id	sid	tid	token	lemma	pos
ejpam-4756	1	1	european	european	PROPN
ejpam-4756	1	2	journal	journal	PROPN
ejpam-4756	1	3	of	of	ADP
ejpam-4756	1	4	pure	pure	ADJ
ejpam-4756	1	5	and	and	CCONJ
ejpam-4756	1	6	applied	apply	VERB
ejpam-4756	1	7	mathematics	mathematic	NOUN
ejpam-4756	1	8	vol	vol	NOUN
ejpam-4756	1	9	.	.	PUNCT
ejpam-4756	2	1	16	16	NUM
ejpam-4756	2	2	,	,	PUNCT
ejpam-4756	2	3	no	no	INTJ
ejpam-4756	2	4	.	.	NOUN
ejpam-4756	2	5	2	2	NUM
ejpam-4756	2	6	,	,	PUNCT
ejpam-4756	2	7	2023	2023	NUM
ejpam-4756	2	8	,	,	PUNCT
ejpam-4756	2	9	1302	1302	NUM
ejpam-4756	2	10	-	-	SYM
ejpam-4756	2	11	1317	1317	NUM
ejpam-4756	2	12	issn	issn	PROPN
ejpam-4756	2	13	1307	1307	NUM
ejpam-4756	2	14	-	-	SYM
ejpam-4756	2	15	5543	5543	NUM
ejpam-4756	2	16	–	–	PUNCT
ejpam-4756	2	17	ejpam.com	ejpam.com	X
ejpam-4756	2	18	published	publish	VERB
ejpam-4756	2	19	by	by	ADP
ejpam-4756	2	20	new	new	PROPN
ejpam-4756	2	21	york	york	PROPN
ejpam-4756	2	22	business	business	PROPN
ejpam-4756	2	23	global	global	ADJ
ejpam-4756	2	24	degree	degree	NOUN
ejpam-4756	2	25	of	of	ADP
ejpam-4756	2	26	convergence	convergence	NOUN
ejpam-4756	2	27	of	of	ADP
ejpam-4756	2	28	a	a	DET
ejpam-4756	2	29	function	function	NOUN
ejpam-4756	2	30	in	in	ADP
ejpam-4756	2	31	generalized	generalized	ADJ
ejpam-4756	2	32	zygmund	zygmund	NOUN
ejpam-4756	2	33	norm	norm	NOUN
ejpam-4756	2	34	using	use	VERB
ejpam-4756	2	35	karamata	karamata	NOUN
ejpam-4756	2	36	-	-	PUNCT
ejpam-4756	2	37	matrix	matrix	NOUN
ejpam-4756	2	38	(	(	PUNCT
ejpam-4756	2	39	kλa	kλa	NOUN
ejpam-4756	2	40	)	)	PUNCT
ejpam-4756	2	41	product	product	NOUN
ejpam-4756	2	42	operator	operator	NOUN
ejpam-4756	2	43	h.	h.	PROPN
ejpam-4756	2	44	k.	k.	PROPN
ejpam-4756	2	45	nigam1	nigam1	PROPN
ejpam-4756	2	46	,	,	PUNCT
ejpam-4756	2	47	manoj	manoj	PROPN
ejpam-4756	2	48	kumar	kumar	PROPN
ejpam-4756	2	49	sah1,∗	sah1,∗	PROPN
ejpam-4756	2	50	1	1	NUM
ejpam-4756	2	51	department	department	NOUN
ejpam-4756	2	52	of	of	ADP
ejpam-4756	2	53	mathematics	mathematic	NOUN
ejpam-4756	2	54	,	,	PUNCT
ejpam-4756	2	55	central	central	ADJ
ejpam-4756	2	56	university	university	NOUN
ejpam-4756	2	57	of	of	ADP
ejpam-4756	2	58	south	south	PROPN
ejpam-4756	2	59	bihar	bihar	PROPN
ejpam-4756	2	60	,	,	PUNCT
ejpam-4756	2	61	gaya	gaya	PROPN
ejpam-4756	2	62	,	,	PUNCT
ejpam-4756	2	63	bihar	bihar	PROPN
ejpam-4756	2	64	,	,	PUNCT
ejpam-4756	2	65	india	india	PROPN
ejpam-4756	2	66	abstract	abstract	NOUN
ejpam-4756	2	67	.	.	PUNCT
ejpam-4756	3	1	in	in	ADP
ejpam-4756	3	2	the	the	DET
ejpam-4756	3	3	present	present	ADJ
ejpam-4756	3	4	paper	paper	NOUN
ejpam-4756	3	5	,	,	PUNCT
ejpam-4756	3	6	we	we	PRON
ejpam-4756	3	7	obtain	obtain	VERB
ejpam-4756	3	8	the	the	DET
ejpam-4756	3	9	results	result	NOUN
ejpam-4756	3	10	on	on	ADP
ejpam-4756	3	11	the	the	DET
ejpam-4756	3	12	degree	degree	NOUN
ejpam-4756	3	13	of	of	ADP
ejpam-4756	3	14	convergence	convergence	NOUN
ejpam-4756	3	15	of	of	ADP
ejpam-4756	3	16	a	a	DET
ejpam-4756	3	17	function	function	NOUN
ejpam-4756	3	18	of	of	ADP
ejpam-4756	3	19	fourier	fourier	ADJ
ejpam-4756	3	20	series	series	NOUN
ejpam-4756	3	21	in	in	ADP
ejpam-4756	3	22	generalized	generalized	ADJ
ejpam-4756	3	23	zygmund	zygmund	NOUN
ejpam-4756	3	24	space	space	NOUN
ejpam-4756	3	25	using	use	VERB
ejpam-4756	3	26	karamata	karamata	NOUN
ejpam-4756	3	27	-	-	PUNCT
ejpam-4756	3	28	matrix	matrix	NOUN
ejpam-4756	3	29	(	(	PUNCT
ejpam-4756	3	30	kλa	kλa	NOUN
ejpam-4756	3	31	)	)	PUNCT
ejpam-4756	3	32	product	product	NOUN
ejpam-4756	3	33	operator	operator	NOUN
ejpam-4756	3	34	.	.	PUNCT
ejpam-4756	4	1	we	we	PRON
ejpam-4756	4	2	also	also	ADV
ejpam-4756	4	3	study	study	VERB
ejpam-4756	4	4	an	an	DET
ejpam-4756	4	5	application	application	NOUN
ejpam-4756	4	6	of	of	ADP
ejpam-4756	4	7	our	our	PRON
ejpam-4756	4	8	main	main	ADJ
ejpam-4756	4	9	result	result	NOUN
ejpam-4756	4	10	.	.	PUNCT
ejpam-4756	5	1	2020	2020	NUM
ejpam-4756	5	2	mathematics	mathematic	NOUN
ejpam-4756	5	3	subject	subject	NOUN
ejpam-4756	5	4	classifications	classification	NOUN
ejpam-4756	5	5	:	:	PUNCT
ejpam-4756	5	6	40c05	40c05	NUM
ejpam-4756	5	7	,	,	PUNCT
ejpam-4756	5	8	40c10	40c10	NUM
ejpam-4756	5	9	,	,	PUNCT
ejpam-4756	5	10	42a10	42a10	DET
ejpam-4756	5	11	key	key	ADJ
ejpam-4756	5	12	words	word	NOUN
ejpam-4756	5	13	and	and	CCONJ
ejpam-4756	5	14	phrases	phrase	NOUN
ejpam-4756	5	15	:	:	PUNCT
ejpam-4756	5	16	degree	degree	NOUN
ejpam-4756	5	17	of	of	ADP
ejpam-4756	5	18	convergence	convergence	NOUN
ejpam-4756	5	19	,	,	PUNCT
ejpam-4756	5	20	generalized	generalized	ADJ
ejpam-4756	5	21	zygmund	zygmund	NOUN
ejpam-4756	5	22	space	space	NOUN
ejpam-4756	5	23	(	(	PUNCT
ejpam-4756	5	24	z	z	NOUN
ejpam-4756	5	25	(	(	PUNCT
ejpam-4756	5	26	η	η	NOUN
ejpam-4756	5	27	)	)	PUNCT
ejpam-4756	5	28	r	r	NOUN
ejpam-4756	5	29	;	;	PUNCT
ejpam-4756	5	30	r	r	NOUN
ejpam-4756	5	31	≥	≥	NOUN
ejpam-4756	5	32	1	1	NUM
ejpam-4756	5	33	)	)	PUNCT
ejpam-4756	5	34	,	,	PUNCT
ejpam-4756	5	35	karamata	karamata	NOUN
ejpam-4756	5	36	-	-	PUNCT
ejpam-4756	5	37	matrix	matrix	NOUN
ejpam-4756	5	38	(	(	PUNCT
ejpam-4756	5	39	kλa	kλa	NOUN
ejpam-4756	5	40	)	)	PUNCT
ejpam-4756	5	41	product	product	NOUN
ejpam-4756	5	42	operator	operator	NOUN
ejpam-4756	5	43	,	,	PUNCT
ejpam-4756	5	44	fourier	fourier	NOUN
ejpam-4756	5	45	series	series	NOUN
ejpam-4756	5	46	,	,	PUNCT
ejpam-4756	5	47	modulus	modulus	NOUN
ejpam-4756	5	48	of	of	ADP
ejpam-4756	5	49	continuity	continuity	NOUN
ejpam-4756	5	50	.	.	PUNCT
ejpam-4756	6	1	1	1	X
ejpam-4756	6	2	.	.	X
ejpam-4756	6	3	introduction	introduction	NOUN
ejpam-4756	6	4	karamata	karamata	NOUN
ejpam-4756	6	5	(	(	PUNCT
ejpam-4756	6	6	[	[	X
ejpam-4756	6	7	3	3	NUM
ejpam-4756	6	8	]	]	PUNCT
ejpam-4756	6	9	)	)	PUNCT
ejpam-4756	6	10	introduced	introduce	VERB
ejpam-4756	6	11	kλ	kλ	VERB
ejpam-4756	6	12	-	-	PUNCT
ejpam-4756	6	13	summability	summability	NOUN
ejpam-4756	6	14	method	method	NOUN
ejpam-4756	6	15	for	for	ADP
ejpam-4756	6	16	the	the	DET
ejpam-4756	6	17	first	first	ADJ
ejpam-4756	6	18	time	time	NOUN
ejpam-4756	6	19	.	.	PUNCT
ejpam-4756	7	1	this	this	DET
ejpam-4756	7	2	method	method	NOUN
ejpam-4756	7	3	was	be	AUX
ejpam-4756	7	4	again	again	ADV
ejpam-4756	7	5	introduced	introduce	VERB
ejpam-4756	7	6	by	by	ADP
ejpam-4756	7	7	lotosky	lotosky	NOUN
ejpam-4756	7	8	(	(	PUNCT
ejpam-4756	7	9	[	[	X
ejpam-4756	7	10	8	8	NUM
ejpam-4756	7	11	]	]	PUNCT
ejpam-4756	7	12	)	)	PUNCT
ejpam-4756	7	13	for	for	ADP
ejpam-4756	7	14	λ	λ	X
ejpam-4756	7	15	=	=	NOUN
ejpam-4756	8	1	1	1	X
ejpam-4756	8	2	.	.	PUNCT
ejpam-4756	8	3	a	a	DET
ejpam-4756	8	4	deep	deep	ADJ
ejpam-4756	8	5	study	study	NOUN
ejpam-4756	8	6	on	on	ADP
ejpam-4756	8	7	kλ	kλ	PROPN
ejpam-4756	8	8	and	and	CCONJ
ejpam-4756	8	9	their	their	PRON
ejpam-4756	8	10	similar	similar	ADJ
ejpam-4756	8	11	cases	case	NOUN
ejpam-4756	8	12	is	be	AUX
ejpam-4756	8	13	studied	study	VERB
ejpam-4756	8	14	after	after	ADP
ejpam-4756	8	15	the	the	DET
ejpam-4756	8	16	publication	publication	NOUN
ejpam-4756	8	17	of	of	ADP
ejpam-4756	8	18	the	the	DET
ejpam-4756	8	19	work	work	NOUN
ejpam-4756	8	20	of	of	ADP
ejpam-4756	8	21	agnew	agnew	PROPN
ejpam-4756	8	22	(	(	PUNCT
ejpam-4756	8	23	[	[	X
ejpam-4756	8	24	1	1	NUM
ejpam-4756	8	25	]	]	NUM
ejpam-4756	8	26	)	)	PUNCT
ejpam-4756	8	27	.	.	PUNCT
ejpam-4756	9	1	the	the	DET
ejpam-4756	9	2	degree	degree	NOUN
ejpam-4756	9	3	of	of	ADP
ejpam-4756	9	4	approximation	approximation	NOUN
ejpam-4756	9	5	of	of	ADP
ejpam-4756	9	6	a	a	DET
ejpam-4756	9	7	function	function	NOUN
ejpam-4756	9	8	in	in	ADP
ejpam-4756	9	9	function	function	NOUN
ejpam-4756	9	10	spaces	space	NOUN
ejpam-4756	9	11	viz	viz	NUM
ejpam-4756	9	12	,	,	PUNCT
ejpam-4756	9	13	lipschitz	lipschitz	NOUN
ejpam-4756	9	14	,	,	PUNCT
ejpam-4756	9	15	hölder	hölder	NOUN
ejpam-4756	9	16	and	and	CCONJ
ejpam-4756	9	17	generalized	generalize	VERB
ejpam-4756	9	18	hölder	hölder	NOUN
ejpam-4756	9	19	using	use	VERB
ejpam-4756	9	20	different	different	ADJ
ejpam-4756	9	21	transforms	transform	NOUN
ejpam-4756	9	22	of	of	ADP
ejpam-4756	9	23	fourier	fouri	ADJ
ejpam-4756	9	24	series	series	NOUN
ejpam-4756	9	25	,	,	PUNCT
ejpam-4756	9	26	has	have	AUX
ejpam-4756	9	27	been	be	AUX
ejpam-4756	9	28	studied	study	VERB
ejpam-4756	9	29	by	by	ADP
ejpam-4756	9	30	the	the	DET
ejpam-4756	9	31	researchers	researcher	NOUN
ejpam-4756	10	1	[	[	X
ejpam-4756	10	2	4–6	4–6	NOUN
ejpam-4756	10	3	,	,	PUNCT
ejpam-4756	10	4	9–12	9–12	PROPN
ejpam-4756	10	5	]	]	PUNCT
ejpam-4756	10	6	etc	etc	X
ejpam-4756	10	7	.	.	X
ejpam-4756	10	8	therefore	therefore	ADV
ejpam-4756	10	9	,	,	PUNCT
ejpam-4756	10	10	in	in	ADP
ejpam-4756	10	11	the	the	DET
ejpam-4756	10	12	present	present	ADJ
ejpam-4756	10	13	paper	paper	NOUN
ejpam-4756	10	14	we	we	PRON
ejpam-4756	10	15	study	study	VERB
ejpam-4756	10	16	the	the	DET
ejpam-4756	10	17	degree	degree	NOUN
ejpam-4756	10	18	of	of	ADP
ejpam-4756	10	19	convergence	convergence	NOUN
ejpam-4756	10	20	of	of	ADP
ejpam-4756	10	21	a	a	DET
ejpam-4756	10	22	function	function	NOUN
ejpam-4756	10	23	in	in	ADP
ejpam-4756	10	24	generalized	generalized	ADJ
ejpam-4756	10	25	zygmund	zygmund	NOUN
ejpam-4756	10	26	space	space	NOUN
ejpam-4756	10	27	(	(	PUNCT
ejpam-4756	10	28	z	z	NOUN
ejpam-4756	10	29	(	(	PUNCT
ejpam-4756	10	30	η	η	NOUN
ejpam-4756	10	31	)	)	PUNCT
ejpam-4756	10	32	r	r	NOUN
ejpam-4756	10	33	;	;	PUNCT
ejpam-4756	11	1	r	r	NOUN
ejpam-4756	11	2	≥	≥	NOUN
ejpam-4756	11	3	1	1	NUM
ejpam-4756	11	4	)	)	PUNCT
ejpam-4756	11	5	using	use	VERB
ejpam-4756	11	6	karamata	karamata	NOUN
ejpam-4756	11	7	-	-	PUNCT
ejpam-4756	11	8	matrix	matrix	NOUN
ejpam-4756	11	9	(	(	PUNCT
ejpam-4756	11	10	kλa	kλa	NOUN
ejpam-4756	11	11	)	)	PUNCT
ejpam-4756	11	12	product	product	NOUN
ejpam-4756	11	13	operator	operator	NOUN
ejpam-4756	11	14	of	of	ADP
ejpam-4756	11	15	fourier	fourier	ADJ
ejpam-4756	11	16	series	series	NOUN
ejpam-4756	11	17	.	.	PUNCT
ejpam-4756	12	1	1.1	1.1	NUM
ejpam-4756	12	2	.	.	PUNCT
ejpam-4756	13	1	fourier	fourier	PROPN
ejpam-4756	13	2	series	series	PROPN
ejpam-4756	13	3	let	let	VERB
ejpam-4756	13	4	g	g	PRON
ejpam-4756	13	5	be	be	AUX
ejpam-4756	13	6	a	a	DET
ejpam-4756	13	7	lebesgue	lebesgue	NOUN
ejpam-4756	13	8	integrable	integrable	ADJ
ejpam-4756	13	9	function	function	NOUN
ejpam-4756	13	10	with	with	ADP
ejpam-4756	13	11	period	period	NOUN
ejpam-4756	13	12	2π	2π	NOUN
ejpam-4756	13	13	on	on	ADP
ejpam-4756	13	14	the	the	DET
ejpam-4756	13	15	interval	interval	NOUN
ejpam-4756	14	1	[	[	X
ejpam-4756	14	2	−π	−π	ADV
ejpam-4756	14	3	,	,	PUNCT
ejpam-4756	14	4	π	π	PROPN
ejpam-4756	14	5	]	]	X
ejpam-4756	14	6	.	.	PUNCT
ejpam-4756	15	1	the	the	DET
ejpam-4756	15	2	fourier	fourier	PROPN
ejpam-4756	15	3	series	series	NOUN
ejpam-4756	15	4	of	of	ADP
ejpam-4756	15	5	a	a	DET
ejpam-4756	15	6	function	function	NOUN
ejpam-4756	15	7	g	g	NOUN
ejpam-4756	15	8	is	be	AUX
ejpam-4756	15	9	given	give	VERB
ejpam-4756	15	10	by	by	ADP
ejpam-4756	15	11	g(t	g(t	PROPN
ejpam-4756	15	12	)	)	PUNCT
ejpam-4756	15	13	∼	∼	NOUN
ejpam-4756	15	14	a0	a0	NOUN
ejpam-4756	15	15	2	2	NUM
ejpam-4756	15	16	+	+	CCONJ
ejpam-4756	15	17	∞∑	∞∑	NUM
ejpam-4756	15	18	ν=1	ν=1	SYM
ejpam-4756	15	19	(	(	PUNCT
ejpam-4756	15	20	aν	aν	NOUN
ejpam-4756	15	21	cos	cos	PROPN
ejpam-4756	15	22	νt+	νt+	PROPN
ejpam-4756	15	23	bν	bν	PROPN
ejpam-4756	15	24	sin	sin	PROPN
ejpam-4756	15	25	νt	νt	PROPN
ejpam-4756	15	26	)	)	PUNCT
ejpam-4756	15	27	,	,	PUNCT
ejpam-4756	15	28	(	(	PUNCT
ejpam-4756	15	29	1	1	X
ejpam-4756	15	30	)	)	PUNCT
ejpam-4756	15	31	∗corresponding	∗corresponde	VERB
ejpam-4756	15	32	author	author	NOUN
ejpam-4756	15	33	.	.	PUNCT
ejpam-4756	16	1	doi	doi	NOUN
ejpam-4756	16	2	:	:	PUNCT
ejpam-4756	16	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4756	https://doi.org/10.29020/nybg.ejpam.v16i2.4756	NOUN
ejpam-4756	16	4	email	email	NOUN
ejpam-4756	16	5	addresses	address	NOUN
ejpam-4756	16	6	:	:	PUNCT
ejpam-4756	16	7	hknigam@cusb.ac.in	hknigam@cusb.ac.in	PUNCT
ejpam-4756	16	8	(	(	PUNCT
ejpam-4756	16	9	h.	h.	PROPN
ejpam-4756	16	10	k.	k.	PROPN
ejpam-4756	16	11	nigam	nigam	PROPN
ejpam-4756	16	12	)	)	PUNCT
ejpam-4756	16	13	,	,	PUNCT
ejpam-4756	16	14	manojsah@cusb.ac.in	manojsah@cusb.ac.in	ADV
ejpam-4756	16	15	(	(	PUNCT
ejpam-4756	16	16	m.	m.	PROPN
ejpam-4756	16	17	k.	k.	PROPN
ejpam-4756	16	18	sah	sah	PROPN
ejpam-4756	16	19	)	)	PUNCT
ejpam-4756	16	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4756	16	21	1302	1302	NUM
ejpam-4756	17	1	©	©	PROPN
ejpam-4756	17	2	2023	2023	NUM
ejpam-4756	17	3	ejpam	ejpam	NOUN
ejpam-4756	17	4	all	all	DET
ejpam-4756	17	5	rights	right	NOUN
ejpam-4756	17	6	reserved	reserve	VERB
ejpam-4756	17	7	.	.	PUNCT
ejpam-4756	18	1	h.	h.	PROPN
ejpam-4756	18	2	k.	k.	PROPN
ejpam-4756	18	3	nigam	nigam	PROPN
ejpam-4756	18	4	,	,	PUNCT
ejpam-4756	18	5	m.	m.	PROPN
ejpam-4756	18	6	k.	k.	PROPN
ejpam-4756	18	7	sah	sah	PROPN
ejpam-4756	18	8	/	/	SYM
ejpam-4756	18	9	eur	eur	PROPN
ejpam-4756	18	10	.	.	PUNCT
ejpam-4756	19	1	j.	j.	PROPN
ejpam-4756	19	2	pure	pure	PROPN
ejpam-4756	19	3	appl	appl	PROPN
ejpam-4756	19	4	.	.	PROPN
ejpam-4756	19	5	math	math	PROPN
ejpam-4756	19	6	,	,	PUNCT
ejpam-4756	19	7	16	16	NUM
ejpam-4756	19	8	(	(	PUNCT
ejpam-4756	19	9	2	2	NUM
ejpam-4756	19	10	)	)	PUNCT
ejpam-4756	19	11	(	(	PUNCT
ejpam-4756	19	12	2023	2023	NUM
ejpam-4756	19	13	)	)	PUNCT
ejpam-4756	19	14	,	,	PUNCT
ejpam-4756	19	15	1302	1302	NUM
ejpam-4756	19	16	-	-	SYM
ejpam-4756	19	17	1317	1317	NUM
ejpam-4756	19	18	1303	1303	NUM
ejpam-4756	19	19	where	where	SCONJ
ejpam-4756	19	20	a0	a0	PROPN
ejpam-4756	19	21	,	,	PUNCT
ejpam-4756	19	22	aν	aν	NOUN
ejpam-4756	19	23	and	and	CCONJ
ejpam-4756	19	24	bν	bν	PROPN
ejpam-4756	19	25	are	be	AUX
ejpam-4756	19	26	fourier	fourier	ADJ
ejpam-4756	19	27	co	co	NOUN
ejpam-4756	19	28	-	-	NOUN
ejpam-4756	19	29	efficients	efficient	NOUN
ejpam-4756	19	30	.	.	PUNCT
ejpam-4756	20	1	the	the	DET
ejpam-4756	20	2	νth	νth	ADJ
ejpam-4756	20	3	partial	partial	ADJ
ejpam-4756	20	4	sum	sum	NOUN
ejpam-4756	20	5	of	of	ADP
ejpam-4756	20	6	(	(	PUNCT
ejpam-4756	20	7	1	1	X
ejpam-4756	20	8	)	)	PUNCT
ejpam-4756	20	9	is	be	AUX
ejpam-4756	20	10	given	give	VERB
ejpam-4756	20	11	(	(	PUNCT
ejpam-4756	20	12	[	[	X
ejpam-4756	20	13	15	15	NUM
ejpam-4756	20	14	]	]	PUNCT
ejpam-4756	20	15	)	)	PUNCT
ejpam-4756	20	16	by	by	ADP
ejpam-4756	20	17	sν(g	sν(g	PROPN
ejpam-4756	20	18	;	;	PUNCT
ejpam-4756	20	19	t	t	X
ejpam-4756	20	20	)	)	PUNCT
ejpam-4756	20	21	=	=	PUNCT
ejpam-4756	21	1	sν(t)−	sν(t)−	PROPN
ejpam-4756	21	2	g(t	g(t	PROPN
ejpam-4756	21	3	)	)	PUNCT
ejpam-4756	22	1	=	=	SYM
ejpam-4756	22	2	1	1	NUM
ejpam-4756	22	3	2π	2π	NUM
ejpam-4756	22	4	∫	∫	PROPN
ejpam-4756	23	1	π	π	NOUN
ejpam-4756	23	2	0	0	PUNCT
ejpam-4756	24	1	ϕ(t	ϕ(t	NUM
ejpam-4756	24	2	,	,	PUNCT
ejpam-4756	24	3	w)dν(w)dw	w)dν(w)dw	PROPN
ejpam-4756	24	4	,	,	PUNCT
ejpam-4756	24	5	(	(	PUNCT
ejpam-4756	24	6	2	2	X
ejpam-4756	24	7	)	)	PUNCT
ejpam-4756	24	8	where	where	SCONJ
ejpam-4756	24	9	ϕ(t	ϕ(t	PROPN
ejpam-4756	24	10	,	,	PUNCT
ejpam-4756	24	11	w	w	NOUN
ejpam-4756	24	12	)	)	PUNCT
ejpam-4756	24	13	=	=	PUNCT
ejpam-4756	25	1	g(t+	g(t+	NUM
ejpam-4756	25	2	w	w	NOUN
ejpam-4756	25	3	)	)	PUNCT
ejpam-4756	26	1	+	+	NUM
ejpam-4756	26	2	g(t−	g(t−	NOUN
ejpam-4756	26	3	w)−	w)−	PROPN
ejpam-4756	26	4	2g(t	2g(t	NUM
ejpam-4756	26	5	)	)	PUNCT
ejpam-4756	26	6	,	,	PUNCT
ejpam-4756	26	7	and	and	CCONJ
ejpam-4756	26	8	dν(w	dν(w	NOUN
ejpam-4756	26	9	)	)	PUNCT
ejpam-4756	26	10	(	(	PUNCT
ejpam-4756	26	11	dirichlet	dirichlet	PROPN
ejpam-4756	26	12	kernal	kernal	PROPN
ejpam-4756	26	13	)	)	PUNCT
ejpam-4756	26	14	is	be	AUX
ejpam-4756	26	15	defined	define	VERB
ejpam-4756	26	16	by	by	ADP
ejpam-4756	26	17	dν(w	dν(w	NOUN
ejpam-4756	26	18	)	)	PUNCT
ejpam-4756	27	1	=	=	VERB
ejpam-4756	27	2	sin	sin	NOUN
ejpam-4756	27	3	(	(	PUNCT
ejpam-4756	27	4	ν	ν	X
ejpam-4756	27	5	+	+	NOUN
ejpam-4756	27	6	1	1	NUM
ejpam-4756	27	7	2	2	NUM
ejpam-4756	27	8	)	)	PUNCT
ejpam-4756	27	9	w	w	NOUN
ejpam-4756	27	10	sin	sin	NOUN
ejpam-4756	27	11	(	(	PUNCT
ejpam-4756	27	12	w	w	NOUN
ejpam-4756	27	13	2	2	NUM
ejpam-4756	27	14	)	)	PUNCT
ejpam-4756	27	15	.	.	PUNCT
ejpam-4756	28	1	(	(	PUNCT
ejpam-4756	28	2	3	3	X
ejpam-4756	28	3	)	)	PUNCT
ejpam-4756	28	4	1.2	1.2	NUM
ejpam-4756	28	5	.	.	PUNCT
ejpam-4756	29	1	summability	summability	NOUN
ejpam-4756	29	2	operator	operator	NOUN
ejpam-4756	29	3	let	let	VERB
ejpam-4756	29	4	u0	u0	ADJ
ejpam-4756	29	5	+	+	CCONJ
ejpam-4756	29	6	u1	u1	NOUN
ejpam-4756	29	7	+	+	CCONJ
ejpam-4756	29	8	u3	u3	NOUN
ejpam-4756	29	9	+	+	CCONJ
ejpam-4756	29	10	·	·	PUNCT
ejpam-4756	29	11	·	·	PUNCT
ejpam-4756	29	12	·	·	PUNCT
ejpam-4756	30	1	=	=	PUNCT
ejpam-4756	30	2	∞∑	∞∑	NUM
ejpam-4756	30	3	ν=0	ν=0	PRON
ejpam-4756	30	4	uν	uν	NOUN
ejpam-4756	30	5	(	(	PUNCT
ejpam-4756	30	6	4	4	X
ejpam-4756	30	7	)	)	PUNCT
ejpam-4756	30	8	be	be	AUX
ejpam-4756	30	9	an	an	DET
ejpam-4756	30	10	infinite	infinite	ADJ
ejpam-4756	30	11	series	series	NOUN
ejpam-4756	30	12	with	with	ADP
ejpam-4756	30	13	the	the	DET
ejpam-4756	30	14	sequence	sequence	NOUN
ejpam-4756	30	15	of	of	ADP
ejpam-4756	30	16	its	its	PRON
ejpam-4756	30	17	νth	νth	ADJ
ejpam-4756	30	18	partial	partial	ADJ
ejpam-4756	30	19	sum	sum	NOUN
ejpam-4756	30	20	sν	sν	NOUN
ejpam-4756	30	21	.	.	PUNCT
ejpam-4756	31	1	1.2.1	1.2.1	NUM
ejpam-4756	31	2	.	.	X
ejpam-4756	32	1	karamata	karamata	PROPN
ejpam-4756	32	2	(	(	PUNCT
ejpam-4756	32	3	kλ	kλ	NOUN
ejpam-4756	32	4	)	)	PUNCT
ejpam-4756	32	5	operator	operator	NOUN
ejpam-4756	32	6	let	let	VERB
ejpam-4756	32	7	us	we	PRON
ejpam-4756	32	8	define	define	VERB
ejpam-4756	32	9	,	,	PUNCT
ejpam-4756	32	10	for	for	ADP
ejpam-4756	32	11	ν	ν	DET
ejpam-4756	32	12	∈	∈	PROPN
ejpam-4756	32	13	n	n	NOUN
ejpam-4756	32	14	∪	∪	X
ejpam-4756	32	15	{	{	PUNCT
ejpam-4756	32	16	0	0	NUM
ejpam-4756	32	17	}	}	PUNCT
ejpam-4756	32	18	,	,	PUNCT
ejpam-4756	32	19	the	the	DET
ejpam-4756	32	20	numbers	number	NOUN
ejpam-4756	32	21	[	[	PUNCT
ejpam-4756	32	22	ν	ν	X
ejpam-4756	32	23	k	k	X
ejpam-4756	32	24	]	]	PUNCT
ejpam-4756	32	25	,	,	PUNCT
ejpam-4756	32	26	for	for	ADP
ejpam-4756	32	27	0	0	NUM
ejpam-4756	32	28	≤	≤	NOUN
