id	sid	tid	token	lemma	pos
ejde-397	1	1	electronic	electronic	ADJ
ejde-397	1	2	journal	journal	NOUN
ejde-397	1	3	of	of	ADP
ejde-397	1	4	differential	differential	ADJ
ejde-397	1	5	equations	equation	NOUN
ejde-397	1	6	,	,	PUNCT
ejde-397	1	7	vol	vol	NOUN
ejde-397	1	8	.	.	PUNCT
ejde-397	1	9	2023	2023	NUM
ejde-397	1	10	(	(	PUNCT
ejde-397	1	11	2023	2023	NUM
ejde-397	1	12	)	)	PUNCT
ejde-397	1	13	,	,	PUNCT
ejde-397	1	14	no	no	INTJ
ejde-397	1	15	.	.	NOUN
ejde-397	1	16	63	63	NUM
ejde-397	1	17	,	,	PUNCT
ejde-397	1	18	pp	pp	ADJ
ejde-397	1	19	.	.	PUNCT
ejde-397	2	1	1–55	1–55	PROPN
ejde-397	2	2	.	.	PUNCT
ejde-397	3	1	issn	issn	PROPN
ejde-397	3	2	:	:	PUNCT
ejde-397	3	3	1072	1072	NUM
ejde-397	3	4	-	-	SYM
ejde-397	3	5	6691	6691	NUM
ejde-397	3	6	.	.	PUNCT
ejde-397	4	1	url	url	PROPN
ejde-397	4	2	:	:	PUNCT
ejde-397	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-397	4	4	,	,	PUNCT
ejde-397	4	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-397	4	6	doi	doi	PROPN
ejde-397	4	7	:	:	PUNCT
ejde-397	4	8	10.58997	10.58997	NUM
ejde-397	4	9	/	/	SYM
ejde-397	4	10	ejde.2023.63	ejde.2023.63	ADJ
ejde-397	4	11	abstract	abstract	ADJ
ejde-397	4	12	degenerate	degenerate	ADJ
ejde-397	4	13	volterra	volterra	NOUN
ejde-397	4	14	inclusions	inclusion	NOUN
ejde-397	4	15	in	in	ADP
ejde-397	4	16	locally	locally	ADV
ejde-397	4	17	convex	convex	PROPN
ejde-397	4	18	spaces	space	NOUN
ejde-397	4	19	marko	marko	PROPN
ejde-397	4	20	kostić	kostić	PROPN
ejde-397	4	21	abstract	abstract	ADJ
ejde-397	4	22	.	.	PUNCT
ejde-397	5	1	in	in	ADP
ejde-397	5	2	this	this	DET
ejde-397	5	3	article	article	NOUN
ejde-397	5	4	,	,	PUNCT
ejde-397	5	5	we	we	PRON
ejde-397	5	6	analyze	analyze	VERB
ejde-397	5	7	the	the	DET
ejde-397	5	8	abstract	abstract	ADJ
ejde-397	5	9	degenerate	degenerate	ADJ
ejde-397	5	10	volterra	volterra	PROPN
ejde-397	5	11	integrodifferential	integrodifferential	ADJ
ejde-397	5	12	equations	equation	NOUN
ejde-397	5	13	in	in	ADP
ejde-397	5	14	sequentially	sequentially	ADV
ejde-397	5	15	complete	complete	ADJ
ejde-397	5	16	locally	locally	ADV
ejde-397	5	17	convex	convex	NOUN
ejde-397	5	18	spaces	space	NOUN
ejde-397	5	19	by	by	ADP
ejde-397	5	20	using	use	VERB
ejde-397	5	21	multivalued	multivalue	VERB
ejde-397	5	22	linear	linear	ADJ
ejde-397	5	23	operators	operator	NOUN
ejde-397	5	24	and	and	CCONJ
ejde-397	5	25	vector	vector	NOUN
ejde-397	5	26	-	-	PUNCT
ejde-397	5	27	valued	value	VERB
ejde-397	5	28	laplace	laplace	NOUN
ejde-397	5	29	transform	transform	NOUN
ejde-397	5	30	.	.	PUNCT
ejde-397	6	1	we	we	PRON
ejde-397	6	2	follow	follow	VERB
ejde-397	6	3	the	the	DET
ejde-397	6	4	method	method	NOUN
ejde-397	6	5	which	which	PRON
ejde-397	6	6	is	be	AUX
ejde-397	6	7	based	base	VERB
ejde-397	6	8	on	on	ADP
ejde-397	6	9	the	the	DET
ejde-397	6	10	use	use	NOUN
ejde-397	6	11	of	of	ADP
ejde-397	6	12	(	(	PUNCT
ejde-397	6	13	a	a	PRON
ejde-397	6	14	,	,	PUNCT
ejde-397	6	15	k)-regularized	k)-regularize	VERB
ejde-397	6	16	c	c	NOUN
ejde-397	6	17	-	-	PUNCT
ejde-397	6	18	resolvent	resolvent	ADJ
ejde-397	6	19	families	family	NOUN
ejde-397	6	20	generated	generate	VERB
ejde-397	6	21	by	by	ADP
ejde-397	6	22	multivalued	multivalued	ADJ
ejde-397	6	23	linear	linear	PROPN
ejde-397	6	24	operators	operator	NOUN
ejde-397	6	25	and	and	CCONJ
ejde-397	6	26	which	which	PRON
ejde-397	6	27	suggests	suggest	VERB
ejde-397	6	28	a	a	DET
ejde-397	6	29	very	very	ADV
ejde-397	6	30	general	general	ADJ
ejde-397	6	31	way	way	NOUN
ejde-397	6	32	of	of	ADP
ejde-397	6	33	approaching	approach	VERB
ejde-397	6	34	abstract	abstract	ADJ
ejde-397	6	35	volterra	volterra	NOUN
ejde-397	6	36	equations	equation	NOUN
ejde-397	6	37	.	.	PUNCT
ejde-397	7	1	among	among	ADP
ejde-397	7	2	many	many	ADJ
ejde-397	7	3	other	other	ADJ
ejde-397	7	4	themes	theme	NOUN
ejde-397	7	5	,	,	PUNCT
ejde-397	7	6	we	we	PRON
ejde-397	7	7	consider	consider	VERB
ejde-397	7	8	the	the	DET
ejde-397	7	9	hille	hille	PROPN
ejde-397	7	10	-	-	PUNCT
ejde-397	7	11	yosida	yosida	PROPN
ejde-397	7	12	type	type	NOUN
ejde-397	7	13	theorems	theorem	NOUN
ejde-397	7	14	for	for	ADP
ejde-397	7	15	(	(	PUNCT
ejde-397	7	16	a	a	DET
ejde-397	7	17	,	,	PUNCT
ejde-397	7	18	k)-regularized	k)-regularize	VERB
ejde-397	7	19	cresolvent	cresolvent	NOUN
ejde-397	7	20	families	family	NOUN
ejde-397	7	21	,	,	PUNCT
ejde-397	7	22	differential	differential	ADJ
ejde-397	7	23	and	and	CCONJ
ejde-397	7	24	analytical	analytical	ADJ
ejde-397	7	25	properties	property	NOUN
ejde-397	7	26	of	of	ADP
ejde-397	7	27	(	(	PUNCT
ejde-397	7	28	a	a	PRON
ejde-397	7	29	,	,	PUNCT
ejde-397	7	30	k)-regularized	k)-regularize	VERB
ejde-397	7	31	c	c	NOUN
ejde-397	7	32	-	-	PUNCT
ejde-397	7	33	resolvent	resolvent	ADJ
ejde-397	7	34	families	family	NOUN
ejde-397	7	35	,	,	PUNCT
ejde-397	7	36	the	the	DET
ejde-397	7	37	generalized	generalized	ADJ
ejde-397	7	38	variation	variation	NOUN
ejde-397	7	39	of	of	ADP
ejde-397	7	40	parameters	parameter	NOUN
ejde-397	7	41	formula	formula	NOUN
ejde-397	7	42	,	,	PUNCT
ejde-397	7	43	and	and	CCONJ
ejde-397	7	44	subordination	subordination	NOUN
ejde-397	7	45	principles	principle	NOUN
ejde-397	7	46	.	.	PUNCT
ejde-397	8	1	we	we	PRON
ejde-397	8	2	also	also	ADV
ejde-397	8	3	introduce	introduce	VERB
ejde-397	8	4	and	and	CCONJ
ejde-397	8	5	analyze	analyze	VERB
ejde-397	8	6	the	the	DET
ejde-397	8	7	class	class	NOUN
ejde-397	8	8	of	of	ADP
ejde-397	8	9	(	(	PUNCT
ejde-397	8	10	a	a	PRON
ejde-397	8	11	,	,	PUNCT
ejde-397	8	12	k)regularized	k)regularize	VERB
ejde-397	8	13	(	(	PUNCT
ejde-397	8	14	c1	c1	NOUN
ejde-397	8	15	,	,	PUNCT
ejde-397	8	16	c2)-existence	c2)-existence	NOUN
ejde-397	8	17	and	and	CCONJ
ejde-397	8	18	uniqueness	uniqueness	NOUN
ejde-397	8	19	families	family	NOUN
ejde-397	8	20	.	.	PUNCT
ejde-397	9	1	the	the	DET
ejde-397	9	2	main	main	ADJ
ejde-397	9	3	purpose	purpose	NOUN
ejde-397	9	4	of	of	ADP
ejde-397	9	5	third	third	ADJ
ejde-397	9	6	section	section	NOUN
ejde-397	9	7	,	,	PUNCT
ejde-397	9	8	which	which	PRON
ejde-397	9	9	can	can	AUX
ejde-397	9	10	be	be	AUX
ejde-397	9	11	viewed	view	VERB
ejde-397	9	12	of	of	ADP
ejde-397	9	13	some	some	DET
ejde-397	9	14	independent	independent	ADJ
ejde-397	9	15	interest	interest	NOUN
ejde-397	9	16	,	,	PUNCT
ejde-397	9	17	is	be	AUX
ejde-397	9	18	to	to	PART
ejde-397	9	19	introduce	introduce	VERB
ejde-397	9	20	a	a	DET
ejde-397	9	21	relatively	relatively	ADV
ejde-397	9	22	simple	simple	ADJ
ejde-397	9	23	and	and	CCONJ
ejde-397	9	24	new	new	ADJ
ejde-397	9	25	theoretical	theoretical	ADJ
ejde-397	9	26	concept	concept	NOUN
ejde-397	9	27	useful	useful	ADJ
ejde-397	9	28	in	in	ADP
ejde-397	9	29	the	the	DET
ejde-397	9	30	analysis	analysis	NOUN
ejde-397	9	31	of	of	ADP
ejde-397	9	32	operational	operational	ADJ
ejde-397	9	33	properties	property	NOUN
ejde-397	9	34	of	of	ADP
ejde-397	9	35	laplace	laplace	NOUN
ejde-397	9	36	transform	transform	NOUN
ejde-397	9	37	of	of	ADP
ejde-397	9	38	non	non	ADJ
ejde-397	9	39	-	-	ADJ
ejde-397	9	40	continuous	continuous	ADJ
ejde-397	9	41	functions	function	NOUN
ejde-397	9	42	with	with	ADP
ejde-397	9	43	values	value	NOUN
ejde-397	9	44	in	in	ADP
ejde-397	9	45	sequentially	sequentially	ADV
ejde-397	9	46	complete	complete	ADJ
ejde-397	9	47	locally	locally	ADV
ejde-397	9	48	convex	convex	ADJ
ejde-397	9	49	spaces	space	NOUN
ejde-397	9	50	.	.	PUNCT
ejde-397	10	1	this	this	DET
ejde-397	10	2	concept	concept	NOUN
ejde-397	10	3	coincides	coincide	VERB
ejde-397	10	4	with	with	ADP
ejde-397	10	5	the	the	DET
ejde-397	10	6	classical	classical	ADJ
ejde-397	10	7	concept	concept	NOUN
ejde-397	10	8	of	of	ADP
ejde-397	10	9	vector	vector	NOUN
ejde-397	10	10	-	-	PUNCT
ejde-397	10	11	valued	value	VERB
ejde-397	10	12	laplace	laplace	NOUN
ejde-397	10	13	transform	transform	NOUN
ejde-397	10	14	in	in	ADP
ejde-397	10	15	the	the	DET
ejde-397	10	16	case	case	NOUN
ejde-397	10	17	that	that	SCONJ
ejde-397	10	18	x	x	PRON
ejde-397	10	19	is	be	AUX
ejde-397	10	20	a	a	DET
ejde-397	10	21	banach	banach	NOUN
ejde-397	10	22	space	space	NOUN
ejde-397	10	23	.	.	PUNCT
ejde-397	11	1	1	1	X
ejde-397	11	2	.	.	X
ejde-397	11	3	introduction	introduction	NOUN
ejde-397	11	4	and	and	CCONJ
ejde-397	11	5	preliminaries	preliminary	NOUN
ejde-397	11	6	the	the	DET
ejde-397	11	7	main	main	ADJ
ejde-397	11	8	aim	aim	NOUN
ejde-397	11	9	of	of	ADP
ejde-397	11	10	this	this	DET
ejde-397	11	11	paper	paper	NOUN
ejde-397	11	12	is	be	AUX
ejde-397	11	13	to	to	PART
ejde-397	11	14	analyze	analyze	VERB
ejde-397	11	15	the	the	DET
ejde-397	11	16	abstract	abstract	ADJ
ejde-397	11	17	degenerate	degenerate	ADJ
ejde-397	11	18	volterra	volterra	PROPN
ejde-397	11	19	integrodifferential	integrodifferential	ADJ
ejde-397	11	20	equations	equation	NOUN
ejde-397	11	21	in	in	ADP
ejde-397	11	22	sequentially	sequentially	ADV
ejde-397	11	23	complete	complete	ADJ
ejde-397	11	24	locally	locally	ADV
ejde-397	11	25	convex	convex	NOUN
ejde-397	11	26	spaces	space	NOUN
ejde-397	11	27	by	by	ADP
ejde-397	11	28	using	use	VERB
ejde-397	11	29	multivalued	multivalue	VERB
ejde-397	11	30	linear	linear	ADJ
ejde-397	11	31	operators	operator	NOUN
ejde-397	11	32	(	(	PUNCT
ejde-397	11	33	cf	cf	NOUN
ejde-397	11	34	.	.	PUNCT
ejde-397	12	1	[	[	X
ejde-397	12	2	68	68	NUM
ejde-397	12	3	]	]	PUNCT
ejde-397	12	4	and	and	CCONJ
ejde-397	12	5	[	[	X
ejde-397	12	6	36	36	NUM
ejde-397	12	7	]	]	PUNCT
ejde-397	12	8	for	for	ADP
ejde-397	12	9	a	a	DET
ejde-397	12	10	comprehensive	comprehensive	ADJ
ejde-397	12	11	survey	survey	NOUN
ejde-397	12	12	of	of	ADP
ejde-397	12	13	results	result	NOUN
ejde-397	12	14	on	on	ADP
ejde-397	12	15	abstract	abstract	ADJ
ejde-397	12	16	non	non	ADJ
ejde-397	12	17	-	-	ADJ
ejde-397	12	18	degenerate	degenerate	ADJ
ejde-397	12	19	volterra	volterra	NOUN
ejde-397	12	20	equations	equation	NOUN
ejde-397	12	21	)	)	PUNCT
ejde-397	12	22	,	,	PUNCT
ejde-397	12	23	as	as	ADV
ejde-397	12	24	well	well	ADV
ejde-397	12	25	as	as	ADP
ejde-397	12	26	to	to	PART
ejde-397	12	27	introduce	introduce	VERB
ejde-397	12	28	a	a	DET
ejde-397	12	29	new	new	ADJ
ejde-397	12	30	theoretical	theoretical	ADJ
ejde-397	12	31	approach	approach	NOUN
ejde-397	12	32	to	to	ADP
ejde-397	12	33	the	the	DET
ejde-397	12	34	laplace	laplace	NOUN
ejde-397	12	35	transform	transform	NOUN
ejde-397	12	36	of	of	ADP
ejde-397	12	37	functions	function	NOUN
ejde-397	12	38	with	with	ADP
ejde-397	12	39	values	value	NOUN
ejde-397	12	40	in	in	ADP
ejde-397	12	41	sequentially	sequentially	ADV
ejde-397	12	42	complete	complete	ADJ
ejde-397	12	43	locally	locally	ADV
ejde-397	12	44	convex	convex	ADJ
ejde-397	12	45	spaces	space	NOUN
ejde-397	12	46	.	.	PUNCT
ejde-397	13	1	to	to	PART
ejde-397	13	2	outline	outline	VERB
ejde-397	13	3	the	the	DET
ejde-397	13	4	motivation	motivation	NOUN
ejde-397	13	5	of	of	ADP
ejde-397	13	6	our	our	PRON
ejde-397	13	7	research	research	NOUN
ejde-397	13	8	,	,	PUNCT
ejde-397	13	9	let	let	VERB
ejde-397	13	10	us	we	PRON
ejde-397	13	11	mention	mention	VERB
ejde-397	13	12	that	that	SCONJ
ejde-397	13	13	there	there	PRON
ejde-397	13	14	exists	exist	VERB
ejde-397	13	15	only	only	ADV
ejde-397	13	16	a	a	DET
ejde-397	13	17	few	few	ADJ
ejde-397	13	18	published	publish	VERB
ejde-397	13	19	papers	paper	NOUN
ejde-397	13	20	in	in	ADP
ejde-397	13	21	the	the	DET
ejde-397	13	22	existing	exist	VERB
ejde-397	13	23	literature	literature	NOUN
ejde-397	13	24	treating	treat	VERB
ejde-397	13	25	the	the	DET
ejde-397	13	26	abstract	abstract	ADJ
ejde-397	13	27	degenerate	degenerate	ADJ
ejde-397	13	28	volterra	volterra	NOUN
ejde-397	13	29	equations	equation	NOUN
ejde-397	13	30	(	(	PUNCT
ejde-397	13	31	[	[	X
ejde-397	13	32	16	16	NUM
ejde-397	13	33	]	]	PUNCT
ejde-397	13	34	,	,	PUNCT
ejde-397	14	1	[	[	X
ejde-397	14	2	18]-[21	18]-[21	X
ejde-397	14	3	]	]	X
ejde-397	14	4	,	,	PUNCT
ejde-397	15	1	[	[	X
ejde-397	15	2	31	31	NUM
ejde-397	15	3	]	]	PUNCT
ejde-397	15	4	)	)	PUNCT
ejde-397	15	5	and	and	CCONJ
ejde-397	15	6	the	the	DET
ejde-397	15	7	abstract	abstract	ADJ
ejde-397	15	8	degenerate	degenerate	ADJ
ejde-397	15	9	fractional	fractional	ADJ
ejde-397	15	10	inclusions	inclusion	NOUN
ejde-397	15	11	associated	associate	VERB
ejde-397	15	12	with	with	ADP
ejde-397	15	13	the	the	DET
ejde-397	15	14	use	use	NOUN
ejde-397	15	15	of	of	ADP
ejde-397	15	16	caputo	caputo	PROPN
ejde-397	15	17	fractional	fractional	ADJ
ejde-397	15	18	derivatives	derivative	NOUN
ejde-397	15	19	(	(	PUNCT
ejde-397	15	20	[	[	X
ejde-397	15	21	45]-[49	45]-[49	X
ejde-397	15	22	]	]	X
ejde-397	15	23	,	,	PUNCT
ejde-397	15	24	[	[	X
ejde-397	15	25	51	51	NUM
ejde-397	15	26	]	]	PUNCT
ejde-397	15	27	)	)	PUNCT
ejde-397	15	28	.	.	PUNCT
ejde-397	16	1	in	in	ADP
ejde-397	16	2	this	this	DET
ejde-397	16	3	paper	paper	NOUN
ejde-397	16	4	,	,	PUNCT
ejde-397	16	5	we	we	PRON
ejde-397	16	6	make	make	VERB
ejde-397	16	7	an	an	DET
ejde-397	16	8	attempt	attempt	NOUN
ejde-397	16	9	to	to	PART
ejde-397	16	10	perform	perform	VERB
ejde-397	16	11	the	the	DET
ejde-397	16	12	first	first	ADJ
ejde-397	16	13	systematic	systematic	ADJ
ejde-397	16	14	exploration	exploration	NOUN
ejde-397	16	15	of	of	ADP
ejde-397	16	16	abstract	abstract	ADJ
ejde-397	16	17	degenerate	degenerate	ADJ
ejde-397	16	18	volterra	volterra	NOUN
ejde-397	16	19	equations	equation	NOUN
ejde-397	16	20	and	and	CCONJ
ejde-397	16	21	abstract	abstract	ADJ
ejde-397	16	22	degenerate	degenerate	ADJ
ejde-397	16	23	fractional	fractional	ADJ
ejde-397	16	24	differential	differential	ADJ
ejde-397	16	25	equations	equation	NOUN
ejde-397	16	26	in	in	ADP
ejde-397	16	27	locally	locally	ADV
ejde-397	16	28	convex	convex	ADJ
ejde-397	16	29	spaces	space	NOUN
ejde-397	16	30	,	,	PUNCT
ejde-397	16	31	contributing	contribute	VERB
ejde-397	16	32	also	also	ADV
ejde-397	16	33	to	to	ADP
ejde-397	16	34	the	the	DET
ejde-397	16	35	theories	theory	NOUN
ejde-397	16	36	of	of	ADP
ejde-397	16	37	abstract	abstract	ADJ
ejde-397	16	38	degenerate	degenerate	ADJ
ejde-397	16	39	differential	differential	ADJ
ejde-397	16	40	equations	equation	NOUN
ejde-397	16	41	of	of	ADP
ejde-397	16	42	first	first	ADJ
ejde-397	16	43	and	and	CCONJ
ejde-397	16	44	second	second	ADJ
ejde-397	16	45	order	order	NOUN
ejde-397	16	46	2020	2020	NUM
ejde-397	16	47	mathematics	mathematic	NOUN
ejde-397	16	48	subject	subject	ADJ
ejde-397	16	49	classification	classification	NOUN
ejde-397	16	50	.	.	PUNCT
ejde-397	17	1	34g25	34g25	NUM
ejde-397	17	2	,	,	PUNCT
ejde-397	17	3	45d05	45d05	NUM
ejde-397	17	4	,	,	PUNCT
ejde-397	17	5	47d06	47d06	NUM
ejde-397	17	6	,	,	PUNCT
ejde-397	17	7	46g12	46g12	NUM
ejde-397	17	8	,	,	PUNCT
ejde-397	17	9	47d60	47d60	NUM
ejde-397	17	10	,	,	PUNCT
ejde-397	17	11	47d62	47d62	NUM
ejde-397	17	12	.	.	PUNCT
ejde-397	18	1	key	key	ADJ
ejde-397	18	2	words	word	NOUN
ejde-397	18	3	and	and	CCONJ
ejde-397	18	4	phrases	phrase	NOUN
ejde-397	18	5	.	.	PUNCT
ejde-397	19	1	abstract	abstract	ADJ
ejde-397	19	2	degenerate	degenerate	ADJ
ejde-397	19	3	volterra	volterra	NOUN
ejde-397	19	4	inclusion	inclusion	NOUN
ejde-397	19	5	;	;	PUNCT
ejde-397	19	6	locally	locally	ADV
ejde-397	19	7	convex	convex	ADJ
ejde-397	19	8	space	space	NOUN
ejde-397	19	9	;	;	PUNCT
ejde-397	19	10	abstract	abstract	ADJ
ejde-397	19	11	degenerate	degenerate	ADJ
ejde-397	19	12	fractional	fractional	ADJ
ejde-397	19	13	differential	differential	NOUN
ejde-397	19	14	equation	equation	NOUN
ejde-397	19	15	;	;	PUNCT
ejde-397	19	16	(	(	PUNCT
ejde-397	19	17	a	a	PRON
ejde-397	19	18	,	,	PUNCT
ejde-397	19	19	k)-regularized	k)-regularize	VERB
ejde-397	19	20	c	c	NOUN
ejde-397	19	21	-	-	PUNCT
ejde-397	19	22	resolvent	resolvent	ADJ
ejde-397	19	23	family	family	NOUN
ejde-397	19	24	;	;	PUNCT
ejde-397	19	25	multivalued	multivalued	ADJ
ejde-397	19	26	linear	linear	ADJ
ejde-397	19	27	operator	operator	NOUN
ejde-397	19	28	.	.	PUNCT
ejde-397	20	1	©	©	ADP
ejde-397	20	2	2023	2023	NUM
ejde-397	20	3	.	.	PUNCT
ejde-397	21	1	this	this	DET
ejde-397	21	2	work	work	NOUN
ejde-397	21	3	is	be	AUX
ejde-397	21	4	licensed	license	VERB
ejde-397	21	5	under	under	ADP
ejde-397	21	6	a	a	DET
ejde-397	21	7	cc	cc	NOUN
ejde-397	21	8	by	by	ADP
ejde-397	21	9	4.0	4.0	NUM
ejde-397	21	10	license	license	NOUN
ejde-397	21	11	.	.	PUNCT
ejde-397	22	1	submitted	submit	VERB
ejde-397	22	2	july	july	PROPN
ejde-397	22	3	10	10	NUM
ejde-397	22	4	,	,	PUNCT
ejde-397	22	5	2022	2022	NUM
ejde-397	22	6	.	.	PUNCT
ejde-397	23	1	published	publish	VERB
ejde-397	23	2	september	september	PROPN
ejde-397	23	3	25	25	NUM
ejde-397	23	4	,	,	PUNCT
ejde-397	23	5	2023	2023	NUM
ejde-397	23	6	.	.	PUNCT
ejde-397	23	7	1	1	NUM
ejde-397	23	8	2	2	NUM
ejde-397	23	9	m.	m.	NOUN
ejde-397	23	10	kostić	kostić	NOUN
ejde-397	24	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	24	2	(	(	PUNCT
ejde-397	24	3	for	for	ADP
ejde-397	24	4	pioneering	pioneer	VERB
ejde-397	24	5	results	result	NOUN
ejde-397	24	6	about	about	ADP
ejde-397	24	7	semigroups	semigroup	NOUN
ejde-397	24	8	of	of	ADP
ejde-397	24	9	operators	operator	NOUN
ejde-397	24	10	in	in	ADP
ejde-397	24	11	locally	locally	ADV
ejde-397	24	12	convex	convex	ADJ
ejde-397	24	13	spaces	space	NOUN
ejde-397	24	14	,	,	PUNCT
ejde-397	24	15	we	we	PRON
ejde-397	24	16	refer	refer	VERB
ejde-397	24	17	the	the	DET
ejde-397	24	18	reader	reader	NOUN
ejde-397	24	19	to	to	ADP
ejde-397	24	20	the	the	DET
ejde-397	24	21	papers	paper	NOUN
ejde-397	24	22	[	[	X
ejde-397	24	23	33	33	NUM
ejde-397	24	24	,	,	PUNCT
ejde-397	24	25	34	34	NUM
ejde-397	24	26	,	,	PUNCT
ejde-397	24	27	82	82	NUM
ejde-397	24	28	]	]	PUNCT
ejde-397	24	29	)	)	PUNCT
ejde-397	24	30	.	.	PUNCT
ejde-397	25	1	a	a	DET
ejde-397	25	2	great	great	ADJ
ejde-397	25	3	number	number	NOUN
ejde-397	25	4	of	of	ADP
ejde-397	25	5	our	our	PRON
ejde-397	25	6	results	result	NOUN
ejde-397	25	7	seems	seem	VERB
ejde-397	25	8	to	to	PART
ejde-397	25	9	be	be	AUX
ejde-397	25	10	new	new	ADJ
ejde-397	25	11	even	even	ADV
ejde-397	25	12	in	in	ADP
ejde-397	25	13	the	the	DET
ejde-397	25	14	bahach	bahach	NOUN
ejde-397	25	15	space	space	NOUN
ejde-397	25	16	setting	setting	NOUN
ejde-397	25	17	.	.	PUNCT
ejde-397	26	1	the	the	DET
ejde-397	26	2	organization	organization	NOUN
ejde-397	26	3	and	and	CCONJ
ejde-397	26	4	main	main	ADJ
ejde-397	26	5	ideas	idea	NOUN
ejde-397	26	6	of	of	ADP
ejde-397	26	7	this	this	DET
ejde-397	26	8	paper	paper	NOUN
ejde-397	26	9	can	can	AUX
ejde-397	26	10	be	be	AUX
ejde-397	26	11	briefly	briefly	ADV
ejde-397	26	12	described	describe	VERB
ejde-397	26	13	as	as	SCONJ
ejde-397	26	14	follows	follow	VERB
ejde-397	26	15	.	.	PUNCT
ejde-397	27	1	in	in	ADP
ejde-397	27	2	the	the	DET
ejde-397	27	3	second	second	ADJ
ejde-397	27	4	section	section	NOUN
ejde-397	27	5	of	of	ADP
ejde-397	27	6	paper	paper	NOUN
ejde-397	27	7	,	,	PUNCT
ejde-397	27	8	we	we	PRON
ejde-397	27	9	will	will	AUX
ejde-397	27	10	take	take	VERB
ejde-397	27	11	a	a	DET
ejde-397	27	12	preliminary	preliminary	ADJ
ejde-397	27	13	and	and	CCONJ
ejde-397	27	14	incomplete	incomplete	ADJ
ejde-397	27	15	look	look	VERB
ejde-397	27	16	at	at	ADP
ejde-397	27	17	the	the	DET
ejde-397	27	18	multivalued	multivalue	VERB
ejde-397	27	19	linear	linear	PROPN
ejde-397	27	20	operators	operator	NOUN
ejde-397	27	21	in	in	ADP
ejde-397	27	22	locally	locally	ADV
ejde-397	27	23	convex	convex	ADJ
ejde-397	27	24	spaces	space	NOUN
ejde-397	27	25	;	;	PUNCT
ejde-397	27	26	for	for	ADP
ejde-397	27	27	more	more	ADJ
ejde-397	27	28	details	detail	NOUN
ejde-397	27	29	,	,	PUNCT
ejde-397	27	30	we	we	PRON
ejde-397	27	31	refer	refer	VERB
ejde-397	27	32	the	the	DET
ejde-397	27	33	reader	reader	NOUN
ejde-397	27	34	to	to	ADP
ejde-397	27	35	the	the	DET
ejde-397	27	36	monographs	monograph	NOUN
ejde-397	28	1	[	[	X
ejde-397	28	2	9	9	NUM
ejde-397	28	3	,	,	PUNCT
ejde-397	28	4	17	17	NUM
ejde-397	28	5	]	]	PUNCT
ejde-397	28	6	.	.	PUNCT
ejde-397	29	1	we	we	PRON
ejde-397	29	2	introduce	introduce	VERB
ejde-397	29	3	the	the	DET
ejde-397	29	4	notion	notion	NOUN
ejde-397	29	5	of	of	ADP
ejde-397	29	6	a	a	DET
ejde-397	29	7	c	c	NOUN
ejde-397	29	8	-	-	NOUN
ejde-397	29	9	resolvent	resolvent	NOUN
ejde-397	29	10	of	of	ADP
ejde-397	29	11	a	a	DET
ejde-397	29	12	multivalued	multivalue	VERB
ejde-397	29	13	linear	linear	ADJ
ejde-397	29	14	operator	operator	NOUN
ejde-397	29	15	,	,	PUNCT
ejde-397	29	16	reconsider	reconsider	VERB
ejde-397	29	17	the	the	DET
ejde-397	29	18	assertions	assertion	NOUN
ejde-397	29	19	from	from	ADP
ejde-397	29	20	[	[	X
ejde-397	29	21	17	17	NUM
ejde-397	29	22	,	,	PUNCT
ejde-397	29	23	chapter	chapter	NOUN
ejde-397	29	24	i	i	PROPN
ejde-397	29	25	]	]	PUNCT
ejde-397	29	26	and	and	CCONJ
ejde-397	29	27	state	state	VERB
ejde-397	29	28	a	a	DET
ejde-397	29	29	generalization	generalization	NOUN
ejde-397	29	30	of	of	ADP
ejde-397	29	31	[	[	X
ejde-397	29	32	36	36	NUM
ejde-397	29	33	,	,	PUNCT
ejde-397	29	34	proposition	proposition	NOUN
ejde-397	29	35	2.1.14	2.1.14	NUM
ejde-397	29	36	]	]	PUNCT
ejde-397	29	37	for	for	ADP
ejde-397	29	38	c	c	NOUN
ejde-397	29	39	-	-	PUNCT
ejde-397	29	40	resolvents	resolvent	NOUN
ejde-397	29	41	of	of	ADP
ejde-397	29	42	multivalued	multivalued	ADJ
ejde-397	29	43	linear	linear	ADJ
ejde-397	29	44	operators	operator	NOUN
ejde-397	29	45	.	.	PUNCT
ejde-397	30	1	following	follow	VERB
ejde-397	30	2	the	the	DET
ejde-397	30	3	approach	approach	NOUN
ejde-397	30	4	of	of	ADP
ejde-397	30	5	knuckles	knuckle	NOUN
ejde-397	30	6	and	and	CCONJ
ejde-397	30	7	neubrander	neubrander	NOUN
ejde-397	30	8	[	[	X
ejde-397	30	9	32	32	NUM
ejde-397	30	10	]	]	PUNCT
ejde-397	30	11	,	,	PUNCT
ejde-397	30	12	we	we	PRON
ejde-397	30	13	introduce	introduce	VERB
ejde-397	30	14	the	the	DET
ejde-397	30	15	notion	notion	NOUN
ejde-397	30	16	of	of	ADP
ejde-397	30	17	a	a	DET
ejde-397	30	18	relatively	relatively	ADV
ejde-397	30	19	closed	closed	ADJ
ejde-397	30	20	multivalued	multivalue	VERB
ejde-397	30	21	linear	linear	ADJ
ejde-397	30	22	operator	operator	NOUN
ejde-397	30	23	in	in	ADP
ejde-397	30	24	locally	locally	ADV
ejde-397	30	25	convex	convex	ADJ
ejde-397	30	26	space	space	NOUN
ejde-397	30	27	.	.	PUNCT
ejde-397	31	1	the	the	DET
ejde-397	31	2	generalized	generalize	VERB
ejde-397	31	3	resolvent	resolvent	ADJ
ejde-397	31	4	equations	equation	NOUN
ejde-397	31	5	continue	continue	VERB
ejde-397	31	6	to	to	PART
ejde-397	31	7	hold	hold	VERB
ejde-397	31	8	in	in	ADP
ejde-397	31	9	our	our	PRON
ejde-397	31	10	framework	framework	NOUN
ejde-397	31	11	.	.	PUNCT
ejde-397	32	1	as	as	SCONJ
ejde-397	32	2	mentioned	mention	VERB
ejde-397	32	3	in	in	ADP
ejde-397	32	4	[	[	X
ejde-397	32	5	36	36	NUM
ejde-397	32	6	,	,	PUNCT
ejde-397	32	7	section	section	NOUN
ejde-397	32	8	1.2	1.2	NUM
ejde-397	32	9	]	]	PUNCT
ejde-397	32	10	,	,	PUNCT
ejde-397	32	11	only	only	ADV
ejde-397	32	12	a	a	DET
ejde-397	32	13	few	few	ADJ
ejde-397	32	14	noteworthy	noteworthy	ADJ
ejde-397	32	15	facts	fact	NOUN
ejde-397	32	16	has	have	AUX
ejde-397	32	17	been	be	AUX
ejde-397	32	18	said	say	VERB
ejde-397	32	19	about	about	ADP
ejde-397	32	20	the	the	DET
ejde-397	32	21	laplace	laplace	NOUN
ejde-397	32	22	transform	transform	NOUN
ejde-397	32	23	of	of	ADP
ejde-397	32	24	functions	function	NOUN
ejde-397	32	25	with	with	ADP
ejde-397	32	26	values	value	NOUN
ejde-397	32	27	in	in	ADP
ejde-397	32	28	sequentially	sequentially	ADV
ejde-397	32	29	complete	complete	ADJ
ejde-397	32	30	locally	locally	ADV
ejde-397	32	31	convex	convex	ADJ
ejde-397	32	32	spaces	space	NOUN
ejde-397	32	33	.	.	PUNCT
ejde-397	33	1	in	in	ADP
ejde-397	33	2	section	section	NOUN
ejde-397	33	3	3	3	NUM
ejde-397	33	4	,	,	PUNCT
ejde-397	33	5	we	we	PRON
ejde-397	33	6	propose	propose	VERB
ejde-397	33	7	a	a	DET
ejde-397	33	8	new	new	ADJ
ejde-397	33	9	theoretical	theoretical	ADJ
ejde-397	33	10	approach	approach	NOUN
ejde-397	33	11	to	to	ADP
ejde-397	33	12	the	the	DET
ejde-397	33	13	laplace	laplace	NOUN
ejde-397	33	14	transform	transform	NOUN
ejde-397	33	15	of	of	ADP
ejde-397	33	16	functions	function	NOUN
ejde-397	33	17	with	with	ADP
ejde-397	33	18	values	value	NOUN
ejde-397	33	19	in	in	ADP
ejde-397	33	20	sequentially	sequentially	ADV
ejde-397	33	21	complete	complete	ADJ
ejde-397	33	22	locally	locally	ADV
ejde-397	33	23	convex	convex	ADJ
ejde-397	33	24	spaces	space	NOUN
ejde-397	33	25	.	.	PUNCT
ejde-397	34	1	this	this	DET
ejde-397	34	2	concept	concept	NOUN
ejde-397	34	3	extends	extend	VERB
ejde-397	34	4	the	the	DET
ejde-397	34	5	corresponding	correspond	VERB
ejde-397	34	6	one	one	NOUN
ejde-397	34	7	introduced	introduce	VERB
ejde-397	34	8	by	by	ADP
ejde-397	34	9	xiao	xiao	PROPN
ejde-397	34	10	and	and	CCONJ
ejde-397	34	11	liang	liang	PROPN
ejde-397	34	12	(	(	PUNCT
ejde-397	34	13	[	[	X
ejde-397	34	14	80	80	NUM
ejde-397	34	15	]	]	PUNCT
ejde-397	34	16	,	,	PUNCT
ejde-397	34	17	1997	1997	NUM
ejde-397	34	18	)	)	PUNCT
ejde-397	34	19	,	,	PUNCT
ejde-397	34	20	and	and	CCONJ
ejde-397	34	21	coincides	coincide	VERB
ejde-397	34	22	with	with	ADP
ejde-397	34	23	the	the	DET
ejde-397	34	24	classical	classical	ADJ
ejde-397	34	25	concept	concept	NOUN
ejde-397	34	26	of	of	ADP
ejde-397	34	27	vector	vector	NOUN
ejde-397	34	28	-	-	PUNCT
ejde-397	34	29	valued	value	VERB
ejde-397	34	30	laplace	laplace	NOUN
ejde-397	34	31	transform	transform	NOUN
ejde-397	34	32	in	in	ADP
ejde-397	34	33	the	the	DET
ejde-397	34	34	case	case	NOUN
ejde-397	34	35	that	that	SCONJ
ejde-397	34	36	the	the	DET
ejde-397	34	37	state	state	NOUN
ejde-397	34	38	space	space	NOUN
ejde-397	34	39	x	x	PUNCT
ejde-397	34	40	is	be	AUX
ejde-397	34	41	one	one	NUM
ejde-397	34	42	of	of	ADP
ejde-397	34	43	banach	banach	NOUN
ejde-397	34	44	’s	’s	X
ejde-397	35	1	[	[	X
ejde-397	35	2	1	1	NUM
ejde-397	35	3	]	]	PUNCT
ejde-397	35	4	.	.	PUNCT
ejde-397	36	1	concerning	concern	VERB
ejde-397	36	2	the	the	DET
ejde-397	36	3	integration	integration	NOUN
ejde-397	36	4	of	of	ADP
ejde-397	36	5	functions	function	NOUN
ejde-397	36	6	with	with	ADP
ejde-397	36	7	values	value	NOUN
ejde-397	36	8	in	in	ADP
ejde-397	36	9	sequentially	sequentially	ADV
ejde-397	36	10	complete	complete	ADJ
ejde-397	36	11	locally	locally	ADV
ejde-397	36	12	convex	convex	ADJ
ejde-397	36	13	spaces	space	NOUN
ejde-397	36	14	,	,	PUNCT
ejde-397	36	15	we	we	PRON
ejde-397	36	16	follow	follow	VERB
ejde-397	36	17	the	the	DET
ejde-397	36	18	approach	approach	NOUN
ejde-397	36	19	of	of	ADP
ejde-397	36	20	martinez	martinez	PROPN
ejde-397	36	21	and	and	CCONJ
ejde-397	36	22	sanz	sanz	PROPN
ejde-397	36	23	(	(	PUNCT
ejde-397	36	24	cf	cf	NOUN
ejde-397	36	25	.	.	PUNCT
ejde-397	37	1	[	[	X
ejde-397	37	2	61	61	NUM
ejde-397	37	3	,	,	PUNCT
ejde-397	37	4	pp	pp	ADJ
ejde-397	37	5	.	.	PUNCT
ejde-397	38	1	99	99	NUM
ejde-397	38	2	-	-	SYM
ejde-397	38	3	102	102	NUM
ejde-397	38	4	]	]	PUNCT
ejde-397	38	5	for	for	ADP
ejde-397	38	6	more	more	ADJ
ejde-397	38	7	details	detail	NOUN
ejde-397	38	8	)	)	PUNCT
ejde-397	38	9	;	;	PUNCT
ejde-397	38	10	for	for	ADP
ejde-397	38	11	pettis	pettis	NOUN
ejde-397	38	12	integration	integration	NOUN
ejde-397	38	13	in	in	ADP
ejde-397	38	14	locally	locally	ADV
ejde-397	38	15	convex	convex	ADJ
ejde-397	38	16	spaces	space	NOUN
ejde-397	38	17	and	and	CCONJ
ejde-397	38	18	some	some	DET
ejde-397	38	19	applications	application	NOUN
ejde-397	38	20	to	to	ADP
ejde-397	38	21	abstract	abstract	ADJ
ejde-397	38	22	differential	differential	ADJ
ejde-397	38	23	inclusions	inclusion	NOUN
ejde-397	38	24	of	of	ADP
ejde-397	38	25	first	first	ADJ
ejde-397	38	26	order	order	NOUN
ejde-397	38	27	,	,	PUNCT
ejde-397	38	28	we	we	PRON
ejde-397	38	29	refer	refer	VERB
ejde-397	38	30	the	the	DET
ejde-397	38	31	reader	reader	NOUN
ejde-397	38	32	to	to	ADP
ejde-397	38	33	[	[	X
ejde-397	38	34	28	28	NUM
ejde-397	38	35	,	,	PUNCT
ejde-397	38	36	29	29	NUM
ejde-397	38	37	,	,	PUNCT
ejde-397	38	38	56	56	NUM
ejde-397	38	39	]	]	PUNCT
ejde-397	38	40	.	.	PUNCT
ejde-397	39	1	once	once	SCONJ
ejde-397	39	2	we	we	PRON
ejde-397	39	3	have	have	AUX
ejde-397	39	4	proved	prove	VERB
ejde-397	39	5	the	the	DET
ejde-397	39	6	formula	formula	NOUN
ejde-397	39	7	for	for	ADP
ejde-397	39	8	partial	partial	ADJ
ejde-397	39	9	integration	integration	NOUN
ejde-397	39	10	in	in	ADP
ejde-397	39	11	theorem	theorem	NOUN
ejde-397	39	12	3.1	3.1	NUM
ejde-397	39	13	,	,	PUNCT
ejde-397	39	14	we	we	PRON
ejde-397	39	15	have	have	VERB
ejde-397	39	16	an	an	DET
ejde-397	39	17	open	open	ADJ
ejde-397	39	18	door	door	NOUN
ejde-397	39	19	to	to	PART
ejde-397	39	20	consider	consider	VERB
ejde-397	39	21	various	various	ADJ
ejde-397	39	22	operational	operational	ADJ
ejde-397	39	23	properties	property	NOUN
ejde-397	39	24	of	of	ADP
ejde-397	39	25	laplace	laplace	NOUN
ejde-397	39	26	transform	transform	NOUN
ejde-397	39	27	by	by	ADP
ejde-397	39	28	using	use	VERB
ejde-397	39	29	the	the	DET
ejde-397	39	30	methods	method	NOUN
ejde-397	39	31	already	already	ADV
ejde-397	39	32	known	know	VERB
ejde-397	39	33	in	in	ADP
ejde-397	39	34	the	the	DET
ejde-397	39	35	banach	banach	NOUN
ejde-397	39	36	space	space	NOUN
ejde-397	39	37	case	case	NOUN
ejde-397	39	38	.	.	PUNCT
ejde-397	40	1	the	the	DET
ejde-397	40	2	non	non	NOUN
ejde-397	40	3	-	-	NOUN
ejde-397	40	4	possibility	possibility	NOUN
ejde-397	40	5	of	of	ADP
ejde-397	40	6	establishing	establish	VERB
ejde-397	40	7	fubini	fubini	ADJ
ejde-397	40	8	-	-	ADJ
ejde-397	40	9	tonelli	tonelli	NOUN
ejde-397	40	10	theorem	theorem	NOUN
ejde-397	40	11	in	in	ADP
ejde-397	40	12	this	this	DET
ejde-397	40	13	concept	concept	NOUN
ejde-397	40	14	of	of	ADP
ejde-397	40	15	integration	integration	NOUN
ejde-397	40	16	additionally	additionally	ADV
ejde-397	40	17	hinders	hinder	VERB
ejde-397	40	18	our	our	PRON
ejde-397	40	19	research	research	NOUN
ejde-397	40	20	and	and	CCONJ
ejde-397	40	21	does	do	AUX
ejde-397	40	22	not	not	PART
ejde-397	40	23	able	able	VERB
ejde-397	40	24	us	we	PRON
ejde-397	40	25	to	to	PART
ejde-397	40	26	fully	fully	ADV
ejde-397	40	27	transfer	transfer	VERB
ejde-397	40	28	some	some	DET
ejde-397	40	29	assertions	assertion	NOUN
ejde-397	40	30	from	from	ADP
ejde-397	40	31	the	the	DET
ejde-397	40	32	banach	banach	NOUN
ejde-397	40	33	space	space	NOUN
ejde-397	40	34	case	case	NOUN
ejde-397	40	35	to	to	ADP
ejde-397	40	36	the	the	DET
ejde-397	40	37	general	general	ADJ
ejde-397	40	38	locally	locally	ADV
ejde-397	40	39	convex	convex	ADJ
ejde-397	40	40	space	space	NOUN
ejde-397	40	41	case	case	NOUN
ejde-397	40	42	;	;	PUNCT
ejde-397	40	43	for	for	ADP
ejde-397	40	44	example	example	NOUN
ejde-397	40	45	,	,	PUNCT
ejde-397	40	46	in	in	ADP
ejde-397	40	47	theorem	theorem	NOUN
ejde-397	40	48	3.3(vi	3.3(vi	NUM
ejde-397	40	49	)	)	PUNCT
ejde-397	40	50	we	we	PRON
ejde-397	40	51	consider	consider	VERB
ejde-397	40	52	the	the	DET
ejde-397	40	53	laplace	laplace	NOUN
ejde-397	40	54	transform	transform	NOUN
ejde-397	40	55	of	of	ADP
ejde-397	40	56	finite	finite	ADJ
ejde-397	40	57	convolution	convolution	NOUN
ejde-397	40	58	product	product	NOUN
ejde-397	40	59	and	and	CCONJ
ejde-397	40	60	there	there	ADV
ejde-397	40	61	it	it	PRON
ejde-397	40	62	is	be	AUX
ejde-397	40	63	almost	almost	ADV
ejde-397	40	64	inevitable	inevitable	ADJ
ejde-397	40	65	to	to	PART
ejde-397	40	66	impose	impose	VERB
ejde-397	40	67	the	the	DET
ejde-397	40	68	condition	condition	NOUN
ejde-397	40	69	that	that	SCONJ
ejde-397	40	70	the	the	DET
ejde-397	40	71	function	function	NOUN
ejde-397	40	72	f(t	f(t	PROPN
ejde-397	40	73	)	)	PUNCT
ejde-397	40	74	is	be	AUX
ejde-397	40	75	continuous	continuous	ADJ
ejde-397	40	76	.	.	PUNCT
ejde-397	41	1	a	a	DET
ejde-397	41	2	large	large	ADJ
ejde-397	41	3	number	number	NOUN
ejde-397	41	4	of	of	ADP
ejde-397	41	5	research	research	NOUN
ejde-397	41	6	papers	paper	NOUN
ejde-397	41	7	,	,	PUNCT
ejde-397	41	8	starting	start	VERB
ejde-397	41	9	presumably	presumably	ADV
ejde-397	41	10	with	with	ADP
ejde-397	41	11	that	that	PRON
ejde-397	41	12	of	of	ADP
ejde-397	41	13	yagi	yagi	NOUN
ejde-397	41	14	[	[	X
ejde-397	41	15	81	81	NUM
ejde-397	41	16	]	]	PUNCT
ejde-397	41	17	,	,	PUNCT
ejde-397	41	18	written	write	VERB
ejde-397	41	19	over	over	ADP
ejde-397	41	20	the	the	DET
ejde-397	41	21	last	last	ADJ
ejde-397	41	22	twenty	twenty	NUM
ejde-397	41	23	five	five	NUM
ejde-397	41	24	years	year	NOUN
ejde-397	41	25	,	,	PUNCT
ejde-397	41	26	have	have	VERB
ejde-397	41	27	concerned	concern	VERB
ejde-397	41	28	applications	application	NOUN
ejde-397	41	29	of	of	ADP
ejde-397	41	30	multivalued	multivalued	ADJ
ejde-397	41	31	linear	linear	ADJ
ejde-397	41	32	operators	operator	NOUN
ejde-397	41	33	to	to	PART
ejde-397	41	34	abstract	abstract	ADJ
ejde-397	41	35	degenerate	degenerate	ADJ
ejde-397	41	36	differential	differential	ADJ
ejde-397	41	37	equations	equation	NOUN
ejde-397	41	38	(	(	PUNCT
ejde-397	41	39	cf	cf	NOUN
ejde-397	41	40	.	.	PUNCT
ejde-397	42	1	[	[	X
ejde-397	42	2	8	8	NUM
ejde-397	42	3	]	]	PUNCT
ejde-397	42	4	,	,	PUNCT
ejde-397	42	5	[	[	X
ejde-397	42	6	13	13	NUM
ejde-397	42	7	]	]	PUNCT
ejde-397	42	8	,	,	PUNCT
ejde-397	42	9	[	[	X
ejde-397	42	10	17	17	NUM
ejde-397	42	11	]	]	PUNCT
ejde-397	42	12	and	and	CCONJ
ejde-397	42	13	[	[	X
ejde-397	42	14	63]-[65	63]-[65	X
ejde-397	42	15	]	]	X
ejde-397	42	16	for	for	ADP
ejde-397	42	17	the	the	DET
ejde-397	42	18	primary	primary	ADJ
ejde-397	42	19	source	source	NOUN
ejde-397	42	20	of	of	ADP
ejde-397	42	21	information	information	NOUN
ejde-397	42	22	on	on	ADP
ejde-397	42	23	this	this	DET
ejde-397	42	24	subject	subject	NOUN
ejde-397	42	25	)	)	PUNCT
ejde-397	42	26	.	.	PUNCT
ejde-397	43	1	in	in	ADP
ejde-397	43	2	section	section	NOUN
ejde-397	43	3	4	4	NUM
ejde-397	43	4	,	,	PUNCT
ejde-397	43	5	we	we	PRON
ejde-397	43	6	analyze	analyze	VERB
ejde-397	43	7	the	the	DET
ejde-397	43	8	abstract	abstract	ADJ
ejde-397	43	9	degenerate	degenerate	ADJ
ejde-397	43	10	volterra	volterra	NOUN
ejde-397	43	11	inclusion	inclusion	NOUN
ejde-397	43	12	bu(t	bu(t	NOUN
ejde-397	43	13	)	)	PUNCT
ejde-397	43	14	⊆	⊆	NUM
ejde-397	43	15	a	a	DET
ejde-397	43	16	∫	∫	PROPN
ejde-397	43	17	t	t	NOUN
ejde-397	43	18	0	0	NUM
ejde-397	43	19	a(t−	a(t−	PROPN
ejde-397	43	20	s)u(s	s)u(s	NOUN
ejde-397	43	21	)	)	PUNCT
ejde-397	43	22	ds+	ds+	ADJ
ejde-397	43	23	f(t	f(t	PROPN
ejde-397	43	24	)	)	PUNCT
ejde-397	43	25	,	,	PUNCT
ejde-397	43	26	t	t	PROPN
ejde-397	43	27	∈	∈	PROPN
ejde-397	44	1	[	[	X
ejde-397	44	2	0	0	NUM
ejde-397	44	3	,	,	PUNCT
ejde-397	44	4	τ	τ	PROPN
ejde-397	44	5	)	)	PUNCT
ejde-397	44	6	,	,	PUNCT
ejde-397	44	7	(	(	PUNCT
ejde-397	44	8	1.1	1.1	NUM
ejde-397	44	9	)	)	PUNCT
ejde-397	44	10	where	where	SCONJ
ejde-397	44	11	a	a	DET
ejde-397	44	12	∈	∈	PROPN
ejde-397	44	13	l1	l1	PROPN
ejde-397	44	14	loc([0	loc([0	PROPN
ejde-397	44	15	,	,	PUNCT
ejde-397	44	16	τ	τ	PROPN
ejde-397	44	17	)	)	PUNCT
ejde-397	44	18	)	)	PUNCT
ejde-397	44	19	,	,	PUNCT
ejde-397	44	20	a	a	PRON
ejde-397	44	21	6=	6=	NUM
ejde-397	44	22	0	0	NUM
ejde-397	44	23	,	,	PUNCT
ejde-397	44	24	a	a	DET
ejde-397	44	25	:	:	PUNCT
ejde-397	44	26	x	x	X
ejde-397	44	27	→	→	X
ejde-397	44	28	p	p	X
ejde-397	44	29	(	(	PUNCT
ejde-397	44	30	y	y	PROPN
ejde-397	44	31	)	)	PUNCT
ejde-397	44	32	and	and	CCONJ
ejde-397	44	33	b	b	X
ejde-397	44	34	:	:	PUNCT
ejde-397	44	35	x	x	X
ejde-397	44	36	→	→	X
ejde-397	44	37	p	p	X
ejde-397	44	38	(	(	PUNCT
ejde-397	44	39	y	y	PROPN
ejde-397	44	40	)	)	PUNCT
ejde-397	44	41	are	be	AUX
ejde-397	44	42	given	give	VERB
ejde-397	44	43	multivalued	multivalued	ADJ
ejde-397	44	44	linear	linear	ADJ
ejde-397	44	45	operators	operator	NOUN
ejde-397	44	46	acting	act	VERB
ejde-397	44	47	between	between	ADP
ejde-397	44	48	sequentially	sequentially	ADV
ejde-397	44	49	complete	complete	ADJ
ejde-397	44	50	locally	locally	ADV
ejde-397	44	51	convex	convex	ADJ
ejde-397	44	52	spaces	space	NOUN
ejde-397	44	53	x	x	PUNCT
ejde-397	44	54	and	and	CCONJ
ejde-397	44	55	y	y	PROPN
ejde-397	44	56	,	,	PUNCT
ejde-397	44	57	and	and	CCONJ
ejde-397	44	58	f	f	X
ejde-397	44	59	:	:	PUNCT
ejde-397	44	60	x	x	X
ejde-397	44	61	→	→	X
ejde-397	44	62	p	p	X
ejde-397	44	63	(	(	PUNCT
ejde-397	44	64	y	y	PROPN
ejde-397	44	65	)	)	PUNCT
ejde-397	44	66	is	be	AUX
ejde-397	44	67	a	a	DET
ejde-397	44	68	given	give	VERB
ejde-397	44	69	mutivalued	mutivalue	VERB
ejde-397	44	70	mapping	mapping	NOUN
ejde-397	44	71	,	,	PUNCT
ejde-397	44	72	as	as	ADV
ejde-397	44	73	well	well	ADV
ejde-397	44	74	as	as	ADP
ejde-397	44	75	the	the	DET
ejde-397	44	76	fractional	fractional	ADJ
ejde-397	44	77	sobolev	sobolev	NOUN
ejde-397	44	78	inclusions	inclusion	NOUN
ejde-397	44	79	dα	dα	ADP
ejde-397	44	80	t	t	PROPN
ejde-397	44	81	bu(t	bu(t	NOUN
ejde-397	44	82	)	)	PUNCT
ejde-397	44	83	∈	∈	NOUN
ejde-397	44	84	au(t	au(t	NUM
ejde-397	44	85	)	)	PUNCT
ejde-397	45	1	+	+	CCONJ
ejde-397	45	2	f(t	f(t	NOUN
ejde-397	45	3	)	)	PUNCT
ejde-397	45	4	,	,	PUNCT
ejde-397	45	5	t	t	PROPN
ejde-397	45	6	≥	≥	NUM
ejde-397	45	7	0	0	NUM
ejde-397	45	8	,	,	PUNCT
ejde-397	45	9	(	(	PUNCT
ejde-397	45	10	bu)(j)(0	bu)(j)(0	ADJ
ejde-397	45	11	)	)	PUNCT
ejde-397	45	12	=	=	SYM
ejde-397	45	13	bxj	bxj	NOUN
ejde-397	45	14	,	,	PUNCT
ejde-397	45	15	0	0	NUM
ejde-397	45	16	≤	≤	NUM
ejde-397	45	17	j	j	PROPN
ejde-397	45	18	≤	≤	PROPN
ejde-397	45	19	dαe	dαe	VERB
ejde-397	45	20	−	−	PROPN
ejde-397	45	21	1	1	NUM
ejde-397	45	22	,	,	PUNCT
ejde-397	45	23	(	(	PUNCT
ejde-397	45	24	1.2	1.2	NUM
ejde-397	45	25	)	)	PUNCT
ejde-397	45	26	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	45	27	abstract	abstract	ADJ
ejde-397	45	28	degenerate	degenerate	ADJ
ejde-397	45	29	volterra	volterra	NOUN
ejde-397	45	30	inclusions	inclusion	NOUN
ejde-397	45	31	3	3	NUM
ejde-397	45	32	where	where	SCONJ
ejde-397	45	33	we	we	PRON
ejde-397	45	34	assume	assume	VERB
ejde-397	45	35	that	that	SCONJ
ejde-397	45	36	b	b	X
ejde-397	45	37	=	=	SYM
ejde-397	45	38	b	b	PROPN
ejde-397	45	39	is	be	AUX
ejde-397	45	40	single	single	ADV
ejde-397	45	41	-	-	PUNCT
ejde-397	45	42	valued	value	VERB
ejde-397	45	43	,	,	PUNCT
ejde-397	45	44	and	and	CCONJ
ejde-397	45	45	bdα	bdα	PROPN
ejde-397	45	46	t	t	PROPN
ejde-397	45	47	u(t	u(t	NOUN
ejde-397	45	48	)	)	PUNCT
ejde-397	45	49	⊆	⊆	NUM
ejde-397	45	50	au(t	au(t	NUM
ejde-397	45	51	)	)	PUNCT
ejde-397	46	1	+	+	CCONJ
ejde-397	46	2	f(t	f(t	NOUN
ejde-397	46	3	)	)	PUNCT
ejde-397	46	4	,	,	PUNCT
ejde-397	46	5	t	t	PROPN
ejde-397	46	6	≥	≥	NUM
ejde-397	46	7	0	0	NUM
ejde-397	46	8	,	,	PUNCT
ejde-397	46	9	u(j)(0	u(j)(0	NUM
ejde-397	46	10	)	)	PUNCT
ejde-397	46	11	=	=	SYM
ejde-397	46	12	xj	xj	PROPN
ejde-397	46	13	,	,	PUNCT
ejde-397	46	14	0	0	NUM
ejde-397	46	15	≤	≤	NUM
ejde-397	46	16	j	j	PROPN
ejde-397	46	17	≤	≤	PROPN
ejde-397	46	18	dαe	dαe	VERB
ejde-397	46	19	−	−	PROPN
ejde-397	46	20	1	1	NUM
ejde-397	46	21	.	.	PUNCT
ejde-397	47	1	(	(	PUNCT
ejde-397	47	2	1.3	1.3	NUM
ejde-397	47	3	)	)	PUNCT
ejde-397	47	4	here	here	ADV
ejde-397	47	5	,	,	PUNCT
ejde-397	47	6	dα	dα	PROPN
ejde-397	47	7	t	t	PROPN
ejde-397	47	8	u(t	u(t	PROPN
ejde-397	47	9	)	)	PUNCT
ejde-397	47	10	denotes	denote	VERB
ejde-397	47	11	the	the	DET
ejde-397	47	12	caputo	caputo	PROPN
ejde-397	47	13	fractional	fractional	PROPN
ejde-397	47	14	derivative	derivative	NOUN
ejde-397	47	15	of	of	ADP
ejde-397	47	16	function	function	NOUN
ejde-397	47	17	u(t	u(t	NOUN
ejde-397	47	18	)	)	PUNCT
ejde-397	47	19	.	.	PUNCT
ejde-397	48	1	we	we	PRON
ejde-397	48	2	define	define	VERB
ejde-397	48	3	various	various	ADJ
ejde-397	48	4	types	type	NOUN
ejde-397	48	5	of	of	ADP
ejde-397	48	6	solutions	solution	NOUN
ejde-397	48	7	of	of	ADP
ejde-397	48	8	problems	problem	NOUN
ejde-397	48	9	(	(	PUNCT
ejde-397	48	10	1.1	1.1	NUM
ejde-397	48	11	)	)	PUNCT
ejde-397	48	12	,	,	PUNCT
ejde-397	48	13	(	(	PUNCT
ejde-397	48	14	1.2	1.2	NUM
ejde-397	48	15	)	)	PUNCT
ejde-397	48	16	and	and	CCONJ
ejde-397	48	17	(	(	PUNCT
ejde-397	48	18	1.3	1.3	NUM
ejde-397	48	19	)	)	PUNCT
ejde-397	48	20	.	.	PUNCT
ejde-397	49	1	in	in	ADP
ejde-397	49	2	theorems	theorem	NOUN
ejde-397	49	3	4.3	4.3	NUM
ejde-397	49	4	and	and	CCONJ
ejde-397	49	5	4.5	4.5	NUM
ejde-397	49	6	,	,	PUNCT
ejde-397	49	7	we	we	PRON
ejde-397	49	8	reconsider	reconsider	VERB
ejde-397	49	9	the	the	DET
ejde-397	49	10	main	main	ADJ
ejde-397	49	11	results	result	NOUN
ejde-397	49	12	of	of	ADP
ejde-397	49	13	research	research	NOUN
ejde-397	49	14	of	of	ADP
ejde-397	49	15	kim	kim	PROPN
ejde-397	50	1	[	[	X
ejde-397	50	2	31	31	NUM
ejde-397	50	3	]	]	PUNCT
ejde-397	50	4	,	,	PUNCT
ejde-397	50	5	while	while	SCONJ
ejde-397	50	6	in	in	ADP
ejde-397	50	7	theorem	theorem	NOUN
ejde-397	50	8	4.6	4.6	NUM
ejde-397	50	9	we	we	PRON
ejde-397	50	10	prove	prove	VERB
ejde-397	50	11	an	an	DET
ejde-397	50	12	extension	extension	NOUN
ejde-397	50	13	of	of	ADP
ejde-397	50	14	[	[	X
ejde-397	50	15	32	32	NUM
ejde-397	50	16	,	,	PUNCT
ejde-397	50	17	theorem	theorem	VERB
ejde-397	50	18	3.5	3.5	NUM
ejde-397	50	19	]	]	PUNCT
ejde-397	50	20	for	for	ADP
ejde-397	50	21	abstract	abstract	ADJ
ejde-397	50	22	degenerate	degenerate	ADJ
ejde-397	50	23	fractional	fractional	ADJ
ejde-397	50	24	differential	differential	ADJ
ejde-397	50	25	inclusions	inclusion	NOUN
ejde-397	50	26	.	.	PUNCT
ejde-397	51	1	subordination	subordination	NOUN
ejde-397	51	2	principles	principle	NOUN
ejde-397	51	3	are	be	AUX
ejde-397	51	4	clarified	clarify	VERB
ejde-397	51	5	in	in	ADP
ejde-397	51	6	theorem	theorem	ADJ
ejde-397	51	7	4.8	4.8	NUM
ejde-397	51	8	and	and	CCONJ
ejde-397	51	9	theorem	theorem	VERB
ejde-397	51	10	4.9	4.9	NUM
ejde-397	51	11	following	follow	VERB
ejde-397	51	12	the	the	DET
ejde-397	51	13	methods	method	NOUN
ejde-397	51	14	proposed	propose	VERB
ejde-397	51	15	by	by	ADP
ejde-397	51	16	prüss	prüss	PROPN
ejde-397	51	17	[	[	X
ejde-397	51	18	68	68	NUM
ejde-397	51	19	,	,	PUNCT
ejde-397	51	20	section	section	NOUN
ejde-397	51	21	4	4	NUM
ejde-397	51	22	]	]	PUNCT
ejde-397	51	23	and	and	CCONJ
ejde-397	51	24	bazhlekova	bazhlekova	X
ejde-397	51	25	[	[	X
ejde-397	51	26	5	5	NUM
ejde-397	51	27	,	,	PUNCT
ejde-397	51	28	section	section	NOUN
ejde-397	51	29	3	3	NUM
ejde-397	51	30	]	]	PUNCT
ejde-397	51	31	(	(	PUNCT
ejde-397	51	32	cf	cf	NOUN
ejde-397	51	33	.	.	PUNCT
ejde-397	52	1	[	[	X
ejde-397	52	2	22	22	NUM
ejde-397	52	3	]	]	PUNCT
ejde-397	52	4	and	and	CCONJ
ejde-397	52	5	[	[	X
ejde-397	52	6	42]-[46	42]-[46	NOUN
ejde-397	52	7	]	]	X
ejde-397	52	8	for	for	ADP
ejde-397	52	9	similar	similar	ADJ
ejde-397	52	10	results	result	NOUN
ejde-397	52	11	known	know	VERB
ejde-397	52	12	in	in	ADP
ejde-397	52	13	degenerate	degenerate	ADJ
ejde-397	52	14	case	case	NOUN
ejde-397	52	15	)	)	PUNCT
ejde-397	52	16	.	.	PUNCT
ejde-397	53	1	following	follow	VERB
ejde-397	53	2	the	the	DET
ejde-397	53	3	old	old	ADJ
ejde-397	53	4	ideas	idea	NOUN
ejde-397	53	5	of	of	ADP
ejde-397	53	6	delaubenfels	delaubenfel	NOUN
ejde-397	53	7	[	[	X
ejde-397	53	8	11	11	NUM
ejde-397	53	9	]	]	PUNCT
ejde-397	53	10	,	,	PUNCT
ejde-397	53	11	in	in	ADP
ejde-397	53	12	section	section	NOUN
ejde-397	53	13	5	5	NUM
ejde-397	53	14	we	we	PRON
ejde-397	53	15	introduce	introduce	VERB
ejde-397	53	16	and	and	CCONJ
ejde-397	53	17	analyze	analyze	VERB
ejde-397	53	18	the	the	DET
ejde-397	53	19	class	class	NOUN
ejde-397	53	20	of	of	ADP
ejde-397	53	21	(	(	PUNCT
ejde-397	53	22	a	a	PRON
ejde-397	53	23	,	,	PUNCT
ejde-397	53	24	k)-regularized	k)-regularize	VERB
ejde-397	53	25	(	(	PUNCT
ejde-397	53	26	c1	c1	NOUN
ejde-397	53	27	,	,	PUNCT
ejde-397	53	28	c2)-existence	c2)-existence	VERB
ejde-397	53	29	and	and	CCONJ
ejde-397	53	30	uniqueness	uniqueness	ADJ
ejde-397	53	31	families	family	NOUN
ejde-397	53	32	(	(	PUNCT
ejde-397	53	33	cf	cf	NOUN
ejde-397	53	34	.	.	PUNCT
ejde-397	54	1	[	[	X
ejde-397	54	2	36	36	NUM
ejde-397	54	3	,	,	PUNCT
ejde-397	54	4	section	section	NOUN
ejde-397	54	5	2.8	2.8	NUM
ejde-397	54	6	]	]	PUNCT
ejde-397	54	7	for	for	ADP
ejde-397	54	8	non	non	ADJ
ejde-397	54	9	-	-	ADJ
ejde-397	54	10	degenerate	degenerate	ADJ
ejde-397	54	11	case	case	NOUN
ejde-397	54	12	)	)	PUNCT
ejde-397	54	13	.	.	PUNCT
ejde-397	55	1	later	later	ADV
ejde-397	55	2	on	on	ADV
ejde-397	55	3	,	,	PUNCT
ejde-397	55	4	we	we	PRON
ejde-397	55	5	single	single	VERB
ejde-397	55	6	out	out	ADP
ejde-397	55	7	the	the	DET
ejde-397	55	8	class	class	NOUN
ejde-397	55	9	of	of	ADP
ejde-397	55	10	(	(	PUNCT
ejde-397	55	11	a	a	PRON
ejde-397	55	12	,	,	PUNCT
ejde-397	55	13	k)regularized	k)regularize	VERB
ejde-397	55	14	c	c	X
ejde-397	55	15	-	-	PUNCT
ejde-397	55	16	resolvent	resolvent	ADJ
ejde-397	55	17	families	family	NOUN
ejde-397	55	18	for	for	ADP
ejde-397	55	19	special	special	ADJ
ejde-397	55	20	considerations	consideration	NOUN
ejde-397	55	21	.	.	PUNCT
ejde-397	56	1	we	we	PRON
ejde-397	56	2	focus	focus	VERB
ejde-397	56	3	our	our	PRON
ejde-397	56	4	attention	attention	NOUN
ejde-397	56	5	on	on	ADP
ejde-397	56	6	the	the	DET
ejde-397	56	7	analysis	analysis	NOUN
ejde-397	56	8	of	of	ADP
ejde-397	56	9	hille	hille	PROPN
ejde-397	56	10	-	-	PUNCT
ejde-397	56	11	yosida	yosida	PROPN
ejde-397	56	12	’s	’s	PART
ejde-397	56	13	type	type	NOUN
ejde-397	56	14	theorems	theorem	NOUN
ejde-397	56	15	for	for	ADP
ejde-397	56	16	(	(	PUNCT
ejde-397	56	17	a	a	PRON
ejde-397	56	18	,	,	PUNCT
ejde-397	56	19	k)-regularized	k)-regularize	VERB
ejde-397	56	20	c	c	NOUN
ejde-397	56	21	-	-	PUNCT
ejde-397	56	22	resolvent	resolvent	ADJ
ejde-397	56	23	families	family	NOUN
ejde-397	56	24	generated	generate	VERB
ejde-397	56	25	by	by	ADP
ejde-397	56	26	multivalued	multivalued	ADJ
ejde-397	56	27	linear	linear	PROPN
ejde-397	56	28	operators	operator	NOUN
ejde-397	56	29	(	(	PUNCT
ejde-397	56	30	as	as	SCONJ
ejde-397	56	31	in	in	ADP
ejde-397	56	32	all	all	DET
ejde-397	56	33	previous	previous	ADJ
ejde-397	56	34	researches	research	NOUN
ejde-397	56	35	of	of	ADP
ejde-397	56	36	non	non	ADJ
ejde-397	56	37	-	-	ADJ
ejde-397	56	38	degenerate	degenerate	ADJ
ejde-397	56	39	case	case	NOUN
ejde-397	56	40	,	,	PUNCT
ejde-397	56	41	we	we	PRON
ejde-397	56	42	introduce	introduce	VERB
ejde-397	56	43	the	the	DET
ejde-397	56	44	notion	notion	NOUN
ejde-397	56	45	of	of	ADP
ejde-397	56	46	a	a	DET
ejde-397	56	47	subgenerator	subgenerator	NOUN
ejde-397	56	48	of	of	ADP
ejde-397	56	49	an	an	DET
ejde-397	56	50	(	(	PUNCT
ejde-397	56	51	a	a	PRON
ejde-397	56	52	,	,	PUNCT
ejde-397	56	53	k)regularized	k)regularize	VERB
ejde-397	56	54	c	c	X
ejde-397	56	55	-	-	PUNCT
ejde-397	56	56	resolvent	resolvent	ADJ
ejde-397	56	57	family	family	NOUN
ejde-397	56	58	and	and	CCONJ
ejde-397	56	59	investigate	investigate	VERB
ejde-397	56	60	the	the	DET
ejde-397	56	61	most	most	ADV
ejde-397	56	62	important	important	ADJ
ejde-397	56	63	properties	property	NOUN
ejde-397	56	64	of	of	ADP
ejde-397	56	65	subgenerators	subgenerator	NOUN
ejde-397	56	66	;	;	PUNCT
ejde-397	56	67	our	our	PRON
ejde-397	56	68	analysis	analysis	NOUN
ejde-397	56	69	is	be	AUX
ejde-397	56	70	based	base	VERB
ejde-397	56	71	on	on	ADP
ejde-397	56	72	the	the	DET
ejde-397	56	73	use	use	NOUN
ejde-397	56	74	of	of	ADP
ejde-397	56	75	vector	vector	NOUN
ejde-397	56	76	-	-	PUNCT
ejde-397	56	77	valued	value	VERB
ejde-397	56	78	laplace	laplace	NOUN
ejde-397	56	79	transform	transform	NOUN
ejde-397	56	80	)	)	PUNCT
ejde-397	56	81	.	.	PUNCT
ejde-397	57	1	it	it	PRON
ejde-397	57	2	is	be	AUX
ejde-397	57	3	well	well	ADV
ejde-397	57	4	known	know	VERB
ejde-397	57	5	(	(	PUNCT
ejde-397	57	6	see	see	VERB
ejde-397	57	7	e.g.	e.g.	ADV
ejde-397	57	8	[	[	X
ejde-397	57	9	17	17	NUM
ejde-397	57	10	,	,	PUNCT
ejde-397	57	11	theorem	theorem	VERB
ejde-397	57	12	2.4	2.4	NUM
ejde-397	57	13	]	]	PUNCT
ejde-397	57	14	,	,	PUNCT
ejde-397	57	15	[	[	X
ejde-397	57	16	32	32	NUM
ejde-397	57	17	,	,	PUNCT
ejde-397	57	18	theorem	theorem	VERB
ejde-397	57	19	3.6	3.6	NUM
ejde-397	57	20	]	]	PUNCT
ejde-397	57	21	and	and	CCONJ
ejde-397	57	22	[	[	X
ejde-397	57	23	31	31	NUM
ejde-397	57	24	,	,	PUNCT
ejde-397	57	25	p.	p.	NOUN
ejde-397	57	26	169	169	NUM
ejde-397	57	27	]	]	PUNCT
ejde-397	57	28	)	)	PUNCT
ejde-397	57	29	that	that	SCONJ
ejde-397	57	30	hille	hille	PROPN
ejde-397	57	31	-	-	PUNCT
ejde-397	57	32	yosida	yosida	PROPN
ejde-397	57	33	’s	’s	PART
ejde-397	57	34	type	type	NOUN
ejde-397	57	35	estimates	estimate	NOUN
ejde-397	57	36	for	for	ADP
ejde-397	57	37	the	the	DET
ejde-397	57	38	resolvent	resolvent	NOUN
ejde-397	57	39	of	of	ADP
ejde-397	57	40	a	a	DET
ejde-397	57	41	multivalued	multivalue	VERB
ejde-397	57	42	operator	operator	NOUN
ejde-397	57	43	a	a	PRON
ejde-397	57	44	immediately	immediately	ADV
ejde-397	57	45	implies	imply	VERB
ejde-397	57	46	that	that	SCONJ
ejde-397	57	47	a	a	PRON
ejde-397	57	48	is	be	AUX
ejde-397	57	49	single	single	ADV
ejde-397	57	50	-	-	PUNCT
ejde-397	57	51	valued	value	VERB
ejde-397	57	52	in	in	ADP
ejde-397	57	53	a	a	DET
ejde-397	57	54	certain	certain	ADJ
ejde-397	57	55	sense	sense	NOUN
ejde-397	57	56	.	.	PUNCT
ejde-397	58	1	in	in	ADP
ejde-397	58	2	part	part	NOUN
ejde-397	58	3	(	(	PUNCT
ejde-397	58	4	ii	ii	NOUN
ejde-397	58	5	)	)	PUNCT
ejde-397	58	6	of	of	ADP
ejde-397	58	7	theorem	theorem	NOUN
ejde-397	58	8	5.12	5.12	NUM
ejde-397	58	9	,	,	PUNCT
ejde-397	58	10	we	we	PRON
ejde-397	58	11	will	will	AUX
ejde-397	58	12	prove	prove	VERB
ejde-397	58	13	a	a	DET
ejde-397	58	14	similar	similar	ADJ
ejde-397	58	15	assertion	assertion	NOUN
ejde-397	58	16	provided	provide	VERB
ejde-397	58	17	that	that	SCONJ
ejde-397	58	18	the	the	DET
ejde-397	58	19	hilleyosida	hilleyosida	PROPN
ejde-397	58	20	condition	condition	NOUN
ejde-397	58	21	(	(	PUNCT
ejde-397	58	22	5.17	5.17	NUM
ejde-397	58	23	)	)	PUNCT
ejde-397	58	24	below	below	ADP
ejde-397	58	25	holds	hold	NOUN
ejde-397	58	26	.	.	PUNCT
ejde-397	59	1	for	for	ADP
ejde-397	59	2	the	the	DET
ejde-397	59	3	validity	validity	NOUN
ejde-397	59	4	of	of	ADP
ejde-397	59	5	theorem	theorem	NOUN
ejde-397	59	6	5.12(ii	5.12(ii	PROPN
ejde-397	59	7	)	)	PUNCT
ejde-397	59	8	,	,	PUNCT
ejde-397	59	9	we	we	PRON
ejde-397	59	10	have	have	AUX
ejde-397	59	11	found	find	VERB
ejde-397	59	12	the	the	DET
ejde-397	59	13	condition	condition	NOUN
ejde-397	59	14	k(0	k(0	PROPN
ejde-397	59	15	)	)	PUNCT
ejde-397	59	16	6=	6=	ADP
ejde-397	59	17	0	0	NUM
ejde-397	59	18	very	very	ADV
ejde-397	59	19	important	important	ADJ
ejde-397	59	20	to	to	PART
ejde-397	59	21	be	be	AUX
ejde-397	59	22	satisfied	satisfied	ADJ
ejde-397	59	23	;	;	PUNCT
ejde-397	59	24	in	in	ADP
ejde-397	59	25	other	other	ADJ
ejde-397	59	26	words	word	NOUN
ejde-397	59	27	,	,	PUNCT
ejde-397	59	28	the	the	DET
ejde-397	59	29	existence	existence	NOUN
ejde-397	59	30	of	of	ADP
ejde-397	59	31	above	above	ADV
ejde-397	59	32	-	-	PUNCT
ejde-397	59	33	mentioned	mention	VERB
ejde-397	59	34	single	single	ADJ
ejde-397	59	35	-	-	PUNCT
ejde-397	59	36	valued	value	VERB
ejde-397	59	37	branch	branch	NOUN
ejde-397	59	38	of	of	ADP
ejde-397	59	39	a	a	PRON
ejde-397	59	40	can	can	AUX
ejde-397	59	41	be	be	AUX
ejde-397	59	42	proved	prove	VERB
ejde-397	59	43	exactly	exactly	ADV
ejde-397	59	44	in	in	ADP
ejde-397	59	45	non	non	ADJ
ejde-397	59	46	-	-	ADJ
ejde-397	59	47	convoluted	convoluted	ADJ
ejde-397	59	48	or	or	CCONJ
ejde-397	59	49	non	non	ADJ
ejde-397	59	50	-	-	ADJ
ejde-397	59	51	integrated	integrated	ADJ
ejde-397	59	52	case	case	NOUN
ejde-397	59	53	,	,	PUNCT
ejde-397	59	54	so	so	SCONJ
ejde-397	59	55	that	that	SCONJ
ejde-397	59	56	we	we	PRON
ejde-397	59	57	have	have	AUX
ejde-397	59	58	arrived	arrive	VERB
ejde-397	59	59	to	to	ADP
ejde-397	59	60	a	a	DET
ejde-397	59	61	diametrically	diametrically	ADV
ejde-397	59	62	opposite	opposite	ADJ
ejde-397	59	63	conclusion	conclusion	NOUN
ejde-397	59	64	to	to	ADP
ejde-397	59	65	that	that	PRON
ejde-397	59	66	stated	state	VERB
ejde-397	59	67	on	on	ADP
ejde-397	59	68	l.	l.	PROPN
ejde-397	59	69	7	7	PROPN
ejde-397	59	70	-	-	SYM
ejde-397	59	71	13	13	NUM
ejde-397	59	72	,	,	PUNCT
ejde-397	59	73	p.	p.	NOUN
ejde-397	59	74	169	169	NUM
ejde-397	59	75	of	of	ADP
ejde-397	59	76	[	[	X
ejde-397	59	77	31	31	NUM
ejde-397	59	78	]	]	PUNCT
ejde-397	59	79	.	.	PUNCT
ejde-397	60	1	nevertheless	nevertheless	ADV
ejde-397	60	2	,	,	PUNCT
ejde-397	60	3	the	the	DET
ejde-397	60	4	existence	existence	NOUN
ejde-397	60	5	or	or	CCONJ
ejde-397	60	6	non	non	NOUN
ejde-397	60	7	-	-	NOUN
ejde-397	60	8	existence	existence	NOUN
ejde-397	60	9	of	of	ADP
ejde-397	60	10	such	such	DET
ejde-397	60	11	a	a	DET
ejde-397	60	12	single	single	ADV
ejde-397	60	13	-	-	PUNCT
ejde-397	60	14	valued	value	VERB
ejde-397	60	15	branch	branch	NOUN
ejde-397	60	16	of	of	ADP
ejde-397	60	17	a	a	PRON
ejde-397	60	18	is	be	AUX
ejde-397	60	19	not	not	PART
ejde-397	60	20	sufficient	sufficient	ADJ
ejde-397	60	21	for	for	ADP
ejde-397	60	22	obtaining	obtain	VERB
ejde-397	60	23	a	a	DET
ejde-397	60	24	fairly	fairly	ADV
ejde-397	60	25	complete	complete	ADJ
ejde-397	60	26	information	information	NOUN
ejde-397	60	27	on	on	ADP
ejde-397	60	28	the	the	DET
ejde-397	60	29	well	well	NOUN
ejde-397	60	30	-	-	PUNCT
ejde-397	60	31	posedness	posedness	NOUN
ejde-397	60	32	of	of	ADP
ejde-397	60	33	inclusion	inclusion	NOUN
ejde-397	60	34	(	(	PUNCT
ejde-397	60	35	1.1	1.1	NUM
ejde-397	60	36	)	)	PUNCT
ejde-397	60	37	with	with	ADP
ejde-397	60	38	b	b	X
ejde-397	60	39	=	=	SYM
ejde-397	60	40	i	i	PROPN
ejde-397	60	41	(	(	PUNCT
ejde-397	60	42	the	the	DET
ejde-397	60	43	reading	reading	NOUN
ejde-397	60	44	of	of	ADP
ejde-397	60	45	papers	paper	NOUN
ejde-397	60	46	[	[	X
ejde-397	60	47	31	31	NUM
ejde-397	60	48	,	,	PUNCT
ejde-397	60	49	32	32	NUM
ejde-397	60	50	]	]	PUNCT
ejde-397	60	51	has	have	AUX
ejde-397	60	52	strongly	strongly	ADV
ejde-397	60	53	influenced	influence	VERB
ejde-397	60	54	us	we	PRON
ejde-397	60	55	to	to	PART
ejde-397	60	56	write	write	VERB
ejde-397	60	57	this	this	DET
ejde-397	60	58	paper	paper	NOUN
ejde-397	60	59	,	,	PUNCT
ejde-397	60	60	and	and	CCONJ
ejde-397	60	61	compared	compare	VERB
ejde-397	60	62	with	with	ADP
ejde-397	60	63	the	the	DET
ejde-397	60	64	results	result	NOUN
ejde-397	60	65	of	of	ADP
ejde-397	60	66	[	[	X
ejde-397	60	67	31	31	NUM
ejde-397	60	68	]	]	PUNCT
ejde-397	60	69	,	,	PUNCT
ejde-397	60	70	here	here	ADV
ejde-397	60	71	we	we	PRON
ejde-397	60	72	do	do	AUX
ejde-397	60	73	not	not	PART
ejde-397	60	74	need	need	VERB
ejde-397	60	75	the	the	DET
ejde-397	60	76	assumption	assumption	NOUN
ejde-397	60	77	that	that	SCONJ
ejde-397	60	78	a(t	a(t	NOUN
ejde-397	60	79	)	)	PUNCT
ejde-397	60	80	is	be	AUX
ejde-397	60	81	a	a	DET
ejde-397	60	82	normalized	normalize	VERB
ejde-397	60	83	function	function	NOUN
ejde-397	60	84	of	of	ADP
ejde-397	60	85	local	local	ADJ
ejde-397	60	86	bounded	bounded	ADJ
ejde-397	60	87	variation	variation	NOUN
ejde-397	60	88	)	)	PUNCT
ejde-397	60	89	.	.	PUNCT
ejde-397	61	1	in	in	ADP
ejde-397	61	2	the	the	DET
ejde-397	61	3	remainder	remainder	NOUN
ejde-397	61	4	of	of	ADP
ejde-397	61	5	section	section	NOUN
ejde-397	61	6	5	5	NUM
ejde-397	61	7	,	,	PUNCT
ejde-397	61	8	we	we	PRON
ejde-397	61	9	enquire	enquire	VERB
ejde-397	61	10	into	into	ADP
ejde-397	61	11	the	the	DET
ejde-397	61	12	possibility	possibility	NOUN
ejde-397	61	13	to	to	PART
ejde-397	61	14	extend	extend	VERB
ejde-397	61	15	the	the	DET
ejde-397	61	16	most	most	ADV
ejde-397	61	17	important	important	ADJ
ejde-397	61	18	results	result	NOUN
ejde-397	61	19	from	from	ADP
ejde-397	61	20	[	[	X
ejde-397	61	21	36	36	NUM
ejde-397	61	22	,	,	PUNCT
ejde-397	61	23	section	section	NOUN
ejde-397	61	24	2.1	2.1	NUM
ejde-397	61	25	,	,	PUNCT
ejde-397	61	26	section	section	NOUN
ejde-397	61	27	2.2	2.2	NUM
ejde-397	61	28	]	]	PUNCT
ejde-397	61	29	to	to	ADP
ejde-397	61	30	(	(	PUNCT
ejde-397	61	31	a	a	PRON
ejde-397	61	32	,	,	PUNCT
ejde-397	61	33	k)-regularized	k)-regularize	VERB
ejde-397	61	34	c	c	NOUN
ejde-397	61	35	-	-	PUNCT
ejde-397	61	36	resolvent	resolvent	ADJ
ejde-397	61	37	families	family	NOUN
ejde-397	61	38	generated	generate	VERB
ejde-397	61	39	by	by	ADP
ejde-397	61	40	multivalued	multivalued	ADJ
ejde-397	61	41	linear	linear	PROPN
ejde-397	61	42	operators	operator	NOUN
ejde-397	61	43	,	,	PUNCT
ejde-397	61	44	and	and	CCONJ
ejde-397	61	45	present	present	VERB
ejde-397	61	46	several	several	ADJ
ejde-397	61	47	examples	example	NOUN
ejde-397	61	48	and	and	CCONJ
ejde-397	61	49	possible	possible	ADJ
ejde-397	61	50	applications	application	NOUN
ejde-397	61	51	of	of	ADP
ejde-397	61	52	our	our	PRON
ejde-397	61	53	abstract	abstract	ADJ
ejde-397	61	54	theoretical	theoretical	ADJ
ejde-397	61	55	results	result	NOUN
ejde-397	61	56	.	.	PUNCT
ejde-397	62	1	we	we	PRON
ejde-397	62	2	clarify	clarify	VERB
ejde-397	62	3	the	the	DET
ejde-397	62	4	complex	complex	ADJ
ejde-397	62	5	characterization	characterization	NOUN
ejde-397	62	6	theorem	theorem	NOUN
ejde-397	62	7	for	for	ADP
ejde-397	62	8	the	the	DET
ejde-397	62	9	generation	generation	NOUN
ejde-397	62	10	of	of	ADP
ejde-397	62	11	exponentially	exponentially	ADV
ejde-397	62	12	equicontinuous	equicontinuous	ADJ
ejde-397	62	13	(	(	PUNCT
ejde-397	62	14	a	a	PRON
ejde-397	62	15	,	,	PUNCT
ejde-397	62	16	k)-regularized	k)-regularize	VERB
ejde-397	62	17	c	c	NOUN
ejde-397	62	18	-	-	PUNCT
ejde-397	62	19	resolvent	resolvent	ADJ
ejde-397	62	20	families	family	NOUN
ejde-397	62	21	,	,	PUNCT
ejde-397	62	22	the	the	DET
ejde-397	62	23	generalized	generalized	ADJ
ejde-397	62	24	variation	variation	NOUN
ejde-397	62	25	of	of	ADP
ejde-397	62	26	parameters	parameter	NOUN
ejde-397	62	27	formula	formula	NOUN
ejde-397	62	28	,	,	PUNCT
ejde-397	62	29	and	and	CCONJ
ejde-397	62	30	subordination	subordination	NOUN
ejde-397	62	31	principles	principle	NOUN
ejde-397	62	32	;	;	PUNCT
ejde-397	62	33	in	in	ADP
ejde-397	62	34	two	two	NUM
ejde-397	62	35	separate	separate	ADJ
ejde-397	62	36	subsections	subsection	NOUN
ejde-397	62	37	,	,	PUNCT
ejde-397	62	38	we	we	PRON
ejde-397	62	39	analyze	analyze	VERB
ejde-397	62	40	differential	differential	ADJ
ejde-397	62	41	and	and	CCONJ
ejde-397	62	42	analytical	analytical	ADJ
ejde-397	62	43	properties	property	NOUN
ejde-397	62	44	of	of	ADP
ejde-397	62	45	(	(	PUNCT
ejde-397	62	46	a	a	PRON
ejde-397	62	47	,	,	PUNCT
ejde-397	62	48	k)-regularized	k)-regularize	VERB
ejde-397	62	49	c	c	NOUN
ejde-397	62	50	-	-	PUNCT
ejde-397	62	51	resolvent	resolvent	ADJ
ejde-397	62	52	families	family	NOUN
ejde-397	62	53	as	as	ADV
ejde-397	62	54	well	well	ADV
ejde-397	62	55	as	as	ADP
ejde-397	62	56	the	the	DET
ejde-397	62	57	case	case	NOUN
ejde-397	62	58	in	in	ADP
ejde-397	62	59	which	which	PRON
ejde-397	62	60	some	some	PRON
ejde-397	62	61	of	of	ADP
ejde-397	62	62	the	the	DET
ejde-397	62	63	regularizing	regularize	VERB
ejde-397	62	64	operators	operator	NOUN
ejde-397	62	65	c	c	PROPN
ejde-397	62	66	and	and	CCONJ
ejde-397	62	67	c2	c2	PROPN
ejde-397	62	68	is	be	AUX
ejde-397	62	69	not	not	PART
ejde-397	62	70	injective	injective	ADJ
ejde-397	62	71	.	.	PUNCT
ejde-397	63	1	we	we	PRON
ejde-397	63	2	provide	provide	VERB
ejde-397	63	3	several	several	ADJ
ejde-397	63	4	illustrative	illustrative	ADJ
ejde-397	63	5	examples	example	NOUN
ejde-397	63	6	,	,	PUNCT
ejde-397	63	7	including	include	VERB
ejde-397	63	8	applications	application	NOUN
ejde-397	63	9	to	to	ADP
ejde-397	63	10	fractional	fractional	PROPN
ejde-397	63	11	maxwell	maxwell	PROPN
ejde-397	63	12	’s	’s	PART
ejde-397	63	13	equations	equation	NOUN
ejde-397	63	14	,	,	PUNCT
ejde-397	63	15	fractional	fractional	ADJ
ejde-397	63	16	linearized	linearize	VERB
ejde-397	63	17	benney	benney	NOUN
ejde-397	63	18	-	-	PUNCT
ejde-397	63	19	luke	luke	VERB
ejde-397	63	20	equation	equation	NOUN
ejde-397	63	21	and	and	CCONJ
ejde-397	63	22	backward	backward	ADJ
ejde-397	63	23	poisson	poisson	NOUN
ejde-397	63	24	heat	heat	NOUN
ejde-397	63	25	equation	equation	NOUN
ejde-397	63	26	.	.	PUNCT
ejde-397	64	1	because	because	SCONJ
ejde-397	64	2	of	of	ADP
ejde-397	64	3	some	some	DET
ejde-397	64	4	similarity	similarity	NOUN
ejde-397	64	5	with	with	ADP
ejde-397	64	6	our	our	PRON
ejde-397	64	7	previous	previous	ADJ
ejde-397	64	8	researches	research	NOUN
ejde-397	64	9	of	of	ADP
ejde-397	64	10	non	non	ADJ
ejde-397	64	11	-	-	ADJ
ejde-397	64	12	degenerate	degenerate	ADJ
ejde-397	64	13	case	case	NOUN
ejde-397	64	14	,	,	PUNCT
ejde-397	64	15	we	we	PRON
ejde-397	64	16	have	have	AUX
ejde-397	64	17	decided	decide	VERB
ejde-397	64	18	to	to	PART
ejde-397	64	19	write	write	VERB
ejde-397	64	20	this	this	DET
ejde-397	64	21	paper	paper	NOUN
ejde-397	64	22	in	in	ADP
ejde-397	64	23	a	a	DET
ejde-397	64	24	half	half	ADJ
ejde-397	64	25	-	-	PUNCT
ejde-397	64	26	expository	expository	NOUN
ejde-397	64	27	manner	manner	NOUN
ejde-397	64	28	,	,	PUNCT
ejde-397	64	29	including	include	VERB
ejde-397	64	30	only	only	ADV
ejde-397	64	31	the	the	DET
ejde-397	64	32	4	4	NUM
ejde-397	64	33	m.	m.	NOUN
ejde-397	64	34	kostić	kostić	NOUN
ejde-397	65	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	65	2	most	most	ADV
ejde-397	65	3	relevant	relevant	ADJ
ejde-397	65	4	details	detail	NOUN
ejde-397	65	5	of	of	ADP
ejde-397	65	6	proofs	proof	NOUN
ejde-397	65	7	of	of	ADP
ejde-397	65	8	our	our	PRON
ejde-397	65	9	structural	structural	ADJ
ejde-397	65	10	results	result	NOUN
ejde-397	65	11	.	.	PUNCT
ejde-397	66	1	the	the	DET
ejde-397	66	2	author	author	NOUN
ejde-397	66	3	would	would	AUX
ejde-397	66	4	like	like	VERB
ejde-397	66	5	to	to	PART
ejde-397	66	6	express	express	VERB
ejde-397	66	7	his	his	PRON
ejde-397	66	8	appreciation	appreciation	NOUN
ejde-397	66	9	and	and	CCONJ
ejde-397	66	10	sincere	sincere	ADJ
ejde-397	66	11	thanks	thank	NOUN
ejde-397	66	12	to	to	ADP
ejde-397	66	13	prof	prof	PROPN
ejde-397	66	14	.	.	PUNCT
ejde-397	67	1	vladimir	vladimir	PROPN
ejde-397	67	2	fedorov	fedorov	PROPN
ejde-397	67	3	(	(	PUNCT
ejde-397	67	4	chelyabinsk	chelyabinsk	PROPN
ejde-397	67	5	,	,	PUNCT
ejde-397	67	6	russia	russia	PROPN
ejde-397	67	7	)	)	PUNCT
ejde-397	67	8	and	and	CCONJ
ejde-397	67	9	prof	prof	PROPN
ejde-397	67	10	.	.	PUNCT
ejde-397	68	1	rodrigo	rodrigo	PROPN
ejde-397	68	2	ponce	ponce	PROPN
ejde-397	68	3	(	(	PUNCT
ejde-397	68	4	talca	talca	ADV
ejde-397	68	5	,	,	PUNCT
ejde-397	68	6	chile	chile	PROPN
ejde-397	68	7	)	)	PUNCT
ejde-397	68	8	for	for	ADP
ejde-397	68	9	many	many	ADJ
ejde-397	68	10	stimulating	stimulating	ADJ
ejde-397	68	11	and	and	CCONJ
ejde-397	68	12	enlightening	enlightening	ADJ
ejde-397	68	13	discussions	discussion	NOUN
ejde-397	68	14	during	during	ADP
ejde-397	68	15	the	the	DET
ejde-397	68	16	research	research	NOUN
ejde-397	68	17	.	.	PUNCT
ejde-397	69	1	we	we	PRON
ejde-397	69	2	use	use	VERB
ejde-397	69	3	the	the	DET
ejde-397	69	4	standard	standard	ADJ
ejde-397	69	5	terminology	terminology	NOUN
ejde-397	69	6	throughout	throughout	ADP
ejde-397	69	7	the	the	DET
ejde-397	69	8	paper	paper	NOUN
ejde-397	69	9	.	.	PUNCT
ejde-397	70	1	by	by	ADP
ejde-397	70	2	x	x	SYM
ejde-397	70	3	we	we	PRON
ejde-397	70	4	denote	denote	VERB
ejde-397	70	5	a	a	DET
ejde-397	70	6	hausdorff	hausdorff	NOUN
ejde-397	70	7	sequentially	sequentially	ADV
ejde-397	70	8	complete	complete	ADJ
ejde-397	70	9	locally	locally	ADV
ejde-397	70	10	convex	convex	ADJ
ejde-397	70	11	space	space	NOUN
ejde-397	70	12	over	over	ADP
ejde-397	70	13	the	the	DET
ejde-397	70	14	field	field	NOUN
ejde-397	70	15	of	of	ADP
ejde-397	70	16	complex	complex	ADJ
ejde-397	70	17	numbers	number	NOUN
ejde-397	70	18	,	,	PUNCT
ejde-397	70	19	sclcs	sclcs	NOUN
ejde-397	70	20	for	for	ADP
ejde-397	70	21	short	short	ADJ
ejde-397	70	22	.	.	PUNCT
ejde-397	71	1	if	if	SCONJ
ejde-397	71	2	y	y	PROPN
ejde-397	71	3	is	be	AUX
ejde-397	71	4	also	also	ADV
ejde-397	71	5	an	an	DET
ejde-397	71	6	sclcs	sclcs	NOUN
ejde-397	71	7	over	over	ADP
ejde-397	71	8	the	the	DET
ejde-397	71	9	same	same	ADJ
ejde-397	71	10	field	field	NOUN
ejde-397	71	11	of	of	ADP
ejde-397	71	12	scalars	scalar	NOUN
ejde-397	71	13	as	as	ADP
ejde-397	71	14	x	x	X
ejde-397	71	15	,	,	PUNCT
ejde-397	71	16	then	then	ADV
ejde-397	71	17	we	we	PRON
ejde-397	71	18	denote	denote	VERB
ejde-397	71	19	by	by	ADP
ejde-397	71	20	l(x	l(x	PROPN
ejde-397	71	21	,	,	PUNCT
ejde-397	71	22	y	y	PROPN
ejde-397	71	23	)	)	PUNCT
ejde-397	71	24	the	the	DET
ejde-397	71	25	space	space	NOUN
ejde-397	71	26	consisting	consist	VERB
ejde-397	71	27	of	of	ADP
ejde-397	71	28	all	all	DET
ejde-397	71	29	continuous	continuous	ADJ
ejde-397	71	30	linear	linear	ADJ
ejde-397	71	31	mappings	mapping	NOUN
ejde-397	71	32	from	from	ADP
ejde-397	71	33	x	x	NOUN
ejde-397	71	34	into	into	ADP
ejde-397	71	35	y	y	PROPN
ejde-397	71	36	;	;	PUNCT
ejde-397	71	37	l(x	l(x	PROPN
ejde-397	71	38	)	)	PUNCT
ejde-397	71	39	≡	≡	PROPN
ejde-397	71	40	l(x	l(x	PROPN
ejde-397	71	41	,	,	PUNCT
ejde-397	71	42	x	x	NOUN
ejde-397	71	43	)	)	PUNCT
ejde-397	71	44	.	.	PUNCT
ejde-397	72	1	by	by	ADP
ejde-397	72	2	~x	~x	NUM
ejde-397	72	3	(	(	PUNCT
ejde-397	72	4	~	~	PUNCT
ejde-397	72	5	,	,	PUNCT
ejde-397	72	6	if	if	SCONJ
ejde-397	72	7	there	there	PRON
ejde-397	72	8	is	be	VERB
ejde-397	72	9	no	no	DET
ejde-397	72	10	risk	risk	NOUN
ejde-397	72	11	for	for	ADP
ejde-397	72	12	confusion	confusion	NOUN
ejde-397	72	13	)	)	PUNCT
ejde-397	72	14	,	,	PUNCT
ejde-397	72	15	we	we	PRON
ejde-397	72	16	denote	denote	VERB
ejde-397	72	17	the	the	DET
ejde-397	72	18	fundamental	fundamental	ADJ
ejde-397	72	19	system	system	NOUN
ejde-397	72	20	of	of	ADP
ejde-397	72	21	seminorms	seminorm	NOUN
ejde-397	72	22	which	which	PRON
ejde-397	72	23	defines	define	VERB
ejde-397	72	24	the	the	DET
ejde-397	72	25	topology	topology	NOUN
ejde-397	72	26	of	of	ADP
ejde-397	72	27	x	x	PROPN
ejde-397	72	28	;	;	PUNCT
ejde-397	72	29	the	the	DET
ejde-397	72	30	fundamental	fundamental	ADJ
ejde-397	72	31	system	system	NOUN
ejde-397	72	32	of	of	ADP
ejde-397	72	33	seminorms	seminorm	NOUN
ejde-397	72	34	which	which	PRON
ejde-397	72	35	defines	define	VERB
ejde-397	72	36	the	the	DET
ejde-397	72	37	topology	topology	NOUN
ejde-397	72	38	on	on	ADP
ejde-397	72	39	an	an	DET
ejde-397	72	40	arbitrary	arbitrary	ADJ
ejde-397	72	41	sclcs	sclcs	NOUN
ejde-397	72	42	z	z	NOUN
ejde-397	72	43	is	be	AUX
ejde-397	72	44	denoted	denote	VERB
ejde-397	72	45	by	by	ADP
ejde-397	72	46	~z	~z	PUNCT
ejde-397	72	47	.	.	PUNCT
ejde-397	73	1	the	the	DET
ejde-397	73	2	symbol	symbol	NOUN
ejde-397	73	3	ix	ix	ADP
ejde-397	73	4	(	(	PUNCT
ejde-397	73	5	iy	iy	INTJ
ejde-397	73	6	)	)	PUNCT
ejde-397	73	7	denotes	denote	VERB
ejde-397	73	8	the	the	DET
ejde-397	73	9	identity	identity	NOUN
ejde-397	73	10	operator	operator	NOUN
ejde-397	73	11	on	on	ADP
ejde-397	73	12	x	x	SYM
ejde-397	73	13	(	(	PUNCT
ejde-397	73	14	y	y	PROPN
ejde-397	73	15	)	)	PUNCT
ejde-397	73	16	;	;	PUNCT
ejde-397	73	17	if	if	SCONJ
ejde-397	73	18	there	there	PRON
ejde-397	73	19	is	be	VERB
ejde-397	73	20	no	no	DET
ejde-397	73	21	risk	risk	NOUN
ejde-397	73	22	for	for	ADP
ejde-397	73	23	confusion	confusion	NOUN
ejde-397	73	24	,	,	PUNCT
ejde-397	73	25	then	then	ADV
ejde-397	73	26	we	we	PRON
ejde-397	73	27	also	also	ADV
ejde-397	73	28	write	write	VERB
ejde-397	73	29	i	i	PRON
ejde-397	73	30	in	in	ADP
ejde-397	73	31	place	place	NOUN
ejde-397	73	32	of	of	ADP
ejde-397	73	33	ix	ix	PROPN
ejde-397	73	34	.	.	PUNCT
ejde-397	74	1	by	by	ADP
ejde-397	74	2	x∗	x∗	PROPN
ejde-397	74	3	we	we	PRON
ejde-397	74	4	denote	denote	VERB
ejde-397	74	5	the	the	DET
ejde-397	74	6	dual	dual	ADJ
ejde-397	74	7	space	space	NOUN
ejde-397	74	8	of	of	ADP
ejde-397	74	9	x.	x.	NOUN
ejde-397	74	10	let	let	VERB
ejde-397	74	11	0	0	PUNCT
ejde-397	74	12	<	<	X
ejde-397	74	13	τ	τ	X
ejde-397	74	14	≤	≤	PUNCT
ejde-397	74	15	∞.	∞.	PROPN
ejde-397	74	16	a	a	DET
ejde-397	74	17	strongly	strongly	ADV
ejde-397	74	18	continuous	continuous	ADJ
ejde-397	74	19	operator	operator	NOUN
ejde-397	74	20	family	family	NOUN
ejde-397	74	21	(	(	PUNCT
ejde-397	74	22	w	w	PROPN
ejde-397	74	23	(	(	PUNCT
ejde-397	74	24	t))t∈[0,τ	t))t∈[0,τ	PROPN
ejde-397	74	25	)	)	PUNCT
ejde-397	74	26	⊆	⊆	NUM
ejde-397	74	27	l(x	l(x	PROPN
ejde-397	74	28	,	,	PUNCT
ejde-397	74	29	y	y	PROPN
ejde-397	74	30	)	)	PUNCT
ejde-397	74	31	is	be	AUX
ejde-397	74	32	said	say	VERB
ejde-397	74	33	to	to	PART
ejde-397	74	34	be	be	AUX
ejde-397	74	35	locally	locally	ADV
ejde-397	74	36	equicontinuous	equicontinuous	ADJ
ejde-397	74	37	if	if	SCONJ
ejde-397	74	38	and	and	CCONJ
ejde-397	74	39	only	only	ADV
ejde-397	74	40	if	if	SCONJ
ejde-397	74	41	,	,	PUNCT
ejde-397	74	42	for	for	ADP
ejde-397	74	43	every	every	DET
ejde-397	74	44	t	t	NOUN
ejde-397	74	45	∈	∈	PROPN
ejde-397	74	46	(	(	PUNCT
ejde-397	74	47	0	0	NUM
ejde-397	74	48	,	,	PUNCT
ejde-397	74	49	τ	τ	PROPN
ejde-397	74	50	)	)	PUNCT
ejde-397	74	51	and	and	CCONJ
ejde-397	74	52	for	for	ADP
ejde-397	74	53	every	every	DET
ejde-397	74	54	p	p	PROPN
ejde-397	74	55	∈	∈	PROPN
ejde-397	74	56	~y	~y	NUM
ejde-397	74	57	,	,	PUNCT
ejde-397	74	58	there	there	PRON
ejde-397	74	59	exist	exist	VERB
ejde-397	74	60	qp	qp	ADP
ejde-397	74	61	∈	∈	PROPN
ejde-397	74	62	~x	~x	PUNCT
ejde-397	74	63	and	and	CCONJ
ejde-397	74	64	cp	cp	INTJ
ejde-397	74	65	>	>	X
ejde-397	74	66	0	0	NUM
ejde-397	74	67	such	such	ADJ
ejde-397	74	68	that	that	SCONJ
ejde-397	74	69	p(w	p(w	PROPN
ejde-397	74	70	(	(	PUNCT
ejde-397	74	71	t)x	t)x	ADJ
ejde-397	74	72	)	)	PUNCT
ejde-397	74	73	≤	≤	NUM
ejde-397	74	74	cpqp(x	cpqp(x	NOUN
ejde-397	74	75	)	)	PUNCT
ejde-397	74	76	,	,	PUNCT
ejde-397	74	77	x	x	PUNCT
ejde-397	74	78	∈	∈	PROPN
ejde-397	74	79	x	x	NOUN
ejde-397	74	80	,	,	PUNCT
ejde-397	74	81	t	t	PROPN
ejde-397	74	82	∈	∈	PROPN
ejde-397	75	1	[	[	X
ejde-397	75	2	0	0	NUM
ejde-397	75	3	,	,	PUNCT
ejde-397	75	4	t	t	X
ejde-397	75	5	]	]	PUNCT
ejde-397	75	6	;	;	PUNCT
ejde-397	75	7	the	the	DET
ejde-397	75	8	notions	notion	NOUN
ejde-397	75	9	of	of	ADP
ejde-397	75	10	equicontinuity	equicontinuity	NOUN
ejde-397	75	11	of	of	ADP
ejde-397	75	12	(	(	PUNCT
ejde-397	75	13	w	w	PROPN
ejde-397	75	14	(	(	PUNCT
ejde-397	75	15	t))t∈[0,τ	t))t∈[0,τ	PROPN
ejde-397	75	16	)	)	PUNCT
ejde-397	75	17	and	and	CCONJ
ejde-397	75	18	the	the	DET
ejde-397	75	19	exponential	exponential	ADJ
ejde-397	75	20	equicontinuity	equicontinuity	NOUN
ejde-397	75	21	of	of	ADP
ejde-397	75	22	(	(	PUNCT
ejde-397	75	23	w	w	PROPN
ejde-397	75	24	(	(	PUNCT
ejde-397	75	25	t))t≥0	t))t≥0	PROPN
ejde-397	75	26	are	be	AUX
ejde-397	75	27	defined	define	VERB
ejde-397	75	28	similarly	similarly	ADV
ejde-397	75	29	.	.	PUNCT
ejde-397	76	1	notice	notice	VERB
ejde-397	76	2	that	that	SCONJ
ejde-397	76	3	(	(	PUNCT
ejde-397	76	4	w	w	PROPN
ejde-397	76	5	(	(	PUNCT
ejde-397	76	6	t))t∈[0,τ	t))t∈[0,τ	PROPN
ejde-397	76	7	)	)	PUNCT
ejde-397	76	8	is	be	AUX
ejde-397	76	9	automatically	automatically	ADV
ejde-397	76	10	locally	locally	ADV
ejde-397	76	11	equicontinuous	equicontinuous	ADJ
ejde-397	76	12	in	in	ADP
ejde-397	76	13	case	case	NOUN
ejde-397	76	14	that	that	SCONJ
ejde-397	76	15	the	the	DET
ejde-397	76	16	space	space	NOUN
ejde-397	76	17	x	x	PUNCT
ejde-397	76	18	is	be	AUX
ejde-397	76	19	barreled	barrel	VERB
ejde-397	76	20	(	(	PUNCT
ejde-397	76	21	[	[	X
ejde-397	76	22	62	62	NUM
ejde-397	76	23	]	]	PUNCT
ejde-397	76	24	)	)	PUNCT
ejde-397	76	25	.	.	PUNCT
ejde-397	77	1	by	by	ADP
ejde-397	77	2	b	b	NOUN
ejde-397	77	3	we	we	PRON
ejde-397	77	4	denote	denote	VERB
ejde-397	77	5	the	the	DET
ejde-397	77	6	family	family	NOUN
ejde-397	77	7	consisting	consist	VERB
ejde-397	77	8	of	of	ADP
ejde-397	77	9	all	all	DET
ejde-397	77	10	bounded	bound	VERB
ejde-397	77	11	subsets	subset	NOUN
ejde-397	77	12	of	of	ADP
ejde-397	77	13	x.	x.	NOUN
ejde-397	77	14	define	define	VERB
ejde-397	77	15	pb(t	pb(t	PUNCT
ejde-397	77	16	)	)	PUNCT
ejde-397	78	1	:	:	PUNCT
ejde-397	78	2	=	=	PUNCT
ejde-397	78	3	supx∈b	supx∈b	PROPN
ejde-397	78	4	p(tx	p(tx	NUM
ejde-397	78	5	)	)	PUNCT
ejde-397	78	6	,	,	PUNCT
ejde-397	78	7	p	p	NOUN
ejde-397	78	8	∈	∈	PROPN
ejde-397	78	9	~y	~y	NUM
ejde-397	78	10	,	,	PUNCT
ejde-397	78	11	b	b	X
ejde-397	78	12	∈	∈	PROPN
ejde-397	78	13	b	b	PROPN
ejde-397	78	14	,	,	PUNCT
ejde-397	78	15	t	t	PROPN
ejde-397	78	16	∈	∈	PROPN
ejde-397	78	17	l(x	l(x	PROPN
ejde-397	78	18	,	,	PUNCT
ejde-397	78	19	y	y	PROPN
ejde-397	78	20	)	)	PUNCT
ejde-397	78	21	.	.	PUNCT
ejde-397	79	1	then	then	ADV
ejde-397	79	2	pb	pb	PROPN
ejde-397	79	3	(	(	PUNCT
ejde-397	79	4	·	·	PUNCT
ejde-397	79	5	)	)	PUNCT
ejde-397	79	6	is	be	AUX
ejde-397	79	7	a	a	DET
ejde-397	79	8	seminorm	seminorm	NOUN
ejde-397	79	9	on	on	ADP
ejde-397	79	10	l(x	l(x	PROPN
ejde-397	79	11	,	,	PUNCT
ejde-397	79	12	y	y	PROPN
ejde-397	79	13	)	)	PUNCT
ejde-397	79	14	and	and	CCONJ
ejde-397	79	15	the	the	DET
ejde-397	79	16	system	system	NOUN
ejde-397	79	17	(	(	PUNCT
ejde-397	79	18	pb)(p	pb)(p	NOUN
ejde-397	79	19	,	,	PUNCT
ejde-397	79	20	b)∈~y	b)∈~y	VERB
ejde-397	79	21	×b	×b	NOUN
ejde-397	79	22	induces	induce	VERB
ejde-397	79	23	the	the	DET
ejde-397	79	24	hausdorff	hausdorff	NOUN
ejde-397	79	25	locally	locally	ADV
ejde-397	79	26	convex	convex	ADJ
ejde-397	79	27	topology	topology	NOUN
ejde-397	79	28	on	on	ADP
ejde-397	79	29	l(x	l(x	PROPN
ejde-397	79	30	,	,	PUNCT
ejde-397	79	31	y	y	PROPN
ejde-397	79	32	)	)	PUNCT
ejde-397	79	33	.	.	PUNCT
ejde-397	80	1	if	if	SCONJ
ejde-397	80	2	y	y	PROPN
ejde-397	80	3	is	be	AUX
ejde-397	80	4	continuously	continuously	ADV
ejde-397	80	5	embedded	embed	VERB
ejde-397	80	6	in	in	ADP
ejde-397	80	7	x	x	PROPN
ejde-397	80	8	,	,	PUNCT
ejde-397	80	9	we	we	PRON
ejde-397	80	10	will	will	AUX
ejde-397	80	11	use	use	VERB
ejde-397	80	12	the	the	DET
ejde-397	80	13	notation	notation	NOUN
ejde-397	80	14	y	y	PROPN
ejde-397	80	15	↪	↪	PROPN
ejde-397	80	16	→	→	SYM
ejde-397	80	17	x.	x.	NOUN
ejde-397	80	18	suppose	suppose	VERB
ejde-397	80	19	that	that	SCONJ
ejde-397	80	20	a	a	PRON
ejde-397	80	21	is	be	AUX
ejde-397	80	22	a	a	DET
ejde-397	80	23	closed	closed	ADJ
ejde-397	80	24	linear	linear	NOUN
ejde-397	80	25	operator	operator	NOUN
ejde-397	80	26	acting	act	VERB
ejde-397	80	27	on	on	ADP
ejde-397	80	28	x.	x.	NOUN
ejde-397	81	1	then	then	ADV
ejde-397	81	2	we	we	PRON
ejde-397	81	3	denote	denote	VERB
ejde-397	81	4	the	the	DET
ejde-397	81	5	domain	domain	NOUN
ejde-397	81	6	,	,	PUNCT
ejde-397	81	7	kernel	kernel	NOUN
ejde-397	81	8	space	space	NOUN
ejde-397	81	9	and	and	CCONJ
ejde-397	81	10	range	range	NOUN
ejde-397	81	11	of	of	ADP
ejde-397	81	12	a	a	PRON
ejde-397	81	13	by	by	ADP
ejde-397	81	14	d(a	d(a	PROPN
ejde-397	81	15	)	)	PUNCT
ejde-397	81	16	,	,	PUNCT
ejde-397	81	17	n(a	n(a	NUM
ejde-397	81	18	)	)	PUNCT
ejde-397	81	19	and	and	CCONJ
ejde-397	81	20	r(a	r(a	PROPN
ejde-397	81	21	)	)	PUNCT
ejde-397	81	22	,	,	PUNCT
ejde-397	81	23	respectively	respectively	ADV
ejde-397	81	24	.	.	PUNCT
ejde-397	82	1	since	since	SCONJ
ejde-397	82	2	no	no	DET
ejde-397	82	3	confusion	confusion	NOUN
ejde-397	82	4	seems	seem	VERB
ejde-397	82	5	likely	likely	ADJ
ejde-397	82	6	,	,	PUNCT
ejde-397	82	7	we	we	PRON
ejde-397	82	8	will	will	AUX
ejde-397	82	9	identify	identify	VERB
ejde-397	82	10	a	a	PRON
ejde-397	82	11	with	with	ADP
ejde-397	82	12	its	its	PRON
ejde-397	82	13	graph	graph	NOUN
ejde-397	82	14	.	.	PUNCT
ejde-397	83	1	set	set	VERB
ejde-397	83	2	pa(x	pa(x	NOUN
ejde-397	83	3	)	)	PUNCT
ejde-397	84	1	:	:	PUNCT
ejde-397	84	2	=	=	SYM
ejde-397	84	3	p(x	p(x	PROPN
ejde-397	84	4	)	)	PUNCT
ejde-397	84	5	+	+	NUM
ejde-397	84	6	p(ax	p(ax	NOUN
ejde-397	84	7	)	)	PUNCT
ejde-397	84	8	,	,	PUNCT
ejde-397	84	9	x	x	PUNCT
ejde-397	84	10	∈	∈	PROPN
ejde-397	84	11	d(a	d(a	PROPN
ejde-397	84	12	)	)	PUNCT
ejde-397	84	13	,	,	PUNCT
ejde-397	84	14	p	p	PROPN
ejde-397	84	15	∈	∈	PROPN
ejde-397	84	16	~.	~.	X
ejde-397	84	17	then	then	ADV
ejde-397	84	18	the	the	DET
ejde-397	84	19	calibration	calibration	NOUN
ejde-397	84	20	(	(	PUNCT
ejde-397	84	21	pa)p∈~	pa)p∈~	PROPN
ejde-397	84	22	induces	induce	VERB
ejde-397	84	23	the	the	DET
ejde-397	84	24	hausdorff	hausdorff	NOUN
ejde-397	84	25	sequentially	sequentially	ADV
ejde-397	84	26	complete	complete	ADJ
ejde-397	84	27	locally	locally	ADV
ejde-397	84	28	convex	convex	ADJ
ejde-397	84	29	topology	topology	NOUN
ejde-397	84	30	on	on	ADP
ejde-397	84	31	d(a	d(a	PROPN
ejde-397	84	32	)	)	PUNCT
ejde-397	84	33	;	;	PUNCT
ejde-397	84	34	we	we	PRON
ejde-397	84	35	denote	denote	VERB
ejde-397	84	36	this	this	DET
ejde-397	84	37	space	space	NOUN
ejde-397	84	38	simply	simply	ADV
ejde-397	84	39	by	by	ADP
ejde-397	84	40	[	[	X
ejde-397	84	41	d(a	d(a	PROPN
ejde-397	84	42	)	)	PUNCT
ejde-397	84	43	]	]	PUNCT
ejde-397	84	44	.	.	PUNCT
ejde-397	85	1	suppose	suppose	VERB
ejde-397	85	2	that	that	SCONJ
ejde-397	85	3	v	v	NOUN
ejde-397	85	4	is	be	AUX
ejde-397	85	5	a	a	DET
ejde-397	85	6	general	general	ADJ
ejde-397	85	7	topological	topological	ADJ
ejde-397	85	8	vector	vector	NOUN
ejde-397	85	9	space	space	NOUN
ejde-397	85	10	(	(	PUNCT
ejde-397	85	11	the	the	DET
ejde-397	85	12	consistent	consistent	ADJ
ejde-397	85	13	and	and	CCONJ
ejde-397	85	14	stable	stable	ADJ
ejde-397	85	15	theory	theory	NOUN
ejde-397	85	16	of	of	ADP
ejde-397	85	17	abstract	abstract	ADJ
ejde-397	85	18	degenerate	degenerate	ADJ
ejde-397	85	19	volterra	volterra	PROPN
ejde-397	85	20	integro	integro	PROPN
ejde-397	85	21	-	-	PUNCT
ejde-397	85	22	differential	differential	NOUN
ejde-397	85	23	equations	equation	NOUN
ejde-397	85	24	in	in	ADP
ejde-397	85	25	non	non	ADJ
ejde-397	85	26	-	-	ADJ
ejde-397	85	27	locally	locally	ADV
ejde-397	85	28	convex	convex	ADJ
ejde-397	85	29	spaces	space	NOUN
ejde-397	85	30	has	have	AUX
ejde-397	85	31	not	not	PART
ejde-397	85	32	been	be	AUX
ejde-397	85	33	yet	yet	ADV
ejde-397	85	34	created	create	VERB
ejde-397	85	35	;	;	PUNCT
ejde-397	85	36	see	see	VERB
ejde-397	85	37	[	[	X
ejde-397	85	38	26	26	NUM
ejde-397	85	39	]	]	PUNCT
ejde-397	85	40	for	for	ADP
ejde-397	85	41	some	some	DET
ejde-397	85	42	results	result	NOUN
ejde-397	85	43	established	establish	VERB
ejde-397	85	44	in	in	ADP
ejde-397	85	45	non	non	ADJ
ejde-397	85	46	-	-	ADJ
ejde-397	85	47	degenerate	degenerate	ADJ
ejde-397	85	48	case	case	NOUN
ejde-397	85	49	)	)	PUNCT
ejde-397	85	50	.	.	PUNCT
ejde-397	86	1	as	as	SCONJ
ejde-397	86	2	it	it	PRON
ejde-397	86	3	is	be	AUX
ejde-397	86	4	well	well	ADV
ejde-397	86	5	-	-	PUNCT
ejde-397	86	6	known	know	VERB
ejde-397	86	7	,	,	PUNCT
ejde-397	86	8	a	a	DET
ejde-397	86	9	function	function	NOUN
ejde-397	86	10	f	f	NOUN
ejde-397	86	11	:	:	PUNCT
ejde-397	86	12	ω	ω	PROPN
ejde-397	86	13	→	→	SYM
ejde-397	86	14	v	v	PROPN
ejde-397	86	15	,	,	PUNCT
ejde-397	86	16	where	where	SCONJ
ejde-397	86	17	ω	ω	PROPN
ejde-397	86	18	is	be	AUX
ejde-397	86	19	an	an	DET
ejde-397	86	20	open	open	ADJ
ejde-397	86	21	non	non	ADJ
ejde-397	86	22	-	-	ADJ
ejde-397	86	23	empty	empty	ADJ
ejde-397	86	24	subset	subset	NOUN
ejde-397	86	25	of	of	ADP
ejde-397	86	26	c	c	PROPN
ejde-397	86	27	,	,	PUNCT
ejde-397	86	28	is	be	AUX
ejde-397	86	29	said	say	VERB
ejde-397	86	30	to	to	PART
ejde-397	86	31	be	be	AUX
ejde-397	86	32	analytic	analytic	ADJ
ejde-397	86	33	if	if	SCONJ
ejde-397	86	34	it	it	PRON
ejde-397	86	35	is	be	AUX
ejde-397	86	36	locally	locally	ADV
ejde-397	86	37	expressible	expressible	ADJ
ejde-397	86	38	in	in	ADP
ejde-397	86	39	a	a	DET
ejde-397	86	40	neighborhood	neighborhood	NOUN
ejde-397	86	41	of	of	ADP
ejde-397	86	42	any	any	DET
ejde-397	86	43	point	point	NOUN
ejde-397	86	44	z	z	NOUN
ejde-397	86	45	∈	∈	NOUN
ejde-397	86	46	ω	ω	X
ejde-397	86	47	by	by	ADP
ejde-397	86	48	a	a	DET
ejde-397	86	49	uniformly	uniformly	ADV
ejde-397	86	50	convergent	convergent	NOUN
ejde-397	86	51	power	power	NOUN
ejde-397	86	52	series	series	NOUN
ejde-397	86	53	with	with	ADP
ejde-397	86	54	coefficients	coefficient	NOUN
ejde-397	86	55	in	in	ADP
ejde-397	86	56	v	v	NOUN
ejde-397	86	57	.	.	PUNCT
ejde-397	87	1	the	the	DET
ejde-397	87	2	reader	reader	NOUN
ejde-397	87	3	may	may	AUX
ejde-397	87	4	consult	consult	VERB
ejde-397	87	5	[	[	X
ejde-397	87	6	1	1	NUM
ejde-397	87	7	]	]	PUNCT
ejde-397	87	8	,	,	PUNCT
ejde-397	87	9	[	[	X
ejde-397	87	10	36	36	NUM
ejde-397	87	11	,	,	PUNCT
ejde-397	87	12	section	section	NOUN
ejde-397	87	13	1.1	1.1	NUM
ejde-397	87	14	]	]	PUNCT
ejde-397	87	15	and	and	CCONJ
ejde-397	87	16	references	reference	NOUN
ejde-397	87	17	cited	cite	VERB
ejde-397	87	18	there	there	ADV
ejde-397	87	19	for	for	ADP
ejde-397	87	20	the	the	DET
ejde-397	87	21	basic	basic	ADJ
ejde-397	87	22	information	information	NOUN
ejde-397	87	23	about	about	ADP
ejde-397	87	24	vector	vector	NOUN
ejde-397	87	25	-	-	PUNCT
ejde-397	87	26	valued	value	VERB
ejde-397	87	27	analytic	analytic	ADJ
ejde-397	87	28	functions	function	NOUN
ejde-397	87	29	.	.	PUNCT
ejde-397	88	1	in	in	ADP
ejde-397	88	2	our	our	PRON
ejde-397	88	3	framework	framework	NOUN
ejde-397	88	4	,	,	PUNCT
ejde-397	88	5	the	the	DET
ejde-397	88	6	analyticity	analyticity	NOUN
ejde-397	88	7	of	of	ADP
ejde-397	88	8	a	a	DET
ejde-397	88	9	mapping	mapping	NOUN
ejde-397	88	10	f	f	NOUN
ejde-397	88	11	:	:	PUNCT
ejde-397	88	12	ω	ω	X
ejde-397	88	13	→	→	PUNCT
ejde-397	88	14	x	x	X
ejde-397	88	15	is	be	AUX
ejde-397	88	16	equivalent	equivalent	ADJ
ejde-397	88	17	with	with	ADP
ejde-397	88	18	its	its	PRON
ejde-397	88	19	weak	weak	ADJ
ejde-397	88	20	analyticity	analyticity	NOUN
ejde-397	88	21	.	.	PUNCT
ejde-397	89	1	a	a	DET
ejde-397	89	2	function	function	NOUN
ejde-397	89	3	f	f	NOUN
ejde-397	89	4	:	:	PUNCT
ejde-397	90	1	[	[	X
ejde-397	90	2	0	0	NUM
ejde-397	90	3	,	,	PUNCT
ejde-397	90	4	t	t	X
ejde-397	90	5	]	]	PUNCT
ejde-397	90	6	→	→	SYM
ejde-397	90	7	x	x	X
ejde-397	90	8	,	,	PUNCT
ejde-397	90	9	where	where	SCONJ
ejde-397	90	10	0	0	X
ejde-397	90	11	<	<	X
ejde-397	90	12	t	t	X
ejde-397	90	13	<	<	X
ejde-397	90	14	∞	∞	PROPN
ejde-397	90	15	,	,	PUNCT
ejde-397	90	16	is	be	AUX
ejde-397	90	17	said	say	VERB
ejde-397	90	18	to	to	PART
ejde-397	90	19	be	be	AUX
ejde-397	90	20	hölder	hölder	NOUN
ejde-397	90	21	continuous	continuous	ADJ
ejde-397	90	22	with	with	ADP
ejde-397	90	23	the	the	DET
ejde-397	90	24	exponent	exponent	NOUN
ejde-397	90	25	r	r	NOUN
ejde-397	90	26	∈	∈	PROPN
ejde-397	90	27	(	(	PUNCT
ejde-397	90	28	0	0	NUM
ejde-397	90	29	,	,	PUNCT
ejde-397	90	30	1	1	NUM
ejde-397	90	31	]	]	PUNCT
ejde-397	90	32	if	if	SCONJ
ejde-397	90	33	for	for	ADP
ejde-397	90	34	each	each	DET
ejde-397	90	35	p	p	PROPN
ejde-397	90	36	∈	∈	PROPN
ejde-397	90	37	~x	~x	PUNCT
ejde-397	90	38	there	there	PRON
ejde-397	90	39	exists	exist	VERB
ejde-397	90	40	m	m	VERB
ejde-397	90	41	≥	≥	NUM
ejde-397	90	42	1	1	NUM
ejde-397	90	43	such	such	ADJ
ejde-397	90	44	that	that	DET
ejde-397	90	45	p(f(t)−	p(f(t)−	PROPN
ejde-397	90	46	f(s	f(s	PROPN
ejde-397	90	47	)	)	PUNCT
ejde-397	90	48	)	)	PUNCT
ejde-397	90	49	≤m	≤m	PROPN
ejde-397	90	50	|t−	|t−	PROPN
ejde-397	90	51	s|r	s|r	VERB
ejde-397	90	52	,	,	PUNCT
ejde-397	90	53	provided	provide	VERB
ejde-397	90	54	0	0	NUM
ejde-397	90	55	≤	≤	NUM
ejde-397	90	56	t	t	PROPN
ejde-397	90	57	,	,	PUNCT
ejde-397	90	58	s	s	PART
ejde-397	90	59	≤	≤	PROPN
ejde-397	90	60	t	t	NOUN
ejde-397	90	61	,	,	PUNCT
ejde-397	90	62	while	while	SCONJ
ejde-397	90	63	a	a	DET
ejde-397	90	64	function	function	NOUN
ejde-397	90	65	f	f	NOUN
ejde-397	90	66	:	:	PUNCT
ejde-397	91	1	[	[	X
ejde-397	91	2	0,∞)→	0,∞)→	NOUN
ejde-397	91	3	x	x	NOUN
ejde-397	91	4	is	be	AUX
ejde-397	91	5	said	say	VERB
ejde-397	91	6	to	to	PART
ejde-397	91	7	be	be	AUX
ejde-397	91	8	locally	locally	ADV
ejde-397	91	9	hölder	hölder	NOUN
ejde-397	91	10	continuous	continuous	ADJ
ejde-397	91	11	with	with	ADP
ejde-397	91	12	the	the	DET
ejde-397	91	13	exponent	exponent	NOUN
ejde-397	91	14	r	r	NOUN
ejde-397	91	15	if	if	SCONJ
ejde-397	91	16	its	its	PRON
ejde-397	91	17	restriction	restriction	NOUN
ejde-397	91	18	on	on	ADP
ejde-397	91	19	any	any	DET
ejde-397	91	20	finite	finite	ADJ
ejde-397	91	21	interval	interval	NOUN
ejde-397	91	22	[	[	X
ejde-397	91	23	0	0	NUM
ejde-397	91	24	,	,	PUNCT
ejde-397	91	25	t	t	PROPN
ejde-397	91	26	]	]	PUNCT
ejde-397	91	27	is	be	AUX
ejde-397	91	28	hölder	hölder	NOUN
ejde-397	91	29	continuous	continuous	ADJ
ejde-397	91	30	with	with	ADP
ejde-397	91	31	the	the	DET
ejde-397	91	32	same	same	ADJ
ejde-397	91	33	exponent	exponent	NOUN
ejde-397	91	34	.	.	PUNCT
ejde-397	92	1	by	by	ADP
ejde-397	92	2	acloc([0,∞	acloc([0,∞	PROPN
ejde-397	92	3	)	)	PUNCT
ejde-397	92	4	)	)	PUNCT
ejde-397	93	1	we	we	PRON
ejde-397	93	2	denote	denote	VERB
ejde-397	93	3	the	the	DET
ejde-397	93	4	space	space	NOUN
ejde-397	93	5	consisting	consist	VERB
ejde-397	93	6	of	of	ADP
ejde-397	93	7	all	all	DET
ejde-397	93	8	functions	function	NOUN
ejde-397	93	9	f	f	NOUN
ejde-397	93	10	:	:	PUNCT
ejde-397	94	1	[	[	X
ejde-397	94	2	0,∞)→	0,∞)→	NOUN
ejde-397	94	3	x	x	X
ejde-397	94	4	whose	whose	DET
ejde-397	94	5	restriction	restriction	NOUN
ejde-397	94	6	on	on	ADP
ejde-397	94	7	any	any	DET
ejde-397	94	8	finite	finite	ADJ
ejde-397	94	9	interval	interval	NOUN
ejde-397	94	10	[	[	X
ejde-397	94	11	0	0	NUM
ejde-397	94	12	,	,	PUNCT
ejde-397	94	13	t	t	NOUN
ejde-397	94	14	]	]	PUNCT
ejde-397	94	15	(	(	PUNCT
ejde-397	94	16	t	t	X
ejde-397	94	17	>	>	X
ejde-397	94	18	0	0	NUM
ejde-397	94	19	)	)	PUNCT
ejde-397	94	20	is	be	AUX
ejde-397	94	21	absolutely	absolutely	ADV
ejde-397	94	22	continuous	continuous	ADJ
ejde-397	94	23	.	.	PUNCT
ejde-397	95	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	95	2	abstract	abstract	ADJ
ejde-397	95	3	degenerate	degenerate	ADJ
ejde-397	95	4	volterra	volterra	NOUN
ejde-397	95	5	inclusions	inclusion	NOUN
ejde-397	95	6	5	5	NUM
ejde-397	95	7	let	let	VERB
ejde-397	95	8	0	0	NUM
ejde-397	95	9	<	<	X
ejde-397	95	10	τ	τ	X
ejde-397	95	11	≤	≤	NOUN
ejde-397	95	12	∞	∞	PROPN
ejde-397	95	13	and	and	CCONJ
ejde-397	95	14	a	a	DET
ejde-397	95	15	∈	∈	PROPN
ejde-397	95	16	l1	l1	PROPN
ejde-397	95	17	loc([0	loc([0	PROPN
ejde-397	95	18	,	,	PUNCT
ejde-397	95	19	τ	τ	PROPN
ejde-397	95	20	)	)	PUNCT
ejde-397	95	21	)	)	PUNCT
ejde-397	95	22	.	.	PUNCT
ejde-397	96	1	then	then	ADV
ejde-397	96	2	we	we	PRON
ejde-397	96	3	say	say	VERB
ejde-397	96	4	that	that	SCONJ
ejde-397	96	5	the	the	DET
ejde-397	96	6	function	function	NOUN
ejde-397	96	7	a(t	a(t	NOUN
ejde-397	96	8	)	)	PUNCT
ejde-397	96	9	is	be	AUX
ejde-397	96	10	a	a	DET
ejde-397	96	11	kernel	kernel	NOUN
ejde-397	96	12	on	on	ADP
ejde-397	96	13	[	[	X
ejde-397	96	14	0	0	NUM
ejde-397	96	15	,	,	PUNCT
ejde-397	96	16	τ	τ	X
ejde-397	96	17	)	)	PUNCT
ejde-397	96	18	if	if	SCONJ
ejde-397	96	19	for	for	ADP
ejde-397	96	20	each	each	DET
ejde-397	96	21	f	f	PROPN
ejde-397	96	22	∈	∈	PROPN
ejde-397	96	23	c([0	c([0	PROPN
ejde-397	96	24	,	,	PUNCT
ejde-397	96	25	τ	τ	PROPN
ejde-397	96	26	)	)	PUNCT
ejde-397	96	27	)	)	PUNCT
ejde-397	97	1	the	the	DET
ejde-397	97	2	assumption	assumption	NOUN
ejde-397	97	3	∫	∫	PROPN
ejde-397	97	4	t	t	PROPN
ejde-397	97	5	0	0	NUM
ejde-397	98	1	a(t	a(t	NOUN
ejde-397	98	2	−	−	NOUN
ejde-397	98	3	s)f(s	s)f(	NOUN
ejde-397	98	4	)	)	PUNCT
ejde-397	98	5	ds	ds	NOUN
ejde-397	98	6	=	=	SYM
ejde-397	98	7	0	0	NUM
ejde-397	98	8	,	,	PUNCT
ejde-397	98	9	t	t	PROPN
ejde-397	98	10	∈	∈	PROPN
ejde-397	99	1	[	[	X
ejde-397	99	2	0	0	NUM
ejde-397	99	3	,	,	PUNCT
ejde-397	99	4	τ	τ	X
ejde-397	99	5	)	)	PUNCT
ejde-397	99	6	implies	imply	VERB
ejde-397	99	7	f(t	f(t	NOUN
ejde-397	99	8	)	)	PUNCT
ejde-397	99	9	=	=	SYM
ejde-397	99	10	0	0	NUM
ejde-397	99	11	,	,	PUNCT
ejde-397	99	12	t	t	PROPN
ejde-397	99	13	∈	∈	PROPN
ejde-397	100	1	[	[	X
ejde-397	100	2	0	0	NUM
ejde-397	100	3	,	,	PUNCT
ejde-397	100	4	τ	τ	PROPN
ejde-397	100	5	)	)	PUNCT
ejde-397	100	6	.	.	PUNCT
ejde-397	101	1	given	give	VERB
ejde-397	101	2	s	s	PRON
ejde-397	101	3	∈	∈	NOUN
ejde-397	101	4	r	r	NOUN
ejde-397	101	5	in	in	ADP
ejde-397	101	6	advance	advance	NOUN
ejde-397	101	7	,	,	PUNCT
ejde-397	101	8	set	set	VERB
ejde-397	101	9	bsc	bsc	PROPN
ejde-397	101	10	:	:	PUNCT
ejde-397	101	11	=	=	SYM
ejde-397	101	12	sup{l	sup{l	NOUN
ejde-397	101	13	∈	∈	PROPN
ejde-397	101	14	z	z	NOUN
ejde-397	101	15	:	:	PUNCT
ejde-397	101	16	l	l	NOUN
ejde-397	101	17	≤	≤	PROPN
ejde-397	101	18	s	s	X
ejde-397	101	19	}	}	PUNCT
ejde-397	101	20	and	and	CCONJ
ejde-397	101	21	dse	dse	PROPN
ejde-397	101	22	:	:	PUNCT
ejde-397	101	23	=	=	SYM
ejde-397	101	24	inf{l	inf{l	PROPN
ejde-397	101	25	∈	∈	PROPN
ejde-397	101	26	z	z	NOUN
ejde-397	101	27	:	:	PUNCT
ejde-397	101	28	s	s	VERB
ejde-397	101	29	≤	≤	NUM
ejde-397	101	30	l	l	NOUN
ejde-397	101	31	}	}	PUNCT
ejde-397	101	32	.	.	PUNCT
ejde-397	102	1	the	the	DET
ejde-397	102	2	gamma	gamma	PROPN
ejde-397	102	3	function	function	NOUN
ejde-397	102	4	is	be	AUX
ejde-397	102	5	denoted	denote	VERB
ejde-397	102	6	by	by	ADP
ejde-397	102	7	γ	γ	PROPN
ejde-397	102	8	(	(	PUNCT
ejde-397	102	9	·	·	PUNCT
ejde-397	102	10	)	)	PUNCT
ejde-397	102	11	and	and	CCONJ
ejde-397	102	12	the	the	DET
ejde-397	102	13	principal	principal	ADJ
ejde-397	102	14	branch	branch	NOUN
ejde-397	102	15	is	be	AUX
ejde-397	102	16	always	always	ADV
ejde-397	102	17	used	use	VERB
ejde-397	102	18	to	to	PART
ejde-397	102	19	take	take	VERB
ejde-397	102	20	the	the	DET
ejde-397	102	21	powers	power	NOUN
ejde-397	102	22	.	.	PUNCT
ejde-397	103	1	set	set	VERB
ejde-397	103	2	gζ(t	gζ(t	NOUN
ejde-397	103	3	)	)	PUNCT
ejde-397	103	4	:	:	PUNCT
ejde-397	103	5	=	=	PUNCT
ejde-397	103	6	tζ−1	tζ−1	PROPN
ejde-397	103	7	/	/	SYM
ejde-397	103	8	γ(ζ	γ(ζ	PROPN
ejde-397	103	9	)	)	PUNCT
ejde-397	103	10	(	(	PUNCT
ejde-397	103	11	ζ	ζ	NOUN
ejde-397	103	12	>	>	SYM
ejde-397	103	13	0	0	NUM
ejde-397	103	14	,	,	PUNCT
ejde-397	103	15	t	t	X
ejde-397	103	16	>	>	X
ejde-397	103	17	0	0	NUM
ejde-397	103	18	)	)	PUNCT
ejde-397	103	19	,	,	PUNCT
ejde-397	103	20	g0(t	g0(t	NOUN
ejde-397	103	21	)	)	PUNCT
ejde-397	103	22	:	:	PUNCT
ejde-397	104	1	=	=	PUNCT
ejde-397	104	2	δ	δ	NOUN
ejde-397	104	3	-	-	PUNCT
ejde-397	104	4	distribution	distribution	NOUN
ejde-397	104	5	and	and	CCONJ
ejde-397	104	6	,	,	PUNCT
ejde-397	104	7	by	by	ADP
ejde-397	104	8	common	common	ADJ
ejde-397	104	9	consent	consent	NOUN
ejde-397	104	10	,	,	PUNCT
ejde-397	104	11	0ζ	0ζ	NOUN
ejde-397	104	12	:	:	PUNCT
ejde-397	104	13	=	=	SYM
ejde-397	104	14	0	0	X
ejde-397	104	15	.	.	PUNCT
ejde-397	105	1	for	for	ADP
ejde-397	105	2	any	any	DET
ejde-397	105	3	angle	angle	NOUN
ejde-397	105	4	α	α	X
ejde-397	105	5	∈	∈	PROPN
ejde-397	105	6	(	(	PUNCT
ejde-397	105	7	0	0	NUM
ejde-397	105	8	,	,	PUNCT
ejde-397	105	9	π	π	PROPN
ejde-397	105	10	]	]	X
ejde-397	105	11	,	,	PUNCT
ejde-397	105	12	we	we	PRON
ejde-397	105	13	define	define	VERB
ejde-397	105	14	σα	σα	PRON
ejde-397	105	15	:	:	PUNCT
ejde-397	105	16	=	=	SYM
ejde-397	105	17	{	{	PUNCT
ejde-397	105	18	z	z	NOUN
ejde-397	105	19	∈	∈	PROPN
ejde-397	106	1	c	c	NOUN
ejde-397	106	2	:	:	PUNCT
ejde-397	106	3	z	z	PROPN
ejde-397	107	1	6=	6=	NUM
ejde-397	107	2	0	0	NUM
ejde-397	107	3	,	,	PUNCT
ejde-397	107	4	|	|	ADV
ejde-397	107	5	arg(z)|	arg(z)|	VERB
ejde-397	107	6	<	<	X
ejde-397	107	7	α	α	NOUN
ejde-397	107	8	}	}	PUNCT
ejde-397	107	9	.	.	PUNCT
ejde-397	108	1	set	set	VERB
ejde-397	108	2	c+	c+	NOUN
ejde-397	108	3	:	:	PUNCT
ejde-397	108	4	=	=	SYM
ejde-397	108	5	{	{	PUNCT
ejde-397	108	6	λ	λ	X
ejde-397	108	7	∈	∈	NOUN
ejde-397	108	8	c	c	NOUN
ejde-397	108	9	:	:	PUNCT
ejde-397	108	10	<	<	X
ejde-397	108	11	λ	λ	X
ejde-397	108	12	>	>	X
ejde-397	108	13	0	0	NUM
ejde-397	108	14	}	}	PUNCT
ejde-397	108	15	.	.	PUNCT
ejde-397	109	1	now	now	ADV
ejde-397	109	2	we	we	PRON
ejde-397	109	3	repeat	repeat	VERB
ejde-397	109	4	some	some	DET
ejde-397	109	5	basic	basic	ADJ
ejde-397	109	6	facts	fact	NOUN
ejde-397	109	7	and	and	CCONJ
ejde-397	109	8	definitions	definition	NOUN
ejde-397	109	9	about	about	ADP
ejde-397	109	10	integration	integration	NOUN
ejde-397	109	11	of	of	ADP
ejde-397	109	12	functions	function	NOUN
ejde-397	109	13	with	with	ADP
ejde-397	109	14	values	value	NOUN
ejde-397	109	15	in	in	ADP
ejde-397	109	16	sclcss	sclcss	PROPN
ejde-397	109	17	.	.	PUNCT
ejde-397	110	1	unless	unless	SCONJ
ejde-397	110	2	stated	state	VERB
ejde-397	110	3	otherwise	otherwise	ADV
ejde-397	110	4	,	,	PUNCT
ejde-397	110	5	by	by	ADP
ejde-397	110	6	ω	ω	NOUN
ejde-397	110	7	we	we	PRON
ejde-397	110	8	denote	denote	VERB
ejde-397	110	9	a	a	DET
ejde-397	110	10	locally	locally	ADV
ejde-397	110	11	compact	compact	ADJ
ejde-397	110	12	,	,	PUNCT
ejde-397	110	13	separable	separable	ADJ
ejde-397	110	14	metric	metric	ADJ
ejde-397	110	15	space	space	NOUN
ejde-397	110	16	and	and	CCONJ
ejde-397	110	17	by	by	ADP
ejde-397	110	18	µ	µ	PROPN
ejde-397	110	19	we	we	PRON
ejde-397	110	20	denote	denote	VERB
ejde-397	110	21	a	a	DET
ejde-397	110	22	locally	locally	ADV
ejde-397	110	23	finite	finite	PROPN
ejde-397	110	24	borel	borel	PROPN
ejde-397	110	25	measure	measure	NOUN
ejde-397	110	26	defined	define	VERB
ejde-397	110	27	on	on	ADP
ejde-397	110	28	ω	ω	NUM
ejde-397	110	29	.	.	PUNCT
ejde-397	111	1	a	a	DET
ejde-397	111	2	function	function	NOUN
ejde-397	111	3	f	f	NOUN
ejde-397	111	4	:	:	PUNCT
ejde-397	111	5	ω→	ω→	PUNCT
ejde-397	111	6	x	x	PUNCT
ejde-397	111	7	is	be	AUX
ejde-397	111	8	said	say	VERB
ejde-397	111	9	to	to	PART
ejde-397	111	10	be	be	AUX
ejde-397	111	11	µ-measurable	µ-measurable	ADJ
ejde-397	111	12	if	if	SCONJ
ejde-397	111	13	and	and	CCONJ
ejde-397	111	14	only	only	ADV
ejde-397	111	15	if	if	SCONJ
ejde-397	111	16	there	there	PRON
ejde-397	111	17	exists	exist	VERB
ejde-397	111	18	a	a	DET
ejde-397	111	19	sequence	sequence	NOUN
ejde-397	111	20	(	(	PUNCT
ejde-397	111	21	fn	fn	NOUN
ejde-397	111	22	)	)	PUNCT
ejde-397	111	23	in	in	ADP
ejde-397	111	24	xω	xω	NUM
ejde-397	111	25	of	of	ADP
ejde-397	111	26	simple	simple	ADJ
ejde-397	111	27	functions	function	NOUN
ejde-397	111	28	(	(	PUNCT
ejde-397	111	29	cf	cf	NOUN
ejde-397	111	30	.	.	PUNCT
ejde-397	112	1	[	[	X
ejde-397	112	2	36	36	NUM
ejde-397	112	3	,	,	PUNCT
ejde-397	112	4	definition	definition	NOUN
ejde-397	112	5	1.1.1(i	1.1.1(i	NUM
ejde-397	112	6	)	)	PUNCT
ejde-397	112	7	]	]	PUNCT
ejde-397	112	8	for	for	ADP
ejde-397	112	9	the	the	DET
ejde-397	112	10	notion	notion	NOUN
ejde-397	112	11	)	)	PUNCT
ejde-397	112	12	such	such	ADJ
ejde-397	112	13	that	that	SCONJ
ejde-397	112	14	limn→∞	limn→∞	PROPN
ejde-397	112	15	fn(t	fn(t	X
ejde-397	112	16	)	)	PUNCT
ejde-397	112	17	=	=	SYM
ejde-397	112	18	f(t	f(t	NOUN
ejde-397	112	19	)	)	PUNCT
ejde-397	112	20	for	for	ADP
ejde-397	112	21	a.e	a.e	PROPN
ejde-397	112	22	.	.	PROPN
ejde-397	112	23	t	t	PROPN
ejde-397	112	24	∈	∈	PROPN
ejde-397	112	25	ω	ω	PROPN
ejde-397	112	26	.	.	PUNCT
ejde-397	112	27	definition	definition	NOUN
ejde-397	112	28	1.1	1.1	NUM
ejde-397	112	29	.	.	PUNCT
ejde-397	113	1	let	let	VERB
ejde-397	113	2	k	k	PROPN
ejde-397	113	3	⊆	⊆	NUM
ejde-397	113	4	ω	ω	NUM
ejde-397	113	5	be	be	AUX
ejde-397	113	6	a	a	DET
ejde-397	113	7	compact	compact	ADJ
ejde-397	113	8	set	set	NOUN
ejde-397	113	9	,	,	PUNCT
ejde-397	113	10	and	and	CCONJ
ejde-397	113	11	let	let	VERB
ejde-397	113	12	a	a	DET
ejde-397	113	13	function	function	NOUN
ejde-397	114	1	f	f	NOUN
ejde-397	114	2	:	:	PUNCT
ejde-397	114	3	k	k	X
ejde-397	114	4	→	→	PUNCT
ejde-397	114	5	x	x	PUNCT
ejde-397	114	6	be	be	AUX
ejde-397	114	7	strongly	strongly	ADV
ejde-397	114	8	measurable	measurable	ADJ
ejde-397	114	9	.	.	PUNCT
ejde-397	115	1	then	then	ADV
ejde-397	115	2	it	it	PRON
ejde-397	115	3	is	be	AUX
ejde-397	115	4	said	say	VERB
ejde-397	115	5	that	that	SCONJ
ejde-397	115	6	f	f	PROPN
ejde-397	115	7	(	(	PUNCT
ejde-397	115	8	·	·	PUNCT
ejde-397	115	9	)	)	PUNCT
ejde-397	115	10	is	be	AUX
ejde-397	115	11	(	(	PUNCT
ejde-397	115	12	µ-)integrable	µ-)integrable	ADJ
ejde-397	115	13	if	if	SCONJ
ejde-397	115	14	there	there	PRON
ejde-397	115	15	is	be	VERB
ejde-397	115	16	a	a	DET
ejde-397	115	17	sequence	sequence	NOUN
ejde-397	115	18	(	(	PUNCT
ejde-397	115	19	fn)n∈n	fn)n∈n	NUM
ejde-397	115	20	of	of	ADP
ejde-397	115	21	simple	simple	ADJ
ejde-397	115	22	functions	function	NOUN
ejde-397	115	23	such	such	ADJ
ejde-397	115	24	that	that	SCONJ
ejde-397	115	25	limn→∞	limn→∞	PROPN
ejde-397	115	26	fn(t	fn(t	X
ejde-397	115	27	)	)	PUNCT
ejde-397	115	28	=	=	SYM
ejde-397	115	29	f(t	f(t	NOUN
ejde-397	115	30	)	)	PUNCT
ejde-397	115	31	a.e	a.e	PROPN
ejde-397	115	32	.	.	PROPN
ejde-397	115	33	t	t	PROPN
ejde-397	115	34	∈	∈	PROPN
ejde-397	115	35	k	k	PROPN
ejde-397	115	36	and	and	CCONJ
ejde-397	115	37	for	for	ADP
ejde-397	115	38	all	all	PRON
ejde-397	115	39	ε	ε	PROPN
ejde-397	115	40	>	>	X
ejde-397	115	41	0	0	PUNCT
ejde-397	115	42	and	and	CCONJ
ejde-397	115	43	each	each	DET
ejde-397	115	44	p	p	NOUN
ejde-397	115	45	∈	∈	PROPN
ejde-397	115	46	~	~	PUNCT
ejde-397	115	47	there	there	PRON
ejde-397	115	48	is	be	VERB
ejde-397	115	49	a	a	DET
ejde-397	115	50	number	number	NOUN
ejde-397	115	51	n0	n0	X
ejde-397	115	52	=	=	SYM
ejde-397	115	53	n0(ε	n0(ε	PROPN
ejde-397	115	54	,	,	PUNCT
ejde-397	115	55	p	p	NOUN
ejde-397	115	56	)	)	PUNCT
ejde-397	115	57	such	such	ADJ
ejde-397	115	58	that∫	that∫	NOUN
ejde-397	116	1	k	k	PROPN
ejde-397	117	1	p	p	X
ejde-397	117	2	(	(	PUNCT
ejde-397	117	3	fn	fn	NOUN
ejde-397	117	4	−	−	PROPN
ejde-397	117	5	fm	fm	PROPN
ejde-397	117	6	)	)	PUNCT
ejde-397	117	7	dµ	dµ	VERB
ejde-397	117	8	≤	≤	PROPN
ejde-397	117	9	ε	ε	PROPN
ejde-397	117	10	(	(	PUNCT
ejde-397	117	11	m	m	PROPN
ejde-397	117	12	,	,	PUNCT
ejde-397	117	13	n	n	PRON
ejde-397	117	14	≥	≥	NOUN
ejde-397	117	15	n0	n0	NUM
ejde-397	117	16	)	)	PUNCT
ejde-397	117	17	.	.	PUNCT
ejde-397	118	1	(	(	PUNCT
ejde-397	118	2	1.4	1.4	NUM
ejde-397	118	3	)	)	PUNCT
ejde-397	118	4	in	in	ADP
ejde-397	118	5	this	this	DET
ejde-397	118	6	case	case	NOUN
ejde-397	118	7	we	we	PRON
ejde-397	118	8	define	define	VERB
ejde-397	118	9	∫	∫	PROPN
ejde-397	119	1	k	k	PROPN
ejde-397	119	2	f	f	PROPN
ejde-397	119	3	dµ	dµ	PROPN
ejde-397	119	4	:	:	PUNCT
ejde-397	120	1	=	=	SYM
ejde-397	120	2	lim	lim	PROPN
ejde-397	120	3	n→∞	n→∞	NUM
ejde-397	121	1	∫	∫	PROPN
ejde-397	121	2	k	k	PROPN
ejde-397	121	3	fn	fn	PROPN
ejde-397	121	4	dµ.	dµ.	PROPN
ejde-397	121	5	from	from	ADP
ejde-397	121	6	(	(	PUNCT
ejde-397	121	7	1.4	1.4	NUM
ejde-397	121	8	)	)	PUNCT
ejde-397	121	9	,	,	PUNCT
ejde-397	121	10	we	we	PRON
ejde-397	121	11	have	have	VERB
ejde-397	121	12	that	that	PRON
ejde-397	121	13	(	(	PUNCT
ejde-397	121	14	p(fn))n∈n	p(fn))n∈n	PROPN
ejde-397	121	15	is	be	AUX
ejde-397	121	16	a	a	DET
ejde-397	121	17	cauchy	cauchy	ADJ
ejde-397	121	18	sequence	sequence	NOUN
ejde-397	121	19	in	in	ADP
ejde-397	121	20	the	the	DET
ejde-397	121	21	space	space	NOUN
ejde-397	121	22	l1(k,µ	l1(k,µ	NOUN
ejde-397	121	23	)	)	PUNCT
ejde-397	121	24	,	,	PUNCT
ejde-397	121	25	so	so	SCONJ
ejde-397	121	26	that	that	SCONJ
ejde-397	121	27	the	the	DET
ejde-397	121	28	limit	limit	NOUN
ejde-397	121	29	p(f	p(f	PROPN
ejde-397	121	30	)	)	PUNCT
ejde-397	122	1	=	=	SYM
ejde-397	122	2	limn→∞	limn→∞	X
ejde-397	122	3	p(fn	p(fn	NOUN
ejde-397	122	4	)	)	PUNCT
ejde-397	122	5	is	be	AUX
ejde-397	122	6	µ-integrable	µ-integrable	ADJ
ejde-397	122	7	.	.	PUNCT
ejde-397	123	1	similarly	similarly	ADV
ejde-397	123	2	we	we	PRON
ejde-397	123	3	can	can	AUX
ejde-397	123	4	prove	prove	VERB
ejde-397	123	5	that	that	SCONJ
ejde-397	123	6	each	each	DET
ejde-397	123	7	function	function	NOUN
ejde-397	123	8	p(fn	p(fn	NOUN
ejde-397	123	9	−	−	PROPN
ejde-397	123	10	f	f	X
ejde-397	123	11	)	)	PUNCT
ejde-397	123	12	is	be	AUX
ejde-397	123	13	µ-integrable	µ-integrable	ADJ
ejde-397	123	14	and	and	CCONJ
ejde-397	123	15	the	the	DET
ejde-397	123	16	sequence	sequence	NOUN
ejde-397	123	17	of	of	ADP
ejde-397	123	18	its	its	PRON
ejde-397	123	19	corresponding	correspond	VERB
ejde-397	123	20	integrals	integral	NOUN
ejde-397	123	21	converges	converge	VERB
ejde-397	123	22	to	to	ADP
ejde-397	123	23	zero	zero	NUM
ejde-397	123	24	.	.	PUNCT
ejde-397	124	1	recall	recall	VERB
ejde-397	124	2	that	that	SCONJ
ejde-397	124	3	every	every	DET
ejde-397	124	4	continuous	continuous	ADJ
ejde-397	124	5	function	function	NOUN
ejde-397	124	6	f	f	NOUN
ejde-397	124	7	:	:	PUNCT
ejde-397	124	8	k	k	X
ejde-397	124	9	→	→	PUNCT
ejde-397	124	10	x	x	X
ejde-397	124	11	is	be	AUX
ejde-397	124	12	µ-integrable	µ-integrable	ADJ
ejde-397	124	13	.	.	PUNCT
ejde-397	125	1	definition	definition	NOUN
ejde-397	125	2	1.2	1.2	NUM
ejde-397	125	3	.	.	PUNCT
ejde-397	126	1	(	(	PUNCT
ejde-397	126	2	i	i	NOUN
ejde-397	126	3	)	)	PUNCT
ejde-397	126	4	a	a	DET
ejde-397	126	5	function	function	NOUN
ejde-397	126	6	f	f	NOUN
ejde-397	126	7	:	:	PUNCT
ejde-397	126	8	ω→	ω→	PUNCT
ejde-397	126	9	x	x	PUNCT
ejde-397	126	10	is	be	AUX
ejde-397	126	11	said	say	VERB
ejde-397	126	12	to	to	PART
ejde-397	126	13	be	be	AUX
ejde-397	126	14	locally	locally	ADV
ejde-397	126	15	µ-integrable	µ-integrable	ADJ
ejde-397	126	16	if	if	SCONJ
ejde-397	126	17	,	,	PUNCT
ejde-397	126	18	for	for	SCONJ
ejde-397	126	19	every	every	DET
ejde-397	126	20	compact	compact	NOUN
ejde-397	126	21	set	set	VERB
ejde-397	126	22	k	k	PROPN
ejde-397	126	23	⊆	⊆	NUM
ejde-397	126	24	ω	ω	NUM
ejde-397	126	25	,	,	PUNCT
ejde-397	126	26	the	the	DET
ejde-397	126	27	restriction	restriction	NOUN
ejde-397	126	28	f|k	f|k	PUNCT
ejde-397	127	1	:	:	PUNCT
ejde-397	127	2	k	k	X
ejde-397	127	3	→	→	PUNCT
ejde-397	127	4	x	x	X
ejde-397	127	5	is	be	AUX
ejde-397	127	6	µ-integrable	µ-integrable	ADJ
ejde-397	127	7	.	.	PUNCT
ejde-397	128	1	(	(	PUNCT
ejde-397	128	2	ii	ii	NOUN
ejde-397	128	3	)	)	PUNCT
ejde-397	128	4	a	a	DET
ejde-397	128	5	function	function	NOUN
ejde-397	128	6	f	f	NOUN
ejde-397	128	7	:	:	PUNCT
ejde-397	128	8	ω→	ω→	PUNCT
ejde-397	128	9	x	x	PUNCT
ejde-397	128	10	is	be	AUX
ejde-397	128	11	said	say	VERB
ejde-397	128	12	to	to	PART
ejde-397	128	13	be	be	AUX
ejde-397	128	14	µ-integrable	µ-integrable	ADJ
ejde-397	128	15	if	if	SCONJ
ejde-397	128	16	it	it	PRON
ejde-397	128	17	is	be	AUX
ejde-397	128	18	locally	locally	ADV
ejde-397	128	19	integrable	integrable	ADJ
ejde-397	128	20	and	and	CCONJ
ejde-397	128	21	if	if	SCONJ
ejde-397	128	22	additionally	additionally	ADV
ejde-397	128	23	∫	∫	PROPN
ejde-397	128	24	ω	ω	NUM
ejde-397	128	25	p(f	p(f	PROPN
ejde-397	128	26	)	)	PUNCT
ejde-397	128	27	dµ	dµ	VERB
ejde-397	128	28	<	<	X
ejde-397	128	29	∞	∞	PROPN
ejde-397	128	30	,	,	PUNCT
ejde-397	128	31	p	p	PROPN
ejde-397	128	32	∈	∈	PROPN
ejde-397	128	33	~.	~.	X
ejde-397	128	34	(	(	PUNCT
ejde-397	128	35	1.5	1.5	NUM
ejde-397	128	36	)	)	PUNCT
ejde-397	128	37	if	if	SCONJ
ejde-397	128	38	this	this	PRON
ejde-397	128	39	is	be	AUX
ejde-397	128	40	the	the	DET
ejde-397	128	41	case	case	NOUN
ejde-397	128	42	,	,	PUNCT
ejde-397	128	43	we	we	PRON
ejde-397	128	44	define	define	VERB
ejde-397	128	45	∫	∫	PROPN
ejde-397	128	46	ω	ω	PROPN
ejde-397	128	47	f	f	PROPN
ejde-397	128	48	dµ	dµ	PROPN
ejde-397	128	49	:	:	PUNCT
ejde-397	129	1	=	=	SYM
ejde-397	129	2	lim	lim	PROPN
ejde-397	129	3	n→∞	n→∞	NUM
ejde-397	130	1	∫	∫	PROPN
ejde-397	130	2	kn	kn	PROPN
ejde-397	130	3	f	f	PROPN
ejde-397	130	4	dµ	dµ	PROPN
ejde-397	130	5	,	,	PUNCT
ejde-397	130	6	with	with	ADP
ejde-397	130	7	(	(	PUNCT
ejde-397	130	8	kn)n∈n	kn)n∈n	PUNCT
ejde-397	130	9	being	be	AUX
ejde-397	130	10	an	an	DET
ejde-397	130	11	expansive	expansive	ADJ
ejde-397	130	12	sequence	sequence	NOUN
ejde-397	130	13	of	of	ADP
ejde-397	130	14	compact	compact	ADJ
ejde-397	130	15	subsets	subset	NOUN
ejde-397	130	16	of	of	ADP
ejde-397	130	17	ω	ω	PROPN
ejde-397	130	18	with	with	ADP
ejde-397	130	19	the	the	DET
ejde-397	130	20	property	property	NOUN
ejde-397	130	21	that	that	PRON
ejde-397	130	22	⋃	⋃	PROPN
ejde-397	130	23	n∈nkn	n∈nkn	PROPN
ejde-397	130	24	=	=	SYM
ejde-397	130	25	ω	ω	PROPN
ejde-397	130	26	.	.	PUNCT
ejde-397	131	1	the	the	DET
ejde-397	131	2	above	above	ADJ
ejde-397	131	3	definition	definition	NOUN
ejde-397	131	4	does	do	AUX
ejde-397	131	5	not	not	PART
ejde-397	131	6	depend	depend	VERB
ejde-397	131	7	on	on	ADP
ejde-397	131	8	the	the	DET
ejde-397	131	9	choice	choice	NOUN
ejde-397	131	10	of	of	ADP
ejde-397	131	11	sequence	sequence	NOUN
ejde-397	131	12	(	(	PUNCT
ejde-397	131	13	kn)n∈n	kn)n∈n	X
ejde-397	131	14	.	.	PUNCT
ejde-397	132	1	moreover	moreover	ADV
ejde-397	132	2	,	,	PUNCT
ejde-397	132	3	p	p	X
ejde-397	132	4	(	(	PUNCT
ejde-397	132	5	∫	∫	PROPN
ejde-397	132	6	ω	ω	PROPN
ejde-397	132	7	f	f	PROPN
ejde-397	132	8	dµ	dµ	PROPN
ejde-397	132	9	)	)	PUNCT
ejde-397	132	10	≤	≤	NUM
ejde-397	132	11	∫	∫	PROPN
ejde-397	133	1	ω	ω	NUM
ejde-397	133	2	p(f	p(f	PROPN
ejde-397	133	3	)	)	PUNCT
ejde-397	133	4	dµ	dµ	PROPN
ejde-397	133	5	,	,	PUNCT
ejde-397	133	6	p	p	PROPN
ejde-397	133	7	∈	∈	PROPN
ejde-397	133	8	~.	~.	X
ejde-397	133	9	(	(	PUNCT
ejde-397	134	1	1.6	1.6	NUM
ejde-397	134	2	)	)	PUNCT
ejde-397	134	3	it	it	PRON
ejde-397	134	4	is	be	AUX
ejde-397	134	5	not	not	PART
ejde-397	134	6	difficult	difficult	ADJ
ejde-397	134	7	to	to	PART
ejde-397	134	8	verify	verify	VERB
ejde-397	134	9	that	that	SCONJ
ejde-397	134	10	the	the	DET
ejde-397	134	11	µ-integrability	µ-integrability	NOUN
ejde-397	134	12	of	of	ADP
ejde-397	134	13	a	a	DET
ejde-397	134	14	function	function	NOUN
ejde-397	134	15	f	f	NOUN
ejde-397	135	1	:	:	PUNCT
ejde-397	135	2	k	k	X
ejde-397	135	3	→	→	SYM
ejde-397	135	4	x	x	PROPN
ejde-397	135	5	,	,	PUNCT
ejde-397	135	6	resp	resp	NOUN
ejde-397	135	7	.	.	PUNCT
ejde-397	136	1	f	f	X
ejde-397	136	2	:	:	PUNCT
ejde-397	137	1	ω→	ω→	PUNCT
ejde-397	137	2	x	x	SYM
ejde-397	137	3	,	,	PUNCT
ejde-397	137	4	implies	imply	VERB
ejde-397	137	5	that	that	SCONJ
ejde-397	137	6	for	for	ADP
ejde-397	137	7	each	each	DET
ejde-397	137	8	x∗	x∗	PROPN
ejde-397	137	9	∈	∈	PROPN
ejde-397	137	10	x∗	x∗	PROPN
ejde-397	137	11	,	,	PUNCT
ejde-397	137	12	one	one	PRON
ejde-397	137	13	has	have	VERB
ejde-397	137	14	:	:	PUNCT
ejde-397	137	15	〈	〈	PROPN
ejde-397	137	16	x∗	x∗	PROPN
ejde-397	137	17	,	,	PUNCT
ejde-397	137	18	∫	∫	PROPN
ejde-397	137	19	k	k	PROPN
ejde-397	137	20	f	f	PROPN
ejde-397	137	21	dµ	dµ	PRON
ejde-397	137	22	〉	〉	NOUN
ejde-397	137	23	=	=	PUNCT
ejde-397	137	24	∫	∫	PROPN
ejde-397	137	25	k	k	PROPN
ejde-397	137	26	〈	〈	PROPN
ejde-397	137	27	x∗	x∗	PROPN
ejde-397	137	28	,	,	PUNCT
ejde-397	137	29	f	f	PROPN
ejde-397	137	30	〉	〉	PROPN
ejde-397	137	31	dµ	dµ	PROPN
ejde-397	137	32	,	,	PUNCT
ejde-397	137	33	resp	resp	NOUN
ejde-397	137	34	.	.	PUNCT
ejde-397	138	1	〈	〈	PROPN
ejde-397	138	2	x∗	x∗	PROPN
ejde-397	138	3	,	,	PUNCT
ejde-397	138	4	∫	∫	PROPN
ejde-397	138	5	ω	ω	PROPN
ejde-397	138	6	f	f	PROPN
ejde-397	138	7	dµ	dµ	PROPN
ejde-397	138	8	〉	〉	NOUN
ejde-397	138	9	=	=	SYM
ejde-397	138	10	∫	∫	PROPN
ejde-397	138	11	ω	ω	NUM
ejde-397	138	12	〈	〈	PROPN
ejde-397	138	13	x∗	x∗	PROPN
ejde-397	138	14	,	,	PUNCT
ejde-397	138	15	f	f	PROPN
ejde-397	138	16	〉	〉	PROPN
ejde-397	138	17	dµ.	dµ.	PROPN
ejde-397	138	18	(	(	PUNCT
ejde-397	138	19	1.7	1.7	NUM
ejde-397	138	20	)	)	PUNCT
ejde-397	138	21	6	6	NUM
ejde-397	138	22	m.	m.	NOUN
ejde-397	138	23	kostić	kostić	NOUN
ejde-397	139	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	139	2	definition	definition	NOUN
ejde-397	139	3	1.2	1.2	NUM
ejde-397	139	4	is	be	AUX
ejde-397	139	5	equivalent	equivalent	ADJ
ejde-397	139	6	with	with	ADP
ejde-397	139	7	the	the	DET
ejde-397	139	8	definition	definition	NOUN
ejde-397	139	9	of	of	ADP
ejde-397	139	10	bochner	bochner	NOUN
ejde-397	139	11	integral	integral	ADJ
ejde-397	139	12	,	,	PUNCT
ejde-397	139	13	provided	provide	VERB
ejde-397	139	14	that	that	SCONJ
ejde-397	139	15	x	x	PRON
ejde-397	139	16	is	be	AUX
ejde-397	139	17	a	a	DET
ejde-397	139	18	banach	banach	NOUN
ejde-397	139	19	space	space	NOUN
ejde-397	139	20	.	.	PUNCT
ejde-397	140	1	furthermore	furthermore	ADV
ejde-397	140	2	,	,	PUNCT
ejde-397	140	3	every	every	DET
ejde-397	140	4	continuous	continuous	ADJ
ejde-397	140	5	function	function	NOUN
ejde-397	140	6	f	f	NOUN
ejde-397	140	7	:	:	PUNCT
ejde-397	140	8	ω→	ω→	PUNCT
ejde-397	140	9	x	x	SYM
ejde-397	140	10	satisfying	satisfy	VERB
ejde-397	140	11	(	(	PUNCT
ejde-397	140	12	1.5	1.5	NUM
ejde-397	140	13	)	)	PUNCT
ejde-397	140	14	is	be	AUX
ejde-397	140	15	µ-integrable	µ-integrable	ADJ
ejde-397	140	16	and	and	CCONJ
ejde-397	140	17	the	the	DET
ejde-397	140	18	following	follow	VERB
ejde-397	140	19	holds	hold	NOUN
ejde-397	140	20	.	.	PUNCT
ejde-397	141	1	theorem	theorem	VERB
ejde-397	141	2	1.3	1.3	NUM
ejde-397	141	3	.	.	PUNCT
ejde-397	142	1	(	(	PUNCT
ejde-397	142	2	i	i	NOUN
ejde-397	142	3	)	)	PUNCT
ejde-397	142	4	(	(	PUNCT
ejde-397	142	5	the	the	DET
ejde-397	142	6	dominated	dominate	VERB
ejde-397	142	7	convergence	convergence	NOUN
ejde-397	142	8	theorem	theorem	VERB
ejde-397	142	9	)	)	PUNCT
ejde-397	142	10	suppose	suppose	VERB
ejde-397	142	11	that	that	SCONJ
ejde-397	142	12	(	(	PUNCT
ejde-397	142	13	fn	fn	NOUN
ejde-397	142	14	)	)	PUNCT
ejde-397	142	15	is	be	AUX
ejde-397	142	16	a	a	DET
ejde-397	142	17	sequence	sequence	NOUN
ejde-397	142	18	of	of	ADP
ejde-397	142	19	µ-integrable	µ-integrable	ADJ
ejde-397	142	20	functions	function	NOUN
ejde-397	142	21	from	from	ADP
ejde-397	142	22	xω	xω	PROPN
ejde-397	142	23	and	and	CCONJ
ejde-397	142	24	(	(	PUNCT
ejde-397	142	25	fn	fn	NOUN
ejde-397	142	26	)	)	PUNCT
ejde-397	142	27	converges	converge	VERB
ejde-397	142	28	pointwise	pointwise	VERB
ejde-397	142	29	to	to	ADP
ejde-397	142	30	a	a	DET
ejde-397	142	31	function	function	NOUN
ejde-397	142	32	f	f	NOUN
ejde-397	142	33	:	:	PUNCT
ejde-397	142	34	ω	ω	X
ejde-397	142	35	→	→	SYM
ejde-397	142	36	x.	x.	NOUN
ejde-397	142	37	assume	assume	VERB
ejde-397	142	38	that	that	SCONJ
ejde-397	142	39	,	,	PUNCT
ejde-397	142	40	for	for	ADP
ejde-397	142	41	every	every	DET
ejde-397	142	42	p	p	PROPN
ejde-397	142	43	∈	∈	PROPN
ejde-397	142	44	~	~	PUNCT
ejde-397	142	45	,	,	PUNCT
ejde-397	142	46	there	there	PRON
ejde-397	142	47	exists	exist	VERB
ejde-397	142	48	a	a	DET
ejde-397	142	49	µ-integrable	µ-integrable	ADJ
ejde-397	142	50	function	function	NOUN
ejde-397	142	51	fp	fp	X
ejde-397	142	52	:	:	PUNCT
ejde-397	142	53	ω→	ω→	PUNCT
ejde-397	143	1	[	[	X
ejde-397	143	2	0,∞	0,∞	X
ejde-397	143	3	)	)	PUNCT
ejde-397	143	4	such	such	ADJ
ejde-397	143	5	that	that	SCONJ
ejde-397	143	6	p(fn	p(fn	NOUN
ejde-397	143	7	)	)	PUNCT
ejde-397	143	8	≤	≤	NUM
ejde-397	143	9	fp	fp	NOUN
ejde-397	143	10	,	,	PUNCT
ejde-397	143	11	n	n	PROPN
ejde-397	143	12	∈	∈	PROPN
ejde-397	143	13	n.	n.	NOUN
ejde-397	144	1	then	then	ADV
ejde-397	144	2	f	f	X
ejde-397	144	3	(	(	PUNCT
ejde-397	144	4	·	·	PUNCT
ejde-397	144	5	)	)	PUNCT
ejde-397	144	6	is	be	AUX
ejde-397	144	7	a	a	DET
ejde-397	144	8	µ-integrable	µ-integrable	ADJ
ejde-397	144	9	function	function	NOUN
ejde-397	144	10	and	and	CCONJ
ejde-397	145	1	limn→∞	limn→∞	PROPN
ejde-397	145	2	∫	∫	PROPN
ejde-397	145	3	ω	ω	PROPN
ejde-397	145	4	fn	fn	PROPN
ejde-397	146	1	dµ	dµ	PROPN
ejde-397	146	2	=	=	SYM
ejde-397	146	3	∫	∫	PROPN
ejde-397	147	1	ω	ω	PROPN
ejde-397	147	2	f	f	PROPN
ejde-397	147	3	dµ.	dµ.	PROPN
ejde-397	147	4	(	(	PUNCT
ejde-397	147	5	ii	ii	NOUN
ejde-397	147	6	)	)	PUNCT
ejde-397	147	7	let	let	VERB
ejde-397	147	8	y	y	PRON
ejde-397	147	9	be	be	AUX
ejde-397	147	10	a	a	DET
ejde-397	147	11	sclcs	sclcs	NOUN
ejde-397	147	12	,	,	PUNCT
ejde-397	147	13	and	and	CCONJ
ejde-397	147	14	let	let	VERB
ejde-397	147	15	t	t	NOUN
ejde-397	147	16	:	:	PUNCT
ejde-397	147	17	x	x	X
ejde-397	147	18	→	→	SYM
ejde-397	147	19	y	y	X
ejde-397	147	20	be	be	AUX
ejde-397	147	21	a	a	DET
ejde-397	147	22	continuous	continuous	ADJ
ejde-397	147	23	linear	linear	ADJ
ejde-397	147	24	mapping	mapping	NOUN
ejde-397	147	25	.	.	PUNCT
ejde-397	148	1	if	if	SCONJ
ejde-397	148	2	f	f	PROPN
ejde-397	148	3	:	:	PUNCT
ejde-397	148	4	ω→	ω→	PUNCT
ejde-397	148	5	x	x	X
ejde-397	148	6	is	be	AUX
ejde-397	148	7	µ-integrable	µ-integrable	ADJ
ejde-397	148	8	,	,	PUNCT
ejde-397	148	9	then	then	ADV
ejde-397	148	10	tf	tf	INTJ
ejde-397	148	11	:	:	PUNCT
ejde-397	148	12	ω→	ω→	PUNCT
ejde-397	148	13	y	y	PROPN
ejde-397	148	14	is	be	AUX
ejde-397	148	15	likewise	likewise	ADV
ejde-397	148	16	µ-integrable	µ-integrable	ADJ
ejde-397	148	17	and	and	CCONJ
ejde-397	148	18	t	t	PROPN
ejde-397	148	19	∫	∫	PROPN
ejde-397	149	1	ω	ω	PROPN
ejde-397	149	2	f	f	PROPN
ejde-397	149	3	dµ	dµ	PROPN
ejde-397	149	4	=	=	SYM
ejde-397	149	5	∫	∫	PROPN
ejde-397	149	6	ω	ω	INTJ
ejde-397	149	7	tf	tf	PROPN
ejde-397	149	8	dµ.	dµ.	PROPN
ejde-397	149	9	(	(	PUNCT
ejde-397	149	10	1.8	1.8	NUM
ejde-397	149	11	)	)	PUNCT
ejde-397	149	12	(	(	PUNCT
ejde-397	149	13	iii	iii	X
ejde-397	149	14	)	)	PUNCT
ejde-397	149	15	let	let	VERB
ejde-397	149	16	y	y	PRON
ejde-397	149	17	be	be	AUX
ejde-397	149	18	a	a	DET
ejde-397	149	19	sclcs	sclcs	NOUN
ejde-397	149	20	,	,	PUNCT
ejde-397	149	21	and	and	CCONJ
ejde-397	149	22	let	let	VERB
ejde-397	149	23	t	t	NOUN
ejde-397	149	24	:	:	PUNCT
ejde-397	149	25	d(t	d(t	PROPN
ejde-397	149	26	)	)	PUNCT
ejde-397	150	1	⊆	⊆	NUM
ejde-397	150	2	x	x	SYM
ejde-397	150	3	→	→	SYM
ejde-397	150	4	y	y	X
ejde-397	150	5	be	be	AUX
ejde-397	150	6	a	a	DET
ejde-397	150	7	closed	closed	ADJ
ejde-397	150	8	linear	linear	ADJ
ejde-397	150	9	mapping	mapping	NOUN
ejde-397	150	10	.	.	PUNCT
ejde-397	151	1	if	if	SCONJ
ejde-397	151	2	f	f	PROPN
ejde-397	151	3	:	:	PUNCT
ejde-397	151	4	ω	ω	PROPN
ejde-397	151	5	→	→	SYM
ejde-397	151	6	d(t	d(t	PROPN
ejde-397	151	7	)	)	PUNCT
ejde-397	151	8	is	be	AUX
ejde-397	151	9	µ-integrable	µ-integrable	ADJ
ejde-397	151	10	and	and	CCONJ
ejde-397	151	11	tf	tf	INTJ
ejde-397	151	12	:	:	PUNCT
ejde-397	151	13	ω	ω	X
ejde-397	151	14	→	→	SYM
ejde-397	151	15	y	y	PROPN
ejde-397	151	16	is	be	AUX
ejde-397	151	17	likewise	likewise	ADV
ejde-397	151	18	µ-integrable	µ-integrable	ADJ
ejde-397	151	19	,	,	PUNCT
ejde-397	152	1	then∫	then∫	NOUN
ejde-397	152	2	ω	ω	NUM
ejde-397	153	1	f	f	PROPN
ejde-397	153	2	dµ	dµ	PROPN
ejde-397	153	3	∈	∈	PROPN
ejde-397	153	4	d(t	d(t	PROPN
ejde-397	153	5	)	)	PUNCT
ejde-397	153	6	and	and	CCONJ
ejde-397	153	7	(	(	PUNCT
ejde-397	153	8	1.8	1.8	NUM
ejde-397	153	9	)	)	PUNCT
ejde-397	153	10	holds	hold	VERB
ejde-397	153	11	.	.	PUNCT
ejde-397	154	1	recent	recent	ADJ
ejde-397	154	2	decades	decade	NOUN
ejde-397	154	3	have	have	AUX
ejde-397	154	4	witnessed	witness	VERB
ejde-397	154	5	a	a	DET
ejde-397	154	6	fast	fast	ADJ
ejde-397	154	7	growing	grow	VERB
ejde-397	154	8	applications	application	NOUN
ejde-397	154	9	of	of	ADP
ejde-397	154	10	fractional	fractional	ADJ
ejde-397	154	11	calculus	calculus	NOUN
ejde-397	154	12	and	and	CCONJ
ejde-397	154	13	fractional	fractional	ADJ
ejde-397	154	14	differential	differential	ADJ
ejde-397	154	15	equations	equation	NOUN
ejde-397	154	16	to	to	PART
ejde-397	154	17	diverse	diverse	VERB
ejde-397	154	18	scientific	scientific	ADJ
ejde-397	154	19	and	and	CCONJ
ejde-397	154	20	engineering	engineering	NOUN
ejde-397	154	21	fields	field	NOUN
ejde-397	154	22	(	(	PUNCT
ejde-397	154	23	cf	cf	NOUN
ejde-397	154	24	.	.	PUNCT
ejde-397	155	1	[	[	X
ejde-397	155	2	5	5	NUM
ejde-397	155	3	,	,	PUNCT
ejde-397	155	4	14	14	NUM
ejde-397	155	5	,	,	PUNCT
ejde-397	155	6	30	30	NUM
ejde-397	155	7	,	,	PUNCT
ejde-397	155	8	67	67	NUM
ejde-397	155	9	,	,	PUNCT
ejde-397	155	10	70	70	NUM
ejde-397	155	11	]	]	PUNCT
ejde-397	155	12	and	and	CCONJ
ejde-397	155	13	references	reference	NOUN
ejde-397	155	14	cited	cite	VERB
ejde-397	155	15	therein	therein	ADV
ejde-397	155	16	for	for	ADP
ejde-397	155	17	further	further	ADJ
ejde-397	155	18	information	information	NOUN
ejde-397	155	19	)	)	PUNCT
ejde-397	155	20	.	.	PUNCT
ejde-397	156	1	in	in	ADP
ejde-397	156	2	this	this	DET
ejde-397	156	3	paper	paper	NOUN
ejde-397	156	4	,	,	PUNCT
ejde-397	156	5	we	we	PRON
ejde-397	156	6	mainly	mainly	ADV
ejde-397	156	7	use	use	VERB
ejde-397	156	8	the	the	DET
ejde-397	156	9	caputo	caputo	PROPN
ejde-397	156	10	fractional	fractional	ADJ
ejde-397	156	11	derivatives	derivative	NOUN
ejde-397	156	12	.	.	PUNCT
ejde-397	157	1	let	let	VERB
ejde-397	157	2	ζ	ζ	PRON
ejde-397	157	3	>	>	X
ejde-397	157	4	0	0	NUM
ejde-397	157	5	.	.	PUNCT
ejde-397	158	1	then	then	ADV
ejde-397	158	2	the	the	DET
ejde-397	158	3	caputo	caputo	PROPN
ejde-397	158	4	fractional	fractional	PROPN
ejde-397	158	5	derivative	derivative	PROPN
ejde-397	158	6	dζ	dζ	PROPN
ejde-397	158	7	tu	tu	PROPN
ejde-397	158	8	[	[	X
ejde-397	158	9	5	5	NUM
ejde-397	158	10	,	,	PUNCT
ejde-397	158	11	36	36	NUM
ejde-397	158	12	]	]	PUNCT
ejde-397	158	13	is	be	AUX
ejde-397	158	14	defined	define	VERB
ejde-397	158	15	for	for	ADP
ejde-397	158	16	those	those	DET
ejde-397	158	17	functions	function	NOUN
ejde-397	158	18	u	u	PROPN
ejde-397	158	19	∈	∈	PROPN
ejde-397	158	20	cdζe−1([0,∞	cdζe−1([0,∞	NOUN
ejde-397	158	21	)	)	PUNCT
ejde-397	158	22	:	:	PUNCT
ejde-397	159	1	x	x	X
ejde-397	159	2	)	)	PUNCT
ejde-397	159	3	for	for	ADP
ejde-397	159	4	which	which	PRON
ejde-397	159	5	gdζe−ζ	gdζe−ζ	ADP
ejde-397	159	6	∗	∗	NOUN
ejde-397	159	7	(	(	PUNCT
ejde-397	159	8	u−	u−	PROPN
ejde-397	159	9	∑dζe−1	∑dζe−1	NOUN
ejde-397	159	10	j=0	j=0	VERB
ejde-397	159	11	u(j)(0)gj+1	u(j)(0)gj+1	PROPN
ejde-397	159	12	)	)	PUNCT
ejde-397	159	13	∈	∈	PROPN
ejde-397	159	14	cdζe([0,∞	cdζe([0,∞	NOUN
ejde-397	159	15	)	)	PUNCT
ejde-397	159	16	:	:	PUNCT
ejde-397	160	1	x	x	X
ejde-397	160	2	)	)	PUNCT
ejde-397	160	3	,	,	PUNCT
ejde-397	160	4	by	by	ADP
ejde-397	160	5	dζ	dζ	PROPN
ejde-397	160	6	tu(t	tu(t	NUM
ejde-397	160	7	)	)	PUNCT
ejde-397	160	8	:	:	PUNCT
ejde-397	161	1	=	=	PUNCT
ejde-397	161	2	ddζe	ddζe	ADV
ejde-397	162	1	dtdζe	dtdζe	VERB
ejde-397	162	2	[	[	PUNCT
ejde-397	162	3	gdζe−ζ	gdζe−ζ	NOUN
ejde-397	162	4	∗	∗	NOUN
ejde-397	162	5	(	(	PUNCT
ejde-397	162	6	u−	u−	PROPN
ejde-397	162	7	dζe−1∑	dζe−1∑	PROPN
ejde-397	162	8	j=0	j=0	PROPN
ejde-397	162	9	u(j)(0)gj+1	u(j)(0)gj+1	PROPN
ejde-397	162	10	)	)	PUNCT
ejde-397	162	11	]	]	PUNCT
ejde-397	162	12	.	.	PUNCT
ejde-397	163	1	define	define	VERB
ejde-397	163	2	cr([0	cr([0	NOUN
ejde-397	163	3	,	,	PUNCT
ejde-397	163	4	t	t	X
ejde-397	163	5	]	]	PUNCT
ejde-397	163	6	:	:	PUNCT
ejde-397	163	7	x	x	X
ejde-397	163	8	)	)	PUNCT
ejde-397	163	9	to	to	PART
ejde-397	163	10	be	be	AUX
ejde-397	163	11	the	the	DET
ejde-397	163	12	vector	vector	NOUN
ejde-397	163	13	space	space	NOUN
ejde-397	163	14	consisting	consist	VERB
ejde-397	163	15	of	of	ADP
ejde-397	163	16	hölder	hölder	NOUN
ejde-397	163	17	continuous	continuous	ADJ
ejde-397	163	18	functions	function	NOUN
ejde-397	163	19	f	f	NOUN
ejde-397	163	20	:	:	PUNCT
ejde-397	164	1	[	[	X
ejde-397	164	2	0	0	NUM
ejde-397	164	3	,	,	PUNCT
ejde-397	164	4	t	t	X
ejde-397	164	5	]	]	PUNCT
ejde-397	164	6	→	→	PUNCT
ejde-397	164	7	x	x	X
ejde-397	164	8	with	with	ADP
ejde-397	164	9	the	the	DET
ejde-397	164	10	exponent	exponent	NOUN
ejde-397	164	11	r	r	NOUN
ejde-397	164	12	;	;	PUNCT
ejde-397	164	13	if	if	SCONJ
ejde-397	164	14	r′	r′	PRON
ejde-397	164	15	∈	∈	PROPN
ejde-397	164	16	(	(	PUNCT
ejde-397	164	17	0,∞	0,∞	NUM
ejde-397	164	18	)	)	PUNCT
ejde-397	164	19	\	\	NOUN
ejde-397	164	20	n	n	CCONJ
ejde-397	164	21	,	,	PUNCT
ejde-397	164	22	then	then	ADV
ejde-397	164	23	we	we	PRON
ejde-397	164	24	define	define	VERB
ejde-397	164	25	cr	cr	NOUN
ejde-397	165	1	′	′	NUM
ejde-397	166	1	(	(	PUNCT
ejde-397	167	1	[	[	X
ejde-397	167	2	0	0	NUM
ejde-397	167	3	,	,	PUNCT
ejde-397	167	4	t	t	X
ejde-397	167	5	]	]	PUNCT
ejde-397	167	6	:	:	PUNCT
ejde-397	168	1	x	x	X
ejde-397	168	2	)	)	PUNCT
ejde-397	168	3	as	as	ADP
ejde-397	168	4	the	the	DET
ejde-397	168	5	vector	vector	NOUN
ejde-397	168	6	space	space	NOUN
ejde-397	168	7	consisting	consist	VERB
ejde-397	168	8	of	of	ADP
ejde-397	168	9	those	those	DET
ejde-397	168	10	functions	function	NOUN
ejde-397	168	11	f	f	NOUN
ejde-397	168	12	:	:	PUNCT
ejde-397	169	1	[	[	X
ejde-397	169	2	0	0	NUM
ejde-397	169	3	,	,	PUNCT
ejde-397	169	4	t	t	X
ejde-397	169	5	]	]	PUNCT
ejde-397	169	6	→	→	PUNCT
ejde-397	169	7	x	x	SYM
ejde-397	169	8	for	for	ADP
ejde-397	169	9	which	which	PRON
ejde-397	169	10	f	f	PROPN
ejde-397	169	11	∈	∈	PROPN
ejde-397	169	12	cbr′c([0	cbr′c([0	NOUN
ejde-397	169	13	,	,	PUNCT
ejde-397	169	14	t	t	X
ejde-397	169	15	]	]	PUNCT
ejde-397	169	16	:	:	PUNCT
ejde-397	169	17	x	x	X
ejde-397	169	18	)	)	PUNCT
ejde-397	169	19	and	and	CCONJ
ejde-397	169	20	f	f	PROPN
ejde-397	169	21	(	(	PUNCT
ejde-397	169	22	br′c	br′c	PROPN
ejde-397	169	23	)	)	PUNCT
ejde-397	169	24	∈	∈	PROPN
ejde-397	169	25	cr′−br′c([0	cr′−br′c([0	PROPN
ejde-397	169	26	,	,	PUNCT
ejde-397	169	27	t	t	NOUN
ejde-397	169	28	]	]	PUNCT
ejde-397	169	29	:	:	PUNCT
ejde-397	169	30	x	x	X
ejde-397	169	31	)	)	PUNCT
ejde-397	169	32	.	.	PUNCT
ejde-397	170	1	without	without	ADP
ejde-397	170	2	going	go	VERB
ejde-397	170	3	into	into	ADP
ejde-397	170	4	further	further	ADJ
ejde-397	170	5	details	detail	NOUN
ejde-397	170	6	,	,	PUNCT
ejde-397	170	7	we	we	PRON
ejde-397	170	8	will	will	AUX
ejde-397	170	9	only	only	ADV
ejde-397	170	10	observe	observe	VERB
ejde-397	170	11	here	here	ADV
ejde-397	170	12	that	that	SCONJ
ejde-397	170	13	the	the	DET
ejde-397	170	14	existence	existence	NOUN
ejde-397	170	15	of	of	ADP
ejde-397	170	16	caputo	caputo	PROPN
ejde-397	170	17	fractional	fractional	PROPN
ejde-397	170	18	derivative	derivative	PROPN
ejde-397	170	19	dζ	dζ	PROPN
ejde-397	170	20	tu	tu	PROPN
ejde-397	170	21	implies	imply	VERB
ejde-397	170	22	u	u	PROPN
ejde-397	170	23	∈	∈	PROPN
ejde-397	170	24	cdζe((0,∞	cdζe((0,∞	NOUN
ejde-397	170	25	)	)	PUNCT
ejde-397	170	26	:	:	PUNCT
ejde-397	171	1	x)∩cζ([0	x)∩cζ([0	NUM
ejde-397	171	2	,	,	PUNCT
ejde-397	171	3	t	t	NOUN
ejde-397	171	4	]	]	PUNCT
ejde-397	171	5	:	:	PUNCT
ejde-397	171	6	e	e	X
ejde-397	171	7	)	)	PUNCT
ejde-397	171	8	,	,	PUNCT
ejde-397	171	9	for	for	ADP
ejde-397	171	10	each	each	DET
ejde-397	171	11	finite	finite	ADJ
ejde-397	171	12	number	number	NOUN
ejde-397	171	13	t	t	PROPN
ejde-397	171	14	>	>	X
ejde-397	171	15	0	0	X
ejde-397	171	16	.	.	PUNCT
ejde-397	172	1	a	a	DET
ejde-397	172	2	proof	proof	NOUN
ejde-397	172	3	is	be	AUX
ejde-397	172	4	left	leave	VERB
ejde-397	172	5	to	to	ADP
ejde-397	172	6	the	the	DET
ejde-397	172	7	interested	interested	ADJ
ejde-397	172	8	reader	reader	NOUN
ejde-397	172	9	.	.	PUNCT
ejde-397	173	1	we	we	PRON
ejde-397	173	2	refer	refer	VERB
ejde-397	173	3	the	the	DET
ejde-397	173	4	reader	reader	NOUN
ejde-397	173	5	to	to	ADP
ejde-397	173	6	[	[	X
ejde-397	173	7	5	5	NUM
ejde-397	173	8	]	]	PUNCT
ejde-397	173	9	for	for	ADP
ejde-397	173	10	the	the	DET
ejde-397	173	11	notion	notion	NOUN
ejde-397	173	12	of	of	ADP
ejde-397	173	13	a	a	DET
ejde-397	173	14	riemann	riemann	PROPN
ejde-397	173	15	-	-	PUNCT
ejde-397	173	16	liouville	liouville	VERB
ejde-397	173	17	fractional	fractional	ADJ
ejde-397	173	18	derivative	derivative	ADJ
ejde-397	173	19	dα	dα	NOUN
ejde-397	173	20	t	t	PROPN
ejde-397	173	21	u(t	u(t	PROPN
ejde-397	173	22	)	)	PUNCT
ejde-397	173	23	of	of	ADP
ejde-397	173	24	order	order	NOUN
ejde-397	173	25	α	α	X
ejde-397	173	26	>	>	X
ejde-397	173	27	0	0	NUM
ejde-397	173	28	.	.	PUNCT
ejde-397	174	1	the	the	DET
ejde-397	174	2	mittag	mittag	ADJ
ejde-397	174	3	-	-	PUNCT
ejde-397	174	4	leffler	leffler	NOUN
ejde-397	174	5	function	function	NOUN
ejde-397	174	6	eβ	eβ	NOUN
ejde-397	174	7	,	,	PUNCT
ejde-397	174	8	γ(z	γ(z	PROPN
ejde-397	174	9	)	)	PUNCT
ejde-397	174	10	(	(	PUNCT
ejde-397	174	11	β	β	X
ejde-397	174	12	>	>	X
ejde-397	174	13	0	0	PROPN
ejde-397	174	14	,	,	PUNCT
ejde-397	174	15	γ	γ	PROPN
ejde-397	174	16	∈	∈	NOUN
ejde-397	174	17	r	r	X
ejde-397	174	18	)	)	PUNCT
ejde-397	174	19	is	be	AUX
ejde-397	174	20	defined	define	VERB
ejde-397	174	21	by	by	ADP
ejde-397	174	22	eβ	eβ	NOUN
ejde-397	174	23	,	,	PUNCT
ejde-397	174	24	γ(z	γ(z	ADJ
ejde-397	174	25	)	)	PUNCT
ejde-397	174	26	:	:	PUNCT
ejde-397	175	1	=	=	NOUN
ejde-397	176	1	∞∑	∞∑	NUM
ejde-397	176	2	k=0	k=0	PUNCT
ejde-397	176	3	zk	zk	PROPN
ejde-397	176	4	γ(βk	γ(βk	PROPN
ejde-397	176	5	+	+	CCONJ
ejde-397	176	6	γ	γ	X
ejde-397	176	7	)	)	PUNCT
ejde-397	176	8	,	,	PUNCT
ejde-397	176	9	z	z	PROPN
ejde-397	176	10	∈	∈	PROPN
ejde-397	176	11	c.	c.	PROPN
ejde-397	176	12	set	set	NOUN
ejde-397	176	13	,	,	PUNCT
ejde-397	176	14	for	for	ADP
ejde-397	176	15	short	short	ADJ
ejde-397	176	16	,	,	PUNCT
ejde-397	176	17	eβ(z	eβ(z	PROPN
ejde-397	176	18	)	)	PUNCT
ejde-397	176	19	:	:	PUNCT
ejde-397	176	20	=	=	PUNCT
ejde-397	176	21	eβ,1(z	eβ,1(z	PROPN
ejde-397	176	22	)	)	PUNCT
ejde-397	176	23	,	,	PUNCT
ejde-397	176	24	z	z	PROPN
ejde-397	176	25	∈	∈	PROPN
ejde-397	176	26	c.	c.	NOUN
ejde-397	176	27	if	if	SCONJ
ejde-397	176	28	β	β	X
ejde-397	176	29	∈	∈	PROPN
ejde-397	176	30	(	(	PUNCT
ejde-397	176	31	0	0	NUM
ejde-397	176	32	,	,	PUNCT
ejde-397	176	33	1	1	NUM
ejde-397	176	34	)	)	PUNCT
ejde-397	176	35	,	,	PUNCT
ejde-397	176	36	then	then	ADV
ejde-397	176	37	we	we	PRON
ejde-397	176	38	define	define	VERB
ejde-397	176	39	the	the	DET
ejde-397	176	40	wright	wright	PROPN
ejde-397	176	41	function	function	PROPN
ejde-397	176	42	φβ	φβ	PROPN
ejde-397	176	43	(	(	PUNCT
ejde-397	176	44	·	·	PUNCT
ejde-397	176	45	)	)	PUNCT
ejde-397	176	46	by	by	ADP
ejde-397	176	47	φβ(t	φβ(t	NOUN
ejde-397	176	48	)	)	PUNCT
ejde-397	176	49	:	:	PUNCT
ejde-397	176	50	=	=	PUNCT
ejde-397	176	51	l−1	l−1	PROPN
ejde-397	176	52	(	(	PUNCT
ejde-397	176	53	eβ(−λ	eβ(−λ	PROPN
ejde-397	176	54	)	)	PUNCT
ejde-397	176	55	)	)	PUNCT
ejde-397	176	56	(	(	PUNCT
ejde-397	176	57	t	t	NOUN
ejde-397	176	58	)	)	PUNCT
ejde-397	176	59	,	,	PUNCT
ejde-397	176	60	t	t	PROPN
ejde-397	176	61	≥	≥	NUM
ejde-397	176	62	0	0	NUM
ejde-397	176	63	,	,	PUNCT
ejde-397	176	64	where	where	SCONJ
ejde-397	176	65	l−1	l−1	PROPN
ejde-397	176	66	denotes	denote	VERB
ejde-397	176	67	the	the	DET
ejde-397	176	68	inverse	inverse	ADJ
ejde-397	176	69	laplace	laplace	NOUN
ejde-397	176	70	transform	transform	NOUN
ejde-397	176	71	.	.	PUNCT
ejde-397	177	1	for	for	ADP
ejde-397	177	2	further	further	ADJ
ejde-397	177	3	information	information	NOUN
ejde-397	177	4	about	about	ADP
ejde-397	177	5	the	the	DET
ejde-397	177	6	mittag	mittag	ADJ
ejde-397	177	7	-	-	PUNCT
ejde-397	177	8	leffler	leffler	NOUN
ejde-397	177	9	and	and	CCONJ
ejde-397	177	10	wright	wright	PROPN
ejde-397	177	11	functions	function	NOUN
ejde-397	177	12	,	,	PUNCT
ejde-397	177	13	we	we	PRON
ejde-397	177	14	refer	refer	VERB
ejde-397	177	15	the	the	DET
ejde-397	177	16	reader	reader	NOUN
ejde-397	177	17	to	to	ADP
ejde-397	177	18	[	[	X
ejde-397	177	19	5	5	NUM
ejde-397	177	20	]	]	PUNCT
ejde-397	177	21	,	,	PUNCT
ejde-397	177	22	[	[	X
ejde-397	177	23	36	36	NUM
ejde-397	177	24	]	]	PUNCT
ejde-397	177	25	and	and	CCONJ
ejde-397	177	26	references	reference	NOUN
ejde-397	177	27	cited	cite	VERB
ejde-397	177	28	there	there	ADV
ejde-397	177	29	.	.	PUNCT
ejde-397	178	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	178	2	abstract	abstract	ADJ
ejde-397	178	3	degenerate	degenerate	ADJ
ejde-397	178	4	volterra	volterra	NOUN
ejde-397	178	5	inclusions	inclusion	NOUN
ejde-397	178	6	7	7	NUM
ejde-397	178	7	2	2	NUM
ejde-397	178	8	.	.	PUNCT
ejde-397	178	9	multivalued	multivalue	VERB
ejde-397	178	10	linear	linear	PROPN
ejde-397	178	11	operators	operator	NOUN
ejde-397	178	12	in	in	ADP
ejde-397	178	13	locally	locally	ADV
ejde-397	178	14	convex	convex	PROPN
ejde-397	178	15	spaces	space	VERB
ejde-397	178	16	a	a	DET
ejde-397	178	17	multivalued	multivalue	VERB
ejde-397	178	18	map	map	NOUN
ejde-397	178	19	(	(	PUNCT
ejde-397	178	20	multimap	multimap	ADJ
ejde-397	178	21	)	)	PUNCT
ejde-397	178	22	a	a	PRON
ejde-397	178	23	:	:	PUNCT
ejde-397	178	24	x	x	X
ejde-397	178	25	→	→	X
ejde-397	178	26	p	p	X
ejde-397	178	27	(	(	PUNCT
ejde-397	178	28	y	y	PROPN
ejde-397	178	29	)	)	PUNCT
ejde-397	178	30	is	be	AUX
ejde-397	178	31	said	say	VERB
ejde-397	178	32	to	to	PART
ejde-397	178	33	be	be	AUX
ejde-397	178	34	a	a	DET
ejde-397	178	35	multivalued	multivalue	VERB
ejde-397	178	36	linear	linear	ADJ
ejde-397	178	37	operator	operator	NOUN
ejde-397	178	38	(	(	PUNCT
ejde-397	178	39	mlo	mlo	PROPN
ejde-397	178	40	)	)	PUNCT
ejde-397	178	41	if	if	SCONJ
ejde-397	178	42	and	and	CCONJ
ejde-397	178	43	only	only	ADV
ejde-397	178	44	if	if	SCONJ
ejde-397	178	45	the	the	DET
ejde-397	178	46	following	follow	VERB
ejde-397	178	47	holds	hold	VERB
ejde-397	178	48	:	:	PUNCT
ejde-397	178	49	(	(	PUNCT
ejde-397	178	50	i	i	NOUN
ejde-397	178	51	)	)	PUNCT
ejde-397	178	52	d(a	d(a	PROPN
ejde-397	178	53	)	)	PUNCT
ejde-397	178	54	:	:	PUNCT
ejde-397	179	1	=	=	SYM
ejde-397	179	2	{	{	PUNCT
ejde-397	179	3	x	x	PUNCT
ejde-397	179	4	∈	∈	PROPN
ejde-397	179	5	x	x	X
ejde-397	179	6	:	:	PUNCT
ejde-397	179	7	ax	ax	NOUN
ejde-397	179	8	6=	6=	PUNCT
ejde-397	179	9	∅	∅	NOUN
ejde-397	179	10	}	}	PUNCT
ejde-397	179	11	is	be	AUX
ejde-397	179	12	a	a	DET
ejde-397	179	13	linear	linear	ADJ
ejde-397	179	14	subspace	subspace	NOUN
ejde-397	179	15	of	of	ADP
ejde-397	179	16	x	x	PRON
ejde-397	179	17	;	;	PUNCT
ejde-397	179	18	(	(	PUNCT
ejde-397	179	19	ii	ii	NOUN
ejde-397	179	20	)	)	PUNCT
ejde-397	179	21	ax+ay	ax+ay	CCONJ
ejde-397	180	1	⊆	⊆	NUM
ejde-397	180	2	a(x+	a(x+	ADP
ejde-397	180	3	y	y	PROPN
ejde-397	180	4	)	)	PUNCT
ejde-397	180	5	,	,	PUNCT
ejde-397	180	6	x	x	X
ejde-397	180	7	,	,	PUNCT
ejde-397	180	8	y	y	PROPN
ejde-397	180	9	∈	∈	PROPN
ejde-397	180	10	d(a	d(a	PROPN
ejde-397	180	11	)	)	PUNCT
ejde-397	180	12	and	and	CCONJ
ejde-397	180	13	λax	λax	PRON
ejde-397	180	14	⊆	⊆	NUM
ejde-397	180	15	a(λx	a(λx	NUM
ejde-397	180	16	)	)	PUNCT
ejde-397	180	17	,	,	PUNCT
ejde-397	180	18	λ	λ	X
ejde-397	180	19	∈	∈	PROPN
ejde-397	180	20	c	c	NOUN
ejde-397	180	21	,	,	PUNCT
ejde-397	180	22	x	x	SYM
ejde-397	180	23	∈	∈	PROPN
ejde-397	180	24	d(a	d(a	PROPN
ejde-397	180	25	)	)	PUNCT
ejde-397	180	26	.	.	PUNCT
ejde-397	181	1	if	if	SCONJ
ejde-397	181	2	x	x	X
ejde-397	181	3	=	=	SYM
ejde-397	181	4	y	y	PROPN
ejde-397	181	5	,	,	PUNCT
ejde-397	181	6	then	then	ADV
ejde-397	181	7	we	we	PRON
ejde-397	181	8	say	say	VERB
ejde-397	181	9	that	that	SCONJ
ejde-397	181	10	a	a	PRON
ejde-397	181	11	is	be	AUX
ejde-397	181	12	an	an	DET
ejde-397	181	13	mlo	mlo	NOUN
ejde-397	181	14	in	in	ADP
ejde-397	181	15	x.	x.	PROPN
ejde-397	181	16	an	an	DET
ejde-397	181	17	almost	almost	ADV
ejde-397	181	18	immediate	immediate	ADJ
ejde-397	181	19	consequence	consequence	NOUN
ejde-397	181	20	of	of	ADP
ejde-397	181	21	definition	definition	NOUN
ejde-397	181	22	is	be	AUX
ejde-397	181	23	that	that	DET
ejde-397	181	24	ax	ax	NOUN
ejde-397	182	1	+	+	NOUN
ejde-397	182	2	ay	ay	NOUN
ejde-397	182	3	=	=	SYM
ejde-397	182	4	a(x	a(x	PROPN
ejde-397	182	5	+	+	NUM
ejde-397	182	6	y	y	NOUN
ejde-397	182	7	)	)	PUNCT
ejde-397	182	8	for	for	ADP
ejde-397	182	9	all	all	DET
ejde-397	182	10	x	x	NOUN
ejde-397	182	11	,	,	PUNCT
ejde-397	182	12	y	y	PROPN
ejde-397	182	13	∈	∈	PROPN
ejde-397	182	14	d(a	d(a	PROPN
ejde-397	182	15	)	)	PUNCT
ejde-397	182	16	and	and	CCONJ
ejde-397	182	17	λax	λax	X
ejde-397	182	18	=	=	SYM
ejde-397	182	19	a(λx	a(λx	PROPN
ejde-397	182	20	)	)	PUNCT
ejde-397	182	21	for	for	ADP
ejde-397	182	22	all	all	DET
ejde-397	182	23	x	x	PROPN
ejde-397	182	24	∈	∈	PROPN
ejde-397	182	25	d(a	d(a	PROPN
ejde-397	182	26	)	)	PUNCT
ejde-397	182	27	,	,	PUNCT
ejde-397	182	28	λ	λ	PROPN
ejde-397	182	29	6=	6=	PROPN
ejde-397	182	30	0	0	NUM
ejde-397	182	31	.	.	PUNCT
ejde-397	183	1	furthermore	furthermore	ADV
ejde-397	183	2	,	,	PUNCT
ejde-397	183	3	for	for	ADP
ejde-397	183	4	any	any	DET
ejde-397	183	5	x	x	NOUN
ejde-397	183	6	,	,	PUNCT
ejde-397	183	7	y	y	PROPN
ejde-397	183	8	∈	∈	PROPN
ejde-397	183	9	d(a	d(a	PROPN
ejde-397	183	10	)	)	PUNCT
ejde-397	183	11	and	and	CCONJ
ejde-397	183	12	λ	λ	PROPN
ejde-397	183	13	,	,	PUNCT
ejde-397	183	14	η	η	PROPN
ejde-397	183	15	∈	∈	PROPN
ejde-397	183	16	c	c	PROPN
ejde-397	183	17	with	with	ADP
ejde-397	183	18	|λ|	|λ|	PROPN
ejde-397	183	19	+	+	CCONJ
ejde-397	183	20	|η|	|η|	PROPN
ejde-397	183	21	6=	6=	ADP
ejde-397	183	22	0	0	NUM
ejde-397	183	23	,	,	PUNCT
ejde-397	183	24	we	we	PRON
ejde-397	183	25	have	have	VERB
ejde-397	183	26	λax	λax	ADJ
ejde-397	183	27	+	+	NUM
ejde-397	183	28	ηay	ηay	NOUN
ejde-397	183	29	=	=	PUNCT
ejde-397	183	30	a(λx	a(λx	PROPN
ejde-397	183	31	+	+	CCONJ
ejde-397	183	32	ηy	ηy	ADJ
ejde-397	183	33	)	)	PUNCT
ejde-397	183	34	.	.	PUNCT
ejde-397	184	1	if	if	SCONJ
ejde-397	184	2	a	a	PRON
ejde-397	184	3	is	be	AUX
ejde-397	184	4	an	an	DET
ejde-397	184	5	mlo	mlo	NOUN
ejde-397	184	6	,	,	PUNCT
ejde-397	184	7	then	then	ADV
ejde-397	184	8	a0	a0	PROPN
ejde-397	184	9	is	be	AUX
ejde-397	184	10	a	a	DET
ejde-397	184	11	linear	linear	ADJ
ejde-397	184	12	manifold	manifold	NOUN
ejde-397	184	13	in	in	ADP
ejde-397	184	14	y	y	PROPN
ejde-397	184	15	and	and	CCONJ
ejde-397	184	16	ax	ax	NOUN
ejde-397	184	17	=	=	SYM
ejde-397	184	18	f	f	PROPN
ejde-397	184	19	+	+	CCONJ
ejde-397	184	20	a0	a0	PROPN
ejde-397	184	21	for	for	ADP
ejde-397	184	22	any	any	DET
ejde-397	184	23	x	x	PROPN
ejde-397	184	24	∈	∈	PROPN
ejde-397	184	25	d(a	d(a	PROPN
ejde-397	184	26	)	)	PUNCT
ejde-397	184	27	and	and	CCONJ
ejde-397	184	28	f	f	PROPN
ejde-397	184	29	∈	∈	PROPN
ejde-397	184	30	ax	ax	NOUN
ejde-397	184	31	.	.	PUNCT
ejde-397	185	1	set	set	PROPN
ejde-397	185	2	r(a	r(a	PROPN
ejde-397	185	3	)	)	PUNCT
ejde-397	186	1	:	:	PUNCT
ejde-397	186	2	=	=	SYM
ejde-397	186	3	{	{	PUNCT
ejde-397	186	4	ax	ax	NOUN
ejde-397	186	5	:	:	PUNCT
ejde-397	186	6	x	x	X
ejde-397	186	7	∈	∈	PROPN
ejde-397	186	8	d(a	d(a	PROPN
ejde-397	186	9	)	)	PUNCT
ejde-397	186	10	}	}	PUNCT
ejde-397	186	11	.	.	PUNCT
ejde-397	187	1	the	the	DET
ejde-397	187	2	set	set	NOUN
ejde-397	187	3	a−10	a−10	PROPN
ejde-397	187	4	=	=	SYM
ejde-397	187	5	{	{	PUNCT
ejde-397	187	6	x	x	PROPN
ejde-397	187	7	∈	∈	PROPN
ejde-397	187	8	d(a	d(a	PROPN
ejde-397	187	9	)	)	PUNCT
ejde-397	187	10	:	:	PUNCT
ejde-397	187	11	0	0	NUM
ejde-397	187	12	∈	∈	NOUN
ejde-397	187	13	ax	ax	NOUN
ejde-397	187	14	}	}	PUNCT
ejde-397	187	15	is	be	AUX
ejde-397	187	16	called	call	VERB
ejde-397	187	17	the	the	DET
ejde-397	187	18	kernel	kernel	NOUN
ejde-397	187	19	of	of	ADP
ejde-397	187	20	a	a	PRON
ejde-397	187	21	and	and	CCONJ
ejde-397	187	22	it	it	PRON
ejde-397	187	23	is	be	AUX
ejde-397	187	24	denoted	denote	VERB
ejde-397	187	25	henceforth	henceforth	ADV
ejde-397	187	26	by	by	ADP
ejde-397	187	27	n(a	n(a	NOUN
ejde-397	187	28	)	)	PUNCT
ejde-397	187	29	or	or	CCONJ
ejde-397	187	30	kern(a	kern(a	PROPN
ejde-397	187	31	)	)	PUNCT
ejde-397	187	32	.	.	PUNCT
ejde-397	188	1	the	the	DET
ejde-397	188	2	inverse	inverse	NOUN
ejde-397	188	3	a−1	a−1	PROPN
ejde-397	188	4	of	of	ADP
ejde-397	188	5	an	an	DET
ejde-397	188	6	mlo	mlo	PROPN
ejde-397	188	7	is	be	AUX
ejde-397	188	8	defined	define	VERB
ejde-397	188	9	by	by	ADP
ejde-397	188	10	d(a−1	d(a−1	NOUN
ejde-397	188	11	)	)	PUNCT
ejde-397	188	12	:	:	PUNCT
ejde-397	189	1	=	=	SYM
ejde-397	189	2	r(a	r(a	X
ejde-397	189	3	)	)	PUNCT
ejde-397	189	4	and	and	CCONJ
ejde-397	189	5	a−1y	a−1y	ADJ
ejde-397	189	6	:	:	PUNCT
ejde-397	189	7	=	=	SYM
ejde-397	189	8	{	{	PUNCT
ejde-397	189	9	x	x	PROPN
ejde-397	189	10	∈	∈	PROPN
ejde-397	189	11	d(a	d(a	PROPN
ejde-397	189	12	)	)	PUNCT
ejde-397	189	13	:	:	PUNCT
ejde-397	189	14	y	y	PROPN
ejde-397	189	15	∈	∈	PROPN
ejde-397	189	16	ax	ax	NOUN
ejde-397	189	17	}	}	PUNCT
ejde-397	189	18	.	.	PUNCT
ejde-397	190	1	it	it	PRON
ejde-397	190	2	is	be	AUX
ejde-397	190	3	checked	check	VERB
ejde-397	190	4	at	at	ADP
ejde-397	190	5	once	once	ADV
ejde-397	190	6	that	that	SCONJ
ejde-397	190	7	a−1	a−1	PROPN
ejde-397	190	8	is	be	AUX
ejde-397	190	9	an	an	DET
ejde-397	190	10	mlo	mlo	NOUN
ejde-397	190	11	in	in	ADP
ejde-397	190	12	x	x	PROPN
ejde-397	190	13	,	,	PUNCT
ejde-397	190	14	as	as	ADV
ejde-397	190	15	well	well	ADV
ejde-397	190	16	as	as	ADP
ejde-397	190	17	that	that	PRON
ejde-397	190	18	n(a−1	n(a−1	NOUN
ejde-397	190	19	)	)	PUNCT
ejde-397	190	20	=	=	SYM
ejde-397	190	21	a0	a0	PROPN
ejde-397	190	22	and	and	CCONJ
ejde-397	190	23	(	(	PUNCT
ejde-397	190	24	a−1)−1	a−1)−1	NOUN
ejde-397	190	25	=	=	PUNCT
ejde-397	190	26	a.	a.	NOUN
ejde-397	190	27	if	if	SCONJ
ejde-397	190	28	n(a	n(a	NOUN
ejde-397	190	29	)	)	PUNCT
ejde-397	190	30	=	=	PUNCT
ejde-397	190	31	{	{	PUNCT
ejde-397	190	32	0	0	NUM
ejde-397	190	33	}	}	PUNCT
ejde-397	190	34	,	,	PUNCT
ejde-397	190	35	i.e.	i.e.	X
ejde-397	190	36	,	,	PUNCT
ejde-397	190	37	if	if	SCONJ
ejde-397	190	38	a−1	a−1	PROPN
ejde-397	190	39	is	be	AUX
ejde-397	190	40	single	single	ADV
ejde-397	190	41	-	-	PUNCT
ejde-397	190	42	valued	value	VERB
ejde-397	190	43	,	,	PUNCT
ejde-397	190	44	then	then	ADV
ejde-397	190	45	a	a	PRON
ejde-397	190	46	is	be	AUX
ejde-397	190	47	said	say	VERB
ejde-397	190	48	to	to	PART
ejde-397	190	49	be	be	AUX
ejde-397	190	50	injective	injective	ADJ
ejde-397	190	51	.	.	PUNCT
ejde-397	191	1	it	it	PRON
ejde-397	191	2	is	be	AUX
ejde-397	191	3	worth	worth	ADJ
ejde-397	191	4	noting	note	VERB
ejde-397	191	5	that	that	SCONJ
ejde-397	191	6	ax	ax	NOUN
ejde-397	191	7	=	=	X
ejde-397	191	8	ay	ay	NOUN
ejde-397	191	9	for	for	ADP
ejde-397	191	10	some	some	DET
ejde-397	191	11	two	two	NUM
ejde-397	191	12	elements	element	NOUN
ejde-397	191	13	x	x	PUNCT
ejde-397	191	14	and	and	CCONJ
ejde-397	191	15	y	y	PROPN
ejde-397	191	16	∈	∈	PROPN
ejde-397	191	17	d(a	d(a	PROPN
ejde-397	191	18	)	)	PUNCT
ejde-397	191	19	,	,	PUNCT
ejde-397	191	20	if	if	SCONJ
ejde-397	191	21	and	and	CCONJ
ejde-397	191	22	only	only	ADV
ejde-397	191	23	if	if	SCONJ
ejde-397	191	24	ax	ax	NOUN
ejde-397	191	25	∩	∩	X
ejde-397	191	26	ay	ay	PROPN
ejde-397	191	27	6=	6=	NOUN
ejde-397	191	28	∅	∅	NOUN
ejde-397	191	29	;	;	PUNCT
ejde-397	191	30	moreover	moreover	ADV
ejde-397	191	31	,	,	PUNCT
ejde-397	191	32	if	if	SCONJ
ejde-397	191	33	a	a	PRON
ejde-397	191	34	is	be	AUX
ejde-397	191	35	injective	injective	ADJ
ejde-397	191	36	,	,	PUNCT
ejde-397	191	37	then	then	ADV
ejde-397	191	38	the	the	DET
ejde-397	191	39	equality	equality	NOUN
ejde-397	191	40	ax	ax	NOUN
ejde-397	191	41	=	=	NOUN
ejde-397	191	42	ay	ay	NOUN
ejde-397	191	43	holds	hold	VERB
ejde-397	191	44	if	if	SCONJ
ejde-397	191	45	and	and	CCONJ
ejde-397	191	46	only	only	ADV
ejde-397	191	47	if	if	SCONJ
ejde-397	191	48	x	x	X
ejde-397	191	49	=	=	PUNCT
ejde-397	191	50	y.	y.	NOUN
ejde-397	191	51	for	for	ADP
ejde-397	191	52	any	any	DET
ejde-397	191	53	mapping	mapping	NOUN
ejde-397	191	54	a	a	PRON
ejde-397	191	55	:	:	PUNCT
ejde-397	191	56	x	x	X
ejde-397	191	57	→	→	X
ejde-397	191	58	p	p	X
ejde-397	191	59	(	(	PUNCT
ejde-397	191	60	y	y	PROPN
ejde-397	191	61	)	)	PUNCT
ejde-397	191	62	we	we	PRON
ejde-397	191	63	define	define	VERB
ejde-397	191	64	ǎ	ǎ	VERB
ejde-397	191	65	:	:	PUNCT
ejde-397	191	66	=	=	SYM
ejde-397	191	67	{	{	PUNCT
ejde-397	191	68	(	(	PUNCT
ejde-397	191	69	x	x	NOUN
ejde-397	191	70	,	,	PUNCT
ejde-397	191	71	y	y	PROPN
ejde-397	191	72	)	)	PUNCT
ejde-397	191	73	:	:	PUNCT
ejde-397	191	74	x	x	X
ejde-397	191	75	∈	∈	PROPN
ejde-397	191	76	d(a	d(a	PROPN
ejde-397	191	77	)	)	PUNCT
ejde-397	191	78	,	,	PUNCT
ejde-397	191	79	y	y	PROPN
ejde-397	191	80	∈	∈	PROPN
ejde-397	191	81	ax	ax	NOUN
ejde-397	191	82	}	}	PUNCT
ejde-397	191	83	.	.	PUNCT
ejde-397	192	1	then	then	ADV
ejde-397	192	2	a	a	PRON
ejde-397	192	3	is	be	AUX
ejde-397	192	4	an	an	DET
ejde-397	192	5	mlo	mlo	NOUN
ejde-397	192	6	if	if	SCONJ
ejde-397	192	7	and	and	CCONJ
ejde-397	192	8	only	only	ADV
ejde-397	192	9	if	if	SCONJ
ejde-397	192	10	ǎ	ǎ	PROPN
ejde-397	192	11	is	be	AUX
ejde-397	192	12	a	a	DET
ejde-397	192	13	linear	linear	ADJ
ejde-397	192	14	relation	relation	NOUN
ejde-397	192	15	in	in	ADP
ejde-397	192	16	x	x	PROPN
ejde-397	192	17	×	×	PROPN
ejde-397	192	18	y	y	PROPN
ejde-397	192	19	,	,	PUNCT
ejde-397	192	20	i.e.	i.e.	X
ejde-397	192	21	,	,	PUNCT
ejde-397	192	22	if	if	SCONJ
ejde-397	192	23	and	and	CCONJ
ejde-397	192	24	only	only	ADV
ejde-397	192	25	if	if	SCONJ
ejde-397	192	26	ǎ	ǎ	PROPN
ejde-397	192	27	is	be	AUX
ejde-397	192	28	a	a	DET
ejde-397	192	29	linear	linear	ADJ
ejde-397	192	30	subspace	subspace	NOUN
ejde-397	192	31	of	of	ADP
ejde-397	192	32	x	x	SYM
ejde-397	192	33	×	×	PROPN
ejde-397	192	34	y	y	PROPN
ejde-397	192	35	.	.	PUNCT
ejde-397	193	1	if	if	SCONJ
ejde-397	193	2	a	a	PRON
ejde-397	193	3	,	,	PUNCT
ejde-397	193	4	b	b	NOUN
ejde-397	193	5	:	:	PUNCT
ejde-397	193	6	x	x	X
ejde-397	193	7	→	→	X
ejde-397	193	8	p	p	X
ejde-397	193	9	(	(	PUNCT
ejde-397	193	10	y	y	PROPN
ejde-397	193	11	)	)	PUNCT
ejde-397	193	12	are	be	AUX
ejde-397	193	13	two	two	NUM
ejde-397	193	14	mlos	mlo	NOUN
ejde-397	193	15	,	,	PUNCT
ejde-397	193	16	then	then	ADV
ejde-397	193	17	we	we	PRON
ejde-397	193	18	define	define	VERB
ejde-397	193	19	its	its	PRON
ejde-397	193	20	sum	sum	NOUN
ejde-397	193	21	a+b	a+b	NUM
ejde-397	193	22	by	by	ADP
ejde-397	193	23	d(a+b	d(a+b	NOUN
ejde-397	193	24	)	)	PUNCT
ejde-397	193	25	:	:	PUNCT
ejde-397	194	1	=	=	SYM
ejde-397	194	2	d(a	d(a	PROPN
ejde-397	194	3	)	)	PUNCT
ejde-397	194	4	∩d(b	∩d(b	PROPN
ejde-397	194	5	)	)	PUNCT
ejde-397	194	6	and	and	CCONJ
ejde-397	194	7	(	(	PUNCT
ejde-397	194	8	a+	a+	PRON
ejde-397	194	9	b)x	b)x	X
ejde-397	194	10	:	:	PUNCT
ejde-397	194	11	=	=	SYM
ejde-397	194	12	ax+	ax+	ADJ
ejde-397	194	13	bx	bx	X
ejde-397	194	14	,	,	PUNCT
ejde-397	194	15	x	x	SYM
ejde-397	194	16	∈	∈	PROPN
ejde-397	194	17	d(a+	d(a+	NOUN
ejde-397	194	18	b	b	NOUN
ejde-397	194	19	)	)	PUNCT
ejde-397	194	20	.	.	PUNCT
ejde-397	195	1	it	it	PRON
ejde-397	195	2	can	can	AUX
ejde-397	195	3	be	be	AUX
ejde-397	195	4	simply	simply	ADV
ejde-397	195	5	verified	verify	VERB
ejde-397	195	6	that	that	SCONJ
ejde-397	195	7	a+	a+	PUNCT
ejde-397	195	8	b	b	NOUN
ejde-397	195	9	is	be	AUX
ejde-397	195	10	likewise	likewise	ADV
ejde-397	195	11	an	an	DET
ejde-397	195	12	mlo	mlo	NOUN
ejde-397	195	13	.	.	PUNCT
ejde-397	196	1	let	let	VERB
ejde-397	196	2	a	a	DET
ejde-397	196	3	:	:	PUNCT
ejde-397	196	4	x	x	X
ejde-397	196	5	→	→	X
ejde-397	196	6	p	p	X
ejde-397	196	7	(	(	PUNCT
ejde-397	196	8	y	y	PROPN
ejde-397	196	9	)	)	PUNCT
ejde-397	196	10	and	and	CCONJ
ejde-397	196	11	b	b	X
ejde-397	196	12	:	:	PUNCT
ejde-397	196	13	y	y	PROPN
ejde-397	196	14	→	→	SYM
ejde-397	196	15	p	p	X
ejde-397	196	16	(	(	PUNCT
ejde-397	196	17	z	z	NOUN
ejde-397	196	18	)	)	PUNCT
ejde-397	196	19	be	be	AUX
ejde-397	196	20	two	two	NUM
ejde-397	196	21	mlos	mlo	NOUN
ejde-397	196	22	,	,	PUNCT
ejde-397	196	23	where	where	SCONJ
ejde-397	196	24	z	z	NOUN
ejde-397	196	25	is	be	AUX
ejde-397	196	26	an	an	DET
ejde-397	196	27	sclcs	sclcs	NOUN
ejde-397	196	28	.	.	PUNCT
ejde-397	197	1	the	the	DET
ejde-397	197	2	product	product	NOUN
ejde-397	197	3	of	of	ADP
ejde-397	197	4	a	a	PRON
ejde-397	197	5	and	and	CCONJ
ejde-397	197	6	b	b	NOUN
ejde-397	197	7	is	be	AUX
ejde-397	197	8	defined	define	VERB
ejde-397	197	9	by	by	ADP
ejde-397	197	10	d(ba	d(ba	NOUN
ejde-397	197	11	)	)	PUNCT
ejde-397	198	1	:	:	PUNCT
ejde-397	198	2	=	=	SYM
ejde-397	198	3	{	{	PUNCT
ejde-397	198	4	x	x	PROPN
ejde-397	198	5	∈	∈	PROPN
ejde-397	198	6	d(a	d(a	PROPN
ejde-397	198	7	)	)	PUNCT
ejde-397	198	8	:	:	PUNCT
ejde-397	199	1	d(b)∩ax	d(b)∩ax	PROPN
ejde-397	199	2	6=	6=	ADP
ejde-397	199	3	∅	∅	NOUN
ejde-397	199	4	}	}	PUNCT
ejde-397	199	5	and	and	CCONJ
ejde-397	199	6	bax	bax	NOUN
ejde-397	199	7	:	:	PUNCT
ejde-397	199	8	=	=	PUNCT
ejde-397	199	9	b(d(b)∩ax	b(d(b)∩ax	PROPN
ejde-397	199	10	)	)	PUNCT
ejde-397	199	11	.	.	PUNCT
ejde-397	200	1	then	then	ADV
ejde-397	200	2	ba	ba	VERB
ejde-397	200	3	:	:	PUNCT
ejde-397	200	4	x	x	X
ejde-397	200	5	→	→	X
ejde-397	200	6	p	p	X
ejde-397	200	7	(	(	PUNCT
ejde-397	200	8	z	z	NOUN
ejde-397	200	9	)	)	PUNCT
ejde-397	200	10	is	be	AUX
ejde-397	200	11	an	an	DET
ejde-397	200	12	mlo	mlo	PROPN
ejde-397	200	13	and	and	CCONJ
ejde-397	200	14	(	(	PUNCT
ejde-397	200	15	ba)−1	ba)−1	ADP
ejde-397	200	16	=	=	SYM
ejde-397	200	17	a−1b−1	a−1b−1	PROPN
ejde-397	200	18	.	.	PUNCT
ejde-397	201	1	the	the	DET
ejde-397	201	2	scalar	scalar	ADJ
ejde-397	201	3	multiplication	multiplication	NOUN
ejde-397	201	4	of	of	ADP
ejde-397	201	5	an	an	DET
ejde-397	201	6	mlo	mlo	PROPN
ejde-397	201	7	a	a	PRON
ejde-397	201	8	:	:	PUNCT
ejde-397	201	9	x	x	X
ejde-397	201	10	→	→	X
ejde-397	201	11	p	p	X
ejde-397	201	12	(	(	PUNCT
ejde-397	201	13	y	y	PROPN
ejde-397	201	14	)	)	PUNCT
ejde-397	201	15	with	with	ADP
ejde-397	201	16	the	the	DET
ejde-397	201	17	number	number	NOUN
ejde-397	201	18	z	z	NOUN
ejde-397	201	19	∈	∈	PROPN
ejde-397	201	20	c	c	X
ejde-397	201	21	,	,	PUNCT
ejde-397	201	22	za	za	PROPN
ejde-397	201	23	for	for	ADP
ejde-397	201	24	short	short	ADJ
ejde-397	201	25	,	,	PUNCT
ejde-397	201	26	is	be	AUX
ejde-397	201	27	defined	define	VERB
ejde-397	201	28	by	by	ADP
ejde-397	201	29	d(za	d(za	PROPN
ejde-397	201	30	)	)	PUNCT
ejde-397	201	31	:	:	PUNCT
ejde-397	202	1	=	=	SYM
ejde-397	202	2	d(a	d(a	PROPN
ejde-397	202	3	)	)	PUNCT
ejde-397	202	4	and	and	CCONJ
ejde-397	202	5	(	(	PUNCT
ejde-397	202	6	za)(x	za)(x	NOUN
ejde-397	202	7	)	)	PUNCT
ejde-397	202	8	:	:	PUNCT
ejde-397	202	9	=	=	SYM
ejde-397	202	10	zax	zax	PROPN
ejde-397	202	11	,	,	PUNCT
ejde-397	202	12	x	x	PROPN
ejde-397	202	13	∈	∈	PROPN
ejde-397	202	14	d(a	d(a	PROPN
ejde-397	202	15	)	)	PUNCT
ejde-397	202	16	.	.	PUNCT
ejde-397	203	1	it	it	PRON
ejde-397	203	2	is	be	AUX
ejde-397	203	3	clear	clear	ADJ
ejde-397	203	4	that	that	SCONJ
ejde-397	203	5	za	za	PROPN
ejde-397	203	6	:	:	PUNCT
ejde-397	203	7	x	x	X
ejde-397	203	8	→	→	X
ejde-397	203	9	p	p	X
ejde-397	203	10	(	(	PUNCT
ejde-397	203	11	y	y	PROPN
ejde-397	203	12	)	)	PUNCT
ejde-397	203	13	is	be	AUX
ejde-397	203	14	an	an	DET
ejde-397	203	15	mlo	mlo	PROPN
ejde-397	203	16	and	and	CCONJ
ejde-397	203	17	(	(	PUNCT
ejde-397	203	18	ωz)a	ωz)a	PROPN
ejde-397	203	19	=	=	SYM
ejde-397	203	20	ω(za	ω(za	NUM
ejde-397	203	21	)	)	PUNCT
ejde-397	203	22	=	=	SYM
ejde-397	203	23	z(ωa	z(ωa	NUM
ejde-397	203	24	)	)	PUNCT
ejde-397	203	25	,	,	PUNCT
ejde-397	203	26	z	z	X
ejde-397	203	27	,	,	PUNCT
ejde-397	203	28	ω	ω	PROPN
ejde-397	203	29	∈	∈	PROPN
ejde-397	203	30	c.	c.	NOUN
ejde-397	203	31	suppose	suppose	VERB
ejde-397	203	32	that	that	SCONJ
ejde-397	203	33	x	x	PRON
ejde-397	203	34	′	′	NOUN
ejde-397	203	35	is	be	AUX
ejde-397	203	36	a	a	DET
ejde-397	203	37	linear	linear	ADJ
ejde-397	203	38	subspace	subspace	NOUN
ejde-397	203	39	of	of	ADP
ejde-397	203	40	x	x	X
ejde-397	203	41	,	,	PUNCT
ejde-397	203	42	and	and	CCONJ
ejde-397	203	43	a	a	PRON
ejde-397	203	44	:	:	PUNCT
ejde-397	203	45	x	x	X
ejde-397	203	46	→	→	X
ejde-397	203	47	p	p	X
ejde-397	203	48	(	(	PUNCT
ejde-397	203	49	y	y	PROPN
ejde-397	203	50	)	)	PUNCT
ejde-397	203	51	is	be	AUX
ejde-397	203	52	an	an	DET
ejde-397	203	53	mlo	mlo	PROPN
ejde-397	203	54	.	.	PUNCT
ejde-397	204	1	then	then	ADV
ejde-397	204	2	we	we	PRON
ejde-397	204	3	define	define	VERB
ejde-397	204	4	the	the	DET
ejde-397	204	5	restriction	restriction	NOUN
ejde-397	204	6	of	of	ADP
ejde-397	204	7	operator	operator	NOUN
ejde-397	204	8	a	a	PRON
ejde-397	204	9	to	to	ADP
ejde-397	204	10	the	the	DET
ejde-397	204	11	subspace	subspace	NOUN
ejde-397	204	12	x	x	PROPN
ejde-397	204	13	′	′	NUM
ejde-397	204	14	,	,	PUNCT
ejde-397	204	15	a|x′	a|x′	X
ejde-397	204	16	for	for	ADP
ejde-397	204	17	short	short	ADJ
ejde-397	204	18	,	,	PUNCT
ejde-397	204	19	by	by	ADP
ejde-397	204	20	d(a|x′	d(a|x′	NOUN
ejde-397	204	21	)	)	PUNCT
ejde-397	204	22	:	:	PUNCT
ejde-397	204	23	=	=	SYM
ejde-397	204	24	d(a)∩x	d(a)∩x	NOUN
ejde-397	204	25	′	′	NOUN
ejde-397	204	26	and	and	CCONJ
ejde-397	204	27	a|x′x	a|x′x	PRON
ejde-397	204	28	:	:	PUNCT
ejde-397	204	29	=	=	SYM
ejde-397	204	30	ax	ax	NOUN
ejde-397	204	31	,	,	PUNCT
ejde-397	204	32	x	x	SYM
ejde-397	204	33	∈	∈	PROPN
ejde-397	204	34	d(a|x′	d(a|x′	NOUN
ejde-397	204	35	)	)	PUNCT
ejde-397	204	36	.	.	PUNCT
ejde-397	205	1	clearly	clearly	ADV
ejde-397	205	2	,	,	PUNCT
ejde-397	205	3	a|x′	a|x′	PUNCT
ejde-397	205	4	:	:	PUNCT
ejde-397	205	5	x	x	X
ejde-397	205	6	′	′	NUM
ejde-397	205	7	→	→	SYM
ejde-397	205	8	p	p	X
ejde-397	205	9	(	(	PUNCT
ejde-397	205	10	y	y	PROPN
ejde-397	205	11	)	)	PUNCT
ejde-397	205	12	is	be	AUX
ejde-397	205	13	an	an	DET
ejde-397	205	14	mlo	mlo	NOUN
ejde-397	205	15	.	.	PUNCT
ejde-397	206	1	it	it	PRON
ejde-397	206	2	is	be	AUX
ejde-397	206	3	well	well	ADV
ejde-397	206	4	known	know	VERB
ejde-397	206	5	that	that	SCONJ
ejde-397	206	6	an	an	DET
ejde-397	206	7	mlo	mlo	PROPN
ejde-397	206	8	a	a	PRON
ejde-397	206	9	:	:	PUNCT
ejde-397	206	10	x	x	X
ejde-397	206	11	→	→	X
ejde-397	206	12	p	p	X
ejde-397	206	13	(	(	PUNCT
ejde-397	206	14	y	y	PROPN
ejde-397	206	15	)	)	PUNCT
ejde-397	206	16	is	be	AUX
ejde-397	206	17	injective	injective	ADJ
ejde-397	206	18	(	(	PUNCT
ejde-397	206	19	resp	resp	NOUN
ejde-397	206	20	.	.	PUNCT
ejde-397	206	21	,	,	PUNCT
ejde-397	206	22	single	single	ADV
ejde-397	206	23	-	-	PUNCT
ejde-397	206	24	valued	value	VERB
ejde-397	206	25	)	)	PUNCT
ejde-397	207	1	if	if	SCONJ
ejde-397	207	2	and	and	CCONJ
ejde-397	207	3	only	only	ADV
ejde-397	207	4	if	if	SCONJ
ejde-397	207	5	a−1a	a−1a	PROPN
ejde-397	207	6	=	=	SYM
ejde-397	207	7	i|d(a	i|d(a	PROPN
ejde-397	207	8	)	)	PUNCT
ejde-397	207	9	(	(	PUNCT
ejde-397	207	10	resp	resp	NOUN
ejde-397	207	11	.	.	PUNCT
ejde-397	207	12	,	,	PUNCT
ejde-397	207	13	aa−1	aa−1	PROPN
ejde-397	207	14	=	=	SYM
ejde-397	207	15	iy|r(a	iy|r(a	PROPN
ejde-397	207	16	)	)	PUNCT
ejde-397	207	17	)	)	PUNCT
ejde-397	207	18	.	.	PUNCT
ejde-397	208	1	the	the	DET
ejde-397	208	2	integer	integer	NOUN
ejde-397	208	3	powers	power	NOUN
ejde-397	208	4	of	of	ADP
ejde-397	208	5	an	an	DET
ejde-397	208	6	mlo	mlo	PROPN
ejde-397	208	7	a	a	PRON
ejde-397	208	8	:	:	PUNCT
ejde-397	208	9	x	x	X
ejde-397	208	10	→	→	X
ejde-397	208	11	p	p	X
ejde-397	208	12	(	(	PUNCT
ejde-397	208	13	x	x	X
ejde-397	208	14	)	)	PUNCT
ejde-397	208	15	are	be	AUX
ejde-397	208	16	defined	define	VERB
ejde-397	208	17	recursively	recursively	ADV
ejde-397	208	18	as	as	SCONJ
ejde-397	208	19	follows	follow	VERB
ejde-397	208	20	:	:	PUNCT
ejde-397	208	21	a0	a0	PROPN
ejde-397	209	1	=	=	NOUN
ejde-397	209	2	:	:	PUNCT
ejde-397	209	3	i	i	PRON
ejde-397	209	4	;	;	PUNCT
ejde-397	209	5	if	if	SCONJ
ejde-397	209	6	an−1	an−1	ADJ
ejde-397	209	7	is	be	AUX
ejde-397	209	8	defined	define	VERB
ejde-397	209	9	,	,	PUNCT
ejde-397	209	10	set	set	VERB
ejde-397	209	11	d(an	d(an	NOUN
ejde-397	209	12	)	)	PUNCT
ejde-397	209	13	:	:	PUNCT
ejde-397	210	1	=	=	SYM
ejde-397	210	2	{	{	PUNCT
ejde-397	210	3	x	x	PUNCT
ejde-397	210	4	∈	∈	NOUN
ejde-397	210	5	d(an−1	d(an−1	NOUN
ejde-397	210	6	)	)	PUNCT
ejde-397	210	7	:	:	PUNCT
ejde-397	211	1	d(a	d(a	PROPN
ejde-397	211	2	)	)	PUNCT
ejde-397	211	3	∩	∩	NOUN
ejde-397	211	4	an−1x	an−1x	PROPN
ejde-397	211	5	6=	6=	SYM
ejde-397	211	6	∅	∅	NOUN
ejde-397	211	7	}	}	PUNCT
ejde-397	211	8	,	,	PUNCT
ejde-397	211	9	and	and	CCONJ
ejde-397	211	10	anx	anx	ADJ
ejde-397	211	11	:	:	PUNCT
ejde-397	211	12	=	=	X
ejde-397	211	13	(	(	PUNCT
ejde-397	211	14	aan−1	aan−1	PROPN
ejde-397	211	15	)	)	PUNCT
ejde-397	211	16	x	x	X
ejde-397	212	1	=	=	PUNCT
ejde-397	212	2	⋃	⋃	PROPN
ejde-397	212	3	y∈d(a)∩an−1x	y∈d(a)∩an−1x	NOUN
ejde-397	212	4	ay	ay	NOUN
ejde-397	212	5	,	,	PUNCT
ejde-397	212	6	x	x	X
ejde-397	212	7	∈	∈	PROPN
ejde-397	212	8	d(an	d(an	PROPN
ejde-397	212	9	)	)	PUNCT
ejde-397	212	10	.	.	PUNCT
ejde-397	213	1	we	we	PRON
ejde-397	213	2	can	can	AUX
ejde-397	213	3	prove	prove	VERB
ejde-397	213	4	inductively	inductively	ADV
ejde-397	213	5	that	that	SCONJ
ejde-397	213	6	(	(	PUNCT
ejde-397	213	7	an)−1	an)−1	NOUN
ejde-397	213	8	=	=	SYM
ejde-397	213	9	(	(	PUNCT
ejde-397	213	10	an−1)−1a−1	an−1)−1a−1	NOUN
ejde-397	213	11	=	=	SYM
ejde-397	213	12	(	(	PUNCT
ejde-397	213	13	a−1)n	a−1)n	X
ejde-397	213	14	=	=	NOUN
ejde-397	213	15	:	:	PUNCT
ejde-397	213	16	a−n	a−n	PROPN
ejde-397	213	17	,	,	PUNCT
ejde-397	213	18	n	n	PROPN
ejde-397	213	19	∈	∈	PROPN
ejde-397	213	20	n	n	NOUN
ejde-397	213	21	and	and	CCONJ
ejde-397	213	22	d((λ−a)n	d((λ−a)n	ADJ
ejde-397	213	23	)	)	PUNCT
ejde-397	213	24	=	=	PUNCT
ejde-397	214	1	d(an	d(an	NOUN
ejde-397	214	2	)	)	PUNCT
ejde-397	214	3	,	,	PUNCT
ejde-397	214	4	n	n	PROPN
ejde-397	214	5	∈	∈	PROPN
ejde-397	214	6	n0	n0	PROPN
ejde-397	214	7	.	.	PUNCT
ejde-397	215	1	moreover	moreover	ADV
ejde-397	215	2	,	,	PUNCT
ejde-397	215	3	if	if	SCONJ
ejde-397	215	4	a	a	PRON
ejde-397	215	5	is	be	AUX
ejde-397	215	6	single	single	ADV
ejde-397	215	7	-	-	PUNCT
ejde-397	215	8	valued	value	VERB
ejde-397	215	9	,	,	PUNCT
ejde-397	215	10	then	then	ADV
ejde-397	215	11	the	the	DET
ejde-397	215	12	above	above	ADJ
ejde-397	215	13	definitions	definition	NOUN
ejde-397	215	14	are	be	AUX
ejde-397	215	15	consistent	consistent	ADJ
ejde-397	215	16	with	with	ADP
ejde-397	215	17	the	the	DET
ejde-397	215	18	usual	usual	ADJ
ejde-397	215	19	definition	definition	NOUN
ejde-397	215	20	of	of	ADP
ejde-397	215	21	powers	power	NOUN
ejde-397	215	22	of	of	ADP
ejde-397	215	23	a.	a.	NOUN
ejde-397	215	24	if	if	SCONJ
ejde-397	215	25	a	a	PRON
ejde-397	215	26	:	:	PUNCT
ejde-397	215	27	x	x	X
ejde-397	215	28	→	→	X
ejde-397	215	29	p	p	X
ejde-397	215	30	(	(	PUNCT
ejde-397	215	31	y	y	PROPN
ejde-397	215	32	)	)	PUNCT
ejde-397	215	33	and	and	CCONJ
ejde-397	215	34	b	b	X
ejde-397	215	35	:	:	PUNCT
ejde-397	215	36	x	x	X
ejde-397	215	37	→	→	X
ejde-397	215	38	p	p	X
ejde-397	215	39	(	(	PUNCT
ejde-397	215	40	y	y	PROPN
ejde-397	215	41	)	)	PUNCT
ejde-397	215	42	are	be	AUX
ejde-397	215	43	two	two	NUM
ejde-397	215	44	mlos	mlo	NOUN
ejde-397	215	45	,	,	PUNCT
ejde-397	215	46	then	then	ADV
ejde-397	215	47	we	we	PRON
ejde-397	215	48	write	write	VERB
ejde-397	215	49	a	a	DET
ejde-397	215	50	⊆	⊆	NUM
ejde-397	215	51	b	b	NOUN
ejde-397	215	52	if	if	SCONJ
ejde-397	216	1	and	and	CCONJ
ejde-397	216	2	only	only	ADV
ejde-397	216	3	if	if	SCONJ
ejde-397	216	4	d(a	d(a	PROPN
ejde-397	216	5	)	)	PUNCT
ejde-397	216	6	⊆	⊆	NUM
ejde-397	216	7	d(b	d(b	NOUN
ejde-397	216	8	)	)	PUNCT
ejde-397	216	9	and	and	CCONJ
ejde-397	216	10	ax	ax	VERB
ejde-397	216	11	⊆	⊆	NUM
ejde-397	216	12	bx	bx	NOUN
ejde-397	216	13	for	for	ADP
ejde-397	216	14	all	all	DET
ejde-397	216	15	x	x	PROPN
ejde-397	216	16	∈	∈	PROPN
ejde-397	216	17	d(a	d(a	PROPN
ejde-397	216	18	)	)	PUNCT
ejde-397	216	19	.	.	PUNCT
ejde-397	217	1	assume	assume	VERB
ejde-397	217	2	now	now	ADV
ejde-397	217	3	that	that	SCONJ
ejde-397	217	4	a	a	DET
ejde-397	217	5	linear	linear	ADJ
ejde-397	217	6	8	8	NUM
ejde-397	217	7	m.	m.	NOUN
ejde-397	217	8	kostić	kostić	NOUN
ejde-397	218	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	218	2	single	single	ADV
ejde-397	218	3	-	-	PUNCT
ejde-397	218	4	valued	value	VERB
ejde-397	218	5	operator	operator	NOUN
ejde-397	218	6	s	s	PART
ejde-397	218	7	:	:	PUNCT
ejde-397	218	8	d(s	d(s	PROPN
ejde-397	218	9	)	)	PUNCT
ejde-397	219	1	⊆	⊆	NUM
ejde-397	219	2	x	x	SYM
ejde-397	219	3	→	→	SYM
ejde-397	219	4	y	y	PROPN
ejde-397	219	5	has	have	AUX
ejde-397	219	6	domain	domain	VERB
ejde-397	219	7	d(s	d(s	PROPN
ejde-397	219	8	)	)	PUNCT
ejde-397	220	1	=	=	SYM
ejde-397	220	2	d(a	d(a	PROPN
ejde-397	220	3	)	)	PUNCT
ejde-397	220	4	and	and	CCONJ
ejde-397	220	5	s	s	VERB
ejde-397	220	6	⊆	⊆	NUM
ejde-397	220	7	a	a	PRON
ejde-397	220	8	,	,	PUNCT
ejde-397	220	9	where	where	SCONJ
ejde-397	220	10	a	a	PRON
ejde-397	220	11	:	:	PUNCT
ejde-397	220	12	x	x	X
ejde-397	220	13	→	→	X
ejde-397	220	14	p	p	X
ejde-397	220	15	(	(	PUNCT
ejde-397	220	16	y	y	PROPN
ejde-397	220	17	)	)	PUNCT
ejde-397	220	18	is	be	AUX
ejde-397	220	19	an	an	DET
ejde-397	220	20	mlo	mlo	PROPN
ejde-397	220	21	.	.	PUNCT
ejde-397	221	1	then	then	ADV
ejde-397	221	2	s	s	VERB
ejde-397	221	3	is	be	AUX
ejde-397	221	4	called	call	VERB
ejde-397	221	5	a	a	DET
ejde-397	221	6	section	section	NOUN
ejde-397	221	7	of	of	ADP
ejde-397	221	8	a	a	PRON
ejde-397	221	9	;	;	PUNCT
ejde-397	221	10	if	if	SCONJ
ejde-397	221	11	this	this	PRON
ejde-397	221	12	is	be	AUX
ejde-397	221	13	the	the	DET
ejde-397	221	14	case	case	NOUN
ejde-397	221	15	,	,	PUNCT
ejde-397	221	16	we	we	PRON
ejde-397	221	17	have	have	VERB
ejde-397	221	18	ax	ax	NOUN
ejde-397	221	19	=	=	PUNCT
ejde-397	221	20	sx+a0	sx+a0	NOUN
ejde-397	221	21	,	,	PUNCT
ejde-397	221	22	x	x	PROPN
ejde-397	221	23	∈	∈	PROPN
ejde-397	221	24	d(a	d(a	PROPN
ejde-397	221	25	)	)	PUNCT
ejde-397	221	26	and	and	CCONJ
ejde-397	221	27	r(a	r(a	PROPN
ejde-397	221	28	)	)	PUNCT
ejde-397	221	29	=	=	SYM
ejde-397	222	1	r(s	r(s	X
ejde-397	222	2	)	)	PUNCT
ejde-397	222	3	+	+	NOUN
ejde-397	222	4	a0	a0	NOUN
ejde-397	222	5	.	.	PUNCT
ejde-397	223	1	we	we	PRON
ejde-397	223	2	say	say	VERB
ejde-397	223	3	that	that	SCONJ
ejde-397	223	4	an	an	DET
ejde-397	223	5	mlo	mlo	PROPN
ejde-397	223	6	operator	operator	NOUN
ejde-397	223	7	a	a	DET
ejde-397	223	8	:	:	PUNCT
ejde-397	223	9	x	x	X
ejde-397	223	10	→	→	X
ejde-397	223	11	p	p	X
ejde-397	223	12	(	(	PUNCT
ejde-397	223	13	y	y	PROPN
ejde-397	223	14	)	)	PUNCT
ejde-397	223	15	is	be	AUX
ejde-397	223	16	closed	close	VERB
ejde-397	223	17	if	if	SCONJ
ejde-397	223	18	for	for	ADP
ejde-397	223	19	any	any	DET
ejde-397	223	20	nets	net	NOUN
ejde-397	223	21	(	(	PUNCT
ejde-397	223	22	xτ	xτ	NOUN
ejde-397	223	23	)	)	PUNCT
ejde-397	223	24	in	in	ADP
ejde-397	223	25	d(a	d(a	PROPN
ejde-397	223	26	)	)	PUNCT
ejde-397	223	27	and	and	CCONJ
ejde-397	223	28	(	(	PUNCT
ejde-397	223	29	yτ	yτ	PROPN
ejde-397	223	30	)	)	PUNCT
ejde-397	223	31	in	in	ADP
ejde-397	223	32	y	y	PRON
ejde-397	223	33	such	such	ADJ
ejde-397	223	34	that	that	SCONJ
ejde-397	223	35	yτ	yτ	PROPN
ejde-397	223	36	∈	∈	PROPN
ejde-397	223	37	axτ	axτ	NOUN
ejde-397	223	38	for	for	ADP
ejde-397	223	39	all	all	PRON
ejde-397	223	40	τ	τ	PROPN
ejde-397	223	41	∈	∈	NOUN
ejde-397	223	42	i	i	PRON
ejde-397	223	43	we	we	PRON
ejde-397	223	44	have	have	VERB
ejde-397	223	45	that	that	SCONJ
ejde-397	223	46	the	the	DET
ejde-397	223	47	suppositions	supposition	NOUN
ejde-397	223	48	limτ→∞	limτ→∞	VERB
ejde-397	223	49	xτ	xτ	X
ejde-397	224	1	=	=	SYM
ejde-397	224	2	x	x	X
ejde-397	224	3	and	and	CCONJ
ejde-397	224	4	limτ→∞	limτ→∞	PROPN
ejde-397	224	5	yτ	yτ	NOUN
ejde-397	225	1	=	=	SYM
ejde-397	225	2	y	y	PROPN
ejde-397	225	3	imply	imply	VERB
ejde-397	225	4	x	x	X
ejde-397	225	5	∈	∈	PROPN
ejde-397	225	6	d(a	d(a	PROPN
ejde-397	225	7	)	)	PUNCT
ejde-397	225	8	and	and	CCONJ
ejde-397	225	9	y	y	PROPN
ejde-397	225	10	∈	∈	PROPN
ejde-397	225	11	ax	ax	NOUN
ejde-397	225	12	.	.	PUNCT
ejde-397	226	1	we	we	PRON
ejde-397	226	2	introduce	introduce	VERB
ejde-397	226	3	the	the	DET
ejde-397	226	4	notion	notion	NOUN
ejde-397	226	5	of	of	ADP
ejde-397	226	6	a	a	DET
ejde-397	226	7	relatively	relatively	ADV
ejde-397	226	8	closed	closed	ADJ
ejde-397	226	9	mlo	mlo	PROPN
ejde-397	226	10	as	as	SCONJ
ejde-397	226	11	follows	follow	VERB
ejde-397	226	12	[	[	X
ejde-397	226	13	32	32	NUM
ejde-397	226	14	]	]	PUNCT
ejde-397	226	15	.	.	PUNCT
ejde-397	227	1	we	we	PRON
ejde-397	227	2	say	say	VERB
ejde-397	227	3	that	that	SCONJ
ejde-397	227	4	an	an	DET
ejde-397	227	5	mlo	mlo	PROPN
ejde-397	227	6	a	a	PRON
ejde-397	227	7	:	:	PUNCT
ejde-397	227	8	x	x	X
ejde-397	227	9	→	→	X
ejde-397	227	10	p	p	X
ejde-397	227	11	(	(	PUNCT
ejde-397	227	12	y	y	PROPN
ejde-397	227	13	)	)	PUNCT
ejde-397	227	14	is	be	AUX
ejde-397	227	15	relatively	relatively	ADV
ejde-397	227	16	closed	closed	ADJ
ejde-397	227	17	if	if	SCONJ
ejde-397	227	18	and	and	CCONJ
ejde-397	227	19	only	only	ADV
ejde-397	227	20	if	if	SCONJ
ejde-397	227	21	there	there	PRON
ejde-397	227	22	exist	exist	VERB
ejde-397	227	23	auxiliary	auxiliary	ADJ
ejde-397	227	24	sclcss	sclcss	PROPN
ejde-397	227	25	xa	xa	PROPN
ejde-397	227	26	and	and	CCONJ
ejde-397	227	27	ya	ya	PRON
ejde-397	227	28	such	such	ADJ
ejde-397	227	29	that	that	SCONJ
ejde-397	227	30	d(a	d(a	PROPN
ejde-397	227	31	)	)	PUNCT
ejde-397	227	32	⊆	⊆	NUM
ejde-397	227	33	xa	xa	X
ejde-397	227	34	↪	↪	PROPN
ejde-397	227	35	→	→	SYM
ejde-397	227	36	x	x	PROPN
ejde-397	227	37	,	,	PUNCT
ejde-397	227	38	r(a	r(a	NUM
ejde-397	227	39	)	)	PUNCT
ejde-397	227	40	⊆	⊆	NUM
ejde-397	227	41	ya	ya	PROPN
ejde-397	227	42	↪	↪	PROPN
ejde-397	227	43	→	→	SYM
ejde-397	227	44	y	y	PROPN
ejde-397	227	45	and	and	CCONJ
ejde-397	227	46	a	a	PRON
ejde-397	227	47	is	be	AUX
ejde-397	227	48	closed	close	VERB
ejde-397	227	49	in	in	ADP
ejde-397	227	50	xa	xa	PROPN
ejde-397	227	51	×	×	PROPN
ejde-397	227	52	ya	ya	PROPN
ejde-397	227	53	;	;	PUNCT
ejde-397	227	54	i.e.	i.e.	X
ejde-397	227	55	,	,	PUNCT
ejde-397	227	56	the	the	DET
ejde-397	227	57	assumptions	assumption	NOUN
ejde-397	227	58	d(a	d(a	PROPN
ejde-397	227	59	)	)	PUNCT
ejde-397	227	60	3	3	NUM
ejde-397	227	61	xτ	xτ	NOUN
ejde-397	227	62	→	→	SYM
ejde-397	227	63	x	x	PROPN
ejde-397	227	64	as	as	ADP
ejde-397	227	65	τ	τ	PROPN
ejde-397	227	66	→	→	SYM
ejde-397	227	67	∞	∞	PROPN
ejde-397	227	68	in	in	ADP
ejde-397	227	69	xa	xa	PROPN
ejde-397	227	70	and	and	CCONJ
ejde-397	227	71	axτ	axτ	NOUN
ejde-397	227	72	3	3	NUM
ejde-397	227	73	yτ	yτ	PROPN
ejde-397	227	74	→	→	SYM
ejde-397	227	75	y	y	PROPN
ejde-397	227	76	as	as	ADP
ejde-397	227	77	τ	τ	PROPN
ejde-397	227	78	→	→	SYM
ejde-397	227	79	∞	∞	PROPN
ejde-397	227	80	in	in	ADP
ejde-397	227	81	ya	ya	PRON
ejde-397	227	82	implies	imply	VERB
ejde-397	227	83	that	that	SCONJ
ejde-397	227	84	x	x	SYM
ejde-397	227	85	∈	∈	PROPN
ejde-397	227	86	d(a	d(a	PROPN
ejde-397	227	87	)	)	PUNCT
ejde-397	227	88	and	and	CCONJ
ejde-397	227	89	y	y	PROPN
ejde-397	227	90	∈	∈	PROPN
ejde-397	227	91	ax	ax	NOUN
ejde-397	227	92	.	.	PUNCT
ejde-397	228	1	a	a	DET
ejde-397	228	2	relatively	relatively	ADV
ejde-397	228	3	closed	closed	ADJ
ejde-397	228	4	operator	operator	NOUN
ejde-397	228	5	will	will	AUX
ejde-397	228	6	also	also	ADV
ejde-397	228	7	be	be	AUX
ejde-397	228	8	called	call	VERB
ejde-397	228	9	xa	xa	PROPN
ejde-397	228	10	×	×	PROPN
ejde-397	228	11	ya	ya	PROPN
ejde-397	228	12	-	-	PUNCT
ejde-397	228	13	closed	closed	ADJ
ejde-397	228	14	.	.	PUNCT
ejde-397	229	1	for	for	ADP
ejde-397	229	2	example	example	NOUN
ejde-397	229	3	,	,	PUNCT
ejde-397	229	4	let	let	VERB
ejde-397	229	5	a	a	DET
ejde-397	229	6	,	,	PUNCT
ejde-397	229	7	b	b	NOUN
ejde-397	229	8	:	:	PUNCT
ejde-397	229	9	d	d	NOUN
ejde-397	229	10	⊆	⊆	NUM
ejde-397	229	11	x	x	SYM
ejde-397	229	12	→	→	SYM
ejde-397	229	13	y	y	PROPN
ejde-397	229	14	be	be	AUX
ejde-397	229	15	closed	close	VERB
ejde-397	229	16	linear	linear	ADJ
ejde-397	229	17	operators	operator	NOUN
ejde-397	229	18	with	with	ADP
ejde-397	229	19	the	the	DET
