id	sid	tid	token	lemma	pos
ejpam-4244	1	1	european	european	PROPN
ejpam-4244	1	2	journal	journal	PROPN
ejpam-4244	1	3	of	of	ADP
ejpam-4244	1	4	pure	pure	ADJ
ejpam-4244	1	5	and	and	CCONJ
ejpam-4244	1	6	applied	apply	VERB
ejpam-4244	1	7	mathematics	mathematic	NOUN
ejpam-4244	1	8	vol	vol	NOUN
ejpam-4244	1	9	.	.	PROPN
ejpam-4244	2	1	15	15	NUM
ejpam-4244	2	2	,	,	PUNCT
ejpam-4244	2	3	no	no	INTJ
ejpam-4244	2	4	.	.	NOUN
ejpam-4244	2	5	1	1	NUM
ejpam-4244	2	6	,	,	PUNCT
ejpam-4244	2	7	2022	2022	NUM
ejpam-4244	2	8	,	,	PUNCT
ejpam-4244	2	9	249	249	NUM
ejpam-4244	2	10	-	-	SYM
ejpam-4244	2	11	260	260	NUM
ejpam-4244	2	12	issn	issn	PROPN
ejpam-4244	2	13	1307	1307	NUM
ejpam-4244	2	14	-	-	SYM
ejpam-4244	2	15	5543	5543	NUM
ejpam-4244	2	16	–	–	PUNCT
ejpam-4244	2	17	ejpam.com	ejpam.com	X
ejpam-4244	2	18	published	publish	VERB
ejpam-4244	2	19	by	by	ADP
ejpam-4244	2	20	new	new	PROPN
ejpam-4244	2	21	york	york	PROPN
ejpam-4244	2	22	business	business	PROPN
ejpam-4244	2	23	global	global	PROPN
ejpam-4244	2	24	on	on	ADP
ejpam-4244	2	25	inductive	inductive	ADJ
ejpam-4244	2	26	limit	limit	NOUN
ejpam-4244	2	27	of	of	ADP
ejpam-4244	2	28	commutative	commutative	ADJ
ejpam-4244	2	29	triples	triple	NOUN
ejpam-4244	2	30	lamine	lamine	PROPN
ejpam-4244	2	31	timite1,∗	timite1,∗	PROPN
ejpam-4244	2	32	,	,	PUNCT
ejpam-4244	2	33	ibrahima	ibrahima	PROPN
ejpam-4244	2	34	toure1	toure1	PROPN
ejpam-4244	2	35	1	1	NUM
ejpam-4244	2	36	department	department	NOUN
ejpam-4244	2	37	of	of	ADP
ejpam-4244	2	38	mathematics	mathematic	NOUN
ejpam-4244	2	39	and	and	CCONJ
ejpam-4244	2	40	informatics	informatic	NOUN
ejpam-4244	2	41	,	,	PUNCT
ejpam-4244	2	42	university	university	NOUN
ejpam-4244	2	43	felix	felix	NOUN
ejpam-4244	2	44	houphouet	houphouet	PROPN
ejpam-4244	3	1	boigny	boigny	PROPN
ejpam-4244	3	2	at	at	ADP
ejpam-4244	3	3	abidjan	abidjan	PROPN
ejpam-4244	3	4	,	,	PUNCT
ejpam-4244	3	5	cote	cote	PROPN
ejpam-4244	3	6	d’ivoire	d’ivoire	NOUN
ejpam-4244	3	7	abstract	abstract	NOUN
ejpam-4244	3	8	.	.	PUNCT
ejpam-4244	4	1	in	in	ADP
ejpam-4244	4	2	this	this	DET
ejpam-4244	4	3	paper	paper	NOUN
ejpam-4244	4	4	,	,	PUNCT
ejpam-4244	4	5	we	we	PRON
ejpam-4244	4	6	extend	extend	VERB
ejpam-4244	4	7	olshanski	olshanski	PROPN
ejpam-4244	4	8	’s	’s	PART
ejpam-4244	4	9	work	work	NOUN
ejpam-4244	4	10	on	on	ADP
ejpam-4244	4	11	gelfand	gelfand	ADJ
ejpam-4244	4	12	pairs	pair	NOUN
ejpam-4244	4	13	to	to	ADP
ejpam-4244	4	14	commutative	commutative	ADJ
ejpam-4244	4	15	triples	triple	NOUN
ejpam-4244	4	16	.	.	PUNCT
ejpam-4244	5	1	we	we	PRON
ejpam-4244	5	2	introduce	introduce	VERB
ejpam-4244	5	3	the	the	DET
ejpam-4244	5	4	notion	notion	NOUN
ejpam-4244	5	5	of	of	ADP
ejpam-4244	5	6	spherical	spherical	ADJ
ejpam-4244	5	7	triples	triple	NOUN
ejpam-4244	5	8	as	as	ADP
ejpam-4244	5	9	a	a	DET
ejpam-4244	5	10	generalization	generalization	NOUN
ejpam-4244	5	11	of	of	ADP
ejpam-4244	5	12	commutative	commutative	ADJ
ejpam-4244	5	13	triples	triple	NOUN
ejpam-4244	5	14	.	.	PUNCT
ejpam-4244	6	1	we	we	PRON
ejpam-4244	6	2	prove	prove	VERB
ejpam-4244	6	3	that	that	SCONJ
ejpam-4244	6	4	inductive	inductive	ADJ
ejpam-4244	6	5	limit	limit	NOUN
ejpam-4244	6	6	of	of	ADP
ejpam-4244	6	7	an	an	DET
ejpam-4244	6	8	increasing	increase	VERB
ejpam-4244	6	9	sequence	sequence	NOUN
ejpam-4244	6	10	of	of	ADP
ejpam-4244	6	11	commutative	commutative	ADJ
ejpam-4244	6	12	triples	triple	NOUN
ejpam-4244	6	13	is	be	AUX
ejpam-4244	6	14	a	a	DET
ejpam-4244	6	15	spherical	spherical	ADJ
ejpam-4244	6	16	triple	triple	NOUN
ejpam-4244	6	17	which	which	PRON
ejpam-4244	6	18	shows	show	VERB
ejpam-4244	6	19	that	that	SCONJ
ejpam-4244	6	20	the	the	DET
ejpam-4244	6	21	former	former	NOUN
ejpam-4244	6	22	is	be	AUX
ejpam-4244	6	23	also	also	ADV
ejpam-4244	6	24	a	a	DET
ejpam-4244	6	25	generalization	generalization	NOUN
ejpam-4244	6	26	of	of	ADP
ejpam-4244	6	27	spherical	spherical	ADJ
ejpam-4244	6	28	pairs	pair	NOUN
ejpam-4244	6	29	.	.	PUNCT
ejpam-4244	7	1	furthermore	furthermore	ADV
ejpam-4244	7	2	,	,	PUNCT
ejpam-4244	7	3	we	we	PRON
ejpam-4244	7	4	define	define	VERB
ejpam-4244	7	5	spherical	spherical	ADJ
ejpam-4244	7	6	functions	function	NOUN
ejpam-4244	7	7	associated	associate	VERB
ejpam-4244	7	8	with	with	ADP
ejpam-4244	7	9	these	these	DET
ejpam-4244	7	10	spherical	spherical	ADJ
ejpam-4244	7	11	triples	triple	NOUN
ejpam-4244	7	12	.	.	PUNCT
ejpam-4244	8	1	finally	finally	ADV
ejpam-4244	8	2	,	,	PUNCT
ejpam-4244	8	3	we	we	PRON
ejpam-4244	8	4	characterize	characterize	VERB
ejpam-4244	8	5	these	these	DET
ejpam-4244	8	6	spherical	spherical	ADJ
ejpam-4244	8	7	functions	function	NOUN
ejpam-4244	8	8	by	by	ADP
ejpam-4244	8	9	a	a	DET
ejpam-4244	8	10	functional	functional	ADJ
ejpam-4244	8	11	equation	equation	NOUN
ejpam-4244	8	12	and	and	CCONJ
ejpam-4244	8	13	we	we	PRON
ejpam-4244	8	14	give	give	VERB
ejpam-4244	8	15	some	some	PRON
ejpam-4244	8	16	of	of	ADP
ejpam-4244	8	17	its	its	PRON
ejpam-4244	8	18	properties	property	NOUN
ejpam-4244	8	19	.	.	PUNCT
ejpam-4244	9	1	2020	2020	NUM
ejpam-4244	9	2	mathematics	mathematic	NOUN
ejpam-4244	9	3	subject	subject	NOUN
ejpam-4244	9	4	classifications	classification	NOUN
ejpam-4244	9	5	:	:	PUNCT
ejpam-4244	9	6	43a30	43a30	NUM
ejpam-4244	9	7	,	,	PUNCT
ejpam-4244	9	8	43a65	43a65	NUM
ejpam-4244	9	9	,	,	PUNCT
ejpam-4244	9	10	43a90	43a90	NUM
ejpam-4244	9	11	,	,	PUNCT
ejpam-4244	9	12	22d10	22d10	NUM
ejpam-4244	9	13	key	key	ADJ
ejpam-4244	9	14	words	word	NOUN
ejpam-4244	9	15	and	and	CCONJ
ejpam-4244	9	16	phrases	phrase	NOUN
ejpam-4244	9	17	:	:	PUNCT
ejpam-4244	9	18	commutative	commutative	ADJ
ejpam-4244	9	19	triple	triple	ADJ
ejpam-4244	9	20	,	,	PUNCT
ejpam-4244	9	21	spherical	spherical	ADJ
ejpam-4244	9	22	function	function	NOUN
ejpam-4244	9	23	,	,	PUNCT
ejpam-4244	9	24	spherical	spherical	ADJ
ejpam-4244	9	25	pair	pair	NOUN
ejpam-4244	9	26	,	,	PUNCT
ejpam-4244	9	27	spherical	spherical	ADJ
ejpam-4244	9	28	triple	triple	ADJ
ejpam-4244	9	29	1	1	NUM
ejpam-4244	9	30	.	.	PUNCT
ejpam-4244	10	1	introduction	introduction	NOUN
ejpam-4244	10	2	the	the	DET
ejpam-4244	10	3	notion	notion	NOUN
ejpam-4244	10	4	of	of	ADP
ejpam-4244	10	5	gelfand	gelfand	ADJ
ejpam-4244	10	6	pairs	pair	NOUN
ejpam-4244	10	7	has	have	AUX
ejpam-4244	10	8	been	be	AUX
ejpam-4244	10	9	introduced	introduce	VERB
ejpam-4244	10	10	by	by	ADP
ejpam-4244	10	11	i.	i.	PROPN
ejpam-4244	10	12	gelfand	gelfand	PROPN
ejpam-4244	10	13	in	in	ADP
ejpam-4244	10	14	1950	1950	NUM
ejpam-4244	10	15	and	and	CCONJ
ejpam-4244	10	16	developed	develop	VERB
ejpam-4244	10	17	by	by	ADP
ejpam-4244	10	18	many	many	ADJ
ejpam-4244	10	19	authors	author	NOUN
ejpam-4244	10	20	.	.	PUNCT
ejpam-4244	11	1	an	an	DET
ejpam-4244	11	2	extension	extension	NOUN
ejpam-4244	11	3	of	of	ADP
ejpam-4244	11	4	gelfand	gelfand	ADJ
ejpam-4244	11	5	pairs	pair	NOUN
ejpam-4244	11	6	is	be	AUX
ejpam-4244	11	7	the	the	DET
ejpam-4244	11	8	notion	notion	NOUN
ejpam-4244	11	9	of	of	ADP
ejpam-4244	11	10	commutative	commutative	ADJ
ejpam-4244	11	11	triples	triple	NOUN
ejpam-4244	11	12	.	.	PUNCT
ejpam-4244	12	1	the	the	DET
ejpam-4244	12	2	notion	notion	NOUN
ejpam-4244	12	3	of	of	ADP
ejpam-4244	12	4	commutative	commutative	ADJ
ejpam-4244	12	5	triples	triple	NOUN
ejpam-4244	12	6	has	have	AUX
ejpam-4244	12	7	been	be	AUX
ejpam-4244	12	8	enough	enough	ADV
ejpam-4244	12	9	studied	study	VERB
ejpam-4244	12	10	by	by	ADP
ejpam-4244	12	11	many	many	ADJ
ejpam-4244	12	12	authors	author	NOUN
ejpam-4244	12	13	such	such	ADJ
ejpam-4244	12	14	as	as	ADP
ejpam-4244	12	15	:	:	PUNCT
ejpam-4244	12	16	r.	r.	NOUN
ejpam-4244	12	17	camporesi	camporesi	X
ejpam-4244	13	1	[	[	X
ejpam-4244	13	2	8	8	NUM
ejpam-4244	13	3	]	]	PUNCT
ejpam-4244	13	4	,	,	PUNCT
ejpam-4244	13	5	j.	j.	PROPN
ejpam-4244	13	6	faraut	faraut	PROPN
ejpam-4244	14	1	[	[	X
ejpam-4244	14	2	1	1	NUM
ejpam-4244	14	3	]	]	PUNCT
ejpam-4244	14	4	,	,	PUNCT
ejpam-4244	14	5	f.	f.	PROPN
ejpam-4244	14	6	ricci[9	ricci[9	PROPN
ejpam-4244	14	7	]	]	X
ejpam-4244	14	8	,	,	PUNCT
ejpam-4244	14	9	i.	i.	PROPN
ejpam-4244	14	10	toure	toure	NOUN
ejpam-4244	15	1	[	[	X
ejpam-4244	15	2	11	11	NUM
ejpam-4244	15	3	]	]	PUNCT
ejpam-4244	15	4	,	,	PUNCT
ejpam-4244	15	5	etc	etc	X
ejpam-4244	15	6	....	....	X
ejpam-4244	15	7	it	it	PRON
ejpam-4244	15	8	has	have	AUX
ejpam-4244	15	9	permitted	permit	VERB
ejpam-4244	15	10	to	to	PART
ejpam-4244	15	11	establish	establish	VERB
ejpam-4244	15	12	a	a	DET
ejpam-4244	15	13	connection	connection	NOUN
ejpam-4244	15	14	between	between	ADP
ejpam-4244	15	15	harmonic	harmonic	ADJ
ejpam-4244	15	16	analysis	analysis	NOUN
ejpam-4244	15	17	on	on	ADP
ejpam-4244	15	18	non	non	PRON
ejpam-4244	15	19	commutative	commutative	ADJ
ejpam-4244	15	20	locally	locally	ADV
ejpam-4244	15	21	compact	compact	ADJ
ejpam-4244	15	22	groups	group	NOUN
ejpam-4244	15	23	and	and	CCONJ
ejpam-4244	15	24	the	the	DET
ejpam-4244	15	25	theory	theory	NOUN
ejpam-4244	15	26	of	of	ADP
ejpam-4244	15	27	commutative	commutative	ADJ
ejpam-4244	15	28	banach	banach	NOUN
ejpam-4244	15	29	algebra	algebra	NOUN
ejpam-4244	15	30	.	.	PUNCT
ejpam-4244	16	1	indeed	indeed	ADV
ejpam-4244	16	2	the	the	DET
ejpam-4244	16	3	spectrum	spectrum	NOUN
ejpam-4244	16	4	of	of	ADP
ejpam-4244	16	5	a	a	DET
ejpam-4244	16	6	commutative	commutative	ADJ
ejpam-4244	16	7	banach	banach	NOUN
ejpam-4244	16	8	subalgebra	subalgebra	NOUN
ejpam-4244	16	9	in	in	ADP
ejpam-4244	16	10	the	the	DET
ejpam-4244	16	11	algebra(for	algebra(for	NOUN
ejpam-4244	16	12	the	the	DET
ejpam-4244	16	13	convolution	convolution	NOUN
ejpam-4244	16	14	product	product	NOUN
ejpam-4244	16	15	)	)	PUNCT
ejpam-4244	16	16	of	of	ADP
ejpam-4244	16	17	integrable	integrable	ADJ
ejpam-4244	16	18	functions	function	NOUN
ejpam-4244	16	19	is	be	AUX
ejpam-4244	16	20	identified	identify	VERB
ejpam-4244	16	21	with	with	ADP
ejpam-4244	16	22	functions	function	NOUN
ejpam-4244	16	23	defined	define	VERB
ejpam-4244	16	24	on	on	ADP
ejpam-4244	16	25	g	g	NOUN
ejpam-4244	16	26	,	,	PUNCT
ejpam-4244	16	27	called	call	VERB
ejpam-4244	16	28	δ	δ	NOUN
ejpam-4244	16	29	-	-	ADJ
ejpam-4244	16	30	spherical	spherical	ADJ
ejpam-4244	16	31	functions	function	NOUN
ejpam-4244	16	32	which	which	PRON
ejpam-4244	16	33	play	play	VERB
ejpam-4244	16	34	the	the	DET
ejpam-4244	16	35	same	same	ADJ
ejpam-4244	16	36	role	role	NOUN
ejpam-4244	16	37	as	as	ADP
ejpam-4244	16	38	exponential	exponential	ADJ
ejpam-4244	16	39	functions	function	NOUN
ejpam-4244	16	40	.	.	PUNCT
ejpam-4244	17	1	this	this	DET
ejpam-4244	17	2	identification	identification	NOUN
ejpam-4244	17	3	has	have	AUX
ejpam-4244	17	4	allowed	allow	VERB
ejpam-4244	17	5	to	to	PART
ejpam-4244	17	6	define	define	VERB
ejpam-4244	17	7	in	in	ADP
ejpam-4244	17	8	the	the	DET
ejpam-4244	17	9	general	general	ADJ
ejpam-4244	17	10	case	case	NOUN
ejpam-4244	17	11	,	,	PUNCT
ejpam-4244	17	12	the	the	DET
ejpam-4244	17	13	δ	δ	PROPN
ejpam-4244	17	14	-	-	ADJ
ejpam-4244	17	15	spherical	spherical	ADJ
ejpam-4244	17	16	fourier	fourier	NOUN
ejpam-4244	17	17	transform	transform	NOUN
ejpam-4244	17	18	and	and	CCONJ
ejpam-4244	17	19	to	to	PART
ejpam-4244	17	20	establish	establish	VERB
ejpam-4244	17	21	the	the	DET
ejpam-4244	17	22	majority	majority	NOUN
ejpam-4244	17	23	of	of	ADP
ejpam-4244	17	24	harmonic	harmonic	ADJ
ejpam-4244	17	25	analysis	analysis	NOUN
ejpam-4244	17	26	results	result	NOUN
ejpam-4244	17	27	on	on	ADP
ejpam-4244	17	28	rn	rn	PROPN
ejpam-4244	17	29	.	.	PUNCT
ejpam-4244	17	30	in	in	ADP
ejpam-4244	17	31	1980	1980	NUM
ejpam-4244	17	32	’s	’s	PART
ejpam-4244	17	33	,	,	PUNCT
ejpam-4244	17	34	olshanski	olshanski	INTJ
ejpam-4244	17	35	(	(	PUNCT
ejpam-4244	17	36	[	[	X
ejpam-4244	17	37	4	4	NUM
ejpam-4244	17	38	]	]	PUNCT
ejpam-4244	17	39	,	,	PUNCT
ejpam-4244	17	40	[	[	X
ejpam-4244	17	41	5	5	NUM
ejpam-4244	17	42	]	]	PUNCT
ejpam-4244	17	43	,	,	PUNCT
ejpam-4244	17	44	[	[	X
ejpam-4244	17	45	6	6	NUM
ejpam-4244	17	46	]	]	PUNCT
ejpam-4244	17	47	has	have	AUX
ejpam-4244	17	48	studied	study	VERB
ejpam-4244	17	49	infinite	infinite	ADJ
ejpam-4244	17	50	dimensional	dimensional	ADJ
ejpam-4244	17	51	unitary	unitary	ADJ
ejpam-4244	17	52	representations	representation	NOUN
ejpam-4244	17	53	for	for	ADP
ejpam-4244	17	54	pairs	pair	NOUN
ejpam-4244	17	55	(	(	PUNCT
ejpam-4244	17	56	g∞,k∞	g∞,k∞	PROPN
ejpam-4244	17	57	)	)	PUNCT
ejpam-4244	17	58	which	which	PRON
ejpam-4244	17	59	are	be	AUX
ejpam-4244	17	60	inductive	inductive	ADJ
ejpam-4244	17	61	limit	limit	NOUN
ejpam-4244	17	62	of	of	ADP
ejpam-4244	17	63	gelfand	gelfand	ADJ
ejpam-4244	17	64	pairs	pair	NOUN
ejpam-4244	17	65	(	(	PUNCT
ejpam-4244	17	66	gn	gn	PROPN
ejpam-4244	17	67	,	,	PUNCT
ejpam-4244	17	68	kn	kn	PROPN
ejpam-4244	17	69	)	)	PUNCT
ejpam-4244	17	70	,	,	PUNCT
ejpam-4244	17	71	where	where	SCONJ
ejpam-4244	17	72	g∞	g∞	X
ejpam-4244	17	73	=	=	SYM
ejpam-4244	17	74	∪∞	∪∞	PUNCT
ejpam-4244	17	75	n=1gn	n=1gn	NUM
ejpam-4244	17	76	and	and	CCONJ
ejpam-4244	17	77	k∞	k∞	PROPN
ejpam-4244	17	78	=	=	PUNCT
ejpam-4244	18	1	∪∞	∪∞	PROPN
ejpam-4244	18	2	n=1kn	n=1kn	PROPN
ejpam-4244	18	3	.	.	PUNCT
ejpam-4244	19	1	olshanski	olshanski	PROPN
ejpam-4244	19	2	has	have	AUX
ejpam-4244	19	3	proved	prove	VERB
ejpam-4244	19	4	that	that	SCONJ
ejpam-4244	19	5	inductive	inductive	ADJ
ejpam-4244	19	6	limit	limit	NOUN
ejpam-4244	19	7	of	of	ADP
ejpam-4244	19	8	increasing	increase	VERB
ejpam-4244	19	9	sequence	sequence	NOUN
ejpam-4244	19	10	of	of	ADP
ejpam-4244	19	11	gelfand	gelfand	ADJ
ejpam-4244	19	12	pairs	pair	NOUN
ejpam-4244	19	13	is	be	AUX
ejpam-4244	19	14	a	a	DET
ejpam-4244	19	15	spherical	spherical	ADJ
ejpam-4244	19	16	pair	pair	NOUN
ejpam-4244	19	17	and	and	CCONJ
ejpam-4244	19	18	has	have	AUX
ejpam-4244	19	19	given	give	VERB
ejpam-4244	19	20	characterizations	characterization	NOUN
ejpam-4244	19	21	of	of	ADP
ejpam-4244	19	22	spherical	spherical	ADJ
ejpam-4244	19	23	functions	function	NOUN
ejpam-4244	19	24	associated	associate	VERB
ejpam-4244	19	25	with	with	ADP
ejpam-4244	19	26	these	these	DET
ejpam-4244	19	27	pairs	pair	NOUN
ejpam-4244	19	28	.	.	PUNCT
ejpam-4244	20	1	some	some	DET
ejpam-4244	20	2	authors	author	NOUN
ejpam-4244	20	3	have	have	AUX
ejpam-4244	20	4	also	also	ADV
ejpam-4244	20	5	obtained	obtain	VERB
ejpam-4244	20	6	some	some	DET
ejpam-4244	20	7	∗corresponding	∗corresponde	VERB
ejpam-4244	20	8	author	author	NOUN
ejpam-4244	20	9	.	.	PUNCT
ejpam-4244	21	1	doi	doi	NOUN
ejpam-4244	21	2	:	:	PUNCT
ejpam-4244	21	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4244	https://doi.org/10.29020/nybg.ejpam.v15i1.4244	PROPN
ejpam-4244	21	4	email	email	NOUN
ejpam-4244	21	5	addresses	address	NOUN
ejpam-4244	21	6	:	:	PUNCT
ejpam-4244	21	7	timite.lamine87@ufhb.edu.ci	timite.lamine87@ufhb.edu.ci	X
ejpam-4244	21	8	(	(	PUNCT
ejpam-4244	21	9	l.	l.	PROPN
ejpam-4244	21	10	timite	timite	PROPN
ejpam-4244	21	11	)	)	PUNCT
ejpam-4244	21	12	,	,	PUNCT
ejpam-4244	21	13	ibrahima.toure@univ-fhb.edu.ci	ibrahima.toure@univ-fhb.edu.ci	NOUN
ejpam-4244	21	14	(	(	PUNCT
ejpam-4244	21	15	i.	i.	NOUN
ejpam-4244	21	16	toure	toure	PROPN
ejpam-4244	21	17	)	)	PUNCT
ejpam-4244	21	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4244	22	1	249	249	NUM
ejpam-4244	22	2	©	©	PROPN
ejpam-4244	22	3	2022	2022	NUM
ejpam-4244	22	4	ejpam	ejpam	VERB
ejpam-4244	22	5	all	all	DET
ejpam-4244	22	6	rights	right	NOUN
ejpam-4244	22	7	reserved	reserve	VERB
ejpam-4244	22	8	.	.	PUNCT
ejpam-4244	23	1	l.	l.	PROPN
ejpam-4244	23	2	timite	timite	PROPN
ejpam-4244	23	3	,	,	PUNCT
ejpam-4244	23	4	i.	i.	PROPN
ejpam-4244	23	5	toure	toure	PROPN
ejpam-4244	23	6	/	/	SYM
ejpam-4244	23	7	eur	eur	PROPN
ejpam-4244	23	8	.	.	PUNCT
ejpam-4244	24	1	j.	j.	PROPN
ejpam-4244	24	2	pure	pure	PROPN
ejpam-4244	24	3	appl	appl	PROPN
ejpam-4244	24	4	.	.	PROPN
ejpam-4244	24	5	math	math	PROPN
ejpam-4244	24	6	,	,	PUNCT
ejpam-4244	24	7	15	15	NUM
ejpam-4244	24	8	(	(	PUNCT
ejpam-4244	24	9	1	1	NUM
ejpam-4244	24	10	)	)	PUNCT
ejpam-4244	24	11	(	(	PUNCT
ejpam-4244	24	12	2022	2022	NUM
ejpam-4244	24	13	)	)	PUNCT
ejpam-4244	24	14	,	,	PUNCT
ejpam-4244	24	15	249	249	NUM
ejpam-4244	24	16	-	-	SYM
ejpam-4244	24	17	260	260	NUM
ejpam-4244	24	18	250	250	NUM
ejpam-4244	24	19	results	result	NOUN
ejpam-4244	24	20	about	about	ADP
ejpam-4244	24	21	inductive	inductive	ADJ
ejpam-4244	24	22	limits	limit	NOUN
ejpam-4244	24	23	of	of	ADP
ejpam-4244	24	24	gelfand	gelfand	ADJ
ejpam-4244	24	25	pairs	pair	NOUN
ejpam-4244	24	26	.	.	PUNCT
ejpam-4244	25	1	we	we	PRON
ejpam-4244	25	2	can	can	AUX
ejpam-4244	25	3	mention	mention	VERB
ejpam-4244	25	4	vershik[5	vershik[5	NOUN
ejpam-4244	25	5	]	]	PUNCT
ejpam-4244	25	6	,	,	PUNCT
ejpam-4244	25	7	s.	s.	PROPN
ejpam-4244	25	8	kerov[2	kerov[2	PROPN
ejpam-4244	25	9	]	]	PUNCT
ejpam-4244	25	10	,	,	PUNCT
ejpam-4244	25	11	j.	j.	PROPN
ejpam-4244	25	12	faraut	faraut	PROPN
ejpam-4244	26	1	[	[	X
ejpam-4244	26	2	1	1	NUM
ejpam-4244	26	3	]	]	PUNCT
ejpam-4244	26	4	,	,	PUNCT
ejpam-4244	26	5	r.	r.	PROPN
ejpam-4244	26	6	marouane[3	marouane[3	NOUN
ejpam-4244	26	7	]	]	PUNCT
ejpam-4244	26	8	etc	etc	X
ejpam-4244	26	9	....	....	X
ejpam-4244	26	10	for	for	ADP
ejpam-4244	26	11	example	example	NOUN
ejpam-4244	26	12	in	in	ADP
ejpam-4244	26	13	2007	2007	NUM
ejpam-4244	26	14	,	,	PUNCT
ejpam-4244	26	15	rabaoui	rabaoui	ADV
ejpam-4244	26	16	has	have	AUX
ejpam-4244	26	17	proved	prove	VERB
ejpam-4244	26	18	a	a	DET
ejpam-4244	26	19	bochner	bochner	NOUN
ejpam-4244	26	20	type	type	NOUN
ejpam-4244	26	21	theorem	theorem	NOUN
ejpam-4244	26	22	for	for	ADP
ejpam-4244	26	23	pairs	pair	NOUN
ejpam-4244	26	24	(	(	PUNCT
ejpam-4244	26	25	g∞,k∞	g∞,k∞	NOUN
ejpam-4244	26	26	)	)	PUNCT
ejpam-4244	26	27	.	.	PUNCT
ejpam-4244	27	1	in	in	ADP
ejpam-4244	27	2	this	this	DET
ejpam-4244	27	3	paper	paper	NOUN
ejpam-4244	27	4	,	,	PUNCT
ejpam-4244	27	5	we	we	PRON
ejpam-4244	27	6	extend	extend	VERB
ejpam-4244	27	7	to	to	ADP
ejpam-4244	27	8	commutative	commutative	ADJ
ejpam-4244	27	9	triples	triple	NOUN
ejpam-4244	27	10	some	some	DET
ejpam-4244	27	11	olshanski	olshanski	NOUN
ejpam-4244	27	12	’s	’s	PART
ejpam-4244	27	13	results([4	results([4	NOUN
ejpam-4244	27	14	]	]	PUNCT
ejpam-4244	27	15	,	,	PUNCT
ejpam-4244	27	16	[	[	X
ejpam-4244	27	17	5	5	NUM
ejpam-4244	27	18	]	]	PUNCT
ejpam-4244	27	19	,	,	PUNCT
ejpam-4244	27	20	[	[	X
ejpam-4244	27	21	6	6	NUM
ejpam-4244	27	22	]	]	PUNCT
ejpam-4244	27	23	.	.	PUNCT
ejpam-4244	28	1	in	in	ADP
ejpam-4244	28	2	second	second	ADJ
ejpam-4244	28	3	section	section	NOUN
ejpam-4244	28	4	,	,	PUNCT
ejpam-4244	28	5	we	we	PRON
ejpam-4244	28	6	give	give	VERB
ejpam-4244	28	7	some	some	DET
ejpam-4244	28	8	definitions	definition	NOUN
ejpam-4244	28	9	and	and	CCONJ
ejpam-4244	28	10	notations	notation	NOUN
ejpam-4244	28	11	which	which	PRON
ejpam-4244	28	12	will	will	AUX
ejpam-4244	28	13	be	be	AUX
ejpam-4244	28	14	useful	useful	ADJ
ejpam-4244	28	15	for	for	ADP
ejpam-4244	28	16	well	well	ADJ
ejpam-4244	28	17	understanding	understanding	NOUN
ejpam-4244	28	18	of	of	ADP
ejpam-4244	28	19	this	this	DET
ejpam-4244	28	20	paper	paper	NOUN
ejpam-4244	28	21	.	.	PUNCT
ejpam-4244	29	1	in	in	ADP
ejpam-4244	29	2	the	the	DET
ejpam-4244	29	3	last	last	ADJ
ejpam-4244	29	4	section	section	NOUN
ejpam-4244	29	5	,	,	PUNCT
ejpam-4244	29	6	we	we	PRON
ejpam-4244	29	7	first	first	ADV
ejpam-4244	29	8	extend	extend	VERB
ejpam-4244	29	9	to	to	ADP
ejpam-4244	29	10	commutative	commutative	ADJ
ejpam-4244	29	11	triples	triple	NOUN
ejpam-4244	29	12	the	the	DET
ejpam-4244	29	13	notion	notion	NOUN
ejpam-4244	29	14	of	of	ADP
ejpam-4244	29	15	spherical	spherical	ADJ
ejpam-4244	29	16	pairs	pair	NOUN
ejpam-4244	29	17	namely	namely	ADV
ejpam-4244	29	18	spherical	spherical	ADJ
ejpam-4244	29	19	triples	triple	NOUN
ejpam-4244	29	20	and	and	CCONJ
ejpam-4244	29	21	we	we	PRON
ejpam-4244	29	22	define	define	VERB
ejpam-4244	29	23	spherical	spherical	ADJ
ejpam-4244	29	24	function	function	NOUN
ejpam-4244	29	25	for	for	ADP
ejpam-4244	29	26	these	these	DET
ejpam-4244	29	27	triples	triple	NOUN
ejpam-4244	29	28	.	.	PUNCT
ejpam-4244	30	1	then	then	ADV
ejpam-4244	30	2	,	,	PUNCT
ejpam-4244	30	3	we	we	PRON
ejpam-4244	30	4	prove	prove	VERB
ejpam-4244	30	5	that	that	SCONJ
ejpam-4244	30	6	inductive	inductive	ADJ
ejpam-4244	30	7	limit	limit	NOUN
ejpam-4244	30	8	of	of	ADP
ejpam-4244	30	9	a	a	DET
ejpam-4244	30	10	sequence	sequence	NOUN
ejpam-4244	30	11	of	of	ADP
ejpam-4244	30	12	commutative	commutative	ADJ
ejpam-4244	30	13	triples	triple	NOUN
ejpam-4244	30	14	is	be	AUX
ejpam-4244	30	15	a	a	DET
ejpam-4244	30	16	spherical	spherical	ADJ
ejpam-4244	30	17	triple	triple	NOUN
ejpam-4244	30	18	.	.	PUNCT
ejpam-4244	31	1	finally	finally	ADV
ejpam-4244	31	2	,	,	PUNCT
ejpam-4244	31	3	we	we	PRON
ejpam-4244	31	4	characterize	characterize	VERB
ejpam-4244	31	5	spherical	spherical	ADJ
ejpam-4244	31	6	functions	function	NOUN
ejpam-4244	31	7	for	for	ADP
ejpam-4244	31	8	these	these	DET
ejpam-4244	31	9	triples	triple	NOUN
ejpam-4244	31	10	by	by	ADP