ejpam-4756	32	29	k	k	NOUN
ejpam-4756	32	30	≤	≤	NUM
ejpam-4756	32	31	ν	ν	NOUN
ejpam-4756	32	32	,	,	PUNCT
ejpam-4756	32	33	by	by	ADP
ejpam-4756	32	34	ν−1∏	ν−1∏	PROPN
ejpam-4756	32	35	p=0	p=0	PROPN
ejpam-4756	32	36	(	(	PUNCT
ejpam-4756	32	37	t+	t+	NOUN
ejpam-4756	32	38	p	p	NOUN
ejpam-4756	32	39	)	)	PUNCT
ejpam-4756	32	40	=	=	PUNCT
ejpam-4756	33	1	t(t+	t(t+	NUM
ejpam-4756	33	2	1	1	NUM
ejpam-4756	33	3	)	)	PUNCT
ejpam-4756	33	4	·	·	PUNCT
ejpam-4756	33	5	·	·	PUNCT
ejpam-4756	33	6	·	·	PUNCT
ejpam-4756	33	7	(	(	PUNCT
ejpam-4756	33	8	t+	t+	ADP
ejpam-4756	33	9	ν	ν	ADP
ejpam-4756	33	10	−	−	PROPN
ejpam-4756	33	11	1	1	NUM
ejpam-4756	33	12	)	)	PUNCT
ejpam-4756	33	13	=	=	SYM
ejpam-4756	33	14	ν∑	ν∑	PROPN
ejpam-4756	33	15	k=0	k=0	PROPN
ejpam-4756	34	1	[	[	PUNCT
ejpam-4756	34	2	ν	ν	X
ejpam-4756	34	3	k	k	X
ejpam-4756	34	4	]	]	X
ejpam-4756	34	5	tk	tk	PROPN
ejpam-4756	34	6	=	=	SYM
ejpam-4756	34	7	γ(t+	γ(t+	PROPN
ejpam-4756	34	8	ν	ν	PROPN
ejpam-4756	34	9	)	)	PUNCT
ejpam-4756	34	10	γt	γt	NOUN
ejpam-4756	34	11	.	.	PUNCT
ejpam-4756	35	1	the	the	DET
ejpam-4756	35	2	numbers	number	NOUN
ejpam-4756	35	3	[	[	PUNCT
ejpam-4756	35	4	ν	ν	X
ejpam-4756	35	5	k	k	X
ejpam-4756	35	6	]	]	X
ejpam-4756	35	7	are	be	AUX
ejpam-4756	35	8	said	say	VERB
ejpam-4756	35	9	to	to	PART
ejpam-4756	35	10	be	be	AUX
ejpam-4756	35	11	the	the	DET
ejpam-4756	35	12	absolute	absolute	ADJ
ejpam-4756	35	13	value	value	NOUN
ejpam-4756	35	14	of	of	ADP
ejpam-4756	35	15	stirling	stirling	NOUN
ejpam-4756	35	16	number	number	NOUN
ejpam-4756	35	17	of	of	ADP
ejpam-4756	35	18	first	first	ADJ
ejpam-4756	35	19	kind	kind	NOUN
ejpam-4756	35	20	.	.	PUNCT
ejpam-4756	36	1	let	let	VERB
ejpam-4756	36	2	{	{	PUNCT
ejpam-4756	36	3	sν	sν	VERB
ejpam-4756	36	4	}	}	PUNCT
ejpam-4756	36	5	be	be	AUX
ejpam-4756	36	6	the	the	DET
ejpam-4756	36	7	seuqence	seuqence	NOUN
ejpam-4756	36	8	of	of	ADP
ejpam-4756	36	9	the	the	DET
ejpam-4756	36	10	partial	partial	ADJ
ejpam-4756	36	11	sums	sum	NOUN
ejpam-4756	36	12	of	of	ADP
ejpam-4756	36	13	the	the	DET
ejpam-4756	36	14	series	series	NOUN
ejpam-4756	36	15	(	(	PUNCT
ejpam-4756	36	16	4	4	NUM
ejpam-4756	36	17	)	)	PUNCT
ejpam-4756	36	18	and	and	CCONJ
ejpam-4756	36	19	we	we	PRON
ejpam-4756	36	20	write	write	VERB
ejpam-4756	36	21	[	[	X
ejpam-4756	36	22	3	3	NUM
ejpam-4756	36	23	,	,	PUNCT
ejpam-4756	36	24	8	8	NUM
ejpam-4756	36	25	]	]	PUNCT
ejpam-4756	36	26	sλν	sλν	NOUN
ejpam-4756	37	1	=	=	SYM
ejpam-4756	37	2	γλ	γλ	NUM
ejpam-4756	37	3	γ(λ+	γ(λ+	NUM
ejpam-4756	37	4	ν	ν	NOUN
ejpam-4756	37	5	)	)	PUNCT
ejpam-4756	37	6	ν∑	ν∑	PUNCT
ejpam-4756	38	1	k=0	k=0	PROPN
ejpam-4756	38	2	[	[	PUNCT
ejpam-4756	38	3	ν	ν	X
ejpam-4756	38	4	k	k	X
ejpam-4756	38	5	]	]	X
ejpam-4756	38	6	λksk	λksk	X
ejpam-4756	38	7	(	(	PUNCT
ejpam-4756	38	8	5	5	NUM
ejpam-4756	38	9	)	)	PUNCT
ejpam-4756	38	10	to	to	PART
ejpam-4756	38	11	denote	denote	VERB
ejpam-4756	38	12	the	the	DET
ejpam-4756	38	13	νth	νth	NOUN
ejpam-4756	38	14	kλ	kλ	NOUN
ejpam-4756	38	15	-	-	NOUN
ejpam-4756	38	16	operator	operator	NOUN
ejpam-4756	38	17	of	of	ADP
ejpam-4756	38	18	order	order	NOUN
ejpam-4756	38	19	λ	λ	X
ejpam-4756	38	20	>	>	X
ejpam-4756	38	21	0	0	PROPN
ejpam-4756	38	22	.	.	PUNCT
ejpam-4756	39	1	if	if	SCONJ
ejpam-4756	39	2	sλν	sλν	NOUN
ejpam-4756	39	3	→	→	SYM
ejpam-4756	39	4	s	s	X
ejpam-4756	39	5	as	as	ADP
ejpam-4756	39	6	ν	ν	NOUN
ejpam-4756	39	7	→	→	SYM
ejpam-4756	39	8	∞	∞	PROPN
ejpam-4756	39	9	,	,	PUNCT
ejpam-4756	39	10	where	where	SCONJ
ejpam-4756	39	11	s	s	NOUN
ejpam-4756	39	12	is	be	AUX
ejpam-4756	39	13	a	a	DET
ejpam-4756	39	14	definite	definite	ADJ
ejpam-4756	39	15	number	number	NOUN
ejpam-4756	39	16	,	,	PUNCT
ejpam-4756	39	17	then	then	ADV
ejpam-4756	39	18	the	the	DET
ejpam-4756	39	19	series	series	NOUN
ejpam-4756	39	20	(	(	PUNCT
ejpam-4756	39	21	4	4	NUM
ejpam-4756	39	22	)	)	PUNCT
ejpam-4756	39	23	is	be	AUX
ejpam-4756	39	24	said	say	VERB
ejpam-4756	39	25	to	to	PART
ejpam-4756	39	26	be	be	AUX
ejpam-4756	39	27	summable	summable	ADJ
ejpam-4756	39	28	by	by	ADP
ejpam-4756	39	29	karamata	karamata	ADJ
ejpam-4756	39	30	metnhod	metnhod	NOUN
ejpam-4756	39	31	(	(	PUNCT
ejpam-4756	39	32	kλ	kλ	NOUN
ejpam-4756	39	33	)	)	PUNCT
ejpam-4756	39	34	of	of	ADP
ejpam-4756	39	35	order	order	NOUN
ejpam-4756	39	36	λ	λ	X
ejpam-4756	39	37	>	>	X
ejpam-4756	39	38	0	0	PUNCT
ejpam-4756	39	39	to	to	ADP
ejpam-4756	39	40	the	the	DET
ejpam-4756	39	41	sum	sum	NOUN
ejpam-4756	39	42	s.	s.	PROPN
ejpam-4756	39	43	thus	thus	ADV
ejpam-4756	39	44	,	,	PUNCT
ejpam-4756	39	45	sλν	sλν	PROPN
ejpam-4756	39	46	→	→	SYM
ejpam-4756	39	47	s(kλ	s(kλ	PROPN
ejpam-4756	39	48	)	)	PUNCT
ejpam-4756	39	49	as	as	ADP
ejpam-4756	39	50	ν	ν	PROPN
ejpam-4756	39	51	→	→	SYM
ejpam-4756	39	52	∞.	∞.	PROPN
ejpam-4756	39	53	(	(	PUNCT
ejpam-4756	39	54	6	6	NUM
ejpam-4756	39	55	)	)	PUNCT
ejpam-4756	39	56	h.	h.	PROPN
ejpam-4756	39	57	k.	k.	PROPN
ejpam-4756	39	58	nigam	nigam	PROPN
ejpam-4756	39	59	,	,	PUNCT
ejpam-4756	39	60	m.	m.	PROPN
ejpam-4756	39	61	k.	k.	PROPN
ejpam-4756	39	62	sah	sah	PROPN
ejpam-4756	39	63	/	/	SYM
ejpam-4756	39	64	eur	eur	PROPN
ejpam-4756	39	65	.	.	PUNCT
ejpam-4756	40	1	j.	j.	PROPN
ejpam-4756	40	2	pure	pure	PROPN
ejpam-4756	40	3	appl	appl	PROPN
ejpam-4756	40	4	.	.	PROPN
ejpam-4756	40	5	math	math	PROPN
ejpam-4756	40	6	,	,	PUNCT
ejpam-4756	40	7	16	16	NUM
ejpam-4756	40	8	(	(	PUNCT
ejpam-4756	40	9	2	2	NUM
ejpam-4756	40	10	)	)	PUNCT
ejpam-4756	40	11	(	(	PUNCT
ejpam-4756	40	12	2023	2023	NUM
ejpam-4756	40	13	)	)	PUNCT
ejpam-4756	40	14	,	,	PUNCT
ejpam-4756	40	15	1302	1302	NUM
ejpam-4756	40	16	-	-	SYM
ejpam-4756	40	17	1317	1317	NUM
ejpam-4756	40	18	1304	1304	NUM
ejpam-4756	40	19	1.2.2	1.2.2	NUM
ejpam-4756	40	20	.	.	PUNCT
ejpam-4756	41	1	matrix	matrix	NOUN
ejpam-4756	41	2	(	(	PUNCT
ejpam-4756	41	3	a	a	DET
ejpam-4756	41	4	)	)	PUNCT
ejpam-4756	41	5	operator	operator	NOUN
ejpam-4756	41	6	let	let	VERB
ejpam-4756	41	7	a	a	PRON
ejpam-4756	41	8	=	=	SYM
ejpam-4756	41	9	(	(	PUNCT
ejpam-4756	41	10	aν	aν	NOUN
ejpam-4756	41	11	,	,	PUNCT
ejpam-4756	41	12	k	k	NOUN
ejpam-4756	41	13	)	)	PUNCT
ejpam-4756	41	14	;	;	PUNCT
ejpam-4756	41	15	ν	ν	X
ejpam-4756	41	16	,	,	PUNCT
ejpam-4756	41	17	k	k	NOUN
ejpam-4756	41	18	=	=	SYM
ejpam-4756	41	19	0	0	NUM
ejpam-4756	41	20	,	,	PUNCT
ejpam-4756	41	21	1	1	NUM
ejpam-4756	41	22	,	,	PUNCT
ejpam-4756	41	23	2	2	NUM
ejpam-4756	41	24	,	,	PUNCT
ejpam-4756	41	25	·	·	PUNCT
ejpam-4756	41	26	·	·	PUNCT
ejpam-4756	41	27	·	·	PUNCT
ejpam-4756	41	28	be	be	AUX
ejpam-4756	41	29	an	an	DET
ejpam-4756	41	30	infinite	infinite	ADJ
ejpam-4756	41	31	lower	low	ADJ
ejpam-4756	41	32	triangular	triangular	NOUN
ejpam-4756	41	33	matrix	matrix	NOUN
ejpam-4756	41	34	satisfying	satisfy	VERB
ejpam-4756	41	35	the	the	DET
ejpam-4756	41	36	silverman	silverman	NOUN
ejpam-4756	41	37	-	-	PUNCT
ejpam-4756	41	38	toeplitz	toeplitz	NOUN
ejpam-4756	42	1	[	[	X
ejpam-4756	42	2	14	14	NUM
ejpam-4756	42	3	]	]	SYM
ejpam-4756	42	4	conditions	condition	NOUN
ejpam-4756	42	5	of	of	ADP
ejpam-4756	42	6	regularity	regularity	NOUN
ejpam-4756	42	7	i.e.	i.e.	X
ejpam-4756	42	8	ν∑	ν∑	X
ejpam-4756	43	1	k=0	k=0	PROPN
ejpam-4756	43	2	aν	aν	PROPN
ejpam-4756	43	3	,	,	PUNCT
ejpam-4756	43	4	k	k	PROPN
ejpam-4756	44	1	=	=	SYM
ejpam-4756	45	1	1	1	NUM
ejpam-4756	46	1	as	as	ADP
ejpam-4756	46	2	ν	ν	NOUN
ejpam-4756	46	3	→	→	SYM
ejpam-4756	46	4	∞	∞	PROPN
ejpam-4756	46	5	,	,	PUNCT
ejpam-4756	46	6	aν	aν	NOUN
ejpam-4756	46	7	,	,	PUNCT
ejpam-4756	46	8	k	k	PROPN
ejpam-4756	46	9	=	=	PUNCT
ejpam-4756	46	10	0	0	PROPN
ejpam-4756	46	11	for	for	ADP
ejpam-4756	46	12	k	k	PROPN
ejpam-4756	46	13	>	>	X
ejpam-4756	46	14	ν	ν	PROPN
ejpam-4756	46	15	,	,	PUNCT
ejpam-4756	46	16	ν∑	ν∑	PROPN
ejpam-4756	46	17	k=0	k=0	PROPN
ejpam-4756	46	18	|aν	|aν	PROPN
ejpam-4756	46	19	,	,	PUNCT
ejpam-4756	46	20	k|	k|	NOUN
ejpam-4756	46	21	≤	≤	NUM
ejpam-4756	46	22	m	m	PROPN
ejpam-4756	46	23	,	,	PUNCT
ejpam-4756	46	24	a	a	DET
ejpam-4756	46	25	finite	finite	NOUN
ejpam-4756	46	26	constant	constant	ADJ
ejpam-4756	46	27	.	.	PUNCT
ejpam-4756	47	1	the	the	DET
ejpam-4756	47	2	sequence	sequence	NOUN
ejpam-4756	47	3	to	to	ADP
ejpam-4756	47	4	sequence	sequence	NOUN
ejpam-4756	47	5	transformation	transformation	NOUN
ejpam-4756	47	6	daν	daν	X
ejpam-4756	47	7	:	:	PUNCT
ejpam-4756	47	8	=	=	SYM
ejpam-4756	47	9	ν∑	ν∑	PROPN
ejpam-4756	47	10	k=0	k=0	PROPN
ejpam-4756	47	11	aν	aν	PROPN
ejpam-4756	47	12	,	,	PUNCT
ejpam-4756	47	13	ksk	ksk	PROPN
ejpam-4756	47	14	(	(	PUNCT
ejpam-4756	47	15	7	7	NUM
ejpam-4756	47	16	)	)	PUNCT
ejpam-4756	47	17	defines	define	VERB
ejpam-4756	47	18	the	the	DET
ejpam-4756	47	19	sequence	sequence	NOUN
ejpam-4756	47	20	daν	daν	NOUN
ejpam-4756	47	21	of	of	ADP
ejpam-4756	47	22	matrix	matrix	NOUN
ejpam-4756	47	23	operator	operator	NOUN
ejpam-4756	47	24	of	of	ADP
ejpam-4756	47	25	the	the	DET
ejpam-4756	47	26	sequence	sequence	NOUN
ejpam-4756	47	27	{	{	PUNCT
ejpam-4756	47	28	sν	sν	NOUN
ejpam-4756	47	29	}	}	PUNCT
ejpam-4756	47	30	obtained	obtain	VERB
ejpam-4756	47	31	by	by	ADP
ejpam-4756	47	32	the	the	DET
ejpam-4756	47	33	sequence	sequence	NOUN
ejpam-4756	47	34	of	of	ADP
ejpam-4756	47	35	co	co	ADJ
ejpam-4756	47	36	-	-	ADJ
ejpam-4756	47	37	efficient	efficient	ADJ
ejpam-4756	47	38	(	(	PUNCT
ejpam-4756	47	39	aν	aν	NOUN
ejpam-4756	47	40	,	,	PUNCT
ejpam-4756	47	41	k	k	NOUN
ejpam-4756	47	42	)	)	PUNCT
ejpam-4756	47	43	.	.	PUNCT
ejpam-4756	48	1	if	if	SCONJ
ejpam-4756	48	2	d	d	PROPN
ejpam-4756	48	3	a	a	DET
ejpam-4756	48	4	ν	ν	X
ejpam-4756	48	5	→	→	SYM
ejpam-4756	48	6	s	s	X
ejpam-4756	48	7	as	as	ADP
ejpam-4756	48	8	n	n	PROPN
ejpam-4756	48	9	→	→	SYM
ejpam-4756	48	10	∞	∞	PROPN
ejpam-4756	48	11	,	,	PUNCT
ejpam-4756	48	12	then	then	ADV
ejpam-4756	48	13	(	(	PUNCT
ejpam-4756	48	14	4	4	X
ejpam-4756	48	15	)	)	PUNCT
ejpam-4756	48	16	is	be	AUX
ejpam-4756	48	17	said	say	VERB
ejpam-4756	48	18	to	to	PART
ejpam-4756	48	19	be	be	AUX
ejpam-4756	48	20	summable	summable	ADJ
ejpam-4756	48	21	by	by	ADP
ejpam-4756	48	22	matrix	matrix	NOUN
ejpam-4756	48	23	(	(	PUNCT
ejpam-4756	48	24	a	a	DET
ejpam-4756	48	25	)	)	PUNCT
ejpam-4756	48	26	method	method	NOUN
ejpam-4756	48	27	to	to	ADP
ejpam-4756	48	28	a	a	DET
ejpam-4756	48	29	definite	definite	ADJ
ejpam-4756	48	30	number	number	NOUN
ejpam-4756	48	31	s.	s.	PROPN
ejpam-4756	48	32	1.2.3	1.2.3	NUM
ejpam-4756	48	33	.	.	PUNCT
ejpam-4756	49	1	karamata	karamata	NOUN
ejpam-4756	49	2	-	-	PUNCT
ejpam-4756	49	3	matrix	matrix	NOUN
ejpam-4756	49	4	(	(	PUNCT
ejpam-4756	49	5	kλa	kλa	NOUN
ejpam-4756	49	6	)	)	PUNCT
ejpam-4756	49	7	product	product	NOUN
ejpam-4756	49	8	operator	operator	NOUN
ejpam-4756	49	9	superimposing	superimpose	VERB
ejpam-4756	49	10	a	a	DET
ejpam-4756	49	11	operator	operator	NOUN
ejpam-4756	49	12	onkλ	onkλ	NOUN
ejpam-4756	49	13	,	,	PUNCT
ejpam-4756	49	14	a	a	DET
ejpam-4756	49	15	karamata	karamata	NOUN
ejpam-4756	49	16	-	-	PUNCT
ejpam-4756	49	17	matrix	matrix	NOUN
ejpam-4756	49	18	(	(	PUNCT
ejpam-4756	49	19	kλa	kλa	NOUN
ejpam-4756	49	20	)	)	PUNCT
ejpam-4756	49	21	product	product	NOUN
ejpam-4756	49	22	operator	operator	NOUN
ejpam-4756	49	23	is	be	AUX
ejpam-4756	49	24	obtained	obtain	VERB
ejpam-4756	49	25	and	and	CCONJ
ejpam-4756	49	26	is	be	AUX
ejpam-4756	49	27	given	give	VERB
ejpam-4756	49	28	by	by	ADP
ejpam-4756	49	29	dk	dk	PROPN
ejpam-4756	49	30	λa	λa	ADP
ejpam-4756	49	31	ν	ν	PROPN
ejpam-4756	50	1	=	=	X
ejpam-4756	50	2	γλ	γλ	NUM
ejpam-4756	50	3	γν	γν	INTJ
ejpam-4756	51	1	+	+	CCONJ
ejpam-4756	51	2	λ	λ	X
ejpam-4756	51	3	ν∑	ν∑	X
ejpam-4756	51	4	k=0	k=0	PROPN
ejpam-4756	52	1	[	[	PUNCT
ejpam-4756	52	2	ν	ν	X
ejpam-4756	52	3	k	k	X
ejpam-4756	52	4	]	]	PUNCT
ejpam-4756	52	5	λk(dak	λk(dak	ADJ
ejpam-4756	52	6	)	)	PUNCT
ejpam-4756	52	7	=	=	SYM
ejpam-4756	53	1	γλ	γλ	NUM
ejpam-4756	53	2	γν	γν	INTJ
ejpam-4756	54	1	+	+	CCONJ
ejpam-4756	54	2	λ	λ	X
ejpam-4756	54	3	ν∑	ν∑	X
ejpam-4756	54	4	k=0	k=0	PROPN
ejpam-4756	55	1	[	[	PUNCT
ejpam-4756	55	2	ν	ν	X
ejpam-4756	55	3	k	k	X
ejpam-4756	55	4	]	]	PUNCT
ejpam-4756	55	5	λk	λk	ADP
ejpam-4756	55	6	k∑	k∑	PROPN
ejpam-4756	55	7	j=0	j=0	PROPN
ejpam-4756	55	8	aν	aν	PROPN
ejpam-4756	55	9	,	,	PUNCT
ejpam-4756	55	10	jsj	jsj	X
ejpam-4756	55	11	.	.	PUNCT
ejpam-4756	56	1	(	(	PUNCT
ejpam-4756	56	2	8)	8)	NUM
ejpam-4756	56	3	if	if	SCONJ
ejpam-4756	56	4	dk	dk	PROPN
ejpam-4756	56	5	λa	λa	X
ejpam-4756	56	6	ν	ν	PROPN
ejpam-4756	56	7	→	→	SYM
ejpam-4756	56	8	s	s	X
ejpam-4756	56	9	as	as	ADP
ejpam-4756	56	10	ν	ν	NOUN
ejpam-4756	56	11	→	→	SYM
ejpam-4756	56	12	∞	∞	PROPN
ejpam-4756	56	13	,	,	PUNCT
ejpam-4756	56	14	then	then	ADV
ejpam-4756	56	15	the	the	DET
ejpam-4756	56	16	series	series	NOUN
ejpam-4756	56	17	(	(	PUNCT
ejpam-4756	56	18	4	4	NUM
ejpam-4756	56	19	)	)	PUNCT
ejpam-4756	56	20	is	be	AUX
ejpam-4756	56	21	said	say	VERB
ejpam-4756	56	22	to	to	PART
ejpam-4756	56	23	be	be	AUX
ejpam-4756	56	24	summable	summable	ADJ
ejpam-4756	56	25	to	to	ADP
ejpam-4756	56	26	s	s	PRON
ejpam-4756	56	27	by	by	ADP
ejpam-4756	56	28	(	(	PUNCT
ejpam-4756	56	29	kλa	kλa	NOUN
ejpam-4756	56	30	)	)	PUNCT
ejpam-4756	56	31	product	product	NOUN
ejpam-4756	56	32	operator	operator	NOUN
ejpam-4756	56	33	.	.	PUNCT
ejpam-4756	57	1	regularity	regularity	NOUN
ejpam-4756	57	2	of	of	ADP
ejpam-4756	57	3	the	the	DET
ejpam-4756	57	4	kλ	kλ	NOUN
ejpam-4756	57	5	and	and	CCONJ
ejpam-4756	57	6	a	a	DET
ejpam-4756	57	7	methods	method	NOUN
ejpam-4756	57	8	implies	imply	VERB
ejpam-4756	57	9	the	the	DET
ejpam-4756	57	10	regularity	regularity	NOUN
ejpam-4756	57	11	of	of	ADP
ejpam-4756	57	12	the	the	DET
ejpam-4756	57	13	kλa	kλa	NOUN
ejpam-4756	57	14	method	method	NOUN
ejpam-4756	57	15	.	.	PUNCT
ejpam-4756	58	1	1.3	1.3	NUM
ejpam-4756	58	2	.	.	PUNCT
ejpam-4756	59	1	generalized	generalize	VERB
ejpam-4756	59	2	zygmund	zygmund	PROPN
ejpam-4756	59	3	space	space	NOUN
ejpam-4756	59	4	let	let	VERB
ejpam-4756	59	5	c2π	c2π	NOUN
ejpam-4756	59	6	denotes	denote	VERB
ejpam-4756	59	7	the	the	DET
ejpam-4756	59	8	banach	banach	NOUN
ejpam-4756	59	9	space	space	NOUN
ejpam-4756	59	10	of	of	ADP
ejpam-4756	59	11	all	all	PRON
ejpam-4756	59	12	continuous	continuous	ADJ
ejpam-4756	59	13	and	and	CCONJ
ejpam-4756	59	14	2π	2π	NOUN
ejpam-4756	59	15	-	-	ADJ
ejpam-4756	59	16	periodic	periodic	ADJ
ejpam-4756	59	17	functions	function	NOUN
ejpam-4756	59	18	defined	define	VERB
ejpam-4756	59	19	on	on	ADP
ejpam-4756	59	20	the	the	DET
ejpam-4756	59	21	interval	interval	NOUN
ejpam-4756	59	22	[	[	X
ejpam-4756	59	23	0	0	NUM
ejpam-4756	59	24	,	,	PUNCT
ejpam-4756	59	25	2π	2π	NOUN
ejpam-4756	59	26	]	]	PUNCT
ejpam-4756	59	27	with	with	ADP
ejpam-4756	59	28	the	the	DET
ejpam-4756	59	29	supremum	supremum	ADJ
ejpam-4756	59	30	norm	norm	NOUN
ejpam-4756	59	31	.	.	PUNCT
ejpam-4756	60	1	the	the	DET
ejpam-4756	60	2	function	function	NOUN
ejpam-4756	60	3	space	space	NOUN
ejpam-4756	60	4	for	for	ADP
ejpam-4756	60	5	0	0	NUM
ejpam-4756	60	6	<	<	X
ejpam-4756	60	7	α	α	X
ejpam-4756	60	8	<	<	X
ejpam-4756	60	9	1	1	NUM
ejpam-4756	60	10	,	,	PUNCT
ejpam-4756	60	11	zα	zα	PROPN
ejpam-4756	60	12	:	:	PUNCT
ejpam-4756	60	13	=	=	SYM
ejpam-4756	60	14	{	{	PUNCT
ejpam-4756	60	15	g	g	NOUN
ejpam-4756	60	16	∈	∈	PROPN
ejpam-4756	60	17	c2π	c2π	NOUN
ejpam-4756	60	18	:	:	PUNCT
ejpam-4756	60	19	|g(t+	|g(t+	NOUN
ejpam-4756	60	20	w	w	NOUN
ejpam-4756	60	21	)	)	PUNCT
ejpam-4756	61	1	+	+	CCONJ
ejpam-4756	61	2	g(t−	g(t−	NOUN
ejpam-4756	61	3	w)−	w)−	PROPN
ejpam-4756	61	4	2g(t)|	2g(t)|	NUM
ejpam-4756	61	5	=	=	SYM
ejpam-4756	61	6	o(|w|α	o(|w|α	NOUN
ejpam-4756	61	7	)	)	PUNCT
ejpam-4756	61	8	}	}	PUNCT
ejpam-4756	61	9	(	(	PUNCT
ejpam-4756	61	10	9	9	X
ejpam-4756	61	11	)	)	PUNCT
ejpam-4756	61	12	h.	h.	PROPN
ejpam-4756	61	13	k.	k.	PROPN
ejpam-4756	61	14	nigam	nigam	PROPN
ejpam-4756	61	15	,	,	PUNCT
ejpam-4756	61	16	m.	m.	PROPN
ejpam-4756	61	17	k.	k.	PROPN
ejpam-4756	61	18	sah	sah	PROPN
ejpam-4756	61	19	/	/	SYM
ejpam-4756	61	20	eur	eur	PROPN
ejpam-4756	61	21	.	.	PUNCT
ejpam-4756	62	1	j.	j.	PROPN
ejpam-4756	62	2	pure	pure	PROPN
ejpam-4756	62	3	appl	appl	PROPN
ejpam-4756	62	4	.	.	PROPN
ejpam-4756	62	5	math	math	PROPN
ejpam-4756	62	6	,	,	PUNCT
ejpam-4756	62	7	16	16	NUM
ejpam-4756	62	8	(	(	PUNCT
ejpam-4756	62	9	2	2	NUM
ejpam-4756	62	10	)	)	PUNCT
ejpam-4756	62	11	(	(	PUNCT
ejpam-4756	62	12	2023	2023	NUM
ejpam-4756	62	13	)	)	PUNCT
ejpam-4756	62	14	,	,	PUNCT
ejpam-4756	62	15	1302	1302	NUM
ejpam-4756	62	16	-	-	SYM
ejpam-4756	62	17	1317	1317	NUM
ejpam-4756	62	18	1305	1305	NUM
ejpam-4756	62	19	is	be	AUX
ejpam-4756	62	20	a	a	DET
ejpam-4756	62	21	banach	banach	NOUN
ejpam-4756	62	22	space	space	NOUN
ejpam-4756	62	23	with	with	ADP
ejpam-4756	62	24	the	the	DET
ejpam-4756	62	25	norm	norm	NOUN
ejpam-4756	62	26	∥	∥	X
ejpam-4756	62	27	·	·	PUNCT
ejpam-4756	62	28	∥(α	∥(α	X
ejpam-4756	62	29	)	)	PUNCT
ejpam-4756	62	30	defined	define	VERB
ejpam-4756	62	31	by	by	ADP
ejpam-4756	62	32	∥g∥(α	∥g∥(α	NOUN
ejpam-4756	62	33	)	)	PUNCT
ejpam-4756	62	34	:	:	PUNCT
ejpam-4756	62	35	=	=	SYM
ejpam-4756	62	36	sup	sup	PROPN
ejpam-4756	62	37	0≤t≤2π	0≤t≤2π	NUM
ejpam-4756	62	38	|g(t)|+	|g(t)|+	PROPN
ejpam-4756	62	39	sup	sup	PROPN
ejpam-4756	62	40	t	t	PROPN
ejpam-4756	62	41	,	,	PUNCT
ejpam-4756	62	42	w	w	PROPN
ejpam-4756	62	43	w	w	PROPN
ejpam-4756	62	44	̸=0	̸=0	ADJ
ejpam-4756	62	45	|g(t+	|g(t+	NOUN
ejpam-4756	62	46	w	w	NOUN
ejpam-4756	62	47	)	)	PUNCT
ejpam-4756	63	1	+	+	CCONJ
ejpam-4756	63	2	g(t−	g(t−	NOUN
ejpam-4756	63	3	w)−	w)−	PROPN
ejpam-4756	63	4	2g(t)|	2g(t)|	NUM
ejpam-4756	63	5	|w|α	|w|α	VERB
ejpam-4756	63	6	the	the	DET
ejpam-4756	63	7	space	space	NOUN
ejpam-4756	63	8	of	of	ADP
ejpam-4756	63	9	all	all	DET
ejpam-4756	63	10	lebesgue	lebesgue	NOUN
ejpam-4756	63	11	integrable	integrable	ADJ
ejpam-4756	63	12	and	and	CCONJ
ejpam-4756	63	13	periodic	periodic	ADJ
ejpam-4756	63	14	functions	function	NOUN
ejpam-4756	63	15	with	with	ADP
ejpam-4756	63	16	period	period	NOUN
ejpam-4756	63	17	2π	2π	NOUN
ejpam-4756	63	18	be	be	VERB
ejpam-4756	63	19	lr	lr	NOUN
ejpam-4756	63	20	:	:	PUNCT
ejpam-4756	63	21	=	=	SYM
ejpam-4756	63	22	{	{	PUNCT
ejpam-4756	63	23	g	g	NOUN
ejpam-4756	63	24	:	:	PUNCT
ejpam-4756	63	25	[	[	X
