id	sid	tid	token	lemma	pos
ejpam-4659	1	1	european	european	PROPN
ejpam-4659	1	2	journal	journal	PROPN
ejpam-4659	1	3	of	of	ADP
ejpam-4659	1	4	pure	pure	ADJ
ejpam-4659	1	5	and	and	CCONJ
ejpam-4659	1	6	applied	apply	VERB
ejpam-4659	1	7	mathematics	mathematic	NOUN
ejpam-4659	1	8	vol	vol	NOUN
ejpam-4659	1	9	.	.	PUNCT
ejpam-4659	2	1	16	16	NUM
ejpam-4659	2	2	,	,	PUNCT
ejpam-4659	2	3	no	no	INTJ
ejpam-4659	2	4	.	.	NOUN
ejpam-4659	2	5	1	1	NUM
ejpam-4659	2	6	,	,	PUNCT
ejpam-4659	2	7	2023	2023	NUM
ejpam-4659	2	8	,	,	PUNCT
ejpam-4659	2	9	538	538	NUM
ejpam-4659	2	10	-	-	SYM
ejpam-4659	2	11	547	547	NUM
ejpam-4659	2	12	issn	issn	PROPN
ejpam-4659	2	13	1307	1307	NUM
ejpam-4659	2	14	-	-	SYM
ejpam-4659	2	15	5543	5543	NUM
ejpam-4659	2	16	–	–	PUNCT
ejpam-4659	2	17	ejpam.com	ejpam.com	X
ejpam-4659	2	18	published	publish	VERB
ejpam-4659	2	19	by	by	ADP
ejpam-4659	2	20	new	new	PROPN
ejpam-4659	2	21	york	york	PROPN
ejpam-4659	2	22	business	business	PROPN
ejpam-4659	2	23	global	global	ADJ
ejpam-4659	2	24	results	result	NOUN
ejpam-4659	2	25	of	of	ADP
ejpam-4659	2	26	semigroup	semigroup	NOUN
ejpam-4659	2	27	of	of	ADP
ejpam-4659	2	28	linear	linear	PROPN
ejpam-4659	2	29	operators	operator	NOUN
ejpam-4659	2	30	generating	generate	VERB
ejpam-4659	2	31	a	a	DET
ejpam-4659	2	32	general	general	ADJ
ejpam-4659	2	33	class	class	NOUN
ejpam-4659	2	34	of	of	ADP
ejpam-4659	2	35	semilinear	semilinear	PROPN
ejpam-4659	2	36	initial	initial	ADJ
ejpam-4659	2	37	value	value	NOUN
ejpam-4659	2	38	problems	problem	NOUN
ejpam-4659	2	39	o.	o.	PROPN
ejpam-4659	2	40	y.	y.	PROPN
ejpam-4659	2	41	saka	saka	PROPN
ejpam-4659	2	42	-	-	PUNCT
ejpam-4659	2	43	balogun1	balogun1	PROPN
ejpam-4659	2	44	,	,	PUNCT
ejpam-4659	2	45	f.	f.	PROPN
ejpam-4659	2	46	h.	h.	PROPN
ejpam-4659	2	47	oyelami1	oyelami1	PROPN
ejpam-4659	2	48	,	,	PUNCT
ejpam-4659	2	49	a.	a.	PROPN
ejpam-4659	2	50	y.	y.	PROPN
ejpam-4659	2	51	akinyele2,∗	akinyele2,∗	PROPN
ejpam-4659	2	52	,	,	PUNCT
ejpam-4659	2	53	j.	j.	PROPN
ejpam-4659	2	54	b.	b.	PROPN
ejpam-4659	2	55	omosowon2	omosowon2	PROPN
ejpam-4659	2	56	1	1	NUM
ejpam-4659	2	57	department	department	NOUN
ejpam-4659	2	58	of	of	ADP
ejpam-4659	2	59	mathematical	mathematical	ADJ
ejpam-4659	2	60	and	and	CCONJ
ejpam-4659	2	61	physical	physical	ADJ
ejpam-4659	2	62	sciences	science	NOUN
ejpam-4659	2	63	,	,	PUNCT
ejpam-4659	2	64	afe	afe	PROPN
ejpam-4659	2	65	babalola	babalola	PROPN
ejpam-4659	2	66	university	university	PROPN
ejpam-4659	2	67	,	,	PUNCT
ejpam-4659	2	68	ado	ado	NOUN
ejpam-4659	2	69	-	-	PUNCT
ejpam-4659	2	70	ekiti	ekiti	PROPN
ejpam-4659	2	71	,	,	PUNCT
ejpam-4659	2	72	nigeria	nigeria	PROPN
ejpam-4659	2	73	2	2	NUM
ejpam-4659	2	74	department	department	NOUN
ejpam-4659	2	75	of	of	ADP
ejpam-4659	2	76	mathematics	mathematic	NOUN
ejpam-4659	2	77	,	,	PUNCT
ejpam-4659	2	78	university	university	NOUN
ejpam-4659	2	79	of	of	ADP
ejpam-4659	2	80	ilorin	ilorin	NOUN
ejpam-4659	2	81	,	,	PUNCT
ejpam-4659	2	82	ilorin	ilorin	PROPN
ejpam-4659	2	83	,	,	PUNCT
ejpam-4659	2	84	nigeria	nigeria	PROPN
ejpam-4659	2	85	abstract	abstract	ADJ
ejpam-4659	2	86	.	.	PUNCT
ejpam-4659	3	1	this	this	DET
ejpam-4659	3	2	paper	paper	NOUN
ejpam-4659	3	3	present	present	ADJ
ejpam-4659	3	4	results	result	NOUN
ejpam-4659	3	5	of	of	ADP
ejpam-4659	3	6	ω	ω	NOUN
ejpam-4659	3	7	-	-	PUNCT
ejpam-4659	3	8	order	order	NOUN
ejpam-4659	3	9	preserving	preserve	VERB
ejpam-4659	3	10	partial	partial	ADJ
ejpam-4659	3	11	contraction	contraction	NOUN
ejpam-4659	3	12	mapping	mapping	NOUN
ejpam-4659	3	13	generating	generate	VERB
ejpam-4659	3	14	a	a	DET
ejpam-4659	3	15	general	general	ADJ
ejpam-4659	3	16	class	class	NOUN
ejpam-4659	3	17	of	of	ADP
ejpam-4659	3	18	semilinear	semilinear	PROPN
ejpam-4659	3	19	initial	initial	ADJ
ejpam-4659	3	20	value	value	NOUN
ejpam-4659	3	21	problems	problem	NOUN
ejpam-4659	3	22	.	.	PUNCT
ejpam-4659	4	1	we	we	PRON
ejpam-4659	4	2	consider	consider	VERB
ejpam-4659	4	3	the	the	DET
ejpam-4659	4	4	use	use	NOUN
ejpam-4659	4	5	of	of	ADP
ejpam-4659	4	6	fractional	fractional	ADJ
ejpam-4659	4	7	powers	power	NOUN
ejpam-4659	4	8	of	of	ADP
ejpam-4659	4	9	unbounded	unbounded	ADJ
ejpam-4659	4	10	linear	linear	PROPN
ejpam-4659	4	11	operators	operator	NOUN
ejpam-4659	4	12	for	for	ADP
ejpam-4659	4	13	its	its	PRON
ejpam-4659	4	14	application	application	NOUN
ejpam-4659	4	15	by	by	ADP
ejpam-4659	4	16	starting	start	VERB
ejpam-4659	4	17	with	with	ADP
ejpam-4659	4	18	some	some	DET
ejpam-4659	4	19	results	result	NOUN
ejpam-4659	4	20	concerning	concern	VERB
ejpam-4659	4	21	such	such	ADJ
ejpam-4659	4	22	fractional	fractional	ADJ
ejpam-4659	4	23	powers	power	NOUN
ejpam-4659	4	24	.	.	PUNCT
ejpam-4659	5	1	we	we	PRON
ejpam-4659	5	2	assume	assume	VERB
ejpam-4659	5	3	a	a	PRON
ejpam-4659	5	4	to	to	PART
ejpam-4659	5	5	be	be	AUX
ejpam-4659	5	6	the	the	DET
ejpam-4659	5	7	infinitesimal	infinitesimal	ADJ
ejpam-4659	5	8	generator	generator	NOUN
ejpam-4659	5	9	of	of	ADP
ejpam-4659	5	10	an	an	DET
ejpam-4659	5	11	analytic	analytic	ADJ
ejpam-4659	5	12	semigroup	semigroup	NOUN
ejpam-4659	5	13	in	in	ADP
ejpam-4659	5	14	a	a	DET
ejpam-4659	5	15	banach	banach	NOUN
ejpam-4659	5	16	space	space	NOUN
ejpam-4659	5	17	x	x	NOUN
ejpam-4659	5	18	,	,	PUNCT
ejpam-4659	5	19	0	0	NUM
ejpam-4659	5	20	∈	∈	PROPN
ejpam-4659	5	21	ρ(a	ρ(a	PROPN
ejpam-4659	5	22	)	)	PUNCT
ejpam-4659	5	23	and	and	CCONJ
ejpam-4659	5	24	defined	define	VERB
ejpam-4659	5	25	the	the	DET
ejpam-4659	5	26	fractional	fractional	ADJ
ejpam-4659	5	27	powers	power	NOUN
ejpam-4659	5	28	of	of	ADP
ejpam-4659	5	29	a	a	PRON
ejpam-4659	5	30	for	for	ADP
ejpam-4659	5	31	0	0	NUM
ejpam-4659	5	32	<	<	X
ejpam-4659	5	33	α	α	PROPN
ejpam-4659	5	34	≤	≤	NUM
ejpam-4659	5	35	1	1	NUM
ejpam-4659	5	36	.	.	PUNCT
ejpam-4659	6	1	we	we	PRON
ejpam-4659	6	2	also	also	ADV
ejpam-4659	6	3	show	show	VERB
ejpam-4659	6	4	that	that	SCONJ
ejpam-4659	6	5	aα	aα	NOUN
ejpam-4659	6	6	is	be	AUX
ejpam-4659	6	7	a	a	DET
ejpam-4659	6	8	closed	closed	ADJ
ejpam-4659	6	9	linear	linear	NOUN
ejpam-4659	6	10	operator	operator	NOUN
ejpam-4659	6	11	whose	whose	DET
ejpam-4659	6	12	domain	domain	NOUN
ejpam-4659	6	13	d(aα	d(aα	PROPN
ejpam-4659	6	14	)	)	PUNCT
ejpam-4659	6	15	⊃	⊃	PROPN
ejpam-4659	6	16	d(a	d(a	PROPN
ejpam-4659	6	17	)	)	PUNCT
ejpam-4659	6	18	is	be	AUX
ejpam-4659	6	19	dense	dense	ADJ
ejpam-4659	6	20	in	in	ADP
ejpam-4659	6	21	x.	x.	NOUN
ejpam-4659	6	22	finally	finally	ADV
ejpam-4659	6	23	we	we	PRON
ejpam-4659	6	24	established	establish	VERB
ejpam-4659	6	25	that	that	SCONJ
ejpam-4659	6	26	the	the	DET
ejpam-4659	6	27	operator	operator	NOUN
ejpam-4659	6	28	is	be	AUX
ejpam-4659	6	29	bounded	bound	VERB
ejpam-4659	6	30	,	,	PUNCT
ejpam-4659	6	31	continuous	continuous	ADJ
ejpam-4659	6	32	and	and	CCONJ
ejpam-4659	6	33	holder	holder	NOUN
ejpam-4659	6	34	continuous	continuous	ADJ
ejpam-4659	6	35	.	.	PUNCT
ejpam-4659	7	1	2020	2020	NUM
ejpam-4659	7	2	mathematics	mathematic	NOUN
ejpam-4659	7	3	subject	subject	NOUN
ejpam-4659	7	4	classifications	classification	NOUN
ejpam-4659	7	5	:	:	PUNCT
ejpam-4659	7	6	06f15	06f15	NUM
ejpam-4659	7	7	,	,	PUNCT
ejpam-4659	7	8	06f05	06f05	NUM
ejpam-4659	7	9	,	,	PUNCT
ejpam-4659	7	10	20m05	20m05	NUM
ejpam-4659	7	11	key	key	ADJ
ejpam-4659	7	12	words	word	NOUN
ejpam-4659	7	13	and	and	CCONJ
ejpam-4659	7	14	phrases	phrase	NOUN
ejpam-4659	7	15	:	:	PUNCT
ejpam-4659	7	16	ω	ω	ADJ
ejpam-4659	7	17	-	-	ADJ
ejpam-4659	7	18	ocpn	ocpn	ADJ
ejpam-4659	7	19	,	,	PUNCT
ejpam-4659	7	20	strongly	strongly	ADV
ejpam-4659	7	21	elliptic	elliptic	ADJ
ejpam-4659	7	22	,	,	PUNCT
ejpam-4659	7	23	c0	c0	PROPN
ejpam-4659	7	24	-	-	PUNCT
ejpam-4659	7	25	semigroup	semigroup	PROPN
ejpam-4659	7	26	,	,	PUNCT
ejpam-4659	7	27	analytic	analytic	ADJ
ejpam-4659	7	28	semigroup	semigroup	NOUN
ejpam-4659	7	29	1	1	NUM
ejpam-4659	7	30	.	.	PUNCT
ejpam-4659	7	31	front	front	ADJ
ejpam-4659	7	32	matter	matter	NOUN
ejpam-4659	7	33	assume	assume	VERB
ejpam-4659	7	34	ω	ω	PROPN
ejpam-4659	7	35	⊂	⊂	PROPN
ejpam-4659	7	36	rn	rn	PROPN
ejpam-4659	7	37	is	be	AUX
ejpam-4659	7	38	a	a	DET
ejpam-4659	7	39	bounded	bounded	ADJ
ejpam-4659	7	40	domain	domain	NOUN
ejpam-4659	7	41	with	with	ADP
ejpam-4659	7	42	smooth	smooth	ADJ
ejpam-4659	7	43	boundary	boundary	ADJ
ejpam-4659	7	44	∂ω	∂ω	PROPN
ejpam-4659	7	45	and	and	CCONJ
ejpam-4659	7	46	let	let	VERB
ejpam-4659	7	47	a(x	a(x	NOUN
ejpam-4659	7	48	,	,	PUNCT
ejpam-4659	7	49	d	d	NOUN
ejpam-4659	7	50	)	)	PUNCT
ejpam-4659	7	51	=	=	SYM
ejpam-4659	7	52	∑	∑	PUNCT
ejpam-4659	7	53	|α|≤2	|α|≤2	X
ejpam-4659	7	54	m	m	VERB
ejpam-4659	7	55	aα(x)d	aα(x)d	ADJ
ejpam-4659	7	56	α	α	PROPN
ejpam-4659	7	57	(	(	PUNCT
ejpam-4659	7	58	1	1	NUM
ejpam-4659	7	59	)	)	PUNCT
ejpam-4659	7	60	be	be	AUX
ejpam-4659	7	61	a	a	DET
ejpam-4659	7	62	strongly	strongly	ADV
ejpam-4659	7	63	elliptic	elliptic	ADJ
ejpam-4659	7	64	differential	differential	NOUN
ejpam-4659	7	65	operator	operator	NOUN
ejpam-4659	7	66	in	in	ADP
ejpam-4659	7	67	ω	ω	PROPN
ejpam-4659	7	68	.	.	PUNCT
ejpam-4659	8	1	for	for	ADP
ejpam-4659	8	2	1	1	NUM
ejpam-4659	8	3	<	<	X
ejpam-4659	8	4	p	p	X
ejpam-4659	8	5	<	<	X
ejpam-4659	8	6	∞	∞	NUM
ejpam-4659	8	7	we	we	PRON
ejpam-4659	8	8	associate	associate	VERB
ejpam-4659	8	9	with	with	ADP
ejpam-4659	8	10	a(x	a(x	NOUN
ejpam-4659	8	11	,	,	PUNCT
ejpam-4659	8	12	d	d	NOUN
ejpam-4659	8	13	)	)	PUNCT
ejpam-4659	8	14	and	and	CCONJ
ejpam-4659	8	15	operator	operator	NOUN
ejpam-4659	8	16	ap	ap	PROPN
ejpam-4659	8	17	in	in	ADP
ejpam-4659	8	18	lp(ω	lp(ω	PROPN
ejpam-4659	8	19	)	)	PUNCT
ejpam-4659	8	20	by	by	ADP
ejpam-4659	8	21	d(ap	d(ap	PROPN
ejpam-4659	8	22	)	)	PUNCT
ejpam-4659	8	23	=	=	PUNCT
ejpam-4659	9	1	w	w	NOUN
ejpam-4659	9	2	2m	2m	NUM
ejpam-4659	9	3	,	,	PUNCT
ejpam-4659	9	4	p(ω	p(ω	PROPN
ejpam-4659	9	5	)	)	PUNCT
ejpam-4659	9	6	∩wm	∩wm	PROPN
ejpam-4659	9	7	,	,	PUNCT
ejpam-4659	9	8	p	p	NOUN
ejpam-4659	9	9	0	0	NUM
ejpam-4659	9	10	(	(	PUNCT
ejpam-4659	9	11	ω	ω	NOUN
ejpam-4659	9	12	)	)	PUNCT
ejpam-4659	9	13	(	(	PUNCT
ejpam-4659	9	14	2	2	NUM
ejpam-4659	9	15	)	)	PUNCT
ejpam-4659	9	16	and	and	CCONJ
ejpam-4659	9	17	apu	apu	PROPN
ejpam-4659	9	18	=	=	SYM
ejpam-4659	9	19	a(x	a(x	PROPN
ejpam-4659	9	20	,	,	PUNCT
ejpam-4659	9	21	d)u	d)u	X
ejpam-4659	9	22	(	(	PUNCT
ejpam-4659	9	23	3	3	X
ejpam-4659	9	24	)	)	PUNCT
ejpam-4659	9	25	∗corresponding	∗corresponde	VERB
ejpam-4659	9	26	author	author	NOUN
ejpam-4659	9	27	.	.	PUNCT
ejpam-4659	10	1	doi	doi	NOUN
ejpam-4659	10	2	:	:	PUNCT
ejpam-4659	10	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4659	https://doi.org/10.29020/nybg.ejpam.v16i1.4659	PROPN
ejpam-4659	10	4	email	email	NOUN
ejpam-4659	10	5	addresses	address	NOUN
ejpam-4659	10	6	:	:	PUNCT
ejpam-4659	10	7	balogunld@yahoo.com	balogunld@yahoo.com	X
ejpam-4659	10	8	(	(	PUNCT
ejpam-4659	10	9	o.	o.	PROPN
ejpam-4659	10	10	y.	y.	PROPN
ejpam-4659	10	11	saka	saka	PROPN
ejpam-4659	10	12	-	-	PUNCT
ejpam-4659	10	13	balogun	balogun	PROPN
ejpam-4659	10	14	)	)	PUNCT
ejpam-4659	10	15	,	,	PUNCT
ejpam-4659	10	16	adefolajufunmilayo@gmail.com	adefolajufunmilayo@gmail.com	X
ejpam-4659	11	1	(	(	PUNCT
ejpam-4659	11	2	f.	f.	PROPN
ejpam-4659	11	3	h.	h.	PROPN
ejpam-4659	11	4	oyelami	oyelami	PROPN
ejpam-4659	11	5	)	)	PUNCT
ejpam-4659	11	6	,	,	PUNCT
ejpam-4659	11	7	jbo0011@mix.wvu.edu	jbo0011@mix.wvu.edu	PROPN
ejpam-4659	11	8	(	(	PUNCT
ejpam-4659	11	9	j.	j.	PROPN
ejpam-4659	11	10	b.	b.	PROPN
ejpam-4659	11	11	omosowon	omosowon	PROPN
ejpam-4659	11	12	)	)	PUNCT
ejpam-4659	11	13	,	,	PUNCT
ejpam-4659	11	14	olaakinyele04@gmail.com	olaakinyele04@gmail.com	X
ejpam-4659	11	15	(	(	PUNCT
ejpam-4659	11	16	a.	a.	PROPN
ejpam-4659	11	17	y.	y.	PROPN
ejpam-4659	11	18	akinyele∗	akinyele∗	PROPN
ejpam-4659	11	19	)	)	PUNCT
ejpam-4659	11	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4659	12	1	538	538	NUM
ejpam-4659	12	2	©	©	PROPN
ejpam-4659	12	3	2023	2023	NUM
ejpam-4659	12	4	ejpam	ejpam	NOUN
ejpam-4659	12	5	all	all	DET
ejpam-4659	12	6	rights	right	NOUN
ejpam-4659	12	7	reserved	reserve	VERB
ejpam-4659	12	8	.	.	PUNCT
ejpam-4659	13	1	a.	a.	PROPN
ejpam-4659	13	2	y.	y.	PROPN
ejpam-4659	13	3	akinyele	akinyele	PROPN
ejpam-4659	13	4	et	et	PROPN
ejpam-4659	13	5	al	al	PROPN
ejpam-4659	13	6	.	.	PUNCT
ejpam-4659	13	7	/	/	SYM
ejpam-4659	13	8	eur	eur	PROPN
ejpam-4659	13	9	.	.	PUNCT
ejpam-4659	14	1	j.	j.	PROPN
ejpam-4659	14	2	pure	pure	PROPN
ejpam-4659	14	3	appl	appl	PROPN
ejpam-4659	14	4	.	.	PROPN
ejpam-4659	14	5	math	math	PROPN
ejpam-4659	14	6	,	,	PUNCT
ejpam-4659	14	7	16	16	NUM
ejpam-4659	14	8	(	(	PUNCT
ejpam-4659	14	9	1	1	NUM
ejpam-4659	14	10	)	)	PUNCT
ejpam-4659	14	11	(	(	PUNCT
ejpam-4659	14	12	2023	2023	NUM
ejpam-4659	14	13	)	)	PUNCT
ejpam-4659	14	14	,	,	PUNCT
ejpam-4659	14	15	538	538	NUM
ejpam-4659	14	16	-	-	SYM
ejpam-4659	14	17	547	547	NUM
ejpam-4659	14	18	539	539	NUM
ejpam-4659	14	19	for	for	ADP
ejpam-4659	14	20	u	u	PROPN
ejpam-4659	14	21	∈	∈	PROPN
ejpam-4659	14	22	d(ap	d(ap	PROPN
ejpam-4659	14	23	)	)	PUNCT
ejpam-4659	14	24	and	and	CCONJ
ejpam-4659	14	25	a	a	DET
ejpam-4659	14	26	∈	∈	PROPN
ejpam-4659	14	27	ω	ω	NUM
ejpam-4659	14	28	−	−	PROPN
ejpam-4659	14	29	ocpn	ocpn	ADJ
ejpam-4659	14	30	.	.	PUNCT
ejpam-4659	14	31	suppose	suppose	VERB
ejpam-4659	14	32	ap	ap	PROPN
ejpam-4659	14	33	is	be	AUX
ejpam-4659	14	34	the	the	DET
ejpam-4659	14	35	infinitesimal	infinitesimal	ADJ
ejpam-4659	14	36	generator	generator	NOUN
ejpam-4659	14	37	of	of	ADP
ejpam-4659	14	38	an	an	DET
ejpam-4659	14	39	analytic	analytic	ADJ
ejpam-4659	14	40	semigroup	semigroup	NOUN
ejpam-4659	14	41	on	on	ADP
ejpam-4659	14	42	lp(ω	lp(ω	PROPN
ejpam-4659	14	43	)	)	PUNCT
ejpam-4659	14	44	.	.	PUNCT
ejpam-4659	15	1	by	by	ADP
ejpam-4659	15	2	adding	add	VERB
ejpam-4659	15	3	to	to	ADP
ejpam-4659	15	4	a(x	a(x	NOUN
ejpam-4659	15	5	,	,	PUNCT
ejpam-4659	15	6	d	d	NOUN
ejpam-4659	15	7	)	)	PUNCT
ejpam-4659	15	8	,	,	PUNCT
ejpam-4659	15	9	and	and	CCONJ
ejpam-4659	15	10	hence	hence	ADV
ejpam-4659	15	11	to	to	ADP
ejpam-4659	15	12	ap	ap	PROPN
ejpam-4659	15	13	,	,	PUNCT
ejpam-4659	15	14	a	a	DET
ejpam-4659	15	15	positive	positive	ADJ
ejpam-4659	15	16	multiple	multiple	NOUN
ejpam-4659	15	17	of	of	ADP
ejpam-4659	15	18	identity	identity	NOUN
ejpam-4659	15	19	,	,	PUNCT
ejpam-4659	15	20	we	we	PRON
ejpam-4659	15	21	obtain	obtain	VERB
ejpam-4659	15	22	an	an	DET
ejpam-4659	15	23	infinitesimal	infinitesimal	ADJ
ejpam-4659	15	24	generator	generator	NOUN
ejpam-4659	15	25	−(ap	−(ap	PROPN
ejpam-4659	15	26	+	+	CCONJ
ejpam-4659	15	27	ki	ki	PROPN
ejpam-4659	15	28	)	)	PUNCT
ejpam-4659	15	29	of	of	ADP
ejpam-4659	15	30	an	an	DET
ejpam-4659	15	31	analytic	analytic	ADJ
ejpam-4659	15	32	semigroup	semigroup	NOUN
ejpam-4659	15	33	,	,	PUNCT
ejpam-4659	15	34	which	which	PRON
ejpam-4659	15	35	is	be	AUX
ejpam-4659	15	36	invertible	invertible	ADJ
ejpam-4659	15	37	.	.	PUNCT
ejpam-4659	16	1	in	in	ADP
ejpam-4659	16	2	the	the	DET
ejpam-4659	16	3	sequel	sequel	NOUN
ejpam-4659	16	4	we	we	PRON
ejpam-4659	16	5	will	will	AUX
ejpam-4659	16	6	tactically	tactically	ADV
ejpam-4659	16	7	assume	assume	VERB
ejpam-4659	16	8	that	that	SCONJ
ejpam-4659	16	9	this	this	PRON
ejpam-4659	16	10	has	have	AUX
ejpam-4659	16	11	been	be	AUX
ejpam-4659	16	12	done	do	VERB
ejpam-4659	16	13	and	and	CCONJ
ejpam-4659	16	14	thus	thus	ADV
ejpam-4659	16	15	assume	assume	VERB
ejpam-4659	16	16	directly	directly	ADV
ejpam-4659	16	17	that	that	SCONJ
ejpam-4659	16	18	ap	ap	PROPN
ejpam-4659	16	19	itself	itself	PRON
ejpam-4659	16	20	is	be	AUX
ejpam-4659	16	21	invertible	invertible	ADJ
ejpam-4659	16	22	.	.	PUNCT
ejpam-4659	17	1	let	let	VERB
ejpam-4659	17	2	a	a	PRON
ejpam-4659	17	3	be	be	AUX
ejpam-4659	17	4	a	a	DET
ejpam-4659	17	5	strongly	strongly	ADV
ejpam-4659	17	6	elliptic	elliptic	ADJ
ejpam-4659	17	7	operator	operator	NOUN
ejpam-4659	17	8	of	of	ADP
ejpam-4659	17	9	order	order	NOUN
ejpam-4659	17	10	2	2	NUM
ejpam-4659	17	11	m	m	VERB
ejpam-4659	17	12	on	on	ADP
ejpam-4659	17	13	a	a	DET
ejpam-4659	17	14	bounded	bounded	ADJ
ejpam-4659	17	15	domain	domain	NOUN
ejpam-4659	17	16	ω	ω	PROPN
ejpam-4659	17	17	with	with	ADP
ejpam-4659	17	18	smooth	smooth	ADJ
ejpam-4659	17	19	boundary	boundary	ADJ
ejpam-4659	17	20	∂ω	∂ω	PROPN
ejpam-4659	17	21	in	in	ADP
ejpam-4659	17	22	rn	rn	PROPN
ejpam-4659	17	23	and	and	CCONJ
ejpam-4659	17	24	let	let	VERB
ejpam-4659	17	25	1	1	NUM
ejpam-4659	17	26	<	<	X
ejpam-4659	17	27	p	p	X
ejpam-4659	17	28	<	<	X
ejpam-4659	17	29	∞.	∞.	PROPN
ejpam-4659	17	30	there	there	PRON
ejpam-4659	17	31	exists	exist	VERB
ejpam-4659	17	32	a	a	DET
ejpam-4659	17	33	constant	constant	ADJ
ejpam-4659	17	34	c	c	NOUN
ejpam-4659	17	35	such	such	ADJ
ejpam-4659	17	36	that	that	SCONJ
ejpam-4659	17	37	∥u∥2m	∥u∥2m	PROPN
ejpam-4659	17	38	,	,	PUNCT
ejpam-4659	17	39	p	p	NOUN
ejpam-4659	17	40	≤	≤	NOUN
ejpam-4659	18	1	c(∥au∥0,p	c(∥au∥0,p	VERB
ejpam-4659	18	2	+	+	X
ejpam-4659	18	3	∥u∥0,p	∥u∥0,p	NOUN
ejpam-4659	18	4	)	)	PUNCT
ejpam-4659	18	5	(	(	PUNCT
ejpam-4659	18	6	4	4	X
ejpam-4659	18	7	)	)	PUNCT
ejpam-4659	18	8	for	for	ADP
ejpam-4659	18	9	every	every	DET
ejpam-4659	18	10	u	u	PROPN
ejpam-4659	18	11	∈	∈	PROPN
ejpam-4659	18	12	d(ap	d(ap	PROPN
ejpam-4659	18	13	)	)	PUNCT
ejpam-4659	18	14	and	and	CCONJ
ejpam-4659	18	15	ap	ap	PROPN
ejpam-4659	18	16	∈	∈	PROPN
ejpam-4659	18	17	ω	ω	PROPN
ejpam-4659	18	18	−ocpn	−ocpn	PROPN
ejpam-4659	18	19	.	.	PUNCT
ejpam-4659	19	1	since	since	SCONJ
ejpam-4659	19	2	we	we	PRON
ejpam-4659	19	3	assume	assume	VERB
ejpam-4659	19	4	now	now	ADV
ejpam-4659	19	5	that	that	SCONJ
ejpam-4659	19	6	ap	ap	PROPN
ejpam-4659	19	7	is	be	AUX
ejpam-4659	19	8	invertible	invertible	ADJ
ejpam-4659	19	9	in	in	ADP
ejpam-4659	19	10	lp(ω	lp(ω	PROPN
ejpam-4659	19	11	)	)	PUNCT
ejpam-4659	19	12	it	it	PRON
ejpam-4659	19	13	follows	follow	VERB
ejpam-4659	19	14	readily	readily	ADV
ejpam-4659	19	15	that	that	SCONJ
ejpam-4659	19	16	c∥u∥0,p	c∥u∥0,p	NOUN
ejpam-4659	19	17	≤	≤	NOUN
ejpam-4659	19	18	∥apu∥0,p	∥apu∥0,p	VERB