ejde-397	229	20	same	same	ADJ
ejde-397	229	21	domain	domain	NOUN
ejde-397	229	22	d.	d.	NOUN
ejde-397	229	23	then	then	ADV
ejde-397	229	24	the	the	DET
ejde-397	229	25	operator	operator	NOUN
ejde-397	229	26	a+b	a+b	VERB
ejde-397	229	27	is	be	AUX
ejde-397	229	28	not	not	PART
ejde-397	229	29	necessarily	necessarily	ADV
ejde-397	229	30	closed	close	VERB
ejde-397	229	31	but	but	CCONJ
ejde-397	229	32	it	it	PRON
ejde-397	229	33	is	be	AUX
ejde-397	229	34	always	always	ADV
ejde-397	229	35	[	[	X
ejde-397	229	36	d(a)]×	d(a)]×	X
ejde-397	229	37	y	y	PROPN
ejde-397	229	38	-closed	-closed	PROPN
ejde-397	229	39	(	(	PUNCT
ejde-397	229	40	cf	cf	NOUN
ejde-397	229	41	.	.	PUNCT
ejde-397	230	1	[	[	X
ejde-397	230	2	31	31	NUM
ejde-397	230	3	,	,	PUNCT
ejde-397	230	4	p.	p.	NOUN
ejde-397	230	5	170	170	NUM
ejde-397	230	6	]	]	PUNCT
ejde-397	230	7	)	)	PUNCT
ejde-397	230	8	.	.	PUNCT
ejde-397	231	1	examples	example	NOUN
ejde-397	231	2	presented	present	VERB
ejde-397	231	3	in	in	ADP
ejde-397	231	4	[	[	X
ejde-397	231	5	32	32	NUM
ejde-397	231	6	]	]	PUNCT
ejde-397	231	7	can	can	AUX
ejde-397	231	8	be	be	AUX
ejde-397	231	9	simply	simply	ADV
ejde-397	231	10	reformulated	reformulate	VERB
ejde-397	231	11	for	for	ADP
ejde-397	231	12	operators	operator	NOUN
ejde-397	231	13	acting	act	VERB
ejde-397	231	14	on	on	ADP
ejde-397	231	15	locally	locally	ADV
ejde-397	231	16	convex	convex	ADJ
ejde-397	231	17	spaces	space	NOUN
ejde-397	231	18	,	,	PUNCT
ejde-397	231	19	as	as	ADV
ejde-397	231	20	well	well	ADV
ejde-397	231	21	:	:	PUNCT
ejde-397	231	22	example	example	NOUN
ejde-397	231	23	2.1	2.1	NUM
ejde-397	231	24	.	.	PUNCT
ejde-397	232	1	(	(	PUNCT
ejde-397	232	2	i	i	NOUN
ejde-397	232	3	)	)	PUNCT
ejde-397	232	4	if	if	SCONJ
ejde-397	232	5	a	a	PRON
ejde-397	232	6	:	:	PUNCT
ejde-397	232	7	x	x	X
ejde-397	232	8	→	→	X
ejde-397	232	9	p	p	X
ejde-397	232	10	(	(	PUNCT
ejde-397	232	11	y	y	PROPN
ejde-397	232	12	)	)	PUNCT
ejde-397	232	13	is	be	AUX
ejde-397	232	14	an	an	DET
ejde-397	232	15	mlo	mlo	NOUN
ejde-397	232	16	,	,	PUNCT
ejde-397	232	17	then	then	ADV
ejde-397	232	18	a	a	PRON
ejde-397	232	19	:	:	PUNCT
ejde-397	232	20	x	x	X
ejde-397	232	21	→	→	X
ejde-397	232	22	p	p	X
ejde-397	232	23	(	(	PUNCT
ejde-397	232	24	y	y	PROPN
ejde-397	232	25	)	)	PUNCT
ejde-397	232	26	is	be	AUX
ejde-397	232	27	likewise	likewise	ADV
ejde-397	232	28	an	an	DET
ejde-397	232	29	mlo	mlo	NOUN
ejde-397	232	30	.	.	PUNCT
ejde-397	233	1	this	this	PRON
ejde-397	233	2	shows	show	VERB
ejde-397	233	3	that	that	SCONJ
ejde-397	233	4	any	any	DET
ejde-397	233	5	mlo	mlo	NOUN
ejde-397	233	6	has	have	VERB
ejde-397	233	7	a	a	DET
ejde-397	233	8	closed	closed	ADJ
ejde-397	233	9	linear	linear	NOUN
ejde-397	233	10	extension	extension	NOUN
ejde-397	233	11	,	,	PUNCT
ejde-397	233	12	in	in	ADP
ejde-397	233	13	contrast	contrast	NOUN
ejde-397	233	14	to	to	ADP
ejde-397	233	15	the	the	DET
ejde-397	233	16	usually	usually	ADV
ejde-397	233	17	considered	consider	VERB
ejde-397	233	18	single	single	ADJ
ejde-397	233	19	-	-	PUNCT
ejde-397	233	20	valued	value	VERB
ejde-397	233	21	linear	linear	PROPN
ejde-397	233	22	operators	operator	NOUN
ejde-397	233	23	.	.	PUNCT
ejde-397	234	1	(	(	PUNCT
ejde-397	234	2	ii	ii	NOUN
ejde-397	234	3	)	)	PUNCT
ejde-397	234	4	let	let	VERB
ejde-397	234	5	a	a	DET
ejde-397	234	6	:	:	PUNCT
ejde-397	234	7	d(a	d(a	PROPN
ejde-397	234	8	)	)	PUNCT
ejde-397	234	9	⊆	⊆	NUM
ejde-397	234	10	x	x	SYM
ejde-397	234	11	→	→	SYM
ejde-397	234	12	y	y	X
ejde-397	234	13	be	be	AUX
ejde-397	234	14	a	a	DET
ejde-397	234	15	single	single	ADV
ejde-397	234	16	-	-	PUNCT
ejde-397	234	17	valued	value	VERB
ejde-397	234	18	linear	linear	NOUN
ejde-397	234	19	operator	operator	NOUN
ejde-397	234	20	that	that	PRON
ejde-397	234	21	is	be	AUX
ejde-397	234	22	xa	xa	PROPN
ejde-397	234	23	×	×	PROPN
ejde-397	234	24	yaclosed	yaclose	VERB
ejde-397	234	25	,	,	PUNCT
ejde-397	234	26	let	let	VERB
ejde-397	234	27	b	b	NOUN
ejde-397	234	28	:	:	PUNCT
ejde-397	234	29	x	x	X
ejde-397	234	30	→	→	X
ejde-397	234	31	p	p	X
ejde-397	234	32	(	(	PUNCT
ejde-397	234	33	y	y	PROPN
ejde-397	234	34	)	)	PUNCT
ejde-397	234	35	be	be	AUX
ejde-397	234	36	an	an	DET
ejde-397	234	37	mlo	mlo	NOUN
ejde-397	234	38	that	that	PRON
ejde-397	234	39	is	be	AUX
ejde-397	234	40	xb	xb	PROPN
ejde-397	234	41	×	×	PROPN
ejde-397	234	42	yb	yb	PROPN
ejde-397	234	43	-	-	PUNCT
ejde-397	234	44	closed	closed	ADJ
ejde-397	234	45	,	,	PUNCT
ejde-397	234	46	and	and	CCONJ
ejde-397	234	47	let	let	VERB
ejde-397	234	48	ya	ya	PRON
ejde-397	234	49	↪	↪	PROPN
ejde-397	234	50	→	→	SYM
ejde-397	234	51	yb	yb	PROPN
ejde-397	234	52	.	.	PUNCT
ejde-397	235	1	then	then	ADV
ejde-397	235	2	the	the	DET
ejde-397	235	3	mlo	mlo	PROPN
ejde-397	235	4	s	s	PART
ejde-397	235	5	=	=	PUNCT
ejde-397	235	6	a	a	PRON
ejde-397	235	7	+	+	NUM
ejde-397	235	8	b	b	NOUN
ejde-397	235	9	is	be	AUX
ejde-397	235	10	xs	xs	PROPN
ejde-397	235	11	×	×	PROPN
ejde-397	235	12	yb	yb	PROPN
ejde-397	235	13	-	-	PUNCT
ejde-397	235	14	closed	closed	ADJ
ejde-397	235	15	,	,	PUNCT
ejde-397	235	16	where	where	SCONJ
ejde-397	235	17	xs	xs	PROPN
ejde-397	235	18	:	:	PUNCT
ejde-397	235	19	=	=	SYM
ejde-397	235	20	d(a	d(a	ADJ
ejde-397	235	21	)	)	PUNCT
ejde-397	235	22	∩	∩	X
ejde-397	235	23	xb	xb	PROPN
ejde-397	235	24	and	and	CCONJ
ejde-397	235	25	the	the	DET
ejde-397	235	26	topology	topology	NOUN
ejde-397	235	27	on	on	ADP
ejde-397	235	28	xs	xs	PROPN
ejde-397	235	29	is	be	AUX
ejde-397	235	30	induced	induce	VERB
ejde-397	235	31	by	by	ADP
ejde-397	235	32	the	the	DET
ejde-397	235	33	system	system	NOUN
ejde-397	235	34	(	(	PUNCT
ejde-397	235	35	sp	sp	NOUN
ejde-397	235	36	,	,	PUNCT
ejde-397	235	37	q	q	NOUN
ejde-397	235	38	,	,	PUNCT
ejde-397	235	39	r	r	NOUN
ejde-397	235	40	)	)	PUNCT
ejde-397	235	41	of	of	ADP
ejde-397	235	42	fundamental	fundamental	ADJ
ejde-397	235	43	seminorms	seminorm	NOUN
ejde-397	235	44	,	,	PUNCT
ejde-397	235	45	defined	define	VERB
ejde-397	235	46	as	as	SCONJ
ejde-397	235	47	follows	follow	VERB
ejde-397	235	48	:	:	PUNCT
ejde-397	235	49	sp	sp	NOUN
ejde-397	235	50	,	,	PUNCT
ejde-397	235	51	q	q	NOUN
ejde-397	235	52	,	,	PUNCT
ejde-397	235	53	r(x	r(x	NOUN
ejde-397	235	54	)	)	PUNCT
ejde-397	236	1	=	=	NOUN
ejde-397	236	2	:	:	PUNCT
ejde-397	236	3	p(x)+p(ax)+q(x)+r(ax	p(x)+p(ax)+q(x)+r(ax	NOUN
ejde-397	236	4	)	)	PUNCT
ejde-397	236	5	,	,	PUNCT
ejde-397	236	6	x	x	PUNCT
ejde-397	236	7	∈	∈	PROPN
ejde-397	236	8	xs	xs	PROPN
ejde-397	236	9	(	(	PUNCT
ejde-397	236	10	p	p	NOUN
ejde-397	236	11	∈	∈	PROPN
ejde-397	236	12	~x	~x	PUNCT
ejde-397	236	13	,	,	PUNCT
ejde-397	236	14	q	q	PROPN
ejde-397	236	15	∈	∈	PROPN
ejde-397	236	16	~xb	~xb	PROPN
ejde-397	236	17	,	,	PUNCT
ejde-397	236	18	r	r	NOUN
ejde-397	236	19	∈	∈	PROPN
ejde-397	236	20	~ya	~ya	PROPN
ejde-397	236	21	)	)	PUNCT
ejde-397	236	22	.	.	PUNCT
ejde-397	237	1	(	(	PUNCT
ejde-397	237	2	iii	iii	X
ejde-397	237	3	)	)	PUNCT
ejde-397	237	4	let	let	VERB
ejde-397	237	5	a	a	DET
ejde-397	237	6	:	:	PUNCT
ejde-397	237	7	d(a	d(a	PROPN
ejde-397	237	8	)	)	PUNCT
ejde-397	237	9	⊆	⊆	NUM
ejde-397	237	10	x	x	SYM
ejde-397	237	11	→	→	SYM
ejde-397	237	12	y	y	X
ejde-397	237	13	be	be	AUX
ejde-397	237	14	a	a	DET
ejde-397	237	15	single	single	ADV
ejde-397	237	16	-	-	PUNCT
ejde-397	237	17	valued	value	VERB
ejde-397	237	18	linear	linear	NOUN
ejde-397	237	19	operator	operator	NOUN
ejde-397	237	20	that	that	PRON
ejde-397	237	21	is	be	AUX
ejde-397	237	22	xa	xa	PROPN
ejde-397	237	23	×	×	PROPN
ejde-397	237	24	yaclosed	yaclose	VERB
ejde-397	237	25	,	,	PUNCT
ejde-397	237	26	let	let	VERB
ejde-397	237	27	b	b	X
ejde-397	237	28	:	:	PUNCT
ejde-397	237	29	y	y	PROPN
ejde-397	237	30	→	→	SYM
ejde-397	237	31	p	p	X
ejde-397	237	32	(	(	PUNCT
ejde-397	237	33	z	z	NOUN
ejde-397	237	34	)	)	PUNCT
ejde-397	237	35	be	be	AUX
ejde-397	237	36	an	an	DET
ejde-397	237	37	mlo	mlo	NOUN
ejde-397	237	38	that	that	PRON
ejde-397	237	39	is	be	AUX
ejde-397	237	40	yb	yb	PROPN
ejde-397	237	41	×	×	PROPN
ejde-397	237	42	zb	zb	NOUN
ejde-397	237	43	-	-	PUNCT
ejde-397	237	44	closed	closed	ADJ
ejde-397	237	45	,	,	PUNCT
ejde-397	237	46	and	and	CCONJ
ejde-397	237	47	let	let	VERB
ejde-397	237	48	yb	yb	PROPN
ejde-397	237	49	↪	↪	PROPN
ejde-397	237	50	→	→	SYM
ejde-397	237	51	ya	ya	PROPN
ejde-397	237	52	.	.	PUNCT
ejde-397	238	1	then	then	ADV
ejde-397	238	2	the	the	DET
ejde-397	238	3	mlo	mlo	PROPN
ejde-397	238	4	c	c	PROPN
ejde-397	238	5	=	=	SYM
ejde-397	238	6	ba	ba	PROPN
ejde-397	238	7	:	:	PUNCT
ejde-397	238	8	x	x	X
ejde-397	238	9	→	→	X
ejde-397	238	10	p	p	X
ejde-397	238	11	(	(	PUNCT
ejde-397	238	12	z	z	NOUN
ejde-397	238	13	)	)	PUNCT
ejde-397	238	14	is	be	AUX
ejde-397	238	15	xc	xc	PROPN
ejde-397	238	16	×	×	PROPN
ejde-397	238	17	zb	zb	PROPN
ejde-397	238	18	-	-	PUNCT
ejde-397	238	19	closed	closed	ADJ
ejde-397	238	20	,	,	PUNCT
ejde-397	238	21	where	where	SCONJ
ejde-397	238	22	xc	xc	PROPN
ejde-397	238	23	:	:	PUNCT
ejde-397	238	24	=	=	SYM
ejde-397	238	25	{	{	PUNCT
ejde-397	238	26	x	x	PROPN
ejde-397	238	27	∈	∈	PROPN
ejde-397	238	28	d(a	d(a	PROPN
ejde-397	238	29	)	)	PUNCT
ejde-397	238	30	:	:	PUNCT
ejde-397	238	31	ax	ax	NOUN
ejde-397	238	32	∈	∈	PROPN
ejde-397	238	33	yb	yb	PROPN
ejde-397	238	34	}	}	PUNCT
ejde-397	238	35	and	and	CCONJ
ejde-397	238	36	the	the	DET
ejde-397	238	37	topology	topology	NOUN
ejde-397	238	38	on	on	ADP
ejde-397	238	39	xc	xc	PROPN
ejde-397	238	40	is	be	AUX
ejde-397	238	41	induced	induce	VERB
ejde-397	238	42	by	by	ADP
ejde-397	238	43	the	the	DET
ejde-397	238	44	system	system	NOUN
ejde-397	238	45	(	(	PUNCT
ejde-397	238	46	sp	sp	NOUN
ejde-397	238	47	,	,	PUNCT
ejde-397	238	48	q	q	NOUN
ejde-397	238	49	)	)	PUNCT
ejde-397	238	50	of	of	ADP
ejde-397	238	51	fundamental	fundamental	ADJ
ejde-397	238	52	seminorms	seminorm	NOUN
ejde-397	238	53	,	,	PUNCT
ejde-397	238	54	defined	define	VERB
ejde-397	238	55	as	as	SCONJ
ejde-397	238	56	follows	follow	VERB
ejde-397	238	57	:	:	PUNCT
ejde-397	238	58	sp	sp	NOUN
ejde-397	238	59	,	,	PUNCT
ejde-397	238	60	q(x	q(x	PROPN
ejde-397	238	61	)	)	PUNCT
ejde-397	239	1	=	=	NOUN
ejde-397	239	2	:	:	PUNCT
ejde-397	239	3	p(x)+p(ax)+q(ax	p(x)+p(ax)+q(ax	NOUN
ejde-397	239	4	)	)	PUNCT
ejde-397	239	5	,	,	PUNCT
ejde-397	239	6	x	x	PUNCT
ejde-397	239	7	∈	∈	PROPN
ejde-397	239	8	xc	xc	X
ejde-397	239	9	(	(	PUNCT
ejde-397	239	10	p	p	X
ejde-397	239	11	∈	∈	PROPN
ejde-397	239	12	~x	~x	PUNCT
ejde-397	239	13	,	,	PUNCT
ejde-397	239	14	q	q	PROPN
ejde-397	239	15	∈	∈	PROPN
ejde-397	239	16	~yb	~yb	NOUN
ejde-397	239	17	)	)	PUNCT
ejde-397	239	18	.	.	PUNCT
ejde-397	240	1	(	(	PUNCT
ejde-397	240	2	iv	iv	X
ejde-397	240	3	)	)	PUNCT
ejde-397	240	4	let	let	VERB
ejde-397	240	5	a	a	DET
ejde-397	240	6	:	:	PUNCT
ejde-397	240	7	d(a	d(a	PROPN
ejde-397	240	8	)	)	PUNCT
ejde-397	240	9	⊆	⊆	NUM
ejde-397	240	10	x	x	SYM
ejde-397	240	11	→	→	SYM
ejde-397	240	12	y	y	PROPN
ejde-397	240	13	and	and	CCONJ
ejde-397	240	14	b	b	NOUN
ejde-397	240	15	:	:	PUNCT
ejde-397	240	16	d(b	d(b	X
ejde-397	240	17	)	)	PUNCT
ejde-397	241	1	⊆	⊆	NUM
ejde-397	241	2	x	x	SYM
ejde-397	241	3	→	→	SYM
ejde-397	241	4	y	y	PROPN
ejde-397	241	5	be	be	AUX
ejde-397	241	6	two	two	NUM
ejde-397	241	7	single	single	ADV
ejde-397	241	8	-	-	PUNCT
ejde-397	241	9	valued	value	VERB
ejde-397	241	10	linear	linear	PROPN
ejde-397	241	11	operators	operator	NOUN
ejde-397	241	12	.	.	PUNCT
ejde-397	242	1	set	set	VERB
ejde-397	242	2	a	a	PRON
ejde-397	242	3	:	:	PUNCT
ejde-397	242	4	=	=	SYM
ejde-397	242	5	b−1a	b−1a	X
ejde-397	242	6	=	=	SYM
ejde-397	242	7	{	{	PUNCT
ejde-397	242	8	(	(	PUNCT
ejde-397	242	9	x	x	NOUN
ejde-397	242	10	,	,	PUNCT
ejde-397	242	11	y	y	PROPN
ejde-397	242	12	)	)	PUNCT
ejde-397	242	13	:	:	PUNCT
ejde-397	243	1	x	x	X
ejde-397	243	2	∈	∈	PROPN
ejde-397	243	3	d(a	d(a	PROPN
ejde-397	243	4	)	)	PUNCT
ejde-397	243	5	,	,	PUNCT
ejde-397	243	6	y	y	PROPN
ejde-397	243	7	∈	∈	PROPN
ejde-397	243	8	d(b	d(b	PROPN
ejde-397	243	9	)	)	PUNCT
ejde-397	243	10	and	and	CCONJ
ejde-397	243	11	ax	ax	NOUN
ejde-397	243	12	=	=	PUNCT
ejde-397	243	13	by	by	ADP
ejde-397	243	14	}	}	PUNCT
ejde-397	243	15	.	.	PUNCT
ejde-397	244	1	then	then	ADV
ejde-397	244	2	a	a	PRON
ejde-397	244	3	is	be	AUX
ejde-397	244	4	an	an	DET
ejde-397	244	5	mlo	mlo	NOUN
ejde-397	244	6	in	in	ADP
ejde-397	244	7	x	x	NOUN
ejde-397	244	8	,	,	PUNCT
ejde-397	244	9	and	and	CCONJ
ejde-397	244	10	the	the	DET
ejde-397	244	11	following	follow	VERB
ejde-397	244	12	holds	hold	VERB
ejde-397	244	13	:	:	PUNCT
ejde-397	244	14	(	(	PUNCT
ejde-397	244	15	a	a	X
ejde-397	244	16	)	)	PUNCT
ejde-397	244	17	if	if	SCONJ
ejde-397	244	18	one	one	NUM
ejde-397	244	19	of	of	ADP
ejde-397	244	20	the	the	DET
ejde-397	244	21	operators	operator	NOUN
ejde-397	244	22	a	a	PRON
ejde-397	244	23	,	,	PUNCT
ejde-397	244	24	b	b	PROPN
ejde-397	244	25	is	be	AUX
ejde-397	244	26	bounded	bound	VERB
ejde-397	244	27	and	and	CCONJ
ejde-397	244	28	the	the	DET
ejde-397	244	29	other	other	ADJ
ejde-397	244	30	closed	close	VERB
ejde-397	244	31	,	,	PUNCT
ejde-397	244	32	then	then	ADV
ejde-397	244	33	a	a	PRON
ejde-397	244	34	is	be	AUX
ejde-397	244	35	closed	closed	ADJ
ejde-397	244	36	.	.	PUNCT
ejde-397	245	1	(	(	PUNCT
ejde-397	245	2	b	b	X
ejde-397	245	3	)	)	PUNCT
ejde-397	245	4	if	if	SCONJ
ejde-397	245	5	a	a	PRON
ejde-397	245	6	is	be	AUX
ejde-397	245	7	closed	closed	ADJ
ejde-397	245	8	and	and	CCONJ
ejde-397	245	9	b	b	NOUN
ejde-397	245	10	is	be	AUX
ejde-397	245	11	xb	xb	PROPN
ejde-397	245	12	×	×	PROPN
ejde-397	245	13	y	y	PROPN
ejde-397	245	14	-closed	-closed	PROPN
ejde-397	245	15	,	,	PUNCT
ejde-397	245	16	then	then	ADV
ejde-397	245	17	a	a	PRON
ejde-397	245	18	is	be	AUX
ejde-397	245	19	[	[	X
ejde-397	245	20	d(a)]×xb	d(a)]×xb	NOUN
ejde-397	245	21	-	-	PUNCT
ejde-397	245	22	closed	closed	ADJ
ejde-397	245	23	.	.	PUNCT
ejde-397	246	1	(	(	PUNCT
ejde-397	246	2	c	c	X
ejde-397	246	3	)	)	PUNCT
ejde-397	246	4	if	if	SCONJ
ejde-397	246	5	b	b	NOUN
ejde-397	246	6	is	be	AUX
ejde-397	246	7	closed	close	VERB
ejde-397	246	8	and	and	CCONJ
ejde-397	246	9	a	a	PRON
ejde-397	246	10	is	be	AUX
ejde-397	246	11	xa	xa	PROPN
ejde-397	246	12	×	×	PROPN
ejde-397	246	13	y	y	PROPN
ejde-397	246	14	-closed	-closed	PROPN
ejde-397	246	15	,	,	PUNCT
ejde-397	246	16	then	then	ADV
ejde-397	246	17	a	a	PRON
ejde-397	246	18	is	be	AUX
ejde-397	246	19	xa	xa	PROPN
ejde-397	246	20	×	×	PROPN
ejde-397	247	1	[	[	X
ejde-397	247	2	d(b)]-closed	d(b)]-close	VERB
ejde-397	247	3	.	.	PUNCT
ejde-397	248	1	(	(	PUNCT
ejde-397	248	2	d	d	X
ejde-397	248	3	)	)	PUNCT
ejde-397	248	4	if	if	SCONJ
ejde-397	248	5	a	a	PRON
ejde-397	248	6	is	be	AUX
ejde-397	248	7	xa	xa	PROPN
ejde-397	248	8	×	×	PROPN
ejde-397	248	9	ya	ya	PROPN
ejde-397	248	10	-	-	PUNCT
ejde-397	248	11	closed	close	VERB
ejde-397	248	12	and	and	CCONJ
ejde-397	248	13	b	b	NOUN
ejde-397	248	14	is	be	AUX
ejde-397	248	15	xb	xb	PROPN
ejde-397	248	16	×	×	PROPN
ejde-397	248	17	yb	yb	PROPN
ejde-397	248	18	-	-	PUNCT
ejde-397	248	19	closed	closed	ADJ
ejde-397	248	20	,	,	PUNCT
ejde-397	248	21	where	where	SCONJ
ejde-397	248	22	yb	yb	PROPN
ejde-397	248	23	↪	↪	PROPN
ejde-397	248	24	→	→	SYM
ejde-397	248	25	ya	ya	PROPN
ejde-397	248	26	,	,	PUNCT
ejde-397	248	27	then	then	ADV
ejde-397	248	28	a	a	PRON
ejde-397	248	29	is	be	AUX
ejde-397	248	30	xc	xc	PROPN
ejde-397	248	31	×xb	×xb	PROPN
ejde-397	248	32	-	-	PUNCT
ejde-397	248	33	closed	closed	ADJ
ejde-397	248	34	,	,	PUNCT
ejde-397	248	35	where	where	SCONJ
ejde-397	248	36	xc	xc	PROPN
ejde-397	248	37	is	be	AUX
ejde-397	248	38	defined	define	VERB
ejde-397	248	39	as	as	ADP
ejde-397	248	40	in	in	ADP
ejde-397	248	41	(	(	PUNCT
ejde-397	248	42	iii	iii	NOUN
ejde-397	248	43	)	)	PUNCT
ejde-397	248	44	.	.	PUNCT
ejde-397	249	1	if	if	SCONJ
ejde-397	249	2	a	a	PRON
ejde-397	249	3	:	:	PUNCT
ejde-397	249	4	x	x	X
ejde-397	249	5	→	→	X
ejde-397	249	6	p	p	X
ejde-397	249	7	(	(	PUNCT
ejde-397	249	8	y	y	PROPN
ejde-397	249	9	)	)	PUNCT
ejde-397	249	10	is	be	AUX
ejde-397	249	11	an	an	DET
ejde-397	249	12	mlo	mlo	NOUN
ejde-397	249	13	,	,	PUNCT
ejde-397	249	14	then	then	ADV
ejde-397	249	15	we	we	PRON
ejde-397	249	16	define	define	VERB
ejde-397	249	17	the	the	DET
ejde-397	249	18	adjoint	adjoint	NOUN
ejde-397	249	19	a∗	a∗	NOUN
ejde-397	249	20	:	:	PUNCT
ejde-397	249	21	y	y	PROPN
ejde-397	249	22	∗	∗	NOUN
ejde-397	249	23	→	→	SYM
ejde-397	249	24	p	p	X
ejde-397	249	25	(	(	PUNCT
ejde-397	249	26	x∗	x∗	PROPN
ejde-397	249	27	)	)	PUNCT
ejde-397	249	28	of	of	ADP
ejde-397	249	29	a	a	PRON
ejde-397	249	30	by	by	ADP
ejde-397	249	31	its	its	PRON
ejde-397	249	32	graph	graph	NOUN
ejde-397	249	33	a∗	a∗	NOUN
ejde-397	249	34	:	:	PUNCT
ejde-397	249	35	=	=	SYM
ejde-397	249	36	{	{	PUNCT
ejde-397	249	37	(	(	PUNCT
ejde-397	249	38	y∗	y∗	PROPN
ejde-397	249	39	,	,	PUNCT
ejde-397	249	40	x∗	x∗	PROPN
ejde-397	249	41	)	)	PUNCT
ejde-397	250	1	∈	∈	PROPN
ejde-397	250	2	y	y	PROPN
ejde-397	250	3	∗	∗	NOUN
ejde-397	250	4	×x∗	×x∗	NOUN
ejde-397	250	5	:	:	PUNCT
ejde-397	250	6	〈	〈	PROPN
ejde-397	250	7	y∗	y∗	PROPN
ejde-397	250	8	,	,	PUNCT
ejde-397	250	9	y	y	PROPN
ejde-397	250	10	〉	〉	NOUN
ejde-397	250	11	=	=	SYM
ejde-397	250	12	〈	〈	PROPN
ejde-397	250	13	x∗	x∗	NOUN
ejde-397	250	14	,	,	PUNCT
ejde-397	250	15	x	x	SYM
ejde-397	250	16	〉	〉	NOUN
ejde-397	250	17	for	for	ADP
ejde-397	250	18	all	all	DET
ejde-397	250	19	pairs	pair	NOUN
ejde-397	250	20	(	(	PUNCT
ejde-397	250	21	x	x	NOUN
ejde-397	250	22	,	,	PUNCT
ejde-397	250	23	y	y	PROPN
ejde-397	250	24	)	)	PUNCT
ejde-397	250	25	∈	∈	PROPN
ejde-397	250	26	a	a	PRON
ejde-397	250	27	}	}	PUNCT
ejde-397	250	28	.	.	PUNCT
ejde-397	251	1	it	it	PRON
ejde-397	251	2	is	be	AUX
ejde-397	251	3	simply	simply	ADV
ejde-397	251	4	verified	verify	VERB
ejde-397	251	5	that	that	SCONJ
ejde-397	251	6	a∗	a∗	PROPN
ejde-397	251	7	is	be	AUX
ejde-397	251	8	a	a	DET
ejde-397	251	9	closed	closed	ADJ
ejde-397	251	10	mlo	mlo	NOUN
ejde-397	251	11	,	,	PUNCT
ejde-397	251	12	and	and	CCONJ
ejde-397	251	13	that	that	SCONJ
ejde-397	251	14	〈	〈	PROPN
ejde-397	251	15	y∗	y∗	PROPN
ejde-397	251	16	,	,	PUNCT
ejde-397	251	17	y	y	PROPN
ejde-397	251	18	〉	〉	NUM
ejde-397	251	19	=	=	SYM
ejde-397	251	20	0	0	PUNCT
ejde-397	251	21	whenever	whenever	SCONJ
ejde-397	251	22	y∗	y∗	PROPN
ejde-397	251	23	∈	∈	PROPN
ejde-397	251	24	d(a∗	d(a∗	X
ejde-397	251	25	)	)	PUNCT
ejde-397	251	26	and	and	CCONJ
ejde-397	251	27	y	y	PROPN
ejde-397	251	28	∈	∈	PROPN
ejde-397	251	29	a0	a0	PROPN
ejde-397	251	30	.	.	PUNCT
ejde-397	252	1	furthermore	furthermore	ADV
ejde-397	252	2	,	,	PUNCT
ejde-397	252	3	a∗	a∗	PROPN
ejde-397	252	4	is	be	AUX
ejde-397	252	5	single	single	ADV
ejde-397	252	6	-	-	PUNCT
ejde-397	252	7	valued	value	VERB
ejde-397	252	8	provided	provide	VERB
ejde-397	252	9	that	that	SCONJ
ejde-397	252	10	a	a	PRON
ejde-397	252	11	is	be	AUX
ejde-397	252	12	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	252	13	abstract	abstract	ADJ
ejde-397	252	14	degenerate	degenerate	ADJ
ejde-397	252	15	volterra	volterra	NOUN
ejde-397	252	16	inclusions	inclusion	NOUN
ejde-397	252	17	9	9	NUM
ejde-397	252	18	densely	densely	ADV
ejde-397	252	19	defined	define	VERB
ejde-397	252	20	,	,	PUNCT
ejde-397	252	21	a∗	a∗	NOUN
ejde-397	252	22	=	=	SYM
ejde-397	252	23	a∗	a∗	NOUN
ejde-397	252	24	and	and	CCONJ
ejde-397	252	25	the	the	DET
ejde-397	252	26	equations	equation	NOUN
ejde-397	253	1	[	[	X
ejde-397	253	2	17	17	NUM
ejde-397	253	3	,	,	PUNCT
ejde-397	253	4	(	(	PUNCT
ejde-397	253	5	1.2)-(1.6	1.2)-(1.6	NUM
ejde-397	253	6	)	)	PUNCT
ejde-397	253	7	]	]	PUNCT
ejde-397	253	8	continue	continue	VERB
ejde-397	253	9	to	to	PART
ejde-397	253	10	hold	hold	VERB
ejde-397	253	11	for	for	ADP
ejde-397	253	12	adjoints	adjoint	NOUN
ejde-397	253	13	of	of	ADP
ejde-397	253	14	mlos	mlo	NOUN
ejde-397	253	15	acting	act	VERB
ejde-397	253	16	on	on	ADP
ejde-397	253	17	locally	locally	ADV
ejde-397	253	18	convex	convex	ADJ
ejde-397	253	19	spaces	space	NOUN
ejde-397	253	20	.	.	PUNCT
ejde-397	254	1	the	the	DET
ejde-397	254	2	following	follow	VERB
ejde-397	254	3	important	important	ADJ
ejde-397	254	4	lemma	lemma	PROPN
ejde-397	254	5	can	can	AUX
ejde-397	254	6	be	be	AUX
ejde-397	254	7	proved	prove	VERB
ejde-397	254	8	by	by	ADP
ejde-397	254	9	using	use	VERB
ejde-397	254	10	the	the	DET
ejde-397	254	11	hahn	hahn	NOUN
ejde-397	254	12	-	-	PUNCT
ejde-397	254	13	banach	banach	NOUN
ejde-397	254	14	theorem	theorem	NOUN
ejde-397	254	15	and	and	CCONJ
ejde-397	254	16	the	the	DET
ejde-397	254	17	argumentation	argumentation	NOUN
ejde-397	254	18	from	from	ADP
ejde-397	254	19	[	[	X
ejde-397	254	20	3	3	NUM
ejde-397	254	21	]	]	PUNCT
ejde-397	254	22	.	.	PUNCT
ejde-397	255	1	lemma	lemma	PROPN
ejde-397	255	2	2.2	2.2	NUM
ejde-397	255	3	.	.	PUNCT
ejde-397	255	4	suppose	suppose	VERB
ejde-397	255	5	that	that	SCONJ
ejde-397	255	6	a	a	PRON
ejde-397	255	7	:	:	PUNCT
ejde-397	255	8	x	x	X
ejde-397	255	9	→	→	X
ejde-397	255	10	p	p	X
ejde-397	255	11	(	(	PUNCT
ejde-397	255	12	y	y	PROPN
ejde-397	255	13	)	)	PUNCT
ejde-397	255	14	is	be	AUX
ejde-397	255	15	an	an	DET
ejde-397	255	16	mlo	mlo	NOUN
ejde-397	255	17	and	and	CCONJ
ejde-397	255	18	a	a	PRON
ejde-397	255	19	is	be	AUX
ejde-397	255	20	xa	xa	PROPN
ejde-397	255	21	×	×	PROPN
ejde-397	255	22	ya	ya	PROPN
ejde-397	255	23	-	-	PUNCT
ejde-397	255	24	closed	closed	ADJ
ejde-397	255	25	.	.	PUNCT
ejde-397	256	1	assume	assume	VERB
ejde-397	256	2	,	,	PUNCT
ejde-397	256	3	further	far	ADV
ejde-397	256	4	,	,	PUNCT
ejde-397	256	5	that	that	SCONJ
ejde-397	256	6	x0	x0	PROPN
ejde-397	256	7	∈	∈	PROPN
ejde-397	256	8	x	x	X
ejde-397	256	9	,	,	PUNCT
ejde-397	256	10	y0	y0	PROPN
ejde-397	256	11	∈	∈	PROPN
ejde-397	256	12	y	y	PROPN
ejde-397	256	13	and	and	CCONJ
ejde-397	256	14	〈	〈	PROPN
ejde-397	256	15	x∗	x∗	PROPN
ejde-397	256	16	,	,	PUNCT
ejde-397	256	17	x0	x0	PROPN
ejde-397	256	18	〉	〉	NOUN
ejde-397	256	19	=	=	PUNCT
ejde-397	256	20	〈	〈	PROPN
ejde-397	256	21	y∗	y∗	ADV
ejde-397	256	22	,	,	PUNCT
ejde-397	256	23	y0	y0	NOUN
ejde-397	256	24	〉	〉	NOUN
ejde-397	256	25	for	for	ADP
ejde-397	256	26	all	all	DET
ejde-397	256	27	pairs	pair	NOUN
ejde-397	256	28	(	(	PUNCT
ejde-397	256	29	x∗	x∗	PROPN
ejde-397	256	30	,	,	PUNCT
ejde-397	256	31	y∗	y∗	PROPN
ejde-397	256	32	)	)	PUNCT
ejde-397	257	1	∈	∈	PROPN
ejde-397	257	2	x∗a	x∗a	PROPN
ejde-397	257	3	×	×	PROPN
ejde-397	257	4	y	y	PROPN
ejde-397	257	5	∗a	∗a	ADJ
ejde-397	257	6	satisfying	satisfy	VERB
ejde-397	257	7	that	that	SCONJ
ejde-397	257	8	〈	〈	PROPN
ejde-397	257	9	x∗	x∗	PROPN
ejde-397	257	10	,	,	PUNCT
ejde-397	257	11	x	x	X
ejde-397	257	12	〉	〉	NOUN
ejde-397	257	13	=	=	SYM
ejde-397	257	14	〈	〈	PROPN
ejde-397	257	15	y∗	y∗	PROPN
ejde-397	257	16	,	,	PUNCT
ejde-397	257	17	y	y	PROPN
ejde-397	257	18	〉	〉	NUM
ejde-397	257	19	whenever	whenever	SCONJ
ejde-397	257	20	y	y	PROPN
ejde-397	257	21	∈	∈	PROPN
ejde-397	257	22	ax	ax	NOUN
ejde-397	257	23	.	.	PUNCT
ejde-397	258	1	then	then	ADV
ejde-397	258	2	y0	y0	PROPN
ejde-397	258	3	∈	∈	NOUN
ejde-397	258	4	ax0	ax0	NOUN
ejde-397	258	5	.	.	PUNCT
ejde-397	259	1	with	with	ADP
ejde-397	259	2	lemma	lemma	PROPN
ejde-397	259	3	2.2	2.2	NUM
ejde-397	259	4	in	in	ADP
ejde-397	259	5	view	view	NOUN
ejde-397	259	6	,	,	PUNCT
ejde-397	259	7	we	we	PRON
ejde-397	259	8	can	can	AUX
ejde-397	259	9	simply	simply	ADV
ejde-397	259	10	prove	prove	VERB
ejde-397	259	11	the	the	DET
ejde-397	259	12	following	follow	VERB
ejde-397	259	13	extension	extension	NOUN
ejde-397	259	14	of	of	ADP
ejde-397	259	15	theorem	theorem	NOUN
ejde-397	259	16	1.3(iii	1.3(iii	NUM
ejde-397	259	17	)	)	PUNCT
ejde-397	259	18	for	for	ADP
ejde-397	259	19	relatively	relatively	ADV
ejde-397	259	20	closed	closed	ADJ
ejde-397	259	21	mlos	mlo	NOUN
ejde-397	259	22	in	in	ADP
ejde-397	259	23	locally	locally	ADV
ejde-397	259	24	convex	convex	ADJ
ejde-397	259	25	spaces	space	NOUN
ejde-397	259	26	.	.	PUNCT
ejde-397	260	1	theorem	theorem	VERB
ejde-397	260	2	2.3	2.3	NUM
ejde-397	260	3	.	.	PUNCT
ejde-397	261	1	suppose	suppose	VERB
ejde-397	261	2	that	that	SCONJ
ejde-397	261	3	a	a	PRON
ejde-397	261	4	:	:	PUNCT
ejde-397	261	5	x	x	X
ejde-397	261	6	→	→	X
ejde-397	261	7	p	p	X
ejde-397	261	8	(	(	PUNCT
ejde-397	261	9	y	y	PROPN
ejde-397	261	10	)	)	PUNCT
ejde-397	261	11	is	be	AUX
ejde-397	261	12	an	an	DET
ejde-397	261	13	mlo	mlo	NOUN
ejde-397	261	14	and	and	CCONJ
ejde-397	261	15	a	a	PRON
ejde-397	261	16	is	be	AUX
ejde-397	261	17	xa×ya	xa×ya	PROPN
ejde-397	261	18	-	-	PUNCT
ejde-397	261	19	closed	closed	ADJ
ejde-397	261	20	.	.	PUNCT
ejde-397	262	1	let	let	VERB
ejde-397	262	2	f	f	NOUN
ejde-397	262	3	:	:	PUNCT
ejde-397	262	4	ω	ω	PROPN
ejde-397	262	5	→	→	SYM
ejde-397	262	6	xa	xa	PROPN
ejde-397	262	7	and	and	CCONJ
ejde-397	262	8	g	g	PROPN
ejde-397	262	9	:	:	PUNCT
ejde-397	262	10	ω	ω	PROPN
ejde-397	262	11	→	→	SYM
ejde-397	262	12	ya	ya	PROPN
ejde-397	262	13	be	be	VERB
ejde-397	262	14	µ-integrable	µ-integrable	ADJ
ejde-397	262	15	,	,	PUNCT
ejde-397	262	16	and	and	CCONJ
ejde-397	262	17	let	let	VERB
ejde-397	262	18	g(x	g(x	NOUN
ejde-397	262	19	)	)	PUNCT
ejde-397	262	20	∈	∈	PROPN
ejde-397	262	21	af(x	af(x	PRON
ejde-397	262	22	)	)	PUNCT
ejde-397	262	23	,	,	PUNCT
ejde-397	263	1	x	x	PUNCT
ejde-397	263	2	∈	∈	PROPN
ejde-397	263	3	ω	ω	X
ejde-397	263	4	.	.	PUNCT
ejde-397	264	1	then	then	ADV
ejde-397	264	2	∫	∫	PROPN
ejde-397	264	3	ω	ω	PROPN
ejde-397	264	4	f	f	PROPN
ejde-397	264	5	dµ	dµ	PROPN
ejde-397	264	6	∈	∈	PROPN
ejde-397	264	7	d(a	d(a	PROPN
ejde-397	264	8	)	)	PUNCT
ejde-397	264	9	and	and	CCONJ
ejde-397	264	10	∫	∫	PROPN
ejde-397	264	11	ω	ω	PROPN
ejde-397	264	12	g	g	PROPN
ejde-397	264	13	dµ	dµ	PROPN
ejde-397	264	14	∈	∈	PROPN
ejde-397	264	15	a	a	DET
ejde-397	264	16	∫	∫	PROPN
ejde-397	264	17	ω	ω	PROPN
ejde-397	264	18	f	f	PROPN
ejde-397	264	19	dµ.	dµ.	PROPN
ejde-397	264	20	in	in	ADP
ejde-397	264	21	the	the	DET
ejde-397	264	22	remaining	remain	VERB
ejde-397	264	23	part	part	NOUN
ejde-397	264	24	of	of	ADP
ejde-397	264	25	this	this	DET
ejde-397	264	26	section	section	NOUN
ejde-397	264	27	,	,	PUNCT
ejde-397	264	28	we	we	PRON
ejde-397	264	29	will	will	AUX
ejde-397	264	30	analyze	analyze	VERB
ejde-397	264	31	the	the	DET
ejde-397	264	32	c	c	NOUN
ejde-397	264	33	-	-	PUNCT
ejde-397	264	34	resolvent	resolvent	ADJ
ejde-397	264	35	sets	set	NOUN
ejde-397	264	36	of	of	ADP
ejde-397	264	37	multivalued	multivalued	ADJ
ejde-397	264	38	linear	linear	ADJ
ejde-397	264	39	operators	operator	NOUN
ejde-397	264	40	in	in	ADP
ejde-397	264	41	locally	locally	ADV
ejde-397	264	42	convex	convex	ADJ
ejde-397	264	43	spaces	space	NOUN
ejde-397	264	44	.	.	PUNCT
ejde-397	265	1	our	our	PRON
ejde-397	265	2	standing	standing	NOUN
ejde-397	265	3	assumptions	assumption	NOUN
ejde-397	265	4	will	will	AUX
ejde-397	265	5	be	be	AUX
ejde-397	265	6	that	that	SCONJ
ejde-397	265	7	a	a	PRON
ejde-397	265	8	is	be	AUX
ejde-397	265	9	an	an	DET
ejde-397	265	10	mlo	mlo	NOUN
ejde-397	265	11	in	in	ADP
ejde-397	265	12	x	x	PROPN
ejde-397	265	13	,	,	PUNCT
ejde-397	265	14	as	as	ADV
ejde-397	265	15	well	well	ADV
ejde-397	265	16	as	as	ADP
ejde-397	265	17	that	that	PRON
ejde-397	265	18	c	c	PROPN
ejde-397	265	19	∈	∈	PROPN
ejde-397	265	20	l(x	l(x	PROPN
ejde-397	265	21	)	)	PUNCT
ejde-397	265	22	is	be	AUX
ejde-397	265	23	injective	injective	ADJ
ejde-397	265	24	(	(	PUNCT
ejde-397	265	25	the	the	DET
ejde-397	265	26	only	only	ADJ
ejde-397	265	27	exception	exception	NOUN
ejde-397	265	28	will	will	AUX
ejde-397	265	29	be	be	AUX
ejde-397	265	30	subsection	subsection	NOUN
ejde-397	265	31	5.2	5.2	NUM
ejde-397	265	32	,	,	PUNCT
ejde-397	265	33	where	where	SCONJ
ejde-397	265	34	c	c	NOUN
ejde-397	265	35	can	can	AUX
ejde-397	265	36	be	be	AUX
ejde-397	265	37	possibly	possibly	ADV
ejde-397	265	38	non	non	ADJ
ejde-397	265	39	-	-	ADJ
ejde-397	265	40	injective	injective	ADJ
ejde-397	265	41	)	)	PUNCT
ejde-397	265	42	and	and	CCONJ
ejde-397	265	43	ca	ca	PROPN
ejde-397	265	44	⊆	⊆	NUM
ejde-397	265	45	ac	ac	PROPN
ejde-397	265	46	(	(	PUNCT
ejde-397	265	47	this	this	PRON
ejde-397	265	48	is	be	AUX
ejde-397	265	49	equivalent	equivalent	ADJ
ejde-397	265	50	to	to	PART
ejde-397	265	51	say	say	VERB
ejde-397	265	52	that	that	SCONJ
ejde-397	265	53	,	,	PUNCT
ejde-397	265	54	for	for	ADP
ejde-397	265	55	any	any	DET
ejde-397	265	56	(	(	PUNCT
ejde-397	265	57	x	x	NOUN
ejde-397	265	58	,	,	PUNCT
ejde-397	265	59	y	y	NOUN
ejde-397	265	60	)	)	PUNCT
ejde-397	265	61	∈	∈	PROPN
ejde-397	265	62	x	x	SYM
ejde-397	265	63	×x	×x	PROPN
ejde-397	265	64	,	,	PUNCT
ejde-397	265	65	we	we	PRON
ejde-397	265	66	have	have	VERB
ejde-397	265	67	the	the	DET
ejde-397	265	68	implication	implication	NOUN
ejde-397	265	69	(	(	PUNCT
ejde-397	265	70	x	x	NOUN
ejde-397	265	71	,	,	PUNCT
ejde-397	265	72	y	y	PROPN
ejde-397	265	73	)	)	PUNCT
ejde-397	265	74	∈	∈	PROPN
ejde-397	265	75	a	a	DET
ejde-397	265	76	⇒	⇒	NOUN
ejde-397	265	77	(	(	PUNCT
ejde-397	265	78	cx	cx	NOUN
ejde-397	265	79	,	,	PUNCT
ejde-397	265	80	cy	cy	PROPN
ejde-397	265	81	)	)	PUNCT
ejde-397	265	82	∈	∈	PROPN
ejde-397	265	83	a	a	PRON
ejde-397	265	84	;	;	PUNCT
ejde-397	265	85	by	by	ADP
ejde-397	265	86	induction	induction	NOUN
ejde-397	265	87	,	,	PUNCT
ejde-397	265	88	we	we	PRON
ejde-397	265	89	immediately	immediately	ADV
ejde-397	265	90	get	get	VERB
ejde-397	265	91	that	that	DET
ejde-397	265	92	cak	cak	PROPN
ejde-397	265	93	⊆	⊆	NUM
ejde-397	265	94	akc	akc	NOUN
ejde-397	265	95	for	for	ADP
ejde-397	265	96	all	all	DET
ejde-397	265	97	k	k	PROPN
ejde-397	265	98	∈	∈	PROPN
ejde-397	265	99	n	n	CCONJ
ejde-397	265	100	)	)	PUNCT
ejde-397	265	101	.	.	PUNCT
ejde-397	266	1	then	then	ADV
ejde-397	266	2	the	the	DET
ejde-397	266	3	c	c	NOUN
ejde-397	266	4	-	-	PUNCT
ejde-397	266	5	resolvent	resolvent	ADJ
ejde-397	266	6	set	set	NOUN
ejde-397	266	7	of	of	ADP
ejde-397	266	8	a	a	DET
ejde-397	266	9	,	,	PUNCT
ejde-397	266	10	ρc(a	ρc(a	NOUN
ejde-397	266	11	)	)	PUNCT
ejde-397	266	12	for	for	ADP
ejde-397	266	13	short	short	ADJ
ejde-397	266	14	,	,	PUNCT
ejde-397	266	15	is	be	AUX
ejde-397	266	16	defined	define	VERB
ejde-397	266	17	as	as	ADP
ejde-397	266	18	the	the	DET
ejde-397	266	19	union	union	NOUN
ejde-397	266	20	of	of	ADP
ejde-397	266	21	those	those	DET
ejde-397	266	22	complex	complex	ADJ
ejde-397	266	23	numbers	number	NOUN
ejde-397	266	24	λ	λ	X
ejde-397	266	25	∈	∈	NOUN
ejde-397	266	26	c	c	NOUN
ejde-397	266	27	for	for	ADP
ejde-397	266	28	which	which	PRON
ejde-397	266	29	(	(	PUNCT
ejde-397	266	30	i	i	NOUN
ejde-397	266	31	)	)	PUNCT
ejde-397	266	32	r(c	r(c	NUM
ejde-397	266	33	)	)	PUNCT
ejde-397	266	34	⊆	⊆	NUM
ejde-397	266	35	r(λ−a	r(λ−a	NUM
ejde-397	266	36	)	)	PUNCT
ejde-397	266	37	;	;	PUNCT
ejde-397	266	38	(	(	PUNCT
ejde-397	266	39	ii	ii	NOUN
ejde-397	266	40	)	)	PUNCT
ejde-397	266	41	(	(	PUNCT
ejde-397	266	42	λ−a)−1c	λ−a)−1c	NOUN
ejde-397	266	43	is	be	AUX
ejde-397	266	44	a	a	DET
ejde-397	266	45	single	single	ADV
ejde-397	266	46	-	-	PUNCT
ejde-397	266	47	valued	value	VERB
ejde-397	266	48	bounded	bounded	ADJ
ejde-397	266	49	operator	operator	NOUN
ejde-397	266	50	on	on	ADP
ejde-397	266	51	x.	x.	NOUN
ejde-397	266	52	the	the	DET
ejde-397	266	53	operator	operator	NOUN
ejde-397	266	54	λ	λ	PROPN
ejde-397	266	55	7→	7→	PROPN
ejde-397	266	56	(	(	PUNCT
ejde-397	266	57	λ	λ	SYM
ejde-397	266	58	−	−	PROPN
ejde-397	266	59	a)−1c	a)−1c	PROPN
ejde-397	266	60	is	be	AUX
ejde-397	266	61	called	call	VERB
ejde-397	266	62	the	the	DET
ejde-397	266	63	c	c	NOUN
ejde-397	266	64	-	-	NOUN
ejde-397	266	65	resolvent	resolvent	NOUN
ejde-397	266	66	of	of	ADP
ejde-397	266	67	a	a	DET
ejde-397	266	68	(	(	PUNCT
ejde-397	266	69	λ	λ	X
ejde-397	266	70	∈	∈	PROPN
ejde-397	266	71	ρc(a	ρc(a	NOUN
ejde-397	266	72	)	)	PUNCT
ejde-397	266	73	)	)	PUNCT
ejde-397	266	74	;	;	PUNCT
ejde-397	266	75	the	the	DET
ejde-397	266	76	resolvent	resolvent	ADJ
ejde-397	266	77	set	set	NOUN
ejde-397	266	78	of	of	ADP
ejde-397	266	79	a	a	PRON
ejde-397	266	80	is	be	AUX
ejde-397	266	81	defined	define	VERB
ejde-397	266	82	by	by	ADP
ejde-397	266	83	ρ(a	ρ(a	PROPN
ejde-397	266	84	)	)	PUNCT
ejde-397	266	85	:	:	PUNCT
ejde-397	266	86	=	=	SYM
ejde-397	266	87	ρi(a	ρi(a	NOUN
ejde-397	266	88	)	)	PUNCT
ejde-397	266	89	,	,	PUNCT
ejde-397	266	90	r(λ	r(λ	PUNCT
ejde-397	266	91	:	:	PUNCT
ejde-397	266	92	a	a	X
ejde-397	266	93	)	)	PUNCT
ejde-397	266	94	≡	≡	PROPN
ejde-397	266	95	(	(	PUNCT
ejde-397	266	96	λ	λ	X
ejde-397	266	97	−a)−1	−a)−1	NOUN
ejde-397	266	98	(	(	PUNCT
ejde-397	266	99	λ	λ	X
ejde-397	266	100	∈	∈	PROPN
ejde-397	266	101	ρ(a	ρ(a	PROPN
ejde-397	266	102	)	)	PUNCT
ejde-397	266	103	)	)	PUNCT
ejde-397	266	104	.	.	PUNCT
ejde-397	267	1	we	we	PRON
ejde-397	267	2	can	can	AUX
ejde-397	267	3	almost	almost	ADV
ejde-397	267	4	trivially	trivially	ADV
ejde-397	267	5	construct	construct	VERB
ejde-397	267	6	examples	example	NOUN
ejde-397	267	7	of	of	ADP
ejde-397	267	8	mlos	mlo	NOUN
ejde-397	267	9	for	for	ADP
ejde-397	267	10	which	which	PRON
ejde-397	267	11	ρ(a	ρ(a	NOUN
ejde-397	267	12	)	)	PUNCT
ejde-397	267	13	=	=	SYM
ejde-397	267	14	∅	∅	NOUN
ejde-397	267	15	and	and	CCONJ
ejde-397	267	16	ρc(a	ρc(a	NOUN
ejde-397	267	17	)	)	PUNCT
ejde-397	267	18	6=	6=	NUM
ejde-397	267	19	∅	∅	NOUN
ejde-397	267	20	;	;	PUNCT
ejde-397	267	21	for	for	ADP
ejde-397	267	22	example	example	NOUN
ejde-397	267	23	,	,	PUNCT
ejde-397	267	24	let	let	VERB
ejde-397	267	25	y	y	PRON
ejde-397	267	26	be	be	AUX
ejde-397	267	27	a	a	DET
ejde-397	267	28	proper	proper	ADJ
ejde-397	267	29	closed	closed	ADJ
ejde-397	267	30	linear	linear	ADJ
ejde-397	267	31	subspace	subspace	NOUN
ejde-397	267	32	of	of	ADP
ejde-397	267	33	x	x	PRON
ejde-397	267	34	,	,	PUNCT
ejde-397	267	35	let	let	VERB
ejde-397	267	36	a	a	PRON
ejde-397	267	37	be	be	AUX
ejde-397	267	38	an	an	DET
ejde-397	267	39	mlo	mlo	NOUN
ejde-397	267	40	in	in	ADP
ejde-397	267	41	y	y	PROPN
ejde-397	267	42	,	,	PUNCT
ejde-397	267	43	and	and	CCONJ
ejde-397	267	44	let	let	VERB
ejde-397	267	45	λ	λ	X
ejde-397	267	46	∈	∈	VERB
ejde-397	267	47	c	c	AUX
ejde-397	267	48	so	so	SCONJ
ejde-397	267	49	that	that	SCONJ
ejde-397	267	50	(	(	PUNCT
ejde-397	267	51	λ	λ	X
ejde-397	267	52	−	−	PROPN
ejde-397	267	53	a)−1	a)−1	NOUN
ejde-397	267	54	∈	∈	PROPN
ejde-397	267	55	l(y	l(y	PROPN
ejde-397	267	56	)	)	PUNCT
ejde-397	267	57	.	.	PUNCT
ejde-397	268	1	taking	take	VERB
ejde-397	268	2	any	any	DET
ejde-397	268	3	injective	injective	ADJ
ejde-397	268	4	operator	operator	NOUN
ejde-397	268	5	c	c	PROPN
ejde-397	268	6	∈	∈	PROPN
ejde-397	268	7	l(x	l(x	PROPN
ejde-397	268	8	)	)	PUNCT
ejde-397	268	9	with	with	ADP
ejde-397	268	10	r(c	r(c	ADJ
ejde-397	268	11	)	)	PUNCT
ejde-397	268	12	⊆	⊆	NUM
ejde-397	268	13	y	y	PROPN
ejde-397	268	14	,	,	PUNCT
ejde-397	268	15	and	and	CCONJ
ejde-397	268	16	looking	look	VERB
ejde-397	268	17	a	a	DET
ejde-397	268	18	=	=	NOUN
ejde-397	268	19	ax	ax	NOUN
ejde-397	268	20	as	as	ADP
ejde-397	268	21	an	an	DET
ejde-397	268	22	mlo	mlo	PROPN
ejde-397	268	23	in	in	ADP
ejde-397	268	24	x	x	NOUN
ejde-397	268	25	,	,	PUNCT
ejde-397	268	26	it	it	PRON
ejde-397	268	27	is	be	AUX
ejde-397	268	28	clear	clear	ADJ
ejde-397	268	29	that	that	SCONJ
ejde-397	268	30	λ	λ	PROPN
ejde-397	268	31	∈	∈	PROPN
ejde-397	268	32	ρc(ax	ρc(ax	NOUN
ejde-397	268	33	)	)	PUNCT
ejde-397	268	34	and	and	CCONJ
ejde-397	268	35	ρ(ax	ρ(ax	NOUN
ejde-397	268	36	)	)	PUNCT
ejde-397	268	37	=	=	PUNCT
ejde-397	268	38	∅.	∅.	NOUN
ejde-397	268	39	in	in	ADP
ejde-397	268	40	general	general	ADJ
ejde-397	268	41	case	case	NOUN
ejde-397	268	42	,	,	PUNCT
ejde-397	268	43	if	if	SCONJ
ejde-397	268	44	ρc(a	ρc(a	NOUN
ejde-397	268	45	)	)	PUNCT
ejde-397	268	46	6=	6=	NUM
ejde-397	268	47	∅	∅	NOUN
ejde-397	268	48	,	,	PUNCT
ejde-397	268	49	then	then	ADV
ejde-397	268	50	for	for	ADP
ejde-397	268	51	any	any	DET
ejde-397	268	52	λ	λ	PROPN
ejde-397	268	53	∈	∈	PROPN
ejde-397	268	54	ρc(a	ρc(a	NOUN
ejde-397	268	55	)	)	PUNCT
ejde-397	268	56	we	we	PRON
ejde-397	268	57	have	have	VERB
ejde-397	268	58	a0	a0	NOUN
ejde-397	268	59	=	=	SYM
ejde-397	268	60	n((λi	n((λi	PROPN
ejde-397	268	61	−	−	ADP
ejde-397	268	62	a)−1c	a)−1c	NOUN
ejde-397	268	63	)	)	PUNCT
ejde-397	268	64	,	,	PUNCT
ejde-397	268	65	as	as	ADV
ejde-397	268	66	well	well	ADV
ejde-397	268	67	as	as	ADP
ejde-397	268	68	λ	λ	PROPN
ejde-397	268	69	∈	∈	PROPN
ejde-397	268	70	ρc(a	ρc(a	NOUN
ejde-397	268	71	)	)	PUNCT
ejde-397	268	72	,	,	PUNCT
ejde-397	268	73	a	a	DET
ejde-397	268	74	⊆	⊆	NUM
ejde-397	268	75	c−1ac	c−1ac	NOUN
ejde-397	268	76	and	and	CCONJ
ejde-397	268	77	(	(	PUNCT
ejde-397	268	78	(	(	PUNCT
ejde-397	268	79	λ−a)−1c)k(d(al	λ−a)−1c)k(d(al	NOUN
ejde-397	268	80	)	)	PUNCT
ejde-397	268	81	)	)	PUNCT
ejde-397	269	1	⊆	⊆	NUM
ejde-397	269	2	d(ak+l	d(ak+l	NOUN
ejde-397	269	3	)	)	PUNCT
ejde-397	269	4	,	,	PUNCT
ejde-397	269	5	k	k	NOUN
ejde-397	269	6	,	,	PUNCT
ejde-397	269	7	l	l	PROPN
ejde-397	269	8	∈	∈	PROPN
ejde-397	269	9	n0	n0	NUM
ejde-397	269	10	;	;	PUNCT
ejde-397	269	11	here	here	ADV
ejde-397	269	12	it	it	PRON
ejde-397	269	13	is	be	AUX
ejde-397	269	14	worth	worth	ADJ
ejde-397	269	15	noting	note	VERB
ejde-397	269	16	that	that	SCONJ
ejde-397	269	17	the	the	DET
ejde-397	269	18	equality	equality	NOUN
ejde-397	269	19	a	a	DET
ejde-397	269	20	=	=	X
ejde-397	269	21	c−1ac	c−1ac	NOUN
ejde-397	269	22	holds	hold	VERB
ejde-397	269	23	provided	provide	VERB
ejde-397	269	24	,	,	PUNCT
ejde-397	269	25	in	in	ADP
ejde-397	269	26	addition	addition	NOUN
ejde-397	269	27	,	,	PUNCT
ejde-397	269	28	that	that	SCONJ
ejde-397	269	29	ρ(a	ρ(a	NOUN
ejde-397	269	30	)	)	PUNCT
ejde-397	269	31	6=	6=	NOUN
ejde-397	269	32	∅	∅	NOUN
ejde-397	269	33	(	(	PUNCT
ejde-397	269	34	see	see	VERB
ejde-397	269	35	the	the	DET
ejde-397	269	36	proofs	proof	NOUN
ejde-397	269	37	of	of	ADP
ejde-397	269	38	[	[	X
ejde-397	269	39	12	12	NUM
ejde-397	269	40	,	,	PUNCT
ejde-397	269	41	proposition	proposition	NOUN
ejde-397	269	42	2.1	2.1	NUM
ejde-397	269	43	,	,	PUNCT
ejde-397	269	44	lemma	lemma	PROPN
ejde-397	269	45	2.3	2.3	NUM
ejde-397	269	46	]	]	PUNCT
ejde-397	269	47	)	)	PUNCT
ejde-397	269	48	.	.	PUNCT
ejde-397	270	1	the	the	DET
ejde-397	270	2	basic	basic	ADJ
ejde-397	270	3	properties	property	NOUN
ejde-397	270	4	of	of	ADP
ejde-397	270	5	c	c	NOUN
ejde-397	270	6	-	-	PUNCT
ejde-397	270	7	resolvent	resolvent	ADJ
ejde-397	270	8	sets	set	NOUN
ejde-397	270	9	of	of	ADP
ejde-397	270	10	single	single	ADV
ejde-397	270	11	-	-	PUNCT
ejde-397	270	12	valued	value	VERB
ejde-397	270	13	linear	linear	PROPN
ejde-397	270	14	operators	operator	NOUN
ejde-397	270	15	[	[	X
ejde-397	270	16	35	35	NUM
ejde-397	270	17	,	,	PUNCT
ejde-397	270	18	36	36	NUM
ejde-397	270	19	]	]	PUNCT
ejde-397	270	20	continue	continue	VERB
ejde-397	270	21	to	to	PART
ejde-397	270	22	hold	hold	VERB
ejde-397	270	23	in	in	ADP
ejde-397	270	24	our	our	PRON
ejde-397	270	25	framework	framework	NOUN
ejde-397	270	26	(	(	PUNCT
ejde-397	270	27	observe	observe	VERB
ejde-397	270	28	,	,	PUNCT
ejde-397	270	29	however	however	ADV
ejde-397	270	30	,	,	PUNCT
ejde-397	270	31	that	that	SCONJ
ejde-397	270	32	there	there	PRON
ejde-397	270	33	exist	exist	VERB
ejde-397	270	34	certain	certain	ADJ
ejde-397	270	35	differences	difference	NOUN
ejde-397	270	36	that	that	SCONJ
ejde-397	270	37	we	we	PRON
ejde-397	270	38	will	will	AUX
ejde-397	270	39	not	not	PART
ejde-397	270	40	discuss	discuss	VERB
ejde-397	270	41	here	here	ADV
ejde-397	270	42	)	)	PUNCT
ejde-397	270	43	.	.	PUNCT
ejde-397	271	1	for	for	ADP
ejde-397	271	2	example	example	NOUN
ejde-397	271	3	,	,	PUNCT
ejde-397	271	4	if	if	SCONJ
ejde-397	271	5	ρ(a	ρ(a	PROPN
ejde-397	271	6	)	)	PUNCT
ejde-397	271	7	6=	6=	ADP
ejde-397	271	8	∅	∅	NOUN
ejde-397	271	9	,	,	PUNCT
ejde-397	271	10	then	then	ADV
ejde-397	271	11	a	a	PRON
ejde-397	271	12	is	be	AUX
ejde-397	271	13	closed	closed	ADJ
ejde-397	271	14	;	;	PUNCT
ejde-397	271	15	it	it	PRON
ejde-397	271	16	is	be	AUX
ejde-397	271	17	well	well	ADV
ejde-397	271	18	known	know	VERB
ejde-397	271	19	that	that	SCONJ
ejde-397	271	20	this	this	DET
ejde-397	271	21	statement	statement	NOUN
ejde-397	271	22	does	do	AUX
ejde-397	271	23	not	not	PART
ejde-397	271	24	hold	hold	VERB
ejde-397	271	25	if	if	SCONJ
ejde-397	271	26	ρc(a	ρc(a	NOUN
ejde-397	271	27	)	)	PUNCT
ejde-397	271	28	6=	6=	ADP
ejde-397	271	29	∅	∅	NOUN
ejde-397	271	30	for	for	ADP
ejde-397	271	31	some	some	DET
ejde-397	271	32	c	c	NOUN
ejde-397	271	33	6=	6=	PROPN
ejde-397	272	1	i	i	PRON
ejde-397	272	2	(	(	PUNCT
ejde-397	272	3	cf	cf	NOUN
ejde-397	272	4	.	.	PUNCT
ejde-397	273	1	[	[	X
ejde-397	273	2	12	12	NUM
ejde-397	273	3	,	,	PUNCT
ejde-397	273	4	example	example	NOUN
ejde-397	273	5	2.2	2.2	NUM
ejde-397	273	6	]	]	PUNCT
ejde-397	273	7	)	)	PUNCT
ejde-397	273	8	.	.	PUNCT
ejde-397	274	1	arguing	argue	VERB
ejde-397	274	2	as	as	ADP
ejde-397	274	3	in	in	ADP
ejde-397	274	4	the	the	DET
ejde-397	274	5	proofs	proof	NOUN
ejde-397	274	6	of	of	ADP
ejde-397	274	7	[	[	X
ejde-397	274	8	17	17	NUM
ejde-397	274	9	,	,	PUNCT
ejde-397	274	10	theorem	theorem	VERB
ejde-397	274	11	1.7	1.7	NUM
ejde-397	274	12	-	-	PUNCT
ejde-397	274	13	theorem	theorem	ADJ
ejde-397	274	14	1.9	1.9	NUM
ejde-397	274	15	]	]	PUNCT
ejde-397	274	16	,	,	PUNCT
ejde-397	274	17	we	we	PRON
ejde-397	274	18	can	can	AUX
ejde-397	274	19	deduce	deduce	VERB
ejde-397	274	20	the	the	DET
ejde-397	274	21	validity	validity	NOUN
ejde-397	274	22	of	of	ADP
ejde-397	274	23	the	the	DET
ejde-397	274	24	following	follow	VERB
ejde-397	274	25	important	important	ADJ
ejde-397	274	26	theorem	theorem	VERB
ejde-397	274	27	,	,	PUNCT
ejde-397	274	28	which	which	PRON
ejde-397	274	29	will	will	AUX
ejde-397	274	30	be	be	AUX
ejde-397	274	31	frequently	frequently	ADV
ejde-397	274	32	used	use	VERB
ejde-397	274	33	in	in	ADP
ejde-397	274	34	the	the	DET
ejde-397	274	35	sequel	sequel	NOUN
ejde-397	274	36	.	.	PUNCT
ejde-397	275	1	theorem	theorem	VERB
ejde-397	275	2	2.4	2.4	NUM
ejde-397	275	3	.	.	PUNCT
ejde-397	276	1	(	(	PUNCT
ejde-397	276	2	i	i	NOUN
ejde-397	276	3	)	)	PUNCT
ejde-397	276	4	we	we	PRON
ejde-397	276	5	have	have	VERB
ejde-397	276	6	(	(	PUNCT
ejde-397	276	7	λ−a	λ−a	PRON
ejde-397	276	8	)	)	PUNCT
ejde-397	277	1	−1	−1	NOUN
ejde-397	277	2	ca	ca	NOUN
ejde-397	277	3	⊆	⊆	NUM
ejde-397	277	4	λ	λ	X
ejde-397	277	5	(	(	PUNCT
ejde-397	277	6	λ−a	λ−a	NOUN
ejde-397	277	7	)	)	PUNCT
ejde-397	278	1	−1	−1	NOUN
ejde-397	278	2	c	c	NOUN
ejde-397	278	3	−	−	NOUN
ejde-397	278	4	c	c	NOUN
ejde-397	278	5	⊆	⊆	NUM
ejde-397	278	6	a	a	DET
ejde-397	278	7	(	(	PUNCT
ejde-397	278	8	λ−a	λ−a	NUM
ejde-397	278	9	)	)	PUNCT
ejde-397	278	10	−1	−1	NOUN
ejde-397	279	1	c	c	NOUN
ejde-397	279	2	,	,	PUNCT
ejde-397	279	3	λ	λ	PROPN
ejde-397	279	4	∈	∈	PROPN
ejde-397	279	5	ρc(a	ρc(a	NOUN
ejde-397	279	6	)	)	PUNCT
ejde-397	279	7	.	.	PUNCT
ejde-397	280	1	the	the	DET
ejde-397	280	2	operator	operator	NOUN
ejde-397	280	3	(	(	PUNCT
ejde-397	280	4	λ−a)−1ca	λ−a)−1ca	NOUN
ejde-397	280	5	is	be	AUX
ejde-397	280	6	single	single	ADV
ejde-397	280	7	-	-	PUNCT
ejde-397	280	8	valued	value	VERB
ejde-397	280	9	on	on	ADP
ejde-397	280	10	d(a	d(a	PROPN
ejde-397	280	11	)	)	PUNCT
ejde-397	280	12	and	and	CCONJ
ejde-397	280	13	(	(	PUNCT
ejde-397	280	14	λ−a)−1cax	λ−a)−1cax	X
ejde-397	280	15	=	=	X
ejde-397	280	16	(	(	PUNCT
ejde-397	280	17	λ−a)−1cy	λ−a)−1cy	PROPN
ejde-397	280	18	,	,	PUNCT
ejde-397	280	19	whenever	whenever	SCONJ
ejde-397	280	20	y	y	PROPN
ejde-397	280	21	∈	∈	PROPN
ejde-397	280	22	ax	ax	NOUN
ejde-397	280	23	and	and	CCONJ
ejde-397	280	24	λ	λ	NOUN
ejde-397	280	25	∈	∈	PROPN
ejde-397	280	26	ρc(a	ρc(a	NOUN
ejde-397	280	27	)	)	PUNCT
ejde-397	280	28	.	.	PUNCT
ejde-397	281	1	(	(	PUNCT
ejde-397	281	2	ii	ii	NOUN
ejde-397	281	3	)	)	PUNCT
ejde-397	281	4	suppose	suppose	VERB
ejde-397	281	5	that	that	SCONJ
ejde-397	281	6	λ	λ	PROPN
ejde-397	281	7	,	,	PUNCT
ejde-397	281	8	µ	µ	X
ejde-397	281	9	∈	∈	NOUN
ejde-397	281	10	ρc(a	ρc(a	NOUN
ejde-397	281	11	)	)	PUNCT
ejde-397	281	12	.	.	PUNCT
ejde-397	282	1	then	then	ADV
ejde-397	282	2	the	the	DET
ejde-397	282	3	resolvent	resolvent	ADJ
ejde-397	282	4	equation	equation	NOUN
ejde-397	282	5	(	(	PUNCT
ejde-397	282	6	λ−a	λ−a	NOUN
ejde-397	282	7	)	)	PUNCT
ejde-397	282	8	−1	−1	NOUN
ejde-397	282	9	c2x−	c2x−	NOUN
ejde-397	282	10	(	(	PUNCT
ejde-397	282	11	µ−a	µ−a	ADJ
ejde-397	282	12	)	)	PUNCT
ejde-397	282	13	−1	−1	NOUN
ejde-397	282	14	c2x	c2x	NOUN
ejde-397	282	15	=	=	PUNCT
ejde-397	282	16	(	(	PUNCT
ejde-397	282	17	µ−	µ−	PROPN
ejde-397	282	18	λ	λ	PROPN
ejde-397	282	19	)	)	PUNCT
ejde-397	282	20	(	(	PUNCT
ejde-397	282	21	λ−a	λ−a	NUM
ejde-397	282	22	)	)	PUNCT
ejde-397	282	23	−1	−1	NOUN
ejde-397	282	24	c	c	NOUN
ejde-397	282	25	(	(	PUNCT
ejde-397	282	26	µ−a	µ−a	ADJ
ejde-397	282	27	)	)	PUNCT
ejde-397	282	28	−1	−1	NOUN
ejde-397	283	1	cx	cx	NOUN
ejde-397	283	2	,	,	PUNCT
ejde-397	283	3	x	x	SYM
ejde-397	283	4	∈	∈	NOUN
ejde-397	283	5	x	x	SYM
ejde-397	283	6	10	10	NUM
ejde-397	283	7	m.	m.	NOUN
ejde-397	283	8	kostić	kostić	NOUN
ejde-397	284	1	ejde-2023/63	ejde-2023/63	PROPN
ejde-397	284	2	holds	hold	VERB
ejde-397	284	3	good	good	ADJ
ejde-397	284	4	.	.	PUNCT
ejde-397	285	1	in	in	ADP
ejde-397	285	2	particular	particular	ADJ
ejde-397	285	3	,	,	PUNCT
ejde-397	285	4	(	(	PUNCT
ejde-397	285	5	λ−a)−1c(µ−a)−1c	λ−a)−1c(µ−a)−1c	X
ejde-397	285	6	=	=	SYM
ejde-397	285	7	(	(	PUNCT
ejde-397	285	8	µ−a)−1c(λ−a	µ−a)−1c(λ−a	PROPN
ejde-397	285	9	)	)	PUNCT
ejde-397	285	10	−1	−1	NOUN
ejde-397	285	11	c.	c.	NOUN
ejde-397	285	12	by	by	ADP
ejde-397	285	13	theorem	theorem	NOUN
ejde-397	285	14	2.4(i	2.4(i	NUM
ejde-397	285	15	)	)	PUNCT
ejde-397	285	16	,	,	PUNCT
ejde-397	285	17	it	it	PRON
ejde-397	285	18	readily	readily	ADV
ejde-397	285	19	follows	follow	VERB
ejde-397	285	20	that	that	SCONJ
ejde-397	285	21	the	the	DET
ejde-397	285	22	operator	operator	NOUN
ejde-397	285	23	λ(λ−a)−1c−c	λ(λ−a)−1c−c	VERB
ejde-397	285	24	∈	∈	PROPN
ejde-397	285	25	l(x	l(x	PROPN
ejde-397	285	26	)	)	PUNCT
ejde-397	285	27	is	be	AUX
ejde-397	285	28	a	a	DET
ejde-397	285	29	bounded	bounded	ADJ
ejde-397	285	30	linear	linear	ADJ
ejde-397	285	31	section	section	NOUN
ejde-397	285	32	of	of	ADP
ejde-397	285	33	the	the	DET
ejde-397	285	34	mloa(λ−a)−1c	mloa(λ−a)−1c	NOUN
ejde-397	285	35	(	(	PUNCT
ejde-397	285	36	λ	λ	X
ejde-397	285	37	∈	∈	PROPN
ejde-397	285	38	ρc(a	ρc(a	NOUN
ejde-397	285	39	)	)	PUNCT
ejde-397	285	40	)	)	PUNCT
ejde-397	285	41	.	.	PUNCT
ejde-397	286	1	inductively	inductively	ADV
ejde-397	286	2	,	,	PUNCT
ejde-397	286	3	we	we	PRON
ejde-397	286	4	can	can	AUX
ejde-397	286	5	prove	prove	VERB
ejde-397	286	6	that	that	SCONJ
ejde-397	286	7	,	,	PUNCT
ejde-397	286	8	for	for	ADP
ejde-397	286	9	every	every	DET
ejde-397	286	10	x	x	SYM
ejde-397	286	11	∈	∈	PROPN
ejde-397	286	12	x	x	NOUN
ejde-397	286	13	,	,	PUNCT
ejde-397	286	14	n	n	PROPN
ejde-397	286	15	∈	∈	PROPN
ejde-397	286	16	n0	n0	NOUN
ejde-397	286	17	and	and	CCONJ
ejde-397	286	18	λ	λ	PROPN
ejde-397	286	19	∈	∈	PROPN
ejde-397	286	20	ρc(a	ρc(a	NOUN
ejde-397	286	21	)	)	PUNCT
ejde-397	286	22	,	,	PUNCT
ejde-397	286	23	we	we	PRON
ejde-397	286	24	have	have	VERB
ejde-397	286	25	card((λ−a)−ncx	card((λ−a)−ncx	NOUN
ejde-397	286	26	)	)	PUNCT
ejde-397	286	27	≤	≤	NUM
ejde-397	286	28	1	1	NUM
ejde-397	286	29	.	.	PUNCT
ejde-397	287	1	having	have	VERB
ejde-397	287	2	in	in	ADP
ejde-397	287	3	mind	mind	NOUN
ejde-397	287	4	this	this	DET
ejde-397	287	5	fact	fact	NOUN
ejde-397	287	6	,	,	PUNCT
ejde-397	287	7	as	as	ADV
ejde-397	287	8	well	well	ADV
ejde-397	287	9	as	as	ADP
ejde-397	287	10	the	the	DET
ejde-397	287	11	argumentation	argumentation	NOUN
ejde-397	287	12	already	already	ADV
ejde-397	287	13	seen	see	VERB
ejde-397	287	14	many	many	ADJ
ejde-397	287	15	times	time	NOUN
ejde-397	287	16	in	in	ADP
ejde-397	287	17	our	our	PRON
ejde-397	287	18	previous	previous	ADJ
ejde-397	287	19	research	research	NOUN
ejde-397	287	20	studies	study	NOUN
ejde-397	287	21	of	of	ADP
ejde-397	287	22	c	c	NOUN
ejde-397	287	23	-	-	PUNCT
ejde-397	287	24	resolvents	resolvent	NOUN
ejde-397	287	25	of	of	ADP
ejde-397	287	26	single	single	ADV
ejde-397	287	27	-	-	PUNCT
ejde-397	287	28	valued	value	VERB
ejde-397	287	29	linear	linear	PROPN
ejde-397	287	30	operators	operator	NOUN
ejde-397	287	31	,	,	PUNCT
ejde-397	287	32	we	we	PRON
ejde-397	287	33	can	can	AUX
ejde-397	287	34	prove	prove	VERB
ejde-397	287	35	the	the	DET
ejde-397	287	36	following	following	ADJ
ejde-397	287	37	extension	extension	NOUN
ejde-397	287	38	of	of	ADP
ejde-397	287	39	[	[	X
ejde-397	287	40	36	36	NUM
ejde-397	287	41	,	,	PUNCT
ejde-397	287	42	proposition	proposition	NOUN
ejde-397	287	43	2.1.14	2.1.14	NUM
ejde-397	287	44	]	]	PUNCT
ejde-397	287	45	for	for	ADP
ejde-397	287	46	mlos	mlo	NOUN
ejde-397	287	47	in	in	ADP
ejde-397	287	48	locally	locally	ADV
ejde-397	287	49	convex	convex	ADJ
ejde-397	287	50	spaces	space	NOUN
ejde-397	287	51	.	.	PUNCT
ejde-397	288	1	proposition	proposition	NOUN
ejde-397	288	2	2.5	2.5	NUM
ejde-397	288	3	.	.	PUNCT
ejde-397	289	1	let	let	AUX
ejde-397	289	2	∅	∅	NOUN
ejde-397	289	3	6=	6=	ADP
ejde-397	289	4	ω	ω	NUM
ejde-397	289	5	⊆	⊆	NUM
ejde-397	289	6	ρc(a	ρc(a	NOUN
ejde-397	289	7	)	)	PUNCT
ejde-397	289	8	be	be	AUX
ejde-397	289	9	open	open	ADJ
ejde-397	289	10	,	,	PUNCT
ejde-397	289	11	and	and	CCONJ
ejde-397	289	12	let	let	VERB
ejde-397	289	13	x	x	X
ejde-397	289	14	∈	∈	PROPN
ejde-397	289	15	x.	x.	NOUN
ejde-397	289	16	(	(	PUNCT
ejde-397	289	17	i	i	NOUN
ejde-397	289	18	)	)	PUNCT
ejde-397	289	19	the	the	DET
ejde-397	289	20	local	local	ADJ
ejde-397	289	21	boundedness	boundedness	NOUN
ejde-397	289	22	of	of	ADP
ejde-397	289	23	the	the	DET
ejde-397	289	24	mapping	mapping	NOUN
ejde-397	289	25	λ	λ	X
ejde-397	289	26	7→	7→	PROPN
ejde-397	289	27	(	(	PUNCT
ejde-397	289	28	λ	λ	X
ejde-397	289	29	−	−	NOUN
ejde-397	289	30	a)−1cx	a)−1cx	NOUN
ejde-397	289	31	,	,	PUNCT
ejde-397	289	32	λ	λ	PROPN
ejde-397	289	33	∈	∈	PROPN
ejde-397	289	34	ω	ω	PROPN
ejde-397	289	35	,	,	PUNCT
ejde-397	289	36	resp	resp	NOUN
ejde-397	289	37	.	.	PUNCT
ejde-397	290	1	the	the	DET
ejde-397	290	2	assumption	assumption	NOUN
ejde-397	290	3	that	that	SCONJ
ejde-397	290	4	x	x	PRON
ejde-397	290	5	is	be	AUX
ejde-397	290	6	barreled	barrel	VERB
ejde-397	290	7	and	and	CCONJ
ejde-397	290	8	the	the	DET
ejde-397	290	9	local	local	ADJ
ejde-397	290	10	boundedness	boundedness	NOUN
ejde-397	290	11	of	of	ADP
ejde-397	290	12	the	the	DET
ejde-397	290	13	mapping	mapping	NOUN
ejde-397	290	14	λ	λ	PROPN
ejde-397	290	15	7→	7→	NUM
ejde-397	290	16	(	(	PUNCT
ejde-397	290	17	λ−	λ−	PROPN
ejde-397	290	18	a)−1c	a)−1c	PROPN
ejde-397	290	19	,	,	PUNCT
ejde-397	290	20	λ	λ	PROPN
ejde-397	290	21	∈	∈	PROPN
ejde-397	290	22	ω	ω	PROPN
ejde-397	290	23	,	,	PUNCT
ejde-397	290	24	implies	imply	VERB
ejde-397	290	25	the	the	DET
ejde-397	290	26	analyticity	analyticity	NOUN
ejde-397	290	27	of	of	ADP
ejde-397	290	28	the	the	DET
ejde-397	290	29	mapping	mapping	NOUN
ejde-397	290	30	λ	λ	X
ejde-397	290	31	7→	7→	PROPN
ejde-397	290	32	(	(	PUNCT
ejde-397	290	33	λ−a)−1c3x	λ−a)−1c3x	PROPN
ejde-397	290	34	,	,	PUNCT
ejde-397	290	35	λ	λ	PROPN
ejde-397	290	36	∈	∈	PROPN
ejde-397	290	37	ω	ω	PROPN
ejde-397	290	38	,	,	PUNCT
ejde-397	290	39	resp	resp	NOUN
ejde-397	290	40	.	.	PUNCT
ejde-397	291	1	λ	λ	X
ejde-397	291	2	7→	7→	NUM
ejde-397	292	1	(	(	PUNCT
ejde-397	292	2	λ−a)−1c3	λ−a)−1c3	PROPN
ejde-397	292	3	,	,	PUNCT
ejde-397	292	4	λ	λ	PROPN
ejde-397	292	5	∈	∈	PROPN
ejde-397	292	6	ω	ω	NOUN
ejde-397	292	7	.	.	PUNCT
ejde-397	293	1	furthermore	furthermore	ADV
ejde-397	293	2	,	,	PUNCT
ejde-397	293	3	if	if	SCONJ
ejde-397	293	4	r(c	r(c	ADJ
ejde-397	293	5	)	)	PUNCT
ejde-397	293	6	is	be	AUX
ejde-397	293	7	dense	dense	ADJ
ejde-397	293	8	in	in	ADP
ejde-397	293	9	x	x	NOUN
ejde-397	293	10	,	,	PUNCT
ejde-397	293	11	resp	resp	NOUN
ejde-397	293	12	.	.	PUNCT
ejde-397	294	1	if	if	SCONJ
ejde-397	294	2	r(c	r(c	PROPN
ejde-397	294	3	)	)	PUNCT
ejde-397	294	4	is	be	AUX
ejde-397	294	5	dense	dense	ADJ
ejde-397	294	6	in	in	ADP
ejde-397	294	7	x	x	PUNCT
ejde-397	294	8	and	and	CCONJ
ejde-397	294	9	x	x	X
ejde-397	294	10	is	be	AUX
ejde-397	294	11	barreled	barrel	VERB
ejde-397	294	12	,	,	PUNCT
ejde-397	294	13	then	then	ADV
ejde-397	294	14	the	the	DET
ejde-397	294	15	mapping	mapping	NOUN
ejde-397	294	16	λ	λ	X
ejde-397	294	17	7→	7→	PROPN
ejde-397	294	18	(	(	PUNCT
ejde-397	294	19	λ	λ	X
ejde-397	294	20	−	−	NOUN
ejde-397	294	21	a)−1cx	a)−1cx	NOUN
ejde-397	294	22	,	,	PUNCT
ejde-397	294	23	λ	λ	PROPN
ejde-397	294	24	∈	∈	PROPN
ejde-397	294	25	ω	ω	PROPN
ejde-397	294	26	is	be	AUX
ejde-397	294	27	analytic	analytic	ADJ
ejde-397	294	28	,	,	PUNCT
ejde-397	294	29	resp	resp	NOUN
ejde-397	294	30	.	.	PUNCT
ejde-397	295	1	the	the	DET
ejde-397	295	2	mapping	mapping	NOUN
ejde-397	295	3	λ	λ	X
ejde-397	295	4	7→	7→	PROPN
ejde-397	295	5	(	(	PUNCT
ejde-397	295	6	λ−a)−1c	λ−a)−1c	PROPN
ejde-397	295	7	,	,	PUNCT
ejde-397	295	8	λ	λ	PROPN
ejde-397	295	9	∈	∈	PROPN
ejde-397	295	10	ω	ω	NOUN
ejde-397	295	11	is	be	AUX
ejde-397	295	12	analytic	analytic	ADJ
ejde-397	295	13	.	.	PUNCT
ejde-397	296	1	(	(	PUNCT
ejde-397	296	2	ii	ii	NOUN
ejde-397	296	3	)	)	PUNCT
ejde-397	296	4	suppose	suppose	VERB
ejde-397	296	5	that	that	SCONJ
ejde-397	296	6	r(c	r(c	PROPN
ejde-397	296	7	)	)	PUNCT
ejde-397	296	8	is	be	AUX
ejde-397	296	9	dense	dense	ADJ
ejde-397	296	10	in	in	ADP
ejde-397	296	11	x.	x.	NOUN
ejde-397	296	12	then	then	ADV
ejde-397	296	13	the	the	DET
ejde-397	296	14	local	local	ADJ
ejde-397	296	15	boundedness	boundedness	NOUN
ejde-397	296	16	of	of	ADP
ejde-397	296	17	the	the	DET
ejde-397	296	18	mapping	mapping	NOUN
ejde-397	296	19	λ	λ	PROPN
ejde-397	296	20	7→	7→	PROPN
ejde-397	296	21	(	(	PUNCT
ejde-397	296	22	λ−a)−1cx	λ−a)−1cx	PROPN
ejde-397	296	23	,	,	PUNCT
ejde-397	296	24	λ	λ	PROPN
ejde-397	296	25	∈	∈	PROPN
ejde-397	296	26	ω	ω	NOUN
ejde-397	296	27	implies	imply	VERB
ejde-397	296	28	its	its	PRON
ejde-397	296	29	analyticity	analyticity	NOUN
ejde-397	296	30	as	as	ADV
ejde-397	296	31	well	well	ADV
ejde-397	296	32	as	as	ADP
ejde-397	296	33	cx	cx	PROPN
ejde-397	296	34	∈	∈	PROPN
ejde-397	296	35	r((λ−a)n	r((λ−a)n	NOUN
ejde-397	296	36	)	)	PUNCT
ejde-397	296	37	,	,	PUNCT
ejde-397	296	38	n	n	PROPN
ejde-397	296	39	∈	∈	PROPN
ejde-397	296	40	n	n	NOUN
ejde-397	296	41	and	and	CCONJ
ejde-397	296	42	dn−1	dn−1	PROPN
ejde-397	296	43	dλn−1	dλn−1	PROPN
ejde-397	296	44	(	(	PUNCT
ejde-397	296	45	λ−a	λ−a	PROPN
ejde-397	296	46	)	)	PUNCT
ejde-397	296	47	−1	−1	NOUN
ejde-397	296	48	cx	cx	NOUN
ejde-397	297	1	=	=	PUNCT
ejde-397	297	2	(	(	PUNCT
ejde-397	297	3	−1)n−1(n−	−1)n−1(n−	NOUN
ejde-397	297	4	1	1	NUM
ejde-397	297	5	)	)	PUNCT
ejde-397	297	6	!	!	PUNCT
ejde-397	298	1	(	(	PUNCT
ejde-397	298	2	λ−a	λ−a	NOUN
ejde-397	298	3	)	)	PUNCT
ejde-397	298	4	−n	−n	PROPN
ejde-397	298	5	cx	cx	NOUN
ejde-397	298	6	,	,	PUNCT
ejde-397	298	7	n	n	PROPN
ejde-397	298	8	∈	∈	PROPN
ejde-397	298	9	n.	n.	NOUN
ejde-397	298	10	(	(	PUNCT
ejde-397	298	11	2.1	2.1	NUM
ejde-397	298	12	)	)	PUNCT
ejde-397	298	13	furthermore	furthermore	ADV
ejde-397	298	14	,	,	PUNCT
ejde-397	298	15	if	if	SCONJ
ejde-397	298	16	x	x	PRON
ejde-397	298	17	is	be	AUX
ejde-397	298	18	barreled	barrel	VERB
ejde-397	298	19	,	,	PUNCT
ejde-397	298	20	then	then	ADV
ejde-397	298	21	the	the	DET
ejde-397	298	22	local	local	ADJ
ejde-397	298	23	boundedness	boundedness	NOUN
ejde-397	298	24	of	of	ADP
ejde-397	298	25	the	the	DET
ejde-397	298	26	mapping	mapping	NOUN
ejde-397	298	27	λ	λ	X
ejde-397	298	28	7→	7→	PROPN
ejde-397	298	29	(	(	PUNCT
ejde-397	298	30	λ−a)−1c	λ−a)−1c	PROPN
ejde-397	298	31	,	,	PUNCT
ejde-397	298	32	λ	λ	PROPN
ejde-397	298	33	∈	∈	PROPN
ejde-397	298	34	ω	ω	NOUN
ejde-397	298	35	implies	imply	VERB
ejde-397	298	36	its	its	PRON
ejde-397	298	37	analyticity	analyticity	NOUN
ejde-397	298	38	as	as	ADV
ejde-397	298	39	well	well	ADV
ejde-397	298	40	as	as	ADP
ejde-397	298	41	r(c	r(c	ADJ
ejde-397	298	42	)	)	PUNCT
ejde-397	298	43	⊆	⊆	NUM
ejde-397	298	44	r((λ−a)n	r((λ−a)n	NOUN
ejde-397	298	45	)	)	PUNCT
ejde-397	298	46	,	,	PUNCT
ejde-397	298	47	n	n	PROPN
ejde-397	298	48	∈	∈	PROPN
ejde-397	298	49	n	n	NOUN
ejde-397	298	50	and	and	CCONJ
ejde-397	298	51	dn−1	dn−1	PROPN
ejde-397	298	52	dλn−1	dλn−1	PROPN
ejde-397	298	53	(	(	PUNCT
ejde-397	298	54	λ−a	λ−a	NOUN
ejde-397	298	55	)	)	PUNCT
ejde-397	298	56	−1	−1	NOUN
ejde-397	298	57	c	c	NOUN
ejde-397	298	58	=	=	SYM
ejde-397	298	59	(	(	PUNCT
ejde-397	298	60	−1)n−1(n−	−1)n−1(n−	NOUN
ejde-397	298	61	1	1	NUM
ejde-397	298	62	)	)	PUNCT
ejde-397	298	63	!	!	PUNCT
ejde-397	299	1	(	(	PUNCT
ejde-397	299	2	λ−a	λ−a	NUM
ejde-397	299	3	)	)	PUNCT
ejde-397	299	4	−n	−n	PROPN
ejde-397	299	5	c	c	PROPN
ejde-397	299	6	∈	∈	PROPN
ejde-397	299	7	l(x	l(x	PROPN
ejde-397	299	8	)	)	PUNCT
ejde-397	299	9	,	,	PUNCT
ejde-397	299	10	n	n	PROPN
ejde-397	299	11	∈	∈	PROPN
ejde-397	299	12	n.	n.	NOUN
ejde-397	299	13	(	(	PUNCT
ejde-397	299	14	2.2	2.2	NUM
ejde-397	299	15	)	)	PUNCT
ejde-397	299	16	(	(	PUNCT
ejde-397	299	17	iii	iii	X
ejde-397	299	18	)	)	PUNCT
ejde-397	299	19	the	the	DET
ejde-397	299	20	continuity	continuity	NOUN
ejde-397	299	21	of	of	ADP
ejde-397	299	22	mapping	map	VERB
ejde-397	299	23	λ	λ	PROPN
ejde-397	299	24	7→	7→	PROPN
ejde-397	299	25	(	(	PUNCT
ejde-397	299	26	λ−a)−1cx	λ−a)−1cx	PROPN
ejde-397	299	27	,	,	PUNCT
ejde-397	299	28	λ	λ	PROPN
ejde-397	299	29	∈	∈	PROPN
ejde-397	299	30	ω	ω	NOUN
ejde-397	299	31	implies	imply	VERB
ejde-397	299	32	its	its	PRON
ejde-397	299	33	analyticity	analyticity	NOUN
ejde-397	299	34	and	and	CCONJ
ejde-397	299	35	(	(	PUNCT
ejde-397	299	36	2.1	2.1	NUM
ejde-397	299	37	)	)	PUNCT
ejde-397	299	38	.	.	PUNCT
ejde-397	300	1	furthermore	furthermore	ADV
ejde-397	300	2	,	,	PUNCT
ejde-397	300	3	if	if	SCONJ
ejde-397	300	4	x	x	PRON
ejde-397	300	5	is	be	AUX
ejde-397	300	6	barreled	barrel	VERB
ejde-397	300	7	,	,	PUNCT
ejde-397	300	8	then	then	ADV
ejde-397	300	9	the	the	DET
ejde-397	300	10	continuity	continuity	NOUN
ejde-397	300	11	of	of	ADP
ejde-397	300	12	mapping	map	VERB
ejde-397	300	13	λ	λ	PROPN
ejde-397	300	14	7→	7→	PROPN
ejde-397	300	15	(	(	PUNCT
ejde-397	300	16	λ−a)−1c	λ−a)−1c	PROPN
ejde-397	300	17	,	,	PUNCT
ejde-397	300	18	λ	λ	PROPN
ejde-397	300	19	∈	∈	PROPN
ejde-397	300	20	ω	ω	NOUN
ejde-397	300	21	implies	imply	VERB
ejde-397	300	22	its	its	PRON
ejde-397	300	23	analyticity	analyticity	NOUN
ejde-397	300	24	and	and	CCONJ
ejde-397	300	25	(	(	PUNCT
ejde-397	300	26	2.2	2.2	NUM
ejde-397	300	27	)	)	PUNCT
ejde-397	300	28	.	.	PUNCT
ejde-397	301	1	it	it	PRON
ejde-397	301	2	is	be	AUX
ejde-397	301	3	well	well	ADV
ejde-397	301	4	known	know	VERB
ejde-397	301	5	that	that	SCONJ
ejde-397	301	6	ρc(a	ρc(a	NOUN
ejde-397	301	7	)	)	PUNCT
ejde-397	301	8	need	need	AUX
ejde-397	301	9	not	not	PART
ejde-397	301	10	be	be	AUX
ejde-397	301	11	an	an	DET
ejde-397	301	12	open	open	ADJ
ejde-397	301	13	subset	subset	NOUN
ejde-397	301	14	of	of	ADP
ejde-397	301	15	c	c	PROPN
ejde-397	301	16	if	if	SCONJ
ejde-397	301	17	c	c	PROPN
ejde-397	301	18	6=	6=	PROPN
ejde-397	302	1	i	i	PRON
ejde-397	302	2	and	and	CCONJ
ejde-397	302	3	a	a	PRON
ejde-397	302	4	is	be	AUX
ejde-397	302	5	a	a	DET
ejde-397	302	6	single	single	ADV
ejde-397	302	7	-	-	PUNCT
ejde-397	302	8	valued	value	VERB
ejde-397	302	9	linear	linear	NOUN
ejde-397	302	10	operator	operator	NOUN
ejde-397	302	11	(	(	PUNCT
ejde-397	302	12	cf	cf	NOUN
ejde-397	302	13	.	.	PUNCT
ejde-397	303	1	[	[	X
ejde-397	303	2	12	12	NUM
ejde-397	303	3	,	,	PUNCT
ejde-397	303	4	example	example	NOUN
ejde-397	303	5	2.5	2.5	NUM
ejde-397	303	6	]	]	PUNCT
ejde-397	303	7	)	)	PUNCT
ejde-397	303	8	and	and	CCONJ
ejde-397	303	9	that	that	SCONJ
ejde-397	303	10	ρ(a	ρ(a	PROPN
ejde-397	303	11	)	)	PUNCT
ejde-397	303	12	is	be	AUX
ejde-397	303	13	an	an	DET
ejde-397	303	14	open	open	ADJ
ejde-397	303	15	subset	subset	NOUN
ejde-397	303	16	of	of	ADP
ejde-397	303	17	c	c	PROPN
ejde-397	303	18	,	,	PUNCT
ejde-397	303	19	provided	provide	VERB
ejde-397	303	20	that	that	SCONJ
ejde-397	303	21	x	x	PRON
ejde-397	303	22	is	be	AUX
ejde-397	303	23	a	a	DET
ejde-397	303	24	banach	banach	NOUN
ejde-397	303	25	space	space	NOUN
ejde-397	303	26	and	and	CCONJ
ejde-397	303	27	a	a	PRON
ejde-397	303	28	is	be	AUX
ejde-397	303	29	an	an	DET
ejde-397	303	30	mlo	mlo	NOUN
ejde-397	303	31	in	in	ADP
ejde-397	303	32	x	x	PROPN
ejde-397	303	33	(	(	PUNCT
ejde-397	303	34	cf	cf	NOUN
ejde-397	303	35	.	.	PUNCT
ejde-397	304	1	[	[	X
ejde-397	304	2	17	17	NUM
ejde-397	304	3	,	,	PUNCT
ejde-397	304	4	theorem	theorem	VERB
ejde-397	304	5	1.6	1.6	NUM
ejde-397	304	6	]	]	PUNCT
ejde-397	304	7	)	)	PUNCT
ejde-397	304	8	.	.	PUNCT
ejde-397	305	1	the	the	DET
ejde-397	305	2	regular	regular	ADJ
ejde-397	305	3	c	c	NOUN
ejde-397	305	4	-	-	PUNCT
ejde-397	305	5	resolvent	resolvent	ADJ
ejde-397	305	6	set	set	NOUN
ejde-397	305	7	of	of	ADP
ejde-397	305	8	a	a	DET
ejde-397	305	9	,	,	PUNCT
ejde-397	305	10	ρrc(a	ρrc(a	NOUN
ejde-397	305	11	)	)	PUNCT
ejde-397	305	12	for	for	ADP
ejde-397	305	13	short	short	ADJ
ejde-397	305	14	,	,	PUNCT
ejde-397	305	15	is	be	AUX
ejde-397	305	16	defined	define	VERB
ejde-397	305	17	as	as	ADP
ejde-397	305	18	the	the	DET
ejde-397	305	19	union	union	NOUN
ejde-397	305	20	of	of	ADP
ejde-397	305	21	those	those	DET
ejde-397	305	22	complex	complex	ADJ
ejde-397	305	23	numbers	number	NOUN
ejde-397	305	24	λ	λ	NOUN
ejde-397	305	25	∈	∈	NOUN
ejde-397	305	26	ρc(a	ρc(a	NOUN
ejde-397	305	27	)	)	PUNCT
ejde-397	305	28	for	for	ADP
ejde-397	305	29	which	which	PRON
ejde-397	305	30	(	(	PUNCT
ejde-397	305	31	λ	λ	X
ejde-397	305	32	−	−	PROPN
ejde-397	305	33	a)−1c	a)−1c	PROPN
ejde-397	305	34	∈	∈	PROPN
ejde-397	305	35	r(x	r(x	PROPN
ejde-397	305	36	)	)	PUNCT
ejde-397	305	37	,	,	PUNCT
ejde-397	305	38	where	where	SCONJ
ejde-397	305	39	r(x	r(x	NOUN
ejde-397	305	40	)	)	PUNCT
ejde-397	305	41	denotes	denote	VERB
ejde-397	305	42	the	the	DET
ejde-397	305	43	set	set	NOUN
ejde-397	305	44	of	of	ADP
ejde-397	305	45	all	all	DET
ejde-397	305	46	regular	regular	ADJ
ejde-397	305	47	bounded	bounded	ADJ
ejde-397	305	48	linear	linear	PROPN
ejde-397	305	49	operators	operator	NOUN
ejde-397	305	50	a	a	DET
ejde-397	305	51	∈	∈	NOUN
ejde-397	305	52	l(x	l(x	PROPN
ejde-397	305	53	)	)	PUNCT
ejde-397	305	54	,	,	PUNCT
ejde-397	305	55	i.e.	i.e.	X
ejde-397	305	56	,	,	PUNCT
ejde-397	305	57	the	the	DET
ejde-397	305	58	operators	operator	NOUN
ejde-397	305	59	a	a	DET
ejde-397	305	60	∈	∈	NOUN
ejde-397	305	61	l(x	l(x	NOUN
ejde-397	305	62	)	)	PUNCT
ejde-397	305	63	for	for	ADP
ejde-397	305	64	which	which	PRON
ejde-397	305	65	there	there	PRON
ejde-397	305	66	exists	exist	VERB
ejde-397	305	67	a	a	DET
ejde-397	305	68	positive	positive	ADJ
ejde-397	305	69	constant	constant	ADJ
ejde-397	305	70	c	c	NOUN
ejde-397	305	71	>	>	X
ejde-397	305	72	0	0	NUM
ejde-397	305	73	such	such	ADJ
ejde-397	305	74	that	that	PRON
ejde-397	305	75	for	for	ADP
ejde-397	305	76	each	each	DET
ejde-397	305	77	seminorm	seminorm	NOUN
ejde-397	305	78	p	p	PROPN
ejde-397	305	79	∈	∈	PROPN
ejde-397	305	80	~	~	PUNCT
ejde-397	305	81	there	there	PRON
ejde-397	305	82	exists	exist	VERB
ejde-397	305	83	another	another	DET
ejde-397	305	84	seminorm	seminorm	NOUN
ejde-397	305	85	q	q	NOUN
ejde-397	305	86	∈	∈	PROPN
ejde-397	305	87	~	~	PUNCT
ejde-397	305	88	such	such	ADJ
ejde-397	305	89	that	that	DET
ejde-397	305	90	p(anx	p(anx	NOUN
ejde-397	305	91	)	)	PUNCT
ejde-397	305	92	≤	≤	NUM
ejde-397	305	93	cnq(x	cnq(x	NOUN
ejde-397	305	94	)	)	PUNCT
ejde-397	305	95	,	,	PUNCT
ejde-397	306	1	x	x	PUNCT
ejde-397	306	2	∈	∈	PROPN
ejde-397	306	3	x	x	X
ejde-397	306	4	,	,	PUNCT
ejde-397	306	5	n	n	PROPN
ejde-397	306	6	∈	∈	PROPN
ejde-397	306	7	n	n	CCONJ
ejde-397	306	8	;	;	PUNCT
ejde-397	306	9	the	the	DET
ejde-397	306	10	regular	regular	ADJ
ejde-397	306	11	resolvent	resolvent	ADJ
ejde-397	306	12	set	set	NOUN
ejde-397	306	13	of	of	ADP
ejde-397	306	14	a	a	PRON
ejde-397	306	15	,	,	PUNCT
ejde-397	306	16	ρr(a	ρr(a	NUM
ejde-397	306	17	)	)	PUNCT
ejde-397	306	18	for	for	ADP
ejde-397	306	19	short	short	ADJ
ejde-397	306	20	,	,	PUNCT
ejde-397	306	21	is	be	AUX
ejde-397	306	22	then	then	ADV
ejde-397	306	23	defined	define	VERB
ejde-397	306	24	by	by	ADP
ejde-397	306	25	ρr(a	ρr(a	NUM
ejde-397	306	26	)	)	PUNCT
ejde-397	306	27	:	:	PUNCT
ejde-397	306	28	=	=	SYM
ejde-397	306	29	ρri(a	ρri(a	X
ejde-397	306	30	)	)	PUNCT
ejde-397	306	31	.	.	PUNCT
ejde-397	307	1	by	by	ADP
ejde-397	307	2	the	the	DET
ejde-397	307	3	argumentation	argumentation	NOUN
ejde-397	307	4	contained	contain	VERB
ejde-397	307	5	in	in	ADP
ejde-397	307	6	the	the	DET
ejde-397	307	7	proof	proof	NOUN
ejde-397	307	8	of	of	ADP
ejde-397	307	9	[	[	X
ejde-397	307	10	17	17	NUM
ejde-397	307	11	,	,	PUNCT
ejde-397	307	12	theorem	theorem	VERB
ejde-397	307	13	1.6	1.6	NUM
ejde-397	307	14	]	]	PUNCT
ejde-397	307	15	,	,	PUNCT
ejde-397	307	16	it	it	PRON
ejde-397	307	17	readily	readily	ADV
ejde-397	307	18	follows	follow	VERB
ejde-397	307	19	that	that	SCONJ
ejde-397	307	20	ρr(a	ρr(a	NUM
ejde-397	307	21	)	)	PUNCT
ejde-397	307	22	is	be	AUX
ejde-397	307	23	always	always	ADV
ejde-397	307	24	an	an	DET
ejde-397	307	25	open	open	ADJ
ejde-397	307	26	subset	subset	NOUN
ejde-397	307	27	of	of	ADP
ejde-397	307	28	c.	c.	PROPN
ejde-397	307	29	the	the	DET
ejde-397	307	30	generalized	generalize	VERB
ejde-397	307	31	resolvent	resolvent	ADJ
ejde-397	307	32	equations	equation	NOUN
ejde-397	307	33	hold	hold	VERB
ejde-397	307	34	for	for	ADP
ejde-397	307	35	c	c	NOUN
ejde-397	307	36	-	-	PUNCT
ejde-397	307	37	resolvents	resolvent	NOUN
ejde-397	307	38	of	of	ADP
ejde-397	307	39	multivalued	multivalued	ADJ
ejde-397	307	40	linear	linear	ADJ
ejde-397	307	41	operators	operator	NOUN
ejde-397	307	42	;	;	PUNCT
ejde-397	307	43	more	more	ADV
ejde-397	307	44	precisely	precisely	ADV
ejde-397	307	45	,	,	PUNCT
ejde-397	307	46	we	we	PRON
ejde-397	307	47	have	have	VERB
ejde-397	307	48	the	the	DET
ejde-397	307	49	following	following	ADJ
ejde-397	307	50	theorem	theorem	NOUN
ejde-397	307	51	which	which	PRON
ejde-397	307	52	can	can	AUX
ejde-397	307	53	be	be	AUX
ejde-397	307	54	proved	prove	VERB
ejde-397	307	55	by	by	ADP
ejde-397	307	56	induction	induction	NOUN
ejde-397	307	57	.	.	PUNCT
ejde-397	308	1	theorem	theorem	VERB
ejde-397	308	2	2.6	2.6	NUM
ejde-397	308	3	.	.	PUNCT
ejde-397	309	1	(	(	PUNCT
ejde-397	309	2	i	i	NOUN
ejde-397	309	3	)	)	PUNCT
ejde-397	309	4	let	let	VERB
ejde-397	309	5	x	x	PUNCT
ejde-397	309	6	∈	∈	PROPN
ejde-397	309	7	x	x	NOUN
ejde-397	309	8	,	,	PUNCT
ejde-397	309	9	k	k	PROPN
ejde-397	309	10	∈	∈	PROPN
ejde-397	309	11	n0	n0	PROPN
ejde-397	309	12	and	and	CCONJ
ejde-397	309	13	λ	λ	PROPN
ejde-397	309	14	,	,	PUNCT
ejde-397	309	15	z	z	NOUN
ejde-397	309	16	∈	∈	PROPN
ejde-397	309	17	ρc(a	ρc(a	NOUN
ejde-397	309	18	)	)	PUNCT
ejde-397	309	19	with	with	ADP
ejde-397	309	20	z	z	PROPN
ejde-397	309	21	6=	6=	PROPN
ejde-397	309	22	λ	λ	PROPN
ejde-397	309	23	.	.	PUNCT
ejde-397	310	1	then	then	ADV
ejde-397	310	2	the	the	DET
ejde-397	310	3	following	follow	VERB
ejde-397	310	4	holds	hold	VERB
ejde-397	310	5	:(	:(	PUNCT
ejde-397	310	6	z	z	NOUN
ejde-397	310	7	−a	−a	NOUN
ejde-397	310	8	)	)	PUNCT
ejde-397	311	1	−1	−1	NOUN
ejde-397	311	2	c	c	NOUN
ejde-397	311	3	(	(	PUNCT
ejde-397	311	4	(	(	PUNCT
ejde-397	311	5	λ−a	λ−a	NOUN
ejde-397	311	6	)	)	PUNCT
ejde-397	311	7	−1	−1	NOUN
ejde-397	312	1	c	c	NOUN
ejde-397	312	2	)	)	PUNCT
ejde-397	313	1	k	k	NOUN
ejde-397	313	2	x	x	PUNCT
ejde-397	313	3	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	313	4	abstract	abstract	ADJ
ejde-397	313	5	degenerate	degenerate	ADJ
ejde-397	313	6	volterra	volterra	NOUN
ejde-397	313	7	inclusions	inclusion	NOUN
ejde-397	313	8	11	11	NUM
ejde-397	313	9	=	=	SYM
ejde-397	313	10	(	(	PUNCT
ejde-397	313	11	−1)k	−1)k	PROPN
ejde-397	313	12	(	(	PUNCT
ejde-397	313	13	z	z	NOUN
ejde-397	313	14	−	−	PROPN
ejde-397	313	15	λ)k	λ)k	NOUN
ejde-397	313	16	(	(	PUNCT
ejde-397	313	17	z	z	NOUN
ejde-397	313	18	−a	−a	NOUN
ejde-397	313	19	)	)	PUNCT
ejde-397	313	20	−1	−1	NOUN
ejde-397	313	21	ck+1x+	ck+1x+	NOUN
ejde-397	313	22	k∑	k∑	VERB
ejde-397	313	23	i=1	i=1	PROPN
ejde-397	314	1	(	(	PUNCT
ejde-397	314	2	−1)k−i	−1)k−i	X
ejde-397	314	3	(	(	PUNCT
ejde-397	314	4	(	(	PUNCT
ejde-397	314	5	λ−a)−1c	λ−a)−1c	NOUN
ejde-397	314	6	)	)	PUNCT
ejde-397	314	7	i	i	PROPN
ejde-397	314	8	ck+1−ix	ck+1−ix	VERB
ejde-397	314	9	(	(	PUNCT
ejde-397	314	10	z	z	NOUN
ejde-397	314	11	−	−	PROPN
ejde-397	314	12	λ	λ	PROPN
ejde-397	314	13	)	)	PUNCT
ejde-397	314	14	k+1−i	k+1−i	PROPN
ejde-397	314	15	.	.	PUNCT
ejde-397	315	1	(	(	PUNCT
ejde-397	315	2	ii	ii	NOUN
ejde-397	315	3	)	)	PUNCT
ejde-397	315	4	let	let	VERB
ejde-397	315	5	k	k	PROPN
ejde-397	315	6	∈	∈	PROPN
ejde-397	315	7	n0	n0	PROPN
ejde-397	315	8	,	,	PUNCT
ejde-397	315	9	x	x	PRON
ejde-397	315	10	,	,	PUNCT
ejde-397	315	11	y	y	PROPN
ejde-397	315	12	∈	∈	PROPN
ejde-397	316	1	x	x	X
ejde-397	316	2	,	,	PUNCT
ejde-397	316	3	y	y	PROPN
ejde-397	316	4	∈	∈	PROPN
ejde-397	316	5	(	(	PUNCT
ejde-397	316	6	λ0	λ0	NOUN
ejde-397	316	7	−	−	PUNCT
ejde-397	316	8	a)kx	a)kx	PROPN
ejde-397	316	9	and	and	CCONJ
ejde-397	316	10	λ0	λ0	NOUN
ejde-397	316	11	,	,	PUNCT
ejde-397	316	12	z	z	NOUN
ejde-397	316	13	∈	∈	PROPN
ejde-397	316	14	ρc(a	ρc(a	NOUN
ejde-397	316	15	)	)	PUNCT
ejde-397	316	16	with	with	ADP
ejde-397	316	17	z	z	NOUN
ejde-397	316	18	6=	6=	NOUN
ejde-397	316	19	λ0	λ0	NOUN
ejde-397	316	20	.	.	PUNCT
ejde-397	317	1	then	then	ADV
ejde-397	317	2	the	the	DET
ejde-397	317	3	following	follow	VERB
ejde-397	317	4	holds	hold	VERB
ejde-397	317	5	:(	:(	PUNCT
ejde-397	317	6	z	z	NOUN
ejde-397	317	7	−a	−a	NOUN
ejde-397	317	8	)	)	PUNCT
ejde-397	317	9	−1	−1	NOUN
ejde-397	317	10	ck+1x	ck+1x	NOUN
ejde-397	317	11	=	=	SYM
ejde-397	317	12	(	(	PUNCT
ejde-397	317	13	−1)k	−1)k	PROPN
ejde-397	317	14	(	(	PUNCT
ejde-397	317	15	z	z	NOUN
ejde-397	317	16	−	−	NOUN
ejde-397	317	17	λ0	λ0	NOUN
ejde-397	317	18	)	)	PUNCT
ejde-397	318	1	k	k	PROPN
ejde-397	318	2	(	(	PUNCT
ejde-397	318	3	z	z	NOUN
ejde-397	318	4	−a)−1	−a)−1	NOUN
ejde-397	318	5	ck+1y	ck+1y	NOUN
ejde-397	318	6	+	+	CCONJ
ejde-397	318	7	k∑	k∑	ADJ
ejde-397	318	8	i=1	i=1	X
ejde-397	318	9	(	(	PUNCT
ejde-397	318	10	−1)k−i	−1)k−i	X
ejde-397	318	11	(	(	PUNCT
ejde-397	318	12	(	(	PUNCT
ejde-397	318	13	λ0	λ0	NOUN
ejde-397	318	14	−a)−1c	−a)−1c	NUM
ejde-397	318	15	)	)	PUNCT
ejde-397	319	1	i	i	PRON
ejde-397	319	2	ck+1−iy	ck+1−iy	VERB
ejde-397	319	3	(	(	PUNCT
ejde-397	319	4	z	z	NOUN
ejde-397	319	5	−	−	NOUN
ejde-397	319	6	λ0	λ0	NOUN
ejde-397	319	7	)	)	PUNCT
ejde-397	319	8	k+1−i	k+1−i	NOUN
ejde-397	319	9	.	.	PUNCT
ejde-397	320	1	we	we	PRON
ejde-397	320	2	close	close	VERB
ejde-397	320	3	this	this	DET
ejde-397	320	4	subsection	subsection	NOUN
ejde-397	320	5	with	with	ADP
ejde-397	320	6	the	the	DET
ejde-397	320	7	observation	observation	NOUN
ejde-397	320	8	that	that	SCONJ
ejde-397	320	9	the	the	DET
ejde-397	320	10	notion	notion	NOUN
ejde-397	320	11	of	of	ADP
ejde-397	320	12	c	c	NOUN
ejde-397	320	13	-	-	PUNCT
ejde-397	320	14	resolvent	resolvent	ADJ
ejde-397	320	15	set	set	NOUN
ejde-397	320	16	of	of	ADP
ejde-397	320	17	a	a	DET
ejde-397	320	18	given	give	VERB
ejde-397	320	19	mlo	mlo	PROPN
ejde-397	320	20	can	can	AUX
ejde-397	320	21	be	be	AUX
ejde-397	320	22	also	also	ADV
ejde-397	320	23	introduced	introduce	VERB
ejde-397	320	24	in	in	ADP
ejde-397	320	25	the	the	DET
ejde-397	320	26	case	case	NOUN
ejde-397	320	27	that	that	SCONJ
ejde-397	320	28	c	c	PROPN
ejde-397	320	29	is	be	AUX
ejde-397	320	30	not	not	PART
ejde-397	320	31	injective	injective	ADJ
ejde-397	320	32	.	.	PUNCT
ejde-397	321	1	if	if	SCONJ
ejde-397	321	2	this	this	PRON
ejde-397	321	3	is	be	AUX
ejde-397	321	4	the	the	DET
ejde-397	321	5	case	case	NOUN
ejde-397	321	6	,	,	PUNCT
ejde-397	321	7	theorem	theorem	VERB
ejde-397	321	8	2.4	2.4	NUM
ejde-397	321	9	,	,	PUNCT
ejde-397	321	10	theorem	theorem	VERB
ejde-397	321	11	2.6	2.6	NUM
ejde-397	321	12	and	and	CCONJ
ejde-397	321	13	an	an	DET
ejde-397	321	14	analogue	analogue	NOUN
ejde-397	321	15	of	of	ADP
ejde-397	321	16	proposition	proposition	NOUN
ejde-397	321	17	2.5	2.5	NUM
ejde-397	321	18	continue	continue	VERB
ejde-397	321	19	to	to	PART
ejde-397	321	20	hold	hold	VERB
ejde-397	321	21	(	(	PUNCT
ejde-397	321	22	[	[	X
ejde-397	321	23	38	38	NUM
ejde-397	321	24	]	]	PUNCT
ejde-397	321	25	)	)	PUNCT
ejde-397	321	26	.	.	PUNCT
ejde-397	322	1	3	3	X
ejde-397	322	2	.	.	X
ejde-397	322	3	laplace	laplace	NOUN
ejde-397	322	4	transform	transform	NOUN
ejde-397	322	5	of	of	ADP
ejde-397	322	6	functions	function	NOUN
ejde-397	322	7	with	with	ADP
ejde-397	322	8	values	value	NOUN
ejde-397	322	9	in	in	ADP
ejde-397	322	10	sequentially	sequentially	ADV
ejde-397	322	11	complete	complete	ADJ
ejde-397	322	12	locally	locally	ADV
ejde-397	322	13	convex	convex	ADJ
ejde-397	322	14	spaces	space	NOUN
ejde-397	322	15	in	in	ADP
ejde-397	322	16	this	this	DET
ejde-397	322	17	section	section	NOUN
ejde-397	322	18	,	,	PUNCT
ejde-397	322	19	we	we	PRON
ejde-397	322	20	assume	assume	VERB
ejde-397	322	21	that	that	SCONJ
ejde-397	322	22	µ	µ	X
ejde-397	322	23	=	=	SYM
ejde-397	322	24	dt	dt	X
ejde-397	322	25	is	be	AUX
ejde-397	322	26	the	the	DET
ejde-397	322	27	lebesgue	lebesgue	ADJ
ejde-397	322	28	measure	measure	NOUN
ejde-397	322	29	on	on	ADP
ejde-397	322	30	ω	ω	PROPN
ejde-397	322	31	=	=	PUNCT
ejde-397	323	1	[	[	X
ejde-397	323	2	0,∞	0,∞	NUM
ejde-397	323	3	)	)	PUNCT
ejde-397	323	4	and	and	CCONJ
ejde-397	323	5	f	f	NOUN
ejde-397	323	6	:	:	PUNCT
ejde-397	324	1	[	[	X
ejde-397	324	2	0,∞	0,∞	NOUN
ejde-397	324	3	)	)	PUNCT
ejde-397	324	4	→	→	PUNCT
ejde-397	324	5	x	x	X
ejde-397	324	6	is	be	AUX
ejde-397	324	7	a	a	DET
ejde-397	324	8	locally	locally	ADV
ejde-397	324	9	lebesgue	lebesgue	ADJ
ejde-397	324	10	integrable	integrable	ADJ
ejde-397	324	11	function	function	NOUN
ejde-397	324	12	(	(	PUNCT
ejde-397	324	13	in	in	ADP
ejde-397	324	14	the	the	DET
ejde-397	324	15	sense	sense	NOUN
ejde-397	324	16	of	of	ADP
ejde-397	324	17	definition	definition	NOUN
ejde-397	324	18	1.2(i	1.2(i	NUM
ejde-397	324	19	)	)	PUNCT
ejde-397	324	20	)	)	PUNCT
ejde-397	324	21	.	.	PUNCT
ejde-397	325	1	as	as	ADP
ejde-397	325	2	in	in	ADP
ejde-397	325	3	the	the	DET
ejde-397	325	4	banach	banach	NOUN
ejde-397	325	5	space	space	NOUN
ejde-397	325	6	case	case	NOUN
ejde-397	325	7	,	,	PUNCT
ejde-397	325	8	we	we	PRON
ejde-397	325	9	will	will	AUX
ejde-397	325	10	denote	denote	VERB
ejde-397	325	11	the	the	DET
ejde-397	325	12	space	space	NOUN
ejde-397	325	13	consisting	consist	VERB
ejde-397	325	14	of	of	ADP
ejde-397	325	15	such	such	ADJ
ejde-397	325	16	functions	function	NOUN
ejde-397	325	17	by	by	ADP
ejde-397	325	18	l1	l1	PROPN
ejde-397	325	19	loc([0,∞	loc([0,∞	PROPN
ejde-397	325	20	)	)	PUNCT
ejde-397	325	21	:	:	PUNCT
ejde-397	326	1	x	x	X
ejde-397	326	2	)	)	PUNCT
ejde-397	326	3	;	;	PUNCT
ejde-397	326	4	similarly	similarly	ADV
ejde-397	326	5	we	we	PRON
ejde-397	326	6	define	define	VERB
ejde-397	326	7	the	the	DET
ejde-397	326	8	space	space	NOUN
ejde-397	326	9	l1([0	l1([0	NOUN
ejde-397	326	10	,	,	PUNCT
ejde-397	326	11	τ	τ	X
ejde-397	326	12	]	]	PUNCT
ejde-397	326	13	:	:	PUNCT
ejde-397	326	14	x	x	X
ejde-397	326	15	)	)	PUNCT
ejde-397	326	16	for	for	ADP
ejde-397	326	17	0	0	NUM
ejde-397	326	18	<	<	X
ejde-397	326	19	τ	τ	X
ejde-397	326	20	<	<	X
ejde-397	326	21	∞.	∞.	PROPN
ejde-397	326	22	it	it	PRON
ejde-397	326	23	is	be	AUX
ejde-397	326	24	clear	clear	ADJ
ejde-397	326	25	that	that	SCONJ
ejde-397	326	26	(	(	PUNCT
ejde-397	326	27	1.7	1.7	NUM
ejde-397	326	28	)	)	PUNCT
ejde-397	326	29	implies	imply	VERB
ejde-397	326	30	〈	〈	PROPN
ejde-397	326	31	x∗	x∗	PROPN
ejde-397	326	32	,	,	PUNCT
ejde-397	326	33	f	f	X
ejde-397	326	34	(	(	PUNCT
ejde-397	326	35	·	·	PUNCT
ejde-397	326	36	)	)	PUNCT
ejde-397	326	37	〉	〉	PROPN
ejde-397	326	38	∈	∈	PROPN
ejde-397	326	39	l1	l1	PROPN
ejde-397	326	40	loc([0,∞	loc([0,∞	PROPN
ejde-397	326	41	)	)	PUNCT
ejde-397	326	42	)	)	PUNCT
ejde-397	326	43	for	for	ADP
ejde-397	326	44	x∗	x∗	PROPN
ejde-397	326	45	∈	∈	PROPN
ejde-397	326	46	x∗.	x∗.	PUNCT
ejde-397	327	1	the	the	DET
ejde-397	327	2	first	first	ADV
ejde-397	327	3	normalized	normalize	VERB
ejde-397	327	4	antiderivative	antiderivative	ADJ
ejde-397	327	5	t	t	NOUN
ejde-397	327	6	7→	7→	NUM
ejde-397	328	1	f	f	PROPN
ejde-397	329	1	[	[	X
ejde-397	329	2	1](t	1](t	NUM
ejde-397	329	3	)	)	PUNCT
ejde-397	329	4	:	:	PUNCT
ejde-397	329	5	=	=	SYM
ejde-397	329	6	f	f	X
ejde-397	329	7	(	(	PUNCT
ejde-397	329	8	t	t	PROPN
ejde-397	329	9	)	)	PUNCT
ejde-397	329	10	:	:	PUNCT
ejde-397	330	1	=	=	SYM
ejde-397	330	2	∫	∫	PROPN
ejde-397	330	3	t	t	PROPN
ejde-397	330	4	0	0	NUM
ejde-397	330	5	f(s	f(	NOUN
ejde-397	330	6	)	)	PUNCT
ejde-397	330	7	ds	ds	PROPN
ejde-397	330	8	,	,	PUNCT
ejde-397	330	9	t	t	PROPN
ejde-397	330	10	≥	≥	NOUN
ejde-397	330	11	0	0	NUM
ejde-397	330	12	of	of	ADP
ejde-397	330	13	f	f	PROPN
ejde-397	330	14	(	(	PUNCT
ejde-397	330	15	·	·	PUNCT
ejde-397	330	16	)	)	PUNCT
ejde-397	330	17	is	be	AUX
ejde-397	330	18	continuous	continuous	ADJ
ejde-397	330	19	for	for	ADP
ejde-397	330	20	t	t	PROPN
ejde-397	330	21	≥	≥	NOUN
ejde-397	330	22	0	0	NUM
ejde-397	330	23	,	,	PUNCT
ejde-397	330	24	and	and	CCONJ
ejde-397	330	25	we	we	PRON
ejde-397	330	26	have	have	VERB
ejde-397	330	27	that	that	PRON
ejde-397	330	28	∫	∫	PROPN
ejde-397	330	29	t	t	PROPN
ejde-397	330	30	0	0	NUM
ejde-397	330	31	p(f	p(f	PROPN
ejde-397	330	32	)	)	PUNCT
ejde-397	330	33	dµ	dµ	VERB
ejde-397	330	34	<	<	X
ejde-397	330	35	∞	∞	PROPN
ejde-397	330	36	for	for	ADP
ejde-397	330	37	any	any	DET
ejde-397	330	38	p	p	NOUN
ejde-397	330	39	∈	∈	PROPN
ejde-397	330	40	~	~	PUNCT
ejde-397	330	41	and	and	CCONJ
ejde-397	330	42	t	t	PROPN
ejde-397	330	43	≥	≥	NUM
ejde-397	330	44	0	0	NUM
ejde-397	330	45	.	.	PUNCT
ejde-397	331	1	set	set	VERB
ejde-397	331	2	f	f	PROPN
ejde-397	332	1	[	[	X
ejde-397	332	2	n](t	n](t	NOUN
ejde-397	332	3	)	)	PUNCT
ejde-397	332	4	:	:	PUNCT
ejde-397	333	1	=	=	SYM
ejde-397	333	2	∫	∫	PROPN
ejde-397	334	1	t	t	PROPN
ejde-397	334	2	0	0	NUM
ejde-397	334	3	gn(t−	gn(t−	VERB
ejde-397	334	4	s)f(s	s)f(	NOUN
ejde-397	334	5	)	)	PUNCT
ejde-397	334	6	ds	ds	PROPN
ejde-397	334	7	,	,	PUNCT
ejde-397	334	8	t	t	PROPN
ejde-397	334	9	≥	≥	NUM
ejde-397	334	10	0	0	NUM
ejde-397	334	11	.	.	PUNCT
ejde-397	335	1	a	a	DET
ejde-397	335	2	few	few	ADJ
ejde-397	335	3	auxiliary	auxiliary	ADJ
ejde-397	335	4	results	result	NOUN
ejde-397	335	5	on	on	ADP
ejde-397	335	6	integration	integration	NOUN
ejde-397	335	7	in	in	ADP
ejde-397	335	8	sequentially	sequentially	ADV
ejde-397	335	9	complete	complete	ADJ
ejde-397	335	10	locally	locally	ADV
ejde-397	335	11	convex	convex	ADJ
ejde-397	335	12	spaces	space	NOUN
ejde-397	335	13	is	be	AUX
ejde-397	335	14	collected	collect	VERB
ejde-397	335	15	in	in	ADP
ejde-397	335	16	the	the	DET
ejde-397	335	17	following	following	NOUN
ejde-397	335	18	theorem	theorem	NOUN
ejde-397	335	19	,	,	PUNCT
ejde-397	335	20	which	which	PRON
ejde-397	335	21	seems	seem	VERB
ejde-397	335	22	to	to	PART
ejde-397	335	23	be	be	AUX
ejde-397	335	24	new	new	ADJ
ejde-397	335	25	and	and	CCONJ
ejde-397	335	26	not	not	PART
ejde-397	335	27	considered	consider	VERB
ejde-397	335	28	elsewhere	elsewhere	ADV
ejde-397	335	29	in	in	ADP
ejde-397	335	30	the	the	DET
ejde-397	335	31	existing	exist	VERB
ejde-397	335	32	literature	literature	NOUN
ejde-397	335	33	:	:	PUNCT
ejde-397	335	34	theorem	theorem	VERB
ejde-397	335	35	3.1	3.1	NUM
ejde-397	335	36	.	.	PUNCT
ejde-397	336	1	(	(	PUNCT
ejde-397	336	2	i	i	NOUN
ejde-397	336	3	)	)	PUNCT
ejde-397	336	4	suppose	suppose	VERB
ejde-397	336	5	that	that	SCONJ
ejde-397	336	6	g	g	PROPN
ejde-397	336	7	∈	∈	PROPN
ejde-397	336	8	c([0,∞	c([0,∞	PROPN
ejde-397	336	9	)	)	PUNCT
ejde-397	336	10	)	)	PUNCT
ejde-397	337	1	and	and	CCONJ
ejde-397	337	2	f	f	PROPN
ejde-397	337	3	∈	∈	PROPN
ejde-397	337	4	l1	l1	PROPN
ejde-397	337	5	loc([0,∞	loc([0,∞	PROPN
ejde-397	337	6	)	)	PUNCT
ejde-397	337	7	:	:	PUNCT
ejde-397	338	1	x	x	X
ejde-397	338	2	)	)	PUNCT
ejde-397	338	3	.	.	PUNCT
ejde-397	339	1	then	then	ADV
ejde-397	339	2	gf	gf	PROPN
ejde-397	339	3	∈	∈	PROPN
ejde-397	339	4	l1	l1	PROPN
ejde-397	339	5	loc([0,∞	loc([0,∞	PROPN
ejde-397	339	6	)	)	PUNCT
ejde-397	339	7	:	:	PUNCT
ejde-397	340	1	x	x	X
ejde-397	340	2	)	)	PUNCT
ejde-397	340	3	.	.	PUNCT
ejde-397	341	1	(	(	PUNCT
ejde-397	341	2	ii	ii	NOUN
ejde-397	341	3	)	)	PUNCT
ejde-397	341	4	if	if	SCONJ
ejde-397	341	5	g	g	PROPN
ejde-397	341	6	∈	∈	PROPN
ejde-397	341	7	l1	l1	PROPN
ejde-397	341	8	loc([0,∞	loc([0,∞	PROPN
ejde-397	341	9	)	)	PUNCT
ejde-397	341	10	)	)	PUNCT
ejde-397	342	1	and	and	CCONJ
ejde-397	342	2	f	f	PROPN
ejde-397	342	3	∈	∈	PROPN
ejde-397	342	4	c([0,∞	c([0,∞	PROPN
ejde-397	342	5	)	)	PUNCT
ejde-397	342	6	:	:	PUNCT
ejde-397	343	1	x	x	X
ejde-397	343	2	)	)	PUNCT
ejde-397	343	3	,	,	PUNCT
ejde-397	343	4	then	then	ADV
ejde-397	343	5	gf	gf	PROPN
ejde-397	343	6	∈	∈	PROPN
ejde-397	343	7	l1	l1	PROPN
ejde-397	343	8	loc([0,∞	loc([0,∞	PROPN
ejde-397	343	9	)	)	PUNCT
ejde-397	343	10	:	:	PUNCT
ejde-397	344	1	x	x	X
ejde-397	344	2	)	)	PUNCT
ejde-397	344	3	.	.	PUNCT
ejde-397	345	1	(	(	PUNCT
ejde-397	345	2	iii	iii	X
ejde-397	345	3	)	)	PUNCT
ejde-397	345	4	(	(	PUNCT
ejde-397	345	5	the	the	DET
ejde-397	345	6	partial	partial	ADJ
ejde-397	345	7	integration	integration	NOUN
ejde-397	345	8	)	)	PUNCT
ejde-397	345	9	suppose	suppose	VERB
ejde-397	345	10	that	that	SCONJ
ejde-397	345	11	g	g	PROPN
ejde-397	345	12	∈	∈	PROPN
ejde-397	345	13	acloc([0,∞	acloc([0,∞	PROPN
ejde-397	345	14	)	)	PUNCT
ejde-397	345	15	)	)	PUNCT
ejde-397	345	16	.	.	PUNCT
ejde-397	346	1	then	then	ADV
ejde-397	346	2	,	,	PUNCT
ejde-397	346	3	for	for	ADP
ejde-397	346	4	every	every	DET
ejde-397	346	5	τ	τ	PROPN
ejde-397	346	6	≥	≥	NOUN
ejde-397	346	7	0	0	NUM
ejde-397	346	8	,	,	PUNCT
ejde-397	346	9	we	we	PRON
ejde-397	346	10	have∫	have∫	VERB
ejde-397	346	11	τ	τ	X
ejde-397	346	12	0	0	NUM
ejde-397	346	13	g(t)f(t	g(t)f(t	NOUN
ejde-397	346	14	)	)	PUNCT
ejde-397	346	15	dt	dt	NOUN
ejde-397	347	1	=	=	PUNCT
ejde-397	347	2	g(τ)f	g(τ)f	PROPN
ejde-397	347	3	(	(	PUNCT
ejde-397	347	4	τ)−	τ)−	PROPN
ejde-397	347	5	∫	∫	PROPN
ejde-397	347	6	τ	τ	PROPN
ejde-397	347	7	0	0	NUM
ejde-397	347	8	g′(t)f	g′(t)f	PROPN
ejde-397	347	9	(	(	PUNCT
ejde-397	347	10	t	t	NOUN
ejde-397	347	11	)	)	PUNCT
ejde-397	347	12	dt	dt	PROPN
ejde-397	347	13	.	.	PUNCT
ejde-397	348	1	(	(	PUNCT
ejde-397	348	2	3.1	3.1	NUM
ejde-397	348	3	)	)	PUNCT
ejde-397	348	4	proof	proof	NOUN
ejde-397	348	5	.	.	PUNCT
ejde-397	349	1	fix	fix	VERB
ejde-397	349	2	a	a	DET
ejde-397	349	3	number	number	NOUN
ejde-397	349	4	τ	τ	X
ejde-397	349	5	∈	∈	PROPN
ejde-397	349	6	(	(	PUNCT
ejde-397	349	7	0,∞	0,∞	NOUN
ejde-397	349	8	)	)	PUNCT
ejde-397	349	9	.	.	PUNCT
ejde-397	350	1	let	let	VERB
ejde-397	350	2	(	(	PUNCT
ejde-397	350	3	fn)n∈n	fn)n∈n	NUM
ejde-397	350	4	be	be	AUX
ejde-397	350	5	a	a	DET
ejde-397	350	6	sequence	sequence	NOUN
ejde-397	350	7	of	of	ADP
ejde-397	350	8	simple	simple	ADJ
ejde-397	350	9	functions	function	NOUN
ejde-397	350	10	in	in	ADP
ejde-397	350	11	x	x	PUNCT
ejde-397	351	1	[	[	X
ejde-397	351	2	0,τ	0,τ	X
ejde-397	351	3	]	]	PUNCT
ejde-397	351	4	such	such	ADJ
ejde-397	351	5	that	that	SCONJ
ejde-397	351	6	limn→∞	limn→∞	PROPN
ejde-397	351	7	fn(t	fn(t	X
ejde-397	351	8	)	)	PUNCT
ejde-397	351	9	=	=	SYM
ejde-397	351	10	f(t	f(t	NOUN
ejde-397	351	11	)	)	PUNCT
ejde-397	351	12	a.e	a.e	PROPN
ejde-397	351	13	.	.	PROPN
ejde-397	351	14	t	t	PROPN
ejde-397	351	15	∈	∈	PROPN
ejde-397	352	1	k	k	X
ejde-397	352	2	=	=	PUNCT
ejde-397	353	1	[	[	X
ejde-397	353	2	0	0	NUM
ejde-397	353	3	,	,	PUNCT
ejde-397	353	4	τ	τ	X
ejde-397	353	5	]	]	PUNCT
ejde-397	353	6	and	and	CCONJ
ejde-397	353	7	for	for	ADP
ejde-397	353	8	all	all	DET
ejde-397	353	9	ε	ε	PROPN
ejde-397	353	10	>	>	X
ejde-397	353	11	0	0	PUNCT
ejde-397	353	12	and	and	CCONJ
ejde-397	353	13	each	each	DET
ejde-397	353	14	p	p	NOUN
ejde-397	353	15	∈	∈	PROPN
ejde-397	353	16	~	~	PUNCT
ejde-397	353	17	there	there	PRON
ejde-397	353	18	is	be	VERB
ejde-397	353	19	a	a	DET
ejde-397	353	20	number	number	NOUN
ejde-397	353	21	n0	n0	X
ejde-397	353	22	=	=	SYM
ejde-397	353	23	n0(ε	n0(ε	PROPN
ejde-397	353	24	,	,	PUNCT
ejde-397	353	25	p	p	NOUN
ejde-397	353	26	)	)	PUNCT
ejde-397	353	27	such	such	ADJ
ejde-397	353	28	that	that	SCONJ
ejde-397	353	29	(	(	PUNCT
ejde-397	353	30	1.4	1.4	NUM
ejde-397	353	31	)	)	PUNCT
ejde-397	353	32	holds	hold	VERB
ejde-397	353	33	.	.	PUNCT
ejde-397	354	1	then	then	ADV
ejde-397	354	2	∫	∫	PROPN
ejde-397	354	3	τ	τ	PROPN
ejde-397	354	4	0	0	NUM
ejde-397	354	5	f(t	f(t	NOUN
ejde-397	354	6	)	)	PUNCT
ejde-397	354	7	dt	dt	NOUN
ejde-397	355	1	=	=	SYM
ejde-397	355	2	limn→∞	limn→∞	PROPN
ejde-397	355	3	∫	∫	PROPN
ejde-397	355	4	τ	τ	X
ejde-397	355	5	0	0	NUM
ejde-397	355	6	fn(t	fn(t	NUM
ejde-397	355	7	)	)	PUNCT
ejde-397	355	8	dt	dt	PROPN
ejde-397	355	9	and	and	CCONJ
ejde-397	355	10	the	the	DET
ejde-397	355	11	sequence	sequence	NOUN
ejde-397	355	12	(	(	PUNCT
ejde-397	355	13	p(fn))n∈n	p(fn))n∈n	PROPN
ejde-397	355	14	is	be	AUX
ejde-397	355	15	convergent	convergent	NOUN
ejde-397	355	16	in	in	ADP
ejde-397	355	17	l1[0	l1[0	PROPN
ejde-397	355	18	,	,	PUNCT
ejde-397	355	19	τ	τ	X
ejde-397	355	20	]	]	PUNCT
ejde-397	355	21	.	.	PUNCT
ejde-397	356	1	by	by	ADP
ejde-397	356	2	the	the	DET
ejde-397	356	3	proof	proof	NOUN
ejde-397	356	4	of	of	ADP
ejde-397	356	5	[	[	X
ejde-397	356	6	61	61	NUM
ejde-397	356	7	,	,	PUNCT
ejde-397	356	8	proposition	proposition	NOUN
ejde-397	356	9	4.4.1	4.4.1	NUM
ejde-397	356	10	]	]	PUNCT
ejde-397	356	11	,	,	PUNCT
ejde-397	356	12	there	there	PRON
ejde-397	356	13	exists	exist	VERB
ejde-397	356	14	a	a	DET
ejde-397	356	15	sequence	sequence	NOUN
ejde-397	356	16	(	(	PUNCT
ejde-397	356	17	sn)n∈n	sn)n∈n	PROPN
ejde-397	356	18	of	of	ADP
ejde-397	356	19	simple	simple	ADJ
ejde-397	356	20	functions	function	NOUN
ejde-397	356	21	in	in	ADP
ejde-397	356	22	c[0,τ	c[0,τ	PROPN
ejde-397	356	23	]	]	PUNCT
ejde-397	356	24	such	such	ADJ
ejde-397	356	25	that	that	SCONJ
ejde-397	356	26	limn→∞	limn→∞	PROPN
ejde-397	356	27	‖sn	‖sn	NUM
ejde-397	356	28	−	−	NOUN
ejde-397	356	29	g‖l∞[0,τ	g‖l∞[0,τ	X
ejde-397	356	30	]	]	PUNCT
ejde-397	357	1	=	=	SYM
ejde-397	357	2	0	0	NUM
ejde-397	357	3	,	,	PUNCT
ejde-397	357	4	supn∈n	supn∈n	NOUN
ejde-397	357	5	‖sn‖l∞[0,τ	‖sn‖l∞[0,τ	NOUN
ejde-397	357	6	]	]	PUNCT
ejde-397	357	7	≤	≤	NUM
ejde-397	357	8	‖g‖l∞[0,τ	‖g‖l∞[0,τ	NOUN
ejde-397	357	9	]	]	PUNCT
ejde-397	357	10	and	and	CCONJ
ejde-397	357	11	that	that	SCONJ
ejde-397	357	12	for	for	ADP
ejde-397	357	13	all	all	DET
ejde-397	357	14	ε	ε	PROPN
ejde-397	357	15	>	>	PUNCT
ejde-397	357	16	0	0	PROPN
ejde-397	357	17	and	and	CCONJ
ejde-397	357	18	p	p	NOUN
ejde-397	357	19	=	=	NOUN
ejde-397	358	1	|	|	NOUN
ejde-397	358	2	·	·	PUNCT
ejde-397	358	3	|	|	ADV
ejde-397	358	4	there	there	PRON
ejde-397	358	5	is	be	VERB
ejde-397	358	6	a	a	DET
ejde-397	358	7	number	number	NOUN
ejde-397	358	8	n0	n0	X
ejde-397	358	9	=	=	SYM
ejde-397	358	10	n0(ε	n0(ε	PROPN
ejde-397	358	11	,	,	PUNCT
ejde-397	358	12	p	p	NOUN
ejde-397	358	13	)	)	PUNCT
ejde-397	358	14	such	such	ADJ
ejde-397	358	15	that	that	SCONJ
ejde-397	358	16	(	(	PUNCT
ejde-397	358	17	1.4	1.4	NUM
ejde-397	358	18	)	)	PUNCT
ejde-397	358	19	holds	hold	VERB
ejde-397	358	20	with	with	ADP
ejde-397	358	21	the	the	DET
ejde-397	358	22	functions	function	NOUN
ejde-397	358	23	fn	fn	NOUN
ejde-397	358	24	(	(	PUNCT
ejde-397	358	25	·	·	PUNCT
ejde-397	358	26	)	)	PUNCT
ejde-397	358	27	and	and	CCONJ
ejde-397	358	28	fm	fm	PROPN
ejde-397	358	29	(	(	PUNCT
ejde-397	358	30	·	·	PUNCT
ejde-397	358	31	)	)	PUNCT
ejde-397	358	32	replaced	replace	VERB
ejde-397	358	33	respectively	respectively	ADV
ejde-397	358	34	with	with	ADP
ejde-397	358	35	sn	sn	PROPN
ejde-397	358	36	(	(	PUNCT
ejde-397	358	37	·	·	PUNCT
ejde-397	358	38	)	)	PUNCT
ejde-397	358	39	and	and	CCONJ
ejde-397	358	40	sm	sm	PROPN
ejde-397	358	41	(	(	PUNCT
ejde-397	358	42	·	·	PUNCT
ejde-397	358	43	)	)	PUNCT
ejde-397	358	44	.	.	PUNCT
ejde-397	359	1	clearly	clearly	ADV
ejde-397	359	2	,	,	PUNCT
ejde-397	359	3	(	(	PUNCT
ejde-397	359	4	snfn)n∈n	snfn)n∈n	NOUN
ejde-397	359	5	is	be	AUX
ejde-397	359	6	a	a	DET
ejde-397	359	7	sequence	sequence	NOUN
ejde-397	359	8	of	of	ADP
ejde-397	359	9	simple	simple	ADJ
ejde-397	359	10	functions	function	NOUN
ejde-397	359	11	in	in	ADP
ejde-397	359	12	x	x	PUNCT
ejde-397	360	1	[	[	X
ejde-397	360	2	0,τ	0,τ	X
ejde-397	360	3	]	]	PUNCT
ejde-397	360	4	such	such	ADJ
ejde-397	360	5	that	that	SCONJ
ejde-397	360	6	12	12	NUM
ejde-397	360	7	m.	m.	NOUN
ejde-397	360	8	kostić	kostić	NOUN
ejde-397	361	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	361	2	limn→∞	limn→∞	PROPN
ejde-397	361	3	sn(t)fn(t	sn(t)fn(t	NOUN
ejde-397	361	4	)	)	PUNCT
ejde-397	361	5	=	=	SYM
ejde-397	361	6	g(t)f(t	g(t)f(t	NOUN
ejde-397	361	7	)	)	PUNCT
ejde-397	361	8	a.e	a.e	PROPN
ejde-397	361	9	.	.	PROPN
ejde-397	361	10	t	t	PROPN
ejde-397	361	11	∈	∈	PROPN
ejde-397	362	1	[	[	X
ejde-397	362	2	0	0	NUM
ejde-397	362	3	,	,	PUNCT
ejde-397	362	4	τ	τ	X
ejde-397	362	5	]	]	PUNCT
ejde-397	362	6	.	.	PUNCT
ejde-397	363	1	furthermore	furthermore	ADV
ejde-397	363	2	,	,	PUNCT
ejde-397	363	3	it	it	PRON
ejde-397	363	4	can	can	AUX
ejde-397	363	5	be	be	AUX
ejde-397	363	6	easily	easily	ADV
ejde-397	363	7	seen	see	VERB
ejde-397	363	8	that∫	that∫	NOUN
ejde-397	363	9	t	t	NOUN
ejde-397	363	10	0	0	PUNCT
ejde-397	364	1	p	p	X
ejde-397	364	2	(	(	PUNCT
ejde-397	364	3	sn(t)fn(t)−	sn(t)fn(t)−	PROPN
ejde-397	364	4	sm(t)fm(t	sm(t)fm(t	NOUN
ejde-397	364	5	)	)	PUNCT
ejde-397	364	6	)	)	PUNCT
ejde-397	365	1	dt	dt	PART
ejde-397	365	2	≤	≤	ADJ
ejde-397	365	3	‖sn‖l∞[0,τ	‖sn‖l∞[0,τ	NOUN
ejde-397	365	4	]	]	PUNCT
ejde-397	366	1	∫	∫	PROPN
ejde-397	366	2	t	t	NOUN
ejde-397	366	3	0	0	PUNCT
ejde-397	367	1	p	p	X
ejde-397	367	2	(	(	PUNCT
ejde-397	367	3	fn(t)−	fn(t)−	PROPN
ejde-397	367	4	fm(t	fm(t	NOUN
ejde-397	367	5	)	)	PUNCT
ejde-397	367	6	)	)	PUNCT
ejde-397	367	7	dt+	dt+	NOUN
ejde-397	367	8	‖sn	‖sn	NUM
ejde-397	368	1	−	−	NOUN
ejde-397	368	2	sm‖l∞[0,τ	sm‖l∞[0,τ	X
ejde-397	368	3	]	]	PUNCT
ejde-397	368	4	∫	∫	PROPN
ejde-397	368	5	t	t	NOUN
ejde-397	368	6	0	0	PUNCT
ejde-397	369	1	p	p	X
ejde-397	369	2	(	(	PUNCT
ejde-397	369	3	fm(t	fm(t	NOUN
ejde-397	369	4	)	)	PUNCT
ejde-397	369	5	)	)	PUNCT
ejde-397	370	1	dt	dt	VERB
ejde-397	370	2	≤	≤	NOUN
ejde-397	370	3	‖g‖l∞[0,τ	‖g‖l∞[0,τ	PROPN
ejde-397	370	4	]	]	X
ejde-397	371	1	∫	∫	PROPN
ejde-397	371	2	t	t	PROPN
ejde-397	371	3	0	0	PUNCT
ejde-397	372	1	p	p	X
ejde-397	372	2	(	(	PUNCT
ejde-397	372	3	fn(t)−	fn(t)−	PROPN
ejde-397	372	4	fm(t	fm(t	NOUN
ejde-397	372	5	)	)	PUNCT
ejde-397	372	6	)	)	PUNCT
ejde-397	373	1	dt	dt	PUNCT
ejde-397	374	1	+	+	CCONJ
ejde-397	374	2	(	(	PUNCT
ejde-397	374	3	‖sn	‖sn	NUM
ejde-397	374	4	−	−	NOUN
ejde-397	374	5	g‖l∞[0,τ	g‖l∞[0,τ	X
ejde-397	374	6	]	]	PUNCT
ejde-397	375	1	+	+	CCONJ
ejde-397	376	1	‖sm	‖sm	NUM
ejde-397	376	2	−	−	NOUN
ejde-397	376	3	g‖l∞[0,τ	g‖l∞[0,τ	X
ejde-397	376	4	]	]	PUNCT
ejde-397	376	5	)	)	PUNCT
ejde-397	377	1	∫	∫	PROPN
ejde-397	377	2	t	t	NOUN
ejde-397	377	3	0	0	NUM
ejde-397	378	1	p	p	X
ejde-397	378	2	(	(	PUNCT
ejde-397	378	3	fm(t	fm(t	NOUN
ejde-397	378	4	)	)	PUNCT
ejde-397	378	5	)	)	PUNCT
ejde-397	379	1	dt	dt	PROPN
ejde-397	379	2	,	,	PUNCT
ejde-397	379	3	m	m	PROPN
ejde-397	379	4	,	,	PUNCT
ejde-397	379	5	n	n	PROPN
ejde-397	379	6	∈	∈	PROPN
ejde-397	379	7	n.	n.	NOUN
ejde-397	379	8	this	this	PRON
ejde-397	379	9	proves	prove	VERB
ejde-397	379	10	(	(	PUNCT
ejde-397	379	11	i	i	NOUN
ejde-397	379	12	)	)	PUNCT
ejde-397	379	13	.	.	PUNCT
ejde-397	380	1	to	to	PART
ejde-397	380	2	prove	prove	VERB
ejde-397	380	3	(	(	PUNCT
ejde-397	380	4	ii	ii	NOUN
ejde-397	380	5	)	)	PUNCT
ejde-397	380	6	,	,	PUNCT
ejde-397	380	7	observe	observe	VERB
ejde-397	380	8	first	first	ADV
ejde-397	380	9	that	that	SCONJ
ejde-397	380	10	using	use	VERB
ejde-397	380	11	definition	definition	NOUN
ejde-397	380	12	1.1	1.1	NUM
ejde-397	380	13	we	we	PRON
ejde-397	380	14	can	can	AUX
ejde-397	380	15	directly	directly	ADV
ejde-397	380	16	prove	prove	VERB
ejde-397	380	17	that	that	SCONJ
ejde-397	380	18	a	a	DET
ejde-397	380	19	function	function	NOUN
ejde-397	380	20	g1f1	g1f1	PROPN
ejde-397	380	21	(	(	PUNCT
ejde-397	380	22	·	·	PUNCT
ejde-397	380	23	)	)	PUNCT
ejde-397	380	24	belongs	belong	VERB
ejde-397	380	25	to	to	ADP
ejde-397	380	26	the	the	DET
ejde-397	380	27	space	space	NOUN
ejde-397	380	28	l1([0	l1([0	NOUN
ejde-397	380	29	,	,	PUNCT
ejde-397	380	30	τ	τ	X
ejde-397	380	31	]	]	PUNCT
ejde-397	380	32	:	:	PUNCT
ejde-397	380	33	x	x	X
ejde-397	380	34	)	)	PUNCT
ejde-397	380	35	,	,	PUNCT
ejde-397	380	36	provided	provide	VERB
ejde-397	380	37	that	that	DET
ejde-397	380	38	f1	f1	NOUN
ejde-397	380	39	:	:	PUNCT
ejde-397	381	1	[	[	X
ejde-397	381	2	0	0	NUM
ejde-397	381	3	,	,	PUNCT
ejde-397	381	4	τ	τ	X
ejde-397	381	5	]	]	PUNCT
ejde-397	381	6	→	→	PUNCT
ejde-397	381	7	x	x	X
ejde-397	381	8	is	be	AUX
ejde-397	381	9	a	a	DET
ejde-397	381	10	simple	simple	ADJ
ejde-397	381	11	function	function	NOUN
ejde-397	381	12	and	and	CCONJ
ejde-397	381	13	g1	g1	PROPN
ejde-397	381	14	∈	∈	PROPN
ejde-397	381	15	l1[0	l1[0	PROPN
ejde-397	381	16	,	,	PUNCT
ejde-397	381	17	τ	τ	X
ejde-397	381	18	]	]	PUNCT
ejde-397	381	19	.	.	PUNCT
ejde-397	382	1	using	use	VERB
ejde-397	382	2	the	the	DET
ejde-397	382	3	arguments	argument	NOUN
ejde-397	382	4	contained	contain	VERB
ejde-397	382	5	in	in	ADP
ejde-397	382	6	the	the	DET
ejde-397	382	7	proof	proof	NOUN
ejde-397	382	8	of	of	ADP
ejde-397	382	9	[	[	X
ejde-397	382	10	61	61	NUM
ejde-397	382	11	,	,	PUNCT
ejde-397	382	12	proposition	proposition	NOUN
ejde-397	382	13	4.4.1	4.4.1	NUM
ejde-397	382	14	]	]	X
ejde-397	382	15	once	once	ADV
ejde-397	382	16	more	more	ADV
ejde-397	382	17	,	,	PUNCT
ejde-397	382	18	we	we	PRON
ejde-397	382	19	can	can	AUX
ejde-397	382	20	find	find	VERB
ejde-397	382	21	a	a	DET
ejde-397	382	22	sequence	sequence	NOUN
ejde-397	382	23	(	(	PUNCT
ejde-397	382	24	fn)n∈n	fn)n∈n	NUM
ejde-397	382	25	of	of	ADP
ejde-397	382	26	simple	simple	ADJ
ejde-397	382	27	functions	function	NOUN
ejde-397	382	28	in	in	ADP
ejde-397	382	29	x	x	PUNCT
ejde-397	383	1	[	[	X
ejde-397	383	2	0,τ	0,τ	X
ejde-397	383	3	]	]	PUNCT
ejde-397	383	4	such	such	ADJ
ejde-397	383	5	that	that	SCONJ
ejde-397	383	6	,	,	PUNCT
ejde-397	383	7	for	for	ADP
ejde-397	383	8	every	every	DET
ejde-397	383	9	p	p	PROPN
ejde-397	383	10	∈	∈	PROPN
ejde-397	383	11	~	~	NOUN
ejde-397	383	12	,	,	PUNCT
ejde-397	383	13	limn→∞	limn→∞	PRON
ejde-397	383	14	p(fn	p(fn	NOUN
ejde-397	383	15	−	−	VERB
ejde-397	383	16	f)l∞[0,τ	f)l∞[0,τ	NOUN
ejde-397	383	17	]	]	PUNCT
ejde-397	383	18	=	=	SYM
ejde-397	383	19	0	0	NUM
ejde-397	383	20	,	,	PUNCT
ejde-397	383	21	supn∈n	supn∈n	NOUN
ejde-397	383	22	p(fn)l∞[0,τ	p(fn)l∞[0,τ	NOUN
ejde-397	383	23	]	]	PUNCT
ejde-397	383	24	≤	≤	NUM
ejde-397	383	25	p(f)l∞[0,τ	p(f)l∞[0,τ	NOUN
ejde-397	383	26	]	]	PUNCT
ejde-397	383	27	and	and	CCONJ
ejde-397	383	28	that	that	SCONJ
ejde-397	383	29	for	for	ADP
ejde-397	383	30	all	all	DET
ejde-397	383	31	ε	ε	PROPN
ejde-397	383	32	>	>	X
ejde-397	383	33	0	0	PUNCT
ejde-397	384	1	there	there	PRON
ejde-397	384	2	is	be	VERB
ejde-397	384	3	a	a	DET
ejde-397	384	4	number	number	NOUN
ejde-397	384	5	n0	n0	X
ejde-397	384	6	=	=	SYM
ejde-397	384	7	n0(ε	n0(ε	PROPN
ejde-397	384	8	,	,	PUNCT
ejde-397	384	9	p	p	NOUN
ejde-397	384	10	)	)	PUNCT
ejde-397	384	11	such	such	ADJ
ejde-397	384	12	that	that	SCONJ
ejde-397	384	13	(	(	PUNCT
ejde-397	384	14	1.4	1.4	NUM
ejde-397	384	15	)	)	PUNCT
ejde-397	384	16	holds	hold	VERB
ejde-397	384	17	.	.	PUNCT
ejde-397	385	1	therefore	therefore	ADV
ejde-397	385	2	,	,	PUNCT
ejde-397	385	3	(	(	PUNCT
ejde-397	385	4	gfn)n∈n	gfn)n∈n	NOUN
ejde-397	385	5	is	be	AUX
ejde-397	385	6	a	a	DET
ejde-397	385	7	sequence	sequence	NOUN
ejde-397	385	8	in	in	ADP
ejde-397	385	9	l1([0	l1([0	NOUN
ejde-397	385	10	,	,	PUNCT
ejde-397	385	11	τ	τ	X
ejde-397	385	12	]	]	PUNCT
ejde-397	385	13	:	:	PUNCT
ejde-397	385	14	x	x	X
ejde-397	385	15	)	)	PUNCT
ejde-397	385	16	and	and	CCONJ
ejde-397	385	17	limn→∞	limn→∞	PROPN
ejde-397	385	18	g(t)fn(t	g(t)fn(t	NOUN
ejde-397	385	19	)	)	PUNCT
ejde-397	385	20	=	=	SYM
ejde-397	385	21	g(t)f(t	g(t)f(t	NOUN
ejde-397	385	22	)	)	PUNCT
ejde-397	385	23	a.e	a.e	PROPN
ejde-397	385	24	.	.	PROPN
ejde-397	385	25	t	t	PROPN
ejde-397	385	26	∈	∈	PROPN
ejde-397	386	1	[	[	X
ejde-397	386	2	0	0	NUM
ejde-397	386	3	,	,	PUNCT
ejde-397	386	4	τ	τ	PROPN
ejde-397	386	5	]	]	PUNCT
ejde-397	386	6	.	.	PUNCT
ejde-397	387	1	making	make	VERB
ejde-397	387	2	use	use	NOUN
ejde-397	387	3	of	of	ADP
ejde-397	387	4	the	the	DET
ejde-397	387	5	dominated	dominate	VERB
ejde-397	387	6	convergence	convergence	NOUN
ejde-397	387	7	theorem	theorem	NOUN
ejde-397	387	8	(	(	PUNCT
ejde-397	387	9	theorem	theorem	NOUN
ejde-397	387	10	1.3(i	1.3(i	NUM
ejde-397	387	11	)	)	PUNCT
ejde-397	387	12	)	)	PUNCT
ejde-397	387	13	,	,	PUNCT
ejde-397	387	14	we	we	PRON
ejde-397	387	15	obtain	obtain	VERB
ejde-397	387	16	that	that	DET
ejde-397	387	17	gf	gf	PROPN
ejde-397	387	18	∈	∈	PROPN
ejde-397	387	19	l1	l1	PROPN
ejde-397	387	20	loc([0,∞	loc([0,∞	PROPN
ejde-397	387	21	)	)	PUNCT
ejde-397	387	22	:	:	PUNCT
ejde-397	388	1	x	x	X
ejde-397	388	2	)	)	PUNCT
ejde-397	388	3	,	,	PUNCT
ejde-397	388	4	as	as	SCONJ
ejde-397	388	5	claimed	claim	VERB
ejde-397	388	6	.	.	PUNCT
ejde-397	389	1	by	by	ADP
ejde-397	389	2	(	(	PUNCT
ejde-397	389	3	i	i	NOUN
ejde-397	389	4	)	)	PUNCT
ejde-397	389	5	and	and	CCONJ
ejde-397	389	6	(	(	PUNCT
ejde-397	389	7	ii	ii	NOUN
ejde-397	389	8	)	)	PUNCT
ejde-397	389	9	,	,	PUNCT
ejde-397	389	10	the	the	DET
ejde-397	389	11	both	both	PRON
ejde-397	389	12	integral	integral	ADJ
ejde-397	389	13	in	in	ADP
ejde-397	389	14	(	(	PUNCT
ejde-397	389	15	3.1	3.1	NUM
ejde-397	389	16	)	)	PUNCT
ejde-397	389	17	are	be	AUX
ejde-397	389	18	well	well	ADV
ejde-397	389	19	-	-	PUNCT
ejde-397	389	20	defined	define	VERB
ejde-397	389	21	.	.	PUNCT
ejde-397	390	1	let	let	VERB
ejde-397	390	2	x∗	x∗	PROPN
ejde-397	390	3	∈	∈	PROPN
ejde-397	390	4	x∗.	x∗.	NOUN
ejde-397	390	5	using	use	VERB
ejde-397	390	6	the	the	DET
ejde-397	390	7	partial	partial	ADJ
ejde-397	390	8	integration	integration	NOUN
ejde-397	390	9	in	in	ADP
ejde-397	390	10	the	the	DET
ejde-397	390	11	lebesgue	lebesgue	NOUN
ejde-397	390	12	integral	integral	ADJ
ejde-397	390	13	and	and	CCONJ
ejde-397	390	14	(	(	PUNCT
ejde-397	390	15	1.7	1.7	NUM
ejde-397	390	16	)	)	PUNCT
ejde-397	390	17	,	,	PUNCT
ejde-397	390	18	we	we	PRON
ejde-397	390	19	obtain	obtain	VERB
ejde-397	390	20	that∫	that∫	PROPN
ejde-397	390	21	τ	τ	PROPN
ejde-397	390	22	0	0	NUM
ejde-397	390	23	g(t	g(t	PROPN
ejde-397	390	24	)	)	PUNCT
ejde-397	390	25	〈	〈	PROPN
ejde-397	390	26	x∗	x∗	NOUN
ejde-397	390	27	,	,	PUNCT
ejde-397	390	28	f(t	f(t	NOUN
ejde-397	390	29	)	)	PUNCT
ejde-397	390	30	〉	〉	NOUN
ejde-397	390	31	dt	dt	NOUN
ejde-397	390	32	=	=	SYM
ejde-397	390	33	g(τ	g(τ	PROPN
ejde-397	390	34	)	)	PUNCT
ejde-397	390	35	〈	〈	NOUN
ejde-397	390	36	x∗	x∗	PROPN
ejde-397	390	37	,	,	PUNCT
ejde-397	390	38	f	f	PROPN
ejde-397	390	39	(	(	PUNCT
ejde-397	390	40	τ	τ	PROPN
ejde-397	390	41	)	)	PUNCT
ejde-397	390	42	〉	〉	NOUN
ejde-397	390	43	−	−	NOUN
ejde-397	391	1	∫	∫	PROPN
ejde-397	392	1	τ	τ	X
ejde-397	392	2	0	0	NUM
ejde-397	392	3	g′(t	g′(t	PROPN
ejde-397	392	4	)	)	PUNCT
ejde-397	392	5	〈	〈	NOUN
ejde-397	392	6	x∗	x∗	PROPN
ejde-397	392	7	,	,	PUNCT
ejde-397	392	8	f	f	PROPN
ejde-397	392	9	(	(	PUNCT
ejde-397	392	10	t	t	NOUN
ejde-397	392	11	)	)	PUNCT
ejde-397	392	12	〉	〉	NOUN
ejde-397	392	13	dt	dt	PROPN
ejde-397	392	14	.	.	PUNCT
ejde-397	393	1	since	since	SCONJ
ejde-397	393	2	x∗	x∗	PROPN
ejde-397	393	3	was	be	AUX
ejde-397	393	4	arbitrary	arbitrary	ADJ
ejde-397	393	5	,	,	PUNCT
ejde-397	393	6	it	it	PRON
ejde-397	393	7	readily	readily	ADV
ejde-397	393	8	follows	follow	VERB
ejde-397	393	9	from	from	ADP
ejde-397	393	10	(	(	PUNCT
ejde-397	393	11	1.7	1.7	NUM
ejde-397	393	12	)	)	PUNCT
ejde-397	393	13	that	that	SCONJ
ejde-397	393	14	(	(	PUNCT
ejde-397	393	15	3.1	3.1	NUM
ejde-397	393	16	)	)	PUNCT
ejde-397	393	17	holds	hold	VERB
ejde-397	393	18	.	.	PUNCT
ejde-397	394	1	the	the	DET
ejde-397	394	2	proof	proof	NOUN
ejde-397	394	3	of	of	ADP
ejde-397	394	4	the	the	DET
ejde-397	394	5	theorem	theorem	NOUN
ejde-397	394	6	is	be	AUX
ejde-397	394	7	thereby	thereby	ADV
ejde-397	394	8	complete	complete	ADJ
ejde-397	394	9	.	.	PUNCT
ejde-397	395	1	�	�	PROPN
ejde-397	395	2	in	in	ADP
ejde-397	395	3	the	the	DET
ejde-397	395	4	remaining	remain	VERB
ejde-397	395	5	part	part	NOUN
ejde-397	395	6	of	of	ADP
ejde-397	395	7	this	this	DET
ejde-397	395	8	section	section	NOUN
ejde-397	395	9	,	,	PUNCT
ejde-397	395	10	we	we	PRON
ejde-397	395	11	are	be	AUX
ejde-397	395	12	concerned	concerned	ADJ
ejde-397	395	13	with	with	ADP
ejde-397	395	14	the	the	DET
ejde-397	395	15	existence	existence	NOUN
ejde-397	395	16	of	of	ADP
ejde-397	395	17	laplace	laplace	NOUN
ejde-397	395	18	integral	integral	ADJ
ejde-397	395	19	(	(	PUNCT
ejde-397	395	20	lf)(λ	lf)(λ	PROPN
ejde-397	395	21	)	)	PUNCT
ejde-397	395	22	:	:	PUNCT
ejde-397	395	23	=	=	PUNCT
ejde-397	395	24	f̃(λ	f̃(λ	PROPN
ejde-397	395	25	)	)	PUNCT
ejde-397	395	26	:	:	PUNCT
ejde-397	396	1	=	=	SYM
ejde-397	396	2	∫	∫	PROPN
ejde-397	396	3	∞	∞	PROPN
ejde-397	396	4	0	0	NUM
ejde-397	396	5	e−λtf(t	e−λtf(t	NUM
ejde-397	396	6	)	)	PUNCT
ejde-397	396	7	dt	dt	PUNCT
ejde-397	396	8	:	:	PUNCT
ejde-397	396	9	=	=	SYM
ejde-397	396	10	lim	lim	PROPN
ejde-397	396	11	τ→∞	τ→∞	NUM
ejde-397	396	12	∫	∫	PROPN
ejde-397	396	13	τ	τ	X
ejde-397	396	14	0	0	NUM
ejde-397	396	15	e−λtf(t	e−λtf(t	NUM
ejde-397	396	16	)	)	PUNCT
ejde-397	396	17	dt	dt	PROPN
ejde-397	396	18	,	,	PUNCT
ejde-397	396	19	for	for	ADP
ejde-397	396	20	λ	λ	PROPN
ejde-397	396	21	∈	∈	PROPN
ejde-397	396	22	c.	c.	NOUN
ejde-397	396	23	if	if	SCONJ
ejde-397	396	24	f̃(λ0	f̃(λ0	ADV
ejde-397	396	25	)	)	PUNCT
ejde-397	396	26	exists	exist	VERB
ejde-397	396	27	for	for	ADP
ejde-397	396	28	some	some	DET
ejde-397	396	29	λ0	λ0	NOUN
ejde-397	396	30	∈	∈	NOUN
ejde-397	396	31	c	c	NOUN
ejde-397	396	32	,	,	PUNCT
ejde-397	396	33	then	then	ADV
ejde-397	396	34	we	we	PRON
ejde-397	396	35	define	define	VERB
ejde-397	396	36	the	the	DET
ejde-397	396	37	abscissa	abscissa	NOUN
ejde-397	396	38	of	of	ADP
ejde-397	396	39	convergence	convergence	NOUN
ejde-397	396	40	of	of	ADP
ejde-397	396	41	f̃	f̃	PROPN
ejde-397	396	42	(	(	PUNCT
ejde-397	396	43	·	·	PUNCT
ejde-397	396	44	)	)	PUNCT
ejde-397	396	45	by	by	ADP
ejde-397	396	46	absx(f	absx(f	NOUN
ejde-397	396	47	)	)	PUNCT
ejde-397	396	48	:	:	PUNCT
ejde-397	396	49	=	=	SYM
ejde-397	396	50	inf	inf	NOUN
ejde-397	396	51	{	{	PUNCT
ejde-397	396	52	<	<	X
ejde-397	396	53	λ	λ	X
ejde-397	396	54	:	:	PUNCT
ejde-397	396	55	f̃(λ	f̃(λ	NOUN
ejde-397	396	56	)	)	PUNCT
ejde-397	396	57	exists	exist	VERB
ejde-397	396	58	}	}	PUNCT
ejde-397	396	59	;	;	PUNCT
ejde-397	396	60	otherwise	otherwise	ADV
ejde-397	396	61	,	,	PUNCT
ejde-397	396	62	absx(f	absx(f	PROPN
ejde-397	396	63	)	)	PUNCT
ejde-397	396	64	:	:	PUNCT
ejde-397	396	65	=	=	PUNCT
ejde-397	397	1	+	+	NUM
ejde-397	397	2	∞.	∞.	PROPN
ejde-397	397	3	it	it	PRON
ejde-397	397	4	is	be	AUX
ejde-397	397	5	said	say	VERB
ejde-397	397	6	that	that	SCONJ
ejde-397	397	7	f	f	PROPN
ejde-397	397	8	(	(	PUNCT
ejde-397	397	9	·	·	PUNCT
ejde-397	397	10	)	)	PUNCT
ejde-397	397	11	is	be	AUX
ejde-397	397	12	laplace	laplace	NOUN
ejde-397	397	13	transformable	transformable	NOUN
ejde-397	397	14	,	,	PUNCT
ejde-397	397	15	or	or	CCONJ
ejde-397	397	16	equivalently	equivalently	ADV
ejde-397	397	17	,	,	PUNCT
ejde-397	397	18	that	that	SCONJ
ejde-397	397	19	f	f	X
ejde-397	397	20	(	(	PUNCT
ejde-397	397	21	·	·	PUNCT
ejde-397	397	22	)	)	PUNCT
ejde-397	397	23	belongs	belong	VERB
ejde-397	397	24	to	to	ADP
ejde-397	397	25	the	the	DET
ejde-397	397	26	class	class	NOUN
ejde-397	397	27	(	(	PUNCT
ejde-397	397	28	p1)-x	p1)-x	NOUN
ejde-397	397	29	,	,	PUNCT
ejde-397	397	30	if	if	SCONJ
ejde-397	397	31	and	and	CCONJ
ejde-397	397	32	only	only	ADV
ejde-397	397	33	if	if	SCONJ
ejde-397	397	34	absx(f	absx(f	NOUN
ejde-397	397	35	)	)	PUNCT
ejde-397	397	36	<	<	AUX
ejde-397	397	37	∞.	∞.	PROPN
ejde-397	397	38	assuming	assume	VERB
ejde-397	397	39	that	that	SCONJ
ejde-397	397	40	there	there	PRON
ejde-397	397	41	exists	exist	VERB
ejde-397	397	42	a	a	DET
ejde-397	397	43	number	number	NOUN
ejde-397	397	44	ω	ω	NUM
ejde-397	397	45	∈	∈	NOUN
ejde-397	397	46	r	r	NOUN
ejde-397	397	47	such	such	ADJ
ejde-397	397	48	that	that	PRON
ejde-397	397	49	for	for	ADP
ejde-397	397	50	each	each	DET
ejde-397	397	51	seminorm	seminorm	NOUN
ejde-397	397	52	p	p	PROPN
ejde-397	397	53	∈	∈	PROPN
ejde-397	397	54	~	~	PUNCT
ejde-397	397	55	there	there	PRON
ejde-397	397	56	exists	exist	VERB
ejde-397	397	57	a	a	DET
ejde-397	397	58	number	number	NOUN
ejde-397	397	59	mp	mp	NOUN
ejde-397	397	60	>	>	X
ejde-397	397	61	0	0	PUNCT
ejde-397	398	1	satisfying	satisfy	VERB
ejde-397	398	2	that	that	SCONJ
ejde-397	398	3	p(f(t	p(f(t	NOUN
ejde-397	398	4	)	)	PUNCT
ejde-397	398	5	)	)	PUNCT
ejde-397	398	6	≤mpe	≤mpe	NUM
ejde-397	398	7	ωt	ωt	PROPN
ejde-397	398	8	,	,	PUNCT
ejde-397	398	9	t	t	PROPN
ejde-397	398	10	≥	≥	PROPN
ejde-397	398	11	0	0	NUM
ejde-397	398	12	,	,	PUNCT
ejde-397	398	13	we	we	PRON
ejde-397	398	14	define	define	VERB
ejde-397	398	15	ωx(f	ωx(f	NOUN
ejde-397	398	16	)	)	PUNCT
ejde-397	398	17	∈	∈	NOUN
ejde-397	399	1	[	[	X
ejde-397	399	2	−∞,∞	−∞,∞	X
ejde-397	399	3	)	)	PUNCT
ejde-397	399	4	as	as	ADP
ejde-397	399	5	the	the	DET
ejde-397	399	6	infimum	infimum	NOUN
ejde-397	399	7	of	of	ADP
ejde-397	399	8	all	all	DET
ejde-397	399	9	numbers	number	NOUN
ejde-397	399	10	ω	ω	X
ejde-397	399	11	∈	∈	NOUN
ejde-397	399	12	r	r	NOUN
ejde-397	399	13	with	with	ADP
ejde-397	399	14	the	the	DET
ejde-397	399	15	above	above	ADJ
ejde-397	399	16	property	property	NOUN
ejde-397	399	17	;	;	PUNCT
ejde-397	399	18	if	if	SCONJ
ejde-397	399	19	there	there	PRON
ejde-397	399	20	is	be	VERB
ejde-397	399	21	no	no	DET
ejde-397	399	22	such	such	DET
ejde-397	399	23	a	a	DET
ejde-397	399	24	number	number	NOUN
ejde-397	399	25	ω	ω	NUM
ejde-397	399	26	∈	∈	PROPN
ejde-397	399	27	r	r	NOUN
ejde-397	399	28	,	,	PUNCT
ejde-397	399	29	then	then	ADV
ejde-397	399	30	we	we	PRON
ejde-397	399	31	define	define	VERB
ejde-397	399	32	ωx(f	ωx(f	NOUN
ejde-397	399	33	)	)	PUNCT
ejde-397	399	34	:	:	PUNCT
ejde-397	400	1	=	=	PUNCT
ejde-397	400	2	+	+	NOUN
ejde-397	400	3	∞.	∞.	PROPN
ejde-397	400	4	further	far	ADV
ejde-397	400	5	on	on	ADV
ejde-397	400	6	,	,	PUNCT
ejde-397	400	7	we	we	PRON
ejde-397	400	8	abbreviate	abbreviate	VERB
ejde-397	400	9	ωx(f	ωx(f	NOUN
ejde-397	400	10	)	)	PUNCT
ejde-397	400	11	(	(	PUNCT
ejde-397	400	12	absx(f	absx(f	NOUN
ejde-397	400	13	)	)	PUNCT
ejde-397	400	14	)	)	PUNCT
ejde-397	400	15	to	to	ADP
ejde-397	400	16	ω(f	ω(f	ADV
ejde-397	400	17	)	)	PUNCT
ejde-397	400	18	(	(	PUNCT
ejde-397	400	19	abs(f	abs(f	PROPN
ejde-397	400	20	)	)	PUNCT
ejde-397	400	21	)	)	PUNCT
ejde-397	400	22	,	,	PUNCT
ejde-397	400	23	if	if	SCONJ
ejde-397	400	24	there	there	PRON
ejde-397	400	25	is	be	VERB
ejde-397	400	26	no	no	DET
ejde-397	400	27	risk	risk	NOUN
ejde-397	400	28	for	for	ADP
ejde-397	400	29	confusion	confusion	NOUN
ejde-397	400	30	.	.	PUNCT
ejde-397	401	1	define	define	VERB
ejde-397	401	2	w	w	PROPN
ejde-397	401	3	abs(f	abs(f	PROPN
ejde-397	401	4	)	)	PUNCT
ejde-397	401	5	:	:	PUNCT
ejde-397	401	6	=	=	SYM
ejde-397	401	7	inf	inf	NOUN
ejde-397	401	8	{	{	PUNCT
ejde-397	401	9	λ	λ	X
ejde-397	401	10	∈	∈	NOUN
ejde-397	401	11	r	r	NOUN
ejde-397	401	12	:	:	PUNCT
ejde-397	401	13	sup	sup	VERB
ejde-397	401	14	t>0	t>0	NOUN
ejde-397	401	15	∣∣∫	∣∣∫	NOUN
ejde-397	401	16	t	t	NOUN
ejde-397	401	17	0	0	PUNCT
ejde-397	401	18	e−λs	e−λ	VERB
ejde-397	401	19	〈	〈	PROPN
ejde-397	401	20	x∗	x∗	NOUN
ejde-397	401	21	,	,	PUNCT
ejde-397	401	22	f(s	f(s	ADV
ejde-397	401	23	)	)	PUNCT
ejde-397	401	24	〉	〉	NOUN
ejde-397	401	25	ds	ds	X
ejde-397	401	26	∣∣	∣∣	NUM
ejde-397	401	27	<	<	X
ejde-397	401	28	∞	∞	NUM
ejde-397	401	29	for	for	ADP
ejde-397	401	30	all	all	DET
ejde-397	401	31	x∗	x∗	PROPN
ejde-397	401	32	∈	∈	PROPN
ejde-397	401	33	x∗	x∗	PROPN
ejde-397	401	34	}	}	PUNCT
ejde-397	401	35	,	,	PUNCT
ejde-397	401	36	f∞	f∞	X
ejde-397	401	37	:	:	PUNCT
ejde-397	401	38	=	=	SYM
ejde-397	401	39	limτ→∞	limτ→∞	ADJ
ejde-397	401	40	f	f	X
ejde-397	401	41	(	(	PUNCT
ejde-397	401	42	τ	τ	PROPN
ejde-397	401	43	)	)	PUNCT
ejde-397	401	44	,	,	PUNCT
ejde-397	401	45	if	if	SCONJ
ejde-397	401	46	the	the	DET
ejde-397	401	47	limit	limit	NOUN
ejde-397	401	48	exists	exist	VERB
ejde-397	401	49	in	in	ADP
ejde-397	401	50	x	x	NOUN
ejde-397	401	51	,	,	PUNCT
ejde-397	401	52	and	and	CCONJ
ejde-397	401	53	f∞	f∞	NOUN
ejde-397	401	54	:	:	PUNCT
ejde-397	401	55	=	=	SYM
ejde-397	401	56	0	0	NUM
ejde-397	401	57	,	,	PUNCT
ejde-397	401	58	otherwise	otherwise	ADV
ejde-397	401	59	.	.	PUNCT
ejde-397	402	1	keeping	keep	VERB
ejde-397	402	2	in	in	ADP
ejde-397	402	3	mind	mind	NOUN
ejde-397	402	4	theorem	theorem	VERB
ejde-397	402	5	3.1	3.1	NUM
ejde-397	402	6	,	,	PUNCT
ejde-397	402	7	we	we	PRON
ejde-397	402	8	can	can	AUX
ejde-397	402	9	repeat	repeat	VERB
ejde-397	402	10	literally	literally	ADV
ejde-397	402	11	the	the	DET
ejde-397	402	12	argumentation	argumentation	NOUN
ejde-397	402	13	from	from	ADP
ejde-397	402	14	[	[	X
ejde-397	402	15	1	1	NUM
ejde-397	402	16	,	,	PUNCT
ejde-397	402	17	section	section	NOUN
ejde-397	402	18	1.4	1.4	NUM
ejde-397	402	19	,	,	PUNCT
ejde-397	402	20	pp	pp	ADJ
ejde-397	402	21	.	.	PUNCT
ejde-397	403	1	27	27	NUM
ejde-397	403	2	-	-	SYM
ejde-397	403	3	30	30	NUM
ejde-397	403	4	]	]	PUNCT
ejde-397	403	5	in	in	ADP
ejde-397	403	6	order	order	NOUN
ejde-397	403	7	to	to	PART
ejde-397	403	8	see	see	VERB
ejde-397	403	9	that	that	SCONJ
ejde-397	403	10	the	the	DET
ejde-397	403	11	following	follow	VERB
ejde-397	403	12	theorem	theorem	NOUN
ejde-397	403	13	holds	hold	VERB
ejde-397	403	14	good	good	ADJ
ejde-397	403	15	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	403	16	abstract	abstract	ADJ
ejde-397	403	17	degenerate	degenerate	ADJ
ejde-397	403	18	volterra	volterra	NOUN
ejde-397	403	19	inclusions	inclusion	NOUN
ejde-397	403	20	13	13	NUM
ejde-397	403	21	(	(	PUNCT
ejde-397	403	22	the	the	DET
ejde-397	403	23	only	only	ADJ
ejde-397	403	24	essential	essential	ADJ
ejde-397	403	25	difference	difference	NOUN
ejde-397	403	26	occurs	occur	VERB
ejde-397	403	27	on	on	ADP
ejde-397	403	28	l.	l.	PROPN
ejde-397	403	29	6	6	NUM
ejde-397	403	30	,	,	PUNCT
ejde-397	403	31	p.	p.	NOUN
ejde-397	403	32	29	29	NUM
ejde-397	403	33	,	,	PUNCT
ejde-397	403	34	where	where	SCONJ
ejde-397	403	35	we	we	PRON
ejde-397	403	36	can	can	AUX
ejde-397	403	37	use	use	VERB
ejde-397	403	38	[	[	PUNCT
ejde-397	403	39	62	62	NUM
ejde-397	403	40	,	,	PUNCT
ejde-397	403	41	mackey	mackey	PROPN
ejde-397	403	42	’s	’s	PART
ejde-397	403	43	theorem	theorem	VERB
ejde-397	403	44	23.15	23.15	NUM
ejde-397	403	45	]	]	PUNCT
ejde-397	403	46	in	in	ADP
ejde-397	403	47	place	place	NOUN
ejde-397	403	48	of	of	ADP
ejde-397	403	49	the	the	DET
ejde-397	403	50	uniform	uniform	PROPN
ejde-397	403	51	boundedness	boundedness	PROPN
ejde-397	403	52	principle	principle	NOUN
ejde-397	403	53	):	):	PUNCT
ejde-397	403	54	theorem	theorem	ADJ
ejde-397	403	55	3.2	3.2	NUM
ejde-397	403	56	.	.	PUNCT
ejde-397	404	1	let	let	VERB
ejde-397	404	2	f	f	PROPN
ejde-397	404	3	∈	∈	PROPN
ejde-397	404	4	l1	l1	PROPN
ejde-397	404	5	loc([0,∞	loc([0,∞	PROPN
ejde-397	404	6	)	)	PUNCT
ejde-397	404	7	:	:	PUNCT
ejde-397	405	1	x	x	X
ejde-397	405	2	)	)	PUNCT
ejde-397	405	3	.	.	PUNCT
ejde-397	406	1	then	then	ADV
ejde-397	406	2	the	the	DET
ejde-397	406	3	following	follow	VERB
ejde-397	406	4	holds	hold	VERB
ejde-397	406	5	:	:	PUNCT
ejde-397	406	6	(	(	PUNCT
ejde-397	406	7	i	i	NOUN
ejde-397	406	8	)	)	PUNCT
ejde-397	406	9	the	the	DET
ejde-397	406	10	laplace	laplace	NOUN
ejde-397	406	11	integral	integral	ADJ
ejde-397	406	12	f̃(λ	f̃(λ	PROPN
ejde-397	406	13	)	)	PUNCT
ejde-397	406	14	converges	converge	VERB
ejde-397	406	15	if	if	SCONJ
ejde-397	406	16	<	<	X
ejde-397	406	17	λ	λ	X
ejde-397	406	18	>	>	X
ejde-397	406	19	abs(f	abs(f	PROPN
ejde-397	406	20	)	)	PUNCT
ejde-397	406	21	and	and	CCONJ
ejde-397	406	22	diverges	diverge	VERB
ejde-397	406	23	if	if	SCONJ
ejde-397	406	24	<	<	X
ejde-397	406	25	λ	λ	X
ejde-397	406	26	<	<	X
ejde-397	406	27	abs(f	abs(f	PROPN
ejde-397	406	28	)	)	PUNCT
ejde-397	406	29	.	.	PUNCT
ejde-397	407	1	if	if	SCONJ
ejde-397	407	2	<	<	X
ejde-397	407	3	λ	λ	X
ejde-397	407	4	=	=	SYM
ejde-397	407	5	abs(f	abs(f	PROPN
ejde-397	407	6	)	)	PUNCT
ejde-397	407	7	,	,	PUNCT
ejde-397	407	8	then	then	ADV
ejde-397	407	9	the	the	DET
ejde-397	407	10	laplace	laplace	NOUN
ejde-397	407	11	integral	integral	ADJ
ejde-397	407	12	may	may	NOUN
ejde-397	407	13	or	or	CCONJ
ejde-397	407	14	may	may	AUX
ejde-397	407	15	not	not	PART
ejde-397	407	16	be	be	AUX
ejde-397	407	17	convergent	convergent	ADJ
ejde-397	407	18	.	.	PUNCT
ejde-397	408	1	(	(	PUNCT
ejde-397	408	2	ii	ii	NOUN
ejde-397	408	3	)	)	PUNCT
ejde-397	408	4	w	w	PROPN
ejde-397	408	5	abs(f	abs(f	PROPN
ejde-397	408	6	)	)	PUNCT
ejde-397	408	7	=	=	SYM
ejde-397	408	8	abs(f	abs(f	PROPN
ejde-397	408	9	)	)	PUNCT
ejde-397	408	10	.	.	PUNCT
ejde-397	409	1	(	(	PUNCT
ejde-397	409	2	iii	iii	X
ejde-397	409	3	)	)	PUNCT
ejde-397	409	4	suppose	suppose	VERB
ejde-397	409	5	that	that	SCONJ
ejde-397	409	6	λ	λ	PROPN
ejde-397	409	7	∈	∈	PROPN
ejde-397	409	8	c	c	NOUN
ejde-397	409	9	and	and	CCONJ
ejde-397	409	10	the	the	DET
ejde-397	409	11	limit	limit	NOUN
ejde-397	409	12	limτ→∞	limτ→∞	PROPN
ejde-397	409	13	∫	∫	PROPN
ejde-397	409	14	t	t	PROPN
ejde-397	409	15	0	0	NUM
ejde-397	409	16	e−λsp(f(s	e−λsp(f(s	NUM
ejde-397	409	17	)	)	PUNCT
ejde-397	409	18	)	)	PUNCT
ejde-397	410	1	ds	ds	NOUN
ejde-397	410	2	exists	exist	VERB
ejde-397	410	3	for	for	ADP
ejde-397	410	4	any	any	DET
ejde-397	410	5	p	p	PROPN
ejde-397	410	6	∈	∈	PROPN
ejde-397	410	7	~.	~.	X
ejde-397	410	8	then	then	ADV
ejde-397	410	9	f̃(λ	f̃(λ	PROPN
ejde-397	410	10	)	)	PUNCT
ejde-397	410	11	exists	exist	VERB
ejde-397	410	12	,	,	PUNCT
ejde-397	410	13	as	as	ADV
ejde-397	410	14	well	well	ADV
ejde-397	410	15	.	.	PUNCT
ejde-397	411	1	(	(	PUNCT
ejde-397	411	2	iv	iv	X
ejde-397	411	3	)	)	PUNCT
ejde-397	411	4	we	we	PRON
ejde-397	411	5	have	have	AUX
ejde-397	411	6	abs(f	abs(f	PROPN
ejde-397	411	7	)	)	PUNCT
ejde-397	411	8	≤	≤	NOUN
ejde-397	411	9	abs(p(f	abs(p(f	PROPN
ejde-397	411	10	)	)	PUNCT
ejde-397	411	11	)	)	PUNCT
ejde-397	412	1	≤	≤	NOUN
ejde-397	412	2	ω(f	ω(f	NUM
ejde-397	412	3	)	)	PUNCT
ejde-397	412	4	,	,	PUNCT
ejde-397	412	5	p	p	PROPN
ejde-397	412	6	∈	∈	PROPN
ejde-397	412	7	~.	~.	PUNCT
ejde-397	412	8	in	in	ADP
ejde-397	412	9	general	general	ADJ
ejde-397	412	10	,	,	PUNCT
ejde-397	412	11	any	any	PRON
ejde-397	412	12	of	of	ADP
ejde-397	412	13	these	these	DET
ejde-397	412	14	two	two	NUM
ejde-397	412	15	inequalities	inequality	NOUN
ejde-397	412	16	can	can	AUX
ejde-397	412	17	be	be	AUX
ejde-397	412	18	strict	strict	ADJ
ejde-397	412	19	.	.	PUNCT
ejde-397	413	1	(	(	PUNCT
ejde-397	413	2	v	v	X
ejde-397	413	3	)	)	PUNCT
ejde-397	413	4	we	we	PRON
ejde-397	413	5	have	have	AUX
ejde-397	413	6	abs(f	abs(f	VERB
ejde-397	413	7	)	)	PUNCT
ejde-397	414	1	=	=	SYM
ejde-397	414	2	ω	ω	PROPN
ejde-397	414	3	(	(	PUNCT
ejde-397	414	4	f	f	PROPN
ejde-397	414	5	−	−	PROPN
ejde-397	414	6	f∞	f∞	X
ejde-397	414	7	)	)	PUNCT
ejde-397	414	8	,	,	PUNCT
ejde-397	414	9	(	(	PUNCT
ejde-397	414	10	3.2	3.2	NUM
ejde-397	414	11	)	)	PUNCT
ejde-397	414	12	f̃(λ	f̃(λ	NOUN
ejde-397	414	13	)	)	PUNCT
ejde-397	414	14	=	=	SYM
ejde-397	415	1	f∞	f∞	X
ejde-397	415	2	+	+	CCONJ
ejde-397	415	3	λ	λ	PROPN
ejde-397	415	4	∫	∫	PROPN
ejde-397	415	5	∞	∞	PROPN
ejde-397	415	6	0	0	PROPN
ejde-397	415	7	e−λt	e−λt	NOUN
ejde-397	415	8	(	(	PUNCT
ejde-397	415	9	f	f	PROPN
ejde-397	415	10	(	(	PUNCT
ejde-397	415	11	t)−	t)−	PROPN
ejde-397	415	12	f∞	f∞	X
ejde-397	415	13	)	)	PUNCT
ejde-397	415	14	dt	dt	PROPN
ejde-397	415	15	,	,	PUNCT
ejde-397	415	16	<	<	X
ejde-397	415	17	λ	λ	X
ejde-397	415	18	>	>	X
ejde-397	415	19	ω	ω	PROPN
ejde-397	415	20	(	(	PUNCT
ejde-397	415	21	f	f	PROPN
ejde-397	415	22	−	−	PROPN
ejde-397	415	23	f∞	f∞	X
ejde-397	415	24	)	)	PUNCT
ejde-397	415	25	,	,	PUNCT
ejde-397	415	26	(	(	PUNCT
ejde-397	415	27	3.3	3.3	NUM
ejde-397	415	28	)	)	PUNCT
ejde-397	415	29	f̃(λ	f̃(λ	NOUN
ejde-397	415	30	)	)	PUNCT
ejde-397	415	31	=	=	PUNCT
ejde-397	416	1	λf̃	λf̃	X
ejde-397	416	2	(	(	PUNCT
ejde-397	416	3	λ	λ	NOUN
ejde-397	416	4	)	)	PUNCT
ejde-397	416	5	,	,	PUNCT
ejde-397	416	6	<	<	X
ejde-397	416	7	λ	λ	X
ejde-397	416	8	>	>	X
ejde-397	416	9	max(abs(f	max(abs(f	NUM
ejde-397	416	10	)	)	PUNCT
ejde-397	416	11	,	,	PUNCT
ejde-397	416	12	0	0	NUM
ejde-397	416	13	)	)	PUNCT
ejde-397	416	14	(	(	PUNCT
ejde-397	416	15	3.4	3.4	NUM
ejde-397	416	16	)	)	PUNCT
ejde-397	416	17	and	and	CCONJ
ejde-397	416	18	abs(f	abs(f	PROPN
ejde-397	416	19	)	)	PUNCT
ejde-397	416	20	≤	≤	NUM
ejde-397	416	21	ω	ω	NUM
ejde-397	416	22	⇔	⇔	X
ejde-397	416	23	ω(f	ω(f	PROPN
ejde-397	416	24	)	)	PUNCT
ejde-397	417	1	≤	≤	NUM
ejde-397	417	2	ω	ω	X
ejde-397	417	3	(	(	PUNCT
ejde-397	417	4	if	if	SCONJ
ejde-397	417	5	ω	ω	PROPN
ejde-397	417	6	≥	≥	NOUN
ejde-397	417	7	0	0	NUM
ejde-397	417	8	)	)	PUNCT
ejde-397	417	9	.	.	PUNCT
ejde-397	418	1	in	in	ADP
ejde-397	418	2	particular	particular	ADJ
ejde-397	418	3	,	,	PUNCT
ejde-397	418	4	f	f	X
ejde-397	418	5	(	(	PUNCT
ejde-397	418	6	·	·	PUNCT
ejde-397	418	7	)	)	PUNCT
ejde-397	418	8	is	be	AUX
ejde-397	418	9	laplace	laplace	NOUN
ejde-397	418	10	transformable	transformable	NOUN
ejde-397	419	1	if	if	SCONJ
ejde-397	419	2	and	and	CCONJ
ejde-397	419	3	only	only	ADV
ejde-397	419	4	if	if	SCONJ
ejde-397	419	5	ω(f	ω(f	NOUN
ejde-397	419	6	)	)	PUNCT
ejde-397	419	7	<	<	AUX
ejde-397	419	8	∞.	∞.	PROPN
ejde-397	419	9	recall	recall	VERB
ejde-397	419	10	[	[	X
ejde-397	419	11	79	79	NUM
ejde-397	419	12	]	]	PUNCT
ejde-397	419	13	,	,	PUNCT
ejde-397	419	14	a	a	DET
ejde-397	419	15	function	function	NOUN
ejde-397	419	16	h	h	NOUN
ejde-397	419	17	(	(	PUNCT
ejde-397	419	18	·	·	PUNCT
ejde-397	419	19	)	)	PUNCT
ejde-397	419	20	belongs	belong	VERB
ejde-397	419	21	to	to	ADP
ejde-397	419	22	the	the	DET
ejde-397	419	23	class	class	NOUN
ejde-397	419	24	lt	lt	NOUN
ejde-397	419	25	−x	−x	NOUN
ejde-397	419	26	if	if	SCONJ
ejde-397	419	27	and	and	CCONJ
ejde-397	419	28	only	only	ADV
ejde-397	419	29	if	if	SCONJ
ejde-397	419	30	there	there	PRON
ejde-397	419	31	exist	exist	VERB
ejde-397	419	32	a	a	DET
ejde-397	419	33	function	function	NOUN
ejde-397	419	34	g	g	PROPN
ejde-397	419	35	∈	∈	PROPN
ejde-397	419	36	c([0,∞	c([0,∞	PROPN
ejde-397	419	37	)	)	PUNCT
ejde-397	419	38	:	:	PUNCT
ejde-397	420	1	x	x	X
ejde-397	420	2	)	)	PUNCT
ejde-397	420	3	and	and	CCONJ
ejde-397	420	4	a	a	DET
ejde-397	420	5	number	number	NOUN
ejde-397	420	6	ω	ω	NUM
ejde-397	420	7	∈	∈	NOUN
ejde-397	420	8	r	r	NOUN
ejde-397	420	9	such	such	ADJ
ejde-397	420	10	that	that	DET
ejde-397	420	11	ω(g	ω(g	NOUN
ejde-397	420	12	)	)	PUNCT
ejde-397	420	13	≤	≤	NOUN
ejde-397	421	1	ω	ω	NUM
ejde-397	421	2	<	<	X
ejde-397	421	3	∞	∞	PROPN
ejde-397	421	4	and	and	CCONJ
ejde-397	421	5	h(λ	h(λ	PROPN
ejde-397	421	6	)	)	PUNCT
ejde-397	422	1	=	=	PRON
ejde-397	422	2	(	(	PUNCT
ejde-397	422	3	lg)(λ	lg)(λ	NOUN
ejde-397	422	4	)	)	PUNCT
ejde-397	422	5	for	for	ADP
ejde-397	422	6	λ	λ	PROPN
ejde-397	422	7	>	>	X
ejde-397	422	8	ω	ω	PROPN
ejde-397	422	9	;	;	PUNCT
ejde-397	422	10	as	as	SCONJ
ejde-397	422	11	observed	observe	VERB
ejde-397	422	12	in	in	ADP
ejde-397	422	13	[	[	X
ejde-397	422	14	36	36	NUM
ejde-397	422	15	,	,	PUNCT
ejde-397	422	16	section	section	NOUN
ejde-397	422	17	1.2	1.2	NUM
ejde-397	422	18	]	]	PUNCT
ejde-397	422	19	,	,	PUNCT
ejde-397	422	20	the	the	DET
ejde-397	422	21	assumption	assumption	NOUN
ejde-397	422	22	h	h	NOUN
ejde-397	422	23	∈	∈	PROPN
ejde-397	422	24	lt	lt	DET
ejde-397	422	25	−	−	NOUN
ejde-397	422	26	x	x	PRON
ejde-397	422	27	immediately	immediately	ADV
ejde-397	422	28	implies	imply	VERB
ejde-397	422	29	that	that	SCONJ
ejde-397	422	30	the	the	DET
ejde-397	422	31	function	function	NOUN
ejde-397	422	32	λ	λ	PROPN
ejde-397	422	33	7→	7→	NUM
ejde-397	422	34	h(λ	h(λ	NOUN
ejde-397	422	35	)	)	PUNCT
ejde-397	422	36	,	,	PUNCT
ejde-397	422	37	λ	λ	X
ejde-397	422	38	>	>	X
ejde-397	422	39	ω	ω	PROPN
ejde-397	422	40	can	can	AUX
ejde-397	422	41	be	be	AUX
ejde-397	422	42	analytically	analytically	ADV
ejde-397	422	43	extended	extend	VERB
ejde-397	422	44	to	to	ADP
ejde-397	422	45	the	the	DET
ejde-397	422	46	right	right	ADJ
ejde-397	422	47	half	half	ADJ
ejde-397	422	48	plane	plane	NOUN
ejde-397	422	49	{	{	PUNCT
ejde-397	422	50	λ	λ	X
ejde-397	422	51	∈	∈	NOUN
ejde-397	422	52	c	c	NOUN
ejde-397	422	53	:	:	PUNCT
ejde-397	422	54	<	<	X
ejde-397	422	55	λ	λ	X
ejde-397	422	56	>	>	X
ejde-397	422	57	ω	ω	PROPN
ejde-397	422	58	}	}	PUNCT
ejde-397	422	59	.	.	PUNCT
ejde-397	423	1	in	in	ADP
ejde-397	423	2	the	the	DET
ejde-397	423	3	sequel	sequel	NOUN
ejde-397	423	4	,	,	PUNCT
ejde-397	423	5	the	the	DET
ejde-397	423	6	set	set	NOUN
ejde-397	423	7	of	of	ADP
ejde-397	423	8	all	all	DET
ejde-397	423	9	originals	original	NOUN
ejde-397	423	10	g	g	PROPN
ejde-397	423	11	(	(	PUNCT
ejde-397	423	12	·	·	PUNCT
ejde-397	423	13	)	)	PUNCT
ejde-397	423	14	whose	whose	DET
ejde-397	423	15	laplace	laplace	NOUN
ejde-397	423	16	transform	transform	NOUN
ejde-397	423	17	belongs	belong	VERB
ejde-397	423	18	to	to	ADP
ejde-397	423	19	the	the	DET
ejde-397	423	20	class	class	NOUN
ejde-397	423	21	lt	lt	NOUN
ejde-397	423	22	−x	−x	NOUN
ejde-397	423	23	will	will	AUX
ejde-397	423	24	be	be	AUX
ejde-397	423	25	abbreviated	abbreviate	VERB
ejde-397	423	26	to	to	ADP
ejde-397	423	27	ltor−x	ltor−x	PROPN
ejde-397	423	28	.	.	PUNCT
ejde-397	424	1	keeping	keep	VERB
ejde-397	424	2	this	this	DET
ejde-397	424	3	observation	observation	NOUN
ejde-397	424	4	and	and	CCONJ
ejde-397	424	5	the	the	DET
ejde-397	424	6	equations	equation	NOUN
ejde-397	424	7	(	(	PUNCT
ejde-397	424	8	3.2)-(3.3	3.2)-(3.3	NUM
ejde-397	424	9	)	)	PUNCT
ejde-397	424	10	in	in	ADP
ejde-397	424	11	mind	mind	NOUN
ejde-397	424	12	,	,	PUNCT
ejde-397	424	13	we	we	PRON
ejde-397	424	14	can	can	AUX
ejde-397	424	15	simply	simply	ADV
ejde-397	424	16	prove	prove	VERB
ejde-397	424	17	that	that	SCONJ
ejde-397	424	18	the	the	DET
ejde-397	424	19	mapping	mapping	NOUN
ejde-397	424	20	λ	λ	PROPN
ejde-397	424	21	7→	7→	PROPN
ejde-397	424	22	f̃(λ	f̃(λ	PROPN
ejde-397	424	23	)	)	PUNCT
ejde-397	424	24	,	,	PUNCT
ejde-397	424	25	<	<	X
ejde-397	424	26	λ	λ	X
ejde-397	424	27	>	>	X
ejde-397	424	28	abs(f	abs(f	PROPN
ejde-397	424	29	)	)	PUNCT
ejde-397	424	30	is	be	AUX
ejde-397	424	31	analytic	analytic	ADJ
ejde-397	424	32	,	,	PUNCT
ejde-397	424	33	provided	provide	VERB
ejde-397	424	34	that	that	SCONJ
ejde-397	424	35	f	f	PROPN
ejde-397	424	36	∈	∈	PROPN
ejde-397	424	37	(	(	PUNCT
ejde-397	424	38	p1)−x	p1)−x	PROPN
ejde-397	424	39	.	.	PUNCT
ejde-397	424	40	if	if	SCONJ
ejde-397	424	41	this	this	PRON
ejde-397	424	42	is	be	AUX
ejde-397	424	43	the	the	DET
ejde-397	424	44	case	case	NOUN
ejde-397	424	45	,	,	PUNCT
ejde-397	424	46	the	the	DET
ejde-397	424	47	following	follow	VERB
ejde-397	424	48	formula	formula	NOUN
ejde-397	424	49	holds	hold	VERB
ejde-397	424	50	:	:	PUNCT
ejde-397	424	51	dn	dn	PROPN
ejde-397	424	52	dλn	dλn	PROPN
ejde-397	424	53	f̃(λ	f̃(λ	PROPN
ejde-397	424	54	)	)	PUNCT
ejde-397	425	1	=	=	PUNCT
ejde-397	425	2	(	(	PUNCT
ejde-397	425	3	−1)n	−1)n	PROPN
ejde-397	425	4	∫	∫	PROPN
ejde-397	425	5	∞	∞	PROPN
ejde-397	425	6	0	0	NUM
ejde-397	425	7	e−λttnf(t	e−λttnf(t	PROPN
ejde-397	425	8	)	)	PUNCT
ejde-397	425	9	dt	dt	PROPN
ejde-397	425	10	,	,	PUNCT
ejde-397	425	11	n	n	PROPN
ejde-397	425	12	∈	∈	PROPN
ejde-397	425	13	n	n	CCONJ
ejde-397	425	14	,	,	PUNCT
ejde-397	426	1	λ	λ	X
ejde-397	426	2	∈	∈	PROPN
ejde-397	426	3	c	c	NOUN
ejde-397	426	4	,	,	PUNCT
ejde-397	426	5	<	<	X
ejde-397	426	6	λ	λ	X
ejde-397	426	7	>	>	X
ejde-397	426	8	abs(f	abs(f	PROPN
ejde-397	426	9	)	)	PUNCT
ejde-397	426	10	.	.	PUNCT
ejde-397	427	1	(	(	PUNCT
ejde-397	427	2	3.5	3.5	NUM
ejde-397	427	3	)	)	PUNCT
ejde-397	427	4	in	in	ADP
ejde-397	427	5	the	the	DET
ejde-397	427	6	following	following	NOUN
ejde-397	427	7	theorem	theorem	NOUN
ejde-397	427	8	,	,	PUNCT
ejde-397	427	9	we	we	PRON
ejde-397	427	10	will	will	AUX
ejde-397	427	11	collect	collect	VERB
ejde-397	427	12	various	various	ADJ
ejde-397	427	13	operational	operational	ADJ
ejde-397	427	14	properties	property	NOUN
ejde-397	427	15	of	of	ADP
ejde-397	427	16	vectorvalued	vectorvalue	VERB
ejde-397	427	17	laplace	laplace	NOUN
ejde-397	427	18	transform	transform	NOUN
ejde-397	427	19	.	.	PUNCT
ejde-397	428	1	theorem	theorem	VERB
ejde-397	428	2	3.3	3.3	NUM
ejde-397	428	3	.	.	PUNCT
ejde-397	429	1	let	let	VERB
ejde-397	429	2	f	f	PROPN
ejde-397	429	3	∈	∈	PROPN
ejde-397	429	4	(	(	PUNCT
ejde-397	429	5	p1)-x	p1)-x	NOUN
ejde-397	429	6	,	,	PUNCT
ejde-397	429	7	z	z	NOUN
ejde-397	429	8	∈	∈	PROPN
ejde-397	429	9	c	c	PROPN
ejde-397	429	10	and	and	CCONJ
ejde-397	429	11	s	s	X
ejde-397	429	12	≥	≥	NOUN
ejde-397	429	13	0	0	NUM
ejde-397	429	14	.	.	PUNCT
ejde-397	430	1	(	(	PUNCT
ejde-397	430	2	i	i	NOUN
ejde-397	430	3	)	)	PUNCT
ejde-397	430	4	put	put	VERB
ejde-397	430	5	g(t	g(t	PROPN
ejde-397	430	6	)	)	PUNCT
ejde-397	430	7	:	:	PUNCT
ejde-397	431	1	=	=	PUNCT
ejde-397	431	2	e−ztf(t	e−ztf(t	NUM
ejde-397	431	3	)	)	PUNCT
ejde-397	431	4	,	,	PUNCT
ejde-397	431	5	t	t	PROPN
ejde-397	431	6	≥	≥	NUM
ejde-397	431	7	0	0	NUM
ejde-397	431	8	.	.	PUNCT
ejde-397	432	1	then	then	ADV
ejde-397	432	2	g	g	PROPN
ejde-397	432	3	(	(	PUNCT
ejde-397	432	4	·	·	PUNCT
ejde-397	432	5	)	)	PUNCT
ejde-397	432	6	is	be	AUX
ejde-397	432	7	laplace	laplace	NOUN
ejde-397	432	8	transformable	transformable	NOUN
ejde-397	432	9	,	,	PUNCT
ejde-397	432	10	abs(g	abs(g	PROPN
ejde-397	432	11	)	)	PUNCT
ejde-397	432	12	=	=	SYM
ejde-397	432	13	abs(f)−<z	abs(f)−<z	X
ejde-397	432	14	and	and	CCONJ
ejde-397	432	15	g̃(λ	g̃(λ	NOUN
ejde-397	432	16	)	)	PUNCT
ejde-397	433	1	=	=	SYM
ejde-397	433	2	f̃(λ+	f̃(λ+	PROPN
ejde-397	433	3	z	z	X
ejde-397	433	4	)	)	PUNCT
ejde-397	433	5	,	,	PUNCT
ejde-397	433	6	λ	λ	PROPN
ejde-397	433	7	∈	∈	PROPN
ejde-397	433	8	c	c	NOUN
ejde-397	433	9	,	,	PUNCT
ejde-397	433	10	<	<	X
ejde-397	433	11	λ	λ	X
ejde-397	433	12	>	>	X
ejde-397	433	13	abs(f)−<z	abs(f)−<z	PROPN
ejde-397	433	14	.	.	PROPN
ejde-397	433	15	(	(	PUNCT
ejde-397	433	16	ii	ii	NOUN
ejde-397	433	17	)	)	PUNCT
ejde-397	433	18	put	put	VERB
ejde-397	433	19	fs(t	fs(t	PUNCT
ejde-397	433	20	)	)	PUNCT
ejde-397	433	21	:	:	PUNCT
ejde-397	434	1	=	=	PUNCT
ejde-397	434	2	f(t	f(t	PROPN
ejde-397	434	3	+	+	CCONJ
ejde-397	434	4	s	s	X
ejde-397	434	5	)	)	PUNCT
ejde-397	434	6	,	,	PUNCT
ejde-397	434	7	t	t	PROPN
ejde-397	434	8	≥	≥	NUM
ejde-397	434	9	0	0	NUM
ejde-397	434	10	,	,	PUNCT
ejde-397	434	11	hs(t	hs(t	NUM
ejde-397	434	12	)	)	PUNCT
ejde-397	434	13	:	:	PUNCT
ejde-397	435	1	=	=	PUNCT
ejde-397	435	2	f(t	f(t	PROPN
ejde-397	435	3	−	−	PROPN
ejde-397	435	4	s	s	PART
ejde-397	435	5	)	)	PUNCT
ejde-397	435	6	,	,	PUNCT
ejde-397	435	7	t	t	PROPN
ejde-397	435	8	≥	≥	NOUN
ejde-397	435	9	s	s	NOUN
ejde-397	435	10	and	and	CCONJ
ejde-397	435	11	hs(t	hs(t	NUM
ejde-397	435	12	)	)	PUNCT
ejde-397	435	13	:	:	PUNCT
ejde-397	436	1	=	=	SYM
ejde-397	436	2	0	0	NUM
ejde-397	436	3	,	,	PUNCT
ejde-397	436	4	s	s	VERB
ejde-397	436	5	∈	∈	PROPN
ejde-397	437	1	[	[	X
ejde-397	437	2	0	0	NUM
ejde-397	437	3	,	,	PUNCT
ejde-397	437	4	t	t	PROPN
ejde-397	437	5	]	]	PUNCT
ejde-397	437	6	.	.	PUNCT
ejde-397	438	1	then	then	ADV
ejde-397	438	2	abs(fs	abs(fs	X
ejde-397	438	3	)	)	PUNCT
ejde-397	438	4	=	=	SYM
ejde-397	438	5	abs(hs	abs(hs	ADJ
ejde-397	438	6	)	)	PUNCT
ejde-397	438	7	=	=	SYM
ejde-397	439	1	abs(f	abs(f	PROPN
ejde-397	439	2	)	)	PUNCT
ejde-397	439	3	,	,	PUNCT
ejde-397	439	4	f̃s(λ	f̃s(λ	CCONJ
ejde-397	439	5	)	)	PUNCT
ejde-397	439	6	=	=	SYM
ejde-397	440	1	eλs(f̃(λ)−	eλs(f̃(λ)−	PROPN
ejde-397	440	2	∫	∫	PROPN
ejde-397	440	3	s	s	PART
ejde-397	440	4	0	0	NUM
ejde-397	440	5	e−λtf(t	e−λtf(t	NUM
ejde-397	440	6	)	)	PUNCT
ejde-397	440	7	dt	dt	NOUN
ejde-397	440	8	)	)	PUNCT
ejde-397	440	9	and	and	CCONJ
ejde-397	440	10	h̃s(λ	h̃s(λ	NUM
ejde-397	440	11	)	)	PUNCT
ejde-397	441	1	=	=	SYM
ejde-397	441	2	e−λsf̃(λ	e−λsf̃(λ	NOUN
ejde-397	441	3	)	)	PUNCT
ejde-397	441	4	(	(	PUNCT
ejde-397	441	5	λ	λ	X
ejde-397	441	6	∈	∈	PROPN
ejde-397	441	7	c	c	X
ejde-397	441	8	,	,	PUNCT
ejde-397	441	9	<	<	X
ejde-397	441	10	λ	λ	X
ejde-397	441	11	>	>	X
ejde-397	441	12	a	a	PROPN
ejde-397	441	13	)	)	PUNCT
ejde-397	441	14	.	.	PUNCT
ejde-397	442	1	(	(	PUNCT
ejde-397	442	2	iii	iii	X
ejde-397	442	3	)	)	PUNCT
ejde-397	442	4	let	let	VERB
ejde-397	442	5	t	t	PROPN
ejde-397	442	6	∈	∈	PROPN
ejde-397	442	7	l(x	l(x	PROPN
ejde-397	442	8	,	,	PUNCT
ejde-397	442	9	y	y	PROPN
ejde-397	442	10	)	)	PUNCT
ejde-397	442	11	.	.	PUNCT
ejde-397	443	1	then	then	ADV
ejde-397	443	2	t	t	PROPN
ejde-397	443	3	◦	◦	NOUN
ejde-397	443	4	f	f	X
ejde-397	443	5	∈	∈	PROPN
ejde-397	443	6	(	(	PUNCT
ejde-397	443	7	p1)-y	p1)-y	X
ejde-397	443	8	and	and	CCONJ
ejde-397	443	9	t	t	PROPN
ejde-397	443	10	f̃(λ	f̃(λ	PROPN
ejde-397	443	11	)	)	PUNCT
ejde-397	443	12	=	=	PUNCT
ejde-397	443	13	˜(t	˜(t	X
ejde-397	443	14	◦	◦	NOUN
ejde-397	443	15	f)(λ	f)(λ	NOUN
ejde-397	443	16	)	)	PUNCT
ejde-397	443	17	for	for	ADP
ejde-397	443	18	λ	λ	PROPN
ejde-397	443	19	∈	∈	PROPN
ejde-397	443	20	c	c	X
ejde-397	443	21	,	,	PUNCT
ejde-397	443	22	<	<	X
ejde-397	443	23	λ	λ	X
ejde-397	443	24	>	>	X
ejde-397	443	25	abs(f	abs(f	PROPN
ejde-397	443	26	)	)	PUNCT
ejde-397	443	27	.	.	PUNCT
ejde-397	444	1	(	(	PUNCT
ejde-397	444	2	iv	iv	X
ejde-397	444	3	)	)	PUNCT
ejde-397	444	4	suppose	suppose	VERB
ejde-397	444	5	that	that	SCONJ
ejde-397	444	6	a	a	PRON
ejde-397	444	7	:	:	PUNCT
ejde-397	444	8	x	x	X
ejde-397	444	9	→	→	X
ejde-397	444	10	p	p	X
ejde-397	444	11	(	(	PUNCT
ejde-397	444	12	y	y	PROPN
ejde-397	444	13	)	)	PUNCT
ejde-397	444	14	is	be	AUX
ejde-397	444	15	an	an	DET
ejde-397	444	16	mlo	mlo	NOUN
ejde-397	444	17	and	and	CCONJ
ejde-397	444	18	a	a	PRON
ejde-397	444	19	is	be	AUX
ejde-397	444	20	xa	xa	PROPN
ejde-397	444	21	×	×	PROPN
ejde-397	444	22	ya	ya	PROPN
ejde-397	444	23	-	-	PUNCT
ejde-397	444	24	closed	closed	ADJ
ejde-397	444	25	,	,	PUNCT
ejde-397	444	26	as	as	ADV
ejde-397	444	27	well	well	ADV
ejde-397	444	28	as	as	ADP
ejde-397	444	29	f	f	PROPN
ejde-397	444	30	∈	∈	PROPN
ejde-397	444	31	(	(	PUNCT
ejde-397	444	32	p1	p1	PROPN
ejde-397	444	33	)	)	PUNCT
ejde-397	444	34	−	−	PROPN
ejde-397	444	35	xa	xa	PROPN
ejde-397	444	36	,	,	PUNCT
ejde-397	444	37	l	l	PROPN
ejde-397	444	38	∈	∈	PROPN
ejde-397	444	39	(	(	PUNCT
ejde-397	444	40	p1	p1	NOUN
ejde-397	444	41	)	)	PUNCT
ejde-397	445	1	−	−	PROPN
ejde-397	445	2	ya	ya	PROPN
ejde-397	445	3	and	and	CCONJ
ejde-397	445	4	(	(	PUNCT
ejde-397	445	5	f(t	f(t	PROPN
ejde-397	445	6	)	)	PUNCT
ejde-397	445	7	,	,	PUNCT
ejde-397	445	8	l(t	l(t	PROPN
ejde-397	445	9	)	)	PUNCT
ejde-397	445	10	)	)	PUNCT
ejde-397	446	1	∈	∈	PROPN
ejde-397	446	2	a	a	PRON
ejde-397	446	3	for	for	ADP
ejde-397	446	4	a.e	a.e	PROPN
ejde-397	446	5	.	.	PROPN
ejde-397	446	6	t	t	PROPN
ejde-397	446	7	≥	≥	PROPN
ejde-397	446	8	0	0	NUM
ejde-397	446	9	.	.	PUNCT
ejde-397	447	1	then	then	ADV
ejde-397	447	2	(	(	PUNCT
ejde-397	447	3	f̃(λ	f̃(λ	NOUN
ejde-397	447	4	)	)	PUNCT
ejde-397	447	5	,	,	PUNCT
ejde-397	447	6	l̃(λ	l̃(λ	PROPN
ejde-397	447	7	)	)	PUNCT
ejde-397	447	8	)	)	PUNCT
ejde-397	448	1	∈	∈	PROPN
ejde-397	448	2	a	a	PRON
ejde-397	448	3	,	,	PUNCT
ejde-397	448	4	λ	λ	PROPN
ejde-397	448	5	∈	∈	PROPN
ejde-397	448	6	c	c	NOUN
ejde-397	448	7	for	for	ADP
ejde-397	448	8	<	<	X
ejde-397	448	9	λ	λ	X
ejde-397	448	10	>	>	X
ejde-397	448	11	max(abs(f	max(abs(f	NUM
ejde-397	448	12	)	)	PUNCT
ejde-397	448	13	,	,	PUNCT
ejde-397	448	14	abs(l	abs(l	PROPN
ejde-397	448	15	)	)	PUNCT
ejde-397	448	16	)	)	PUNCT
ejde-397	448	17	.	.	PUNCT
ejde-397	449	1	14	14	NUM
ejde-397	449	2	m.	m.	NOUN
ejde-397	449	3	kostić	kostić	NOUN
ejde-397	450	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	450	2	(	(	PUNCT
ejde-397	450	3	v	v	NOUN
ejde-397	450	4	)	)	PUNCT
ejde-397	450	5	suppose	suppose	VERB
ejde-397	450	6	,	,	PUNCT
ejde-397	450	7	in	in	ADP
ejde-397	450	8	addition	addition	NOUN
ejde-397	450	9	,	,	PUNCT
ejde-397	450	10	ω(f	ω(f	NUM
ejde-397	450	11	)	)	PUNCT
ejde-397	451	1	<	<	X
ejde-397	451	2	∞.	∞.	PROPN
ejde-397	451	3	put	put	VERB
ejde-397	451	4	j(t	j(t	PROPN
ejde-397	451	5	)	)	PUNCT
ejde-397	451	6	:	:	PUNCT
ejde-397	452	1	=	=	SYM
ejde-397	452	2	∫	∫	PROPN
ejde-397	452	3	∞	∞	PROPN
ejde-397	452	4	0	0	NUM
ejde-397	452	5	e−s	e−s	PROPN
ejde-397	452	6	2/4	2/4	NUM
ejde-397	452	7	t	t	NOUN
ejde-397	452	8	√	√	NOUN
ejde-397	452	9	πt	πt	ADP
ejde-397	452	10	f(s	f(	NOUN
ejde-397	452	11	)	)	PUNCT
ejde-397	453	1	ds	ds	ADJ
ejde-397	453	2	:	:	PUNCT
ejde-397	453	3	=	=	SYM
ejde-397	453	4	lim	lim	PROPN
ejde-397	453	5	τ→∞	τ→∞	NUM
ejde-397	453	6	∫	∫	PROPN
ejde-397	453	7	τ	τ	PROPN
ejde-397	453	8	0	0	PROPN
ejde-397	453	9	e−s	e−s	PROPN
ejde-397	453	10	2/4	2/4	NUM
ejde-397	453	11	t	t	NOUN
ejde-397	453	12	√	√	NOUN
ejde-397	453	13	πt	πt	ADP
ejde-397	453	14	f(s	f(	NOUN
ejde-397	453	15	)	)	PUNCT
ejde-397	453	16	ds	ds	PROPN
ejde-397	453	17	,	,	PUNCT
ejde-397	453	18	t	t	X
ejde-397	453	19	>	>	X
ejde-397	453	20	0	0	NUM
ejde-397	453	21	,	,	PUNCT
ejde-397	453	22	k(t	k(t	PROPN
ejde-397	453	23	)	)	PUNCT
ejde-397	453	24	:	:	PUNCT
ejde-397	454	1	=	=	SYM
ejde-397	454	2	∫	∫	PROPN
ejde-397	454	3	∞	∞	NUM
ejde-397	454	4	0	0	NUM
ejde-397	454	5	se−s	se−s	PROPN
ejde-397	454	6	2/4	2/4	NUM
ejde-397	454	7	t	t	NOUN
ejde-397	454	8	2	2	NUM
ejde-397	454	9	√	√	NUM
ejde-397	454	10	πt	πt	ADP
ejde-397	454	11	3	3	NUM
ejde-397	454	12	2	2	NUM
ejde-397	454	13	f(s	f(	NOUN
ejde-397	454	14	)	)	PUNCT
ejde-397	455	1	ds	ds	ADJ
ejde-397	455	2	:	:	PUNCT
ejde-397	455	3	=	=	SYM
ejde-397	455	4	lim	lim	PROPN
ejde-397	455	5	τ→∞	τ→∞	NUM
ejde-397	455	6	∫	∫	PROPN
ejde-397	455	7	τ	τ	PROPN
ejde-397	455	8	0	0	NUM
ejde-397	455	9	se−s	se−s	PROPN
ejde-397	455	10	2/4	2/4	NUM
ejde-397	455	11	t	t	NOUN
ejde-397	455	12	2	2	NUM
ejde-397	455	13	√	√	NUM
ejde-397	455	14	πt	πt	ADP
ejde-397	455	15	3	3	NUM
ejde-397	455	16	2	2	NUM
ejde-397	455	17	f(s	f(	NOUN
ejde-397	455	18	)	)	PUNCT
ejde-397	455	19	ds	ds	PROPN
ejde-397	455	20	,	,	PUNCT
ejde-397	455	21	t	t	X
ejde-397	455	22	>	>	X
ejde-397	455	23	0	0	PROPN
ejde-397	455	24	.	.	PUNCT
ejde-397	456	1	then	then	ADV
ejde-397	456	2	j	j	X
ejde-397	456	3	(	(	PUNCT
ejde-397	456	4	·	·	PUNCT
ejde-397	456	5	)	)	PUNCT
ejde-397	456	6	and	and	CCONJ
ejde-397	456	7	k	k	X
ejde-397	456	8	(	(	PUNCT
ejde-397	456	9	·	·	PUNCT
ejde-397	456	10	)	)	PUNCT
ejde-397	456	11	are	be	AUX
ejde-397	456	12	laplace	laplace	NOUN
ejde-397	456	13	transformable	transformable	NOUN
ejde-397	456	14	,	,	PUNCT
ejde-397	456	15	max(abs(j	max(abs(j	PROPN
ejde-397	456	16	)	)	PUNCT
ejde-397	456	17	,	,	PUNCT
ejde-397	456	18	abs(k	abs(k	PROPN
ejde-397	456	19	)	)	PUNCT
ejde-397	456	20	)	)	PUNCT
ejde-397	457	1	≤	≤	NOUN
ejde-397	457	2	(	(	PUNCT
ejde-397	457	3	max(ω(f	max(ω(f	NOUN
ejde-397	457	4	)	)	PUNCT
ejde-397	457	5	,	,	PUNCT
ejde-397	457	6	0	0	NUM
ejde-397	457	7	)	)	PUNCT
ejde-397	457	8	)	)	PUNCT
ejde-397	457	9	2	2	NUM
ejde-397	457	10	,	,	PUNCT
ejde-397	457	11	j̃(λ	j̃(λ	NOUN
ejde-397	457	12	)	)	PUNCT
ejde-397	457	13	=	=	PUNCT
ejde-397	458	1	f̃	f̃	PROPN
ejde-397	458	2	(	(	PUNCT
ejde-397	458	3	√	√	PROPN
ejde-397	458	4	λ	λ	PROPN
ejde-397	458	5	)	)	PUNCT
ejde-397	458	6	√	√	ADP
ejde-397	458	7	λ	λ	INTJ
ejde-397	458	8	,	,	PUNCT
ejde-397	458	9	k̃(λ	k̃(λ	NOUN
ejde-397	458	10	)	)	PUNCT
ejde-397	458	11	=	=	SYM
ejde-397	458	12	f̃	f̃	PROPN
ejde-397	458	13	(	(	PUNCT
ejde-397	458	14	√	√	PROPN
ejde-397	458	15	λ	λ	PROPN
ejde-397	458	16	)	)	PUNCT
ejde-397	458	17	for	for	ADP
ejde-397	458	18	all	all	DET
ejde-397	458	19	λ	λ	PROPN
ejde-397	458	20	∈	∈	PROPN
ejde-397	458	21	c	c	NOUN
ejde-397	458	22	with	with	ADP
ejde-397	458	23	<	<	X
ejde-397	458	24	λ	λ	X
ejde-397	458	25	>	>	X
ejde-397	458	26	(	(	PUNCT
ejde-397	458	27	max(ω(f	max(ω(f	NOUN
ejde-397	458	28	)	)	PUNCT
ejde-397	458	29	,	,	PUNCT
ejde-397	458	30	0))2	0))2	NUM
ejde-397	458	31	.	.	PUNCT
ejde-397	459	1	(	(	PUNCT
ejde-397	459	2	vi	vi	X
ejde-397	459	3	)	)	PUNCT
ejde-397	459	4	let	let	VERB
ejde-397	459	5	f	f	PROPN
ejde-397	459	6	∈	∈	PROPN
ejde-397	459	7	(	(	PUNCT
ejde-397	459	8	p1)-x	p1)-x	NOUN
ejde-397	459	9	,	,	PUNCT
ejde-397	459	10	h	h	NOUN
ejde-397	459	11	∈	∈	PROPN
ejde-397	459	12	l1	l1	PROPN
ejde-397	459	13	loc([0,∞	loc([0,∞	PROPN
ejde-397	459	14	)	)	PUNCT
ejde-397	459	15	)	)	PUNCT
ejde-397	459	16	and	and	CCONJ
ejde-397	459	17	abs(|h|	abs(|h|	NUM
ejde-397	459	18	)	)	PUNCT
ejde-397	460	1	<	<	X
ejde-397	460	2	∞.	∞.	PROPN
ejde-397	460	3	suppose	suppose	VERB
ejde-397	460	4	,	,	PUNCT
ejde-397	460	5	in	in	ADP
ejde-397	460	6	addition	addition	NOUN
ejde-397	460	7	,	,	PUNCT
ejde-397	460	8	that	that	SCONJ
ejde-397	460	9	f	f	PROPN
ejde-397	460	10	∈	∈	PROPN
ejde-397	460	11	c([0,∞	c([0,∞	PROPN
ejde-397	460	12	)	)	PUNCT
ejde-397	460	13	:	:	PUNCT
ejde-397	461	1	x	x	X
ejde-397	461	2	)	)	PUNCT
ejde-397	461	3	.	.	PUNCT
ejde-397	462	1	put	put	NOUN
ejde-397	462	2	(	(	PUNCT
ejde-397	462	3	h	h	NOUN
ejde-397	462	4	∗	∗	NOUN
ejde-397	462	5	f)(t	f)(t	PROPN
ejde-397	462	6	)	)	PUNCT
ejde-397	462	7	:	:	PUNCT
ejde-397	463	1	=	=	SYM
ejde-397	463	2	∫	∫	PROPN
ejde-397	463	3	t	t	PROPN
ejde-397	463	4	0	0	NUM
ejde-397	464	1	h(t−	h(t−	PRON
ejde-397	464	2	s)f(s	s)f(	NOUN
ejde-397	464	3	)	)	PUNCT
ejde-397	464	4	ds	ds	PROPN
ejde-397	464	5	,	,	PUNCT
ejde-397	464	6	t	t	PROPN
ejde-397	464	7	≥	≥	NUM
ejde-397	464	8	0	0	NUM
ejde-397	464	9	.	.	PUNCT
ejde-397	465	1	then	then	ADV
ejde-397	465	2	the	the	DET
ejde-397	465	3	mapping	mapping	NOUN
ejde-397	465	4	t	t	PROPN
ejde-397	465	5	7→	7→	NUM
ejde-397	465	6	(	(	PUNCT
ejde-397	465	7	h	h	NOUN
ejde-397	465	8	∗	∗	NOUN
ejde-397	465	9	f)(t	f)(t	PROPN
ejde-397	465	10	)	)	PUNCT
ejde-397	465	11	,	,	PUNCT
ejde-397	465	12	t	t	PROPN
ejde-397	465	13	≥	≥	NOUN
ejde-397	465	14	0	0	NUM
ejde-397	465	15	is	be	AUX
ejde-397	465	16	continuous	continuous	ADJ
ejde-397	465	17	,	,	PUNCT
ejde-397	465	18	h	h	PROPN
ejde-397	465	19	∗	∗	NOUN
ejde-397	466	1	f	f	PROPN
ejde-397	466	2	∈	∈	PROPN
ejde-397	466	3	(	(	PUNCT
ejde-397	466	4	p1)-x	p1)-x	NOUN
ejde-397	466	5	,	,	PUNCT
ejde-397	466	6	and	and	CCONJ
ejde-397	466	7	h̃	h̃	PROPN
ejde-397	466	8	∗	∗	NOUN
ejde-397	466	9	f(λ	f(λ	NOUN
ejde-397	466	10	)	)	PUNCT
ejde-397	466	11	=	=	SYM
ejde-397	466	12	h̃(λ)f̃(λ	h̃(λ)f̃(λ	NOUN
ejde-397	466	13	)	)	PUNCT
ejde-397	466	14	,	,	PUNCT
ejde-397	466	15	λ	λ	X
ejde-397	466	16	∈	∈	PROPN
ejde-397	466	17	c	c	NOUN
ejde-397	466	18	,	,	PUNCT
ejde-397	466	19	<	<	X
ejde-397	466	20	λ	λ	X
ejde-397	466	21	>	>	X
ejde-397	466	22	max	max	PROPN
ejde-397	466	23	(	(	PUNCT
ejde-397	466	24	abs(|h|	abs(|h|	NUM
ejde-397	466	25	)	)	PUNCT
ejde-397	466	26	,	,	PUNCT
ejde-397	466	27	abs(f	abs(f	PROPN
ejde-397	466	28	)	)	PUNCT
ejde-397	466	29	)	)	PUNCT
ejde-397	466	30	.	.	PUNCT
ejde-397	467	1	proof	proof	NOUN
ejde-397	467	2	.	.	PUNCT
ejde-397	468	1	keeping	keep	VERB
ejde-397	468	2	in	in	ADP
ejde-397	468	3	mind	mind	NOUN
ejde-397	468	4	theorem	theorem	VERB
ejde-397	468	5	3.1	3.1	NUM
ejde-397	468	6	,	,	PUNCT
ejde-397	468	7	theorem	theorem	VERB
ejde-397	468	8	1.3(ii	1.3(ii	NUM
ejde-397	468	9	)	)	PUNCT
ejde-397	468	10	and	and	CCONJ
ejde-397	468	11	theorem	theorem	VERB
ejde-397	468	12	2.3	2.3	NUM
ejde-397	468	13	,	,	PUNCT
ejde-397	468	14	the	the	DET
ejde-397	468	15	assertions	assertion	NOUN
ejde-397	468	16	(	(	PUNCT
ejde-397	468	17	i)-(iv	i)-(iv	X
ejde-397	468	18	)	)	PUNCT
ejde-397	468	19	can	can	AUX
ejde-397	468	20	be	be	AUX
ejde-397	468	21	proved	prove	VERB
ejde-397	468	22	as	as	ADP
ejde-397	468	23	in	in	ADP
ejde-397	468	24	the	the	DET
ejde-397	468	25	banach	banach	NOUN
ejde-397	468	26	space	space	NOUN
ejde-397	468	27	case	case	NOUN
ejde-397	468	28	(	(	PUNCT
ejde-397	468	29	cf	cf	NOUN
ejde-397	468	30	.	.	PUNCT
ejde-397	469	1	[	[	X
ejde-397	469	2	1	1	NUM
ejde-397	469	3	,	,	PUNCT
ejde-397	469	4	proposition	proposition	NOUN
ejde-397	469	5	1.6.1	1.6.1	NUM
ejde-397	469	6	-	-	NOUN
ejde-397	469	7	proposition	proposition	NOUN
ejde-397	469	8	1.6.3	1.6.3	NUM
ejde-397	469	9	]	]	PUNCT
ejde-397	469	10	for	for	ADP
ejde-397	469	11	more	more	ADJ
ejde-397	469	12	details	detail	NOUN
ejde-397	469	13	)	)	PUNCT
ejde-397	469	14	.	.	PUNCT
ejde-397	470	1	consider	consider	VERB
ejde-397	470	2	now	now	ADV
ejde-397	470	3	the	the	DET
ejde-397	470	4	part	part	NOUN
ejde-397	470	5	(	(	PUNCT
ejde-397	470	6	v	v	NOUN
ejde-397	470	7	)	)	PUNCT
ejde-397	470	8	.	.	PUNCT
ejde-397	471	1	let	let	VERB
ejde-397	471	2	λ	λ	X
ejde-397	471	3	∈	∈	PROPN
ejde-397	471	4	c	c	NOUN
ejde-397	471	5	with	with	ADP
ejde-397	471	6	<	<	X
ejde-397	471	7	λ	λ	X
ejde-397	471	8	>	>	X
ejde-397	471	9	(	(	PUNCT
ejde-397	471	10	max(ω(f	max(ω(f	NOUN
ejde-397	471	11	)	)	PUNCT
ejde-397	471	12	,	,	PUNCT
ejde-397	471	13	0))2	0))2	PRON
ejde-397	471	14	be	be	AUX
ejde-397	471	15	fixed	fix	VERB
ejde-397	471	16	.	.	PUNCT
ejde-397	472	1	then	then	ADV
ejde-397	472	2	<	<	X
ejde-397	472	3	(	(	PUNCT
ejde-397	472	4	√	√	NUM
ejde-397	472	5	λ	λ	NOUN
ejde-397	472	6	)	)	PUNCT
ejde-397	472	7	>	>	X
ejde-397	472	8	max(ω(f	max(ω(f	PROPN
ejde-397	472	9	)	)	PUNCT
ejde-397	472	10	,	,	PUNCT
ejde-397	472	11	0	0	X
ejde-397	472	12	)	)	PUNCT
ejde-397	472	13	≥	≥	PROPN
ejde-397	472	14	max(ω(f	max(ω(f	NOUN
ejde-397	472	15	)	)	PUNCT
ejde-397	472	16	,	,	PUNCT
ejde-397	472	17	0	0	NUM
ejde-397	472	18	)	)	PUNCT
ejde-397	472	19	so	so	SCONJ
ejde-397	472	20	that	that	SCONJ
ejde-397	472	21	[	[	X
ejde-397	472	22	36	36	NUM
ejde-397	472	23	,	,	PUNCT
ejde-397	472	24	theorem	theorem	ADJ
ejde-397	472	25	1.2.1(v	1.2.1(v	NUM
ejde-397	472	26	)	)	PUNCT
ejde-397	472	27	]	]	PUNCT
ejde-397	473	1	implies	imply	VERB
ejde-397	473	2	in	in	ADP
ejde-397	473	3	combination	combination	NOUN
ejde-397	473	4	with	with	ADP
ejde-397	473	5	(	(	PUNCT
ejde-397	473	6	3.4	3.4	NUM
ejde-397	473	7	)	)	PUNCT
ejde-397	473	8	that	that	PRON
ejde-397	473	9	f̃	f̃	PROPN
ejde-397	473	10	(	(	PUNCT
ejde-397	473	11	√	√	NUM
ejde-397	473	12	λ	λ	NOUN
ejde-397	473	13	)	)	PUNCT
ejde-397	473	14	exists	exist	VERB
ejde-397	473	15	,	,	PUNCT
ejde-397	473	16	as	as	ADV
ejde-397	473	17	well	well	ADV
ejde-397	473	18	as	as	ADP
ejde-397	474	1	that	that	DET
ejde-397	474	2	f̃	f̃	PROPN
ejde-397	474	3	(	(	PUNCT
ejde-397	474	4	√	√	PROPN
ejde-397	474	5	λ	λ	PROPN
ejde-397	474	6	)	)	PUNCT
ejde-397	474	7	=	=	SYM
ejde-397	474	8	f̃	f̃	PROPN
ejde-397	474	9	(	(	PUNCT
ejde-397	474	10	√	√	PROPN
ejde-397	474	11	λ	λ	PROPN
ejde-397	474	12	)	)	PUNCT
ejde-397	474	13	√	√	ADP
ejde-397	475	1	λ	λ	X
ejde-397	475	2	=	=	SYM
ejde-397	475	3	∫	∫	PROPN
ejde-397	475	4	∞	∞	PROPN
ejde-397	475	5	0	0	PROPN
ejde-397	475	6	e−λt	e−λt	NOUN
ejde-397	475	7	∫	∫	PROPN
ejde-397	475	8	∞	∞	PROPN
ejde-397	475	9	0	0	NUM
ejde-397	475	10	e−s	e−s	PROPN
ejde-397	475	11	2/4	2/4	NUM
ejde-397	475	12	t	t	NOUN
ejde-397	475	13	√	√	NOUN
ejde-397	475	14	πt	πt	ADP
ejde-397	475	15	f(s	f(	NOUN
ejde-397	475	16	)	)	PUNCT
ejde-397	475	17	ds	ds	ADJ
ejde-397	475	18	dt	dt	PROPN
ejde-397	475	19	.	.	PUNCT
ejde-397	476	1	on	on	ADP
ejde-397	476	2	the	the	DET
ejde-397	476	3	other	other	ADJ
ejde-397	476	4	hand	hand	NOUN
ejde-397	476	5	,	,	PUNCT
ejde-397	476	6	we	we	PRON
ejde-397	476	7	can	can	AUX
ejde-397	476	8	use	use	VERB
ejde-397	476	9	the	the	DET
ejde-397	476	10	dominated	dominate	VERB
ejde-397	476	11	convergence	convergence	NOUN
ejde-397	476	12	theorem	theorem	NOUN
ejde-397	476	13	and	and	CCONJ
ejde-397	476	14	an	an	DET
ejde-397	476	15	elementary	elementary	ADJ
ejde-397	476	16	argumentation	argumentation	NOUN
ejde-397	476	17	to	to	PART
ejde-397	476	18	prove	prove	VERB
ejde-397	476	19	that	that	SCONJ
ejde-397	476	20	the	the	DET
ejde-397	476	21	mapping	mapping	NOUN
ejde-397	476	22	t	t	X
ejde-397	476	23	7→	7→	NUM
ejde-397	476	24	k(t	k(t	NOUN
ejde-397	476	25	)	)	PUNCT
ejde-397	476	26	,	,	PUNCT
ejde-397	476	27	t	t	PROPN
ejde-397	476	28	>	>	X
ejde-397	476	29	0	0	PUNCT
ejde-397	476	30	is	be	AUX
ejde-397	476	31	continuous	continuous	ADJ
ejde-397	476	32	as	as	ADV
ejde-397	476	33	well	well	ADV
ejde-397	476	34	as	as	ADP
ejde-397	476	35	that	that	PRON
ejde-397	476	36	for	for	ADP
ejde-397	476	37	each	each	DET
ejde-397	476	38	seminorm	seminorm	NOUN
ejde-397	476	39	p	p	PROPN
ejde-397	476	40	∈	∈	PROPN
ejde-397	476	41	~	~	PUNCT
ejde-397	476	42	there	there	PRON
ejde-397	476	43	exists	exist	VERB
ejde-397	476	44	a	a	DET
ejde-397	476	45	finite	finite	ADJ
ejde-397	476	46	number	number	NOUN
ejde-397	476	47	mp	mp	PROPN
ejde-397	476	48	>	>	X
ejde-397	476	49	0	0	NUM
ejde-397	477	1	such	such	ADJ
ejde-397	477	2	that	that	DET
ejde-397	477	3	p(k(t	p(k(t	PROPN
ejde-397	477	4	)	)	PUNCT
ejde-397	477	5	)	)	PUNCT
ejde-397	478	1	≤	≤	NUM
ejde-397	478	2	mpt	mpt	PROPN
ejde-397	478	3	(	(	PUNCT
ejde-397	478	4	−1)/2	−1)/2	PROPN
ejde-397	478	5	,	,	PUNCT
ejde-397	478	6	t	t	PROPN
ejde-397	478	7	∈	∈	PROPN
ejde-397	478	8	(	(	PUNCT
ejde-397	478	9	0	0	NUM
ejde-397	478	10	,	,	PUNCT
ejde-397	478	11	1	1	NUM
ejde-397	478	12	]	]	PUNCT
ejde-397	478	13	.	.	PUNCT
ejde-397	479	1	this	this	PRON
ejde-397	479	2	simply	simply	ADV
ejde-397	479	3	implies	imply	VERB
ejde-397	479	4	k	k	PROPN
ejde-397	479	5	∈	∈	PROPN
ejde-397	479	6	l1	l1	PROPN
ejde-397	479	7	loc([0,∞	loc([0,∞	PROPN
ejde-397	479	8	)	)	PUNCT
ejde-397	479	9	:	:	PUNCT
ejde-397	480	1	x	x	X
ejde-397	480	2	)	)	PUNCT
ejde-397	480	3	.	.	PUNCT
ejde-397	480	4	since∫	since∫	VERB
ejde-397	480	5	∞	∞	PROPN
ejde-397	480	6	0	0	NUM
ejde-397	480	7	e−λt	e−λt	NOUN
ejde-397	480	8	〈	〈	PROPN
ejde-397	480	9	x∗	x∗	NOUN
ejde-397	480	10	,	,	PUNCT
ejde-397	480	11	k(t	k(t	NOUN
ejde-397	480	12	)	)	PUNCT
ejde-397	480	13	〉	〉	NOUN
ejde-397	480	14	dt	dt	NOUN
ejde-397	480	15	=	=	SYM
ejde-397	481	1	∫	∫	PROPN
ejde-397	481	2	∞	∞	NOUN
ejde-397	481	3	0	0	NUM
ejde-397	482	1	e−	e−	CCONJ
ejde-397	482	2	√	√	VERB
ejde-397	482	3	λt	λt	ADP
ejde-397	482	4	〈	〈	PROPN
ejde-397	482	5	x∗	x∗	NOUN
ejde-397	482	6	,	,	PUNCT
ejde-397	482	7	f(t	f(t	PROPN
ejde-397	482	8	)	)	PUNCT
ejde-397	482	9	〉	〉	NOUN
ejde-397	482	10	dt	dt	PROPN
ejde-397	482	11	,	,	PUNCT
ejde-397	482	12	x∗	x∗	PROPN
ejde-397	482	13	∈	∈	PROPN
ejde-397	482	14	x∗	x∗	PROPN
ejde-397	482	15	,	,	PUNCT
ejde-397	482	16	(	(	PUNCT
ejde-397	482	17	3.6	3.6	NUM
ejde-397	482	18	)	)	PUNCT
ejde-397	482	19	we	we	PRON
ejde-397	482	20	obtain	obtain	VERB
ejde-397	482	21	lim	lim	PROPN
ejde-397	482	22	τ→∞	τ→∞	NUM
ejde-397	482	23	〈	〈	PROPN
ejde-397	482	24	x∗	x∗	PROPN
ejde-397	482	25	,	,	PUNCT
ejde-397	482	26	∫	∫	PROPN
ejde-397	482	27	τ	τ	X
ejde-397	482	28	0	0	NUM
ejde-397	482	29	e−λtk(t	e−λtk(t	X
ejde-397	482	30	)	)	PUNCT
ejde-397	482	31	dt	dt	X
ejde-397	482	32	〉	〉	NOUN
ejde-397	482	33	=	=	SYM
ejde-397	482	34	〈	〈	PROPN
ejde-397	482	35	x∗	x∗	PROPN
ejde-397	482	36	,	,	PUNCT
ejde-397	482	37	f̃	f̃	PROPN
ejde-397	482	38	(	(	PUNCT
ejde-397	482	39	√	√	PROPN
ejde-397	482	40	λ	λ	PROPN
ejde-397	482	41	)	)	PUNCT
ejde-397	482	42	〉	〉	PROPN
ejde-397	482	43	,	,	PUNCT
ejde-397	482	44	x∗	x∗	PROPN
ejde-397	482	45	∈	∈	PROPN
ejde-397	482	46	x∗.	x∗.	PUNCT
ejde-397	482	47	by	by	ADP
ejde-397	482	48	theorem	theorem	NOUN
ejde-397	482	49	3.1(i	3.1(i	NUM
ejde-397	482	50	)	)	PUNCT
ejde-397	482	51	,	,	PUNCT
ejde-397	482	52	we	we	PRON
ejde-397	482	53	obtain	obtain	VERB
ejde-397	482	54	that	that	SCONJ
ejde-397	482	55	the	the	DET
ejde-397	482	56	mapping	mapping	NOUN
ejde-397	482	57	τ	τ	PROPN
ejde-397	482	58	7→	7→	NUM
ejde-397	482	59	∫	∫	NOUN
ejde-397	482	60	τ	τ	PROPN
ejde-397	482	61	0	0	NUM
ejde-397	482	62	e−λtk(t	e−λtk(t	X
ejde-397	482	63	)	)	PUNCT
ejde-397	482	64	dt	dt	PROPN
ejde-397	482	65	,	,	PUNCT
ejde-397	482	66	τ	τ	PROPN
ejde-397	482	67	≥	≥	X
ejde-397	482	68	0	0	NUM
ejde-397	482	69	is	be	AUX
ejde-397	482	70	continuous	continuous	ADJ
ejde-397	482	71	so	so	SCONJ
ejde-397	482	72	that	that	SCONJ
ejde-397	482	73	the	the	DET
ejde-397	482	74	previous	previous	ADJ
ejde-397	482	75	equality	equality	NOUN
ejde-397	482	76	implies	imply	VERB
ejde-397	482	77	supτ≥0	supτ≥0	PROPN
ejde-397	482	78	|〈x∗	|〈x∗	PROPN
ejde-397	482	79	,	,	PUNCT
ejde-397	482	80	∫	∫	PROPN
ejde-397	482	81	τ	τ	X
ejde-397	482	82	0	0	NUM
ejde-397	482	83	e−λtk(t	e−λtk(t	PRON
ejde-397	482	84	)	)	PUNCT
ejde-397	482	85	dt〉|	dt〉|	NOUN
ejde-397	482	86	<	<	X
ejde-397	482	87	∞	∞	PROPN
ejde-397	482	88	for	for	ADP
ejde-397	482	89	all	all	DET
ejde-397	482	90	x∗	x∗	PROPN
ejde-397	482	91	∈	∈	PROPN
ejde-397	482	92	x∗.	x∗.	PUNCT
ejde-397	483	1	therefore	therefore	ADV
ejde-397	483	2	,	,	PUNCT
ejde-397	483	3	theorem	theorem	VERB
ejde-397	483	4	3.2(ii	3.2(ii	NUM
ejde-397	483	5	)	)	PUNCT
ejde-397	483	6	shows	show	VERB
ejde-397	483	7	that	that	SCONJ
ejde-397	483	8	λ	λ	PROPN
ejde-397	483	9	>	>	X
ejde-397	483	10	w	w	PROPN
ejde-397	483	11	abs(k	abs(k	PROPN
ejde-397	483	12	)	)	PUNCT
ejde-397	483	13	=	=	SYM
ejde-397	483	14	abs(k	abs(k	PROPN
ejde-397	483	15	)	)	PUNCT
ejde-397	483	16	and	and	CCONJ
ejde-397	483	17	k̃(λ	k̃(λ	NOUN
ejde-397	483	18	)	)	PUNCT
ejde-397	483	19	exists	exist	VERB
ejde-397	483	20	.	.	PUNCT
ejde-397	484	1	using	use	VERB
ejde-397	484	2	again	again	ADV
ejde-397	484	3	(	(	PUNCT
ejde-397	484	4	3.6	3.6	NUM
ejde-397	484	5	)	)	PUNCT
ejde-397	484	6	,	,	PUNCT
ejde-397	484	7	it	it	PRON
ejde-397	484	8	readily	readily	ADV
ejde-397	484	9	follows	follow	VERB
ejde-397	484	10	that	that	SCONJ
ejde-397	484	11	k̃(λ	k̃(λ	NOUN
ejde-397	484	12	)	)	PUNCT
ejde-397	485	1	=	=	SYM
ejde-397	485	2	f	f	X
ejde-397	485	3	(	(	PUNCT
ejde-397	485	4	√	√	PROPN
ejde-397	485	5	λ	λ	NOUN
ejde-397	485	6	)	)	PUNCT
ejde-397	485	7	,	,	PUNCT
ejde-397	485	8	as	as	SCONJ
ejde-397	485	9	claimed	claim	VERB
ejde-397	485	10	.	.	PUNCT
ejde-397	486	1	similarly	similarly	ADV
ejde-397	486	2	we	we	PRON
ejde-397	486	3	can	can	AUX
ejde-397	486	4	prove	prove	VERB
ejde-397	486	5	that	that	DET
ejde-397	486	6	j̃(λ	j̃(λ	NOUN
ejde-397	486	7	)	)	PUNCT
ejde-397	487	1	=	=	SYM
ejde-397	488	1	f	f	X
ejde-397	488	2	(	(	PUNCT
ejde-397	488	3	√	√	INTJ
ejde-397	488	4	λ)/	λ)/	X
ejde-397	488	5	√	√	NUM
ejde-397	488	6	λ	λ	INTJ
ejde-397	488	7	.	.	PUNCT
ejde-397	488	8	suppose	suppose	VERB
ejde-397	488	9	,	,	PUNCT
ejde-397	488	10	finally	finally	ADV
ejde-397	488	11	,	,	PUNCT
ejde-397	488	12	that	that	SCONJ
ejde-397	488	13	the	the	DET
ejde-397	488	14	requirements	requirement	NOUN
ejde-397	488	15	of	of	ADP
ejde-397	488	16	(	(	PUNCT
ejde-397	488	17	vi	vi	NOUN
ejde-397	488	18	)	)	PUNCT
ejde-397	488	19	hold	hold	NOUN
ejde-397	488	20	.	.	PUNCT
ejde-397	489	1	then	then	ADV
ejde-397	489	2	it	it	PRON
ejde-397	489	3	is	be	AUX
ejde-397	489	4	very	very	ADV
ejde-397	489	5	simple	simple	ADJ
ejde-397	489	6	to	to	PART
ejde-397	489	7	prove	prove	VERB
ejde-397	489	8	that	that	SCONJ
ejde-397	489	9	the	the	DET
ejde-397	489	10	mapping	mapping	NOUN
ejde-397	489	11	t	t	PROPN
ejde-397	489	12	7→	7→	NUM
ejde-397	489	13	(	(	PUNCT
ejde-397	489	14	h∗f)(t	h∗f)(t	PROPN
ejde-397	489	15	)	)	PUNCT
ejde-397	489	16	,	,	PUNCT
ejde-397	489	17	t	t	PROPN
ejde-397	489	18	≥	≥	NOUN
ejde-397	489	19	0	0	NUM
ejde-397	489	20	is	be	AUX
ejde-397	489	21	continuous	continuous	ADJ
ejde-397	489	22	as	as	ADV
ejde-397	489	23	well	well	ADV
ejde-397	489	24	as	as	ADP
ejde-397	489	25	that	that	PRON
ejde-397	489	26	ω(1	ω(1	PROPN
ejde-397	489	27	∗	∗	NOUN
ejde-397	489	28	h	h	NOUN
ejde-397	489	29	∗	∗	X
ejde-397	489	30	f	f	NOUN
ejde-397	489	31	)	)	PUNCT
ejde-397	489	32	=	=	SYM
ejde-397	489	33	ω(h	ω(h	PROPN
ejde-397	489	34	∗	∗	NOUN
ejde-397	489	35	(	(	PUNCT
ejde-397	489	36	1	1	NUM
ejde-397	489	37	∗	∗	NOUN
ejde-397	489	38	f	f	NOUN
ejde-397	489	39	)	)	PUNCT
ejde-397	489	40	)	)	PUNCT
ejde-397	490	1	<	<	X
ejde-397	490	2	∞.	∞.	PROPN
ejde-397	490	3	an	an	DET
ejde-397	490	4	application	application	NOUN
ejde-397	490	5	of	of	ADP
ejde-397	490	6	theorem	theorem	PROPN
ejde-397	490	7	3.2(v	3.2(v	NUM
ejde-397	490	8	)	)	PUNCT
ejde-397	490	9	yields	yield	NOUN
ejde-397	490	10	that	that	PRON
ejde-397	490	11	h	h	NOUN
ejde-397	490	12	∗	∗	VERB
ejde-397	490	13	f	f	PROPN
ejde-397	490	14	∈	∈	PROPN
ejde-397	490	15	(	(	PUNCT
ejde-397	490	16	p1)-x	p1)-x	NOUN
ejde-397	490	17	.	.	PUNCT
ejde-397	491	1	fix	fix	NOUN
ejde-397	491	2	now	now	ADV
ejde-397	491	3	a	a	DET
ejde-397	491	4	number	number	NOUN
ejde-397	491	5	λ	λ	X
ejde-397	491	6	∈	∈	NOUN
ejde-397	491	7	c	c	NOUN
ejde-397	491	8	with	with	ADP
ejde-397	491	9	<	<	X
ejde-397	491	10	λ	λ	X
ejde-397	491	11	>	>	X
ejde-397	491	12	max(abs(|h|	max(abs(|h|	PROPN
ejde-397	491	13	)	)	PUNCT
ejde-397	491	14	,	,	PUNCT
ejde-397	491	15	abs(f	abs(f	PROPN
ejde-397	491	16	)	)	PUNCT
ejde-397	491	17	)	)	PUNCT
ejde-397	491	18	.	.	PUNCT
ejde-397	492	1	since	since	SCONJ
ejde-397	492	2	abs(〈x∗	abs(〈x∗	PROPN
ejde-397	492	3	,	,	PUNCT
ejde-397	492	4	f	f	X
ejde-397	492	5	(	(	PUNCT
ejde-397	492	6	·	·	PUNCT
ejde-397	492	7	)	)	SYM
ejde-397	492	8	〉	〉	PROPN
ejde-397	492	9	)	)	PUNCT
ejde-397	492	10	≤	≤	PUNCT
ejde-397	492	11	abs(f	abs(f	PROPN
ejde-397	492	12	)	)	PUNCT
ejde-397	492	13	for	for	ADP
ejde-397	492	14	all	all	DET
ejde-397	492	15	x∗	x∗	PROPN
ejde-397	492	16	∈	∈	PROPN
ejde-397	492	17	x∗	x∗	PROPN
ejde-397	492	18	,	,	PUNCT
ejde-397	492	19	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	492	20	abstract	abstract	ADJ
ejde-397	492	21	degenerate	degenerate	ADJ
ejde-397	492	22	volterra	volterra	NOUN
ejde-397	492	23	inclusions	inclusion	NOUN
ejde-397	492	24	15	15	NUM
ejde-397	492	25	[	[	SYM
ejde-397	492	26	1	1	NUM
ejde-397	492	27	,	,	PUNCT
ejde-397	492	28	proposition	proposition	NOUN
ejde-397	492	29	1.6.4	1.6.4	NUM
ejde-397	492	30	]	]	PUNCT
ejde-397	492	31	implies	imply	VERB
ejde-397	492	32	that	that	SCONJ
ejde-397	492	33	(	(	PUNCT
ejde-397	492	34	l(h	l(h	PROPN
ejde-397	492	35	∗	∗	NOUN
ejde-397	492	36	〈	〈	PROPN
ejde-397	492	37	x∗	x∗	PROPN
ejde-397	492	38	,	,	PUNCT
ejde-397	492	39	f(·)〉))(λ	f(·)〉))(λ	NOUN
ejde-397	492	40	)	)	PUNCT
ejde-397	492	41	exists	exist	VERB
ejde-397	492	42	.	.	PUNCT
ejde-397	493	1	using	use	VERB
ejde-397	493	2	this	this	DET
ejde-397	493	3	fact	fact	NOUN
ejde-397	493	4	,	,	PUNCT
ejde-397	493	5	it	it	PRON
ejde-397	493	6	readily	readily	ADV
ejde-397	493	7	follows	follow	VERB
ejde-397	493	8	that	that	SCONJ
ejde-397	493	9	sup	sup	NOUN
ejde-397	493	10	t>0	t>0	NOUN
ejde-397	493	11	∣∣∣∫	∣∣∣∫	NOUN
ejde-397	493	12	t	t	NOUN
ejde-397	493	13	0	0	PUNCT
ejde-397	493	14	e−s	e−s	PROPN
ejde-397	493	15	<	<	X
ejde-397	493	16	λ	λ	X
ejde-397	493	17	(	(	PUNCT
ejde-397	493	18	h	h	PROPN
ejde-397	493	19	∗	∗	NOUN
ejde-397	493	20	〈	〈	PROPN
ejde-397	493	21	x∗	x∗	NOUN
ejde-397	493	22	,	,	PUNCT
ejde-397	493	23	f	f	X
ejde-397	493	24	(	(	PUNCT
ejde-397	493	25	·	·	PUNCT
ejde-397	493	26	)	)	PUNCT
ejde-397	493	27	〉	〉	NOUN
ejde-397	493	28	)	)	PUNCT
ejde-397	493	29	(	(	PUNCT
ejde-397	493	30	s	s	X
ejde-397	493	31	)	)	PUNCT
ejde-397	493	32	ds	ds	ADJ
ejde-397	493	33	∣∣∣	∣∣∣	NOUN
ejde-397	493	34	<	<	X
ejde-397	493	35	∞	∞	PROPN
ejde-397	493	36	,	,	PUNCT
ejde-397	493	37	x∗	x∗	PROPN
ejde-397	493	38	∈	∈	PROPN
ejde-397	493	39	x∗.	x∗.	PUNCT
ejde-397	493	40	by	by	ADP
ejde-397	493	41	theorem	theorem	PROPN
ejde-397	493	42	3.2(ii	3.2(ii	PROPN
ejde-397	493	43	)	)	PUNCT
ejde-397	493	44	,	,	PUNCT
ejde-397	493	45	we	we	PRON
ejde-397	493	46	obtain	obtain	VERB
ejde-397	493	47	that	that	SCONJ
ejde-397	493	48	h̃	h̃	PROPN
ejde-397	493	49	∗	∗	NOUN
ejde-397	493	50	f(λ	f(λ	NOUN
ejde-397	493	51	)	)	PUNCT
ejde-397	493	52	exists	exist	VERB
ejde-397	493	53	.	.	PUNCT
ejde-397	494	1	the	the	DET
ejde-397	494	2	equality	equality	NOUN
ejde-397	494	3	h̃	h̃	PROPN
ejde-397	494	4	∗	∗	NOUN
ejde-397	494	5	f(λ	f(λ	NOUN
ejde-397	494	6	)	)	PUNCT
ejde-397	494	7	=	=	SYM
ejde-397	494	8	h̃(λ)f̃(λ	h̃(λ)f̃(λ	NOUN
ejde-397	494	9	)	)	PUNCT
ejde-397	494	10	can	can	AUX
ejde-397	494	11	be	be	AUX
ejde-397	494	12	proved	prove	VERB
ejde-397	494	13	in	in	ADP
ejde-397	494	14	a	a	DET
ejde-397	494	15	routine	routine	ADJ
ejde-397	494	16	manner	manner	NOUN
ejde-397	494	17	.	.	PUNCT
ejde-397	495	1	�	�	PROPN
ejde-397	495	2	for	for	ADP
ejde-397	495	3	the	the	DET
ejde-397	495	4	sequel	sequel	NOUN
ejde-397	495	5	,	,	PUNCT
ejde-397	495	6	we	we	PRON
ejde-397	495	7	need	need	VERB
ejde-397	495	8	the	the	DET
ejde-397	495	9	notion	notion	NOUN
ejde-397	495	10	of	of	ADP
ejde-397	495	11	a	a	DET
ejde-397	495	12	lebesgue	lebesgue	NOUN
ejde-397	495	13	point	point	NOUN
ejde-397	495	14	of	of	ADP
ejde-397	495	15	a	a	DET
ejde-397	495	16	function	function	NOUN
ejde-397	495	17	f	f	PROPN
ejde-397	495	18	∈	∈	PROPN
ejde-397	495	19	l1	l1	PROPN
ejde-397	495	20	loc([0,∞	loc([0,∞	PROPN
ejde-397	495	21	)	)	PUNCT
ejde-397	495	22	:	:	PUNCT
ejde-397	496	1	x	x	X
ejde-397	496	2	)	)	PUNCT
ejde-397	496	3	.	.	PUNCT
ejde-397	497	1	a	a	DET
ejde-397	497	2	point	point	NOUN
ejde-397	497	3	t	t	PROPN
ejde-397	497	4	≥	≥	NOUN
ejde-397	497	5	0	0	NUM
ejde-397	497	6	is	be	AUX
ejde-397	497	7	said	say	VERB
ejde-397	497	8	to	to	PART
ejde-397	497	9	be	be	AUX
ejde-397	497	10	a	a	DET
ejde-397	497	11	lebesgue	lebesgue	ADJ
ejde-397	497	12	point	point	NOUN
ejde-397	497	13	of	of	ADP
ejde-397	497	14	f	f	PROPN
ejde-397	497	15	(	(	PUNCT
ejde-397	497	16	·	·	PUNCT
ejde-397	497	17	)	)	PUNCT
ejde-397	497	18	if	if	SCONJ
ejde-397	497	19	and	and	CCONJ
ejde-397	497	20	only	only	ADV
ejde-397	497	21	if	if	SCONJ
ejde-397	497	22	for	for	ADP
ejde-397	497	23	each	each	DET
ejde-397	497	24	seminorm	seminorm	NOUN
ejde-397	497	25	p	p	PROPN
ejde-397	497	26	∈	∈	PROPN
ejde-397	498	1	~	~	PUNCT
ejde-397	498	2	,	,	PUNCT
ejde-397	498	3	we	we	PRON
ejde-397	498	4	have	have	VERB
ejde-397	498	5	lim	lim	NOUN
ejde-397	498	6	h→0	h→0	ADV
ejde-397	498	7	1	1	NUM
ejde-397	498	8	h	h	NOUN
ejde-397	498	9	∫	∫	PROPN
ejde-397	498	10	t+h	t+h	X
ejde-397	499	1	t	t	PROPN
ejde-397	499	2	p	p	X
ejde-397	499	3	(	(	PUNCT
ejde-397	499	4	f(s)−	f(s)−	ADP
ejde-397	499	5	f(t	f(t	PROPN
ejde-397	499	6	)	)	PUNCT
ejde-397	499	7	)	)	PUNCT
ejde-397	499	8	ds	ds	NOUN
ejde-397	499	9	=	=	NOUN
ejde-397	499	10	0	0	PROPN
ejde-397	499	11	.	.	PUNCT
ejde-397	500	1	(	(	PUNCT
ejde-397	500	2	3.7	3.7	NUM
ejde-397	500	3	)	)	PUNCT
ejde-397	500	4	it	it	PRON
ejde-397	500	5	is	be	AUX
ejde-397	500	6	clear	clear	ADJ
ejde-397	500	7	that	that	SCONJ
ejde-397	500	8	any	any	DET
ejde-397	500	9	point	point	NOUN
ejde-397	500	10	of	of	ADP
ejde-397	500	11	continuity	continuity	NOUN
ejde-397	500	12	of	of	ADP
ejde-397	500	13	function	function	NOUN
ejde-397	500	14	f	f	X
ejde-397	500	15	(	(	PUNCT
ejde-397	500	16	·	·	PUNCT
ejde-397	500	17	)	)	PUNCT
ejde-397	500	18	is	be	AUX
ejde-397	500	19	one	one	NUM
ejde-397	500	20	of	of	ADP
ejde-397	500	21	lebesgue	lebesgue	NOUN
ejde-397	500	22	’s	’s	PART
ejde-397	500	23	points	point	NOUN
ejde-397	500	24	of	of	ADP
ejde-397	500	25	f	f	X
ejde-397	500	26	(	(	PUNCT
ejde-397	500	27	·	·	PUNCT
ejde-397	500	28	)	)	PUNCT
ejde-397	500	29	,	,	PUNCT
ejde-397	500	30	as	as	ADV
ejde-397	500	31	well	well	ADV
ejde-397	500	32	as	as	ADP
ejde-397	500	33	that	that	SCONJ
ejde-397	500	34	the	the	DET
ejde-397	500	35	mapping	mapping	NOUN
ejde-397	500	36	t	t	PROPN
ejde-397	500	37	7→	7→	NUM
ejde-397	500	38	f	f	PROPN
ejde-397	500	39	(	(	PUNCT
ejde-397	500	40	t	t	PROPN
ejde-397	500	41	)	)	PUNCT
ejde-397	500	42	,	,	PUNCT
ejde-397	500	43	t	t	PROPN
ejde-397	500	44	≥	≥	NOUN
ejde-397	500	45	0	0	NUM
ejde-397	500	46	is	be	AUX
ejde-397	500	47	differentiable	differentiable	ADJ
ejde-397	500	48	at	at	ADP
ejde-397	500	49	any	any	DET
ejde-397	500	50	lebesgue	lebesgue	NOUN
ejde-397	500	51	’s	’s	PART
ejde-397	500	52	point	point	NOUN
ejde-397	500	53	of	of	ADP
ejde-397	500	54	f	f	PROPN
ejde-397	500	55	(	(	PUNCT
ejde-397	500	56	·	·	PUNCT
ejde-397	500	57	)	)	PUNCT
ejde-397	500	58	.	.	PUNCT
ejde-397	501	1	furthermore	furthermore	ADV
ejde-397	501	2	,	,	PUNCT
ejde-397	501	3	a	a	DET
ejde-397	501	4	slight	slight	ADJ
ejde-397	501	5	modification	modification	NOUN
ejde-397	501	6	of	of	ADP
ejde-397	501	7	the	the	DET
ejde-397	501	8	proof	proof	NOUN
ejde-397	501	9	of	of	ADP
ejde-397	501	10	[	[	X
ejde-397	501	11	1	1	NUM
ejde-397	501	12	,	,	PUNCT
ejde-397	501	13	proposition	proposition	NOUN
ejde-397	501	14	1.2.2	1.2.2	NUM
ejde-397	501	15	;	;	PUNCT
ejde-397	501	16	a)/b	a)/b	PROPN
ejde-397	501	17	)	)	PUNCT
ejde-397	501	18	]	]	PUNCT
ejde-397	501	19	shows	show	VERB
ejde-397	501	20	that	that	SCONJ
ejde-397	501	21	the	the	DET
ejde-397	501	22	following	follow	VERB
ejde-397	501	23	holds	hold	VERB
ejde-397	501	24	:	:	PUNCT
ejde-397	501	25	(	(	PUNCT
ejde-397	501	26	q1	q1	NOUN
ejde-397	501	27	)	)	PUNCT
ejde-397	501	28	for	for	ADP
ejde-397	501	29	each	each	DET
ejde-397	501	30	seminorm	seminorm	NOUN
ejde-397	501	31	p	p	PROPN
ejde-397	501	32	∈	∈	PROPN
ejde-397	501	33	~	~	PUNCT
ejde-397	501	34	there	there	PRON
ejde-397	501	35	exists	exist	VERB
ejde-397	501	36	a	a	DET
ejde-397	501	37	set	set	NOUN
ejde-397	501	38	np	np	PRON
ejde-397	501	39	⊆	⊆	NUM
ejde-397	501	40	[	[	X
ejde-397	501	41	0,∞	0,∞	NOUN
ejde-397	501	42	)	)	PUNCT
ejde-397	501	43	of	of	ADP
ejde-397	501	44	lebesgue	lebesgue	PROPN
ejde-397	501	45	’s	’s	PART
ejde-397	501	46	measure	measure	NOUN
ejde-397	501	47	zero	zero	NUM
ejde-397	501	48	such	such	ADJ
ejde-397	501	49	that	that	SCONJ
ejde-397	501	50	lim	lim	PROPN
ejde-397	501	51	h→0	h→0	ADV
ejde-397	501	52	p	p	X
ejde-397	501	53	(	(	PUNCT
ejde-397	501	54	1	1	NUM
ejde-397	501	55	h	h	NOUN
ejde-397	501	56	∫	∫	PROPN