ejpam-4756	63	26	0	0	NUM
ejpam-4756	63	27	,	,	PUNCT
ejpam-4756	63	28	2π	2π	NOUN
ejpam-4756	63	29	]	]	PUNCT
ejpam-4756	63	30	→	→	SYM
ejpam-4756	63	31	r	r	NOUN
ejpam-4756	63	32	;	;	PUNCT
ejpam-4756	63	33	∫	∫	PROPN
ejpam-4756	63	34	2π	2π	PROPN
ejpam-4756	63	35	0	0	NUM
ejpam-4756	63	36	|g(t)|rdt	|g(t)|rdt	ADJ
ejpam-4756	63	37	<	<	X
ejpam-4756	63	38	∞	∞	PROPN
ejpam-4756	63	39	,	,	PUNCT
ejpam-4756	63	40	r	r	NOUN
ejpam-4756	63	41	≥	≥	NOUN
ejpam-4756	63	42	1	1	NUM
ejpam-4756	63	43	}	}	PUNCT
ejpam-4756	63	44	.	.	PUNCT
ejpam-4756	64	1	(	(	PUNCT
ejpam-4756	64	2	10	10	NUM
ejpam-4756	64	3	)	)	PUNCT
ejpam-4756	64	4	the	the	DET
ejpam-4756	64	5	norm	norm	NOUN
ejpam-4756	64	6	of	of	ADP
ejpam-4756	64	7	(	(	PUNCT
ejpam-4756	64	8	10	10	NUM
ejpam-4756	64	9	)	)	PUNCT
ejpam-4756	64	10	is	be	AUX
ejpam-4756	64	11	defined	define	VERB
ejpam-4756	64	12	by	by	ADP
ejpam-4756	64	13	∥g∥r	∥g∥r	NOUN
ejpam-4756	64	14	=	=	PUNCT
ejpam-4756	64	15			PUNCT
ejpam-4756	64	16	{	{	PUNCT
ejpam-4756	64	17	1	1	NUM
ejpam-4756	64	18	2π	2π	NUM
ejpam-4756	64	19	∫	∫	PROPN
ejpam-4756	64	20	2π	2π	PROPN
ejpam-4756	64	21	0	0	NUM
ejpam-4756	64	22	|g(t)|rdt	|g(t)|rdt	ADJ
ejpam-4756	64	23	}	}	PUNCT
ejpam-4756	64	24	1	1	NUM
ejpam-4756	64	25	r	r	NOUN
ejpam-4756	64	26	for	for	ADP
ejpam-4756	64	27	1	1	NUM
ejpam-4756	64	28	≤	≤	NOUN
ejpam-4756	64	29	r	r	NOUN
ejpam-4756	64	30	<	<	X
ejpam-4756	64	31	∞	∞	PROPN
ejpam-4756	64	32	,	,	PUNCT
ejpam-4756	64	33	ess	ess	PROPN
ejpam-4756	64	34	supt∈[0,2π	supt∈[0,2π	NOUN
ejpam-4756	64	35	]	]	X
ejpam-4756	65	1	|g(t)|	|g(t)|	ADV
ejpam-4756	65	2	for	for	ADP
ejpam-4756	65	3	r	r	NOUN
ejpam-4756	65	4	=	=	SYM
ejpam-4756	65	5	∞.	∞.	PROPN
ejpam-4756	65	6	we	we	PRON
ejpam-4756	65	7	define	define	VERB
ejpam-4756	65	8	z(α),r	z(α),r	NOUN
ejpam-4756	65	9	:	:	PUNCT
ejpam-4756	65	10	=	=	SYM
ejpam-4756	65	11	g	g	PROPN
ejpam-4756	65	12	∈	∈	PROPN
ejpam-4756	65	13	lr[0	lr[0	PROPN
ejpam-4756	65	14	,	,	PUNCT
ejpam-4756	65	15	2π	2π	NOUN
ejpam-4756	65	16	]	]	PUNCT
ejpam-4756	65	17	:	:	PUNCT
ejpam-4756	65	18	(	(	PUNCT
ejpam-4756	65	19	∫	∫	PROPN
ejpam-4756	65	20	2π	2π	PROPN
ejpam-4756	65	21	0	0	NUM
ejpam-4756	65	22	|g(t+	|g(t+	NOUN
ejpam-4756	65	23	w	w	NOUN
ejpam-4756	65	24	)	)	PUNCT
ejpam-4756	66	1	+	+	CCONJ
ejpam-4756	66	2	g(t−	g(t−	NOUN
ejpam-4756	66	3	w)−	w)−	PROPN
ejpam-4756	66	4	2g(t)|rdt	2g(t)|rdt	NUM
ejpam-4756	66	5	)	)	PUNCT
ejpam-4756	66	6	1	1	NUM
ejpam-4756	66	7	r	r	NOUN
ejpam-4756	66	8	=	=	SYM
ejpam-4756	66	9	o(|w|α	o(|w|α	PROPN
ejpam-4756	66	10	)	)	PUNCT
ejpam-4756	66	11			NOUN
ejpam-4756	66	12	.	.	PUNCT
ejpam-4756	67	1	(	(	PUNCT
ejpam-4756	67	2	11	11	NUM
ejpam-4756	67	3	)	)	PUNCT
ejpam-4756	67	4	the	the	DET
ejpam-4756	67	5	space	space	NOUN
ejpam-4756	67	6	z(α),r	z(α),r	NOUN
ejpam-4756	67	7	,	,	PUNCT
ejpam-4756	67	8	r	r	NOUN
ejpam-4756	67	9	≥	≥	NOUN
ejpam-4756	67	10	1	1	NUM
ejpam-4756	67	11	,	,	PUNCT
ejpam-4756	67	12	0	0	NUM
ejpam-4756	67	13	<	<	X
ejpam-4756	67	14	α	α	PROPN
ejpam-4756	67	15	≤	≤	ADJ
ejpam-4756	67	16	1	1	NUM
ejpam-4756	67	17	is	be	AUX
ejpam-4756	67	18	a	a	DET
ejpam-4756	67	19	banach	banach	NOUN
ejpam-4756	67	20	space	space	NOUN
ejpam-4756	67	21	with	with	ADP
ejpam-4756	67	22	the	the	DET
ejpam-4756	67	23	norm	norm	NOUN
ejpam-4756	67	24	∥	∥	X
ejpam-4756	67	25	·	·	PUNCT
ejpam-4756	67	26	∥α	∥α	NOUN
ejpam-4756	67	27	,	,	PUNCT
ejpam-4756	67	28	r	r	NOUN
ejpam-4756	67	29	:	:	PUNCT
ejpam-4756	67	30	∥g∥α	∥g∥α	NOUN
ejpam-4756	67	31	,	,	PUNCT
ejpam-4756	67	32	r	r	NOUN
ejpam-4756	67	33	:	:	PUNCT
ejpam-4756	67	34	=	=	NOUN
ejpam-4756	67	35	∥g∥r	∥g∥r	NOUN
ejpam-4756	68	1	+	+	CCONJ
ejpam-4756	68	2	sup	sup	NOUN
ejpam-4756	68	3	w	w	ADP
ejpam-4756	68	4	̸=0	̸=0	ADV
ejpam-4756	68	5	∥g(t+	∥g(t+	NOUN
ejpam-4756	68	6	w	w	NOUN
ejpam-4756	68	7	)	)	PUNCT
ejpam-4756	68	8	+	+	CCONJ
ejpam-4756	68	9	g(t−	g(t−	NOUN
ejpam-4756	68	10	w)−	w)−	PROPN
ejpam-4756	68	11	2g(t)∥r	2g(t)∥r	NUM
ejpam-4756	68	12	|w|α	|w|α	PROPN
ejpam-4756	68	13	.	.	PUNCT
ejpam-4756	69	1	∥g∥α	∥g∥α	NOUN
ejpam-4756	69	2	,	,	PUNCT
ejpam-4756	69	3	r	r	NOUN
ejpam-4756	69	4	:	:	PUNCT
ejpam-4756	69	5	=	=	NOUN
ejpam-4756	69	6	∥g∥r	∥g∥r	X
ejpam-4756	69	7	.	.	PUNCT
ejpam-4756	70	1	the	the	DET
ejpam-4756	70	2	function	function	NOUN
ejpam-4756	70	3	space	space	NOUN
ejpam-4756	70	4	z(η1	z(η1	NOUN
ejpam-4756	70	5	)	)	PUNCT
ejpam-4756	70	6	is	be	AUX
ejpam-4756	70	7	a	a	DET
ejpam-4756	70	8	defined	define	VERB
ejpam-4756	70	9	as	as	ADP
ejpam-4756	70	10	z(η1	z(η1	NOUN
ejpam-4756	70	11	)	)	PUNCT
ejpam-4756	70	12	:	:	PUNCT
ejpam-4756	71	1	=	=	SYM
ejpam-4756	71	2	{	{	PUNCT
ejpam-4756	71	3	g	g	NOUN
ejpam-4756	71	4	∈	∈	PROPN
ejpam-4756	71	5	c2π	c2π	NOUN
ejpam-4756	71	6	:	:	PUNCT
ejpam-4756	71	7	|g(t+	|g(t+	NOUN
ejpam-4756	71	8	w	w	NOUN
ejpam-4756	71	9	)	)	PUNCT
ejpam-4756	72	1	+	+	CCONJ
ejpam-4756	72	2	g(t−	g(t−	NOUN
ejpam-4756	72	3	w)−	w)−	PROPN
ejpam-4756	72	4	2g(t)|	2g(t)|	NUM
ejpam-4756	72	5	=	=	SYM
ejpam-4756	72	6	o(η1(w	o(η1(w	NOUN
ejpam-4756	72	7	)	)	PUNCT
ejpam-4756	72	8	)	)	PUNCT
ejpam-4756	72	9	}	}	PUNCT
ejpam-4756	72	10	where	where	SCONJ
ejpam-4756	72	11	η1	η1	NOUN
ejpam-4756	72	12	is	be	AUX
ejpam-4756	72	13	a	a	DET
ejpam-4756	72	14	integral	integral	ADJ
ejpam-4756	72	15	modulus	modulus	NOUN
ejpam-4756	72	16	of	of	ADP
ejpam-4756	72	17	continuity	continuity	NOUN
ejpam-4756	72	18	,	,	PUNCT
ejpam-4756	72	19	that	that	ADV
ejpam-4756	72	20	is	is	ADV
ejpam-4756	72	21	,	,	PUNCT
ejpam-4756	72	22	η1	η1	NOUN
ejpam-4756	72	23	is	be	AUX
ejpam-4756	72	24	a	a	DET
ejpam-4756	72	25	non	non	ADJ
ejpam-4756	72	26	-	-	ADJ
ejpam-4756	72	27	decreasing	decrease	VERB
ejpam-4756	72	28	continuous	continuous	ADJ
ejpam-4756	72	29	function	function	NOUN
ejpam-4756	72	30	together	together	ADV
ejpam-4756	72	31	with	with	ADP
ejpam-4756	72	32	the	the	DET
ejpam-4756	72	33	property	property	NOUN
ejpam-4756	72	34	η1(0	η1(0	NOUN
ejpam-4756	72	35	)	)	PUNCT
ejpam-4756	72	36	=	=	SYM
ejpam-4756	73	1	0	0	NUM
ejpam-4756	73	2	,	,	PUNCT
ejpam-4756	73	3	η1(w1	η1(w1	PRON
ejpam-4756	73	4	+	+	NOUN
ejpam-4756	73	5	w2	w2	NOUN
ejpam-4756	73	6	)	)	PUNCT
ejpam-4756	73	7	≤	≤	NUM
ejpam-4756	74	1	η1(w1	η1(w1	NOUN
ejpam-4756	74	2	)	)	PUNCT
ejpam-4756	74	3	+	+	SYM
ejpam-4756	74	4	η1(w2	η1(w2	NOUN
ejpam-4756	74	5	)	)	PUNCT
ejpam-4756	74	6	.	.	PUNCT
ejpam-4756	75	1	let	let	VERB
ejpam-4756	75	2	η1	η1	NOUN
ejpam-4756	75	3	:	:	PUNCT
ejpam-4756	76	1	[	[	X
ejpam-4756	76	2	0	0	NUM
ejpam-4756	76	3	,	,	PUNCT
ejpam-4756	76	4	2π	2π	NOUN
ejpam-4756	76	5	]	]	PUNCT
ejpam-4756	76	6	→	→	PUNCT
ejpam-4756	76	7	r	r	NOUN
ejpam-4756	76	8	be	be	AUX
ejpam-4756	76	9	a	a	DET
ejpam-4756	76	10	real	real	ADV
ejpam-4756	76	11	valued	value	VERB
ejpam-4756	76	12	arbitrary	arbitrary	ADJ
ejpam-4756	76	13	function	function	NOUN
ejpam-4756	76	14	with	with	ADP
ejpam-4756	76	15	η1(w	η1(w	NOUN
ejpam-4756	76	16	)	)	PUNCT
ejpam-4756	76	17	>	>	X
ejpam-4756	76	18	0	0	PUNCT
ejpam-4756	76	19	for	for	ADP
ejpam-4756	76	20	0	0	NUM
ejpam-4756	76	21	<	<	X
ejpam-4756	76	22	w	w	PROPN
ejpam-4756	76	23	≤	≤	ADJ
ejpam-4756	76	24	2π	2π	NOUN
ejpam-4756	76	25	and	and	CCONJ
ejpam-4756	76	26	limn→0	limn→0	PROPN
ejpam-4756	76	27	+	+	CCONJ
ejpam-4756	76	28	η1(w	η1(w	NOUN
ejpam-4756	76	29	)	)	PUNCT
ejpam-4756	76	30	=	=	SYM
ejpam-4756	76	31	η1(0	η1(0	NOUN
ejpam-4756	76	32	)	)	PUNCT
ejpam-4756	76	33	=	=	SYM
ejpam-4756	77	1	0	0	X
ejpam-4756	77	2	.	.	PUNCT
ejpam-4756	78	1	now	now	ADV
ejpam-4756	78	2	,	,	PUNCT
ejpam-4756	78	3	we	we	PRON
ejpam-4756	78	4	define	define	VERB
ejpam-4756	78	5	(	(	PUNCT
ejpam-4756	78	6	[	[	X
ejpam-4756	78	7	15	15	NUM
ejpam-4756	78	8	]	]	SYM
ejpam-4756	78	9	)	)	PUNCT
ejpam-4756	78	10	z(η1	z(η1	X
ejpam-4756	78	11	)	)	PUNCT
ejpam-4756	78	12	r	r	NOUN
ejpam-4756	78	13	=	=	PUNCT
ejpam-4756	78	14	{	{	PUNCT
ejpam-4756	78	15	g	g	PROPN
ejpam-4756	78	16	∈	∈	PROPN
ejpam-4756	78	17	lr[0	lr[0	PROPN
ejpam-4756	78	18	,	,	PUNCT
ejpam-4756	78	19	2π	2π	NOUN
ejpam-4756	78	20	]	]	PUNCT
ejpam-4756	78	21	:	:	PUNCT
ejpam-4756	78	22	sup	sup	NOUN
ejpam-4756	78	23	w	w	ADP
ejpam-4756	78	24	̸=0	̸=0	ADV
ejpam-4756	78	25	∥g(·+	∥g(·+	PROPN
ejpam-4756	78	26	w	w	PROPN
ejpam-4756	78	27	)	)	PUNCT
ejpam-4756	79	1	+	+	CCONJ
ejpam-4756	79	2	g	g	PROPN
ejpam-4756	79	3	(	(	PUNCT
ejpam-4756	79	4	·	·	PUNCT
ejpam-4756	79	5	−	−	PROPN
ejpam-4756	79	6	w)−	w)−	PROPN
ejpam-4756	79	7	2g(·)∥r	2g(·)∥r	NUM
ejpam-4756	79	8	η1(w	η1(w	NUM
ejpam-4756	79	9	)	)	PUNCT
ejpam-4756	79	10	<	<	X
ejpam-4756	79	11	∞	∞	PROPN
ejpam-4756	79	12	,	,	PUNCT
ejpam-4756	79	13	r	r	NOUN
ejpam-4756	79	14	≥	≥	NOUN
ejpam-4756	79	15	1	1	NUM
ejpam-4756	79	16	}	}	PUNCT
ejpam-4756	79	17	,	,	PUNCT
ejpam-4756	79	18	(	(	PUNCT
ejpam-4756	79	19	12	12	NUM
ejpam-4756	79	20	)	)	PUNCT
ejpam-4756	79	21	with	with	ADP
ejpam-4756	79	22	its	its	PRON
ejpam-4756	79	23	norm	norm	NOUN
ejpam-4756	79	24	given	give	VERB
ejpam-4756	79	25	by	by	ADP
ejpam-4756	79	26	∥g∥(η1)r	∥g∥(η1)r	PROPN
ejpam-4756	79	27	=	=	SYM
ejpam-4756	79	28	∥g∥r	∥g∥r	PROPN
ejpam-4756	79	29	+	+	CCONJ
ejpam-4756	79	30	sup	sup	NOUN
ejpam-4756	79	31	w	w	ADP
ejpam-4756	79	32	̸=0	̸=0	ADV
ejpam-4756	79	33	∥g(·+	∥g(·+	PROPN
ejpam-4756	79	34	w	w	PROPN
ejpam-4756	79	35	)	)	PUNCT
ejpam-4756	79	36	+	+	CCONJ
ejpam-4756	79	37	g	g	PROPN
ejpam-4756	79	38	(	(	PUNCT
ejpam-4756	79	39	·	·	PUNCT
ejpam-4756	79	40	−	−	PROPN
ejpam-4756	79	41	w)−	w)−	PROPN
ejpam-4756	79	42	2g(·)∥r	2g(·)∥r	PROPN
ejpam-4756	79	43	η1(w	η1(w	NUM
ejpam-4756	79	44	)	)	PUNCT
ejpam-4756	79	45	,	,	PUNCT
ejpam-4756	79	46	r	r	NOUN
ejpam-4756	79	47	≥	≥	NOUN
ejpam-4756	79	48	1	1	NUM
ejpam-4756	79	49	.	.	PUNCT
ejpam-4756	80	1	(	(	PUNCT
ejpam-4756	80	2	13	13	NUM
ejpam-4756	80	3	)	)	PUNCT
ejpam-4756	80	4	h.	h.	PROPN
ejpam-4756	80	5	k.	k.	PROPN
ejpam-4756	80	6	nigam	nigam	PROPN
ejpam-4756	80	7	,	,	PUNCT
ejpam-4756	80	8	m.	m.	PROPN
ejpam-4756	80	9	k.	k.	PROPN
ejpam-4756	80	10	sah	sah	PROPN
ejpam-4756	80	11	/	/	SYM
ejpam-4756	80	12	eur	eur	PROPN
ejpam-4756	80	13	.	.	PUNCT
ejpam-4756	81	1	j.	j.	PROPN
ejpam-4756	81	2	pure	pure	PROPN
ejpam-4756	81	3	appl	appl	PROPN
ejpam-4756	81	4	.	.	PROPN
ejpam-4756	81	5	math	math	PROPN
ejpam-4756	81	6	,	,	PUNCT
ejpam-4756	81	7	16	16	NUM
ejpam-4756	81	8	(	(	PUNCT
ejpam-4756	81	9	2	2	NUM
ejpam-4756	81	10	)	)	PUNCT
ejpam-4756	81	11	(	(	PUNCT
ejpam-4756	81	12	2023	2023	NUM
ejpam-4756	81	13	)	)	PUNCT
ejpam-4756	81	14	,	,	PUNCT
ejpam-4756	81	15	1302	1302	NUM
ejpam-4756	81	16	-	-	SYM
ejpam-4756	81	17	1317	1317	NUM
ejpam-4756	81	18	1306	1306	NUM
ejpam-4756	81	19	hence	hence	ADV
ejpam-4756	81	20	,	,	PUNCT
ejpam-4756	81	21	the	the	DET
ejpam-4756	81	22	generalized	generalized	ADJ
ejpam-4756	81	23	zygmund	zygmund	NOUN
ejpam-4756	81	24	space	space	NOUN
ejpam-4756	81	25	(	(	PUNCT
ejpam-4756	81	26	12	12	NUM
ejpam-4756	81	27	)	)	PUNCT
ejpam-4756	81	28	with	with	ADP
ejpam-4756	81	29	(	(	PUNCT
ejpam-4756	81	30	13	13	NUM
ejpam-4756	81	31	)	)	PUNCT
ejpam-4756	81	32	is	be	AUX
ejpam-4756	81	33	a	a	DET
ejpam-4756	81	34	banach	banach	NOUN
ejpam-4756	81	35	space	space	NOUN
ejpam-4756	81	36	.	.	PUNCT
ejpam-4756	82	1	the	the	DET
ejpam-4756	82	2	space	space	NOUN
ejpam-4756	82	3	∥	∥	PUNCT
ejpam-4756	82	4	·	·	PUNCT
ejpam-4756	82	5	∥(η1)r	∥(η1)r	NUM
ejpam-4756	82	6	is	be	AUX
ejpam-4756	82	7	complete	complete	ADJ
ejpam-4756	82	8	in	in	ADP
ejpam-4756	82	9	view	view	NOUN
ejpam-4756	82	10	of	of	ADP
ejpam-4756	82	11	lr(r	lr(r	NOUN
ejpam-4756	82	12	≥	≥	NOUN
ejpam-4756	82	13	1	1	NUM
ejpam-4756	82	14	)	)	PUNCT
ejpam-4756	82	15	space	space	NOUN
ejpam-4756	82	16	.	.	PUNCT
ejpam-4756	83	1	note	note	VERB
ejpam-4756	83	2	1	1	NUM
ejpam-4756	83	3	:	:	PUNCT
ejpam-4756	83	4	η1(w	η1(w	NUM
ejpam-4756	83	5	)	)	PUNCT
ejpam-4756	83	6	and	and	CCONJ
ejpam-4756	83	7	η2(w	η2(w	NUM
ejpam-4756	83	8	)	)	PUNCT
ejpam-4756	83	9	denote	denote	VERB
ejpam-4756	83	10	the	the	DET
ejpam-4756	83	11	moduli	modulus	NOUN
ejpam-4756	83	12	of	of	ADP
ejpam-4756	83	13	continuity	continuity	NOUN
ejpam-4756	83	14	of	of	ADP
ejpam-4756	83	15	order	order	NOUN
ejpam-4756	83	16	two	two	NUM
ejpam-4756	83	17	(	(	PUNCT
ejpam-4756	83	18	[	[	X
ejpam-4756	83	19	15	15	NUM
ejpam-4756	83	20	]	]	NUM
ejpam-4756	83	21	)	)	PUNCT
ejpam-4756	83	22	.	.	PUNCT
ejpam-4756	84	1	if	if	SCONJ
ejpam-4756	84	2	η1(w	η1(w	NUM
ejpam-4756	84	3	)	)	PUNCT
ejpam-4756	84	4	η2(w	η2(w	NOUN
ejpam-4756	84	5	)	)	PUNCT
ejpam-4756	84	6	be	be	VERB
ejpam-4756	84	7	non	non	ADJ
ejpam-4756	84	8	-	-	ADJ
ejpam-4756	84	9	decreasing	decrease	VERB
ejpam-4756	84	10	and	and	CCONJ
ejpam-4756	84	11	positive	positive	ADJ
ejpam-4756	84	12	,	,	PUNCT
ejpam-4756	84	13	then	then	ADV
ejpam-4756	84	14	∥g∥(η2)r	∥g∥(η2)r	PROPN
ejpam-4756	84	15	≤	≤	ADJ
ejpam-4756	84	16	max	max	PROPN
ejpam-4756	84	17	(	(	PUNCT
ejpam-4756	84	18	1	1	NUM
ejpam-4756	84	19	,	,	PUNCT
ejpam-4756	84	20	η1(2π	η1(2π	NOUN
ejpam-4756	84	21	)	)	PUNCT
ejpam-4756	84	22	η2(2π	η2(2π	NOUN
ejpam-4756	84	23	)	)	PUNCT
ejpam-4756	84	24	)	)	PUNCT
ejpam-4756	85	1	∥g∥(η1)r	∥g∥(η1)r	PROPN
ejpam-4756	85	2	<	<	X
ejpam-4756	85	3	∞.	∞.	PROPN
ejpam-4756	85	4	note	note	VERB
ejpam-4756	85	5	2	2	NUM
ejpam-4756	85	6	:	:	PUNCT
ejpam-4756	85	7	we	we	PRON
ejpam-4756	85	8	observe	observe	VERB
ejpam-4756	85	9	that	that	SCONJ
ejpam-4756	85	10	z(η1	z(η1	NOUN
ejpam-4756	85	11	)	)	PUNCT
ejpam-4756	86	1	r	r	NOUN
ejpam-4756	86	2	⊂	⊂	PROPN
ejpam-4756	86	3	z(η2	z(η2	NOUN
ejpam-4756	86	4	)	)	PUNCT
ejpam-4756	87	1	r	r	NOUN
ejpam-4756	87	2	⊂	⊂	PROPN
ejpam-4756	87	3	lr	lr	NOUN
ejpam-4756	87	4	,	,	PUNCT
ejpam-4756	87	5	r	r	NOUN
ejpam-4756	87	6	≥	≥	NOUN
ejpam-4756	87	7	1	1	NUM
ejpam-4756	87	8	.	.	PUNCT
ejpam-4756	87	9	remark	remark	NOUN
ejpam-4756	87	10	1	1	NUM
ejpam-4756	87	11	:	:	PUNCT
ejpam-4756	87	12	(	(	PUNCT
ejpam-4756	87	13	i	i	NOUN
ejpam-4756	87	14	)	)	PUNCT
ejpam-4756	87	15	if	if	SCONJ
ejpam-4756	87	16	r	r	NOUN
ejpam-4756	87	17	→	→	SYM
ejpam-4756	87	18	∞	∞	PROPN
ejpam-4756	87	19	in	in	ADP
ejpam-4756	87	20	z	z	PROPN
ejpam-4756	87	21	(	(	PUNCT
ejpam-4756	87	22	η1	η1	NOUN
ejpam-4756	87	23	)	)	PUNCT
ejpam-4756	87	24	r	r	NOUN
ejpam-4756	87	25	then	then	ADV
ejpam-4756	87	26	z	z	PROPN
ejpam-4756	87	27	(	(	PUNCT
ejpam-4756	87	28	η1	η1	NOUN
ejpam-4756	87	29	)	)	PUNCT
ejpam-4756	87	30	r	r	NOUN
ejpam-4756	87	31	reduces	reduce	VERB
ejpam-4756	87	32	to	to	ADP
ejpam-4756	87	33	z(η1	z(η1	NUM
ejpam-4756	87	34	)	)	PUNCT
ejpam-4756	87	35	.	.	PUNCT
ejpam-4756	88	1	(	(	PUNCT
ejpam-4756	88	2	ii	ii	NOUN
ejpam-4756	88	3	)	)	PUNCT
ejpam-4756	88	4	if	if	SCONJ
ejpam-4756	88	5	η1(w	η1(w	PRON
ejpam-4756	88	6	)	)	PUNCT
ejpam-4756	88	7	=	=	SYM
ejpam-4756	88	8	wα	wα	NOUN
ejpam-4756	88	9	in	in	ADP
ejpam-4756	88	10	z(η1	z(η1	NOUN
ejpam-4756	88	11	)	)	PUNCT
ejpam-4756	88	12	then	then	ADV
ejpam-4756	88	13	z(η1	z(η1	X
ejpam-4756	88	14	)	)	PUNCT
ejpam-4756	88	15	reduces	reduce	VERB
ejpam-4756	88	16	to	to	ADP
ejpam-4756	88	17	zα	zα	PRON
ejpam-4756	88	18	.	.	PUNCT
ejpam-4756	89	1	(	(	PUNCT
ejpam-4756	89	2	iii	iii	X
ejpam-4756	89	3	)	)	PUNCT
ejpam-4756	89	4	if	if	SCONJ
ejpam-4756	89	5	η1(w	η1(w	PRON
ejpam-4756	89	6	)	)	PUNCT
ejpam-4756	89	7	=	=	SYM
ejpam-4756	89	8	wα	wα	NOUN
ejpam-4756	89	9	in	in	ADP
ejpam-4756	89	10	z	z	PROPN
ejpam-4756	89	11	(	(	PUNCT
ejpam-4756	89	12	η1	η1	NOUN
ejpam-4756	89	13	)	)	PUNCT
ejpam-4756	89	14	r	r	NOUN
ejpam-4756	89	15	then	then	ADV
ejpam-4756	89	16	z	z	PROPN
ejpam-4756	89	17	(	(	PUNCT
ejpam-4756	89	18	η1	η1	NOUN
ejpam-4756	89	19	)	)	PUNCT
ejpam-4756	89	20	r	r	NOUN
ejpam-4756	89	21	reduces	reduce	VERB
ejpam-4756	89	22	to	to	ADP
ejpam-4756	89	23	zα	zα	PRON
ejpam-4756	89	24	,	,	PUNCT
ejpam-4756	89	25	r.	r.	PROPN
ejpam-4756	89	26	(	(	PUNCT
ejpam-4756	89	27	iv	iv	X
ejpam-4756	89	28	)	)	PUNCT
ejpam-4756	89	29	if	if	SCONJ
ejpam-4756	89	30	r	r	NOUN
ejpam-4756	89	31	→	→	SYM
ejpam-4756	89	32	∞	∞	PROPN
ejpam-4756	89	33	in	in	ADP
ejpam-4756	89	34	zα	zα	NUM
ejpam-4756	89	35	,	,	PUNCT
ejpam-4756	89	36	r	r	NOUN
ejpam-4756	89	37	then	then	ADV
ejpam-4756	89	38	zα	zα	NUM
ejpam-4756	89	39	,	,	PUNCT
ejpam-4756	89	40	r	r	NOUN
ejpam-4756	89	41	reduces	reduce	VERB
ejpam-4756	89	42	to	to	ADP
ejpam-4756	89	43	zα	zα	PROPN
ejpam-4756	89	44	.	.	PUNCT
ejpam-4756	90	1	(	(	PUNCT
ejpam-4756	90	2	v	v	NOUN
ejpam-4756	90	3	)	)	PUNCT
ejpam-4756	90	4	if	if	SCONJ
ejpam-4756	90	5	η1(w	η1(w	PRON
ejpam-4756	90	6	)	)	PUNCT
ejpam-4756	90	7	=	=	VERB
ejpam-4756	90	8	wα1	wα1	NOUN
ejpam-4756	90	9	,	,	PUNCT
ejpam-4756	90	10	η2(w	η2(w	X
ejpam-4756	90	11	)	)	PUNCT
ejpam-4756	90	12	=	=	SYM
ejpam-4756	91	1	wα2	wα2	NOUN
ejpam-4756	91	2	,	,	PUNCT
ejpam-4756	91	3	r	r	NOUN
ejpam-4756	91	4	→	→	SYM
ejpam-4756	91	5	∞	∞	PROPN
ejpam-4756	91	6	and	and	CCONJ
ejpam-4756	91	7	α2	α2	NOUN
ejpam-4756	91	8	=	=	SYM
ejpam-4756	91	9	0	0	NUM
ejpam-4756	92	1	in	in	ADP
ejpam-4756	92	2	zα	zα	PROPN
ejpam-4756	92	3	,	,	PUNCT
ejpam-4756	92	4	r	r	NOUN
ejpam-4756	92	5	then	then	ADV
ejpam-4756	92	6	z	z	PROPN
ejpam-4756	92	7	(	(	PUNCT
ejpam-4756	92	8	η1	η1	NOUN
ejpam-4756	92	9	)	)	PUNCT
ejpam-4756	92	10	r	r	NOUN
ejpam-4756	92	11	reduces	reduce	VERB
ejpam-4756	92	12	to	to	ADP
ejpam-4756	92	13	lip(α	lip(α	PROPN
ejpam-4756	92	14	)	)	PUNCT
ejpam-4756	92	15	.	.	PUNCT
ejpam-4756	93	1	(	(	PUNCT
ejpam-4756	93	2	vi	vi	X
ejpam-4756	93	3	)	)	PUNCT
ejpam-4756	93	4	let	let	VERB
ejpam-4756	93	5	0	0	NUM
ejpam-4756	93	6	≤	≤	ADV
ejpam-4756	93	7	δ2	δ2	VERB
ejpam-4756	93	8	<	<	X
ejpam-4756	93	9	δ1	δ1	NOUN
ejpam-4756	93	10	<	<	X
ejpam-4756	93	11	1	1	NUM
ejpam-4756	93	12	,	,	PUNCT
ejpam-4756	93	13	if	if	SCONJ
ejpam-4756	93	14	η1(w	η1(w	ADP
ejpam-4756	93	15	)	)	PUNCT
ejpam-4756	93	16	=	=	SYM
ejpam-4756	93	17	wδ1	wδ1	NOUN
ejpam-4756	93	18	and	and	CCONJ
ejpam-4756	93	19	η2(w	η2(w	NOUN
ejpam-4756	93	20	)	)	PUNCT
ejpam-4756	94	1	=	=	SYM
ejpam-4756	95	1	wδ2	wδ2	NOUN
ejpam-4756	95	2	then	then	ADV
ejpam-4756	95	3	η1(w	η1(w	NOUN
ejpam-4756	95	4	)	)	PUNCT
ejpam-4756	95	5	η2(w	η2(w	NOUN
ejpam-4756	95	6	)	)	PUNCT
ejpam-4756	95	7	is	be	AUX
ejpam-4756	95	8	non	non	ADJ
ejpam-4756	95	9	-	-	ADJ
ejpam-4756	95	10	decreasing	decrease	VERB
ejpam-4756	95	11	,	,	PUNCT
ejpam-4756	95	12	while	while	SCONJ