ejpam-4659	19	19	for	for	ADP
ejpam-4659	19	20	some	some	DET
ejpam-4659	19	21	constant	constant	ADJ
ejpam-4659	19	22	c	c	NOUN
ejpam-4659	19	23	>	>	PUNCT
ejpam-4659	19	24	0	0	PUNCT
ejpam-4659	20	1	and	and	CCONJ
ejpam-4659	20	2	therefore	therefore	ADV
ejpam-4659	20	3	we	we	PRON
ejpam-4659	20	4	have	have	VERB
ejpam-4659	20	5	∥u∥2m	∥u∥2m	NOUN
ejpam-4659	20	6	,	,	PUNCT
ejpam-4659	20	7	p	p	ADJ
ejpam-4659	20	8	≤	≤	NUM
ejpam-4659	20	9	c∥apu∥0,p	c∥apu∥0,p	NOUN
ejpam-4659	20	10	for	for	ADP
ejpam-4659	20	11	u	u	PROPN
ejpam-4659	20	12	∈	∈	PROPN
ejpam-4659	20	13	d(ap	d(ap	PROPN
ejpam-4659	20	14	)	)	PUNCT
ejpam-4659	20	15	.	.	PUNCT
ejpam-4659	21	1	(	(	PUNCT
ejpam-4659	21	2	5	5	X
ejpam-4659	21	3	)	)	PUNCT
ejpam-4659	21	4	suppose	suppose	VERB
ejpam-4659	21	5	x	x	PRON
ejpam-4659	21	6	is	be	AUX
ejpam-4659	21	7	a	a	DET
ejpam-4659	21	8	banach	banach	NOUN
ejpam-4659	21	9	space	space	NOUN
ejpam-4659	21	10	,	,	PUNCT
ejpam-4659	21	11	xn	xn	PROPN
ejpam-4659	22	1	⊆	⊆	NUM
ejpam-4659	22	2	x	x	X
ejpam-4659	22	3	is	be	AUX
ejpam-4659	22	4	a	a	DET
ejpam-4659	22	5	finite	finite	ADJ
ejpam-4659	22	6	set	set	NOUN
ejpam-4659	22	7	,	,	PUNCT
ejpam-4659	22	8	ω	ω	PROPN
ejpam-4659	22	9	−ocpn	−ocpn	PROPN
ejpam-4659	22	10	the	the	DET
ejpam-4659	22	11	ω	ω	NOUN
ejpam-4659	22	12	-	-	PUNCT
ejpam-4659	22	13	order	order	NOUN
ejpam-4659	22	14	preserving	preserve	VERB
ejpam-4659	22	15	partial	partial	ADJ
ejpam-4659	22	16	contraction	contraction	NOUN
ejpam-4659	22	17	mapping	mapping	NOUN
ejpam-4659	22	18	,	,	PUNCT
ejpam-4659	22	19	mm	mm	PROPN
ejpam-4659	22	20	be	be	AUX
ejpam-4659	22	21	a	a	DET
ejpam-4659	22	22	matrix	matrix	NOUN
ejpam-4659	22	23	,	,	PUNCT
ejpam-4659	22	24	l(x	l(x	PROPN
ejpam-4659	22	25	)	)	PUNCT
ejpam-4659	22	26	be	be	VERB
ejpam-4659	22	27	a	a	DET
ejpam-4659	22	28	bounded	bounded	ADJ
ejpam-4659	22	29	linear	linear	ADJ
ejpam-4659	22	30	operator	operator	NOUN
ejpam-4659	22	31	on	on	ADP
ejpam-4659	22	32	x	x	PROPN
ejpam-4659	22	33	,	,	PUNCT
ejpam-4659	22	34	pn	pn	PROPN
ejpam-4659	22	35	a	a	DET
ejpam-4659	22	36	partial	partial	ADJ
ejpam-4659	22	37	transformation	transformation	NOUN
ejpam-4659	22	38	semigroup	semigroup	NOUN
ejpam-4659	22	39	,	,	PUNCT
ejpam-4659	22	40	ρ(a	ρ(a	PROPN
ejpam-4659	22	41	)	)	PUNCT
ejpam-4659	22	42	a	a	DET
ejpam-4659	22	43	resolvent	resolvent	ADJ
ejpam-4659	22	44	set	set	NOUN
ejpam-4659	22	45	,	,	PUNCT
ejpam-4659	22	46	σ(a	σ(a	PROPN
ejpam-4659	22	47	)	)	PUNCT
ejpam-4659	22	48	a	a	DET
ejpam-4659	22	49	spectrum	spectrum	NOUN
ejpam-4659	22	50	of	of	ADP
ejpam-4659	22	51	a.	a.	NOUN
ejpam-4659	22	52	this	this	DET
ejpam-4659	22	53	paper	paper	NOUN
ejpam-4659	22	54	consist	consist	NOUN
ejpam-4659	22	55	of	of	ADP
ejpam-4659	22	56	results	result	NOUN
ejpam-4659	22	57	of	of	ADP
ejpam-4659	22	58	ω	ω	NOUN
ejpam-4659	22	59	-	-	PUNCT
ejpam-4659	22	60	order	order	NOUN
ejpam-4659	22	61	preserving	preserve	VERB
ejpam-4659	22	62	partial	partial	ADJ
ejpam-4659	22	63	contraction	contraction	NOUN
ejpam-4659	22	64	mapping	mapping	NOUN
ejpam-4659	22	65	generating	generate	VERB
ejpam-4659	22	66	a	a	DET
ejpam-4659	22	67	general	general	ADJ
ejpam-4659	22	68	class	class	NOUN
ejpam-4659	22	69	of	of	ADP
ejpam-4659	22	70	semilinear	semilinear	PROPN
ejpam-4659	22	71	initial	initial	ADJ
ejpam-4659	22	72	value	value	NOUN
ejpam-4659	22	73	problems	problem	NOUN
ejpam-4659	22	74	.	.	PUNCT
ejpam-4659	23	1	akinyele	akinyele	PROPN
ejpam-4659	23	2	et	et	PROPN
ejpam-4659	23	3	al	al	PROPN
ejpam-4659	23	4	.	.	PUNCT
ejpam-4659	24	1	[	[	X
ejpam-4659	24	2	1	1	NUM
ejpam-4659	24	3	]	]	PUNCT
ejpam-4659	24	4	,	,	PUNCT
ejpam-4659	24	5	characterized	characterize	VERB
ejpam-4659	24	6	ω	ω	NUM
ejpam-4659	24	7	-	-	PUNCT
ejpam-4659	24	8	order	order	NOUN
ejpam-4659	24	9	reversing	reverse	VERB
ejpam-4659	24	10	partial	partial	ADJ
ejpam-4659	24	11	contraction	contraction	NOUN
ejpam-4659	24	12	mapping	mapping	NOUN
ejpam-4659	24	13	as	as	ADP
ejpam-4659	24	14	a	a	DET
ejpam-4659	24	15	compact	compact	ADJ
ejpam-4659	24	16	semigroup	semigroup	NOUN
ejpam-4659	24	17	of	of	ADP
ejpam-4659	24	18	linear	linear	ADJ
ejpam-4659	24	19	operator	operator	NOUN
ejpam-4659	24	20	and	and	CCONJ
ejpam-4659	24	21	also	also	ADV
ejpam-4659	24	22	in	in	ADP
ejpam-4659	24	23	[	[	X
ejpam-4659	24	24	2	2	NUM
ejpam-4659	24	25	]	]	PUNCT
ejpam-4659	24	26	,	,	PUNCT
ejpam-4659	24	27	akinyele	akinyele	PROPN
ejpam-4659	24	28	et	et	PROPN
ejpam-4659	24	29	al	al	PROPN
ejpam-4659	24	30	.	.	PROPN
ejpam-4659	24	31	,	,	PUNCT
ejpam-4659	24	32	obtained	obtain	VERB
ejpam-4659	24	33	differentiable	differentiable	ADJ
ejpam-4659	24	34	and	and	CCONJ
ejpam-4659	24	35	analytic	analytic	ADJ
ejpam-4659	24	36	results	result	NOUN
ejpam-4659	24	37	on	on	ADP
ejpam-4659	24	38	ω	ω	ADJ
ejpam-4659	24	39	-	-	PUNCT
ejpam-4659	24	40	order	order	NOUN
ejpam-4659	24	41	preserving	preserve	VERB
ejpam-4659	24	42	partial	partial	ADJ
ejpam-4659	24	43	contraction	contraction	NOUN
ejpam-4659	24	44	mapping	mapping	NOUN
ejpam-4659	24	45	in	in	ADP
ejpam-4659	24	46	semigroup	semigroup	NOUN
ejpam-4659	24	47	of	of	ADP
ejpam-4659	24	48	linear	linear	PROPN
ejpam-4659	24	49	operator	operator	NOUN
ejpam-4659	24	50	.	.	PUNCT
ejpam-4659	25	1	balakrishnan	balakrishnan	PROPN
ejpam-4659	26	1	[	[	X
ejpam-4659	26	2	3	3	NUM
ejpam-4659	26	3	]	]	PUNCT
ejpam-4659	26	4	,	,	PUNCT
ejpam-4659	26	5	presented	present	VERB
ejpam-4659	26	6	an	an	DET
ejpam-4659	26	7	operator	operator	NOUN
ejpam-4659	26	8	calculus	calculus	NOUN
ejpam-4659	26	9	for	for	ADP
ejpam-4659	26	10	infinitesimal	infinitesimal	ADJ
ejpam-4659	26	11	generators	generator	NOUN
ejpam-4659	26	12	of	of	ADP
ejpam-4659	26	13	semigroup	semigroup	PROPN
ejpam-4659	26	14	.	.	PUNCT
ejpam-4659	27	1	banach	banach	NOUN
ejpam-4659	28	1	[	[	X
ejpam-4659	28	2	4	4	NUM
ejpam-4659	28	3	]	]	PUNCT
ejpam-4659	28	4	,	,	PUNCT
ejpam-4659	28	5	established	establish	VERB
ejpam-4659	28	6	and	and	CCONJ
ejpam-4659	28	7	introduced	introduce	VERB
ejpam-4659	28	8	the	the	DET
ejpam-4659	28	9	concept	concept	NOUN
ejpam-4659	28	10	of	of	ADP
ejpam-4659	28	11	banach	banach	NOUN
ejpam-4659	28	12	spaces	space	NOUN
ejpam-4659	28	13	.	.	PUNCT
ejpam-4659	29	1	brezis	brezis	NOUN
ejpam-4659	29	2	and	and	CCONJ
ejpam-4659	29	3	gallouet	gallouet	VERB
ejpam-4659	29	4	[	[	X
ejpam-4659	29	5	5	5	NUM
ejpam-4659	29	6	]	]	PUNCT
ejpam-4659	29	7	,	,	PUNCT
ejpam-4659	29	8	generated	generate	VERB
ejpam-4659	29	9	nonlinear	nonlinear	ADJ
ejpam-4659	29	10	schrödinger	schrödinger	NOUN
ejpam-4659	29	11	evolution	evolution	NOUN
ejpam-4659	29	12	equation	equation	NOUN
ejpam-4659	29	13	.	.	PUNCT
ejpam-4659	30	1	chill	chill	NOUN
ejpam-4659	30	2	and	and	CCONJ
ejpam-4659	30	3	tomilov	tomilov	NOUN
ejpam-4659	31	1	[	[	X
ejpam-4659	31	2	6	6	NUM
ejpam-4659	31	3	]	]	PUNCT
ejpam-4659	31	4	,	,	PUNCT
ejpam-4659	31	5	presented	present	VERB
ejpam-4659	31	6	some	some	DET
ejpam-4659	31	7	resolvent	resolvent	ADJ
ejpam-4659	31	8	approach	approach	NOUN
ejpam-4659	31	9	to	to	ADP
ejpam-4659	31	10	stability	stability	NOUN
ejpam-4659	31	11	operator	operator	NOUN
ejpam-4659	31	12	semigroup	semigroup	PROPN
ejpam-4659	31	13	.	.	PUNCT
ejpam-4659	32	1	davies	davy	NOUN
ejpam-4659	33	1	[	[	X
ejpam-4659	33	2	7	7	NUM
ejpam-4659	33	3	]	]	PUNCT
ejpam-4659	33	4	,	,	PUNCT
ejpam-4659	33	5	obtained	obtain	VERB
ejpam-4659	33	6	linear	linear	PROPN
ejpam-4659	33	7	operators	operator	NOUN
ejpam-4659	33	8	and	and	CCONJ
ejpam-4659	33	9	their	their	PRON
ejpam-4659	33	10	spectra	spectra	PROPN
ejpam-4659	33	11	.	.	PUNCT
ejpam-4659	33	12	engel	engel	PROPN
ejpam-4659	33	13	and	and	CCONJ
ejpam-4659	33	14	nagel	nagel	PROPN
ejpam-4659	34	1	[	[	X
ejpam-4659	34	2	8	8	NUM
ejpam-4659	34	3	]	]	PUNCT
ejpam-4659	34	4	,	,	PUNCT
ejpam-4659	34	5	introduced	introduce	VERB
ejpam-4659	34	6	one	one	NUM
ejpam-4659	34	7	-	-	PUNCT
ejpam-4659	34	8	parameter	parameter	NOUN
ejpam-4659	34	9	semigroup	semigroup	NOUN
ejpam-4659	34	10	for	for	ADP
ejpam-4659	34	11	linear	linear	PROPN
ejpam-4659	34	12	evolution	evolution	NOUN
ejpam-4659	34	13	equations	equation	NOUN
ejpam-4659	34	14	.	.	PUNCT
ejpam-4659	35	1	omosowon	omosowon	PROPN
ejpam-4659	35	2	et	et	PROPN
ejpam-4659	35	3	al	al	PROPN
ejpam-4659	35	4	.	.	PUNCT
ejpam-4659	36	1	[	[	X
ejpam-4659	36	2	13	13	NUM
ejpam-4659	36	3	]	]	PUNCT
ejpam-4659	36	4	,	,	PUNCT
ejpam-4659	36	5	generated	generate	VERB
ejpam-4659	36	6	some	some	DET
ejpam-4659	36	7	analytic	analytic	ADJ
ejpam-4659	36	8	results	result	NOUN
ejpam-4659	36	9	of	of	ADP
ejpam-4659	36	10	semigroup	semigroup	NOUN
ejpam-4659	36	11	of	of	ADP
ejpam-4659	36	12	linear	linear	ADJ
ejpam-4659	36	13	operator	operator	NOUN
ejpam-4659	36	14	with	with	ADP
ejpam-4659	36	15	dynamic	dynamic	ADJ
ejpam-4659	36	16	boundary	boundary	ADJ
ejpam-4659	36	17	conditions	condition	NOUN
ejpam-4659	36	18	,	,	PUNCT
ejpam-4659	36	19	and	and	CCONJ
ejpam-4659	36	20	also	also	ADV
ejpam-4659	36	21	in	in	ADP
ejpam-4659	36	22	[	[	PUNCT
ejpam-4659	36	23	11	11	NUM
ejpam-4659	36	24	]	]	PUNCT
ejpam-4659	36	25	,	,	PUNCT
ejpam-4659	36	26	omosowon	omosowon	PROPN
ejpam-4659	36	27	et	et	PROPN
ejpam-4659	36	28	al	al	PROPN
ejpam-4659	36	29	.	.	PROPN
ejpam-4659	36	30	,	,	PUNCT
ejpam-4659	36	31	introduced	introduce	VERB
ejpam-4659	36	32	dual	dual	ADJ
ejpam-4659	36	33	properties	property	NOUN
ejpam-4659	36	34	of	of	ADP
ejpam-4659	36	35	ω	ω	NOUN
ejpam-4659	36	36	-	-	PUNCT
ejpam-4659	36	37	order	order	NOUN
ejpam-4659	36	38	reversing	reverse	VERB
ejpam-4659	36	39	partial	partial	ADJ
ejpam-4659	36	40	contraction	contraction	NOUN
ejpam-4659	36	41	mapping	mapping	NOUN
ejpam-4659	36	42	in	in	ADP
ejpam-4659	36	43	semigroup	semigroup	NOUN
ejpam-4659	36	44	of	of	ADP
ejpam-4659	36	45	linear	linear	PROPN
ejpam-4659	36	46	operator	operator	NOUN
ejpam-4659	36	47	.	.	PUNCT
ejpam-4659	37	1	omosowon	omosowon	PROPN
ejpam-4659	37	2	et	et	PROPN
ejpam-4659	37	3	al	al	PROPN
ejpam-4659	37	4	.	.	PUNCT
ejpam-4659	38	1	[	[	X
ejpam-4659	38	2	10	10	NUM
ejpam-4659	38	3	]	]	PUNCT
ejpam-4659	38	4	,	,	PUNCT
ejpam-4659	38	5	established	establish	VERB
ejpam-4659	38	6	a	a	DET
ejpam-4659	38	7	regular	regular	ADJ
ejpam-4659	38	8	weak*-continuous	weak*-continuous	ADJ
ejpam-4659	38	9	semigroup	semigroup	NOUN
ejpam-4659	38	10	of	of	ADP
ejpam-4659	38	11	linear	linear	PROPN
ejpam-4659	38	12	operators	operator	NOUN
ejpam-4659	38	13	,	,	PUNCT
ejpam-4659	38	14	and	and	CCONJ
ejpam-4659	38	15	also	also	ADV
ejpam-4659	38	16	in	in	ADP
ejpam-4659	38	17	[	[	PUNCT
ejpam-4659	38	18	9	9	NUM
ejpam-4659	38	19	]	]	PUNCT
ejpam-4659	38	20	,	,	PUNCT
ejpam-4659	38	21	omosowon	omosowon	PROPN
ejpam-4659	38	22	et	et	PROPN
ejpam-4659	38	23	al	al	PROPN
ejpam-4659	38	24	.	.	PROPN
ejpam-4659	38	25	,	,	PUNCT
ejpam-4659	38	26	obtained	obtain	VERB
ejpam-4659	38	27	a	a	DET
ejpam-4659	38	28	quasilinear	quasilinear	ADJ
ejpam-4659	38	29	equations	equation	NOUN
ejpam-4659	38	30	of	of	ADP
ejpam-4659	38	31	evolution	evolution	NOUN
ejpam-4659	38	32	on	on	ADP
ejpam-4659	38	33	semigroup	semigroup	NOUN
ejpam-4659	38	34	of	of	ADP
ejpam-4659	38	35	linear	linear	PROPN
ejpam-4659	38	36	operator.reversing	operator.reverse	VERB
ejpam-4659	38	37	partial	partial	ADJ
ejpam-4659	38	38	contraction	contraction	NOUN
ejpam-4659	38	39	mapping	mapping	NOUN
ejpam-4659	38	40	generating	generate	VERB
ejpam-4659	38	41	a	a	DET
ejpam-4659	38	42	differential	differential	ADJ
ejpam-4659	38	43	operator	operator	NOUN
ejpam-4659	38	44	.	.	PUNCT
ejpam-4659	39	1	omosowon	omosowon	PROPN
ejpam-4659	39	2	et	et	PROPN
ejpam-4659	39	3	al	al	PROPN
ejpam-4659	39	4	.	.	PUNCT
ejpam-4659	40	1	[	[	X
ejpam-4659	40	2	12	12	NUM
ejpam-4659	40	3	]	]	PUNCT
ejpam-4659	40	4	,	,	PUNCT
ejpam-4659	40	5	deduced	deduce	VERB
ejpam-4659	40	6	results	result	NOUN
ejpam-4659	40	7	of	of	ADP
ejpam-4659	40	8	semigroup	semigroup	NOUN
ejpam-4659	40	9	of	of	ADP
ejpam-4659	40	10	linear	linear	PROPN
ejpam-4659	40	11	equation	equation	NOUN
ejpam-4659	40	12	generating	generate	VERB
ejpam-4659	40	13	a	a	DET
ejpam-4659	40	14	wave	wave	NOUN
ejpam-4659	40	15	equation	equation	NOUN
ejpam-4659	40	16	.	.	PUNCT
ejpam-4659	41	1	pazy	pazy	NOUN
ejpam-4659	42	1	[	[	X
ejpam-4659	42	2	14	14	NUM
ejpam-4659	42	3	]	]	PUNCT
ejpam-4659	42	4	,	,	PUNCT
ejpam-4659	42	5	presented	present	VERB
ejpam-4659	42	6	asymptotic	asymptotic	ADJ
ejpam-4659	42	7	behavior	behavior	NOUN
ejpam-4659	42	8	of	of	ADP
ejpam-4659	42	9	the	the	DET
ejpam-4659	42	10	solution	solution	NOUN
ejpam-4659	42	11	of	of	ADP
ejpam-4659	42	12	an	an	DET
ejpam-4659	42	13	abstract	abstract	ADJ
ejpam-4659	42	14	evolution	evolution	NOUN
ejpam-4659	42	15	and	and	CCONJ
ejpam-4659	42	16	some	some	DET
ejpam-4659	42	17	applications	application	NOUN
ejpam-4659	42	18	and	and	CCONJ
ejpam-4659	42	19	also	also	ADV
ejpam-4659	42	20	in	in	ADP
ejpam-4659	42	21	[	[	X
ejpam-4659	42	22	15	15	NUM
ejpam-4659	42	23	]	]	PUNCT
ejpam-4659	42	24	,	,	PUNCT
ejpam-4659	42	25	obtained	obtain	VERB
ejpam-4659	42	26	a	a	DET
ejpam-4659	42	27	class	class	NOUN
ejpam-4659	42	28	of	of	ADP
ejpam-4659	42	29	semi	semi	ADJ
ejpam-4659	42	30	-	-	ADJ
ejpam-4659	42	31	linear	linear	ADJ
ejpam-4659	42	32	equations	equation	NOUN
ejpam-4659	42	33	of	of	ADP
ejpam-4659	42	34	evolution	evolution	NOUN
ejpam-4659	42	35	.	.	PUNCT
ejpam-4659	43	1	rauf	rauf	PROPN
ejpam-4659	43	2	and	and	CCONJ
ejpam-4659	43	3	akinyele	akinyele	PROPN
ejpam-4659	44	1	[	[	X
ejpam-4659	44	2	16	16	NUM
ejpam-4659	44	3	]	]	PUNCT
ejpam-4659	44	4	,	,	PUNCT
ejpam-4659	44	5	introduced	introduce	VERB
ejpam-4659	44	6	ω	ω	NUM
ejpam-4659	44	7	-	-	PUNCT
ejpam-4659	44	8	order	order	NOUN
ejpam-4659	44	9	preserving	preserve	VERB
ejpam-4659	44	10	partial	partial	ADJ
ejpam-4659	44	11	contraction	contraction	NOUN
ejpam-4659	44	12	mapping	mapping	NOUN
ejpam-4659	44	13	and	and	CCONJ
ejpam-4659	44	14	obtained	obtain	VERB
ejpam-4659	44	15	its	its	PRON
ejpam-4659	44	16	properties	property	NOUN
ejpam-4659	44	17	,	,	PUNCT
ejpam-4659	44	18	also	also	ADV
ejpam-4659	44	19	in	in	ADP
ejpam-4659	44	20	[	[	X
ejpam-4659	44	21	17	17	NUM
ejpam-4659	44	22	]	]	PUNCT
ejpam-4659	44	23	,	,	PUNCT
ejpam-4659	44	24	rauf	rauf	PROPN
ejpam-4659	44	25	et	et	PROPN
ejpam-4659	44	26	al	al	PROPN
ejpam-4659	44	27	.	.	PROPN
ejpam-4659	44	28	,	,	PUNCT
ejpam-4659	44	29	established	establish	VERB
ejpam-4659	44	30	some	some	DET
ejpam-4659	44	31	results	result	NOUN
ejpam-4659	44	32	of	of	ADP
ejpam-4659	44	33	stability	stability	NOUN
ejpam-4659	44	34	and	and	CCONJ
ejpam-4659	44	35	spectra	spectra	ADJ
ejpam-4659	44	36	properties	property	NOUN
ejpam-4659	44	37	on	on	ADP
ejpam-4659	44	38	semigroup	semigroup	NOUN
ejpam-4659	44	39	of	of	ADP
ejpam-4659	44	40	linear	linear	PROPN
ejpam-4659	44	41	operator	operator	NOUN
ejpam-4659	44	42	.	.	PUNCT
ejpam-4659	45	1	vrabie	vrabie	PROPN
ejpam-4659	46	1	[	[	X
ejpam-4659	46	2	18	18	NUM
ejpam-4659	46	3	]	]	PUNCT
ejpam-4659	46	4	,	,	PUNCT
ejpam-4659	46	5	proved	prove	VERB
ejpam-4659	46	6	some	some	DET
ejpam-4659	46	7	results	result	NOUN
ejpam-4659	46	8	of	of	ADP
ejpam-4659	46	9	c0	c0	NOUN
ejpam-4659	46	10	-	-	PUNCT
ejpam-4659	46	11	semigroup	semigroup	PROPN
ejpam-4659	46	12	and	and	CCONJ
ejpam-4659	46	13	its	its	PRON
ejpam-4659	46	14	applications	application	NOUN
ejpam-4659	46	15	.	.	PUNCT
ejpam-4659	47	1	yosida	yosida	PROPN
ejpam-4659	48	1	[	[	X
ejpam-4659	48	2	19	19	NUM
ejpam-4659	48	3	]	]	PUNCT
ejpam-4659	48	4	,	,	PUNCT
ejpam-4659	48	5	deduced	deduce	VERB
ejpam-4659	48	6	some	some	DET
ejpam-4659	48	7	results	result	NOUN
ejpam-4659	48	8	on	on	ADP
ejpam-4659	48	9	differentiability	differentiability	NOUN
ejpam-4659	48	10	and	and	CCONJ
ejpam-4659	48	11	representation	representation	NOUN
ejpam-4659	48	12	of	of	ADP
ejpam-4659	48	13	one	one	NUM
ejpam-4659	48	14	-	-	PUNCT
ejpam-4659	48	15	parameter	parameter	NOUN
ejpam-4659	48	16	semigroup	semigroup	NOUN
ejpam-4659	48	17	of	of	ADP
ejpam-4659	48	18	linear	linear	PROPN
ejpam-4659	48	19	operators	operator	NOUN
ejpam-4659	48	20	.	.	PUNCT
ejpam-4659	49	1	a.	a.	PROPN
ejpam-4659	49	2	y.	y.	PROPN
ejpam-4659	49	3	akinyele	akinyele	PROPN
ejpam-4659	49	4	et	et	PROPN
ejpam-4659	49	5	al	al	PROPN
ejpam-4659	49	6	.	.	PUNCT
ejpam-4659	49	7	/	/	SYM
ejpam-4659	49	8	eur	eur	PROPN
ejpam-4659	49	9	.	.	PUNCT
ejpam-4659	50	1	j.	j.	PROPN
ejpam-4659	50	2	pure	pure	PROPN
ejpam-4659	50	3	appl	appl	PROPN
ejpam-4659	50	4	.	.	PROPN
ejpam-4659	50	5	math	math	PROPN
ejpam-4659	50	6	,	,	PUNCT
ejpam-4659	50	7	16	16	NUM
ejpam-4659	50	8	(	(	PUNCT
ejpam-4659	50	9	1	1	NUM
ejpam-4659	50	10	)	)	PUNCT
ejpam-4659	50	11	(	(	PUNCT
ejpam-4659	50	12	2023	2023	NUM
ejpam-4659	50	13	)	)	PUNCT
ejpam-4659	50	14	,	,	PUNCT
ejpam-4659	50	15	538	538	NUM
ejpam-4659	50	16	-	-	SYM
ejpam-4659	50	17	547	547	NUM
ejpam-4659	50	18	540	540	NUM
ejpam-4659	50	19	2	2	NUM
ejpam-4659	50	20	.	.	PUNCT
ejpam-4659	51	1	preliminaries	preliminary	NOUN
ejpam-4659	51	2	definition	definition	NOUN
ejpam-4659	51	3	2.2	2.2	NUM
ejpam-4659	51	4	(	(	PUNCT
ejpam-4659	51	5	c0	c0	NOUN
ejpam-4659	51	6	-	-	PUNCT
ejpam-4659	51	7	semigroup	semigroup	NOUN
ejpam-4659	51	8	)	)	PUNCT
ejpam-4659	52	1	[	[	X
ejpam-4659	52	2	18	18	NUM
ejpam-4659	52	3	]	]	PUNCT
ejpam-4659	52	4	a	a	DET
ejpam-4659	52	5	c0	c0	NOUN
ejpam-4659	52	6	-	-	PUNCT
ejpam-4659	52	7	semigroup	semigroup	PROPN
ejpam-4659	52	8	is	be	AUX
ejpam-4659	52	9	a	a	DET
ejpam-4659	52	10	strongly	strongly	ADV
ejpam-4659	52	11	continuous	continuous	ADJ
ejpam-4659	52	12	one	one	NUM
ejpam-4659	52	13	parameter	parameter	NOUN
ejpam-4659	52	14	semigroup	semigroup	NOUN
ejpam-4659	52	15	of	of	ADP
ejpam-4659	52	16	bounded	bounded	ADJ
ejpam-4659	52	17	linear	linear	ADJ
ejpam-4659	52	18	operator	operator	NOUN
ejpam-4659	52	19	on	on	ADP
ejpam-4659	52	20	banach	banach	NOUN
ejpam-4659	52	21	space	space	NOUN
ejpam-4659	52	22	.	.	PUNCT
ejpam-4659	53	1	definition	definition	NOUN
ejpam-4659	53	2	2.3	2.3	NUM
ejpam-4659	53	3	(	(	PUNCT