ejde-397	501	57	t+h	t+h	X
ejde-397	501	58	t	t	PROPN
ejde-397	501	59	f(s	f(	NOUN
ejde-397	501	60	)	)	PUNCT
ejde-397	501	61	ds−	ds−	PROPN
ejde-397	501	62	f(t	f(t	NOUN
ejde-397	501	63	)	)	PUNCT
ejde-397	501	64	)	)	PUNCT
ejde-397	502	1	=	=	PUNCT
ejde-397	502	2	0	0	NUM
ejde-397	502	3	,	,	PUNCT
ejde-397	502	4	t	t	PROPN
ejde-397	502	5	∈	∈	PROPN
ejde-397	503	1	[	[	X
ejde-397	503	2	0,∞	0,∞	NUM
ejde-397	503	3	)	)	PUNCT
ejde-397	503	4	\np	\np	PROPN
ejde-397	503	5	and	and	CCONJ
ejde-397	503	6	that	that	SCONJ
ejde-397	503	7	(	(	PUNCT
ejde-397	503	8	3.7	3.7	NUM
ejde-397	503	9	)	)	PUNCT
ejde-397	503	10	holds	hold	VERB
ejde-397	503	11	for	for	ADP
ejde-397	503	12	t	t	PROPN
ejde-397	503	13	∈	∈	PROPN
ejde-397	503	14	[	[	X
ejde-397	503	15	0,∞	0,∞	NOUN
ejde-397	503	16	)	)	PUNCT
ejde-397	503	17	\np	\np	PROPN
ejde-397	503	18	.	.	PUNCT
ejde-397	504	1	in	in	ADP
ejde-397	504	2	the	the	DET
ejde-397	504	3	case	case	NOUN
ejde-397	504	4	that	that	SCONJ
ejde-397	504	5	x	x	PRON
ejde-397	504	6	is	be	AUX
ejde-397	504	7	a	a	DET
ejde-397	504	8	fréchet	fréchet	NOUN
ejde-397	504	9	space	space	NOUN
ejde-397	504	10	,	,	PUNCT
ejde-397	504	11	(	(	PUNCT
ejde-397	504	12	q1	q1	PROPN
ejde-397	504	13	)	)	PUNCT
ejde-397	504	14	immediately	immediately	ADV
ejde-397	504	15	implies	imply	VERB
ejde-397	504	16	that	that	SCONJ
ejde-397	504	17	almost	almost	ADV
ejde-397	504	18	every	every	DET
ejde-397	504	19	point	point	NOUN
ejde-397	504	20	t	t	X
ejde-397	504	21	>	>	X
ejde-397	504	22	0	0	PUNCT
ejde-397	504	23	is	be	AUX
ejde-397	504	24	a	a	DET
ejde-397	504	25	lebesgue	lebesgue	ADJ
ejde-397	504	26	point	point	NOUN
ejde-397	504	27	of	of	ADP
ejde-397	504	28	f	f	PROPN
ejde-397	504	29	(	(	PUNCT
ejde-397	504	30	·	·	PUNCT
ejde-397	504	31	)	)	PUNCT
ejde-397	504	32	.	.	PUNCT
ejde-397	505	1	using	use	VERB
ejde-397	505	2	the	the	DET
ejde-397	505	3	proof	proof	NOUN
ejde-397	505	4	of	of	ADP
ejde-397	505	5	[	[	X
ejde-397	505	6	1	1	NUM
ejde-397	505	7	,	,	PUNCT
ejde-397	505	8	theorem	theorem	VERB
ejde-397	505	9	1.7.7	1.7.7	NUM
ejde-397	505	10	]	]	PUNCT
ejde-397	505	11	,	,	PUNCT
ejde-397	505	12	theorem	theorem	VERB
ejde-397	505	13	3.1(iii	3.1(iii	NUM
ejde-397	505	14	)	)	PUNCT
ejde-397	505	15	,	,	PUNCT
ejde-397	505	16	as	as	ADV
ejde-397	505	17	well	well	ADV
ejde-397	505	18	as	as	ADP
ejde-397	505	19	the	the	DET
ejde-397	505	20	equations	equation	NOUN
ejde-397	505	21	(	(	PUNCT
ejde-397	505	22	1.6	1.6	NUM
ejde-397	505	23	)	)	PUNCT
ejde-397	505	24	and	and	CCONJ
ejde-397	505	25	(	(	PUNCT
ejde-397	505	26	3.5	3.5	NUM
ejde-397	505	27	)	)	PUNCT
ejde-397	505	28	,	,	PUNCT
ejde-397	505	29	we	we	PRON
ejde-397	505	30	can	can	AUX
ejde-397	505	31	simply	simply	ADV
ejde-397	505	32	prove	prove	VERB
ejde-397	505	33	that	that	SCONJ
ejde-397	505	34	the	the	DET
ejde-397	505	35	post	post	ADJ
ejde-397	505	36	-	-	ADJ
ejde-397	505	37	widder	widder	ADJ
ejde-397	505	38	inversion	inversion	NOUN
ejde-397	505	39	formula	formula	NOUN
ejde-397	505	40	holds	hold	VERB
ejde-397	505	41	in	in	ADP
ejde-397	505	42	our	our	PRON
ejde-397	505	43	framework	framework	NOUN
ejde-397	505	44	:	:	PUNCT
ejde-397	505	45	theorem	theorem	VERB
ejde-397	505	46	3.4	3.4	NUM
ejde-397	505	47	(	(	PUNCT
ejde-397	505	48	post	post	ADJ
ejde-397	505	49	-	-	ADJ
ejde-397	505	50	widder	widder	NOUN
ejde-397	505	51	)	)	PUNCT
ejde-397	505	52	.	.	PUNCT
ejde-397	506	1	suppose	suppose	VERB
ejde-397	506	2	f	f	PROPN
ejde-397	506	3	∈	∈	PROPN
ejde-397	506	4	(	(	PUNCT
ejde-397	506	5	p1)−x	p1)−x	PROPN
ejde-397	506	6	and	and	CCONJ
ejde-397	506	7	t	t	PROPN
ejde-397	506	8	>	>	X
ejde-397	506	9	0	0	PUNCT
ejde-397	506	10	is	be	AUX
ejde-397	506	11	a	a	DET
ejde-397	506	12	lebesgue	lebesgue	ADJ
ejde-397	506	13	point	point	NOUN
ejde-397	506	14	of	of	ADP
ejde-397	506	15	f	f	PROPN
ejde-397	506	16	(	(	PUNCT
ejde-397	506	17	·	·	PUNCT
ejde-397	506	18	)	)	PUNCT
ejde-397	506	19	.	.	PUNCT
ejde-397	507	1	then	then	ADV
ejde-397	507	2	f(t	f(t	NOUN
ejde-397	507	3	)	)	PUNCT
ejde-397	508	1	=	=	SYM
ejde-397	508	2	lim	lim	PROPN
ejde-397	508	3	n→∞	n→∞	X
ejde-397	508	4	(	(	PUNCT
ejde-397	508	5	−1)n	−1)n	PROPN
ejde-397	508	6	1	1	NUM
ejde-397	508	7	n	n	NOUN
ejde-397	508	8	!	!	PUNCT
ejde-397	509	1	(	(	PUNCT
ejde-397	509	2	n	n	X
ejde-397	509	3	t	t	NOUN
ejde-397	509	4	)	)	PUNCT
ejde-397	510	1	n+1	n+1	PROPN
ejde-397	510	2	f̃	f̃	PROPN
ejde-397	510	3	(	(	PUNCT
ejde-397	510	4	n	n	CCONJ
ejde-397	510	5	)	)	PUNCT
ejde-397	510	6	(	(	PUNCT
ejde-397	510	7	n	n	X
ejde-397	510	8	t	t	PROPN
ejde-397	510	9	)	)	PUNCT
ejde-397	510	10	.	.	PUNCT
ejde-397	511	1	the	the	DET
ejde-397	511	2	situation	situation	NOUN
ejde-397	511	3	is	be	AUX
ejde-397	511	4	much	much	ADV
ejde-397	511	5	more	more	ADV
ejde-397	511	6	complicated	complicated	ADJ
ejde-397	511	7	if	if	SCONJ
ejde-397	511	8	we	we	PRON
ejde-397	511	9	consider	consider	VERB
ejde-397	511	10	the	the	DET
ejde-397	511	11	phragmén	phragmén	PROPN
ejde-397	511	12	-	-	PUNCT
ejde-397	511	13	doetsch	doetsch	NOUN
ejde-397	511	14	inversion	inversion	NOUN
ejde-397	511	15	formula	formula	NOUN
ejde-397	511	16	for	for	ADP
ejde-397	511	17	the	the	DET
ejde-397	511	18	laplace	laplace	NOUN
ejde-397	511	19	transform	transform	NOUN
ejde-397	511	20	of	of	ADP
ejde-397	511	21	functions	function	NOUN
ejde-397	511	22	with	with	ADP
ejde-397	511	23	values	value	NOUN
ejde-397	511	24	in	in	ADP
ejde-397	511	25	sclcss	sclcss	PROPN
ejde-397	511	26	.	.	PUNCT
ejde-397	512	1	the	the	DET
ejde-397	512	2	following	following	ADJ
ejde-397	512	3	result	result	NOUN
ejde-397	512	4	of	of	ADP
ejde-397	512	5	this	this	DET
ejde-397	512	6	type	type	NOUN
ejde-397	512	7	will	will	AUX
ejde-397	512	8	be	be	AUX
ejde-397	512	9	sufficiently	sufficiently	ADV
ejde-397	512	10	general	general	ADJ
ejde-397	512	11	for	for	ADP
ejde-397	512	12	our	our	PRON
ejde-397	512	13	purposes	purpose	NOUN
ejde-397	512	14	:	:	PUNCT
ejde-397	512	15	theorem	theorem	VERB
ejde-397	512	16	3.5	3.5	NUM
ejde-397	512	17	.	.	PUNCT
ejde-397	513	1	let	let	VERB
ejde-397	513	2	f	f	PROPN
ejde-397	513	3	∈	∈	PROPN
ejde-397	513	4	(	(	PUNCT
ejde-397	513	5	p1)-x	p1)-x	NOUN
ejde-397	513	6	and	and	CCONJ
ejde-397	513	7	t	t	NOUN
ejde-397	513	8	≥	≥	NUM
ejde-397	513	9	0	0	NUM
ejde-397	513	10	.	.	PUNCT
ejde-397	514	1	then	then	ADV
ejde-397	514	2	the	the	DET
ejde-397	514	3	following	follow	VERB
ejde-397	514	4	holds	hold	VERB
ejde-397	514	5	:	:	PUNCT
ejde-397	514	6	f	f	PROPN
ejde-397	515	1	[	[	X
ejde-397	515	2	2](t	2](t	NUM
ejde-397	515	3	)	)	PUNCT
ejde-397	515	4	=	=	SYM
ejde-397	515	5	lim	lim	PROPN
ejde-397	515	6	λ→∞	λ→∞	NUM
ejde-397	515	7	∞∑	∞∑	PROPN
ejde-397	515	8	n=1	n=1	PROPN
ejde-397	515	9	(	(	PUNCT
ejde-397	515	10	−1)n−1n!−1enλt	−1)n−1n!−1enλt	NOUN
ejde-397	515	11	f̃(nλ	f̃(nλ	PROPN
ejde-397	515	12	)	)	PUNCT
ejde-397	515	13	nλ	nλ	INTJ
ejde-397	515	14	.	.	PUNCT
ejde-397	516	1	proof	proof	NOUN
ejde-397	516	2	.	.	PUNCT
ejde-397	517	1	due	due	ADP
ejde-397	517	2	to	to	ADP
ejde-397	517	3	theorem	theorem	ADJ
ejde-397	517	4	3.2(v	3.2(v	NUM
ejde-397	517	5	)	)	PUNCT
ejde-397	517	6	,	,	PUNCT
ejde-397	517	7	we	we	PRON
ejde-397	517	8	have	have	VERB
ejde-397	517	9	f	f	PROPN
ejde-397	517	10	∈	∈	PROPN
ejde-397	517	11	c([0,∞	c([0,∞	PROPN
ejde-397	517	12	)	)	PUNCT
ejde-397	517	13	:	:	PUNCT
ejde-397	518	1	x	x	X
ejde-397	518	2	)	)	PUNCT
ejde-397	518	3	and	and	CCONJ
ejde-397	518	4	ω(f	ω(f	PROPN
ejde-397	518	5	)	)	PUNCT
ejde-397	518	6	<	<	X
ejde-397	518	7	∞.	∞.	PROPN
ejde-397	518	8	the	the	DET
ejde-397	518	9	result	result	NOUN
ejde-397	518	10	now	now	ADV
ejde-397	518	11	follows	follow	VERB
ejde-397	518	12	easily	easily	ADV
ejde-397	518	13	from	from	ADP
ejde-397	518	14	[	[	X
ejde-397	518	15	36	36	NUM
ejde-397	518	16	,	,	PUNCT
ejde-397	518	17	theorem	theorem	VERB
ejde-397	518	18	1.2.1(ix	1.2.1(ix	NUM
ejde-397	518	19	)	)	PUNCT
ejde-397	518	20	]	]	PUNCT
ejde-397	518	21	.	.	PUNCT
ejde-397	519	1	�	�	PROPN
ejde-397	519	2	now	now	ADV
ejde-397	519	3	we	we	PRON
ejde-397	519	4	will	will	AUX
ejde-397	519	5	state	state	VERB
ejde-397	519	6	and	and	CCONJ
ejde-397	519	7	prove	prove	VERB
ejde-397	519	8	the	the	DET
ejde-397	519	9	following	follow	VERB
ejde-397	519	10	uniqueness	uniqueness	NOUN
ejde-397	519	11	type	type	NOUN
ejde-397	519	12	theorem	theorem	NOUN
ejde-397	519	13	for	for	ADP
ejde-397	519	14	the	the	DET
ejde-397	519	15	laplace	laplace	NOUN
ejde-397	519	16	transform	transform	NOUN
ejde-397	519	17	.	.	PUNCT
ejde-397	520	1	16	16	NUM
ejde-397	520	2	m.	m.	NOUN
ejde-397	520	3	kostić	kostić	NOUN
ejde-397	520	4	ejde-2023/63	ejde-2023/63	PROPN
ejde-397	520	5	theorem	theorem	ADJ
ejde-397	520	6	3.6	3.6	NUM
ejde-397	520	7	(	(	PUNCT
ejde-397	520	8	uniqueness	uniqueness	NOUN
ejde-397	520	9	theorem	theorem	VERB
ejde-397	520	10	for	for	ADP
ejde-397	520	11	the	the	DET
ejde-397	520	12	laplace	laplace	NOUN
ejde-397	520	13	transform	transform	NOUN
ejde-397	520	14	)	)	PUNCT
ejde-397	520	15	.	.	PUNCT
ejde-397	520	16	suppose	suppose	VERB
ejde-397	520	17	that	that	SCONJ
ejde-397	520	18	f	f	PROPN
ejde-397	520	19	∈	∈	PROPN
ejde-397	520	20	(	(	PUNCT
ejde-397	520	21	p1)−x	p1)−x	NOUN
ejde-397	520	22	,	,	PUNCT
ejde-397	520	23	λ0	λ0	NOUN
ejde-397	520	24	>	>	X
ejde-397	520	25	abs(f	abs(f	PROPN
ejde-397	520	26	)	)	PUNCT
ejde-397	520	27	and	and	CCONJ
ejde-397	520	28	f̃(λ	f̃(λ	PROPN
ejde-397	520	29	)	)	PUNCT
ejde-397	520	30	=	=	SYM
ejde-397	520	31	0	0	NUM
ejde-397	520	32	for	for	ADP
ejde-397	520	33	all	all	DET
ejde-397	520	34	λ	λ	PROPN
ejde-397	520	35	>	>	X
ejde-397	520	36	λ0	λ0	NOUN
ejde-397	520	37	.	.	PUNCT
ejde-397	521	1	then	then	ADV
ejde-397	521	2	f	f	PROPN
ejde-397	521	3	(	(	PUNCT
ejde-397	521	4	t	t	PROPN
ejde-397	521	5	)	)	PUNCT
ejde-397	521	6	=	=	SYM
ejde-397	521	7	0	0	NUM
ejde-397	521	8	,	,	PUNCT
ejde-397	521	9	t	t	PROPN
ejde-397	521	10	≥	≥	NUM
ejde-397	521	11	0	0	NUM
ejde-397	521	12	,	,	PUNCT
ejde-397	521	13	f(t	f(t	PROPN
ejde-397	521	14	)	)	PUNCT
ejde-397	522	1	=	=	SYM
ejde-397	522	2	0	0	PUNCT
ejde-397	523	1	if	if	SCONJ
ejde-397	523	2	t	t	PROPN
ejde-397	523	3	>	>	X
ejde-397	523	4	0	0	PUNCT
ejde-397	523	5	is	be	AUX
ejde-397	523	6	a	a	DET
ejde-397	523	7	lebesgue	lebesgue	ADJ
ejde-397	523	8	point	point	NOUN
ejde-397	523	9	of	of	ADP
ejde-397	523	10	f	f	PROPN
ejde-397	523	11	(	(	PUNCT
ejde-397	523	12	·	·	PUNCT
ejde-397	523	13	)	)	PUNCT
ejde-397	523	14	,	,	PUNCT
ejde-397	523	15	and	and	CCONJ
ejde-397	523	16	for	for	ADP
ejde-397	523	17	each	each	DET
ejde-397	523	18	seminorm	seminorm	NOUN
ejde-397	523	19	p	p	PROPN
ejde-397	523	20	∈	∈	PROPN
ejde-397	523	21	~	~	PUNCT
ejde-397	523	22	there	there	PRON
ejde-397	523	23	exists	exist	VERB
ejde-397	523	24	a	a	DET
ejde-397	523	25	set	set	NOUN
ejde-397	523	26	np	np	PRON
ejde-397	523	27	⊆	⊆	NUM
ejde-397	523	28	[	[	X
ejde-397	523	29	0,∞	0,∞	NOUN
ejde-397	523	30	)	)	PUNCT
ejde-397	523	31	of	of	ADP
ejde-397	523	32	lebesgue	lebesgue	PROPN
ejde-397	523	33	’s	’s	PART
ejde-397	523	34	measure	measure	NOUN
ejde-397	523	35	zero	zero	NUM
ejde-397	523	36	such	such	ADJ
ejde-397	523	37	that	that	DET
ejde-397	523	38	p(f(t	p(f(t	NOUN
ejde-397	523	39	)	)	PUNCT
ejde-397	523	40	)	)	PUNCT
ejde-397	524	1	=	=	SYM
ejde-397	524	2	0	0	NUM
ejde-397	524	3	,	,	PUNCT
ejde-397	524	4	t	t	PROPN
ejde-397	524	5	∈	∈	PROPN
ejde-397	525	1	[	[	X
ejde-397	525	2	0,∞	0,∞	NOUN
ejde-397	525	3	)	)	PUNCT
ejde-397	525	4	\np	\np	PROPN
ejde-397	525	5	.	.	PUNCT
ejde-397	526	1	in	in	ADP
ejde-397	526	2	particular	particular	ADJ
ejde-397	526	3	,	,	PUNCT
ejde-397	526	4	if	if	SCONJ
ejde-397	526	5	x	x	PRON
ejde-397	526	6	is	be	AUX
ejde-397	526	7	a	a	DET
ejde-397	526	8	fréchet	fréchet	NOUN
ejde-397	526	9	space	space	NOUN
ejde-397	526	10	,	,	PUNCT
ejde-397	526	11	then	then	ADV
ejde-397	526	12	f(t	f(t	NOUN
ejde-397	526	13	)	)	PUNCT
ejde-397	527	1	=	=	SYM
ejde-397	527	2	0	0	NUM
ejde-397	528	1	for	for	ADP
ejde-397	528	2	a.e	a.e	PROPN
ejde-397	528	3	.	.	PROPN
ejde-397	528	4	t	t	PROPN
ejde-397	528	5	≥	≥	PROPN
ejde-397	528	6	0	0	NUM
ejde-397	528	7	.	.	PUNCT
ejde-397	528	8	proof	proof	NOUN
ejde-397	528	9	.	.	PUNCT
ejde-397	529	1	the	the	DET
ejde-397	529	2	function	function	NOUN
ejde-397	529	3	t	t	PROPN
ejde-397	529	4	7→	7→	NUM
ejde-397	529	5	f	f	PROPN
ejde-397	529	6	(	(	PUNCT
ejde-397	529	7	t	t	PROPN
ejde-397	529	8	)	)	PUNCT
ejde-397	529	9	,	,	PUNCT
ejde-397	529	10	t	t	PROPN
ejde-397	529	11	≥	≥	NOUN
ejde-397	529	12	0	0	NUM
ejde-397	529	13	is	be	AUX
ejde-397	529	14	continuous	continuous	ADJ
ejde-397	529	15	and	and	CCONJ
ejde-397	529	16	by	by	ADP
ejde-397	529	17	theorem	theorem	NOUN
ejde-397	529	18	3.2(v	3.2(v	NUM
ejde-397	529	19	)	)	PUNCT
ejde-397	529	20	we	we	PRON
ejde-397	529	21	obtain	obtain	VERB
ejde-397	529	22	that	that	DET
ejde-397	529	23	ω(f	ω(f	NUM
ejde-397	529	24	)	)	PUNCT
ejde-397	529	25	<	<	X
ejde-397	529	26	∞	∞	PROPN
ejde-397	529	27	and	and	CCONJ
ejde-397	529	28	f̃	f̃	PROPN
ejde-397	529	29	(	(	PUNCT
ejde-397	529	30	λ	λ	NOUN
ejde-397	529	31	)	)	PUNCT
ejde-397	529	32	=	=	SYM
ejde-397	529	33	0	0	NUM
ejde-397	529	34	,	,	PUNCT
ejde-397	529	35	λ	λ	X
ejde-397	529	36	>	>	X
ejde-397	529	37	max(λ0	max(λ0	PROPN
ejde-397	529	38	,	,	PUNCT
ejde-397	529	39	0	0	NUM
ejde-397	529	40	)	)	PUNCT
ejde-397	529	41	.	.	PUNCT
ejde-397	530	1	now	now	ADV
ejde-397	530	2	we	we	PRON
ejde-397	530	3	can	can	AUX
ejde-397	530	4	apply	apply	VERB
ejde-397	530	5	theorem	theorem	ADJ
ejde-397	530	6	3.4	3.4	NUM
ejde-397	530	7	in	in	ADP
ejde-397	530	8	order	order	NOUN
ejde-397	530	9	to	to	PART
ejde-397	530	10	see	see	VERB
ejde-397	530	11	that	that	SCONJ
ejde-397	530	12	f	f	PROPN
ejde-397	530	13	(	(	PUNCT
ejde-397	530	14	t	t	PROPN
ejde-397	530	15	)	)	PUNCT
ejde-397	530	16	=	=	SYM
ejde-397	530	17	0	0	NUM
ejde-397	530	18	,	,	PUNCT
ejde-397	530	19	t	t	PROPN
ejde-397	530	20	≥	≥	NUM
ejde-397	530	21	0	0	NUM
ejde-397	530	22	.	.	PUNCT
ejde-397	531	1	the	the	DET
ejde-397	531	2	remaining	remain	VERB
ejde-397	531	3	part	part	NOUN
ejde-397	531	4	of	of	ADP
ejde-397	531	5	proof	proof	NOUN
ejde-397	531	6	is	be	AUX
ejde-397	531	7	simple	simple	ADJ
ejde-397	531	8	and	and	CCONJ
ejde-397	531	9	therefore	therefore	ADV
ejde-397	531	10	omitted	omit	VERB
ejde-397	531	11	.	.	PUNCT
ejde-397	532	1	�	�	PROPN
ejde-397	532	2	remark	remark	VERB
ejde-397	532	3	3.7	3.7	NUM
ejde-397	532	4	.	.	PUNCT
ejde-397	533	1	suppose	suppose	VERB
ejde-397	533	2	that	that	SCONJ
ejde-397	533	3	f	f	PROPN
ejde-397	533	4	∈	∈	PROPN
ejde-397	533	5	l1	l1	PROPN
ejde-397	533	6	loc([0,∞	loc([0,∞	PROPN
ejde-397	533	7	)	)	PUNCT
ejde-397	533	8	:	:	PUNCT
ejde-397	534	1	x	x	X
ejde-397	534	2	)	)	PUNCT
ejde-397	534	3	and	and	CCONJ
ejde-397	534	4	for	for	ADP
ejde-397	534	5	each	each	DET
ejde-397	534	6	seminorm	seminorm	NOUN
ejde-397	534	7	p	p	PROPN
ejde-397	534	8	∈	∈	PROPN
ejde-397	534	9	~	~	PUNCT
ejde-397	534	10	there	there	PRON
ejde-397	534	11	exists	exist	VERB
ejde-397	534	12	a	a	DET
ejde-397	534	13	set	set	NOUN
ejde-397	534	14	np	np	PRON
ejde-397	534	15	⊆	⊆	NUM
ejde-397	534	16	[	[	X
ejde-397	534	17	0,∞	0,∞	NOUN
ejde-397	534	18	)	)	PUNCT
ejde-397	534	19	of	of	ADP
ejde-397	534	20	lebesgue	lebesgue	PROPN
ejde-397	534	21	’s	’s	PART
ejde-397	534	22	measure	measure	NOUN
ejde-397	534	23	zero	zero	NUM
ejde-397	534	24	such	such	ADJ
ejde-397	534	25	that	that	DET
ejde-397	534	26	p(f(t	p(f(t	NOUN
ejde-397	534	27	)	)	PUNCT
ejde-397	534	28	)	)	PUNCT
ejde-397	535	1	=	=	SYM
ejde-397	535	2	0	0	NUM
ejde-397	535	3	,	,	PUNCT
ejde-397	535	4	t	t	PROPN
ejde-397	535	5	∈	∈	PROPN
ejde-397	536	1	[	[	X
ejde-397	536	2	0,∞	0,∞	NUM
ejde-397	536	3	)	)	PUNCT
ejde-397	536	4	\	\	PROPN
ejde-397	537	1	np	np	PROPN
ejde-397	537	2	.	.	PUNCT
ejde-397	537	3	then	then	ADV
ejde-397	537	4	abs(f	abs(f	PROPN
ejde-397	537	5	)	)	PUNCT
ejde-397	538	1	=	=	SYM
ejde-397	538	2	abs(p(f	abs(p(f	PROPN
ejde-397	538	3	)	)	PUNCT
ejde-397	538	4	)	)	PUNCT
ejde-397	539	1	=	=	PUNCT
ejde-397	539	2	−∞	−∞	X
ejde-397	539	3	(	(	PUNCT
ejde-397	539	4	p	p	X
ejde-397	539	5	∈	∈	PROPN
ejde-397	539	6	~	~	PUNCT
ejde-397	539	7	)	)	PUNCT
ejde-397	539	8	and	and	CCONJ
ejde-397	539	9	f̃(λ	f̃(λ	PROPN
ejde-397	539	10	)	)	PUNCT
ejde-397	539	11	=	=	SYM
ejde-397	539	12	0	0	NUM
ejde-397	539	13	for	for	ADP
ejde-397	539	14	all	all	DET
ejde-397	539	15	λ	λ	PROPN
ejde-397	539	16	∈	∈	PROPN
ejde-397	539	17	c.	c.	NOUN
ejde-397	539	18	the	the	DET
ejde-397	539	19	following	follow	VERB
ejde-397	539	20	converse	converse	NOUN
ejde-397	539	21	of	of	ADP
ejde-397	539	22	theorem	theorem	PROPN
ejde-397	539	23	3.3(iv	3.3(iv	NUM
ejde-397	539	24	)	)	PUNCT
ejde-397	539	25	simply	simply	ADV
ejde-397	539	26	follows	follow	VERB
ejde-397	539	27	from	from	ADP
ejde-397	539	28	an	an	DET
ejde-397	539	29	application	application	NOUN
ejde-397	539	30	of	of	ADP
ejde-397	539	31	theorem	theorem	ADJ
ejde-397	539	32	3.5	3.5	NUM
ejde-397	539	33	.	.	PUNCT
ejde-397	540	1	proposition	proposition	NOUN
ejde-397	540	2	3.8	3.8	NUM
ejde-397	540	3	.	.	PUNCT
ejde-397	540	4	suppose	suppose	VERB
ejde-397	540	5	that	that	SCONJ
ejde-397	540	6	a	a	PRON
ejde-397	540	7	:	:	PUNCT
ejde-397	540	8	x	x	X
ejde-397	540	9	→	→	X
ejde-397	540	10	p	p	X
ejde-397	540	11	(	(	PUNCT
ejde-397	540	12	y	y	PROPN
ejde-397	540	13	)	)	PUNCT
ejde-397	540	14	is	be	AUX
ejde-397	540	15	an	an	DET
ejde-397	540	16	mlo	mlo	NOUN
ejde-397	540	17	and	and	CCONJ
ejde-397	540	18	a	a	PRON
ejde-397	540	19	is	be	AUX
ejde-397	540	20	xa	xa	PROPN
ejde-397	540	21	×	×	NOUN
ejde-397	540	22	yaclosed	yaclose	VERB
ejde-397	540	23	,	,	PUNCT
ejde-397	540	24	as	as	ADV
ejde-397	540	25	well	well	ADV
ejde-397	540	26	as	as	ADP
ejde-397	540	27	f	f	PROPN
ejde-397	540	28	∈	∈	PROPN
ejde-397	540	29	(	(	PUNCT
ejde-397	540	30	p1	p1	PROPN
ejde-397	540	31	)	)	PUNCT
ejde-397	540	32	−xa	−xa	PROPN
ejde-397	540	33	,	,	PUNCT
ejde-397	540	34	l	l	PROPN
ejde-397	540	35	∈	∈	PROPN
ejde-397	540	36	(	(	PUNCT
ejde-397	540	37	p1	p1	NOUN
ejde-397	540	38	)	)	PUNCT
ejde-397	541	1	−	−	PROPN
ejde-397	541	2	ya	ya	PROPN
ejde-397	541	3	and	and	CCONJ
ejde-397	541	4	(	(	PUNCT
ejde-397	541	5	f̃(λ	f̃(λ	PROPN
ejde-397	541	6	)	)	PUNCT
ejde-397	541	7	,	,	PUNCT
ejde-397	541	8	l̃(λ	l̃(λ	PROPN
ejde-397	541	9	)	)	PUNCT
ejde-397	541	10	)	)	PUNCT
ejde-397	542	1	∈	∈	PROPN
ejde-397	542	2	a	a	PRON
ejde-397	542	3	,	,	PUNCT
ejde-397	542	4	λ	λ	PROPN
ejde-397	542	5	∈	∈	PROPN
ejde-397	542	6	c	c	NOUN
ejde-397	542	7	for	for	ADP
ejde-397	542	8	<	<	X
ejde-397	542	9	λ	λ	X
ejde-397	542	10	>	>	X
ejde-397	542	11	max(abs(f	max(abs(f	NUM
ejde-397	542	12	)	)	PUNCT
ejde-397	542	13	,	,	PUNCT
ejde-397	542	14	abs(l	abs(l	PROPN
ejde-397	542	15	)	)	PUNCT
ejde-397	542	16	)	)	PUNCT
ejde-397	542	17	.	.	PUNCT
ejde-397	543	1	then	then	ADV
ejde-397	543	2	af	af	VERB
ejde-397	543	3	[	[	X
ejde-397	543	4	1](t	1](t	NUM
ejde-397	543	5	)	)	PUNCT
ejde-397	543	6	=	=	SYM
ejde-397	543	7	l[1](t	l[1](t	PROPN
ejde-397	543	8	)	)	PUNCT
ejde-397	543	9	,	,	PUNCT
ejde-397	543	10	t	t	PROPN
ejde-397	543	11	≥	≥	NOUN
ejde-397	543	12	0	0	NUM
ejde-397	543	13	and	and	CCONJ
ejde-397	543	14	af(t	af(t	NUM
ejde-397	543	15	)	)	PUNCT
ejde-397	543	16	=	=	SYM
ejde-397	543	17	l(t	l(t	PROPN
ejde-397	543	18	)	)	PUNCT
ejde-397	543	19	for	for	ADP
ejde-397	543	20	any	any	DET
ejde-397	543	21	t	t	NOUN
ejde-397	543	22	>	>	X
ejde-397	543	23	0	0	NUM
ejde-397	543	24	which	which	PRON
ejde-397	543	25	is	be	AUX
ejde-397	543	26	a	a	DET
ejde-397	543	27	lebesgue	lebesgue	ADJ
ejde-397	543	28	point	point	NOUN
ejde-397	543	29	of	of	ADP
ejde-397	543	30	both	both	DET
ejde-397	543	31	functions	function	NOUN
ejde-397	543	32	f(t	f(t	NOUN
ejde-397	543	33	)	)	PUNCT
ejde-397	543	34	and	and	CCONJ
ejde-397	543	35	l(t	l(t	NOUN
ejde-397	543	36	)	)	PUNCT
ejde-397	543	37	.	.	PUNCT
ejde-397	544	1	the	the	DET
ejde-397	544	2	method	method	NOUN
ejde-397	544	3	proposed	propose	VERB
ejde-397	544	4	by	by	ADP
ejde-397	544	5	xiao	xiao	PROPN
ejde-397	544	6	and	and	CCONJ
ejde-397	544	7	liang	liang	PROPN
ejde-397	544	8	in	in	ADP
ejde-397	544	9	[	[	X
ejde-397	544	10	80	80	NUM
ejde-397	544	11	]	]	PUNCT
ejde-397	544	12	provides	provide	VERB
ejde-397	544	13	a	a	DET
ejde-397	544	14	sufficiently	sufficiently	ADV
ejde-397	544	15	enough	enough	ADJ
ejde-397	544	16	framework	framework	NOUN
ejde-397	544	17	for	for	ADP
ejde-397	544	18	the	the	DET
ejde-397	544	19	theoretical	theoretical	ADJ
ejde-397	544	20	study	study	NOUN
ejde-397	544	21	of	of	ADP
ejde-397	544	22	real	real	ADJ
ejde-397	544	23	and	and	CCONJ
ejde-397	544	24	complex	complex	ADJ
ejde-397	544	25	inversion	inversion	NOUN
ejde-397	544	26	methods	method	NOUN
ejde-397	544	27	for	for	ADP
ejde-397	544	28	the	the	DET
ejde-397	544	29	laplace	laplace	NOUN
ejde-397	544	30	transform	transform	NOUN
ejde-397	544	31	of	of	ADP
ejde-397	544	32	functions	function	NOUN
ejde-397	544	33	with	with	ADP
ejde-397	544	34	values	value	NOUN
ejde-397	544	35	in	in	ADP
ejde-397	544	36	sclscs	sclsc	NOUN
ejde-397	544	37	,	,	PUNCT
ejde-397	544	38	as	as	ADV
ejde-397	544	39	well	well	ADV
ejde-397	544	40	as	as	ADP
ejde-397	544	41	for	for	ADP
ejde-397	544	42	the	the	DET
ejde-397	544	43	studies	study	NOUN
ejde-397	544	44	of	of	ADP
ejde-397	544	45	analytical	analytical	ADJ
ejde-397	544	46	properties	property	NOUN
ejde-397	544	47	and	and	CCONJ
ejde-397	544	48	approximation	approximation	NOUN
ejde-397	544	49	of	of	ADP
ejde-397	544	50	laplace	laplace	NOUN
ejde-397	544	51	transform	transform	NOUN
ejde-397	544	52	(	(	PUNCT
ejde-397	544	53	see	see	VERB
ejde-397	544	54	e.g.	e.g.	ADV
ejde-397	544	55	[	[	X
ejde-397	544	56	79	79	NUM
ejde-397	544	57	,	,	PUNCT
ejde-397	544	58	section	section	NOUN
ejde-397	544	59	1.1.1	1.1.1	NUM
ejde-397	544	60	]	]	PUNCT
ejde-397	544	61	and	and	CCONJ
ejde-397	544	62	[	[	X
ejde-397	544	63	36	36	NUM
ejde-397	544	64	,	,	PUNCT
ejde-397	544	65	section	section	NOUN
ejde-397	544	66	1.2	1.2	NUM
ejde-397	544	67	]	]	PUNCT
ejde-397	544	68	for	for	ADP
ejde-397	544	69	more	more	ADJ
ejde-397	544	70	details	detail	NOUN
ejde-397	544	71	)	)	PUNCT
ejde-397	544	72	;	;	PUNCT
ejde-397	544	73	this	this	DET
ejde-397	544	74	method	method	NOUN
ejde-397	544	75	can	can	AUX
ejde-397	544	76	be	be	AUX
ejde-397	544	77	successfully	successfully	ADV
ejde-397	544	78	applied	apply	VERB
ejde-397	544	79	in	in	ADP
ejde-397	544	80	the	the	DET
ejde-397	544	81	analysis	analysis	NOUN
ejde-397	544	82	of	of	ADP
ejde-397	544	83	subordination	subordination	NOUN
ejde-397	544	84	principles	principle	NOUN
ejde-397	544	85	for	for	ADP
ejde-397	544	86	abstract	abstract	ADJ
ejde-397	544	87	time	time	NOUN
ejde-397	544	88	-	-	PUNCT
ejde-397	544	89	fractional	fractional	ADJ
ejde-397	544	90	inclusions	inclusion	NOUN
ejde-397	544	91	,	,	PUNCT
ejde-397	544	92	as	as	ADV
ejde-397	544	93	well	well	ADV
ejde-397	544	94	(	(	PUNCT
ejde-397	544	95	cf	cf	NOUN
ejde-397	544	96	.	.	PUNCT
ejde-397	544	97	theorem	theorem	VERB
ejde-397	544	98	4.8	4.8	NUM
ejde-397	544	99	below	below	ADV
ejde-397	544	100	)	)	PUNCT
ejde-397	544	101	.	.	PUNCT
ejde-397	545	1	it	it	PRON
ejde-397	545	2	is	be	AUX
ejde-397	545	3	also	also	ADV
ejde-397	545	4	worth	worth	ADJ
ejde-397	545	5	noting	note	VERB
ejde-397	545	6	that	that	SCONJ
ejde-397	545	7	there	there	PRON
ejde-397	545	8	exists	exist	VERB
ejde-397	545	9	a	a	DET
ejde-397	545	10	great	great	ADJ
ejde-397	545	11	number	number	NOUN
ejde-397	545	12	of	of	ADP
ejde-397	545	13	theoretical	theoretical	ADJ
ejde-397	545	14	results	result	NOUN
ejde-397	545	15	from	from	ADP
ejde-397	545	16	the	the	DET
ejde-397	545	17	monograph	monograph	NOUN
ejde-397	546	1	[	[	X
ejde-397	546	2	1	1	NUM
ejde-397	546	3	]	]	PUNCT
ejde-397	546	4	,	,	PUNCT
ejde-397	546	5	not	not	PART
ejde-397	546	6	mentioned	mention	VERB
ejde-397	546	7	so	so	ADV
ejde-397	546	8	far	far	ADV
ejde-397	546	9	,	,	PUNCT
ejde-397	546	10	which	which	PRON
ejde-397	546	11	can	can	AUX
ejde-397	546	12	be	be	AUX
ejde-397	546	13	reconsidered	reconsider	VERB
ejde-397	546	14	for	for	ADP
ejde-397	546	15	the	the	DET
ejde-397	546	16	laplace	laplace	NOUN
ejde-397	546	17	transformable	transformable	ADJ
ejde-397	546	18	functions	function	NOUN
ejde-397	546	19	with	with	ADP
ejde-397	546	20	values	value	NOUN
ejde-397	546	21	in	in	ADP
ejde-397	546	22	sclscs	sclsc	NOUN
ejde-397	546	23	;	;	PUNCT
ejde-397	546	24	for	for	ADP
ejde-397	546	25	example	example	NOUN
ejde-397	546	26	,	,	PUNCT
ejde-397	546	27	all	all	DET
ejde-397	546	28	structural	structural	ADJ
ejde-397	546	29	results	result	NOUN
ejde-397	546	30	from	from	ADP
ejde-397	546	31	[	[	X
ejde-397	546	32	1	1	NUM
ejde-397	546	33	,	,	PUNCT
ejde-397	546	34	section	section	NOUN
ejde-397	546	35	4.1	4.1	NUM
ejde-397	546	36	]	]	PUNCT
ejde-397	546	37	continue	continue	VERB
ejde-397	546	38	to	to	PART
ejde-397	546	39	hold	hold	VERB
ejde-397	546	40	in	in	ADP
ejde-397	546	41	our	our	PRON
ejde-397	546	42	framework	framework	NOUN
ejde-397	546	43	.	.	PUNCT
ejde-397	547	1	due	due	ADJ
ejde-397	547	2	primarily	primarily	ADV
ejde-397	547	3	to	to	ADP
ejde-397	547	4	the	the	DET
ejde-397	547	5	space	space	NOUN
ejde-397	547	6	limitations	limitation	NOUN
ejde-397	547	7	,	,	PUNCT
ejde-397	547	8	in	in	ADP
ejde-397	547	9	this	this	DET
ejde-397	547	10	paper	paper	NOUN
ejde-397	547	11	we	we	PRON
ejde-397	547	12	will	will	AUX
ejde-397	547	13	not	not	PART
ejde-397	547	14	be	be	AUX
ejde-397	547	15	able	able	ADJ
ejde-397	547	16	to	to	PART
ejde-397	547	17	consider	consider	VERB
ejde-397	547	18	many	many	ADJ
ejde-397	547	19	other	other	ADJ
ejde-397	547	20	important	important	ADJ
ejde-397	547	21	questions	question	NOUN
ejde-397	547	22	concerning	concern	VERB
ejde-397	547	23	the	the	DET
ejde-397	547	24	vector	vector	NOUN
ejde-397	547	25	-	-	PUNCT
ejde-397	547	26	valued	value	VERB
ejde-397	547	27	laplace	laplace	NOUN
ejde-397	547	28	transform	transform	NOUN
ejde-397	547	29	of	of	ADP
ejde-397	547	30	functions	function	NOUN
ejde-397	547	31	with	with	ADP
ejde-397	547	32	values	value	NOUN
ejde-397	547	33	in	in	ADP
ejde-397	547	34	sclcss	sclcss	PROPN
ejde-397	547	35	.	.	PUNCT
ejde-397	548	1	at	at	ADP
ejde-397	548	2	the	the	DET
ejde-397	548	3	end	end	NOUN
ejde-397	548	4	of	of	ADP
ejde-397	548	5	this	this	DET
ejde-397	548	6	section	section	NOUN
ejde-397	548	7	,	,	PUNCT
ejde-397	548	8	we	we	PRON
ejde-397	548	9	would	would	AUX
ejde-397	548	10	like	like	VERB
ejde-397	548	11	to	to	PART
ejde-397	548	12	briefly	briefly	ADV
ejde-397	548	13	explain	explain	VERB
ejde-397	548	14	how	how	SCONJ
ejde-397	548	15	we	we	PRON
ejde-397	548	16	can	can	AUX
ejde-397	548	17	extend	extend	VERB
ejde-397	548	18	the	the	DET
ejde-397	548	19	definition	definition	NOUN
ejde-397	548	20	of	of	ADP
ejde-397	548	21	laplace	laplace	NOUN
ejde-397	548	22	transformable	transformable	ADJ
ejde-397	548	23	functions	function	NOUN
ejde-397	548	24	to	to	ADP
ejde-397	548	25	the	the	DET
ejde-397	548	26	multivalued	multivalued	ADJ
ejde-397	548	27	ones	one	NOUN
ejde-397	548	28	.	.	PUNCT
ejde-397	549	1	let	let	VERB
ejde-397	549	2	0	0	NUM
ejde-397	549	3	<	<	X
ejde-397	549	4	τ	τ	X
ejde-397	549	5	≤	≤	NOUN
ejde-397	549	6	∞	∞	PROPN
ejde-397	549	7	and	and	CCONJ
ejde-397	549	8	f	f	NOUN
ejde-397	549	9	:	:	PUNCT
ejde-397	550	1	[	[	X
ejde-397	550	2	0	0	NUM
ejde-397	550	3	,	,	PUNCT
ejde-397	550	4	τ	τ	X
ejde-397	550	5	)	)	PUNCT
ejde-397	550	6	→	→	SYM
ejde-397	550	7	p	p	X
ejde-397	550	8	(	(	PUNCT
ejde-397	550	9	x	x	NOUN
ejde-397	550	10	)	)	PUNCT
ejde-397	550	11	.	.	PUNCT
ejde-397	551	1	a	a	DET
ejde-397	551	2	single	single	ADV
ejde-397	551	3	-	-	PUNCT
ejde-397	551	4	valued	value	VERB
ejde-397	551	5	function	function	NOUN
ejde-397	551	6	f	f	NOUN
ejde-397	551	7	:	:	PUNCT
ejde-397	552	1	[	[	X
ejde-397	552	2	0	0	NUM
ejde-397	552	3	,	,	PUNCT
ejde-397	552	4	τ	τ	X
ejde-397	552	5	)	)	PUNCT
ejde-397	552	6	→	→	PUNCT
ejde-397	552	7	x	x	X
ejde-397	552	8	is	be	AUX
ejde-397	552	9	called	call	VERB
ejde-397	552	10	a	a	DET
ejde-397	552	11	section	section	NOUN
ejde-397	552	12	of	of	ADP
ejde-397	552	13	f	f	PROPN
ejde-397	552	14	if	if	SCONJ
ejde-397	552	15	and	and	CCONJ
ejde-397	552	16	only	only	ADV
ejde-397	552	17	if	if	SCONJ
ejde-397	552	18	f(t	f(t	NOUN
ejde-397	552	19	)	)	PUNCT
ejde-397	552	20	∈	∈	PROPN
ejde-397	552	21	f(t	f(t	PROPN
ejde-397	552	22	)	)	PUNCT
ejde-397	552	23	for	for	ADP
ejde-397	552	24	all	all	DET
ejde-397	552	25	t	t	NOUN
ejde-397	552	26	∈	∈	PROPN
ejde-397	553	1	[	[	X
ejde-397	553	2	0	0	NUM
ejde-397	553	3	,	,	PUNCT
ejde-397	553	4	τ	τ	PROPN
ejde-397	553	5	)	)	PUNCT
ejde-397	553	6	.	.	PUNCT
ejde-397	554	1	we	we	PRON
ejde-397	554	2	denote	denote	VERB
ejde-397	554	3	the	the	DET
ejde-397	554	4	set	set	NOUN
ejde-397	554	5	of	of	ADP
ejde-397	554	6	all	all	DET
ejde-397	554	7	sections	section	NOUN
ejde-397	554	8	,	,	PUNCT
ejde-397	554	9	resp	resp	NOUN
ejde-397	554	10	.	.	PUNCT
ejde-397	555	1	,	,	PUNCT
ejde-397	555	2	all	all	DET
ejde-397	555	3	continuous	continuous	ADJ
ejde-397	555	4	sections	section	NOUN
ejde-397	555	5	,	,	PUNCT
ejde-397	555	6	of	of	ADP
ejde-397	555	7	f	f	PROPN
ejde-397	555	8	by	by	ADP
ejde-397	555	9	sec(f	sec(f	PROPN
ejde-397	555	10	)	)	PUNCT
ejde-397	555	11	,	,	PUNCT
ejde-397	555	12	resp	resp	NOUN
ejde-397	555	13	.	.	PUNCT
ejde-397	555	14	,	,	PUNCT
ejde-397	555	15	secc(f	secc(f	PROPN
ejde-397	555	16	)	)	PUNCT
ejde-397	555	17	.	.	PUNCT
ejde-397	555	18	suppose	suppose	VERB
ejde-397	555	19	now	now	ADV
ejde-397	555	20	that	that	SCONJ
ejde-397	555	21	τ	τ	PROPN
ejde-397	555	22	=	=	NUM
ejde-397	555	23	∞	∞	PROPN
ejde-397	555	24	and	and	CCONJ
ejde-397	555	25	any	any	DET
ejde-397	555	26	function	function	NOUN
ejde-397	555	27	f	f	PROPN
ejde-397	555	28	∈	∈	PROPN
ejde-397	555	29	sec(f	sec(f	PROPN
ejde-397	555	30	)	)	PUNCT
ejde-397	555	31	belongs	belong	VERB
ejde-397	555	32	to	to	ADP
ejde-397	555	33	the	the	DET
ejde-397	555	34	class	class	NOUN
ejde-397	555	35	(	(	PUNCT
ejde-397	555	36	p1)-x	p1)-x	NOUN
ejde-397	555	37	.	.	PUNCT
ejde-397	556	1	then	then	ADV
ejde-397	556	2	we	we	PRON
ejde-397	556	3	define	define	VERB
ejde-397	556	4	absx(f	absx(f	NOUN
ejde-397	556	5	)	)	PUNCT
ejde-397	556	6	:	:	PUNCT
ejde-397	556	7	=	=	SYM
ejde-397	556	8	sup{absx(f	sup{absx(f	PROPN
ejde-397	556	9	)	)	PUNCT
ejde-397	556	10	:	:	PUNCT
ejde-397	557	1	f	f	PROPN
ejde-397	557	2	∈	∈	PROPN
ejde-397	557	3	sec(v	sec(v	PROPN
ejde-397	557	4	)	)	PUNCT
ejde-397	557	5	}	}	PUNCT
ejde-397	557	6	;	;	PUNCT
ejde-397	557	7	f	f	X
ejde-397	557	8	(	(	PUNCT
ejde-397	557	9	·	·	PUNCT
ejde-397	557	10	)	)	PUNCT
ejde-397	557	11	is	be	AUX
ejde-397	557	12	said	say	VERB
ejde-397	557	13	to	to	PART
ejde-397	557	14	be	be	AUX
ejde-397	557	15	laplace	laplace	NOUN
ejde-397	557	16	transformable	transformable	ADJ
ejde-397	557	17	if	if	SCONJ
ejde-397	557	18	and	and	CCONJ
ejde-397	557	19	only	only	ADV
ejde-397	557	20	if	if	SCONJ
ejde-397	557	21	absx(f	absx(f	NOUN
ejde-397	557	22	)	)	PUNCT
ejde-397	558	1	<	<	X
ejde-397	558	2	∞.	∞.	PROPN
ejde-397	558	3	4	4	NUM
ejde-397	558	4	.	.	PUNCT
ejde-397	558	5	abstract	abstract	ADJ
ejde-397	558	6	degenerate	degenerate	PROPN
ejde-397	558	7	volterra	volterra	PROPN
ejde-397	558	8	integro	integro	PROPN
ejde-397	558	9	-	-	PUNCT
ejde-397	558	10	differential	differential	NOUN
ejde-397	558	11	inclusions	inclusion	NOUN
ejde-397	558	12	in	in	ADP
ejde-397	558	13	the	the	DET
ejde-397	558	14	following	follow	VERB
ejde-397	558	15	general	general	ADJ
ejde-397	558	16	definition	definition	NOUN
ejde-397	558	17	,	,	PUNCT
ejde-397	558	18	we	we	PRON
ejde-397	558	19	introduce	introduce	VERB
ejde-397	558	20	various	various	ADJ
ejde-397	558	21	types	type	NOUN
ejde-397	558	22	of	of	ADP
ejde-397	558	23	solutions	solution	NOUN
ejde-397	558	24	to	to	ADP
ejde-397	558	25	the	the	DET
ejde-397	558	26	abstract	abstract	ADJ
ejde-397	558	27	degenerate	degenerate	ADJ
ejde-397	558	28	inclusions	inclusion	NOUN
ejde-397	558	29	(	(	PUNCT
ejde-397	558	30	1.1	1.1	NUM
ejde-397	558	31	)	)	PUNCT
ejde-397	558	32	,	,	PUNCT
ejde-397	558	33	(	(	PUNCT
ejde-397	558	34	1.2	1.2	NUM
ejde-397	558	35	)	)	PUNCT
ejde-397	558	36	and	and	CCONJ
ejde-397	558	37	(	(	PUNCT
ejde-397	558	38	1.3	1.3	NUM
ejde-397	558	39	)	)	PUNCT
ejde-397	558	40	.	.	PUNCT
ejde-397	559	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	559	2	abstract	abstract	ADJ
ejde-397	559	3	degenerate	degenerate	ADJ
ejde-397	559	4	volterra	volterra	NOUN
ejde-397	559	5	inclusions	inclusion	NOUN
ejde-397	559	6	17	17	NUM
ejde-397	559	7	definition	definition	NOUN
ejde-397	559	8	4.1	4.1	NUM
ejde-397	559	9	.	.	PUNCT
ejde-397	560	1	let	let	VERB
ejde-397	560	2	0	0	NUM
ejde-397	560	3	<	<	X
ejde-397	560	4	τ	τ	PROPN
ejde-397	560	5	≤	≤	NOUN
ejde-397	560	6	∞	∞	PROPN
ejde-397	560	7	,	,	PUNCT
ejde-397	560	8	α	α	X
ejde-397	560	9	>	>	X
ejde-397	560	10	0	0	PROPN
ejde-397	560	11	,	,	PUNCT
ejde-397	560	12	a	a	DET
ejde-397	560	13	∈	∈	PROPN
ejde-397	560	14	l1	l1	PROPN
ejde-397	560	15	loc([0	loc([0	PROPN
ejde-397	560	16	,	,	PUNCT
ejde-397	560	17	τ	τ	PROPN
ejde-397	560	18	)	)	PUNCT
ejde-397	560	19	)	)	PUNCT
ejde-397	560	20	,	,	PUNCT
ejde-397	560	21	a	a	DET
ejde-397	560	22	6=	6=	NUM
ejde-397	560	23	0	0	NUM
ejde-397	560	24	,	,	PUNCT
ejde-397	560	25	f	f	X
ejde-397	560	26	:	:	PUNCT
ejde-397	561	1	[	[	X
ejde-397	561	2	0	0	NUM
ejde-397	561	3	,	,	PUNCT
ejde-397	561	4	τ)→	τ)→	PUNCT
ejde-397	561	5	p	p	X
ejde-397	561	6	(	(	PUNCT
ejde-397	561	7	y	y	PROPN
ejde-397	561	8	)	)	PUNCT
ejde-397	561	9	,	,	PUNCT
ejde-397	561	10	and	and	CCONJ
ejde-397	561	11	let	let	VERB
ejde-397	561	12	a	a	PRON
ejde-397	561	13	:	:	PUNCT
ejde-397	561	14	x	x	X
ejde-397	561	15	→	→	X
ejde-397	561	16	p	p	X
ejde-397	561	17	(	(	PUNCT
ejde-397	561	18	y	y	PROPN
ejde-397	561	19	)	)	PUNCT
ejde-397	561	20	,	,	PUNCT
ejde-397	561	21	b	b	X
ejde-397	561	22	:	:	PUNCT
ejde-397	561	23	x	x	X
ejde-397	561	24	→	→	X
ejde-397	561	25	p	p	X
ejde-397	561	26	(	(	PUNCT
ejde-397	561	27	y	y	PROPN
ejde-397	561	28	)	)	PUNCT
ejde-397	561	29	be	be	AUX
ejde-397	561	30	two	two	NUM
ejde-397	561	31	given	give	VERB
ejde-397	561	32	mappings	mapping	NOUN
ejde-397	561	33	(	(	PUNCT
ejde-397	561	34	possibly	possibly	ADV
ejde-397	561	35	non	non	ADJ
ejde-397	561	36	-	-	ADJ
ejde-397	561	37	linear	linear	ADJ
ejde-397	561	38	)	)	PUNCT
ejde-397	561	39	.	.	PUNCT
ejde-397	562	1	(	(	PUNCT
ejde-397	562	2	i	i	NOUN
ejde-397	562	3	)	)	PUNCT
ejde-397	562	4	a	a	DET
ejde-397	562	5	function	function	NOUN
ejde-397	562	6	u	u	PROPN
ejde-397	562	7	∈	∈	PROPN
ejde-397	562	8	c([0	c([0	NOUN
ejde-397	562	9	,	,	PUNCT
ejde-397	562	10	τ	τ	PROPN
ejde-397	562	11	)	)	PUNCT
ejde-397	562	12	:	:	PUNCT
ejde-397	562	13	x	x	X
ejde-397	562	14	)	)	PUNCT
ejde-397	562	15	is	be	AUX
ejde-397	562	16	said	say	VERB
ejde-397	562	17	to	to	PART
ejde-397	562	18	be	be	AUX
ejde-397	562	19	a	a	DET
ejde-397	562	20	pre	pre	NOUN
ejde-397	562	21	-	-	NOUN
ejde-397	562	22	solution	solution	NOUN
ejde-397	562	23	of	of	ADP
ejde-397	562	24	(	(	PUNCT
ejde-397	562	25	1.1	1.1	NUM
ejde-397	562	26	)	)	PUNCT
ejde-397	562	27	if	if	SCONJ
ejde-397	562	28	and	and	CCONJ
ejde-397	562	29	only	only	ADV
ejde-397	562	30	if	if	SCONJ
ejde-397	562	31	(	(	PUNCT
ejde-397	562	32	a∗u)(t	a∗u)(t	ADJ
ejde-397	562	33	)	)	PUNCT
ejde-397	562	34	∈	∈	PROPN
ejde-397	562	35	d(a	d(a	PROPN
ejde-397	562	36	)	)	PUNCT
ejde-397	562	37	and	and	CCONJ
ejde-397	562	38	u(t	u(t	NOUN
ejde-397	562	39	)	)	PUNCT
ejde-397	562	40	∈	∈	PROPN
ejde-397	562	41	d(b	d(b	PROPN
ejde-397	562	42	)	)	PUNCT
ejde-397	562	43	for	for	ADP
ejde-397	562	44	t	t	PROPN
ejde-397	562	45	∈	∈	PROPN
ejde-397	563	1	[	[	X
ejde-397	563	2	0	0	NUM
ejde-397	563	3	,	,	PUNCT
ejde-397	563	4	τ	τ	PROPN
ejde-397	563	5	)	)	PUNCT
ejde-397	563	6	,	,	PUNCT
ejde-397	563	7	as	as	ADV
ejde-397	563	8	well	well	ADV
ejde-397	563	9	as	as	ADP
ejde-397	563	10	(	(	PUNCT
ejde-397	563	11	1.1	1.1	NUM
ejde-397	563	12	)	)	PUNCT
ejde-397	563	13	holds	hold	VERB
ejde-397	563	14	.	.	PUNCT
ejde-397	564	1	by	by	ADP
ejde-397	564	2	a	a	DET
ejde-397	564	3	solution	solution	NOUN
ejde-397	564	4	of	of	ADP
ejde-397	564	5	(	(	PUNCT
ejde-397	564	6	1.1	1.1	NUM
ejde-397	564	7	)	)	PUNCT
ejde-397	564	8	,	,	PUNCT
ejde-397	564	9	we	we	PRON
ejde-397	564	10	mean	mean	VERB
ejde-397	564	11	any	any	DET
ejde-397	564	12	pre	pre	NOUN
ejde-397	564	13	-	-	NOUN
ejde-397	564	14	solution	solution	ADJ
ejde-397	564	15	u	u	NOUN
ejde-397	564	16	(	(	PUNCT
ejde-397	564	17	·	·	PUNCT
ejde-397	564	18	)	)	PUNCT
ejde-397	564	19	of	of	ADP
ejde-397	564	20	(	(	PUNCT
ejde-397	564	21	1.1	1.1	NUM
ejde-397	564	22	)	)	PUNCT
ejde-397	564	23	satisfying	satisfy	VERB
ejde-397	564	24	additionally	additionally	ADV
ejde-397	564	25	that	that	SCONJ
ejde-397	564	26	there	there	PRON
ejde-397	564	27	exist	exist	VERB
ejde-397	564	28	functions	function	NOUN
ejde-397	564	29	ub	ub	ADP
ejde-397	564	30	∈	∈	PROPN
ejde-397	564	31	c([0	c([0	PROPN
ejde-397	564	32	,	,	PUNCT
ejde-397	564	33	τ	τ	PROPN
ejde-397	564	34	)	)	PUNCT
ejde-397	564	35	:	:	PUNCT
ejde-397	564	36	y	y	X
ejde-397	564	37	)	)	PUNCT
ejde-397	564	38	and	and	CCONJ
ejde-397	564	39	ua	ua	PROPN
ejde-397	564	40	,	,	PUNCT
ejde-397	564	41	a	a	DET
ejde-397	564	42	∈	∈	PROPN
ejde-397	564	43	c([0	c([0	NOUN
ejde-397	564	44	,	,	PUNCT
ejde-397	564	45	τ	τ	PROPN
ejde-397	564	46	)	)	PUNCT
ejde-397	564	47	:	:	PUNCT
ejde-397	564	48	y	y	X
ejde-397	564	49	)	)	PUNCT
ejde-397	564	50	such	such	ADJ
ejde-397	564	51	that	that	PRON
ejde-397	564	52	ub(t	ub(t	NOUN
ejde-397	564	53	)	)	PUNCT
ejde-397	564	54	∈	∈	PROPN
ejde-397	564	55	bu(t	bu(t	NOUN
ejde-397	564	56	)	)	PUNCT
ejde-397	564	57	and	and	CCONJ
ejde-397	564	58	ua	ua	PROPN
ejde-397	564	59	,	,	PUNCT
ejde-397	564	60	a(t	a(t	PROPN
ejde-397	564	61	)	)	PUNCT
ejde-397	564	62	∈	∈	PROPN
ejde-397	564	63	a	a	DET
ejde-397	564	64	∫	∫	PROPN
ejde-397	564	65	t	t	NOUN
ejde-397	564	66	0	0	NUM
ejde-397	564	67	a(t−	a(t−	PROPN
ejde-397	564	68	s)u(s	s)u(s	NOUN
ejde-397	564	69	)	)	PUNCT
ejde-397	564	70	ds	ds	NOUN
ejde-397	564	71	for	for	ADP
ejde-397	564	72	t	t	PROPN
ejde-397	564	73	∈	∈	PROPN
ejde-397	565	1	[	[	X
ejde-397	565	2	0	0	NUM
ejde-397	565	3	,	,	PUNCT
ejde-397	565	4	τ	τ	PROPN
ejde-397	565	5	)	)	PUNCT
ejde-397	565	6	,	,	PUNCT
ejde-397	565	7	as	as	ADV
ejde-397	565	8	well	well	ADV
ejde-397	565	9	as	as	ADP
ejde-397	565	10	ub(t	ub(t	NOUN
ejde-397	565	11	)	)	PUNCT
ejde-397	565	12	∈	∈	PROPN
ejde-397	565	13	ua	ua	PROPN
ejde-397	565	14	,	,	PUNCT
ejde-397	565	15	a(t	a(t	PROPN
ejde-397	565	16	)	)	PUNCT
ejde-397	566	1	+	+	CCONJ
ejde-397	566	2	f(t	f(t	NOUN
ejde-397	566	3	)	)	PUNCT
ejde-397	566	4	,	,	PUNCT
ejde-397	566	5	t	t	PROPN
ejde-397	566	6	∈	∈	PROPN
ejde-397	567	1	[	[	X
ejde-397	567	2	0	0	NUM
ejde-397	567	3	,	,	PUNCT
ejde-397	567	4	τ	τ	PROPN
ejde-397	567	5	)	)	PUNCT
ejde-397	567	6	.	.	PUNCT
ejde-397	568	1	strong	strong	ADJ
ejde-397	568	2	solution	solution	NOUN
ejde-397	568	3	of	of	ADP
ejde-397	568	4	(	(	PUNCT
ejde-397	568	5	1.1	1.1	NUM
ejde-397	568	6	)	)	PUNCT
ejde-397	568	7	is	be	AUX
ejde-397	568	8	any	any	DET
ejde-397	568	9	function	function	NOUN
ejde-397	568	10	u	u	PROPN
ejde-397	568	11	∈	∈	PROPN
ejde-397	568	12	c([0	c([0	NOUN
ejde-397	568	13	,	,	PUNCT
ejde-397	568	14	τ	τ	PROPN
ejde-397	568	15	)	)	PUNCT
ejde-397	568	16	:	:	PUNCT
ejde-397	569	1	x	x	X
ejde-397	569	2	)	)	PUNCT
ejde-397	569	3	satisfying	satisfy	VERB
ejde-397	569	4	that	that	SCONJ
ejde-397	569	5	there	there	PRON
ejde-397	569	6	exist	exist	VERB
ejde-397	569	7	two	two	NUM
ejde-397	569	8	continuous	continuous	ADJ
ejde-397	569	9	functions	function	NOUN
ejde-397	569	10	ub	ub	ADP
ejde-397	569	11	∈	∈	PROPN
ejde-397	569	12	c([0	c([0	PROPN
ejde-397	569	13	,	,	PUNCT
ejde-397	569	14	τ	τ	PROPN
ejde-397	569	15	)	)	PUNCT
ejde-397	569	16	:	:	PUNCT
ejde-397	569	17	y	y	X
ejde-397	569	18	)	)	PUNCT
ejde-397	569	19	and	and	CCONJ
ejde-397	569	20	ua	ua	PROPN
ejde-397	569	21	∈	∈	PROPN
ejde-397	569	22	c([0	c([0	PROPN
ejde-397	569	23	,	,	PUNCT
ejde-397	569	24	τ	τ	PROPN
ejde-397	569	25	)	)	PUNCT
ejde-397	569	26	:	:	PUNCT
ejde-397	569	27	y	y	X
ejde-397	569	28	)	)	PUNCT
ejde-397	569	29	such	such	ADJ
ejde-397	569	30	that	that	PRON
ejde-397	569	31	ub(t	ub(t	NOUN
ejde-397	569	32	)	)	PUNCT
ejde-397	569	33	∈	∈	PROPN
ejde-397	569	34	bu(t	bu(t	NOUN
ejde-397	569	35	)	)	PUNCT
ejde-397	569	36	,	,	PUNCT
ejde-397	569	37	ua(t	ua(t	NOUN
ejde-397	569	38	)	)	PUNCT
ejde-397	569	39	∈	∈	PROPN
ejde-397	569	40	au(t	au(t	NUM
ejde-397	569	41	)	)	PUNCT
ejde-397	569	42	for	for	ADP
ejde-397	569	43	all	all	DET
ejde-397	569	44	t	t	NOUN
ejde-397	569	45	∈	∈	PROPN
ejde-397	569	46	[	[	X
ejde-397	569	47	0	0	NUM
ejde-397	569	48	,	,	PUNCT
ejde-397	569	49	τ	τ	PROPN
ejde-397	569	50	)	)	PUNCT
ejde-397	569	51	,	,	PUNCT
ejde-397	569	52	and	and	CCONJ
ejde-397	569	53	ub(t	ub(t	X
ejde-397	569	54	)	)	PUNCT
ejde-397	569	55	∈	∈	PROPN
ejde-397	569	56	(	(	PUNCT
ejde-397	569	57	a	a	DET
ejde-397	569	58	∗	∗	NOUN
ejde-397	569	59	ua)(t	ua)(t	PROPN
ejde-397	569	60	)	)	PUNCT
ejde-397	569	61	+	+	CCONJ
ejde-397	569	62	f(t	f(t	NOUN
ejde-397	569	63	)	)	PUNCT
ejde-397	569	64	,	,	PUNCT
ejde-397	569	65	t	t	PROPN
ejde-397	569	66	∈	∈	PROPN
ejde-397	570	1	[	[	X
ejde-397	570	2	0	0	NUM
ejde-397	570	3	,	,	PUNCT
ejde-397	570	4	τ	τ	PROPN
ejde-397	570	5	)	)	PUNCT
ejde-397	570	6	.	.	PUNCT
ejde-397	571	1	(	(	PUNCT
ejde-397	571	2	ii	ii	NOUN
ejde-397	571	3	)	)	PUNCT
ejde-397	571	4	let	let	VERB
ejde-397	571	5	b	b	NOUN
ejde-397	571	6	=	=	SYM
ejde-397	571	7	b	b	PROPN
ejde-397	571	8	be	be	AUX
ejde-397	571	9	single	single	ADV
ejde-397	571	10	-	-	PUNCT
ejde-397	571	11	valued	value	VERB
ejde-397	571	12	.	.	PUNCT
ejde-397	572	1	by	by	ADP
ejde-397	572	2	a	a	DET
ejde-397	572	3	p	p	NOUN
ejde-397	572	4	-	-	PUNCT
ejde-397	572	5	solution	solution	NOUN
ejde-397	572	6	of	of	ADP
ejde-397	572	7	(	(	PUNCT
ejde-397	572	8	1.2	1.2	NUM
ejde-397	572	9	)	)	PUNCT
ejde-397	572	10	,	,	PUNCT
ejde-397	572	11	we	we	PRON
ejde-397	572	12	mean	mean	VERB
ejde-397	572	13	any	any	DET
ejde-397	572	14	x	x	ADJ
ejde-397	572	15	-	-	PUNCT
ejde-397	572	16	valued	value	VERB
ejde-397	572	17	function	function	NOUN
ejde-397	572	18	t	t	PROPN
ejde-397	572	19	7→	7→	NUM
ejde-397	572	20	u(t	u(t	NOUN
ejde-397	572	21	)	)	PUNCT
ejde-397	572	22	,	,	PUNCT
ejde-397	572	23	t	t	PROPN
ejde-397	572	24	≥	≥	NUM
ejde-397	572	25	0	0	NUM
ejde-397	573	1	such	such	ADJ
ejde-397	573	2	that	that	SCONJ
ejde-397	573	3	the	the	DET
ejde-397	573	4	term	term	NOUN
ejde-397	573	5	t	t	PROPN
ejde-397	573	6	7→	7→	NUM
ejde-397	573	7	dα	dα	NOUN
ejde-397	573	8	t	t	PROPN
ejde-397	573	9	bu(t	bu(t	NOUN
ejde-397	573	10	)	)	PUNCT
ejde-397	573	11	,	,	PUNCT
ejde-397	573	12	t	t	PROPN
ejde-397	573	13	≥	≥	PROPN
ejde-397	573	14	0	0	NUM
ejde-397	573	15	is	be	AUX
ejde-397	573	16	well	well	ADV
ejde-397	573	17	-	-	PUNCT
ejde-397	573	18	defined	define	VERB
ejde-397	573	19	,	,	PUNCT
ejde-397	573	20	u(t	u(t	NOUN
ejde-397	573	21	)	)	PUNCT
ejde-397	573	22	∈	∈	PROPN
ejde-397	573	23	d(a	d(a	PROPN
ejde-397	573	24	)	)	PUNCT
ejde-397	573	25	for	for	ADP
ejde-397	573	26	t	t	PROPN
ejde-397	573	27	≥	≥	PROPN
ejde-397	573	28	0	0	NUM
ejde-397	573	29	,	,	PUNCT
ejde-397	573	30	and	and	CCONJ
ejde-397	573	31	the	the	DET
ejde-397	573	32	requirements	requirement	NOUN
ejde-397	573	33	of	of	ADP
ejde-397	573	34	(	(	PUNCT
ejde-397	573	35	1.2	1.2	NUM
ejde-397	573	36	)	)	PUNCT
ejde-397	573	37	hold	hold	VERB
ejde-397	573	38	;	;	PUNCT
ejde-397	573	39	a	a	DET
ejde-397	573	40	pre	pre	NOUN
ejde-397	573	41	-	-	NOUN
ejde-397	573	42	solution	solution	NOUN
ejde-397	573	43	of	of	ADP
ejde-397	573	44	(	(	PUNCT
ejde-397	573	45	1.2	1.2	NUM
ejde-397	573	46	)	)	PUNCT
ejde-397	573	47	is	be	AUX
ejde-397	573	48	any	any	DET
ejde-397	573	49	p	p	NOUN
ejde-397	573	50	-	-	PUNCT
ejde-397	573	51	solution	solution	NOUN
ejde-397	573	52	of	of	ADP
ejde-397	573	53	(	(	PUNCT
ejde-397	573	54	1.2	1.2	NUM
ejde-397	573	55	)	)	PUNCT
ejde-397	573	56	that	that	PRON
ejde-397	573	57	is	be	AUX
ejde-397	573	58	continuous	continuous	ADJ
ejde-397	573	59	for	for	ADP
ejde-397	573	60	t	t	PROPN
ejde-397	573	61	≥	≥	NOUN
ejde-397	573	62	0	0	NUM
ejde-397	573	63	.	.	PUNCT
ejde-397	574	1	finally	finally	ADV
ejde-397	574	2	,	,	PUNCT
ejde-397	574	3	a	a	DET
ejde-397	574	4	solution	solution	NOUN
ejde-397	574	5	of	of	ADP
ejde-397	574	6	(	(	PUNCT
ejde-397	574	7	1.2	1.2	NUM
ejde-397	574	8	)	)	PUNCT
ejde-397	574	9	is	be	AUX
ejde-397	574	10	any	any	DET
ejde-397	574	11	pre	pre	ADJ
ejde-397	574	12	-	-	NOUN
ejde-397	574	13	solution	solution	ADJ
ejde-397	574	14	u	u	NOUN
ejde-397	574	15	(	(	PUNCT
ejde-397	574	16	·	·	PUNCT
ejde-397	574	17	)	)	PUNCT
ejde-397	574	18	of	of	ADP
ejde-397	574	19	(	(	PUNCT
ejde-397	574	20	1.2	1.2	NUM
ejde-397	574	21	)	)	PUNCT
ejde-397	574	22	satisfying	satisfy	VERB
ejde-397	574	23	additionally	additionally	ADV
ejde-397	574	24	that	that	SCONJ
ejde-397	574	25	there	there	PRON
ejde-397	574	26	exists	exist	VERB
ejde-397	574	27	a	a	DET
ejde-397	574	28	function	function	NOUN
ejde-397	574	29	ua	ua	PROPN
ejde-397	574	30	∈	∈	PROPN
ejde-397	574	31	c([0,∞	c([0,∞	PROPN
ejde-397	574	32	)	)	PUNCT
ejde-397	574	33	:	:	PUNCT
ejde-397	575	1	y	y	X
ejde-397	575	2	)	)	PUNCT
ejde-397	575	3	such	such	ADJ
ejde-397	575	4	that	that	PRON
ejde-397	575	5	ua(t	ua(t	PROPN
ejde-397	575	6	)	)	PUNCT
ejde-397	575	7	∈	∈	PROPN
ejde-397	575	8	au(t	au(t	NUM
ejde-397	575	9	)	)	PUNCT
ejde-397	575	10	for	for	ADP
ejde-397	575	11	t	t	PROPN
ejde-397	575	12	≥	≥	NOUN
ejde-397	575	13	0	0	NUM
ejde-397	575	14	,	,	PUNCT
ejde-397	575	15	and	and	CCONJ
ejde-397	575	16	dα	dα	PROPN
ejde-397	575	17	t	t	PROPN
ejde-397	575	18	bu(t	bu(t	NOUN
ejde-397	575	19	)	)	PUNCT
ejde-397	575	20	∈	∈	PROPN
ejde-397	575	21	ua(t)+f(t	ua(t)+f(t	NOUN
ejde-397	575	22	)	)	PUNCT
ejde-397	575	23	,	,	PUNCT
ejde-397	575	24	t	t	PROPN
ejde-397	575	25	≥	≥	PROPN
ejde-397	575	26	0	0	NUM
ejde-397	575	27	.	.	PUNCT
ejde-397	575	28	(	(	PUNCT
ejde-397	575	29	iii	iii	NOUN
ejde-397	575	30	)	)	PUNCT
ejde-397	575	31	by	by	ADP
ejde-397	575	32	a	a	DET
ejde-397	575	33	pre	pre	NOUN
ejde-397	575	34	-	-	NOUN
ejde-397	575	35	solution	solution	NOUN
ejde-397	575	36	of	of	ADP
ejde-397	575	37	(	(	PUNCT
ejde-397	575	38	1.3	1.3	NUM
ejde-397	575	39	)	)	PUNCT
ejde-397	575	40	,	,	PUNCT
ejde-397	575	41	we	we	PRON
ejde-397	575	42	mean	mean	VERB
ejde-397	575	43	any	any	DET
ejde-397	575	44	continuous	continuous	ADJ
ejde-397	575	45	x	x	ADV
ejde-397	575	46	-	-	PUNCT
ejde-397	575	47	valued	value	VERB
ejde-397	575	48	function	function	NOUN
ejde-397	575	49	t	t	PROPN
ejde-397	575	50	7→	7→	NUM
ejde-397	575	51	u(t	u(t	NOUN
ejde-397	575	52	)	)	PUNCT
ejde-397	575	53	,	,	PUNCT
ejde-397	575	54	t	t	PROPN
ejde-397	575	55	≥	≥	NUM
ejde-397	575	56	0	0	NUM
ejde-397	575	57	such	such	ADJ
ejde-397	575	58	that	that	SCONJ
ejde-397	575	59	the	the	DET
ejde-397	575	60	term	term	NOUN
ejde-397	575	61	t	t	PROPN
ejde-397	575	62	7→	7→	NUM
ejde-397	575	63	dα	dα	ADP
ejde-397	575	64	t	t	PROPN
ejde-397	575	65	u(t	u(t	PROPN
ejde-397	575	66	)	)	PUNCT
ejde-397	575	67	,	,	PUNCT
ejde-397	575	68	t	t	PROPN
ejde-397	575	69	≥	≥	PROPN
ejde-397	575	70	0	0	NUM
ejde-397	575	71	is	be	AUX
ejde-397	575	72	well	well	ADV
ejde-397	575	73	defined	define	VERB
ejde-397	575	74	and	and	CCONJ
ejde-397	575	75	continuous	continuous	ADJ
ejde-397	575	76	,	,	PUNCT
ejde-397	575	77	as	as	ADV
ejde-397	575	78	well	well	ADV
ejde-397	575	79	as	as	ADP
ejde-397	575	80	that	that	PRON
ejde-397	575	81	dα	dα	ADP
ejde-397	575	82	t	t	PROPN
ejde-397	575	83	u(t	u(t	PROPN
ejde-397	575	84	)	)	PUNCT
ejde-397	575	85	∈	∈	PROPN
ejde-397	575	86	d(b	d(b	PROPN
ejde-397	575	87	)	)	PUNCT
ejde-397	575	88	and	and	CCONJ
ejde-397	575	89	u(t	u(t	NOUN
ejde-397	575	90	)	)	PUNCT
ejde-397	575	91	∈	∈	PROPN
ejde-397	575	92	d(a	d(a	PROPN
ejde-397	575	93	)	)	PUNCT
ejde-397	575	94	for	for	ADP
ejde-397	575	95	t	t	PROPN
ejde-397	575	96	≥	≥	PROPN
ejde-397	575	97	0	0	NUM
ejde-397	575	98	,	,	PUNCT
ejde-397	575	99	and	and	CCONJ
ejde-397	575	100	that	that	SCONJ
ejde-397	575	101	the	the	DET
ejde-397	575	102	requirements	requirement	NOUN
ejde-397	575	103	of	of	ADP
ejde-397	575	104	(	(	PUNCT
ejde-397	575	105	1.3	1.3	NUM
ejde-397	575	106	)	)	PUNCT
ejde-397	575	107	hold	hold	VERB
ejde-397	575	108	;	;	PUNCT
ejde-397	575	109	a	a	DET
ejde-397	575	110	solution	solution	NOUN
ejde-397	575	111	of	of	ADP
ejde-397	575	112	(	(	PUNCT
ejde-397	575	113	1.3	1.3	NUM
ejde-397	575	114	)	)	PUNCT
ejde-397	575	115	is	be	AUX
ejde-397	575	116	any	any	DET
ejde-397	575	117	pre	pre	ADJ
ejde-397	575	118	-	-	NOUN
ejde-397	575	119	solution	solution	ADJ
ejde-397	575	120	u	u	NOUN
ejde-397	575	121	(	(	PUNCT
ejde-397	575	122	·	·	PUNCT
ejde-397	575	123	)	)	PUNCT
ejde-397	575	124	of	of	ADP
ejde-397	575	125	(	(	PUNCT
ejde-397	575	126	1.3	1.3	NUM
ejde-397	575	127	)	)	PUNCT
ejde-397	575	128	satisfying	satisfy	VERB
ejde-397	575	129	additionally	additionally	ADV
ejde-397	575	130	that	that	SCONJ
ejde-397	575	131	there	there	PRON
ejde-397	575	132	exist	exist	VERB
ejde-397	575	133	functions	function	NOUN
ejde-397	575	134	uα	uα	PROPN
ejde-397	575	135	,	,	PUNCT
ejde-397	575	136	b	b	PROPN
ejde-397	575	137	∈	∈	PROPN
ejde-397	575	138	c([0,∞	c([0,∞	PROPN
ejde-397	575	139	)	)	PUNCT
ejde-397	575	140	:	:	PUNCT
ejde-397	576	1	y	y	X
ejde-397	576	2	)	)	PUNCT
ejde-397	576	3	and	and	CCONJ
ejde-397	576	4	ua	ua	PROPN
ejde-397	576	5	∈	∈	PROPN
ejde-397	576	6	c([0,∞	c([0,∞	PROPN
ejde-397	576	7	)	)	PUNCT
ejde-397	576	8	:	:	PUNCT
ejde-397	576	9	y	y	X
ejde-397	576	10	)	)	PUNCT
ejde-397	576	11	such	such	ADJ
ejde-397	576	12	that	that	SCONJ
ejde-397	576	13	uα	uα	PROPN
ejde-397	576	14	,	,	PUNCT
ejde-397	576	15	b(t	b(t	NOUN
ejde-397	576	16	)	)	PUNCT
ejde-397	576	17	∈	∈	PROPN
ejde-397	576	18	bdα	bdα	PROPN
ejde-397	576	19	t	t	PROPN
ejde-397	576	20	u(t	u(t	PROPN
ejde-397	576	21	)	)	PUNCT
ejde-397	576	22	and	and	CCONJ
ejde-397	576	23	ua(t	ua(t	NOUN
ejde-397	576	24	)	)	PUNCT
ejde-397	576	25	∈	∈	PROPN
ejde-397	576	26	au(t	au(t	NUM
ejde-397	576	27	)	)	PUNCT
ejde-397	576	28	for	for	ADP
ejde-397	576	29	t	t	PROPN
ejde-397	576	30	≥	≥	NOUN
ejde-397	576	31	0	0	NUM
ejde-397	576	32	,	,	PUNCT
ejde-397	576	33	as	as	ADV
ejde-397	576	34	well	well	ADV
ejde-397	576	35	as	as	ADP
ejde-397	576	36	that	that	PRON
ejde-397	576	37	uα	uα	PROPN
ejde-397	576	38	,	,	PUNCT
ejde-397	576	39	b(t	b(t	NOUN
ejde-397	576	40	)	)	PUNCT
ejde-397	576	41	∈	∈	PROPN
ejde-397	576	42	ua(t	ua(t	PROPN
ejde-397	576	43	)	)	PUNCT
ejde-397	576	44	+	+	CCONJ
ejde-397	576	45	f(t	f(t	NOUN
ejde-397	576	46	)	)	PUNCT
ejde-397	576	47	,	,	PUNCT
ejde-397	576	48	t	t	PROPN
ejde-397	576	49	≥	≥	NUM
ejde-397	576	50	0	0	NUM
ejde-397	576	51	.	.	PUNCT
ejde-397	577	1	before	before	ADP
ejde-397	577	2	proceeding	proceed	VERB
ejde-397	577	3	further	far	ADV
ejde-397	577	4	,	,	PUNCT
ejde-397	577	5	we	we	PRON
ejde-397	577	6	want	want	VERB
ejde-397	577	7	to	to	PART
ejde-397	577	8	observe	observe	VERB
ejde-397	577	9	that	that	SCONJ
ejde-397	577	10	the	the	DET
ejde-397	577	11	existence	existence	NOUN
ejde-397	577	12	of	of	ADP
ejde-397	577	13	solutions	solution	NOUN
ejde-397	577	14	to	to	ADP
ejde-397	577	15	(	(	PUNCT
ejde-397	577	16	1.1	1.1	NUM
ejde-397	577	17	)	)	PUNCT
ejde-397	577	18	,	,	PUNCT
ejde-397	577	19	(	(	PUNCT
ejde-397	577	20	1.2	1.2	NUM
ejde-397	577	21	)	)	PUNCT
ejde-397	577	22	or	or	CCONJ
ejde-397	577	23	(	(	PUNCT
ejde-397	577	24	1.3	1.3	NUM
ejde-397	577	25	)	)	PUNCT
ejde-397	577	26	immediately	immediately	ADV
ejde-397	577	27	implies	imply	VERB
ejde-397	577	28	that	that	PRON
ejde-397	577	29	secc(f	secc(f	PROPN
ejde-397	577	30	)	)	PUNCT
ejde-397	577	31	6=	6=	ADP
ejde-397	577	32	∅	∅	NOUN
ejde-397	577	33	,	,	PUNCT
ejde-397	577	34	as	as	ADV
ejde-397	577	35	well	well	ADV
ejde-397	577	36	as	as	ADP
ejde-397	577	37	that	that	SCONJ
ejde-397	577	38	any	any	DET
ejde-397	577	39	strong	strong	ADJ
ejde-397	577	40	solution	solution	NOUN
ejde-397	577	41	of	of	ADP
ejde-397	577	42	(	(	PUNCT
ejde-397	577	43	1.1	1.1	NUM
ejde-397	577	44	)	)	PUNCT
ejde-397	577	45	is	be	AUX
ejde-397	577	46	already	already	ADV
ejde-397	577	47	a	a	DET
ejde-397	577	48	solution	solution	NOUN
ejde-397	577	49	of	of	ADP
ejde-397	577	50	(	(	PUNCT
ejde-397	577	51	1.1	1.1	NUM
ejde-397	577	52	)	)	PUNCT
ejde-397	577	53	,	,	PUNCT
ejde-397	577	54	provided	provide	VERB
ejde-397	577	55	that	that	SCONJ
ejde-397	577	56	a	a	PRON
ejde-397	577	57	and	and	CCONJ
ejde-397	577	58	b	b	NOUN
ejde-397	577	59	are	be	AUX
ejde-397	577	60	mlos	mlo	NOUN
ejde-397	577	61	with	with	ADP
ejde-397	577	62	a	a	DET
ejde-397	577	63	being	be	AUX
ejde-397	577	64	closed	close	VERB
ejde-397	577	65	;	;	PUNCT
ejde-397	577	66	this	this	PRON
ejde-397	577	67	can	can	AUX
ejde-397	577	68	be	be	AUX
ejde-397	577	69	simply	simply	ADV
ejde-397	577	70	verified	verify	VERB
ejde-397	577	71	with	with	ADP
ejde-397	577	72	the	the	DET
ejde-397	577	73	help	help	NOUN
ejde-397	577	74	of	of	ADP
ejde-397	577	75	theorem	theorem	ADJ
ejde-397	577	76	2.3	2.3	NUM
ejde-397	577	77	.	.	PUNCT
ejde-397	578	1	the	the	DET
ejde-397	578	2	notion	notion	NOUN
ejde-397	578	3	of	of	ADP
ejde-397	578	4	a	a	DET
ejde-397	578	5	(	(	PUNCT
ejde-397	578	6	pre-)solution	pre-)solution	NOUN
ejde-397	578	7	of	of	ADP
ejde-397	578	8	problems	problem	NOUN
ejde-397	578	9	(	(	PUNCT
ejde-397	578	10	1.2	1.2	NUM
ejde-397	578	11	)	)	PUNCT
ejde-397	578	12	and	and	CCONJ
ejde-397	578	13	(	(	PUNCT
ejde-397	578	14	1.3	1.3	NUM
ejde-397	578	15	)	)	PUNCT
ejde-397	578	16	can	can	AUX
ejde-397	578	17	be	be	AUX
ejde-397	578	18	similarly	similarly	ADV
ejde-397	578	19	defined	define	VERB
ejde-397	578	20	on	on	ADP
ejde-397	578	21	any	any	DET
ejde-397	578	22	finite	finite	ADJ
ejde-397	578	23	interval	interval	NOUN
ejde-397	578	24	[	[	X
ejde-397	578	25	0	0	NUM
ejde-397	578	26	,	,	PUNCT
ejde-397	578	27	τ	τ	X
ejde-397	578	28	)	)	PUNCT
ejde-397	578	29	or	or	CCONJ
ejde-397	578	30	[	[	X
ejde-397	578	31	0	0	NUM
ejde-397	578	32	,	,	PUNCT
ejde-397	578	33	τ	τ	PROPN
ejde-397	578	34	]	]	X
ejde-397	578	35	,	,	PUNCT
ejde-397	578	36	where	where	SCONJ
ejde-397	578	37	0	0	X
ejde-397	578	38	<	<	X
ejde-397	578	39	τ	τ	X
ejde-397	578	40	<	<	X
ejde-397	578	41	∞	∞	PROPN
ejde-397	578	42	,	,	PUNCT
ejde-397	578	43	and	and	CCONJ
ejde-397	578	44	extends	extend	VERB
ejde-397	578	45	so	so	SCONJ
ejde-397	578	46	the	the	DET
ejde-397	578	47	notion	notion	NOUN
ejde-397	578	48	of	of	ADP
ejde-397	578	49	a	a	DET
ejde-397	578	50	strict	strict	ADJ
ejde-397	578	51	solution	solution	NOUN
ejde-397	578	52	of	of	ADP
ejde-397	578	53	[	[	X
ejde-397	578	54	17	17	NUM
ejde-397	578	55	,	,	PUNCT
ejde-397	578	56	problem	problem	NOUN
ejde-397	578	57	(	(	PUNCT
ejde-397	578	58	e	e	NOUN
ejde-397	578	59	)	)	PUNCT
ejde-397	579	1	pp	pp	ADV
ejde-397	579	2	.	.	PUNCT
ejde-397	580	1	33	33	NUM
ejde-397	580	2	-	-	SYM
ejde-397	580	3	34	34	NUM
ejde-397	580	4	]	]	PUNCT
ejde-397	580	5	(	(	PUNCT
ejde-397	580	6	b	b	X
ejde-397	580	7	=	=	SYM
ejde-397	580	8	i	i	PROPN
ejde-397	580	9	,	,	PUNCT
ejde-397	580	10	α	α	NOUN
ejde-397	580	11	=	=	SYM
ejde-397	580	12	1	1	NUM
ejde-397	580	13	,	,	PUNCT
ejde-397	580	14	f(t	f(t	PROPN
ejde-397	580	15	)	)	PUNCT
ejde-397	580	16	=	=	SYM
ejde-397	580	17	f(t	f(t	NOUN
ejde-397	580	18	)	)	PUNCT
ejde-397	580	19	is	be	AUX
ejde-397	580	20	continuous	continuous	ADJ
ejde-397	580	21	single	single	ADV
ejde-397	580	22	-	-	PUNCT
ejde-397	580	23	valued	value	VERB
ejde-397	580	24	)	)	PUNCT
ejde-397	580	25	.	.	PUNCT
ejde-397	581	1	we	we	PRON
ejde-397	581	2	refer	refer	VERB
ejde-397	581	3	the	the	DET
ejde-397	581	4	reader	reader	NOUN
ejde-397	581	5	to	to	ADP
ejde-397	581	6	[	[	X
ejde-397	581	7	23]-[24	23]-[24	X
ejde-397	581	8	]	]	PUNCT
ejde-397	581	9	and	and	CCONJ
ejde-397	581	10	[	[	X
ejde-397	581	11	45	45	NUM
ejde-397	581	12	]	]	PUNCT
ejde-397	581	13	for	for	ADP
ejde-397	581	14	related	related	ADJ
ejde-397	581	15	results	result	NOUN
ejde-397	581	16	about	about	ADP
ejde-397	581	17	the	the	DET
ejde-397	581	18	wellposedness	wellposedness	NOUN
ejde-397	581	19	of	of	ADP
ejde-397	581	20	problem	problem	NOUN
ejde-397	581	21	(	(	PUNCT
ejde-397	581	22	1.2	1.2	NUM
ejde-397	581	23	)	)	PUNCT
ejde-397	581	24	,	,	PUNCT
ejde-397	581	25	as	as	ADV
ejde-397	581	26	well	well	ADV
ejde-397	581	27	as	as	ADP
ejde-397	581	28	to	to	ADP
ejde-397	581	29	the	the	DET
ejde-397	581	30	monograph	monograph	NOUN
ejde-397	582	1	[	[	X
ejde-397	582	2	15	15	NUM
ejde-397	582	3	]	]	PUNCT
ejde-397	582	4	by	by	ADP
ejde-397	582	5	dragoni	dragoni	ADJ
ejde-397	582	6	,	,	PUNCT
ejde-397	582	7	macki	macki	NOUN
ejde-397	582	8	,	,	PUNCT
ejde-397	582	9	nistri	nistri	NOUN
ejde-397	582	10	and	and	CCONJ
ejde-397	582	11	zecca	zecca	NOUN
ejde-397	582	12	for	for	ADP
ejde-397	582	13	some	some	DET
ejde-397	582	14	other	other	ADJ
ejde-397	582	15	concepts	concept	NOUN
ejde-397	582	16	of	of	ADP
ejde-397	582	17	solutions	solution	NOUN
ejde-397	582	18	to	to	ADP
ejde-397	582	19	the	the	DET
ejde-397	582	20	abstract	abstract	ADJ
ejde-397	582	21	differential	differential	ADJ
ejde-397	582	22	inclusions	inclusion	NOUN
ejde-397	582	23	in	in	ADP
ejde-397	582	24	abstract	abstract	ADJ
ejde-397	582	25	spaces	space	NOUN
ejde-397	582	26	.	.	PUNCT
ejde-397	583	1	in	in	ADP
ejde-397	583	2	our	our	PRON
ejde-397	583	3	further	further	ADJ
ejde-397	583	4	work	work	NOUN
ejde-397	583	5	,	,	PUNCT
ejde-397	583	6	it	it	PRON
ejde-397	583	7	will	will	AUX
ejde-397	583	8	be	be	AUX
ejde-397	583	9	assumed	assume	VERB
ejde-397	583	10	that	that	SCONJ
ejde-397	583	11	a	a	PRON
ejde-397	583	12	and	and	CCONJ
ejde-397	583	13	b	b	NOUN
ejde-397	583	14	are	be	AUX
ejde-397	583	15	multivalued	multivalued	ADJ
ejde-397	583	16	linear	linear	PROPN
ejde-397	583	17	operators	operator	NOUN
ejde-397	583	18	.	.	PUNCT
ejde-397	584	1	observe	observe	VERB
ejde-397	584	2	that	that	SCONJ
ejde-397	584	3	we	we	PRON
ejde-397	584	4	can	can	AUX
ejde-397	584	5	not	not	PART
ejde-397	584	6	consider	consider	VERB
ejde-397	584	7	the	the	DET
ejde-397	584	8	qualitative	qualitative	ADJ
ejde-397	584	9	properties	property	NOUN
ejde-397	584	10	of	of	ADP
ejde-397	584	11	solutions	solution	NOUN
ejde-397	584	12	of	of	ADP
ejde-397	584	13	problems	problem	NOUN
ejde-397	584	14	(	(	PUNCT
ejde-397	584	15	1.1	1.1	NUM
ejde-397	584	16	)	)	PUNCT
ejde-397	584	17	,	,	PUNCT
ejde-397	584	18	(	(	PUNCT
ejde-397	584	19	1.2	1.2	NUM
ejde-397	584	20	)	)	PUNCT
ejde-397	584	21	or	or	CCONJ
ejde-397	584	22	(	(	PUNCT
ejde-397	584	23	1.3	1.3	NUM
ejde-397	584	24	)	)	PUNCT
ejde-397	584	25	in	in	ADP
ejde-397	584	26	full	full	ADJ
ejde-397	584	27	generality	generality	NOUN
ejde-397	584	28	by	by	ADP
ejde-397	584	29	a	a	DET
ejde-397	584	30	simple	simple	ADJ
ejde-397	584	31	passing	passing	NOUN
ejde-397	584	32	to	to	ADP
ejde-397	584	33	the	the	DET
ejde-397	584	34	multivalued	multivalue	VERB
ejde-397	584	35	linear	linear	PROPN
ejde-397	584	36	operators	operator	NOUN
ejde-397	584	37	b−1a	b−1a	ADV
ejde-397	584	38	or	or	CCONJ
ejde-397	584	39	ab−1	ab−1	PROPN
ejde-397	584	40	(	(	PUNCT
ejde-397	584	41	see	see	VERB
ejde-397	584	42	the	the	DET
ejde-397	584	43	definition	definition	NOUN
ejde-397	584	44	of	of	ADP
ejde-397	584	45	a	a	DET
ejde-397	584	46	solution	solution	NOUN
ejde-397	584	47	of	of	ADP
ejde-397	584	48	(	(	PUNCT
ejde-397	584	49	1.1	1.1	NUM
ejde-397	584	50	)	)	PUNCT
ejde-397	584	51	)	)	PUNCT
ejde-397	584	52	.	.	PUNCT
ejde-397	585	1	concerning	concern	VERB
ejde-397	585	2	this	this	DET
ejde-397	585	3	question	question	NOUN
ejde-397	585	4	,	,	PUNCT
ejde-397	585	5	we	we	PRON
ejde-397	585	6	have	have	VERB
ejde-397	585	7	the	the	DET
ejde-397	585	8	following	follow	VERB
ejde-397	585	9	remark	remark	NOUN
ejde-397	585	10	.	.	PUNCT
ejde-397	586	1	remark	remark	VERB
ejde-397	586	2	4.2	4.2	NUM
ejde-397	586	3	.	.	PUNCT
ejde-397	587	1	suppose	suppose	VERB
ejde-397	587	2	that	that	SCONJ
ejde-397	587	3	0	0	NUM
ejde-397	588	1	<	<	X
ejde-397	588	2	τ	τ	PROPN
ejde-397	588	3	≤	≤	NOUN
ejde-397	588	4	∞	∞	PROPN
ejde-397	588	5	,	,	PUNCT
ejde-397	588	6	α	α	X
ejde-397	588	7	>	>	X
ejde-397	588	8	0	0	NUM
ejde-397	588	9	,	,	PUNCT
ejde-397	588	10	as	as	ADV
ejde-397	588	11	well	well	ADV
ejde-397	588	12	as	as	ADP
ejde-397	588	13	that	that	PRON
ejde-397	588	14	a	a	PRON
ejde-397	588	15	:	:	PUNCT
ejde-397	588	16	d(a	d(a	PROPN
ejde-397	588	17	)	)	PUNCT
ejde-397	588	18	⊆	⊆	NUM
ejde-397	588	19	x	x	SYM
ejde-397	588	20	→	→	SYM
ejde-397	588	21	y	y	PROPN
ejde-397	588	22	and	and	CCONJ
ejde-397	588	23	b	b	NOUN
ejde-397	588	24	:	:	PUNCT
ejde-397	588	25	d(b	d(b	X
ejde-397	588	26	)	)	PUNCT
ejde-397	589	1	⊆	⊆	NUM
ejde-397	589	2	x	x	SYM
ejde-397	589	3	→	→	SYM
ejde-397	589	4	y	y	PROPN
ejde-397	589	5	are	be	AUX
ejde-397	589	6	two	two	NUM
ejde-397	589	7	single	single	ADV
ejde-397	589	8	-	-	PUNCT
ejde-397	589	9	valued	value	VERB
ejde-397	589	10	linear	linear	PROPN
ejde-397	589	11	operators	operator	NOUN
ejde-397	589	12	.	.	PUNCT
ejde-397	590	1	then	then	ADV
ejde-397	590	2	b−1a	b−1a	ADV
ejde-397	590	3	is	be	AUX
ejde-397	590	4	an	an	DET
ejde-397	590	5	mlo	mlo	NOUN
ejde-397	590	6	in	in	ADP
ejde-397	590	7	x	x	NOUN
ejde-397	590	8	,	,	PUNCT
ejde-397	590	9	and	and	CCONJ
ejde-397	590	10	ab−1	ab−1	PROPN
ejde-397	590	11	is	be	AUX
ejde-397	590	12	an	an	DET
ejde-397	590	13	mlo	mlo	NOUN
ejde-397	590	14	in	in	ADP
ejde-397	590	15	y	y	PROPN
ejde-397	590	16	.	.	PUNCT
ejde-397	591	1	18	18	NUM
ejde-397	591	2	m.	m.	NOUN
ejde-397	591	3	kostić	kostić	NOUN
ejde-397	591	4	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	591	5	(	(	PUNCT
ejde-397	591	6	i	i	NOUN
ejde-397	591	7	)	)	PUNCT
ejde-397	591	8	suppose	suppose	VERB
ejde-397	591	9	that	that	SCONJ
ejde-397	591	10	u	u	PROPN
ejde-397	591	11	(	(	PUNCT
ejde-397	591	12	·	·	PUNCT
ejde-397	591	13	)	)	PUNCT
ejde-397	591	14	is	be	AUX
ejde-397	591	15	a	a	DET
ejde-397	591	16	pre	pre	NOUN
ejde-397	591	17	-	-	NOUN
ejde-397	591	18	solution	solution	NOUN
ejde-397	591	19	(	(	PUNCT
ejde-397	591	20	or	or	CCONJ
ejde-397	591	21	,	,	PUNCT
ejde-397	591	22	equivalently	equivalently	ADV
ejde-397	591	23	,	,	PUNCT
ejde-397	591	24	solution	solution	NOUN
ejde-397	591	25	)	)	PUNCT
ejde-397	591	26	of	of	ADP
ejde-397	591	27	problem	problem	NOUN
ejde-397	591	28	(	(	PUNCT
ejde-397	591	29	1.1	1.1	NUM
ejde-397	591	30	)	)	PUNCT
ejde-397	591	31	with	with	ADP
ejde-397	591	32	b	b	NOUN
ejde-397	591	33	=	=	SYM
ejde-397	591	34	ix	ix	PROPN
ejde-397	591	35	,	,	PUNCT
ejde-397	591	36	a	a	PRON
ejde-397	591	37	=	=	X
ejde-397	591	38	b−1a	b−1a	X
ejde-397	591	39	and	and	CCONJ
ejde-397	591	40	f	f	X
ejde-397	591	41	=	=	SYM
ejde-397	591	42	f	f	X
ejde-397	591	43	:	:	PUNCT
ejde-397	592	1	[	[	X
ejde-397	592	2	0	0	NUM
ejde-397	592	3	,	,	PUNCT
ejde-397	592	4	τ	τ	PROPN
ejde-397	592	5	)	)	PUNCT
ejde-397	592	6	→	→	SYM
ejde-397	592	7	d(b	d(b	X
ejde-397	592	8	)	)	PUNCT
ejde-397	592	9	being	be	AUX
ejde-397	592	10	singlevalued	singlevalue	VERB
ejde-397	592	11	.	.	PUNCT
ejde-397	593	1	then	then	ADV
ejde-397	593	2	u	u	PROPN
ejde-397	593	3	∈	∈	PROPN
ejde-397	593	4	c([0	c([0	NOUN
ejde-397	593	5	,	,	PUNCT
ejde-397	593	6	τ	τ	PROPN
ejde-397	593	7	)	)	PUNCT
ejde-397	593	8	:	:	PUNCT
ejde-397	594	1	x	x	X
ejde-397	594	2	)	)	PUNCT
ejde-397	594	3	and	and	CCONJ
ejde-397	594	4	bu(t	bu(t	NUM
ejde-397	594	5	)	)	PUNCT
ejde-397	594	6	=	=	SYM
ejde-397	594	7	a(a	a(a	PROPN
ejde-397	594	8	∗	∗	NOUN
ejde-397	594	9	u)(t	u)(t	NOUN
ejde-397	594	10	)	)	PUNCT
ejde-397	595	1	+	+	NOUN
ejde-397	595	2	bf(t	bf(t	NOUN
ejde-397	595	3	)	)	PUNCT
ejde-397	595	4	,	,	PUNCT
ejde-397	595	5	t	t	PROPN
ejde-397	595	6	∈	∈	PROPN
ejde-397	596	1	[	[	X
ejde-397	596	2	0	0	NUM
ejde-397	596	3	,	,	PUNCT
ejde-397	596	4	τ	τ	PROPN
ejde-397	596	5	)	)	PUNCT
ejde-397	596	6	.	.	PUNCT
ejde-397	597	1	if	if	SCONJ
ejde-397	597	2	,	,	PUNCT
ejde-397	597	3	in	in	ADP
ejde-397	597	4	addition	addition	NOUN
ejde-397	597	5	to	to	ADP
ejde-397	597	6	this	this	PRON
ejde-397	597	7	,	,	PUNCT
ejde-397	597	8	b	b	PROPN
ejde-397	597	9	∈	∈	PROPN
ejde-397	597	10	l(x	l(x	PROPN
ejde-397	597	11	,	,	PUNCT
ejde-397	597	12	y	y	PROPN
ejde-397	597	13	)	)	PUNCT
ejde-397	597	14	and	and	CCONJ
ejde-397	597	15	u	u	NOUN
ejde-397	597	16	(	(	PUNCT
ejde-397	597	17	·	·	PUNCT
ejde-397	597	18	)	)	PUNCT
ejde-397	597	19	is	be	AUX
ejde-397	597	20	a	a	DET
ejde-397	597	21	strong	strong	ADJ
ejde-397	597	22	solution	solution	NOUN
ejde-397	597	23	of	of	ADP
ejde-397	597	24	problem	problem	NOUN
ejde-397	597	25	(	(	PUNCT
ejde-397	597	26	1.1	1.1	NUM
ejde-397	597	27	)	)	PUNCT
ejde-397	597	28	with	with	ADP
ejde-397	597	29	the	the	DET
ejde-397	597	30	above	above	ADJ
ejde-397	597	31	requirements	requirement	NOUN
ejde-397	597	32	being	be	AUX
ejde-397	597	33	satisfied	satisfied	ADJ
ejde-397	597	34	,	,	PUNCT
ejde-397	597	35	then	then	ADV
ejde-397	597	36	the	the	DET
ejde-397	597	37	mappings	mapping	NOUN
ejde-397	597	38	t	t	X
ejde-397	597	39	7→	7→	NUM
ejde-397	597	40	au(t	au(t	NUM
ejde-397	597	41	)	)	PUNCT
ejde-397	597	42	,	,	PUNCT
ejde-397	597	43	t	t	PROPN
ejde-397	597	44	∈	∈	PROPN
ejde-397	598	1	[	[	X
ejde-397	598	2	0	0	NUM
ejde-397	598	3	,	,	PUNCT
ejde-397	598	4	τ	τ	X
ejde-397	598	5	)	)	PUNCT
ejde-397	598	6	and	and	CCONJ
ejde-397	598	7	t	t	PROPN
ejde-397	598	8	7→	7→	NUM
ejde-397	598	9	bu(t	bu(t	NUM
ejde-397	598	10	)	)	PUNCT
ejde-397	598	11	,	,	PUNCT
ejde-397	598	12	t	t	PROPN
ejde-397	598	13	∈	∈	PROPN
ejde-397	599	1	[	[	X
ejde-397	599	2	0	0	NUM
ejde-397	599	3	,	,	PUNCT
ejde-397	599	4	τ	τ	X
ejde-397	599	5	)	)	PUNCT
ejde-397	599	6	are	be	AUX
ejde-397	599	7	continuous	continuous	ADJ
ejde-397	599	8	,	,	PUNCT
ejde-397	599	9	and	and	CCONJ
ejde-397	599	10	(	(	PUNCT
ejde-397	599	11	a	a	DET
ejde-397	599	12	∗au)(t	∗au)(t	NUM
ejde-397	599	13	)	)	PUNCT
ejde-397	599	14	=	=	SYM
ejde-397	599	15	bu(t)−bf(t	bu(t)−bf(t	NOUN
ejde-397	599	16	)	)	PUNCT
ejde-397	599	17	,	,	PUNCT
ejde-397	599	18	t	t	PROPN
ejde-397	599	19	∈	∈	PROPN
ejde-397	600	1	[	[	X
ejde-397	600	2	0	0	NUM
ejde-397	600	3	,	,	PUNCT
ejde-397	600	4	τ	τ	PROPN
ejde-397	600	5	)	)	PUNCT
ejde-397	600	6	.	.	PUNCT
ejde-397	601	1	(	(	PUNCT
ejde-397	601	2	ii	ii	NOUN
ejde-397	601	3	)	)	PUNCT
ejde-397	601	4	suppose	suppose	VERB
ejde-397	601	5	that	that	SCONJ
ejde-397	601	6	v	v	NOUN
ejde-397	601	7	(	(	PUNCT
ejde-397	601	8	·	·	PUNCT
ejde-397	601	9	)	)	PUNCT
ejde-397	601	10	is	be	AUX
ejde-397	601	11	a	a	DET
ejde-397	601	12	pre	pre	NOUN
ejde-397	601	13	-	-	NOUN
ejde-397	601	14	solution	solution	NOUN
ejde-397	601	15	(	(	PUNCT
ejde-397	601	16	solution	solution	NOUN
ejde-397	601	17	)	)	PUNCT
ejde-397	601	18	of	of	ADP
ejde-397	601	19	(	(	PUNCT
ejde-397	601	20	1.2	1.2	NUM
ejde-397	601	21	)	)	PUNCT
ejde-397	601	22	with	with	ADP
ejde-397	601	23	b	b	PROPN
ejde-397	601	24	=	=	SYM
ejde-397	601	25	iy	iy	PROPN
ejde-397	601	26	,	,	PUNCT
ejde-397	601	27	a	a	DET
ejde-397	601	28	=	=	X
ejde-397	601	29	ab−1	ab−1	PROPN
ejde-397	601	30	,	,	PUNCT
ejde-397	602	1	f	f	PROPN
ejde-397	602	2	=	=	SYM
ejde-397	602	3	f	f	X
ejde-397	602	4	:	:	PUNCT
ejde-397	603	1	[	[	X
ejde-397	603	2	0	0	NUM
ejde-397	603	3	,	,	PUNCT
ejde-397	603	4	τ	τ	X
ejde-397	603	5	)	)	PUNCT
ejde-397	603	6	→	→	PUNCT
ejde-397	603	7	y	y	X
ejde-397	603	8	being	be	AUX
ejde-397	603	9	single	single	ADV
ejde-397	603	10	-	-	PUNCT
ejde-397	603	11	valued	value	VERB
ejde-397	603	12	,	,	PUNCT
ejde-397	603	13	and	and	CCONJ
ejde-397	603	14	vj	vj	PROPN
ejde-397	603	15	=	=	PUNCT
ejde-397	603	16	bxj	bxj	NOUN
ejde-397	603	17	(	(	PUNCT
ejde-397	603	18	0	0	NUM
ejde-397	603	19	≤	≤	NUM
ejde-397	603	20	j	j	PROPN
ejde-397	603	21	≤	≤	PROPN
ejde-397	603	22	dαe	dαe	VERB
ejde-397	603	23	−	−	PROPN
ejde-397	603	24	1	1	NUM
ejde-397	603	25	)	)	PUNCT
ejde-397	603	26	.	.	PUNCT
ejde-397	604	1	let	let	VERB
ejde-397	604	2	b−1	b−1	PROPN
ejde-397	604	3	∈	∈	PROPN
ejde-397	604	4	l(y	l(y	PROPN
ejde-397	604	5	,	,	PUNCT
ejde-397	604	6	x	x	NOUN
ejde-397	604	7	)	)	PUNCT
ejde-397	604	8	.	.	PUNCT
ejde-397	605	1	then	then	ADV
ejde-397	605	2	the	the	DET
ejde-397	605	3	function	function	NOUN
ejde-397	605	4	u(t	u(t	NOUN
ejde-397	605	5	)	)	PUNCT
ejde-397	605	6	:	:	PUNCT
ejde-397	605	7	=	=	PUNCT
ejde-397	605	8	b−1v(t	b−1v(t	NOUN
ejde-397	605	9	)	)	PUNCT
ejde-397	605	10	,	,	PUNCT
ejde-397	605	11	t	t	PROPN
ejde-397	605	12	≥	≥	PROPN
ejde-397	605	13	0	0	NUM
ejde-397	605	14	is	be	AUX
ejde-397	605	15	a	a	DET
ejde-397	605	16	pre	pre	NOUN
ejde-397	605	17	-	-	NOUN
ejde-397	605	18	solution	solution	NOUN
ejde-397	605	19	(	(	PUNCT
ejde-397	605	20	solution	solution	NOUN
ejde-397	605	21	)	)	PUNCT
ejde-397	605	22	of	of	ADP
ejde-397	605	23	(	(	PUNCT
ejde-397	605	24	1.2	1.2	NUM
ejde-397	605	25	)	)	PUNCT
ejde-397	605	26	with	with	ADP
ejde-397	605	27	b	b	PROPN
ejde-397	605	28	=	=	SYM
ejde-397	605	29	b	b	PROPN
ejde-397	605	30	and	and	CCONJ
ejde-397	605	31	a	a	DET
ejde-397	605	32	=	=	NOUN
ejde-397	605	33	a.	a.	NOUN
ejde-397	605	34	(	(	PUNCT
ejde-397	605	35	iii	iii	NOUN
ejde-397	605	36	)	)	PUNCT
ejde-397	605	37	suppose	suppose	VERB
ejde-397	605	38	that	that	SCONJ
ejde-397	605	39	f	f	PROPN
ejde-397	605	40	=	=	SYM
ejde-397	605	41	f	f	X
ejde-397	605	42	:	:	PUNCT
ejde-397	606	1	[	[	X
ejde-397	606	2	0	0	NUM
ejde-397	606	3	,	,	PUNCT
ejde-397	606	4	τ	τ	PROPN
ejde-397	606	5	)	)	PUNCT
ejde-397	606	6	→	→	SYM
ejde-397	606	7	d(b	d(b	X
ejde-397	606	8	)	)	PUNCT
ejde-397	606	9	is	be	AUX
ejde-397	606	10	single	single	ADV
ejde-397	606	11	-	-	PUNCT
ejde-397	606	12	valued	value	VERB
ejde-397	606	13	and	and	CCONJ
ejde-397	606	14	u	u	NOUN
ejde-397	606	15	(	(	PUNCT
ejde-397	606	16	·	·	PUNCT
ejde-397	606	17	)	)	PUNCT
ejde-397	606	18	is	be	AUX
ejde-397	606	19	a	a	DET
ejde-397	606	20	presolution	presolution	NOUN
ejde-397	606	21	of	of	ADP
ejde-397	606	22	problem	problem	NOUN
ejde-397	606	23	(	(	PUNCT
ejde-397	606	24	dfp)l	dfp)l	PROPN
ejde-397	606	25	with	with	ADP
ejde-397	606	26	b	b	NOUN
ejde-397	606	27	=	=	PUNCT
ejde-397	606	28	ix	ix	PROPN
ejde-397	606	29	and	and	CCONJ
ejde-397	606	30	a	a	DET
ejde-397	606	31	=	=	X
ejde-397	606	32	b−1a	b−1a	NOUN
ejde-397	606	33	.	.	PUNCT
ejde-397	607	1	then	then	ADV
ejde-397	607	2	u	u	X
ejde-397	607	3	(	(	PUNCT
ejde-397	607	4	·	·	PUNCT
ejde-397	607	5	)	)	PUNCT
ejde-397	607	6	is	be	AUX
ejde-397	607	7	a	a	DET
ejde-397	607	8	pre	pre	NOUN
ejde-397	607	9	-	-	NOUN
ejde-397	607	10	solution	solution	NOUN
ejde-397	607	11	of	of	ADP
ejde-397	607	12	problem	problem	NOUN
ejde-397	607	13	(	(	PUNCT
ejde-397	607	14	dfp)l	dfp)l	PROPN
ejde-397	607	15	with	with	ADP
ejde-397	607	16	b	b	PROPN
ejde-397	607	17	=	=	SYM
ejde-397	607	18	b	b	PROPN
ejde-397	607	19	,	,	PUNCT
ejde-397	607	20	a	a	DET
ejde-397	607	21	=	=	PUNCT
ejde-397	607	22	a	a	NOUN
ejde-397	607	23	and	and	CCONJ
ejde-397	607	24	f(t	f(t	NOUN
ejde-397	607	25	)	)	PUNCT
ejde-397	608	1	=	=	PUNCT
ejde-397	608	2	bf(t	bf(t	NOUN
ejde-397	608	3	)	)	PUNCT
ejde-397	608	4	,	,	PUNCT
ejde-397	608	5	t	t	PROPN
ejde-397	608	6	∈	∈	PROPN
ejde-397	609	1	[	[	X
ejde-397	609	2	0	0	NUM
ejde-397	609	3	,	,	PUNCT
ejde-397	609	4	τ	τ	PROPN
ejde-397	609	5	)	)	PUNCT
ejde-397	609	6	.	.	PUNCT
ejde-397	610	1	if	if	SCONJ
ejde-397	610	2	,	,	PUNCT
ejde-397	610	3	in	in	ADP
ejde-397	610	4	addition	addition	NOUN
ejde-397	610	5	to	to	ADP
ejde-397	610	6	this	this	PRON
ejde-397	610	7	,	,	PUNCT
ejde-397	610	8	b	b	PROPN
ejde-397	610	9	∈	∈	PROPN
ejde-397	610	10	l(x	l(x	PROPN
ejde-397	610	11	,	,	PUNCT
ejde-397	610	12	y	y	PROPN
ejde-397	610	13	)	)	PUNCT
ejde-397	610	14	and	and	CCONJ
ejde-397	610	15	u	u	NOUN
ejde-397	610	16	(	(	PUNCT
ejde-397	610	17	·	·	PUNCT
ejde-397	610	18	)	)	PUNCT
ejde-397	610	19	is	be	AUX
ejde-397	610	20	a	a	DET
ejde-397	610	21	solution	solution	NOUN
ejde-397	610	22	of	of	ADP
ejde-397	610	23	problem	problem	NOUN
ejde-397	610	24	(	(	PUNCT
ejde-397	610	25	1.3	1.3	NUM
ejde-397	610	26	)	)	PUNCT
ejde-397	610	27	with	with	ADP
ejde-397	610	28	the	the	DET
ejde-397	610	29	above	above	ADJ
ejde-397	610	30	requirements	requirement	NOUN
ejde-397	610	31	being	be	AUX
ejde-397	610	32	satisfied	satisfied	ADJ
ejde-397	610	33	,	,	PUNCT
ejde-397	610	34	then	then	ADV
ejde-397	610	35	u	u	NOUN
ejde-397	610	36	(	(	PUNCT
ejde-397	610	37	·	·	PUNCT
ejde-397	610	38	)	)	PUNCT
ejde-397	610	39	is	be	AUX
ejde-397	610	40	a	a	DET
ejde-397	610	41	solution	solution	NOUN
ejde-397	610	42	of	of	ADP
ejde-397	610	43	problem	problem	NOUN
ejde-397	610	44	(	(	PUNCT
ejde-397	610	45	dfp)l	dfp)l	PROPN
ejde-397	610	46	with	with	ADP
ejde-397	610	47	b	b	PROPN
ejde-397	610	48	=	=	SYM
ejde-397	610	49	b	b	PROPN
ejde-397	610	50	,	,	PUNCT
ejde-397	610	51	a	a	DET
ejde-397	610	52	=	=	PUNCT
ejde-397	610	53	a	a	NOUN
ejde-397	610	54	and	and	CCONJ
ejde-397	610	55	f(t	f(t	NOUN
ejde-397	610	56	)	)	PUNCT
ejde-397	611	1	=	=	PUNCT
ejde-397	611	2	bf(t	bf(t	NOUN
ejde-397	611	3	)	)	PUNCT
ejde-397	611	4	,	,	PUNCT
ejde-397	611	5	t	t	PROPN
ejde-397	611	6	∈	∈	PROPN
ejde-397	612	1	[	[	X
ejde-397	612	2	0	0	NUM
ejde-397	612	3	,	,	PUNCT
ejde-397	612	4	τ	τ	PROPN
ejde-397	612	5	)	)	PUNCT
ejde-397	612	6	.	.	PUNCT
ejde-397	613	1	(	(	PUNCT
ejde-397	613	2	iv	iv	X
ejde-397	613	3	)	)	PUNCT
ejde-397	613	4	suppose	suppose	VERB
ejde-397	613	5	that	that	SCONJ
ejde-397	613	6	u	u	NOUN
ejde-397	613	7	:	:	PUNCT
ejde-397	614	1	[	[	X
ejde-397	614	2	0,∞	0,∞	NUM
ejde-397	614	3	)	)	PUNCT
ejde-397	614	4	→	→	SYM
ejde-397	614	5	d(a	d(a	PROPN
ejde-397	614	6	)	)	PUNCT
ejde-397	614	7	∩	∩	NOUN
ejde-397	614	8	d(b	d(b	PROPN
ejde-397	614	9	)	)	PUNCT
ejde-397	614	10	.	.	PUNCT
ejde-397	615	1	then	then	ADV
ejde-397	615	2	u	u	X
ejde-397	615	3	(	(	PUNCT
ejde-397	615	4	·	·	PUNCT
ejde-397	615	5	)	)	PUNCT
ejde-397	615	6	is	be	AUX
ejde-397	615	7	a	a	DET
ejde-397	615	8	p	p	NOUN
ejde-397	615	9	-	-	PUNCT
ejde-397	615	10	solution	solution	NOUN
ejde-397	615	11	of	of	ADP
ejde-397	615	12	problem	problem	NOUN
ejde-397	615	13	(	(	PUNCT
ejde-397	615	14	dfp)r	dfp)r	NOUN
ejde-397	615	15	with	with	ADP
ejde-397	615	16	b	b	NOUN
ejde-397	615	17	=	=	SYM
ejde-397	615	18	b	b	PROPN
ejde-397	615	19	and	and	CCONJ
ejde-397	615	20	a	a	DET
ejde-397	615	21	=	=	NOUN
ejde-397	615	22	a	a	DET
ejde-397	615	23	if	if	NOUN
ejde-397	616	1	and	and	CCONJ
ejde-397	616	2	only	only	ADV
ejde-397	616	3	if	if	SCONJ
ejde-397	616	4	v	v	NOUN
ejde-397	616	5	=	=	SYM
ejde-397	616	6	bu	bu	PROPN
ejde-397	616	7	(	(	PUNCT
ejde-397	616	8	·	·	PUNCT
ejde-397	616	9	)	)	PUNCT
ejde-397	616	10	is	be	AUX
ejde-397	616	11	a	a	DET
ejde-397	616	12	pre	pre	NOUN
ejde-397	616	13	-	-	NOUN
ejde-397	616	14	solution	solution	NOUN
ejde-397	616	15	of	of	ADP
ejde-397	616	16	problem	problem	NOUN
ejde-397	616	17	dα	dα	ADP
ejde-397	616	18	t	t	PROPN
ejde-397	616	19	v(t	v(t	PROPN
ejde-397	616	20	)	)	PUNCT
ejde-397	616	21	∈	∈	PROPN
ejde-397	616	22	ab−1v(t	ab−1v(t	NOUN
ejde-397	616	23	)	)	PUNCT
ejde-397	617	1	+	+	CCONJ
ejde-397	617	2	f(t	f(t	NOUN
ejde-397	617	3	)	)	PUNCT
ejde-397	617	4	,	,	PUNCT
ejde-397	617	5	t	t	PROPN
ejde-397	617	6	≥	≥	NUM
ejde-397	617	7	0	0	NUM
ejde-397	617	8	,	,	PUNCT
ejde-397	617	9	v(j)(0	v(j)(0	PROPN
ejde-397	617	10	)	)	PUNCT
ejde-397	617	11	=	=	NOUN
ejde-397	617	12	bxj	bxj	NOUN
ejde-397	617	13	,	,	PUNCT
ejde-397	617	14	0	0	NUM
ejde-397	617	15	≤	≤	NUM
ejde-397	617	16	j	j	PROPN
ejde-397	617	17	≤	≤	PROPN
ejde-397	617	18	dαe	dαe	VERB
ejde-397	617	19	−	−	PROPN
ejde-397	617	20	1	1	NUM
ejde-397	617	21	.	.	PUNCT
ejde-397	618	1	(	(	PUNCT
ejde-397	618	2	v	v	NOUN
ejde-397	618	3	)	)	PUNCT
ejde-397	618	4	suppose	suppose	VERB
ejde-397	618	5	that	that	SCONJ
ejde-397	618	6	cy	cy	PROPN
ejde-397	618	7	∈	∈	PROPN
ejde-397	618	8	l(y	l(y	PROPN
ejde-397	618	9	)	)	PUNCT
ejde-397	618	10	is	be	AUX
ejde-397	618	11	injective	injective	ADJ
ejde-397	618	12	and	and	CCONJ
ejde-397	618	13	the	the	DET
ejde-397	618	14	closed	closed	ADJ
ejde-397	618	15	graph	graph	NOUN
ejde-397	618	16	theorem	theorem	NOUN
ejde-397	618	17	holds	hold	NOUN
ejde-397	618	18	for	for	ADP
ejde-397	618	19	the	the	DET
ejde-397	618	20	mappings	mapping	NOUN
ejde-397	618	21	from	from	ADP
ejde-397	618	22	y	y	PROPN
ejde-397	618	23	into	into	ADP
ejde-397	618	24	y	y	PROPN
ejde-397	618	25	.	.	PUNCT
ejde-397	619	1	then	then	ADV
ejde-397	619	2	we	we	PRON
ejde-397	619	3	define	define	VERB
ejde-397	619	4	the	the	DET
ejde-397	619	5	set	set	ADJ
ejde-397	619	6	ρbcy	ρbcy	NOUN
ejde-397	619	7	(	(	PUNCT
ejde-397	619	8	a	a	X
ejde-397	619	9	)	)	PUNCT
ejde-397	619	10	:	:	PUNCT
ejde-397	619	11	=	=	SYM
ejde-397	619	12	{	{	PUNCT
ejde-397	619	13	λ	λ	X
ejde-397	619	14	∈	∈	NOUN
ejde-397	619	15	c	c	NOUN
ejde-397	619	16	:	:	PUNCT
ejde-397	620	1	λb	λb	ADP
ejde-397	620	2	−	−	PROPN
ejde-397	620	3	a	a	PRON
ejde-397	620	4	is	be	AUX
ejde-397	620	5	injective	injective	ADJ
ejde-397	620	6	and	and	CCONJ
ejde-397	620	7	(	(	PUNCT
ejde-397	620	8	λb	λb	INTJ
ejde-397	620	9	−	−	PROPN
ejde-397	620	10	a)−1cy	a)−1cy	PROPN
ejde-397	620	11	∈	∈	PROPN
ejde-397	620	12	l(y	l(y	PROPN
ejde-397	620	13	)	)	PUNCT
ejde-397	620	14	}	}	PUNCT
ejde-397	620	15	.	.	PUNCT
ejde-397	621	1	it	it	PRON
ejde-397	621	2	can	can	AUX
ejde-397	621	3	be	be	AUX
ejde-397	621	4	simply	simply	ADV
ejde-397	621	5	checked	check	VERB
ejde-397	621	6	that	that	DET
ejde-397	621	7	ρbcy	ρbcy	NOUN
ejde-397	621	8	(	(	PUNCT
ejde-397	621	9	a	a	X
ejde-397	621	10	)	)	PUNCT
ejde-397	621	11	⊆	⊆	NUM
ejde-397	621	12	ρcy	ρcy	NOUN
ejde-397	621	13	(	(	PUNCT
ejde-397	621	14	ab−1	ab−1	PROPN
ejde-397	621	15	)	)	PUNCT
ejde-397	621	16	,	,	PUNCT
ejde-397	621	17	as	as	ADV
ejde-397	621	18	well	well	ADV
ejde-397	621	19	as	as	ADP
ejde-397	621	20	that	that	PRON
ejde-397	621	21	(	(	PUNCT
ejde-397	621	22	λ−ab−1	λ−ab−1	NOUN
ejde-397	621	23	)	)	PUNCT
ejde-397	621	24	−1	−1	NOUN
ejde-397	621	25	cy	cy	NOUN
ejde-397	621	26	=	=	SYM
ejde-397	621	27	b	b	PROPN
ejde-397	621	28	(	(	PUNCT
ejde-397	621	29	λb	λb	ADV
ejde-397	621	30	−a	−a	ADJ
ejde-397	621	31	)	)	PUNCT
ejde-397	621	32	−1	−1	NOUN
ejde-397	621	33	cy	cy	PROPN
ejde-397	621	34	,	,	PUNCT
ejde-397	621	35	λ	λ	PROPN
ejde-397	621	36	∈	∈	NOUN
ejde-397	621	37	ρbcy	ρbcy	NOUN
ejde-397	621	38	(	(	PUNCT
ejde-397	621	39	a	a	NOUN
ejde-397	621	40	)	)	PUNCT
ejde-397	621	41	.	.	PUNCT
ejde-397	622	1	(	(	PUNCT
ejde-397	622	2	4.1	4.1	NUM
ejde-397	622	3	)	)	PUNCT
ejde-397	622	4	this	this	PRON
ejde-397	622	5	is	be	AUX
ejde-397	622	6	an	an	DET
ejde-397	622	7	extension	extension	NOUN
ejde-397	622	8	of	of	ADP
ejde-397	622	9	[	[	X
ejde-397	622	10	17	17	NUM
ejde-397	622	11	,	,	PUNCT
ejde-397	622	12	theorem	theorem	VERB
ejde-397	622	13	1.14	1.14	NUM
ejde-397	622	14	]	]	PUNCT
ejde-397	622	15	and	and	CCONJ
ejde-397	622	16	holds	hold	VERB
ejde-397	622	17	even	even	ADV
ejde-397	622	18	in	in	ADP
ejde-397	622	19	the	the	DET
ejde-397	622	20	case	case	NOUN
ejde-397	622	21	that	that	SCONJ
ejde-397	622	22	the	the	DET
ejde-397	622	23	operator	operator	NOUN
ejde-397	622	24	cy	cy	VERB
ejde-397	622	25	does	do	AUX
ejde-397	622	26	not	not	PART
ejde-397	622	27	commute	commute	VERB
ejde-397	622	28	with	with	ADP
ejde-397	622	29	ab−1	ab−1	NOUN
ejde-397	622	30	,	,	PUNCT
ejde-397	622	31	when	when	SCONJ
ejde-397	622	32	we	we	PRON
ejde-397	622	33	define	define	VERB
ejde-397	622	34	the	the	DET
ejde-397	622	35	cy	cy	PROPN
ejde-397	622	36	resolvent	resolvent	ADJ
ejde-397	622	37	set	set	NOUN
ejde-397	622	38	of	of	ADP
ejde-397	622	39	the	the	DET
ejde-397	622	40	operator	operator	NOUN
ejde-397	622	41	λ−ab−1	λ−ab−1	NOUN
ejde-397	622	42	in	in	ADP
ejde-397	622	43	the	the	DET
ejde-397	622	44	same	same	ADJ
ejde-397	622	45	way	way	NOUN
ejde-397	622	46	as	as	ADP
ejde-397	622	47	before	before	ADV
ejde-397	622	48	.	.	PUNCT
ejde-397	623	1	observe	observe	VERB
ejde-397	623	2	also	also	ADV
ejde-397	623	3	that	that	SCONJ
ejde-397	623	4	the	the	DET
ejde-397	623	5	assumption	assumption	NOUN
ejde-397	623	6	d(a	d(a	PROPN
ejde-397	623	7	)	)	PUNCT
ejde-397	623	8	⊆	⊆	NUM
ejde-397	623	9	d(b	d(b	NOUN
ejde-397	623	10	)	)	PUNCT
ejde-397	623	11	,	,	PUNCT
ejde-397	623	12	which	which	PRON
ejde-397	623	13	has	have	AUX
ejde-397	623	14	been	be	AUX
ejde-397	623	15	used	use	VERB
ejde-397	623	16	in	in	ADP
ejde-397	623	17	[	[	X
ejde-397	623	18	17	17	NUM
ejde-397	623	19	,	,	PUNCT
ejde-397	623	20	section	section	NOUN
ejde-397	623	21	1.6	1.6	NUM
ejde-397	623	22	]	]	PUNCT
ejde-397	623	23	,	,	PUNCT
ejde-397	623	24	is	be	AUX
ejde-397	623	25	not	not	PART
ejde-397	623	26	necessary	necessary	ADJ
ejde-397	623	27	for	for	ADP
ejde-397	623	28	the	the	DET
ejde-397	623	29	validity	validity	NOUN
ejde-397	623	30	of	of	ADP
ejde-397	623	31	(	(	PUNCT
ejde-397	623	32	4.1	4.1	NUM
ejde-397	623	33	)	)	PUNCT
ejde-397	623	34	.	.	PUNCT
ejde-397	624	1	(	(	PUNCT
ejde-397	624	2	vi	vi	X
ejde-397	624	3	)	)	PUNCT
ejde-397	624	4	suppose	suppose	VERB
ejde-397	624	5	that	that	SCONJ
ejde-397	624	6	x	x	PROPN
ejde-397	624	7	=	=	SYM
ejde-397	624	8	y	y	PROPN
ejde-397	624	9	,	,	PUNCT
ejde-397	624	10	c	c	PROPN
ejde-397	624	11	∈	∈	PROPN
ejde-397	624	12	l(x	l(x	PROPN
ejde-397	624	13	)	)	PUNCT
ejde-397	624	14	is	be	AUX
ejde-397	624	15	injective	injective	ADJ
ejde-397	624	16	,	,	PUNCT
ejde-397	624	17	b	b	PROPN
ejde-397	624	18	∈	∈	PROPN
ejde-397	624	19	l(x	l(x	PROPN
ejde-397	624	20	)	)	PUNCT
ejde-397	624	21	,	,	PUNCT
ejde-397	624	22	ca	can	AUX
ejde-397	624	23	⊆	⊆	NUM
ejde-397	624	24	ac	ac	PROPN
ejde-397	624	25	and	and	CCONJ
ejde-397	624	26	cb	cb	PROPN
ejde-397	624	27	⊆	⊆	NUM
ejde-397	624	28	bc	bc	PROPN
ejde-397	624	29	.	.	PROPN
ejde-397	624	30	define	define	VERB
ejde-397	624	31	the	the	DET
ejde-397	624	32	set	set	ADJ
ejde-397	624	33	ρbc(a	ρbc(a	PROPN
ejde-397	624	34	)	)	PUNCT
ejde-397	624	35	as	as	ADP
ejde-397	624	36	above	above	ADV
ejde-397	624	37	.	.	PUNCT
ejde-397	625	1	then	then	ADV
ejde-397	625	2	we	we	PRON
ejde-397	625	3	have	have	VERB
ejde-397	625	4	ρbc(a	ρbc(a	PROPN
ejde-397	625	5	)	)	PUNCT
ejde-397	625	6	⊆	⊆	NUM
ejde-397	625	7	ρc(b−1a	ρc(b−1a	NOUN
ejde-397	625	8	)	)	PUNCT
ejde-397	625	9	and	and	CCONJ
ejde-397	625	10	(	(	PUNCT
ejde-397	625	11	λ−b−1a	λ−b−1a	ADJ
ejde-397	625	12	)	)	PUNCT
ejde-397	625	13	−1	−1	NOUN
ejde-397	625	14	cx	cx	NOUN
ejde-397	626	1	=	=	PUNCT
ejde-397	626	2	(	(	PUNCT
ejde-397	626	3	λb	λb	ADV
ejde-397	626	4	−a	−a	ADJ
ejde-397	626	5	)	)	PUNCT
ejde-397	626	6	−1	−1	NOUN
ejde-397	626	7	cbx	cbx	PROPN
ejde-397	626	8	,	,	PUNCT
ejde-397	626	9	x	x	SYM
ejde-397	626	10	∈	∈	PROPN
ejde-397	626	11	x.	x.	NOUN
ejde-397	626	12	furthermore	furthermore	ADV
ejde-397	626	13	,	,	PUNCT
ejde-397	626	14	if	if	SCONJ
ejde-397	626	15	c	c	NOUN
ejde-397	626	16	=	=	SYM
ejde-397	626	17	i	i	PROPN
ejde-397	626	18	,	,	PUNCT
ejde-397	626	19	x	x	PROPN
ejde-397	626	20	6=	6=	NUM
ejde-397	626	21	y	y	PROPN
ejde-397	626	22	and	and	CCONJ
ejde-397	626	23	b	b	PROPN
ejde-397	626	24	∈	∈	PROPN
ejde-397	626	25	l(x	l(x	PROPN
ejde-397	626	26	,	,	PUNCT
ejde-397	626	27	y	y	PROPN
ejde-397	626	28	)	)	PUNCT
ejde-397	626	29	,	,	PUNCT
ejde-397	626	30	then	then	ADV
ejde-397	626	31	ρb(a	ρb(a	PUNCT
ejde-397	626	32	)	)	PUNCT
ejde-397	626	33	⊆	⊆	NUM
ejde-397	626	34	ρ(b−1a	ρ(b−1a	NUM
ejde-397	626	35	)	)	PUNCT
ejde-397	626	36	and	and	CCONJ
ejde-397	626	37	the	the	DET
ejde-397	626	38	previous	previous	ADJ
ejde-397	626	39	equality	equality	NOUN
ejde-397	626	40	holds	hold	VERB
ejde-397	626	41	.	.	PUNCT
ejde-397	627	1	consider	consider	VERB
ejde-397	627	2	now	now	ADV
ejde-397	627	3	the	the	DET
ejde-397	627	4	case	case	NOUN
ejde-397	627	5	in	in	ADP
ejde-397	627	6	which	which	PRON
ejde-397	627	7	the	the	DET
ejde-397	627	8	operator	operator	NOUN
ejde-397	627	9	a	a	NOUN
ejde-397	627	10	is	be	AUX
ejde-397	627	11	closed	closed	ADJ
ejde-397	627	12	,	,	PUNCT
ejde-397	627	13	the	the	DET
ejde-397	627	14	operator	operator	NOUN
ejde-397	627	15	b	b	PROPN
ejde-397	627	16	=	=	SYM
ejde-397	627	17	b	b	PROPN
ejde-397	627	18	is	be	AUX
ejde-397	627	19	single	single	ADV
ejde-397	627	20	-	-	PUNCT
ejde-397	627	21	valued	value	VERB
ejde-397	627	22	and	and	CCONJ
ejde-397	627	23	the	the	DET
ejde-397	627	24	function	function	NOUN
ejde-397	627	25	f(t	f(t	NOUN
ejde-397	627	26	)	)	PUNCT
ejde-397	628	1	=	=	SYM
ejde-397	628	2	f(t	f(t	NOUN
ejde-397	628	3	)	)	PUNCT
ejde-397	628	4	is	be	AUX
ejde-397	628	5	y	y	PROPN
ejde-397	628	6	-continuous	-continuous	ADJ
ejde-397	628	7	at	at	ADP
ejde-397	628	8	each	each	DET
ejde-397	628	9	point	point	NOUN
ejde-397	628	10	t	t	PROPN
ejde-397	628	11	≥	≥	NOUN
ejde-397	628	12	0	0	NUM
ejde-397	628	13	.	.	PUNCT
ejde-397	629	1	then	then	ADV
ejde-397	629	2	any	any	DET
ejde-397	629	3	pre	pre	ADJ
ejde-397	629	4	-	-	NOUN
ejde-397	629	5	solution	solution	ADJ
ejde-397	629	6	u	u	NOUN
ejde-397	629	7	(	(	PUNCT
ejde-397	629	8	·	·	PUNCT
ejde-397	629	9	)	)	PUNCT
ejde-397	629	10	of	of	ADP
ejde-397	629	11	problem	problem	NOUN
ejde-397	629	12	(	(	PUNCT
ejde-397	629	13	1.2	1.2	NUM
ejde-397	629	14	)	)	PUNCT
ejde-397	629	15	is	be	AUX
ejde-397	629	16	already	already	ADV
ejde-397	629	17	a	a	DET
ejde-397	629	18	solution	solution	NOUN
ejde-397	629	19	of	of	ADP
ejde-397	629	20	this	this	DET
ejde-397	629	21	problem	problem	NOUN
ejde-397	629	22	,	,	PUNCT
ejde-397	629	23	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	629	24	abstract	abstract	ADJ
ejde-397	629	25	degenerate	degenerate	ADJ
ejde-397	629	26	volterra	volterra	NOUN
ejde-397	629	27	inclusions	inclusion	NOUN
ejde-397	629	28	19	19	NUM
ejde-397	629	29	and	and	CCONJ
ejde-397	629	30	theorem	theorem	VERB
ejde-397	629	31	2.3	2.3	NUM
ejde-397	629	32	in	in	ADP
ejde-397	629	33	combination	combination	NOUN
ejde-397	629	34	with	with	ADP
ejde-397	629	35	the	the	DET
ejde-397	629	36	identity	identity	NOUN
ejde-397	629	37	[	[	X
ejde-397	629	38	5	5	NUM
ejde-397	629	39	,	,	PUNCT
ejde-397	629	40	(	(	PUNCT
ejde-397	629	41	1.21	1.21	NUM
ejde-397	629	42	)	)	PUNCT
ejde-397	629	43	]	]	PUNCT
ejde-397	629	44	implies	imply	VERB
ejde-397	630	1	that	that	SCONJ
ejde-397	630	2	bu(t)−	bu(t)−	PROPN
ejde-397	630	3	dαe−1∑	dαe−1∑	VERB
ejde-397	630	4	k=0	k=0	PROPN
ejde-397	630	5	gk+1(t)bxj	gk+1(t)bxj	PROPN
ejde-397	630	6	−	−	PROPN
ejde-397	630	7	(	(	PUNCT
ejde-397	630	8	gα	gα	ADP
ejde-397	630	9	∗	∗	NOUN
ejde-397	630	10	f	f	PROPN
ejde-397	630	11	)	)	PUNCT
ejde-397	630	12	(	(	PUNCT
ejde-397	630	13	t	t	X
ejde-397	630	14	)	)	PUNCT
ejde-397	630	15	∈	∈	PROPN
ejde-397	630	16	a	a	DET
ejde-397	630	17	(	(	PUNCT
ejde-397	630	18	gα	gα	ADP
ejde-397	630	19	∗	∗	NOUN
ejde-397	630	20	u	u	NOUN
ejde-397	630	21	)	)	PUNCT
ejde-397	630	22	(	(	PUNCT
ejde-397	630	23	t	t	PROPN
ejde-397	630	24	)	)	PUNCT
ejde-397	630	25	,	,	PUNCT
ejde-397	630	26	t	t	PROPN
ejde-397	630	27	≥	≥	PROPN
ejde-397	630	28	0	0	NUM
ejde-397	630	29	.	.	PUNCT
ejde-397	630	30	suppose	suppose	VERB
ejde-397	630	31	,	,	PUNCT
ejde-397	630	32	conversely	conversely	ADV
ejde-397	630	33	,	,	PUNCT
ejde-397	630	34	that	that	SCONJ
ejde-397	630	35	there	there	PRON
ejde-397	630	36	exists	exist	VERB
ejde-397	630	37	a	a	DET
ejde-397	630	38	function	function	NOUN
ejde-397	630	39	ua	ua	PROPN
ejde-397	630	40	∈	∈	PROPN
ejde-397	630	41	c([0,∞	c([0,∞	PROPN
ejde-397	630	42	)	)	PUNCT
ejde-397	630	43	:	:	PUNCT
ejde-397	631	1	y	y	X
ejde-397	631	2	)	)	PUNCT
ejde-397	631	3	such	such	ADJ
ejde-397	631	4	that	that	PRON
ejde-397	631	5	ua(t	ua(t	PROPN
ejde-397	631	6	)	)	PUNCT
ejde-397	631	7	∈	∈	PROPN
ejde-397	631	8	au(t	au(t	NUM
ejde-397	631	9	)	)	PUNCT
ejde-397	631	10	,	,	PUNCT
ejde-397	631	11	t	t	PROPN
ejde-397	631	12	≥	≥	NOUN
ejde-397	631	13	0	0	NUM
ejde-397	631	14	and	and	CCONJ
ejde-397	631	15	bu(t)−	bu(t)−	PROPN
ejde-397	631	16	dαe−1∑	dαe−1∑	ADJ
ejde-397	631	17	k=0	k=0	PROPN
ejde-397	632	1	gk+1(t)bxj	gk+1(t)bxj	PROPN
ejde-397	632	2	−	−	PROPN
ejde-397	632	3	(	(	PUNCT
ejde-397	632	4	gα	gα	ADP
ejde-397	632	5	∗	∗	NOUN
ejde-397	632	6	f	f	PROPN
ejde-397	632	7	)	)	PUNCT
ejde-397	632	8	(	(	PUNCT
ejde-397	632	9	t	t	NOUN
ejde-397	632	10	)	)	PUNCT
ejde-397	632	11	=	=	PUNCT
ejde-397	632	12	(	(	PUNCT
ejde-397	632	13	gα	gα	ADP
ejde-397	632	14	∗	∗	X
ejde-397	632	15	ua	ua	PROPN
ejde-397	632	16	)	)	PUNCT
ejde-397	632	17	(	(	PUNCT
ejde-397	632	18	t	t	PROPN
ejde-397	632	19	)	)	PUNCT
ejde-397	632	20	,	,	PUNCT
ejde-397	632	21	t	t	PROPN
ejde-397	632	22	≥	≥	NUM
ejde-397	632	23	0	0	NUM
ejde-397	632	24	.	.	PUNCT
ejde-397	633	1	then	then	ADV
ejde-397	633	2	it	it	PRON
ejde-397	633	3	can	can	AUX
ejde-397	633	4	be	be	AUX
ejde-397	633	5	simply	simply	ADV
ejde-397	633	6	verified	verify	VERB
ejde-397	633	7	that	that	SCONJ
ejde-397	633	8	u	u	NOUN
ejde-397	633	9	(	(	PUNCT
ejde-397	633	10	·	·	PUNCT
ejde-397	633	11	)	)	PUNCT
ejde-397	633	12	is	be	AUX
ejde-397	633	13	a	a	DET
ejde-397	633	14	solution	solution	NOUN
ejde-397	633	15	of	of	ADP
ejde-397	633	16	problem	problem	NOUN
ejde-397	633	17	(	(	PUNCT
ejde-397	633	18	1.2	1.2	NUM
ejde-397	633	19	)	)	PUNCT
ejde-397	633	20	;	;	PUNCT
ejde-397	633	21	it	it	PRON
ejde-397	633	22	is	be	AUX
ejde-397	633	23	noteworthy	noteworthy	ADJ
ejde-397	633	24	that	that	SCONJ
ejde-397	633	25	we	we	PRON
ejde-397	633	26	do	do	AUX
ejde-397	633	27	not	not	PART
ejde-397	633	28	need	need	VERB
ejde-397	633	29	the	the	DET
ejde-397	633	30	assumption	assumption	NOUN
ejde-397	633	31	on	on	ADP
ejde-397	633	32	closedness	closedness	NOUN
ejde-397	633	33	of	of	ADP
ejde-397	633	34	a	a	PRON
ejde-397	633	35	in	in	ADP
ejde-397	633	36	this	this	DET
ejde-397	633	37	direction	direction	NOUN
ejde-397	633	38	.	.	PUNCT
ejde-397	634	1	even	even	ADV
ejde-397	634	2	in	in	ADP
ejde-397	634	3	the	the	DET
ejde-397	634	4	case	case	NOUN
ejde-397	634	5	that	that	SCONJ
ejde-397	634	6	a	a	DET
ejde-397	634	7	=	=	X
ejde-397	634	8	a	a	PRON
ejde-397	634	9	is	be	AUX
ejde-397	634	10	a	a	DET
ejde-397	634	11	closed	closed	ADJ
ejde-397	634	12	single	single	ADV
ejde-397	634	13	-	-	PUNCT
ejde-397	634	14	valued	value	VERB
ejde-397	634	15	linear	linear	NOUN
ejde-397	634	16	operator	operator	NOUN
ejde-397	634	17	,	,	PUNCT
ejde-397	634	18	a	a	DET
ejde-397	634	19	corresponding	correspond	VERB
ejde-397	634	20	statement	statement	NOUN
ejde-397	634	21	for	for	ADP
ejde-397	634	22	the	the	DET
ejde-397	634	23	problem	problem	NOUN
ejde-397	634	24	(	(	PUNCT
ejde-397	634	25	1.3	1.3	NUM
ejde-397	634	26	)	)	PUNCT
ejde-397	634	27	can	can	AUX
ejde-397	634	28	not	not	PART
ejde-397	634	29	be	be	AUX
ejde-397	634	30	proved	prove	VERB
ejde-397	634	31	.	.	PUNCT
ejde-397	635	1	suppose	suppose	VERB
ejde-397	635	2	,	,	PUNCT
ejde-397	635	3	finally	finally	ADV
ejde-397	635	4	,	,	PUNCT
ejde-397	635	5	that	that	SCONJ
ejde-397	635	6	the	the	DET
ejde-397	635	7	operators	operator	NOUN
ejde-397	635	8	a	a	PRON
ejde-397	635	9	and	and	CCONJ
ejde-397	635	10	b	b	NOUN
ejde-397	635	11	are	be	AUX
ejde-397	635	12	closed	closed	ADJ
ejde-397	635	13	,	,	PUNCT
ejde-397	635	14	u	u	NOUN
ejde-397	635	15	(	(	PUNCT
ejde-397	635	16	·	·	PUNCT
ejde-397	635	17	)	)	PUNCT
ejde-397	635	18	is	be	AUX
ejde-397	635	19	a	a	DET
ejde-397	635	20	solution	solution	NOUN
ejde-397	635	21	of	of	ADP
ejde-397	635	22	problem	problem	NOUN
ejde-397	635	23	(	(	PUNCT
ejde-397	635	24	1.2	1.2	NUM
ejde-397	635	25	)	)	PUNCT
ejde-397	635	26	,	,	PUNCT
ejde-397	635	27	the	the	DET
ejde-397	635	28	function	function	NOUN
ejde-397	635	29	f(t	f(t	NOUN
ejde-397	635	30	)	)	PUNCT
ejde-397	635	31	=	=	SYM
ejde-397	636	1	f(t	f(t	NOUN
ejde-397	636	2	)	)	PUNCT
ejde-397	636	3	is	be	AUX
ejde-397	636	4	y	y	PROPN
ejde-397	636	5	-continuous	-continuous	ADJ
ejde-397	636	6	at	at	ADP
ejde-397	636	7	each	each	DET
ejde-397	636	8	point	point	NOUN
ejde-397	636	9	t	t	PROPN
ejde-397	636	10	≥	≥	NOUN
ejde-397	636	11	0	0	NUM
ejde-397	636	12	,	,	PUNCT
ejde-397	636	13	as	as	ADV
ejde-397	636	14	well	well	ADV
ejde-397	636	15	as	as	ADP
ejde-397	636	16	the	the	DET
ejde-397	636	17	functions	function	NOUN
ejde-397	636	18	uα	uα	PROPN
ejde-397	636	19	,	,	PUNCT
ejde-397	636	20	b	b	PROPN
ejde-397	636	21	∈	∈	PROPN
ejde-397	636	22	c([0,∞	c([0,∞	PROPN
ejde-397	636	23	)	)	PUNCT
ejde-397	636	24	:	:	PUNCT
ejde-397	636	25	y	y	X
ejde-397	636	26	)	)	PUNCT
ejde-397	636	27	and	and	CCONJ
ejde-397	636	28	ua	ua	PROPN
ejde-397	636	29	∈	∈	PROPN
ejde-397	636	30	c([0,∞	c([0,∞	PROPN
ejde-397	636	31	)	)	PUNCT
ejde-397	636	32	:	:	PUNCT
ejde-397	636	33	y	y	X
ejde-397	636	34	)	)	PUNCT
ejde-397	636	35	satisfy	satisfy	VERB
ejde-397	636	36	the	the	DET
ejde-397	636	37	requirements	requirement	NOUN
ejde-397	636	38	stated	state	VERB
ejde-397	636	39	in	in	ADP
ejde-397	636	40	definition	definition	NOUN
ejde-397	636	41	4.1(iii	4.1(iii	NUM
ejde-397	636	42	)	)	PUNCT
ejde-397	636	43	.	.	PUNCT
ejde-397	637	1	using	use	VERB
ejde-397	637	2	again	again	ADV
ejde-397	637	3	theorem	theorem	VERB
ejde-397	637	4	2.3	2.3	NUM
ejde-397	637	5	and	and	CCONJ
ejde-397	637	6	the	the	DET
ejde-397	637	7	identity	identity	NOUN
ejde-397	637	8	[	[	X
ejde-397	637	9	5	5	NUM
ejde-397	637	10	,	,	PUNCT
ejde-397	637	11	(	(	PUNCT
ejde-397	637	12	1.21	1.21	NUM
ejde-397	637	13	)	)	PUNCT
ejde-397	637	14	]	]	PUNCT
ejde-397	637	15	,	,	PUNCT
ejde-397	637	16	it	it	PRON
ejde-397	637	17	readily	readily	ADV
ejde-397	637	18	follows	follow	VERB
ejde-397	637	19	that	that	SCONJ
ejde-397	638	1	b	b	X
ejde-397	638	2	[	[	PUNCT
ejde-397	638	3	u(t)−	u(t)−	PROPN
ejde-397	638	4	dαe−1∑	dαe−1∑	VERB
ejde-397	638	5	k=0	k=0	PROPN
ejde-397	638	6	gk+1(t)xj	gk+1(t)xj	PROPN
ejde-397	638	7	]	]	PUNCT
ejde-397	638	8	3	3	NUM
ejde-397	638	9	(	(	PUNCT
ejde-397	638	10	gα	gα	ADP
ejde-397	638	11	∗	∗	NOUN
ejde-397	638	12	uα	uα	PROPN
ejde-397	638	13	,	,	PUNCT
ejde-397	638	14	b	b	NOUN
ejde-397	638	15	)	)	PUNCT
ejde-397	638	16	(	(	PUNCT
ejde-397	638	17	t	t	NOUN
ejde-397	638	18	)	)	PUNCT
ejde-397	638	19	=	=	PUNCT
ejde-397	638	20	(	(	PUNCT
ejde-397	638	21	gα	gα	ADP
ejde-397	638	22	∗	∗	X
ejde-397	638	23	ua	ua	PROPN
ejde-397	638	24	)	)	PUNCT
ejde-397	638	25	(	(	PUNCT
ejde-397	638	26	t	t	NOUN
ejde-397	638	27	)	)	PUNCT
ejde-397	638	28	+	+	CCONJ
ejde-397	638	29	(	(	PUNCT
ejde-397	638	30	gα	gα	ADP
ejde-397	638	31	∗	∗	NOUN
ejde-397	638	32	f	f	PROPN
ejde-397	638	33	)	)	PUNCT
ejde-397	638	34	(	(	PUNCT
ejde-397	638	35	t	t	X
ejde-397	638	36	)	)	PUNCT
ejde-397	638	37	∈	∈	PROPN
ejde-397	638	38	a	a	DET
ejde-397	638	39	(	(	PUNCT
ejde-397	638	40	gα	gα	ADP
ejde-397	638	41	∗	∗	NOUN
ejde-397	638	42	u	u	NOUN
ejde-397	638	43	)	)	PUNCT
ejde-397	638	44	(	(	PUNCT
ejde-397	638	45	t	t	PROPN
ejde-397	638	46	)	)	PUNCT
ejde-397	639	1	+	+	CCONJ
ejde-397	639	2	(	(	PUNCT
ejde-397	639	3	gα	gα	ADP
ejde-397	639	4	∗	∗	NOUN
ejde-397	639	5	f	f	PROPN
ejde-397	639	6	)	)	PUNCT
ejde-397	639	7	(	(	PUNCT
ejde-397	639	8	t	t	PROPN
ejde-397	639	9	)	)	PUNCT
ejde-397	639	10	,	,	PUNCT
ejde-397	639	11	t	t	PROPN
ejde-397	639	12	≥	≥	NUM
ejde-397	639	13	0	0	NUM
ejde-397	639	14	.	.	PUNCT
ejde-397	640	1	the	the	DET
ejde-397	640	2	proof	proof	NOUN
ejde-397	640	3	of	of	ADP
ejde-397	640	4	following	follow	VERB
ejde-397	640	5	important	important	ADJ
ejde-397	640	6	theorem	theorem	NOUN
ejde-397	640	7	can	can	AUX
ejde-397	640	8	be	be	AUX
ejde-397	640	9	deduced	deduce	VERB
ejde-397	640	10	by	by	ADP
ejde-397	640	11	using	use	VERB
ejde-397	640	12	theorem	theorem	ADJ
ejde-397	640	13	2.3	2.3	NUM
ejde-397	640	14	,	,	PUNCT
ejde-397	640	15	theorem	theorem	ADJ
ejde-397	640	16	3.3[(iv),(vi	3.3[(iv),(vi	NUM
ejde-397	640	17	)	)	PUNCT
ejde-397	640	18	]	]	PUNCT
ejde-397	640	19	,	,	PUNCT
ejde-397	640	20	theorem	theorem	VERB
ejde-397	640	21	3.5	3.5	NUM
ejde-397	640	22	and	and	CCONJ
ejde-397	640	23	the	the	DET
ejde-397	640	24	argumentation	argumentation	NOUN
ejde-397	640	25	already	already	ADV
ejde-397	640	26	seen	see	VERB
ejde-397	640	27	in	in	ADP
ejde-397	640	28	the	the	DET
ejde-397	640	29	proof	proof	NOUN
ejde-397	640	30	of	of	ADP
ejde-397	640	31	[	[	X
ejde-397	640	32	31	31	NUM
ejde-397	640	33	,	,	PUNCT
ejde-397	640	34	theorem	theorem	VERB
ejde-397	640	35	3.1	3.1	NUM
ejde-397	640	36	]	]	PUNCT
ejde-397	640	37	(	(	PUNCT
ejde-397	640	38	cf	cf	NOUN
ejde-397	640	39	.	.	PUNCT
ejde-397	641	1	also	also	ADV
ejde-397	641	2	[	[	X
ejde-397	641	3	32	32	NUM
ejde-397	641	4	,	,	PUNCT
ejde-397	641	5	fundamental	fundamental	ADJ
ejde-397	641	6	lemma	lemma	PROPN
ejde-397	641	7	3.1	3.1	NUM
ejde-397	641	8	]	]	PUNCT
ejde-397	641	9	)	)	PUNCT
ejde-397	641	10	;	;	PUNCT
ejde-397	641	11	observe	observe	VERB
ejde-397	641	12	that	that	SCONJ
ejde-397	641	13	we	we	PRON
ejde-397	641	14	do	do	AUX
ejde-397	641	15	not	not	PART
ejde-397	641	16	use	use	VERB
ejde-397	641	17	the	the	DET
ejde-397	641	18	assumption	assumption	NOUN
ejde-397	641	19	on	on	ADP
ejde-397	641	20	the	the	DET
ejde-397	641	21	exponential	exponential	ADJ
ejde-397	641	22	boundedness	boundedness	NOUN
ejde-397	641	23	of	of	ADP
ejde-397	641	24	function	function	NOUN
ejde-397	641	25	u(t	u(t	NOUN
ejde-397	641	26	)	)	PUNCT
ejde-397	641	27	here	here	ADV
ejde-397	641	28	.	.	PUNCT
ejde-397	642	1	after	after	ADP
ejde-397	642	2	formulation	formulation	NOUN
ejde-397	642	3	,	,	PUNCT
ejde-397	642	4	we	we	PRON
ejde-397	642	5	will	will	AUX
ejde-397	642	6	only	only	ADV
ejde-397	642	7	include	include	VERB
ejde-397	642	8	the	the	DET
ejde-397	642	9	most	most	ADV
ejde-397	642	10	relevant	relevant	ADJ
ejde-397	642	11	details	detail	NOUN
ejde-397	642	12	needed	need	VERB
ejde-397	642	13	for	for	ADP
ejde-397	642	14	the	the	DET
ejde-397	642	15	proof	proof	NOUN
ejde-397	642	16	of	of	ADP
ejde-397	642	17	implication	implication	NOUN
ejde-397	642	18	(	(	PUNCT
ejde-397	642	19	iii	iii	NOUN
ejde-397	642	20	)	)	PUNCT
ejde-397	642	21	⇒	⇒	NOUN
ejde-397	642	22	(	(	PUNCT
ejde-397	642	23	iv	iv	X
ejde-397	642	24	)	)	PUNCT
ejde-397	642	25	.	.	PUNCT
ejde-397	643	1	theorem	theorem	VERB
ejde-397	643	2	4.3	4.3	NUM
ejde-397	643	3	.	.	PUNCT
ejde-397	644	1	suppose	suppose	VERB
ejde-397	644	2	that	that	SCONJ
ejde-397	644	3	a	a	PRON
ejde-397	644	4	:	:	PUNCT
ejde-397	644	5	x	x	X
ejde-397	644	6	→	→	X
ejde-397	644	7	p	p	X
ejde-397	644	8	(	(	PUNCT
ejde-397	644	9	y	y	PROPN
ejde-397	644	10	)	)	PUNCT
ejde-397	644	11	and	and	CCONJ
ejde-397	644	12	b	b	X
ejde-397	644	13	:	:	PUNCT
ejde-397	644	14	x	x	X
ejde-397	644	15	→	→	X
ejde-397	644	16	p	p	X
ejde-397	644	17	(	(	PUNCT
ejde-397	644	18	y	y	PROPN
ejde-397	644	19	)	)	PUNCT
ejde-397	644	20	are	be	AUX
ejde-397	644	21	mlos	mlo	NOUN
ejde-397	644	22	,	,	PUNCT
ejde-397	644	23	as	as	ADV
ejde-397	644	24	well	well	ADV
ejde-397	644	25	as	as	ADP
ejde-397	644	26	that	that	PRON
ejde-397	644	27	a	a	PRON
ejde-397	644	28	is	be	AUX
ejde-397	644	29	xa	xa	PROPN
ejde-397	644	30	×	×	PROPN
ejde-397	644	31	ya	ya	PROPN
ejde-397	644	32	-	-	PUNCT
ejde-397	644	33	closed	closed	ADJ
ejde-397	644	34	.	.	PUNCT
ejde-397	645	1	assume	assume	VERB
ejde-397	645	2	,	,	PUNCT
ejde-397	645	3	further	far	ADV
ejde-397	645	4	,	,	PUNCT
ejde-397	645	5	that	that	SCONJ
ejde-397	645	6	a	a	DET
ejde-397	645	7	∈	∈	PROPN
ejde-397	645	8	l1	l1	PROPN
ejde-397	645	9	loc([0,∞	loc([0,∞	PROPN
ejde-397	645	10	)	)	PUNCT
ejde-397	645	11	)	)	PUNCT
ejde-397	645	12	,	,	PUNCT
ejde-397	645	13	a	a	DET
ejde-397	645	14	6=	6=	NUM
ejde-397	645	15	0	0	NUM
ejde-397	645	16	,	,	PUNCT
ejde-397	645	17	abs(|a|	abs(|a|	ADJ
ejde-397	645	18	)	)	PUNCT
ejde-397	645	19	<	<	X
ejde-397	645	20	∞	∞	PROPN
ejde-397	645	21	,	,	PUNCT
ejde-397	645	22	u	u	PROPN
ejde-397	645	23	∈	∈	PROPN
ejde-397	645	24	c([0,∞	c([0,∞	PROPN
ejde-397	645	25	)	)	PUNCT
ejde-397	645	26	:	:	PUNCT
ejde-397	646	1	x	x	X
ejde-397	646	2	)	)	PUNCT
ejde-397	646	3	,	,	PUNCT
ejde-397	646	4	u	u	PROPN
ejde-397	646	5	∈	∈	PROPN
ejde-397	646	6	(	(	PUNCT
ejde-397	646	7	p1	p1	NOUN
ejde-397	646	8	)	)	PUNCT
ejde-397	646	9	−	−	NOUN
ejde-397	647	1	x	x	SYM
ejde-397	647	2	,	,	PUNCT
ejde-397	647	3	as	as	ADV
ejde-397	647	4	well	well	ADV
ejde-397	647	5	as	as	ADP
ejde-397	647	6	that	that	DET
ejde-397	647	7	u(t	u(t	NOUN
ejde-397	647	8	)	)	PUNCT
ejde-397	647	9	∈	∈	PROPN
ejde-397	647	10	d(b	d(b	PROPN
ejde-397	647	11	)	)	PUNCT
ejde-397	647	12	,	,	PUNCT
ejde-397	647	13	t	t	PROPN
ejde-397	647	14	≥	≥	NUM
ejde-397	647	15	0	0	NUM
ejde-397	647	16	,	,	PUNCT
ejde-397	647	17	a	a	DET
ejde-397	647	18	∗u	∗u	PROPN
ejde-397	647	19	∈	∈	PROPN
ejde-397	647	20	c([0,∞	c([0,∞	PROPN
ejde-397	647	21	)	)	PUNCT
ejde-397	647	22	:	:	PUNCT
ejde-397	647	23	xa	xa	PROPN
ejde-397	647	24	)	)	PUNCT
ejde-397	647	25	,	,	PUNCT
ejde-397	647	26	a	a	DET
ejde-397	647	27	∗u	∗u	PROPN
ejde-397	647	28	∈	∈	PROPN
ejde-397	647	29	(	(	PUNCT
ejde-397	647	30	p1)−xa	p1)−xa	X
ejde-397	647	31	,	,	PUNCT
ejde-397	647	32	absya(bu	absya(bu	NOUN
ejde-397	647	33	)	)	PUNCT
ejde-397	647	34	<	<	X
ejde-397	647	35	∞	∞	PROPN
ejde-397	647	36	,	,	PUNCT
ejde-397	647	37	absya(f	absya(f	NOUN
ejde-397	647	38	)	)	PUNCT
ejde-397	647	39	<	<	X
ejde-397	647	40	∞	∞	PROPN
ejde-397	647	41	,	,	PUNCT
ejde-397	647	42	and	and	CCONJ
ejde-397	647	43	ω	ω	NOUN
ejde-397	647	44	>	>	X
ejde-397	647	45	max(0	max(0	NOUN
ejde-397	647	46	,	,	PUNCT
ejde-397	647	47	ωx(u	ωx(u	NOUN
ejde-397	647	48	)	)	PUNCT
ejde-397	647	49	,	,	PUNCT
ejde-397	647	50	absya(bu	absya(bu	NOUN
ejde-397	647	51	)	)	PUNCT
ejde-397	647	52	,	,	PUNCT
ejde-397	647	53	absya(f	absya(f	NOUN
ejde-397	647	54	)	)	PUNCT
ejde-397	647	55	,	,	PUNCT
ejde-397	647	56	absxa(a∗u	absxa(a∗u	PROPN
ejde-397	647	57	)	)	PUNCT
ejde-397	647	58	)	)	PUNCT
ejde-397	647	59	.	.	PUNCT
ejde-397	648	1	consider	consider	VERB
ejde-397	648	2	the	the	DET
ejde-397	648	3	following	follow	VERB
ejde-397	648	4	assertions	assertion	NOUN
ejde-397	648	5	:	:	PUNCT
ejde-397	648	6	(	(	PUNCT
ejde-397	648	7	i	i	NOUN
ejde-397	648	8	)	)	PUNCT
ejde-397	648	9	u	u	NOUN
ejde-397	648	10	(	(	PUNCT
ejde-397	648	11	·	·	PUNCT
ejde-397	648	12	)	)	PUNCT
ejde-397	648	13	is	be	AUX
ejde-397	648	14	a	a	DET
ejde-397	648	15	solution	solution	NOUN
ejde-397	648	16	of	of	ADP
ejde-397	648	17	(	(	PUNCT
ejde-397	648	18	1.1	1.1	NUM
ejde-397	648	19	)	)	PUNCT
ejde-397	648	20	with	with	ADP
ejde-397	648	21	τ	τ	PROPN
ejde-397	648	22	=	=	PRON
ejde-397	648	23	∞.	∞.	PROPN
ejde-397	648	24	(	(	PUNCT
ejde-397	648	25	ii	ii	NOUN
ejde-397	648	26	)	)	PUNCT
ejde-397	648	27	u	u	NOUN
ejde-397	648	28	(	(	PUNCT
ejde-397	648	29	·	·	PUNCT
ejde-397	648	30	)	)	PUNCT
ejde-397	648	31	is	be	AUX
ejde-397	648	32	a	a	DET
ejde-397	648	33	pre	pre	NOUN
ejde-397	648	34	-	-	NOUN
ejde-397	648	35	solution	solution	NOUN
ejde-397	648	36	of	of	ADP
ejde-397	648	37	(	(	PUNCT
ejde-397	648	38	1.1	1.1	NUM
ejde-397	648	39	)	)	PUNCT
ejde-397	648	40	with	with	ADP
ejde-397	648	41	τ	τ	PROPN
ejde-397	648	42	=	=	PRON
ejde-397	648	43	∞.	∞.	PROPN
ejde-397	648	44	(	(	PUNCT
ejde-397	648	45	iii	iii	NOUN
ejde-397	648	46	)	)	PUNCT
ejde-397	648	47	for	for	ADP
ejde-397	648	48	any	any	DET
ejde-397	648	49	section	section	NOUN
ejde-397	648	50	ub	ub	ADP
ejde-397	648	51	∈	∈	PROPN
ejde-397	648	52	sec(bu	sec(bu	NOUN
ejde-397	648	53	)	)	PUNCT
ejde-397	648	54	there	there	PRON
ejde-397	648	55	is	be	VERB
ejde-397	648	56	a	a	DET
ejde-397	648	57	section	section	NOUN
ejde-397	648	58	f	f	PROPN
ejde-397	648	59	∈	∈	PROPN
ejde-397	648	60	sec(f	sec(f	PROPN
ejde-397	648	61	)	)	PUNCT
ejde-397	648	62	such	such	ADJ
ejde-397	648	63	that	that	DET
ejde-397	648	64	ũb(λ)−	ũb(λ)−	PROPN
ejde-397	648	65	f̃(λ	f̃(λ	PROPN
ejde-397	648	66	)	)	PUNCT
ejde-397	648	67	∈	∈	PROPN
ejde-397	648	68	ã(λ)aũ(λ	ã(λ)aũ(λ	NOUN
ejde-397	648	69	)	)	PUNCT
ejde-397	648	70	,	,	PUNCT
ejde-397	648	71	<	<	X
ejde-397	648	72	λ	λ	X
ejde-397	648	73	>	>	X
ejde-397	648	74	ω	ω	PROPN
ejde-397	648	75	,	,	PUNCT
ejde-397	648	76	ã(λ	ã(λ	PROPN
ejde-397	648	77	)	)	PUNCT
ejde-397	648	78	6=	6=	ADP
ejde-397	648	79	0	0	NUM
ejde-397	648	80	.	.	PUNCT
ejde-397	649	1	(	(	PUNCT
ejde-397	649	2	iv	iv	X
ejde-397	649	3	)	)	PUNCT
ejde-397	649	4	for	for	ADP
ejde-397	649	5	any	any	DET
ejde-397	649	6	section	section	NOUN
ejde-397	649	7	ub	ub	ADP
ejde-397	649	8	∈	∈	PROPN
ejde-397	649	9	sec(bu	sec(bu	NOUN
ejde-397	649	10	)	)	PUNCT
ejde-397	649	11	there	there	PRON
ejde-397	649	12	is	be	VERB
ejde-397	649	13	a	a	DET
ejde-397	649	14	section	section	NOUN
ejde-397	649	15	f	f	PROPN
ejde-397	649	16	∈	∈	PROPN
ejde-397	649	17	sec(f	sec(f	PROPN
ejde-397	649	18	)	)	PUNCT
ejde-397	649	19	such	such	ADJ
ejde-397	649	20	that	that	DET
ejde-397	649	21	ũb(λ)−	ũb(λ)−	PROPN
ejde-397	649	22	f̃(λ	f̃(λ	PROPN
ejde-397	649	23	)	)	PUNCT
ejde-397	649	24	∈	∈	PROPN
ejde-397	649	25	ã(λ)aũ(λ	ã(λ)aũ(λ	NOUN
ejde-397	649	26	)	)	PUNCT
ejde-397	649	27	,	,	PUNCT
ejde-397	649	28	λ	λ	PROPN
ejde-397	649	29	∈	∈	PROPN
ejde-397	649	30	n	n	CCONJ
ejde-397	649	31	,	,	PUNCT
ejde-397	649	32	λ	λ	X
ejde-397	649	33	>	>	X
ejde-397	649	34	ω	ω	PROPN
ejde-397	649	35	,	,	PUNCT
ejde-397	649	36	ã(λ	ã(λ	PROPN
ejde-397	649	37	)	)	PUNCT
ejde-397	649	38	6=	6=	ADP
ejde-397	649	39	0	0	NUM
ejde-397	649	40	.	.	PUNCT
ejde-397	650	1	(	(	PUNCT
ejde-397	650	2	4.2	4.2	NUM
ejde-397	650	3	)	)	PUNCT
ejde-397	650	4	(	(	PUNCT
ejde-397	650	5	v	v	NOUN
ejde-397	650	6	)	)	PUNCT
ejde-397	650	7	for	for	ADP
ejde-397	650	8	any	any	DET
ejde-397	650	9	section	section	NOUN
ejde-397	650	10	ub	ub	ADP
ejde-397	650	11	∈	∈	PROPN
ejde-397	650	12	sec(bu	sec(bu	NOUN
ejde-397	650	13	)	)	PUNCT
ejde-397	650	14	there	there	PRON
ejde-397	650	15	is	be	VERB
ejde-397	650	16	a	a	DET
ejde-397	650	17	section	section	NOUN
ejde-397	650	18	f	f	PROPN
ejde-397	650	19	∈	∈	PROPN
ejde-397	650	20	sec(f	sec(f	PROPN
ejde-397	650	21	)	)	PUNCT
ejde-397	650	22	such	such	ADJ
ejde-397	650	23	that	that	SCONJ
ejde-397	650	24	(	(	PUNCT
ejde-397	650	25	1	1	NUM
ejde-397	650	26	∗	∗	NOUN
ejde-397	650	27	ub	ub	NOUN
ejde-397	650	28	)	)	PUNCT
ejde-397	650	29	(	(	PUNCT
ejde-397	650	30	t)−	t)−	PROPN
ejde-397	650	31	(	(	PUNCT
ejde-397	650	32	1	1	NUM
ejde-397	650	33	∗	∗	NOUN
ejde-397	650	34	f)(t	f)(t	PROPN
ejde-397	650	35	)	)	PUNCT
ejde-397	650	36	∈	∈	PROPN
ejde-397	650	37	a(1	a(1	NOUN
ejde-397	650	38	∗	∗	VERB
ejde-397	650	39	a	a	DET
ejde-397	650	40	∗	∗	NOUN
ejde-397	650	41	u)(t	u)(t	NOUN
ejde-397	650	42	)	)	PUNCT
ejde-397	650	43	,	,	PUNCT
ejde-397	650	44	t	t	PROPN
ejde-397	650	45	≥	≥	PROPN
ejde-397	650	46	0	0	NUM
ejde-397	650	47	.	.	PUNCT
ejde-397	651	1	(	(	PUNCT
ejde-397	651	2	4.3	4.3	NUM
ejde-397	651	3	)	)	PUNCT
ejde-397	651	4	then	then	ADV
ejde-397	651	5	we	we	PRON
ejde-397	651	6	have	have	VERB
ejde-397	651	7	(	(	PUNCT
ejde-397	651	8	i	i	NOUN
ejde-397	651	9	)	)	PUNCT
ejde-397	651	10	⇒	⇒	PROPN
ejde-397	651	11	(	(	PUNCT
ejde-397	651	12	ii	ii	NOUN
ejde-397	651	13	)	)	PUNCT
ejde-397	651	14	⇒	⇒	NOUN
ejde-397	651	15	(	(	PUNCT
ejde-397	651	16	iii	iii	NOUN
ejde-397	651	17	)	)	PUNCT
ejde-397	651	18	⇒	⇒	NOUN
ejde-397	651	19	(	(	PUNCT
ejde-397	651	20	iv	iv	X
ejde-397	651	21	)	)	PUNCT
ejde-397	651	22	⇒	⇒	NOUN
ejde-397	651	23	(	(	PUNCT
ejde-397	651	24	v	v	NOUN
ejde-397	651	25	)	)	PUNCT
ejde-397	651	26	.	.	PUNCT
ejde-397	652	1	furthermore	furthermore	ADV
ejde-397	652	2	,	,	PUNCT
ejde-397	652	3	if	if	SCONJ
ejde-397	652	4	b	b	PROPN
ejde-397	652	5	=	=	SYM
ejde-397	652	6	b	b	PROPN
ejde-397	652	7	is	be	AUX
ejde-397	652	8	singlevalued	singlevalue	VERB
ejde-397	652	9	,	,	PUNCT
ejde-397	652	10	bu	bu	PROPN
ejde-397	652	11	∈	∈	PROPN
ejde-397	652	12	c([0,∞	c([0,∞	PROPN
ejde-397	652	13	)	)	PUNCT
ejde-397	652	14	:	:	PUNCT
ejde-397	653	1	ya	ya	PROPN
ejde-397	653	2	)	)	PUNCT
ejde-397	653	3	and	and	CCONJ
ejde-397	653	4	f	f	X
ejde-397	653	5	=	=	SYM
ejde-397	653	6	f	f	PROPN
ejde-397	653	7	∈	∈	PROPN
ejde-397	653	8	c([0,∞	c([0,∞	PROPN
ejde-397	653	9	)	)	PUNCT
ejde-397	653	10	:	:	PUNCT
ejde-397	653	11	ya	ya	PROPN
ejde-397	653	12	)	)	PUNCT
ejde-397	653	13	is	be	AUX
ejde-397	653	14	single	single	ADV
ejde-397	653	15	-	-	PUNCT
ejde-397	653	16	valued	value	VERB
ejde-397	653	17	,	,	PUNCT
ejde-397	653	18	then	then	ADV
ejde-397	653	19	the	the	DET
ejde-397	653	20	above	above	ADJ
ejde-397	653	21	is	be	AUX
ejde-397	653	22	equivalent	equivalent	ADJ
ejde-397	653	23	.	.	PUNCT
ejde-397	654	1	20	20	NUM
ejde-397	654	2	m.	m.	NOUN
ejde-397	654	3	kostić	kostić	NOUN
ejde-397	655	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	655	2	sketch	sketch	NOUN
ejde-397	655	3	of	of	ADP
ejde-397	655	4	proof	proof	NOUN
ejde-397	655	5	for	for	ADP
ejde-397	655	6	(	(	PUNCT
ejde-397	655	7	iv	iv	X
ejde-397	655	8	)	)	PUNCT
ejde-397	655	9	⇒	⇒	NOUN
ejde-397	655	10	(	(	PUNCT
ejde-397	655	11	v	v	NOUN
ejde-397	655	12	)	)	PUNCT
ejde-397	655	13	.	.	PUNCT
ejde-397	656	1	suppose	suppose	VERB
ejde-397	656	2	that	that	SCONJ
ejde-397	656	3	for	for	ADP
ejde-397	656	4	any	any	DET
ejde-397	656	5	section	section	NOUN
ejde-397	656	6	ub	ub	ADP
ejde-397	656	7	∈	∈	PROPN
ejde-397	656	8	sec(bu	sec(bu	NOUN
ejde-397	656	9	)	)	PUNCT
ejde-397	656	10	there	there	PRON
ejde-397	656	11	is	be	VERB
ejde-397	656	12	a	a	DET
ejde-397	656	13	section	section	NOUN
ejde-397	656	14	f	f	PROPN
ejde-397	656	15	∈	∈	PROPN
ejde-397	656	16	sec(f	sec(f	PROPN
ejde-397	656	17	)	)	PUNCT
ejde-397	656	18	such	such	ADJ
ejde-397	656	19	that	that	SCONJ
ejde-397	656	20	(	(	PUNCT
ejde-397	656	21	4.2	4.2	NUM
ejde-397	656	22	)	)	PUNCT
ejde-397	656	23	holds	hold	VERB
ejde-397	656	24	.	.	PUNCT
ejde-397	657	1	let	let	VERB
ejde-397	657	2	a	a	DET
ejde-397	657	3	number	number	NOUN
ejde-397	657	4	λ	λ	X
ejde-397	657	5	∈	∈	NOUN
ejde-397	657	6	n	n	NOUN
ejde-397	657	7	with	with	ADP
ejde-397	657	8	λ	λ	PROPN
ejde-397	657	9	>	>	X
ejde-397	657	10	ω	ω	PROPN
ejde-397	657	11	and	and	CCONJ
ejde-397	657	12	ã(λ	ã(λ	PROPN
ejde-397	657	13	)	)	PUNCT
ejde-397	658	1	=	=	SYM
ejde-397	658	2	0	0	NUM
ejde-397	658	3	be	be	AUX
ejde-397	658	4	temorarily	temorarily	ADV
ejde-397	658	5	fixed	fix	VERB
ejde-397	658	6	.	.	PUNCT
ejde-397	659	1	then	then	ADV
ejde-397	659	2	there	there	PRON
ejde-397	659	3	exists	exist	VERB
ejde-397	659	4	a	a	DET
ejde-397	659	5	sequence	sequence	NOUN
ejde-397	659	6	(	(	PUNCT
ejde-397	659	7	λn)n∈n	λn)n∈n	NUM
ejde-397	659	8	in	in	ADP
ejde-397	659	9	(	(	PUNCT
ejde-397	659	10	λ,∞	λ,∞	SYM
ejde-397	659	11	)	)	PUNCT
ejde-397	659	12	such	such	ADJ
ejde-397	659	13	that	that	DET
ejde-397	659	14	ã(λn	ã(λn	NOUN
ejde-397	659	15	)	)	PUNCT
ejde-397	659	16	6=	6=	ADP
ejde-397	659	17	0	0	NUM
ejde-397	660	1	and	and	CCONJ
ejde-397	660	2	limn→+∞	limn→+∞	VERB
ejde-397	660	3	λn	λn	NOUN
ejde-397	660	4	=	=	PUNCT
ejde-397	660	5	λ	λ	PROPN
ejde-397	660	6	.	.	PUNCT
ejde-397	661	1	since	since	SCONJ
ejde-397	661	2	(	(	PUNCT
ejde-397	661	3	ã(λn)ũ(λn	ã(λn)ũ(λn	NOUN
ejde-397	661	4	)	)	PUNCT
ejde-397	661	5	,	,	PUNCT
ejde-397	661	6	ũb(λn	ũb(λn	NOUN
ejde-397	661	7	)	)	PUNCT
ejde-397	661	8	−	−	PRON
ejde-397	661	9	f̃(λn	f̃(λn	NOUN
ejde-397	661	10	)	)	PUNCT
ejde-397	661	11	)	)	PUNCT
ejde-397	662	1	∈	∈	PROPN
ejde-397	662	2	a	a	PRON
ejde-397	662	3	,	,	PUNCT
ejde-397	662	4	n	n	PROPN
ejde-397	662	5	∈	∈	PROPN
ejde-397	662	6	n	n	CCONJ
ejde-397	662	7	,	,	PUNCT
ejde-397	662	8	i.e.	i.e.	X
ejde-397	662	9	,	,	PUNCT
ejde-397	662	10	(	(	PUNCT
ejde-397	662	11	ã	ã	PROPN
ejde-397	662	12	∗	∗	PROPN
ejde-397	662	13	u(λn	u(λn	PROPN
ejde-397	662	14	)	)	PUNCT
ejde-397	662	15	,	,	PUNCT
ejde-397	662	16	ũb(λn	ũb(λn	NOUN
ejde-397	662	17	)	)	PUNCT
ejde-397	662	18	−	−	PRON
ejde-397	662	19	f̃(λn	f̃(λn	NOUN
ejde-397	662	20	)	)	PUNCT
ejde-397	662	21	)	)	PUNCT
ejde-397	663	1	∈	∈	PROPN
ejde-397	663	2	a	a	PRON
ejde-397	663	3	,	,	PUNCT
ejde-397	663	4	n	n	PROPN
ejde-397	663	5	∈	∈	PROPN
ejde-397	663	6	n	n	CCONJ
ejde-397	663	7	,	,	PUNCT
ejde-397	663	8	and	and	CCONJ
ejde-397	663	9	a	a	PRON
ejde-397	663	10	is	be	AUX
ejde-397	663	11	xa	xa	PROPN
ejde-397	663	12	×	×	PROPN
ejde-397	663	13	ya	ya	PROPN
ejde-397	663	14	-	-	PUNCT
ejde-397	663	15	closed	closed	ADJ
ejde-397	663	16	,	,	PUNCT
ejde-397	663	17	it	it	PRON
ejde-397	663	18	readily	readily	ADV
ejde-397	663	19	folows	folow	VERB
ejde-397	663	20	that	that	SCONJ
ejde-397	663	21	(	(	PUNCT
ejde-397	663	22	ã	ã	PROPN
ejde-397	663	23	∗	∗	VERB
ejde-397	663	24	u(λ	u(λ	PROPN
ejde-397	663	25	)	)	PUNCT
ejde-397	663	26	,	,	PUNCT
ejde-397	663	27	ũb(λ	ũb(λ	PROPN
ejde-397	663	28	)	)	PUNCT
ejde-397	663	29	−	−	PROPN
ejde-397	663	30	f̃(λ	f̃(λ	NOUN
ejde-397	663	31	)	)	PUNCT
ejde-397	663	32	)	)	PUNCT
ejde-397	664	1	∈	∈	PROPN
ejde-397	664	2	a	a	PRON
ejde-397	664	3	;	;	PUNCT
ejde-397	664	4	in	in	ADP
ejde-397	664	5	other	other	ADJ
ejde-397	664	6	words	word	NOUN
ejde-397	664	7	,	,	PUNCT
ejde-397	664	8	(	(	PUNCT
ejde-397	664	9	0	0	NUM
ejde-397	664	10	,	,	PUNCT
ejde-397	664	11	ũb(λ	ũb(λ	NOUN
ejde-397	664	12	)	)	PUNCT
ejde-397	664	13	−	−	PROPN
ejde-397	664	14	f̃(λ	f̃(λ	NOUN
ejde-397	664	15	)	)	PUNCT
ejde-397	664	16	)	)	PUNCT
ejde-397	665	1	∈	∈	PROPN
ejde-397	665	2	a.	a.	NOUN
ejde-397	665	3	by	by	ADP
ejde-397	665	4	the	the	DET
ejde-397	665	5	foregoing	foregoing	NOUN
ejde-397	665	6	,	,	PUNCT
ejde-397	665	7	we	we	PRON
ejde-397	665	8	have	have	VERB
ejde-397	665	9	that	that	PRON
ejde-397	665	10	(	(	PUNCT
ejde-397	665	11	ã	ã	PROPN
ejde-397	665	12	∗	∗	VERB
ejde-397	665	13	u(λ	u(λ	PROPN
ejde-397	665	14	)	)	PUNCT
ejde-397	665	15	,	,	PUNCT
ejde-397	665	16	ũb(λ	ũb(λ	PROPN
ejde-397	665	17	)	)	PUNCT
ejde-397	665	18	−	−	PROPN
ejde-397	665	19	f̃(λ	f̃(λ	NOUN
ejde-397	665	20	)	)	PUNCT
ejde-397	665	21	)	)	PUNCT
ejde-397	666	1	∈	∈	PROPN
ejde-397	666	2	a	a	PRON
ejde-397	666	3	for	for	ADP
ejde-397	666	4	all	all	DET
ejde-397	666	5	λ	λ	PROPN
ejde-397	666	6	∈	∈	PROPN
ejde-397	666	7	n	n	NOUN
ejde-397	666	8	with	with	ADP
ejde-397	666	9	λ	λ	PROPN
ejde-397	666	10	>	>	X
ejde-397	666	11	ω	ω	PROPN
ejde-397	666	12	.	.	PUNCT
ejde-397	667	1	using	use	VERB
ejde-397	667	2	theorem	theorem	NOUN
ejde-397	667	3	2.3	2.3	NUM
ejde-397	667	4	,	,	PUNCT
ejde-397	667	5	we	we	PRON
ejde-397	667	6	obtain	obtain	VERB
ejde-397	667	7	that	that	DET
ejde-397	667	8	∫∞	∫∞	NOUN
ejde-397	667	9	0	0	PUNCT
ejde-397	668	1	e−λt(ub	e−λt(ub	PROPN
ejde-397	668	2	−	−	PROPN
ejde-397	668	3	f)[2](t	f)[2](t	PROPN
ejde-397	668	4	)	)	PUNCT
ejde-397	668	5	dt	dt	VERB
ejde-397	669	1	∈	∈	PROPN
ejde-397	669	2	a	a	DET
ejde-397	669	3	∫∞	∫∞	NOUN
ejde-397	669	4	0	0	NUM
ejde-397	669	5	e−λt(a	e−λt(a	NOUN
ejde-397	669	6	∗	∗	X
ejde-397	669	7	u)[2](t	u)[2](t	NOUN
ejde-397	669	8	)	)	PUNCT
ejde-397	669	9	dt	dt	PUNCT
ejde-397	670	1	(	(	PUNCT
ejde-397	670	2	λ	λ	X
ejde-397	670	3	∈	∈	PROPN
ejde-397	670	4	n	n	CCONJ
ejde-397	670	5	,	,	PUNCT
ejde-397	670	6	λ	λ	X
ejde-397	670	7	>	>	X
ejde-397	670	8	ω	ω	NUM
ejde-397	670	9	)	)	PUNCT
ejde-397	670	10	and	and	CCONJ
ejde-397	670	11	now	now	ADV
ejde-397	670	12	we	we	PRON
ejde-397	670	13	can	can	AUX
ejde-397	670	14	apply	apply	VERB
ejde-397	670	15	theorem	theorem	ADJ
ejde-397	670	16	3.5	3.5	NUM
ejde-397	670	17	,	,	PUNCT
ejde-397	670	18	along	along	ADP
ejde-397	670	19	with	with	ADP
ejde-397	670	20	the	the	DET
ejde-397	670	21	xa×ya	xa×ya	PROPN
ejde-397	670	22	-	-	PUNCT
ejde-397	670	23	closedness	closedness	ADJ
ejde-397	670	24	ofa	ofa	PROPN
ejde-397	670	25	,	,	PUNCT
ejde-397	670	26	in	in	ADP
ejde-397	670	27	order	order	NOUN
ejde-397	670	28	to	to	PART
ejde-397	670	29	see	see	VERB
ejde-397	670	30	that	that	SCONJ
ejde-397	670	31	u	u	NOUN
ejde-397	671	1	[	[	X
ejde-397	671	2	2	2	NUM
ejde-397	671	3	]	]	SYM
ejde-397	671	4	b	b	NOUN
ejde-397	671	5	(	(	PUNCT
ejde-397	671	6	t)−f	t)−f	PROPN
ejde-397	671	7	[	[	X
ejde-397	671	8	2](t	2](t	NUM
ejde-397	671	9	)	)	PUNCT
ejde-397	671	10	∈	∈	PROPN
ejde-397	671	11	a(a∗u)[2](t	a(a∗u)[2](t	PROPN
ejde-397	671	12	)	)	PUNCT
ejde-397	671	13	,	,	PUNCT
ejde-397	671	14	t	t	PROPN
ejde-397	671	15	≥	≥	NUM
ejde-397	671	16	0	0	NUM
ejde-397	671	17	.	.	PUNCT
ejde-397	672	1	this	this	PRON
ejde-397	672	2	simply	simply	ADV
ejde-397	672	3	implies	imply	VERB
ejde-397	672	4	(	(	PUNCT
ejde-397	672	5	4.3	4.3	NUM
ejde-397	672	6	)	)	PUNCT
ejde-397	672	7	.	.	PUNCT
ejde-397	673	1	remark	remark	PROPN
ejde-397	673	2	4.4	4.4	NUM
ejde-397	673	3	.	.	PUNCT
ejde-397	674	1	observe	observe	VERB
ejde-397	674	2	that	that	SCONJ
ejde-397	674	3	we	we	PRON
ejde-397	674	4	do	do	AUX
ejde-397	674	5	not	not	PART
ejde-397	674	6	require	require	VERB
ejde-397	674	7	any	any	DET
ejde-397	674	8	type	type	NOUN
ejde-397	674	9	of	of	ADP
ejde-397	674	10	closedness	closedness	NOUN
ejde-397	674	11	of	of	ADP
ejde-397	674	12	the	the	DET
ejde-397	674	13	operator	operator	NOUN
ejde-397	674	14	b	b	PROPN
ejde-397	674	15	in	in	ADP
ejde-397	674	16	the	the	DET
ejde-397	674	17	formulation	formulation	NOUN
ejde-397	674	18	of	of	ADP
ejde-397	674	19	theorem	theorem	NOUN
ejde-397	674	20	4.3	4.3	NUM
ejde-397	674	21	.	.	PUNCT
ejde-397	675	1	even	even	ADV
ejde-397	675	2	in	in	ADP
ejde-397	675	3	the	the	DET
ejde-397	675	4	case	case	NOUN
ejde-397	675	5	that	that	SCONJ
ejde-397	675	6	x	x	X
ejde-397	675	7	=	=	SYM
ejde-397	675	8	y	y	PROPN
ejde-397	675	9	and	and	CCONJ
ejde-397	675	10	b	b	X
ejde-397	675	11	=	=	SYM
ejde-397	675	12	b	b	PROPN
ejde-397	675	13	=	=	SYM
ejde-397	675	14	i	i	PROPN
ejde-397	675	15	,	,	PUNCT
ejde-397	675	16	we	we	PRON
ejde-397	675	17	can	can	AUX
ejde-397	675	18	not	not	PART
ejde-397	675	19	differentiate	differentiate	VERB
ejde-397	675	20	the	the	DET
ejde-397	675	21	equation	equation	NOUN
ejde-397	675	22	(	(	PUNCT
ejde-397	675	23	4.3	4.3	NUM
ejde-397	675	24	)	)	PUNCT
ejde-397	675	25	once	once	ADV
ejde-397	675	26	more	more	ADV
ejde-397	675	27	without	without	ADP
ejde-397	675	28	making	make	VERB
ejde-397	675	29	an	an	DET
ejde-397	675	30	additional	additional	ADJ
ejde-397	675	31	assumption	assumption	NOUN
ejde-397	675	32	that	that	SCONJ
ejde-397	675	33	f	f	PROPN
ejde-397	675	34	=	=	SYM
ejde-397	675	35	f	f	PROPN
ejde-397	675	36	∈	∈	PROPN
ejde-397	675	37	c([0,∞	c([0,∞	PROPN
ejde-397	675	38	)	)	PUNCT
ejde-397	675	39	:	:	PUNCT
ejde-397	675	40	ya	ya	PROPN
ejde-397	675	41	)	)	PUNCT
ejde-397	675	42	is	be	AUX
ejde-397	675	43	single	single	ADV
ejde-397	675	44	-	-	PUNCT
ejde-397	675	45	valued	value	VERB
ejde-397	675	46	(	(	PUNCT
ejde-397	675	47	cf	cf	NOUN
ejde-397	675	48	.	.	PUNCT
ejde-397	676	1	[	[	X
ejde-397	676	2	31	31	NUM
ejde-397	676	3	,	,	PUNCT
ejde-397	676	4	l.	l.	PROPN
ejde-397	676	5	-1	-1	PROPN
ejde-397	676	6	,	,	PUNCT
ejde-397	676	7	p.	p.	NOUN
ejde-397	676	8	173	173	NUM
ejde-397	676	9	;	;	PUNCT
ejde-397	676	10	l.	l.	PROPN
ejde-397	676	11	1	1	NUM
ejde-397	676	12	-	-	SYM
ejde-397	676	13	3	3	NUM
ejde-397	676	14	,	,	PUNCT
ejde-397	676	15	p.	p.	NOUN
ejde-397	676	16	174	174	NUM
ejde-397	676	17	]	]	PUNCT
ejde-397	676	18	,	,	PUNCT
ejde-397	676	19	where	where	SCONJ
ejde-397	676	20	the	the	DET
ejde-397	676	21	author	author	NOUN
ejde-397	676	22	has	have	AUX
ejde-397	676	23	made	make	VERB
ejde-397	676	24	a	a	DET
ejde-397	676	25	small	small	ADJ
ejde-397	676	26	mistake	mistake	NOUN
ejde-397	676	27	in	in	ADP
ejde-397	676	28	the	the	DET
ejde-397	676	29	consideration	consideration	NOUN
ejde-397	676	30	;	;	PUNCT
ejde-397	676	31	in	in	ADP
ejde-397	676	32	actual	actual	ADJ
ejde-397	676	33	fact	fact	NOUN
ejde-397	676	34	,	,	PUNCT
ejde-397	676	35	the	the	DET
ejde-397	676	36	equation	equation	NOUN
ejde-397	676	37	[	[	X
ejde-397	676	38	31	31	NUM
ejde-397	676	39	,	,	PUNCT
ejde-397	676	40	(	(	PUNCT
ejde-397	676	41	3.1	3.1	NUM
ejde-397	676	42	)	)	PUNCT
ejde-397	676	43	]	]	PUNCT
ejde-397	676	44	has	have	VERB
ejde-397	676	45	to	to	PART
ejde-397	676	46	be	be	AUX
ejde-397	676	47	valid	valid	ADJ
ejde-397	676	48	for	for	ADP
ejde-397	676	49	some	some	DET
ejde-397	676	50	f	f	PROPN
ejde-397	676	51	∈	∈	PROPN
ejde-397	676	52	secc(f	secc(f	PROPN
ejde-397	676	53	)	)	PUNCT
ejde-397	676	54	in	in	ADP
ejde-397	676	55	order	order	NOUN
ejde-397	676	56	for	for	ADP
ejde-397	676	57	the	the	DET
ejde-397	676	58	proof	proof	NOUN
ejde-397	676	59	of	of	ADP
ejde-397	676	60	implication	implication	NOUN
ejde-397	676	61	(	(	PUNCT
ejde-397	676	62	iii	iii	NOUN
ejde-397	676	63	)	)	PUNCT
ejde-397	676	64	⇒	⇒	NOUN
ejde-397	676	65	(	(	PUNCT
ejde-397	676	66	i	i	NOUN
ejde-397	676	67	)	)	PUNCT
ejde-397	676	68	of	of	ADP
ejde-397	676	69	[	[	X
ejde-397	676	70	31	31	NUM
ejde-397	676	71	,	,	PUNCT
ejde-397	676	72	theorem	theorem	VERB
ejde-397	676	73	3.1	3.1	NUM
ejde-397	676	74	]	]	PUNCT
ejde-397	676	75	to	to	PART
ejde-397	676	76	work	work	VERB
ejde-397	676	77	)	)	PUNCT
ejde-397	676	78	.	.	PUNCT
ejde-397	677	1	if	if	SCONJ
ejde-397	677	2	ω	ω	PROPN
ejde-397	677	3	is	be	AUX
ejde-397	677	4	a	a	DET
ejde-397	677	5	non	non	ADJ
ejde-397	677	6	-	-	ADJ
ejde-397	677	7	empty	empty	ADJ
ejde-397	677	8	open	open	ADJ
ejde-397	677	9	subset	subset	NOUN
ejde-397	677	10	of	of	ADP
ejde-397	677	11	c	c	PROPN
ejde-397	677	12	and	and	CCONJ
ejde-397	677	13	g	g	PROPN
ejde-397	677	14	:	:	PUNCT
ejde-397	677	15	ω	ω	PROPN
ejde-397	677	16	→	→	PUNCT
ejde-397	677	17	x	x	X
ejde-397	677	18	is	be	AUX
ejde-397	677	19	an	an	DET
ejde-397	677	20	analytic	analytic	ADJ
ejde-397	677	21	mapping	mapping	NOUN
ejde-397	677	22	that	that	SCONJ
ejde-397	677	23	it	it	PRON
ejde-397	677	24	is	be	AUX
ejde-397	677	25	not	not	PART
ejde-397	677	26	identically	identically	ADV
ejde-397	677	27	equal	equal	ADJ
ejde-397	677	28	to	to	ADP
ejde-397	677	29	the	the	DET
ejde-397	677	30	zero	zero	NUM
ejde-397	677	31	function	function	NOUN
ejde-397	677	32	,	,	PUNCT
ejde-397	677	33	then	then	ADV
ejde-397	677	34	we	we	PRON
ejde-397	677	35	can	can	AUX
ejde-397	677	36	simply	simply	ADV
ejde-397	677	37	prove	prove	VERB
ejde-397	677	38	that	that	SCONJ
ejde-397	677	39	for	for	ADP
ejde-397	677	40	each	each	DET
ejde-397	677	41	zero	zero	NUM
ejde-397	677	42	λ0	λ0	NOUN
ejde-397	677	43	of	of	ADP
ejde-397	677	44	g	g	PROPN
ejde-397	677	45	(	(	PUNCT
ejde-397	677	46	·	·	PUNCT
ejde-397	677	47	)	)	PUNCT
ejde-397	677	48	there	there	PRON
ejde-397	677	49	exists	exist	VERB
ejde-397	677	50	a	a	DET
ejde-397	677	51	uniquely	uniquely	ADV
ejde-397	677	52	determined	determined	ADJ
ejde-397	677	53	natural	natural	ADJ
ejde-397	677	54	number	number	NOUN
ejde-397	677	55	n	n	CCONJ
ejde-397	677	56	∈	∈	NOUN
ejde-397	677	57	n	n	PRON
ejde-397	677	58	such	such	ADJ
ejde-397	677	59	that	that	DET
ejde-397	677	60	g(j)(λ0	g(j)(λ0	NOUN
ejde-397	677	61	)	)	PUNCT
ejde-397	677	62	=	=	SYM
ejde-397	677	63	0	0	NUM
ejde-397	677	64	for	for	ADP
ejde-397	677	65	0	0	NUM
ejde-397	677	66	≤	≤	NUM
ejde-397	677	67	j	j	PROPN
ejde-397	677	68	≤	≤	ADJ
ejde-397	677	69	n−	n−	PROPN
ejde-397	677	70	1	1	NUM
ejde-397	677	71	and	and	CCONJ
ejde-397	677	72	g(n)(λ0	g(n)(λ0	NOUN
ejde-397	677	73	)	)	PUNCT
ejde-397	677	74	6=	6=	ADP
ejde-397	677	75	0	0	NUM
ejde-397	677	76	.	.	PUNCT
ejde-397	678	1	owing	owe	VERB
ejde-397	678	2	to	to	ADP
ejde-397	678	3	this	this	DET
ejde-397	678	4	fact	fact	NOUN
ejde-397	678	5	,	,	PUNCT
ejde-397	678	6	we	we	PRON
ejde-397	678	7	can	can	AUX
ejde-397	678	8	repeat	repeat	VERB
ejde-397	678	9	almost	almost	ADV
ejde-397	678	10	literally	literally	ADV
ejde-397	678	11	the	the	DET
ejde-397	678	12	arguments	argument	NOUN
ejde-397	678	13	given	give	VERB
ejde-397	678	14	in	in	ADP
ejde-397	678	15	the	the	DET
ejde-397	678	16	proof	proof	NOUN
ejde-397	678	17	of	of	ADP
ejde-397	678	18	[	[	X
ejde-397	678	19	31	31	NUM
ejde-397	678	20	,	,	PUNCT
ejde-397	678	21	theorem	theorem	VERB
ejde-397	678	22	3.2	3.2	NUM
ejde-397	678	23	]	]	PUNCT
ejde-397	678	24	to	to	PART
ejde-397	678	25	verify	verify	VERB
ejde-397	678	26	the	the	DET
ejde-397	678	27	validity	validity	NOUN
ejde-397	678	28	of	of	ADP
ejde-397	678	29	the	the	DET
ejde-397	678	30	following	follow	VERB
ejde-397	678	31	ljubich	ljubich	PROPN
ejde-397	678	32	uniqueness	uniqueness	PROPN
ejde-397	678	33	type	type	NOUN
ejde-397	678	34	theorem	theorem	NOUN
ejde-397	678	35	:	:	PUNCT
ejde-397	678	36	theorem	theorem	ADJ
ejde-397	678	37	4.5	4.5	NUM
ejde-397	678	38	.	.	PUNCT
ejde-397	679	1	suppose	suppose	VERB
ejde-397	679	2	a	a	DET
ejde-397	679	3	:	:	PUNCT
ejde-397	679	4	x	x	SYM
ejde-397	679	5	→	→	X
ejde-397	679	6	p	p	X
ejde-397	679	7	(	(	PUNCT
ejde-397	679	8	y	y	PROPN
ejde-397	679	9	)	)	PUNCT
ejde-397	679	10	is	be	AUX
ejde-397	679	11	an	an	DET
ejde-397	679	12	mlo	mlo	PROPN
ejde-397	679	13	,	,	PUNCT
ejde-397	679	14	b	b	PROPN
ejde-397	679	15	=	=	SYM
ejde-397	679	16	b	b	PROPN
ejde-397	679	17	:	:	PUNCT
ejde-397	679	18	d(b	d(b	X
ejde-397	679	19	)	)	PUNCT
ejde-397	680	1	⊆	⊆	NUM
ejde-397	680	2	x	x	SYM
ejde-397	680	3	→	→	SYM
ejde-397	680	4	y	y	PROPN
ejde-397	680	5	is	be	AUX
ejde-397	680	6	a	a	DET
ejde-397	680	7	single	single	ADV
ejde-397	680	8	-	-	PUNCT
ejde-397	680	9	valued	value	VERB
ejde-397	680	10	linear	linear	NOUN
ejde-397	680	11	operator	operator	NOUN
ejde-397	680	12	,	,	PUNCT
ejde-397	680	13	a	a	PRON
ejde-397	680	14	is	be	AUX
ejde-397	680	15	xa	xa	PROPN
ejde-397	680	16	×	×	PROPN
ejde-397	680	17	ya	ya	PROPN
ejde-397	680	18	-	-	PUNCT
ejde-397	680	19	closed	close	VERB
ejde-397	680	20	and	and	CCONJ
ejde-397	680	21	b	b	NOUN
ejde-397	680	22	is	be	AUX
ejde-397	680	23	xb	xb	PROPN
ejde-397	680	24	×	×	PROPN
ejde-397	680	25	yb	yb	PROPN
ejde-397	680	26	-	-	PUNCT
ejde-397	680	27	closed	closed	ADJ
ejde-397	680	28	,	,	PUNCT
ejde-397	680	29	where	where	SCONJ
ejde-397	680	30	ya	ya	PROPN
ejde-397	680	31	↪	↪	PROPN
ejde-397	680	32	→	→	SYM
ejde-397	680	33	yb	yb	PROPN
ejde-397	680	34	.	.	PROPN
ejde-397	680	35	assume	assume	VERB
ejde-397	680	36	,	,	PUNCT
ejde-397	680	37	further	far	ADV
ejde-397	680	38	,	,	PUNCT
ejde-397	680	39	that	that	SCONJ
ejde-397	680	40	a	a	DET
ejde-397	680	41	∈	∈	PROPN
ejde-397	680	42	l1	l1	PROPN
ejde-397	680	43	loc([0,∞	loc([0,∞	PROPN
ejde-397	680	44	)	)	PUNCT
ejde-397	680	45	)	)	PUNCT
ejde-397	680	46	,	,	PUNCT
ejde-397	680	47	a	a	DET
ejde-397	680	48	6=	6=	NUM
ejde-397	680	49	0	0	NUM
ejde-397	680	50	,	,	PUNCT
ejde-397	680	51	abs(|a|	abs(|a|	ADJ
ejde-397	680	52	)	)	PUNCT
ejde-397	680	53	<	<	X
ejde-397	680	54	∞	∞	PROPN
ejde-397	680	55	,	,	PUNCT
ejde-397	680	56	f	f	X
ejde-397	680	57	=	=	SYM
ejde-397	680	58	f	f	PROPN
ejde-397	680	59	∈	∈	PROPN
ejde-397	680	60	c([0,∞	c([0,∞	PROPN
ejde-397	680	61	)	)	PUNCT
ejde-397	680	62	:	:	PUNCT
ejde-397	680	63	ya	ya	PROPN
ejde-397	680	64	)	)	PUNCT
ejde-397	680	65	is	be	AUX
ejde-397	680	66	single	single	ADV
ejde-397	680	67	-	-	PUNCT
ejde-397	680	68	valued	value	VERB
ejde-397	680	69	,	,	PUNCT
ejde-397	680	70	absya(f	absya(f	NOUN
ejde-397	680	71	)	)	PUNCT
ejde-397	680	72	<	<	X
ejde-397	680	73	∞	∞	PROPN
ejde-397	680	74	,	,	PUNCT
ejde-397	680	75	and	and	CCONJ
ejde-397	680	76	there	there	PRON
ejde-397	680	77	exist	exist	VERB
ejde-397	680	78	a	a	DET
ejde-397	680	79	sequence	sequence	NOUN
ejde-397	680	80	(	(	PUNCT
ejde-397	680	81	λk)k∈n	λk)k∈n	NUM
ejde-397	680	82	of	of	ADP
ejde-397	680	83	complex	complex	ADJ
ejde-397	680	84	numbers	number	NOUN
ejde-397	680	85	and	and	CCONJ
ejde-397	680	86	a	a	DET
ejde-397	680	87	number	number	NOUN
ejde-397	680	88	ω	ω	PROPN
ejde-397	680	89	>	>	X
ejde-397	680	90	abs(|a|	abs(|a|	PROPN
ejde-397	680	91	)	)	PUNCT
ejde-397	680	92	such	such	ADJ
ejde-397	680	93	that	that	DET
ejde-397	680	94	limk→∞<λk	limk→∞<λk	NOUN
ejde-397	680	95	=	=	PUNCT
ejde-397	681	1	+	+	NUM
ejde-397	681	2	∞	∞	PROPN
ejde-397	681	3	,	,	PUNCT
ejde-397	681	4	ã(λk	ã(λk	NOUN
ejde-397	681	5	)	)	PUNCT
ejde-397	681	6	6=	6=	ADP
ejde-397	681	7	0	0	NUM
ejde-397	681	8	,	,	PUNCT
ejde-397	681	9	k	k	PROPN
ejde-397	681	10	∈	∈	PROPN
ejde-397	681	11	n	n	CCONJ
ejde-397	681	12	,	,	PUNCT
ejde-397	681	13	and	and	CCONJ
ejde-397	681	14	1	1	NUM
ejde-397	681	15	ã(λk	ã(λk	NOUN
ejde-397	681	16	)	)	PUNCT
ejde-397	682	1	bx	bx	NOUN
ejde-397	682	2	/∈	/∈	PUNCT
ejde-397	682	3	ax	ax	NOUN
ejde-397	682	4	,	,	PUNCT
ejde-397	682	5	k	k	PROPN
ejde-397	682	6	∈	∈	PROPN
ejde-397	682	7	n	n	CCONJ
ejde-397	682	8	,	,	PUNCT
ejde-397	682	9	0	0	NUM
ejde-397	683	1	6=	6=	NUM
ejde-397	683	2	x	x	SYM
ejde-397	683	3	∈	∈	PROPN
ejde-397	683	4	d(a	d(a	PROPN
ejde-397	683	5	)	)	PUNCT
ejde-397	683	6	∩d(b	∩d(b	PROPN
ejde-397	683	7	)	)	PUNCT
ejde-397	683	8	.	.	PUNCT
ejde-397	684	1	then	then	ADV
ejde-397	684	2	there	there	PRON
ejde-397	684	3	exists	exist	VERB
ejde-397	684	4	a	a	DET
ejde-397	684	5	unique	unique	ADJ
ejde-397	684	6	pre	pre	NOUN
ejde-397	684	7	-	-	NOUN
ejde-397	684	8	solution	solution	NOUN
ejde-397	684	9	of	of	ADP
ejde-397	684	10	(	(	PUNCT
ejde-397	684	11	1.1	1.1	NUM
ejde-397	684	12	)	)	PUNCT
ejde-397	684	13	,	,	PUNCT
ejde-397	684	14	with	with	ADP
ejde-397	684	15	τ	τ	PROPN
ejde-397	684	16	=	=	SYM
ejde-397	684	17	∞	∞	PROPN
ejde-397	684	18	,	,	PUNCT
ejde-397	684	19	satisfying	satisfy	VERB
ejde-397	684	20	that	that	SCONJ
ejde-397	684	21	u	u	PROPN
ejde-397	684	22	∈	∈	PROPN
ejde-397	684	23	(	(	PUNCT
ejde-397	684	24	p1	p1	NOUN
ejde-397	684	25	)	)	PUNCT
ejde-397	684	26	−	−	PROPN
ejde-397	684	27	xb	xb	PROPN
ejde-397	684	28	,	,	PUNCT
ejde-397	684	29	u(t	u(t	PROPN
ejde-397	684	30	)	)	PUNCT
ejde-397	684	31	∈	∈	PROPN
ejde-397	684	32	d(b	d(b	PROPN
ejde-397	684	33	)	)	PUNCT
ejde-397	684	34	,	,	PUNCT
ejde-397	684	35	t	t	PROPN
ejde-397	684	36	≥	≥	NUM
ejde-397	684	37	0	0	NUM
ejde-397	684	38	,	,	PUNCT
ejde-397	684	39	bu	bu	PROPN
ejde-397	684	40	∈	∈	PROPN
ejde-397	684	41	c([0,∞	c([0,∞	PROPN
ejde-397	684	42	)	)	PUNCT
ejde-397	684	43	:	:	PUNCT
ejde-397	684	44	ya	ya	PROPN
ejde-397	684	45	)	)	PUNCT
ejde-397	684	46	,	,	PUNCT
ejde-397	684	47	a	a	DET
ejde-397	684	48	∗	∗	NOUN
ejde-397	684	49	u	u	NOUN
ejde-397	684	50	∈	∈	PROPN
ejde-397	684	51	c([0,∞	c([0,∞	PROPN
ejde-397	684	52	)	)	PUNCT
ejde-397	684	53	:	:	PUNCT
ejde-397	685	1	xa	xa	PROPN
ejde-397	685	2	)	)	PUNCT
ejde-397	685	3	,	,	PUNCT
ejde-397	685	4	a	a	DET
ejde-397	685	5	∗	∗	NOUN
ejde-397	685	6	u	u	NOUN
ejde-397	685	7	∈	∈	PROPN
ejde-397	685	8	(	(	PUNCT
ejde-397	685	9	p1)−xa	p1)−xa	X
ejde-397	685	10	and	and	CCONJ
ejde-397	685	11	absya(bu	absya(bu	PROPN
ejde-397	685	12	)	)	PUNCT
ejde-397	686	1	<	<	X
ejde-397	686	2	∞.	∞.	PROPN
ejde-397	686	3	in	in	ADP
ejde-397	686	4	the	the	DET
ejde-397	686	5	following	follow	VERB
ejde-397	686	6	extension	extension	NOUN
ejde-397	686	7	of	of	ADP
ejde-397	686	8	[	[	X
ejde-397	686	9	36	36	NUM
ejde-397	686	10	,	,	PUNCT
ejde-397	686	11	theorem	theorem	VERB
ejde-397	686	12	2.1.34	2.1.34	NUM
ejde-397	686	13	]	]	PUNCT
ejde-397	686	14	,	,	PUNCT
ejde-397	686	15	we	we	PRON
ejde-397	686	16	will	will	AUX
ejde-397	686	17	prove	prove	VERB
ejde-397	686	18	one	one	NUM
ejde-397	686	19	more	more	ADV
ejde-397	686	20	ljubich	ljubich	ADJ
ejde-397	686	21	’s	’s	PART
ejde-397	686	22	uniqueness	uniqueness	PROPN
ejde-397	686	23	criterium	criterium	NOUN
ejde-397	686	24	for	for	ADP
ejde-397	686	25	abstract	abstract	ADJ
ejde-397	686	26	cauchy	cauchy	ADJ
ejde-397	686	27	problems	problem	NOUN
ejde-397	686	28	with	with	ADP
ejde-397	686	29	multivalued	multivalued	ADJ
ejde-397	686	30	linear	linear	ADJ
ejde-397	686	31	operators	operator	NOUN
ejde-397	686	32	(	(	PUNCT
ejde-397	686	33	cf	cf	NOUN
ejde-397	686	34	.	.	PUNCT
ejde-397	687	1	also	also	ADV
ejde-397	687	2	[	[	X
ejde-397	687	3	32	32	NUM
ejde-397	687	4	,	,	PUNCT
ejde-397	687	5	theorem	theorem	VERB
ejde-397	687	6	3.5	3.5	NUM
ejde-397	687	7	]	]	PUNCT
ejde-397	687	8	and	and	CCONJ
ejde-397	687	9	[	[	X
ejde-397	687	10	36	36	NUM
ejde-397	687	11	,	,	PUNCT
ejde-397	687	12	theorem	theorem	VERB
ejde-397	687	13	2.10.44	2.10.44	NOUN
ejde-397	687	14	]	]	NUM
ejde-397	687	15	)	)	PUNCT
ejde-397	687	16	.	.	PUNCT
ejde-397	688	1	theorem	theorem	VERB
ejde-397	688	2	4.6	4.6	NUM
ejde-397	688	3	.	.	PUNCT
ejde-397	689	1	suppose	suppose	VERB
ejde-397	689	2	α	α	PRON
ejde-397	689	3	>	>	X
ejde-397	689	4	0	0	PROPN
ejde-397	689	5	,	,	PUNCT
ejde-397	689	6	λ	λ	X
ejde-397	689	7	>	>	X
ejde-397	689	8	0	0	PROPN
ejde-397	689	9	,	,	PUNCT
ejde-397	689	10	a	a	PRON
ejde-397	689	11	is	be	AUX
ejde-397	689	12	an	an	DET
ejde-397	689	13	mlo	mlo	NOUN
ejde-397	689	14	in	in	ADP
ejde-397	689	15	x	x	NOUN
ejde-397	689	16	,	,	PUNCT
ejde-397	689	17	{	{	PUNCT
ejde-397	689	18	(	(	PUNCT
ejde-397	689	19	nλ)α	nλ)α	NOUN
ejde-397	689	20	:	:	PUNCT
ejde-397	689	21	n	n	CCONJ
ejde-397	689	22	∈	∈	PROPN
ejde-397	689	23	n	n	CCONJ
ejde-397	689	24	}	}	PUNCT
ejde-397	689	25	⊆	⊆	NUM
ejde-397	689	26	ρc(a	ρc(a	NOUN
ejde-397	689	27	)	)	PUNCT
ejde-397	689	28	and	and	CCONJ
ejde-397	689	29	,	,	PUNCT
ejde-397	689	30	for	for	ADP
ejde-397	689	31	every	every	DET
ejde-397	689	32	σ	σ	NOUN
ejde-397	689	33	>	>	X
ejde-397	689	34	0	0	PUNCT
ejde-397	690	1	and	and	CCONJ
ejde-397	690	2	x	x	SYM
ejde-397	690	3	∈	∈	PROPN
ejde-397	690	4	x	x	NOUN
ejde-397	690	5	,	,	PUNCT
ejde-397	690	6	lim	lim	PROPN
ejde-397	690	7	n→∞	n→∞	X
ejde-397	690	8	(	(	PUNCT
ejde-397	690	9	(	(	PUNCT
ejde-397	690	10	nλ)α	nλ)α	NOUN
ejde-397	690	11	−a	−a	NOUN
ejde-397	690	12	)	)	PUNCT
ejde-397	690	13	−1	−1	NOUN
ejde-397	690	14	cx	cx	PROPN
ejde-397	690	15	enλσ	enλσ	NOUN
ejde-397	690	16	=	=	NOUN
ejde-397	690	17	0	0	PROPN
ejde-397	690	18	.	.	PUNCT
ejde-397	691	1	then	then	ADV
ejde-397	691	2	,	,	PUNCT
ejde-397	691	3	for	for	ADP
ejde-397	691	4	every	every	DET
ejde-397	691	5	x0	x0	PROPN
ejde-397	691	6	,	,	PUNCT
ejde-397	691	7	·	·	PUNCT
ejde-397	691	8	·	·	PUNCT
ejde-397	691	9	·	·	PUNCT
ejde-397	691	10	,	,	PUNCT
ejde-397	691	11	xdαe−1	xdαe−1	PROPN
ejde-397	691	12	∈	∈	PROPN
ejde-397	691	13	x	x	PRON
ejde-397	691	14	,	,	PUNCT
ejde-397	691	15	there	there	PRON
ejde-397	691	16	exists	exist	VERB
ejde-397	691	17	at	at	ADP
ejde-397	691	18	most	most	ADJ
ejde-397	691	19	one	one	NUM
ejde-397	691	20	pre	pre	NOUN
ejde-397	691	21	-	-	NOUN
ejde-397	691	22	solution	solution	NOUN
ejde-397	691	23	of	of	ADP
ejde-397	691	24	the	the	DET
ejde-397	691	25	initial	initial	ADJ
ejde-397	691	26	value	value	NOUN
ejde-397	691	27	problem	problem	NOUN
ejde-397	691	28	(	(	PUNCT
ejde-397	691	29	1.2	1.2	NUM
ejde-397	691	30	)	)	PUNCT
ejde-397	691	31	with	with	ADP
ejde-397	691	32	b	b	PROPN
ejde-397	691	33	=	=	SYM
ejde-397	691	34	i.	i.	NOUN
ejde-397	691	35	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	691	36	abstract	abstract	ADJ
ejde-397	691	37	degenerate	degenerate	ADJ
ejde-397	691	38	volterra	volterra	NOUN
ejde-397	691	39	inclusions	inclusion	NOUN
ejde-397	691	40	21	21	NUM
ejde-397	691	41	proof	proof	NOUN
ejde-397	691	42	.	.	PUNCT
ejde-397	692	1	it	it	PRON
ejde-397	692	2	suffices	suffice	VERB
ejde-397	692	3	to	to	PART
ejde-397	692	4	show	show	VERB
ejde-397	692	5	that	that	SCONJ
ejde-397	692	6	the	the	DET
ejde-397	692	7	zero	zero	NUM
ejde-397	692	8	function	function	NOUN
ejde-397	692	9	is	be	AUX
ejde-397	692	10	the	the	DET
ejde-397	692	11	only	only	ADJ
ejde-397	692	12	pre	pre	NOUN
ejde-397	692	13	-	-	NOUN
ejde-397	692	14	solution	solution	NOUN
ejde-397	692	15	of	of	ADP
ejde-397	692	16	problem	problem	NOUN
ejde-397	692	17	(	(	PUNCT
ejde-397	692	18	1.2	1.2	NUM
ejde-397	692	19	)	)	PUNCT
ejde-397	692	20	with	with	ADP
ejde-397	692	21	b	b	NOUN
ejde-397	692	22	=	=	SYM
ejde-397	692	23	i	i	PROPN
ejde-397	692	24	and	and	CCONJ
ejde-397	692	25	the	the	DET
ejde-397	692	26	initial	initial	ADJ
ejde-397	692	27	values	value	NOUN
ejde-397	692	28	x0	x0	PROPN
ejde-397	692	29	,	,	PUNCT
ejde-397	692	30	·	·	PUNCT
ejde-397	692	31	·	·	PUNCT
ejde-397	692	32	·	·	PUNCT
ejde-397	692	33	,	,	PUNCT
ejde-397	692	34	xdαe−1	xdαe−1	PROPN
ejde-397	692	35	chosen	choose	VERB
ejde-397	692	36	to	to	PART
ejde-397	692	37	be	be	AUX
ejde-397	692	38	zeroes	zero	NOUN
ejde-397	692	39	.	.	PUNCT
ejde-397	693	1	let	let	VERB
ejde-397	693	2	u	u	PRON
ejde-397	693	3	(	(	PUNCT
ejde-397	693	4	·	·	PUNCT
ejde-397	693	5	)	)	PUNCT
ejde-397	693	6	be	be	AUX
ejde-397	693	7	a	a	DET
ejde-397	693	8	pre	pre	NOUN
ejde-397	693	9	-	-	NOUN
ejde-397	693	10	solution	solution	NOUN
ejde-397	693	11	of	of	ADP
ejde-397	693	12	such	such	DET
ejde-397	693	13	a	a	DET
ejde-397	693	14	problem	problem	NOUN
ejde-397	693	15	.	.	PUNCT
ejde-397	694	1	set	set	NOUN
ejde-397	694	2	zn(t	zn(t	NUM
ejde-397	694	3	)	)	PUNCT
ejde-397	694	4	:	:	PUNCT
ejde-397	695	1	=	=	SYM
ejde-397	695	2	(	(	PUNCT
ejde-397	695	3	(	(	PUNCT
ejde-397	695	4	nλ)α	nλ)α	NOUN
ejde-397	695	5	−a)−1cu(t	−a)−1cu(t	PROPN
ejde-397	695	6	)	)	PUNCT
ejde-397	695	7	,	,	PUNCT
ejde-397	695	8	t	t	PROPN
ejde-397	695	9	≥	≥	NUM
ejde-397	695	10	0	0	NUM
ejde-397	695	11	,	,	PUNCT
ejde-397	695	12	n	n	DET
ejde-397	695	13	∈	∈	PROPN
ejde-397	695	14	n.	n.	NOUN
ejde-397	695	15	then	then	ADV
ejde-397	695	16	it	it	PRON
ejde-397	695	17	can	can	AUX
ejde-397	695	18	be	be	AUX
ejde-397	695	19	easily	easily	ADV
ejde-397	695	20	checked	check	VERB
ejde-397	695	21	with	with	ADP
ejde-397	695	22	the	the	DET
ejde-397	695	23	help	help	NOUN
ejde-397	695	24	of	of	ADP
ejde-397	695	25	theorem	theorem	NOUN
ejde-397	695	26	2.4(i	2.4(i	NUM
ejde-397	695	27	)	)	PUNCT
ejde-397	695	28	that	that	SCONJ
ejde-397	695	29	zn	zn	PROPN
ejde-397	695	30	(	(	PUNCT
ejde-397	695	31	·	·	PUNCT
ejde-397	695	32	)	)	PUNCT
ejde-397	695	33	is	be	AUX
ejde-397	695	34	a	a	DET
ejde-397	695	35	solution	solution	NOUN
ejde-397	695	36	of	of	ADP
ejde-397	695	37	the	the	DET
ejde-397	695	38	initial	initial	ADJ
ejde-397	695	39	value	value	NOUN
ejde-397	695	40	problem	problem	NOUN
ejde-397	695	41	:	:	PUNCT
ejde-397	695	42	zn	zn	PROPN
ejde-397	695	43	∈	∈	PROPN
ejde-397	695	44	cdαe((0,∞	cdαe((0,∞	PROPN
ejde-397	695	45	)	)	PUNCT
ejde-397	695	46	:	:	PUNCT
ejde-397	696	1	x	x	X
ejde-397	696	2	)	)	PUNCT
ejde-397	696	3	∩	∩	NOUN
ejde-397	696	4	cdαe−1([0,∞	cdαe−1([0,∞	NOUN
ejde-397	696	5	)	)	PUNCT
ejde-397	696	6	:	:	PUNCT
ejde-397	697	1	x	x	X
ejde-397	697	2	)	)	PUNCT
ejde-397	697	3	,	,	PUNCT
ejde-397	697	4	dα	dα	PROPN
ejde-397	697	5	t	t	PROPN
ejde-397	697	6	zn(t	zn(t	NUM
ejde-397	697	7	)	)	PUNCT
ejde-397	697	8	=	=	PRON
ejde-397	698	1	(	(	PUNCT
ejde-397	698	2	nλ)αzn(t)−	nλ)αzn(t)−	PROPN
ejde-397	698	3	cu(t	cu(t	PUNCT
ejde-397	698	4	)	)	PUNCT
ejde-397	698	5	,	,	PUNCT
ejde-397	698	6	t	t	X
ejde-397	698	7	>	>	X
ejde-397	698	8	0	0	NUM
ejde-397	698	9	,	,	PUNCT
ejde-397	698	10	z(j	z(j	NOUN
ejde-397	698	11	)	)	PUNCT
ejde-397	698	12	n	n	CCONJ
ejde-397	698	13	(	(	PUNCT
ejde-397	698	14	0	0	NUM
ejde-397	698	15	)	)	PUNCT
ejde-397	698	16	=	=	SYM
ejde-397	698	17	0	0	NUM
ejde-397	698	18	,	,	PUNCT
ejde-397	698	19	0	0	NUM
ejde-397	698	20	≤	≤	NUM
ejde-397	698	21	j	j	PROPN
ejde-397	698	22	≤	≤	PROPN
ejde-397	698	23	dαe	dαe	VERB
ejde-397	698	24	−	−	PROPN
ejde-397	698	25	1	1	NUM
ejde-397	698	26	.	.	PUNCT
ejde-397	699	1	this	this	PRON
ejde-397	699	2	implies	imply	VERB
ejde-397	699	3	zn(t	zn(t	NOUN
ejde-397	699	4	)	)	PUNCT
ejde-397	700	1	=	=	PUNCT
ejde-397	700	2	−(u	−(u	NOUN
ejde-397	700	3	∗	∗	X
ejde-397	700	4	·	·	SYM
ejde-397	700	5	α−1eα	α−1eα	NOUN
ejde-397	700	6	,	,	PUNCT
ejde-397	700	7	α((nλ)α·α−1))(t	α((nλ)α·α−1))(t	PROPN
ejde-397	700	8	)	)	PUNCT
ejde-397	700	9	,	,	PUNCT
ejde-397	700	10	t	t	PROPN
ejde-397	700	11	≥	≥	NUM
ejde-397	700	12	0	0	NUM
ejde-397	700	13	,	,	PUNCT
ejde-397	700	14	n	n	PRON
ejde-397	700	15	∈	∈	PROPN
ejde-397	700	16	n	n	NOUN
ejde-397	700	17	and	and	CCONJ
ejde-397	700	18	lim	lim	PROPN
ejde-397	700	19	n→∞	n→∞	NUM
ejde-397	701	1	e−nλσ	e−nλσ	PROPN
ejde-397	701	2	∫	∫	PROPN
ejde-397	701	3	t	t	PROPN
ejde-397	701	4	0	0	NUM
ejde-397	701	5	sα−1eα	sα−1eα	PROPN
ejde-397	701	6	,	,	PUNCT
ejde-397	701	7	α	α	PROPN
ejde-397	701	8	(	(	PUNCT
ejde-397	701	9	(	(	PUNCT
ejde-397	701	10	nλ)αsα	nλ)αsα	ADV
ejde-397	701	11	)	)	PUNCT
ejde-397	701	12	cu(t−	cu(t−	PROPN
ejde-397	702	1	s	s	X
ejde-397	702	2	)	)	PUNCT
ejde-397	702	3	ds	ds	NOUN
ejde-397	702	4	=	=	SYM
ejde-397	702	5	0	0	NUM
ejde-397	702	6	(	(	PUNCT
ejde-397	702	7	t	t	X
ejde-397	702	8	>	>	X
ejde-397	702	9	0	0	PROPN
ejde-397	702	10	,	,	PUNCT
ejde-397	702	11	σ	σ	X
ejde-397	702	12	>	>	X
ejde-397	702	13	0	0	NUM
ejde-397	702	14	)	)	PUNCT
ejde-397	702	15	.	.	PUNCT
ejde-397	703	1	now	now	ADV
ejde-397	703	2	we	we	PRON
ejde-397	703	3	can	can	AUX
ejde-397	703	4	argue	argue	VERB
ejde-397	703	5	as	as	ADP
ejde-397	703	6	in	in	ADP
ejde-397	703	7	the	the	DET
ejde-397	703	8	second	second	ADJ
ejde-397	703	9	part	part	NOUN
ejde-397	703	10	of	of	ADP
ejde-397	703	11	proof	proof	NOUN
ejde-397	703	12	of	of	ADP
ejde-397	703	13	[	[	X
ejde-397	703	14	36	36	NUM
ejde-397	703	15	,	,	PUNCT
ejde-397	703	16	theorem	theorem	VERB
ejde-397	703	17	2.1.34	2.1.34	NUM
ejde-397	703	18	]	]	PUNCT
ejde-397	703	19	so	so	SCONJ
ejde-397	703	20	as	as	SCONJ
ejde-397	703	21	to	to	PART
ejde-397	703	22	conclude	conclude	VERB
ejde-397	703	23	that	that	SCONJ
ejde-397	703	24	u(t	u(t	NOUN
ejde-397	703	25	)	)	PUNCT
ejde-397	703	26	=	=	SYM
ejde-397	703	27	0	0	NUM
ejde-397	703	28	,	,	PUNCT
ejde-397	703	29	t	t	PROPN
ejde-397	703	30	≥	≥	NOUN
ejde-397	703	31	0	0	PUNCT
ejde-397	703	32	(	(	PUNCT
ejde-397	703	33	in	in	ADP
ejde-397	703	34	the	the	DET
ejde-397	703	35	case	case	NOUN
ejde-397	703	36	that	that	SCONJ
ejde-397	703	37	α	α	PROPN
ejde-397	703	38	∈	∈	PROPN
ejde-397	703	39	n	n	CCONJ
ejde-397	703	40	,	,	PUNCT
ejde-397	703	41	the	the	DET
ejde-397	703	42	assertion	assertion	NOUN
ejde-397	703	43	can	can	AUX
ejde-397	703	44	be	be	AUX
ejde-397	703	45	proved	prove	VERB
ejde-397	703	46	by	by	ADP
ejde-397	703	47	a	a	DET
ejde-397	703	48	trustworthy	trustworthy	ADJ
ejde-397	703	49	passing	passing	NOUN
ejde-397	703	50	to	to	ADP
ejde-397	703	51	the	the	DET
ejde-397	703	52	theory	theory	NOUN
ejde-397	703	53	of	of	ADP
ejde-397	703	54	abstract	abstract	ADJ
ejde-397	703	55	cauchy	cauchy	ADJ
ejde-397	703	56	problems	problem	NOUN
ejde-397	703	57	of	of	ADP
ejde-397	703	58	first	first	ADJ
ejde-397	703	59	order	order	NOUN
ejde-397	703	60	since	since	SCONJ
ejde-397	703	61	[	[	X
ejde-397	703	62	36	36	NUM
ejde-397	703	63	,	,	PUNCT
ejde-397	703	64	lemma	lemma	PROPN
ejde-397	703	65	2.1.33(i	2.1.33(i	NUM
ejde-397	703	66	)	)	PUNCT
ejde-397	703	67	]	]	PUNCT
ejde-397	703	68	admits	admit	VERB
ejde-397	703	69	an	an	DET
ejde-397	703	70	extension	extension	NOUN
ejde-397	703	71	to	to	ADP
ejde-397	703	72	multivalued	multivalued	ADJ
ejde-397	703	73	linear	linear	ADJ
ejde-397	703	74	operators	operator	NOUN
ejde-397	703	75	)	)	PUNCT
ejde-397	703	76	.	.	PUNCT
ejde-397	704	1	�	�	PROPN
ejde-397	704	2	remark	remark	VERB
ejde-397	704	3	4.7	4.7	NUM
ejde-397	704	4	.	.	PUNCT
ejde-397	705	1	observe	observe	VERB
ejde-397	705	2	that	that	SCONJ
ejde-397	705	3	,	,	PUNCT
ejde-397	705	4	in	in	ADP
ejde-397	705	5	the	the	DET
ejde-397	705	6	formulation	formulation	NOUN
ejde-397	705	7	of	of	ADP
ejde-397	705	8	theorem	theorem	NOUN
ejde-397	705	9	4.6	4.6	NUM
ejde-397	705	10	,	,	PUNCT
ejde-397	705	11	we	we	PRON
ejde-397	705	12	do	do	AUX
ejde-397	705	13	not	not	PART
ejde-397	705	14	require	require	VERB
ejde-397	705	15	any	any	DET
ejde-397	705	16	type	type	NOUN
ejde-397	705	17	of	of	ADP
ejde-397	705	18	closedness	closedness	NOUN
ejde-397	705	19	of	of	ADP
ejde-397	705	20	the	the	DET
ejde-397	705	21	operator	operator	NOUN
ejde-397	705	22	a.	a.	NOUN
ejde-397	705	23	the	the	DET
ejde-397	705	24	following	follow	VERB
ejde-397	705	25	theorem	theorem	NOUN
ejde-397	705	26	is	be	AUX
ejde-397	705	27	very	very	ADV
ejde-397	705	28	similar	similar	ADJ
ejde-397	705	29	to	to	ADP
ejde-397	705	30	[	[	X
ejde-397	705	31	5	5	NUM
ejde-397	705	32	,	,	PUNCT
ejde-397	705	33	theorem	theorem	VERB
ejde-397	705	34	3.1	3.1	NUM
ejde-397	705	35	,	,	PUNCT
ejde-397	705	36	theorem	theorem	VERB
ejde-397	705	37	3.3	3.3	NUM
ejde-397	705	38	]	]	PUNCT
ejde-397	705	39	and	and	CCONJ
ejde-397	705	40	[	[	X
ejde-397	705	41	36	36	NUM
ejde-397	705	42	,	,	PUNCT
ejde-397	705	43	theorem	theorem	VERB
ejde-397	705	44	2.4.2	2.4.2	NOUN
ejde-397	705	45	]	]	PUNCT
ejde-397	705	46	.	.	PUNCT
ejde-397	706	1	because	because	SCONJ
ejde-397	706	2	of	of	ADP
ejde-397	706	3	its	its	PRON
ejde-397	706	4	importance	importance	NOUN
ejde-397	706	5	,	,	PUNCT
ejde-397	706	6	we	we	PRON
ejde-397	706	7	will	will	AUX
ejde-397	706	8	include	include	VERB
ejde-397	706	9	the	the	DET
ejde-397	706	10	most	most	ADV
ejde-397	706	11	relevant	relevant	ADJ
ejde-397	706	12	details	detail	NOUN
ejde-397	706	13	of	of	ADP
ejde-397	706	14	proof	proof	NOUN
ejde-397	706	15	.	.	PUNCT
ejde-397	707	1	theorem	theorem	VERB
ejde-397	707	2	4.8	4.8	NUM
ejde-397	707	3	(	(	PUNCT
ejde-397	707	4	subordination	subordination	NOUN
ejde-397	707	5	principle	principle	NOUN
ejde-397	707	6	for	for	ADP
ejde-397	707	7	abstract	abstract	ADJ
ejde-397	707	8	time	time	NOUN
ejde-397	707	9	-	-	PUNCT
ejde-397	707	10	fractional	fractional	ADJ
ejde-397	707	11	inclusions	inclusion	NOUN
ejde-397	707	12	)	)	PUNCT
ejde-397	707	13	.	.	PUNCT
ejde-397	708	1	suppose	suppose	VERB
ejde-397	708	2	that	that	SCONJ
ejde-397	708	3	0	0	NUM
ejde-397	708	4	<	<	X
ejde-397	708	5	α	α	X
ejde-397	708	6	<	<	X
ejde-397	708	7	β	β	X
ejde-397	708	8	,	,	PUNCT
ejde-397	708	9	γ	γ	X
ejde-397	708	10	=	=	SYM
ejde-397	708	11	α	α	PROPN
ejde-397	708	12	/	/	SYM
ejde-397	708	13	β	β	PROPN
ejde-397	708	14	,	,	PUNCT
ejde-397	708	15	a	a	PRON
ejde-397	708	16	:	:	PUNCT
ejde-397	708	17	x	x	X
ejde-397	708	18	→	→	X
ejde-397	708	19	p	p	X
ejde-397	708	20	(	(	PUNCT
ejde-397	708	21	y	y	PROPN
ejde-397	708	22	)	)	PUNCT
ejde-397	708	23	is	be	AUX
ejde-397	708	24	an	an	DET
ejde-397	708	25	mlo	mlo	PROPN
ejde-397	708	26	,	,	PUNCT
ejde-397	708	27	b	b	PROPN
ejde-397	708	28	=	=	SYM
ejde-397	708	29	b	b	PROPN
ejde-397	708	30	:	:	PUNCT
ejde-397	708	31	d(b	d(b	X
ejde-397	708	32	)	)	PUNCT
ejde-397	709	1	⊆	⊆	NUM
ejde-397	709	2	x	x	SYM
ejde-397	709	3	→	→	SYM
ejde-397	709	4	y	y	PROPN
ejde-397	709	5	is	be	AUX
ejde-397	709	6	a	a	DET
ejde-397	709	7	single	single	ADV
ejde-397	709	8	-	-	PUNCT
ejde-397	709	9	valued	value	VERB
ejde-397	709	10	linear	linear	NOUN
ejde-397	709	11	operator	operator	NOUN
ejde-397	709	12	,	,	PUNCT
ejde-397	709	13	a	a	PRON
ejde-397	709	14	is	be	AUX
ejde-397	709	15	xa×ya	xa×ya	PROPN
ejde-397	709	16	-	-	PUNCT
ejde-397	709	17	closed	closed	ADJ
ejde-397	709	18	and	and	CCONJ
ejde-397	709	19	b	b	NOUN
ejde-397	709	20	is	be	AUX
ejde-397	709	21	xb	xb	PROPN
ejde-397	709	22	×ybclosed	×ybclose	VERB
ejde-397	709	23	,	,	PUNCT
ejde-397	709	24	where	where	SCONJ
ejde-397	709	25	xa	xa	PROPN
ejde-397	709	26	↪	↪	PROPN
ejde-397	709	27	→	→	SYM
ejde-397	709	28	xb	xb	PROPN
ejde-397	709	29	and	and	CCONJ
ejde-397	709	30	ya	ya	PROPN
ejde-397	709	31	↪	↪	PROPN
ejde-397	709	32	→	→	SYM
ejde-397	709	33	yb	yb	PROPN
ejde-397	709	34	.	.	PROPN
ejde-397	709	35	assume	assume	VERB
ejde-397	709	36	,	,	PUNCT
ejde-397	709	37	further	far	ADV
ejde-397	709	38	,	,	PUNCT
ejde-397	709	39	that	that	SCONJ
ejde-397	709	40	fβ	fβ	PROPN
ejde-397	709	41	∈	∈	PROPN
ejde-397	709	42	ltor	ltor	NOUN
ejde-397	709	43	−	−	PROPN
ejde-397	709	44	ya	ya	PROPN
ejde-397	709	45	is	be	AUX
ejde-397	709	46	single	single	ADV
ejde-397	709	47	-	-	PUNCT
ejde-397	709	48	valued	value	VERB
ejde-397	709	49	and	and	CCONJ
ejde-397	709	50	there	there	PRON
ejde-397	709	51	exists	exist	VERB
ejde-397	709	52	a	a	DET
ejde-397	709	53	presolution	presolution	NOUN
ejde-397	709	54	(	(	PUNCT
ejde-397	709	55	or	or	CCONJ
ejde-397	709	56	,	,	PUNCT
ejde-397	709	57	equivalently	equivalently	ADV
ejde-397	709	58	,	,	PUNCT
ejde-397	709	59	solution	solution	NOUN
ejde-397	709	60	)	)	PUNCT
ejde-397	709	61	u(t	u(t	NOUN
ejde-397	709	62	)	)	PUNCT
ejde-397	709	63	:	:	PUNCT
ejde-397	709	64	=	=	NOUN
ejde-397	709	65	uβ(t	uβ(t	X
ejde-397	709	66	)	)	PUNCT
ejde-397	709	67	of	of	ADP
ejde-397	709	68	(	(	PUNCT
ejde-397	709	69	1.1	1.1	NUM
ejde-397	709	70	)	)	PUNCT
ejde-397	709	71	,	,	PUNCT
ejde-397	709	72	with	with	ADP
ejde-397	709	73	τ	τ	PROPN
ejde-397	709	74	=	=	SYM
ejde-397	709	75	∞	∞	PROPN
ejde-397	709	76	,	,	PUNCT
ejde-397	709	77	a(t	a(t	NOUN
ejde-397	709	78	)	)	PUNCT
ejde-397	709	79	=	=	SYM
ejde-397	709	80	gβ(t	gβ(t	NOUN
ejde-397	709	81	)	)	PUNCT
ejde-397	709	82	and	and	CCONJ
ejde-397	709	83	f	f	X
ejde-397	709	84	=	=	SYM
ejde-397	709	85	fβ	fβ	ADJ
ejde-397	709	86	,	,	PUNCT
ejde-397	709	87	satisfying	satisfy	VERB
ejde-397	709	88	that	that	SCONJ
ejde-397	709	89	uβ	uβ	PROPN
ejde-397	709	90	∈	∈	PROPN
ejde-397	709	91	ltor−xb	ltor−xb	ADJ
ejde-397	709	92	,	,	PUNCT
ejde-397	709	93	buβ	buβ	NOUN
ejde-397	709	94	∈	∈	PROPN
ejde-397	709	95	ltor−ya	ltor−ya	NOUN
ejde-397	709	96	,	,	PUNCT
ejde-397	709	97	gβ∗uβ	gβ∗uβ	PROPN
ejde-397	709	98	∈	∈	PROPN
ejde-397	709	99	ltor−xa	ltor−xa	NOUN
ejde-397	709	100	and	and	CCONJ
ejde-397	709	101	that	that	SCONJ
ejde-397	709	102	for	for	ADP
ejde-397	709	103	each	each	DET
ejde-397	709	104	seminorm	seminorm	NOUN
ejde-397	709	105	p	p	PROPN
ejde-397	709	106	∈	∈	PROPN
ejde-397	709	107	~xb	~xb	PROPN
ejde-397	709	108	there	there	PRON
ejde-397	709	109	exists	exist	VERB
ejde-397	709	110	ωp	ωp	PRON
ejde-397	709	111	≥	≥	NOUN
ejde-397	709	112	0	0	NUM
ejde-397	709	113	such	such	ADJ
ejde-397	709	114	that	that	SCONJ
ejde-397	709	115	p(uβ(t	p(uβ(t	NOUN
ejde-397	709	116	)	)	PUNCT
ejde-397	709	117	)	)	PUNCT
ejde-397	710	1	=	=	SYM
ejde-397	710	2	o(eωpt	o(eωpt	PROPN
ejde-397	710	3	)	)	PUNCT
ejde-397	710	4	,	,	PUNCT
ejde-397	710	5	t	t	PROPN
ejde-397	710	6	≥	≥	NUM
ejde-397	710	7	0	0	NUM
ejde-397	710	8	,	,	PUNCT
ejde-397	710	9	p	p	PRON
ejde-397	710	10	∈	∈	PROPN
ejde-397	710	11	~xb	~xb	PROPN
ejde-397	710	12	.	.	PUNCT
ejde-397	711	1	we	we	PRON
ejde-397	711	2	define	define	VERB
ejde-397	711	3	uα(t	uα(t	NOUN
ejde-397	711	4	)	)	PUNCT
ejde-397	711	5	:	:	PUNCT
ejde-397	712	1	=	=	SYM
ejde-397	712	2	∫	∫	PROPN
ejde-397	712	3	∞	∞	NUM
ejde-397	712	4	0	0	NUM
ejde-397	712	5	t−γφγ	t−γφγ	NOUN
ejde-397	712	6	(	(	PUNCT
ejde-397	712	7	st−γ	st−γ	NOUN
ejde-397	712	8	)	)	PUNCT
ejde-397	712	9	uβ(s	uβ(s	PUNCT
ejde-397	712	10	)	)	PUNCT
ejde-397	712	11	ds	ds	PROPN
ejde-397	712	12	,	,	PUNCT
ejde-397	712	13	t	t	NOUN
ejde-397	712	14	>	>	X
ejde-397	712	15	0	0	PUNCT
ejde-397	712	16	and	and	CCONJ
ejde-397	712	17	uα(0	uα(0	PROPN
ejde-397	712	18	)	)	PUNCT
ejde-397	712	19	:	:	PUNCT
ejde-397	712	20	=	=	SYM
ejde-397	712	21	uβ(0	uβ(0	NOUN
ejde-397	712	22	)	)	PUNCT
ejde-397	712	23	;	;	PUNCT
ejde-397	713	1	fα(t)x	fα(t)x	X
ejde-397	713	2	:	:	PUNCT
ejde-397	713	3	=	=	SYM
ejde-397	713	4	∫	∫	PROPN
ejde-397	713	5	∞	∞	NUM
ejde-397	713	6	0	0	NUM
ejde-397	713	7	t−γφγ	t−γφγ	NOUN
ejde-397	713	8	(	(	PUNCT
ejde-397	713	9	st−γ	st−γ	NOUN
ejde-397	713	10	)	)	PUNCT
ejde-397	713	11	fβ(s	fβ(	NOUN
ejde-397	713	12	)	)	PUNCT
ejde-397	713	13	ds	ds	PROPN
ejde-397	713	14	,	,	PUNCT
ejde-397	713	15	t	t	NOUN
ejde-397	713	16	>	>	X
ejde-397	713	17	0	0	PUNCT
ejde-397	713	18	and	and	CCONJ
ejde-397	713	19	fα(0	fα(0	NOUN
ejde-397	713	20	)	)	PUNCT
ejde-397	713	21	:	:	PUNCT
ejde-397	713	22	=	=	SYM
ejde-397	713	23	fβ(0	fβ(0	NOUN
ejde-397	713	24	)	)	PUNCT
ejde-397	713	25	.	.	PUNCT
ejde-397	714	1	then	then	ADV
ejde-397	714	2	uα(t	uα(t	VERB
ejde-397	714	3	)	)	PUNCT
ejde-397	714	4	is	be	AUX
ejde-397	714	5	a	a	DET
ejde-397	714	6	solution	solution	NOUN
ejde-397	714	7	of	of	ADP
ejde-397	714	8	(	(	PUNCT
ejde-397	714	9	1.1	1.1	NUM
ejde-397	714	10	)	)	PUNCT
ejde-397	714	11	,	,	PUNCT
ejde-397	714	12	with	with	ADP
ejde-397	714	13	τ	τ	PROPN
ejde-397	714	14	=	=	SYM
ejde-397	714	15	∞	∞	PROPN
ejde-397	714	16	,	,	PUNCT
ejde-397	714	17	a(t	a(t	NOUN
ejde-397	714	18	)	)	PUNCT
ejde-397	714	19	=	=	SYM
ejde-397	714	20	gα(t	gα(t	NOUN
ejde-397	714	21	)	)	PUNCT
ejde-397	714	22	and	and	CCONJ
ejde-397	714	23	f(t	f(t	NOUN
ejde-397	714	24	)	)	PUNCT
ejde-397	714	25	=	=	PUNCT
ejde-397	714	26	fα(t	fα(t	X
ejde-397	714	27	)	)	PUNCT
ejde-397	714	28	∈	∈	PROPN
ejde-397	714	29	ltor−ya	ltor−ya	NOUN
ejde-397	714	30	,	,	PUNCT
ejde-397	714	31	satisfying	satisfy	VERB
ejde-397	714	32	additionally	additionally	ADV
ejde-397	714	33	that	that	SCONJ
ejde-397	714	34	uα	uα	PROPN
ejde-397	714	35	∈	∈	PROPN
ejde-397	714	36	ltor−xb	ltor−xb	ADV
ejde-397	714	37	,	,	PUNCT
ejde-397	714	38	buα	buα	NOUN
ejde-397	714	39	∈	∈	PROPN
ejde-397	714	40	ltor−ya	ltor−ya	NOUN
ejde-397	714	41	,	,	PUNCT
ejde-397	714	42	gα∗uα	gα∗uα	PROPN
ejde-397	714	43	∈	∈	PROPN
ejde-397	714	44	ltor	ltor	NOUN
ejde-397	714	45	−xa	−xa	PROPN
ejde-397	714	46	and	and	CCONJ
ejde-397	714	47	p	p	X
ejde-397	714	48	(	(	PUNCT
ejde-397	714	49	uα(t	uα(t	X
ejde-397	714	50	)	)	PUNCT
ejde-397	714	51	)	)	PUNCT
ejde-397	715	1	=	=	PUNCT
ejde-397	715	2	o	o	NOUN
ejde-397	715	3	(	(	PUNCT
ejde-397	715	4	exp	exp	X
ejde-397	715	5	(	(	PUNCT
ejde-397	715	6	ω1	ω1	PROPN
ejde-397	715	7	/	/	SYM
ejde-397	715	8	γ	γ	PROPN
ejde-397	715	9	p	p	PROPN
ejde-397	715	10	t	t	PROPN
ejde-397	715	11	)	)	PUNCT
ejde-397	715	12	)	)	PUNCT
ejde-397	715	13	,	,	PUNCT
ejde-397	715	14	p	p	PROPN
ejde-397	715	15	∈	∈	PROPN
ejde-397	715	16	~xb	~xb	PROPN
ejde-397	715	17	,	,	PUNCT
ejde-397	715	18	t	t	PROPN
ejde-397	715	19	≥	≥	PROPN
ejde-397	715	20	0	0	NUM
ejde-397	715	21	.	.	PUNCT
ejde-397	716	1	(	(	PUNCT
ejde-397	716	2	4.4	4.4	NUM
ejde-397	716	3	)	)	PUNCT
ejde-397	716	4	let	let	VERB
ejde-397	716	5	p	p	X
ejde-397	716	6	∈	∈	PROPN
ejde-397	716	7	~xb	~xb	PROPN
ejde-397	716	8	be	be	AUX
ejde-397	716	9	fixed	fix	VERB
ejde-397	716	10	.	.	PUNCT
ejde-397	717	1	then	then	ADV
ejde-397	717	2	the	the	DET
ejde-397	717	3	condition	condition	NOUN
ejde-397	717	4	p	p	X
ejde-397	717	5	(	(	PUNCT
ejde-397	717	6	uβ(t	uβ(t	PUNCT
ejde-397	717	7	)	)	PUNCT
ejde-397	717	8	)	)	PUNCT
ejde-397	718	1	=	=	PUNCT
ejde-397	718	2	o	o	X
ejde-397	718	3	(	(	PUNCT
ejde-397	718	4	(	(	PUNCT
ejde-397	718	5	1	1	NUM
ejde-397	718	6	+	+	NUM
ejde-397	718	7	tξp	tξp	NOUN
ejde-397	718	8	)	)	PUNCT
ejde-397	718	9	eωpt	eωpt	NOUN
ejde-397	718	10	)	)	PUNCT
ejde-397	718	11	for	for	ADP
ejde-397	718	12	some	some	DET
ejde-397	718	13	ξp	ξp	NOUN
ejde-397	718	14	≥	≥	NOUN
ejde-397	718	15	0	0	NUM
ejde-397	718	16	,	,	PUNCT
ejde-397	718	17	(	(	PUNCT
ejde-397	718	18	4.5	4.5	NUM
ejde-397	718	19	)	)	PUNCT
ejde-397	718	20	22	22	NUM
ejde-397	718	21	m.	m.	NOUN
ejde-397	718	22	kostić	kostić	NOUN
ejde-397	719	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	719	2	resp	resp	NOUN
ejde-397	719	3	.	.	PUNCT
ejde-397	719	4	,	,	PUNCT
ejde-397	719	5	p	p	X
ejde-397	719	6	(	(	PUNCT
ejde-397	719	7	uβ(t	uβ(t	PUNCT
ejde-397	719	8	)	)	PUNCT
ejde-397	719	9	)	)	PUNCT
ejde-397	720	1	=	=	PUNCT
ejde-397	720	2	o	o	X
ejde-397	720	3	(	(	PUNCT
ejde-397	720	4	tξpeωpt	tξpeωpt	PROPN
ejde-397	720	5	)	)	PUNCT
ejde-397	720	6	,	,	PUNCT
ejde-397	720	7	t	t	PROPN
ejde-397	720	8	≥	≥	NUM
ejde-397	720	9	0	0	NUM
ejde-397	720	10	(	(	PUNCT
ejde-397	720	11	4.6	4.6	NUM
ejde-397	720	12	)	)	PUNCT
ejde-397	720	13	implies	imply	VERB
ejde-397	720	14	that	that	SCONJ
ejde-397	720	15	p	p	X
ejde-397	720	16	(	(	PUNCT
ejde-397	720	17	uα(t	uα(t	NUM
ejde-397	720	18	)	)	PUNCT
ejde-397	720	19	)	)	PUNCT
ejde-397	721	1	=	=	PUNCT
ejde-397	721	2	o	o	X
ejde-397	721	3	(	(	PUNCT
ejde-397	721	4	(	(	PUNCT
ejde-397	721	5	1	1	NUM
ejde-397	721	6	+	+	CCONJ
ejde-397	721	7	tξpγ	tξpγ	ADJ
ejde-397	721	8	)	)	PUNCT
ejde-397	721	9	(	(	PUNCT
ejde-397	721	10	1	1	NUM
ejde-397	721	11	+	+	CCONJ
ejde-397	721	12	ωpt	ωpt	NOUN
ejde-397	721	13	ξp(1−γ	ξp(1−γ	NOUN
ejde-397	721	14	)	)	PUNCT
ejde-397	721	15	)	)	PUNCT
ejde-397	721	16	exp	exp	NOUN
ejde-397	721	17	(	(	PUNCT
ejde-397	721	18	ω1	ω1	PROPN
ejde-397	721	19	/	/	SYM
ejde-397	721	20	γ	γ	PROPN
ejde-397	721	21	p	p	PROPN
ejde-397	721	22	t	t	PROPN
ejde-397	721	23	)	)	PUNCT
ejde-397	721	24	)	)	PUNCT
ejde-397	721	25	,	,	PUNCT
ejde-397	721	26	t	t	PROPN
ejde-397	721	27	≥	≥	NUM
ejde-397	721	28	0	0	NUM
ejde-397	721	29	,	,	PUNCT
ejde-397	721	30	(	(	PUNCT
ejde-397	721	31	4.7	4.7	NUM
ejde-397	721	32	)	)	PUNCT
ejde-397	721	33	resp	resp	NOUN
ejde-397	721	34	.	.	PUNCT
ejde-397	721	35	,	,	PUNCT
ejde-397	721	36	p	p	X
ejde-397	721	37	(	(	PUNCT
ejde-397	721	38	uα(t	uα(t	X
ejde-397	721	39	)	)	PUNCT
ejde-397	721	40	)	)	PUNCT
ejde-397	722	1	=	=	PUNCT
ejde-397	722	2	o	o	NOUN
ejde-397	722	3	(	(	PUNCT
ejde-397	722	4	tξpγ	tξpγ	X
ejde-397	722	5	(	(	PUNCT
ejde-397	722	6	1	1	NUM
ejde-397	722	7	+	+	NUM
ejde-397	722	8	ωpt	ωpt	NOUN
ejde-397	722	9	ξp(1−γ	ξp(1−γ	NOUN
ejde-397	722	10	)	)	PUNCT
ejde-397	722	11	)	)	PUNCT
ejde-397	723	1	exp	exp	NOUN
ejde-397	723	2	(	(	PUNCT
ejde-397	723	3	ω1	ω1	PROPN
ejde-397	723	4	/	/	SYM
ejde-397	723	5	γ	γ	PROPN
ejde-397	723	6	p	p	PROPN
ejde-397	723	7	t	t	PROPN
ejde-397	723	8	)	)	PUNCT
ejde-397	723	9	)	)	PUNCT
ejde-397	723	10	,	,	PUNCT
ejde-397	723	11	t	t	PROPN
ejde-397	723	12	≥	≥	PROPN
ejde-397	723	13	0	0	NUM
ejde-397	723	14	.	.	PUNCT
ejde-397	724	1	(	(	PUNCT
ejde-397	724	2	4.8	4.8	NUM
ejde-397	724	3	)	)	PUNCT
ejde-397	724	4	furthermore	furthermore	ADV
ejde-397	724	5	,	,	PUNCT
ejde-397	724	6	the	the	DET
ejde-397	724	7	following	follow	VERB
ejde-397	724	8	holds	hold	VERB
ejde-397	724	9	:	:	PUNCT
ejde-397	724	10	(	(	PUNCT
ejde-397	724	11	i	i	NOUN
ejde-397	724	12	)	)	PUNCT
ejde-397	724	13	the	the	DET
ejde-397	724	14	mapping	mapping	NOUN
ejde-397	724	15	t	t	PROPN
ejde-397	724	16	7→	7→	NUM
ejde-397	724	17	uα(t	uα(t	NOUN
ejde-397	724	18	)	)	PUNCT
ejde-397	724	19	,	,	PUNCT
ejde-397	724	20	t	t	PROPN
ejde-397	724	21	>	>	X
ejde-397	724	22	0	0	PUNCT
ejde-397	724	23	admits	admit	VERB
ejde-397	724	24	an	an	DET
ejde-397	724	25	extension	extension	NOUN
ejde-397	724	26	to	to	PART
ejde-397	724	27	σmin	σmin	VERB
ejde-397	724	28	(	(	PUNCT
ejde-397	724	29	(	(	PUNCT
ejde-397	724	30	1	1	NUM
ejde-397	724	31	γ−1)π2	γ−1)π2	NUM
ejde-397	724	32	,	,	PUNCT
ejde-397	724	33	π	π	PROPN
ejde-397	724	34	)	)	PUNCT
ejde-397	724	35	and	and	CCONJ
ejde-397	724	36	the	the	DET
ejde-397	724	37	mapping	mapping	NOUN
ejde-397	724	38	z	z	NOUN
ejde-397	724	39	7→	7→	NUM
ejde-397	724	40	uα(z	uα(z	NOUN
ejde-397	724	41	)	)	PUNCT
ejde-397	724	42	,	,	PUNCT
ejde-397	724	43	z	z	PROPN
ejde-397	724	44	∈	∈	PROPN
ejde-397	724	45	σmin	σmin	NOUN
ejde-397	724	46	(	(	PUNCT
ejde-397	724	47	(	(	PUNCT
ejde-397	724	48	1	1	NUM
ejde-397	724	49	γ−1)π2	γ−1)π2	NUM
ejde-397	724	50	,	,	PUNCT
ejde-397	724	51	π	π	X
ejde-397	724	52	)	)	PUNCT
ejde-397	724	53	is	be	AUX
ejde-397	724	54	analytic	analytic	ADJ
ejde-397	724	55	.	.	PUNCT
ejde-397	725	1	(	(	PUNCT
ejde-397	725	2	ii	ii	NOUN
ejde-397	725	3	)	)	PUNCT
ejde-397	725	4	let	let	VERB
ejde-397	725	5	ε	ε	PROPN
ejde-397	725	6	∈	∈	PROPN
ejde-397	725	7	(	(	PUNCT
ejde-397	725	8	0,min	0,min	PROPN
ejde-397	725	9	(	(	PUNCT
ejde-397	725	10	(	(	PUNCT
ejde-397	725	11	1	1	NUM
ejde-397	725	12	γ	γ	PROPN
ejde-397	725	13	−	−	PROPN
ejde-397	725	14	1)π2	1)π2	PROPN
ejde-397	725	15	,	,	PUNCT
ejde-397	725	16	π	π	PROPN
ejde-397	725	17	)	)	PUNCT
ejde-397	725	18	)	)	PUNCT
ejde-397	725	19	.	.	PUNCT
ejde-397	726	1	if	if	SCONJ
ejde-397	726	2	,	,	PUNCT
ejde-397	726	3	for	for	ADP
ejde-397	726	4	every	every	DET
ejde-397	726	5	p	p	PROPN
ejde-397	726	6	∈	∈	PROPN
ejde-397	726	7	~	~	PUNCT
ejde-397	726	8	,	,	PUNCT
ejde-397	726	9	one	one	NUM
ejde-397	726	10	has	have	VERB
ejde-397	726	11	ωp	ωp	NOUN
ejde-397	726	12	=	=	SYM
ejde-397	726	13	0	0	NUM
ejde-397	726	14	,	,	PUNCT
ejde-397	726	15	then	then	ADV
ejde-397	726	16	for	for	ADP
ejde-397	726	17	each	each	DET
ejde-397	726	18	θ	θ	PROPN
ejde-397	726	19	∈	∈	PROPN
ejde-397	726	20	(	(	PUNCT
ejde-397	726	21	0,min	0,min	PROPN
ejde-397	726	22	(	(	PUNCT
ejde-397	726	23	(	(	PUNCT
ejde-397	726	24	1	1	NUM
ejde-397	726	25	γ	γ	PROPN
ejde-397	726	26	−	−	PROPN
ejde-397	726	27	1)π2	1)π2	PROPN
ejde-397	726	28	,	,	PUNCT
ejde-397	726	29	π	π	PROPN
ejde-397	726	30	)	)	PUNCT
ejde-397	726	31	)	)	PUNCT
ejde-397	727	1	the	the	DET
ejde-397	727	2	following	follow	VERB
ejde-397	727	3	holds	hold	VERB
ejde-397	727	4	:	:	PUNCT
ejde-397	727	5	limz→0,z∈σθ	limz→0,z∈σθ	ADJ
ejde-397	727	6	uα(z	uα(z	NOUN
ejde-397	727	7	)	)	PUNCT
ejde-397	727	8	=	=	SYM
ejde-397	728	1	uα(0	uα(0	PROPN
ejde-397	728	2	)	)	PUNCT
ejde-397	728	3	.	.	PUNCT
ejde-397	729	1	(	(	PUNCT
ejde-397	729	2	iii	iii	X
ejde-397	729	3	)	)	PUNCT
ejde-397	729	4	if	if	SCONJ
ejde-397	729	5	ωp	ωp	ADV
ejde-397	729	6	>	>	X
ejde-397	729	7	0	0	PUNCT
ejde-397	729	8	for	for	ADP
ejde-397	729	9	some	some	DET
ejde-397	729	10	p	p	NOUN
ejde-397	729	11	∈	∈	PROPN
ejde-397	730	1	~	~	PUNCT
ejde-397	730	2	,	,	PUNCT
ejde-397	730	3	then	then	ADV
ejde-397	730	4	for	for	ADP
ejde-397	730	5	each	each	DET
ejde-397	730	6	θ	θ	PROPN
ejde-397	730	7	∈	∈	PROPN
ejde-397	730	8	(	(	PUNCT
ejde-397	730	9	0,min	0,min	PROPN
ejde-397	730	10	(	(	PUNCT
ejde-397	730	11	(	(	PUNCT
ejde-397	730	12	1	1	NUM
ejde-397	730	13	γ	γ	PROPN
ejde-397	730	14	−	−	PROPN
ejde-397	730	15	1)π2	1)π2	PROPN
ejde-397	730	16	,	,	PUNCT
ejde-397	730	17	π	π	PROPN
ejde-397	730	18	2	2	NUM
ejde-397	730	19	)	)	PUNCT
ejde-397	730	20	)	)	PUNCT
ejde-397	731	1	the	the	DET
ejde-397	731	2	following	follow	VERB
ejde-397	731	3	holds	hold	VERB
ejde-397	731	4	:	:	PUNCT
ejde-397	731	5	limz→0,z∈σθ	limz→0,z∈σθ	ADJ
ejde-397	731	6	uα(z	uα(z	NOUN
ejde-397	731	7	)	)	PUNCT
ejde-397	731	8	=	=	SYM
ejde-397	732	1	uα(0	uα(0	ADJ
ejde-397	732	2	)	)	PUNCT
ejde-397	732	3	.	.	PUNCT
ejde-397	733	1	proof	proof	NOUN
ejde-397	733	2	.	.	PUNCT
ejde-397	734	1	the	the	DET
ejde-397	734	2	proofs	proof	NOUN
ejde-397	734	3	of	of	ADP
ejde-397	734	4	(	(	PUNCT
ejde-397	734	5	i)-(iii	i)-(iii	NOUN
ejde-397	734	6	)	)	PUNCT
ejde-397	734	7	follows	follow	VERB
ejde-397	734	8	similarly	similarly	ADV
ejde-397	734	9	as	as	ADP
ejde-397	734	10	in	in	ADP
ejde-397	734	11	that	that	PRON
ejde-397	734	12	of	of	ADP
ejde-397	734	13	[	[	X
ejde-397	734	14	5	5	NUM
ejde-397	734	15	,	,	PUNCT
ejde-397	734	16	theorem	theorem	VERB
ejde-397	734	17	3.3	3.3	NUM
ejde-397	734	18	]	]	PUNCT
ejde-397	734	19	,	,	PUNCT
ejde-397	734	20	while	while	SCONJ
ejde-397	734	21	the	the	DET
ejde-397	734	22	proof	proof	NOUN
ejde-397	734	23	that	that	SCONJ
ejde-397	734	24	the	the	DET
ejde-397	734	25	condition	condition	NOUN
ejde-397	734	26	(	(	PUNCT
ejde-397	734	27	4.5	4.5	NUM
ejde-397	734	28	)	)	PUNCT
ejde-397	734	29	,	,	PUNCT
ejde-397	734	30	resp	resp	NOUN
ejde-397	734	31	.	.	PUNCT
ejde-397	734	32	(	(	PUNCT
ejde-397	734	33	4.6	4.6	NUM
ejde-397	734	34	)	)	PUNCT
ejde-397	734	35	,	,	PUNCT
ejde-397	734	36	implies	imply	VERB
ejde-397	734	37	(	(	PUNCT
ejde-397	734	38	4.7	4.7	NUM
ejde-397	734	39	)	)	PUNCT
ejde-397	734	40	,	,	PUNCT
ejde-397	734	41	resp	resp	NOUN
ejde-397	734	42	.	.	PUNCT
ejde-397	735	1	(	(	PUNCT
ejde-397	735	2	4.8	4.8	NUM