ejpam-4756	95	13	η1(w	η1(w	PRON
ejpam-4756	95	14	)	)	PUNCT
ejpam-4756	95	15	wη2(w	wη2(w	PROPN
ejpam-4756	95	16	)	)	PUNCT
ejpam-4756	95	17	is	be	AUX
ejpam-4756	95	18	non	non	ADJ
ejpam-4756	95	19	-	-	ADJ
ejpam-4756	95	20	increasing	increase	VERB
ejpam-4756	95	21	.	.	PUNCT
ejpam-4756	96	1	1.4	1.4	NUM
ejpam-4756	96	2	.	.	PUNCT
ejpam-4756	96	3	degree	degree	NOUN
ejpam-4756	96	4	of	of	ADP
ejpam-4756	96	5	convergence	convergence	NOUN
ejpam-4756	96	6	the	the	DET
ejpam-4756	96	7	degree	degree	NOUN
ejpam-4756	96	8	of	of	ADP
ejpam-4756	96	9	convergence	convergence	NOUN
ejpam-4756	96	10	of	of	ADP
ejpam-4756	96	11	a	a	DET
ejpam-4756	96	12	summation	summation	NOUN
ejpam-4756	96	13	method	method	NOUN
ejpam-4756	96	14	to	to	ADP
ejpam-4756	96	15	a	a	DET
ejpam-4756	96	16	given	give	VERB
ejpam-4756	96	17	function	function	NOUN
ejpam-4756	96	18	g	g	PROPN
ejpam-4756	96	19	is	be	AUX
ejpam-4756	96	20	a	a	DET
ejpam-4756	96	21	measure	measure	NOUN
ejpam-4756	96	22	that	that	SCONJ
ejpam-4756	96	23	how	how	SCONJ
ejpam-4756	96	24	fast	fast	ADJ
ejpam-4756	96	25	wν	wν	NOUN
ejpam-4756	96	26	converges	converge	VERB
ejpam-4756	96	27	to	to	ADP
ejpam-4756	96	28	g	g	NOUN
ejpam-4756	96	29	,	,	PUNCT
ejpam-4756	96	30	which	which	PRON
ejpam-4756	96	31	is	be	AUX
ejpam-4756	96	32	given	give	VERB
ejpam-4756	96	33	by	by	ADP
ejpam-4756	96	34	(	(	PUNCT
ejpam-4756	96	35	[	[	X
ejpam-4756	96	36	7	7	NUM
ejpam-4756	96	37	]	]	SYM
ejpam-4756	96	38	)	)	PUNCT
ejpam-4756	96	39	∥g	∥g	PROPN
ejpam-4756	96	40	−	−	PROPN
ejpam-4756	96	41	wν∥	wν∥	PROPN
ejpam-4756	96	42	=	=	PROPN
ejpam-4756	96	43	o	o	PROPN
ejpam-4756	96	44	(	(	PUNCT
ejpam-4756	96	45	1	1	NUM
ejpam-4756	96	46	γν	γν	NOUN
ejpam-4756	96	47	)	)	PUNCT
ejpam-4756	96	48	,	,	PUNCT
ejpam-4756	96	49	where	where	SCONJ
ejpam-4756	96	50	γν	γν	PRON
ejpam-4756	96	51	→	→	SYM
ejpam-4756	96	52	∞	∞	PROPN
ejpam-4756	96	53	as	as	ADP
ejpam-4756	96	54	ν	ν	NOUN
ejpam-4756	96	55	→	→	SYM
ejpam-4756	96	56	∞.	∞.	PROPN
ejpam-4756	96	57	we	we	PRON
ejpam-4756	96	58	write	write	VERB
ejpam-4756	96	59	φ(w	φ(w	PROPN
ejpam-4756	96	60	)	)	PUNCT
ejpam-4756	96	61	=	=	SYM
ejpam-4756	97	1	ϕ(t	ϕ(t	PROPN
ejpam-4756	97	2	,	,	PUNCT
ejpam-4756	97	3	w	w	NOUN
ejpam-4756	97	4	)	)	PUNCT
ejpam-4756	97	5	=	=	PUNCT
ejpam-4756	98	1	g(t+	g(t+	NUM
ejpam-4756	98	2	w	w	NOUN
ejpam-4756	98	3	)	)	PUNCT
ejpam-4756	99	1	+	+	NUM
ejpam-4756	99	2	g(t−	g(t−	NOUN
ejpam-4756	99	3	w)−	w)−	PROPN
ejpam-4756	99	4	2g(t	2g(t	NUM
ejpam-4756	99	5	)	)	PUNCT
ejpam-4756	99	6	;	;	PUNCT
ejpam-4756	99	7	φ(t	φ(t	X
ejpam-4756	99	8	)	)	PUNCT
ejpam-4756	100	1	=	=	SYM
ejpam-4756	101	1	∫	∫	PROPN
ejpam-4756	101	2	t	t	PROPN
ejpam-4756	101	3	0	0	NUM
ejpam-4756	101	4	|ϕ(u)|du	|ϕ(u)|du	NUM
ejpam-4756	101	5	;	;	PUNCT
ejpam-4756	101	6	mν(w	mν(w	NOUN
ejpam-4756	101	7	)	)	PUNCT
ejpam-4756	101	8	=	=	SYM
ejpam-4756	101	9	1	1	NUM
ejpam-4756	101	10	2π	2π	NUM
ejpam-4756	101	11	ν∑	ν∑	PUNCT
ejpam-4756	102	1	k=0	k=0	PUNCT
ejpam-4756	102	2	[	[	PUNCT
ejpam-4756	102	3	ν	ν	X
ejpam-4756	102	4	k	k	X
ejpam-4756	102	5	]	]	PUNCT
ejpam-4756	102	6	λk	λk	PROPN
ejpam-4756	102	7	k∑	k∑	PROPN
ejpam-4756	102	8	j=0	j=0	PROPN
ejpam-4756	102	9	ak	ak	PROPN
ejpam-4756	102	10	,	,	PUNCT
ejpam-4756	102	11	j	j	PROPN
ejpam-4756	102	12	sin	sin	NOUN
ejpam-4756	102	13	(	(	PUNCT
ejpam-4756	102	14	j	j	NOUN
ejpam-4756	102	15	+	+	CCONJ
ejpam-4756	102	16	1	1	NUM
ejpam-4756	102	17	2	2	NUM
ejpam-4756	102	18	)	)	PUNCT
ejpam-4756	102	19	w	w	ADP
ejpam-4756	102	20	sin(w2	sin(w2	ADJ
ejpam-4756	102	21	)	)	PUNCT
ejpam-4756	102	22	.	.	PUNCT
ejpam-4756	103	1	the	the	DET
ejpam-4756	103	2	organization	organization	NOUN
ejpam-4756	103	3	of	of	ADP
ejpam-4756	103	4	the	the	DET
ejpam-4756	103	5	paper	paper	NOUN
ejpam-4756	103	6	is	be	AUX
ejpam-4756	103	7	as	as	SCONJ
ejpam-4756	103	8	follows	follow	VERB
ejpam-4756	103	9	:	:	PUNCT
ejpam-4756	103	10	in	in	ADP
ejpam-4756	103	11	section	section	NOUN
ejpam-4756	103	12	2	2	NUM
ejpam-4756	103	13	,	,	PUNCT
ejpam-4756	103	14	we	we	PRON
ejpam-4756	103	15	give	give	VERB
ejpam-4756	103	16	a	a	DET
ejpam-4756	103	17	motivation	motivation	NOUN
ejpam-4756	103	18	and	and	CCONJ
ejpam-4756	103	19	propose	propose	VERB
ejpam-4756	103	20	our	our	PRON
ejpam-4756	103	21	main	main	ADJ
ejpam-4756	103	22	results	result	NOUN
ejpam-4756	103	23	.	.	PUNCT
ejpam-4756	104	1	in	in	ADP
ejpam-4756	104	2	section	section	NOUN
ejpam-4756	104	3	3	3	NUM
ejpam-4756	104	4	,	,	PUNCT
ejpam-4756	104	5	we	we	PRON
ejpam-4756	104	6	establish	establish	VERB
ejpam-4756	104	7	two	two	NUM
ejpam-4756	104	8	lemmas	lemma	NOUN
ejpam-4756	104	9	,	,	PUNCT
ejpam-4756	104	10	which	which	PRON
ejpam-4756	104	11	are	be	AUX
ejpam-4756	104	12	used	use	VERB
ejpam-4756	104	13	in	in	ADP
ejpam-4756	104	14	the	the	DET
ejpam-4756	104	15	proofs	proof	NOUN
ejpam-4756	104	16	of	of	ADP
ejpam-4756	104	17	our	our	PRON
ejpam-4756	104	18	main	main	ADJ
ejpam-4756	104	19	results	result	NOUN
ejpam-4756	104	20	.	.	PUNCT
ejpam-4756	105	1	in	in	ADP
ejpam-4756	105	2	section	section	NOUN
ejpam-4756	105	3	4	4	NUM
ejpam-4756	105	4	,	,	PUNCT
ejpam-4756	105	5	we	we	PRON
ejpam-4756	105	6	establish	establish	VERB
ejpam-4756	105	7	our	our	PRON
ejpam-4756	105	8	main	main	ADJ
ejpam-4756	105	9	results	result	NOUN
ejpam-4756	105	10	.	.	PUNCT
ejpam-4756	106	1	in	in	ADP
ejpam-4756	106	2	section	section	NOUN
ejpam-4756	106	3	5	5	NUM
ejpam-4756	106	4	,	,	PUNCT
ejpam-4756	106	5	we	we	PRON
ejpam-4756	106	6	give	give	VERB
ejpam-4756	106	7	applications	application	NOUN
ejpam-4756	106	8	of	of	ADP
ejpam-4756	106	9	our	our	PRON
ejpam-4756	106	10	main	main	ADJ
ejpam-4756	106	11	results	result	NOUN
ejpam-4756	106	12	and	and	CCONJ
ejpam-4756	106	13	in	in	ADP
ejpam-4756	106	14	section	section	NOUN
ejpam-4756	106	15	6	6	NUM
ejpam-4756	106	16	,	,	PUNCT
ejpam-4756	106	17	we	we	PRON
ejpam-4756	106	18	give	give	VERB
ejpam-4756	106	19	a	a	DET
ejpam-4756	106	20	conclusion	conclusion	NOUN
ejpam-4756	106	21	of	of	ADP
ejpam-4756	106	22	the	the	DET
ejpam-4756	106	23	main	main	ADJ
ejpam-4756	106	24	results	result	NOUN
ejpam-4756	106	25	.	.	PUNCT
ejpam-4756	107	1	h.	h.	PROPN
ejpam-4756	107	2	k.	k.	PROPN
ejpam-4756	107	3	nigam	nigam	PROPN
ejpam-4756	107	4	,	,	PUNCT
ejpam-4756	107	5	m.	m.	PROPN
ejpam-4756	107	6	k.	k.	PROPN
ejpam-4756	107	7	sah	sah	PROPN
ejpam-4756	107	8	/	/	SYM
ejpam-4756	107	9	eur	eur	PROPN
ejpam-4756	107	10	.	.	PUNCT
ejpam-4756	108	1	j.	j.	PROPN
ejpam-4756	108	2	pure	pure	PROPN
ejpam-4756	108	3	appl	appl	PROPN
ejpam-4756	108	4	.	.	PROPN
ejpam-4756	108	5	math	math	PROPN
ejpam-4756	108	6	,	,	PUNCT
ejpam-4756	108	7	16	16	NUM
ejpam-4756	108	8	(	(	PUNCT
ejpam-4756	108	9	2	2	NUM
ejpam-4756	108	10	)	)	PUNCT
ejpam-4756	108	11	(	(	PUNCT
ejpam-4756	108	12	2023	2023	NUM
ejpam-4756	108	13	)	)	PUNCT
ejpam-4756	108	14	,	,	PUNCT
ejpam-4756	108	15	1302	1302	NUM
ejpam-4756	108	16	-	-	SYM
ejpam-4756	108	17	1317	1317	NUM
ejpam-4756	108	18	1307	1307	NUM
ejpam-4756	108	19	2	2	NUM
ejpam-4756	108	20	.	.	X
ejpam-4756	108	21	main	main	ADJ
ejpam-4756	108	22	results	result	NOUN
ejpam-4756	108	23	in	in	ADP
ejpam-4756	108	24	this	this	DET
ejpam-4756	108	25	section	section	NOUN
ejpam-4756	108	26	,	,	PUNCT
ejpam-4756	108	27	we	we	PRON
ejpam-4756	108	28	state	state	VERB
ejpam-4756	108	29	our	our	PRON
ejpam-4756	108	30	main	main	ADJ
ejpam-4756	108	31	results	result	NOUN
ejpam-4756	108	32	:	:	PUNCT
ejpam-4756	108	33	theorem	theorem	NOUN
ejpam-4756	108	34	1	1	NUM
ejpam-4756	108	35	.	.	PUNCT
ejpam-4756	109	1	let	let	VERB
ejpam-4756	109	2	g	g	PRON
ejpam-4756	109	3	be	be	AUX
ejpam-4756	109	4	a	a	DET
ejpam-4756	109	5	lebesgue	lebesgue	NOUN
ejpam-4756	109	6	integrable	integrable	ADJ
ejpam-4756	109	7	function	function	NOUN
ejpam-4756	109	8	with	with	ADP
ejpam-4756	109	9	period	period	NOUN
ejpam-4756	109	10	2π	2π	PROPN
ejpam-4756	109	11	then	then	ADV
ejpam-4756	109	12	the	the	DET
ejpam-4756	109	13	degree	degree	NOUN
ejpam-4756	109	14	of	of	ADP
ejpam-4756	109	15	convergence	convergence	NOUN
ejpam-4756	109	16	of	of	ADP
ejpam-4756	109	17	g	g	NOUN
ejpam-4756	109	18	of	of	ADP
ejpam-4756	109	19	fourier	fourier	ADJ
ejpam-4756	109	20	series	series	NOUN
ejpam-4756	109	21	in	in	ADP
ejpam-4756	109	22	the	the	DET
ejpam-4756	109	23	generalized	generalized	ADJ
ejpam-4756	109	24	zygmund	zygmund	NOUN
ejpam-4756	109	25	space	space	NOUN
ejpam-4756	109	26	(	(	PUNCT
ejpam-4756	109	27	z	z	NOUN
ejpam-4756	109	28	(	(	PUNCT
ejpam-4756	109	29	η1	η1	NOUN
ejpam-4756	109	30	)	)	PUNCT
ejpam-4756	109	31	r	r	NOUN
ejpam-4756	109	32	,	,	PUNCT
ejpam-4756	109	33	r	r	NOUN
ejpam-4756	109	34	≥	≥	NOUN
ejpam-4756	109	35	1	1	NUM
ejpam-4756	109	36	)	)	PUNCT
ejpam-4756	109	37	using	use	VERB
ejpam-4756	109	38	(	(	PUNCT
ejpam-4756	109	39	kλa	kλa	NOUN
ejpam-4756	109	40	)	)	PUNCT
ejpam-4756	109	41	operator	operator	NOUN
ejpam-4756	109	42	,	,	PUNCT
ejpam-4756	109	43	is	be	AUX
ejpam-4756	109	44	given	give	VERB
ejpam-4756	109	45	by	by	ADP
ejpam-4756	109	46	∥dkλa	∥dkλa	NOUN
ejpam-4756	109	47	ν	ν	X
ejpam-4756	109	48	(	(	PUNCT
ejpam-4756	109	49	g	g	NOUN
ejpam-4756	109	50	;	;	PUNCT
ejpam-4756	109	51	·	·	PUNCT
ejpam-4756	109	52	)	)	PUNCT
ejpam-4756	110	1	−	−	PROPN
ejpam-4756	111	1	g(·)∥(η2)r	g(·)∥(η2)r	PROPN
ejpam-4756	111	2	=	=	PUNCT
ejpam-4756	112	1	o	o	X
ejpam-4756	113	1	[	[	X
ejpam-4756	113	2	(	(	PUNCT
ejpam-4756	113	3	(	(	PUNCT
ejpam-4756	113	4	1	1	NUM
ejpam-4756	113	5	+	+	NUM
ejpam-4756	113	6	γλ){2π(ν	γλ){2π(ν	NOUN
ejpam-4756	113	7	+	+	X
ejpam-4756	114	1	1)−	1)−	NUM
ejpam-4756	114	2	1	1	NUM
ejpam-4756	114	3	}	}	PUNCT
ejpam-4756	114	4	(	(	PUNCT
ejpam-4756	114	5	ν	ν	X
ejpam-4756	114	6	+	+	NOUN
ejpam-4756	114	7	1)γλ{π(ν	1)γλ{π(ν	NUM
ejpam-4756	114	8	+	+	SYM
ejpam-4756	114	9	1)−	1)−	NUM
ejpam-4756	114	10	1	1	NUM
ejpam-4756	114	11	}	}	PUNCT
ejpam-4756	114	12	)	)	PUNCT
ejpam-4756	114	13	∫	∫	PROPN
ejpam-4756	115	1	π	π	NOUN
ejpam-4756	115	2	1	1	NUM
ejpam-4756	115	3	ν+1	ν+1	NUM
ejpam-4756	115	4	η1(w	η1(w	NOUN
ejpam-4756	115	5	)	)	PUNCT
ejpam-4756	115	6	η2(w	η2(w	PROPN
ejpam-4756	115	7	)	)	PUNCT
ejpam-4756	115	8	1	1	NUM
ejpam-4756	115	9	w2	w2	NOUN
ejpam-4756	115	10	dw	dw	PROPN
ejpam-4756	115	11	]	]	PUNCT
ejpam-4756	115	12	,	,	PUNCT
ejpam-4756	115	13	(	(	PUNCT
ejpam-4756	115	14	14	14	NUM
ejpam-4756	115	15	)	)	PUNCT
ejpam-4756	115	16	where	where	SCONJ
ejpam-4756	115	17	η1(w	η1(w	X
ejpam-4756	115	18	)	)	PUNCT
ejpam-4756	115	19	and	and	CCONJ
ejpam-4756	115	20	η2(w	η2(w	NOUN
ejpam-4756	115	21	)	)	PUNCT
ejpam-4756	115	22	are	be	AUX
ejpam-4756	115	23	as	as	ADV
ejpam-4756	115	24	defined	define	VERB
ejpam-4756	115	25	in	in	ADP
ejpam-4756	115	26	note	note	NOUN
ejpam-4756	115	27	1	1	NUM
ejpam-4756	115	28	and	and	CCONJ
ejpam-4756	115	29	η1(w	η1(w	NUM
ejpam-4756	115	30	)	)	PUNCT
ejpam-4756	115	31	η2(w	η2(w	NOUN
ejpam-4756	115	32	)	)	PUNCT
ejpam-4756	115	33	is	be	AUX
ejpam-4756	115	34	positive	positive	ADJ
ejpam-4756	115	35	and	and	CCONJ
ejpam-4756	115	36	non	non	ADJ
ejpam-4756	115	37	-	-	ADJ
ejpam-4756	115	38	decreasing	decrease	VERB
ejpam-4756	115	39	.	.	PUNCT
ejpam-4756	116	1	theorem	theorem	NOUN
ejpam-4756	116	2	2	2	NUM
ejpam-4756	116	3	.	.	PUNCT
ejpam-4756	117	1	following	follow	VERB
ejpam-4756	117	2	the	the	DET
ejpam-4756	117	3	conditions	condition	NOUN
ejpam-4756	117	4	of	of	ADP
ejpam-4756	117	5	theorem	theorem	NOUN
ejpam-4756	117	6	1	1	NUM
ejpam-4756	117	7	,	,	PUNCT
ejpam-4756	117	8	if	if	SCONJ
ejpam-4756	117	9	η1(w	η1(w	ADP
ejpam-4756	117	10	)	)	PUNCT
ejpam-4756	117	11	wη2(w	wη2(w	PROPN
ejpam-4756	117	12	)	)	PUNCT
ejpam-4756	117	13	is	be	AUX
ejpam-4756	117	14	non	non	ADJ
ejpam-4756	117	15	-	-	ADJ
ejpam-4756	117	16	increasing	increase	VERB
ejpam-4756	117	17	,	,	PUNCT
ejpam-4756	117	18	then	then	ADV
ejpam-4756	117	19	the	the	DET
ejpam-4756	117	20	degree	degree	NOUN
ejpam-4756	117	21	of	of	ADP
ejpam-4756	117	22	convergence	convergence	NOUN
ejpam-4756	117	23	of	of	ADP
ejpam-4756	117	24	g	g	NOUN
ejpam-4756	117	25	of	of	ADP
ejpam-4756	117	26	fourier	fourier	ADJ
ejpam-4756	117	27	series	series	NOUN
ejpam-4756	117	28	in	in	ADP
ejpam-4756	117	29	the	the	DET
ejpam-4756	117	30	generalized	generalized	ADJ
ejpam-4756	117	31	zygmund	zygmund	NOUN
ejpam-4756	117	32	space	space	NOUN
ejpam-4756	117	33	(	(	PUNCT
ejpam-4756	117	34	z	z	NOUN
ejpam-4756	117	35	(	(	PUNCT
ejpam-4756	117	36	η1	η1	NOUN
ejpam-4756	117	37	)	)	PUNCT
ejpam-4756	117	38	r	r	NOUN
ejpam-4756	117	39	,	,	PUNCT
ejpam-4756	117	40	r	r	NOUN
ejpam-4756	117	41	≥	≥	NOUN
ejpam-4756	117	42	1	1	NUM
ejpam-4756	117	43	)	)	PUNCT
ejpam-4756	117	44	using	use	VERB
ejpam-4756	117	45	(	(	PUNCT
ejpam-4756	117	46	kλa	kλa	NOUN
ejpam-4756	117	47	)	)	PUNCT
ejpam-4756	117	48	operator	operator	NOUN
ejpam-4756	117	49	,	,	PUNCT
ejpam-4756	117	50	is	be	AUX
ejpam-4756	117	51	given	give	VERB
ejpam-4756	117	52	by	by	ADP
ejpam-4756	117	53	∥dkλa	∥dkλa	NOUN
ejpam-4756	117	54	ν	ν	X
ejpam-4756	117	55	(	(	PUNCT
ejpam-4756	117	56	g	g	NOUN
ejpam-4756	117	57	;	;	PUNCT
ejpam-4756	117	58	·	·	PUNCT
ejpam-4756	117	59	)	)	PUNCT
ejpam-4756	117	60	−	−	PROPN
ejpam-4756	118	1	g(·)∥(η2)r	g(·)∥(η2)r	PROPN
ejpam-4756	118	2	=	=	PUNCT
ejpam-4756	119	1	o	o	X
ejpam-4756	120	1	[	[	X
ejpam-4756	120	2	(	(	PUNCT
ejpam-4756	120	3	(	(	PUNCT
ejpam-4756	120	4	1	1	NUM
ejpam-4756	120	5	+	+	NUM
ejpam-4756	120	6	γλ){2π(ν	γλ){2π(ν	NOUN
ejpam-4756	121	1	+	+	ADJ
ejpam-4756	122	1	1)−	1)−	NUM
ejpam-4756	122	2	1	1	NUM
ejpam-4756	122	3	}	}	PUNCT
ejpam-4756	122	4	γλ{π(ν	γλ{π(ν	PROPN
ejpam-4756	123	1	+	+	PROPN
ejpam-4756	123	2	1)−	1)−	NUM
ejpam-4756	123	3	1	1	NUM
ejpam-4756	123	4	}	}	PUNCT
ejpam-4756	123	5	)	)	PUNCT
ejpam-4756	123	6	η1	η1	NOUN
ejpam-4756	123	7	(	(	PUNCT
ejpam-4756	123	8	1	1	NUM
ejpam-4756	123	9	ν+1	ν+1	PROPN
ejpam-4756	123	10	)	)	PUNCT
ejpam-4756	123	11	η2	η2	PROPN
ejpam-4756	123	12	(	(	PUNCT
ejpam-4756	123	13	1	1	NUM
ejpam-4756	123	14	ν+1	ν+1	NUM
ejpam-4756	123	15	)	)	PUNCT
ejpam-4756	123	16	log{(ν	log{(ν	NOUN
ejpam-4756	123	17	+	+	CCONJ
ejpam-4756	123	18	1)π	1)π	NUM
ejpam-4756	123	19	}	}	PUNCT
ejpam-4756	123	20	]	]	PUNCT
ejpam-4756	123	21	.	.	PUNCT
ejpam-4756	124	1	(	(	PUNCT
ejpam-4756	124	2	15	15	NUM
ejpam-4756	124	3	)	)	PUNCT
ejpam-4756	124	4	3	3	NUM
ejpam-4756	124	5	.	.	PUNCT
ejpam-4756	124	6	lemmas	lemmas	PROPN
ejpam-4756	124	7	in	in	ADP
ejpam-4756	124	8	this	this	DET
ejpam-4756	124	9	section	section	NOUN
ejpam-4756	124	10	,	,	PUNCT
ejpam-4756	124	11	we	we	PRON
ejpam-4756	124	12	prove	prove	VERB
ejpam-4756	124	13	the	the	DET
ejpam-4756	124	14	following	follow	VERB
ejpam-4756	124	15	lemmas	lemmas	NOUN
ejpam-4756	124	16	:	:	PUNCT
ejpam-4756	124	17	lemma	lemma	PROPN
ejpam-4756	124	18	1	1	NUM
ejpam-4756	124	19	.	.	PUNCT
ejpam-4756	125	1	(	(	PUNCT
ejpam-4756	125	2	[	[	X
ejpam-4756	125	3	6	6	NUM
ejpam-4756	125	4	]	]	PUNCT
ejpam-4756	125	5	)	)	PUNCT
ejpam-4756	125	6	let	let	VERB
ejpam-4756	125	7	f	f	PROPN
ejpam-4756	125	8	∈	∈	PROPN
ejpam-4756	125	9	z	z	PROPN
ejpam-4756	125	10	(	(	PUNCT
ejpam-4756	125	11	η1	η1	NOUN
ejpam-4756	125	12	)	)	PUNCT
ejpam-4756	125	13	r	r	NOUN
ejpam-4756	125	14	,	,	PUNCT
ejpam-4756	125	15	then	then	ADV
ejpam-4756	125	16	for	for	ADP
ejpam-4756	125	17	0	0	NUM
ejpam-4756	125	18	<	<	X
ejpam-4756	125	19	w	w	PROPN
ejpam-4756	125	20	≤	≤	NUM
ejpam-4756	125	21	π	π	NOUN
ejpam-4756	125	22	.	.	PUNCT
ejpam-4756	126	1	if	if	SCONJ
ejpam-4756	126	2	η1(w	η1(w	PROPN
ejpam-4756	126	3	)	)	PUNCT
ejpam-4756	126	4	and	and	CCONJ
ejpam-4756	126	5	η2(w	η2(w	NOUN
ejpam-4756	126	6	)	)	PUNCT
ejpam-4756	126	7	are	be	AUX
ejpam-4756	126	8	as	as	ADV
ejpam-4756	126	9	defined	define	VERB
ejpam-4756	126	10	in	in	ADP
ejpam-4756	126	11	note	note	NOUN
ejpam-4756	126	12	1	1	NUM
ejpam-4756	126	13	,	,	PUNCT
ejpam-4756	126	14	then	then	ADV
ejpam-4756	126	15	∥ϕ(·+	∥ϕ(·+	PROPN
ejpam-4756	126	16	z	z	PROPN
ejpam-4756	126	17	,	,	PUNCT
ejpam-4756	126	18	w	w	PROPN
ejpam-4756	126	19	)	)	PUNCT
ejpam-4756	127	1	+	+	CCONJ
ejpam-4756	127	2	ϕ	ϕ	X
ejpam-4756	127	3	(	(	PUNCT
ejpam-4756	127	4	·	·	PUNCT
ejpam-4756	127	5	−	−	PROPN
ejpam-4756	128	1	z	z	X
ejpam-4756	128	2	,	,	PUNCT
ejpam-4756	128	3	w)−	w)−	PROPN
ejpam-4756	128	4	2ϕ	2ϕ	NUM
ejpam-4756	128	5	(	(	PUNCT
ejpam-4756	128	6	·	·	PUNCT
ejpam-4756	128	7	,	,	PUNCT
ejpam-4756	128	8	w)∥r	w)∥r	ADP
ejpam-4756	128	9	=	=	SYM
ejpam-4756	128	10	o	o	X
ejpam-4756	128	11	(	(	PUNCT
ejpam-4756	128	12	η2(|z|	η2(|z|	NOUN
ejpam-4756	128	13	)	)	PUNCT
ejpam-4756	128	14	η1(w	η1(w	NOUN
ejpam-4756	128	15	)	)	PUNCT
ejpam-4756	128	16	η2(w	η2(w	NOUN
ejpam-4756	128	17	)	)	PUNCT
ejpam-4756	128	18	)	)	PUNCT
ejpam-4756	128	19	.	.	PUNCT
ejpam-4756	129	1	lemma	lemma	PROPN
ejpam-4756	129	2	2	2	NUM
ejpam-4756	129	3	.	.	PUNCT
ejpam-4756	129	4	|mν(w)|	|mν(w)|	PROPN
ejpam-4756	129	5	=	=	X
ejpam-4756	130	1	o	o	X
ejpam-4756	130	2	(	(	PUNCT
ejpam-4756	130	3	ν+1	ν+1	PROPN
ejpam-4756	130	4	γλ	γλ	PROPN
ejpam-4756	130	5	)	)	PUNCT
ejpam-4756	130	6	for	for	ADP
ejpam-4756	130	7	0	0	NUM
ejpam-4756	130	8	<	<	X
ejpam-4756	130	9	w	w	PROPN
ejpam-4756	130	10	≤	≤	NUM
ejpam-4756	130	11	1	1	NUM
ejpam-4756	130	12	ν+1	ν+1	PROPN
ejpam-4756	130	13	.	.	PUNCT
ejpam-4756	131	1	proof	proof	NOUN
ejpam-4756	131	2	.	.	PUNCT
ejpam-4756	132	1	for	for	ADP
ejpam-4756	132	2	0	0	NUM
ejpam-4756	132	3	<	<	X
ejpam-4756	132	4	w	w	PROPN
ejpam-4756	132	5	≤	≤	NUM
ejpam-4756	132	6	1	1	NUM
ejpam-4756	132	7	ν+1	ν+1	PROPN
ejpam-4756	132	8	,	,	PUNCT
ejpam-4756	132	9	sin	sin	NOUN
ejpam-4756	132	10	(	(	PUNCT
ejpam-4756	132	11	w	w	NOUN
ejpam-4756	132	12	2	2	NUM
ejpam-4756	132	13	)	)	PUNCT
ejpam-4756	132	14	≥	≥	NOUN
ejpam-4756	132	15	w	w	PROPN
ejpam-4756	132	16	π	π	PROPN
ejpam-4756	132	17	,	,	PUNCT
ejpam-4756	132	18	|	|	ADV
ejpam-4756	132	19	sin(νw)|	sin(νw)|	X
ejpam-4756	132	20	≤	≤	X
ejpam-4756	132	21	νw	νw	PROPN
ejpam-4756	132	22	.	.	PUNCT
ejpam-4756	132	23	|mν(w)|	|mν(w)|	PROPN
ejpam-4756	132	24	=	=	SYM
ejpam-4756	132	25	1	1	NUM
ejpam-4756	132	26	2π	2π	NOUN
ejpam-4756	132	27	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	132	28	ν∑	ν∑	PROPN
ejpam-4756	132	29	k=0	k=0	PROPN
ejpam-4756	133	1	[	[	PUNCT
ejpam-4756	133	2	ν	ν	X