ejpam-4659	53	4	ω	ω	ADJ
ejpam-4659	53	5	-	-	ADJ
ejpam-4659	53	6	ocpn	ocpn	ADJ
ejpam-4659	53	7	)	)	PUNCT
ejpam-4659	54	1	[	[	X
ejpam-4659	54	2	16	16	NUM
ejpam-4659	54	3	]	]	PUNCT
ejpam-4659	54	4	a	a	DET
ejpam-4659	54	5	transformation	transformation	NOUN
ejpam-4659	54	6	α	α	X
ejpam-4659	54	7	∈	∈	PROPN
ejpam-4659	54	8	pn	pn	PROPN
ejpam-4659	54	9	is	be	AUX
ejpam-4659	54	10	called	call	VERB
ejpam-4659	54	11	ω	ω	NOUN
ejpam-4659	54	12	-	-	PUNCT
ejpam-4659	54	13	order	order	NOUN
ejpam-4659	54	14	preserving	preserve	VERB
ejpam-4659	54	15	partial	partial	ADJ
ejpam-4659	54	16	contraction	contraction	NOUN
ejpam-4659	54	17	mapping	mapping	NOUN
ejpam-4659	54	18	if	if	SCONJ
ejpam-4659	54	19	∀x	∀x	NUM
ejpam-4659	54	20	,	,	PUNCT
ejpam-4659	54	21	y	y	PROPN
ejpam-4659	54	22	∈	∈	PROPN
ejpam-4659	54	23	domα	domα	NOUN
ejpam-4659	54	24	:	:	PUNCT
ejpam-4659	55	1	x	x	SYM
ejpam-4659	55	2	≤	≤	X
ejpam-4659	55	3	y	y	NOUN
ejpam-4659	55	4	=	=	PRON
ejpam-4659	55	5	⇒	⇒	VERB
ejpam-4659	55	6	αx	αx	ADV
ejpam-4659	55	7	≤	≤	ADJ
ejpam-4659	55	8	αy	αy	ADV
ejpam-4659	55	9	and	and	CCONJ
ejpam-4659	55	10	at	at	ADV
ejpam-4659	55	11	least	least	ADJ
ejpam-4659	55	12	one	one	NUM
ejpam-4659	55	13	of	of	ADP
ejpam-4659	55	14	its	its	PRON
ejpam-4659	55	15	transformation	transformation	NOUN
ejpam-4659	55	16	must	must	AUX
ejpam-4659	55	17	satisfy	satisfy	VERB
ejpam-4659	55	18	αy	αy	ADP
ejpam-4659	56	1	=	=	PUNCT
ejpam-4659	56	2	y	y	PROPN
ejpam-4659	56	3	such	such	ADJ
ejpam-4659	56	4	that	that	DET
ejpam-4659	56	5	t	t	PROPN
ejpam-4659	56	6	(	(	PUNCT
ejpam-4659	56	7	t	t	PROPN
ejpam-4659	56	8	+	+	NUM
ejpam-4659	56	9	s	s	X
ejpam-4659	56	10	)	)	PUNCT
ejpam-4659	56	11	=	=	SYM
ejpam-4659	56	12	t	t	PROPN
ejpam-4659	56	13	(	(	PUNCT
ejpam-4659	56	14	t)t	t)t	X
ejpam-4659	56	15	(	(	PUNCT
ejpam-4659	56	16	s	s	X
ejpam-4659	56	17	)	)	PUNCT
ejpam-4659	56	18	whenever	whenever	SCONJ
ejpam-4659	56	19	t	t	PROPN
ejpam-4659	56	20	,	,	PUNCT
ejpam-4659	56	21	s	s	PART
ejpam-4659	56	22	>	>	X
ejpam-4659	56	23	0	0	PUNCT
ejpam-4659	56	24	and	and	CCONJ
ejpam-4659	56	25	otherwise	otherwise	ADV
ejpam-4659	56	26	for	for	ADP
ejpam-4659	56	27	t	t	PROPN
ejpam-4659	56	28	(	(	PUNCT
ejpam-4659	56	29	0	0	NUM
ejpam-4659	56	30	)	)	PUNCT
ejpam-4659	56	31	=	=	SYM
ejpam-4659	56	32	i.	i.	NOUN
ejpam-4659	56	33	definition	definition	NOUN
ejpam-4659	56	34	2.4	2.4	NUM
ejpam-4659	56	35	(	(	PUNCT
ejpam-4659	56	36	evolution	evolution	NOUN
ejpam-4659	56	37	equation	equation	NOUN
ejpam-4659	56	38	)	)	PUNCT
ejpam-4659	57	1	[	[	X
ejpam-4659	57	2	14	14	NUM
ejpam-4659	57	3	]	]	X
ejpam-4659	57	4	an	an	DET
ejpam-4659	57	5	evolution	evolution	NOUN
ejpam-4659	57	6	equation	equation	NOUN
ejpam-4659	57	7	is	be	AUX
ejpam-4659	57	8	an	an	DET
ejpam-4659	57	9	equation	equation	NOUN
ejpam-4659	57	10	that	that	PRON
ejpam-4659	57	11	can	can	AUX
ejpam-4659	57	12	be	be	AUX
ejpam-4659	57	13	interpreted	interpret	VERB
ejpam-4659	57	14	as	as	ADP
ejpam-4659	57	15	the	the	DET
ejpam-4659	57	16	differential	differential	ADJ
ejpam-4659	57	17	law	law	NOUN
ejpam-4659	57	18	of	of	ADP
ejpam-4659	57	19	the	the	DET
ejpam-4659	57	20	development	development	NOUN
ejpam-4659	57	21	(	(	PUNCT
ejpam-4659	57	22	evolution	evolution	NOUN
ejpam-4659	57	23	)	)	PUNCT
ejpam-4659	57	24	in	in	ADP
ejpam-4659	57	25	time	time	NOUN
ejpam-4659	57	26	of	of	ADP
ejpam-4659	57	27	a	a	DET
ejpam-4659	57	28	system	system	NOUN
ejpam-4659	57	29	.	.	PUNCT
ejpam-4659	58	1	the	the	DET
ejpam-4659	58	2	class	class	NOUN
ejpam-4659	58	3	of	of	ADP
ejpam-4659	58	4	evolution	evolution	NOUN
ejpam-4659	58	5	equations	equation	NOUN
ejpam-4659	58	6	includes	include	VERB
ejpam-4659	58	7	,	,	PUNCT
ejpam-4659	58	8	first	first	ADV
ejpam-4659	58	9	of	of	ADP
ejpam-4659	58	10	all	all	PRON
ejpam-4659	58	11	,	,	PUNCT
ejpam-4659	58	12	ordinary	ordinary	ADJ
ejpam-4659	58	13	differential	differential	ADJ
ejpam-4659	58	14	equations	equation	NOUN
ejpam-4659	58	15	and	and	CCONJ
ejpam-4659	58	16	systems	system	NOUN
ejpam-4659	58	17	of	of	ADP
ejpam-4659	58	18	the	the	DET
ejpam-4659	58	19	form	form	NOUN
ejpam-4659	58	20	u	u	NOUN
ejpam-4659	58	21	=	=	PUNCT
ejpam-4659	58	22	f(t	f(t	NOUN
ejpam-4659	58	23	,	,	PUNCT
ejpam-4659	58	24	u	u	NOUN
ejpam-4659	58	25	)	)	PUNCT
ejpam-4659	58	26	,	,	PUNCT
ejpam-4659	58	27	u	u	NOUN
ejpam-4659	58	28	=	=	PUNCT
ejpam-4659	58	29	f(t	f(t	NOUN
ejpam-4659	58	30	,	,	PUNCT
ejpam-4659	58	31	u	u	NOUN
ejpam-4659	58	32	,	,	PUNCT
ejpam-4659	58	33	u	u	NOUN
ejpam-4659	58	34	)	)	PUNCT
ejpam-4659	58	35	,	,	PUNCT
ejpam-4659	58	36	etc	etc	X
ejpam-4659	58	37	.	.	X
ejpam-4659	58	38	,	,	PUNCT
ejpam-4659	58	39	in	in	ADP
ejpam-4659	58	40	the	the	DET
ejpam-4659	58	41	case	case	NOUN
ejpam-4659	58	42	where	where	SCONJ
ejpam-4659	58	43	u(t	u(t	NOUN
ejpam-4659	58	44	)	)	PUNCT
ejpam-4659	58	45	can	can	AUX
ejpam-4659	58	46	be	be	AUX
ejpam-4659	58	47	regarded	regard	VERB
ejpam-4659	58	48	naturally	naturally	ADV
ejpam-4659	58	49	as	as	ADP
ejpam-4659	58	50	the	the	DET
ejpam-4659	58	51	solution	solution	NOUN
ejpam-4659	58	52	of	of	ADP
ejpam-4659	58	53	the	the	DET
ejpam-4659	58	54	cauchy	cauchy	ADJ
ejpam-4659	58	55	problem	problem	NOUN
ejpam-4659	58	56	;	;	PUNCT
ejpam-4659	58	57	these	these	DET
ejpam-4659	58	58	equations	equation	NOUN
ejpam-4659	58	59	describe	describe	VERB
ejpam-4659	58	60	the	the	DET
ejpam-4659	58	61	evolution	evolution	NOUN
ejpam-4659	58	62	of	of	ADP
ejpam-4659	58	63	systems	system	NOUN
ejpam-4659	58	64	with	with	ADP
ejpam-4659	58	65	finitely	finitely	ADV
ejpam-4659	58	66	many	many	ADJ
ejpam-4659	58	67	degrees	degree	NOUN
ejpam-4659	58	68	of	of	ADP
ejpam-4659	58	69	freedom	freedom	NOUN
ejpam-4659	58	70	.	.	PUNCT
ejpam-4659	59	1	definition	definition	NOUN
ejpam-4659	59	2	2.5	2.5	NUM
ejpam-4659	59	3	(	(	PUNCT
ejpam-4659	59	4	mild	mild	ADJ
ejpam-4659	59	5	solution	solution	NOUN
ejpam-4659	59	6	)	)	PUNCT
ejpam-4659	60	1	[	[	X
ejpam-4659	60	2	15	15	NUM
ejpam-4659	60	3	]	]	X
ejpam-4659	60	4	a	a	DET
ejpam-4659	60	5	continuous	continuous	ADJ
ejpam-4659	60	6	solution	solution	NOUN
ejpam-4659	60	7	u	u	NOUN
ejpam-4659	60	8	of	of	ADP
ejpam-4659	60	9	the	the	DET
ejpam-4659	60	10	integral	integral	ADJ
ejpam-4659	60	11	equation	equation	NOUN
ejpam-4659	60	12	.	.	PUNCT
ejpam-4659	61	1	u(t	u(t	NOUN
ejpam-4659	61	2	)	)	PUNCT
ejpam-4659	62	1	=	=	SYM
ejpam-4659	62	2	t	t	PROPN
ejpam-4659	62	3	(	(	PUNCT
ejpam-4659	62	4	t−	t−	PROPN
ejpam-4659	62	5	t0)u0	t0)u0	ADJ
ejpam-4659	62	6	+	+	NUM
ejpam-4659	62	7	∫	∫	PROPN
ejpam-4659	62	8	t	t	PROPN
ejpam-4659	62	9	t0	t0	PROPN
ejpam-4659	62	10	t	t	PROPN
ejpam-4659	62	11	(	(	PUNCT
ejpam-4659	62	12	t−	t−	X
ejpam-4659	62	13	s)f(s	s)f(	NOUN
ejpam-4659	62	14	,	,	PUNCT
ejpam-4659	62	15	u(s))ds	u(s))ds	PROPN
ejpam-4659	62	16	will	will	AUX
ejpam-4659	62	17	be	be	AUX
ejpam-4659	62	18	called	call	VERB
ejpam-4659	62	19	a	a	DET
ejpam-4659	62	20	mild	mild	ADJ
ejpam-4659	62	21	solution	solution	NOUN
ejpam-4659	62	22	of	of	ADP
ejpam-4659	62	23	the	the	DET
ejpam-4659	62	24	initial	initial	ADJ
ejpam-4659	62	25	value	value	NOUN
ejpam-4659	62	26	problem	problem	NOUN
ejpam-4659	62	27	{	{	PUNCT
ejpam-4659	62	28	du(t	du(t	NOUN
ejpam-4659	62	29	)	)	PUNCT
ejpam-4659	62	30	dt	dt	X
ejpam-4659	63	1	+	+	NOUN
ejpam-4659	63	2	au(t	au(t	NUM
ejpam-4659	63	3	)	)	PUNCT
ejpam-4659	63	4	=	=	SYM
ejpam-4659	63	5	f(t	f(t	NOUN
ejpam-4659	63	6	,	,	PUNCT
ejpam-4659	63	7	u(t	u(t	NOUN
ejpam-4659	63	8	)	)	PUNCT
ejpam-4659	63	9	)	)	PUNCT
ejpam-4659	63	10	,	,	PUNCT
ejpam-4659	63	11	t	t	PROPN
ejpam-4659	63	12	>	>	X
ejpam-4659	63	13	t0	t0	PROPN
ejpam-4659	63	14	u(t0	u(t0	NOUN
ejpam-4659	63	15	)	)	PUNCT
ejpam-4659	63	16	=	=	PUNCT
ejpam-4659	63	17	u0	u0	ADJ
ejpam-4659	63	18	if	if	SCONJ
ejpam-4659	63	19	the	the	DET
ejpam-4659	63	20	solution	solution	NOUN
ejpam-4659	63	21	is	be	AUX
ejpam-4659	63	22	a	a	DET
ejpam-4659	63	23	lipschitz	lipschitz	ADJ
ejpam-4659	63	24	continuous	continuous	ADJ
ejpam-4659	63	25	function	function	NOUN
ejpam-4659	63	26	.	.	PUNCT
ejpam-4659	64	1	definition	definition	NOUN
ejpam-4659	64	2	2.6(analytic	2.6(analytic	PROPN
ejpam-4659	64	3	semigroup	semigroup	NOUN
ejpam-4659	64	4	)	)	PUNCT
ejpam-4659	65	1	[	[	X
ejpam-4659	65	2	18	18	NUM
ejpam-4659	65	3	]	]	PUNCT
ejpam-4659	65	4	we	we	PRON
ejpam-4659	65	5	say	say	VERB
ejpam-4659	65	6	that	that	SCONJ
ejpam-4659	65	7	a	a	DET
ejpam-4659	65	8	c0	c0	NOUN
ejpam-4659	65	9	-	-	PUNCT
ejpam-4659	65	10	semigroup	semigroup	PROPN
ejpam-4659	65	11	{	{	PUNCT
ejpam-4659	65	12	t	t	PROPN
ejpam-4659	65	13	(	(	PUNCT
ejpam-4659	65	14	t	t	PROPN
ejpam-4659	65	15	)	)	PUNCT
ejpam-4659	65	16	;	;	PUNCT
ejpam-4659	65	17	t	t	PROPN
ejpam-4659	65	18	≥	≥	NUM
ejpam-4659	65	19	0	0	NUM
ejpam-4659	65	20	}	}	PUNCT
ejpam-4659	65	21	is	be	AUX
ejpam-4659	65	22	analytic	analytic	ADJ
ejpam-4659	65	23	if	if	SCONJ
ejpam-4659	65	24	there	there	PRON
ejpam-4659	65	25	exists	exist	VERB
ejpam-4659	65	26	0	0	PUNCT
ejpam-4659	65	27	<	<	X
ejpam-4659	65	28	θ	θ	X
ejpam-4659	65	29	≤	≤	NUM
ejpam-4659	65	30	π	π	PROPN
ejpam-4659	65	31	,	,	PUNCT
ejpam-4659	65	32	and	and	CCONJ
ejpam-4659	65	33	a	a	DET
ejpam-4659	65	34	mapping	mapping	NOUN
ejpam-4659	65	35	s	s	VERB
ejpam-4659	65	36	:	:	PUNCT
ejpam-4659	65	37	c̄θ	c̄θ	VERB
ejpam-4659	65	38	→	→	SYM
ejpam-4659	65	39	l(x	l(x	PROPN
ejpam-4659	65	40	)	)	PUNCT
ejpam-4659	65	41	such	such	ADJ
ejpam-4659	65	42	that	that	SCONJ
ejpam-4659	65	43	:	:	PUNCT
ejpam-4659	65	44	(	(	PUNCT
ejpam-4659	65	45	i	i	NOUN
ejpam-4659	65	46	)	)	PUNCT
ejpam-4659	65	47	t	t	PROPN
ejpam-4659	65	48	(	(	PUNCT
ejpam-4659	65	49	t	t	PROPN
ejpam-4659	65	50	)	)	PUNCT
ejpam-4659	65	51	=	=	SYM
ejpam-4659	65	52	s(t	s(t	PROPN
ejpam-4659	65	53	)	)	PUNCT
ejpam-4659	65	54	for	for	ADP
ejpam-4659	65	55	each	each	DET
ejpam-4659	65	56	t	t	PROPN
ejpam-4659	65	57	≥	≥	NOUN
ejpam-4659	65	58	0	0	NUM
ejpam-4659	65	59	;	;	PUNCT
ejpam-4659	65	60	(	(	PUNCT
ejpam-4659	65	61	ii	ii	NOUN
ejpam-4659	65	62	)	)	PUNCT
ejpam-4659	65	63	s(z1	s(z1	NOUN
ejpam-4659	66	1	+	+	CCONJ
ejpam-4659	66	2	z2	z2	ADJ
ejpam-4659	66	3	)	)	PUNCT
ejpam-4659	66	4	=	=	SYM
ejpam-4659	66	5	s(z1)s(z2	s(z1)s(z2	NOUN
ejpam-4659	66	6	)	)	PUNCT
ejpam-4659	66	7	for	for	ADP
ejpam-4659	66	8	z1	z1	PROPN
ejpam-4659	66	9	,	,	PUNCT
ejpam-4659	66	10	z2	z2	PROPN
ejpam-4659	66	11	∈	∈	PROPN
ejpam-4659	66	12	c̄θ	c̄θ	VERB
ejpam-4659	66	13	;	;	PUNCT
ejpam-4659	66	14	(	(	PUNCT
ejpam-4659	66	15	iii	iii	NOUN
ejpam-4659	66	16	)	)	PUNCT
ejpam-4659	66	17	limz1∈c̄θ	limz1∈c̄θ	VERB
ejpam-4659	66	18	,	,	PUNCT
ejpam-4659	66	19	z1→0s(z1)x	z1→0s(z1)x	NOUN
ejpam-4659	66	20	=	=	SYM
ejpam-4659	66	21	x	x	SYM
ejpam-4659	66	22	for	for	ADP
ejpam-4659	66	23	x	x	SYM
ejpam-4659	66	24	∈	∈	PROPN
ejpam-4659	66	25	x	x	NOUN
ejpam-4659	66	26	;	;	PUNCT
ejpam-4659	66	27	and	and	CCONJ
ejpam-4659	66	28	(	(	PUNCT
ejpam-4659	66	29	iv	iv	X
ejpam-4659	66	30	)	)	PUNCT
ejpam-4659	66	31	the	the	DET
ejpam-4659	66	32	mapping	map	VERB
ejpam-4659	66	33	z1	z1	NOUN
ejpam-4659	66	34	→	→	PUNCT
ejpam-4659	66	35	s(z1	s(z1	NOUN
ejpam-4659	66	36	)	)	PUNCT
ejpam-4659	66	37	is	be	AUX
ejpam-4659	66	38	analytic	analytic	ADJ
ejpam-4659	66	39	from	from	ADP
ejpam-4659	66	40	c̄θ	c̄θ	VERB
ejpam-4659	66	41	to	to	ADP
ejpam-4659	66	42	l(x	l(x	PROPN
ejpam-4659	66	43	)	)	PUNCT
ejpam-4659	66	44	.	.	PUNCT
ejpam-4659	67	1	in	in	ADP
ejpam-4659	67	2	addition	addition	NOUN
ejpam-4659	67	3	,	,	PUNCT
ejpam-4659	67	4	for	for	ADP
ejpam-4659	67	5	each	each	DET
ejpam-4659	67	6	0	0	NUM
ejpam-4659	67	7	<	<	X
ejpam-4659	67	8	δ	δ	X
ejpam-4659	67	9	<	<	X
ejpam-4659	67	10	θ	θ	PROPN
ejpam-4659	67	11	,	,	PUNCT
ejpam-4659	67	12	the	the	DET
ejpam-4659	67	13	mapping	mapping	NOUN
ejpam-4659	67	14	z1	z1	NOUN
ejpam-4659	67	15	→	→	PUNCT
ejpam-4659	67	16	s(z1	s(z1	NOUN
ejpam-4659	67	17	)	)	PUNCT
ejpam-4659	67	18	is	be	AUX
ejpam-4659	67	19	bounded	bound	VERB
ejpam-4659	67	20	from	from	ADP
ejpam-4659	67	21	cδ	cδ	NOUN
ejpam-4659	67	22	to	to	ADP
ejpam-4659	67	23	l(x	l(x	PROPN
ejpam-4659	67	24	)	)	PUNCT
ejpam-4659	67	25	,	,	PUNCT
ejpam-4659	67	26	then	then	ADV
ejpam-4659	67	27	the	the	DET
ejpam-4659	67	28	c0	c0	PROPN
ejpam-4659	67	29	-	-	PUNCT
ejpam-4659	67	30	semigroup	semigroup	PROPN
ejpam-4659	67	31	{	{	PUNCT
ejpam-4659	67	32	t	t	PROPN
ejpam-4659	67	33	(	(	PUNCT
ejpam-4659	67	34	t	t	PROPN
ejpam-4659	67	35	)	)	PUNCT
ejpam-4659	67	36	;	;	PUNCT
ejpam-4659	67	37	t	t	PROPN
ejpam-4659	67	38	≥	≥	NOUN
ejpam-4659	67	39	0	0	NUM
ejpam-4659	67	40	}	}	PUNCT
ejpam-4659	67	41	is	be	AUX
ejpam-4659	67	42	called	call	VERB
ejpam-4659	67	43	analytic	analytic	ADJ
ejpam-4659	67	44	and	and	CCONJ
ejpam-4659	67	45	uniformly	uniformly	ADV
ejpam-4659	67	46	bounded	bound	VERB
ejpam-4659	67	47	.	.	PUNCT
ejpam-4659	68	1	definition	definition	NOUN
ejpam-4659	68	2	2.7(strongly	2.7(strongly	PROPN
ejpam-4659	68	3	elliptic	elliptic	ADJ
ejpam-4659	68	4	)	)	PUNCT
ejpam-4659	69	1	[	[	X
ejpam-4659	69	2	15	15	NUM
ejpam-4659	69	3	]	]	X
ejpam-4659	69	4	the	the	DET
ejpam-4659	69	5	operator	operator	NOUN
ejpam-4659	69	6	a(x	a(x	NOUN
ejpam-4659	69	7	,	,	PUNCT
ejpam-4659	69	8	d	d	NOUN
ejpam-4659	69	9	)	)	PUNCT
ejpam-4659	69	10	is	be	AUX
ejpam-4659	69	11	strongly	strongly	ADV
ejpam-4659	69	12	elliptic	elliptic	ADJ
ejpam-4659	69	13	if	if	SCONJ
ejpam-4659	69	14	there	there	PRON
ejpam-4659	69	15	exists	exist	VERB
ejpam-4659	69	16	a	a	DET
ejpam-4659	69	17	constant	constant	ADJ
ejpam-4659	69	18	c	c	NOUN
ejpam-4659	69	19	>	>	X
ejpam-4659	69	20	0	0	NUM
ejpam-4659	69	21	such	such	ADJ
ejpam-4659	69	22	that	that	DET
ejpam-4659	69	23	re(−1)ma1(x	re(−1)ma1(x	NOUN
ejpam-4659	69	24	,	,	PUNCT
ejpam-4659	69	25	ξ	ξ	X
ejpam-4659	69	26	)	)	PUNCT
ejpam-4659	69	27	≥	≥	NOUN
ejpam-4659	70	1	c|ξ|2	c|ξ|2	PROPN
ejpam-4659	70	2	m	m	PROPN
ejpam-4659	70	3	a.	a.	NOUN
ejpam-4659	70	4	y.	y.	PROPN
ejpam-4659	70	5	akinyele	akinyele	PROPN
ejpam-4659	70	6	et	et	PROPN
ejpam-4659	70	7	al	al	PROPN
ejpam-4659	70	8	.	.	PUNCT
ejpam-4659	70	9	/	/	SYM
ejpam-4659	70	10	eur	eur	PROPN
ejpam-4659	70	11	.	.	PUNCT
ejpam-4659	71	1	j.	j.	PROPN
ejpam-4659	71	2	pure	pure	PROPN
ejpam-4659	71	3	appl	appl	PROPN
ejpam-4659	71	4	.	.	PROPN
ejpam-4659	71	5	math	math	PROPN
ejpam-4659	71	6	,	,	PUNCT
ejpam-4659	71	7	16	16	NUM
ejpam-4659	71	8	(	(	PUNCT
ejpam-4659	71	9	1	1	NUM
ejpam-4659	71	10	)	)	PUNCT
ejpam-4659	71	11	(	(	PUNCT
ejpam-4659	71	12	2023	2023	NUM
ejpam-4659	71	13	)	)	PUNCT
ejpam-4659	71	14	,	,	PUNCT
ejpam-4659	71	15	538	538	NUM
ejpam-4659	71	16	-	-	SYM
ejpam-4659	71	17	547	547	NUM
ejpam-4659	71	18	541	541	NUM
ejpam-4659	71	19	for	for	ADP
ejpam-4659	71	20	all	all	DET
ejpam-4659	71	21	x	x	SYM
ejpam-4659	71	22	∈	∈	PROPN
ejpam-4659	71	23	ω	ω	NOUN
ejpam-4659	71	24	and	and	CCONJ
ejpam-4659	71	25	ξ	ξ	PROPN
ejpam-4659	71	26	∈	∈	PROPN
ejpam-4659	71	27	rn	rn	PROPN
ejpam-4659	71	28	.	.	PROPN
ejpam-4659	71	29	example	example	NOUN
ejpam-4659	71	30	1	1	NUM
ejpam-4659	71	31	for	for	ADP
ejpam-4659	71	32	every	every	DET
ejpam-4659	71	33	2×	2×	NUM
ejpam-4659	71	34	2	2	NUM
ejpam-4659	71	35	matrix	matrix	NOUN
ejpam-4659	71	36	in	in	ADP
ejpam-4659	71	37	[	[	X
ejpam-4659	71	38	mm(rn	mm(rn	PROPN
ejpam-4659	71	39	)	)	PUNCT
ejpam-4659	71	40	]	]	PUNCT
ejpam-4659	71	41	.	.	PUNCT
ejpam-4659	71	42	suppose	suppose	VERB
ejpam-4659	71	43	a	a	DET
ejpam-4659	71	44	=	=	X
ejpam-4659	71	45	(	(	PUNCT
ejpam-4659	71	46	2	2	NUM
ejpam-4659	71	47	0	0	NUM
ejpam-4659	71	48	∆	∆	X
ejpam-4659	71	49	2	2	NUM
ejpam-4659	71	50	)	)	PUNCT
ejpam-4659	71	51	and	and	CCONJ
ejpam-4659	71	52	let	let	VERB
ejpam-4659	71	53	t	t	PROPN
ejpam-4659	71	54	(	(	PUNCT
ejpam-4659	71	55	t	t	PROPN
ejpam-4659	71	56	)	)	PUNCT
ejpam-4659	71	57	=	=	SYM
ejpam-4659	71	58	eta	eta	PROPN
ejpam-4659	71	59	,	,	PUNCT
ejpam-4659	71	60	then	then	ADV
ejpam-4659	71	61	we	we	PRON
ejpam-4659	71	62	have	have	VERB
ejpam-4659	71	63	eta	eta	NOUN
ejpam-4659	71	64	=	=	X
ejpam-4659	71	65	(	(	PUNCT
ejpam-4659	71	66	e2	e2	PROPN
ejpam-4659	71	67	t	t	PROPN
ejpam-4659	71	68	i	i	PRON
ejpam-4659	71	69	e∆t	e∆t	PROPN
ejpam-4659	71	70	e2	e2	PROPN
ejpam-4659	71	71	t	t	PROPN
ejpam-4659	71	72	)	)	PUNCT
ejpam-4659	71	73	.	.	PUNCT
ejpam-4659	72	1	example	example	NOUN
ejpam-4659	72	2	2	2	NUM
ejpam-4659	72	3	for	for	ADP
ejpam-4659	72	4	every	every	DET
ejpam-4659	72	5	3×	3×	NUM
ejpam-4659	72	6	3	3	NUM
ejpam-4659	72	7	matrix	matrix	NOUN
ejpam-4659	72	8	in	in	ADP
ejpam-4659	72	9	[	[	X
ejpam-4659	72	10	mm(c	mm(c	X
ejpam-4659	72	11	)	)	PUNCT
ejpam-4659	72	12	]	]	PUNCT
ejpam-4659	72	13	,	,	PUNCT
ejpam-4659	72	14	we	we	PRON
ejpam-4659	72	15	have	have	VERB
ejpam-4659	72	16	for	for	ADP
ejpam-4659	72	17	each	each	DET
ejpam-4659	72	18	λ	λ	PROPN
ejpam-4659	72	19	>	>	X
ejpam-4659	72	20	0	0	NUM
ejpam-4659	73	1	such	such	ADJ
ejpam-4659	73	2	that	that	SCONJ
ejpam-4659	73	3	λ	λ	PROPN
ejpam-4659	73	4	∈	∈	PROPN
ejpam-4659	73	5	ρ(a	ρ(a	PROPN
ejpam-4659	73	6	)	)	PUNCT
ejpam-4659	73	7	where	where	SCONJ
ejpam-4659	73	8	ρ(a	ρ(a	NOUN
ejpam-4659	73	9	)	)	PUNCT
ejpam-4659	73	10	is	be	AUX
ejpam-4659	73	11	a	a	DET
ejpam-4659	73	12	resolvent	resolvent	ADJ
ejpam-4659	73	13	set	set	NOUN
ejpam-4659	73	14	on	on	ADP
ejpam-4659	73	15	x.	x.	NOUN
ejpam-4659	73	16	suppose	suppose	VERB
ejpam-4659	73	17	we	we	PRON
ejpam-4659	73	18	have	have	VERB
ejpam-4659	73	19	a	a	DET
ejpam-4659	73	20	=	=	SYM
ejpam-4659	73	21			PROPN
ejpam-4659	73	22	2	2	NUM
ejpam-4659	73	23	2	2	NUM
ejpam-4659	73	24	i	i	NOUN
ejpam-4659	73	25	2	2	NUM
ejpam-4659	73	26	2	2	NUM
ejpam-4659	73	27	2	2	NUM
ejpam-4659	73	28	∆	∆	X
ejpam-4659	73	29	2	2	NUM
ejpam-4659	73	30	2	2	NUM
ejpam-4659	73	31			PROPN
ejpam-4659	73	32	and	and	CCONJ
ejpam-4659	73	33	let	let	VERB
ejpam-4659	73	34	t	t	PROPN
ejpam-4659	73	35	(	(	PUNCT
ejpam-4659	73	36	t	t	PROPN
ejpam-4659	73	37	)	)	PUNCT
ejpam-4659	74	1	=	=	PUNCT
ejpam-4659	74	2	etaλ	etaλ	NOUN
ejpam-4659	74	3	,	,	PUNCT
ejpam-4659	74	4	then	then	ADV
ejpam-4659	74	5	we	we	PRON
ejpam-4659	74	6	have	have	AUX
ejpam-4659	74	7	etaλ	etaλ	VERB