ejpam-4244	31	11	a	a	DET
ejpam-4244	31	12	functional	functional	ADJ
ejpam-4244	31	13	equation	equation	NOUN
ejpam-4244	31	14	and	and	CCONJ
ejpam-4244	31	15	we	we	PRON
ejpam-4244	31	16	give	give	VERB
ejpam-4244	31	17	some	some	DET
ejpam-4244	31	18	properties	property	NOUN
ejpam-4244	31	19	of	of	ADP
ejpam-4244	31	20	these	these	DET
ejpam-4244	31	21	spherical	spherical	ADJ
ejpam-4244	31	22	functions	function	NOUN
ejpam-4244	31	23	.	.	PUNCT
ejpam-4244	32	1	2	2	X
ejpam-4244	32	2	.	.	X
ejpam-4244	32	3	preliminaries	preliminary	NOUN
ejpam-4244	32	4	in	in	ADP
ejpam-4244	32	5	this	this	DET
ejpam-4244	32	6	section	section	NOUN
ejpam-4244	32	7	,	,	PUNCT
ejpam-4244	32	8	we	we	PRON
ejpam-4244	32	9	give	give	VERB
ejpam-4244	32	10	some	some	DET
ejpam-4244	32	11	notations	notation	NOUN
ejpam-4244	32	12	and	and	CCONJ
ejpam-4244	32	13	definitions	definition	NOUN
ejpam-4244	32	14	for	for	ADP
ejpam-4244	32	15	the	the	DET
ejpam-4244	32	16	well	well	ADV
ejpam-4244	32	17	-	-	PUNCT
ejpam-4244	32	18	understanding	understanding	NOUN
ejpam-4244	32	19	of	of	ADP
ejpam-4244	32	20	this	this	DET
ejpam-4244	32	21	paper	paper	NOUN
ejpam-4244	32	22	.	.	PUNCT
ejpam-4244	33	1	let	let	VERB
ejpam-4244	33	2	g	g	PRON
ejpam-4244	33	3	be	be	AUX
ejpam-4244	33	4	a	a	DET
ejpam-4244	33	5	locally	locally	ADV
ejpam-4244	33	6	compact	compact	ADJ
ejpam-4244	33	7	group	group	NOUN
ejpam-4244	33	8	and	and	CCONJ
ejpam-4244	33	9	let	let	VERB
ejpam-4244	33	10	k	k	PRON
ejpam-4244	33	11	be	be	AUX
ejpam-4244	33	12	a	a	DET
ejpam-4244	33	13	compact	compact	ADJ
ejpam-4244	33	14	subgroup	subgroup	NOUN
ejpam-4244	33	15	of	of	ADP
ejpam-4244	33	16	g.	g.	PROPN
ejpam-4244	33	17	g	g	PROPN
ejpam-4244	33	18	is	be	AUX
ejpam-4244	33	19	equipped	equip	VERB
ejpam-4244	33	20	with	with	ADP
ejpam-4244	33	21	a	a	DET
ejpam-4244	33	22	left	left	ADJ
ejpam-4244	33	23	haar	haar	NOUN
ejpam-4244	33	24	measure	measure	NOUN
ejpam-4244	33	25	dx	dx	PROPN
ejpam-4244	33	26	and	and	CCONJ
ejpam-4244	33	27	k	k	PROPN
ejpam-4244	33	28	is	be	AUX
ejpam-4244	33	29	equipped	equip	VERB
ejpam-4244	33	30	with	with	ADP
ejpam-4244	33	31	its	its	PRON
ejpam-4244	33	32	normalized	normalize	VERB
ejpam-4244	33	33	haar	haar	PROPN
ejpam-4244	33	34	measure	measure	NOUN
ejpam-4244	33	35	α	α	X
ejpam-4244	33	36	.	.	PUNCT
ejpam-4244	34	1	let	let	VERB
ejpam-4244	34	2	δ	δ	PRON
ejpam-4244	34	3	be	be	AUX
ejpam-4244	34	4	a	a	DET
ejpam-4244	34	5	unitary	unitary	ADJ
ejpam-4244	34	6	irreducible	irreducible	ADJ
ejpam-4244	34	7	representation	representation	NOUN
ejpam-4244	34	8	of	of	ADP
ejpam-4244	34	9	k	k	PROPN
ejpam-4244	34	10	and	and	CCONJ
ejpam-4244	34	11	let	let	VERB
ejpam-4244	34	12	us	we	PRON
ejpam-4244	34	13	denote	denote	VERB
ejpam-4244	34	14	by	by	ADP
ejpam-4244	34	15	eδ	eδ	NOUN
ejpam-4244	34	16	the	the	DET
ejpam-4244	34	17	realization	realization	NOUN
ejpam-4244	34	18	space	space	NOUN
ejpam-4244	34	19	of	of	ADP
ejpam-4244	34	20	the	the	DET
ejpam-4244	34	21	representation	representation	NOUN
ejpam-4244	34	22	δ	δ	PROPN
ejpam-4244	34	23	.	.	PUNCT
ejpam-4244	35	1	we	we	PRON
ejpam-4244	35	2	put	put	VERB
ejpam-4244	35	3	end(eδ	end(eδ	NOUN
ejpam-4244	35	4	)	)	PUNCT
ejpam-4244	35	5	,	,	PUNCT
ejpam-4244	35	6	the	the	DET
ejpam-4244	35	7	space	space	NOUN
ejpam-4244	35	8	of	of	ADP
ejpam-4244	35	9	endomorphisms	endomorphism	NOUN
ejpam-4244	35	10	of	of	ADP
ejpam-4244	35	11	eδ	eδ	NOUN
ejpam-4244	35	12	and	and	CCONJ
ejpam-4244	35	13	denote	denote	VERB
ejpam-4244	35	14	by	by	ADP
ejpam-4244	35	15	cc(g	cc(g	NOUN
ejpam-4244	35	16	,	,	PUNCT
ejpam-4244	35	17	end(eδ	end(eδ	NOUN
ejpam-4244	35	18	)	)	PUNCT
ejpam-4244	35	19	)	)	PUNCT
ejpam-4244	35	20	the	the	DET
ejpam-4244	35	21	space	space	NOUN
ejpam-4244	35	22	of	of	ADP
ejpam-4244	35	23	compactly	compactly	ADV
ejpam-4244	35	24	supported	support	VERB
ejpam-4244	35	25	continuous	continuous	ADJ
ejpam-4244	35	26	functions	function	NOUN
ejpam-4244	35	27	of	of	ADP
ejpam-4244	35	28	g	g	NOUN
ejpam-4244	35	29	with	with	ADP
ejpam-4244	35	30	values	value	NOUN
ejpam-4244	35	31	in	in	ADP
ejpam-4244	35	32	end(eδ	end(eδ	NOUN
ejpam-4244	35	33	)	)	PUNCT
ejpam-4244	35	34	.	.	PUNCT
ejpam-4244	36	1	cc(g	cc(g	PUNCT
ejpam-4244	36	2	,	,	PUNCT
ejpam-4244	36	3	end(eδ	end(eδ	NOUN
ejpam-4244	36	4	)	)	PUNCT
ejpam-4244	36	5	)	)	PUNCT
ejpam-4244	36	6	is	be	AUX
ejpam-4244	36	7	a	a	DET
ejpam-4244	36	8	convolution	convolution	NOUN
ejpam-4244	36	9	algebra	algebra	NOUN
ejpam-4244	36	10	where	where	SCONJ
ejpam-4244	36	11	the	the	DET
ejpam-4244	36	12	convolution	convolution	NOUN
ejpam-4244	36	13	is	be	AUX
ejpam-4244	36	14	defined	define	VERB
ejpam-4244	36	15	by	by	ADP
ejpam-4244	36	16	:	:	PUNCT
ejpam-4244	36	17	for	for	ADP
ejpam-4244	36	18	f	f	PROPN
ejpam-4244	36	19	,	,	PUNCT
ejpam-4244	36	20	h	h	NOUN
ejpam-4244	36	21	∈	∈	PROPN
ejpam-4244	36	22	cc(g	cc(g	NOUN
ejpam-4244	36	23	,	,	PUNCT
ejpam-4244	36	24	end(eδ	end(eδ	NOUN
ejpam-4244	36	25	)	)	PUNCT
ejpam-4244	36	26	)	)	PUNCT
ejpam-4244	36	27	and	and	CCONJ
ejpam-4244	36	28	x	x	PUNCT
ejpam-4244	36	29	∈	∈	PROPN
ejpam-4244	36	30	g	g	PROPN
ejpam-4244	36	31	,	,	PUNCT
ejpam-4244	36	32	f	f	PROPN
ejpam-4244	36	33	∗h(x	∗h(x	PROPN
ejpam-4244	36	34	)	)	PUNCT
ejpam-4244	37	1	=	=	SYM
ejpam-4244	38	1	∫	∫	PROPN
ejpam-4244	38	2	g	g	PROPN
ejpam-4244	38	3	f	f	PROPN
ejpam-4244	38	4	(	(	PUNCT
ejpam-4244	38	5	y−1x)h(y)dy	y−1x)h(y)dy	PROPN
ejpam-4244	38	6	we	we	PRON
ejpam-4244	38	7	set	set	VERB
ejpam-4244	38	8	,	,	PUNCT
ejpam-4244	38	9	cc(g	cc(g	X
ejpam-4244	38	10	,	,	PUNCT
ejpam-4244	38	11	k	k	PROPN
ejpam-4244	38	12	,	,	PUNCT
ejpam-4244	38	13	δ	δ	PROPN
ejpam-4244	38	14	,	,	PUNCT
ejpam-4244	38	15	δ	δ	PROPN
ejpam-4244	38	16	)	)	PUNCT
ejpam-4244	38	17	:	:	PUNCT
ejpam-4244	39	1	=	=	X
ejpam-4244	39	2	{	{	PUNCT
ejpam-4244	39	3	f	f	PROPN
ejpam-4244	39	4	∈	∈	PROPN
ejpam-4244	39	5	cc(g	cc(g	NOUN
ejpam-4244	39	6	,	,	PUNCT
ejpam-4244	39	7	end(eδ	end(eδ	NOUN
ejpam-4244	39	8	)	)	PUNCT
ejpam-4244	39	9	)	)	PUNCT
ejpam-4244	39	10	:	:	PUNCT
ejpam-4244	40	1	f	f	X
ejpam-4244	40	2	(	(	PUNCT
ejpam-4244	40	3	kxk′	kxk′	X
ejpam-4244	40	4	)	)	PUNCT
ejpam-4244	40	5	=	=	SYM
ejpam-4244	40	6	δ(k′−1)f	δ(k′−1)f	X
ejpam-4244	40	7	(	(	PUNCT
ejpam-4244	40	8	x)δ(k−1)∀k	x)δ(k−1)∀k	PROPN
ejpam-4244	40	9	,	,	PUNCT
ejpam-4244	40	10	k′	k′	PROPN
ejpam-4244	40	11	∈	∈	PROPN
ejpam-4244	40	12	k	k	PROPN
ejpam-4244	40	13	,	,	PUNCT
ejpam-4244	40	14	∀x	∀x	VERB
ejpam-4244	40	15	∈	∈	PROPN
ejpam-4244	40	16	g	g	NOUN
ejpam-4244	40	17	}	}	PUNCT
ejpam-4244	40	18	,	,	PUNCT
ejpam-4244	40	19	the	the	DET
ejpam-4244	40	20	space	space	NOUN
ejpam-4244	40	21	of	of	ADP
ejpam-4244	40	22	continuous	continuous	ADJ
ejpam-4244	40	23	δ	δ	NOUN
ejpam-4244	40	24	-	-	PUNCT
ejpam-4244	40	25	radial	radial	ADJ
ejpam-4244	40	26	functions	function	NOUN
ejpam-4244	40	27	of	of	ADP
ejpam-4244	40	28	g	g	NOUN
ejpam-4244	40	29	with	with	ADP
ejpam-4244	40	30	compact	compact	ADJ
ejpam-4244	40	31	support	support	NOUN
ejpam-4244	40	32	.	.	PUNCT
ejpam-4244	41	1	cc(g	cc(g	PUNCT
ejpam-4244	41	2	,	,	PUNCT
ejpam-4244	41	3	k	k	PROPN
ejpam-4244	41	4	,	,	PUNCT
ejpam-4244	41	5	δ	δ	PROPN
ejpam-4244	41	6	,	,	PUNCT
ejpam-4244	41	7	δ	δ	PROPN
ejpam-4244	41	8	)	)	PUNCT
ejpam-4244	41	9	is	be	AUX
ejpam-4244	41	10	a	a	DET
ejpam-4244	41	11	subalgebra	subalgebra	NOUN
ejpam-4244	41	12	of	of	ADP
ejpam-4244	41	13	the	the	DET
ejpam-4244	41	14	convolution	convolution	NOUN
ejpam-4244	41	15	algebra	algebra	NOUN
ejpam-4244	41	16	cc(g	cc(g	ADJ
ejpam-4244	41	17	,	,	PUNCT
ejpam-4244	41	18	end(eδ	end(eδ	NOUN
ejpam-4244	41	19	)	)	PUNCT
ejpam-4244	41	20	)	)	PUNCT
ejpam-4244	41	21	.	.	PUNCT
ejpam-4244	42	1	we	we	PRON
ejpam-4244	42	2	say	say	VERB
ejpam-4244	42	3	that	that	SCONJ
ejpam-4244	42	4	(	(	PUNCT
ejpam-4244	42	5	g	g	NOUN
ejpam-4244	42	6	,	,	PUNCT
ejpam-4244	42	7	k	k	PROPN
ejpam-4244	42	8	,	,	PUNCT
ejpam-4244	42	9	δ	δ	PROPN
ejpam-4244	42	10	)	)	PUNCT
ejpam-4244	42	11	is	be	AUX
ejpam-4244	42	12	a	a	DET
ejpam-4244	42	13	commutative	commutative	ADJ
ejpam-4244	42	14	triple	triple	NOUN
ejpam-4244	42	15	if	if	SCONJ
ejpam-4244	42	16	the	the	DET
ejpam-4244	42	17	convolution	convolution	NOUN
ejpam-4244	42	18	algebra	algebra	NOUN
ejpam-4244	42	19	cc(g	cc(g	ADJ
ejpam-4244	42	20	,	,	PUNCT
ejpam-4244	42	21	k	k	PROPN
ejpam-4244	42	22	,	,	PUNCT
ejpam-4244	42	23	δ	δ	PROPN
ejpam-4244	42	24	,	,	PUNCT
ejpam-4244	42	25	δ	δ	PROPN
ejpam-4244	42	26	)	)	PUNCT
ejpam-4244	42	27	is	be	AUX
ejpam-4244	42	28	commutative	commutative	ADJ
ejpam-4244	42	29	.	.	PUNCT
ejpam-4244	43	1	if	if	SCONJ
ejpam-4244	43	2	δ	δ	PROPN
ejpam-4244	43	3	is	be	AUX
ejpam-4244	43	4	the	the	DET
ejpam-4244	43	5	one	one	NUM
ejpam-4244	43	6	dimensional	dimensional	ADJ
ejpam-4244	43	7	trivial	trivial	ADJ
ejpam-4244	43	8	representation	representation	NOUN
ejpam-4244	43	9	then	then	ADV
ejpam-4244	43	10	we	we	PRON
ejpam-4244	43	11	obtain	obtain	VERB
ejpam-4244	43	12	the	the	DET
ejpam-4244	43	13	classical	classical	ADJ
ejpam-4244	43	14	notion	notion	NOUN
ejpam-4244	43	15	of	of	ADP
ejpam-4244	43	16	gelfand	gelfand	ADJ
ejpam-4244	43	17	pairs	pair	NOUN
ejpam-4244	43	18	.	.	PUNCT
ejpam-4244	44	1	let	let	VERB
ejpam-4244	44	2	us	we	PRON
ejpam-4244	44	3	put	put	VERB
ejpam-4244	44	4	χδ	χδ	PROPN
ejpam-4244	44	5	:	:	PUNCT
ejpam-4244	45	1	=	=	SYM
ejpam-4244	45	2	d(δ)ξδ	d(δ)ξδ	PROPN
ejpam-4244	45	3	,	,	PUNCT
ejpam-4244	45	4	where	where	SCONJ
ejpam-4244	45	5	d(δ	d(δ	PROPN
ejpam-4244	45	6	)	)	PUNCT
ejpam-4244	45	7	is	be	AUX
ejpam-4244	45	8	the	the	DET
ejpam-4244	45	9	degree	degree	NOUN
ejpam-4244	45	10	of	of	ADP
ejpam-4244	45	11	δ	δ	PROPN
ejpam-4244	45	12	and	and	CCONJ
ejpam-4244	45	13	ξδ	ξδ	ADP
ejpam-4244	45	14	the	the	DET
ejpam-4244	45	15	character	character	NOUN
ejpam-4244	45	16	of	of	ADP
ejpam-4244	45	17	δ	δ	PROPN
ejpam-4244	45	18	.	.	PUNCT
ejpam-4244	46	1	let	let	VERB
ejpam-4244	46	2	us	we	PRON
ejpam-4244	46	3	denote	denote	VERB
ejpam-4244	46	4	by	by	ADP
ejpam-4244	46	5	ĝ(resp.k̂	ĝ(resp.k̂	PROPN
ejpam-4244	46	6	)	)	PUNCT
ejpam-4244	46	7	the	the	DET
ejpam-4244	46	8	unitary	unitary	ADJ
ejpam-4244	46	9	dual	dual	NOUN
ejpam-4244	46	10	of	of	ADP
ejpam-4244	46	11	g(resp	g(resp	NOUN
ejpam-4244	46	12	.	.	PUNCT
ejpam-4244	47	1	k	k	X
ejpam-4244	47	2	)	)	PUNCT
ejpam-4244	47	3	.	.	PUNCT
ejpam-4244	48	1	for	for	ADP
ejpam-4244	48	2	u	u	PROPN
ejpam-4244	48	3	∈	∈	PROPN
ejpam-4244	48	4	ĝ	ĝ	NOUN
ejpam-4244	48	5	,	,	PUNCT
ejpam-4244	48	6	we	we	PRON
ejpam-4244	48	7	denote	denote	VERB
ejpam-4244	48	8	by	by	ADP
ejpam-4244	48	9	mtp(δ	mtp(δ	PROPN
ejpam-4244	48	10	,	,	PUNCT
ejpam-4244	48	11	u	u	NOUN
ejpam-4244	48	12	)	)	PUNCT
ejpam-4244	48	13	the	the	DET
ejpam-4244	48	14	multiplicity	multiplicity	NOUN
ejpam-4244	48	15	of	of	ADP
ejpam-4244	48	16	δ	δ	PROPN
ejpam-4244	48	17	in	in	ADP
ejpam-4244	48	18	u|k	u|k	NOUN
ejpam-4244	48	19	.	.	PUNCT
ejpam-4244	49	1	we	we	PRON
ejpam-4244	49	2	know	know	VERB
ejpam-4244	49	3	by	by	ADP
ejpam-4244	49	4	(	(	PUNCT
ejpam-4244	49	5	[	[	X
ejpam-4244	49	6	9	9	NUM
ejpam-4244	49	7	]	]	PUNCT
ejpam-4244	49	8	,	,	PUNCT
ejpam-4244	49	9	theorem	theorem	VERB
ejpam-4244	49	10	1.1	1.1	NUM
ejpam-4244	49	11	,	,	PUNCT
ejpam-4244	49	12	page	page	NOUN
ejpam-4244	49	13	4	4	NUM
ejpam-4244	49	14	)	)	PUNCT
ejpam-4244	49	15	that	that	SCONJ
ejpam-4244	49	16	(	(	PUNCT
ejpam-4244	49	17	g	g	NOUN
ejpam-4244	49	18	,	,	PUNCT
ejpam-4244	49	19	k	k	PROPN
ejpam-4244	49	20	,	,	PUNCT
ejpam-4244	49	21	δ	δ	PROPN
ejpam-4244	49	22	)	)	PUNCT
ejpam-4244	49	23	is	be	AUX
ejpam-4244	49	24	commutative	commutative	ADJ
ejpam-4244	49	25	if	if	SCONJ
ejpam-4244	49	26	and	and	CCONJ
ejpam-4244	49	27	only	only	ADV
ejpam-4244	49	28	if	if	SCONJ
ejpam-4244	49	29	mtp(δ	mtp(δ	PROPN
ejpam-4244	49	30	,	,	PUNCT
ejpam-4244	49	31	u	u	NOUN
ejpam-4244	49	32	)	)	PUNCT
ejpam-4244	49	33	≤	≤	NUM
ejpam-4244	49	34	1	1	NUM
ejpam-4244	49	35	for	for	ADP
ejpam-4244	49	36	all	all	DET
ejpam-4244	49	37	u	u	PROPN
ejpam-4244	49	38	∈	∈	PROPN
ejpam-4244	49	39	ĝ.	ĝ.	NOUN
ejpam-4244	49	40	let	let	VERB
ejpam-4244	49	41	ĝ(δ	ĝ(δ	PRON
ejpam-4244	49	42	)	)	PUNCT
ejpam-4244	49	43	be	be	AUX
ejpam-4244	49	44	the	the	DET
ejpam-4244	49	45	subset	subset	NOUN
ejpam-4244	49	46	of	of	ADP
ejpam-4244	49	47	ĝ	ĝ	PROPN
ejpam-4244	49	48	consisting	consist	VERB
ejpam-4244	49	49	of	of	ADP
ejpam-4244	49	50	those	those	DET
ejpam-4244	49	51	u	u	PROPN
ejpam-4244	49	52	∈	∈	PROPN
ejpam-4244	49	53	ĝ	ĝ	NOUN
ejpam-4244	49	54	that	that	PRON
ejpam-4244	49	55	contains	contain	VERB
ejpam-4244	49	56	δ	δ	PROPN
ejpam-4244	49	57	upon	upon	SCONJ
ejpam-4244	49	58	restriction	restriction	NOUN
ejpam-4244	49	59	to	to	ADP
ejpam-4244	49	60	k.	k.	PROPN
ejpam-4244	49	61	for	for	ADP
ejpam-4244	49	62	u	u	PROPN
ejpam-4244	49	63	∈	∈	PROPN
ejpam-4244	49	64	ĝ(δ	ĝ(δ	ADV
ejpam-4244	49	65	)	)	PUNCT
ejpam-4244	49	66	and	and	CCONJ
ejpam-4244	49	67	h	h	VERB
ejpam-4244	49	68	its	its	PRON
ejpam-4244	49	69	realization	realization	NOUN
ejpam-4244	49	70	space	space	NOUN
ejpam-4244	49	71	,	,	PUNCT
ejpam-4244	49	72	we	we	PRON
ejpam-4244	49	73	designate	designate	VERB
ejpam-4244	49	74	by	by	ADP
ejpam-4244	49	75	h(δ	h(δ	NOUN
ejpam-4244	49	76	)	)	PUNCT
ejpam-4244	49	77	the	the	DET
ejpam-4244	49	78	isotypic	isotypic	NOUN
ejpam-4244	49	79	component	component	NOUN
ejpam-4244	49	80	of	of	ADP
ejpam-4244	49	81	δ	δ	PROPN
ejpam-4244	49	82	that	that	PRON
ejpam-4244	49	83	is	be	AUX
ejpam-4244	49	84	the	the	DET
ejpam-4244	49	85	subspace	subspace	NOUN
ejpam-4244	49	86	of	of	ADP
ejpam-4244	49	87	vectors	vector	NOUN
ejpam-4244	49	88	which	which	PRON
ejpam-4244	49	89	transform	transform	VERB
ejpam-4244	49	90	under	under	ADP
ejpam-4244	49	91	k	k	NOUN
ejpam-4244	49	92	according	accord	VERB
ejpam-4244	49	93	to	to	ADP
ejpam-4244	49	94	δ	δ	PROPN
ejpam-4244	49	95	.	.	PUNCT
ejpam-4244	50	1	the	the	DET
ejpam-4244	50	2	projection	projection	NOUN
ejpam-4244	50	3	p	p	NOUN
ejpam-4244	50	4	from	from	ADP
ejpam-4244	50	5	h	h	NOUN
ejpam-4244	50	6	onto	onto	ADP
ejpam-4244	50	7	h(δ	h(δ	NOUN
ejpam-4244	50	8	)	)	PUNCT
ejpam-4244	50	9	is	be	AUX
ejpam-4244	50	10	defined	define	VERB
ejpam-4244	50	11	by	by	ADP
ejpam-4244	50	12	:	:	PUNCT
ejpam-4244	50	13	p	p	X
ejpam-4244	50	14	=	=	PUNCT
ejpam-4244	50	15	∫	∫	PROPN
ejpam-4244	50	16	k	k	PROPN
ejpam-4244	50	17	χδ(k	χδ(k	PUNCT
ejpam-4244	50	18	−1)u(k)dk	−1)u(k)dk	X
ejpam-4244	50	19	.	.	PUNCT
ejpam-4244	51	1	a	a	DET
ejpam-4244	51	2	function	function	NOUN
ejpam-4244	51	3	φ	φ	NOUN
ejpam-4244	51	4	:	:	PUNCT
ejpam-4244	51	5	g	g	PROPN
ejpam-4244	51	6	−→	−→	PROPN
ejpam-4244	51	7	end(eδ	end(eδ	NOUN
ejpam-4244	51	8	)	)	PUNCT
ejpam-4244	51	9	is	be	AUX
ejpam-4244	51	10	said	say	VERB
ejpam-4244	51	11	to	to	PART
ejpam-4244	51	12	be	be	AUX
ejpam-4244	51	13	unitary	unitary	ADJ
ejpam-4244	51	14	if	if	SCONJ
ejpam-4244	51	15	∀g	∀g	NOUN
ejpam-4244	51	16	∈	∈	PROPN
ejpam-4244	51	17	g	g	NOUN
ejpam-4244	51	18	,	,	PUNCT
ejpam-4244	51	19	φ(g)∗	φ(g)∗	NOUN
ejpam-4244	51	20	=	=	SYM
ejpam-4244	51	21	φ(g−1	φ(g−1	NUM
ejpam-4244	51	22	)	)	PUNCT
ejpam-4244	51	23	,	,	PUNCT
ejpam-4244	51	24	where	where	SCONJ
ejpam-4244	51	25	φ(g)∗	φ(g)∗	NOUN
ejpam-4244	51	26	designates	designate	VERB
ejpam-4244	51	27	the	the	DET
ejpam-4244	51	28	adjoint	adjoint	NOUN
ejpam-4244	51	29	of	of	ADP
ejpam-4244	51	30	φ(g	φ(g	PROPN
ejpam-4244	51	31	)	)	PUNCT
ejpam-4244	51	32	.	.	PUNCT
ejpam-4244	52	1	l.	l.	PROPN
ejpam-4244	52	2	timite	timite	PROPN
ejpam-4244	52	3	,	,	PUNCT
ejpam-4244	52	4	i.	i.	PROPN
ejpam-4244	52	5	toure	toure	PROPN
ejpam-4244	52	6	/	/	SYM
ejpam-4244	52	7	eur	eur	PROPN
ejpam-4244	52	8	.	.	PUNCT
ejpam-4244	53	1	j.	j.	PROPN
ejpam-4244	53	2	pure	pure	PROPN
ejpam-4244	53	3	appl	appl	PROPN
ejpam-4244	53	4	.	.	PROPN
ejpam-4244	53	5	math	math	PROPN
ejpam-4244	53	6	,	,	PUNCT
ejpam-4244	53	7	15	15	NUM
ejpam-4244	53	8	(	(	PUNCT
ejpam-4244	53	9	1	1	NUM
ejpam-4244	53	10	)	)	PUNCT
ejpam-4244	53	11	(	(	PUNCT
ejpam-4244	53	12	2022	2022	NUM
ejpam-4244	53	13	)	)	PUNCT
ejpam-4244	53	14	,	,	PUNCT
ejpam-4244	53	15	249	249	NUM
ejpam-4244	53	16	-	-	SYM
ejpam-4244	53	17	260	260	NUM
ejpam-4244	53	18	251	251	NUM
ejpam-4244	53	19	3	3	NUM
ejpam-4244	53	20	.	.	PUNCT
ejpam-4244	54	1	spherical	spherical	ADJ
ejpam-4244	54	2	triples	triple	NOUN
ejpam-4244	54	3	in	in	ADP
ejpam-4244	54	4	this	this	DET
ejpam-4244	54	5	section	section	NOUN
ejpam-4244	54	6	,	,	PUNCT
ejpam-4244	54	7	we	we	PRON
ejpam-4244	54	8	extend	extend	VERB
ejpam-4244	54	9	to	to	ADP
ejpam-4244	54	10	commutative	commutative	ADJ
ejpam-4244	54	11	triples	triple	NOUN
ejpam-4244	54	12	some	some	PRON
ejpam-4244	54	13	of	of	ADP
ejpam-4244	54	14	olshanski	olshanski	PROPN
ejpam-4244	54	15	’s	’s	PART
ejpam-4244	54	16	results	result	NOUN
ejpam-4244	54	17	.	.	PUNCT
ejpam-4244	55	1	that	that	PRON
ejpam-4244	55	2	will	will	AUX
ejpam-4244	55	3	permit	permit	VERB
ejpam-4244	55	4	us	we	PRON
ejpam-4244	55	5	to	to	PART
ejpam-4244	55	6	introduce	introduce	VERB
ejpam-4244	55	7	the	the	DET
ejpam-4244	55	8	notion	notion	NOUN
ejpam-4244	55	9	of	of	ADP
ejpam-4244	55	10	spherical	spherical	ADJ
ejpam-4244	55	11	triples	triple	NOUN
ejpam-4244	55	12	.	.	PUNCT
ejpam-4244	56	1	we	we	PRON
ejpam-4244	56	2	recall	recall	VERB
ejpam-4244	56	3	first	first	ADV
ejpam-4244	56	4	the	the	DET
ejpam-4244	56	5	definition	definition	NOUN
ejpam-4244	56	6	of	of	ADP
ejpam-4244	56	7	an	an	DET
ejpam-4244	56	8	admissible	admissible	ADJ
ejpam-4244	56	9	representation	representation	NOUN
ejpam-4244	56	10	for	for	ADP
ejpam-4244	56	11	the	the	DET
ejpam-4244	56	12	pair	pair	NOUN
ejpam-4244	56	13	(	(	PUNCT
ejpam-4244	56	14	g	g	NOUN
ejpam-4244	56	15	,	,	PUNCT
ejpam-4244	56	16	k	k	NOUN
ejpam-4244	56	17	)	)	PUNCT
ejpam-4244	56	18	.	.	PUNCT
ejpam-4244	57	1	in	in	ADP
ejpam-4244	57	2	fact	fact	NOUN
ejpam-4244	57	3	,	,	PUNCT
ejpam-4244	57	4	if	if	SCONJ
ejpam-4244	57	5	g	g	PROPN
ejpam-4244	57	6	is	be	AUX
ejpam-4244	57	7	a	a	DET
ejpam-4244	57	8	topological	topological	ADJ
ejpam-4244	57	9	hausdorff	hausdorff	NOUN
ejpam-4244	57	10	group	group	NOUN
ejpam-4244	57	11	(	(	PUNCT
ejpam-4244	57	12	not	not	PART
ejpam-4244	57	13	necessary	necessary	ADJ
ejpam-4244	57	14	localement	localement	ADJ
ejpam-4244	57	15	compact	compact	NOUN
ejpam-4244	57	16	)	)	PUNCT
ejpam-4244	57	17	and	and	CCONJ
ejpam-4244	57	18	k	k	X
ejpam-4244	57	19	a	a	DET
ejpam-4244	57	20	closed	closed	ADJ
ejpam-4244	57	21	subgroup	subgroup	NOUN
ejpam-4244	57	22	of	of	ADP
ejpam-4244	57	23	g	g	PROPN
ejpam-4244	57	24	,	,	PUNCT
ejpam-4244	57	25	a	a	DET
ejpam-4244	57	26	unitary	unitary	ADJ
ejpam-4244	57	27	representation	representation	NOUN
ejpam-4244	57	28	of	of	ADP
ejpam-4244	57	29	g	g	PROPN
ejpam-4244	57	30	is	be	AUX
ejpam-4244	57	31	an	an	DET
ejpam-4244	57	32	admissible	admissible	ADJ
ejpam-4244	57	33	representation	representation	NOUN
ejpam-4244	57	34	of	of	ADP
ejpam-4244	57	35	the	the	DET
ejpam-4244	57	36	pair	pair	NOUN
ejpam-4244	57	37	(	(	PUNCT
ejpam-4244	57	38	g	g	NOUN
ejpam-4244	57	39	,	,	PUNCT
ejpam-4244	57	40	k	k	NOUN
ejpam-4244	57	41	)	)	PUNCT
ejpam-4244	57	42	if	if	SCONJ
ejpam-4244	57	43	its	its	PRON
ejpam-4244	57	44	restriction	restriction	NOUN
ejpam-4244	57	45	to	to	ADP
ejpam-4244	57	46	k	k	PROPN
ejpam-4244	57	47	is	be	AUX
ejpam-4244	57	48	a	a	DET
ejpam-4244	57	49	discrete	discrete	ADJ
ejpam-4244	57	50	direct	direct	ADJ
ejpam-4244	57	51	sum	sum	NOUN
ejpam-4244	57	52	of	of	ADP
ejpam-4244	57	53	irreducible	irreducible	ADJ
ejpam-4244	57	54	representations	representation	NOUN
ejpam-4244	57	55	.	.	PUNCT
ejpam-4244	58	1	definition	definition	NOUN
ejpam-4244	58	2	1	1	NUM
ejpam-4244	58	3	.	.	PUNCT
ejpam-4244	59	1	let	let	VERB
ejpam-4244	59	2	g	g	PRON
ejpam-4244	59	3	be	be	AUX
ejpam-4244	59	4	a	a	DET
ejpam-4244	59	5	hausdorff	hausdorff	NOUN
ejpam-4244	59	6	topological	topological	ADJ
ejpam-4244	59	7	group	group	NOUN
ejpam-4244	59	8	,	,	PUNCT
ejpam-4244	59	9	k	k	PROPN
ejpam-4244	59	10	be	be	AUX
ejpam-4244	59	11	a	a	DET
ejpam-4244	59	12	closed	closed	ADJ
ejpam-4244	59	13	subgroup	subgroup	NOUN
ejpam-4244	59	14	of	of	ADP
ejpam-4244	59	15	g	g	PROPN
ejpam-4244	59	16	and	and	CCONJ
ejpam-4244	59	17	(	(	PUNCT
ejpam-4244	59	18	δ	δ	PROPN
ejpam-4244	59	19	,	,	PUNCT
ejpam-4244	59	20	eδ	eδ	NOUN
ejpam-4244	59	21	)	)	PUNCT
ejpam-4244	59	22	a	a	DET
ejpam-4244	59	23	unitary	unitary	ADJ
ejpam-4244	59	24	irreducible	irreducible	ADJ
ejpam-4244	59	25	representation	representation	NOUN
ejpam-4244	59	26	of	of	ADP
ejpam-4244	59	27	k.	k.	PROPN
ejpam-4244	59	28	(	(	PUNCT
ejpam-4244	59	29	g	g	PROPN
ejpam-4244	59	30	,	,	PUNCT
ejpam-4244	59	31	k	k	PROPN
ejpam-4244	59	32	,	,	PUNCT
ejpam-4244	59	33	δ	δ	PROPN
ejpam-4244	59	34	)	)	PUNCT
ejpam-4244	59	35	is	be	AUX
ejpam-4244	59	36	a	a	DET
ejpam-4244	59	37	spherical	spherical	ADJ
ejpam-4244	59	38	triple	triple	NOUN
ejpam-4244	59	39	if	if	SCONJ
ejpam-4244	59	40	for	for	ADP
ejpam-4244	59	41	any	any	DET
ejpam-4244	59	42	unitary	unitary	ADJ
ejpam-4244	59	43	irreducible	irreducible	ADJ
ejpam-4244	59	44	admissible	admissible	ADJ