ejpam-4756	133	3	k	k	X
ejpam-4756	133	4	]	]	PUNCT
ejpam-4756	133	5	λk	λk	PROPN
ejpam-4756	133	6	k∑	k∑	PROPN
ejpam-4756	133	7	j=0	j=0	PROPN
ejpam-4756	133	8	ak	ak	PROPN
ejpam-4756	133	9	,	,	PUNCT
ejpam-4756	133	10	j	j	PROPN
ejpam-4756	133	11	sin	sin	NOUN
ejpam-4756	133	12	(	(	PUNCT
ejpam-4756	133	13	j	j	NOUN
ejpam-4756	133	14	+	+	CCONJ
ejpam-4756	133	15	1	1	NUM
ejpam-4756	133	16	2	2	NUM
ejpam-4756	133	17	)	)	PUNCT
ejpam-4756	133	18	w	w	ADP
ejpam-4756	133	19	γ(n+	γ(n+	NUM
ejpam-4756	133	20	λ	λ	NOUN
ejpam-4756	133	21	)	)	PUNCT
ejpam-4756	133	22	sin(w2	sin(w2	ADJ
ejpam-4756	133	23	)	)	PUNCT
ejpam-4756	133	24	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	133	25	≤	≤	ADV
ejpam-4756	133	26	1	1	NUM
ejpam-4756	133	27	2π	2π	NUM
ejpam-4756	133	28	1	1	NUM
ejpam-4756	133	29	γ(ν	γ(ν	PROPN
ejpam-4756	133	30	+	+	PROPN
ejpam-4756	133	31	λ	λ	PROPN
ejpam-4756	133	32	)	)	PUNCT
ejpam-4756	133	33	ν∑	ν∑	PUNCT
ejpam-4756	134	1	k=0	k=0	PROPN
ejpam-4756	134	2	[	[	PUNCT
ejpam-4756	134	3	ν	ν	X
ejpam-4756	134	4	k	k	X
ejpam-4756	134	5	]	]	PUNCT
ejpam-4756	134	6	λk	λk	ADP
ejpam-4756	134	7	j∑	j∑	PROPN
ejpam-4756	134	8	q=0	q=0	PROPN
ejpam-4756	134	9	ak	ak	PROPN
ejpam-4756	134	10	,	,	PUNCT
ejpam-4756	134	11	j	j	PROPN
ejpam-4756	134	12	|	|	ADV
ejpam-4756	134	13	sin	sin	NOUN
ejpam-4756	134	14	(	(	PUNCT
ejpam-4756	134	15	j	j	NOUN
ejpam-4756	134	16	+	+	CCONJ
ejpam-4756	134	17	1	1	NUM
ejpam-4756	134	18	2	2	NUM
ejpam-4756	134	19	)	)	PUNCT
ejpam-4756	134	20	w|	w|	NOUN
ejpam-4756	134	21	|	|	ADV
ejpam-4756	134	22	sin(w2	sin(w2	ADJ
ejpam-4756	134	23	)	)	PUNCT
ejpam-4756	134	24	|	|	ADV
ejpam-4756	134	25	≤	≤	NUM
ejpam-4756	134	26	1	1	NUM
ejpam-4756	134	27	2π	2π	NUM
ejpam-4756	134	28	1	1	NUM
ejpam-4756	134	29	γ(ν	γ(ν	PROPN
ejpam-4756	134	30	+	+	PROPN
ejpam-4756	134	31	λ	λ	PROPN
ejpam-4756	134	32	)	)	PUNCT
ejpam-4756	134	33	ν∑	ν∑	PUNCT
ejpam-4756	135	1	k=0	k=0	PROPN
ejpam-4756	135	2	[	[	PUNCT
ejpam-4756	135	3	ν	ν	X
ejpam-4756	135	4	k	k	X
ejpam-4756	135	5	]	]	PUNCT
ejpam-4756	135	6	λk	λk	PROPN
ejpam-4756	135	7	k∑	k∑	PROPN
ejpam-4756	135	8	j=0	j=0	PROPN
ejpam-4756	135	9	ak	ak	PROPN
ejpam-4756	135	10	,	,	PUNCT
ejpam-4756	135	11	j	j	PROPN
ejpam-4756	135	12	(	(	PUNCT
ejpam-4756	135	13	j	j	PROPN
ejpam-4756	135	14	+	+	CCONJ
ejpam-4756	135	15	1	1	NUM
ejpam-4756	135	16	2	2	NUM
ejpam-4756	135	17	)	)	PUNCT
ejpam-4756	135	18	w	w	PROPN
ejpam-4756	135	19	w	w	PROPN
ejpam-4756	135	20	π	π	PROPN
ejpam-4756	135	21	h.	h.	PROPN
ejpam-4756	135	22	k.	k.	PROPN
ejpam-4756	135	23	nigam	nigam	PROPN
ejpam-4756	135	24	,	,	PUNCT
ejpam-4756	135	25	m.	m.	PROPN
ejpam-4756	135	26	k.	k.	PROPN
ejpam-4756	135	27	sah	sah	PROPN
ejpam-4756	135	28	/	/	SYM
ejpam-4756	135	29	eur	eur	PROPN
ejpam-4756	135	30	.	.	PUNCT
ejpam-4756	136	1	j.	j.	PROPN
ejpam-4756	136	2	pure	pure	PROPN
ejpam-4756	136	3	appl	appl	PROPN
ejpam-4756	136	4	.	.	PROPN
ejpam-4756	136	5	math	math	PROPN
ejpam-4756	136	6	,	,	PUNCT
ejpam-4756	136	7	16	16	NUM
ejpam-4756	136	8	(	(	PUNCT
ejpam-4756	136	9	2	2	NUM
ejpam-4756	136	10	)	)	PUNCT
ejpam-4756	136	11	(	(	PUNCT
ejpam-4756	136	12	2023	2023	NUM
ejpam-4756	136	13	)	)	PUNCT
ejpam-4756	136	14	,	,	PUNCT
ejpam-4756	136	15	1302	1302	NUM
ejpam-4756	136	16	-	-	SYM
ejpam-4756	136	17	1317	1317	NUM
ejpam-4756	136	18	1308	1308	NUM
ejpam-4756	136	19	≤	≤	NUM
ejpam-4756	136	20	1	1	NUM
ejpam-4756	136	21	4	4	NUM
ejpam-4756	136	22	1	1	NUM
ejpam-4756	136	23	γ(ν	γ(ν	PROPN
ejpam-4756	136	24	+	+	PROPN
ejpam-4756	136	25	λ	λ	PROPN
ejpam-4756	136	26	)	)	PUNCT
ejpam-4756	136	27	ν∑	ν∑	PUNCT
ejpam-4756	137	1	k=0	k=0	PROPN
ejpam-4756	137	2	[	[	PUNCT
ejpam-4756	137	3	ν	ν	X
ejpam-4756	137	4	k	k	X
ejpam-4756	137	5	]	]	PUNCT
ejpam-4756	137	6	λk	λk	PROPN
ejpam-4756	137	7	k∑	k∑	PROPN
ejpam-4756	137	8	j=0	j=0	PROPN
ejpam-4756	137	9	ak	ak	PROPN
ejpam-4756	137	10	,	,	PUNCT
ejpam-4756	137	11	j(2j	j(2j	PRON
ejpam-4756	137	12	+	+	ADJ
ejpam-4756	137	13	1	1	NUM
ejpam-4756	137	14	)	)	PUNCT
ejpam-4756	137	15	≤	≤	NUM
ejpam-4756	137	16	1	1	NUM
ejpam-4756	137	17	4	4	NUM
ejpam-4756	137	18	1	1	NUM
ejpam-4756	137	19	γ(ν	γ(ν	PROPN
ejpam-4756	137	20	+	+	PROPN
ejpam-4756	137	21	λ	λ	PROPN
ejpam-4756	137	22	)	)	PUNCT
ejpam-4756	137	23	ν∑	ν∑	PUNCT
ejpam-4756	138	1	k=0	k=0	PROPN
ejpam-4756	138	2	[	[	PUNCT
ejpam-4756	138	3	ν	ν	X
ejpam-4756	138	4	k	k	X
ejpam-4756	138	5	]	]	PUNCT
ejpam-4756	138	6	λk	λk	ADP
ejpam-4756	138	7	2	2	PROPN
ejpam-4756	138	8	k∑	k∑	PROPN
ejpam-4756	138	9	j=0	j=0	PROPN
ejpam-4756	138	10	jak	jak	PROPN
ejpam-4756	138	11	,	,	PUNCT
ejpam-4756	138	12	j	j	PROPN
ejpam-4756	138	13	+	+	CCONJ
ejpam-4756	138	14	k∑	k∑	PROPN
ejpam-4756	138	15	j=0	j=0	PROPN
ejpam-4756	138	16	ak	ak	PROPN
ejpam-4756	138	17	,	,	PUNCT
ejpam-4756	138	18	j	j	PROPN
ejpam-4756	139	1			PROPN
ejpam-4756	139	2	≤	≤	NUM
ejpam-4756	139	3	1	1	NUM
ejpam-4756	139	4	4	4	NUM
ejpam-4756	139	5	1	1	NUM
ejpam-4756	139	6	γ(ν	γ(ν	PROPN
ejpam-4756	139	7	+	+	PROPN
ejpam-4756	139	8	λ	λ	PROPN
ejpam-4756	139	9	)	)	PUNCT
ejpam-4756	139	10	ν∑	ν∑	PUNCT
ejpam-4756	140	1	k=0	k=0	PROPN
ejpam-4756	140	2	[	[	PUNCT
ejpam-4756	140	3	ν	ν	X
ejpam-4756	140	4	k	k	X
ejpam-4756	140	5	]	]	PUNCT
ejpam-4756	140	6	λk	λk	X
ejpam-4756	140	7	{	{	PUNCT
ejpam-4756	140	8	2(ak,1	2(ak,1	NOUN
ejpam-4756	140	9	+	+	CCONJ
ejpam-4756	140	10	2ak,2	2ak,2	NOUN
ejpam-4756	140	11	+	+	X
ejpam-4756	140	12	·	·	PUNCT
ejpam-4756	140	13	·	·	PUNCT
ejpam-4756	140	14	·	·	PUNCT
ejpam-4756	140	15	+	+	NUM
ejpam-4756	140	16	kak	kak	PROPN
ejpam-4756	140	17	,	,	PUNCT
ejpam-4756	140	18	k	k	PROPN
ejpam-4756	140	19	)	)	PUNCT
ejpam-4756	140	20	+	+	CCONJ
ejpam-4756	140	21	1	1	NUM
ejpam-4756	140	22	}	}	PUNCT
ejpam-4756	140	23	≤	≤	NUM
ejpam-4756	140	24	1	1	NUM
ejpam-4756	140	25	4	4	NUM
ejpam-4756	140	26	1	1	NUM
ejpam-4756	140	27	γ(ν	γ(ν	PROPN
ejpam-4756	140	28	+	+	PROPN
ejpam-4756	140	29	λ	λ	PROPN
ejpam-4756	140	30	)	)	PUNCT
ejpam-4756	140	31	ν∑	ν∑	PUNCT
ejpam-4756	141	1	k=0	k=0	PROPN
ejpam-4756	141	2	[	[	PUNCT
ejpam-4756	141	3	ν	ν	X
ejpam-4756	141	4	k	k	X
ejpam-4756	141	5	]	]	PUNCT
ejpam-4756	141	6	λk	λk	X
ejpam-4756	141	7	{	{	PUNCT
ejpam-4756	141	8	2(kak,1	2(kak,1	NUM
ejpam-4756	141	9	+	+	CCONJ
ejpam-4756	141	10	kak,2	kak,2	X
ejpam-4756	141	11	+	+	CCONJ
ejpam-4756	141	12	·	·	PUNCT
ejpam-4756	141	13	·	·	PUNCT
ejpam-4756	141	14	·	·	PUNCT
ejpam-4756	141	15	+	+	NUM
ejpam-4756	141	16	kak	kak	PROPN
ejpam-4756	141	17	,	,	PUNCT
ejpam-4756	141	18	k	k	PROPN
ejpam-4756	141	19	)	)	PUNCT
ejpam-4756	141	20	+	+	CCONJ
ejpam-4756	141	21	1	1	NUM
ejpam-4756	141	22	}	}	PUNCT
ejpam-4756	141	23	≤	≤	NUM
ejpam-4756	141	24	1	1	NUM
ejpam-4756	141	25	4	4	NUM
ejpam-4756	141	26	1	1	NUM
ejpam-4756	141	27	γ(ν	γ(ν	PROPN
ejpam-4756	141	28	+	+	PROPN
ejpam-4756	141	29	λ	λ	PROPN
ejpam-4756	141	30	)	)	PUNCT
ejpam-4756	141	31	ν∑	ν∑	PUNCT
ejpam-4756	142	1	k=0	k=0	PROPN
ejpam-4756	142	2	[	[	PUNCT
ejpam-4756	142	3	ν	ν	X
ejpam-4756	142	4	k	k	X
ejpam-4756	142	5	]	]	PUNCT
ejpam-4756	142	6	λk	λk	X
ejpam-4756	142	7	{	{	PUNCT
ejpam-4756	142	8	2k(ak,0	2k(ak,0	PROPN
ejpam-4756	142	9	+	+	CCONJ
ejpam-4756	142	10	ak,1	ak,1	PROPN
ejpam-4756	142	11	+	+	NUM
ejpam-4756	142	12	ak,2	ak,2	NOUN
ejpam-4756	142	13	+	+	X
ejpam-4756	142	14	·	·	PUNCT
ejpam-4756	142	15	·	·	PUNCT
ejpam-4756	142	16	·	·	PUNCT
ejpam-4756	142	17	+	+	NUM
ejpam-4756	142	18	ak	ak	PROPN
ejpam-4756	142	19	,	,	PUNCT
ejpam-4756	142	20	k)−	k)−	PROPN
ejpam-4756	142	21	2kak,0	2kak,0	PROPN
ejpam-4756	142	22	+	+	CCONJ
ejpam-4756	142	23	1	1	NUM
ejpam-4756	142	24	}	}	PUNCT
ejpam-4756	142	25	≤	≤	NUM
ejpam-4756	142	26	1	1	NUM
ejpam-4756	142	27	4	4	NUM
ejpam-4756	142	28	1	1	NUM
ejpam-4756	142	29	γ(ν	γ(ν	PROPN
ejpam-4756	142	30	+	+	PROPN
ejpam-4756	142	31	λ	λ	PROPN
ejpam-4756	142	32	)	)	PUNCT
ejpam-4756	142	33	ν∑	ν∑	PUNCT
ejpam-4756	143	1	k=0	k=0	PROPN
ejpam-4756	143	2	[	[	PUNCT
ejpam-4756	143	3	ν	ν	X
ejpam-4756	143	4	k	k	X
ejpam-4756	143	5	]	]	X
ejpam-4756	143	6	λk2k	λk2k	X
ejpam-4756	143	7	{	{	PUNCT
ejpam-4756	143	8	(	(	PUNCT
ejpam-4756	143	9	ak,0	ak,0	PROPN
ejpam-4756	143	10	+	+	CCONJ
ejpam-4756	143	11	ak,1	ak,1	PROPN
ejpam-4756	143	12	+	+	NUM
ejpam-4756	143	13	ak,2	ak,2	NOUN
ejpam-4756	143	14	+	+	X
ejpam-4756	143	15	·	·	PUNCT
ejpam-4756	143	16	·	·	PUNCT
ejpam-4756	143	17	·	·	PUNCT
ejpam-4756	143	18	+	+	NUM
ejpam-4756	143	19	ak	ak	PROPN
ejpam-4756	143	20	,	,	PUNCT
ejpam-4756	143	21	k)−	k)−	PROPN
ejpam-4756	143	22	ak,0}+	ak,0}+	PROPN
ejpam-4756	143	23	1	1	NUM
ejpam-4756	143	24	≤	≤	NUM
ejpam-4756	143	25	1	1	NUM
ejpam-4756	143	26	4	4	NUM
ejpam-4756	143	27	1	1	NUM
ejpam-4756	143	28	γ(ν	γ(ν	PROPN
ejpam-4756	143	29	+	+	PROPN
ejpam-4756	143	30	λ	λ	PROPN
ejpam-4756	143	31	)	)	PUNCT
ejpam-4756	143	32	ν∑	ν∑	PUNCT
ejpam-4756	144	1	k=0	k=0	PROPN
ejpam-4756	144	2	[	[	PUNCT
ejpam-4756	144	3	ν	ν	X
ejpam-4756	144	4	k	k	X
ejpam-4756	144	5	]	]	X
ejpam-4756	144	6	λk2k	λk2k	PROPN
ejpam-4756	144	7	{	{	PUNCT
ejpam-4756	144	8	1−	1−	NUM
ejpam-4756	144	9	ak,0}+	ak,0}+	PROPN
ejpam-4756	144	10	1	1	NUM
ejpam-4756	144	11	≤	≤	NUM
ejpam-4756	144	12	1	1	NUM
ejpam-4756	144	13	4	4	NUM
ejpam-4756	144	14	1	1	NUM
ejpam-4756	144	15	γ(ν	γ(ν	PROPN
ejpam-4756	144	16	+	+	PROPN
ejpam-4756	144	17	λ	λ	PROPN
ejpam-4756	144	18	)	)	PUNCT
ejpam-4756	144	19	ν∑	ν∑	PUNCT
ejpam-4756	145	1	k=0	k=0	PROPN
ejpam-4756	145	2	[	[	PUNCT
ejpam-4756	145	3	ν	ν	X
ejpam-4756	145	4	k	k	X
ejpam-4756	145	5	]	]	PUNCT
ejpam-4756	145	6	λk(2k	λk(2k	X
ejpam-4756	145	7	+	+	NOUN
ejpam-4756	145	8	1	1	NUM
ejpam-4756	145	9	)	)	PUNCT
ejpam-4756	145	10	≤	≤	NOUN
ejpam-4756	145	11	(	(	PUNCT
ejpam-4756	145	12	2n+	2n+	NUM
ejpam-4756	145	13	1	1	NUM
ejpam-4756	145	14	)	)	PUNCT
ejpam-4756	145	15	4	4	NUM
ejpam-4756	145	16	1	1	NUM
ejpam-4756	145	17	γ(ν	γ(ν	PROPN
ejpam-4756	145	18	+	+	PROPN
ejpam-4756	145	19	λ	λ	PROPN
ejpam-4756	145	20	)	)	PUNCT
ejpam-4756	145	21	ν∑	ν∑	PUNCT
ejpam-4756	146	1	k=0	k=0	PROPN
ejpam-4756	146	2	[	[	PUNCT
ejpam-4756	146	3	ν	ν	X
ejpam-4756	146	4	k	k	X
ejpam-4756	146	5	]	]	PUNCT
ejpam-4756	146	6	λk	λk	ADP
ejpam-4756	146	7	≤	≤	NUM
ejpam-4756	146	8	(	(	PUNCT
ejpam-4756	146	9	2n+	2n+	NUM
ejpam-4756	146	10	1	1	NUM
ejpam-4756	146	11	)	)	PUNCT
ejpam-4756	146	12	4	4	NUM
ejpam-4756	146	13	1	1	NUM
ejpam-4756	146	14	γ(ν	γ(ν	PROPN
ejpam-4756	146	15	+	+	PROPN
ejpam-4756	146	16	λ	λ	PROPN
ejpam-4756	146	17	)	)	PUNCT
ejpam-4756	146	18	γ(ν	γ(ν	PROPN
ejpam-4756	146	19	+	+	PROPN
ejpam-4756	146	20	λ	λ	X
ejpam-4756	146	21	)	)	PUNCT
ejpam-4756	146	22	γλ	γλ	PROPN
ejpam-4756	146	23	=	=	SYM
ejpam-4756	146	24	o	o	PROPN
ejpam-4756	146	25	(	(	PUNCT
ejpam-4756	146	26	ν	ν	X
ejpam-4756	146	27	+	+	NOUN
ejpam-4756	146	28	1	1	NUM
ejpam-4756	146	29	γλ	γλ	NUM
ejpam-4756	146	30	)	)	PUNCT
ejpam-4756	146	31	.	.	PUNCT
ejpam-4756	147	1	lemma	lemma	PROPN
ejpam-4756	147	2	3	3	X
ejpam-4756	147	3	.	.	PUNCT
ejpam-4756	147	4	|mν(w)|	|mν(w)|	PROPN
ejpam-4756	147	5	=	=	X
ejpam-4756	147	6	o	o	X
ejpam-4756	147	7	(	(	PUNCT
ejpam-4756	147	8	1	1	NUM
ejpam-4756	147	9	w2(ν+1)γλ	w2(ν+1)γλ	NOUN
ejpam-4756	147	10	)	)	PUNCT
ejpam-4756	147	11	for	for	ADP
ejpam-4756	147	12	1	1	NUM
ejpam-4756	147	13	ν+1	ν+1	PROPN
ejpam-4756	147	14	<	<	X
ejpam-4756	147	15	w	w	PROPN
ejpam-4756	147	16	≤	≤	NUM
ejpam-4756	147	17	π	π	NOUN
ejpam-4756	147	18	.	.	PUNCT
ejpam-4756	148	1	proof	proof	NOUN
ejpam-4756	148	2	.	.	PUNCT
ejpam-4756	149	1	for	for	ADP
ejpam-4756	149	2	1	1	NUM
ejpam-4756	149	3	ν+1	ν+1	PROPN
ejpam-4756	149	4	<	<	X
ejpam-4756	149	5	w	w	X
ejpam-4756	149	6	≤	≤	NUM
ejpam-4756	149	7	π	π	NOUN
ejpam-4756	149	8	,	,	PUNCT
ejpam-4756	149	9	sin(w2	sin(w2	ADJ
ejpam-4756	149	10	)	)	PUNCT
ejpam-4756	149	11	≥	≥	PROPN
ejpam-4756	149	12	w	w	PROPN
ejpam-4756	149	13	π	π	PROPN
ejpam-4756	149	14	.	.	PUNCT
ejpam-4756	150	1	|mν(w)|	|mν(w)|	ADJ
ejpam-4756	150	2	=	=	SYM
ejpam-4756	150	3	1	1	NUM
ejpam-4756	150	4	2π	2π	NOUN
ejpam-4756	150	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	150	6	ν∑	ν∑	PROPN
ejpam-4756	150	7	k=0	k=0	PROPN
ejpam-4756	150	8	[	[	PUNCT
ejpam-4756	150	9	ν	ν	X
ejpam-4756	150	10	k	k	X
ejpam-4756	150	11	]	]	PUNCT
ejpam-4756	151	1	λk	λk	ADP
ejpam-4756	151	2	k∑	k∑	PROPN
ejpam-4756	151	3	j=0	j=0	PROPN
ejpam-4756	151	4	akbj	akbj	VERB
ejpam-4756	151	5	sin	sin	NOUN
ejpam-4756	151	6	(	(	PUNCT
ejpam-4756	151	7	j	j	NOUN
ejpam-4756	152	1	+	+	CCONJ
ejpam-4756	152	2	1	1	NUM
ejpam-4756	152	3	2	2	NUM
ejpam-4756	152	4	)	)	PUNCT
ejpam-4756	152	5	w	w	ADP
ejpam-4756	152	6	γ(ν	γ(ν	PROPN
ejpam-4756	152	7	+	+	CCONJ
ejpam-4756	152	8	λ	λ	NOUN
ejpam-4756	152	9	)	)	PUNCT
ejpam-4756	152	10	sin(w2	sin(w2	NOUN
ejpam-4756	152	11	)	)	PUNCT
ejpam-4756	153	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	153	2	≤	≤	ADV
ejpam-4756	153	3	1	1	NUM
ejpam-4756	153	4	2π	2π	NUM
ejpam-4756	153	5	1	1	NUM
ejpam-4756	153	6	γ(ν	γ(ν	PROPN
ejpam-4756	153	7	+	+	PROPN
ejpam-4756	153	8	λ	λ	PROPN
ejpam-4756	153	9	)	)	PUNCT
ejpam-4756	153	10	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	153	11	ν∑	ν∑	PUNCT
ejpam-4756	153	12	k=0	k=0	PROPN
ejpam-4756	153	13	[	[	PUNCT
ejpam-4756	153	14	ν	ν	X
ejpam-4756	153	15	k	k	X
ejpam-4756	153	16	]	]	PUNCT
ejpam-4756	153	17	λk	λk	PROPN
ejpam-4756	153	18	k∑	k∑	PROPN
ejpam-4756	153	19	j=0	j=0	PROPN
ejpam-4756	153	20	ak	ak	PROPN
ejpam-4756	153	21	,	,	PUNCT
ejpam-4756	153	22	j	j	PROPN
ejpam-4756	153	23	sin	sin	NOUN
ejpam-4756	153	24	(	(	PUNCT
ejpam-4756	153	25	j	j	NOUN
ejpam-4756	153	26	+	+	CCONJ
ejpam-4756	153	27	1	1	NUM
ejpam-4756	153	28	2	2	NUM
ejpam-4756	153	29	)	)	PUNCT
ejpam-4756	153	30	w	w	NOUN
ejpam-4756	153	31	|	|	ADV
ejpam-4756	153	32	sin(w2	sin(w2	ADJ
ejpam-4756	153	33	)	)	PUNCT
ejpam-4756	153	34	|	|	CCONJ
ejpam-4756	153	35	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	153	36	≤	≤	ADV
ejpam-4756	153	37	1	1	NUM
ejpam-4756	153	38	2π	2π	NUM
ejpam-4756	153	39	1	1	NUM
ejpam-4756	153	40	γ(ν	γ(ν	PROPN
ejpam-4756	153	41	+	+	PROPN
ejpam-4756	153	42	λ	λ	PROPN
ejpam-4756	153	43	)	)	PUNCT
ejpam-4756	153	44	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	153	45	ν∑	ν∑	PUNCT
ejpam-4756	153	46	k=0	k=0	PROPN
ejpam-4756	153	47	[	[	PUNCT
ejpam-4756	153	48	ν	ν	X
ejpam-4756	153	49	k	k	X
ejpam-4756	153	50	]	]	PUNCT
ejpam-4756	153	51	λk	λk	PROPN
ejpam-4756	153	52	k∑	k∑	PROPN
ejpam-4756	153	53	j=0	j=0	PROPN
ejpam-4756	153	54	ak	ak	PROPN
ejpam-4756	153	55	,	,	PUNCT
ejpam-4756	153	56	j	j	PROPN
ejpam-4756	153	57	sin	sin	NOUN
ejpam-4756	153	58	(	(	PUNCT
ejpam-4756	153	59	j	j	NOUN
ejpam-4756	153	60	+	+	CCONJ
ejpam-4756	153	61	1	1	NUM
ejpam-4756	153	62	2	2	NUM
ejpam-4756	153	63	)	)	PUNCT
ejpam-4756	153	64	w	w	PROPN
ejpam-4756	153	65	w	w	PROPN
ejpam-4756	153	66	π	π	PROPN
ejpam-4756	153	67	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4756	153	68	h.	h.	PROPN
ejpam-4756	153	69	k.	k.	PROPN
ejpam-4756	153	70	nigam	nigam	PROPN
ejpam-4756	153	71	,	,	PUNCT
ejpam-4756	153	72	m.	m.	PROPN
ejpam-4756	153	73	k.	k.	PROPN
ejpam-4756	153	74	sah	sah	PROPN
ejpam-4756	153	75	/	/	SYM
ejpam-4756	153	76	eur	eur	PROPN
ejpam-4756	153	77	.	.	PUNCT
ejpam-4756	154	1	j.	j.	PROPN
ejpam-4756	154	2	pure	pure	PROPN
ejpam-4756	154	3	appl	appl	PROPN
ejpam-4756	154	4	.	.	PROPN
ejpam-4756	154	5	math	math	PROPN
ejpam-4756	154	6	,	,	PUNCT
ejpam-4756	154	7	16	16	NUM
ejpam-4756	154	8	(	(	PUNCT
ejpam-4756	154	9	2	2	NUM
ejpam-4756	154	10	)	)	PUNCT
ejpam-4756	154	11	(	(	PUNCT
ejpam-4756	154	12	2023	2023	NUM
ejpam-4756	154	13	)	)	PUNCT
ejpam-4756	154	14	,	,	PUNCT
ejpam-4756	154	15	1302	1302	NUM
ejpam-4756	154	16	-	-	SYM
ejpam-4756	154	17	1317	1317	NUM
ejpam-4756	154	18	1309	1309	NUM
ejpam-4756	154	19	≤	≤	NUM
ejpam-4756	154	20	1	1	NUM
ejpam-4756	154	21	2w	2w	NUM
ejpam-4756	154	22	1	1	NUM
ejpam-4756	154	23	γ(ν	γ(ν	PROPN
ejpam-4756	154	24	+	+	PROPN
ejpam-4756	154	25	λ	λ	PROPN
ejpam-4756	154	26	)	)	PUNCT
ejpam-4756	154	27	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	154	28	ν∑	ν∑	PUNCT
ejpam-4756	155	1	k=0	k=0	PROPN
ejpam-4756	155	2	[	[	PUNCT
ejpam-4756	155	3	ν	ν	X
ejpam-4756	155	4	k	k	X
ejpam-4756	155	5	]	]	PUNCT
ejpam-4756	155	6	λk	λk	PROPN
ejpam-4756	155	7	k∑	k∑	PROPN
ejpam-4756	155	8	j=0	j=0	PROPN
ejpam-4756	155	9	ak	ak	PROPN
ejpam-4756	155	10	,	,	PUNCT
ejpam-4756	155	11	j	j	PROPN
ejpam-4756	155	12	sin	sin	NOUN
ejpam-4756	155	13	(	(	PUNCT
ejpam-4756	155	14	j	j	NOUN
ejpam-4756	155	15	+	+	CCONJ
ejpam-4756	155	16	1	1	NUM
ejpam-4756	155	17	2	2	NUM
ejpam-4756	155	18	)	)	PUNCT
ejpam-4756	155	19	w	w	ADP
ejpam-4756	155	20	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4756	155	21	by	by	ADP
ejpam-4756	155	22	abel	abel	PROPN
ejpam-4756	155	23	’s	’s	PART
ejpam-4756	155	24	lemma	lemma	PROPN
ejpam-4756	155	25	,	,	PUNCT
ejpam-4756	155	26	we	we	PRON
ejpam-4756	155	27	get	get	VERB
ejpam-4756	155	28	|mν(w)|	|mν(w)|	ADJ
ejpam-4756	155	29	≤	≤	ADJ
ejpam-4756	155	30	1	1	NUM
ejpam-4756	155	31	2w	2w	NUM
ejpam-4756	155	32	1	1	NUM
ejpam-4756	155	33	γ(ν	γ(ν	PROPN
ejpam-4756	155	34	+	+	PROPN
ejpam-4756	155	35	λ	λ	PROPN
ejpam-4756	155	36	)	)	PUNCT
ejpam-4756	155	37	[	[	PUNCT
ejpam-4756	155	38	ν∑	ν∑	X
ejpam-4756	156	1	k=0	k=0	PROPN
ejpam-4756	156	2	[	[	PUNCT
ejpam-4756	156	3	ν	ν	X
ejpam-4756	156	4	k	k	X
ejpam-4756	156	5	]	]	PUNCT
ejpam-4756	156	6	λk	λk	X
ejpam-4756	156	7	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4756	156	8	k−1∑	k−1∑	PROPN
ejpam-4756	156	9	j=0	j=0	PROPN
ejpam-4756	156	10	(	(	PUNCT
ejpam-4756	156	11	ak	ak	PROPN
ejpam-4756	156	12	,	,	PUNCT
ejpam-4756	156	13	j	j	PROPN
ejpam-4756	156	14	−	−	PROPN
ejpam-4756	156	15	ak−1,j+1	ak−1,j+1	PROPN
ejpam-4756	156	16	)	)	PUNCT
ejpam-4756	156	17	j∑	j∑	PROPN
ejpam-4756	157	1	p=0	p=0	PROPN
ejpam-4756	157	2	sin	sin	NOUN
ejpam-4756	157	3	(	(	PUNCT
ejpam-4756	157	4	p+	p+	NOUN
ejpam-4756	157	5	1	1	NUM
ejpam-4756	157	6	2	2	NUM
ejpam-4756	157	7	)	)	PUNCT
ejpam-4756	157	8	w	w	ADP
ejpam-4756	157	9	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4756	157	10	+	+	PROPN
ejpam-4756	157	11	ak	ak	PROPN
ejpam-4756	157	12	,	,	PUNCT
ejpam-4756	157	13	k	k	PROPN
ejpam-4756	157	14	k∑	k∑	PROPN
ejpam-4756	157	15	j=0	j=0	PROPN
ejpam-4756	157	16	sin	sin	NOUN
ejpam-4756	157	17	(	(	PUNCT