ejde-397	735	3	)	)	PUNCT
ejde-397	735	4	,	,	PUNCT
ejde-397	735	5	follows	follow	VERB
ejde-397	735	6	similarly	similarly	ADV
ejde-397	735	7	as	as	ADP
ejde-397	735	8	in	in	ADP
ejde-397	735	9	that	that	PRON
ejde-397	735	10	of	of	ADP
ejde-397	735	11	[	[	X
ejde-397	735	12	36	36	NUM
ejde-397	735	13	,	,	PUNCT
ejde-397	735	14	theorem	theorem	VERB
ejde-397	735	15	2.4.2	2.4.2	NOUN
ejde-397	735	16	]	]	PUNCT
ejde-397	735	17	.	.	PUNCT
ejde-397	736	1	furthermore	furthermore	ADV
ejde-397	736	2	,	,	PUNCT
ejde-397	736	3	it	it	PRON
ejde-397	736	4	can	can	AUX
ejde-397	736	5	be	be	AUX
ejde-397	736	6	easily	easily	ADV
ejde-397	736	7	seen	see	VERB
ejde-397	736	8	that	that	SCONJ
ejde-397	736	9	the	the	DET
ejde-397	736	10	estimate	estimate	NOUN
ejde-397	736	11	(	(	PUNCT
ejde-397	736	12	4.4	4.4	NUM
ejde-397	736	13	)	)	PUNCT
ejde-397	736	14	holds	hold	VERB
ejde-397	736	15	for	for	ADP
ejde-397	736	16	solution	solution	NOUN
ejde-397	736	17	uα	uα	PROPN
ejde-397	736	18	(	(	PUNCT
ejde-397	736	19	·	·	PUNCT
ejde-397	736	20	)	)	PUNCT
ejde-397	736	21	.	.	PUNCT
ejde-397	737	1	by	by	ADP
ejde-397	737	2	theorem	theorem	NOUN
ejde-397	737	3	4.3	4.3	NUM
ejde-397	737	4	,	,	PUNCT
ejde-397	737	5	we	we	PRON
ejde-397	737	6	should	should	AUX
ejde-397	737	7	only	only	ADV
ejde-397	737	8	show	show	VERB
ejde-397	737	9	that	that	SCONJ
ejde-397	737	10	uα	uα	PROPN
ejde-397	737	11	∈	∈	PROPN
ejde-397	737	12	ltor	ltor	NOUN
ejde-397	737	13	−xb	−xb	ADV
ejde-397	737	14	,	,	PUNCT
ejde-397	737	15	buα	buα	PROPN
ejde-397	737	16	∈	∈	PROPN
ejde-397	737	17	ltor	ltor	NOUN
ejde-397	737	18	−	−	PROPN
ejde-397	737	19	ya	ya	PROPN
ejde-397	737	20	,	,	PUNCT
ejde-397	737	21	fα	fα	ADP
ejde-397	737	22	∈	∈	NOUN
ejde-397	737	23	ltor	ltor	NOUN
ejde-397	737	24	−	−	PROPN
ejde-397	737	25	ya	ya	PROPN
ejde-397	737	26	,	,	PUNCT
ejde-397	737	27	gα	gα	ADP
ejde-397	737	28	∗	∗	NOUN
ejde-397	737	29	uα	uα	PROPN
ejde-397	737	30	∈	∈	PROPN
ejde-397	737	31	ltor	ltor	NOUN
ejde-397	737	32	−xa	−xa	PROPN
ejde-397	737	33	and	and	CCONJ
ejde-397	737	34	b̃uα(λ)−	b̃uα(λ)−	ADV
ejde-397	737	35	f̃α(λ	f̃α(λ	NUM
ejde-397	737	36	)	)	PUNCT
ejde-397	737	37	∈	∈	PROPN
ejde-397	737	38	λ−αaũα(λ	λ−αaũα(λ	PROPN
ejde-397	737	39	)	)	PUNCT
ejde-397	737	40	,	,	PUNCT
ejde-397	737	41	λ	λ	X
ejde-397	737	42	>	>	X
ejde-397	737	43	ω	ω	PROPN
ejde-397	737	44	suff	suff	PROPN
ejde-397	737	45	.	.	PUNCT
ejde-397	738	1	large	large	ADJ
ejde-397	738	2	.	.	PUNCT
ejde-397	739	1	(	(	PUNCT
ejde-397	739	2	4.9	4.9	NUM
ejde-397	739	3	)	)	PUNCT
ejde-397	739	4	since	since	SCONJ
ejde-397	739	5	uβ	uβ	PROPN
ejde-397	739	6	∈	∈	PROPN
ejde-397	739	7	ltor	ltor	NOUN
ejde-397	739	8	−	−	PROPN
ejde-397	739	9	xb	xb	PROPN
ejde-397	739	10	,	,	PUNCT
ejde-397	739	11	the	the	DET
ejde-397	739	12	proof	proof	NOUN
ejde-397	739	13	of	of	ADP
ejde-397	739	14	[	[	X
ejde-397	739	15	5	5	NUM
ejde-397	739	16	,	,	PUNCT
ejde-397	739	17	theorem	theorem	VERB
ejde-397	739	18	3.1	3.1	NUM
ejde-397	739	19	]	]	PUNCT
ejde-397	739	20	immediately	immediately	ADV
ejde-397	739	21	implies	imply	VERB
ejde-397	739	22	that	that	SCONJ
ejde-397	739	23	uα	uα	PROPN
ejde-397	739	24	∈	∈	PROPN
ejde-397	739	25	ltor	ltor	NOUN
ejde-397	739	26	−xb	−xb	ADV
ejde-397	739	27	,	,	PUNCT
ejde-397	739	28	as	as	ADV
ejde-397	739	29	well	well	ADV
ejde-397	739	30	as	as	ADP
ejde-397	739	31	that	that	PRON
ejde-397	739	32	ũα(λ	ũα(λ	PROPN
ejde-397	739	33	)	)	PUNCT
ejde-397	740	1	=	=	SYM
ejde-397	740	2	λγ−1ũβ(λβ	λγ−1ũβ(λβ	PROPN
ejde-397	740	3	)	)	PUNCT
ejde-397	740	4	,	,	PUNCT
ejde-397	740	5	λ	λ	X
ejde-397	740	6	>	>	X
ejde-397	740	7	ω	ω	PROPN
ejde-397	740	8	suff	suff	PROPN
ejde-397	740	9	.	.	PUNCT
ejde-397	741	1	large	large	ADJ
ejde-397	741	2	.	.	PUNCT
ejde-397	742	1	similarly	similarly	ADV
ejde-397	742	2	,	,	PUNCT
ejde-397	742	3	we	we	PRON
ejde-397	742	4	have	have	VERB
ejde-397	742	5	that	that	PRON
ejde-397	742	6	fα	fα	ADP
ejde-397	742	7	∈	∈	NOUN
ejde-397	742	8	ltor	ltor	NOUN
ejde-397	742	9	−	−	PROPN
ejde-397	742	10	ya	ya	PROPN
ejde-397	742	11	and	and	CCONJ
ejde-397	742	12	f̃α(λ	f̃α(λ	NUM
ejde-397	742	13	)	)	PUNCT
ejde-397	742	14	=	=	SYM
ejde-397	742	15	λγ−1f̃β(λβ	λγ−1f̃β(λβ	PROPN
ejde-397	742	16	)	)	PUNCT
ejde-397	742	17	,	,	PUNCT
ejde-397	742	18	λ	λ	X
ejde-397	742	19	>	>	X
ejde-397	742	20	ω	ω	PROPN
ejde-397	742	21	suff	suff	PROPN
ejde-397	742	22	.	.	PUNCT
ejde-397	743	1	large	large	ADJ
ejde-397	743	2	.	.	PUNCT
ejde-397	744	1	keeping	keep	VERB
ejde-397	744	2	in	in	ADP
ejde-397	744	3	mind	mind	NOUN
ejde-397	744	4	that	that	SCONJ
ejde-397	744	5	xa	xa	PROPN
ejde-397	744	6	↪	↪	PROPN
ejde-397	744	7	→	→	SYM
ejde-397	744	8	xb	xb	PROPN
ejde-397	744	9	and	and	CCONJ
ejde-397	744	10	gβ	gβ	PROPN
ejde-397	744	11	∗	∗	NOUN
ejde-397	744	12	uβ	uβ	PROPN
ejde-397	744	13	∈	∈	PROPN
ejde-397	744	14	ltor	ltor	NOUN
ejde-397	744	15	−xa	−xa	PROPN
ejde-397	744	16	,	,	PUNCT
ejde-397	744	17	we	we	PRON
ejde-397	744	18	can	can	AUX
ejde-397	744	19	prove	prove	VERB
ejde-397	744	20	that	that	SCONJ
ejde-397	744	21	(	(	PUNCT
ejde-397	744	22	gα	gα	ADP
ejde-397	744	23	∗	∗	NOUN
ejde-397	744	24	uα	uα	PROPN
ejde-397	744	25	)	)	PUNCT
ejde-397	744	26	(	(	PUNCT
ejde-397	744	27	t	t	NOUN
ejde-397	744	28	)	)	PUNCT
ejde-397	744	29	=	=	SYM
ejde-397	745	1	∫	∫	PROPN
ejde-397	745	2	∞	∞	NUM
ejde-397	745	3	0	0	NUM
ejde-397	745	4	t−γφγ	t−γφγ	NOUN
ejde-397	745	5	(	(	PUNCT
ejde-397	745	6	st−γ	st−γ	NOUN
ejde-397	745	7	)	)	PUNCT
ejde-397	745	8	(	(	PUNCT
ejde-397	745	9	gβ	gβ	NOUN
ejde-397	745	10	∗	∗	X
ejde-397	745	11	uβ	uβ	PROPN
ejde-397	745	12	)	)	PUNCT
ejde-397	745	13	(	(	PUNCT
ejde-397	745	14	s	s	X
ejde-397	745	15	)	)	PUNCT
ejde-397	745	16	ds	ds	PROPN
ejde-397	745	17	,	,	PUNCT
ejde-397	745	18	t	t	X
ejde-397	745	19	>	>	X
ejde-397	745	20	0	0	PUNCT
ejde-397	745	21	by	by	ADP
ejde-397	745	22	performing	perform	VERB
ejde-397	745	23	the	the	DET
ejde-397	745	24	laplace	laplace	NOUN
ejde-397	745	25	transform	transform	NOUN
ejde-397	745	26	(	(	PUNCT
ejde-397	745	27	the	the	DET
ejde-397	745	28	convergence	convergence	NOUN
ejde-397	745	29	of	of	ADP
ejde-397	745	30	last	last	ADJ
ejde-397	745	31	integral	integral	NOUN
ejde-397	745	32	is	be	AUX
ejde-397	745	33	taken	take	VERB
ejde-397	745	34	for	for	ADP
ejde-397	745	35	the	the	DET
ejde-397	745	36	topology	topology	NOUN
ejde-397	745	37	of	of	ADP
ejde-397	745	38	xa	xa	PROPN
ejde-397	745	39	)	)	PUNCT
ejde-397	745	40	.	.	PUNCT
ejde-397	746	1	this	this	PRON
ejde-397	746	2	simply	simply	ADV
ejde-397	746	3	implies	imply	VERB
ejde-397	746	4	that	that	SCONJ
ejde-397	746	5	gα	gα	ADP
ejde-397	746	6	∗	∗	NOUN
ejde-397	746	7	uα	uα	PROPN
ejde-397	746	8	∈	∈	PROPN
ejde-397	746	9	ltor	ltor	NOUN
ejde-397	746	10	−	−	PROPN
ejde-397	746	11	xa	xa	PROPN
ejde-397	746	12	and	and	CCONJ
ejde-397	746	13	(	(	PUNCT
ejde-397	746	14	l(gα	l(gα	X
ejde-397	746	15	∗	∗	X
ejde-397	746	16	uα))(λ	uα))(λ	PROPN
ejde-397	746	17	)	)	PUNCT
ejde-397	746	18	=	=	SYM
ejde-397	747	1	λγ−1(l(gβ	λγ−1(l(gβ	PROPN
ejde-397	747	2	∗	∗	NOUN
ejde-397	747	3	uβ))(λγ	uβ))(λγ	PROPN
ejde-397	747	4	)	)	PUNCT
ejde-397	747	5	,	,	PUNCT
ejde-397	747	6	λ	λ	X
ejde-397	747	7	>	>	X
ejde-397	747	8	ω	ω	PROPN
ejde-397	747	9	suff	suff	PROPN
ejde-397	747	10	.	.	PUNCT
ejde-397	748	1	large	large	ADJ
ejde-397	748	2	.	.	PUNCT
ejde-397	749	1	since	since	SCONJ
ejde-397	749	2	ya	ya	PROPN
ejde-397	749	3	↪	↪	PROPN
ejde-397	749	4	→	→	SYM
ejde-397	749	5	yb	yb	PROPN
ejde-397	749	6	,	,	PUNCT
ejde-397	749	7	a	a	DET
ejde-397	749	8	similar	similar	ADJ
ejde-397	749	9	line	line	NOUN
ejde-397	749	10	of	of	ADP
ejde-397	749	11	reasoning	reasoning	NOUN
ejde-397	749	12	shows	show	VERB
ejde-397	749	13	that	that	SCONJ
ejde-397	749	14	buα(t	buα(t	VERB
ejde-397	749	15	)	)	PUNCT
ejde-397	749	16	=	=	SYM
ejde-397	749	17	∫	∫	PROPN
ejde-397	749	18	∞	∞	PROPN
ejde-397	749	19	0	0	NUM
ejde-397	749	20	t−γφγ	t−γφγ	NOUN
ejde-397	749	21	(	(	PUNCT
ejde-397	749	22	st−γ	st−γ	NOUN
ejde-397	749	23	)	)	PUNCT
ejde-397	749	24	(	(	PUNCT
ejde-397	749	25	buβ	buβ	INTJ
ejde-397	749	26	)	)	PUNCT
ejde-397	749	27	(	(	PUNCT
ejde-397	749	28	s	s	X
ejde-397	749	29	)	)	PUNCT
ejde-397	749	30	ds	ds	PROPN
ejde-397	749	31	,	,	PUNCT
ejde-397	749	32	t	t	X
ejde-397	749	33	>	>	X
ejde-397	749	34	0	0	PUNCT
ejde-397	750	1	(	(	PUNCT
ejde-397	750	2	the	the	DET
ejde-397	750	3	convergence	convergence	NOUN
ejde-397	750	4	of	of	ADP
ejde-397	750	5	this	this	DET
ejde-397	750	6	integral	integral	NOUN
ejde-397	750	7	is	be	AUX
ejde-397	750	8	taken	take	VERB
ejde-397	750	9	for	for	ADP
ejde-397	750	10	the	the	DET
ejde-397	750	11	topology	topology	NOUN
ejde-397	750	12	of	of	ADP
ejde-397	750	13	ya	ya	PROPN
ejde-397	750	14	)	)	PUNCT
ejde-397	750	15	and	and	CCONJ
ejde-397	750	16	b̃uα(λ	b̃uα(λ	NOUN
ejde-397	750	17	)	)	PUNCT
ejde-397	750	18	=	=	PUNCT
ejde-397	750	19	bũα(λ	bũα(λ	X
ejde-397	750	20	)	)	PUNCT
ejde-397	750	21	for	for	ADP
ejde-397	750	22	all	all	DET
ejde-397	750	23	sufficiently	sufficiently	ADV
ejde-397	750	24	large	large	ADJ
ejde-397	750	25	values	value	NOUN
ejde-397	750	26	of	of	ADP
ejde-397	750	27	λ	λ	PROPN
ejde-397	750	28	>	>	X
ejde-397	750	29	ω	ω	PROPN
ejde-397	750	30	.	.	PUNCT
ejde-397	751	1	the	the	DET
ejde-397	751	2	proof	proof	NOUN
ejde-397	751	3	of	of	ADP
ejde-397	751	4	(	(	PUNCT
ejde-397	751	5	4.9	4.9	NUM
ejde-397	751	6	)	)	PUNCT
ejde-397	751	7	now	now	ADV
ejde-397	751	8	follows	follow	VERB
ejde-397	751	9	from	from	ADP
ejde-397	751	10	a	a	DET
ejde-397	751	11	simple	simple	ADJ
ejde-397	751	12	computation	computation	NOUN
ejde-397	751	13	.	.	PUNCT
ejde-397	752	1	�	�	PROPN
ejde-397	752	2	we	we	PRON
ejde-397	752	3	can	can	AUX
ejde-397	752	4	similarly	similarly	ADV
ejde-397	752	5	prove	prove	VERB
ejde-397	752	6	the	the	DET
ejde-397	752	7	following	follow	VERB
ejde-397	752	8	subordination	subordination	NOUN
ejde-397	752	9	principles	principle	NOUN
ejde-397	752	10	for	for	ADP
ejde-397	752	11	abstract	abstract	ADJ
ejde-397	752	12	degenerate	degenerate	ADJ
ejde-397	752	13	volterra	volterra	NOUN
ejde-397	752	14	inclusions	inclusion	NOUN
ejde-397	752	15	in	in	ADP
ejde-397	752	16	locally	locally	ADV
ejde-397	752	17	convex	convex	ADJ
ejde-397	752	18	spaces	space	NOUN
ejde-397	752	19	(	(	PUNCT
ejde-397	752	20	cf	cf	NOUN
ejde-397	752	21	.	.	PUNCT
ejde-397	753	1	[	[	X
ejde-397	753	2	68	68	NUM
ejde-397	753	3	,	,	PUNCT
ejde-397	753	4	section	section	NOUN
ejde-397	753	5	4	4	NUM
ejde-397	753	6	]	]	PUNCT
ejde-397	753	7	and	and	CCONJ
ejde-397	753	8	[	[	X
ejde-397	753	9	36	36	NUM
ejde-397	753	10	,	,	PUNCT
ejde-397	753	11	theorem	theorem	VERB
ejde-397	753	12	2.1.8	2.1.8	NUM
ejde-397	753	13	,	,	PUNCT
ejde-397	753	14	theorem	theorem	VERB
ejde-397	753	15	2.8.7	2.8.7	NUM
ejde-397	753	16	]	]	PUNCT
ejde-397	753	17	for	for	ADP
ejde-397	753	18	more	more	ADJ
ejde-397	753	19	details	detail	NOUN
ejde-397	753	20	concerning	concern	VERB
ejde-397	753	21	non	non	ADJ
ejde-397	753	22	-	-	ADJ
ejde-397	753	23	degenerate	degenerate	ADJ
ejde-397	753	24	case	case	NOUN
ejde-397	753	25	and	and	CCONJ
ejde-397	753	26	,	,	PUNCT
ejde-397	753	27	especially	especially	ADV
ejde-397	753	28	,	,	PUNCT
ejde-397	753	29	the	the	DET
ejde-397	753	30	case	case	NOUN
ejde-397	753	31	in	in	ADP
ejde-397	753	32	which	which	PRON
ejde-397	753	33	b(t	b(t	NOUN
ejde-397	753	34	)	)	PUNCT
ejde-397	753	35	=	=	PUNCT
ejde-397	753	36	g1(t	g1(t	PROPN
ejde-397	753	37	)	)	PUNCT
ejde-397	753	38	or	or	CCONJ
ejde-397	753	39	b(t	b(t	VERB
ejde-397	753	40	)	)	PUNCT
ejde-397	753	41	=	=	SYM
ejde-397	753	42	g2(t	g2(t	PROPN
ejde-397	753	43	)	)	PUNCT
ejde-397	753	44	)	)	PUNCT
ejde-397	753	45	.	.	PUNCT
ejde-397	754	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	754	2	abstract	abstract	ADJ
ejde-397	754	3	degenerate	degenerate	ADJ
ejde-397	754	4	volterra	volterra	NOUN
ejde-397	754	5	inclusions	inclusion	NOUN
ejde-397	754	6	23	23	NUM
ejde-397	754	7	theorem	theorem	NOUN
ejde-397	754	8	4.9	4.9	NUM
ejde-397	754	9	.	.	PUNCT
ejde-397	755	1	let	let	VERB
ejde-397	755	2	b(t	b(t	PROPN
ejde-397	755	3	)	)	PUNCT
ejde-397	755	4	and	and	CCONJ
ejde-397	755	5	c(t	c(t	PROPN
ejde-397	755	6	)	)	PUNCT
ejde-397	755	7	satisfy	satisfy	NOUN
ejde-397	755	8	(	(	PUNCT
ejde-397	755	9	p1)-c	p1)-c	VERB
ejde-397	755	10	,	,	PUNCT
ejde-397	755	11	let	let	VERB
ejde-397	755	12	∫∞	∫∞	NOUN
ejde-397	755	13	0	0	PUNCT
ejde-397	756	1	e−βt|b(t)|	e−βt|b(t)|	PROPN
ejde-397	756	2	dt	dt	X
ejde-397	757	1	<	<	X
ejde-397	757	2	∞	∞	PROPN
ejde-397	757	3	for	for	ADP
ejde-397	757	4	some	some	DET
ejde-397	757	5	β	β	NOUN
ejde-397	757	6	≥	≥	NOUN
ejde-397	757	7	0	0	NUM
ejde-397	757	8	,	,	PUNCT
ejde-397	757	9	and	and	CCONJ
ejde-397	757	10	let	let	VERB
ejde-397	757	11	α	α	NOUN
ejde-397	757	12	=	=	SYM
ejde-397	757	13	c̃−1	c̃−1	PROPN
ejde-397	757	14	(	(	PUNCT
ejde-397	757	15	1	1	NUM
ejde-397	757	16	β	β	X
ejde-397	757	17	)	)	PUNCT
ejde-397	757	18	if	if	SCONJ
ejde-397	757	19	∫	∫	PROPN
ejde-397	757	20	∞	∞	PROPN
ejde-397	757	21	0	0	PUNCT
ejde-397	757	22	c(t	c(t	PROPN
ejde-397	757	23	)	)	PUNCT
ejde-397	757	24	dt	dt	NOUN
ejde-397	757	25	>	>	X
ejde-397	757	26	1	1	NUM
ejde-397	757	27	β	β	X
ejde-397	757	28	,	,	PUNCT
ejde-397	757	29	α	α	X
ejde-397	757	30	=	=	SYM
ejde-397	757	31	0	0	PUNCT
ejde-397	757	32	otherwise	otherwise	ADV
ejde-397	757	33	.	.	PUNCT
ejde-397	758	1	suppose	suppose	VERB
ejde-397	758	2	that	that	SCONJ
ejde-397	758	3	abs(|a|	abs(|a|	VERB
ejde-397	758	4	)	)	PUNCT
ejde-397	758	5	<	<	X
ejde-397	758	6	∞	∞	PROPN
ejde-397	758	7	,	,	PUNCT
ejde-397	758	8	ã(λ	ã(λ	PROPN
ejde-397	758	9	)	)	PUNCT
ejde-397	758	10	=	=	SYM
ejde-397	759	1	b̃	b̃	PROPN
ejde-397	759	2	(	(	PUNCT
ejde-397	759	3	1	1	NUM
ejde-397	759	4	c̃(λ	c̃(λ	PROPN
ejde-397	759	5	)	)	PUNCT
ejde-397	759	6	)	)	PUNCT
ejde-397	759	7	,	,	PUNCT
ejde-397	759	8	λ	λ	X
ejde-397	759	9	>	>	X
ejde-397	759	10	α	α	PROPN
ejde-397	759	11	,	,	PUNCT
ejde-397	759	12	a	a	PRON
ejde-397	759	13	:	:	PUNCT
ejde-397	759	14	x	x	X
ejde-397	759	15	→	→	X
ejde-397	759	16	p	p	X
ejde-397	759	17	(	(	PUNCT
ejde-397	759	18	y	y	PROPN
ejde-397	759	19	)	)	PUNCT
ejde-397	759	20	is	be	AUX
ejde-397	759	21	an	an	DET
ejde-397	759	22	mlo	mlo	PROPN
ejde-397	759	23	,	,	PUNCT
ejde-397	759	24	b	b	PROPN
ejde-397	759	25	=	=	SYM
ejde-397	759	26	b	b	PROPN
ejde-397	759	27	:	:	PUNCT
ejde-397	759	28	d(b	d(b	X
ejde-397	759	29	)	)	PUNCT
ejde-397	760	1	⊆	⊆	NUM
ejde-397	760	2	x	x	SYM
ejde-397	760	3	→	→	SYM
ejde-397	760	4	y	y	PROPN
ejde-397	760	5	is	be	AUX
ejde-397	760	6	a	a	DET
ejde-397	760	7	single	single	ADV
ejde-397	760	8	-	-	PUNCT
ejde-397	760	9	valued	value	VERB
ejde-397	760	10	linear	linear	NOUN
ejde-397	760	11	operator	operator	NOUN
ejde-397	760	12	,	,	PUNCT
ejde-397	760	13	a	a	PRON
ejde-397	760	14	is	be	AUX
ejde-397	760	15	xa	xa	PROPN
ejde-397	760	16	×	×	PROPN
ejde-397	760	17	ya	ya	PROPN
ejde-397	760	18	-	-	PUNCT
ejde-397	760	19	closed	close	VERB
ejde-397	760	20	and	and	CCONJ
ejde-397	760	21	b	b	NOUN
ejde-397	760	22	is	be	AUX
ejde-397	760	23	xb	xb	PROPN
ejde-397	760	24	×	×	PROPN
ejde-397	760	25	yb	yb	PROPN
ejde-397	760	26	-	-	PUNCT
ejde-397	760	27	closed	closed	ADJ
ejde-397	760	28	,	,	PUNCT
ejde-397	760	29	where	where	SCONJ
ejde-397	760	30	xa	xa	PROPN
ejde-397	760	31	↪	↪	PROPN
ejde-397	760	32	→	→	SYM
ejde-397	760	33	xb	xb	PROPN
ejde-397	760	34	and	and	CCONJ
ejde-397	760	35	ya	ya	PROPN
ejde-397	760	36	↪	↪	PROPN
ejde-397	760	37	→	→	SYM
ejde-397	760	38	yb	yb	PROPN
ejde-397	760	39	.	.	PROPN
ejde-397	761	1	assume	assume	VERB
ejde-397	761	2	,	,	PUNCT
ejde-397	761	3	further	far	ADV
ejde-397	761	4	,	,	PUNCT
ejde-397	761	5	that	that	SCONJ
ejde-397	761	6	fβ	fβ	PROPN
ejde-397	761	7	∈	∈	PROPN
ejde-397	761	8	ltor	ltor	NOUN
ejde-397	761	9	−	−	PROPN
ejde-397	761	10	ya	ya	PROPN
ejde-397	761	11	is	be	AUX
ejde-397	761	12	single	single	ADV
ejde-397	761	13	-	-	PUNCT
ejde-397	761	14	valued	value	VERB
ejde-397	761	15	and	and	CCONJ
ejde-397	761	16	there	there	PRON
ejde-397	761	17	exists	exist	VERB
ejde-397	761	18	a	a	DET
ejde-397	761	19	presolution	presolution	NOUN
ejde-397	761	20	(	(	PUNCT
ejde-397	761	21	or	or	CCONJ
ejde-397	761	22	,	,	PUNCT
ejde-397	761	23	equivalently	equivalently	ADV
ejde-397	761	24	,	,	PUNCT
ejde-397	761	25	solution	solution	NOUN
ejde-397	761	26	)	)	PUNCT
ejde-397	761	27	u(t	u(t	NOUN
ejde-397	761	28	)	)	PUNCT
ejde-397	762	1	:	:	PUNCT
ejde-397	762	2	=	=	SYM
ejde-397	762	3	ub(t	ub(t	X
ejde-397	762	4	)	)	PUNCT
ejde-397	762	5	of	of	ADP
ejde-397	762	6	(	(	PUNCT
ejde-397	762	7	1.1	1.1	NUM
ejde-397	762	8	)	)	PUNCT
ejde-397	762	9	,	,	PUNCT
ejde-397	762	10	with	with	ADP
ejde-397	762	11	τ	τ	PROPN
ejde-397	762	12	=	=	SYM
ejde-397	762	13	∞	∞	PROPN
ejde-397	762	14	,	,	PUNCT
ejde-397	762	15	a(t	a(t	NOUN
ejde-397	762	16	)	)	PUNCT
ejde-397	762	17	replaced	replace	VERB
ejde-397	762	18	with	with	ADP
ejde-397	762	19	b(t	b(t	NOUN
ejde-397	762	20	)	)	PUNCT
ejde-397	762	21	therein	therein	ADV
ejde-397	762	22	,	,	PUNCT
ejde-397	762	23	and	and	CCONJ
ejde-397	762	24	f	f	X
ejde-397	762	25	=	=	SYM
ejde-397	762	26	fb	fb	INTJ
ejde-397	762	27	,	,	PUNCT
ejde-397	762	28	satisfying	satisfy	VERB
ejde-397	762	29	that	that	SCONJ
ejde-397	762	30	ub	ub	PROPN
ejde-397	762	31	∈	∈	PROPN
ejde-397	762	32	ltor	ltor	NOUN
ejde-397	762	33	−xb	−xb	ADV
ejde-397	762	34	,	,	PUNCT
ejde-397	762	35	bub	bub	NOUN
ejde-397	762	36	∈	∈	PROPN
ejde-397	762	37	ltor	ltor	NOUN
ejde-397	762	38	−	−	PROPN
ejde-397	762	39	ya	ya	PROPN
ejde-397	762	40	,	,	PUNCT
ejde-397	762	41	b	b	PROPN
ejde-397	762	42	∗	∗	X
ejde-397	762	43	ub	ub	X
ejde-397	762	44	∈	∈	PROPN
ejde-397	762	45	ltor	ltor	NOUN
ejde-397	762	46	−xa	−xa	PROPN
ejde-397	762	47	and	and	CCONJ
ejde-397	762	48	the	the	DET
ejde-397	762	49	family	family	NOUN
ejde-397	762	50	{	{	PUNCT
ejde-397	762	51	e−ωbtub(t	e−ωbtub(t	PROPN
ejde-397	762	52	)	)	PUNCT
ejde-397	762	53	:	:	PUNCT
ejde-397	762	54	t	t	X
ejde-397	762	55	≥	≥	NOUN
ejde-397	762	56	0	0	NUM
ejde-397	762	57	}	}	PUNCT
ejde-397	762	58	is	be	AUX
ejde-397	762	59	bounded	bound	VERB
ejde-397	762	60	in	in	ADP
ejde-397	762	61	xb	xb	PROPN
ejde-397	762	62	(	(	PUNCT
ejde-397	762	63	ωb	ωb	PRON
ejde-397	762	64	≥	≥	NOUN
ejde-397	762	65	0	0	NUM
ejde-397	762	66	)	)	PUNCT
ejde-397	762	67	.	.	PUNCT
ejde-397	763	1	let	let	VERB
ejde-397	763	2	c(t	c(t	PROPN
ejde-397	763	3	)	)	PUNCT
ejde-397	763	4	be	be	AUX
ejde-397	763	5	completely	completely	ADV
ejde-397	763	6	positive	positive	ADJ
ejde-397	763	7	and	and	CCONJ
ejde-397	763	8	let	let	VERB
ejde-397	763	9	there	there	PRON
ejde-397	763	10	exist	exist	VERB
ejde-397	763	11	a	a	DET
ejde-397	763	12	function	function	NOUN
ejde-397	763	13	fa	fa	PROPN
ejde-397	763	14	∈	∈	PROPN
ejde-397	763	15	ltor−ya	ltor−ya	NOUN
ejde-397	764	1	such	such	ADJ
ejde-397	764	2	that	that	PRON
ejde-397	764	3	f̃a(λ	f̃a(λ	NOUN
ejde-397	764	4	)	)	PUNCT
ejde-397	764	5	=	=	SYM
ejde-397	764	6	1	1	NUM
ejde-397	764	7	λc̃(λ	λc̃(λ	NOUN
ejde-397	764	8	)	)	PUNCT
ejde-397	764	9	f̃b	f̃b	NOUN
ejde-397	764	10	(	(	PUNCT
ejde-397	764	11	1	1	NUM
ejde-397	764	12	c̃(λ	c̃(λ	PROPN
ejde-397	764	13	)	)	PUNCT
ejde-397	764	14	)	)	PUNCT
ejde-397	764	15	,	,	PUNCT
ejde-397	764	16	λ	λ	X
ejde-397	764	17	>	>	X
ejde-397	764	18	ω0	ω0	PROPN
ejde-397	764	19	,	,	PUNCT
ejde-397	764	20	f̃b	f̃b	X
ejde-397	764	21	(	(	PUNCT
ejde-397	764	22	1	1	NUM
ejde-397	764	23	c̃(λ	c̃(λ	PROPN
ejde-397	764	24	)	)	PUNCT
ejde-397	764	25	)	)	PUNCT
ejde-397	764	26	6=	6=	ADP
ejde-397	764	27	0	0	NUM
ejde-397	764	28	,	,	PUNCT
ejde-397	764	29	for	for	ADP
ejde-397	764	30	some	some	DET
ejde-397	764	31	ω0	ω0	NOUN
ejde-397	764	32	>	>	X
ejde-397	764	33	0	0	X
ejde-397	764	34	.	.	PUNCT
ejde-397	765	1	let	let	VERB
ejde-397	765	2	ωa	ωa	ADV
ejde-397	765	3	=	=	SYM
ejde-397	765	4	c̃−1	c̃−1	PROPN
ejde-397	765	5	(	(	PUNCT
ejde-397	765	6	1	1	NUM
ejde-397	765	7	ωb	ωb	NOUN
ejde-397	765	8	)	)	PUNCT
ejde-397	766	1	if	if	SCONJ
ejde-397	766	2	∫	∫	PROPN
ejde-397	766	3	∞	∞	PROPN
ejde-397	766	4	0	0	PUNCT
ejde-397	766	5	c(t	c(t	PROPN
ejde-397	766	6	)	)	PUNCT
ejde-397	766	7	dt	dt	NOUN
ejde-397	766	8	>	>	X
ejde-397	766	9	1	1	NUM
ejde-397	766	10	ωb	ωb	NOUN
ejde-397	766	11	,	,	PUNCT
ejde-397	766	12	ωa	ωa	PROPN
ejde-397	766	13	=	=	SYM
ejde-397	766	14	0	0	PUNCT
ejde-397	767	1	otherwise	otherwise	ADV
ejde-397	767	2	.	.	PUNCT
ejde-397	768	1	then	then	ADV
ejde-397	768	2	,	,	PUNCT
ejde-397	768	3	for	for	ADP
ejde-397	768	4	every	every	DET
ejde-397	768	5	r	r	NOUN
ejde-397	768	6	∈	∈	PROPN
ejde-397	768	7	(	(	PUNCT
ejde-397	768	8	0	0	NUM
ejde-397	768	9	,	,	PUNCT
ejde-397	768	10	1	1	NUM
ejde-397	768	11	]	]	PUNCT
ejde-397	768	12	,	,	PUNCT
ejde-397	768	13	there	there	PRON
ejde-397	768	14	exists	exist	VERB
ejde-397	768	15	a	a	DET
ejde-397	768	16	solution	solution	NOUN
ejde-397	768	17	u(t	u(t	NOUN
ejde-397	768	18	)	)	PUNCT
ejde-397	768	19	:	:	PUNCT
ejde-397	768	20	=	=	SYM
ejde-397	768	21	ua	ua	PROPN
ejde-397	768	22	,	,	PUNCT
ejde-397	768	23	r(t	r(t	NOUN
ejde-397	768	24	)	)	PUNCT
ejde-397	768	25	of	of	ADP
ejde-397	768	26	(	(	PUNCT
ejde-397	768	27	1.1	1.1	NUM
ejde-397	768	28	)	)	PUNCT
ejde-397	768	29	,	,	PUNCT
ejde-397	768	30	with	with	ADP
ejde-397	768	31	τ	τ	PROPN
ejde-397	768	32	=	=	SYM
ejde-397	768	33	∞	∞	PROPN
ejde-397	768	34	,	,	PUNCT
ejde-397	768	35	a(t	a(t	NOUN
ejde-397	768	36	)	)	PUNCT
ejde-397	768	37	and	and	CCONJ
ejde-397	768	38	f	f	X
ejde-397	768	39	=	=	NOUN
ejde-397	768	40	fr	fr	NOUN
ejde-397	768	41	:	:	PUNCT
ejde-397	768	42	=	=	SYM
ejde-397	768	43	gr	gr	ADP
ejde-397	768	44	∗	∗	X
ejde-397	768	45	fa	fa	PROPN
ejde-397	768	46	,	,	PUNCT
ejde-397	768	47	satisfying	satisfy	VERB
ejde-397	768	48	that	that	SCONJ
ejde-397	768	49	ua	ua	PRON
ejde-397	768	50	,	,	PUNCT
ejde-397	768	51	r	r	NOUN
ejde-397	768	52	∈	∈	PROPN
ejde-397	768	53	ltor	ltor	NOUN
ejde-397	768	54	−	−	PROPN
ejde-397	768	55	xb	xb	PROPN
ejde-397	768	56	,	,	PUNCT
ejde-397	768	57	bua	bua	PROPN
ejde-397	768	58	,	,	PUNCT
ejde-397	768	59	r	r	NOUN
ejde-397	768	60	∈	∈	PROPN
ejde-397	768	61	ltor	ltor	NOUN
ejde-397	768	62	−	−	PROPN
ejde-397	768	63	ya	ya	PROPN
ejde-397	768	64	,	,	PUNCT
ejde-397	768	65	a	a	DET
ejde-397	768	66	∗	∗	X
ejde-397	768	67	ua	ua	PROPN
ejde-397	768	68	,	,	PUNCT
ejde-397	768	69	r	r	NOUN
ejde-397	768	70	∈	∈	PROPN
ejde-397	768	71	ltor	ltor	NOUN
ejde-397	768	72	−xa	−xa	PROPN
ejde-397	768	73	and	and	CCONJ
ejde-397	768	74	the	the	DET
ejde-397	768	75	set	set	NOUN
ejde-397	768	76	{	{	PUNCT
ejde-397	768	77	e−ωatua	e−ωatua	NOUN
ejde-397	768	78	,	,	PUNCT
ejde-397	768	79	r(t	r(t	NOUN
ejde-397	768	80	)	)	PUNCT
ejde-397	768	81	:	:	PUNCT
ejde-397	768	82	t	t	X
ejde-397	768	83	≥	≥	NOUN
ejde-397	768	84	0	0	NUM
ejde-397	768	85	}	}	PUNCT
ejde-397	768	86	is	be	AUX
ejde-397	768	87	bounded	bound	VERB
ejde-397	768	88	in	in	ADP
ejde-397	768	89	xb	xb	PROPN
ejde-397	768	90	,	,	PUNCT
ejde-397	768	91	if	if	SCONJ
ejde-397	768	92	ωb	ωb	ADV
ejde-397	768	93	=	=	SYM
ejde-397	768	94	0	0	NUM
ejde-397	768	95	or	or	CCONJ
ejde-397	768	96	ωbc̃(0	ωbc̃(0	NOUN
ejde-397	768	97	)	)	PUNCT
ejde-397	768	98	6=	6=	ADP
ejde-397	768	99	1	1	NUM
ejde-397	768	100	,	,	PUNCT
ejde-397	768	101	resp	resp	NOUN
ejde-397	768	102	.	.	PUNCT
ejde-397	768	103	,	,	PUNCT
ejde-397	768	104	the	the	DET
ejde-397	768	105	set	set	NOUN
ejde-397	768	106	{	{	PUNCT
ejde-397	768	107	e−εtua	e−εtua	PROPN
ejde-397	768	108	,	,	PUNCT
ejde-397	768	109	r(t	r(t	NOUN
ejde-397	768	110	)	)	PUNCT
ejde-397	768	111	:	:	PUNCT
ejde-397	769	1	t	t	X
ejde-397	769	2	≥	≥	NOUN
ejde-397	769	3	0	0	NUM
ejde-397	769	4	}	}	PUNCT
ejde-397	769	5	is	be	AUX
ejde-397	769	6	bounded	bound	VERB
ejde-397	769	7	in	in	ADP
ejde-397	769	8	xb	xb	PROPN
ejde-397	769	9	for	for	ADP
ejde-397	769	10	any	any	DET
ejde-397	769	11	ε	ε	PROPN
ejde-397	769	12	>	>	X
ejde-397	769	13	0	0	PROPN
ejde-397	769	14	,	,	PUNCT
ejde-397	769	15	if	if	SCONJ
ejde-397	769	16	ωb	ωb	ADV
ejde-397	769	17	>	>	X
ejde-397	769	18	0	0	PUNCT
ejde-397	769	19	and	and	CCONJ
ejde-397	769	20	ωbc̃(0	ωbc̃(0	NOUN
ejde-397	769	21	)	)	PUNCT
ejde-397	769	22	=	=	SYM
ejde-397	769	23	1	1	X
ejde-397	769	24	.	.	PUNCT
ejde-397	770	1	furthermore	furthermore	ADV
ejde-397	770	2	,	,	PUNCT
ejde-397	770	3	the	the	DET
ejde-397	770	4	function	function	NOUN
ejde-397	770	5	t	t	PROPN
ejde-397	770	6	7→	7→	NUM
ejde-397	770	7	ua	ua	PROPN
ejde-397	770	8	,	,	PUNCT
ejde-397	770	9	r(t	r(t	NOUN
ejde-397	770	10	)	)	PUNCT
ejde-397	770	11	∈	∈	PROPN
ejde-397	770	12	xb	xb	PROPN
ejde-397	770	13	,	,	PUNCT
ejde-397	770	14	t	t	PROPN
ejde-397	770	15	≥	≥	PROPN
ejde-397	770	16	0	0	NUM
ejde-397	770	17	is	be	AUX
ejde-397	770	18	locally	locally	ADV
ejde-397	770	19	hölder	hölder	NOUN
ejde-397	770	20	continuous	continuous	ADJ
ejde-397	770	21	with	with	ADP
ejde-397	770	22	the	the	DET
ejde-397	770	23	exponent	exponent	NOUN
ejde-397	770	24	r	r	NOUN
ejde-397	770	25	∈	∈	PROPN
ejde-397	770	26	(	(	PUNCT
ejde-397	770	27	0	0	NUM
ejde-397	770	28	,	,	PUNCT
ejde-397	770	29	1	1	NUM
ejde-397	770	30	]	]	PUNCT
ejde-397	770	31	.	.	PUNCT
ejde-397	771	1	remark	remark	PROPN
ejde-397	771	2	4.10	4.10	NUM
ejde-397	771	3	.	.	PUNCT
ejde-397	772	1	(	(	PUNCT
ejde-397	772	2	i	i	NOUN
ejde-397	772	3	)	)	PUNCT
ejde-397	772	4	in	in	ADP
ejde-397	772	5	theorem	theorem	ADJ
ejde-397	772	6	4.8	4.8	NUM
ejde-397	772	7	and	and	CCONJ
ejde-397	772	8	theorem	theorem	VERB
ejde-397	772	9	4.9	4.9	NUM
ejde-397	772	10	,	,	PUNCT
ejde-397	772	11	we	we	PRON
ejde-397	772	12	have	have	AUX
ejde-397	772	13	only	only	ADV
ejde-397	772	14	proved	prove	VERB
ejde-397	772	15	the	the	DET
ejde-397	772	16	existence	existence	NOUN
ejde-397	772	17	of	of	ADP
ejde-397	772	18	a	a	DET
ejde-397	772	19	solution	solution	NOUN
ejde-397	772	20	of	of	ADP
ejde-397	772	21	the	the	DET
ejde-397	772	22	subordinated	subordinate	VERB
ejde-397	772	23	inclusion	inclusion	NOUN
ejde-397	772	24	.	.	PUNCT
ejde-397	773	1	the	the	DET
ejde-397	773	2	uniqueness	uniqueness	NOUN
ejde-397	773	3	of	of	ADP
ejde-397	773	4	solutions	solution	NOUN
ejde-397	773	5	can	can	AUX
ejde-397	773	6	be	be	AUX
ejde-397	773	7	proved	prove	VERB
ejde-397	773	8	,	,	PUNCT
ejde-397	773	9	for	for	ADP
ejde-397	773	10	example	example	NOUN
ejde-397	773	11	,	,	PUNCT
ejde-397	773	12	by	by	ADP
ejde-397	773	13	using	use	VERB
ejde-397	773	14	theorem	theorem	ADJ
ejde-397	773	15	4.5	4.5	NUM
ejde-397	773	16	,	,	PUNCT
ejde-397	773	17	theorem	theorem	VERB
ejde-397	773	18	4.6	4.6	NUM
ejde-397	773	19	or	or	CCONJ
ejde-397	773	20	[	[	X
ejde-397	773	21	36	36	NUM
ejde-397	773	22	,	,	PUNCT
ejde-397	773	23	theorem	theorem	VERB
ejde-397	773	24	2.2.6	2.2.6	NUM
ejde-397	773	25	]	]	PUNCT
ejde-397	773	26	.	.	PUNCT
ejde-397	774	1	(	(	PUNCT
ejde-397	774	2	ii	ii	NOUN
ejde-397	774	3	)	)	PUNCT
ejde-397	774	4	in	in	ADP
ejde-397	774	5	theorem	theorem	NOUN
ejde-397	774	6	4.9	4.9	NUM
ejde-397	774	7	,	,	PUNCT
ejde-397	774	8	we	we	PRON
ejde-397	774	9	have	have	AUX
ejde-397	774	10	faced	face	VERB
ejde-397	774	11	ourselves	ourselves	PRON
ejde-397	774	12	with	with	ADP
ejde-397	774	13	a	a	DET
ejde-397	774	14	loss	loss	NOUN
ejde-397	774	15	of	of	ADP
ejde-397	774	16	regularity	regularity	NOUN
ejde-397	774	17	for	for	ADP
ejde-397	774	18	solutions	solution	NOUN
ejde-397	774	19	of	of	ADP
ejde-397	774	20	the	the	DET
ejde-397	774	21	subordinated	subordinated	ADJ
ejde-397	774	22	problem	problem	NOUN
ejde-397	774	23	.	.	PUNCT
ejde-397	775	1	even	even	ADV
ejde-397	775	2	in	in	ADP
ejde-397	775	3	the	the	DET
ejde-397	775	4	case	case	NOUN
ejde-397	775	5	that	that	SCONJ
ejde-397	775	6	x	x	X
ejde-397	775	7	=	=	SYM
ejde-397	775	8	y	y	PROPN
ejde-397	775	9	and	and	CCONJ
ejde-397	775	10	b	b	X
ejde-397	775	11	=	=	SYM
ejde-397	775	12	i	i	PROPN
ejde-397	775	13	,	,	PUNCT
ejde-397	775	14	it	it	PRON
ejde-397	775	15	is	be	AUX
ejde-397	775	16	not	not	PART
ejde-397	775	17	so	so	ADV
ejde-397	775	18	simple	simple	ADJ
ejde-397	775	19	to	to	PART
ejde-397	775	20	prove	prove	VERB
ejde-397	775	21	the	the	DET
ejde-397	775	22	existence	existence	NOUN
ejde-397	775	23	of	of	ADP
ejde-397	775	24	a	a	DET
ejde-397	775	25	solution	solution	NOUN
ejde-397	775	26	of	of	ADP
ejde-397	775	27	problem	problem	NOUN
ejde-397	775	28	(	(	PUNCT
ejde-397	775	29	1.1	1.1	NUM
ejde-397	775	30	)	)	PUNCT
ejde-397	775	31	,	,	PUNCT
ejde-397	775	32	with	with	ADP
ejde-397	775	33	τ	τ	PROPN
ejde-397	775	34	=	=	SYM
ejde-397	775	35	∞	∞	PROPN
ejde-397	775	36	,	,	PUNCT
ejde-397	775	37	a(t	a(t	NOUN
ejde-397	775	38	)	)	PUNCT
ejde-397	775	39	and	and	CCONJ
ejde-397	775	40	f	f	X
ejde-397	775	41	=	=	SYM
ejde-397	775	42	fa	fa	PROPN
ejde-397	775	43	,	,	PUNCT
ejde-397	775	44	without	without	ADP
ejde-397	775	45	imposing	impose	VERB
ejde-397	775	46	some	some	DET
ejde-397	775	47	additional	additional	ADJ
ejde-397	775	48	unpleasant	unpleasant	ADJ
ejde-397	775	49	conditions	condition	NOUN
ejde-397	775	50	.	.	PUNCT
ejde-397	776	1	in	in	ADP
ejde-397	776	2	the	the	DET
ejde-397	776	3	next	next	ADJ
ejde-397	776	4	section	section	NOUN
ejde-397	776	5	,	,	PUNCT
ejde-397	776	6	we	we	PRON
ejde-397	776	7	will	will	AUX
ejde-397	776	8	introduce	introduce	VERB
ejde-397	776	9	various	various	ADJ
ejde-397	776	10	types	type	NOUN
ejde-397	776	11	of	of	ADP
ejde-397	776	12	solution	solution	NOUN
ejde-397	776	13	operator	operator	NOUN
ejde-397	776	14	families	family	NOUN
ejde-397	776	15	for	for	ADP
ejde-397	776	16	the	the	DET
ejde-397	776	17	abstract	abstract	ADJ
ejde-397	776	18	volterra	volterra	NOUN
ejde-397	776	19	inclusion	inclusion	NOUN
ejde-397	776	20	(	(	PUNCT
ejde-397	776	21	1.1	1.1	NUM
ejde-397	776	22	)	)	PUNCT
ejde-397	776	23	and	and	CCONJ
ejde-397	776	24	there	there	ADV
ejde-397	776	25	we	we	PRON
ejde-397	776	26	will	will	AUX
ejde-397	776	27	reconsider	reconsider	VERB
ejde-397	776	28	the	the	DET
ejde-397	776	29	problem	problem	NOUN
ejde-397	776	30	of	of	ADP
ejde-397	776	31	loss	loss	NOUN
ejde-397	776	32	of	of	ADP
ejde-397	776	33	regularity	regularity	NOUN
ejde-397	776	34	for	for	ADP
ejde-397	776	35	solutions	solution	NOUN
ejde-397	776	36	of	of	ADP
ejde-397	776	37	the	the	DET
ejde-397	776	38	subordinated	subordinated	ADJ
ejde-397	776	39	problem	problem	NOUN
ejde-397	776	40	once	once	ADV
ejde-397	776	41	more	more	ADV
ejde-397	776	42	(	(	PUNCT
ejde-397	776	43	cf	cf	NOUN
ejde-397	776	44	.	.	PUNCT
ejde-397	777	1	theorem	theorem	NOUN
ejde-397	777	2	5.7	5.7	NUM
ejde-397	777	3	)	)	PUNCT
ejde-397	777	4	.	.	PUNCT
ejde-397	778	1	5	5	X
ejde-397	778	2	.	.	NUM
ejde-397	778	3	multivalued	multivalue	VERB
ejde-397	778	4	linear	linear	PROPN
ejde-397	778	5	operators	operator	NOUN
ejde-397	778	6	as	as	ADP
ejde-397	778	7	subgenerators	subgenerator	NOUN
ejde-397	778	8	of	of	ADP
ejde-397	778	9	(	(	PUNCT
ejde-397	778	10	a	a	PRON
ejde-397	778	11	,	,	PUNCT
ejde-397	778	12	k)-regularized	k)-regularize	VERB
ejde-397	778	13	c	c	NOUN
ejde-397	778	14	-	-	PUNCT
ejde-397	778	15	resolvent	resolvent	ADJ
ejde-397	778	16	solution	solution	NOUN
ejde-397	778	17	operator	operator	NOUN
ejde-397	778	18	families	family	NOUN
ejde-397	778	19	in	in	ADP
ejde-397	778	20	[	[	X
ejde-397	778	21	36	36	NUM
ejde-397	778	22	,	,	PUNCT
ejde-397	778	23	section	section	NOUN
ejde-397	778	24	2.8	2.8	NUM
ejde-397	778	25	]	]	PUNCT
ejde-397	778	26	,	,	PUNCT
ejde-397	778	27	the	the	DET
ejde-397	778	28	class	class	NOUN
ejde-397	778	29	of	of	ADP
ejde-397	778	30	(	(	PUNCT
ejde-397	778	31	a	a	PRON
ejde-397	778	32	,	,	PUNCT
ejde-397	778	33	k)-regularized	k)-regularize	VERB
ejde-397	778	34	(	(	PUNCT
ejde-397	778	35	c1	c1	NOUN
ejde-397	778	36	,	,	PUNCT
ejde-397	778	37	c2)-existence	c2)-existence	VERB
ejde-397	778	38	and	and	CCONJ
ejde-397	778	39	uniqueness	uniqueness	NOUN
ejde-397	778	40	families	family	NOUN
ejde-397	778	41	has	have	AUX
ejde-397	778	42	been	be	AUX
ejde-397	778	43	introduced	introduce	VERB
ejde-397	778	44	and	and	CCONJ
ejde-397	778	45	analyzed	analyze	VERB
ejde-397	778	46	within	within	ADP
ejde-397	778	47	the	the	DET
ejde-397	778	48	theory	theory	NOUN
ejde-397	778	49	of	of	ADP
ejde-397	778	50	abstract	abstract	ADJ
ejde-397	778	51	nondegenerate	nondegenerate	PROPN
ejde-397	778	52	volterra	volterra	PROPN
ejde-397	778	53	equations	equation	NOUN
ejde-397	778	54	.	.	PUNCT
ejde-397	779	1	the	the	DET
ejde-397	779	2	main	main	ADJ
ejde-397	779	3	aim	aim	NOUN
ejde-397	779	4	of	of	ADP
ejde-397	779	5	this	this	DET
ejde-397	779	6	section	section	NOUN
ejde-397	779	7	is	be	AUX
ejde-397	779	8	to	to	PART
ejde-397	779	9	consider	consider	VERB
ejde-397	779	10	multivalued	multivalued	ADJ
ejde-397	779	11	linear	linear	ADJ
ejde-397	779	12	operators	operator	NOUN
ejde-397	779	13	in	in	ADP
ejde-397	779	14	locally	locally	ADV
ejde-397	779	15	convex	convex	ADJ
ejde-397	779	16	spaces	space	NOUN
ejde-397	779	17	as	as	ADP
ejde-397	779	18	subgenerators	subgenerator	NOUN
ejde-397	779	19	of	of	ADP
ejde-397	779	20	(	(	PUNCT
ejde-397	779	21	a	a	PRON
ejde-397	779	22	,	,	PUNCT
ejde-397	779	23	k)-regularized	k)-regularize	VERB
ejde-397	779	24	(	(	PUNCT
ejde-397	779	25	c1	c1	NOUN
ejde-397	779	26	,	,	PUNCT
ejde-397	779	27	c2)-existence	c2)-existence	NOUN
ejde-397	779	28	and	and	CCONJ
ejde-397	779	29	uniqueness	uniqueness	NOUN
ejde-397	779	30	families	family	NOUN
ejde-397	779	31	,	,	PUNCT
ejde-397	779	32	as	as	ADV
ejde-397	779	33	well	well	ADV
ejde-397	779	34	as	as	ADP
ejde-397	779	35	to	to	PART
ejde-397	779	36	consider	consider	VERB
ejde-397	779	37	in	in	ADP
ejde-397	779	38	more	more	ADJ
ejde-397	779	39	detail	detail	NOUN
ejde-397	779	40	the	the	DET
ejde-397	779	41	class	class	NOUN
ejde-397	779	42	of	of	ADP
ejde-397	779	43	(	(	PUNCT
ejde-397	779	44	a	a	PRON
ejde-397	779	45	,	,	PUNCT
ejde-397	779	46	k)-regularized	k)-regularize	VERB
ejde-397	779	47	c	c	NOUN
ejde-397	779	48	-	-	PUNCT
ejde-397	779	49	resolvent	resolvent	ADJ
ejde-397	779	50	families	family	NOUN
ejde-397	779	51	.	.	PUNCT
ejde-397	780	1	unless	unless	SCONJ
ejde-397	780	2	specified	specify	VERB
ejde-397	780	3	otherwise	otherwise	ADV
ejde-397	780	4	,	,	PUNCT
ejde-397	780	5	we	we	PRON
ejde-397	780	6	assume	assume	VERB
ejde-397	780	7	that	that	SCONJ
ejde-397	780	8	0	0	NUM
ejde-397	780	9	<	<	X
ejde-397	780	10	τ	τ	PROPN
ejde-397	780	11	≤	≤	NOUN
ejde-397	780	12	∞	∞	PROPN
ejde-397	780	13	,	,	PUNCT
ejde-397	780	14	k	k	PROPN
ejde-397	780	15	∈	∈	PROPN
ejde-397	780	16	c([0	c([0	PROPN
ejde-397	780	17	,	,	PUNCT
ejde-397	780	18	τ	τ	PROPN
ejde-397	780	19	)	)	PUNCT
ejde-397	780	20	)	)	PUNCT
ejde-397	780	21	,	,	PUNCT
ejde-397	781	1	k	k	PROPN
ejde-397	781	2	6=	6=	PROPN
ejde-397	781	3	0	0	NUM
ejde-397	781	4	,	,	PUNCT
ejde-397	781	5	a	a	DET
ejde-397	781	6	∈	∈	PROPN
ejde-397	781	7	l1	l1	PROPN
ejde-397	781	8	loc([0	loc([0	PROPN
ejde-397	781	9	,	,	PUNCT
ejde-397	781	10	τ	τ	PROPN
ejde-397	781	11	)	)	PUNCT
ejde-397	781	12	)	)	PUNCT
ejde-397	781	13	,	,	PUNCT
ejde-397	781	14	a	a	PRON
ejde-397	781	15	6=	6=	NUM
ejde-397	781	16	0	0	NUM
ejde-397	781	17	,	,	PUNCT
ejde-397	781	18	a	a	PRON
ejde-397	781	19	:	:	PUNCT
ejde-397	781	20	x	x	X
ejde-397	781	21	→	→	X
ejde-397	781	22	p	p	X
ejde-397	781	23	(	(	PUNCT
ejde-397	781	24	x	x	NOUN
ejde-397	781	25	)	)	PUNCT
ejde-397	781	26	24	24	NUM
ejde-397	781	27	m.	m.	NOUN
ejde-397	781	28	kostić	kostić	NOUN
ejde-397	782	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	782	2	is	be	AUX
ejde-397	782	3	an	an	DET
ejde-397	782	4	mlo	mlo	PROPN
ejde-397	782	5	,	,	PUNCT
ejde-397	782	6	c1	c1	PROPN
ejde-397	782	7	∈	∈	PROPN
ejde-397	782	8	l(y	l(y	PROPN
ejde-397	782	9	,	,	PUNCT
ejde-397	782	10	x	x	NOUN
ejde-397	782	11	)	)	PUNCT
ejde-397	782	12	,	,	PUNCT
ejde-397	782	13	c2	c2	PROPN
ejde-397	782	14	∈	∈	PROPN
ejde-397	782	15	l(x	l(x	PROPN
ejde-397	782	16	)	)	PUNCT
ejde-397	782	17	is	be	AUX
ejde-397	782	18	injective	injective	ADJ
ejde-397	782	19	,	,	PUNCT
ejde-397	782	20	c	c	PROPN
ejde-397	782	21	∈	∈	PROPN
ejde-397	782	22	l(x	l(x	PROPN
ejde-397	782	23	)	)	PUNCT
ejde-397	782	24	is	be	AUX
ejde-397	782	25	injective	injective	ADJ
ejde-397	782	26	and	and	CCONJ
ejde-397	782	27	ca	ca	PROPN
ejde-397	782	28	⊆	⊆	NUM
ejde-397	782	29	ac	ac	NOUN
ejde-397	782	30	.	.	PUNCT
ejde-397	783	1	the	the	DET
ejde-397	783	2	following	follow	VERB
ejde-397	783	3	definition	definition	NOUN
ejde-397	783	4	is	be	AUX
ejde-397	783	5	an	an	DET
ejde-397	783	6	extension	extension	NOUN
ejde-397	783	7	of	of	ADP
ejde-397	783	8	[	[	X
ejde-397	783	9	36	36	NUM
ejde-397	783	10	,	,	PUNCT
ejde-397	783	11	definition	definition	NOUN
ejde-397	783	12	2.8.2	2.8.2	NUM
ejde-397	783	13	]	]	PUNCT
ejde-397	783	14	(	(	PUNCT
ejde-397	783	15	x	x	SYM
ejde-397	783	16	=	=	SYM
ejde-397	783	17	y	y	PROPN
ejde-397	783	18	,	,	PUNCT
ejde-397	783	19	a	a	PRON
ejde-397	783	20	is	be	AUX
ejde-397	783	21	a	a	DET
ejde-397	783	22	closed	closed	ADJ
ejde-397	783	23	single	single	ADV
ejde-397	783	24	-	-	PUNCT
ejde-397	783	25	valued	value	VERB
ejde-397	783	26	linear	linear	NOUN
ejde-397	783	27	operator	operator	NOUN
ejde-397	783	28	on	on	ADP
ejde-397	783	29	x	x	NOUN
ejde-397	783	30	)	)	PUNCT
ejde-397	783	31	and	and	CCONJ
ejde-397	783	32	[	[	X
ejde-397	783	33	72	72	NUM
ejde-397	783	34	,	,	PUNCT
ejde-397	783	35	definition	definition	NOUN
ejde-397	783	36	3.5	3.5	NUM
ejde-397	783	37	]	]	PUNCT
ejde-397	783	38	(	(	PUNCT
ejde-397	783	39	x	x	X
ejde-397	783	40	=	=	SYM
ejde-397	783	41	y	y	PROPN
ejde-397	783	42	,	,	PUNCT
ejde-397	783	43	c	c	PROPN
ejde-397	783	44	=	=	SYM
ejde-397	783	45	c1	c1	PROPN
ejde-397	783	46	,	,	PUNCT
ejde-397	783	47	a(t	a(t	NOUN
ejde-397	783	48	)	)	PUNCT
ejde-397	783	49	=	=	PUNCT
ejde-397	784	1	k(t	k(t	X
ejde-397	784	2	)	)	PUNCT
ejde-397	784	3	=	=	SYM
ejde-397	784	4	1	1	NUM
ejde-397	784	5	)	)	PUNCT
ejde-397	784	6	.	.	PUNCT
ejde-397	785	1	definition	definition	NOUN
ejde-397	785	2	5.1	5.1	NUM
ejde-397	785	3	.	.	PUNCT
ejde-397	785	4	suppose	suppose	VERB
ejde-397	785	5	0	0	PUNCT
ejde-397	786	1	<	<	X
ejde-397	786	2	τ	τ	PROPN
ejde-397	786	3	≤	≤	NOUN
ejde-397	786	4	∞	∞	PROPN
ejde-397	786	5	,	,	PUNCT
ejde-397	786	6	k	k	PROPN
ejde-397	786	7	∈	∈	PROPN
ejde-397	786	8	c([0	c([0	PROPN
ejde-397	786	9	,	,	PUNCT
ejde-397	786	10	τ	τ	PROPN
ejde-397	786	11	)	)	PUNCT
ejde-397	786	12	)	)	PUNCT
ejde-397	786	13	,	,	PUNCT
ejde-397	787	1	k	k	PROPN
ejde-397	787	2	6=	6=	PROPN
ejde-397	787	3	0	0	NUM
ejde-397	787	4	,	,	PUNCT
ejde-397	787	5	a	a	DET
ejde-397	787	6	∈	∈	PROPN
ejde-397	787	7	l1	l1	PROPN
ejde-397	787	8	loc([0	loc([0	PROPN
ejde-397	787	9	,	,	PUNCT
ejde-397	787	10	τ	τ	PROPN
ejde-397	787	11	)	)	PUNCT
ejde-397	787	12	)	)	PUNCT
ejde-397	787	13	,	,	PUNCT
ejde-397	787	14	a	a	PRON
ejde-397	787	15	6=	6=	NUM
ejde-397	787	16	0	0	NUM
ejde-397	787	17	,	,	PUNCT
ejde-397	787	18	a	a	PRON
ejde-397	787	19	:	:	PUNCT
ejde-397	787	20	x	x	X
ejde-397	787	21	→	→	X
ejde-397	787	22	p	p	X
ejde-397	787	23	(	(	PUNCT
ejde-397	787	24	x	x	X
ejde-397	787	25	)	)	PUNCT
ejde-397	787	26	is	be	AUX
ejde-397	787	27	an	an	DET
ejde-397	787	28	mlo	mlo	PROPN
ejde-397	787	29	,	,	PUNCT
ejde-397	787	30	c1	c1	PROPN
ejde-397	787	31	∈	∈	PROPN
ejde-397	787	32	l(y	l(y	PROPN
ejde-397	787	33	,	,	PUNCT
ejde-397	787	34	x	x	NOUN
ejde-397	787	35	)	)	PUNCT
ejde-397	787	36	,	,	PUNCT
ejde-397	787	37	and	and	CCONJ
ejde-397	787	38	c2	c2	PROPN
ejde-397	787	39	∈	∈	PROPN
ejde-397	787	40	l(x	l(x	PROPN
ejde-397	787	41	)	)	PUNCT
ejde-397	788	1	is	be	AUX
ejde-397	788	2	injective	injective	ADJ
ejde-397	788	3	.	.	PUNCT
ejde-397	789	1	(	(	PUNCT
ejde-397	789	2	i	i	NOUN
ejde-397	789	3	)	)	PUNCT
ejde-397	789	4	then	then	ADV
ejde-397	789	5	it	it	PRON
ejde-397	789	6	is	be	AUX
ejde-397	789	7	said	say	VERB
ejde-397	789	8	that	that	SCONJ
ejde-397	789	9	a	a	PRON
ejde-397	789	10	is	be	AUX
ejde-397	789	11	a	a	DET
ejde-397	789	12	subgenerator	subgenerator	NOUN
ejde-397	789	13	of	of	ADP
ejde-397	789	14	a	a	DET
ejde-397	789	15	(	(	PUNCT
ejde-397	789	16	local	local	ADJ
ejde-397	789	17	,	,	PUNCT
ejde-397	789	18	if	if	SCONJ
ejde-397	789	19	τ	τ	PROPN
ejde-397	789	20	<	<	X
ejde-397	789	21	∞	∞	PROPN
ejde-397	789	22	)	)	PUNCT
ejde-397	789	23	mild	mild	NOUN
ejde-397	789	24	(	(	PUNCT
ejde-397	789	25	a	a	PRON
ejde-397	789	26	,	,	PUNCT
ejde-397	789	27	k)regularized	k)regularize	VERB
ejde-397	789	28	(	(	PUNCT
ejde-397	789	29	c1	c1	NOUN
ejde-397	789	30	,	,	PUNCT
ejde-397	789	31	c2)-existence	c2)-existence	VERB
ejde-397	789	32	and	and	CCONJ
ejde-397	789	33	uniqueness	uniqueness	VERB
ejde-397	789	34	family	family	NOUN
ejde-397	789	35	(	(	PUNCT
ejde-397	789	36	r1(t	r1(t	PROPN
ejde-397	789	37	)	)	PUNCT
ejde-397	789	38	,	,	PUNCT
ejde-397	789	39	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	789	40	)	)	PUNCT
ejde-397	789	41	⊆	⊆	NUM
ejde-397	789	42	l(y	l(y	PROPN
ejde-397	789	43	,	,	PUNCT
ejde-397	789	44	x)×	x)×	SYM
ejde-397	789	45	l(x	l(x	PROPN
ejde-397	789	46	)	)	PUNCT
ejde-397	790	1	if	if	SCONJ
ejde-397	790	2	and	and	CCONJ
ejde-397	790	3	only	only	ADV
ejde-397	790	4	if	if	SCONJ
ejde-397	790	5	the	the	DET
ejde-397	790	6	mappings	mapping	NOUN
ejde-397	790	7	t	t	X
ejde-397	790	8	7→	7→	NUM
ejde-397	790	9	r1(t)y	r1(t)y	PROPN
ejde-397	790	10	,	,	PUNCT
ejde-397	790	11	t	t	PROPN
ejde-397	790	12	≥	≥	NOUN
ejde-397	790	13	0	0	NUM
ejde-397	790	14	and	and	CCONJ
ejde-397	790	15	t	t	PROPN
ejde-397	790	16	7→	7→	NUM
ejde-397	790	17	r2(t)x	r2(t)x	NOUN
ejde-397	790	18	,	,	PUNCT
ejde-397	790	19	t	t	PROPN
ejde-397	790	20	∈	∈	PROPN
ejde-397	791	1	[	[	X
ejde-397	791	2	0	0	NUM
ejde-397	791	3	,	,	PUNCT
ejde-397	791	4	τ	τ	X
ejde-397	791	5	)	)	PUNCT
ejde-397	791	6	are	be	AUX
ejde-397	791	7	continuous	continuous	ADJ
ejde-397	791	8	for	for	SCONJ
ejde-397	791	9	every	every	DET
ejde-397	791	10	fixed	fix	VERB
ejde-397	791	11	x	x	SYM
ejde-397	791	12	∈	∈	PROPN
ejde-397	791	13	x	x	X
ejde-397	791	14	and	and	CCONJ
ejde-397	791	15	y	y	PROPN
ejde-397	791	16	∈	∈	PROPN
ejde-397	791	17	y	y	PROPN
ejde-397	791	18	,	,	PUNCT
ejde-397	791	19	as	as	ADV
ejde-397	791	20	well	well	ADV
ejde-397	791	21	as	as	ADP
ejde-397	791	22	the	the	DET
ejde-397	791	23	following	follow	VERB
ejde-397	791	24	conditions	condition	NOUN
ejde-397	791	25	hold	hold	VERB
ejde-397	791	26	:	:	PUNCT
ejde-397	791	27	(	(	PUNCT
ejde-397	791	28	∫	∫	PROPN
ejde-397	791	29	t	t	PROPN
ejde-397	791	30	0	0	NUM
ejde-397	791	31	a(t−	a(t−	PROPN
ejde-397	791	32	s)r1(s)y	s)r1(s)y	PROPN
ejde-397	791	33	ds	ds	PROPN
ejde-397	791	34	,	,	PUNCT
ejde-397	791	35	r1(t)y	r1(t)y	NOUN
ejde-397	791	36	−	−	PROPN
ejde-397	791	37	k(t)c1y	k(t)c1y	PROPN
ejde-397	791	38	)	)	PUNCT
ejde-397	791	39	∈	∈	PROPN
ejde-397	792	1	a	a	PRON
ejde-397	792	2	,	,	PUNCT
ejde-397	792	3	t	t	PROPN
ejde-397	792	4	∈	∈	PROPN
ejde-397	793	1	[	[	X
ejde-397	793	2	0	0	NUM
ejde-397	793	3	,	,	PUNCT
ejde-397	793	4	τ	τ	PROPN
ejde-397	793	5	)	)	PUNCT
ejde-397	793	6	,	,	PUNCT
ejde-397	793	7	y	y	PROPN
ejde-397	793	8	∈	∈	PROPN
ejde-397	793	9	y	y	PROPN
ejde-397	793	10	;	;	PUNCT
ejde-397	793	11	(	(	PUNCT
ejde-397	793	12	5.1)∫	5.1)∫	NUM
ejde-397	793	13	t	t	NOUN
ejde-397	793	14	0	0	NUM
ejde-397	793	15	a(t−	a(t−	NOUN
ejde-397	793	16	s)r2(s)y	s)r2(s)y	NOUN
ejde-397	793	17	ds	ds	ADJ
ejde-397	793	18	=	=	SYM
ejde-397	793	19	r2(t)x−	r2(t)x−	PROPN
ejde-397	793	20	k(t)c2x	k(t)c2x	NOUN
ejde-397	793	21	,	,	PUNCT
ejde-397	793	22	whenever	whenever	SCONJ
ejde-397	793	23	t	t	PROPN
ejde-397	793	24	∈	∈	PROPN
ejde-397	794	1	[	[	X
ejde-397	794	2	0	0	NUM
ejde-397	794	3	,	,	PUNCT
ejde-397	794	4	τ	τ	X
ejde-397	794	5	)	)	PUNCT
ejde-397	794	6	and	and	CCONJ
ejde-397	794	7	(	(	PUNCT
ejde-397	794	8	x	x	NOUN
ejde-397	794	9	,	,	PUNCT
ejde-397	794	10	y	y	NOUN
ejde-397	794	11	)	)	PUNCT
ejde-397	794	12	∈	∈	PROPN
ejde-397	794	13	a.	a.	NOUN
ejde-397	794	14	(	(	PUNCT
ejde-397	794	15	5.2	5.2	NUM
ejde-397	794	16	)	)	PUNCT
ejde-397	794	17	(	(	PUNCT
ejde-397	794	18	ii	ii	NOUN
ejde-397	794	19	)	)	PUNCT
ejde-397	794	20	let	let	VERB
ejde-397	794	21	(	(	PUNCT
ejde-397	794	22	r1(t))t∈[0,τ	r1(t))t∈[0,τ	NOUN
ejde-397	794	23	)	)	PUNCT
ejde-397	794	24	⊆	⊆	NUM
ejde-397	794	25	l(y	l(y	PROPN
ejde-397	794	26	,	,	PUNCT
ejde-397	794	27	x	x	PRON
ejde-397	794	28	)	)	PUNCT
ejde-397	794	29	be	be	AUX
ejde-397	794	30	strongly	strongly	ADV
ejde-397	794	31	continuous	continuous	ADJ
ejde-397	794	32	.	.	PUNCT
ejde-397	795	1	then	then	ADV
ejde-397	795	2	it	it	PRON
ejde-397	795	3	is	be	AUX
ejde-397	795	4	said	say	VERB
ejde-397	795	5	that	that	SCONJ
ejde-397	795	6	a	a	PRON
ejde-397	795	7	is	be	AUX
ejde-397	795	8	a	a	DET
ejde-397	795	9	subgenerator	subgenerator	NOUN
ejde-397	795	10	of	of	ADP
ejde-397	795	11	a	a	DET
ejde-397	795	12	(	(	PUNCT
ejde-397	795	13	local	local	ADJ
ejde-397	795	14	,	,	PUNCT
ejde-397	795	15	if	if	SCONJ
ejde-397	795	16	τ	τ	PROPN
ejde-397	795	17	<	<	X
ejde-397	795	18	∞	∞	NOUN
ejde-397	795	19	)	)	PUNCT
ejde-397	795	20	mild	mild	NOUN
ejde-397	795	21	(	(	PUNCT
ejde-397	795	22	a	a	DET
ejde-397	795	23	,	,	PUNCT
ejde-397	795	24	k)-regularized	k)-regularize	VERB
ejde-397	795	25	c1	c1	NOUN
ejde-397	795	26	-	-	PUNCT
ejde-397	795	27	existence	existence	NOUN
ejde-397	795	28	family	family	NOUN
ejde-397	795	29	(	(	PUNCT
ejde-397	795	30	r1(t))t∈[0,τ	r1(t))t∈[0,τ	PROPN
ejde-397	795	31	)	)	PUNCT
ejde-397	796	1	if	if	SCONJ
ejde-397	796	2	and	and	CCONJ
ejde-397	796	3	only	only	ADV
ejde-397	796	4	if	if	SCONJ
ejde-397	796	5	(	(	PUNCT
ejde-397	796	6	5.1	5.1	NUM
ejde-397	796	7	)	)	PUNCT
ejde-397	796	8	holds	hold	VERB
ejde-397	796	9	.	.	PUNCT
ejde-397	797	1	(	(	PUNCT
ejde-397	797	2	iii	iii	X
ejde-397	797	3	)	)	PUNCT
ejde-397	797	4	let	let	VERB
ejde-397	797	5	(	(	PUNCT
ejde-397	797	6	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	797	7	)	)	PUNCT
ejde-397	797	8	⊆	⊆	NUM
ejde-397	797	9	l(x	l(x	PROPN
ejde-397	797	10	)	)	PUNCT
ejde-397	797	11	be	be	AUX
ejde-397	797	12	strongly	strongly	ADV
ejde-397	797	13	continuous	continuous	ADJ
ejde-397	797	14	.	.	PUNCT
ejde-397	798	1	then	then	ADV
ejde-397	798	2	it	it	PRON
ejde-397	798	3	is	be	AUX
ejde-397	798	4	said	say	VERB
ejde-397	798	5	that	that	SCONJ
ejde-397	798	6	a	a	PRON
ejde-397	798	7	is	be	AUX
ejde-397	798	8	a	a	DET
ejde-397	798	9	subgenerator	subgenerator	NOUN
ejde-397	798	10	of	of	ADP
ejde-397	798	11	a	a	DET
ejde-397	798	12	(	(	PUNCT
ejde-397	798	13	local	local	ADJ
ejde-397	798	14	,	,	PUNCT
ejde-397	798	15	if	if	SCONJ
ejde-397	798	16	τ	τ	PROPN
ejde-397	798	17	<	<	X
ejde-397	798	18	∞	∞	PROPN
ejde-397	798	19	)	)	PUNCT
ejde-397	798	20	mild	mild	NOUN
ejde-397	798	21	(	(	PUNCT
ejde-397	798	22	a	a	PRON
ejde-397	798	23	,	,	PUNCT
ejde-397	798	24	k)-regularized	k)-regularize	VERB
ejde-397	798	25	c2	c2	PROPN
ejde-397	798	26	-	-	PUNCT
ejde-397	798	27	uniqueness	uniqueness	PROPN
ejde-397	798	28	family	family	NOUN
ejde-397	798	29	(	(	PUNCT
ejde-397	798	30	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	798	31	)	)	PUNCT
ejde-397	798	32	if	if	SCONJ
ejde-397	798	33	and	and	CCONJ
ejde-397	798	34	only	only	ADV
ejde-397	798	35	if	if	SCONJ
ejde-397	798	36	(	(	PUNCT
ejde-397	798	37	5.2	5.2	NUM
ejde-397	798	38	)	)	PUNCT
ejde-397	798	39	holds	hold	VERB
ejde-397	798	40	.	.	PUNCT
ejde-397	799	1	as	as	ADP
ejde-397	799	2	an	an	DET
ejde-397	799	3	immediate	immediate	ADJ
ejde-397	799	4	consequence	consequence	NOUN
ejde-397	799	5	of	of	ADP
ejde-397	799	6	definition	definition	NOUN
ejde-397	799	7	,	,	PUNCT
ejde-397	799	8	we	we	PRON
ejde-397	799	9	have	have	VERB
ejde-397	799	10	that	that	DET
ejde-397	799	11	r(r1(0)−k(0)c1	r(r1(0)−k(0)c1	NOUN
ejde-397	799	12	)	)	PUNCT
ejde-397	799	13	⊆	⊆	NUM
ejde-397	799	14	a0	a0	NOUN
ejde-397	799	15	as	as	ADV
ejde-397	799	16	well	well	ADV
ejde-397	799	17	as	as	ADP
ejde-397	799	18	that	that	DET
ejde-397	799	19	r2(t)a	r2(t)a	ADJ
ejde-397	799	20	is	be	AUX
ejde-397	799	21	single	single	ADV
ejde-397	799	22	-	-	PUNCT
ejde-397	799	23	valued	value	VERB
ejde-397	799	24	for	for	ADP
ejde-397	799	25	any	any	DET
ejde-397	799	26	t	t	PROPN
ejde-397	799	27	≥	≥	NOUN
ejde-397	799	28	0	0	NUM
ejde-397	799	29	,	,	PUNCT
ejde-397	799	30	and	and	CCONJ
ejde-397	799	31	r2(t)y	r2(t)y	ADP
ejde-397	799	32	=	=	SYM
ejde-397	799	33	0	0	NUM
ejde-397	799	34	for	for	ADP
ejde-397	799	35	any	any	DET
ejde-397	799	36	y	y	PROPN
ejde-397	799	37	∈	∈	PROPN
ejde-397	799	38	a0	a0	PROPN
ejde-397	799	39	and	and	CCONJ
ejde-397	799	40	t	t	PROPN
ejde-397	799	41	≥	≥	NUM
ejde-397	799	42	0	0	NUM
ejde-397	799	43	.	.	PUNCT
ejde-397	800	1	now	now	ADV
ejde-397	800	2	we	we	PRON
ejde-397	800	3	will	will	AUX
ejde-397	800	4	extend	extend	VERB
ejde-397	800	5	the	the	DET
ejde-397	800	6	definition	definition	NOUN
ejde-397	800	7	of	of	ADP
ejde-397	800	8	an	an	DET
ejde-397	800	9	(	(	PUNCT
ejde-397	800	10	a	a	DET
ejde-397	800	11	,	,	PUNCT
ejde-397	800	12	k)-regularized	k)-regularize	VERB
ejde-397	800	13	c	c	NOUN
ejde-397	800	14	-	-	PUNCT
ejde-397	800	15	resolvent	resolvent	ADJ
ejde-397	800	16	family	family	NOUN
ejde-397	800	17	subgenerated	subgenerate	VERB
ejde-397	800	18	by	by	ADP
ejde-397	800	19	a	a	DET
ejde-397	800	20	single	single	ADV
ejde-397	800	21	-	-	PUNCT
ejde-397	800	22	valued	value	VERB
ejde-397	800	23	linear	linear	NOUN
ejde-397	800	24	operator	operator	NOUN
ejde-397	800	25	(	(	PUNCT
ejde-397	800	26	cf	cf	NOUN
ejde-397	800	27	.	.	PUNCT
ejde-397	801	1	[	[	X
ejde-397	801	2	36	36	NUM
ejde-397	801	3	,	,	PUNCT
ejde-397	801	4	definition	definition	NOUN
ejde-397	801	5	2.1.1	2.1.1	NUM
ejde-397	801	6	]	]	PUNCT
ejde-397	801	7	)	)	PUNCT
ejde-397	801	8	.	.	PUNCT
ejde-397	802	1	definition	definition	NOUN
ejde-397	802	2	5.2	5.2	NUM
ejde-397	802	3	.	.	PUNCT
ejde-397	802	4	suppose	suppose	VERB
ejde-397	802	5	that	that	SCONJ
ejde-397	802	6	0	0	NUM
ejde-397	802	7	<	<	X
ejde-397	802	8	τ	τ	PROPN
ejde-397	802	9	≤	≤	NOUN
ejde-397	802	10	∞	∞	PROPN
ejde-397	802	11	,	,	PUNCT
ejde-397	802	12	k	k	PROPN
ejde-397	802	13	∈	∈	PROPN
ejde-397	802	14	c([0	c([0	PROPN
ejde-397	802	15	,	,	PUNCT
ejde-397	802	16	τ	τ	PROPN
ejde-397	802	17	)	)	PUNCT
ejde-397	802	18	)	)	PUNCT
ejde-397	802	19	,	,	PUNCT
ejde-397	802	20	k	k	PROPN
ejde-397	802	21	6=	6=	PROPN
ejde-397	802	22	0	0	NUM
ejde-397	802	23	,	,	PUNCT
ejde-397	802	24	a	a	DET
ejde-397	802	25	∈	∈	PROPN
ejde-397	802	26	l1	l1	PROPN
ejde-397	802	27	loc([0	loc([0	PROPN
ejde-397	802	28	,	,	PUNCT
ejde-397	802	29	τ	τ	PROPN
ejde-397	802	30	)	)	PUNCT
ejde-397	802	31	)	)	PUNCT
ejde-397	802	32	,	,	PUNCT
ejde-397	802	33	a	a	PRON
ejde-397	802	34	6=	6=	NUM
ejde-397	802	35	0	0	NUM
ejde-397	802	36	,	,	PUNCT
ejde-397	802	37	a	a	PRON
ejde-397	802	38	:	:	PUNCT
ejde-397	802	39	x	x	X
ejde-397	802	40	→	→	X
ejde-397	802	41	p	p	X
ejde-397	802	42	(	(	PUNCT
ejde-397	802	43	x	x	X
ejde-397	802	44	)	)	PUNCT
ejde-397	802	45	is	be	AUX
ejde-397	802	46	an	an	DET
ejde-397	802	47	mlo	mlo	NOUN
ejde-397	802	48	,	,	PUNCT
ejde-397	802	49	c	c	PROPN
ejde-397	802	50	∈	∈	PROPN
ejde-397	802	51	l(x	l(x	PROPN
ejde-397	802	52	)	)	PUNCT
ejde-397	802	53	is	be	AUX
ejde-397	802	54	injective	injective	ADJ
ejde-397	802	55	and	and	CCONJ
ejde-397	802	56	ca	ca	NOUN
ejde-397	802	57	⊆	⊆	NUM
ejde-397	802	58	ac	ac	PROPN
ejde-397	802	59	.	.	PUNCT
ejde-397	803	1	then	then	ADV
ejde-397	803	2	it	it	PRON
ejde-397	803	3	is	be	AUX
ejde-397	803	4	said	say	VERB
ejde-397	803	5	that	that	SCONJ
ejde-397	803	6	a	a	DET
ejde-397	803	7	strongly	strongly	ADV
ejde-397	803	8	continuous	continuous	ADJ
ejde-397	803	9	operator	operator	NOUN
ejde-397	803	10	family	family	NOUN
ejde-397	803	11	(	(	PUNCT
ejde-397	803	12	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	803	13	)	)	PUNCT
ejde-397	803	14	⊆	⊆	NUM
ejde-397	803	15	l(x	l(x	PROPN
ejde-397	803	16	)	)	PUNCT
ejde-397	803	17	is	be	AUX
ejde-397	803	18	an	an	DET
ejde-397	803	19	(	(	PUNCT
ejde-397	803	20	a	a	PRON
ejde-397	803	21	,	,	PUNCT
ejde-397	803	22	k)regularized	k)regularize	VERB
ejde-397	803	23	c	c	X
ejde-397	803	24	-	-	PUNCT
ejde-397	803	25	resolvent	resolvent	ADJ
ejde-397	803	26	family	family	NOUN
ejde-397	803	27	with	with	ADP
ejde-397	803	28	a	a	DET
ejde-397	803	29	subgenerator	subgenerator	NOUN
ejde-397	803	30	a	a	DET
ejde-397	803	31	if	if	NOUN
ejde-397	803	32	and	and	CCONJ
ejde-397	803	33	only	only	ADV
ejde-397	803	34	if	if	SCONJ
ejde-397	803	35	(	(	PUNCT
ejde-397	803	36	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	803	37	)	)	PUNCT
ejde-397	803	38	is	be	AUX
ejde-397	803	39	a	a	DET
ejde-397	803	40	mild	mild	ADJ
ejde-397	803	41	(	(	PUNCT
ejde-397	803	42	a	a	PRON
ejde-397	803	43	,	,	PUNCT
ejde-397	803	44	k)-regularized	k)-regularize	VERB
ejde-397	803	45	c	c	NOUN
ejde-397	803	46	-	-	PUNCT
ejde-397	803	47	uniqueness	uniqueness	NOUN
ejde-397	803	48	family	family	NOUN
ejde-397	803	49	having	have	VERB
ejde-397	803	50	a	a	DET
ejde-397	803	51	as	as	ADP
ejde-397	803	52	subgenerator	subgenerator	NOUN
ejde-397	803	53	,	,	PUNCT
ejde-397	803	54	r(t)c	r(t)c	NOUN
ejde-397	803	55	=	=	SYM
ejde-397	803	56	cr(t	cr(t	NOUN
ejde-397	803	57	)	)	PUNCT
ejde-397	803	58	and	and	CCONJ
ejde-397	803	59	r(t)a	r(t)a	NOUN
ejde-397	803	60	⊆	⊆	NUM
ejde-397	803	61	ar(t	ar(t	NOUN
ejde-397	803	62	)	)	PUNCT
ejde-397	803	63	(	(	PUNCT
ejde-397	803	64	t	t	X
ejde-397	803	65	≥	≥	PROPN
ejde-397	803	66	0	0	NUM
ejde-397	803	67	)	)	PUNCT
ejde-397	803	68	.	.	PUNCT
ejde-397	804	1	an	an	PRON
ejde-397	804	2	(	(	PUNCT
ejde-397	804	3	a	a	PRON
ejde-397	804	4	,	,	PUNCT
ejde-397	804	5	k)-regularized	k)-regularize	VERB
ejde-397	804	6	c	c	NOUN
ejde-397	804	7	-	-	PUNCT
ejde-397	804	8	resolvent	resolvent	ADJ
ejde-397	804	9	family	family	NOUN
ejde-397	804	10	(	(	PUNCT
ejde-397	804	11	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	804	12	)	)	PUNCT
ejde-397	804	13	is	be	AUX
ejde-397	804	14	said	say	VERB
ejde-397	804	15	to	to	PART
ejde-397	804	16	be	be	AUX
ejde-397	804	17	locally	locally	ADV
ejde-397	804	18	equicontinuous	equicontinuous	ADJ
ejde-397	804	19	if	if	SCONJ
ejde-397	804	20	and	and	CCONJ
ejde-397	804	21	only	only	ADV
ejde-397	804	22	if	if	SCONJ
ejde-397	804	23	,	,	PUNCT
ejde-397	804	24	for	for	ADP
ejde-397	804	25	every	every	DET
ejde-397	804	26	t	t	NOUN
ejde-397	804	27	∈	∈	PROPN
ejde-397	804	28	(	(	PUNCT
ejde-397	804	29	0	0	NUM
ejde-397	804	30	,	,	PUNCT
ejde-397	804	31	τ	τ	PROPN
ejde-397	804	32	)	)	PUNCT
ejde-397	804	33	,	,	PUNCT
ejde-397	804	34	the	the	DET
ejde-397	804	35	family	family	NOUN
ejde-397	804	36	{	{	PUNCT
ejde-397	804	37	r(s	r(s	PROPN
ejde-397	804	38	)	)	PUNCT
ejde-397	804	39	:	:	PUNCT
ejde-397	804	40	s	s	VERB
ejde-397	804	41	∈	∈	PROPN
ejde-397	805	1	[	[	X
ejde-397	805	2	0	0	NUM
ejde-397	805	3	,	,	PUNCT
ejde-397	805	4	t	t	PROPN
ejde-397	805	5	]	]	PUNCT
ejde-397	805	6	}	}	PUNCT
ejde-397	805	7	is	be	AUX
ejde-397	805	8	equicontinuous	equicontinuous	ADJ
ejde-397	805	9	.	.	PUNCT
ejde-397	806	1	in	in	ADP
ejde-397	806	2	the	the	DET
ejde-397	806	3	case	case	NOUN
ejde-397	806	4	τ	τ	X
ejde-397	806	5	=	=	SYM
ejde-397	806	6	∞	∞	PROPN
ejde-397	806	7	,	,	PUNCT
ejde-397	806	8	(	(	PUNCT
ejde-397	806	9	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	806	10	is	be	AUX
ejde-397	806	11	said	say	VERB
ejde-397	806	12	to	to	PART
ejde-397	806	13	be	be	AUX
ejde-397	806	14	exponentially	exponentially	ADV
ejde-397	806	15	equicontinuous	equicontinuous	ADJ
ejde-397	806	16	(	(	PUNCT
ejde-397	806	17	equicontinuous	equicontinuous	ADJ
ejde-397	806	18	)	)	PUNCT
ejde-397	806	19	if	if	SCONJ
ejde-397	806	20	there	there	PRON
ejde-397	806	21	exists	exist	VERB
ejde-397	806	22	ω	ω	NUM
ejde-397	806	23	∈	∈	PROPN
ejde-397	806	24	r	r	NOUN
ejde-397	806	25	(	(	PUNCT
ejde-397	806	26	ω	ω	NOUN
ejde-397	806	27	=	=	SYM
ejde-397	806	28	0	0	NUM
ejde-397	806	29	)	)	PUNCT
ejde-397	806	30	such	such	ADJ
ejde-397	806	31	that	that	SCONJ
ejde-397	806	32	the	the	DET
ejde-397	806	33	family	family	NOUN
ejde-397	806	34	{	{	PUNCT
ejde-397	806	35	e−ωtr(t	e−ωtr(t	NUM
ejde-397	806	36	)	)	PUNCT
ejde-397	806	37	:	:	PUNCT
ejde-397	806	38	t	t	X
ejde-397	806	39	≥	≥	NOUN
ejde-397	806	40	0	0	NUM
ejde-397	806	41	}	}	PUNCT
ejde-397	806	42	is	be	AUX
ejde-397	806	43	equicontinuous	equicontinuous	ADJ
ejde-397	806	44	;	;	PUNCT
ejde-397	806	45	the	the	DET
ejde-397	806	46	infimum	infimum	ADJ
ejde-397	806	47	of	of	ADP
ejde-397	806	48	such	such	ADJ
ejde-397	806	49	numbers	number	NOUN
ejde-397	806	50	is	be	AUX
ejde-397	806	51	said	say	VERB
ejde-397	806	52	to	to	PART
ejde-397	806	53	be	be	AUX
ejde-397	806	54	the	the	DET
ejde-397	806	55	exponential	exponential	ADJ
ejde-397	806	56	type	type	NOUN
ejde-397	806	57	of	of	ADP
ejde-397	806	58	(	(	PUNCT
ejde-397	806	59	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	806	60	.	.	PUNCT
ejde-397	807	1	the	the	DET
ejde-397	807	2	above	above	ADJ
ejde-397	807	3	notion	notion	NOUN
ejde-397	807	4	can	can	AUX
ejde-397	807	5	be	be	AUX
ejde-397	807	6	simply	simply	ADV
ejde-397	807	7	understood	understand	VERB
ejde-397	807	8	for	for	ADP
ejde-397	807	9	the	the	DET
ejde-397	807	10	classes	class	NOUN
ejde-397	807	11	of	of	ADP
ejde-397	807	12	mild	mild	ADJ
ejde-397	807	13	(	(	PUNCT
ejde-397	807	14	a	a	PRON
ejde-397	807	15	,	,	PUNCT
ejde-397	807	16	k)-regularized	k)-regularize	VERB
ejde-397	807	17	c1	c1	NOUN
ejde-397	807	18	-	-	PUNCT
ejde-397	807	19	existence	existence	NOUN
ejde-397	807	20	families	family	NOUN
ejde-397	807	21	and	and	CCONJ
ejde-397	807	22	mild	mild	ADJ
ejde-397	807	23	(	(	PUNCT
ejde-397	807	24	a	a	PRON
ejde-397	807	25	,	,	PUNCT
ejde-397	807	26	k)-regularized	k)-regularize	VERB
ejde-397	807	27	c2	c2	PROPN
ejde-397	807	28	-	-	PUNCT
ejde-397	807	29	uniqueness	uniqueness	NOUN
ejde-397	807	30	families	family	NOUN
ejde-397	807	31	;	;	PUNCT
ejde-397	807	32	a	a	DET
ejde-397	807	33	mild	mild	ADJ
ejde-397	807	34	(	(	PUNCT
ejde-397	807	35	a	a	PRON
ejde-397	807	36	,	,	PUNCT
ejde-397	807	37	k)-regularized	k)-regularize	VERB
ejde-397	807	38	(	(	PUNCT
ejde-397	807	39	c1	c1	NOUN
ejde-397	807	40	,	,	PUNCT
ejde-397	807	41	c2)-existence	c2)-existence	VERB
ejde-397	807	42	and	and	CCONJ
ejde-397	807	43	uniqueness	uniqueness	VERB
ejde-397	807	44	family	family	NOUN
ejde-397	807	45	(	(	PUNCT
ejde-397	807	46	r1(t	r1(t	PROPN
ejde-397	807	47	)	)	PUNCT
ejde-397	807	48	,	,	PUNCT
ejde-397	807	49	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	807	50	)	)	PUNCT
ejde-397	807	51	⊆	⊆	NUM
ejde-397	807	52	l(y	l(y	PROPN
ejde-397	807	53	,	,	PUNCT
ejde-397	807	54	x	x	NOUN
ejde-397	807	55	)	)	PUNCT
ejde-397	807	56	×	×	NOUN
ejde-397	807	57	l(x	l(x	PROPN
ejde-397	807	58	)	)	PUNCT
ejde-397	807	59	is	be	AUX
ejde-397	807	60	said	say	VERB
ejde-397	807	61	to	to	PART
ejde-397	807	62	be	be	AUX
ejde-397	807	63	locally	locally	ADV
ejde-397	807	64	equicontinuous	equicontinuous	ADJ
ejde-397	807	65	(	(	PUNCT
ejde-397	807	66	exponentially	exponentially	ADV
ejde-397	807	67	equicontinuous	equicontinuous	ADJ
ejde-397	807	68	,	,	PUNCT
ejde-397	807	69	provided	provide	VERB
ejde-397	807	70	that	that	SCONJ
ejde-397	807	71	τ	τ	PROPN
ejde-397	807	72	=	=	SYM
ejde-397	807	73	∞	∞	PROPN
ejde-397	807	74	)	)	PUNCT
ejde-397	808	1	if	if	SCONJ
ejde-397	808	2	and	and	CCONJ
ejde-397	808	3	only	only	ADV
ejde-397	808	4	if	if	SCONJ
ejde-397	808	5	both	both	DET
ejde-397	808	6	operator	operator	NOUN
ejde-397	808	7	families	family	NOUN
ejde-397	808	8	(	(	PUNCT
ejde-397	808	9	r1(t))t≥0	r1(t))t≥0	ADJ
ejde-397	808	10	and	and	CCONJ
ejde-397	808	11	(	(	PUNCT
ejde-397	808	12	r2(t))t≥0	r2(t))t≥0	NOUN
ejde-397	808	13	are	be	AUX
ejde-397	808	14	.	.	PUNCT
ejde-397	809	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	809	2	abstract	abstract	ADJ
ejde-397	809	3	degenerate	degenerate	ADJ
ejde-397	809	4	volterra	volterra	NOUN
ejde-397	809	5	inclusions	inclusion	NOUN
ejde-397	809	6	25	25	NUM
ejde-397	810	1	it	it	PRON
ejde-397	810	2	would	would	AUX
ejde-397	810	3	take	take	VERB
ejde-397	810	4	too	too	ADV
ejde-397	810	5	long	long	ADJ
ejde-397	810	6	to	to	PART
ejde-397	810	7	consider	consider	VERB
ejde-397	810	8	the	the	DET
ejde-397	810	9	notion	notion	NOUN
ejde-397	810	10	of	of	ADP
ejde-397	810	11	q	q	ADJ
ejde-397	810	12	-	-	ADJ
ejde-397	810	13	exponential	exponential	ADJ
ejde-397	810	14	equicontinuity	equicontinuity	NOUN
ejde-397	810	15	for	for	ADP
ejde-397	810	16	the	the	DET
ejde-397	810	17	classes	class	NOUN
ejde-397	810	18	of	of	ADP
ejde-397	810	19	mild	mild	ADJ
ejde-397	810	20	(	(	PUNCT
ejde-397	810	21	a	a	PRON
ejde-397	810	22	,	,	PUNCT
ejde-397	810	23	k)-regularized	k)-regularize	VERB
ejde-397	810	24	c1	c1	NOUN
ejde-397	810	25	-	-	PUNCT
ejde-397	810	26	existence	existence	NOUN
ejde-397	810	27	families	family	NOUN
ejde-397	810	28	and	and	CCONJ
ejde-397	810	29	mild	mild	ADJ
ejde-397	810	30	(	(	PUNCT
ejde-397	810	31	a	a	PRON
ejde-397	810	32	,	,	PUNCT
ejde-397	810	33	k)regularized	k)regularize	VERB
ejde-397	810	34	c2	c2	PROPN
ejde-397	810	35	-	-	PUNCT
ejde-397	810	36	uniqueness	uniqueness	NOUN
ejde-397	810	37	families	family	NOUN
ejde-397	810	38	(	(	PUNCT
ejde-397	810	39	cf	cf	NOUN
ejde-397	810	40	.	.	PUNCT
ejde-397	811	1	[	[	X
ejde-397	811	2	36	36	NUM
ejde-397	811	3	,	,	PUNCT
ejde-397	811	4	section	section	NOUN
ejde-397	811	5	2.4	2.4	NUM
ejde-397	811	6	]	]	PUNCT
ejde-397	811	7	for	for	ADP
ejde-397	811	8	more	more	ADJ
ejde-397	811	9	details	detail	NOUN
ejde-397	811	10	about	about	ADP
ejde-397	811	11	non	non	ADJ
ejde-397	811	12	-	-	ADJ
ejde-397	811	13	degenerate	degenerate	ADJ
ejde-397	811	14	case	case	NOUN
ejde-397	811	15	)	)	PUNCT
ejde-397	811	16	.	.	PUNCT
ejde-397	812	1	if	if	SCONJ
ejde-397	812	2	k(t	k(t	NOUN
ejde-397	812	3	)	)	PUNCT
ejde-397	813	1	=	=	SYM
ejde-397	813	2	gα+1(t	gα+1(t	PROPN
ejde-397	813	3	)	)	PUNCT
ejde-397	813	4	,	,	PUNCT
ejde-397	813	5	where	where	SCONJ
ejde-397	813	6	α	α	PRON
ejde-397	813	7	≥	≥	NOUN
ejde-397	813	8	0	0	NUM
ejde-397	813	9	,	,	PUNCT
ejde-397	813	10	then	then	ADV
ejde-397	813	11	it	it	PRON
ejde-397	813	12	is	be	AUX
ejde-397	813	13	also	also	ADV
ejde-397	813	14	said	say	VERB
ejde-397	813	15	that	that	SCONJ
ejde-397	813	16	(	(	PUNCT
ejde-397	813	17	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	813	18	)	)	PUNCT
ejde-397	813	19	is	be	AUX
ejde-397	813	20	an	an	DET
ejde-397	813	21	α	α	NUM
ejde-397	813	22	-	-	PUNCT
ejde-397	813	23	times	time	NOUN
ejde-397	813	24	integrated	integrate	VERB
ejde-397	813	25	(	(	PUNCT
ejde-397	813	26	a	a	DET
ejde-397	813	27	,	,	PUNCT
ejde-397	813	28	c)-resolvent	c)-resolvent	ADJ
ejde-397	813	29	family	family	NOUN
ejde-397	813	30	;	;	PUNCT
ejde-397	813	31	0	0	NUM
ejde-397	813	32	-	-	PUNCT
ejde-397	813	33	times	time	NOUN
ejde-397	813	34	integrated	integrated	ADJ
ejde-397	813	35	(	(	PUNCT
ejde-397	813	36	a	a	PRON
ejde-397	813	37	,	,	PUNCT
ejde-397	813	38	c)-resolvent	c)-resolvent	ADJ
ejde-397	813	39	family	family	NOUN
ejde-397	813	40	is	be	AUX
ejde-397	813	41	further	far	ADV
ejde-397	813	42	abbreviated	abbreviate	VERB
ejde-397	813	43	to	to	ADP
ejde-397	813	44	(	(	PUNCT
ejde-397	813	45	a	a	DET
ejde-397	813	46	,	,	PUNCT
ejde-397	813	47	c)-resolvent	c)-resolvent	ADJ
ejde-397	813	48	family	family	NOUN
ejde-397	813	49	.	.	PUNCT
ejde-397	814	1	we	we	PRON
ejde-397	814	2	will	will	AUX
ejde-397	814	3	accept	accept	VERB
ejde-397	814	4	a	a	DET
ejde-397	814	5	similar	similar	ADJ
ejde-397	814	6	terminology	terminology	NOUN
ejde-397	814	7	for	for	ADP
ejde-397	814	8	the	the	DET
ejde-397	814	9	classes	class	NOUN
ejde-397	814	10	of	of	ADP
ejde-397	814	11	mild	mild	ADJ
ejde-397	814	12	(	(	PUNCT
ejde-397	814	13	a	a	PRON
ejde-397	814	14	,	,	PUNCT
ejde-397	814	15	k)-regularized	k)-regularize	VERB
ejde-397	814	16	c1	c1	NOUN
ejde-397	814	17	-	-	PUNCT
ejde-397	814	18	existence	existence	NOUN
ejde-397	814	19	families	family	NOUN
ejde-397	814	20	and	and	CCONJ
ejde-397	814	21	mild	mild	ADJ
ejde-397	814	22	(	(	PUNCT
ejde-397	814	23	a	a	PRON
ejde-397	814	24	,	,	PUNCT
ejde-397	814	25	k)-regularized	k)-regularize	VERB
ejde-397	814	26	c2	c2	PROPN
ejde-397	814	27	-	-	PUNCT
ejde-397	814	28	uniqueness	uniqueness	NOUN
ejde-397	814	29	families	family	NOUN
ejde-397	814	30	;	;	PUNCT
ejde-397	814	31	in	in	ADP
ejde-397	814	32	the	the	DET
ejde-397	814	33	case	case	NOUN
ejde-397	814	34	of	of	ADP
ejde-397	814	35	consideration	consideration	NOUN
ejde-397	814	36	of	of	ADP
ejde-397	814	37	convoluted	convoluted	ADJ
ejde-397	814	38	c	c	NOUN
ejde-397	814	39	-	-	PUNCT
ejde-397	814	40	semigroups	semigroup	NOUN
ejde-397	814	41	,	,	PUNCT
ejde-397	814	42	it	it	PRON
ejde-397	814	43	will	will	AUX
ejde-397	814	44	be	be	AUX
ejde-397	814	45	always	always	ADV
ejde-397	814	46	assumed	assume	VERB
ejde-397	814	47	that	that	SCONJ
ejde-397	814	48	the	the	DET
ejde-397	814	49	condition	condition	NOUN
ejde-397	814	50	(	(	PUNCT
ejde-397	814	51	5.1	5.1	NUM
ejde-397	814	52	)	)	PUNCT
ejde-397	814	53	holds	hold	VERB
ejde-397	814	54	with	with	ADP
ejde-397	814	55	a(t	a(t	NOUN
ejde-397	814	56	)	)	PUNCT
ejde-397	814	57	=	=	SYM
ejde-397	814	58	1	1	NUM
ejde-397	814	59	and	and	CCONJ
ejde-397	814	60	the	the	DET
ejde-397	814	61	operator	operator	NOUN
ejde-397	814	62	c1	c1	NOUN
ejde-397	814	63	replaced	replace	VERB
ejde-397	814	64	by	by	ADP
ejde-397	814	65	c.	c.	PROPN
ejde-397	814	66	let	let	VERB
ejde-397	814	67	us	we	PRON
ejde-397	814	68	mention	mention	VERB
ejde-397	814	69	in	in	ADP
ejde-397	814	70	passing	pass	VERB
ejde-397	814	71	that	that	SCONJ
ejde-397	814	72	the	the	DET
ejde-397	814	73	operator	operator	NOUN
ejde-397	814	74	semigroups	semigroup	NOUN
ejde-397	814	75	generated	generate	VERB
ejde-397	814	76	by	by	ADP
ejde-397	814	77	multivalued	multivalued	ADJ
ejde-397	814	78	linear	linear	PROPN
ejde-397	814	79	operators	operator	NOUN
ejde-397	814	80	have	have	AUX
ejde-397	814	81	been	be	AUX
ejde-397	814	82	analyzed	analyze	VERB
ejde-397	814	83	by	by	ADP
ejde-397	814	84	a.	a.	PROPN
ejde-397	814	85	g.	g.	PROPN
ejde-397	814	86	baskakov	baskakov	PROPN
ejde-397	814	87	in	in	ADP
ejde-397	814	88	[	[	X
ejde-397	814	89	4	4	NUM
ejde-397	814	90	]	]	PUNCT
ejde-397	814	91	.	.	PUNCT
ejde-397	815	1	the	the	DET
ejde-397	815	2	following	follow	VERB
ejde-397	815	3	proposition	proposition	NOUN
ejde-397	815	4	can	can	AUX
ejde-397	815	5	be	be	AUX
ejde-397	815	6	proved	prove	VERB
ejde-397	815	7	with	with	ADP
ejde-397	815	8	the	the	DET
ejde-397	815	9	help	help	NOUN
ejde-397	815	10	of	of	ADP
ejde-397	815	11	theorems	theorem	NOUN
ejde-397	815	12	2.3	2.3	NUM
ejde-397	815	13	and	and	CCONJ
ejde-397	815	14	3.1(ii	3.1(ii	NUM
ejde-397	815	15	)	)	PUNCT
ejde-397	815	16	.	.	PUNCT
ejde-397	816	1	proposition	proposition	NOUN
ejde-397	816	2	5.3	5.3	NUM
ejde-397	816	3	.	.	PUNCT
ejde-397	816	4	suppose	suppose	VERB
ejde-397	816	5	that	that	SCONJ
ejde-397	816	6	(	(	PUNCT
ejde-397	816	7	r1(t	r1(t	PROPN
ejde-397	816	8	)	)	PUNCT
ejde-397	816	9	,	,	PUNCT
ejde-397	816	10	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	816	11	)	)	PUNCT
ejde-397	816	12	⊆	⊆	NUM
ejde-397	816	13	l(y	l(y	PROPN
ejde-397	816	14	,	,	PUNCT
ejde-397	816	15	x	x	NOUN
ejde-397	816	16	)	)	PUNCT
ejde-397	816	17	×	×	NOUN
ejde-397	816	18	l(x	l(x	PROPN
ejde-397	816	19	)	)	PUNCT
ejde-397	816	20	is	be	AUX
ejde-397	816	21	a	a	DET
ejde-397	816	22	mild	mild	ADJ
ejde-397	816	23	(	(	PUNCT
ejde-397	816	24	a	a	PRON
ejde-397	816	25	,	,	PUNCT
ejde-397	816	26	k)-regularized	k)-regularize	VERB
ejde-397	816	27	(	(	PUNCT
ejde-397	816	28	c1	c1	NOUN
ejde-397	816	29	,	,	PUNCT
ejde-397	816	30	c2)-existence	c2)-existence	VERB
ejde-397	816	31	and	and	CCONJ
ejde-397	816	32	uniqueness	uniqueness	VERB
ejde-397	816	33	family	family	NOUN
ejde-397	816	34	with	with	ADP
ejde-397	816	35	a	a	DET
ejde-397	816	36	subgenerator	subgenerator	NOUN
ejde-397	816	37	a	a	PRON
ejde-397	816	38	and	and	CCONJ
ejde-397	816	39	(	(	PUNCT
ejde-397	816	40	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	816	41	)	)	PUNCT
ejde-397	816	42	⊆	⊆	NUM
ejde-397	816	43	l(x	l(x	PROPN
ejde-397	816	44	)	)	PUNCT
ejde-397	816	45	is	be	AUX
ejde-397	816	46	an	an	DET
ejde-397	816	47	(	(	PUNCT
ejde-397	816	48	a	a	DET
ejde-397	816	49	,	,	PUNCT
ejde-397	816	50	k)-regularized	k)-regularize	VERB
ejde-397	816	51	c	c	NOUN
ejde-397	816	52	-	-	PUNCT
ejde-397	816	53	resolvent	resolvent	ADJ
ejde-397	816	54	family	family	NOUN
ejde-397	816	55	with	with	ADP
ejde-397	816	56	a	a	DET
ejde-397	816	57	subgenerator	subgenerator	NOUN
ejde-397	816	58	a.	a.	NOUN
ejde-397	816	59	let	let	VERB
ejde-397	816	60	b	b	PROPN
ejde-397	816	61	∈	∈	PROPN
ejde-397	816	62	l1	l1	PROPN
ejde-397	816	63	loc([0	loc([0	PROPN
ejde-397	816	64	,	,	PUNCT
ejde-397	816	65	τ	τ	PROPN
ejde-397	816	66	)	)	PUNCT
ejde-397	816	67	)	)	PUNCT
ejde-397	816	68	be	be	AUX
ejde-397	816	69	such	such	ADJ
ejde-397	816	70	that	that	SCONJ
ejde-397	816	71	a	a	DET
ejde-397	816	72	∗	∗	NOUN
ejde-397	816	73	b	b	NOUN
ejde-397	816	74	6=	6=	ADP
ejde-397	816	75	0	0	NUM
ejde-397	816	76	in	in	ADP
ejde-397	816	77	l1([0	l1([0	NOUN
ejde-397	816	78	,	,	PUNCT
ejde-397	816	79	τ	τ	NOUN
ejde-397	816	80	)	)	PUNCT
ejde-397	816	81	)	)	PUNCT
ejde-397	816	82	and	and	CCONJ
ejde-397	816	83	k	k	PROPN
ejde-397	816	84	∗	∗	PROPN
ejde-397	816	85	b	b	PROPN
ejde-397	816	86	6=	6=	ADP
ejde-397	816	87	0	0	NUM
ejde-397	816	88	in	in	ADP
ejde-397	816	89	c([0	c([0	PROPN
ejde-397	816	90	,	,	PUNCT
ejde-397	816	91	τ	τ	PROPN
ejde-397	816	92	)	)	PUNCT
ejde-397	816	93	)	)	PUNCT
ejde-397	816	94	.	.	PUNCT
ejde-397	817	1	then	then	ADV
ejde-397	817	2	(	(	PUNCT
ejde-397	817	3	(	(	PUNCT
ejde-397	817	4	b	b	NOUN
ejde-397	817	5	∗	∗	NOUN
ejde-397	817	6	r2)(t))t≥0	r2)(t))t≥0	NOUN
ejde-397	817	7	is	be	AUX
ejde-397	817	8	a	a	DET
ejde-397	817	9	mild	mild	ADJ
ejde-397	817	10	(	(	PUNCT
ejde-397	817	11	a	a	DET
ejde-397	817	12	,	,	PUNCT
ejde-397	817	13	k)-regularized	k)-regularize	VERB
ejde-397	817	14	c2	c2	PROPN
ejde-397	817	15	-	-	PUNCT
ejde-397	817	16	uniqueness	uniqueness	PROPN
ejde-397	817	17	family	family	NOUN
ejde-397	817	18	with	with	ADP
ejde-397	817	19	a	a	DET
ejde-397	817	20	subgenerator	subgenerator	NOUN
ejde-397	817	21	a.	a.	NOUN
ejde-397	817	22	furthermore	furthermore	ADV
ejde-397	817	23	,	,	PUNCT
ejde-397	817	24	the	the	DET
ejde-397	817	25	following	follow	VERB
ejde-397	817	26	holds	hold	VERB
ejde-397	817	27	:	:	PUNCT
ejde-397	817	28	(	(	PUNCT
ejde-397	817	29	i	i	NOUN
ejde-397	817	30	)	)	PUNCT
ejde-397	817	31	let	let	VERB
ejde-397	817	32	a	a	PRON
ejde-397	817	33	be	be	AUX
ejde-397	817	34	x1	x1	PRON
ejde-397	817	35	a	a	DET
ejde-397	817	36	×	×	NOUN
ejde-397	818	1	x2	x2	PROPN
ejde-397	818	2	a	a	ADV
ejde-397	818	3	-	-	PUNCT
ejde-397	818	4	closed	closed	ADJ
ejde-397	818	5	.	.	PUNCT
ejde-397	819	1	suppose	suppose	VERB
ejde-397	819	2	that	that	SCONJ
ejde-397	819	3	,	,	PUNCT
ejde-397	819	4	for	for	ADP
ejde-397	819	5	every	every	DET
ejde-397	819	6	y	y	PROPN
ejde-397	819	7	∈	∈	PROPN
ejde-397	819	8	y	y	PROPN
ejde-397	819	9	,	,	PUNCT
ejde-397	819	10	the	the	DET
ejde-397	819	11	mapping	mapping	NOUN
ejde-397	819	12	t	t	PROPN
ejde-397	819	13	7→	7→	NUM
ejde-397	819	14	(	(	PUNCT
ejde-397	819	15	a∗r1)(t)y	a∗r1)(t)y	PROPN
ejde-397	819	16	,	,	PUNCT
ejde-397	819	17	t	t	PROPN
ejde-397	819	18	∈	∈	PROPN
ejde-397	820	1	[	[	X
ejde-397	820	2	0	0	NUM
ejde-397	820	3	,	,	PUNCT
ejde-397	820	4	τ	τ	X
ejde-397	820	5	)	)	PUNCT
ejde-397	820	6	is	be	AUX
ejde-397	820	7	continuous	continuous	ADJ
ejde-397	820	8	in	in	ADP
ejde-397	820	9	x1	x1	PROPN
ejde-397	820	10	a	a	PRON
ejde-397	820	11	and	and	CCONJ
ejde-397	820	12	the	the	DET
ejde-397	820	13	mapping	mapping	NOUN
ejde-397	820	14	t	t	PROPN
ejde-397	820	15	7→	7→	NUM
ejde-397	820	16	r1(t)y	r1(t)y	PROPN
ejde-397	820	17	,	,	PUNCT
ejde-397	820	18	t	t	PROPN
ejde-397	820	19	∈	∈	PROPN
ejde-397	821	1	[	[	X
ejde-397	821	2	0	0	NUM
ejde-397	821	3	,	,	PUNCT
ejde-397	821	4	τ	τ	X
ejde-397	821	5	)	)	PUNCT
ejde-397	821	6	is	be	AUX
ejde-397	821	7	continuous	continuous	ADJ
ejde-397	821	8	in	in	ADP
ejde-397	821	9	x2	x2	PROPN
ejde-397	821	10	a.	a.	NOUN
ejde-397	821	11	then	then	ADV
ejde-397	821	12	(	(	PUNCT
ejde-397	821	13	(	(	PUNCT
ejde-397	821	14	b	b	NOUN
ejde-397	821	15	∗	∗	NOUN
ejde-397	821	16	r1)(t))t≥0	r1)(t))t≥0	NOUN
ejde-397	821	17	is	be	AUX
ejde-397	821	18	a	a	DET
ejde-397	821	19	mild	mild	ADJ
ejde-397	821	20	(	(	PUNCT
ejde-397	821	21	a	a	DET
ejde-397	821	22	,	,	PUNCT
ejde-397	821	23	k)regularized	k)regularize	VERB
ejde-397	821	24	c1	c1	NOUN
ejde-397	821	25	-	-	PUNCT
ejde-397	821	26	existence	existence	NOUN
ejde-397	821	27	family	family	NOUN
ejde-397	821	28	with	with	ADP
ejde-397	821	29	a	a	DET
ejde-397	821	30	subgenerator	subgenerator	NOUN
ejde-397	821	31	a.	a.	NOUN
ejde-397	821	32	(	(	PUNCT
ejde-397	821	33	ii	ii	NOUN
ejde-397	821	34	)	)	PUNCT
ejde-397	821	35	let	let	VERB
ejde-397	821	36	a	a	PRON
ejde-397	821	37	be	be	AUX
ejde-397	821	38	x1	x1	NUM
ejde-397	821	39	a×x2	a×x2	ADP
ejde-397	821	40	a	a	PRON
ejde-397	821	41	-	-	PUNCT
ejde-397	821	42	closed	closed	ADJ
ejde-397	821	43	.	.	PUNCT
ejde-397	822	1	suppose	suppose	VERB
ejde-397	822	2	that	that	SCONJ
ejde-397	822	3	,	,	PUNCT
ejde-397	822	4	for	for	ADP
ejde-397	822	5	every	every	DET
ejde-397	822	6	x	x	PROPN
ejde-397	822	7	∈	∈	PROPN
ejde-397	822	8	d(a	d(a	PROPN
ejde-397	822	9	)	)	PUNCT
ejde-397	822	10	and	and	CCONJ
ejde-397	822	11	y	y	PROPN
ejde-397	822	12	∈	∈	PROPN
ejde-397	822	13	r(a	r(a	PROPN
ejde-397	822	14	)	)	PUNCT
ejde-397	822	15	,	,	PUNCT
ejde-397	822	16	the	the	DET
ejde-397	822	17	mapping	mapping	NOUN
ejde-397	822	18	t	t	NOUN
ejde-397	822	19	7→	7→	NUM
ejde-397	822	20	r(t)x	r(t)x	PROPN
ejde-397	822	21	,	,	PUNCT
ejde-397	822	22	t	t	PROPN
ejde-397	822	23	∈	∈	PROPN
ejde-397	823	1	[	[	X
ejde-397	823	2	0	0	NUM
ejde-397	823	3	,	,	PUNCT
ejde-397	823	4	τ	τ	X
ejde-397	823	5	)	)	PUNCT
ejde-397	823	6	is	be	AUX
ejde-397	823	7	continuous	continuous	ADJ
ejde-397	823	8	in	in	ADP
ejde-397	823	9	x1	x1	PROPN
ejde-397	823	10	a	a	PRON
ejde-397	823	11	and	and	CCONJ
ejde-397	823	12	the	the	DET
ejde-397	823	13	mapping	mapping	NOUN
ejde-397	823	14	t	t	PROPN
ejde-397	823	15	7→	7→	NUM
ejde-397	824	1	r(t)y	r(t)y	PROPN
ejde-397	824	2	,	,	PUNCT
ejde-397	824	3	t	t	PROPN
ejde-397	824	4	∈	∈	PROPN
ejde-397	825	1	[	[	X
ejde-397	825	2	0	0	NUM
ejde-397	825	3	,	,	PUNCT
ejde-397	825	4	τ	τ	X
ejde-397	825	5	)	)	PUNCT
ejde-397	825	6	is	be	AUX
ejde-397	825	7	continuous	continuous	ADJ
ejde-397	825	8	in	in	ADP
ejde-397	825	9	x2	x2	PROPN
ejde-397	825	10	a.	a.	NOUN
ejde-397	825	11	then	then	ADV
ejde-397	825	12	(	(	PUNCT
ejde-397	825	13	(	(	PUNCT
ejde-397	825	14	b	b	X
ejde-397	825	15	∗r)(t))t≥0	∗r)(t))t≥0	PROPN
ejde-397	825	16	is	be	AUX
ejde-397	825	17	a	a	DET
ejde-397	825	18	(	(	PUNCT
ejde-397	825	19	a	a	PRON
ejde-397	825	20	,	,	PUNCT
ejde-397	825	21	k)regularized	k)regularize	VERB
ejde-397	825	22	c	c	X
ejde-397	825	23	-	-	PUNCT
ejde-397	825	24	regularized	regularize	VERB
ejde-397	825	25	family	family	NOUN
ejde-397	825	26	with	with	ADP
ejde-397	825	27	a	a	DET
ejde-397	825	28	subgenerator	subgenerator	NOUN
ejde-397	825	29	a.	a.	NOUN
ejde-397	825	30	although	although	SCONJ
ejde-397	825	31	the	the	DET
ejde-397	825	32	parts	part	NOUN
ejde-397	825	33	(	(	PUNCT
ejde-397	825	34	i	i	NOUN
ejde-397	825	35	)	)	PUNCT
ejde-397	825	36	and	and	CCONJ
ejde-397	825	37	(	(	PUNCT
ejde-397	825	38	ii	ii	NOUN
ejde-397	825	39	)	)	PUNCT
ejde-397	825	40	of	of	ADP
ejde-397	825	41	the	the	DET
ejde-397	825	42	above	above	ADJ
ejde-397	825	43	proposition	proposition	NOUN
ejde-397	825	44	have	have	AUX
ejde-397	825	45	been	be	AUX
ejde-397	825	46	stated	state	VERB
ejde-397	825	47	for	for	ADP
ejde-397	825	48	x1	x1	DET
ejde-397	825	49	a	a	DET
ejde-397	825	50	×x2	×x2	ADJ
ejde-397	825	51	a	a	PRON
ejde-397	825	52	-	-	PUNCT
ejde-397	825	53	closed	close	VERB
ejde-397	825	54	subgenerators	subgenerator	NOUN
ejde-397	825	55	,	,	PUNCT
ejde-397	825	56	the	the	DET
ejde-397	825	57	most	most	ADV
ejde-397	825	58	important	important	ADJ
ejde-397	825	59	case	case	NOUN
ejde-397	825	60	in	in	ADP
ejde-397	825	61	our	our	PRON
ejde-397	825	62	further	further	ADJ
ejde-397	825	63	study	study	NOUN
ejde-397	825	64	will	will	AUX
ejde-397	825	65	be	be	AUX
ejde-397	825	66	that	that	SCONJ
ejde-397	825	67	in	in	ADP
ejde-397	825	68	which	which	PRON
ejde-397	825	69	x1	x1	NOUN
ejde-397	825	70	a	a	X
ejde-397	825	71	=	=	X
ejde-397	825	72	x2	x2	INTJ
ejde-397	825	73	a	a	NOUN
ejde-397	826	1	=	=	PUNCT
ejde-397	826	2	x.	x.	NOUN
ejde-397	826	3	this	this	PRON
ejde-397	826	4	is	be	AUX
ejde-397	826	5	primarily	primarily	ADV
ejde-397	826	6	caused	cause	VERB
ejde-397	826	7	by	by	ADP
ejde-397	826	8	the	the	DET
ejde-397	826	9	following	following	ADJ
ejde-397	826	10	fact	fact	NOUN
ejde-397	826	11	:	:	PUNCT
ejde-397	826	12	let	let	VERB
ejde-397	826	13	a	a	PRON
ejde-397	826	14	be	be	AUX
ejde-397	826	15	a	a	DET
ejde-397	826	16	subgenerator	subgenerator	NOUN
ejde-397	826	17	of	of	ADP
ejde-397	826	18	a	a	DET
ejde-397	826	19	mild	mild	ADJ
ejde-397	826	20	(	(	PUNCT
ejde-397	826	21	a	a	DET
ejde-397	826	22	,	,	PUNCT
ejde-397	826	23	k)-regularized	k)-regularize	VERB
ejde-397	826	24	c1	c1	NOUN
ejde-397	826	25	-	-	PUNCT
ejde-397	826	26	existence	existence	NOUN
ejde-397	826	27	family	family	NOUN
ejde-397	826	28	(	(	PUNCT
ejde-397	826	29	mild	mild	ADJ
ejde-397	826	30	(	(	PUNCT
ejde-397	826	31	a	a	DET
ejde-397	826	32	,	,	PUNCT
ejde-397	826	33	k)-regularized	k)-regularize	VERB
ejde-397	826	34	c2	c2	PROPN
ejde-397	826	35	-	-	PUNCT
ejde-397	826	36	uniqueness	uniqueness	PROPN
ejde-397	826	37	family	family	NOUN
ejde-397	826	38	;	;	PUNCT
ejde-397	826	39	mild	mild	ADJ
ejde-397	826	40	(	(	PUNCT
ejde-397	826	41	a	a	PRON
ejde-397	826	42	,	,	PUNCT
ejde-397	826	43	k)-regularized	k)-regularize	VERB
ejde-397	826	44	c	c	NOUN
ejde-397	826	45	-	-	PUNCT
ejde-397	826	46	resolvent	resolvent	ADJ
ejde-397	826	47	family	family	NOUN
ejde-397	826	48	)	)	PUNCT
ejde-397	826	49	(	(	PUNCT
ejde-397	826	50	r1(t))t∈[0,τ	r1(t))t∈[0,τ	NOUN
ejde-397	826	51	)	)	PUNCT
ejde-397	826	52	(	(	PUNCT
ejde-397	826	53	(	(	PUNCT
ejde-397	826	54	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	826	55	)	)	PUNCT
ejde-397	826	56	;	;	PUNCT
ejde-397	826	57	(	(	PUNCT
ejde-397	826	58	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	826	59	)	)	PUNCT
ejde-397	826	60	)	)	PUNCT
ejde-397	826	61	.	.	PUNCT
ejde-397	827	1	then	then	ADV
ejde-397	827	2	a	a	PRON
ejde-397	827	3	is	be	AUX
ejde-397	827	4	likewise	likewise	ADV
ejde-397	827	5	a	a	DET
ejde-397	827	6	subgenerator	subgenerator	NOUN
ejde-397	827	7	of	of	ADP
ejde-397	827	8	(	(	PUNCT
ejde-397	827	9	r1(t))t∈[0,τ	r1(t))t∈[0,τ	PROPN
ejde-397	827	10	)	)	PUNCT
ejde-397	827	11	(	(	PUNCT
ejde-397	827	12	(	(	PUNCT
ejde-397	827	13	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	827	14	)	)	PUNCT
ejde-397	827	15	;	;	PUNCT
ejde-397	827	16	(	(	PUNCT
ejde-397	827	17	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	827	18	)	)	PUNCT
ejde-397	827	19	,	,	PUNCT
ejde-397	827	20	provided	provide	VERB
ejde-397	827	21	in	in	ADP
ejde-397	827	22	addition	addition	NOUN
ejde-397	827	23	that	that	SCONJ
ejde-397	827	24	(	(	PUNCT
ejde-397	827	25	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	827	26	)	)	PUNCT
ejde-397	827	27	;	;	PUNCT
ejde-397	827	28	(	(	PUNCT
ejde-397	827	29	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	827	30	)	)	PUNCT
ejde-397	827	31	is	be	AUX
ejde-397	827	32	locally	locally	ADV
ejde-397	827	33	equicontinuous	equicontinuous	ADJ
ejde-397	827	34	)	)	PUNCT
ejde-397	827	35	.	.	PUNCT
ejde-397	828	1	suppose	suppose	VERB
ejde-397	828	2	that	that	SCONJ
ejde-397	828	3	(	(	PUNCT
ejde-397	828	4	r1(t	r1(t	PROPN
ejde-397	828	5	)	)	PUNCT
ejde-397	828	6	,	,	PUNCT
ejde-397	828	7	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	828	8	)	)	PUNCT
ejde-397	828	9	is	be	AUX
ejde-397	828	10	a	a	DET
ejde-397	828	11	mild	mild	ADJ
ejde-397	828	12	(	(	PUNCT
ejde-397	828	13	a	a	PRON
ejde-397	828	14	,	,	PUNCT
ejde-397	828	15	k)-regularized	k)-regularize	VERB
ejde-397	828	16	(	(	PUNCT
ejde-397	828	17	c1	c1	NOUN
ejde-397	828	18	,	,	PUNCT
ejde-397	828	19	c2)-existence	c2)-existence	VERB
ejde-397	828	20	and	and	CCONJ
ejde-397	828	21	uniqueness	uniqueness	VERB
ejde-397	828	22	family	family	NOUN
ejde-397	828	23	with	with	ADP
ejde-397	828	24	a	a	DET
ejde-397	828	25	subgenerator	subgenerator	NOUN
ejde-397	828	26	a.	a.	NOUN
ejde-397	828	27	arguing	arguing	NOUN
ejde-397	828	28	as	as	ADP
ejde-397	828	29	in	in	ADP
ejde-397	828	30	non	non	ADJ
ejde-397	828	31	-	-	ADJ
ejde-397	828	32	degenerate	degenerate	ADJ
ejde-397	828	33	case	case	NOUN
ejde-397	828	34	(	(	PUNCT
ejde-397	828	35	cf	cf	NOUN
ejde-397	828	36	.	.	PUNCT
ejde-397	829	1	the	the	DET
ejde-397	829	2	paragraph	paragraph	NOUN
ejde-397	829	3	directly	directly	ADV
ejde-397	829	4	preceding	precede	VERB
ejde-397	829	5	[	[	X
ejde-397	829	6	36	36	NUM
ejde-397	829	7	,	,	PUNCT
ejde-397	829	8	definition	definition	NOUN
ejde-397	829	9	2.8.3	2.8.3	NUM
ejde-397	829	10	]	]	PUNCT
ejde-397	829	11	)	)	PUNCT
ejde-397	829	12	,	,	PUNCT
ejde-397	829	13	we	we	PRON
ejde-397	829	14	may	may	AUX
ejde-397	829	15	conclude	conclude	VERB
ejde-397	829	16	that	that	SCONJ
ejde-397	829	17	(	(	PUNCT
ejde-397	829	18	a	a	DET
ejde-397	829	19	∗r2	∗r2	NOUN
ejde-397	829	20	)	)	PUNCT
ejde-397	829	21	(	(	PUNCT
ejde-397	829	22	s)r1(t)y	s)r1(t)y	NOUN
ejde-397	829	23	−r2(s	−r2(s	NOUN
ejde-397	829	24	)	)	PUNCT
ejde-397	829	25	(	(	PUNCT
ejde-397	829	26	a	a	DET
ejde-397	829	27	∗r1	∗r1	NOUN
ejde-397	829	28	)	)	PUNCT
ejde-397	829	29	(	(	PUNCT
ejde-397	829	30	t)y	t)y	PUNCT
ejde-397	829	31	=	=	PUNCT
ejde-397	829	32	k(t	k(t	NOUN
ejde-397	829	33	)	)	PUNCT
ejde-397	829	34	(	(	PUNCT
ejde-397	829	35	a	a	DET
ejde-397	829	36	∗r2	∗r2	NOUN
ejde-397	829	37	)	)	PUNCT
ejde-397	829	38	(	(	PUNCT
ejde-397	829	39	s)c1y	s)c1y	PROPN
ejde-397	829	40	−	−	PROPN
ejde-397	829	41	k(s)c2	k(s)c2	PROPN
ejde-397	829	42	(	(	PUNCT
ejde-397	829	43	a	a	DET
ejde-397	829	44	∗r1	∗r1	NOUN
ejde-397	829	45	)	)	PUNCT
ejde-397	829	46	(	(	PUNCT
ejde-397	829	47	t)y	t)y	PROPN
ejde-397	829	48	,	,	PUNCT
ejde-397	829	49	t	t	PROPN
ejde-397	829	50	∈	∈	PROPN
ejde-397	830	1	[	[	X
ejde-397	830	2	0	0	NUM
ejde-397	830	3	,	,	PUNCT
ejde-397	830	4	τ	τ	PROPN
ejde-397	830	5	)	)	PUNCT
ejde-397	830	6	,	,	PUNCT
ejde-397	830	7	y	y	PROPN
ejde-397	830	8	∈	∈	PROPN
ejde-397	830	9	y.	y.	NOUN
ejde-397	830	10	(	(	PUNCT
ejde-397	830	11	5.3	5.3	NUM
ejde-397	830	12	)	)	PUNCT
ejde-397	830	13	the	the	DET
ejde-397	830	14	integral	integral	ADJ
ejde-397	830	15	generator	generator	NOUN
ejde-397	830	16	of	of	ADP
ejde-397	830	17	mild	mild	ADJ
ejde-397	830	18	(	(	PUNCT
ejde-397	830	19	a	a	PRON
ejde-397	830	20	,	,	PUNCT
ejde-397	830	21	k)-regularized	k)-regularize	VERB
ejde-397	830	22	c2	c2	PROPN
ejde-397	830	23	-	-	PUNCT
ejde-397	830	24	uniqueness	uniqueness	PROPN
ejde-397	830	25	family	family	NOUN
ejde-397	830	26	(	(	PUNCT
ejde-397	830	27	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	830	28	)	)	PUNCT
ejde-397	830	29	(	(	PUNCT
ejde-397	830	30	mild	mild	ADJ
ejde-397	830	31	(	(	PUNCT
ejde-397	830	32	a	a	PRON
ejde-397	830	33	,	,	PUNCT
ejde-397	830	34	k)-regularized	k)-regularize	VERB
ejde-397	830	35	(	(	PUNCT
ejde-397	830	36	c1	c1	NOUN
ejde-397	830	37	,	,	PUNCT
ejde-397	830	38	c2)-existence	c2)-existence	VERB
ejde-397	830	39	and	and	CCONJ
ejde-397	830	40	uniqueness	uniqueness	VERB
ejde-397	830	41	family	family	NOUN
ejde-397	830	42	(	(	PUNCT
ejde-397	830	43	r1(t	r1(t	PROPN
ejde-397	830	44	)	)	PUNCT
ejde-397	830	45	,	,	PUNCT
ejde-397	830	46	r2(t))t∈[0,τ	r2(t))t∈[0,τ	NOUN
ejde-397	830	47	)	)	PUNCT
ejde-397	830	48	)	)	PUNCT
ejde-397	830	49	is	be	AUX
ejde-397	830	50	defined	define	VERB
ejde-397	830	51	by	by	ADP
ejde-397	830	52	ai	be	VERB
ejde-397	830	53	nt	not	PART
ejde-397	830	54	:	:	PUNCT
ejde-397	830	55	=	=	SYM
ejde-397	830	56	{	{	PUNCT
ejde-397	830	57	(	(	PUNCT
ejde-397	830	58	x	x	NOUN
ejde-397	830	59	,	,	PUNCT
ejde-397	830	60	y	y	NOUN
ejde-397	830	61	)	)	PUNCT
ejde-397	830	62	∈	∈	PROPN
ejde-397	830	63	x	x	X
ejde-397	830	64	×x	×x	X
ejde-397	830	65	:	:	PUNCT
ejde-397	830	66	r2(t)x−	r2(t)x−	PROPN
ejde-397	830	67	k(t)c2x	k(t)c2x	NOUN
ejde-397	830	68	=	=	SYM
ejde-397	830	69	∫	∫	PROPN
ejde-397	830	70	t	t	NOUN
ejde-397	830	71	0	0	NUM
ejde-397	830	72	a(t−	a(t−	PROPN
ejde-397	830	73	s)r2(s)y	s)r2(s)y	NOUN
ejde-397	830	74	ds	ds	PROPN
ejde-397	830	75	,	,	PUNCT
ejde-397	830	76	t	t	PROPN
ejde-397	830	77	∈	∈	PROPN
ejde-397	831	1	[	[	X
ejde-397	831	2	0	0	NUM
ejde-397	831	3	,	,	PUNCT
ejde-397	831	4	τ	τ	PROPN
ejde-397	831	5	)	)	PUNCT
ejde-397	831	6	}	}	PUNCT
ejde-397	831	7	;	;	PUNCT
ejde-397	831	8	26	26	NUM
ejde-397	831	9	m.	m.	NOUN
ejde-397	831	10	kostić	kostić	PUNCT
ejde-397	831	11	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	831	12	we	we	PRON
ejde-397	831	13	define	define	VERB
ejde-397	831	14	the	the	DET
ejde-397	831	15	integral	integral	ADJ
ejde-397	831	16	generator	generator	NOUN
ejde-397	831	17	of	of	ADP
ejde-397	831	18	an	an	DET
ejde-397	831	19	(	(	PUNCT
ejde-397	831	20	a	a	PRON
ejde-397	831	21	,	,	PUNCT
ejde-397	831	22	k)-regularized	k)-regularize	VERB
ejde-397	831	23	c	c	X
ejde-397	831	24	-	-	PUNCT
ejde-397	831	25	regularized	regularize	VERB
ejde-397	831	26	family	family	NOUN
ejde-397	831	27	(	(	PUNCT
ejde-397	831	28	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	831	29	)	)	PUNCT
ejde-397	831	30	in	in	ADP
ejde-397	831	31	the	the	DET
ejde-397	831	32	same	same	ADJ
ejde-397	831	33	way	way	NOUN
ejde-397	831	34	as	as	ADP
ejde-397	831	35	above	above	ADV
ejde-397	831	36	.	.	PUNCT
ejde-397	832	1	the	the	DET
ejde-397	832	2	integral	integral	ADJ
ejde-397	832	3	generator	generator	NOUN
ejde-397	832	4	ai	be	AUX
ejde-397	832	5	nt	not	PART
ejde-397	832	6	is	be	AUX
ejde-397	832	7	an	an	DET
ejde-397	832	8	mlo	mlo	NOUN
ejde-397	832	9	in	in	ADP
ejde-397	832	10	x	x	PUNCT
ejde-397	832	11	which	which	PRON
ejde-397	832	12	is	be	AUX
ejde-397	832	13	,	,	PUNCT
ejde-397	832	14	in	in	ADP
ejde-397	832	15	fact	fact	NOUN
ejde-397	832	16	,	,	PUNCT
ejde-397	832	17	the	the	DET
ejde-397	832	18	maximal	maximal	ADJ
ejde-397	832	19	subgenerator	subgenerator	NOUN
ejde-397	832	20	of	of	ADP
ejde-397	832	21	(	(	PUNCT
ejde-397	832	22	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	832	23	)	)	PUNCT
ejde-397	832	24	(	(	PUNCT
ejde-397	832	25	(	(	PUNCT
ejde-397	832	26	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	832	27	)	)	PUNCT
ejde-397	832	28	)	)	PUNCT
ejde-397	832	29	with	with	ADP
ejde-397	832	30	respect	respect	NOUN
ejde-397	832	31	to	to	ADP
ejde-397	832	32	the	the	DET
ejde-397	832	33	set	set	NOUN
ejde-397	832	34	inclusion	inclusion	NOUN
ejde-397	832	35	;	;	PUNCT
ejde-397	832	36	furthermore	furthermore	ADV
ejde-397	832	37	,	,	PUNCT
ejde-397	832	38	the	the	DET
ejde-397	832	39	assumption	assumption	NOUN
ejde-397	832	40	r2(t)c2	r2(t)c2	X
ejde-397	832	41	=	=	SYM
ejde-397	832	42	c2r2(t	c2r2(t	NOUN
ejde-397	832	43	)	)	PUNCT
ejde-397	832	44	,	,	PUNCT
ejde-397	832	45	t	t	PROPN
ejde-397	832	46	∈	∈	PROPN
ejde-397	833	1	[	[	X
ejde-397	833	2	0	0	NUM
ejde-397	833	3	,	,	PUNCT
ejde-397	833	4	τ	τ	X
ejde-397	833	5	)	)	PUNCT
ejde-397	833	6	implies	imply	VERB
ejde-397	833	7	that	that	SCONJ
ejde-397	833	8	c−1	c−1	PROPN
ejde-397	833	9	2	2	NUM
ejde-397	833	10	aintc2	aintc2	NOUN
ejde-397	833	11	=	=	PRON
ejde-397	833	12	ai	be	VERB
ejde-397	833	13	nt	not	PART
ejde-397	833	14	so	so	SCONJ
ejde-397	833	15	that	that	DET
ejde-397	833	16	c−1aintc	c−1aintc	NOUN
ejde-397	834	1	=	=	PUNCT
ejde-397	834	2	ai	be	VERB
ejde-397	834	3	nt	not	PART
ejde-397	834	4	for	for	ADP
ejde-397	834	5	resolvent	resolvent	ADJ
ejde-397	834	6	families	family	NOUN
ejde-397	834	7	.	.	PUNCT
ejde-397	835	1	the	the	DET
ejde-397	835	2	local	local	ADJ
ejde-397	835	3	equicontinuity	equicontinuity	NOUN
ejde-397	835	4	of	of	ADP
ejde-397	835	5	(	(	PUNCT
ejde-397	835	6	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	835	7	)	)	PUNCT
ejde-397	835	8	(	(	PUNCT
ejde-397	835	9	(	(	PUNCT
ejde-397	835	10	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	835	11	)	)	PUNCT
ejde-397	835	12	)	)	PUNCT
ejde-397	835	13	immediately	immediately	ADV
ejde-397	835	14	implies	imply	VERB
ejde-397	835	15	that	that	SCONJ
ejde-397	835	16	ai	be	AUX
ejde-397	835	17	nt	not	PART
ejde-397	835	18	is	be	AUX
ejde-397	835	19	closed	closed	ADJ
ejde-397	835	20	.	.	PUNCT
ejde-397	836	1	observe	observe	VERB
ejde-397	836	2	that	that	SCONJ
ejde-397	836	3	,	,	PUNCT
ejde-397	836	4	in	in	ADP
ejde-397	836	5	the	the	DET
ejde-397	836	6	above	above	ADJ
ejde-397	836	7	definition	definition	NOUN
ejde-397	836	8	of	of	ADP
ejde-397	836	9	integral	integral	ADJ
ejde-397	836	10	generator	generator	NOUN
ejde-397	836	11	,	,	PUNCT
ejde-397	836	12	we	we	PRON
ejde-397	836	13	do	do	AUX
ejde-397	836	14	not	not	PART
ejde-397	836	15	require	require	VERB
ejde-397	836	16	that	that	SCONJ
ejde-397	836	17	the	the	DET
ejde-397	836	18	function	function	NOUN
ejde-397	836	19	a(t	a(t	NOUN
ejde-397	836	20	)	)	PUNCT
ejde-397	836	21	is	be	AUX
ejde-397	836	22	a	a	DET
ejde-397	836	23	kernel	kernel	NOUN
ejde-397	836	24	on	on	ADP
ejde-397	836	25	[	[	X
ejde-397	836	26	0	0	NUM
ejde-397	836	27	,	,	PUNCT
ejde-397	836	28	τ	τ	PROPN
ejde-397	836	29	)	)	PUNCT
ejde-397	836	30	,	,	PUNCT
ejde-397	836	31	as	as	ADP
ejde-397	836	32	in	in	ADP
ejde-397	836	33	non	non	ADJ
ejde-397	836	34	-	-	ADJ
ejde-397	836	35	degenerate	degenerate	ADJ
ejde-397	836	36	case	case	NOUN
ejde-397	836	37	.	.	PUNCT
ejde-397	837	1	in	in	ADP
ejde-397	837	2	the	the	DET
ejde-397	837	3	case	case	NOUN
ejde-397	837	4	of	of	ADP
ejde-397	837	5	resolvent	resolvent	ADJ
ejde-397	837	6	families	family	NOUN
ejde-397	837	7	,	,	PUNCT
ejde-397	837	8	the	the	DET
ejde-397	837	9	following	follow	VERB
ejde-397	837	10	holds	hold	VERB
ejde-397	837	11	:	:	PUNCT
ejde-397	837	12	(	(	PUNCT
ejde-397	837	13	i	i	NOUN
ejde-397	837	14	)	)	PUNCT
ejde-397	837	15	suppose	suppose	VERB
ejde-397	837	16	that	that	SCONJ
ejde-397	837	17	(	(	PUNCT
ejde-397	837	18	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	837	19	)	)	PUNCT
ejde-397	837	20	is	be	AUX
ejde-397	837	21	locally	locally	ADV
ejde-397	837	22	equicontinuous	equicontinuous	ADJ
ejde-397	837	23	and	and	CCONJ
ejde-397	837	24	a	a	PRON
ejde-397	837	25	is	be	AUX
ejde-397	837	26	a	a	DET
ejde-397	837	27	closed	closed	ADJ
ejde-397	837	28	subgenerator	subgenerator	NOUN
ejde-397	837	29	of	of	ADP
ejde-397	837	30	(	(	PUNCT
ejde-397	837	31	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	837	32	)	)	PUNCT
ejde-397	837	33	.	.	PUNCT
ejde-397	838	1	then(∫	then(∫	NOUN
ejde-397	838	2	t	t	NOUN
ejde-397	838	3	0	0	NUM
ejde-397	838	4	a(t−	a(t−	NOUN
ejde-397	838	5	s)r(s)x	s)r(s)x	NOUN
ejde-397	838	6	ds	ds	ADJ
ejde-397	838	7	,	,	PUNCT
ejde-397	838	8	r(t)x−	r(t)x−	NOUN
ejde-397	838	9	k(t)cx	k(t)cx	NOUN
ejde-397	838	10	)	)	PUNCT
ejde-397	838	11	∈	∈	PROPN
ejde-397	838	12	a	a	PRON
ejde-397	838	13	,	,	PUNCT
ejde-397	838	14	(	(	PUNCT
ejde-397	838	15	5.4	5.4	NUM
ejde-397	838	16	)	)	PUNCT
ejde-397	838	17	for	for	ADP
ejde-397	838	18	t	t	PROPN
ejde-397	838	19	∈	∈	PROPN
ejde-397	839	1	[	[	X
ejde-397	839	2	0	0	NUM
ejde-397	839	3	,	,	PUNCT
ejde-397	839	4	τ	τ	PROPN
ejde-397	839	5	)	)	PUNCT
ejde-397	839	6	,	,	PUNCT
ejde-397	839	7	x	x	PUNCT
ejde-397	839	8	∈	∈	PROPN
ejde-397	839	9	d(a	d(a	PROPN
ejde-397	839	10	)	)	PUNCT
ejde-397	839	11	.	.	PUNCT
ejde-397	840	1	(	(	PUNCT
ejde-397	840	2	ii	ii	NOUN
ejde-397	840	3	)	)	PUNCT
ejde-397	840	4	if	if	SCONJ
ejde-397	840	5	a	a	PRON
ejde-397	840	6	is	be	AUX
ejde-397	840	7	a	a	DET
ejde-397	840	8	subgenerator	subgenerator	NOUN
ejde-397	840	9	of	of	ADP
ejde-397	840	10	(	(	PUNCT
ejde-397	840	11	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	840	12	)	)	PUNCT
ejde-397	840	13	,	,	PUNCT
ejde-397	840	14	then	then	ADV
ejde-397	840	15	c−1ac	c−1ac	PROPN
ejde-397	840	16	is	be	AUX
ejde-397	840	17	a	a	DET
ejde-397	840	18	subgenerator	subgenerator	NOUN
ejde-397	840	19	of	of	ADP
ejde-397	840	20	(	(	PUNCT
ejde-397	840	21	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	840	22	)	)	PUNCT
ejde-397	840	23	,	,	PUNCT
ejde-397	840	24	too	too	ADV
ejde-397	840	25	.	.	PUNCT
ejde-397	841	1	(	(	PUNCT
ejde-397	841	2	iii	iii	X
ejde-397	841	3	)	)	PUNCT
ejde-397	841	4	suppose	suppose	VERB
ejde-397	841	5	that	that	SCONJ
ejde-397	841	6	a(t	a(t	NOUN
ejde-397	841	7	)	)	PUNCT
ejde-397	841	8	is	be	AUX
ejde-397	841	9	a	a	DET
ejde-397	841	10	kernel	kernel	NOUN
ejde-397	841	11	on	on	ADP
ejde-397	841	12	[	[	X
ejde-397	841	13	0	0	NUM
ejde-397	841	14	,	,	PUNCT
ejde-397	841	15	τ	τ	PROPN
ejde-397	841	16	)	)	PUNCT
ejde-397	841	17	,	,	PUNCT
ejde-397	841	18	a	a	PRON
ejde-397	841	19	and	and	CCONJ
ejde-397	841	20	b	b	NOUN
ejde-397	841	21	are	be	AUX
ejde-397	841	22	two	two	NUM
ejde-397	841	23	subgenerators	subgenerator	NOUN
ejde-397	841	24	of	of	ADP
ejde-397	841	25	(	(	PUNCT
ejde-397	841	26	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	841	27	)	)	PUNCT
ejde-397	841	28	,	,	PUNCT
ejde-397	841	29	and	and	CCONJ
ejde-397	841	30	x	x	PUNCT
ejde-397	841	31	∈	∈	PROPN
ejde-397	841	32	d(a	d(a	PROPN
ejde-397	841	33	)	)	PUNCT
ejde-397	841	34	∩	∩	NOUN
ejde-397	841	35	d(b	d(b	PROPN
ejde-397	841	36	)	)	PUNCT
ejde-397	841	37	.	.	PUNCT
ejde-397	842	1	then	then	ADV
ejde-397	842	2	r(t)(y	r(t)(y	ADJ
ejde-397	842	3	−	−	PROPN
ejde-397	842	4	z	z	NOUN
ejde-397	842	5	)	)	PUNCT
ejde-397	842	6	=	=	SYM
ejde-397	842	7	0	0	NUM
ejde-397	842	8	,	,	PUNCT
ejde-397	842	9	t	t	PROPN
ejde-397	842	10	∈	∈	PROPN
ejde-397	843	1	[	[	X
ejde-397	843	2	0	0	NUM
ejde-397	843	3	,	,	PUNCT
ejde-397	843	4	τ	τ	PROPN
ejde-397	843	5	)	)	PUNCT
ejde-397	843	6	for	for	ADP
ejde-397	843	7	each	each	DET
ejde-397	843	8	y	y	PROPN
ejde-397	843	9	∈	∈	PROPN
ejde-397	843	10	ax	ax	NOUN
ejde-397	843	11	and	and	CCONJ
ejde-397	843	12	z	z	NOUN
ejde-397	843	13	∈	∈	PROPN
ejde-397	843	14	bx	bx	PROPN
ejde-397	843	15	.	.	PUNCT
ejde-397	843	16	(	(	PUNCT
ejde-397	843	17	iv	iv	X
ejde-397	843	18	)	)	PUNCT
ejde-397	843	19	let	let	VERB
ejde-397	843	20	a	a	PRON
ejde-397	843	21	be	be	AUX
ejde-397	843	22	a	a	DET
ejde-397	843	23	subgenerator	subgenerator	NOUN
ejde-397	843	24	of	of	ADP
ejde-397	843	25	(	(	PUNCT
ejde-397	843	26	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	843	27	)	)	PUNCT
ejde-397	843	28	,	,	PUNCT
ejde-397	843	29	and	and	CCONJ
ejde-397	843	30	let	let	VERB
ejde-397	843	31	λ	λ	PROPN
ejde-397	843	32	∈	∈	PROPN
ejde-397	843	33	ρc(a	ρc(a	NOUN
ejde-397	843	34	)	)	PUNCT
ejde-397	843	35	(	(	PUNCT
ejde-397	843	36	λ	λ	PROPN
ejde-397	843	37	∈	∈	PROPN
ejde-397	843	38	ρ(a	ρ(a	PROPN
ejde-397	843	39	)	)	PUNCT
ejde-397	843	40	)	)	PUNCT
ejde-397	843	41	.	.	PUNCT
ejde-397	844	1	suppose	suppose	VERB
ejde-397	844	2	that	that	SCONJ
ejde-397	844	3	x	x	PUNCT
ejde-397	844	4	∈	∈	PROPN
ejde-397	844	5	x	x	X
ejde-397	844	6	,	,	PUNCT
ejde-397	844	7	y	y	PROPN
ejde-397	844	8	=	=	SYM
ejde-397	844	9	(	(	PUNCT
ejde-397	844	10	λ−a)−1cx	λ−a)−1cx	X
ejde-397	844	11	(	(	PUNCT
ejde-397	844	12	y	y	NOUN
ejde-397	844	13	=	=	SYM
ejde-397	844	14	(	(	PUNCT
ejde-397	844	15	λ−a)−1x	λ−a)−1x	NOUN
ejde-397	844	16	)	)	PUNCT
ejde-397	844	17	and	and	CCONJ
ejde-397	844	18	z	z	NOUN
ejde-397	844	19	∈	∈	PROPN
ejde-397	844	20	ay	ay	PROPN
ejde-397	844	21	.	.	PUNCT
ejde-397	844	22	then	then	ADV
ejde-397	844	23	theorem	theorem	VERB
ejde-397	844	24	2.4(i	2.4(i	NUM
ejde-397	844	25	)	)	PUNCT
ejde-397	844	26	implies	imply	VERB
ejde-397	844	27	that	that	SCONJ
ejde-397	844	28	λ(λ	λ(λ	PROPN
ejde-397	844	29	−	−	PROPN
ejde-397	844	30	a)−1cx	a)−1cx	X
ejde-397	844	31	−	−	PROPN
ejde-397	844	32	cx	cx	PROPN
ejde-397	844	33	∈	∈	PROPN
ejde-397	844	34	a(λ	a(λ	ADV
ejde-397	844	35	−	−	NOUN
ejde-397	844	36	a)−1cx	a)−1cx	X
ejde-397	844	37	=	=	SYM
ejde-397	844	38	ay	ay	PROPN
ejde-397	844	39	(	(	PUNCT
ejde-397	844	40	λ(λ−a)−1x−x	λ(λ−a)−1x−x	PROPN
ejde-397	844	41	∈	∈	PROPN
ejde-397	844	42	a(λ−a)−1x	a(λ−a)−1x	PROPN
ejde-397	844	43	=	=	SYM
ejde-397	844	44	ay	ay	PROPN
ejde-397	844	45	)	)	PUNCT
ejde-397	844	46	,	,	PUNCT
ejde-397	844	47	so	so	SCONJ
ejde-397	844	48	that	that	SCONJ
ejde-397	844	49	r(t)y−k(t)cy	r(t)y−k(t)cy	PROPN
ejde-397	844	50	∈	∈	PROPN
ejde-397	844	51	a	a	DET
ejde-397	844	52	∫	∫	PROPN
ejde-397	844	53	t	t	PROPN
ejde-397	844	54	0	0	NUM
ejde-397	844	55	a(t−	a(t−	NOUN
ejde-397	844	56	s)r(s)[λ(λ	s)r(s)[λ(λ	VERB
ejde-397	844	57	−	−	PROPN
ejde-397	844	58	a)−1cx	a)−1cx	X
ejde-397	844	59	−	−	PROPN
ejde-397	844	60	cx	cx	NOUN
ejde-397	844	61	]	]	X
ejde-397	844	62	ds	ds	PROPN
ejde-397	845	1	=	=	SYM
ejde-397	845	2	a{λ(λ	a{λ(λ	PRON
ejde-397	845	3	−	−	PROPN
ejde-397	845	4	a)−1c	a)−1c	PROPN
ejde-397	846	1	∫	∫	PROPN
ejde-397	846	2	t	t	PROPN
ejde-397	846	3	0	0	NUM
ejde-397	846	4	a(t	a(t	NOUN
ejde-397	846	5	−	−	NOUN
ejde-397	846	6	s)r(s)x	s)r(s)x	ADV
ejde-397	846	7	ds	ds	ADJ
ejde-397	846	8	−∫	−∫	NOUN
ejde-397	846	9	t	t	NOUN
ejde-397	846	10	0	0	SYM
ejde-397	846	11	a(t−s)r(s)cxds	a(t−s)r(s)cxds	PROPN
ejde-397	846	12	}	}	PUNCT
ejde-397	846	13	,	,	PUNCT
ejde-397	846	14	t	t	PROPN
ejde-397	846	15	∈	∈	PROPN
ejde-397	847	1	[	[	X
ejde-397	847	2	0	0	NUM
ejde-397	847	3	,	,	PUNCT
ejde-397	847	4	τ	τ	X
ejde-397	847	5	)	)	PUNCT
ejde-397	847	6	and	and	CCONJ
ejde-397	847	7	∫	∫	PROPN
ejde-397	847	8	t	t	PROPN
ejde-397	847	9	0	0	NUM
ejde-397	847	10	a(t−s)r(s)cxds	a(t−s)r(s)cxds	PROPN
ejde-397	847	11	∈	∈	PROPN
ejde-397	847	12	d(a	d(a	PROPN
ejde-397	847	13	)	)	PUNCT
ejde-397	847	14	,	,	PUNCT
ejde-397	847	15	t	t	PROPN
ejde-397	847	16	∈	∈	PROPN
ejde-397	848	1	[	[	X
ejde-397	848	2	0	0	NUM
ejde-397	848	3	,	,	PUNCT
ejde-397	848	4	τ	τ	PROPN
ejde-397	848	5	)	)	PUNCT
ejde-397	848	6	;	;	PUNCT
ejde-397	848	7	from	from	ADP
ejde-397	848	8	this	this	PRON
ejde-397	848	9	,	,	PUNCT
ejde-397	848	10	we	we	PRON
ejde-397	848	11	may	may	AUX
ejde-397	848	12	conclude	conclude	VERB
ejde-397	848	13	that	that	PRON
ejde-397	848	14	r(t)cx	r(t)cx	VERB
ejde-397	848	15	−	−	NOUN
ejde-397	848	16	k(t)c2x	k(t)c2x	NOUN
ejde-397	848	17	∈	∈	NOUN
ejde-397	848	18	(	(	PUNCT
ejde-397	848	19	λ	λ	X
ejde-397	848	20	−	−	NOUN
ejde-397	848	21	a)a(λ	a)a(λ	ADP
ejde-397	848	22	−	−	PROPN
ejde-397	849	1	a)−1c	a)−1c	PROPN
ejde-397	849	2	∫	∫	PROPN
ejde-397	849	3	t	t	PROPN
ejde-397	849	4	0	0	NUM
ejde-397	849	5	a(t	a(t	NOUN
ejde-397	849	6	−	−	NOUN
ejde-397	849	7	s)r(s)x	s)r(s)x	NOUN
ejde-397	849	8	ds	ds	ADJ
ejde-397	849	9	,	,	PUNCT
ejde-397	849	10	t	t	PROPN
ejde-397	849	11	∈	∈	PROPN
ejde-397	850	1	[	[	X
ejde-397	850	2	0	0	NUM
ejde-397	850	3	,	,	PUNCT
ejde-397	850	4	τ	τ	PROPN
ejde-397	850	5	)	)	PUNCT
ejde-397	850	6	;	;	PUNCT
ejde-397	850	7	similarly	similarly	ADV
ejde-397	850	8	,	,	PUNCT
ejde-397	850	9	we	we	PRON
ejde-397	850	10	have	have	VERB
ejde-397	850	11	that	that	PRON
ejde-397	850	12	∫	∫	PROPN
ejde-397	850	13	t	t	NOUN
ejde-397	850	14	0	0	NUM
ejde-397	851	1	a(t	a(t	NOUN
ejde-397	851	2	−	−	NOUN
ejde-397	851	3	s)r(s)x	s)r(s)x	NOUN
ejde-397	851	4	ds	ds	ADP
ejde-397	851	5	∈	∈	PROPN
ejde-397	851	6	d(a	d(a	PROPN
ejde-397	851	7	)	)	PUNCT
ejde-397	851	8	and	and	CCONJ
ejde-397	851	9	r(t)x	r(t)x	PROPN
ejde-397	851	10	−	−	PROPN
ejde-397	851	11	k(t)cx	k(t)cx	X
ejde-397	851	12	∈	∈	PROPN
ejde-397	851	13	(	(	PUNCT
ejde-397	851	14	λ	λ	X
ejde-397	851	15	−	−	NOUN
ejde-397	851	16	a)a(λ	a)a(λ	NOUN
ejde-397	851	17	−	−	PROPN
ejde-397	851	18	a)−1	a)−1	NOUN
ejde-397	851	19	∫	∫	PROPN
ejde-397	851	20	t	t	PROPN
ejde-397	851	21	0	0	NUM
ejde-397	852	1	a(t	a(t	NOUN
ejde-397	852	2	−	−	NOUN
ejde-397	852	3	s)r(s)x	s)r(s)x	NOUN
ejde-397	852	4	ds	ds	ADJ
ejde-397	852	5	,	,	PUNCT
ejde-397	852	6	t	t	PROPN
ejde-397	852	7	∈	∈	PROPN
ejde-397	853	1	[	[	X
ejde-397	853	2	0	0	NUM
ejde-397	853	3	,	,	PUNCT
ejde-397	853	4	τ	τ	PROPN
ejde-397	853	5	)	)	PUNCT
ejde-397	853	6	,	,	PUNCT
ejde-397	853	7	provided	provide	VERB
ejde-397	853	8	that	that	SCONJ
ejde-397	853	9	λ	λ	PROPN
ejde-397	853	10	∈	∈	PROPN
ejde-397	853	11	ρ(a	ρ(a	PROPN
ejde-397	853	12	)	)	PUNCT
ejde-397	853	13	.	.	PUNCT
ejde-397	854	1	the	the	DET
ejde-397	854	2	following	follow	VERB
ejde-397	854	3	extensions	extension	NOUN
ejde-397	854	4	of	of	ADP
ejde-397	854	5	[	[	X
ejde-397	854	6	36	36	NUM
ejde-397	854	7	,	,	PUNCT
ejde-397	854	8	theorems	theorem	NOUN
ejde-397	854	9	2.8.5	2.8.5	NUM
ejde-397	854	10	and	and	CCONJ
ejde-397	854	11	2.1.5	2.1.5	NUM
ejde-397	854	12	]	]	PUNCT
ejde-397	854	13	are	be	AUX
ejde-397	854	14	stated	state	VERB
ejde-397	854	15	without	without	ADP
ejde-397	854	16	proofs	proof	NOUN
ejde-397	854	17	.	.	PUNCT
ejde-397	855	1	theorem	theorem	VERB
ejde-397	855	2	5.4	5.4	NUM
ejde-397	855	3	.	.	PUNCT
ejde-397	856	1	suppose	suppose	VERB
ejde-397	856	2	a	a	PRON
ejde-397	856	3	is	be	AUX
ejde-397	856	4	a	a	DET
ejde-397	856	5	closed	closed	ADJ
ejde-397	856	6	mlo	mlo	NOUN
ejde-397	856	7	in	in	ADP
ejde-397	856	8	x	x	PROPN
ejde-397	856	9	,	,	PUNCT
ejde-397	856	10	c1	c1	PROPN
ejde-397	856	11	∈	∈	PROPN
ejde-397	856	12	l(y	l(y	PROPN
ejde-397	856	13	,	,	PUNCT
ejde-397	856	14	x	x	NOUN
ejde-397	856	15	)	)	PUNCT
ejde-397	856	16	,	,	PUNCT
ejde-397	856	17	c2	c2	PROPN
ejde-397	856	18	∈	∈	PROPN
ejde-397	856	19	l(x	l(x	PROPN
ejde-397	856	20	)	)	PUNCT
ejde-397	856	21	,	,	PUNCT
ejde-397	856	22	c2	c2	PROPN
ejde-397	856	23	is	be	AUX
ejde-397	856	24	injective	injective	ADJ
ejde-397	856	25	,	,	PUNCT
ejde-397	856	26	ω0	ω0	ADV
ejde-397	856	27	≥	≥	NOUN
ejde-397	856	28	0	0	NUM
ejde-397	856	29	and	and	CCONJ
ejde-397	856	30	ω	ω	NUM
ejde-397	856	31	≥	≥	NOUN
ejde-397	856	32	max(ω0	max(ω0	PROPN
ejde-397	856	33	,	,	PUNCT
ejde-397	856	34	abs(|a|	abs(|a|	ADJ
ejde-397	856	35	)	)	PUNCT
ejde-397	856	36	,	,	PUNCT
ejde-397	856	37	abs(k	abs(k	PROPN
ejde-397	856	38	)	)	PUNCT
ejde-397	856	39	)	)	PUNCT
ejde-397	856	40	.	.	PUNCT
ejde-397	857	1	(	(	PUNCT
ejde-397	857	2	i	i	NOUN
ejde-397	857	3	)	)	PUNCT
ejde-397	857	4	let	let	VERB
ejde-397	857	5	(	(	PUNCT
ejde-397	857	6	r1(t	r1(t	PROPN
ejde-397	857	7	)	)	PUNCT
ejde-397	857	8	,	,	PUNCT
ejde-397	857	9	r2(t))t≥0	r2(t))t≥0	PROPN
ejde-397	857	10	⊆	⊆	NUM
ejde-397	857	11	l(y	l(y	PROPN
ejde-397	857	12	,	,	PUNCT
ejde-397	857	13	x	x	NOUN
ejde-397	857	14	)	)	PUNCT
ejde-397	857	15	×	×	NOUN
ejde-397	857	16	l(x	l(x	PROPN
ejde-397	857	17	)	)	PUNCT
ejde-397	857	18	be	be	AUX
ejde-397	857	19	strongly	strongly	ADV
ejde-397	857	20	continuous	continuous	ADJ
ejde-397	857	21	,	,	PUNCT
ejde-397	857	22	and	and	CCONJ
ejde-397	857	23	let	let	VERB
ejde-397	857	24	the	the	DET
ejde-397	857	25	family	family	NOUN
ejde-397	857	26	{	{	PUNCT
ejde-397	857	27	e−ωtri(t	e−ωtri(t	PROPN
ejde-397	857	28	)	)	PUNCT
ejde-397	857	29	:	:	PUNCT
ejde-397	858	1	t	t	X
ejde-397	858	2	≥	≥	NOUN
ejde-397	858	3	0	0	NUM
ejde-397	858	4	}	}	PUNCT
ejde-397	858	5	be	be	AUX
ejde-397	858	6	equicontinuous	equicontinuous	ADJ
ejde-397	858	7	for	for	ADP
ejde-397	858	8	i	i	PROPN
ejde-397	858	9	=	=	NOUN
ejde-397	858	10	1	1	NUM
ejde-397	858	11	,	,	PUNCT
ejde-397	858	12	2	2	NUM
ejde-397	858	13	.	.	PUNCT
ejde-397	859	1	(	(	PUNCT
ejde-397	859	2	a	a	X
ejde-397	859	3	)	)	PUNCT
ejde-397	859	4	suppose	suppose	VERB
ejde-397	859	5	(	(	PUNCT
ejde-397	859	6	r1(t	r1(t	PROPN
ejde-397	859	7	)	)	PUNCT
ejde-397	859	8	,	,	PUNCT
ejde-397	859	9	r2(t))t≥0	r2(t))t≥0	PROPN
ejde-397	859	10	is	be	AUX
ejde-397	859	11	a	a	DET
ejde-397	859	12	mild	mild	ADJ
ejde-397	859	13	(	(	PUNCT
ejde-397	859	14	a	a	PRON
ejde-397	859	15	,	,	PUNCT
ejde-397	859	16	k)-regularized	k)-regularize	VERB
ejde-397	859	17	(	(	PUNCT
ejde-397	859	18	c1	c1	NOUN
ejde-397	859	19	,	,	PUNCT
ejde-397	859	20	c2)-existence	c2)-existence	VERB
ejde-397	859	21	and	and	CCONJ
ejde-397	859	22	uniqueness	uniqueness	VERB
ejde-397	859	23	family	family	NOUN
ejde-397	859	24	with	with	ADP
ejde-397	859	25	a	a	DET
ejde-397	859	26	subgenerator	subgenerator	NOUN
ejde-397	859	27	a.	a.	NOUN
ejde-397	859	28	then	then	ADV
ejde-397	859	29	,	,	PUNCT
ejde-397	859	30	for	for	ADP
ejde-397	859	31	every	every	DET
ejde-397	859	32	λ	λ	PROPN
ejde-397	859	33	∈	∈	PROPN
ejde-397	859	34	c	c	NOUN
ejde-397	859	35	with	with	ADP
ejde-397	859	36	<	<	X
ejde-397	859	37	λ	λ	X
ejde-397	859	38	>	>	X
ejde-397	859	39	ω	ω	PROPN
ejde-397	859	40	and	and	CCONJ
ejde-397	859	41	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	859	42	)	)	PUNCT
ejde-397	860	1	6=	6=	ADP
ejde-397	860	2	0	0	NUM
ejde-397	860	3	,	,	PUNCT
ejde-397	860	4	the	the	DET
ejde-397	860	5	operator	operator	NOUN
ejde-397	860	6	i	i	PRON
ejde-397	860	7	−	−	VERB
ejde-397	860	8	ã(λ)a	ã(λ)a	ADP
ejde-397	860	9	is	be	AUX
ejde-397	860	10	injective	injective	ADJ
ejde-397	860	11	,	,	PUNCT
ejde-397	860	12	r(c1	r(c1	NOUN
ejde-397	860	13	)	)	PUNCT
ejde-397	860	14	⊆	⊆	NUM
ejde-397	860	15	r(i	r(i	PROPN
ejde-397	860	16	−	−	PROPN
ejde-397	860	17	ã(λ)a	ã(λ)a	NUM
ejde-397	860	18	)	)	PUNCT
ejde-397	860	19	,	,	PUNCT
ejde-397	860	20	k̃(λ	k̃(λ	PROPN
ejde-397	860	21	)	)	PUNCT
ejde-397	860	22	(	(	PUNCT
ejde-397	860	23	i	i	PRON
ejde-397	860	24	−	−	VERB
ejde-397	860	25	ã(λ)a	ã(λ)a	ADP
ejde-397	860	26	)	)	PUNCT
ejde-397	860	27	−1	−1	NOUN
ejde-397	860	28	c1y	c1y	NOUN
ejde-397	860	29	=	=	SYM
ejde-397	861	1	∫	∫	PROPN
ejde-397	861	2	∞	∞	NUM
ejde-397	861	3	0	0	NUM
ejde-397	862	1	e−λtr1(t)y	e−λtr1(t)y	ADV
ejde-397	862	2	dt	dt	NOUN
ejde-397	862	3	,	,	PUNCT
ejde-397	862	4	y	y	PROPN
ejde-397	862	5	∈	∈	PROPN
ejde-397	862	6	y	y	PROPN
ejde-397	862	7	,	,	PUNCT
ejde-397	862	8	(	(	PUNCT
ejde-397	862	9	5.5	5.5	NUM
ejde-397	862	10	)	)	PUNCT
ejde-397	862	11	{	{	PUNCT
ejde-397	862	12	1	1	NUM
ejde-397	862	13	ã(z	ã(z	PROPN
ejde-397	862	14	)	)	PUNCT
ejde-397	862	15	:	:	PUNCT
ejde-397	863	1	<	<	X
ejde-397	863	2	z	z	X
ejde-397	863	3	>	>	X
ejde-397	863	4	ω	ω	PROPN
ejde-397	863	5	,	,	PUNCT
ejde-397	863	6	k̃(z)ã(z	k̃(z)ã(z	PROPN
ejde-397	863	7	)	)	PUNCT
ejde-397	863	8	6=	6=	ADP
ejde-397	863	9	0	0	NUM
ejde-397	863	10	}	}	PUNCT
ejde-397	863	11	⊆	⊆	NUM
ejde-397	863	12	ρc1	ρc1	X
ejde-397	863	13	(	(	PUNCT
ejde-397	863	14	a	a	X
ejde-397	863	15	)	)	PUNCT
ejde-397	863	16	,	,	PUNCT
ejde-397	863	17	(	(	PUNCT
ejde-397	863	18	5.6	5.6	NUM
ejde-397	863	19	)	)	PUNCT
ejde-397	863	20	k̃(λ)c2x	k̃(λ)c2x	NOUN
ejde-397	864	1	=	=	PUNCT
ejde-397	864	2	∫	∫	PROPN
ejde-397	864	3	∞	∞	PROPN
ejde-397	864	4	0	0	PROPN
ejde-397	864	5	e−λt	e−λt	NOUN
ejde-397	864	6	[	[	PUNCT
ejde-397	864	7	r2(t)x−	r2(t)x−	PROPN
ejde-397	864	8	(	(	PUNCT
ejde-397	864	9	a	a	DET
ejde-397	864	10	∗r2	∗r2	NOUN
ejde-397	864	11	)	)	PUNCT
ejde-397	864	12	(	(	PUNCT
ejde-397	864	13	t)y	t)y	PUNCT
ejde-397	864	14	]	]	X
ejde-397	865	1	dt	dt	X
ejde-397	865	2	,	,	PUNCT
ejde-397	865	3	(	(	PUNCT
ejde-397	865	4	5.7	5.7	NUM
ejde-397	865	5	)	)	PUNCT
ejde-397	865	6	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	865	7	abstract	abstract	ADJ
ejde-397	865	8	degenerate	degenerate	ADJ
ejde-397	865	9	volterra	volterra	NOUN
ejde-397	865	10	inclusions	inclusion	NOUN
ejde-397	865	11	27	27	NUM
ejde-397	865	12	whenever	whenever	SCONJ
ejde-397	865	13	(	(	PUNCT
ejde-397	865	14	x	x	NOUN
ejde-397	865	15	,	,	PUNCT
ejde-397	865	16	y	y	NOUN
ejde-397	865	17	)	)	PUNCT
ejde-397	865	18	∈	∈	PROPN
ejde-397	865	19	a.	a.	NOUN
ejde-397	865	20	here	here	ADV
ejde-397	865	21	,	,	PUNCT
ejde-397	865	22	ρc1	ρc1	ADJ
ejde-397	865	23	(	(	PUNCT
ejde-397	865	24	a	a	X
ejde-397	865	25	)	)	PUNCT
ejde-397	865	26	is	be	AUX
ejde-397	865	27	defined	define	VERB
ejde-397	865	28	in	in	ADP
ejde-397	865	29	the	the	DET
ejde-397	865	30	obvious	obvious	ADJ
ejde-397	865	31	way	way	NOUN
ejde-397	865	32	.	.	PUNCT
ejde-397	866	1	(	(	PUNCT
ejde-397	866	2	b	b	X
ejde-397	866	3	)	)	PUNCT
ejde-397	866	4	let	let	VERB
ejde-397	866	5	(	(	PUNCT
ejde-397	866	6	5.6	5.6	NUM
ejde-397	866	7	)	)	PUNCT
ejde-397	866	8	hold	hold	VERB
ejde-397	866	9	,	,	PUNCT
ejde-397	866	10	and	and	CCONJ
ejde-397	866	11	let	let	VERB
ejde-397	866	12	(	(	PUNCT
ejde-397	866	13	5.5	5.5	NUM
ejde-397	866	14	)	)	PUNCT
ejde-397	866	15	and	and	CCONJ
ejde-397	866	16	(	(	PUNCT
ejde-397	866	17	5.7	5.7	NUM
ejde-397	866	18	)	)	PUNCT
ejde-397	866	19	hold	hold	VERB
ejde-397	866	20	for	for	ADP
ejde-397	866	21	any	any	DET
ejde-397	866	22	λ	λ	PROPN
ejde-397	866	23	∈	∈	PROPN
ejde-397	866	24	c	c	NOUN
ejde-397	866	25	with	with	ADP
ejde-397	866	26	<	<	X
ejde-397	866	27	λ	λ	X
ejde-397	866	28	>	>	X
ejde-397	866	29	ω	ω	PROPN
ejde-397	866	30	and	and	CCONJ
ejde-397	866	31	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	866	32	)	)	PUNCT
ejde-397	866	33	6=	6=	ADP
ejde-397	866	34	0	0	X
ejde-397	866	35	.	.	PUNCT
ejde-397	867	1	then	then	ADV
ejde-397	867	2	(	(	PUNCT
ejde-397	867	3	r1(t	r1(t	PROPN
ejde-397	867	4	)	)	PUNCT
ejde-397	867	5	,	,	PUNCT
ejde-397	867	6	r2(t))t≥0	r2(t))t≥0	PROPN
ejde-397	867	7	is	be	AUX
ejde-397	867	8	a	a	DET
ejde-397	867	9	mild	mild	ADJ
ejde-397	867	10	(	(	PUNCT
ejde-397	867	11	a	a	PRON
ejde-397	867	12	,	,	PUNCT
ejde-397	867	13	k)-regularized	k)-regularize	VERB
ejde-397	867	14	(	(	PUNCT
ejde-397	867	15	c1	c1	NOUN
ejde-397	867	16	,	,	PUNCT
ejde-397	867	17	c2)existence	c2)existence	NOUN
ejde-397	867	18	and	and	CCONJ
ejde-397	867	19	uniqueness	uniqueness	ADJ
ejde-397	867	20	family	family	NOUN
ejde-397	867	21	with	with	ADP
ejde-397	867	22	a	a	DET
ejde-397	867	23	subgenerator	subgenerator	NOUN
ejde-397	867	24	a.	a.	NOUN
ejde-397	867	25	(	(	PUNCT
ejde-397	867	26	ii	ii	NOUN
ejde-397	867	27	)	)	PUNCT
ejde-397	867	28	let	let	VERB
ejde-397	867	29	(	(	PUNCT
ejde-397	867	30	r1(t))t≥0	r1(t))t≥0	VERB
ejde-397	867	31	be	be	AUX
ejde-397	867	32	strongly	strongly	ADV
ejde-397	867	33	continuous	continuous	ADJ
ejde-397	867	34	,	,	PUNCT
ejde-397	867	35	and	and	CCONJ
ejde-397	867	36	let	let	VERB
ejde-397	867	37	the	the	DET
ejde-397	867	38	family	family	NOUN
ejde-397	867	39	{	{	PUNCT
ejde-397	867	40	e−ωtr1(t	e−ωtr1(t	PROPN
ejde-397	867	41	)	)	PUNCT
ejde-397	867	42	:	:	PUNCT
ejde-397	868	1	t	t	X
ejde-397	868	2	≥	≥	NOUN
ejde-397	868	3	0	0	NUM
ejde-397	868	4	}	}	PUNCT
ejde-397	868	5	be	be	AUX
ejde-397	868	6	equicontinuous	equicontinuous	ADJ
ejde-397	868	7	.	.	PUNCT
ejde-397	869	1	then	then	ADV
ejde-397	869	2	(	(	PUNCT
ejde-397	869	3	r1(t))t≥0	r1(t))t≥0	PROPN
ejde-397	869	4	is	be	AUX
ejde-397	869	5	a	a	DET
ejde-397	869	6	mild	mild	ADJ
ejde-397	869	7	(	(	PUNCT
ejde-397	869	8	a	a	DET
ejde-397	869	9	,	,	PUNCT
ejde-397	869	10	k)-regularized	k)-regularize	VERB
ejde-397	869	11	c1	c1	NOUN
ejde-397	869	12	-	-	PUNCT
ejde-397	869	13	existence	existence	NOUN
ejde-397	869	14	family	family	NOUN
ejde-397	869	15	with	with	ADP
ejde-397	869	16	a	a	DET
ejde-397	869	17	subgenerator	subgenerator	NOUN
ejde-397	869	18	a	a	DET
ejde-397	869	19	if	if	NOUN
ejde-397	870	1	and	and	CCONJ
ejde-397	870	2	only	only	ADV
ejde-397	870	3	if	if	SCONJ
ejde-397	870	4	for	for	ADP
ejde-397	870	5	every	every	DET
ejde-397	870	6	λ	λ	PROPN
ejde-397	870	7	∈	∈	PROPN
ejde-397	870	8	c	c	NOUN
ejde-397	870	9	with	with	ADP
ejde-397	870	10	<	<	X
ejde-397	870	11	λ	λ	X
ejde-397	870	12	>	>	X
ejde-397	870	13	ω	ω	PROPN
ejde-397	870	14	and	and	CCONJ
ejde-397	870	15	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	870	16	)	)	PUNCT
ejde-397	870	17	6=	6=	ADP
ejde-397	870	18	0	0	NUM
ejde-397	870	19	,	,	PUNCT
ejde-397	870	20	one	one	PRON
ejde-397	870	21	has	have	VERB
ejde-397	870	22	r(c1	r(c1	NOUN
ejde-397	870	23	)	)	PUNCT
ejde-397	870	24	⊆	⊆	NUM
ejde-397	870	25	r(i	r(i	PROPN
ejde-397	870	26	−	−	PROPN
ejde-397	870	27	ã(λ)a	ã(λ)a	PROPN
ejde-397	870	28	)	)	PUNCT
ejde-397	870	29	and	and	CCONJ
ejde-397	870	30	k̃(λ)c1y	k̃(λ)c1y	PROPN
ejde-397	870	31	∈	∈	PROPN
ejde-397	870	32	(	(	PUNCT
ejde-397	870	33	i	i	PRON
ejde-397	870	34	−	−	VERB
ejde-397	870	35	ã(λ)a	ã(λ)a	ADP
ejde-397	870	36	)	)	PUNCT
ejde-397	870	37	∫	∫	PROPN
ejde-397	871	1	∞	∞	PROPN
ejde-397	871	2	0	0	NUM
ejde-397	872	1	e−λtr1(t)y	e−λtr1(t)y	ADV
ejde-397	872	2	dt	dt	NOUN
ejde-397	872	3	,	,	PUNCT
ejde-397	872	4	y	y	PROPN
ejde-397	872	5	∈	∈	PROPN
ejde-397	872	6	y.	y.	PROPN
ejde-397	872	7	(	(	PUNCT
ejde-397	872	8	iii	iii	NOUN
ejde-397	872	9	)	)	PUNCT
ejde-397	872	10	let	let	VERB
ejde-397	872	11	(	(	PUNCT
ejde-397	872	12	r2(t))t≥0	r2(t))t≥0	VERB
ejde-397	872	13	be	be	AUX
ejde-397	872	14	strongly	strongly	ADV
ejde-397	872	15	continuous	continuous	ADJ
ejde-397	872	16	,	,	PUNCT
ejde-397	872	17	and	and	CCONJ
ejde-397	872	18	let	let	VERB
ejde-397	872	19	the	the	DET
ejde-397	872	20	family	family	NOUN
ejde-397	872	21	{	{	PUNCT
ejde-397	872	22	e−ωtr2(t	e−ωtr2(t	PROPN
ejde-397	872	23	)	)	PUNCT
ejde-397	872	24	:	:	PUNCT
ejde-397	873	1	t	t	X
ejde-397	873	2	≥	≥	NOUN
ejde-397	873	3	0	0	NUM
ejde-397	873	4	}	}	PUNCT
ejde-397	873	5	be	be	AUX
ejde-397	873	6	equicontinuous	equicontinuous	ADJ
ejde-397	873	7	.	.	PUNCT
ejde-397	874	1	then	then	ADV
ejde-397	874	2	(	(	PUNCT
ejde-397	874	3	r2(t))t≥0	r2(t))t≥0	NOUN
ejde-397	874	4	is	be	AUX
ejde-397	874	5	a	a	DET
ejde-397	874	6	mild	mild	ADJ
ejde-397	874	7	(	(	PUNCT
ejde-397	874	8	a	a	DET
ejde-397	874	9	,	,	PUNCT
ejde-397	874	10	k)-regularized	k)-regularize	VERB
ejde-397	874	11	c2	c2	PROPN
ejde-397	874	12	-	-	PUNCT
ejde-397	874	13	uniqueness	uniqueness	PROPN
ejde-397	874	14	family	family	NOUN
ejde-397	874	15	with	with	ADP
ejde-397	874	16	a	a	DET
ejde-397	874	17	subgenerator	subgenerator	NOUN
ejde-397	874	18	a	a	DET
ejde-397	874	19	if	if	NOUN
ejde-397	875	1	and	and	CCONJ
ejde-397	875	2	only	only	ADV
ejde-397	875	3	if	if	SCONJ
ejde-397	875	4	for	for	ADP
ejde-397	875	5	every	every	DET
ejde-397	875	6	λ	λ	PROPN
ejde-397	875	7	∈	∈	PROPN
ejde-397	875	8	c	c	NOUN
ejde-397	875	9	with	with	ADP
ejde-397	875	10	<	<	X
ejde-397	875	11	λ	λ	X
ejde-397	875	12	>	>	X
ejde-397	875	13	ω	ω	PROPN
ejde-397	875	14	and	and	CCONJ
ejde-397	875	15	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	875	16	)	)	PUNCT
ejde-397	875	17	6=	6=	ADP
ejde-397	875	18	0	0	NUM
ejde-397	875	19	,	,	PUNCT
ejde-397	875	20	the	the	DET
ejde-397	875	21	operator	operator	NOUN
ejde-397	875	22	i	i	PRON
ejde-397	875	23	−	−	VERB
ejde-397	875	24	ã(λ)a	ã(λ)a	ADP
ejde-397	875	25	is	be	AUX
ejde-397	875	26	injective	injective	ADJ
ejde-397	875	27	and	and	CCONJ
ejde-397	875	28	(	(	PUNCT
ejde-397	875	29	5.7	5.7	NUM
ejde-397	875	30	)	)	PUNCT
ejde-397	875	31	holds	hold	VERB
ejde-397	875	32	.	.	PUNCT
ejde-397	876	1	theorem	theorem	VERB
ejde-397	876	2	5.5	5.5	NUM
ejde-397	876	3	.	.	PUNCT
ejde-397	877	1	let	let	AUX
ejde-397	877	2	(	(	PUNCT
ejde-397	877	3	r(t))t≥0	r(t))t≥0	NOUN
ejde-397	877	4	⊆	⊆	NUM
ejde-397	877	5	l(x	l(x	PROPN
ejde-397	877	6	)	)	PUNCT
ejde-397	877	7	be	be	AUX
ejde-397	877	8	a	a	DET
ejde-397	877	9	strongly	strongly	ADV
ejde-397	877	10	continuous	continuous	ADJ
ejde-397	877	11	operator	operator	NOUN
ejde-397	877	12	family	family	NOUN
ejde-397	877	13	such	such	ADJ
ejde-397	877	14	that	that	SCONJ
ejde-397	877	15	there	there	PRON
ejde-397	877	16	exists	exist	VERB
ejde-397	877	17	ω	ω	PROPN
ejde-397	877	18	≥	≥	NOUN
ejde-397	877	19	0	0	NUM
ejde-397	877	20	satisfying	satisfy	VERB
ejde-397	877	21	that	that	SCONJ
ejde-397	877	22	the	the	DET
ejde-397	877	23	family	family	NOUN
ejde-397	877	24	{	{	PUNCT
ejde-397	877	25	e−ωtr(t	e−ωtr(t	NUM
ejde-397	877	26	)	)	PUNCT
ejde-397	877	27	:	:	PUNCT
ejde-397	877	28	t	t	X
ejde-397	877	29	≥	≥	NOUN
ejde-397	877	30	0	0	NUM
ejde-397	877	31	}	}	PUNCT
ejde-397	877	32	is	be	AUX
ejde-397	877	33	equicontinuous	equicontinuous	ADJ
ejde-397	877	34	,	,	PUNCT
ejde-397	877	35	and	and	CCONJ
ejde-397	877	36	let	let	VERB
ejde-397	877	37	ω0	ω0	ADV
ejde-397	877	38	>	>	ADV
ejde-397	877	39	max(ω	max(ω	PROPN
ejde-397	877	40	,	,	PUNCT
ejde-397	877	41	abs(|a|	abs(|a|	ADJ
ejde-397	877	42	)	)	PUNCT
ejde-397	877	43	,	,	PUNCT
ejde-397	877	44	abs(k	abs(k	PROPN
ejde-397	877	45	)	)	PUNCT
ejde-397	877	46	)	)	PUNCT
ejde-397	877	47	.	.	PUNCT
ejde-397	878	1	suppose	suppose	VERB
ejde-397	878	2	that	that	SCONJ
ejde-397	878	3	a	a	PRON
ejde-397	878	4	is	be	AUX
ejde-397	878	5	a	a	DET
ejde-397	878	6	closed	closed	ADJ
ejde-397	878	7	mlo	mlo	NOUN
ejde-397	878	8	in	in	ADP
ejde-397	878	9	x	x	PROPN
ejde-397	878	10	and	and	CCONJ
ejde-397	878	11	ca	ca	PROPN
ejde-397	878	12	⊆	⊆	NUM
ejde-397	878	13	ac	ac	NOUN
ejde-397	878	14	.	.	PUNCT
ejde-397	879	1	(	(	PUNCT
ejde-397	879	2	i	i	NOUN
ejde-397	879	3	)	)	PUNCT
ejde-397	879	4	assume	assume	VERB
ejde-397	879	5	that	that	SCONJ
ejde-397	879	6	a	a	PRON
ejde-397	879	7	is	be	AUX
ejde-397	879	8	a	a	DET
ejde-397	879	9	subgenerator	subgenerator	NOUN
ejde-397	879	10	of	of	ADP
ejde-397	879	11	the	the	DET
ejde-397	879	12	global	global	ADJ
ejde-397	879	13	(	(	PUNCT
ejde-397	879	14	a	a	PRON
ejde-397	879	15	,	,	PUNCT
ejde-397	879	16	k)-regularized	k)-regularize	VERB
ejde-397	879	17	c	c	NOUN
ejde-397	879	18	-	-	PUNCT
ejde-397	879	19	resolvent	resolvent	ADJ
ejde-397	879	20	family	family	NOUN
ejde-397	879	21	(	(	PUNCT
ejde-397	879	22	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	879	23	satisfying	satisfying	NOUN
ejde-397	879	24	(	(	PUNCT
ejde-397	879	25	5.1	5.1	NUM
ejde-397	879	26	)	)	PUNCT
ejde-397	879	27	for	for	ADP
ejde-397	879	28	all	all	PRON
ejde-397	879	29	x	x	PUNCT
ejde-397	879	30	=	=	SYM
ejde-397	879	31	y	y	PROPN
ejde-397	879	32	∈	∈	PROPN
ejde-397	879	33	x.	x.	NOUN
ejde-397	879	34	then	then	ADV
ejde-397	879	35	,	,	PUNCT
ejde-397	879	36	for	for	ADP
ejde-397	879	37	every	every	DET
ejde-397	879	38	λ	λ	PROPN
ejde-397	879	39	∈	∈	PROPN
ejde-397	879	40	c	c	NOUN
ejde-397	879	41	with	with	ADP
ejde-397	879	42	<	<	X
ejde-397	879	43	λ	λ	X
ejde-397	879	44	>	>	X
ejde-397	879	45	ω0	ω0	PROPN
ejde-397	879	46	and	and	CCONJ
ejde-397	879	47	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	879	48	)	)	PUNCT
ejde-397	879	49	6=	6=	ADP
ejde-397	879	50	0	0	NUM
ejde-397	879	51	,	,	PUNCT
ejde-397	879	52	the	the	DET
ejde-397	879	53	operator	operator	NOUN
ejde-397	879	54	i	i	PRON
ejde-397	879	55	−	−	VERB
ejde-397	879	56	ã(λ)a	ã(λ)a	ADP
ejde-397	879	57	is	be	AUX
ejde-397	879	58	injective	injective	ADJ
ejde-397	879	59	,	,	PUNCT
ejde-397	879	60	r(c	r(c	NUM
ejde-397	879	61	)	)	PUNCT
ejde-397	879	62	⊆	⊆	NUM
ejde-397	879	63	r(i	r(i	PROPN
ejde-397	879	64	−	−	PROPN
ejde-397	879	65	ã(λ)a	ã(λ)a	NUM
ejde-397	879	66	)	)	PUNCT
ejde-397	879	67	,	,	PUNCT
ejde-397	879	68	k̃(λ	k̃(λ	PROPN
ejde-397	879	69	)	)	PUNCT
ejde-397	879	70	(	(	PUNCT
ejde-397	879	71	i	i	PRON
ejde-397	879	72	−	−	VERB
ejde-397	879	73	ã(λ)a	ã(λ)a	ADP
ejde-397	879	74	)	)	PUNCT
ejde-397	879	75	−1	−1	NOUN
ejde-397	880	1	cx	cx	NOUN
ejde-397	881	1	=	=	PUNCT
ejde-397	882	1	∫	∫	PROPN
ejde-397	883	1	∞	∞	PROPN
ejde-397	883	2	0	0	NUM
ejde-397	883	3	e−λtr(t)x	e−λtr(t)x	PUNCT
ejde-397	883	4	dt	dt	PROPN
ejde-397	883	5	,	,	PUNCT
ejde-397	883	6	(	(	PUNCT
ejde-397	883	7	5.8	5.8	NUM
ejde-397	883	8	)	)	PUNCT
ejde-397	883	9	for	for	ADP
ejde-397	883	10	x	x	PROPN
ejde-397	883	11	∈	∈	PROPN
ejde-397	883	12	x	x	X
ejde-397	883	13	,	,	PUNCT
ejde-397	883	14	<	<	X
ejde-397	883	15	λ	λ	X
ejde-397	883	16	>	>	X
ejde-397	883	17	ω0	ω0	PROPN
ejde-397	883	18	,	,	PUNCT
ejde-397	883	19	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	883	20	)	)	PUNCT
ejde-397	883	21	6=	6=	ADP
ejde-397	883	22	0	0	NUM
ejde-397	883	23	,	,	PUNCT
ejde-397	883	24	{	{	PUNCT
ejde-397	883	25	1	1	NUM
ejde-397	883	26	ã(λ	ã(λ	PROPN
ejde-397	883	27	)	)	PUNCT
ejde-397	883	28	:	:	PUNCT
ejde-397	884	1	<	<	X
ejde-397	884	2	λ	λ	X
ejde-397	884	3	>	>	X
ejde-397	884	4	ω0	ω0	PROPN
ejde-397	884	5	,	,	PUNCT
ejde-397	884	6	k̃(λ)ã(λ	k̃(λ)ã(λ	PROPN
ejde-397	884	7	)	)	PUNCT
ejde-397	884	8	6=	6=	ADP
ejde-397	884	9	0	0	NUM
ejde-397	884	10	}	}	PUNCT
ejde-397	884	11	⊆	⊆	NUM
ejde-397	884	12	ρc(a	ρc(a	NOUN
ejde-397	884	13	)	)	PUNCT
ejde-397	884	14	(	(	PUNCT
ejde-397	884	15	5.9	5.9	NUM
ejde-397	884	16	)	)	PUNCT
ejde-397	884	17	and	and	CCONJ
ejde-397	884	18	r(s)r(t	r(s)r(t	NOUN
ejde-397	884	19	)	)	PUNCT
ejde-397	884	20	=	=	SYM
ejde-397	884	21	r(t)r(s	r(t)r(s	NOUN
ejde-397	884	22	)	)	PUNCT
ejde-397	884	23	for	for	ADP
ejde-397	884	24	t	t	PROPN
ejde-397	884	25	,	,	PUNCT
ejde-397	884	26	s	s	PART
ejde-397	884	27	≥	≥	NOUN
ejde-397	884	28	0	0	NUM
ejde-397	884	29	.	.	PUNCT
ejde-397	884	30	(	(	PUNCT
ejde-397	884	31	ii	ii	NOUN
ejde-397	884	32	)	)	PUNCT
ejde-397	884	33	assume	assume	VERB
ejde-397	884	34	(	(	PUNCT
ejde-397	884	35	5.8	5.8	NUM
ejde-397	884	36	)	)	PUNCT
ejde-397	884	37	and	and	CCONJ
ejde-397	884	38	(	(	PUNCT
ejde-397	884	39	5.9	5.9	NUM
ejde-397	884	40	)	)	PUNCT
ejde-397	884	41	.	.	PUNCT
ejde-397	885	1	then	then	ADV
ejde-397	885	2	a	a	PRON
ejde-397	885	3	is	be	AUX
ejde-397	885	4	a	a	DET
ejde-397	885	5	subgenerator	subgenerator	NOUN
ejde-397	885	6	of	of	ADP
ejde-397	885	7	the	the	DET
ejde-397	885	8	global	global	ADJ
ejde-397	885	9	(	(	PUNCT
ejde-397	885	10	a	a	PRON
ejde-397	885	11	,	,	PUNCT
ejde-397	885	12	k)regularized	k)regularize	VERB
ejde-397	885	13	c	c	X
ejde-397	885	14	-	-	PUNCT
ejde-397	885	15	resolvent	resolvent	ADJ
ejde-397	885	16	family	family	NOUN
ejde-397	885	17	(	(	PUNCT
ejde-397	885	18	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	885	19	satisfying	satisfying	NOUN
ejde-397	885	20	(	(	PUNCT
ejde-397	885	21	5.1	5.1	NUM
ejde-397	885	22	)	)	PUNCT
ejde-397	885	23	for	for	ADP
ejde-397	885	24	all	all	PRON
ejde-397	885	25	x	x	PUNCT
ejde-397	885	26	=	=	PUNCT
ejde-397	885	27	y	y	PROPN
ejde-397	885	28	∈	∈	PROPN
ejde-397	885	29	x	x	X
ejde-397	885	30	and	and	CCONJ
ejde-397	885	31	r(s)r(t	r(s)r(t	NOUN
ejde-397	885	32	)	)	PUNCT
ejde-397	885	33	=	=	SYM
ejde-397	885	34	r(t)r(s	r(t)r(s	NOUN
ejde-397	885	35	)	)	PUNCT
ejde-397	885	36	,	,	PUNCT
ejde-397	885	37	t	t	PROPN
ejde-397	885	38	,	,	PUNCT
ejde-397	885	39	s	s	PART
ejde-397	885	40	≥	≥	NOUN
ejde-397	885	41	0	0	NUM
ejde-397	885	42	.	.	PUNCT
ejde-397	885	43	remark	remark	PROPN
ejde-397	885	44	5.6	5.6	NUM
ejde-397	885	45	.	.	PUNCT
ejde-397	886	1	(	(	PUNCT
ejde-397	886	2	i	i	NOUN
ejde-397	886	3	)	)	PUNCT
ejde-397	886	4	suppose	suppose	VERB
ejde-397	886	5	that	that	SCONJ
ejde-397	886	6	(	(	PUNCT
ejde-397	886	7	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	886	8	is	be	AUX
ejde-397	886	9	a	a	DET
ejde-397	886	10	degenerate	degenerate	ADJ
ejde-397	886	11	exponentially	exponentially	ADV
ejde-397	886	12	equicontinuous	equicontinuous	ADJ
ejde-397	886	13	(	(	PUNCT
ejde-397	886	14	a	a	PRON
ejde-397	886	15	,	,	PUNCT
ejde-397	886	16	k)-regularized	k)-regularize	VERB
ejde-397	886	17	c	c	NOUN
ejde-397	886	18	-	-	PUNCT
ejde-397	886	19	resolvent	resolvent	ADJ
ejde-397	886	20	family	family	NOUN
ejde-397	886	21	in	in	ADP
ejde-397	886	22	the	the	DET
ejde-397	886	23	sense	sense	NOUN
ejde-397	886	24	of	of	ADP
ejde-397	886	25	[	[	X
ejde-397	886	26	45	45	NUM
ejde-397	886	27	,	,	PUNCT
ejde-397	886	28	definition	definition	NOUN
ejde-397	886	29	2.2	2.2	NUM
ejde-397	886	30	]	]	PUNCT
ejde-397	886	31	,	,	PUNCT
ejde-397	886	32	and	and	CCONJ
ejde-397	886	33	b	b	X
ejde-397	886	34	∈	∈	PROPN
ejde-397	886	35	l(x	l(x	PROPN
ejde-397	886	36	)	)	PUNCT
ejde-397	886	37	.	.	PUNCT
ejde-397	887	1	using	use	VERB
ejde-397	887	2	remark	remark	NOUN
ejde-397	887	3	2.1(iv)/(a	2.1(iv)/(a	NUM
ejde-397	887	4	)	)	PUNCT
ejde-397	887	5	,	,	PUNCT
ejde-397	887	6	remark	remark	NOUN
ejde-397	887	7	4.2(iv	4.2(iv	NUM
ejde-397	887	8	)	)	PUNCT
ejde-397	887	9	and	and	CCONJ
ejde-397	887	10	theorem	theorem	VERB
ejde-397	887	11	5.5(ii	5.5(ii	NUM
ejde-397	887	12	)	)	PUNCT
ejde-397	887	13	,	,	PUNCT
ejde-397	887	14	it	it	PRON
ejde-397	887	15	can	can	AUX
ejde-397	887	16	be	be	AUX
ejde-397	887	17	easily	easily	ADV
ejde-397	887	18	seen	see	VERB
ejde-397	887	19	that	that	SCONJ
ejde-397	887	20	(	(	PUNCT
ejde-397	887	21	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	887	22	is	be	AUX
ejde-397	887	23	an	an	DET
ejde-397	887	24	exponentially	exponentially	ADV
ejde-397	887	25	equicontinuous	equicontinuous	ADJ
ejde-397	887	26	(	(	PUNCT
ejde-397	887	27	a	a	DET
ejde-397	887	28	,	,	PUNCT
ejde-397	887	29	k)-regularized	k)-regularize	VERB
ejde-397	887	30	c	c	NOUN
ejde-397	887	31	-	-	PUNCT
ejde-397	887	32	resolvent	resolvent	ADJ
ejde-397	887	33	family	family	NOUN
ejde-397	887	34	with	with	ADP
ejde-397	887	35	a	a	DET
ejde-397	887	36	closed	closed	ADJ
ejde-397	887	37	subgenerator	subgenerator	NOUN
ejde-397	887	38	b−1a	b−1a	NOUN
ejde-397	887	39	.	.	PUNCT
ejde-397	888	1	(	(	PUNCT
ejde-397	888	2	ii	ii	NOUN
ejde-397	888	3	)	)	PUNCT
ejde-397	888	4	suppose	suppose	VERB
ejde-397	888	5	that	that	SCONJ
ejde-397	888	6	n	n	PROPN
ejde-397	888	7	∈	∈	PROPN
ejde-397	888	8	n	n	CCONJ
ejde-397	888	9	,	,	PUNCT
ejde-397	888	10	x	x	PUNCT
ejde-397	888	11	and	and	CCONJ
ejde-397	888	12	y	y	PROPN
ejde-397	888	13	are	be	AUX
ejde-397	888	14	banach	banach	NOUN
ejde-397	888	15	spaces	space	NOUN
ejde-397	888	16	,	,	PUNCT
ejde-397	888	17	a	a	DET
ejde-397	888	18	:	:	PUNCT
ejde-397	888	19	d(a	d(a	PROPN
ejde-397	888	20	)	)	PUNCT
ejde-397	888	21	⊆	⊆	NUM
ejde-397	888	22	x	x	SYM
ejde-397	888	23	→	→	SYM
ejde-397	888	24	y	y	PROPN
ejde-397	888	25	is	be	AUX
ejde-397	888	26	closed	close	VERB
ejde-397	888	27	,	,	PUNCT
ejde-397	888	28	b	b	X
ejde-397	888	29	∈	∈	PROPN
ejde-397	888	30	l(x	l(x	PROPN
ejde-397	888	31	,	,	PUNCT
ejde-397	888	32	y	y	PROPN
ejde-397	888	33	)	)	PUNCT
ejde-397	888	34	and	and	CCONJ
ejde-397	888	35	(	(	PUNCT
ejde-397	888	36	v	v	NOUN
ejde-397	888	37	(	(	PUNCT
ejde-397	888	38	t))t≥0	t))t≥0	NOUN
ejde-397	888	39	⊆	⊆	NUM
ejde-397	888	40	l(x	l(x	PROPN
ejde-397	888	41	)	)	PUNCT
ejde-397	888	42	is	be	AUX
ejde-397	888	43	a	a	DET
ejde-397	888	44	degenerate	degenerate	ADJ
ejde-397	888	45	exponentially	exponentially	ADV
ejde-397	888	46	bounded	bound	VERB
ejde-397	888	47	n	n	CCONJ
ejde-397	888	48	-	-	PUNCT
ejde-397	888	49	times	time	NOUN
ejde-397	888	50	integrated	integrate	VERB
ejde-397	888	51	semigroup	semigroup	NOUN
ejde-397	888	52	generated	generate	VERB
ejde-397	888	53	by	by	ADP
ejde-397	888	54	linear	linear	PROPN
ejde-397	888	55	operators	operator	NOUN
ejde-397	888	56	a	a	DET
ejde-397	888	57	,	,	PUNCT
ejde-397	888	58	b	b	NOUN
ejde-397	888	59	,	,	PUNCT
ejde-397	888	60	in	in	ADP
ejde-397	888	61	the	the	DET
ejde-397	888	62	sense	sense	NOUN
ejde-397	888	63	of	of	ADP
ejde-397	888	64	[	[	X
ejde-397	888	65	63	63	NUM
ejde-397	888	66	,	,	PUNCT
ejde-397	888	67	definition	definition	NOUN
ejde-397	888	68	1.5.3	1.5.3	NUM
ejde-397	888	69	]	]	PUNCT
ejde-397	888	70	.	.	PUNCT
ejde-397	889	1	then	then	ADV
ejde-397	889	2	the	the	DET
ejde-397	889	3	arguments	argument	NOUN
ejde-397	889	4	mentioned	mention	VERB
ejde-397	889	5	above	above	ADP
ejde-397	889	6	show	show	VERB
ejde-397	889	7	that	that	SCONJ
ejde-397	889	8	(	(	PUNCT
ejde-397	889	9	v	v	X
ejde-397	889	10	(	(	PUNCT
ejde-397	889	11	t))t≥0	t))t≥0	PROPN
ejde-397	889	12	is	be	AUX
ejde-397	889	13	an	an	DET
ejde-397	889	14	exponentially	exponentially	ADV
ejde-397	889	15	bounded	bound	VERB
ejde-397	889	16	n	n	CCONJ
ejde-397	889	17	-	-	PUNCT
ejde-397	889	18	times	times	NOUN
ejde-397	889	19	integrated	integrated	ADJ
ejde-397	889	20	(	(	PUNCT
ejde-397	889	21	g1	g1	PROPN
ejde-397	889	22	,	,	PUNCT
ejde-397	889	23	i)-regularized	i)-regularize	VERB
ejde-397	889	24	family	family	NOUN
ejde-397	889	25	(	(	PUNCT
ejde-397	889	26	semigroup	semigroup	PROPN
ejde-397	889	27	)	)	PUNCT
ejde-397	889	28	with	with	ADP
ejde-397	889	29	a	a	DET
ejde-397	889	30	closed	closed	ADJ
ejde-397	889	31	subgenerator	subgenerator	NOUN
ejde-397	889	32	b−1a	b−1a	NOUN
ejde-397	889	33	.	.	PUNCT
ejde-397	890	1	(	(	PUNCT
ejde-397	890	2	iii	iii	X
ejde-397	890	3	)	)	PUNCT
ejde-397	890	4	let	let	VERB
ejde-397	890	5	n	n	PRON
ejde-397	890	6	∈	∈	PROPN
ejde-397	890	7	n0	n0	PROPN
ejde-397	890	8	.	.	PUNCT
ejde-397	891	1	due	due	ADP
ejde-397	891	2	to	to	ADP
ejde-397	891	3	theorem	theorem	ADJ
ejde-397	891	4	5.5(ii	5.5(ii	NUM
ejde-397	891	5	)	)	PUNCT
ejde-397	891	6	,	,	PUNCT
ejde-397	891	7	the	the	DET
ejde-397	891	8	notion	notion	NOUN
ejde-397	891	9	of	of	ADP
ejde-397	891	10	an	an	DET
ejde-397	891	11	exponentially	exponentially	ADV
ejde-397	891	12	bounded	bound	VERB
ejde-397	891	13	(	(	PUNCT
ejde-397	891	14	a	a	PRON
ejde-397	891	15	,	,	PUNCT
ejde-397	891	16	k)-regularized	k)-regularize	VERB
ejde-397	891	17	c	c	NOUN
ejde-397	891	18	-	-	PUNCT
ejde-397	891	19	resolvent	resolvent	ADJ
ejde-397	891	20	family	family	NOUN
ejde-397	891	21	extends	extend	VERB
ejde-397	891	22	the	the	DET
ejde-397	891	23	notion	notion	NOUN
ejde-397	891	24	of	of	ADP
ejde-397	891	25	a	a	DET
ejde-397	891	26	degenerate	degenerate	ADJ
ejde-397	891	27	exponentially	exponentially	ADV
ejde-397	891	28	bounded	bound	VERB
ejde-397	891	29	n	n	CCONJ
ejde-397	891	30	-	-	PUNCT
ejde-397	891	31	times	time	NOUN
ejde-397	891	32	integrated	integrate	VERB
ejde-397	891	33	semigroup	semigroup	NOUN
ejde-397	891	34	generated	generate	VERB
ejde-397	891	35	by	by	ADP
ejde-397	891	36	an	an	DET
ejde-397	891	37	mlo	mlo	PROPN
ejde-397	891	38	,	,	PUNCT
ejde-397	891	39	introduced	introduce	VERB
ejde-397	891	40	in	in	ADP
ejde-397	891	41	[	[	X
ejde-397	891	42	63	63	NUM
ejde-397	891	43	,	,	PUNCT
ejde-397	891	44	definition	definition	NOUN
ejde-397	891	45	1.6.6	1.6.6	NUM
ejde-397	891	46	,	,	PUNCT
ejde-397	891	47	definition	definition	NOUN
ejde-397	891	48	1.6.8	1.6.8	NUM
ejde-397	891	49	]	]	PUNCT
ejde-397	891	50	.	.	PUNCT
ejde-397	892	1	28	28	NUM
ejde-397	892	2	m.	m.	NOUN
ejde-397	892	3	kostić	kostić	NOUN
ejde-397	893	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	893	2	(	(	PUNCT
ejde-397	893	3	iv	iv	X
ejde-397	893	4	)	)	PUNCT
ejde-397	893	5	suppose	suppose	VERB
ejde-397	893	6	that	that	SCONJ
ejde-397	893	7	(	(	PUNCT
ejde-397	893	8	r(t))t≥0	r(t))t≥0	NOUN
ejde-397	893	9	⊆	⊆	NUM
ejde-397	893	10	l(x	l(x	PROPN
ejde-397	893	11	,	,	PUNCT
ejde-397	893	12	[	[	X
ejde-397	893	13	d(b	d(b	X
ejde-397	893	14	)	)	PUNCT
ejde-397	893	15	]	]	PUNCT
ejde-397	893	16	)	)	PUNCT
ejde-397	893	17	is	be	AUX
ejde-397	893	18	an	an	DET
ejde-397	893	19	exponentially	exponentially	ADV
ejde-397	893	20	equicontinuous	equicontinuous	ADJ
ejde-397	893	21	(	(	PUNCT
ejde-397	893	22	a	a	PRON
ejde-397	893	23	,	,	PUNCT
ejde-397	893	24	k)-regularized	k)-regularize	VERB
ejde-397	893	25	c	c	NOUN
ejde-397	893	26	-	-	PUNCT
ejde-397	893	27	resolvent	resolvent	ADJ
ejde-397	893	28	family	family	NOUN
ejde-397	893	29	generated	generate	VERB
ejde-397	893	30	by	by	ADP
ejde-397	893	31	a	a	DET
ejde-397	893	32	,	,	PUNCT
ejde-397	893	33	b	b	NOUN
ejde-397	893	34	,	,	PUNCT
ejde-397	893	35	in	in	ADP
ejde-397	893	36	the	the	DET
ejde-397	893	37	sense	sense	NOUN
ejde-397	893	38	of	of	ADP
ejde-397	893	39	[	[	X
ejde-397	893	40	46	46	NUM
ejde-397	893	41	,	,	PUNCT
ejde-397	893	42	definition	definition	NOUN
ejde-397	893	43	2.5	2.5	NUM
ejde-397	893	44	]	]	PUNCT
ejde-397	893	45	.	.	PUNCT
ejde-397	894	1	then	then	ADV
ejde-397	894	2	[	[	X
ejde-397	894	3	46	46	NUM
ejde-397	894	4	,	,	PUNCT
ejde-397	894	5	theorem	theorem	VERB
ejde-397	894	6	2.3(i	2.3(i	NUM
ejde-397	894	7	)	)	PUNCT
ejde-397	894	8	]	]	PUNCT
ejde-397	894	9	in	in	ADP
ejde-397	894	10	combination	combination	NOUN
ejde-397	894	11	with	with	ADP
ejde-397	894	12	remark	remark	NOUN
ejde-397	894	13	4.2(v	4.2(v	NUM
ejde-397	894	14	)	)	PUNCT
ejde-397	894	15	and	and	CCONJ
ejde-397	894	16	theorem	theorem	VERB
ejde-397	894	17	5.5(ii	5.5(ii	NUM
ejde-397	894	18	)	)	PUNCT
ejde-397	894	19	implies	imply	VERB
ejde-397	894	20	that	that	SCONJ
ejde-397	894	21	(	(	PUNCT
ejde-397	894	22	br(t))t≥0	br(t))t≥0	PROPN
ejde-397	894	23	is	be	AUX
ejde-397	894	24	an	an	DET
ejde-397	894	25	exponentially	exponentially	ADV
ejde-397	894	26	equicontinuous	equicontinuous	ADJ
ejde-397	894	27	(	(	PUNCT
ejde-397	894	28	a	a	PRON
ejde-397	894	29	,	,	PUNCT
ejde-397	894	30	k)regularized	k)regularize	VERB
ejde-397	894	31	c	c	X
ejde-397	894	32	-	-	PUNCT
ejde-397	894	33	resolvent	resolvent	ADJ
ejde-397	894	34	family	family	NOUN
ejde-397	894	35	generated	generate	VERB
ejde-397	894	36	by	by	ADP
ejde-397	894	37	b−1a	b−1a	INTJ
ejde-397	894	38	(	(	PUNCT
ejde-397	894	39	recall	recall	VERB
ejde-397	894	40	that	that	SCONJ
ejde-397	894	41	b−1a	b−1a	ADV
ejde-397	894	42	is	be	AUX
ejde-397	894	43	closed	closed	ADJ
ejde-397	894	44	provided	provide	VERB
ejde-397	894	45	that	that	SCONJ
ejde-397	894	46	c	c	NOUN
ejde-397	894	47	=	=	SYM
ejde-397	894	48	i	i	PROPN
ejde-397	894	49	)	)	PUNCT
ejde-397	894	50	.	.	PUNCT
ejde-397	895	1	the	the	DET
ejde-397	895	2	proof	proof	NOUN
ejde-397	895	3	of	of	ADP
ejde-397	895	4	following	follow	VERB
ejde-397	895	5	extension	extension	NOUN
ejde-397	895	6	of	of	ADP
ejde-397	895	7	[	[	X
ejde-397	895	8	36	36	NUM
ejde-397	895	9	,	,	PUNCT
ejde-397	895	10	theorems	theorem	NOUN
ejde-397	895	11	2.1.8(i	2.1.8(i	NUM
ejde-397	895	12	)	)	PUNCT
ejde-397	895	13	and	and	CCONJ
ejde-397	895	14	2.8.7(i	2.8.7(i	NUM
ejde-397	895	15	)	)	PUNCT
ejde-397	895	16	]	]	PUNCT
ejde-397	895	17	is	be	AUX
ejde-397	895	18	standard	standard	ADJ
ejde-397	895	19	and	and	CCONJ
ejde-397	895	20	therefore	therefore	ADV
ejde-397	895	21	omitted	omit	VERB
ejde-397	895	22	;	;	PUNCT
ejde-397	895	23	we	we	PRON
ejde-397	895	24	can	can	AUX
ejde-397	895	25	similarly	similarly	ADV
ejde-397	895	26	reformulate	reformulate	VERB
ejde-397	895	27	theorem	theorem	ADJ
ejde-397	895	28	4.8	4.8	NUM
ejde-397	895	29	and	and	CCONJ
ejde-397	895	30	[	[	X
ejde-397	895	31	36	36	NUM
ejde-397	895	32	,	,	PUNCT
ejde-397	895	33	proposition	proposition	NOUN
ejde-397	895	34	2.1.16	2.1.16	NUM
ejde-397	895	35	]	]	PUNCT
ejde-397	895	36	for	for	ADP
ejde-397	895	37	the	the	DET
ejde-397	895	38	class	class	NOUN
ejde-397	895	39	of	of	ADP
ejde-397	895	40	mild	mild	ADJ
ejde-397	895	41	(	(	PUNCT
ejde-397	895	42	a	a	PRON
ejde-397	895	43	,	,	PUNCT
ejde-397	895	44	k)-regularized	k)-regularize	VERB
ejde-397	895	45	(	(	PUNCT
ejde-397	895	46	c1	c1	NOUN
ejde-397	895	47	,	,	PUNCT
ejde-397	895	48	c2)-existence	c2)-existence	VERB
ejde-397	895	49	and	and	CCONJ
ejde-397	895	50	uniqueness	uniqueness	ADJ
ejde-397	895	51	families	family	NOUN
ejde-397	895	52	(	(	PUNCT
ejde-397	895	53	(	(	PUNCT
ejde-397	895	54	a	a	PRON
ejde-397	895	55	,	,	PUNCT
ejde-397	895	56	k)-regularized	k)-regularize	VERB
ejde-397	895	57	c	c	NOUN
ejde-397	895	58	-	-	PUNCT
ejde-397	895	59	resolvent	resolvent	ADJ
ejde-397	895	60	families	family	NOUN
ejde-397	895	61	)	)	PUNCT
ejde-397	895	62	.	.	PUNCT
ejde-397	896	1	here	here	ADV
ejde-397	896	2	it	it	PRON
ejde-397	896	3	is	be	AUX
ejde-397	896	4	only	only	ADV
ejde-397	896	5	worth	worth	ADJ
ejde-397	896	6	noting	note	VERB
ejde-397	896	7	that	that	SCONJ
ejde-397	896	8	the	the	DET
ejde-397	896	9	existence	existence	NOUN
ejde-397	896	10	of	of	ADP
ejde-397	896	11	a	a	DET
ejde-397	896	12	mild	mild	ADJ
ejde-397	896	13	(	(	PUNCT
ejde-397	896	14	a	a	DET
ejde-397	896	15	,	,	PUNCT
ejde-397	896	16	k1)-regularized	k1)-regularize	VERB
ejde-397	896	17	c1	c1	NOUN
ejde-397	896	18	-	-	PUNCT
ejde-397	896	19	existence	existence	NOUN
ejde-397	896	20	family	family	NOUN
ejde-397	896	21	(	(	PUNCT
ejde-397	896	22	r0,1(t))t≥0	r0,1(t))t≥0	NOUN
ejde-397	896	23	in	in	ADP
ejde-397	896	24	the	the	DET
ejde-397	896	25	second	second	ADJ
ejde-397	896	26	part	part	NOUN
ejde-397	896	27	of	of	ADP
ejde-397	896	28	theorem	theorem	NOUN
ejde-397	896	29	is	be	AUX
ejde-397	896	30	not	not	PART
ejde-397	896	31	automatically	automatically	ADV
ejde-397	896	32	guaranteed	guarantee	VERB
ejde-397	896	33	by	by	ADP
ejde-397	896	34	the	the	DET
ejde-397	896	35	denseness	denseness	NOUN
ejde-397	896	36	of	of	ADP
ejde-397	896	37	a	a	PRON
ejde-397	896	38	(	(	PUNCT
ejde-397	896	39	even	even	ADV
ejde-397	896	40	in	in	ADP
ejde-397	896	41	the	the	DET
ejde-397	896	42	case	case	NOUN
ejde-397	896	43	that	that	SCONJ
ejde-397	896	44	the	the	DET
ejde-397	896	45	operator	operator	NOUN
ejde-397	897	1	a	a	PRON
ejde-397	897	2	=	=	NOUN
ejde-397	897	3	a	a	NOUN
ejde-397	897	4	is	be	AUX
ejde-397	897	5	single	single	ADV
ejde-397	897	6	-	-	PUNCT
ejde-397	897	7	valued	value	VERB
ejde-397	897	8	,	,	PUNCT
ejde-397	897	9	it	it	PRON
ejde-397	897	10	seems	seem	VERB
ejde-397	897	11	that	that	SCONJ
ejde-397	897	12	the	the	DET
ejde-397	897	13	condition	condition	NOUN
ejde-397	897	14	c1a	c1a	VERB
ejde-397	897	15	⊆	⊆	NUM
ejde-397	897	16	ac1	ac1	PROPN
ejde-397	897	17	is	be	AUX
ejde-397	897	18	necessary	necessary	ADJ
ejde-397	897	19	for	for	SCONJ
ejde-397	897	20	such	such	DET
ejde-397	897	21	a	a	DET
ejde-397	897	22	mild	mild	ADJ
ejde-397	897	23	existence	existence	NOUN
ejde-397	897	24	family	family	NOUN
ejde-397	897	25	to	to	PART
ejde-397	897	26	exist	exist	VERB
ejde-397	897	27	)	)	PUNCT
ejde-397	897	28	.	.	PUNCT
ejde-397	898	1	theorem	theorem	VERB
ejde-397	898	2	5.7	5.7	NUM
ejde-397	898	3	.	.	PUNCT
ejde-397	899	1	suppose	suppose	VERB
ejde-397	899	2	c1	c1	PROPN
ejde-397	899	3	∈	∈	PROPN
ejde-397	899	4	l(y	l(y	PROPN
ejde-397	899	5	,	,	PUNCT
ejde-397	899	6	x	x	NOUN
ejde-397	899	7	)	)	PUNCT
ejde-397	899	8	,	,	PUNCT
ejde-397	899	9	c2	c2	PROPN
ejde-397	899	10	∈	∈	PROPN
ejde-397	899	11	l(x	l(x	PROPN
ejde-397	899	12	)	)	PUNCT
ejde-397	899	13	is	be	AUX
ejde-397	899	14	injective	injective	ADJ
ejde-397	899	15	,	,	PUNCT
ejde-397	899	16	a	a	PRON
ejde-397	899	17	is	be	AUX
ejde-397	899	18	a	a	DET
ejde-397	899	19	closed	closed	ADJ
ejde-397	899	20	mlo	mlo	NOUN
ejde-397	899	21	in	in	ADP
ejde-397	899	22	x	x	PROPN
ejde-397	899	23	,	,	PUNCT
ejde-397	899	24	c	c	PROPN
ejde-397	899	25	∈	∈	PROPN
ejde-397	899	26	l(x	l(x	PROPN
ejde-397	899	27	)	)	PUNCT
ejde-397	899	28	is	be	AUX
ejde-397	899	29	injective	injective	ADJ
ejde-397	899	30	and	and	CCONJ
ejde-397	899	31	ca	ca	PROPN
ejde-397	899	32	⊆	⊆	NUM
ejde-397	899	33	ac	ac	PROPN
ejde-397	899	34	.	.	PUNCT
ejde-397	900	1	let	let	VERB
ejde-397	900	2	b(t	b(t	PROPN
ejde-397	900	3	)	)	PUNCT
ejde-397	900	4	and	and	CCONJ
ejde-397	900	5	c(t	c(t	PROPN
ejde-397	900	6	)	)	PUNCT
ejde-397	900	7	satisfy	satisfy	NOUN
ejde-397	900	8	(	(	PUNCT
ejde-397	900	9	p1)-c	p1)-c	PROPN
ejde-397	900	10	,	,	PUNCT
ejde-397	900	11	let∫∞	let∫∞	PRON
ejde-397	900	12	0	0	PUNCT
ejde-397	901	1	e−βt|b(t)|	e−βt|b(t)|	NUM
ejde-397	901	2	dt	dt	X
ejde-397	901	3	<	<	X
ejde-397	901	4	∞	∞	PROPN
ejde-397	901	5	for	for	ADP
ejde-397	901	6	some	some	DET
ejde-397	901	7	β	β	NOUN
ejde-397	901	8	≥	≥	NOUN
ejde-397	901	9	0	0	NUM
ejde-397	901	10	,	,	PUNCT
ejde-397	901	11	and	and	CCONJ
ejde-397	901	12	let	let	VERB
ejde-397	901	13	α	α	NOUN
ejde-397	901	14	=	=	SYM
ejde-397	901	15	c̃−1	c̃−1	PROPN
ejde-397	901	16	(	(	PUNCT
ejde-397	901	17	1	1	NUM
ejde-397	901	18	β	β	X
ejde-397	901	19	)	)	PUNCT
ejde-397	901	20	if	if	SCONJ
ejde-397	901	21	∫	∫	PROPN
ejde-397	901	22	∞	∞	PROPN
ejde-397	901	23	0	0	PUNCT
ejde-397	901	24	c(t	c(t	PROPN
ejde-397	901	25	)	)	PUNCT
ejde-397	901	26	dt	dt	NOUN
ejde-397	901	27	>	>	X
ejde-397	901	28	1	1	NUM
ejde-397	901	29	β	β	X
ejde-397	901	30	,	,	PUNCT
ejde-397	901	31	α	α	X
ejde-397	901	32	=	=	SYM
ejde-397	901	33	0	0	NUM
ejde-397	901	34	otherwise	otherwise	ADV
ejde-397	901	35	.	.	PUNCT
ejde-397	902	1	suppose	suppose	VERB
ejde-397	902	2	,	,	PUNCT
ejde-397	902	3	further	far	ADV
ejde-397	902	4	,	,	PUNCT
ejde-397	902	5	that	that	PRON
ejde-397	902	6	abs(|a|	abs(|a|	VERB
ejde-397	902	7	)	)	PUNCT
ejde-397	902	8	<	<	X
ejde-397	902	9	∞	∞	PROPN
ejde-397	902	10	and	and	CCONJ
ejde-397	902	11	ã(λ	ã(λ	PROPN
ejde-397	902	12	)	)	PUNCT
ejde-397	903	1	=	=	SYM
ejde-397	903	2	b̃	b̃	PROPN
ejde-397	903	3	(	(	PUNCT
ejde-397	903	4	1	1	NUM
ejde-397	903	5	c̃(λ	c̃(λ	PROPN
ejde-397	903	6	)	)	PUNCT
ejde-397	903	7	)	)	PUNCT
ejde-397	903	8	,	,	PUNCT
ejde-397	903	9	λ	λ	PROPN
ejde-397	903	10	≥	≥	PROPN
ejde-397	903	11	α	α	X
ejde-397	903	12	.	.	PUNCT
ejde-397	904	1	let	let	VERB
ejde-397	904	2	a	a	PRON
ejde-397	904	3	be	be	AUX
ejde-397	904	4	a	a	DET
ejde-397	904	5	subgenerator	subgenerator	NOUN
ejde-397	904	6	of	of	ADP
ejde-397	904	7	a	a	DET
ejde-397	904	8	(	(	PUNCT
ejde-397	904	9	b	b	NOUN
ejde-397	904	10	,	,	PUNCT
ejde-397	904	11	k)-regularized	k)-regularize	VERB
ejde-397	904	12	c1	c1	NOUN
ejde-397	904	13	-	-	PUNCT
ejde-397	904	14	existence	existence	NOUN
ejde-397	904	15	family	family	NOUN
ejde-397	904	16	(	(	PUNCT
ejde-397	904	17	r1(t))t≥0	r1(t))t≥0	PROPN
ejde-397	904	18	(	(	PUNCT
ejde-397	904	19	(	(	PUNCT
ejde-397	904	20	b	b	NOUN
ejde-397	904	21	,	,	PUNCT
ejde-397	904	22	k)-regularized	k)-regularize	VERB
ejde-397	904	23	c2	c2	PROPN
ejde-397	904	24	-	-	PUNCT
ejde-397	904	25	uniqueness	uniqueness	PROPN
ejde-397	904	26	family	family	NOUN
ejde-397	904	27	(	(	PUNCT
ejde-397	904	28	r2(t))t≥0	r2(t))t≥0	NOUN
ejde-397	904	29	;	;	PUNCT
ejde-397	904	30	(	(	PUNCT
ejde-397	904	31	b	b	NOUN
ejde-397	904	32	,	,	PUNCT
ejde-397	904	33	k)-regularized	k)-regularize	VERB
ejde-397	904	34	c	c	NOUN
ejde-397	904	35	-	-	PUNCT
ejde-397	904	36	resolvent	resolvent	ADJ
ejde-397	904	37	family	family	NOUN
ejde-397	904	38	(	(	PUNCT
ejde-397	904	39	r0(t))t≥0	r0(t))t≥0	PROPN
ejde-397	904	40	with	with	ADP
ejde-397	904	41	the	the	DET
ejde-397	904	42	property	property	NOUN
ejde-397	904	43	that	that	PRON
ejde-397	904	44	(	(	PUNCT
ejde-397	904	45	5.1	5.1	NUM
ejde-397	904	46	)	)	PUNCT
ejde-397	904	47	holds	hold	VERB
ejde-397	904	48	for	for	ADP
ejde-397	904	49	r1	r1	PROPN
ejde-397	904	50	(	(	PUNCT
ejde-397	904	51	·	·	PUNCT
ejde-397	904	52	)	)	PUNCT
ejde-397	904	53	replaced	replace	VERB
ejde-397	904	54	with	with	ADP
ejde-397	904	55	r0	r0	NOUN
ejde-397	904	56	(	(	PUNCT
ejde-397	904	57	·	·	PUNCT
ejde-397	904	58	)	)	PUNCT
ejde-397	904	59	and	and	CCONJ
ejde-397	904	60	each	each	DET
ejde-397	904	61	x	x	PUNCT
ejde-397	904	62	=	=	PUNCT
ejde-397	904	63	y	y	PROPN
ejde-397	904	64	∈	∈	PROPN
ejde-397	904	65	x	x	X
ejde-397	904	66	)	)	PUNCT
ejde-397	904	67	satisfying	satisfy	VERB
ejde-397	904	68	that	that	SCONJ
ejde-397	904	69	the	the	DET
ejde-397	904	70	family	family	NOUN
ejde-397	904	71	{	{	PUNCT
ejde-397	904	72	e−ωbtr1(t	e−ωbtr1(t	PROPN
ejde-397	904	73	)	)	PUNCT
ejde-397	904	74	:	:	PUNCT
ejde-397	904	75	t	t	X
ejde-397	904	76	≥	≥	NOUN
ejde-397	904	77	0	0	NUM
ejde-397	904	78	}	}	PUNCT
ejde-397	904	79	(	(	PUNCT
ejde-397	904	80	{	{	PUNCT
ejde-397	904	81	e−ωbtr2(t	e−ωbtr2(t	PROPN
ejde-397	904	82	)	)	PUNCT
ejde-397	904	83	:	:	PUNCT
ejde-397	904	84	t	t	X
ejde-397	904	85	≥	≥	NOUN
ejde-397	904	86	0	0	NUM
ejde-397	904	87	}	}	PUNCT
ejde-397	904	88	;	;	PUNCT
ejde-397	904	89	{	{	PUNCT
ejde-397	904	90	e−ωbtr(t	e−ωbtr(t	PROPN
ejde-397	904	91	)	)	PUNCT
ejde-397	904	92	:	:	PUNCT
ejde-397	904	93	t	t	X
ejde-397	904	94	≥	≥	NOUN
ejde-397	904	95	0	0	NUM
ejde-397	904	96	}	}	PUNCT
ejde-397	904	97	)	)	PUNCT
ejde-397	904	98	is	be	AUX
ejde-397	904	99	equicontinuous	equicontinuous	ADJ
ejde-397	904	100	for	for	ADP
ejde-397	904	101	some	some	DET
ejde-397	904	102	ωb	ωb	NOUN
ejde-397	904	103	≥	≥	NOUN
ejde-397	904	104	0	0	NUM
ejde-397	904	105	.	.	PUNCT
ejde-397	905	1	assume	assume	VERB
ejde-397	905	2	,	,	PUNCT
ejde-397	905	3	further	far	ADV
ejde-397	905	4	,	,	PUNCT
ejde-397	905	5	that	that	PRON
ejde-397	905	6	c(t	c(t	PROPN
ejde-397	905	7	)	)	PUNCT
ejde-397	905	8	is	be	AUX
ejde-397	905	9	completely	completely	ADV
ejde-397	905	10	positive	positive	ADJ
ejde-397	905	11	and	and	CCONJ
ejde-397	905	12	that	that	SCONJ
ejde-397	905	13	there	there	PRON
ejde-397	905	14	exists	exist	VERB
ejde-397	905	15	a	a	DET
ejde-397	905	16	scalarvalued	scalarvalue	VERB
ejde-397	905	17	continuous	continuous	ADJ
ejde-397	905	18	kernel	kernel	NOUN
ejde-397	905	19	k1(t	k1(t	PROPN
ejde-397	905	20	)	)	PUNCT
ejde-397	905	21	satisfying	satisfy	VERB
ejde-397	905	22	(	(	PUNCT
ejde-397	905	23	p1)-c	p1)-c	ADJ
ejde-397	905	24	and	and	CCONJ
ejde-397	905	25	k̃1(λ	k̃1(λ	PROPN
ejde-397	905	26	)	)	PUNCT
ejde-397	905	27	=	=	SYM
ejde-397	905	28	1	1	NUM
ejde-397	905	29	λc̃(λ	λc̃(λ	NOUN
ejde-397	905	30	)	)	PUNCT
ejde-397	905	31	k̃	k̃	PROPN
ejde-397	905	32	(	(	PUNCT
ejde-397	905	33	1	1	NUM
ejde-397	905	34	c̃(λ	c̃(λ	PROPN
ejde-397	905	35	)	)	PUNCT
ejde-397	905	36	)	)	PUNCT
ejde-397	905	37	,	,	PUNCT
ejde-397	905	38	λ	λ	X
ejde-397	905	39	>	>	X
ejde-397	905	40	ω0	ω0	PROPN
ejde-397	905	41	,	,	PUNCT
ejde-397	905	42	k̃	k̃	PROPN
ejde-397	905	43	(	(	PUNCT
ejde-397	905	44	1	1	NUM
ejde-397	905	45	c̃(λ	c̃(λ	PROPN
ejde-397	905	46	)	)	PUNCT
ejde-397	905	47	)	)	PUNCT
ejde-397	906	1	6=	6=	ADP
ejde-397	906	2	0	0	NUM
ejde-397	906	3	,	,	PUNCT
ejde-397	906	4	for	for	ADP
ejde-397	906	5	some	some	DET
ejde-397	906	6	ω0	ω0	NOUN
ejde-397	906	7	>	>	X
ejde-397	906	8	0	0	X
ejde-397	906	9	.	.	PUNCT
ejde-397	907	1	let	let	VERB
ejde-397	907	2	ωa	ωa	ADV
ejde-397	907	3	=	=	SYM
ejde-397	907	4	c̃−1	c̃−1	PROPN
ejde-397	907	5	(	(	PUNCT
ejde-397	907	6	1	1	NUM
ejde-397	907	7	ωb	ωb	NOUN
ejde-397	907	8	)	)	PUNCT
ejde-397	908	1	if	if	SCONJ
ejde-397	908	2	∫	∫	PROPN
ejde-397	908	3	∞	∞	PROPN
ejde-397	908	4	0	0	PUNCT
ejde-397	908	5	c(t	c(t	PROPN
ejde-397	908	6	)	)	PUNCT
ejde-397	908	7	dt	dt	NOUN
ejde-397	908	8	>	>	X
ejde-397	908	9	1	1	NUM
ejde-397	908	10	ωb	ωb	NOUN
ejde-397	908	11	,	,	PUNCT
ejde-397	908	12	ωa	ωa	PROPN
ejde-397	908	13	=	=	SYM
ejde-397	908	14	0	0	PUNCT
ejde-397	909	1	otherwise	otherwise	ADV
ejde-397	909	2	.	.	PUNCT
ejde-397	910	1	then	then	ADV
ejde-397	910	2	,	,	PUNCT
ejde-397	910	3	for	for	ADP
ejde-397	910	4	every	every	DET
ejde-397	910	5	r	r	NOUN
ejde-397	910	6	∈	∈	PROPN
ejde-397	910	7	(	(	PUNCT
ejde-397	910	8	0	0	NUM
ejde-397	910	9	,	,	PUNCT
ejde-397	910	10	1	1	NUM
ejde-397	910	11	]	]	PUNCT
ejde-397	910	12	,	,	PUNCT
ejde-397	910	13	a	a	PRON
ejde-397	910	14	is	be	AUX
ejde-397	910	15	a	a	DET
ejde-397	910	16	subgenerator	subgenerator	NOUN
ejde-397	910	17	of	of	ADP
ejde-397	910	18	a	a	DET
ejde-397	910	19	global	global	ADJ
ejde-397	910	20	(	(	PUNCT
ejde-397	910	21	a	a	PROPN
ejde-397	910	22	,	,	PUNCT
ejde-397	910	23	k1	k1	PROPN
ejde-397	910	24	∗gr)-regularized	∗gr)-regularize	VERB
ejde-397	910	25	c1existence	c1existence	PROPN
ejde-397	910	26	family	family	NOUN
ejde-397	910	27	(	(	PUNCT
ejde-397	910	28	rr,1(t))t≥0	rr,1(t))t≥0	X
ejde-397	910	29	(	(	PUNCT
ejde-397	910	30	(	(	PUNCT
ejde-397	910	31	a	a	PRON
ejde-397	910	32	,	,	PUNCT
ejde-397	910	33	k1	k1	PROPN
ejde-397	910	34	∗	∗	NOUN
ejde-397	910	35	gr)-regularized	gr)-regularize	VERB
ejde-397	910	36	c2	c2	PROPN
ejde-397	910	37	-	-	PUNCT
ejde-397	910	38	uniqueness	uniqueness	PROPN
ejde-397	910	39	family	family	NOUN
ejde-397	910	40	(	(	PUNCT
ejde-397	910	41	rr,2(t))t≥0	rr,2(t))t≥0	PROPN
ejde-397	910	42	;	;	PUNCT
ejde-397	910	43	(	(	PUNCT
ejde-397	910	44	a	a	X
ejde-397	910	45	,	,	PUNCT
ejde-397	910	46	k1	k1	PROPN
ejde-397	910	47	∗	∗	NOUN
ejde-397	910	48	gr)-regularized	gr)-regularize	VERB
ejde-397	910	49	c	c	NOUN
ejde-397	910	50	-	-	PUNCT
ejde-397	910	51	resolvent	resolvent	ADJ
ejde-397	910	52	family	family	NOUN
ejde-397	910	53	(	(	PUNCT
ejde-397	910	54	rr,0(t))t≥0	rr,0(t))t≥0	NOUN
ejde-397	910	55	with	with	ADP
ejde-397	910	56	the	the	DET
ejde-397	910	57	property	property	NOUN
ejde-397	910	58	that	that	PRON
ejde-397	910	59	(	(	PUNCT
ejde-397	910	60	5.1	5.1	NUM
ejde-397	910	61	)	)	PUNCT
ejde-397	910	62	holds	hold	VERB
ejde-397	910	63	for	for	ADP
ejde-397	910	64	r1	r1	PROPN
ejde-397	910	65	(	(	PUNCT
ejde-397	910	66	·	·	PUNCT
ejde-397	910	67	)	)	PUNCT
ejde-397	910	68	replaced	replace	VERB
ejde-397	910	69	with	with	ADP
ejde-397	910	70	rr,0	rr,0	PROPN
ejde-397	910	71	(	(	PUNCT
ejde-397	910	72	·	·	PUNCT
ejde-397	910	73	)	)	PUNCT
ejde-397	910	74	and	and	CCONJ
ejde-397	910	75	each	each	PRON
ejde-397	910	76	x	x	PUNCT
ejde-397	911	1	=	=	PUNCT
ejde-397	911	2	y	y	PROPN
ejde-397	911	3	∈	∈	PROPN
ejde-397	911	4	x	x	NOUN
ejde-397	911	5	)	)	PUNCT
ejde-397	911	6	such	such	ADJ
ejde-397	911	7	that	that	SCONJ
ejde-397	911	8	the	the	DET
ejde-397	911	9	family	family	NOUN
ejde-397	911	10	{	{	PUNCT
ejde-397	911	11	e−ωatrr	e−ωatrr	PROPN
ejde-397	911	12	,	,	PUNCT
ejde-397	911	13	i(t	i(t	PROPN
ejde-397	911	14	)	)	PUNCT
ejde-397	911	15	:	:	PUNCT
ejde-397	911	16	t	t	X
ejde-397	911	17	≥	≥	NOUN
ejde-397	911	18	0	0	NUM
ejde-397	911	19	}	}	PUNCT
ejde-397	911	20	is	be	AUX
ejde-397	911	21	equicontinuous	equicontinuous	ADJ
ejde-397	911	22	and	and	CCONJ
ejde-397	911	23	that	that	SCONJ
ejde-397	911	24	the	the	DET
ejde-397	911	25	mapping	mapping	NOUN
ejde-397	911	26	t	t	PROPN
ejde-397	911	27	7→	7→	NUM
ejde-397	911	28	rr	rr	PROPN
ejde-397	911	29	,	,	PUNCT
ejde-397	911	30	i(t	i(t	PROPN
ejde-397	911	31	)	)	PUNCT
ejde-397	911	32	,	,	PUNCT
ejde-397	911	33	t	t	PROPN
ejde-397	911	34	≥	≥	PROPN
ejde-397	911	35	0	0	NUM
ejde-397	911	36	is	be	AUX
ejde-397	911	37	locally	locally	ADV
ejde-397	911	38	hölder	hölder	NOUN
ejde-397	911	39	continuous	continuous	ADJ
ejde-397	911	40	with	with	ADP
ejde-397	911	41	exponent	exponent	NOUN
ejde-397	911	42	r	r	NOUN
ejde-397	911	43	,	,	PUNCT
ejde-397	911	44	if	if	SCONJ
ejde-397	911	45	ωb	ωb	ADV
ejde-397	911	46	=	=	SYM
ejde-397	911	47	0	0	NUM
ejde-397	911	48	or	or	CCONJ
ejde-397	911	49	ωbc̃(0	ωbc̃(0	NOUN
ejde-397	911	50	)	)	PUNCT
ejde-397	911	51	6=	6=	ADP
ejde-397	911	52	1	1	NUM
ejde-397	911	53	(	(	PUNCT
ejde-397	911	54	i	i	NOUN
ejde-397	911	55	=	=	NOUN
ejde-397	911	56	0	0	NUM
ejde-397	911	57	,	,	PUNCT
ejde-397	911	58	1	1	NUM
ejde-397	911	59	,	,	PUNCT
ejde-397	911	60	2	2	NUM
ejde-397	911	61	)	)	PUNCT
ejde-397	911	62	,	,	PUNCT
ejde-397	911	63	resp	resp	NOUN
ejde-397	911	64	.	.	PUNCT
ejde-397	911	65	,	,	PUNCT
ejde-397	911	66	for	for	ADP
ejde-397	911	67	every	every	DET
ejde-397	911	68	ε	ε	PROPN
ejde-397	911	69	>	>	X
ejde-397	911	70	0	0	PROPN
ejde-397	911	71	,	,	PUNCT
ejde-397	911	72	there	there	PRON
ejde-397	911	73	exists	exist	VERB
ejde-397	911	74	mε	mε	PROPN
ejde-397	911	75	≥	≥	NUM
ejde-397	911	76	1	1	NUM
ejde-397	911	77	such	such	ADJ
ejde-397	911	78	that	that	SCONJ
ejde-397	911	79	the	the	DET
ejde-397	911	80	family	family	NOUN
ejde-397	911	81	{	{	PUNCT
ejde-397	911	82	e−εtrr	e−εtrr	PROPN
ejde-397	911	83	,	,	PUNCT
ejde-397	911	84	i(t	i(t	PROPN
ejde-397	911	85	)	)	PUNCT
ejde-397	911	86	:	:	PUNCT
ejde-397	911	87	t	t	X
ejde-397	911	88	≥	≥	NOUN
ejde-397	911	89	0	0	NUM
ejde-397	911	90	}	}	PUNCT
ejde-397	911	91	is	be	AUX
ejde-397	911	92	equicontinuous	equicontinuous	ADJ
ejde-397	911	93	and	and	CCONJ
ejde-397	911	94	that	that	SCONJ
ejde-397	911	95	the	the	DET
ejde-397	911	96	mapping	mapping	NOUN
ejde-397	911	97	t	t	PROPN
ejde-397	911	98	7→	7→	NUM
ejde-397	911	99	rr	rr	PROPN
ejde-397	911	100	,	,	PUNCT
ejde-397	911	101	i(t	i(t	PROPN
ejde-397	911	102	)	)	PUNCT
ejde-397	911	103	,	,	PUNCT
ejde-397	911	104	t	t	PROPN
ejde-397	911	105	≥	≥	PROPN
ejde-397	911	106	0	0	NUM
ejde-397	911	107	is	be	AUX
ejde-397	911	108	locally	locally	ADV
ejde-397	911	109	hölder	hölder	NOUN
ejde-397	911	110	continuous	continuous	ADJ
ejde-397	911	111	with	with	ADP
ejde-397	911	112	exponent	exponent	NOUN
ejde-397	911	113	r	r	NOUN
ejde-397	911	114	,	,	PUNCT
ejde-397	911	115	if	if	SCONJ
ejde-397	911	116	ωb	ωb	ADV
ejde-397	911	117	>	>	X
ejde-397	911	118	0	0	PUNCT
ejde-397	911	119	and	and	CCONJ
ejde-397	911	120	ωbc̃(0	ωbc̃(0	NOUN
ejde-397	911	121	)	)	PUNCT
ejde-397	912	1	=	=	SYM
ejde-397	912	2	1	1	NUM
ejde-397	912	3	(	(	PUNCT
ejde-397	912	4	i	i	NOUN
ejde-397	912	5	=	=	NOUN
ejde-397	912	6	0	0	NUM
ejde-397	912	7	,	,	PUNCT
ejde-397	912	8	1	1	NUM
ejde-397	912	9	,	,	PUNCT
ejde-397	912	10	2	2	NUM
ejde-397	912	11	)	)	PUNCT
ejde-397	912	12	.	.	PUNCT
ejde-397	913	1	furthermore	furthermore	ADV
ejde-397	913	2	,	,	PUNCT
ejde-397	913	3	if	if	SCONJ
ejde-397	913	4	a	a	PRON
ejde-397	913	5	is	be	AUX
ejde-397	913	6	densely	densely	ADV
ejde-397	913	7	defined	define	VERB
ejde-397	913	8	,	,	PUNCT
ejde-397	913	9	then	then	ADV
ejde-397	913	10	a	a	PRON
ejde-397	913	11	is	be	AUX
ejde-397	913	12	a	a	DET
ejde-397	913	13	subgenerator	subgenerator	NOUN
ejde-397	913	14	of	of	ADP
ejde-397	913	15	a	a	DET
ejde-397	913	16	global	global	ADJ
ejde-397	913	17	(	(	PUNCT
ejde-397	913	18	a	a	PRON
ejde-397	913	19	,	,	PUNCT
ejde-397	913	20	k1)regularized	k1)regularize	VERB
ejde-397	913	21	c2	c2	PROPN
ejde-397	913	22	-	-	PUNCT
ejde-397	913	23	uniqueness	uniqueness	PROPN
ejde-397	913	24	family	family	NOUN
ejde-397	913	25	(	(	PUNCT
ejde-397	913	26	r0,2(t))t≥0	r0,2(t))t≥0	PROPN
ejde-397	913	27	(	(	PUNCT
ejde-397	913	28	(	(	PUNCT
ejde-397	913	29	a	a	PRON
ejde-397	913	30	,	,	PUNCT
ejde-397	913	31	k1)-regularized	k1)-regularize	VERB
ejde-397	913	32	c	c	NOUN
ejde-397	913	33	-	-	PUNCT
ejde-397	913	34	resolvent	resolvent	ADJ
ejde-397	913	35	family	family	NOUN
ejde-397	913	36	(	(	PUNCT
ejde-397	913	37	r0,0(t))t≥0	r0,0(t))t≥0	PROPN
ejde-397	913	38	with	with	ADP
ejde-397	913	39	the	the	DET
ejde-397	913	40	property	property	NOUN
ejde-397	913	41	that	that	PRON
ejde-397	913	42	(	(	PUNCT
ejde-397	913	43	5.1	5.1	NUM
ejde-397	913	44	)	)	PUNCT
ejde-397	913	45	holds	hold	VERB
ejde-397	913	46	for	for	ADP
ejde-397	913	47	r1	r1	PROPN
ejde-397	913	48	(	(	PUNCT
ejde-397	913	49	·	·	PUNCT
ejde-397	913	50	)	)	PUNCT
ejde-397	913	51	replaced	replace	VERB
ejde-397	913	52	with	with	ADP
ejde-397	913	53	r0,0	r0,0	NOUN
ejde-397	913	54	(	(	PUNCT
ejde-397	913	55	·	·	PUNCT
ejde-397	913	56	)	)	PUNCT
ejde-397	913	57	and	and	CCONJ
ejde-397	913	58	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	913	59	abstract	abstract	ADJ
ejde-397	913	60	degenerate	degenerate	ADJ
ejde-397	913	61	volterra	volterra	NOUN
ejde-397	913	62	inclusions	inclusion	NOUN
ejde-397	913	63	29	29	NUM
ejde-397	913	64	each	each	PRON
ejde-397	913	65	x	x	PUNCT
ejde-397	913	66	=	=	PUNCT
ejde-397	913	67	y	y	PROPN
ejde-397	913	68	∈	∈	PROPN
ejde-397	913	69	x	x	NOUN
ejde-397	913	70	)	)	PUNCT
ejde-397	913	71	such	such	ADJ
ejde-397	913	72	that	that	SCONJ
ejde-397	913	73	the	the	DET
ejde-397	913	74	family	family	NOUN
ejde-397	913	75	{	{	PUNCT
ejde-397	913	76	e−ωatri(t	e−ωatri(t	PROPN
ejde-397	913	77	)	)	PUNCT
ejde-397	913	78	:	:	PUNCT
ejde-397	913	79	t	t	X
ejde-397	913	80	≥	≥	NOUN
ejde-397	913	81	0	0	NUM
ejde-397	913	82	}	}	PUNCT
ejde-397	913	83	is	be	AUX
ejde-397	913	84	equicontinuous	equicontinuous	ADJ
ejde-397	913	85	,	,	PUNCT
ejde-397	913	86	resp	resp	NOUN
ejde-397	913	87	.	.	PUNCT
ejde-397	913	88	,	,	PUNCT
ejde-397	913	89	for	for	ADP
ejde-397	913	90	every	every	DET
ejde-397	913	91	ε	ε	PROPN
ejde-397	913	92	>	>	X
ejde-397	913	93	0	0	PROPN
ejde-397	913	94	,	,	PUNCT
ejde-397	913	95	the	the	DET
ejde-397	913	96	family	family	NOUN
ejde-397	913	97	{	{	PUNCT
ejde-397	913	98	e−εtri(t	e−εtri(t	PROPN
ejde-397	913	99	)	)	PUNCT
ejde-397	913	100	:	:	PUNCT
ejde-397	914	1	t	t	X
ejde-397	914	2	≥	≥	NOUN
ejde-397	914	3	0	0	NUM
ejde-397	914	4	}	}	PUNCT
ejde-397	914	5	is	be	AUX
ejde-397	914	6	equicontinuous	equicontinuous	ADJ
ejde-397	914	7	(	(	PUNCT
ejde-397	914	8	i	i	NOUN
ejde-397	914	9	=	=	NOUN
ejde-397	914	10	1	1	NUM
ejde-397	914	11	,	,	PUNCT
ejde-397	914	12	2	2	NUM
ejde-397	914	13	)	)	PUNCT
ejde-397	914	14	.	.	PUNCT
ejde-397	915	1	let	let	VERB
ejde-397	915	2	(	(	PUNCT
ejde-397	915	3	r1(t	r1(t	PROPN
ejde-397	915	4	)	)	PUNCT
ejde-397	915	5	,	,	PUNCT
ejde-397	915	6	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	915	7	)	)	PUNCT
ejde-397	915	8	be	be	VERB
ejde-397	915	9	a	a	DET
ejde-397	915	10	mild	mild	ADJ
ejde-397	915	11	(	(	PUNCT
ejde-397	915	12	a	a	PRON
ejde-397	915	13	,	,	PUNCT
ejde-397	915	14	k)-regularized	k)-regularize	VERB
ejde-397	915	15	(	(	PUNCT
ejde-397	915	16	c1	c1	NOUN
ejde-397	915	17	,	,	PUNCT
ejde-397	915	18	c2)-existence	c2)-existence	VERB
ejde-397	915	19	and	and	CCONJ
ejde-397	915	20	uniqueness	uniqueness	VERB
ejde-397	915	21	family	family	NOUN
ejde-397	915	22	with	with	ADP
ejde-397	915	23	a	a	DET
ejde-397	915	24	subgenerator	subgenerator	NOUN
ejde-397	915	25	a.	a.	NOUN
ejde-397	916	1	then	then	ADV
ejde-397	916	2	it	it	PRON
ejde-397	916	3	is	be	AUX
ejde-397	916	4	straightforward	straightforward	ADJ
ejde-397	916	5	to	to	PART
ejde-397	916	6	see	see	VERB
ejde-397	916	7	that	that	SCONJ
ejde-397	916	8	the	the	DET
ejde-397	916	9	function	function	NOUN
ejde-397	916	10	t	t	PROPN
ejde-397	916	11	7→	7→	NUM
ejde-397	916	12	r1(t)y	r1(t)y	PROPN
ejde-397	916	13	,	,	PUNCT
ejde-397	916	14	t	t	PROPN
ejde-397	916	15	∈	∈	PROPN
ejde-397	917	1	[	[	X
ejde-397	917	2	0	0	NUM
ejde-397	917	3	,	,	PUNCT
ejde-397	917	4	τ	τ	X
ejde-397	917	5	)	)	PUNCT
ejde-397	917	6	(	(	PUNCT
ejde-397	917	7	y	y	PROPN
ejde-397	917	8	∈	∈	PROPN
ejde-397	917	9	y	y	PROPN
ejde-397	917	10	)	)	PUNCT
ejde-397	917	11	,	,	PUNCT
ejde-397	917	12	resp	resp	NOUN
ejde-397	917	13	.	.	PUNCT
ejde-397	918	1	t	t	PROPN
ejde-397	918	2	7→	7→	NUM
ejde-397	918	3	r2(t)x	r2(t)x	NOUN
ejde-397	918	4	,	,	PUNCT
ejde-397	918	5	t	t	PROPN
ejde-397	918	6	∈	∈	PROPN
ejde-397	919	1	[	[	X
ejde-397	919	2	0	0	NUM
ejde-397	919	3	,	,	PUNCT
ejde-397	919	4	τ	τ	X
ejde-397	919	5	)	)	PUNCT
ejde-397	919	6	(	(	PUNCT
ejde-397	919	7	x	x	SYM
ejde-397	919	8	∈	∈	PROPN
ejde-397	919	9	d(a	d(a	PROPN
ejde-397	919	10	)	)	PUNCT
ejde-397	919	11	)	)	PUNCT
ejde-397	919	12	,	,	PUNCT
ejde-397	919	13	is	be	AUX
ejde-397	919	14	a	a	DET
ejde-397	919	15	solution	solution	NOUN
ejde-397	919	16	of	of	ADP
ejde-397	919	17	problem	problem	NOUN
ejde-397	919	18	(	(	PUNCT
ejde-397	919	19	1.1	1.1	NUM
ejde-397	919	20	)	)	PUNCT
ejde-397	919	21	with	with	ADP
ejde-397	919	22	b	b	NOUN
ejde-397	919	23	=	=	SYM
ejde-397	919	24	i	i	PROPN
ejde-397	919	25	and	and	CCONJ
ejde-397	919	26	f(t	f(t	PROPN
ejde-397	919	27	)	)	PUNCT
ejde-397	920	1	=	=	SYM
ejde-397	920	2	k(t)c1y	k(t)c1y	PROPN
ejde-397	920	3	,	,	PUNCT
ejde-397	920	4	t	t	PROPN
ejde-397	920	5	∈	∈	PROPN
ejde-397	921	1	[	[	X
ejde-397	921	2	0	0	NUM
ejde-397	921	3	,	,	PUNCT
ejde-397	921	4	τ	τ	PROPN
ejde-397	921	5	)	)	PUNCT
ejde-397	921	6	,	,	PUNCT
ejde-397	921	7	resp	resp	NOUN
ejde-397	921	8	.	.	PUNCT
ejde-397	922	1	a	a	DET
ejde-397	922	2	strong	strong	ADJ
ejde-397	922	3	solution	solution	NOUN
ejde-397	922	4	of	of	ADP
ejde-397	922	5	(	(	PUNCT
ejde-397	922	6	1.1	1.1	NUM
ejde-397	922	7	)	)	PUNCT
ejde-397	922	8	with	with	ADP
ejde-397	922	9	b	b	NOUN
ejde-397	922	10	=	=	SYM
ejde-397	922	11	i	i	PROPN
ejde-397	922	12	and	and	CCONJ
ejde-397	922	13	f(t	f(t	NOUN
ejde-397	922	14	)	)	PUNCT
ejde-397	922	15	=	=	SYM
ejde-397	922	16	k(t)c2x	k(t)c2x	NOUN
ejde-397	922	17	,	,	PUNCT
ejde-397	922	18	t	t	PROPN
ejde-397	922	19	∈	∈	PROPN
ejde-397	923	1	[	[	X
ejde-397	923	2	0	0	NUM
ejde-397	923	3	,	,	PUNCT
ejde-397	923	4	τ	τ	PROPN
ejde-397	923	5	)	)	PUNCT
ejde-397	923	6	,	,	PUNCT
ejde-397	923	7	provided	provide	VERB
ejde-397	923	8	additionally	additionally	ADV
ejde-397	923	9	in	in	ADP
ejde-397	923	10	the	the	DET
ejde-397	923	11	last	last	ADJ
ejde-397	923	12	case	case	NOUN
ejde-397	923	13	that	that	SCONJ
ejde-397	923	14	r2(t)x	r2(t)x	PROPN
ejde-397	923	15	∈	∈	PROPN
ejde-397	923	16	d(a	d(a	PROPN
ejde-397	923	17	)	)	PUNCT
ejde-397	923	18	,	,	PUNCT
ejde-397	923	19	t	t	PROPN
ejde-397	923	20	∈	∈	PROPN
ejde-397	924	1	[	[	X
ejde-397	924	2	0	0	NUM
ejde-397	924	3	,	,	PUNCT
ejde-397	924	4	τ	τ	X
ejde-397	924	5	)	)	PUNCT
ejde-397	924	6	and	and	CCONJ
ejde-397	924	7	r2(t)ax	r2(t)ax	ADV
ejde-397	924	8	⊆	⊆	X
ejde-397	924	9	ar2(t)x	ar2(t)x	PROPN
ejde-397	924	10	,	,	PUNCT
ejde-397	924	11	t	t	PROPN
ejde-397	924	12	∈	∈	PROPN
ejde-397	925	1	[	[	X
ejde-397	925	2	0	0	NUM
ejde-397	925	3	,	,	PUNCT
ejde-397	925	4	τ	τ	PROPN
ejde-397	925	5	)	)	PUNCT
ejde-397	925	6	.	.	PUNCT
ejde-397	926	1	furthermore	furthermore	ADV
ejde-397	926	2	,	,	PUNCT
ejde-397	926	3	it	it	PRON
ejde-397	926	4	is	be	AUX
ejde-397	926	5	very	very	ADV
ejde-397	926	6	simple	simple	ADJ
ejde-397	926	7	to	to	PART
ejde-397	926	8	transmit	transmit	VERB
ejde-397	926	9	the	the	DET
ejde-397	926	10	assertions	assertion	NOUN
ejde-397	926	11	of	of	ADP
ejde-397	926	12	[	[	X
ejde-397	926	13	36	36	NUM
ejde-397	926	14	,	,	PUNCT
ejde-397	926	15	proposition	proposition	NOUN
ejde-397	926	16	2.8.8	2.8.8	NUM
ejde-397	926	17	,	,	PUNCT
ejde-397	926	18	proposition	proposition	NOUN
ejde-397	926	19	2.8.9	2.8.9	NUM
ejde-397	926	20	]	]	PUNCT
ejde-397	926	21	to	to	AUX
ejde-397	926	22	mild	mild	ADJ
ejde-397	926	23	(	(	PUNCT
ejde-397	926	24	a	a	PRON
ejde-397	926	25	,	,	PUNCT
ejde-397	926	26	k)-regularized	k)-regularize	VERB
ejde-397	926	27	(	(	PUNCT
ejde-397	926	28	c1	c1	NOUN
ejde-397	926	29	,	,	PUNCT
ejde-397	926	30	c2)-existence	c2)-existence	VERB
ejde-397	926	31	and	and	CCONJ
ejde-397	926	32	uniqueness	uniqueness	ADJ
ejde-397	926	33	families	family	NOUN
ejde-397	926	34	subgenerated	subgenerate	VERB
ejde-397	926	35	by	by	ADP
ejde-397	926	36	multivalued	multivalued	ADJ
ejde-397	926	37	linear	linear	PROPN
ejde-397	926	38	operators	operator	NOUN
ejde-397	926	39	:	:	PUNCT
ejde-397	926	40	proposition	proposition	NOUN
ejde-397	926	41	5.8	5.8	NUM
ejde-397	926	42	.	.	PUNCT
ejde-397	927	1	(	(	PUNCT
ejde-397	927	2	i	i	NOUN
ejde-397	927	3	)	)	PUNCT
ejde-397	927	4	suppose	suppose	VERB
ejde-397	927	5	that	that	SCONJ
ejde-397	927	6	(	(	PUNCT
ejde-397	927	7	r1(t	r1(t	PROPN
ejde-397	927	8	)	)	PUNCT
ejde-397	927	9	,	,	PUNCT
ejde-397	927	10	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	927	11	)	)	PUNCT
ejde-397	927	12	is	be	AUX
ejde-397	927	13	a	a	DET
ejde-397	927	14	mild	mild	ADJ
ejde-397	927	15	(	(	PUNCT
ejde-397	927	16	a	a	PRON
ejde-397	927	17	,	,	PUNCT
ejde-397	927	18	k)-regularized	k)-regularize	VERB
ejde-397	927	19	(	(	PUNCT
ejde-397	927	20	c1	c1	NOUN
ejde-397	927	21	,	,	PUNCT
ejde-397	927	22	c2)-existence	c2)-existence	VERB
ejde-397	927	23	and	and	CCONJ
ejde-397	927	24	uniqueness	uniqueness	VERB
ejde-397	927	25	family	family	NOUN
ejde-397	927	26	with	with	ADP
ejde-397	927	27	a	a	DET
ejde-397	927	28	subgenerator	subgenerator	NOUN
ejde-397	927	29	a	a	ADV
ejde-397	927	30	,	,	PUNCT
ejde-397	927	31	as	as	ADV
ejde-397	927	32	well	well	ADV
ejde-397	927	33	as	as	ADP
ejde-397	927	34	that	that	PRON
ejde-397	927	35	(	(	PUNCT
ejde-397	927	36	r2(t))t∈[0,τ	r2(t))t∈[0,τ	NOUN