ejpam-4244	59	45	representation	representation	NOUN
ejpam-4244	59	46	(	(	PUNCT
ejpam-4244	59	47	u	u	NOUN
ejpam-4244	59	48	,	,	PUNCT
ejpam-4244	59	49	h	h	NOUN
ejpam-4244	59	50	)	)	PUNCT
ejpam-4244	59	51	of	of	ADP
ejpam-4244	59	52	g	g	PROPN
ejpam-4244	59	53	,	,	PUNCT
ejpam-4244	59	54	mtp(δ	mtp(δ	PROPN
ejpam-4244	59	55	,	,	PUNCT
ejpam-4244	59	56	u|k	u|k	NOUN
ejpam-4244	59	57	)	)	PUNCT
ejpam-4244	59	58	≤	≤	NUM
ejpam-4244	59	59	1	1	NUM
ejpam-4244	59	60	.	.	PUNCT
ejpam-4244	60	1	if	if	SCONJ
ejpam-4244	60	2	mtp(δ	mtp(δ	PROPN
ejpam-4244	60	3	,	,	PUNCT
ejpam-4244	60	4	u|k	u|k	NOUN
ejpam-4244	60	5	)	)	PUNCT
ejpam-4244	60	6	=	=	SYM
ejpam-4244	60	7	1	1	NUM
ejpam-4244	60	8	,	,	PUNCT
ejpam-4244	60	9	u	u	NOUN
ejpam-4244	60	10	is	be	AUX
ejpam-4244	60	11	called	call	VERB
ejpam-4244	60	12	a	a	DET
ejpam-4244	60	13	δ	δ	NOUN
ejpam-4244	60	14	-	-	ADJ
ejpam-4244	60	15	spherical	spherical	ADJ
ejpam-4244	60	16	representation	representation	NOUN
ejpam-4244	60	17	.	.	PUNCT
ejpam-4244	61	1	remark	remark	NOUN
ejpam-4244	61	2	1	1	NUM
ejpam-4244	61	3	.	.	PUNCT
ejpam-4244	62	1	if	if	SCONJ
ejpam-4244	62	2	g	g	PROPN
ejpam-4244	62	3	is	be	AUX
ejpam-4244	62	4	a	a	DET
ejpam-4244	62	5	locally	locally	ADV
ejpam-4244	62	6	compact	compact	ADJ
ejpam-4244	62	7	group	group	NOUN
ejpam-4244	62	8	and	and	CCONJ
ejpam-4244	62	9	k	k	PROPN
ejpam-4244	62	10	is	be	AUX
ejpam-4244	62	11	a	a	DET
ejpam-4244	62	12	compact	compact	ADJ
ejpam-4244	62	13	subgroup	subgroup	NOUN
ejpam-4244	62	14	of	of	ADP
ejpam-4244	62	15	g	g	PROPN
ejpam-4244	62	16	,	,	PUNCT
ejpam-4244	62	17	(	(	PUNCT
ejpam-4244	62	18	g	g	NOUN
ejpam-4244	62	19	,	,	PUNCT
ejpam-4244	62	20	k	k	PROPN
ejpam-4244	62	21	,	,	PUNCT
ejpam-4244	62	22	δ	δ	PROPN
ejpam-4244	62	23	)	)	PUNCT
ejpam-4244	62	24	is	be	AUX
ejpam-4244	62	25	a	a	DET
ejpam-4244	62	26	spherical	spherical	ADJ
ejpam-4244	62	27	triple	triple	NOUN
ejpam-4244	62	28	if	if	SCONJ
ejpam-4244	63	1	and	and	CCONJ
ejpam-4244	63	2	only	only	ADV
ejpam-4244	63	3	if	if	SCONJ
ejpam-4244	63	4	(	(	PUNCT
ejpam-4244	63	5	g	g	NOUN
ejpam-4244	63	6	,	,	PUNCT
ejpam-4244	63	7	k	k	PROPN
ejpam-4244	63	8	,	,	PUNCT
ejpam-4244	63	9	δ	δ	PROPN
ejpam-4244	63	10	)	)	PUNCT
ejpam-4244	63	11	is	be	AUX
ejpam-4244	63	12	a	a	DET
ejpam-4244	63	13	commutative	commutative	ADJ
ejpam-4244	63	14	triple	triple	ADJ
ejpam-4244	63	15	.	.	PUNCT
ejpam-4244	64	1	remark	remark	NOUN
ejpam-4244	64	2	2	2	NUM
ejpam-4244	64	3	.	.	PUNCT
ejpam-4244	65	1	let	let	VERB
ejpam-4244	65	2	us	we	PRON
ejpam-4244	65	3	also	also	ADV
ejpam-4244	65	4	mention	mention	VERB
ejpam-4244	65	5	that	that	SCONJ
ejpam-4244	65	6	the	the	DET
ejpam-4244	65	7	notion	notion	NOUN
ejpam-4244	65	8	of	of	ADP
ejpam-4244	65	9	spherical	spherical	ADJ
ejpam-4244	65	10	triples	triple	NOUN
ejpam-4244	65	11	is	be	AUX
ejpam-4244	65	12	a	a	DET
ejpam-4244	65	13	generalization	generalization	NOUN
ejpam-4244	65	14	of	of	ADP
ejpam-4244	65	15	spherical	spherical	ADJ
ejpam-4244	65	16	pairs	pair	NOUN
ejpam-4244	65	17	which	which	PRON
ejpam-4244	65	18	corresponds	correspond	VERB
ejpam-4244	65	19	to	to	ADP
ejpam-4244	65	20	the	the	DET
ejpam-4244	65	21	case	case	NOUN
ejpam-4244	65	22	when	when	SCONJ
ejpam-4244	65	23	δ	δ	PROPN
ejpam-4244	65	24	is	be	AUX
ejpam-4244	65	25	the	the	DET
ejpam-4244	65	26	one	one	NUM
ejpam-4244	65	27	dimensional	dimensional	ADJ
ejpam-4244	65	28	trivial	trivial	ADJ
ejpam-4244	65	29	representation	representation	NOUN
ejpam-4244	65	30	.	.	PUNCT
ejpam-4244	66	1	in	in	ADP
ejpam-4244	66	2	fact	fact	NOUN
ejpam-4244	66	3	,	,	PUNCT
ejpam-4244	66	4	if	if	SCONJ
ejpam-4244	66	5	mtp(1k	mtp(1k	ADJ
ejpam-4244	66	6	,	,	PUNCT
ejpam-4244	66	7	u|k	u|k	NOUN
ejpam-4244	66	8	)	)	PUNCT
ejpam-4244	66	9	≤	≤	NUM
ejpam-4244	66	10	1	1	NUM
ejpam-4244	66	11	then	then	ADV
ejpam-4244	66	12	dimhk	dimhk	VERB
ejpam-4244	66	13	≤	≤	ADV
ejpam-4244	66	14	1	1	NUM
ejpam-4244	66	15	,	,	PUNCT
ejpam-4244	66	16	where	where	SCONJ
ejpam-4244	66	17	hk	hk	PROPN
ejpam-4244	66	18	is	be	AUX
ejpam-4244	66	19	the	the	DET
ejpam-4244	66	20	space	space	NOUN
ejpam-4244	66	21	of	of	ADP
ejpam-4244	66	22	k	k	ADJ
ejpam-4244	66	23	-	-	PUNCT
ejpam-4244	66	24	invariant	invariant	ADJ
ejpam-4244	66	25	vectors	vector	NOUN
ejpam-4244	66	26	of	of	ADP
ejpam-4244	66	27	h.	h.	PROPN
ejpam-4244	66	28	in	in	ADP
ejpam-4244	66	29	what	what	PRON
ejpam-4244	66	30	follows	follow	VERB
ejpam-4244	66	31	,	,	PUNCT
ejpam-4244	66	32	we	we	PRON
ejpam-4244	66	33	define	define	VERB
ejpam-4244	66	34	δ	δ	NOUN
ejpam-4244	66	35	-	-	ADJ
ejpam-4244	66	36	spherical	spherical	ADJ
ejpam-4244	66	37	functions	function	NOUN
ejpam-4244	66	38	for	for	ADP
ejpam-4244	66	39	spherical	spherical	ADJ
ejpam-4244	66	40	triples	triple	NOUN
ejpam-4244	66	41	.	.	PUNCT
ejpam-4244	67	1	let	let	VERB
ejpam-4244	67	2	us	we	PRON
ejpam-4244	67	3	mention	mention	VERB
ejpam-4244	67	4	that	that	SCONJ
ejpam-4244	67	5	if	if	SCONJ
ejpam-4244	67	6	mtp(δ	mtp(δ	PROPN
ejpam-4244	67	7	,	,	PUNCT
ejpam-4244	67	8	u|k	u|k	NOUN
ejpam-4244	67	9	)	)	PUNCT
ejpam-4244	67	10	=	=	SYM
ejpam-4244	67	11	1	1	NUM
ejpam-4244	67	12	then	then	ADV
ejpam-4244	67	13	h(δ	h(δ	NOUN
ejpam-4244	67	14	)	)	PUNCT
ejpam-4244	67	15	is	be	AUX
ejpam-4244	67	16	isomorphic	isomorphic	ADJ
ejpam-4244	67	17	to	to	ADP
ejpam-4244	67	18	eδ	eδ	NOUN
ejpam-4244	67	19	.	.	PUNCT
ejpam-4244	68	1	definition	definition	NOUN
ejpam-4244	68	2	2	2	NUM
ejpam-4244	68	3	.	.	PUNCT
ejpam-4244	69	1	let	let	AUX
ejpam-4244	69	2	(	(	PUNCT
ejpam-4244	69	3	g	g	NOUN
ejpam-4244	69	4	,	,	PUNCT
ejpam-4244	69	5	k	k	PROPN
ejpam-4244	69	6	,	,	PUNCT
ejpam-4244	69	7	δ	δ	PROPN
ejpam-4244	69	8	)	)	PUNCT
ejpam-4244	69	9	be	be	VERB
ejpam-4244	69	10	a	a	DET
ejpam-4244	69	11	spherical	spherical	ADJ
ejpam-4244	69	12	triple	triple	NOUN
ejpam-4244	69	13	.	.	PUNCT
ejpam-4244	70	1	a	a	DET
ejpam-4244	70	2	function	function	NOUN
ejpam-4244	70	3	φ	φ	NOUN
ejpam-4244	70	4	:	:	PUNCT
ejpam-4244	70	5	g	g	PROPN
ejpam-4244	70	6	−→	−→	PROPN
ejpam-4244	70	7	end(eδ	end(eδ	NOUN
ejpam-4244	70	8	)	)	PUNCT
ejpam-4244	70	9	is	be	AUX
ejpam-4244	70	10	a	a	DET
ejpam-4244	70	11	δ	δ	NOUN
ejpam-4244	70	12	-	-	NOUN
ejpam-4244	70	13	spherical	spherical	ADJ
ejpam-4244	70	14	if	if	SCONJ
ejpam-4244	70	15	there	there	PRON
ejpam-4244	70	16	exists	exist	VERB
ejpam-4244	70	17	a	a	DET
ejpam-4244	70	18	δ	δ	NOUN
ejpam-4244	70	19	-	-	ADJ
ejpam-4244	70	20	spherical	spherical	ADJ
ejpam-4244	70	21	representation	representation	NOUN
ejpam-4244	70	22	(	(	PUNCT
ejpam-4244	70	23	u	u	NOUN
ejpam-4244	70	24	,	,	PUNCT
ejpam-4244	70	25	h	h	NOUN
ejpam-4244	70	26	)	)	PUNCT
ejpam-4244	70	27	of	of	ADP
ejpam-4244	70	28	g	g	PROPN
ejpam-4244	70	29	such	such	ADJ
ejpam-4244	70	30	that	that	SCONJ
ejpam-4244	70	31	φ(g)u	φ(g)u	PROPN
ejpam-4244	70	32	=	=	PUNCT
ejpam-4244	70	33	pu(g−1)u,∀g	pu(g−1)u,∀g	NOUN
ejpam-4244	70	34	∈	∈	PROPN
ejpam-4244	70	35	g	g	PROPN
ejpam-4244	70	36	,	,	PUNCT
ejpam-4244	70	37	∀u	∀u	NOUN
ejpam-4244	70	38	∈	∈	NOUN
ejpam-4244	70	39	eδ	eδ	NOUN
ejpam-4244	70	40	,	,	PUNCT
ejpam-4244	70	41	where	where	SCONJ
ejpam-4244	70	42	p	p	NOUN
ejpam-4244	70	43	is	be	AUX
ejpam-4244	70	44	the	the	DET
ejpam-4244	70	45	orthogonal	orthogonal	ADJ
ejpam-4244	70	46	projection	projection	NOUN
ejpam-4244	70	47	of	of	ADP
ejpam-4244	70	48	h	h	NOUN
ejpam-4244	70	49	onto	onto	ADP
ejpam-4244	70	50	eδ	eδ	NOUN
ejpam-4244	70	51	.	.	PUNCT
ejpam-4244	71	1	the	the	DET
ejpam-4244	71	2	following	follow	VERB
ejpam-4244	71	3	theorem	theorem	NOUN
ejpam-4244	71	4	gives	give	VERB
ejpam-4244	71	5	some	some	DET
ejpam-4244	71	6	properties	property	NOUN
ejpam-4244	71	7	of	of	ADP
ejpam-4244	71	8	δ	δ	NOUN
ejpam-4244	71	9	-	-	ADJ
ejpam-4244	71	10	spherical	spherical	ADJ
ejpam-4244	71	11	functions	function	NOUN
ejpam-4244	71	12	.	.	PUNCT
ejpam-4244	72	1	theorem	theorem	NOUN
ejpam-4244	72	2	1	1	NUM
ejpam-4244	72	3	.	.	PUNCT
ejpam-4244	73	1	let	let	VERB
ejpam-4244	73	2	φ	φ	NOUN
ejpam-4244	73	3	:	:	PUNCT
ejpam-4244	73	4	g	g	PROPN
ejpam-4244	73	5	−→	−→	NOUN
ejpam-4244	73	6	end(eδ	end(eδ	NOUN
ejpam-4244	73	7	)	)	PUNCT
ejpam-4244	73	8	be	be	VERB
ejpam-4244	73	9	a	a	DET
ejpam-4244	73	10	δ	δ	NOUN
ejpam-4244	73	11	-	-	ADJ
ejpam-4244	73	12	spherical	spherical	ADJ
ejpam-4244	73	13	function	function	NOUN
ejpam-4244	73	14	.	.	PUNCT
ejpam-4244	74	1	then	then	ADV
ejpam-4244	74	2	i	i	PRON
ejpam-4244	74	3	)	)	PUNCT
ejpam-4244	74	4	φ(e	φ(e	ADV
ejpam-4244	74	5	)	)	PUNCT
ejpam-4244	75	1	=	=	SYM
ejpam-4244	75	2	i	i	PROPN
ejpam-4244	75	3	,	,	PUNCT
ejpam-4244	75	4	where	where	SCONJ
ejpam-4244	75	5	i	i	PRON
ejpam-4244	75	6	is	be	AUX
ejpam-4244	75	7	the	the	DET
ejpam-4244	75	8	identity	identity	NOUN
ejpam-4244	75	9	operator	operator	NOUN
ejpam-4244	75	10	of	of	ADP
ejpam-4244	75	11	eδ	eδ	PROPN
ejpam-4244	75	12	.	.	PUNCT
ejpam-4244	75	13	ii	ii	PROPN
ejpam-4244	75	14	)	)	PUNCT
ejpam-4244	75	15	φ	φ	PROPN
ejpam-4244	75	16	is	be	AUX
ejpam-4244	75	17	δ	δ	NOUN
ejpam-4244	75	18	-	-	PUNCT
ejpam-4244	75	19	radial	radial	ADJ
ejpam-4244	75	20	.	.	PUNCT
ejpam-4244	76	1	proof	proof	NOUN
ejpam-4244	76	2	.	.	PUNCT
ejpam-4244	77	1	let	let	VERB
ejpam-4244	77	2	φ	φ	NOUN
ejpam-4244	77	3	:	:	PUNCT
ejpam-4244	77	4	g	g	PROPN
ejpam-4244	77	5	−→	−→	NOUN
ejpam-4244	77	6	end(eδ	end(eδ	NOUN
ejpam-4244	77	7	)	)	PUNCT
ejpam-4244	77	8	be	be	VERB
ejpam-4244	77	9	a	a	DET
ejpam-4244	77	10	δ	δ	NOUN
ejpam-4244	77	11	-	-	ADJ
ejpam-4244	77	12	spherical	spherical	ADJ
ejpam-4244	77	13	function	function	NOUN
ejpam-4244	77	14	.	.	PUNCT
ejpam-4244	78	1	i	i	PRON
ejpam-4244	78	2	)	)	PUNCT
ejpam-4244	78	3	then	then	ADV
ejpam-4244	78	4	there	there	PRON
ejpam-4244	78	5	exits	exit	VERB
ejpam-4244	78	6	a	a	DET
ejpam-4244	78	7	δ	δ	NOUN
ejpam-4244	78	8	-	-	ADJ
ejpam-4244	78	9	spherical	spherical	ADJ
ejpam-4244	78	10	representation	representation	NOUN
ejpam-4244	78	11	(	(	PUNCT
ejpam-4244	78	12	u	u	NOUN
ejpam-4244	78	13	,	,	PUNCT
ejpam-4244	78	14	h	h	NOUN
ejpam-4244	78	15	)	)	PUNCT
ejpam-4244	78	16	of	of	ADP
ejpam-4244	78	17	g	g	PROPN
ejpam-4244	78	18	such	such	ADJ
ejpam-4244	78	19	that	that	SCONJ
ejpam-4244	78	20	φ(g)u	φ(g)u	PROPN
ejpam-4244	78	21	=	=	SYM
ejpam-4244	78	22	pu(g−1)u	pu(g−1)u	NOUN
ejpam-4244	78	23	,	,	PUNCT
ejpam-4244	78	24	∀g	∀g	X
ejpam-4244	78	25	∈	∈	PROPN
ejpam-4244	78	26	g	g	NOUN
ejpam-4244	78	27	,	,	PUNCT
ejpam-4244	78	28	∀u	∀u	NOUN
ejpam-4244	78	29	∈	∈	NOUN
ejpam-4244	78	30	eδ	eδ	NOUN
ejpam-4244	78	31	.	.	PUNCT
ejpam-4244	79	1	∀v	∀v	PROPN
ejpam-4244	79	2	∈	∈	PROPN
ejpam-4244	79	3	eδ	eδ	NOUN
ejpam-4244	79	4	,	,	PUNCT
ejpam-4244	79	5	φ(e)v	φ(e)v	PROPN
ejpam-4244	79	6	=	=	PUNCT
ejpam-4244	80	1	pu(e)v	pu(e)v	PROPN
ejpam-4244	80	2	=	=	PUNCT
ejpam-4244	80	3	pv	pv	NOUN
ejpam-4244	80	4	=	=	PUNCT
ejpam-4244	80	5	v.	v.	ADP
ejpam-4244	80	6	hence	hence	ADV
ejpam-4244	80	7	φ(e	φ(e	NUM
ejpam-4244	80	8	)	)	PUNCT
ejpam-4244	80	9	=	=	SYM
ejpam-4244	80	10	i.	i.	PROPN
ejpam-4244	80	11	l.	l.	PROPN
ejpam-4244	80	12	timite	timite	PROPN
ejpam-4244	80	13	,	,	PUNCT
ejpam-4244	80	14	i.	i.	PROPN
ejpam-4244	80	15	toure	toure	PROPN
ejpam-4244	80	16	/	/	SYM
ejpam-4244	80	17	eur	eur	PROPN
ejpam-4244	80	18	.	.	PUNCT
ejpam-4244	81	1	j.	j.	PROPN
ejpam-4244	81	2	pure	pure	PROPN
ejpam-4244	81	3	appl	appl	PROPN
ejpam-4244	81	4	.	.	PROPN
ejpam-4244	81	5	math	math	PROPN
ejpam-4244	81	6	,	,	PUNCT
ejpam-4244	81	7	15	15	NUM
ejpam-4244	81	8	(	(	PUNCT
ejpam-4244	81	9	1	1	NUM
ejpam-4244	81	10	)	)	PUNCT
ejpam-4244	81	11	(	(	PUNCT
ejpam-4244	81	12	2022	2022	NUM
ejpam-4244	81	13	)	)	PUNCT
ejpam-4244	81	14	,	,	PUNCT
ejpam-4244	81	15	249	249	NUM
ejpam-4244	81	16	-	-	SYM
ejpam-4244	81	17	260	260	NUM
ejpam-4244	81	18	252	252	NUM
ejpam-4244	81	19	ii	ii	NOUN
ejpam-4244	81	20	)	)	PUNCT
ejpam-4244	82	1	∀k1	∀k1	PROPN
ejpam-4244	82	2	,	,	PUNCT
ejpam-4244	82	3	k2	k2	PROPN
ejpam-4244	82	4	∈	∈	PROPN
ejpam-4244	82	5	k,∀x	k,∀x	ADP
ejpam-4244	82	6	∈	∈	PROPN
ejpam-4244	82	7	g	g	NOUN
ejpam-4244	82	8	and	and	CCONJ
ejpam-4244	82	9	∀u	∀u	NOUN
ejpam-4244	82	10	∈	∈	NOUN
ejpam-4244	82	11	eδ	eδ	NOUN
ejpam-4244	82	12	,	,	PUNCT
ejpam-4244	82	13	φ(k1xk2)u	φ(k1xk2)u	PROPN
ejpam-4244	82	14	=	=	PUNCT
ejpam-4244	82	15	pu(k−1	pu(k−1	PROPN
ejpam-4244	82	16	2	2	NUM
ejpam-4244	82	17	x−1k−1	x−1k−1	NUM
ejpam-4244	82	18	1	1	NUM
ejpam-4244	82	19	)	)	PUNCT
ejpam-4244	82	20	u	u	NOUN
ejpam-4244	83	1	=	=	NOUN
ejpam-4244	83	2	pu(k−1	pu(k−1	PROPN
ejpam-4244	83	3	2	2	NUM
ejpam-4244	83	4	)	)	PUNCT
ejpam-4244	83	5	u(x−1)u(k−1	u(x−1)u(k−1	PROPN
ejpam-4244	83	6	1	1	NUM
ejpam-4244	83	7	)	)	PUNCT
ejpam-4244	83	8	u	u	NOUN
ejpam-4244	83	9	=	=	PUNCT
ejpam-4244	83	10	u(k−1	u(k−1	PROPN
ejpam-4244	83	11	2	2	NUM
ejpam-4244	83	12	)	)	PUNCT
ejpam-4244	83	13	pu(x−1)u(k−1	pu(x−1)u(k−1	NUM
ejpam-4244	83	14	1	1	X
ejpam-4244	83	15	)	)	PUNCT
ejpam-4244	83	16	u	u	NOUN
ejpam-4244	83	17	=	=	NOUN
ejpam-4244	83	18	δ(k−1	δ(k−1	VERB
ejpam-4244	83	19	2	2	NUM
ejpam-4244	83	20	)	)	PUNCT
ejpam-4244	83	21	pu(x−1)δ(k−1	pu(x−1)δ(k−1	PROPN
ejpam-4244	83	22	1	1	NUM
ejpam-4244	83	23	)	)	PUNCT
ejpam-4244	83	24	u	u	NOUN
ejpam-4244	83	25	=	=	NOUN
ejpam-4244	83	26	δ(k−1	δ(k−1	VERB
ejpam-4244	83	27	2	2	NUM
ejpam-4244	83	28	)	)	PUNCT
ejpam-4244	83	29	φ(x)δ(k−1	φ(x)δ(k−1	PROPN
ejpam-4244	83	30	1	1	NUM
ejpam-4244	83	31	)	)	PUNCT
ejpam-4244	83	32	u	u	NOUN
ejpam-4244	83	33	hence	hence	ADV
ejpam-4244	83	34	φ	φ	PROPN
ejpam-4244	83	35	is	be	AUX
ejpam-4244	83	36	a	a	DET
ejpam-4244	83	37	δ	δ	NOUN
ejpam-4244	83	38	-	-	PUNCT
ejpam-4244	83	39	radial	radial	ADJ
ejpam-4244	83	40	function	function	NOUN
ejpam-4244	83	41	.	.	PUNCT
ejpam-4244	84	1	now	now	ADV
ejpam-4244	84	2	,	,	PUNCT
ejpam-4244	84	3	let	let	VERB
ejpam-4244	84	4	g1	g1	PROPN
ejpam-4244	84	5	⊆	⊆	NUM
ejpam-4244	84	6	g2	g2	PROPN
ejpam-4244	84	7	⊆	⊆	NUM
ejpam-4244	84	8	...	...	PUNCT
ejpam-4244	84	9	⊆	⊆	NUM
ejpam-4244	84	10	gn	gn	PROPN
ejpam-4244	84	11	⊆	⊆	NUM
ejpam-4244	84	12	...	...	PUNCT
ejpam-4244	84	13	be	be	AUX
ejpam-4244	84	14	an	an	DET
ejpam-4244	84	15	increasing	increase	VERB
ejpam-4244	84	16	sequence	sequence	NOUN
ejpam-4244	84	17	of	of	ADP
ejpam-4244	84	18	locally	locally	ADV
ejpam-4244	84	19	compact	compact	ADJ
ejpam-4244	84	20	groups	group	NOUN
ejpam-4244	84	21	such	such	ADJ
ejpam-4244	84	22	that	that	PRON
ejpam-4244	84	23	for	for	ADP
ejpam-4244	84	24	each	each	DET
ejpam-4244	84	25	n	n	CCONJ
ejpam-4244	84	26	,	,	PUNCT
ejpam-4244	84	27	gn	gn	PROPN
ejpam-4244	84	28	is	be	AUX
ejpam-4244	84	29	a	a	DET
ejpam-4244	84	30	closed	closed	ADJ
ejpam-4244	84	31	subgroup	subgroup	NOUN
ejpam-4244	84	32	of	of	ADP
ejpam-4244	84	33	gn+1	gn+1	PROPN
ejpam-4244	84	34	.	.	PUNCT
ejpam-4244	85	1	we	we	PRON
ejpam-4244	85	2	consider	consider	VERB
ejpam-4244	85	3	again	again	ADV
ejpam-4244	85	4	k1	k1	VERB
ejpam-4244	85	5	⊆	⊆	NUM
ejpam-4244	85	6	k2	k2	NOUN
ejpam-4244	85	7	⊆	⊆	NUM
ejpam-4244	85	8	...	...	PUNCT
ejpam-4244	85	9	⊆	⊆	NUM
ejpam-4244	85	10	kn	kn	PROPN
ejpam-4244	85	11	⊆	⊆	NUM
ejpam-4244	85	12	...	...	PUNCT
ejpam-4244	85	13	an	an	DET
ejpam-4244	85	14	increasing	increase	VERB
ejpam-4244	85	15	sequence	sequence	NOUN
ejpam-4244	85	16	of	of	ADP
ejpam-4244	85	17	compact	compact	ADJ
ejpam-4244	85	18	groups	group	NOUN
ejpam-4244	85	19	such	such	ADJ
ejpam-4244	85	20	that	that	PRON
ejpam-4244	85	21	for	for	ADP
ejpam-4244	85	22	each	each	DET
ejpam-4244	85	23	n	n	CCONJ
ejpam-4244	85	24	,	,	PUNCT
ejpam-4244	85	25	kn	kn	PROPN
ejpam-4244	85	26	is	be	AUX
ejpam-4244	85	27	a	a	DET
ejpam-4244	85	28	compact	compact	ADJ
ejpam-4244	85	29	subgroup	subgroup	NOUN
ejpam-4244	85	30	of	of	ADP
ejpam-4244	85	31	gn	gn	PROPN
ejpam-4244	85	32	and	and	CCONJ
ejpam-4244	85	33	kn	kn	PROPN
ejpam-4244	85	34	=	=	PROPN
ejpam-4244	85	35	gn	gn	PROPN
ejpam-4244	85	36	∩kn+1	∩kn+1	PROPN
ejpam-4244	85	37	.	.	PUNCT
ejpam-4244	86	1	the	the	DET
ejpam-4244	86	2	family	family	NOUN
ejpam-4244	86	3	of	of	ADP
ejpam-4244	86	4	pairs	pair	NOUN
ejpam-4244	86	5	(	(	PUNCT
ejpam-4244	86	6	gn	gn	INTJ
ejpam-4244	86	7	,	,	PUNCT
ejpam-4244	86	8	kn)n≥1	kn)n≥1	NOUN
ejpam-4244	86	9	that	that	PRON
ejpam-4244	86	10	we	we	PRON
ejpam-4244	86	11	consider	consider	VERB
ejpam-4244	86	12	,	,	PUNCT
ejpam-4244	86	13	equipped	equip	VERB
ejpam-4244	86	14	with	with	ADP
ejpam-4244	86	15	the	the	DET
ejpam-4244	86	16	system	system	NOUN
ejpam-4244	86	17	of	of	ADP
ejpam-4244	86	18	canonical	canonical	ADJ
ejpam-4244	86	19	continuous	continuous	ADJ
ejpam-4244	86	20	embeddings	embedding	NOUN
ejpam-4244	86	21	tm	tm	NOUN
ejpam-4244	86	22	,	,	PUNCT
ejpam-4244	86	23	n	n	PROPN
ejpam-4244	86	24	:	:	PUNCT
ejpam-4244	86	25	gn	gn	INTJ
ejpam-4244	86	26	−→	−→	ADJ
ejpam-4244	86	27	gm	gm	PROPN
ejpam-4244	86	28	,	,	PUNCT
ejpam-4244	86	29	n	n	CCONJ
ejpam-4244	86	30	,	,	PUNCT
ejpam-4244	86	31	m	m	PROPN
ejpam-4244	86	32	∈	∈	PROPN
ejpam-4244	86	33	n∗	n∗	PROPN
ejpam-4244	86	34	,	,	PUNCT
ejpam-4244	86	35	n	n	CCONJ
ejpam-4244	86	36	≤	≤	NOUN
ejpam-4244	86	37	m	m	NOUN
ejpam-4244	86	38	,	,	PUNCT
ejpam-4244	86	39	constitutes	constitute	VERB
ejpam-4244	86	40	an	an	DET
ejpam-4244	86	41	inductive	inductive	ADJ
ejpam-4244	86	42	countable	countable	ADJ
ejpam-4244	86	43	system	system	NOUN
ejpam-4244	86	44	of	of	ADP
ejpam-4244	86	45	topological	topological	ADJ
ejpam-4244	86	46	groups	group	NOUN
ejpam-4244	86	47	.	.	PUNCT
ejpam-4244	87	1	hence	hence	ADV
ejpam-4244	87	2	,	,	PUNCT
ejpam-4244	87	3	we	we	PRON
ejpam-4244	87	4	can	can	AUX
ejpam-4244	87	5	define	define	VERB
ejpam-4244	87	6	the	the	DET
ejpam-4244	87	7	following	following	ADJ
ejpam-4244	87	8	inductive	inductive	ADJ
ejpam-4244	87	9	limit	limit	NOUN
ejpam-4244	87	10	groups	group	NOUN
ejpam-4244	87	11	:	:	PUNCT
ejpam-4244	88	1	g∞	g∞	X
ejpam-4244	88	2	=	=	PUNCT
ejpam-4244	88	3	⋃	⋃	ADP
ejpam-4244	88	4	n≥1	n≥1	NOUN
ejpam-4244	88	5	gn	gn	PROPN
ejpam-4244	88	6	k∞	k∞	PROPN
ejpam-4244	88	7	=	=	SYM
ejpam-4244	89	1	⋃	⋃	ADP
ejpam-4244	89	2	n≥1	n≥1	PROPN
ejpam-4244	89	3	kn	kn	PROPN
ejpam-4244	89	4	.	.	PUNCT
ejpam-4244	90	1	the	the	DET
ejpam-4244	90	2	topology	topology	NOUN
ejpam-4244	90	3	defined	define	VERB
ejpam-4244	90	4	on	on	ADP
ejpam-4244	90	5	g∞	g∞	PROPN
ejpam-4244	90	6	is	be	AUX
ejpam-4244	90	7	the	the	DET
ejpam-4244	90	8	inductive	inductive	ADJ
ejpam-4244	90	9	limit	limit	NOUN
ejpam-4244	90	10	topology	topology	NOUN
ejpam-4244	90	11	.	.	PUNCT
ejpam-4244	91	1	let	let	VERB
ejpam-4244	91	2	(	(	PUNCT
ejpam-4244	91	3	eδn	eδn	ADV
ejpam-4244	91	4	)	)	PUNCT
ejpam-4244	91	5	be	be	AUX
ejpam-4244	91	6	an	an	DET
ejpam-4244	91	7	increasing	increase	VERB
ejpam-4244	91	8	sequence	sequence	NOUN
ejpam-4244	91	9	of	of	ADP
ejpam-4244	91	10	hilbert	hilbert	NOUN
ejpam-4244	91	11	spaces	space	NOUN
ejpam-4244	91	12	and	and	CCONJ
ejpam-4244	91	13	for	for	ADP
ejpam-4244	91	14	any	any	DET
ejpam-4244	91	15	n	n	PRON
ejpam-4244	91	16	≥	≥	NOUN
ejpam-4244	91	17	1	1	NUM
ejpam-4244	91	18	,	,	PUNCT
ejpam-4244	91	19	let	let	VERB
ejpam-4244	91	20	us	we	PRON
ejpam-4244	91	21	consider	consider	VERB
ejpam-4244	91	22	a	a	DET
ejpam-4244	91	23	unitary	unitary	ADJ
ejpam-4244	91	24	representation	representation	NOUN
ejpam-4244	91	25	(	(	PUNCT
ejpam-4244	91	26	δn	δn	NOUN
ejpam-4244	91	27	,	,	PUNCT
ejpam-4244	91	28	eδn	eδn	ADJ
ejpam-4244	91	29	)	)	PUNCT
ejpam-4244	91	30	of	of	ADP
ejpam-4244	91	31	kn	kn	PROPN
ejpam-4244	91	32	.	.	PROPN
ejpam-4244	92	1	for	for	ADP
ejpam-4244	92	2	each	each	DET
ejpam-4244	92	3	n	n	PRON
ejpam-4244	92	4	≥	≥	NOUN
ejpam-4244	92	5	1	1	NUM
ejpam-4244	92	6	,	,	PUNCT
ejpam-4244	92	7	we	we	PRON
ejpam-4244	92	8	consider	consider	VERB
ejpam-4244	92	9	an	an	DET
ejpam-4244	92	10	isometric	isometric	ADJ
ejpam-4244	92	11	embedding	embed	VERB
ejpam-4244	92	12	in	in	ADP
ejpam-4244	92	13	:	:	PUNCT
ejpam-4244	92	14	eδn	eδn	VERB
ejpam-4244	92	15	−→	−→	NOUN
ejpam-4244	92	16	eδn+1	eδn+1	PROPN
ejpam-4244	92	17	commuting	commute	VERB
ejpam-4244	92	18	with	with	ADP
ejpam-4244	92	19	the	the	DET
ejpam-4244	92	20	action	action	NOUN
ejpam-4244	92	21	of	of	ADP
ejpam-4244	92	22	kn	kn	PROPN
ejpam-4244	92	23	.	.	PUNCT
ejpam-4244	93	1	let	let	VERB
ejpam-4244	93	2	us	we	PRON
ejpam-4244	93	3	put	put	VERB
ejpam-4244	93	4	eδ∞	eδ∞	PROPN
ejpam-4244	93	5	=	=	PUNCT
ejpam-4244	94	1	⋃	⋃	NOUN
ejpam-4244	94	2	n∈n∗	n∈n∗	PUNCT
ejpam-4244	94	3	eδn	eδn	VERB
ejpam-4244	94	4	the	the	DET
ejpam-4244	94	5	hilbert	hilbert	PROPN
ejpam-4244	94	6	completion	completion	NOUN
ejpam-4244	94	7	of	of	ADP
ejpam-4244	94	8	⋃	⋃	NOUN
ejpam-4244	94	9	n∈n∗	n∈n∗	PART
ejpam-4244	94	10	eδn	eδn	NOUN
ejpam-4244	94	11	.	.	PUNCT
ejpam-4244	95	1	then	then	ADV
ejpam-4244	95	2	there	there	PRON
ejpam-4244	95	3	exists	exist	VERB
ejpam-4244	95	4	a	a	DET
ejpam-4244	95	5	unique	unique	ADJ
ejpam-4244	95	6	representation	representation	NOUN
ejpam-4244	95	7	δ∞	δ∞	NOUN
ejpam-4244	95	8	of	of	ADP
ejpam-4244	95	9	g∞	g∞	PROPN
ejpam-4244	95	10	such	such	ADJ
ejpam-4244	95	11	that	that	DET
ejpam-4244	95	12	δ∞(k)u	δ∞(k)u	NOUN
ejpam-4244	95	13	=	=	PUNCT
ejpam-4244	95	14	δn(k)u,∀k	δn(k)u,∀k	PROPN
ejpam-4244	95	15	∈	∈	PROPN
ejpam-4244	95	16	kn,∀u	kn,∀u	PROPN
ejpam-4244	95	17	∈	∈	PROPN