ejpam-4756	157	18	j	j	NOUN
ejpam-4756	157	19	+	+	CCONJ
ejpam-4756	157	20	1	1	NUM
ejpam-4756	157	21	2	2	NUM
ejpam-4756	157	22	)	)	PUNCT
ejpam-4756	157	23	w	w	ADP
ejpam-4756	157	24	]	]	PUNCT
ejpam-4756	157	25	≤	≤	NUM
ejpam-4756	157	26	1	1	NUM
ejpam-4756	157	27	2w	2w	NUM
ejpam-4756	157	28	1	1	NUM
ejpam-4756	157	29	γ(ν	γ(ν	PROPN
ejpam-4756	157	30	+	+	PROPN
ejpam-4756	157	31	λ	λ	PROPN
ejpam-4756	157	32	)	)	PUNCT
ejpam-4756	157	33	ν∑	ν∑	PUNCT
ejpam-4756	158	1	k=0	k=0	PROPN
ejpam-4756	158	2	[	[	PUNCT
ejpam-4756	158	3	ν	ν	X
ejpam-4756	158	4	k	k	X
ejpam-4756	158	5	]	]	PUNCT
ejpam-4756	158	6	λk	λk	X
ejpam-4756	158	7	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4756	158	8	k−1∑	k−1∑	PROPN
ejpam-4756	158	9	j=0	j=0	PROPN
ejpam-4756	158	10	∆ak	∆ak	PROPN
ejpam-4756	158	11	,	,	PUNCT
ejpam-4756	158	12	j	j	PROPN
ejpam-4756	158	13	j∑	j∑	PROPN
ejpam-4756	158	14	p=0	p=0	PROPN
ejpam-4756	158	15	sin	sin	NOUN
ejpam-4756	158	16	(	(	PUNCT
ejpam-4756	158	17	p+	p+	NOUN
ejpam-4756	158	18	1	1	NUM
ejpam-4756	158	19	2	2	NUM
ejpam-4756	158	20	)	)	PUNCT
ejpam-4756	158	21	w	w	PROPN
ejpam-4756	158	22	∣∣∣∣∣∣+	∣∣∣∣∣∣+	PROPN
ejpam-4756	158	23	ak	ak	PROPN
ejpam-4756	158	24	,	,	PUNCT
ejpam-4756	158	25	k	k	PROPN
ejpam-4756	158	26	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4756	158	27	k∑	k∑	PROPN
ejpam-4756	158	28	j=0	j=0	PROPN
ejpam-4756	158	29	sin	sin	NOUN
ejpam-4756	158	30	(	(	PUNCT
ejpam-4756	158	31	j	j	NOUN
ejpam-4756	158	32	+	+	CCONJ
ejpam-4756	158	33	1	1	NUM
ejpam-4756	158	34	2	2	NUM
ejpam-4756	158	35	)	)	PUNCT
ejpam-4756	158	36	w	w	ADP
ejpam-4756	158	37	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	158	38	≤	≤	ADV
ejpam-4756	158	39	1	1	NUM
ejpam-4756	158	40	2w	2w	NUM
ejpam-4756	158	41	1	1	NUM
ejpam-4756	158	42	γ(ν	γ(ν	PROPN
ejpam-4756	158	43	+	+	PROPN
ejpam-4756	158	44	λ	λ	PROPN
ejpam-4756	158	45	)	)	PUNCT
ejpam-4756	158	46	ν∑	ν∑	PUNCT
ejpam-4756	159	1	k=0	k=0	PROPN
ejpam-4756	159	2	[	[	PUNCT
ejpam-4756	159	3	ν	ν	X
ejpam-4756	159	4	k	k	X
ejpam-4756	159	5	]	]	PUNCT
ejpam-4756	159	6	λk	λk	ADP
ejpam-4756	159	7	k−1∑	k−1∑	PROPN
ejpam-4756	159	8	j=0	j=0	PROPN
ejpam-4756	159	9	|∆ak	|∆ak	PROPN
ejpam-4756	159	10	,	,	PUNCT
ejpam-4756	159	11	j	j	PROPN
ejpam-4756	159	12	|+	|+	PROPN
ejpam-4756	159	13	ak	ak	PROPN
ejpam-4756	159	14	,	,	PUNCT
ejpam-4756	159	15	k	k	PROPN
ejpam-4756	159	16			NOUN
ejpam-4756	159	17	max	max	PROPN
ejpam-4756	159	18	0≤p≤m	0≤p≤m	PROPN
ejpam-4756	159	19	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4756	159	20	m∑	m∑	CCONJ
ejpam-4756	159	21	p=0	p=0	PROPN
ejpam-4756	159	22	sin	sin	NOUN
ejpam-4756	159	23	(	(	PUNCT
ejpam-4756	159	24	p+	p+	NOUN
ejpam-4756	159	25	1	1	NUM
ejpam-4756	159	26	2	2	NUM
ejpam-4756	159	27	)	)	PUNCT
ejpam-4756	159	28	l	l	NOUN
ejpam-4756	159	29	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4756	159	30	≤	≤	ADV
ejpam-4756	159	31	1	1	NUM
ejpam-4756	159	32	2w	2w	NUM
ejpam-4756	159	33	1	1	NUM
ejpam-4756	159	34	γ(ν	γ(ν	PROPN
ejpam-4756	159	35	+	+	PROPN
ejpam-4756	159	36	λ	λ	PROPN
ejpam-4756	159	37	)	)	PUNCT
ejpam-4756	159	38	ν∑	ν∑	PUNCT
ejpam-4756	160	1	k=0	k=0	PROPN
ejpam-4756	160	2	[	[	PUNCT
ejpam-4756	160	3	ν	ν	X
ejpam-4756	160	4	k	k	X
ejpam-4756	160	5	]	]	PUNCT
ejpam-4756	160	6	λk	λk	X
ejpam-4756	160	7	[	[	PUNCT
ejpam-4756	160	8	o	o	X
ejpam-4756	160	9	(	(	PUNCT
ejpam-4756	160	10	1	1	NUM
ejpam-4756	160	11	k	k	NOUN
ejpam-4756	160	12	+	+	NOUN
ejpam-4756	160	13	1	1	X
ejpam-4756	160	14	)	)	PUNCT
ejpam-4756	161	1	+	+	NOUN
ejpam-4756	161	2	o	o	X
ejpam-4756	161	3	(	(	PUNCT
ejpam-4756	161	4	1	1	NUM
ejpam-4756	161	5	k	k	NOUN
ejpam-4756	161	6	+	+	NOUN
ejpam-4756	161	7	1	1	NUM
ejpam-4756	161	8	)	)	PUNCT
ejpam-4756	161	9	]	]	PUNCT
ejpam-4756	161	10	·	·	PUNCT
ejpam-4756	161	11	1	1	NUM
ejpam-4756	161	12	w	w	NOUN
ejpam-4756	161	13	≤	≤	NUM
ejpam-4756	161	14	1	1	NUM
ejpam-4756	161	15	w2	w2	NOUN
ejpam-4756	161	16	1	1	NUM
ejpam-4756	161	17	γ(ν	γ(ν	PROPN
ejpam-4756	161	18	+	+	PROPN
ejpam-4756	161	19	λ	λ	PROPN
ejpam-4756	161	20	)	)	PUNCT
ejpam-4756	161	21	ν∑	ν∑	PUNCT
ejpam-4756	162	1	k=0	k=0	PROPN
ejpam-4756	162	2	[	[	PUNCT
ejpam-4756	162	3	ν	ν	X
ejpam-4756	162	4	k	k	X
ejpam-4756	162	5	]	]	X
ejpam-4756	162	6	λk	λk	X
ejpam-4756	162	7	(	(	PUNCT
ejpam-4756	162	8	1	1	NUM
ejpam-4756	162	9	k	k	X
ejpam-4756	162	10	+	+	NOUN
ejpam-4756	162	11	1	1	NUM
ejpam-4756	162	12	)	)	PUNCT
ejpam-4756	162	13	.	.	PUNCT
ejpam-4756	163	1	≤	≤	ADV
ejpam-4756	163	2	1	1	NUM
ejpam-4756	163	3	w2(ν	w2(ν	X
ejpam-4756	163	4	+	+	CCONJ
ejpam-4756	163	5	1	1	X
ejpam-4756	163	6	)	)	PUNCT
ejpam-4756	163	7	1	1	NUM
ejpam-4756	163	8	γ(ν	γ(ν	PROPN
ejpam-4756	163	9	+	+	PROPN
ejpam-4756	163	10	λ	λ	PROPN
ejpam-4756	163	11	)	)	PUNCT
ejpam-4756	163	12	ν∑	ν∑	PUNCT
ejpam-4756	164	1	k=0	k=0	PROPN
ejpam-4756	164	2	[	[	PUNCT
ejpam-4756	164	3	ν	ν	X
ejpam-4756	164	4	k	k	X
ejpam-4756	164	5	]	]	PUNCT
ejpam-4756	164	6	λk	λk	ADP
ejpam-4756	164	7	≤	≤	NUM
ejpam-4756	164	8	1	1	NUM
ejpam-4756	164	9	w2(ν	w2(ν	X
ejpam-4756	164	10	+	+	CCONJ
ejpam-4756	164	11	1	1	X
ejpam-4756	164	12	)	)	PUNCT
ejpam-4756	164	13	1	1	NUM
ejpam-4756	164	14	γ(ν	γ(ν	PROPN
ejpam-4756	164	15	+	+	PROPN
ejpam-4756	164	16	λ	λ	PROPN
ejpam-4756	164	17	)	)	PUNCT
ejpam-4756	164	18	γ(ν	γ(ν	PROPN
ejpam-4756	164	19	+	+	PROPN
ejpam-4756	164	20	λ	λ	X
ejpam-4756	164	21	)	)	PUNCT
ejpam-4756	164	22	γλ	γλ	PROPN
ejpam-4756	164	23	=	=	SYM
ejpam-4756	164	24	o	o	X
ejpam-4756	164	25	(	(	PUNCT
ejpam-4756	164	26	1	1	NUM
ejpam-4756	164	27	w2(ν	w2(ν	X
ejpam-4756	164	28	+	+	CCONJ
ejpam-4756	164	29	1)γλ	1)γλ	NUM
ejpam-4756	164	30	)	)	PUNCT
ejpam-4756	164	31	.	.	PUNCT
ejpam-4756	165	1	4	4	X
ejpam-4756	165	2	.	.	X
ejpam-4756	165	3	proof	proof	NOUN
ejpam-4756	165	4	of	of	ADP
ejpam-4756	165	5	main	main	ADJ
ejpam-4756	165	6	results	result	NOUN
ejpam-4756	165	7	proof	proof	NOUN
ejpam-4756	165	8	.	.	PUNCT
ejpam-4756	166	1	[	[	X
ejpam-4756	166	2	proof	proof	NOUN
ejpam-4756	166	3	of	of	ADP
ejpam-4756	166	4	theorem	theorem	NOUN
ejpam-4756	166	5	1	1	NUM
ejpam-4756	166	6	]	]	PUNCT
ejpam-4756	166	7	by	by	ADP
ejpam-4756	166	8	using	use	VERB
ejpam-4756	166	9	the	the	DET
ejpam-4756	166	10	integral	integral	ADJ
ejpam-4756	166	11	representation	representation	NOUN
ejpam-4756	166	12	(	(	PUNCT
ejpam-4756	166	13	[	[	X
ejpam-4756	166	14	13	13	NUM
ejpam-4756	166	15	]	]	SYM
ejpam-4756	166	16	)	)	PUNCT
ejpam-4756	166	17	of	of	ADP
ejpam-4756	166	18	sν(g	sν(g	PROPN
ejpam-4756	166	19	;	;	PUNCT
ejpam-4756	166	20	t	t	PROPN
ejpam-4756	166	21	)	)	PUNCT
ejpam-4756	166	22	,	,	PUNCT
ejpam-4756	166	23	we	we	PRON
ejpam-4756	166	24	have	have	VERB
ejpam-4756	166	25	sν(g	sν(g	NOUN
ejpam-4756	166	26	;	;	PUNCT
ejpam-4756	166	27	t)−	t)−	PROPN
ejpam-4756	166	28	g(t	g(t	PROPN
ejpam-4756	166	29	)	)	PUNCT
ejpam-4756	166	30	=	=	SYM
ejpam-4756	167	1	1	1	NUM
ejpam-4756	167	2	2π	2π	NUM
ejpam-4756	167	3	∫	∫	PROPN
ejpam-4756	168	1	π	π	NOUN
ejpam-4756	168	2	0	0	PUNCT
ejpam-4756	169	1	ϕ(t	ϕ(t	NUM
ejpam-4756	169	2	,	,	PUNCT
ejpam-4756	169	3	w	w	NOUN
ejpam-4756	169	4	)	)	PUNCT
ejpam-4756	169	5	sin(n+	sin(n+	NOUN
ejpam-4756	169	6	1	1	NUM
ejpam-4756	169	7	2)w	2)w	NUM
ejpam-4756	169	8	sin(w2	sin(w2	X
ejpam-4756	169	9	)	)	PUNCT
ejpam-4756	170	1	dw	dw	PROPN
ejpam-4756	170	2	.	.	PROPN
ejpam-4756	171	1	(	(	PUNCT
ejpam-4756	171	2	16	16	NUM
ejpam-4756	171	3	)	)	PUNCT
ejpam-4756	171	4	denoting	denote	VERB
ejpam-4756	171	5	kλa	kλa	NOUN
ejpam-4756	171	6	operator	operator	NOUN
ejpam-4756	171	7	of	of	ADP
ejpam-4756	171	8	sν(g	sν(g	PROPN
ejpam-4756	171	9	;	;	PUNCT
ejpam-4756	171	10	t	t	PROPN
ejpam-4756	171	11	)	)	PUNCT
ejpam-4756	171	12	by	by	ADP
ejpam-4756	171	13	dk	dk	PROPN
ejpam-4756	171	14	λa	λa	PROPN
ejpam-4756	171	15	ν	ν	NOUN
ejpam-4756	171	16	,	,	PUNCT
ejpam-4756	171	17	we	we	PRON
ejpam-4756	171	18	get	get	VERB
ejpam-4756	171	19	dk	dk	PROPN
ejpam-4756	171	20	λa	λa	ADP
ejpam-4756	171	21	ν	ν	X
ejpam-4756	171	22	(	(	PUNCT
ejpam-4756	171	23	g	g	NOUN
ejpam-4756	171	24	;	;	PUNCT
ejpam-4756	171	25	t)−	t)−	PROPN
ejpam-4756	171	26	g(t	g(t	PROPN
ejpam-4756	171	27	)	)	PUNCT
ejpam-4756	172	1	=	=	PRON
ejpam-4756	173	1	γλ	γλ	NUM
ejpam-4756	173	2	γν	γν	INTJ
ejpam-4756	174	1	+	+	CCONJ
ejpam-4756	174	2	λ	λ	X
ejpam-4756	174	3	ν∑	ν∑	X
ejpam-4756	174	4	k=0	k=0	PROPN
ejpam-4756	174	5	[	[	PUNCT
ejpam-4756	174	6	ν	ν	X
ejpam-4756	174	7	k	k	X
ejpam-4756	174	8	]	]	PUNCT
ejpam-4756	174	9	λk	λk	PROPN
ejpam-4756	174	10	k∑	k∑	PROPN
ejpam-4756	174	11	j=0	j=0	PROPN
ejpam-4756	174	12	ak	ak	PROPN
ejpam-4756	174	13	,	,	PUNCT
ejpam-4756	174	14	j	j	PROPN
ejpam-4756	174	15	{	{	PUNCT
ejpam-4756	174	16	sj(f	sj(f	PROPN
ejpam-4756	174	17	;	;	PUNCT
ejpam-4756	174	18	t)−	t)−	PROPN
ejpam-4756	174	19	f(t	f(t	PROPN
ejpam-4756	174	20	)	)	PUNCT
ejpam-4756	174	21	}	}	PUNCT
ejpam-4756	175	1	h.	h.	PROPN
ejpam-4756	175	2	k.	k.	PROPN
ejpam-4756	175	3	nigam	nigam	PROPN
ejpam-4756	175	4	,	,	PUNCT
ejpam-4756	175	5	m.	m.	PROPN
ejpam-4756	175	6	k.	k.	PROPN
ejpam-4756	175	7	sah	sah	PROPN
ejpam-4756	175	8	/	/	SYM
ejpam-4756	175	9	eur	eur	PROPN
ejpam-4756	175	10	.	.	PUNCT
ejpam-4756	176	1	j.	j.	PROPN
ejpam-4756	176	2	pure	pure	PROPN
ejpam-4756	176	3	appl	appl	PROPN
ejpam-4756	176	4	.	.	PROPN
ejpam-4756	176	5	math	math	PROPN
ejpam-4756	176	6	,	,	PUNCT
ejpam-4756	176	7	16	16	NUM
ejpam-4756	176	8	(	(	PUNCT
ejpam-4756	176	9	2	2	NUM
ejpam-4756	176	10	)	)	PUNCT
ejpam-4756	176	11	(	(	PUNCT
ejpam-4756	176	12	2023	2023	NUM
ejpam-4756	176	13	)	)	PUNCT
ejpam-4756	176	14	,	,	PUNCT
ejpam-4756	176	15	1302	1302	NUM
ejpam-4756	176	16	-	-	SYM
ejpam-4756	176	17	1317	1317	NUM
ejpam-4756	176	18	1310	1310	NUM
ejpam-4756	176	19	=	=	SYM
ejpam-4756	177	1	γλ	γλ	NUM
ejpam-4756	177	2	γν	γν	INTJ
ejpam-4756	178	1	+	+	CCONJ
ejpam-4756	178	2	λ	λ	X
ejpam-4756	178	3	ν∑	ν∑	X
ejpam-4756	178	4	k=0	k=0	PROPN
ejpam-4756	178	5	[	[	PUNCT
ejpam-4756	178	6	ν	ν	X
ejpam-4756	178	7	k	k	X
ejpam-4756	178	8	]	]	PUNCT
ejpam-4756	178	9	λk	λk	PROPN
ejpam-4756	178	10	k∑	k∑	PROPN
ejpam-4756	178	11	j=0	j=0	PROPN
ejpam-4756	178	12	ak	ak	PROPN
ejpam-4756	178	13	,	,	PUNCT
ejpam-4756	178	14	j	j	PROPN
ejpam-4756	178	15	{	{	PUNCT
ejpam-4756	178	16	1	1	NUM
ejpam-4756	178	17	2π	2π	NUM
ejpam-4756	178	18	∫	∫	PROPN
ejpam-4756	179	1	π	π	NOUN
ejpam-4756	179	2	0	0	PUNCT
ejpam-4756	180	1	ϕ(t	ϕ(t	NUM
ejpam-4756	180	2	,	,	PUNCT
ejpam-4756	180	3	w	w	NOUN
ejpam-4756	180	4	)	)	PUNCT
ejpam-4756	180	5	sin(j	sin(j	VERB
ejpam-4756	181	1	+	+	CCONJ
ejpam-4756	181	2	1	1	NUM
ejpam-4756	181	3	2)w	2)w	NUM
ejpam-4756	181	4	sin(w2	sin(w2	X
ejpam-4756	181	5	)	)	PUNCT
ejpam-4756	181	6	dw	dw	NOUN
ejpam-4756	181	7	}	}	PUNCT
ejpam-4756	181	8	=	=	PUNCT
ejpam-4756	182	1	γλ	γλ	NUM
ejpam-4756	182	2	∫	∫	PROPN
ejpam-4756	182	3	π	π	NOUN
ejpam-4756	182	4	0	0	PUNCT
ejpam-4756	183	1	ϕ(t	ϕ(t	NUM
ejpam-4756	183	2	,	,	PUNCT
ejpam-4756	183	3	w	w	NOUN
ejpam-4756	183	4	)	)	PUNCT
ejpam-4756	183	5	1	1	NUM
ejpam-4756	183	6	2π	2π	NOUN
ejpam-4756	183	7	ν∑	ν∑	PUNCT
ejpam-4756	184	1	k=0	k=0	PUNCT
ejpam-4756	184	2	[	[	PUNCT
ejpam-4756	184	3	ν	ν	X
ejpam-4756	184	4	k	k	X
ejpam-4756	184	5	]	]	PUNCT
ejpam-4756	184	6	λk	λk	PROPN
ejpam-4756	184	7	k∑	k∑	PROPN
ejpam-4756	184	8	j=0	j=0	PROPN
ejpam-4756	184	9	ak	ak	PROPN
ejpam-4756	184	10	,	,	PUNCT
ejpam-4756	184	11	j	j	PROPN
ejpam-4756	184	12	sin(j	sin(j	PROPN
ejpam-4756	185	1	+	+	CCONJ
ejpam-4756	185	2	1	1	NUM
ejpam-4756	185	3	2)w	2)w	NUM
ejpam-4756	185	4	γν	γν	NOUN
ejpam-4756	185	5	+	+	CCONJ
ejpam-4756	185	6	λ	λ	X
ejpam-4756	185	7	·	·	PUNCT
ejpam-4756	185	8	sin(w2	sin(w2	X
ejpam-4756	185	9	)	)	PUNCT
ejpam-4756	185	10	dw	dw	PROPN
ejpam-4756	185	11	=	=	NOUN
ejpam-4756	186	1	γλ	γλ	PROPN
ejpam-4756	186	2	∫	∫	PROPN
ejpam-4756	186	3	π	π	NOUN
ejpam-4756	186	4	0	0	PUNCT
ejpam-4756	187	1	ϕ(t	ϕ(t	NUM
ejpam-4756	187	2	,	,	PUNCT
ejpam-4756	187	3	w)mν(w)dw	w)mν(w)dw	PROPN
ejpam-4756	187	4	.	.	PUNCT
ejpam-4756	188	1	let	let	VERB
ejpam-4756	188	2	ρν(t	ρν(t	NUM
ejpam-4756	188	3	)	)	PUNCT
ejpam-4756	188	4	:	:	PUNCT
ejpam-4756	189	1	=	=	PUNCT
ejpam-4756	189	2	dk	dk	X
ejpam-4756	189	3	λa	λa	X
ejpam-4756	189	4	ν	ν	X
ejpam-4756	189	5	(	(	PUNCT
ejpam-4756	189	6	g	g	NOUN
ejpam-4756	189	7	;	;	PUNCT
ejpam-4756	189	8	t)−	t)−	PROPN
ejpam-4756	189	9	g(t	g(t	PROPN
ejpam-4756	189	10	)	)	PUNCT
ejpam-4756	189	11	=	=	VERB
ejpam-4756	190	1	γλ	γλ	NUM
ejpam-4756	190	2	∫	∫	PROPN
ejpam-4756	190	3	π	π	NOUN
ejpam-4756	190	4	0	0	PUNCT
ejpam-4756	191	1	ϕ(t	ϕ(t	NUM
ejpam-4756	191	2	,	,	PUNCT
ejpam-4756	191	3	w)mν(w)dw	w)mν(w)dw	PROPN
ejpam-4756	191	4	.	.	PUNCT
ejpam-4756	192	1	(	(	PUNCT
ejpam-4756	192	2	17	17	NUM
ejpam-4756	192	3	)	)	PUNCT
ejpam-4756	192	4	now	now	ADV
ejpam-4756	192	5	,	,	PUNCT
ejpam-4756	192	6	ρν(t+	ρν(t+	PROPN
ejpam-4756	192	7	z	z	PROPN
ejpam-4756	192	8	)	)	PUNCT
ejpam-4756	193	1	+	+	NUM
ejpam-4756	193	2	ρν(t−	ρν(t−	NOUN
ejpam-4756	194	1	z)−	z)−	NUM
ejpam-4756	194	2	2ρν(t	2ρν(t	NUM
ejpam-4756	194	3	)	)	PUNCT
ejpam-4756	194	4	=	=	VERB
ejpam-4756	195	1	γλ	γλ	NUM
ejpam-4756	195	2	∫	∫	PROPN
ejpam-4756	195	3	π	π	PROPN
ejpam-4756	195	4	0	0	NUM
ejpam-4756	195	5	{	{	PUNCT
ejpam-4756	195	6	ϕ(t+	ϕ(t+	NOUN
ejpam-4756	195	7	z	z	PROPN
ejpam-4756	195	8	,	,	PUNCT
ejpam-4756	195	9	w	w	PROPN
ejpam-4756	195	10	)	)	PUNCT
ejpam-4756	195	11	+	+	CCONJ
ejpam-4756	196	1	ϕ(t−	ϕ(t−	PROPN
ejpam-4756	196	2	z	z	NOUN
ejpam-4756	196	3	,	,	PUNCT
ejpam-4756	196	4	w)−	w)−	PROPN
ejpam-4756	196	5	2ϕ(t	2ϕ(t	NUM
ejpam-4756	196	6	,	,	PUNCT
ejpam-4756	196	7	w)}mν(w)dw	w)}mν(w)dw	PROPN
ejpam-4756	196	8	.	.	PUNCT
ejpam-4756	197	1	using	use	VERB
ejpam-4756	197	2	generalized	generalized	ADJ
ejpam-4756	197	3	minkowski	minkowski	ADJ
ejpam-4756	197	4	inequality	inequality	NOUN
ejpam-4756	197	5	(	(	PUNCT
ejpam-4756	197	6	[	[	X
ejpam-4756	197	7	2	2	NUM
ejpam-4756	197	8	]	]	NUM
ejpam-4756	197	9	)	)	PUNCT
ejpam-4756	197	10	,	,	PUNCT
ejpam-4756	197	11	we	we	PRON
ejpam-4756	197	12	can	can	AUX
ejpam-4756	197	13	write	write	VERB
ejpam-4756	197	14	∥ρν(·+	∥ρν(·+	PROPN
ejpam-4756	197	15	z	z	PROPN
ejpam-4756	197	16	)	)	PUNCT
ejpam-4756	198	1	+	+	NOUN
ejpam-4756	198	2	ρν	ρν	PROPN
ejpam-4756	198	3	(	(	PUNCT
ejpam-4756	198	4	·	·	PUNCT
ejpam-4756	198	5	−	−	PUNCT
ejpam-4756	199	1	z)−	z)−	PROPN
ejpam-4756	199	2	2ρν(·)∥r	2ρν(·)∥r	NUM
ejpam-4756	199	3	≤	≤	NUM
ejpam-4756	200	1	γλ	γλ	NUM
ejpam-4756	200	2	∫	∫	PROPN
ejpam-4756	201	1	1	1	NUM
ejpam-4756	201	2	ν+1	ν+1	PROPN
ejpam-4756	201	3	0	0	NUM
ejpam-4756	201	4	∥ϕ(·+	∥ϕ(·+	PROPN
ejpam-4756	201	5	z	z	PROPN
ejpam-4756	201	6	,	,	PUNCT
ejpam-4756	201	7	w	w	PROPN
ejpam-4756	201	8	)	)	PUNCT
ejpam-4756	201	9	+	+	CCONJ
ejpam-4756	201	10	ϕ	ϕ	X
ejpam-4756	201	11	(	(	PUNCT
ejpam-4756	201	12	·	·	PUNCT
ejpam-4756	201	13	−	−	PROPN
ejpam-4756	202	1	z	z	X
ejpam-4756	202	2	,	,	PUNCT
ejpam-4756	202	3	w)−	w)−	PROPN
ejpam-4756	202	4	2ϕ	2ϕ	NUM
ejpam-4756	202	5	(	(	PUNCT
ejpam-4756	202	6	·	·	PUNCT
ejpam-4756	202	7	,	,	PUNCT
ejpam-4756	202	8	w)∥r|mν(w)|dw	w)∥r|mν(w)|dw	NOUN
ejpam-4756	202	9	+	+	CCONJ
ejpam-4756	202	10	γλ	γλ	NUM
ejpam-4756	202	11	∫	∫	PROPN
ejpam-4756	202	12	π	π	PROPN
ejpam-4756	202	13	1	1	NUM
ejpam-4756	202	14	ν+1	ν+1	PROPN
ejpam-4756	202	15	∥ϕ(·+	∥ϕ(·+	PROPN
ejpam-4756	202	16	z	z	PROPN
ejpam-4756	202	17	,	,	PUNCT
ejpam-4756	202	18	w	w	PROPN
ejpam-4756	202	19	)	)	PUNCT
ejpam-4756	202	20	+	+	CCONJ
ejpam-4756	202	21	ϕ	ϕ	X
ejpam-4756	202	22	(	(	PUNCT
ejpam-4756	202	23	·	·	PUNCT
ejpam-4756	203	1	−	−	PROPN
ejpam-4756	204	1	z	z	X
ejpam-4756	204	2	,	,	PUNCT
ejpam-4756	204	3	w)−	w)−	PROPN
ejpam-4756	204	4	2ϕ	2ϕ	NUM
ejpam-4756	204	5	(	(	PUNCT
ejpam-4756	204	6	·	·	PUNCT
ejpam-4756	204	7	,	,	PUNCT
ejpam-4756	204	8	w)∥r|mν(w)|dw	w)∥r|mν(w)|dw	PROPN
ejpam-4756	204	9	=	=	PROPN
ejpam-4756	204	10	i1	i1	PROPN
ejpam-4756	204	11	+	+	CCONJ
ejpam-4756	204	12	i2	i2	PROPN
ejpam-4756	204	13	.	.	PUNCT
ejpam-4756	205	1	(	(	PUNCT
ejpam-4756	205	2	18	18	NUM
ejpam-4756	205	3	)	)	PUNCT
ejpam-4756	205	4	now	now	ADV
ejpam-4756	205	5	,	,	PUNCT
ejpam-4756	205	6	using	use	VERB
ejpam-4756	205	7	lemmas	lemmas	PROPN
ejpam-4756	205	8	1	1	NUM
ejpam-4756	205	9	and	and	CCONJ
ejpam-4756	205	10	2	2	NUM
ejpam-4756	205	11	,	,	PUNCT
ejpam-4756	205	12	we	we	PRON
ejpam-4756	205	13	have	have	VERB
ejpam-4756	205	14	i1	i1	PROPN
ejpam-4756	205	15	=	=	PUNCT
ejpam-4756	206	1	[	[	PUNCT
ejpam-4756	206	2	γλ	γλ	NUM
ejpam-4756	206	3	∫	∫	PROPN
ejpam-4756	206	4	1	1	NUM
ejpam-4756	206	5	ν+1	ν+1	PROPN
ejpam-4756	206	6	0	0	NUM
ejpam-4756	206	7	η2(|z|	η2(|z|	NOUN
ejpam-4756	206	8	)	)	PUNCT
ejpam-4756	206	9	η1(w	η1(w	NOUN
ejpam-4756	206	10	)	)	PUNCT
ejpam-4756	206	11	η2(w	η2(w	NOUN
ejpam-4756	206	12	)	)	PUNCT
ejpam-4756	206	13	(	(	PUNCT
ejpam-4756	206	14	ν	ν	X
ejpam-4756	206	15	+	+	NOUN
ejpam-4756	206	16	1	1	X
ejpam-4756	206	17	)	)	PUNCT
ejpam-4756	206	18	γλ	γλ	INTJ
ejpam-4756	206	19	dw	dw	NOUN
ejpam-4756	206	20	]	]	PUNCT
ejpam-4756	207	1	=	=	PUNCT
ejpam-4756	207	2	o	o	X
ejpam-4756	207	3	[	[	PUNCT
ejpam-4756	207	4	(	(	PUNCT
ejpam-4756	207	5	ν	ν	X
ejpam-4756	207	6	+	+	NOUN
ejpam-4756	207	7	1)η2(|z|	1)η2(|z|	NUM
ejpam-4756	207	8	)	)	PUNCT
ejpam-4756	207	9	∫	∫	PROPN
ejpam-4756	208	1	1	1	NUM
ejpam-4756	208	2	ν+1	ν+1	PROPN
ejpam-4756	208	3	0	0	NUM
ejpam-4756	208	4	η1(w	η1(w	NOUN
ejpam-4756	208	5	)	)	PUNCT
ejpam-4756	208	6	η2(w	η2(w	PROPN
ejpam-4756	208	7	)	)	PUNCT
ejpam-4756	208	8	dw	dw	NOUN
ejpam-4756	208	9	]	]	PUNCT
ejpam-4756	209	1	=	=	PUNCT
ejpam-4756	209	2	o	o	NOUN
ejpam-4756	209	3	(ν	(ν	NOUN
ejpam-4756	209	4	+	+	CCONJ
ejpam-4756	209	5	1)η2(|z|	1)η2(|z|	NUM
ejpam-4756	209	6	)	)	PUNCT
ejpam-4756	209	7	η1	η1	NOUN
ejpam-4756	209	8	(	(	PUNCT
ejpam-4756	209	9	1	1	NUM
ejpam-4756	209	10	ν+1	ν+1	PROPN
ejpam-4756	209	11	)	)	PUNCT
ejpam-4756	209	12	η2	η2	PROPN
ejpam-4756	209	13	(	(	PUNCT
ejpam-4756	209	14	1	1	NUM
ejpam-4756	209	15	ν+1	ν+1	PROPN
ejpam-4756	209	16	)	)	PUNCT
ejpam-4756	209	17	∫	∫	PROPN
ejpam-4756	209	18	1	1	NUM
ejpam-4756	209	19	ν+1	ν+1	PROPN
ejpam-4756	209	20	0	0	NUM
ejpam-4756	209	21	dw	dw	NOUN
ejpam-4756	209	22			NOUN
ejpam-4756	209	23	=	=	PUNCT
ejpam-4756	210	1	o	o	PUNCT
ejpam-4756	210	2	η2(|z|)η1	η2(|z|)η1	PROPN
ejpam-4756	210	3	(	(	PUNCT