ejpam-4659	74	8	=	=	SYM
ejpam-4659	74	9	e2tλ	e2tλ	X
ejpam-4659	74	10	e2tλ	e2tλ	PUNCT
ejpam-4659	75	1	i	i	PRON
ejpam-4659	75	2	e2tλ	e2tλ	X
ejpam-4659	75	3	e2tλ	e2tλ	X
ejpam-4659	75	4	e2tλ	e2tλ	NUM
ejpam-4659	75	5	e∆tλ	e∆tλ	ADJ
ejpam-4659	75	6	e2tλ	e2tλ	X
ejpam-4659	75	7	e2tλ	e2tλ	NUM
ejpam-4659	76	1			PROPN
ejpam-4659	76	2	.	.	PUNCT
ejpam-4659	76	3	example	example	NOUN
ejpam-4659	77	1	3	3	NUM
ejpam-4659	77	2	let	let	VERB
ejpam-4659	77	3	x	x	NOUN
ejpam-4659	77	4	=	=	SYM
ejpam-4659	77	5	cub(n∪{0	cub(n∪{0	NOUN
ejpam-4659	77	6	}	}	PUNCT
ejpam-4659	77	7	)	)	PUNCT
ejpam-4659	77	8	be	be	AUX
ejpam-4659	77	9	the	the	DET
ejpam-4659	77	10	space	space	NOUN
ejpam-4659	77	11	of	of	ADP
ejpam-4659	77	12	all	all	DET
ejpam-4659	77	13	bounded	bounded	ADJ
ejpam-4659	77	14	and	and	CCONJ
ejpam-4659	77	15	uniformly	uniformly	ADV
ejpam-4659	77	16	continuous	continuous	ADJ
ejpam-4659	77	17	function	function	NOUN
ejpam-4659	77	18	from	from	ADP
ejpam-4659	77	19	n∪{0	n∪{0	NOUN
ejpam-4659	77	20	}	}	PUNCT
ejpam-4659	77	21	to	to	ADP
ejpam-4659	77	22	r	r	NOUN
ejpam-4659	77	23	,	,	PUNCT
ejpam-4659	77	24	endowed	endow	VERB
ejpam-4659	77	25	with	with	ADP
ejpam-4659	77	26	the	the	DET
ejpam-4659	77	27	sup	sup	ADJ
ejpam-4659	77	28	-	-	PUNCT
ejpam-4659	77	29	norm	norm	NOUN
ejpam-4659	77	30	∥	∥	NOUN
ejpam-4659	77	31	·	·	PUNCT
ejpam-4659	77	32	∥∞	∥∞	ADJ
ejpam-4659	77	33	and	and	CCONJ
ejpam-4659	77	34	let	let	VERB
ejpam-4659	77	35	{	{	PUNCT
ejpam-4659	77	36	t	t	PROPN
ejpam-4659	77	37	(	(	PUNCT
ejpam-4659	77	38	t	t	PROPN
ejpam-4659	77	39	)	)	PUNCT
ejpam-4659	77	40	;	;	PUNCT
ejpam-4659	77	41	t	t	PROPN
ejpam-4659	77	42	∈	∈	PROPN
ejpam-4659	77	43	r+	r+	PUNCT
ejpam-4659	77	44	}	}	PUNCT
ejpam-4659	77	45	⊆	⊆	NUM
ejpam-4659	77	46	l(x	l(x	PROPN
ejpam-4659	77	47	)	)	PUNCT
ejpam-4659	77	48	be	be	AUX
ejpam-4659	77	49	defined	define	VERB
ejpam-4659	77	50	by	by	ADP
ejpam-4659	77	51	[	[	X
ejpam-4659	77	52	t	t	X
ejpam-4659	77	53	(	(	PUNCT
ejpam-4659	77	54	t)f	t)f	X
ejpam-4659	77	55	]	]	X
ejpam-4659	77	56	(	(	PUNCT
ejpam-4659	77	57	s	s	X
ejpam-4659	77	58	)	)	PUNCT
ejpam-4659	77	59	=	=	PUNCT
ejpam-4659	77	60	f(t+	f(t+	NUM
ejpam-4659	77	61	s	s	X
ejpam-4659	77	62	)	)	PUNCT
ejpam-4659	77	63	for	for	ADP
ejpam-4659	77	64	each	each	DET
ejpam-4659	77	65	f	f	PROPN
ejpam-4659	77	66	∈	∈	PROPN
ejpam-4659	77	67	x	x	X
ejpam-4659	77	68	and	and	CCONJ
ejpam-4659	77	69	each	each	DET
ejpam-4659	77	70	t	t	PROPN
ejpam-4659	77	71	,	,	PUNCT
ejpam-4659	77	72	s	s	PART
ejpam-4659	77	73	∈	∈	PROPN
ejpam-4659	77	74	r+	r+	NOUN
ejpam-4659	77	75	,	,	PUNCT
ejpam-4659	77	76	one	one	PRON
ejpam-4659	77	77	may	may	AUX
ejpam-4659	77	78	easily	easily	ADV
ejpam-4659	77	79	verify	verify	VERB
ejpam-4659	77	80	that	that	SCONJ
ejpam-4659	77	81	{	{	PUNCT
ejpam-4659	77	82	t	t	PROPN
ejpam-4659	77	83	(	(	PUNCT
ejpam-4659	77	84	t	t	PROPN
ejpam-4659	77	85	)	)	PUNCT
ejpam-4659	77	86	;	;	PUNCT
ejpam-4659	77	87	t	t	PROPN
ejpam-4659	77	88	∈	∈	PROPN
ejpam-4659	77	89	r+	r+	PUNCT
ejpam-4659	77	90	}	}	PUNCT
ejpam-4659	77	91	satisfies	satisfy	VERB
ejpam-4659	77	92	examples	example	NOUN
ejpam-4659	77	93	1	1	NUM
ejpam-4659	77	94	and	and	CCONJ
ejpam-4659	77	95	2	2	NUM
ejpam-4659	77	96	above	above	ADV
ejpam-4659	77	97	.	.	PUNCT
ejpam-4659	78	1	lemma	lemma	PROPN
ejpam-4659	78	2	2.1	2.1	NUM
ejpam-4659	78	3	let	let	VERB
ejpam-4659	78	4	ω	ω	NUM
ejpam-4659	78	5	be	be	AUX
ejpam-4659	78	6	a	a	DET
ejpam-4659	78	7	bounded	bounded	ADJ
ejpam-4659	78	8	domain	domain	NOUN
ejpam-4659	78	9	in	in	ADP
ejpam-4659	78	10	rn	rn	PROPN
ejpam-4659	78	11	with	with	ADP
ejpam-4659	78	12	boundary	boundary	ADJ
ejpam-4659	78	13	∂ω	∂ω	PROPN
ejpam-4659	78	14	of	of	ADP
ejpam-4659	78	15	class	class	NOUN
ejpam-4659	78	16	cm	cm	NOUN
ejpam-4659	78	17	and	and	CCONJ
ejpam-4659	78	18	let	let	VERB
ejpam-4659	78	19	u	u	PRON
ejpam-4659	78	20	∈	∈	PROPN
ejpam-4659	78	21	wm	wm	PROPN
ejpam-4659	78	22	,	,	PUNCT
ejpam-4659	78	23	r(ω	r(ω	ADJ
ejpam-4659	78	24	)	)	PUNCT
ejpam-4659	78	25	∩	∩	NOUN
ejpam-4659	78	26	lq(ω	lq(ω	NOUN
ejpam-4659	78	27	)	)	PUNCT
ejpam-4659	78	28	where	where	SCONJ
ejpam-4659	78	29	1	1	NUM
ejpam-4659	78	30	≤	≤	NOUN
ejpam-4659	78	31	r	r	NOUN
ejpam-4659	78	32	,	,	PUNCT
ejpam-4659	78	33	q	q	ADJ
ejpam-4659	78	34	≤	≤	NUM
ejpam-4659	78	35	∞.	∞.	PROPN
ejpam-4659	78	36	for	for	ADP
ejpam-4659	78	37	any	any	DET
ejpam-4659	78	38	integer	integer	PROPN
ejpam-4659	78	39	j	j	PROPN
ejpam-4659	78	40	,	,	PUNCT
ejpam-4659	78	41	0	0	NUM
ejpam-4659	78	42	≤	≤	NUM
ejpam-4659	78	43	j	j	X
ejpam-4659	78	44	<	<	X
ejpam-4659	78	45	m	m	VERB
ejpam-4659	78	46	and	and	CCONJ
ejpam-4659	78	47	any	any	DET
ejpam-4659	78	48	j	j	PROPN
ejpam-4659	78	49	m	m	VERB
ejpam-4659	78	50	≤	≤	NOUN
ejpam-4659	78	51	ϑ	ϑ	PRON
ejpam-4659	78	52	≤	≤	NUM
ejpam-4659	78	53	1	1	NUM
ejpam-4659	78	54	we	we	PRON
ejpam-4659	78	55	have	have	VERB
ejpam-4659	78	56	∥dju∥0,p	∥dju∥0,p	NOUN
ejpam-4659	78	57	≤	≤	NOUN
ejpam-4659	78	58	c∥u∥ϑm	c∥u∥ϑm	PROPN
ejpam-4659	78	59	,	,	PUNCT
ejpam-4659	78	60	r∥u∥1−ϑ	r∥u∥1−ϑ	NOUN
ejpam-4659	78	61	0,q	0,q	PUNCT
ejpam-4659	79	1	(	(	PUNCT
ejpam-4659	79	2	6	6	NUM
ejpam-4659	79	3	)	)	PUNCT
ejpam-4659	79	4	provided	provide	VERB
ejpam-4659	79	5	that	that	SCONJ
ejpam-4659	79	6	1	1	NUM
ejpam-4659	79	7	p	p	NOUN
ejpam-4659	79	8	=	=	PUNCT
ejpam-4659	79	9	j	j	PROPN
ejpam-4659	79	10	n	n	PROPN
ejpam-4659	79	11	+	+	CCONJ
ejpam-4659	79	12	ϑ	ϑ	X
ejpam-4659	79	13	(	(	PUNCT
ejpam-4659	79	14	1	1	NUM
ejpam-4659	79	15	r	r	NOUN
ejpam-4659	79	16	−	−	NOUN
ejpam-4659	79	17	m	m	NOUN
ejpam-4659	79	18	n	n	NUM
ejpam-4659	79	19	)	)	PUNCT
ejpam-4659	80	1	+	+	CCONJ
ejpam-4659	80	2	(	(	PUNCT
ejpam-4659	80	3	1−	1−	NUM
ejpam-4659	80	4	ϑ	ϑ	NOUN
ejpam-4659	80	5	)	)	PUNCT
ejpam-4659	80	6	1	1	NUM
ejpam-4659	80	7	q	q	NOUN
ejpam-4659	80	8	(	(	PUNCT
ejpam-4659	80	9	7	7	NUM
ejpam-4659	80	10	)	)	PUNCT
ejpam-4659	80	11	a.	a.	NOUN
ejpam-4659	80	12	y.	y.	PROPN
ejpam-4659	80	13	akinyele	akinyele	PROPN
ejpam-4659	80	14	et	et	PROPN
ejpam-4659	80	15	al	al	PROPN
ejpam-4659	80	16	.	.	PUNCT
ejpam-4659	80	17	/	/	SYM
ejpam-4659	80	18	eur	eur	PROPN
ejpam-4659	80	19	.	.	PUNCT
ejpam-4659	81	1	j.	j.	PROPN
ejpam-4659	81	2	pure	pure	PROPN
ejpam-4659	81	3	appl	appl	PROPN
ejpam-4659	81	4	.	.	PROPN
ejpam-4659	81	5	math	math	PROPN
ejpam-4659	81	6	,	,	PUNCT
ejpam-4659	81	7	16	16	NUM
ejpam-4659	81	8	(	(	PUNCT
ejpam-4659	81	9	1	1	NUM
ejpam-4659	81	10	)	)	PUNCT
ejpam-4659	81	11	(	(	PUNCT
ejpam-4659	81	12	2023	2023	NUM
ejpam-4659	81	13	)	)	PUNCT
ejpam-4659	81	14	,	,	PUNCT
ejpam-4659	81	15	538	538	NUM
ejpam-4659	81	16	-	-	SYM
ejpam-4659	81	17	547	547	NUM
ejpam-4659	81	18	542	542	NUM
ejpam-4659	81	19	and	and	CCONJ
ejpam-4659	81	20	m−	m−	PROPN
ejpam-4659	81	21	j	j	PROPN
ejpam-4659	81	22	−	−	PROPN
ejpam-4659	82	1	n	n	PRON
ejpam-4659	82	2	r	r	NOUN
ejpam-4659	82	3	is	be	AUX
ejpam-4659	82	4	not	not	PART
ejpam-4659	82	5	a	a	DET
ejpam-4659	82	6	nonnegative	nonnegative	ADJ
ejpam-4659	82	7	integer	integer	NOUN
ejpam-4659	82	8	,	,	PUNCT
ejpam-4659	82	9	the	the	DET
ejpam-4659	82	10	(	(	PUNCT
ejpam-4659	82	11	6	6	NUM
ejpam-4659	82	12	)	)	PUNCT
ejpam-4659	82	13	holds	hold	VERB
ejpam-4659	82	14	with	with	ADP
ejpam-4659	82	15	ϑ	ϑ	PROPN
ejpam-4659	82	16	=	=	X
ejpam-4659	82	17	j	j	PROPN
ejpam-4659	82	18	m	m	PROPN
ejpam-4659	82	19	.	.	PUNCT
ejpam-4659	83	1	theorem	theorem	VERB
ejpam-4659	83	2	2.2	2.2	NUM
ejpam-4659	83	3	[	[	PUNCT
ejpam-4659	83	4	sobolev	sobolev	NOUN
ejpam-4659	83	5	]	]	PUNCT
ejpam-4659	83	6	let	let	VERB
ejpam-4659	83	7	ω	ω	PRON
ejpam-4659	83	8	be	be	AUX
ejpam-4659	83	9	a	a	DET
ejpam-4659	83	10	bounded	bounded	ADJ
ejpam-4659	83	11	domain	domain	NOUN
ejpam-4659	83	12	in	in	ADP
ejpam-4659	83	13	rn	rn	PROPN
ejpam-4659	83	14	with	with	ADP
ejpam-4659	83	15	smooth	smooth	ADJ
ejpam-4659	83	16	boundary	boundary	ADJ
ejpam-4659	83	17	∂ω	∂ω	PROPN
ejpam-4659	83	18	(	(	PUNCT
ejpam-4659	83	19	e.g.	e.g.	ADV
ejpam-4659	83	20	∂ω	∂ω	PROPN
ejpam-4659	83	21	is	be	AUX
ejpam-4659	83	22	of	of	ADP
ejpam-4659	83	23	class	class	NOUN
ejpam-4659	83	24	cm	cm	NOUN
ejpam-4659	83	25	)	)	PUNCT
ejpam-4659	83	26	,	,	PUNCT
ejpam-4659	83	27	then	then	ADV
ejpam-4659	83	28	w	w	PROPN
ejpam-4659	83	29	k	k	PROPN
ejpam-4659	83	30	,	,	PUNCT
ejpam-4659	83	31	p	p	X
ejpam-4659	83	32	⊂	⊂	X
ejpam-4659	83	33	lnp/(n−kp)(ω	lnp/(n−kp)(ω	X
ejpam-4659	83	34	)	)	PUNCT
ejpam-4659	83	35	for	for	ADP
ejpam-4659	83	36	kp	kp	PROPN
ejpam-4659	83	37	<	<	X
ejpam-4659	83	38	n	n	PROPN
ejpam-4659	83	39	(	(	PUNCT
ejpam-4659	83	40	8)	8)	NUM
ejpam-4659	83	41	and	and	CCONJ
ejpam-4659	83	42	w	w	PROPN
ejpam-4659	83	43	k	k	PROPN
ejpam-4659	83	44	,	,	PUNCT
ejpam-4659	83	45	p(ω	p(ω	PROPN
ejpam-4659	83	46	)	)	PUNCT
ejpam-4659	83	47	⊂	⊂	PROPN
ejpam-4659	83	48	cm(ω	cm(ω	ADV
ejpam-4659	83	49	)	)	PUNCT
ejpam-4659	83	50	for	for	ADP
ejpam-4659	83	51	0	0	NUM
ejpam-4659	83	52	≤	≤	NUM
ejpam-4659	83	53	m	m	VERB
ejpam-4659	83	54	<	<	X
ejpam-4659	83	55	k	k	X
ejpam-4659	83	56	−	−	PROPN
ejpam-4659	84	1	n	n	PRON
ejpam-4659	84	2	p	p	NOUN
ejpam-4659	84	3	.	.	PUNCT
ejpam-4659	85	1	(	(	PUNCT
ejpam-4659	85	2	9	9	NUM
ejpam-4659	85	3	)	)	PUNCT
ejpam-4659	85	4	moreover	moreover	ADV
ejpam-4659	85	5	,	,	PUNCT
ejpam-4659	85	6	there	there	PRON
ejpam-4659	85	7	exists	exist	VERB
ejpam-4659	85	8	a	a	DET
ejpam-4659	85	9	constant	constant	ADJ
ejpam-4659	85	10	c1	c1	NOUN
ejpam-4659	85	11	and	and	CCONJ
ejpam-4659	85	12	c2	c2	PROPN
ejpam-4659	85	13	such	such	ADJ
ejpam-4659	85	14	that	that	PRON
ejpam-4659	85	15	for	for	ADP
ejpam-4659	85	16	any	any	DET
ejpam-4659	85	17	u	u	PROPN
ejpam-4659	85	18	∈	∈	PROPN
ejpam-4659	85	19	wm	wm	PROPN
ejpam-4659	85	20	,	,	PUNCT
ejpam-4659	85	21	p(ω	p(ω	PROPN
ejpam-4659	85	22	)	)	PUNCT
ejpam-4659	85	23	∥u∥0,n	∥u∥0,n	PROPN
ejpam-4659	85	24	,	,	PUNCT
ejpam-4659	85	25	p/(n−kp	p/(n−kp	PROPN
ejpam-4659	85	26	)	)	PUNCT
ejpam-4659	85	27	≤	≤	PROPN
ejpam-4659	85	28	c1∥u∥k	c1∥u∥k	PROPN
ejpam-4659	85	29	,	,	PUNCT
ejpam-4659	85	30	p	p	NOUN
ejpam-4659	85	31	for	for	ADP
ejpam-4659	85	32	kp	kp	PROPN
ejpam-4659	85	33	<	<	X
ejpam-4659	85	34	n	n	PROPN
ejpam-4659	85	35	(	(	PUNCT
ejpam-4659	85	36	10	10	NUM
ejpam-4659	85	37	)	)	PUNCT
ejpam-4659	85	38	and	and	CCONJ
ejpam-4659	85	39	sup(|dα	sup(|dα	VERB
ejpam-4659	85	40	αu(x)|	αu(x)|	PUNCT
ejpam-4659	85	41	:	:	PUNCT
ejpam-4659	85	42	|α|	|α|	PROPN
ejpam-4659	85	43	≤	≤	NUM
ejpam-4659	85	44	m	m	NOUN
ejpam-4659	85	45	,	,	PUNCT
ejpam-4659	85	46	x	x	AUX
ejpam-4659	85	47	∈	∈	PROPN
ejpam-4659	85	48	ω	ω	NUM
ejpam-4659	85	49	)	)	PUNCT
ejpam-4659	85	50	≤	≤	NOUN
ejpam-4659	85	51	c2∥u∥k	c2∥u∥k	PROPN
ejpam-4659	85	52	,	,	PUNCT
ejpam-4659	85	53	p	p	NOUN
ejpam-4659	85	54	for	for	ADP
ejpam-4659	85	55	0	0	NUM
ejpam-4659	85	56	≤	≤	NUM
ejpam-4659	85	57	m	m	VERB
ejpam-4659	85	58	<	<	X
ejpam-4659	85	59	k	k	X
ejpam-4659	85	60	−	−	PROPN
ejpam-4659	85	61	n	n	PRON
ejpam-4659	85	62	p	p	NOUN
ejpam-4659	85	63	.	.	PUNCT
ejpam-4659	86	1	(	(	PUNCT
ejpam-4659	86	2	11	11	NUM
ejpam-4659	86	3	)	)	SYM
ejpam-4659	86	4	3	3	NUM
ejpam-4659	86	5	.	.	X
ejpam-4659	86	6	main	main	ADJ
ejpam-4659	86	7	results	result	NOUN
ejpam-4659	86	8	this	this	DET
ejpam-4659	86	9	section	section	NOUN
ejpam-4659	86	10	present	present	ADJ
ejpam-4659	86	11	results	result	NOUN
ejpam-4659	86	12	of	of	ADP
ejpam-4659	86	13	semigroup	semigroup	NOUN
ejpam-4659	86	14	of	of	ADP
ejpam-4659	86	15	linear	linear	ADJ
ejpam-4659	86	16	operator	operator	NOUN
ejpam-4659	86	17	by	by	ADP
ejpam-4659	86	18	using	use	VERB
ejpam-4659	86	19	ω	ω	PROPN
ejpam-4659	86	20	-	-	ADJ
ejpam-4659	86	21	ocpn	ocpn	ADJ
ejpam-4659	86	22	to	to	PART
ejpam-4659	86	23	generates	generate	VERB
ejpam-4659	86	24	a	a	DET
ejpam-4659	86	25	general	general	ADJ
ejpam-4659	86	26	class	class	NOUN
ejpam-4659	86	27	of	of	ADP
ejpam-4659	86	28	semilinear	semilinear	PROPN
ejpam-4659	86	29	initial	initial	ADJ
ejpam-4659	86	30	value	value	NOUN
ejpam-4659	86	31	problems	problem	NOUN
ejpam-4659	86	32	:	:	PUNCT
ejpam-4659	86	33	theorem	theorem	VERB
ejpam-4659	86	34	3.1	3.1	NUM
ejpam-4659	86	35	suppose	suppose	VERB
ejpam-4659	86	36	ap	ap	PROPN
ejpam-4659	86	37	:	:	PUNCT
ejpam-4659	86	38	d(ap	d(ap	PROPN
ejpam-4659	86	39	)	)	PUNCT
ejpam-4659	86	40	⊆	⊆	NUM
ejpam-4659	86	41	x	x	SYM
ejpam-4659	86	42	→	→	PUNCT
ejpam-4659	86	43	x	x	SYM
ejpam-4659	86	44	is	be	AUX
ejpam-4659	86	45	the	the	DET
ejpam-4659	86	46	infinitesimal	infinitesimal	ADJ
ejpam-4659	86	47	generator	generator	NOUN
ejpam-4659	86	48	of	of	ADP
ejpam-4659	86	49	an	an	DET
ejpam-4659	86	50	analytic	analytic	ADJ
ejpam-4659	86	51	semigroup	semigroup	NOUN
ejpam-4659	86	52	{	{	PUNCT
ejpam-4659	86	53	t	t	PROPN
ejpam-4659	86	54	(	(	PUNCT
ejpam-4659	86	55	t	t	PROPN
ejpam-4659	86	56	)	)	PUNCT
ejpam-4659	86	57	;	;	PUNCT
ejpam-4659	86	58	t	t	PROPN
ejpam-4659	86	59	≥	≥	NOUN
ejpam-4659	86	60	0	0	NUM
ejpam-4659	86	61	}	}	PUNCT
ejpam-4659	86	62	.	.	PUNCT
ejpam-4659	87	1	assume	assume	VERB
ejpam-4659	87	2	1	1	NUM
ejpam-4659	87	3	<	<	X
ejpam-4659	87	4	p	p	X
ejpam-4659	87	5	<	<	X
ejpam-4659	87	6	∞	∞	PROPN
ejpam-4659	87	7	and	and	CCONJ
ejpam-4659	87	8	let	let	VERB
ejpam-4659	87	9	ap	ap	PROPN
ejpam-4659	87	10	be	be	AUX
ejpam-4659	87	11	the	the	DET
ejpam-4659	87	12	operator	operator	NOUN
ejpam-4659	87	13	defined	define	VERB
ejpam-4659	87	14	in	in	ADP
ejpam-4659	87	15	lemma	lemma	PROPN
ejpam-4659	87	16	2.1	2.1	NUM
ejpam-4659	87	17	.	.	PUNCT
ejpam-4659	88	1	for	for	ADP
ejpam-4659	88	2	any	any	DET
ejpam-4659	88	3	multi	multi	ADJ
ejpam-4659	88	4	-	-	NOUN
ejpam-4659	88	5	index	index	ADJ
ejpam-4659	88	6	β	β	NOUN
ejpam-4659	88	7	,	,	PUNCT
ejpam-4659	88	8	|β|	|β|	PROPN
ejpam-4659	88	9	=	=	SYM
ejpam-4659	88	10	j	j	X
ejpam-4659	88	11	<	<	X
ejpam-4659	88	12	2	2	NUM
ejpam-4659	88	13	m	m	NOUN
ejpam-4659	88	14	and	and	CCONJ
ejpam-4659	88	15	any	any	DET
ejpam-4659	88	16	j/2	j/2	NOUN
ejpam-4659	88	17	m	m	NOUN
ejpam-4659	88	18	<	<	X
ejpam-4659	88	19	α	α	X
ejpam-4659	88	20	≤	≤	NUM
ejpam-4659	88	21	1	1	NUM
ejpam-4659	88	22	we	we	PRON
ejpam-4659	88	23	have	have	VERB
ejpam-4659	88	24	∥dβa−α	∥dβa−α	PROPN
ejpam-4659	88	25	p	p	NOUN
ejpam-4659	88	26	u∥0,p	u∥0,p	PROPN
ejpam-4659	88	27	≤	≤	PROPN
ejpam-4659	88	28	c∥u∥0,p	c∥u∥0,p	NOUN
ejpam-4659	88	29	(	(	PUNCT
ejpam-4659	88	30	12	12	NUM
ejpam-4659	88	31	)	)	PUNCT
ejpam-4659	88	32	for	for	ADP
ejpam-4659	88	33	u	u	PROPN
ejpam-4659	88	34	∈	∈	PROPN
ejpam-4659	88	35	d(ap	d(ap	PROPN
ejpam-4659	88	36	)	)	PUNCT
ejpam-4659	88	37	and	and	CCONJ
ejpam-4659	88	38	ap	ap	PROPN
ejpam-4659	88	39	∈	∈	PROPN
ejpam-4659	88	40	ω	ω	PROPN
ejpam-4659	88	41	−ocpn	−ocpn	NOUN
ejpam-4659	88	42	.	.	PUNCT
ejpam-4659	89	1	proof	proof	NOUN
ejpam-4659	89	2	:	:	PUNCT
ejpam-4659	89	3	set	set	NOUN
ejpam-4659	89	4	b	b	NOUN
ejpam-4659	89	5	=	=	SYM
ejpam-4659	89	6	dβ	dβ	PROPN
ejpam-4659	89	7	.	.	PUNCT
ejpam-4659	89	8	since	since	SCONJ
ejpam-4659	89	9	|β|	|β|	PRON
ejpam-4659	89	10	<	<	X
ejpam-4659	89	11	2	2	NUM
ejpam-4659	89	12	m	m	PRON
ejpam-4659	89	13	,	,	PUNCT
ejpam-4659	89	14	it	it	PRON
ejpam-4659	89	15	is	be	AUX
ejpam-4659	89	16	clear	clear	ADJ
ejpam-4659	89	17	that	that	SCONJ
ejpam-4659	89	18	d(b	d(b	PRON
ejpam-4659	89	19	)	)	PUNCT
ejpam-4659	89	20	⊃	⊃	PROPN
ejpam-4659	89	21	d(ap	d(ap	PROPN
ejpam-4659	89	22	)	)	PUNCT
ejpam-4659	89	23	for	for	ADP
ejpam-4659	89	24	all	all	DET
ejpam-4659	89	25	a	a	DET
ejpam-4659	89	26	,	,	PUNCT
ejpam-4659	89	27	b	b	PROPN
ejpam-4659	89	28	∈	∈	PROPN
ejpam-4659	89	29	ω	ω	NOUN
ejpam-4659	90	1	−	−	PROPN
ejpam-4659	91	1	ocpn	ocpn	ADJ
ejpam-4659	91	2	.	.	PUNCT
ejpam-4659	92	1	from	from	ADP
ejpam-4659	92	2	lemma	lemma	PROPN
ejpam-4659	92	3	2.1	2.1	NUM
ejpam-4659	92	4	,	,	PUNCT
ejpam-4659	92	5	we	we	PRON
ejpam-4659	92	6	have	have	VERB
ejpam-4659	92	7	∥dβu∥0,p	∥dβu∥0,p	ADJ
ejpam-4659	93	1	≤	≤	ADJ
ejpam-4659	93	2	c∥u∥j/2m2m	c∥u∥j/2m2m	NOUN
ejpam-4659	93	3	,	,	PUNCT
ejpam-4659	93	4	p	p	NOUN
ejpam-4659	93	5	∥u∥	∥u∥	NOUN
ejpam-4659	93	6	1−j/2	1−j/2	NUM
ejpam-4659	93	7	m	m	NOUN
ejpam-4659	93	8	0,p	0,p	NOUN
ejpam-4659	93	9	.	.	PUNCT
ejpam-4659	94	1	(	(	PUNCT
ejpam-4659	94	2	13	13	NUM
ejpam-4659	94	3	)	)	PUNCT
ejpam-4659	94	4	polarization	polarization	NOUN
ejpam-4659	94	5	of	of	ADP
ejpam-4659	94	6	(	(	PUNCT
ejpam-4659	94	7	13	13	NUM
ejpam-4659	94	8	)	)	PUNCT
ejpam-4659	94	9	together	together	ADV
ejpam-4659	94	10	with	with	ADP
ejpam-4659	94	11	estimate	estimate	NOUN
ejpam-4659	94	12	(	(	PUNCT
ejpam-4659	94	13	5	5	NUM
ejpam-4659	94	14	)	)	PUNCT
ejpam-4659	94	15	yields	yield	NOUN
ejpam-4659	94	16	∥dβu∥0,p	∥dβu∥0,p	SYM
ejpam-4659	94	17	≤	≤	NUM
ejpam-4659	94	18	c(ρ−1+j/2m∥apu∥0,p	c(ρ−1+j/2m∥apu∥0,p	X
ejpam-4659	94	19	+	+	CCONJ
ejpam-4659	94	20	ρj/2m∥u∥0,p	ρj/2m∥u∥0,p	NUM
ejpam-4659	94	21	)	)	PUNCT
ejpam-4659	94	22	(	(	PUNCT
ejpam-4659	94	23	14	14	NUM
ejpam-4659	94	24	)	)	PUNCT
ejpam-4659	94	25	for	for	ADP
ejpam-4659	94	26	p	p	PROPN
ejpam-4659	94	27	>	>	X
ejpam-4659	94	28	0	0	PROPN
ejpam-4659	94	29	,	,	PUNCT
ejpam-4659	94	30	u	u	PROPN
ejpam-4659	94	31	∈	∈	PROPN
ejpam-4659	94	32	d(ap	d(ap	PROPN
ejpam-4659	94	33	)	)	PUNCT
ejpam-4659	94	34	and	and	CCONJ
ejpam-4659	94	35	ap	ap	PROPN
ejpam-4659	94	36	∈	∈	PROPN
ejpam-4659	94	37	ω−ocpn	ω−ocpn	PROPN
ejpam-4659	94	38	.	.	PROPN
ejpam-4659	94	39	suppose	suppose	VERB
ejpam-4659	94	40	b	b	NOUN
ejpam-4659	94	41	is	be	AUX
ejpam-4659	94	42	a	a	DET
ejpam-4659	94	43	closed	closed	ADJ
ejpam-4659	94	44	linear	linear	ADJ
ejpam-4659	94	45	operator	operator	NOUN
ejpam-4659	94	46	satisfiying	satisfiying	PROPN
ejpam-4659	94	47	d(b	d(b	PROPN
ejpam-4659	94	48	)	)	PUNCT
ejpam-4659	94	49	⊃	⊃	PROPN
ejpam-4659	94	50	d(a	d(a	PROPN
ejpam-4659	94	51	)	)	PUNCT
ejpam-4659	94	52	.	.	PUNCT
ejpam-4659	95	1	if	if	SCONJ
ejpam-4659	95	2	for	for	ADP
ejpam-4659	95	3	some	some	DET
ejpam-4659	95	4	γ	γ	NOUN
ejpam-4659	95	5	,	,	PUNCT
ejpam-4659	95	6	0	0	NUM
ejpam-4659	95	7	<	<	X
ejpam-4659	95	8	γ	γ	X
ejpam-4659	95	9	<	<	X
ejpam-4659	95	10	1	1	NUM
ejpam-4659	95	11	,	,	PUNCT
ejpam-4659	95	12	and	and	CCONJ