ejpam-4244	95	18	eδn	eδn	VERB
ejpam-4244	95	19	.	.	PUNCT
ejpam-4244	96	1	δ∞	δ∞	PRON
ejpam-4244	96	2	is	be	AUX
ejpam-4244	96	3	the	the	DET
ejpam-4244	96	4	inductive	inductive	ADJ
ejpam-4244	96	5	limit	limit	NOUN
ejpam-4244	96	6	of	of	ADP
ejpam-4244	96	7	sequence	sequence	NOUN
ejpam-4244	96	8	of	of	ADP
ejpam-4244	96	9	representations	representation	NOUN
ejpam-4244	96	10	(	(	PUNCT
ejpam-4244	96	11	δn)n∈n∗	δn)n∈n∗	NOUN
ejpam-4244	96	12	.	.	PUNCT
ejpam-4244	97	1	(	(	PUNCT
ejpam-4244	97	2	g∞,k∞	g∞,k∞	PROPN
ejpam-4244	97	3	,	,	PUNCT
ejpam-4244	97	4	δ∞	δ∞	PROPN
ejpam-4244	97	5	)	)	PUNCT
ejpam-4244	97	6	will	will	AUX
ejpam-4244	97	7	be	be	AUX
ejpam-4244	97	8	called	call	VERB
ejpam-4244	97	9	the	the	DET
ejpam-4244	97	10	inductive	inductive	ADJ
ejpam-4244	97	11	limit	limit	NOUN
ejpam-4244	97	12	of	of	ADP
ejpam-4244	97	13	(	(	PUNCT
ejpam-4244	97	14	gn	gn	PROPN
ejpam-4244	97	15	,	,	PUNCT
ejpam-4244	97	16	kn	kn	PROPN
ejpam-4244	97	17	,	,	PUNCT
ejpam-4244	97	18	δn)n∈n∗	δn)n∈n∗	PROPN
ejpam-4244	97	19	.	.	PUNCT
ejpam-4244	98	1	in	in	ADP
ejpam-4244	98	2	what	what	PRON
ejpam-4244	98	3	follows	follow	VERB
ejpam-4244	98	4	,	,	PUNCT
ejpam-4244	98	5	we	we	PRON
ejpam-4244	98	6	assume	assume	VERB
ejpam-4244	98	7	that	that	SCONJ
ejpam-4244	98	8	(	(	PUNCT
ejpam-4244	98	9	gn	gn	PROPN
ejpam-4244	98	10	,	,	PUNCT
ejpam-4244	98	11	kn	kn	PROPN
ejpam-4244	98	12	,	,	PUNCT
ejpam-4244	98	13	δn	δn	PROPN
ejpam-4244	98	14	)	)	PUNCT
ejpam-4244	98	15	is	be	AUX
ejpam-4244	98	16	a	a	DET
ejpam-4244	98	17	commutative	commutative	ADJ
ejpam-4244	98	18	triple	triple	NOUN
ejpam-4244	98	19	for	for	ADP
ejpam-4244	98	20	each	each	DET
ejpam-4244	98	21	n	n	DET
ejpam-4244	98	22	∈	∈	PROPN
ejpam-4244	98	23	n∗.	n∗.	NOUN
ejpam-4244	98	24	we	we	PRON
ejpam-4244	98	25	recall	recall	VERB
ejpam-4244	98	26	the	the	DET
ejpam-4244	98	27	notion	notion	NOUN
ejpam-4244	98	28	of	of	ADP
ejpam-4244	98	29	approximation	approximation	NOUN
ejpam-4244	98	30	of	of	ADP
ejpam-4244	98	31	irreducible	irreducible	ADJ
ejpam-4244	98	32	representations	representation	NOUN
ejpam-4244	98	33	for	for	ADP
ejpam-4244	98	34	inductive	inductive	ADJ
ejpam-4244	98	35	limits	limit	NOUN
ejpam-4244	98	36	.	.	PUNCT
ejpam-4244	99	1	let	let	VERB
ejpam-4244	99	2	us	we	PRON
ejpam-4244	99	3	consider	consider	VERB
ejpam-4244	99	4	(	(	PUNCT
ejpam-4244	99	5	t	t	PROPN
ejpam-4244	99	6	,	,	PUNCT
ejpam-4244	99	7	h	h	NOUN
ejpam-4244	99	8	)	)	PUNCT
ejpam-4244	99	9	a	a	DET
ejpam-4244	99	10	unitary	unitary	ADJ
ejpam-4244	99	11	representation	representation	NOUN
ejpam-4244	99	12	of	of	ADP
ejpam-4244	99	13	g∞	g∞	PROPN
ejpam-4244	99	14	and	and	CCONJ
ejpam-4244	99	15	(	(	PUNCT
ejpam-4244	99	16	tn	tn	PROPN
ejpam-4244	99	17	,	,	PUNCT
ejpam-4244	99	18	hn	hn	PROPN
ejpam-4244	99	19	)	)	PUNCT
ejpam-4244	99	20	a	a	DET
ejpam-4244	99	21	sequence	sequence	NOUN
ejpam-4244	99	22	of	of	ADP
ejpam-4244	99	23	unitary	unitary	ADJ
ejpam-4244	99	24	representations	representation	NOUN
ejpam-4244	99	25	of	of	ADP
ejpam-4244	99	26	groups	group	NOUN
ejpam-4244	100	1	gn	gn	PROPN
ejpam-4244	100	2	.	.	PROPN
ejpam-4244	100	3	let	let	VERB
ejpam-4244	100	4	us	we	PRON
ejpam-4244	100	5	put	put	VERB
ejpam-4244	100	6	σ	σ	NOUN
ejpam-4244	100	7	=	=	PUNCT
ejpam-4244	100	8	{	{	PUNCT
ejpam-4244	100	9	ξ1	ξ1	NOUN
ejpam-4244	100	10	,	,	PUNCT
ejpam-4244	100	11	...	...	PUNCT
ejpam-4244	100	12	,	,	PUNCT
ejpam-4244	100	13	ξs	ξs	VERB
ejpam-4244	100	14	}	}	PUNCT
ejpam-4244	100	15	⊂	⊂	PROPN
ejpam-4244	100	16	h	h	NOUN
ejpam-4244	100	17	and	and	CCONJ
ejpam-4244	100	18	σn	σn	NOUN
ejpam-4244	100	19	=	=	SYM
ejpam-4244	100	20	{	{	PUNCT
ejpam-4244	100	21	ξ1n	ξ1n	ADJ
ejpam-4244	100	22	,	,	PUNCT
ejpam-4244	100	23	...	...	PUNCT
ejpam-4244	100	24	,	,	PUNCT
ejpam-4244	100	25	ξsn	ξsn	ADP
ejpam-4244	100	26	}	}	PUNCT
ejpam-4244	100	27	⊂	⊂	PROPN
ejpam-4244	100	28	hn	hn	PROPN
ejpam-4244	100	29	,	,	PUNCT
ejpam-4244	100	30	n	n	NOUN
ejpam-4244	100	31	=	=	SYM
ejpam-4244	100	32	1	1	NUM
ejpam-4244	100	33	,	,	PUNCT
ejpam-4244	100	34	2	2	NUM
ejpam-4244	100	35	,	,	PUNCT
ejpam-4244	100	36	...	...	PUNCT
ejpam-4244	101	1	we	we	PRON
ejpam-4244	101	2	shall	shall	AUX
ejpam-4244	101	3	write	write	VERB
ejpam-4244	101	4	(	(	PUNCT
ejpam-4244	101	5	tn	tn	PROPN
ejpam-4244	101	6	,	,	PUNCT
ejpam-4244	101	7	σn	σn	NOUN
ejpam-4244	101	8	)	)	PUNCT
ejpam-4244	101	9	−→	−→	NOUN
ejpam-4244	101	10	(	(	PUNCT
ejpam-4244	101	11	t	t	PROPN
ejpam-4244	101	12	,	,	PUNCT
ejpam-4244	101	13	σ	σ	PROPN
ejpam-4244	101	14	)	)	PUNCT
ejpam-4244	101	15	if	if	SCONJ
ejpam-4244	101	16	(	(	PUNCT
ejpam-4244	101	17	tn(g)ξin	tn(g)ξin	ADJ
ejpam-4244	101	18	,	,	PUNCT
ejpam-4244	101	19	ξjn	ξjn	ADJ
ejpam-4244	101	20	)	)	PUNCT
ejpam-4244	101	21	converges	converge	NOUN
ejpam-4244	101	22	to	to	ADP
ejpam-4244	101	23	(	(	PUNCT
ejpam-4244	101	24	t	t	PROPN
ejpam-4244	101	25	(	(	PUNCT
ejpam-4244	101	26	g)ξi	g)ξi	PROPN
ejpam-4244	101	27	,	,	PUNCT
ejpam-4244	101	28	ξj	ξj	NOUN
ejpam-4244	101	29	)	)	PUNCT
ejpam-4244	101	30	uniformly	uniformly	ADV
ejpam-4244	101	31	on	on	ADP
ejpam-4244	101	32	compact	compact	ADJ
ejpam-4244	101	33	sets	set	NOUN
ejpam-4244	101	34	in	in	ADP
ejpam-4244	101	35	g∞	g∞	PROPN
ejpam-4244	101	36	(	(	PUNCT
ejpam-4244	101	37	1	1	NUM
ejpam-4244	101	38	≤	≤	NUM
ejpam-4244	101	39	i	i	PRON
ejpam-4244	101	40	,	,	PUNCT
ejpam-4244	101	41	j	j	PROPN
ejpam-4244	101	42	≤	≤	PROPN
ejpam-4244	101	43	s	s	PROPN
ejpam-4244	101	44	,	,	PUNCT
ejpam-4244	101	45	g	g	PROPN
ejpam-4244	101	46	∈	∈	PROPN
ejpam-4244	101	47	g∞	g∞	PROPN
ejpam-4244	101	48	)	)	PUNCT
ejpam-4244	101	49	.(the	.(the	PROPN
ejpam-4244	101	50	reader	reader	NOUN
ejpam-4244	101	51	can	can	AUX
ejpam-4244	101	52	refer	refer	VERB
ejpam-4244	101	53	to	to	ADP
ejpam-4244	101	54	[	[	X
ejpam-4244	101	55	6	6	NUM
ejpam-4244	101	56	]	]	PUNCT
ejpam-4244	101	57	for	for	ADP
ejpam-4244	101	58	more	more	ADJ
ejpam-4244	101	59	details	detail	NOUN
ejpam-4244	101	60	)	)	PUNCT
ejpam-4244	102	1	we	we	PRON
ejpam-4244	102	2	say	say	VERB
ejpam-4244	102	3	that	that	SCONJ
ejpam-4244	102	4	the	the	DET
ejpam-4244	102	5	sequence	sequence	NOUN
ejpam-4244	102	6	(	(	PUNCT
ejpam-4244	102	7	tn	tn	NOUN
ejpam-4244	102	8	)	)	PUNCT
ejpam-4244	102	9	of	of	ADP
ejpam-4244	102	10	unitary	unitary	ADJ
ejpam-4244	102	11	representations	representation	NOUN
ejpam-4244	102	12	of	of	ADP
ejpam-4244	102	13	groups	group	NOUN
ejpam-4244	102	14	gn	gn	PROPN
ejpam-4244	102	15	approximates	approximate	VERB
ejpam-4244	102	16	the	the	DET
ejpam-4244	102	17	l.	l.	PROPN
ejpam-4244	102	18	timite	timite	PROPN
ejpam-4244	102	19	,	,	PUNCT
ejpam-4244	102	20	i.	i.	PROPN
ejpam-4244	102	21	toure	toure	PROPN
ejpam-4244	102	22	/	/	SYM
ejpam-4244	102	23	eur	eur	PROPN
ejpam-4244	102	24	.	.	PUNCT
ejpam-4244	103	1	j.	j.	PROPN
ejpam-4244	103	2	pure	pure	PROPN
ejpam-4244	103	3	appl	appl	PROPN
ejpam-4244	103	4	.	.	PROPN
ejpam-4244	103	5	math	math	PROPN
ejpam-4244	103	6	,	,	PUNCT
ejpam-4244	103	7	15	15	NUM
ejpam-4244	103	8	(	(	PUNCT
ejpam-4244	103	9	1	1	NUM
ejpam-4244	103	10	)	)	PUNCT
ejpam-4244	103	11	(	(	PUNCT
ejpam-4244	103	12	2022	2022	NUM
ejpam-4244	103	13	)	)	PUNCT
ejpam-4244	103	14	,	,	PUNCT
ejpam-4244	103	15	249	249	NUM
ejpam-4244	103	16	-	-	SYM
ejpam-4244	103	17	260	260	NUM
ejpam-4244	103	18	253	253	NUM
ejpam-4244	103	19	unitary	unitary	ADJ
ejpam-4244	103	20	representation	representation	NOUN
ejpam-4244	103	21	t	t	PROPN
ejpam-4244	103	22	of	of	ADP
ejpam-4244	103	23	group	group	NOUN
ejpam-4244	103	24	g∞	g∞	PROPN
ejpam-4244	103	25	if	if	SCONJ
ejpam-4244	103	26	for	for	ADP
ejpam-4244	103	27	any	any	DET
ejpam-4244	103	28	finite	finite	NOUN
ejpam-4244	103	29	subset	subset	NOUN
ejpam-4244	104	1	σ	σ	PROPN
ejpam-4244	104	2	⊂	⊂	PROPN
ejpam-4244	104	3	h	h	NOUN
ejpam-4244	104	4	,	,	PUNCT
ejpam-4244	104	5	it	it	PRON
ejpam-4244	104	6	is	be	AUX
ejpam-4244	104	7	possible	possible	ADJ
ejpam-4244	104	8	to	to	PART
ejpam-4244	104	9	select	select	VERB
ejpam-4244	104	10	finite	finite	ADJ
ejpam-4244	104	11	subsets	subset	NOUN
ejpam-4244	104	12	σn	σn	X
ejpam-4244	104	13	⊂	⊂	PROPN
ejpam-4244	104	14	hn	hn	PROPN
ejpam-4244	104	15	of	of	ADP
ejpam-4244	104	16	the	the	DET
ejpam-4244	104	17	same	same	ADJ
ejpam-4244	104	18	cardinalitiy	cardinalitiy	NOUN
ejpam-4244	104	19	such	such	ADJ
ejpam-4244	104	20	that	that	PRON
ejpam-4244	104	21	(	(	PUNCT
ejpam-4244	104	22	tn	tn	NOUN
ejpam-4244	104	23	,	,	PUNCT
ejpam-4244	104	24	σn	σn	NOUN
ejpam-4244	104	25	)	)	PUNCT
ejpam-4244	104	26	−→	−→	NOUN
ejpam-4244	104	27	(	(	PUNCT
ejpam-4244	104	28	t	t	PROPN
ejpam-4244	104	29	,	,	PUNCT
ejpam-4244	104	30	σ	σ	PROPN
ejpam-4244	104	31	)	)	PUNCT
ejpam-4244	104	32	.	.	PUNCT
ejpam-4244	105	1	we	we	PRON
ejpam-4244	105	2	know	know	VERB
ejpam-4244	105	3	by	by	ADP
ejpam-4244	105	4	(	(	PUNCT
ejpam-4244	105	5	[	[	X
ejpam-4244	105	6	6	6	NUM
ejpam-4244	105	7	]	]	PUNCT
ejpam-4244	105	8	,	,	PUNCT
ejpam-4244	105	9	theorem	theorem	VERB
ejpam-4244	105	10	22.9	22.9	NUM
ejpam-4244	105	11	,	,	PUNCT
ejpam-4244	105	12	page	page	NOUN
ejpam-4244	105	13	434	434	NUM
ejpam-4244	105	14	)	)	PUNCT
ejpam-4244	105	15	that	that	SCONJ
ejpam-4244	105	16	,	,	PUNCT
ejpam-4244	105	17	for	for	ADP
ejpam-4244	105	18	any	any	DET
ejpam-4244	105	19	irreducible	irreducible	ADJ
ejpam-4244	105	20	unitary	unitary	ADJ
ejpam-4244	105	21	representation	representation	NOUN
ejpam-4244	105	22	t	t	NOUN
ejpam-4244	105	23	of	of	ADP
ejpam-4244	105	24	the	the	DET
ejpam-4244	105	25	group	group	NOUN
ejpam-4244	105	26	g∞	g∞	PROPN
ejpam-4244	105	27	,	,	PUNCT
ejpam-4244	105	28	there	there	PRON
ejpam-4244	105	29	exists	exist	VERB
ejpam-4244	105	30	a	a	DET
ejpam-4244	105	31	sequence	sequence	NOUN
ejpam-4244	105	32	(	(	PUNCT
ejpam-4244	105	33	tn	tn	NOUN
ejpam-4244	105	34	)	)	PUNCT
ejpam-4244	105	35	of	of	ADP
ejpam-4244	105	36	irreducible	irreducible	ADJ
ejpam-4244	105	37	unitary	unitary	ADJ
ejpam-4244	105	38	representations	representation	NOUN
ejpam-4244	105	39	of	of	ADP
ejpam-4244	105	40	groups	group	NOUN
ejpam-4244	105	41	gn	gn	INTJ
ejpam-4244	105	42	approximating	approximate	VERB
ejpam-4244	105	43	t.	t.	NOUN
ejpam-4244	105	44	in	in	ADP
ejpam-4244	105	45	the	the	DET
ejpam-4244	105	46	following	following	NOUN
ejpam-4244	105	47	theorem	theorem	NOUN
ejpam-4244	105	48	,	,	PUNCT
ejpam-4244	105	49	we	we	PRON
ejpam-4244	105	50	prove	prove	VERB
ejpam-4244	105	51	that	that	SCONJ
ejpam-4244	105	52	(	(	PUNCT
ejpam-4244	105	53	g∞,k∞	g∞,k∞	PROPN
ejpam-4244	105	54	,	,	PUNCT
ejpam-4244	105	55	δ∞	δ∞	PROPN
ejpam-4244	105	56	)	)	PUNCT
ejpam-4244	105	57	is	be	AUX
ejpam-4244	105	58	a	a	DET
ejpam-4244	105	59	spherical	spherical	ADJ
ejpam-4244	105	60	triple	triple	NOUN
ejpam-4244	105	61	and	and	CCONJ
ejpam-4244	105	62	we	we	PRON
ejpam-4244	105	63	characterize	characterize	VERB
ejpam-4244	105	64	δ∞-spherical	δ∞-spherical	ADJ
ejpam-4244	105	65	functions	function	NOUN
ejpam-4244	105	66	for	for	ADP
ejpam-4244	105	67	(	(	PUNCT
ejpam-4244	105	68	g∞,k∞	g∞,k∞	PROPN
ejpam-4244	105	69	,	,	PUNCT
ejpam-4244	105	70	δ∞	δ∞	PROPN
ejpam-4244	105	71	)	)	PUNCT
ejpam-4244	105	72	.	.	PUNCT
ejpam-4244	106	1	theorem	theorem	NOUN
ejpam-4244	106	2	2	2	NUM
ejpam-4244	106	3	.	.	X
ejpam-4244	107	1	i	i	PRON
ejpam-4244	107	2	)	)	PUNCT
ejpam-4244	107	3	the	the	DET
ejpam-4244	107	4	inductive	inductive	ADJ
ejpam-4244	107	5	limit	limit	NOUN
ejpam-4244	107	6	(	(	PUNCT
ejpam-4244	107	7	g∞,k∞	g∞,k∞	PROPN
ejpam-4244	107	8	,	,	PUNCT
ejpam-4244	107	9	δ∞	δ∞	PROPN
ejpam-4244	107	10	)	)	PUNCT
ejpam-4244	107	11	of	of	ADP
ejpam-4244	107	12	an	an	DET
ejpam-4244	107	13	increasing	increase	VERB
ejpam-4244	107	14	sequence	sequence	NOUN
ejpam-4244	107	15	of	of	ADP
ejpam-4244	107	16	commutative	commutative	ADJ
ejpam-4244	107	17	triples	triple	NOUN
ejpam-4244	107	18	(	(	PUNCT
ejpam-4244	107	19	gn	gn	PROPN
ejpam-4244	107	20	,	,	PUNCT
ejpam-4244	107	21	kn	kn	PROPN
ejpam-4244	107	22	,	,	PUNCT
ejpam-4244	107	23	δn	δn	PROPN
ejpam-4244	107	24	)	)	PUNCT
ejpam-4244	107	25	is	be	AUX
ejpam-4244	107	26	a	a	DET
ejpam-4244	107	27	spherical	spherical	ADJ
ejpam-4244	107	28	triple	triple	NOUN
ejpam-4244	107	29	.	.	PUNCT
ejpam-4244	108	1	ii	ii	X
ejpam-4244	108	2	)	)	PUNCT
ejpam-4244	108	3	a	a	DET
ejpam-4244	108	4	δ∞-radial	δ∞-radial	ADJ
ejpam-4244	108	5	unitary	unitary	ADJ
ejpam-4244	108	6	function	function	NOUN
ejpam-4244	108	7	of	of	ADP
ejpam-4244	108	8	positive	positive	ADJ
ejpam-4244	108	9	type	type	NOUN
ejpam-4244	108	10	φ	φ	NOUN
ejpam-4244	108	11	:	:	PUNCT
ejpam-4244	108	12	g∞	g∞	PROPN
ejpam-4244	108	13	−→	−→	NOUN
ejpam-4244	108	14	end(eδ∞	end(eδ∞	PROPN
ejpam-4244	108	15	)	)	PUNCT
ejpam-4244	108	16	is	be	AUX
ejpam-4244	108	17	δ∞-spherical	δ∞-spherical	ADJ
ejpam-4244	108	18	if	if	SCONJ
ejpam-4244	108	19	and	and	CCONJ
ejpam-4244	108	20	only	only	ADV
ejpam-4244	108	21	if	if	SCONJ
ejpam-4244	108	22	φ(e	φ(e	NUM
ejpam-4244	108	23	)	)	PUNCT
ejpam-4244	108	24	=	=	SYM
ejpam-4244	108	25	i∞	i∞	NOUN
ejpam-4244	108	26	and	and	CCONJ
ejpam-4244	108	27	∀x	∀x	NUM
ejpam-4244	108	28	,	,	PUNCT
ejpam-4244	108	29	y	y	PROPN
ejpam-4244	108	30	∈	∈	PROPN
ejpam-4244	108	31	g∞,φ(y)φ(x	g∞,φ(y)φ(x	PROPN
ejpam-4244	108	32	)	)	PUNCT
ejpam-4244	109	1	=	=	PROPN
ejpam-4244	109	2	lim	lim	PROPN
ejpam-4244	109	3	n→∞	n→∞	NUM
ejpam-4244	110	1	∫	∫	PROPN
ejpam-4244	110	2	kn	kn	PROPN
ejpam-4244	110	3	χδn(k)φ(xky)dαn(k	χδn(k)φ(xky)dαn(k	PROPN
ejpam-4244	110	4	)	)	PUNCT
ejpam-4244	110	5	,	,	PUNCT
ejpam-4244	110	6	where	where	SCONJ
ejpam-4244	110	7	i∞	i∞	NOUN
ejpam-4244	110	8	is	be	AUX
ejpam-4244	110	9	the	the	DET
ejpam-4244	110	10	identity	identity	NOUN
ejpam-4244	110	11	operator	operator	NOUN
ejpam-4244	110	12	of	of	ADP
ejpam-4244	110	13	eδ∞	eδ∞	PROPN
ejpam-4244	110	14	.	.	PUNCT
ejpam-4244	111	1	the	the	DET
ejpam-4244	111	2	following	follow	VERB
ejpam-4244	111	3	lemmas	lemma	NOUN
ejpam-4244	111	4	are	be	AUX
ejpam-4244	111	5	useful	useful	ADJ
ejpam-4244	111	6	to	to	PART
ejpam-4244	111	7	prove	prove	VERB
ejpam-4244	111	8	this	this	DET
ejpam-4244	111	9	theorem	theorem	NOUN
ejpam-4244	111	10	.	.	PUNCT
ejpam-4244	112	1	lemma	lemma	PROPN
ejpam-4244	112	2	1	1	X
ejpam-4244	112	3	.	.	PUNCT
ejpam-4244	113	1	let	let	VERB
ejpam-4244	113	2	(	(	PUNCT
ejpam-4244	113	3	hn	hn	NOUN
ejpam-4244	113	4	)	)	PUNCT
ejpam-4244	113	5	be	be	AUX
ejpam-4244	113	6	an	an	DET
ejpam-4244	113	7	increasing	increase	VERB
ejpam-4244	113	8	sequence	sequence	NOUN
ejpam-4244	113	9	of	of	ADP
ejpam-4244	113	10	subspaces	subspace	NOUN
ejpam-4244	113	11	of	of	ADP
ejpam-4244	113	12	a	a	DET
ejpam-4244	113	13	hilbert	hilbert	NOUN
ejpam-4244	113	14	space	space	NOUN
ejpam-4244	113	15	h.	h.	NOUN
ejpam-4244	113	16	we	we	PRON
ejpam-4244	113	17	put	put	VERB
ejpam-4244	113	18	:	:	PUNCT
ejpam-4244	113	19	h∞	h∞	X
ejpam-4244	113	20	=	=	SYM
ejpam-4244	113	21	⋃	⋃	ADP
ejpam-4244	113	22	n≥1	n≥1	NOUN
ejpam-4244	113	23	hn	hn	PROPN
ejpam-4244	113	24	the	the	DET
ejpam-4244	113	25	hilbert	hilbert	PROPN
ejpam-4244	113	26	completion	completion	NOUN
ejpam-4244	113	27	of	of	ADP
ejpam-4244	113	28	⋃	⋃	PROPN
ejpam-4244	113	29	n≥1hn	n≥1hn	PROPN
ejpam-4244	113	30	and	and	CCONJ
ejpam-4244	113	31	p	p	NOUN
ejpam-4244	113	32	:	:	PUNCT
ejpam-4244	114	1	h	h	NOUN
ejpam-4244	114	2	−→	−→	NOUN
ejpam-4244	114	3	h∞	h∞	PUNCT
ejpam-4244	115	1	the	the	DET
ejpam-4244	115	2	projection	projection	NOUN
ejpam-4244	115	3	of	of	ADP
ejpam-4244	115	4	h	h	NOUN
ejpam-4244	115	5	onto	onto	ADP
ejpam-4244	115	6	h∞.	h∞.	PRON
ejpam-4244	115	7	for	for	ADP
ejpam-4244	115	8	any	any	DET
ejpam-4244	115	9	n	n	CCONJ
ejpam-4244	115	10	,	,	PUNCT
ejpam-4244	115	11	we	we	PRON
ejpam-4244	115	12	denote	denote	VERB
ejpam-4244	115	13	by	by	ADP
ejpam-4244	115	14	pn	pn	PROPN
ejpam-4244	115	15	:	:	PUNCT
ejpam-4244	115	16	h	h	PROPN
ejpam-4244	116	1	−→	−→	ADV
ejpam-4244	116	2	hn	hn	PRON
ejpam-4244	116	3	the	the	DET
ejpam-4244	116	4	projection	projection	NOUN
ejpam-4244	116	5	of	of	ADP
ejpam-4244	116	6	h	h	NOUN
ejpam-4244	116	7	onto	onto	ADP
ejpam-4244	116	8	hn	hn	PROPN
ejpam-4244	116	9	.	.	PUNCT
ejpam-4244	117	1	then	then	ADV
ejpam-4244	117	2	pn	pn	PROPN
ejpam-4244	117	3	strongly	strongly	ADV
ejpam-4244	117	4	converges	converge	VERB
ejpam-4244	117	5	to	to	ADP
ejpam-4244	117	6	p.	p.	NOUN
ejpam-4244	117	7	proof	proof	NOUN
ejpam-4244	117	8	.	.	PUNCT
ejpam-4244	118	1	let	let	VERB
ejpam-4244	118	2	v	v	NUM
ejpam-4244	118	3	∈	∈	PROPN
ejpam-4244	118	4	h	h	NOUN
ejpam-4244	118	5	,	,	PUNCT
ejpam-4244	118	6	then	then	ADV
ejpam-4244	118	7	pv	pv	INTJ
ejpam-4244	118	8	∈	∈	PROPN
ejpam-4244	118	9	h∞.	h∞.	INTJ
ejpam-4244	118	10	since	since	SCONJ
ejpam-4244	118	11	⋃∞	⋃∞	SYM
ejpam-4244	118	12	n=1hn	n=1hn	PRON
ejpam-4244	118	13	is	be	AUX
ejpam-4244	118	14	dense	dense	ADJ
ejpam-4244	118	15	in	in	ADP
ejpam-4244	118	16	h∞	h∞	PROPN
ejpam-4244	118	17	,	,	PUNCT
ejpam-4244	118	18	there	there	PRON
ejpam-4244	118	19	exists	exist	VERB
ejpam-4244	118	20	a	a	DET
ejpam-4244	118	21	sequence	sequence	NOUN
ejpam-4244	118	22	(	(	PUNCT
ejpam-4244	118	23	vm)m	vm)m	PROPN
ejpam-4244	118	24	⊂	⊂	PROPN
ejpam-4244	118	25	⋃∞	⋃∞	X
ejpam-4244	118	26	n=1hn	n=1hn	PRON
ejpam-4244	118	27	such	such	ADJ
ejpam-4244	118	28	that	that	SCONJ
ejpam-4244	118	29	limm→+∞	limm→+∞	VERB
ejpam-4244	118	30	||vm	||vm	PROPN
ejpam-4244	118	31	−	−	PROPN
ejpam-4244	118	32	pv||h	pv||h	NOUN
ejpam-4244	118	33	=	=	NOUN
ejpam-4244	118	34	0	0	X
ejpam-4244	118	35	.	.	PUNCT
ejpam-4244	119	1	since	since	SCONJ
ejpam-4244	119	2	(	(	PUNCT
ejpam-4244	119	3	hn	hn	PROPN
ejpam-4244	119	4	)	)	PUNCT
ejpam-4244	119	5	is	be	AUX
ejpam-4244	119	6	an	an	DET
ejpam-4244	119	7	increasing	increase	VERB
ejpam-4244	119	8	sequence	sequence	NOUN
ejpam-4244	119	9	then	then	ADV
ejpam-4244	119	10	for	for	ADP
ejpam-4244	119	11	any	any	DET
ejpam-4244	119	12	m	m	PROPN
ejpam-4244	119	13	∈	∈	PROPN
ejpam-4244	119	14	n∗	n∗	NOUN
ejpam-4244	119	15	,	,	PUNCT
ejpam-4244	119	16	there	there	PRON
ejpam-4244	119	17	exists	exist	VERB
ejpam-4244	119	18	nm	nm	ADP
ejpam-4244	119	19	∈	∈	PROPN
ejpam-4244	119	20	n∗	n∗	VERB
ejpam-4244	119	21	such	such	ADJ
ejpam-4244	119	22	that	that	SCONJ
ejpam-4244	119	23	∀n	∀n	NUM
ejpam-4244	119	24	≥	≥	NOUN
ejpam-4244	119	25	nm	nm	PROPN
ejpam-4244	119	26	,	,	PUNCT
ejpam-4244	119	27	vm	vm	PROPN
ejpam-4244	119	28	∈	∈	PROPN
ejpam-4244	120	1	hn	hn	INTJ
ejpam-4244	120	2	.	.	PUNCT
ejpam-4244	120	3	let	let	VERB
ejpam-4244	120	4	us	we	PRON
ejpam-4244	120	5	fix	fix	VERB
ejpam-4244	120	6	n	n	PRON
ejpam-4244	120	7	such	such	ADJ
ejpam-4244	120	8	that	that	SCONJ
ejpam-4244	120	9	nm	nm	ADJ
ejpam-4244	120	10	≤	≤	NUM
ejpam-4244	120	11	n	n	PRON
ejpam-4244	120	12	≤	≤	NOUN
ejpam-4244	120	13	m.	m.	NOUN
ejpam-4244	120	14	since	since	SCONJ
ejpam-4244	120	15	vm	vm	PROPN
ejpam-4244	120	16	∈	∈	PROPN
ejpam-4244	120	17	hn	hn	PROPN
ejpam-4244	120	18	,	,	PUNCT
ejpam-4244	120	19	we	we	PRON
ejpam-4244	120	20	have	have	VERB
ejpam-4244	120	21	:	:	PUNCT
ejpam-4244	120	22	pnvm	pnvm	PROPN
ejpam-4244	120	23	=	=	SYM
ejpam-4244	120	24	vm	vm	PROPN
ejpam-4244	120	25	.	.	PROPN
ejpam-4244	121	1	hence	hence	ADV
ejpam-4244	121	2	||pnpv	||pnpv	PROPN
ejpam-4244	121	3	−	−	PROPN
ejpam-4244	121	4	pv||h	pv||h	PROPN
ejpam-4244	121	5	=	=	PUNCT
ejpam-4244	121	6	||pnpv	||pnpv	PROPN
ejpam-4244	121	7	−	−	PROPN
ejpam-4244	121	8	pnvm	pnvm	PROPN
ejpam-4244	121	9	+	+	CCONJ
ejpam-4244	121	10	vm	vm	NOUN
ejpam-4244	121	11	−	−	PROPN
ejpam-4244	121	12	pv||h	pv||h	PROPN
ejpam-4244	121	13	≤	≤	PUNCT
ejpam-4244	121	14	||pnpv	||pnpv	PROPN
ejpam-4244	121	15	−	−	PROPN
ejpam-4244	121	16	pnvm||h	pnvm||h	ADJ
ejpam-4244	121	17	+	+	CCONJ
ejpam-4244	121	18	||vm	||vm	PROPN
ejpam-4244	121	19	−	−	NOUN
ejpam-4244	121	20	pv||h	pv||h	NOUN
ejpam-4244	121	21	≤	≤	NOUN
ejpam-4244	121	22	(	(	PUNCT
ejpam-4244	121	23	||pn||+	||pn||+	PROPN
ejpam-4244	121	24	1)||pv	1)||pv	NUM
ejpam-4244	121	25	−	−	NOUN
ejpam-4244	121	26	vm||h	vm||h	NOUN
ejpam-4244	121	27	=	=	NOUN
ejpam-4244	121	28	2||pv	2||pv	PROPN
ejpam-4244	121	29	−	−	PROPN
ejpam-4244	121	30	vm||h	vm||h	NOUN
ejpam-4244	121	31	.	.	PUNCT
ejpam-4244	122	1	if	if	SCONJ
ejpam-4244	122	2	n	n	PRON
ejpam-4244	122	3	−→	−→	VERB
ejpam-4244	122	4	+	+	NOUN
ejpam-4244	122	5	∞	∞	PROPN
ejpam-4244	122	6	then	then	ADV
ejpam-4244	122	7	m	m	VERB
ejpam-4244	122	8	−→	−→	ADJ
ejpam-4244	122	9	+	+	SYM
ejpam-4244	122	10	∞.	∞.	PROPN
ejpam-4244	122	11	since	since	SCONJ
ejpam-4244	122	12	limm→+∞	limm→+∞	PROPN
ejpam-4244	122	13	||vm	||vm	PROPN
ejpam-4244	122	14	−	−	PROPN
ejpam-4244	122	15	pv||h	pv||h	NOUN
ejpam-4244	123	1	=	=	NOUN
ejpam-4244	123	2	0	0	NUM
ejpam-4244	123	3	then	then	ADV
ejpam-4244	123	4	limn→+∞	limn→+∞	VERB
ejpam-4244	123	5	||pnpv	||pnpv	PROPN
ejpam-4244	123	6	−	−	PROPN
ejpam-4244	123	7	pv||h	pv||h	PROPN
ejpam-4244	123	8	=	=	NOUN
ejpam-4244	123	9	0	0	X
ejpam-4244	123	10	.	.	PUNCT
ejpam-4244	124	1	hence	hence	ADV
ejpam-4244	124	2	pnp	pnp	PROPN
ejpam-4244	124	3	converges	converge	VERB
ejpam-4244	124	4	strongly	strongly	ADV
ejpam-4244	124	5	to	to	ADP
ejpam-4244	124	6	p.	p.	NOUN