ejde-397	927	37	)	)	PUNCT
ejde-397	927	38	is	be	AUX
ejde-397	927	39	locally	locally	ADV
ejde-397	927	40	equicontinuous	equicontinuous	ADJ
ejde-397	927	41	and	and	CCONJ
ejde-397	927	42	the	the	DET
ejde-397	927	43	functions	function	NOUN
ejde-397	927	44	a(t	a(t	VERB
ejde-397	927	45	)	)	PUNCT
ejde-397	927	46	and	and	CCONJ
ejde-397	927	47	k(t	k(t	NOUN
ejde-397	927	48	)	)	PUNCT
ejde-397	927	49	are	be	AUX
ejde-397	927	50	kernels	kernel	NOUN
ejde-397	927	51	on	on	ADP
ejde-397	927	52	[	[	X
ejde-397	927	53	0	0	NUM
ejde-397	927	54	,	,	PUNCT
ejde-397	927	55	τ	τ	PROPN
ejde-397	927	56	)	)	PUNCT
ejde-397	927	57	.	.	PUNCT
ejde-397	928	1	then	then	ADV
ejde-397	928	2	c2r1(t	c2r1(t	VERB
ejde-397	928	3	)	)	PUNCT
ejde-397	928	4	=	=	SYM
ejde-397	928	5	r2(t)c1	r2(t)c1	NOUN
ejde-397	928	6	,	,	PUNCT
ejde-397	928	7	t	t	PROPN
ejde-397	928	8	∈	∈	PROPN
ejde-397	929	1	[	[	X
ejde-397	929	2	0	0	NUM
ejde-397	929	3	,	,	PUNCT
ejde-397	929	4	τ	τ	PROPN
ejde-397	929	5	)	)	PUNCT
ejde-397	929	6	.	.	PUNCT
ejde-397	930	1	(	(	PUNCT
ejde-397	930	2	ii	ii	NOUN
ejde-397	930	3	)	)	PUNCT
ejde-397	930	4	suppose	suppose	VERB
ejde-397	930	5	that	that	SCONJ
ejde-397	930	6	(	(	PUNCT
ejde-397	930	7	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	930	8	)	)	PUNCT
ejde-397	930	9	is	be	AUX
ejde-397	930	10	a	a	DET
ejde-397	930	11	locally	locally	ADV
ejde-397	930	12	equicontinuous	equicontinuous	ADJ
ejde-397	930	13	mild	mild	ADJ
ejde-397	930	14	(	(	PUNCT
ejde-397	930	15	a	a	DET
ejde-397	930	16	,	,	PUNCT
ejde-397	930	17	k)-regularized	k)-regularize	VERB
ejde-397	930	18	c2	c2	PROPN
ejde-397	930	19	-	-	PUNCT
ejde-397	930	20	uniqueness	uniqueness	PROPN
ejde-397	930	21	family	family	NOUN
ejde-397	930	22	with	with	ADP
ejde-397	930	23	a	a	DET
ejde-397	930	24	subgenerator	subgenerator	NOUN
ejde-397	930	25	a.	a.	NOUN
ejde-397	930	26	then	then	ADV
ejde-397	930	27	every	every	DET
ejde-397	930	28	strong	strong	ADJ
ejde-397	930	29	solution	solution	NOUN
ejde-397	930	30	u(t	u(t	NOUN
ejde-397	930	31	)	)	PUNCT
ejde-397	930	32	of	of	ADP
ejde-397	930	33	(	(	PUNCT
ejde-397	930	34	1.1	1.1	NUM
ejde-397	930	35	)	)	PUNCT
ejde-397	930	36	with	with	ADP
ejde-397	930	37	b	b	NOUN
ejde-397	930	38	=	=	SYM
ejde-397	930	39	i	i	PROPN
ejde-397	930	40	and	and	CCONJ
ejde-397	930	41	f	f	NOUN
ejde-397	930	42	=	=	SYM
ejde-397	930	43	f	f	PROPN
ejde-397	930	44	∈	∈	PROPN
ejde-397	930	45	c([0	c([0	PROPN
ejde-397	930	46	,	,	PUNCT
ejde-397	930	47	τ	τ	PROPN
ejde-397	930	48	)	)	PUNCT
ejde-397	930	49	:	:	PUNCT
ejde-397	930	50	x	x	X
ejde-397	930	51	)	)	PUNCT
ejde-397	930	52	satisfies	satisfie	NOUN
ejde-397	930	53	(	(	PUNCT
ejde-397	930	54	r2	r2	PROPN
ejde-397	930	55	∗	∗	PROPN
ejde-397	930	56	f	f	PROPN
ejde-397	930	57	)	)	PUNCT
ejde-397	930	58	(	(	PUNCT
ejde-397	930	59	t	t	NOUN
ejde-397	930	60	)	)	PUNCT
ejde-397	930	61	=	=	PUNCT
ejde-397	930	62	(	(	PUNCT
ejde-397	930	63	kc2	kc2	PROPN
ejde-397	930	64	∗	∗	X
ejde-397	930	65	u	u	PROPN
ejde-397	930	66	)	)	PUNCT
ejde-397	930	67	(	(	PUNCT
ejde-397	930	68	t	t	PROPN
ejde-397	930	69	)	)	PUNCT
ejde-397	930	70	,	,	PUNCT
ejde-397	930	71	0	0	NUM
ejde-397	930	72	≤	≤	NUM
ejde-397	930	73	t	t	PROPN
ejde-397	930	74	<	<	X
ejde-397	930	75	τ	τ	X
ejde-397	930	76	.	.	PUNCT
ejde-397	931	1	(	(	PUNCT
ejde-397	931	2	5.10	5.10	NUM
ejde-397	931	3	)	)	PUNCT
ejde-397	931	4	furthermore	furthermore	ADV
ejde-397	931	5	,	,	PUNCT
ejde-397	931	6	the	the	DET
ejde-397	931	7	problem	problem	NOUN
ejde-397	931	8	(	(	PUNCT
ejde-397	931	9	1.1	1.1	NUM
ejde-397	931	10	)	)	PUNCT
ejde-397	931	11	has	have	AUX
ejde-397	931	12	at	at	ADP
ejde-397	931	13	most	most	ADJ
ejde-397	931	14	one	one	NUM
ejde-397	931	15	pre	pre	ADJ
ejde-397	931	16	-	-	NOUN
ejde-397	931	17	solution	solution	NOUN
ejde-397	931	18	provided	provide	VERB
ejde-397	931	19	,	,	PUNCT
ejde-397	931	20	in	in	ADP
ejde-397	931	21	addition	addition	NOUN
ejde-397	931	22	,	,	PUNCT
ejde-397	931	23	that	that	SCONJ
ejde-397	931	24	the	the	DET
ejde-397	931	25	functions	function	NOUN
ejde-397	931	26	a(t	a(t	VERB
ejde-397	931	27	)	)	PUNCT
ejde-397	931	28	and	and	CCONJ
ejde-397	931	29	k(t	k(t	NOUN
ejde-397	931	30	)	)	PUNCT
ejde-397	931	31	are	be	AUX
ejde-397	931	32	kernels	kernel	NOUN
ejde-397	931	33	on	on	ADP
ejde-397	931	34	on	on	ADP
ejde-397	931	35	[	[	X
ejde-397	931	36	0	0	NUM
ejde-397	931	37	,	,	PUNCT
ejde-397	931	38	τ	τ	X
ejde-397	931	39	)	)	PUNCT
ejde-397	931	40	and	and	CCONJ
ejde-397	931	41	the	the	DET
ejde-397	931	42	function	function	NOUN
ejde-397	931	43	f(t	f(t	PROPN
ejde-397	931	44	)	)	PUNCT
ejde-397	931	45	is	be	AUX
ejde-397	931	46	single	single	ADV
ejde-397	931	47	-	-	PUNCT
ejde-397	931	48	valued	value	VERB
ejde-397	931	49	.	.	PUNCT
ejde-397	932	1	the	the	DET
ejde-397	932	2	first	first	ADJ
ejde-397	932	3	part	part	NOUN
ejde-397	932	4	of	of	ADP
ejde-397	932	5	the	the	DET
ejde-397	932	6	following	follow	VERB
ejde-397	932	7	theorem	theorem	NOUN
ejde-397	932	8	is	be	AUX
ejde-397	932	9	an	an	DET
ejde-397	932	10	extension	extension	NOUN
ejde-397	932	11	of	of	ADP
ejde-397	932	12	[	[	X
ejde-397	932	13	36	36	NUM
ejde-397	932	14	,	,	PUNCT
ejde-397	932	15	theorem	theorem	VERB
ejde-397	932	16	2.1.28(ii	2.1.28(ii	NUM
ejde-397	932	17	)	)	PUNCT
ejde-397	932	18	]	]	PUNCT
ejde-397	932	19	and	and	CCONJ
ejde-397	932	20	its	its	PRON
ejde-397	932	21	validity	validity	NOUN
ejde-397	932	22	can	can	AUX
ejde-397	932	23	be	be	AUX
ejde-397	932	24	verified	verify	VERB
ejde-397	932	25	with	with	ADP
ejde-397	932	26	the	the	DET
ejde-397	932	27	help	help	NOUN
ejde-397	932	28	of	of	ADP
ejde-397	932	29	proof	proof	NOUN
ejde-397	932	30	of	of	ADP
ejde-397	932	31	[	[	X
ejde-397	932	32	59	59	NUM
ejde-397	932	33	,	,	PUNCT
ejde-397	932	34	theorem	theorem	VERB
ejde-397	932	35	2.7	2.7	NUM
ejde-397	932	36	]	]	PUNCT
ejde-397	932	37	,	,	PUNCT
ejde-397	932	38	lemma	lemma	PROPN
ejde-397	932	39	2.2	2.2	NUM
ejde-397	932	40	and	and	CCONJ
ejde-397	932	41	theorem	theorem	VERB
ejde-397	932	42	2.3	2.3	NUM
ejde-397	932	43	;	;	PUNCT
ejde-397	932	44	the	the	DET
ejde-397	932	45	second	second	ADJ
ejde-397	932	46	part	part	NOUN
ejde-397	932	47	of	of	ADP
ejde-397	932	48	theorem	theorem	NOUN
ejde-397	932	49	is	be	AUX
ejde-397	932	50	an	an	DET
ejde-397	932	51	extension	extension	NOUN
ejde-397	932	52	of	of	ADP
ejde-397	932	53	[	[	X
ejde-397	932	54	36	36	NUM
ejde-397	932	55	,	,	PUNCT
ejde-397	932	56	proposition	proposition	NOUN
ejde-397	932	57	2.1.31	2.1.31	NUM
ejde-397	932	58	]	]	PUNCT
ejde-397	932	59	and	and	CCONJ
ejde-397	932	60	can	can	AUX
ejde-397	932	61	be	be	AUX
ejde-397	932	62	shown	show	VERB
ejde-397	932	63	by	by	ADP
ejde-397	932	64	the	the	DET
ejde-397	932	65	arguments	argument	NOUN
ejde-397	932	66	contained	contain	VERB
ejde-397	932	67	in	in	ADP
ejde-397	932	68	the	the	DET
ejde-397	932	69	proof	proof	NOUN
ejde-397	932	70	of	of	ADP
ejde-397	932	71	[	[	X
ejde-397	932	72	66	66	NUM
ejde-397	932	73	,	,	PUNCT
ejde-397	932	74	theorem	theorem	VERB
ejde-397	932	75	2.5	2.5	NUM
ejde-397	932	76	]	]	PUNCT
ejde-397	932	77	,	,	PUNCT
ejde-397	932	78	along	along	ADP
ejde-397	932	79	with	with	ADP
ejde-397	932	80	lemma	lemma	PROPN
ejde-397	932	81	2.2	2.2	NUM
ejde-397	932	82	.	.	PUNCT
ejde-397	933	1	theorem	theorem	VERB
ejde-397	933	2	5.9	5.9	NUM
ejde-397	933	3	.	.	PUNCT
ejde-397	934	1	(	(	PUNCT
ejde-397	934	2	i	i	NOUN
ejde-397	934	3	)	)	PUNCT
ejde-397	934	4	suppose	suppose	VERB
ejde-397	934	5	that	that	SCONJ
ejde-397	934	6	(	(	PUNCT
ejde-397	934	7	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	934	8	)	)	PUNCT
ejde-397	934	9	is	be	AUX
ejde-397	934	10	a	a	DET
ejde-397	934	11	locally	locally	ADV
ejde-397	934	12	equicontinuous	equicontinuous	ADJ
ejde-397	934	13	(	(	PUNCT
ejde-397	934	14	a	a	PRON
ejde-397	934	15	,	,	PUNCT
ejde-397	934	16	k)-regularized	k)-regularize	VERB
ejde-397	934	17	c	c	NOUN
ejde-397	934	18	-	-	PUNCT
ejde-397	934	19	resolvent	resolvent	ADJ
ejde-397	934	20	family	family	NOUN
ejde-397	934	21	generated	generate	VERB
ejde-397	934	22	by	by	ADP
ejde-397	934	23	a	a	PRON
ejde-397	934	24	,	,	PUNCT
ejde-397	934	25	the	the	DET
ejde-397	934	26	equation	equation	NOUN
ejde-397	934	27	(	(	PUNCT
ejde-397	934	28	5.1	5.1	NUM
ejde-397	934	29	)	)	PUNCT
ejde-397	934	30	holds	hold	VERB
ejde-397	934	31	for	for	ADP
ejde-397	934	32	each	each	PRON
ejde-397	934	33	y	y	NOUN
ejde-397	934	34	=	=	PUNCT
ejde-397	934	35	x	x	SYM
ejde-397	934	36	∈	∈	PROPN
ejde-397	934	37	x	x	NOUN
ejde-397	934	38	,	,	PUNCT
ejde-397	934	39	with	with	ADP
ejde-397	934	40	r1	r1	PROPN
ejde-397	934	41	(	(	PUNCT
ejde-397	934	42	·	·	PUNCT
ejde-397	934	43	)	)	PUNCT
ejde-397	934	44	and	and	CCONJ
ejde-397	934	45	c1	c1	PROPN
ejde-397	934	46	replaced	replace	VERB
ejde-397	934	47	therein	therein	ADV
ejde-397	934	48	with	with	ADP
ejde-397	934	49	r	r	NOUN
ejde-397	934	50	(	(	PUNCT
ejde-397	934	51	·	·	PUNCT
ejde-397	934	52	)	)	PUNCT
ejde-397	934	53	and	and	CCONJ
ejde-397	934	54	c	c	NOUN
ejde-397	934	55	,	,	PUNCT
ejde-397	934	56	respectively	respectively	ADV
ejde-397	934	57	,	,	PUNCT
ejde-397	934	58	k(t	k(t	PROPN
ejde-397	934	59	)	)	PUNCT
ejde-397	934	60	is	be	AUX
ejde-397	934	61	a	a	DET
ejde-397	934	62	kernel	kernel	NOUN
ejde-397	934	63	on	on	ADP
ejde-397	934	64	[	[	X
ejde-397	934	65	0	0	NUM
ejde-397	934	66	,	,	PUNCT
ejde-397	934	67	τ	τ	PROPN
ejde-397	934	68	)	)	PUNCT
ejde-397	934	69	,	,	PUNCT
ejde-397	934	70	u	u	NOUN
ejde-397	934	71	,	,	PUNCT
ejde-397	934	72	f	f	PROPN
ejde-397	934	73	∈	∈	PROPN
ejde-397	934	74	c([0	c([0	PROPN
ejde-397	934	75	,	,	PUNCT
ejde-397	934	76	τ	τ	PROPN
ejde-397	934	77	)	)	PUNCT
ejde-397	934	78	:	:	PUNCT
ejde-397	935	1	x	x	X
ejde-397	935	2	)	)	PUNCT
ejde-397	935	3	,	,	PUNCT
ejde-397	935	4	and	and	CCONJ
ejde-397	935	5	(	(	PUNCT
ejde-397	935	6	5.10	5.10	NUM
ejde-397	935	7	)	)	PUNCT
ejde-397	935	8	holds	hold	VERB
ejde-397	935	9	with	with	ADP
ejde-397	935	10	r2	r2	PROPN
ejde-397	935	11	(	(	PUNCT
ejde-397	935	12	·	·	PUNCT
ejde-397	935	13	)	)	PUNCT
ejde-397	935	14	and	and	CCONJ
ejde-397	935	15	c2	c2	PROPN
ejde-397	935	16	replaced	replace	VERB
ejde-397	935	17	therein	therein	ADV
ejde-397	935	18	with	with	ADP
ejde-397	935	19	r	r	NOUN
ejde-397	935	20	(	(	PUNCT
ejde-397	935	21	·	·	PUNCT
ejde-397	935	22	)	)	PUNCT
ejde-397	935	23	and	and	CCONJ
ejde-397	935	24	c	c	NOUN
ejde-397	935	25	,	,	PUNCT
ejde-397	935	26	respectively	respectively	ADV
ejde-397	935	27	.	.	PUNCT
ejde-397	936	1	then	then	ADV
ejde-397	936	2	u(t	u(t	NOUN
ejde-397	936	3	)	)	PUNCT
ejde-397	936	4	is	be	AUX
ejde-397	936	5	a	a	DET
ejde-397	936	6	solution	solution	NOUN
ejde-397	936	7	of	of	ADP
ejde-397	936	8	the	the	DET
ejde-397	936	9	abstract	abstract	ADJ
ejde-397	936	10	volterra	volterra	NOUN
ejde-397	936	11	inclusion	inclusion	NOUN
ejde-397	936	12	(	(	PUNCT
ejde-397	936	13	1.1	1.1	NUM
ejde-397	936	14	)	)	PUNCT
ejde-397	936	15	with	with	ADP
ejde-397	936	16	b	b	NOUN
ejde-397	936	17	=	=	SYM
ejde-397	936	18	i	i	PROPN
ejde-397	936	19	and	and	CCONJ
ejde-397	936	20	f	f	PROPN
ejde-397	936	21	=	=	SYM
ejde-397	936	22	f	f	PROPN
ejde-397	936	23	.	.	PUNCT
ejde-397	937	1	(	(	PUNCT
ejde-397	937	2	ii	ii	NOUN
ejde-397	937	3	)	)	PUNCT
ejde-397	937	4	suppose	suppose	VERB
ejde-397	937	5	that	that	SCONJ
ejde-397	937	6	the	the	DET
ejde-397	937	7	functions	function	NOUN
ejde-397	937	8	a(t	a(t	VERB
ejde-397	937	9	)	)	PUNCT
ejde-397	937	10	and	and	CCONJ
ejde-397	937	11	k(t	k(t	NOUN
ejde-397	937	12	)	)	PUNCT
ejde-397	937	13	are	be	AUX
ejde-397	937	14	kernels	kernel	NOUN
ejde-397	937	15	on	on	ADP
ejde-397	937	16	[	[	X
ejde-397	937	17	0	0	NUM
ejde-397	937	18	,	,	PUNCT
ejde-397	937	19	τ	τ	PROPN
ejde-397	937	20	)	)	PUNCT
ejde-397	937	21	,	,	PUNCT
ejde-397	937	22	and	and	CCONJ
ejde-397	937	23	a	a	PRON
ejde-397	937	24	is	be	AUX
ejde-397	937	25	a	a	DET
ejde-397	937	26	closed	closed	ADJ
ejde-397	937	27	mlo	mlo	NOUN
ejde-397	937	28	in	in	ADP
ejde-397	937	29	x.	x.	PROPN
ejde-397	937	30	consider	consider	VERB
ejde-397	937	31	the	the	DET
ejde-397	937	32	following	follow	VERB
ejde-397	937	33	assertions	assertion	NOUN
ejde-397	937	34	:	:	PUNCT
ejde-397	937	35	(	(	PUNCT
ejde-397	937	36	a	a	X
ejde-397	937	37	)	)	PUNCT
ejde-397	937	38	a	a	PRON
ejde-397	937	39	is	be	AUX
ejde-397	937	40	a	a	DET
ejde-397	937	41	subgenerator	subgenerator	NOUN
ejde-397	937	42	of	of	ADP
ejde-397	937	43	a	a	DET
ejde-397	937	44	locally	locally	ADV
ejde-397	937	45	equicontinuous	equicontinuous	ADJ
ejde-397	937	46	(	(	PUNCT
ejde-397	937	47	a	a	PRON
ejde-397	937	48	,	,	PUNCT
ejde-397	937	49	k)-regularized	k)-regularize	VERB
ejde-397	937	50	c	c	NOUN
ejde-397	937	51	-	-	PUNCT
ejde-397	937	52	resolvent	resolvent	ADJ
ejde-397	937	53	family	family	NOUN
ejde-397	937	54	(	(	PUNCT
ejde-397	937	55	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	937	56	)	)	PUNCT
ejde-397	937	57	satisfying	satisfy	VERB
ejde-397	937	58	the	the	DET
ejde-397	937	59	equation	equation	NOUN
ejde-397	937	60	(	(	PUNCT
ejde-397	937	61	5.1	5.1	NUM
ejde-397	937	62	)	)	PUNCT
ejde-397	937	63	for	for	ADP
ejde-397	937	64	each	each	PRON
ejde-397	937	65	y	y	NOUN
ejde-397	937	66	=	=	PUNCT
ejde-397	937	67	x	x	SYM
ejde-397	937	68	∈	∈	PROPN
ejde-397	937	69	x	x	NOUN
ejde-397	937	70	,	,	PUNCT
ejde-397	937	71	with	with	ADP
ejde-397	937	72	r1	r1	PROPN
ejde-397	937	73	(	(	PUNCT
ejde-397	937	74	·	·	PUNCT
ejde-397	937	75	)	)	PUNCT
ejde-397	937	76	and	and	CCONJ
ejde-397	937	77	c1	c1	PROPN
ejde-397	937	78	replaced	replace	VERB
ejde-397	937	79	therein	therein	ADV
ejde-397	937	80	by	by	ADP
ejde-397	937	81	r	r	NOUN
ejde-397	937	82	(	(	PUNCT
ejde-397	937	83	·	·	PUNCT
ejde-397	937	84	)	)	PUNCT
ejde-397	937	85	and	and	CCONJ
ejde-397	937	86	c	c	NOUN
ejde-397	937	87	,	,	PUNCT
ejde-397	937	88	respectively	respectively	ADV
ejde-397	937	89	.	.	PUNCT
ejde-397	938	1	(	(	PUNCT
ejde-397	938	2	b	b	X
ejde-397	938	3	)	)	PUNCT
ejde-397	938	4	for	for	ADP
ejde-397	938	5	every	every	DET
ejde-397	938	6	x	x	SYM
ejde-397	938	7	∈	∈	PROPN
ejde-397	938	8	x	x	NOUN
ejde-397	938	9	,	,	PUNCT
ejde-397	938	10	there	there	PRON
ejde-397	938	11	exists	exist	VERB
ejde-397	938	12	a	a	DET
ejde-397	938	13	unique	unique	ADJ
ejde-397	938	14	solution	solution	NOUN
ejde-397	938	15	of	of	ADP
ejde-397	938	16	(	(	PUNCT
ejde-397	938	17	1.1	1.1	NUM
ejde-397	938	18	)	)	PUNCT
ejde-397	938	19	with	with	ADP
ejde-397	938	20	b	b	NOUN
ejde-397	938	21	=	=	SYM
ejde-397	938	22	i	i	PROPN
ejde-397	938	23	and	and	CCONJ
ejde-397	938	24	f(t	f(t	NOUN
ejde-397	938	25	)	)	PUNCT
ejde-397	939	1	=	=	SYM
ejde-397	939	2	f(t	f(t	NOUN
ejde-397	939	3	)	)	PUNCT
ejde-397	939	4	=	=	SYM
ejde-397	939	5	k(t)cx	k(t)cx	PROPN
ejde-397	939	6	,	,	PUNCT
ejde-397	939	7	t	t	PROPN
ejde-397	939	8	∈	∈	PROPN
ejde-397	940	1	[	[	X
ejde-397	940	2	0	0	NUM
ejde-397	940	3	,	,	PUNCT
ejde-397	940	4	τ	τ	PROPN
ejde-397	940	5	)	)	PUNCT
ejde-397	940	6	.	.	PUNCT
ejde-397	941	1	then	then	ADV
ejde-397	941	2	(	(	PUNCT
ejde-397	941	3	a)⇒	a)⇒	PROPN
ejde-397	941	4	(	(	PUNCT
ejde-397	941	5	b	b	NOUN
ejde-397	941	6	)	)	PUNCT
ejde-397	941	7	.	.	PUNCT
ejde-397	942	1	if	if	SCONJ
ejde-397	942	2	,	,	PUNCT
ejde-397	942	3	in	in	ADP
ejde-397	942	4	addition	addition	NOUN
ejde-397	942	5	,	,	PUNCT
ejde-397	942	6	x	x	PRON
ejde-397	942	7	is	be	AUX
ejde-397	942	8	a	a	DET
ejde-397	942	9	fréchet	fréchet	NOUN
ejde-397	942	10	space	space	NOUN
ejde-397	942	11	,	,	PUNCT
ejde-397	942	12	then	then	ADV
ejde-397	942	13	the	the	DET
ejde-397	942	14	above	above	ADJ
ejde-397	942	15	are	be	AUX
ejde-397	942	16	equivalent	equivalent	ADJ
ejde-397	942	17	.	.	PUNCT
ejde-397	943	1	before	before	ADP
ejde-397	943	2	proceeding	proceed	VERB
ejde-397	943	3	further	far	ADV
ejde-397	943	4	,	,	PUNCT
ejde-397	943	5	it	it	PRON
ejde-397	943	6	should	should	AUX
ejde-397	943	7	be	be	AUX
ejde-397	943	8	noticed	notice	VERB
ejde-397	943	9	that	that	SCONJ
ejde-397	943	10	some	some	DET
ejde-397	943	11	additional	additional	ADJ
ejde-397	943	12	conditions	condition	NOUN
ejde-397	943	13	ensure	ensure	VERB
ejde-397	943	14	the	the	DET
ejde-397	943	15	validity	validity	NOUN
ejde-397	943	16	of	of	ADP
ejde-397	943	17	implication	implication	NOUN
ejde-397	943	18	(	(	PUNCT
ejde-397	943	19	b	b	NOUN
ejde-397	943	20	)	)	PUNCT
ejde-397	943	21	⇒	⇒	NOUN
ejde-397	943	22	(	(	PUNCT
ejde-397	943	23	a	a	X
ejde-397	943	24	)	)	PUNCT
ejde-397	943	25	in	in	ADP
ejde-397	943	26	complete	complete	ADJ
ejde-397	943	27	locally	locally	ADV
ejde-397	943	28	convex	convex	ADJ
ejde-397	943	29	spaces	space	NOUN
ejde-397	943	30	.	.	PUNCT
ejde-397	944	1	we	we	PRON
ejde-397	944	2	will	will	AUX
ejde-397	944	3	explain	explain	VERB
ejde-397	944	4	this	this	DET
ejde-397	944	5	fact	fact	NOUN
ejde-397	944	6	for	for	ADP
ejde-397	944	7	the	the	DET
ejde-397	944	8	problem	problem	NOUN
ejde-397	944	9	(	(	PUNCT
ejde-397	944	10	1.3	1.3	NUM
ejde-397	944	11	)	)	PUNCT
ejde-397	944	12	,	,	PUNCT
ejde-397	944	13	where	where	SCONJ
ejde-397	944	14	after	after	ADP
ejde-397	944	15	integration	integration	NOUN
ejde-397	944	16	we	we	PRON
ejde-397	944	17	have	have	AUX
ejde-397	944	18	a(t	a(t	VERB
ejde-397	944	19	)	)	PUNCT
ejde-397	944	20	=	=	SYM
ejde-397	944	21	gα(t	gα(t	NOUN
ejde-397	944	22	)	)	PUNCT
ejde-397	944	23	.	.	PUNCT
ejde-397	945	1	assume	assume	VERB
ejde-397	945	2	that	that	SCONJ
ejde-397	945	3	there	there	PRON
ejde-397	945	4	exists	exist	VERB
ejde-397	945	5	a	a	DET
ejde-397	945	6	unique	unique	ADJ
ejde-397	945	7	solution	solution	NOUN
ejde-397	945	8	of	of	ADP
ejde-397	945	9	problem	problem	NOUN
ejde-397	945	10	(	(	PUNCT
ejde-397	945	11	1.3	1.3	NUM
ejde-397	945	12	)	)	PUNCT
ejde-397	945	13	with	with	ADP
ejde-397	945	14	30	30	NUM
ejde-397	945	15	m.	m.	NOUN
ejde-397	945	16	kostić	kostić	NOUN
ejde-397	946	1	ejde-2023/63	ejde-2023/63	PROPN
ejde-397	946	2	b	b	PROPN
ejde-397	946	3	=	=	SYM
ejde-397	946	4	i	i	PROPN
ejde-397	946	5	,	,	PUNCT
ejde-397	946	6	f(t	f(t	PROPN
ejde-397	946	7	)	)	PUNCT
ejde-397	946	8	≡	≡	PROPN
ejde-397	946	9	0	0	NUM
ejde-397	946	10	,	,	PUNCT
ejde-397	946	11	x0	x0	PROPN
ejde-397	946	12	∈	∈	PROPN
ejde-397	946	13	c(d(a	c(d(a	PROPN
ejde-397	946	14	)	)	PUNCT
ejde-397	946	15	)	)	PUNCT
ejde-397	946	16	and	and	CCONJ
ejde-397	946	17	xj	xj	PROPN
ejde-397	946	18	=	=	SYM
ejde-397	946	19	0	0	PROPN
ejde-397	946	20	,	,	PUNCT
ejde-397	946	21	1	1	NUM
ejde-397	946	22	≤	≤	NUM
ejde-397	946	23	j	j	PROPN
ejde-397	946	24	≤	≤	PROPN
ejde-397	946	25	dαe−1	dαe−1	PROPN
ejde-397	946	26	.	.	PUNCT
ejde-397	947	1	if	if	SCONJ
ejde-397	947	2	,	,	PUNCT
ejde-397	947	3	in	in	ADP
ejde-397	947	4	addition	addition	NOUN
ejde-397	947	5	to	to	ADP
ejde-397	947	6	this	this	PRON
ejde-397	947	7	,	,	PUNCT
ejde-397	947	8	x	x	PRON
ejde-397	947	9	is	be	AUX
ejde-397	947	10	complete	complete	ADJ
ejde-397	947	11	,	,	PUNCT
ejde-397	947	12	a	a	PRON
ejde-397	947	13	is	be	AUX
ejde-397	947	14	closed	closed	ADJ
ejde-397	947	15	,	,	PUNCT
ejde-397	947	16	ca	can	AUX
ejde-397	947	17	⊆	⊆	NUM
ejde-397	947	18	ac	ac	PROPN
ejde-397	947	19	and	and	CCONJ
ejde-397	947	20	for	for	ADP
ejde-397	947	21	each	each	DET
ejde-397	947	22	seminorm	seminorm	NOUN
ejde-397	947	23	p	p	X
ejde-397	947	24	∈	∈	PROPN
ejde-397	947	25	~	~	PUNCT
ejde-397	947	26	and	and	CCONJ
ejde-397	947	27	t	t	X
ejde-397	947	28	>	>	X
ejde-397	947	29	0	0	PUNCT
ejde-397	948	1	there	there	PRON
ejde-397	948	2	exist	exist	VERB
ejde-397	948	3	q	q	PROPN
ejde-397	948	4	∈	∈	NOUN
ejde-397	948	5	~	~	PUNCT
ejde-397	948	6	and	and	CCONJ
ejde-397	948	7	c	c	X
ejde-397	948	8	>	>	X
ejde-397	948	9	0	0	NUM
ejde-397	948	10	such	such	ADJ
ejde-397	948	11	that	that	DET
ejde-397	948	12	p(u(t;cx	p(u(t;cx	NOUN
ejde-397	948	13	)	)	PUNCT
ejde-397	948	14	)	)	PUNCT
ejde-397	948	15	≤	≤	NOUN
ejde-397	948	16	cq(x	cq(x	PUNCT
ejde-397	948	17	)	)	PUNCT
ejde-397	948	18	,	,	PUNCT
ejde-397	948	19	x	x	PROPN
ejde-397	948	20	∈	∈	PROPN
ejde-397	948	21	d(a	d(a	PROPN
ejde-397	948	22	)	)	PUNCT
ejde-397	948	23	,	,	PUNCT
ejde-397	948	24	t	t	PROPN
ejde-397	948	25	∈	∈	PROPN
ejde-397	949	1	[	[	X
ejde-397	949	2	0	0	NUM
ejde-397	949	3	,	,	PUNCT
ejde-397	949	4	t	t	X
ejde-397	949	5	]	]	PUNCT
ejde-397	949	6	,	,	PUNCT
ejde-397	949	7	then	then	ADV
ejde-397	949	8	the	the	DET
ejde-397	949	9	arguments	argument	NOUN
ejde-397	949	10	used	use	VERB
ejde-397	949	11	in	in	ADP
ejde-397	949	12	non	non	ADJ
ejde-397	949	13	-	-	ADJ
ejde-397	949	14	degenerate	degenerate	ADJ
ejde-397	949	15	case	case	NOUN
ejde-397	949	16	(	(	PUNCT
ejde-397	949	17	see	see	VERB
ejde-397	949	18	e.g.	e.g.	ADV
ejde-397	949	19	[	[	X
ejde-397	949	20	40	40	NUM
ejde-397	949	21	,	,	PUNCT
ejde-397	949	22	p.	p.	NOUN
ejde-397	949	23	304	304	NUM
ejde-397	949	24	]	]	PUNCT
ejde-397	949	25	)	)	PUNCT
ejde-397	949	26	show	show	VERB
ejde-397	949	27	that	that	SCONJ
ejde-397	949	28	a	a	PRON
ejde-397	949	29	is	be	AUX
ejde-397	949	30	a	a	DET
ejde-397	949	31	subgenerator	subgenerator	NOUN
ejde-397	949	32	of	of	ADP
ejde-397	949	33	a	a	DET
ejde-397	949	34	locally	locally	ADV
ejde-397	949	35	equicontinuous	equicontinuous	ADJ
ejde-397	949	36	(	(	PUNCT
ejde-397	949	37	gα	gα	NOUN
ejde-397	949	38	,	,	PUNCT
ejde-397	949	39	c)-resolvent	c)-resolvent	NOUN
ejde-397	949	40	family	family	NOUN
ejde-397	949	41	(	(	PUNCT
ejde-397	949	42	rα(t))t≥0	rα(t))t≥0	PROPN
ejde-397	949	43	.	.	PUNCT
ejde-397	950	1	the	the	DET
ejde-397	950	2	proof	proof	NOUN
ejde-397	950	3	of	of	ADP
ejde-397	950	4	following	follow	VERB
ejde-397	950	5	complex	complex	ADJ
ejde-397	950	6	characterization	characterization	NOUN
ejde-397	950	7	theorem	theorem	NOUN
ejde-397	950	8	for	for	ADP
ejde-397	950	9	(	(	PUNCT
ejde-397	950	10	a	a	PRON
ejde-397	950	11	,	,	PUNCT
ejde-397	950	12	k)-regularized	k)-regularize	VERB
ejde-397	950	13	c	c	NOUN
ejde-397	950	14	-	-	PUNCT
ejde-397	950	15	resolvent	resolvent	ADJ
ejde-397	950	16	families	family	NOUN
ejde-397	950	17	is	be	AUX
ejde-397	950	18	left	leave	VERB
ejde-397	950	19	to	to	ADP
ejde-397	950	20	the	the	DET
ejde-397	950	21	reader	reader	NOUN
ejde-397	950	22	as	as	ADP
ejde-397	950	23	an	an	DET
ejde-397	950	24	easy	easy	ADJ
ejde-397	950	25	exercise	exercise	NOUN
ejde-397	950	26	.	.	PUNCT
ejde-397	951	1	theorem	theorem	VERB
ejde-397	951	2	5.10	5.10	NUM
ejde-397	951	3	.	.	PUNCT
ejde-397	952	1	let	let	VERB
ejde-397	952	2	ω0	ω0	ADV
ejde-397	952	3	>	>	X
ejde-397	952	4	max(0	max(0	NOUN
ejde-397	952	5	,	,	PUNCT
ejde-397	952	6	abs(|a|	abs(|a|	ADJ
ejde-397	952	7	)	)	PUNCT
ejde-397	952	8	,	,	PUNCT
ejde-397	952	9	abs(k	abs(k	PROPN
ejde-397	952	10	)	)	PUNCT
ejde-397	952	11	)	)	PUNCT
ejde-397	952	12	,	,	PUNCT
ejde-397	952	13	and	and	CCONJ
ejde-397	952	14	let	let	VERB
ejde-397	952	15	a	a	PRON
ejde-397	952	16	be	be	AUX
ejde-397	952	17	a	a	DET
ejde-397	952	18	closed	closed	ADJ
ejde-397	952	19	mlo	mlo	NOUN
ejde-397	952	20	in	in	ADP
ejde-397	952	21	x.	x.	PROPN
ejde-397	952	22	assume	assume	VERB
ejde-397	952	23	that	that	SCONJ
ejde-397	952	24	,	,	PUNCT
ejde-397	952	25	for	for	ADP
ejde-397	952	26	every	every	DET
ejde-397	952	27	λ	λ	PROPN
ejde-397	952	28	∈	∈	PROPN
ejde-397	952	29	c	c	NOUN
ejde-397	952	30	with	with	ADP
ejde-397	952	31	<	<	X
ejde-397	952	32	λ	λ	X
ejde-397	952	33	>	>	X
ejde-397	952	34	ω0	ω0	PROPN
ejde-397	952	35	and	and	CCONJ
ejde-397	952	36	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	952	37	)	)	PUNCT
ejde-397	952	38	6=	6=	ADP
ejde-397	952	39	0	0	NUM
ejde-397	952	40	,	,	PUNCT
ejde-397	952	41	the	the	DET
ejde-397	952	42	operator	operator	NOUN
ejde-397	952	43	i−	i−	PROPN
ejde-397	952	44	ã(λ)a	ã(λ)a	PROPN
ejde-397	952	45	is	be	AUX
ejde-397	952	46	injective	injective	ADJ
ejde-397	952	47	and	and	CCONJ
ejde-397	952	48	r(c	r(c	ADJ
ejde-397	952	49	)	)	PUNCT
ejde-397	952	50	⊆	⊆	NUM
ejde-397	952	51	r(i−	r(i−	NOUN
ejde-397	952	52	ã(λ)a	ã(λ)a	NUM
ejde-397	952	53	)	)	PUNCT
ejde-397	952	54	.	.	PUNCT
ejde-397	953	1	if	if	SCONJ
ejde-397	953	2	there	there	PRON
ejde-397	953	3	exists	exist	VERB
ejde-397	953	4	a	a	DET
ejde-397	953	5	function	function	NOUN
ejde-397	953	6	υ	υ	NOUN
ejde-397	953	7	:	:	PUNCT
ejde-397	953	8	{	{	PUNCT
ejde-397	953	9	λ	λ	X
ejde-397	953	10	∈	∈	NOUN
ejde-397	953	11	c	c	NOUN
ejde-397	953	12	:	:	PUNCT
ejde-397	953	13	<	<	X
ejde-397	953	14	λ	λ	X
ejde-397	953	15	>	>	X
ejde-397	953	16	ω0	ω0	PROPN
ejde-397	953	17	}	}	PUNCT
ejde-397	953	18	→	→	SYM
ejde-397	953	19	l(x	l(x	PROPN
ejde-397	953	20	)	)	PUNCT
ejde-397	953	21	which	which	PRON
ejde-397	953	22	satisfies	satisfy	VERB
ejde-397	953	23	:	:	PUNCT
ejde-397	953	24	(	(	PUNCT
ejde-397	953	25	i	i	NOUN
ejde-397	953	26	)	)	PUNCT
ejde-397	953	27	υ(λ	υ(λ	PROPN
ejde-397	953	28	)	)	PUNCT
ejde-397	954	1	=	=	PUNCT
ejde-397	954	2	k̃(λ)(i	k̃(λ)(i	PROPN
ejde-397	954	3	−	−	PROPN
ejde-397	954	4	ã(λ)a)−1c	ã(λ)a)−1c	PROPN
ejde-397	954	5	,	,	PUNCT
ejde-397	954	6	<	<	X
ejde-397	954	7	λ	λ	X
ejde-397	954	8	>	>	X
ejde-397	954	9	ω0	ω0	PROPN
ejde-397	954	10	,	,	PUNCT
ejde-397	954	11	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	954	12	)	)	PUNCT
ejde-397	954	13	6=	6=	ADP
ejde-397	954	14	0	0	NUM
ejde-397	954	15	,	,	PUNCT
ejde-397	954	16	(	(	PUNCT
ejde-397	954	17	ii	ii	NOUN
ejde-397	954	18	)	)	PUNCT
ejde-397	954	19	the	the	DET
ejde-397	954	20	mapping	mapping	NOUN
ejde-397	954	21	λ	λ	PROPN
ejde-397	954	22	7→	7→	NUM
ejde-397	954	23	υ(λ)x	υ(λ)x	NOUN
ejde-397	954	24	,	,	PUNCT
ejde-397	954	25	<	<	X
ejde-397	954	26	λ	λ	X
ejde-397	954	27	>	>	X
ejde-397	954	28	ω0	ω0	PROPN
ejde-397	954	29	is	be	AUX
ejde-397	954	30	analytic	analytic	ADJ
ejde-397	954	31	for	for	SCONJ
ejde-397	954	32	every	every	DET
ejde-397	954	33	fixed	fix	VERB
ejde-397	954	34	x	x	SYM
ejde-397	954	35	∈	∈	PROPN
ejde-397	954	36	x	x	X
ejde-397	954	37	,	,	PUNCT
ejde-397	954	38	(	(	PUNCT
ejde-397	954	39	iii	iii	X
ejde-397	954	40	)	)	PUNCT
ejde-397	954	41	there	there	PRON
ejde-397	954	42	exists	exist	VERB
ejde-397	954	43	r	r	NOUN
ejde-397	954	44	≥	≥	NOUN
ejde-397	954	45	−1	−1	NOUN
ejde-397	954	46	such	such	ADJ
ejde-397	954	47	that	that	SCONJ
ejde-397	954	48	the	the	DET
ejde-397	954	49	family	family	NOUN
ejde-397	954	50	{	{	PUNCT
ejde-397	954	51	λ−rυ(λ	λ−rυ(λ	PROPN
ejde-397	954	52	)	)	PUNCT
ejde-397	954	53	:	:	PUNCT
ejde-397	954	54	<	<	X
ejde-397	954	55	λ	λ	X
ejde-397	954	56	>	>	X
ejde-397	954	57	ω0	ω0	PROPN
ejde-397	954	58	}	}	PUNCT
ejde-397	954	59	⊆	⊆	NUM
ejde-397	954	60	l(x	l(x	PROPN
ejde-397	954	61	)	)	PUNCT
ejde-397	954	62	is	be	AUX
ejde-397	954	63	equicontinuous	equicontinuous	ADJ
ejde-397	954	64	,	,	PUNCT
ejde-397	954	65	then	then	ADV
ejde-397	954	66	,	,	PUNCT
ejde-397	954	67	for	for	ADP
ejde-397	954	68	every	every	DET
ejde-397	954	69	α	α	PROPN
ejde-397	954	70	>	>	X
ejde-397	954	71	1	1	NUM
ejde-397	954	72	,	,	PUNCT
ejde-397	954	73	a	a	PRON
ejde-397	954	74	is	be	AUX
ejde-397	954	75	a	a	DET
ejde-397	954	76	subgenerator	subgenerator	NOUN
ejde-397	954	77	of	of	ADP
ejde-397	954	78	a	a	DET
ejde-397	954	79	global	global	ADJ
ejde-397	954	80	(	(	PUNCT
ejde-397	954	81	a	a	PROPN
ejde-397	954	82	,	,	PUNCT
ejde-397	954	83	k	k	PROPN
ejde-397	954	84	∗	∗	X
ejde-397	954	85	gα+r)-regularized	gα+r)-regularize	VERB
ejde-397	954	86	cresolvent	cresolvent	NOUN
ejde-397	954	87	family	family	NOUN
ejde-397	954	88	(	(	PUNCT
ejde-397	954	89	rα(t))t≥0	rα(t))t≥0	PROPN
ejde-397	954	90	which	which	PRON
ejde-397	954	91	satisfies	satisfy	VERB
ejde-397	954	92	that	that	SCONJ
ejde-397	954	93	the	the	DET
ejde-397	954	94	family	family	NOUN
ejde-397	954	95	{	{	PUNCT
ejde-397	954	96	e−ω0trα(t	e−ω0trα(t	PROPN
ejde-397	954	97	)	)	PUNCT
ejde-397	954	98	:	:	PUNCT
ejde-397	954	99	t	t	X
ejde-397	954	100	≥	≥	NUM
ejde-397	954	101	0	0	NUM
ejde-397	954	102	}	}	PUNCT
ejde-397	954	103	⊆	⊆	NUM
ejde-397	954	104	l(x	l(x	PROPN
ejde-397	954	105	)	)	PUNCT
ejde-397	954	106	is	be	AUX
ejde-397	954	107	equicontinuous	equicontinuous	ADJ
ejde-397	954	108	.	.	PUNCT
ejde-397	955	1	furthermore	furthermore	ADV
ejde-397	955	2	,	,	PUNCT
ejde-397	955	3	(	(	PUNCT
ejde-397	955	4	rα(t))t≥0	rα(t))t≥0	PROPN
ejde-397	955	5	is	be	AUX
ejde-397	955	6	a	a	DET
ejde-397	955	7	mild	mild	ADJ
ejde-397	955	8	(	(	PUNCT
ejde-397	955	9	a	a	PRON
ejde-397	955	10	,	,	PUNCT
ejde-397	955	11	k	k	PROPN
ejde-397	955	12	∗gα+r)-regularized	∗gα+r)-regularize	VERB
ejde-397	955	13	c	c	NOUN
ejde-397	955	14	-	-	PUNCT
ejde-397	955	15	existence	existence	NOUN
ejde-397	955	16	family	family	NOUN
ejde-397	955	17	having	have	VERB
ejde-397	955	18	a	a	DET
ejde-397	955	19	as	as	ADP
ejde-397	955	20	subgenerator	subgenerator	NOUN
ejde-397	955	21	.	.	PUNCT
ejde-397	956	1	in	in	ADP
ejde-397	956	2	the	the	DET
ejde-397	956	3	first	first	ADJ
ejde-397	956	4	part	part	NOUN
ejde-397	956	5	of	of	ADP
ejde-397	956	6	following	follow	VERB
ejde-397	956	7	example	example	NOUN
ejde-397	956	8	,	,	PUNCT
ejde-397	956	9	we	we	PRON
ejde-397	956	10	will	will	AUX
ejde-397	956	11	briefly	briefly	ADV
ejde-397	956	12	explain	explain	VERB
ejde-397	956	13	how	how	SCONJ
ejde-397	956	14	one	one	PRON
ejde-397	956	15	can	can	AUX
ejde-397	956	16	use	use	VERB
ejde-397	956	17	multiplication	multiplication	NOUN
ejde-397	956	18	operators	operator	NOUN
ejde-397	956	19	for	for	ADP
ejde-397	956	20	construction	construction	NOUN
ejde-397	956	21	of	of	ADP
ejde-397	956	22	local	local	ADJ
ejde-397	956	23	integrated	integrate	VERB
ejde-397	956	24	semigroups	semigroup	NOUN
ejde-397	956	25	generated	generate	VERB
ejde-397	956	26	by	by	ADP
ejde-397	956	27	multivalued	multivalued	ADJ
ejde-397	956	28	operators	operator	NOUN
ejde-397	956	29	;	;	PUNCT
ejde-397	956	30	in	in	ADP
ejde-397	956	31	the	the	DET
ejde-397	956	32	second	second	ADJ
ejde-397	956	33	part	part	NOUN
ejde-397	956	34	of	of	ADP
ejde-397	956	35	example	example	NOUN
ejde-397	956	36	,	,	PUNCT
ejde-397	956	37	we	we	PRON
ejde-397	956	38	will	will	AUX
ejde-397	956	39	apply	apply	VERB
ejde-397	956	40	the	the	DET
ejde-397	956	41	complex	complex	ADJ
ejde-397	956	42	characterization	characterization	NOUN
ejde-397	956	43	theorem	theorem	NOUN
ejde-397	956	44	for	for	ADP
ejde-397	956	45	proving	prove	VERB
ejde-397	956	46	the	the	DET
ejde-397	956	47	existence	existence	NOUN
ejde-397	956	48	of	of	ADP
ejde-397	956	49	a	a	DET
ejde-397	956	50	very	very	ADV
ejde-397	956	51	specific	specific	ADJ
ejde-397	956	52	exponentially	exponentially	ADV
ejde-397	956	53	equicontinuous	equicontinuous	ADJ
ejde-397	956	54	,	,	PUNCT
ejde-397	956	55	convoluted	convoluted	ADJ
ejde-397	956	56	fractional	fractional	ADJ
ejde-397	956	57	resolvent	resolvent	ADJ
ejde-397	956	58	family	family	NOUN
ejde-397	956	59	(	(	PUNCT
ejde-397	956	60	cf	cf	NOUN
ejde-397	956	61	.	.	PUNCT
ejde-397	957	1	[	[	X
ejde-397	957	2	42	42	NUM
ejde-397	957	3	,	,	PUNCT
ejde-397	957	4	example	example	NOUN
ejde-397	957	5	2.5	2.5	NUM
ejde-397	957	6	]	]	PUNCT
ejde-397	957	7	for	for	ADP
ejde-397	957	8	an	an	DET
ejde-397	957	9	example	example	NOUN
ejde-397	957	10	of	of	ADP
ejde-397	957	11	a	a	DET
ejde-397	957	12	locally	locally	ADV
ejde-397	957	13	defined	define	VERB
ejde-397	957	14	solution	solution	NOUN
ejde-397	957	15	of	of	ADP
ejde-397	957	16	an	an	DET
ejde-397	957	17	abstract	abstract	ADJ
ejde-397	957	18	degenerate	degenerate	ADJ
ejde-397	957	19	multi	multi	ADJ
ejde-397	957	20	-	-	ADJ
ejde-397	957	21	term	term	ADJ
ejde-397	957	22	fractional	fractional	ADJ
ejde-397	957	23	problem	problem	NOUN
ejde-397	957	24	)	)	PUNCT
ejde-397	957	25	.	.	PUNCT
ejde-397	958	1	example	example	NOUN
ejde-397	959	1	5.11	5.11	NUM
ejde-397	959	2	.	.	PUNCT
ejde-397	960	1	(	(	PUNCT
ejde-397	960	2	i	i	NOUN
ejde-397	960	3	)	)	PUNCT
ejde-397	960	4	(	(	PUNCT
ejde-397	960	5	cf	cf	NOUN
ejde-397	960	6	.	.	PUNCT
ejde-397	961	1	also	also	ADV
ejde-397	961	2	[	[	X
ejde-397	961	3	2	2	NUM
ejde-397	961	4	,	,	PUNCT
ejde-397	961	5	example	example	NOUN
ejde-397	961	6	4.4(c	4.4(c	NUM
ejde-397	961	7	)	)	PUNCT
ejde-397	961	8	]	]	PUNCT
ejde-397	961	9	)	)	PUNCT
ejde-397	961	10	suppose	suppose	VERB
ejde-397	961	11	that	that	SCONJ
ejde-397	961	12	1	1	NUM
ejde-397	961	13	≤	≤	NOUN
ejde-397	961	14	p	p	NOUN
ejde-397	961	15	≤	≤	NUM
ejde-397	961	16	∞	∞	PROPN
ejde-397	961	17	,	,	PUNCT
ejde-397	961	18	x	x	X
ejde-397	961	19	:	:	PUNCT
ejde-397	961	20	=	=	NOUN
ejde-397	961	21	lp(1,∞	lp(1,∞	NOUN
ejde-397	961	22	)	)	PUNCT
ejde-397	961	23	,	,	PUNCT
ejde-397	961	24	1	1	NUM
ejde-397	961	25	<	<	X
ejde-397	961	26	a	a	PRON
ejde-397	961	27	<	<	X
ejde-397	961	28	b	b	X
ejde-397	961	29	<	<	X
ejde-397	961	30	∞	∞	PROPN
ejde-397	961	31	,	,	PUNCT
ejde-397	961	32	j	j	NOUN
ejde-397	961	33	:	:	PUNCT
ejde-397	961	34	=	=	SYM
ejde-397	962	1	[	[	X
ejde-397	962	2	a	a	X
ejde-397	962	3	,	,	PUNCT
ejde-397	962	4	b	b	NOUN
ejde-397	962	5	]	]	X
ejde-397	962	6	,	,	PUNCT
ejde-397	962	7	mb(x	mb(x	NUM
ejde-397	962	8	)	)	PUNCT
ejde-397	962	9	:	:	PUNCT
ejde-397	963	1	=	=	NOUN
ejde-397	963	2	χj(x	χj(x	PUNCT
ejde-397	963	3	)	)	PUNCT
ejde-397	963	4	and	and	CCONJ
ejde-397	963	5	ma(x	ma(x	NOUN
ejde-397	963	6	)	)	PUNCT
ejde-397	963	7	:	:	PUNCT
ejde-397	964	1	=	=	SYM
ejde-397	964	2	x	x	SYM
ejde-397	964	3	+	+	NUM
ejde-397	964	4	iex	iex	PROPN
ejde-397	964	5	(	(	PUNCT
ejde-397	964	6	x	x	X
ejde-397	964	7	>	>	X
ejde-397	964	8	1	1	NUM
ejde-397	964	9	)	)	PUNCT
ejde-397	964	10	.	.	PUNCT
ejde-397	965	1	consider	consider	VERB
ejde-397	965	2	the	the	DET
ejde-397	965	3	multiplication	multiplication	NOUN
ejde-397	965	4	operators	operator	NOUN
ejde-397	965	5	a	a	DET
ejde-397	965	6	:	:	PUNCT
ejde-397	965	7	d(a	d(a	PROPN
ejde-397	965	8	)	)	PUNCT
ejde-397	965	9	→	→	SYM
ejde-397	965	10	x	x	SYM
ejde-397	965	11	and	and	CCONJ
ejde-397	965	12	b	b	X
ejde-397	965	13	∈	∈	PROPN
ejde-397	965	14	l(x	l(x	PROPN
ejde-397	965	15	)	)	PUNCT
ejde-397	965	16	,	,	PUNCT
ejde-397	965	17	where	where	SCONJ
ejde-397	965	18	d(a	d(a	PROPN
ejde-397	965	19	)	)	PUNCT
ejde-397	965	20	:	:	PUNCT
ejde-397	965	21	=	=	SYM
ejde-397	965	22	{	{	PUNCT
ejde-397	965	23	f(x	f(x	PROPN
ejde-397	965	24	)	)	PUNCT
ejde-397	965	25	∈	∈	PROPN
ejde-397	965	26	x	x	X
ejde-397	965	27	:	:	PUNCT
ejde-397	965	28	(	(	PUNCT
ejde-397	965	29	x	x	X
ejde-397	965	30	+	+	NUM
ejde-397	965	31	iex)f(x	iex)f(x	PROPN
ejde-397	965	32	)	)	PUNCT
ejde-397	965	33	∈	∈	PROPN
ejde-397	965	34	x	x	X
ejde-397	965	35	}	}	PUNCT
ejde-397	965	36	,	,	PUNCT
ejde-397	965	37	af(x	af(x	ADV
ejde-397	965	38	)	)	PUNCT
ejde-397	965	39	:	:	PUNCT
ejde-397	966	1	=	=	SYM
ejde-397	966	2	(	(	PUNCT
ejde-397	966	3	x	x	X
ejde-397	966	4	+	+	NUM
ejde-397	966	5	iex)f(x	iex)f(x	PROPN
ejde-397	966	6	)	)	PUNCT
ejde-397	966	7	and	and	CCONJ
ejde-397	966	8	bf(x	bf(x	PRON
ejde-397	966	9	)	)	PUNCT
ejde-397	966	10	:	:	PUNCT
ejde-397	966	11	=	=	SYM
ejde-397	966	12	mb(x)f(x	mb(x)f(x	NOUN
ejde-397	966	13	)	)	PUNCT
ejde-397	966	14	(	(	PUNCT
ejde-397	966	15	x	x	X
ejde-397	966	16	>	>	X
ejde-397	966	17	1	1	NUM
ejde-397	966	18	,	,	PUNCT
ejde-397	966	19	f	f	PROPN
ejde-397	966	20	∈	∈	PROPN
ejde-397	966	21	x	x	PROPN
ejde-397	966	22	)	)	PUNCT
ejde-397	966	23	.	.	PUNCT
ejde-397	967	1	then	then	ADV
ejde-397	967	2	it	it	PRON
ejde-397	967	3	is	be	AUX
ejde-397	967	4	very	very	ADV
ejde-397	967	5	simple	simple	ADJ
ejde-397	967	6	to	to	PART
ejde-397	967	7	prove	prove	VERB
ejde-397	967	8	that	that	SCONJ
ejde-397	967	9	,	,	PUNCT
ejde-397	967	10	for	for	ADP
ejde-397	967	11	every	every	DET
ejde-397	967	12	α	α	PROPN
ejde-397	967	13	∈	∈	PROPN
ejde-397	967	14	(	(	PUNCT
ejde-397	967	15	0	0	NUM
ejde-397	967	16	,	,	PUNCT
ejde-397	967	17	1	1	NUM
ejde-397	967	18	)	)	PUNCT
ejde-397	967	19	,	,	PUNCT
ejde-397	967	20	the	the	DET
ejde-397	967	21	resolvent	resolvent	ADJ
ejde-397	967	22	set	set	NOUN
ejde-397	967	23	of	of	ADP
ejde-397	967	24	the	the	DET
ejde-397	967	25	multivalued	multivalue	VERB
ejde-397	967	26	linear	linear	ADJ
ejde-397	967	27	operator	operator	NOUN
ejde-397	967	28	a	a	PRON
ejde-397	967	29	:	:	PUNCT
ejde-397	967	30	=	=	SYM
ejde-397	967	31	b−1a	b−1a	X
ejde-397	967	32	contains	contain	VERB
ejde-397	967	33	the	the	DET
ejde-397	967	34	exponential	exponential	ADJ
ejde-397	967	35	region	region	NOUN
ejde-397	967	36	e(α	e(α	PROPN
ejde-397	967	37	,	,	PUNCT
ejde-397	967	38	1	1	NUM
ejde-397	967	39	)	)	PUNCT
ejde-397	967	40	:	:	PUNCT
ejde-397	967	41	=	=	SYM
ejde-397	967	42	{	{	PUNCT
ejde-397	967	43	x	x	X
ejde-397	967	44	+	+	X
ejde-397	967	45	iy	iy	X
ejde-397	967	46	:	:	PUNCT
ejde-397	967	47	x	x	X
ejde-397	967	48	≥	≥	NUM
ejde-397	967	49	1	1	NUM
ejde-397	967	50	,	,	PUNCT
ejde-397	967	51	|y|	|y|	ADJ
ejde-397	967	52	≤	≤	NUM
ejde-397	967	53	eαx	eαx	PROPN
ejde-397	967	54	}	}	PUNCT
ejde-397	967	55	,	,	PUNCT
ejde-397	967	56	as	as	ADV
ejde-397	967	57	well	well	ADV
ejde-397	967	58	as	as	ADP
ejde-397	967	59	that	that	PRON
ejde-397	967	60	(	(	PUNCT
ejde-397	967	61	λ−a)−1f(x	λ−a)−1f(x	NOUN
ejde-397	967	62	)	)	PUNCT
ejde-397	967	63	=	=	SYM
ejde-397	967	64	(	(	PUNCT
ejde-397	967	65	λb	λb	X
ejde-397	967	66	−a)−1bf(x	−a)−1bf(x	NOUN
ejde-397	967	67	)	)	PUNCT
ejde-397	968	1	=	=	SYM
ejde-397	968	2	mb(x)f(x)/λmb(x)−ma(x	mb(x)f(x)/λmb(x)−ma(x	NOUN
ejde-397	968	3	)	)	PUNCT
ejde-397	968	4	for	for	ADP
ejde-397	968	5	x	x	SYM
ejde-397	968	6	>	>	X
ejde-397	968	7	1	1	NUM
ejde-397	968	8	,	,	PUNCT
ejde-397	968	9	f	f	PROPN
ejde-397	968	10	∈	∈	PROPN
ejde-397	968	11	x.	x.	NOUN
ejde-397	969	1	furthermore	furthermore	ADV
ejde-397	969	2	,	,	PUNCT
ejde-397	969	3	the	the	DET
ejde-397	969	4	operator	operator	NOUN
ejde-397	969	5	a	a	DET
ejde-397	969	6	generates	generate	VERB
ejde-397	969	7	a	a	DET
ejde-397	969	8	local	local	ADJ
ejde-397	969	9	once	once	ADV
ejde-397	969	10	integrated	integrate	VERB
ejde-397	969	11	semigroup	semigroup	NOUN
ejde-397	969	12	(	(	PUNCT
ejde-397	969	13	s1(t))t∈[0,1	s1(t))t∈[0,1	ADV
ejde-397	969	14	]	]	PUNCT
ejde-397	969	15	,	,	PUNCT
ejde-397	969	16	given	give	VERB
ejde-397	969	17	by	by	ADP
ejde-397	969	18	(	(	PUNCT
ejde-397	969	19	s1(t)f)(x	s1(t)f)(x	PROPN
ejde-397	969	20	)	)	PUNCT
ejde-397	969	21	=	=	PRON
ejde-397	969	22	{	{	PUNCT
ejde-397	969	23	(	(	PUNCT
ejde-397	969	24	x+	x+	PROPN
ejde-397	969	25	iex	iex	PROPN
ejde-397	969	26	)	)	PUNCT
ejde-397	969	27	−1	−1	NOUN
ejde-397	969	28	[	[	PUNCT
ejde-397	969	29	et(x+iex	et(x+iex	NOUN
ejde-397	969	30	)	)	PUNCT
ejde-397	969	31	−	−	PROPN
ejde-397	970	1	1	1	NUM
ejde-397	970	2	]	]	PUNCT
ejde-397	970	3	f(x	f(x	PROPN
ejde-397	970	4	)	)	PUNCT
ejde-397	970	5	,	,	PUNCT
ejde-397	970	6	t	t	PROPN
ejde-397	970	7	∈	∈	PROPN
ejde-397	971	1	[	[	X
ejde-397	971	2	0	0	NUM
ejde-397	971	3	,	,	PUNCT
ejde-397	971	4	1	1	NUM
ejde-397	971	5	]	]	PUNCT
ejde-397	971	6	,	,	PUNCT
ejde-397	971	7	x	x	PROPN
ejde-397	971	8	/∈	/∈	PROPN
ejde-397	971	9	j	j	PROPN
ejde-397	971	10	,	,	PUNCT
ejde-397	971	11	f	f	PROPN
ejde-397	971	12	∈	∈	PROPN
ejde-397	971	13	x	x	X
ejde-397	971	14	,	,	PUNCT
ejde-397	971	15	0	0	NUM
ejde-397	971	16	,	,	PUNCT
ejde-397	971	17	t	t	PROPN
ejde-397	971	18	∈	∈	PROPN
ejde-397	972	1	[	[	X
ejde-397	972	2	0	0	NUM
ejde-397	972	3	,	,	PUNCT
ejde-397	972	4	1	1	NUM
ejde-397	972	5	]	]	PUNCT
ejde-397	972	6	,	,	PUNCT
ejde-397	972	7	x	x	SYM
ejde-397	972	8	∈	∈	PROPN
ejde-397	972	9	j	j	PROPN
ejde-397	972	10	,	,	PUNCT
ejde-397	972	11	f	f	PROPN
ejde-397	972	12	∈	∈	PROPN
ejde-397	972	13	x.	x.	NOUN
ejde-397	972	14	(	(	PUNCT
ejde-397	972	15	ii	ii	NOUN
ejde-397	972	16	)	)	PUNCT
ejde-397	972	17	put	put	NOUN
ejde-397	972	18	x	x	PUNCT
ejde-397	972	19	:	:	PUNCT
ejde-397	972	20	=	=	SYM
ejde-397	972	21	{	{	PUNCT
ejde-397	972	22	f	f	PROPN
ejde-397	972	23	∈	∈	PROPN
ejde-397	972	24	c∞([0,∞	c∞([0,∞	PROPN
ejde-397	972	25	)	)	PUNCT
ejde-397	972	26	)	)	PUNCT
ejde-397	972	27	:	:	PUNCT
ejde-397	973	1	limx→+∞	limx→+∞	X
ejde-397	973	2	f	f	X
ejde-397	973	3	(	(	PUNCT
ejde-397	973	4	k)(x	k)(x	PROPN
ejde-397	973	5	)	)	PUNCT
ejde-397	973	6	=	=	SYM
ejde-397	973	7	0	0	NUM
ejde-397	973	8	for	for	ADP
ejde-397	973	9	all	all	DET
ejde-397	973	10	k	k	PROPN
ejde-397	973	11	∈	∈	PROPN
ejde-397	973	12	n0	n0	PROPN
ejde-397	973	13	}	}	PUNCT
ejde-397	973	14	and	and	CCONJ
ejde-397	973	15	||f	||f	ADJ
ejde-397	973	16	||k	||k	NOUN
ejde-397	973	17	:	:	PUNCT
ejde-397	974	1	=	=	SYM
ejde-397	974	2	∑k	∑k	PROPN
ejde-397	974	3	j=0	j=0	PROPN
ejde-397	974	4	supx≥0	supx≥0	PROPN
ejde-397	974	5	|f	|f	PROPN
ejde-397	974	6	(	(	PUNCT
ejde-397	974	7	j)(x)|	j)(x)|	PROPN
ejde-397	974	8	,	,	PUNCT
ejde-397	974	9	f	f	PROPN
ejde-397	974	10	∈	∈	PROPN
ejde-397	974	11	x	x	X
ejde-397	974	12	,	,	PUNCT
ejde-397	974	13	k	k	PROPN
ejde-397	974	14	∈	∈	PROPN
ejde-397	974	15	n0	n0	PROPN
ejde-397	974	16	.	.	PUNCT
ejde-397	975	1	then	then	ADV
ejde-397	975	2	the	the	DET
ejde-397	975	3	topology	topology	NOUN
ejde-397	975	4	induced	induce	VERB
ejde-397	975	5	by	by	ADP
ejde-397	975	6	these	these	DET
ejde-397	975	7	norms	norm	NOUN
ejde-397	975	8	turns	turn	VERB
ejde-397	975	9	x	x	PUNCT
ejde-397	975	10	into	into	ADP
ejde-397	975	11	a	a	DET
ejde-397	975	12	fréchet	fréchet	NOUN
ejde-397	975	13	space	space	NOUN
ejde-397	975	14	(	(	PUNCT
ejde-397	975	15	cf	cf	NOUN
ejde-397	975	16	.	.	PUNCT
ejde-397	976	1	also	also	ADV
ejde-397	976	2	[	[	X
ejde-397	976	3	36	36	NUM
ejde-397	976	4	,	,	PUNCT
ejde-397	976	5	example	example	NOUN
ejde-397	976	6	2.4.6(ii	2.4.6(ii	NUM
ejde-397	976	7	)	)	PUNCT
ejde-397	976	8	]	]	PUNCT
ejde-397	976	9	)	)	PUNCT
ejde-397	976	10	.	.	PUNCT
ejde-397	977	1	let	let	VERB
ejde-397	977	2	α	α	PRON
ejde-397	977	3	∈	∈	PROPN
ejde-397	977	4	(	(	PUNCT
ejde-397	977	5	0	0	NUM
ejde-397	977	6	,	,	PUNCT
ejde-397	977	7	1	1	NUM
ejde-397	977	8	)	)	PUNCT
ejde-397	977	9	and	and	CCONJ
ejde-397	977	10	j	j	X
ejde-397	978	1	=	=	PUNCT
ejde-397	979	1	[	[	X
ejde-397	979	2	a	a	X
ejde-397	979	3	,	,	PUNCT
ejde-397	979	4	b	b	NOUN
ejde-397	979	5	]	]	PUNCT
ejde-397	979	6	⊆	⊆	NUM
ejde-397	979	7	[	[	X
ejde-397	979	8	0,∞	0,∞	NOUN
ejde-397	979	9	)	)	PUNCT
ejde-397	979	10	be	be	VERB
ejde-397	979	11	such	such	ADJ
ejde-397	979	12	that	that	SCONJ
ejde-397	979	13	σαπ/2∩{x+iex	σαπ/2∩{x+iex	ADV
ejde-397	979	14	:	:	PUNCT
ejde-397	979	15	x	x	SYM
ejde-397	979	16	∈	∈	PROPN
ejde-397	979	17	j	j	PROPN
ejde-397	979	18	}	}	PUNCT
ejde-397	979	19	=	=	SYM
ejde-397	979	20	∅	∅	NOUN
ejde-397	979	21	,	,	PUNCT
ejde-397	979	22	and	and	CCONJ
ejde-397	979	23	let	let	VERB
ejde-397	979	24	mb	mb	ADP
ejde-397	979	25	∈	∈	PROPN
ejde-397	979	26	c∞([0,∞	c∞([0,∞	NOUN
ejde-397	979	27	)	)	PUNCT
ejde-397	979	28	)	)	PUNCT
ejde-397	980	1	satisfy	satisfy	VERB
ejde-397	980	2	0	0	NUM
ejde-397	980	3	≤	≤	NUM
ejde-397	980	4	mb(x	mb(x	NUM
ejde-397	980	5	)	)	PUNCT
ejde-397	980	6	≤	≤	NUM
ejde-397	980	7	1	1	NUM
ejde-397	980	8	,	,	PUNCT
ejde-397	980	9	x	x	X
ejde-397	980	10	≥	≥	NOUN
ejde-397	980	11	0	0	NUM
ejde-397	980	12	,	,	PUNCT
ejde-397	980	13	mb(x	mb(x	NUM
ejde-397	980	14	)	)	PUNCT
ejde-397	980	15	=	=	SYM
ejde-397	980	16	1	1	NUM
ejde-397	980	17	,	,	PUNCT
ejde-397	980	18	x	x	PROPN
ejde-397	980	19	/∈	/∈	PROPN
ejde-397	980	20	j	j	PROPN
ejde-397	980	21	and	and	CCONJ
ejde-397	980	22	mb(x	mb(x	NUM
ejde-397	980	23	)	)	PUNCT
ejde-397	980	24	=	=	SYM
ejde-397	980	25	0	0	NUM
ejde-397	980	26	,	,	PUNCT
ejde-397	980	27	x	x	X
ejde-397	980	28	∈	∈	PROPN
ejde-397	980	29	[	[	X
ejde-397	980	30	a+	a+	X
ejde-397	980	31	ε	ε	PROPN
ejde-397	980	32	,	,	PUNCT
ejde-397	980	33	b−	b−	PROPN
ejde-397	980	34	ε	ε	PROPN
ejde-397	980	35	]	]	PUNCT
ejde-397	980	36	for	for	ADP
ejde-397	980	37	some	some	DET
ejde-397	980	38	ε	ε	PROPN
ejde-397	980	39	>	>	X
ejde-397	980	40	0	0	PROPN
ejde-397	980	41	.	.	PUNCT
ejde-397	981	1	as	as	ADP
ejde-397	981	2	in	in	ADP
ejde-397	981	3	the	the	DET
ejde-397	981	4	first	first	ADJ
ejde-397	981	5	part	part	NOUN
ejde-397	981	6	of	of	ADP
ejde-397	981	7	this	this	DET
ejde-397	981	8	example	example	NOUN
ejde-397	981	9	,	,	PUNCT
ejde-397	981	10	we	we	PRON
ejde-397	981	11	consider	consider	VERB
ejde-397	981	12	the	the	DET
ejde-397	981	13	multiplication	multiplication	NOUN
ejde-397	981	14	operators	operator	NOUN
ejde-397	981	15	a	a	PRON
ejde-397	981	16	:	:	PUNCT
ejde-397	981	17	d(a)→	d(a)→	PUNCT
ejde-397	981	18	x	x	X
ejde-397	981	19	and	and	CCONJ
ejde-397	981	20	b	b	X
ejde-397	981	21	∈	∈	PROPN
ejde-397	981	22	l(x	l(x	PROPN
ejde-397	981	23	)	)	PUNCT
ejde-397	981	24	,	,	PUNCT
ejde-397	981	25	where	where	SCONJ
ejde-397	981	26	d(a	d(a	PROPN
ejde-397	981	27	)	)	PUNCT
ejde-397	981	28	=	=	PRON
ejde-397	982	1	{	{	PUNCT
ejde-397	982	2	f(x	f(x	PROPN
ejde-397	982	3	)	)	PUNCT
ejde-397	982	4	∈	∈	PROPN
ejde-397	982	5	e	e	NOUN
ejde-397	982	6	:	:	PUNCT
ejde-397	982	7	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	982	8	abstract	abstract	ADJ
ejde-397	982	9	degenerate	degenerate	ADJ
ejde-397	982	10	volterra	volterra	NOUN
ejde-397	982	11	inclusions	inclusion	NOUN
ejde-397	982	12	31	31	NUM
ejde-397	982	13	(	(	PUNCT
ejde-397	982	14	x+	x+	X
ejde-397	982	15	iex)f(x	iex)f(x	PROPN
ejde-397	982	16	)	)	PUNCT
ejde-397	982	17	∈	∈	PROPN
ejde-397	982	18	x	x	X
ejde-397	982	19	}	}	PUNCT
ejde-397	982	20	,	,	PUNCT
ejde-397	982	21	af(x	af(x	ADV
ejde-397	982	22	)	)	PUNCT
ejde-397	982	23	:	:	PUNCT
ejde-397	982	24	=	=	SYM
ejde-397	982	25	(	(	PUNCT
ejde-397	982	26	x+	x+	X
ejde-397	982	27	iex)f(x	iex)f(x	PROPN
ejde-397	982	28	)	)	PUNCT
ejde-397	982	29	and	and	CCONJ
ejde-397	982	30	bf(x	bf(x	PRON
ejde-397	982	31	)	)	PUNCT
ejde-397	982	32	:	:	PUNCT
ejde-397	982	33	=	=	SYM
ejde-397	982	34	mb(x)f(x	mb(x)f(x	NOUN
ejde-397	982	35	)	)	PUNCT
ejde-397	982	36	(	(	PUNCT
ejde-397	982	37	x	x	X
ejde-397	982	38	≥	≥	NOUN
ejde-397	982	39	0	0	NUM
ejde-397	982	40	,	,	PUNCT
ejde-397	982	41	f	f	PROPN
ejde-397	982	42	∈	∈	PROPN
ejde-397	982	43	x	x	NOUN
ejde-397	982	44	)	)	PUNCT
ejde-397	982	45	.	.	PUNCT
ejde-397	983	1	in	in	ADP
ejde-397	983	2	a	a	DET
ejde-397	983	3	recent	recent	ADJ
ejde-397	983	4	research	research	NOUN
ejde-397	983	5	study	study	NOUN
ejde-397	983	6	with	with	ADP
ejde-397	983	7	pilipović	pilipović	ADJ
ejde-397	983	8	and	and	CCONJ
ejde-397	983	9	velinov	velinov	NOUN
ejde-397	983	10	[	[	X
ejde-397	983	11	53	53	NUM
ejde-397	983	12	]	]	PUNCT
ejde-397	983	13	,	,	PUNCT
ejde-397	983	14	we	we	PRON
ejde-397	983	15	have	have	AUX
ejde-397	983	16	shown	show	VERB
ejde-397	983	17	that	that	SCONJ
ejde-397	983	18	a	a	PRON
ejde-397	983	19	can	can	AUX
ejde-397	983	20	not	not	PART
ejde-397	983	21	be	be	AUX
ejde-397	983	22	the	the	DET
ejde-397	983	23	generator	generator	NOUN
ejde-397	983	24	of	of	ADP
ejde-397	983	25	any	any	DET
ejde-397	983	26	local	local	ADJ
ejde-397	983	27	integrated	integrate	VERB
ejde-397	983	28	semigroup	semigroup	NOUN
ejde-397	983	29	in	in	ADP
ejde-397	983	30	x	x	PROPN
ejde-397	983	31	,	,	PUNCT
ejde-397	983	32	as	as	ADV
ejde-397	983	33	well	well	ADV
ejde-397	983	34	as	as	ADP
ejde-397	983	35	that	that	PRON
ejde-397	983	36	a	a	PRON
ejde-397	983	37	generates	generate	VERB
ejde-397	983	38	an	an	DET
ejde-397	983	39	ultradistribution	ultradistribution	NOUN
ejde-397	983	40	semigroup	semigroup	NOUN
ejde-397	983	41	of	of	ADP
ejde-397	983	42	beurling	beurling	ADJ
ejde-397	983	43	class	class	NOUN
ejde-397	983	44	.	.	PUNCT
ejde-397	984	1	set	set	VERB
ejde-397	984	2	a	a	DET
ejde-397	984	3	:	:	PUNCT
ejde-397	984	4	=	=	X
ejde-397	984	5	b−1a	b−1a	X
ejde-397	984	6	.	.	PUNCT
ejde-397	985	1	we	we	PRON
ejde-397	985	2	will	will	AUX
ejde-397	985	3	prove	prove	VERB
ejde-397	985	4	that	that	SCONJ
ejde-397	985	5	there	there	PRON
ejde-397	985	6	exists	exist	VERB
ejde-397	985	7	a	a	DET
ejde-397	985	8	sufficiently	sufficiently	ADV
ejde-397	985	9	large	large	ADJ
ejde-397	985	10	number	number	NOUN
ejde-397	985	11	ω	ω	PROPN
ejde-397	985	12	>	>	X
ejde-397	985	13	0	0	NUM
ejde-397	985	14	such	such	ADJ
ejde-397	985	15	that	that	PRON
ejde-397	985	16	for	for	ADP
ejde-397	985	17	each	each	PRON
ejde-397	985	18	s	s	X
ejde-397	985	19	>	>	X
ejde-397	985	20	1	1	NUM
ejde-397	985	21	and	and	CCONJ
ejde-397	985	22	d	d	X
ejde-397	985	23	>	>	X
ejde-397	985	24	0	0	PUNCT
ejde-397	986	1	the	the	DET
ejde-397	986	2	operator	operator	NOUN
ejde-397	986	3	family	family	NOUN
ejde-397	986	4	{	{	PUNCT
ejde-397	986	5	e−d|λ|1	e−d|λ|1	PROPN
ejde-397	986	6	/	/	SYM
ejde-397	986	7	s(λ	s(λ	PROPN
ejde-397	986	8	−a)−1	−a)−1	NOUN
ejde-397	986	9	:	:	PUNCT
ejde-397	986	10	<	<	X
ejde-397	986	11	λ	λ	X
ejde-397	986	12	>	>	X
ejde-397	986	13	ω	ω	PROPN
ejde-397	986	14	,	,	PUNCT
ejde-397	986	15	λ	λ	PROPN
ejde-397	986	16	∈	∈	PROPN
ejde-397	986	17	σαπ/2	σαπ/2	PROPN
ejde-397	986	18	}	}	PUNCT
ejde-397	986	19	⊆	⊆	NUM
ejde-397	986	20	l(x	l(x	PROPN
ejde-397	986	21	)	)	PUNCT
ejde-397	986	22	is	be	AUX
ejde-397	986	23	equicontinuous	equicontinuous	ADJ
ejde-397	986	24	,	,	PUNCT
ejde-397	986	25	which	which	PRON
ejde-397	986	26	immediately	immediately	ADV
ejde-397	986	27	implies	imply	VERB
ejde-397	986	28	by	by	ADP
ejde-397	986	29	theorem	theorem	NOUN
ejde-397	986	30	5.10	5.10	NUM
ejde-397	986	31	that	that	PRON
ejde-397	986	32	a	a	DET
ejde-397	986	33	generates	generate	VERB
ejde-397	986	34	an	an	DET
ejde-397	986	35	exponentially	exponentially	ADV
ejde-397	986	36	equicontinuous	equicontinuous	ADJ
ejde-397	986	37	(	(	PUNCT
ejde-397	986	38	gα	gα	NOUN
ejde-397	986	39	,	,	PUNCT
ejde-397	986	40	l−1(e−d|λ|	l−1(e−d|λ|	PROPN
ejde-397	986	41	α	α	NOUN
ejde-397	986	42	/	/	SYM
ejde-397	986	43	s	s	PART
ejde-397	986	44	)	)	PUNCT
ejde-397	986	45	)	)	PUNCT
ejde-397	987	1	-regularized	-regularized	ADJ
ejde-397	987	2	resolvent	resolvent	ADJ
ejde-397	987	3	family	family	NOUN
ejde-397	987	4	.	.	PUNCT
ejde-397	988	1	it	it	PRON
ejde-397	988	2	is	be	AUX
ejde-397	988	3	clear	clear	ADJ
ejde-397	988	4	that	that	SCONJ
ejde-397	988	5	the	the	DET
ejde-397	988	6	resolvent	resolvent	NOUN
ejde-397	988	7	of	of	ADP
ejde-397	988	8	a	a	PRON
ejde-397	988	9	will	will	AUX
ejde-397	988	10	be	be	AUX
ejde-397	988	11	given	give	VERB
ejde-397	988	12	by	by	ADP
ejde-397	988	13	(	(	PUNCT
ejde-397	988	14	λ−a)−1f(x	λ−a)−1f(x	NOUN
ejde-397	988	15	)	)	PUNCT
ejde-397	989	1	=	=	SYM
ejde-397	989	2	(	(	PUNCT
ejde-397	989	3	λb−a)−1bf(x	λb−a)−1bf(x	NOUN
ejde-397	989	4	)	)	PUNCT
ejde-397	989	5	=	=	SYM
ejde-397	989	6	mb(x)f(x)/λmb(x)−ma(x	mb(x)f(x)/λmb(x)−ma(x	NOUN
ejde-397	989	7	)	)	PUNCT
ejde-397	989	8	for	for	ADP
ejde-397	989	9	x	x	X
ejde-397	989	10	≥	≥	NOUN
ejde-397	989	11	0	0	NUM
ejde-397	989	12	,	,	PUNCT
ejde-397	989	13	f	f	PROPN
ejde-397	989	14	∈	∈	PROPN
ejde-397	989	15	x.	x.	NOUN
ejde-397	989	16	since	since	SCONJ
ejde-397	989	17	mb(x)f(x)/λmb(x)−ma(x	mb(x)f(x)/λmb(x)−ma(x	NOUN
ejde-397	989	18	)	)	PUNCT
ejde-397	989	19	=	=	SYM
ejde-397	989	20	1	1	NUM
ejde-397	989	21	/	/	SYM
ejde-397	989	22	λ−(x+iex	λ−(x+iex	ADV
ejde-397	989	23	)	)	PUNCT
ejde-397	989	24	for	for	ADP
ejde-397	989	25	x	x	PROPN
ejde-397	989	26	/∈	/∈	PROPN
ejde-397	989	27	j	j	PROPN
ejde-397	989	28	,	,	PUNCT
ejde-397	989	29	our	our	PRON
ejde-397	989	30	first	first	ADJ
ejde-397	989	31	task	task	NOUN
ejde-397	989	32	will	will	AUX
ejde-397	989	33	be	be	AUX
ejde-397	989	34	to	to	PART
ejde-397	989	35	estimate	estimate	VERB
ejde-397	989	36	the	the	DET
ejde-397	989	37	derivatives	derivative	NOUN
ejde-397	989	38	of	of	ADP
ejde-397	989	39	function	function	NOUN
ejde-397	989	40	1	1	NUM
ejde-397	989	41	/	/	SYM
ejde-397	989	42	λ	λ	X
ejde-397	990	1	−	−	PROPN
ejde-397	990	2	(	(	PUNCT
ejde-397	990	3	·	·	PUNCT
ejde-397	990	4	+	+	CCONJ
ejde-397	990	5	ie	ie	X
ejde-397	990	6	·	·	SYM
ejde-397	990	7	)	)	PUNCT
ejde-397	990	8	outside	outside	ADP
ejde-397	990	9	the	the	DET
ejde-397	990	10	interval	interval	NOUN
ejde-397	990	11	j	j	PROPN
ejde-397	990	12	.	.	PUNCT
ejde-397	991	1	in	in	ADP
ejde-397	991	2	order	order	NOUN
ejde-397	991	3	to	to	PART
ejde-397	991	4	do	do	AUX
ejde-397	991	5	that	that	PRON
ejde-397	991	6	,	,	PUNCT
ejde-397	991	7	observe	observe	VERB
ejde-397	991	8	first	first	ADV
ejde-397	991	9	that	that	SCONJ
ejde-397	991	10	any	any	DET
ejde-397	991	11	complex	complex	ADJ
ejde-397	991	12	number	number	NOUN
ejde-397	991	13	λ	λ	X
ejde-397	991	14	∈	∈	NOUN
ejde-397	991	15	c	c	NOUN
ejde-397	991	16	\	\	PROPN
ejde-397	991	17	s	s	PROPN
ejde-397	991	18	,	,	PUNCT
ejde-397	991	19	where	where	SCONJ
ejde-397	991	20	s	s	VERB
ejde-397	991	21	:	:	PUNCT
ejde-397	991	22	=	=	SYM
ejde-397	991	23	{	{	PUNCT
ejde-397	991	24	x+	x+	PROPN
ejde-397	991	25	iex	iex	NOUN
ejde-397	991	26	:	:	PUNCT
ejde-397	991	27	x	x	X
ejde-397	991	28	≥	≥	NOUN
ejde-397	991	29	0	0	NUM
ejde-397	991	30	}	}	PUNCT
ejde-397	991	31	,	,	PUNCT
ejde-397	991	32	belongs	belong	VERB
ejde-397	991	33	to	to	ADP
ejde-397	991	34	the	the	DET
ejde-397	991	35	resolvent	resolvent	ADJ
ejde-397	991	36	set	set	NOUN
ejde-397	991	37	of	of	ADP
ejde-397	991	38	a	a	DET
ejde-397	991	39	and	and	CCONJ
ejde-397	991	40	(	(	PUNCT
ejde-397	991	41	λ−a	λ−a	NUM
ejde-397	991	42	)	)	PUNCT
ejde-397	991	43	−1	−1	NOUN
ejde-397	991	44	f(x	f(x	PROPN
ejde-397	991	45	)	)	PUNCT
ejde-397	992	1	=	=	SYM
ejde-397	992	2	f(x	f(x	PROPN
ejde-397	992	3	)	)	PUNCT
ejde-397	993	1	λ−	λ−	PROPN
ejde-397	993	2	(	(	PUNCT
ejde-397	993	3	x+	x+	PROPN
ejde-397	993	4	iex	iex	PROPN
ejde-397	993	5	)	)	PUNCT
ejde-397	993	6	,	,	PUNCT
ejde-397	994	1	λ	λ	X
ejde-397	994	2	∈	∈	PROPN
ejde-397	994	3	c	c	NOUN
ejde-397	994	4	\	\	PROPN
ejde-397	994	5	s	s	PROPN
ejde-397	994	6	,	,	PUNCT
ejde-397	994	7	x	x	X
ejde-397	994	8	≥	≥	NOUN
ejde-397	994	9	0	0	NUM
ejde-397	994	10	.	.	PUNCT
ejde-397	995	1	fix	fix	VERB
ejde-397	995	2	,	,	PUNCT
ejde-397	995	3	after	after	ADP
ejde-397	995	4	that	that	PRON
ejde-397	995	5	,	,	PUNCT
ejde-397	995	6	numbers	number	NOUN
ejde-397	995	7	s	s	PART
ejde-397	995	8	>	>	X
ejde-397	995	9	1	1	NUM
ejde-397	995	10	,	,	PUNCT
ejde-397	995	11	d	d	X
ejde-397	995	12	>	>	X
ejde-397	995	13	0	0	PROPN
ejde-397	995	14	,	,	PUNCT
ejde-397	995	15	a	a	PRON
ejde-397	995	16	>	>	X
ejde-397	995	17	0	0	NUM
ejde-397	995	18	,	,	PUNCT
ejde-397	995	19	b	b	X
ejde-397	995	20	>	>	X
ejde-397	995	21	1	1	NUM
ejde-397	995	22	satisfying	satisfy	VERB
ejde-397	995	23	that	that	SCONJ
ejde-397	995	24	x	x	X
ejde-397	996	1	−	−	PRON
ejde-397	996	2	ln(((x	ln(((x	NOUN
ejde-397	996	3	−	−	NOUN
ejde-397	996	4	b)/a)s	b)/a)s	NOUN
ejde-397	996	5	+	+	CCONJ
ejde-397	996	6	1	1	X
ejde-397	996	7	)	)	PUNCT
ejde-397	996	8	≥	≥	NOUN
ejde-397	996	9	1	1	NUM
ejde-397	996	10	,	,	PUNCT
ejde-397	996	11	x	x	X
ejde-397	996	12	≥	≥	PROPN
ejde-397	996	13	b.	b.	PROPN
ejde-397	996	14	set	set	VERB
ejde-397	996	15	ω	ω	PROPN
ejde-397	996	16	:	:	PUNCT
ejde-397	996	17	=	=	SYM
ejde-397	996	18	{	{	PUNCT
ejde-397	996	19	λ	λ	X
ejde-397	996	20	∈	∈	NOUN
ejde-397	996	21	c	c	NOUN
ejde-397	996	22	:	:	PUNCT
ejde-397	996	23	<	<	X
ejde-397	996	24	λ	λ	X
ejde-397	996	25	≥	≥	NOUN
ejde-397	996	26	a|=λ|1	a|=λ|1	PROPN
ejde-397	996	27	/	/	SYM
ejde-397	996	28	s	s	PART
ejde-397	996	29	+	+	NUM
ejde-397	996	30	b	b	NOUN
ejde-397	996	31	}	}	PUNCT
ejde-397	996	32	and	and	CCONJ
ejde-397	996	33	denote	denote	VERB
ejde-397	996	34	by	by	ADP
ejde-397	996	35	γ	γ	PROPN
ejde-397	996	36	the	the	DET
ejde-397	996	37	upwards	upwards	ADV
ejde-397	996	38	oriented	orient	VERB
ejde-397	996	39	boundary	boundary	NOUN
ejde-397	996	40	of	of	ADP
ejde-397	996	41	the	the	DET
ejde-397	996	42	region	region	NOUN
ejde-397	996	43	ω	ω	PROPN
ejde-397	996	44	.	.	PUNCT
ejde-397	997	1	inductively	inductively	ADV
ejde-397	997	2	,	,	PUNCT
ejde-397	997	3	we	we	PRON
ejde-397	997	4	can	can	AUX
ejde-397	997	5	prove	prove	VERB
ejde-397	997	6	that	that	SCONJ
ejde-397	997	7	for	for	ADP
ejde-397	997	8	each	each	DET
ejde-397	997	9	number	number	NOUN
ejde-397	997	10	n	n	ADP
ejde-397	997	11	∈	∈	NOUN
ejde-397	997	12	n	n	CCONJ
ejde-397	997	13	there	there	PRON
ejde-397	997	14	exist	exist	VERB
ejde-397	997	15	complex	complex	ADJ
ejde-397	997	16	polynomials	polynomial	NOUN
ejde-397	997	17	pj(z	pj(z	NOUN
ejde-397	997	18	)	)	PUNCT
ejde-397	997	19	=	=	PUNCT
ejde-397	998	1	∑j	∑j	PROPN
ejde-397	998	2	l=0	l=0	PROPN
ejde-397	998	3	aj	aj	PROPN
ejde-397	998	4	,	,	PUNCT
ejde-397	998	5	lz	lz	ADP
ejde-397	998	6	l	l	PROPN
ejde-397	998	7	(	(	PUNCT
ejde-397	998	8	1	1	NUM
ejde-397	998	9	≤	≤	NUM
ejde-397	998	10	j	j	PROPN
ejde-397	998	11	≤	≤	NUM
ejde-397	998	12	n	n	CCONJ
ejde-397	998	13	)	)	PUNCT
ejde-397	998	14	such	such	ADJ
ejde-397	998	15	that	that	DET
ejde-397	998	16	deg(pj	deg(pj	NOUN
ejde-397	998	17	)	)	PUNCT
ejde-397	998	18	=	=	SYM
ejde-397	998	19	j	j	PROPN
ejde-397	998	20	,	,	PUNCT
ejde-397	998	21	|aj	|aj	NUM
ejde-397	998	22	,	,	PUNCT
ejde-397	998	23	l|	l|	ADJ
ejde-397	998	24	≤	≤	NUM
ejde-397	998	25	(	(	PUNCT
ejde-397	998	26	n+	n+	NOUN
ejde-397	998	27	1	1	NUM
ejde-397	998	28	)	)	PUNCT
ejde-397	998	29	!	!	PUNCT
ejde-397	999	1	(	(	PUNCT
ejde-397	999	2	1	1	NUM
ejde-397	999	3	≤	≤	NUM
ejde-397	999	4	j	j	PROPN
ejde-397	999	5	≤	≤	NUM
ejde-397	999	6	n	n	CCONJ
ejde-397	999	7	,	,	PUNCT
ejde-397	999	8	0	0	NUM
ejde-397	999	9	≤	≤	NUM
ejde-397	999	10	l	l	NOUN
ejde-397	999	11	≤	≤	PROPN
ejde-397	999	12	j	j	NOUN
ejde-397	999	13	)	)	PUNCT
ejde-397	999	14	and	and	CCONJ
ejde-397	999	15	dn	dn	PROPN
ejde-397	999	16	dxn	dxn	PROPN
ejde-397	999	17	(	(	PUNCT
ejde-397	999	18	λ−	λ−	PROPN
ejde-397	999	19	(	(	PUNCT
ejde-397	999	20	x+iex	x+iex	NUM
ejde-397	999	21	)	)	PUNCT
ejde-397	999	22	)	)	PUNCT
ejde-397	1000	1	−1	−1	NOUN
ejde-397	1001	1	=	=	SYM
ejde-397	1001	2	n+1∑	n+1∑	PROPN
ejde-397	1001	3	j=1	j=1	NOUN
ejde-397	1001	4	(	(	PUNCT
ejde-397	1001	5	λ−	λ−	PROPN
ejde-397	1001	6	(	(	PUNCT
ejde-397	1001	7	x+iex	x+iex	PROPN
ejde-397	1001	8	)	)	PUNCT
ejde-397	1001	9	)	)	PUNCT
ejde-397	1002	1	−j−1	−j−1	NUM
ejde-397	1002	2	pj	pj	PROPN
ejde-397	1002	3	(	(	PUNCT
ejde-397	1002	4	ex	ex	X
ejde-397	1002	5	)	)	PUNCT
ejde-397	1002	6	,	,	PUNCT
ejde-397	1002	7	x	x	X
ejde-397	1002	8	≥	≥	NOUN
ejde-397	1002	9	0	0	NUM
ejde-397	1002	10	,	,	PUNCT
ejde-397	1002	11	λ	λ	PROPN
ejde-397	1002	12	∈	∈	PROPN
ejde-397	1002	13	c\s	c\s	NOUN
ejde-397	1002	14	.	.	PUNCT
ejde-397	1002	15	(	(	PUNCT
ejde-397	1002	16	5.11	5.11	NUM
ejde-397	1002	17	)	)	PUNCT
ejde-397	1002	18	suppose	suppose	VERB
ejde-397	1002	19	λ	λ	X
ejde-397	1002	20	∈	∈	PROPN
ejde-397	1002	21	ω	ω	PROPN
ejde-397	1002	22	and	and	CCONJ
ejde-397	1002	23	x	x	PRON
ejde-397	1002	24	≥	≥	NOUN
ejde-397	1002	25	0	0	NUM
ejde-397	1002	26	.	.	PUNCT
ejde-397	1003	1	if	if	SCONJ
ejde-397	1003	2	|=λ−	|=λ−	PROPN
ejde-397	1003	3	ex|	ex|	PROPN
ejde-397	1003	4	≥	≥	NUM
ejde-397	1003	5	1	1	NUM
ejde-397	1003	6	,	,	PUNCT
ejde-397	1003	7	then	then	ADV
ejde-397	1003	8	we	we	PRON
ejde-397	1003	9	have	have	VERB
ejde-397	1003	10	the	the	DET
ejde-397	1003	11	estimate	estimate	NOUN
ejde-397	1003	12	e2jx	e2jx	PUNCT
ejde-397	1003	13	(	(	PUNCT
ejde-397	1003	14	<	<	X
ejde-397	1003	15	λ−	λ−	PROPN
ejde-397	1003	16	x	x	SYM
ejde-397	1003	17	)	)	PUNCT
ejde-397	1003	18	2k	2k	NOUN
ejde-397	1003	19	+	+	CCONJ
ejde-397	1003	20	(	(	PUNCT
ejde-397	1003	21	=	=	NOUN
ejde-397	1003	22	λ−	λ−	PROPN
ejde-397	1003	23	ex	ex	X
ejde-397	1003	24	)	)	PUNCT
ejde-397	1003	25	2k	2k	PROPN
ejde-397	1003	26	≤	≤	NOUN
ejde-397	1003	27	e2jx	e2jx	PUNCT
ejde-397	1003	28	(	(	PUNCT
ejde-397	1003	29	=	=	NOUN
ejde-397	1003	30	λ−	λ−	PROPN
ejde-397	1003	31	ex	ex	X
ejde-397	1003	32	)	)	PUNCT
ejde-397	1003	33	2k	2k	PROPN
ejde-397	1003	34	≤	≤	NOUN
ejde-397	1003	35	22j	22j	NOUN
ejde-397	1003	36	(	(	PUNCT
ejde-397	1003	37	1	1	NUM
ejde-397	1003	38	+	+	NUM
ejde-397	1003	39	|=λ|	|=λ|	NOUN
ejde-397	1003	40	)	)	PUNCT
ejde-397	1003	41	2j	2j	NOUN
ejde-397	1003	42	,	,	PUNCT
ejde-397	1003	43	k	k	PROPN
ejde-397	1003	44	∈	∈	PROPN
ejde-397	1003	45	n0	n0	PROPN
ejde-397	1003	46	,	,	PUNCT
ejde-397	1003	47	0	0	NUM
ejde-397	1003	48	≤	≤	NUM
ejde-397	1003	49	j	j	PROPN
ejde-397	1003	50	<	<	X
ejde-397	1003	51	k.	k.	PROPN
ejde-397	1003	52	(	(	PUNCT
ejde-397	1003	53	5.12	5.12	NUM
ejde-397	1003	54	)	)	PUNCT
ejde-397	1003	55	if	if	SCONJ
ejde-397	1003	56	|=λ−	|=λ−	PROPN
ejde-397	1003	57	ex|	ex|	PROPN
ejde-397	1003	58	<	<	X
ejde-397	1003	59	1	1	NUM
ejde-397	1003	60	,	,	PUNCT
ejde-397	1003	61	then	then	ADV
ejde-397	1003	62	=	=	X
ejde-397	1003	63	λ	λ	X
ejde-397	1003	64	>	>	X
ejde-397	1003	65	0	0	NUM
ejde-397	1003	66	,	,	PUNCT
ejde-397	1003	67	0	0	NUM
ejde-397	1003	68	≤	≤	NUM
ejde-397	1003	69	x	x	PUNCT
ejde-397	1003	70	<	<	X
ejde-397	1003	71	ln(=λ+	ln(=λ+	PROPN
ejde-397	1003	72	1	1	NUM
ejde-397	1003	73	)	)	PUNCT
ejde-397	1003	74	,	,	PUNCT
ejde-397	1003	75	and	and	CCONJ
ejde-397	1003	76	e2jx	e2jx	X
ejde-397	1003	77	(	(	PUNCT
ejde-397	1003	78	<	<	X
ejde-397	1003	79	λ−	λ−	PROPN
ejde-397	1003	80	x	x	SYM
ejde-397	1003	81	)	)	PUNCT
ejde-397	1003	82	2k	2k	NOUN
ejde-397	1003	83	+	+	CCONJ
ejde-397	1003	84	(	(	PUNCT
ejde-397	1003	85	=	=	NOUN
ejde-397	1003	86	λ−	λ−	PROPN
ejde-397	1003	87	ex	ex	X
ejde-397	1003	88	)	)	PUNCT
ejde-397	1003	89	2k	2k	PROPN
ejde-397	1003	90	≤	≤	NOUN
ejde-397	1003	91	e2jx	e2jx	PUNCT
ejde-397	1003	92	(	(	PUNCT
ejde-397	1003	93	<	<	X
ejde-397	1003	94	λ−	λ−	PROPN
ejde-397	1003	95	x	x	SYM
ejde-397	1003	96	)	)	PUNCT
ejde-397	1003	97	2k	2k	NOUN
ejde-397	1003	98	≤	≤	NOUN
ejde-397	1003	99	(	(	PUNCT
ejde-397	1003	100	=	=	NOUN
ejde-397	1003	101	λ+	λ+	NUM
ejde-397	1003	102	1	1	NUM
ejde-397	1003	103	)	)	PUNCT
ejde-397	1003	104	j	j	PROPN
ejde-397	1004	1	<	<	X
ejde-397	1004	2	λ−	λ−	PROPN
ejde-397	1004	3	ln	ln	INTJ
ejde-397	1004	4	(	(	PUNCT
ejde-397	1004	5	(	(	PUNCT
ejde-397	1004	6	(	(	PUNCT
ejde-397	1004	7	<	<	X
ejde-397	1004	8	λ−	λ−	PROPN
ejde-397	1004	9	b)/a)s	b)/a)s	NOUN
ejde-397	1004	10	+	+	CCONJ
ejde-397	1004	11	1	1	X
ejde-397	1004	12	)	)	PUNCT
ejde-397	1004	13	≤	≤	NOUN
ejde-397	1004	14	(	(	PUNCT
ejde-397	1004	15	=	=	NOUN
ejde-397	1004	16	λ+	λ+	NUM
ejde-397	1004	17	1	1	NUM
ejde-397	1004	18	)	)	PUNCT
ejde-397	1004	19	j	j	NOUN
ejde-397	1004	20	,	,	PUNCT
ejde-397	1004	21	k	k	PROPN
ejde-397	1004	22	∈	∈	PROPN
ejde-397	1004	23	n0	n0	PROPN
ejde-397	1004	24	,	,	PUNCT
ejde-397	1004	25	0	0	NUM
ejde-397	1004	26	≤	≤	NUM
ejde-397	1004	27	j	j	PROPN
ejde-397	1004	28	<	<	X
ejde-397	1004	29	k.	k.	PROPN
ejde-397	1004	30	(	(	PUNCT
ejde-397	1004	31	5.13	5.13	NUM
ejde-397	1004	32	)	)	PUNCT
ejde-397	1004	33	let	let	VERB
ejde-397	1004	34	ω′	ω′	PRON
ejde-397	1004	35	>	>	X
ejde-397	1004	36	0	0	PUNCT
ejde-397	1004	37	be	be	AUX
ejde-397	1004	38	such	such	ADJ
ejde-397	1004	39	that	that	SCONJ
ejde-397	1004	40	{	{	PUNCT
ejde-397	1004	41	λ	λ	X
ejde-397	1004	42	∈	∈	PROPN
ejde-397	1004	43	σαπ/2	σαπ/2	NOUN
ejde-397	1004	44	:	:	PUNCT
ejde-397	1004	45	<	<	X
ejde-397	1004	46	λ	λ	X
ejde-397	1004	47	>	>	X
ejde-397	1004	48	ω′	ω′	PROPN
ejde-397	1004	49	}	}	PUNCT
ejde-397	1004	50	⊆	⊆	NUM
ejde-397	1004	51	ω	ω	NOUN
ejde-397	1004	52	.	.	PUNCT
ejde-397	1005	1	combining	combine	VERB
ejde-397	1005	2	(	(	PUNCT
ejde-397	1005	3	5.11)-(5.13	5.11)-(5.13	NUM
ejde-397	1005	4	)	)	PUNCT
ejde-397	1005	5	,	,	PUNCT
ejde-397	1005	6	it	it	PRON
ejde-397	1005	7	can	can	AUX
ejde-397	1005	8	be	be	AUX
ejde-397	1005	9	simply	simply	ADV
ejde-397	1005	10	proved	prove	VERB
ejde-397	1005	11	that	that	SCONJ
ejde-397	1005	12	for	for	ADP
ejde-397	1005	13	each	each	DET
ejde-397	1005	14	number	number	NOUN
ejde-397	1005	15	n	n	ADP
ejde-397	1005	16	∈	∈	PRON
ejde-397	1005	17	n	n	CCONJ
ejde-397	1005	18	there	there	PRON
ejde-397	1005	19	exists	exist	VERB
ejde-397	1005	20	a	a	DET
ejde-397	1005	21	finite	finite	PROPN
ejde-397	1005	22	constant	constant	NOUN
ejde-397	1006	1	cn	cn	PROPN
ejde-397	1006	2	>	>	X
ejde-397	1006	3	0	0	NUM
ejde-397	1007	1	such	such	ADJ
ejde-397	1007	2	that	that	SCONJ
ejde-397	1007	3	n∑	n∑	PROPN
ejde-397	1007	4	k=0	k=0	PROPN
ejde-397	1007	5	sup	sup	NOUN
ejde-397	1007	6	x≥0,x/∈j	x≥0,x/∈j	PROPN
ejde-397	1007	7	∣∣	∣∣	NUM
ejde-397	1007	8	dn	dn	ADP
ejde-397	1007	9	dxn	dxn	PROPN
ejde-397	1007	10	(	(	PUNCT
ejde-397	1007	11	λ−	λ−	PROPN
ejde-397	1007	12	(	(	PUNCT
ejde-397	1007	13	x+	x+	PROPN
ejde-397	1007	14	iex	iex	PROPN
ejde-397	1007	15	)	)	PUNCT
ejde-397	1007	16	)	)	PUNCT
ejde-397	1008	1	−1∣∣	−1∣∣	ADJ
ejde-397	1008	2	≤	≤	NOUN
ejde-397	1008	3	cned|λ|1	cned|λ|1	PROPN
ejde-397	1008	4	/	/	SYM
ejde-397	1008	5	s	s	NOUN
ejde-397	1008	6	,	,	PUNCT
ejde-397	1008	7	(	(	PUNCT
ejde-397	1008	8	5.14	5.14	NUM
ejde-397	1008	9	)	)	PUNCT
ejde-397	1008	10	for	for	ADP
ejde-397	1008	11	λ	λ	PROPN
ejde-397	1008	12	∈	∈	PROPN
ejde-397	1008	13	σαπ/2	σαπ/2	NOUN
ejde-397	1008	14	and	and	CCONJ
ejde-397	1008	15	<	<	X
ejde-397	1008	16	λ	λ	X
ejde-397	1008	17	>	>	X
ejde-397	1008	18	ω′.	ω′.	VERB
ejde-397	1008	19	we	we	PRON
ejde-397	1008	20	can	can	AUX
ejde-397	1008	21	similarly	similarly	ADV
ejde-397	1008	22	prove	prove	VERB
ejde-397	1008	23	an	an	DET
ejde-397	1008	24	estimate	estimate	NOUN
ejde-397	1008	25	of	of	ADP
ejde-397	1008	26	type	type	NOUN
ejde-397	1008	27	(	(	PUNCT
ejde-397	1008	28	5.14	5.14	NUM
ejde-397	1008	29	)	)	PUNCT
ejde-397	1008	30	for	for	ADP
ejde-397	1008	31	the	the	DET
ejde-397	1008	32	derivatives	derivative	NOUN
ejde-397	1008	33	of	of	ADP
ejde-397	1008	34	function	function	NOUN
ejde-397	1008	35	(	(	PUNCT
ejde-397	1008	36	λmb(x)−(x+iex))−1	λmb(x)−(x+iex))−1	X
ejde-397	1008	37	on	on	ADP
ejde-397	1008	38	the	the	DET
ejde-397	1008	39	interval	interval	NOUN
ejde-397	1008	40	j	j	PROPN
ejde-397	1008	41	,	,	PUNCT
ejde-397	1008	42	which	which	PRON
ejde-397	1008	43	is	be	AUX
ejde-397	1008	44	well	well	ADV
ejde-397	1008	45	-	-	PUNCT
ejde-397	1008	46	defined	define	VERB
ejde-397	1008	47	for	for	ADP
ejde-397	1008	48	λ	λ	PROPN
ejde-397	1008	49	∈	∈	PROPN
ejde-397	1008	50	σαπ/2	σαπ/2	NOUN
ejde-397	1008	51	because	because	SCONJ
ejde-397	1008	52	32	32	NUM
ejde-397	1008	53	m.	m.	NOUN
ejde-397	1008	54	kostić	kostić	NOUN
ejde-397	1009	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1009	2	of	of	ADP
ejde-397	1009	3	assumption	assumption	NOUN
ejde-397	1009	4	0	0	NUM
ejde-397	1009	5	≤	≤	NOUN
ejde-397	1009	6	mb(x	mb(x	CCONJ
ejde-397	1009	7	)	)	PUNCT
ejde-397	1009	8	≤	≤	NUM
ejde-397	1009	9	1	1	NUM
ejde-397	1009	10	,	,	PUNCT
ejde-397	1009	11	x	x	X
ejde-397	1009	12	≥	≥	NOUN
ejde-397	1009	13	0	0	NUM
ejde-397	1009	14	and	and	CCONJ
ejde-397	1009	15	the	the	DET
ejde-397	1009	16	condition	condition	NOUN
ejde-397	1009	17	σαπ/2∩{x+iex	σαπ/2∩{x+iex	VERB
ejde-397	1009	18	:	:	PUNCT
ejde-397	1010	1	x	x	SYM
ejde-397	1010	2	∈	∈	PROPN
ejde-397	1010	3	j	j	PROPN
ejde-397	1010	4	}	}	PUNCT
ejde-397	1010	5	=	=	PUNCT
ejde-397	1010	6	∅.	∅.	NOUN
ejde-397	1010	7	in	in	ADP
ejde-397	1010	8	actual	actual	ADJ
ejde-397	1010	9	fact	fact	NOUN
ejde-397	1010	10	,	,	PUNCT
ejde-397	1010	11	an	an	DET
ejde-397	1010	12	induction	induction	NOUN
ejde-397	1010	13	argument	argument	NOUN
ejde-397	1010	14	shows	show	VERB
ejde-397	1010	15	that	that	SCONJ
ejde-397	1010	16	for	for	ADP
ejde-397	1010	17	each	each	DET
ejde-397	1010	18	number	number	NOUN
ejde-397	1010	19	n	n	ADP
ejde-397	1010	20	∈	∈	NOUN
ejde-397	1010	21	n	n	CCONJ
ejde-397	1010	22	there	there	PRON
ejde-397	1010	23	exist	exist	VERB
ejde-397	1010	24	numbers	number	NOUN
ejde-397	1010	25	aj	aj	PROPN
ejde-397	1010	26	,	,	PUNCT
ejde-397	1010	27	l1,···,ls	l1,···,ls	ADV
ejde-397	1010	28	such	such	ADJ
ejde-397	1010	29	that	that	SCONJ
ejde-397	1010	30	|aj	|aj	NOUN
ejde-397	1010	31	,	,	PUNCT
ejde-397	1010	32	l1,···,ls	l1,···,ls	ADV
ejde-397	1010	33	|	|	ADV
ejde-397	1010	34	≤	≤	NUM
ejde-397	1010	35	(	(	PUNCT
ejde-397	1010	36	n	n	NOUN
ejde-397	1010	37	+	+	NOUN
ejde-397	1010	38	1	1	NUM
ejde-397	1010	39	)	)	PUNCT
ejde-397	1010	40	!	!	PUNCT
ejde-397	1011	1	(	(	PUNCT
ejde-397	1011	2	1	1	NUM
ejde-397	1011	3	≤	≤	NUM
ejde-397	1011	4	j	j	PROPN
ejde-397	1011	5	≤	≤	NUM
ejde-397	1011	6	n	n	CCONJ
ejde-397	1011	7	,	,	PUNCT
ejde-397	1011	8	0	0	NUM
ejde-397	1011	9	≤	≤	NUM
ejde-397	1011	10	l	l	NOUN
ejde-397	1011	11	≤	≤	PROPN
ejde-397	1011	12	j	j	NOUN
ejde-397	1011	13	)	)	PUNCT
ejde-397	1011	14	and	and	CCONJ
ejde-397	1011	15	that	that	SCONJ
ejde-397	1011	16	,	,	PUNCT
ejde-397	1011	17	for	for	ADP
ejde-397	1011	18	every	every	DET
ejde-397	1011	19	x	x	SYM
ejde-397	1011	20	∈	∈	PROPN
ejde-397	1011	21	j	j	PROPN
ejde-397	1011	22	and	and	CCONJ
ejde-397	1011	23	λ	λ	PROPN
ejde-397	1011	24	∈	∈	PROPN
ejde-397	1011	25	σαπ/2	σαπ/2	PROPN
ejde-397	1011	26	,	,	PUNCT
ejde-397	1011	27	dn	dn	PROPN
ejde-397	1011	28	dxn	dxn	PROPN
ejde-397	1011	29	(	(	PUNCT
ejde-397	1011	30	λmb(x)−	λmb(x)−	PROPN
ejde-397	1011	31	(	(	PUNCT
ejde-397	1011	32	x+	x+	PROPN
ejde-397	1011	33	iex	iex	PROPN
ejde-397	1011	34	)	)	PUNCT
ejde-397	1011	35	)	)	PUNCT
ejde-397	1011	36	−1	−1	NOUN
ejde-397	1012	1	=	=	SYM
ejde-397	1012	2	n+1∑	n+1∑	PROPN
ejde-397	1012	3	j=1	j=1	NOUN
ejde-397	1012	4	(	(	PUNCT
ejde-397	1012	5	λmb(x)−	λmb(x)−	PROPN
ejde-397	1012	6	(	(	PUNCT
ejde-397	1012	7	x+	x+	PROPN
ejde-397	1012	8	iex	iex	PROPN
ejde-397	1012	9	)	)	PUNCT
ejde-397	1012	10	)	)	PUNCT
ejde-397	1012	11	−j−1	−j−1	NUM
ejde-397	1012	12	×	×	NOUN
ejde-397	1012	13	j∑	j∑	PROPN
ejde-397	1012	14	l=0	l=0	PROPN
ejde-397	1012	15	aj	aj	PROPN
ejde-397	1012	16	,	,	PUNCT
ejde-397	1012	17	l1,···,ls	l1,···,ls	PRON
ejde-397	1012	18	∏	∏	PROPN
ejde-397	1012	19	l1m1+···+lsms	l1m1+···+lsm	NOUN
ejde-397	1012	20	=	=	NOUN
ejde-397	1012	21	n	n	NOUN
ejde-397	1012	22	(	(	PUNCT
ejde-397	1012	23	λm	λm	X
ejde-397	1012	24	(	(	PUNCT
ejde-397	1012	25	lj	lj	PROPN
ejde-397	1012	26	)	)	PUNCT
ejde-397	1012	27	b	b	PROPN
ejde-397	1012	28	(	(	PUNCT
ejde-397	1012	29	x)−m(lj	x)−m(lj	PROPN
ejde-397	1012	30	)	)	PUNCT
ejde-397	1012	31	a	a	DET
ejde-397	1012	32	(	(	PUNCT
ejde-397	1012	33	x	x	NOUN
ejde-397	1012	34	)	)	PUNCT
ejde-397	1012	35	)	)	PUNCT
ejde-397	1013	1	mj	mj	INTJ
ejde-397	1013	2	.	.	PUNCT
ejde-397	1014	1	(	(	PUNCT
ejde-397	1014	2	5.15	5.15	NUM
ejde-397	1014	3	)	)	PUNCT
ejde-397	1014	4	since	since	SCONJ
ejde-397	1014	5	d	d	NOUN
ejde-397	1014	6	:	:	PUNCT
ejde-397	1014	7	=	=	SYM
ejde-397	1014	8	dist(σαπ/2	dist(σαπ/2	PROPN
ejde-397	1014	9	,	,	PUNCT
ejde-397	1014	10	{	{	PUNCT
ejde-397	1014	11	x+	x+	PROPN
ejde-397	1014	12	iex	iex	NOUN
ejde-397	1014	13	:	:	PUNCT
ejde-397	1014	14	x	x	SYM
ejde-397	1014	15	∈	∈	PROPN
ejde-397	1014	16	j	j	NOUN
ejde-397	1014	17	}	}	PUNCT
ejde-397	1014	18	)	)	PUNCT
ejde-397	1014	19	is	be	AUX
ejde-397	1014	20	a	a	DET
ejde-397	1014	21	positive	positive	ADJ
ejde-397	1014	22	real	real	ADJ
ejde-397	1014	23	number	number	NOUN
ejde-397	1014	24	and	and	CCONJ
ejde-397	1014	25	|(λm(lj	|(λm(lj	NOUN
ejde-397	1014	26	)	)	PUNCT
ejde-397	1014	27	b	b	PROPN
ejde-397	1014	28	(	(	PUNCT
ejde-397	1014	29	x)−	x)−	PROPN
ejde-397	1014	30	m	m	PROPN
ejde-397	1014	31	(	(	PUNCT
ejde-397	1014	32	lj	lj	PROPN
ejde-397	1014	33	)	)	PUNCT
ejde-397	1014	34	a	a	PRON
ejde-397	1014	35	(	(	PUNCT
ejde-397	1014	36	x))mj	x))mj	PROPN
ejde-397	1014	37	|	|	ADV
ejde-397	1014	38	≤	≤	X
ejde-397	1014	39	cmj	cmj	VERB
ejde-397	1014	40	|λ|mj	|λ|mj	PROPN
ejde-397	1014	41	for	for	ADP
ejde-397	1014	42	all	all	DET
ejde-397	1014	43	λ	λ	PROPN
ejde-397	1014	44	∈	∈	PROPN
ejde-397	1014	45	σαπ/2	σαπ/2	NOUN
ejde-397	1014	46	with	with	ADP
ejde-397	1014	47	<	<	X
ejde-397	1014	48	λ	λ	X
ejde-397	1014	49	>	>	X
ejde-397	1014	50	ω	ω	PROPN
ejde-397	1014	51	,	,	PUNCT
ejde-397	1014	52	where	where	SCONJ
ejde-397	1014	53	the	the	DET
ejde-397	1014	54	number	number	NOUN
ejde-397	1014	55	ω	ω	PROPN
ejde-397	1014	56	>	>	X
ejde-397	1014	57	ω′	ω′	PROPN
ejde-397	1014	58	is	be	AUX
ejde-397	1014	59	sufficiently	sufficiently	ADV
ejde-397	1014	60	large	large	ADJ
ejde-397	1014	61	,	,	PUNCT
ejde-397	1014	62	(	(	PUNCT
ejde-397	1014	63	5.15	5.15	NUM
ejde-397	1014	64	)	)	PUNCT
ejde-397	1014	65	shows	show	VERB
ejde-397	1014	66	that	that	SCONJ
ejde-397	1014	67	for	for	ADP
ejde-397	1014	68	each	each	DET
ejde-397	1014	69	number	number	NOUN
ejde-397	1014	70	n	n	ADP
ejde-397	1014	71	∈	∈	PRON
ejde-397	1014	72	n	n	CCONJ
ejde-397	1014	73	there	there	PRON
ejde-397	1014	74	exists	exist	VERB
ejde-397	1014	75	a	a	DET
ejde-397	1014	76	finite	finite	ADJ
ejde-397	1014	77	number	number	NOUN
ejde-397	1014	78	c′n	c′n	PROPN
ejde-397	1014	79	>	>	X
ejde-397	1014	80	0	0	NUM
ejde-397	1014	81	such	such	ADJ
ejde-397	1014	82	that	that	SCONJ
ejde-397	1014	83	n∑	n∑	PROPN
ejde-397	1014	84	k=0	k=0	PROPN
ejde-397	1014	85	sup	sup	PROPN
ejde-397	1014	86	x≥0,x∈j	x≥0,x∈j	PROPN
ejde-397	1014	87	∣∣∣	∣∣∣	PROPN
ejde-397	1014	88	dn	dn	PROPN
ejde-397	1014	89	dxn	dxn	PROPN
ejde-397	1014	90	(	(	PUNCT
ejde-397	1014	91	λmb(x)−	λmb(x)−	PROPN
ejde-397	1014	92	(	(	PUNCT
ejde-397	1014	93	x+	x+	PROPN
ejde-397	1014	94	iex	iex	PROPN
ejde-397	1014	95	)	)	PUNCT
ejde-397	1014	96	)	)	PUNCT
ejde-397	1014	97	−1∣∣∣	−1∣∣∣	PROPN
ejde-397	1014	98	≤	≤	PROPN
ejde-397	1014	99	c′ned|λ|1	c′ned|λ|1	NOUN
ejde-397	1014	100	/	/	SYM
ejde-397	1014	101	s	s	NOUN
ejde-397	1014	102	,	,	PUNCT
ejde-397	1014	103	(	(	PUNCT
ejde-397	1014	104	5.16	5.16	NUM
ejde-397	1014	105	)	)	PUNCT
ejde-397	1014	106	for	for	ADP
ejde-397	1014	107	λ	λ	PROPN
ejde-397	1014	108	∈	∈	PROPN
ejde-397	1014	109	σαπ/2	σαπ/2	NOUN
ejde-397	1014	110	and	and	CCONJ
ejde-397	1014	111	<	<	X
ejde-397	1014	112	λ	λ	X
ejde-397	1014	113	>	>	X
ejde-397	1014	114	ω	ω	PROPN
ejde-397	1014	115	.	.	PUNCT
ejde-397	1015	1	by	by	ADP
ejde-397	1015	2	(	(	PUNCT
ejde-397	1015	3	5.14	5.14	NUM
ejde-397	1015	4	)	)	PUNCT
ejde-397	1015	5	and	and	CCONJ
ejde-397	1015	6	(	(	PUNCT
ejde-397	1015	7	5.16	5.16	NUM
ejde-397	1015	8	)	)	PUNCT
ejde-397	1015	9	,	,	PUNCT
ejde-397	1015	10	we	we	PRON
ejde-397	1015	11	have	have	VERB
ejde-397	1015	12	that	that	SCONJ
ejde-397	1015	13	the	the	DET
ejde-397	1015	14	operator	operator	NOUN
ejde-397	1015	15	family	family	NOUN
ejde-397	1015	16	{	{	PUNCT
ejde-397	1015	17	e−d|λ|1	e−d|λ|1	PROPN
ejde-397	1015	18	/	/	SYM
ejde-397	1015	19	s(λ−a)−1	s(λ−a)−1	PUNCT
ejde-397	1015	20	:	:	PUNCT
ejde-397	1015	21	λ	λ	X
ejde-397	1015	22	∈	∈	PROPN
ejde-397	1015	23	σαπ/2	σαπ/2	NOUN
ejde-397	1015	24	,	,	PUNCT
ejde-397	1015	25	<	<	X
ejde-397	1015	26	λ	λ	X
ejde-397	1015	27	>	>	X
ejde-397	1015	28	ω	ω	PROPN
ejde-397	1015	29	}	}	PUNCT
ejde-397	1015	30	⊆	⊆	NUM
ejde-397	1015	31	l(x	l(x	PROPN
ejde-397	1015	32	)	)	PUNCT
ejde-397	1015	33	is	be	AUX
ejde-397	1015	34	equicontinuous	equicontinuous	ADJ
ejde-397	1015	35	,	,	PUNCT
ejde-397	1015	36	as	as	SCONJ
ejde-397	1015	37	claimed	claim	VERB
ejde-397	1015	38	.	.	PUNCT
ejde-397	1016	1	now	now	ADV
ejde-397	1016	2	we	we	PRON
ejde-397	1016	3	would	would	AUX
ejde-397	1016	4	like	like	VERB
ejde-397	1016	5	to	to	PART
ejde-397	1016	6	tell	tell	VERB
ejde-397	1016	7	something	something	PRON
ejde-397	1016	8	more	more	ADJ
ejde-397	1016	9	about	about	ADP
ejde-397	1016	10	the	the	DET
ejde-397	1016	11	importance	importance	NOUN
ejde-397	1016	12	of	of	ADP
ejde-397	1016	13	condition	condition	NOUN
ejde-397	1016	14	k(0	k(0	PROPN
ejde-397	1016	15	)	)	PUNCT
ejde-397	1016	16	6=	6=	ADP
ejde-397	1016	17	0	0	NUM
ejde-397	1016	18	in	in	ADP
ejde-397	1016	19	the	the	DET
ejde-397	1016	20	part	part	NOUN
ejde-397	1016	21	(	(	PUNCT
ejde-397	1016	22	ii	ii	NOUN
ejde-397	1016	23	)	)	PUNCT
ejde-397	1016	24	of	of	ADP
ejde-397	1016	25	subsequent	subsequent	ADJ
ejde-397	1016	26	theorem	theorem	NOUN
ejde-397	1016	27	.	.	PUNCT
ejde-397	1017	1	if	if	SCONJ
ejde-397	1017	2	all	all	DET
ejde-397	1017	3	the	the	DET
ejde-397	1017	4	necessary	necessary	ADJ
ejde-397	1017	5	requirements	requirement	NOUN
ejde-397	1017	6	hold	hold	VERB
ejde-397	1017	7	,	,	PUNCT
ejde-397	1017	8	the	the	DET
ejde-397	1017	9	arguments	argument	NOUN
ejde-397	1017	10	contained	contain	VERB
ejde-397	1017	11	in	in	ADP
ejde-397	1017	12	the	the	DET
ejde-397	1017	13	proof	proof	NOUN
ejde-397	1017	14	of	of	ADP
ejde-397	1017	15	[	[	X
ejde-397	1017	16	32	32	NUM
ejde-397	1017	17	,	,	PUNCT
ejde-397	1017	18	theorem	theorem	VERB
ejde-397	1017	19	3.6	3.6	NUM
ejde-397	1017	20	]	]	PUNCT
ejde-397	1017	21	imply	imply	VERB
ejde-397	1017	22	the	the	DET
ejde-397	1017	23	existence	existence	NOUN
ejde-397	1017	24	of	of	ADP
ejde-397	1017	25	a	a	DET
ejde-397	1017	26	global	global	ADJ
ejde-397	1017	27	(	(	PUNCT
ejde-397	1017	28	a	a	PROPN
ejde-397	1017	29	,	,	PUNCT
ejde-397	1017	30	k	k	PROPN
ejde-397	1017	31	∗	∗	NOUN
ejde-397	1017	32	g1)-regularized	g1)-regularize	VERB
ejde-397	1017	33	c	c	X
ejde-397	1017	34	-	-	PUNCT
ejde-397	1017	35	resolvent	resolvent	ADJ
ejde-397	1017	36	family	family	NOUN
ejde-397	1017	37	(	(	PUNCT
ejde-397	1017	38	r1(t))t≥0	r1(t))t≥0	PROPN
ejde-397	1017	39	subgenerated	subgenerate	VERB
ejde-397	1017	40	by	by	ADP
ejde-397	1017	41	a	a	PRON
ejde-397	1017	42	,	,	PUNCT
ejde-397	1017	43	which	which	PRON
ejde-397	1017	44	additionally	additionally	ADV
ejde-397	1017	45	satisfies	satisfy	VERB
ejde-397	1017	46	that	that	SCONJ
ejde-397	1017	47	for	for	ADP
ejde-397	1017	48	each	each	DET
ejde-397	1017	49	t	t	PROPN
ejde-397	1017	50	≥	≥	NOUN
ejde-397	1017	51	0	0	PUNCT
ejde-397	1017	52	the	the	DET
ejde-397	1017	53	operator	operator	NOUN
ejde-397	1017	54	r1(t)a	r1(t)a	NOUN
ejde-397	1017	55	is	be	AUX
ejde-397	1017	56	single	single	ADV
ejde-397	1017	57	-	-	PUNCT
ejde-397	1017	58	valued	value	VERB
ejde-397	1017	59	on	on	ADP
ejde-397	1017	60	d(a	d(a	PROPN
ejde-397	1017	61	)	)	PUNCT
ejde-397	1017	62	.	.	PUNCT
ejde-397	1018	1	then	then	ADV
ejde-397	1018	2	it	it	PRON
ejde-397	1018	3	is	be	AUX
ejde-397	1018	4	necessary	necessary	ADJ
ejde-397	1018	5	to	to	PART
ejde-397	1018	6	differentiate	differentiate	VERB
ejde-397	1018	7	the	the	DET
ejde-397	1018	8	equality	equality	NOUN
ejde-397	1018	9	r1(t)x−	r1(t)x−	PROPN
ejde-397	1018	10	(	(	PUNCT
ejde-397	1018	11	k	k	PROPN
ejde-397	1018	12	∗g1)(t)cx	∗g1)(t)cx	PROPN
ejde-397	1018	13	=	=	PROPN
ejde-397	1018	14	∫	∫	PROPN
ejde-397	1018	15	t	t	PROPN
ejde-397	1018	16	0	0	NUM
ejde-397	1018	17	a(t−s)r1(s)ax	a(t−s)r1(s)ax	X
ejde-397	1018	18	ds	ds	PROPN
ejde-397	1018	19	,	,	PUNCT
ejde-397	1018	20	t	t	PROPN
ejde-397	1018	21	≥	≥	NUM
ejde-397	1018	22	0	0	NUM
ejde-397	1018	23	,	,	PUNCT
ejde-397	1018	24	x	x	PROPN
ejde-397	1018	25	∈	∈	PROPN
ejde-397	1018	26	d(a	d(a	PROPN
ejde-397	1018	27	)	)	PUNCT
ejde-397	1018	28	and	and	CCONJ
ejde-397	1018	29	to	to	PART
ejde-397	1018	30	employ	employ	VERB
ejde-397	1018	31	the	the	DET
ejde-397	1018	32	fact	fact	NOUN
ejde-397	1018	33	that	that	SCONJ
ejde-397	1018	34	(	(	PUNCT
ejde-397	1018	35	ddtr1(t)x)t=0	ddtr1(t)x)t=0	NOUN
ejde-397	1018	36	=	=	SYM
ejde-397	1018	37	k(0)cx	k(0)cx	NOUN
ejde-397	1018	38	(	(	PUNCT
ejde-397	1018	39	x	x	SYM
ejde-397	1018	40	∈	∈	PROPN
ejde-397	1018	41	d(a	d(a	PROPN
ejde-397	1018	42	)	)	PUNCT
ejde-397	1018	43	)	)	PUNCT
ejde-397	1018	44	(	(	PUNCT
ejde-397	1018	45	cf	cf	X
ejde-397	1018	46	.	.	PUNCT
ejde-397	1019	1	the	the	DET
ejde-397	1019	2	proof	proof	NOUN
ejde-397	1019	3	of	of	ADP
ejde-397	1019	4	[	[	X
ejde-397	1019	5	32	32	NUM
ejde-397	1019	6	,	,	PUNCT
ejde-397	1019	7	theorem	theorem	VERB
ejde-397	1019	8	3.6	3.6	NUM
ejde-397	1019	9	]	]	PUNCT
ejde-397	1019	10	,	,	PUNCT
ejde-397	1019	11	as	as	ADV
ejde-397	1019	12	well	well	ADV
ejde-397	1019	13	as	as	ADP
ejde-397	1019	14	the	the	DET
ejde-397	1019	15	proofs	proof	NOUN
ejde-397	1019	16	of	of	ADP
ejde-397	1019	17	[	[	X
ejde-397	1019	18	17	17	NUM
ejde-397	1019	19	,	,	PUNCT
ejde-397	1019	20	proposition	proposition	NOUN
ejde-397	1019	21	2.1	2.1	NUM
ejde-397	1019	22	]	]	PUNCT
ejde-397	1019	23	and	and	CCONJ
ejde-397	1019	24	[	[	X
ejde-397	1019	25	36	36	NUM
ejde-397	1019	26	,	,	PUNCT
ejde-397	1019	27	proposition	proposition	NOUN
ejde-397	1019	28	2.1.7	2.1.7	NUM
ejde-397	1019	29	]	]	PUNCT
ejde-397	1019	30	)	)	PUNCT
ejde-397	1019	31	in	in	ADP
ejde-397	1019	32	order	order	NOUN
ejde-397	1019	33	to	to	PART
ejde-397	1019	34	see	see	VERB
ejde-397	1019	35	that	that	SCONJ
ejde-397	1019	36	the	the	DET
ejde-397	1019	37	function	function	NOUN
ejde-397	1019	38	r	r	NOUN
ejde-397	1019	39	:	:	PUNCT
ejde-397	1019	40	d(r	d(r	PROPN
ejde-397	1019	41	)	)	PUNCT
ejde-397	1019	42	≡	≡	PROPN
ejde-397	1019	43	{	{	PUNCT
ejde-397	1019	44	ã(λ)−1	ã(λ)−1	NOUN
ejde-397	1019	45	:	:	PUNCT
ejde-397	1019	46	λ	λ	X
ejde-397	1019	47	>	>	X
ejde-397	1019	48	b	b	PROPN
ejde-397	1019	49	,	,	PUNCT
ejde-397	1019	50	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1019	51	)	)	PUNCT
ejde-397	1019	52	6=	6=	ADP
ejde-397	1019	53	0	0	NUM
ejde-397	1019	54	}	}	PUNCT
ejde-397	1019	55	→	→	SYM
ejde-397	1019	56	l(d(a	l(d(a	PROPN
ejde-397	1019	57	)	)	PUNCT
ejde-397	1019	58	)	)	PUNCT
ejde-397	1019	59	,	,	PUNCT
ejde-397	1019	60	given	give	VERB
ejde-397	1019	61	by	by	ADP
ejde-397	1019	62	r(ã(λ)−1	r(ã(λ)−1	NOUN
ejde-397	1019	63	)	)	PUNCT
ejde-397	1019	64	:	:	PUNCT
ejde-397	1020	1	=	=	SYM
ejde-397	1020	2	(	(	PUNCT
ejde-397	1020	3	ã(λ)−1	ã(λ)−1	NOUN
ejde-397	1020	4	−a)−1c	−a)−1c	NOUN
ejde-397	1020	5	,	,	PUNCT
ejde-397	1020	6	λ	λ	PROPN
ejde-397	1020	7	∈	∈	PROPN
ejde-397	1020	8	d(r	d(r	PROPN
ejde-397	1020	9	)	)	PUNCT
ejde-397	1020	10	,	,	PUNCT
ejde-397	1020	11	is	be	AUX
ejde-397	1020	12	a	a	DET
ejde-397	1020	13	c	c	NOUN
ejde-397	1020	14	-	-	NOUN
ejde-397	1020	15	pseudoresolvent	pseudoresolvent	NOUN
ejde-397	1020	16	in	in	ADP
ejde-397	1020	17	the	the	DET
ejde-397	1020	18	sense	sense	NOUN
ejde-397	1020	19	of	of	ADP
ejde-397	1020	20	[	[	X
ejde-397	1020	21	57	57	NUM
ejde-397	1020	22	,	,	PUNCT
ejde-397	1020	23	definition	definition	NOUN
ejde-397	1020	24	3.1	3.1	NUM
ejde-397	1020	25	]	]	PUNCT
ejde-397	1020	26	,	,	PUNCT
ejde-397	1020	27	satisfying	satisfy	VERB
ejde-397	1020	28	additionally	additionally	ADV
ejde-397	1020	29	that	that	SCONJ
ejde-397	1020	30	n(r(λ	n(r(λ	NOUN
ejde-397	1020	31	)	)	PUNCT
ejde-397	1020	32	)	)	PUNCT
ejde-397	1021	1	=	=	PRON
ejde-397	1021	2	{	{	PUNCT
ejde-397	1021	3	0	0	NUM
ejde-397	1021	4	}	}	PUNCT
ejde-397	1021	5	,	,	PUNCT
ejde-397	1021	6	λ	λ	PROPN
ejde-397	1021	7	∈	∈	PROPN
ejde-397	1021	8	d(r	d(r	PROPN
ejde-397	1021	9	)	)	PUNCT
ejde-397	1021	10	.	.	PUNCT
ejde-397	1022	1	only	only	ADV
ejde-397	1022	2	after	after	ADP
ejde-397	1022	3	that	that	PRON
ejde-397	1022	4	,	,	PUNCT
ejde-397	1022	5	we	we	PRON
ejde-397	1022	6	can	can	AUX
ejde-397	1022	7	use	use	VERB
ejde-397	1022	8	[	[	X
ejde-397	1022	9	57	57	NUM
ejde-397	1022	10	,	,	PUNCT
ejde-397	1022	11	theorem	theorem	VERB
ejde-397	1022	12	3.4	3.4	NUM
ejde-397	1022	13	]	]	PUNCT
ejde-397	1022	14	with	with	ADP
ejde-397	1022	15	a	a	DET
ejde-397	1022	16	view	view	NOUN
ejde-397	1022	17	to	to	PART
ejde-397	1022	18	prove	prove	VERB
ejde-397	1022	19	the	the	DET
ejde-397	1022	20	existence	existence	NOUN
ejde-397	1022	21	of	of	ADP
ejde-397	1022	22	a	a	DET
ejde-397	1022	23	single	single	ADV
ejde-397	1022	24	-	-	PUNCT
ejde-397	1022	25	valued	value	VERB
ejde-397	1022	26	linear	linear	NOUN
ejde-397	1022	27	operator	operator	NOUN
ejde-397	1022	28	a	a	PRON
ejde-397	1022	29	,	,	PUNCT
ejde-397	1022	30	with	with	ADP
ejde-397	1022	31	domain	domain	NOUN
ejde-397	1022	32	and	and	CCONJ
ejde-397	1022	33	range	range	NOUN
ejde-397	1022	34	contained	contain	VERB
ejde-397	1022	35	in	in	ADP
ejde-397	1022	36	d(a	d(a	PROPN
ejde-397	1022	37	)	)	PUNCT
ejde-397	1022	38	,	,	PUNCT
ejde-397	1022	39	which	which	PRON
ejde-397	1022	40	satisfies	satisfy	VERB
ejde-397	1022	41	the	the	DET
ejde-397	1022	42	properties	property	NOUN
ejde-397	1022	43	required	require	VERB
ejde-397	1022	44	in	in	ADP
ejde-397	1022	45	(	(	PUNCT
ejde-397	1022	46	ii	ii	NOUN
ejde-397	1022	47	):	):	PUNCT
ejde-397	1022	48	this	this	DET
ejde-397	1022	49	consideration	consideration	NOUN
ejde-397	1022	50	shows	show	VERB
ejde-397	1022	51	the	the	DET
ejde-397	1022	52	full	full	ADJ
ejde-397	1022	53	importance	importance	NOUN
ejde-397	1022	54	of	of	ADP
ejde-397	1022	55	concepts	concept	NOUN
ejde-397	1022	56	introduced	introduce	VERB
ejde-397	1022	57	in	in	ADP
ejde-397	1022	58	definition	definition	NOUN
ejde-397	1022	59	5.1	5.1	NUM
ejde-397	1022	60	and	and	CCONJ
ejde-397	1022	61	definition	definition	NOUN
ejde-397	1022	62	5.2	5.2	NUM
ejde-397	1022	63	in	in	ADP
ejde-397	1022	64	integrated	integrated	ADJ
ejde-397	1022	65	and	and	CCONJ
ejde-397	1022	66	convoluted	convoluted	ADJ
ejde-397	1022	67	case	case	NOUN
ejde-397	1022	68	k(0	k(0	PROPN
ejde-397	1022	69	)	)	PUNCT
ejde-397	1022	70	=	=	SYM
ejde-397	1023	1	0	0	X
ejde-397	1023	2	.	.	X
ejde-397	1024	1	keeping	keep	VERB
ejde-397	1024	2	in	in	ADP
ejde-397	1024	3	mind	mind	NOUN
ejde-397	1024	4	theorem	theorem	VERB
ejde-397	1024	5	2.4(i	2.4(i	NUM
ejde-397	1024	6	)	)	PUNCT
ejde-397	1024	7	and	and	CCONJ
ejde-397	1024	8	the	the	DET
ejde-397	1024	9	argumentation	argumentation	NOUN
ejde-397	1024	10	contained	contain	VERB
ejde-397	1024	11	in	in	ADP
ejde-397	1024	12	the	the	DET
ejde-397	1024	13	proofs	proof	NOUN
ejde-397	1024	14	of	of	ADP
ejde-397	1024	15	[	[	X
ejde-397	1024	16	32	32	NUM
ejde-397	1024	17	,	,	PUNCT
ejde-397	1024	18	theorem	theorem	VERB
ejde-397	1024	19	3.6	3.6	NUM
ejde-397	1024	20	]	]	PUNCT
ejde-397	1024	21	and	and	CCONJ
ejde-397	1024	22	[	[	X
ejde-397	1024	23	36	36	NUM
ejde-397	1024	24	,	,	PUNCT
ejde-397	1024	25	theorem	theorem	VERB
ejde-397	1024	26	1.2.6	1.2.6	NUM
ejde-397	1024	27	]	]	PUNCT
ejde-397	1024	28	,	,	PUNCT
ejde-397	1024	29	the	the	DET
ejde-397	1024	30	remaining	remain	VERB
ejde-397	1024	31	parts	part	NOUN
ejde-397	1024	32	of	of	ADP
ejde-397	1024	33	following	follow	VERB
ejde-397	1024	34	theorem	theorem	NOUN
ejde-397	1024	35	can	can	AUX
ejde-397	1024	36	be	be	AUX
ejde-397	1024	37	deduced	deduce	VERB
ejde-397	1024	38	,	,	PUNCT
ejde-397	1024	39	more	more	ADJ
ejde-397	1024	40	or	or	CCONJ
ejde-397	1024	41	less	less	ADJ
ejde-397	1024	42	,	,	PUNCT
ejde-397	1024	43	as	as	ADP
ejde-397	1024	44	in	in	ADP
ejde-397	1024	45	non	non	ADJ
ejde-397	1024	46	-	-	ADJ
ejde-397	1024	47	degenerate	degenerate	ADJ
ejde-397	1024	48	case	case	NOUN
ejde-397	1024	49	.	.	PUNCT
ejde-397	1025	1	theorem	theorem	VERB
ejde-397	1025	2	5.12	5.12	NUM
ejde-397	1025	3	.	.	PUNCT
ejde-397	1026	1	suppose	suppose	VERB
ejde-397	1026	2	ω	ω	NUM
ejde-397	1026	3	∈	∈	PROPN
ejde-397	1026	4	r	r	X
ejde-397	1026	5	,	,	PUNCT
ejde-397	1026	6	abs(k	abs(k	PROPN
ejde-397	1026	7	)	)	PUNCT
ejde-397	1026	8	<	<	X
ejde-397	1026	9	∞	∞	PROPN
ejde-397	1026	10	,	,	PUNCT
ejde-397	1026	11	abs(|a|	abs(|a|	ADJ
ejde-397	1026	12	)	)	PUNCT
ejde-397	1026	13	<	<	X
ejde-397	1026	14	∞	∞	PROPN
ejde-397	1026	15	,	,	PUNCT
ejde-397	1026	16	a	a	PRON
ejde-397	1026	17	is	be	AUX
ejde-397	1026	18	a	a	DET
ejde-397	1026	19	closed	closed	ADJ
ejde-397	1026	20	mlo	mlo	NOUN
ejde-397	1026	21	in	in	ADP
ejde-397	1026	22	x	x	NOUN
ejde-397	1026	23	,	,	PUNCT
ejde-397	1026	24	λ0	λ0	NOUN
ejde-397	1026	25	∈	∈	NOUN
ejde-397	1026	26	ρc(a	ρc(a	NOUN
ejde-397	1026	27	)	)	PUNCT
ejde-397	1026	28	,	,	PUNCT
ejde-397	1026	29	b	b	PROPN
ejde-397	1026	30	≥	≥	NOUN
ejde-397	1026	31	max(0	max(0	NOUN
ejde-397	1026	32	,	,	PUNCT
ejde-397	1026	33	ω	ω	PROPN
ejde-397	1026	34	,	,	PUNCT
ejde-397	1026	35	abs(|a|	abs(|a|	ADJ
ejde-397	1026	36	)	)	PUNCT
ejde-397	1026	37	,	,	PUNCT
ejde-397	1026	38	abs(k	abs(k	PROPN
ejde-397	1026	39	)	)	PUNCT
ejde-397	1026	40	)	)	PUNCT
ejde-397	1026	41	,	,	PUNCT
ejde-397	1026	42	{	{	PUNCT
ejde-397	1026	43	1	1	NUM
ejde-397	1026	44	ã(λ	ã(λ	PROPN
ejde-397	1026	45	)	)	PUNCT
ejde-397	1026	46	:	:	PUNCT
ejde-397	1027	1	λ	λ	X
ejde-397	1027	2	>	>	X
ejde-397	1027	3	b	b	PROPN
ejde-397	1027	4	,	,	PUNCT
ejde-397	1027	5	k̃(λ)ã(λ	k̃(λ)ã(λ	PROPN
ejde-397	1027	6	)	)	PUNCT
ejde-397	1027	7	6=	6=	ADP
ejde-397	1027	8	0	0	NUM
ejde-397	1027	9	}	}	PUNCT
ejde-397	1027	10	⊆	⊆	NUM
ejde-397	1027	11	ρc(a	ρc(a	NOUN
ejde-397	1027	12	)	)	PUNCT
ejde-397	1027	13	,	,	PUNCT
ejde-397	1027	14	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1027	15	abstract	abstract	ADJ
ejde-397	1027	16	degenerate	degenerate	ADJ
ejde-397	1027	17	volterra	volterra	NOUN
ejde-397	1027	18	inclusions	inclusion	NOUN
ejde-397	1027	19	33	33	NUM
ejde-397	1027	20	the	the	DET
ejde-397	1027	21	function	function	NOUN
ejde-397	1027	22	h	h	NOUN
ejde-397	1027	23	:	:	PUNCT
ejde-397	1027	24	d(h	d(h	PROPN
ejde-397	1027	25	)	)	PUNCT
ejde-397	1027	26	≡	≡	PROPN
ejde-397	1027	27	{	{	PUNCT
ejde-397	1027	28	λ	λ	X
ejde-397	1027	29	>	>	X
ejde-397	1027	30	b	b	PROPN
ejde-397	1027	31	:	:	PUNCT
ejde-397	1027	32	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1027	33	)	)	PUNCT
ejde-397	1027	34	6=	6=	ADP
ejde-397	1027	35	0	0	NUM
ejde-397	1027	36	}	}	PUNCT
ejde-397	1027	37	→	→	SYM
ejde-397	1027	38	l(x	l(x	PROPN
ejde-397	1027	39	)	)	PUNCT
ejde-397	1027	40	,	,	PUNCT
ejde-397	1027	41	given	give	VERB
ejde-397	1027	42	by	by	ADP
ejde-397	1027	43	h(λ)x	h(λ)x	PROPN
ejde-397	1027	44	=	=	PUNCT
ejde-397	1027	45	k̃(λ)(i	k̃(λ)(i	PROPN
ejde-397	1027	46	−	−	PROPN
ejde-397	1027	47	ã(λ)a)−1cx	ã(λ)a)−1cx	PROPN
ejde-397	1027	48	,	,	PUNCT
ejde-397	1027	49	x	x	SYM
ejde-397	1027	50	∈	∈	NOUN
ejde-397	1027	51	x	x	X
ejde-397	1027	52	,	,	PUNCT
ejde-397	1027	53	λ	λ	PROPN
ejde-397	1027	54	∈	∈	PROPN
ejde-397	1027	55	d(h	d(h	PROPN
ejde-397	1027	56	)	)	PUNCT
ejde-397	1027	57	,	,	PUNCT
ejde-397	1027	58	satisfies	satisfy	VERB
ejde-397	1027	59	that	that	SCONJ
ejde-397	1027	60	the	the	DET
ejde-397	1027	61	mapping	mapping	NOUN
ejde-397	1027	62	λ	λ	PROPN
ejde-397	1027	63	7→	7→	PROPN
ejde-397	1027	64	h(λ)x	h(λ)x	PROPN
ejde-397	1027	65	,	,	PUNCT
ejde-397	1027	66	λ	λ	PROPN
ejde-397	1027	67	∈	∈	PROPN
ejde-397	1027	68	d(h	d(h	PROPN
ejde-397	1027	69	)	)	PUNCT
ejde-397	1027	70	is	be	AUX
ejde-397	1027	71	infinitely	infinitely	ADV
ejde-397	1027	72	differentiable	differentiable	ADJ
ejde-397	1027	73	for	for	ADP
ejde-397	1027	74	every	every	DET
ejde-397	1027	75	fixed	fix	VERB
ejde-397	1027	76	x	x	SYM
ejde-397	1027	77	∈	∈	PROPN
ejde-397	1027	78	x	x	X
ejde-397	1027	79	and	and	CCONJ
ejde-397	1027	80	,	,	PUNCT
ejde-397	1027	81	for	for	ADP
ejde-397	1027	82	every	every	DET
ejde-397	1027	83	p	p	PROPN
ejde-397	1027	84	∈	∈	PROPN
ejde-397	1028	1	~	~	PUNCT
ejde-397	1028	2	,	,	PUNCT
ejde-397	1028	3	there	there	PRON
ejde-397	1028	4	exist	exist	VERB
ejde-397	1028	5	cp	cp	PROPN
ejde-397	1028	6	>	>	X
ejde-397	1028	7	0	0	PUNCT
ejde-397	1029	1	and	and	CCONJ
ejde-397	1029	2	rp	rp	NOUN
ejde-397	1029	3	∈	∈	PROPN
ejde-397	1029	4	~	~	PUNCT
ejde-397	1029	5	such	such	ADJ
ejde-397	1029	6	that	that	SCONJ
ejde-397	1029	7	p	p	NOUN
ejde-397	1029	8	(	(	PUNCT
ejde-397	1029	9	l!−1(λ−	l!−1(λ−	NUM
ejde-397	1029	10	ω)l+1	ω)l+1	X
ejde-397	1030	1	d	d	X
ejde-397	1030	2	l	l	NOUN
ejde-397	1030	3	dλl	dλl	VERB
ejde-397	1030	4	h(λ)x	h(λ)x	PROPN
ejde-397	1030	5	)	)	PUNCT
ejde-397	1030	6	≤	≤	NUM
ejde-397	1030	7	cprp(x	cprp(x	NOUN
ejde-397	1030	8	)	)	PUNCT
ejde-397	1030	9	,	,	PUNCT
ejde-397	1030	10	x	x	PUNCT
ejde-397	1030	11	∈	∈	NOUN
ejde-397	1030	12	x	x	X
ejde-397	1030	13	,	,	PUNCT
ejde-397	1030	14	λ	λ	PROPN
ejde-397	1030	15	∈	∈	PROPN
ejde-397	1030	16	d(h	d(h	PROPN
ejde-397	1030	17	)	)	PUNCT
ejde-397	1030	18	,	,	PUNCT
ejde-397	1030	19	l	l	PROPN
ejde-397	1030	20	∈	∈	PROPN
ejde-397	1030	21	n0	n0	PROPN
ejde-397	1030	22	.	.	PUNCT
ejde-397	1031	1	(	(	PUNCT
ejde-397	1031	2	5.17	5.17	NUM
ejde-397	1031	3	)	)	PUNCT
ejde-397	1031	4	then	then	ADV
ejde-397	1031	5	,	,	PUNCT
ejde-397	1031	6	for	for	ADP
ejde-397	1031	7	every	every	DET
ejde-397	1031	8	r	r	NOUN
ejde-397	1031	9	∈	∈	PROPN
ejde-397	1031	10	(	(	PUNCT
ejde-397	1031	11	0	0	NUM
ejde-397	1031	12	,	,	PUNCT
ejde-397	1031	13	1	1	NUM
ejde-397	1031	14	]	]	PUNCT
ejde-397	1031	15	,	,	PUNCT
ejde-397	1031	16	the	the	DET
ejde-397	1031	17	operator	operator	NOUN
ejde-397	1031	18	a	a	PRON
ejde-397	1031	19	is	be	AUX
ejde-397	1031	20	a	a	DET
ejde-397	1031	21	subgenerator	subgenerator	NOUN
ejde-397	1031	22	of	of	ADP
ejde-397	1031	23	a	a	DET
ejde-397	1031	24	global	global	ADJ
ejde-397	1031	25	(	(	PUNCT
ejde-397	1031	26	a	a	PROPN
ejde-397	1031	27	,	,	PUNCT
ejde-397	1031	28	k	k	PROPN
ejde-397	1031	29	∗gr)regularized	∗gr)regularize	VERB
ejde-397	1031	30	c	c	NOUN
ejde-397	1031	31	-	-	PUNCT
ejde-397	1031	32	resolvent	resolvent	ADJ
ejde-397	1031	33	family	family	NOUN
ejde-397	1031	34	(	(	PUNCT
ejde-397	1031	35	rr(t))t≥0	rr(t))t≥0	PROPN
ejde-397	1031	36	satisfying	satisfy	VERB
ejde-397	1031	37	that	that	SCONJ
ejde-397	1031	38	,	,	PUNCT
ejde-397	1031	39	for	for	ADP
ejde-397	1031	40	every	every	DET
ejde-397	1031	41	p	p	PROPN
ejde-397	1031	42	∈	∈	PROPN
ejde-397	1031	43	~	~	PUNCT
ejde-397	1031	44	,	,	PUNCT
ejde-397	1031	45	p	p	X
ejde-397	1031	46	(	(	PUNCT
ejde-397	1031	47	rr(t+	rr(t+	PROPN
ejde-397	1031	48	h)x−rr(t)x	h)x−rr(t)x	PROPN
ejde-397	1031	49	)	)	PUNCT
ejde-397	1031	50	≤	≤	NOUN
ejde-397	1031	51	2cprp(x	2cprp(x	NUM
ejde-397	1031	52	)	)	PUNCT
ejde-397	1031	53	rγ(r	rγ(r	NOUN
ejde-397	1031	54	)	)	PUNCT
ejde-397	1031	55	max	max	PROPN
ejde-397	1031	56	(	(	PUNCT
ejde-397	1031	57	eω(t+h	eω(t+h	PROPN
ejde-397	1031	58	)	)	PUNCT
ejde-397	1031	59	,	,	PUNCT
ejde-397	1031	60	1	1	X
ejde-397	1031	61	)	)	PUNCT
ejde-397	1031	62	hr	hr	NOUN
ejde-397	1031	63	,	,	PUNCT
ejde-397	1031	64	t	t	PROPN
ejde-397	1031	65	≥	≥	PROPN
ejde-397	1031	66	0	0	NUM
ejde-397	1031	67	,	,	PUNCT
ejde-397	1031	68	h	h	NOUN
ejde-397	1031	69	>	>	X
ejde-397	1031	70	0	0	NUM
ejde-397	1031	71	,	,	PUNCT
ejde-397	1031	72	x	x	X
ejde-397	1031	73	∈	∈	NOUN
ejde-397	1031	74	x	x	NOUN
ejde-397	1031	75	,	,	PUNCT
ejde-397	1031	76	and	and	CCONJ
ejde-397	1031	77	that	that	SCONJ
ejde-397	1031	78	,	,	PUNCT
ejde-397	1031	79	for	for	ADP
ejde-397	1031	80	every	every	DET
ejde-397	1031	81	p	p	NOUN
ejde-397	1031	82	∈	∈	PROPN
ejde-397	1031	83	~	~	PUNCT
ejde-397	1031	84	and	and	CCONJ
ejde-397	1031	85	b	b	X
ejde-397	1031	86	∈	∈	PROPN
ejde-397	1031	87	b	b	PROPN
ejde-397	1031	88	,	,	PUNCT
ejde-397	1031	89	the	the	DET
ejde-397	1031	90	mapping	mapping	NOUN
ejde-397	1031	91	t	t	NOUN
ejde-397	1031	92	7→	7→	NUM
ejde-397	1031	93	pb(rr(t	pb(rr(t	NOUN
ejde-397	1031	94	)	)	PUNCT
ejde-397	1031	95	)	)	PUNCT
ejde-397	1031	96	,	,	PUNCT
ejde-397	1031	97	t	t	PROPN
ejde-397	1031	98	≥	≥	PROPN
ejde-397	1031	99	0	0	NUM
ejde-397	1031	100	is	be	AUX
ejde-397	1031	101	locally	locally	ADV
ejde-397	1031	102	hölder	hölder	NOUN
ejde-397	1031	103	continuous	continuous	ADJ
ejde-397	1031	104	with	with	ADP
ejde-397	1031	105	exponent	exponent	ADJ
ejde-397	1031	106	r	r	NOUN
ejde-397	1031	107	;	;	PUNCT
ejde-397	1031	108	furthermore	furthermore	ADV
ejde-397	1031	109	,	,	PUNCT
ejde-397	1031	110	(	(	PUNCT
ejde-397	1031	111	rr(t))t≥0	rr(t))t≥0	PROPN
ejde-397	1031	112	is	be	AUX
ejde-397	1031	113	a	a	DET
ejde-397	1031	114	mild	mild	ADJ
ejde-397	1031	115	(	(	PUNCT
ejde-397	1031	116	a	a	X
ejde-397	1031	117	,	,	PUNCT
ejde-397	1031	118	k	k	PROPN
ejde-397	1031	119	∗	∗	NOUN
ejde-397	1031	120	gr)regularized	gr)regularize	VERB
ejde-397	1031	121	c	c	NOUN
ejde-397	1031	122	-	-	PUNCT
ejde-397	1031	123	existence	existence	NOUN
ejde-397	1031	124	family	family	NOUN
ejde-397	1031	125	having	have	VERB
ejde-397	1031	126	a	a	DET
ejde-397	1031	127	as	as	ADP
ejde-397	1031	128	subgenerator	subgenerator	NOUN
ejde-397	1031	129	,	,	PUNCT
ejde-397	1031	130	and	and	CCONJ
ejde-397	1031	131	the	the	DET
ejde-397	1031	132	following	follow	VERB
ejde-397	1031	133	holds	hold	VERB
ejde-397	1031	134	:	:	PUNCT
ejde-397	1031	135	(	(	PUNCT
ejde-397	1031	136	i	i	NOUN
ejde-397	1031	137	)	)	PUNCT
ejde-397	1031	138	suppose	suppose	VERB
ejde-397	1031	139	that	that	SCONJ
ejde-397	1031	140	a	a	PRON
ejde-397	1031	141	is	be	AUX
ejde-397	1031	142	densely	densely	ADV
ejde-397	1031	143	defined	define	VERB
ejde-397	1031	144	.	.	PUNCT
ejde-397	1032	1	then	then	ADV
ejde-397	1032	2	a	a	PRON
ejde-397	1032	3	is	be	AUX
ejde-397	1032	4	a	a	DET
ejde-397	1032	5	subgenerator	subgenerator	NOUN
ejde-397	1032	6	of	of	ADP
ejde-397	1032	7	a	a	DET
ejde-397	1032	8	global	global	ADJ
ejde-397	1032	9	(	(	PUNCT
ejde-397	1032	10	a	a	PRON
ejde-397	1032	11	,	,	PUNCT
ejde-397	1032	12	k)-regularized	k)-regularize	VERB
ejde-397	1032	13	c	c	NOUN
ejde-397	1032	14	-	-	PUNCT
ejde-397	1032	15	resolvent	resolvent	ADJ
ejde-397	1032	16	family	family	NOUN
ejde-397	1032	17	(	(	PUNCT
ejde-397	1032	18	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	1032	19	⊆	⊆	NUM
ejde-397	1032	20	l(x	l(x	PROPN
ejde-397	1032	21	)	)	PUNCT
ejde-397	1032	22	satisfying	satisfy	VERB
ejde-397	1032	23	that	that	SCONJ
ejde-397	1032	24	the	the	DET
ejde-397	1032	25	family	family	NOUN
ejde-397	1032	26	{	{	PUNCT
ejde-397	1032	27	e−ωtr(t	e−ωtr(t	NUM
ejde-397	1032	28	)	)	PUNCT
ejde-397	1032	29	:	:	PUNCT
ejde-397	1032	30	t	t	X
ejde-397	1032	31	≥	≥	NUM
ejde-397	1032	32	0	0	NUM
ejde-397	1032	33	}	}	PUNCT
ejde-397	1032	34	⊆	⊆	NUM
ejde-397	1032	35	l(x	l(x	PROPN
ejde-397	1032	36	)	)	PUNCT
ejde-397	1032	37	is	be	AUX
ejde-397	1032	38	equicontinuous	equicontinuous	ADJ
ejde-397	1032	39	.	.	PUNCT
ejde-397	1033	1	furthermore	furthermore	ADV
ejde-397	1033	2	,	,	PUNCT
ejde-397	1033	3	(	(	PUNCT
ejde-397	1033	4	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	1033	5	is	be	AUX
ejde-397	1033	6	a	a	DET
ejde-397	1033	7	mild	mild	ADJ
ejde-397	1033	8	(	(	PUNCT
ejde-397	1033	9	a	a	PRON
ejde-397	1033	10	,	,	PUNCT
ejde-397	1033	11	k)-regularized	k)-regularize	VERB
ejde-397	1033	12	c	c	NOUN
ejde-397	1033	13	-	-	PUNCT
ejde-397	1033	14	existence	existence	NOUN
ejde-397	1033	15	family	family	NOUN
ejde-397	1033	16	having	have	VERB
ejde-397	1033	17	a	a	DET
ejde-397	1033	18	as	as	ADP
ejde-397	1033	19	subgenerator	subgenerator	NOUN
ejde-397	1033	20	.	.	PUNCT
ejde-397	1034	1	(	(	PUNCT
ejde-397	1034	2	ii	ii	NOUN
ejde-397	1034	3	)	)	PUNCT
ejde-397	1034	4	suppose	suppose	VERB
ejde-397	1034	5	that	that	SCONJ
ejde-397	1034	6	k(0	k(0	PROPN
ejde-397	1034	7	)	)	PUNCT
ejde-397	1034	8	6=	6=	ADP
ejde-397	1034	9	0	0	X
ejde-397	1034	10	.	.	PUNCT
ejde-397	1035	1	then	then	ADV
ejde-397	1035	2	the	the	DET
ejde-397	1035	3	operator	operator	NOUN
ejde-397	1035	4	c	c	NOUN
ejde-397	1035	5	′	′	NOUN
ejde-397	1035	6	:	:	PUNCT
ejde-397	1036	1	=	=	SYM
ejde-397	1036	2	c|d(a	c|d(a	ADJ
ejde-397	1036	3	)	)	PUNCT
ejde-397	1036	4	∈	∈	PROPN
ejde-397	1036	5	l(d(a	l(d(a	PROPN
ejde-397	1036	6	)	)	PUNCT
ejde-397	1036	7	)	)	PUNCT
ejde-397	1036	8	is	be	AUX
ejde-397	1036	9	injective	injective	ADJ
ejde-397	1036	10	,	,	PUNCT
ejde-397	1036	11	a0	a0	PROPN
ejde-397	1036	12	is	be	AUX
ejde-397	1036	13	a	a	DET
ejde-397	1036	14	closed	closed	ADJ
ejde-397	1036	15	subspace	subspace	NOUN
ejde-397	1036	16	of	of	ADP
ejde-397	1036	17	x	x	PRON
ejde-397	1036	18	,	,	PUNCT
ejde-397	1036	19	d(a)∩a0	d(a)∩a0	PROPN
ejde-397	1036	20	=	=	SYM
ejde-397	1036	21	{	{	PUNCT
ejde-397	1036	22	0	0	NUM
ejde-397	1036	23	}	}	PUNCT
ejde-397	1036	24	,	,	PUNCT
ejde-397	1036	25	and	and	CCONJ
ejde-397	1036	26	we	we	PRON
ejde-397	1036	27	have	have	VERB
ejde-397	1036	28	the	the	DET
ejde-397	1036	29	following	following	NOUN
ejde-397	1036	30	:	:	PUNCT
ejde-397	1036	31	define	define	VERB
ejde-397	1036	32	the	the	DET
ejde-397	1036	33	operator	operator	NOUN
ejde-397	1036	34	a	a	DET
ejde-397	1036	35	:	:	PUNCT
ejde-397	1036	36	d(a	d(a	PROPN
ejde-397	1036	37	)	)	PUNCT
ejde-397	1036	38	⊆	⊆	NUM
ejde-397	1036	39	d(a)→	d(a)→	PUNCT
ejde-397	1036	40	d(a	d(a	PROPN
ejde-397	1036	41	)	)	PUNCT
ejde-397	1036	42	by	by	ADP
ejde-397	1036	43	d(a	d(a	PROPN
ejde-397	1036	44	)	)	PUNCT
ejde-397	1036	45	:	:	PUNCT
ejde-397	1037	1	=	=	SYM
ejde-397	1037	2	{	{	PUNCT
ejde-397	1037	3	x	x	PUNCT
ejde-397	1037	4	∈	∈	PROPN
ejde-397	1037	5	d(a	d(a	PROPN
ejde-397	1037	6	)	)	PUNCT
ejde-397	1037	7	:	:	PUNCT
ejde-397	1038	1	cx	cx	X
ejde-397	1038	2	=	=	PUNCT
ejde-397	1038	3	(	(	PUNCT
ejde-397	1038	4	λ0	λ0	NOUN
ejde-397	1038	5	−a	−a	NOUN
ejde-397	1038	6	)	)	PUNCT
ejde-397	1038	7	−1	−1	NOUN
ejde-397	1038	8	cy	cy	NOUN
ejde-397	1038	9	for	for	ADP
ejde-397	1038	10	some	some	DET
ejde-397	1038	11	y	y	PROPN
ejde-397	1038	12	∈	∈	PROPN
ejde-397	1038	13	d(a	d(a	PROPN
ejde-397	1038	14	)	)	PUNCT
ejde-397	1038	15	}	}	PUNCT
ejde-397	1038	16	and	and	CCONJ
ejde-397	1038	17	ax	ax	NOUN
ejde-397	1038	18	:	:	PUNCT
ejde-397	1038	19	=	=	SYM
ejde-397	1039	1	c−1acx	c−1acx	X
ejde-397	1039	2	,	,	PUNCT
ejde-397	1039	3	x	x	PROPN
ejde-397	1039	4	∈	∈	PROPN
ejde-397	1039	5	d(a	d(a	PROPN
ejde-397	1039	6	)	)	PUNCT
ejde-397	1039	7	.	.	PUNCT
ejde-397	1040	1	then	then	ADV
ejde-397	1040	2	a	a	PRON
ejde-397	1040	3	is	be	AUX
ejde-397	1040	4	a	a	DET
ejde-397	1040	5	well	well	ADV
ejde-397	1040	6	-	-	PUNCT
ejde-397	1040	7	defined	define	VERB
ejde-397	1040	8	single	single	ADV
ejde-397	1040	9	-	-	PUNCT
ejde-397	1040	10	valued	value	VERB
ejde-397	1040	11	closed	close	VERB
ejde-397	1040	12	linear	linear	ADJ
ejde-397	1040	13	operator	operator	NOUN
ejde-397	1040	14	in	in	ADP
ejde-397	1040	15	d(a	d(a	PROPN
ejde-397	1040	16	)	)	PUNCT
ejde-397	1040	17	,	,	PUNCT
ejde-397	1040	18	and	and	CCONJ
ejde-397	1040	19	moreover	moreover	ADV
ejde-397	1040	20	,	,	PUNCT
ejde-397	1040	21	a	a	PRON
ejde-397	1040	22	is	be	AUX
ejde-397	1040	23	the	the	DET
ejde-397	1040	24	integral	integral	ADJ
ejde-397	1040	25	generator	generator	NOUN
ejde-397	1040	26	of	of	ADP
ejde-397	1040	27	a	a	DET
ejde-397	1040	28	global	global	ADJ
ejde-397	1040	29	(	(	PUNCT
ejde-397	1040	30	a	a	PRON
ejde-397	1040	31	,	,	PUNCT
ejde-397	1040	32	k)-regularized	k)-regularize	VERB
ejde-397	1040	33	c	c	PROPN
ejde-397	1040	34	′-resolvent	′-resolvent	PROPN
ejde-397	1040	35	family	family	NOUN
ejde-397	1040	36	(	(	PUNCT
ejde-397	1040	37	s(t))t≥0	s(t))t≥0	PROPN
ejde-397	1040	38	⊆	⊆	NUM
ejde-397	1040	39	l(d(a	l(d(a	PROPN
ejde-397	1040	40	)	)	PUNCT
ejde-397	1040	41	)	)	PUNCT
ejde-397	1041	1	satisfying	satisfy	VERB
ejde-397	1041	2	that	that	SCONJ
ejde-397	1041	3	the	the	DET
ejde-397	1041	4	family	family	NOUN
ejde-397	1041	5	{	{	PUNCT
ejde-397	1041	6	e−ωts(t	e−ωts(t	PROPN
ejde-397	1041	7	)	)	PUNCT
ejde-397	1041	8	:	:	PUNCT
ejde-397	1041	9	t	t	X
ejde-397	1041	10	≥	≥	NUM
ejde-397	1041	11	0	0	NUM
ejde-397	1041	12	}	}	PUNCT
ejde-397	1041	13	⊆	⊆	NUM
ejde-397	1041	14	l(d(a	l(d(a	NUM
ejde-397	1041	15	)	)	PUNCT
ejde-397	1041	16	)	)	PUNCT
ejde-397	1041	17	is	be	AUX
ejde-397	1041	18	equicontinuous	equicontinuous	ADJ
ejde-397	1041	19	,	,	PUNCT
ejde-397	1041	20	a	a	DET
ejde-397	1041	21	∫	∫	PROPN
ejde-397	1041	22	t	t	NOUN
ejde-397	1041	23	0	0	NUM
ejde-397	1041	24	a(t	a(t	NOUN
ejde-397	1041	25	−	−	NOUN
ejde-397	1041	26	s)s(s)x	s)s(s)x	NOUN
ejde-397	1041	27	ds	ds	NOUN
ejde-397	1041	28	=	=	SYM
ejde-397	1041	29	s(t)x	s(t)x	PROPN
ejde-397	1041	30	−	−	PROPN
ejde-397	1041	31	k(t)cx	k(t)cx	PROPN
ejde-397	1041	32	,	,	PUNCT
ejde-397	1041	33	t	t	PROPN
ejde-397	1041	34	∈	∈	PROPN
ejde-397	1042	1	[	[	X
ejde-397	1042	2	0	0	NUM
ejde-397	1042	3	,	,	PUNCT
ejde-397	1042	4	τ	τ	PROPN
ejde-397	1042	5	)	)	PUNCT
ejde-397	1042	6	,	,	PUNCT
ejde-397	1042	7	x	x	PROPN
ejde-397	1042	8	∈	∈	PROPN
ejde-397	1042	9	d(a	d(a	PROPN
ejde-397	1042	10	)	)	PUNCT
ejde-397	1042	11	and	and	CCONJ
ejde-397	1042	12	r1(t)x	r1(t)x	PROPN
ejde-397	1042	13	=	=	SYM
ejde-397	1042	14	∫	∫	PROPN
ejde-397	1042	15	t	t	PROPN
ejde-397	1042	16	0	0	PUNCT
ejde-397	1042	17	s(s)x	s(s)x	ADV
ejde-397	1042	18	ds	ds	PROPN
ejde-397	1042	19	,	,	PUNCT
ejde-397	1042	20	t	t	PROPN
ejde-397	1042	21	≥	≥	NUM
ejde-397	1042	22	0	0	NUM
ejde-397	1042	23	,	,	PUNCT
ejde-397	1042	24	x	x	PROPN
ejde-397	1042	25	∈	∈	PROPN
ejde-397	1042	26	d(a	d(a	PROPN
ejde-397	1042	27	)	)	PUNCT
ejde-397	1042	28	.	.	PUNCT
ejde-397	1043	1	in	in	ADP
ejde-397	1043	2	the	the	DET
ejde-397	1043	3	following	follow	VERB
ejde-397	1043	4	proposition	proposition	NOUN
ejde-397	1043	5	,	,	PUNCT
ejde-397	1043	6	which	which	PRON
ejde-397	1043	7	extends	extend	VERB
ejde-397	1043	8	the	the	DET
ejde-397	1043	9	assertions	assertion	NOUN
ejde-397	1043	10	of	of	ADP
ejde-397	1043	11	[	[	X
ejde-397	1043	12	59	59	NUM
ejde-397	1043	13	,	,	PUNCT
ejde-397	1043	14	proposition	proposition	NOUN
ejde-397	1043	15	2.5	2.5	NUM
ejde-397	1043	16	]	]	PUNCT
ejde-397	1043	17	and	and	CCONJ
ejde-397	1043	18	[	[	X
ejde-397	1043	19	36	36	NUM
ejde-397	1043	20	,	,	PUNCT
ejde-397	1043	21	proposition	proposition	NOUN
ejde-397	1043	22	2.1.4(ii	2.1.4(ii	NUM
ejde-397	1043	23	)	)	PUNCT
ejde-397	1043	24	]	]	PUNCT
ejde-397	1043	25	,	,	PUNCT
ejde-397	1043	26	we	we	PRON
ejde-397	1043	27	will	will	AUX
ejde-397	1043	28	reconsider	reconsider	VERB
ejde-397	1043	29	the	the	DET
ejde-397	1043	30	condition	condition	NOUN
ejde-397	1043	31	k(0	k(0	PROPN
ejde-397	1043	32	)	)	PUNCT
ejde-397	1043	33	6=	6=	ADP
ejde-397	1043	34	0	0	NUM
ejde-397	1043	35	from	from	ADP
ejde-397	1043	36	theorem	theorem	ADJ
ejde-397	1043	37	5.12	5.12	NUM
ejde-397	1043	38	once	once	ADV
ejde-397	1043	39	more	more	ADJ
ejde-397	1043	40	.	.	PUNCT
ejde-397	1044	1	a	a	DET
ejde-397	1044	2	straightforward	straightforward	ADJ
ejde-397	1044	3	proof	proof	NOUN
ejde-397	1044	4	is	be	AUX
ejde-397	1044	5	omitted	omit	VERB
ejde-397	1044	6	.	.	PUNCT
ejde-397	1045	1	proposition	proposition	NOUN
ejde-397	1045	2	5.13	5.13	NUM
ejde-397	1045	3	.	.	PUNCT
ejde-397	1046	1	let	let	VERB
ejde-397	1046	2	a	a	DET
ejde-397	1046	3	be	be	AUX
ejde-397	1046	4	a	a	DET
ejde-397	1046	5	closed	closed	ADJ
ejde-397	1046	6	subgenerator	subgenerator	NOUN
ejde-397	1046	7	of	of	ADP
ejde-397	1046	8	a	a	DET
ejde-397	1046	9	mild	mild	ADJ
ejde-397	1046	10	(	(	PUNCT
ejde-397	1046	11	a	a	DET
ejde-397	1046	12	,	,	PUNCT
ejde-397	1046	13	k)-regularized	k)-regularize	VERB
ejde-397	1046	14	c1	c1	NOUN
ejde-397	1046	15	-	-	PUNCT
ejde-397	1046	16	resolvent	resolvent	NOUN
ejde-397	1046	17	family	family	NOUN
ejde-397	1046	18	(	(	PUNCT
ejde-397	1046	19	r1(t))t∈[0,τ	r1(t))t∈[0,τ	PROPN
ejde-397	1046	20	)	)	PUNCT
ejde-397	1046	21	(	(	PUNCT
ejde-397	1046	22	mild	mild	ADJ
ejde-397	1046	23	(	(	PUNCT
ejde-397	1046	24	a	a	PRON
ejde-397	1046	25	,	,	PUNCT
ejde-397	1046	26	k)-regularized	k)-regularize	VERB
ejde-397	1046	27	c2	c2	PROPN
ejde-397	1046	28	-	-	PUNCT
ejde-397	1046	29	uniqueness	uniqueness	PROPN
ejde-397	1046	30	family	family	NOUN
ejde-397	1046	31	(	(	PUNCT
ejde-397	1046	32	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	1046	33	)	)	PUNCT
ejde-397	1046	34	;	;	PUNCT
ejde-397	1046	35	(	(	PUNCT
ejde-397	1046	36	a	a	DET
ejde-397	1046	37	,	,	PUNCT
ejde-397	1046	38	k)-regularized	k)-regularize	VERB
ejde-397	1046	39	c	c	NOUN
ejde-397	1046	40	-	-	PUNCT
ejde-397	1046	41	resolvent	resolvent	ADJ
ejde-397	1046	42	family	family	NOUN
ejde-397	1046	43	(	(	PUNCT
ejde-397	1046	44	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1046	45	)	)	PUNCT
ejde-397	1046	46	)	)	PUNCT
ejde-397	1046	47	.	.	PUNCT
ejde-397	1047	1	if	if	SCONJ
ejde-397	1047	2	k(t	k(t	PROPN
ejde-397	1047	3	)	)	PUNCT
ejde-397	1047	4	is	be	AUX
ejde-397	1047	5	absolutely	absolutely	ADV
ejde-397	1047	6	continuous	continuous	ADJ
ejde-397	1047	7	and	and	CCONJ
ejde-397	1047	8	k(0	k(0	PROPN
ejde-397	1047	9	)	)	PUNCT
ejde-397	1047	10	6=	6=	ADP
ejde-397	1047	11	0	0	NUM
ejde-397	1047	12	,	,	PUNCT
ejde-397	1047	13	then	then	ADV
ejde-397	1047	14	a	a	PRON
ejde-397	1047	15	is	be	AUX
ejde-397	1047	16	a	a	DET
ejde-397	1047	17	subgenerator	subgenerator	NOUN
ejde-397	1047	18	of	of	ADP
ejde-397	1047	19	a	a	DET
ejde-397	1047	20	mild	mild	ADJ
ejde-397	1047	21	(	(	PUNCT
ejde-397	1047	22	a	a	DET
ejde-397	1047	23	,	,	PUNCT
ejde-397	1047	24	g1)regularized	g1)regularize	VERB
ejde-397	1047	25	c1	c1	NOUN
ejde-397	1047	26	-	-	PUNCT
ejde-397	1047	27	resolvent	resolvent	NOUN
ejde-397	1047	28	family	family	NOUN
ejde-397	1047	29	(	(	PUNCT
ejde-397	1047	30	r1(t))t∈[0,τ	r1(t))t∈[0,τ	PROPN
ejde-397	1047	31	)	)	PUNCT
ejde-397	1047	32	(	(	PUNCT
ejde-397	1047	33	mild	mild	ADJ
ejde-397	1047	34	(	(	PUNCT
ejde-397	1047	35	a	a	PRON
ejde-397	1047	36	,	,	PUNCT
ejde-397	1047	37	g1)-regularized	g1)-regularize	VERB
ejde-397	1047	38	c2	c2	PROPN
ejde-397	1047	39	-	-	PUNCT
ejde-397	1047	40	uniqueness	uniqueness	PROPN
ejde-397	1047	41	family	family	NOUN
ejde-397	1047	42	(	(	PUNCT
ejde-397	1047	43	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	1047	44	)	)	PUNCT
ejde-397	1047	45	;	;	PUNCT
ejde-397	1047	46	(	(	PUNCT
ejde-397	1047	47	a	a	DET
ejde-397	1047	48	,	,	PUNCT
ejde-397	1047	49	g1)-regularized	g1)-regularized	ADJ
ejde-397	1047	50	c	c	X
ejde-397	1047	51	-	-	PUNCT
ejde-397	1047	52	resolvent	resolvent	ADJ
ejde-397	1047	53	family	family	NOUN
ejde-397	1047	54	(	(	PUNCT
ejde-397	1047	55	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1047	56	)	)	PUNCT
ejde-397	1047	57	)	)	PUNCT
ejde-397	1047	58	.	.	PUNCT
ejde-397	1048	1	now	now	ADV
ejde-397	1048	2	we	we	PRON
ejde-397	1048	3	would	would	AUX
ejde-397	1048	4	like	like	VERB
ejde-397	1048	5	to	to	PART
ejde-397	1048	6	present	present	VERB
ejde-397	1048	7	some	some	DET
ejde-397	1048	8	illustrative	illustrative	ADJ
ejde-397	1048	9	applications	application	NOUN
ejde-397	1048	10	of	of	ADP
ejde-397	1048	11	results	result	NOUN
ejde-397	1048	12	obtained	obtain	VERB
ejde-397	1048	13	so	so	ADV
ejde-397	1048	14	far	far	ADV
ejde-397	1048	15	.	.	PUNCT
ejde-397	1049	1	example	example	NOUN
ejde-397	1049	2	5.14	5.14	NUM
ejde-397	1049	3	.	.	PUNCT
ejde-397	1050	1	let	let	VERB
ejde-397	1050	2	α	α	PRON
ejde-397	1050	3	∈	∈	PROPN
ejde-397	1050	4	(	(	PUNCT
ejde-397	1050	5	0	0	NUM
ejde-397	1050	6	,	,	PUNCT
ejde-397	1050	7	1	1	NUM
ejde-397	1050	8	)	)	PUNCT
ejde-397	1050	9	.	.	PUNCT
ejde-397	1051	1	34	34	NUM
ejde-397	1051	2	m.	m.	NOUN
ejde-397	1051	3	kostić	kostić	NOUN
ejde-397	1051	4	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1051	5	(	(	PUNCT
ejde-397	1051	6	i	i	NOUN
ejde-397	1051	7	)	)	PUNCT
ejde-397	1051	8	(	(	PUNCT
ejde-397	1052	1	[	[	X
ejde-397	1052	2	17	17	NUM
ejde-397	1052	3	]	]	PUNCT
ejde-397	1052	4	)	)	PUNCT
ejde-397	1052	5	consider	consider	VERB
ejde-397	1052	6	the	the	DET
ejde-397	1052	7	following	follow	VERB
ejde-397	1052	8	time	time	NOUN
ejde-397	1052	9	-	-	PUNCT
ejde-397	1052	10	fractional	fractional	ADJ
ejde-397	1052	11	analogue	analogue	NOUN
ejde-397	1052	12	of	of	ADP
ejde-397	1052	13	homogeneous	homogeneous	ADJ
ejde-397	1052	14	counterpart	counterpart	NOUN
ejde-397	1052	15	of	of	ADP
ejde-397	1052	16	problem	problem	NOUN
ejde-397	1052	17	[	[	X
ejde-397	1052	18	17	17	NUM
ejde-397	1052	19	,	,	PUNCT
ejde-397	1052	20	example	example	NOUN
ejde-397	1052	21	2.1	2.1	NUM
ejde-397	1052	22	,	,	PUNCT
ejde-397	1052	23	(	(	PUNCT
ejde-397	1052	24	2.18	2.18	NUM
ejde-397	1052	25	)	)	PUNCT
ejde-397	1052	26	]	]	PUNCT
ejde-397	1052	27	:	:	PUNCT
ejde-397	1053	1	dα	dα	PROPN
ejde-397	1053	2	t	t	PROPN
ejde-397	1053	3	[	[	X
ejde-397	1053	4	m(x)vα(t	m(x)vα(t	PROPN
ejde-397	1053	5	,	,	PUNCT
ejde-397	1053	6	x	x	NOUN
ejde-397	1053	7	)	)	PUNCT
ejde-397	1053	8	]	]	PUNCT
ejde-397	1054	1	=	=	PUNCT
ejde-397	1054	2	−	−	NOUN
ejde-397	1054	3	∂	∂	NOUN
ejde-397	1054	4	∂x	∂x	PROPN
ejde-397	1054	5	vα(t	vα(t	NUM
ejde-397	1054	6	,	,	PUNCT
ejde-397	1054	7	x	x	NOUN
ejde-397	1054	8	)	)	PUNCT
ejde-397	1054	9	,	,	PUNCT
ejde-397	1054	10	t	t	PROPN
ejde-397	1054	11	≥	≥	NUM
ejde-397	1054	12	0	0	NUM
ejde-397	1054	13	,	,	PUNCT
ejde-397	1054	14	x	x	X
ejde-397	1054	15	∈	∈	NOUN
ejde-397	1054	16	r	r	NOUN
ejde-397	1054	17	;	;	PUNCT
ejde-397	1054	18	m(x)vα(0	m(x)vα(0	NOUN
ejde-397	1054	19	,	,	PUNCT
ejde-397	1054	20	x	x	X
ejde-397	1054	21	)	)	PUNCT
ejde-397	1054	22	=	=	SYM
ejde-397	1054	23	u0(x	u0(x	NUM
ejde-397	1054	24	)	)	PUNCT
ejde-397	1054	25	,	,	PUNCT
ejde-397	1054	26	x	x	PROPN
ejde-397	1054	27	∈	∈	PROPN
ejde-397	1054	28	r.	r.	PROPN
ejde-397	1054	29	(	(	PUNCT
ejde-397	1054	30	5.18	5.18	NUM
ejde-397	1054	31	)	)	PUNCT
ejde-397	1054	32	let	let	VERB
ejde-397	1054	33	x	x	SYM
ejde-397	1054	34	=	=	PUNCT
ejde-397	1054	35	y	y	NOUN
ejde-397	1054	36	:	:	PUNCT
ejde-397	1054	37	=	=	SYM
ejde-397	1054	38	l2(r	l2(r	NOUN
ejde-397	1054	39	)	)	PUNCT
ejde-397	1054	40	,	,	PUNCT
ejde-397	1054	41	and	and	CCONJ
ejde-397	1054	42	let	let	VERB
ejde-397	1054	43	the	the	DET
ejde-397	1054	44	operator	operator	NOUN
ejde-397	1054	45	a	a	DET
ejde-397	1054	46	:	:	PUNCT
ejde-397	1054	47	=	=	SYM
ejde-397	1054	48	−d	−d	PROPN
ejde-397	1054	49	/	/	SYM
ejde-397	1054	50	dx	dx	PROPN
ejde-397	1054	51	act	act	VERB
ejde-397	1054	52	on	on	ADP
ejde-397	1054	53	x	x	PUNCT
ejde-397	1054	54	with	with	ADP
ejde-397	1054	55	its	its	PRON
ejde-397	1054	56	maximal	maximal	ADJ
ejde-397	1054	57	distributional	distributional	ADJ
ejde-397	1054	58	domain	domain	NOUN
ejde-397	1054	59	h1(r	h1(r	NOUN
ejde-397	1054	60	)	)	PUNCT
ejde-397	1054	61	.	.	PUNCT
ejde-397	1055	1	(	(	PUNCT
ejde-397	1055	2	a	a	X
ejde-397	1055	3	)	)	PUNCT
ejde-397	1055	4	suppose	suppose	VERB
ejde-397	1055	5	first	first	ADV
ejde-397	1055	6	that	that	SCONJ
ejde-397	1055	7	(	(	PUNCT
ejde-397	1055	8	bf)(x	bf)(x	PROPN
ejde-397	1055	9	)	)	PUNCT
ejde-397	1055	10	:	:	PUNCT
ejde-397	1055	11	=	=	SYM
ejde-397	1055	12	χ(−∞,a)∩(b,∞)(x)f(x	χ(−∞,a)∩(b,∞)(x)f(x	PROPN
ejde-397	1055	13	)	)	PUNCT
ejde-397	1055	14	,	,	PUNCT
ejde-397	1055	15	x	x	PUNCT
ejde-397	1055	16	∈	∈	NOUN
ejde-397	1055	17	r	r	NOUN
ejde-397	1055	18	(	(	PUNCT
ejde-397	1055	19	f	f	PROPN
ejde-397	1055	20	∈	∈	PROPN
ejde-397	1055	21	x	x	NOUN
ejde-397	1055	22	)	)	PUNCT
ejde-397	1055	23	,	,	PUNCT
ejde-397	1055	24	where	where	SCONJ
ejde-397	1055	25	−∞	−∞	ADP
ejde-397	1055	26	<	<	X
ejde-397	1055	27	a	a	DET
ejde-397	1055	28	<	<	X
ejde-397	1055	29	b	b	X
ejde-397	1055	30	<	<	X
ejde-397	1055	31	∞.	∞.	PROPN
ejde-397	1055	32	then	then	ADV
ejde-397	1055	33	b	b	PROPN
ejde-397	1055	34	∈	∈	PROPN
ejde-397	1055	35	l(x	l(x	PROPN
ejde-397	1055	36	)	)	PUNCT
ejde-397	1055	37	,	,	PUNCT
ejde-397	1055	38	b	b	X
ejde-397	1055	39	=	=	SYM
ejde-397	1055	40	b∗	b∗	ADJ
ejde-397	1055	41	,	,	PUNCT
ejde-397	1055	42	b2	b2	NOUN
ejde-397	1055	43	=	=	SYM
ejde-397	1055	44	b	b	PROPN
ejde-397	1055	45	and	and	CCONJ
ejde-397	1055	46	(	(	PUNCT
ejde-397	1055	47	5.18	5.18	NUM
ejde-397	1055	48	)	)	PUNCT
ejde-397	1055	49	is	be	AUX
ejde-397	1055	50	formulated	formulate	VERB
ejde-397	1055	51	in	in	ADP
ejde-397	1055	52	x	x	PUNCT
ejde-397	1055	53	in	in	ADP
ejde-397	1055	54	the	the	DET
ejde-397	1055	55	abstract	abstract	ADJ
ejde-397	1055	56	form	form	NOUN
ejde-397	1055	57	b∗dα	b∗dα	PROPN
ejde-397	1055	58	t	t	NOUN
ejde-397	1055	59	bvα(t	bvα(t	PROPN
ejde-397	1055	60	)	)	PUNCT
ejde-397	1055	61	=	=	PUNCT
ejde-397	1056	1	dα	dα	NOUN
ejde-397	1056	2	t	t	NOUN
ejde-397	1056	3	bvα(t	bvα(t	PROPN
ejde-397	1056	4	)	)	PUNCT
ejde-397	1056	5	=	=	SYM
ejde-397	1056	6	avα(t	avα(t	PROPN
ejde-397	1056	7	)	)	PUNCT
ejde-397	1056	8	,	,	PUNCT
ejde-397	1056	9	t	t	PROPN
ejde-397	1056	10	≥	≥	NUM
ejde-397	1056	11	0	0	NUM
ejde-397	1056	12	;	;	PUNCT
ejde-397	1056	13	bvα(0	bvα(0	NUM
ejde-397	1056	14	)	)	PUNCT
ejde-397	1057	1	=	=	PUNCT
ejde-397	1057	2	u0	u0	ADJ
ejde-397	1057	3	.	.	PUNCT
ejde-397	1058	1	(	(	PUNCT
ejde-397	1058	2	5.19	5.19	NUM
ejde-397	1058	3	)	)	PUNCT
ejde-397	1058	4	further	far	ADV
ejde-397	1058	5	on	on	ADV
ejde-397	1058	6	,	,	PUNCT
ejde-397	1058	7	the	the	DET
ejde-397	1058	8	multivalued	multivalue	VERB
ejde-397	1058	9	linear	linear	ADJ
ejde-397	1058	10	operator	operator	NOUN
ejde-397	1058	11	a	a	PRON
ejde-397	1058	12	:	:	PUNCT
ejde-397	1058	13	=	=	SYM
ejde-397	1058	14	(	(	PUNCT
ejde-397	1058	15	b∗)−1ab−1	b∗)−1ab−1	PROPN
ejde-397	1058	16	is	be	AUX
ejde-397	1058	17	maximal	maximal	ADJ
ejde-397	1058	18	dissipative	dissipative	NOUN
ejde-397	1058	19	in	in	ADP
ejde-397	1058	20	the	the	DET
ejde-397	1058	21	sense	sense	NOUN
ejde-397	1058	22	of	of	ADP
ejde-397	1058	23	[	[	X
ejde-397	1058	24	17	17	NUM
ejde-397	1058	25	,	,	PUNCT
ejde-397	1058	26	definition	definition	NOUN
ejde-397	1058	27	,	,	PUNCT
ejde-397	1058	28	p.	p.	NOUN
ejde-397	1058	29	35	35	NUM
ejde-397	1058	30	]	]	PUNCT
ejde-397	1058	31	and	and	CCONJ
ejde-397	1058	32	‖(λ	‖(λ	NOUN
ejde-397	1059	1	−	−	NOUN
ejde-397	1060	1	a)−1‖	a)−1‖	VERB
ejde-397	1060	2	≤	≤	NUM
ejde-397	1061	1	λ−1	λ−1	PROPN
ejde-397	1061	2	,	,	PUNCT
ejde-397	1061	3	λ	λ	X
ejde-397	1061	4	>	>	X
ejde-397	1061	5	0	0	NUM
ejde-397	1061	6	.	.	PUNCT
ejde-397	1062	1	by	by	ADP
ejde-397	1062	2	the	the	DET
ejde-397	1062	3	foregoing	foregoing	NOUN
ejde-397	1062	4	,	,	PUNCT
ejde-397	1062	5	we	we	PRON
ejde-397	1062	6	know	know	VERB
ejde-397	1062	7	that	that	SCONJ
ejde-397	1062	8	the	the	DET
ejde-397	1062	9	operator	operator	NOUN
ejde-397	1062	10	a	a	PRON
ejde-397	1062	11	is	be	AUX
ejde-397	1062	12	single	single	ADV
ejde-397	1062	13	-	-	PUNCT
ejde-397	1062	14	valued	value	VERB
ejde-397	1062	15	on	on	ADP
ejde-397	1062	16	d(a	d(a	PROPN
ejde-397	1062	17	)	)	PUNCT
ejde-397	1062	18	;	;	PUNCT
ejde-397	1062	19	with	with	ADP
ejde-397	1062	20	a	a	DET
ejde-397	1062	21	little	little	ADJ
ejde-397	1062	22	abuse	abuse	NOUN
ejde-397	1062	23	of	of	ADP
ejde-397	1062	24	notation	notation	NOUN
ejde-397	1062	25	,	,	PUNCT
ejde-397	1062	26	we	we	PRON
ejde-397	1062	27	will	will	AUX
ejde-397	1062	28	denote	denote	VERB
ejde-397	1062	29	by	by	ADP
ejde-397	1062	30	t	t	PROPN
ejde-397	1062	31	⊆	⊆	NUM
ejde-397	1062	32	a	a	DET
ejde-397	1062	33	the	the	DET
ejde-397	1062	34	single	single	ADV
ejde-397	1062	35	-	-	PUNCT
ejde-397	1062	36	valued	value	VERB
ejde-397	1062	37	linear	linear	NOUN
ejde-397	1062	38	operator	operator	NOUN
ejde-397	1062	39	which	which	PRON
ejde-397	1062	40	generates	generate	VERB
ejde-397	1062	41	a	a	DET
ejde-397	1062	42	bounded	bounded	ADJ
ejde-397	1062	43	strongly	strongly	ADV
ejde-397	1062	44	continuous	continuous	ADJ
ejde-397	1062	45	semigroup	semigroup	NOUN
ejde-397	1062	46	(	(	PUNCT
ejde-397	1062	47	t	t	PROPN
ejde-397	1062	48	(	(	PUNCT
ejde-397	1062	49	t))t≥0	t))t≥0	NOUN
ejde-397	1062	50	on	on	ADP
ejde-397	1062	51	d(a	d(a	PROPN
ejde-397	1062	52	)	)	PUNCT
ejde-397	1062	53	(	(	PUNCT
ejde-397	1062	54	cf	cf	NOUN
ejde-397	1062	55	.	.	PUNCT
ejde-397	1062	56	theorem	theorem	PROPN
ejde-397	1062	57	5.12(ii	5.12(ii	NUM
ejde-397	1062	58	)	)	PUNCT
ejde-397	1062	59	,	,	PUNCT
ejde-397	1062	60	where	where	SCONJ
ejde-397	1062	61	we	we	PRON
ejde-397	1062	62	have	have	AUX
ejde-397	1062	63	denoted	denote	VERB
ejde-397	1062	64	this	this	DET
ejde-397	1062	65	operator	operator	NOUN
ejde-397	1062	66	by	by	ADP
ejde-397	1062	67	a	a	PRON
ejde-397	1062	68	)	)	PUNCT
ejde-397	1062	69	.	.	PUNCT
ejde-397	1063	1	using	use	VERB
ejde-397	1063	2	[	[	X
ejde-397	1063	3	32	32	NUM
ejde-397	1063	4	,	,	PUNCT
ejde-397	1063	5	theorem	theorem	ADJ
ejde-397	1063	6	3.6(a	3.6(a	NUM
ejde-397	1063	7	)	)	PUNCT
ejde-397	1063	8	]	]	PUNCT
ejde-397	1063	9	and	and	CCONJ
ejde-397	1063	10	the	the	DET
ejde-397	1063	11	consideration	consideration	NOUN
ejde-397	1063	12	from	from	ADP
ejde-397	1063	13	the	the	DET
ejde-397	1063	14	paragraph	paragraph	NOUN
ejde-397	1063	15	directly	directly	ADV
ejde-397	1063	16	preceding	precede	VERB
ejde-397	1063	17	the	the	DET
ejde-397	1063	18	formulation	formulation	NOUN
ejde-397	1063	19	of	of	ADP
ejde-397	1063	20	[	[	X
ejde-397	1063	21	17	17	NUM
ejde-397	1063	22	,	,	PUNCT
ejde-397	1063	23	theorem	theorem	VERB
ejde-397	1063	24	2.8	2.8	NUM
ejde-397	1063	25	]	]	PUNCT
ejde-397	1063	26	,	,	PUNCT
ejde-397	1063	27	it	it	PRON
ejde-397	1063	28	readily	readily	ADV
ejde-397	1063	29	follows	follow	VERB
ejde-397	1063	30	that	that	SCONJ
ejde-397	1063	31	d(t	d(t	PROPN
ejde-397	1063	32	)	)	PUNCT
ejde-397	1064	1	=	=	SYM
ejde-397	1064	2	d(a	d(a	PROPN
ejde-397	1064	3	)	)	PUNCT
ejde-397	1064	4	.	.	PUNCT
ejde-397	1064	5	suppose	suppose	VERB
ejde-397	1064	6	now	now	ADV
ejde-397	1064	7	that	that	SCONJ
ejde-397	1064	8	u0	u0	ADJ
ejde-397	1064	9	=	=	PROPN
ejde-397	1064	10	bv0	bv0	PROPN
ejde-397	1064	11	,	,	PUNCT
ejde-397	1064	12	where	where	SCONJ
ejde-397	1064	13	v0	v0	PROPN
ejde-397	1064	14	∈	∈	PROPN
ejde-397	1064	15	d(a	d(a	PROPN
ejde-397	1064	16	)	)	PUNCT
ejde-397	1064	17	and	and	CCONJ
ejde-397	1064	18	av0	av0	PRON
ejde-397	1064	19	∈	∈	PROPN
ejde-397	1064	20	r(b∗	r(b∗	NOUN
ejde-397	1064	21	)	)	PUNCT
ejde-397	1064	22	,	,	PUNCT
ejde-397	1064	23	i.e.	i.e.	X
ejde-397	1064	24	,	,	PUNCT
ejde-397	1064	25	that	that	SCONJ
ejde-397	1064	26	u0	u0	PROPN
ejde-397	1064	27	∈	∈	PROPN
ejde-397	1064	28	d(a	d(a	PROPN
ejde-397	1064	29	)	)	PUNCT
ejde-397	1064	30	=	=	SYM
ejde-397	1064	31	d(t	d(t	PROPN
ejde-397	1064	32	)	)	PUNCT
ejde-397	1064	33	(	(	PUNCT
ejde-397	1064	34	cf	cf	X
ejde-397	1064	35	.	.	PUNCT
ejde-397	1065	1	the	the	DET
ejde-397	1065	2	proof	proof	NOUN
ejde-397	1065	3	of	of	ADP
ejde-397	1065	4	[	[	X
ejde-397	1065	5	17	17	NUM
ejde-397	1065	6	,	,	PUNCT
ejde-397	1065	7	theorem	theorem	VERB
ejde-397	1065	8	2.10	2.10	NUM
ejde-397	1065	9	]	]	PUNCT
ejde-397	1065	10	)	)	PUNCT
ejde-397	1065	11	.	.	PUNCT
ejde-397	1066	1	from	from	ADP
ejde-397	1066	2	[	[	X
ejde-397	1066	3	17	17	NUM
ejde-397	1066	4	,	,	PUNCT
ejde-397	1066	5	theorem	theorem	VERB
ejde-397	1066	6	2.8	2.8	NUM
ejde-397	1066	7	,	,	PUNCT
ejde-397	1066	8	theorem	theorem	VERB
ejde-397	1066	9	2.10	2.10	NUM
ejde-397	1066	10	]	]	PUNCT
ejde-397	1066	11	,	,	PUNCT
ejde-397	1066	12	the	the	DET
ejde-397	1066	13	problem	problem	NOUN
ejde-397	1066	14	(	(	PUNCT
ejde-397	1066	15	5.19	5.19	NUM
ejde-397	1066	16	)	)	PUNCT
ejde-397	1066	17	,	,	PUNCT
ejde-397	1066	18	with	with	ADP
ejde-397	1066	19	α	α	NOUN
ejde-397	1066	20	=	=	SYM
ejde-397	1066	21	1	1	NUM
ejde-397	1066	22	,	,	PUNCT
ejde-397	1066	23	has	have	VERB
ejde-397	1066	24	a	a	DET
ejde-397	1066	25	unique	unique	ADJ
ejde-397	1066	26	solution	solution	NOUN
ejde-397	1066	27	v1(t	v1(t	PART
ejde-397	1066	28	)	)	PUNCT
ejde-397	1066	29	satisfying	satisfy	VERB
ejde-397	1066	30	bv1(t	bv1(t	PROPN
ejde-397	1066	31	)	)	PUNCT
ejde-397	1067	1	=	=	SYM
ejde-397	1067	2	t	t	PROPN
ejde-397	1067	3	(	(	PUNCT
ejde-397	1067	4	t)u0	t)u0	ADV
ejde-397	1067	5	;	;	PUNCT
ejde-397	1067	6	moreover	moreover	ADV
ejde-397	1067	7	,	,	PUNCT
ejde-397	1067	8	(	(	PUNCT
ejde-397	1067	9	d	d	X
ejde-397	1067	10	/	/	SYM
ejde-397	1067	11	dt)bv1(t	dt)bv1(t	PROPN
ejde-397	1067	12	)	)	PUNCT
ejde-397	1068	1	=	=	PUNCT
ejde-397	1068	2	b∗(d	b∗(d	PROPN
ejde-397	1068	3	/	/	SYM
ejde-397	1068	4	dt)bv1(t	dt)bv1(t	PROPN
ejde-397	1068	5	)	)	PUNCT
ejde-397	1069	1	=	=	SYM
ejde-397	1069	2	av1(t	av1(t	X
ejde-397	1069	3	)	)	PUNCT
ejde-397	1069	4	=	=	SYM
ejde-397	1070	1	(	(	PUNCT
ejde-397	1070	2	d	d	X
ejde-397	1070	3	/	/	SYM
ejde-397	1070	4	dt)t	dt)t	PROPN
ejde-397	1070	5	(	(	PUNCT
ejde-397	1070	6	t)u0	t)u0	NOUN
ejde-397	1070	7	=	=	SYM
ejde-397	1070	8	t	t	PROPN
ejde-397	1070	9	(	(	PUNCT
ejde-397	1070	10	t)tu0	t)tu0	PROPN
ejde-397	1070	11	,	,	PUNCT
ejde-397	1070	12	(	(	PUNCT
ejde-397	1070	13	5.20	5.20	NUM
ejde-397	1070	14	)	)	PUNCT
ejde-397	1070	15	for	for	ADP
ejde-397	1070	16	t	t	PROPN
ejde-397	1070	17	≥	≥	NOUN
ejde-397	1070	18	0	0	NUM
ejde-397	1070	19	.	.	PUNCT
ejde-397	1071	1	since	since	SCONJ
ejde-397	1071	2	condition	condition	NOUN
ejde-397	1071	3	[	[	X
ejde-397	1071	4	17	17	NUM
ejde-397	1071	5	,	,	PUNCT
ejde-397	1071	6	(	(	PUNCT
ejde-397	1071	7	2.14	2.14	NUM
ejde-397	1071	8	)	)	PUNCT
ejde-397	1071	9	]	]	PUNCT
ejde-397	1071	10	holds	hold	VERB
ejde-397	1071	11	,	,	PUNCT
ejde-397	1071	12	we	we	PRON
ejde-397	1071	13	obtain	obtain	VERB
ejde-397	1071	14	that	that	SCONJ
ejde-397	1071	15	there	there	PRON
ejde-397	1071	16	exists	exist	VERB
ejde-397	1071	17	λ0	λ0	NOUN
ejde-397	1071	18	>	>	X
ejde-397	1071	19	0	0	NUM
ejde-397	1071	20	such	such	ADJ
ejde-397	1071	21	that	that	SCONJ
ejde-397	1071	22	(	(	PUNCT
ejde-397	1071	23	λ0b	λ0b	PUNCT
ejde-397	1071	24	−	−	PROPN
ejde-397	1071	25	a)−1	a)−1	NOUN
ejde-397	1071	26	∈	∈	PROPN
ejde-397	1071	27	l(x	l(x	PROPN
ejde-397	1071	28	)	)	PUNCT
ejde-397	1071	29	;	;	PUNCT
ejde-397	1071	30	hence	hence	ADV
ejde-397	1071	31	,	,	PUNCT
ejde-397	1071	32	v1	v1	PROPN
ejde-397	1071	33	(	(	PUNCT
ejde-397	1071	34	·	·	PUNCT
ejde-397	1071	35	)	)	PUNCT
ejde-397	1071	36	=	=	PUNCT
ejde-397	1072	1	(	(	PUNCT
ejde-397	1072	2	λ0b	λ0b	PUNCT
ejde-397	1072	3	−	−	PROPN
ejde-397	1072	4	a)−1(λ0b	a)−1(λ0b	PROPN
ejde-397	1072	5	−	−	PROPN
ejde-397	1073	1	a)v1	a)v1	PROPN
ejde-397	1073	2	(	(	PUNCT
ejde-397	1073	3	·	·	PUNCT
ejde-397	1073	4	)	)	PUNCT
ejde-397	1073	5	∈	∈	PROPN
ejde-397	1073	6	c([0,∞	c([0,∞	PROPN
ejde-397	1073	7	)	)	PUNCT
ejde-397	1073	8	:	:	PUNCT
ejde-397	1074	1	x	x	X
ejde-397	1074	2	)	)	PUNCT
ejde-397	1074	3	is	be	AUX
ejde-397	1074	4	bounded	bound	VERB
ejde-397	1074	5	,	,	PUNCT
ejde-397	1074	6	as	as	ADV
ejde-397	1074	7	well	well	ADV
ejde-397	1074	8	as	as	ADP
ejde-397	1074	9	(	(	PUNCT
ejde-397	1074	10	d	d	NOUN
ejde-397	1074	11	/	/	SYM
ejde-397	1074	12	dt)bv1(t	dt)bv1(t	PROPN
ejde-397	1074	13	)	)	PUNCT
ejde-397	1074	14	,	,	PUNCT
ejde-397	1074	15	bv1(t	bv1(t	PROPN
ejde-397	1074	16	)	)	PUNCT
ejde-397	1074	17	and	and	CCONJ
ejde-397	1074	18	av1(t	av1(t	PRON
ejde-397	1074	19	)	)	PUNCT
ejde-397	1074	20	are	be	AUX
ejde-397	1074	21	continuous	continuous	ADJ
ejde-397	1074	22	and	and	CCONJ
ejde-397	1074	23	bounded	bound	VERB
ejde-397	1074	24	for	for	ADP
ejde-397	1074	25	t	t	PROPN
ejde-397	1074	26	≥	≥	PROPN
ejde-397	1074	27	0	0	NUM
ejde-397	1074	28	.	.	PUNCT
ejde-397	1075	1	define	define	VERB
ejde-397	1075	2	vα(t	vα(t	NOUN
ejde-397	1075	3	)	)	PUNCT
ejde-397	1075	4	:	:	PUNCT
ejde-397	1076	1	=	=	SYM
ejde-397	1076	2	∫∞	∫∞	NOUN
ejde-397	1076	3	0	0	SYM
ejde-397	1076	4	t−αφα(st−α)v1(s	t−αφα(st−α)v1(s	ADJ
ejde-397	1076	5	)	)	PUNCT
ejde-397	1076	6	ds	ds	PROPN
ejde-397	1076	7	,	,	PUNCT
ejde-397	1076	8	t	t	NOUN
ejde-397	1076	9	>	>	X
ejde-397	1076	10	0	0	PROPN
ejde-397	1076	11	and	and	CCONJ
ejde-397	1076	12	vα(0	vα(0	NOUN
ejde-397	1076	13	)	)	PUNCT
ejde-397	1076	14	:	:	PUNCT
ejde-397	1076	15	=	=	PUNCT
ejde-397	1076	16	v1(0	v1(0	PROPN
ejde-397	1076	17	)	)	PUNCT
ejde-397	1076	18	.	.	PUNCT
ejde-397	1077	1	using	use	VERB
ejde-397	1077	2	theorem	theorem	ADJ
ejde-397	1077	3	4.8	4.8	NUM
ejde-397	1077	4	and	and	CCONJ
ejde-397	1077	5	the	the	DET
ejde-397	1077	6	arguments	argument	NOUN
ejde-397	1077	7	contained	contain	VERB
ejde-397	1077	8	in	in	ADP
ejde-397	1077	9	its	its	PRON
ejde-397	1077	10	proof	proof	NOUN
ejde-397	1077	11	,	,	PUNCT
ejde-397	1077	12	it	it	PRON
ejde-397	1077	13	readily	readily	ADV
ejde-397	1077	14	follows	follow	VERB
ejde-397	1077	15	that	that	SCONJ
ejde-397	1077	16	the	the	DET
ejde-397	1077	17	function	function	NOUN
ejde-397	1077	18	vα	vα	PROPN
ejde-397	1077	19	(	(	PUNCT
ejde-397	1077	20	·	·	PUNCT
ejde-397	1077	21	)	)	PUNCT
ejde-397	1077	22	is	be	AUX
ejde-397	1077	23	a	a	DET
ejde-397	1077	24	bounded	bounded	ADJ
ejde-397	1077	25	solution	solution	NOUN
ejde-397	1077	26	of	of	ADP
ejde-397	1077	27	problem	problem	NOUN
ejde-397	1077	28	(	(	PUNCT
ejde-397	1077	29	5.19	5.19	NUM
ejde-397	1077	30	)	)	PUNCT
ejde-397	1077	31	,	,	PUNCT
ejde-397	1077	32	satisfying	satisfy	VERB
ejde-397	1077	33	in	in	ADP
ejde-397	1077	34	addition	addition	NOUN
ejde-397	1077	35	that	that	SCONJ
ejde-397	1077	36	the	the	DET
ejde-397	1077	37	functions	function	NOUN
ejde-397	1077	38	t	t	X
ejde-397	1077	39	7→	7→	NUM
ejde-397	1077	40	vα	vα	PROPN
ejde-397	1077	41	(	(	PUNCT
ejde-397	1077	42	·	·	PUNCT
ejde-397	1077	43	)	)	PUNCT
ejde-397	1077	44	,	,	PUNCT
ejde-397	1077	45	t	t	PROPN
ejde-397	1077	46	>	>	X
ejde-397	1077	47	0	0	PUNCT
ejde-397	1078	1	and	and	CCONJ
ejde-397	1078	2	t	t	PROPN
ejde-397	1078	3	7→	7→	NUM
ejde-397	1078	4	avα	avα	PROPN
ejde-397	1078	5	(	(	PUNCT
ejde-397	1078	6	·	·	PUNCT
ejde-397	1078	7	)	)	PUNCT
ejde-397	1078	8	,	,	PUNCT
ejde-397	1078	9	t	t	PROPN
ejde-397	1078	10	>	>	X
ejde-397	1078	11	0	0	NUM
ejde-397	1078	12	can	can	AUX
ejde-397	1078	13	be	be	AUX
ejde-397	1078	14	analytically	analytically	ADV
ejde-397	1078	15	extended	extend	VERB
ejde-397	1078	16	to	to	ADP
ejde-397	1078	17	the	the	DET
ejde-397	1078	18	sector	sector	NOUN
ejde-397	1078	19	σmin	σmin	NOUN
ejde-397	1078	20	(	(	PUNCT
ejde-397	1078	21	(	(	PUNCT
ejde-397	1078	22	1	1	NUM
ejde-397	1078	23	α−1)π2	α−1)π2	NUM
ejde-397	1078	24	,	,	PUNCT
ejde-397	1078	25	π	π	PROPN
ejde-397	1078	26	)	)	PUNCT
ejde-397	1078	27	.	.	PUNCT
ejde-397	1079	1	the	the	DET
ejde-397	1079	2	uniqueness	uniqueness	NOUN
ejde-397	1079	3	of	of	ADP
ejde-397	1079	4	solutions	solution	NOUN
ejde-397	1079	5	of	of	ADP
ejde-397	1079	6	problem	problem	NOUN
ejde-397	1079	7	(	(	PUNCT
ejde-397	1079	8	5.19	5.19	NUM
ejde-397	1079	9	)	)	PUNCT
ejde-397	1079	10	can	can	AUX
ejde-397	1079	11	be	be	AUX
ejde-397	1079	12	proved	prove	VERB
ejde-397	1079	13	with	with	ADP
ejde-397	1079	14	the	the	DET
ejde-397	1079	15	help	help	NOUN
ejde-397	1079	16	of	of	ADP
ejde-397	1079	17	theorem	theorem	ADJ
ejde-397	1079	18	4.6	4.6	NUM
ejde-397	1079	19	.	.	PUNCT
ejde-397	1080	1	(	(	PUNCT
ejde-397	1080	2	b	b	X
ejde-397	1080	3	)	)	PUNCT
ejde-397	1080	4	suppose	suppose	VERB
ejde-397	1080	5	now	now	ADV
ejde-397	1080	6	that	that	SCONJ
ejde-397	1080	7	(	(	PUNCT
ejde-397	1080	8	bf)(x	bf)(x	PROPN
ejde-397	1080	9	)	)	PUNCT
ejde-397	1080	10	:	:	PUNCT
ejde-397	1080	11	=	=	PUNCT
ejde-397	1080	12	χ(a,∞,a)(x)f(x	χ(a,∞,a)(x)f(x	PROPN
ejde-397	1080	13	)	)	PUNCT
ejde-397	1080	14	,	,	PUNCT
ejde-397	1080	15	x	x	PUNCT
ejde-397	1080	16	∈	∈	NOUN
ejde-397	1080	17	r	r	NOUN
ejde-397	1080	18	(	(	PUNCT
ejde-397	1080	19	f	f	PROPN
ejde-397	1080	20	∈	∈	PROPN
ejde-397	1080	21	x	x	NOUN
ejde-397	1080	22	)	)	PUNCT
ejde-397	1080	23	,	,	PUNCT
ejde-397	1080	24	where	where	SCONJ
ejde-397	1080	25	−∞	−∞	ADP
ejde-397	1080	26	<	<	X
ejde-397	1080	27	a	a	X
ejde-397	1080	28	<	<	X
ejde-397	1080	29	∞.	∞.	PROPN
ejde-397	1080	30	then	then	ADV
ejde-397	1080	31	b	b	PROPN
ejde-397	1080	32	∈	∈	PROPN
ejde-397	1080	33	l(x	l(x	PROPN
ejde-397	1080	34	)	)	PUNCT
ejde-397	1080	35	,	,	PUNCT
ejde-397	1080	36	b	b	X
ejde-397	1080	37	=	=	SYM
ejde-397	1080	38	b∗	b∗	ADJ
ejde-397	1080	39	,	,	PUNCT
ejde-397	1080	40	b2	b2	NOUN
ejde-397	1080	41	=	=	SYM
ejde-397	1080	42	b	b	PROPN
ejde-397	1080	43	and	and	CCONJ
ejde-397	1080	44	the	the	DET
ejde-397	1080	45	conclusions	conclusion	NOUN
ejde-397	1080	46	established	establish	VERB
ejde-397	1080	47	in	in	ADP
ejde-397	1080	48	the	the	DET
ejde-397	1080	49	part	part	NOUN
ejde-397	1080	50	(	(	PUNCT
ejde-397	1080	51	a	a	NOUN
ejde-397	1080	52	)	)	PUNCT
ejde-397	1080	53	of	of	ADP
ejde-397	1080	54	this	this	DET
ejde-397	1080	55	example	example	NOUN
ejde-397	1080	56	,	,	PUNCT
ejde-397	1080	57	ending	end	VERB
ejde-397	1080	58	with	with	ADP
ejde-397	1080	59	the	the	DET
ejde-397	1080	60	equation	equation	NOUN
ejde-397	1080	61	(	(	PUNCT
ejde-397	1080	62	5.20	5.20	NUM
ejde-397	1080	63	)	)	PUNCT
ejde-397	1080	64	,	,	PUNCT
ejde-397	1080	65	continue	continue	VERB
ejde-397	1080	66	to	to	PART
ejde-397	1080	67	hold	hold	VERB
ejde-397	1080	68	.	.	PUNCT
ejde-397	1081	1	in	in	ADP
ejde-397	1081	2	our	our	PRON
ejde-397	1081	3	concrete	concrete	ADJ
ejde-397	1081	4	situation	situation	NOUN
ejde-397	1081	5	,	,	PUNCT
ejde-397	1081	6	we	we	PRON
ejde-397	1081	7	have	have	VERB
ejde-397	1081	8	the	the	DET
ejde-397	1081	9	validity	validity	NOUN
ejde-397	1081	10	of	of	ADP
ejde-397	1081	11	condition	condition	NOUN
ejde-397	1081	12	[	[	X
ejde-397	1081	13	17	17	NUM
ejde-397	1081	14	,	,	PUNCT
ejde-397	1081	15	(	(	PUNCT
ejde-397	1081	16	2.11	2.11	NUM
ejde-397	1081	17	)	)	PUNCT
ejde-397	1081	18	]	]	PUNCT
ejde-397	1081	19	but	but	CCONJ
ejde-397	1081	20	not	not	PART
ejde-397	1081	21	the	the	DET
ejde-397	1081	22	condition	condition	NOUN
ejde-397	1081	23	[	[	X
ejde-397	1081	24	17	17	NUM
ejde-397	1081	25	,	,	PUNCT
ejde-397	1081	26	(	(	PUNCT
ejde-397	1081	27	2.14	2.14	NUM
ejde-397	1081	28	)	)	PUNCT
ejde-397	1081	29	]	]	PUNCT
ejde-397	1081	30	,	,	PUNCT
ejde-397	1081	31	in	in	ADP
ejde-397	1081	32	general	general	ADJ
ejde-397	1081	33	.	.	PUNCT
ejde-397	1082	1	define	define	VERB
ejde-397	1082	2	fα(t	fα(t	PUNCT
ejde-397	1082	3	)	)	PUNCT
ejde-397	1082	4	:	:	PUNCT
ejde-397	1082	5	=	=	SYM
ejde-397	1082	6	∫∞	∫∞	NOUN
ejde-397	1082	7	0	0	X
ejde-397	1083	1	t−αφα(st−α)bv1(s	t−αφα(st−α)bv1(s	PROPN
ejde-397	1083	2	)	)	PUNCT
ejde-397	1083	3	ds	ds	PROPN
ejde-397	1083	4	,	,	PUNCT
ejde-397	1083	5	t	t	X
ejde-397	1083	6	>	>	X
ejde-397	1083	7	0	0	PROPN
ejde-397	1083	8	,	,	PUNCT
ejde-397	1083	9	fα(0	fα(0	PROPN
ejde-397	1083	10	)	)	PUNCT
ejde-397	1083	11	:	:	PUNCT
ejde-397	1083	12	=	=	SYM
ejde-397	1083	13	bv1(0	bv1(0	NOUN
ejde-397	1083	14	)	)	PUNCT
ejde-397	1083	15	=	=	SYM
ejde-397	1083	16	u0	u0	ADJ
ejde-397	1083	17	,	,	PUNCT
ejde-397	1083	18	hα(t	hα(t	NUM
ejde-397	1083	19	)	)	PUNCT
ejde-397	1083	20	:	:	PUNCT
ejde-397	1084	1	=	=	SYM
ejde-397	1084	2	∫∞	∫∞	NOUN
ejde-397	1084	3	0	0	X
ejde-397	1084	4	t−αφα(st−α)av1(s	t−αφα(st−α)av1(s	PROPN
ejde-397	1084	5	)	)	PUNCT
ejde-397	1084	6	ds	ds	PROPN
ejde-397	1084	7	,	,	PUNCT
ejde-397	1084	8	t	t	NOUN
ejde-397	1084	9	>	>	X
ejde-397	1084	10	0	0	PUNCT
ejde-397	1084	11	and	and	CCONJ
ejde-397	1084	12	hα(0	hα(0	NOUN
ejde-397	1084	13	)	)	PUNCT
ejde-397	1084	14	:	:	PUNCT
ejde-397	1085	1	=	=	NOUN
ejde-397	1085	2	av1(0	av1(0	NOUN
ejde-397	1085	3	)	)	PUNCT
ejde-397	1085	4	.	.	PUNCT
ejde-397	1086	1	by	by	ADP
ejde-397	1086	2	the	the	DET
ejde-397	1086	3	foregoing	foregoing	NOUN
ejde-397	1086	4	,	,	PUNCT
ejde-397	1086	5	we	we	PRON
ejde-397	1086	6	have	have	VERB
ejde-397	1086	7	that	that	PRON
ejde-397	1086	8	fα	fα	NOUN
ejde-397	1086	9	,	,	PUNCT
ejde-397	1086	10	hα	hα	ADP
ejde-397	1086	11	∈	∈	PROPN
ejde-397	1086	12	c([0,∞	c([0,∞	PROPN
ejde-397	1086	13	)	)	PUNCT
ejde-397	1086	14	:	:	PUNCT
ejde-397	1087	1	x	x	X
ejde-397	1087	2	)	)	PUNCT
ejde-397	1087	3	are	be	AUX
ejde-397	1087	4	bounded	bound	VERB
ejde-397	1087	5	and	and	CCONJ
ejde-397	1087	6	dα	dα	PROPN
ejde-397	1087	7	t	t	NOUN
ejde-397	1087	8	fα(t	fα(t	PUNCT
ejde-397	1087	9	)	)	PUNCT
ejde-397	1087	10	=	=	SYM
ejde-397	1087	11	hα(t	hα(t	X
ejde-397	1087	12	)	)	PUNCT
ejde-397	1087	13	,	,	PUNCT
ejde-397	1087	14	t	t	PROPN
ejde-397	1087	15	≥	≥	NUM
ejde-397	1087	16	0	0	NUM
ejde-397	1087	17	,	,	PUNCT
ejde-397	1087	18	which	which	PRON
ejde-397	1087	19	simply	simply	ADV
ejde-397	1087	20	implies	imply	VERB
ejde-397	1087	21	bhα(t	bhα(t	NOUN
ejde-397	1087	22	)	)	PUNCT
ejde-397	1087	23	=	=	SYM
ejde-397	1087	24	hα(t	hα(t	NUM
ejde-397	1087	25	)	)	PUNCT
ejde-397	1087	26	,	,	PUNCT
ejde-397	1087	27	t	t	PROPN
ejde-397	1087	28	≥	≥	NUM
ejde-397	1087	29	0	0	NUM
ejde-397	1087	30	.	.	PUNCT
ejde-397	1088	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1088	2	abstract	abstract	ADJ
ejde-397	1088	3	degenerate	degenerate	ADJ
ejde-397	1088	4	volterra	volterra	NOUN
ejde-397	1088	5	inclusions	inclusion	NOUN
ejde-397	1088	6	35	35	NUM
ejde-397	1088	7	by	by	ADP
ejde-397	1088	8	(	(	PUNCT
ejde-397	1088	9	5.20	5.20	NUM
ejde-397	1088	10	)	)	PUNCT
ejde-397	1088	11	,	,	PUNCT
ejde-397	1088	12	we	we	PRON
ejde-397	1088	13	have	have	VERB
ejde-397	1088	14	that	that	PRON
ejde-397	1088	15	av1(t	av1(t	ADV
ejde-397	1088	16	)	)	PUNCT
ejde-397	1089	1	=	=	SYM
ejde-397	1089	2	t	t	PROPN
ejde-397	1089	3	(	(	PUNCT
ejde-397	1089	4	t)tu0	t)tu0	PROPN
ejde-397	1089	5	∈	∈	PROPN
ejde-397	1089	6	b−1[av1(t	b−1[av1(t	ADJ
ejde-397	1089	7	)	)	PUNCT
ejde-397	1089	8	]	]	PUNCT
ejde-397	1089	9	and	and	CCONJ
ejde-397	1089	10	bav1(t	bav1(t	NUM
ejde-397	1089	11	)	)	PUNCT
ejde-397	1089	12	=	=	SYM
ejde-397	1089	13	av1(t	av1(t	X
ejde-397	1089	14	)	)	PUNCT
ejde-397	1089	15	(	(	PUNCT
ejde-397	1089	16	t	t	X
ejde-397	1089	17	≥	≥	PROPN
ejde-397	1089	18	0	0	NUM
ejde-397	1089	19	)	)	PUNCT
ejde-397	1089	20	,	,	PUNCT
ejde-397	1089	21	whence	whence	SCONJ
ejde-397	1089	22	we	we	PRON
ejde-397	1089	23	may	may	AUX
ejde-397	1089	24	conclude	conclude	VERB
ejde-397	1089	25	that	that	PRON
ejde-397	1089	26	av1(t	av1(t	ADV
ejde-397	1089	27	)	)	PUNCT
ejde-397	1089	28	∈	∈	PROPN
ejde-397	1089	29	a[bv1(t	a[bv1(t	PROPN
ejde-397	1089	30	)	)	PUNCT
ejde-397	1089	31	]	]	PUNCT
ejde-397	1090	1	(	(	PUNCT
ejde-397	1090	2	t	t	X
ejde-397	1090	3	≥	≥	PROPN
ejde-397	1090	4	0	0	NUM
ejde-397	1090	5	)	)	PUNCT
ejde-397	1090	6	.	.	PUNCT
ejde-397	1091	1	since	since	SCONJ
ejde-397	1091	2	a	a	PRON
ejde-397	1091	3	is	be	AUX
ejde-397	1091	4	closed	close	VERB
ejde-397	1091	5	,	,	PUNCT
ejde-397	1091	6	an	an	DET
ejde-397	1091	7	application	application	NOUN
ejde-397	1091	8	of	of	ADP
ejde-397	1091	9	theorem	theorem	ADJ
ejde-397	1091	10	2.3	2.3	NUM
ejde-397	1091	11	yields	yield	NOUN
ejde-397	1091	12	that	that	PRON
ejde-397	1091	13	hα(t	hα(t	VERB
ejde-397	1091	14	)	)	PUNCT
ejde-397	1091	15	=	=	SYM
ejde-397	1091	16	bhα(t	bhα(t	X
ejde-397	1091	17	)	)	PUNCT
ejde-397	1091	18	∈	∈	NOUN
ejde-397	1091	19	ab−1fα(t	ab−1fα(t	NOUN
ejde-397	1091	20	)	)	PUNCT
ejde-397	1091	21	(	(	PUNCT
ejde-397	1091	22	t	t	PROPN
ejde-397	1091	23	≥	≥	PROPN
ejde-397	1091	24	0	0	NUM
ejde-397	1091	25	)	)	PUNCT
ejde-397	1091	26	;	;	PUNCT
ejde-397	1091	27	consequently	consequently	ADV
ejde-397	1091	28	,	,	PUNCT
ejde-397	1091	29	the	the	DET
ejde-397	1091	30	function	function	NOUN
ejde-397	1091	31	t	t	PROPN
ejde-397	1091	32	7→	7→	NUM
ejde-397	1091	33	fα(t	fα(t	NUM
ejde-397	1091	34	)	)	PUNCT
ejde-397	1091	35	,	,	PUNCT
ejde-397	1091	36	t	t	PROPN
ejde-397	1091	37	≥	≥	PROPN
ejde-397	1091	38	0	0	NUM
ejde-397	1091	39	is	be	AUX
ejde-397	1091	40	a	a	DET
ejde-397	1091	41	pre	pre	NOUN
ejde-397	1091	42	-	-	NOUN
ejde-397	1091	43	solution	solution	NOUN
ejde-397	1091	44	of	of	ADP
ejde-397	1091	45	problem	problem	NOUN
ejde-397	1091	46	(	(	PUNCT
ejde-397	1091	47	1.2	1.2	NUM
ejde-397	1091	48	)	)	PUNCT
ejde-397	1091	49	with	with	ADP
ejde-397	1091	50	b	b	PROPN
ejde-397	1091	51	≡	≡	PROPN
ejde-397	1091	52	i	i	PROPN
ejde-397	1091	53	,	,	PUNCT
ejde-397	1091	54	f(t	f(t	PROPN
ejde-397	1091	55	)	)	PUNCT
ejde-397	1091	56	≡	≡	PROPN
ejde-397	1091	57	0	0	PUNCT
ejde-397	1092	1	and	and	CCONJ
ejde-397	1092	2	,	,	PUNCT
ejde-397	1092	3	by	by	ADP
ejde-397	1092	4	remark	remark	NOUN
ejde-397	1092	5	4.2(iv	4.2(iv	NUM
ejde-397	1092	6	)	)	PUNCT
ejde-397	1092	7	,	,	PUNCT
ejde-397	1092	8	the	the	DET
ejde-397	1092	9	problem	problem	NOUN
ejde-397	1092	10	(	(	PUNCT
ejde-397	1092	11	5.19	5.19	NUM
ejde-397	1092	12	)	)	PUNCT
ejde-397	1092	13	has	have	VERB
ejde-397	1092	14	a	a	DET
ejde-397	1092	15	bounded	bounded	ADJ
ejde-397	1092	16	p	p	NOUN
ejde-397	1092	17	-	-	PUNCT
ejde-397	1092	18	solution	solution	NOUN
ejde-397	1092	19	vα	vα	PROPN
ejde-397	1092	20	(	(	PUNCT
ejde-397	1092	21	·	·	PUNCT
ejde-397	1092	22	)	)	PUNCT
ejde-397	1093	1	satisfying	satisfying	NOUN
ejde-397	1093	2	,	,	PUNCT
ejde-397	1093	3	in	in	ADP
ejde-397	1093	4	addition	addition	NOUN
ejde-397	1093	5	,	,	PUNCT
ejde-397	1093	6	that	that	SCONJ
ejde-397	1093	7	the	the	DET
ejde-397	1093	8	functions	function	NOUN
ejde-397	1093	9	t	t	X
ejde-397	1093	10	7→	7→	NUM
ejde-397	1093	11	bvα	bvα	PROPN
ejde-397	1093	12	(	(	PUNCT
ejde-397	1093	13	·	·	PUNCT
ejde-397	1093	14	)	)	PUNCT
ejde-397	1093	15	,	,	PUNCT
ejde-397	1093	16	t	t	PROPN
ejde-397	1093	17	>	>	X
ejde-397	1093	18	0	0	PUNCT
ejde-397	1094	1	and	and	CCONJ
ejde-397	1094	2	t	t	PROPN
ejde-397	1094	3	7→	7→	NUM
ejde-397	1094	4	avα	avα	PROPN
ejde-397	1094	5	(	(	PUNCT
ejde-397	1094	6	·	·	PUNCT
ejde-397	1094	7	)	)	PUNCT
ejde-397	1094	8	,	,	PUNCT
ejde-397	1094	9	t	t	PROPN
ejde-397	1094	10	>	>	X
ejde-397	1094	11	0	0	NUM
ejde-397	1094	12	can	can	AUX
ejde-397	1094	13	be	be	AUX
ejde-397	1094	14	analytically	analytically	ADV
ejde-397	1094	15	extended	extend	VERB
ejde-397	1094	16	to	to	ADP
ejde-397	1094	17	the	the	DET
ejde-397	1094	18	sector	sector	NOUN
ejde-397	1094	19	σmin	σmin	NOUN
ejde-397	1094	20	(	(	PUNCT
ejde-397	1094	21	(	(	PUNCT
ejde-397	1094	22	1	1	NUM
ejde-397	1094	23	α−1)π2	α−1)π2	NUM
ejde-397	1094	24	,	,	PUNCT
ejde-397	1094	25	π	π	PROPN
ejde-397	1094	26	)	)	PUNCT
ejde-397	1094	27	.	.	PUNCT
ejde-397	1095	1	the	the	DET
ejde-397	1095	2	uniqueness	uniqueness	NOUN
ejde-397	1095	3	follows	follow	VERB
ejde-397	1095	4	again	again	ADV
ejde-397	1095	5	from	from	ADP
ejde-397	1095	6	an	an	DET
ejde-397	1095	7	essential	essential	ADJ
ejde-397	1095	8	application	application	NOUN
ejde-397	1095	9	of	of	ADP
ejde-397	1095	10	theorem	theorem	NOUN
ejde-397	1095	11	4.6	4.6	NUM
ejde-397	1095	12	.	.	PUNCT
ejde-397	1096	1	(	(	PUNCT
ejde-397	1096	2	ii	ii	NOUN
ejde-397	1096	3	)	)	PUNCT
ejde-397	1096	4	(	(	PUNCT
ejde-397	1097	1	[	[	X
ejde-397	1097	2	31]-[32	31]-[32	PROPN
ejde-397	1097	3	]	]	PUNCT
ejde-397	1097	4	)	)	PUNCT
ejde-397	1097	5	here	here	ADV
ejde-397	1097	6	we	we	PRON
ejde-397	1097	7	would	would	AUX
ejde-397	1097	8	like	like	VERB
ejde-397	1097	9	to	to	PART
ejde-397	1097	10	observe	observe	VERB
ejde-397	1097	11	,	,	PUNCT
ejde-397	1097	12	without	without	ADP
ejde-397	1097	13	going	go	VERB
ejde-397	1097	14	into	into	ADP
ejde-397	1097	15	full	full	ADJ
ejde-397	1097	16	details	detail	NOUN
ejde-397	1097	17	,	,	PUNCT
ejde-397	1097	18	that	that	SCONJ
ejde-397	1097	19	we	we	PRON
ejde-397	1097	20	can	can	AUX
ejde-397	1097	21	similarly	similarly	ADV
ejde-397	1097	22	prove	prove	VERB
ejde-397	1097	23	some	some	DET
ejde-397	1097	24	results	result	NOUN
ejde-397	1097	25	on	on	ADP
ejde-397	1097	26	the	the	DET
ejde-397	1097	27	existence	existence	NOUN
ejde-397	1097	28	and	and	CCONJ
ejde-397	1097	29	uniqueness	uniqueness	NOUN
ejde-397	1097	30	of	of	ADP
ejde-397	1097	31	analytical	analytical	ADJ
ejde-397	1097	32	solutions	solution	NOUN
ejde-397	1097	33	of	of	ADP
ejde-397	1097	34	the	the	DET
ejde-397	1097	35	abstract	abstract	ADJ
ejde-397	1097	36	volterra	volterra	NOUN
ejde-397	1097	37	equation	equation	NOUN
ejde-397	1097	38	∂	∂	NOUN
ejde-397	1098	1	∂r	∂r	PROPN
ejde-397	1098	2	vα(t	vα(t	NOUN
ejde-397	1098	3	,	,	PUNCT
ejde-397	1098	4	r	r	NOUN
ejde-397	1098	5	)	)	PUNCT
ejde-397	1098	6	=	=	SYM
ejde-397	1098	7	a(r	a(r	NOUN
ejde-397	1098	8	)	)	PUNCT
ejde-397	1098	9	∫	∫	PROPN
ejde-397	1099	1	t	t	PROPN
ejde-397	1099	2	0	0	NUM
ejde-397	1099	3	gα(t−	gα(t−	NOUN
ejde-397	1099	4	s)vα(s	s)vα(s	NUM
ejde-397	1099	5	,	,	PUNCT
ejde-397	1099	6	r	r	NOUN
ejde-397	1099	7	)	)	PUNCT
ejde-397	1099	8	ds+	ds+	ADJ
ejde-397	1099	9	f(t	f(t	NOUN
ejde-397	1099	10	,	,	PUNCT
ejde-397	1099	11	r	r	NOUN
ejde-397	1099	12	)	)	PUNCT
ejde-397	1099	13	,	,	PUNCT
ejde-397	1099	14	t	t	PROPN
ejde-397	1099	15	≥	≥	NUM
ejde-397	1099	16	0	0	NUM
ejde-397	1099	17	,	,	PUNCT
ejde-397	1099	18	r	r	NOUN
ejde-397	1099	19	∈	∈	PROPN
ejde-397	1100	1	[	[	X
ejde-397	1100	2	0	0	NUM
ejde-397	1100	3	,	,	PUNCT
ejde-397	1100	4	1	1	NUM
ejde-397	1100	5	]	]	PUNCT
ejde-397	1100	6	,	,	PUNCT
ejde-397	1100	7	on	on	ADP
ejde-397	1100	8	the	the	DET
ejde-397	1100	9	sector	sector	NOUN
ejde-397	1100	10	σmin	σmin	NOUN
ejde-397	1100	11	(	(	PUNCT
ejde-397	1100	12	(	(	PUNCT
ejde-397	1100	13	1	1	NUM
ejde-397	1100	14	α−1)π2	α−1)π2	NUM
ejde-397	1100	15	,	,	PUNCT
ejde-397	1100	16	π	π	PROPN
ejde-397	1100	17	)	)	PUNCT
ejde-397	1100	18	,	,	PUNCT
ejde-397	1100	19	where	where	SCONJ
ejde-397	1100	20	a	a	DET
ejde-397	1100	21	∈	∈	NOUN
ejde-397	1100	22	c1[0	c1[0	PROPN
ejde-397	1100	23	,	,	PUNCT
ejde-397	1100	24	1	1	NUM
ejde-397	1100	25	]	]	PUNCT
ejde-397	1100	26	and	and	CCONJ
ejde-397	1100	27	the	the	DET
ejde-397	1100	28	mapping	mapping	NOUN
ejde-397	1100	29	t	t	NOUN
ejde-397	1100	30	7→	7→	NUM
ejde-397	1100	31	f(t	f(t	NOUN
ejde-397	1100	32	,	,	PUNCT
ejde-397	1100	33	·	·	PUNCT
ejde-397	1100	34	)	)	PUNCT
ejde-397	1100	35	,	,	PUNCT
ejde-397	1100	36	t	t	PROPN
ejde-397	1100	37	≥	≥	NOUN
ejde-397	1100	38	0	0	NUM
ejde-397	1100	39	is	be	AUX
ejde-397	1100	40	continuous	continuous	ADJ
ejde-397	1100	41	and	and	CCONJ
ejde-397	1100	42	exponentially	exponentially	ADV
ejde-397	1100	43	bounded	bound	VERB
ejde-397	1100	44	with	with	ADP
ejde-397	1100	45	the	the	DET
ejde-397	1100	46	values	value	NOUN
ejde-397	1100	47	in	in	ADP
ejde-397	1100	48	the	the	DET
ejde-397	1100	49	banach	banach	NOUN
ejde-397	1100	50	space	space	NOUN
ejde-397	1100	51	c[0	c[0	PROPN
ejde-397	1100	52	,	,	PUNCT
ejde-397	1100	53	1	1	NUM
ejde-397	1100	54	]	]	PUNCT
ejde-397	1100	55	(	(	PUNCT
ejde-397	1100	56	cf	cf	NOUN
ejde-397	1100	57	.	.	PUNCT
ejde-397	1101	1	[	[	X
ejde-397	1101	2	31	31	NUM
ejde-397	1101	3	,	,	PUNCT
ejde-397	1101	4	example	example	NOUN
ejde-397	1101	5	1	1	NUM
ejde-397	1101	6	]	]	PUNCT
ejde-397	1101	7	and	and	CCONJ
ejde-397	1101	8	theorem	theorem	VERB
ejde-397	1101	9	4.8	4.8	NUM
ejde-397	1101	10	)	)	PUNCT
ejde-397	1101	11	;	;	PUNCT
ejde-397	1101	12	using	use	VERB
ejde-397	1101	13	theorem	theorem	NOUN
ejde-397	1101	14	4.9	4.9	NUM
ejde-397	1101	15	instead	instead	ADV
ejde-397	1101	16	of	of	ADP
ejde-397	1101	17	theorem	theorem	NOUN
ejde-397	1101	18	4.8	4.8	NUM
ejde-397	1101	19	,	,	PUNCT
ejde-397	1101	20	we	we	PRON
ejde-397	1101	21	can	can	AUX
ejde-397	1101	22	consider	consider	VERB
ejde-397	1101	23	the	the	DET
ejde-397	1101	24	well	well	NOUN
ejde-397	1101	25	-	-	PUNCT
ejde-397	1101	26	posedness	posedness	NOUN
ejde-397	1101	27	in	in	ADP
ejde-397	1101	28	c[0	c[0	PROPN
ejde-397	1101	29	,	,	PUNCT
ejde-397	1101	30	1	1	NUM
ejde-397	1101	31	]	]	PUNCT
ejde-397	1101	32	for	for	ADP
ejde-397	1101	33	the	the	DET
ejde-397	1101	34	equation	equation	NOUN
ejde-397	1101	35	∂	∂	NOUN
ejde-397	1102	1	∂r	∂r	NUM
ejde-397	1102	2	vc(t	vc(t	NOUN
ejde-397	1102	3	,	,	PUNCT
ejde-397	1102	4	r	r	NOUN
ejde-397	1102	5	)	)	PUNCT
ejde-397	1102	6	=	=	SYM
ejde-397	1102	7	a(r	a(r	NOUN
ejde-397	1102	8	)	)	PUNCT
ejde-397	1103	1	∫	∫	PROPN
ejde-397	1103	2	t	t	PROPN
ejde-397	1103	3	0	0	NUM
ejde-397	1103	4	c(t−	c(t−	PROPN
ejde-397	1103	5	s)vc(s	s)vc(s	ADJ
ejde-397	1103	6	,	,	PUNCT
ejde-397	1103	7	r	r	NOUN
ejde-397	1103	8	)	)	PUNCT
ejde-397	1103	9	ds+	ds+	ADJ
ejde-397	1103	10	f(t	f(t	NOUN
ejde-397	1103	11	,	,	PUNCT
ejde-397	1103	12	r	r	NOUN
ejde-397	1103	13	)	)	PUNCT
ejde-397	1103	14	,	,	PUNCT
ejde-397	1103	15	t	t	PROPN
ejde-397	1103	16	≥	≥	NUM
ejde-397	1103	17	0	0	NUM
ejde-397	1103	18	,	,	PUNCT
ejde-397	1103	19	r	r	NOUN
ejde-397	1103	20	∈	∈	PROPN
ejde-397	1104	1	[	[	X
ejde-397	1104	2	0	0	NUM
ejde-397	1104	3	,	,	PUNCT
ejde-397	1104	4	1	1	NUM
ejde-397	1104	5	]	]	PUNCT
ejde-397	1104	6	,	,	PUNCT
ejde-397	1104	7	where	where	SCONJ
ejde-397	1104	8	c	c	X
ejde-397	1104	9	(	(	PUNCT
ejde-397	1104	10	·	·	PUNCT
ejde-397	1104	11	)	)	PUNCT
ejde-397	1104	12	is	be	AUX
ejde-397	1104	13	a	a	DET
ejde-397	1104	14	completely	completely	ADV
ejde-397	1104	15	positive	positive	ADJ
ejde-397	1104	16	function	function	NOUN
ejde-397	1104	17	.	.	PUNCT
ejde-397	1105	1	fractional	fractional	PROPN
ejde-397	1105	2	maxwell	maxwell	PROPN
ejde-397	1105	3	’s	’s	PART
ejde-397	1105	4	equations	equation	NOUN
ejde-397	1105	5	have	have	AUX
ejde-397	1105	6	gained	gain	VERB
ejde-397	1105	7	much	much	ADJ
ejde-397	1105	8	attention	attention	NOUN
ejde-397	1105	9	in	in	ADP
ejde-397	1105	10	recent	recent	ADJ
ejde-397	1105	11	years	year	NOUN
ejde-397	1105	12	(	(	PUNCT
ejde-397	1105	13	see	see	VERB
ejde-397	1105	14	e.g.	e.g.	ADV
ejde-397	1105	15	[	[	X
ejde-397	1105	16	10	10	NUM
ejde-397	1105	17	]	]	PUNCT
ejde-397	1105	18	,	,	PUNCT
ejde-397	1105	19	[	[	X
ejde-397	1105	20	27	27	NUM
ejde-397	1105	21	]	]	PUNCT
ejde-397	1105	22	,	,	PUNCT
ejde-397	1105	23	[	[	X
ejde-397	1105	24	60	60	NUM
ejde-397	1105	25	]	]	PUNCT
ejde-397	1105	26	,	,	PUNCT
ejde-397	1105	27	[	[	X
ejde-397	1105	28	74	74	NUM
ejde-397	1105	29	]	]	PUNCT
ejde-397	1105	30	,	,	PUNCT
ejde-397	1105	31	[	[	X
ejde-397	1105	32	83	83	NUM
ejde-397	1105	33	]	]	PUNCT
ejde-397	1105	34	and	and	CCONJ
ejde-397	1105	35	references	reference	NOUN
ejde-397	1105	36	cited	cite	VERB
ejde-397	1105	37	therein	therein	ADV
ejde-397	1105	38	for	for	ADP
ejde-397	1105	39	more	more	ADJ
ejde-397	1105	40	details	detail	NOUN
ejde-397	1105	41	on	on	ADP
ejde-397	1105	42	the	the	DET
ejde-397	1105	43	subject	subject	NOUN
ejde-397	1105	44	)	)	PUNCT
ejde-397	1105	45	.	.	PUNCT
ejde-397	1106	1	here	here	ADV
ejde-397	1106	2	we	we	PRON
ejde-397	1106	3	want	want	VERB
ejde-397	1106	4	to	to	PART
ejde-397	1106	5	briefly	briefly	ADV
ejde-397	1106	6	explain	explain	VERB
ejde-397	1106	7	how	how	SCONJ
ejde-397	1106	8	we	we	PRON
ejde-397	1106	9	can	can	AUX
ejde-397	1106	10	use	use	VERB
ejde-397	1106	11	the	the	DET
ejde-397	1106	12	analysis	analysis	NOUN
ejde-397	1106	13	of	of	ADP
ejde-397	1106	14	favini	favini	NOUN
ejde-397	1106	15	and	and	CCONJ
ejde-397	1106	16	yagi	yagi	ADJ
ejde-397	1106	17	[	[	X
ejde-397	1106	18	17	17	NUM
ejde-397	1106	19	,	,	PUNCT
ejde-397	1106	20	exampe	exampe	NOUN
ejde-397	1106	21	2.2	2.2	NUM
ejde-397	1106	22	]	]	PUNCT
ejde-397	1106	23	for	for	ADP
ejde-397	1106	24	proving	prove	VERB
ejde-397	1106	25	the	the	DET
ejde-397	1106	26	existence	existence	NOUN
ejde-397	1106	27	and	and	CCONJ
ejde-397	1106	28	uniqueness	uniqueness	NOUN
ejde-397	1106	29	of	of	ADP
ejde-397	1106	30	analytical	analytical	ADJ
ejde-397	1106	31	solutions	solution	NOUN
ejde-397	1106	32	of	of	ADP
ejde-397	1106	33	certain	certain	ADJ
ejde-397	1106	34	classes	class	NOUN
ejde-397	1106	35	of	of	ADP
ejde-397	1106	36	inhomogeneous	inhomogeneous	ADJ
ejde-397	1106	37	abstract	abstract	ADJ
ejde-397	1106	38	time	time	NOUN
ejde-397	1106	39	-	-	PUNCT
ejde-397	1106	40	fractional	fractional	ADJ
ejde-397	1106	41	maxwell	maxwell	PROPN
ejde-397	1106	42	’s	’s	PART
ejde-397	1106	43	equations	equation	NOUN
ejde-397	1106	44	in	in	ADP
ejde-397	1106	45	r3	r3	PROPN
ejde-397	1106	46	;	;	PUNCT
ejde-397	1106	47	the	the	DET
ejde-397	1106	48	time	time	NOUN
ejde-397	1106	49	-	-	PUNCT
ejde-397	1106	50	fractional	fractional	ADJ
ejde-397	1106	51	analogues	analogue	NOUN
ejde-397	1106	52	of	of	ADP
ejde-397	1106	53	poisson	poisson	ADJ
ejde-397	1106	54	-	-	PUNCT
ejde-397	1106	55	wave	wave	NOUN
ejde-397	1106	56	equations	equation	NOUN
ejde-397	1106	57	(	(	PUNCT
ejde-397	1106	58	see	see	VERB
ejde-397	1106	59	e.g.	e.g.	ADV
ejde-397	1106	60	[	[	X
ejde-397	1106	61	17	17	NUM
ejde-397	1106	62	,	,	PUNCT
ejde-397	1106	63	example	example	NOUN
ejde-397	1106	64	2.3	2.3	NUM
ejde-397	1106	65	,	,	PUNCT
ejde-397	1106	66	example	example	NOUN
ejde-397	1106	67	6.23	6.23	NUM
ejde-397	1106	68	]	]	PUNCT
ejde-397	1106	69	)	)	PUNCT
ejde-397	1106	70	will	will	AUX
ejde-397	1106	71	be	be	AUX
ejde-397	1106	72	considered	consider	VERB
ejde-397	1106	73	somewhere	somewhere	ADV
ejde-397	1106	74	else	else	ADV
ejde-397	1106	75	.	.	PUNCT
ejde-397	1107	1	consider	consider	VERB
ejde-397	1107	2	the	the	DET
ejde-397	1107	3	following	follow	VERB
ejde-397	1107	4	abstract	abstract	ADJ
ejde-397	1107	5	time	time	NOUN
ejde-397	1107	6	-	-	PUNCT
ejde-397	1107	7	fractional	fractional	ADJ
ejde-397	1107	8	maxwell	maxwell	PROPN
ejde-397	1107	9	’s	’s	PART
ejde-397	1107	10	equations	equation	NOUN
ejde-397	1107	11	:	:	PUNCT
ejde-397	1107	12	rote	rote	VERB
ejde-397	1107	13	=	=	PUNCT
ejde-397	1107	14	−dα	−dα	PROPN
ejde-397	1107	15	t	t	PROPN
ejde-397	1107	16	b	b	NUM
ejde-397	1107	17	,	,	PUNCT
ejde-397	1107	18	roth	roth	PROPN
ejde-397	1107	19	=	=	PUNCT
ejde-397	1108	1	dα	dα	ADP
ejde-397	1108	2	t	t	PROPN
ejde-397	1108	3	d	d	PROPN
ejde-397	1109	1	+	+	CCONJ
ejde-397	1109	2	j	j	PROPN
ejde-397	1109	3	(	(	PUNCT
ejde-397	1109	4	5.21	5.21	NUM
ejde-397	1109	5	)	)	PUNCT
ejde-397	1109	6	in	in	ADP
ejde-397	1109	7	r3	r3	PROPN
ejde-397	1109	8	,	,	PUNCT
ejde-397	1109	9	where	where	SCONJ
ejde-397	1109	10	e	e	X
ejde-397	1109	11	(	(	PUNCT
ejde-397	1109	12	resp	resp	NOUN
ejde-397	1109	13	.	.	PUNCT
ejde-397	1110	1	h	h	X
ejde-397	1110	2	)	)	PUNCT
ejde-397	1110	3	denotes	denote	VERB
ejde-397	1110	4	the	the	DET
ejde-397	1110	5	electric	electric	PROPN
ejde-397	1110	6	(	(	PUNCT
ejde-397	1110	7	resp	resp	NOUN
ejde-397	1110	8	.	.	PUNCT
ejde-397	1111	1	magnetic	magnetic	ADJ
ejde-397	1111	2	)	)	PUNCT
ejde-397	1111	3	field	field	NOUN
ejde-397	1111	4	intensity	intensity	NOUN
ejde-397	1111	5	,	,	PUNCT
ejde-397	1111	6	b	b	PROPN
ejde-397	1111	7	(	(	PUNCT
ejde-397	1111	8	resp	resp	NOUN
ejde-397	1111	9	.	.	PUNCT
ejde-397	1112	1	d	d	X
ejde-397	1112	2	)	)	PUNCT
ejde-397	1112	3	denotes	denote	VERB
ejde-397	1112	4	the	the	DET
ejde-397	1112	5	electric	electric	PROPN
ejde-397	1112	6	(	(	PUNCT
ejde-397	1112	7	resp	resp	NOUN
ejde-397	1112	8	.	.	PUNCT
ejde-397	1113	1	magnetic	magnetic	ADJ
ejde-397	1113	2	)	)	PUNCT
ejde-397	1113	3	flux	flux	PROPN
ejde-397	1113	4	density	density	NOUN
ejde-397	1113	5	,	,	PUNCT
ejde-397	1113	6	and	and	CCONJ
ejde-397	1113	7	where	where	SCONJ
ejde-397	1113	8	j	j	PROPN
ejde-397	1113	9	is	be	AUX
ejde-397	1113	10	the	the	DET
ejde-397	1113	11	current	current	ADJ
ejde-397	1113	12	density	density	NOUN
ejde-397	1113	13	.	.	PUNCT
ejde-397	1114	1	it	it	PRON
ejde-397	1114	2	is	be	AUX
ejde-397	1114	3	assumed	assume	VERB
ejde-397	1114	4	that	that	SCONJ
ejde-397	1114	5	the	the	DET
ejde-397	1114	6	medium	medium	NOUN
ejde-397	1114	7	which	which	PRON
ejde-397	1114	8	fills	fill	VERB
ejde-397	1114	9	the	the	DET
ejde-397	1114	10	space	space	NOUN
ejde-397	1114	11	r3	r3	PROPN
ejde-397	1114	12	is	be	AUX
ejde-397	1114	13	linear	linear	ADJ
ejde-397	1114	14	but	but	CCONJ
ejde-397	1114	15	possibly	possibly	ADV
ejde-397	1114	16	anisotropic	anisotropic	VERB
ejde-397	1114	17	and	and	CCONJ
ejde-397	1114	18	nonhomogeneous	nonhomogeneous	NOUN
ejde-397	1114	19	,	,	PUNCT
ejde-397	1114	20	which	which	PRON
ejde-397	1114	21	means	mean	VERB
ejde-397	1114	22	that	that	SCONJ
ejde-397	1114	23	d	d	PROPN
ejde-397	1114	24	=	=	PUNCT
ejde-397	1114	25	εe	εe	PROPN
ejde-397	1114	26	,	,	PUNCT
ejde-397	1114	27	b	b	X
ejde-397	1114	28	=	=	SYM
ejde-397	1114	29	µh	µh	PROPN
ejde-397	1114	30	and	and	CCONJ
ejde-397	1114	31	j	j	PROPN
ejde-397	1114	32	=	=	NOUN
ejde-397	1114	33	σe	σe	PROPN
ejde-397	1115	1	+	+	NUM
ejde-397	1115	2	j	j	NOUN
ejde-397	1115	3	′	′	NOUN
ejde-397	1115	4	with	with	ADP
ejde-397	1115	5	some	some	DET
ejde-397	1115	6	3	3	NUM
ejde-397	1115	7	×	×	NOUN
ejde-397	1115	8	3	3	NUM
ejde-397	1115	9	real	real	ADJ
ejde-397	1115	10	matrices	matrix	NOUN
ejde-397	1115	11	ε(x	ε(x	NOUN
ejde-397	1115	12	)	)	PUNCT
ejde-397	1115	13	,	,	PUNCT
ejde-397	1115	14	µ(x	µ(x	NOUN
ejde-397	1115	15	)	)	PUNCT
ejde-397	1115	16	,	,	PUNCT
ejde-397	1115	17	σ(x	σ(x	PROPN
ejde-397	1115	18	)	)	PUNCT
ejde-397	1115	19	(	(	PUNCT
ejde-397	1115	20	x	x	SYM
ejde-397	1115	21	∈	∈	PROPN
ejde-397	1115	22	r3	r3	PROPN
ejde-397	1115	23	)	)	PUNCT
ejde-397	1115	24	and	and	CCONJ
ejde-397	1115	25	j	j	PROPN
ejde-397	1116	1	′	′	NUM
ejde-397	1116	2	being	be	AUX
ejde-397	1116	3	a	a	DET
ejde-397	1116	4	given	give	VERB
ejde-397	1116	5	forced	force	VERB
ejde-397	1116	6	current	current	ADJ
ejde-397	1116	7	density	density	NOUN
ejde-397	1116	8	.	.	PUNCT
ejde-397	1117	1	let	let	VERB
ejde-397	1117	2	any	any	DET
ejde-397	1117	3	component	component	NOUN
ejde-397	1117	4	of	of	ADP
ejde-397	1117	5	ε(x	ε(x	NOUN
ejde-397	1117	6	)	)	PUNCT
ejde-397	1117	7	,	,	PUNCT
ejde-397	1117	8	µ(x	µ(x	NOUN
ejde-397	1117	9	)	)	PUNCT
ejde-397	1117	10	,	,	PUNCT
ejde-397	1117	11	σ(x	σ(x	PROPN
ejde-397	1117	12	)	)	PUNCT
ejde-397	1117	13	be	be	VERB
ejde-397	1117	14	a	a	DET
ejde-397	1117	15	bounded	bounded	ADJ
ejde-397	1117	16	,	,	PUNCT
ejde-397	1117	17	measurable	measurable	ADJ
ejde-397	1117	18	function	function	NOUN
ejde-397	1117	19	in	in	ADP
ejde-397	1117	20	r3	r3	PROPN
ejde-397	1117	21	,	,	PUNCT
ejde-397	1117	22	let	let	VERB
ejde-397	1117	23	the	the	DET
ejde-397	1117	24	conditions	condition	NOUN
ejde-397	1117	25	[	[	X
ejde-397	1117	26	17	17	NUM
ejde-397	1117	27	,	,	PUNCT
ejde-397	1117	28	(	(	PUNCT
ejde-397	1117	29	2.23)-(2.25	2.23)-(2.25	NOUN
ejde-397	1117	30	)	)	PUNCT
ejde-397	1117	31	]	]	PUNCT
ejde-397	1117	32	hold	hold	VERB
ejde-397	1117	33	,	,	PUNCT
ejde-397	1117	34	and	and	CCONJ
ejde-397	1117	35	let	let	VERB
ejde-397	1117	36	f(t	f(t	NOUN
ejde-397	1117	37	)	)	PUNCT
ejde-397	1118	1	=	=	SYM
ejde-397	1118	2	−(j	−(j	NOUN
ejde-397	1118	3	′	′	NUM
ejde-397	1118	4	(	(	PUNCT
ejde-397	1118	5	·	·	PROPN
ejde-397	1118	6	,	,	PUNCT
ejde-397	1118	7	t	t	PROPN
ejde-397	1118	8	)	)	PUNCT
ejde-397	1118	9	0)t	0)t	NOUN
ejde-397	1118	10	.	.	PUNCT
ejde-397	1119	1	then	then	ADV
ejde-397	1119	2	we	we	PRON
ejde-397	1119	3	can	can	AUX
ejde-397	1119	4	formulate	formulate	VERB
ejde-397	1119	5	the	the	DET
ejde-397	1119	6	problem	problem	NOUN
ejde-397	1119	7	(	(	PUNCT
ejde-397	1119	8	5.21	5.21	NUM
ejde-397	1119	9	)	)	PUNCT
ejde-397	1119	10	in	in	ADP
ejde-397	1119	11	the	the	DET
ejde-397	1119	12	abstract	abstract	ADJ
ejde-397	1119	13	form	form	NOUN
ejde-397	1119	14	b∗dα	b∗dα	PROPN
ejde-397	1119	15	t	t	X
ejde-397	1119	16	bv1(t	bv1(t	PROPN
ejde-397	1119	17	)	)	PUNCT
ejde-397	1119	18	=	=	PUNCT
ejde-397	1119	19	av1(t	av1(t	X
ejde-397	1119	20	)	)	PUNCT
ejde-397	1120	1	+	+	CCONJ
ejde-397	1120	2	f(t	f(t	NOUN
ejde-397	1120	3	)	)	PUNCT
ejde-397	1120	4	,	,	PUNCT
ejde-397	1120	5	t	t	PROPN
ejde-397	1120	6	≥	≥	NUM
ejde-397	1120	7	0	0	NUM
ejde-397	1120	8	;	;	PUNCT
ejde-397	1120	9	bv1(0	bv1(0	NOUN
ejde-397	1120	10	)	)	PUNCT
ejde-397	1121	1	=	=	SYM
ejde-397	1122	1	u0	u0	ADJ
ejde-397	1122	2	,	,	PUNCT
ejde-397	1122	3	(	(	PUNCT
ejde-397	1122	4	5.22	5.22	NUM
ejde-397	1122	5	)	)	PUNCT
ejde-397	1122	6	in	in	ADP
ejde-397	1122	7	the	the	DET
ejde-397	1122	8	space	space	NOUN
ejde-397	1122	9	x	x	NOUN
ejde-397	1122	10	:	:	PUNCT
ejde-397	1122	11	=	=	X
ejde-397	1122	12	{	{	PUNCT
ejde-397	1122	13	l2(r3)}6	l2(r3)}6	NOUN
ejde-397	1122	14	,	,	PUNCT
ejde-397	1122	15	using	use	VERB
ejde-397	1122	16	the	the	DET
ejde-397	1122	17	bounded	bounded	ADJ
ejde-397	1122	18	self	self	NOUN
ejde-397	1122	19	-	-	PUNCT
ejde-397	1122	20	adjoint	adjoint	NOUN
ejde-397	1122	21	operator	operator	NOUN
ejde-397	1122	22	b	b	PROPN
ejde-397	1122	23	of	of	ADP
ejde-397	1122	24	multiplication	multiplication	NOUN
ejde-397	1122	25	by	by	ADP
ejde-397	1122	26	√	√	ADP
ejde-397	1122	27	c(x	c(x	NOUN
ejde-397	1122	28	)	)	PUNCT
ejde-397	1122	29	acting	act	VERB
ejde-397	1122	30	in	in	ADP
ejde-397	1122	31	x	x	NOUN
ejde-397	1122	32	,	,	PUNCT
ejde-397	1122	33	and	and	CCONJ
ejde-397	1122	34	a	a	DET
ejde-397	1122	35	being	be	AUX
ejde-397	1122	36	the	the	DET
ejde-397	1122	37	closed	closed	ADJ
ejde-397	1122	38	linear	linear	ADJ
ejde-397	1122	39	operator	operator	NOUN
ejde-397	1122	40	in	in	ADP
ejde-397	1122	41	x	x	PUNCT
ejde-397	1122	42	given	give	VERB
ejde-397	1122	43	by	by	ADP
ejde-397	1122	44	[	[	X
ejde-397	1122	45	17	17	NUM
ejde-397	1122	46	,	,	PUNCT
ejde-397	1122	47	(	(	PUNCT
ejde-397	1122	48	2.27	2.27	NUM
ejde-397	1122	49	)	)	PUNCT
ejde-397	1122	50	]	]	PUNCT
ejde-397	1122	51	.	.	PUNCT
ejde-397	1123	1	36	36	NUM
ejde-397	1123	2	m.	m.	NOUN
ejde-397	1123	3	kostić	kostić	NOUN
ejde-397	1123	4	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1123	5	in	in	ADP
ejde-397	1123	6	our	our	PRON
ejde-397	1123	7	concrete	concrete	ADJ
ejde-397	1123	8	situation	situation	NOUN
ejde-397	1123	9	,	,	PUNCT
ejde-397	1123	10	the	the	DET
ejde-397	1123	11	conditions	condition	NOUN
ejde-397	1123	12	[	[	X
ejde-397	1123	13	17	17	NUM
ejde-397	1123	14	,	,	PUNCT
ejde-397	1123	15	(	(	PUNCT
ejde-397	1123	16	2.10	2.10	NUM
ejde-397	1123	17	)	)	PUNCT
ejde-397	1123	18	and	and	CCONJ
ejde-397	1123	19	(	(	PUNCT
ejde-397	1123	20	2.14	2.14	NUM
ejde-397	1123	21	)	)	PUNCT
ejde-397	1123	22	]	]	PUNCT
ejde-397	1123	23	hold	hold	VERB
ejde-397	1123	24	,	,	PUNCT
ejde-397	1123	25	so	so	SCONJ
ejde-397	1123	26	that	that	SCONJ
ejde-397	1123	27	the	the	DET
ejde-397	1123	28	assumptions	assumption	NOUN
ejde-397	1123	29	f	f	X
ejde-397	1123	30	∈	∈	PROPN
ejde-397	1123	31	c2([0,∞	c2([0,∞	NOUN
ejde-397	1123	32	)	)	PUNCT
ejde-397	1123	33	:	:	PUNCT
ejde-397	1123	34	x	x	X
ejde-397	1123	35	)	)	PUNCT
ejde-397	1123	36	and	and	CCONJ
ejde-397	1123	37	u0	u0	ADJ
ejde-397	1123	38	=	=	NOUN
ejde-397	1123	39	bv0	bv0	NOUN
ejde-397	1123	40	for	for	ADP
ejde-397	1123	41	some	some	DET
ejde-397	1123	42	v0	v0	NOUN
ejde-397	1123	43	∈	∈	PROPN
ejde-397	1123	44	d(a	d(a	PROPN
ejde-397	1123	45	)	)	PUNCT
ejde-397	1123	46	satisfying	satisfy	VERB
ejde-397	1123	47	av0	av0	PROPN
ejde-397	1123	48	+	+	CCONJ
ejde-397	1123	49	f(0	f(0	NOUN
ejde-397	1123	50	)	)	PUNCT
ejde-397	1123	51	∈	∈	PROPN
ejde-397	1123	52	r(b∗	r(b∗	NOUN
ejde-397	1123	53	)	)	PUNCT
ejde-397	1123	54	ensure	ensure	VERB
ejde-397	1123	55	by	by	ADP
ejde-397	1123	56	[	[	X
ejde-397	1123	57	17	17	NUM
ejde-397	1123	58	,	,	PUNCT
ejde-397	1123	59	corollary	corollary	NOUN
ejde-397	1123	60	2.11	2.11	NUM
ejde-397	1123	61	]	]	PUNCT
ejde-397	1123	62	that	that	SCONJ
ejde-397	1123	63	the	the	DET
ejde-397	1123	64	problem	problem	NOUN
ejde-397	1123	65	(	(	PUNCT
ejde-397	1123	66	5.22	5.22	NUM
ejde-397	1123	67	)	)	PUNCT
ejde-397	1123	68	has	have	VERB
ejde-397	1123	69	a	a	DET
ejde-397	1123	70	unique	unique	ADJ
ejde-397	1123	71	strict	strict	ADJ
ejde-397	1123	72	solution	solution	NOUN
ejde-397	1123	73	v1	v1	NOUN
ejde-397	1123	74	(	(	PUNCT
ejde-397	1123	75	·	·	PUNCT
ejde-397	1123	76	)	)	PUNCT
ejde-397	1123	77	in	in	ADP
ejde-397	1123	78	the	the	DET
ejde-397	1123	79	sense	sense	NOUN
ejde-397	1123	80	of	of	ADP
ejde-397	1123	81	equation	equation	NOUN
ejde-397	1123	82	[	[	X
ejde-397	1123	83	17	17	NUM
ejde-397	1123	84	,	,	PUNCT
ejde-397	1123	85	(	(	PUNCT
ejde-397	1123	86	2.13	2.13	NUM
ejde-397	1123	87	)	)	PUNCT
ejde-397	1123	88	]	]	PUNCT
ejde-397	1123	89	.	.	PUNCT
ejde-397	1124	1	suppose	suppose	VERB
ejde-397	1124	2	,	,	PUNCT
ejde-397	1124	3	additionally	additionally	ADV
ejde-397	1124	4	,	,	PUNCT
ejde-397	1124	5	that	that	SCONJ
ejde-397	1124	6	the	the	DET
ejde-397	1124	7	function	function	NOUN
ejde-397	1124	8	f	f	PROPN
ejde-397	1124	9	′′(t	′′(t	PROPN
ejde-397	1124	10	)	)	PUNCT
ejde-397	1124	11	is	be	AUX
ejde-397	1124	12	exponentially	exponentially	ADV
ejde-397	1124	13	bounded	bound	VERB
ejde-397	1124	14	.	.	PUNCT
ejde-397	1125	1	then	then	ADV
ejde-397	1125	2	we	we	PRON
ejde-397	1125	3	can	can	AUX
ejde-397	1125	4	use	use	VERB
ejde-397	1125	5	[	[	X
ejde-397	1125	6	17	17	NUM
ejde-397	1125	7	,	,	PUNCT
ejde-397	1125	8	theorem	theorem	VERB
ejde-397	1125	9	2.5	2.5	NUM
ejde-397	1125	10	]	]	PUNCT
ejde-397	1125	11	,	,	PUNCT
ejde-397	1125	12	the	the	DET
ejde-397	1125	13	proof	proof	NOUN
ejde-397	1125	14	of	of	ADP
ejde-397	1125	15	[	[	X
ejde-397	1125	16	17	17	NUM