ejpam-4659	95	13	every	every	DET
ejpam-4659	95	14	ρ	ρ	PROPN
ejpam-4659	95	15	≥	≥	NOUN
ejpam-4659	95	16	ρ0	ρ0	NOUN
ejpam-4659	95	17	>	>	X
ejpam-4659	95	18	0	0	NUM
ejpam-4659	95	19	we	we	PRON
ejpam-4659	95	20	have	have	VERB
ejpam-4659	95	21	∥bx∥	∥bx∥	ADV
ejpam-4659	95	22	≤	≤	NUM
ejpam-4659	95	23	c(ργ∥x∥+	c(ργ∥x∥+	PROPN
ejpam-4659	95	24	ργ−1∥ax∥	ργ−1∥ax∥	NOUN
ejpam-4659	95	25	)	)	PUNCT
ejpam-4659	95	26	(	(	PUNCT
ejpam-4659	95	27	15	15	NUM
ejpam-4659	95	28	)	)	PUNCT
ejpam-4659	95	29	a.	a.	NOUN
ejpam-4659	95	30	y.	y.	PROPN
ejpam-4659	95	31	akinyele	akinyele	PROPN
ejpam-4659	95	32	et	et	PROPN
ejpam-4659	95	33	al	al	PROPN
ejpam-4659	95	34	.	.	PUNCT
ejpam-4659	95	35	/	/	SYM
ejpam-4659	95	36	eur	eur	PROPN
ejpam-4659	95	37	.	.	PUNCT
ejpam-4659	96	1	j.	j.	PROPN
ejpam-4659	96	2	pure	pure	PROPN
ejpam-4659	96	3	appl	appl	PROPN
ejpam-4659	96	4	.	.	PROPN
ejpam-4659	96	5	math	math	PROPN
ejpam-4659	96	6	,	,	PUNCT
ejpam-4659	96	7	16	16	NUM
ejpam-4659	96	8	(	(	PUNCT
ejpam-4659	96	9	1	1	NUM
ejpam-4659	96	10	)	)	PUNCT
ejpam-4659	96	11	(	(	PUNCT
ejpam-4659	96	12	2023	2023	NUM
ejpam-4659	96	13	)	)	PUNCT
ejpam-4659	96	14	,	,	PUNCT
ejpam-4659	96	15	538	538	NUM
ejpam-4659	96	16	-	-	SYM
ejpam-4659	96	17	547	547	NUM
ejpam-4659	96	18	543	543	NUM
ejpam-4659	96	19	for	for	ADP
ejpam-4659	96	20	x	x	PROPN
ejpam-4659	96	21	∈	∈	PROPN
ejpam-4659	96	22	d(a	d(a	PROPN
ejpam-4659	96	23	)	)	PUNCT
ejpam-4659	96	24	and	and	CCONJ
ejpam-4659	96	25	a	a	DET
ejpam-4659	96	26	∈	∈	PROPN
ejpam-4659	96	27	ω	ω	NUM
ejpam-4659	96	28	−ocpn	−ocpn	PROPN
ejpam-4659	96	29	,	,	PUNCT
ejpam-4659	96	30	then	then	ADV
ejpam-4659	96	31	d(b	d(b	X
ejpam-4659	96	32	)	)	PUNCT
ejpam-4659	96	33	⊃	⊃	PROPN
ejpam-4659	96	34	d(aα	d(aα	PROPN
ejpam-4659	96	35	)	)	PUNCT
ejpam-4659	96	36	for	for	ADP
ejpam-4659	96	37	every	every	DET
ejpam-4659	96	38	γ	γ	PROPN
ejpam-4659	96	39	≤	≤	NOUN
ejpam-4659	96	40	1	1	NUM
ejpam-4659	96	41	.	.	PUNCT
ejpam-4659	97	1	(	(	PUNCT
ejpam-4659	97	2	16	16	NUM
ejpam-4659	97	3	)	)	PUNCT
ejpam-4659	97	4	it	it	PRON
ejpam-4659	97	5	follows	follow	VERB
ejpam-4659	97	6	now	now	ADV
ejpam-4659	97	7	that	that	SCONJ
ejpam-4659	97	8	d(b	d(b	PRON
ejpam-4659	97	9	)	)	PUNCT
ejpam-4659	97	10	⊃	⊃	PROPN
ejpam-4659	97	11	d(aα	d(aα	PROPN
ejpam-4659	97	12	p	p	NOUN
ejpam-4659	97	13	)	)	PUNCT
ejpam-4659	97	14	for	for	ADP
ejpam-4659	97	15	j/2	j/2	DET
ejpam-4659	97	16	m	m	PROPN
ejpam-4659	97	17	<	<	X
ejpam-4659	97	18	α≤	α≤	PROPN
ejpam-4659	97	19	1	1	NUM
ejpam-4659	97	20	,	,	PUNCT
ejpam-4659	97	21	that	that	PRON
ejpam-4659	97	22	,	,	PUNCT
ejpam-4659	97	23	is	be	AUX
ejpam-4659	97	24	ba−α	ba−α	PROPN
ejpam-4659	97	25	p	p	NOUN
ejpam-4659	97	26	is	be	AUX
ejpam-4659	97	27	bounded	bound	VERB
ejpam-4659	97	28	for	for	ADP
ejpam-4659	97	29	these	these	DET
ejpam-4659	97	30	values	value	NOUN
ejpam-4659	97	31	of	of	ADP
ejpam-4659	97	32	α	α	NOUN
ejpam-4659	97	33	and	and	CCONJ
ejpam-4659	97	34	this	this	PRON
ejpam-4659	97	35	achieved	achieve	VERB
ejpam-4659	97	36	the	the	DET
ejpam-4659	97	37	proof	proof	NOUN
ejpam-4659	97	38	.	.	PUNCT
ejpam-4659	98	1	theorem	theorem	ADJ
ejpam-4659	98	2	3.2	3.2	NUM
ejpam-4659	98	3	assume	assume	VERB
ejpam-4659	98	4	ap	ap	PROPN
ejpam-4659	98	5	:	:	PUNCT
ejpam-4659	98	6	d(ap	d(ap	PROPN
ejpam-4659	98	7	)	)	PUNCT
ejpam-4659	98	8	⊆	⊆	NUM
ejpam-4659	98	9	lp(ω	lp(ω	NUM
ejpam-4659	98	10	)	)	PUNCT
ejpam-4659	98	11	→	→	SYM
ejpam-4659	98	12	lp(ω	lp(ω	X
ejpam-4659	98	13	)	)	PUNCT
ejpam-4659	98	14	is	be	AUX
ejpam-4659	98	15	the	the	DET
ejpam-4659	98	16	infinitesimal	infinitesimal	ADJ
ejpam-4659	98	17	generator	generator	NOUN
ejpam-4659	98	18	of	of	ADP
ejpam-4659	98	19	a	a	DET
ejpam-4659	98	20	semigroup	semigroup	NOUN
ejpam-4659	98	21	{	{	PUNCT
ejpam-4659	98	22	t	t	PROPN
ejpam-4659	98	23	(	(	PUNCT
ejpam-4659	98	24	t	t	PROPN
ejpam-4659	98	25	)	)	PUNCT
ejpam-4659	98	26	;	;	PUNCT
ejpam-4659	98	27	t	t	PROPN
ejpam-4659	98	28	≥	≥	NUM
ejpam-4659	98	29	}	}	PUNCT
ejpam-4659	98	30	.	.	PUNCT
ejpam-4659	99	1	let	let	VERB
ejpam-4659	99	2	ω	ω	PROPN
ejpam-4659	99	3	⊂	⊂	PROPN
ejpam-4659	99	4	rn	rn	AUX
ejpam-4659	99	5	be	be	AUX
ejpam-4659	99	6	a	a	DET
ejpam-4659	99	7	bounded	bounded	ADJ
ejpam-4659	99	8	domain	domain	NOUN
ejpam-4659	99	9	with	with	ADP
ejpam-4659	99	10	smooth	smooth	ADJ
ejpam-4659	99	11	boundary	boundary	ADJ
ejpam-4659	99	12	∂ω	∂ω	PROPN
ejpam-4659	99	13	such	such	ADJ
ejpam-4659	99	14	that	that	SCONJ
ejpam-4659	99	15	a	a	DET
ejpam-4659	99	16	∈	∈	PROPN
ejpam-4659	99	17	ω	ω	NUM
ejpam-4659	99	18	−ocpn	−ocpn	NOUN
ejpam-4659	99	19	.	.	PUNCT
ejpam-4659	100	1	if	if	SCONJ
ejpam-4659	100	2	0	0	NUM
ejpam-4659	100	3	≤	≤	NUM
ejpam-4659	100	4	α	α	NOUN
ejpam-4659	100	5	≤	≤	NUM
ejpam-4659	100	6	1	1	NUM
ejpam-4659	100	7	,	,	PUNCT
ejpam-4659	100	8	then	then	ADV
ejpam-4659	100	9	xα	xα	PUNCT
ejpam-4659	101	1	⊂	⊂	PROPN
ejpam-4659	101	2	w	w	PROPN
ejpam-4659	101	3	k	k	PROPN
ejpam-4659	101	4	,	,	PUNCT
ejpam-4659	101	5	q(ω	q(ω	PROPN
ejpam-4659	101	6	)	)	PUNCT
ejpam-4659	101	7	for	for	ADP
ejpam-4659	101	8	k	k	PROPN
ejpam-4659	101	9	−	−	PROPN
ejpam-4659	101	10	n	n	CCONJ
ejpam-4659	101	11	q	q	NOUN
ejpam-4659	101	12	<	<	X
ejpam-4659	101	13	2mα−	2mα−	NUM
ejpam-4659	102	1	n	n	DET
ejpam-4659	102	2	p	p	NOUN
ejpam-4659	102	3	,	,	PUNCT
ejpam-4659	102	4	q	q	X
ejpam-4659	102	5	≥	≥	X
ejpam-4659	102	6	p	p	X
ejpam-4659	102	7	(	(	PUNCT
ejpam-4659	102	8	17	17	NUM
ejpam-4659	102	9	)	)	PUNCT
ejpam-4659	102	10	xα	xα	PUNCT
ejpam-4659	103	1	⊂	⊂	PROPN
ejpam-4659	103	2	cp(ω	cp(ω	PROPN
ejpam-4659	103	3	)	)	PUNCT
ejpam-4659	103	4	for	for	ADP
ejpam-4659	103	5	0	0	NUM
ejpam-4659	103	6	≤	≤	NUM
ejpam-4659	103	7	v	v	ADP
ejpam-4659	103	8	<	<	X
ejpam-4659	103	9	2mα−	2mα−	NUM
ejpam-4659	103	10	n	n	PRON
ejpam-4659	103	11	p	p	NOUN
ejpam-4659	103	12	,	,	PUNCT
ejpam-4659	103	13	(	(	PUNCT
ejpam-4659	103	14	18	18	NUM
ejpam-4659	103	15	)	)	PUNCT
ejpam-4659	103	16	and	and	CCONJ
ejpam-4659	103	17	the	the	DET
ejpam-4659	103	18	embeddings	embedding	NOUN
ejpam-4659	103	19	are	be	AUX
ejpam-4659	103	20	continuous	continuous	ADJ
ejpam-4659	103	21	.	.	PUNCT
ejpam-4659	104	1	proof	proof	NOUN
ejpam-4659	104	2	:	:	PUNCT
ejpam-4659	104	3	from	from	ADP
ejpam-4659	104	4	theorem	theorem	NOUN
ejpam-4659	104	5	3.1	3.1	NUM
ejpam-4659	104	6	it	it	PRON
ejpam-4659	104	7	follows	follow	VERB
ejpam-4659	104	8	readily	readily	ADV
ejpam-4659	104	9	that	that	SCONJ
ejpam-4659	104	10	xα	xα	PUNCT
ejpam-4659	105	1	⊂	⊂	PROPN
ejpam-4659	105	2	w	w	PROPN
ejpam-4659	105	3	j	j	PROPN
ejpam-4659	105	4	,	,	PUNCT
ejpam-4659	105	5	p(ω	p(ω	PROPN
ejpam-4659	105	6	)	)	PUNCT
ejpam-4659	105	7	provided	provide	VERB
ejpam-4659	105	8	that	that	SCONJ
ejpam-4659	105	9	j	j	PROPN
ejpam-4659	105	10	<	<	X
ejpam-4659	105	11	2mα	2mα	NOUN
ejpam-4659	105	12	and	and	CCONJ
ejpam-4659	105	13	the	the	DET
ejpam-4659	105	14	imbedding	imbedding	NOUN
ejpam-4659	105	15	is	be	AUX
ejpam-4659	105	16	continuous	continuous	ADJ
ejpam-4659	105	17	.	.	PUNCT
ejpam-4659	106	1	since	since	SCONJ
ejpam-4659	106	2	ω	ω	PROPN
ejpam-4659	106	3	is	be	AUX
ejpam-4659	106	4	a	a	DET
ejpam-4659	106	5	bounded	bounded	ADJ
ejpam-4659	106	6	domain	domain	NOUN
ejpam-4659	106	7	in	in	ADP
ejpam-4659	106	8	rn	rn	PROPN
ejpam-4659	106	9	with	with	ADP
ejpam-4659	106	10	smooth	smooth	ADJ
ejpam-4659	106	11	boundary	boundary	ADJ
ejpam-4659	106	12	∂ω	∂ω	PROPN
ejpam-4659	106	13	,	,	PUNCT
ejpam-4659	106	14	assume	assume	VERB
ejpam-4659	106	15	∂ω	∂ω	PROPN
ejpam-4659	106	16	is	be	AUX
ejpam-4659	106	17	of	of	ADP
ejpam-4659	106	18	class	class	NOUN
ejpam-4659	106	19	c	c	NOUN
ejpam-4659	106	20	′	′	NOUN
ejpam-4659	106	21	and	and	CCONJ
ejpam-4659	106	22	let	let	VERB
ejpam-4659	106	23	1	1	NUM
ejpam-4659	106	24	≤	≤	NOUN
ejpam-4659	106	25	r	r	NOUN
ejpam-4659	106	26	,	,	PUNCT
ejpam-4659	106	27	p	p	X
ejpam-4659	106	28	<	<	X
ejpam-4659	106	29	∞.	∞.	PROPN
ejpam-4659	106	30	if	if	SCONJ
ejpam-4659	106	31	j	j	PROPN
ejpam-4659	106	32	,	,	PUNCT
ejpam-4659	106	33	m	m	VERB
ejpam-4659	106	34	are	be	AUX
ejpam-4659	106	35	integers	integer	NOUN
ejpam-4659	106	36	such	such	ADJ
ejpam-4659	106	37	that	that	SCONJ
ejpam-4659	106	38	0	0	NUM
ejpam-4659	106	39	≤	≤	NUM
ejpam-4659	106	40	r	r	NOUN
ejpam-4659	106	41	,	,	PUNCT
ejpam-4659	106	42	j	j	NOUN
ejpam-4659	106	43	<	<	X
ejpam-4659	106	44	m	m	VERB
ejpam-4659	106	45	and	and	CCONJ
ejpam-4659	106	46	1	1	NUM
ejpam-4659	106	47	p	p	X
ejpam-4659	106	48	>	>	X
ejpam-4659	106	49	1	1	NUM
ejpam-4659	106	50	r	r	NOUN
ejpam-4659	106	51	+	+	NUM
ejpam-4659	106	52	j	j	PROPN
ejpam-4659	106	53	n	n	CCONJ
ejpam-4659	106	54	−	−	PROPN
ejpam-4659	106	55	m	m	VERB
ejpam-4659	106	56	n	n	CCONJ
ejpam-4659	106	57	(	(	PUNCT
ejpam-4659	106	58	19	19	NUM
ejpam-4659	106	59	)	)	PUNCT
ejpam-4659	106	60	then	then	ADV
ejpam-4659	106	61	wm	wm	PROPN
ejpam-4659	106	62	,	,	PUNCT
ejpam-4659	106	63	r(ω	r(ω	ADV
ejpam-4659	106	64	)	)	PUNCT
ejpam-4659	106	65	⊃	⊃	PROPN
ejpam-4659	106	66	w	w	PROPN
ejpam-4659	106	67	j	j	PROPN
ejpam-4659	106	68	,	,	PUNCT
ejpam-4659	106	69	p(ω	p(ω	PROPN
ejpam-4659	106	70	)	)	PUNCT
ejpam-4659	106	71	and	and	CCONJ
ejpam-4659	106	72	the	the	DET
ejpam-4659	106	73	imbedding	imbedding	NOUN
ejpam-4659	106	74	is	be	AUX
ejpam-4659	106	75	compact	compact	ADJ
ejpam-4659	106	76	.	.	PUNCT
ejpam-4659	107	1	it	it	PRON
ejpam-4659	107	2	follows	follow	VERB
ejpam-4659	107	3	that	that	SCONJ
ejpam-4659	107	4	w	w	PROPN
ejpam-4659	107	5	j	j	PROPN
ejpam-4659	107	6	,	,	PUNCT
ejpam-4659	107	7	p(ω	p(ω	PROPN
ejpam-4659	107	8	)	)	PUNCT
ejpam-4659	107	9	is	be	AUX
ejpam-4659	107	10	continuously	continuously	ADV
ejpam-4659	107	11	imbedded	imbed	VERB
ejpam-4659	107	12	in	in	ADP
ejpam-4659	107	13	w	w	PROPN
ejpam-4659	107	14	k	k	PROPN
ejpam-4659	107	15	,	,	PUNCT
ejpam-4659	107	16	q(ω	q(ω	PROPN
ejpam-4659	107	17	)	)	PUNCT
ejpam-4659	107	18	provided	provide	VERB
ejpam-4659	107	19	that	that	SCONJ
ejpam-4659	107	20	k	k	PROPN
ejpam-4659	107	21	−	−	PROPN
ejpam-4659	107	22	n	n	CCONJ
ejpam-4659	107	23	/	/	SYM
ejpam-4659	107	24	q	q	X
ejpam-4659	107	25	<	<	X
ejpam-4659	107	26	j	j	PROPN
ejpam-4659	107	27	−	−	PROPN
ejpam-4659	107	28	n	n	CCONJ
ejpam-4659	107	29	/	/	SYM
ejpam-4659	107	30	p	p	X
ejpam-4659	107	31	and	and	CCONJ
ejpam-4659	107	32	(	(	PUNCT
ejpam-4659	107	33	17	17	NUM
ejpam-4659	107	34	)	)	PUNCT
ejpam-4659	107	35	follows	follow	VERB
ejpam-4659	107	36	.	.	PUNCT
ejpam-4659	108	1	from	from	ADP
ejpam-4659	108	2	theorem	theorem	ADJ
ejpam-4659	108	3	2.2	2.2	NUM
ejpam-4659	108	4	(	(	PUNCT
ejpam-4659	108	5	sobolev	sobolev	NOUN
ejpam-4659	108	6	)	)	PUNCT
ejpam-4659	108	7	,	,	PUNCT
ejpam-4659	108	8	it	it	PRON
ejpam-4659	108	9	follows	follow	VERB
ejpam-4659	108	10	that	that	SCONJ
ejpam-4659	108	11	w	w	PROPN
ejpam-4659	108	12	j	j	PROPN
ejpam-4659	108	13	,	,	PUNCT
ejpam-4659	108	14	p(ω	p(ω	PROPN
ejpam-4659	108	15	)	)	PUNCT
ejpam-4659	108	16	is	be	AUX
ejpam-4659	108	17	continuously	continuously	ADV
ejpam-4659	108	18	imbedded	imbed	VERB
ejpam-4659	108	19	in	in	ADP
ejpam-4659	108	20	cv(ω	cv(ω	NOUN
ejpam-4659	108	21	)	)	PUNCT
ejpam-4659	108	22	for	for	ADP
ejpam-4659	108	23	0	0	NUM
ejpam-4659	108	24	≤	≤	NUM
ejpam-4659	108	25	v	v	ADP
ejpam-4659	108	26	<	<	X
ejpam-4659	108	27	j	j	PROPN
ejpam-4659	108	28	−	−	PROPN
ejpam-4659	108	29	n	n	CCONJ
ejpam-4659	108	30	/	/	SYM
ejpam-4659	108	31	p	p	X
ejpam-4659	108	32	and	and	CCONJ
ejpam-4659	108	33	(	(	PUNCT
ejpam-4659	108	34	18	18	NUM
ejpam-4659	108	35	)	)	PUNCT
ejpam-4659	108	36	follows	follow	VERB
ejpam-4659	108	37	.	.	PUNCT
ejpam-4659	109	1	hence	hence	ADV
ejpam-4659	109	2	,	,	PUNCT
ejpam-4659	109	3	the	the	DET
ejpam-4659	109	4	proof	proof	NOUN
ejpam-4659	109	5	is	be	AUX
ejpam-4659	109	6	completed	complete	VERB
ejpam-4659	109	7	.	.	PUNCT
ejpam-4659	110	1	theorem	theorem	VERB
ejpam-4659	110	2	3.3	3.3	NUM
ejpam-4659	110	3	let	let	VERB
ejpam-4659	110	4	a(x	a(x	NOUN
ejpam-4659	110	5	,	,	PUNCT
ejpam-4659	110	6	d	d	NOUN
ejpam-4659	110	7	)	)	PUNCT
ejpam-4659	110	8	be	be	AUX
ejpam-4659	110	9	a	a	DET
ejpam-4659	110	10	strongly	strongly	ADV
ejpam-4659	110	11	elliptic	elliptic	ADJ
ejpam-4659	110	12	operator	operator	NOUN
ejpam-4659	110	13	given	give	VERB
ejpam-4659	110	14	by	by	ADP
ejpam-4659	110	15	a(x	a(x	NOUN
ejpam-4659	110	16	,	,	PUNCT
ejpam-4659	110	17	d	d	NOUN
ejpam-4659	110	18	)	)	PUNCT
ejpam-4659	111	1	=	=	SYM
ejpam-4659	111	2	−	−	PROPN
ejpam-4659	111	3	3∑	3∑	NUM
ejpam-4659	111	4	k	k	NOUN
ejpam-4659	111	5	,	,	PUNCT
ejpam-4659	111	6	l=1	l=1	PROPN
ejpam-4659	111	7	∂	∂	NUM
ejpam-4659	111	8	∂xk	∂xk	PROPN
ejpam-4659	111	9	ak	ak	PROPN
ejpam-4659	111	10	,	,	PUNCT
ejpam-4659	111	11	l(x	l(x	PROPN
ejpam-4659	111	12	)	)	PUNCT
ejpam-4659	111	13	∂	∂	NUM
ejpam-4659	111	14	∂xl	∂xl	PROPN
ejpam-4659	111	15	.	.	PUNCT
ejpam-4659	112	1	let	let	VERB
ejpam-4659	112	2	ω	ω	PRON
ejpam-4659	112	3	be	be	AUX
ejpam-4659	112	4	a	a	DET
ejpam-4659	112	5	bounded	bounded	ADJ
ejpam-4659	112	6	domain	domain	NOUN
ejpam-4659	112	7	in	in	ADP
ejpam-4659	112	8	r3	r3	PROPN
ejpam-4659	112	9	with	with	ADP
ejpam-4659	112	10	smooth	smooth	ADJ
ejpam-4659	112	11	boundary	boundary	ADJ
ejpam-4659	112	12	∂ω	∂ω	PROPN
ejpam-4659	112	13	such	such	ADJ
ejpam-4659	112	14	that	that	SCONJ
ejpam-4659	112	15	a	a	DET
ejpam-4659	112	16	∈	∈	PROPN
ejpam-4659	112	17	ω	ω	NOUN
ejpam-4659	112	18	−	−	PROPN
ejpam-4659	112	19	ocpn	ocpn	ADJ
ejpam-4659	112	20	where	where	SCONJ
ejpam-4659	112	21	ak	ak	PROPN
ejpam-4659	112	22	,	,	PUNCT
ejpam-4659	112	23	l(x	l(x	PROPN
ejpam-4659	112	24	)	)	PUNCT
ejpam-4659	112	25	=	=	SYM
ejpam-4659	112	26	al	al	PROPN
ejpam-4659	112	27	,	,	PUNCT
ejpam-4659	112	28	k(x	k(x	PROPN
ejpam-4659	112	29	)	)	PUNCT
ejpam-4659	112	30	are	be	AUX
ejpam-4659	112	31	real	real	ADV
ejpam-4659	112	32	valued	value	VERB
ejpam-4659	112	33	and	and	CCONJ
ejpam-4659	112	34	continuously	continuously	ADV
ejpam-4659	112	35	differentiable	differentiable	VERB
ejpam-4659	112	36	in	in	ADP
ejpam-4659	112	37	ω	ω	PROPN
ejpam-4659	112	38	.	.	PUNCT
ejpam-4659	113	1	let	let	VERB
ejpam-4659	113	2	f(t	f(t	PROPN
ejpam-4659	113	3	,	,	PUNCT
ejpam-4659	113	4	x	x	X
ejpam-4659	113	5	,	,	PUNCT
ejpam-4659	113	6	u	u	NOUN
ejpam-4659	113	7	,	,	PUNCT
ejpam-4659	113	8	p	p	NOUN
ejpam-4659	113	9	)	)	PUNCT
ejpam-4659	113	10	,	,	PUNCT
ejpam-4659	113	11	p	p	PROPN
ejpam-4659	113	12	∈	∈	PROPN
ejpam-4659	113	13	r3	r3	PROPN
ejpam-4659	113	14	,	,	PUNCT
ejpam-4659	113	15	be	be	AUX
ejpam-4659	113	16	locally	locally	ADV
ejpam-4659	113	17	lipschitz	lipschitz	VERB
ejpam-4659	113	18	continuous	continuous	ADJ
ejpam-4659	113	19	function	function	NOUN
ejpam-4659	113	20	of	of	ADP
ejpam-4659	113	21	all	all	DET
ejpam-4659	113	22	its	its	PRON
ejpam-4659	113	23	arguments	argument	NOUN
ejpam-4659	113	24	and	and	CCONJ
ejpam-4659	113	25	assume	assume	VERB
ejpam-4659	113	26	further	far	ADV
ejpam-4659	113	27	that	that	SCONJ
ejpam-4659	113	28	there	there	PRON
ejpam-4659	113	29	is	be	VERB
ejpam-4659	113	30	a	a	DET
ejpam-4659	113	31	continuous	continuous	ADJ
ejpam-4659	113	32	function	function	NOUN
ejpam-4659	113	33	ρ(t	ρ(t	NUM
ejpam-4659	113	34	,	,	PUNCT
ejpam-4659	113	35	r	r	NOUN
ejpam-4659	113	36	)	)	PUNCT
ejpam-4659	113	37	:	:	PUNCT
ejpam-4659	113	38	r	r	NOUN
ejpam-4659	113	39	×	×	NOUN
ejpam-4659	113	40	r	r	NOUN
ejpam-4659	113	41	→	→	PUNCT
ejpam-4659	113	42	r+	r+	NOUN
ejpam-4659	113	43	and	and	CCONJ
ejpam-4659	113	44	a	a	DET
ejpam-4659	113	45	real	real	ADV
ejpam-4659	113	46	constant	constant	ADJ
ejpam-4659	113	47	1	1	NUM
ejpam-4659	113	48	≤	≤	NOUN
ejpam-4659	113	49	r	r	NOUN
ejpam-4659	113	50	<	<	X
ejpam-4659	113	51	3	3	NUM
ejpam-4659	113	52	such	such	ADJ
ejpam-4659	113	53	that	that	SCONJ
ejpam-4659	113	54	|f(t	|f(t	PROPN
ejpam-4659	113	55	,	,	PUNCT
ejpam-4659	113	56	x	x	NOUN
ejpam-4659	113	57	,	,	PUNCT
ejpam-4659	113	58	u	u	NOUN
ejpam-4659	113	59	,	,	PUNCT
ejpam-4659	113	60	p)|	p)|	NOUN
ejpam-4659	113	61	≤	≤	NOUN
ejpam-4659	113	62	ρ(t	ρ(t	PROPN
ejpam-4659	113	63	,	,	PUNCT
ejpam-4659	113	64	|u|)(1	|u|)(1	PROPN
ejpam-4659	113	65	+	+	CCONJ
ejpam-4659	113	66	|p|γ	|p|γ	PROPN
ejpam-4659	113	67	)	)	PUNCT
ejpam-4659	113	68	(	(	PUNCT
ejpam-4659	113	69	20	20	NUM
ejpam-4659	113	70	)	)	PUNCT
ejpam-4659	113	71	|f(t	|f(t	NOUN
ejpam-4659	113	72	,	,	PUNCT
ejpam-4659	113	73	x	x	NOUN
ejpam-4659	113	74	,	,	PUNCT
ejpam-4659	113	75	u	u	NOUN
ejpam-4659	113	76	,	,	PUNCT
ejpam-4659	113	77	p)−	p)−	ADJ
ejpam-4659	113	78	f(t	f(t	NOUN
ejpam-4659	113	79	,	,	PUNCT
ejpam-4659	113	80	x	x	X
ejpam-4659	113	81	,	,	PUNCT
ejpam-4659	113	82	u	u	NOUN
ejpam-4659	113	83	,	,	PUNCT
ejpam-4659	113	84	q)|	q)|	VERB
ejpam-4659	113	85	≤	≤	NOUN
ejpam-4659	113	86	ρ(t	ρ(t	PROPN
ejpam-4659	113	87	,	,	PUNCT
ejpam-4659	113	88	|u|)(1	|u|)(1	NOUN
ejpam-4659	114	1	+	+	CCONJ
ejpam-4659	114	2	|p|γ−1	|p|γ−1	NUM
ejpam-4659	114	3	+	+	CCONJ
ejpam-4659	114	4	|q|γ−1)|p−	|q|γ−1)|p−	PROPN
ejpam-4659	114	5	q|	q|	PROPN
ejpam-4659	114	6	(	(	PUNCT
ejpam-4659	114	7	21	21	NUM
ejpam-4659	114	8	)	)	PUNCT
ejpam-4659	114	9	a.	a.	NOUN
ejpam-4659	114	10	y.	y.	PROPN
ejpam-4659	114	11	akinyele	akinyele	PROPN
ejpam-4659	114	12	et	et	PROPN
ejpam-4659	114	13	al	al	PROPN
ejpam-4659	114	14	.	.	PUNCT
ejpam-4659	114	15	/	/	SYM
ejpam-4659	114	16	eur	eur	PROPN
ejpam-4659	114	17	.	.	PUNCT
ejpam-4659	115	1	j.	j.	PROPN
ejpam-4659	115	2	pure	pure	PROPN
ejpam-4659	115	3	appl	appl	PROPN
ejpam-4659	115	4	.	.	PROPN
ejpam-4659	115	5	math	math	PROPN
ejpam-4659	115	6	,	,	PUNCT
ejpam-4659	115	7	16	16	NUM
ejpam-4659	115	8	(	(	PUNCT
ejpam-4659	115	9	1	1	NUM
ejpam-4659	115	10	)	)	PUNCT
ejpam-4659	115	11	(	(	PUNCT
ejpam-4659	115	12	2023	2023	NUM
ejpam-4659	115	13	)	)	PUNCT
ejpam-4659	115	14	,	,	PUNCT
ejpam-4659	115	15	538	538	NUM
ejpam-4659	115	16	-	-	SYM
ejpam-4659	115	17	547	547	NUM
ejpam-4659	115	18	544	544	NUM
ejpam-4659	115	19	|f(t	|f(t	NOUN
ejpam-4659	115	20	,	,	PUNCT
ejpam-4659	115	21	x	x	NOUN
ejpam-4659	115	22	,	,	PUNCT
ejpam-4659	115	23	u	u	NOUN
ejpam-4659	115	24	,	,	PUNCT
ejpam-4659	115	25	p)−	p)−	ADJ