ejpam-4244	124	7	consequently	consequently	ADV
ejpam-4244	124	8	pn	pn	PROPN
ejpam-4244	124	9	converges	converge	VERB
ejpam-4244	124	10	strongly	strongly	ADV
ejpam-4244	124	11	to	to	ADP
ejpam-4244	124	12	p	p	NOUN
ejpam-4244	124	13	because	because	SCONJ
ejpam-4244	124	14	for	for	ADP
ejpam-4244	124	15	any	any	DET
ejpam-4244	124	16	n	n	PRON
ejpam-4244	124	17	≥	≥	NOUN
ejpam-4244	124	18	1	1	NUM
ejpam-4244	124	19	,	,	PUNCT
ejpam-4244	124	20	pnp	pnp	PROPN
ejpam-4244	124	21	=	=	SYM
ejpam-4244	124	22	pn	pn	PROPN
ejpam-4244	124	23	.	.	PROPN
ejpam-4244	124	24	l.	l.	PROPN
ejpam-4244	124	25	timite	timite	PROPN
ejpam-4244	124	26	,	,	PUNCT
ejpam-4244	124	27	i.	i.	PROPN
ejpam-4244	124	28	toure	toure	PROPN
ejpam-4244	124	29	/	/	SYM
ejpam-4244	124	30	eur	eur	PROPN
ejpam-4244	124	31	.	.	PUNCT
ejpam-4244	125	1	j.	j.	PROPN
ejpam-4244	125	2	pure	pure	PROPN
ejpam-4244	125	3	appl	appl	PROPN
ejpam-4244	125	4	.	.	PROPN
ejpam-4244	125	5	math	math	PROPN
ejpam-4244	125	6	,	,	PUNCT
ejpam-4244	125	7	15	15	NUM
ejpam-4244	125	8	(	(	PUNCT
ejpam-4244	125	9	1	1	NUM
ejpam-4244	125	10	)	)	PUNCT
ejpam-4244	125	11	(	(	PUNCT
ejpam-4244	125	12	2022	2022	NUM
ejpam-4244	125	13	)	)	PUNCT
ejpam-4244	125	14	,	,	PUNCT
ejpam-4244	125	15	249	249	NUM
ejpam-4244	125	16	-	-	SYM
ejpam-4244	125	17	260	260	NUM
ejpam-4244	125	18	254	254	NUM
ejpam-4244	125	19	lemma	lemma	PROPN
ejpam-4244	125	20	2	2	NUM
ejpam-4244	125	21	.	.	PUNCT
ejpam-4244	126	1	let	let	VERB
ejpam-4244	126	2	φ	φ	NOUN
ejpam-4244	126	3	:	:	PUNCT
ejpam-4244	126	4	g∞	g∞	PROPN
ejpam-4244	126	5	−→	−→	NOUN
ejpam-4244	126	6	end(eδ∞	end(eδ∞	PROPN
ejpam-4244	126	7	)	)	PUNCT
ejpam-4244	126	8	be	be	VERB
ejpam-4244	126	9	a	a	DET
ejpam-4244	126	10	function	function	NOUN
ejpam-4244	126	11	verifying	verify	VERB
ejpam-4244	126	12	φ(e	φ(e	NUM
ejpam-4244	126	13	)	)	PUNCT
ejpam-4244	126	14	=	=	SYM
ejpam-4244	126	15	i∞	i∞	NOUN
ejpam-4244	126	16	and	and	CCONJ
ejpam-4244	126	17	∀x	∀x	NUM
ejpam-4244	126	18	,	,	PUNCT
ejpam-4244	126	19	y	y	PROPN
ejpam-4244	126	20	∈	∈	PROPN
ejpam-4244	126	21	g∞,φ(y)φ(x	g∞,φ(y)φ(x	PROPN
ejpam-4244	126	22	)	)	PUNCT
ejpam-4244	127	1	=	=	PROPN
ejpam-4244	127	2	lim	lim	PROPN
ejpam-4244	127	3	n→∞	n→∞	NUM
ejpam-4244	128	1	∫	∫	PROPN
ejpam-4244	128	2	kn	kn	PROPN
ejpam-4244	128	3	χδn(k)φ(xky)dαn(k	χδn(k)φ(xky)dαn(k	PROPN
ejpam-4244	128	4	)	)	PUNCT
ejpam-4244	128	5	.	.	PUNCT
ejpam-4244	129	1	then	then	ADV
ejpam-4244	129	2	i	i	PRON
ejpam-4244	129	3	)	)	PUNCT
ejpam-4244	129	4	i∞	i∞	NOUN
ejpam-4244	130	1	=	=	PUNCT
ejpam-4244	130	2	limn→∞	limn→∞	PROPN
ejpam-4244	130	3	∫	∫	PROPN
ejpam-4244	130	4	kn	kn	PROPN
ejpam-4244	130	5	χδn(k)φ(k)dαn(k	χδn(k)φ(k)dαn(k	PROPN
ejpam-4244	130	6	)	)	PUNCT
ejpam-4244	130	7	,	,	PUNCT
ejpam-4244	130	8	where	where	SCONJ
ejpam-4244	130	9	i∞	i∞	NOUN
ejpam-4244	130	10	is	be	AUX
ejpam-4244	130	11	the	the	DET
ejpam-4244	130	12	operator	operator	NOUN
ejpam-4244	130	13	identity	identity	NOUN
ejpam-4244	130	14	of	of	ADP
ejpam-4244	130	15	eδ∞	eδ∞	PROPN
ejpam-4244	130	16	.	.	PUNCT
ejpam-4244	131	1	ii	ii	X
ejpam-4244	131	2	)	)	PUNCT
ejpam-4244	131	3	∀x	∀x	VERB
ejpam-4244	131	4	∈	∈	PROPN
ejpam-4244	131	5	g∞	g∞	NOUN
ejpam-4244	131	6	,	,	PUNCT
ejpam-4244	131	7	φ(x	φ(x	NOUN
ejpam-4244	131	8	)	)	PUNCT
ejpam-4244	131	9	=	=	VERB
ejpam-4244	132	1	lim	lim	PROPN
ejpam-4244	132	2	n→∞	n→∞	NUM
ejpam-4244	133	1	∫	∫	PROPN
ejpam-4244	133	2	kn	kn	PROPN
ejpam-4244	133	3	χδn(k)φ(kx)dαn(k	χδn(k)φ(kx)dαn(k	PROPN
ejpam-4244	133	4	)	)	PUNCT
ejpam-4244	134	1	=	=	PROPN
ejpam-4244	134	2	lim	lim	PROPN
ejpam-4244	134	3	n→∞	n→∞	NUM
ejpam-4244	135	1	∫	∫	PROPN
ejpam-4244	135	2	kn	kn	PROPN
ejpam-4244	135	3	χδn(k)φ(xk)dαn(k	χδn(k)φ(xk)dαn(k	PROPN
ejpam-4244	135	4	)	)	PUNCT
ejpam-4244	135	5	iii	iii	PROPN
ejpam-4244	135	6	)	)	PUNCT
ejpam-4244	135	7	∀x	∀x	VERB
ejpam-4244	135	8	∈	∈	PROPN
ejpam-4244	135	9	g∞	g∞	PROPN
ejpam-4244	135	10	,	,	PUNCT
ejpam-4244	135	11	∀k	∀k	NOUN
ejpam-4244	135	12	∈	∈	PROPN
ejpam-4244	135	13	k∞	k∞	PROPN
ejpam-4244	135	14	,	,	PUNCT
ejpam-4244	135	15	φ(xk	φ(xk	NUM
ejpam-4244	135	16	)	)	PUNCT
ejpam-4244	135	17	=	=	PRON
ejpam-4244	135	18	φ(k)φ(x)and	φ(k)φ(x)and	X
ejpam-4244	135	19	φ(kx	φ(kx	PROPN
ejpam-4244	135	20	)	)	PUNCT
ejpam-4244	135	21	=	=	SYM
ejpam-4244	135	22	φ(x)φ(k	φ(x)φ(k	NOUN
ejpam-4244	135	23	)	)	PUNCT
ejpam-4244	135	24	.	.	PUNCT
ejpam-4244	136	1	proof	proof	NOUN
ejpam-4244	136	2	.	.	PUNCT
ejpam-4244	137	1	i	i	PRON
ejpam-4244	137	2	)	)	PUNCT
ejpam-4244	137	3	i∞	i∞	NOUN
ejpam-4244	138	1	=	=	NOUN
ejpam-4244	138	2	φ(e)φ(e	φ(e)φ(e	NOUN
ejpam-4244	138	3	)	)	PUNCT
ejpam-4244	138	4	=	=	SYM
ejpam-4244	139	1	limn→∞	limn→∞	PROPN
ejpam-4244	139	2	∫	∫	PROPN
ejpam-4244	139	3	kn	kn	PROPN
ejpam-4244	139	4	χδn(k)φ(k)dαn(k	χδn(k)φ(k)dαn(k	PROPN
ejpam-4244	139	5	)	)	PUNCT
ejpam-4244	139	6	ii	ii	PROPN
ejpam-4244	139	7	)	)	PUNCT
ejpam-4244	140	1	∀x	∀x	VERB
ejpam-4244	140	2	∈	∈	PROPN
ejpam-4244	140	3	g∞	g∞	PROPN
ejpam-4244	140	4	,	,	PUNCT
ejpam-4244	140	5	we	we	PRON
ejpam-4244	140	6	have	have	AUX
ejpam-4244	140	7	:	:	PUNCT
ejpam-4244	140	8	φ(x	φ(x	VERB
ejpam-4244	140	9	)	)	PUNCT
ejpam-4244	140	10	=	=	SYM
ejpam-4244	140	11	φ(e)φ(x	φ(e)φ(x	X
ejpam-4244	140	12	)	)	PUNCT
ejpam-4244	140	13	=	=	VERB
ejpam-4244	140	14	lim	lim	PROPN
ejpam-4244	140	15	n→∞	n→∞	NUM
ejpam-4244	141	1	∫	∫	PROPN
ejpam-4244	141	2	kn	kn	PROPN
ejpam-4244	141	3	χδn(k)φ(xk)dαn(k	χδn(k)φ(xk)dαn(k	PROPN
ejpam-4244	141	4	)	)	PUNCT
ejpam-4244	141	5	.	.	PUNCT
ejpam-4244	142	1	in	in	ADP
ejpam-4244	142	2	the	the	DET
ejpam-4244	142	3	same	same	ADJ
ejpam-4244	142	4	way	way	NOUN
ejpam-4244	142	5	∀x	∀x	X
ejpam-4244	142	6	∈	∈	PROPN
ejpam-4244	142	7	g∞,φ(x	g∞,φ(x	NOUN
ejpam-4244	142	8	)	)	PUNCT
ejpam-4244	143	1	=	=	PUNCT
ejpam-4244	143	2	φ(x)φ(e	φ(x)φ(e	NOUN
ejpam-4244	143	3	)	)	PUNCT
ejpam-4244	144	1	=	=	VERB
ejpam-4244	144	2	lim	lim	PROPN
ejpam-4244	144	3	n→∞	n→∞	NUM
ejpam-4244	145	1	∫	∫	PROPN
ejpam-4244	145	2	kn	kn	PROPN
ejpam-4244	145	3	χδn(k)φ(kx)dαn(k	χδn(k)φ(kx)dαn(k	PROPN
ejpam-4244	145	4	)	)	PUNCT
ejpam-4244	145	5	.	.	PUNCT
ejpam-4244	146	1	iii	iii	X
ejpam-4244	146	2	)	)	PUNCT
ejpam-4244	146	3	∀k	∀k	NOUN
ejpam-4244	146	4	,	,	PUNCT
ejpam-4244	146	5	k′	k′	PROPN
ejpam-4244	146	6	∈	∈	PROPN
ejpam-4244	146	7	kn	kn	PROPN
ejpam-4244	146	8	,	,	PUNCT
ejpam-4244	146	9	χδn(kk	χδn(kk	VERB
ejpam-4244	146	10	′	′	NUM
ejpam-4244	146	11	)	)	PUNCT
ejpam-4244	147	1	=	=	SYM
ejpam-4244	147	2	χδn(k	χδn(k	NOUN
ejpam-4244	147	3	′k	′k	NOUN
ejpam-4244	147	4	)	)	PUNCT
ejpam-4244	147	5	.	.	PUNCT
ejpam-4244	148	1	consequently	consequently	ADV
ejpam-4244	148	2	∀x	∀x	X
ejpam-4244	148	3	∈	∈	PROPN
ejpam-4244	148	4	g∞	g∞	NOUN
ejpam-4244	148	5	and	and	CCONJ
ejpam-4244	148	6	∀k	∀k	NOUN
ejpam-4244	148	7	∈	∈	PROPN
ejpam-4244	148	8	k∞	k∞	PROPN
ejpam-4244	148	9	,	,	PUNCT
ejpam-4244	148	10	we	we	PRON
ejpam-4244	148	11	have	have	VERB
ejpam-4244	148	12	:	:	PUNCT
ejpam-4244	148	13	φ(kx	φ(kx	NUM
ejpam-4244	148	14	)	)	PUNCT
ejpam-4244	148	15	=	=	SYM
ejpam-4244	148	16	φ(kx)φ(e	φ(kx)φ(e	ADJ
ejpam-4244	148	17	)	)	PUNCT
ejpam-4244	149	1	=	=	SYM
ejpam-4244	149	2	lim	lim	PROPN
ejpam-4244	149	3	n→∞	n→∞	NUM
ejpam-4244	150	1	∫	∫	PROPN
ejpam-4244	150	2	kn	kn	PROPN
ejpam-4244	150	3	χδn(k1)φ(k1kx)dαn(k1	χδn(k1)φ(k1kx)dαn(k1	PROPN
ejpam-4244	150	4	)	)	PUNCT
ejpam-4244	151	1	=	=	PROPN
ejpam-4244	151	2	lim	lim	PROPN
ejpam-4244	151	3	n→∞	n→∞	NUM
ejpam-4244	152	1	∫	∫	PROPN
ejpam-4244	152	2	kn	kn	PROPN
ejpam-4244	152	3	χδn(k1k	χδn(k1k	PROPN
ejpam-4244	152	4	−1)φ(k1x)dαn(k1	−1)φ(k1x)dαn(k1	PROPN
ejpam-4244	152	5	)	)	PUNCT
ejpam-4244	153	1	=	=	VERB
ejpam-4244	153	2	lim	lim	PROPN
ejpam-4244	153	3	n→∞	n→∞	NUM
ejpam-4244	154	1	∫	∫	PROPN
ejpam-4244	154	2	kn	kn	PROPN
ejpam-4244	154	3	χδn(k	χδn(k	PROPN
ejpam-4244	154	4	−1k1)φ(k1x)dαn(k1	−1k1)φ(k1x)dαn(k1	PROPN
ejpam-4244	154	5	)	)	PUNCT
ejpam-4244	155	1	=	=	VERB
ejpam-4244	155	2	lim	lim	PROPN
ejpam-4244	155	3	n→∞	n→∞	NUM
ejpam-4244	156	1	∫	∫	PROPN
ejpam-4244	156	2	kn	kn	PROPN
ejpam-4244	156	3	χδn(k1)φ(kk1x)dαn(k1	χδn(k1)φ(kk1x)dαn(k1	PROPN
ejpam-4244	156	4	)	)	PUNCT
ejpam-4244	157	1	=	=	SYM
ejpam-4244	157	2	φ(x)φ(k	φ(x)φ(k	NOUN
ejpam-4244	157	3	)	)	PUNCT
ejpam-4244	157	4	φ(xk	φ(xk	NUM
ejpam-4244	157	5	)	)	PUNCT
ejpam-4244	157	6	=	=	SYM
ejpam-4244	157	7	φ(e)φ(xk	φ(e)φ(xk	ADJ
ejpam-4244	157	8	)	)	PUNCT
ejpam-4244	157	9	=	=	VERB
ejpam-4244	157	10	lim	lim	PROPN
ejpam-4244	157	11	n→∞	n→∞	NUM
ejpam-4244	158	1	∫	∫	PROPN
ejpam-4244	158	2	kn	kn	PROPN
ejpam-4244	158	3	χδn(k1)φ(xkk1)dαn(k1	χδn(k1)φ(xkk1)dαn(k1	PROPN
ejpam-4244	158	4	)	)	PUNCT
ejpam-4244	158	5	l.	l.	PROPN
ejpam-4244	158	6	timite	timite	PROPN
ejpam-4244	158	7	,	,	PUNCT
ejpam-4244	158	8	i.	i.	PROPN
ejpam-4244	158	9	toure	toure	PROPN
ejpam-4244	158	10	/	/	SYM
ejpam-4244	158	11	eur	eur	PROPN
ejpam-4244	158	12	.	.	PUNCT
ejpam-4244	159	1	j.	j.	PROPN
ejpam-4244	159	2	pure	pure	PROPN
ejpam-4244	159	3	appl	appl	PROPN
ejpam-4244	159	4	.	.	PROPN
ejpam-4244	159	5	math	math	PROPN
ejpam-4244	159	6	,	,	PUNCT
ejpam-4244	159	7	15	15	NUM
ejpam-4244	159	8	(	(	PUNCT
ejpam-4244	159	9	1	1	NUM
ejpam-4244	159	10	)	)	PUNCT
ejpam-4244	159	11	(	(	PUNCT
ejpam-4244	159	12	2022	2022	NUM
ejpam-4244	159	13	)	)	PUNCT
ejpam-4244	159	14	,	,	PUNCT
ejpam-4244	159	15	249	249	NUM
ejpam-4244	159	16	-	-	SYM
ejpam-4244	159	17	260	260	NUM
ejpam-4244	159	18	255	255	NUM
ejpam-4244	159	19	=	=	SYM
ejpam-4244	159	20	lim	lim	PROPN
ejpam-4244	159	21	n→∞	n→∞	NUM
ejpam-4244	160	1	∫	∫	PROPN
ejpam-4244	160	2	kn	kn	PROPN
ejpam-4244	160	3	χδn(k	χδn(k	PROPN
ejpam-4244	160	4	−1k1)φ(xk1)dαn(k1	−1k1)φ(xk1)dαn(k1	PROPN
ejpam-4244	160	5	)	)	PUNCT
ejpam-4244	161	1	=	=	VERB
ejpam-4244	161	2	lim	lim	PROPN
ejpam-4244	161	3	n→∞	n→∞	NUM
ejpam-4244	162	1	∫	∫	PROPN
ejpam-4244	162	2	kn	kn	PROPN
ejpam-4244	162	3	χδn(k1k	χδn(k1k	PROPN
ejpam-4244	162	4	−1)φ(xk1)dαn(k1	−1)φ(xk1)dαn(k1	PROPN
ejpam-4244	162	5	)	)	PUNCT
ejpam-4244	163	1	=	=	VERB
ejpam-4244	163	2	lim	lim	PROPN
ejpam-4244	163	3	n→∞	n→∞	NUM
ejpam-4244	164	1	∫	∫	PROPN
ejpam-4244	164	2	kn	kn	PROPN
ejpam-4244	164	3	χδn(k1)φ(xk1k)dαn(k1	χδn(k1)φ(xk1k)dαn(k1	PROPN
ejpam-4244	164	4	)	)	PUNCT
ejpam-4244	164	5	=	=	SYM
ejpam-4244	164	6	φ(k)φ(x	φ(k)φ(x	NUM
ejpam-4244	164	7	)	)	PUNCT
ejpam-4244	164	8	we	we	PRON
ejpam-4244	164	9	come	come	VERB
ejpam-4244	164	10	back	back	ADV
ejpam-4244	164	11	to	to	ADP
ejpam-4244	164	12	the	the	DET
ejpam-4244	164	13	proof	proof	NOUN
ejpam-4244	164	14	of	of	ADP
ejpam-4244	164	15	theorem	theorem	ADJ
ejpam-4244	164	16	2	2	NUM
ejpam-4244	164	17	.	.	PUNCT
ejpam-4244	165	1	proof	proof	NOUN
ejpam-4244	165	2	.	.	PUNCT
ejpam-4244	166	1	i	i	PRON
ejpam-4244	166	2	)	)	PUNCT
ejpam-4244	166	3	let	let	VERB
ejpam-4244	166	4	(	(	PUNCT
ejpam-4244	166	5	g∞,k∞	g∞,k∞	PROPN
ejpam-4244	166	6	,	,	PUNCT
ejpam-4244	166	7	δ∞	δ∞	X
ejpam-4244	166	8	)	)	PUNCT
ejpam-4244	166	9	be	be	VERB
ejpam-4244	166	10	the	the	DET
ejpam-4244	166	11	inductive	inductive	ADJ
ejpam-4244	166	12	limit	limit	NOUN
ejpam-4244	166	13	of	of	ADP
ejpam-4244	166	14	an	an	DET
ejpam-4244	166	15	increasing	increase	VERB
ejpam-4244	166	16	sequence	sequence	NOUN
ejpam-4244	166	17	of	of	ADP
ejpam-4244	166	18	commutative	commutative	ADJ
ejpam-4244	166	19	triples	triple	NOUN
ejpam-4244	166	20	(	(	PUNCT
ejpam-4244	166	21	gn	gn	PROPN
ejpam-4244	166	22	,	,	PUNCT
ejpam-4244	166	23	kn	kn	PROPN
ejpam-4244	166	24	,	,	PUNCT
ejpam-4244	166	25	δn	δn	PROPN
ejpam-4244	166	26	)	)	PUNCT
ejpam-4244	166	27	.	.	PUNCT
ejpam-4244	167	1	let	let	VERB
ejpam-4244	167	2	us	we	PRON
ejpam-4244	167	3	consider	consider	VERB
ejpam-4244	167	4	(	(	PUNCT
ejpam-4244	167	5	π	π	NOUN
ejpam-4244	167	6	,	,	PUNCT
ejpam-4244	167	7	h	h	NOUN
ejpam-4244	167	8	)	)	PUNCT
ejpam-4244	167	9	a	a	DET
ejpam-4244	167	10	unitary	unitary	ADJ
ejpam-4244	167	11	irreducible	irreducible	ADJ
ejpam-4244	167	12	admissible	admissible	ADJ
ejpam-4244	167	13	representation	representation	NOUN
ejpam-4244	167	14	of	of	ADP
ejpam-4244	167	15	g∞	g∞	PROPN
ejpam-4244	167	16	and	and	CCONJ
ejpam-4244	167	17	h(δ∞	h(δ∞	NOUN
ejpam-4244	167	18	)	)	PUNCT
ejpam-4244	167	19	the	the	DET
ejpam-4244	167	20	isotypic	isotypic	NOUN
ejpam-4244	167	21	component	component	NOUN
ejpam-4244	167	22	of	of	ADP
ejpam-4244	167	23	δ∞	δ∞	NOUN
ejpam-4244	167	24	in	in	ADP
ejpam-4244	167	25	h.	h.	PROPN
ejpam-4244	167	26	let	let	VERB
ejpam-4244	167	27	us	we	PRON
ejpam-4244	167	28	assume	assume	VERB
ejpam-4244	167	29	that	that	SCONJ
ejpam-4244	167	30	mtp(δ∞	mtp(δ∞	NOUN
ejpam-4244	167	31	,	,	PUNCT
ejpam-4244	167	32	π|k∞	π|k∞	NOUN
ejpam-4244	167	33	)	)	PUNCT
ejpam-4244	167	34	>	>	X
ejpam-4244	168	1	1	1	X
ejpam-4244	168	2	.	.	PUNCT
ejpam-4244	168	3	let	let	VERB
ejpam-4244	168	4	ξ1	ξ1	NOUN
ejpam-4244	168	5	,	,	PUNCT
ejpam-4244	168	6	ξ2	ξ2	PROPN
ejpam-4244	168	7	be	be	AUX
ejpam-4244	168	8	two	two	NUM
ejpam-4244	168	9	non	non	ADJ
ejpam-4244	168	10	-	-	ADJ
ejpam-4244	168	11	zero	zero	NUM
ejpam-4244	168	12	vectors	vector	NOUN
ejpam-4244	168	13	of	of	ADP
ejpam-4244	168	14	h(δ∞	h(δ∞	NOUN
ejpam-4244	168	15	)	)	PUNCT
ejpam-4244	168	16	.	.	PUNCT
ejpam-4244	169	1	let	let	VERB
ejpam-4244	169	2	us	we	PRON
ejpam-4244	169	3	denote	denote	VERB
ejpam-4244	169	4	by	by	ADP
ejpam-4244	169	5	eξ1	eξ1	PROPN
ejpam-4244	170	1	=	=	PUNCT
ejpam-4244	170	2	〈	〈	PROPN
ejpam-4244	170	3	δ∞(k)ξ1	δ∞(k)ξ1	NOUN
ejpam-4244	170	4	,	,	PUNCT
ejpam-4244	170	5	k	k	PROPN
ejpam-4244	170	6	∈	∈	PROPN
ejpam-4244	170	7	k∞	k∞	PROPN
ejpam-4244	170	8	〉	〉	PROPN
ejpam-4244	170	9	,	,	PUNCT
ejpam-4244	170	10	the	the	DET
ejpam-4244	170	11	hilbert	hilbert	NOUN
ejpam-4244	170	12	completion	completion	NOUN
ejpam-4244	170	13	of	of	ADP
ejpam-4244	170	14	vector	vector	NOUN
ejpam-4244	170	15	subspace	subspace	NOUN
ejpam-4244	170	16	generated	generate	VERB
ejpam-4244	170	17	by	by	ADP
ejpam-4244	170	18	the	the	DET
ejpam-4244	170	19	set	set	NOUN
ejpam-4244	170	20	{	{	PUNCT
ejpam-4244	170	21	δ∞(k)ξ1	δ∞(k)ξ1	NOUN
ejpam-4244	170	22	,	,	PUNCT
ejpam-4244	170	23	k	k	PROPN
ejpam-4244	170	24	∈	∈	PROPN
ejpam-4244	170	25	k∞	k∞	PROPN
ejpam-4244	170	26	}	}	PUNCT
ejpam-4244	170	27	and	and	CCONJ
ejpam-4244	170	28	eξ2	eξ2	NOUN
ejpam-4244	170	29	=	=	SYM
ejpam-4244	170	30	〈	〈	PROPN
ejpam-4244	170	31	δ∞(k)ξ2	δ∞(k)ξ2	NOUN
ejpam-4244	170	32	,	,	PUNCT
ejpam-4244	170	33	k	k	PROPN
ejpam-4244	170	34	∈	∈	PROPN
ejpam-4244	170	35	k∞	k∞	PROPN
ejpam-4244	170	36	〉	〉	NOUN
ejpam-4244	170	37	the	the	DET
ejpam-4244	170	38	hilbert	hilbert	PROPN
ejpam-4244	170	39	completion	completion	NOUN
ejpam-4244	170	40	of	of	ADP
ejpam-4244	170	41	vector	vector	NOUN
ejpam-4244	170	42	subspace	subspace	NOUN
ejpam-4244	170	43	generated	generate	VERB
ejpam-4244	170	44	by	by	ADP
ejpam-4244	170	45	the	the	DET
ejpam-4244	170	46	set	set	NOUN
ejpam-4244	170	47	{	{	PUNCT
ejpam-4244	170	48	δ∞(k)ξ2	δ∞(k)ξ2	PROPN
ejpam-4244	170	49	,	,	PUNCT
ejpam-4244	170	50	k	k	PROPN
ejpam-4244	170	51	∈	∈	PROPN
ejpam-4244	170	52	k∞	k∞	PROPN
ejpam-4244	170	53	}	}	PUNCT
ejpam-4244	170	54	.	.	PUNCT
ejpam-4244	171	1	eξ1	eξ1	NOUN
ejpam-4244	171	2	and	and	CCONJ
ejpam-4244	171	3	eξ2	eξ2	PROPN
ejpam-4244	171	4	are	be	AUX
ejpam-4244	171	5	two	two	NUM
ejpam-4244	171	6	distinct	distinct	ADJ
ejpam-4244	171	7	copies	copy	NOUN
ejpam-4244	171	8	of	of	ADP
ejpam-4244	171	9	eδ∞	eδ∞	PROPN
ejpam-4244	171	10	in	in	ADP
ejpam-4244	171	11	h.	h.	NOUN
ejpam-4244	171	12	since	since	SCONJ
ejpam-4244	171	13	(	(	PUNCT
ejpam-4244	171	14	π	π	PROPN
ejpam-4244	171	15	,	,	PUNCT
ejpam-4244	171	16	h	h	NOUN
ejpam-4244	171	17	)	)	PUNCT
ejpam-4244	171	18	is	be	AUX
ejpam-4244	171	19	a	a	DET
ejpam-4244	171	20	unitary	unitary	ADJ
ejpam-4244	171	21	irreducible	irreducible	ADJ
ejpam-4244	171	22	representation	representation	NOUN
ejpam-4244	171	23	of	of	ADP
ejpam-4244	171	24	g∞	g∞	PROPN
ejpam-4244	171	25	then	then	ADV
ejpam-4244	171	26	by	by	ADP
ejpam-4244	171	27	(	(	PUNCT
ejpam-4244	171	28	[	[	X
ejpam-4244	171	29	6	6	NUM
ejpam-4244	171	30	]	]	PUNCT
ejpam-4244	171	31	,	,	PUNCT
ejpam-4244	171	32	theorem	theorem	VERB
ejpam-4244	171	33	22.9	22.9	NUM
ejpam-4244	171	34	,	,	PUNCT
ejpam-4244	171	35	page	page	NOUN
ejpam-4244	171	36	434	434	NUM
ejpam-4244	171	37	)	)	PUNCT
ejpam-4244	171	38	,	,	PUNCT
ejpam-4244	171	39	there	there	PRON
ejpam-4244	171	40	exists	exist	VERB
ejpam-4244	171	41	a	a	DET
ejpam-4244	171	42	sequence	sequence	NOUN
ejpam-4244	171	43	(	(	PUNCT
ejpam-4244	171	44	πn	πn	INTJ
ejpam-4244	171	45	,	,	PUNCT
ejpam-4244	171	46	hn	hn	PROPN
ejpam-4244	171	47	)	)	PUNCT
ejpam-4244	171	48	of	of	ADP
ejpam-4244	171	49	unitary	unitary	ADJ
ejpam-4244	171	50	irreducible	irreducible	ADJ
ejpam-4244	171	51	representations	representation	NOUN
ejpam-4244	171	52	of	of	ADP
ejpam-4244	171	53	groups	group	NOUN
ejpam-4244	171	54	gn	gn	INTJ
ejpam-4244	171	55	approximating	approximate	VERB
ejpam-4244	171	56	(	(	PUNCT
ejpam-4244	171	57	π	π	PROPN
ejpam-4244	171	58	,	,	PUNCT
ejpam-4244	171	59	h	h	NOUN
ejpam-4244	171	60	)	)	PUNCT
ejpam-4244	171	61	.	.	PUNCT
ejpam-4244	172	1	since	since	SCONJ
ejpam-4244	172	2	{	{	PUNCT
ejpam-4244	172	3	ξ1	ξ1	NOUN
ejpam-4244	172	4	,	,	PUNCT
ejpam-4244	172	5	ξ2	ξ2	ADJ
ejpam-4244	172	6	}	}	PUNCT
ejpam-4244	173	1	⊂	⊂	PROPN
ejpam-4244	174	1	h	h	NOUN
ejpam-4244	174	2	then	then	ADV
ejpam-4244	174	3	there	there	PRON
ejpam-4244	174	4	exists	exist	VERB
ejpam-4244	174	5	a	a	DET
ejpam-4244	174	6	sequence	sequence	NOUN
ejpam-4244	174	7	{	{	PUNCT
ejpam-4244	174	8	ξn1	ξn1	PROPN
ejpam-4244	174	9	,	,	PUNCT
ejpam-4244	174	10	ξn2	ξn2	NOUN
ejpam-4244	174	11	}	}	PUNCT
ejpam-4244	174	12	⊂	⊂	PROPN
ejpam-4244	174	13	hn	hn	PROPN
ejpam-4244	174	14	such	such	ADJ
ejpam-4244	174	15	that	that	PRON
ejpam-4244	174	16	(	(	PUNCT
ejpam-4244	174	17	πn(k)ξ	πn(k)ξ	PROPN
ejpam-4244	174	18	n	n	VERB
ejpam-4244	174	19	i	i	PRON
ejpam-4244	174	20	,	,	PUNCT
ejpam-4244	174	21	ξ	ξ	PROPN
ejpam-4244	174	22	n	n	PRON
ejpam-4244	174	23	j	j	NOUN
ejpam-4244	174	24	)	)	PUNCT
ejpam-4244	174	25	−→	−→	ADP
ejpam-4244	174	26	n→∞	n→∞	X
ejpam-4244	174	27	(	(	PUNCT
ejpam-4244	174	28	π(k)ξi	π(k)ξi	PROPN
ejpam-4244	174	29	,	,	PUNCT
ejpam-4244	174	30	ξj	ξj	NOUN
ejpam-4244	174	31	)	)	PUNCT
ejpam-4244	174	32	,	,	PUNCT
ejpam-4244	174	33	∀k	∀k	PROPN
ejpam-4244	174	34	∈	∈	PROPN
ejpam-4244	174	35	k∞,∀i	k∞,∀i	PROPN
ejpam-4244	174	36	,	,	PUNCT
ejpam-4244	174	37	j	j	PROPN
ejpam-4244	174	38	∈	∈	PROPN
ejpam-4244	174	39	{	{	PUNCT
ejpam-4244	174	40	1	1	NUM
ejpam-4244	174	41	;	;	PUNCT
ejpam-4244	174	42	2	2	NUM
ejpam-4244	174	43	}	}	PUNCT
ejpam-4244	174	44	uniformly	uniformly	ADV
ejpam-4244	174	45	on	on	ADP
ejpam-4244	174	46	compact	compact	ADJ
ejpam-4244	174	47	sets	set	NOUN
ejpam-4244	174	48	.	.	PUNCT
ejpam-4244	175	1	hence	hence	ADV
ejpam-4244	175	2	(	(	PUNCT
ejpam-4244	175	3	πn(k)ξ	πn(k)ξ	PROPN
ejpam-4244	175	4	n	n	PROPN
ejpam-4244	175	5	i	i	PRON
ejpam-4244	175	6	,	,	PUNCT
ejpam-4244	175	7	ξ	ξ	PROPN
ejpam-4244	175	8	n	n	PRON
ejpam-4244	175	9	j	j	NOUN
ejpam-4244	175	10	)	)	PUNCT
ejpam-4244	176	1	−→	−→	ADP
ejpam-4244	176	2	n→∞	n→∞	X
ejpam-4244	176	3	(	(	PUNCT
ejpam-4244	176	4	δ∞(k)ξi	δ∞(k)ξi	PROPN
ejpam-4244	176	5	,	,	PUNCT
ejpam-4244	176	6	ξj),∀k	ξj),∀k	PROPN
ejpam-4244	176	7	∈	∈	PROPN
ejpam-4244	176	8	k∞	k∞	PROPN
ejpam-4244	176	9	,	,	PUNCT
ejpam-4244	176	10	∀i	∀i	NOUN
ejpam-4244	176	11	,	,	PUNCT
ejpam-4244	176	12	j	j	PROPN
ejpam-4244	176	13	∈	∈	PROPN
ejpam-4244	176	14	{	{	PUNCT
ejpam-4244	176	15	1	1	NUM
ejpam-4244	176	16	;	;	PUNCT
ejpam-4244	176	17	2	2	NUM
ejpam-4244	176	18	}	}	PUNCT
ejpam-4244	176	19	.	.	PUNCT
ejpam-4244	177	1	in	in	ADP
ejpam-4244	177	2	particular	particular	ADJ
ejpam-4244	177	3	,	,	PUNCT
ejpam-4244	177	4	if	if	SCONJ
ejpam-4244	177	5	i	i	PRON
ejpam-4244	177	6	=	=	SYM
ejpam-4244	177	7	j	j	PROPN
ejpam-4244	177	8	,	,	PUNCT
ejpam-4244	177	9	we	we	PRON
ejpam-4244	177	10	have	have	VERB
ejpam-4244	177	11	:	:	PUNCT
ejpam-4244	177	12	(	(	PUNCT
ejpam-4244	177	13	πn(k)ξ	πn(k)ξ	PROPN
ejpam-4244	177	14	n	n	VERB
ejpam-4244	177	15	i	i	PRON
ejpam-4244	177	16	,	,	PUNCT
ejpam-4244	177	17	ξ	ξ	PROPN
ejpam-4244	177	18	n	n	PROPN
ejpam-4244	177	19	i	i	PRON
ejpam-4244	177	20	)	)	PUNCT
ejpam-4244	178	1	−→	−→	ADV
ejpam-4244	178	2	n→∞	n→∞	X
ejpam-4244	178	3	(	(	PUNCT
ejpam-4244	178	4	δ∞(k)ξi	δ∞(k)ξi	ADJ
ejpam-4244	178	5	,	,	PUNCT
ejpam-4244	178	6	ξi	ξi	NOUN
ejpam-4244	178	7	)	)	PUNCT
ejpam-4244	178	8	.	.	PUNCT
ejpam-4244	179	1	let	let	VERB
ejpam-4244	179	2	us	we	PRON
ejpam-4244	179	3	put	put	VERB
ejpam-4244	179	4	hni	hni	PROPN
ejpam-4244	179	5	=	=	PROPN
ejpam-4244	179	6	ξni	ξni	NOUN
ejpam-4244	179	7	−	−	PROPN
ejpam-4244	179	8	phn(δn)(ξ	phn(δn)(ξ	PROPN
ejpam-4244	179	9	n	n	PROPN
ejpam-4244	179	10	i	i	PROPN
ejpam-4244	179	11	)	)	PUNCT
ejpam-4244	179	12	,	,	PUNCT
ejpam-4244	179	13	where	where	SCONJ
ejpam-4244	179	14	hn(δn	hn(δn	NOUN
ejpam-4244	179	15	)	)	PUNCT
ejpam-4244	179	16	is	be	AUX
ejpam-4244	179	17	the	the	DET
ejpam-4244	179	18	isotypic	isotypic	ADJ
ejpam-4244	179	19	component	component	NOUN
ejpam-4244	179	20	of	of	ADP
ejpam-4244	179	21	δn	δn	NOUN