ejde-397	1125	17	,	,	PUNCT
ejde-397	1125	18	corollary	corollary	NOUN
ejde-397	1125	19	2.11	2.11	NUM
ejde-397	1125	20	]	]	PUNCT
ejde-397	1125	21	and	and	CCONJ
ejde-397	1125	22	the	the	DET
ejde-397	1125	23	arguments	argument	NOUN
ejde-397	1125	24	from	from	ADP
ejde-397	1125	25	the	the	DET
ejde-397	1125	26	part	part	NOUN
ejde-397	1125	27	(	(	PUNCT
ejde-397	1125	28	i)/(a	i)/(a	NOUN
ejde-397	1125	29	)	)	PUNCT
ejde-397	1125	30	of	of	ADP
ejde-397	1125	31	this	this	DET
ejde-397	1125	32	example	example	NOUN
ejde-397	1125	33	in	in	ADP
ejde-397	1125	34	order	order	NOUN
ejde-397	1125	35	to	to	PART
ejde-397	1125	36	see	see	VERB
ejde-397	1125	37	that	that	SCONJ
ejde-397	1125	38	the	the	DET
ejde-397	1125	39	solution	solution	NOUN
ejde-397	1125	40	v1	v1	PROPN
ejde-397	1125	41	∈	∈	PROPN
ejde-397	1125	42	c([0,∞	c([0,∞	NOUN
ejde-397	1125	43	)	)	PUNCT
ejde-397	1125	44	:	:	PUNCT
ejde-397	1125	45	x	x	X
ejde-397	1125	46	)	)	PUNCT
ejde-397	1125	47	is	be	AUX
ejde-397	1125	48	exponentially	exponentially	ADV
ejde-397	1125	49	bounded	bound	VERB
ejde-397	1125	50	,	,	PUNCT
ejde-397	1125	51	as	as	ADV
ejde-397	1125	52	well	well	ADV
ejde-397	1125	53	as	as	ADP
ejde-397	1125	54	that	that	PRON
ejde-397	1125	55	h(t	h(t	PROPN
ejde-397	1125	56	)	)	PUNCT
ejde-397	1125	57	:	:	PUNCT
ejde-397	1126	1	=	=	PUNCT
ejde-397	1126	2	(	(	PUNCT
ejde-397	1126	3	d	d	X
ejde-397	1126	4	/	/	SYM
ejde-397	1126	5	dt)bv1(t	dt)bv1(t	PROPN
ejde-397	1126	6	)	)	PUNCT
ejde-397	1126	7	,	,	PUNCT
ejde-397	1126	8	bv1(t	bv1(t	PROPN
ejde-397	1126	9	)	)	PUNCT
ejde-397	1126	10	and	and	CCONJ
ejde-397	1126	11	av1(t	av1(t	PRON
ejde-397	1126	12	)	)	PUNCT
ejde-397	1126	13	are	be	AUX
ejde-397	1126	14	continuous	continuous	ADJ
ejde-397	1126	15	and	and	CCONJ
ejde-397	1126	16	exponentially	exponentially	ADV
ejde-397	1126	17	bounded	bound	VERB
ejde-397	1126	18	for	for	ADP
ejde-397	1126	19	t	t	PROPN
ejde-397	1126	20	≥	≥	PROPN
ejde-397	1126	21	0	0	NUM
ejde-397	1126	22	.	.	PUNCT
ejde-397	1127	1	define	define	VERB
ejde-397	1127	2	vα(t	vα(t	NOUN
ejde-397	1127	3	)	)	PUNCT
ejde-397	1127	4	and	and	CCONJ
ejde-397	1127	5	fα(t	fα(t	NOUN
ejde-397	1127	6	)	)	PUNCT
ejde-397	1127	7	as	as	ADP
ejde-397	1127	8	before	before	ADV
ejde-397	1127	9	,	,	PUNCT
ejde-397	1127	10	hα(t	hα(t	NUM
ejde-397	1127	11	)	)	PUNCT
ejde-397	1127	12	:	:	PUNCT
ejde-397	1128	1	=	=	SYM
ejde-397	1128	2	∫∞	∫∞	NOUN
ejde-397	1128	3	0	0	PUNCT
ejde-397	1128	4	t−αφα(st−α)h(s	t−αφα(st−α)h(	NOUN
ejde-397	1128	5	)	)	PUNCT
ejde-397	1128	6	ds	ds	PROPN
ejde-397	1128	7	,	,	PUNCT
ejde-397	1128	8	t	t	NOUN
ejde-397	1128	9	>	>	X
ejde-397	1128	10	0	0	PUNCT
ejde-397	1128	11	and	and	CCONJ
ejde-397	1128	12	hα(0	hα(0	NOUN
ejde-397	1128	13	)	)	PUNCT
ejde-397	1128	14	:	:	PUNCT
ejde-397	1128	15	=	=	PUNCT
ejde-397	1128	16	h(0	h(0	PROPN
ejde-397	1128	17	)	)	PUNCT
ejde-397	1128	18	.	.	PUNCT
ejde-397	1129	1	performing	perform	VERB
ejde-397	1129	2	the	the	DET
ejde-397	1129	3	laplace	laplace	NOUN
ejde-397	1129	4	transform	transform	NOUN
ejde-397	1129	5	,	,	PUNCT
ejde-397	1129	6	it	it	PRON
ejde-397	1129	7	can	can	AUX
ejde-397	1129	8	be	be	AUX
ejde-397	1129	9	simply	simply	ADV
ejde-397	1129	10	verifed	verife	VERB
ejde-397	1129	11	that	that	SCONJ
ejde-397	1129	12	(	(	PUNCT
ejde-397	1129	13	g1−α	g1−α	PROPN
ejde-397	1129	14	∗	∗	NOUN
ejde-397	1129	15	(	(	PUNCT
ejde-397	1129	16	bvα	bvα	NOUN
ejde-397	1129	17	−	−	NOUN
ejde-397	1129	18	u0))(t	u0))(t	SYM
ejde-397	1129	19	)	)	PUNCT
ejde-397	1130	1	=	=	NOUN
ejde-397	1130	2	∫	∫	PROPN
ejde-397	1130	3	t	t	PROPN
ejde-397	1130	4	0	0	NUM
ejde-397	1130	5	hα(s	hα(s	SYM
ejde-397	1130	6	)	)	PUNCT
ejde-397	1130	7	ds	ds	PROPN
ejde-397	1130	8	,	,	PUNCT
ejde-397	1130	9	t	t	PROPN
ejde-397	1130	10	≥	≥	NUM
ejde-397	1130	11	0	0	NUM
ejde-397	1130	12	,	,	PUNCT
ejde-397	1130	13	so	so	SCONJ
ejde-397	1130	14	that	that	SCONJ
ejde-397	1130	15	dα	dα	DET
ejde-397	1130	16	t	t	NOUN
ejde-397	1130	17	bvα(t	bvα(t	PROPN
ejde-397	1130	18	)	)	PUNCT
ejde-397	1130	19	exists	exist	VERB
ejde-397	1130	20	and	and	CCONJ
ejde-397	1130	21	equals	equal	VERB
ejde-397	1130	22	to	to	PART
ejde-397	1130	23	hα(t	hα(t	VERB
ejde-397	1130	24	)	)	PUNCT
ejde-397	1130	25	.	.	PUNCT
ejde-397	1131	1	on	on	ADP
ejde-397	1131	2	the	the	DET
ejde-397	1131	3	other	other	ADJ
ejde-397	1131	4	hand	hand	NOUN
ejde-397	1131	5	,	,	PUNCT
ejde-397	1131	6	we	we	PRON
ejde-397	1131	7	have	have	VERB
ejde-397	1131	8	b∗bv1(t	b∗bv1(t	PROPN
ejde-397	1131	9	)	)	PUNCT
ejde-397	1132	1	=	=	SYM
ejde-397	1132	2	a	a	PRON
ejde-397	1132	3	(	(	PUNCT
ejde-397	1132	4	g1	g1	PROPN
ejde-397	1132	5	∗	∗	NOUN
ejde-397	1132	6	v1	v1	NOUN
ejde-397	1132	7	)	)	PUNCT
ejde-397	1132	8	(	(	PUNCT
ejde-397	1132	9	t	t	X
ejde-397	1132	10	)	)	PUNCT
ejde-397	1132	11	+	+	NOUN
ejde-397	1132	12	b∗u0	b∗u0	PROPN
ejde-397	1132	13	+	+	CCONJ
ejde-397	1132	14	∫	∫	PROPN
ejde-397	1132	15	t	t	PROPN
ejde-397	1132	16	0	0	NUM
ejde-397	1132	17	f(s	f(	NOUN
ejde-397	1132	18	)	)	PUNCT
ejde-397	1132	19	ds	ds	PROPN
ejde-397	1132	20	,	,	PUNCT
ejde-397	1132	21	t	t	PROPN
ejde-397	1132	22	≥	≥	NUM
ejde-397	1132	23	0	0	NUM
ejde-397	1132	24	,	,	PUNCT
ejde-397	1132	25	so	so	SCONJ
ejde-397	1132	26	that	that	SCONJ
ejde-397	1132	27	b∗bvα(t	b∗bvα(t	NOUN
ejde-397	1132	28	)	)	PUNCT
ejde-397	1132	29	=	=	SYM
ejde-397	1133	1	a	a	PRON
ejde-397	1133	2	(	(	PUNCT
ejde-397	1133	3	gα	gα	ADP
ejde-397	1133	4	∗	∗	NOUN
ejde-397	1133	5	vα	vα	PROPN
ejde-397	1133	6	)	)	PUNCT
ejde-397	1133	7	(	(	PUNCT
ejde-397	1133	8	t	t	X
ejde-397	1133	9	)	)	PUNCT
ejde-397	1134	1	+	+	NOUN
ejde-397	1134	2	b∗u0	b∗u0	PROPN
ejde-397	1134	3	+	+	CCONJ
ejde-397	1134	4	∫	∫	PROPN
ejde-397	1134	5	t	t	PROPN
ejde-397	1134	6	0	0	NUM
ejde-397	1134	7	fα(s	fα(s	CCONJ
ejde-397	1134	8	)	)	PUNCT
ejde-397	1134	9	ds	ds	PROPN
ejde-397	1134	10	,	,	PUNCT
ejde-397	1134	11	t	t	PROPN
ejde-397	1134	12	≥	≥	NOUN
ejde-397	1134	13	0	0	NUM
ejde-397	1134	14	by	by	ADP
ejde-397	1134	15	theorem	theorem	NOUN
ejde-397	1134	16	4.8	4.8	NUM
ejde-397	1134	17	.	.	PUNCT
ejde-397	1135	1	this	this	PRON
ejde-397	1135	2	implies	imply	VERB
ejde-397	1135	3	dα	dα	ADP
ejde-397	1135	4	t	t	PROPN
ejde-397	1135	5	b	b	PROPN
ejde-397	1135	6	∗bvα(t	∗bvα(t	X
ejde-397	1135	7	)	)	PUNCT
ejde-397	1135	8	=	=	SYM
ejde-397	1135	9	avα(t	avα(t	PROPN
ejde-397	1135	10	)	)	PUNCT
ejde-397	1135	11	+	+	PUNCT
ejde-397	1135	12	fα(t	fα(t	X
ejde-397	1135	13	)	)	PUNCT
ejde-397	1135	14	and	and	CCONJ
ejde-397	1135	15	,	,	PUNCT
ejde-397	1135	16	since	since	SCONJ
ejde-397	1135	17	dα	dα	DET
ejde-397	1135	18	t	t	PROPN
ejde-397	1135	19	bvα(t	bvα(t	PROPN
ejde-397	1135	20	)	)	PUNCT
ejde-397	1135	21	exists	exist	VERB
ejde-397	1135	22	,	,	PUNCT
ejde-397	1135	23	b∗dα	b∗dα	PRON
ejde-397	1135	24	t	t	NOUN
ejde-397	1135	25	bvα(t	bvα(t	PROPN
ejde-397	1135	26	)	)	PUNCT
ejde-397	1135	27	=	=	SYM
ejde-397	1135	28	avα(t	avα(t	PROPN
ejde-397	1135	29	)	)	PUNCT
ejde-397	1135	30	+	+	CCONJ
ejde-397	1135	31	fα(t	fα(t	NUM
ejde-397	1135	32	)	)	PUNCT
ejde-397	1135	33	,	,	PUNCT
ejde-397	1135	34	t	t	PROPN
ejde-397	1135	35	≥	≥	NUM
ejde-397	1135	36	0	0	NUM
ejde-397	1135	37	.	.	PUNCT
ejde-397	1136	1	clearly	clearly	ADV
ejde-397	1136	2	,	,	PUNCT
ejde-397	1136	3	bvα(0	bvα(0	ADJ
ejde-397	1136	4	)	)	PUNCT
ejde-397	1137	1	=	=	PUNCT
ejde-397	1137	2	u0	u0	ADJ
ejde-397	1137	3	so	so	SCONJ
ejde-397	1137	4	that	that	SCONJ
ejde-397	1137	5	vα	vα	INTJ
ejde-397	1137	6	∈	∈	PROPN
ejde-397	1137	7	c([0,∞	c([0,∞	PROPN
ejde-397	1137	8	)	)	PUNCT
ejde-397	1137	9	:	:	PUNCT
ejde-397	1138	1	x	x	X
ejde-397	1138	2	)	)	PUNCT
ejde-397	1138	3	is	be	AUX
ejde-397	1138	4	an	an	DET
ejde-397	1138	5	exponentially	exponentially	ADV
ejde-397	1138	6	bounded	bound	VERB
ejde-397	1138	7	solution	solution	NOUN
ejde-397	1138	8	of	of	ADP
ejde-397	1138	9	problem	problem	NOUN
ejde-397	1138	10	b∗dα	b∗dα	PROPN
ejde-397	1138	11	t	t	NOUN
ejde-397	1138	12	bvα(t	bvα(t	PROPN
ejde-397	1138	13	)	)	PUNCT
ejde-397	1138	14	=	=	SYM
ejde-397	1138	15	avα(t	avα(t	PROPN
ejde-397	1138	16	)	)	PUNCT
ejde-397	1138	17	+	+	CCONJ
ejde-397	1138	18	fα(t	fα(t	NUM
ejde-397	1138	19	)	)	PUNCT
ejde-397	1138	20	,	,	PUNCT
ejde-397	1138	21	t	t	PROPN
ejde-397	1138	22	≥	≥	NUM
ejde-397	1138	23	0	0	NUM
ejde-397	1138	24	;	;	PUNCT
ejde-397	1138	25	bvα(0	bvα(0	NUM
ejde-397	1138	26	)	)	PUNCT
ejde-397	1139	1	=	=	PUNCT
ejde-397	1139	2	u0	u0	ADJ
ejde-397	1139	3	,	,	PUNCT
ejde-397	1139	4	(	(	PUNCT
ejde-397	1139	5	5.23	5.23	NUM
ejde-397	1139	6	)	)	PUNCT
ejde-397	1139	7	that	that	PRON
ejde-397	1139	8	is	be	AUX
ejde-397	1139	9	analytically	analytically	ADV
ejde-397	1139	10	extensible	extensible	ADJ
ejde-397	1139	11	on	on	ADP
ejde-397	1139	12	the	the	DET
ejde-397	1139	13	sector	sector	NOUN
ejde-397	1139	14	σmin	σmin	NOUN
ejde-397	1139	15	(	(	PUNCT
ejde-397	1139	16	(	(	PUNCT
ejde-397	1139	17	1	1	NUM
ejde-397	1139	18	α−1)π2	α−1)π2	NUM
ejde-397	1139	19	,	,	PUNCT
ejde-397	1139	20	π	π	NOUN
ejde-397	1139	21	)	)	PUNCT
ejde-397	1139	22	and	and	CCONJ
ejde-397	1139	23	satisfies	satisfie	NOUN
ejde-397	1139	24	,	,	PUNCT
ejde-397	1139	25	in	in	ADP
ejde-397	1139	26	addition	addition	NOUN
ejde-397	1139	27	,	,	PUNCT
ejde-397	1139	28	that	that	SCONJ
ejde-397	1139	29	the	the	DET
ejde-397	1139	30	mapping	mapping	NOUN
ejde-397	1139	31	avα	avα	NOUN
ejde-397	1139	32	∈	∈	PROPN
ejde-397	1139	33	c([0,∞	c([0,∞	PROPN
ejde-397	1139	34	)	)	PUNCT
ejde-397	1139	35	:	:	PUNCT
ejde-397	1140	1	x	x	X
ejde-397	1140	2	)	)	PUNCT
ejde-397	1140	3	is	be	AUX
ejde-397	1140	4	exponentially	exponentially	ADV
ejde-397	1140	5	bounded	bound	VERB
ejde-397	1140	6	and	and	CCONJ
ejde-397	1140	7	analytically	analytically	ADV
ejde-397	1140	8	extensible	extensible	ADJ
ejde-397	1140	9	on	on	ADP
ejde-397	1140	10	the	the	DET
ejde-397	1140	11	same	same	ADJ
ejde-397	1140	12	sector	sector	NOUN
ejde-397	1140	13	,	,	PUNCT
ejde-397	1140	14	as	as	ADV
ejde-397	1140	15	well	well	ADV
ejde-397	1140	16	.	.	PUNCT
ejde-397	1141	1	the	the	DET
ejde-397	1141	2	uniqueness	uniqueness	NOUN
ejde-397	1141	3	of	of	ADP
ejde-397	1141	4	solutions	solution	NOUN
ejde-397	1141	5	of	of	ADP
ejde-397	1141	6	problem	problem	NOUN
ejde-397	1141	7	(	(	PUNCT
ejde-397	1141	8	pα	pα	NOUN
ejde-397	1141	9	)	)	PUNCT
ejde-397	1141	10	follows	follow	VERB
ejde-397	1141	11	from	from	ADP
ejde-397	1141	12	theorem	theorem	ADJ
ejde-397	1141	13	4.6	4.6	NUM
ejde-397	1141	14	.	.	PUNCT
ejde-397	1142	1	we	we	PRON
ejde-397	1142	2	end	end	VERB
ejde-397	1142	3	this	this	DET
ejde-397	1142	4	example	example	NOUN
ejde-397	1142	5	with	with	ADP
ejde-397	1142	6	the	the	DET
ejde-397	1142	7	observation	observation	NOUN
ejde-397	1142	8	that	that	PRON
ejde-397	1142	9	theorem	theorem	VERB
ejde-397	1142	10	4.8	4.8	NUM
ejde-397	1142	11	and	and	CCONJ
ejde-397	1142	12	theorem	theorem	VERB
ejde-397	1142	13	4.9	4.9	NUM
ejde-397	1142	14	can	can	AUX
ejde-397	1142	15	be	be	AUX
ejde-397	1142	16	successfully	successfully	ADV
ejde-397	1142	17	applied	apply	VERB
ejde-397	1142	18	in	in	ADP
ejde-397	1142	19	the	the	DET
ejde-397	1142	20	analysis	analysis	NOUN
ejde-397	1142	21	of	of	ADP
ejde-397	1142	22	a	a	DET
ejde-397	1142	23	large	large	ADJ
ejde-397	1142	24	class	class	NOUN
ejde-397	1142	25	of	of	ADP
ejde-397	1142	26	abstract	abstract	ADJ
ejde-397	1142	27	degenerate	degenerate	ADJ
ejde-397	1142	28	volterra	volterra	PROPN
ejde-397	1142	29	integro	integro	PROPN
ejde-397	1142	30	-	-	PUNCT
ejde-397	1142	31	differential	differential	NOUN
ejde-397	1142	32	equations	equation	NOUN
ejde-397	1142	33	that	that	PRON
ejde-397	1142	34	are	be	AUX
ejde-397	1142	35	subordinated	subordinate	VERB
ejde-397	1142	36	,	,	PUNCT
ejde-397	1142	37	in	in	ADP
ejde-397	1142	38	a	a	DET
ejde-397	1142	39	certain	certain	ADJ
ejde-397	1142	40	sense	sense	NOUN
ejde-397	1142	41	,	,	PUNCT
ejde-397	1142	42	to	to	PART
ejde-397	1142	43	degenerate	degenerate	VERB
ejde-397	1142	44	differential	differential	ADJ
ejde-397	1142	45	equations	equation	NOUN
ejde-397	1142	46	of	of	ADP
ejde-397	1142	47	first	first	ADJ
ejde-397	1142	48	and	and	CCONJ
ejde-397	1142	49	second	second	ADJ
ejde-397	1142	50	order	order	NOUN
ejde-397	1142	51	for	for	ADP
ejde-397	1142	52	which	which	PRON
ejde-397	1142	53	we	we	PRON
ejde-397	1142	54	know	know	VERB
ejde-397	1142	55	that	that	PRON
ejde-397	1142	56	are	be	AUX
ejde-397	1142	57	well	well	ADV
ejde-397	1142	58	posed	pose	VERB
ejde-397	1142	59	[	[	X
ejde-397	1142	60	17	17	NUM
ejde-397	1142	61	,	,	PUNCT
ejde-397	1142	62	22	22	NUM
ejde-397	1142	63	,	,	PUNCT
ejde-397	1142	64	25	25	NUM
ejde-397	1142	65	,	,	PUNCT
ejde-397	1142	66	71	71	NUM
ejde-397	1142	67	,	,	PUNCT
ejde-397	1142	68	73	73	NUM
ejde-397	1142	69	,	,	PUNCT
ejde-397	1142	70	75	75	NUM
ejde-397	1142	71	,	,	PUNCT
ejde-397	1142	72	76	76	NUM
ejde-397	1142	73	]	]	PUNCT
ejde-397	1142	74	.	.	PUNCT
ejde-397	1143	1	concerning	concern	VERB
ejde-397	1143	2	the	the	DET
ejde-397	1143	3	adjoint	adjoint	NOUN
ejde-397	1143	4	type	type	NOUN
ejde-397	1143	5	theorems	theorem	NOUN
ejde-397	1143	6	,	,	PUNCT
ejde-397	1143	7	it	it	PRON
ejde-397	1143	8	should	should	AUX
ejde-397	1143	9	be	be	AUX
ejde-397	1143	10	noticed	notice	VERB
ejde-397	1143	11	that	that	SCONJ
ejde-397	1143	12	the	the	DET
ejde-397	1143	13	assertions	assertion	NOUN
ejde-397	1143	14	of	of	ADP
ejde-397	1143	15	[	[	X
ejde-397	1143	16	36	36	NUM
ejde-397	1143	17	,	,	PUNCT
ejde-397	1143	18	theorem	theorem	VERB
ejde-397	1143	19	2.1.12(i)/(ii	2.1.12(i)/(ii	NUM
ejde-397	1143	20	)	)	PUNCT
ejde-397	1143	21	;	;	PUNCT
ejde-397	1143	22	theorem	theorem	VERB
ejde-397	1143	23	2.1.13	2.1.13	NUM
ejde-397	1143	24	]	]	PUNCT
ejde-397	1143	25	continue	continue	VERB
ejde-397	1143	26	to	to	PART
ejde-397	1143	27	hold	hold	VERB
ejde-397	1143	28	for	for	ADP
ejde-397	1143	29	(	(	PUNCT
ejde-397	1143	30	a	a	PRON
ejde-397	1143	31	,	,	PUNCT
ejde-397	1143	32	k)-regularized	k)-regularize	VERB
ejde-397	1143	33	c	c	X
ejde-397	1143	34	-	-	PUNCT
ejde-397	1143	35	regularized	regularize	VERB
ejde-397	1143	36	families	family	NOUN
ejde-397	1143	37	subgenerated	subgenerate	VERB
ejde-397	1143	38	by	by	ADP
ejde-397	1143	39	closed	close	VERB
ejde-397	1143	40	multivalued	multivalued	ADJ
ejde-397	1143	41	linear	linear	PROPN
ejde-397	1143	42	operators	operator	NOUN
ejde-397	1143	43	.	.	PUNCT
ejde-397	1144	1	furthermore	furthermore	ADV
ejde-397	1144	2	,	,	PUNCT
ejde-397	1144	3	it	it	PRON
ejde-397	1144	4	is	be	AUX
ejde-397	1144	5	not	not	PART
ejde-397	1144	6	necessary	necessary	ADJ
ejde-397	1144	7	to	to	PART
ejde-397	1144	8	assume	assume	VERB
ejde-397	1144	9	that	that	SCONJ
ejde-397	1144	10	the	the	DET
ejde-397	1144	11	operator	operator	NOUN
ejde-397	1144	12	a	a	PRON
ejde-397	1144	13	is	be	AUX
ejde-397	1144	14	densely	densely	ADV
ejde-397	1144	15	defined	define	VERB
ejde-397	1144	16	in	in	ADP
ejde-397	1144	17	the	the	DET
ejde-397	1144	18	case	case	NOUN
ejde-397	1144	19	of	of	ADP
ejde-397	1144	20	consideration	consideration	NOUN
ejde-397	1144	21	of	of	ADP
ejde-397	1144	22	[	[	X
ejde-397	1144	23	36	36	NUM
ejde-397	1144	24	,	,	PUNCT
ejde-397	1144	25	theorem	theorem	VERB
ejde-397	1144	26	2.1.12(i	2.1.12(i	NUM
ejde-397	1144	27	)	)	PUNCT
ejde-397	1144	28	]	]	PUNCT
ejde-397	1144	29	.	.	PUNCT
ejde-397	1145	1	suppose	suppose	VERB
ejde-397	1145	2	now	now	ADV
ejde-397	1145	3	that	that	SCONJ
ejde-397	1145	4	a	a	PRON
ejde-397	1145	5	is	be	AUX
ejde-397	1145	6	a	a	DET
ejde-397	1145	7	subgenerator	subgenerator	NOUN
ejde-397	1145	8	of	of	ADP
ejde-397	1145	9	an	an	DET
ejde-397	1145	10	(	(	PUNCT
ejde-397	1145	11	a	a	PRON
ejde-397	1145	12	,	,	PUNCT
ejde-397	1145	13	k)-regularized	k)-regularize	VERB
ejde-397	1145	14	c	c	NOUN
ejde-397	1145	15	-	-	PUNCT
ejde-397	1145	16	resolvent	resolvent	ADJ
ejde-397	1145	17	family	family	NOUN
ejde-397	1145	18	(	(	PUNCT
ejde-397	1145	19	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1145	20	)	)	PUNCT
ejde-397	1145	21	,	,	PUNCT
ejde-397	1145	22	n	n	PROPN
ejde-397	1145	23	∈	∈	PROPN
ejde-397	1145	24	n	n	NOUN
ejde-397	1145	25	and	and	CCONJ
ejde-397	1145	26	xj	xj	PROPN
ejde-397	1145	27	∈	∈	PROPN
ejde-397	1145	28	axj−1	axj−1	PROPN
ejde-397	1145	29	for	for	ADP
ejde-397	1145	30	1	1	NUM
ejde-397	1145	31	≤	≤	NUM
ejde-397	1145	32	j	j	PROPN
ejde-397	1145	33	≤	≤	PROPN
ejde-397	1145	34	n.	n.	NOUN
ejde-397	1145	35	then	then	ADV
ejde-397	1145	36	we	we	PRON
ejde-397	1145	37	can	can	AUX
ejde-397	1145	38	prove	prove	VERB
ejde-397	1145	39	inductively	inductively	ADV
ejde-397	1145	40	that	that	SCONJ
ejde-397	1145	41	,	,	PUNCT
ejde-397	1145	42	for	for	ADP
ejde-397	1145	43	every	every	DET
ejde-397	1145	44	t	t	NOUN
ejde-397	1145	45	∈	∈	PROPN
ejde-397	1146	1	[	[	X
ejde-397	1146	2	0	0	NUM
ejde-397	1146	3	,	,	PUNCT
ejde-397	1146	4	τ	τ	PROPN
ejde-397	1146	5	)	)	PUNCT
ejde-397	1146	6	,	,	PUNCT
ejde-397	1146	7	r(t)x	r(t)x	PROPN
ejde-397	1146	8	=	=	PUNCT
ejde-397	1146	9	k(t)cx0	k(t)cx0	NOUN
ejde-397	1146	10	+	+	CCONJ
ejde-397	1146	11	n−1∑	n−1∑	ADJ
ejde-397	1146	12	j=1	j=1	NOUN
ejde-397	1146	13	(	(	PUNCT
ejde-397	1146	14	a∗,j	a∗,j	PROPN
ejde-397	1146	15	∗	∗	PROPN
ejde-397	1146	16	k	k	PROPN
ejde-397	1146	17	)	)	PUNCT
ejde-397	1146	18	(	(	PUNCT
ejde-397	1146	19	t)cxj	t)cxj	PROPN
ejde-397	1146	20	+	+	CCONJ
ejde-397	1146	21	(	(	PUNCT
ejde-397	1146	22	a∗,n	a∗,n	INTJ
ejde-397	1146	23	∗r(·)xn	∗r(·)xn	NOUN
ejde-397	1146	24	)	)	PUNCT
ejde-397	1146	25	(	(	PUNCT
ejde-397	1146	26	t	t	NOUN
ejde-397	1146	27	)	)	PUNCT
ejde-397	1146	28	.	.	PUNCT
ejde-397	1147	1	(	(	PUNCT
ejde-397	1147	2	5.24	5.24	X
ejde-397	1147	3	)	)	PUNCT
ejde-397	1147	4	keeping	keep	VERB
ejde-397	1147	5	in	in	ADP
ejde-397	1147	6	mind	mind	NOUN
ejde-397	1147	7	the	the	DET
ejde-397	1147	8	identity	identity	NOUN
ejde-397	1147	9	(	(	PUNCT
ejde-397	1147	10	5.24	5.24	NUM
ejde-397	1147	11	)	)	PUNCT
ejde-397	1147	12	,	,	PUNCT
ejde-397	1147	13	theorem	theorem	VERB
ejde-397	1147	14	2.3	2.3	NUM
ejde-397	1147	15	and	and	CCONJ
ejde-397	1147	16	proposition	proposition	NOUN
ejde-397	1147	17	5.8(ii	5.8(ii	NUM
ejde-397	1147	18	)	)	PUNCT
ejde-397	1147	19	,	,	PUNCT
ejde-397	1147	20	it	it	PRON
ejde-397	1147	21	is	be	AUX
ejde-397	1147	22	almost	almost	ADV
ejde-397	1147	23	straightforward	straightforward	ADJ
ejde-397	1147	24	to	to	PART
ejde-397	1147	25	transfer	transfer	VERB
ejde-397	1147	26	the	the	DET
ejde-397	1147	27	assertion	assertion	NOUN
ejde-397	1147	28	of	of	ADP
ejde-397	1147	29	[	[	X
ejde-397	1147	30	36	36	NUM
ejde-397	1147	31	,	,	PUNCT
ejde-397	1147	32	proposition	proposition	NOUN
ejde-397	1147	33	2.1.32	2.1.32	NUM
ejde-397	1147	34	]	]	PUNCT
ejde-397	1147	35	to	to	PART
ejde-397	1147	36	degenerate	degenerate	ADJ
ejde-397	1147	37	case	case	NOUN
ejde-397	1147	38	.	.	PUNCT
ejde-397	1148	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1148	2	abstract	abstract	ADJ
ejde-397	1148	3	degenerate	degenerate	ADJ
ejde-397	1148	4	volterra	volterra	NOUN
ejde-397	1148	5	inclusions	inclusion	VERB
ejde-397	1148	6	37	37	NUM
ejde-397	1148	7	proposition	proposition	NOUN
ejde-397	1148	8	5.15	5.15	NUM
ejde-397	1148	9	.	.	PUNCT
ejde-397	1149	1	(	(	PUNCT
ejde-397	1149	2	i	i	NOUN
ejde-397	1149	3	)	)	PUNCT
ejde-397	1149	4	suppose	suppose	VERB
ejde-397	1149	5	α	α	PRON
ejde-397	1149	6	∈	∈	PROPN
ejde-397	1149	7	(	(	PUNCT
ejde-397	1149	8	0,∞	0,∞	NUM
ejde-397	1149	9	)	)	PUNCT
ejde-397	1149	10	\	\	NOUN
ejde-397	1149	11	n	n	CCONJ
ejde-397	1149	12	,	,	PUNCT
ejde-397	1149	13	x	x	PROPN
ejde-397	1149	14	∈	∈	PROPN
ejde-397	1149	15	d(a	d(a	PROPN
ejde-397	1149	16	)	)	PUNCT
ejde-397	1149	17	as	as	ADV
ejde-397	1149	18	well	well	ADV
ejde-397	1149	19	as	as	ADP
ejde-397	1149	20	c−1f	c−1f	PROPN
ejde-397	1149	21	,	,	PUNCT
ejde-397	1149	22	fa	fa	PROPN
ejde-397	1149	23	∈	∈	PROPN
ejde-397	1149	24	c([0	c([0	PROPN
ejde-397	1149	25	,	,	PUNCT
ejde-397	1149	26	τ	τ	PROPN
ejde-397	1149	27	)	)	PUNCT
ejde-397	1149	28	:	:	PUNCT
ejde-397	1149	29	x	x	X
ejde-397	1149	30	)	)	PUNCT
ejde-397	1149	31	,	,	PUNCT
ejde-397	1149	32	fa(t	fa(t	NOUN
ejde-397	1149	33	)	)	PUNCT
ejde-397	1149	34	∈	∈	PROPN
ejde-397	1149	35	ac−1f(t	ac−1f(t	NOUN
ejde-397	1149	36	)	)	PUNCT
ejde-397	1149	37	,	,	PUNCT
ejde-397	1149	38	t	t	PROPN
ejde-397	1149	39	∈	∈	PROPN
ejde-397	1150	1	[	[	X
ejde-397	1150	2	0	0	NUM
ejde-397	1150	3	,	,	PUNCT
ejde-397	1150	4	τ	τ	PROPN
ejde-397	1150	5	)	)	PUNCT
ejde-397	1150	6	and	and	CCONJ
ejde-397	1150	7	a	a	PRON
ejde-397	1150	8	is	be	AUX
ejde-397	1150	9	a	a	DET
ejde-397	1150	10	closed	closed	ADJ
ejde-397	1150	11	subgenerator	subgenerator	NOUN
ejde-397	1150	12	of	of	ADP
ejde-397	1150	13	a	a	DET
ejde-397	1150	14	(	(	PUNCT
ejde-397	1150	15	gα	gα	NOUN
ejde-397	1150	16	,	,	PUNCT
ejde-397	1150	17	c)-regularized	c)-regularize	VERB
ejde-397	1150	18	resolvent	resolvent	ADJ
ejde-397	1150	19	family	family	NOUN
ejde-397	1150	20	(	(	PUNCT
ejde-397	1150	21	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1150	22	)	)	PUNCT
ejde-397	1150	23	.	.	PUNCT
ejde-397	1151	1	set	set	VERB
ejde-397	1151	2	v(t	v(t	NOUN
ejde-397	1151	3	)	)	PUNCT
ejde-397	1151	4	:	:	PUNCT
ejde-397	1152	1	=	=	SYM
ejde-397	1152	2	(	(	PUNCT
ejde-397	1152	3	gdαe−α	gdαe−α	PROPN
ejde-397	1152	4	∗	∗	PROPN
ejde-397	1152	5	f)(t	f)(t	PROPN
ejde-397	1152	6	)	)	PUNCT
ejde-397	1152	7	,	,	PUNCT
ejde-397	1152	8	t	t	PROPN
ejde-397	1152	9	∈	∈	PROPN
ejde-397	1153	1	[	[	X
ejde-397	1153	2	0	0	NUM
ejde-397	1153	3	,	,	PUNCT
ejde-397	1153	4	τ	τ	PROPN
ejde-397	1153	5	)	)	PUNCT
ejde-397	1153	6	.	.	PUNCT
ejde-397	1154	1	if	if	SCONJ
ejde-397	1154	2	v	v	NUM
ejde-397	1154	3	∈	∈	PROPN
ejde-397	1154	4	cdαe−1([0	cdαe−1([0	X
ejde-397	1154	5	,	,	PUNCT
ejde-397	1154	6	τ	τ	PROPN
ejde-397	1154	7	)	)	PUNCT
ejde-397	1154	8	:	:	PUNCT
ejde-397	1155	1	x	x	X
ejde-397	1155	2	)	)	PUNCT
ejde-397	1155	3	and	and	CCONJ
ejde-397	1155	4	v(k)(0	v(k)(0	NUM
ejde-397	1155	5	)	)	PUNCT
ejde-397	1155	6	=	=	SYM
ejde-397	1155	7	0	0	NUM
ejde-397	1155	8	for	for	ADP
ejde-397	1155	9	1	1	NUM
ejde-397	1155	10	≤	≤	NUM
ejde-397	1155	11	k	k	PROPN
ejde-397	1155	12	≤	≤	PROPN
ejde-397	1155	13	dαe	dαe	VERB
ejde-397	1155	14	−	−	PROPN
ejde-397	1155	15	2	2	NUM
ejde-397	1155	16	,	,	PUNCT
ejde-397	1155	17	then	then	ADV
ejde-397	1155	18	the	the	DET
ejde-397	1155	19	function	function	NOUN
ejde-397	1155	20	u(t	u(t	NOUN
ejde-397	1155	21	)	)	PUNCT
ejde-397	1155	22	:	:	PUNCT
ejde-397	1156	1	=	=	PUNCT
ejde-397	1156	2	r(t)x	r(t)x	X
ejde-397	1156	3	+	+	PUNCT
ejde-397	1156	4	(	(	PUNCT
ejde-397	1156	5	r	r	NOUN
ejde-397	1156	6	∗	∗	NOUN
ejde-397	1156	7	c−1f)(t	c−1f)(t	PROPN
ejde-397	1156	8	)	)	PUNCT
ejde-397	1156	9	,	,	PUNCT
ejde-397	1156	10	t	t	PROPN
ejde-397	1156	11	∈	∈	PROPN
ejde-397	1157	1	[	[	X
ejde-397	1157	2	0	0	NUM
ejde-397	1157	3	,	,	PUNCT
ejde-397	1157	4	τ	τ	X
ejde-397	1157	5	)	)	PUNCT
ejde-397	1157	6	is	be	AUX
ejde-397	1157	7	a	a	DET
ejde-397	1157	8	unique	unique	ADJ
ejde-397	1157	9	solution	solution	NOUN
ejde-397	1157	10	of	of	ADP
ejde-397	1157	11	the	the	DET
ejde-397	1157	12	following	following	ADJ
ejde-397	1157	13	abstract	abstract	ADJ
ejde-397	1157	14	time	time	NOUN
ejde-397	1157	15	-	-	PUNCT
ejde-397	1157	16	fractional	fractional	ADJ
ejde-397	1157	17	inclusion	inclusion	NOUN
ejde-397	1157	18	:	:	PUNCT
ejde-397	1157	19	u	u	PROPN
ejde-397	1157	20	∈	∈	PROPN
ejde-397	1157	21	cdαe((0	cdαe((0	PROPN
ejde-397	1157	22	,	,	PUNCT
ejde-397	1157	23	τ	τ	PROPN
ejde-397	1157	24	)	)	PUNCT
ejde-397	1157	25	:	:	PUNCT
ejde-397	1157	26	x	x	X
ejde-397	1157	27	)	)	PUNCT
ejde-397	1157	28	∩	∩	NOUN
ejde-397	1157	29	cdαe−1([0	cdαe−1([0	VERB
ejde-397	1157	30	,	,	PUNCT
ejde-397	1157	31	τ	τ	X
ejde-397	1157	32	)	)	PUNCT
ejde-397	1157	33	:	:	PUNCT
ejde-397	1158	1	x	x	X
ejde-397	1158	2	)	)	PUNCT
ejde-397	1158	3	,	,	PUNCT
ejde-397	1158	4	dα	dα	PROPN
ejde-397	1158	5	t	t	PROPN
ejde-397	1158	6	u(t	u(t	PROPN
ejde-397	1158	7	)	)	PUNCT
ejde-397	1158	8	∈	∈	NOUN
ejde-397	1158	9	au(t	au(t	PRON
ejde-397	1158	10	)	)	PUNCT
ejde-397	1159	1	+	+	CCONJ
ejde-397	1159	2	ddαe−1	ddαe−1	PROPN
ejde-397	1159	3	dtdαe−1	dtdαe−1	PROPN
ejde-397	1159	4	(	(	PUNCT
ejde-397	1159	5	gdαe−α	gdαe−α	PROPN
ejde-397	1159	6	∗	∗	PROPN
ejde-397	1159	7	f	f	PROPN
ejde-397	1159	8	)	)	PUNCT
ejde-397	1159	9	(	(	PUNCT
ejde-397	1159	10	t	t	PROPN
ejde-397	1159	11	)	)	PUNCT
ejde-397	1159	12	,	,	PUNCT
ejde-397	1159	13	t	t	PROPN
ejde-397	1159	14	∈	∈	PROPN
ejde-397	1160	1	[	[	X
ejde-397	1160	2	0	0	NUM
ejde-397	1160	3	,	,	PUNCT
ejde-397	1160	4	τ	τ	PROPN
ejde-397	1160	5	)	)	PUNCT
ejde-397	1160	6	,	,	PUNCT
ejde-397	1160	7	u(0	u(0	PROPN
ejde-397	1160	8	)	)	PUNCT
ejde-397	1160	9	=	=	SYM
ejde-397	1160	10	cx	cx	PROPN
ejde-397	1160	11	,	,	PUNCT
ejde-397	1160	12	u(k)(0	u(k)(0	PROPN
ejde-397	1160	13	)	)	PUNCT
ejde-397	1160	14	=	=	SYM
ejde-397	1160	15	0	0	NUM
ejde-397	1160	16	,	,	PUNCT
ejde-397	1160	17	1	1	NUM
ejde-397	1160	18	≤	≤	NUM
ejde-397	1160	19	k	k	X
ejde-397	1160	20	≤	≤	PROPN
ejde-397	1160	21	dαe	dαe	VERB
ejde-397	1160	22	−	−	PROPN
ejde-397	1160	23	1	1	NUM
ejde-397	1160	24	.	.	PUNCT
ejde-397	1160	25	(	(	PUNCT
ejde-397	1160	26	ii	ii	NOUN
ejde-397	1160	27	)	)	PUNCT
ejde-397	1160	28	suppose	suppose	VERB
ejde-397	1160	29	r	r	NOUN
ejde-397	1160	30	≥	≥	NOUN
ejde-397	1160	31	0	0	NUM
ejde-397	1160	32	,	,	PUNCT
ejde-397	1160	33	n	n	PRON
ejde-397	1160	34	∈	∈	PROPN
ejde-397	1160	35	n	n	CCONJ
ejde-397	1160	36	\	\	NOUN
ejde-397	1160	37	{	{	PUNCT
ejde-397	1160	38	1	1	NUM
ejde-397	1160	39	}	}	PUNCT
ejde-397	1160	40	,	,	PUNCT
ejde-397	1160	41	xj	xj	PROPN
ejde-397	1160	42	∈	∈	PROPN
ejde-397	1160	43	axj−1	axj−1	PROPN
ejde-397	1160	44	for	for	ADP
ejde-397	1160	45	1	1	NUM
ejde-397	1160	46	≤	≤	NUM
ejde-397	1160	47	j	j	PROPN
ejde-397	1160	48	≤	≤	PROPN
ejde-397	1160	49	n	n	CCONJ
ejde-397	1160	50	,	,	PUNCT
ejde-397	1160	51	fj(t	fj(t	X
ejde-397	1160	52	)	)	PUNCT
ejde-397	1160	53	∈	∈	PROPN
ejde-397	1160	54	afj−1(t	afj−1(t	NOUN
ejde-397	1160	55	)	)	PUNCT
ejde-397	1160	56	for	for	ADP
ejde-397	1160	57	t	t	PROPN
ejde-397	1160	58	∈	∈	PROPN
ejde-397	1161	1	[	[	X
ejde-397	1161	2	0	0	NUM
ejde-397	1161	3	,	,	PUNCT
ejde-397	1161	4	τ	τ	X
ejde-397	1161	5	)	)	PUNCT
ejde-397	1161	6	and	and	CCONJ
ejde-397	1161	7	1	1	NUM
ejde-397	1161	8	≤	≤	NUM
ejde-397	1161	9	j	j	PROPN
ejde-397	1161	10	≤	≤	NUM
ejde-397	1161	11	n	n	CCONJ
ejde-397	1161	12	,	,	PUNCT
ejde-397	1161	13	fj	fj	PROPN
ejde-397	1161	14	∈	∈	PROPN
ejde-397	1161	15	c([0	c([0	PROPN
ejde-397	1161	16	,	,	PUNCT
ejde-397	1161	17	τ	τ	PROPN
ejde-397	1161	18	)	)	PUNCT
ejde-397	1161	19	:	:	PUNCT
ejde-397	1162	1	x	x	X
ejde-397	1162	2	)	)	PUNCT
ejde-397	1162	3	for	for	ADP
ejde-397	1162	4	0	0	NUM
ejde-397	1162	5	≤	≤	NUM
ejde-397	1162	6	j	j	PROPN
ejde-397	1162	7	≤	≤	NUM
ejde-397	1162	8	n	n	CCONJ
ejde-397	1162	9	,	,	PUNCT
ejde-397	1162	10	and	and	CCONJ
ejde-397	1162	11	a	a	PRON
ejde-397	1162	12	is	be	AUX
ejde-397	1162	13	a	a	DET
ejde-397	1162	14	closed	closed	ADJ
ejde-397	1162	15	subgenerator	subgenerator	NOUN
ejde-397	1162	16	of	of	ADP
ejde-397	1162	17	a	a	DET
ejde-397	1162	18	(	(	PUNCT
ejde-397	1162	19	g1	g1	PROPN
ejde-397	1162	20	/	/	SYM
ejde-397	1162	21	n	n	CCONJ
ejde-397	1162	22	,	,	PUNCT
ejde-397	1162	23	gr+1)-regularized	gr+1)-regularized	ADJ
ejde-397	1162	24	c	c	NOUN
ejde-397	1162	25	-	-	PUNCT
ejde-397	1162	26	resolvent	resolvent	ADJ
ejde-397	1162	27	family	family	NOUN
ejde-397	1162	28	(	(	PUNCT
ejde-397	1162	29	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1162	30	)	)	PUNCT
ejde-397	1162	31	.	.	PUNCT
ejde-397	1163	1	then	then	ADV
ejde-397	1163	2	the	the	DET
ejde-397	1163	3	function	function	NOUN
ejde-397	1163	4	v(t	v(t	NOUN
ejde-397	1163	5	)	)	PUNCT
ejde-397	1163	6	:	:	PUNCT
ejde-397	1164	1	=	=	PUNCT
ejde-397	1164	2	r(t)x	r(t)x	X
ejde-397	1164	3	+	+	PUNCT
ejde-397	1164	4	(	(	PUNCT
ejde-397	1164	5	r	r	NOUN
ejde-397	1164	6	∗	∗	NOUN
ejde-397	1164	7	c−1f)(t)x	c−1f)(t)x	PROPN
ejde-397	1164	8	,	,	PUNCT
ejde-397	1164	9	t	t	PROPN
ejde-397	1164	10	∈	∈	PROPN
ejde-397	1165	1	[	[	X
ejde-397	1165	2	0	0	NUM
ejde-397	1165	3	,	,	PUNCT
ejde-397	1165	4	τ	τ	X
ejde-397	1165	5	)	)	PUNCT
ejde-397	1165	6	is	be	AUX
ejde-397	1165	7	a	a	DET
ejde-397	1165	8	unique	unique	ADJ
ejde-397	1165	9	solution	solution	NOUN
ejde-397	1165	10	of	of	ADP
ejde-397	1165	11	the	the	DET
ejde-397	1165	12	following	following	ADJ
ejde-397	1165	13	abstract	abstract	ADJ
ejde-397	1165	14	time	time	NOUN
ejde-397	1165	15	-	-	PUNCT
ejde-397	1165	16	fractional	fractional	ADJ
ejde-397	1165	17	inclusion	inclusion	NOUN
ejde-397	1165	18	v	v	ADP
ejde-397	1165	19	∈	∈	PROPN
ejde-397	1165	20	c1((0	c1((0	NOUN
ejde-397	1165	21	,	,	PUNCT
ejde-397	1165	22	τ	τ	X
ejde-397	1165	23	)	)	PUNCT
ejde-397	1165	24	:	:	PUNCT
ejde-397	1165	25	x	x	X
ejde-397	1165	26	)	)	PUNCT
ejde-397	1165	27	∩	∩	NOUN
ejde-397	1165	28	c([0	c([0	PROPN
ejde-397	1165	29	,	,	PUNCT
ejde-397	1165	30	τ	τ	PROPN
ejde-397	1165	31	)	)	PUNCT
ejde-397	1165	32	:	:	PUNCT
ejde-397	1166	1	x	x	X
ejde-397	1166	2	)	)	PUNCT
ejde-397	1166	3	,	,	PUNCT
ejde-397	1166	4	v′(t	v′(t	PROPN
ejde-397	1166	5	)	)	PUNCT
ejde-397	1166	6	∈	∈	PROPN
ejde-397	1166	7	av(t	av(t	NOUN
ejde-397	1166	8	)	)	PUNCT
ejde-397	1166	9	+	+	CCONJ
ejde-397	1166	10	n−1∑	n−1∑	NUM
ejde-397	1166	11	j=1	j=1	NOUN
ejde-397	1166	12	g(j	g(j	PROPN
ejde-397	1166	13	/	/	SYM
ejde-397	1166	14	n)+r(t)cxj	n)+r(t)cxj	PROPN
ejde-397	1166	15	+	+	CCONJ
ejde-397	1167	1	n−1∑	n−1∑	PROPN
ejde-397	1167	2	j=0	j=0	PROPN
ejde-397	1167	3	(	(	PUNCT
ejde-397	1167	4	g(j	g(j	PROPN
ejde-397	1167	5	/	/	SYM
ejde-397	1167	6	n)+r	n)+r	PROPN
ejde-397	1167	7	∗	∗	NOUN
ejde-397	1167	8	fj	fj	PROPN
ejde-397	1167	9	)	)	PUNCT
ejde-397	1167	10	(	(	PUNCT
ejde-397	1167	11	t	t	NOUN
ejde-397	1167	12	)	)	PUNCT
ejde-397	1167	13	+	+	NOUN
ejde-397	1167	14	d	d	ADP
ejde-397	1167	15	dt	dt	X
ejde-397	1167	16	gr+1(t)cx	gr+1(t)cx	NOUN
ejde-397	1167	17	,	,	PUNCT
ejde-397	1167	18	t	t	PROPN
ejde-397	1167	19	∈	∈	PROPN
ejde-397	1167	20	(	(	PUNCT
ejde-397	1167	21	0	0	NUM
ejde-397	1167	22	,	,	PUNCT
ejde-397	1167	23	τ	τ	PROPN
ejde-397	1167	24	)	)	PUNCT
ejde-397	1167	25	,	,	PUNCT
ejde-397	1167	26	v(0	v(0	NOUN
ejde-397	1167	27	)	)	PUNCT
ejde-397	1167	28	=	=	PUNCT
ejde-397	1168	1	gr+1(0)cx	gr+1(0)cx	PROPN
ejde-397	1168	2	.	.	PUNCT
ejde-397	1169	1	furthermore	furthermore	ADV
ejde-397	1169	2	,	,	PUNCT
ejde-397	1169	3	v	v	PROPN
ejde-397	1169	4	∈	∈	PROPN
ejde-397	1169	5	c1([0	c1([0	PROPN
ejde-397	1169	6	,	,	PUNCT
ejde-397	1169	7	τ	τ	X
ejde-397	1169	8	)	)	PUNCT
ejde-397	1169	9	:	:	PUNCT
ejde-397	1169	10	x	x	X
ejde-397	1169	11	)	)	PUNCT
ejde-397	1169	12	provided	provide	VERB
ejde-397	1169	13	that	that	SCONJ
ejde-397	1169	14	r	r	NOUN
ejde-397	1169	15	≥	≥	NUM
ejde-397	1169	16	1	1	NUM
ejde-397	1169	17	or	or	CCONJ
ejde-397	1169	18	x	x	SYM
ejde-397	1169	19	=	=	SYM
ejde-397	1169	20	0	0	NUM
ejde-397	1169	21	and	and	CCONJ
ejde-397	1169	22	r	r	NOUN
ejde-397	1169	23	≥	≥	NOUN
ejde-397	1169	24	0	0	NUM
ejde-397	1169	25	.	.	PUNCT
ejde-397	1170	1	5.1	5.1	NUM
ejde-397	1170	2	.	.	PUNCT
ejde-397	1171	1	differential	differential	ADJ
ejde-397	1171	2	and	and	CCONJ
ejde-397	1171	3	analytical	analytical	ADJ
ejde-397	1171	4	properties	property	NOUN
ejde-397	1171	5	of	of	ADP
ejde-397	1171	6	(	(	PUNCT
ejde-397	1171	7	a	a	PRON
ejde-397	1171	8	,	,	PUNCT
ejde-397	1171	9	k)-regularized	k)-regularize	VERB
ejde-397	1171	10	c	c	NOUN
ejde-397	1171	11	-	-	PUNCT
ejde-397	1171	12	resolvent	resolvent	ADJ
ejde-397	1171	13	families	family	NOUN
ejde-397	1171	14	.	.	PUNCT
ejde-397	1172	1	the	the	DET
ejde-397	1172	2	main	main	ADJ
ejde-397	1172	3	structural	structural	ADJ
ejde-397	1172	4	characterizations	characterization	NOUN
ejde-397	1172	5	of	of	ADP
ejde-397	1172	6	differential	differential	NOUN
ejde-397	1172	7	and	and	CCONJ
ejde-397	1172	8	analytical	analytical	ADJ
ejde-397	1172	9	(	(	PUNCT
ejde-397	1172	10	a	a	PRON
ejde-397	1172	11	,	,	PUNCT
ejde-397	1172	12	k)regularized	k)regularize	VERB
ejde-397	1172	13	c	c	X
ejde-397	1172	14	-	-	PUNCT
ejde-397	1172	15	resolvent	resolvent	ADJ
ejde-397	1172	16	families	family	NOUN
ejde-397	1172	17	generated	generate	VERB
ejde-397	1172	18	by	by	ADP
ejde-397	1172	19	single	single	ADJ
ejde-397	1172	20	-	-	PUNCT
ejde-397	1172	21	valued	value	VERB
ejde-397	1172	22	linear	linear	PROPN
ejde-397	1172	23	operators	operator	NOUN
ejde-397	1172	24	continue	continue	VERB
ejde-397	1172	25	to	to	PART
ejde-397	1172	26	hold	hold	VERB
ejde-397	1172	27	in	in	ADP
ejde-397	1172	28	our	our	PRON
ejde-397	1172	29	framework	framework	NOUN
ejde-397	1172	30	(	(	PUNCT
ejde-397	1172	31	cf	cf	NOUN
ejde-397	1172	32	.	.	PUNCT
ejde-397	1173	1	[	[	X
ejde-397	1173	2	17	17	NUM
ejde-397	1173	3	,	,	PUNCT
ejde-397	1173	4	chapter	chapter	NOUN
ejde-397	1173	5	iii	iii	NOUN
ejde-397	1173	6	]	]	X
ejde-397	1173	7	,	,	PUNCT
ejde-397	1173	8	[	[	X
ejde-397	1173	9	6	6	NUM
ejde-397	1173	10	,	,	PUNCT
ejde-397	1173	11	7	7	NUM
ejde-397	1173	12	,	,	PUNCT
ejde-397	1173	13	19	19	NUM
ejde-397	1173	14	]	]	PUNCT
ejde-397	1173	15	for	for	ADP
ejde-397	1173	16	some	some	DET
ejde-397	1173	17	references	reference	NOUN
ejde-397	1173	18	on	on	ADP
ejde-397	1173	19	infinitely	infinitely	ADV
ejde-397	1173	20	differentiable	differentiable	ADJ
ejde-397	1173	21	semigroups	semigroup	NOUN
ejde-397	1173	22	generated	generate	VERB
ejde-397	1173	23	by	by	ADP
ejde-397	1173	24	mlos	mlo	NOUN
ejde-397	1173	25	)	)	PUNCT
ejde-397	1173	26	.	.	PUNCT
ejde-397	1174	1	we	we	PRON
ejde-397	1174	2	will	will	AUX
ejde-397	1174	3	use	use	VERB
ejde-397	1174	4	the	the	DET
ejde-397	1174	5	following	follow	VERB
ejde-397	1174	6	definition	definition	NOUN
ejde-397	1174	7	.	.	PUNCT
ejde-397	1175	1	definition	definition	NOUN
ejde-397	1175	2	5.16	5.16	NUM
ejde-397	1175	3	.	.	PUNCT
ejde-397	1176	1	(	(	PUNCT
ejde-397	1176	2	see	see	VERB
ejde-397	1176	3	[	[	X
ejde-397	1176	4	36	36	NUM
ejde-397	1176	5	,	,	PUNCT
ejde-397	1176	6	definition	definition	NOUN
ejde-397	1176	7	2.2.1	2.2.1	NUM
ejde-397	1176	8	]	]	PUNCT
ejde-397	1176	9	for	for	ADP
ejde-397	1176	10	non	non	ADJ
ejde-397	1176	11	-	-	ADJ
ejde-397	1176	12	degenerate	degenerate	ADJ
ejde-397	1176	13	case	case	NOUN
ejde-397	1176	14	)	)	PUNCT
ejde-397	1176	15	(	(	PUNCT
ejde-397	1176	16	i	i	NOUN
ejde-397	1176	17	)	)	PUNCT
ejde-397	1176	18	suppose	suppose	VERB
ejde-397	1176	19	that	that	SCONJ
ejde-397	1176	20	a	a	PRON
ejde-397	1176	21	is	be	AUX
ejde-397	1176	22	an	an	DET
ejde-397	1176	23	mlo	mlo	PROPN
ejde-397	1176	24	in	in	ADP
ejde-397	1176	25	x.	x.	NOUN
ejde-397	1176	26	let	let	VERB
ejde-397	1176	27	α	α	PRON
ejde-397	1176	28	∈	∈	PROPN
ejde-397	1176	29	(	(	PUNCT
ejde-397	1176	30	0	0	NUM
ejde-397	1176	31	,	,	PUNCT
ejde-397	1176	32	π	π	NOUN
ejde-397	1176	33	]	]	X
ejde-397	1176	34	,	,	PUNCT
ejde-397	1176	35	and	and	CCONJ
ejde-397	1176	36	let	let	VERB
ejde-397	1176	37	(	(	PUNCT
ejde-397	1176	38	r(t))t≥0	r(t))t≥0	NOUN
ejde-397	1176	39	be	be	AUX
ejde-397	1176	40	an	an	DET
ejde-397	1176	41	(	(	PUNCT
ejde-397	1176	42	a	a	DET
ejde-397	1176	43	,	,	PUNCT
ejde-397	1176	44	k)-regularized	k)-regularize	VERB
ejde-397	1176	45	c	c	NOUN
ejde-397	1176	46	-	-	PUNCT
ejde-397	1176	47	resolvent	resolvent	ADJ
ejde-397	1176	48	family	family	NOUN
ejde-397	1176	49	which	which	PRON
ejde-397	1176	50	do	do	AUX
ejde-397	1176	51	have	have	VERB
ejde-397	1176	52	a	a	PRON
ejde-397	1176	53	as	as	ADP
ejde-397	1176	54	a	a	DET
ejde-397	1176	55	subgenerator	subgenerator	NOUN
ejde-397	1176	56	.	.	PUNCT
ejde-397	1177	1	then	then	ADV
ejde-397	1177	2	it	it	PRON
ejde-397	1177	3	is	be	AUX
ejde-397	1177	4	said	say	VERB
ejde-397	1177	5	that	that	SCONJ
ejde-397	1177	6	(	(	PUNCT
ejde-397	1177	7	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	1177	8	is	be	AUX
ejde-397	1177	9	an	an	DET
ejde-397	1177	10	analytic	analytic	ADJ
ejde-397	1177	11	(	(	PUNCT
ejde-397	1177	12	a	a	PRON
ejde-397	1177	13	,	,	PUNCT
ejde-397	1177	14	k)-regularized	k)-regularize	VERB
ejde-397	1177	15	c	c	NOUN
ejde-397	1177	16	-	-	PUNCT
ejde-397	1177	17	resolvent	resolvent	ADJ
ejde-397	1177	18	family	family	NOUN
ejde-397	1177	19	of	of	ADP
ejde-397	1177	20	angle	angle	PROPN
ejde-397	1177	21	α	α	NOUN
ejde-397	1177	22	,	,	PUNCT
ejde-397	1177	23	if	if	SCONJ
ejde-397	1177	24	there	there	PRON
ejde-397	1177	25	exists	exist	VERB
ejde-397	1177	26	a	a	DET
ejde-397	1177	27	function	function	NOUN
ejde-397	1177	28	r	r	NOUN
ejde-397	1177	29	:	:	PUNCT
ejde-397	1177	30	σα	σα	PROPN
ejde-397	1177	31	→	→	SYM
ejde-397	1177	32	l(x	l(x	PROPN
ejde-397	1177	33	)	)	PUNCT
ejde-397	1177	34	which	which	PRON
ejde-397	1177	35	satisfies	satisfy	VERB
ejde-397	1177	36	that	that	SCONJ
ejde-397	1177	37	,	,	PUNCT
ejde-397	1177	38	for	for	ADP
ejde-397	1177	39	every	every	DET
ejde-397	1177	40	x	x	SYM
ejde-397	1177	41	∈	∈	PROPN
ejde-397	1177	42	x	x	NOUN
ejde-397	1177	43	,	,	PUNCT
ejde-397	1177	44	the	the	DET
ejde-397	1177	45	mapping	mapping	NOUN
ejde-397	1177	46	z	z	PROPN
ejde-397	1177	47	7→	7→	PROPN
ejde-397	1177	48	r(z)x	r(z)x	PROPN
ejde-397	1177	49	,	,	PUNCT
ejde-397	1177	50	z	z	PROPN
ejde-397	1177	51	∈	∈	PROPN
ejde-397	1177	52	σα	σα	PROPN
ejde-397	1177	53	is	be	AUX
ejde-397	1177	54	analytic	analytic	ADJ
ejde-397	1177	55	as	as	ADV
ejde-397	1177	56	well	well	ADV
ejde-397	1177	57	as	as	ADP
ejde-397	1177	58	that	that	PRON
ejde-397	1177	59	:	:	PUNCT
ejde-397	1177	60	(	(	PUNCT
ejde-397	1177	61	a	a	X
ejde-397	1177	62	)	)	PUNCT
ejde-397	1177	63	r(t	r(t	NOUN
ejde-397	1177	64	)	)	PUNCT
ejde-397	1177	65	=	=	SYM
ejde-397	1177	66	r(t	r(t	NOUN
ejde-397	1177	67	)	)	PUNCT
ejde-397	1177	68	,	,	PUNCT
ejde-397	1177	69	t	t	PROPN
ejde-397	1177	70	>	>	X
ejde-397	1177	71	0	0	PUNCT
ejde-397	1178	1	and	and	CCONJ
ejde-397	1178	2	(	(	PUNCT
ejde-397	1178	3	b	b	X
ejde-397	1178	4	)	)	PUNCT
ejde-397	1178	5	limz→0,z∈σγ	limz→0,z∈σγ	PROPN
ejde-397	1178	6	r(z)x	r(z)x	NOUN
ejde-397	1178	7	=	=	SYM
ejde-397	1178	8	k(0)cx	k(0)cx	PROPN
ejde-397	1178	9	for	for	ADP
ejde-397	1178	10	all	all	DET
ejde-397	1178	11	γ	γ	X
ejde-397	1178	12	∈	∈	PROPN
ejde-397	1178	13	(	(	PUNCT
ejde-397	1178	14	0	0	NUM
ejde-397	1178	15	,	,	PUNCT
ejde-397	1178	16	α	α	NOUN
ejde-397	1178	17	)	)	PUNCT
ejde-397	1178	18	and	and	CCONJ
ejde-397	1178	19	x	x	PUNCT
ejde-397	1178	20	∈	∈	PROPN
ejde-397	1178	21	x.	x.	NOUN
ejde-397	1178	22	(	(	PUNCT
ejde-397	1178	23	ii	ii	NOUN
ejde-397	1178	24	)	)	PUNCT
ejde-397	1178	25	let	let	VERB
ejde-397	1178	26	(	(	PUNCT
ejde-397	1178	27	r(t))t≥0	r(t))t≥0	NOUN
ejde-397	1178	28	be	be	AUX
ejde-397	1178	29	an	an	DET
ejde-397	1178	30	analytic	analytic	ADJ
ejde-397	1178	31	(	(	PUNCT
ejde-397	1178	32	a	a	PRON
ejde-397	1178	33	,	,	PUNCT
ejde-397	1178	34	k)-regularized	k)-regularize	VERB
ejde-397	1178	35	c	c	NOUN
ejde-397	1178	36	-	-	PUNCT
ejde-397	1178	37	resolvent	resolvent	ADJ
ejde-397	1178	38	family	family	NOUN
ejde-397	1178	39	of	of	ADP
ejde-397	1178	40	angle	angle	NOUN
ejde-397	1178	41	α	α	PROPN
ejde-397	1178	42	∈	∈	PROPN
ejde-397	1178	43	(	(	PUNCT
ejde-397	1178	44	0	0	NUM
ejde-397	1178	45	,	,	PUNCT
ejde-397	1178	46	π	π	NOUN
ejde-397	1178	47	]	]	X
ejde-397	1178	48	.	.	PUNCT
ejde-397	1179	1	then	then	ADV
ejde-397	1179	2	it	it	PRON
ejde-397	1179	3	is	be	AUX
ejde-397	1179	4	said	say	VERB
ejde-397	1179	5	that	that	SCONJ
ejde-397	1179	6	(	(	PUNCT
ejde-397	1179	7	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	1179	8	is	be	AUX
ejde-397	1179	9	an	an	DET
ejde-397	1179	10	exponentially	exponentially	ADV
ejde-397	1179	11	equicontinuous	equicontinuous	ADJ
ejde-397	1179	12	,	,	PUNCT
ejde-397	1179	13	analytic	analytic	ADJ
ejde-397	1179	14	(	(	PUNCT
ejde-397	1179	15	a	a	PRON
ejde-397	1179	16	,	,	PUNCT
ejde-397	1179	17	k)-regularized	k)-regularize	VERB
ejde-397	1179	18	c	c	NOUN
ejde-397	1179	19	-	-	PUNCT
ejde-397	1179	20	resolvent	resolvent	ADJ
ejde-397	1179	21	family	family	NOUN
ejde-397	1179	22	of	of	ADP
ejde-397	1179	23	angle	angle	PROPN
ejde-397	1179	24	α	α	PROPN
ejde-397	1179	25	,	,	PUNCT
ejde-397	1179	26	resp	resp	NOUN
ejde-397	1179	27	.	.	PUNCT
ejde-397	1180	1	equicontinuous	equicontinuous	ADJ
ejde-397	1180	2	analytic	analytic	ADJ
ejde-397	1180	3	(	(	PUNCT
ejde-397	1180	4	a	a	PRON
ejde-397	1180	5	,	,	PUNCT
ejde-397	1180	6	k)-regularized	k)-regularize	VERB
ejde-397	1180	7	c	c	NOUN
ejde-397	1180	8	-	-	PUNCT
ejde-397	1180	9	resolvent	resolvent	ADJ
ejde-397	1180	10	family	family	NOUN
ejde-397	1180	11	of	of	ADP
ejde-397	1180	12	angle	angle	PROPN
ejde-397	1180	13	α	α	NOUN
ejde-397	1180	14	,	,	PUNCT
ejde-397	1180	15	if	if	SCONJ
ejde-397	1180	16	for	for	ADP
ejde-397	1180	17	every	every	DET
ejde-397	1180	18	γ	γ	X
ejde-397	1180	19	∈	∈	PROPN
ejde-397	1180	20	(	(	PUNCT
ejde-397	1180	21	0	0	NUM
ejde-397	1180	22	,	,	PUNCT
ejde-397	1180	23	α	α	NOUN
ejde-397	1180	24	)	)	PUNCT
ejde-397	1180	25	,	,	PUNCT
ejde-397	1180	26	there	there	PRON
ejde-397	1180	27	exists	exist	VERB
ejde-397	1180	28	ωγ	ωγ	ADP
ejde-397	1180	29	≥	≥	NOUN
ejde-397	1180	30	0	0	NUM
ejde-397	1180	31	,	,	PUNCT
ejde-397	1180	32	resp	resp	NOUN
ejde-397	1180	33	.	.	PUNCT
ejde-397	1181	1	ωγ	ωγ	ADP
ejde-397	1181	2	=	=	SYM
ejde-397	1181	3	0	0	PROPN
ejde-397	1181	4	,	,	PUNCT
ejde-397	1181	5	such	such	ADJ
ejde-397	1182	1	that	that	SCONJ
ejde-397	1182	2	the	the	DET
ejde-397	1182	3	family	family	NOUN
ejde-397	1182	4	{	{	PUNCT
ejde-397	1182	5	e−ωγ	e−ωγ	PROPN
ejde-397	1182	6	<	<	X
ejde-397	1182	7	zr(z	zr(z	X
ejde-397	1182	8	)	)	PUNCT
ejde-397	1182	9	:	:	PUNCT
ejde-397	1182	10	z	z	PROPN
ejde-397	1182	11	∈	∈	PROPN
ejde-397	1182	12	σγ	σγ	PROPN
ejde-397	1182	13	}	}	PUNCT
ejde-397	1182	14	⊆	⊆	NUM
ejde-397	1182	15	l(x	l(x	PROPN
ejde-397	1182	16	)	)	PUNCT
ejde-397	1182	17	is	be	AUX
ejde-397	1182	18	equicontinuous	equicontinuous	ADJ
ejde-397	1182	19	.	.	PUNCT
ejde-397	1183	1	since	since	SCONJ
ejde-397	1183	2	there	there	PRON
ejde-397	1183	3	is	be	VERB
ejde-397	1183	4	no	no	DET
ejde-397	1183	5	risk	risk	NOUN
ejde-397	1183	6	for	for	ADP
ejde-397	1183	7	confusion	confusion	NOUN
ejde-397	1183	8	,	,	PUNCT
ejde-397	1183	9	we	we	PRON
ejde-397	1183	10	will	will	AUX
ejde-397	1183	11	identify	identify	VERB
ejde-397	1183	12	in	in	ADP
ejde-397	1183	13	the	the	DET
ejde-397	1183	14	sequel	sequel	NOUN
ejde-397	1183	15	r	r	NOUN
ejde-397	1183	16	(	(	PUNCT
ejde-397	1183	17	·	·	PUNCT
ejde-397	1183	18	)	)	PUNCT
ejde-397	1183	19	and	and	CCONJ
ejde-397	1183	20	r	r	NOUN
ejde-397	1183	21	(	(	PUNCT
ejde-397	1183	22	·	·	PUNCT
ejde-397	1183	23	)	)	PUNCT
ejde-397	1183	24	.	.	PUNCT
ejde-397	1184	1	38	38	NUM
ejde-397	1184	2	m.	m.	NOUN
ejde-397	1184	3	kostić	kostić	NOUN
ejde-397	1184	4	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1184	5	in	in	ADP
ejde-397	1184	6	the	the	DET
ejde-397	1184	7	following	follow	VERB
ejde-397	1184	8	example	example	NOUN
ejde-397	1184	9	,	,	PUNCT
ejde-397	1184	10	we	we	PRON
ejde-397	1184	11	consider	consider	VERB
ejde-397	1184	12	a	a	DET
ejde-397	1184	13	time	time	NOUN
ejde-397	1184	14	-	-	PUNCT
ejde-397	1184	15	fractional	fractional	ADJ
ejde-397	1184	16	analogue	analogue	NOUN
ejde-397	1184	17	of	of	ADP
ejde-397	1184	18	the	the	DET
ejde-397	1184	19	linearized	linearize	VERB
ejde-397	1184	20	benney	benney	NOUN
ejde-397	1184	21	-	-	PUNCT
ejde-397	1184	22	luke	luke	VERB
ejde-397	1184	23	equation	equation	NOUN
ejde-397	1184	24	in	in	ADP
ejde-397	1184	25	l2	l2	NOUN
ejde-397	1184	26	-	-	PUNCT
ejde-397	1184	27	spaces	space	NOUN
ejde-397	1184	28	and	and	CCONJ
ejde-397	1184	29	there	there	ADV
ejde-397	1184	30	we	we	PRON
ejde-397	1184	31	will	will	AUX
ejde-397	1184	32	meet	meet	VERB
ejde-397	1184	33	some	some	DET
ejde-397	1184	34	interesting	interesting	ADJ
ejde-397	1184	35	examples	example	NOUN
ejde-397	1184	36	of	of	ADP
ejde-397	1184	37	exponentially	exponentially	ADV
ejde-397	1184	38	bounded	bound	VERB
ejde-397	1184	39	,	,	PUNCT
ejde-397	1184	40	analytic	analytic	ADJ
ejde-397	1184	41	fractional	fractional	ADJ
ejde-397	1184	42	resolvent	resolvent	ADJ
ejde-397	1184	43	families	family	NOUN
ejde-397	1184	44	of	of	ADP
ejde-397	1184	45	bounded	bounded	ADJ
ejde-397	1184	46	operators	operator	NOUN
ejde-397	1184	47	whose	whose	DET
ejde-397	1184	48	angle	angle	NOUN
ejde-397	1184	49	of	of	ADP
ejde-397	1184	50	analyticity	analyticity	NOUN
ejde-397	1184	51	can	can	AUX
ejde-397	1184	52	be	be	AUX
ejde-397	1184	53	strictly	strictly	ADV
ejde-397	1184	54	greater	great	ADJ
ejde-397	1184	55	than	than	ADP
ejde-397	1184	56	π/2	π/2	NUM
ejde-397	1184	57	;	;	PUNCT
ejde-397	1184	58	in	in	ADP
ejde-397	1184	59	our	our	PRON
ejde-397	1184	60	approach	approach	NOUN
ejde-397	1184	61	,	,	PUNCT
ejde-397	1184	62	we	we	PRON
ejde-397	1184	63	do	do	AUX
ejde-397	1184	64	not	not	PART
ejde-397	1184	65	use	use	VERB
ejde-397	1184	66	neither	neither	CCONJ
ejde-397	1184	67	multivalued	multivalued	ADJ
ejde-397	1184	68	linear	linear	ADJ
ejde-397	1184	69	operators	operator	NOUN
ejde-397	1184	70	nor	nor	CCONJ
ejde-397	1184	71	relatively	relatively	ADV
ejde-397	1184	72	p	p	NOUN
ejde-397	1184	73	-	-	PUNCT
ejde-397	1184	74	radial	radial	ADJ
ejde-397	1184	75	operators	operator	NOUN
ejde-397	1184	76	(	(	PUNCT
ejde-397	1184	77	[	[	X
ejde-397	1184	78	17	17	NUM
ejde-397	1184	79	]	]	PUNCT
ejde-397	1184	80	,	,	PUNCT
ejde-397	1184	81	[	[	X
ejde-397	1184	82	73	73	NUM
ejde-397	1184	83	]	]	PUNCT
ejde-397	1184	84	)	)	PUNCT
ejde-397	1184	85	.	.	PUNCT
ejde-397	1185	1	the	the	DET
ejde-397	1185	2	method	method	NOUN
ejde-397	1185	3	employed	employ	VERB
ejde-397	1185	4	by	by	ADP
ejde-397	1185	5	g.	g.	PROPN
ejde-397	1185	6	a.	a.	PROPN
ejde-397	1185	7	sviridyuk	sviridyuk	PROPN
ejde-397	1185	8	and	and	CCONJ
ejde-397	1185	9	v.	v.	ADP
ejde-397	1185	10	e.	e.	PROPN
ejde-397	1185	11	fedorov	fedorov	PROPN
ejde-397	1186	1	[	[	X
ejde-397	1186	2	73	73	NUM
ejde-397	1186	3	]	]	PUNCT
ejde-397	1186	4	for	for	ADP
ejde-397	1186	5	the	the	DET
ejde-397	1186	6	usually	usually	ADV
ejde-397	1186	7	considered	consider	VERB
ejde-397	1186	8	benney	benney	NOUN
ejde-397	1186	9	-	-	PUNCT
ejde-397	1186	10	luke	luke	VERB
ejde-397	1186	11	equation	equation	NOUN
ejde-397	1186	12	of	of	ADP
ejde-397	1186	13	first	first	ADJ
ejde-397	1186	14	order	order	NOUN
ejde-397	1186	15	can	can	AUX
ejde-397	1186	16	be	be	AUX
ejde-397	1186	17	very	very	ADV
ejde-397	1186	18	hepful	hepful	ADJ
ejde-397	1186	19	for	for	ADP
ejde-397	1186	20	achieving	achieve	VERB
ejde-397	1186	21	the	the	DET
ejde-397	1186	22	final	final	ADJ
ejde-397	1186	23	conclusions	conclusion	NOUN
ejde-397	1186	24	stated	state	VERB
ejde-397	1186	25	in	in	ADP
ejde-397	1186	26	(	(	PUNCT
ejde-397	1186	27	i)-(ii	i)-(ii	NOUN
ejde-397	1186	28	)	)	PUNCT
ejde-397	1186	29	,	,	PUNCT
ejde-397	1186	30	as	as	ADV
ejde-397	1186	31	well	well	ADV
ejde-397	1186	32	as	as	ADP
ejde-397	1186	33	for	for	ADP
ejde-397	1186	34	the	the	DET
ejde-397	1186	35	concrete	concrete	ADJ
ejde-397	1186	36	choice	choice	NOUN
ejde-397	1186	37	of	of	ADP
ejde-397	1186	38	the	the	DET
ejde-397	1186	39	state	state	NOUN
ejde-397	1186	40	space	space	NOUN
ejde-397	1186	41	x0	x0	PROPN
ejde-397	1186	42	below	below	ADV
ejde-397	1186	43	(	(	PUNCT
ejde-397	1186	44	cf	cf	NOUN
ejde-397	1186	45	.	.	PUNCT
ejde-397	1187	1	also	also	ADV
ejde-397	1187	2	[	[	X
ejde-397	1187	3	38	38	NUM
ejde-397	1187	4	,	,	PUNCT
ejde-397	1187	5	example	example	NOUN
ejde-397	1187	6	2.2.49	2.2.49	NUM
ejde-397	1187	7	,	,	PUNCT
ejde-397	1187	8	example	example	NOUN
ejde-397	1187	9	2.2.53	2.2.53	NUM
ejde-397	1187	10	]	]	PUNCT
ejde-397	1187	11	for	for	ADP
ejde-397	1187	12	our	our	PRON
ejde-397	1187	13	recent	recent	ADJ
ejde-397	1187	14	study	study	NOUN
ejde-397	1187	15	of	of	ADP
ejde-397	1187	16	fractional	fractional	ADJ
ejde-397	1187	17	analogues	analogue	NOUN
ejde-397	1187	18	of	of	ADP
ejde-397	1187	19	the	the	DET
ejde-397	1187	20	abstract	abstract	ADJ
ejde-397	1187	21	barenblatt	barenblatt	PROPN
ejde-397	1187	22	-	-	PUNCT
ejde-397	1187	23	zheltov	zheltov	ADV
ejde-397	1187	24	-	-	PUNCT
ejde-397	1187	25	kochina	kochina	PROPN
ejde-397	1187	26	equation	equation	NOUN
ejde-397	1187	27	in	in	ADP
ejde-397	1187	28	finite	finite	ADJ
ejde-397	1187	29	domains	domain	NOUN
ejde-397	1187	30	,	,	PUNCT
ejde-397	1187	31	where	where	SCONJ
ejde-397	1187	32	we	we	PRON
ejde-397	1187	33	have	have	AUX
ejde-397	1187	34	used	use	VERB
ejde-397	1187	35	the	the	DET
ejde-397	1187	36	pure	pure	ADJ
ejde-397	1187	37	laplace	laplace	NOUN
ejde-397	1187	38	transform	transform	VERB
ejde-397	1187	39	techniques	technique	NOUN
ejde-397	1187	40	from	from	ADP
ejde-397	1187	41	[	[	X
ejde-397	1187	42	42	42	NUM
ejde-397	1187	43	]	]	PUNCT
ejde-397	1187	44	)	)	PUNCT
ejde-397	1187	45	.	.	PUNCT
ejde-397	1188	1	example	example	NOUN
ejde-397	1189	1	5.17	5.17	NUM
ejde-397	1189	2	.	.	PUNCT
ejde-397	1189	3	suppose	suppose	VERB
ejde-397	1189	4	that	that	SCONJ
ejde-397	1189	5	∅	∅	NOUN
ejde-397	1189	6	6=	6=	ADP
ejde-397	1189	7	ω	ω	PROPN
ejde-397	1189	8	⊆	⊆	NUM
ejde-397	1189	9	rn	rn	NOUN
ejde-397	1189	10	is	be	AUX
ejde-397	1189	11	a	a	DET
ejde-397	1189	12	bounded	bounded	ADJ
ejde-397	1189	13	domain	domain	NOUN
ejde-397	1189	14	with	with	ADP
ejde-397	1189	15	smooth	smooth	ADJ
ejde-397	1189	16	boundary	boundary	NOUN
ejde-397	1189	17	,	,	PUNCT
ejde-397	1189	18	and	and	CCONJ
ejde-397	1189	19	∆	∆	PROPN
ejde-397	1189	20	is	be	AUX
ejde-397	1189	21	the	the	DET
ejde-397	1189	22	dirichlet	dirichlet	PROPN
ejde-397	1189	23	laplacian	laplacian	NOUN
ejde-397	1189	24	in	in	ADP
ejde-397	1189	25	x	x	X
ejde-397	1189	26	:	:	PUNCT
ejde-397	1189	27	=	=	SYM
ejde-397	1189	28	l2(ω	l2(ω	NOUN
ejde-397	1189	29	)	)	PUNCT
ejde-397	1189	30	,	,	PUNCT
ejde-397	1189	31	acting	act	VERB
ejde-397	1189	32	with	with	ADP
ejde-397	1189	33	domain	domain	NOUN
ejde-397	1189	34	h2(ω	h2(ω	NOUN
ejde-397	1189	35	)	)	PUNCT
ejde-397	1189	36	∩	∩	NOUN
ejde-397	1189	37	h1	h1	NOUN
ejde-397	1189	38	0	0	NUM
ejde-397	1189	39	(	(	PUNCT
ejde-397	1189	40	ω	ω	NOUN
ejde-397	1189	41	)	)	PUNCT
ejde-397	1189	42	.	.	PUNCT
ejde-397	1190	1	by	by	ADP
ejde-397	1190	2	{	{	PUNCT
ejde-397	1190	3	λk}[=	λk}[=	PROPN
ejde-397	1190	4	σ(∆	σ(∆	PROPN
ejde-397	1190	5	)	)	PUNCT
ejde-397	1190	6	]	]	PUNCT
ejde-397	1191	1	we	we	PRON
ejde-397	1191	2	denote	denote	VERB
ejde-397	1191	3	the	the	DET
ejde-397	1191	4	eigenvalues	eigenvalue	NOUN
ejde-397	1191	5	of	of	ADP
ejde-397	1191	6	∆	∆	PROPN
ejde-397	1191	7	in	in	ADP
ejde-397	1191	8	l2(ω	l2(ω	PROPN
ejde-397	1191	9	)	)	PUNCT
ejde-397	1191	10	(	(	PUNCT
ejde-397	1191	11	recall	recall	VERB
ejde-397	1191	12	that	that	PRON
ejde-397	1191	13	0	0	NUM
ejde-397	1191	14	<	<	X
ejde-397	1191	15	−λ1	−λ1	X
ejde-397	1191	16	≤	≤	PUNCT
ejde-397	1191	17	−λ2	−λ2	X
ejde-397	1191	18	·	·	PUNCT
ejde-397	1191	19	·	·	PUNCT
ejde-397	1191	20	·	·	PUNCT
ejde-397	1191	21	≤	≤	NUM
ejde-397	1191	22	−λk	−λk	VERB
ejde-397	1191	23	≤	≤	NUM
ejde-397	1191	24	·	·	PUNCT
ejde-397	1191	25	·	·	PUNCT
ejde-397	1191	26	·	·	PUNCT
ejde-397	1192	1	→	→	PUNCT
ejde-397	1192	2	+	+	NUM
ejde-397	1192	3	∞	∞	PROPN
ejde-397	1192	4	as	as	ADP
ejde-397	1192	5	k	k	PROPN
ejde-397	1192	6	→	→	SYM
ejde-397	1192	7	∞	∞	PROPN
ejde-397	1192	8	;	;	PUNCT
ejde-397	1192	9	cf	cf	X
ejde-397	1192	10	.	.	PUNCT
ejde-397	1193	1	[	[	X
ejde-397	1193	2	77	77	NUM
ejde-397	1193	3	,	,	PUNCT
ejde-397	1193	4	section	section	NOUN
ejde-397	1193	5	5.6	5.6	NUM
ejde-397	1193	6	]	]	PUNCT
ejde-397	1193	7	,	,	PUNCT
ejde-397	1193	8	[	[	X
ejde-397	1193	9	1	1	NUM
ejde-397	1193	10	,	,	PUNCT
ejde-397	1193	11	section	section	NOUN
ejde-397	1193	12	6	6	NUM
ejde-397	1193	13	]	]	PUNCT
ejde-397	1193	14	and	and	CCONJ
ejde-397	1193	15	[	[	X
ejde-397	1193	16	73	73	NUM
ejde-397	1193	17	,	,	PUNCT
ejde-397	1193	18	section	section	NOUN
ejde-397	1193	19	1.3	1.3	NUM
ejde-397	1193	20	]	]	PUNCT
ejde-397	1193	21	for	for	ADP
ejde-397	1193	22	more	more	ADJ
ejde-397	1193	23	details	detail	NOUN
ejde-397	1193	24	)	)	PUNCT
ejde-397	1193	25	numbered	number	VERB
ejde-397	1193	26	in	in	ADP
ejde-397	1193	27	nonascending	nonascende	VERB
ejde-397	1193	28	order	order	NOUN
ejde-397	1193	29	with	with	ADP
ejde-397	1193	30	regard	regard	NOUN
ejde-397	1193	31	to	to	ADP
ejde-397	1193	32	multiplicities	multiplicity	NOUN
ejde-397	1193	33	.	.	PUNCT
ejde-397	1194	1	by	by	ADP
ejde-397	1194	2	{	{	PUNCT
ejde-397	1194	3	φk	φk	ADP
ejde-397	1194	4	}	}	PUNCT
ejde-397	1194	5	⊆	⊆	NUM
ejde-397	1194	6	c∞(ω	c∞(ω	NOUN
ejde-397	1194	7	)	)	PUNCT
ejde-397	1194	8	we	we	PRON
ejde-397	1194	9	denote	denote	VERB
ejde-397	1194	10	the	the	DET
ejde-397	1194	11	corresponding	corresponding	ADJ
ejde-397	1194	12	set	set	NOUN
ejde-397	1194	13	of	of	ADP
ejde-397	1194	14	mutually	mutually	ADV
ejde-397	1194	15	orthogonal	orthogonal	ADJ
ejde-397	1194	16	eigenfunctions	eigenfunction	NOUN
ejde-397	1194	17	.	.	PUNCT
ejde-397	1195	1	then	then	ADV
ejde-397	1195	2	,	,	PUNCT
ejde-397	1195	3	for	for	ADP
ejde-397	1195	4	every	every	DET
ejde-397	1195	5	ζ	ζ	NOUN
ejde-397	1195	6	>	>	X
ejde-397	1195	7	0	0	NUM
ejde-397	1195	8	,	,	PUNCT
ejde-397	1195	9	we	we	PRON
ejde-397	1195	10	define	define	VERB
ejde-397	1195	11	the	the	DET
ejde-397	1195	12	spectral	spectral	ADJ
ejde-397	1195	13	fractional	fractional	ADJ
ejde-397	1195	14	power	power	NOUN
ejde-397	1195	15	cζ	cζ	ADP
ejde-397	1195	16	∈	∈	PROPN
ejde-397	1195	17	l(x	l(x	PROPN
ejde-397	1195	18	)	)	PUNCT
ejde-397	1195	19	of	of	ADP
ejde-397	1195	20	−∆	−∆	NOUN
ejde-397	1195	21	by	by	ADP
ejde-397	1195	22	cζ	cζ	X
ejde-397	1195	23	·	·	PUNCT
ejde-397	1195	24	:	:	PUNCT
ejde-397	1195	25	=	=	SYM
ejde-397	1195	26	(	(	PUNCT
ejde-397	1195	27	−∆)−(ζ)/2	−∆)−(ζ)/2	PROPN
ejde-397	1195	28	·	·	PUNCT
ejde-397	1195	29	:	:	PUNCT
ejde-397	1196	1	=	=	X
ejde-397	1196	2	∑	∑	PART
ejde-397	1196	3	k≥1	k≥1	PROPN
ejde-397	1196	4	〈	〈	PROPN
ejde-397	1196	5	·	·	SYM
ejde-397	1196	6	,	,	PUNCT
ejde-397	1196	7	φk〉(−λk)−(ζ/2)φk	φk〉(−λk)−(ζ/2)φk	PROPN
ejde-397	1196	8	(	(	PUNCT
ejde-397	1196	9	cf	cf	NOUN
ejde-397	1196	10	.	.	PUNCT
ejde-397	1197	1	[	[	X
ejde-397	1197	2	69	69	NUM
ejde-397	1197	3	]	]	PUNCT
ejde-397	1197	4	for	for	ADP
ejde-397	1197	5	more	more	ADJ
ejde-397	1197	6	details	detail	NOUN
ejde-397	1197	7	)	)	PUNCT
ejde-397	1197	8	.	.	PUNCT
ejde-397	1198	1	then	then	ADV
ejde-397	1198	2	cζ	cζ	PROPN
ejde-397	1198	3	is	be	AUX
ejde-397	1198	4	injective	injective	ADJ
ejde-397	1198	5	and	and	CCONJ
ejde-397	1198	6	r(c	r(c	ADJ
ejde-397	1198	7	)	)	PUNCT
ejde-397	1198	8	=	=	NOUN
ejde-397	1198	9	:	:	PUNCT
ejde-397	1198	10	d((−∆)ζ/2	d((−∆)ζ/2	NUM
ejde-397	1198	11	)	)	PUNCT
ejde-397	1198	12	=	=	PRON
ejde-397	1199	1	{	{	PUNCT
ejde-397	1199	2	f	f	PROPN
ejde-397	1199	3	∈	∈	PROPN
ejde-397	1199	4	l2(ω	l2(ω	PROPN
ejde-397	1199	5	)	)	PUNCT
ejde-397	1199	6	:	:	PUNCT
ejde-397	1199	7	∑	∑	PUNCT
ejde-397	1199	8	k≥1	k≥1	PROPN
ejde-397	1199	9	|〈f	|〈f	VERB
ejde-397	1199	10	,	,	PUNCT
ejde-397	1199	11	φk〉|2(−λk)ζ	φk〉|2(−λk)ζ	PROPN
ejde-397	1199	12	<	<	X
ejde-397	1199	13	∞	∞	NUM
ejde-397	1199	14	}	}	PUNCT
ejde-397	1199	15	.	.	PUNCT
ejde-397	1200	1	let	let	VERB
ejde-397	1200	2	λ	λ	X
ejde-397	1200	3	∈	∈	PROPN
ejde-397	1200	4	σ(∆	σ(∆	PROPN
ejde-397	1200	5	)	)	PUNCT
ejde-397	1200	6	,	,	PUNCT
ejde-397	1200	7	let	let	VERB
ejde-397	1200	8	0	0	NUM
ejde-397	1200	9	<	<	X
ejde-397	1200	10	η	η	PROPN
ejde-397	1200	11	≤	≤	PROPN
ejde-397	1200	12	2	2	NUM
ejde-397	1200	13	,	,	PUNCT
ejde-397	1200	14	and	and	CCONJ
ejde-397	1200	15	let	let	VERB
ejde-397	1200	16	α	α	PRON
ejde-397	1200	17	,	,	PUNCT
ejde-397	1200	18	β	β	X
ejde-397	1200	19	>	>	X
ejde-397	1200	20	0	0	X
ejde-397	1200	21	.	.	PUNCT
ejde-397	1200	22	consider	consider	VERB
ejde-397	1200	23	the	the	DET
ejde-397	1200	24	time	time	NOUN
ejde-397	1200	25	-	-	PUNCT
ejde-397	1200	26	fractional	fractional	ADJ
ejde-397	1200	27	analogue	analogue	NOUN
ejde-397	1200	28	of	of	ADP
ejde-397	1200	29	the	the	DET
ejde-397	1200	30	linearized	linearize	VERB
ejde-397	1200	31	benney	benney	NOUN
ejde-397	1200	32	-	-	PUNCT
ejde-397	1200	33	luke	luke	VERB
ejde-397	1200	34	equation	equation	NOUN
ejde-397	1200	35	(	(	PUNCT
ejde-397	1200	36	λ−∆)dη	λ−∆)dη	PROPN
ejde-397	1200	37	t	t	PROPN
ejde-397	1200	38	u(t	u(t	NOUN
ejde-397	1200	39	,	,	PUNCT
ejde-397	1200	40	x	x	NOUN
ejde-397	1200	41	)	)	PUNCT
ejde-397	1200	42	=	=	SYM
ejde-397	1200	43	(	(	PUNCT
ejde-397	1200	44	α∆−	α∆−	NUM
ejde-397	1200	45	β∆2	β∆2	NUM
ejde-397	1200	46	)	)	PUNCT
ejde-397	1200	47	u(t	u(t	NOUN
ejde-397	1200	48	,	,	PUNCT
ejde-397	1200	49	x	x	NOUN
ejde-397	1200	50	)	)	PUNCT
ejde-397	1201	1	+	+	CCONJ
ejde-397	1201	2	f(t	f(t	NOUN
ejde-397	1201	3	,	,	PUNCT
ejde-397	1201	4	x	x	NOUN
ejde-397	1201	5	)	)	PUNCT
ejde-397	1201	6	,	,	PUNCT
ejde-397	1201	7	t	t	PROPN
ejde-397	1201	8	≥	≥	NUM
ejde-397	1201	9	0	0	NUM
ejde-397	1201	10	,	,	PUNCT
ejde-397	1201	11	x	x	X
ejde-397	1201	12	∈	∈	PROPN
ejde-397	1201	13	ω	ω	PROPN
ejde-397	1201	14	,	,	PUNCT
ejde-397	1201	15	(	(	PUNCT
ejde-397	1201	16	∂k	∂k	PROPN
ejde-397	1201	17	∂tk	∂tk	PROPN
ejde-397	1201	18	u(t	u(t	NOUN
ejde-397	1201	19	,	,	PUNCT
ejde-397	1201	20	x	x	NOUN
ejde-397	1201	21	)	)	PUNCT
ejde-397	1201	22	)	)	PUNCT
ejde-397	1202	1	t=0	t=0	PROPN
ejde-397	1202	2	=	=	PUNCT
ejde-397	1202	3	uk(x	uk(x	NOUN
ejde-397	1202	4	)	)	PUNCT
ejde-397	1202	5	,	,	PUNCT
ejde-397	1202	6	x	x	PUNCT
ejde-397	1202	7	∈	∈	PROPN
ejde-397	1202	8	ω	ω	PROPN
ejde-397	1202	9	,	,	PUNCT
ejde-397	1202	10	0	0	NUM
ejde-397	1202	11	≤	≤	NUM
ejde-397	1202	12	k	k	X
ejde-397	1202	13	≤	≤	PROPN
ejde-397	1202	14	dηe	dηe	VERB
ejde-397	1202	15	−	−	PROPN
ejde-397	1202	16	1	1	NUM
ejde-397	1202	17	,	,	PUNCT
ejde-397	1202	18	u(t	u(t	NOUN
ejde-397	1202	19	,	,	PUNCT
ejde-397	1202	20	x	x	NOUN
ejde-397	1202	21	)	)	PUNCT
ejde-397	1202	22	=	=	SYM
ejde-397	1202	23	∆u(t	∆u(t	PROPN
ejde-397	1202	24	,	,	PUNCT
ejde-397	1202	25	x	x	NOUN
ejde-397	1202	26	)	)	PUNCT
ejde-397	1202	27	=	=	SYM
ejde-397	1202	28	0	0	NUM
ejde-397	1202	29	,	,	PUNCT
ejde-397	1202	30	t	t	PROPN
ejde-397	1202	31	≥	≥	NUM
ejde-397	1202	32	0	0	NUM
ejde-397	1202	33	,	,	PUNCT
ejde-397	1202	34	x	x	X
ejde-397	1202	35	∈	∈	PROPN
ejde-397	1202	36	∂ω	∂ω	PROPN
ejde-397	1202	37	,	,	PUNCT
ejde-397	1202	38	(	(	PUNCT
ejde-397	1202	39	5.25	5.25	NUM
ejde-397	1202	40	)	)	PUNCT
ejde-397	1202	41	for	for	ADP
ejde-397	1202	42	which	which	PRON
ejde-397	1202	43	is	be	AUX
ejde-397	1202	44	known	know	VERB
ejde-397	1202	45	that	that	PRON
ejde-397	1202	46	plays	play	VERB
ejde-397	1202	47	an	an	DET
ejde-397	1202	48	important	important	ADJ
ejde-397	1202	49	role	role	NOUN
ejde-397	1202	50	in	in	ADP
ejde-397	1202	51	evolution	evolution	NOUN
ejde-397	1202	52	modeling	modeling	NOUN
ejde-397	1202	53	of	of	ADP
ejde-397	1202	54	some	some	DET
ejde-397	1202	55	problems	problem	NOUN
ejde-397	1202	56	appearing	appear	VERB
ejde-397	1202	57	in	in	ADP
ejde-397	1202	58	the	the	DET
ejde-397	1202	59	theory	theory	NOUN
ejde-397	1202	60	of	of	ADP
ejde-397	1202	61	liquid	liquid	ADJ
ejde-397	1202	62	filtration	filtration	NOUN
ejde-397	1202	63	.	.	PUNCT
ejde-397	1203	1	denote	denote	VERB
ejde-397	1203	2	by	by	ADP
ejde-397	1203	3	x0	x0	PROPN
ejde-397	1203	4	the	the	DET
ejde-397	1203	5	vector	vector	NOUN
ejde-397	1203	6	space	space	NOUN
ejde-397	1203	7	of	of	ADP
ejde-397	1203	8	those	those	DET
ejde-397	1203	9	functions	function	NOUN
ejde-397	1203	10	from	from	ADP
ejde-397	1203	11	x	x	PUNCT
ejde-397	1203	12	that	that	PRON
ejde-397	1203	13	are	be	AUX
ejde-397	1203	14	orthogonal	orthogonal	ADJ
ejde-397	1203	15	to	to	ADP
ejde-397	1203	16	the	the	DET
ejde-397	1203	17	eigenfunctions	eigenfunction	NOUN
ejde-397	1203	18	φk	φk	ADP
ejde-397	1203	19	(	(	PUNCT
ejde-397	1203	20	·	·	PUNCT
ejde-397	1203	21	)	)	PUNCT
ejde-397	1203	22	for	for	ADP
ejde-397	1203	23	λk	λk	PROPN
ejde-397	1203	24	=	=	SYM
ejde-397	1203	25	λ	λ	PROPN
ejde-397	1203	26	.	.	PUNCT
ejde-397	1204	1	then	then	ADV
ejde-397	1204	2	x0	x0	PROPN
ejde-397	1204	3	is	be	AUX
ejde-397	1204	4	a	a	DET
ejde-397	1204	5	closed	closed	ADJ
ejde-397	1204	6	subspace	subspace	NOUN
ejde-397	1204	7	of	of	ADP
ejde-397	1204	8	x	x	PRON
ejde-397	1204	9	,	,	PUNCT
ejde-397	1204	10	and	and	CCONJ
ejde-397	1204	11	therefore	therefore	ADV
ejde-397	1204	12	,	,	PUNCT
ejde-397	1204	13	becomes	become	VERB
ejde-397	1204	14	the	the	DET
ejde-397	1204	15	banach	banach	NOUN
ejde-397	1204	16	space	space	NOUN
ejde-397	1204	17	equipped	equip	VERB
ejde-397	1204	18	with	with	ADP
ejde-397	1204	19	the	the	DET
ejde-397	1204	20	topology	topology	NOUN
ejde-397	1204	21	inherited	inherit	VERB
ejde-397	1204	22	by	by	ADP
ejde-397	1204	23	the	the	DET
ejde-397	1204	24	x	x	NOUN
ejde-397	1204	25	-	-	NOUN
ejde-397	1204	26	norm	norm	NOUN
ejde-397	1204	27	(	(	PUNCT
ejde-397	1204	28	cf	cf	NOUN
ejde-397	1204	29	.	.	PUNCT
ejde-397	1205	1	[	[	X
ejde-397	1205	2	73	73	NUM
ejde-397	1205	3	,	,	PUNCT
ejde-397	1205	4	example	example	NOUN
ejde-397	1205	5	5.3.1	5.3.1	NUM
ejde-397	1205	6	,	,	PUNCT
ejde-397	1205	7	theorem	theorem	VERB
ejde-397	1205	8	5.3.2	5.3.2	NUM
ejde-397	1205	9	]	]	PUNCT
ejde-397	1205	10	for	for	ADP
ejde-397	1205	11	the	the	DET
ejde-397	1205	12	case	case	NOUN
ejde-397	1205	13	η	η	NOUN
ejde-397	1205	14	=	=	PROPN
ejde-397	1205	15	1	1	NUM
ejde-397	1205	16	)	)	PUNCT
ejde-397	1205	17	.	.	PUNCT
ejde-397	1206	1	on	on	ADP
ejde-397	1206	2	the	the	DET
ejde-397	1206	3	other	other	ADJ
ejde-397	1206	4	hand	hand	NOUN
ejde-397	1206	5	,	,	PUNCT
ejde-397	1206	6	the	the	DET
ejde-397	1206	7	operators	operator	NOUN
ejde-397	1206	8	a	a	DET
ejde-397	1206	9	:	:	PUNCT
ejde-397	1206	10	=	=	SYM
ejde-397	1206	11	α∆−β∆2	α∆−β∆2	NOUN
ejde-397	1206	12	and	and	CCONJ
ejde-397	1206	13	b	b	NOUN
ejde-397	1206	14	:	:	PUNCT
ejde-397	1206	15	=	=	SYM
ejde-397	1206	16	λ−∆	λ−∆	NOUN
ejde-397	1206	17	,	,	PUNCT
ejde-397	1206	18	acting	act	VERB
ejde-397	1206	19	with	with	ADP
ejde-397	1206	20	maximal	maximal	ADJ
ejde-397	1206	21	domains	domain	NOUN
ejde-397	1206	22	,	,	PUNCT
ejde-397	1206	23	are	be	AUX
ejde-397	1206	24	closed	close	VERB
ejde-397	1206	25	in	in	ADP
ejde-397	1206	26	l2(ω	l2(ω	NOUN
ejde-397	1206	27	)	)	PUNCT
ejde-397	1206	28	.	.	PUNCT
ejde-397	1207	1	set	set	VERB
ejde-397	1207	2	θ	θ	NOUN
ejde-397	1207	3	:	:	PUNCT
ejde-397	1207	4	=	=	SYM
ejde-397	1207	5	min((π	min((π	PROPN
ejde-397	1207	6	/	/	SYM
ejde-397	1207	7	η)−	η)−	PROPN
ejde-397	1207	8	(	(	PUNCT
ejde-397	1207	9	π/2	π/2	NUM
ejde-397	1207	10	)	)	PUNCT
ejde-397	1207	11	,	,	PUNCT
ejde-397	1207	12	π	π	X
ejde-397	1207	13	)	)	PUNCT
ejde-397	1207	14	.	.	PUNCT
ejde-397	1208	1	using	use	VERB
ejde-397	1208	2	the	the	DET
ejde-397	1208	3	parseval	parseval	NOUN
ejde-397	1208	4	equality	equality	NOUN
ejde-397	1208	5	,	,	PUNCT
ejde-397	1208	6	the	the	DET
ejde-397	1208	7	asymptotic	asymptotic	ADJ
ejde-397	1208	8	expansion	expansion	NOUN
ejde-397	1208	9	formula	formula	NOUN
ejde-397	1208	10	[	[	X
ejde-397	1208	11	5	5	NUM
ejde-397	1208	12	,	,	PUNCT
ejde-397	1208	13	(	(	PUNCT
ejde-397	1208	14	1.28	1.28	NUM
ejde-397	1208	15	)	)	PUNCT
ejde-397	1208	16	]	]	PUNCT
ejde-397	1208	17	and	and	CCONJ
ejde-397	1208	18	an	an	DET
ejde-397	1208	19	elementary	elementary	ADJ
ejde-397	1208	20	argumentation	argumentation	NOUN
ejde-397	1208	21	,	,	PUNCT
ejde-397	1208	22	we	we	PRON
ejde-397	1208	23	can	can	AUX
ejde-397	1208	24	simply	simply	ADV
ejde-397	1208	25	prove	prove	VERB
ejde-397	1208	26	that	that	SCONJ
ejde-397	1208	27	the	the	DET
ejde-397	1208	28	operator	operator	NOUN
ejde-397	1208	29	family	family	NOUN
ejde-397	1208	30	(	(	PUNCT
ejde-397	1208	31	tη(z))z∈σθ∪{0	tη(z))z∈σθ∪{0	NOUN
ejde-397	1208	32	}	}	PUNCT
ejde-397	1208	33	⊆	⊆	NUM
ejde-397	1208	34	l(x0	l(x0	NOUN
ejde-397	1208	35	)	)	PUNCT
ejde-397	1208	36	,	,	PUNCT
ejde-397	1208	37	given	give	VERB
ejde-397	1208	38	by	by	ADP
ejde-397	1208	39	t	t	PROPN
ejde-397	1208	40	7→	7→	NUM
ejde-397	1208	41	tη(z	tη(z	NUM
ejde-397	1208	42	)	)	PUNCT
ejde-397	1208	43	·	·	PUNCT
ejde-397	1208	44	:	:	PUNCT
ejde-397	1208	45	=	=	PUNCT
ejde-397	1208	46	∑	∑	PUNCT
ejde-397	1208	47	k|λk	k|λk	PROPN
ejde-397	1208	48	6	6	NUM
ejde-397	1208	49	=	=	SYM
ejde-397	1208	50	λ	λ	PART
ejde-397	1208	51	eη	eη	NOUN
ejde-397	1208	52	(	(	PUNCT
ejde-397	1208	53	αλk	αλk	PROPN
ejde-397	1208	54	−	−	NOUN
ejde-397	1208	55	βλ2	βλ2	VERB
ejde-397	1208	56	k	k	PROPN
ejde-397	1208	57	λ−	λ−	PROPN
ejde-397	1208	58	λk	λk	INTJ
ejde-397	1208	59	zη	zη	NOUN
ejde-397	1208	60	)	)	PUNCT
ejde-397	1208	61	〈	〈	PROPN
ejde-397	1208	62	·	·	SYM
ejde-397	1208	63	,	,	PUNCT
ejde-397	1208	64	φk〉φk	φk〉φk	PROPN
ejde-397	1208	65	,	,	PUNCT
ejde-397	1208	66	z	z	PROPN
ejde-397	1208	67	∈	∈	PROPN
ejde-397	1208	68	σθ	σθ	NOUN
ejde-397	1208	69	∪	∪	X
ejde-397	1208	70	{	{	PUNCT
ejde-397	1208	71	0	0	NUM
ejde-397	1208	72	}	}	PUNCT
ejde-397	1208	73	,	,	PUNCT
ejde-397	1208	74	is	be	AUX
ejde-397	1208	75	well	well	ADV
ejde-397	1208	76	-	-	PUNCT
ejde-397	1208	77	defined	define	VERB
ejde-397	1208	78	,	,	PUNCT
ejde-397	1208	79	provided	provide	VERB
ejde-397	1208	80	η	η	PROPN
ejde-397	1208	81	∈	∈	PROPN
ejde-397	1208	82	(	(	PUNCT
ejde-397	1208	83	0	0	NUM
ejde-397	1208	84	,	,	PUNCT
ejde-397	1208	85	2	2	NUM
ejde-397	1208	86	)	)	PUNCT
ejde-397	1208	87	.	.	PUNCT
ejde-397	1209	1	if	if	SCONJ
ejde-397	1209	2	η	η	PROPN
ejde-397	1209	3	=	=	PROPN
ejde-397	1209	4	2	2	NUM
ejde-397	1209	5	,	,	PUNCT
ejde-397	1209	6	then	then	ADV
ejde-397	1209	7	we	we	PRON
ejde-397	1209	8	define	define	VERB
ejde-397	1209	9	(	(	PUNCT
ejde-397	1209	10	t2(t))t≥0	t2(t))t≥0	NOUN
ejde-397	1209	11	⊆	⊆	NUM
ejde-397	1209	12	l(x0	l(x0	NOUN
ejde-397	1209	13	)	)	PUNCT
ejde-397	1209	14	in	in	ADP
ejde-397	1209	15	the	the	DET
ejde-397	1209	16	same	same	ADJ
ejde-397	1209	17	way	way	NOUN
ejde-397	1209	18	as	as	ADP
ejde-397	1209	19	above	above	ADV
ejde-397	1209	20	;	;	PUNCT
ejde-397	1209	21	since	since	SCONJ
ejde-397	1209	22	e2(z2	e2(z2	NOUN
ejde-397	1209	23	)	)	PUNCT
ejde-397	1209	24	=	=	SYM
ejde-397	1209	25	cosh(z	cosh(z	PROPN
ejde-397	1209	26	)	)	PUNCT
ejde-397	1209	27	,	,	PUNCT
ejde-397	1209	28	we	we	PRON
ejde-397	1209	29	have	have	VERB
ejde-397	1209	30	that	that	PRON
ejde-397	1209	31	,	,	PUNCT
ejde-397	1209	32	for	for	ADP
ejde-397	1209	33	every	every	DET
ejde-397	1209	34	t	t	PROPN
ejde-397	1209	35	≥	≥	NOUN
ejde-397	1209	36	0	0	NUM
ejde-397	1209	37	,	,	PUNCT
ejde-397	1209	38	t2(t	t2(t	NOUN
ejde-397	1209	39	)	)	PUNCT
ejde-397	1209	40	·	·	PUNCT
ejde-397	1210	1	=	=	SYM
ejde-397	1210	2	1	1	NUM
ejde-397	1210	3	2	2	NUM
ejde-397	1210	4	∑	∑	NUM
ejde-397	1210	5	k|λk	k|λk	PROPN
ejde-397	1210	6	6	6	NUM
ejde-397	1210	7	=	=	SYM
ejde-397	1210	8	λ	λ	X
ejde-397	1210	9	[	[	PUNCT
ejde-397	1210	10	eit	eit	X
ejde-397	1210	11	(	(	PUNCT
ejde-397	1210	12	(	(	PUNCT
ejde-397	1210	13	βλ2−αλk)/(λ−λk	βλ2−αλk)/(λ−λk	PROPN
ejde-397	1210	14	)	)	PUNCT
ejde-397	1210	15	)	)	PUNCT
ejde-397	1211	1	1/2	1/2	NUM
ejde-397	1211	2	−	−	PROPN
ejde-397	1211	3	e−it	e−it	INTJ
ejde-397	1211	4	(	(	PUNCT
ejde-397	1211	5	(	(	PUNCT
ejde-397	1211	6	βλ2−αλk)/(λ−λk	βλ2−αλk)/(λ−λk	PROPN
ejde-397	1211	7	)	)	PUNCT
ejde-397	1211	8	)	)	PUNCT
ejde-397	1211	9	1/2	1/2	NUM
ejde-397	1211	10	]	]	PUNCT
ejde-397	1211	11	〈	〈	PROPN
ejde-397	1211	12	·	·	SYM
ejde-397	1211	13	,	,	PUNCT
ejde-397	1211	14	φk〉φk	φk〉φk	PROPN
ejde-397	1211	15	,	,	PUNCT
ejde-397	1211	16	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1211	17	abstract	abstract	ADJ
ejde-397	1211	18	degenerate	degenerate	ADJ
ejde-397	1211	19	volterra	volterra	NOUN
ejde-397	1211	20	inclusions	inclusion	NOUN
ejde-397	1211	21	39	39	NUM
ejde-397	1211	22	and	and	CCONJ
ejde-397	1211	23	that	that	SCONJ
ejde-397	1211	24	(	(	PUNCT
ejde-397	1211	25	t2(t))t≥0	t2(t))t≥0	PROPN
ejde-397	1211	26	is	be	AUX
ejde-397	1211	27	bounded	bound	VERB
ejde-397	1211	28	in	in	ADP
ejde-397	1211	29	the	the	DET
ejde-397	1211	30	uniform	uniform	ADJ
ejde-397	1211	31	operator	operator	NOUN
ejde-397	1211	32	norm	norm	NOUN
ejde-397	1211	33	.	.	PUNCT
ejde-397	1212	1	differentiating	differentiate	VERB
ejde-397	1212	2	t2(t	t2(t	NOUN
ejde-397	1212	3	)	)	PUNCT
ejde-397	1212	4	term	term	NOUN
ejde-397	1212	5	by	by	ADP
ejde-397	1212	6	term	term	NOUN
ejde-397	1212	7	,	,	PUNCT
ejde-397	1212	8	it	it	PRON
ejde-397	1212	9	can	can	AUX
ejde-397	1212	10	be	be	AUX
ejde-397	1212	11	easily	easily	ADV
ejde-397	1212	12	seen	see	VERB
ejde-397	1212	13	that	that	SCONJ
ejde-397	1212	14	the	the	DET
ejde-397	1212	15	mapping	mapping	NOUN
ejde-397	1212	16	t	t	NOUN
ejde-397	1212	17	7→	7→	NUM
ejde-397	1212	18	t2(t)f	t2(t)f	NUM
ejde-397	1212	19	,	,	PUNCT
ejde-397	1212	20	t	t	PROPN
ejde-397	1212	21	≥	≥	NOUN
ejde-397	1212	22	0	0	NUM
ejde-397	1212	23	is	be	AUX
ejde-397	1212	24	continuously	continuously	ADV
ejde-397	1212	25	differentiable	differentiable	ADJ
ejde-397	1212	26	for	for	ADP
ejde-397	1212	27	any	any	DET
ejde-397	1212	28	f	f	PROPN
ejde-397	1212	29	∈	∈	PROPN
ejde-397	1212	30	d((−∆)1/2	d((−∆)1/2	PROPN
ejde-397	1212	31	)	)	PUNCT
ejde-397	1212	32	∩	∩	NOUN
ejde-397	1212	33	x0	x0	PROPN
ejde-397	1212	34	,	,	PUNCT
ejde-397	1212	35	and	and	CCONJ
ejde-397	1212	36	therefore	therefore	ADV
ejde-397	1212	37	,	,	PUNCT
ejde-397	1212	38	continuous	continuous	ADJ
ejde-397	1212	39	.	.	PUNCT
ejde-397	1213	1	since	since	SCONJ
ejde-397	1213	2	d((−∆)1/2	d((−∆)1/2	PROPN
ejde-397	1213	3	)	)	PUNCT
ejde-397	1213	4	∩	∩	NOUN
ejde-397	1213	5	x0	x0	PROPN
ejde-397	1213	6	is	be	AUX
ejde-397	1213	7	dense	dense	ADJ
ejde-397	1213	8	in	in	ADP
ejde-397	1213	9	x0	x0	PROPN
ejde-397	1213	10	and	and	CCONJ
ejde-397	1213	11	(	(	PUNCT
ejde-397	1213	12	t2(t))t≥0	t2(t))t≥0	PROPN
ejde-397	1213	13	is	be	AUX
ejde-397	1213	14	bounded	bound	VERB
ejde-397	1213	15	,	,	PUNCT
ejde-397	1213	16	the	the	DET
ejde-397	1213	17	usual	usual	ADJ
ejde-397	1213	18	arguments	argument	NOUN
ejde-397	1213	19	shows	show	VERB
ejde-397	1213	20	that	that	SCONJ
ejde-397	1213	21	(	(	PUNCT
ejde-397	1213	22	t2(t))t≥0	t2(t))t≥0	X
ejde-397	1213	23	is	be	AUX
ejde-397	1213	24	strongly	strongly	ADV
ejde-397	1213	25	continuous	continuous	ADJ
ejde-397	1213	26	.	.	PUNCT
ejde-397	1214	1	now	now	ADV
ejde-397	1214	2	we	we	PRON
ejde-397	1214	3	can	can	AUX
ejde-397	1214	4	proceed	proceed	VERB
ejde-397	1214	5	as	as	ADP
ejde-397	1214	6	in	in	ADP
ejde-397	1214	7	the	the	DET
ejde-397	1214	8	proof	proof	NOUN
ejde-397	1214	9	of	of	ADP
ejde-397	1214	10	theorem	theorem	ADJ
ejde-397	1214	11	4.8	4.8	NUM
ejde-397	1214	12	in	in	ADP
ejde-397	1214	13	order	order	NOUN
ejde-397	1214	14	to	to	PART
ejde-397	1214	15	see	see	VERB
ejde-397	1214	16	that	that	PRON
ejde-397	1214	17	,	,	PUNCT
ejde-397	1214	18	for	for	ADP
ejde-397	1214	19	every	every	DET
ejde-397	1214	20	η	η	PROPN
ejde-397	1214	21	∈	∈	PROPN
ejde-397	1214	22	(	(	PUNCT
ejde-397	1214	23	0	0	NUM
ejde-397	1214	24	,	,	PUNCT
ejde-397	1214	25	2	2	NUM
ejde-397	1214	26	)	)	PUNCT
ejde-397	1214	27	,	,	PUNCT
ejde-397	1214	28	(	(	PUNCT
ejde-397	1214	29	tη(t))t≥0	tη(t))t≥0	PROPN
ejde-397	1214	30	is	be	AUX
ejde-397	1214	31	an	an	DET
ejde-397	1214	32	exponentially	exponentially	ADV
ejde-397	1214	33	bounded	bound	VERB
ejde-397	1214	34	,	,	PUNCT
ejde-397	1214	35	analytic	analytic	ADJ
ejde-397	1214	36	(	(	PUNCT
ejde-397	1214	37	gη	gη	NOUN
ejde-397	1214	38	,	,	PUNCT
ejde-397	1214	39	i)-regularized	i)-regularize	VERB
ejde-397	1214	40	resolvent	resolvent	ADJ
ejde-397	1214	41	family	family	NOUN
ejde-397	1214	42	of	of	ADP
ejde-397	1214	43	angle	angle	PROPN
ejde-397	1214	44	θ	θ	PROPN
ejde-397	1214	45	.	.	PUNCT
ejde-397	1215	1	a	a	DET
ejde-397	1215	2	straightforward	straightforward	ADJ
ejde-397	1215	3	computation	computation	NOUN
ejde-397	1215	4	shows	show	VERB
ejde-397	1215	5	that	that	SCONJ
ejde-397	1215	6	,	,	PUNCT
ejde-397	1215	7	for	for	ADP
ejde-397	1215	8	every	every	DET
ejde-397	1215	9	η	η	PROPN
ejde-397	1215	10	∈	∈	PROPN
ejde-397	1215	11	(	(	PUNCT
ejde-397	1215	12	0	0	NUM
ejde-397	1215	13	,	,	PUNCT
ejde-397	1215	14	2	2	NUM
ejde-397	1215	15	]	]	PUNCT
ejde-397	1215	16	,	,	PUNCT
ejde-397	1215	17	the	the	DET
ejde-397	1215	18	integral	integral	ADJ
ejde-397	1215	19	generator	generator	NOUN
ejde-397	1215	20	a	a	PRON
ejde-397	1215	21	of	of	ADP
ejde-397	1215	22	(	(	PUNCT
ejde-397	1215	23	tη(t))t≥0	tη(t))t≥0	PROPN
ejde-397	1215	24	is	be	AUX
ejde-397	1215	25	a	a	DET
ejde-397	1215	26	closed	closed	ADJ
ejde-397	1215	27	single	single	ADV
ejde-397	1215	28	-	-	PUNCT
ejde-397	1215	29	valued	value	VERB
ejde-397	1215	30	operator	operator	NOUN
ejde-397	1215	31	in	in	ADP
ejde-397	1215	32	x0	x0	PROPN
ejde-397	1215	33	,	,	PUNCT
ejde-397	1215	34	given	give	VERB
ejde-397	1215	35	by	by	ADP
ejde-397	1215	36	a	a	DET
ejde-397	1215	37	=	=	X
ejde-397	1215	38	{	{	PUNCT
ejde-397	1215	39	(	(	PUNCT
ejde-397	1215	40	f	f	X
ejde-397	1215	41	,	,	PUNCT
ejde-397	1215	42	g	g	NOUN
ejde-397	1215	43	)	)	PUNCT
ejde-397	1215	44	∈	∈	NOUN
ejde-397	1215	45	x0	x0	NOUN
ejde-397	1216	1	×x0	×x0	NOUN
ejde-397	1216	2	:	:	PUNCT
ejde-397	1216	3	(	(	PUNCT
ejde-397	1216	4	λ−	λ−	PROPN
ejde-397	1216	5	λk)〈g	λk)〈g	PROPN
ejde-397	1216	6	,	,	PUNCT
ejde-397	1216	7	φk	φk	ADP
ejde-397	1216	8	〉	〉	NOUN
ejde-397	1216	9	=	=	SYM
ejde-397	1216	10	(	(	PUNCT
ejde-397	1216	11	αλk	αλk	PROPN
ejde-397	1216	12	−	−	PROPN
ejde-397	1216	13	βλ2	βλ2	X
ejde-397	1217	1	k)〈f	k)〈f	PROPN
ejde-397	1217	2	,	,	PUNCT
ejde-397	1217	3	φk	φk	ADP
ejde-397	1217	4	〉	〉	NOUN
ejde-397	1217	5	for	for	ADP
ejde-397	1217	6	all	all	DET
ejde-397	1217	7	k	k	PROPN
ejde-397	1217	8	∈	∈	PROPN
ejde-397	1217	9	n	n	INTJ
ejde-397	1217	10	with	with	ADP
ejde-397	1217	11	λk	λk	PROPN
ejde-397	1217	12	6=	6=	SYM
ejde-397	1217	13	λ	λ	PROPN
ejde-397	1217	14	}	}	PUNCT
ejde-397	1217	15	;	;	PUNCT
ejde-397	1217	16	in	in	ADP
ejde-397	1217	17	particular	particular	ADJ
ejde-397	1217	18	,	,	PUNCT
ejde-397	1217	19	a	a	PRON
ejde-397	1217	20	is	be	AUX
ejde-397	1217	21	an	an	DET
ejde-397	1217	22	extension	extension	NOUN
ejde-397	1217	23	of	of	ADP
ejde-397	1217	24	the	the	DET
ejde-397	1217	25	operator	operator	NOUN
ejde-397	1217	26	b−1a|x0	b−1a|x0	NOUN
ejde-397	1217	27	.	.	PUNCT
ejde-397	1218	1	it	it	PRON
ejde-397	1218	2	is	be	AUX
ejde-397	1218	3	also	also	ADV
ejde-397	1218	4	clear	clear	ADJ
ejde-397	1218	5	that	that	SCONJ
ejde-397	1218	6	(	(	PUNCT
ejde-397	1218	7	tη(t))t≥0	tη(t))t≥0	PROPN
ejde-397	1218	8	is	be	AUX
ejde-397	1218	9	a	a	DET
ejde-397	1218	10	mild	mild	ADJ
ejde-397	1218	11	(	(	PUNCT
ejde-397	1218	12	gη	gη	NOUN
ejde-397	1218	13	,	,	PUNCT
ejde-397	1218	14	i)-existence	i)-existence	PUNCT
ejde-397	1218	15	family	family	NOUN
ejde-397	1218	16	generated	generate	VERB
ejde-397	1218	17	by	by	ADP
ejde-397	1218	18	a.	a.	NOUN
ejde-397	1218	19	keeping	keeping	NOUN
ejde-397	1218	20	in	in	ADP
ejde-397	1218	21	mind	mind	NOUN
ejde-397	1218	22	the	the	DET
ejde-397	1218	23	identity	identity	NOUN
ejde-397	1218	24	[	[	X
ejde-397	1218	25	5	5	NUM
ejde-397	1218	26	,	,	PUNCT
ejde-397	1218	27	(	(	PUNCT
ejde-397	1218	28	1.25	1.25	NUM
ejde-397	1218	29	)	)	PUNCT
ejde-397	1218	30	]	]	PUNCT
ejde-397	1218	31	,	,	PUNCT
ejde-397	1218	32	we	we	PRON
ejde-397	1218	33	can	can	AUX
ejde-397	1218	34	carry	carry	VERB
ejde-397	1218	35	out	out	ADP
ejde-397	1218	36	a	a	DET
ejde-397	1218	37	direct	direct	ADJ
ejde-397	1218	38	computation	computation	NOUN
ejde-397	1218	39	showing	show	VERB
ejde-397	1218	40	that	that	SCONJ
ejde-397	1218	41	the	the	DET
ejde-397	1218	42	homogeneous	homogeneous	ADJ
ejde-397	1218	43	counterpart	counterpart	NOUN
ejde-397	1218	44	of	of	ADP
ejde-397	1218	45	problem	problem	NOUN
ejde-397	1218	46	(	(	PUNCT
ejde-397	1218	47	5.25	5.25	NUM
ejde-397	1218	48	)	)	PUNCT
ejde-397	1218	49	≡	≡	PROPN
ejde-397	1218	50	(	(	PUNCT
ejde-397	1218	51	5.25	5.25	NUM
ejde-397	1218	52	)	)	PUNCT
ejde-397	1218	53	with	with	ADP
ejde-397	1218	54	xj	xj	PROPN
ejde-397	1218	55	=	=	SYM
ejde-397	1218	56	0	0	NUM
ejde-397	1218	57	for	for	ADP
ejde-397	1218	58	1	1	NUM
ejde-397	1218	59	≤	≤	NUM
ejde-397	1218	60	j	j	PROPN
ejde-397	1218	61	≤	≤	PROPN
ejde-397	1218	62	dζe	dζe	ADV
ejde-397	1218	63	−	−	PROPN
ejde-397	1218	64	1	1	NUM
ejde-397	1218	65	,	,	PUNCT
ejde-397	1218	66	has	have	VERB
ejde-397	1218	67	an	an	DET
ejde-397	1218	68	exponentially	exponentially	ADV
ejde-397	1218	69	bounded	bound	VERB
ejde-397	1218	70	pre	pre	ADJ
ejde-397	1218	71	-	-	NOUN
ejde-397	1218	72	solution	solution	ADJ
ejde-397	1218	73	uh,0(t	uh,0(t	PROPN
ejde-397	1218	74	)	)	PUNCT
ejde-397	1218	75	=	=	SYM
ejde-397	1218	76	tη(t)x0	tη(t)x0	PROPN
ejde-397	1218	77	,	,	PUNCT
ejde-397	1218	78	t	t	PROPN
ejde-397	1218	79	≥	≥	NOUN
ejde-397	1218	80	0	0	NUM
ejde-397	1218	81	for	for	ADP
ejde-397	1218	82	any	any	DET
ejde-397	1218	83	xk	xk	PROPN
ejde-397	1218	84	∈	∈	PROPN
ejde-397	1218	85	d(a)∩x0	d(a)∩x0	PROPN
ejde-397	1218	86	(	(	PUNCT
ejde-397	1218	87	0	0	NUM
ejde-397	1218	88	≤	≤	NUM
ejde-397	1218	89	k	k	X
ejde-397	1218	90	≤	≤	NUM
ejde-397	1218	91	dηe−1	dηe−1	PROPN
ejde-397	1218	92	)	)	PUNCT
ejde-397	1218	93	,	,	PUNCT
ejde-397	1218	94	which	which	PRON
ejde-397	1218	95	seems	seem	VERB
ejde-397	1218	96	to	to	PART
ejde-397	1218	97	be	be	AUX
ejde-397	1218	98	an	an	DET
ejde-397	1218	99	optimal	optimal	ADJ
ejde-397	1218	100	result	result	NOUN
ejde-397	1218	101	in	in	ADP
ejde-397	1218	102	the	the	DET
ejde-397	1218	103	case	case	NOUN
ejde-397	1218	104	that	that	SCONJ
ejde-397	1218	105	η	η	PROPN
ejde-397	1218	106	≤	≤	PROPN
ejde-397	1218	107	1	1	NUM
ejde-397	1218	108	.	.	PUNCT
ejde-397	1219	1	concerning	concern	VERB
ejde-397	1219	2	the	the	DET
ejde-397	1219	3	homogeneous	homogeneous	ADJ
ejde-397	1219	4	counterpart	counterpart	NOUN
ejde-397	1219	5	of	of	ADP
ejde-397	1219	6	problem	problem	NOUN
ejde-397	1219	7	(	(	PUNCT
ejde-397	1219	8	5.25	5.25	NUM
ejde-397	1219	9	)	)	PUNCT
ejde-397	1219	10	with	with	ADP
ejde-397	1219	11	x0	x0	PROPN
ejde-397	1219	12	=	=	SYM
ejde-397	1219	13	0	0	PROPN
ejde-397	1219	14	,	,	PUNCT
ejde-397	1219	15	its	its	PRON
ejde-397	1219	16	solution	solution	NOUN
ejde-397	1219	17	uh,1(t	uh,1(t	PROPN
ejde-397	1219	18	)	)	PUNCT
ejde-397	1219	19	has	have	VERB
ejde-397	1219	20	to	to	PART
ejde-397	1219	21	be	be	AUX
ejde-397	1219	22	find	find	VERB
ejde-397	1219	23	in	in	ADP
ejde-397	1219	24	the	the	DET
ejde-397	1219	25	form	form	NOUN
ejde-397	1219	26	uh,1(t	uh,1(t	PROPN
ejde-397	1219	27	)	)	PUNCT
ejde-397	1220	1	=	=	SYM
ejde-397	1221	1	∫	∫	PROPN
ejde-397	1221	2	t	t	NOUN
ejde-397	1221	3	0	0	NUM
ejde-397	1221	4	tη(s)x1	tη(s)x1	NOUN
ejde-397	1221	5	ds	ds	PROPN
ejde-397	1221	6	,	,	PUNCT
ejde-397	1221	7	t	t	PROPN
ejde-397	1221	8	≥	≥	NUM
ejde-397	1221	9	0	0	NUM
ejde-397	1221	10	.	.	PUNCT
ejde-397	1222	1	consider	consider	VERB
ejde-397	1222	2	first	first	ADV
ejde-397	1222	3	the	the	DET
ejde-397	1222	4	case	case	NOUN
ejde-397	1222	5	η	η	PROPN
ejde-397	1222	6	∈	∈	PROPN
ejde-397	1222	7	(	(	PUNCT
ejde-397	1222	8	1	1	NUM
ejde-397	1222	9	,	,	PUNCT
ejde-397	1222	10	2	2	NUM
ejde-397	1222	11	)	)	PUNCT
ejde-397	1222	12	.	.	PUNCT
ejde-397	1223	1	then	then	ADV
ejde-397	1223	2	for	for	ADP
ejde-397	1223	3	each	each	DET
ejde-397	1223	4	k	k	PROPN
ejde-397	1223	5	∈	∈	PROPN
ejde-397	1223	6	n	n	INTJ
ejde-397	1223	7	with	with	ADP
ejde-397	1223	8	λk	λk	PROPN
ejde-397	1223	9	6=	6=	SYM
ejde-397	1223	10	λ	λ	PROPN
ejde-397	1223	11	,	,	PUNCT
ejde-397	1223	12	we	we	PRON
ejde-397	1223	13	have	have	VERB
ejde-397	1223	14	d2	d2	PROPN
ejde-397	1223	15	dt2	dt2	PROPN
ejde-397	1223	16	[	[	PUNCT
ejde-397	1223	17	g2−η	g2−η	PROPN
ejde-397	1223	18	∗	∗	NOUN
ejde-397	1223	19	(	(	PUNCT
ejde-397	1223	20	eη	eη	NOUN
ejde-397	1223	21	(	(	PUNCT
ejde-397	1223	22	αλk	αλk	PROPN
ejde-397	1223	23	−	−	NOUN
ejde-397	1223	24	βλ2	βλ2	VERB
ejde-397	1223	25	k	k	PROPN
ejde-397	1224	1	λ−	λ−	PROPN
ejde-397	1224	2	λk	λk	PROPN
ejde-397	1224	3	·	·	SYM
ejde-397	1224	4	η	η	PROPN
ejde-397	1224	5	)	)	PUNCT
ejde-397	1225	1	−	−	PROPN
ejde-397	1225	2	1	1	NUM
ejde-397	1225	3	)	)	PUNCT
ejde-397	1225	4	]	]	PUNCT
ejde-397	1225	5	(	(	PUNCT
ejde-397	1225	6	t	t	NOUN
ejde-397	1225	7	)	)	PUNCT
ejde-397	1225	8	=	=	PUNCT
ejde-397	1226	1	dη	dη	PRON
ejde-397	1226	2	teη	teη	NOUN
ejde-397	1226	3	(	(	PUNCT
ejde-397	1226	4	αλk	αλk	NUM
ejde-397	1226	5	−	−	NOUN
ejde-397	1226	6	βλ2	βλ2	VERB
ejde-397	1226	7	k	k	PROPN
ejde-397	1227	1	λ−	λ−	PROPN
ejde-397	1227	2	λk	λk	X
ejde-397	1227	3	tη	tη	PROPN
ejde-397	1227	4	)	)	PUNCT
ejde-397	1228	1	=	=	PUNCT
ejde-397	1228	2	αλk	αλk	NUM
ejde-397	1228	3	−	−	NOUN
ejde-397	1228	4	βλ2	βλ2	VERB
ejde-397	1228	5	k	k	PROPN
ejde-397	1229	1	λ−	λ−	PROPN
ejde-397	1229	2	λk	λk	INTJ
ejde-397	1229	3	eη	eη	NOUN
ejde-397	1229	4	(	(	PUNCT
ejde-397	1229	5	αλk	αλk	PROPN
ejde-397	1229	6	−	−	NOUN
ejde-397	1229	7	βλ2	βλ2	VERB
ejde-397	1229	8	k	k	PROPN
ejde-397	1230	1	λ−	λ−	PROPN
ejde-397	1230	2	λk	λk	X
ejde-397	1230	3	tη	tη	PROPN
ejde-397	1230	4	)	)	PUNCT
ejde-397	1230	5	,	,	PUNCT
ejde-397	1230	6	t	t	PROPN
ejde-397	1230	7	≥	≥	NUM
ejde-397	1230	8	0	0	NUM
ejde-397	1230	9	.	.	PUNCT
ejde-397	1231	1	on	on	ADP
ejde-397	1231	2	the	the	DET
ejde-397	1231	3	other	other	ADJ
ejde-397	1231	4	hand	hand	NOUN
ejde-397	1231	5	,	,	PUNCT
ejde-397	1231	6	expanding	expand	VERB
ejde-397	1231	7	the	the	DET
ejde-397	1231	8	function	function	NOUN
ejde-397	1231	9	eη	eη	NOUN
ejde-397	1231	10	(	(	PUNCT
ejde-397	1231	11	αλk−βλ2	αλk−βλ2	PROPN
ejde-397	1231	12	k	k	X
ejde-397	1231	13	λ−λk	λ−λk	AUX
ejde-397	1231	14	·	·	PUNCT
ejde-397	1231	15	η)−	η)−	ADP
ejde-397	1231	16	1	1	NUM
ejde-397	1231	17	in	in	ADP
ejde-397	1231	18	a	a	DET
ejde-397	1231	19	power	power	NOUN
ejde-397	1231	20	series	series	NOUN
ejde-397	1231	21	we	we	PRON
ejde-397	1231	22	obtain	obtain	VERB
ejde-397	1231	23	that	that	PRON
ejde-397	1231	24	d	d	NOUN
ejde-397	1231	25	dt	dt	X
ejde-397	1231	26	[	[	PUNCT
ejde-397	1231	27	g2−η	g2−η	PROPN
ejde-397	1231	28	∗	∗	NOUN
ejde-397	1231	29	(	(	PUNCT
ejde-397	1231	30	eη	eη	NOUN
ejde-397	1231	31	(	(	PUNCT
ejde-397	1231	32	αλk	αλk	PROPN
ejde-397	1231	33	−	−	NOUN
ejde-397	1231	34	βλ2	βλ2	VERB
ejde-397	1231	35	k	k	PROPN
ejde-397	1231	36	λ−	λ−	PROPN
ejde-397	1231	37	λk	λk	PROPN
ejde-397	1231	38	·	·	SYM
ejde-397	1231	39	η	η	PROPN
ejde-397	1231	40	)	)	PUNCT
ejde-397	1231	41	−	−	PROPN
ejde-397	1231	42	1	1	NUM
ejde-397	1231	43	)	)	PUNCT
ejde-397	1231	44	]	]	PUNCT
ejde-397	1231	45	(	(	PUNCT
ejde-397	1231	46	t	t	NOUN
ejde-397	1231	47	)	)	PUNCT
ejde-397	1231	48	=	=	PUNCT
ejde-397	1231	49	t	t	PROPN
ejde-397	1231	50	∞∑	∞∑	PROPN
ejde-397	1231	51	n=0	n=0	PUNCT
ejde-397	1231	52	(	(	PUNCT
ejde-397	1231	53	αλk−βλ2	αλk−βλ2	PROPN
ejde-397	1231	54	k	k	PROPN
ejde-397	1231	55	λ−λk	λ−λk	VERB
ejde-397	1231	56	tη	tη	NOUN
ejde-397	1231	57	)	)	PUNCT
ejde-397	1232	1	n+1	n+1	PROPN
ejde-397	1232	2	tnη	tnη	NOUN
ejde-397	1232	3	γ(nη	γ(nη	VERB
ejde-397	1232	4	+	+	CCONJ
ejde-397	1232	5	2	2	NUM
ejde-397	1232	6	)	)	PUNCT
ejde-397	1232	7	,	,	PUNCT
ejde-397	1232	8	t	t	PROPN
ejde-397	1232	9	≥	≥	NUM
ejde-397	1232	10	0	0	NUM
ejde-397	1232	11	.	.	PUNCT
ejde-397	1233	1	the	the	DET
ejde-397	1233	2	previous	previous	ADJ
ejde-397	1233	3	two	two	NUM
ejde-397	1233	4	equalities	equality	NOUN
ejde-397	1233	5	together	together	ADV
ejde-397	1233	6	imply	imply	VERB
ejde-397	1233	7	that	that	PRON
ejde-397	1233	8	d	d	NOUN
ejde-397	1233	9	dt	dt	X
ejde-397	1234	1	[	[	PUNCT
ejde-397	1234	2	g2−η	g2−η	PROPN
ejde-397	1234	3	∗(eη	∗(eη	PROPN
ejde-397	1234	4	(	(	PUNCT
ejde-397	1234	5	αλk−βλ2	αλk−βλ2	PROPN
ejde-397	1234	6	k	k	X
ejde-397	1234	7	λ−λk	λ−λk	PROPN
ejde-397	1234	8	·	·	PUNCT
ejde-397	1234	9	η)−1)](t	η)−1)](t	INTJ
ejde-397	1234	10	)	)	PUNCT
ejde-397	1234	11	=	=	PUNCT
ejde-397	1235	1	αλk−βλ2	αλk−βλ2	NUM
ejde-397	1235	2	k	k	PROPN
ejde-397	1235	3	λ−λk	λ−λk	PROPN
ejde-397	1235	4	∫	∫	PROPN
ejde-397	1235	5	t	t	PROPN
ejde-397	1235	6	0	0	NUM
ejde-397	1235	7	eη	eη	PROPN
ejde-397	1235	8	(	(	PUNCT
ejde-397	1235	9	αλk−βλ2	αλk−βλ2	PROPN
ejde-397	1235	10	k	k	PROPN
ejde-397	1235	11	λ−λk	λ−λk	PROPN
ejde-397	1235	12	sη	sη	NOUN
ejde-397	1235	13	)	)	PUNCT
ejde-397	1235	14	ds	ds	PROPN
ejde-397	1235	15	,	,	PUNCT
ejde-397	1235	16	t	t	PROPN
ejde-397	1235	17	≥	≥	NOUN
ejde-397	1235	18	0	0	NUM
ejde-397	1236	1	and	and	CCONJ
ejde-397	1236	2	dη	dη	ADP
ejde-397	1236	3	t	t	PROPN
ejde-397	1236	4	[	[	PUNCT
ejde-397	1236	5	g1	g1	PROPN
ejde-397	1236	6	∗	∗	NOUN
ejde-397	1236	7	tη(·)x1	tη(·)x1	NOUN
ejde-397	1236	8	]	]	PUNCT
ejde-397	1236	9	(	(	PUNCT
ejde-397	1236	10	t	t	NOUN
ejde-397	1236	11	)	)	PUNCT
ejde-397	1236	12	=	=	PUNCT
ejde-397	1237	1	∑	∑	PUNCT
ejde-397	1237	2	k|λk	k|λk	PROPN
ejde-397	1237	3	6	6	NUM
ejde-397	1237	4	=	=	SYM
ejde-397	1237	5	λ	λ	X
ejde-397	1237	6	αλk	αλk	NUM
ejde-397	1237	7	−	−	NOUN
ejde-397	1237	8	βλ2	βλ2	PROPN
ejde-397	1237	9	k	k	PROPN
ejde-397	1237	10	λ−	λ−	PROPN
ejde-397	1238	1	λk	λk	ADV
ejde-397	1238	2	∫	∫	PROPN
ejde-397	1238	3	t	t	PROPN
ejde-397	1238	4	0	0	NUM
ejde-397	1238	5	eη	eη	NOUN
ejde-397	1238	6	(	(	PUNCT
ejde-397	1238	7	αλk	αλk	PROPN
ejde-397	1238	8	−	−	NOUN
ejde-397	1238	9	βλ2	βλ2	VERB
ejde-397	1238	10	k	k	PROPN
ejde-397	1239	1	λ−	λ−	PROPN
ejde-397	1239	2	λk	λk	INTJ
ejde-397	1239	3	sη	sη	NOUN
ejde-397	1239	4	)	)	PUNCT
ejde-397	1239	5	ds	ds	PROPN
ejde-397	1239	6	〈	〈	PROPN
ejde-397	1239	7	x1	x1	PROPN
ejde-397	1239	8	,	,	PUNCT
ejde-397	1239	9	φk	φk	ADP
ejde-397	1239	10	〉	〉	NOUN
ejde-397	1239	11	φk	φk	ADP
ejde-397	1239	12	=	=	PUNCT
ejde-397	1239	13	∑	∑	PROPN
ejde-397	1239	14	k|λk	k|λk	PROPN
ejde-397	1239	15	6	6	NUM
ejde-397	1239	16	=	=	SYM
ejde-397	1239	17	λ	λ	X
ejde-397	1239	18	αλk	αλk	NUM
ejde-397	1239	19	−	−	NOUN
ejde-397	1239	20	βλ2	βλ2	VERB
ejde-397	1239	21	k	k	PROPN
ejde-397	1240	1	λ−	λ−	PROPN
ejde-397	1240	2	λk	λk	PROPN
ejde-397	1240	3	teη,2	teη,2	NOUN
ejde-397	1240	4	(	(	PUNCT
ejde-397	1240	5	αλk	αλk	PROPN
ejde-397	1240	6	−	−	NOUN
ejde-397	1240	7	βλ2	βλ2	VERB
ejde-397	1240	8	k	k	PROPN
ejde-397	1241	1	λ−	λ−	PROPN
ejde-397	1241	2	λk	λk	X
ejde-397	1241	3	tη	tη	PROPN
ejde-397	1241	4	)	)	PUNCT
ejde-397	1241	5	〈	〈	PROPN
ejde-397	1241	6	x1	x1	PROPN
ejde-397	1241	7	,	,	PUNCT
ejde-397	1241	8	φk	φk	ADP
ejde-397	1241	9	〉	〉	NOUN
ejde-397	1241	10	φk	φk	ADP
ejde-397	1241	11	,	,	PUNCT
ejde-397	1241	12	t	t	PROPN
ejde-397	1241	13	≥	≥	NUM
ejde-397	1241	14	0	0	NUM
ejde-397	1241	15	.	.	PUNCT
ejde-397	1242	1	using	use	VERB
ejde-397	1242	2	again	again	ADV
ejde-397	1242	3	the	the	DET
ejde-397	1242	4	asymptotic	asymptotic	ADJ
ejde-397	1242	5	expansion	expansion	NOUN
ejde-397	1242	6	formula	formula	NOUN
ejde-397	1242	7	[	[	X
ejde-397	1242	8	5	5	NUM
ejde-397	1242	9	,	,	PUNCT
ejde-397	1242	10	(	(	PUNCT
ejde-397	1242	11	1.28	1.28	NUM
ejde-397	1242	12	)	)	PUNCT
ejde-397	1242	13	]	]	PUNCT
ejde-397	1242	14	,	,	PUNCT
ejde-397	1242	15	we	we	PRON
ejde-397	1242	16	obtain	obtain	VERB
ejde-397	1242	17	that	that	SCONJ
ejde-397	1242	18	the	the	DET
ejde-397	1242	19	above	above	ADJ
ejde-397	1242	20	series	series	NOUN
ejde-397	1242	21	converges	converge	VERB
ejde-397	1242	22	for	for	ADP
ejde-397	1242	23	any	any	DET
ejde-397	1242	24	x1	x1	PROPN
ejde-397	1242	25	∈	∈	PROPN
ejde-397	1242	26	x0	x0	PROPN
ejde-397	1242	27	and	and	CCONJ
ejde-397	1242	28	belongs	belong	VERB
ejde-397	1242	29	to	to	ADP
ejde-397	1242	30	d(b	d(b	PROPN
ejde-397	1242	31	)	)	PUNCT
ejde-397	1242	32	provided	provide	VERB
ejde-397	1242	33	,	,	PUNCT
ejde-397	1242	34	in	in	ADP
ejde-397	1242	35	addition	addition	NOUN
ejde-397	1242	36	,	,	PUNCT
ejde-397	1242	37	that	that	SCONJ
ejde-397	1242	38	x1	x1	PROPN
ejde-397	1242	39	∈	∈	PROPN
ejde-397	1242	40	d(b	d(b	PROPN
ejde-397	1242	41	)	)	PUNCT
ejde-397	1242	42	∩	∩	NOUN
ejde-397	1242	43	x0	x0	PROPN
ejde-397	1242	44	.	.	PUNCT
ejde-397	1243	1	in	in	ADP
ejde-397	1243	2	this	this	DET
ejde-397	1243	3	case	case	NOUN
ejde-397	1243	4	,	,	PUNCT
ejde-397	1243	5	the	the	DET
ejde-397	1243	6	equality	equality	NOUN
ejde-397	1243	7	bdη	bdη	PROPN
ejde-397	1243	8	t	t	PROPN
ejde-397	1243	9	uh,1(t	uh,1(t	PROPN
ejde-397	1243	10	)	)	PUNCT
ejde-397	1243	11	=	=	SYM
ejde-397	1243	12	auh,1(t	auh,1(t	NUM
ejde-397	1243	13	)	)	PUNCT
ejde-397	1243	14	,	,	PUNCT
ejde-397	1243	15	t	t	PROPN
ejde-397	1243	16	≥	≥	NOUN
ejde-397	1243	17	0	0	NUM
ejde-397	1243	18	readily	readily	ADV
ejde-397	1243	19	follows	follow	VERB
ejde-397	1243	20	,	,	PUNCT
ejde-397	1243	21	so	so	SCONJ
ejde-397	1243	22	that	that	SCONJ
ejde-397	1243	23	the	the	DET
ejde-397	1243	24	function	function	NOUN
ejde-397	1243	25	uh(t	uh(t	PUNCT
ejde-397	1243	26	)	)	PUNCT
ejde-397	1243	27	:	:	PUNCT
ejde-397	1243	28	=	=	SYM
ejde-397	1243	29	uh,0(t	uh,0(t	PROPN
ejde-397	1243	30	)	)	PUNCT
ejde-397	1243	31	+	+	SYM
ejde-397	1243	32	uh,1(t	uh,1(t	PROPN
ejde-397	1243	33	)	)	PUNCT
ejde-397	1243	34	,	,	PUNCT
ejde-397	1243	35	t	t	PROPN
ejde-397	1243	36	≥	≥	PROPN
ejde-397	1243	37	0	0	NUM
ejde-397	1243	38	is	be	AUX
ejde-397	1243	39	a	a	DET
ejde-397	1243	40	pre	pre	NOUN
ejde-397	1243	41	-	-	NOUN
ejde-397	1243	42	solution	solution	NOUN
ejde-397	1243	43	of	of	ADP
ejde-397	1243	44	problem	problem	NOUN
ejde-397	1243	45	(	(	PUNCT
ejde-397	1243	46	1.3	1.3	NUM
ejde-397	1243	47	)	)	PUNCT
ejde-397	1243	48	provided	provide	VERB
ejde-397	1243	49	that	that	SCONJ
ejde-397	1243	50	x0	x0	PROPN
ejde-397	1243	51	∈	∈	PROPN
ejde-397	1243	52	d(a	d(a	PROPN
ejde-397	1243	53	)	)	PUNCT
ejde-397	1243	54	∩x0	∩x0	PROPN
ejde-397	1243	55	and	and	CCONJ
ejde-397	1243	56	x1	x1	PROPN
ejde-397	1243	57	∈	∈	PROPN
ejde-397	1243	58	d(b	d(b	PROPN
ejde-397	1243	59	)	)	PUNCT
ejde-397	1243	60	∩x0	∩x0	NOUN
ejde-397	1243	61	(	(	PUNCT
ejde-397	1243	62	with	with	ADP
ejde-397	1243	63	x	x	X
ejde-397	1243	64	=	=	PUNCT
ejde-397	1243	65	y	y	PROPN
ejde-397	1243	66	=	=	SYM
ejde-397	1243	67	l2(ω	l2(ω	PROPN
ejde-397	1243	68	)	)	PUNCT
ejde-397	1243	69	in	in	ADP
ejde-397	1243	70	definition	definition	NOUN
ejde-397	1243	71	4.1(iii	4.1(iii	NUM
ejde-397	1243	72	)	)	PUNCT
ejde-397	1243	73	)	)	PUNCT
ejde-397	1243	74	;	;	PUNCT
ejde-397	1243	75	furthermore	furthermore	ADV
ejde-397	1243	76	,	,	PUNCT
ejde-397	1243	77	the	the	DET
ejde-397	1243	78	mappings	mapping	NOUN
ejde-397	1243	79	t	t	X
ejde-397	1243	80	7→	7→	NUM
ejde-397	1243	81	uh(t	uh(t	PART
ejde-397	1243	82	)	)	PUNCT
ejde-397	1243	83	∈	∈	PROPN
ejde-397	1243	84	l2(ω	l2(ω	PROPN
ejde-397	1243	85	)	)	PUNCT
ejde-397	1243	86	,	,	PUNCT
ejde-397	1243	87	t	t	PROPN
ejde-397	1243	88	>	>	X
ejde-397	1243	89	0	0	PUNCT
ejde-397	1243	90	and	and	CCONJ
ejde-397	1243	91	t	t	PROPN
ejde-397	1243	92	7→	7→	PROPN
ejde-397	1243	93	buh(t	buh(t	PROPN
ejde-397	1243	94	)	)	PUNCT
ejde-397	1243	95	∈	∈	PROPN
ejde-397	1243	96	l2(ω	l2(ω	PROPN
ejde-397	1243	97	)	)	PUNCT
ejde-397	1243	98	,	,	PUNCT
ejde-397	1243	99	t	t	PROPN
ejde-397	1243	100	>	>	X
ejde-397	1243	101	0	0	NUM
ejde-397	1243	102	can	can	AUX
ejde-397	1243	103	be	be	AUX
ejde-397	1243	104	analytically	analytically	ADV
ejde-397	1243	105	extended	extend	VERB
ejde-397	1243	106	to	to	ADP
ejde-397	1243	107	the	the	DET
ejde-397	1243	108	sector	sector	NOUN
ejde-397	1243	109	σθ	σθ	PROPN
ejde-397	1243	110	.	.	PUNCT
ejde-397	1244	1	the	the	DET
ejde-397	1244	2	40	40	NUM
ejde-397	1244	3	m.	m.	NOUN
ejde-397	1244	4	kostić	kostić	NOUN
ejde-397	1244	5	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1244	6	situation	situation	NOUN
ejde-397	1244	7	is	be	AUX
ejde-397	1244	8	slightly	slightly	ADV
ejde-397	1244	9	different	different	ADJ
ejde-397	1244	10	in	in	ADP
ejde-397	1244	11	the	the	DET
ejde-397	1244	12	case	case	NOUN
ejde-397	1244	13	that	that	SCONJ
ejde-397	1244	14	η	η	PROPN
ejde-397	1244	15	=	=	PROPN
ejde-397	1244	16	2	2	NUM
ejde-397	1244	17	since	since	SCONJ
ejde-397	1244	18	we	we	PRON
ejde-397	1244	19	can	can	AUX
ejde-397	1244	20	not	not	PART
ejde-397	1244	21	use	use	VERB
ejde-397	1244	22	the	the	DET
ejde-397	1244	23	formula	formula	NOUN
ejde-397	1244	24	[	[	X
ejde-397	1244	25	5	5	NUM
ejde-397	1244	26	,	,	PUNCT
ejde-397	1244	27	(	(	PUNCT
ejde-397	1244	28	1.28	1.28	NUM
ejde-397	1244	29	)	)	PUNCT
ejde-397	1244	30	]	]	PUNCT
ejde-397	1244	31	;	;	PUNCT
ejde-397	1244	32	then	then	ADV
ejde-397	1244	33	a	a	DET
ejde-397	1244	34	simple	simple	ADJ
ejde-397	1244	35	computation	computation	NOUN
ejde-397	1244	36	shows	show	VERB
ejde-397	1244	37	that	that	SCONJ
ejde-397	1244	38	,	,	PUNCT
ejde-397	1244	39	formally	formally	ADV
ejde-397	1244	40	,	,	PUNCT
ejde-397	1244	41	for	for	ADP
ejde-397	1244	42	every	every	DET
ejde-397	1244	43	t	t	PROPN
ejde-397	1244	44	≥	≥	NOUN
ejde-397	1244	45	0	0	NUM
ejde-397	1244	46	,	,	PUNCT
ejde-397	1244	47	bu′′h,1(t	bu′′h,1(t	NUM
ejde-397	1244	48	)	)	PUNCT
ejde-397	1244	49	=	=	SYM
ejde-397	1244	50	auh,1(t	auh,1(t	X
ejde-397	1244	51	)	)	PUNCT
ejde-397	1244	52	=	=	SYM
ejde-397	1245	1	1	1	NUM
ejde-397	1245	2	2	2	NUM
ejde-397	1245	3	∑	∑	NUM
ejde-397	1245	4	k|λk	k|λk	PROPN
ejde-397	1245	5	6	6	NUM
ejde-397	1245	6	=	=	SYM
ejde-397	1245	7	λ	λ	X
ejde-397	1245	8	[	[	PUNCT
ejde-397	1245	9	i	i	PRON
ejde-397	1245	10	(	(	PUNCT
ejde-397	1245	11	(	(	PUNCT
ejde-397	1245	12	βλ2	βλ2	NOUN
ejde-397	1245	13	−	−	NOUN
ejde-397	1245	14	αλk)/(λ−	αλk)/(λ−	PUNCT
ejde-397	1245	15	λk	λk	NOUN
ejde-397	1245	16	)	)	PUNCT
ejde-397	1245	17	)	)	PUNCT
ejde-397	1245	18	1/2	1/2	NUM
ejde-397	1245	19	eit((βλ	eit((βλ	NOUN
ejde-397	1246	1	2−αλk)/(λ−λk))1/2	2−αλk)/(λ−λk))1/2	NUM
ejde-397	1246	2	−	−	NOUN
ejde-397	1247	1	i	i	PRON
ejde-397	1247	2	(	(	PUNCT
ejde-397	1247	3	(	(	PUNCT
ejde-397	1247	4	βλ2	βλ2	NOUN
ejde-397	1247	5	−	−	NOUN
ejde-397	1247	6	αλk)/(λ−	αλk)/(λ−	PUNCT
ejde-397	1247	7	λk	λk	NOUN
ejde-397	1247	8	)	)	PUNCT
ejde-397	1247	9	)	)	PUNCT
ejde-397	1247	10	1/2	1/2	NUM
ejde-397	1247	11	e−it((βλ	e−it((βλ	NOUN
ejde-397	1247	12	2−αλk)/(λ−λk))1/2	2−αλk)/(λ−λk))1/2	NUM
ejde-397	1247	13	]	]	PUNCT
ejde-397	1247	14	〈	〈	PROPN
ejde-397	1247	15	x1	x1	PROPN
ejde-397	1247	16	,	,	PUNCT
ejde-397	1247	17	φk〉φk	φk〉φk	PROPN
ejde-397	1247	18	.	.	PUNCT
ejde-397	1248	1	hence	hence	ADV
ejde-397	1248	2	,	,	PUNCT
ejde-397	1248	3	the	the	DET
ejde-397	1248	4	function	function	NOUN
ejde-397	1248	5	uh(t	uh(t	PUNCT
ejde-397	1248	6	)	)	PUNCT
ejde-397	1248	7	:	:	PUNCT
ejde-397	1248	8	=	=	SYM
ejde-397	1248	9	uh,0(t)+uh,1(t	uh,0(t)+uh,1(t	ADJ
ejde-397	1248	10	)	)	PUNCT
ejde-397	1248	11	,	,	PUNCT
ejde-397	1248	12	t	t	PROPN
ejde-397	1248	13	≥	≥	PROPN
ejde-397	1248	14	0	0	NUM
ejde-397	1248	15	is	be	AUX
ejde-397	1248	16	a	a	DET
ejde-397	1248	17	pre	pre	NOUN
ejde-397	1248	18	-	-	NOUN
ejde-397	1248	19	solution	solution	NOUN
ejde-397	1248	20	of	of	ADP
ejde-397	1248	21	problem	problem	NOUN
ejde-397	1248	22	(	(	PUNCT
ejde-397	1248	23	1.3	1.3	NUM
ejde-397	1248	24	)	)	PUNCT
ejde-397	1248	25	with	with	ADP
ejde-397	1248	26	x0	x0	PROPN
ejde-397	1248	27	∈	∈	PROPN
ejde-397	1248	28	d(a	d(a	PROPN
ejde-397	1248	29	)	)	PUNCT
ejde-397	1248	30	∩	∩	NOUN
ejde-397	1248	31	x0	x0	PROPN
ejde-397	1248	32	and	and	CCONJ
ejde-397	1248	33	x1	x1	PROPN
ejde-397	1248	34	∈	∈	PROPN
ejde-397	1248	35	d((−∆)3/2	d((−∆)3/2	ADJ
ejde-397	1248	36	)	)	PUNCT
ejde-397	1248	37	∩	∩	NOUN
ejde-397	1248	38	x0	x0	PROPN
ejde-397	1248	39	.	.	PUNCT
ejde-397	1249	1	the	the	DET
ejde-397	1249	2	range	range	NOUN
ejde-397	1249	3	of	of	ADP
ejde-397	1249	4	any	any	DET
ejde-397	1249	5	pre	pre	NOUN
ejde-397	1249	6	-	-	NOUN
ejde-397	1249	7	solution	solution	NOUN
ejde-397	1249	8	of	of	ADP
ejde-397	1249	9	problem	problem	NOUN
ejde-397	1249	10	(	(	PUNCT
ejde-397	1249	11	5.25	5.25	NUM
ejde-397	1249	12	)	)	PUNCT
ejde-397	1249	13	with	with	ADP
ejde-397	1249	14	f	f	PROPN
ejde-397	1249	15	=	=	SYM
ejde-397	1249	16	0	0	PROPN
ejde-397	1249	17	must	must	AUX
ejde-397	1249	18	be	be	AUX
ejde-397	1249	19	contained	contain	VERB
ejde-397	1249	20	in	in	ADP
ejde-397	1249	21	x0	x0	PROPN
ejde-397	1249	22	,	,	PUNCT
ejde-397	1249	23	so	so	SCONJ
ejde-397	1249	24	that	that	SCONJ
ejde-397	1249	25	the	the	DET
ejde-397	1249	26	uniqueness	uniqueness	NOUN
ejde-397	1249	27	of	of	ADP
ejde-397	1249	28	solutions	solution	NOUN
ejde-397	1249	29	of	of	ADP
ejde-397	1249	30	problem	problem	NOUN
ejde-397	1249	31	(	(	PUNCT
ejde-397	1249	32	5.25	5.25	NUM
ejde-397	1249	33	)	)	PUNCT
ejde-397	1249	34	follows	follow	VERB
ejde-397	1249	35	from	from	ADP
ejde-397	1249	36	its	its	PRON
ejde-397	1249	37	linearity	linearity	NOUN
ejde-397	1249	38	and	and	CCONJ
ejde-397	1249	39	proposition	proposition	NOUN
ejde-397	1249	40	5.8(ii	5.8(ii	NUM
ejde-397	1249	41	)	)	PUNCT
ejde-397	1249	42	.	.	PUNCT
ejde-397	1250	1	before	before	ADP
ejde-397	1250	2	considering	consider	VERB
ejde-397	1250	3	the	the	DET
ejde-397	1250	4	inhomogeneous	inhomogeneous	ADJ
ejde-397	1250	5	problem	problem	NOUN
ejde-397	1250	6	(	(	PUNCT
ejde-397	1250	7	5.25	5.25	NUM
ejde-397	1250	8	)	)	PUNCT
ejde-397	1250	9	,	,	PUNCT
ejde-397	1250	10	we	we	PRON
ejde-397	1250	11	would	would	AUX
ejde-397	1250	12	like	like	VERB
ejde-397	1250	13	to	to	PART
ejde-397	1250	14	observe	observe	VERB
ejde-397	1250	15	that	that	SCONJ
ejde-397	1250	16	the	the	DET
ejde-397	1250	17	assumptions	assumption	NOUN
ejde-397	1250	18	(	(	PUNCT
ejde-397	1250	19	x	x	NOUN
ejde-397	1250	20	,	,	PUNCT
ejde-397	1250	21	y	y	PROPN
ejde-397	1250	22	)	)	PUNCT
ejde-397	1250	23	∈	∈	PROPN
ejde-397	1250	24	a	a	PRON
ejde-397	1250	25	and	and	CCONJ
ejde-397	1250	26	x	x	PROPN
ejde-397	1250	27	∈	∈	PROPN
ejde-397	1250	28	d(a	d(a	PROPN
ejde-397	1250	29	)	)	PUNCT
ejde-397	1250	30	imply	imply	INTJ
ejde-397	1250	31	(	(	PUNCT
ejde-397	1250	32	x	x	NOUN
ejde-397	1250	33	,	,	PUNCT
ejde-397	1250	34	y	y	NOUN
ejde-397	1250	35	)	)	PUNCT
ejde-397	1250	36	∈	∈	PROPN
ejde-397	1250	37	b−1a|x0	b−1a|x0	NOUN
ejde-397	1250	38	.	.	PUNCT
ejde-397	1251	1	keeping	keep	VERB
ejde-397	1251	2	in	in	ADP
ejde-397	1251	3	mind	mind	NOUN
ejde-397	1251	4	this	this	DET
ejde-397	1251	5	remark	remark	NOUN
ejde-397	1251	6	,	,	PUNCT
ejde-397	1251	7	theorem	theorem	VERB
ejde-397	1251	8	2.3	2.3	NUM
ejde-397	1251	9	,	,	PUNCT
ejde-397	1251	10	as	as	ADV
ejde-397	1251	11	well	well	ADV
ejde-397	1251	12	as	as	ADP
ejde-397	1251	13	the	the	DET
ejde-397	1251	14	fact	fact	NOUN
ejde-397	1251	15	that	that	SCONJ
ejde-397	1251	16	the	the	DET
ejde-397	1251	17	assertion	assertion	NOUN
ejde-397	1251	18	of	of	ADP
ejde-397	1251	19	[	[	X
ejde-397	1251	20	68	68	NUM
ejde-397	1251	21	,	,	PUNCT
ejde-397	1251	22	proposition	proposition	NOUN
ejde-397	1251	23	2.1(iii	2.1(iii	NUM
ejde-397	1251	24	)	)	PUNCT
ejde-397	1251	25	]	]	PUNCT
ejde-397	1251	26	admits	admit	VERB
ejde-397	1251	27	a	a	DET
ejde-397	1251	28	reformulation	reformulation	NOUN
ejde-397	1251	29	in	in	ADP
ejde-397	1251	30	our	our	PRON
ejde-397	1251	31	framework	framework	NOUN
ejde-397	1251	32	,	,	PUNCT
ejde-397	1251	33	we	we	PRON
ejde-397	1251	34	can	can	AUX
ejde-397	1251	35	simply	simply	ADV
ejde-397	1251	36	prove	prove	VERB
ejde-397	1251	37	that	that	SCONJ
ejde-397	1251	38	for	for	ADP
ejde-397	1251	39	any	any	DET
ejde-397	1251	40	function	function	NOUN
ejde-397	1251	41	h	h	NOUN
ejde-397	1251	42	∈w	∈w	VERB
ejde-397	1251	43	1,1	1,1	NUM
ejde-397	1251	44	loc	loc	NOUN
ejde-397	1251	45	(	(	PUNCT
ejde-397	1251	46	[	[	X
ejde-397	1251	47	0,∞	0,∞	NOUN
ejde-397	1251	48	)	)	PUNCT
ejde-397	1251	49	:	:	PUNCT
ejde-397	1252	1	x0	x0	PROPN
ejde-397	1252	2	)	)	PUNCT
ejde-397	1252	3	satisfying	satisfy	VERB
ejde-397	1252	4	that	that	SCONJ
ejde-397	1252	5	t	t	PROPN
ejde-397	1252	6	7→	7→	NUM
ejde-397	1252	7	∑	∑	PROPN
ejde-397	1252	8	k|λk	k|λk	PROPN
ejde-397	1252	9	6	6	NUM
ejde-397	1252	10	=	=	SYM
ejde-397	1252	11	λ	λ	X
ejde-397	1252	12	(	(	PUNCT
ejde-397	1252	13	αλk	αλk	NUM
ejde-397	1252	14	−	−	PROPN
ejde-397	1252	15	βλ2	βλ2	X
ejde-397	1252	16	k	k	X
ejde-397	1252	17	)	)	PUNCT
ejde-397	1252	18	〈	〈	PROPN
ejde-397	1253	1	d	d	NOUN
ejde-397	1253	2	dt	dt	X
ejde-397	1253	3	(	(	PUNCT
ejde-397	1253	4	gη	gη	NOUN
ejde-397	1253	5	∗	∗	NOUN
ejde-397	1253	6	h)(t	h)(t	NOUN
ejde-397	1253	7	)	)	PUNCT
ejde-397	1253	8	,	,	PUNCT
ejde-397	1253	9	φk	φk	ADP
ejde-397	1253	10	〉	〉	NOUN
ejde-397	1253	11	φk	φk	ADP
ejde-397	1253	12	∈	∈	PROPN
ejde-397	1253	13	l1	l1	PROPN
ejde-397	1253	14	loc([0,∞	loc([0,∞	PROPN
ejde-397	1253	15	)	)	PUNCT
ejde-397	1253	16	:	:	PUNCT
ejde-397	1254	1	x0	x0	PROPN
ejde-397	1254	2	)	)	PUNCT
ejde-397	1254	3	,	,	PUNCT
ejde-397	1254	4	(	(	PUNCT
ejde-397	1254	5	5.26	5.26	NUM
ejde-397	1254	6	)	)	PUNCT
ejde-397	1254	7	the	the	DET
ejde-397	1254	8	function	function	NOUN
ejde-397	1254	9	ubh(t	ubh(t	PROPN
ejde-397	1254	10	)	)	PUNCT
ejde-397	1254	11	:	:	PUNCT
ejde-397	1255	1	=	=	SYM
ejde-397	1255	2	∫	∫	PROPN
ejde-397	1255	3	t	t	PROPN
ejde-397	1255	4	0	0	NUM
ejde-397	1255	5	tη(t	tη(t	PUNCT
ejde-397	1255	6	−	−	PROPN
ejde-397	1255	7	s	s	NOUN
ejde-397	1255	8	)	)	PUNCT
ejde-397	1255	9	dds	dds	PROPN
ejde-397	1255	10	(	(	PUNCT
ejde-397	1255	11	gη	gη	NOUN
ejde-397	1255	12	∗	∗	NOUN
ejde-397	1255	13	h	h	NOUN
ejde-397	1255	14	)	)	PUNCT
ejde-397	1255	15	ds	ds	PROPN
ejde-397	1255	16	,	,	PUNCT
ejde-397	1255	17	t	t	PROPN
ejde-397	1255	18	≥	≥	NOUN
ejde-397	1255	19	0	0	NUM
ejde-397	1255	20	is	be	AUX
ejde-397	1255	21	a	a	DET
ejde-397	1255	22	solution	solution	NOUN
ejde-397	1255	23	of	of	ADP
ejde-397	1255	24	problem	problem	NOUN
ejde-397	1255	25	(	(	PUNCT
ejde-397	1255	26	5.25	5.25	NUM
ejde-397	1255	27	)	)	PUNCT
ejde-397	1255	28	with	with	ADP
ejde-397	1255	29	f	f	PROPN
ejde-397	1255	30	=	=	SYM
ejde-397	1255	31	bh	bh	PROPN
ejde-397	1255	32	.	.	PROPN
ejde-397	1256	1	on	on	ADP
ejde-397	1256	2	the	the	DET
ejde-397	1256	3	other	other	ADJ
ejde-397	1256	4	hand	hand	NOUN
ejde-397	1256	5	,	,	PUNCT
ejde-397	1256	6	the	the	DET
ejde-397	1256	7	operator	operator	NOUN
ejde-397	1256	8	b	b	NOUN
ejde-397	1256	9	annihilates	annihilate	VERB
ejde-397	1256	10	any	any	DET
ejde-397	1256	11	function	function	NOUN
ejde-397	1256	12	from	from	ADP
ejde-397	1256	13	span{φk	span{φk	NOUN
ejde-397	1256	14	:	:	PUNCT
ejde-397	1256	15	k|λ	k|λ	X
ejde-397	1256	16	=	=	PUNCT
ejde-397	1256	17	λk	λk	X
ejde-397	1256	18	}	}	PUNCT
ejde-397	1256	19	so	so	SCONJ
ejde-397	1256	20	that	that	SCONJ
ejde-397	1256	21	the	the	DET
ejde-397	1256	22	function	function	NOUN
ejde-397	1256	23	t	t	PROPN
ejde-397	1256	24	7→	7→	NUM
ejde-397	1256	25	∑	∑	PUNCT
ejde-397	1256	26	k|λk	k|λk	X
ejde-397	1256	27	=	=	SYM
ejde-397	1256	28	λ	λ	X
ejde-397	1256	29	〈	〈	NOUN
ejde-397	1256	30	f(t),φk	f(t),φk	PROPN
ejde-397	1256	31	〉	〉	PROPN
ejde-397	1256	32	βλ2	βλ2	PUNCT
ejde-397	1256	33	k−αλk	k−αλk	PROPN
ejde-397	1256	34	φk	φk	ADP
ejde-397	1256	35	,	,	PUNCT
ejde-397	1256	36	t	t	PROPN
ejde-397	1256	37	≥	≥	PROPN
ejde-397	1256	38	0	0	NUM
ejde-397	1256	39	is	be	AUX
ejde-397	1256	40	a	a	DET
ejde-397	1256	41	pre	pre	NOUN
ejde-397	1256	42	-	-	NOUN
ejde-397	1256	43	solution	solution	NOUN
ejde-397	1256	44	of	of	ADP
ejde-397	1256	45	problem	problem	NOUN
ejde-397	1256	46	(	(	PUNCT
ejde-397	1256	47	5.25	5.25	NUM
ejde-397	1256	48	)	)	PUNCT
ejde-397	1256	49	with	with	ADP
ejde-397	1256	50	f	f	PROPN
ejde-397	1256	51	=	=	PUNCT
ejde-397	1256	52	∑	∑	PUNCT
ejde-397	1256	53	k|λk	k|λk	X
ejde-397	1256	54	=	=	PRON
ejde-397	1256	55	λ〈f	λ〈f	X
ejde-397	1256	56	(	(	PUNCT
ejde-397	1256	57	·	·	PUNCT
ejde-397	1256	58	)	)	PUNCT
ejde-397	1256	59	,	,	PUNCT
ejde-397	1256	60	φk〉φk	φk〉φk	PROPN
ejde-397	1256	61	,	,	PUNCT
ejde-397	1256	62	provided	provide	VERB
ejde-397	1256	63	that	that	SCONJ
ejde-397	1256	64	the	the	DET
ejde-397	1256	65	following	follow	VERB
ejde-397	1256	66	condition	condition	NOUN
ejde-397	1256	67	holds	hold	VERB
ejde-397	1256	68	(	(	PUNCT
ejde-397	1256	69	a1	a1	NOUN
ejde-397	1256	70	)	)	PUNCT
ejde-397	1256	71	:	:	PUNCT
ejde-397	1257	1	dη	dη	ADP
ejde-397	1257	2	t	t	PROPN
ejde-397	1257	3	〈	〈	PROPN
ejde-397	1257	4	f(t	f(t	PROPN
ejde-397	1257	5	)	)	PUNCT
ejde-397	1257	6	,	,	PUNCT
ejde-397	1257	7	φk	φk	ADP
ejde-397	1257	8	〉	〉	PROPN
ejde-397	1257	9	exists	exist	VERB
ejde-397	1257	10	in	in	ADP
ejde-397	1257	11	l2(ω	l2(ω	NOUN
ejde-397	1257	12	)	)	PUNCT
ejde-397	1257	13	for	for	ADP
ejde-397	1257	14	k|λ	k|λ	X
ejde-397	1257	15	=	=	SYM
ejde-397	1257	16	λk	λk	X
ejde-397	1257	17	,	,	PUNCT
ejde-397	1257	18	〈	〈	PROPN
ejde-397	1257	19	x0	x0	PROPN
ejde-397	1257	20	,	,	PUNCT
ejde-397	1257	21	φk	φk	ADP
ejde-397	1257	22	〉	〉	NOUN
ejde-397	1257	23	=	=	SYM
ejde-397	1257	24	0	0	NUM
ejde-397	1257	25	for	for	ADP
ejde-397	1257	26	k|λ	k|λ	X
ejde-397	1257	27	6=	6=	ADP
ejde-397	1257	28	λk	λk	ADV
ejde-397	1257	29	,	,	PUNCT
ejde-397	1257	30	〈	〈	PROPN
ejde-397	1257	31	x1	x1	PROPN
ejde-397	1257	32	,	,	PUNCT
ejde-397	1257	33	φk	φk	ADP
ejde-397	1257	34	〉	〉	NOUN
ejde-397	1257	35	=	=	SYM
ejde-397	1257	36	0	0	NUM
ejde-397	1257	37	for	for	ADP
ejde-397	1257	38	k|λ	k|λ	X
ejde-397	1257	39	6=	6=	ADP
ejde-397	1257	40	λk	λk	ADP
ejde-397	1257	41	,	,	PUNCT
ejde-397	1257	42	1	1	NUM
ejde-397	1257	43	<	<	X
ejde-397	1257	44	η	η	PROPN
ejde-397	1257	45	≤	≤	PROPN
ejde-397	1257	46	2	2	NUM
ejde-397	1257	47	,	,	PUNCT
ejde-397	1257	48	〈	〈	PROPN
ejde-397	1257	49	x0	x0	PROPN
ejde-397	1257	50	,	,	PUNCT
ejde-397	1257	51	φk	φk	ADP
ejde-397	1257	52	〉	〉	NOUN
ejde-397	1257	53	=	=	SYM
ejde-397	1257	54	〈	〈	PROPN
ejde-397	1257	55	f(0),φk	f(0),φk	PROPN
ejde-397	1257	56	〉	〉	PROPN
ejde-397	1257	57	βλ2	βλ2	PUNCT
ejde-397	1257	58	k−αλk	k−αλk	PROPN
ejde-397	1257	59	for	for	ADP
ejde-397	1257	60	k|λ	k|λ	PROPN
ejde-397	1257	61	=	=	PUNCT
ejde-397	1257	62	λk	λk	ADP
ejde-397	1257	63	,	,	PUNCT
ejde-397	1257	64	and	and	CCONJ
ejde-397	1257	65	〈	〈	PROPN
ejde-397	1257	66	x1	x1	PROPN
ejde-397	1257	67	,	,	PUNCT
ejde-397	1257	68	φk	φk	ADP
ejde-397	1257	69	〉	〉	NOUN
ejde-397	1257	70	=	=	SYM
ejde-397	1257	71	〈	〈	PROPN
ejde-397	1257	72	f	f	PROPN
ejde-397	1257	73	′(0),φk	′(0),φk	PROPN
ejde-397	1257	74	〉	〉	PROPN
ejde-397	1257	75	βλ2	βλ2	PUNCT
ejde-397	1257	76	k−αλk	k−αλk	PROPN
ejde-397	1257	77	for	for	ADP
ejde-397	1257	78	k|λ	k|λ	PROPN
ejde-397	1257	79	=	=	PUNCT
ejde-397	1257	80	λk	λk	PROPN
ejde-397	1257	81	,	,	PUNCT
ejde-397	1257	82	1	1	NUM
ejde-397	1257	83	<	<	X
ejde-397	1257	84	η	η	PROPN
ejde-397	1257	85	≤	≤	PROPN
ejde-397	1257	86	2	2	NUM
ejde-397	1257	87	.	.	PUNCT
ejde-397	1258	1	summa	summa	PROPN
ejde-397	1258	2	summarum	summarum	PROPN
ejde-397	1258	3	,	,	PUNCT
ejde-397	1258	4	we	we	PRON
ejde-397	1258	5	have	have	VERB
ejde-397	1258	6	the	the	DET
ejde-397	1258	7	following	following	NOUN
ejde-397	1258	8	:	:	PUNCT
ejde-397	1258	9	(	(	PUNCT
ejde-397	1258	10	i	i	NOUN
ejde-397	1258	11	)	)	PUNCT
ejde-397	1258	12	0	0	PUNCT
ejde-397	1258	13	<	<	X
ejde-397	1258	14	η	η	X
ejde-397	1258	15	<	<	X
ejde-397	1258	16	2	2	NUM
ejde-397	1258	17	:	:	PUNCT
ejde-397	1258	18	suppose	suppose	VERB
ejde-397	1258	19	that	that	SCONJ
ejde-397	1258	20	x0	x0	PROPN
ejde-397	1258	21	∈	∈	PROPN
ejde-397	1258	22	d(a	d(a	PROPN
ejde-397	1258	23	)	)	PUNCT
ejde-397	1258	24	∩	∩	NOUN
ejde-397	1258	25	x0	x0	PROPN
ejde-397	1258	26	,	,	PUNCT
ejde-397	1258	27	x1	x1	PROPN
ejde-397	1258	28	∈	∈	PROPN
ejde-397	1258	29	d(b	d(b	PROPN
ejde-397	1258	30	)	)	PUNCT
ejde-397	1258	31	∩	∩	NOUN
ejde-397	1258	32	x0	x0	PROPN
ejde-397	1258	33	,	,	PUNCT
ejde-397	1258	34	if	if	SCONJ
ejde-397	1258	35	η	η	PROPN
ejde-397	1258	36	>	>	X
ejde-397	1258	37	1	1	NUM
ejde-397	1258	38	,	,	PUNCT
ejde-397	1258	39	∑	∑	ADP
ejde-397	1258	40	k|λk	k|λk	PROPN
ejde-397	1258	41	6	6	NUM
ejde-397	1258	42	=	=	SYM
ejde-397	1258	43	λ	λ	X
ejde-397	1258	44	〈	〈	PROPN
ejde-397	1258	45	f(·),φk	f(·),φk	PROPN
ejde-397	1258	46	〉	〉	PROPN
ejde-397	1258	47	λ−λk	λ−λk	VERB
ejde-397	1258	48	φk	φk	ADP
ejde-397	1258	49	=	=	PUNCT
ejde-397	1258	50	h	h	NOUN
ejde-397	1258	51	∈	∈	PROPN
ejde-397	1258	52	w	w	PROPN
ejde-397	1258	53	1,1	1,1	NUM
ejde-397	1258	54	loc	loc	X
ejde-397	1258	55	(	(	PUNCT
ejde-397	1258	56	[	[	X
ejde-397	1258	57	0,∞	0,∞	NOUN
ejde-397	1258	58	)	)	PUNCT
ejde-397	1258	59	:	:	PUNCT
ejde-397	1258	60	x0	x0	PROPN
ejde-397	1258	61	)	)	PUNCT
ejde-397	1258	62	satisfies	satisfie	NOUN
ejde-397	1258	63	(	(	PUNCT
ejde-397	1258	64	5.26	5.26	NUM
ejde-397	1258	65	)	)	PUNCT
ejde-397	1258	66	,	,	PUNCT
ejde-397	1258	67	and	and	CCONJ
ejde-397	1258	68	the	the	DET
ejde-397	1258	69	condition	condition	NOUN
ejde-397	1258	70	(	(	PUNCT
ejde-397	1258	71	a1	a1	NOUN
ejde-397	1258	72	)	)	PUNCT
ejde-397	1258	73	holds	hold	NOUN
ejde-397	1258	74	.	.	PUNCT
ejde-397	1259	1	then	then	ADV
ejde-397	1259	2	there	there	PRON
ejde-397	1259	3	exists	exist	VERB
ejde-397	1259	4	a	a	DET
ejde-397	1259	5	unique	unique	ADJ
ejde-397	1259	6	pre	pre	NOUN
ejde-397	1259	7	-	-	NOUN
ejde-397	1259	8	solution	solution	NOUN
ejde-397	1259	9	of	of	ADP
ejde-397	1259	10	problem	problem	NOUN
ejde-397	1259	11	(	(	PUNCT
ejde-397	1259	12	5.25	5.25	NUM
ejde-397	1259	13	)	)	PUNCT
ejde-397	1259	14	.	.	PUNCT
ejde-397	1260	1	(	(	PUNCT
ejde-397	1260	2	ii	ii	X
ejde-397	1260	3	)	)	PUNCT
ejde-397	1260	4	η	η	PROPN
ejde-397	1260	5	=	=	SYM
ejde-397	1260	6	2	2	NUM
ejde-397	1260	7	:	:	PUNCT
ejde-397	1260	8	suppose	suppose	VERB
ejde-397	1260	9	x1	x1	PROPN
ejde-397	1260	10	∈	∈	PROPN
ejde-397	1260	11	d((−∆)3/2	d((−∆)3/2	ADJ
ejde-397	1260	12	)	)	PUNCT
ejde-397	1260	13	∩	∩	NOUN
ejde-397	1260	14	x0	x0	PROPN
ejde-397	1260	15	and	and	CCONJ
ejde-397	1260	16	the	the	DET
ejde-397	1260	17	remaining	remain	VERB
ejde-397	1260	18	assumptions	assumption	NOUN
ejde-397	1260	19	from	from	ADP
ejde-397	1260	20	(	(	PUNCT
ejde-397	1260	21	i	i	NOUN
ejde-397	1260	22	)	)	PUNCT
ejde-397	1260	23	hold	hold	VERB
ejde-397	1260	24	.	.	PUNCT
ejde-397	1261	1	then	then	ADV
ejde-397	1261	2	there	there	PRON
ejde-397	1261	3	exists	exist	VERB
ejde-397	1261	4	a	a	DET
ejde-397	1261	5	unique	unique	ADJ
ejde-397	1261	6	pre	pre	NOUN
ejde-397	1261	7	-	-	NOUN
ejde-397	1261	8	solution	solution	NOUN
ejde-397	1261	9	of	of	ADP
ejde-397	1261	10	problem	problem	NOUN
ejde-397	1261	11	(	(	PUNCT
ejde-397	1261	12	5.25	5.25	NUM
ejde-397	1261	13	)	)	PUNCT
ejde-397	1261	14	.	.	PUNCT
ejde-397	1262	1	observe	observe	VERB
ejde-397	1262	2	also	also	ADV
ejde-397	1262	3	that	that	SCONJ
ejde-397	1262	4	our	our	PRON
ejde-397	1262	5	results	result	NOUN
ejde-397	1262	6	on	on	ADP
ejde-397	1262	7	the	the	DET
ejde-397	1262	8	well	well	NOUN
ejde-397	1262	9	-	-	PUNCT
ejde-397	1262	10	posedness	posedness	NOUN
ejde-397	1262	11	of	of	ADP
ejde-397	1262	12	fractional	fractional	ADJ
ejde-397	1262	13	analogue	analogue	NOUN
ejde-397	1262	14	of	of	ADP
ejde-397	1262	15	the	the	DET
ejde-397	1262	16	benney	benney	NOUN
ejde-397	1262	17	-	-	PUNCT
ejde-397	1262	18	luke	luke	PROPN
ejde-397	1262	19	equation	equation	NOUN
ejde-397	1262	20	,	,	PUNCT
ejde-397	1262	21	based	base	VERB
ejde-397	1262	22	on	on	ADP
ejde-397	1262	23	a	a	DET
ejde-397	1262	24	very	very	ADV
ejde-397	1262	25	simple	simple	ADJ
ejde-397	1262	26	approach	approach	NOUN
ejde-397	1262	27	,	,	PUNCT
ejde-397	1262	28	are	be	AUX
ejde-397	1262	29	completely	completely	ADV
ejde-397	1262	30	new	new	ADJ
ejde-397	1262	31	provided	provide	VERB
ejde-397	1262	32	that	that	SCONJ
ejde-397	1262	33	η	η	PROPN
ejde-397	1262	34	>	>	X
ejde-397	1262	35	1	1	NUM
ejde-397	1262	36	,	,	PUNCT
ejde-397	1262	37	as	as	ADV
ejde-397	1262	38	well	well	ADV
ejde-397	1262	39	as	as	ADP
ejde-397	1262	40	that	that	SCONJ
ejde-397	1262	41	we	we	PRON
ejde-397	1262	42	have	have	AUX
ejde-397	1262	43	obtained	obtain	VERB
ejde-397	1262	44	some	some	DET
ejde-397	1262	45	new	new	ADJ
ejde-397	1262	46	results	result	NOUN
ejde-397	1262	47	on	on	ADP
ejde-397	1262	48	the	the	DET
ejde-397	1262	49	wellposedness	wellposedness	NOUN
ejde-397	1262	50	of	of	ADP
ejde-397	1262	51	the	the	DET
ejde-397	1262	52	inhomogeneous	inhomogeneous	ADJ
ejde-397	1262	53	cauchy	cauchy	PROPN
ejde-397	1262	54	problem	problem	NOUN
ejde-397	1262	55	pη	pη	ADP
ejde-397	1262	56	,	,	PUNCT
ejde-397	1262	57	f	f	PROPN
ejde-397	1262	58	in	in	ADP
ejde-397	1262	59	the	the	DET
ejde-397	1262	60	case	case	NOUN
ejde-397	1262	61	that	that	SCONJ
ejde-397	1262	62	η	η	PROPN
ejde-397	1262	63	<	<	X
ejde-397	1262	64	1	1	NUM
ejde-397	1262	65	(	(	PUNCT
ejde-397	1262	66	cf	cf	NOUN
ejde-397	1262	67	.	.	PUNCT
ejde-397	1263	1	[	[	X
ejde-397	1263	2	22	22	NUM
ejde-397	1263	3	,	,	PUNCT
ejde-397	1263	4	theorem	theorem	VERB
ejde-397	1263	5	4.2	4.2	NUM
ejde-397	1263	6	]	]	PUNCT
ejde-397	1263	7	for	for	ADP
ejde-397	1263	8	the	the	DET
ejde-397	1263	9	first	first	ADJ
ejde-397	1263	10	result	result	NOUN
ejde-397	1263	11	in	in	ADP
ejde-397	1263	12	this	this	DET
ejde-397	1263	13	direction	direction	NOUN
ejde-397	1263	14	)	)	PUNCT
ejde-397	1263	15	.	.	PUNCT
ejde-397	1264	1	the	the	DET
ejde-397	1264	2	following	follow	VERB
ejde-397	1264	3	theorem	theorem	NOUN
ejde-397	1264	4	can	can	AUX
ejde-397	1264	5	be	be	AUX
ejde-397	1264	6	deduced	deduce	VERB
ejde-397	1264	7	by	by	ADP
ejde-397	1264	8	making	make	VERB
ejde-397	1264	9	use	use	NOUN
ejde-397	1264	10	of	of	ADP
ejde-397	1264	11	the	the	DET
ejde-397	1264	12	argumentation	argumentation	NOUN
ejde-397	1264	13	contained	contain	VERB
ejde-397	1264	14	in	in	ADP
ejde-397	1264	15	the	the	DET
ejde-397	1264	16	proof	proof	NOUN
ejde-397	1264	17	of	of	ADP
ejde-397	1264	18	[	[	X
ejde-397	1264	19	39	39	NUM
ejde-397	1264	20	,	,	PUNCT
ejde-397	1264	21	theorem	theorem	VERB
ejde-397	1264	22	2.16	2.16	NUM
ejde-397	1264	23	]	]	PUNCT
ejde-397	1264	24	.	.	PUNCT
ejde-397	1265	1	here	here	ADV
ejde-397	1265	2	we	we	PRON
ejde-397	1265	3	would	would	AUX
ejde-397	1265	4	like	like	VERB
ejde-397	1265	5	to	to	PART
ejde-397	1265	6	observe	observe	VERB
ejde-397	1265	7	that	that	SCONJ
ejde-397	1265	8	the	the	DET
ejde-397	1265	9	equality	equality	NOUN
ejde-397	1265	10	rλ,µ	rλ,µ	NOUN
ejde-397	1265	11	=	=	SYM
ejde-397	1265	12	0	0	NUM
ejde-397	1265	13	,	,	PUNCT
ejde-397	1265	14	stated	state	VERB
ejde-397	1265	15	on	on	ADP
ejde-397	1265	16	[	[	X
ejde-397	1265	17	39	39	NUM
ejde-397	1265	18	,	,	PUNCT
ejde-397	1265	19	p.	p.	NOUN
ejde-397	1265	20	12	12	NUM
ejde-397	1265	21	,	,	PUNCT
ejde-397	1265	22	l.	l.	NOUN
ejde-397	1265	23	4	4	NUM
ejde-397	1265	24	]	]	PUNCT
ejde-397	1265	25	,	,	PUNCT
ejde-397	1265	26	can	can	AUX
ejde-397	1265	27	be	be	AUX
ejde-397	1265	28	proved	prove	VERB
ejde-397	1265	29	by	by	ADP
ejde-397	1265	30	taking	take	VERB
ejde-397	1265	31	the	the	DET
ejde-397	1265	32	laplace	laplace	NOUN
ejde-397	1265	33	transform	transform	NOUN
ejde-397	1265	34	of	of	ADP
ejde-397	1265	35	term	term	NOUN
ejde-397	1265	36	appearing	appear	VERB
ejde-397	1265	37	on	on	ADP
ejde-397	1265	38	[	[	X
ejde-397	1265	39	39	39	NUM
ejde-397	1265	40	,	,	PUNCT
ejde-397	1265	41	p.	p.	NOUN
ejde-397	1265	42	12	12	NUM
ejde-397	1265	43	,	,	PUNCT
ejde-397	1265	44	l.	l.	PROPN
ejde-397	1265	45	1	1	NUM
ejde-397	1265	46	-	-	SYM
ejde-397	1265	47	2	2	NUM
ejde-397	1265	48	]	]	PUNCT
ejde-397	1265	49	in	in	ADP
ejde-397	1265	50	variable	variable	ADJ
ejde-397	1265	51	µ	µ	NOUN
ejde-397	1265	52	,	,	PUNCT
ejde-397	1265	53	and	and	CCONJ
ejde-397	1265	54	by	by	ADP
ejde-397	1265	55	using	use	VERB
ejde-397	1265	56	the	the	DET
ejde-397	1265	57	strong	strong	ADJ
ejde-397	1265	58	analyticity	analyticity	NOUN
ejde-397	1265	59	of	of	ADP
ejde-397	1265	60	mapping	map	VERB
ejde-397	1265	61	λ	λ	PROPN
ejde-397	1265	62	7→	7→	NUM
ejde-397	1265	63	f	f	PROPN
ejde-397	1265	64	(	(	PUNCT
ejde-397	1265	65	λ	λ	NOUN
ejde-397	1265	66	)	)	PUNCT
ejde-397	1265	67	∈	∈	PROPN
ejde-397	1265	68	l(x	l(x	PROPN
ejde-397	1265	69	)	)	PUNCT
ejde-397	1265	70	,	,	PUNCT
ejde-397	1266	1	λ	λ	PROPN
ejde-397	1266	2	∈	∈	PROPN
ejde-397	1266	3	n	n	CCONJ
ejde-397	1266	4	,	,	PUNCT
ejde-397	1266	5	along	along	ADP
ejde-397	1266	6	with	with	ADP
ejde-397	1266	7	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1266	8	abstract	abstract	ADJ
ejde-397	1266	9	degenerate	degenerate	ADJ
ejde-397	1266	10	volterra	volterra	NOUN
ejde-397	1266	11	inclusions	inclusion	NOUN
ejde-397	1266	12	41	41	NUM
ejde-397	1266	13	the	the	DET
ejde-397	1266	14	equality	equality	NOUN
ejde-397	1266	15	rλ,µ	rλ,µ	NOUN
ejde-397	1266	16	=	=	NOUN
ejde-397	1266	17	0	0	NUM
ejde-397	1266	18	for	for	ADP
ejde-397	1266	19	<	<	X
ejde-397	1266	20	λ	λ	X
ejde-397	1266	21	>	>	X
ejde-397	1266	22	ω	ω	PROPN
ejde-397	1266	23	,	,	PUNCT
ejde-397	1266	24	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1266	25	)	)	PUNCT
ejde-397	1266	26	6=	6=	ADP
ejde-397	1266	27	0	0	NUM
ejde-397	1266	28	(	(	PUNCT
ejde-397	1266	29	the	the	DET
ejde-397	1266	30	repeated	repeat	VERB
ejde-397	1266	31	use	use	NOUN
ejde-397	1266	32	of	of	ADP
ejde-397	1266	33	identity	identity	NOUN
ejde-397	1266	34	[	[	X
ejde-397	1266	35	39	39	NUM
ejde-397	1266	36	,	,	PUNCT
ejde-397	1266	37	(	(	PUNCT
ejde-397	1266	38	2.30	2.30	NUM
ejde-397	1266	39	)	)	PUNCT
ejde-397	1266	40	]	]	PUNCT
ejde-397	1266	41	on	on	ADP
ejde-397	1266	42	[	[	X
ejde-397	1266	43	39	39	NUM
ejde-397	1266	44	,	,	PUNCT
ejde-397	1266	45	p.	p.	NOUN
ejde-397	1266	46	12	12	NUM
ejde-397	1266	47	,	,	PUNCT
ejde-397	1266	48	l.4	l.4	X
ejde-397	1266	49	]	]	PUNCT
ejde-397	1266	50	is	be	AUX
ejde-397	1266	51	wrong	wrong	ADJ
ejde-397	1266	52	and	and	CCONJ
ejde-397	1266	53	makes	make	VERB
ejde-397	1266	54	a	a	DET
ejde-397	1266	55	circulus	circulus	NOUN
ejde-397	1266	56	vitiosus	vitiosus	NOUN
ejde-397	1266	57	):	):	PUNCT
ejde-397	1266	58	theorem	theorem	VERB
ejde-397	1266	59	5.18	5.18	NUM
ejde-397	1266	60	.	.	PUNCT
ejde-397	1267	1	(	(	PUNCT
ejde-397	1267	2	see	see	VERB
ejde-397	1267	3	[	[	X
ejde-397	1267	4	36	36	NUM
ejde-397	1267	5	,	,	PUNCT
ejde-397	1267	6	theorem	theorem	VERB
ejde-397	1267	7	2.2.4	2.2.4	NUM
ejde-397	1267	8	]	]	PUNCT
ejde-397	1267	9	for	for	ADP
ejde-397	1267	10	non	non	ADJ
ejde-397	1267	11	-	-	ADJ
ejde-397	1267	12	degenerate	degenerate	ADJ
ejde-397	1267	13	case	case	NOUN
ejde-397	1267	14	)	)	PUNCT
ejde-397	1267	15	suppose	suppose	VERB
ejde-397	1267	16	that	that	SCONJ
ejde-397	1267	17	α	α	PROPN
ejde-397	1267	18	∈	∈	PROPN
ejde-397	1267	19	(	(	PUNCT
ejde-397	1267	20	0	0	NUM
ejde-397	1267	21	,	,	PUNCT
ejde-397	1267	22	π/2	π/2	NUM
ejde-397	1267	23	]	]	PUNCT
ejde-397	1267	24	,	,	PUNCT
ejde-397	1267	25	abs(k	abs(k	PROPN
ejde-397	1267	26	)	)	PUNCT
ejde-397	1267	27	<	<	X
ejde-397	1267	28	∞	∞	PROPN
ejde-397	1267	29	,	,	PUNCT
ejde-397	1267	30	abs(|a|	abs(|a|	ADJ
ejde-397	1267	31	)	)	PUNCT
ejde-397	1267	32	<	<	X
ejde-397	1267	33	∞	∞	PROPN
ejde-397	1267	34	,	,	PUNCT
ejde-397	1267	35	and	and	CCONJ
ejde-397	1267	36	k̃(λ	k̃(λ	NOUN
ejde-397	1267	37	)	)	PUNCT
ejde-397	1267	38	can	can	AUX
ejde-397	1267	39	be	be	AUX
ejde-397	1267	40	analytically	analytically	ADV
ejde-397	1267	41	continued	continue	VERB
ejde-397	1267	42	to	to	ADP
ejde-397	1267	43	a	a	DET
ejde-397	1267	44	function	function	NOUN
ejde-397	1267	45	g	g	NOUN
ejde-397	1267	46	:	:	PUNCT
ejde-397	1267	47	ω	ω	PROPN
ejde-397	1267	48	+	+	CCONJ
ejde-397	1267	49	σπ	σπ	PROPN
ejde-397	1267	50	2	2	NUM
ejde-397	1267	51	+	+	NOUN
ejde-397	1267	52	α	α	NOUN
ejde-397	1267	53	→	→	SYM
ejde-397	1267	54	c	c	X
ejde-397	1267	55	,	,	PUNCT
ejde-397	1267	56	where	where	SCONJ
ejde-397	1267	57	ω	ω	PROPN
ejde-397	1267	58	≥	≥	NOUN
ejde-397	1267	59	max(0	max(0	NOUN
ejde-397	1267	60	,	,	PUNCT
ejde-397	1267	61	abs(k	abs(k	PROPN
ejde-397	1267	62	)	)	PUNCT
ejde-397	1267	63	,	,	PUNCT
ejde-397	1267	64	abs(|a|	abs(|a|	ADJ
ejde-397	1267	65	)	)	PUNCT
ejde-397	1267	66	)	)	PUNCT
ejde-397	1267	67	.	.	PUNCT
ejde-397	1268	1	suppose	suppose	VERB
ejde-397	1268	2	,	,	PUNCT
ejde-397	1268	3	further	far	ADV
ejde-397	1268	4	,	,	PUNCT
ejde-397	1268	5	that	that	SCONJ
ejde-397	1268	6	a	a	PRON
ejde-397	1268	7	is	be	AUX
ejde-397	1268	8	a	a	DET
ejde-397	1268	9	closed	closed	ADJ
ejde-397	1268	10	subgenerator	subgenerator	NOUN
ejde-397	1268	11	of	of	ADP
ejde-397	1268	12	an	an	DET
ejde-397	1268	13	analytic	analytic	ADJ
ejde-397	1268	14	(	(	PUNCT
ejde-397	1268	15	a	a	PRON
ejde-397	1268	16	,	,	PUNCT
ejde-397	1268	17	k)-regularized	k)-regularize	VERB
ejde-397	1268	18	c	c	NOUN
ejde-397	1268	19	-	-	PUNCT
ejde-397	1268	20	resolvent	resolvent	ADJ
ejde-397	1268	21	family	family	NOUN
ejde-397	1268	22	(	(	PUNCT
ejde-397	1268	23	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	1268	24	of	of	ADP
ejde-397	1268	25	angle	angle	NOUN
ejde-397	1268	26	α	α	PROPN
ejde-397	1268	27	satisfying	satisfy	VERB
ejde-397	1268	28	that	that	SCONJ
ejde-397	1268	29	the	the	DET
ejde-397	1268	30	family	family	NOUN
ejde-397	1268	31	{	{	PUNCT
ejde-397	1268	32	e−ωzr(z	e−ωzr(z	PROPN
ejde-397	1268	33	)	)	PUNCT
ejde-397	1268	34	:	:	PUNCT
ejde-397	1268	35	z	z	X
ejde-397	1268	36	∈	∈	PROPN
ejde-397	1268	37	σγ	σγ	PROPN
ejde-397	1268	38	}	}	PUNCT
ejde-397	1268	39	⊆	⊆	NUM
ejde-397	1268	40	l(x	l(x	PROPN
ejde-397	1268	41	)	)	PUNCT
ejde-397	1268	42	is	be	AUX
ejde-397	1268	43	equicontinuous	equicontinuous	ADJ
ejde-397	1268	44	for	for	ADP
ejde-397	1268	45	all	all	DET
ejde-397	1268	46	angles	angle	NOUN
ejde-397	1268	47	γ	γ	X
ejde-397	1268	48	∈	∈	PROPN
ejde-397	1268	49	(	(	PUNCT
ejde-397	1268	50	0	0	NUM
ejde-397	1268	51	,	,	PUNCT
ejde-397	1268	52	α	α	NOUN
ejde-397	1268	53	)	)	PUNCT
ejde-397	1268	54	,	,	PUNCT
ejde-397	1268	55	as	as	ADV
ejde-397	1268	56	well	well	ADV
ejde-397	1268	57	as	as	ADP
ejde-397	1268	58	that	that	DET
ejde-397	1268	59	equation	equation	NOUN
ejde-397	1268	60	(	(	PUNCT
ejde-397	1268	61	5.1	5.1	NUM
ejde-397	1268	62	)	)	PUNCT
ejde-397	1268	63	holds	hold	VERB
ejde-397	1268	64	for	for	ADP
ejde-397	1268	65	each	each	PRON
ejde-397	1268	66	y	y	NOUN
ejde-397	1268	67	=	=	PUNCT
ejde-397	1268	68	x	x	SYM
ejde-397	1268	69	∈	∈	PROPN
ejde-397	1268	70	x	x	NOUN
ejde-397	1268	71	,	,	PUNCT
ejde-397	1268	72	with	with	ADP
ejde-397	1268	73	r1	r1	PROPN
ejde-397	1268	74	(	(	PUNCT
ejde-397	1268	75	·	·	PUNCT
ejde-397	1268	76	)	)	PUNCT
ejde-397	1268	77	and	and	CCONJ
ejde-397	1268	78	c1	c1	PROPN
ejde-397	1268	79	replaced	replace	VERB
ejde-397	1268	80	therein	therein	ADV
ejde-397	1268	81	by	by	ADP
ejde-397	1268	82	r	r	NOUN
ejde-397	1268	83	(	(	PUNCT
ejde-397	1268	84	·	·	PUNCT
ejde-397	1268	85	)	)	PUNCT
ejde-397	1268	86	and	and	CCONJ
ejde-397	1268	87	c	c	NOUN
ejde-397	1268	88	,	,	PUNCT
ejde-397	1268	89	respectively	respectively	ADV
ejde-397	1268	90	.	.	PUNCT
ejde-397	1269	1	set	set	VERB
ejde-397	1269	2	n	n	NOUN
ejde-397	1269	3	:	:	PUNCT
ejde-397	1269	4	=	=	SYM
ejde-397	1269	5	{	{	PUNCT
ejde-397	1269	6	λ	λ	X
ejde-397	1269	7	∈	∈	PROPN
ejde-397	1269	8	ω	ω	NOUN
ejde-397	1269	9	+	+	CCONJ
ejde-397	1269	10	σπ	σπ	PROPN
ejde-397	1269	11	2	2	NUM
ejde-397	1269	12	+	+	NOUN
ejde-397	1269	13	α	α	NOUN
ejde-397	1269	14	:	:	PUNCT
ejde-397	1269	15	g(λ	g(λ	PROPN
ejde-397	1269	16	)	)	PUNCT
ejde-397	1269	17	6=	6=	ADP
ejde-397	1269	18	0	0	NUM
ejde-397	1269	19	}	}	PUNCT
ejde-397	1269	20	.	.	PUNCT
ejde-397	1270	1	then	then	ADV
ejde-397	1270	2	n	n	PRON
ejde-397	1270	3	is	be	AUX
ejde-397	1270	4	an	an	DET
ejde-397	1270	5	open	open	ADJ
ejde-397	1270	6	connected	connected	ADJ
ejde-397	1270	7	subset	subset	NOUN
ejde-397	1270	8	of	of	ADP
ejde-397	1270	9	c.	c.	PROPN
ejde-397	1270	10	furthermore	furthermore	ADV
ejde-397	1270	11	,	,	PUNCT
ejde-397	1270	12	the	the	DET
ejde-397	1270	13	existence	existence	NOUN
ejde-397	1270	14	of	of	ADP
ejde-397	1270	15	an	an	DET
ejde-397	1270	16	analytic	analytic	ADJ
ejde-397	1270	17	function	function	NOUN
ejde-397	1270	18	â	â	PROPN
ejde-397	1270	19	:	:	PUNCT
ejde-397	1270	20	n	n	X
ejde-397	1270	21	→	→	SYM
ejde-397	1270	22	c	c	NOUN
ejde-397	1270	23	such	such	ADJ
ejde-397	1270	24	that	that	SCONJ
ejde-397	1270	25	â(λ	â(λ	VERB
ejde-397	1270	26	)	)	PUNCT
ejde-397	1270	27	=	=	SYM
ejde-397	1270	28	ã(λ	ã(λ	PROPN
ejde-397	1270	29	)	)	PUNCT
ejde-397	1270	30	,	,	PUNCT
ejde-397	1270	31	<	<	X
ejde-397	1270	32	λ	λ	X
ejde-397	1270	33	>	>	X
ejde-397	1270	34	ω	ω	PROPN
ejde-397	1270	35	implies	imply	VERB
ejde-397	1270	36	that	that	SCONJ
ejde-397	1270	37	the	the	DET
ejde-397	1270	38	operator	operator	NOUN
ejde-397	1270	39	i	i	PRON
ejde-397	1270	40	−	−	PROPN
ejde-397	1271	1	â(λ)a	â(λ)a	PROPN
ejde-397	1271	2	is	be	AUX
ejde-397	1271	3	injective	injective	ADJ
ejde-397	1271	4	for	for	ADP
ejde-397	1271	5	every	every	DET
ejde-397	1271	6	λ	λ	PROPN
ejde-397	1271	7	∈	∈	PROPN
ejde-397	1271	8	n	n	NOUN
ejde-397	1271	9	,	,	PUNCT
ejde-397	1271	10	r(c	r(c	PROPN
ejde-397	1271	11	)	)	PUNCT
ejde-397	1271	12	⊆	⊆	NUM
ejde-397	1271	13	r(i	r(i	PROPN
ejde-397	1271	14	−	−	PROPN
ejde-397	1271	15	â(λ)c−1ac	â(λ)c−1ac	NUM
ejde-397	1271	16	)	)	PUNCT
ejde-397	1271	17	for	for	ADP
ejde-397	1271	18	every	every	DET
ejde-397	1271	19	λ	λ	PROPN
ejde-397	1271	20	∈	∈	PROPN
ejde-397	1271	21	n1	n1	NOUN
ejde-397	1271	22	:	:	PUNCT
ejde-397	1271	23	=	=	SYM
ejde-397	1271	24	{	{	PUNCT
ejde-397	1271	25	λ	λ	X
ejde-397	1271	26	∈	∈	NOUN
ejde-397	1271	27	n	n	NOUN
ejde-397	1271	28	:	:	PUNCT
ejde-397	1271	29	â(λ	â(λ	X
ejde-397	1271	30	)	)	PUNCT
ejde-397	1271	31	6=	6=	ADP
ejde-397	1271	32	0	0	NUM
ejde-397	1271	33	}	}	PUNCT
ejde-397	1271	34	,	,	PUNCT
ejde-397	1271	35	the	the	DET
ejde-397	1271	36	operator	operator	NOUN
ejde-397	1271	37	(	(	PUNCT
ejde-397	1271	38	i	i	PRON
ejde-397	1271	39	−	−	PROPN
ejde-397	1271	40	â(λ)c−1ac)−1c	â(λ)c−1ac)−1c	PROPN
ejde-397	1271	41	∈	∈	PROPN
ejde-397	1271	42	l(x	l(x	PROPN
ejde-397	1271	43	)	)	PUNCT
ejde-397	1271	44	is	be	AUX
ejde-397	1271	45	single	single	ADV
ejde-397	1271	46	-	-	PUNCT
ejde-397	1271	47	valued	value	VERB
ejde-397	1271	48	(	(	PUNCT
ejde-397	1271	49	λ	λ	PROPN
ejde-397	1271	50	∈	∈	PROPN
ejde-397	1271	51	n1	n1	NOUN
ejde-397	1271	52	)	)	PUNCT
ejde-397	1271	53	,	,	PUNCT
ejde-397	1271	54	the	the	DET
ejde-397	1271	55	family	family	NOUN
ejde-397	1271	56	{	{	PUNCT
ejde-397	1271	57	(	(	PUNCT
ejde-397	1271	58	λ−	λ−	PROPN
ejde-397	1271	59	ω)g(λ	ω)g(λ	PROPN
ejde-397	1271	60	)	)	PUNCT
ejde-397	1271	61	(	(	PUNCT
ejde-397	1271	62	i	i	PRON
ejde-397	1271	63	−	−	PROPN
ejde-397	1271	64	â(λ)c−1ac	â(λ)c−1ac	PUNCT
ejde-397	1271	65	)	)	PUNCT
ejde-397	1271	66	−1	−1	NOUN
ejde-397	1271	67	c	c	NOUN
ejde-397	1271	68	:	:	PUNCT
ejde-397	1271	69	λ	λ	PROPN
ejde-397	1271	70	∈	∈	NOUN
ejde-397	1271	71	n1	n1	NOUN
ejde-397	1271	72	∩	∩	NOUN
ejde-397	1271	73	(	(	PUNCT
ejde-397	1271	74	ω	ω	NOUN
ejde-397	1271	75	+	+	CCONJ
ejde-397	1271	76	σπ	σπ	PROPN
ejde-397	1271	77	2	2	NUM
ejde-397	1271	78	+	+	NOUN
ejde-397	1271	79	γ1	γ1	NOUN
ejde-397	1271	80	)	)	PUNCT
ejde-397	1271	81	}	}	PUNCT
ejde-397	1271	82	⊆	⊆	NUM
ejde-397	1271	83	l(x	l(x	PROPN
ejde-397	1271	84	)	)	PUNCT
ejde-397	1271	85	is	be	AUX
ejde-397	1271	86	equicontinuous	equicontinuous	ADJ
ejde-397	1271	87	for	for	ADP
ejde-397	1271	88	every	every	DET
ejde-397	1271	89	angle	angle	NOUN
ejde-397	1271	90	γ1	γ1	PROPN
ejde-397	1271	91	∈	∈	PROPN
ejde-397	1271	92	(	(	PUNCT
ejde-397	1271	93	0	0	NUM
ejde-397	1271	94	,	,	PUNCT
ejde-397	1271	95	α	α	NOUN
ejde-397	1271	96	)	)	PUNCT
ejde-397	1271	97	,	,	PUNCT
ejde-397	1271	98	the	the	DET
ejde-397	1271	99	mapping	mapping	NOUN
ejde-397	1271	100	λ	λ	X
ejde-397	1271	101	7→	7→	NUM
ejde-397	1271	102	(	(	PUNCT
ejde-397	1271	103	i	i	PRON
ejde-397	1271	104	−	−	PROPN
ejde-397	1271	105	â(λ)c−1ac	â(λ)c−1ac	NUM
ejde-397	1271	106	)	)	PUNCT
ejde-397	1271	107	−1	−1	NOUN
ejde-397	1271	108	cx	cx	NOUN
ejde-397	1271	109	,	,	PUNCT
ejde-397	1271	110	λ	λ	PROPN
ejde-397	1271	111	∈	∈	NOUN
ejde-397	1271	112	n1	n1	NOUN
ejde-397	1271	113	is	be	AUX
ejde-397	1271	114	analytic	analytic	ADJ
ejde-397	1271	115	for	for	ADP
ejde-397	1271	116	every	every	DET
ejde-397	1271	117	x	x	SYM
ejde-397	1271	118	∈	∈	PROPN
ejde-397	1271	119	x	x	NOUN
ejde-397	1271	120	,	,	PUNCT
ejde-397	1271	121	and	and	CCONJ
ejde-397	1271	122	lim	lim	PROPN
ejde-397	1271	123	λ→+∞,ã(λ)k̃(λ)6=0	λ→+∞,ã(λ)k̃(λ)6=0	PROPN
ejde-397	1271	124	λk̃(λ	λk̃(λ	PROPN
ejde-397	1271	125	)	)	PUNCT
ejde-397	1271	126	(	(	PUNCT
ejde-397	1271	127	i	i	PRON
ejde-397	1271	128	−	−	VERB
ejde-397	1271	129	ã(λ)a	ã(λ)a	ADP
ejde-397	1271	130	)	)	PUNCT
ejde-397	1271	131	−1	−1	NOUN
ejde-397	1271	132	cx	cx	NOUN
ejde-397	1271	133	=	=	SYM
ejde-397	1271	134	r(0)x	r(0)x	PROPN
ejde-397	1271	135	,	,	PUNCT
ejde-397	1271	136	x	x	SYM
ejde-397	1271	137	∈	∈	NOUN
ejde-397	1271	138	x.	x.	NOUN
ejde-397	1271	139	keeping	keep	VERB
ejde-397	1271	140	in	in	ADP
ejde-397	1271	141	mind	mind	NOUN
ejde-397	1271	142	lemma	lemma	PROPN
ejde-397	1271	143	2.2	2.2	NUM
ejde-397	1271	144	,	,	PUNCT
ejde-397	1271	145	theorem	theorem	VERB
ejde-397	1271	146	2.3	2.3	NUM
ejde-397	1271	147	and	and	CCONJ
ejde-397	1271	148	theorem	theorem	VERB
ejde-397	1271	149	5.5	5.5	NUM
ejde-397	1271	150	,	,	PUNCT
ejde-397	1271	151	we	we	PRON
ejde-397	1271	152	can	can	AUX
ejde-397	1271	153	repeat	repeat	VERB
ejde-397	1271	154	almost	almost	ADV
ejde-397	1271	155	literally	literally	ADV
ejde-397	1271	156	the	the	DET
ejde-397	1271	157	proof	proof	NOUN
ejde-397	1271	158	of	of	ADP
ejde-397	1271	159	[	[	X
ejde-397	1271	160	36	36	NUM
ejde-397	1271	161	,	,	PUNCT
ejde-397	1271	162	theorem	theorem	VERB
ejde-397	1271	163	2.2.5	2.2.5	NUM
ejde-397	1271	164	]	]	PUNCT
ejde-397	1271	165	in	in	ADP
ejde-397	1271	166	order	order	NOUN
ejde-397	1271	167	to	to	PART
ejde-397	1271	168	see	see	VERB
ejde-397	1271	169	that	that	SCONJ
ejde-397	1271	170	the	the	DET
ejde-397	1271	171	following	follow	VERB
ejde-397	1271	172	result	result	NOUN
ejde-397	1271	173	holds	hold	VERB
ejde-397	1271	174	.	.	PUNCT
ejde-397	1272	1	theorem	theorem	NOUN
ejde-397	1272	2	5.19	5.19	NUM
ejde-397	1272	3	.	.	PUNCT
ejde-397	1273	1	assume	assume	VERB
ejde-397	1273	2	that	that	SCONJ
ejde-397	1273	3	a	a	PRON
ejde-397	1273	4	is	be	AUX
ejde-397	1273	5	a	a	DET
ejde-397	1273	6	closed	closed	ADJ
ejde-397	1273	7	mlo	mlo	NOUN
ejde-397	1273	8	in	in	ADP
ejde-397	1273	9	x	x	NOUN
ejde-397	1273	10	,	,	PUNCT
ejde-397	1273	11	ca	ca	PROPN
ejde-397	1273	12	⊆	⊆	NUM
ejde-397	1273	13	ac	ac	PROPN
ejde-397	1273	14	,	,	PUNCT
ejde-397	1273	15	α	α	PROPN
ejde-397	1273	16	∈	∈	PROPN
ejde-397	1273	17	(	(	PUNCT
ejde-397	1273	18	0	0	NUM
ejde-397	1273	19	,	,	PUNCT
ejde-397	1273	20	π/2	π/2	NUM
ejde-397	1273	21	]	]	PUNCT
ejde-397	1273	22	,	,	PUNCT
ejde-397	1273	23	abs(k	abs(k	PROPN
ejde-397	1273	24	)	)	PUNCT
ejde-397	1273	25	<	<	X
ejde-397	1273	26	∞	∞	PROPN
ejde-397	1273	27	,	,	PUNCT
ejde-397	1273	28	abs(|a|	abs(|a|	ADJ
ejde-397	1273	29	)	)	PUNCT
ejde-397	1273	30	<	<	X
ejde-397	1273	31	∞	∞	NUM
ejde-397	1273	32	and	and	CCONJ
ejde-397	1273	33	ω	ω	NUM
ejde-397	1273	34	≥	≥	NOUN
ejde-397	1273	35	max(0	max(0	NOUN
ejde-397	1273	36	,	,	PUNCT
ejde-397	1273	37	abs(k	abs(k	PROPN
ejde-397	1273	38	)	)	PUNCT
ejde-397	1273	39	,	,	PUNCT
ejde-397	1273	40	abs(|a|	abs(|a|	ADJ
ejde-397	1273	41	)	)	PUNCT
ejde-397	1273	42	)	)	PUNCT
ejde-397	1273	43	.	.	PUNCT
ejde-397	1274	1	assume	assume	VERB
ejde-397	1274	2	,	,	PUNCT
ejde-397	1274	3	further	far	ADV
ejde-397	1274	4	,	,	PUNCT
ejde-397	1274	5	that	that	SCONJ
ejde-397	1274	6	for	for	ADP
ejde-397	1274	7	every	every	DET
ejde-397	1274	8	λ	λ	PROPN
ejde-397	1274	9	∈	∈	PROPN
ejde-397	1274	10	c	c	NOUN
ejde-397	1274	11	with	with	ADP
ejde-397	1274	12	<	<	X
ejde-397	1274	13	λ	λ	X
ejde-397	1274	14	>	>	X
ejde-397	1274	15	ω	ω	PROPN
ejde-397	1274	16	and	and	CCONJ
ejde-397	1274	17	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1274	18	)	)	PUNCT
ejde-397	1274	19	6=	6=	ADP
ejde-397	1274	20	0	0	NUM
ejde-397	1274	21	,	,	PUNCT
ejde-397	1274	22	the	the	DET
ejde-397	1274	23	operator	operator	NOUN
ejde-397	1274	24	i	i	PRON
ejde-397	1274	25	−	−	VERB
ejde-397	1274	26	ã(λ)a	ã(λ)a	ADP
ejde-397	1274	27	is	be	AUX
ejde-397	1274	28	injective	injective	ADJ
ejde-397	1274	29	with	with	ADP
ejde-397	1274	30	r(c	r(c	ADJ
ejde-397	1274	31	)	)	PUNCT
ejde-397	1274	32	⊆	⊆	NUM
ejde-397	1274	33	r(i	r(i	PROPN
ejde-397	1274	34	−	−	PROPN
ejde-397	1274	35	ã(λ)a	ã(λ)a	NUM
ejde-397	1274	36	)	)	PUNCT
ejde-397	1274	37	.	.	PUNCT
ejde-397	1275	1	if	if	SCONJ
ejde-397	1275	2	there	there	PRON
ejde-397	1275	3	exist	exist	VERB
ejde-397	1275	4	a	a	DET
ejde-397	1275	5	function	function	NOUN
ejde-397	1275	6	q	q	NOUN
ejde-397	1275	7	:	:	PUNCT
ejde-397	1275	8	ω	ω	NOUN
ejde-397	1275	9	+	+	CCONJ
ejde-397	1275	10	σπ	σπ	PROPN
ejde-397	1275	11	2	2	NUM
ejde-397	1275	12	+	+	PROPN
ejde-397	1275	13	α	α	NOUN
ejde-397	1275	14	→	→	SYM
ejde-397	1275	15	l(x	l(x	PROPN
ejde-397	1275	16	)	)	PUNCT
ejde-397	1275	17	and	and	CCONJ
ejde-397	1275	18	an	an	DET
ejde-397	1275	19	operator	operator	NOUN
ejde-397	1275	20	d	d	PROPN
ejde-397	1275	21	∈	∈	PROPN
ejde-397	1275	22	l(x	l(x	PROPN
ejde-397	1275	23	)	)	PUNCT
ejde-397	1275	24	such	such	ADJ
ejde-397	1275	25	that	that	SCONJ
ejde-397	1275	26	,	,	PUNCT
ejde-397	1275	27	for	for	ADP
ejde-397	1275	28	every	every	DET
ejde-397	1275	29	x	x	SYM
ejde-397	1275	30	∈	∈	PROPN
ejde-397	1275	31	x	x	NOUN
ejde-397	1275	32	,	,	PUNCT
ejde-397	1275	33	the	the	DET
ejde-397	1275	34	mapping	mapping	NOUN
ejde-397	1275	35	λ	λ	PROPN
ejde-397	1275	36	7→	7→	PROPN
ejde-397	1275	37	q(λ)x	q(λ)x	PROPN
ejde-397	1275	38	,	,	PUNCT
ejde-397	1275	39	λ	λ	PROPN
ejde-397	1275	40	∈	∈	PROPN
ejde-397	1275	41	ω	ω	NOUN
ejde-397	1276	1	+	+	CCONJ
ejde-397	1276	2	σπ	σπ	PROPN
ejde-397	1276	3	2	2	NUM
ejde-397	1276	4	+	+	NOUN
ejde-397	1276	5	α	α	NOUN
ejde-397	1276	6	is	be	AUX
ejde-397	1276	7	analytic	analytic	ADJ
ejde-397	1276	8	as	as	ADV
ejde-397	1276	9	well	well	ADV
ejde-397	1276	10	as	as	ADP
ejde-397	1276	11	that	that	PRON
ejde-397	1276	12	q(λ)x	q(λ)x	PROPN
ejde-397	1276	13	=	=	PROPN
ejde-397	1276	14	k̃(λ	k̃(λ	PROPN
ejde-397	1276	15	)	)	PUNCT
ejde-397	1277	1	(	(	PUNCT
ejde-397	1277	2	i	i	PRON
ejde-397	1277	3	−	−	VERB
ejde-397	1277	4	ã(λ)a	ã(λ)a	ADP
ejde-397	1277	5	)	)	PUNCT
ejde-397	1277	6	−1	−1	NOUN
ejde-397	1277	7	cx	cx	NOUN
ejde-397	1277	8	,	,	PUNCT
ejde-397	1277	9	<	<	X
ejde-397	1277	10	λ	λ	X
ejde-397	1277	11	>	>	X
ejde-397	1277	12	ω	ω	PROPN
ejde-397	1277	13	,	,	PUNCT
ejde-397	1277	14	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1277	15	)	)	PUNCT
ejde-397	1277	16	6=	6=	ADP
ejde-397	1277	17	0	0	NUM
ejde-397	1277	18	,	,	PUNCT
ejde-397	1277	19	x	x	SYM
ejde-397	1277	20	∈	∈	NOUN
ejde-397	1277	21	x	x	NOUN
ejde-397	1277	22	,	,	PUNCT
ejde-397	1277	23	for	for	ADP
ejde-397	1277	24	every	every	DET
ejde-397	1277	25	γ	γ	X
ejde-397	1277	26	∈	∈	PROPN
ejde-397	1277	27	(	(	PUNCT
ejde-397	1277	28	0	0	NUM
ejde-397	1277	29	,	,	PUNCT
ejde-397	1277	30	α	α	NOUN
ejde-397	1277	31	)	)	PUNCT
ejde-397	1277	32	,	,	PUNCT
ejde-397	1277	33	the	the	DET
ejde-397	1277	34	family	family	NOUN
ejde-397	1277	35	{	{	PUNCT
ejde-397	1277	36	(	(	PUNCT
ejde-397	1277	37	λ	λ	X
ejde-397	1277	38	−	−	NOUN
ejde-397	1277	39	ω)q(λ	ω)q(λ	NUM
ejde-397	1277	40	)	)	PUNCT
ejde-397	1277	41	:	:	PUNCT
ejde-397	1277	42	λ	λ	X
ejde-397	1277	43	∈	∈	PROPN
ejde-397	1277	44	ω	ω	NOUN
ejde-397	1277	45	+	+	CCONJ
ejde-397	1277	46	σπ	σπ	PROPN
ejde-397	1277	47	2	2	NUM
ejde-397	1277	48	+	+	NOUN
ejde-397	1277	49	γ	γ	NOUN
ejde-397	1277	50	}	}	PUNCT
ejde-397	1277	51	⊆	⊆	NUM
ejde-397	1277	52	l(x	l(x	PROPN
ejde-397	1277	53	)	)	PUNCT
ejde-397	1277	54	is	be	AUX
ejde-397	1277	55	equicontinuous	equicontinuous	ADJ
ejde-397	1277	56	and	and	CCONJ
ejde-397	1277	57	lim	lim	PROPN
ejde-397	1277	58	λ→+∞	λ→+∞	PROPN
ejde-397	1277	59	λq(λ)x	λq(λ)x	PROPN
ejde-397	1277	60	=	=	SYM
ejde-397	1277	61	dx	dx	PROPN
ejde-397	1277	62	,	,	PUNCT
ejde-397	1277	63	x	x	X
ejde-397	1277	64	∈	∈	NOUN
ejde-397	1277	65	x	x	SYM
ejde-397	1277	66	,	,	PUNCT
ejde-397	1277	67	if	if	SCONJ
ejde-397	1277	68	d(a	d(a	PROPN
ejde-397	1277	69	)	)	PUNCT
ejde-397	1277	70	6=	6=	PUNCT
ejde-397	1278	1	x	x	SYM
ejde-397	1278	2	,	,	PUNCT
ejde-397	1278	3	then	then	ADV
ejde-397	1278	4	a	a	PRON
ejde-397	1278	5	is	be	AUX
ejde-397	1278	6	a	a	DET
ejde-397	1278	7	subgenerator	subgenerator	NOUN
ejde-397	1278	8	of	of	ADP
ejde-397	1278	9	an	an	DET
ejde-397	1278	10	exponentially	exponentially	ADV
ejde-397	1278	11	equicontinuous	equicontinuous	ADJ
ejde-397	1278	12	,	,	PUNCT
ejde-397	1278	13	analytic	analytic	ADJ
ejde-397	1278	14	(	(	PUNCT
ejde-397	1278	15	a	a	PRON
ejde-397	1278	16	,	,	PUNCT
ejde-397	1278	17	k)-regularized	k)-regularize	VERB
ejde-397	1278	18	c	c	NOUN
ejde-397	1278	19	-	-	PUNCT
ejde-397	1278	20	resolvent	resolvent	ADJ
ejde-397	1278	21	family	family	NOUN
ejde-397	1278	22	(	(	PUNCT
ejde-397	1278	23	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	1278	24	of	of	ADP
ejde-397	1278	25	angle	angle	NOUN
ejde-397	1278	26	α	α	PROPN
ejde-397	1278	27	satisfying	satisfy	VERB
ejde-397	1279	1	that	that	SCONJ
ejde-397	1279	2	r(z)a	r(z)a	ADP
ejde-397	1279	3	⊆	⊆	NUM
ejde-397	1279	4	ar(z	ar(z	NUM
ejde-397	1279	5	)	)	PUNCT
ejde-397	1279	6	,	,	PUNCT
ejde-397	1279	7	z	z	PROPN
ejde-397	1279	8	∈	∈	PROPN
ejde-397	1279	9	σα	σα	PROPN
ejde-397	1279	10	,	,	PUNCT
ejde-397	1279	11	the	the	DET
ejde-397	1279	12	family	family	NOUN
ejde-397	1279	13	{	{	PUNCT
ejde-397	1279	14	e−ωzr(z	e−ωzr(z	PROPN
ejde-397	1279	15	)	)	PUNCT
ejde-397	1279	16	:	:	PUNCT
ejde-397	1279	17	z	z	X
ejde-397	1279	18	∈	∈	PROPN
ejde-397	1279	19	σγ	σγ	PROPN
ejde-397	1279	20	}	}	PUNCT
ejde-397	1279	21	⊆	⊆	NUM
ejde-397	1279	22	l(x	l(x	PROPN
ejde-397	1279	23	)	)	PUNCT
ejde-397	1279	24	is	be	AUX
ejde-397	1279	25	equicontinuous	equicontinuous	ADJ
ejde-397	1279	26	for	for	ADP
ejde-397	1279	27	all	all	DET
ejde-397	1279	28	angles	angle	NOUN
ejde-397	1279	29	γ	γ	X
ejde-397	1279	30	∈	∈	PROPN
ejde-397	1279	31	(	(	PUNCT
ejde-397	1279	32	0	0	NUM
ejde-397	1279	33	,	,	PUNCT
ejde-397	1279	34	α	α	NOUN
ejde-397	1279	35	)	)	PUNCT
ejde-397	1279	36	,	,	PUNCT
ejde-397	1279	37	as	as	ADV
ejde-397	1279	38	well	well	ADV
ejde-397	1279	39	as	as	ADP
ejde-397	1279	40	that	that	DET
ejde-397	1279	41	equation	equation	NOUN
ejde-397	1279	42	(	(	PUNCT
ejde-397	1279	43	5.1	5.1	NUM
ejde-397	1279	44	)	)	PUNCT
ejde-397	1279	45	holds	hold	VERB
ejde-397	1279	46	for	for	ADP
ejde-397	1279	47	each	each	PRON
ejde-397	1279	48	y	y	NOUN
ejde-397	1279	49	=	=	PUNCT
ejde-397	1279	50	x	x	SYM
ejde-397	1279	51	∈	∈	PROPN
ejde-397	1279	52	x	x	NOUN
ejde-397	1279	53	,	,	PUNCT
ejde-397	1279	54	with	with	ADP
ejde-397	1279	55	r1	r1	PROPN
ejde-397	1279	56	(	(	PUNCT
ejde-397	1279	57	·	·	PUNCT
ejde-397	1279	58	)	)	PUNCT
ejde-397	1279	59	and	and	CCONJ
ejde-397	1279	60	c1	c1	PROPN
ejde-397	1279	61	replaced	replace	VERB
ejde-397	1279	62	therein	therein	ADV
ejde-397	1279	63	by	by	ADP
ejde-397	1279	64	r	r	NOUN
ejde-397	1279	65	(	(	PUNCT
ejde-397	1279	66	·	·	PUNCT
ejde-397	1279	67	)	)	PUNCT
ejde-397	1279	68	and	and	CCONJ
ejde-397	1279	69	c	c	NOUN
ejde-397	1279	70	,	,	PUNCT
ejde-397	1279	71	respectively	respectively	ADV
ejde-397	1279	72	.	.	PUNCT
ejde-397	1280	1	42	42	NUM
ejde-397	1280	2	m.	m.	NOUN
ejde-397	1280	3	kostić	kostić	PUNCT
ejde-397	1280	4	ejde-2023/63	ejde-2023/63	PROPN
ejde-397	1280	5	suppose	suppose	VERB
ejde-397	1280	6	that	that	SCONJ
ejde-397	1280	7	∅	∅	NOUN
ejde-397	1280	8	6=	6=	ADP
ejde-397	1280	9	ω	ω	PROPN
ejde-397	1280	10	⊆	⊆	NUM
ejde-397	1280	11	rn	rn	NOUN
ejde-397	1280	12	is	be	AUX
ejde-397	1280	13	a	a	DET
ejde-397	1280	14	bounded	bounded	ADJ
ejde-397	1280	15	domain	domain	NOUN
ejde-397	1280	16	with	with	ADP
ejde-397	1280	17	smooth	smooth	ADJ
ejde-397	1280	18	boundary	boundary	NOUN
ejde-397	1280	19	.	.	PUNCT
ejde-397	1281	1	as	as	SCONJ
ejde-397	1281	2	explained	explain	VERB
ejde-397	1281	3	by	by	ADP
ejde-397	1281	4	falaleev	falaleev	NOUN
ejde-397	1281	5	and	and	CCONJ
ejde-397	1281	6	orlov	orlov	NOUN
ejde-397	1281	7	in	in	ADP
ejde-397	1281	8	[	[	X
ejde-397	1281	9	16	16	NUM
ejde-397	1281	10	]	]	PUNCT
ejde-397	1281	11	,	,	PUNCT
ejde-397	1281	12	the	the	DET
ejde-397	1281	13	equation	equation	NOUN
ejde-397	1281	14	(	(	PUNCT
ejde-397	1281	15	α−∆)utt	α−∆)utt	NUM
ejde-397	1281	16	=	=	SYM
ejde-397	1281	17	β∆ut	β∆ut	NOUN
ejde-397	1281	18	+	+	NUM
ejde-397	1281	19	∆u+	∆u+	NOUN
ejde-397	1281	20	∫	∫	PROPN
ejde-397	1281	21	t	t	PROPN
ejde-397	1281	22	0	0	NUM
ejde-397	1281	23	g(t−	g(t−	PROPN
ejde-397	1281	24	s)∆u(s	s)∆u(s	ADJ
ejde-397	1281	25	,	,	PUNCT
ejde-397	1281	26	x	x	X
ejde-397	1281	27	)	)	PUNCT
ejde-397	1281	28	ds	ds	PROPN
ejde-397	1281	29	,	,	PUNCT
ejde-397	1281	30	t	t	X
ejde-397	1281	31	>	>	X
ejde-397	1281	32	0	0	PROPN
ejde-397	1281	33	,	,	PUNCT
ejde-397	1281	34	x	x	X
ejde-397	1281	35	∈	∈	PROPN
ejde-397	1281	36	ω	ω	PROPN
ejde-397	1281	37	;	;	PUNCT
ejde-397	1281	38	u(0	u(0	PROPN
ejde-397	1281	39	,	,	PUNCT
ejde-397	1281	40	x	x	NOUN
ejde-397	1281	41	)	)	PUNCT
ejde-397	1281	42	=	=	SYM
ejde-397	1281	43	φ(x	φ(x	NOUN
ejde-397	1281	44	)	)	PUNCT
ejde-397	1281	45	,	,	PUNCT
ejde-397	1281	46	ut(0	ut(0	PROPN
ejde-397	1281	47	,	,	PUNCT
ejde-397	1281	48	x	x	NOUN
ejde-397	1281	49	)	)	PUNCT
ejde-397	1281	50	=	=	SYM
ejde-397	1281	51	ψ(x	ψ(x	NOUN
ejde-397	1281	52	)	)	PUNCT
ejde-397	1281	53	,	,	PUNCT
ejde-397	1281	54	(	(	PUNCT
ejde-397	1281	55	5.27	5.27	NUM
ejde-397	1281	56	)	)	PUNCT
ejde-397	1281	57	where	where	SCONJ
ejde-397	1281	58	g	g	PROPN
ejde-397	1281	59	∈	∈	PROPN
ejde-397	1281	60	l1	l1	PROPN
ejde-397	1281	61	loc([0,∞	loc([0,∞	PROPN
ejde-397	1281	62	)	)	PUNCT
ejde-397	1281	63	)	)	PUNCT
ejde-397	1281	64	,	,	PUNCT
ejde-397	1281	65	α	α	PROPN
ejde-397	1281	66	∈	∈	NOUN
ejde-397	1281	67	r	r	NOUN
ejde-397	1281	68	and	and	CCONJ
ejde-397	1281	69	β	β	X
ejde-397	1281	70	∈	∈	PROPN
ejde-397	1281	71	r\{0	r\{0	PROPN
ejde-397	1281	72	}	}	PUNCT
ejde-397	1281	73	,	,	PUNCT
ejde-397	1281	74	appears	appear	VERB
ejde-397	1281	75	in	in	ADP
ejde-397	1281	76	some	some	DET
ejde-397	1281	77	models	model	NOUN
ejde-397	1281	78	of	of	ADP
ejde-397	1281	79	nonlinear	nonlinear	ADJ
ejde-397	1281	80	viscoelasticity	viscoelasticity	NOUN
ejde-397	1281	81	provided	provide	VERB
ejde-397	1281	82	that	that	SCONJ
ejde-397	1281	83	n	n	NOUN
ejde-397	1281	84	=	=	SYM
ejde-397	1281	85	3	3	X
ejde-397	1281	86	.	.	PUNCT
ejde-397	1282	1	in	in	ADP
ejde-397	1282	2	the	the	DET
ejde-397	1282	3	following	follow	VERB
ejde-397	1282	4	illustrative	illustrative	ADJ
ejde-397	1282	5	example	example	NOUN
ejde-397	1282	6	,	,	PUNCT
ejde-397	1282	7	we	we	PRON
ejde-397	1282	8	will	will	AUX
ejde-397	1282	9	consider	consider	VERB
ejde-397	1282	10	the	the	DET
ejde-397	1282	11	well	well	NOUN
ejde-397	1282	12	-	-	PUNCT
ejde-397	1282	13	posedness	posedness	NOUN
ejde-397	1282	14	of	of	ADP
ejde-397	1282	15	equation	equation	NOUN
ejde-397	1282	16	(	(	PUNCT
ejde-397	1282	17	5.27	5.27	NUM
ejde-397	1282	18	)	)	PUNCT
ejde-397	1282	19	following	follow	VERB
ejde-397	1282	20	the	the	DET
ejde-397	1282	21	approaches	approach	NOUN
ejde-397	1282	22	from	from	ADP
ejde-397	1282	23	[	[	X
ejde-397	1282	24	42	42	NUM
ejde-397	1282	25	]	]	PUNCT
ejde-397	1282	26	and	and	CCONJ
ejde-397	1282	27	this	this	DET
ejde-397	1282	28	article	article	NOUN
ejde-397	1282	29	.	.	PUNCT
ejde-397	1282	30	example	example	NOUN
ejde-397	1282	31	5.20	5.20	NUM
ejde-397	1282	32	.	.	PUNCT
ejde-397	1283	1	let	let	VERB
ejde-397	1283	2	∆	∆	PROPN
ejde-397	1283	3	be	be	AUX
ejde-397	1283	4	the	the	DET
ejde-397	1283	5	dirichlet	dirichlet	PROPN
ejde-397	1283	6	laplacian	laplacian	NOUN
ejde-397	1283	7	in	in	ADP
ejde-397	1283	8	x	x	X
ejde-397	1283	9	:	:	PUNCT
ejde-397	1283	10	=	=	SYM
ejde-397	1283	11	l2(ω	l2(ω	NOUN
ejde-397	1283	12	)	)	PUNCT
ejde-397	1283	13	,	,	PUNCT
ejde-397	1283	14	acting	act	VERB
ejde-397	1283	15	with	with	ADP
ejde-397	1283	16	domain	domain	NOUN
ejde-397	1283	17	h2(ω	h2(ω	NOUN
ejde-397	1283	18	)	)	PUNCT
ejde-397	1283	19	∩	∩	NOUN
ejde-397	1283	20	h1	h1	NOUN
ejde-397	1283	21	0	0	NUM
ejde-397	1283	22	(	(	PUNCT
ejde-397	1283	23	ω	ω	NOUN
ejde-397	1283	24	)	)	PUNCT
ejde-397	1283	25	.	.	PUNCT
ejde-397	1284	1	as	as	ADP
ejde-397	1284	2	in	in	ADP
ejde-397	1284	3	example	example	NOUN
ejde-397	1284	4	5.17	5.17	NUM
ejde-397	1284	5	,	,	PUNCT
ejde-397	1284	6	we	we	PRON
ejde-397	1284	7	will	will	AUX
ejde-397	1284	8	denote	denote	VERB
ejde-397	1284	9	by	by	ADP
ejde-397	1284	10	{	{	PUNCT
ejde-397	1284	11	λk	λk	NOUN
ejde-397	1284	12	}	}	PUNCT
ejde-397	1284	13	[=	[=	X
ejde-397	1284	14	σ(∆	σ(∆	PROPN
ejde-397	1284	15	)	)	PUNCT
ejde-397	1284	16	]	]	PUNCT
ejde-397	1285	1	the	the	DET
ejde-397	1285	2	eigenvalues	eigenvalue	NOUN
ejde-397	1285	3	of	of	ADP
ejde-397	1285	4	∆	∆	PROPN
ejde-397	1285	5	in	in	ADP
ejde-397	1285	6	l2(ω	l2(ω	NOUN
ejde-397	1285	7	)	)	PUNCT
ejde-397	1285	8	numbered	number	VERB
ejde-397	1285	9	in	in	ADP
ejde-397	1285	10	nonascending	nonascende	VERB
ejde-397	1285	11	order	order	NOUN
ejde-397	1285	12	with	with	ADP
ejde-397	1285	13	regard	regard	NOUN
ejde-397	1285	14	to	to	ADP
ejde-397	1285	15	multiplicities	multiplicity	NOUN
ejde-397	1285	16	;	;	PUNCT
ejde-397	1285	17	{	{	PUNCT
ejde-397	1285	18	φk	φk	ADP
ejde-397	1285	19	}	}	PUNCT
ejde-397	1285	20	⊆	⊆	NUM
ejde-397	1285	21	c∞(ω	c∞(ω	NOUN
ejde-397	1285	22	)	)	PUNCT
ejde-397	1285	23	denotes	denote	VERB
ejde-397	1285	24	the	the	DET
ejde-397	1285	25	corresponding	correspond	VERB
ejde-397	1285	26	set	set	NOUN
ejde-397	1285	27	of	of	ADP
ejde-397	1285	28	mutually	mutually	ADV
ejde-397	1285	29	orthogonal	orthogonal	ADJ
ejde-397	1285	30	eigenfunctions	eigenfunction	NOUN
ejde-397	1285	31	.	.	PUNCT
ejde-397	1286	1	integrating	integrate	VERB
ejde-397	1286	2	(	(	PUNCT
ejde-397	1286	3	5.27	5.27	NUM
ejde-397	1286	4	)	)	PUNCT
ejde-397	1286	5	twice	twice	ADV
ejde-397	1286	6	with	with	ADP
ejde-397	1286	7	the	the	DET
ejde-397	1286	8	respect	respect	NOUN
ejde-397	1286	9	to	to	ADP
ejde-397	1286	10	the	the	DET
ejde-397	1286	11	time	time	NOUN
ejde-397	1286	12	-	-	PUNCT
ejde-397	1286	13	variable	variable	NOUN
ejde-397	1286	14	t	t	PROPN
ejde-397	1286	15	,	,	PUNCT
ejde-397	1286	16	we	we	PRON
ejde-397	1286	17	obtain	obtain	VERB
ejde-397	1286	18	the	the	DET
ejde-397	1286	19	associated	associated	ADJ
ejde-397	1286	20	integral	integral	ADJ
ejde-397	1286	21	equation	equation	NOUN
ejde-397	1286	22	(	(	PUNCT
ejde-397	1286	23	α−∆)u(t	α−∆)u(t	PROPN
ejde-397	1286	24	)	)	PUNCT
ejde-397	1286	25	=	=	SYM
ejde-397	1286	26	(	(	PUNCT
ejde-397	1286	27	α+	α+	X
ejde-397	1286	28	(	(	PUNCT
ejde-397	1286	29	β	β	NOUN
ejde-397	1286	30	−	−	NOUN
ejde-397	1286	31	1)∆)φ(x	1)∆)φ(x	NUM
ejde-397	1286	32	)	)	PUNCT
ejde-397	1286	33	+	+	NUM
ejde-397	1286	34	t(α−∆)ψ	t(α−∆)ψ	NUM
ejde-397	1286	35	+	+	CCONJ
ejde-397	1286	36	β∆	β∆	NUM
ejde-397	1286	37	(	(	PUNCT
ejde-397	1286	38	g1	g1	PROPN
ejde-397	1286	39	∗	∗	NOUN
ejde-397	1286	40	u	u	NOUN
ejde-397	1286	41	)	)	PUNCT
ejde-397	1286	42	(	(	PUNCT
ejde-397	1286	43	t	t	PROPN
ejde-397	1286	44	)	)	PUNCT
ejde-397	1286	45	+	+	CCONJ
ejde-397	1287	1	∆	∆	PROPN
ejde-397	1288	1	(	(	PUNCT
ejde-397	1288	2	g2	g2	PROPN
ejde-397	1288	3	∗	∗	NOUN
ejde-397	1288	4	u	u	PROPN
ejde-397	1288	5	)	)	PUNCT
ejde-397	1288	6	(	(	PUNCT
ejde-397	1288	7	t	t	PROPN
ejde-397	1288	8	)	)	PUNCT
ejde-397	1288	9	+	+	CCONJ
ejde-397	1288	10	∆	∆	PROPN
ejde-397	1288	11	(	(	PUNCT
ejde-397	1288	12	g2	g2	PROPN
ejde-397	1288	13	∗	∗	VERB
ejde-397	1288	14	g	g	PROPN
ejde-397	1288	15	∗	∗	X
ejde-397	1288	16	u	u	NOUN
ejde-397	1288	17	)	)	PUNCT
ejde-397	1288	18	(	(	PUNCT
ejde-397	1288	19	t	t	PROPN
ejde-397	1288	20	)	)	PUNCT
ejde-397	1288	21	,	,	PUNCT
ejde-397	1288	22	t	t	PROPN
ejde-397	1288	23	≥	≥	PROPN
ejde-397	1288	24	0	0	NUM
ejde-397	1288	25	.	.	PUNCT
ejde-397	1289	1	(	(	PUNCT
ejde-397	1289	2	5.28	5.28	NUM
ejde-397	1289	3	)	)	PUNCT
ejde-397	1289	4	set	set	NOUN
ejde-397	1289	5	b	b	NOUN
ejde-397	1289	6	:	:	PUNCT
ejde-397	1289	7	=	=	SYM
ejde-397	1289	8	α	α	NOUN
ejde-397	1289	9	−	−	NOUN
ejde-397	1289	10	∆	∆	PROPN
ejde-397	1289	11	,	,	PUNCT
ejde-397	1289	12	a2	a2	PROPN
ejde-397	1289	13	:	:	PUNCT
ejde-397	1289	14	=	=	SYM
ejde-397	1289	15	β∆	β∆	ADJ
ejde-397	1289	16	,	,	PUNCT
ejde-397	1289	17	a1	a1	NOUN
ejde-397	1289	18	=	=	SYM
ejde-397	1289	19	a0	a0	NOUN
ejde-397	1289	20	:	:	PUNCT
ejde-397	1289	21	=	=	SYM
ejde-397	1289	22	∆	∆	PROPN
ejde-397	1289	23	(	(	PUNCT
ejde-397	1289	24	acting	act	VERB
ejde-397	1289	25	with	with	ADP
ejde-397	1289	26	the	the	DET
ejde-397	1289	27	dirichlet	dirichlet	PROPN
ejde-397	1289	28	boundary	boundary	PROPN
ejde-397	1289	29	conditions	condition	NOUN
ejde-397	1289	30	)	)	PUNCT
ejde-397	1289	31	,	,	PUNCT
ejde-397	1289	32	a2(t	a2(t	PROPN
ejde-397	1289	33	)	)	PUNCT
ejde-397	1289	34	:	:	PUNCT
ejde-397	1289	35	=	=	PUNCT
ejde-397	1289	36	g1(t	g1(t	NOUN
ejde-397	1289	37	)	)	PUNCT
ejde-397	1289	38	,	,	PUNCT
ejde-397	1289	39	a1(t	a1(t	PROPN
ejde-397	1289	40	)	)	PUNCT
ejde-397	1289	41	:	:	PUNCT
ejde-397	1289	42	=	=	SYM
ejde-397	1289	43	g2(t	g2(t	NOUN
ejde-397	1289	44	)	)	PUNCT
ejde-397	1289	45	,	,	PUNCT
ejde-397	1289	46	a0(t	a0(t	PROPN
ejde-397	1289	47	)	)	PUNCT
ejde-397	1289	48	:	:	PUNCT
ejde-397	1289	49	=	=	SYM
ejde-397	1289	50	(	(	PUNCT
ejde-397	1289	51	g2	g2	PROPN
ejde-397	1289	52	∗	∗	PROPN
ejde-397	1289	53	g)(t	g)(t	PROPN
ejde-397	1289	54	)	)	PUNCT
ejde-397	1289	55	,	,	PUNCT
ejde-397	1289	56	and	and	CCONJ
ejde-397	1289	57	pλ	pλ	INTJ
ejde-397	1289	58	:	:	PUNCT
ejde-397	1289	59	=	=	SYM
ejde-397	1289	60	λ2	λ2	NOUN
ejde-397	1289	61	+	+	CCONJ
ejde-397	1289	62	βλ+	βλ+	ADJ
ejde-397	1289	63	g̃(λ	g̃(λ	NOUN
ejde-397	1289	64	)	)	PUNCT
ejde-397	1289	65	+	+	CCONJ
ejde-397	1289	66	1	1	NUM
ejde-397	1289	67	λ2	λ2	NOUN
ejde-397	1289	68	[	[	PUNCT
ejde-397	1289	69	αλ2	αλ2	NOUN
ejde-397	1289	70	λ2	λ2	NOUN
ejde-397	1289	71	+	+	CCONJ
ejde-397	1289	72	βλ+	βλ+	ADJ
ejde-397	1289	73	g̃(λ	g̃(λ	NOUN
ejde-397	1289	74	)	)	PUNCT
ejde-397	1289	75	+	+	CCONJ
ejde-397	1289	76	1	1	NUM
ejde-397	1289	77	−∆	−∆	NOUN
ejde-397	1289	78	]	]	PUNCT
ejde-397	1289	79	.	.	PUNCT
ejde-397	1289	80	suppose	suppose	VERB
ejde-397	1289	81	that	that	SCONJ
ejde-397	1289	82	α	α	NOUN
ejde-397	1289	83	=	=	NOUN
ejde-397	1289	84	λk0	λk0	NOUN
ejde-397	1289	85	∈	∈	PROPN
ejde-397	1289	86	σ(∆	σ(∆	PROPN
ejde-397	1289	87	)	)	PUNCT
ejde-397	1289	88	for	for	ADP
ejde-397	1289	89	some	some	DET
ejde-397	1289	90	k0	k0	PROPN
ejde-397	1289	91	∈	∈	PROPN
ejde-397	1289	92	n	n	CCONJ
ejde-397	1289	93	and	and	CCONJ
ejde-397	1289	94	the	the	DET
ejde-397	1289	95	function	function	NOUN
ejde-397	1289	96	g(t	g(t	PROPN
ejde-397	1289	97	)	)	PUNCT
ejde-397	1289	98	is	be	AUX
ejde-397	1289	99	laplace	laplace	NOUN
ejde-397	1289	100	transformable	transformable	ADJ
ejde-397	1289	101	(	(	PUNCT
ejde-397	1289	102	in	in	ADP
ejde-397	1289	103	[	[	X
ejde-397	1289	104	42	42	NUM
ejde-397	1289	105	,	,	PUNCT
ejde-397	1289	106	example	example	NOUN
ejde-397	1289	107	3.15	3.15	NUM
ejde-397	1289	108	]	]	PUNCT
ejde-397	1289	109	,	,	PUNCT
ejde-397	1289	110	we	we	PRON
ejde-397	1289	111	have	have	AUX
ejde-397	1289	112	considered	consider	VERB
ejde-397	1289	113	the	the	DET
ejde-397	1289	114	case	case	NOUN
ejde-397	1289	115	α	α	X
ejde-397	1289	116	>	>	X
ejde-397	1289	117	0	0	NUM
ejde-397	1289	118	,	,	PUNCT
ejde-397	1289	119	with	with	ADP
ejde-397	1289	120	the	the	DET
ejde-397	1289	121	state	state	NOUN
ejde-397	1289	122	space	space	NOUN
ejde-397	1289	123	being	be	AUX
ejde-397	1289	124	lp(ω	lp(ω	PRON
ejde-397	1289	125	)	)	PUNCT
ejde-397	1289	126	for	for	ADP
ejde-397	1289	127	some	some	DET
ejde-397	1289	128	1	1	NUM
ejde-397	1289	129	≤	≤	NOUN
ejde-397	1289	130	p	p	X
ejde-397	1289	131	<	<	X
ejde-397	1289	132	∞	∞	PROPN
ejde-397	1289	133	)	)	PUNCT
ejde-397	1289	134	.	.	PUNCT
ejde-397	1290	1	then	then	ADV
ejde-397	1290	2	there	there	PRON
ejde-397	1290	3	exist	exist	VERB
ejde-397	1290	4	constants	constant	NOUN
ejde-397	1290	5	m	m	VERB
ejde-397	1290	6	≥	≥	NOUN
ejde-397	1290	7	1	1	NUM
ejde-397	1290	8	and	and	CCONJ
ejde-397	1290	9	ω	ω	NUM
ejde-397	1290	10	≥	≥	NOUN
ejde-397	1290	11	0	0	NUM
ejde-397	1290	12	such	such	ADJ
ejde-397	1290	13	that	that	SCONJ
ejde-397	1290	14	|	|	ADV
ejde-397	1290	15	∫	∫	PROPN
ejde-397	1290	16	t	t	PROPN
ejde-397	1290	17	0	0	NUM
ejde-397	1290	18	g(s	g(s	PROPN
ejde-397	1290	19	)	)	PUNCT
ejde-397	1290	20	ds|	ds|	NOUN
ejde-397	1290	21	≤meωt	≤meωt	PROPN
ejde-397	1290	22	,	,	PUNCT
ejde-397	1290	23	t	t	PROPN
ejde-397	1290	24	≥	≥	NOUN
ejde-397	1290	25	0	0	NUM
ejde-397	1291	1	and	and	CCONJ
ejde-397	1291	2	λ	λ	X
ejde-397	1291	3	∫	∫	PROPN
ejde-397	1291	4	∞	∞	PROPN
ejde-397	1291	5	0	0	PROPN
ejde-397	1291	6	e−λt	e−λt	PROPN
ejde-397	1291	7	∫	∫	PROPN
ejde-397	1291	8	t	t	PROPN
ejde-397	1291	9	0	0	NUM
ejde-397	1291	10	g(s	g(s	PROPN
ejde-397	1291	11	)	)	PUNCT
ejde-397	1291	12	ds	ds	ADJ
ejde-397	1291	13	dt	dt	NOUN
ejde-397	1291	14	=	=	SYM
ejde-397	1291	15	∫	∫	PROPN
ejde-397	1291	16	∞	∞	PROPN
ejde-397	1291	17	0	0	NUM
ejde-397	1292	1	e−λtg(t	e−λtg(t	NUM
ejde-397	1292	2	)	)	PUNCT
ejde-397	1293	1	dt	dt	NOUN
ejde-397	1293	2	,	,	PUNCT
ejde-397	1293	3	and	and	CCONJ
ejde-397	1293	4	λ	λ	X
ejde-397	1293	5	>	>	X
ejde-397	1293	6	ω	ω	PROPN
ejde-397	1293	7	,	,	PUNCT
ejde-397	1293	8	which	which	PRON
ejde-397	1293	9	simply	simply	ADV
ejde-397	1293	10	implies	imply	VERB
ejde-397	1293	11	that	that	SCONJ
ejde-397	1293	12	the	the	DET
ejde-397	1293	13	set	set	NOUN
ejde-397	1293	14	{	{	PUNCT
ejde-397	1293	15	g̃(λ	g̃(λ	PROPN
ejde-397	1293	16	)	)	PUNCT
ejde-397	1293	17	:	:	PUNCT
ejde-397	1294	1	λ	λ	X
ejde-397	1294	2	>	>	X
ejde-397	1294	3	ω	ω	PROPN
ejde-397	1294	4	+	+	CCONJ
ejde-397	1294	5	1	1	NUM
ejde-397	1294	6	}	}	PUNCT
ejde-397	1294	7	is	be	AUX
ejde-397	1294	8	bounded	bound	VERB
ejde-397	1294	9	.	.	PUNCT
ejde-397	1295	1	define	define	VERB
ejde-397	1295	2	d	d	PROPN
ejde-397	1295	3	:	:	PUNCT
ejde-397	1295	4	l2(ω)→	l2(ω)→	PROPN
ejde-397	1295	5	l2(ω	l2(ω	PROPN
ejde-397	1295	6	)	)	PUNCT
ejde-397	1295	7	by	by	ADP
ejde-397	1295	8	df	df	NOUN
ejde-397	1295	9	:	:	PUNCT
ejde-397	1295	10	=	=	SYM
ejde-397	1295	11	(	(	PUNCT
ejde-397	1295	12	−1)β−1	−1)β−1	NOUN
ejde-397	1295	13	∑∞	∑∞	NOUN
ejde-397	1295	14	k=1〈φk	k=1〈φk	NOUN
ejde-397	1295	15	,	,	PUNCT
ejde-397	1295	16	f〉φk	f〉φk	PROPN
ejde-397	1295	17	,	,	PUNCT
ejde-397	1295	18	f	f	PROPN
ejde-397	1295	19	∈	∈	PROPN
ejde-397	1295	20	l2(ω	l2(ω	PROPN
ejde-397	1295	21	)	)	PUNCT
ejde-397	1295	22	.	.	PUNCT
ejde-397	1296	1	using	use	VERB
ejde-397	1296	2	parseval	parseval	NOUN
ejde-397	1296	3	’s	’s	PART
ejde-397	1296	4	equality	equality	NOUN
ejde-397	1296	5	,	,	PUNCT
ejde-397	1296	6	it	it	PRON
ejde-397	1296	7	can	can	AUX
ejde-397	1296	8	be	be	AUX
ejde-397	1296	9	simply	simply	ADV
ejde-397	1296	10	verified	verify	VERB
ejde-397	1296	11	that	that	SCONJ
ejde-397	1296	12	d	d	X
ejde-397	1296	13	,	,	PUNCT
ejde-397	1296	14	bd	bd	PROPN
ejde-397	1296	15	∈	∈	PROPN
ejde-397	1296	16	l(l2(ω	l(l2(ω	PROPN
ejde-397	1296	17	)	)	PUNCT
ejde-397	1296	18	)	)	PUNCT
ejde-397	1296	19	;	;	PUNCT
ejde-397	1297	1	furthermore	furthermore	ADV
ejde-397	1297	2	,	,	PUNCT
ejde-397	1297	3	‖r(λ	‖r(λ	NUM
ejde-397	1297	4	:	:	PUNCT
ejde-397	1297	5	∆)‖	∆)‖	PROPN
ejde-397	1297	6	=	=	SYM
ejde-397	1297	7	o	o	PROPN
ejde-397	1297	8	(	(	PUNCT
ejde-397	1297	9	|α	|α	NOUN
ejde-397	1297	10	−	−	NOUN
ejde-397	1297	11	λ|−1	λ|−1	NOUN
ejde-397	1297	12	)	)	PUNCT
ejde-397	1297	13	as	as	ADP
ejde-397	1297	14	λ	λ	PROPN
ejde-397	1297	15	→	→	SYM
ejde-397	1297	16	α	α	PROPN
ejde-397	1297	17	(	(	PUNCT
ejde-397	1297	18	see	see	VERB
ejde-397	1297	19	[	[	X
ejde-397	1297	20	44	44	NUM
ejde-397	1297	21	,	,	PUNCT
ejde-397	1297	22	example	example	NOUN
ejde-397	1297	23	,	,	PUNCT
ejde-397	1297	24	pp	pp	ADJ
ejde-397	1297	25	.	.	PUNCT
ejde-397	1298	1	57	57	NUM
ejde-397	1298	2	-	-	SYM
ejde-397	1298	3	58	58	NUM
ejde-397	1298	4	]	]	PUNCT
ejde-397	1298	5	)	)	PUNCT
ejde-397	1298	6	.	.	PUNCT
ejde-397	1299	1	using	use	VERB
ejde-397	1299	2	the	the	DET
ejde-397	1299	3	resolvent	resolvent	ADJ
ejde-397	1299	4	equation	equation	NOUN
ejde-397	1299	5	and	and	CCONJ
ejde-397	1299	6	these	these	DET
ejde-397	1299	7	facts	fact	NOUN
ejde-397	1299	8	,	,	PUNCT
ejde-397	1299	9	we	we	PRON
ejde-397	1299	10	obtain	obtain	VERB
ejde-397	1299	11	the	the	DET
ejde-397	1299	12	existence	existence	NOUN
ejde-397	1299	13	of	of	ADP
ejde-397	1299	14	a	a	DET
ejde-397	1299	15	sufficiently	sufficiently	ADV
ejde-397	1299	16	large	large	ADJ
ejde-397	1299	17	real	real	ADJ
ejde-397	1299	18	number	number	NOUN
ejde-397	1299	19	r	r	NOUN
ejde-397	1299	20	>	>	X
ejde-397	1299	21	0	0	NUM
ejde-397	1300	1	such	such	ADJ
ejde-397	1300	2	that	that	SCONJ
ejde-397	1300	3	p−1	p−1	PROPN
ejde-397	1300	4	λ	λ	PROPN
ejde-397	1300	5	∈	∈	PROPN
ejde-397	1300	6	l(l2(ω	l(l2(ω	PROPN
ejde-397	1300	7	)	)	PUNCT
ejde-397	1300	8	)	)	PUNCT
ejde-397	1300	9	for	for	ADP
ejde-397	1300	10	|λ|	|λ|	PROPN
ejde-397	1300	11	≥	≥	PRON
ejde-397	1300	12	r	r	NOUN
ejde-397	1300	13	,	,	PUNCT
ejde-397	1300	14	as	as	ADV
ejde-397	1300	15	well	well	ADV
ejde-397	1300	16	as	as	ADP
ejde-397	1300	17	that	that	DET
ejde-397	1300	18	|λ|−2	|λ|−2	NUM
ejde-397	1300	19	[	[	PUNCT
ejde-397	1300	20	‖p−1	‖p−1	PUNCT
ejde-397	1300	21	λ	λ	PROPN
ejde-397	1300	22	‖+	‖+	PROPN
ejde-397	1300	23	‖bp−1	‖bp−1	PROPN
ejde-397	1300	24	λ	λ	PROPN
ejde-397	1300	25	‖+	‖+	PROPN
ejde-397	1300	26	2∑	2∑	NUM
ejde-397	1300	27	j=0	j=0	VERB
ejde-397	1300	28	‖ãj(λ)ajp−1	‖ãj(λ)ajp−1	PRON
ejde-397	1300	29	λ	λ	PROPN
ejde-397	1300	30	‖	‖	PROPN
ejde-397	1300	31	]	]	X
ejde-397	1300	32	≤m	≤m	PROPN
ejde-397	1300	33	,	,	PUNCT
ejde-397	1300	34	|λ|	|λ|	NOUN
ejde-397	1300	35	≥	≥	NUM
ejde-397	1300	36	r	r	NOUN
ejde-397	1300	37	,	,	PUNCT
ejde-397	1300	38	lim	lim	PROPN
ejde-397	1300	39	|λ|→∞	|λ|→∞	NOUN
ejde-397	1301	1	λ−1p−1	λ−1p−1	PROPN
ejde-397	1301	2	λ	λ	X
ejde-397	1301	3	f	f	X
ejde-397	1301	4	=	=	SYM
ejde-397	1301	5	df	df	PROPN
ejde-397	1301	6	,	,	PUNCT
ejde-397	1301	7	lim	lim	PROPN
ejde-397	1301	8	|λ|→∞	|λ|→∞	PROPN
ejde-397	1302	1	λ−1bp−1	λ−1bp−1	PROPN
ejde-397	1302	2	λ	λ	X
ejde-397	1302	3	f	f	X
ejde-397	1302	4	=	=	SYM
ejde-397	1302	5	bdf	bdf	PROPN
ejde-397	1302	6	,	,	PUNCT
ejde-397	1302	7	lim	lim	PROPN
ejde-397	1302	8	|λ|→∞	|λ|→∞	NOUN
ejde-397	1303	1	λ−1ãj(λ)p−1	λ−1ãj(λ)p−1	PROPN
ejde-397	1303	2	λ	λ	X
ejde-397	1303	3	f	f	X
ejde-397	1303	4	=	=	SYM
ejde-397	1303	5	0	0	NUM
ejde-397	1303	6	,	,	PUNCT
ejde-397	1303	7	0	0	NUM
ejde-397	1303	8	≤	≤	NUM
ejde-397	1303	9	j	j	PROPN
ejde-397	1303	10	≤	≤	ADV
ejde-397	1303	11	2	2	NUM
ejde-397	1303	12	(	(	PUNCT
ejde-397	1303	13	f	f	PROPN
ejde-397	1303	14	∈	∈	PROPN
ejde-397	1303	15	l2(ω	l2(ω	PROPN
ejde-397	1303	16	)	)	PUNCT
ejde-397	1303	17	)	)	PUNCT
ejde-397	1303	18	.	.	PUNCT
ejde-397	1304	1	(	(	PUNCT
ejde-397	1304	2	5.29	5.29	NUM
ejde-397	1304	3	)	)	PUNCT
ejde-397	1304	4	using	use	VERB
ejde-397	1304	5	[	[	X
ejde-397	1304	6	42	42	NUM
ejde-397	1304	7	,	,	PUNCT
ejde-397	1304	8	theorem	theorem	VERB
ejde-397	1304	9	3.9	3.9	NUM
ejde-397	1304	10	]	]	PUNCT
ejde-397	1304	11	,	,	PUNCT
ejde-397	1304	12	we	we	PRON
ejde-397	1304	13	obtain	obtain	VERB
ejde-397	1304	14	that	that	SCONJ
ejde-397	1304	15	there	there	PRON
ejde-397	1304	16	exists	exist	VERB
ejde-397	1304	17	an	an	DET
ejde-397	1304	18	exponentially	exponentially	ADV
ejde-397	1304	19	bounded	bound	VERB
ejde-397	1304	20	once	once	ADV
ejde-397	1304	21	integrated	integrate	VERB
ejde-397	1304	22	i	i	PROPN
ejde-397	1304	23	-	-	PUNCT
ejde-397	1304	24	existence	existence	NOUN
ejde-397	1304	25	family	family	NOUN
ejde-397	1304	26	(	(	PUNCT
ejde-397	1304	27	e1(t))t≥0	e1(t))t≥0	X
ejde-397	1304	28	for	for	ADP
ejde-397	1304	29	(	(	PUNCT
ejde-397	1304	30	5.28	5.28	NUM
ejde-397	1304	31	)	)	PUNCT
ejde-397	1304	32	,	,	PUNCT
ejde-397	1304	33	in	in	ADP
ejde-397	1304	34	the	the	DET
ejde-397	1304	35	sense	sense	NOUN
ejde-397	1304	36	of	of	ADP
ejde-397	1304	37	[	[	X
ejde-397	1304	38	42	42	NUM
ejde-397	1304	39	,	,	PUNCT
ejde-397	1304	40	definition	definition	NOUN
ejde-397	1304	41	3.8(i	3.8(i	NUM
ejde-397	1304	42	)	)	PUNCT
ejde-397	1304	43	]	]	PUNCT
ejde-397	1304	44	,	,	PUNCT
ejde-397	1304	45	satisfying	satisfy	VERB
ejde-397	1304	46	additionally	additionally	ADV
ejde-397	1304	47	that	that	SCONJ
ejde-397	1304	48	for	for	ADP
ejde-397	1304	49	each	each	DET
ejde-397	1304	50	f	f	PROPN
ejde-397	1304	51	∈	∈	PROPN
ejde-397	1304	52	l2(ω	l2(ω	PROPN
ejde-397	1304	53	)	)	PUNCT
ejde-397	1304	54	the	the	DET
ejde-397	1304	55	mappings	mapping	NOUN
ejde-397	1304	56	t	t	X
ejde-397	1304	57	7→	7→	NUM
ejde-397	1304	58	e1(t)f	e1(t)f	PROPN
ejde-397	1304	59	,	,	PUNCT
ejde-397	1304	60	t	t	PROPN
ejde-397	1304	61	>	>	X
ejde-397	1304	62	0	0	PROPN
ejde-397	1304	63	,	,	PUNCT
ejde-397	1304	64	t	t	NOUN
ejde-397	1304	65	7→	7→	NUM
ejde-397	1304	66	be1(t)f	be1(t)f	PROPN
ejde-397	1304	67	,	,	PUNCT
ejde-397	1304	68	t	t	PROPN
ejde-397	1304	69	>	>	X
ejde-397	1304	70	0	0	PUNCT
ejde-397	1305	1	and	and	CCONJ
ejde-397	1305	2	t	t	PROPN
ejde-397	1305	3	7→	7→	NUM
ejde-397	1305	4	aj(aj	aj(aj	PROPN
ejde-397	1305	5	∗	∗	NOUN
ejde-397	1305	6	e1)(t)f	e1)(t)f	PROPN
ejde-397	1305	7	,	,	PUNCT
ejde-397	1305	8	t	t	PROPN
ejde-397	1305	9	>	>	X
ejde-397	1305	10	0	0	NUM
ejde-397	1305	11	can	can	AUX
ejde-397	1305	12	be	be	AUX
ejde-397	1305	13	analytically	analytically	ADV
ejde-397	1305	14	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1305	15	abstract	abstract	ADJ
ejde-397	1305	16	degenerate	degenerate	ADJ
ejde-397	1305	17	volterra	volterra	NOUN
ejde-397	1305	18	inclusions	inclusion	NOUN
ejde-397	1305	19	43	43	NUM
ejde-397	1305	20	extended	extend	VERB
ejde-397	1305	21	to	to	ADP
ejde-397	1305	22	the	the	DET
ejde-397	1305	23	sector	sector	NOUN
ejde-397	1305	24	σπ/2	σπ/2	NOUN
ejde-397	1305	25	;	;	PUNCT
ejde-397	1305	26	furthermore	furthermore	ADV
ejde-397	1305	27	,	,	PUNCT
ejde-397	1305	28	(	(	PUNCT
ejde-397	1305	29	e1(t))t≥0	e1(t))t≥0	PROPN
ejde-397	1305	30	is	be	AUX
ejde-397	1305	31	an	an	DET
ejde-397	1305	32	exponentially	exponentially	ADV
ejde-397	1305	33	bounded	bound	VERB
ejde-397	1305	34	once	once	ADV
ejde-397	1305	35	integrated	integrate	VERB
ejde-397	1305	36	i	i	NOUN
ejde-397	1305	37	-	-	PUNCT
ejde-397	1305	38	uniqueness	uniqueness	PROPN
ejde-397	1305	39	family	family	NOUN
ejde-397	1305	40	for	for	ADP
ejde-397	1305	41	(	(	PUNCT
ejde-397	1305	42	5.28	5.28	NUM
ejde-397	1305	43	)	)	PUNCT
ejde-397	1305	44	,	,	PUNCT
ejde-397	1305	45	in	in	ADP
ejde-397	1305	46	the	the	DET
ejde-397	1305	47	sense	sense	NOUN
ejde-397	1305	48	of	of	ADP
ejde-397	1305	49	[	[	X
ejde-397	1305	50	42	42	NUM