ejpam-4659	115	26	f(t	f(t	NOUN
ejpam-4659	115	27	,	,	PUNCT
ejpam-4659	115	28	x	x	NOUN
ejpam-4659	115	29	,	,	PUNCT
ejpam-4659	115	30	v	v	NOUN
ejpam-4659	115	31	,	,	PUNCT
ejpam-4659	115	32	p)|	p)|	NOUN
ejpam-4659	115	33	≤	≤	NOUN
ejpam-4659	115	34	ρ(t	ρ(t	NUM
ejpam-4659	115	35	,	,	PUNCT
ejpam-4659	115	36	|u|+	|u|+	NOUN
ejpam-4659	115	37	|v|)(1	|v|)(1	X
ejpam-4659	116	1	+	+	PUNCT
ejpam-4659	116	2	|p|γ)|u−	|p|γ)|u−	NOUN
ejpam-4659	116	3	v|	v|	NOUN
ejpam-4659	116	4	.	.	PUNCT
ejpam-4659	117	1	(	(	PUNCT
ejpam-4659	117	2	22	22	NUM
ejpam-4659	117	3	)	)	PUNCT
ejpam-4659	117	4	then	then	ADV
ejpam-4659	117	5	for	for	ADP
ejpam-4659	117	6	every	every	DET
ejpam-4659	117	7	u0	u0	PROPN
ejpam-4659	117	8	∈	∈	PROPN
ejpam-4659	117	9	h2(ω	h2(ω	NOUN
ejpam-4659	117	10	)	)	PUNCT
ejpam-4659	117	11	∩h1	∩h1	NOUN
ejpam-4659	117	12	0	0	NUM
ejpam-4659	117	13	(	(	PUNCT
ejpam-4659	117	14	ω	ω	NOUN
ejpam-4659	117	15	)	)	PUNCT
ejpam-4659	117	16	,	,	PUNCT
ejpam-4659	117	17	the	the	DET
ejpam-4659	117	18	initial	initial	ADJ
ejpam-4659	117	19	value	value	NOUN
ejpam-4659	117	20	problem	problem	PUNCT
ejpam-4659	117	21	∂u	∂u	PROPN
ejpam-4659	117	22	∂t	∂t	PROPN
ejpam-4659	117	23	=	=	SYM
ejpam-4659	117	24	a(x	a(x	PROPN
ejpam-4659	117	25	,	,	PUNCT
ejpam-4659	117	26	d)u+	d)u+	PRON
ejpam-4659	117	27	f(t	f(t	NOUN
ejpam-4659	117	28	,	,	PUNCT
ejpam-4659	117	29	x	x	X
ejpam-4659	117	30	,	,	PUNCT
ejpam-4659	117	31	u	u	NOUN
ejpam-4659	117	32	,	,	PUNCT
ejpam-4659	117	33	grad	grad	NOUN
ejpam-4659	117	34	u	u	NOUN
ejpam-4659	117	35	)	)	PUNCT
ejpam-4659	117	36	in	in	ADP
ejpam-4659	117	37	ω	ω	PROPN
ejpam-4659	117	38	u(t	u(t	NOUN
ejpam-4659	117	39	,	,	PUNCT
ejpam-4659	117	40	x	x	NOUN
ejpam-4659	117	41	)	)	PUNCT
ejpam-4659	117	42	=	=	SYM
ejpam-4659	117	43	0	0	NUM
ejpam-4659	117	44	on	on	ADP
ejpam-4659	117	45	∂ω	∂ω	PROPN
ejpam-4659	117	46	u(0	u(0	PROPN
ejpam-4659	117	47	,	,	PUNCT
ejpam-4659	117	48	x	x	NOUN
ejpam-4659	117	49	)	)	PUNCT
ejpam-4659	117	50	=	=	SYM
ejpam-4659	117	51	u0(x	u0(x	NOUN
ejpam-4659	117	52	)	)	PUNCT
ejpam-4659	117	53	in	in	ADP
ejpam-4659	117	54	ω	ω	PROPN
ejpam-4659	117	55	(	(	PUNCT
ejpam-4659	117	56	23	23	NUM
ejpam-4659	117	57	)	)	PUNCT
ejpam-4659	117	58	has	have	VERB
ejpam-4659	117	59	a	a	DET
ejpam-4659	117	60	unique	unique	ADJ
ejpam-4659	117	61	local	local	ADJ
ejpam-4659	117	62	strong	strong	ADJ
ejpam-4659	117	63	solution	solution	NOUN
ejpam-4659	117	64	in	in	ADP
ejpam-4659	117	65	l2(ω	l2(ω	NOUN
ejpam-4659	117	66	)	)	PUNCT
ejpam-4659	117	67	.	.	PUNCT
ejpam-4659	118	1	proof	proof	NOUN
ejpam-4659	118	2	:	:	PUNCT
ejpam-4659	118	3	we	we	PRON
ejpam-4659	118	4	recall	recall	VERB
ejpam-4659	118	5	that	that	SCONJ
ejpam-4659	118	6	with	with	ADP
ejpam-4659	118	7	the	the	DET
ejpam-4659	118	8	strongly	strongly	ADV
ejpam-4659	118	9	elliptic	elliptic	ADJ
ejpam-4659	118	10	operator	operator	NOUN
ejpam-4659	118	11	a(x	a(x	NOUN
ejpam-4659	118	12	,	,	PUNCT
ejpam-4659	118	13	d	d	NOUN
ejpam-4659	118	14	)	)	PUNCT
ejpam-4659	118	15	,	,	PUNCT
ejpam-4659	118	16	we	we	PRON
ejpam-4659	118	17	associate	associate	VERB
ejpam-4659	118	18	an	an	DET
ejpam-4659	118	19	operator	operator	NOUN
ejpam-4659	118	20	a	a	PRON
ejpam-4659	118	21	in	in	ADP
ejpam-4659	118	22	l2(ω	l2(ω	NOUN
ejpam-4659	118	23	)	)	PUNCT
ejpam-4659	118	24	by	by	ADP
ejpam-4659	118	25	d(a	d(a	PROPN
ejpam-4659	118	26	)	)	PUNCT
ejpam-4659	118	27	=	=	SYM
ejpam-4659	119	1	h2(ω	h2(ω	NOUN
ejpam-4659	119	2	)	)	PUNCT
ejpam-4659	119	3	∩h1	∩h1	NOUN
ejpam-4659	119	4	0	0	NUM
ejpam-4659	119	5	(	(	PUNCT
ejpam-4659	119	6	ω	ω	NOUN
ejpam-4659	119	7	)	)	PUNCT
ejpam-4659	119	8	and	and	CCONJ
ejpam-4659	119	9	au	au	X
ejpam-4659	119	10	=	=	SYM
ejpam-4659	119	11	a(x	a(x	NOUN
ejpam-4659	119	12	,	,	PUNCT
ejpam-4659	119	13	d)u	d)u	ADJ
ejpam-4659	119	14	for	for	ADP
ejpam-4659	119	15	u	u	PROPN
ejpam-4659	119	16	∈	∈	PROPN
ejpam-4659	119	17	d(a	d(a	PROPN
ejpam-4659	119	18	)	)	PUNCT
ejpam-4659	119	19	and	and	CCONJ
ejpam-4659	119	20	a	a	DET
ejpam-4659	119	21	∈	∈	PROPN
ejpam-4659	119	22	ω	ω	NUM
ejpam-4659	119	23	−ocpn	−ocpn	NOUN
ejpam-4659	119	24	.	.	PUNCT
ejpam-4659	120	1	let	let	VERB
ejpam-4659	120	2	1	1	NUM
ejpam-4659	120	3	<	<	X
ejpam-4659	120	4	p	p	X
ejpam-4659	120	5	<	<	X
ejpam-4659	120	6	∞	∞	PROPN
ejpam-4659	120	7	,	,	PUNCT
ejpam-4659	120	8	the	the	DET
ejpam-4659	120	9	operator	operator	NOUN
ejpam-4659	120	10	a	a	PRON
ejpam-4659	120	11	is	be	AUX
ejpam-4659	120	12	the	the	DET
ejpam-4659	120	13	infinitesimal	infinitesimal	ADJ
ejpam-4659	120	14	generator	generator	NOUN
ejpam-4659	120	15	of	of	ADP
ejpam-4659	120	16	an	an	DET
ejpam-4659	120	17	analytic	analytic	ADJ
ejpam-4659	120	18	semigroup	semigroup	NOUN
ejpam-4659	120	19	of	of	ADP
ejpam-4659	120	20	contractions	contraction	NOUN
ejpam-4659	120	21	on	on	ADP
ejpam-4659	120	22	lp(ω	lp(ω	PROPN
ejpam-4659	120	23	)	)	PUNCT
ejpam-4659	120	24	,	,	PUNCT
ejpam-4659	120	25	then	then	ADV
ejpam-4659	120	26	it	it	PRON
ejpam-4659	120	27	follows	follow	VERB
ejpam-4659	120	28	that	that	SCONJ
ejpam-4659	120	29	a	a	PRON
ejpam-4659	120	30	is	be	AUX
ejpam-4659	120	31	the	the	DET
ejpam-4659	120	32	infinitesimal	infinitesimal	ADJ
ejpam-4659	120	33	generator	generator	NOUN
ejpam-4659	120	34	of	of	ADP
ejpam-4659	120	35	an	an	DET
ejpam-4659	120	36	analytic	analytic	ADJ
ejpam-4659	120	37	semigroup	semigroup	NOUN
ejpam-4659	120	38	on	on	ADP
ejpam-4659	120	39	l2(ω	l2(ω	PROPN
ejpam-4659	120	40	)	)	PUNCT
ejpam-4659	120	41	.	.	PUNCT
ejpam-4659	121	1	from	from	ADP
ejpam-4659	121	2	the	the	DET
ejpam-4659	121	3	strong	strong	ADJ
ejpam-4659	121	4	ellipticity	ellipticity	NOUN
ejpam-4659	121	5	together	together	ADV
ejpam-4659	121	6	with	with	ADP
ejpam-4659	121	7	poincare	poincare	PROPN
ejpam-4659	121	8	’s	’s	PART
ejpam-4659	121	9	inequality	inequality	NOUN
ejpam-4659	121	10	it	it	PRON
ejpam-4659	121	11	follows	follow	VERB
ejpam-4659	121	12	readily	readily	ADV
ejpam-4659	121	13	that	that	SCONJ
ejpam-4659	121	14	a	a	PRON
ejpam-4659	121	15	is	be	AUX
ejpam-4659	121	16	also	also	ADV
ejpam-4659	121	17	invertible	invertible	ADJ
ejpam-4659	121	18	.	.	PUNCT
ejpam-4659	122	1	from	from	ADP
ejpam-4659	122	2	theorem	theorem	ADJ
ejpam-4659	122	3	3.2	3.2	NUM
ejpam-4659	122	4	it	it	PRON
ejpam-4659	122	5	follows	follow	VERB
ejpam-4659	122	6	that	that	SCONJ
ejpam-4659	122	7	if	if	SCONJ
ejpam-4659	122	8	α	α	PROPN
ejpam-4659	122	9	>	>	X
ejpam-4659	122	10	3/4	3/4	NUM
ejpam-4659	122	11	,	,	PUNCT
ejpam-4659	122	12	then	then	ADV
ejpam-4659	122	13	xα	xα	CCONJ
ejpam-4659	123	1	⊂	⊂	PROPN
ejpam-4659	123	2	l∞(ω	l∞(ω	X
ejpam-4659	123	3	)	)	PUNCT
ejpam-4659	123	4	and	and	CCONJ
ejpam-4659	123	5	if	if	SCONJ
ejpam-4659	123	6	also	also	ADV
ejpam-4659	123	7	1	1	NUM
ejpam-4659	123	8	/	/	SYM
ejpam-4659	123	9	q	q	X
ejpam-4659	123	10	>	>	X
ejpam-4659	123	11	(	(	PUNCT
ejpam-4659	123	12	5−	5−	NUM
ejpam-4659	123	13	4α)/6	4α)/6	NOUN
ejpam-4659	123	14	,	,	PUNCT
ejpam-4659	123	15	then	then	ADV
ejpam-4659	123	16	xα	xα	PUNCT
ejpam-4659	123	17	⊂	⊂	PROPN
ejpam-4659	123	18	w	w	PROPN
ejpam-4659	123	19	1,q(ω	1,q(ω	PROPN
ejpam-4659	123	20	)	)	PUNCT
ejpam-4659	123	21	.	.	PUNCT
ejpam-4659	124	1	thus	thus	ADV
ejpam-4659	124	2	for	for	ADP
ejpam-4659	124	3	max(3/4	max(3/4	PROPN
ejpam-4659	124	4	,	,	PUNCT
ejpam-4659	124	5	(	(	PUNCT
ejpam-4659	124	6	5γ	5γ	NOUN
ejpam-4659	124	7	−	−	PROPN
ejpam-4659	124	8	3)/4γ	3)/4γ	NUM
ejpam-4659	124	9	)	)	PUNCT
ejpam-4659	124	10	<	<	X
ejpam-4659	124	11	a	a	DET
ejpam-4659	124	12	<	<	X
ejpam-4659	124	13	1	1	NUM
ejpam-4659	124	14	,	,	PUNCT
ejpam-4659	124	15	we	we	PRON
ejpam-4659	124	16	have	have	VERB
ejpam-4659	124	17	xα	xα	PUNCT
ejpam-4659	125	1	⊂	⊂	PRON
ejpam-4659	125	2	w	w	NOUN
ejpam-4659	125	3	1,2γ(ω	1,2γ(ω	NOUN
ejpam-4659	125	4	)	)	PUNCT
ejpam-4659	125	5	∩	∩	NOUN
ejpam-4659	125	6	l∞(ω	l∞(ω	NOUN
ejpam-4659	125	7	)	)	PUNCT
ejpam-4659	125	8	.	.	PUNCT
ejpam-4659	126	1	(	(	PUNCT
ejpam-4659	126	2	24	24	NUM
ejpam-4659	126	3	)	)	PUNCT
ejpam-4659	126	4	in	in	ADP
ejpam-4659	126	5	order	order	NOUN
ejpam-4659	126	6	to	to	PART
ejpam-4659	126	7	show	show	VERB
ejpam-4659	126	8	that	that	SCONJ
ejpam-4659	126	9	the	the	DET
ejpam-4659	126	10	initial	initial	ADJ
ejpam-4659	126	11	value	value	NOUN
ejpam-4659	126	12	problem	problem	NOUN
ejpam-4659	126	13	has	have	VERB
ejpam-4659	126	14	a	a	DET
ejpam-4659	126	15	unique	unique	ADJ
ejpam-4659	126	16	local	local	ADJ
ejpam-4659	126	17	solution	solution	NOUN
ejpam-4659	126	18	,	,	PUNCT
ejpam-4659	126	19	we	we	PRON
ejpam-4659	126	20	have	have	VERB
ejpam-4659	126	21	to	to	PART
ejpam-4659	126	22	show	show	VERB
ejpam-4659	126	23	that	that	SCONJ
ejpam-4659	126	24	the	the	DET
ejpam-4659	126	25	mapping	mapping	NOUN
ejpam-4659	126	26	f	f	X
ejpam-4659	126	27	(	(	PUNCT
ejpam-4659	126	28	t	t	PROPN
ejpam-4659	126	29	,	,	PUNCT
ejpam-4659	126	30	u)(x	u)(x	PROPN
ejpam-4659	126	31	)	)	PUNCT
ejpam-4659	126	32	=	=	PUNCT
ejpam-4659	126	33	f(t	f(t	NOUN
ejpam-4659	126	34	,	,	PUNCT
ejpam-4659	126	35	x	x	PRON
ejpam-4659	126	36	,	,	PUNCT
ejpam-4659	126	37	x(x),∇u(x	x(x),∇u(x	PROPN
ejpam-4659	126	38	)	)	PUNCT
ejpam-4659	126	39	)	)	PUNCT
ejpam-4659	126	40	,	,	PUNCT
ejpam-4659	126	41	x	x	PUNCT
ejpam-4659	126	42	∈	∈	PROPN
ejpam-4659	126	43	ω	ω	PROPN
ejpam-4659	126	44	(	(	PUNCT
ejpam-4659	126	45	25	25	NUM
ejpam-4659	126	46	)	)	PUNCT
ejpam-4659	126	47	is	be	AUX
ejpam-4659	126	48	well	well	ADV
ejpam-4659	126	49	defined	define	VERB
ejpam-4659	126	50	on	on	ADP
ejpam-4659	126	51	r+	r+	NOUN
ejpam-4659	126	52	×xα	×xα	NOUN
ejpam-4659	126	53	and	and	CCONJ
ejpam-4659	126	54	satisfies	satisfy	VERB
ejpam-4659	126	55	a	a	DET
ejpam-4659	126	56	local	local	ADJ
ejpam-4659	126	57	holder	holder	NOUN
ejpam-4659	126	58	condition	condition	NOUN
ejpam-4659	126	59	.	.	PUNCT
ejpam-4659	127	1	from	from	ADP
ejpam-4659	127	2	(	(	PUNCT
ejpam-4659	127	3	20	20	NUM
ejpam-4659	127	4	)	)	PUNCT
ejpam-4659	127	5	and	and	CCONJ
ejpam-4659	127	6	(	(	PUNCT
ejpam-4659	127	7	24	24	NUM
ejpam-4659	127	8	)	)	PUNCT
ejpam-4659	127	9	,	,	PUNCT
ejpam-4659	127	10	we	we	PRON
ejpam-4659	127	11	have	have	VERB
ejpam-4659	127	12	for	for	ADP
ejpam-4659	127	13	every	every	DET
ejpam-4659	127	14	u	u	NOUN
ejpam-4659	127	15	∈	∈	PROPN
ejpam-4659	127	16	xα	xα	PUNCT
ejpam-4659	128	1	∥f	∥f	PROPN
ejpam-4659	128	2	(	(	PUNCT
ejpam-4659	128	3	t	t	PROPN
ejpam-4659	128	4	,	,	PUNCT
ejpam-4659	128	5	u)∥0,2	u)∥0,2	ADJ
ejpam-4659	128	6	≤	≤	ADJ
ejpam-4659	128	7	2p(t	2p(t	NUM
ejpam-4659	128	8	,	,	PUNCT
ejpam-4659	128	9	∥u∥0,∞)(m1/2	∥u∥0,∞)(m1/2	PROPN
ejpam-4659	128	10	+	+	SYM
ejpam-4659	128	11	∥u∥γ1,2γ	∥u∥γ1,2γ	NOUN
ejpam-4659	128	12	)	)	PUNCT
ejpam-4659	128	13	where	where	SCONJ
ejpam-4659	128	14	m	m	NOUN
ejpam-4659	128	15	is	be	AUX
ejpam-4659	128	16	the	the	DET
ejpam-4659	128	17	measure	measure	NOUN
ejpam-4659	128	18	of	of	ADP
ejpam-4659	128	19	ω	ω	PROPN
ejpam-4659	128	20	.	.	PUNCT
ejpam-4659	129	1	therefore	therefore	ADV
ejpam-4659	129	2	f	f	PROPN
ejpam-4659	129	3	is	be	AUX
ejpam-4659	129	4	well	well	ADV
ejpam-4659	129	5	defined	define	VERB
ejpam-4659	129	6	on	on	ADP
ejpam-4659	129	7	r+	r+	X
ejpam-4659	129	8	×xα	×xα	PROPN
ejpam-4659	129	9	.	.	PUNCT
ejpam-4659	130	1	to	to	PART
ejpam-4659	130	2	show	show	VERB
ejpam-4659	130	3	that	that	SCONJ
ejpam-4659	130	4	f	f	PROPN
ejpam-4659	130	5	satisfies	satisfy	VERB
ejpam-4659	130	6	a	a	DET
ejpam-4659	130	7	local	local	ADJ
ejpam-4659	130	8	hölder	hölder	NOUN
ejpam-4659	130	9	condition	condition	NOUN
ejpam-4659	130	10	we	we	PRON
ejpam-4659	130	11	note	note	VERB
ejpam-4659	130	12	that	that	SCONJ
ejpam-4659	131	1	∥f	∥f	PROPN
ejpam-4659	131	2	(	(	PUNCT
ejpam-4659	131	3	t	t	PROPN
ejpam-4659	131	4	,	,	PUNCT
ejpam-4659	131	5	u)−	u)−	PROPN
ejpam-4659	131	6	f	f	PROPN
ejpam-4659	131	7	(	(	PUNCT
ejpam-4659	131	8	t	t	PROPN
ejpam-4659	131	9	,	,	PUNCT
ejpam-4659	131	10	v)∥20,2	v)∥20,2	PROPN
ejpam-4659	131	11	≤	≤	ADJ
ejpam-4659	131	12	2	2	NUM
ejpam-4659	131	13	∫	∫	NOUN
ejpam-4659	131	14	0	0	NUM
ejpam-4659	132	1	|f(t	|f(t	PROPN
ejpam-4659	132	2	,	,	PUNCT
ejpam-4659	132	3	x	x	SYM
ejpam-4659	132	4	,	,	PUNCT
ejpam-4659	132	5	u,∇u)−	u,∇u)−	ADJ
ejpam-4659	132	6	f(t	f(t	NOUN
ejpam-4659	132	7	,	,	PUNCT
ejpam-4659	132	8	x	x	PRON
ejpam-4659	132	9	,	,	PUNCT
ejpam-4659	132	10	u,∇v)|2dx	u,∇v)|2dx	ADJ
ejpam-4659	132	11	+	+	NUM
ejpam-4659	132	12	2	2	NUM
ejpam-4659	132	13	∫	∫	NOUN
ejpam-4659	132	14	ω	ω	X
ejpam-4659	132	15	|f(t	|f(t	PROPN
ejpam-4659	132	16	,	,	PUNCT
ejpam-4659	132	17	x	x	PRON
ejpam-4659	132	18	,	,	PUNCT
ejpam-4659	132	19	u,∇v)−	u,∇v)−	ADJ
ejpam-4659	132	20	f(t	f(t	NOUN
ejpam-4659	132	21	,	,	PUNCT
ejpam-4659	132	22	x	x	PRON
ejpam-4659	132	23	,	,	PUNCT
ejpam-4659	132	24	v,∇v)|2dx	v,∇v)|2dx	ADJ
ejpam-4659	132	25	(	(	PUNCT
ejpam-4659	132	26	26	26	NUM
ejpam-4659	132	27	)	)	PUNCT
ejpam-4659	132	28	and	and	CCONJ
ejpam-4659	132	29	estimate	estimate	VERB
ejpam-4659	132	30	each	each	PRON
ejpam-4659	132	31	of	of	ADP
ejpam-4659	132	32	the	the	DET
ejpam-4659	132	33	two	two	NUM
ejpam-4659	132	34	terms	term	NOUN
ejpam-4659	132	35	on	on	ADP
ejpam-4659	132	36	the	the	DET
ejpam-4659	132	37	right	right	NOUN
ejpam-4659	132	38	of	of	ADP
ejpam-4659	132	39	(	(	PUNCT
ejpam-4659	132	40	26	26	NUM
ejpam-4659	132	41	)	)	PUNCT
ejpam-4659	132	42	separately	separately	ADV
ejpam-4659	132	43	.	.	PUNCT
ejpam-4659	133	1	from	from	ADP
ejpam-4659	133	2	(	(	PUNCT
ejpam-4659	133	3	21	21	NUM
ejpam-4659	133	4	)	)	PUNCT
ejpam-4659	133	5	and	and	CCONJ
ejpam-4659	133	6	(	(	PUNCT
ejpam-4659	133	7	23	23	NUM
ejpam-4659	133	8	)	)	PUNCT
ejpam-4659	133	9	we	we	PRON
ejpam-4659	133	10	have∫	have∫	VERB
ejpam-4659	133	11	ω	ω	PUNCT
ejpam-4659	133	12	|f(t	|f(t	PROPN
ejpam-4659	133	13	,	,	PUNCT
ejpam-4659	133	14	x	x	SYM
ejpam-4659	133	15	,	,	PUNCT
ejpam-4659	133	16	u,∇u)−	u,∇u)−	ADJ
ejpam-4659	133	17	f(t	f(t	NOUN
ejpam-4659	133	18	,	,	PUNCT
ejpam-4659	133	19	x	x	PRON
ejpam-4659	133	20	,	,	PUNCT
ejpam-4659	133	21	u,∇v)|2dx	u,∇v)|2dx	PROPN
ejpam-4659	133	22	a.	a.	NOUN
ejpam-4659	133	23	y.	y.	PROPN
ejpam-4659	133	24	akinyele	akinyele	PROPN
ejpam-4659	133	25	et	et	PROPN
ejpam-4659	133	26	al	al	PROPN
ejpam-4659	133	27	.	.	PUNCT
ejpam-4659	133	28	/	/	SYM
ejpam-4659	133	29	eur	eur	PROPN
ejpam-4659	133	30	.	.	PUNCT
ejpam-4659	134	1	j.	j.	PROPN
ejpam-4659	134	2	pure	pure	PROPN
ejpam-4659	134	3	appl	appl	PROPN
ejpam-4659	134	4	.	.	PROPN
ejpam-4659	134	5	math	math	PROPN
ejpam-4659	134	6	,	,	PUNCT
ejpam-4659	134	7	16	16	NUM
ejpam-4659	134	8	(	(	PUNCT
ejpam-4659	134	9	1	1	NUM
ejpam-4659	134	10	)	)	PUNCT
ejpam-4659	134	11	(	(	PUNCT
ejpam-4659	134	12	2023	2023	NUM
ejpam-4659	134	13	)	)	PUNCT
ejpam-4659	134	14	,	,	PUNCT
ejpam-4659	134	15	538	538	NUM
ejpam-4659	134	16	-	-	SYM
ejpam-4659	134	17	547	547	NUM
ejpam-4659	134	18	545	545	NUM
ejpam-4659	134	19	≤	≤	NOUN
ejpam-4659	134	20	c	c	X
ejpam-4659	134	21	·	·	PUNCT
ejpam-4659	134	22	ρ(t	ρ(t	NUM
ejpam-4659	134	23	,	,	PUNCT
ejpam-4659	134	24	∥u∥0,∞)2	∥u∥0,∞)2	NOUN
ejpam-4659	134	25	∫	∫	PROPN
ejpam-4659	134	26	ω	ω	PROPN
ejpam-4659	134	27	(	(	PUNCT
ejpam-4659	134	28	1	1	NUM
ejpam-4659	134	29	+	+	CCONJ
ejpam-4659	134	30	|∇u|2γ−2	|∇u|2γ−2	PROPN
ejpam-4659	134	31	+	+	CCONJ
ejpam-4659	134	32	|∇v|2γ−2)|∇(u−	|∇v|2γ−2)|∇(u−	PRON
ejpam-4659	134	33	v)|2dx	v)|2dx	ADV
ejpam-4659	134	34	≤	≤	X
ejpam-4659	134	35	c	c	X
ejpam-4659	134	36	·	·	PUNCT
ejpam-4659	134	37	ρ(t	ρ(t	NUM
ejpam-4659	134	38	,	,	PUNCT
ejpam-4659	134	39	∥u∥0,∞)2(m1	∥u∥0,∞)2(m1	NOUN
ejpam-4659	134	40	+	+	CCONJ
ejpam-4659	134	41	∥∇u∥2γ−2	∥∇u∥2γ−2	X
ejpam-4659	134	42	0,2γ	0,2γ	NOUN
ejpam-4659	134	43	+	+	CCONJ
ejpam-4659	134	44	∥∇v∥2γ−2	∥∇v∥2γ−2	NUM
ejpam-4659	134	45	0,2γ	0,2γ	NUM
ejpam-4659	134	46	)	)	PUNCT
ejpam-4659	135	1	∥∇(u−	∥∇(u−	PROPN
ejpam-4659	135	2	v)∥20,2γdx	v)∥20,2γdx	NOUN
ejpam-4659	135	3	≤	≤	ADJ
ejpam-4659	135	4	l(∥u∥α	l(∥u∥α	NOUN
ejpam-4659	135	5	,	,	PUNCT
ejpam-4659	135	6	∥v∥α)∥u−	∥v∥α)∥u−	NOUN
ejpam-4659	135	7	v∥21,2γ	v∥21,2γ	NOUN
ejpam-4659	135	8	≤	≤	ADJ
ejpam-4659	135	9	l(∥u∥α	l(∥u∥α	NOUN
ejpam-4659	135	10	,	,	PUNCT
ejpam-4659	135	11	∥v∥α)∥u−	∥v∥α)∥u−	NOUN
ejpam-4659	135	12	v∥2α	v∥2α	NOUN
ejpam-4659	135	13	(	(	PUNCT
ejpam-4659	135	14	27	27	NUM
ejpam-4659	135	15	)	)	PUNCT
ejpam-4659	135	16	where	where	SCONJ
ejpam-4659	135	17	∥	∥	PUNCT
ejpam-4659	135	18	∥α	∥α	NOUN
ejpam-4659	135	19	denotes	denote	VERB
ejpam-4659	135	20	the	the	DET
ejpam-4659	135	21	norm	norm	NOUN
ejpam-4659	135	22	in	in	ADP
ejpam-4659	135	23	xα	xα	PUNCT
ejpam-4659	135	24	and	and	CCONJ
ejpam-4659	135	25	l	l	NOUN
ejpam-4659	135	26	is	be	AUX
ejpam-4659	135	27	a	a	DET
ejpam-4659	135	28	constant	constant	ADJ
ejpam-4659	135	29	depending	depend	VERB
ejpam-4659	135	30	on	on	ADP
ejpam-4659	135	31	∥u∥α	∥u∥α	NOUN
ejpam-4659	135	32	and	and	CCONJ
ejpam-4659	135	33	∥v∥α	∥v∥α	NOUN
ejpam-4659	135	34	.	.	PUNCT
ejpam-4659	136	1	to	to	PART
ejpam-4659	136	2	obtain	obtain	VERB
ejpam-4659	136	3	the	the	DET
ejpam-4659	136	4	second	second	ADJ
ejpam-4659	136	5	inequality	inequality	NOUN
ejpam-4659	136	6	we	we	PRON
ejpam-4659	136	7	used	use	VERB
ejpam-4659	136	8	hölder	hölder	NOUN
ejpam-4659	136	9	’s	’s	PART
ejpam-4659	136	10	inequality	inequality	NOUN
ejpam-4659	136	11	.	.	PUNCT
ejpam-4659	137	1	the	the	DET
ejpam-4659	137	2	last	last	ADJ
ejpam-4659	137	3	inequality	inequality	NOUN
ejpam-4659	137	4	(	(	PUNCT
ejpam-4659	137	5	27	27	NUM
ejpam-4659	137	6	)	)	PUNCT
ejpam-4659	137	7	is	be	AUX
ejpam-4659	137	8	a	a	DET
ejpam-4659	137	9	consequence	consequence	NOUN
ejpam-4659	137	10	of	of	ADP
ejpam-4659	137	11	the	the	DET
ejpam-4659	137	12	continuous	continuous	ADJ
ejpam-4659	137	13	imbedding	imbedding	NOUN
ejpam-4659	137	14	of	of	ADP
ejpam-4659	137	15	xα	xα	INTJ
ejpam-4659	137	16	in	in	ADP
ejpam-4659	137	17	w	w	NOUN
ejpam-4659	137	18	1,2γ(ω	1,2γ(ω	NUM
ejpam-4659	137	19	)	)	PUNCT
ejpam-4659	137	20	.	.	PUNCT
ejpam-4659	138	1	similarly	similarly	ADV
ejpam-4659	138	2	for	for	ADP
ejpam-4659	138	3	the	the	DET
ejpam-4659	138	4	second	second	ADJ