ejpam-4244	179	22	in	in	ADP
ejpam-4244	179	23	hn	hn	PROPN
ejpam-4244	179	24	and	and	CCONJ
ejpam-4244	179	25	phn(δn	phn(δn	NOUN
ejpam-4244	179	26	)	)	PUNCT
ejpam-4244	179	27	is	be	AUX
ejpam-4244	179	28	the	the	DET
ejpam-4244	179	29	projection	projection	NOUN
ejpam-4244	179	30	of	of	ADP
ejpam-4244	179	31	h	h	NOUN
ejpam-4244	179	32	onto	onto	ADP
ejpam-4244	179	33	hn(δn	hn(δn	NOUN
ejpam-4244	179	34	)	)	PUNCT
ejpam-4244	179	35	.	.	PUNCT
ejpam-4244	180	1	since	since	SCONJ
ejpam-4244	180	2	for	for	ADP
ejpam-4244	180	3	any	any	DET
ejpam-4244	180	4	n	n	CCONJ
ejpam-4244	180	5	,	,	PUNCT
ejpam-4244	180	6	(	(	PUNCT
ejpam-4244	180	7	gn	gn	PROPN
ejpam-4244	180	8	,	,	PUNCT
ejpam-4244	180	9	kn	kn	PROPN
ejpam-4244	180	10	,	,	PUNCT
ejpam-4244	180	11	δn	δn	PROPN
ejpam-4244	180	12	)	)	PUNCT
ejpam-4244	180	13	is	be	AUX
ejpam-4244	180	14	a	a	DET
ejpam-4244	180	15	commutative	commutative	ADJ
ejpam-4244	180	16	triple	triple	NOUN
ejpam-4244	180	17	then	then	ADV
ejpam-4244	180	18	∀n	∀n	NUM
ejpam-4244	180	19	,	,	PUNCT
ejpam-4244	180	20	eδn	eδn	PRON
ejpam-4244	180	21	'	'	PUNCT
ejpam-4244	180	22	hn(δn	hn(δn	NOUN
ejpam-4244	180	23	)	)	PUNCT
ejpam-4244	180	24	.	.	PUNCT
ejpam-4244	181	1	since	since	SCONJ
ejpam-4244	181	2	(	(	PUNCT
ejpam-4244	181	3	eδn	eδn	PROPN
ejpam-4244	181	4	)	)	PUNCT
ejpam-4244	181	5	is	be	AUX
ejpam-4244	181	6	an	an	DET
ejpam-4244	181	7	increasing	increase	VERB
ejpam-4244	181	8	sequence	sequence	NOUN
ejpam-4244	181	9	of	of	ADP
ejpam-4244	181	10	vector	vector	NOUN
ejpam-4244	181	11	spaces	space	NOUN
ejpam-4244	181	12	then	then	ADV
ejpam-4244	181	13	the	the	DET
ejpam-4244	181	14	sequence	sequence	NOUN
ejpam-4244	181	15	(	(	PUNCT
ejpam-4244	181	16	hn(δn	hn(δn	PROPN
ejpam-4244	181	17	)	)	PUNCT
ejpam-4244	181	18	)	)	PUNCT
ejpam-4244	181	19	is	be	AUX
ejpam-4244	181	20	also	also	ADV
ejpam-4244	181	21	increasing	increase	VERB
ejpam-4244	181	22	.	.	PUNCT
ejpam-4244	182	1	then	then	ADV
ejpam-4244	182	2	by	by	ADP
ejpam-4244	182	3	the	the	DET
ejpam-4244	182	4	lemma	lemma	PROPN
ejpam-4244	182	5	1	1	NUM
ejpam-4244	182	6	,	,	PUNCT
ejpam-4244	182	7	phn(δn	phn(δn	NUM
ejpam-4244	182	8	)	)	PUNCT
ejpam-4244	182	9	converges	converge	VERB
ejpam-4244	182	10	strongly	strongly	ADV
ejpam-4244	182	11	to	to	ADP
ejpam-4244	182	12	ph∞	ph∞	PROPN
ejpam-4244	182	13	,	,	PUNCT
ejpam-4244	182	14	where	where	SCONJ
ejpam-4244	182	15	ph∞	ph∞	PROPN
ejpam-4244	182	16	is	be	AUX
ejpam-4244	182	17	the	the	DET
ejpam-4244	182	18	projection	projection	NOUN
ejpam-4244	182	19	of	of	ADP
ejpam-4244	182	20	h	h	NOUN
ejpam-4244	182	21	onto	onto	ADP
ejpam-4244	182	22	h∞	h∞	PROPN
ejpam-4244	182	23	l.	l.	PROPN
ejpam-4244	182	24	timite	timite	PROPN
ejpam-4244	182	25	,	,	PUNCT
ejpam-4244	182	26	i.	i.	PROPN
ejpam-4244	182	27	toure	toure	PROPN
ejpam-4244	182	28	/	/	SYM
ejpam-4244	182	29	eur	eur	PROPN
ejpam-4244	182	30	.	.	PUNCT
ejpam-4244	183	1	j.	j.	PROPN
ejpam-4244	183	2	pure	pure	PROPN
ejpam-4244	183	3	appl	appl	PROPN
ejpam-4244	183	4	.	.	PROPN
ejpam-4244	183	5	math	math	PROPN
ejpam-4244	183	6	,	,	PUNCT
ejpam-4244	183	7	15	15	NUM
ejpam-4244	183	8	(	(	PUNCT
ejpam-4244	183	9	1	1	NUM
ejpam-4244	183	10	)	)	PUNCT
ejpam-4244	183	11	(	(	PUNCT
ejpam-4244	183	12	2022	2022	NUM
ejpam-4244	183	13	)	)	PUNCT
ejpam-4244	183	14	,	,	PUNCT
ejpam-4244	183	15	249	249	NUM
ejpam-4244	183	16	-	-	SYM
ejpam-4244	183	17	260	260	NUM
ejpam-4244	183	18	256	256	NUM
ejpam-4244	183	19	and	and	CCONJ
ejpam-4244	183	20	h∞	h∞	PROPN
ejpam-4244	183	21	is	be	AUX
ejpam-4244	183	22	the	the	DET
ejpam-4244	183	23	hilbert	hilbert	NOUN
ejpam-4244	183	24	completion	completion	NOUN
ejpam-4244	183	25	of	of	ADP
ejpam-4244	183	26	⋃	⋃	NOUN
ejpam-4244	183	27	n≥1hn(δn	n≥1hn(δn	NOUN
ejpam-4244	183	28	)	)	PUNCT
ejpam-4244	183	29	.	.	PUNCT
ejpam-4244	184	1	for	for	ADP
ejpam-4244	184	2	n	n	PRON
ejpam-4244	184	3	sufficiently	sufficiently	ADV
ejpam-4244	184	4	large	large	ADJ
ejpam-4244	184	5	,	,	PUNCT
ejpam-4244	184	6	we	we	PRON
ejpam-4244	184	7	have	have	VERB
ejpam-4244	184	8	(	(	PUNCT
ejpam-4244	184	9	πn(k)h	πn(k)h	PUNCT
ejpam-4244	184	10	n	n	VERB
ejpam-4244	184	11	i	i	PRON
ejpam-4244	184	12	,	,	PUNCT
ejpam-4244	184	13	h	h	PROPN
ejpam-4244	185	1	n	n	NOUN
ejpam-4244	185	2	i	i	PRON
ejpam-4244	185	3	)	)	PUNCT
ejpam-4244	186	1	=	=	PUNCT
ejpam-4244	186	2	(	(	PUNCT
ejpam-4244	186	3	πn(k)ξ	πn(k)ξ	PROPN
ejpam-4244	186	4	n	n	PRON
ejpam-4244	186	5	i	i	PRON
ejpam-4244	186	6	,	,	PUNCT
ejpam-4244	186	7	ξ	ξ	PROPN
ejpam-4244	186	8	n	n	PROPN
ejpam-4244	186	9	i	i	NOUN
ejpam-4244	186	10	)	)	PUNCT
ejpam-4244	186	11	−	−	PROPN
ejpam-4244	186	12	(	(	PUNCT
ejpam-4244	186	13	πn(k)ξ	πn(k)ξ	PROPN
ejpam-4244	186	14	n	n	PRON
ejpam-4244	186	15	i	i	PRON
ejpam-4244	186	16	,	,	PUNCT
ejpam-4244	186	17	phn(δn)(ξ	phn(δn)(ξ	PROPN
ejpam-4244	186	18	n	n	PROPN
ejpam-4244	186	19	i	i	PROPN
ejpam-4244	186	20	)	)	PUNCT
ejpam-4244	186	21	)	)	PUNCT
ejpam-4244	186	22	−	−	PROPN
ejpam-4244	187	1	(	(	PUNCT
ejpam-4244	187	2	πn(k)phn(δn)(ξ	πn(k)phn(δn)(ξ	NOUN
ejpam-4244	187	3	n	n	PROPN
ejpam-4244	187	4	i	i	PROPN
ejpam-4244	187	5	)	)	PUNCT
ejpam-4244	187	6	,	,	PUNCT
ejpam-4244	187	7	ξ	ξ	PROPN
ejpam-4244	187	8	n	n	X
ejpam-4244	187	9	i	i	PRON
ejpam-4244	187	10	)	)	PUNCT
ejpam-4244	188	1	+	+	CCONJ
ejpam-4244	188	2	(	(	PUNCT
ejpam-4244	188	3	πn(k)phn(δn)(ξ	πn(k)phn(δn)(ξ	NOUN
ejpam-4244	188	4	n	n	PROPN
ejpam-4244	188	5	i	i	PROPN
ejpam-4244	188	6	)	)	PUNCT
ejpam-4244	188	7	,	,	PUNCT
ejpam-4244	188	8	phn(δn)(ξ	phn(δn)(ξ	PROPN
ejpam-4244	188	9	n	n	PROPN
ejpam-4244	188	10	i	i	PROPN
ejpam-4244	188	11	)	)	PUNCT
ejpam-4244	188	12	)	)	PUNCT
ejpam-4244	188	13	.	.	PUNCT
ejpam-4244	189	1	then	then	ADV
ejpam-4244	189	2	(	(	PUNCT
ejpam-4244	189	3	πn(k)h	πn(k)h	PUNCT
ejpam-4244	189	4	n	n	VERB
ejpam-4244	189	5	i	i	PRON
ejpam-4244	189	6	,	,	PUNCT
ejpam-4244	189	7	h	h	PROPN
ejpam-4244	189	8	n	n	NOUN
ejpam-4244	189	9	i	i	PRON
ejpam-4244	189	10	)	)	PUNCT
ejpam-4244	189	11	−→	−→	ADV
ejpam-4244	189	12	n→∞	n→∞	X
ejpam-4244	189	13	(	(	PUNCT
ejpam-4244	189	14	δ∞(k)ξi	δ∞(k)ξi	ADJ
ejpam-4244	189	15	,	,	PUNCT
ejpam-4244	189	16	ξi)−	ξi)−	NUM
ejpam-4244	189	17	(	(	PUNCT
ejpam-4244	189	18	π(k)ξi	π(k)ξi	PROPN
ejpam-4244	189	19	,	,	PUNCT
ejpam-4244	189	20	ph(δ∞)(ξi))−	ph(δ∞)(ξi))−	X
ejpam-4244	189	21	(	(	PUNCT
ejpam-4244	189	22	π(k)ph(δ∞)(ξi	π(k)ph(δ∞)(ξi	PROPN
ejpam-4244	189	23	)	)	PUNCT
ejpam-4244	189	24	,	,	PUNCT
ejpam-4244	189	25	ξi	ξi	NOUN
ejpam-4244	189	26	)	)	PUNCT
ejpam-4244	190	1	+	+	CCONJ
ejpam-4244	190	2	(	(	PUNCT
ejpam-4244	190	3	π(k)ph(δ∞(ξi	π(k)ph(δ∞(ξi	ADJ
ejpam-4244	190	4	)	)	PUNCT
ejpam-4244	190	5	,	,	PUNCT
ejpam-4244	190	6	ph(δ∞)(ξi	ph(δ∞)(ξi	PROPN
ejpam-4244	190	7	)	)	PUNCT
ejpam-4244	190	8	)	)	PUNCT
ejpam-4244	190	9	.	.	PUNCT
ejpam-4244	191	1	since	since	SCONJ
ejpam-4244	191	2	ph(δ∞)(ξi	ph(δ∞)(ξi	PROPN
ejpam-4244	191	3	)	)	PUNCT
ejpam-4244	191	4	=	=	PUNCT
ejpam-4244	191	5	ξi	ξi	NOUN
ejpam-4244	191	6	then	then	ADV
ejpam-4244	191	7	(	(	PUNCT
ejpam-4244	191	8	δ∞(k)ξi	δ∞(k)ξi	PROPN
ejpam-4244	191	9	,	,	PUNCT
ejpam-4244	191	10	ξi)−(π(k)ξi	ξi)−(π(k)ξi	PRON
ejpam-4244	191	11	,	,	PUNCT
ejpam-4244	191	12	ph(δ∞)(ξi))−(π(k)ph(δ∞)(ξi	ph(δ∞)(ξi))−(π(k)ph(δ∞)(ξi	ADJ
ejpam-4244	191	13	)	)	PUNCT
ejpam-4244	191	14	,	,	PUNCT
ejpam-4244	191	15	ξi)+	ξi)+	NOUN
ejpam-4244	191	16	(	(	PUNCT
ejpam-4244	191	17	π(k)ph(δ∞(ξi	π(k)ph(δ∞(ξi	PROPN
ejpam-4244	191	18	)	)	PUNCT
ejpam-4244	191	19	,	,	PUNCT
ejpam-4244	191	20	ph(δ∞)(ξi	ph(δ∞)(ξi	PROPN
ejpam-4244	191	21	)	)	PUNCT
ejpam-4244	191	22	)	)	PUNCT
ejpam-4244	192	1	=	=	PUNCT
ejpam-4244	192	2	0	0	X
ejpam-4244	192	3	.	.	PUNCT
ejpam-4244	193	1	hence	hence	ADV
ejpam-4244	193	2	(	(	PUNCT
ejpam-4244	193	3	πn(k)h	πn(k)h	PUNCT
ejpam-4244	193	4	n	n	VERB
ejpam-4244	193	5	i	i	PRON
ejpam-4244	193	6	,	,	PUNCT
ejpam-4244	193	7	h	h	PROPN
ejpam-4244	193	8	n	n	NOUN
ejpam-4244	193	9	i	i	PRON
ejpam-4244	193	10	)	)	PUNCT
ejpam-4244	194	1	−→	−→	ADV
ejpam-4244	194	2	n→∞	n→∞	NUM
ejpam-4244	194	3	0	0	NUM
ejpam-4244	194	4	.	.	PUNCT
ejpam-4244	195	1	in	in	ADP
ejpam-4244	195	2	particular	particular	ADJ
ejpam-4244	195	3	,	,	PUNCT
ejpam-4244	195	4	if	if	SCONJ
ejpam-4244	195	5	k	k	PROPN
ejpam-4244	195	6	=	=	SYM
ejpam-4244	195	7	e	e	X
ejpam-4244	195	8	,	,	PUNCT
ejpam-4244	195	9	we	we	PRON
ejpam-4244	195	10	have	have	VERB
ejpam-4244	195	11	||hni	||hni	NOUN
ejpam-4244	195	12	||	||	ADP
ejpam-4244	196	1	−→	−→	ADJ
ejpam-4244	196	2	n→∞	n→∞	NUM
ejpam-4244	196	3	0	0	NUM
ejpam-4244	196	4	.	.	PUNCT
ejpam-4244	197	1	therefore	therefore	ADV
ejpam-4244	197	2	for	for	ADP
ejpam-4244	197	3	n	n	PRON
ejpam-4244	197	4	sufficiently	sufficiently	ADV
ejpam-4244	197	5	large	large	ADJ
ejpam-4244	197	6	,	,	PUNCT
ejpam-4244	197	7	ξni	ξni	NOUN
ejpam-4244	197	8	is	be	AUX
ejpam-4244	197	9	arbitrarily	arbitrarily	ADV
ejpam-4244	197	10	close	close	ADJ
ejpam-4244	197	11	to	to	ADP
ejpam-4244	197	12	phn(δn)(ξ	phn(δn)(ξ	PROPN
ejpam-4244	197	13	n	n	PROPN
ejpam-4244	197	14	i	i	PROPN
ejpam-4244	197	15	)	)	PUNCT
ejpam-4244	197	16	.	.	PUNCT
ejpam-4244	198	1	so	so	ADV
ejpam-4244	198	2	that	that	SCONJ
ejpam-4244	198	3	we	we	PRON
ejpam-4244	198	4	can	can	AUX
ejpam-4244	198	5	assume	assume	VERB
ejpam-4244	198	6	for	for	ADP
ejpam-4244	198	7	n	n	PRON
ejpam-4244	198	8	sufficiently	sufficiently	ADV
ejpam-4244	198	9	large	large	ADJ
ejpam-4244	198	10	,	,	PUNCT
ejpam-4244	198	11	ξni	ξni	PROPN
ejpam-4244	198	12	∈	∈	PROPN
ejpam-4244	198	13	hn(δn	hn(δn	PROPN
ejpam-4244	198	14	)	)	PUNCT
ejpam-4244	198	15	.	.	PUNCT
ejpam-4244	199	1	let	let	VERB
ejpam-4244	199	2	us	we	PRON
ejpam-4244	199	3	put	put	VERB
ejpam-4244	199	4	en	en	ADV
ejpam-4244	199	5	i	i	NOUN
ejpam-4244	199	6	=	=	SYM
ejpam-4244	200	1	〈	〈	PROPN
ejpam-4244	200	2	πn(k)ξni	πn(k)ξni	NOUN
ejpam-4244	200	3	,	,	PUNCT
ejpam-4244	200	4	k	k	PROPN
ejpam-4244	200	5	∈	∈	PROPN
ejpam-4244	200	6	kn	kn	PROPN
ejpam-4244	200	7	〉	〉	PROPN
ejpam-4244	200	8	,	,	PUNCT
ejpam-4244	200	9	i	i	PRON
ejpam-4244	200	10	=	=	NOUN
ejpam-4244	200	11	1	1	NUM
ejpam-4244	200	12	,	,	PUNCT
ejpam-4244	200	13	2	2	NUM
ejpam-4244	200	14	,	,	PUNCT
ejpam-4244	200	15	the	the	DET
ejpam-4244	200	16	hilbert	hilbert	NOUN
ejpam-4244	200	17	completion	completion	NOUN
ejpam-4244	200	18	of	of	ADP
ejpam-4244	200	19	the	the	DET
ejpam-4244	200	20	vector	vector	NOUN
ejpam-4244	200	21	subspace	subspace	NOUN
ejpam-4244	200	22	generated	generate	VERB
ejpam-4244	200	23	by	by	ADP
ejpam-4244	200	24	the	the	DET
ejpam-4244	200	25	family	family	NOUN
ejpam-4244	200	26	{	{	PUNCT
ejpam-4244	200	27	πn(k)ξni	πn(k)ξni	PROPN
ejpam-4244	200	28	,	,	PUNCT
ejpam-4244	200	29	k	k	PROPN
ejpam-4244	200	30	∈	∈	PROPN
ejpam-4244	200	31	kn	kn	PROPN
ejpam-4244	200	32	}	}	PUNCT
ejpam-4244	200	33	.	.	PUNCT
ejpam-4244	201	1	for	for	ADP
ejpam-4244	201	2	any	any	DET
ejpam-4244	201	3	i	i	PROPN
ejpam-4244	201	4	,	,	PUNCT
ejpam-4244	201	5	en	en	ADV
ejpam-4244	201	6	i	i	PRON
ejpam-4244	201	7	is	be	AUX
ejpam-4244	201	8	copy	copy	NOUN
ejpam-4244	201	9	of	of	ADP
ejpam-4244	201	10	eδn	eδn	NOUN
ejpam-4244	201	11	in	in	ADP
ejpam-4244	201	12	hn	hn	PROPN
ejpam-4244	201	13	.	.	PUNCT
ejpam-4244	202	1	let	let	VERB
ejpam-4244	202	2	us	we	PRON
ejpam-4244	202	3	suppose	suppose	VERB
ejpam-4244	202	4	that	that	SCONJ
ejpam-4244	202	5	there	there	PRON
ejpam-4244	202	6	exists	exist	VERB
ejpam-4244	202	7	k	k	PROPN
ejpam-4244	202	8	,	,	PUNCT
ejpam-4244	202	9	k1	k1	PROPN
ejpam-4244	202	10	∈	∈	PROPN
ejpam-4244	202	11	kn	kn	PROPN
ejpam-4244	202	12	such	such	ADJ
ejpam-4244	202	13	that	that	SCONJ
ejpam-4244	202	14	ξn	ξn	NOUN
ejpam-4244	202	15	=	=	SYM
ejpam-4244	202	16	πn(k)ξ	πn(k)ξ	PROPN
ejpam-4244	202	17	n	n	PRON
ejpam-4244	202	18	1	1	NUM
ejpam-4244	202	19	=	=	PUNCT
ejpam-4244	202	20	πn(k1)ξ	πn(k1)ξ	NOUN
ejpam-4244	202	21	n	n	PROPN
ejpam-4244	202	22	2	2	NUM
ejpam-4244	202	23	.	.	PUNCT
ejpam-4244	203	1	(	(	PUNCT
ejpam-4244	203	2	ξn	ξn	PROPN
ejpam-4244	203	3	,	,	PUNCT
ejpam-4244	203	4	ξn	ξn	PROPN
ejpam-4244	203	5	)	)	PUNCT
ejpam-4244	203	6	=	=	PUNCT
ejpam-4244	203	7	(	(	PUNCT
ejpam-4244	203	8	πn(k)ξ	πn(k)ξ	PROPN
ejpam-4244	203	9	n	n	PRON
ejpam-4244	203	10	1	1	NUM
ejpam-4244	203	11	,	,	PUNCT
ejpam-4244	203	12	πn(k1)ξ	πn(k1)ξ	PRON
ejpam-4244	203	13	n	n	ADV
ejpam-4244	203	14	2	2	NUM
ejpam-4244	203	15	)	)	PUNCT
ejpam-4244	203	16	=	=	SYM
ejpam-4244	203	17	(	(	PUNCT
ejpam-4244	203	18	πn(k	πn(k	NOUN
ejpam-4244	203	19	−1	−1	NOUN
ejpam-4244	203	20	1	1	NUM
ejpam-4244	203	21	k)ξn1	k)ξn1	NOUN
ejpam-4244	203	22	,	,	PUNCT
ejpam-4244	203	23	ξ	ξ	PROPN
ejpam-4244	203	24	n	n	PRON
ejpam-4244	203	25	2	2	NUM
ejpam-4244	203	26	)	)	PUNCT
ejpam-4244	203	27	−→	−→	NOUN
ejpam-4244	203	28	n→∞	n→∞	X
ejpam-4244	203	29	(	(	PUNCT
ejpam-4244	203	30	δ∞(k)ξ1	δ∞(k)ξ1	NOUN
ejpam-4244	203	31	,	,	PUNCT
ejpam-4244	203	32	ξ2	ξ2	NOUN
ejpam-4244	203	33	)	)	PUNCT
ejpam-4244	203	34	=	=	SYM
ejpam-4244	204	1	0	0	X
ejpam-4244	204	2	.	.	PUNCT
ejpam-4244	204	3	consequently	consequently	ADV
ejpam-4244	204	4	||ξn||	||ξn||	VERB
ejpam-4244	204	5	−→	−→	ADJ
ejpam-4244	204	6	n→∞	n→∞	NOUN
ejpam-4244	204	7	0	0	NUM
ejpam-4244	204	8	.	.	PUNCT
ejpam-4244	205	1	so	so	ADV
ejpam-4244	205	2	en	en	PROPN
ejpam-4244	205	3	1	1	NUM
ejpam-4244	205	4	and	and	CCONJ
ejpam-4244	205	5	en	en	PROPN
ejpam-4244	205	6	2	2	NUM
ejpam-4244	205	7	are	be	AUX
ejpam-4244	205	8	distinct	distinct	ADJ
ejpam-4244	205	9	.	.	PUNCT
ejpam-4244	206	1	it	it	PRON
ejpam-4244	206	2	follows	follow	VERB
ejpam-4244	206	3	that	that	SCONJ
ejpam-4244	206	4	hn	hn	PROPN
ejpam-4244	206	5	contains	contain	VERB
ejpam-4244	206	6	two	two	NUM
ejpam-4244	206	7	distinct	distinct	ADJ
ejpam-4244	206	8	copies	copy	NOUN
ejpam-4244	206	9	of	of	ADP
ejpam-4244	206	10	eδn	eδn	NOUN
ejpam-4244	206	11	,	,	PUNCT
ejpam-4244	206	12	which	which	PRON
ejpam-4244	206	13	is	be	AUX
ejpam-4244	206	14	absurd	absurd	ADJ
ejpam-4244	206	15	because	because	SCONJ
ejpam-4244	206	16	(	(	PUNCT
ejpam-4244	206	17	gn	gn	PROPN
ejpam-4244	206	18	,	,	PUNCT
ejpam-4244	206	19	kn	kn	PROPN
ejpam-4244	206	20	,	,	PUNCT
ejpam-4244	206	21	δn	δn	PROPN
ejpam-4244	206	22	)	)	PUNCT
ejpam-4244	206	23	is	be	AUX
ejpam-4244	206	24	a	a	DET
ejpam-4244	206	25	commutative	commutative	ADJ
ejpam-4244	206	26	triple	triple	NOUN
ejpam-4244	206	27	for	for	ADP
ejpam-4244	206	28	any	any	DET
ejpam-4244	206	29	n	n	NOUN
ejpam-4244	207	1	and	and	CCONJ
ejpam-4244	207	2	so	so	ADV
ejpam-4244	207	3	the	the	DET
ejpam-4244	207	4	multiplicity	multiplicity	NOUN
ejpam-4244	207	5	of	of	ADP
ejpam-4244	207	6	δn	δn	NOUN
ejpam-4244	207	7	in	in	ADP
ejpam-4244	207	8	π|kn	π|kn	NUM
ejpam-4244	207	9	is	be	AUX
ejpam-4244	207	10	at	at	ADP
ejpam-4244	207	11	most	most	ADJ
ejpam-4244	207	12	1	1	NUM
ejpam-4244	207	13	.	.	X
ejpam-4244	207	14	ii	ii	NOUN
ejpam-4244	207	15	)	)	PUNCT
ejpam-4244	207	16	let	let	VERB
ejpam-4244	207	17	us	we	PRON
ejpam-4244	207	18	assume	assume	VERB
ejpam-4244	207	19	that	that	SCONJ
ejpam-4244	207	20	φ	φ	PROPN
ejpam-4244	207	21	is	be	AUX
ejpam-4244	207	22	a	a	DET
ejpam-4244	207	23	δ∞-spherical	δ∞-spherical	ADJ
ejpam-4244	207	24	function	function	NOUN
ejpam-4244	207	25	.	.	PUNCT
ejpam-4244	208	1	then	then	ADV
ejpam-4244	208	2	there	there	PRON
ejpam-4244	208	3	exists	exist	VERB
ejpam-4244	208	4	a	a	DET
ejpam-4244	208	5	δ∞-spherical	δ∞-spherical	ADJ
ejpam-4244	208	6	representation	representation	NOUN
ejpam-4244	208	7	(	(	PUNCT
ejpam-4244	208	8	u	u	NOUN
ejpam-4244	208	9	,	,	PUNCT
ejpam-4244	208	10	h	h	NOUN
ejpam-4244	208	11	)	)	PUNCT
ejpam-4244	208	12	of	of	ADP
ejpam-4244	208	13	g∞	g∞	PROPN
ejpam-4244	208	14	such	such	ADJ
ejpam-4244	208	15	that	that	SCONJ
ejpam-4244	208	16	∀g	∀g	NOUN
ejpam-4244	208	17	∈	∈	PROPN
ejpam-4244	208	18	g,∀u	g,∀u	NOUN
ejpam-4244	208	19	∈	∈	PROPN
ejpam-4244	208	20	eδ∞	eδ∞	PROPN
ejpam-4244	208	21	,	,	PUNCT
ejpam-4244	208	22	φ(g)u	φ(g)u	NOUN
ejpam-4244	208	23	=	=	SYM
ejpam-4244	208	24	pu(g−1)u	pu(g−1)u	NOUN
ejpam-4244	208	25	,	,	PUNCT
ejpam-4244	208	26	where	where	SCONJ
ejpam-4244	208	27	p	p	NOUN
ejpam-4244	208	28	is	be	AUX
ejpam-4244	208	29	the	the	DET
ejpam-4244	208	30	projection	projection	NOUN
ejpam-4244	208	31	of	of	ADP
ejpam-4244	208	32	h	h	NOUN
ejpam-4244	208	33	onto	onto	ADP
ejpam-4244	208	34	eδ∞	eδ∞	PROPN
ejpam-4244	208	35	.	.	PUNCT
ejpam-4244	209	1	for	for	ADP
ejpam-4244	209	2	any	any	DET
ejpam-4244	209	3	n	n	PRON
ejpam-4244	209	4	≥	≥	NOUN
ejpam-4244	209	5	1	1	NUM
ejpam-4244	209	6	,	,	PUNCT
ejpam-4244	209	7	pn	pn	PROPN
ejpam-4244	209	8	=	=	SYM
ejpam-4244	209	9	∫	∫	PROPN
ejpam-4244	209	10	kn	kn	PROPN
ejpam-4244	209	11	χδn(k	χδn(k	PROPN
ejpam-4244	209	12	−1)u(k)dαn(k	−1)u(k)dαn(k	NOUN
ejpam-4244	209	13	)	)	PUNCT
ejpam-4244	209	14	is	be	AUX
ejpam-4244	209	15	the	the	DET
ejpam-4244	209	16	projection	projection	NOUN
ejpam-4244	209	17	of	of	ADP
ejpam-4244	209	18	h	h	NOUN
ejpam-4244	209	19	onto	onto	ADP
ejpam-4244	209	20	eδn	eδn	NOUN
ejpam-4244	209	21	,	,	PUNCT
ejpam-4244	209	22	where	where	SCONJ
ejpam-4244	209	23	αn	αn	NOUN
ejpam-4244	209	24	is	be	AUX
ejpam-4244	209	25	the	the	DET
ejpam-4244	209	26	normalized	normalize	VERB
ejpam-4244	209	27	haar	haar	NOUN
ejpam-4244	209	28	measure	measure	NOUN
ejpam-4244	209	29	on	on	ADP
ejpam-4244	209	30	kn	kn	PROPN
ejpam-4244	209	31	.	.	PROPN
ejpam-4244	209	32	∀x	∀x	PROPN
ejpam-4244	209	33	,	,	PUNCT
ejpam-4244	209	34	y	y	PROPN
ejpam-4244	209	35	∈	∈	PROPN
ejpam-4244	209	36	g	g	NOUN
ejpam-4244	209	37	,	,	PUNCT
ejpam-4244	209	38	and	and	CCONJ
ejpam-4244	209	39	∀v	∀v	PROPN
ejpam-4244	209	40	∈	∈	PROPN
ejpam-4244	209	41	eδ	eδ	NOUN
ejpam-4244	209	42	,	,	PUNCT
ejpam-4244	209	43	φ(y)φ(x)v	φ(y)φ(x)v	PROPN
ejpam-4244	209	44	=	=	SYM
ejpam-4244	209	45	pu(y−1)pu(x−1)v	pu(y−1)pu(x−1)v	PROPN
ejpam-4244	209	46	=	=	SYM
ejpam-4244	209	47	lim	lim	PROPN
ejpam-4244	209	48	n→∞	n→∞	NUM
ejpam-4244	209	49	pu(y−1)pnu(x−1)v	pu(y−1)pnu(x−1)v	PROPN
ejpam-4244	209	50	=	=	SYM
ejpam-4244	209	51	lim	lim	PROPN
ejpam-4244	209	52	n→∞	n→∞	X
ejpam-4244	210	1	p	p	NOUN
ejpam-4244	210	2	∫	∫	PROPN
ejpam-4244	210	3	kn	kn	PROPN
ejpam-4244	210	4	χδn(k	χδn(k	PROPN
ejpam-4244	210	5	−1)u(y−1kx−1)dαn(k)v	−1)u(y−1kx−1)dαn(k)v	PROPN
ejpam-4244	210	6	l.	l.	PROPN
ejpam-4244	210	7	timite	timite	PROPN
ejpam-4244	210	8	,	,	PUNCT
ejpam-4244	210	9	i.	i.	PROPN
ejpam-4244	210	10	toure	toure	PROPN
ejpam-4244	210	11	/	/	SYM
ejpam-4244	210	12	eur	eur	PROPN
ejpam-4244	210	13	.	.	PUNCT
ejpam-4244	211	1	j.	j.	PROPN
ejpam-4244	211	2	pure	pure	PROPN
ejpam-4244	211	3	appl	appl	PROPN
ejpam-4244	211	4	.	.	PROPN
ejpam-4244	211	5	math	math	PROPN
ejpam-4244	211	6	,	,	PUNCT
ejpam-4244	211	7	15	15	NUM
ejpam-4244	211	8	(	(	PUNCT
ejpam-4244	211	9	1	1	NUM
ejpam-4244	211	10	)	)	PUNCT
ejpam-4244	211	11	(	(	PUNCT
ejpam-4244	211	12	2022	2022	NUM
ejpam-4244	211	13	)	)	PUNCT
ejpam-4244	211	14	,	,	PUNCT
ejpam-4244	211	15	249	249	NUM
ejpam-4244	211	16	-	-	SYM
ejpam-4244	211	17	260	260	NUM
ejpam-4244	211	18	257	257	NUM
ejpam-4244	211	19	=	=	NOUN
ejpam-4244	212	1	lim	lim	PROPN
ejpam-4244	212	2	n→∞	n→∞	NUM
ejpam-4244	213	1	∫	∫	PROPN
ejpam-4244	213	2	kn	kn	PROPN
ejpam-4244	213	3	χδn(k	χδn(k	PROPN
ejpam-4244	213	4	−1)pu(y−1kx−1)dαn(k)v	−1)pu(y−1kx−1)dαn(k)v	PROPN
ejpam-4244	213	5	=	=	SYM
ejpam-4244	213	6	lim	lim	PROPN
ejpam-4244	213	7	n→∞	n→∞	NUM
ejpam-4244	214	1	∫	∫	PROPN
ejpam-4244	214	2	kn	kn	PROPN
ejpam-4244	215	1	χδn(k	χδn(k	PROPN
ejpam-4244	215	2	−1)φ(xk−1y)dαn(k)v	−1)φ(xk−1y)dαn(k)v	PUNCT
ejpam-4244	215	3	=	=	SYM
ejpam-4244	215	4	lim	lim	PROPN
ejpam-4244	215	5	n→∞	n→∞	NUM
ejpam-4244	216	1	∫	∫	PROPN
ejpam-4244	216	2	kn	kn	PROPN
ejpam-4244	216	3	χδn(k)φ(xky)dαn(k)v	χδn(k)φ(xky)dαn(k)v	PROPN
ejpam-4244	216	4	hence	hence	ADV
ejpam-4244	216	5	∀x	∀x	NUM
ejpam-4244	216	6	,	,	PUNCT
ejpam-4244	216	7	y	y	PROPN
ejpam-4244	216	8	∈	∈	PROPN
ejpam-4244	216	9	g∞	g∞	PROPN
ejpam-4244	216	10	,	,	PUNCT
ejpam-4244	216	11	φ(y)φ(x	φ(y)φ(x	NUM
ejpam-4244	216	12	)	)	PUNCT
ejpam-4244	216	13	=	=	VERB
ejpam-4244	217	1	lim	lim	PROPN
ejpam-4244	217	2	n→∞	n→∞	NUM
ejpam-4244	218	1	∫	∫	PROPN
ejpam-4244	218	2	kn	kn	PROPN
ejpam-4244	218	3	χδn(k)φ(xky)dαn(k	χδn(k)φ(xky)dαn(k	PROPN
ejpam-4244	218	4	)	)	PUNCT
ejpam-4244	218	5	.	.	PUNCT
ejpam-4244	219	1	conversely	conversely	ADV
ejpam-4244	219	2	,	,	PUNCT
ejpam-4244	219	3	let	let	VERB
ejpam-4244	219	4	us	we	PRON
ejpam-4244	219	5	assume	assume	VERB
ejpam-4244	219	6	that	that	SCONJ
ejpam-4244	219	7	φ	φ	PROPN
ejpam-4244	219	8	is	be	AUX
ejpam-4244	219	9	a	a	DET
ejpam-4244	219	10	δ∞-radial	δ∞-radial	ADJ
ejpam-4244	219	11	unitary	unitary	ADJ
ejpam-4244	219	12	function	function	NOUN
ejpam-4244	219	13	of	of	ADP
ejpam-4244	219	14	positive	positive	ADJ
ejpam-4244	219	15	type	type	NOUN
ejpam-4244	219	16	verifying	verifying	NOUN
ejpam-4244	219	17	φ(e	φ(e	NOUN
ejpam-4244	219	18	)	)	PUNCT
ejpam-4244	219	19	=	=	SYM
ejpam-4244	219	20	i∞	i∞	NOUN
ejpam-4244	219	21	and	and	CCONJ
ejpam-4244	219	22	limn→∞	limn→∞	PROPN
ejpam-4244	219	23	∫	∫	PROPN
ejpam-4244	219	24	kn	kn	PROPN
ejpam-4244	219	25	χδn(k)φ(xky)dαn(k	χδn(k)φ(xky)dαn(k	PROPN