ejpam-4756	210	4	1	1	NUM
ejpam-4756	210	5	ν+1	ν+1	PROPN
ejpam-4756	210	6	)	)	PUNCT
ejpam-4756	210	7	η2	η2	PROPN
ejpam-4756	210	8	(	(	PUNCT
ejpam-4756	210	9	1	1	NUM
ejpam-4756	210	10	ν+1	ν+1	NOUN
ejpam-4756	210	11	)	)	PUNCT
ejpam-4756	210	12			NOUN
ejpam-4756	210	13	.	.	PUNCT
ejpam-4756	211	1	(	(	PUNCT
ejpam-4756	211	2	19	19	NUM
ejpam-4756	211	3	)	)	PUNCT
ejpam-4756	211	4	h.	h.	PROPN
ejpam-4756	211	5	k.	k.	PROPN
ejpam-4756	211	6	nigam	nigam	PROPN
ejpam-4756	211	7	,	,	PUNCT
ejpam-4756	211	8	m.	m.	PROPN
ejpam-4756	211	9	k.	k.	PROPN
ejpam-4756	211	10	sah	sah	PROPN
ejpam-4756	211	11	/	/	SYM
ejpam-4756	211	12	eur	eur	PROPN
ejpam-4756	211	13	.	.	PUNCT
ejpam-4756	212	1	j.	j.	PROPN
ejpam-4756	212	2	pure	pure	PROPN
ejpam-4756	212	3	appl	appl	PROPN
ejpam-4756	212	4	.	.	PROPN
ejpam-4756	212	5	math	math	PROPN
ejpam-4756	212	6	,	,	PUNCT
ejpam-4756	212	7	16	16	NUM
ejpam-4756	212	8	(	(	PUNCT
ejpam-4756	212	9	2	2	NUM
ejpam-4756	212	10	)	)	PUNCT
ejpam-4756	212	11	(	(	PUNCT
ejpam-4756	212	12	2023	2023	NUM
ejpam-4756	212	13	)	)	PUNCT
ejpam-4756	212	14	,	,	PUNCT
ejpam-4756	212	15	1302	1302	NUM
ejpam-4756	212	16	-	-	SYM
ejpam-4756	212	17	1317	1317	NUM
ejpam-4756	212	18	1311	1311	NUM
ejpam-4756	212	19	now	now	ADV
ejpam-4756	212	20	,	,	PUNCT
ejpam-4756	212	21	using	use	VERB
ejpam-4756	212	22	lemmas	lemmas	PROPN
ejpam-4756	212	23	1	1	NUM
ejpam-4756	212	24	and	and	CCONJ
ejpam-4756	212	25	3	3	NUM
ejpam-4756	212	26	,	,	PUNCT
ejpam-4756	212	27	we	we	PRON
ejpam-4756	212	28	have	have	VERB
ejpam-4756	212	29	i2	i2	PROPN
ejpam-4756	213	1	=	=	PUNCT
ejpam-4756	213	2	o	o	PROPN
ejpam-4756	213	3	[	[	PUNCT
ejpam-4756	213	4	γλ	γλ	NUM
ejpam-4756	213	5	∫	∫	PROPN
ejpam-4756	213	6	π	π	PROPN
ejpam-4756	213	7	1	1	NUM
ejpam-4756	213	8	ν+1	ν+1	NUM
ejpam-4756	213	9	η2(|z|	η2(|z|	NOUN
ejpam-4756	213	10	)	)	PUNCT
ejpam-4756	213	11	η1(w	η1(w	NOUN
ejpam-4756	213	12	)	)	PUNCT
ejpam-4756	213	13	η2(w	η2(w	NOUN
ejpam-4756	213	14	)	)	PUNCT
ejpam-4756	213	15	{	{	PUNCT
ejpam-4756	213	16	1	1	NUM
ejpam-4756	213	17	w2(ν	w2(ν	X
ejpam-4756	213	18	+	+	CCONJ
ejpam-4756	213	19	1)γλ	1)γλ	PROPN
ejpam-4756	213	20	}	}	PUNCT
ejpam-4756	213	21	dw	dw	NOUN
ejpam-4756	213	22	]	]	PUNCT
ejpam-4756	214	1	=	=	PUNCT
ejpam-4756	214	2	o	o	X
ejpam-4756	214	3	[	[	PUNCT
ejpam-4756	214	4	η2(|z|	η2(|z|	NOUN
ejpam-4756	214	5	)	)	PUNCT
ejpam-4756	214	6	(	(	PUNCT
ejpam-4756	214	7	ν	ν	X
ejpam-4756	214	8	+	+	NOUN
ejpam-4756	214	9	1	1	NUM
ejpam-4756	214	10	)	)	PUNCT
ejpam-4756	214	11	∫	∫	PROPN
ejpam-4756	215	1	π	π	PROPN
ejpam-4756	215	2	1	1	NUM
ejpam-4756	215	3	n+1	n+1	PROPN
ejpam-4756	215	4	η1(w	η1(w	NUM
ejpam-4756	215	5	)	)	PUNCT
ejpam-4756	215	6	η2(w	η2(w	NOUN
ejpam-4756	215	7	)	)	PUNCT
ejpam-4756	215	8	1	1	NUM
ejpam-4756	215	9	w2	w2	NOUN
ejpam-4756	215	10	dw	dw	NOUN
ejpam-4756	215	11	]	]	PUNCT
ejpam-4756	215	12	.	.	PUNCT
ejpam-4756	216	1	(	(	PUNCT
ejpam-4756	216	2	20	20	X
ejpam-4756	216	3	)	)	PUNCT
ejpam-4756	216	4	combining	combine	VERB
ejpam-4756	216	5	(	(	PUNCT
ejpam-4756	216	6	18)-(20	18)-(20	NUM
ejpam-4756	216	7	)	)	PUNCT
ejpam-4756	216	8	,	,	PUNCT
ejpam-4756	216	9	we	we	PRON
ejpam-4756	216	10	have	have	VERB
ejpam-4756	216	11	∥ρν(·+	∥ρν(·+	PROPN
ejpam-4756	216	12	z)+ρν	z)+ρν	PROPN
ejpam-4756	216	13	(	(	PUNCT
ejpam-4756	216	14	·	·	PUNCT
ejpam-4756	216	15	−	−	PUNCT
ejpam-4756	217	1	z)−	z)−	NOUN
ejpam-4756	217	2	2ρν(·)∥r	2ρν(·)∥r	NUM
ejpam-4756	218	1	=	=	PUNCT
ejpam-4756	218	2	o	o	PUNCT
ejpam-4756	219	1	η2(|z|)η1	η2(|z|)η1	PROPN
ejpam-4756	219	2	(	(	PUNCT
ejpam-4756	219	3	1	1	NUM
ejpam-4756	219	4	ν+1	ν+1	PROPN
ejpam-4756	219	5	)	)	PUNCT
ejpam-4756	219	6	η2	η2	PROPN
ejpam-4756	219	7	(	(	PUNCT
ejpam-4756	219	8	1	1	NUM
ejpam-4756	219	9	ν+1	ν+1	NOUN
ejpam-4756	219	10	)	)	PUNCT
ejpam-4756	219	11			VERB
ejpam-4756	220	1	+	+	ADP
ejpam-4756	220	2	o	o	X
ejpam-4756	220	3	[	[	PUNCT
ejpam-4756	220	4	η2(|z|	η2(|z|	NOUN
ejpam-4756	220	5	)	)	PUNCT
ejpam-4756	220	6	(	(	PUNCT
ejpam-4756	220	7	v	v	X
ejpam-4756	220	8	+	+	CCONJ
ejpam-4756	220	9	1	1	NUM
ejpam-4756	220	10	)	)	PUNCT
ejpam-4756	220	11	∫	∫	PROPN
ejpam-4756	221	1	π	π	NOUN
ejpam-4756	221	2	1	1	NUM
ejpam-4756	221	3	ν+1	ν+1	NUM
ejpam-4756	221	4	η1(w	η1(w	NOUN
ejpam-4756	221	5	)	)	PUNCT
ejpam-4756	221	6	η2(w	η2(w	PROPN
ejpam-4756	221	7	)	)	PUNCT
ejpam-4756	221	8	1	1	NUM
ejpam-4756	221	9	w2	w2	NOUN
ejpam-4756	221	10	dw	dw	NOUN
ejpam-4756	221	11	]	]	PUNCT
ejpam-4756	221	12	.	.	PUNCT
ejpam-4756	222	1	(	(	PUNCT
ejpam-4756	222	2	21	21	NUM
ejpam-4756	222	3	)	)	PUNCT
ejpam-4756	222	4	now	now	ADV
ejpam-4756	222	5	,	,	PUNCT
ejpam-4756	222	6	sup	sup	NOUN
ejpam-4756	222	7	z	z	NOUN
ejpam-4756	222	8	̸=0	̸=0	NOUN
ejpam-4756	222	9	∥ρν(·+	∥ρν(·+	PROPN
ejpam-4756	222	10	z	z	PROPN
ejpam-4756	222	11	)	)	PUNCT
ejpam-4756	223	1	+	+	NOUN
ejpam-4756	223	2	ρν	ρν	PROPN
ejpam-4756	223	3	(	(	PUNCT
ejpam-4756	223	4	·	·	PUNCT
ejpam-4756	223	5	−	−	PUNCT
ejpam-4756	224	1	z)−	z)−	PROPN
ejpam-4756	224	2	2ρν(·)∥r	2ρν(·)∥r	NUM
ejpam-4756	224	3	η2(|z|	η2(|z|	NOUN
ejpam-4756	224	4	)	)	PUNCT
ejpam-4756	224	5	=	=	SYM
ejpam-4756	224	6	o	o	X
ejpam-4756	224	7	η1	η1	X
ejpam-4756	224	8	(	(	PUNCT
ejpam-4756	224	9	1	1	NUM
ejpam-4756	224	10	ν+1	ν+1	NOUN
ejpam-4756	224	11	)	)	PUNCT
ejpam-4756	224	12	η2	η2	PROPN
ejpam-4756	224	13	(	(	PUNCT
ejpam-4756	224	14	1	1	NUM
ejpam-4756	224	15	ν+1	ν+1	PROPN
ejpam-4756	224	16	)	)	PUNCT
ejpam-4756	225	1	+o	+o	PROPN
ejpam-4756	225	2	[	[	PUNCT
ejpam-4756	225	3	1	1	NUM
ejpam-4756	225	4	(	(	PUNCT
ejpam-4756	225	5	n+	n+	NOUN
ejpam-4756	225	6	1	1	NUM
ejpam-4756	225	7	)	)	PUNCT
ejpam-4756	225	8	∫	∫	PROPN
ejpam-4756	226	1	π	π	NOUN
ejpam-4756	226	2	1	1	NUM
ejpam-4756	226	3	ν+1	ν+1	NUM
ejpam-4756	226	4	η1(w	η1(w	NOUN
ejpam-4756	226	5	)	)	PUNCT
ejpam-4756	226	6	η2(w	η2(w	PROPN
ejpam-4756	226	7	)	)	PUNCT
ejpam-4756	226	8	1	1	NUM
ejpam-4756	226	9	w2	w2	NOUN
ejpam-4756	226	10	dw	dw	NOUN
ejpam-4756	226	11	]	]	PUNCT
ejpam-4756	226	12	.	.	PUNCT
ejpam-4756	227	1	(	(	PUNCT
ejpam-4756	227	2	22	22	NUM
ejpam-4756	227	3	)	)	PUNCT
ejpam-4756	227	4	now	now	ADV
ejpam-4756	227	5	,	,	PUNCT
ejpam-4756	227	6	∥ρν(·)∥r	∥ρν(·)∥r	NOUN
ejpam-4756	227	7	≤	≤	NUM
ejpam-4756	227	8	∫	∫	PROPN
ejpam-4756	228	1	π	π	NOUN
ejpam-4756	228	2	0	0	PUNCT
ejpam-4756	228	3	∥ϕ	∥ϕ	PROPN
ejpam-4756	228	4	(	(	PUNCT
ejpam-4756	228	5	·	·	PUNCT
ejpam-4756	228	6	,	,	PUNCT
ejpam-4756	228	7	w)∥r|mν(w)|dw	w)∥r|mν(w)|dw	X
ejpam-4756	228	8	=	=	PUNCT
ejpam-4756	228	9	o	o	X
ejpam-4756	229	1	[	[	X
ejpam-4756	229	2	∫	∫	X
ejpam-4756	229	3	1	1	NUM
ejpam-4756	229	4	ν+1	ν+1	PROPN
ejpam-4756	229	5	0	0	NUM
ejpam-4756	229	6	∥ϕ	∥ϕ	PROPN
ejpam-4756	229	7	(	(	PUNCT
ejpam-4756	229	8	·	·	PUNCT
ejpam-4756	229	9	,	,	PUNCT
ejpam-4756	229	10	w)∥r|mν(w)|dw	w)∥r|mν(w)|dw	NOUN
ejpam-4756	229	11	]	]	PUNCT
ejpam-4756	230	1	+	+	CCONJ
ejpam-4756	230	2	[	[	X
ejpam-4756	230	3	∫	∫	X
ejpam-4756	230	4	π	π	PROPN
ejpam-4756	230	5	1	1	NUM
ejpam-4756	230	6	ν+1	ν+1	PROPN
ejpam-4756	230	7	∥ϕ	∥ϕ	PROPN
ejpam-4756	230	8	(	(	PUNCT
ejpam-4756	230	9	·	·	PUNCT
ejpam-4756	230	10	,	,	PUNCT
ejpam-4756	230	11	w)∥r|mν(w)|dw	w)∥r|mν(w)|dw	X
ejpam-4756	230	12	]	]	PUNCT
ejpam-4756	230	13	=	=	SYM
ejpam-4756	230	14	j1	j1	PROPN
ejpam-4756	230	15	+	+	CCONJ
ejpam-4756	230	16	j2	j2	PROPN
ejpam-4756	230	17	.	.	PUNCT
ejpam-4756	231	1	(	(	PUNCT
ejpam-4756	231	2	23	23	NUM
ejpam-4756	231	3	)	)	PUNCT
ejpam-4756	231	4	using	use	VERB
ejpam-4756	231	5	lemma	lemma	PROPN
ejpam-4756	231	6	2	2	NUM
ejpam-4756	231	7	,	,	PUNCT
ejpam-4756	231	8	we	we	PRON
ejpam-4756	231	9	get	get	VERB
ejpam-4756	231	10	j1	j1	NOUN
ejpam-4756	231	11	=	=	PUNCT
ejpam-4756	231	12	o	o	X
ejpam-4756	232	1	[	[	X
ejpam-4756	232	2	∫	∫	X
ejpam-4756	232	3	1	1	NUM
ejpam-4756	232	4	ν+1	ν+1	PROPN
ejpam-4756	232	5	0	0	NUM
ejpam-4756	232	6	∥ϕ	∥ϕ	PROPN
ejpam-4756	232	7	(	(	PUNCT
ejpam-4756	232	8	·	·	PUNCT
ejpam-4756	232	9	,	,	PUNCT
ejpam-4756	232	10	w)∥r|mν(w)|dw	w)∥r|mν(w)|dw	NOUN
ejpam-4756	232	11	]	]	PUNCT
ejpam-4756	232	12	=	=	PUNCT
ejpam-4756	233	1	o	o	X
ejpam-4756	233	2	[	[	PUNCT
ejpam-4756	233	3	(	(	PUNCT
ejpam-4756	233	4	ν	ν	X
ejpam-4756	233	5	+	+	NOUN
ejpam-4756	233	6	1	1	X
ejpam-4756	233	7	)	)	PUNCT
ejpam-4756	233	8	γλ	γλ	VERB
ejpam-4756	233	9	∫	∫	PROPN
ejpam-4756	233	10	1	1	NUM
ejpam-4756	233	11	ν+1	ν+1	PROPN
ejpam-4756	233	12	0	0	NUM
ejpam-4756	233	13	η1(w)dw	η1(w)dw	NOUN
ejpam-4756	233	14	]	]	PUNCT
ejpam-4756	234	1	=	=	PUNCT
ejpam-4756	234	2	o	o	X
ejpam-4756	234	3	[	[	PUNCT
ejpam-4756	234	4	(	(	PUNCT
ejpam-4756	234	5	ν	ν	X
ejpam-4756	234	6	+	+	NOUN
ejpam-4756	234	7	1	1	X
ejpam-4756	234	8	)	)	PUNCT
ejpam-4756	234	9	γλ	γλ	NUM
ejpam-4756	234	10	η1	η1	NOUN
ejpam-4756	234	11	(	(	PUNCT
ejpam-4756	234	12	1	1	NUM
ejpam-4756	234	13	ν	ν	NOUN
ejpam-4756	234	14	+	+	NOUN
ejpam-4756	234	15	1	1	NUM
ejpam-4756	234	16	)	)	PUNCT
ejpam-4756	234	17	∫	∫	PROPN
ejpam-4756	234	18	1	1	NUM
ejpam-4756	234	19	ν+1	ν+1	PROPN
ejpam-4756	234	20	0	0	NUM
ejpam-4756	234	21	dw	dw	NOUN
ejpam-4756	234	22	]	]	PUNCT
ejpam-4756	235	1	=	=	PUNCT
ejpam-4756	235	2	o	o	X
ejpam-4756	235	3	[	[	PUNCT
ejpam-4756	235	4	1	1	NUM
ejpam-4756	235	5	γλ	γλ	NOUN
ejpam-4756	235	6	η1	η1	NOUN
ejpam-4756	235	7	(	(	PUNCT
ejpam-4756	235	8	1	1	NUM
ejpam-4756	235	9	ν	ν	NOUN
ejpam-4756	235	10	+	+	NOUN
ejpam-4756	235	11	1	1	NUM
ejpam-4756	235	12	)	)	PUNCT
ejpam-4756	235	13	]	]	PUNCT
ejpam-4756	235	14	.	.	PUNCT
ejpam-4756	236	1	(	(	PUNCT
ejpam-4756	236	2	24	24	NUM
ejpam-4756	236	3	)	)	PUNCT
ejpam-4756	236	4	h.	h.	PROPN
ejpam-4756	236	5	k.	k.	PROPN
ejpam-4756	236	6	nigam	nigam	PROPN
ejpam-4756	236	7	,	,	PUNCT
ejpam-4756	236	8	m.	m.	PROPN
ejpam-4756	236	9	k.	k.	PROPN
ejpam-4756	236	10	sah	sah	PROPN
ejpam-4756	236	11	/	/	SYM
ejpam-4756	236	12	eur	eur	PROPN
ejpam-4756	236	13	.	.	PUNCT
ejpam-4756	237	1	j.	j.	PROPN
ejpam-4756	237	2	pure	pure	PROPN
ejpam-4756	237	3	appl	appl	PROPN
ejpam-4756	237	4	.	.	PROPN
ejpam-4756	237	5	math	math	PROPN
ejpam-4756	237	6	,	,	PUNCT
ejpam-4756	237	7	16	16	NUM
ejpam-4756	237	8	(	(	PUNCT
ejpam-4756	237	9	2	2	NUM
ejpam-4756	237	10	)	)	PUNCT
ejpam-4756	237	11	(	(	PUNCT
ejpam-4756	237	12	2023	2023	NUM
ejpam-4756	237	13	)	)	PUNCT
ejpam-4756	237	14	,	,	PUNCT
ejpam-4756	237	15	1302	1302	NUM
ejpam-4756	237	16	-	-	SYM
ejpam-4756	237	17	1317	1317	NUM
ejpam-4756	237	18	1312	1312	NUM
ejpam-4756	237	19	using	use	VERB
ejpam-4756	237	20	lemma	lemma	PROPN
ejpam-4756	237	21	3	3	NUM
ejpam-4756	237	22	,	,	PUNCT
ejpam-4756	237	23	we	we	PRON
ejpam-4756	237	24	get	get	VERB
ejpam-4756	237	25	j2	j2	NOUN
ejpam-4756	237	26	=	=	PUNCT
ejpam-4756	237	27	o	o	X
ejpam-4756	238	1	[	[	X
ejpam-4756	238	2	∫	∫	X
ejpam-4756	238	3	π	π	PROPN
ejpam-4756	238	4	1	1	NUM
ejpam-4756	238	5	ν+1	ν+1	PROPN
ejpam-4756	238	6	∥ϕ	∥ϕ	PROPN
ejpam-4756	238	7	(	(	PUNCT
ejpam-4756	238	8	·	·	PUNCT
ejpam-4756	238	9	,	,	PUNCT
ejpam-4756	238	10	w)∥r|mν(w)|dw	w)∥r|mν(w)|dw	NOUN
ejpam-4756	238	11	]	]	PUNCT
ejpam-4756	238	12	=	=	PUNCT
ejpam-4756	238	13	o	o	X
ejpam-4756	239	1	[	[	X
ejpam-4756	239	2	∫	∫	X
ejpam-4756	239	3	π	π	PROPN
ejpam-4756	239	4	1	1	NUM
ejpam-4756	239	5	ν+1	ν+1	PROPN
ejpam-4756	239	6	{	{	PUNCT
ejpam-4756	239	7	1	1	NUM
ejpam-4756	239	8	w2(ν	w2(ν	X
ejpam-4756	239	9	+	+	CCONJ
ejpam-4756	239	10	1)γλ	1)γλ	VERB
ejpam-4756	239	11	}	}	PUNCT
ejpam-4756	239	12	η1(w)dw	η1(w)dw	NOUN
ejpam-4756	239	13	]	]	PUNCT
ejpam-4756	240	1	=	=	PUNCT
ejpam-4756	240	2	o	o	X
ejpam-4756	240	3	[	[	PUNCT
ejpam-4756	240	4	1	1	NUM
ejpam-4756	240	5	(	(	PUNCT
ejpam-4756	240	6	ν	ν	NOUN
ejpam-4756	240	7	+	+	CCONJ
ejpam-4756	241	1	1)γλ	1)γλ	PROPN
ejpam-4756	241	2	∫	∫	PROPN
ejpam-4756	241	3	π	π	NOUN
ejpam-4756	241	4	1	1	NUM
ejpam-4756	241	5	ν+1	ν+1	NUM
ejpam-4756	241	6	η1(w	η1(w	NOUN
ejpam-4756	241	7	)	)	PUNCT
ejpam-4756	241	8	w2	w2	NOUN
ejpam-4756	241	9	dw	dw	NOUN
ejpam-4756	241	10	]	]	PUNCT
ejpam-4756	241	11	.	.	PUNCT
ejpam-4756	242	1	(	(	PUNCT
ejpam-4756	242	2	25	25	NUM
ejpam-4756	242	3	)	)	PUNCT
ejpam-4756	242	4	combining	combine	VERB
ejpam-4756	242	5	(	(	PUNCT
ejpam-4756	242	6	23)-(25	23)-(25	NUM
ejpam-4756	242	7	)	)	PUNCT
ejpam-4756	242	8	,	,	PUNCT
ejpam-4756	242	9	we	we	PRON
ejpam-4756	242	10	have	have	VERB
ejpam-4756	242	11	∥ρν(·)∥r	∥ρν(·)∥r	NOUN
ejpam-4756	242	12	=	=	PUNCT
ejpam-4756	243	1	o	o	X
ejpam-4756	243	2	[	[	PUNCT
ejpam-4756	243	3	1	1	NUM
ejpam-4756	243	4	γλ	γλ	NOUN
ejpam-4756	243	5	η1	η1	NOUN
ejpam-4756	243	6	(	(	PUNCT
ejpam-4756	243	7	1	1	NUM
ejpam-4756	243	8	ν	ν	NOUN
ejpam-4756	243	9	+	+	NOUN
ejpam-4756	243	10	1	1	NUM
ejpam-4756	243	11	)	)	PUNCT
ejpam-4756	243	12	]	]	PUNCT
ejpam-4756	244	1	+	+	PUNCT
ejpam-4756	244	2	o	o	X
ejpam-4756	244	3	[	[	PUNCT
ejpam-4756	244	4	1	1	NUM
ejpam-4756	244	5	(	(	PUNCT
ejpam-4756	244	6	ν	ν	NOUN
ejpam-4756	244	7	+	+	CCONJ
ejpam-4756	244	8	1)γλ	1)γλ	PROPN
ejpam-4756	244	9	∫	∫	PROPN
ejpam-4756	244	10	π	π	NOUN
ejpam-4756	244	11	1	1	NUM
ejpam-4756	244	12	ν+1	ν+1	NUM
ejpam-4756	244	13	η1(w	η1(w	NOUN
ejpam-4756	244	14	)	)	PUNCT
ejpam-4756	244	15	w2	w2	NOUN
ejpam-4756	244	16	dw	dw	NOUN
ejpam-4756	244	17	]	]	PUNCT
ejpam-4756	244	18	.	.	PUNCT
ejpam-4756	245	1	(	(	PUNCT
ejpam-4756	245	2	26	26	NUM
ejpam-4756	245	3	)	)	PUNCT
ejpam-4756	245	4	now	now	ADV
ejpam-4756	245	5	,	,	PUNCT
ejpam-4756	245	6	we	we	PRON
ejpam-4756	245	7	have	have	VERB
ejpam-4756	245	8	∥ρν(·)∥(η2)r	∥ρν(·)∥(η2)r	NOUN
ejpam-4756	245	9	=	=	PUNCT
ejpam-4756	245	10	∥ρν(·)∥r	∥ρν(·)∥r	NOUN
ejpam-4756	245	11	+	+	CCONJ
ejpam-4756	245	12	sup	sup	NOUN
ejpam-4756	245	13	z	z	NOUN
ejpam-4756	246	1	̸=0	̸=0	NOUN
ejpam-4756	246	2	∥ρν(·+	∥ρν(·+	PROPN
ejpam-4756	246	3	z	z	PROPN
ejpam-4756	246	4	)	)	PUNCT
ejpam-4756	247	1	+	+	NOUN
ejpam-4756	247	2	ρν	ρν	PROPN
ejpam-4756	247	3	(	(	PUNCT
ejpam-4756	247	4	·	·	PUNCT
ejpam-4756	247	5	−	−	PUNCT
ejpam-4756	248	1	z)−	z)−	PROPN
ejpam-4756	248	2	2ρν(·)∥r	2ρν(·)∥r	NUM
ejpam-4756	248	3	η2(|z|	η2(|z|	NOUN
ejpam-4756	248	4	)	)	PUNCT
ejpam-4756	248	5	.	.	PUNCT
ejpam-4756	249	1	from	from	ADP
ejpam-4756	249	2	(	(	PUNCT
ejpam-4756	249	3	22	22	NUM
ejpam-4756	249	4	)	)	PUNCT
ejpam-4756	249	5	and	and	CCONJ
ejpam-4756	249	6	(	(	PUNCT
ejpam-4756	249	7	26	26	NUM
ejpam-4756	249	8	)	)	PUNCT
ejpam-4756	249	9	,	,	PUNCT
ejpam-4756	249	10	we	we	PRON
ejpam-4756	249	11	get	get	VERB
ejpam-4756	249	12	∥ρv(·)∥(η2)r	∥ρv(·)∥(η2)r	NOUN
ejpam-4756	250	1	=	=	PUNCT
ejpam-4756	250	2	o	o	X
ejpam-4756	250	3	[	[	PUNCT
ejpam-4756	250	4	1	1	NUM
ejpam-4756	250	5	γλ	γλ	NOUN
ejpam-4756	250	6	η1	η1	NOUN
ejpam-4756	250	7	(	(	PUNCT
ejpam-4756	250	8	1	1	NUM
ejpam-4756	250	9	ν	ν	NOUN
ejpam-4756	250	10	+	+	NOUN
ejpam-4756	250	11	1	1	NUM
ejpam-4756	250	12	)	)	PUNCT
ejpam-4756	250	13	]	]	PUNCT
ejpam-4756	251	1	+	+	PUNCT
ejpam-4756	251	2	o	o	X
ejpam-4756	251	3	[	[	PUNCT
ejpam-4756	251	4	1	1	NUM
ejpam-4756	251	5	(	(	PUNCT
ejpam-4756	251	6	ν	ν	NOUN
ejpam-4756	251	7	+	+	CCONJ
ejpam-4756	251	8	1)γλ	1)γλ	PROPN
ejpam-4756	251	9	∫	∫	PROPN
ejpam-4756	251	10	π	π	NOUN
ejpam-4756	251	11	1	1	NUM
ejpam-4756	251	12	ν+1	ν+1	NUM
ejpam-4756	251	13	η1(w	η1(w	NOUN
ejpam-4756	251	14	)	)	PUNCT
ejpam-4756	251	15	w2	w2	NOUN
ejpam-4756	251	16	dw	dw	NOUN
ejpam-4756	251	17	]	]	PUNCT
ejpam-4756	251	18	=	=	PUNCT
ejpam-4756	251	19	o	o	X
ejpam-4756	251	20	η1	η1	X
ejpam-4756	251	21	(	(	PUNCT
ejpam-4756	251	22	1	1	NUM
ejpam-4756	251	23	ν+1	ν+1	NOUN
ejpam-4756	251	24	)	)	PUNCT
ejpam-4756	251	25	η2	η2	PROPN
ejpam-4756	251	26	(	(	PUNCT
ejpam-4756	251	27	1	1	NUM
ejpam-4756	251	28	ν+1	ν+1	PROPN
ejpam-4756	251	29	)	)	PUNCT
ejpam-4756	252	1	+o	+o	PROPN
ejpam-4756	252	2	[	[	PUNCT
ejpam-4756	252	3	1	1	NUM
ejpam-4756	252	4	(	(	PUNCT
ejpam-4756	252	5	ν	ν	X
ejpam-4756	252	6	+	+	NOUN
ejpam-4756	252	7	1	1	NUM
ejpam-4756	252	8	)	)	PUNCT
ejpam-4756	252	9	∫	∫	PROPN
ejpam-4756	253	1	π	π	NOUN
ejpam-4756	253	2	1	1	NUM
ejpam-4756	253	3	ν+1	ν+1	NUM
ejpam-4756	253	4	η1(w	η1(w	NOUN
ejpam-4756	253	5	)	)	PUNCT
ejpam-4756	253	6	η2(w	η2(w	PROPN
ejpam-4756	253	7	)	)	PUNCT
ejpam-4756	253	8	1	1	NUM
ejpam-4756	253	9	w2	w2	NOUN
ejpam-4756	253	10	dw	dw	NOUN
ejpam-4756	253	11	]	]	PUNCT
ejpam-4756	253	12	.	.	PUNCT
ejpam-4756	254	1	in	in	ADP
ejpam-4756	254	2	view	view	NOUN
ejpam-4756	254	3	of	of	ADP
ejpam-4756	254	4	monotonicity	monotonicity	NOUN
ejpam-4756	254	5	of	of	ADP
ejpam-4756	254	6	η2(w	η2(w	NOUN
ejpam-4756	254	7	)	)	PUNCT
ejpam-4756	254	8	,	,	PUNCT
ejpam-4756	254	9	we	we	PRON
ejpam-4756	254	10	have	have	VERB
ejpam-4756	254	11	η1(w	η1(w	PRON
ejpam-4756	254	12	)	)	PUNCT
ejpam-4756	254	13	=	=	SYM
ejpam-4756	255	1	η1(w	η1(w	NOUN
ejpam-4756	255	2	)	)	PUNCT
ejpam-4756	255	3	η2(w)η2(w	η2(w)η2(w	NOUN
ejpam-4756	255	4	)	)	PUNCT
ejpam-4756	255	5	≤	≤	NOUN
ejpam-4756	256	1	η2(π	η2(π	NUM
ejpam-4756	256	2	)	)	PUNCT
ejpam-4756	256	3	η1(w	η1(w	NOUN
ejpam-4756	256	4	)	)	PUNCT
ejpam-4756	256	5	η2(w	η2(w	NUM
ejpam-4756	256	6	)	)	PUNCT
ejpam-4756	257	1	=	=	SYM
ejpam-4756	257	2	o	o	X
ejpam-4756	257	3	(	(	PUNCT
ejpam-4756	257	4	η1(w	η1(w	NOUN
ejpam-4756	257	5	)	)	PUNCT
ejpam-4756	257	6	η2(w	η2(w	NOUN
ejpam-4756	257	7	)	)	PUNCT
ejpam-4756	257	8	)	)	PUNCT
ejpam-4756	257	9	for	for	ADP
ejpam-4756	257	10	0	0	NUM
ejpam-4756	257	11	<	<	X
ejpam-4756	257	12	w	w	PROPN
ejpam-4756	257	13	≤	≤	NUM
ejpam-4756	257	14	π	π	X
ejpam-4756	257	15	.	.	PUNCT
ejpam-4756	258	1	hence	hence	ADV
ejpam-4756	258	2	,	,	PUNCT
ejpam-4756	258	3	∥ρν(·)∥(η2)r	∥ρν(·)∥(η2)r	PROPN
ejpam-4756	258	4	=	=	PUNCT
ejpam-4756	258	5	o	o	X
ejpam-4756	258	6			PROPN
ejpam-4756	258	7	1	1	NUM
ejpam-4756	258	8	γλ	γλ	NOUN
ejpam-4756	258	9	η1	η1	NOUN
ejpam-4756	258	10	(	(	PUNCT
ejpam-4756	258	11	1	1	NUM
ejpam-4756	258	12	ν+1	ν+1	PROPN
ejpam-4756	258	13	)	)	PUNCT
ejpam-4756	258	14	η2	η2	PROPN
ejpam-4756	258	15	(	(	PUNCT
ejpam-4756	258	16	1	1	NUM
ejpam-4756	258	17	ν+1	ν+1	PROPN
ejpam-4756	258	18	)	)	PUNCT
ejpam-4756	259	1	+o	+o	PROPN
ejpam-4756	259	2	[	[	PUNCT
ejpam-4756	259	3	1	1	NUM
ejpam-4756	259	4	(	(	PUNCT
ejpam-4756	259	5	ν	ν	NOUN
ejpam-4756	259	6	+	+	CCONJ
ejpam-4756	260	1	1)γλ	1)γλ	PROPN
ejpam-4756	260	2	∫	∫	PROPN
ejpam-4756	260	3	π	π	NOUN
ejpam-4756	260	4	1	1	NUM
ejpam-4756	260	5	ν+1	ν+1	PROPN
ejpam-4756	260	6	η1(w	η1(w	NOUN