ejpam-4659	138	5	term	term	NOUN
ejpam-4659	138	6	we	we	PRON
ejpam-4659	138	7	have	have	VERB
ejpam-4659	138	8	(	(	PUNCT
ejpam-4659	138	9	22	22	NUM
ejpam-4659	138	10	)	)	PUNCT
ejpam-4659	138	11	and	and	CCONJ
ejpam-4659	138	12	(	(	PUNCT
ejpam-4659	138	13	24	24	NUM
ejpam-4659	138	14	)	)	PUNCT
ejpam-4659	138	15	,	,	PUNCT
ejpam-4659	138	16	then	then	ADV
ejpam-4659	138	17	we	we	PRON
ejpam-4659	138	18	have∫	have∫	VERB
ejpam-4659	138	19	ω	ω	PUNCT
ejpam-4659	138	20	|f(t	|f(t	PROPN
ejpam-4659	138	21	,	,	PUNCT
ejpam-4659	138	22	x	x	NOUN
ejpam-4659	138	23	,	,	PUNCT
ejpam-4659	138	24	u,∇v)−	u,∇v)−	ADJ
ejpam-4659	138	25	f(t	f(t	NOUN
ejpam-4659	138	26	,	,	PUNCT
ejpam-4659	138	27	x	x	PRON
ejpam-4659	138	28	,	,	PUNCT
ejpam-4659	138	29	v,∇v)|2dx	v,∇v)|2dx	ADJ
ejpam-4659	138	30	≤	≤	NOUN
ejpam-4659	138	31	cρ(t	cρ(t	PUNCT
ejpam-4659	138	32	,	,	PUNCT
ejpam-4659	138	33	∥u∥0,∞	∥u∥0,∞	X
ejpam-4659	139	1	+	+	PUNCT
ejpam-4659	139	2	∥v∥0,∞)2	∥v∥0,∞)2	ADJ
ejpam-4659	139	3	∫	∫	PROPN
ejpam-4659	139	4	ω	ω	PROPN
ejpam-4659	139	5	(	(	PUNCT
ejpam-4659	139	6	1	1	NUM
ejpam-4659	139	7	+	+	ADP
ejpam-4659	139	8	|∇u|2γ)|u−	|∇u|2γ)|u−	NOUN
ejpam-4659	139	9	v|2dx	v|2dx	ADJ
ejpam-4659	139	10	≤	≤	NOUN
ejpam-4659	139	11	cρ(t	cρ(t	PUNCT
ejpam-4659	139	12	,	,	PUNCT
ejpam-4659	139	13	∥u∥0,∞	∥u∥0,∞	X
ejpam-4659	139	14	+	+	CCONJ
ejpam-4659	139	15	∥v∥0,∞)2∥u−	∥v∥0,∞)2∥u−	NUM
ejpam-4659	139	16	v∥20,∞(1	v∥20,∞(1	NOUN
ejpam-4659	139	17	+	+	CCONJ
ejpam-4659	139	18	∥v∥2γ1,2γ	∥v∥2γ1,2γ	NOUN
ejpam-4659	139	19	)	)	PUNCT
ejpam-4659	139	20	≤	≤	NOUN
ejpam-4659	139	21	l(∥u∥α	l(∥u∥α	NOUN
ejpam-4659	139	22	,	,	PUNCT
ejpam-4659	139	23	∥v∥α)∥u−	∥v∥α)∥u−	NOUN
ejpam-4659	139	24	v∥2α	v∥2α	PROPN
ejpam-4659	139	25	(	(	PUNCT
ejpam-4659	139	26	28	28	NUM
ejpam-4659	139	27	)	)	PUNCT
ejpam-4659	139	28	and	and	CCONJ
ejpam-4659	139	29	therefore	therefore	ADV
ejpam-4659	139	30	,	,	PUNCT
ejpam-4659	139	31	∥f	∥f	PROPN
ejpam-4659	139	32	(	(	PUNCT
ejpam-4659	139	33	t	t	PROPN
ejpam-4659	139	34	,	,	PUNCT
ejpam-4659	139	35	u)−	u)−	PROPN
ejpam-4659	139	36	f	f	PROPN
ejpam-4659	139	37	(	(	PUNCT
ejpam-4659	139	38	t	t	PROPN
ejpam-4659	139	39	,	,	PUNCT
ejpam-4659	139	40	v)∥0,2	v)∥0,2	PROPN
ejpam-4659	139	41	≤	≤	PROPN
ejpam-4659	139	42	l(∥u∥α	l(∥u∥α	PROPN
ejpam-4659	139	43	,	,	PUNCT
ejpam-4659	139	44	∥v∥α)∥u−	∥v∥α)∥u−	PRON
ejpam-4659	139	45	v∥	v∥	NOUN
ejpam-4659	139	46	(	(	PUNCT
ejpam-4659	139	47	29	29	NUM
ejpam-4659	139	48	)	)	PUNCT
ejpam-4659	139	49	and	and	CCONJ
ejpam-4659	139	50	the	the	DET
ejpam-4659	139	51	existence	existence	NOUN
ejpam-4659	139	52	of	of	ADP
ejpam-4659	139	53	the	the	DET
ejpam-4659	139	54	strong	strong	ADJ
ejpam-4659	139	55	local	local	ADJ
ejpam-4659	139	56	solution	solution	NOUN
ejpam-4659	139	57	(	(	PUNCT
ejpam-4659	139	58	23	23	NUM
ejpam-4659	139	59	)	)	PUNCT
ejpam-4659	139	60	is	be	AUX
ejpam-4659	139	61	a	a	DET
ejpam-4659	139	62	direct	direct	ADJ
ejpam-4659	139	63	consequence	consequence	NOUN
ejpam-4659	139	64	that	that	SCONJ
ejpam-4659	139	65	the	the	DET
ejpam-4659	139	66	initial	initial	ADJ
ejpam-4659	139	67	value	value	NOUN
ejpam-4659	139	68	problem	problem	NOUN
ejpam-4659	139	69	(	(	PUNCT
ejpam-4659	139	70	23	23	NUM
ejpam-4659	139	71	)	)	PUNCT
ejpam-4659	139	72	has	have	AUX
ejpam-4659	139	73	a	a	DET
ejpam-4659	139	74	unique	unique	ADJ
ejpam-4659	139	75	local	local	ADJ
ejpam-4659	139	76	solution	solution	NOUN
ejpam-4659	139	77	u.	u.	VERB
ejpam-4659	139	78	hence	hence	ADV
ejpam-4659	139	79	the	the	DET
ejpam-4659	139	80	proof	proof	NOUN
ejpam-4659	139	81	is	be	AUX
ejpam-4659	139	82	completed	complete	VERB
ejpam-4659	139	83	.	.	PUNCT
ejpam-4659	140	1	theorem	theorem	VERB
ejpam-4659	140	2	3.4	3.4	NUM
ejpam-4659	140	3	assume	assume	VERB
ejpam-4659	140	4	a	a	DET
ejpam-4659	140	5	:	:	PUNCT
ejpam-4659	140	6	d(a	d(a	PROPN
ejpam-4659	140	7	)	)	PUNCT
ejpam-4659	140	8	⊆	⊆	NUM
ejpam-4659	140	9	h2(ω	h2(ω	NOUN
ejpam-4659	140	10	)	)	PUNCT
ejpam-4659	140	11	→	→	SYM
ejpam-4659	140	12	h2(ω	h2(ω	NOUN
ejpam-4659	140	13	)	)	PUNCT
ejpam-4659	140	14	is	be	AUX
ejpam-4659	140	15	the	the	DET
ejpam-4659	140	16	infinitesimal	infinitesimal	ADJ
ejpam-4659	140	17	generator	generator	NOUN
ejpam-4659	140	18	of	of	ADP
ejpam-4659	140	19	a	a	DET
ejpam-4659	140	20	c0	c0	NOUN
ejpam-4659	140	21	-	-	PUNCT
ejpam-4659	140	22	semigroup	semigroup	PROPN
ejpam-4659	140	23	{	{	PUNCT
ejpam-4659	140	24	t	t	PROPN
ejpam-4659	140	25	(	(	PUNCT
ejpam-4659	140	26	t)t≥0	t)t≥0	PROPN
ejpam-4659	140	27	}	}	PUNCT
ejpam-4659	140	28	.	.	PUNCT
ejpam-4659	141	1	let	let	VERB
ejpam-4659	141	2	f(u	f(u	NOUN
ejpam-4659	141	3	)	)	PUNCT
ejpam-4659	142	1	=	=	PUNCT
ejpam-4659	143	1	3∑	3∑	NUM
ejpam-4659	143	2	i=1	i=1	NUM
ejpam-4659	143	3	u	u	NOUN
ejpam-4659	143	4	∂u	∂u	PROPN
ejpam-4659	143	5	∂xi	∂xi	PROPN
ejpam-4659	143	6	.	.	PUNCT
ejpam-4659	144	1	(	(	PUNCT
ejpam-4659	144	2	30	30	NUM
ejpam-4659	144	3	)	)	PUNCT
ejpam-4659	144	4	if	if	SCONJ
ejpam-4659	144	5	γ	γ	X
ejpam-4659	144	6	>	>	X
ejpam-4659	144	7	3	3	NUM
ejpam-4659	144	8	4	4	NUM
ejpam-4659	144	9	,	,	PUNCT
ejpam-4659	144	10	u	u	PROPN
ejpam-4659	144	11	∈	∈	PROPN
ejpam-4659	144	12	d(a	d(a	PROPN
ejpam-4659	144	13	)	)	PUNCT
ejpam-4659	144	14	and	and	CCONJ
ejpam-4659	144	15	a	a	DET
ejpam-4659	144	16	∈	∈	PROPN
ejpam-4659	144	17	ω	ω	NUM
ejpam-4659	144	18	−ocpn	−ocpn	PROPN
ejpam-4659	144	19	,	,	PUNCT
ejpam-4659	144	20	then	then	ADV
ejpam-4659	144	21	f(u	f(u	PROPN
ejpam-4659	144	22	)	)	PUNCT
ejpam-4659	144	23	is	be	AUX
ejpam-4659	144	24	well	well	ADV
ejpam-4659	144	25	defined	define	VERB
ejpam-4659	144	26	and	and	CCONJ
ejpam-4659	144	27	∥f(u)∥	∥f(u)∥	ADJ
ejpam-4659	144	28	≤	≤	NOUN
ejpam-4659	144	29	c∥aγu∥∥a	c∥aγu∥∥a	NOUN
ejpam-4659	144	30	1	1	NUM
ejpam-4659	144	31	2u∥.	2u∥.	NUM
ejpam-4659	144	32	(	(	PUNCT
ejpam-4659	144	33	31	31	NUM
ejpam-4659	144	34	)	)	PUNCT
ejpam-4659	144	35	if	if	SCONJ
ejpam-4659	144	36	u	u	NOUN
ejpam-4659	144	37	,	,	PUNCT
ejpam-4659	144	38	v	v	PROPN
ejpam-4659	144	39	∈	∈	PROPN
ejpam-4659	144	40	d(a	d(a	PROPN
ejpam-4659	144	41	)	)	PUNCT
ejpam-4659	144	42	and	and	CCONJ
ejpam-4659	144	43	a	a	DET
ejpam-4659	144	44	∈	∈	PROPN
ejpam-4659	144	45	ω	ω	NUM
ejpam-4659	144	46	−ocpn	−ocpn	PROPN
ejpam-4659	144	47	,	,	PUNCT
ejpam-4659	144	48	then	then	ADV
ejpam-4659	144	49	∥f(u)−	∥f(u)−	NOUN
ejpam-4659	144	50	f(v)∥	f(v)∥	ADV
ejpam-4659	144	51	≤	≤	PROPN
ejpam-4659	144	52	c(∥aγu∥∥a	c(∥aγu∥∥a	X
ejpam-4659	144	53	1	1	NUM
ejpam-4659	144	54	2u−a	2u−a	NUM
ejpam-4659	144	55	1	1	NUM
ejpam-4659	144	56	2	2	NUM
ejpam-4659	144	57	v∥+	v∥+	CCONJ
ejpam-4659	144	58	∥a	∥a	PROPN
ejpam-4659	144	59	1	1	NUM
ejpam-4659	144	60	2	2	NUM
ejpam-4659	144	61	v∥∥aγu−aγv∥	v∥∥aγu−aγv∥	NOUN
ejpam-4659	144	62	)	)	PUNCT
ejpam-4659	144	63	.	.	PUNCT
ejpam-4659	145	1	(	(	PUNCT
ejpam-4659	145	2	32	32	NUM
ejpam-4659	145	3	)	)	PUNCT
ejpam-4659	145	4	proof	proof	NOUN
ejpam-4659	145	5	:	:	PUNCT
ejpam-4659	145	6	since	since	SCONJ
ejpam-4659	145	7	d(a	d(a	PROPN
ejpam-4659	145	8	)	)	PUNCT
ejpam-4659	145	9	⊂	⊂	PROPN
ejpam-4659	145	10	h2(ω	h2(ω	PROPN
ejpam-4659	145	11	)	)	PUNCT
ejpam-4659	145	12	,	,	PUNCT
ejpam-4659	145	13	then	then	ADV
ejpam-4659	145	14	it	it	PRON
ejpam-4659	145	15	follows	follow	VERB
ejpam-4659	145	16	from	from	ADP
ejpam-4659	145	17	sobolev	sobolev	PROPN
ejpam-4659	145	18	’s	’s	PART
ejpam-4659	145	19	theorem	theorem	NOUN
ejpam-4659	145	20	which	which	PRON
ejpam-4659	145	21	states	state	VERB
ejpam-4659	145	22	that	that	SCONJ
ejpam-4659	145	23	if	if	SCONJ
ejpam-4659	145	24	ω	ω	PROPN
ejpam-4659	145	25	is	be	AUX
ejpam-4659	145	26	a	a	DET
ejpam-4659	145	27	bounded	bounded	ADJ
ejpam-4659	145	28	domain	domain	NOUN
ejpam-4659	145	29	in	in	ADP
ejpam-4659	145	30	rn	rn	PROPN
ejpam-4659	145	31	with	with	ADP
ejpam-4659	145	32	a	a	DET
ejpam-4659	145	33	smooth	smooth	ADJ
ejpam-4659	145	34	boundary	boundary	ADJ
ejpam-4659	145	35	∂ω	∂ω	PROPN
ejpam-4659	145	36	of	of	ADP
ejpam-4659	145	37	class	class	NOUN
ejpam-4659	145	38	cm	cm	PROPN
ejpam-4659	145	39	,	,	PUNCT
ejpam-4659	145	40	then	then	ADV
ejpam-4659	145	41	w	w	PROPN
ejpam-4659	145	42	k	k	PROPN
ejpam-4659	145	43	,	,	PUNCT
ejpam-4659	145	44	p(ω	p(ω	PROPN
ejpam-4659	145	45	)	)	PUNCT
ejpam-4659	145	46	⊂	⊂	PROPN
ejpam-4659	146	1	lnp/(n−kp)(ω	lnp/(n−kp)(ω	X
ejpam-4659	146	2	)	)	PUNCT
ejpam-4659	146	3	for	for	ADP
ejpam-4659	146	4	kp	kp	PROPN
ejpam-4659	146	5	<	<	X
ejpam-4659	146	6	n	n	PROPN
ejpam-4659	146	7	(	(	PUNCT
ejpam-4659	146	8	33	33	NUM
ejpam-4659	146	9	)	)	PUNCT
ejpam-4659	146	10	references	reference	NOUN
ejpam-4659	146	11	546	546	NUM
ejpam-4659	146	12	and	and	CCONJ
ejpam-4659	146	13	w	w	PROPN
ejpam-4659	146	14	k	k	PROPN
ejpam-4659	146	15	,	,	PUNCT
ejpam-4659	146	16	p(ω	p(ω	PROPN
ejpam-4659	146	17	)	)	PUNCT
ejpam-4659	147	1	⊂	⊂	PROPN
ejpam-4659	147	2	cm(ω	cm(ω	ADV
ejpam-4659	147	3	)	)	PUNCT
ejpam-4659	147	4	for	for	ADP
ejpam-4659	147	5	0	0	NUM
ejpam-4659	147	6	≤	≤	NUM
ejpam-4659	147	7	m	m	VERB
ejpam-4659	147	8	<	<	X
ejpam-4659	147	9	k	k	X
ejpam-4659	147	10	−	−	PROPN
ejpam-4659	148	1	n	n	PRON
ejpam-4659	148	2	p	p	NOUN
ejpam-4659	148	3	.	.	PUNCT
ejpam-4659	149	1	(	(	PUNCT
ejpam-4659	149	2	34	34	NUM
ejpam-4659	149	3	)	)	PUNCT
ejpam-4659	149	4	moreover	moreover	ADV
ejpam-4659	149	5	,	,	PUNCT
ejpam-4659	149	6	there	there	PRON
ejpam-4659	149	7	exist	exist	VERB
ejpam-4659	149	8	constants	constant	NOUN
ejpam-4659	149	9	c1	c1	PROPN
ejpam-4659	149	10	and	and	CCONJ
ejpam-4659	149	11	c2	c2	PROPN
ejpam-4659	149	12	such	such	ADJ
ejpam-4659	149	13	that	that	PRON
ejpam-4659	149	14	for	for	ADP
ejpam-4659	149	15	any	any	DET
ejpam-4659	149	16	u	u	PROPN
ejpam-4659	149	17	∈	∈	PROPN
ejpam-4659	149	18	wm	wm	PROPN
ejpam-4659	149	19	,	,	PUNCT
ejpam-4659	149	20	p(ω	p(ω	PROPN
ejpam-4659	149	21	)	)	PUNCT
ejpam-4659	149	22	,	,	PUNCT
ejpam-4659	149	23	∥u∥0,np/(n−kp	∥u∥0,np/(n−kp	NOUN
ejpam-4659	149	24	)	)	PUNCT
ejpam-4659	149	25	≤	≤	NOUN
ejpam-4659	149	26	c1∥u∥k	c1∥u∥k	PROPN
ejpam-4659	149	27	,	,	PUNCT
ejpam-4659	149	28	p	p	NOUN
ejpam-4659	149	29	for	for	ADP
ejpam-4659	149	30	kp	kp	PROPN
ejpam-4659	149	31	<	<	X
ejpam-4659	149	32	n	n	PROPN
ejpam-4659	149	33	(	(	PUNCT
ejpam-4659	149	34	35	35	NUM
ejpam-4659	149	35	)	)	PUNCT
ejpam-4659	149	36	and	and	CCONJ
ejpam-4659	149	37	sup{|dαu(x)|	sup{|dαu(x)|	PROPN
ejpam-4659	149	38	:	:	PUNCT
ejpam-4659	150	1	|α|	|α|	NOUN
ejpam-4659	150	2	≤	≤	NUM
ejpam-4659	150	3	m	m	NOUN
ejpam-4659	150	4	,	,	PUNCT
ejpam-4659	150	5	x	x	SYM
ejpam-4659	150	6	∈	∈	PROPN
ejpam-4659	150	7	ω	ω	X
ejpam-4659	150	8	≤	≤	PROPN
ejpam-4659	150	9	c2∥u∥k	c2∥u∥k	PROPN
ejpam-4659	150	10	,	,	PUNCT
ejpam-4659	150	11	p	p	X
ejpam-4659	150	12	}	}	PUNCT
ejpam-4659	150	13	(	(	PUNCT
ejpam-4659	150	14	36	36	NUM
ejpam-4659	150	15	)	)	PUNCT
ejpam-4659	150	16	for	for	ADP
ejpam-4659	150	17	0	0	NUM
ejpam-4659	150	18	≤	≤	NUM
ejpam-4659	150	19	m	m	VERB
ejpam-4659	150	20	<	<	X
ejpam-4659	150	21	k	k	X
ejpam-4659	150	22	−	−	PROPN
ejpam-4659	150	23	n	n	PRON
ejpam-4659	150	24	p	p	NOUN
ejpam-4659	150	25	and	and	CCONJ
ejpam-4659	150	26	it	it	PRON
ejpam-4659	150	27	follows	follow	VERB
ejpam-4659	150	28	that	that	SCONJ
ejpam-4659	150	29	u	u	PROPN
ejpam-4659	150	30	∈	∈	PROPN
ejpam-4659	150	31	l∞(ω	l∞(ω	NOUN
ejpam-4659	150	32	)	)	PUNCT
ejpam-4659	150	33	and	and	CCONJ
ejpam-4659	150	34	therefore	therefore	ADV
ejpam-4659	150	35	f(u	f(u	PROPN
ejpam-4659	150	36	)	)	PUNCT
ejpam-4659	150	37	∈	∈	PROPN
ejpam-4659	150	38	l2(ω	l2(ω	NOUN
ejpam-4659	150	39	)	)	PUNCT
ejpam-4659	150	40	is	be	AUX
ejpam-4659	150	41	thus	thus	ADV
ejpam-4659	150	42	well	well	ADV
ejpam-4659	150	43	-	-	PUNCT
ejpam-4659	150	44	defined	define	VERB
ejpam-4659	150	45	.	.	PUNCT
ejpam-4659	151	1	moreover	moreover	ADV
ejpam-4659	151	2	,	,	PUNCT
ejpam-4659	151	3	from	from	ADP
ejpam-4659	151	4	theorem	theorem	ADJ
ejpam-4659	151	5	3.3	3.3	NUM
ejpam-4659	151	6	we	we	PRON
ejpam-4659	151	7	have	have	VERB
ejpam-4659	151	8	∥f(u)∥	∥f(u)∥	VERB
ejpam-4659	151	9	≤	≤	ADJ
ejpam-4659	151	10	∥u∥0,∞∥∇u∥	∥u∥0,∞∥∇u∥	NOUN
ejpam-4659	151	11	≤	≤	NUM
ejpam-4659	151	12	c∥aγu∥∥∇u∥	c∥aγu∥∥∇u∥	NOUN
ejpam-4659	152	1	=	=	PUNCT
ejpam-4659	153	1	c∥aγu∥∥a	c∥aγu∥∥a	VERB
ejpam-4659	153	2	1	1	NUM
ejpam-4659	153	3	2u∥.	2u∥.	NUM
ejpam-4659	153	4	also	also	ADV
ejpam-4659	153	5	∥f(u)−	∥f(u)−	VERB
ejpam-4659	153	6	f(v)∥	f(v)∥	AUX
ejpam-4659	153	7	≤	≤	ADJ
ejpam-4659	153	8	∥u∥0,∞∥∇(u−	∥u∥0,∞∥∇(u−	NUM
ejpam-4659	153	9	v)∥+	v)∥+	ADJ
ejpam-4659	153	10	∥u−	∥u−	PROPN
ejpam-4659	153	11	v∥0,∞∥∇u∥	v∥0,∞∥∇u∥	NUM
ejpam-4659	153	12	≤	≤	NUM
ejpam-4659	153	13	c(∥aγu∥∥a	c(∥aγu∥∥a	X
ejpam-4659	153	14	1	1	NUM
ejpam-4659	153	15	2u−a	2u−a	NUM
ejpam-4659	153	16	1	1	NUM
ejpam-4659	153	17	2	2	NUM
ejpam-4659	153	18	vv∥+	vv∥+	NOUN
ejpam-4659	153	19	∥a	∥a	PROPN
ejpam-4659	153	20	1	1	NUM
ejpam-4659	153	21	2	2	NUM
ejpam-4659	153	22	v∥∥aγu−aγv∥	v∥∥aγu−aγv∥	NOUN
ejpam-4659	153	23	)	)	PUNCT
ejpam-4659	153	24	.	.	PUNCT
ejpam-4659	154	1	(	(	PUNCT
ejpam-4659	154	2	37	37	NUM
ejpam-4659	154	3	)	)	PUNCT
ejpam-4659	154	4	hence	hence	ADV
ejpam-4659	154	5	the	the	DET
ejpam-4659	154	6	proof	proof	NOUN
ejpam-4659	154	7	in	in	ADP
ejpam-4659	154	8	completed	complete	VERB
ejpam-4659	154	9	.	.	PUNCT
ejpam-4659	155	1	4	4	X
ejpam-4659	155	2	.	.	X
ejpam-4659	155	3	conclusion	conclusion	NOUN
ejpam-4659	155	4	in	in	ADP
ejpam-4659	155	5	this	this	DET
ejpam-4659	155	6	paper	paper	NOUN
ejpam-4659	155	7	,	,	PUNCT
ejpam-4659	155	8	it	it	PRON
ejpam-4659	155	9	has	have	AUX
ejpam-4659	155	10	been	be	AUX
ejpam-4659	155	11	established	establish	VERB
ejpam-4659	155	12	that	that	SCONJ
ejpam-4659	155	13	ω	ω	ADJ
ejpam-4659	155	14	-	-	PUNCT
ejpam-4659	155	15	order	order	NOUN
ejpam-4659	155	16	preserving	preserve	VERB
ejpam-4659	155	17	partial	partial	ADJ
ejpam-4659	155	18	contraction	contraction	NOUN
ejpam-4659	155	19	mapping	mapping	NOUN
ejpam-4659	155	20	generates	generate	VERB
ejpam-4659	155	21	some	some	DET
ejpam-4659	155	22	results	result	NOUN
ejpam-4659	155	23	of	of	ADP
ejpam-4659	155	24	a	a	DET
ejpam-4659	155	25	general	general	ADJ
ejpam-4659	155	26	class	class	NOUN
ejpam-4659	155	27	of	of	ADP
ejpam-4659	155	28	semilinear	semilinear	PROPN
ejpam-4659	155	29	initial	initial	ADJ
ejpam-4659	155	30	value	value	NOUN
ejpam-4659	155	31	problems	problem	NOUN
ejpam-4659	155	32	.	.	PUNCT
ejpam-4659	156	1	references	reference	NOUN
ejpam-4659	156	2	[	[	X
ejpam-4659	156	3	1	1	NUM
ejpam-4659	156	4	]	]	X
ejpam-4659	156	5	j	j	PROPN
ejpam-4659	156	6	b	b	PROPN
ejpam-4659	156	7	omosowon	omosowon	VERB
ejpam-4659	156	8	a	a	DET
ejpam-4659	156	9	y	y	PROPN
ejpam-4659	156	10	akinyele	akinyele	PROPN
ejpam-4659	156	11	,	,	PUNCT
ejpam-4659	156	12	o	o	PROPN
ejpam-4659	156	13	e	e	NOUN
ejpam-4659	156	14	jimoh	jimoh	NOUN
ejpam-4659	156	15	and	and	CCONJ
ejpam-4659	156	16	k	k	PROPN
ejpam-4659	156	17	a	a	DET
ejpam-4659	156	18	bello	bello	PROPN
ejpam-4659	156	19	.	.	PUNCT
ejpam-4659	157	1	results	result	NOUN
ejpam-4659	157	2	of	of	ADP
ejpam-4659	157	3	semigroup	semigroup	NOUN
ejpam-4659	157	4	of	of	ADP
ejpam-4659	157	5	linear	linear	ADJ
ejpam-4659	157	6	operator	operator	NOUN
ejpam-4659	157	7	generating	generate	VERB
ejpam-4659	157	8	a	a	DET
ejpam-4659	157	9	continuous	continuous	ADJ
ejpam-4659	157	10	time	time	NOUN
ejpam-4659	157	11	markov	markov	PROPN
ejpam-4659	157	12	semigroup	semigroup	PROPN
ejpam-4659	157	13	.	.	PUNCT
ejpam-4659	157	14	earthline	earthline	PROPN
ejpam-4659	157	15	journal	journal	PROPN
ejpam-4659	157	16	of	of	ADP
ejpam-4659	157	17	mathematical	mathematical	ADJ
ejpam-4659	157	18	sciences	sciences	PROPN
ejpam-4659	157	19	,	,	PUNCT
ejpam-4659	157	20	10(1):97–108	10(1):97–108	NUM
ejpam-4659	157	21	,	,	PUNCT
ejpam-4659	157	22	2022	2022	NUM
ejpam-4659	157	23	.	.	PUNCT
ejpam-4659	158	1	[	[	X
ejpam-4659	158	2	2	2	X
ejpam-4659	158	3	]	]	PUNCT
ejpam-4659	158	4	a	a	DET
ejpam-4659	158	5	y	y	PROPN
ejpam-4659	158	6	akinyele	akinyele	PROPN
ejpam-4659	158	7	,	,	PUNCT
ejpam-4659	158	8	k	k	PROPN
ejpam-4659	158	9	rauf	rauf	PROPN
ejpam-4659	158	10	,	,	PUNCT
ejpam-4659	158	11	j	j	PROPN
ejpam-4659	158	12	b	b	PROPN
ejpam-4659	158	13	omosowon	omosowon	PROPN
ejpam-4659	158	14	,	,	PUNCT
ejpam-4659	158	15	b	b	PROPN
ejpam-4659	158	16	sambo	sambo	NOUN
ejpam-4659	158	17	,	,	PUNCT
ejpam-4659	158	18	and	and	CCONJ
ejpam-4659	158	19	g	g	PROPN
ejpam-4659	158	20	o	o	PROPN
ejpam-4659	158	21	ibrahim	ibrahim	PROPN
ejpam-4659	158	22	.	.	PUNCT
ejpam-4659	159	1	differentiable	differentiable	ADJ
ejpam-4659	159	2	and	and	CCONJ
ejpam-4659	159	3	analytic	analytic	ADJ
ejpam-4659	159	4	results	result	NOUN
ejpam-4659	159	5	on	on	ADP
ejpam-4659	159	6	ω	ω	ADJ
ejpam-4659	159	7	-	-	PUNCT
ejpam-4659	159	8	order	order	NOUN
ejpam-4659	159	9	preserving	preserve	VERB
ejpam-4659	159	10	partial	partial	ADJ
ejpam-4659	159	11	contraction	contraction	NOUN
ejpam-4659	159	12	mapping	mapping	NOUN
ejpam-4659	159	13	in	in	ADP
ejpam-4659	159	14	semigroup	semigroup	NOUN
ejpam-4659	159	15	of	of	ADP
ejpam-4659	159	16	linear	linear	PROPN
ejpam-4659	159	17	operator	operator	NOUN
ejpam-4659	159	18	.	.	PUNCT
ejpam-4659	160	1	asian	asian	PROPN
ejpam-4659	160	2	pacific	pacific	PROPN
ejpam-4659	160	3	journal	journal	PROPN
ejpam-4659	160	4	of	of	ADP
ejpam-4659	160	5	mathematics	mathematic	NOUN
ejpam-4659	160	6	and	and	CCONJ
ejpam-4659	160	7	applications	application	NOUN
ejpam-4659	160	8	,	,	PUNCT
ejpam-4659	160	9	8(2):1–13	8(2):1–13	NUM
ejpam-4659	160	10	,	,	PUNCT
ejpam-4659	160	11	2021	2021	NUM
ejpam-4659	160	12	.	.	PUNCT
ejpam-4659	161	1	[	[	X
ejpam-4659	161	2	3	3	X
ejpam-4659	161	3	]	]	PUNCT
ejpam-4659	161	4	a	a	DET
ejpam-4659	161	5	v	v	NOUN
ejpam-4659	161	6	balakrishnan	balakrishnan	PROPN
ejpam-4659	161	7	.	.	PUNCT
ejpam-4659	162	1	an	an	DET
ejpam-4659	162	2	operator	operator	NOUN
ejpam-4659	162	3	calculus	calculus	NOUN
ejpam-4659	162	4	for	for	ADP
ejpam-4659	162	5	infinitesimal	infinitesimal	ADJ
ejpam-4659	162	6	generators	generator	NOUN
ejpam-4659	162	7	of	of	ADP