ejpam-4244	219	26	)	)	PUNCT
ejpam-4244	219	27	=	=	SYM
ejpam-4244	219	28	φ(y)φ(x	φ(y)φ(x	PROPN
ejpam-4244	219	29	)	)	PUNCT
ejpam-4244	219	30	.	.	PUNCT
ejpam-4244	220	1	let	let	VERB
ejpam-4244	220	2	v	v	X
ejpam-4244	220	3	∈	∈	PROPN
ejpam-4244	220	4	eδ∞	eδ∞	PROPN
ejpam-4244	220	5	.	.	PUNCT
ejpam-4244	221	1	let	let	VERB
ejpam-4244	221	2	us	we	PRON
ejpam-4244	221	3	put	put	VERB
ejpam-4244	221	4	l(x	l(x	PROPN
ejpam-4244	221	5	)	)	PUNCT
ejpam-4244	222	1	=	=	PRON
ejpam-4244	222	2	(	(	PUNCT
ejpam-4244	222	3	φ(x)v	φ(x)v	PROPN
ejpam-4244	222	4	,	,	PUNCT
ejpam-4244	222	5	v	v	NOUN
ejpam-4244	222	6	)	)	PUNCT
ejpam-4244	222	7	,	,	PUNCT
ejpam-4244	222	8	∀x	∀x	VERB
ejpam-4244	222	9	∈	∈	PROPN
ejpam-4244	223	1	g∞.	g∞.	INTJ
ejpam-4244	223	2	since	since	SCONJ
ejpam-4244	223	3	φ	φ	PROPN
ejpam-4244	223	4	is	be	AUX
ejpam-4244	223	5	of	of	ADP
ejpam-4244	223	6	positive	positive	ADJ
ejpam-4244	223	7	type	type	NOUN
ejpam-4244	223	8	,	,	PUNCT
ejpam-4244	223	9	l	l	NOUN
ejpam-4244	223	10	is	be	AUX
ejpam-4244	223	11	also	also	ADV
ejpam-4244	223	12	of	of	ADP
ejpam-4244	223	13	positive	positive	ADJ
ejpam-4244	223	14	type	type	NOUN
ejpam-4244	223	15	.	.	PUNCT
ejpam-4244	224	1	hence	hence	ADV
ejpam-4244	224	2	there	there	PRON
ejpam-4244	224	3	exists	exist	VERB
ejpam-4244	224	4	a	a	DET
ejpam-4244	224	5	unitary	unitary	ADJ
ejpam-4244	224	6	representation	representation	NOUN
ejpam-4244	224	7	(	(	PUNCT
ejpam-4244	224	8	u	u	NOUN
ejpam-4244	224	9	l	l	NOUN
ejpam-4244	224	10	,	,	PUNCT
ejpam-4244	224	11	hl	hl	NOUN
ejpam-4244	224	12	)	)	PUNCT
ejpam-4244	224	13	with	with	ADP
ejpam-4244	224	14	a	a	DET
ejpam-4244	224	15	cylic	cylic	ADJ
ejpam-4244	224	16	vector	vector	NOUN
ejpam-4244	224	17	ξl	ξl	NOUN
ejpam-4244	224	18	such	such	ADJ
ejpam-4244	224	19	that	that	SCONJ
ejpam-4244	224	20	∀x	∀x	VERB
ejpam-4244	224	21	∈	∈	PROPN
ejpam-4244	224	22	g∞	g∞	PROPN
ejpam-4244	224	23	,	,	PUNCT
ejpam-4244	224	24	(	(	PUNCT
ejpam-4244	224	25	φ(x)v	φ(x)v	PROPN
ejpam-4244	224	26	,	,	PUNCT
ejpam-4244	224	27	v	v	NOUN
ejpam-4244	224	28	)	)	PUNCT
ejpam-4244	224	29	=	=	SYM
ejpam-4244	224	30	l(x	l(x	PROPN
ejpam-4244	224	31	)	)	PUNCT
ejpam-4244	224	32	=	=	SYM
ejpam-4244	224	33	(	(	PUNCT
ejpam-4244	224	34	ξl	ξl	NOUN
ejpam-4244	224	35	,	,	PUNCT
ejpam-4244	224	36	u	u	NOUN
ejpam-4244	224	37	l(x)ξl	l(x)ξl	NOUN
ejpam-4244	224	38	)	)	PUNCT
ejpam-4244	224	39	.	.	PUNCT
ejpam-4244	225	1	we	we	PRON
ejpam-4244	225	2	know	know	VERB
ejpam-4244	225	3	by	by	ADP
ejpam-4244	225	4	the	the	DET
ejpam-4244	225	5	lemma	lemma	PROPN
ejpam-4244	225	6	2	2	NUM
ejpam-4244	225	7	iii	iii	NOUN
ejpam-4244	225	8	)	)	PUNCT
ejpam-4244	225	9	,	,	PUNCT
ejpam-4244	225	10	φ(k1xk2	φ(k1xk2	PROPN
ejpam-4244	225	11	)	)	PUNCT
ejpam-4244	225	12	=	=	SYM
ejpam-4244	226	1	φ(k2)φ(x)φ(k1),∀k1	φ(k2)φ(x)φ(k1),∀k1	PROPN
ejpam-4244	226	2	,	,	PUNCT
ejpam-4244	226	3	k2	k2	PROPN
ejpam-4244	226	4	∈	∈	PROPN
ejpam-4244	226	5	k∞	k∞	PROPN
ejpam-4244	226	6	,	,	PUNCT
ejpam-4244	226	7	∀x	∀x	X
ejpam-4244	226	8	∈	∈	PROPN
ejpam-4244	226	9	g∞	g∞	NOUN
ejpam-4244	226	10	and	and	CCONJ
ejpam-4244	226	11	by	by	ADP
ejpam-4244	226	12	the	the	DET
ejpam-4244	226	13	lemma	lemma	PROPN
ejpam-4244	226	14	2	2	NUM
ejpam-4244	226	15	i	i	NOUN
ejpam-4244	226	16	)	)	PUNCT
ejpam-4244	226	17	,	,	PUNCT
ejpam-4244	226	18	i∞	i∞	NOUN
ejpam-4244	226	19	=	=	SYM
ejpam-4244	226	20	lim	lim	PROPN
ejpam-4244	226	21	n→∞	n→∞	NUM
ejpam-4244	227	1	∫	∫	PROPN
ejpam-4244	227	2	kn	kn	PROPN
ejpam-4244	227	3	χδn(k)φ(k)dαn(k	χδn(k)φ(k)dαn(k	PROPN
ejpam-4244	227	4	)	)	PUNCT
ejpam-4244	227	5	.	.	PUNCT
ejpam-4244	228	1	so	so	ADV
ejpam-4244	228	2	we	we	PRON
ejpam-4244	228	3	have	have	VERB
ejpam-4244	228	4	:	:	PUNCT
ejpam-4244	228	5	(	(	PUNCT
ejpam-4244	228	6	φ(x)v	φ(x)v	PROPN
ejpam-4244	228	7	,	,	PUNCT
ejpam-4244	228	8	v	v	NOUN
ejpam-4244	228	9	)	)	PUNCT
ejpam-4244	228	10	=	=	VERB
ejpam-4244	229	1	lim	lim	PROPN
ejpam-4244	229	2	n→∞	n→∞	NUM
ejpam-4244	229	3	m→∞	m→∞	NUM
ejpam-4244	229	4	∫	∫	PROPN
ejpam-4244	230	1	kn	kn	PROPN
ejpam-4244	230	2	∫	∫	PROPN
ejpam-4244	230	3	km	km	PROPN
ejpam-4244	230	4	χδn(k1)χδm(k	χδn(k1)χδm(k	PROPN
ejpam-4244	230	5	−1	−1	NOUN
ejpam-4244	230	6	2	2	NUM
ejpam-4244	230	7	)	)	PUNCT
ejpam-4244	230	8	(	(	PUNCT
ejpam-4244	230	9	φ(x)φ(k1)v	φ(x)φ(k1)v	VERB
ejpam-4244	230	10	,	,	PUNCT
ejpam-4244	230	11	φ(k2)v)dαn(k1)dαm(k2	φ(k2)v)dαn(k1)dαm(k2	NOUN
ejpam-4244	230	12	)	)	PUNCT
ejpam-4244	230	13	=	=	SYM
ejpam-4244	230	14	lim	lim	PROPN
ejpam-4244	230	15	n→∞	n→∞	NUM
ejpam-4244	230	16	m→∞	m→∞	NUM
ejpam-4244	230	17	∫	∫	PROPN
ejpam-4244	230	18	kn	kn	PROPN
ejpam-4244	230	19	∫	∫	PROPN
ejpam-4244	230	20	km	km	PROPN
ejpam-4244	230	21	χδn(k1)χδm(k	χδn(k1)χδm(k	PROPN
ejpam-4244	230	22	−1	−1	NOUN
ejpam-4244	230	23	2	2	NUM
ejpam-4244	230	24	)	)	PUNCT
ejpam-4244	230	25	(	(	PUNCT
ejpam-4244	230	26	φ(k−1	φ(k−1	PROPN
ejpam-4244	230	27	2	2	NUM
ejpam-4244	230	28	)	)	PUNCT
ejpam-4244	230	29	φ(x)φ(k1)v	φ(x)φ(k1)v	VERB
ejpam-4244	230	30	,	,	PUNCT
ejpam-4244	230	31	v)dαn(k1)dαm(k2	v)dαn(k1)dαm(k2	NOUN
ejpam-4244	230	32	)	)	PUNCT
ejpam-4244	231	1	=	=	SYM
ejpam-4244	231	2	lim	lim	PROPN
ejpam-4244	231	3	n→∞	n→∞	NUM
ejpam-4244	231	4	m→∞	m→∞	NUM
ejpam-4244	231	5	∫	∫	PROPN
ejpam-4244	232	1	kn	kn	PROPN
ejpam-4244	232	2	∫	∫	PROPN
ejpam-4244	232	3	km	km	PROPN
ejpam-4244	232	4	χδn(k1)χδm(k	χδn(k1)χδm(k	PROPN
ejpam-4244	232	5	−1	−1	NOUN
ejpam-4244	232	6	2	2	NUM
ejpam-4244	232	7	)	)	PUNCT
ejpam-4244	232	8	(	(	PUNCT
ejpam-4244	232	9	φ(k1xk	φ(k1xk	NUM
ejpam-4244	232	10	−1	−1	NOUN
ejpam-4244	232	11	2	2	NUM
ejpam-4244	232	12	)	)	PUNCT
ejpam-4244	232	13	v	v	NOUN
ejpam-4244	232	14	,	,	PUNCT
ejpam-4244	232	15	v)dαn(k1)dαm(k2	v)dαn(k1)dαm(k2	NOUN
ejpam-4244	232	16	)	)	PUNCT
ejpam-4244	232	17	=	=	SYM
ejpam-4244	232	18	lim	lim	PROPN
ejpam-4244	232	19	n→∞	n→∞	NUM
ejpam-4244	232	20	m→∞	m→∞	NUM
ejpam-4244	233	1	∫	∫	PROPN
ejpam-4244	233	2	kn	kn	PROPN
ejpam-4244	233	3	∫	∫	PROPN
ejpam-4244	233	4	km	km	PROPN
ejpam-4244	233	5	χδn(k1)χδm(k	χδn(k1)χδm(k	PROPN
ejpam-4244	233	6	−1	−1	NOUN
ejpam-4244	233	7	2	2	NUM
ejpam-4244	233	8	)	)	PUNCT
ejpam-4244	233	9	(	(	PUNCT
ejpam-4244	233	10	ξl	ξl	NOUN
ejpam-4244	233	11	,	,	PUNCT
ejpam-4244	233	12	u	u	NOUN
ejpam-4244	233	13	l(k1xk	l(k1xk	X
ejpam-4244	233	14	−1	−1	NOUN
ejpam-4244	233	15	2	2	NUM
ejpam-4244	233	16	)	)	PUNCT
ejpam-4244	233	17	ξl)dαn(k1)dαm(k2	ξl)dαn(k1)dαm(k2	NOUN
ejpam-4244	233	18	)	)	PUNCT
ejpam-4244	234	1	=	=	SYM
ejpam-4244	234	2	lim	lim	PROPN
ejpam-4244	234	3	n→∞	n→∞	NUM
ejpam-4244	234	4	m→∞	m→∞	NUM
ejpam-4244	234	5	∫	∫	PROPN
ejpam-4244	235	1	kn	kn	PROPN
ejpam-4244	235	2	∫	∫	PROPN
ejpam-4244	235	3	km	km	PROPN
ejpam-4244	235	4	χδn(k1)χδm(k	χδn(k1)χδm(k	PROPN
ejpam-4244	235	5	−1	−1	NOUN
ejpam-4244	235	6	2	2	NUM
ejpam-4244	235	7	)	)	PUNCT
ejpam-4244	235	8	(	(	PUNCT
ejpam-4244	235	9	u	u	NOUN
ejpam-4244	235	10	l(k−1	l(k−1	PROPN
ejpam-4244	235	11	1	1	NUM
ejpam-4244	235	12	)	)	PUNCT
ejpam-4244	235	13	,	,	PUNCT
ejpam-4244	235	14	u	u	PROPN
ejpam-4244	235	15	l(x)u	l(x)u	PROPN
ejpam-4244	235	16	l(k−1	l(k−1	PROPN
ejpam-4244	235	17	2	2	NUM
ejpam-4244	235	18	)	)	PUNCT
ejpam-4244	235	19	ξl)dαn(k1)dαm(k2	ξl)dαn(k1)dαm(k2	NOUN
ejpam-4244	235	20	)	)	PUNCT
ejpam-4244	236	1	=	=	SYM
ejpam-4244	236	2	lim	lim	PROPN
ejpam-4244	236	3	n→∞	n→∞	NUM
ejpam-4244	236	4	m→∞	m→∞	NOUN
ejpam-4244	236	5	(	(	PUNCT
ejpam-4244	236	6	u	u	NOUN
ejpam-4244	236	7	l(x−1)pnξ	l(x−1)pnξ	NOUN
ejpam-4244	236	8	l	l	NOUN
ejpam-4244	236	9	,	,	PUNCT
ejpam-4244	236	10	pmξl	pmξl	NOUN
ejpam-4244	236	11	)	)	PUNCT
ejpam-4244	236	12	=	=	PUNCT
ejpam-4244	236	13	(	(	PUNCT
ejpam-4244	236	14	u	u	NOUN
ejpam-4244	236	15	l(x−1)pξl	l(x−1)pξl	PROPN
ejpam-4244	236	16	,	,	PUNCT
ejpam-4244	236	17	p	p	NOUN
ejpam-4244	236	18	ξl	ξl	NOUN
ejpam-4244	236	19	)	)	PUNCT
ejpam-4244	236	20	=	=	SYM
ejpam-4244	236	21	(	(	PUNCT
ejpam-4244	236	22	pu	pu	PROPN
ejpam-4244	236	23	l(x−1)pξl	l(x−1)pξl	PROPN
ejpam-4244	236	24	,	,	PUNCT
ejpam-4244	236	25	ξl	ξl	NOUN
ejpam-4244	236	26	)	)	PUNCT
ejpam-4244	236	27	therefore	therefore	ADV
ejpam-4244	236	28	we	we	PRON
ejpam-4244	236	29	can	can	AUX
ejpam-4244	236	30	assume	assume	VERB
ejpam-4244	236	31	ξl	ξl	NUM
ejpam-4244	236	32	∈	∈	PROPN
ejpam-4244	236	33	hl(δ∞	hl(δ∞	NOUN
ejpam-4244	236	34	)	)	PUNCT
ejpam-4244	236	35	by	by	ADP
ejpam-4244	236	36	changing	change	VERB
ejpam-4244	236	37	hl	hl	NOUN
ejpam-4244	236	38	by	by	ADP
ejpam-4244	236	39	the	the	DET
ejpam-4244	236	40	subspace	subspace	NOUN
ejpam-4244	236	41	generated	generate	VERB
ejpam-4244	236	42	by	by	ADP
ejpam-4244	236	43	pξl	pξl	PROPN
ejpam-4244	236	44	.	.	PUNCT
ejpam-4244	237	1	let	let	VERB
ejpam-4244	237	2	us	we	PRON
ejpam-4244	237	3	put	put	VERB
ejpam-4244	237	4	φu	φu	ADP
ejpam-4244	237	5	l	l	NOUN
ejpam-4244	237	6	(	(	PUNCT
ejpam-4244	237	7	x	x	X
ejpam-4244	237	8	)	)	PUNCT
ejpam-4244	237	9	=	=	SYM
ejpam-4244	237	10	pu	pu	PROPN
ejpam-4244	237	11	l(x−1)p	l(x−1)p	PROPN
ejpam-4244	237	12	,	,	PUNCT
ejpam-4244	237	13	∀x	∀x	VERB
ejpam-4244	237	14	∈	∈	PROPN
ejpam-4244	237	15	g∞.	g∞.	PROPN
ejpam-4244	237	16	l.	l.	PROPN
ejpam-4244	237	17	timite	timite	PROPN
ejpam-4244	237	18	,	,	PUNCT
ejpam-4244	237	19	i.	i.	PROPN
ejpam-4244	237	20	toure	toure	PROPN
ejpam-4244	237	21	/	/	SYM
ejpam-4244	237	22	eur	eur	PROPN
ejpam-4244	237	23	.	.	PUNCT
ejpam-4244	238	1	j.	j.	PROPN
ejpam-4244	238	2	pure	pure	PROPN
ejpam-4244	238	3	appl	appl	PROPN
ejpam-4244	238	4	.	.	PROPN
ejpam-4244	238	5	math	math	PROPN
ejpam-4244	238	6	,	,	PUNCT
ejpam-4244	238	7	15	15	NUM
ejpam-4244	238	8	(	(	PUNCT
ejpam-4244	238	9	1	1	NUM
ejpam-4244	238	10	)	)	PUNCT
ejpam-4244	238	11	(	(	PUNCT
ejpam-4244	238	12	2022	2022	NUM
ejpam-4244	238	13	)	)	PUNCT
ejpam-4244	238	14	,	,	PUNCT
ejpam-4244	238	15	249	249	NUM
ejpam-4244	238	16	-	-	SYM
ejpam-4244	238	17	260	260	NUM
ejpam-4244	238	18	258	258	NUM
ejpam-4244	238	19	hence	hence	ADV
ejpam-4244	238	20	(	(	PUNCT
ejpam-4244	238	21	φ(x)v	φ(x)v	PROPN
ejpam-4244	238	22	,	,	PUNCT
ejpam-4244	238	23	v	v	NOUN
ejpam-4244	238	24	)	)	PUNCT
ejpam-4244	238	25	=	=	PUNCT
ejpam-4244	238	26	(	(	PUNCT
ejpam-4244	238	27	φu	φu	NOUN
ejpam-4244	238	28	l	l	NOUN
ejpam-4244	238	29	(	(	PUNCT
ejpam-4244	238	30	x)ξl	x)ξl	PROPN
ejpam-4244	238	31	,	,	PUNCT
ejpam-4244	238	32	ξl	ξl	NOUN
ejpam-4244	238	33	)	)	PUNCT
ejpam-4244	238	34	,	,	PUNCT
ejpam-4244	238	35	∀x	∀x	VERB
ejpam-4244	238	36	∈	∈	PROPN
ejpam-4244	238	37	g∞	g∞	X
ejpam-4244	238	38	(	(	PUNCT
ejpam-4244	238	39	3.1	3.1	NUM
ejpam-4244	238	40	)	)	PUNCT
ejpam-4244	238	41	thanks	thank	NOUN
ejpam-4244	238	42	to	to	ADP
ejpam-4244	238	43	lemma	lemma	PROPN
ejpam-4244	238	44	2	2	PROPN
ejpam-4244	238	45	ii	ii	NOUN
ejpam-4244	238	46	)	)	PUNCT
ejpam-4244	238	47	,	,	PUNCT
ejpam-4244	238	48	we	we	PRON
ejpam-4244	238	49	have	have	AUX
ejpam-4244	238	50	φ(k	φ(k	PROPN
ejpam-4244	238	51	)	)	PUNCT
ejpam-4244	238	52	=	=	SYM
ejpam-4244	238	53	δ(k−1	δ(k−1	PROPN
ejpam-4244	238	54	)	)	PUNCT
ejpam-4244	238	55	,	,	PUNCT
ejpam-4244	238	56	∀k	∀k	X
ejpam-4244	238	57	∈	∈	NOUN
ejpam-4244	238	58	k∞.	k∞.	X
ejpam-4244	238	59	thus	thus	ADV
ejpam-4244	238	60	any	any	DET
ejpam-4244	238	61	vector	vector	NOUN
ejpam-4244	238	62	u	u	NOUN
ejpam-4244	238	63	of	of	ADP
ejpam-4244	238	64	e∞	e∞	PROPN
ejpam-4244	238	65	can	can	AUX
ejpam-4244	238	66	be	be	AUX
ejpam-4244	238	67	expressed	express	VERB
ejpam-4244	238	68	as	as	ADP
ejpam-4244	238	69	a	a	DET
ejpam-4244	238	70	linear	linear	ADJ
ejpam-4244	238	71	combination	combination	NOUN
ejpam-4244	238	72	∑	∑	PUNCT
ejpam-4244	238	73	iφ(ki)v	iφ(ki)v	VERB
ejpam-4244	238	74	,	,	PUNCT
ejpam-4244	238	75	where	where	SCONJ
ejpam-4244	238	76	ki	ki	PROPN
ejpam-4244	238	77	∈	∈	PROPN
ejpam-4244	238	78	k∞,∀i	k∞,∀i	PROPN
ejpam-4244	238	79	.	.	PUNCT
ejpam-4244	239	1	let	let	VERB
ejpam-4244	239	2	t	t	NOUN
ejpam-4244	239	3	:	:	PUNCT
ejpam-4244	239	4	eδ∞	eδ∞	VERB
ejpam-4244	239	5	−→	−→	ADJ
ejpam-4244	239	6	hl(δ∞	hl(δ∞	NOUN
ejpam-4244	239	7	)	)	PUNCT
ejpam-4244	239	8	be	be	VERB
ejpam-4244	239	9	the	the	DET
ejpam-4244	239	10	function	function	NOUN
ejpam-4244	239	11	defined	define	VERB
ejpam-4244	239	12	by	by	ADP
ejpam-4244	239	13	:	:	PUNCT
ejpam-4244	239	14	t	t	PROPN
ejpam-4244	239	15	(	(	PUNCT
ejpam-4244	239	16	∑	∑	PUNCT
ejpam-4244	239	17	i	i	PRON
ejpam-4244	239	18	aiφ(ki)v	aiφ(ki)v	VERB
ejpam-4244	239	19	)	)	PUNCT
ejpam-4244	240	1	=	=	PUNCT
ejpam-4244	240	2	∑	∑	PUNCT
ejpam-4244	241	1	i	i	PRON
ejpam-4244	241	2	aiφ	aiφ	ADV
ejpam-4244	241	3	u	u	VERB
ejpam-4244	241	4	l	l	NOUN
ejpam-4244	241	5	(	(	PUNCT
ejpam-4244	241	6	ki)ξ	ki)ξ	PROPN
ejpam-4244	241	7	l	l	NOUN
ejpam-4244	241	8	,	,	PUNCT
ejpam-4244	241	9	where	where	SCONJ
ejpam-4244	241	10	ai	ai	VERB
ejpam-4244	241	11	∈	∈	PROPN
ejpam-4244	241	12	c	c	NOUN
ejpam-4244	241	13	,	,	PUNCT
ejpam-4244	241	14	and	and	CCONJ
ejpam-4244	241	15	ki	ki	PROPN
ejpam-4244	241	16	∈	∈	PROPN
ejpam-4244	241	17	k∞	k∞	PROPN
ejpam-4244	241	18	,	,	PUNCT
ejpam-4244	241	19	∀i	∀i	NOUN
ejpam-4244	241	20	.	.	PUNCT
ejpam-4244	242	1	let	let	VERB
ejpam-4244	242	2	us	we	PRON
ejpam-4244	242	3	show	show	VERB
ejpam-4244	242	4	that	that	SCONJ
ejpam-4244	242	5	t	t	PROPN
ejpam-4244	242	6	is	be	AUX
ejpam-4244	242	7	well	well	ADV
ejpam-4244	242	8	-	-	PUNCT
ejpam-4244	242	9	defined	define	VERB
ejpam-4244	242	10	.	.	PUNCT
ejpam-4244	243	1	for	for	ADP
ejpam-4244	243	2	that	that	PRON
ejpam-4244	243	3	we	we	PRON
ejpam-4244	243	4	assume	assume	VERB
ejpam-4244	243	5	that	that	SCONJ
ejpam-4244	243	6	∑	∑	PROPN
ejpam-4244	243	7	i	i	PRON
ejpam-4244	243	8	aiφ(ki)v	aiφ(ki)v	VERB
ejpam-4244	243	9	=	=	PUNCT
ejpam-4244	243	10	0	0	X
ejpam-4244	243	11	.	.	PUNCT
ejpam-4244	244	1	by	by	ADP
ejpam-4244	244	2	the	the	DET
ejpam-4244	244	3	equation	equation	NOUN
ejpam-4244	244	4	(	(	PUNCT
ejpam-4244	244	5	3.1	3.1	NUM
ejpam-4244	244	6	)	)	PUNCT
ejpam-4244	244	7	,	,	PUNCT
ejpam-4244	244	8	we	we	PRON
ejpam-4244	244	9	have	have	VERB
ejpam-4244	244	10	χδn(k)(φ(ykx)v	χδn(k)(φ(ykx)v	NUM
ejpam-4244	244	11	,	,	PUNCT
ejpam-4244	244	12	v	v	NOUN
ejpam-4244	244	13	)	)	PUNCT
ejpam-4244	244	14	=	=	PUNCT
ejpam-4244	245	1	χδn(k)(φ	χδn(k)(φ	PRON
ejpam-4244	245	2	u	u	NOUN
ejpam-4244	245	3	l	l	NOUN
ejpam-4244	245	4	(	(	PUNCT
ejpam-4244	245	5	ykx)ξl	ykx)ξl	ADJ
ejpam-4244	245	6	,	,	PUNCT
ejpam-4244	245	7	ξl),∀x	ξl),∀x	PROPN
ejpam-4244	245	8	,	,	PUNCT
ejpam-4244	245	9	y	y	PROPN
ejpam-4244	245	10	∈	∈	PROPN
ejpam-4244	245	11	g∞	g∞	PROPN
ejpam-4244	245	12	,	,	PUNCT
ejpam-4244	245	13	k	k	PROPN
ejpam-4244	245	14	∈	∈	PROPN
ejpam-4244	245	15	kn	kn	PROPN
ejpam-4244	245	16	.	.	PUNCT
ejpam-4244	245	17	(	(	PUNCT
ejpam-4244	245	18	3.2	3.2	NUM
ejpam-4244	245	19	)	)	PUNCT
ejpam-4244	245	20	by	by	ADP
ejpam-4244	245	21	applying	apply	VERB
ejpam-4244	245	22	integral	integral	ADJ
ejpam-4244	245	23	and	and	CCONJ
ejpam-4244	245	24	limit	limit	NOUN
ejpam-4244	245	25	on	on	ADP
ejpam-4244	245	26	both	both	DET
ejpam-4244	245	27	sides	side	NOUN
ejpam-4244	245	28	of	of	ADP
ejpam-4244	245	29	the	the	DET
ejpam-4244	245	30	equation	equation	NOUN
ejpam-4244	245	31	(	(	PUNCT
ejpam-4244	245	32	3.2	3.2	NUM
ejpam-4244	245	33	)	)	PUNCT
ejpam-4244	245	34	,	,	PUNCT
ejpam-4244	245	35	we	we	PRON
ejpam-4244	245	36	get	get	VERB
ejpam-4244	245	37	(	(	PUNCT
ejpam-4244	245	38	φ(x)φ(y)v	φ(x)φ(y)v	PROPN
ejpam-4244	245	39	,	,	PUNCT
ejpam-4244	245	40	v	v	NOUN
ejpam-4244	245	41	)	)	PUNCT
ejpam-4244	245	42	=	=	PUNCT
ejpam-4244	245	43	(	(	PUNCT
ejpam-4244	245	44	φu	φu	NOUN
ejpam-4244	245	45	l	l	NOUN
ejpam-4244	245	46	(	(	PUNCT
ejpam-4244	245	47	x)φu	x)φu	PROPN
ejpam-4244	245	48	l	l	PROPN
ejpam-4244	245	49	(	(	PUNCT
ejpam-4244	245	50	y)ξl	y)ξl	PROPN
ejpam-4244	245	51	,	,	PUNCT
ejpam-4244	245	52	ξl	ξl	NOUN
ejpam-4244	245	53	)	)	PUNCT
ejpam-4244	245	54	,	,	PUNCT
ejpam-4244	245	55	∀x	∀x	X
ejpam-4244	245	56	,	,	PUNCT
ejpam-4244	245	57	y	y	PROPN
ejpam-4244	245	58	∈	∈	PROPN
ejpam-4244	246	1	g∞.	g∞.	INTJ
ejpam-4244	246	2	hence	hence	ADV
ejpam-4244	246	3	(	(	PUNCT
ejpam-4244	246	4	φ(y)v	φ(y)v	PROPN
ejpam-4244	246	5	,	,	PUNCT
ejpam-4244	246	6	φ(x−1)v	φ(x−1)v	PROPN
ejpam-4244	246	7	)	)	PUNCT
ejpam-4244	246	8	=	=	PUNCT
ejpam-4244	247	1	(	(	PUNCT
ejpam-4244	247	2	φu	φu	NOUN
ejpam-4244	247	3	l	l	NOUN
ejpam-4244	247	4	(	(	PUNCT
ejpam-4244	247	5	y)ξl	y)ξl	PROPN
ejpam-4244	247	6	,	,	PUNCT
ejpam-4244	247	7	φu	φu	ADP
ejpam-4244	247	8	l	l	NOUN
ejpam-4244	247	9	(	(	PUNCT
ejpam-4244	247	10	x−1)ξl),∀x	x−1)ξl),∀x	PROPN
ejpam-4244	247	11	,	,	PUNCT
ejpam-4244	247	12	y	y	PROPN
ejpam-4244	247	13	∈	∈	PROPN
ejpam-4244	247	14	g∞.	g∞.	PROPN
ejpam-4244	247	15	(	(	PUNCT
ejpam-4244	247	16	3.3	3.3	NUM
ejpam-4244	247	17	)	)	PUNCT
ejpam-4244	247	18	we	we	PRON
ejpam-4244	247	19	deduce	deduce	VERB
ejpam-4244	247	20	that	that	PRON
ejpam-4244	247	21	0	0	NUM
ejpam-4244	248	1	=	=	SYM
ejpam-4244	248	2	(	(	PUNCT
ejpam-4244	248	3	∑	∑	PUNCT
ejpam-4244	248	4	i	i	PRON
ejpam-4244	248	5	aiφ(ki)v	aiφ(ki)v	PROPN
ejpam-4244	248	6	,	,	PUNCT
ejpam-4244	248	7	∑	∑	PROPN
ejpam-4244	248	8	j	j	PROPN
ejpam-4244	248	9	bjφ(c	bjφ(c	PROPN
ejpam-4244	248	10	−1	−1	PROPN
ejpam-4244	248	11	j	j	PROPN
ejpam-4244	248	12	)	)	PUNCT
ejpam-4244	248	13	v	v	NOUN
ejpam-4244	248	14	)	)	PUNCT
ejpam-4244	248	15	=	=	SYM
ejpam-4244	248	16	(	(	PUNCT
ejpam-4244	248	17	∑	∑	PUNCT
ejpam-4244	248	18	i	i	PRON
ejpam-4244	248	19	aiφ	aiφ	ADV
ejpam-4244	248	20	u	u	VERB
ejpam-4244	248	21	l	l	NOUN
ejpam-4244	248	22	(	(	PUNCT
ejpam-4244	248	23	ki)ξ	ki)ξ	PROPN
ejpam-4244	248	24	l	l	PROPN
ejpam-4244	248	25	,	,	PUNCT
ejpam-4244	248	26	∑	∑	PUNCT
ejpam-4244	248	27	j	j	PROPN
ejpam-4244	248	28	bjφ	bjφ	PROPN
ejpam-4244	248	29	u	u	NOUN
ejpam-4244	248	30	l	l	NOUN
ejpam-4244	248	31	(	(	PUNCT
ejpam-4244	248	32	c−1	c−1	PROPN
ejpam-4244	248	33	j	j	PROPN
ejpam-4244	248	34	)	)	PUNCT
ejpam-4244	248	35	ξl	ξl	PROPN
ejpam-4244	248	36	)	)	PUNCT
ejpam-4244	248	37	,	,	PUNCT
ejpam-4244	248	38	where	where	SCONJ
ejpam-4244	248	39	cj	cj	NOUN
ejpam-4244	248	40	,	,	PUNCT
ejpam-4244	248	41	ki	ki	PROPN
ejpam-4244	248	42	∈	∈	PROPN
ejpam-4244	248	43	k∞	k∞	PROPN
ejpam-4244	248	44	and	and	CCONJ
ejpam-4244	248	45	ai	ai	VERB
ejpam-4244	248	46	,	,	PUNCT
ejpam-4244	248	47	bj	bj	ADP
ejpam-4244	248	48	∈	∈	PROPN
ejpam-4244	248	49	c	c	X
ejpam-4244	248	50	;	;	PUNCT
ejpam-4244	248	51	∀i,∀j	∀i,∀j	NOUN
ejpam-4244	248	52	.	.	PUNCT
ejpam-4244	249	1	hence	hence	ADV
ejpam-4244	249	2	t	t	PROPN
ejpam-4244	249	3	(	(	PUNCT
ejpam-4244	249	4	∑	∑	PUNCT
ejpam-4244	249	5	i	i	PRON
ejpam-4244	249	6	aiφ(ki)v	aiφ(ki)v	NOUN
ejpam-4244	249	7	)	)	PUNCT
ejpam-4244	249	8	=	=	PUNCT
ejpam-4244	250	1	∑	∑	PUNCT
ejpam-4244	250	2	i	i	PRON
ejpam-4244	250	3	aiφ	aiφ	ADV
ejpam-4244	250	4	u	u	VERB
ejpam-4244	250	5	l	l	NOUN
ejpam-4244	250	6	(	(	PUNCT
ejpam-4244	250	7	ki)ξ	ki)ξ	X
ejpam-4244	250	8	l	l	NOUN
ejpam-4244	250	9	=	=	SYM
ejpam-4244	250	10	0	0	X
ejpam-4244	250	11	.	.	PUNCT
ejpam-4244	251	1	thus	thus	ADV
ejpam-4244	251	2	t	t	PROPN
ejpam-4244	251	3	is	be	AUX
ejpam-4244	251	4	well	well	ADV
ejpam-4244	251	5	defined	define	VERB
ejpam-4244	251	6	.	.	PUNCT
ejpam-4244	252	1	t	t	PROPN
ejpam-4244	252	2	is	be	AUX
ejpam-4244	252	3	obviously	obviously	ADV
ejpam-4244	252	4	linear	linear	ADJ
ejpam-4244	252	5	.	.	PUNCT
ejpam-4244	253	1	now	now	ADV
ejpam-4244	253	2	,	,	PUNCT
ejpam-4244	253	3	let	let	VERB
ejpam-4244	253	4	’s	’s	NOUN
ejpam-4244	253	5	show	show	VERB
ejpam-4244	253	6	that	that	SCONJ
ejpam-4244	253	7	t	t	PROPN
ejpam-4244	253	8	is	be	AUX
ejpam-4244	253	9	bijective	bijective	ADJ
ejpam-4244	253	10	.	.	PUNCT
ejpam-4244	254	1	for	for	ADP
ejpam-4244	254	2	that	that	PRON
ejpam-4244	254	3	we	we	PRON
ejpam-4244	254	4	assume	assume	VERB
ejpam-4244	254	5	that	that	SCONJ
ejpam-4244	254	6	t	t	PROPN
ejpam-4244	254	7	(	(	PUNCT
ejpam-4244	254	8	∑	∑	PUNCT
ejpam-4244	254	9	i	i	PRON
ejpam-4244	254	10	aiφ(ki)v	aiφ(ki)v	NOUN
ejpam-4244	254	11	)	)	PUNCT
ejpam-4244	254	12	=	=	PUNCT
ejpam-4244	255	1	∑	∑	PUNCT
ejpam-4244	255	2	i	i	PRON
ejpam-4244	255	3	aiφ	aiφ	ADV
ejpam-4244	255	4	u	u	VERB
ejpam-4244	255	5	l	l	NOUN
ejpam-4244	255	6	(	(	PUNCT
ejpam-4244	255	7	ki)ξ	ki)ξ	X
ejpam-4244	255	8	l	l	NOUN
ejpam-4244	255	9	=	=	PUNCT
ejpam-4244	255	10	0	0	X
ejpam-4244	255	11	.	.	PUNCT
ejpam-4244	256	1	then	then	ADV
ejpam-4244	256	2	we	we	PRON
ejpam-4244	256	3	claim	claim	VERB
ejpam-4244	256	4	that∑	that∑	VERB
ejpam-4244	256	5	i	i	PRON
ejpam-4244	256	6	aiφ(ki)v	aiφ(ki)v	VERB
ejpam-4244	256	7	=	=	PUNCT
ejpam-4244	256	8	0	0	X
ejpam-4244	256	9	.	.	PUNCT
ejpam-4244	257	1	by	by	ADP
ejpam-4244	257	2	the	the	DET
ejpam-4244	257	3	equation	equation	NOUN
ejpam-4244	257	4	(	(	PUNCT
ejpam-4244	257	5	3.3	3.3	NUM
ejpam-4244	257	6	)	)	PUNCT
ejpam-4244	257	7	,	,	PUNCT
ejpam-4244	257	8	we	we	PRON
ejpam-4244	257	9	have	have	VERB
ejpam-4244	257	10	(	(	PUNCT
ejpam-4244	257	11	φ(y)v	φ(y)v	PROPN
ejpam-4244	257	12	,	,	PUNCT
ejpam-4244	257	13	φ(x−1)v	φ(x−1)v	PROPN
ejpam-4244	257	14	)	)	PUNCT
ejpam-4244	257	15	=	=	PUNCT
ejpam-4244	258	1	(	(	PUNCT
ejpam-4244	258	2	φu	φu	NOUN
ejpam-4244	258	3	l	l	NOUN