ejde-397	1305	51	,	,	PUNCT
ejde-397	1305	52	definition	definition	NOUN
ejde-397	1305	53	3.8(ii	3.8(ii	NUM
ejde-397	1305	54	)	)	PUNCT
ejde-397	1305	55	]	]	PUNCT
ejde-397	1305	56	.	.	PUNCT
ejde-397	1306	1	therefore	therefore	ADV
ejde-397	1306	2	,	,	PUNCT
ejde-397	1306	3	for	for	ADP
ejde-397	1306	4	every	every	DET
ejde-397	1306	5	φ	φ	PROPN
ejde-397	1306	6	,	,	PUNCT
ejde-397	1306	7	ψ	ψ	PROPN
ejde-397	1306	8	∈	∈	PROPN
ejde-397	1306	9	h2(ω	h2(ω	NOUN
ejde-397	1306	10	)	)	PUNCT
ejde-397	1306	11	∩h1	∩h1	NOUN
ejde-397	1306	12	0	0	NUM
ejde-397	1306	13	(	(	PUNCT
ejde-397	1306	14	ω	ω	NOUN
ejde-397	1306	15	)	)	PUNCT
ejde-397	1306	16	,	,	PUNCT
ejde-397	1306	17	there	there	PRON
ejde-397	1306	18	exists	exist	VERB
ejde-397	1306	19	a	a	DET
ejde-397	1306	20	unique	unique	ADJ
ejde-397	1306	21	strong	strong	ADJ
ejde-397	1306	22	solution	solution	NOUN
ejde-397	1306	23	of	of	ADP
ejde-397	1306	24	the	the	DET
ejde-397	1306	25	associated	associate	VERB
ejde-397	1306	26	once	once	ADV
ejde-397	1306	27	integrated	integrate	VERB
ejde-397	1306	28	problem	problem	NOUN
ejde-397	1306	29	(	(	PUNCT
ejde-397	1306	30	5.28	5.28	NUM
ejde-397	1306	31	)	)	PUNCT
ejde-397	1306	32	(	(	PUNCT
ejde-397	1306	33	α−∆)u(t	α−∆)u(t	PROPN
ejde-397	1306	34	)	)	PUNCT
ejde-397	1306	35	=	=	SYM
ejde-397	1306	36	t(α+	t(α+	PRON
ejde-397	1306	37	(	(	PUNCT
ejde-397	1306	38	β	β	NOUN
ejde-397	1306	39	−	−	NOUN
ejde-397	1306	40	1)∆)φ(x	1)∆)φ(x	NUM
ejde-397	1306	41	)	)	PUNCT
ejde-397	1307	1	+	+	CCONJ
ejde-397	1307	2	t2	t2	NOUN
ejde-397	1307	3	2	2	NUM
ejde-397	1307	4	(	(	PUNCT
ejde-397	1307	5	α−∆)ψ	α−∆)ψ	NOUN
ejde-397	1307	6	+	+	CCONJ
ejde-397	1307	7	β∆	β∆	ADJ
ejde-397	1307	8	(	(	PUNCT
ejde-397	1307	9	g1	g1	PROPN
ejde-397	1307	10	∗	∗	NOUN
ejde-397	1307	11	u	u	NOUN
ejde-397	1307	12	)	)	PUNCT
ejde-397	1307	13	(	(	PUNCT
ejde-397	1307	14	t	t	PROPN
ejde-397	1307	15	)	)	PUNCT
ejde-397	1307	16	+	+	CCONJ
ejde-397	1307	17	∆	∆	PROPN
ejde-397	1307	18	(	(	PUNCT
ejde-397	1307	19	g2	g2	PROPN
ejde-397	1307	20	∗	∗	NOUN
ejde-397	1307	21	u	u	PROPN
ejde-397	1307	22	)	)	PUNCT
ejde-397	1307	23	(	(	PUNCT
ejde-397	1307	24	t	t	PROPN
ejde-397	1307	25	)	)	PUNCT
ejde-397	1307	26	+	+	CCONJ
ejde-397	1307	27	∆	∆	PROPN
ejde-397	1307	28	(	(	PUNCT
ejde-397	1307	29	g2	g2	PROPN
ejde-397	1307	30	∗	∗	VERB
ejde-397	1307	31	g	g	PROPN
ejde-397	1307	32	∗	∗	X
ejde-397	1307	33	u	u	NOUN
ejde-397	1307	34	)	)	PUNCT
ejde-397	1307	35	(	(	PUNCT
ejde-397	1307	36	t	t	PROPN
ejde-397	1307	37	)	)	PUNCT
ejde-397	1307	38	,	,	PUNCT
ejde-397	1307	39	t	t	PROPN
ejde-397	1307	40	≥	≥	NUM
ejde-397	1307	41	0	0	NUM
ejde-397	1307	42	,	,	PUNCT
ejde-397	1307	43	(	(	PUNCT
ejde-397	1307	44	5.30	5.30	NUM
ejde-397	1307	45	)	)	PUNCT
ejde-397	1307	46	given	give	VERB
ejde-397	1307	47	by	by	ADP
ejde-397	1307	48	u(t	u(t	NOUN
ejde-397	1307	49	)	)	PUNCT
ejde-397	1307	50	=	=	PUNCT
ejde-397	1307	51	e1(t)(α+	e1(t)(α+	PROPN
ejde-397	1307	52	(	(	PUNCT
ejde-397	1307	53	β	β	NOUN
ejde-397	1307	54	−	−	PROPN
ejde-397	1307	55	1)∆)φ+	1)∆)φ+	NUM
ejde-397	1307	56	∫	∫	PROPN
ejde-397	1307	57	t	t	PROPN
ejde-397	1307	58	0	0	NUM
ejde-397	1307	59	e1(s)(α−∆)ψ	e1(s)(α−∆)ψ	PROPN
ejde-397	1307	60	ds	ds	PROPN
ejde-397	1307	61	,	,	PUNCT
ejde-397	1307	62	t	t	PROPN
ejde-397	1307	63	≥	≥	NOUN
ejde-397	1307	64	0	0	NUM
ejde-397	1307	65	.	.	PUNCT
ejde-397	1308	1	on	on	ADP
ejde-397	1308	2	the	the	DET
ejde-397	1308	3	other	other	ADJ
ejde-397	1308	4	hand	hand	NOUN
ejde-397	1308	5	,	,	PUNCT
ejde-397	1308	6	equation	equation	NOUN
ejde-397	1308	7	(	(	PUNCT
ejde-397	1308	8	5.29	5.29	NUM
ejde-397	1308	9	)	)	PUNCT
ejde-397	1308	10	taken	take	VERB
ejde-397	1308	11	together	together	ADV
ejde-397	1308	12	with	with	ADP
ejde-397	1308	13	the	the	DET
ejde-397	1308	14	equality	equality	NOUN
ejde-397	1308	15	lim|λ|→∞	lim|λ|→∞	NOUN
ejde-397	1308	16	λ−1bp−1	λ−1bp−1	PROPN
ejde-397	1308	17	λ	λ	X
ejde-397	1308	18	f	f	NOUN
ejde-397	1308	19	=	=	PUNCT
ejde-397	1308	20	bdf	bdf	NOUN
ejde-397	1308	21	,	,	PUNCT
ejde-397	1308	22	theorem	theorem	VERB
ejde-397	1308	23	5.19	5.19	NUM
ejde-397	1308	24	and	and	CCONJ
ejde-397	1308	25	remark	remark	NOUN
ejde-397	1308	26	4.2(v	4.2(v	NUM
ejde-397	1308	27	)	)	PUNCT
ejde-397	1308	28	implies	imply	VERB
ejde-397	1308	29	that	that	SCONJ
ejde-397	1308	30	for	for	ADP
ejde-397	1308	31	each	each	DET
ejde-397	1308	32	θ	θ	PROPN
ejde-397	1308	33	∈	∈	PROPN
ejde-397	1308	34	(	(	PUNCT
ejde-397	1308	35	−π	−π	PROPN
ejde-397	1308	36	,	,	PUNCT
ejde-397	1308	37	π	π	X
ejde-397	1308	38	]	]	X
ejde-397	1308	39	the	the	DET
ejde-397	1308	40	mlo	mlo	PROPN
ejde-397	1308	41	eiθab−1	eiθab−1	PROPN
ejde-397	1308	42	generates	generate	VERB
ejde-397	1308	43	an	an	DET
ejde-397	1308	44	exponentially	exponentially	ADV
ejde-397	1308	45	bounded	bound	VERB
ejde-397	1308	46	,	,	PUNCT
ejde-397	1308	47	analytic	analytic	ADJ
ejde-397	1308	48	once	once	ADV
ejde-397	1308	49	integrated	integrate	VERB
ejde-397	1308	50	(	(	PUNCT
ejde-397	1308	51	b	b	NOUN
ejde-397	1308	52	+	+	CCONJ
ejde-397	1308	53	g2(t	g2(t	NOUN
ejde-397	1308	54	)	)	PUNCT
ejde-397	1309	1	+	+	CCONJ
ejde-397	1309	2	(	(	PUNCT
ejde-397	1309	3	g2	g2	PROPN
ejde-397	1309	4	∗	∗	PROPN
ejde-397	1309	5	g)(t	g)(t	PROPN
ejde-397	1309	6	)	)	PUNCT
ejde-397	1309	7	,	,	PUNCT
ejde-397	1309	8	i)-regularized	i)-regularize	VERB
ejde-397	1309	9	resolvent	resolvent	ADJ
ejde-397	1309	10	family	family	NOUN
ejde-397	1309	11	(	(	PUNCT
ejde-397	1309	12	e1,b(t	e1,b(t	NOUN
ejde-397	1309	13	)	)	PUNCT
ejde-397	1309	14	≡	≡	PROPN
ejde-397	1309	15	be1(t))t≥0	be1(t))t≥0	PROPN
ejde-397	1309	16	of	of	ADP
ejde-397	1309	17	angle	angle	NOUN
ejde-397	1309	18	π/2	π/2	NUM
ejde-397	1309	19	.	.	PUNCT
ejde-397	1310	1	since	since	SCONJ
ejde-397	1310	2	[	[	X
ejde-397	1310	3	36	36	NUM
ejde-397	1310	4	,	,	PUNCT
ejde-397	1310	5	theorem	theorem	ADJ
ejde-397	1310	6	2.1.29(ii	2.1.29(ii	NOUN
ejde-397	1310	7	)	)	PUNCT
ejde-397	1310	8	]	]	PUNCT
ejde-397	1310	9	holds	hold	VERB
ejde-397	1310	10	in	in	ADP
ejde-397	1310	11	our	our	PRON
ejde-397	1310	12	framework	framework	NOUN
ejde-397	1310	13	,	,	PUNCT
ejde-397	1310	14	this	this	PRON
ejde-397	1310	15	immediately	immediately	ADV
ejde-397	1310	16	yields	yield	VERB
ejde-397	1310	17	some	some	DET
ejde-397	1310	18	results	result	NOUN
ejde-397	1310	19	on	on	ADP
ejde-397	1310	20	the	the	DET
ejde-397	1310	21	existence	existence	NOUN
ejde-397	1310	22	and	and	CCONJ
ejde-397	1310	23	uniqueness	uniqueness	NOUN
ejde-397	1310	24	of	of	ADP
ejde-397	1310	25	analytical	analytical	ADJ
ejde-397	1310	26	(	(	PUNCT
ejde-397	1310	27	possible	possible	ADJ
ejde-397	1310	28	,	,	PUNCT
ejde-397	1310	29	entire	entire	ADJ
ejde-397	1310	30	,	,	PUNCT
ejde-397	1310	31	cf	cf	NOUN
ejde-397	1310	32	.	.	PUNCT
ejde-397	1311	1	[	[	X
ejde-397	1311	2	44	44	NUM
ejde-397	1311	3	,	,	PUNCT
ejde-397	1311	4	theorem	theorem	VERB
ejde-397	1311	5	2.2	2.2	NUM
ejde-397	1311	6	]	]	PUNCT
ejde-397	1311	7	)	)	PUNCT
ejde-397	1311	8	solutions	solution	NOUN
ejde-397	1311	9	of	of	ADP
ejde-397	1311	10	the	the	DET
ejde-397	1311	11	problem	problem	NOUN
ejde-397	1311	12	(	(	PUNCT
ejde-397	1311	13	5.30	5.30	NUM
ejde-397	1311	14	)	)	PUNCT
ejde-397	1311	15	with	with	ADP
ejde-397	1311	16	the	the	DET
ejde-397	1311	17	term	term	NOUN
ejde-397	1311	18	t(α	t(α	PROPN
ejde-397	1311	19	+	+	CCONJ
ejde-397	1311	20	(	(	PUNCT
ejde-397	1311	21	β	β	NOUN
ejde-397	1311	22	−	−	PROPN
ejde-397	1311	23	1)∆)φ	1)∆)φ	NOUN
ejde-397	1312	1	+	+	CCONJ
ejde-397	1312	2	t2	t2	PROPN
ejde-397	1312	3	2	2	NUM
ejde-397	1312	4	(	(	PUNCT
ejde-397	1312	5	α−∆)ψ	α−∆)ψ	NOUN
ejde-397	1312	6	replaced	replace	VERB
ejde-397	1312	7	by	by	ADP
ejde-397	1312	8	a	a	DET
ejde-397	1312	9	general	general	ADJ
ejde-397	1312	10	inhomogeneity	inhomogeneity	NOUN
ejde-397	1312	11	f(t	f(t	PROPN
ejde-397	1312	12	)	)	PUNCT
ejde-397	1312	13	.	.	PUNCT
ejde-397	1313	1	the	the	DET
ejde-397	1313	2	classes	class	NOUN
ejde-397	1313	3	of	of	ADP
ejde-397	1313	4	exponentially	exponentially	ADV
ejde-397	1313	5	equicontinuous	equicontinuous	ADJ
ejde-397	1313	6	,	,	PUNCT
ejde-397	1313	7	analytic	analytic	ADJ
ejde-397	1313	8	(	(	PUNCT
ejde-397	1313	9	a	a	PRON
ejde-397	1313	10	,	,	PUNCT
ejde-397	1313	11	k)-regularized	k)-regularize	VERB
ejde-397	1313	12	c1	c1	NOUN
ejde-397	1313	13	-	-	PUNCT
ejde-397	1313	14	existence	existence	NOUN
ejde-397	1313	15	families	family	NOUN
ejde-397	1313	16	and	and	CCONJ
ejde-397	1313	17	(	(	PUNCT
ejde-397	1313	18	a	a	PRON
ejde-397	1313	19	,	,	PUNCT
ejde-397	1313	20	k)-regularized	k)-regularize	VERB
ejde-397	1313	21	c2	c2	PROPN
ejde-397	1313	22	-	-	PUNCT
ejde-397	1313	23	uniqueness	uniqueness	NOUN
ejde-397	1313	24	families	family	NOUN
ejde-397	1313	25	can	can	AUX
ejde-397	1313	26	be	be	AUX
ejde-397	1313	27	introduced	introduce	VERB
ejde-397	1313	28	and	and	CCONJ
ejde-397	1313	29	analyzed	analyze	VERB
ejde-397	1313	30	,	,	PUNCT
ejde-397	1313	31	as	as	ADV
ejde-397	1313	32	well	well	ADV
ejde-397	1313	33	.	.	PUNCT
ejde-397	1314	1	for	for	ADP
ejde-397	1314	2	the	the	DET
ejde-397	1314	3	sequel	sequel	NOUN
ejde-397	1314	4	,	,	PUNCT
ejde-397	1314	5	we	we	PRON
ejde-397	1314	6	need	need	VERB
ejde-397	1314	7	the	the	DET
ejde-397	1314	8	following	following	ADJ
ejde-397	1314	9	notion	notion	NOUN
ejde-397	1314	10	.	.	PUNCT
ejde-397	1315	1	definition	definition	NOUN
ejde-397	1315	2	5.21	5.21	NUM
ejde-397	1315	3	.	.	PUNCT
ejde-397	1316	1	let	let	VERB
ejde-397	1316	2	x	x	SYM
ejde-397	1316	3	=	=	PUNCT
ejde-397	1316	4	y	y	PROPN
ejde-397	1316	5	,	,	PUNCT
ejde-397	1316	6	and	and	CCONJ
ejde-397	1316	7	let	let	VERB
ejde-397	1316	8	a	a	PRON
ejde-397	1316	9	be	be	AUX
ejde-397	1316	10	a	a	DET
ejde-397	1316	11	subgenerator	subgenerator	NOUN
ejde-397	1316	12	of	of	ADP
ejde-397	1316	13	a	a	DET
ejde-397	1316	14	c1	c1	NOUN
ejde-397	1316	15	-	-	PUNCT
ejde-397	1316	16	existence	existence	NOUN
ejde-397	1316	17	family	family	NOUN
ejde-397	1316	18	(	(	PUNCT
ejde-397	1316	19	r1(t))t≥0	r1(t))t≥0	PROPN
ejde-397	1316	20	(	(	PUNCT
ejde-397	1316	21	cf	cf	NOUN
ejde-397	1316	22	.	.	PUNCT
ejde-397	1317	1	definition	definition	NOUN
ejde-397	1317	2	5.1(i	5.1(i	NUM
ejde-397	1317	3	)	)	PUNCT
ejde-397	1317	4	with	with	ADP
ejde-397	1317	5	a(t	a(t	NOUN
ejde-397	1317	6	)	)	PUNCT
ejde-397	1317	7	≡	≡	PROPN
ejde-397	1317	8	1	1	NUM
ejde-397	1317	9	and	and	CCONJ
ejde-397	1317	10	k(t	k(t	PROPN
ejde-397	1317	11	)	)	PUNCT
ejde-397	1317	12	≡	≡	PROPN
ejde-397	1317	13	1	1	NUM
ejde-397	1317	14	)	)	PUNCT
ejde-397	1317	15	.	.	PUNCT
ejde-397	1318	1	then	then	ADV
ejde-397	1318	2	(	(	PUNCT
ejde-397	1318	3	r1(t))t≥0	r1(t))t≥0	PROPN
ejde-397	1318	4	is	be	AUX
ejde-397	1318	5	said	say	VERB
ejde-397	1318	6	to	to	PART
ejde-397	1318	7	be	be	AUX
ejde-397	1318	8	entire	entire	ADJ
ejde-397	1318	9	if	if	SCONJ
ejde-397	1318	10	,	,	PUNCT
ejde-397	1318	11	for	for	ADP
ejde-397	1318	12	every	every	DET
ejde-397	1318	13	x	x	SYM
ejde-397	1318	14	∈	∈	PROPN
ejde-397	1318	15	x	x	NOUN
ejde-397	1318	16	,	,	PUNCT
ejde-397	1318	17	the	the	DET
ejde-397	1318	18	mapping	mapping	NOUN
ejde-397	1318	19	t	t	NOUN
ejde-397	1318	20	7→	7→	NUM
ejde-397	1318	21	r1(t)x	r1(t)x	NOUN
ejde-397	1318	22	,	,	PUNCT
ejde-397	1318	23	t	t	PROPN
ejde-397	1318	24	≥	≥	NOUN
ejde-397	1318	25	0	0	NUM
ejde-397	1318	26	can	can	AUX
ejde-397	1318	27	be	be	AUX
ejde-397	1318	28	analytically	analytically	ADV
ejde-397	1318	29	extended	extend	VERB
ejde-397	1318	30	to	to	ADP
ejde-397	1318	31	the	the	DET
ejde-397	1318	32	whole	whole	ADJ
ejde-397	1318	33	complex	complex	ADJ
ejde-397	1318	34	plane	plane	NOUN
ejde-397	1318	35	.	.	PUNCT
ejde-397	1319	1	using	use	VERB
ejde-397	1319	2	the	the	DET
ejde-397	1319	3	arguments	argument	NOUN
ejde-397	1319	4	in	in	ADP
ejde-397	1319	5	the	the	DET
ejde-397	1319	6	proof	proof	NOUN
ejde-397	1319	7	of	of	ADP
ejde-397	1319	8	[	[	X
ejde-397	1319	9	41	41	NUM
ejde-397	1319	10	,	,	PUNCT
ejde-397	1319	11	theorem	theorem	VERB
ejde-397	1319	12	3.15	3.15	NUM
ejde-397	1319	13	]	]	PUNCT
ejde-397	1319	14	,	,	PUNCT
ejde-397	1319	15	we	we	PRON
ejde-397	1319	16	can	can	AUX
ejde-397	1319	17	deduce	deduce	VERB
ejde-397	1319	18	the	the	DET
ejde-397	1319	19	following	follow	VERB
ejde-397	1319	20	result	result	NOUN
ejde-397	1319	21	.	.	PUNCT
ejde-397	1320	1	theorem	theorem	VERB
ejde-397	1320	2	5.22	5.22	NUM
ejde-397	1320	3	.	.	PUNCT
ejde-397	1321	1	suppose	suppose	VERB
ejde-397	1321	2	r	r	NOUN
ejde-397	1321	3	≥	≥	NOUN
ejde-397	1321	4	0	0	NUM
ejde-397	1321	5	,	,	PUNCT
ejde-397	1321	6	θ	θ	PROPN
ejde-397	1321	7	∈	∈	PROPN
ejde-397	1321	8	(	(	PUNCT
ejde-397	1321	9	0	0	NUM
ejde-397	1321	10	,	,	PUNCT
ejde-397	1321	11	π/2	π/2	NUM
ejde-397	1321	12	)	)	PUNCT
ejde-397	1321	13	,	,	PUNCT
ejde-397	1321	14	a	a	PRON
ejde-397	1321	15	is	be	AUX
ejde-397	1321	16	a	a	DET
ejde-397	1321	17	closed	closed	ADJ
ejde-397	1321	18	mlo	mlo	NOUN
ejde-397	1321	19	and	and	CCONJ
ejde-397	1321	20	−a	−a	NOUN
ejde-397	1321	21	is	be	AUX
ejde-397	1321	22	a	a	DET
ejde-397	1321	23	subgenerator	subgenerator	NOUN
ejde-397	1321	24	of	of	ADP
ejde-397	1321	25	an	an	DET
ejde-397	1321	26	exponentially	exponentially	ADV
ejde-397	1321	27	equicontinuous	equicontinuous	ADJ
ejde-397	1321	28	,	,	PUNCT
ejde-397	1321	29	analytic	analytic	ADJ
ejde-397	1321	30	r	r	NOUN
ejde-397	1321	31	-	-	PUNCT
ejde-397	1321	32	times	time	NOUN
ejde-397	1321	33	integrated	integrated	ADJ
ejde-397	1321	34	csemigroup	csemigroup	NOUN
ejde-397	1321	35	(	(	PUNCT
ejde-397	1321	36	sr(t))t≥0	sr(t))t≥0	PROPN
ejde-397	1321	37	of	of	ADP
ejde-397	1321	38	angle	angle	PROPN
ejde-397	1321	39	θ	θ	PROPN
ejde-397	1321	40	.	.	PUNCT
ejde-397	1322	1	then	then	ADV
ejde-397	1322	2	there	there	PRON
ejde-397	1322	3	exists	exist	VERB
ejde-397	1322	4	an	an	DET
ejde-397	1322	5	operator	operator	NOUN
ejde-397	1322	6	c1	c1	NOUN
ejde-397	1322	7	∈	∈	PROPN
ejde-397	1322	8	l(x	l(x	PROPN
ejde-397	1322	9	)	)	PUNCT
ejde-397	1322	10	such	such	ADJ
ejde-397	1322	11	that	that	SCONJ
ejde-397	1322	12	a	a	PRON
ejde-397	1322	13	is	be	AUX
ejde-397	1322	14	a	a	DET
ejde-397	1322	15	subgenerator	subgenerator	NOUN
ejde-397	1322	16	of	of	ADP
ejde-397	1322	17	an	an	DET
ejde-397	1322	18	entire	entire	ADJ
ejde-397	1322	19	c1	c1	NOUN
ejde-397	1322	20	-	-	PUNCT
ejde-397	1322	21	existence	existence	NOUN
ejde-397	1322	22	family	family	NOUN
ejde-397	1322	23	in	in	ADP
ejde-397	1322	24	x.	x.	PROPN
ejde-397	1322	25	remark	remark	PROPN
ejde-397	1322	26	5.23	5.23	NUM
ejde-397	1322	27	.	.	PUNCT
ejde-397	1323	1	(	(	PUNCT
ejde-397	1323	2	i	i	NOUN
ejde-397	1323	3	)	)	PUNCT
ejde-397	1323	4	it	it	PRON
ejde-397	1323	5	ought	ought	AUX
ejde-397	1323	6	to	to	PART
ejde-397	1323	7	be	be	AUX
ejde-397	1323	8	observed	observe	VERB
ejde-397	1323	9	that	that	SCONJ
ejde-397	1323	10	we	we	PRON
ejde-397	1323	11	do	do	AUX
ejde-397	1323	12	not	not	PART
ejde-397	1323	13	require	require	VERB
ejde-397	1323	14	the	the	DET
ejde-397	1323	15	injectivity	injectivity	NOUN
ejde-397	1323	16	of	of	ADP
ejde-397	1323	17	operator	operator	NOUN
ejde-397	1323	18	c1	c1	PROPN
ejde-397	1323	19	here	here	ADV
ejde-397	1323	20	.	.	PUNCT
ejde-397	1324	1	the	the	DET
ejde-397	1324	2	operators	operator	NOUN
ejde-397	1324	3	tα(z	tα(z	NOUN
ejde-397	1324	4	)	)	PUNCT
ejde-397	1324	5	and	and	CCONJ
ejde-397	1324	6	sα	sα	ADP
ejde-397	1324	7	,	,	PUNCT
ejde-397	1324	8	z0(z	z0(z	NUM
ejde-397	1324	9	)	)	PUNCT
ejde-397	1324	10	,	,	PUNCT
ejde-397	1324	11	appearing	appear	VERB
ejde-397	1324	12	in	in	ADP
ejde-397	1324	13	the	the	DET
ejde-397	1324	14	proof	proof	NOUN
ejde-397	1324	15	of	of	ADP
ejde-397	1324	16	[	[	X
ejde-397	1324	17	41	41	NUM
ejde-397	1324	18	,	,	PUNCT
ejde-397	1324	19	theorem	theorem	VERB
ejde-397	1324	20	3.15	3.15	NUM
ejde-397	1324	21	]	]	PUNCT
ejde-397	1324	22	,	,	PUNCT
ejde-397	1324	23	annulate	annulate	ADJ
ejde-397	1324	24	on	on	ADP
ejde-397	1324	25	the	the	DET
ejde-397	1324	26	subspace	subspace	PROPN
ejde-397	1324	27	a0	a0	PROPN
ejde-397	1324	28	.	.	PUNCT
ejde-397	1325	1	(	(	PUNCT
ejde-397	1325	2	ii	ii	NOUN
ejde-397	1325	3	)	)	PUNCT
ejde-397	1325	4	theorem	theorem	VERB
ejde-397	1325	5	5.22	5.22	NUM
ejde-397	1325	6	is	be	AUX
ejde-397	1325	7	closely	closely	ADV
ejde-397	1325	8	linked	link	VERB
ejde-397	1325	9	with	with	ADP
ejde-397	1325	10	the	the	DET
ejde-397	1325	11	assertions	assertion	NOUN
ejde-397	1325	12	of	of	ADP
ejde-397	1325	13	[	[	X
ejde-397	1325	14	40	40	NUM
ejde-397	1325	15	,	,	PUNCT
ejde-397	1325	16	theorem	theorem	VERB
ejde-397	1325	17	2.1	2.1	NUM
ejde-397	1325	18	,	,	PUNCT
ejde-397	1325	19	theorem	theorem	VERB
ejde-397	1325	20	2.2	2.2	NUM
ejde-397	1325	21	]	]	PUNCT
ejde-397	1325	22	.	.	PUNCT
ejde-397	1326	1	these	these	DET
ejde-397	1326	2	results	result	NOUN
ejde-397	1326	3	can	can	AUX
ejde-397	1326	4	be	be	AUX
ejde-397	1326	5	extended	extend	VERB
ejde-397	1326	6	to	to	ADP
ejde-397	1326	7	abstract	abstract	ADJ
ejde-397	1326	8	degenerate	degenerate	ADJ
ejde-397	1326	9	fractional	fractional	ADJ
ejde-397	1326	10	differential	differential	ADJ
ejde-397	1326	11	inclusions	inclusion	NOUN
ejde-397	1326	12	,	,	PUNCT
ejde-397	1326	13	as	as	ADV
ejde-397	1326	14	well	well	ADV
ejde-397	1326	15	.	.	PUNCT
ejde-397	1327	1	example	example	NOUN
ejde-397	1327	2	5.24	5.24	NUM
ejde-397	1327	3	.	.	PUNCT
ejde-397	1328	1	in	in	ADP
ejde-397	1328	2	a	a	DET
ejde-397	1328	3	great	great	ADJ
ejde-397	1328	4	number	number	NOUN
ejde-397	1328	5	of	of	ADP
ejde-397	1328	6	research	research	NOUN
ejde-397	1328	7	papers	paper	NOUN
ejde-397	1328	8	,	,	PUNCT
ejde-397	1328	9	many	many	ADJ
ejde-397	1328	10	authors	author	NOUN
ejde-397	1328	11	have	have	AUX
ejde-397	1328	12	considered	consider	VERB
ejde-397	1328	13	infinitely	infinitely	ADV
ejde-397	1328	14	differentiable	differentiable	ADJ
ejde-397	1328	15	semigroups	semigroup	NOUN
ejde-397	1328	16	generated	generate	VERB
ejde-397	1328	17	by	by	ADP
ejde-397	1328	18	multivalued	multivalued	ADJ
ejde-397	1328	19	linear	linear	ADJ
ejde-397	1328	20	operators	operator	NOUN
ejde-397	1328	21	of	of	ADP
ejde-397	1328	22	form	form	NOUN
ejde-397	1328	23	ab−1	ab−1	NOUN
ejde-397	1328	24	or	or	CCONJ
ejde-397	1328	25	b−1a	b−1a	ADV
ejde-397	1328	26	,	,	PUNCT
ejde-397	1328	27	where	where	SCONJ
ejde-397	1328	28	the	the	DET
ejde-397	1328	29	operators	operator	NOUN
ejde-397	1328	30	a	a	PRON
ejde-397	1328	31	and	and	CCONJ
ejde-397	1328	32	b	b	NOUN
ejde-397	1328	33	satisfy	satisfy	VERB
ejde-397	1328	34	the	the	DET
ejde-397	1328	35	condition	condition	NOUN
ejde-397	1328	36	[	[	X
ejde-397	1328	37	17	17	NUM
ejde-397	1328	38	,	,	PUNCT
ejde-397	1328	39	(	(	PUNCT
ejde-397	1328	40	3.14	3.14	NUM
ejde-397	1328	41	)	)	PUNCT
ejde-397	1328	42	]	]	PUNCT
ejde-397	1328	43	,	,	PUNCT
ejde-397	1328	44	or	or	CCONJ
ejde-397	1328	45	its	its	PRON
ejde-397	1328	46	slight	slight	ADJ
ejde-397	1328	47	modification	modification	NOUN
ejde-397	1328	48	,	,	PUNCT
ejde-397	1328	49	with	with	ADP
ejde-397	1328	50	certain	certain	ADJ
ejde-397	1328	51	real	real	ADJ
ejde-397	1328	52	constants	constant	NOUN
ejde-397	1328	53	0	0	PUNCT
ejde-397	1328	54	<	<	X
ejde-397	1328	55	β	β	X
ejde-397	1328	56	≤	≤	NUM
ejde-397	1328	57	α	α	PRON
ejde-397	1328	58	≤	≤	NUM
ejde-397	1328	59	1	1	NUM
ejde-397	1328	60	,	,	PUNCT
ejde-397	1328	61	γ	γ	X
ejde-397	1328	62	∈	∈	NOUN
ejde-397	1328	63	r	r	NOUN
ejde-397	1328	64	and	and	CCONJ
ejde-397	1328	65	c	c	NOUN
ejde-397	1328	66	,	,	PUNCT
ejde-397	1328	67	c	c	X
ejde-397	1328	68	>	>	X
ejde-397	1328	69	0	0	PUNCT
ejde-397	1329	1	(	(	PUNCT
ejde-397	1329	2	in	in	ADP
ejde-397	1329	3	our	our	PRON
ejde-397	1329	4	notation	notation	NOUN
ejde-397	1329	5	,	,	PUNCT
ejde-397	1329	6	we	we	PRON
ejde-397	1329	7	have	have	VERB
ejde-397	1329	8	a	a	DET
ejde-397	1329	9	=	=	NOUN
ejde-397	1329	10	l	l	NOUN
ejde-397	1329	11	and	and	CCONJ
ejde-397	1329	12	b	b	NOUN
ejde-397	1329	13	=	=	SYM
ejde-397	1329	14	m	m	PROPN
ejde-397	1329	15	)	)	PUNCT
ejde-397	1329	16	.	.	PUNCT
ejde-397	1330	1	the	the	DET
ejde-397	1330	2	validity	validity	NOUN
ejde-397	1330	3	of	of	ADP
ejde-397	1330	4	this	this	DET
ejde-397	1330	5	condition	condition	NOUN
ejde-397	1330	6	with	with	ADP
ejde-397	1330	7	α	α	PROPN
ejde-397	1330	8	=	=	SYM
ejde-397	1330	9	1	1	NUM
ejde-397	1330	10	(	(	PUNCT
ejde-397	1330	11	see	see	VERB
ejde-397	1330	12	e.g.	e.g.	ADV
ejde-397	1330	13	[	[	X
ejde-397	1330	14	17	17	NUM
ejde-397	1330	15	,	,	PUNCT
ejde-397	1330	16	example	example	NOUN
ejde-397	1330	17	3.3	3.3	NUM
ejde-397	1330	18	,	,	PUNCT
ejde-397	1330	19	3.6	3.6	NUM
ejde-397	1330	20	]	]	PUNCT
ejde-397	1330	21	)	)	PUNCT
ejde-397	1330	22	immediately	immediately	ADV
ejde-397	1330	23	implies	imply	VERB
ejde-397	1330	24	by	by	ADP
ejde-397	1330	25	theorem	theorem	ADJ
ejde-397	1330	26	5.19	5.19	NUM
ejde-397	1330	27	and	and	CCONJ
ejde-397	1330	28	remark	remark	NOUN
ejde-397	1330	29	4.2(v	4.2(v	NUM
ejde-397	1330	30	)	)	PUNCT
ejde-397	1330	31	that	that	SCONJ
ejde-397	1330	32	the	the	DET
ejde-397	1330	33	operator	operator	NOUN
ejde-397	1330	34	ab−1	ab−1	NOUN
ejde-397	1330	35	generates	generate	VERB
ejde-397	1330	36	an	an	DET
ejde-397	1330	37	exponentially	exponentially	ADV
ejde-397	1330	38	bounded	bound	VERB
ejde-397	1330	39	,	,	PUNCT
ejde-397	1330	40	analytic	analytic	ADJ
ejde-397	1330	41	σ	σ	PROPN
ejde-397	1330	42	-	-	PUNCT
ejde-397	1330	43	times	time	NOUN
ejde-397	1330	44	integrated	integrate	VERB
ejde-397	1330	45	semigroup	semigroup	NOUN
ejde-397	1330	46	of	of	ADP
ejde-397	1330	47	angle	angle	NOUN
ejde-397	1330	48	σarcctan(1	σarcctan(1	PROPN
ejde-397	1330	49	/	/	SYM
ejde-397	1330	50	c	c	NOUN
ejde-397	1330	51	)	)	PUNCT
ejde-397	1330	52	,	,	PUNCT
ejde-397	1330	53	provided	provide	VERB
ejde-397	1330	54	that	that	SCONJ
ejde-397	1330	55	σ	σ	NOUN
ejde-397	1330	56	>	>	X
ejde-397	1330	57	1−	1−	NUM
ejde-397	1330	58	β	β	X
ejde-397	1330	59	;	;	PUNCT
ejde-397	1330	60	in	in	ADP
ejde-397	1330	61	the	the	DET
ejde-397	1330	62	concrete	concrete	ADJ
ejde-397	1330	63	situation	situation	NOUN
ejde-397	1330	64	of	of	ADP
ejde-397	1330	65	[	[	X
ejde-397	1330	66	17	17	NUM
ejde-397	1330	67	,	,	PUNCT
ejde-397	1330	68	example	example	NOUN
ejde-397	1330	69	3.4	3.4	NUM
ejde-397	1330	70	,	,	PUNCT
ejde-397	1330	71	3.5	3.5	NUM
ejde-397	1330	72	]	]	PUNCT
ejde-397	1330	73	,	,	PUNCT
ejde-397	1330	74	the	the	DET
ejde-397	1330	75	above	above	ADJ
ejde-397	1330	76	holds	hold	VERB
ejde-397	1330	77	with	with	ADP
ejde-397	1330	78	the	the	DET
ejde-397	1330	79	operator	operator	NOUN
ejde-397	1330	80	ab−1	ab−1	NOUN
ejde-397	1330	81	replaced	replace	VERB
ejde-397	1330	82	by	by	ADP
ejde-397	1330	83	b−1a	b−1a	PROPN
ejde-397	1330	84	.	.	PROPN
ejde-397	1330	85	44	44	NUM
ejde-397	1330	86	m.	m.	NOUN
ejde-397	1330	87	kostić	kostić	NOUN
ejde-397	1331	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1331	2	unfortunately	unfortunately	ADV
ejde-397	1331	3	,	,	PUNCT
ejde-397	1331	4	this	this	DET
ejde-397	1331	5	fact	fact	NOUN
ejde-397	1331	6	is	be	AUX
ejde-397	1331	7	not	not	PART
ejde-397	1331	8	sufficiently	sufficiently	ADV
ejde-397	1331	9	enough	enough	ADJ
ejde-397	1331	10	for	for	ADP
ejde-397	1331	11	taking	take	VERB
ejde-397	1331	12	up	up	ADP
ejde-397	1331	13	a	a	DET
ejde-397	1331	14	fairly	fairly	ADV
ejde-397	1331	15	complete	complete	ADJ
ejde-397	1331	16	study	study	NOUN
ejde-397	1331	17	of	of	ADP
ejde-397	1331	18	the	the	DET
ejde-397	1331	19	abstract	abstract	ADJ
ejde-397	1331	20	degenerate	degenerate	ADJ
ejde-397	1331	21	cauchy	cauchy	NOUN
ejde-397	1331	22	problems	problem	NOUN
ejde-397	1331	23	that	that	PRON
ejde-397	1331	24	are	be	AUX
ejde-397	1331	25	subordinated	subordinate	VERB
ejde-397	1331	26	to	to	ADP
ejde-397	1331	27	those	those	PRON
ejde-397	1331	28	appearing	appear	VERB
ejde-397	1331	29	in	in	ADP
ejde-397	1331	30	the	the	DET
ejde-397	1331	31	above	above	ADV
ejde-397	1331	32	-	-	PUNCT
ejde-397	1331	33	mentioned	mention	VERB
ejde-397	1331	34	examples	example	NOUN
ejde-397	1331	35	and	and	CCONJ
ejde-397	1331	36	,	,	PUNCT
ejde-397	1331	37	concerning	concern	VERB
ejde-397	1331	38	this	this	DET
ejde-397	1331	39	question	question	NOUN
ejde-397	1331	40	,	,	PUNCT
ejde-397	1331	41	we	we	PRON
ejde-397	1331	42	will	will	AUX
ejde-397	1331	43	only	only	ADV
ejde-397	1331	44	want	want	VERB
ejde-397	1331	45	to	to	PART
ejde-397	1331	46	mention	mention	VERB
ejde-397	1331	47	that	that	SCONJ
ejde-397	1331	48	the	the	DET
ejde-397	1331	49	subordination	subordination	NOUN
ejde-397	1331	50	fractional	fractional	ADJ
ejde-397	1331	51	operator	operator	NOUN
ejde-397	1331	52	families	family	NOUN
ejde-397	1331	53	can	can	AUX
ejde-397	1331	54	be	be	AUX
ejde-397	1331	55	constructed	construct	VERB
ejde-397	1331	56	since	since	SCONJ
ejde-397	1331	57	the	the	DET
ejde-397	1331	58	semigroups	semigroup	NOUN
ejde-397	1331	59	considered	consider	VERB
ejde-397	1331	60	in	in	ADP
ejde-397	1331	61	[	[	X
ejde-397	1331	62	17	17	NUM
ejde-397	1331	63	,	,	PUNCT
ejde-397	1331	64	chapter	chapter	NOUN
ejde-397	1331	65	iii	iii	PROPN
ejde-397	1331	66	]	]	PUNCT
ejde-397	1331	67	have	have	VERB
ejde-397	1331	68	a	a	DET
ejde-397	1331	69	removable	removable	ADJ
ejde-397	1331	70	singularity	singularity	NOUN
ejde-397	1331	71	at	at	ADP
ejde-397	1331	72	zero	zero	NUM
ejde-397	1331	73	(	(	PUNCT
ejde-397	1331	74	cf	cf	NOUN
ejde-397	1331	75	.	.	PUNCT
ejde-397	1332	1	the	the	DET
ejde-397	1332	2	proof	proof	NOUN
ejde-397	1332	3	of	of	ADP
ejde-397	1332	4	[	[	X
ejde-397	1332	5	5	5	NUM
ejde-397	1332	6	,	,	PUNCT
ejde-397	1332	7	theorem	theorem	VERB
ejde-397	1332	8	3.1	3.1	NUM
ejde-397	1332	9	]	]	PUNCT
ejde-397	1332	10	,	,	PUNCT
ejde-397	1332	11	[	[	X
ejde-397	1332	12	47	47	NUM
ejde-397	1332	13	]	]	PUNCT
ejde-397	1332	14	and	and	CCONJ
ejde-397	1332	15	the	the	DET
ejde-397	1332	16	forthcoming	forthcoming	ADJ
ejde-397	1332	17	monograph	monograph	NOUN
ejde-397	1333	1	[	[	X
ejde-397	1333	2	38	38	NUM
ejde-397	1333	3	]	]	PUNCT
ejde-397	1333	4	for	for	ADP
ejde-397	1333	5	more	more	ADJ
ejde-397	1333	6	details	detail	NOUN
ejde-397	1333	7	)	)	PUNCT
ejde-397	1333	8	.	.	PUNCT
ejde-397	1334	1	on	on	ADP
ejde-397	1334	2	the	the	DET
ejde-397	1334	3	other	other	ADJ
ejde-397	1334	4	hand	hand	NOUN
ejde-397	1334	5	,	,	PUNCT
ejde-397	1334	6	from	from	ADP
ejde-397	1334	7	the	the	DET
ejde-397	1334	8	point	point	NOUN
ejde-397	1334	9	of	of	ADP
ejde-397	1334	10	view	view	NOUN
ejde-397	1334	11	of	of	ADP
ejde-397	1334	12	possible	possible	ADJ
ejde-397	1334	13	applications	application	NOUN
ejde-397	1334	14	of	of	ADP
ejde-397	1334	15	theorem	theorem	NOUN
ejde-397	1334	16	5.22	5.22	NUM
ejde-397	1334	17	,	,	PUNCT
ejde-397	1334	18	it	it	PRON
ejde-397	1334	19	is	be	AUX
ejde-397	1334	20	very	very	ADV
ejde-397	1334	21	important	important	ADJ
ejde-397	1334	22	to	to	PART
ejde-397	1334	23	know	know	VERB
ejde-397	1334	24	that	that	SCONJ
ejde-397	1334	25	the	the	DET
ejde-397	1334	26	operators	operator	NOUN
ejde-397	1334	27	ab−1	ab−1	NOUN
ejde-397	1334	28	or	or	CCONJ
ejde-397	1334	29	b−1a	b−1a	AUX
ejde-397	1334	30	generate	generate	VERB
ejde-397	1334	31	exponentially	exponentially	ADV
ejde-397	1334	32	bounded	bound	VERB
ejde-397	1334	33	,	,	PUNCT
ejde-397	1334	34	analytic	analytic	ADJ
ejde-397	1334	35	integrated	integrate	VERB
ejde-397	1334	36	semigroups	semigroup	NOUN
ejde-397	1334	37	.	.	PUNCT
ejde-397	1335	1	this	this	PRON
ejde-397	1335	2	enables	enable	VERB
ejde-397	1335	3	us	we	PRON
ejde-397	1335	4	to	to	PART
ejde-397	1335	5	consider	consider	VERB
ejde-397	1335	6	the	the	DET
ejde-397	1335	7	abstract	abstract	ADJ
ejde-397	1335	8	degenerate	degenerate	ADJ
ejde-397	1335	9	cauchy	cauchy	NOUN
ejde-397	1335	10	problems	problem	NOUN
ejde-397	1335	11	that	that	PRON
ejde-397	1335	12	are	be	AUX
ejde-397	1335	13	backward	backward	ADJ
ejde-397	1335	14	to	to	ADP
ejde-397	1335	15	those	those	PRON
ejde-397	1335	16	appearing	appear	VERB
ejde-397	1335	17	in	in	ADP
ejde-397	1335	18	[	[	X
ejde-397	1335	19	17	17	NUM
ejde-397	1335	20	,	,	PUNCT
ejde-397	1335	21	examples	example	NOUN
ejde-397	1335	22	3.3–3.6	3.3–3.6	NUM
ejde-397	1335	23	]	]	PUNCT
ejde-397	1335	24	.	.	PUNCT
ejde-397	1336	1	for	for	ADP
ejde-397	1336	2	example	example	NOUN
ejde-397	1336	3	,	,	PUNCT
ejde-397	1336	4	we	we	PRON
ejde-397	1336	5	can	can	AUX
ejde-397	1336	6	consider	consider	VERB
ejde-397	1336	7	the	the	DET
ejde-397	1336	8	following	follow	VERB
ejde-397	1336	9	modification	modification	NOUN
ejde-397	1336	10	of	of	ADP
ejde-397	1336	11	the	the	DET
ejde-397	1336	12	backward	backward	ADJ
ejde-397	1336	13	poisson	poisson	NOUN
ejde-397	1336	14	heat	heat	NOUN
ejde-397	1336	15	equation	equation	NOUN
ejde-397	1336	16	in	in	ADP
ejde-397	1336	17	the	the	DET
ejde-397	1336	18	space	space	NOUN
ejde-397	1336	19	lp(ω	lp(ω	NUM
ejde-397	1336	20	):	):	PUNCT
ejde-397	1336	21	∂	∂	NUM
ejde-397	1336	22	∂t	∂t	PROPN
ejde-397	1337	1	[	[	X
ejde-397	1337	2	m(x)v(t	m(x)v(t	X
ejde-397	1337	3	,	,	PUNCT
ejde-397	1337	4	x	x	NOUN
ejde-397	1337	5	)	)	PUNCT
ejde-397	1337	6	]	]	PUNCT
ejde-397	1338	1	=	=	PUNCT
ejde-397	1338	2	−∆v	−∆v	X
ejde-397	1339	1	+	+	CCONJ
ejde-397	1339	2	bv	bv	PROPN
ejde-397	1339	3	,	,	PUNCT
ejde-397	1339	4	t	t	PROPN
ejde-397	1339	5	≥	≥	NUM
ejde-397	1339	6	0	0	NUM
ejde-397	1339	7	,	,	PUNCT
ejde-397	1339	8	x	x	X
ejde-397	1339	9	∈	∈	PROPN
ejde-397	1339	10	ω	ω	PROPN
ejde-397	1339	11	;	;	PUNCT
ejde-397	1339	12	v(t	v(t	NUM
ejde-397	1339	13	,	,	PUNCT
ejde-397	1339	14	x	x	NOUN
ejde-397	1339	15	)	)	PUNCT
ejde-397	1339	16	=	=	SYM
ejde-397	1339	17	0	0	NUM
ejde-397	1339	18	,	,	PUNCT
ejde-397	1339	19	(	(	PUNCT
ejde-397	1339	20	t	t	PROPN
ejde-397	1339	21	,	,	PUNCT
ejde-397	1339	22	x	x	NOUN
ejde-397	1339	23	)	)	PUNCT
ejde-397	1339	24	∈	∈	PROPN
ejde-397	1340	1	[	[	X
ejde-397	1340	2	0,∞)×	0,∞)×	NUM
ejde-397	1340	3	∂ω	∂ω	ADJ
ejde-397	1340	4	,	,	PUNCT
ejde-397	1340	5	m(x)v(0	m(x)v(0	NOUN
ejde-397	1340	6	,	,	PUNCT
ejde-397	1340	7	x	x	NOUN
ejde-397	1340	8	)	)	PUNCT
ejde-397	1340	9	=	=	SYM
ejde-397	1340	10	u0(x	u0(x	NUM
ejde-397	1340	11	)	)	PUNCT
ejde-397	1340	12	,	,	PUNCT
ejde-397	1341	1	x	x	PUNCT
ejde-397	1341	2	∈	∈	PROPN
ejde-397	1341	3	ω	ω	PROPN
ejde-397	1341	4	,	,	PUNCT
ejde-397	1341	5	(	(	PUNCT
ejde-397	1341	6	5.31	5.31	NUM
ejde-397	1341	7	)	)	PUNCT
ejde-397	1341	8	where	where	SCONJ
ejde-397	1341	9	ω	ω	PROPN
ejde-397	1341	10	is	be	AUX
ejde-397	1341	11	a	a	DET
ejde-397	1341	12	bounded	bounded	ADJ
ejde-397	1341	13	domain	domain	NOUN
ejde-397	1341	14	in	in	ADP
ejde-397	1341	15	rn	rn	PROPN
ejde-397	1341	16	,	,	PUNCT
ejde-397	1341	17	b	b	PROPN
ejde-397	1341	18	>	>	X
ejde-397	1341	19	0	0	NUM
ejde-397	1341	20	,	,	PUNCT
ejde-397	1341	21	m(x	m(x	PROPN
ejde-397	1341	22	)	)	PUNCT
ejde-397	1341	23	≥	≥	NOUN
ejde-397	1341	24	0	0	NUM
ejde-397	1342	1	a.e	a.e	PROPN
ejde-397	1342	2	.	.	PUNCT
ejde-397	1342	3	x	x	PUNCT
ejde-397	1342	4	∈	∈	PROPN
ejde-397	1342	5	ω	ω	PROPN
ejde-397	1342	6	,	,	PUNCT
ejde-397	1342	7	m	m	PROPN
ejde-397	1342	8	∈	∈	NOUN
ejde-397	1342	9	l∞(ω	l∞(ω	NOUN
ejde-397	1342	10	)	)	PUNCT
ejde-397	1342	11	and	and	CCONJ
ejde-397	1342	12	1	1	NUM
ejde-397	1342	13	<	<	X
ejde-397	1342	14	p	p	X
ejde-397	1342	15	<	<	X
ejde-397	1342	16	∞.	∞.	PROPN
ejde-397	1342	17	let	let	VERB
ejde-397	1342	18	b	b	NOUN
ejde-397	1342	19	be	be	AUX
ejde-397	1342	20	the	the	DET
ejde-397	1342	21	multiplication	multiplication	NOUN
ejde-397	1342	22	in	in	ADP
ejde-397	1342	23	lp(ω	lp(ω	PROPN
ejde-397	1342	24	)	)	PUNCT
ejde-397	1342	25	with	with	ADP
ejde-397	1342	26	m(x	m(x	PROPN
ejde-397	1342	27	)	)	PUNCT
ejde-397	1342	28	,	,	PUNCT
ejde-397	1342	29	and	and	CCONJ
ejde-397	1342	30	let	let	VERB
ejde-397	1342	31	a	a	DET
ejde-397	1342	32	=	=	SYM
ejde-397	1342	33	∆	∆	PROPN
ejde-397	1343	1	−	−	PROPN
ejde-397	1344	1	b	b	X
ejde-397	1344	2	act	act	VERB
ejde-397	1344	3	with	with	ADP
ejde-397	1344	4	the	the	DET
ejde-397	1344	5	dirichlet	dirichlet	PROPN
ejde-397	1344	6	boundary	boundary	PROPN
ejde-397	1344	7	conditions	condition	NOUN
ejde-397	1344	8	.	.	PUNCT
ejde-397	1345	1	then	then	ADV
ejde-397	1345	2	theorem	theorem	VERB
ejde-397	1345	3	5.22	5.22	NUM
ejde-397	1345	4	implies	imply	VERB
ejde-397	1345	5	that	that	SCONJ
ejde-397	1345	6	there	there	PRON
ejde-397	1345	7	exists	exist	VERB
ejde-397	1345	8	an	an	DET
ejde-397	1345	9	operator	operator	NOUN
ejde-397	1345	10	c1	c1	NOUN
ejde-397	1345	11	∈	∈	PROPN
ejde-397	1345	12	l(lp(ω	l(lp(ω	PROPN
ejde-397	1345	13	)	)	PUNCT
ejde-397	1345	14	)	)	PUNCT
ejde-397	1345	15	such	such	ADJ
ejde-397	1345	16	that	that	SCONJ
ejde-397	1345	17	a	a	DET
ejde-397	1345	18	=	=	NOUN
ejde-397	1345	19	−ab−1	−ab−1	NOUN
ejde-397	1345	20	is	be	AUX
ejde-397	1345	21	a	a	DET
ejde-397	1345	22	subgenerator	subgenerator	NOUN
ejde-397	1345	23	of	of	ADP
ejde-397	1345	24	an	an	DET
ejde-397	1345	25	entire	entire	ADJ
ejde-397	1345	26	c1	c1	NOUN
ejde-397	1345	27	-	-	PUNCT
ejde-397	1345	28	existence	existence	NOUN
ejde-397	1345	29	family	family	NOUN
ejde-397	1345	30	;	;	PUNCT
ejde-397	1345	31	hence	hence	ADV
ejde-397	1345	32	,	,	PUNCT
ejde-397	1345	33	for	for	ADP
ejde-397	1345	34	every	every	DET
ejde-397	1345	35	u0	u0	PROPN
ejde-397	1345	36	∈	∈	PROPN
ejde-397	1345	37	r(c1	r(c1	NOUN
ejde-397	1345	38	)	)	PUNCT
ejde-397	1345	39	,	,	PUNCT
ejde-397	1345	40	the	the	DET
ejde-397	1345	41	problem	problem	NOUN
ejde-397	1345	42	(	(	PUNCT
ejde-397	1345	43	5.31	5.31	NUM
ejde-397	1345	44	)	)	PUNCT
ejde-397	1345	45	has	have	VERB
ejde-397	1345	46	a	a	DET
ejde-397	1345	47	unique	unique	ADJ
ejde-397	1345	48	solution	solution	NOUN
ejde-397	1345	49	t	t	PROPN
ejde-397	1345	50	7→	7→	NUM
ejde-397	1345	51	u(t	u(t	NOUN
ejde-397	1345	52	)	)	PUNCT
ejde-397	1345	53	,	,	PUNCT
ejde-397	1345	54	t	t	PROPN
ejde-397	1345	55	≥	≥	NUM
ejde-397	1345	56	0	0	NUM
ejde-397	1345	57	which	which	PRON
ejde-397	1345	58	can	can	AUX
ejde-397	1345	59	be	be	AUX
ejde-397	1345	60	extended	extend	VERB
ejde-397	1345	61	entirely	entirely	ADV
ejde-397	1345	62	to	to	ADP
ejde-397	1345	63	the	the	DET
ejde-397	1345	64	whole	whole	ADJ
ejde-397	1345	65	complex	complex	ADJ
ejde-397	1345	66	plane	plane	NOUN
ejde-397	1345	67	.	.	PUNCT
ejde-397	1346	1	furthermore	furthermore	ADV
ejde-397	1346	2	,	,	PUNCT
ejde-397	1346	3	it	it	PRON
ejde-397	1346	4	can	can	AUX
ejde-397	1346	5	be	be	AUX
ejde-397	1346	6	proved	prove	VERB
ejde-397	1346	7	that	that	SCONJ
ejde-397	1346	8	the	the	DET
ejde-397	1346	9	set	set	NOUN
ejde-397	1346	10	of	of	ADP
ejde-397	1346	11	all	all	DET
ejde-397	1346	12	initial	initial	ADJ
ejde-397	1346	13	values	value	NOUN
ejde-397	1346	14	u0	u0	ADJ
ejde-397	1346	15	for	for	ADP
ejde-397	1346	16	which	which	PRON
ejde-397	1346	17	there	there	PRON
ejde-397	1346	18	exists	exist	VERB
ejde-397	1346	19	a	a	DET
ejde-397	1346	20	unique	unique	ADJ
ejde-397	1346	21	solution	solution	NOUN
ejde-397	1346	22	of	of	ADP
ejde-397	1346	23	problem	problem	NOUN
ejde-397	1346	24	(	(	PUNCT
ejde-397	1346	25	5.31	5.31	NUM
ejde-397	1346	26	)	)	PUNCT
ejde-397	1346	27	is	be	AUX
ejde-397	1346	28	dense	dense	ADJ
ejde-397	1346	29	in	in	ADP
ejde-397	1346	30	lp(ω	lp(ω	PROPN
ejde-397	1346	31	)	)	PUNCT
ejde-397	1346	32	provided	provide	VERB
ejde-397	1346	33	that	that	SCONJ
ejde-397	1346	34	there	there	PRON
ejde-397	1346	35	exists	exist	VERB
ejde-397	1346	36	a	a	DET
ejde-397	1346	37	constant	constant	ADJ
ejde-397	1346	38	d	d	X
ejde-397	1346	39	>	>	X
ejde-397	1346	40	0	0	NUM
ejde-397	1347	1	such	such	ADJ
ejde-397	1347	2	that	that	SCONJ
ejde-397	1347	3	|m(x)|	|m(x)|	PROPN
ejde-397	1347	4	≥	≥	X
ejde-397	1347	5	d	d	X
ejde-397	1347	6	a.e	a.e	PROPN
ejde-397	1347	7	.	.	PROPN
ejde-397	1347	8	x	x	SYM
ejde-397	1347	9	∈	∈	PROPN
ejde-397	1347	10	ω	ω	NOUN
ejde-397	1347	11	.	.	PUNCT
ejde-397	1348	1	in	in	ADP
ejde-397	1348	2	the	the	DET
ejde-397	1348	3	following	follow	VERB
ejde-397	1348	4	example	example	NOUN
ejde-397	1348	5	,	,	PUNCT
ejde-397	1348	6	we	we	PRON
ejde-397	1348	7	consider	consider	VERB
ejde-397	1348	8	the	the	DET
ejde-397	1348	9	existence	existence	NOUN
ejde-397	1348	10	and	and	CCONJ
ejde-397	1348	11	uniqueness	uniqueness	NOUN
ejde-397	1348	12	of	of	ADP
ejde-397	1348	13	solutions	solution	NOUN
ejde-397	1348	14	of	of	ADP
ejde-397	1348	15	abstract	abstract	ADJ
ejde-397	1348	16	degenerate	degenerate	ADJ
ejde-397	1348	17	relaxation	relaxation	NOUN
ejde-397	1348	18	cauchy	cauchy	NOUN
ejde-397	1348	19	problems	problem	NOUN
ejde-397	1348	20	that	that	PRON
ejde-397	1348	21	are	be	AUX
ejde-397	1348	22	not	not	PART
ejde-397	1348	23	subordinated	subordinate	VERB
ejde-397	1348	24	to	to	ADP
ejde-397	1348	25	those	those	PRON
ejde-397	1348	26	of	of	ADP
ejde-397	1348	27	first	first	ADJ
ejde-397	1348	28	order	order	NOUN
ejde-397	1348	29	.	.	PUNCT
ejde-397	1349	1	example	example	NOUN
ejde-397	1350	1	5.25	5.25	NUM
ejde-397	1350	2	.	.	PUNCT
ejde-397	1351	1	it	it	PRON
ejde-397	1351	2	is	be	AUX
ejde-397	1351	3	clear	clear	ADJ
ejde-397	1351	4	that	that	SCONJ
ejde-397	1351	5	the	the	DET
ejde-397	1351	6	examples	example	NOUN
ejde-397	1351	7	presented	present	VERB
ejde-397	1351	8	in	in	ADP
ejde-397	1351	9	[	[	X
ejde-397	1351	10	17	17	NUM
ejde-397	1351	11	,	,	PUNCT
ejde-397	1351	12	chapter	chapter	NOUN
ejde-397	1351	13	iii	iii	PROPN
ejde-397	1351	14	]	]	PUNCT
ejde-397	1351	15	can	can	AUX
ejde-397	1351	16	serve	serve	VERB
ejde-397	1351	17	one	one	NUM
ejde-397	1351	18	for	for	ADP
ejde-397	1351	19	consideration	consideration	NOUN
ejde-397	1351	20	of	of	ADP
ejde-397	1351	21	a	a	DET
ejde-397	1351	22	wide	wide	ADJ
ejde-397	1351	23	class	class	NOUN
ejde-397	1351	24	of	of	ADP
ejde-397	1351	25	abstract	abstract	ADJ
ejde-397	1351	26	degenerate	degenerate	ADJ
ejde-397	1351	27	relaxation	relaxation	NOUN
ejde-397	1351	28	equations	equation	NOUN
ejde-397	1351	29	that	that	PRON
ejde-397	1351	30	are	be	AUX
ejde-397	1351	31	not	not	PART
ejde-397	1351	32	subordinated	subordinate	VERB
ejde-397	1351	33	to	to	ADP
ejde-397	1351	34	the	the	DET
ejde-397	1351	35	problems	problem	NOUN
ejde-397	1351	36	of	of	ADP
ejde-397	1351	37	first	first	ADJ
ejde-397	1351	38	order	order	NOUN
ejde-397	1351	39	(	(	PUNCT
ejde-397	1351	40	a	a	DET
ejde-397	1351	41	fairly	fairly	ADV
ejde-397	1351	42	complete	complete	ADJ
ejde-397	1351	43	analysis	analysis	NOUN
ejde-397	1351	44	of	of	ADP
ejde-397	1351	45	such	such	ADJ
ejde-397	1351	46	equations	equation	NOUN
ejde-397	1351	47	is	be	AUX
ejde-397	1351	48	quite	quite	PRON
ejde-397	1351	49	non	non	ADJ
ejde-397	1351	50	-	-	ADJ
ejde-397	1351	51	trivial	trivial	ADJ
ejde-397	1351	52	and	and	CCONJ
ejde-397	1351	53	we	we	PRON
ejde-397	1351	54	shall	shall	AUX
ejde-397	1351	55	skip	skip	VERB
ejde-397	1351	56	all	all	DET
ejde-397	1351	57	related	related	ADJ
ejde-397	1351	58	details	detail	NOUN
ejde-397	1351	59	for	for	ADP
ejde-397	1351	60	convenience	convenience	NOUN
ejde-397	1351	61	):	):	PUNCT
ejde-397	1351	62	suppose	suppose	VERB
ejde-397	1351	63	that	that	SCONJ
ejde-397	1351	64	the	the	DET
ejde-397	1351	65	condition	condition	NOUN
ejde-397	1351	66	[	[	X
ejde-397	1351	67	17	17	NUM
ejde-397	1351	68	,	,	PUNCT
ejde-397	1351	69	(	(	PUNCT
ejde-397	1351	70	3.1	3.1	NUM
ejde-397	1351	71	)	)	PUNCT
ejde-397	1351	72	]	]	PUNCT
ejde-397	1351	73	holds	hold	VERB
ejde-397	1351	74	with	with	ADP
ejde-397	1351	75	certain	certain	ADJ
ejde-397	1351	76	real	real	ADJ
ejde-397	1351	77	constants	constant	NOUN
ejde-397	1351	78	0	0	PUNCT
ejde-397	1351	79	<	<	X
ejde-397	1351	80	β	β	X
ejde-397	1351	81	≤	≤	NUM
ejde-397	1351	82	α	α	DET
ejde-397	1351	83	≤	≤	NUM
ejde-397	1351	84	1	1	NUM
ejde-397	1351	85	,	,	PUNCT
ejde-397	1351	86	c	c	X
ejde-397	1351	87	,	,	PUNCT
ejde-397	1351	88	m	m	VERB
ejde-397	1351	89	>	>	X
ejde-397	1351	90	0	0	NUM
ejde-397	1351	91	,	,	PUNCT
ejde-397	1351	92	as	as	ADV
ejde-397	1351	93	well	well	ADV
ejde-397	1351	94	as	as	ADP
ejde-397	1351	95	that	that	DET
ejde-397	1351	96	θ	θ	PROPN
ejde-397	1351	97	∈	∈	PROPN
ejde-397	1351	98	(	(	PUNCT
ejde-397	1351	99	π/2	π/2	NUM
ejde-397	1351	100	,	,	PUNCT
ejde-397	1351	101	0	0	NUM
ejde-397	1351	102	)	)	PUNCT
ejde-397	1351	103	,	,	PUNCT
ejde-397	1351	104	ζ	ζ	PROPN
ejde-397	1351	105	∈	∈	PROPN
ejde-397	1351	106	(	(	PUNCT
ejde-397	1351	107	0	0	NUM
ejde-397	1351	108	,	,	PUNCT
ejde-397	1351	109	1	1	NUM
ejde-397	1351	110	)	)	PUNCT
ejde-397	1351	111	and	and	CCONJ
ejde-397	1351	112	π	π	PROPN
ejde-397	1351	113	2	2	X
ejde-397	1351	114	>	>	X
ejde-397	1351	115	π−arctan	π−arctan	PROPN
ejde-397	1351	116	1	1	NUM
ejde-397	1351	117	c	c	X
ejde-397	1351	118	+	+	NOUN
ejde-397	1351	119	θ	θ	X
ejde-397	1351	120	>	>	X
ejde-397	1351	121	1	1	NUM
ejde-397	1351	122	2πζ	2πζ	NOUN
ejde-397	1351	123	.	.	PUNCT
ejde-397	1352	1	then	then	ADV
ejde-397	1352	2	σπ−arctan	σπ−arctan	PROPN
ejde-397	1352	3	1	1	NUM
ejde-397	1352	4	c+θ	c+θ	NOUN
ejde-397	1352	5	⊆	⊆	NUM
ejde-397	1352	6	ρ(eiθa	ρ(eiθa	NUM
ejde-397	1352	7	)	)	PUNCT
ejde-397	1352	8	and	and	CCONJ
ejde-397	1352	9	,	,	PUNCT
ejde-397	1352	10	in	in	ADP
ejde-397	1352	11	general	general	ADJ
ejde-397	1352	12	,	,	PUNCT
ejde-397	1352	13	ρ(eiθa	ρ(eiθa	PROPN
ejde-397	1352	14	)	)	PUNCT
ejde-397	1352	15	does	do	AUX
ejde-397	1352	16	not	not	PART
ejde-397	1352	17	contain	contain	VERB
ejde-397	1352	18	any	any	DET
ejde-397	1352	19	right	right	ADJ
ejde-397	1352	20	half	half	ADJ
ejde-397	1352	21	-	-	PUNCT
ejde-397	1352	22	plane	plane	NOUN
ejde-397	1352	23	.	.	PUNCT
ejde-397	1353	1	an	an	DET
ejde-397	1353	2	application	application	NOUN
ejde-397	1353	3	of	of	ADP
ejde-397	1353	4	theorem	theorem	ADJ
ejde-397	1353	5	5.19	5.19	NUM
ejde-397	1353	6	shows	show	VERB
ejde-397	1353	7	that	that	SCONJ
ejde-397	1353	8	the	the	DET
ejde-397	1353	9	operator	operator	NOUN
ejde-397	1353	10	eiθa	eiθa	PROPN
ejde-397	1353	11	generates	generate	VERB
ejde-397	1353	12	an	an	DET
ejde-397	1353	13	exponentially	exponentially	ADV
ejde-397	1353	14	bounded	bound	VERB
ejde-397	1353	15	,	,	PUNCT
ejde-397	1353	16	analytic	analytic	ADJ
ejde-397	1353	17	(	(	PUNCT
ejde-397	1353	18	gζ	gζ	PROPN
ejde-397	1353	19	,	,	PUNCT
ejde-397	1353	20	gr+1)-regularized	gr+1)-regularized	ADJ
ejde-397	1353	21	resolvent	resolvent	ADJ
ejde-397	1353	22	family	family	NOUN
ejde-397	1353	23	of	of	ADP
ejde-397	1353	24	angle	angle	NOUN
ejde-397	1353	25	θ′	θ′	NOUN
ejde-397	1353	26	:	:	PUNCT
ejde-397	1353	27	=	=	PUNCT
ejde-397	1353	28	min((π	min((π	X
ejde-397	1353	29	−	−	PROPN
ejde-397	1353	30	arctan(1	arctan(1	NOUN
ejde-397	1353	31	/	/	SYM
ejde-397	1353	32	c	c	X
ejde-397	1353	33	)	)	PUNCT
ejde-397	1354	1	+	+	NUM
ejde-397	1354	2	θ	θ	PROPN
ejde-397	1354	3	−	−	PROPN
ejde-397	1354	4	(	(	PUNCT
ejde-397	1354	5	πζ/2))/ζ	πζ/2))/ζ	PROPN
ejde-397	1354	6	,	,	PUNCT
ejde-397	1354	7	π/2	π/2	NUM
ejde-397	1354	8	)	)	PUNCT
ejde-397	1354	9	,	,	PUNCT
ejde-397	1354	10	where	where	SCONJ
ejde-397	1354	11	r	r	NOUN
ejde-397	1354	12	>	>	X
ejde-397	1354	13	ζ(1	ζ(1	PROPN
ejde-397	1354	14	−	−	NOUN
ejde-397	1354	15	β	β	NOUN
ejde-397	1354	16	)	)	PUNCT
ejde-397	1354	17	,	,	PUNCT
ejde-397	1354	18	if	if	SCONJ
ejde-397	1354	19	a	a	PRON
ejde-397	1354	20	is	be	AUX
ejde-397	1354	21	not	not	PART
ejde-397	1354	22	densely	densely	ADV
ejde-397	1354	23	defined	define	VERB
ejde-397	1354	24	,	,	PUNCT
ejde-397	1354	25	and	and	CCONJ
ejde-397	1354	26	r	r	NOUN
ejde-397	1354	27	=	=	SYM
ejde-397	1354	28	ζ(1−	ζ(1−	NOUN
ejde-397	1354	29	β	β	X
ejde-397	1354	30	)	)	PUNCT
ejde-397	1354	31	,	,	PUNCT
ejde-397	1354	32	otherwise	otherwise	ADV
ejde-397	1354	33	.	.	PUNCT
ejde-397	1355	1	suppose	suppose	VERB
ejde-397	1355	2	now	now	ADV
ejde-397	1355	3	that	that	SCONJ
ejde-397	1355	4	x	x	PUNCT
ejde-397	1355	5	∈	∈	PROPN
ejde-397	1355	6	e	e	NOUN
ejde-397	1355	7	,	,	PUNCT
ejde-397	1355	8	1	1	NUM
ejde-397	1355	9	−	−	NOUN
ejde-397	1355	10	ζ	ζ	NOUN
ejde-397	1355	11	>	>	PUNCT
ejde-397	1355	12	η	η	PROPN
ejde-397	1355	13	>	>	X
ejde-397	1355	14	1	1	NUM
ejde-397	1355	15	−	−	PROPN
ejde-397	1355	16	ζβ	ζβ	PROPN
ejde-397	1355	17	,	,	PUNCT
ejde-397	1355	18	δ	δ	PROPN
ejde-397	1355	19	>	>	X
ejde-397	1355	20	0	0	NUM
ejde-397	1355	21	,	,	PUNCT
ejde-397	1355	22	0	0	NUM
ejde-397	1355	23	<	<	X
ejde-397	1355	24	γ	γ	X
ejde-397	1355	25	<	<	X
ejde-397	1355	26	θ′	θ′	NOUN
ejde-397	1355	27	,	,	PUNCT
ejde-397	1355	28	t	t	PROPN
ejde-397	1355	29	>	>	X
ejde-397	1355	30	0	0	NUM
ejde-397	1355	31	is	be	AUX
ejde-397	1355	32	fixed	fix	VERB
ejde-397	1355	33	temporarily	temporarily	ADV
ejde-397	1355	34	,	,	PUNCT
ejde-397	1355	35	γ1	γ1	PROPN
ejde-397	1355	36	:	:	PUNCT
ejde-397	1355	37	=	=	PRON
ejde-397	1355	38	{	{	PUNCT
ejde-397	1355	39	rei((π/2)+γ	rei((π/2)+γ	NOUN
ejde-397	1355	40	)	)	PUNCT
ejde-397	1355	41	:	:	PUNCT
ejde-397	1356	1	r	r	NOUN
ejde-397	1356	2	≥	≥	NUM
ejde-397	1356	3	t−1	t−1	NOUN
ejde-397	1356	4	}	}	PUNCT
ejde-397	1356	5	∪	∪	VERB
ejde-397	1356	6	{	{	PUNCT
ejde-397	1356	7	t−1eiθ	t−1eiθ	PROPN
ejde-397	1356	8	:	:	PUNCT
ejde-397	1356	9	θ	θ	PROPN
ejde-397	1356	10	∈	∈	PROPN
ejde-397	1357	1	[	[	X
ejde-397	1357	2	0	0	NUM
ejde-397	1357	3	,	,	PUNCT
ejde-397	1357	4	(	(	PUNCT
ejde-397	1357	5	π/2	π/2	NUM
ejde-397	1357	6	)	)	PUNCT
ejde-397	1357	7	+	+	CCONJ
ejde-397	1357	8	γ	γ	X
ejde-397	1357	9	]	]	X
ejde-397	1357	10	}	}	PUNCT
ejde-397	1357	11	,	,	PUNCT
ejde-397	1357	12	γ2	γ2	NOUN
ejde-397	1357	13	:	:	PUNCT
ejde-397	1357	14	=	=	SYM
ejde-397	1357	15	{	{	PUNCT
ejde-397	1357	16	re−i((π/2)+γ	re−i((π/2)+γ	PROPN
ejde-397	1357	17	)	)	PUNCT
ejde-397	1357	18	:	:	PUNCT
ejde-397	1358	1	r	r	NOUN
ejde-397	1358	2	≥	≥	NUM
ejde-397	1358	3	t−1	t−1	NOUN
ejde-397	1358	4	}	}	PUNCT
ejde-397	1358	5	∪	∪	VERB
ejde-397	1358	6	{	{	PUNCT
ejde-397	1358	7	t−1eiθ	t−1eiθ	PROPN
ejde-397	1358	8	:	:	PUNCT
ejde-397	1358	9	θ	θ	PROPN
ejde-397	1358	10	∈	∈	PROPN
ejde-397	1359	1	[	[	X
ejde-397	1359	2	−(π/2)−	−(π/2)−	VERB
ejde-397	1359	3	γ	γ	NOUN
ejde-397	1359	4	,	,	PUNCT
ejde-397	1359	5	0	0	NUM
ejde-397	1359	6	]	]	PUNCT
ejde-397	1359	7	}	}	PUNCT
ejde-397	1359	8	and	and	CCONJ
ejde-397	1359	9	γ	γ	X
ejde-397	1359	10	:	:	PUNCT
ejde-397	1359	11	=	=	SYM
ejde-397	1359	12	γ1	γ1	PROPN
ejde-397	1359	13	∪	∪	ADP
ejde-397	1359	14	γ2	γ2	PROPN
ejde-397	1359	15	is	be	AUX
ejde-397	1359	16	oriented	orient	VERB
ejde-397	1359	17	counterclockwise	counterclockwise	NOUN
ejde-397	1359	18	.	.	PUNCT
ejde-397	1360	1	define	define	VERB
ejde-397	1360	2	u(0	u(0	NOUN
ejde-397	1360	3	)	)	PUNCT
ejde-397	1360	4	:	:	PUNCT
ejde-397	1361	1	=	=	SYM
ejde-397	1361	2	0	0	NUM
ejde-397	1361	3	and	and	CCONJ
ejde-397	1361	4	u(t	u(t	NOUN
ejde-397	1361	5	)	)	PUNCT
ejde-397	1361	6	:	:	PUNCT
ejde-397	1361	7	=	=	SYM
ejde-397	1361	8	1	1	NUM
ejde-397	1361	9	2πi	2πi	ADJ
ejde-397	1361	10	∫	∫	PROPN
ejde-397	1361	11	γ	γ	X
ejde-397	1361	12	eλtλ−η	eλtλ−η	X
ejde-397	1361	13	(	(	PUNCT
ejde-397	1361	14	λζ	λζ	ADP
ejde-397	1361	15	−	−	PROPN
ejde-397	1361	16	eiθa	eiθa	PROPN
ejde-397	1361	17	)	)	PUNCT
ejde-397	1361	18	−1	−1	NOUN
ejde-397	1361	19	x	x	SYM
ejde-397	1361	20	dλ	dλ	NOUN
ejde-397	1361	21	.	.	PUNCT
ejde-397	1362	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1362	2	abstract	abstract	ADJ
ejde-397	1362	3	degenerate	degenerate	ADJ
ejde-397	1362	4	volterra	volterra	NOUN
ejde-397	1362	5	inclusions	inclusion	NOUN
ejde-397	1362	6	45	45	NUM
ejde-397	1362	7	arguing	argue	VERB
ejde-397	1362	8	as	as	ADP
ejde-397	1362	9	in	in	ADP
ejde-397	1362	10	[	[	X
ejde-397	1362	11	1	1	NUM
ejde-397	1362	12	,	,	PUNCT
ejde-397	1362	13	theorem	theorem	VERB
ejde-397	1362	14	2.6.1	2.6.1	NUM
ejde-397	1362	15	,	,	PUNCT
ejde-397	1362	16	theorem	theorem	VERB
ejde-397	1362	17	2.6.4	2.6.4	NUM
ejde-397	1362	18	]	]	PUNCT
ejde-397	1362	19	,	,	PUNCT
ejde-397	1362	20	it	it	PRON
ejde-397	1362	21	readily	readily	ADV
ejde-397	1362	22	follows	follow	VERB
ejde-397	1362	23	that	that	SCONJ
ejde-397	1362	24	u	u	PROPN
ejde-397	1362	25	∈	∈	PROPN
ejde-397	1362	26	c([0,∞	c([0,∞	PROPN
ejde-397	1362	27	)	)	PUNCT
ejde-397	1362	28	:	:	PUNCT
ejde-397	1363	1	e	e	X
ejde-397	1363	2	)	)	PUNCT
ejde-397	1363	3	,	,	PUNCT
ejde-397	1363	4	‖u(t)‖	‖u(t)‖	NOUN
ejde-397	1363	5	=	=	SYM
ejde-397	1363	6	o(tη+ζβ−1	o(tη+ζβ−1	NUM
ejde-397	1363	7	)	)	PUNCT
ejde-397	1363	8	,	,	PUNCT
ejde-397	1363	9	t	t	PROPN
ejde-397	1363	10	≥	≥	NOUN
ejde-397	1363	11	0	0	PUNCT
ejde-397	1363	12	and	and	CCONJ
ejde-397	1363	13	that	that	SCONJ
ejde-397	1363	14	the	the	DET
ejde-397	1363	15	mapping	mapping	NOUN
ejde-397	1363	16	t	t	NOUN
ejde-397	1363	17	7→	7→	NUM
ejde-397	1363	18	u(t	u(t	NOUN
ejde-397	1363	19	)	)	PUNCT
ejde-397	1363	20	,	,	PUNCT
ejde-397	1363	21	t	t	PROPN
ejde-397	1363	22	>	>	X
ejde-397	1363	23	0	0	NUM
ejde-397	1363	24	can	can	AUX
ejde-397	1363	25	be	be	AUX
ejde-397	1363	26	analytically	analytically	ADV
ejde-397	1363	27	extended	extend	VERB
ejde-397	1363	28	to	to	ADP
ejde-397	1363	29	the	the	DET
ejde-397	1363	30	sector	sector	NOUN
ejde-397	1363	31	σθ′	σθ′	NOUN
ejde-397	1363	32	.	.	PUNCT
ejde-397	1364	1	keeping	keep	VERB
ejde-397	1364	2	in	in	ADP
ejde-397	1364	3	mind	mind	NOUN
ejde-397	1364	4	theorem	theorem	VERB
ejde-397	1364	5	2.3	2.3	NUM
ejde-397	1364	6	and	and	CCONJ
ejde-397	1364	7	theorem	theorem	VERB
ejde-397	1364	8	2.4(i	2.4(i	NUM
ejde-397	1364	9	)	)	PUNCT
ejde-397	1364	10	,	,	PUNCT
ejde-397	1364	11	we	we	PRON
ejde-397	1364	12	obtain	obtain	VERB
ejde-397	1364	13	that	that	SCONJ
ejde-397	1364	14	there	there	PRON
ejde-397	1364	15	exists	exist	VERB
ejde-397	1364	16	a	a	DET
ejde-397	1364	17	continuous	continuous	ADJ
ejde-397	1364	18	section	section	NOUN
ejde-397	1364	19	t	t	PROPN
ejde-397	1364	20	7→	7→	PROPN
ejde-397	1364	21	ua	ua	PROPN
ejde-397	1364	22	,	,	PUNCT
ejde-397	1364	23	θ	θ	PROPN
ejde-397	1364	24	,	,	PUNCT
ejde-397	1364	25	ζ(t	ζ(t	PROPN
ejde-397	1364	26	)	)	PUNCT
ejde-397	1364	27	,	,	PUNCT
ejde-397	1364	28	t	t	PROPN
ejde-397	1364	29	>	>	X
ejde-397	1364	30	0	0	NUM
ejde-397	1365	1	of	of	ADP
ejde-397	1365	2	the	the	DET
ejde-397	1365	3	multivalued	multivalue	VERB
ejde-397	1365	4	mapping	mapping	NOUN
ejde-397	1365	5	t	t	NOUN
ejde-397	1365	6	7→	7→	NOUN
ejde-397	1365	7	eiθa(gζ	eiθa(gζ	PROPN
ejde-397	1365	8	∗u)(t	∗u)(t	NOUN
ejde-397	1365	9	)	)	PUNCT
ejde-397	1365	10	,	,	PUNCT
ejde-397	1365	11	t	t	X
ejde-397	1365	12	>	>	X
ejde-397	1365	13	0	0	NUM
ejde-397	1365	14	,	,	PUNCT
ejde-397	1365	15	with	with	SCONJ
ejde-397	1365	16	the	the	DET
ejde-397	1365	17	meaning	meaning	NOUN
ejde-397	1365	18	clear	clear	ADJ
ejde-397	1365	19	,	,	PUNCT
ejde-397	1365	20	such	such	ADJ
ejde-397	1365	21	that	that	SCONJ
ejde-397	1365	22	u(t	u(t	NOUN
ejde-397	1365	23	)	)	PUNCT
ejde-397	1365	24	=	=	SYM
ejde-397	1365	25	ua	ua	PROPN
ejde-397	1365	26	,	,	PUNCT
ejde-397	1365	27	θ	θ	PROPN
ejde-397	1365	28	,	,	PUNCT
ejde-397	1365	29	ζ(t	ζ(t	PROPN
ejde-397	1365	30	)	)	PUNCT
ejde-397	1365	31	+	+	NUM
ejde-397	1365	32	gη+ζ(t)x	gη+ζ(t)x	NOUN
ejde-397	1365	33	,	,	PUNCT
ejde-397	1365	34	t	t	X
ejde-397	1365	35	>	>	X
ejde-397	1365	36	0	0	X
ejde-397	1365	37	.	.	PUNCT
ejde-397	1366	1	observe	observe	VERB
ejde-397	1366	2	,	,	PUNCT
ejde-397	1366	3	finally	finally	ADV
ejde-397	1366	4	,	,	PUNCT
ejde-397	1366	5	that	that	SCONJ
ejde-397	1366	6	the	the	DET
ejde-397	1366	7	riemann	riemann	PROPN
ejde-397	1366	8	-	-	PUNCT
ejde-397	1366	9	liouville	liouville	VERB
ejde-397	1366	10	fractional	fractional	ADJ
ejde-397	1366	11	derivative	derivative	ADJ
ejde-397	1366	12	dζ	dζ	PROPN
ejde-397	1366	13	t	t	PROPN
ejde-397	1366	14	u(t	u(t	PROPN
ejde-397	1366	15	)	)	PUNCT
ejde-397	1366	16	need	need	AUX
ejde-397	1366	17	not	not	PART
ejde-397	1366	18	be	be	AUX
ejde-397	1366	19	defined	define	VERB
ejde-397	1366	20	here	here	ADV
ejde-397	1366	21	.	.	PUNCT
ejde-397	1367	1	in	in	ADP
ejde-397	1367	2	the	the	DET
ejde-397	1367	3	sequel	sequel	NOUN
ejde-397	1367	4	,	,	PUNCT
ejde-397	1367	5	we	we	PRON
ejde-397	1367	6	need	need	VERB
ejde-397	1367	7	the	the	DET
ejde-397	1367	8	following	following	ADJ
ejde-397	1367	9	notion	notion	NOUN
ejde-397	1367	10	.	.	PUNCT
ejde-397	1368	1	suppose	suppose	VERB
ejde-397	1368	2	that	that	SCONJ
ejde-397	1368	3	a	a	DET
ejde-397	1368	4	sequence	sequence	NOUN
ejde-397	1368	5	(	(	PUNCT
ejde-397	1368	6	mn)n∈n0	mn)n∈n0	ADP
ejde-397	1368	7	of	of	ADP
ejde-397	1368	8	positive	positive	ADJ
ejde-397	1368	9	real	real	ADJ
ejde-397	1368	10	numbers	number	NOUN
ejde-397	1368	11	satisfies	satisfy	VERB
ejde-397	1368	12	m0	m0	NOUN
ejde-397	1368	13	=	=	SYM
ejde-397	1368	14	1	1	NUM
ejde-397	1368	15	,	,	PUNCT
ejde-397	1368	16	as	as	ADV
ejde-397	1368	17	well	well	ADV
ejde-397	1368	18	as	as	ADP
ejde-397	1368	19	the	the	DET
ejde-397	1368	20	following	following	ADJ
ejde-397	1368	21	conditions	condition	NOUN
ejde-397	1368	22	:	:	PUNCT
ejde-397	1368	23	(	(	PUNCT
ejde-397	1368	24	a2	a2	PROPN
ejde-397	1368	25	)	)	PUNCT
ejde-397	1368	26	m2	m2	PROPN
ejde-397	1368	27	p	p	PROPN
ejde-397	1368	28	≤mp+1mp−1	≤mp+1mp−1	PROPN
ejde-397	1368	29	,	,	PUNCT
ejde-397	1368	30	p	p	PROPN
ejde-397	1368	31	∈	∈	PROPN
ejde-397	1368	32	n	n	CCONJ
ejde-397	1368	33	,	,	PUNCT
ejde-397	1368	34	(	(	PUNCT
ejde-397	1368	35	a2	a2	PROPN
ejde-397	1368	36	)	)	PUNCT
ejde-397	1368	37	mp	mp	PROPN
ejde-397	1368	38	≤	≤	PROPN
ejde-397	1368	39	ahp	ahp	PROPN
ejde-397	1368	40	minp1,p2∈n	minp1,p2∈n	PROPN
ejde-397	1368	41	,	,	PUNCT
ejde-397	1368	42	p1+p2	p1+p2	PROPN
ejde-397	1368	43	=	=	SYM
ejde-397	1368	44	pmp1mp2	pmp1mp2	PROPN
ejde-397	1368	45	,	,	PUNCT
ejde-397	1368	46	n	n	PROPN
ejde-397	1368	47	∈	∈	PROPN
ejde-397	1368	48	n	n	CCONJ
ejde-397	1368	49	,	,	PUNCT
ejde-397	1368	50	for	for	ADP
ejde-397	1368	51	some	some	DET
ejde-397	1368	52	a	a	DET
ejde-397	1368	53	>	>	SYM
ejde-397	1368	54	1	1	NUM
ejde-397	1368	55	and	and	CCONJ
ejde-397	1368	56	h	h	NOUN
ejde-397	1368	57	>	>	X
ejde-397	1368	58	1	1	NUM
ejde-397	1368	59	,	,	PUNCT
ejde-397	1368	60	(	(	PUNCT
ejde-397	1368	61	a2	a2	NOUN
ejde-397	1368	62	)	)	PUNCT
ejde-397	1368	63	’	'	PUNCT
ejde-397	1368	64	∑∞	∑∞	NOUN
ejde-397	1368	65	p=1	p=1	PUNCT
ejde-397	1369	1	mp−1	mp−1	ADV
ejde-397	1369	2	mp	mp	PROPN
ejde-397	1369	3	<	<	AUX
ejde-397	1369	4	∞.	∞.	PROPN
ejde-397	1369	5	set	set	VERB
ejde-397	1369	6	ωl(t	ωl(t	PUNCT
ejde-397	1369	7	)	)	PUNCT
ejde-397	1369	8	:	:	PUNCT
ejde-397	1370	1	=	=	NOUN
ejde-397	1370	2	∞∑	∞∑	NUM
ejde-397	1370	3	n=0	n=0	NUM
ejde-397	1370	4	tn	tn	NOUN
ejde-397	1370	5	mn	mn	PROPN
ejde-397	1370	6	,	,	PUNCT
ejde-397	1370	7	t	t	PROPN
ejde-397	1370	8	≥	≥	NUM
ejde-397	1370	9	0	0	NUM
ejde-397	1370	10	.	.	PUNCT
ejde-397	1371	1	the	the	DET
ejde-397	1371	2	most	most	ADV
ejde-397	1371	3	important	important	ADJ
ejde-397	1371	4	results	result	NOUN
ejde-397	1371	5	concerning	concern	VERB
ejde-397	1371	6	differential	differential	NOUN
ejde-397	1371	7	properties	property	NOUN
ejde-397	1371	8	of	of	ADP
ejde-397	1371	9	non	non	ADJ
ejde-397	1371	10	-	-	ADJ
ejde-397	1371	11	degenerate	degenerate	ADJ
ejde-397	1371	12	(	(	PUNCT
ejde-397	1371	13	a	a	PRON
ejde-397	1371	14	,	,	PUNCT
ejde-397	1371	15	k)-regularized	k)-regularize	VERB
ejde-397	1371	16	c	c	NOUN
ejde-397	1371	17	-	-	PUNCT
ejde-397	1371	18	resolvent	resolvent	ADJ
ejde-397	1371	19	families	family	NOUN
ejde-397	1371	20	remain	remain	VERB
ejde-397	1371	21	true	true	ADJ
ejde-397	1371	22	,	,	PUNCT
ejde-397	1371	23	with	with	ADP
ejde-397	1371	24	almost	almost	ADV
ejde-397	1371	25	minimal	minimal	ADJ
ejde-397	1371	26	reformulations	reformulation	NOUN
ejde-397	1371	27	,	,	PUNCT
ejde-397	1371	28	in	in	ADP
ejde-397	1371	29	our	our	PRON
ejde-397	1371	30	new	new	ADJ
ejde-397	1371	31	setting	setting	NOUN
ejde-397	1371	32	.	.	PUNCT
ejde-397	1372	1	the	the	DET
ejde-397	1372	2	proofs	proof	NOUN
ejde-397	1372	3	of	of	ADP
ejde-397	1372	4	following	follow	VERB
ejde-397	1372	5	extensions	extension	NOUN
ejde-397	1372	6	of	of	ADP
ejde-397	1372	7	[	[	X
ejde-397	1372	8	36	36	NUM
ejde-397	1372	9	,	,	PUNCT
ejde-397	1372	10	theorem	theorem	VERB
ejde-397	1372	11	2.2.15	2.2.15	NUM
ejde-397	1372	12	,	,	PUNCT
ejde-397	1372	13	theorem	theorem	VERB
ejde-397	1372	14	2.2.17	2.2.17	NUM
ejde-397	1372	15	]	]	PUNCT
ejde-397	1372	16	are	be	AUX
ejde-397	1372	17	omitted	omit	VERB
ejde-397	1372	18	.	.	PUNCT
ejde-397	1373	1	theorem	theorem	VERB
ejde-397	1373	2	5.26	5.26	NUM
ejde-397	1373	3	.	.	PUNCT
ejde-397	1374	1	suppose	suppose	VERB
ejde-397	1374	2	that	that	SCONJ
ejde-397	1374	3	a	a	PRON
ejde-397	1374	4	is	be	AUX
ejde-397	1374	5	a	a	DET
ejde-397	1374	6	closed	closed	ADJ
ejde-397	1374	7	mlo	mlo	NOUN
ejde-397	1374	8	in	in	ADP
ejde-397	1374	9	x	x	PROPN
ejde-397	1374	10	,	,	PUNCT
ejde-397	1374	11	abs(k	abs(k	PROPN
ejde-397	1374	12	)	)	PUNCT
ejde-397	1374	13	<	<	X
ejde-397	1374	14	∞	∞	PROPN
ejde-397	1374	15	,	,	PUNCT
ejde-397	1374	16	abs(|a|	abs(|a|	ADJ
ejde-397	1374	17	)	)	PUNCT
ejde-397	1374	18	<	<	X
ejde-397	1374	19	∞	∞	PROPN
ejde-397	1374	20	,	,	PUNCT
ejde-397	1374	21	r	r	NOUN
ejde-397	1374	22	≥	≥	NOUN
ejde-397	1374	23	−1	−1	NOUN
ejde-397	1374	24	and	and	CCONJ
ejde-397	1374	25	there	there	PRON
ejde-397	1374	26	exists	exist	VERB
ejde-397	1374	27	ω	ω	PROPN
ejde-397	1374	28	≥	≥	NOUN
ejde-397	1374	29	max(0	max(0	NOUN
ejde-397	1374	30	,	,	PUNCT
ejde-397	1374	31	abs(k	abs(k	PROPN
ejde-397	1374	32	)	)	PUNCT
ejde-397	1374	33	,	,	PUNCT
ejde-397	1374	34	abs(|a|	abs(|a|	ADJ
ejde-397	1374	35	)	)	PUNCT
ejde-397	1374	36	)	)	PUNCT
ejde-397	1374	37	such	such	ADJ
ejde-397	1374	38	that	that	SCONJ
ejde-397	1374	39	,	,	PUNCT
ejde-397	1374	40	for	for	ADP
ejde-397	1374	41	every	every	DET
ejde-397	1374	42	z	z	PROPN
ejde-397	1374	43	∈	∈	PROPN
ejde-397	1374	44	{	{	PUNCT
ejde-397	1374	45	λ	λ	X
ejde-397	1374	46	∈	∈	PROPN
ejde-397	1374	47	c	c	NOUN
ejde-397	1374	48	:	:	PUNCT
ejde-397	1374	49	<	<	X
ejde-397	1374	50	λ	λ	X
ejde-397	1374	51	>	>	X
ejde-397	1374	52	ω	ω	PROPN
ejde-397	1374	53	,	,	PUNCT
ejde-397	1374	54	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1374	55	)	)	PUNCT
ejde-397	1374	56	6=	6=	ADP
ejde-397	1374	57	0	0	NUM
ejde-397	1374	58	}	}	PUNCT
ejde-397	1374	59	,	,	PUNCT
ejde-397	1374	60	we	we	PRON
ejde-397	1374	61	have	have	VERB
ejde-397	1374	62	that	that	SCONJ
ejde-397	1374	63	the	the	DET
ejde-397	1374	64	operator	operator	NOUN
ejde-397	1374	65	i	i	PRON
ejde-397	1374	66	−	−	VERB
ejde-397	1374	67	ã(z)a	ã(z)a	ADJ
ejde-397	1374	68	is	be	AUX
ejde-397	1374	69	injective	injective	ADJ
ejde-397	1374	70	and	and	CCONJ
ejde-397	1374	71	r(c	r(c	ADJ
ejde-397	1374	72	)	)	PUNCT
ejde-397	1374	73	⊆	⊆	NUM
ejde-397	1374	74	r(i	r(i	NOUN
ejde-397	1374	75	−	−	PROPN
ejde-397	1374	76	ã(z)a	ã(z)a	ADJ
ejde-397	1374	77	)	)	PUNCT
ejde-397	1374	78	.	.	PUNCT
ejde-397	1375	1	if	if	SCONJ
ejde-397	1375	2	,	,	PUNCT
ejde-397	1375	3	additionally	additionally	ADV
ejde-397	1375	4	,	,	PUNCT
ejde-397	1375	5	for	for	ADP
ejde-397	1375	6	every	every	DET
ejde-397	1375	7	σ	σ	PROPN
ejde-397	1375	8	>	>	X
ejde-397	1375	9	0	0	PROPN
ejde-397	1375	10	,	,	PUNCT
ejde-397	1375	11	there	there	PRON
ejde-397	1375	12	exist	exist	VERB
ejde-397	1375	13	cσ	cσ	ADP
ejde-397	1375	14	>	>	X
ejde-397	1375	15	0	0	PUNCT
ejde-397	1375	16	and	and	CCONJ
ejde-397	1375	17	an	an	DET
ejde-397	1375	18	open	open	ADJ
ejde-397	1375	19	neighborhood	neighborhood	NOUN
ejde-397	1375	20	ωσ	ωσ	PROPN
ejde-397	1375	21	,	,	PUNCT
ejde-397	1375	22	ω	ω	NUM
ejde-397	1375	23	of	of	ADP
ejde-397	1375	24	the	the	DET
ejde-397	1375	25	region	region	NOUN
ejde-397	1375	26	λσ	λσ	PROPN
ejde-397	1375	27	,	,	PUNCT
ejde-397	1375	28	ω	ω	NOUN
ejde-397	1375	29	:	:	PUNCT
ejde-397	1375	30	=	=	SYM
ejde-397	1375	31	{	{	PUNCT
ejde-397	1375	32	λ	λ	X
ejde-397	1375	33	∈	∈	NOUN
ejde-397	1375	34	c	c	NOUN
ejde-397	1375	35	:	:	PUNCT
ejde-397	1375	36	<	<	X
ejde-397	1375	37	λ	λ	X
ejde-397	1375	38	≤	≤	PROPN
ejde-397	1375	39	ω	ω	PROPN
ejde-397	1375	40	,	,	PUNCT
ejde-397	1375	41	<	<	X
ejde-397	1375	42	λ	λ	X
ejde-397	1375	43	≥	≥	NOUN
ejde-397	1375	44	−σ	−σ	NOUN
ejde-397	1375	45	ln	ln	PROPN
ejde-397	1375	46	|=λ|+	|=λ|+	ADV
ejde-397	1375	47	cσ	cσ	ADP
ejde-397	1375	48	}	}	PUNCT
ejde-397	1375	49	∪	∪	X
ejde-397	1375	50	{	{	PUNCT
ejde-397	1375	51	λ	λ	X
ejde-397	1375	52	∈	∈	NOUN
ejde-397	1375	53	c	c	NOUN
ejde-397	1375	54	:	:	PUNCT
ejde-397	1375	55	<	<	X
ejde-397	1375	56	λ	λ	X
ejde-397	1375	57	≥	≥	NOUN
ejde-397	1375	58	ω	ω	NUM
ejde-397	1375	59	}	}	PUNCT
ejde-397	1375	60	,	,	PUNCT
ejde-397	1375	61	and	and	CCONJ
ejde-397	1375	62	a	a	DET
ejde-397	1375	63	function	function	NOUN
ejde-397	1375	64	hσ	hσ	NOUN
ejde-397	1375	65	:	:	PUNCT
ejde-397	1375	66	ωσ	ωσ	PROPN
ejde-397	1375	67	,	,	PUNCT
ejde-397	1375	68	ω	ω	PROPN
ejde-397	1375	69	→	→	SYM
ejde-397	1375	70	l(x	l(x	PROPN
ejde-397	1375	71	)	)	PUNCT
ejde-397	1375	72	such	such	ADJ
ejde-397	1375	73	that	that	SCONJ
ejde-397	1375	74	,	,	PUNCT
ejde-397	1375	75	for	for	ADP
ejde-397	1375	76	every	every	DET
ejde-397	1375	77	x	x	SYM
ejde-397	1375	78	∈	∈	PROPN
ejde-397	1375	79	x	x	NOUN
ejde-397	1375	80	,	,	PUNCT
ejde-397	1375	81	the	the	DET
ejde-397	1375	82	mapping	mapping	NOUN
ejde-397	1375	83	λ	λ	PROPN
ejde-397	1375	84	7→	7→	PROPN
ejde-397	1375	85	hσ(λ)x	hσ(λ)x	NOUN
ejde-397	1375	86	,	,	PUNCT
ejde-397	1375	87	λ	λ	PROPN
ejde-397	1375	88	∈	∈	PROPN
ejde-397	1375	89	ωσ	ωσ	PRON
ejde-397	1375	90	,	,	PUNCT
ejde-397	1375	91	ω	ω	PROPN
ejde-397	1375	92	is	be	AUX
ejde-397	1375	93	analytic	analytic	ADJ
ejde-397	1375	94	as	as	ADV
ejde-397	1375	95	well	well	ADV
ejde-397	1375	96	as	as	ADP
ejde-397	1375	97	that	that	PRON
ejde-397	1375	98	hσ(λ	hσ(λ	PUNCT
ejde-397	1375	99	)	)	PUNCT
ejde-397	1376	1	=	=	PUNCT
ejde-397	1376	2	k̃(λ)(i	k̃(λ)(i	PROPN
ejde-397	1376	3	−	−	PROPN
ejde-397	1376	4	ã(λ)a)−1c	ã(λ)a)−1c	PROPN
ejde-397	1376	5	,	,	PUNCT
ejde-397	1376	6	<	<	X
ejde-397	1376	7	λ	λ	X
ejde-397	1376	8	>	>	X
ejde-397	1376	9	ω	ω	PROPN
ejde-397	1376	10	,	,	PUNCT
ejde-397	1376	11	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1376	12	)	)	PUNCT
ejde-397	1376	13	6=	6=	ADP
ejde-397	1376	14	0	0	NUM
ejde-397	1376	15	,	,	PUNCT
ejde-397	1376	16	and	and	CCONJ
ejde-397	1376	17	that	that	SCONJ
ejde-397	1376	18	the	the	DET
ejde-397	1376	19	family	family	NOUN
ejde-397	1376	20	{	{	PUNCT
ejde-397	1376	21	|λ|−rhσ(λ	|λ|−rhσ(λ	NUM
ejde-397	1376	22	)	)	PUNCT
ejde-397	1376	23	:	:	PUNCT
ejde-397	1376	24	λ	λ	X
ejde-397	1376	25	∈	∈	PROPN
ejde-397	1376	26	λσ	λσ	PRON
ejde-397	1376	27	,	,	PUNCT
ejde-397	1376	28	ω	ω	NOUN
ejde-397	1376	29	}	}	PUNCT
ejde-397	1376	30	is	be	AUX
ejde-397	1376	31	equicontinuous	equicontinuous	ADJ
ejde-397	1376	32	,	,	PUNCT
ejde-397	1376	33	then	then	ADV
ejde-397	1376	34	,	,	PUNCT
ejde-397	1376	35	for	for	ADP
ejde-397	1376	36	every	every	DET
ejde-397	1376	37	ζ	ζ	NOUN
ejde-397	1376	38	>	>	X
ejde-397	1376	39	1	1	NUM
ejde-397	1376	40	,	,	PUNCT
ejde-397	1376	41	a	a	PRON
ejde-397	1376	42	is	be	AUX
ejde-397	1376	43	a	a	DET
ejde-397	1376	44	subgenerator	subgenerator	NOUN
ejde-397	1376	45	of	of	ADP
ejde-397	1376	46	an	an	DET
ejde-397	1376	47	exponentially	exponentially	ADV
ejde-397	1376	48	equicontinuous	equicontinuous	ADJ
ejde-397	1376	49	(	(	PUNCT
ejde-397	1376	50	a	a	PRON
ejde-397	1376	51	,	,	PUNCT
ejde-397	1376	52	k	k	PROPN
ejde-397	1376	53	∗	∗	NOUN
ejde-397	1376	54	gζ+r)-regularized	gζ+r)-regularize	VERB
ejde-397	1376	55	c	c	NOUN
ejde-397	1376	56	-	-	PUNCT
ejde-397	1376	57	resolvent	resolvent	ADJ
ejde-397	1376	58	family	family	NOUN
ejde-397	1376	59	(	(	PUNCT
ejde-397	1376	60	rζ(t))t≥0	rζ(t))t≥0	PROPN
ejde-397	1376	61	satisfying	satisfy	VERB
ejde-397	1376	62	that	that	SCONJ
ejde-397	1376	63	the	the	DET
ejde-397	1376	64	mapping	mapping	NOUN
ejde-397	1376	65	t	t	PROPN
ejde-397	1376	66	7→	7→	NUM
ejde-397	1376	67	rζ(t	rζ(t	NOUN
ejde-397	1376	68	)	)	PUNCT
ejde-397	1376	69	,	,	PUNCT
ejde-397	1376	70	t	t	PROPN
ejde-397	1376	71	>	>	X
ejde-397	1376	72	0	0	PUNCT
ejde-397	1376	73	is	be	AUX
ejde-397	1376	74	infinitely	infinitely	ADV
ejde-397	1376	75	differentiable	differentiable	ADJ
ejde-397	1376	76	in	in	ADP
ejde-397	1376	77	l(x	l(x	PROPN
ejde-397	1376	78	)	)	PUNCT
ejde-397	1376	79	.	.	PUNCT
ejde-397	1377	1	theorem	theorem	VERB
ejde-397	1377	2	5.27	5.27	NUM
ejde-397	1377	3	.	.	PUNCT
ejde-397	1378	1	let	let	VERB
ejde-397	1378	2	(	(	PUNCT
ejde-397	1378	3	mn)n∈n0	mn)n∈n0	NOUN
ejde-397	1378	4	satisfy	satisfy	NOUN
ejde-397	1378	5	(	(	PUNCT
ejde-397	1378	6	m.1	m.1	NOUN
ejde-397	1378	7	)	)	PUNCT
ejde-397	1378	8	,	,	PUNCT
ejde-397	1378	9	(	(	PUNCT
ejde-397	1378	10	m.2	m.2	NOUN
ejde-397	1378	11	)	)	PUNCT
ejde-397	1378	12	and	and	CCONJ
ejde-397	1378	13	(	(	PUNCT
ejde-397	1378	14	m.3	m.3	NOUN
ejde-397	1378	15	)	)	PUNCT
ejde-397	1378	16	’	'	PUNCT
ejde-397	1378	17	.	.	PUNCT
ejde-397	1379	1	(	(	PUNCT
ejde-397	1379	2	i	i	NOUN
ejde-397	1379	3	)	)	PUNCT
ejde-397	1379	4	suppose	suppose	VERB
ejde-397	1379	5	that	that	SCONJ
ejde-397	1379	6	abs(k	abs(k	PROPN
ejde-397	1379	7	)	)	PUNCT
ejde-397	1379	8	<	<	X
ejde-397	1379	9	∞	∞	PROPN
ejde-397	1379	10	,	,	PUNCT
ejde-397	1379	11	abs(|a|	abs(|a|	ADJ
ejde-397	1379	12	)	)	PUNCT
ejde-397	1379	13	<	<	X
ejde-397	1379	14	∞	∞	PROPN
ejde-397	1379	15	,	,	PUNCT
ejde-397	1379	16	a	a	PRON
ejde-397	1379	17	is	be	AUX
ejde-397	1379	18	a	a	DET
ejde-397	1379	19	closed	closed	ADJ
ejde-397	1379	20	subgenerator	subgenerator	NOUN
ejde-397	1379	21	of	of	ADP
ejde-397	1379	22	a	a	DET
ejde-397	1379	23	(	(	PUNCT
ejde-397	1379	24	local	local	ADJ
ejde-397	1379	25	)	)	PUNCT
ejde-397	1379	26	(	(	PUNCT
ejde-397	1379	27	a	a	PRON
ejde-397	1379	28	,	,	PUNCT
ejde-397	1379	29	k)-regularized	k)-regularize	VERB
ejde-397	1379	30	c	c	NOUN
ejde-397	1379	31	-	-	PUNCT
ejde-397	1379	32	resolvent	resolvent	ADJ
ejde-397	1379	33	family	family	NOUN
ejde-397	1379	34	(	(	PUNCT
ejde-397	1379	35	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1379	36	)	)	PUNCT
ejde-397	1379	37	,	,	PUNCT
ejde-397	1379	38	ω	ω	X
ejde-397	1379	39	>	>	X
ejde-397	1379	40	max(0	max(0	PROPN
ejde-397	1379	41	,	,	PUNCT
ejde-397	1379	42	abs(k	abs(k	PROPN
ejde-397	1379	43	)	)	PUNCT
ejde-397	1379	44	,	,	PUNCT
ejde-397	1379	45	abs(|a|	abs(|a|	ADJ
ejde-397	1379	46	)	)	PUNCT
ejde-397	1379	47	)	)	PUNCT
ejde-397	1380	1	and	and	CCONJ
ejde-397	1380	2	m	m	PROPN
ejde-397	1380	3	∈	∈	PROPN
ejde-397	1380	4	n.	n.	NOUN
ejde-397	1380	5	denote	denote	NOUN
ejde-397	1380	6	,	,	PUNCT
ejde-397	1380	7	for	for	ADP
ejde-397	1380	8	every	every	DET
ejde-397	1380	9	ε	ε	PROPN
ejde-397	1380	10	∈	∈	PROPN
ejde-397	1380	11	(	(	PUNCT
ejde-397	1380	12	0	0	NUM
ejde-397	1380	13	,	,	PUNCT
ejde-397	1380	14	1	1	NUM
ejde-397	1380	15	)	)	PUNCT
ejde-397	1380	16	and	and	CCONJ
ejde-397	1380	17	a	a	DET
ejde-397	1380	18	corresponding	correspond	VERB
ejde-397	1380	19	kε	kε	X
ejde-397	1380	20	>	>	X
ejde-397	1380	21	0	0	PROPN
ejde-397	1380	22	,	,	PUNCT
ejde-397	1380	23	fε	fε	NOUN
ejde-397	1380	24	,	,	PUNCT
ejde-397	1380	25	ω	ω	NOUN
ejde-397	1380	26	:	:	PUNCT
ejde-397	1380	27	=	=	SYM
ejde-397	1380	28	{	{	PUNCT
ejde-397	1381	1	λ	λ	X
ejde-397	1381	2	∈	∈	NOUN
ejde-397	1381	3	c	c	NOUN
ejde-397	1381	4	:	:	PUNCT
ejde-397	1382	1	<	<	X
ejde-397	1382	2	λ	λ	X
ejde-397	1382	3	≥	≥	NOUN
ejde-397	1382	4	−	−	NOUN
ejde-397	1382	5	lnωl	lnωl	NOUN
ejde-397	1382	6	(	(	PUNCT
ejde-397	1382	7	kε|=λ|	kε|=λ|	PROPN
ejde-397	1382	8	)	)	PUNCT
ejde-397	1383	1	+	+	CCONJ
ejde-397	1383	2	ω	ω	NUM
ejde-397	1383	3	}	}	PUNCT
ejde-397	1383	4	.	.	PUNCT
ejde-397	1384	1	assume	assume	VERB
ejde-397	1384	2	that	that	SCONJ
ejde-397	1384	3	,	,	PUNCT
ejde-397	1384	4	for	for	ADP
ejde-397	1384	5	every	every	DET
ejde-397	1384	6	ε	ε	PROPN
ejde-397	1384	7	∈	∈	PROPN
ejde-397	1384	8	(	(	PUNCT
ejde-397	1384	9	0	0	NUM
ejde-397	1384	10	,	,	PUNCT
ejde-397	1384	11	1	1	NUM
ejde-397	1384	12	)	)	PUNCT
ejde-397	1384	13	,	,	PUNCT
ejde-397	1384	14	there	there	PRON
ejde-397	1384	15	exist	exist	VERB
ejde-397	1384	16	kε	kε	PROPN
ejde-397	1384	17	>	>	X
ejde-397	1384	18	0	0	PROPN
ejde-397	1384	19	,	,	PUNCT
ejde-397	1384	20	an	an	DET
ejde-397	1384	21	open	open	ADJ
ejde-397	1384	22	neighborhood	neighborhood	NOUN
ejde-397	1384	23	oε	oε	NOUN
ejde-397	1384	24	,	,	PUNCT
ejde-397	1384	25	ω	ω	NUM
ejde-397	1384	26	of	of	ADP
ejde-397	1384	27	the	the	DET
ejde-397	1384	28	region	region	NOUN
ejde-397	1384	29	gε	gε	PROPN
ejde-397	1384	30	,	,	PUNCT
ejde-397	1384	31	ω	ω	NOUN
ejde-397	1384	32	:	:	PUNCT
ejde-397	1384	33	=	=	SYM
ejde-397	1384	34	{	{	PUNCT
ejde-397	1384	35	λ	λ	X
ejde-397	1384	36	∈	∈	NOUN
ejde-397	1384	37	c	c	NOUN
ejde-397	1384	38	:	:	PUNCT
ejde-397	1385	1	<	<	X
ejde-397	1385	2	λ	λ	X
ejde-397	1385	3	≥	≥	PROPN
ejde-397	1385	4	ω	ω	NUM
ejde-397	1385	5	,	,	PUNCT
ejde-397	1385	6	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1385	7	)	)	PUNCT
ejde-397	1385	8	6=	6=	ADP
ejde-397	1385	9	0	0	NUM
ejde-397	1385	10	}	}	PUNCT
ejde-397	1385	11	∪	∪	X
ejde-397	1385	12	{	{	PUNCT
ejde-397	1385	13	λ	λ	PROPN
ejde-397	1385	14	∈	∈	PROPN
ejde-397	1385	15	fε	fε	NOUN
ejde-397	1385	16	,	,	PUNCT
ejde-397	1385	17	ω	ω	NOUN
ejde-397	1385	18	:	:	PUNCT
ejde-397	1385	19	<	<	X
ejde-397	1385	20	λ	λ	X
ejde-397	1385	21	≤	≤	NOUN
ejde-397	1385	22	ω	ω	NUM
ejde-397	1385	23	}	}	PUNCT
ejde-397	1385	24	,	,	PUNCT
ejde-397	1385	25	a	a	DET
ejde-397	1385	26	mapping	mapping	NOUN
ejde-397	1385	27	hε	hε	ADP
ejde-397	1385	28	:	:	PUNCT
ejde-397	1385	29	oε	oε	PROPN
ejde-397	1385	30	,	,	PUNCT
ejde-397	1385	31	ω	ω	PROPN
ejde-397	1385	32	→	→	SYM
ejde-397	1385	33	l(e	l(e	NOUN
ejde-397	1385	34	)	)	PUNCT
ejde-397	1385	35	and	and	CCONJ
ejde-397	1385	36	analytic	analytic	ADJ
ejde-397	1385	37	mappings	mapping	NOUN
ejde-397	1385	38	fε	fε	NOUN
ejde-397	1385	39	:	:	PUNCT
ejde-397	1385	40	oε	oε	PROPN
ejde-397	1385	41	,	,	PUNCT
ejde-397	1385	42	ω	ω	PROPN
ejde-397	1385	43	→	→	SYM
ejde-397	1385	44	c	c	PROPN
ejde-397	1385	45	,	,	PUNCT
ejde-397	1385	46	gε	gε	X
ejde-397	1385	47	:	:	PUNCT
ejde-397	1385	48	oε	oε	PROPN
ejde-397	1385	49	,	,	PUNCT
ejde-397	1385	50	ω	ω	PROPN
ejde-397	1385	51	→	→	SYM
ejde-397	1385	52	c	c	NOUN
ejde-397	1385	53	such	such	ADJ
ejde-397	1385	54	that	that	PRON
ejde-397	1385	55	:	:	PUNCT
ejde-397	1385	56	(	(	PUNCT
ejde-397	1385	57	a	a	X
ejde-397	1385	58	)	)	PUNCT
ejde-397	1385	59	fε(λ	fε(λ	NOUN
ejde-397	1385	60	)	)	PUNCT
ejde-397	1385	61	=	=	SYM
ejde-397	1385	62	k̃(λ	k̃(λ	PROPN
ejde-397	1385	63	)	)	PUNCT
ejde-397	1385	64	,	,	PUNCT
ejde-397	1385	65	<	<	X
ejde-397	1385	66	λ	λ	X
ejde-397	1385	67	>	>	X
ejde-397	1385	68	ω	ω	PROPN
ejde-397	1385	69	;	;	PUNCT
ejde-397	1385	70	gε(λ	gε(λ	X
ejde-397	1385	71	)	)	PUNCT
ejde-397	1385	72	=	=	SYM
ejde-397	1385	73	ã(λ	ã(λ	PROPN
ejde-397	1385	74	)	)	PUNCT
ejde-397	1385	75	,	,	PUNCT
ejde-397	1385	76	<	<	X
ejde-397	1385	77	λ	λ	X
ejde-397	1385	78	>	>	X
ejde-397	1385	79	ω	ω	PROPN
ejde-397	1385	80	,	,	PUNCT
ejde-397	1385	81	46	46	NUM
ejde-397	1385	82	m.	m.	NOUN
ejde-397	1385	83	kostić	kostić	NOUN
ejde-397	1386	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1386	2	(	(	PUNCT
ejde-397	1386	3	b	b	NOUN
ejde-397	1386	4	)	)	PUNCT
ejde-397	1386	5	for	for	ADP
ejde-397	1386	6	every	every	DET
ejde-397	1386	7	λ	λ	PROPN
ejde-397	1386	8	∈	∈	PROPN
ejde-397	1386	9	fε	fε	NOUN
ejde-397	1386	10	,	,	PUNCT
ejde-397	1386	11	ω	ω	PROPN
ejde-397	1386	12	,	,	PUNCT
ejde-397	1386	13	the	the	DET
ejde-397	1386	14	operator	operator	NOUN
ejde-397	1387	1	i	i	PRON
ejde-397	1387	2	−	−	PROPN
ejde-397	1388	1	gε(λ)a	gε(λ)a	PROPN
ejde-397	1388	2	is	be	AUX
ejde-397	1388	3	injective	injective	ADJ
ejde-397	1388	4	and	and	CCONJ
ejde-397	1388	5	r(c	r(c	ADJ
ejde-397	1388	6	)	)	PUNCT
ejde-397	1388	7	⊆	⊆	NUM
ejde-397	1388	8	r(i	r(i	NOUN
ejde-397	1388	9	−	−	PROPN
ejde-397	1388	10	gε(λ)a	gε(λ)a	NOUN
ejde-397	1388	11	)	)	PUNCT
ejde-397	1388	12	,	,	PUNCT
ejde-397	1388	13	(	(	PUNCT
ejde-397	1388	14	c	c	X
ejde-397	1388	15	)	)	PUNCT
ejde-397	1388	16	for	for	ADP
ejde-397	1388	17	every	every	DET
ejde-397	1388	18	x	x	SYM
ejde-397	1388	19	∈	∈	PROPN
ejde-397	1388	20	x	x	NOUN
ejde-397	1388	21	,	,	PUNCT
ejde-397	1388	22	the	the	DET
ejde-397	1388	23	mapping	mapping	NOUN
ejde-397	1388	24	λ	λ	NOUN
ejde-397	1388	25	7→	7→	NUM
ejde-397	1388	26	hε(λ)x	hε(λ)x	NOUN
ejde-397	1388	27	,	,	PUNCT
ejde-397	1388	28	λ	λ	PROPN
ejde-397	1388	29	∈	∈	PROPN
ejde-397	1388	30	gε	gε	PROPN
ejde-397	1388	31	,	,	PUNCT
ejde-397	1388	32	ω	ω	PROPN
ejde-397	1388	33	is	be	AUX
ejde-397	1388	34	analytic	analytic	ADJ
ejde-397	1388	35	,	,	PUNCT
ejde-397	1388	36	hε(λ	hε(λ	NOUN
ejde-397	1388	37	)	)	PUNCT
ejde-397	1389	1	=	=	SYM
ejde-397	1389	2	fε(λ)(i	fε(λ)(i	PROPN
ejde-397	1390	1	−	−	PROPN
ejde-397	1390	2	gε(λ)a)−1c	gε(λ)a)−1c	PROPN
ejde-397	1390	3	,	,	PUNCT
ejde-397	1390	4	λ	λ	PROPN
ejde-397	1390	5	∈	∈	PROPN
ejde-397	1390	6	gε	gε	PROPN
ejde-397	1390	7	,	,	PUNCT
ejde-397	1390	8	ω	ω	PROPN
ejde-397	1390	9	,	,	PUNCT
ejde-397	1390	10	(	(	PUNCT
ejde-397	1390	11	d	d	X
ejde-397	1390	12	)	)	PUNCT
ejde-397	1390	13	the	the	DET
ejde-397	1390	14	family	family	NOUN
ejde-397	1390	15	{	{	PUNCT
ejde-397	1390	16	(	(	PUNCT
ejde-397	1390	17	1	1	NUM
ejde-397	1390	18	+	+	NUM
ejde-397	1390	19	|λ|)−me−ε|<λ|hε(λ	|λ|)−me−ε|<λ|hε(λ	PROPN
ejde-397	1390	20	)	)	PUNCT
ejde-397	1390	21	:	:	PUNCT
ejde-397	1391	1	λ	λ	X
ejde-397	1391	2	∈	∈	PROPN
ejde-397	1391	3	fε	fε	NOUN
ejde-397	1391	4	,	,	PUNCT
ejde-397	1391	5	ω	ω	PROPN
ejde-397	1391	6	,	,	PUNCT
ejde-397	1391	7	<	<	X
ejde-397	1391	8	λ	λ	X
ejde-397	1391	9	≤	≤	NOUN
ejde-397	1391	10	ω	ω	NUM
ejde-397	1391	11	}	}	PUNCT
ejde-397	1391	12	⊆	⊆	NUM
ejde-397	1391	13	l(x	l(x	PROPN
ejde-397	1391	14	)	)	PUNCT
ejde-397	1391	15	is	be	AUX
ejde-397	1391	16	equicontinuous	equicontinuous	ADJ
ejde-397	1391	17	and	and	CCONJ
ejde-397	1391	18	the	the	DET
ejde-397	1391	19	family	family	NOUN
ejde-397	1391	20	{	{	PUNCT
ejde-397	1391	21	(	(	PUNCT
ejde-397	1391	22	1	1	NUM
ejde-397	1391	23	+	+	NUM
ejde-397	1391	24	|λ|)−mhε(λ	|λ|)−mhε(λ	NOUN
ejde-397	1391	25	)	)	PUNCT
ejde-397	1391	26	:	:	PUNCT
ejde-397	1392	1	λ	λ	X
ejde-397	1392	2	∈	∈	PROPN
ejde-397	1392	3	c	c	X
ejde-397	1392	4	,	,	PUNCT
ejde-397	1392	5	<	<	X
ejde-397	1392	6	λ	λ	X
ejde-397	1392	7	≥	≥	NOUN
ejde-397	1392	8	ω	ω	NUM
ejde-397	1392	9	}	}	PUNCT
ejde-397	1392	10	⊆	⊆	NUM
ejde-397	1392	11	l(x	l(x	PROPN
ejde-397	1392	12	)	)	PUNCT
ejde-397	1392	13	is	be	AUX
ejde-397	1392	14	equicontinuous	equicontinuous	ADJ
ejde-397	1392	15	.	.	PUNCT
ejde-397	1393	1	then	then	ADV
ejde-397	1393	2	the	the	DET
ejde-397	1393	3	mapping	mapping	NOUN
ejde-397	1393	4	t	t	NOUN
ejde-397	1393	5	7→	7→	NUM
ejde-397	1393	6	r(t	r(t	NOUN
ejde-397	1393	7	)	)	PUNCT
ejde-397	1393	8	,	,	PUNCT
ejde-397	1393	9	t	t	PROPN
ejde-397	1393	10	∈	∈	PROPN
ejde-397	1393	11	(	(	PUNCT
ejde-397	1393	12	0	0	NUM
ejde-397	1393	13	,	,	PUNCT
ejde-397	1393	14	τ	τ	X
ejde-397	1393	15	)	)	PUNCT
ejde-397	1393	16	is	be	AUX
ejde-397	1393	17	infinitely	infinitely	ADV
ejde-397	1393	18	differentiable	differentiable	ADJ
ejde-397	1393	19	in	in	ADP
ejde-397	1393	20	l(x	l(x	PROPN
ejde-397	1393	21	)	)	PUNCT
ejde-397	1393	22	and	and	CCONJ
ejde-397	1393	23	,	,	PUNCT
ejde-397	1393	24	for	for	SCONJ
ejde-397	1393	25	every	every	DET
ejde-397	1393	26	compact	compact	NOUN
ejde-397	1393	27	set	set	VERB
ejde-397	1393	28	k	k	PROPN
ejde-397	1393	29	⊆	⊆	NUM
ejde-397	1393	30	(	(	PUNCT
ejde-397	1393	31	0	0	NUM
ejde-397	1393	32	,	,	PUNCT
ejde-397	1393	33	τ	τ	PROPN
ejde-397	1393	34	)	)	PUNCT
ejde-397	1393	35	,	,	PUNCT
ejde-397	1393	36	there	there	PRON
ejde-397	1393	37	exists	exist	VERB
ejde-397	1393	38	hk	hk	PROPN
ejde-397	1393	39	>	>	X
ejde-397	1393	40	0	0	NUM
ejde-397	1394	1	such	such	ADJ
ejde-397	1394	2	that	that	SCONJ
ejde-397	1394	3	the	the	DET
ejde-397	1394	4	set	set	NOUN
ejde-397	1394	5	{	{	PUNCT
ejde-397	1394	6	h	h	NOUN
ejde-397	1394	7	n	n	CCONJ
ejde-397	1394	8	k	k	PROPN
ejde-397	1394	9	dn	dn	PROPN
ejde-397	1394	10	dtnr(t	dtnr(t	PROPN
ejde-397	1394	11	)	)	PUNCT
ejde-397	1394	12	mn	mn	PROPN
ejde-397	1394	13	:	:	PUNCT
ejde-397	1394	14	t	t	PROPN
ejde-397	1394	15	∈	∈	PROPN
ejde-397	1394	16	k	k	PROPN
ejde-397	1394	17	,	,	PUNCT
ejde-397	1394	18	n	n	PROPN
ejde-397	1394	19	∈	∈	PROPN
ejde-397	1394	20	n0	n0	PROPN
ejde-397	1394	21	}	}	PUNCT
ejde-397	1394	22	is	be	AUX
ejde-397	1394	23	equicontinuous	equicontinuous	ADJ
ejde-397	1394	24	.	.	PUNCT
ejde-397	1395	1	(	(	PUNCT
ejde-397	1395	2	ii	ii	NOUN
ejde-397	1395	3	)	)	PUNCT
ejde-397	1395	4	suppose	suppose	VERB
ejde-397	1395	5	that	that	SCONJ
ejde-397	1395	6	abs(k	abs(k	PROPN
ejde-397	1395	7	)	)	PUNCT
ejde-397	1395	8	<	<	X
ejde-397	1395	9	∞	∞	PROPN
ejde-397	1395	10	,	,	PUNCT
ejde-397	1395	11	abs(|a|	abs(|a|	ADJ
ejde-397	1395	12	)	)	PUNCT
ejde-397	1395	13	<	<	X
ejde-397	1395	14	∞	∞	PROPN
ejde-397	1395	15	,	,	PUNCT
ejde-397	1395	16	a	a	PRON
ejde-397	1395	17	is	be	AUX
ejde-397	1395	18	a	a	DET
ejde-397	1395	19	closed	closed	ADJ
ejde-397	1395	20	subgenerator	subgenerator	NOUN
ejde-397	1395	21	of	of	ADP
ejde-397	1395	22	a	a	DET
ejde-397	1395	23	(	(	PUNCT
ejde-397	1395	24	local	local	ADJ
ejde-397	1395	25	)	)	PUNCT
ejde-397	1395	26	(	(	PUNCT
ejde-397	1395	27	a	a	PRON
ejde-397	1395	28	,	,	PUNCT
ejde-397	1395	29	k)-regularized	k)-regularize	VERB
ejde-397	1395	30	c	c	NOUN
ejde-397	1395	31	-	-	PUNCT
ejde-397	1395	32	resolvent	resolvent	ADJ
ejde-397	1395	33	family	family	NOUN
ejde-397	1395	34	(	(	PUNCT
ejde-397	1395	35	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1395	36	)	)	PUNCT
ejde-397	1395	37	,	,	PUNCT
ejde-397	1395	38	ω	ω	X
ejde-397	1395	39	>	>	X
ejde-397	1395	40	max(0	max(0	PROPN
ejde-397	1395	41	,	,	PUNCT
ejde-397	1395	42	abs(k	abs(k	PROPN
ejde-397	1395	43	)	)	PUNCT
ejde-397	1395	44	,	,	PUNCT
ejde-397	1395	45	abs(|a|	abs(|a|	ADJ
ejde-397	1395	46	)	)	PUNCT
ejde-397	1395	47	)	)	PUNCT
ejde-397	1395	48	and	and	CCONJ
ejde-397	1395	49	m	m	PROPN
ejde-397	1395	50	∈	∈	PROPN
ejde-397	1395	51	n.	n.	NOUN
ejde-397	1395	52	denote	denote	NOUN
ejde-397	1395	53	,	,	PUNCT
ejde-397	1395	54	for	for	ADP
ejde-397	1395	55	every	every	DET
ejde-397	1395	56	ε	ε	PROPN
ejde-397	1395	57	∈	∈	PROPN
ejde-397	1395	58	(	(	PUNCT
ejde-397	1395	59	0	0	NUM
ejde-397	1395	60	,	,	PUNCT
ejde-397	1395	61	1	1	NUM
ejde-397	1395	62	)	)	PUNCT
ejde-397	1395	63	,	,	PUNCT
ejde-397	1395	64	ρ	ρ	PROPN
ejde-397	1395	65	∈	∈	PROPN
ejde-397	1396	1	[	[	X
ejde-397	1396	2	1,∞	1,∞	NUM
ejde-397	1396	3	)	)	PUNCT
ejde-397	1396	4	and	and	CCONJ
ejde-397	1396	5	a	a	DET
ejde-397	1396	6	corresponding	correspond	VERB
ejde-397	1396	7	kε	kε	X
ejde-397	1396	8	>	>	X
ejde-397	1396	9	0	0	PROPN
ejde-397	1396	10	,	,	PUNCT
ejde-397	1396	11	fε	fε	PROPN
ejde-397	1396	12	,	,	PUNCT
ejde-397	1396	13	ω	ω	PROPN
ejde-397	1396	14	,	,	PUNCT
ejde-397	1396	15	ρ	ρ	NOUN
ejde-397	1396	16	:	:	PUNCT
ejde-397	1396	17	=	=	SYM
ejde-397	1396	18	{	{	PUNCT
ejde-397	1396	19	λ	λ	X
ejde-397	1396	20	∈	∈	NOUN
ejde-397	1396	21	c	c	NOUN
ejde-397	1396	22	:	:	PUNCT
ejde-397	1397	1	<	<	X
ejde-397	1397	2	λ	λ	X
ejde-397	1397	3	≥	≥	X
ejde-397	1397	4	−kε|=λ|1	−kε|=λ|1	X
ejde-397	1397	5	/	/	SYM
ejde-397	1397	6	ρ	ρ	PROPN
ejde-397	1397	7	+	+	X
ejde-397	1397	8	ω	ω	NUM
ejde-397	1397	9	}	}	PUNCT
ejde-397	1397	10	.	.	PUNCT
ejde-397	1398	1	assume	assume	VERB
ejde-397	1398	2	that	that	SCONJ
ejde-397	1398	3	,	,	PUNCT
ejde-397	1398	4	for	for	ADP
ejde-397	1398	5	every	every	DET
ejde-397	1398	6	ε	ε	PROPN
ejde-397	1398	7	∈	∈	PROPN
ejde-397	1398	8	(	(	PUNCT
ejde-397	1398	9	0	0	NUM
ejde-397	1398	10	,	,	PUNCT
ejde-397	1398	11	1	1	NUM
ejde-397	1398	12	)	)	PUNCT
ejde-397	1398	13	,	,	PUNCT
ejde-397	1398	14	there	there	PRON
ejde-397	1398	15	exist	exist	VERB
ejde-397	1398	16	kε	kε	PROPN
ejde-397	1398	17	>	>	X
ejde-397	1398	18	0	0	PROPN
ejde-397	1398	19	,	,	PUNCT
ejde-397	1398	20	an	an	DET
ejde-397	1398	21	open	open	ADJ
ejde-397	1398	22	neighborhood	neighborhood	NOUN
ejde-397	1398	23	oε	oε	NOUN
ejde-397	1398	24	,	,	PUNCT
ejde-397	1398	25	ω	ω	NUM
ejde-397	1398	26	of	of	ADP
ejde-397	1398	27	the	the	DET
ejde-397	1398	28	region	region	NOUN
ejde-397	1398	29	gε	gε	PROPN
ejde-397	1398	30	,	,	PUNCT
ejde-397	1398	31	ω	ω	PROPN
ejde-397	1398	32	,	,	PUNCT
ejde-397	1398	33	ρ	ρ	NOUN
ejde-397	1398	34	:	:	PUNCT
ejde-397	1398	35	=	=	SYM
ejde-397	1398	36	{	{	PUNCT
ejde-397	1398	37	λ	λ	X
ejde-397	1398	38	∈	∈	NOUN
ejde-397	1398	39	c	c	NOUN
ejde-397	1398	40	:	:	PUNCT
ejde-397	1399	1	<	<	X
ejde-397	1399	2	λ	λ	X
ejde-397	1399	3	≥	≥	PROPN
ejde-397	1399	4	ω	ω	NUM
ejde-397	1399	5	,	,	PUNCT
ejde-397	1399	6	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1399	7	)	)	PUNCT
ejde-397	1399	8	6=	6=	ADP
ejde-397	1399	9	0	0	NUM
ejde-397	1399	10	}	}	PUNCT
ejde-397	1399	11	∪	∪	X
ejde-397	1399	12	{	{	PUNCT
ejde-397	1399	13	λ	λ	PROPN
ejde-397	1399	14	∈	∈	PROPN
ejde-397	1399	15	fε	fε	NOUN
ejde-397	1399	16	,	,	PUNCT
ejde-397	1399	17	ω	ω	PROPN
ejde-397	1399	18	,	,	PUNCT
ejde-397	1399	19	ρ	ρ	NOUN
ejde-397	1399	20	:	:	PUNCT
ejde-397	1399	21	<	<	X
ejde-397	1399	22	λ	λ	X
ejde-397	1399	23	≤	≤	NOUN
ejde-397	1399	24	ω	ω	NUM
ejde-397	1399	25	}	}	PUNCT
ejde-397	1399	26	,	,	PUNCT
ejde-397	1399	27	a	a	DET
ejde-397	1399	28	mapping	mapping	NOUN
ejde-397	1399	29	hε	hε	ADP
ejde-397	1399	30	:	:	PUNCT
ejde-397	1399	31	oε	oε	PROPN
ejde-397	1399	32	,	,	PUNCT
ejde-397	1399	33	ω	ω	PROPN
ejde-397	1399	34	→	→	SYM
ejde-397	1399	35	l(x	l(x	PROPN
ejde-397	1399	36	)	)	PUNCT
ejde-397	1399	37	and	and	CCONJ
ejde-397	1399	38	analytic	analytic	ADJ
ejde-397	1399	39	mappings	mapping	NOUN
ejde-397	1399	40	fε	fε	NOUN
ejde-397	1399	41	:	:	PUNCT
ejde-397	1399	42	oε	oε	PROPN
ejde-397	1399	43	,	,	PUNCT
ejde-397	1399	44	ω	ω	PROPN
ejde-397	1399	45	→	→	SYM
ejde-397	1399	46	c	c	PROPN
ejde-397	1399	47	and	and	CCONJ
ejde-397	1399	48	gε	gε	INTJ
ejde-397	1399	49	:	:	PUNCT
ejde-397	1399	50	oε	oε	PROPN
ejde-397	1399	51	,	,	PUNCT
ejde-397	1399	52	ω	ω	PROPN
ejde-397	1399	53	→	→	SYM
ejde-397	1399	54	c	c	NOUN
ejde-397	1399	55	such	such	ADJ
ejde-397	1399	56	that	that	SCONJ
ejde-397	1399	57	the	the	DET
ejde-397	1399	58	conditions	condition	NOUN
ejde-397	1399	59	(	(	PUNCT
ejde-397	1399	60	i)(a)-(d	i)(a)-(d	NOUN
ejde-397	1399	61	)	)	PUNCT
ejde-397	1399	62	of	of	ADP
ejde-397	1399	63	this	this	PRON
ejde-397	1399	64	theorem	theorem	VERB
ejde-397	1399	65	hold	hold	NOUN
ejde-397	1399	66	with	with	ADP
ejde-397	1399	67	fε	fε	NOUN
ejde-397	1399	68	,	,	PUNCT
ejde-397	1399	69	ω	ω	PROPN
ejde-397	1399	70	,	,	PUNCT
ejde-397	1399	71	resp	resp	NOUN
ejde-397	1399	72	.	.	PUNCT
ejde-397	1400	1	gε	gε	PROPN
ejde-397	1400	2	,	,	PUNCT
ejde-397	1400	3	ω	ω	PROPN
ejde-397	1400	4	,	,	PUNCT
ejde-397	1400	5	replaced	replace	VERB
ejde-397	1400	6	by	by	ADP
ejde-397	1400	7	fε	fε	NOUN
ejde-397	1400	8	,	,	PUNCT
ejde-397	1400	9	ω	ω	PROPN
ejde-397	1400	10	,	,	PUNCT
ejde-397	1400	11	ρ	ρ	PROPN
ejde-397	1400	12	,	,	PUNCT
ejde-397	1400	13	resp	resp	NOUN
ejde-397	1400	14	.	.	PUNCT
ejde-397	1401	1	gε	gε	PROPN
ejde-397	1401	2	,	,	PUNCT
ejde-397	1401	3	ω	ω	PROPN
ejde-397	1401	4	,	,	PUNCT
ejde-397	1401	5	ρ	ρ	PROPN
ejde-397	1401	6	.	.	PUNCT
ejde-397	1402	1	then	then	ADV
ejde-397	1402	2	the	the	DET
ejde-397	1402	3	mapping	mapping	NOUN
ejde-397	1402	4	t	t	NOUN
ejde-397	1402	5	7→	7→	NUM
ejde-397	1402	6	r(t	r(t	NOUN
ejde-397	1402	7	)	)	PUNCT
ejde-397	1402	8	,	,	PUNCT
ejde-397	1402	9	t	t	PROPN
ejde-397	1402	10	∈	∈	PROPN
ejde-397	1402	11	(	(	PUNCT
ejde-397	1402	12	0	0	NUM
ejde-397	1402	13	,	,	PUNCT
ejde-397	1402	14	τ	τ	X
ejde-397	1402	15	)	)	PUNCT
ejde-397	1402	16	is	be	AUX
ejde-397	1402	17	infinitely	infinitely	ADV
ejde-397	1402	18	differentiable	differentiable	ADJ
ejde-397	1402	19	in	in	ADP
ejde-397	1402	20	l(x	l(x	PROPN
ejde-397	1402	21	)	)	PUNCT
ejde-397	1402	22	and	and	CCONJ
ejde-397	1402	23	,	,	PUNCT
ejde-397	1402	24	for	for	SCONJ
ejde-397	1402	25	every	every	DET
ejde-397	1402	26	compact	compact	NOUN
ejde-397	1402	27	set	set	VERB
ejde-397	1402	28	k	k	PROPN
ejde-397	1402	29	⊆	⊆	NUM
ejde-397	1402	30	(	(	PUNCT
ejde-397	1402	31	0	0	NUM
ejde-397	1402	32	,	,	PUNCT
ejde-397	1402	33	τ	τ	PROPN
ejde-397	1402	34	)	)	PUNCT
ejde-397	1402	35	,	,	PUNCT
ejde-397	1402	36	there	there	PRON
ejde-397	1402	37	exists	exist	VERB
ejde-397	1402	38	hk	hk	PROPN
ejde-397	1402	39	>	>	X
ejde-397	1402	40	0	0	NUM
ejde-397	1403	1	such	such	ADJ
ejde-397	1403	2	that	that	SCONJ
ejde-397	1403	3	the	the	DET
ejde-397	1403	4	set	set	NOUN
ejde-397	1403	5	{	{	PUNCT
ejde-397	1403	6	h	h	NOUN
ejde-397	1403	7	n	n	CCONJ
ejde-397	1403	8	k	k	PROPN
ejde-397	1403	9	dn	dn	PROPN
ejde-397	1403	10	dtnr(t	dtnr(t	PROPN
ejde-397	1403	11	)	)	PUNCT
ejde-397	1403	12	n!ρ	n!ρ	PROPN
ejde-397	1403	13	:	:	PUNCT
ejde-397	1403	14	t	t	PROPN
ejde-397	1403	15	∈	∈	PROPN
ejde-397	1403	16	k	k	PROPN
ejde-397	1403	17	,	,	PUNCT
ejde-397	1403	18	n	n	PROPN
ejde-397	1403	19	∈	∈	PROPN
ejde-397	1403	20	n0	n0	PROPN
ejde-397	1403	21	}	}	PUNCT
ejde-397	1403	22	is	be	AUX
ejde-397	1403	23	equicontinuous	equicontinuous	ADJ
ejde-397	1403	24	.	.	PUNCT
ejde-397	1404	1	let	let	VERB
ejde-397	1404	2	us	we	PRON
ejde-397	1404	3	recall	recall	VERB
ejde-397	1404	4	that	that	SCONJ
ejde-397	1404	5	the	the	DET
ejde-397	1404	6	case	case	NOUN
ejde-397	1404	7	ρ	ρ	X
ejde-397	1404	8	=	=	SYM
ejde-397	1404	9	1	1	NUM
ejde-397	1404	10	in	in	ADP
ejde-397	1404	11	theorem	theorem	NOUN
ejde-397	1404	12	5.27	5.27	NUM
ejde-397	1404	13	is	be	AUX
ejde-397	1404	14	very	very	ADV
ejde-397	1404	15	important	important	ADJ
ejde-397	1404	16	because	because	SCONJ
ejde-397	1404	17	it	it	PRON
ejde-397	1404	18	gives	give	VERB
ejde-397	1404	19	a	a	DET
ejde-397	1404	20	sufficient	sufficient	ADJ
ejde-397	1404	21	condition	condition	NOUN
ejde-397	1404	22	for	for	SCONJ
ejde-397	1404	23	an	an	DET
ejde-397	1404	24	(	(	PUNCT
ejde-397	1404	25	a	a	DET
ejde-397	1404	26	,	,	PUNCT
ejde-397	1404	27	k)-regularized	k)-regularize	VERB
ejde-397	1404	28	c	c	NOUN
ejde-397	1404	29	-	-	PUNCT
ejde-397	1404	30	resolvent	resolvent	ADJ
ejde-397	1404	31	family	family	NOUN
ejde-397	1404	32	to	to	PART
ejde-397	1404	33	be	be	AUX
ejde-397	1404	34	real	real	ADJ
ejde-397	1404	35	analytic	analytic	ADJ
ejde-397	1404	36	.	.	PUNCT
ejde-397	1405	1	suppose	suppose	VERB
ejde-397	1405	2	now	now	ADV
ejde-397	1405	3	that	that	SCONJ
ejde-397	1405	4	n	n	X
ejde-397	1405	5	∈	∈	PROPN
ejde-397	1405	6	n	n	CCONJ
ejde-397	1405	7	,	,	PUNCT
ejde-397	1405	8	|a|(t	|a|(t	NOUN
ejde-397	1405	9	)	)	PUNCT
ejde-397	1405	10	satisfies	satisfie	NOUN
ejde-397	1405	11	(	(	PUNCT
ejde-397	1405	12	p1)-c	p1)-c	VERB
ejde-397	1405	13	and	and	CCONJ
ejde-397	1405	14	abs(a	abs(a	PROPN
ejde-397	1405	15	)	)	PUNCT
ejde-397	1405	16	=	=	NOUN
ejde-397	1405	17	0	0	X
ejde-397	1405	18	.	.	PUNCT
ejde-397	1405	19	following	follow	VERB
ejde-397	1405	20	[	[	X
ejde-397	1405	21	68	68	NUM
ejde-397	1405	22	,	,	PUNCT
ejde-397	1405	23	definition	definition	NOUN
ejde-397	1405	24	3.3	3.3	NUM
ejde-397	1405	25	,	,	PUNCT
ejde-397	1405	26	p.	p.	NOUN
ejde-397	1405	27	69	69	NUM
ejde-397	1405	28	]	]	PUNCT
ejde-397	1405	29	,	,	PUNCT
ejde-397	1405	30	we	we	PRON
ejde-397	1405	31	say	say	VERB
ejde-397	1405	32	that	that	SCONJ
ejde-397	1405	33	a(t	a(t	NOUN
ejde-397	1405	34	)	)	PUNCT
ejde-397	1405	35	is	be	AUX
ejde-397	1405	36	n	n	ADV
ejde-397	1405	37	-	-	PUNCT
ejde-397	1405	38	regular	regular	ADJ
ejde-397	1405	39	if	if	SCONJ
ejde-397	1405	40	and	and	CCONJ
ejde-397	1405	41	only	only	ADV
ejde-397	1405	42	if	if	SCONJ
ejde-397	1405	43	there	there	PRON
ejde-397	1405	44	exists	exist	VERB
ejde-397	1405	45	c	c	NOUN
ejde-397	1405	46	>	>	X
ejde-397	1405	47	0	0	NUM
ejde-397	1405	48	such	such	ADJ
ejde-397	1405	49	that	that	SCONJ
ejde-397	1405	50	|λmâ(m)(λ)|	|λmâ(m)(λ)|	PROPN
ejde-397	1405	51	≤	≤	NUM
ejde-397	1405	52	c|â(λ)|	c|â(λ)|	PROPN
ejde-397	1405	53	,	,	PUNCT
ejde-397	1405	54	λ	λ	PROPN
ejde-397	1405	55	∈	∈	NOUN
ejde-397	1405	56	c+	c+	NOUN
ejde-397	1405	57	,	,	PUNCT
ejde-397	1405	58	1	1	NUM
ejde-397	1405	59	≤	≤	NUM
ejde-397	1405	60	m	m	VERB
ejde-397	1405	61	≤	≤	PROPN
ejde-397	1405	62	n.	n.	NOUN
ejde-397	1405	63	set	set	VERB
ejde-397	1405	64	a(−1)(t	a(−1)(t	PROPN
ejde-397	1405	65	)	)	PUNCT
ejde-397	1405	66	:	:	PUNCT
ejde-397	1406	1	=	=	PUNCT
ejde-397	1406	2	∫	∫	PROPN
ejde-397	1406	3	t	t	PROPN
ejde-397	1406	4	0	0	NUM
ejde-397	1406	5	a(s	a(s	ADJ
ejde-397	1406	6	)	)	PUNCT
ejde-397	1406	7	ds	ds	PROPN
ejde-397	1406	8	,	,	PUNCT
ejde-397	1406	9	t	t	PROPN
ejde-397	1406	10	≥	≥	NOUN
ejde-397	1406	11	0	0	PUNCT
ejde-397	1406	12	and	and	CCONJ
ejde-397	1406	13	suppose	suppose	VERB
ejde-397	1406	14	that	that	SCONJ
ejde-397	1406	15	a(t	a(t	NOUN
ejde-397	1406	16	)	)	PUNCT
ejde-397	1406	17	and	and	CCONJ
ejde-397	1406	18	b(t	b(t	NOUN
ejde-397	1406	19	)	)	PUNCT
ejde-397	1406	20	are	be	AUX
ejde-397	1406	21	n	n	ADV
ejde-397	1406	22	-	-	PUNCT
ejde-397	1406	23	regular	regular	ADJ
ejde-397	1406	24	for	for	ADP
ejde-397	1406	25	some	some	DET
ejde-397	1406	26	n	n	PRON
ejde-397	1406	27	∈	∈	PROPN
ejde-397	1406	28	n.	n.	NOUN
ejde-397	1406	29	then	then	ADV
ejde-397	1406	30	we	we	PRON
ejde-397	1406	31	know	know	VERB
ejde-397	1406	32	that	that	SCONJ
ejde-397	1406	33	â(λ	â(λ	VERB
ejde-397	1406	34	)	)	PUNCT
ejde-397	1406	35	6=	6=	ADP
ejde-397	1406	36	0	0	NUM
ejde-397	1406	37	,	,	PUNCT
ejde-397	1406	38	λ	λ	PROPN
ejde-397	1406	39	∈	∈	NOUN
ejde-397	1406	40	c+	c+	NOUN
ejde-397	1406	41	,	,	PUNCT
ejde-397	1406	42	as	as	ADV
ejde-397	1406	43	well	well	ADV
ejde-397	1406	44	as	as	ADP
ejde-397	1406	45	that	that	PRON
ejde-397	1406	46	(	(	PUNCT
ejde-397	1406	47	a	a	DET
ejde-397	1406	48	∗	∗	NOUN
ejde-397	1406	49	b)(t	b)(t	NOUN
ejde-397	1406	50	)	)	PUNCT
ejde-397	1406	51	and	and	CCONJ
ejde-397	1406	52	a(−1)(t	a(−1)(t	ADJ
ejde-397	1406	53	)	)	PUNCT
ejde-397	1406	54	are	be	AUX
ejde-397	1406	55	n	n	ADV
ejde-397	1406	56	-	-	PUNCT
ejde-397	1406	57	regular	regular	ADJ
ejde-397	1406	58	,	,	PUNCT
ejde-397	1406	59	and	and	CCONJ
ejde-397	1406	60	that	that	SCONJ
ejde-397	1406	61	a′(t	a′(t	ADP
ejde-397	1406	62	)	)	PUNCT
ejde-397	1406	63	is	be	AUX
ejde-397	1406	64	n	n	ADV
ejde-397	1406	65	-	-	PUNCT
ejde-397	1406	66	regular	regular	NOUN
ejde-397	1406	67	provided	provide	VERB
ejde-397	1406	68	that	that	DET
ejde-397	1406	69	abs(a′	abs(a′	NOUN
ejde-397	1406	70	)	)	PUNCT
ejde-397	1407	1	=	=	SYM
ejde-397	1407	2	0	0	X
ejde-397	1407	3	.	.	PUNCT
ejde-397	1407	4	following	follow	VERB
ejde-397	1407	5	[	[	X
ejde-397	1407	6	68	68	NUM
ejde-397	1407	7	,	,	PUNCT
ejde-397	1407	8	definition	definition	NOUN
ejde-397	1407	9	3.1	3.1	NUM
ejde-397	1407	10	,	,	PUNCT
ejde-397	1407	11	p.	p.	NOUN
ejde-397	1407	12	68	68	NUM
ejde-397	1407	13	]	]	PUNCT
ejde-397	1407	14	and	and	CCONJ
ejde-397	1407	15	[	[	X
ejde-397	1407	16	36	36	NUM
ejde-397	1407	17	,	,	PUNCT
ejde-397	1407	18	definition	definition	NOUN
ejde-397	1407	19	2.1.23	2.1.23	NUM
ejde-397	1407	20	]	]	PUNCT
ejde-397	1407	21	,	,	PUNCT
ejde-397	1407	22	it	it	PRON
ejde-397	1407	23	will	will	AUX
ejde-397	1407	24	be	be	AUX
ejde-397	1407	25	said	say	VERB
ejde-397	1407	26	that	that	SCONJ
ejde-397	1407	27	the	the	DET
ejde-397	1407	28	abstract	abstract	ADJ
ejde-397	1407	29	volterra	volterra	NOUN
ejde-397	1407	30	inclusion	inclusion	NOUN
ejde-397	1407	31	(	(	PUNCT
ejde-397	1407	32	1.1	1.1	NUM
ejde-397	1407	33	)	)	PUNCT
ejde-397	1407	34	with	with	ADP
ejde-397	1407	35	b	b	X
ejde-397	1407	36	=	=	SYM
ejde-397	1407	37	i	i	PROPN
ejde-397	1407	38	(	(	PUNCT
ejde-397	1407	39	denoted	denote	VERB
ejde-397	1407	40	henceforth	henceforth	ADV
ejde-397	1407	41	by	by	ADP
ejde-397	1407	42	the	the	DET
ejde-397	1407	43	same	same	ADJ
ejde-397	1407	44	symbol	symbol	NOUN
ejde-397	1407	45	)	)	PUNCT
ejde-397	1407	46	is	be	AUX
ejde-397	1407	47	(	(	PUNCT
ejde-397	1407	48	kc)-parabolic	kc)-parabolic	VERB
ejde-397	1407	49	if	if	SCONJ
ejde-397	1407	50	and	and	CCONJ
ejde-397	1407	51	only	only	ADV
ejde-397	1407	52	if	if	SCONJ
ejde-397	1407	53	the	the	DET
ejde-397	1407	54	following	follow	VERB
ejde-397	1407	55	holds	hold	VERB
ejde-397	1407	56	:	:	PUNCT
ejde-397	1407	57	(	(	PUNCT
ejde-397	1407	58	i	i	NOUN
ejde-397	1407	59	)	)	PUNCT
ejde-397	1407	60	|a|(t	|a|(t	NOUN
ejde-397	1407	61	)	)	PUNCT
ejde-397	1407	62	and	and	CCONJ
ejde-397	1407	63	k(t	k(t	PROPN
ejde-397	1407	64	)	)	PUNCT
ejde-397	1407	65	satisfy	satisfy	NOUN
ejde-397	1407	66	(	(	PUNCT
ejde-397	1407	67	p1)-c	p1)-c	VERB
ejde-397	1407	68	and	and	CCONJ
ejde-397	1407	69	there	there	PRON
ejde-397	1407	70	exist	exist	VERB
ejde-397	1407	71	meromorphic	meromorphic	ADJ
ejde-397	1407	72	extensions	extension	NOUN
ejde-397	1407	73	of	of	ADP
ejde-397	1407	74	the	the	DET
ejde-397	1407	75	functions	function	NOUN
ejde-397	1407	76	ã(λ	ã(λ	PROPN
ejde-397	1407	77	)	)	PUNCT
ejde-397	1407	78	and	and	CCONJ
ejde-397	1407	79	k̃(λ	k̃(λ	NOUN
ejde-397	1407	80	)	)	PUNCT
ejde-397	1407	81	on	on	ADP
ejde-397	1407	82	c+	c+	PROPN
ejde-397	1407	83	,	,	PUNCT
ejde-397	1407	84	denoted	denote	VERB
ejde-397	1407	85	by	by	ADP
ejde-397	1407	86	â(λ	â(λ	NOUN
ejde-397	1407	87	)	)	PUNCT
ejde-397	1407	88	and	and	CCONJ
ejde-397	1407	89	k̂(λ	k̂(λ	NOUN
ejde-397	1407	90	)	)	PUNCT
ejde-397	1407	91	.	.	PUNCT
ejde-397	1408	1	let	let	VERB
ejde-397	1408	2	n	n	PRON
ejde-397	1408	3	be	be	AUX
ejde-397	1408	4	the	the	DET
ejde-397	1408	5	subset	subset	NOUN
ejde-397	1408	6	of	of	ADP
ejde-397	1408	7	c+	c+	NOUN
ejde-397	1408	8	which	which	PRON
ejde-397	1408	9	consists	consist	VERB
ejde-397	1408	10	of	of	ADP
ejde-397	1408	11	all	all	DET
ejde-397	1408	12	zeros	zero	NOUN
ejde-397	1408	13	and	and	CCONJ
ejde-397	1408	14	possible	possible	ADJ
ejde-397	1408	15	poles	pole	NOUN
ejde-397	1408	16	of	of	ADP
ejde-397	1408	17	â(λ	â(λ	NUM
ejde-397	1408	18	)	)	PUNCT
ejde-397	1408	19	and	and	CCONJ
ejde-397	1408	20	k̂(λ	k̂(λ	NOUN
ejde-397	1408	21	)	)	PUNCT
ejde-397	1408	22	.	.	PUNCT
ejde-397	1409	1	(	(	PUNCT
ejde-397	1409	2	ii	ii	X
ejde-397	1409	3	)	)	PUNCT
ejde-397	1409	4	there	there	PRON
ejde-397	1409	5	exists	exist	VERB
ejde-397	1409	6	m	m	VERB
ejde-397	1409	7	≥	≥	NUM
ejde-397	1409	8	1	1	NUM
ejde-397	1409	9	such	such	ADJ
ejde-397	1409	10	that	that	SCONJ
ejde-397	1409	11	,	,	PUNCT
ejde-397	1409	12	for	for	ADP
ejde-397	1409	13	every	every	DET
ejde-397	1409	14	λ	λ	PROPN
ejde-397	1409	15	∈	∈	NOUN
ejde-397	1409	16	c+	c+	X
ejde-397	1409	17	\n	\n	PUNCT
ejde-397	1409	18	,	,	PUNCT
ejde-397	1409	19	1	1	X
ejde-397	1409	20	/	/	SYM
ejde-397	1409	21	â(λ	â(λ	NUM
ejde-397	1409	22	)	)	PUNCT
ejde-397	1409	23	∈	∈	NOUN
ejde-397	1409	24	ρc(a	ρc(a	NOUN
ejde-397	1409	25	)	)	PUNCT
ejde-397	1409	26	and	and	CCONJ
ejde-397	1409	27	||k̂(λ)(i	||k̂(λ)(i	ADP
ejde-397	1409	28	−	−	PROPN
ejde-397	1409	29	â(λ)a)−1c||	â(λ)a)−1c||	X
ejde-397	1409	30	≤m/|λ|	≤m/|λ|	PROPN
ejde-397	1409	31	.	.	PUNCT
ejde-397	1410	1	if	if	SCONJ
ejde-397	1410	2	k(t	k(t	NOUN
ejde-397	1410	3	)	)	PUNCT
ejde-397	1410	4	≡	≡	PROPN
ejde-397	1410	5	1	1	NUM
ejde-397	1410	6	,	,	PUNCT
ejde-397	1410	7	resp	resp	NOUN
ejde-397	1410	8	.	.	PUNCT
ejde-397	1411	1	c	c	X
ejde-397	1412	1	=	=	SYM
ejde-397	1412	2	i	i	PROPN
ejde-397	1412	3	,	,	PUNCT
ejde-397	1412	4	then	then	ADV
ejde-397	1412	5	it	it	PRON
ejde-397	1412	6	is	be	AUX
ejde-397	1412	7	also	also	ADV
ejde-397	1412	8	said	say	VERB
ejde-397	1412	9	that	that	SCONJ
ejde-397	1412	10	(	(	PUNCT
ejde-397	1412	11	1.1	1.1	NUM
ejde-397	1412	12	)	)	PUNCT
ejde-397	1412	13	is	be	AUX
ejde-397	1412	14	c	c	NOUN
ejde-397	1412	15	-	-	PUNCT
ejde-397	1412	16	parabolic	parabolic	ADJ
ejde-397	1412	17	,	,	PUNCT
ejde-397	1412	18	resp	resp	NOUN
ejde-397	1412	19	.	.	PUNCT
ejde-397	1413	1	k	k	X
ejde-397	1413	2	-	-	NOUN
ejde-397	1413	3	parabolic	parabolic	NOUN
ejde-397	1413	4	.	.	PUNCT
ejde-397	1414	1	now	now	ADV
ejde-397	1414	2	we	we	PRON
ejde-397	1414	3	are	be	AUX
ejde-397	1414	4	ready	ready	ADJ
ejde-397	1414	5	to	to	PART
ejde-397	1414	6	formulate	formulate	VERB
ejde-397	1414	7	the	the	DET
ejde-397	1414	8	following	following	ADJ
ejde-397	1414	9	extension	extension	NOUN
ejde-397	1414	10	of	of	ADP
ejde-397	1414	11	[	[	X
ejde-397	1414	12	36	36	NUM
ejde-397	1414	13	,	,	PUNCT
ejde-397	1414	14	theorem	theorem	VERB
ejde-397	1414	15	2.1.24	2.1.24	NUM
ejde-397	1414	16	]	]	PUNCT
ejde-397	1414	17	.	.	PUNCT
ejde-397	1415	1	theorem	theorem	NOUN
ejde-397	1415	2	5.28	5.28	NUM
ejde-397	1415	3	.	.	PUNCT
ejde-397	1416	1	assume	assume	VERB
ejde-397	1416	2	n	n	PRON
ejde-397	1416	3	∈	∈	PROPN
ejde-397	1416	4	n	n	CCONJ
ejde-397	1416	5	,	,	PUNCT
ejde-397	1416	6	a(t	a(t	NOUN
ejde-397	1416	7	)	)	PUNCT
ejde-397	1416	8	is	be	AUX
ejde-397	1416	9	n	n	ADV
ejde-397	1416	10	-	-	PUNCT
ejde-397	1416	11	regular	regular	ADJ
ejde-397	1416	12	,	,	PUNCT
ejde-397	1416	13	(	(	PUNCT
ejde-397	1416	14	x	x	X
ejde-397	1416	15	,	,	PUNCT
ejde-397	1416	16	‖	‖	PROPN
ejde-397	1416	17	·	·	PUNCT
ejde-397	1416	18	‖	‖	NUM
ejde-397	1416	19	)	)	PUNCT
ejde-397	1417	1	is	be	AUX
ejde-397	1417	2	a	a	DET
ejde-397	1417	3	banach	banach	NOUN
ejde-397	1417	4	space	space	NOUN
ejde-397	1417	5	,	,	PUNCT
ejde-397	1417	6	a	a	PRON
ejde-397	1417	7	is	be	AUX
ejde-397	1417	8	a	a	DET
ejde-397	1417	9	closed	closed	ADJ
ejde-397	1417	10	mlo	mlo	NOUN
ejde-397	1417	11	in	in	ADP
ejde-397	1417	12	x	x	PROPN
ejde-397	1417	13	,	,	PUNCT
ejde-397	1417	14	the	the	DET
ejde-397	1417	15	abstract	abstract	ADJ
ejde-397	1417	16	volterra	volterra	NOUN
ejde-397	1417	17	inclusion	inclusion	NOUN
ejde-397	1417	18	(	(	PUNCT
ejde-397	1417	19	1.1	1.1	NUM
ejde-397	1417	20	)	)	PUNCT
ejde-397	1417	21	is	be	AUX
ejde-397	1417	22	c	c	NOUN
ejde-397	1417	23	-	-	NOUN
ejde-397	1417	24	parabolic	parabolic	ADJ
ejde-397	1417	25	,	,	PUNCT
ejde-397	1417	26	and	and	CCONJ
ejde-397	1417	27	the	the	DET
ejde-397	1417	28	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1417	29	abstract	abstract	ADJ
ejde-397	1417	30	degenerate	degenerate	ADJ
ejde-397	1417	31	volterra	volterra	NOUN
ejde-397	1417	32	inclusions	inclusion	NOUN
ejde-397	1417	33	47	47	NUM
ejde-397	1417	34	mapping	mapping	NOUN
ejde-397	1417	35	λ	λ	X
ejde-397	1417	36	7→	7→	NUM
ejde-397	1417	37	(	(	PUNCT
ejde-397	1417	38	i−	i−	PROPN
ejde-397	1417	39	ã(λ)a)−1c	ã(λ)a)−1c	PROPN
ejde-397	1417	40	,	,	PUNCT
ejde-397	1417	41	λ	λ	PROPN
ejde-397	1417	42	∈	∈	NOUN
ejde-397	1417	43	c+	c+	NOUN
ejde-397	1417	44	is	be	AUX
ejde-397	1417	45	continuous	continuous	ADJ
ejde-397	1417	46	.	.	PUNCT
ejde-397	1418	1	then	then	ADV
ejde-397	1418	2	,	,	PUNCT
ejde-397	1418	3	for	for	ADP
ejde-397	1418	4	every	every	DET
ejde-397	1418	5	α	α	PROPN
ejde-397	1418	6	∈	∈	PROPN
ejde-397	1418	7	(	(	PUNCT
ejde-397	1418	8	0	0	NUM
ejde-397	1418	9	,	,	PUNCT
ejde-397	1418	10	1	1	NUM
ejde-397	1418	11	]	]	PUNCT
ejde-397	1418	12	,	,	PUNCT
ejde-397	1418	13	a	a	PRON
ejde-397	1418	14	is	be	AUX
ejde-397	1418	15	a	a	DET
ejde-397	1418	16	subgenerator	subgenerator	NOUN
ejde-397	1418	17	of	of	ADP
ejde-397	1418	18	an	an	DET
ejde-397	1418	19	(	(	PUNCT
ejde-397	1418	20	a	a	PRON
ejde-397	1418	21	,	,	PUNCT
ejde-397	1418	22	gα+1)-regularized	gα+1)-regularize	VERB
ejde-397	1418	23	c2	c2	PROPN
ejde-397	1418	24	-	-	PUNCT
ejde-397	1418	25	resolvent	resolvent	NOUN
ejde-397	1418	26	family	family	NOUN
ejde-397	1418	27	(	(	PUNCT
ejde-397	1418	28	sα(t))t≥0	sα(t))t≥0	PROPN
ejde-397	1418	29	which	which	PRON
ejde-397	1418	30	satisfies	satisfy	VERB
ejde-397	1418	31	suph>0,t≥0	suph>0,t≥0	NOUN
ejde-397	1418	32	h	h	NOUN
ejde-397	1418	33	−α||sα(t	−α||sα(t	VERB
ejde-397	1418	34	+	+	NUM
ejde-397	1418	35	h	h	NOUN
ejde-397	1418	36	)	)	PUNCT
ejde-397	1418	37	−	−	PROPN
ejde-397	1419	1	sα(t)||	sα(t)||	PROPN
ejde-397	1419	2	<	<	X
ejde-397	1419	3	∞	∞	PROPN
ejde-397	1419	4	,	,	PUNCT
ejde-397	1419	5	dα	dα	ADP
ejde-397	1419	6	t	t	PROPN
ejde-397	1419	7	sα(t)ck−1	sα(t)ck−1	PROPN
ejde-397	1419	8	∈	∈	PROPN
ejde-397	1419	9	ck−1((0,∞	ck−1((0,∞	PROPN
ejde-397	1419	10	)	)	PUNCT
ejde-397	1419	11	:	:	PUNCT
ejde-397	1419	12	l(x	l(x	PROPN
ejde-397	1419	13	)	)	PUNCT
ejde-397	1419	14	)	)	PUNCT
ejde-397	1419	15	,	,	PUNCT
ejde-397	1419	16	1	1	NUM
ejde-397	1419	17	≤	≤	NUM
ejde-397	1419	18	k	k	NOUN
ejde-397	1419	19	≤	≤	PROPN
ejde-397	1419	20	n	n	CCONJ
ejde-397	1419	21	as	as	ADV
ejde-397	1419	22	well	well	ADV
ejde-397	1419	23	as	as	ADP
ejde-397	1419	24	:	:	PUNCT
ejde-397	1419	25	‖tjdj	‖tjdj	VERB
ejde-397	1419	26	td	td	NOUN
ejde-397	1419	27	α	α	PROPN
ejde-397	1419	28	t	t	PROPN
ejde-397	1419	29	sα(t)ck−1‖	sα(t)ck−1‖	PROPN
ejde-397	1419	30	≤m	≤m	PROPN
ejde-397	1419	31	,	,	PUNCT
ejde-397	1419	32	t	t	PROPN
ejde-397	1419	33	≥	≥	NUM
ejde-397	1419	34	0	0	NUM
ejde-397	1419	35	,	,	PUNCT
ejde-397	1419	36	1	1	NUM
ejde-397	1419	37	≤	≤	NUM
ejde-397	1419	38	k	k	X
ejde-397	1419	39	≤	≤	PROPN
ejde-397	1419	40	n	n	CCONJ
ejde-397	1419	41	,	,	PUNCT
ejde-397	1419	42	0	0	NUM
ejde-397	1419	43	≤	≤	NUM
ejde-397	1419	44	j	j	PROPN
ejde-397	1419	45	≤	≤	PROPN
ejde-397	1419	46	k	k	NOUN
ejde-397	1420	1	−	−	PROPN
ejde-397	1420	2	1	1	NUM
ejde-397	1420	3	,	,	PUNCT
ejde-397	1420	4	(	(	PUNCT
ejde-397	1420	5	5.32	5.32	NUM
ejde-397	1420	6	)	)	PUNCT
ejde-397	1420	7	‖tkdk−1	‖tkdk−1	PROPN
ejde-397	1421	1	t	t	PROPN
ejde-397	1421	2	dα	dα	PROPN
ejde-397	1421	3	t	t	PROPN
ejde-397	1421	4	sα(t)ck−1	sα(t)ck−1	ADV
ejde-397	1421	5	−	−	PROPN
ejde-397	1421	6	skdk−1	skdk−1	PROPN
ejde-397	1421	7	s	s	PART
ejde-397	1421	8	dα	dα	ADP
ejde-397	1421	9	s	s	PART
ejde-397	1421	10	sα(s)ck−1‖	sα(s)ck−1‖	NOUN
ejde-397	1421	11	≤m	≤m	PROPN
ejde-397	1421	12	|t−	|t−	PROPN
ejde-397	1421	13	s|	s|	VERB
ejde-397	1421	14	(	(	PUNCT
ejde-397	1421	15	1	1	NUM
ejde-397	1421	16	+	+	CCONJ
ejde-397	1421	17	ln	ln	ADJ
ejde-397	1421	18	t	t	NOUN
ejde-397	1421	19	t−	t−	PROPN
ejde-397	1421	20	s	s	PART
ejde-397	1421	21	)	)	PUNCT
ejde-397	1421	22	,	,	PUNCT
ejde-397	1421	23	0	0	NUM
ejde-397	1421	24	≤	≤	NOUN
ejde-397	1421	25	s	s	X
ejde-397	1421	26	<	<	X
ejde-397	1421	27	t	t	X
ejde-397	1421	28	<	<	X
ejde-397	1421	29	∞	∞	PROPN
ejde-397	1421	30	,	,	PUNCT
ejde-397	1421	31	1	1	NUM
ejde-397	1421	32	≤	≤	NUM
ejde-397	1421	33	k	k	NOUN
ejde-397	1421	34	≤	≤	PROPN
ejde-397	1421	35	n	n	CCONJ
ejde-397	1421	36	,	,	PUNCT
ejde-397	1421	37	(	(	PUNCT
ejde-397	1421	38	5.33	5.33	NUM
ejde-397	1421	39	)	)	PUNCT
ejde-397	1421	40	and	and	CCONJ
ejde-397	1421	41	,	,	PUNCT
ejde-397	1421	42	for	for	ADP
ejde-397	1421	43	every	every	DET
ejde-397	1421	44	t	t	NOUN
ejde-397	1421	45	>	>	X
ejde-397	1421	46	0	0	PROPN
ejde-397	1421	47	,	,	PUNCT
ejde-397	1421	48	ε	ε	PROPN
ejde-397	1421	49	>	>	PUNCT
ejde-397	1421	50	0	0	PROPN
ejde-397	1422	1	and	and	CCONJ
ejde-397	1422	2	k	k	PROPN
ejde-397	1422	3	∈	∈	PROPN
ejde-397	1422	4	nn	nn	PROPN
ejde-397	1422	5	,	,	PUNCT
ejde-397	1422	6	there	there	PRON
ejde-397	1422	7	exists	exist	VERB
ejde-397	1422	8	mε	mε	PROPN
ejde-397	1422	9	t	t	PROPN
ejde-397	1422	10	,	,	PUNCT
ejde-397	1422	11	k	k	PROPN
ejde-397	1422	12	>	>	X
ejde-397	1422	13	0	0	NUM
ejde-397	1423	1	such	such	ADJ
ejde-397	1423	2	that	that	SCONJ
ejde-397	1423	3	‖tkdk−1	‖tkdk−1	VERB
ejde-397	1423	4	t	t	PROPN
ejde-397	1423	5	dα	dα	PROPN
ejde-397	1423	6	t	t	PROPN
ejde-397	1423	7	sα(t)ck−1	sα(t)ck−1	ADV
ejde-397	1423	8	−	−	PROPN
ejde-397	1424	1	skdk−1	skdk−1	PROPN
ejde-397	1424	2	s	s	PART
ejde-397	1424	3	dα	dα	PRON
ejde-397	1424	4	s	s	PART
ejde-397	1424	5	sα(s)ck−1‖	sα(s)ck−1‖	NOUN
ejde-397	1424	6	≤mε	≤mε	PROPN
ejde-397	1424	7	t	t	PROPN
ejde-397	1424	8	,	,	PUNCT
ejde-397	1424	9	k(t−	k(t−	PROPN
ejde-397	1424	10	s)1−ε	s)1−ε	PROPN
ejde-397	1424	11	,	,	PUNCT
ejde-397	1424	12	0	0	NUM
ejde-397	1424	13	≤	≤	NOUN
ejde-397	1424	14	s	s	PART
ejde-397	1424	15	<	<	X
ejde-397	1424	16	t	t	X
ejde-397	1424	17	≤	≤	X
ejde-397	1424	18	t	t	PROPN
ejde-397	1424	19	,	,	PUNCT
ejde-397	1424	20	1	1	NUM
ejde-397	1424	21	≤	≤	NUM
ejde-397	1424	22	k	k	PROPN
ejde-397	1424	23	≤	≤	PROPN
ejde-397	1424	24	n.	n.	NOUN
ejde-397	1424	25	(	(	PUNCT
ejde-397	1424	26	5.34	5.34	NUM
ejde-397	1424	27	)	)	PUNCT
ejde-397	1424	28	furthermore	furthermore	ADV
ejde-397	1424	29	,	,	PUNCT
ejde-397	1424	30	if	if	SCONJ
ejde-397	1424	31	a	a	PRON
ejde-397	1424	32	is	be	AUX
ejde-397	1424	33	densely	densely	ADV
ejde-397	1424	34	defined	define	VERB
ejde-397	1424	35	,	,	PUNCT
ejde-397	1424	36	then	then	ADV
ejde-397	1424	37	a	a	PRON
ejde-397	1424	38	is	be	AUX
ejde-397	1424	39	a	a	DET
ejde-397	1424	40	subgenerator	subgenerator	NOUN
ejde-397	1424	41	of	of	ADP
ejde-397	1424	42	a	a	DET
ejde-397	1424	43	bounded	bounded	ADJ
ejde-397	1424	44	(	(	PUNCT
ejde-397	1424	45	a	a	DET
ejde-397	1424	46	,	,	PUNCT
ejde-397	1424	47	c2)regularized	c2)regularize	VERB
ejde-397	1424	48	resolvent	resolvent	ADJ
ejde-397	1424	49	family	family	NOUN
ejde-397	1424	50	(	(	PUNCT
ejde-397	1424	51	s(t))t≥0	s(t))t≥0	PROPN
ejde-397	1424	52	,	,	PUNCT
ejde-397	1424	53	satisfying	satisfy	VERB
ejde-397	1424	54	additionally	additionally	ADV
ejde-397	1424	55	that	that	SCONJ
ejde-397	1424	56	the	the	DET
ejde-397	1424	57	mapping	mapping	NOUN
ejde-397	1424	58	t	t	PROPN
ejde-397	1424	59	7→	7→	NUM
ejde-397	1424	60	s(t)ck−1	s(t)ck−1	NOUN
ejde-397	1424	61	,	,	PUNCT
ejde-397	1424	62	t	t	PROPN
ejde-397	1424	63	>	>	X
ejde-397	1424	64	0	0	PUNCT
ejde-397	1424	65	is	be	AUX
ejde-397	1424	66	in	in	ADP
ejde-397	1424	67	class	class	NOUN
ejde-397	1424	68	ck−1((0,∞	ck−1((0,∞	PROPN
ejde-397	1424	69	)	)	PUNCT
ejde-397	1424	70	:	:	PUNCT
ejde-397	1424	71	l(x	l(x	PROPN
ejde-397	1424	72	)	)	PUNCT
ejde-397	1424	73	)	)	PUNCT
ejde-397	1424	74	,	,	PUNCT
ejde-397	1424	75	1	1	NUM
ejde-397	1424	76	≤	≤	NUM
ejde-397	1424	77	k	k	NOUN
ejde-397	1424	78	≤	≤	NOUN
ejde-397	1424	79	n	n	CCONJ
ejde-397	1424	80	and	and	CCONJ
ejde-397	1424	81	that	that	SCONJ
ejde-397	1424	82	(	(	PUNCT
ejde-397	1424	83	5.32)-(5.34	5.32)-(5.34	NUM
ejde-397	1424	84	)	)	PUNCT
ejde-397	1424	85	hold	hold	VERB
ejde-397	1424	86	with	with	ADP
ejde-397	1424	87	dα	dα	DET
ejde-397	1424	88	t	t	PROPN
ejde-397	1424	89	sα(t)ck−1	sα(t)ck−1	ADV
ejde-397	1424	90	replaced	replace	VERB
ejde-397	1424	91	by	by	ADP
ejde-397	1424	92	s(t)ck−1	s(t)ck−1	NOUN
ejde-397	1424	93	(	(	PUNCT
ejde-397	1424	94	1	1	NUM
ejde-397	1424	95	≤	≤	NUM
ejde-397	1424	96	k	k	NOUN
ejde-397	1424	97	≤	≤	NUM
ejde-397	1424	98	n	n	CCONJ
ejde-397	1424	99	)	)	PUNCT
ejde-397	1424	100	therein	therein	ADV
ejde-397	1424	101	.	.	PUNCT
ejde-397	1425	1	the	the	DET
ejde-397	1425	2	representation	representation	NOUN
ejde-397	1425	3	formula	formula	NOUN
ejde-397	1425	4	[	[	X
ejde-397	1425	5	68	68	NUM
ejde-397	1425	6	,	,	PUNCT
ejde-397	1425	7	(	(	PUNCT
ejde-397	1425	8	3.41	3.41	NUM
ejde-397	1425	9	)	)	PUNCT
ejde-397	1425	10	,	,	PUNCT
ejde-397	1425	11	p.	p.	NOUN
ejde-397	1425	12	81	81	NUM
ejde-397	1425	13	]	]	PUNCT
ejde-397	1425	14	and	and	CCONJ
ejde-397	1425	15	the	the	DET
ejde-397	1425	16	assertions	assertion	NOUN
ejde-397	1425	17	of	of	ADP
ejde-397	1425	18	[	[	X
ejde-397	1425	19	68	68	NUM
ejde-397	1425	20	,	,	PUNCT
ejde-397	1425	21	corollary	corollary	ADJ
ejde-397	1425	22	3.2	3.2	NUM
ejde-397	1425	23	-	-	PUNCT
ejde-397	1425	24	corollary	corollary	ADJ
ejde-397	1425	25	3.3	3.3	NUM
ejde-397	1425	26	,	,	PUNCT
ejde-397	1425	27	pp	pp	ADJ
ejde-397	1425	28	.	.	PUNCT
ejde-397	1426	1	74	74	NUM
ejde-397	1426	2	-	-	SYM
ejde-397	1426	3	75	75	NUM
ejde-397	1426	4	]	]	PUNCT
ejde-397	1426	5	can	can	AUX
ejde-397	1426	6	be	be	AUX
ejde-397	1426	7	extended	extend	VERB
ejde-397	1426	8	to	to	PART
ejde-397	1426	9	exponentially	exponentially	ADV
ejde-397	1426	10	bounded	bound	VERB
ejde-397	1426	11	(	(	PUNCT
ejde-397	1426	12	a	a	DET
ejde-397	1426	13	,	,	PUNCT
ejde-397	1426	14	c)regularized	c)regularize	VERB
ejde-397	1426	15	resolvent	resolvent	ADJ
ejde-397	1426	16	families	family	NOUN
ejde-397	1426	17	subgenerated	subgenerate	VERB
ejde-397	1426	18	by	by	ADP
ejde-397	1426	19	multivalued	multivalued	ADJ
ejde-397	1426	20	linear	linear	PROPN
ejde-397	1426	21	operators	operator	NOUN
ejde-397	1426	22	,	,	PUNCT
ejde-397	1426	23	as	as	ADV
ejde-397	1426	24	well	well	ADV
ejde-397	1426	25	.	.	PUNCT
ejde-397	1427	1	for	for	ADP
ejde-397	1427	2	more	more	ADJ
ejde-397	1427	3	details	detail	NOUN
ejde-397	1427	4	about	about	ADP
ejde-397	1427	5	parabolicity	parabolicity	NOUN
ejde-397	1427	6	of	of	ADP
ejde-397	1427	7	abstract	abstract	ADJ
ejde-397	1427	8	non	non	ADJ
ejde-397	1427	9	-	-	ADJ
ejde-397	1427	10	degenerate	degenerate	ADJ
ejde-397	1427	11	volterra	volterra	NOUN
ejde-397	1427	12	equations	equation	NOUN
ejde-397	1427	13	,	,	PUNCT
ejde-397	1427	14	we	we	PRON
ejde-397	1427	15	refer	refer	VERB
ejde-397	1427	16	the	the	DET
ejde-397	1427	17	reader	reader	NOUN
ejde-397	1427	18	to	to	ADP
ejde-397	1427	19	[	[	X
ejde-397	1427	20	68	68	NUM
ejde-397	1427	21	,	,	PUNCT
ejde-397	1427	22	chapter	chapter	NOUN
ejde-397	1427	23	i	i	PROPN
ejde-397	1427	24	,	,	PUNCT
ejde-397	1427	25	section	section	NOUN
ejde-397	1427	26	3	3	NUM
ejde-397	1427	27	]	]	PUNCT
ejde-397	1427	28	.	.	PUNCT
ejde-397	1428	1	5.2	5.2	NUM
ejde-397	1428	2	.	.	PUNCT
ejde-397	1429	1	non	non	ADJ
ejde-397	1429	2	-	-	NOUN
ejde-397	1429	3	injectivity	injectivity	NOUN
ejde-397	1429	4	of	of	ADP
ejde-397	1429	5	regularizing	regularize	VERB
ejde-397	1429	6	operators	operator	NOUN
ejde-397	1429	7	c2	c2	PROPN
ejde-397	1429	8	and	and	CCONJ
ejde-397	1429	9	c.	c.	NOUN
ejde-397	1429	10	in	in	ADP
ejde-397	1429	11	this	this	DET
ejde-397	1429	12	subsection	subsection	NOUN
ejde-397	1429	13	,	,	PUNCT
ejde-397	1429	14	we	we	PRON
ejde-397	1429	15	consider	consider	VERB
ejde-397	1429	16	multivalued	multivalued	ADJ
ejde-397	1429	17	linear	linear	ADJ
ejde-397	1429	18	operators	operator	NOUN
ejde-397	1429	19	as	as	ADP
ejde-397	1429	20	subgenerators	subgenerator	NOUN
ejde-397	1429	21	of	of	ADP
ejde-397	1429	22	mild	mild	ADJ
ejde-397	1429	23	(	(	PUNCT
ejde-397	1429	24	a	a	PRON
ejde-397	1429	25	,	,	PUNCT
ejde-397	1429	26	k)regularized	k)regularize	VERB
ejde-397	1429	27	(	(	PUNCT
ejde-397	1429	28	c1	c1	NOUN
ejde-397	1429	29	,	,	PUNCT
ejde-397	1429	30	c2)-resolvent	c2)-resolvent	NOUN
ejde-397	1429	31	operator	operator	NOUN
ejde-397	1429	32	families	family	NOUN
ejde-397	1429	33	and	and	CCONJ
ejde-397	1429	34	(	(	PUNCT
ejde-397	1429	35	a	a	PRON
ejde-397	1429	36	,	,	PUNCT
ejde-397	1429	37	k)-regularized	k)-regularize	VERB
ejde-397	1429	38	c	c	NOUN
ejde-397	1429	39	-	-	PUNCT
ejde-397	1429	40	resolvent	resolvent	ADJ
ejde-397	1429	41	operator	operator	NOUN
ejde-397	1429	42	families	family	NOUN
ejde-397	1429	43	.	.	PUNCT
ejde-397	1430	1	we	we	PRON
ejde-397	1430	2	use	use	VERB
ejde-397	1430	3	the	the	DET
ejde-397	1430	4	same	same	ADJ
ejde-397	1430	5	notion	notion	NOUN
ejde-397	1430	6	and	and	CCONJ
ejde-397	1430	7	notation	notation	NOUN
ejde-397	1430	8	as	as	ADP
ejde-397	1430	9	before	before	ADV
ejde-397	1430	10	but	but	CCONJ
ejde-397	1430	11	now	now	ADV
ejde-397	1430	12	we	we	PRON
ejde-397	1430	13	allow	allow	VERB
ejde-397	1430	14	that	that	SCONJ
ejde-397	1430	15	the	the	DET
ejde-397	1430	16	operators	operator	NOUN
ejde-397	1430	17	c2	c2	PROPN
ejde-397	1430	18	and	and	CCONJ
ejde-397	1430	19	c	c	PROPN
ejde-397	1430	20	are	be	AUX
ejde-397	1430	21	possibly	possibly	ADV
ejde-397	1430	22	non	non	ADJ
ejde-397	1430	23	-	-	ADJ
ejde-397	1430	24	injective	injective	ADJ
ejde-397	1430	25	(	(	PUNCT
ejde-397	1430	26	see	see	VERB
ejde-397	1430	27	definition	definition	NOUN
ejde-397	1430	28	5.1	5.1	NUM
ejde-397	1430	29	-	-	PUNCT
ejde-397	1430	30	definition	definition	NOUN
ejde-397	1430	31	5.2	5.2	NUM
ejde-397	1430	32	)	)	PUNCT
ejde-397	1430	33	.	.	PUNCT
ejde-397	1431	1	without	without	ADP
ejde-397	1431	2	any	any	DET
ejde-397	1431	3	doubt	doubt	NOUN
ejde-397	1431	4	,	,	PUNCT
ejde-397	1431	5	this	this	DET
ejde-397	1431	6	choice	choice	NOUN
ejde-397	1431	7	has	have	VERB
ejde-397	1431	8	some	some	DET
ejde-397	1431	9	obvious	obvious	ADJ
ejde-397	1431	10	displeasing	displeasing	ADJ
ejde-397	1431	11	consequences	consequence	NOUN
ejde-397	1431	12	on	on	ADP
ejde-397	1431	13	the	the	DET
ejde-397	1431	14	uniqueness	uniqueness	NOUN
ejde-397	1431	15	of	of	ADP
ejde-397	1431	16	corresponding	corresponding	ADJ
ejde-397	1431	17	abstract	abstract	PROPN
ejde-397	1431	18	volterra	volterra	PROPN
ejde-397	1431	19	integro	integro	PROPN
ejde-397	1431	20	-	-	PUNCT
ejde-397	1431	21	differential	differential	NOUN
ejde-397	1431	22	inclusions	inclusion	NOUN
ejde-397	1431	23	(	(	PUNCT
ejde-397	1431	24	see	see	VERB
ejde-397	1431	25	proposition	proposition	NOUN
ejde-397	1431	26	5.8(ii	5.8(ii	NUM
ejde-397	1431	27	)	)	PUNCT
ejde-397	1431	28	and	and	CCONJ
ejde-397	1431	29	theorem	theorem	VERB
ejde-397	1431	30	5.9(ii	5.9(ii	NUM
ejde-397	1431	31	)	)	PUNCT
ejde-397	1431	32	)	)	PUNCT
ejde-397	1431	33	.	.	PUNCT
ejde-397	1432	1	as	as	ADP
ejde-397	1432	2	before	before	ADV
ejde-397	1432	3	,	,	PUNCT
ejde-397	1432	4	we	we	PRON
ejde-397	1432	5	assume	assume	VERB
ejde-397	1432	6	that	that	SCONJ
ejde-397	1432	7	x	x	PRON
ejde-397	1432	8	and	and	CCONJ
ejde-397	1432	9	y	y	PROPN
ejde-397	1432	10	are	be	AUX
ejde-397	1432	11	two	two	NUM
ejde-397	1432	12	sclcss	sclcss	NOUN
ejde-397	1432	13	,	,	PUNCT
ejde-397	1432	14	0	0	PUNCT
ejde-397	1432	15	<	<	X
ejde-397	1432	16	τ	τ	PROPN
ejde-397	1432	17	≤	≤	NOUN
ejde-397	1432	18	∞	∞	PROPN
ejde-397	1432	19	,	,	PUNCT
ejde-397	1432	20	k	k	PROPN
ejde-397	1432	21	∈	∈	PROPN
ejde-397	1432	22	c([0	c([0	PROPN
ejde-397	1432	23	,	,	PUNCT
ejde-397	1432	24	τ	τ	PROPN
ejde-397	1432	25	)	)	PUNCT
ejde-397	1432	26	)	)	PUNCT
ejde-397	1432	27	,	,	PUNCT
ejde-397	1432	28	k	k	PROPN
ejde-397	1432	29	6=	6=	PROPN
ejde-397	1432	30	0	0	NUM
ejde-397	1432	31	,	,	PUNCT
ejde-397	1432	32	a	a	DET
ejde-397	1432	33	∈	∈	PROPN
ejde-397	1432	34	l1	l1	PROPN
ejde-397	1432	35	loc([0	loc([0	PROPN
ejde-397	1432	36	,	,	PUNCT
ejde-397	1432	37	τ	τ	PROPN
ejde-397	1432	38	)	)	PUNCT
ejde-397	1432	39	)	)	PUNCT
ejde-397	1432	40	,	,	PUNCT
ejde-397	1432	41	a	a	PRON
ejde-397	1432	42	6=	6=	NUM
ejde-397	1432	43	0	0	NUM
ejde-397	1432	44	,	,	PUNCT
ejde-397	1432	45	a	a	PRON
ejde-397	1432	46	:	:	PUNCT
ejde-397	1432	47	x	x	X
ejde-397	1432	48	→	→	X
ejde-397	1432	49	p	p	X
ejde-397	1432	50	(	(	PUNCT
ejde-397	1432	51	x	x	X
ejde-397	1432	52	)	)	PUNCT
ejde-397	1432	53	is	be	AUX
ejde-397	1432	54	an	an	DET
ejde-397	1432	55	mlo	mlo	PROPN
ejde-397	1432	56	,	,	PUNCT
ejde-397	1432	57	c1	c1	PROPN
ejde-397	1432	58	∈	∈	PROPN
ejde-397	1432	59	l(y	l(y	PROPN
ejde-397	1432	60	,	,	PUNCT
ejde-397	1432	61	x	x	NOUN
ejde-397	1432	62	)	)	PUNCT
ejde-397	1432	63	,	,	PUNCT
ejde-397	1433	1	c	c	X
ejde-397	1433	2	,	,	PUNCT
ejde-397	1433	3	c2	c2	PROPN
ejde-397	1433	4	∈	∈	PROPN
ejde-397	1433	5	l(x	l(x	PROPN
ejde-397	1433	6	)	)	PUNCT
ejde-397	1433	7	and	and	CCONJ
ejde-397	1433	8	ca	ca	PROPN
ejde-397	1433	9	⊆	⊆	NUM
ejde-397	1433	10	ac	ac	NOUN
ejde-397	1433	11	.	.	PUNCT
ejde-397	1434	1	we	we	PRON
ejde-397	1434	2	define	define	VERB
ejde-397	1434	3	the	the	DET
ejde-397	1434	4	integral	integral	ADJ
ejde-397	1434	5	generator	generator	NOUN
ejde-397	1434	6	ai	be	VERB
ejde-397	1434	7	nt	not	PART
ejde-397	1434	8	of	of	ADP
ejde-397	1434	9	a	a	DET
ejde-397	1434	10	mild	mild	ADJ
ejde-397	1434	11	(	(	PUNCT
ejde-397	1434	12	a	a	PRON
ejde-397	1434	13	,	,	PUNCT
ejde-397	1434	14	k)-regularized	k)-regularize	VERB
ejde-397	1434	15	c2	c2	PROPN
ejde-397	1434	16	-	-	PUNCT
ejde-397	1434	17	uniqueness	uniqueness	PROPN
ejde-397	1434	18	family	family	NOUN
ejde-397	1434	19	(	(	PUNCT
ejde-397	1434	20	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	1434	21	)	)	PUNCT
ejde-397	1434	22	(	(	PUNCT
ejde-397	1434	23	mild	mild	ADJ
ejde-397	1434	24	(	(	PUNCT
ejde-397	1434	25	a	a	PRON
ejde-397	1434	26	,	,	PUNCT
ejde-397	1434	27	k)-regularized	k)-regularize	VERB
ejde-397	1434	28	(	(	PUNCT
ejde-397	1434	29	c1	c1	NOUN
ejde-397	1434	30	,	,	PUNCT
ejde-397	1434	31	c2)-existence	c2)-existence	VERB
ejde-397	1434	32	and	and	CCONJ
ejde-397	1434	33	uniqueness	uniqueness	VERB
ejde-397	1434	34	family	family	NOUN
ejde-397	1434	35	(	(	PUNCT
ejde-397	1434	36	r1(t	r1(t	PROPN
ejde-397	1434	37	)	)	PUNCT
ejde-397	1434	38	,	,	PUNCT
ejde-397	1434	39	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	1434	40	)	)	PUNCT
ejde-397	1434	41	;	;	PUNCT
ejde-397	1434	42	(	(	PUNCT
ejde-397	1434	43	a	a	PRON
ejde-397	1434	44	,	,	PUNCT
ejde-397	1434	45	k)-regularized	k)-regularized	ADJ
ejde-397	1434	46	cregularized	cregularize	VERB
ejde-397	1434	47	family	family	NOUN
ejde-397	1434	48	(	(	PUNCT
ejde-397	1434	49	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1434	50	)	)	PUNCT
ejde-397	1434	51	)	)	PUNCT
ejde-397	1434	52	in	in	ADP
ejde-397	1434	53	the	the	DET
ejde-397	1434	54	same	same	ADJ
ejde-397	1434	55	way	way	NOUN
ejde-397	1434	56	as	as	ADP
ejde-397	1434	57	for	for	ADP
ejde-397	1434	58	injective	injective	ADJ
ejde-397	1434	59	operators	operator	NOUN
ejde-397	1434	60	c	c	PROPN
ejde-397	1434	61	and	and	CCONJ
ejde-397	1434	62	c2	c2	PROPN
ejde-397	1434	63	.	.	PUNCT
ejde-397	1435	1	then	then	ADV
ejde-397	1435	2	we	we	PRON
ejde-397	1435	3	have	have	VERB
ejde-397	1435	4	that	that	PRON
ejde-397	1435	5	ai	be	VERB
ejde-397	1435	6	nt	not	PART
ejde-397	1435	7	⊆	⊆	NUM
ejde-397	1435	8	c−1	c−1	PROPN
ejde-397	1435	9	2	2	NUM
ejde-397	1435	10	aintc2	aintc2	NOUN
ejde-397	1435	11	(	(	PUNCT
ejde-397	1435	12	ai	be	VERB
ejde-397	1435	13	nt	not	PART
ejde-397	1435	14	⊆	⊆	NUM
ejde-397	1435	15	c−1aintc	c−1aintc	NOUN
ejde-397	1435	16	)	)	PUNCT
ejde-397	1435	17	is	be	AUX
ejde-397	1435	18	still	still	ADV
ejde-397	1435	19	the	the	DET
ejde-397	1435	20	maximal	maximal	ADJ
ejde-397	1435	21	subgenerator	subgenerator	NOUN
ejde-397	1435	22	of	of	ADP
ejde-397	1435	23	(	(	PUNCT
ejde-397	1435	24	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	1435	25	)	)	PUNCT
ejde-397	1435	26	(	(	PUNCT
ejde-397	1435	27	(	(	PUNCT
ejde-397	1435	28	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1435	29	)	)	PUNCT
ejde-397	1435	30	)	)	PUNCT
ejde-397	1435	31	with	with	ADP
ejde-397	1435	32	respect	respect	NOUN
ejde-397	1435	33	to	to	ADP
ejde-397	1435	34	the	the	DET
ejde-397	1435	35	set	set	VERB
ejde-397	1435	36	inclusion	inclusion	NOUN
ejde-397	1435	37	and	and	CCONJ
ejde-397	1435	38	the	the	DET
ejde-397	1435	39	local	local	ADJ
ejde-397	1435	40	equicontinuity	equicontinuity	NOUN
ejde-397	1435	41	of	of	ADP
ejde-397	1435	42	(	(	PUNCT
ejde-397	1435	43	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	1435	44	)	)	PUNCT
ejde-397	1435	45	(	(	PUNCT
ejde-397	1435	46	(	(	PUNCT
ejde-397	1435	47	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1435	48	)	)	PUNCT
ejde-397	1435	49	)	)	PUNCT
ejde-397	1436	1	implies	imply	VERB
ejde-397	1436	2	that	that	SCONJ
ejde-397	1436	3	ai	be	AUX
ejde-397	1436	4	nt	not	PART
ejde-397	1436	5	is	be	AUX
ejde-397	1436	6	closed	close	VERB
ejde-397	1436	7	;	;	PUNCT
ejde-397	1436	8	as	as	ADP
ejde-397	1436	9	the	the	DET
ejde-397	1436	10	next	next	ADJ
ejde-397	1436	11	illustrative	illustrative	ADJ
ejde-397	1436	12	example	example	NOUN
ejde-397	1436	13	shows	show	NOUN
ejde-397	1436	14	,	,	PUNCT
ejde-397	1436	15	c−1aintc	c−1aintc	PROPN
ejde-397	1436	16	need	need	AUX
ejde-397	1436	17	not	not	PART
ejde-397	1436	18	be	be	AUX
ejde-397	1436	19	a	a	DET
ejde-397	1436	20	subgenerator	subgenerator	NOUN
ejde-397	1436	21	of	of	ADP
ejde-397	1436	22	(	(	PUNCT
ejde-397	1436	23	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1436	24	)	)	PUNCT
ejde-397	1436	25	and	and	CCONJ
ejde-397	1436	26	the	the	DET
ejde-397	1436	27	inclusion	inclusion	NOUN
ejde-397	1436	28	c−1aintc	c−1aintc	NOUN
ejde-397	1436	29	⊆	⊆	NUM
ejde-397	1436	30	ai	be	AUX
ejde-397	1436	31	nt	not	PART
ejde-397	1436	32	is	be	AUX
ejde-397	1436	33	not	not	PART
ejde-397	1436	34	true	true	ADJ
ejde-397	1436	35	for	for	ADP
ejde-397	1436	36	resolvent	resolvent	ADJ
ejde-397	1436	37	operator	operator	NOUN
ejde-397	1436	38	families	family	NOUN
ejde-397	1436	39	,	,	PUNCT
ejde-397	1436	40	in	in	ADP
ejde-397	1436	41	general	general	ADJ
ejde-397	1437	1	[	[	X
ejde-397	1437	2	50	50	NUM
ejde-397	1437	3	]	]	PUNCT
ejde-397	1437	4	.	.	PUNCT
ejde-397	1438	1	suppose	suppose	VERB
ejde-397	1438	2	that	that	SCONJ
ejde-397	1438	3	a(t	a(t	NOUN
ejde-397	1438	4	)	)	PUNCT
ejde-397	1438	5	is	be	AUX
ejde-397	1438	6	a	a	DET
ejde-397	1438	7	kernel	kernel	NOUN
ejde-397	1438	8	on	on	ADP
ejde-397	1438	9	[	[	X
ejde-397	1438	10	0	0	NUM
ejde-397	1438	11	,	,	PUNCT
ejde-397	1438	12	τ	τ	PROPN
ejde-397	1438	13	)	)	PUNCT
ejde-397	1438	14	,	,	PUNCT
ejde-397	1438	15	a	a	PRON
ejde-397	1438	16	and	and	CCONJ
ejde-397	1438	17	b	b	NOUN
ejde-397	1438	18	are	be	AUX
ejde-397	1438	19	two	two	NUM
ejde-397	1438	20	subgenerators	subgenerator	NOUN
ejde-397	1438	21	of	of	ADP
ejde-397	1438	22	an	an	DET
ejde-397	1438	23	(	(	PUNCT
ejde-397	1438	24	a	a	PRON
ejde-397	1438	25	,	,	PUNCT
ejde-397	1438	26	k)-regularized	k)-regularize	VERB
ejde-397	1438	27	c	c	NOUN
ejde-397	1438	28	-	-	PUNCT
ejde-397	1438	29	resolvent	resolvent	ADJ
ejde-397	1438	30	family	family	NOUN
ejde-397	1438	31	(	(	PUNCT
ejde-397	1438	32	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1438	33	)	)	PUNCT
ejde-397	1438	34	,	,	PUNCT
ejde-397	1438	35	and	and	CCONJ
ejde-397	1438	36	x	x	PUNCT
ejde-397	1438	37	∈	∈	PROPN
ejde-397	1438	38	d(a	d(a	PROPN
ejde-397	1438	39	)	)	PUNCT
ejde-397	1438	40	∩	∩	NOUN
ejde-397	1438	41	d(b	d(b	PROPN
ejde-397	1438	42	)	)	PUNCT
ejde-397	1438	43	.	.	PUNCT
ejde-397	1439	1	then	then	ADV
ejde-397	1439	2	r(t)(y	r(t)(y	ADJ
ejde-397	1439	3	−	−	PROPN
ejde-397	1439	4	z	z	NOUN
ejde-397	1439	5	)	)	PUNCT
ejde-397	1439	6	=	=	SYM
ejde-397	1439	7	0	0	NUM
ejde-397	1439	8	,	,	PUNCT
ejde-397	1439	9	t	t	PROPN
ejde-397	1439	10	∈	∈	PROPN
ejde-397	1440	1	[	[	X
ejde-397	1440	2	0	0	NUM
ejde-397	1440	3	,	,	PUNCT
ejde-397	1440	4	τ	τ	PROPN
ejde-397	1440	5	)	)	PUNCT
ejde-397	1440	6	for	for	ADP
ejde-397	1440	7	each	each	DET
ejde-397	1440	8	y	y	PROPN
ejde-397	1440	9	∈	∈	PROPN
ejde-397	1440	10	ax	ax	NOUN
ejde-397	1440	11	and	and	CCONJ
ejde-397	1440	12	z	z	NOUN
ejde-397	1440	13	∈	∈	PROPN
ejde-397	1440	14	bx	bx	PROPN
ejde-397	1440	15	.	.	PUNCT
ejde-397	1441	1	furthermore	furthermore	ADV
ejde-397	1441	2	,	,	PUNCT
ejde-397	1441	3	the	the	DET
ejde-397	1441	4	local	local	ADJ
ejde-397	1441	5	equicontinuity	equicontinuity	NOUN
ejde-397	1441	6	of	of	ADP
ejde-397	1441	7	(	(	PUNCT
ejde-397	1441	8	r(t))t∈[0,τ	r(t))t∈[0,τ	PROPN
ejde-397	1441	9	)	)	PUNCT
ejde-397	1441	10	and	and	CCONJ
ejde-397	1441	11	the	the	DET
ejde-397	1441	12	closedness	closedness	NOUN
ejde-397	1441	13	of	of	ADP
ejde-397	1441	14	a	a	DET
ejde-397	1441	15	imply	imply	NOUN
ejde-397	1441	16	that	that	SCONJ
ejde-397	1441	17	the	the	DET
ejde-397	1441	18	inclusion	inclusion	NOUN
ejde-397	1441	19	(	(	PUNCT
ejde-397	1441	20	5.4	5.4	NUM
ejde-397	1441	21	)	)	PUNCT
ejde-397	1441	22	continues	continue	VERB
ejde-397	1441	23	to	to	PART
ejde-397	1441	24	hold	hold	VERB
ejde-397	1441	25	without	without	ADP
ejde-397	1441	26	injectivity	injectivity	NOUN
ejde-397	1441	27	of	of	ADP
ejde-397	1441	28	c	c	PROPN
ejde-397	1441	29	being	be	AUX
ejde-397	1441	30	assumed	assume	VERB
ejde-397	1441	31	.	.	PUNCT
ejde-397	1442	1	48	48	NUM
ejde-397	1442	2	m.	m.	NOUN
ejde-397	1442	3	kostić	kostić	NOUN
ejde-397	1442	4	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1442	5	in	in	ADP
ejde-397	1442	6	the	the	DET
ejde-397	1442	7	following	follow	VERB
ejde-397	1442	8	definition	definition	NOUN
ejde-397	1442	9	,	,	PUNCT
ejde-397	1442	10	we	we	PRON
ejde-397	1442	11	introduce	introduce	VERB
ejde-397	1442	12	the	the	DET
ejde-397	1442	13	notion	notion	NOUN
ejde-397	1442	14	of	of	ADP
ejde-397	1442	15	an	an	DET
ejde-397	1442	16	(	(	PUNCT
ejde-397	1442	17	a	a	PROPN
ejde-397	1442	18	,	,	PUNCT
ejde-397	1442	19	k	k	PROPN
ejde-397	1442	20	,	,	PUNCT
ejde-397	1442	21	c)-subgenerator	c)-subgenerator	NOUN
ejde-397	1442	22	of	of	ADP
ejde-397	1442	23	any	any	DET
ejde-397	1442	24	strongly	strongly	ADV
ejde-397	1442	25	continuous	continuous	ADJ
ejde-397	1442	26	operator	operator	NOUN
ejde-397	1442	27	family	family	NOUN
ejde-397	1442	28	(	(	PUNCT
ejde-397	1442	29	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1442	30	)	)	PUNCT
ejde-397	1442	31	⊆	⊆	NUM
ejde-397	1442	32	l(x	l(x	PROPN
ejde-397	1442	33	)	)	PUNCT
ejde-397	1442	34	.	.	PUNCT
ejde-397	1443	1	this	this	DET
ejde-397	1443	2	definition	definition	NOUN
ejde-397	1443	3	extends	extend	VERB
ejde-397	1443	4	the	the	DET
ejde-397	1443	5	corresponding	corresponding	ADJ
ejde-397	1443	6	ones	one	NOUN
ejde-397	1443	7	introduced	introduce	VERB
ejde-397	1443	8	by	by	ADP
ejde-397	1443	9	kuo	kuo	PROPN
ejde-397	1444	1	[	[	X
ejde-397	1444	2	54	54	NUM
ejde-397	1444	3	,	,	PUNCT
ejde-397	1444	4	55	55	NUM
ejde-397	1444	5	,	,	PUNCT
ejde-397	1444	6	definition	definition	NOUN
ejde-397	1444	7	2.4	2.4	NUM
ejde-397	1444	8	]	]	PUNCT
ejde-397	1444	9	in	in	ADP
ejde-397	1444	10	the	the	DET
ejde-397	1444	11	setting	setting	NOUN
ejde-397	1444	12	of	of	ADP
ejde-397	1444	13	banach	banach	NOUN
ejde-397	1444	14	spaces	space	NOUN
ejde-397	1444	15	,	,	PUNCT
ejde-397	1444	16	where	where	SCONJ
ejde-397	1444	17	it	it	PRON
ejde-397	1444	18	has	have	AUX
ejde-397	1444	19	also	also	ADV
ejde-397	1444	20	been	be	AUX
ejde-397	1444	21	assumed	assume	VERB
ejde-397	1444	22	that	that	SCONJ
ejde-397	1444	23	the	the	DET
ejde-397	1444	24	operator	operator	NOUN
ejde-397	1445	1	a	a	PRON
ejde-397	1445	2	=	=	NOUN
ejde-397	1445	3	a	a	NOUN
ejde-397	1445	4	is	be	AUX
ejde-397	1445	5	linear	linear	ADJ
ejde-397	1445	6	and	and	CCONJ
ejde-397	1445	7	single	single	ADV
ejde-397	1445	8	-	-	PUNCT
ejde-397	1445	9	valued	value	VERB
ejde-397	1445	10	.	.	PUNCT
ejde-397	1446	1	definition	definition	NOUN
ejde-397	1446	2	5.29	5.29	NUM
ejde-397	1446	3	.	.	PUNCT
ejde-397	1447	1	let	let	VERB
ejde-397	1447	2	0	0	NUM
ejde-397	1447	3	<	<	X
ejde-397	1447	4	τ	τ	PROPN
ejde-397	1447	5	≤	≤	NOUN
ejde-397	1447	6	∞	∞	PROPN
ejde-397	1447	7	,	,	PUNCT
ejde-397	1447	8	c	c	PROPN
ejde-397	1447	9	∈	∈	PROPN
ejde-397	1447	10	l(x	l(x	PROPN
ejde-397	1447	11	)	)	PUNCT
ejde-397	1447	12	,	,	PUNCT
ejde-397	1447	13	a	a	DET
ejde-397	1447	14	∈	∈	PROPN
ejde-397	1447	15	l1	l1	PROPN
ejde-397	1447	16	loc([0	loc([0	PROPN
ejde-397	1447	17	,	,	PUNCT
ejde-397	1447	18	τ	τ	PROPN
ejde-397	1447	19	)	)	PUNCT
ejde-397	1447	20	)	)	PUNCT
ejde-397	1447	21	,	,	PUNCT
ejde-397	1447	22	a	a	DET
ejde-397	1447	23	6=	6=	NUM
ejde-397	1447	24	0	0	NUM
ejde-397	1447	25	,	,	PUNCT
ejde-397	1447	26	k	k	PROPN
ejde-397	1447	27	∈	∈	PROPN
ejde-397	1447	28	c([0	c([0	PROPN
ejde-397	1447	29	,	,	PUNCT
ejde-397	1447	30	τ	τ	PROPN
ejde-397	1447	31	)	)	PUNCT
ejde-397	1447	32	)	)	PUNCT
ejde-397	1447	33	and	and	CCONJ
ejde-397	1447	34	k	k	X
ejde-397	1447	35	6=	6=	PROPN
ejde-397	1447	36	0	0	X
ejde-397	1447	37	.	.	PUNCT
ejde-397	1447	38	suppose	suppose	VERB
ejde-397	1447	39	that	that	SCONJ
ejde-397	1447	40	(	(	PUNCT
ejde-397	1447	41	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1447	42	)	)	PUNCT
ejde-397	1447	43	⊆	⊆	NUM
ejde-397	1447	44	l(x	l(x	PROPN
ejde-397	1447	45	)	)	PUNCT
ejde-397	1447	46	is	be	AUX
ejde-397	1447	47	a	a	DET
ejde-397	1447	48	strongly	strongly	ADV
ejde-397	1447	49	continuous	continuous	ADJ
ejde-397	1447	50	operator	operator	NOUN
ejde-397	1447	51	family	family	NOUN
ejde-397	1447	52	.	.	PUNCT
ejde-397	1448	1	by	by	ADP
ejde-397	1448	2	an	an	DET
ejde-397	1448	3	(	(	PUNCT
ejde-397	1448	4	a	a	PROPN
ejde-397	1448	5	,	,	PUNCT
ejde-397	1448	6	k	k	PROPN
ejde-397	1448	7	,	,	PUNCT
ejde-397	1448	8	c)-subgenerator	c)-subgenerator	NOUN
ejde-397	1448	9	of	of	ADP
ejde-397	1448	10	(	(	PUNCT
ejde-397	1448	11	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1448	12	)	)	PUNCT
ejde-397	1448	13	we	we	PRON
ejde-397	1448	14	mean	mean	VERB
ejde-397	1448	15	any	any	DET
ejde-397	1448	16	mlo	mlo	PROPN
ejde-397	1448	17	a	a	PRON
ejde-397	1448	18	in	in	ADP
ejde-397	1448	19	x	x	PUNCT
ejde-397	1448	20	satisfying	satisfy	VERB
ejde-397	1448	21	the	the	DET
ejde-397	1448	22	following	follow	VERB
ejde-397	1448	23	two	two	NUM
ejde-397	1448	24	conditions	condition	NOUN
ejde-397	1448	25	:	:	PUNCT
ejde-397	1448	26	(	(	PUNCT
ejde-397	1448	27	i	i	NOUN
ejde-397	1448	28	)	)	PUNCT
ejde-397	1448	29	z(t)x−	z(t)x−	NOUN
ejde-397	1448	30	k(t)cx	k(t)cx	X
ejde-397	1448	31	=	=	SYM
ejde-397	1448	32	∫	∫	PROPN
ejde-397	1448	33	t	t	PROPN
ejde-397	1448	34	0	0	NUM
ejde-397	1449	1	a(t−	a(t−	PROPN
ejde-397	1449	2	s)z(s)y	s)z(s)y	PROPN
ejde-397	1449	3	ds	ds	NOUN
ejde-397	1449	4	,	,	PUNCT
ejde-397	1449	5	whenever	whenever	SCONJ
ejde-397	1449	6	t	t	PROPN
ejde-397	1449	7	∈	∈	PROPN
ejde-397	1450	1	[	[	X
ejde-397	1450	2	0	0	NUM
ejde-397	1450	3	,	,	PUNCT
ejde-397	1450	4	τ	τ	X
ejde-397	1450	5	)	)	PUNCT
ejde-397	1450	6	and	and	CCONJ
ejde-397	1450	7	y	y	PROPN
ejde-397	1450	8	∈	∈	PROPN
ejde-397	1450	9	ax	ax	NOUN
ejde-397	1450	10	.	.	PUNCT
ejde-397	1450	11	(	(	PUNCT
ejde-397	1450	12	ii	ii	NOUN
ejde-397	1450	13	)	)	PUNCT
ejde-397	1450	14	for	for	ADP
ejde-397	1450	15	all	all	DET
ejde-397	1450	16	x	x	SYM
ejde-397	1450	17	∈	∈	PROPN
ejde-397	1450	18	x	x	X
ejde-397	1450	19	and	and	CCONJ
ejde-397	1450	20	t	t	PROPN
ejde-397	1450	21	∈	∈	PROPN
ejde-397	1451	1	[	[	X
ejde-397	1451	2	0	0	NUM
ejde-397	1451	3	,	,	PUNCT
ejde-397	1451	4	τ	τ	PROPN
ejde-397	1451	5	)	)	PUNCT
ejde-397	1451	6	,	,	PUNCT
ejde-397	1451	7	we	we	PRON
ejde-397	1451	8	have	have	VERB
ejde-397	1451	9	∫	∫	PROPN
ejde-397	1451	10	t	t	NOUN
ejde-397	1451	11	0	0	NUM
ejde-397	1452	1	a(t	a(t	NOUN
ejde-397	1452	2	−	−	NOUN
ejde-397	1452	3	s)z(s)x	s)z(s)x	ADV
ejde-397	1452	4	ds	ds	ADJ
ejde-397	1452	5	∈	∈	PROPN
ejde-397	1452	6	d(a	d(a	PROPN
ejde-397	1452	7	)	)	PUNCT
ejde-397	1452	8	and	and	CCONJ
ejde-397	1452	9	z(t)x−	z(t)x−	NOUN
ejde-397	1452	10	k(t)cx	k(t)cx	PROPN
ejde-397	1452	11	∈	∈	PROPN
ejde-397	1452	12	a	a	DET
ejde-397	1452	13	∫	∫	PROPN
ejde-397	1452	14	t	t	NOUN
ejde-397	1452	15	0	0	NUM
ejde-397	1452	16	a(t−	a(t−	NOUN
ejde-397	1452	17	s)z(s)x	s)z(s)x	ADV
ejde-397	1452	18	ds	ds	PROPN
ejde-397	1452	19	.	.	PUNCT
ejde-397	1453	1	the	the	DET
ejde-397	1453	2	(	(	PUNCT
ejde-397	1453	3	a	a	PROPN
ejde-397	1453	4	,	,	PUNCT
ejde-397	1453	5	k	k	NOUN
ejde-397	1453	6	,	,	PUNCT
ejde-397	1453	7	c)-integral	c)-integral	ADJ
ejde-397	1453	8	generator	generator	NOUN
ejde-397	1453	9	ai	be	VERB
ejde-397	1453	10	nt	not	PART
ejde-397	1453	11	of	of	ADP
ejde-397	1453	12	(	(	PUNCT
ejde-397	1453	13	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1453	14	)	)	PUNCT
ejde-397	1453	15	(	(	PUNCT
ejde-397	1453	16	integral	integral	ADJ
ejde-397	1453	17	generator	generator	NOUN
ejde-397	1453	18	,	,	PUNCT
ejde-397	1453	19	if	if	SCONJ
ejde-397	1453	20	there	there	PRON
ejde-397	1453	21	is	be	VERB
ejde-397	1453	22	no	no	DET
ejde-397	1453	23	risk	risk	NOUN
ejde-397	1453	24	for	for	ADP
ejde-397	1453	25	confusion	confusion	NOUN
ejde-397	1453	26	)	)	PUNCT
ejde-397	1453	27	is	be	AUX
ejde-397	1453	28	defined	define	VERB
ejde-397	1453	29	by	by	ADP
ejde-397	1453	30	ai	be	VERB
ejde-397	1453	31	nt	not	PART
ejde-397	1453	32	:	:	PUNCT
ejde-397	1453	33	=	=	SYM
ejde-397	1453	34	{	{	PUNCT
ejde-397	1453	35	(	(	PUNCT
ejde-397	1453	36	x	x	NOUN
ejde-397	1453	37	,	,	PUNCT
ejde-397	1453	38	y	y	NOUN
ejde-397	1453	39	)	)	PUNCT
ejde-397	1453	40	∈	∈	PROPN
ejde-397	1453	41	x	x	X
ejde-397	1453	42	×x	×x	X
ejde-397	1453	43	:	:	PUNCT
ejde-397	1453	44	z(t)x−	z(t)x−	NOUN
ejde-397	1453	45	k(t)cx	k(t)cx	X
ejde-397	1453	46	=	=	SYM
ejde-397	1453	47	∫	∫	PROPN
ejde-397	1453	48	t	t	PROPN
ejde-397	1453	49	0	0	NUM
ejde-397	1453	50	a(t−	a(t−	NOUN
ejde-397	1453	51	s)z(s)y	s)z(s)y	NOUN
ejde-397	1453	52	ds	ds	NOUN
ejde-397	1453	53	for	for	ADP
ejde-397	1453	54	all	all	DET
ejde-397	1453	55	t	t	NOUN
ejde-397	1453	56	∈	∈	PROPN
ejde-397	1454	1	[	[	X
ejde-397	1454	2	0	0	NUM
ejde-397	1454	3	,	,	PUNCT
ejde-397	1454	4	τ	τ	PROPN
ejde-397	1454	5	)	)	PUNCT
ejde-397	1454	6	}	}	PUNCT
ejde-397	1454	7	.	.	PUNCT
ejde-397	1455	1	if	if	SCONJ
ejde-397	1455	2	a	a	PRON
ejde-397	1455	3	is	be	AUX
ejde-397	1455	4	a	a	DET
ejde-397	1455	5	subgenerator	subgenerator	NOUN
ejde-397	1455	6	of	of	ADP
ejde-397	1455	7	(	(	PUNCT
ejde-397	1455	8	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1455	9	)	)	PUNCT
ejde-397	1455	10	,	,	PUNCT
ejde-397	1455	11	then	then	ADV
ejde-397	1455	12	it	it	PRON
ejde-397	1455	13	is	be	AUX
ejde-397	1455	14	clear	clear	ADJ
ejde-397	1455	15	that	that	SCONJ
ejde-397	1455	16	(	(	PUNCT
ejde-397	1455	17	z(t))t∈[0,τ	z(t))t∈[0,τ	NOUN
ejde-397	1455	18	)	)	PUNCT
ejde-397	1455	19	is	be	AUX
ejde-397	1455	20	a	a	DET
ejde-397	1455	21	mild	mild	ADJ
ejde-397	1455	22	(	(	PUNCT
ejde-397	1455	23	a	a	PRON
ejde-397	1455	24	,	,	PUNCT
ejde-397	1455	25	k)-regularized	k)-regularize	VERB
ejde-397	1455	26	(	(	PUNCT
ejde-397	1455	27	c	c	NOUN
ejde-397	1455	28	,	,	PUNCT
ejde-397	1455	29	c)-existence	c)-existence	NOUN
ejde-397	1455	30	and	and	CCONJ
ejde-397	1455	31	uniqueness	uniqueness	PROPN
ejde-397	1455	32	family	family	NOUN
ejde-397	1455	33	which	which	PRON
ejde-397	1455	34	do	do	AUX
ejde-397	1455	35	have	have	VERB
ejde-397	1455	36	a	a	DET
ejde-397	1455	37	as	as	ADP
ejde-397	1455	38	subgenerator	subgenerator	NOUN
ejde-397	1455	39	.	.	PUNCT
ejde-397	1456	1	since	since	SCONJ
ejde-397	1456	2	we	we	PRON
ejde-397	1456	3	have	have	AUX
ejde-397	1456	4	not	not	PART
ejde-397	1456	5	assumed	assume	VERB
ejde-397	1456	6	that	that	SCONJ
ejde-397	1456	7	a	a	DET
ejde-397	1456	8	commutes	commute	NOUN
ejde-397	1456	9	with	with	ADP
ejde-397	1456	10	c	c	PROPN
ejde-397	1456	11	or	or	CCONJ
ejde-397	1456	12	(	(	PUNCT
ejde-397	1456	13	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1456	14	)	)	PUNCT
ejde-397	1456	15	,	,	PUNCT
ejde-397	1456	16	it	it	PRON
ejde-397	1456	17	does	do	AUX
ejde-397	1456	18	not	not	PART
ejde-397	1456	19	follow	follow	VERB
ejde-397	1456	20	automatically	automatically	ADV
ejde-397	1456	21	from	from	ADP
ejde-397	1456	22	definition	definition	NOUN
ejde-397	1456	23	5.29	5.29	NUM
ejde-397	1456	24	that	that	PRON
ejde-397	1456	25	(	(	PUNCT
ejde-397	1456	26	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1456	27	)	)	PUNCT
ejde-397	1456	28	is	be	AUX
ejde-397	1456	29	an	an	DET
ejde-397	1456	30	(	(	PUNCT
ejde-397	1456	31	a	a	DET
ejde-397	1456	32	,	,	PUNCT
ejde-397	1456	33	k)regularized	k)regularize	VERB
ejde-397	1456	34	c	c	X
ejde-397	1456	35	-	-	PUNCT
ejde-397	1456	36	resolvent	resolvent	ADJ
ejde-397	1456	37	family	family	NOUN
ejde-397	1456	38	with	with	ADP
ejde-397	1456	39	subgenerator	subgenerator	NOUN
ejde-397	1456	40	a.	a.	NOUN
ejde-397	1456	41	by	by	ADP
ejde-397	1456	42	χ(z	χ(z	PROPN
ejde-397	1456	43	)	)	PUNCT
ejde-397	1456	44	we	we	PRON
ejde-397	1456	45	denote	denote	VERB
ejde-397	1456	46	the	the	DET
ejde-397	1456	47	set	set	NOUN
ejde-397	1456	48	consisting	consisting	NOUN
ejde-397	1456	49	of	of	ADP
ejde-397	1456	50	all	all	DET
ejde-397	1456	51	subgenerators	subgenerator	NOUN
ejde-397	1456	52	of	of	ADP
ejde-397	1456	53	(	(	PUNCT
ejde-397	1456	54	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1456	55	)	)	PUNCT
ejde-397	1456	56	.	.	PUNCT
ejde-397	1457	1	the	the	DET
ejde-397	1457	2	local	local	ADJ
ejde-397	1457	3	equicontinuity	equicontinuity	NOUN
ejde-397	1457	4	of	of	ADP
ejde-397	1457	5	(	(	PUNCT
ejde-397	1457	6	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1457	7	)	)	PUNCT
ejde-397	1457	8	yields	yield	VERB
ejde-397	1457	9	that	that	PRON
ejde-397	1457	10	for	for	ADP
ejde-397	1457	11	each	each	DET
ejde-397	1457	12	subgenerator	subgenerator	NOUN
ejde-397	1457	13	a	a	DET
ejde-397	1457	14	∈	∈	NOUN
ejde-397	1457	15	χ(z	χ(z	PROPN
ejde-397	1457	16	)	)	PUNCT
ejde-397	1457	17	we	we	PRON
ejde-397	1457	18	have	have	VERB
ejde-397	1457	19	a	a	DET
ejde-397	1457	20	∈	∈	ADJ
ejde-397	1457	21	χ(z	χ(z	PROPN
ejde-397	1457	22	)	)	PUNCT
ejde-397	1457	23	.	.	PUNCT
ejde-397	1458	1	the	the	DET
ejde-397	1458	2	set	set	NOUN
ejde-397	1458	3	χ(z	χ(z	PROPN
ejde-397	1458	4	)	)	PUNCT
ejde-397	1458	5	can	can	AUX
ejde-397	1458	6	have	have	VERB
ejde-397	1458	7	infinitely	infinitely	ADV
ejde-397	1458	8	many	many	ADJ
ejde-397	1458	9	elements	element	NOUN
ejde-397	1458	10	;	;	PUNCT
ejde-397	1458	11	if	if	SCONJ
ejde-397	1458	12	a	a	DET
ejde-397	1458	13	∈	∈	PROPN
ejde-397	1458	14	χ(z	χ(z	PROPN
ejde-397	1458	15	)	)	PUNCT
ejde-397	1458	16	,	,	PUNCT
ejde-397	1458	17	then	then	ADV
ejde-397	1458	18	a	a	DET
ejde-397	1458	19	⊆	⊆	NUM
ejde-397	1458	20	ai	be	VERB
ejde-397	1458	21	nt	not	PART
ejde-397	1458	22	(	(	PUNCT
ejde-397	1458	23	cf	cf	NOUN
ejde-397	1458	24	.	.	PUNCT
ejde-397	1459	1	[	[	X
ejde-397	1459	2	58	58	NUM
ejde-397	1459	3	,	,	PUNCT
ejde-397	1459	4	example	example	NOUN
ejde-397	1459	5	4.10	4.10	NUM
ejde-397	1459	6	,	,	PUNCT
ejde-397	1459	7	4.11	4.11	NUM
ejde-397	1459	8	]	]	PUNCT
ejde-397	1459	9	;	;	PUNCT
ejde-397	1459	10	in	in	ADP
ejde-397	1459	11	these	these	DET
ejde-397	1459	12	examples	example	NOUN
ejde-397	1459	13	,	,	PUNCT
ejde-397	1459	14	the	the	DET
ejde-397	1459	15	partially	partially	ADV
ejde-397	1459	16	ordered	order	VERB
ejde-397	1459	17	set	set	NOUN
ejde-397	1459	18	(	(	PUNCT
ejde-397	1459	19	χsv(z),⊆	χsv(z),⊆	NOUN
ejde-397	1459	20	)	)	PUNCT
ejde-397	1459	21	,	,	PUNCT
ejde-397	1459	22	where	where	SCONJ
ejde-397	1459	23	χsv(z	χsv(z	NOUN
ejde-397	1459	24	)	)	PUNCT
ejde-397	1459	25	denotes	denote	VERB
ejde-397	1459	26	the	the	DET
ejde-397	1459	27	set	set	NOUN
ejde-397	1459	28	consisting	consist	VERB
ejde-397	1459	29	of	of	ADP
ejde-397	1459	30	all	all	DET
ejde-397	1459	31	single	single	ADV
ejde-397	1459	32	-	-	PUNCT
ejde-397	1459	33	valued	value	VERB
ejde-397	1459	34	linear	linear	ADJ
ejde-397	1459	35	subgenerators	subgenerator	NOUN
ejde-397	1459	36	of	of	ADP
ejde-397	1459	37	(	(	PUNCT
ejde-397	1459	38	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1459	39	)	)	PUNCT
ejde-397	1459	40	,	,	PUNCT
ejde-397	1459	41	does	do	AUX
ejde-397	1459	42	not	not	PART
ejde-397	1459	43	have	have	VERB
ejde-397	1459	44	the	the	DET
ejde-397	1459	45	greatest	great	ADJ
ejde-397	1459	46	element	element	NOUN
ejde-397	1459	47	)	)	PUNCT
ejde-397	1459	48	and	and	CCONJ
ejde-397	1459	49	,	,	PUNCT
ejde-397	1459	50	if	if	SCONJ
ejde-397	1459	51	χ(z	χ(z	NOUN
ejde-397	1459	52	)	)	PUNCT
ejde-397	1459	53	is	be	AUX
ejde-397	1459	54	finite	finite	ADJ
ejde-397	1459	55	,	,	PUNCT
ejde-397	1459	56	then	then	ADV
ejde-397	1459	57	it	it	PRON
ejde-397	1459	58	need	need	AUX
ejde-397	1459	59	not	not	PART
ejde-397	1459	60	be	be	AUX
ejde-397	1459	61	a	a	DET
ejde-397	1459	62	singleton	singleton	NOUN
ejde-397	1459	63	[	[	X
ejde-397	1459	64	35	35	NUM
ejde-397	1459	65	]	]	PUNCT
ejde-397	1459	66	.	.	PUNCT
ejde-397	1460	1	in	in	ADP
ejde-397	1460	2	general	general	ADJ
ejde-397	1460	3	,	,	PUNCT
ejde-397	1460	4	the	the	DET
ejde-397	1460	5	set	set	NOUN
ejde-397	1460	6	χ(z	χ(z	PROPN
ejde-397	1460	7	)	)	PUNCT
ejde-397	1460	8	can	can	AUX
ejde-397	1460	9	be	be	AUX
ejde-397	1460	10	empty	empty	ADJ
ejde-397	1460	11	and	and	CCONJ
ejde-397	1460	12	the	the	DET
ejde-397	1460	13	integral	integral	ADJ
ejde-397	1460	14	generator	generator	NOUN
ejde-397	1460	15	of	of	ADP
ejde-397	1460	16	(	(	PUNCT
ejde-397	1460	17	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1460	18	)	)	PUNCT
ejde-397	1460	19	need	need	AUX
ejde-397	1460	20	not	not	PART
ejde-397	1460	21	be	be	AUX
ejde-397	1460	22	a	a	DET
ejde-397	1460	23	subgenerator	subgenerator	NOUN
ejde-397	1460	24	of	of	ADP
ejde-397	1460	25	(	(	PUNCT
ejde-397	1460	26	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1460	27	)	)	PUNCT
ejde-397	1460	28	in	in	ADP
ejde-397	1460	29	the	the	DET
ejde-397	1460	30	case	case	NOUN
ejde-397	1460	31	that	that	SCONJ
ejde-397	1460	32	τ	τ	PROPN
ejde-397	1460	33	<	<	X
ejde-397	1460	34	∞	∞	PROPN
ejde-397	1460	35	;	;	PUNCT
ejde-397	1460	36	see	see	VERB
ejde-397	1460	37	[	[	X
ejde-397	1460	38	50	50	NUM
ejde-397	1460	39	]	]	PUNCT
ejde-397	1460	40	for	for	ADP
ejde-397	1460	41	a	a	DET
ejde-397	1460	42	counterexample	counterexample	NOUN
ejde-397	1460	43	given	give	VERB
ejde-397	1460	44	for	for	ADP
ejde-397	1460	45	local	local	ADJ
ejde-397	1460	46	c	c	NOUN
ejde-397	1460	47	-	-	PUNCT
ejde-397	1460	48	regularized	regularize	VERB
ejde-397	1460	49	semigroups	semigroup	NOUN
ejde-397	1460	50	.	.	PUNCT
ejde-397	1461	1	if	if	SCONJ
ejde-397	1461	2	a	a	PRON
ejde-397	1461	3	and	and	CCONJ
ejde-397	1461	4	b	b	NOUN
ejde-397	1461	5	are	be	AUX
ejde-397	1461	6	subgenerators	subgenerator	NOUN
ejde-397	1461	7	of	of	ADP
ejde-397	1461	8	(	(	PUNCT
ejde-397	1461	9	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1461	10	)	)	PUNCT
ejde-397	1461	11	,	,	PUNCT
ejde-397	1461	12	then	then	ADV
ejde-397	1461	13	for	for	SCONJ
ejde-397	1461	14	any	any	DET
ejde-397	1461	15	complex	complex	ADJ
ejde-397	1461	16	numbers	number	NOUN
ejde-397	1461	17	α	α	NOUN
ejde-397	1461	18	,	,	PUNCT
ejde-397	1461	19	β	β	PROPN
ejde-397	1461	20	such	such	ADJ
ejde-397	1461	21	that	that	PRON
ejde-397	1461	22	α+β	α+β	NUM
ejde-397	1461	23	=	=	SYM
ejde-397	1461	24	1	1	NUM
ejde-397	1461	25	we	we	PRON
ejde-397	1461	26	have	have	VERB
ejde-397	1461	27	that	that	SCONJ
ejde-397	1461	28	αa+βb	αa+βb	PRON
ejde-397	1461	29	is	be	AUX
ejde-397	1461	30	a	a	DET
ejde-397	1461	31	subgenerator	subgenerator	NOUN
ejde-397	1461	32	of	of	ADP
ejde-397	1461	33	(	(	PUNCT
ejde-397	1461	34	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1461	35	)	)	PUNCT
ejde-397	1461	36	.	.	PUNCT
ejde-397	1462	1	set	set	VERB
ejde-397	1462	2	a∧	a∧	PROPN
ejde-397	1462	3	b	b	PROPN
ejde-397	1462	4	:	:	PUNCT
ejde-397	1462	5	=	=	SYM
ejde-397	1462	6	(	(	PUNCT
ejde-397	1462	7	1/2)a+(1/2)b	1/2)a+(1/2)b	NUM
ejde-397	1462	8	.	.	PUNCT
ejde-397	1463	1	we	we	PRON
ejde-397	1463	2	define	define	VERB
ejde-397	1463	3	the	the	DET
ejde-397	1463	4	operator	operator	NOUN
ejde-397	1463	5	a∨0b	a∨0b	PROPN
ejde-397	1463	6	by	by	ADP
ejde-397	1463	7	d(a∨0b	d(a∨0b	NOUN
ejde-397	1463	8	)	)	PUNCT
ejde-397	1463	9	:	:	PUNCT
ejde-397	1464	1	=	=	SYM
ejde-397	1464	2	span[d(a)∪	span[d(a)∪	PRON
ejde-397	1464	3	d(b	d(b	NOUN
ejde-397	1464	4	)	)	PUNCT
ejde-397	1464	5	]	]	PUNCT
ejde-397	1464	6	and	and	CCONJ
ejde-397	1464	7	a	a	DET
ejde-397	1464	8	∨0	∨0	NOUN
ejde-397	1464	9	b(ax+	b(ax+	NOUN
ejde-397	1464	10	by	by	ADP
ejde-397	1464	11	)	)	PUNCT
ejde-397	1464	12	:	:	PUNCT
ejde-397	1464	13	=	=	PUNCT
ejde-397	1464	14	aax+	aax+	PROPN
ejde-397	1464	15	bby	bby	PROPN
ejde-397	1464	16	,	,	PUNCT
ejde-397	1464	17	x	x	PROPN
ejde-397	1464	18	∈	∈	PROPN
ejde-397	1464	19	d(a	d(a	PROPN
ejde-397	1464	20	)	)	PUNCT
ejde-397	1464	21	,	,	PUNCT
ejde-397	1464	22	y	y	PROPN
ejde-397	1464	23	∈	∈	PROPN
ejde-397	1464	24	d(b	d(b	PROPN
ejde-397	1464	25	)	)	PUNCT
ejde-397	1464	26	,	,	PUNCT
ejde-397	1464	27	a	a	DET
ejde-397	1464	28	,	,	PUNCT
ejde-397	1464	29	b	b	X
ejde-397	1464	30	∈	∈	PROPN
ejde-397	1464	31	c	c	NOUN
ejde-397	1464	32	;	;	PUNCT
ejde-397	1464	33	a	a	DET
ejde-397	1464	34	∨	∨	NUM
ejde-397	1464	35	b	b	NOUN
ejde-397	1464	36	:	:	PUNCT
ejde-397	1464	37	=	=	SYM
ejde-397	1464	38	a	a	DET
ejde-397	1464	39	∨0	∨0	PROPN
ejde-397	1464	40	b.	b.	PROPN
ejde-397	1464	41	then	then	ADV
ejde-397	1464	42	a	a	DET
ejde-397	1464	43	∨0	∨0	PROPN
ejde-397	1464	44	b	b	PROPN
ejde-397	1464	45	is	be	AUX
ejde-397	1464	46	a	a	DET
ejde-397	1464	47	subgenerator	subgenerator	NOUN
ejde-397	1464	48	of	of	ADP
ejde-397	1464	49	(	(	PUNCT
ejde-397	1464	50	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1464	51	)	)	PUNCT
ejde-397	1464	52	,	,	PUNCT
ejde-397	1464	53	and	and	CCONJ
ejde-397	1464	54	a	a	DET
ejde-397	1464	55	∨	∨	NUM
ejde-397	1464	56	b	b	NOUN
ejde-397	1464	57	is	be	AUX
ejde-397	1464	58	a	a	DET
ejde-397	1464	59	subgenerator	subgenerator	NOUN
ejde-397	1464	60	of	of	ADP
ejde-397	1464	61	(	(	PUNCT
ejde-397	1464	62	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1464	63	)	)	PUNCT
ejde-397	1464	64	,	,	PUNCT
ejde-397	1464	65	provided	provide	VERB
ejde-397	1464	66	that	that	SCONJ
ejde-397	1464	67	(	(	PUNCT
ejde-397	1464	68	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1464	69	)	)	PUNCT
ejde-397	1464	70	is	be	AUX
ejde-397	1464	71	locally	locally	ADV
ejde-397	1464	72	equicontinuous	equicontinuous	ADJ
ejde-397	1464	73	.	.	PUNCT
ejde-397	1465	1	in	in	ADP
ejde-397	1465	2	the	the	DET
ejde-397	1465	3	case	case	NOUN
ejde-397	1465	4	of	of	ADP
ejde-397	1465	5	non	non	ADJ
ejde-397	1465	6	-	-	ADJ
ejde-397	1465	7	degenerate	degenerate	ADJ
ejde-397	1465	8	k	k	ADV
ejde-397	1465	9	-	-	ADJ
ejde-397	1465	10	convoluted	convoluted	ADJ
ejde-397	1465	11	c	c	NOUN
ejde-397	1465	12	-	-	PUNCT
ejde-397	1465	13	semigroups	semigroup	NOUN
ejde-397	1465	14	,	,	PUNCT
ejde-397	1465	15	c	c	NOUN
ejde-397	1465	16	injective	injective	ADJ
ejde-397	1465	17	,	,	PUNCT
ejde-397	1465	18	it	it	PRON
ejde-397	1465	19	is	be	AUX
ejde-397	1465	20	well	well	ADV
ejde-397	1465	21	known	know	VERB
ejde-397	1465	22	that	that	SCONJ
ejde-397	1465	23	the	the	DET
ejde-397	1465	24	set	set	NOUN
ejde-397	1465	25	χ(z	χ(z	PROPN
ejde-397	1465	26	)	)	PUNCT
ejde-397	1465	27	,	,	PUNCT
ejde-397	1465	28	equipped	equip	VERB
ejde-397	1465	29	with	with	ADP
ejde-397	1465	30	the	the	DET
ejde-397	1465	31	operations	operation	NOUN
ejde-397	1465	32	∧	∧	PROPN
ejde-397	1465	33	and	and	CCONJ
ejde-397	1465	34	∨	∨	NUM
ejde-397	1465	35	,	,	PUNCT
ejde-397	1465	36	forms	form	VERB
ejde-397	1465	37	a	a	DET
ejde-397	1465	38	complete	complete	ADJ
ejde-397	1465	39	boolean	boolean	ADJ
ejde-397	1465	40	lattice	lattice	NOUN
ejde-397	1465	41	(	(	PUNCT
ejde-397	1465	42	[	[	X
ejde-397	1465	43	78	78	NUM
ejde-397	1465	44	]	]	PUNCT
ejde-397	1465	45	,	,	PUNCT
ejde-397	1465	46	[	[	X
ejde-397	1465	47	35	35	NUM
ejde-397	1465	48	,	,	PUNCT
ejde-397	1465	49	remark	remark	NOUN
ejde-397	1465	50	2.1.8(ii)-(iii	2.1.8(ii)-(iii	NUM
ejde-397	1465	51	)	)	PUNCT
ejde-397	1465	52	]	]	PUNCT
ejde-397	1465	53	)	)	PUNCT
ejde-397	1465	54	.	.	PUNCT
ejde-397	1466	1	we	we	PRON
ejde-397	1466	2	will	will	AUX
ejde-397	1466	3	not	not	PART
ejde-397	1466	4	discuss	discuss	VERB
ejde-397	1466	5	the	the	DET
ejde-397	1466	6	properties	property	NOUN
ejde-397	1466	7	of	of	ADP
ejde-397	1466	8	(	(	PUNCT
ejde-397	1466	9	χ(z),∧,∨	χ(z),∧,∨	PROPN
ejde-397	1466	10	)	)	PUNCT
ejde-397	1466	11	in	in	ADP
ejde-397	1466	12	general	general	ADJ
ejde-397	1466	13	case	case	NOUN
ejde-397	1466	14	.	.	PUNCT
ejde-397	1467	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1467	2	abstract	abstract	ADJ
ejde-397	1467	3	degenerate	degenerate	ADJ
ejde-397	1467	4	volterra	volterra	NOUN
ejde-397	1467	5	inclusions	inclusion	NOUN
ejde-397	1467	6	49	49	NUM
ejde-397	1467	7	if	if	SCONJ
ejde-397	1467	8	a	a	PRON
ejde-397	1467	9	is	be	AUX
ejde-397	1467	10	a	a	DET
ejde-397	1467	11	closed	closed	ADJ
ejde-397	1467	12	,	,	PUNCT
ejde-397	1467	13	a	a	DET
ejde-397	1467	14	∈	∈	NOUN
ejde-397	1467	15	χ(z	χ(z	PROPN
ejde-397	1467	16	)	)	PUNCT
ejde-397	1467	17	,	,	PUNCT
ejde-397	1467	18	0	0	NUM
ejde-397	1467	19	∈	∈	PROPN
ejde-397	1467	20	supp(a	supp(a	NOUN
ejde-397	1467	21	)	)	PUNCT
ejde-397	1467	22	and	and	CCONJ
ejde-397	1467	23	y	y	PROPN
ejde-397	1467	24	∈	∈	PROPN
ejde-397	1467	25	ax	ax	NOUN
ejde-397	1467	26	,	,	PUNCT
ejde-397	1467	27	then	then	ADV
ejde-397	1467	28	we	we	PRON
ejde-397	1467	29	have	have	VERB
ejde-397	1467	30	(	(	PUNCT
ejde-397	1467	31	∫	∫	PROPN
ejde-397	1467	32	t	t	PROPN
ejde-397	1467	33	0	0	NUM
ejde-397	1467	34	a(t	a(t	NOUN
ejde-397	1467	35	−	−	NOUN
ejde-397	1467	36	s)z(s)x	s)z(s)x	ADV
ejde-397	1467	37	ds	ds	ADJ
ejde-397	1467	38	,	,	PUNCT
ejde-397	1467	39	z(t)x−	z(t)x−	NOUN
ejde-397	1467	40	k(t)cx	k(t)cx	PROPN
ejde-397	1467	41	)	)	PUNCT
ejde-397	1467	42	∈	∈	PROPN
ejde-397	1467	43	a	a	X
ejde-397	1467	44	,	,	PUNCT
ejde-397	1467	45	t	t	PROPN
ejde-397	1467	46	∈	∈	PROPN
ejde-397	1468	1	[	[	X
ejde-397	1468	2	0	0	NUM
ejde-397	1468	3	,	,	PUNCT
ejde-397	1468	4	τ	τ	PROPN
ejde-397	1468	5	)	)	PUNCT
ejde-397	1468	6	,	,	PUNCT
ejde-397	1468	7	i.e.	i.e.	X
ejde-397	1468	8	,(∫	,(∫	PUNCT
ejde-397	1468	9	t	t	PROPN
ejde-397	1468	10	0	0	NUM
ejde-397	1468	11	a(t−	a(t−	NOUN
ejde-397	1468	12	s)z(s)x	s)z(s)x	ADV
ejde-397	1468	13	ds	ds	PROPN
ejde-397	1468	14	,	,	PUNCT
ejde-397	1468	15	∫	∫	PROPN
ejde-397	1468	16	t	t	PROPN
ejde-397	1468	17	0	0	NUM
ejde-397	1468	18	a(t−	a(t−	NOUN
ejde-397	1468	19	s)z(s)y	s)z(s)y	NOUN
ejde-397	1468	20	ds	ds	ADJ
ejde-397	1468	21	)	)	PUNCT
ejde-397	1468	22	∈	∈	PROPN
ejde-397	1468	23	a	a	X
ejde-397	1468	24	,	,	PUNCT
ejde-397	1468	25	t	t	PROPN
ejde-397	1468	26	∈	∈	PROPN
ejde-397	1469	1	[	[	X
ejde-397	1469	2	0	0	NUM
ejde-397	1469	3	,	,	PUNCT
ejde-397	1469	4	τ	τ	PROPN
ejde-397	1469	5	)	)	PUNCT
ejde-397	1469	6	.	.	PUNCT
ejde-397	1470	1	(	(	PUNCT
ejde-397	1470	2	5.35	5.35	NUM
ejde-397	1470	3	)	)	PUNCT
ejde-397	1470	4	suppose	suppose	VERB
ejde-397	1470	5	now	now	ADV
ejde-397	1470	6	that	that	SCONJ
ejde-397	1470	7	τ0	τ0	NOUN
ejde-397	1470	8	∈	∈	PROPN
ejde-397	1470	9	(	(	PUNCT
ejde-397	1470	10	0	0	NUM
ejde-397	1470	11	,	,	PUNCT
ejde-397	1470	12	τ	τ	PROPN
ejde-397	1470	13	)	)	PUNCT
ejde-397	1470	14	.	.	PUNCT
ejde-397	1471	1	by	by	ADP
ejde-397	1471	2	[	[	X
ejde-397	1471	3	35	35	NUM
ejde-397	1471	4	,	,	PUNCT
ejde-397	1471	5	theorem	theorem	VERB
ejde-397	1471	6	3.4.40	3.4.40	NUM
ejde-397	1471	7	]	]	PUNCT
ejde-397	1471	8	,	,	PUNCT
ejde-397	1471	9	there	there	PRON
ejde-397	1471	10	exists	exist	VERB
ejde-397	1471	11	a	a	DET
ejde-397	1471	12	sequence	sequence	NOUN
ejde-397	1471	13	(	(	PUNCT
ejde-397	1471	14	fn)n∈n	fn)n∈n	NUM
ejde-397	1471	15	in	in	ADP
ejde-397	1471	16	l1[0	l1[0	PROPN
ejde-397	1471	17	,	,	PUNCT
ejde-397	1471	18	τ0	τ0	NOUN
ejde-397	1471	19	]	]	PUNCT
ejde-397	1471	20	such	such	ADJ
ejde-397	1471	21	that	that	SCONJ
ejde-397	1471	22	(	(	PUNCT
ejde-397	1471	23	a	a	DET
ejde-397	1471	24	∗	∗	NOUN
ejde-397	1471	25	fn)(t	fn)(t	NOUN
ejde-397	1471	26	)	)	PUNCT
ejde-397	1471	27	→	→	SYM
ejde-397	1471	28	g1(t	g1(t	X
ejde-397	1471	29	)	)	PUNCT
ejde-397	1471	30	in	in	ADP
ejde-397	1471	31	l1[0	l1[0	PROPN
ejde-397	1471	32	,	,	PUNCT
ejde-397	1471	33	τ0	τ0	NOUN
ejde-397	1471	34	]	]	PUNCT
ejde-397	1471	35	.	.	PUNCT
ejde-397	1472	1	then	then	ADV
ejde-397	1472	2	the	the	DET
ejde-397	1472	3	closedness	closedness	NOUN
ejde-397	1472	4	of	of	ADP
ejde-397	1472	5	a	a	DET
ejde-397	1472	6	along	along	NOUN
ejde-397	1472	7	with	with	ADP
ejde-397	1472	8	(	(	PUNCT
ejde-397	1472	9	5.35	5.35	NUM
ejde-397	1472	10	)	)	PUNCT
ejde-397	1472	11	shows	show	VERB
ejde-397	1472	12	that	that	SCONJ
ejde-397	1472	13	(	(	PUNCT
ejde-397	1472	14	∫	∫	PROPN
ejde-397	1472	15	t	t	PROPN
ejde-397	1472	16	0	0	NUM
ejde-397	1472	17	g1(t−	g1(t−	VERB
ejde-397	1472	18	s)z(s)x	s)z(s)x	ADV
ejde-397	1472	19	ds	ds	ADJ
ejde-397	1472	20	,	,	PUNCT
ejde-397	1472	21	∫	∫	PROPN
ejde-397	1472	22	t	t	PROPN
ejde-397	1472	23	0	0	NUM
ejde-397	1472	24	g1(t−	g1(t−	ADJ
ejde-397	1472	25	s)z(s)y	s)z(s)y	PROPN
ejde-397	1472	26	ds	ds	ADJ
ejde-397	1472	27	)	)	PUNCT
ejde-397	1472	28	∈	∈	PROPN
ejde-397	1472	29	a	a	X
ejde-397	1472	30	,	,	PUNCT
ejde-397	1472	31	t	t	PROPN
ejde-397	1472	32	∈	∈	PROPN
ejde-397	1473	1	[	[	X
ejde-397	1473	2	0	0	NUM
ejde-397	1473	3	,	,	PUNCT
ejde-397	1473	4	τ0	τ0	NOUN
ejde-397	1473	5	]	]	PUNCT
ejde-397	1473	6	.	.	PUNCT
ejde-397	1474	1	after	after	ADP
ejde-397	1474	2	differentiation	differentiation	NOUN
ejde-397	1474	3	,	,	PUNCT
ejde-397	1474	4	we	we	PRON
ejde-397	1474	5	obtain	obtain	VERB
ejde-397	1474	6	that	that	PRON
ejde-397	1474	7	(	(	PUNCT
ejde-397	1474	8	z(t)x	z(t)x	PROPN
ejde-397	1474	9	,	,	PUNCT
ejde-397	1474	10	z(t)y	z(t)y	PROPN
ejde-397	1474	11	)	)	PUNCT
ejde-397	1474	12	∈	∈	PROPN
ejde-397	1475	1	a	a	PRON
ejde-397	1475	2	,	,	PUNCT
ejde-397	1475	3	t	t	PROPN
ejde-397	1475	4	∈	∈	PROPN
ejde-397	1476	1	[	[	X
ejde-397	1476	2	0	0	NUM
ejde-397	1476	3	,	,	PUNCT
ejde-397	1476	4	τ0	τ0	NOUN
ejde-397	1476	5	]	]	PUNCT
ejde-397	1476	6	and	and	CCONJ
ejde-397	1476	7	since	since	SCONJ
ejde-397	1476	8	τ0	τ0	NOUN
ejde-397	1476	9	was	be	AUX
ejde-397	1476	10	arbitrary	arbitrary	ADJ
ejde-397	1476	11	,	,	PUNCT
ejde-397	1476	12	we	we	PRON
ejde-397	1476	13	have	have	VERB
ejde-397	1476	14	that	that	DET
ejde-397	1476	15	z(t)a	z(t)a	PROPN
ejde-397	1476	16	⊆	⊆	NUM
ejde-397	1476	17	az(t	az(t	NOUN
ejde-397	1476	18	)	)	PUNCT
ejde-397	1476	19	,	,	PUNCT
ejde-397	1476	20	t	t	PROPN
ejde-397	1476	21	∈	∈	PROPN
ejde-397	1477	1	[	[	X
ejde-397	1477	2	0	0	NUM
ejde-397	1477	3	,	,	PUNCT
ejde-397	1477	4	τ	τ	PROPN
ejde-397	1477	5	)	)	PUNCT
ejde-397	1477	6	for	for	ADP
ejde-397	1477	7	any	any	DET
ejde-397	1477	8	closed	closed	ADJ
ejde-397	1477	9	subgenerator	subgenerator	NOUN
ejde-397	1477	10	a	a	PRON
ejde-397	1477	11	of	of	ADP
ejde-397	1477	12	(	(	PUNCT
ejde-397	1477	13	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1477	14	)	)	PUNCT
ejde-397	1477	15	.	.	PUNCT
ejde-397	1478	1	if	if	SCONJ
ejde-397	1478	2	this	this	PRON
ejde-397	1478	3	is	be	AUX
ejde-397	1478	4	the	the	DET
ejde-397	1478	5	case	case	NOUN
ejde-397	1478	6	and	and	CCONJ
ejde-397	1478	7	z(t)c	z(t)c	PROPN
ejde-397	1478	8	=	=	SYM
ejde-397	1478	9	cz(t	cz(t	X
ejde-397	1478	10	)	)	PUNCT
ejde-397	1478	11	,	,	PUNCT
ejde-397	1478	12	t	t	PROPN
ejde-397	1478	13	∈	∈	PROPN
ejde-397	1479	1	[	[	X
ejde-397	1479	2	0	0	NUM
ejde-397	1479	3	,	,	PUNCT
ejde-397	1479	4	τ	τ	PROPN
ejde-397	1479	5	)	)	PUNCT
ejde-397	1479	6	,	,	PUNCT
ejde-397	1479	7	then	then	ADV
ejde-397	1479	8	c−1ac	c−1ac	PROPN
ejde-397	1479	9	also	also	ADV
ejde-397	1479	10	commutes	commute	VERB
ejde-397	1479	11	with	with	ADP
ejde-397	1479	12	z(t	z(t	NOUN
ejde-397	1479	13	):	):	PUNCT
ejde-397	1479	14	suppose	suppose	VERB
ejde-397	1479	15	that	that	SCONJ
ejde-397	1479	16	(	(	PUNCT
ejde-397	1479	17	x	x	X
ejde-397	1479	18	,	,	PUNCT
ejde-397	1479	19	y	y	NOUN
ejde-397	1479	20	)	)	PUNCT
ejde-397	1479	21	∈	∈	PROPN
ejde-397	1479	22	c−1ac	c−1ac	NOUN
ejde-397	1479	23	.	.	PUNCT
ejde-397	1480	1	then	then	ADV
ejde-397	1480	2	cy	cy	PROPN
ejde-397	1480	3	∈	∈	PROPN
ejde-397	1480	4	acx	acx	PROPN
ejde-397	1480	5	,	,	PUNCT
ejde-397	1480	6	cz(t)x	cz(t)x	X
ejde-397	1480	7	=	=	SYM
ejde-397	1480	8	z(t)cx	z(t)cx	NUM
ejde-397	1480	9	∈	∈	PROPN
ejde-397	1480	10	d(a	d(a	PROPN
ejde-397	1480	11	)	)	PUNCT
ejde-397	1480	12	,	,	PUNCT
ejde-397	1480	13	t	t	PROPN
ejde-397	1480	14	∈	∈	PROPN
ejde-397	1481	1	[	[	X
ejde-397	1481	2	0	0	NUM
ejde-397	1481	3	,	,	PUNCT
ejde-397	1481	4	τ	τ	X
ejde-397	1481	5	)	)	PUNCT
ejde-397	1481	6	and	and	CCONJ
ejde-397	1481	7	cz(t)y	cz(t)y	PUNCT
ejde-397	1481	8	=	=	SYM
ejde-397	1481	9	z(t)cy	z(t)cy	NUM
ejde-397	1481	10	∈	∈	NOUN
ejde-397	1481	11	z(t)acx	z(t)acx	NOUN
ejde-397	1481	12	⊆	⊆	NUM
ejde-397	1481	13	acz(t)x	acz(t)x	NOUN
ejde-397	1481	14	=	=	PUNCT
ejde-397	1481	15	az(t)cx	az(t)cx	NOUN
ejde-397	1481	16	,	,	PUNCT
ejde-397	1481	17	t	t	PROPN
ejde-397	1481	18	∈	∈	PROPN
ejde-397	1482	1	[	[	X
ejde-397	1482	2	0	0	NUM
ejde-397	1482	3	,	,	PUNCT
ejde-397	1482	4	τ	τ	PROPN
ejde-397	1482	5	)	)	PUNCT
ejde-397	1483	1	so	so	SCONJ
ejde-397	1483	2	that	that	SCONJ
ejde-397	1483	3	z(t)y	z(t)y	PROPN
ejde-397	1483	4	∈	∈	PROPN
ejde-397	1483	5	c−1acz(t)x	c−1acz(t)x	NOUN
ejde-397	1483	6	,	,	PUNCT
ejde-397	1483	7	t	t	PROPN
ejde-397	1483	8	∈	∈	PROPN
ejde-397	1484	1	[	[	X
ejde-397	1484	2	0	0	NUM
ejde-397	1484	3	,	,	PUNCT
ejde-397	1484	4	τ	τ	X
ejde-397	1484	5	)	)	PUNCT
ejde-397	1484	6	and	and	CCONJ
ejde-397	1484	7	z(t)[c−1ac	z(t)[c−1ac	PROPN
ejde-397	1484	8	]	]	PUNCT
ejde-397	1484	9	⊆	⊆	NUM
ejde-397	1484	10	[	[	X
ejde-397	1484	11	c−1ac]z(t	c−1ac]z(t	NOUN
ejde-397	1484	12	)	)	PUNCT
ejde-397	1484	13	,	,	PUNCT
ejde-397	1484	14	t	t	PROPN
ejde-397	1484	15	∈	∈	PROPN
ejde-397	1485	1	[	[	X
ejde-397	1485	2	0	0	NUM
ejde-397	1485	3	,	,	PUNCT
ejde-397	1485	4	τ	τ	PROPN
ejde-397	1485	5	)	)	PUNCT
ejde-397	1485	6	.	.	PUNCT
ejde-397	1486	1	suppose	suppose	VERB
ejde-397	1486	2	again	again	ADV
ejde-397	1486	3	that	that	SCONJ
ejde-397	1486	4	a	a	PRON
ejde-397	1486	5	is	be	AUX
ejde-397	1486	6	a	a	DET
ejde-397	1486	7	closed	closed	ADJ
ejde-397	1486	8	subgenerator	subgenerator	NOUN
ejde-397	1486	9	of	of	ADP
ejde-397	1486	10	(	(	PUNCT
ejde-397	1486	11	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1486	12	)	)	PUNCT
ejde-397	1486	13	,	,	PUNCT
ejde-397	1486	14	0	0	NUM
ejde-397	1486	15	∈	∈	PROPN
ejde-397	1486	16	supp(a	supp(a	NOUN
ejde-397	1486	17	)	)	PUNCT
ejde-397	1486	18	and	and	CCONJ
ejde-397	1486	19	y	y	PROPN
ejde-397	1486	20	∈	∈	PROPN
ejde-397	1486	21	ax	ax	NOUN
ejde-397	1486	22	.	.	PUNCT
ejde-397	1487	1	then	then	ADV
ejde-397	1487	2	(	(	PUNCT
ejde-397	1487	3	∫	∫	PROPN
ejde-397	1487	4	t	t	PROPN
ejde-397	1487	5	0	0	NUM
ejde-397	1487	6	a(t	a(t	NOUN
ejde-397	1487	7	−	−	PROPN
ejde-397	1487	8	s)z(s)y	s)z(s)y	NOUN
ejde-397	1487	9	ds	ds	NOUN
ejde-397	1487	10	,	,	PUNCT
ejde-397	1487	11	z(t)y	z(t)y	PROPN
ejde-397	1487	12	−	−	NOUN
ejde-397	1487	13	k(t)cy	k(t)cy	PROPN
ejde-397	1487	14	)	)	PUNCT
ejde-397	1487	15	=	=	PUNCT
ejde-397	1487	16	(	(	PUNCT
ejde-397	1487	17	z(t)x	z(t)x	PROPN
ejde-397	1487	18	−	−	NOUN
ejde-397	1487	19	k(t)cx	k(t)cx	NOUN
ejde-397	1487	20	,	,	PUNCT
ejde-397	1487	21	z(t)y	z(t)y	PROPN
ejde-397	1487	22	−	−	NOUN
ejde-397	1487	23	k(t)cy	k(t)cy	PROPN
ejde-397	1487	24	)	)	PUNCT
ejde-397	1487	25	∈	∈	PROPN
ejde-397	1487	26	a	a	X
ejde-397	1487	27	,	,	PUNCT
ejde-397	1487	28	t	t	PROPN
ejde-397	1487	29	∈	∈	PROPN
ejde-397	1488	1	[	[	X
ejde-397	1488	2	0	0	NUM
ejde-397	1488	3	,	,	PUNCT
ejde-397	1488	4	τ	τ	PROPN
ejde-397	1488	5	)	)	PUNCT
ejde-397	1488	6	.	.	PUNCT
ejde-397	1489	1	since	since	SCONJ
ejde-397	1489	2	(	(	PUNCT
ejde-397	1489	3	z(t)x	z(t)x	PROPN
ejde-397	1489	4	,	,	PUNCT
ejde-397	1489	5	z(t)y	z(t)y	PROPN
ejde-397	1489	6	)	)	PUNCT
ejde-397	1489	7	∈	∈	PROPN
ejde-397	1489	8	a	a	PRON
ejde-397	1489	9	,	,	PUNCT
ejde-397	1489	10	t	t	PROPN
ejde-397	1489	11	∈	∈	PROPN
ejde-397	1490	1	[	[	X
ejde-397	1490	2	0	0	NUM
ejde-397	1490	3	,	,	PUNCT
ejde-397	1490	4	τ	τ	PROPN
ejde-397	1490	5	)	)	PUNCT
ejde-397	1490	6	,	,	PUNCT
ejde-397	1490	7	the	the	DET
ejde-397	1490	8	above	above	ADV
ejde-397	1490	9	easily	easily	ADV
ejde-397	1490	10	implies	imply	VERB
ejde-397	1490	11	that	that	SCONJ
ejde-397	1490	12	(	(	PUNCT
ejde-397	1490	13	cx	cx	NOUN
ejde-397	1490	14	,	,	PUNCT
ejde-397	1490	15	cy	cy	PROPN
ejde-397	1490	16	)	)	PUNCT
ejde-397	1490	17	∈	∈	PROPN
ejde-397	1490	18	a	a	DET
ejde-397	1490	19	so	so	ADV
ejde-397	1491	1	that	that	SCONJ
ejde-397	1491	2	ca	can	AUX
ejde-397	1491	3	⊆	⊆	NUM
ejde-397	1491	4	ac	ac	PROPN
ejde-397	1491	5	,	,	PUNCT
ejde-397	1491	6	i.e.	i.e.	X
ejde-397	1491	7	,	,	PUNCT
ejde-397	1491	8	a	a	DET
ejde-397	1491	9	⊆	⊆	NUM
ejde-397	1491	10	c−1ac	c−1ac	NOUN
ejde-397	1491	11	.	.	PUNCT
ejde-397	1492	1	now	now	ADV
ejde-397	1492	2	we	we	PRON
ejde-397	1492	3	proceed	proceed	VERB
ejde-397	1492	4	by	by	ADP
ejde-397	1492	5	repeating	repeat	VERB
ejde-397	1492	6	some	some	DET
ejde-397	1492	7	parts	part	NOUN
ejde-397	1492	8	of	of	ADP
ejde-397	1492	9	the	the	DET
ejde-397	1492	10	proof	proof	NOUN
ejde-397	1492	11	of	of	ADP
ejde-397	1492	12	[	[	X
ejde-397	1492	13	35	35	NUM
ejde-397	1492	14	,	,	PUNCT
ejde-397	1492	15	proposition	proposition	NOUN
ejde-397	1492	16	2.1.6(i	2.1.6(i	NUM
ejde-397	1492	17	)	)	PUNCT
ejde-397	1492	18	]	]	PUNCT
ejde-397	1492	19	.	.	PUNCT
ejde-397	1493	1	let	let	VERB
ejde-397	1493	2	(	(	PUNCT
ejde-397	1493	3	x	x	NOUN
ejde-397	1493	4	,	,	PUNCT
ejde-397	1493	5	y	y	PROPN
ejde-397	1493	6	)	)	PUNCT
ejde-397	1493	7	∈	∈	PROPN
ejde-397	1493	8	ai	be	VERB
ejde-397	1493	9	nt	not	PART
ejde-397	1493	10	.	.	PUNCT
ejde-397	1494	1	as	as	ADP
ejde-397	1494	2	above	above	ADV
ejde-397	1494	3	,	,	PUNCT
ejde-397	1494	4	we	we	PRON
ejde-397	1494	5	have	have	VERB
ejde-397	1494	6	(	(	PUNCT
ejde-397	1494	7	∫	∫	PROPN
ejde-397	1494	8	t	t	PROPN
ejde-397	1494	9	0	0	NUM
ejde-397	1495	1	a(t	a(t	NOUN
ejde-397	1495	2	−	−	NOUN
ejde-397	1495	3	s)z(s)x	s)z(s)x	ADV
ejde-397	1495	4	ds	ds	ADJ
ejde-397	1495	5	,	,	PUNCT
ejde-397	1495	6	∫	∫	PROPN
ejde-397	1495	7	t	t	NOUN
ejde-397	1495	8	0	0	NUM
ejde-397	1495	9	a(t	a(t	NOUN
ejde-397	1495	10	−	−	NOUN
ejde-397	1495	11	s)z(s)y	s)z(s)y	NOUN
ejde-397	1495	12	ds	ds	ADJ
ejde-397	1495	13	)	)	PUNCT
ejde-397	1495	14	∈	∈	PROPN
ejde-397	1495	15	a	a	X
ejde-397	1495	16	,	,	PUNCT
ejde-397	1495	17	t	t	PROPN
ejde-397	1495	18	∈	∈	PROPN
ejde-397	1496	1	[	[	X
ejde-397	1496	2	0	0	NUM
ejde-397	1496	3	,	,	PUNCT
ejde-397	1496	4	τ	τ	X
ejde-397	1496	5	)	)	PUNCT
ejde-397	1496	6	and	and	CCONJ
ejde-397	1496	7	(	(	PUNCT
ejde-397	1496	8	z(t)x	z(t)x	PROPN
ejde-397	1496	9	,	,	PUNCT
ejde-397	1496	10	z(t)y	z(t)y	PROPN
ejde-397	1496	11	)	)	PUNCT
ejde-397	1496	12	∈	∈	PROPN
ejde-397	1496	13	a	a	DET
ejde-397	1496	14	=	=	X
ejde-397	1496	15	a	a	NOUN
ejde-397	1496	16	,	,	PUNCT
ejde-397	1496	17	t	t	PROPN
ejde-397	1496	18	∈	∈	PROPN
ejde-397	1497	1	[	[	X
ejde-397	1497	2	0	0	NUM
ejde-397	1497	3	,	,	PUNCT
ejde-397	1497	4	τ	τ	PROPN
ejde-397	1497	5	)	)	PUNCT
ejde-397	1497	6	.	.	PUNCT
ejde-397	1498	1	this	this	PRON
ejde-397	1498	2	implies	imply	VERB
ejde-397	1498	3	z(t)y	z(t)y	PROPN
ejde-397	1498	4	∈	∈	PROPN
ejde-397	1498	5	az(t)x	az(t)x	PUNCT
ejde-397	1499	1	=	=	PRON
ejde-397	1499	2	a[θ(t)cx	a[θ(t)cx	NOUN
ejde-397	1499	3	+	+	PROPN
ejde-397	1500	1	∫	∫	PROPN
ejde-397	1500	2	t	t	NOUN
ejde-397	1500	3	0	0	NUM
ejde-397	1500	4	a(t	a(t	NOUN
ejde-397	1500	5	−	−	PROPN
ejde-397	1500	6	s)z(s)y	s)z(s)y	PROPN
ejde-397	1500	7	ds	ds	NOUN
ejde-397	1500	8	]	]	PUNCT
ejde-397	1500	9	,	,	PUNCT
ejde-397	1500	10	t	t	PROPN
ejde-397	1500	11	∈	∈	PROPN
ejde-397	1501	1	[	[	X
ejde-397	1501	2	0	0	NUM
ejde-397	1501	3	,	,	PUNCT
ejde-397	1501	4	τ	τ	X
ejde-397	1501	5	)	)	PUNCT
ejde-397	1501	6	and	and	CCONJ
ejde-397	1501	7	,	,	PUNCT
ejde-397	1501	8	since	since	SCONJ
ejde-397	1501	9	∫	∫	PROPN
ejde-397	1501	10	t	t	PROPN
ejde-397	1501	11	0	0	NUM
ejde-397	1501	12	a(t	a(t	NOUN
ejde-397	1501	13	−	−	NOUN
ejde-397	1501	14	s)z(s)y	s)z(s)y	NOUN