ejpam-4659	162	8	semigroup	semigroup	PROPN
ejpam-4659	162	9	.	.	PUNCT
ejpam-4659	163	1	trans	trans	PROPN
ejpam-4659	163	2	amer	amer	PROPN
ejpam-4659	163	3	.	.	PROPN
ejpam-4659	163	4	math	math	PROPN
ejpam-4659	163	5	.	.	PUNCT
ejpam-4659	164	1	soc	soc	PROPN
ejpam-4659	164	2	.	.	PROPN
ejpam-4659	164	3	,	,	PUNCT
ejpam-4659	164	4	91:330–353	91:330–353	PROPN
ejpam-4659	164	5	,	,	PUNCT
ejpam-4659	164	6	1959	1959	NUM
ejpam-4659	164	7	.	.	PUNCT
ejpam-4659	165	1	[	[	X
ejpam-4659	165	2	4	4	NUM
ejpam-4659	165	3	]	]	PUNCT
ejpam-4659	165	4	s	s	VERB
ejpam-4659	165	5	banach	banach	NOUN
ejpam-4659	165	6	.	.	PUNCT
ejpam-4659	166	1	surles	surle	NOUN
ejpam-4659	166	2	operation	operation	NOUN
ejpam-4659	166	3	dam	dam	PROPN
ejpam-4659	166	4	les	les	PROPN
ejpam-4659	166	5	eusembles	eusemble	NOUN
ejpam-4659	166	6	abstracts	abstract	NOUN
ejpam-4659	166	7	et	et	PROPN
ejpam-4659	166	8	lear	lear	PROPN
ejpam-4659	166	9	application	application	PROPN
ejpam-4659	166	10	aus	aus	PROPN
ejpam-4659	166	11	equation	equation	NOUN
ejpam-4659	166	12	integrals	integral	NOUN
ejpam-4659	166	13	.	.	PUNCT
ejpam-4659	167	1	fund	fund	PROPN
ejpam-4659	167	2	.	.	PUNCT
ejpam-4659	168	1	math	math	NOUN
ejpam-4659	168	2	.	.	PUNCT
ejpam-4659	168	3	,	,	PUNCT
ejpam-4659	169	1	3:133–181	3:133–181	NUM
ejpam-4659	169	2	,	,	PUNCT
ejpam-4659	169	3	1922	1922	NUM
ejpam-4659	169	4	.	.	PUNCT
ejpam-4659	170	1	[	[	X
ejpam-4659	170	2	5	5	NUM
ejpam-4659	170	3	]	]	PUNCT
ejpam-4659	170	4	h	h	NOUN
ejpam-4659	170	5	brezis	brezis	NOUN
ejpam-4659	170	6	and	and	CCONJ
ejpam-4659	170	7	t	t	NOUN
ejpam-4659	170	8	gallouet	gallouet	NOUN
ejpam-4659	170	9	.	.	PUNCT
ejpam-4659	171	1	nonlinear	nonlinear	ADJ
ejpam-4659	171	2	schrödinger	schrödinger	NOUN
ejpam-4659	171	3	evolution	evolution	NOUN
ejpam-4659	171	4	equation	equation	NOUN
ejpam-4659	171	5	.	.	PUNCT
ejpam-4659	172	1	nonlinear	nonlinear	ADJ
ejpam-4659	172	2	anal	anal	PROPN
ejpam-4659	172	3	.	.	PUNCT
ejpam-4659	173	1	tma	tma	PROPN
ejpam-4659	173	2	,	,	PUNCT
ejpam-4659	173	3	84:677–682	84:677–682	PROPN
ejpam-4659	173	4	,	,	PUNCT
ejpam-4659	173	5	1980	1980	NUM
ejpam-4659	173	6	.	.	PUNCT
ejpam-4659	174	1	references	reference	NOUN
ejpam-4659	174	2	547	547	NUM
ejpam-4659	174	3	[	[	X
ejpam-4659	174	4	6	6	NUM
ejpam-4659	174	5	]	]	SYM
ejpam-4659	174	6	r	r	NOUN
ejpam-4659	174	7	chill	chill	NOUN
ejpam-4659	174	8	and	and	CCONJ
ejpam-4659	174	9	y	y	PROPN
ejpam-4659	174	10	tomilov	tomilov	ADJ
ejpam-4659	174	11	.	.	PUNCT
ejpam-4659	175	1	stability	stability	NOUN
ejpam-4659	175	2	operator	operator	NOUN
ejpam-4659	175	3	semigroups	semigroup	NOUN
ejpam-4659	175	4	.	.	PUNCT
ejpam-4659	176	1	banach	banach	NOUN
ejpam-4659	176	2	center	center	NOUN
ejpam-4659	176	3	publication	publication	NOUN
ejpam-4659	176	4	75	75	NUM
ejpam-4659	176	5	,	,	PUNCT
ejpam-4659	176	6	polish	polish	PROPN
ejpam-4659	176	7	academy	academy	PROPN
ejpam-4659	176	8	of	of	ADP
ejpam-4659	176	9	sciences	sciences	PROPN
ejpam-4659	176	10	,	,	PUNCT
ejpam-4659	176	11	warsaw	warsaw	PROPN
ejpam-4659	176	12	,	,	PUNCT
ejpam-4659	176	13	2007	2007	NUM
ejpam-4659	176	14	.	.	PUNCT
ejpam-4659	177	1	[	[	X
ejpam-4659	177	2	7	7	NUM
ejpam-4659	177	3	]	]	X
ejpam-4659	177	4	e	e	PROPN
ejpam-4659	177	5	b	b	PROPN
ejpam-4659	177	6	davies	davy	NOUN
ejpam-4659	177	7	.	.	PUNCT
ejpam-4659	178	1	linear	linear	ADJ
ejpam-4659	178	2	operator	operator	NOUN
ejpam-4659	178	3	and	and	CCONJ
ejpam-4659	178	4	their	their	PRON
ejpam-4659	178	5	spectra	spectra	PROPN
ejpam-4659	178	6	.	.	PROPN
ejpam-4659	179	1	cambridge	cambridge	PROPN
ejpam-4659	179	2	university	university	PROPN
ejpam-4659	179	3	press	press	PROPN
ejpam-4659	179	4	,	,	PUNCT
ejpam-4659	179	5	new	new	PROPN
ejpam-4659	179	6	york	york	PROPN
ejpam-4659	179	7	,	,	PUNCT
ejpam-4659	179	8	2007	2007	NUM
ejpam-4659	179	9	.	.	PUNCT
ejpam-4659	180	1	[	[	X
ejpam-4659	180	2	8	8	NUM
ejpam-4659	180	3	]	]	X
ejpam-4659	180	4	k	k	PROPN
ejpam-4659	180	5	engel	engel	PROPN
ejpam-4659	180	6	and	and	CCONJ
ejpam-4659	180	7	r	r	PROPN
ejpam-4659	180	8	nagel	nagel	PROPN
ejpam-4659	180	9	.	.	PUNCT
ejpam-4659	181	1	one	one	NUM
ejpam-4659	181	2	-	-	PUNCT
ejpam-4659	181	3	parameter	parameter	NOUN
ejpam-4659	181	4	semigroups	semigroup	NOUN
ejpam-4659	181	5	for	for	ADP
ejpam-4659	181	6	linear	linear	PROPN
ejpam-4659	181	7	equations	equation	NOUN
ejpam-4659	181	8	.	.	PUNCT
ejpam-4659	182	1	springer	springer	NOUN
ejpam-4659	182	2	,	,	PUNCT
ejpam-4659	182	3	new	new	PROPN
ejpam-4659	182	4	york	york	PROPN
ejpam-4659	182	5	,	,	PUNCT
ejpam-4659	182	6	2000	2000	NUM
ejpam-4659	182	7	.	.	PUNCT
ejpam-4659	183	1	[	[	X
ejpam-4659	183	2	9	9	NUM
ejpam-4659	183	3	]	]	X
ejpam-4659	183	4	j	j	PROPN
ejpam-4659	183	5	b	b	PROPN
ejpam-4659	183	6	omosowon	omosowon	PROPN
ejpam-4659	183	7	,	,	PUNCT
ejpam-4659	183	8	a	a	DET
ejpam-4659	183	9	y	y	PROPN
ejpam-4659	183	10	akinyele	akinyele	PROPN
ejpam-4659	183	11	,	,	PUNCT
ejpam-4659	183	12	k	k	PROPN
ejpam-4659	183	13	a	a	PROPN
ejpam-4659	183	14	bello	bello	PROPN
ejpam-4659	183	15	,	,	PUNCT
ejpam-4659	183	16	and	and	CCONJ
ejpam-4659	183	17	b	b	X
ejpam-4659	183	18	m	m	VERB
ejpam-4659	183	19	ahmed	ahme	VERB
ejpam-4659	183	20	.	.	PUNCT
ejpam-4659	184	1	results	result	NOUN
ejpam-4659	184	2	of	of	ADP
ejpam-4659	184	3	semigroup	semigroup	NOUN
ejpam-4659	184	4	of	of	ADP
ejpam-4659	184	5	linear	linear	ADJ
ejpam-4659	184	6	operator	operator	NOUN
ejpam-4659	184	7	generating	generate	VERB
ejpam-4659	184	8	a	a	DET
ejpam-4659	184	9	quasilinear	quasilinear	NOUN
ejpam-4659	184	10	equations	equation	NOUN
ejpam-4659	184	11	of	of	ADP
ejpam-4659	184	12	evolution	evolution	NOUN
ejpam-4659	184	13	,	,	PUNCT
ejpam-4659	184	14	.	.	PUNCT
ejpam-4659	185	1	earthline	earthline	PROPN
ejpam-4659	185	2	journal	journal	PROPN
ejpam-4659	185	3	of	of	ADP
ejpam-4659	185	4	mathematical	mathematical	ADJ
ejpam-4659	185	5	sciences	sciences	PROPN
ejpam-4659	185	6	,	,	PUNCT
ejpam-4659	185	7	10(2):409–421	10(2):409–421	NUM
ejpam-4659	185	8	,	,	PUNCT
ejpam-4659	185	9	2022	2022	NUM
ejpam-4659	185	10	.	.	PUNCT
ejpam-4659	186	1	[	[	X
ejpam-4659	186	2	10	10	NUM
ejpam-4659	186	3	]	]	X
ejpam-4659	186	4	j	j	PROPN
ejpam-4659	186	5	b	b	PROPN
ejpam-4659	186	6	omosowon	omosowon	PROPN
ejpam-4659	186	7	,	,	PUNCT
ejpam-4659	186	8	a	a	DET
ejpam-4659	186	9	y	y	PROPN
ejpam-4659	186	10	akinyele	akinyele	PROPN
ejpam-4659	186	11	,	,	PUNCT
ejpam-4659	186	12	k	k	PROPN
ejpam-4659	186	13	a	a	PROPN
ejpam-4659	186	14	bello	bello	PROPN
ejpam-4659	186	15	,	,	PUNCT
ejpam-4659	186	16	and	and	CCONJ
ejpam-4659	186	17	b	b	X
ejpam-4659	186	18	m	m	VERB
ejpam-4659	186	19	ahmed	ahme	VERB
ejpam-4659	186	20	.	.	PUNCT
ejpam-4659	187	1	results	result	NOUN
ejpam-4659	187	2	of	of	ADP
ejpam-4659	187	3	semigroup	semigroup	NOUN
ejpam-4659	187	4	of	of	ADP
ejpam-4659	187	5	linear	linear	PROPN
ejpam-4659	187	6	operators	operator	NOUN
ejpam-4659	187	7	generating	generate	VERB
ejpam-4659	187	8	a	a	DET
ejpam-4659	187	9	regular	regular	ADJ
ejpam-4659	187	10	weak*-continuous	weak*-continuous	ADJ
ejpam-4659	187	11	semigroup	semigroup	NOUN
ejpam-4659	187	12	.	.	PUNCT
ejpam-4659	187	13	earthline	earthline	PROPN
ejpam-4659	187	14	journal	journal	PROPN
ejpam-4659	187	15	of	of	ADP
ejpam-4659	187	16	mathematical	mathematical	ADJ
ejpam-4659	187	17	sciences	science	NOUN
ejpam-4659	187	18	,	,	PUNCT
ejpam-4659	187	19	10(2):289–304	10(2):289–304	NUM
ejpam-4659	187	20	,	,	PUNCT
ejpam-4659	187	21	2022	2022	NUM
ejpam-4659	187	22	.	.	PUNCT
ejpam-4659	188	1	[	[	X
ejpam-4659	188	2	11	11	NUM
ejpam-4659	188	3	]	]	X
ejpam-4659	188	4	j	j	PROPN
ejpam-4659	188	5	b	b	PROPN
ejpam-4659	188	6	omosowon	omosowon	PROPN
ejpam-4659	188	7	,	,	PUNCT
ejpam-4659	188	8	a	a	DET
ejpam-4659	188	9	y	y	NOUN
ejpam-4659	188	10	akinyele	akinyele	NOUN
ejpam-4659	188	11	,	,	PUNCT
ejpam-4659	188	12	and	and	CCONJ
ejpam-4659	188	13	f	f	PROPN
ejpam-4659	188	14	m	m	PROPN
ejpam-4659	188	15	jimoh	jimoh	ADJ
ejpam-4659	188	16	.	.	PUNCT
ejpam-4659	189	1	dual	dual	ADJ
ejpam-4659	189	2	properties	property	NOUN
ejpam-4659	189	3	of	of	ADP
ejpam-4659	189	4	ω	ω	NOUN
ejpam-4659	189	5	-	-	PUNCT
ejpam-4659	189	6	order	order	NOUN
ejpam-4659	189	7	reversing	reverse	VERB
ejpam-4659	189	8	partial	partial	ADJ
ejpam-4659	189	9	contraction	contraction	NOUN
ejpam-4659	189	10	mapping	mapping	NOUN
ejpam-4659	189	11	in	in	ADP
ejpam-4659	189	12	semigroup	semigroup	NOUN
ejpam-4659	189	13	of	of	ADP
ejpam-4659	189	14	linear	linear	PROPN
ejpam-4659	189	15	operator	operator	NOUN
ejpam-4659	189	16	.	.	PUNCT
ejpam-4659	190	1	asian	asian	ADJ
ejpam-4659	190	2	journal	journal	PROPN
ejpam-4659	190	3	of	of	ADP
ejpam-4659	190	4	mathematics	mathematic	NOUN
ejpam-4659	190	5	and	and	CCONJ
ejpam-4659	190	6	applications	application	NOUN
ejpam-4659	190	7	,	,	PUNCT
ejpam-4659	190	8	ama0566:1–10	ama0566:1–10	PROPN
ejpam-4659	190	9	,	,	PUNCT
ejpam-4659	190	10	2020	2020	NUM
ejpam-4659	190	11	.	.	PUNCT
ejpam-4659	191	1	[	[	X
ejpam-4659	191	2	12	12	NUM
ejpam-4659	191	3	]	]	X
ejpam-4659	191	4	j	j	PROPN
ejpam-4659	191	5	b	b	PROPN
ejpam-4659	191	6	omosowon	omosowon	PROPN
ejpam-4659	191	7	,	,	PUNCT
ejpam-4659	191	8	a	a	DET
ejpam-4659	191	9	y	y	NOUN
ejpam-4659	191	10	akinyele	akinyele	NOUN
ejpam-4659	191	11	,	,	PUNCT
ejpam-4659	191	12	and	and	CCONJ
ejpam-4659	191	13	o	o	PROPN
ejpam-4659	191	14	y	y	PROPN
ejpam-4659	191	15	saka	saka	PROPN
ejpam-4659	191	16	-	-	PUNCT
ejpam-4659	191	17	balogun	balogun	PROPN
ejpam-4659	191	18	.	.	PUNCT
ejpam-4659	192	1	results	result	NOUN
ejpam-4659	192	2	of	of	ADP
ejpam-4659	192	3	semigroup	semigroup	NOUN
ejpam-4659	192	4	of	of	ADP
ejpam-4659	192	5	linear	linear	ADJ
ejpam-4659	192	6	operator	operator	NOUN
ejpam-4659	192	7	generating	generate	VERB
ejpam-4659	192	8	a	a	DET
ejpam-4659	192	9	wave	wave	NOUN
ejpam-4659	192	10	equation	equation	NOUN
ejpam-4659	192	11	.	.	PUNCT
ejpam-4659	193	1	earthline	earthline	PROPN
ejpam-4659	193	2	journal	journal	PROPN
ejpam-4659	193	3	of	of	ADP
ejpam-4659	193	4	mathematical	mathematical	ADJ
ejpam-4659	193	5	sciences	sciences	PROPN
ejpam-4659	193	6	,	,	PUNCT
ejpam-4659	193	7	11(1):173–182	11(1):173–182	PROPN
ejpam-4659	193	8	,	,	PUNCT
ejpam-4659	193	9	2023	2023	NUM
ejpam-4659	193	10	.	.	PUNCT
ejpam-4659	194	1	[	[	X
ejpam-4659	194	2	13	13	NUM
ejpam-4659	194	3	]	]	X
ejpam-4659	194	4	j	j	PROPN
ejpam-4659	194	5	b	b	PROPN
ejpam-4659	194	6	omosowon	omosowon	PROPN
ejpam-4659	194	7	,	,	PUNCT
ejpam-4659	194	8	a	a	DET
ejpam-4659	194	9	y	y	PROPN
ejpam-4659	194	10	akinyele	akinyele	PROPN
ejpam-4659	194	11	,	,	PUNCT
ejpam-4659	194	12	o	o	PROPN
ejpam-4659	194	13	y	y	PROPN
ejpam-4659	194	14	saka	saka	PROPN
ejpam-4659	194	15	-	-	PUNCT
ejpam-4659	194	16	balogun	balogun	ADJ
ejpam-4659	194	17	,	,	PUNCT
ejpam-4659	194	18	and	and	CCONJ
ejpam-4659	194	19	m	m	VERB
ejpam-4659	194	20	a	a	DET
ejpam-4659	194	21	ganiyu	ganiyu	NOUN
ejpam-4659	194	22	.	.	PUNCT
ejpam-4659	195	1	analytic	analytic	ADJ
ejpam-4659	195	2	results	result	NOUN
ejpam-4659	195	3	of	of	ADP
ejpam-4659	195	4	semigroup	semigroup	NOUN
ejpam-4659	195	5	of	of	ADP
ejpam-4659	195	6	linear	linear	ADJ
ejpam-4659	195	7	operator	operator	NOUN
ejpam-4659	195	8	with	with	ADP
ejpam-4659	195	9	dynamic	dynamic	ADJ
ejpam-4659	195	10	boundary	boundary	ADJ
ejpam-4659	195	11	conditions	condition	NOUN
ejpam-4659	195	12	.	.	PUNCT
ejpam-4659	196	1	asian	asian	ADJ
ejpam-4659	196	2	journal	journal	PROPN
ejpam-4659	196	3	of	of	ADP
ejpam-4659	196	4	mathematics	mathematic	NOUN
ejpam-4659	196	5	and	and	CCONJ
ejpam-4659	196	6	applications	application	NOUN
ejpam-4659	196	7	,	,	PUNCT
ejpam-4659	196	8	ama0561:1–10	ama0561:1–10	NOUN
ejpam-4659	196	9	,	,	PUNCT
ejpam-4659	196	10	2020	2020	NUM
ejpam-4659	196	11	.	.	PUNCT
ejpam-4659	197	1	[	[	X
ejpam-4659	197	2	14	14	NUM
ejpam-4659	197	3	]	]	X
ejpam-4659	197	4	a	a	DET
ejpam-4659	197	5	pazy	pazy	NOUN
ejpam-4659	197	6	.	.	PUNCT
ejpam-4659	198	1	asymptotic	asymptotic	ADJ
ejpam-4659	198	2	behavior	behavior	NOUN
ejpam-4659	198	3	of	of	ADP
ejpam-4659	198	4	the	the	DET
ejpam-4659	198	5	solution	solution	NOUN
ejpam-4659	198	6	of	of	ADP
ejpam-4659	198	7	an	an	DET
ejpam-4659	198	8	abstract	abstract	ADJ
ejpam-4659	198	9	evolution	evolution	NOUN
ejpam-4659	198	10	and	and	CCONJ
ejpam-4659	198	11	some	some	DET
ejpam-4659	198	12	applications	application	NOUN
ejpam-4659	198	13	.	.	PUNCT
ejpam-4659	199	1	j.	j.	PROPN
ejpam-4659	199	2	diff	diff	PROPN
ejpam-4659	199	3	.	.	PUNCT
ejpam-4659	200	1	eqs	eqs	PROPN
ejpam-4659	200	2	.	.	PROPN
ejpam-4659	200	3	,	,	PUNCT
ejpam-4659	200	4	4:493–509	4:493–509	NOUN
ejpam-4659	200	5	,	,	PUNCT
ejpam-4659	200	6	1968	1968	NUM
ejpam-4659	200	7	.	.	PUNCT
ejpam-4659	201	1	[	[	X
ejpam-4659	201	2	15	15	NUM
ejpam-4659	201	3	]	]	X
ejpam-4659	201	4	a	a	DET
ejpam-4659	201	5	pazy	pazy	NOUN
ejpam-4659	201	6	.	.	PUNCT
ejpam-4659	202	1	a	a	DET
ejpam-4659	202	2	class	class	NOUN
ejpam-4659	202	3	of	of	ADP
ejpam-4659	202	4	semi	semi	ADJ
ejpam-4659	202	5	-	-	ADJ
ejpam-4659	202	6	linear	linear	ADJ
ejpam-4659	202	7	equations	equation	NOUN
ejpam-4659	202	8	of	of	ADP
ejpam-4659	202	9	evolution	evolution	NOUN
ejpam-4659	202	10	.	.	PUNCT
ejpam-4659	203	1	isreal	isreal	PROPN
ejpam-4659	203	2	j.	j.	PROPN
ejpam-4659	203	3	math	math	PROPN
ejpam-4659	203	4	.	.	PROPN
ejpam-4659	203	5	,	,	PUNCT
ejpam-4659	203	6	20:23–36	20:23–36	NUM
ejpam-4659	203	7	,	,	PUNCT
ejpam-4659	203	8	1975	1975	NUM
ejpam-4659	203	9	.	.	PUNCT
ejpam-4659	204	1	[	[	X
ejpam-4659	204	2	16	16	NUM
ejpam-4659	204	3	]	]	X
ejpam-4659	204	4	k	k	PROPN
ejpam-4659	204	5	rauf	rauf	PROPN
ejpam-4659	204	6	and	and	CCONJ
ejpam-4659	204	7	a	a	DET
ejpam-4659	204	8	y	y	PROPN
ejpam-4659	204	9	akinyele	akinyele	PROPN
ejpam-4659	204	10	.	.	PUNCT
ejpam-4659	205	1	properties	property	NOUN
ejpam-4659	205	2	of	of	ADP
ejpam-4659	205	3	ω	ω	ADJ
ejpam-4659	205	4	-	-	PUNCT
ejpam-4659	205	5	order	order	NOUN
ejpam-4659	205	6	-	-	PUNCT
ejpam-4659	205	7	preserving	preserve	VERB
ejpam-4659	205	8	partial	partial	ADJ
ejpam-4659	205	9	contraction	contraction	NOUN
ejpam-4659	205	10	mapping	mapping	NOUN
ejpam-4659	205	11	and	and	CCONJ
ejpam-4659	205	12	its	its	PRON
ejpam-4659	205	13	relation	relation	NOUN
ejpam-4659	205	14	to	to	ADP
ejpam-4659	205	15	c0	c0	PROPN
ejpam-4659	205	16	-	-	PUNCT
ejpam-4659	205	17	semigroup	semigroup	NOUN
ejpam-4659	205	18	.	.	PUNCT
ejpam-4659	206	1	international	international	ADJ
ejpam-4659	206	2	journal	journal	PROPN
ejpam-4659	206	3	of	of	ADP
ejpam-4659	206	4	mathematics	mathematic	NOUN
ejpam-4659	206	5	and	and	CCONJ
ejpam-4659	206	6	computer	computer	NOUN
ejpam-4659	206	7	science	science	NOUN
ejpam-4659	206	8	,	,	PUNCT
ejpam-4659	206	9	14(1):61–68	14(1):61–68	NUM
ejpam-4659	206	10	,	,	PUNCT
ejpam-4659	206	11	2019	2019	NUM
ejpam-4659	206	12	.	.	PUNCT
ejpam-4659	207	1	[	[	X
ejpam-4659	207	2	17	17	NUM
ejpam-4659	207	3	]	]	X
ejpam-4659	207	4	k	k	PROPN
ejpam-4659	207	5	rauf	rauf	PROPN
ejpam-4659	207	6	,	,	PUNCT
ejpam-4659	207	7	a	a	DET
ejpam-4659	207	8	y	y	PROPN
ejpam-4659	207	9	akinyele	akinyele	PROPN
ejpam-4659	207	10	,	,	PUNCT
ejpam-4659	207	11	m	m	VERB
ejpam-4659	207	12	o	o	NOUN
ejpam-4659	207	13	etuk	etuk	NOUN
ejpam-4659	207	14	,	,	PUNCT
ejpam-4659	207	15	r	r	NOUN
ejpam-4659	207	16	o	o	X
ejpam-4659	207	17	zubair	zubair	PROPN
ejpam-4659	207	18	,	,	PUNCT
ejpam-4659	207	19	and	and	CCONJ
ejpam-4659	207	20	m	m	VERB
ejpam-4659	207	21	a	a	DET
ejpam-4659	207	22	aasa	aasa	NOUN
ejpam-4659	207	23	.	.	PUNCT
ejpam-4659	208	1	some	some	DET
ejpam-4659	208	2	result	result	NOUN
ejpam-4659	208	3	of	of	ADP
ejpam-4659	208	4	stability	stability	NOUN
ejpam-4659	208	5	and	and	CCONJ
ejpam-4659	208	6	spectra	spectra	ADJ
ejpam-4659	208	7	properties	property	NOUN
ejpam-4659	208	8	on	on	ADP
ejpam-4659	208	9	semigroup	semigroup	NOUN
ejpam-4659	208	10	of	of	ADP
ejpam-4659	208	11	linear	linear	PROPN
ejpam-4659	208	12	operator	operator	NOUN
ejpam-4659	208	13	.	.	PUNCT
ejpam-4659	209	1	advances	advance	NOUN
ejpam-4659	209	2	in	in	ADP
ejpam-4659	209	3	pure	pure	ADJ
ejpam-4659	209	4	mathematics	mathematic	NOUN
ejpam-4659	209	5	,	,	PUNCT
ejpam-4659	209	6	9:43–51	9:43–51	NUM
ejpam-4659	209	7	,	,	PUNCT
ejpam-4659	209	8	2019	2019	NUM
ejpam-4659	209	9	.	.	PUNCT
ejpam-4659	210	1	[	[	X
ejpam-4659	210	2	18	18	NUM
ejpam-4659	210	3	]	]	X
ejpam-4659	210	4	i	i	PRON
ejpam-4659	210	5	i	i	PROPN
ejpam-4659	210	6	vrabie	vrabie	VERB
ejpam-4659	210	7	.	.	PUNCT
ejpam-4659	211	1	c0	c0	PROPN
ejpam-4659	211	2	-	-	PUNCT
ejpam-4659	211	3	semigroup	semigroup	PROPN
ejpam-4659	211	4	and	and	CCONJ
ejpam-4659	211	5	application	application	NOUN
ejpam-4659	211	6	.	.	PUNCT
ejpam-4659	212	1	elsevier	elsevier	NOUN
ejpam-4659	212	2	,	,	PUNCT
ejpam-4659	212	3	north	north	NOUN
ejpam-4659	212	4	-	-	PUNCT
ejpam-4659	212	5	holland	holland	PROPN
ejpam-4659	212	6	,	,	PUNCT
ejpam-4659	212	7	2003	2003	NUM
ejpam-4659	212	8	.	.	PUNCT
ejpam-4659	213	1	[	[	X
ejpam-4659	213	2	19	19	NUM
ejpam-4659	213	3	]	]	PUNCT
ejpam-4659	213	4	k.	k.	PROPN
ejpam-4659	213	5	yosida	yosida	PROPN
ejpam-4659	213	6	.	.	PUNCT
ejpam-4659	214	1	on	on	ADP
ejpam-4659	214	2	the	the	DET
ejpam-4659	214	3	differentiability	differentiability	NOUN
ejpam-4659	214	4	and	and	CCONJ
ejpam-4659	214	5	representation	representation	NOUN
ejpam-4659	214	6	of	of	ADP
ejpam-4659	214	7	one	one	NUM
ejpam-4659	214	8	-	-	PUNCT
ejpam-4659	214	9	parameter	parameter	NOUN
ejpam-4659	214	10	semigroups	semigroup	NOUN
ejpam-4659	214	11	of	of	ADP
ejpam-4659	214	12	linear	linear	PROPN
ejpam-4659	214	13	operators	operator	NOUN
ejpam-4659	214	14	.	.	PUNCT
ejpam-4659	215	1	j.	j.	PROPN
ejpam-4659	215	2	math	math	PROPN
ejpam-4659	215	3	.	.	PUNCT
ejpam-4659	216	1	soc	soc	PROPN
ejpam-4659	216	2	.	.	PUNCT
ejpam-4659	216	3	,	,	PUNCT
ejpam-4659	216	4	1:15–21	1:15–21	NUM
ejpam-4659	216	5	,	,	PUNCT
ejpam-4659	216	6	1948	1948	NUM
ejpam-4659	216	7	.	.	PUNCT