ejpam-4244	258	4	(	(	PUNCT
ejpam-4244	258	5	y)ξl	y)ξl	PROPN
ejpam-4244	258	6	,	,	PUNCT
ejpam-4244	258	7	φu	φu	ADP
ejpam-4244	258	8	l	l	NOUN
ejpam-4244	258	9	(	(	PUNCT
ejpam-4244	258	10	x−1)ξl),∀x	x−1)ξl),∀x	PROPN
ejpam-4244	258	11	,	,	PUNCT
ejpam-4244	258	12	y	y	PROPN
ejpam-4244	258	13	∈	∈	PROPN
ejpam-4244	259	1	g∞.	g∞.	INTJ
ejpam-4244	259	2	hence	hence	ADV
ejpam-4244	259	3	0	0	NUM
ejpam-4244	260	1	=	=	SYM
ejpam-4244	260	2	(	(	PUNCT
ejpam-4244	260	3	∑	∑	PUNCT
ejpam-4244	260	4	i	i	PRON
ejpam-4244	260	5	aiφ(ki)v	aiφ(ki)v	PROPN
ejpam-4244	260	6	,	,	PUNCT
ejpam-4244	260	7	∑	∑	PROPN
ejpam-4244	260	8	j	j	PROPN
ejpam-4244	260	9	bjφ(c	bjφ(c	PROPN
ejpam-4244	260	10	−1	−1	PROPN
ejpam-4244	260	11	j	j	PROPN
ejpam-4244	260	12	)	)	PUNCT
ejpam-4244	260	13	v	v	NOUN
ejpam-4244	260	14	)	)	PUNCT
ejpam-4244	260	15	=	=	SYM
ejpam-4244	260	16	(	(	PUNCT
ejpam-4244	260	17	∑	∑	PUNCT
ejpam-4244	260	18	i	i	PRON
ejpam-4244	260	19	aiφ	aiφ	ADV
ejpam-4244	260	20	u	u	VERB
ejpam-4244	260	21	l	l	NOUN
ejpam-4244	260	22	(	(	PUNCT
ejpam-4244	260	23	ki)ξ	ki)ξ	PROPN
ejpam-4244	260	24	l	l	PROPN
ejpam-4244	260	25	,	,	PUNCT
ejpam-4244	260	26	∑	∑	PUNCT
ejpam-4244	260	27	j	j	PROPN
ejpam-4244	260	28	bjφ	bjφ	PROPN
ejpam-4244	260	29	u	u	NOUN
ejpam-4244	260	30	l	l	NOUN
ejpam-4244	260	31	(	(	PUNCT
ejpam-4244	260	32	c−1	c−1	PROPN
ejpam-4244	260	33	j	j	PROPN
ejpam-4244	260	34	)	)	PUNCT
ejpam-4244	260	35	ξl	ξl	PROPN
ejpam-4244	260	36	)	)	PUNCT
ejpam-4244	260	37	,	,	PUNCT
ejpam-4244	260	38	where	where	SCONJ
ejpam-4244	260	39	cj	cj	NOUN
ejpam-4244	260	40	,	,	PUNCT
ejpam-4244	260	41	ki	ki	PROPN
ejpam-4244	260	42	∈	∈	PROPN
ejpam-4244	260	43	k∞,∀i,∀j	k∞,∀i,∀j	PROPN
ejpam-4244	260	44	.	.	PUNCT
ejpam-4244	261	1	then	then	ADV
ejpam-4244	261	2	∑	∑	PUNCT
ejpam-4244	261	3	i	i	PRON
ejpam-4244	261	4	aiφ(ki)v	aiφ(ki)v	VERB
ejpam-4244	261	5	=	=	PUNCT
ejpam-4244	261	6	0	0	X
ejpam-4244	261	7	.	.	PUNCT
ejpam-4244	262	1	consequently	consequently	ADV
ejpam-4244	262	2	t	t	PROPN
ejpam-4244	262	3	is	be	AUX
ejpam-4244	262	4	bijective	bijective	ADJ
ejpam-4244	262	5	.	.	PUNCT
ejpam-4244	263	1	in	in	ADP
ejpam-4244	263	2	other	other	ADJ
ejpam-4244	263	3	hand	hand	NOUN
ejpam-4244	263	4	,	,	PUNCT
ejpam-4244	263	5	we	we	PRON
ejpam-4244	263	6	have	have	VERB
ejpam-4244	263	7	(	(	PUNCT
ejpam-4244	263	8	t	t	PROPN
ejpam-4244	263	9	∑	∑	PUNCT
ejpam-4244	263	10	i	i	PRON
ejpam-4244	263	11	aiφ(ki)v	aiφ(ki)v	PROPN
ejpam-4244	263	12	,	,	PUNCT
ejpam-4244	263	13	t	t	PROPN
ejpam-4244	263	14	∑	∑	PROPN
ejpam-4244	263	15	j	j	PROPN
ejpam-4244	263	16	bjφ(cj)v	bjφ(cj)v	PROPN
ejpam-4244	263	17	)	)	PUNCT
ejpam-4244	263	18	=	=	PRON
ejpam-4244	264	1	(	(	PUNCT
ejpam-4244	264	2	∑	∑	PUNCT
ejpam-4244	264	3	i	i	PRON
ejpam-4244	264	4	aiφ	aiφ	ADV
ejpam-4244	264	5	u	u	VERB
ejpam-4244	264	6	l	l	NOUN
ejpam-4244	264	7	(	(	PUNCT
ejpam-4244	264	8	ki)ξ	ki)ξ	PROPN
ejpam-4244	264	9	l	l	PROPN
ejpam-4244	264	10	,	,	PUNCT
ejpam-4244	264	11	∑	∑	PUNCT
ejpam-4244	264	12	j	j	PROPN
ejpam-4244	264	13	bjφ	bjφ	PROPN
ejpam-4244	264	14	u	u	PROPN
ejpam-4244	264	15	l	l	PROPN
ejpam-4244	264	16	(	(	PUNCT
ejpam-4244	264	17	cj)ξ	cj)ξ	PROPN
ejpam-4244	264	18	l	l	NOUN
ejpam-4244	264	19	)	)	PUNCT
ejpam-4244	264	20	references	reference	VERB
ejpam-4244	264	21	259	259	NUM
ejpam-4244	264	22	=	=	SYM
ejpam-4244	264	23	∑	∑	PUNCT
ejpam-4244	264	24	i	i	PRON
ejpam-4244	264	25	∑	∑	PUNCT
ejpam-4244	264	26	j	j	PROPN
ejpam-4244	264	27	aibj(φ	aibj(φ	NUM
ejpam-4244	264	28	u	u	NOUN
ejpam-4244	264	29	l	l	NOUN
ejpam-4244	264	30	(	(	PUNCT
ejpam-4244	264	31	c−1	c−1	PROPN
ejpam-4244	264	32	j	j	PROPN
ejpam-4244	264	33	ki)ξ	ki)ξ	PROPN
ejpam-4244	264	34	l	l	PROPN
ejpam-4244	264	35	,	,	PUNCT
ejpam-4244	264	36	ξl	ξl	NOUN
ejpam-4244	264	37	)	)	PUNCT
ejpam-4244	264	38	=	=	PUNCT
ejpam-4244	265	1	∑	∑	PUNCT
ejpam-4244	265	2	i	i	X
ejpam-4244	265	3	∑	∑	PROPN
ejpam-4244	265	4	j	j	PROPN
ejpam-4244	265	5	aibj(φ(c	aibj(φ(c	PROPN
ejpam-4244	265	6	−1	−1	NOUN
ejpam-4244	265	7	j	j	PROPN
ejpam-4244	265	8	ki)v	ki)v	PROPN
ejpam-4244	265	9	,	,	PUNCT
ejpam-4244	265	10	v	v	NOUN
ejpam-4244	265	11	)	)	PUNCT
ejpam-4244	265	12	=	=	PUNCT
ejpam-4244	266	1	(	(	PUNCT
ejpam-4244	266	2	∑	∑	PUNCT
ejpam-4244	266	3	i	i	PRON
ejpam-4244	266	4	aiφ(ki)v	aiφ(ki)v	PROPN
ejpam-4244	266	5	,	,	PUNCT
ejpam-4244	266	6	∑	∑	PROPN
ejpam-4244	266	7	j	j	PROPN
ejpam-4244	266	8	bjφ(cj)v	bjφ(cj)v	PROPN
ejpam-4244	266	9	)	)	PUNCT
ejpam-4244	266	10	then	then	ADV
ejpam-4244	266	11	t	t	PROPN
ejpam-4244	266	12	is	be	AUX
ejpam-4244	266	13	a	a	DET
ejpam-4244	266	14	unitary	unitary	ADJ
ejpam-4244	266	15	linear	linear	ADJ
ejpam-4244	266	16	isomorphism	isomorphism	NOUN
ejpam-4244	266	17	.	.	PUNCT
ejpam-4244	267	1	for	for	ADP
ejpam-4244	267	2	any	any	DET
ejpam-4244	267	3	g	g	PROPN
ejpam-4244	267	4	∈	∈	PROPN
ejpam-4244	267	5	g∞	g∞	PROPN
ejpam-4244	267	6	,	,	PUNCT
ejpam-4244	267	7	we	we	PRON
ejpam-4244	267	8	have	have	VERB
ejpam-4244	267	9	tφ(g	tφ(g	PUNCT
ejpam-4244	267	10	)	)	PUNCT
ejpam-4244	268	1	∑	∑	PUNCT
ejpam-4244	268	2	i	i	PRON
ejpam-4244	268	3	aiφ(ki)v	aiφ(ki)v	NOUN
ejpam-4244	268	4	=	=	PUNCT
ejpam-4244	268	5	lim	lim	PROPN
ejpam-4244	268	6	n→∞	n→∞	NUM
ejpam-4244	268	7	∑	∑	PROPN
ejpam-4244	268	8	i	i	PRON
ejpam-4244	268	9	ai	ai	VERB
ejpam-4244	268	10	∫	∫	PROPN
ejpam-4244	268	11	kn	kn	PROPN
ejpam-4244	268	12	χδn(k)tφ(kikg)vdαn(k	χδn(k)tφ(kikg)vdαn(k	PROPN
ejpam-4244	268	13	)	)	PUNCT
ejpam-4244	269	1	=	=	VERB
ejpam-4244	269	2	lim	lim	PROPN
ejpam-4244	269	3	n→∞	n→∞	NUM
ejpam-4244	269	4	∑	∑	PROPN
ejpam-4244	270	1	i	i	PRON
ejpam-4244	270	2	ai	ai	VERB
ejpam-4244	270	3	∫	∫	PROPN
ejpam-4244	270	4	kn	kn	PROPN
ejpam-4244	270	5	χδn(k)φ	χδn(k)φ	PROPN
ejpam-4244	270	6	u	u	PROPN
ejpam-4244	270	7	l	l	NOUN
ejpam-4244	270	8	(	(	PUNCT
ejpam-4244	270	9	kikg)ξ	kikg)ξ	PROPN
ejpam-4244	270	10	ldαn(k	ldαn(k	PROPN
ejpam-4244	270	11	)	)	PUNCT
ejpam-4244	270	12	=	=	SYM
ejpam-4244	270	13	φu	φu	NOUN
ejpam-4244	270	14	l	l	NOUN
ejpam-4244	270	15	(	(	PUNCT
ejpam-4244	270	16	g	g	NOUN
ejpam-4244	270	17	)	)	PUNCT
ejpam-4244	270	18	∑	∑	PUNCT
ejpam-4244	270	19	i	i	PRON
ejpam-4244	270	20	aiφ	aiφ	VERB
ejpam-4244	270	21	u	u	VERB
ejpam-4244	270	22	l	l	NOUN
ejpam-4244	270	23	(	(	PUNCT
ejpam-4244	270	24	ki)ξ	ki)ξ	X
ejpam-4244	270	25	l	l	NOUN
ejpam-4244	270	26	=	=	PUNCT
ejpam-4244	270	27	φu	φu	PROPN
ejpam-4244	270	28	l	l	NOUN
ejpam-4244	270	29	(	(	PUNCT
ejpam-4244	270	30	g)t	g)t	X
ejpam-4244	270	31	∑	∑	ADP
ejpam-4244	270	32	i	i	PROPN
ejpam-4244	270	33	aiφ(ki)v	aiφ(ki)v	NOUN
ejpam-4244	270	34	,	,	PUNCT
ejpam-4244	270	35	consequently	consequently	ADV
ejpam-4244	270	36	φ	φ	PROPN
ejpam-4244	270	37	is	be	AUX
ejpam-4244	270	38	unitarily	unitarily	ADV
ejpam-4244	270	39	equivalent	equivalent	ADJ
ejpam-4244	270	40	to	to	ADP
ejpam-4244	270	41	φu	φu	ADP
ejpam-4244	270	42	l	l	NOUN
ejpam-4244	270	43	which	which	PRON
ejpam-4244	270	44	is	be	AUX
ejpam-4244	270	45	a	a	DET
ejpam-4244	270	46	δ∞-spherical	δ∞-spherical	ADJ
ejpam-4244	270	47	function	function	NOUN
ejpam-4244	270	48	.	.	PUNCT
ejpam-4244	271	1	therefore	therefore	ADV
ejpam-4244	271	2	φ	φ	PROPN
ejpam-4244	271	3	is	be	AUX
ejpam-4244	271	4	a	a	DET
ejpam-4244	271	5	δ∞-spherical	δ∞-spherical	ADJ
ejpam-4244	271	6	function	function	NOUN
ejpam-4244	271	7	.	.	PUNCT
ejpam-4244	272	1	references	reference	NOUN
ejpam-4244	272	2	[	[	X
ejpam-4244	272	3	1	1	X
ejpam-4244	272	4	]	]	PUNCT
ejpam-4244	272	5	j.	j.	PROPN
ejpam-4244	272	6	faraut	faraut	PROPN
ejpam-4244	272	7	.	.	PUNCT
ejpam-4244	273	1	infinite	infinite	ADJ
ejpam-4244	273	2	dimensional	dimensional	ADJ
ejpam-4244	273	3	harmonic	harmonic	ADJ
ejpam-4244	273	4	analysis	analysis	NOUN
ejpam-4244	273	5	and	and	CCONJ
ejpam-4244	273	6	probability	probability	NOUN
ejpam-4244	273	7	in	in	ADP
ejpam-4244	273	8	probability	probability	NOUN
ejpam-4244	273	9	measures	measure	NOUN
ejpam-4244	273	10	on	on	ADP
ejpam-4244	273	11	groups	group	NOUN
ejpam-4244	273	12	:	:	PUNCT
ejpam-4244	273	13	proceedings	proceeding	NOUN
ejpam-4244	273	14	of	of	ADP
ejpam-4244	273	15	the	the	DET
ejpam-4244	273	16	cimpa	cimpa	NOUN
ejpam-4244	273	17	-	-	PUNCT
ejpam-4244	273	18	tifr	tifr	NOUN
ejpam-4244	273	19	school	school	NOUN
ejpam-4244	273	20	on	on	ADP
ejpam-4244	273	21	probabilty	probabilty	NOUN
ejpam-4244	273	22	measures	measure	NOUN
ejpam-4244	273	23	on	on	ADP
ejpam-4244	273	24	groups	group	NOUN
ejpam-4244	273	25	.	.	PUNCT
ejpam-4244	274	1	recent	recent	ADJ
ejpam-4244	274	2	directions	direction	NOUN
ejpam-4244	274	3	and	and	CCONJ
ejpam-4244	274	4	trends	trend	NOUN
ejpam-4244	274	5	.	.	PUNCT
ejpam-4244	275	1	tifr	tifr	PROPN
ejpam-4244	275	2	,	,	PUNCT
ejpam-4244	275	3	mumbai	mumbai	PROPN
ejpam-4244	275	4	,	,	PUNCT
ejpam-4244	275	5	narosa	narosa	PROPN
ejpam-4244	275	6	publishing	publishing	PROPN
ejpam-4244	275	7	house	house	PROPN
ejpam-4244	275	8	,	,	PUNCT
ejpam-4244	275	9	2006	2006	NUM
ejpam-4244	275	10	.	.	PUNCT
ejpam-4244	276	1	[	[	X
ejpam-4244	276	2	2	2	X
ejpam-4244	276	3	]	]	PUNCT
ejpam-4244	276	4	s.	s.	PROPN
ejpam-4244	276	5	kerov	kerov	PROPN
ejpam-4244	276	6	,	,	PUNCT
ejpam-4244	276	7	g.	g.	PROPN
ejpam-4244	276	8	olshanski	olshanski	PROPN
ejpam-4244	276	9	,	,	PUNCT
ejpam-4244	276	10	a	a	DET
ejpam-4244	276	11	vershik	vershik	ADV
ejpam-4244	276	12	.	.	PUNCT
ejpam-4244	277	1	harmonic	harmonic	ADJ
ejpam-4244	277	2	analysis	analysis	NOUN
ejpam-4244	277	3	on	on	ADP
ejpam-4244	277	4	the	the	DET
ejpam-4244	277	5	infinite	infinite	ADJ
ejpam-4244	277	6	symmetric	symmetric	ADJ
ejpam-4244	277	7	group	group	NOUN
ejpam-4244	277	8	.	.	PUNCT
ejpam-4244	278	1	invent	invent	NOUN
ejpam-4244	278	2	.	.	PUNCT
ejpam-4244	279	1	math	math	NOUN
ejpam-4244	279	2	.	.	PUNCT
ejpam-4244	280	1	158	158	NUM
ejpam-4244	280	2	,	,	PUNCT
ejpam-4244	280	3	no	no	DET
ejpam-4244	280	4	3(2004	3(2004	NUM
ejpam-4244	280	5	)	)	PUNCT
ejpam-4244	280	6	,	,	PUNCT
ejpam-4244	280	7	551	551	NUM
ejpam-4244	280	8	-	-	SYM
ejpam-4244	280	9	642	642	NUM
ejpam-4244	280	10	.	.	PUNCT
ejpam-4244	281	1	[	[	X
ejpam-4244	281	2	3	3	NUM
ejpam-4244	281	3	]	]	X
ejpam-4244	281	4	r.	r.	PROPN
ejpam-4244	281	5	marouane	marouane	PROPN
ejpam-4244	281	6	,	,	PUNCT
ejpam-4244	281	7	analyse	analyse	PROPN
ejpam-4244	281	8	harmonique	harmonique	PROPN
ejpam-4244	281	9	en	en	PROPN
ejpam-4244	281	10	dimension	dimension	PROPN
ejpam-4244	281	11	infinie	infinie	PROPN
ejpam-4244	281	12	:	:	PUNCT
ejpam-4244	281	13	paires	paire	NOUN
ejpam-4244	281	14	de	de	PROPN
ejpam-4244	281	15	gelfand	gelfand	PROPN
ejpam-4244	281	16	généralisées	généralisées	PROPN
ejpam-4244	281	17	.	.	PUNCT
ejpam-4244	282	1	thèse	thèse	PROPN
ejpam-4244	282	2	de	de	X
ejpam-4244	282	3	doctorat	doctorat	PROPN
ejpam-4244	282	4	de	de	X
ejpam-4244	282	5	l’université	l’université	PROPN
ejpam-4244	282	6	paul	paul	PROPN
ejpam-4244	282	7	verlaine	verlaine	PROPN
ejpam-4244	282	8	-	-	PUNCT
ejpam-4244	282	9	metz	metz	PROPN
ejpam-4244	282	10	ile	ile	PROPN
ejpam-4244	282	11	du	du	PROPN
ejpam-4244	282	12	sauley	sauley	PROPN
ejpam-4244	282	13	,	,	PUNCT
ejpam-4244	282	14	f-57045	f-57045	ADJ
ejpam-4244	282	15	metz	metz	NOUN
ejpam-4244	282	16	cedex	cedex	NOUN
ejpam-4244	282	17	1	1	NUM
ejpam-4244	282	18	,	,	PUNCT
ejpam-4244	282	19	2007	2007	NUM
ejpam-4244	282	20	.	.	PUNCT
ejpam-4244	283	1	[	[	X
ejpam-4244	283	2	4	4	X
ejpam-4244	283	3	]	]	X
ejpam-4244	283	4	g.	g.	NOUN
ejpam-4244	283	5	olshanski	olshanski	PROPN
ejpam-4244	283	6	.	.	PUNCT
ejpam-4244	284	1	the	the	DET
ejpam-4244	284	2	problem	problem	NOUN
ejpam-4244	284	3	of	of	ADP
ejpam-4244	284	4	harmonic	harmonic	ADJ
ejpam-4244	284	5	analysis	analysis	NOUN
ejpam-4244	284	6	on	on	ADP
ejpam-4244	284	7	the	the	DET
ejpam-4244	284	8	infinite	infinite	ADJ
ejpam-4244	284	9	dimensional	dimensional	ADJ
ejpam-4244	284	10	unitary	unitary	ADJ
ejpam-4244	284	11	group	group	NOUN
ejpam-4244	284	12	.	.	PUNCT
ejpam-4244	285	1	j.	j.	PROPN
ejpam-4244	285	2	funct	funct	PROPN
ejpam-4244	285	3	.	.	PUNCT
ejpam-4244	286	1	anal	anal	PROPN
ejpam-4244	286	2	.	.	PUNCT
ejpam-4244	287	1	205	205	NUM
ejpam-4244	287	2	,	,	PUNCT
ejpam-4244	287	3	no	no	DET
ejpam-4244	287	4	2(2003	2(2003	NOUN
ejpam-4244	287	5	)	)	PUNCT
ejpam-4244	287	6	,	,	PUNCT
ejpam-4244	287	7	464	464	NUM
ejpam-4244	287	8	-	-	SYM
ejpam-4244	287	9	524	524	NUM
ejpam-4244	287	10	.	.	PUNCT
ejpam-4244	288	1	[	[	X
ejpam-4244	288	2	5	5	X
ejpam-4244	288	3	]	]	X
ejpam-4244	288	4	g.	g.	NOUN
ejpam-4244	288	5	olshanski	olshanski	PROPN
ejpam-4244	288	6	,	,	PUNCT
ejpam-4244	288	7	a.	a.	NOUN
ejpam-4244	288	8	vershik	vershik	ADV
ejpam-4244	288	9	.	.	PUNCT
ejpam-4244	289	1	ergodic	ergodic	ADJ
ejpam-4244	289	2	unitarily	unitarily	ADV
ejpam-4244	289	3	invariant	invariant	ADJ
ejpam-4244	289	4	measures	measure	NOUN
ejpam-4244	289	5	on	on	ADP
ejpam-4244	289	6	the	the	DET
ejpam-4244	289	7	space	space	NOUN
ejpam-4244	289	8	of	of	ADP
ejpam-4244	289	9	infinite	infinite	ADJ
ejpam-4244	289	10	hermitian	hermitian	ADJ
ejpam-4244	289	11	matrices	matrix	NOUN
ejpam-4244	289	12	.	.	PUNCT
ejpam-4244	290	1	contemporary	contemporary	ADJ
ejpam-4244	290	2	mathematical	mathematical	PROPN
ejpam-4244	290	3	physics	physics	PROPN
ejpam-4244	290	4	(	(	PUNCT
ejpam-4244	290	5	r.	r.	PROPN
ejpam-4244	290	6	l.	l.	PROPN
ejpam-4244	290	7	dobroshin	dobroshin	PROPN
ejpam-4244	290	8	,	,	PUNCT
ejpam-4244	290	9	r.	r.	PROPN
ejpam-4244	290	10	a.	a.	PROPN
ejpam-4244	290	11	minlos	minlos	PROPN
ejpam-4244	290	12	,	,	PUNCT
ejpam-4244	290	13	m.	m.	PROPN
ejpam-4244	290	14	a.	a.	PROPN
ejpam-4244	290	15	shubin	shubin	PROPN
ejpam-4244	290	16	,	,	PUNCT
ejpam-4244	290	17	m.	m.	NOUN
ejpam-4244	290	18	a.	a.	NOUN
ejpam-4244	290	19	vershik	vershik	ADV
ejpam-4244	290	20	)	)	PUNCT
ejpam-4244	290	21	.	.	PUNCT
ejpam-4244	291	1	amer	amer	PROPN
ejpam-4244	291	2	.	.	PUNCT
ejpam-4244	291	3	math	math	PROPN
ejpam-4244	291	4	.	.	PUNCT
ejpam-4244	292	1	soc	soc	NOUN
ejpam-4244	292	2	.	.	PUNCT
ejpam-4244	293	1	translations	translation	NOUN
ejpam-4244	293	2	2	2	NUM
ejpam-4244	293	3	.	.	NUM
ejpam-4244	293	4	175	175	NUM
ejpam-4244	293	5	(	(	PUNCT
ejpam-4244	293	6	1996	1996	NUM
ejpam-4244	293	7	)	)	PUNCT
ejpam-4244	293	8	,	,	PUNCT
ejpam-4244	293	9	137	137	NUM
ejpam-4244	293	10	-	-	SYM
ejpam-4244	293	11	175	175	NUM
ejpam-4244	293	12	.	.	PUNCT
ejpam-4244	294	1	references	reference	NOUN
ejpam-4244	294	2	260	260	NUM
ejpam-4244	294	3	[	[	X
ejpam-4244	294	4	6	6	NUM
ejpam-4244	294	5	]	]	PUNCT
ejpam-4244	294	6	g.	g.	NOUN
ejpam-4244	294	7	olshanski	olshanski	PROPN
ejpam-4244	294	8	.	.	PUNCT
ejpam-4244	295	1	unitary	unitary	ADJ
ejpam-4244	295	2	representation	representation	NOUN
ejpam-4244	295	3	of	of	ADP
ejpam-4244	295	4	infinite	infinite	ADJ
ejpam-4244	295	5	dimensional	dimensional	ADJ
ejpam-4244	295	6	pairs	pair	NOUN
ejpam-4244	295	7	(	(	PUNCT
ejpam-4244	295	8	g	g	NOUN
ejpam-4244	295	9	,	,	PUNCT
ejpam-4244	295	10	k	k	NOUN
ejpam-4244	295	11	)	)	PUNCT
ejpam-4244	295	12	and	and	CCONJ
ejpam-4244	295	13	the	the	DET
ejpam-4244	295	14	formalism	formalism	NOUN
ejpam-4244	295	15	of	of	ADP
ejpam-4244	295	16	r.	r.	PROPN
ejpam-4244	295	17	howe	howe	PROPN
ejpam-4244	295	18	.	.	PUNCT
ejpam-4244	296	1	representation	representation	NOUN
ejpam-4244	296	2	of	of	ADP
ejpam-4244	296	3	lie	lie	NOUN
ejpam-4244	296	4	groups	group	NOUN
ejpam-4244	296	5	and	and	CCONJ
ejpam-4244	296	6	related	related	ADJ
ejpam-4244	296	7	topics	topic	NOUN
ejpam-4244	296	8	.	.	PUNCT
ejpam-4244	297	1	(	(	PUNCT
ejpam-4244	297	2	eds	ed	NOUN
ejpam-4244	297	3	.	.	PUNCT
ejpam-4244	297	4	a.	a.	NOUN
ejpam-4244	297	5	m.	m.	PROPN
ejpam-4244	297	6	vershik	vershik	ADV
ejpam-4244	297	7	,	,	PUNCT
ejpam-4244	297	8	d.	d.	PROPN
ejpam-4244	297	9	p.	p.	PROPN
ejpam-4244	297	10	zhelobenko	zhelobenko	PROPN
ejpam-4244	297	11	)	)	PUNCT
ejpam-4244	297	12	,	,	PUNCT
ejpam-4244	297	13	advanced	advanced	ADJ
ejpam-4244	297	14	studies	study	NOUN
ejpam-4244	297	15	in	in	ADP
ejpam-4244	297	16	contemporary	contemporary	ADJ
ejpam-4244	297	17	mathematics	mathematic	NOUN
ejpam-4244	297	18	.	.	PUNCT
ejpam-4244	298	1	vol	vol	NOUN
ejpam-4244	298	2	7	7	NUM
ejpam-4244	298	3	.	.	PUNCT
ejpam-4244	299	1	gordon	gordon	PROPN
ejpam-4244	299	2	and	and	CCONJ
ejpam-4244	299	3	breach	breach	VERB
ejpam-4244	299	4	,	,	PUNCT
ejpam-4244	299	5	1990	1990	NUM
ejpam-4244	299	6	.	.	PUNCT
ejpam-4244	300	1	[	[	X
ejpam-4244	300	2	7	7	X
ejpam-4244	300	3	]	]	X
ejpam-4244	300	4	e.	e.	PROPN
ejpam-4244	300	5	pedon	pedon	PROPN
ejpam-4244	300	6	,	,	PUNCT
ejpam-4244	300	7	analyse	analyse	PROPN
ejpam-4244	300	8	harmonique	harmonique	PROPN
ejpam-4244	300	9	des	des	X
ejpam-4244	300	10	formes	forme	NOUN
ejpam-4244	300	11	différentielles	différentielles	PROPN
ejpam-4244	300	12	sur	sur	PROPN
ejpam-4244	300	13	l’espace	l’espace	PROPN
ejpam-4244	300	14	hyperbolique	hyperbolique	PROPN
ejpam-4244	300	15	réel	réel	PROPN
ejpam-4244	300	16	,	,	PUNCT
ejpam-4244	300	17	thèse	thèse	PROPN
ejpam-4244	300	18	de	de	X
ejpam-4244	300	19	doctorat	doctorat	PROPN
ejpam-4244	300	20	de	de	X
ejpam-4244	300	21	l’université	l’université	PROPN
ejpam-4244	300	22	henri	henri	PROPN
ejpam-4244	300	23	poincaré	poincaré	PROPN
ejpam-4244	300	24	nancy	nancy	PROPN
ejpam-4244	300	25	1	1	NUM
ejpam-4244	300	26	,	,	PUNCT
ejpam-4244	300	27	1997	1997	NUM
ejpam-4244	300	28	.	.	PUNCT
ejpam-4244	301	1	[	[	X
ejpam-4244	301	2	8	8	NUM
ejpam-4244	301	3	]	]	X
ejpam-4244	301	4	c.	c.	PROPN
ejpam-4244	301	5	roberto	roberto	PROPN
ejpam-4244	301	6	.	.	PUNCT
ejpam-4244	302	1	the	the	DET
ejpam-4244	302	2	spherical	spherical	ADJ
ejpam-4244	302	3	transform	transform	NOUN
ejpam-4244	302	4	for	for	ADP
ejpam-4244	302	5	homogeneous	homogeneous	ADJ
ejpam-4244	302	6	vector	vector	NOUN
ejpam-4244	302	7	bundles	bundle	NOUN
ejpam-4244	302	8	over	over	ADP
ejpam-4244	302	9	riemannian	riemannian	ADJ
ejpam-4244	302	10	symetric	symetric	ADJ
ejpam-4244	302	11	spaces	space	NOUN
ejpam-4244	302	12	.	.	PUNCT
ejpam-4244	303	1	heldermann	heldermann	PROPN
ejpam-4244	303	2	verlag	verlag	PROPN
ejpam-4244	303	3	,	,	PUNCT
ejpam-4244	303	4	1997	1997	NUM
ejpam-4244	303	5	.	.	PUNCT
ejpam-4244	304	1	[	[	X
ejpam-4244	304	2	9	9	NUM
ejpam-4244	304	3	]	]	X
ejpam-4244	304	4	f.	f.	PROPN
ejpam-4244	304	5	ricci	ricci	PROPN
ejpam-4244	304	6	and	and	CCONJ
ejpam-4244	304	7	a.	a.	PROPN
ejpam-4244	304	8	samata	samata	PROPN
ejpam-4244	304	9	,	,	PUNCT
ejpam-4244	304	10	spherical	spherical	ADJ
ejpam-4244	304	11	analysis	analysis	NOUN
ejpam-4244	304	12	on	on	ADP
ejpam-4244	304	13	homogeneous	homogeneous	ADJ
ejpam-4244	304	14	vector	vector	NOUN
ejpam-4244	304	15	bundles	bundle	NOUN
ejpam-4244	304	16	,	,	PUNCT
ejpam-4244	304	17	[	[	X
ejpam-4244	304	18	math.rt	math.rt	X
ejpam-4244	304	19	]	]	X
ejpam-4244	304	20	22	22	NUM
ejpam-4244	304	21	apr	apr	NOUN
ejpam-4244	304	22	2016	2016	NUM
ejpam-4244	304	23	.	.	PUNCT
ejpam-4244	305	1	[	[	X
ejpam-4244	305	2	10	10	NUM
ejpam-4244	305	3	]	]	X
ejpam-4244	305	4	p.	p.	NOUN
ejpam-4244	305	5	roman	roman	PROPN
ejpam-4244	305	6	and	and	CCONJ
ejpam-4244	305	7	j.	j.	PROPN
ejpam-4244	305	8	tirao	tirao	PROPN
ejpam-4244	305	9	,	,	PUNCT
ejpam-4244	305	10	spherical	spherical	ADJ
ejpam-4244	305	11	functions	function	NOUN
ejpam-4244	305	12	,	,	PUNCT
ejpam-4244	305	13	the	the	DET
ejpam-4244	305	14	complex	complex	ADJ
ejpam-4244	305	15	hyperbolic	hyperbolic	ADJ
ejpam-4244	305	16	plane	plane	NOUN
ejpam-4244	305	17	and	and	CCONJ
ejpam-4244	305	18	the	the	DET
ejpam-4244	305	19	hypergeometric	hypergeometric	ADJ
ejpam-4244	305	20	operator	operator	NOUN
ejpam-4244	305	21	,	,	PUNCT
ejpam-4244	305	22	internat	internat	PROPN
ejpam-4244	305	23	.	.	PUNCT
ejpam-4244	306	1	j.	j.	PROPN
ejpam-4244	306	2	math	math	PROPN
ejpam-4244	306	3	.	.	PUNCT
ejpam-4244	307	1	17	17	NUM
ejpam-4244	307	2	,	,	PUNCT
ejpam-4244	307	3	no	no	INTJ
ejpam-4244	307	4	.	.	NOUN
ejpam-4244	308	1	10	10	NUM
ejpam-4244	308	2	1151	1151	NUM
ejpam-4244	308	3	-	-	SYM
ejpam-4244	308	4	1173	1173	NUM
ejpam-4244	308	5	(	(	PUNCT
ejpam-4244	308	6	2006	2006	NUM
ejpam-4244	308	7	)	)	PUNCT
ejpam-4244	308	8	.	.	PUNCT
ejpam-4244	309	1	[	[	X
ejpam-4244	309	2	11	11	NUM
ejpam-4244	309	3	]	]	PUNCT
ejpam-4244	309	4	i.	i.	NOUN
ejpam-4244	309	5	toure	toure	PROPN
ejpam-4244	309	6	,	,	PUNCT
ejpam-4244	309	7	k.	k.	PROPN
ejpam-4244	309	8	kangni	kangni	PROPN
ejpam-4244	309	9	,	,	PUNCT
ejpam-4244	309	10	”	"	PUNCT
ejpam-4244	309	11	a	a	DET
ejpam-4244	309	12	necessary	necessary	ADJ
ejpam-4244	309	13	condition	condition	NOUN
ejpam-4244	309	14	on	on	ADP
ejpam-4244	309	15	gelfand	gelfand	PROPN
ejpam-4244	309	16	triple	triple	ADJ
ejpam-4244	309	17	”	"	PUNCT
ejpam-4244	309	18	,	,	PUNCT
ejpam-4244	309	19	far	far	ADV
ejpam-4244	309	20	east	east	PROPN
ejpam-4244	309	21	j.	j.	PROPN
ejpam-4244	309	22	math	math	PROPN
ejpam-4244	309	23	,	,	PUNCT
ejpam-4244	309	24	2016	2016	NUM
ejpam-4244	309	25	,	,	PUNCT
ejpam-4244	309	26	99	99	NUM
ejpam-4244	309	27	,	,	PUNCT
ejpam-4244	309	28	735	735	NUM
ejpam-4244	309	29	-	-	SYM
ejpam-4244	309	30	742	742	NUM
ejpam-4244	309	31	.	.	PUNCT