ejde-397	1501	15	ds	ds	PROPN
ejde-397	1501	16	∈	∈	PROPN
ejde-397	1501	17	d(a	d(a	PROPN
ejde-397	1501	18	)	)	PUNCT
ejde-397	1501	19	for	for	ADP
ejde-397	1501	20	t	t	PROPN
ejde-397	1501	21	∈	∈	PROPN
ejde-397	1502	1	[	[	X
ejde-397	1502	2	0	0	NUM
ejde-397	1502	3	,	,	PUNCT
ejde-397	1502	4	τ	τ	PROPN
ejde-397	1502	5	)	)	PUNCT
ejde-397	1502	6	,	,	PUNCT
ejde-397	1502	7	cx	cx	PROPN
ejde-397	1502	8	∈	∈	PROPN
ejde-397	1502	9	d(a	d(a	PROPN
ejde-397	1502	10	)	)	PUNCT
ejde-397	1502	11	as	as	ADV
ejde-397	1502	12	well	well	ADV
ejde-397	1502	13	as	as	ADP
ejde-397	1502	14	0	0	NUM
ejde-397	1502	15	∈	∈	PROPN
ejde-397	1503	1	a[θ(t)cx+	a[θ(t)cx+	NUM
ejde-397	1503	2	∫	∫	NOUN
ejde-397	1503	3	t	t	NOUN
ejde-397	1503	4	0	0	NUM
ejde-397	1503	5	a(t−	a(t−	PROPN
ejde-397	1503	6	s)z(s)y	s)z(s)y	PROPN
ejde-397	1503	7	ds−	ds−	PROPN
ejde-397	1503	8	∫	∫	PROPN
ejde-397	1503	9	t	t	NOUN
ejde-397	1503	10	0	0	NUM
ejde-397	1503	11	a(t−	a(t−	PROPN
ejde-397	1503	12	s)z(s)y	s)z(s)y	PROPN
ejde-397	1503	13	ds]−	ds]−	NOUN
ejde-397	1503	14	θ(t)cy	θ(t)cy	PROPN
ejde-397	1503	15	,	,	PUNCT
ejde-397	1503	16	t	t	PROPN
ejde-397	1503	17	∈	∈	PROPN
ejde-397	1504	1	[	[	X
ejde-397	1504	2	0	0	NUM
ejde-397	1504	3	,	,	PUNCT
ejde-397	1504	4	τ	τ	PROPN
ejde-397	1504	5	)	)	PUNCT
ejde-397	1504	6	.	.	PUNCT
ejde-397	1505	1	hence	hence	ADV
ejde-397	1505	2	,	,	PUNCT
ejde-397	1505	3	cy	cy	PROPN
ejde-397	1505	4	∈	∈	PROPN
ejde-397	1505	5	acx	acx	PROPN
ejde-397	1505	6	and	and	CCONJ
ejde-397	1505	7	ai	be	VERB
ejde-397	1505	8	nt	not	PART
ejde-397	1505	9	⊆	⊆	NUM
ejde-397	1505	10	c−1ac	c−1ac	NOUN
ejde-397	1505	11	.	.	PUNCT
ejde-397	1506	1	if	if	SCONJ
ejde-397	1506	2	,	,	PUNCT
ejde-397	1506	3	additionally	additionally	ADV
ejde-397	1506	4	,	,	PUNCT
ejde-397	1506	5	the	the	DET
ejde-397	1506	6	operator	operator	NOUN
ejde-397	1506	7	c	c	NOUN
ejde-397	1506	8	is	be	AUX
ejde-397	1506	9	injective	injective	ADJ
ejde-397	1506	10	and	and	CCONJ
ejde-397	1506	11	z(t)c	z(t)c	NUM
ejde-397	1506	12	=	=	SYM
ejde-397	1506	13	cz(t	cz(t	X
ejde-397	1506	14	)	)	PUNCT
ejde-397	1506	15	,	,	PUNCT
ejde-397	1506	16	t	t	PROPN
ejde-397	1506	17	∈	∈	PROPN
ejde-397	1507	1	[	[	X
ejde-397	1507	2	0	0	NUM
ejde-397	1507	3	,	,	PUNCT
ejde-397	1507	4	τ	τ	PROPN
ejde-397	1507	5	)	)	PUNCT
ejde-397	1507	6	,	,	PUNCT
ejde-397	1507	7	then	then	ADV
ejde-397	1507	8	we	we	PRON
ejde-397	1507	9	can	can	AUX
ejde-397	1507	10	simply	simply	ADV
ejde-397	1507	11	verify	verify	VERB
ejde-397	1507	12	that	that	PRON
ejde-397	1507	13	c−1ac	c−1ac	NOUN
ejde-397	1507	14	is	be	AUX
ejde-397	1507	15	likewise	likewise	ADV
ejde-397	1507	16	a	a	DET
ejde-397	1507	17	closed	closed	ADJ
ejde-397	1507	18	subgenerator	subgenerator	NOUN
ejde-397	1507	19	of	of	ADP
ejde-397	1507	20	(	(	PUNCT
ejde-397	1507	21	w	w	PROPN
ejde-397	1507	22	(	(	PUNCT
ejde-397	1507	23	t))t∈[0,τ	t))t∈[0,τ	PROPN
ejde-397	1507	24	)	)	PUNCT
ejde-397	1507	25	,	,	PUNCT
ejde-397	1507	26	so	so	SCONJ
ejde-397	1507	27	that	that	PRON
ejde-397	1507	28	ai	be	VERB
ejde-397	1507	29	nt	not	PART
ejde-397	1507	30	=	=	SYM
ejde-397	1507	31	c−1ac	c−1ac	ADJ
ejde-397	1507	32	by	by	ADP
ejde-397	1507	33	previously	previously	ADV
ejde-397	1507	34	proved	prove	VERB
ejde-397	1507	35	inclusion	inclusion	NOUN
ejde-397	1507	36	â	â	ADP
ejde-397	1507	37	⊆	⊆	NUM
ejde-397	1507	38	c−1ac	c−1ac	NOUN
ejde-397	1507	39	and	and	CCONJ
ejde-397	1507	40	the	the	DET
ejde-397	1507	41	fact	fact	NOUN
ejde-397	1507	42	that	that	SCONJ
ejde-397	1507	43	ai	be	AUX
ejde-397	1507	44	nt	not	PART
ejde-397	1507	45	extends	extend	VERB
ejde-397	1507	46	any	any	DET
ejde-397	1507	47	subgenerator	subgenerator	NOUN
ejde-397	1507	48	from	from	ADP
ejde-397	1507	49	χ(w	χ(w	PROPN
ejde-397	1507	50	)	)	PUNCT
ejde-397	1507	51	.	.	PUNCT
ejde-397	1508	1	let	let	VERB
ejde-397	1508	2	a	a	PRON
ejde-397	1508	3	and	and	CCONJ
ejde-397	1508	4	b	b	NOUN
ejde-397	1508	5	be	be	AUX
ejde-397	1508	6	two	two	NUM
ejde-397	1508	7	subgenerators	subgenerator	NOUN
ejde-397	1508	8	of	of	ADP
ejde-397	1508	9	(	(	PUNCT
ejde-397	1508	10	z(t))t∈[0,τ	z(t))t∈[0,τ	PROPN
ejde-397	1508	11	)	)	PUNCT
ejde-397	1508	12	,	,	PUNCT
ejde-397	1508	13	let	let	VERB
ejde-397	1508	14	b	b	NOUN
ejde-397	1508	15	be	be	AUX
ejde-397	1508	16	closed	close	VERB
ejde-397	1508	17	,	,	PUNCT
ejde-397	1508	18	and	and	CCONJ
ejde-397	1508	19	let	let	VERB
ejde-397	1508	20	a(t	a(t	NOUN
ejde-397	1508	21	)	)	PUNCT
ejde-397	1508	22	kernel	kernel	NOUN
ejde-397	1508	23	on	on	ADP
ejde-397	1508	24	[	[	X
ejde-397	1508	25	0	0	NUM
ejde-397	1508	26	,	,	PUNCT
ejde-397	1508	27	τ	τ	PROPN
ejde-397	1508	28	)	)	PUNCT
ejde-397	1508	29	.	.	PUNCT
ejde-397	1509	1	suppose	suppose	VERB
ejde-397	1509	2	that	that	SCONJ
ejde-397	1509	3	y	y	PROPN
ejde-397	1509	4	∈	∈	PROPN
ejde-397	1509	5	ax	ax	NOUN
ejde-397	1509	6	.	.	PUNCT
ejde-397	1510	1	then	then	ADV
ejde-397	1510	2	(	(	PUNCT
ejde-397	1510	3	∫	∫	PROPN
ejde-397	1510	4	t	t	PROPN
ejde-397	1510	5	0	0	NUM
ejde-397	1510	6	a(t−s)z(s)y	a(t−s)z(s)y	PROPN
ejde-397	1510	7	ds	ds	PROPN
ejde-397	1510	8	,	,	PUNCT
ejde-397	1510	9	z(t)y−k(t)cy	z(t)y−k(t)cy	NUM
ejde-397	1510	10	)	)	PUNCT
ejde-397	1510	11	=	=	SYM
ejde-397	1510	12	(	(	PUNCT
ejde-397	1510	13	z(t)x−k(t)cx	z(t)x−k(t)cx	NOUN
ejde-397	1510	14	,	,	PUNCT
ejde-397	1510	15	z(t)y−k(t)cy	z(t)y−k(t)cy	NUM
ejde-397	1510	16	)	)	PUNCT
ejde-397	1510	17	∈	∈	PROPN
ejde-397	1510	18	b	b	PROPN
ejde-397	1510	19	,	,	PUNCT
ejde-397	1510	20	t	t	PROPN
ejde-397	1510	21	∈	∈	PROPN
ejde-397	1511	1	[	[	X
ejde-397	1511	2	0	0	NUM
ejde-397	1511	3	,	,	PUNCT
ejde-397	1511	4	τ	τ	PROPN
ejde-397	1511	5	)	)	PUNCT
ejde-397	1511	6	,	,	PUNCT
ejde-397	1511	7	which	which	PRON
ejde-397	1511	8	implies	imply	VERB
ejde-397	1511	9	by	by	ADP
ejde-397	1511	10	theorem	theorem	ADJ
ejde-397	1511	11	2.3	2.3	NUM
ejde-397	1511	12	that	that	PRON
ejde-397	1511	13	(	(	PUNCT
ejde-397	1511	14	(	(	PUNCT
ejde-397	1511	15	a∗z)(t)x−(a∗k)(t)cx	a∗z)(t)x−(a∗k)(t)cx	NOUN
ejde-397	1511	16	,	,	PUNCT
ejde-397	1511	17	(	(	PUNCT
ejde-397	1511	18	a∗z)(t)y−(a∗k)(t)cy	a∗z)(t)y−(a∗k)(t)cy	NOUN
ejde-397	1511	19	)	)	PUNCT
ejde-397	1511	20	∈	∈	PROPN
ejde-397	1511	21	b	b	PROPN
ejde-397	1511	22	,	,	PUNCT
ejde-397	1511	23	t	t	PROPN
ejde-397	1511	24	∈	∈	PROPN
ejde-397	1512	1	[	[	X
ejde-397	1512	2	0	0	NUM
ejde-397	1512	3	,	,	PUNCT
ejde-397	1512	4	τ	τ	PROPN
ejde-397	1512	5	)	)	PUNCT
ejde-397	1512	6	.	.	PUNCT
ejde-397	1513	1	since	since	SCONJ
ejde-397	1513	2	(	(	PUNCT
ejde-397	1513	3	a∗z)(t)x	a∗z)(t)x	PROPN
ejde-397	1513	4	∈	∈	PROPN
ejde-397	1513	5	d(b	d(b	PROPN
ejde-397	1513	6	)	)	PUNCT
ejde-397	1513	7	,	,	PUNCT
ejde-397	1513	8	t	t	PROPN
ejde-397	1513	9	∈	∈	PROPN
ejde-397	1514	1	[	[	X
ejde-397	1514	2	0	0	NUM
ejde-397	1514	3	,	,	PUNCT
ejde-397	1514	4	τ	τ	PROPN
ejde-397	1514	5	)	)	PUNCT
ejde-397	1514	6	,	,	PUNCT
ejde-397	1514	7	the	the	DET
ejde-397	1514	8	above	above	ADJ
ejde-397	1514	9	implies	imply	VERB
ejde-397	1514	10	that	that	SCONJ
ejde-397	1514	11	cx	cx	PROPN
ejde-397	1514	12	∈	∈	PROPN
ejde-397	1514	13	d(b	d(b	PROPN
ejde-397	1514	14	)	)	PUNCT
ejde-397	1514	15	.	.	PUNCT
ejde-397	1515	1	hence	hence	ADV
ejde-397	1515	2	,	,	PUNCT
ejde-397	1515	3	c(d(a	c(d(a	PROPN
ejde-397	1515	4	)	)	PUNCT
ejde-397	1515	5	)	)	PUNCT
ejde-397	1516	1	⊆	⊆	NUM
ejde-397	1516	2	d(b	d(b	NOUN
ejde-397	1516	3	)	)	PUNCT
ejde-397	1516	4	.	.	PUNCT
ejde-397	1517	1	we	we	PRON
ejde-397	1517	2	continue	continue	VERB
ejde-397	1517	3	by	by	ADP
ejde-397	1517	4	observing	observe	VERB
ejde-397	1517	5	that	that	DET
ejde-397	1517	6	proposition	proposition	NOUN
ejde-397	1517	7	5.3	5.3	NUM
ejde-397	1517	8	,	,	PUNCT
ejde-397	1517	9	proposition	proposition	NOUN
ejde-397	1517	10	5.8	5.8	NUM
ejde-397	1517	11	,	,	PUNCT
ejde-397	1517	12	proposition	proposition	NOUN
ejde-397	1517	13	5.13	5.13	NUM
ejde-397	1517	14	,	,	PUNCT
ejde-397	1517	15	the	the	DET
ejde-397	1517	16	equation	equation	NOUN
ejde-397	1517	17	(	(	PUNCT
ejde-397	1517	18	5.3	5.3	NUM
ejde-397	1517	19	)	)	PUNCT
ejde-397	1517	20	and	and	CCONJ
ejde-397	1517	21	assertions	assertion	NOUN
ejde-397	1517	22	clarified	clarify	VERB
ejde-397	1517	23	in	in	ADP
ejde-397	1517	24	the	the	DET
ejde-397	1517	25	paragraph	paragraph	NOUN
ejde-397	1517	26	directly	directly	ADV
ejde-397	1517	27	after	after	ADP
ejde-397	1517	28	theorem	theorem	ADJ
ejde-397	1517	29	5.7	5.7	NUM
ejde-397	1517	30	continue	continue	VERB
ejde-397	1517	31	to	to	PART
ejde-397	1517	32	hold	hold	VERB
ejde-397	1517	33	without	without	ADP
ejde-397	1517	34	any	any	DET
ejde-397	1517	35	terminological	terminological	ADJ
ejde-397	1517	36	changes	change	NOUN
ejde-397	1517	37	.	.	PUNCT
ejde-397	1518	1	if	if	SCONJ
ejde-397	1518	2	(	(	PUNCT
ejde-397	1518	3	r1(t	r1(t	PROPN
ejde-397	1518	4	)	)	PUNCT
ejde-397	1518	5	,	,	PUNCT
ejde-397	1518	6	r2(t))t∈[0,τ	r2(t))t∈[0,τ	PROPN
ejde-397	1518	7	)	)	PUNCT
ejde-397	1518	8	is	be	AUX
ejde-397	1518	9	strongly	strongly	ADV
ejde-397	1518	10	continuous	continuous	ADJ
ejde-397	1518	11	and	and	CCONJ
ejde-397	1518	12	(	(	PUNCT
ejde-397	1518	13	5.3	5.3	NUM
ejde-397	1518	14	)	)	PUNCT
ejde-397	1518	15	holds	hold	VERB
ejde-397	1518	16	,	,	PUNCT
ejde-397	1518	17	then	then	ADV
ejde-397	1518	18	it	it	PRON
ejde-397	1518	19	can	can	AUX
ejde-397	1518	20	be	be	AUX
ejde-397	1518	21	easily	easily	ADV
ejde-397	1518	22	seen	see	VERB
ejde-397	1518	23	that	that	SCONJ
ejde-397	1518	24	the	the	DET
ejde-397	1518	25	integral	integral	ADJ
ejde-397	1518	26	generator	generator	NOUN
ejde-397	1518	27	ai	be	VERB
ejde-397	1518	28	nt	not	PART
ejde-397	1518	29	of	of	ADP
ejde-397	1518	30	(	(	PUNCT
ejde-397	1518	31	r2(t))t∈[0,τ	r2(t))t∈[0,τ	NOUN
ejde-397	1518	32	)	)	PUNCT
ejde-397	1518	33	is	be	AUX
ejde-397	1518	34	a	a	DET
ejde-397	1518	35	subgenerator	subgenerator	NOUN
ejde-397	1518	36	of	of	ADP
ejde-397	1518	37	a	a	DET
ejde-397	1518	38	mild	mild	ADJ
ejde-397	1518	39	(	(	PUNCT
ejde-397	1518	40	a	a	PRON
ejde-397	1518	41	,	,	PUNCT
ejde-397	1518	42	k)-regularized	k)-regularize	VERB
ejde-397	1518	43	(	(	PUNCT
ejde-397	1518	44	c1	c1	NOUN
ejde-397	1518	45	,	,	PUNCT
ejde-397	1518	46	c2)-existence	c2)-existence	VERB
ejde-397	1518	47	and	and	CCONJ
ejde-397	1518	48	uniqueness	uniqueness	VERB
ejde-397	1518	49	family	family	NOUN
ejde-397	1518	50	(	(	PUNCT
ejde-397	1518	51	r1(t	r1(t	PROPN
ejde-397	1518	52	)	)	PUNCT
ejde-397	1518	53	,	,	PUNCT
ejde-397	1518	54	r2(t))t∈[0,τ	r2(t))t∈[0,τ	NOUN
ejde-397	1518	55	)	)	PUNCT
ejde-397	1518	56	.	.	PUNCT
ejde-397	1519	1	this	this	PRON
ejde-397	1519	2	is	be	AUX
ejde-397	1519	3	no	no	ADV
ejde-397	1519	4	longer	long	ADV
ejde-397	1519	5	true	true	ADJ
ejde-397	1519	6	if	if	SCONJ
ejde-397	1519	7	(	(	PUNCT
ejde-397	1519	8	5.3	5.3	NUM
ejde-397	1519	9	)	)	PUNCT
ejde-397	1519	10	holds	hold	VERB
ejde-397	1519	11	only	only	ADV
ejde-397	1519	12	for	for	ADP
ejde-397	1519	13	0	0	NUM
ejde-397	1519	14	≤	≤	NUM
ejde-397	1519	15	t	t	PROPN
ejde-397	1519	16	,	,	PUNCT
ejde-397	1519	17	s	s	AUX
ejde-397	1519	18	,	,	PUNCT
ejde-397	1519	19	t+	t+	PUNCT
ejde-397	1519	20	s	s	VERB
ejde-397	1519	21	<	<	X
ejde-397	1519	22	τ	τ	X
ejde-397	1519	23	;	;	PUNCT
ejde-397	1519	24	see	see	VERB
ejde-397	1519	25	[	[	X
ejde-397	1519	26	50	50	NUM
ejde-397	1519	27	]	]	PUNCT
ejde-397	1519	28	for	for	ADP
ejde-397	1519	29	more	more	ADJ
ejde-397	1519	30	details	detail	NOUN
ejde-397	1519	31	.	.	PUNCT
ejde-397	1520	1	proposition	proposition	NOUN
ejde-397	1520	2	5.30	5.30	NUM
ejde-397	1520	3	.	.	PUNCT
ejde-397	1520	4	suppose	suppose	VERB
ejde-397	1520	5	that	that	SCONJ
ejde-397	1520	6	a	a	PRON
ejde-397	1520	7	is	be	AUX
ejde-397	1520	8	a	a	DET
ejde-397	1520	9	closed	closed	ADJ
ejde-397	1520	10	mlo	mlo	NOUN
ejde-397	1520	11	,	,	PUNCT
ejde-397	1520	12	0	0	PUNCT
ejde-397	1520	13	<	<	X
ejde-397	1520	14	τ	τ	PROPN
ejde-397	1520	15	≤	≤	NOUN
ejde-397	1520	16	∞	∞	PROPN
ejde-397	1520	17	,	,	PUNCT
ejde-397	1520	18	a	a	DET
ejde-397	1520	19	∈	∈	PROPN
ejde-397	1520	20	l1	l1	PROPN
ejde-397	1520	21	loc([0	loc([0	PROPN
ejde-397	1520	22	,	,	PUNCT
ejde-397	1520	23	τ	τ	PROPN
ejde-397	1520	24	)	)	PUNCT
ejde-397	1520	25	)	)	PUNCT
ejde-397	1520	26	,	,	PUNCT
ejde-397	1520	27	a	a	DET
ejde-397	1520	28	∗	∗	NOUN
ejde-397	1520	29	a	a	DET
ejde-397	1520	30	6=	6=	NOUN
ejde-397	1520	31	0	0	NUM
ejde-397	1520	32	in	in	ADP
ejde-397	1520	33	l1	l1	PROPN
ejde-397	1520	34	loc([0	loc([0	PROPN
ejde-397	1520	35	,	,	PUNCT
ejde-397	1520	36	τ	τ	PROPN
ejde-397	1520	37	)	)	PUNCT
ejde-397	1520	38	)	)	PUNCT
ejde-397	1520	39	,	,	PUNCT
ejde-397	1520	40	k	k	PROPN
ejde-397	1520	41	∈	∈	PROPN
ejde-397	1520	42	c([0	c([0	PROPN
ejde-397	1520	43	,	,	PUNCT
ejde-397	1520	44	τ	τ	PROPN
ejde-397	1520	45	)	)	PUNCT
ejde-397	1520	46	)	)	PUNCT
ejde-397	1520	47	and	and	CCONJ
ejde-397	1520	48	k	k	X
ejde-397	1520	49	6=	6=	PROPN
ejde-397	1520	50	0	0	NUM
ejde-397	1520	51	.	.	PUNCT
ejde-397	1521	1	if	if	SCONJ
ejde-397	1521	2	±a	±a	PROPN
ejde-397	1521	3	are	be	AUX
ejde-397	1521	4	subgenerators	subgenerator	NOUN
ejde-397	1521	5	of	of	ADP
ejde-397	1521	6	mild	mild	ADJ
ejde-397	1521	7	(	(	PUNCT
ejde-397	1521	8	a	a	PRON
ejde-397	1521	9	,	,	PUNCT
ejde-397	1521	10	k)-regularized	k)-regularize	VERB
ejde-397	1521	11	c1	c1	NOUN
ejde-397	1521	12	-	-	PUNCT
ejde-397	1521	13	existence	existence	NOUN
ejde-397	1521	14	families	family	NOUN
ejde-397	1521	15	(	(	PUNCT
ejde-397	1521	16	r1,±(t))t∈[0,τ	r1,±(t))t∈[0,τ	NOUN
ejde-397	1521	17	)	)	PUNCT
ejde-397	1521	18	(	(	PUNCT
ejde-397	1521	19	mild	mild	ADJ
ejde-397	1521	20	(	(	PUNCT
ejde-397	1521	21	a	a	PRON
ejde-397	1521	22	,	,	PUNCT
ejde-397	1521	23	k)-regularized	k)-regularize	VERB
ejde-397	1521	24	c2uniqueness	c2uniqueness	NOUN
ejde-397	1521	25	families	family	NOUN
ejde-397	1521	26	(	(	PUNCT
ejde-397	1521	27	r2,±(t))t∈[0,τ	r2,±(t))t∈[0,τ	NOUN
ejde-397	1521	28	)	)	PUNCT
ejde-397	1521	29	;	;	PUNCT
ejde-397	1521	30	(	(	PUNCT
ejde-397	1521	31	a	a	PRON
ejde-397	1521	32	,	,	PUNCT
ejde-397	1521	33	k)-regularized	k)-regularize	VERB
ejde-397	1521	34	c	c	NOUN
ejde-397	1521	35	-	-	PUNCT
ejde-397	1521	36	resolvent	resolvent	ADJ
ejde-397	1521	37	families	family	NOUN
ejde-397	1521	38	(	(	PUNCT
ejde-397	1521	39	r±(t))t∈[0,τ	r±(t))t∈[0,τ	NOUN
ejde-397	1521	40	)	)	PUNCT
ejde-397	1521	41	)	)	PUNCT
ejde-397	1521	42	,	,	PUNCT
ejde-397	1521	43	then	then	ADV
ejde-397	1521	44	a2	a2	PROPN
ejde-397	1521	45	is	be	AUX
ejde-397	1521	46	a	a	DET
ejde-397	1521	47	subgenerator	subgenerator	NOUN
ejde-397	1521	48	of	of	ADP
ejde-397	1521	49	a	a	DET
ejde-397	1521	50	mild	mild	ADJ
ejde-397	1521	51	(	(	PUNCT
ejde-397	1521	52	a∗a	a∗a	NUM
ejde-397	1521	53	,	,	PUNCT
ejde-397	1521	54	k)-regularized	k)-regularize	VERB
ejde-397	1521	55	c1	c1	NOUN
ejde-397	1521	56	-	-	PUNCT
ejde-397	1521	57	existence	existence	NOUN
ejde-397	1521	58	50	50	NUM
ejde-397	1521	59	m.	m.	NOUN
ejde-397	1521	60	kostić	kostić	NOUN
ejde-397	1522	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1522	2	family	family	NOUN
ejde-397	1522	3	(	(	PUNCT
ejde-397	1522	4	r1(t	r1(t	PROPN
ejde-397	1522	5	)	)	PUNCT
ejde-397	1522	6	≡	≡	PROPN
ejde-397	1522	7	(	(	PUNCT
ejde-397	1522	8	1/2)r1(t	1/2)r1(t	NUM
ejde-397	1522	9	)	)	PUNCT
ejde-397	1522	10	+	+	CCONJ
ejde-397	1522	11	(	(	PUNCT
ejde-397	1522	12	1/2)r1,−(t))t∈[0,τ	1/2)r1,−(t))t∈[0,τ	NUM
ejde-397	1522	13	)	)	PUNCT
ejde-397	1522	14	(	(	PUNCT
ejde-397	1522	15	mild	mild	ADJ
ejde-397	1522	16	(	(	PUNCT
ejde-397	1522	17	a	a	DET
ejde-397	1522	18	∗	∗	NOUN
ejde-397	1522	19	a	a	PRON
ejde-397	1522	20	,	,	PUNCT
ejde-397	1522	21	k)-regularized	k)-regularize	VERB
ejde-397	1522	22	c2uniqueness	c2uniqueness	NOUN
ejde-397	1522	23	family	family	NOUN
ejde-397	1522	24	(	(	PUNCT
ejde-397	1522	25	r2(t	r2(t	PROPN
ejde-397	1522	26	)	)	PUNCT
ejde-397	1522	27	≡	≡	PROPN
ejde-397	1522	28	(	(	PUNCT
ejde-397	1522	29	1/2)r2(t	1/2)r2(t	NUM
ejde-397	1522	30	)	)	PUNCT
ejde-397	1522	31	+	+	CCONJ
ejde-397	1522	32	(	(	PUNCT
ejde-397	1522	33	1/2)r2,−(t))t∈[0,τ	1/2)r2,−(t))t∈[0,τ	NUM
ejde-397	1522	34	)	)	PUNCT
ejde-397	1522	35	;	;	PUNCT
ejde-397	1522	36	mild	mild	ADJ
ejde-397	1522	37	(	(	PUNCT
ejde-397	1522	38	a	a	DET
ejde-397	1522	39	∗	∗	NOUN
ejde-397	1522	40	a	a	NOUN
ejde-397	1522	41	,	,	PUNCT
ejde-397	1522	42	k)-regularized	k)-regularize	VERB
ejde-397	1522	43	c	c	NOUN
ejde-397	1522	44	-	-	PUNCT
ejde-397	1522	45	resolvent	resolvent	ADJ
ejde-397	1522	46	family	family	NOUN
ejde-397	1522	47	(	(	PUNCT
ejde-397	1522	48	r(t	r(t	NOUN
ejde-397	1522	49	)	)	PUNCT
ejde-397	1522	50	≡	≡	PROPN
ejde-397	1522	51	(	(	PUNCT
ejde-397	1522	52	1/2)r+(t	1/2)r+(t	NUM
ejde-397	1522	53	)	)	PUNCT
ejde-397	1523	1	+	+	CCONJ
ejde-397	1523	2	(	(	PUNCT
ejde-397	1523	3	1/2)r−(t))t∈[0,τ	1/2)r−(t))t∈[0,τ	NUM
ejde-397	1523	4	)	)	PUNCT
ejde-397	1523	5	)	)	PUNCT
ejde-397	1523	6	.	.	PUNCT
ejde-397	1524	1	proof	proof	NOUN
ejde-397	1524	2	.	.	PUNCT
ejde-397	1525	1	we	we	PRON
ejde-397	1525	2	prove	prove	VERB
ejde-397	1525	3	the	the	DET
ejde-397	1525	4	proposition	proposition	NOUN
ejde-397	1525	5	only	only	ADV
ejde-397	1525	6	for	for	ADP
ejde-397	1525	7	mild	mild	ADJ
ejde-397	1525	8	(	(	PUNCT
ejde-397	1525	9	a	a	PRON
ejde-397	1525	10	,	,	PUNCT
ejde-397	1525	11	k)-regularized	k)-regularize	VERB
ejde-397	1525	12	c1	c1	NOUN
ejde-397	1525	13	-	-	PUNCT
ejde-397	1525	14	existence	existence	NOUN
ejde-397	1525	15	families	family	NOUN
ejde-397	1525	16	.	.	PUNCT
ejde-397	1526	1	let	let	VERB
ejde-397	1526	2	x	x	SYM
ejde-397	1526	3	∈	∈	PROPN
ejde-397	1526	4	e	e	NOUN
ejde-397	1526	5	and	and	CCONJ
ejde-397	1526	6	t	t	PROPN
ejde-397	1526	7	∈	∈	PROPN
ejde-397	1527	1	[	[	X
ejde-397	1527	2	0	0	NUM
ejde-397	1527	3	,	,	PUNCT
ejde-397	1527	4	τ	τ	X
ejde-397	1527	5	)	)	PUNCT
ejde-397	1527	6	be	be	AUX
ejde-397	1527	7	fixed	fix	VERB
ejde-397	1527	8	.	.	PUNCT
ejde-397	1528	1	then	then	ADV
ejde-397	1528	2	1	1	NUM
ejde-397	1528	3	2	2	NUM
ejde-397	1528	4	[	[	X
ejde-397	1528	5	r1,+(t)x−r1,−(t)x	r1,+(t)x−r1,−(t)x	X
ejde-397	1528	6	]	]	X
ejde-397	1528	7	=	=	SYM
ejde-397	1528	8	1	1	NUM
ejde-397	1528	9	2	2	NUM
ejde-397	1528	10	[	[	X
ejde-397	1528	11	r1,+(t)x−	r1,+(t)x−	NOUN
ejde-397	1528	12	k(t)c1x]−	k(t)c1x]−	X
ejde-397	1529	1	[	[	X
ejde-397	1529	2	r1,−(t)x−k(t)c1x	r1,−(t)x−k(t)c1x	X
ejde-397	1529	3	]	]	X
ejde-397	1529	4	∈	∈	PROPN
ejde-397	1529	5	1	1	NUM
ejde-397	1529	6	2a(a∗r1,+(·)x)(t)+	2a(a∗r1,+(·)x)(t)+	NUM
ejde-397	1529	7	1	1	NUM
ejde-397	1529	8	2a(a∗r1,−(·)x)(t	2a(a∗r1,−(·)x)(t	NUM
ejde-397	1529	9	)	)	PUNCT
ejde-397	1529	10	=	=	NOUN
ejde-397	1529	11	a(a∗	a(a∗	X
ejde-397	1529	12	r1(·)x)(t	r1(·)x)(t	PROPN
ejde-397	1529	13	)	)	PUNCT
ejde-397	1529	14	.	.	PUNCT
ejde-397	1530	1	applying	apply	VERB
ejde-397	1530	2	theorem	theorem	NOUN
ejde-397	1530	3	2.3	2.3	NUM
ejde-397	1530	4	,	,	PUNCT
ejde-397	1530	5	we	we	PRON
ejde-397	1530	6	obtain	obtain	VERB
ejde-397	1530	7	that	that	DET
ejde-397	1530	8	1	1	NUM
ejde-397	1530	9	2	2	NUM
ejde-397	1530	10	(	(	PUNCT
ejde-397	1530	11	a	a	DET
ejde-397	1530	12	∗	∗	NOUN
ejde-397	1530	13	[	[	X
ejde-397	1530	14	r1,+(·)x−r1,−(·)x])(t	r1,+(·)x−r1,−(·)x])(t	NOUN
ejde-397	1530	15	)	)	PUNCT
ejde-397	1530	16	∈	∈	PROPN
ejde-397	1530	17	a(a	a(a	PROPN
ejde-397	1530	18	∗	∗	VERB
ejde-397	1530	19	a	a	DET
ejde-397	1530	20	∗	∗	NOUN
ejde-397	1530	21	r1(·)x)(t	r1(·)x)(t	NOUN
ejde-397	1530	22	)	)	PUNCT
ejde-397	1530	23	.	.	PUNCT
ejde-397	1531	1	since	since	SCONJ
ejde-397	1531	2	±a	±a	PROPN
ejde-397	1531	3	are	be	AUX
ejde-397	1531	4	subgenerators	subgenerator	NOUN
ejde-397	1531	5	of	of	ADP
ejde-397	1531	6	mild	mild	ADJ
ejde-397	1531	7	(	(	PUNCT
ejde-397	1531	8	a	a	PRON
ejde-397	1531	9	,	,	PUNCT
ejde-397	1531	10	k)-regularized	k)-regularize	VERB
ejde-397	1531	11	c1existence	c1existence	NOUN
ejde-397	1531	12	families	family	NOUN
ejde-397	1531	13	(	(	PUNCT
ejde-397	1531	14	r1,±(t))t∈[0,τ	r1,±(t))t∈[0,τ	NOUN
ejde-397	1531	15	)	)	PUNCT
ejde-397	1531	16	,	,	PUNCT
ejde-397	1531	17	the	the	DET
ejde-397	1531	18	above	above	ADJ
ejde-397	1531	19	inclusion	inclusion	NOUN
ejde-397	1531	20	implies	imply	VERB
ejde-397	1531	21	(	(	PUNCT
ejde-397	1531	22	a	a	DET
ejde-397	1531	23	∗	∗	NOUN
ejde-397	1531	24	a	a	DET
ejde-397	1531	25	∗	∗	NOUN
ejde-397	1531	26	r1(·)x)(t	r1(·)x)(t	NOUN
ejde-397	1531	27	)	)	PUNCT
ejde-397	1531	28	∈	∈	NOUN
ejde-397	1531	29	d(a2	d(a2	NOUN
ejde-397	1531	30	)	)	PUNCT
ejde-397	1531	31	and	and	CCONJ
ejde-397	1531	32	1	1	NUM
ejde-397	1531	33	2	2	NUM
ejde-397	1531	34	(	(	PUNCT
ejde-397	1531	35	[	[	X
ejde-397	1531	36	r1,+(t)x	r1,+(t)x	X
ejde-397	1531	37	−	−	NOUN
ejde-397	1531	38	k(t)c1x	k(t)c1x	NOUN
ejde-397	1531	39	]	]	PUNCT
ejde-397	1532	1	+	+	CCONJ
ejde-397	1533	1	[	[	X
ejde-397	1533	2	r1,−(t)x	r1,−(t)x	X
ejde-397	1533	3	−	−	PROPN
ejde-397	1533	4	k(t)c1x	k(t)c1x	NOUN
ejde-397	1533	5	]	]	PUNCT
ejde-397	1533	6	)	)	PUNCT
ejde-397	1533	7	=	=	PUNCT
ejde-397	1534	1	r1(t)x	r1(t)x	VERB
ejde-397	1534	2	−	−	NUM
ejde-397	1534	3	k(t)c1x	k(t)c1x	PROPN
ejde-397	1534	4	∈	∈	PROPN
ejde-397	1535	1	a2(a	a2(a	NOUN
ejde-397	1535	2	∗	∗	VERB
ejde-397	1535	3	a	a	DET
ejde-397	1535	4	∗r1(·)x)(t	∗r1(·)x)(t	NOUN
ejde-397	1535	5	)	)	PUNCT
ejde-397	1535	6	,	,	PUNCT
ejde-397	1535	7	as	as	SCONJ
ejde-397	1535	8	required	require	VERB
ejde-397	1535	9	.	.	PUNCT
ejde-397	1536	1	�	�	PROPN
ejde-397	1537	1	the	the	DET
ejde-397	1537	2	following	follow	VERB
ejde-397	1537	3	analogues	analogue	NOUN
ejde-397	1537	4	of	of	ADP
ejde-397	1537	5	theorems	theorem	NOUN
ejde-397	1537	6	5.4[(i),(iii	5.4[(i),(iii	NUM
ejde-397	1537	7	)	)	PUNCT
ejde-397	1537	8	]	]	PUNCT
ejde-397	1537	9	and	and	CCONJ
ejde-397	1537	10	5.5	5.5	NUM
ejde-397	1537	11	hold	hold	NOUN
ejde-397	1537	12	.	.	PUNCT
ejde-397	1538	1	theorem	theorem	VERB
ejde-397	1538	2	5.31	5.31	NUM
ejde-397	1538	3	.	.	PUNCT
ejde-397	1539	1	suppose	suppose	VERB
ejde-397	1539	2	that	that	SCONJ
ejde-397	1539	3	a	a	PRON
ejde-397	1539	4	is	be	AUX
ejde-397	1539	5	a	a	DET
ejde-397	1539	6	closed	closed	ADJ
ejde-397	1539	7	mlo	mlo	NOUN
ejde-397	1539	8	in	in	ADP
ejde-397	1539	9	x	x	PROPN
ejde-397	1539	10	,	,	PUNCT
ejde-397	1539	11	c1	c1	PROPN
ejde-397	1539	12	∈	∈	PROPN
ejde-397	1539	13	l(y	l(y	PROPN
ejde-397	1539	14	,	,	PUNCT
ejde-397	1539	15	x	x	NOUN
ejde-397	1539	16	)	)	PUNCT
ejde-397	1539	17	,	,	PUNCT
ejde-397	1539	18	c2	c2	PROPN
ejde-397	1539	19	∈	∈	PROPN
ejde-397	1539	20	l(x	l(x	PROPN
ejde-397	1539	21	)	)	PUNCT
ejde-397	1539	22	,	,	PUNCT
ejde-397	1539	23	|a(t)|	|a(t)|	NOUN
ejde-397	1539	24	and	and	CCONJ
ejde-397	1539	25	k(t	k(t	PROPN
ejde-397	1539	26	)	)	PUNCT
ejde-397	1539	27	satisfy	satisfy	NOUN
ejde-397	1539	28	(	(	PUNCT
ejde-397	1539	29	p1	p1	PROPN
ejde-397	1539	30	)	)	PUNCT
ejde-397	1539	31	,	,	PUNCT
ejde-397	1539	32	as	as	ADV
ejde-397	1539	33	well	well	ADV
ejde-397	1539	34	as	as	ADP
ejde-397	1539	35	that	that	PRON
ejde-397	1539	36	(	(	PUNCT
ejde-397	1539	37	r1(t	r1(t	PROPN
ejde-397	1539	38	)	)	PUNCT
ejde-397	1539	39	,	,	PUNCT
ejde-397	1539	40	r2(t))t≥0	r2(t))t≥0	PROPN
ejde-397	1539	41	⊆	⊆	NUM
ejde-397	1539	42	l(y	l(y	PROPN
ejde-397	1539	43	,	,	PUNCT
ejde-397	1539	44	x)×	x)×	SYM
ejde-397	1539	45	l(x	l(x	PROPN
ejde-397	1539	46	)	)	PUNCT
ejde-397	1539	47	is	be	AUX
ejde-397	1539	48	strongly	strongly	ADV
ejde-397	1539	49	continuous	continuous	ADJ
ejde-397	1539	50	.	.	PUNCT
ejde-397	1540	1	let	let	VERB
ejde-397	1540	2	ω	ω	NUM
ejde-397	1540	3	≥	≥	NOUN
ejde-397	1540	4	max(0	max(0	NOUN
ejde-397	1540	5	,	,	PUNCT
ejde-397	1540	6	abs(|a|	abs(|a|	ADJ
ejde-397	1540	7	)	)	PUNCT
ejde-397	1540	8	,	,	PUNCT
ejde-397	1540	9	abs(k	abs(k	PROPN
ejde-397	1540	10	)	)	PUNCT
ejde-397	1540	11	)	)	PUNCT
ejde-397	1540	12	be	be	AUX
ejde-397	1540	13	such	such	ADJ
ejde-397	1540	14	that	that	SCONJ
ejde-397	1540	15	the	the	DET
ejde-397	1540	16	operator	operator	NOUN
ejde-397	1540	17	family	family	NOUN
ejde-397	1540	18	{	{	PUNCT
ejde-397	1540	19	e−ωtri(t	e−ωtri(t	PROPN
ejde-397	1540	20	)	)	PUNCT
ejde-397	1540	21	:	:	PUNCT
ejde-397	1540	22	t	t	X
ejde-397	1540	23	≥	≥	NOUN
ejde-397	1540	24	0	0	NUM
ejde-397	1540	25	}	}	PUNCT
ejde-397	1540	26	is	be	AUX
ejde-397	1540	27	equicontinuous	equicontinuous	ADJ
ejde-397	1540	28	for	for	ADP
ejde-397	1540	29	i	i	PROPN
ejde-397	1540	30	=	=	NOUN
ejde-397	1540	31	1	1	NUM
ejde-397	1540	32	,	,	PUNCT
ejde-397	1540	33	2	2	NUM
ejde-397	1540	34	.	.	PUNCT
ejde-397	1541	1	then	then	ADV
ejde-397	1541	2	the	the	DET
ejde-397	1541	3	following	follow	VERB
ejde-397	1541	4	holds	hold	VERB
ejde-397	1541	5	:	:	PUNCT
ejde-397	1541	6	(	(	PUNCT
ejde-397	1541	7	i	i	NOUN
ejde-397	1541	8	)	)	PUNCT
ejde-397	1541	9	(	(	PUNCT
ejde-397	1541	10	r1(t	r1(t	PROPN
ejde-397	1541	11	)	)	PUNCT
ejde-397	1541	12	,	,	PUNCT
ejde-397	1541	13	r2(t))t≥0	r2(t))t≥0	PROPN
ejde-397	1541	14	is	be	AUX
ejde-397	1541	15	a	a	DET
ejde-397	1541	16	mild	mild	ADJ
ejde-397	1541	17	(	(	PUNCT
ejde-397	1541	18	a	a	PRON
ejde-397	1541	19	,	,	PUNCT
ejde-397	1541	20	k)-regularized	k)-regularize	VERB
ejde-397	1541	21	(	(	PUNCT
ejde-397	1541	22	c1	c1	NOUN
ejde-397	1541	23	,	,	PUNCT
ejde-397	1541	24	c2)-existence	c2)-existence	VERB
ejde-397	1541	25	and	and	CCONJ
ejde-397	1541	26	uniqueness	uniqueness	VERB
ejde-397	1541	27	family	family	NOUN
ejde-397	1541	28	with	with	ADP
ejde-397	1541	29	a	a	DET
ejde-397	1541	30	subgenerator	subgenerator	NOUN
ejde-397	1541	31	a	a	DET
ejde-397	1541	32	if	if	NOUN
ejde-397	1542	1	and	and	CCONJ
ejde-397	1542	2	only	only	ADV
ejde-397	1542	3	if	if	SCONJ
ejde-397	1542	4	for	for	ADP
ejde-397	1542	5	every	every	DET
ejde-397	1542	6	λ	λ	PROPN
ejde-397	1542	7	∈	∈	PROPN
ejde-397	1542	8	c	c	NOUN
ejde-397	1542	9	with	with	ADP
ejde-397	1542	10	<	<	X
ejde-397	1542	11	λ	λ	X
ejde-397	1542	12	>	>	X
ejde-397	1542	13	ω	ω	PROPN
ejde-397	1542	14	and	and	CCONJ
ejde-397	1542	15	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1542	16	)	)	PUNCT
ejde-397	1542	17	6=	6=	ADP
ejde-397	1542	18	0	0	NUM
ejde-397	1542	19	,	,	PUNCT
ejde-397	1542	20	we	we	PRON
ejde-397	1542	21	have	have	VERB
ejde-397	1542	22	r(c1	r(c1	NOUN
ejde-397	1542	23	)	)	PUNCT
ejde-397	1542	24	⊆	⊆	NUM
ejde-397	1542	25	r(i	r(i	PROPN
ejde-397	1542	26	−	−	PROPN
ejde-397	1542	27	ã(λ)a),∫	ã(λ)a),∫	NOUN
ejde-397	1542	28	∞	∞	NOUN
ejde-397	1542	29	0	0	PUNCT
ejde-397	1543	1	e−λtr1(t)y	e−λtr1(t)y	ADV
ejde-397	1543	2	dt	dt	PUNCT
ejde-397	1543	3	∈	∈	PROPN
ejde-397	1543	4	k̃(λ	k̃(λ	PROPN
ejde-397	1543	5	)	)	PUNCT
ejde-397	1544	1	(	(	PUNCT
ejde-397	1544	2	i	i	PRON
ejde-397	1544	3	−	−	VERB
ejde-397	1544	4	ã(λ)a	ã(λ)a	ADP
ejde-397	1544	5	)	)	PUNCT
ejde-397	1544	6	−1	−1	NOUN
ejde-397	1544	7	c1y	c1y	NOUN
ejde-397	1544	8	,	,	PUNCT
ejde-397	1544	9	y	y	PROPN
ejde-397	1544	10	∈	∈	PROPN
ejde-397	1544	11	y	y	PROPN
ejde-397	1544	12	,	,	PUNCT
ejde-397	1544	13	(	(	PUNCT
ejde-397	1544	14	5.36	5.36	NUM
ejde-397	1544	15	)	)	PUNCT
ejde-397	1544	16	k̃(λ)c2x	k̃(λ)c2x	NOUN
ejde-397	1545	1	=	=	PUNCT
ejde-397	1545	2	∫	∫	PROPN
ejde-397	1545	3	∞	∞	PROPN
ejde-397	1545	4	0	0	PROPN
ejde-397	1545	5	e−λt	e−λt	NOUN
ejde-397	1545	6	[	[	PUNCT
ejde-397	1545	7	r2(t)x−	r2(t)x−	PROPN
ejde-397	1545	8	(	(	PUNCT
ejde-397	1545	9	a	a	DET
ejde-397	1545	10	∗r2	∗r2	NOUN
ejde-397	1545	11	)	)	PUNCT
ejde-397	1545	12	(	(	PUNCT
ejde-397	1545	13	t)y	t)y	PUNCT
ejde-397	1545	14	]	]	X
ejde-397	1546	1	dt	dt	X
ejde-397	1546	2	,	,	PUNCT
ejde-397	1546	3	whenever	whenever	SCONJ
ejde-397	1546	4	(	(	PUNCT
ejde-397	1546	5	x	x	NOUN
ejde-397	1546	6	,	,	PUNCT
ejde-397	1546	7	y	y	NOUN
ejde-397	1546	8	)	)	PUNCT
ejde-397	1546	9	∈	∈	PROPN
ejde-397	1546	10	a.	a.	NOUN
ejde-397	1546	11	(	(	PUNCT
ejde-397	1546	12	5.37	5.37	NUM
ejde-397	1546	13	)	)	PUNCT
ejde-397	1546	14	(	(	PUNCT
ejde-397	1546	15	ii	ii	NOUN
ejde-397	1546	16	)	)	PUNCT
ejde-397	1546	17	(	(	PUNCT
ejde-397	1546	18	r2(t))t≥0	r2(t))t≥0	NOUN
ejde-397	1546	19	is	be	VERB
ejde-397	1546	20	a	a	DET
ejde-397	1546	21	mild	mild	ADJ
ejde-397	1546	22	(	(	PUNCT
ejde-397	1546	23	a	a	DET
ejde-397	1546	24	,	,	PUNCT
ejde-397	1546	25	k)-regularized	k)-regularize	VERB
ejde-397	1546	26	c2	c2	PROPN
ejde-397	1546	27	-	-	PUNCT
ejde-397	1546	28	uniqueness	uniqueness	PROPN
ejde-397	1546	29	family	family	NOUN
ejde-397	1546	30	with	with	ADP
ejde-397	1546	31	a	a	DET
ejde-397	1546	32	subgenerator	subgenerator	NOUN
ejde-397	1546	33	a	a	DET
ejde-397	1546	34	if	if	NOUN
ejde-397	1546	35	and	and	CCONJ
ejde-397	1546	36	only	only	ADV
ejde-397	1546	37	if	if	SCONJ
ejde-397	1546	38	(	(	PUNCT
ejde-397	1546	39	5.37	5.37	NUM
ejde-397	1546	40	)	)	PUNCT
ejde-397	1546	41	holds	hold	VERB
ejde-397	1546	42	for	for	ADP
ejde-397	1546	43	<	<	X
ejde-397	1546	44	λ	λ	X
ejde-397	1546	45	>	>	X
ejde-397	1546	46	ω	ω	PROPN
ejde-397	1546	47	.	.	PUNCT
ejde-397	1546	48	theorem	theorem	PROPN
ejde-397	1546	49	5.32	5.32	NUM
ejde-397	1546	50	.	.	PUNCT
ejde-397	1546	51	suppose	suppose	VERB
ejde-397	1546	52	that	that	SCONJ
ejde-397	1546	53	a	a	PRON
ejde-397	1546	54	is	be	AUX
ejde-397	1546	55	a	a	DET
ejde-397	1546	56	closed	closed	ADJ
ejde-397	1546	57	mlo	mlo	NOUN
ejde-397	1546	58	in	in	ADP
ejde-397	1546	59	x	x	PROPN
ejde-397	1546	60	,	,	PUNCT
ejde-397	1546	61	c	c	PROPN
ejde-397	1546	62	∈	∈	PROPN
ejde-397	1546	63	l(x	l(x	PROPN
ejde-397	1546	64	)	)	PUNCT
ejde-397	1546	65	,	,	PUNCT
ejde-397	1546	66	ca	can	AUX
ejde-397	1546	67	⊆	⊆	NUM
ejde-397	1546	68	ac	ac	PROPN
ejde-397	1546	69	,	,	PUNCT
ejde-397	1546	70	|a(t)|	|a(t)|	NOUN
ejde-397	1546	71	and	and	CCONJ
ejde-397	1546	72	k(t	k(t	PROPN
ejde-397	1546	73	)	)	PUNCT
ejde-397	1546	74	satisfy	satisfy	NOUN
ejde-397	1546	75	(	(	PUNCT
ejde-397	1546	76	p1	p1	PROPN
ejde-397	1546	77	)	)	PUNCT
ejde-397	1546	78	,	,	PUNCT
ejde-397	1546	79	as	as	ADV
ejde-397	1546	80	well	well	ADV
ejde-397	1546	81	as	as	ADP
ejde-397	1546	82	that	that	PRON
ejde-397	1546	83	(	(	PUNCT
ejde-397	1546	84	r(t))t≥0	r(t))t≥0	NOUN
ejde-397	1546	85	⊆	⊆	NUM
ejde-397	1546	86	l(x	l(x	PROPN
ejde-397	1546	87	)	)	PUNCT
ejde-397	1546	88	is	be	AUX
ejde-397	1546	89	strongly	strongly	ADV
ejde-397	1546	90	continuous	continuous	ADJ
ejde-397	1546	91	and	and	CCONJ
ejde-397	1546	92	commutes	commute	NOUN
ejde-397	1546	93	with	with	ADP
ejde-397	1546	94	c	c	PROPN
ejde-397	1546	95	on	on	ADP
ejde-397	1546	96	x.	x.	NOUN
ejde-397	1546	97	let	let	VERB
ejde-397	1546	98	ω	ω	NUM
ejde-397	1546	99	≥	≥	NOUN
ejde-397	1546	100	max(0	max(0	NOUN
ejde-397	1546	101	,	,	PUNCT
ejde-397	1546	102	abs(|a|	abs(|a|	ADJ
ejde-397	1546	103	)	)	PUNCT
ejde-397	1546	104	,	,	PUNCT
ejde-397	1546	105	abs(k	abs(k	PROPN
ejde-397	1546	106	)	)	PUNCT
ejde-397	1546	107	)	)	PUNCT
ejde-397	1546	108	be	be	AUX
ejde-397	1546	109	such	such	ADJ
ejde-397	1546	110	that	that	SCONJ
ejde-397	1546	111	the	the	DET
ejde-397	1546	112	operator	operator	NOUN
ejde-397	1546	113	family	family	NOUN
ejde-397	1546	114	{	{	PUNCT
ejde-397	1546	115	e−ωtr(t	e−ωtr(t	NUM
ejde-397	1546	116	)	)	PUNCT
ejde-397	1546	117	:	:	PUNCT
ejde-397	1546	118	t	t	X
ejde-397	1546	119	≥	≥	NOUN
ejde-397	1546	120	0	0	NUM
ejde-397	1546	121	}	}	PUNCT
ejde-397	1546	122	is	be	AUX
ejde-397	1546	123	equicontinuous	equicontinuous	ADJ
ejde-397	1546	124	.	.	PUNCT
ejde-397	1547	1	then	then	ADV
ejde-397	1547	2	(	(	PUNCT
ejde-397	1547	3	r(t))t≥0	r(t))t≥0	PROPN
ejde-397	1547	4	is	be	AUX
ejde-397	1547	5	an	an	DET
ejde-397	1547	6	(	(	PUNCT
ejde-397	1547	7	a	a	PRON
ejde-397	1547	8	,	,	PUNCT
ejde-397	1547	9	k)regularized	k)regularize	VERB
ejde-397	1547	10	c	c	X
ejde-397	1547	11	-	-	PUNCT
ejde-397	1547	12	resolvent	resolvent	ADJ
ejde-397	1547	13	family	family	NOUN
ejde-397	1547	14	with	with	ADP
ejde-397	1547	15	a	a	DET
ejde-397	1547	16	subgenerator	subgenerator	NOUN
ejde-397	1547	17	a	a	DET
ejde-397	1547	18	if	if	NOUN
ejde-397	1548	1	and	and	CCONJ
ejde-397	1548	2	only	only	ADV
ejde-397	1548	3	if	if	SCONJ
ejde-397	1548	4	for	for	ADP
ejde-397	1548	5	every	every	DET
ejde-397	1548	6	λ	λ	PROPN
ejde-397	1548	7	∈	∈	PROPN
ejde-397	1548	8	c	c	NOUN
ejde-397	1548	9	with	with	ADP
ejde-397	1548	10	<	<	X
ejde-397	1548	11	λ	λ	X
ejde-397	1548	12	>	>	X
ejde-397	1548	13	ω	ω	PROPN
ejde-397	1548	14	and	and	CCONJ
ejde-397	1548	15	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1548	16	)	)	PUNCT
ejde-397	1548	17	6=	6=	ADP
ejde-397	1548	18	0	0	NUM
ejde-397	1548	19	,	,	PUNCT
ejde-397	1548	20	we	we	PRON
ejde-397	1548	21	have	have	AUX
ejde-397	1548	22	r(c	r(c	VERB
ejde-397	1548	23	)	)	PUNCT
ejde-397	1548	24	⊆	⊆	NUM
ejde-397	1548	25	r(i	r(i	PROPN
ejde-397	1548	26	−	−	PROPN
ejde-397	1548	27	ã(λ)a	ã(λ)a	NUM
ejde-397	1548	28	)	)	PUNCT
ejde-397	1548	29	,	,	PUNCT
ejde-397	1548	30	(	(	PUNCT
ejde-397	1548	31	5.36	5.36	NUM
ejde-397	1548	32	)	)	PUNCT
ejde-397	1548	33	holds	hold	VERB
ejde-397	1548	34	with	with	ADP
ejde-397	1548	35	r1	r1	PROPN
ejde-397	1548	36	(	(	PUNCT
ejde-397	1548	37	·	·	PUNCT
ejde-397	1548	38	)	)	PUNCT
ejde-397	1548	39	,	,	PUNCT
ejde-397	1548	40	c1	c1	PROPN
ejde-397	1548	41	and	and	CCONJ
ejde-397	1548	42	y	y	PROPN
ejde-397	1548	43	,	,	PUNCT
ejde-397	1548	44	y	y	PROPN
ejde-397	1548	45	replaced	replace	VERB
ejde-397	1548	46	with	with	ADP
ejde-397	1548	47	r	r	NOUN
ejde-397	1548	48	(	(	PUNCT
ejde-397	1548	49	·	·	PUNCT
ejde-397	1548	50	)	)	PUNCT
ejde-397	1548	51	,	,	PUNCT
ejde-397	1548	52	c	c	PROPN
ejde-397	1548	53	and	and	CCONJ
ejde-397	1548	54	x	x	X
ejde-397	1548	55	,	,	PUNCT
ejde-397	1548	56	x	x	X
ejde-397	1548	57	therein	therein	ADV
ejde-397	1548	58	,	,	PUNCT
ejde-397	1548	59	as	as	ADV
ejde-397	1548	60	well	well	ADV
ejde-397	1548	61	as	as	ADP
ejde-397	1548	62	(	(	PUNCT
ejde-397	1548	63	5.37	5.37	NUM
ejde-397	1548	64	)	)	PUNCT
ejde-397	1548	65	holds	hold	VERB
ejde-397	1548	66	with	with	ADP
ejde-397	1548	67	r2	r2	PROPN
ejde-397	1548	68	(	(	PUNCT
ejde-397	1548	69	·	·	PUNCT
ejde-397	1548	70	)	)	PUNCT
ejde-397	1548	71	and	and	CCONJ
ejde-397	1548	72	c2	c2	PROPN
ejde-397	1548	73	replaced	replace	VERB
ejde-397	1548	74	with	with	ADP
ejde-397	1548	75	r	r	NOUN
ejde-397	1548	76	(	(	PUNCT
ejde-397	1548	77	·	·	PUNCT
ejde-397	1548	78	)	)	PUNCT
ejde-397	1548	79	and	and	CCONJ
ejde-397	1548	80	c	c	NOUN
ejde-397	1548	81	therein	therein	ADV
ejde-397	1548	82	.	.	PUNCT
ejde-397	1549	1	keeping	keep	VERB
ejde-397	1549	2	in	in	ADP
ejde-397	1549	3	mind	mind	NOUN
ejde-397	1549	4	theorem	theorem	VERB
ejde-397	1549	5	5.32	5.32	NUM
ejde-397	1549	6	and	and	CCONJ
ejde-397	1549	7	[	[	X
ejde-397	1549	8	36	36	NUM
ejde-397	1549	9	,	,	PUNCT
ejde-397	1549	10	theorem	theorem	VERB
ejde-397	1549	11	1.2.2	1.2.2	NUM
ejde-397	1549	12	]	]	PUNCT
ejde-397	1549	13	,	,	PUNCT
ejde-397	1549	14	it	it	PRON
ejde-397	1549	15	is	be	AUX
ejde-397	1549	16	very	very	ADV
ejde-397	1549	17	simple	simple	ADJ
ejde-397	1549	18	to	to	PART
ejde-397	1549	19	prove	prove	VERB
ejde-397	1549	20	the	the	DET
ejde-397	1549	21	following	follow	VERB
ejde-397	1549	22	complex	complex	ADJ
ejde-397	1549	23	characterization	characterization	NOUN
ejde-397	1549	24	theorem	theorem	NOUN
ejde-397	1549	25	(	(	PUNCT
ejde-397	1549	26	cf	cf	NOUN
ejde-397	1549	27	.	.	PUNCT
ejde-397	1550	1	theorem	theorem	VERB
ejde-397	1550	2	5.10	5.10	NUM
ejde-397	1550	3	):	):	PUNCT
ejde-397	1550	4	theorem	theorem	ADJ
ejde-397	1550	5	5.33	5.33	NUM
ejde-397	1550	6	.	.	PUNCT
ejde-397	1551	1	suppose	suppose	VERB
ejde-397	1551	2	that	that	SCONJ
ejde-397	1551	3	a	a	PRON
ejde-397	1551	4	is	be	AUX
ejde-397	1551	5	a	a	DET
ejde-397	1551	6	closed	closed	ADJ
ejde-397	1551	7	mlo	mlo	NOUN
ejde-397	1551	8	in	in	ADP
ejde-397	1551	9	x	x	PROPN
ejde-397	1551	10	,	,	PUNCT
ejde-397	1551	11	c	c	PROPN
ejde-397	1551	12	∈	∈	PROPN
ejde-397	1551	13	l(x	l(x	PROPN
ejde-397	1551	14	)	)	PUNCT
ejde-397	1551	15	,	,	PUNCT
ejde-397	1551	16	ca	can	AUX
ejde-397	1551	17	⊆	⊆	NUM
ejde-397	1551	18	ac	ac	PROPN
ejde-397	1551	19	,	,	PUNCT
ejde-397	1551	20	|a(t)|	|a(t)|	NOUN
ejde-397	1551	21	and	and	CCONJ
ejde-397	1551	22	k(t	k(t	PROPN
ejde-397	1551	23	)	)	PUNCT
ejde-397	1551	24	satisfy	satisfy	NOUN
ejde-397	1551	25	(	(	PUNCT
ejde-397	1551	26	p1	p1	PROPN
ejde-397	1551	27	)	)	PUNCT
ejde-397	1551	28	,	,	PUNCT
ejde-397	1551	29	ω0	ω0	ADV
ejde-397	1551	30	>	>	SYM
ejde-397	1551	31	max(0	max(0	NOUN
ejde-397	1551	32	,	,	PUNCT
ejde-397	1551	33	abs(|a|	abs(|a|	ADJ
ejde-397	1551	34	)	)	PUNCT
ejde-397	1551	35	,	,	PUNCT
ejde-397	1551	36	abs(k	abs(k	PROPN
ejde-397	1551	37	)	)	PUNCT
ejde-397	1551	38	)	)	PUNCT
ejde-397	1552	1	and	and	CCONJ
ejde-397	1552	2	,	,	PUNCT
ejde-397	1552	3	for	for	ADP
ejde-397	1552	4	every	every	DET
ejde-397	1552	5	λ	λ	PROPN
ejde-397	1552	6	∈	∈	PROPN
ejde-397	1552	7	c	c	NOUN
ejde-397	1552	8	with	with	ADP
ejde-397	1552	9	<	<	X
ejde-397	1552	10	λ	λ	X
ejde-397	1552	11	>	>	X
ejde-397	1552	12	ω0	ω0	PROPN
ejde-397	1552	13	and	and	CCONJ
ejde-397	1552	14	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1552	15	)	)	PUNCT
ejde-397	1552	16	6=	6=	ADP
ejde-397	1552	17	0	0	NUM
ejde-397	1552	18	,	,	PUNCT
ejde-397	1552	19	we	we	PRON
ejde-397	1552	20	have	have	AUX
ejde-397	1552	21	r(c	r(c	VERB
ejde-397	1552	22	)	)	PUNCT
ejde-397	1552	23	⊆	⊆	NUM
ejde-397	1552	24	r(i	r(i	PROPN
ejde-397	1552	25	−	−	PROPN
ejde-397	1552	26	ã(λ)a	ã(λ)a	NUM
ejde-397	1552	27	)	)	PUNCT
ejde-397	1552	28	.	.	PUNCT
ejde-397	1553	1	if	if	SCONJ
ejde-397	1553	2	there	there	PRON
ejde-397	1553	3	exists	exist	VERB
ejde-397	1553	4	a	a	DET
ejde-397	1553	5	function	function	NOUN
ejde-397	1553	6	υ	υ	NOUN
ejde-397	1553	7	:	:	PUNCT
ejde-397	1553	8	{	{	PUNCT
ejde-397	1553	9	λ	λ	X
ejde-397	1553	10	∈	∈	NOUN
ejde-397	1553	11	c	c	NOUN
ejde-397	1553	12	:	:	PUNCT
ejde-397	1553	13	<	<	X
ejde-397	1553	14	λ	λ	X
ejde-397	1553	15	>	>	X
ejde-397	1553	16	ω0	ω0	PROPN
ejde-397	1553	17	}	}	PUNCT
ejde-397	1553	18	→	→	SYM
ejde-397	1553	19	l(x	l(x	PROPN
ejde-397	1553	20	)	)	PUNCT
ejde-397	1553	21	which	which	PRON
ejde-397	1553	22	satisfies	satisfy	VERB
ejde-397	1553	23	:	:	PUNCT
ejde-397	1553	24	(	(	PUNCT
ejde-397	1553	25	a	a	X
ejde-397	1553	26	)	)	PUNCT
ejde-397	1553	27	υ(λ)x	υ(λ)x	PROPN
ejde-397	1553	28	∈	∈	NOUN
ejde-397	1553	29	k̃(λ)(i	k̃(λ)(i	PROPN
ejde-397	1553	30	−	−	PUNCT
ejde-397	1553	31	ã(λ)a)−1cx	ã(λ)a)−1cx	PROPN
ejde-397	1553	32	for	for	ADP
ejde-397	1553	33	<	<	X
ejde-397	1553	34	λ	λ	X
ejde-397	1553	35	>	>	X
ejde-397	1553	36	ω0	ω0	PROPN
ejde-397	1553	37	,	,	PUNCT
ejde-397	1553	38	ã(λ)k̃(λ	ã(λ)k̃(λ	PROPN
ejde-397	1553	39	)	)	PUNCT
ejde-397	1553	40	6=	6=	ADP
ejde-397	1553	41	0	0	NUM
ejde-397	1553	42	,	,	PUNCT
ejde-397	1553	43	x	x	SYM
ejde-397	1553	44	∈	∈	NOUN
ejde-397	1553	45	x	x	X
ejde-397	1553	46	,	,	PUNCT
ejde-397	1553	47	(	(	PUNCT
ejde-397	1553	48	b	b	X
ejde-397	1553	49	)	)	PUNCT
ejde-397	1553	50	the	the	DET
ejde-397	1553	51	mapping	mapping	NOUN
ejde-397	1553	52	λ	λ	PROPN
ejde-397	1553	53	7→	7→	NUM
ejde-397	1553	54	υ(λ)x	υ(λ)x	NOUN
ejde-397	1553	55	,	,	PUNCT
ejde-397	1553	56	<	<	X
ejde-397	1553	57	λ	λ	X
ejde-397	1553	58	>	>	X
ejde-397	1553	59	ω0	ω0	PROPN
ejde-397	1553	60	is	be	AUX
ejde-397	1553	61	analytic	analytic	ADJ
ejde-397	1553	62	for	for	SCONJ
ejde-397	1553	63	every	every	DET
ejde-397	1553	64	fixed	fix	VERB
ejde-397	1553	65	x	x	SYM
ejde-397	1553	66	∈	∈	PROPN
ejde-397	1553	67	x	x	X
ejde-397	1553	68	,	,	PUNCT
ejde-397	1553	69	(	(	PUNCT
ejde-397	1553	70	c	c	X
ejde-397	1553	71	)	)	PUNCT
ejde-397	1553	72	there	there	PRON
ejde-397	1553	73	exists	exist	VERB
ejde-397	1553	74	r	r	NOUN
ejde-397	1553	75	≥	≥	NOUN
ejde-397	1553	76	−1	−1	NOUN
ejde-397	1553	77	such	such	ADJ
ejde-397	1553	78	that	that	SCONJ
ejde-397	1553	79	the	the	DET
ejde-397	1553	80	family	family	NOUN
ejde-397	1553	81	{	{	PUNCT
ejde-397	1553	82	λ−rυ(λ	λ−rυ(λ	PROPN
ejde-397	1553	83	)	)	PUNCT
ejde-397	1553	84	:	:	PUNCT
ejde-397	1553	85	<	<	X
ejde-397	1553	86	λ	λ	X
ejde-397	1553	87	>	>	X
ejde-397	1553	88	ω0	ω0	PROPN
ejde-397	1553	89	}	}	PUNCT
ejde-397	1553	90	⊆	⊆	NUM
ejde-397	1553	91	l(x	l(x	PROPN
ejde-397	1553	92	)	)	PUNCT
ejde-397	1553	93	is	be	AUX
ejde-397	1553	94	equicontinuous	equicontinuous	ADJ
ejde-397	1553	95	,	,	PUNCT
ejde-397	1553	96	(	(	PUNCT
ejde-397	1553	97	d	d	NOUN
ejde-397	1553	98	)	)	PUNCT
ejde-397	1553	99	υ(λ)x−	υ(λ)x−	NOUN
ejde-397	1553	100	ã(λ)υ(λ)y	ã(λ)υ(λ)y	NOUN
ejde-397	1553	101	=	=	SYM
ejde-397	1553	102	k̃(λ)cx	k̃(λ)cx	NOUN
ejde-397	1553	103	for	for	ADP
ejde-397	1553	104	<	<	X
ejde-397	1553	105	λ	λ	X
ejde-397	1553	106	>	>	X
ejde-397	1553	107	ω0	ω0	PROPN
ejde-397	1553	108	,	,	PUNCT
ejde-397	1553	109	(	(	PUNCT
ejde-397	1553	110	x	x	NOUN
ejde-397	1553	111	,	,	PUNCT
ejde-397	1553	112	y	y	PROPN
ejde-397	1553	113	)	)	PUNCT
ejde-397	1553	114	∈	∈	PROPN
ejde-397	1553	115	a	a	PRON
ejde-397	1553	116	,	,	PUNCT
ejde-397	1553	117	and	and	CCONJ
ejde-397	1553	118	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1553	119	abstract	abstract	ADJ
ejde-397	1553	120	degenerate	degenerate	ADJ
ejde-397	1553	121	volterra	volterra	NOUN
ejde-397	1553	122	inclusions	inclusion	NOUN
ejde-397	1553	123	51	51	NUM
ejde-397	1553	124	(	(	PUNCT
ejde-397	1553	125	e	e	NOUN
ejde-397	1553	126	)	)	PUNCT
ejde-397	1553	127	υ(λ)cx	υ(λ)cx	PROPN
ejde-397	1553	128	=	=	SYM
ejde-397	1553	129	cυ(λ)x	cυ(λ)x	PROPN
ejde-397	1553	130	for	for	ADP
ejde-397	1553	131	<	<	X
ejde-397	1553	132	λ	λ	X
ejde-397	1553	133	>	>	X
ejde-397	1553	134	ω0	ω0	PROPN
ejde-397	1553	135	,	,	PUNCT
ejde-397	1553	136	x	x	X
ejde-397	1553	137	∈	∈	NOUN
ejde-397	1553	138	x	x	NOUN
ejde-397	1553	139	,	,	PUNCT
ejde-397	1553	140	then	then	ADV
ejde-397	1553	141	,	,	PUNCT
ejde-397	1553	142	for	for	ADP
ejde-397	1553	143	every	every	DET
ejde-397	1553	144	α	α	PROPN
ejde-397	1553	145	>	>	X
ejde-397	1553	146	1	1	NUM
ejde-397	1553	147	,	,	PUNCT
ejde-397	1553	148	a	a	PRON
ejde-397	1553	149	is	be	AUX
ejde-397	1553	150	a	a	DET
ejde-397	1553	151	subgenerator	subgenerator	NOUN
ejde-397	1553	152	of	of	ADP
ejde-397	1553	153	a	a	DET
ejde-397	1553	154	global	global	ADJ
ejde-397	1553	155	(	(	PUNCT
ejde-397	1553	156	a	a	PROPN
ejde-397	1553	157	,	,	PUNCT
ejde-397	1553	158	k	k	PROPN
ejde-397	1553	159	∗	∗	X
ejde-397	1553	160	gα+r)-regularized	gα+r)-regularize	VERB
ejde-397	1553	161	cresolvent	cresolvent	NOUN
ejde-397	1553	162	family	family	NOUN
ejde-397	1553	163	(	(	PUNCT
ejde-397	1553	164	rα(t))t≥0	rα(t))t≥0	PROPN
ejde-397	1553	165	which	which	PRON
ejde-397	1553	166	satisfies	satisfy	VERB
ejde-397	1553	167	that	that	SCONJ
ejde-397	1553	168	the	the	DET
ejde-397	1553	169	family	family	NOUN
ejde-397	1553	170	{	{	PUNCT
ejde-397	1553	171	e−ω0trα(t	e−ω0trα(t	PROPN
ejde-397	1553	172	)	)	PUNCT
ejde-397	1553	173	:	:	PUNCT
ejde-397	1553	174	t	t	X
ejde-397	1553	175	≥	≥	NUM
ejde-397	1553	176	0	0	NUM
ejde-397	1553	177	}	}	PUNCT
ejde-397	1553	178	⊆	⊆	NUM
ejde-397	1553	179	l(x	l(x	PROPN
ejde-397	1553	180	)	)	PUNCT
ejde-397	1553	181	is	be	AUX
ejde-397	1553	182	equicontinuous	equicontinuous	ADJ
ejde-397	1553	183	.	.	PUNCT
ejde-397	1554	1	the	the	DET
ejde-397	1554	2	real	real	ADJ
ejde-397	1554	3	representation	representation	NOUN
ejde-397	1554	4	theorem	theorem	NOUN
ejde-397	1554	5	for	for	ADP
ejde-397	1554	6	generation	generation	NOUN
ejde-397	1554	7	of	of	ADP
ejde-397	1554	8	degenerate	degenerate	ADJ
ejde-397	1554	9	(	(	PUNCT
ejde-397	1554	10	a	a	PRON
ejde-397	1554	11	,	,	PUNCT
ejde-397	1554	12	k)-regularized	k)-regularize	VERB
ejde-397	1554	13	c	c	NOUN
ejde-397	1554	14	-	-	PUNCT
ejde-397	1554	15	resolvent	resolvent	ADJ
ejde-397	1554	16	families	family	NOUN
ejde-397	1554	17	can	can	AUX
ejde-397	1554	18	be	be	AUX
ejde-397	1554	19	also	also	ADV
ejde-397	1554	20	formulated	formulate	VERB
ejde-397	1554	21	but	but	CCONJ
ejde-397	1554	22	the	the	DET
ejde-397	1554	23	assertion	assertion	NOUN
ejde-397	1554	24	of	of	ADP
ejde-397	1554	25	theorem	theorem	NOUN
ejde-397	1554	26	5.12(ii	5.12(ii	PROPN
ejde-397	1554	27	)	)	PUNCT
ejde-397	1554	28	is	be	AUX
ejde-397	1554	29	not	not	PART
ejde-397	1554	30	attainable	attainable	ADJ
ejde-397	1554	31	in	in	ADP
ejde-397	1554	32	the	the	DET
ejde-397	1554	33	case	case	NOUN
ejde-397	1554	34	that	that	SCONJ
ejde-397	1554	35	the	the	DET
ejde-397	1554	36	operator	operator	NOUN
ejde-397	1554	37	c	c	NOUN
ejde-397	1554	38	is	be	AUX
ejde-397	1554	39	not	not	PART
ejde-397	1554	40	injective	injective	ADJ
ejde-397	1554	41	.	.	PUNCT
ejde-397	1555	1	the	the	DET
ejde-397	1555	2	assertion	assertion	NOUN
ejde-397	1555	3	of	of	ADP
ejde-397	1555	4	theorem	theorem	ADJ
ejde-397	1555	5	5.7	5.7	NUM
ejde-397	1555	6	continues	continue	VERB
ejde-397	1555	7	to	to	PART
ejde-397	1555	8	hold	hold	VERB
ejde-397	1555	9	with	with	ADP
ejde-397	1555	10	minimal	minimal	ADJ
ejde-397	1555	11	terminological	terminological	ADJ
ejde-397	1555	12	changes	change	NOUN
ejde-397	1555	13	.	.	PUNCT
ejde-397	1556	1	since	since	SCONJ
ejde-397	1556	2	the	the	DET
ejde-397	1556	3	identity	identity	NOUN
ejde-397	1556	4	(	(	PUNCT
ejde-397	1556	5	5.24	5.24	NUM
ejde-397	1556	6	)	)	PUNCT
ejde-397	1556	7	holds	hold	VERB
ejde-397	1556	8	for	for	ADP
ejde-397	1556	9	degenerate	degenerate	ADJ
ejde-397	1556	10	(	(	PUNCT
ejde-397	1556	11	a	a	PRON
ejde-397	1556	12	,	,	PUNCT
ejde-397	1556	13	k)-regularized	k)-regularize	VERB
ejde-397	1556	14	c	c	NOUN
ejde-397	1556	15	-	-	PUNCT
ejde-397	1556	16	resolvent	resolvent	ADJ
ejde-397	1556	17	families	family	NOUN
ejde-397	1556	18	,	,	PUNCT
ejde-397	1556	19	with	with	ADP
ejde-397	1556	20	c	c	PROPN
ejde-397	1556	21	being	be	AUX
ejde-397	1556	22	not	not	PART
ejde-397	1556	23	injective	injective	ADJ
ejde-397	1556	24	,	,	PUNCT
ejde-397	1556	25	proposition	proposition	NOUN
ejde-397	1556	26	5.15	5.15	NUM
ejde-397	1556	27	can	can	AUX
ejde-397	1556	28	be	be	AUX
ejde-397	1556	29	reformulated	reformulate	VERB
ejde-397	1556	30	without	without	ADP
ejde-397	1556	31	substantial	substantial	ADJ
ejde-397	1556	32	difficulties	difficulty	NOUN
ejde-397	1556	33	,	,	PUNCT
ejde-397	1556	34	as	as	ADV
ejde-397	1556	35	well	well	ADV
ejde-397	1556	36	,	,	PUNCT
ejde-397	1556	37	but	but	CCONJ
ejde-397	1556	38	we	we	PRON
ejde-397	1556	39	can	can	AUX
ejde-397	1556	40	not	not	PART
ejde-397	1556	41	prove	prove	VERB
ejde-397	1556	42	the	the	DET
ejde-397	1556	43	uniqueness	uniqueness	NOUN
ejde-397	1556	44	of	of	ADP
ejde-397	1556	45	solutions	solution	NOUN
ejde-397	1556	46	of	of	ADP
ejde-397	1556	47	corresponding	corresponding	ADJ
ejde-397	1556	48	abstract	abstract	ADJ
ejde-397	1556	49	time	time	NOUN
ejde-397	1556	50	-	-	PUNCT
ejde-397	1556	51	fractional	fractional	ADJ
ejde-397	1556	52	inclusions	inclusion	NOUN
ejde-397	1556	53	.	.	PUNCT
ejde-397	1557	1	as	as	SCONJ
ejde-397	1557	2	already	already	ADV
ejde-397	1557	3	mentioned	mention	VERB
ejde-397	1557	4	,	,	PUNCT
ejde-397	1557	5	the	the	DET
ejde-397	1557	6	adjoint	adjoint	NOUN
ejde-397	1557	7	type	type	NOUN
ejde-397	1557	8	theorems	theorem	NOUN
ejde-397	1558	1	[	[	X
ejde-397	1558	2	36	36	NUM
ejde-397	1558	3	,	,	PUNCT
ejde-397	1558	4	theorem	theorem	VERB
ejde-397	1558	5	2.1.12(i)/(ii	2.1.12(i)/(ii	NUM
ejde-397	1558	6	)	)	PUNCT
ejde-397	1558	7	;	;	PUNCT
ejde-397	1558	8	theorem	theorem	VERB
ejde-397	1558	9	2.1.13	2.1.13	NUM
ejde-397	1558	10	]	]	PUNCT
ejde-397	1558	11	continue	continue	VERB
ejde-397	1558	12	to	to	PART
ejde-397	1558	13	hold	hold	VERB
ejde-397	1558	14	for	for	ADP
ejde-397	1558	15	(	(	PUNCT
ejde-397	1558	16	a	a	PRON
ejde-397	1558	17	,	,	PUNCT
ejde-397	1558	18	k)-regularized	k)-regularize	VERB
ejde-397	1558	19	c	c	X
ejde-397	1558	20	-	-	PUNCT
ejde-397	1558	21	regularized	regularize	VERB
ejde-397	1558	22	families	family	NOUN
ejde-397	1558	23	subgenerated	subgenerate	VERB
ejde-397	1558	24	by	by	ADP
ejde-397	1558	25	closed	close	VERB
ejde-397	1558	26	multivalued	multivalue	VERB
ejde-397	1558	27	linear	linear	ADJ
ejde-397	1558	28	operators	operator	NOUN
ejde-397	1558	29	and	and	CCONJ
ejde-397	1558	30	it	it	PRON
ejde-397	1558	31	is	be	AUX
ejde-397	1558	32	not	not	PART
ejde-397	1558	33	necessary	necessary	ADJ
ejde-397	1558	34	to	to	PART
ejde-397	1558	35	assume	assume	VERB
ejde-397	1558	36	that	that	SCONJ
ejde-397	1558	37	the	the	DET
ejde-397	1558	38	operator	operator	NOUN
ejde-397	1558	39	a	a	PRON
ejde-397	1558	40	is	be	AUX
ejde-397	1558	41	densely	densely	ADV
ejde-397	1558	42	defined	define	VERB
ejde-397	1558	43	in	in	ADP
ejde-397	1558	44	the	the	DET
ejde-397	1558	45	case	case	NOUN
ejde-397	1558	46	of	of	ADP
ejde-397	1558	47	consideration	consideration	NOUN
ejde-397	1558	48	of	of	ADP
ejde-397	1558	49	[	[	X
ejde-397	1558	50	36	36	NUM
ejde-397	1558	51	,	,	PUNCT
ejde-397	1558	52	theorem	theorem	VERB
ejde-397	1558	53	2.1.12(i	2.1.12(i	NUM
ejde-397	1558	54	)	)	PUNCT
ejde-397	1558	55	]	]	PUNCT
ejde-397	1558	56	.	.	PUNCT
ejde-397	1559	1	all	all	DET
ejde-397	1559	2	this	this	PRON
ejde-397	1559	3	remains	remain	VERB
ejde-397	1559	4	true	true	ADJ
ejde-397	1559	5	if	if	SCONJ
ejde-397	1559	6	the	the	DET
ejde-397	1559	7	operator	operator	NOUN
ejde-397	1559	8	c	c	NOUN
ejde-397	1559	9	is	be	AUX
ejde-397	1559	10	not	not	PART
ejde-397	1559	11	injective	injective	ADJ
ejde-397	1559	12	,	,	PUNCT
ejde-397	1559	13	when	when	SCONJ
ejde-397	1559	14	we	we	PRON
ejde-397	1559	15	also	also	ADV
ejde-397	1559	16	do	do	AUX
ejde-397	1559	17	not	not	PART
ejde-397	1559	18	need	need	VERB
ejde-397	1559	19	to	to	PART
ejde-397	1559	20	assume	assume	VERB
ejde-397	1559	21	that	that	SCONJ
ejde-397	1559	22	r(c	r(c	ADJ
ejde-397	1559	23	)	)	PUNCT
ejde-397	1559	24	is	be	AUX
ejde-397	1559	25	dense	dense	ADJ
ejde-397	1559	26	in	in	ADP
ejde-397	1559	27	x.	x.	NOUN
ejde-397	1559	28	if	if	SCONJ
ejde-397	1559	29	c	c	PROPN
ejde-397	1559	30	is	be	AUX
ejde-397	1559	31	not	not	PART
ejde-397	1559	32	injective	injective	ADJ
ejde-397	1559	33	,	,	PUNCT
ejde-397	1559	34	then	then	ADV
ejde-397	1559	35	we	we	PRON
ejde-397	1559	36	introduce	introduce	VERB
ejde-397	1559	37	the	the	DET
ejde-397	1559	38	notion	notion	NOUN
ejde-397	1559	39	of	of	ADP
ejde-397	1559	40	(	(	PUNCT
ejde-397	1559	41	exponential	exponential	ADJ
ejde-397	1559	42	equicontinuous	equicontinuous	ADJ
ejde-397	1559	43	)	)	PUNCT
ejde-397	1559	44	analyticity	analyticity	NOUN
ejde-397	1559	45	of	of	ADP
ejde-397	1559	46	degenerate	degenerate	ADJ
ejde-397	1559	47	(	(	PUNCT
ejde-397	1559	48	a	a	PRON
ejde-397	1559	49	,	,	PUNCT
ejde-397	1559	50	k)-regularized	k)-regularize	VERB
ejde-397	1559	51	c	c	NOUN
ejde-397	1559	52	-	-	PUNCT
ejde-397	1559	53	resolvent	resolvent	ADJ
ejde-397	1559	54	families	family	NOUN
ejde-397	1559	55	in	in	ADP
ejde-397	1559	56	the	the	DET
ejde-397	1559	57	same	same	ADJ
ejde-397	1559	58	way	way	NOUN
ejde-397	1559	59	as	as	ADP
ejde-397	1559	60	in	in	ADP
ejde-397	1559	61	definition	definition	NOUN
ejde-397	1559	62	5.16	5.16	NUM
ejde-397	1559	63	.	.	PUNCT
ejde-397	1560	1	then	then	ADV
ejde-397	1560	2	theorem	theorem	VERB
ejde-397	1560	3	5.18	5.18	NUM
ejde-397	1560	4	does	do	AUX
ejde-397	1560	5	not	not	PART
ejde-397	1560	6	admit	admit	VERB
ejde-397	1560	7	a	a	DET
ejde-397	1560	8	satisfactory	satisfactory	ADJ
ejde-397	1560	9	reformulation	reformulation	NOUN
ejde-397	1560	10	in	in	ADP
ejde-397	1560	11	our	our	PRON
ejde-397	1560	12	new	new	ADJ
ejde-397	1560	13	frame	frame	NOUN
ejde-397	1560	14	.	.	PUNCT
ejde-397	1561	1	on	on	ADP
ejde-397	1561	2	the	the	DET
ejde-397	1561	3	other	other	ADJ
ejde-397	1561	4	hand	hand	NOUN
ejde-397	1561	5	,	,	PUNCT
ejde-397	1561	6	the	the	DET
ejde-397	1561	7	assertion	assertion	NOUN
ejde-397	1561	8	of	of	ADP
ejde-397	1561	9	theorem	theorem	NOUN
ejde-397	1561	10	5.19	5.19	NUM
ejde-397	1561	11	can	can	AUX
ejde-397	1561	12	be	be	AUX
ejde-397	1561	13	rephrased	rephrase	VERB
ejde-397	1561	14	by	by	ADP
ejde-397	1561	15	taking	take	VERB
ejde-397	1561	16	into	into	ADP
ejde-397	1561	17	consideration	consideration	NOUN
ejde-397	1561	18	the	the	DET
ejde-397	1561	19	conditions	condition	NOUN
ejde-397	1561	20	(	(	PUNCT
ejde-397	1561	21	d)-(e	d)-(e	PROPN
ejde-397	1561	22	)	)	PUNCT
ejde-397	1561	23	from	from	ADP
ejde-397	1561	24	theorem	theorem	ADJ
ejde-397	1561	25	5.33	5.33	NUM
ejde-397	1561	26	.	.	PUNCT
ejde-397	1561	27	differential	differential	ADJ
ejde-397	1561	28	properties	property	NOUN
ejde-397	1561	29	of	of	ADP
ejde-397	1561	30	degenerate	degenerate	ADJ
ejde-397	1561	31	(	(	PUNCT
ejde-397	1561	32	a	a	DET
ejde-397	1561	33	,	,	PUNCT
ejde-397	1561	34	k)-regularized	k)-regularize	VERB
ejde-397	1561	35	c	c	NOUN
ejde-397	1561	36	-	-	PUNCT
ejde-397	1561	37	resolvent	resolvent	ADJ
ejde-397	1561	38	families	family	NOUN
ejde-397	1561	39	clarified	clarify	VERB
ejde-397	1561	40	in	in	ADP
ejde-397	1561	41	theorem	theorem	ADJ
ejde-397	1561	42	5.26	5.26	NUM
ejde-397	1561	43	-	-	PUNCT
ejde-397	1561	44	theorem	theorem	ADJ
ejde-397	1561	45	5.27	5.27	NUM
ejde-397	1561	46	continue	continue	VERB
ejde-397	1561	47	to	to	PART
ejde-397	1561	48	hold	hold	VERB
ejde-397	1561	49	after	after	ADP
ejde-397	1561	50	a	a	DET
ejde-397	1561	51	reformulation	reformulation	NOUN
ejde-397	1561	52	of	of	ADP
ejde-397	1561	53	the	the	DET
ejde-397	1561	54	same	same	ADJ
ejde-397	1561	55	type	type	NOUN
ejde-397	1561	56	.	.	PUNCT
ejde-397	1562	1	during	during	ADP
ejde-397	1562	2	the	the	DET
ejde-397	1562	3	peer	peer	NOUN
ejde-397	1562	4	-	-	PUNCT
ejde-397	1562	5	review	review	NOUN
ejde-397	1562	6	process	process	NOUN
ejde-397	1562	7	,	,	PUNCT
ejde-397	1562	8	the	the	DET
ejde-397	1562	9	author	author	NOUN
ejde-397	1562	10	has	have	AUX
ejde-397	1562	11	published	publish	VERB
ejde-397	1562	12	several	several	ADJ
ejde-397	1562	13	research	research	NOUN
ejde-397	1562	14	papers	paper	NOUN
ejde-397	1562	15	about	about	ADP
ejde-397	1562	16	degenerate	degenerate	ADJ
ejde-397	1562	17	(	(	PUNCT
ejde-397	1562	18	a	a	PRON
ejde-397	1562	19	,	,	PUNCT
ejde-397	1562	20	k)-regularized	k)-regularize	VERB
ejde-397	1562	21	c	c	NOUN
ejde-397	1562	22	-	-	PUNCT
ejde-397	1562	23	resolvent	resolvent	ADJ
ejde-397	1562	24	families	family	NOUN
ejde-397	1562	25	and	and	CCONJ
ejde-397	1562	26	their	their	PRON
ejde-397	1562	27	applications	application	NOUN
ejde-397	1562	28	.	.	PUNCT
ejde-397	1563	1	various	various	ADJ
ejde-397	1563	2	subclasses	subclass	NOUN
ejde-397	1563	3	of	of	ADP
ejde-397	1563	4	degenerate	degenerate	ADJ
ejde-397	1563	5	convoluted	convoluted	ADJ
ejde-397	1563	6	c	c	NOUN
ejde-397	1563	7	-	-	PUNCT
ejde-397	1563	8	semigroups	semigroup	NOUN
ejde-397	1563	9	and	and	CCONJ
ejde-397	1563	10	degenerate	degenerate	ADJ
ejde-397	1563	11	convoluted	convoluted	ADJ
ejde-397	1563	12	c	c	NOUN
ejde-397	1563	13	-	-	PUNCT
ejde-397	1563	14	cosine	cosine	NOUN
ejde-397	1563	15	functions	function	NOUN
ejde-397	1563	16	in	in	ADP
ejde-397	1563	17	locally	locally	ADV
ejde-397	1563	18	convex	convex	ADJ
ejde-397	1563	19	spaces	space	NOUN
ejde-397	1563	20	have	have	AUX
ejde-397	1563	21	been	be	AUX
ejde-397	1563	22	investigated	investigate	VERB
ejde-397	1563	23	in	in	ADP
ejde-397	1563	24	[	[	X
ejde-397	1563	25	50	50	NUM
ejde-397	1563	26	]	]	PUNCT
ejde-397	1563	27	.	.	PUNCT
ejde-397	1564	1	perturbation	perturbation	NOUN
ejde-397	1564	2	results	result	NOUN
ejde-397	1564	3	for	for	ADP
ejde-397	1564	4	abstract	abstract	ADJ
ejde-397	1564	5	degenerate	degenerate	ADJ
ejde-397	1564	6	volterra	volterra	PROPN
ejde-397	1564	7	integro	integro	PROPN
ejde-397	1564	8	-	-	PUNCT
ejde-397	1564	9	differential	differential	NOUN
ejde-397	1564	10	equations	equation	NOUN
ejde-397	1564	11	have	have	AUX
ejde-397	1564	12	been	be	AUX
ejde-397	1564	13	examined	examine	VERB
ejde-397	1564	14	in	in	ADP
ejde-397	1564	15	[	[	X
ejde-397	1564	16	51	51	NUM
ejde-397	1564	17	]	]	PUNCT
ejde-397	1564	18	,	,	PUNCT
ejde-397	1564	19	while	while	SCONJ
ejde-397	1564	20	the	the	DET
ejde-397	1564	21	approximation	approximation	NOUN
ejde-397	1564	22	and	and	CCONJ
ejde-397	1564	23	convergence	convergence	NOUN
ejde-397	1564	24	of	of	ADP
ejde-397	1564	25	degenerate	degenerate	ADJ
ejde-397	1564	26	(	(	PUNCT
ejde-397	1564	27	a	a	PRON
ejde-397	1564	28	,	,	PUNCT
ejde-397	1564	29	k)-regularized	k)-regularize	VERB
ejde-397	1564	30	c	c	NOUN
ejde-397	1564	31	-	-	PUNCT
ejde-397	1564	32	resolvent	resolvent	ADJ
ejde-397	1564	33	families	family	NOUN
ejde-397	1564	34	have	have	AUX
ejde-397	1564	35	been	be	AUX
ejde-397	1564	36	examined	examine	VERB
ejde-397	1564	37	in	in	ADP
ejde-397	1564	38	[	[	X
ejde-397	1564	39	52	52	NUM
ejde-397	1564	40	]	]	PUNCT
ejde-397	1564	41	.	.	PUNCT
ejde-397	1565	1	6	6	NUM
ejde-397	1565	2	.	.	X
ejde-397	1565	3	conclusions	conclusion	NOUN
ejde-397	1565	4	and	and	CCONJ
ejde-397	1565	5	final	final	ADJ
ejde-397	1565	6	remarks	remark	NOUN
ejde-397	1565	7	in	in	ADP
ejde-397	1565	8	this	this	DET
ejde-397	1565	9	research	research	NOUN
ejde-397	1565	10	article	article	NOUN
ejde-397	1565	11	,	,	PUNCT
ejde-397	1565	12	we	we	PRON
ejde-397	1565	13	have	have	AUX
ejde-397	1565	14	analyzed	analyze	VERB
ejde-397	1565	15	the	the	DET
ejde-397	1565	16	abstract	abstract	ADJ
ejde-397	1565	17	degenerate	degenerate	ADJ
ejde-397	1565	18	volterra	volterra	PROPN
ejde-397	1565	19	integrodifferential	integrodifferential	ADJ
ejde-397	1565	20	equations	equation	NOUN
ejde-397	1565	21	in	in	ADP
ejde-397	1565	22	sequentially	sequentially	ADV
ejde-397	1565	23	complete	complete	ADJ
ejde-397	1565	24	locally	locally	ADV
ejde-397	1565	25	convex	convex	ADJ
ejde-397	1565	26	spaces	space	NOUN
ejde-397	1565	27	.	.	PUNCT
ejde-397	1566	1	we	we	PRON
ejde-397	1566	2	have	have	AUX
ejde-397	1566	3	systematically	systematically	ADV
ejde-397	1566	4	investigated	investigate	VERB
ejde-397	1566	5	the	the	DET
ejde-397	1566	6	class	class	NOUN
ejde-397	1566	7	of	of	ADP
ejde-397	1566	8	degenerate	degenerate	ADJ
ejde-397	1566	9	(	(	PUNCT
ejde-397	1566	10	a	a	PRON
ejde-397	1566	11	,	,	PUNCT
ejde-397	1566	12	k)-regularized	k)-regularize	VERB
ejde-397	1566	13	c	c	NOUN
ejde-397	1566	14	-	-	PUNCT
ejde-397	1566	15	resolvent	resolvent	ADJ
ejde-397	1566	16	families	family	NOUN
ejde-397	1566	17	subgenerated	subgenerate	VERB
ejde-397	1566	18	by	by	ADP
ejde-397	1566	19	multivalued	multivalued	ADJ
ejde-397	1566	20	linear	linear	PROPN
ejde-397	1566	21	operators	operator	NOUN
ejde-397	1566	22	and	and	CCONJ
ejde-397	1566	23	examined	examine	VERB
ejde-397	1566	24	many	many	ADJ
ejde-397	1566	25	interesting	interesting	ADJ
ejde-397	1566	26	topics	topic	NOUN
ejde-397	1566	27	including	include	VERB
ejde-397	1566	28	the	the	DET
ejde-397	1566	29	generation	generation	NOUN
ejde-397	1566	30	of	of	ADP
ejde-397	1566	31	(	(	PUNCT
ejde-397	1566	32	a	a	PRON
ejde-397	1566	33	,	,	PUNCT
ejde-397	1566	34	k)-regularized	k)-regularize	VERB
ejde-397	1566	35	c	c	NOUN
ejde-397	1566	36	-	-	PUNCT
ejde-397	1566	37	resolvent	resolvent	ADJ
ejde-397	1566	38	families	family	NOUN
ejde-397	1566	39	,	,	PUNCT
ejde-397	1566	40	smoothing	smooth	VERB
ejde-397	1566	41	properties	property	NOUN
ejde-397	1566	42	of	of	ADP
ejde-397	1566	43	(	(	PUNCT
ejde-397	1566	44	a	a	PRON
ejde-397	1566	45	,	,	PUNCT
ejde-397	1566	46	k)-regularized	k)-regularize	VERB
ejde-397	1566	47	c	c	NOUN
ejde-397	1566	48	-	-	PUNCT
ejde-397	1566	49	resolvent	resolvent	ADJ
ejde-397	1566	50	families	family	NOUN
ejde-397	1566	51	and	and	CCONJ
ejde-397	1566	52	subordination	subordination	NOUN
ejde-397	1566	53	principles	principle	NOUN
ejde-397	1566	54	.	.	PUNCT
ejde-397	1567	1	we	we	PRON
ejde-397	1567	2	have	have	AUX
ejde-397	1567	3	also	also	ADV
ejde-397	1567	4	examined	examine	VERB
ejde-397	1567	5	the	the	DET
ejde-397	1567	6	class	class	NOUN
ejde-397	1567	7	of	of	ADP
ejde-397	1567	8	mild	mild	ADJ
ejde-397	1567	9	(	(	PUNCT
ejde-397	1567	10	a	a	PRON
ejde-397	1567	11	,	,	PUNCT
ejde-397	1567	12	k)-regularized	k)-regularize	VERB
ejde-397	1567	13	c1	c1	NOUN
ejde-397	1567	14	-	-	PUNCT
ejde-397	1567	15	existence	existence	NOUN
ejde-397	1567	16	families	family	NOUN
ejde-397	1567	17	,	,	PUNCT
ejde-397	1567	18	the	the	DET
ejde-397	1567	19	class	class	NOUN
ejde-397	1567	20	of	of	ADP
ejde-397	1567	21	mild	mild	ADJ
ejde-397	1567	22	(	(	PUNCT
ejde-397	1567	23	a	a	DET
ejde-397	1567	24	,	,	PUNCT
ejde-397	1567	25	k)-regularized	k)-regularize	VERB
ejde-397	1567	26	c2	c2	PROPN
ejde-397	1567	27	-	-	PUNCT
ejde-397	1567	28	uniqueness	uniqueness	NOUN
ejde-397	1567	29	families	family	NOUN
ejde-397	1567	30	and	and	CCONJ
ejde-397	1567	31	provided	provide	VERB
ejde-397	1567	32	a	a	DET
ejde-397	1567	33	new	new	ADJ
ejde-397	1567	34	theoretical	theoretical	ADJ
ejde-397	1567	35	concept	concept	NOUN
ejde-397	1567	36	of	of	ADP
ejde-397	1567	37	vector	vector	NOUN
ejde-397	1567	38	-	-	PUNCT
ejde-397	1567	39	valued	value	VERB
ejde-397	1567	40	laplace	laplace	NOUN
ejde-397	1567	41	transform	transform	NOUN
ejde-397	1567	42	.	.	PUNCT
ejde-397	1568	1	in	in	ADP
ejde-397	1568	2	addition	addition	NOUN
ejde-397	1568	3	to	to	ADP
ejde-397	1568	4	the	the	DET
ejde-397	1568	5	above	above	NOUN
ejde-397	1568	6	,	,	PUNCT
ejde-397	1568	7	we	we	PRON
ejde-397	1568	8	have	have	AUX
ejde-397	1568	9	presented	present	VERB
ejde-397	1568	10	many	many	ADJ
ejde-397	1568	11	useful	useful	ADJ
ejde-397	1568	12	comments	comment	NOUN
ejde-397	1568	13	,	,	PUNCT
ejde-397	1568	14	open	open	ADJ
ejde-397	1568	15	problems	problem	NOUN
ejde-397	1568	16	,	,	PUNCT
ejde-397	1568	17	examples	example	NOUN
ejde-397	1568	18	and	and	CCONJ
ejde-397	1568	19	illustrative	illustrative	ADJ
ejde-397	1568	20	applications	application	NOUN
ejde-397	1568	21	of	of	ADP
ejde-397	1568	22	our	our	PRON
ejde-397	1568	23	theoretical	theoretical	ADJ
ejde-397	1568	24	results	result	NOUN
ejde-397	1568	25	.	.	PUNCT
ejde-397	1569	1	the	the	DET
ejde-397	1569	2	material	material	NOUN
ejde-397	1569	3	of	of	ADP
ejde-397	1569	4	this	this	DET
ejde-397	1569	5	paper	paper	NOUN
ejde-397	1569	6	has	have	AUX
ejde-397	1569	7	recently	recently	ADV
ejde-397	1569	8	been	be	AUX
ejde-397	1569	9	published	publish	VERB
ejde-397	1569	10	as	as	ADP
ejde-397	1569	11	a	a	DET
ejde-397	1569	12	part	part	NOUN
ejde-397	1569	13	of	of	ADP
ejde-397	1569	14	the	the	DET
ejde-397	1569	15	research	research	NOUN
ejde-397	1569	16	monograph	monograph	NOUN
ejde-397	1570	1	[	[	X
ejde-397	1570	2	38	38	NUM
ejde-397	1570	3	]	]	PUNCT
ejde-397	1570	4	;	;	PUNCT
ejde-397	1570	5	the	the	DET
ejde-397	1570	6	almost	almost	ADV
ejde-397	1570	7	periodic	periodic	ADJ
ejde-397	1570	8	type	type	NOUN
ejde-397	1570	9	solutions	solution	NOUN
ejde-397	1570	10	of	of	ADP
ejde-397	1570	11	the	the	DET
ejde-397	1570	12	abstract	abstract	ADJ
ejde-397	1570	13	degenerate	degenerate	ADJ
ejde-397	1570	14	52	52	NUM
ejde-397	1570	15	m.	m.	NOUN
ejde-397	1570	16	kostić	kostić	NOUN
ejde-397	1570	17	ejde-2023/63	ejde-2023/63	PROPN
ejde-397	1570	18	volterra	volterra	PROPN
ejde-397	1570	19	integro	integro	PROPN
ejde-397	1570	20	-	-	PUNCT
ejde-397	1570	21	differential	differential	NOUN
ejde-397	1570	22	equations	equation	NOUN
ejde-397	1570	23	have	have	AUX
ejde-397	1570	24	recently	recently	ADV
ejde-397	1570	25	been	be	AUX
ejde-397	1570	26	analyzed	analyze	VERB
ejde-397	1570	27	in	in	ADP
ejde-397	1570	28	the	the	DET
ejde-397	1570	29	research	research	NOUN
ejde-397	1570	30	monograph	monograph	NOUN
ejde-397	1571	1	[	[	X
ejde-397	1571	2	37	37	NUM
ejde-397	1571	3	]	]	PUNCT
ejde-397	1571	4	.	.	PUNCT
ejde-397	1572	1	we	we	PRON
ejde-397	1572	2	close	close	VERB
ejde-397	1572	3	the	the	DET
ejde-397	1572	4	paper	paper	NOUN
ejde-397	1572	5	with	with	ADP
ejde-397	1572	6	the	the	DET
ejde-397	1572	7	observation	observation	NOUN
ejde-397	1572	8	that	that	SCONJ
ejde-397	1572	9	we	we	PRON
ejde-397	1572	10	have	have	AUX
ejde-397	1572	11	obeyed	obey	VERB
ejde-397	1572	12	the	the	DET
ejde-397	1572	13	multivalued	multivalue	VERB
ejde-397	1572	14	linear	linear	PROPN
ejde-397	1572	15	operators	operator	NOUN
ejde-397	1572	16	approach	approach	VERB
ejde-397	1572	17	here	here	ADV
ejde-397	1572	18	;	;	PUNCT
ejde-397	1572	19	this	this	DET
ejde-397	1572	20	approach	approach	NOUN
ejde-397	1572	21	,	,	PUNCT
ejde-397	1572	22	although	although	SCONJ
ejde-397	1572	23	very	very	ADV
ejde-397	1572	24	dominant	dominant	ADJ
ejde-397	1572	25	when	when	SCONJ
ejde-397	1572	26	compared	compare	VERB
ejde-397	1572	27	with	with	ADP
ejde-397	1572	28	the	the	DET
ejde-397	1572	29	other	other	ADJ
ejde-397	1572	30	existing	exist	VERB
ejde-397	1572	31	methods	method	NOUN
ejde-397	1572	32	and	and	CCONJ
ejde-397	1572	33	theoretical	theoretical	ADJ
ejde-397	1572	34	strategies	strategy	NOUN
ejde-397	1572	35	in	in	ADP
ejde-397	1572	36	this	this	DET
ejde-397	1572	37	theory	theory	NOUN
ejde-397	1572	38	,	,	PUNCT
ejde-397	1572	39	is	be	AUX
ejde-397	1572	40	not	not	PART
ejde-397	1572	41	sufficiently	sufficiently	ADV
ejde-397	1572	42	adequate	adequate	ADJ
ejde-397	1572	43	to	to	PART
ejde-397	1572	44	cover	cover	VERB
ejde-397	1572	45	all	all	DET
ejde-397	1572	46	related	related	ADJ
ejde-397	1572	47	problems	problem	NOUN
ejde-397	1572	48	regarding	regard	VERB
ejde-397	1572	49	the	the	DET
ejde-397	1572	50	abstract	abstract	ADJ
ejde-397	1572	51	degenerate	degenerate	ADJ
ejde-397	1572	52	volterra	volterra	PROPN
ejde-397	1572	53	integro	integro	PROPN
ejde-397	1572	54	-	-	PUNCT
ejde-397	1572	55	differential	differential	NOUN
ejde-397	1572	56	equations	equation	NOUN
ejde-397	1572	57	.	.	PUNCT
ejde-397	1573	1	for	for	ADP
ejde-397	1573	2	some	some	DET
ejde-397	1573	3	other	other	ADJ
ejde-397	1573	4	concepts	concept	NOUN
ejde-397	1573	5	of	of	ADP
ejde-397	1573	6	solution	solution	NOUN
ejde-397	1573	7	operator	operator	NOUN
ejde-397	1573	8	families	family	NOUN
ejde-397	1573	9	,	,	PUNCT
ejde-397	1573	10	we	we	PRON
ejde-397	1573	11	may	may	AUX
ejde-397	1573	12	refer	refer	VERB
ejde-397	1573	13	to	to	ADP
ejde-397	1573	14	[	[	X
ejde-397	1573	15	42	42	NUM
ejde-397	1573	16	,	,	PUNCT
ejde-397	1573	17	43	43	NUM
ejde-397	1573	18	,	,	PUNCT
ejde-397	1573	19	45	45	NUM
ejde-397	1573	20	,	,	PUNCT
ejde-397	1573	21	46	46	NUM
ejde-397	1573	22	]	]	PUNCT
ejde-397	1573	23	.	.	PUNCT
ejde-397	1574	1	finally	finally	ADV
ejde-397	1574	2	,	,	PUNCT
ejde-397	1574	3	we	we	PRON
ejde-397	1574	4	would	would	AUX
ejde-397	1574	5	like	like	VERB
ejde-397	1574	6	to	to	PART
ejde-397	1574	7	emphasize	emphasize	VERB
ejde-397	1574	8	that	that	SCONJ
ejde-397	1574	9	almost	almost	ADV
ejde-397	1574	10	anything	anything	PRON
ejde-397	1574	11	relevant	relevant	ADJ
ejde-397	1574	12	has	have	AUX
ejde-397	1574	13	been	be	AUX
ejde-397	1574	14	said	say	VERB
ejde-397	1574	15	about	about	ADP
ejde-397	1574	16	the	the	DET
ejde-397	1574	17	existence	existence	NOUN
ejde-397	1574	18	and	and	CCONJ
ejde-397	1574	19	uniqueness	uniqueness	NOUN
ejde-397	1574	20	of	of	ADP
ejde-397	1574	21	the	the	DET
ejde-397	1574	22	positive	positive	ADJ
ejde-397	1574	23	solutions	solution	NOUN
ejde-397	1574	24	to	to	ADP
ejde-397	1574	25	the	the	DET
ejde-397	1574	26	abstract	abstract	ADJ
ejde-397	1574	27	degenerate	degenerate	ADJ
ejde-397	1574	28	volterra	volterra	PROPN
ejde-397	1574	29	integro	integro	PROPN
ejde-397	1574	30	-	-	PUNCT
ejde-397	1574	31	differential	differential	NOUN
ejde-397	1574	32	equations	equation	NOUN
ejde-397	1574	33	in	in	ADP
ejde-397	1574	34	ordered	order	VERB
ejde-397	1574	35	banach	banach	NOUN
ejde-397	1574	36	spaces	space	VERB
ejde-397	1574	37	.	.	PUNCT
ejde-397	1575	1	acknowledgments	acknowledgment	NOUN
ejde-397	1575	2	.	.	PUNCT
ejde-397	1576	1	this	this	DET
ejde-397	1576	2	research	research	NOUN
ejde-397	1576	3	was	be	AUX
ejde-397	1576	4	partially	partially	ADV
ejde-397	1576	5	supported	support	VERB
ejde-397	1576	6	by	by	ADP
ejde-397	1576	7	grant	grant	NOUN
ejde-397	1576	8	no	no	NOUN
ejde-397	1576	9	.	.	PUNCT
ejde-397	1576	10	451	451	NUM
ejde-397	1576	11	-	-	SYM
ejde-397	1576	12	0368/2020/14/200156	0368/2020/14/200156	NUM
ejde-397	1576	13	,	,	PUNCT
ejde-397	1576	14	ministry	ministry	PROPN
ejde-397	1576	15	of	of	ADP
ejde-397	1576	16	science	science	NOUN
ejde-397	1576	17	and	and	CCONJ
ejde-397	1576	18	technological	technological	ADJ
ejde-397	1576	19	development	development	NOUN
ejde-397	1576	20	,	,	PUNCT
ejde-397	1576	21	republic	republic	NOUN
ejde-397	1576	22	of	of	ADP
ejde-397	1576	23	serbia	serbia	PROPN
ejde-397	1576	24	.	.	PUNCT
ejde-397	1577	1	references	reference	NOUN
ejde-397	1577	2	[	[	X
ejde-397	1577	3	1	1	NUM
ejde-397	1577	4	]	]	PUNCT
ejde-397	1577	5	w.	w.	PROPN
ejde-397	1577	6	arendt	arendt	PROPN
ejde-397	1577	7	,	,	PUNCT
ejde-397	1577	8	c.	c.	PROPN
ejde-397	1577	9	j.	j.	PROPN
ejde-397	1577	10	k.	k.	PROPN
ejde-397	1577	11	batty	batty	PROPN
ejde-397	1577	12	,	,	PUNCT
ejde-397	1577	13	m.	m.	NOUN
ejde-397	1577	14	hieber	hieber	PROPN
ejde-397	1577	15	,	,	PUNCT
ejde-397	1577	16	f.	f.	PROPN
ejde-397	1577	17	neubrander	neubrander	PROPN
ejde-397	1577	18	;	;	PUNCT
ejde-397	1577	19	vector	vector	NOUN
ejde-397	1577	20	-	-	PUNCT
ejde-397	1577	21	valued	value	VERB
ejde-397	1577	22	laplace	laplace	NOUN
ejde-397	1577	23	transforms	transform	VERB
ejde-397	1577	24	and	and	CCONJ
ejde-397	1577	25	cauchy	cauchy	NOUN
ejde-397	1577	26	problems	problem	NOUN
ejde-397	1577	27	,	,	PUNCT
ejde-397	1577	28	monographs	monograph	NOUN
ejde-397	1577	29	in	in	ADP
ejde-397	1577	30	mathematics	mathematic	NOUN
ejde-397	1577	31	,	,	PUNCT
ejde-397	1577	32	vol	vol	NOUN
ejde-397	1577	33	.	.	PROPN
ejde-397	1577	34	96	96	NUM
ejde-397	1577	35	,	,	PUNCT
ejde-397	1577	36	birkhäuser	birkhäuser	NOUN
ejde-397	1577	37	,	,	PUNCT
ejde-397	1577	38	basel	basel	PROPN
ejde-397	1577	39	,	,	PUNCT
ejde-397	1577	40	2001	2001	NUM
ejde-397	1577	41	.	.	PUNCT
ejde-397	1578	1	[	[	X
ejde-397	1578	2	2	2	NUM
ejde-397	1578	3	]	]	PUNCT
ejde-397	1578	4	w.	w.	PROPN
ejde-397	1578	5	arendt	arendt	PROPN
ejde-397	1578	6	,	,	PUNCT
ejde-397	1578	7	o.	o.	PROPN
ejde-397	1578	8	el	el	PROPN
ejde-397	1578	9	–	–	PUNCT
ejde-397	1578	10	mennaoui	mennaoui	NOUN
ejde-397	1578	11	,	,	PUNCT
ejde-397	1578	12	v.	v.	ADP
ejde-397	1578	13	keyantuo	keyantuo	PROPN
ejde-397	1578	14	;	;	PUNCT
ejde-397	1578	15	local	local	ADJ
ejde-397	1578	16	integrated	integrate	VERB
ejde-397	1578	17	semigroups	semigroup	NOUN
ejde-397	1578	18	:	:	PUNCT
ejde-397	1578	19	evolution	evolution	NOUN
ejde-397	1578	20	with	with	ADP
ejde-397	1578	21	jumps	jump	NOUN
ejde-397	1578	22	of	of	ADP
ejde-397	1578	23	regularity	regularity	NOUN
ejde-397	1578	24	,	,	PUNCT
ejde-397	1578	25	j.	j.	PROPN
ejde-397	1578	26	math	math	PROPN
ejde-397	1578	27	.	.	PUNCT
ejde-397	1579	1	anal	anal	PROPN
ejde-397	1579	2	.	.	PUNCT
ejde-397	1580	1	appl	appl	PROPN
ejde-397	1580	2	.	.	PROPN
ejde-397	1580	3	,	,	PUNCT
ejde-397	1580	4	186(2	186(2	NUM
ejde-397	1580	5	)	)	PUNCT
ejde-397	1580	6	(	(	PUNCT
ejde-397	1580	7	1994	1994	NUM
ejde-397	1580	8	)	)	PUNCT
ejde-397	1580	9	,	,	PUNCT
ejde-397	1580	10	572	572	NUM
ejde-397	1580	11	-	-	SYM
ejde-397	1580	12	595	595	NUM
ejde-397	1580	13	.	.	PUNCT
ejde-397	1581	1	[	[	X
ejde-397	1581	2	3	3	X
ejde-397	1581	3	]	]	X
ejde-397	1581	4	j.	j.	PROPN
ejde-397	1581	5	m.	m.	PROPN
ejde-397	1581	6	ball	ball	PROPN
ejde-397	1581	7	;	;	PUNCT
ejde-397	1581	8	strongly	strongly	ADV
ejde-397	1581	9	continuous	continuous	ADJ
ejde-397	1581	10	semigroups	semigroup	NOUN
ejde-397	1581	11	,	,	PUNCT
ejde-397	1581	12	weak	weak	ADJ
ejde-397	1581	13	solutions	solution	NOUN
ejde-397	1581	14	,	,	PUNCT
ejde-397	1581	15	and	and	CCONJ
ejde-397	1581	16	the	the	DET
ejde-397	1581	17	variation	variation	NOUN
ejde-397	1581	18	of	of	ADP
ejde-397	1581	19	constants	constant	NOUN
ejde-397	1581	20	formula	formula	NOUN
ejde-397	1581	21	,	,	PUNCT
ejde-397	1581	22	proc	proc	NOUN
ejde-397	1581	23	.	.	PUNCT
ejde-397	1582	1	amer	amer	PROPN
ejde-397	1582	2	.	.	PUNCT
ejde-397	1582	3	math	math	PROPN
ejde-397	1582	4	.	.	PUNCT
ejde-397	1583	1	soc	soc	PROPN
ejde-397	1583	2	.	.	PUNCT
ejde-397	1583	3	,	,	PUNCT
ejde-397	1583	4	63(2	63(2	NUM
ejde-397	1583	5	)	)	PUNCT
ejde-397	1583	6	(	(	PUNCT
ejde-397	1583	7	1997	1997	NUM
ejde-397	1583	8	)	)	PUNCT
ejde-397	1583	9	,	,	PUNCT
ejde-397	1583	10	370	370	NUM
ejde-397	1583	11	-	-	SYM
ejde-397	1583	12	373	373	NUM
ejde-397	1583	13	.	.	PUNCT
ejde-397	1584	1	[	[	X
ejde-397	1584	2	4	4	NUM
ejde-397	1584	3	]	]	PUNCT
ejde-397	1584	4	a.	a.	NOUN
ejde-397	1584	5	g.	g.	PROPN
ejde-397	1584	6	baskakov	baskakov	PROPN
ejde-397	1584	7	;	;	PUNCT
ejde-397	1584	8	linear	linear	PROPN
ejde-397	1584	9	relations	relation	NOUN
ejde-397	1584	10	as	as	ADP
ejde-397	1584	11	generators	generator	NOUN
ejde-397	1584	12	of	of	ADP
ejde-397	1584	13	semigroups	semigroup	NOUN
ejde-397	1584	14	of	of	ADP
ejde-397	1584	15	operators	operator	NOUN
ejde-397	1584	16	,	,	PUNCT
ejde-397	1584	17	math	math	NOUN
ejde-397	1584	18	.	.	PUNCT
ejde-397	1585	1	notes	note	NOUN
ejde-397	1585	2	,	,	PUNCT
ejde-397	1585	3	84(1	84(1	NUM
ejde-397	1585	4	-	-	SYM
ejde-397	1585	5	2	2	NUM
ejde-397	1585	6	)	)	PUNCT
ejde-397	1585	7	(	(	PUNCT
ejde-397	1585	8	2008	2008	NUM
ejde-397	1585	9	)	)	PUNCT
ejde-397	1585	10	,	,	PUNCT
ejde-397	1585	11	166	166	NUM
ejde-397	1585	12	-	-	SYM
ejde-397	1585	13	183	183	NUM
ejde-397	1585	14	.	.	PUNCT
ejde-397	1586	1	[	[	X
ejde-397	1586	2	5	5	X
ejde-397	1586	3	]	]	PUNCT
ejde-397	1586	4	e.	e.	PROPN
ejde-397	1586	5	bazhlekova	bazhlekova	PROPN
ejde-397	1586	6	;	;	PUNCT
ejde-397	1586	7	fractional	fractional	ADJ
ejde-397	1586	8	evolution	evolution	NOUN
ejde-397	1586	9	equations	equation	NOUN
ejde-397	1586	10	in	in	ADP
ejde-397	1586	11	banach	banach	NOUN
ejde-397	1586	12	spaces	space	NOUN
ejde-397	1586	13	,	,	PUNCT
ejde-397	1586	14	thesis	thesis	NOUN
ejde-397	1586	15	,	,	PUNCT
ejde-397	1586	16	eindhoven	eindhoven	ADJ
ejde-397	1586	17	university	university	NOUN
ejde-397	1586	18	of	of	ADP
ejde-397	1586	19	technology	technology	NOUN
ejde-397	1586	20	,	,	PUNCT
ejde-397	1586	21	eindhoven	eindhoven	VERB
ejde-397	1586	22	,	,	PUNCT
ejde-397	1586	23	2001	2001	NUM
ejde-397	1586	24	.	.	PUNCT
ejde-397	1587	1	[	[	X
ejde-397	1587	2	6	6	NUM
ejde-397	1587	3	]	]	PUNCT
ejde-397	1587	4	m.	m.	NOUN
ejde-397	1587	5	s.	s.	PROPN
ejde-397	1587	6	bichegkuev	bichegkuev	PROPN
ejde-397	1587	7	;	;	PUNCT
ejde-397	1587	8	on	on	ADP
ejde-397	1587	9	some	some	DET
ejde-397	1587	10	classes	class	NOUN
ejde-397	1587	11	of	of	ADP
ejde-397	1587	12	infinitely	infinitely	ADV
ejde-397	1587	13	differentiable	differentiable	ADJ
ejde-397	1587	14	operator	operator	NOUN
ejde-397	1587	15	semigroups	semigroup	NOUN
ejde-397	1587	16	,	,	PUNCT
ejde-397	1587	17	differ	differ	VERB
ejde-397	1587	18	.	.	PUNCT
ejde-397	1588	1	equ	equ	PROPN
ejde-397	1588	2	.	.	PROPN
ejde-397	1588	3	,	,	PUNCT
ejde-397	1588	4	46(2	46(2	NOUN
ejde-397	1588	5	)	)	PUNCT
ejde-397	1588	6	(	(	PUNCT
ejde-397	1588	7	2010	2010	NUM
ejde-397	1588	8	)	)	PUNCT
ejde-397	1588	9	,	,	PUNCT
ejde-397	1588	10	224	224	NUM
ejde-397	1588	11	-	-	SYM
ejde-397	1588	12	238	238	NUM
ejde-397	1588	13	.	.	PUNCT
ejde-397	1589	1	[	[	X
ejde-397	1589	2	7	7	X
ejde-397	1589	3	]	]	PUNCT
ejde-397	1589	4	m.	m.	NOUN
ejde-397	1589	5	s.	s.	PROPN
ejde-397	1589	6	bichegkuev	bichegkuev	PROPN
ejde-397	1589	7	;	;	PUNCT
ejde-397	1589	8	to	to	ADP
ejde-397	1589	9	the	the	DET
ejde-397	1589	10	theory	theory	NOUN
ejde-397	1589	11	of	of	ADP
ejde-397	1589	12	infinitely	infinitely	ADV
ejde-397	1589	13	differentiable	differentiable	ADJ
ejde-397	1589	14	semigroups	semigroup	NOUN
ejde-397	1589	15	of	of	ADP
ejde-397	1589	16	operators	operator	NOUN
ejde-397	1589	17	,	,	PUNCT
ejde-397	1589	18	st	st	PROPN
ejde-397	1589	19	.	.	PROPN
ejde-397	1589	20	petersburg	petersburg	PROPN
ejde-397	1589	21	math	math	PROPN
ejde-397	1589	22	.	.	PUNCT
ejde-397	1590	1	j.	j.	PROPN
ejde-397	1590	2	,	,	PUNCT
ejde-397	1590	3	22(2	22(2	NUM
ejde-397	1590	4	)	)	PUNCT
ejde-397	1590	5	(	(	PUNCT
ejde-397	1590	6	2011	2011	NUM
ejde-397	1590	7	)	)	PUNCT
ejde-397	1590	8	,	,	PUNCT
ejde-397	1590	9	175	175	NUM
ejde-397	1590	10	-	-	SYM
ejde-397	1590	11	182	182	NUM
ejde-397	1590	12	.	.	PUNCT
ejde-397	1591	1	[	[	X
ejde-397	1591	2	8	8	NUM
ejde-397	1591	3	]	]	X
ejde-397	1591	4	r.	r.	PROPN
ejde-397	1591	5	w.	w.	PROPN
ejde-397	1591	6	carroll	carroll	PROPN
ejde-397	1591	7	,	,	PUNCT
ejde-397	1591	8	r.	r.	PROPN
ejde-397	1591	9	w.	w.	PROPN
ejde-397	1591	10	showalter	showalter	PROPN
ejde-397	1591	11	;	;	PUNCT
ejde-397	1591	12	singular	singular	NOUN
ejde-397	1591	13	and	and	CCONJ
ejde-397	1591	14	degenerate	degenerate	ADJ
ejde-397	1591	15	cauchy	cauchy	NOUN
ejde-397	1591	16	problems	problem	NOUN
ejde-397	1591	17	,	,	PUNCT
ejde-397	1591	18	academic	academic	ADJ
ejde-397	1591	19	press	press	NOUN
ejde-397	1591	20	,	,	PUNCT
ejde-397	1591	21	new	new	PROPN
ejde-397	1591	22	york	york	PROPN
ejde-397	1591	23	,	,	PUNCT
ejde-397	1591	24	1976	1976	NUM
ejde-397	1591	25	.	.	PUNCT
ejde-397	1592	1	[	[	X
ejde-397	1592	2	9	9	NUM
ejde-397	1592	3	]	]	X
ejde-397	1592	4	r.	r.	PROPN
ejde-397	1592	5	cross	cross	PROPN
ejde-397	1592	6	;	;	PUNCT
ejde-397	1592	7	multivalued	multivalued	ADJ
ejde-397	1592	8	linear	linear	PROPN
ejde-397	1592	9	operators	operator	NOUN
ejde-397	1592	10	,	,	PUNCT
ejde-397	1592	11	marcel	marcel	PROPN
ejde-397	1592	12	dekker	dekker	PROPN
ejde-397	1592	13	inc	inc	PROPN
ejde-397	1592	14	.	.	PROPN
ejde-397	1592	15	,	,	PUNCT
ejde-397	1592	16	new	new	PROPN
ejde-397	1592	17	york	york	PROPN
ejde-397	1592	18	,	,	PUNCT
ejde-397	1592	19	1998	1998	NUM
ejde-397	1592	20	.	.	PUNCT
ejde-397	1593	1	[	[	X
ejde-397	1593	2	10	10	NUM
ejde-397	1593	3	]	]	X
ejde-397	1593	4	s.	s.	PROPN
ejde-397	1593	5	das	das	PROPN
ejde-397	1593	6	;	;	PUNCT
ejde-397	1593	7	functional	functional	ADJ
ejde-397	1593	8	fractional	fractional	ADJ
ejde-397	1593	9	calculus	calculus	NOUN
ejde-397	1593	10	,	,	PUNCT
ejde-397	1593	11	springer	springer	NOUN
ejde-397	1593	12	-	-	PUNCT
ejde-397	1593	13	verlag	verlag	PROPN
ejde-397	1593	14	,	,	PUNCT
ejde-397	1593	15	berlin	berlin	PROPN
ejde-397	1593	16	,	,	PUNCT
ejde-397	1593	17	2011	2011	NUM
ejde-397	1593	18	.	.	PUNCT
ejde-397	1594	1	[	[	X
ejde-397	1594	2	11	11	NUM
ejde-397	1594	3	]	]	X
ejde-397	1594	4	r.	r.	NOUN
ejde-397	1594	5	delaubenfels	delaubenfels	PROPN
ejde-397	1594	6	;	;	PUNCT
ejde-397	1594	7	existence	existence	NOUN
ejde-397	1594	8	families	family	NOUN
ejde-397	1594	9	,	,	PUNCT
ejde-397	1594	10	functional	functional	ADJ
ejde-397	1594	11	calculi	calculi	NOUN
ejde-397	1594	12	and	and	CCONJ
ejde-397	1594	13	evolution	evolution	NOUN
ejde-397	1594	14	equations	equation	NOUN
ejde-397	1594	15	,	,	PUNCT
ejde-397	1594	16	lecture	lecture	NOUN
ejde-397	1594	17	notes	note	NOUN
ejde-397	1594	18	in	in	ADP
ejde-397	1594	19	mathematics	mathematics	NOUN
ejde-397	1594	20	1570	1570	NUM
ejde-397	1594	21	,	,	PUNCT
ejde-397	1594	22	springer	springer	NOUN
ejde-397	1594	23	-	-	PUNCT
ejde-397	1594	24	verlag	verlag	PROPN
ejde-397	1594	25	,	,	PUNCT
ejde-397	1594	26	new	new	PROPN
ejde-397	1594	27	york	york	PROPN
ejde-397	1594	28	,	,	PUNCT
ejde-397	1594	29	1994	1994	NUM
ejde-397	1594	30	.	.	PUNCT
ejde-397	1595	1	[	[	X
ejde-397	1595	2	12	12	NUM
ejde-397	1595	3	]	]	X
ejde-397	1595	4	r.	r.	PROPN
ejde-397	1595	5	delaubenfels	delaubenfels	PROPN
ejde-397	1595	6	,	,	PUNCT
ejde-397	1595	7	f.	f.	PROPN
ejde-397	1595	8	yao	yao	PROPN
ejde-397	1595	9	,	,	PUNCT
ejde-397	1595	10	s.	s.	PROPN
ejde-397	1595	11	w.	w.	PROPN
ejde-397	1595	12	wang	wang	PROPN
ejde-397	1595	13	;	;	PUNCT
ejde-397	1595	14	fractional	fractional	ADJ
ejde-397	1595	15	powers	power	NOUN
ejde-397	1595	16	of	of	ADP
ejde-397	1595	17	operators	operator	NOUN
ejde-397	1595	18	of	of	ADP
ejde-397	1595	19	regularized	regularize	VERB
ejde-397	1595	20	type	type	NOUN
ejde-397	1595	21	,	,	PUNCT
ejde-397	1595	22	j.	j.	PROPN
ejde-397	1595	23	math	math	PROPN
ejde-397	1595	24	.	.	PUNCT
ejde-397	1596	1	anal	anal	PROPN
ejde-397	1596	2	.	.	PUNCT
ejde-397	1597	1	appl	appl	PROPN
ejde-397	1597	2	.	.	PROPN
ejde-397	1597	3	,	,	PUNCT
ejde-397	1597	4	199(3	199(3	NUM
ejde-397	1597	5	)	)	PUNCT
ejde-397	1597	6	(	(	PUNCT
ejde-397	1597	7	1996	1996	NUM
ejde-397	1597	8	)	)	PUNCT
ejde-397	1597	9	,	,	PUNCT
ejde-397	1597	10	910	910	NUM
ejde-397	1597	11	-	-	SYM
ejde-397	1597	12	933	933	NUM
ejde-397	1597	13	.	.	PUNCT
ejde-397	1598	1	[	[	X
ejde-397	1598	2	13	13	NUM
ejde-397	1598	3	]	]	X
ejde-397	1598	4	g.	g.	PROPN
ejde-397	1598	5	v.	v.	PROPN
ejde-397	1598	6	demidenko	demidenko	PROPN
ejde-397	1598	7	,	,	PUNCT
ejde-397	1598	8	s.	s.	PROPN
ejde-397	1598	9	v.	v.	PROPN
ejde-397	1598	10	uspenskii	uspenskii	PROPN
ejde-397	1598	11	;	;	PUNCT
ejde-397	1598	12	partial	partial	ADJ
ejde-397	1598	13	differential	differential	ADJ
ejde-397	1598	14	equations	equation	NOUN
ejde-397	1598	15	and	and	CCONJ
ejde-397	1598	16	systems	system	NOUN
ejde-397	1598	17	not	not	PART
ejde-397	1598	18	solvable	solvable	ADJ
ejde-397	1598	19	with	with	ADP
ejde-397	1598	20	respect	respect	NOUN
ejde-397	1598	21	to	to	ADP
ejde-397	1598	22	the	the	DET
ejde-397	1598	23	highest	high	ADJ
ejde-397	1598	24	-	-	PUNCT
ejde-397	1598	25	order	order	NOUN
ejde-397	1598	26	derivative	derivative	ADJ
ejde-397	1598	27	,	,	PUNCT
ejde-397	1598	28	vol	vol	NOUN
ejde-397	1598	29	.	.	PROPN
ejde-397	1599	1	256	256	NUM
ejde-397	1599	2	of	of	ADP
ejde-397	1599	3	pure	pure	ADJ
ejde-397	1599	4	and	and	CCONJ
ejde-397	1599	5	applied	applied	ADJ
ejde-397	1599	6	mathematics	mathematic	NOUN
ejde-397	1599	7	series	series	NOUN
ejde-397	1599	8	,	,	PUNCT
ejde-397	1599	9	crc	crc	NOUN
ejde-397	1599	10	press	press	PROPN
ejde-397	1599	11	,	,	PUNCT
ejde-397	1599	12	new	new	PROPN
ejde-397	1599	13	york	york	PROPN
ejde-397	1599	14	,	,	PUNCT
ejde-397	1599	15	2003	2003	NUM
ejde-397	1599	16	.	.	PUNCT
ejde-397	1600	1	[	[	X
ejde-397	1600	2	14	14	NUM
ejde-397	1600	3	]	]	PUNCT
ejde-397	1600	4	k.	k.	PROPN
ejde-397	1600	5	diethelm	diethelm	PROPN
ejde-397	1600	6	;	;	PUNCT
ejde-397	1600	7	the	the	DET
ejde-397	1600	8	analysis	analysis	NOUN
ejde-397	1600	9	of	of	ADP
ejde-397	1600	10	fractional	fractional	ADJ
ejde-397	1600	11	differential	differential	ADJ
ejde-397	1600	12	equations	equation	NOUN
ejde-397	1600	13	.	.	PUNCT
ejde-397	1601	1	an	an	DET
ejde-397	1601	2	application	application	NOUN
ejde-397	1601	3	-	-	PUNCT
ejde-397	1601	4	oriented	orient	VERB
ejde-397	1601	5	exposition	exposition	NOUN
ejde-397	1601	6	using	use	VERB
ejde-397	1601	7	differential	differential	ADJ
ejde-397	1601	8	operators	operator	NOUN
ejde-397	1601	9	of	of	ADP
ejde-397	1601	10	caputo	caputo	PROPN
ejde-397	1601	11	type	type	PROPN
ejde-397	1601	12	,	,	PUNCT
ejde-397	1601	13	springer	springer	NOUN
ejde-397	1601	14	-	-	PUNCT
ejde-397	1601	15	verlag	verlag	PROPN
ejde-397	1601	16	,	,	PUNCT
ejde-397	1601	17	berlin	berlin	PROPN
ejde-397	1601	18	,	,	PUNCT
ejde-397	1601	19	2010	2010	NUM
ejde-397	1601	20	.	.	PUNCT
ejde-397	1602	1	[	[	X
ejde-397	1602	2	15	15	NUM
ejde-397	1602	3	]	]	X
ejde-397	1602	4	r.	r.	PROPN
ejde-397	1602	5	dragoni	dragoni	PROPN
ejde-397	1602	6	,	,	PUNCT
ejde-397	1602	7	j.	j.	PROPN
ejde-397	1602	8	w.	w.	PROPN
ejde-397	1602	9	macki	macki	PROPN
ejde-397	1602	10	,	,	PUNCT
ejde-397	1602	11	p.	p.	NOUN
ejde-397	1602	12	nistri	nistri	PROPN
ejde-397	1602	13	,	,	PUNCT
ejde-397	1602	14	p.	p.	PROPN
ejde-397	1602	15	zecca	zecca	NOUN
ejde-397	1602	16	;	;	PUNCT
ejde-397	1602	17	solution	solution	NOUN
ejde-397	1602	18	sets	set	NOUN
ejde-397	1602	19	of	of	ADP
ejde-397	1602	20	differential	differential	ADJ
ejde-397	1602	21	equations	equation	NOUN
ejde-397	1602	22	in	in	ADP
ejde-397	1602	23	abstract	abstract	ADJ
ejde-397	1602	24	spaces	space	NOUN
ejde-397	1602	25	,	,	PUNCT
ejde-397	1602	26	vol	vol	NOUN
ejde-397	1602	27	.	.	PROPN
ejde-397	1602	28	342	342	NUM
ejde-397	1602	29	,	,	PUNCT
ejde-397	1602	30	crc	crc	NOUN
ejde-397	1602	31	press	press	PROPN
ejde-397	1602	32	,	,	PUNCT
ejde-397	1602	33	boca	boca	PROPN
ejde-397	1602	34	raton	raton	PROPN
ejde-397	1602	35	,	,	PUNCT
ejde-397	1602	36	1996	1996	NUM
ejde-397	1602	37	.	.	PUNCT
ejde-397	1603	1	[	[	X
ejde-397	1603	2	16	16	NUM
ejde-397	1603	3	]	]	X
ejde-397	1603	4	m.	m.	NOUN
ejde-397	1603	5	v.	v.	ADP
ejde-397	1603	6	falaleev	falaleev	PROPN
ejde-397	1603	7	,	,	PUNCT
ejde-397	1603	8	s.	s.	PROPN
ejde-397	1603	9	s.	s.	PROPN
ejde-397	1603	10	orlov	orlov	PROPN
ejde-397	1603	11	;	;	PUNCT
ejde-397	1603	12	continuous	continuous	ADJ
ejde-397	1603	13	and	and	CCONJ
ejde-397	1603	14	generalized	generalized	ADJ
ejde-397	1603	15	solutions	solution	NOUN
ejde-397	1603	16	of	of	ADP
ejde-397	1603	17	singular	singular	ADJ
ejde-397	1603	18	integrodifferential	integrodifferential	ADJ
ejde-397	1603	19	equations	equation	NOUN
ejde-397	1603	20	in	in	ADP
ejde-397	1603	21	banach	banach	NOUN
ejde-397	1603	22	spaces	space	NOUN
ejde-397	1603	23	,	,	PUNCT
ejde-397	1603	24	iigu	iigu	PROPN
ejde-397	1603	25	ser	ser	PROPN
ejde-397	1603	26	.	.	PROPN
ejde-397	1604	1	matematika	matematika	PROPN
ejde-397	1604	2	,	,	PUNCT
ejde-397	1604	3	5(1	5(1	NUM
ejde-397	1604	4	)	)	PUNCT
ejde-397	1604	5	(	(	PUNCT
ejde-397	1604	6	2012	2012	NUM
ejde-397	1604	7	)	)	PUNCT
ejde-397	1604	8	,	,	PUNCT
ejde-397	1604	9	62	62	NUM
ejde-397	1604	10	-	-	SYM
ejde-397	1604	11	74	74	NUM
ejde-397	1604	12	.	.	PUNCT
ejde-397	1605	1	[	[	X
ejde-397	1605	2	17	17	NUM
ejde-397	1605	3	]	]	PUNCT
ejde-397	1605	4	a.	a.	NOUN
ejde-397	1605	5	favini	favini	PROPN
ejde-397	1605	6	,	,	PUNCT
ejde-397	1605	7	a.	a.	NOUN
ejde-397	1605	8	yagi	yagi	NOUN
ejde-397	1605	9	;	;	PUNCT
ejde-397	1605	10	degenerate	degenerate	ADJ
ejde-397	1605	11	differential	differential	ADJ
ejde-397	1605	12	equations	equation	NOUN
ejde-397	1605	13	in	in	ADP
ejde-397	1605	14	banach	banach	NOUN
ejde-397	1605	15	spaces	space	NOUN
ejde-397	1605	16	,	,	PUNCT
ejde-397	1605	17	chapman	chapman	NOUN
ejde-397	1605	18	and	and	CCONJ
ejde-397	1605	19	hall	hall	PROPN
ejde-397	1605	20	/	/	SYM
ejde-397	1605	21	crc	crc	NOUN
ejde-397	1605	22	pure	pure	ADJ
ejde-397	1605	23	and	and	CCONJ
ejde-397	1605	24	applied	applied	ADJ
ejde-397	1605	25	mathematics	mathematic	NOUN
ejde-397	1605	26	,	,	PUNCT
ejde-397	1605	27	new	new	PROPN
ejde-397	1605	28	york	york	PROPN
ejde-397	1605	29	,	,	PUNCT
ejde-397	1605	30	1998	1998	NUM
ejde-397	1605	31	.	.	PUNCT
ejde-397	1606	1	[	[	X
ejde-397	1606	2	18	18	NUM
ejde-397	1606	3	]	]	PUNCT
ejde-397	1606	4	a.	a.	NOUN
ejde-397	1606	5	favini	favini	PROPN
ejde-397	1606	6	,	,	PUNCT
ejde-397	1606	7	h.	h.	PROPN
ejde-397	1606	8	tanabe	tanabe	PROPN
ejde-397	1606	9	;	;	PUNCT
ejde-397	1606	10	degenerate	degenerate	ADJ
ejde-397	1606	11	volterra	volterra	NOUN
ejde-397	1606	12	equations	equation	NOUN
ejde-397	1606	13	in	in	ADP
ejde-397	1606	14	banach	banach	NOUN
ejde-397	1606	15	spaces	space	NOUN
ejde-397	1606	16	,	,	PUNCT
ejde-397	1606	17	differ	differ	VERB
ejde-397	1606	18	.	.	PUNCT
ejde-397	1607	1	integral	integral	PROPN
ejde-397	1607	2	equ	equ	PROPN
ejde-397	1607	3	.	.	PROPN
ejde-397	1607	4	,	,	PUNCT
ejde-397	1607	5	14(5	14(5	PROPN
ejde-397	1607	6	)	)	PUNCT
ejde-397	1607	7	(	(	PUNCT
ejde-397	1607	8	2001	2001	NUM
ejde-397	1607	9	)	)	PUNCT
ejde-397	1607	10	,	,	PUNCT
ejde-397	1607	11	613	613	NUM
ejde-397	1607	12	-	-	SYM
ejde-397	1607	13	640	640	NUM
ejde-397	1607	14	.	.	PUNCT
ejde-397	1608	1	[	[	X
ejde-397	1608	2	19	19	NUM
ejde-397	1608	3	]	]	PUNCT
ejde-397	1608	4	a.	a.	NOUN
ejde-397	1608	5	favaron	favaron	PROPN
ejde-397	1608	6	,	,	PUNCT
ejde-397	1608	7	a.	a.	NOUN
ejde-397	1608	8	favini	favini	PROPN
ejde-397	1608	9	;	;	PUNCT
ejde-397	1608	10	on	on	ADP
ejde-397	1608	11	the	the	DET
ejde-397	1608	12	behaviour	behaviour	NOUN
ejde-397	1608	13	of	of	ADP
ejde-397	1608	14	singular	singular	ADJ
ejde-397	1608	15	semigroups	semigroup	NOUN
ejde-397	1608	16	in	in	ADP
ejde-397	1608	17	intermediate	intermediate	ADJ
ejde-397	1608	18	and	and	CCONJ
ejde-397	1608	19	interpolation	interpolation	NOUN
ejde-397	1608	20	spaces	space	NOUN
ejde-397	1608	21	and	and	CCONJ
ejde-397	1608	22	its	its	PRON
ejde-397	1608	23	applications	application	NOUN
ejde-397	1608	24	to	to	PART
ejde-397	1608	25	maximal	maximal	ADJ
ejde-397	1608	26	regularity	regularity	NOUN
ejde-397	1608	27	for	for	ADP
ejde-397	1608	28	degenerate	degenerate	ADJ
ejde-397	1608	29	integro	integro	ADJ
ejde-397	1608	30	-	-	PUNCT
ejde-397	1608	31	differential	differential	NOUN
ejde-397	1608	32	evolution	evolution	NOUN
ejde-397	1608	33	equations	equation	NOUN
ejde-397	1608	34	,	,	PUNCT
ejde-397	1608	35	abstr	abstr	PROPN
ejde-397	1608	36	.	.	PUNCT
ejde-397	1609	1	appl	appl	PROPN
ejde-397	1609	2	.	.	PUNCT
ejde-397	1610	1	anal	anal	PROPN
ejde-397	1610	2	.	.	PUNCT
ejde-397	1610	3	,	,	PUNCT
ejde-397	1610	4	vol	vol	NOUN
ejde-397	1610	5	.	.	PROPN
ejde-397	1610	6	2013	2013	NUM
ejde-397	1610	7	,	,	PUNCT
ejde-397	1610	8	art	art	NOUN
ejde-397	1610	9	.	.	PUNCT
ejde-397	1611	1	i	i	PRON
ejde-397	1611	2	d	d	PROPN
ejde-397	1611	3	275494	275494	NUM
ejde-397	1611	4	,	,	PUNCT
ejde-397	1611	5	37	37	NUM
ejde-397	1611	6	pp	pp	NOUN
ejde-397	1611	7	.	.	PUNCT
ejde-397	1612	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1612	2	abstract	abstract	ADJ
ejde-397	1612	3	degenerate	degenerate	ADJ
ejde-397	1612	4	volterra	volterra	NOUN
ejde-397	1612	5	inclusions	inclusion	NOUN
ejde-397	1612	6	53	53	NUM
ejde-397	1612	7	[	[	SYM
ejde-397	1612	8	20	20	NUM
ejde-397	1612	9	]	]	PUNCT
ejde-397	1612	10	a.	a.	NOUN
ejde-397	1612	11	favini	favini	PROPN
ejde-397	1612	12	,	,	PUNCT
ejde-397	1612	13	a.	a.	NOUN
ejde-397	1612	14	lorenzi	lorenzi	PROPN
ejde-397	1612	15	,	,	PUNCT
ejde-397	1612	16	h.	h.	PROPN
ejde-397	1612	17	tanabe	tanabe	PROPN
ejde-397	1612	18	;	;	PUNCT
ejde-397	1612	19	degenerate	degenerate	ADJ
ejde-397	1612	20	integrodifferential	integrodifferential	ADJ
ejde-397	1612	21	equations	equation	NOUN
ejde-397	1612	22	of	of	ADP
ejde-397	1612	23	parabolic	parabolic	ADJ
ejde-397	1612	24	type	type	NOUN
ejde-397	1612	25	,	,	PUNCT
ejde-397	1612	26	in	in	ADP
ejde-397	1612	27	:	:	PUNCT
ejde-397	1612	28	differential	differential	ADJ
ejde-397	1612	29	equations	equation	NOUN
ejde-397	1612	30	:	:	PUNCT
ejde-397	1612	31	inverse	inverse	NOUN
ejde-397	1612	32	and	and	CCONJ
ejde-397	1612	33	direct	direct	ADJ
ejde-397	1612	34	problems	problem	NOUN
ejde-397	1612	35	,	,	PUNCT
ejde-397	1612	36	chapman	chapman	NOUN
ejde-397	1612	37	and	and	CCONJ
ejde-397	1612	38	hall	hall	PROPN
ejde-397	1612	39	/	/	SYM
ejde-397	1612	40	crc	crc	PROPN
ejde-397	1612	41	press	press	PROPN
ejde-397	1612	42	,	,	PUNCT
ejde-397	1612	43	boca	boca	PROPN
ejde-397	1612	44	raton	raton	PROPN
ejde-397	1612	45	,	,	PUNCT
ejde-397	1612	46	2006	2006	NUM
ejde-397	1612	47	,	,	PUNCT
ejde-397	1612	48	pp	pp	ADJ
ejde-397	1612	49	.	.	PUNCT
ejde-397	1613	1	91	91	NUM
ejde-397	1613	2	-	-	SYM
ejde-397	1613	3	109	109	NUM
ejde-397	1613	4	.	.	PUNCT
ejde-397	1614	1	[	[	X
ejde-397	1614	2	21	21	NUM
ejde-397	1614	3	]	]	PUNCT
ejde-397	1614	4	a.	a.	NOUN
ejde-397	1614	5	favini	favini	PROPN
ejde-397	1614	6	,	,	PUNCT
ejde-397	1614	7	a.	a.	NOUN
ejde-397	1614	8	lorenzi	lorenzi	PROPN
ejde-397	1614	9	,	,	PUNCT
ejde-397	1614	10	h.	h.	PROPN
ejde-397	1614	11	tanabe	tanabe	PROPN
ejde-397	1614	12	;	;	PUNCT
ejde-397	1614	13	degenerate	degenerate	ADJ
ejde-397	1614	14	integrodifferential	integrodifferential	ADJ
ejde-397	1614	15	equations	equation	NOUN
ejde-397	1614	16	of	of	ADP
ejde-397	1614	17	parabolic	parabolic	ADJ
ejde-397	1614	18	type	type	NOUN
ejde-397	1614	19	with	with	ADP
ejde-397	1614	20	robin	robin	PROPN
ejde-397	1614	21	boundary	boundary	PROPN
ejde-397	1614	22	conditions	condition	NOUN
ejde-397	1614	23	:	:	PUNCT
ejde-397	1614	24	l2	l2	NOUN
ejde-397	1614	25	-	-	PUNCT
ejde-397	1614	26	theory	theory	NOUN
ejde-397	1614	27	,	,	PUNCT
ejde-397	1614	28	j.	j.	PROPN
ejde-397	1614	29	math	math	PROPN
ejde-397	1614	30	.	.	PUNCT
ejde-397	1615	1	soc	soc	PROPN
ejde-397	1615	2	.	.	PUNCT
ejde-397	1616	1	japan	japan	PROPN
ejde-397	1616	2	,	,	PUNCT
ejde-397	1616	3	61(1	61(1	NOUN
ejde-397	1616	4	)	)	PUNCT
ejde-397	1616	5	(	(	PUNCT
ejde-397	1616	6	2009	2009	NUM
ejde-397	1616	7	)	)	PUNCT
ejde-397	1616	8	,	,	PUNCT
ejde-397	1616	9	133	133	NUM
ejde-397	1616	10	-	-	SYM
ejde-397	1616	11	176	176	NUM
ejde-397	1616	12	.	.	PUNCT
ejde-397	1617	1	[	[	X
ejde-397	1617	2	22	22	NUM
ejde-397	1617	3	]	]	PUNCT
ejde-397	1617	4	v.	v.	PROPN
ejde-397	1617	5	e.	e.	PROPN
ejde-397	1617	6	fedorov	fedorov	PROPN
ejde-397	1617	7	,	,	PUNCT
ejde-397	1617	8	a.	a.	NOUN
ejde-397	1617	9	debbouche	debbouche	PROPN
ejde-397	1617	10	;	;	PUNCT
ejde-397	1617	11	a	a	DET
ejde-397	1617	12	class	class	NOUN
ejde-397	1617	13	of	of	ADP
ejde-397	1617	14	degenerate	degenerate	ADJ
ejde-397	1617	15	fractional	fractional	ADJ
ejde-397	1617	16	evolution	evolution	NOUN
ejde-397	1617	17	systems	system	NOUN
ejde-397	1617	18	in	in	ADP
ejde-397	1617	19	banach	banach	NOUN
ejde-397	1617	20	spaces	space	NOUN
ejde-397	1617	21	,	,	PUNCT
ejde-397	1617	22	differ	differ	VERB
ejde-397	1617	23	.	.	PUNCT
ejde-397	1618	1	equ	equ	PROPN
ejde-397	1618	2	.	.	PROPN
ejde-397	1618	3	,	,	PUNCT
ejde-397	1618	4	49(12	49(12	NUM
ejde-397	1618	5	)	)	PUNCT
ejde-397	1618	6	(	(	PUNCT
ejde-397	1618	7	2013	2013	NUM
ejde-397	1618	8	)	)	PUNCT
ejde-397	1618	9	,	,	PUNCT
ejde-397	1618	10	1569	1569	NUM
ejde-397	1618	11	-	-	SYM
ejde-397	1618	12	1576	1576	NUM
ejde-397	1618	13	.	.	PUNCT
ejde-397	1619	1	[	[	X
ejde-397	1619	2	23	23	X
ejde-397	1619	3	]	]	X
ejde-397	1619	4	v.	v.	PROPN
ejde-397	1619	5	e.	e.	PROPN
ejde-397	1619	6	fedorov	fedorov	PROPN
ejde-397	1619	7	,	,	PUNCT
ejde-397	1619	8	d.	d.	PROPN
ejde-397	1619	9	m.	m.	PROPN
ejde-397	1619	10	gordievskikh	gordievskikh	PROPN
ejde-397	1619	11	;	;	PUNCT
ejde-397	1619	12	resolving	resolve	VERB
ejde-397	1619	13	operators	operator	NOUN
ejde-397	1619	14	of	of	ADP
ejde-397	1619	15	degenerate	degenerate	ADJ
ejde-397	1619	16	evolution	evolution	NOUN
ejde-397	1619	17	equations	equation	NOUN
ejde-397	1619	18	with	with	ADP
ejde-397	1619	19	fractional	fractional	ADJ
ejde-397	1619	20	derivative	derivative	NOUN
ejde-397	1619	21	with	with	ADP
ejde-397	1619	22	respect	respect	NOUN
ejde-397	1619	23	to	to	ADP
ejde-397	1619	24	time	time	NOUN
ejde-397	1619	25	,	,	PUNCT
ejde-397	1619	26	russian	russian	ADJ
ejde-397	1619	27	math	math	NOUN
ejde-397	1619	28	.	.	PUNCT
ejde-397	1620	1	(	(	PUNCT
ejde-397	1620	2	iz	iz	INTJ
ejde-397	1620	3	.	.	PUNCT
ejde-397	1620	4	vuz	vuz	PROPN
ejde-397	1620	5	)	)	PUNCT
ejde-397	1620	6	,	,	PUNCT
ejde-397	1620	7	1(1	1(1	NUM
ejde-397	1620	8	)	)	PUNCT
ejde-397	1620	9	(	(	PUNCT
ejde-397	1620	10	2015	2015	NUM
ejde-397	1620	11	)	)	PUNCT
ejde-397	1620	12	,	,	PUNCT
ejde-397	1620	13	7183	7183	NUM
ejde-397	1620	14	.	.	PUNCT
ejde-397	1620	15	,	,	PUNCT
ejde-397	1621	1	[	[	X
ejde-397	1621	2	24	24	NUM
ejde-397	1621	3	]	]	PUNCT
ejde-397	1621	4	v.	v.	PROPN
ejde-397	1621	5	e.	e.	PROPN
ejde-397	1621	6	fedorov	fedorov	PROPN
ejde-397	1621	7	,	,	PUNCT
ejde-397	1621	8	d.	d.	PROPN
ejde-397	1621	9	m.	m.	PROPN
ejde-397	1621	10	gordievskikh	gordievskikh	PROPN
ejde-397	1621	11	,	,	PUNCT
ejde-397	1621	12	m.	m.	NOUN
ejde-397	1621	13	v.	v.	ADP
ejde-397	1621	14	plekhanova	plekhanova	PROPN
ejde-397	1621	15	;	;	PUNCT
ejde-397	1621	16	equations	equation	NOUN
ejde-397	1621	17	in	in	ADP
ejde-397	1621	18	banach	banach	NOUN
ejde-397	1621	19	spaces	space	NOUN
ejde-397	1621	20	with	with	ADP
ejde-397	1621	21	a	a	DET
ejde-397	1621	22	degenerate	degenerate	ADJ
ejde-397	1621	23	operator	operator	NOUN
ejde-397	1621	24	under	under	ADP
ejde-397	1621	25	a	a	DET
ejde-397	1621	26	fractional	fractional	ADJ
ejde-397	1621	27	derivative	derivative	NOUN
ejde-397	1621	28	,	,	PUNCT
ejde-397	1621	29	differ	differ	VERB
ejde-397	1621	30	.	.	PUNCT
ejde-397	1622	1	equ	equ	PROPN
ejde-397	1622	2	.	.	PROPN
ejde-397	1622	3	,	,	PUNCT
ejde-397	1622	4	51(10	51(10	NUM
ejde-397	1622	5	)	)	PUNCT
ejde-397	1622	6	(	(	PUNCT
ejde-397	1622	7	2015	2015	NUM
ejde-397	1622	8	)	)	PUNCT
ejde-397	1622	9	,	,	PUNCT
ejde-397	1622	10	1360	1360	NUM
ejde-397	1622	11	-	-	SYM
ejde-397	1622	12	1368	1368	NUM
ejde-397	1622	13	.	.	PUNCT
ejde-397	1623	1	[	[	X
ejde-397	1623	2	25	25	NUM
ejde-397	1623	3	]	]	PUNCT
ejde-397	1623	4	v.	v.	PROPN
ejde-397	1623	5	e.	e.	PROPN
ejde-397	1623	6	fedorov	fedorov	PROPN
ejde-397	1623	7	;	;	PUNCT
ejde-397	1623	8	strongly	strongly	ADV
ejde-397	1623	9	holomorphic	holomorphic	ADJ
ejde-397	1623	10	groups	group	NOUN
ejde-397	1623	11	of	of	ADP
ejde-397	1623	12	linear	linear	ADJ
ejde-397	1623	13	equations	equation	NOUN
ejde-397	1623	14	of	of	ADP
ejde-397	1623	15	sobolev	sobolev	ADJ
ejde-397	1623	16	type	type	NOUN
ejde-397	1623	17	in	in	ADP
ejde-397	1623	18	locally	locally	ADV
ejde-397	1623	19	convex	convex	ADJ
ejde-397	1623	20	spaces	space	NOUN
ejde-397	1623	21	,	,	PUNCT
ejde-397	1623	22	differ	differ	VERB
ejde-397	1623	23	.	.	PUNCT
ejde-397	1624	1	equ	equ	PROPN
ejde-397	1624	2	.	.	PROPN
ejde-397	1624	3	,	,	PUNCT
ejde-397	1624	4	40(5	40(5	NOUN
ejde-397	1624	5	)	)	PUNCT
ejde-397	1624	6	(	(	PUNCT
ejde-397	1624	7	2004	2004	NUM
ejde-397	1624	8	)	)	PUNCT
ejde-397	1624	9	,	,	PUNCT
ejde-397	1624	10	753	753	NUM
ejde-397	1624	11	-	-	SYM
ejde-397	1624	12	765	765	NUM
ejde-397	1624	13	.	.	PUNCT
ejde-397	1625	1	[	[	X
ejde-397	1625	2	26	26	NUM
ejde-397	1625	3	]	]	PUNCT
ejde-397	1625	4	s.	s.	PROPN
ejde-397	1625	5	g.	g.	PROPN
ejde-397	1625	6	gal	gal	PROPN
ejde-397	1625	7	,	,	PUNCT
ejde-397	1625	8	j.	j.	PROPN
ejde-397	1625	9	a.	a.	PROPN
ejde-397	1625	10	goldstein	goldstein	PROPN
ejde-397	1625	11	;	;	PUNCT
ejde-397	1625	12	semigroups	semigroup	NOUN
ejde-397	1625	13	of	of	ADP
ejde-397	1625	14	linear	linear	PROPN
ejde-397	1625	15	operators	operator	NOUN
ejde-397	1625	16	on	on	ADP
ejde-397	1625	17	p	p	ADJ
ejde-397	1625	18	-	-	PUNCT
ejde-397	1625	19	fréchet	fréchet	NOUN
ejde-397	1625	20	spaces	space	NOUN
ejde-397	1625	21	,	,	PUNCT
ejde-397	1625	22	0	0	PUNCT
ejde-397	1625	23	<	<	X
ejde-397	1625	24	p	p	X
ejde-397	1625	25	<	<	X
ejde-397	1625	26	1	1	NUM
ejde-397	1625	27	,	,	PUNCT
ejde-397	1625	28	acta	acta	PROPN
ejde-397	1625	29	math	math	PROPN
ejde-397	1625	30	.	.	PUNCT
ejde-397	1626	1	hungar	hungar	PROPN
ejde-397	1626	2	.	.	PUNCT
ejde-397	1626	3	,	,	PUNCT
ejde-397	1626	4	114(1	114(1	NUM
ejde-397	1626	5	)	)	PUNCT
ejde-397	1626	6	(	(	PUNCT
ejde-397	1626	7	2007	2007	NUM
ejde-397	1626	8	)	)	PUNCT
ejde-397	1626	9	,	,	PUNCT
ejde-397	1626	10	13	13	NUM
ejde-397	1626	11	-	-	SYM
ejde-397	1626	12	36	36	NUM
ejde-397	1626	13	.	.	PUNCT
ejde-397	1627	1	[	[	X
ejde-397	1627	2	27	27	NUM
ejde-397	1627	3	]	]	X
ejde-397	1627	4	r.	r.	PROPN
ejde-397	1627	5	hermann	hermann	PROPN
ejde-397	1627	6	;	;	PUNCT
ejde-397	1627	7	fractional	fractional	ADJ
ejde-397	1627	8	calculus	calculus	NOUN
ejde-397	1627	9	:	:	PUNCT
ejde-397	1627	10	an	an	DET
ejde-397	1627	11	introduction	introduction	NOUN
ejde-397	1627	12	for	for	ADP
ejde-397	1627	13	physicists	physicist	NOUN
ejde-397	1627	14	,	,	PUNCT
ejde-397	1627	15	world	world	NOUN
ejde-397	1627	16	scientific	scientific	ADJ
ejde-397	1627	17	,	,	PUNCT
ejde-397	1627	18	2nd	2nd	ADJ
ejde-397	1627	19	edition	edition	NOUN
ejde-397	1627	20	,	,	PUNCT
ejde-397	1627	21	singapore	singapore	PROPN
ejde-397	1627	22	,	,	PUNCT
ejde-397	1627	23	2014	2014	NUM
ejde-397	1627	24	.	.	PUNCT
ejde-397	1628	1	[	[	X
ejde-397	1628	2	28	28	NUM
ejde-397	1628	3	]	]	X
ejde-397	1628	4	sk	sk	PROPN
ejde-397	1628	5	.	.	PROPN
ejde-397	1628	6	jaker	jaker	PROPN
ejde-397	1628	7	ali	ali	PROPN
ejde-397	1628	8	,	,	PUNCT
ejde-397	1628	9	n.	n.	PROPN
ejde-397	1628	10	d.	d.	PROPN
ejde-397	1628	11	chakraborty	chakraborty	PROPN
ejde-397	1628	12	;	;	PUNCT
ejde-397	1628	13	pettis	pettis	NOUN
ejde-397	1628	14	integration	integration	NOUN
ejde-397	1628	15	in	in	ADP
ejde-397	1628	16	locally	locally	ADV
ejde-397	1628	17	convex	convex	ADJ
ejde-397	1628	18	spaces	space	NOUN
ejde-397	1628	19	,	,	PUNCT
ejde-397	1628	20	anal	anal	NOUN
ejde-397	1628	21	.	.	PUNCT
ejde-397	1628	22	math	math	NOUN
ejde-397	1628	23	.	.	PUNCT
ejde-397	1628	24	,	,	PUNCT
ejde-397	1628	25	23	23	NUM
ejde-397	1628	26	(	(	PUNCT
ejde-397	1628	27	1997	1997	NUM
ejde-397	1628	28	)	)	PUNCT
ejde-397	1628	29	,	,	PUNCT
ejde-397	1628	30	241	241	NUM
ejde-397	1628	31	-	-	SYM
ejde-397	1628	32	257	257	NUM
ejde-397	1628	33	.	.	PUNCT
ejde-397	1629	1	[	[	X
ejde-397	1629	2	29	29	NUM
ejde-397	1629	3	]	]	PUNCT
ejde-397	1629	4	m.	m.	NOUN
ejde-397	1629	5	kazimierz	kazimierz	PROPN
ejde-397	1629	6	;	;	PUNCT
ejde-397	1629	7	vitali	vitali	PROPN
ejde-397	1629	8	and	and	CCONJ
ejde-397	1629	9	lebesgue	lebesgue	PROPN
ejde-397	1629	10	convergence	convergence	NOUN
ejde-397	1629	11	theorems	theorem	NOUN
ejde-397	1629	12	for	for	ADP
ejde-397	1629	13	pettis	pettis	NOUN
ejde-397	1629	14	integral	integral	ADJ
ejde-397	1629	15	in	in	ADP
ejde-397	1629	16	locally	locally	ADV
ejde-397	1629	17	convex	convex	ADJ
ejde-397	1629	18	spaces	space	NOUN
ejde-397	1629	19	,	,	PUNCT
ejde-397	1629	20	atti	atti	PROPN
ejde-397	1629	21	sem	sem	PROPN
ejde-397	1629	22	.	.	PROPN
ejde-397	1630	1	mat	mat	PROPN
ejde-397	1630	2	.	.	PROPN
ejde-397	1630	3	fis	fis	PROPN
ejde-397	1630	4	.	.	PUNCT
ejde-397	1631	1	univ	univ	PROPN
ejde-397	1631	2	.	.	PUNCT
ejde-397	1632	1	modena	modena	PROPN
ejde-397	1632	2	,	,	PUNCT
ejde-397	1632	3	35	35	NUM
ejde-397	1632	4	(	(	PUNCT
ejde-397	1632	5	1987	1987	NUM
ejde-397	1632	6	)	)	PUNCT
ejde-397	1632	7	,	,	PUNCT
ejde-397	1632	8	159	159	NUM
ejde-397	1632	9	-	-	SYM
ejde-397	1632	10	165	165	NUM
ejde-397	1632	11	.	.	PUNCT
ejde-397	1633	1	[	[	X
ejde-397	1633	2	30	30	NUM
ejde-397	1633	3	]	]	PUNCT
ejde-397	1633	4	a.	a.	NOUN
ejde-397	1633	5	a.	a.	NOUN
ejde-397	1633	6	kilbas	kilbas	PROPN
ejde-397	1633	7	,	,	PUNCT
ejde-397	1633	8	h.	h.	PROPN
ejde-397	1633	9	m.	m.	PROPN
ejde-397	1633	10	srivastava	srivastava	PROPN
ejde-397	1633	11	,	,	PUNCT
ejde-397	1633	12	j.	j.	PROPN
ejde-397	1633	13	j.	j.	PROPN
ejde-397	1633	14	trujillo	trujillo	PROPN
ejde-397	1633	15	;	;	PUNCT
ejde-397	1633	16	theory	theory	NOUN
ejde-397	1633	17	and	and	CCONJ
ejde-397	1633	18	applications	application	NOUN
ejde-397	1633	19	of	of	ADP
ejde-397	1633	20	fractional	fractional	ADJ
ejde-397	1633	21	differential	differential	ADJ
ejde-397	1633	22	equations	equation	NOUN
ejde-397	1633	23	,	,	PUNCT
ejde-397	1633	24	elsevier	elsevier	PROPN
ejde-397	1633	25	science	science	PROPN
ejde-397	1633	26	b.v	b.v	PROPN
ejde-397	1633	27	.	.	PROPN
ejde-397	1633	28	,	,	PUNCT
ejde-397	1633	29	amsterdam	amsterdam	PROPN
ejde-397	1633	30	,	,	PUNCT
ejde-397	1633	31	2006	2006	NUM
ejde-397	1633	32	.	.	PUNCT
ejde-397	1634	1	[	[	X
ejde-397	1634	2	31	31	NUM
ejde-397	1634	3	]	]	PUNCT
ejde-397	1634	4	m.	m.	NOUN
ejde-397	1634	5	kim	kim	PROPN
ejde-397	1634	6	,	,	PUNCT
ejde-397	1634	7	volterra	volterra	NOUN
ejde-397	1634	8	inclusions	inclusion	NOUN
ejde-397	1634	9	in	in	ADP
ejde-397	1634	10	banach	banach	NOUN
ejde-397	1634	11	spaces	space	NOUN
ejde-397	1634	12	,	,	PUNCT
ejde-397	1634	13	rocky	rocky	ADJ
ejde-397	1634	14	mountain	mountain	NOUN
ejde-397	1634	15	j.	j.	PROPN
ejde-397	1634	16	math	math	PROPN
ejde-397	1634	17	.	.	PUNCT
ejde-397	1634	18	,	,	PUNCT
ejde-397	1634	19	32(1	32(1	NUM
ejde-397	1634	20	)	)	PUNCT
ejde-397	1634	21	(	(	PUNCT
ejde-397	1634	22	2002	2002	NUM
ejde-397	1634	23	)	)	PUNCT
ejde-397	1634	24	,	,	PUNCT
ejde-397	1634	25	167–178	167–178	NUM
ejde-397	1634	26	.	.	PUNCT
ejde-397	1635	1	[	[	X
ejde-397	1635	2	32	32	NUM
ejde-397	1635	3	]	]	X
ejde-397	1635	4	c.	c.	PROPN
ejde-397	1635	5	knuckles	knuckles	PROPN
ejde-397	1635	6	,	,	PUNCT
ejde-397	1635	7	f.	f.	PROPN
ejde-397	1635	8	neubrander	neubrander	PROPN
ejde-397	1635	9	;	;	PUNCT
ejde-397	1635	10	remarks	remark	NOUN
ejde-397	1635	11	on	on	ADP
ejde-397	1635	12	the	the	DET
ejde-397	1635	13	cauchy	cauchy	ADJ
ejde-397	1635	14	problem	problem	NOUN
ejde-397	1635	15	for	for	ADP
ejde-397	1635	16	multi	multi	ADJ
ejde-397	1635	17	-	-	ADJ
ejde-397	1635	18	valued	value	VERB
ejde-397	1635	19	linear	linear	PROPN
ejde-397	1635	20	operators	operator	NOUN
ejde-397	1635	21	,	,	PUNCT
ejde-397	1635	22	https://www.math.lsu.edu/	https://www.math.lsu.edu/	PROPN
ejde-397	1635	23	neubrand	neubrand	NOUN
ejde-397	1635	24	/	/	SYM
ejde-397	1635	25	knne94.ps	knne94.ps	PROPN
ejde-397	1635	26	;	;	PUNCT
ejde-397	1635	27	in	in	ADP
ejde-397	1635	28	:	:	PUNCT
ejde-397	1635	29	partial	partial	ADJ
ejde-397	1635	30	differential	differential	NOUN
ejde-397	1635	31	equations	equation	NOUN
ejde-397	1635	32	(	(	PUNCT
ejde-397	1635	33	hansurlesse	hansurlesse	NOUN
ejde-397	1635	34	,	,	PUNCT
ejde-397	1635	35	1993	1993	NUM
ejde-397	1635	36	)	)	PUNCT
ejde-397	1635	37	,	,	PUNCT
ejde-397	1635	38	pages	page	NOUN
ejde-397	1635	39	174–187	174–187	NUM
ejde-397	1635	40	,	,	PUNCT
ejde-397	1635	41	akademie	akademie	PROPN
ejde-397	1635	42	-	-	PUNCT
ejde-397	1635	43	verlag	verlag	PROPN
ejde-397	1635	44	,	,	PUNCT
ejde-397	1635	45	berlin	berlin	PROPN
ejde-397	1635	46	,	,	PUNCT
ejde-397	1635	47	1994	1994	NUM
ejde-397	1635	48	.	.	PUNCT
ejde-397	1636	1	[	[	X
ejde-397	1636	2	33	33	NUM
ejde-397	1636	3	]	]	PUNCT
ejde-397	1636	4	h.	h.	PROPN
ejde-397	1636	5	komatsu	komatsu	PROPN
ejde-397	1636	6	;	;	PUNCT
ejde-397	1636	7	semi	semi	NOUN
ejde-397	1636	8	-	-	NOUN
ejde-397	1636	9	groups	group	NOUN
ejde-397	1636	10	of	of	ADP
ejde-397	1636	11	operators	operator	NOUN
ejde-397	1636	12	in	in	ADP
ejde-397	1636	13	locally	locally	ADV
ejde-397	1636	14	convex	convex	ADJ
ejde-397	1636	15	spaces	space	NOUN
ejde-397	1636	16	,	,	PUNCT
ejde-397	1636	17	j.	j.	PROPN
ejde-397	1636	18	math	math	PROPN
ejde-397	1636	19	.	.	PUNCT
ejde-397	1637	1	soc	soc	PROPN
ejde-397	1637	2	.	.	PUNCT
ejde-397	1638	1	japan	japan	PROPN
ejde-397	1638	2	,	,	PUNCT
ejde-397	1638	3	16	16	NUM
ejde-397	1638	4	(	(	PUNCT
ejde-397	1638	5	1964	1964	NUM
ejde-397	1638	6	)	)	PUNCT
ejde-397	1638	7	,	,	PUNCT
ejde-397	1638	8	230	230	NUM
ejde-397	1638	9	-	-	SYM
ejde-397	1638	10	262	262	NUM
ejde-397	1638	11	.	.	PUNCT
ejde-397	1639	1	[	[	X
ejde-397	1639	2	34	34	NUM
ejde-397	1639	3	]	]	X
ejde-397	1639	4	t.	t.	PROPN
ejde-397	1639	5	kōmura	kōmura	PROPN
ejde-397	1639	6	;	;	PUNCT
ejde-397	1639	7	semigroups	semigroup	NOUN
ejde-397	1639	8	of	of	ADP
ejde-397	1639	9	operators	operator	NOUN
ejde-397	1639	10	in	in	ADP
ejde-397	1639	11	locally	locally	ADV
ejde-397	1639	12	convex	convex	ADJ
ejde-397	1639	13	spaces	space	NOUN
ejde-397	1639	14	,	,	PUNCT
ejde-397	1639	15	j.	j.	PROPN
ejde-397	1639	16	funct	funct	PROPN
ejde-397	1639	17	.	.	PUNCT
ejde-397	1640	1	anal	anal	PROPN
ejde-397	1640	2	.	.	PROPN
ejde-397	1640	3	,	,	PUNCT
ejde-397	1640	4	2	2	NUM
ejde-397	1640	5	(	(	PUNCT
ejde-397	1640	6	1968	1968	NUM
ejde-397	1640	7	)	)	PUNCT
ejde-397	1640	8	,	,	PUNCT
ejde-397	1640	9	258	258	NUM
ejde-397	1640	10	-	-	SYM
ejde-397	1640	11	296	296	NUM
ejde-397	1640	12	.	.	PUNCT
ejde-397	1641	1	[	[	X
ejde-397	1641	2	35	35	NUM
ejde-397	1641	3	]	]	PUNCT
ejde-397	1641	4	m.	m.	NOUN
ejde-397	1641	5	kostić	kostić	NOUN
ejde-397	1641	6	;	;	PUNCT
ejde-397	1641	7	generalized	generalize	VERB
ejde-397	1641	8	semigroups	semigroup	NOUN
ejde-397	1641	9	and	and	CCONJ
ejde-397	1641	10	cosine	cosine	NOUN
ejde-397	1641	11	functions	function	NOUN
ejde-397	1641	12	,	,	PUNCT
ejde-397	1641	13	mathematical	mathematical	PROPN
ejde-397	1641	14	institute	institute	PROPN
ejde-397	1641	15	sanu	sanu	PROPN
ejde-397	1641	16	,	,	PUNCT
ejde-397	1641	17	belgrade	belgrade	PROPN
ejde-397	1641	18	,	,	PUNCT
ejde-397	1641	19	2011	2011	NUM
ejde-397	1641	20	.	.	PUNCT
ejde-397	1642	1	[	[	X
ejde-397	1642	2	36	36	NUM
ejde-397	1642	3	]	]	PUNCT
ejde-397	1642	4	m.	m.	NOUN
ejde-397	1642	5	kostić	kostić	NOUN
ejde-397	1642	6	;	;	PUNCT
ejde-397	1642	7	abstract	abstract	PROPN
ejde-397	1642	8	volterra	volterra	NOUN
ejde-397	1642	9	integro	integro	PROPN
ejde-397	1642	10	-	-	PUNCT
ejde-397	1642	11	differential	differential	NOUN
ejde-397	1642	12	equations	equation	NOUN
ejde-397	1642	13	,	,	PUNCT
ejde-397	1642	14	taylor	taylor	PROPN
ejde-397	1642	15	and	and	CCONJ
ejde-397	1642	16	francis	francis	PROPN
ejde-397	1642	17	group	group	PROPN
ejde-397	1642	18	/	/	SYM
ejde-397	1642	19	crc	crc	PROPN
ejde-397	1642	20	press	press	NOUN
ejde-397	1642	21	/	/	SYM
ejde-397	1642	22	science	science	NOUN
ejde-397	1642	23	publishers	publisher	NOUN
ejde-397	1642	24	,	,	PUNCT
ejde-397	1642	25	boca	boca	PROPN
ejde-397	1642	26	raton	raton	PROPN
ejde-397	1642	27	,	,	PUNCT
ejde-397	1642	28	fl	fl	PROPN
ejde-397	1642	29	,	,	PUNCT
ejde-397	1642	30	2015	2015	NUM
ejde-397	1642	31	.	.	PUNCT
ejde-397	1643	1	[	[	X
ejde-397	1643	2	37	37	NUM
ejde-397	1643	3	]	]	PUNCT
ejde-397	1643	4	m.	m.	NOUN
ejde-397	1643	5	kostić	kostić	NOUN
ejde-397	1643	6	;	;	PUNCT
ejde-397	1643	7	almost	almost	ADV
ejde-397	1643	8	periodic	periodic	ADJ
ejde-397	1643	9	and	and	CCONJ
ejde-397	1643	10	almost	almost	ADV
ejde-397	1643	11	automorphic	automorphic	ADJ
ejde-397	1643	12	solutions	solution	NOUN
ejde-397	1643	13	to	to	ADP
ejde-397	1643	14	integro	integro	ADJ
ejde-397	1643	15	-	-	PUNCT
ejde-397	1643	16	differential	differential	NOUN
ejde-397	1643	17	equations	equation	NOUN
ejde-397	1643	18	,	,	PUNCT
ejde-397	1643	19	w.	w.	PROPN
ejde-397	1643	20	de	de	PROPN
ejde-397	1643	21	gruyter	gruyter	PROPN
ejde-397	1643	22	,	,	PUNCT
ejde-397	1643	23	berlin	berlin	PROPN
ejde-397	1643	24	,	,	PUNCT
ejde-397	1643	25	2019	2019	NUM
ejde-397	1643	26	.	.	PUNCT
ejde-397	1644	1	[	[	X
ejde-397	1644	2	38	38	NUM
ejde-397	1644	3	]	]	PUNCT
ejde-397	1644	4	m.	m.	NOUN
ejde-397	1644	5	kostić	kostić	NOUN
ejde-397	1644	6	;	;	PUNCT
ejde-397	1644	7	abstract	abstract	ADJ
ejde-397	1644	8	degenerate	degenerate	PROPN
ejde-397	1644	9	volterra	volterra	PROPN
ejde-397	1644	10	integro	integro	PROPN
ejde-397	1644	11	-	-	PUNCT
ejde-397	1644	12	differential	differential	NOUN
ejde-397	1644	13	equations	equation	NOUN
ejde-397	1644	14	,	,	PUNCT
ejde-397	1644	15	mathematical	mathematical	PROPN
ejde-397	1644	16	institute	institute	PROPN
ejde-397	1644	17	sanu	sanu	PROPN
ejde-397	1644	18	,	,	PUNCT
ejde-397	1644	19	belgrade	belgrade	PROPN
ejde-397	1644	20	,	,	PUNCT
ejde-397	1644	21	2020	2020	NUM
ejde-397	1644	22	.	.	PUNCT
ejde-397	1645	1	[	[	X
ejde-397	1645	2	39	39	NUM
ejde-397	1645	3	]	]	PUNCT
ejde-397	1645	4	m.	m.	NOUN
ejde-397	1645	5	kostić	kostić	NOUN
ejde-397	1645	6	;	;	PUNCT
ejde-397	1645	7	(	(	PUNCT
ejde-397	1645	8	a	a	PRON
ejde-397	1645	9	,	,	PUNCT
ejde-397	1645	10	k)-regularized	k)-regularize	VERB
ejde-397	1645	11	c	c	NOUN
ejde-397	1645	12	-	-	PUNCT
ejde-397	1645	13	resolvent	resolvent	ADJ
ejde-397	1645	14	families	family	NOUN
ejde-397	1645	15	:	:	PUNCT
ejde-397	1645	16	regularity	regularity	NOUN
ejde-397	1645	17	and	and	CCONJ
ejde-397	1645	18	local	local	ADJ
ejde-397	1645	19	properties	property	NOUN
ejde-397	1645	20	,	,	PUNCT
ejde-397	1645	21	abstr	abstr	PROPN
ejde-397	1645	22	.	.	PUNCT
ejde-397	1646	1	appl	appl	PROPN
ejde-397	1646	2	.	.	PUNCT
ejde-397	1647	1	anal	anal	PROPN
ejde-397	1647	2	.	.	PUNCT
ejde-397	1647	3	,	,	PUNCT
ejde-397	1647	4	vol	vol	NOUN
ejde-397	1647	5	.	.	PROPN
ejde-397	1647	6	2009	2009	NUM
ejde-397	1647	7	,	,	PUNCT
ejde-397	1647	8	article	article	NOUN
ejde-397	1647	9	i	i	PROPN
ejde-397	1647	10	d	d	PROPN
ejde-397	1647	11	858242	858242	NUM
ejde-397	1647	12	,	,	PUNCT
ejde-397	1647	13	27	27	NUM
ejde-397	1647	14	pages	page	NOUN
ejde-397	1647	15	,	,	PUNCT
ejde-397	1647	16	2009	2009	NUM
ejde-397	1647	17	.	.	PUNCT
ejde-397	1648	1	[	[	X
ejde-397	1648	2	40	40	NUM
ejde-397	1648	3	]	]	PUNCT
ejde-397	1648	4	m.	m.	NOUN
ejde-397	1648	5	kostić	kostić	NOUN
ejde-397	1648	6	;	;	PUNCT
ejde-397	1648	7	abstract	abstract	ADJ
ejde-397	1648	8	time	time	NOUN
ejde-397	1648	9	-	-	PUNCT
ejde-397	1648	10	fractional	fractional	ADJ
ejde-397	1648	11	equations	equation	NOUN
ejde-397	1648	12	:	:	PUNCT
ejde-397	1648	13	existence	existence	NOUN
ejde-397	1648	14	and	and	CCONJ
ejde-397	1648	15	growth	growth	NOUN
ejde-397	1648	16	of	of	ADP
ejde-397	1648	17	solutions	solution	NOUN
ejde-397	1648	18	,	,	PUNCT
ejde-397	1648	19	fract	fract	NOUN
ejde-397	1648	20	.	.	PUNCT
ejde-397	1649	1	calc	calc	PROPN
ejde-397	1649	2	.	.	PUNCT
ejde-397	1650	1	appl	appl	PROPN
ejde-397	1650	2	.	.	PUNCT
ejde-397	1651	1	anal	anal	PROPN
ejde-397	1651	2	.	.	PROPN
ejde-397	1651	3	,	,	PUNCT
ejde-397	1651	4	14(2	14(2	NUM
ejde-397	1651	5	)	)	PUNCT
ejde-397	1651	6	(	(	PUNCT
ejde-397	1651	7	2011	2011	NUM
ejde-397	1651	8	)	)	PUNCT
ejde-397	1651	9	,	,	PUNCT
ejde-397	1651	10	301	301	NUM
ejde-397	1651	11	-	-	SYM
ejde-397	1651	12	316	316	NUM
ejde-397	1651	13	.	.	PUNCT
ejde-397	1652	1	[	[	X
ejde-397	1652	2	41	41	NUM
ejde-397	1652	3	]	]	PUNCT
ejde-397	1652	4	m.	m.	NOUN
ejde-397	1652	5	kostić	kostić	NOUN
ejde-397	1652	6	;	;	PUNCT
ejde-397	1652	7	abstract	abstract	ADJ
ejde-397	1652	8	volterra	volterra	NOUN
ejde-397	1652	9	equations	equation	NOUN
ejde-397	1652	10	in	in	ADP
ejde-397	1652	11	locally	locally	ADV
ejde-397	1652	12	convex	convex	ADJ
ejde-397	1652	13	spaces	space	NOUN
ejde-397	1652	14	,	,	PUNCT
ejde-397	1652	15	sci	sci	PROPN
ejde-397	1652	16	.	.	PUNCT
ejde-397	1653	1	china	china	PROPN
ejde-397	1653	2	math	math	PROPN
ejde-397	1653	3	.	.	PUNCT
ejde-397	1653	4	,	,	PUNCT
ejde-397	1653	5	55(1	55(1	NUM
ejde-397	1653	6	)	)	PUNCT
ejde-397	1653	7	(	(	PUNCT
ejde-397	1653	8	2012	2012	NUM
ejde-397	1653	9	)	)	PUNCT
ejde-397	1653	10	,	,	PUNCT
ejde-397	1653	11	1797	1797	NUM
ejde-397	1653	12	-	-	SYM
ejde-397	1653	13	1825	1825	NUM
ejde-397	1653	14	.	.	PUNCT
ejde-397	1654	1	[	[	X
ejde-397	1654	2	42	42	NUM
ejde-397	1654	3	]	]	PUNCT
ejde-397	1654	4	m.	m.	NOUN
ejde-397	1654	5	kostić	kostić	NOUN
ejde-397	1654	6	;	;	PUNCT
ejde-397	1654	7	degenerate	degenerate	ADJ
ejde-397	1654	8	k	k	NOUN
ejde-397	1654	9	-	-	ADJ
ejde-397	1654	10	regularized	regularized	ADJ
ejde-397	1654	11	(	(	PUNCT
ejde-397	1654	12	c1	c1	NOUN
ejde-397	1654	13	,	,	PUNCT
ejde-397	1654	14	c2)-existence	c2)-existence	NOUN
ejde-397	1654	15	and	and	CCONJ
ejde-397	1654	16	uniqueness	uniqueness	NOUN
ejde-397	1654	17	families	family	NOUN
ejde-397	1654	18	,	,	PUNCT
ejde-397	1654	19	cubo	cubo	NOUN
ejde-397	1654	20	,	,	PUNCT
ejde-397	1654	21	17(03	17(03	PROPN
ejde-397	1654	22	)	)	PUNCT
ejde-397	1654	23	(	(	PUNCT
ejde-397	1654	24	2015	2015	NUM
ejde-397	1654	25	)	)	PUNCT
ejde-397	1654	26	,	,	PUNCT
ejde-397	1654	27	15	15	NUM
ejde-397	1654	28	-	-	SYM
ejde-397	1654	29	41	41	NUM
ejde-397	1654	30	.	.	PUNCT
ejde-397	1655	1	[	[	X
ejde-397	1655	2	43	43	NUM
ejde-397	1655	3	]	]	PUNCT
ejde-397	1655	4	m.	m.	NOUN
ejde-397	1655	5	kostić	kostić	NOUN
ejde-397	1655	6	;	;	PUNCT
ejde-397	1655	7	abstract	abstract	ADJ
ejde-397	1655	8	degenerate	degenerate	ADJ
ejde-397	1655	9	non	non	ADJ
ejde-397	1655	10	-	-	ADJ
ejde-397	1655	11	scalar	scalar	ADJ
ejde-397	1655	12	volterra	volterra	NOUN
ejde-397	1655	13	equation	equation	NOUN
ejde-397	1655	14	,	,	PUNCT
ejde-397	1655	15	chelyabinsk	chelyabinsk	PROPN
ejde-397	1655	16	phy	phy	PROPN
ejde-397	1655	17	.	.	PROPN
ejde-397	1655	18	math	math	PROPN
ejde-397	1655	19	.	.	PUNCT
ejde-397	1656	1	j.	j.	PROPN
ejde-397	1656	2	,	,	PUNCT
ejde-397	1656	3	1(1	1(1	NUM
ejde-397	1656	4	)	)	PUNCT
ejde-397	1656	5	(	(	PUNCT
ejde-397	1656	6	2016	2016	NUM
ejde-397	1656	7	)	)	PUNCT
ejde-397	1656	8	,	,	PUNCT
ejde-397	1656	9	99	99	NUM
ejde-397	1656	10	-	-	SYM
ejde-397	1656	11	106	106	NUM
ejde-397	1656	12	.	.	PUNCT
ejde-397	1657	1	[	[	X
ejde-397	1657	2	44	44	NUM
ejde-397	1657	3	]	]	PUNCT
ejde-397	1657	4	m.	m.	NOUN
ejde-397	1657	5	kostić	kostić	NOUN
ejde-397	1657	6	;	;	PUNCT
ejde-397	1657	7	on	on	ADP
ejde-397	1657	8	entire	entire	ADJ
ejde-397	1657	9	solutions	solution	NOUN
ejde-397	1657	10	of	of	ADP
ejde-397	1657	11	abstract	abstract	ADJ
ejde-397	1657	12	degenerate	degenerate	ADJ
ejde-397	1657	13	differential	differential	ADJ
ejde-397	1657	14	equations	equation	NOUN
ejde-397	1657	15	of	of	ADP
ejde-397	1657	16	higher	high	ADJ
ejde-397	1657	17	order	order	NOUN
ejde-397	1657	18	,	,	PUNCT
ejde-397	1657	19	funct	funct	ADJ
ejde-397	1657	20	.	.	PUNCT
ejde-397	1658	1	anal	anal	PROPN
ejde-397	1658	2	.	.	PUNCT
ejde-397	1659	1	approx	approx	PROPN
ejde-397	1659	2	.	.	PUNCT
ejde-397	1660	1	comput	comput	PROPN
ejde-397	1660	2	.	.	PUNCT
ejde-397	1660	3	,	,	PUNCT
ejde-397	1660	4	8(1	8(1	NUM
ejde-397	1660	5	)	)	PUNCT
ejde-397	1660	6	(	(	PUNCT
ejde-397	1660	7	2016	2016	NUM
ejde-397	1660	8	)	)	PUNCT
ejde-397	1660	9	,	,	PUNCT
ejde-397	1660	10	51	51	NUM
ejde-397	1660	11	-	-	SYM
ejde-397	1660	12	60	60	NUM
ejde-397	1660	13	.	.	PUNCT
ejde-397	1661	1	[	[	X
ejde-397	1661	2	45	45	NUM
ejde-397	1661	3	]	]	PUNCT
ejde-397	1661	4	m.	m.	NOUN
ejde-397	1661	5	kostić	kostić	NOUN
ejde-397	1661	6	;	;	PUNCT
ejde-397	1661	7	degenerate	degenerate	ADJ
ejde-397	1661	8	abstract	abstract	ADJ
ejde-397	1661	9	volterra	volterra	NOUN
ejde-397	1661	10	equations	equation	NOUN
ejde-397	1661	11	in	in	ADP
ejde-397	1661	12	locally	locally	ADV
ejde-397	1661	13	convex	convex	ADJ
ejde-397	1661	14	spaces	space	NOUN
ejde-397	1661	15	,	,	PUNCT
ejde-397	1661	16	filomat	filomat	NOUN
ejde-397	1661	17	,	,	PUNCT
ejde-397	1661	18	31(3	31(3	NUM
ejde-397	1661	19	)	)	PUNCT
ejde-397	1661	20	(	(	PUNCT
ejde-397	1661	21	2017	2017	NUM
ejde-397	1661	22	)	)	PUNCT
ejde-397	1661	23	,	,	PUNCT
ejde-397	1661	24	597	597	NUM
ejde-397	1661	25	-	-	SYM
ejde-397	1661	26	619	619	NUM
ejde-397	1661	27	.	.	PUNCT
ejde-397	1662	1	[	[	X
ejde-397	1662	2	46	46	NUM
ejde-397	1662	3	]	]	PUNCT
ejde-397	1662	4	m.	m.	NOUN
ejde-397	1662	5	kostić	kostić	NOUN
ejde-397	1662	6	;	;	PUNCT
ejde-397	1662	7	degenerate	degenerate	ADJ
ejde-397	1662	8	multi	multi	ADJ
ejde-397	1662	9	-	-	ADJ
ejde-397	1662	10	term	term	ADJ
ejde-397	1662	11	fractional	fractional	ADJ
ejde-397	1662	12	differential	differential	NOUN
ejde-397	1662	13	equations	equation	NOUN
ejde-397	1662	14	in	in	ADP
ejde-397	1662	15	locally	locally	ADV
ejde-397	1662	16	convex	convex	ADJ
ejde-397	1662	17	spaces	space	NOUN
ejde-397	1662	18	,	,	PUNCT
ejde-397	1662	19	publ	publ	PROPN
ejde-397	1662	20	.	.	PUNCT
ejde-397	1663	1	inst	inst	PROPN
ejde-397	1663	2	.	.	PUNCT
ejde-397	1664	1	math	math	NOUN
ejde-397	1664	2	.	.	PUNCT
ejde-397	1665	1	,	,	PUNCT
ejde-397	1665	2	nouv	nouv	NOUN
ejde-397	1665	3	.	.	PUNCT
ejde-397	1666	1	sér	sér	PROPN
ejde-397	1666	2	.	.	PUNCT
ejde-397	1666	3	,	,	PUNCT
ejde-397	1666	4	100(114	100(114	NUM
ejde-397	1666	5	)	)	PUNCT
ejde-397	1666	6	(	(	PUNCT
ejde-397	1666	7	2016	2016	NUM
ejde-397	1666	8	)	)	PUNCT
ejde-397	1666	9	,	,	PUNCT
ejde-397	1666	10	49	49	NUM
ejde-397	1666	11	-	-	SYM
ejde-397	1666	12	75	75	NUM
ejde-397	1666	13	.	.	PUNCT
ejde-397	1667	1	54	54	NUM
ejde-397	1667	2	m.	m.	NOUN
ejde-397	1667	3	kostić	kostić	NOUN
ejde-397	1667	4	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1668	1	[	[	X
ejde-397	1668	2	47	47	NUM
ejde-397	1668	3	]	]	PUNCT
ejde-397	1668	4	m.	m.	NOUN
ejde-397	1668	5	kostić	kostić	NOUN
ejde-397	1668	6	;	;	PUNCT
ejde-397	1668	7	on	on	ADP
ejde-397	1668	8	a	a	DET
ejde-397	1668	9	class	class	NOUN
ejde-397	1668	10	of	of	ADP
ejde-397	1668	11	abstract	abstract	ADJ
ejde-397	1668	12	degenerate	degenerate	ADJ
ejde-397	1668	13	fractional	fractional	ADJ
ejde-397	1668	14	differential	differential	ADJ
ejde-397	1668	15	equations	equation	NOUN
ejde-397	1668	16	of	of	ADP
ejde-397	1668	17	parabolic	parabolic	ADJ
ejde-397	1668	18	type	type	NOUN
ejde-397	1668	19	,	,	PUNCT
ejde-397	1668	20	comment	comment	NOUN
ejde-397	1668	21	.	.	PUNCT
ejde-397	1669	1	math	math	NOUN
ejde-397	1669	2	.	.	PUNCT
ejde-397	1670	1	univ	univ	PROPN
ejde-397	1670	2	.	.	PUNCT
ejde-397	1671	1	carolin	carolin	PROPN
ejde-397	1671	2	.	.	PROPN
ejde-397	1672	1	,	,	PUNCT
ejde-397	1672	2	59(1	59(1	NUM
ejde-397	1672	3	)	)	PUNCT
ejde-397	1672	4	(	(	PUNCT
ejde-397	1672	5	2018	2018	NUM
ejde-397	1672	6	)	)	PUNCT
ejde-397	1672	7	,	,	PUNCT
ejde-397	1672	8	81	81	NUM
ejde-397	1672	9	-	-	SYM
ejde-397	1672	10	101	101	NUM
ejde-397	1672	11	.	.	PUNCT
ejde-397	1673	1	[	[	X
ejde-397	1673	2	48	48	NUM
ejde-397	1673	3	]	]	PUNCT
ejde-397	1673	4	m.	m.	NOUN
ejde-397	1673	5	kostić	kostić	NOUN
ejde-397	1673	6	;	;	PUNCT
ejde-397	1673	7	abstract	abstract	ADJ
ejde-397	1673	8	degenerate	degenerate	ADJ
ejde-397	1673	9	fractional	fractional	ADJ
ejde-397	1673	10	differential	differential	ADJ
ejde-397	1673	11	inclusions	inclusion	NOUN
ejde-397	1673	12	,	,	PUNCT
ejde-397	1673	13	appl	appl	PROPN
ejde-397	1673	14	.	.	PROPN
ejde-397	1674	1	anal	anal	PROPN
ejde-397	1674	2	.	.	PUNCT
ejde-397	1675	1	discrete	discrete	ADJ
ejde-397	1675	2	math	math	NOUN
ejde-397	1675	3	.	.	PUNCT
ejde-397	1675	4	,	,	PUNCT
ejde-397	1675	5	11(1	11(1	NUM
ejde-397	1675	6	)	)	PUNCT
ejde-397	1675	7	(	(	PUNCT
ejde-397	1675	8	2017	2017	NUM
ejde-397	1675	9	)	)	PUNCT
ejde-397	1675	10	,	,	PUNCT
ejde-397	1675	11	39	39	NUM
ejde-397	1675	12	-	-	SYM
ejde-397	1675	13	61	61	NUM
ejde-397	1675	14	.	.	PUNCT
ejde-397	1676	1	[	[	X
ejde-397	1676	2	49	49	NUM
ejde-397	1676	3	]	]	PUNCT
ejde-397	1676	4	m.	m.	NOUN
ejde-397	1676	5	kostić	kostić	NOUN
ejde-397	1676	6	;	;	PUNCT
ejde-397	1676	7	some	some	DET
ejde-397	1676	8	contributions	contribution	NOUN
ejde-397	1676	9	to	to	ADP
ejde-397	1676	10	the	the	DET
ejde-397	1676	11	theory	theory	NOUN
ejde-397	1676	12	of	of	ADP
ejde-397	1676	13	abstract	abstract	ADJ
ejde-397	1676	14	degenerate	degenerate	ADJ
ejde-397	1676	15	volterra	volterra	PROPN
ejde-397	1676	16	integrodifferential	integrodifferential	PROPN
ejde-397	1676	17	equations	equation	NOUN
ejde-397	1676	18	,	,	PUNCT
ejde-397	1676	19	j.	j.	PROPN
ejde-397	1676	20	math	math	PROPN
ejde-397	1676	21	.	.	PUNCT
ejde-397	1677	1	stat	stat	PROPN
ejde-397	1677	2	.	.	PUNCT
ejde-397	1677	3	,	,	PUNCT
ejde-397	1677	4	12(2	12(2	NUM
ejde-397	1677	5	)	)	PUNCT
ejde-397	1677	6	(	(	PUNCT
ejde-397	1677	7	2016	2016	NUM
ejde-397	1677	8	)	)	PUNCT
ejde-397	1677	9	,	,	PUNCT
ejde-397	1677	10	65	65	NUM
ejde-397	1677	11	-	-	SYM
ejde-397	1677	12	76	76	NUM
ejde-397	1677	13	.	.	PUNCT
ejde-397	1678	1	[	[	X
ejde-397	1678	2	50	50	NUM
ejde-397	1678	3	]	]	PUNCT
ejde-397	1678	4	m.	m.	NOUN
ejde-397	1678	5	kostić	kostić	NOUN
ejde-397	1678	6	,	,	PUNCT
ejde-397	1678	7	;	;	PUNCT
ejde-397	1678	8	degenerate	degenerate	ADJ
ejde-397	1678	9	k	k	ADV
ejde-397	1678	10	-	-	ADJ
ejde-397	1678	11	convoluted	convoluted	ADJ
ejde-397	1678	12	c	c	NOUN
ejde-397	1678	13	-	-	PUNCT
ejde-397	1678	14	semigroups	semigroup	NOUN
ejde-397	1678	15	and	and	CCONJ
ejde-397	1678	16	degenerate	degenerate	ADJ
ejde-397	1678	17	k	k	ADV
ejde-397	1678	18	-	-	ADJ
ejde-397	1678	19	convoluted	convoluted	ADJ
ejde-397	1678	20	c	c	NOUN
ejde-397	1678	21	-	-	PUNCT
ejde-397	1678	22	cosine	cosine	NOUN
ejde-397	1678	23	functions	function	NOUN
ejde-397	1678	24	in	in	ADP
ejde-397	1678	25	locally	locally	ADV
ejde-397	1678	26	convex	convex	ADJ
ejde-397	1678	27	spaces	space	NOUN
ejde-397	1678	28	,	,	PUNCT
ejde-397	1678	29	chelyabinsk	chelyabinsk	PROPN
ejde-397	1678	30	phy	phy	PROPN
ejde-397	1678	31	.	.	PROPN
ejde-397	1678	32	math	math	PROPN
ejde-397	1678	33	.	.	PUNCT
ejde-397	1679	1	j.	j.	PROPN
ejde-397	1679	2	,	,	PUNCT
ejde-397	1679	3	3(1	3(1	NUM
ejde-397	1679	4	)	)	PUNCT
ejde-397	1679	5	(	(	PUNCT
ejde-397	1679	6	2018	2018	NUM
ejde-397	1679	7	)	)	PUNCT
ejde-397	1679	8	,	,	PUNCT
ejde-397	1679	9	90	90	NUM
ejde-397	1679	10	-	-	SYM
ejde-397	1679	11	110	110	NUM
ejde-397	1679	12	.	.	PUNCT
ejde-397	1680	1	[	[	X
ejde-397	1680	2	51	51	NUM
ejde-397	1680	3	]	]	PUNCT
ejde-397	1680	4	m.	m.	NOUN
ejde-397	1680	5	kostić	kostić	NOUN
ejde-397	1680	6	;	;	PUNCT
ejde-397	1680	7	perturbation	perturbation	NOUN
ejde-397	1680	8	results	result	NOUN
ejde-397	1680	9	for	for	ADP
ejde-397	1680	10	abstract	abstract	ADJ
ejde-397	1680	11	degenerate	degenerate	ADJ
ejde-397	1680	12	volterra	volterra	PROPN
ejde-397	1680	13	integro	integro	PROPN
ejde-397	1680	14	-	-	PUNCT
ejde-397	1680	15	differential	differential	NOUN
ejde-397	1680	16	equations	equation	NOUN
ejde-397	1680	17	,	,	PUNCT
ejde-397	1680	18	j.	j.	PROPN
ejde-397	1680	19	fract	fract	PROPN
ejde-397	1680	20	.	.	PUNCT
ejde-397	1681	1	calc	calc	PROPN
ejde-397	1681	2	.	.	PUNCT
ejde-397	1682	1	appl	appl	PROPN
ejde-397	1682	2	.	.	PROPN
ejde-397	1682	3	,	,	PUNCT
ejde-397	1682	4	9(1	9(1	NUM
ejde-397	1682	5	)	)	PUNCT
ejde-397	1682	6	(	(	PUNCT
ejde-397	1682	7	2018	2018	NUM
ejde-397	1682	8	)	)	PUNCT
ejde-397	1682	9	,	,	PUNCT
ejde-397	1682	10	237	237	NUM
ejde-397	1682	11	-	-	SYM
ejde-397	1682	12	252	252	NUM
ejde-397	1682	13	.	.	PUNCT
ejde-397	1683	1	[	[	X
ejde-397	1683	2	52	52	NUM
ejde-397	1683	3	]	]	PUNCT
ejde-397	1683	4	m.	m.	NOUN
ejde-397	1683	5	kostić	kostić	NOUN
ejde-397	1683	6	;	;	PUNCT
ejde-397	1683	7	approximation	approximation	NOUN
ejde-397	1683	8	and	and	CCONJ
ejde-397	1683	9	convergence	convergence	NOUN
ejde-397	1683	10	of	of	ADP
ejde-397	1683	11	degenerate	degenerate	ADJ
ejde-397	1683	12	(	(	PUNCT
ejde-397	1683	13	a	a	PRON
ejde-397	1683	14	,	,	PUNCT
ejde-397	1683	15	k)-regularized	k)-regularize	VERB
ejde-397	1683	16	c	c	NOUN
ejde-397	1683	17	-	-	PUNCT
ejde-397	1683	18	resolvent	resolvent	ADJ
ejde-397	1683	19	families	family	NOUN
ejde-397	1683	20	,	,	PUNCT
ejde-397	1683	21	bull	bull	NOUN
ejde-397	1683	22	.	.	PUNCT
ejde-397	1684	1	cl	cl	NOUN
ejde-397	1684	2	.	.	PUNCT
ejde-397	1685	1	sci	sci	PROPN
ejde-397	1685	2	.	.	PUNCT
ejde-397	1685	3	math	math	PROPN
ejde-397	1685	4	.	.	PUNCT
ejde-397	1686	1	nat	nat	PROPN
ejde-397	1686	2	.	.	PUNCT
ejde-397	1687	1	sci	sci	PROPN
ejde-397	1687	2	.	.	PUNCT
ejde-397	1687	3	math	math	PROPN
ejde-397	1687	4	.	.	PUNCT
ejde-397	1688	1	,	,	PUNCT
ejde-397	1688	2	42	42	NUM
ejde-397	1688	3	(	(	PUNCT
ejde-397	1688	4	2017	2017	NUM
ejde-397	1688	5	)	)	PUNCT
ejde-397	1688	6	,	,	PUNCT
ejde-397	1688	7	69	69	NUM
ejde-397	1688	8	-	-	SYM
ejde-397	1688	9	83	83	NUM
ejde-397	1688	10	.	.	PUNCT
ejde-397	1689	1	[	[	X
ejde-397	1689	2	53	53	NUM
ejde-397	1689	3	]	]	PUNCT
ejde-397	1689	4	m.	m.	NOUN
ejde-397	1689	5	kostić	kostić	PROPN
ejde-397	1689	6	,	,	PUNCT
ejde-397	1689	7	s.	s.	PROPN
ejde-397	1689	8	pilipović	pilipović	PROPN
ejde-397	1689	9	,	,	PUNCT
ejde-397	1689	10	d.	d.	PROPN
ejde-397	1689	11	velinov	velinov	PROPN
ejde-397	1689	12	;	;	PUNCT
ejde-397	1689	13	c	c	X
ejde-397	1689	14	-	-	PUNCT
ejde-397	1689	15	distribution	distribution	NOUN
ejde-397	1689	16	semigroups	semigroup	NOUN
ejde-397	1689	17	and	and	CCONJ
ejde-397	1689	18	c	c	NOUN
ejde-397	1689	19	-	-	PUNCT
ejde-397	1689	20	ultradistribution	ultradistribution	NOUN
ejde-397	1689	21	semigroups	semigroup	NOUN
ejde-397	1689	22	in	in	ADP
ejde-397	1689	23	locally	locally	ADV
ejde-397	1689	24	convex	convex	ADJ
ejde-397	1689	25	spaces	space	NOUN
ejde-397	1689	26	,	,	PUNCT
ejde-397	1689	27	siberain	siberain	NOUN
ejde-397	1689	28	math	math	PROPN
ejde-397	1689	29	.	.	PUNCT
ejde-397	1690	1	j.	j.	PROPN
ejde-397	1690	2	,	,	PUNCT
ejde-397	1690	3	58(3	58(3	NUM
ejde-397	1690	4	)	)	PUNCT
ejde-397	1690	5	(	(	PUNCT
ejde-397	1690	6	2017	2017	NUM
ejde-397	1690	7	)	)	PUNCT
ejde-397	1690	8	,	,	PUNCT
ejde-397	1690	9	476	476	NUM
ejde-397	1690	10	-	-	SYM
ejde-397	1690	11	492	492	NUM
ejde-397	1690	12	.	.	PUNCT
ejde-397	1691	1	[	[	X
ejde-397	1691	2	54	54	NUM
ejde-397	1691	3	]	]	X
ejde-397	1691	4	c.-c	c.-c	NOUN
ejde-397	1691	5	.	.	PUNCT
ejde-397	1692	1	kuo	kuo	PROPN
ejde-397	1692	2	;	;	PUNCT
ejde-397	1692	3	local	local	ADJ
ejde-397	1692	4	k	k	ADV
ejde-397	1692	5	-	-	ADJ
ejde-397	1692	6	convoluted	convoluted	ADJ
ejde-397	1692	7	c	c	NOUN
ejde-397	1692	8	-	-	PUNCT
ejde-397	1692	9	semigroups	semigroup	NOUN
ejde-397	1692	10	and	and	CCONJ
ejde-397	1692	11	abstract	abstract	ADJ
ejde-397	1692	12	cauchy	cauchy	PROPN
ejde-397	1692	13	problems	problem	NOUN
ejde-397	1692	14	,	,	PUNCT
ejde-397	1692	15	taiwanese	taiwanese	PROPN
ejde-397	1692	16	j.	j.	PROPN
ejde-397	1692	17	math	math	PROPN
ejde-397	1692	18	.	.	PUNCT
ejde-397	1692	19	,	,	PUNCT
ejde-397	1692	20	19(4	19(4	PROPN
ejde-397	1692	21	)	)	PUNCT
ejde-397	1692	22	(	(	PUNCT
ejde-397	1692	23	2015	2015	NUM
ejde-397	1692	24	)	)	PUNCT
ejde-397	1692	25	,	,	PUNCT
ejde-397	1692	26	1227	1227	NUM
ejde-397	1692	27	-	-	SYM
ejde-397	1692	28	1245	1245	NUM
ejde-397	1692	29	.	.	PUNCT
ejde-397	1693	1	[	[	X
ejde-397	1693	2	55	55	NUM
ejde-397	1693	3	]	]	X
ejde-397	1693	4	c.-c	c.-c	NOUN
ejde-397	1693	5	.	.	PUNCT
ejde-397	1694	1	kuo	kuo	PROPN
ejde-397	1694	2	;	;	PUNCT
ejde-397	1694	3	local	local	ADJ
ejde-397	1694	4	k	k	ADV
ejde-397	1694	5	-	-	ADJ
ejde-397	1694	6	convoluted	convoluted	ADJ
ejde-397	1694	7	c	c	NOUN
ejde-397	1694	8	-	-	PUNCT
ejde-397	1694	9	cosine	cosine	NOUN
ejde-397	1694	10	functions	function	NOUN
ejde-397	1694	11	and	and	CCONJ
ejde-397	1694	12	abstract	abstract	ADJ
ejde-397	1694	13	cauchy	cauchy	PROPN
ejde-397	1694	14	problems	problem	NOUN
ejde-397	1694	15	,	,	PUNCT
ejde-397	1694	16	filomat	filomat	NOUN
ejde-397	1694	17	,	,	PUNCT
ejde-397	1694	18	30(9	30(9	NUM
ejde-397	1694	19	)	)	PUNCT
ejde-397	1694	20	(	(	PUNCT
ejde-397	1694	21	2016	2016	NUM
ejde-397	1694	22	)	)	PUNCT
ejde-397	1694	23	,	,	PUNCT
ejde-397	1694	24	2583	2583	NUM
ejde-397	1694	25	-	-	SYM
ejde-397	1694	26	2598	2598	NUM
ejde-397	1694	27	.	.	PUNCT
ejde-397	1695	1	[	[	X
ejde-397	1695	2	56	56	NUM
ejde-397	1695	3	]	]	PUNCT
ejde-397	1695	4	m.	m.	NOUN
ejde-397	1695	5	kunze	kunze	PROPN
ejde-397	1695	6	;	;	PUNCT
ejde-397	1695	7	a	a	DET
ejde-397	1695	8	pettis	pettis	NOUN
ejde-397	1695	9	-	-	PUNCT
ejde-397	1695	10	type	type	NOUN
ejde-397	1695	11	integral	integral	ADJ
ejde-397	1695	12	and	and	CCONJ
ejde-397	1695	13	applications	application	NOUN
ejde-397	1695	14	to	to	ADP
ejde-397	1695	15	transition	transition	NOUN
ejde-397	1695	16	semigroups	semigroup	NOUN
ejde-397	1695	17	,	,	PUNCT
ejde-397	1695	18	czechoslovak	czechoslovak	ADJ
ejde-397	1695	19	math	math	NOUN
ejde-397	1695	20	.	.	PUNCT
ejde-397	1696	1	j.	j.	PROPN
ejde-397	1696	2	,	,	PUNCT
ejde-397	1696	3	61(136	61(136	NOUN
ejde-397	1696	4	)	)	PUNCT
ejde-397	1696	5	(	(	PUNCT
ejde-397	1696	6	2011	2011	NUM
ejde-397	1696	7	)	)	PUNCT
ejde-397	1696	8	,	,	PUNCT
ejde-397	1696	9	437	437	NUM
ejde-397	1696	10	-	-	SYM
ejde-397	1696	11	459	459	NUM
ejde-397	1696	12	.	.	PUNCT
ejde-397	1697	1	[	[	X
ejde-397	1697	2	57	57	NUM
ejde-397	1697	3	]	]	PUNCT
ejde-397	1697	4	y.-c	y.-c	PROPN
ejde-397	1697	5	.	.	PUNCT
ejde-397	1698	1	li	li	PROPN
ejde-397	1698	2	,	,	PUNCT
ejde-397	1698	3	s.-y	s.-y	NOUN
ejde-397	1698	4	.	.	PUNCT
ejde-397	1699	1	shaw	shaw	PROPN
ejde-397	1699	2	;	;	PUNCT
ejde-397	1699	3	n	n	NUM
ejde-397	1699	4	-times	-time	NOUN
ejde-397	1699	5	integrated	integrate	VERB
ejde-397	1699	6	c	c	NOUN
ejde-397	1699	7	-	-	PUNCT
ejde-397	1699	8	semigroups	semigroup	NOUN
ejde-397	1699	9	and	and	CCONJ
ejde-397	1699	10	the	the	DET
ejde-397	1699	11	abstract	abstract	ADJ
ejde-397	1699	12	cauchy	cauchy	PROPN
ejde-397	1699	13	problem	problem	NOUN
ejde-397	1699	14	,	,	PUNCT
ejde-397	1699	15	taiwanese	taiwanese	PROPN
ejde-397	1699	16	j.	j.	PROPN
ejde-397	1699	17	math	math	PROPN
ejde-397	1699	18	.	.	PROPN
ejde-397	1699	19	,	,	PUNCT
ejde-397	1699	20	1(1	1(1	NUM
ejde-397	1699	21	)	)	PUNCT
ejde-397	1699	22	(	(	PUNCT
ejde-397	1699	23	1997	1997	NUM
ejde-397	1699	24	)	)	PUNCT
ejde-397	1699	25	,	,	PUNCT
ejde-397	1699	26	75	75	NUM
ejde-397	1699	27	-	-	SYM
ejde-397	1699	28	102	102	NUM
ejde-397	1699	29	.	.	PUNCT
ejde-397	1700	1	[	[	X
ejde-397	1700	2	58	58	NUM
ejde-397	1700	3	]	]	PUNCT
ejde-397	1700	4	y.-c	y.-c	PROPN
ejde-397	1700	5	.	.	PUNCT
ejde-397	1701	1	li	li	PROPN
ejde-397	1701	2	,	,	PUNCT
ejde-397	1701	3	s.-y	s.-y	NOUN
ejde-397	1701	4	.	.	PUNCT
ejde-397	1702	1	shaw	shaw	PROPN
ejde-397	1702	2	;	;	PUNCT
ejde-397	1702	3	on	on	ADP
ejde-397	1702	4	characterization	characterization	NOUN
ejde-397	1702	5	and	and	CCONJ
ejde-397	1702	6	perturbation	perturbation	NOUN
ejde-397	1702	7	of	of	ADP
ejde-397	1702	8	local	local	ADJ
ejde-397	1702	9	c	c	NOUN
ejde-397	1702	10	-	-	PUNCT
ejde-397	1702	11	semigroups	semigroup	NOUN
ejde-397	1702	12	,	,	PUNCT
ejde-397	1702	13	proc	proc	NOUN
ejde-397	1702	14	.	.	PUNCT
ejde-397	1703	1	amer	amer	PROPN
ejde-397	1703	2	.	.	PUNCT
ejde-397	1703	3	math	math	PROPN
ejde-397	1703	4	.	.	PUNCT
ejde-397	1704	1	soc	soc	PROPN
ejde-397	1704	2	.	.	PUNCT
ejde-397	1704	3	,	,	PUNCT
ejde-397	1704	4	135(4	135(4	NUM
ejde-397	1704	5	)	)	PUNCT
ejde-397	1704	6	(	(	PUNCT
ejde-397	1704	7	2007	2007	NUM
ejde-397	1704	8	)	)	PUNCT
ejde-397	1704	9	,	,	PUNCT
ejde-397	1704	10	1097	1097	NUM
ejde-397	1704	11	-	-	SYM
ejde-397	1704	12	1106	1106	NUM
ejde-397	1704	13	.	.	PUNCT
ejde-397	1705	1	[	[	X
ejde-397	1705	2	59	59	NUM
ejde-397	1705	3	]	]	PUNCT
ejde-397	1705	4	c.	c.	PROPN
ejde-397	1705	5	lizama	lizama	NOUN
ejde-397	1705	6	;	;	PUNCT
ejde-397	1705	7	regularized	regularize	VERB
ejde-397	1705	8	solutions	solution	NOUN
ejde-397	1705	9	for	for	ADP
ejde-397	1705	10	abstract	abstract	ADJ
ejde-397	1705	11	volterra	volterra	PROPN
ejde-397	1705	12	equations	equation	NOUN
ejde-397	1705	13	,	,	PUNCT
ejde-397	1705	14	j.	j.	PROPN
ejde-397	1705	15	math	math	PROPN
ejde-397	1705	16	.	.	PUNCT
ejde-397	1706	1	anal	anal	PROPN
ejde-397	1706	2	.	.	PUNCT
ejde-397	1707	1	appl	appl	PROPN
ejde-397	1707	2	.	.	PROPN
ejde-397	1707	3	,	,	PUNCT
ejde-397	1707	4	243(2	243(2	NUM
ejde-397	1707	5	)	)	PUNCT
ejde-397	1707	6	(	(	PUNCT
ejde-397	1707	7	2000	2000	NUM
ejde-397	1707	8	)	)	PUNCT
ejde-397	1707	9	,	,	PUNCT
ejde-397	1708	1	278–292	278–292	NUM
ejde-397	1708	2	.	.	PUNCT
ejde-397	1709	1	[	[	X
ejde-397	1709	2	60	60	NUM
ejde-397	1709	3	]	]	X
ejde-397	1709	4	r.	r.	PROPN
ejde-397	1709	5	madbouly	madbouly	PROPN
ejde-397	1709	6	,	,	PUNCT
ejde-397	1709	7	a.	a.	NOUN
ejde-397	1709	8	g.	g.	PROPN
ejde-397	1709	9	radwan	radwan	PROPN
ejde-397	1709	10	,	,	PUNCT
ejde-397	1709	11	r.	r.	PROPN
ejde-397	1709	12	a.	a.	PROPN
ejde-397	1709	13	el	el	PROPN
ejde-397	1709	14	barkouky	barkouky	NOUN
ejde-397	1709	15	;	;	PUNCT
ejde-397	1709	16	on	on	ADP
ejde-397	1709	17	some	some	DET
ejde-397	1709	18	fractional	fractional	ADJ
ejde-397	1709	19	-	-	PUNCT
ejde-397	1709	20	order	order	NOUN
ejde-397	1709	21	electromagnetic	electromagnetic	ADJ
ejde-397	1709	22	problems	problem	NOUN
ejde-397	1709	23	,	,	PUNCT
ejde-397	1709	24	lambert	lambert	PROPN
ejde-397	1709	25	academic	academic	ADJ
ejde-397	1709	26	publishing	publishing	NOUN
ejde-397	1709	27	,	,	PUNCT
ejde-397	1709	28	2015	2015	NUM
ejde-397	1709	29	.	.	PUNCT
ejde-397	1710	1	[	[	X
ejde-397	1710	2	61	61	NUM
ejde-397	1710	3	]	]	X
ejde-397	1710	4	c.	c.	PROPN
ejde-397	1710	5	martinez	martinez	PROPN
ejde-397	1710	6	,	,	PUNCT
ejde-397	1710	7	m.	m.	PROPN
ejde-397	1710	8	sanz	sanz	PROPN
ejde-397	1710	9	;	;	PUNCT
ejde-397	1710	10	the	the	DET
ejde-397	1710	11	theory	theory	NOUN
ejde-397	1710	12	of	of	ADP
ejde-397	1710	13	fractional	fractional	ADJ
ejde-397	1710	14	powers	power	NOUN
ejde-397	1710	15	of	of	ADP
ejde-397	1710	16	operators	operator	NOUN
ejde-397	1710	17	,	,	PUNCT
ejde-397	1710	18	north	north	PROPN
ejde-397	1710	19	–	–	PUNCT
ejde-397	1710	20	holland	holland	PROPN
ejde-397	1710	21	math	math	PROPN
ejde-397	1710	22	.	.	PUNCT
ejde-397	1710	23	stud	stud	PROPN
ejde-397	1710	24	.	.	PUNCT
ejde-397	1711	1	187	187	NUM
ejde-397	1711	2	,	,	PUNCT
ejde-397	1711	3	elseiver	elseiver	NOUN
ejde-397	1711	4	,	,	PUNCT
ejde-397	1711	5	amsterdam	amsterdam	PROPN
ejde-397	1711	6	,	,	PUNCT
ejde-397	1711	7	2001	2001	NUM
ejde-397	1711	8	.	.	PUNCT
ejde-397	1712	1	[	[	X
ejde-397	1712	2	62	62	NUM
ejde-397	1712	3	]	]	PUNCT
ejde-397	1712	4	r.	r.	PROPN
ejde-397	1712	5	meise	meise	PROPN
ejde-397	1712	6	,	,	PUNCT
ejde-397	1712	7	d.	d.	PROPN
ejde-397	1712	8	vogt	vogt	PROPN
ejde-397	1712	9	;	;	PUNCT
ejde-397	1712	10	introduction	introduction	NOUN
ejde-397	1712	11	to	to	ADP
ejde-397	1712	12	functional	functional	ADJ
ejde-397	1712	13	analysis	analysis	NOUN
ejde-397	1712	14	,	,	PUNCT
ejde-397	1712	15	translated	translate	VERB
ejde-397	1712	16	from	from	ADP
ejde-397	1712	17	the	the	DET
ejde-397	1712	18	german	german	NOUN
ejde-397	1712	19	by	by	ADP
ejde-397	1712	20	m.	m.	PROPN
ejde-397	1712	21	s.	s.	PROPN
ejde-397	1712	22	ramanujan	ramanujan	PROPN
ejde-397	1712	23	and	and	CCONJ
ejde-397	1712	24	revised	revise	VERB
ejde-397	1712	25	by	by	ADP
ejde-397	1712	26	the	the	DET
ejde-397	1712	27	authors	author	NOUN
ejde-397	1712	28	.	.	PUNCT
ejde-397	1713	1	oxf	oxf	PROPN
ejde-397	1713	2	.	.	PUNCT
ejde-397	1713	3	grad	grad	PROPN
ejde-397	1713	4	.	.	PUNCT
ejde-397	1714	1	texts	text	NOUN
ejde-397	1714	2	math	math	PROPN
ejde-397	1714	3	.	.	PUNCT
ejde-397	1714	4	,	,	PUNCT
ejde-397	1714	5	clarendon	clarendon	PROPN
ejde-397	1714	6	press	press	PROPN
ejde-397	1714	7	,	,	PUNCT
ejde-397	1714	8	new	new	PROPN
ejde-397	1714	9	york	york	PROPN
ejde-397	1714	10	,	,	PUNCT
ejde-397	1714	11	1997	1997	NUM
ejde-397	1714	12	.	.	PUNCT
ejde-397	1715	1	[	[	X
ejde-397	1715	2	63	63	NUM
ejde-397	1715	3	]	]	PUNCT
ejde-397	1715	4	i.	i.	PROPN
ejde-397	1715	5	v.	v.	PROPN
ejde-397	1715	6	melnikova	melnikova	PROPN
ejde-397	1715	7	,	,	PUNCT
ejde-397	1715	8	a.	a.	PROPN
ejde-397	1715	9	i.	i.	PROPN
ejde-397	1715	10	filinkov	filinkov	PROPN
ejde-397	1715	11	;	;	PUNCT
ejde-397	1715	12	abstract	abstract	ADJ
ejde-397	1715	13	cauchy	cauchy	PROPN
ejde-397	1715	14	problems	problem	NOUN
ejde-397	1715	15	:	:	PUNCT
ejde-397	1715	16	three	three	NUM
ejde-397	1715	17	approaches	approach	NOUN
ejde-397	1715	18	,	,	PUNCT
ejde-397	1715	19	chapman	chapman	NOUN
ejde-397	1715	20	and	and	CCONJ
ejde-397	1715	21	hall	hall	PROPN
ejde-397	1715	22	/	/	SYM
ejde-397	1715	23	crc	crc	PROPN
ejde-397	1715	24	,	,	PUNCT
ejde-397	1715	25	boca	boca	PROPN
ejde-397	1715	26	raton	raton	PROPN
ejde-397	1715	27	,	,	PUNCT
ejde-397	1715	28	2001	2001	NUM
ejde-397	1715	29	.	.	PUNCT
ejde-397	1716	1	[	[	X
ejde-397	1716	2	64	64	NUM
ejde-397	1716	3	]	]	PUNCT
ejde-397	1716	4	i.	i.	PROPN
ejde-397	1716	5	v.	v.	PROPN
ejde-397	1716	6	melnikova	melnikova	PROPN
ejde-397	1716	7	;	;	PUNCT
ejde-397	1716	8	the	the	DET
ejde-397	1716	9	cauchy	cauchy	PROPN
ejde-397	1716	10	problem	problem	NOUN
ejde-397	1716	11	for	for	ADP
ejde-397	1716	12	differential	differential	ADJ
ejde-397	1716	13	inclusion	inclusion	NOUN
ejde-397	1716	14	in	in	ADP
ejde-397	1716	15	banach	banach	NOUN
ejde-397	1716	16	space	space	NOUN
ejde-397	1716	17	and	and	CCONJ
ejde-397	1716	18	distribution	distribution	NOUN
ejde-397	1716	19	spaces	space	NOUN
ejde-397	1716	20	,	,	PUNCT
ejde-397	1716	21	siberian	siberian	ADJ
ejde-397	1716	22	math	math	NOUN
ejde-397	1716	23	.	.	PUNCT
ejde-397	1717	1	j.	j.	PROPN
ejde-397	1717	2	,	,	PUNCT
ejde-397	1717	3	42(4	42(4	PROPN
ejde-397	1717	4	)	)	PUNCT
ejde-397	1717	5	(	(	PUNCT
ejde-397	1717	6	2001	2001	NUM
ejde-397	1717	7	)	)	PUNCT
ejde-397	1717	8	,	,	PUNCT
ejde-397	1717	9	751	751	NUM
ejde-397	1717	10	-	-	SYM
ejde-397	1717	11	765	765	NUM
ejde-397	1717	12	.	.	PUNCT
ejde-397	1718	1	[	[	X
ejde-397	1718	2	65	65	NUM
ejde-397	1718	3	]	]	X
ejde-397	1718	4	v.	v.	CCONJ
ejde-397	1718	5	obukhovskii	obukhovskii	PROPN
ejde-397	1718	6	,	,	PUNCT
ejde-397	1718	7	p.	p.	NOUN
ejde-397	1718	8	zecca	zecca	NOUN
ejde-397	1718	9	;	;	PUNCT
ejde-397	1718	10	on	on	ADP
ejde-397	1718	11	boundary	boundary	ADJ
ejde-397	1718	12	value	value	NOUN
ejde-397	1718	13	problems	problem	NOUN
ejde-397	1718	14	for	for	ADP
ejde-397	1718	15	degenerate	degenerate	ADJ
ejde-397	1718	16	differential	differential	ADJ
ejde-397	1718	17	inclusions	inclusion	NOUN
ejde-397	1718	18	in	in	ADP
ejde-397	1718	19	banach	banach	NOUN
ejde-397	1718	20	spaces	space	NOUN
ejde-397	1718	21	,	,	PUNCT
ejde-397	1718	22	abstr	abstr	PROPN
ejde-397	1718	23	.	.	PUNCT
ejde-397	1719	1	appl	appl	PROPN
ejde-397	1719	2	.	.	PUNCT
ejde-397	1720	1	anal	anal	PROPN
ejde-397	1720	2	.	.	PROPN
ejde-397	1720	3	,	,	PUNCT
ejde-397	1720	4	13	13	NUM
ejde-397	1720	5	(	(	PUNCT
ejde-397	1720	6	2003	2003	NUM
ejde-397	1720	7	)	)	PUNCT
ejde-397	1720	8	,	,	PUNCT
ejde-397	1720	9	769	769	NUM
ejde-397	1720	10	-	-	SYM
ejde-397	1720	11	784	784	NUM
ejde-397	1720	12	.	.	PUNCT
ejde-397	1721	1	[	[	X
ejde-397	1721	2	66	66	NUM
ejde-397	1721	3	]	]	PUNCT
ejde-397	1721	4	h.	h.	PROPN
ejde-397	1721	5	oka	oka	PROPN
ejde-397	1721	6	;	;	PUNCT
ejde-397	1721	7	linear	linear	PROPN
ejde-397	1721	8	volterra	volterra	PROPN
ejde-397	1721	9	equations	equation	NOUN
ejde-397	1721	10	and	and	CCONJ
ejde-397	1721	11	integrated	integrate	VERB
ejde-397	1721	12	solution	solution	NOUN
ejde-397	1721	13	families	family	NOUN
ejde-397	1721	14	,	,	PUNCT
ejde-397	1721	15	semigroup	semigroup	PROPN
ejde-397	1721	16	forum	forum	PROPN
ejde-397	1721	17	,	,	PUNCT
ejde-397	1721	18	53(1	53(1	PROPN
ejde-397	1721	19	)	)	PUNCT
ejde-397	1721	20	(	(	PUNCT
ejde-397	1721	21	1996	1996	NUM
ejde-397	1721	22	)	)	PUNCT
ejde-397	1721	23	,	,	PUNCT
ejde-397	1721	24	278	278	NUM
ejde-397	1721	25	-	-	SYM
ejde-397	1721	26	297	297	NUM
ejde-397	1721	27	.	.	PUNCT
ejde-397	1722	1	[	[	X
ejde-397	1722	2	67	67	NUM
ejde-397	1722	3	]	]	X
ejde-397	1722	4	i.	i.	NOUN
ejde-397	1722	5	podlubny	podlubny	PROPN
ejde-397	1722	6	;	;	PUNCT
ejde-397	1722	7	fractional	fractional	ADJ
ejde-397	1722	8	differential	differential	NOUN
ejde-397	1722	9	equations	equation	NOUN
ejde-397	1722	10	,	,	PUNCT
ejde-397	1722	11	academic	academic	ADJ
ejde-397	1722	12	press	press	NOUN
ejde-397	1722	13	,	,	PUNCT
ejde-397	1722	14	new	new	PROPN
ejde-397	1722	15	york	york	PROPN
ejde-397	1722	16	,	,	PUNCT
ejde-397	1722	17	1999	1999	NUM
ejde-397	1722	18	.	.	PUNCT
ejde-397	1723	1	[	[	X
ejde-397	1723	2	68	68	NUM
ejde-397	1723	3	]	]	PUNCT
ejde-397	1723	4	j.	j.	PROPN
ejde-397	1723	5	prüss	prüss	PROPN
ejde-397	1723	6	,	,	PUNCT
ejde-397	1723	7	evolutionary	evolutionary	ADJ
ejde-397	1723	8	integral	integral	ADJ
ejde-397	1723	9	equations	equation	NOUN
ejde-397	1723	10	and	and	CCONJ
ejde-397	1723	11	applications	application	NOUN
ejde-397	1723	12	,	,	PUNCT
ejde-397	1723	13	birkhäuser	birkhäuser	NOUN
ejde-397	1723	14	-	-	PUNCT
ejde-397	1723	15	verlag	verlag	NOUN
ejde-397	1723	16	,	,	PUNCT
ejde-397	1723	17	basel	basel	PROPN
ejde-397	1723	18	,	,	PUNCT
ejde-397	1723	19	1993	1993	NUM
ejde-397	1723	20	.	.	PUNCT
ejde-397	1724	1	[	[	X
ejde-397	1724	2	69	69	NUM
ejde-397	1724	3	]	]	X
ejde-397	1724	4	r.	r.	PROPN
ejde-397	1724	5	servadeia	servadeia	PROPN
ejde-397	1724	6	,	,	PUNCT
ejde-397	1724	7	e.	e.	PROPN
ejde-397	1724	8	valdinoci	valdinoci	PROPN
ejde-397	1724	9	;	;	PUNCT
ejde-397	1724	10	on	on	ADP
ejde-397	1724	11	the	the	DET
ejde-397	1724	12	spectrum	spectrum	NOUN
ejde-397	1724	13	of	of	ADP
ejde-397	1724	14	two	two	NUM
ejde-397	1724	15	different	different	ADJ
ejde-397	1724	16	fractional	fractional	ADJ
ejde-397	1724	17	operators	operator	NOUN
ejde-397	1724	18	,	,	PUNCT
ejde-397	1724	19	proc	proc	NOUN
ejde-397	1724	20	.	.	PUNCT
ejde-397	1725	1	royal	royal	ADJ
ejde-397	1725	2	soc	soc	PROPN
ejde-397	1725	3	.	.	PUNCT
ejde-397	1726	1	edinburgh	edinburgh	PROPN
ejde-397	1726	2	,	,	PUNCT
ejde-397	1726	3	144(4	144(4	NUM
ejde-397	1726	4	)	)	PUNCT
ejde-397	1726	5	(	(	PUNCT
ejde-397	1726	6	2014	2014	NUM
ejde-397	1726	7	)	)	PUNCT
ejde-397	1726	8	,	,	PUNCT
ejde-397	1726	9	831	831	NUM
ejde-397	1726	10	-	-	SYM
ejde-397	1726	11	855	855	NUM
ejde-397	1726	12	.	.	PUNCT
ejde-397	1727	1	[	[	X
ejde-397	1727	2	70	70	NUM
ejde-397	1727	3	]	]	PUNCT
ejde-397	1727	4	s.	s.	PROPN
ejde-397	1727	5	g.	g.	PROPN
ejde-397	1727	6	samko	samko	PROPN
ejde-397	1727	7	,	,	PUNCT
ejde-397	1727	8	a.	a.	NOUN
ejde-397	1727	9	a.	a.	NOUN
ejde-397	1727	10	kilbas	kilbas	PROPN
ejde-397	1727	11	,	,	PUNCT
ejde-397	1727	12	o.	o.	PROPN
ejde-397	1727	13	i.	i.	PROPN
ejde-397	1727	14	marichev	marichev	PROPN
ejde-397	1727	15	;	;	PUNCT
ejde-397	1727	16	fractional	fractional	ADJ
ejde-397	1727	17	derivatives	derivative	NOUN
ejde-397	1727	18	and	and	CCONJ
ejde-397	1727	19	integrals	integral	NOUN
ejde-397	1727	20	:	:	PUNCT
ejde-397	1727	21	theory	theory	NOUN
ejde-397	1727	22	and	and	CCONJ
ejde-397	1727	23	applications	application	NOUN
ejde-397	1727	24	,	,	PUNCT
ejde-397	1727	25	gordon	gordon	PROPN
ejde-397	1727	26	and	and	CCONJ
ejde-397	1727	27	breach	breach	PROPN
ejde-397	1727	28	,	,	PUNCT
ejde-397	1727	29	new	new	PROPN
ejde-397	1727	30	york	york	PROPN
ejde-397	1727	31	,	,	PUNCT
ejde-397	1727	32	1993	1993	NUM
ejde-397	1727	33	.	.	PUNCT
ejde-397	1728	1	[	[	X
ejde-397	1728	2	71	71	NUM
ejde-397	1728	3	]	]	X
ejde-397	1728	4	n.	n.	PROPN
ejde-397	1728	5	sauer	sauer	PROPN
ejde-397	1728	6	;	;	PUNCT
ejde-397	1728	7	linear	linear	ADJ
ejde-397	1728	8	evolution	evolution	NOUN
ejde-397	1728	9	equations	equation	NOUN
ejde-397	1728	10	in	in	ADP
ejde-397	1728	11	two	two	NUM
ejde-397	1728	12	banach	banach	NOUN
ejde-397	1728	13	spaces	space	NOUN
ejde-397	1728	14	,	,	PUNCT
ejde-397	1728	15	proc	proc	NOUN
ejde-397	1728	16	.	.	PUNCT
ejde-397	1729	1	royal	royal	ADJ
ejde-397	1729	2	soc	soc	PROPN
ejde-397	1729	3	.	.	PUNCT
ejde-397	1730	1	edinburgh	edinburgh	PROPN
ejde-397	1730	2	,	,	PUNCT
ejde-397	1730	3	91a(3	91a(3	NOUN
ejde-397	1730	4	-	-	SYM
ejde-397	1730	5	4	4	NUM
ejde-397	1730	6	)	)	PUNCT
ejde-397	1730	7	(	(	PUNCT
ejde-397	1730	8	1982	1982	NUM
ejde-397	1730	9	)	)	PUNCT
ejde-397	1730	10	,	,	PUNCT
ejde-397	1730	11	287	287	NUM
ejde-397	1730	12	-	-	SYM
ejde-397	1730	13	303	303	NUM
ejde-397	1730	14	.	.	PUNCT
ejde-397	1731	1	[	[	X
ejde-397	1731	2	72	72	NUM
ejde-397	1731	3	]	]	X
ejde-397	1731	4	f.	f.	PROPN
ejde-397	1731	5	schwenninger	schwenninger	PROPN
ejde-397	1731	6	;	;	PUNCT
ejde-397	1731	7	generalisations	generalisation	NOUN
ejde-397	1731	8	of	of	ADP
ejde-397	1731	9	semigroups	semigroup	NOUN
ejde-397	1731	10	of	of	ADP
ejde-397	1731	11	operators	operator	NOUN
ejde-397	1731	12	in	in	ADP
ejde-397	1731	13	the	the	DET
ejde-397	1731	14	view	view	NOUN
ejde-397	1731	15	of	of	ADP
ejde-397	1731	16	linear	linear	PROPN
ejde-397	1731	17	relations	relation	NOUN
ejde-397	1731	18	,	,	PUNCT
ejde-397	1731	19	technischen	technischen	NOUN
ejde-397	1731	20	universiträt	universiträt	PROPN
ejde-397	1731	21	wien	wien	PROPN
ejde-397	1731	22	diplomarbeit	diplomarbeit	NOUN
ejde-397	1731	23	,	,	PUNCT
ejde-397	1731	24	2011	2011	NUM
ejde-397	1731	25	.	.	PUNCT
ejde-397	1732	1	[	[	X
ejde-397	1732	2	73	73	NUM
ejde-397	1732	3	]	]	PUNCT
ejde-397	1732	4	g.	g.	PROPN
ejde-397	1732	5	a.	a.	PROPN
ejde-397	1732	6	sviridyuk	sviridyuk	PROPN
ejde-397	1732	7	,	,	PUNCT
ejde-397	1732	8	v.	v.	PROPN
ejde-397	1732	9	e.	e.	PROPN
ejde-397	1732	10	fedorov	fedorov	PROPN
ejde-397	1732	11	;	;	PUNCT
ejde-397	1732	12	linear	linear	PROPN
ejde-397	1732	13	sobolev	sobolev	ADJ
ejde-397	1732	14	type	type	NOUN
ejde-397	1732	15	equations	equation	NOUN
ejde-397	1732	16	and	and	CCONJ
ejde-397	1732	17	degenerate	degenerate	ADJ
ejde-397	1732	18	semigroups	semigroup	NOUN
ejde-397	1732	19	of	of	ADP
ejde-397	1732	20	operators	operator	NOUN
ejde-397	1732	21	,	,	PUNCT
ejde-397	1732	22	inverse	inverse	NOUN
ejde-397	1732	23	and	and	CCONJ
ejde-397	1732	24	ill	ill	ADV
ejde-397	1732	25	-	-	PUNCT
ejde-397	1732	26	posed	pose	VERB
ejde-397	1732	27	problems	problem	NOUN
ejde-397	1732	28	(	(	PUNCT
ejde-397	1732	29	book	book	NOUN
ejde-397	1732	30	42	42	NUM
ejde-397	1732	31	)	)	PUNCT
ejde-397	1732	32	,	,	PUNCT
ejde-397	1732	33	vsp	vsp	NOUN
ejde-397	1732	34	,	,	PUNCT
ejde-397	1732	35	utrecht	utrecht	PROPN
ejde-397	1732	36	,	,	PUNCT
ejde-397	1732	37	boston	boston	PROPN
ejde-397	1732	38	,	,	PUNCT
ejde-397	1732	39	2003	2003	NUM
ejde-397	1732	40	.	.	PUNCT
ejde-397	1733	1	[	[	X
ejde-397	1733	2	74	74	X
ejde-397	1733	3	]	]	PUNCT
ejde-397	1733	4	v.	v.	PROPN
ejde-397	1733	5	e.	e.	PROPN
ejde-397	1733	6	tarasov	tarasov	PROPN
ejde-397	1733	7	;	;	PUNCT
ejde-397	1733	8	fractional	fractional	ADJ
ejde-397	1733	9	dynamics	dynamic	NOUN
ejde-397	1733	10	:	:	PUNCT
ejde-397	1733	11	applications	application	NOUN
ejde-397	1733	12	of	of	ADP
ejde-397	1733	13	fractional	fractional	ADJ
ejde-397	1733	14	calculus	calculus	NOUN
ejde-397	1733	15	to	to	ADP
ejde-397	1733	16	dynamics	dynamic	NOUN
ejde-397	1733	17	of	of	ADP
ejde-397	1733	18	particles	particle	NOUN
ejde-397	1733	19	,	,	PUNCT
ejde-397	1733	20	fields	field	NOUN
ejde-397	1733	21	and	and	CCONJ
ejde-397	1733	22	media	medium	NOUN
ejde-397	1733	23	,	,	PUNCT
ejde-397	1733	24	springer	springer	NOUN
ejde-397	1733	25	-	-	PUNCT
ejde-397	1733	26	verlag	verlag	PROPN
ejde-397	1733	27	,	,	PUNCT
ejde-397	1733	28	berlin	berlin	PROPN
ejde-397	1733	29	,	,	PUNCT
ejde-397	1733	30	2010	2010	NUM
ejde-397	1733	31	.	.	PUNCT
ejde-397	1734	1	[	[	X
ejde-397	1734	2	75	75	NUM
ejde-397	1734	3	]	]	PUNCT
ejde-397	1734	4	b.	b.	NOUN
ejde-397	1734	5	thaller	thaller	NOUN
ejde-397	1734	6	,	,	PUNCT
ejde-397	1734	7	s.	s.	PROPN
ejde-397	1734	8	thaller	thaller	NOUN
ejde-397	1734	9	;	;	PUNCT
ejde-397	1734	10	factorization	factorization	NOUN
ejde-397	1734	11	of	of	ADP
ejde-397	1734	12	degenerate	degenerate	ADJ
ejde-397	1734	13	cauchy	cauchy	NOUN
ejde-397	1734	14	problems	problem	NOUN
ejde-397	1734	15	:	:	PUNCT
ejde-397	1734	16	the	the	DET
ejde-397	1734	17	linear	linear	ADJ
ejde-397	1734	18	case	case	NOUN
ejde-397	1734	19	,	,	PUNCT
ejde-397	1734	20	j.	j.	PROPN
ejde-397	1734	21	operator	operator	PROPN
ejde-397	1734	22	theory	theory	NOUN
ejde-397	1734	23	,	,	PUNCT
ejde-397	1734	24	36(1	36(1	NUM
ejde-397	1734	25	)	)	PUNCT
ejde-397	1734	26	(	(	PUNCT
ejde-397	1734	27	1996	1996	NUM
ejde-397	1734	28	)	)	PUNCT
ejde-397	1734	29	,	,	PUNCT
ejde-397	1734	30	121	121	NUM
ejde-397	1734	31	-	-	SYM
ejde-397	1734	32	146	146	NUM
ejde-397	1734	33	.	.	PUNCT
ejde-397	1735	1	ejde-2023/63	ejde-2023/63	ADJ
ejde-397	1735	2	abstract	abstract	ADJ
ejde-397	1735	3	degenerate	degenerate	ADJ
ejde-397	1735	4	volterra	volterra	NOUN
ejde-397	1735	5	inclusions	inclusion	NOUN
ejde-397	1735	6	55	55	NUM
ejde-397	1735	7	[	[	X
ejde-397	1735	8	76	76	NUM
ejde-397	1735	9	]	]	X
ejde-397	1735	10	b.	b.	NOUN
ejde-397	1735	11	thaller	thaller	NOUN
ejde-397	1735	12	,	,	PUNCT
ejde-397	1735	13	s.	s.	PROPN
ejde-397	1735	14	thaller	thaller	PROPN
ejde-397	1735	15	;	;	PUNCT
ejde-397	1735	16	semigroup	semigroup	PROPN
ejde-397	1735	17	theory	theory	NOUN
ejde-397	1735	18	of	of	ADP
ejde-397	1735	19	degenerate	degenerate	ADJ
ejde-397	1735	20	linear	linear	PROPN
ejde-397	1735	21	cauchy	cauchy	PROPN
ejde-397	1735	22	problems	problem	NOUN
ejde-397	1735	23	,	,	PUNCT
ejde-397	1735	24	semigroup	semigroup	PROPN
ejde-397	1735	25	forum	forum	PROPN
ejde-397	1735	26	,	,	PUNCT
ejde-397	1735	27	62(3	62(3	NOUN
ejde-397	1735	28	)	)	PUNCT
ejde-397	1735	29	(	(	PUNCT
ejde-397	1735	30	2001	2001	NUM
ejde-397	1735	31	)	)	PUNCT
ejde-397	1735	32	,	,	PUNCT
ejde-397	1735	33	375	375	NUM
ejde-397	1735	34	-	-	SYM
ejde-397	1735	35	398	398	NUM
ejde-397	1735	36	.	.	PUNCT
ejde-397	1736	1	[	[	X
ejde-397	1736	2	77	77	NUM
ejde-397	1736	3	]	]	X
ejde-397	1736	4	h.	h.	PROPN
ejde-397	1736	5	triebel	triebel	NOUN
ejde-397	1736	6	;	;	PUNCT
ejde-397	1736	7	interpolation	interpolation	NOUN
ejde-397	1736	8	theory	theory	NOUN
ejde-397	1736	9	.	.	PUNCT
ejde-397	1737	1	function	function	NOUN
ejde-397	1737	2	spaces	space	NOUN
ejde-397	1737	3	.	.	PUNCT
ejde-397	1738	1	differential	differential	ADJ
ejde-397	1738	2	operators	operator	NOUN
ejde-397	1738	3	,	,	PUNCT
ejde-397	1738	4	north	north	NOUN
ejde-397	1738	5	-	-	PUNCT
ejde-397	1738	6	holland	holland	PROPN
ejde-397	1738	7	publ	publ	NOUN
ejde-397	1738	8	.	.	PUNCT
ejde-397	1739	1	company	company	NOUN
ejde-397	1739	2	,	,	PUNCT
ejde-397	1739	3	1978	1978	NUM
ejde-397	1739	4	.	.	PUNCT
ejde-397	1740	1	[	[	X
ejde-397	1740	2	78	78	NUM
ejde-397	1740	3	]	]	PUNCT
ejde-397	1740	4	s.	s.	PROPN
ejde-397	1740	5	wang	wang	PROPN
ejde-397	1740	6	;	;	PUNCT
ejde-397	1740	7	properties	property	NOUN
ejde-397	1740	8	of	of	ADP
ejde-397	1740	9	subgenerators	subgenerator	NOUN
ejde-397	1740	10	of	of	ADP
ejde-397	1740	11	c	c	NOUN
ejde-397	1740	12	-	-	PUNCT
ejde-397	1740	13	regularized	regularize	VERB
ejde-397	1740	14	semigroups	semigroup	NOUN
ejde-397	1740	15	,	,	PUNCT
ejde-397	1740	16	proc	proc	NOUN
ejde-397	1740	17	.	.	PUNCT
ejde-397	1741	1	amer	amer	PROPN
ejde-397	1741	2	.	.	PUNCT
ejde-397	1741	3	math	math	PROPN
ejde-397	1741	4	.	.	PUNCT
ejde-397	1742	1	soc	soc	PROPN
ejde-397	1742	2	.	.	PUNCT
ejde-397	1742	3	,	,	PUNCT
ejde-397	1742	4	126(2	126(2	NUM
ejde-397	1742	5	)	)	PUNCT
ejde-397	1742	6	(	(	PUNCT
ejde-397	1742	7	1998	1998	NUM
ejde-397	1742	8	)	)	PUNCT
ejde-397	1742	9	,	,	PUNCT
ejde-397	1742	10	453–460	453–460	NUM
ejde-397	1742	11	.	.	PUNCT
ejde-397	1743	1	[	[	X
ejde-397	1743	2	79	79	NUM
ejde-397	1743	3	]	]	X
ejde-397	1743	4	t.-j	t.-j	PROPN
ejde-397	1743	5	.	.	PUNCT
ejde-397	1744	1	xiao	xiao	PROPN
ejde-397	1744	2	,	,	PUNCT
ejde-397	1744	3	j.	j.	PROPN
ejde-397	1744	4	liang	liang	PROPN
ejde-397	1744	5	;	;	PUNCT
ejde-397	1744	6	the	the	DET
ejde-397	1744	7	cauchy	cauchy	PROPN
ejde-397	1744	8	problem	problem	NOUN
ejde-397	1744	9	for	for	ADP
ejde-397	1744	10	higher	high	ADJ
ejde-397	1744	11	–	–	PUNCT
ejde-397	1744	12	order	order	NOUN
ejde-397	1744	13	abstract	abstract	ADJ
ejde-397	1744	14	differential	differential	NOUN
ejde-397	1744	15	equations	equation	NOUN
ejde-397	1744	16	,	,	PUNCT
ejde-397	1744	17	springer	springer	NOUN
ejde-397	1744	18	–	–	PUNCT
ejde-397	1744	19	verlag	verlag	PROPN
ejde-397	1744	20	,	,	PUNCT
ejde-397	1744	21	berlin	berlin	PROPN
ejde-397	1744	22	,	,	PUNCT
ejde-397	1744	23	1998	1998	NUM
ejde-397	1744	24	.	.	PUNCT
ejde-397	1745	1	[	[	X
ejde-397	1745	2	80	80	NUM
ejde-397	1745	3	]	]	X
ejde-397	1745	4	t.-j	t.-j	PROPN
ejde-397	1745	5	.	.	PUNCT
ejde-397	1746	1	xiao	xiao	PROPN
ejde-397	1746	2	,	,	PUNCT
ejde-397	1746	3	j.	j.	PROPN
ejde-397	1746	4	liang	liang	PROPN
ejde-397	1746	5	;	;	PUNCT
ejde-397	1746	6	laplace	laplace	NOUN
ejde-397	1746	7	transforms	transform	VERB
ejde-397	1746	8	and	and	CCONJ
ejde-397	1746	9	integrated	integrate	VERB
ejde-397	1746	10	,	,	PUNCT
ejde-397	1746	11	regularized	regularize	VERB
ejde-397	1746	12	semigroups	semigroup	NOUN
ejde-397	1746	13	in	in	ADP
ejde-397	1746	14	locally	locally	ADV
ejde-397	1746	15	convex	convex	ADJ
ejde-397	1746	16	spaces	space	NOUN
ejde-397	1746	17	,	,	PUNCT
ejde-397	1746	18	j.	j.	PROPN
ejde-397	1746	19	funct	funct	PROPN
ejde-397	1746	20	.	.	PUNCT
ejde-397	1747	1	anal	anal	PROPN
ejde-397	1747	2	.	.	PROPN
ejde-397	1747	3	,	,	PUNCT
ejde-397	1747	4	148(2	148(2	NUM
ejde-397	1747	5	)	)	PUNCT
ejde-397	1747	6	(	(	PUNCT
ejde-397	1747	7	1997	1997	NUM
ejde-397	1747	8	)	)	PUNCT
ejde-397	1747	9	,	,	PUNCT
ejde-397	1747	10	448	448	NUM
ejde-397	1747	11	-	-	SYM
ejde-397	1747	12	479	479	NUM
ejde-397	1747	13	.	.	PUNCT
ejde-397	1748	1	[	[	X
ejde-397	1748	2	81	81	NUM
ejde-397	1748	3	]	]	PUNCT
ejde-397	1748	4	a.	a.	NOUN
ejde-397	1748	5	yagi	yagi	NOUN
ejde-397	1748	6	;	;	PUNCT
ejde-397	1748	7	generation	generation	NOUN
ejde-397	1748	8	theorem	theorem	NOUN
ejde-397	1748	9	of	of	ADP
ejde-397	1748	10	semigroup	semigroup	NOUN
ejde-397	1748	11	for	for	ADP
ejde-397	1748	12	multivalued	multivalued	ADJ
ejde-397	1748	13	linear	linear	PROPN
ejde-397	1748	14	operators	operator	NOUN
ejde-397	1748	15	,	,	PUNCT
ejde-397	1748	16	osaka	osaka	PROPN
ejde-397	1748	17	j.	j.	PROPN
ejde-397	1748	18	math	math	PROPN
ejde-397	1748	19	.	.	PROPN
ejde-397	1748	20	,	,	PUNCT
ejde-397	1748	21	28(2	28(2	NUM
ejde-397	1748	22	)	)	PUNCT
ejde-397	1748	23	(	(	PUNCT
ejde-397	1748	24	1991	1991	NUM
ejde-397	1748	25	)	)	PUNCT
ejde-397	1748	26	,	,	PUNCT
ejde-397	1748	27	385	385	NUM
ejde-397	1748	28	-	-	SYM
ejde-397	1748	29	410	410	NUM
ejde-397	1748	30	.	.	PUNCT
ejde-397	1749	1	[	[	X
ejde-397	1749	2	82	82	NUM
ejde-397	1749	3	]	]	PUNCT
ejde-397	1749	4	k.	k.	PROPN
ejde-397	1749	5	yosida	yosida	PROPN
ejde-397	1749	6	;	;	PUNCT
ejde-397	1749	7	holomorphic	holomorphic	ADJ
ejde-397	1749	8	semigroups	semigroup	NOUN
ejde-397	1749	9	in	in	ADP
ejde-397	1749	10	a	a	DET
ejde-397	1749	11	locally	locally	ADV
ejde-397	1749	12	convex	convex	ADJ
ejde-397	1749	13	linear	linear	PROPN
ejde-397	1749	14	topological	topological	ADJ
ejde-397	1749	15	space	space	NOUN
ejde-397	1749	16	,	,	PUNCT
ejde-397	1749	17	osaka	osaka	PROPN
ejde-397	1749	18	math	math	PROPN
ejde-397	1749	19	.	.	PUNCT
ejde-397	1750	1	j.	j.	PROPN
ejde-397	1750	2	,	,	PUNCT
ejde-397	1750	3	15(1	15(1	NUM
ejde-397	1750	4	)	)	PUNCT
ejde-397	1750	5	(	(	PUNCT
ejde-397	1750	6	1963	1963	NUM
ejde-397	1750	7	)	)	PUNCT
ejde-397	1750	8	,	,	PUNCT
ejde-397	1750	9	51	51	NUM
ejde-397	1750	10	-	-	SYM
ejde-397	1750	11	57	57	NUM
ejde-397	1750	12	.	.	PUNCT
ejde-397	1751	1	[	[	X
ejde-397	1751	2	83	83	NUM
ejde-397	1751	3	]	]	PUNCT
ejde-397	1751	4	m.	m.	PROPN
ejde-397	1751	5	zubair	zubair	PROPN
ejde-397	1751	6	,	,	PUNCT
ejde-397	1751	7	m.	m.	PROPN
ejde-397	1751	8	j.	j.	PROPN
ejde-397	1751	9	mughal	mughal	PROPN
ejde-397	1751	10	,	,	PUNCT
ejde-397	1751	11	q.	q.	PROPN
ejde-397	1751	12	a.	a.	NOUN
ejde-397	1751	13	naqvi	naqvi	PROPN
ejde-397	1751	14	;	;	PUNCT
ejde-397	1751	15	electromagnetic	electromagnetic	ADJ
ejde-397	1751	16	fields	field	NOUN
ejde-397	1751	17	and	and	CCONJ
ejde-397	1751	18	waves	wave	NOUN
ejde-397	1751	19	in	in	ADP
ejde-397	1751	20	fractional	fractional	ADJ
ejde-397	1751	21	dimensional	dimensional	ADJ
ejde-397	1751	22	space	space	NOUN
ejde-397	1751	23	,	,	PUNCT
ejde-397	1751	24	springer	springer	NOUN
ejde-397	1751	25	-	-	PUNCT
ejde-397	1751	26	verlag	verlag	PROPN
ejde-397	1751	27	,	,	PUNCT
ejde-397	1751	28	berlin	berlin	PROPN
ejde-397	1751	29	,	,	PUNCT
ejde-397	1751	30	2012	2012	NUM
ejde-397	1751	31	.	.	PUNCT
ejde-397	1752	1	marko	marko	PROPN
ejde-397	1752	2	kostić	kostić	PROPN
ejde-397	1752	3	university	university	PROPN
ejde-397	1752	4	of	of	ADP
ejde-397	1752	5	novi	novi	PROPN
ejde-397	1752	6	sad	sad	PROPN
ejde-397	1752	7	,	,	PUNCT
ejde-397	1752	8	faculty	faculty	NOUN
ejde-397	1752	9	of	of	ADP
ejde-397	1752	10	technical	technical	ADJ
ejde-397	1752	11	sciences	science	NOUN
ejde-397	1752	12	,	,	PUNCT
ejde-397	1752	13	trg	trg	PROPN
ejde-397	1752	14	d.	d.	PROPN
ejde-397	1752	15	obradovića	obradovića	PROPN
ejde-397	1752	16	6	6	NUM
ejde-397	1752	17	,	,	PUNCT
ejde-397	1752	18	21125	21125	NUM
ejde-397	1752	19	novi	novi	PROPN
ejde-397	1752	20	sad	sad	PROPN
ejde-397	1752	21	,	,	PUNCT
ejde-397	1752	22	serbia	serbia	PROPN
ejde-397	1752	23	email	email	NOUN
ejde-397	1752	24	address	address	NOUN
ejde-397	1752	25	:	:	PUNCT
ejde-397	1752	26	markokostic121@yahoo.com	markokostic121@yahoo.com	X
ejde-397	1752	27	1	1	X
ejde-397	1752	28	.	.	X
ejde-397	1752	29	introduction	introduction	NOUN
ejde-397	1752	30	and	and	CCONJ
ejde-397	1752	31	preliminaries	preliminary	NOUN
ejde-397	1752	32	2	2	NUM
ejde-397	1752	33	.	.	PUNCT
ejde-397	1752	34	multivalued	multivalue	VERB
ejde-397	1752	35	linear	linear	PROPN
ejde-397	1752	36	operators	operator	NOUN
ejde-397	1752	37	in	in	ADP
ejde-397	1752	38	locally	locally	ADV
ejde-397	1752	39	convex	convex	ADJ
ejde-397	1752	40	spaces	space	VERB
ejde-397	1752	41	3	3	NUM
ejde-397	1752	42	.	.	PUNCT
ejde-397	1752	43	laplace	laplace	NOUN
ejde-397	1752	44	transform	transform	NOUN
ejde-397	1752	45	of	of	ADP
ejde-397	1752	46	functions	function	NOUN
ejde-397	1752	47	with	with	ADP
ejde-397	1752	48	values	value	NOUN
ejde-397	1752	49	in	in	ADP
ejde-397	1752	50	sequentially	sequentially	ADV
ejde-397	1752	51	complete	complete	ADJ
ejde-397	1752	52	locally	locally	ADV
ejde-397	1752	53	convex	convex	NOUN
ejde-397	1752	54	spaces	space	VERB
ejde-397	1752	55	4	4	NUM
ejde-397	1752	56	.	.	PUNCT
ejde-397	1752	57	abstract	abstract	ADJ
ejde-397	1752	58	degenerate	degenerate	PROPN
ejde-397	1752	59	volterra	volterra	PROPN
ejde-397	1752	60	integro	integro	PROPN
ejde-397	1752	61	-	-	PUNCT
ejde-397	1752	62	differential	differential	NOUN
ejde-397	1752	63	inclusions	inclusion	NOUN
ejde-397	1752	64	5	5	NUM
ejde-397	1752	65	.	.	PUNCT
ejde-397	1752	66	multivalued	multivalue	VERB
ejde-397	1752	67	linear	linear	PROPN
ejde-397	1752	68	operators	operator	NOUN
ejde-397	1752	69	as	as	ADP
ejde-397	1752	70	subgenerators	subgenerator	NOUN
ejde-397	1752	71	of	of	ADP
ejde-397	1752	72	(	(	PUNCT
ejde-397	1752	73	a	a	PRON
ejde-397	1752	74	,	,	PUNCT
ejde-397	1752	75	k)-regularized	k)-regularize	VERB
ejde-397	1752	76	c	c	NOUN
ejde-397	1752	77	-	-	PUNCT
ejde-397	1752	78	resolvent	resolvent	ADJ
ejde-397	1752	79	solution	solution	NOUN
ejde-397	1752	80	operator	operator	NOUN
ejde-397	1752	81	families	family	NOUN
ejde-397	1752	82	5.1	5.1	NUM
ejde-397	1752	83	.	.	PUNCT
ejde-397	1753	1	differential	differential	ADJ
ejde-397	1753	2	and	and	CCONJ
ejde-397	1753	3	analytical	analytical	ADJ
ejde-397	1753	4	properties	property	NOUN
ejde-397	1753	5	of	of	ADP
ejde-397	1753	6	(	(	PUNCT
ejde-397	1753	7	a	a	PRON
ejde-397	1753	8	,	,	PUNCT
ejde-397	1753	9	k)-regularized	k)-regularize	VERB
ejde-397	1753	10	c	c	NOUN
ejde-397	1753	11	-	-	PUNCT
ejde-397	1753	12	resolvent	resolvent	ADJ
ejde-397	1753	13	families	family	NOUN
ejde-397	1753	14	5.2	5.2	NUM
ejde-397	1753	15	.	.	PUNCT
ejde-397	1754	1	non	non	ADJ
ejde-397	1754	2	-	-	NOUN
ejde-397	1754	3	injectivity	injectivity	NOUN
ejde-397	1754	4	of	of	ADP
ejde-397	1754	5	regularizing	regularize	VERB
ejde-397	1754	6	operators	operator	NOUN
ejde-397	1754	7	c2	c2	PROPN
ejde-397	1754	8	and	and	CCONJ
ejde-397	1754	9	c	c	PROPN
ejde-397	1754	10	6	6	NUM
ejde-397	1754	11	.	.	PUNCT
ejde-397	1755	1	conclusions	conclusion	NOUN
ejde-397	1755	2	and	and	CCONJ
ejde-397	1755	3	final	final	ADJ
ejde-397	1755	4	remarks	remark	NOUN
ejde-397	1755	5	acknowledgments	acknowledgment	NOUN
ejde-397	1755	6	references	reference	NOUN