ejpam-4756	260	7	)	)	PUNCT
ejpam-4756	260	8	η2(w	η2(w	PROPN
ejpam-4756	260	9	)	)	PUNCT
ejpam-4756	260	10	1	1	NUM
ejpam-4756	260	11	w2	w2	NOUN
ejpam-4756	260	12	dw	dw	X
ejpam-4756	260	13	]	]	PUNCT
ejpam-4756	261	1	+	+	ADJ
ejpam-4756	261	2	o	o	X
ejpam-4756	261	3	η1	η1	X
ejpam-4756	261	4	(	(	PUNCT
ejpam-4756	261	5	1	1	NUM
ejpam-4756	261	6	ν+1	ν+1	NOUN
ejpam-4756	261	7	)	)	PUNCT
ejpam-4756	261	8	η2	η2	PROPN
ejpam-4756	261	9	(	(	PUNCT
ejpam-4756	261	10	1	1	NUM
ejpam-4756	261	11	ν+1	ν+1	PROPN
ejpam-4756	261	12	)	)	PUNCT
ejpam-4756	262	1	+o	+o	PROPN
ejpam-4756	262	2	[	[	PUNCT
ejpam-4756	262	3	1	1	NUM
ejpam-4756	262	4	(	(	PUNCT
ejpam-4756	262	5	ν	ν	X
ejpam-4756	262	6	+	+	NOUN
ejpam-4756	262	7	1	1	NUM
ejpam-4756	262	8	)	)	PUNCT
ejpam-4756	262	9	∫	∫	PROPN
ejpam-4756	263	1	π	π	NOUN
ejpam-4756	263	2	1	1	NUM
ejpam-4756	263	3	ν+1	ν+1	NUM
ejpam-4756	263	4	η1(w	η1(w	NOUN
ejpam-4756	263	5	)	)	PUNCT
ejpam-4756	263	6	η2(w	η2(w	PROPN
ejpam-4756	263	7	)	)	PUNCT
ejpam-4756	263	8	1	1	NUM
ejpam-4756	263	9	w2	w2	NOUN
ejpam-4756	263	10	dw	dw	NOUN
ejpam-4756	263	11	]	]	PUNCT
ejpam-4756	263	12	.	.	PUNCT
ejpam-4756	264	1	(	(	PUNCT
ejpam-4756	264	2	27	27	NUM
ejpam-4756	264	3	)	)	PUNCT
ejpam-4756	264	4	since	since	SCONJ
ejpam-4756	264	5	η1	η1	NOUN
ejpam-4756	264	6	and	and	CCONJ
ejpam-4756	264	7	η2	η2	NOUN
ejpam-4756	264	8	are	be	AUX
ejpam-4756	264	9	as	as	ADV
ejpam-4756	264	10	defined	define	VERB
ejpam-4756	264	11	in	in	ADP
ejpam-4756	264	12	note	note	NOUN
ejpam-4756	264	13	1	1	NUM
ejpam-4756	264	14	and	and	CCONJ
ejpam-4756	264	15	η1(w	η1(w	NUM
ejpam-4756	264	16	)	)	PUNCT
ejpam-4756	264	17	η2(w	η2(w	NOUN
ejpam-4756	264	18	)	)	PUNCT
ejpam-4756	264	19	is	be	AUX
ejpam-4756	264	20	positive	positive	ADJ
ejpam-4756	264	21	,	,	PUNCT
ejpam-4756	264	22	non	non	ADJ
ejpam-4756	264	23	-	-	ADJ
ejpam-4756	264	24	decreasing	decrease	VERB
ejpam-4756	264	25	,	,	PUNCT
ejpam-4756	264	26	therefore	therefore	ADV
ejpam-4756	264	27	,	,	PUNCT
ejpam-4756	264	28	∫	∫	PROPN
ejpam-4756	265	1	π	π	PROPN
ejpam-4756	265	2	1	1	NUM
ejpam-4756	265	3	ν+1	ν+1	NUM
ejpam-4756	265	4	η1(w	η1(w	NOUN
ejpam-4756	265	5	)	)	PUNCT
ejpam-4756	265	6	η2(w	η2(w	PROPN
ejpam-4756	265	7	)	)	PUNCT
ejpam-4756	265	8	1	1	NUM
ejpam-4756	265	9	w2	w2	PROPN
ejpam-4756	265	10	dw	dw	PROPN
ejpam-4756	265	11	≥	≥	PROPN
ejpam-4756	265	12	η1	η1	NOUN
ejpam-4756	265	13	(	(	PUNCT
ejpam-4756	265	14	1	1	NUM
ejpam-4756	265	15	ν+1	ν+1	PROPN
ejpam-4756	265	16	)	)	PUNCT
ejpam-4756	265	17	η2	η2	PROPN
ejpam-4756	265	18	(	(	PUNCT
ejpam-4756	265	19	1	1	NUM
ejpam-4756	265	20	ν+1	ν+1	PROPN
ejpam-4756	265	21	)	)	PUNCT
ejpam-4756	265	22	∫	∫	PROPN
ejpam-4756	266	1	π	π	NOUN
ejpam-4756	266	2	1	1	NUM
ejpam-4756	266	3	ν+1	ν+1	PROPN
ejpam-4756	266	4	1	1	NUM
ejpam-4756	266	5	w2	w2	PROPN
ejpam-4756	266	6	dw	dw	PROPN
ejpam-4756	266	7	h.	h.	PROPN
ejpam-4756	266	8	k.	k.	PROPN
ejpam-4756	266	9	nigam	nigam	PROPN
ejpam-4756	266	10	,	,	PUNCT
ejpam-4756	266	11	m.	m.	PROPN
ejpam-4756	266	12	k.	k.	PROPN
ejpam-4756	266	13	sah	sah	PROPN
ejpam-4756	266	14	/	/	SYM
ejpam-4756	266	15	eur	eur	PROPN
ejpam-4756	266	16	.	.	PUNCT
ejpam-4756	267	1	j.	j.	PROPN
ejpam-4756	267	2	pure	pure	PROPN
ejpam-4756	267	3	appl	appl	PROPN
ejpam-4756	267	4	.	.	PROPN
ejpam-4756	267	5	math	math	PROPN
ejpam-4756	267	6	,	,	PUNCT
ejpam-4756	267	7	16	16	NUM
ejpam-4756	267	8	(	(	PUNCT
ejpam-4756	267	9	2	2	NUM
ejpam-4756	267	10	)	)	PUNCT
ejpam-4756	267	11	(	(	PUNCT
ejpam-4756	267	12	2023	2023	NUM
ejpam-4756	267	13	)	)	PUNCT
ejpam-4756	267	14	,	,	PUNCT
ejpam-4756	267	15	1302	1302	NUM
ejpam-4756	267	16	-	-	SYM
ejpam-4756	267	17	1317	1317	NUM
ejpam-4756	267	18	1313	1313	NUM
ejpam-4756	267	19	≥	≥	NOUN
ejpam-4756	267	20	η1	η1	NOUN
ejpam-4756	267	21	(	(	PUNCT
ejpam-4756	267	22	1	1	NUM
ejpam-4756	267	23	n+1	n+1	X
ejpam-4756	267	24	)	)	PUNCT
ejpam-4756	267	25	η2	η2	PROPN
ejpam-4756	267	26	(	(	PUNCT
ejpam-4756	267	27	1	1	NUM
ejpam-4756	267	28	ν+1	ν+1	NOUN
ejpam-4756	267	29	)	)	PUNCT
ejpam-4756	268	1	[	[	X
ejpam-4756	268	2	−	−	X
ejpam-4756	268	3	1	1	NUM
ejpam-4756	268	4	π	π	NOUN
ejpam-4756	268	5	+	+	CCONJ
ejpam-4756	268	6	(	(	PUNCT
ejpam-4756	268	7	ν	ν	X
ejpam-4756	268	8	+	+	NOUN
ejpam-4756	268	9	1	1	NUM
ejpam-4756	268	10	)	)	PUNCT
ejpam-4756	268	11	]	]	PUNCT
ejpam-4756	268	12	≥	≥	NOUN
ejpam-4756	268	13	η1	η1	NOUN
ejpam-4756	268	14	(	(	PUNCT
ejpam-4756	268	15	1	1	NUM
ejpam-4756	268	16	ν+1	ν+1	PROPN
ejpam-4756	268	17	)	)	PUNCT
ejpam-4756	268	18	η2	η2	PROPN
ejpam-4756	268	19	(	(	PUNCT
ejpam-4756	268	20	1	1	NUM
ejpam-4756	268	21	ν+1	ν+1	NOUN
ejpam-4756	268	22	)	)	PUNCT
ejpam-4756	269	1	[	[	X
ejpam-4756	269	2	π(ν	π(ν	ADJ
ejpam-4756	269	3	+	+	X
ejpam-4756	269	4	1)−	1)−	NUM
ejpam-4756	269	5	1	1	NUM
ejpam-4756	269	6	π	π	NOUN
ejpam-4756	269	7	]	]	PUNCT
ejpam-4756	269	8	.	.	PUNCT
ejpam-4756	270	1	then	then	ADV
ejpam-4756	270	2	,	,	PUNCT
ejpam-4756	270	3	η1	η1	NOUN
ejpam-4756	270	4	(	(	PUNCT
ejpam-4756	270	5	1	1	NUM
ejpam-4756	270	6	ν+1	ν+1	PROPN
ejpam-4756	270	7	)	)	PUNCT
ejpam-4756	270	8	η2	η2	PROPN
ejpam-4756	270	9	(	(	PUNCT
ejpam-4756	270	10	1	1	NUM
ejpam-4756	270	11	ν+1	ν+1	PROPN
ejpam-4756	270	12	)	)	PUNCT
ejpam-4756	271	1	=	=	PUNCT
ejpam-4756	272	1	o	o	X
ejpam-4756	273	1	[	[	PUNCT
ejpam-4756	273	2	π	π	X
ejpam-4756	273	3	{	{	PUNCT
ejpam-4756	273	4	π(ν	π(ν	PROPN
ejpam-4756	273	5	+	+	PROPN
ejpam-4756	273	6	1)−	1)−	NUM
ejpam-4756	273	7	1	1	NUM
ejpam-4756	273	8	}	}	PUNCT
ejpam-4756	273	9	∫	∫	PROPN
ejpam-4756	273	10	π	π	PROPN
ejpam-4756	273	11	1	1	NUM
ejpam-4756	273	12	ν+1	ν+1	PROPN
ejpam-4756	273	13	η1(w	η1(w	NOUN
ejpam-4756	273	14	)	)	PUNCT
ejpam-4756	273	15	η2(w	η2(w	PROPN
ejpam-4756	273	16	)	)	PUNCT
ejpam-4756	273	17	1	1	NUM
ejpam-4756	273	18	w2	w2	NOUN
ejpam-4756	273	19	dw	dw	NOUN
ejpam-4756	273	20	]	]	PUNCT
ejpam-4756	273	21	.	.	PUNCT
ejpam-4756	274	1	(	(	PUNCT
ejpam-4756	274	2	28	28	NUM
ejpam-4756	274	3	)	)	PUNCT
ejpam-4756	274	4	from	from	ADP
ejpam-4756	274	5	(	(	PUNCT
ejpam-4756	274	6	27	27	NUM
ejpam-4756	274	7	)	)	PUNCT
ejpam-4756	274	8	and	and	CCONJ
ejpam-4756	274	9	(	(	PUNCT
ejpam-4756	274	10	28	28	NUM
ejpam-4756	274	11	)	)	PUNCT
ejpam-4756	274	12	,	,	PUNCT
ejpam-4756	274	13	we	we	PRON
ejpam-4756	274	14	get	get	VERB
ejpam-4756	274	15	∥ρν(·)∥(η2)r	∥ρν(·)∥(η2)r	NOUN
ejpam-4756	275	1	=	=	NOUN
ejpam-4756	275	2	o	o	X
ejpam-4756	275	3	[	[	PUNCT
ejpam-4756	275	4	1	1	NUM
ejpam-4756	275	5	γλ	γλ	PROPN
ejpam-4756	275	6	π	π	PROPN
ejpam-4756	275	7	{	{	PUNCT
ejpam-4756	275	8	π(ν	π(ν	PROPN
ejpam-4756	276	1	+	+	PROPN
ejpam-4756	276	2	1)−	1)−	NUM
ejpam-4756	276	3	1	1	NUM
ejpam-4756	276	4	}	}	PUNCT
ejpam-4756	276	5	∫	∫	PROPN
ejpam-4756	276	6	π	π	PROPN
ejpam-4756	276	7	1	1	NUM
ejpam-4756	276	8	ν+1	ν+1	PROPN
ejpam-4756	276	9	η1(w	η1(w	NOUN
ejpam-4756	276	10	)	)	PUNCT
ejpam-4756	276	11	η2(w	η2(w	PROPN
ejpam-4756	276	12	)	)	PUNCT
ejpam-4756	276	13	1	1	NUM
ejpam-4756	276	14	w2	w2	NOUN
ejpam-4756	276	15	dw	dw	X
ejpam-4756	276	16	]	]	PUNCT
ejpam-4756	277	1	+	+	PUNCT
ejpam-4756	277	2	o	o	X
ejpam-4756	277	3	[	[	PUNCT
ejpam-4756	277	4	1	1	NUM
ejpam-4756	277	5	(	(	PUNCT
ejpam-4756	277	6	ν	ν	NOUN
ejpam-4756	277	7	+	+	CCONJ
ejpam-4756	277	8	1)γλ	1)γλ	PROPN
ejpam-4756	277	9	∫	∫	PROPN
ejpam-4756	277	10	π	π	NOUN
ejpam-4756	277	11	1	1	NUM
ejpam-4756	277	12	ν+1	ν+1	PROPN
ejpam-4756	277	13	η1(w	η1(w	NOUN
ejpam-4756	277	14	)	)	PUNCT
ejpam-4756	277	15	η2(w	η2(w	PROPN
ejpam-4756	277	16	)	)	PUNCT
ejpam-4756	277	17	1	1	NUM
ejpam-4756	277	18	w2	w2	NOUN
ejpam-4756	277	19	dw	dw	X
ejpam-4756	277	20	]	]	PUNCT
ejpam-4756	278	1	+	+	PUNCT
ejpam-4756	278	2	o	o	X
ejpam-4756	278	3	[	[	PUNCT
ejpam-4756	278	4	π	π	X
ejpam-4756	278	5	{	{	PUNCT
ejpam-4756	278	6	π(ν	π(ν	PROPN
ejpam-4756	278	7	+	+	PROPN
ejpam-4756	278	8	1)−	1)−	NUM
ejpam-4756	278	9	1	1	NUM
ejpam-4756	278	10	}	}	PUNCT
ejpam-4756	278	11	∫	∫	PROPN
ejpam-4756	278	12	π	π	PROPN
ejpam-4756	278	13	1	1	NUM
ejpam-4756	278	14	ν+1	ν+1	PROPN
ejpam-4756	278	15	η1(w	η1(w	NOUN
ejpam-4756	278	16	)	)	PUNCT
ejpam-4756	278	17	η2(w	η2(w	PROPN
ejpam-4756	278	18	)	)	PUNCT
ejpam-4756	278	19	1	1	NUM
ejpam-4756	278	20	w2	w2	NOUN
ejpam-4756	278	21	dw	dw	X
ejpam-4756	278	22	]	]	PUNCT
ejpam-4756	279	1	+	+	PUNCT
ejpam-4756	279	2	o	o	X
ejpam-4756	279	3	[	[	PUNCT
ejpam-4756	279	4	1	1	NUM
ejpam-4756	279	5	(	(	PUNCT
ejpam-4756	279	6	ν	ν	X
ejpam-4756	279	7	+	+	NOUN
ejpam-4756	279	8	1	1	NUM
ejpam-4756	279	9	)	)	PUNCT
ejpam-4756	279	10	∫	∫	PROPN
ejpam-4756	279	11	π	π	NOUN
ejpam-4756	279	12	1	1	NUM
ejpam-4756	279	13	ν+1	ν+1	NUM
ejpam-4756	279	14	η1(w	η1(w	NOUN
ejpam-4756	279	15	)	)	PUNCT
ejpam-4756	279	16	η2(w	η2(w	PROPN
ejpam-4756	279	17	)	)	PUNCT
ejpam-4756	279	18	1	1	NUM
ejpam-4756	279	19	w2	w2	NOUN
ejpam-4756	279	20	dw	dw	NOUN
ejpam-4756	279	21	]	]	PUNCT
ejpam-4756	280	1	=	=	PUNCT
ejpam-4756	280	2	o	o	X
ejpam-4756	281	1	[	[	X
ejpam-4756	281	2	(	(	PUNCT
ejpam-4756	281	3	π	π	PROPN
ejpam-4756	281	4	γλ{π(ν	γλ{π(ν	PROPN
ejpam-4756	281	5	+	+	PROPN
ejpam-4756	281	6	1)−	1)−	PROPN
ejpam-4756	281	7	1	1	NUM
ejpam-4756	281	8	}	}	PUNCT
ejpam-4756	281	9	+	+	NUM
ejpam-4756	281	10	1	1	NUM
ejpam-4756	281	11	γλ(ν	γλ(ν	NOUN
ejpam-4756	281	12	+	+	CCONJ
ejpam-4756	281	13	1	1	X
ejpam-4756	281	14	)	)	PUNCT
ejpam-4756	281	15	+	+	CCONJ
ejpam-4756	281	16	π	π	X
ejpam-4756	281	17	{	{	PUNCT
ejpam-4756	281	18	π(ν	π(ν	ADJ
ejpam-4756	281	19	+	+	PROPN
ejpam-4756	281	20	1)−	1)−	NUM
ejpam-4756	281	21	1	1	NUM
ejpam-4756	281	22	}	}	PUNCT
ejpam-4756	281	23	+	+	NUM
ejpam-4756	281	24	1	1	NUM
ejpam-4756	281	25	(	(	PUNCT
ejpam-4756	281	26	ν	ν	X
ejpam-4756	281	27	+	+	NOUN
ejpam-4756	281	28	1	1	NUM
ejpam-4756	281	29	)	)	PUNCT
ejpam-4756	281	30	)	)	PUNCT
ejpam-4756	281	31	∫	∫	PROPN
ejpam-4756	282	1	π	π	NOUN
ejpam-4756	282	2	1	1	NUM
ejpam-4756	282	3	ν+1	ν+1	NUM
ejpam-4756	282	4	η1(w	η1(w	NOUN
ejpam-4756	282	5	)	)	PUNCT
ejpam-4756	282	6	η2(w	η2(w	PROPN
ejpam-4756	282	7	)	)	PUNCT
ejpam-4756	282	8	1	1	NUM
ejpam-4756	282	9	w2	w2	NOUN
ejpam-4756	282	10	dw	dw	NOUN
ejpam-4756	282	11	]	]	PUNCT
ejpam-4756	282	12	=	=	PUNCT
ejpam-4756	283	1	o	o	X
ejpam-4756	283	2	[	[	X
ejpam-4756	283	3	(	(	PUNCT
ejpam-4756	283	4	(	(	PUNCT
ejpam-4756	283	5	1	1	NUM
ejpam-4756	283	6	+	+	NUM
ejpam-4756	283	7	γλ){2π(ν	γλ){2π(ν	NOUN
ejpam-4756	283	8	+	+	X
ejpam-4756	284	1	1)−	1)−	NUM
ejpam-4756	284	2	1	1	NUM
ejpam-4756	284	3	}	}	PUNCT
ejpam-4756	284	4	(	(	PUNCT
ejpam-4756	284	5	ν	ν	X
ejpam-4756	284	6	+	+	NOUN
ejpam-4756	284	7	1)γλ{π(ν	1)γλ{π(ν	NUM
ejpam-4756	284	8	+	+	SYM
ejpam-4756	284	9	1)−	1)−	NUM
ejpam-4756	284	10	1	1	NUM
ejpam-4756	284	11	}	}	PUNCT
ejpam-4756	284	12	)	)	PUNCT
ejpam-4756	284	13	∫	∫	PROPN
ejpam-4756	285	1	π	π	NOUN
ejpam-4756	285	2	1	1	NUM
ejpam-4756	285	3	ν+1	ν+1	NUM
ejpam-4756	285	4	η1(w	η1(w	NOUN
ejpam-4756	285	5	)	)	PUNCT
ejpam-4756	285	6	η2(w	η2(w	PROPN
ejpam-4756	285	7	)	)	PUNCT
ejpam-4756	285	8	1	1	NUM
ejpam-4756	285	9	w2	w2	NOUN
ejpam-4756	285	10	dw	dw	NOUN
ejpam-4756	285	11	]	]	PUNCT
ejpam-4756	285	12	.	.	PUNCT
ejpam-4756	286	1	proof	proof	NOUN
ejpam-4756	286	2	.	.	PUNCT
ejpam-4756	287	1	[	[	X
ejpam-4756	287	2	proof	proof	NOUN
ejpam-4756	287	3	of	of	ADP
ejpam-4756	287	4	theorem	theorem	NOUN
ejpam-4756	287	5	2	2	NUM
ejpam-4756	287	6	]	]	PUNCT
ejpam-4756	287	7	following	follow	VERB
ejpam-4756	287	8	the	the	DET
ejpam-4756	287	9	proof	proof	NOUN
ejpam-4756	287	10	of	of	ADP
ejpam-4756	287	11	theorem	theorem	NOUN
ejpam-4756	287	12	1	1	NUM
ejpam-4756	287	13	,	,	PUNCT
ejpam-4756	287	14	we	we	PRON
ejpam-4756	287	15	have	have	VERB
ejpam-4756	287	16	eν(g	eν(g	NOUN
ejpam-4756	287	17	)	)	PUNCT
ejpam-4756	288	1	=	=	PUNCT
ejpam-4756	289	1	o	o	X
ejpam-4756	290	1	[	[	X
ejpam-4756	290	2	(	(	PUNCT
ejpam-4756	290	3	(	(	PUNCT
ejpam-4756	290	4	1	1	NUM
ejpam-4756	290	5	+	+	NUM
ejpam-4756	290	6	γλ){2π(ν	γλ){2π(ν	NOUN
ejpam-4756	290	7	+	+	X
ejpam-4756	291	1	1)−	1)−	NUM
ejpam-4756	291	2	1	1	NUM
ejpam-4756	291	3	}	}	PUNCT
ejpam-4756	291	4	(	(	PUNCT
ejpam-4756	291	5	ν	ν	X
ejpam-4756	291	6	+	+	NOUN
ejpam-4756	291	7	1)γλ{π(ν	1)γλ{π(ν	NUM
ejpam-4756	291	8	+	+	SYM
ejpam-4756	291	9	1)−	1)−	NUM
ejpam-4756	291	10	1	1	NUM
ejpam-4756	291	11	}	}	PUNCT
ejpam-4756	291	12	)	)	PUNCT
ejpam-4756	291	13	∫	∫	PROPN
ejpam-4756	292	1	π	π	NOUN
ejpam-4756	292	2	1	1	NUM
ejpam-4756	292	3	ν+1	ν+1	NUM
ejpam-4756	292	4	η1(w	η1(w	NOUN
ejpam-4756	292	5	)	)	PUNCT
ejpam-4756	292	6	η2(w	η2(w	PROPN
ejpam-4756	292	7	)	)	PUNCT
ejpam-4756	292	8	1	1	NUM
ejpam-4756	292	9	w2	w2	NOUN
ejpam-4756	292	10	dw	dw	NOUN
ejpam-4756	292	11	]	]	PUNCT
ejpam-4756	292	12	.	.	PUNCT
ejpam-4756	293	1	since	since	SCONJ
ejpam-4756	293	2	η1(w	η1(w	NUM
ejpam-4756	293	3	)	)	PUNCT
ejpam-4756	293	4	wη2(w	wη2(w	PROPN
ejpam-4756	293	5	)	)	PUNCT
ejpam-4756	293	6	is	be	AUX
ejpam-4756	293	7	non	non	ADJ
ejpam-4756	293	8	-	-	ADJ
ejpam-4756	293	9	increasing	increase	VERB
ejpam-4756	293	10	and	and	CCONJ
ejpam-4756	293	11	positive	positive	ADJ
ejpam-4756	293	12	,	,	PUNCT
ejpam-4756	293	13	thus	thus	ADV
ejpam-4756	293	14	using	use	VERB
ejpam-4756	293	15	second	second	ADJ
ejpam-4756	293	16	mean	mean	NOUN
ejpam-4756	293	17	value	value	NOUN
ejpam-4756	293	18	theorem	theorem	NOUN
ejpam-4756	293	19	of	of	ADP
ejpam-4756	293	20	the	the	DET
ejpam-4756	293	21	integral	integral	ADJ
ejpam-4756	293	22	calculus	calculus	NOUN
ejpam-4756	293	23	,	,	PUNCT
ejpam-4756	293	24	we	we	PRON
ejpam-4756	293	25	have	have	VERB
ejpam-4756	293	26	eν(g	eν(g	NOUN
ejpam-4756	293	27	)	)	PUNCT
ejpam-4756	294	1	=	=	PUNCT
ejpam-4756	295	1	o	o	X
ejpam-4756	296	1	[	[	X
ejpam-4756	296	2	(	(	PUNCT
ejpam-4756	296	3	(	(	PUNCT
ejpam-4756	296	4	1	1	NUM
ejpam-4756	296	5	+	+	NUM
ejpam-4756	296	6	γλ){2π(ν	γλ){2π(ν	NOUN
ejpam-4756	296	7	+	+	X
ejpam-4756	297	1	1)−	1)−	NUM
ejpam-4756	297	2	1	1	NUM
ejpam-4756	297	3	}	}	PUNCT
ejpam-4756	297	4	(	(	PUNCT
ejpam-4756	297	5	ν	ν	X
ejpam-4756	297	6	+	+	NOUN
ejpam-4756	297	7	1)γλ{π(ν	1)γλ{π(ν	NUM
ejpam-4756	297	8	+	+	SYM
ejpam-4756	297	9	1)−	1)−	NUM
ejpam-4756	297	10	1	1	NUM
ejpam-4756	297	11	}	}	PUNCT
ejpam-4756	297	12	)	)	PUNCT
ejpam-4756	297	13	(	(	PUNCT
ejpam-4756	297	14	ν	ν	X
ejpam-4756	297	15	+	+	NOUN
ejpam-4756	297	16	1	1	NUM
ejpam-4756	297	17	)	)	PUNCT
ejpam-4756	297	18	η1	η1	NOUN
ejpam-4756	297	19	(	(	PUNCT
ejpam-4756	297	20	1	1	NUM
ejpam-4756	297	21	ν+1	ν+1	PROPN
ejpam-4756	297	22	)	)	PUNCT
ejpam-4756	297	23	η2	η2	PROPN
ejpam-4756	297	24	(	(	PUNCT
ejpam-4756	297	25	1	1	NUM
ejpam-4756	297	26	ν+1	ν+1	PROPN
ejpam-4756	297	27	)	)	PUNCT
ejpam-4756	297	28	∫	∫	PROPN
ejpam-4756	298	1	π	π	NOUN
ejpam-4756	298	2	1	1	NUM
ejpam-4756	298	3	ν+1	ν+1	PROPN
ejpam-4756	298	4	1	1	NUM
ejpam-4756	298	5	w	w	PROPN
ejpam-4756	298	6	dw	dw	PROPN
ejpam-4756	298	7	]	]	PUNCT
ejpam-4756	298	8	h.	h.	PROPN
ejpam-4756	298	9	k.	k.	PROPN
ejpam-4756	298	10	nigam	nigam	PROPN
ejpam-4756	298	11	,	,	PUNCT
ejpam-4756	298	12	m.	m.	PROPN
ejpam-4756	298	13	k.	k.	PROPN
ejpam-4756	298	14	sah	sah	PROPN
ejpam-4756	298	15	/	/	SYM
ejpam-4756	298	16	eur	eur	PROPN
ejpam-4756	298	17	.	.	PUNCT
ejpam-4756	299	1	j.	j.	PROPN
ejpam-4756	299	2	pure	pure	PROPN
ejpam-4756	299	3	appl	appl	PROPN
ejpam-4756	299	4	.	.	PROPN
ejpam-4756	299	5	math	math	PROPN
ejpam-4756	299	6	,	,	PUNCT
ejpam-4756	299	7	16	16	NUM
ejpam-4756	299	8	(	(	PUNCT
ejpam-4756	299	9	2	2	NUM
ejpam-4756	299	10	)	)	PUNCT
ejpam-4756	299	11	(	(	PUNCT
ejpam-4756	299	12	2023	2023	NUM
ejpam-4756	299	13	)	)	PUNCT
ejpam-4756	299	14	,	,	PUNCT
ejpam-4756	299	15	1302	1302	NUM
ejpam-4756	299	16	-	-	SYM
ejpam-4756	299	17	1317	1317	NUM
ejpam-4756	299	18	1314	1314	NUM
ejpam-4756	299	19	=	=	SYM
ejpam-4756	300	1	o	o	X
ejpam-4756	300	2	[	[	X
ejpam-4756	300	3	(	(	PUNCT
ejpam-4756	300	4	(	(	PUNCT
ejpam-4756	300	5	1	1	NUM
ejpam-4756	300	6	+	+	NUM
ejpam-4756	300	7	γλ){2π(ν	γλ){2π(ν	NOUN
ejpam-4756	301	1	+	+	ADJ
ejpam-4756	301	2	1)−	1)−	NUM
ejpam-4756	301	3	1	1	NUM
ejpam-4756	301	4	}	}	PUNCT
ejpam-4756	301	5	γλ{π(ν	γλ{π(ν	PROPN
ejpam-4756	302	1	+	+	PROPN
ejpam-4756	302	2	1)−	1)−	NUM
ejpam-4756	302	3	1	1	NUM
ejpam-4756	302	4	}	}	PUNCT
ejpam-4756	302	5	)	)	PUNCT
ejpam-4756	302	6	η1	η1	NOUN
ejpam-4756	302	7	(	(	PUNCT
ejpam-4756	302	8	1	1	NUM
ejpam-4756	302	9	ν+1	ν+1	PROPN
ejpam-4756	302	10	)	)	PUNCT
ejpam-4756	302	11	η2	η2	PROPN
ejpam-4756	302	12	(	(	PUNCT
ejpam-4756	302	13	1	1	NUM
ejpam-4756	302	14	ν+1	ν+1	NUM
ejpam-4756	302	15	)	)	PUNCT
ejpam-4756	302	16	log{(ν	log{(ν	NOUN
ejpam-4756	302	17	+	+	CCONJ
ejpam-4756	302	18	1)π	1)π	NUM
ejpam-4756	302	19	}	}	PUNCT
ejpam-4756	302	20	]	]	PUNCT
ejpam-4756	302	21	.	.	PUNCT
ejpam-4756	302	22	.	.	PUNCT
ejpam-4756	303	1	5	5	X
ejpam-4756	303	2	.	.	X
ejpam-4756	303	3	application	application	NOUN
ejpam-4756	303	4	in	in	ADP
ejpam-4756	303	5	this	this	DET
ejpam-4756	303	6	section	section	NOUN
ejpam-4756	303	7	,	,	PUNCT
ejpam-4756	303	8	we	we	PRON
ejpam-4756	303	9	study	study	VERB
ejpam-4756	303	10	an	an	DET
ejpam-4756	303	11	application	application	NOUN
ejpam-4756	303	12	of	of	ADP
ejpam-4756	303	13	our	our	PRON
ejpam-4756	303	14	main	main	ADJ
ejpam-4756	303	15	result	result	NOUN
ejpam-4756	303	16	.	.	PUNCT
ejpam-4756	304	1	we	we	PRON
ejpam-4756	304	2	take	take	VERB
ejpam-4756	304	3	η1	η1	NOUN
ejpam-4756	304	4	(	(	PUNCT
ejpam-4756	304	5	1	1	NUM
ejpam-4756	304	6	ν+1	ν+1	NOUN
ejpam-4756	304	7	)	)	PUNCT
ejpam-4756	304	8	=	=	PUNCT
ejpam-4756	304	9	(	(	PUNCT
ejpam-4756	304	10	1	1	NUM
ejpam-4756	304	11	ν+1	ν+1	NUM
ejpam-4756	304	12	)	)	PUNCT
ejpam-4756	304	13	δ1	δ1	NOUN
ejpam-4756	304	14	,	,	PUNCT
ejpam-4756	304	15	η2	η2	X
ejpam-4756	304	16	(	(	PUNCT
ejpam-4756	304	17	1	1	NUM
ejpam-4756	304	18	ν+1	ν+1	NOUN
ejpam-4756	304	19	)	)	PUNCT
ejpam-4756	304	20	=	=	PUNCT
ejpam-4756	304	21	(	(	PUNCT
ejpam-4756	304	22	1	1	NUM
ejpam-4756	304	23	ν+1	ν+1	NOUN
ejpam-4756	304	24	)	)	PUNCT
ejpam-4756	304	25	δ2	δ2	VERB
ejpam-4756	304	26	,	,	PUNCT
ejpam-4756	304	27	δ1	δ1	NOUN
ejpam-4756	304	28	=	=	SYM
ejpam-4756	304	29	1	1	NUM
ejpam-4756	304	30	,	,	PUNCT
ejpam-4756	304	31	δ2	δ2	VERB
ejpam-4756	304	32	=	=	SYM
ejpam-4756	304	33	0	0	NUM
ejpam-4756	304	34	,	,	PUNCT
ejpam-4756	304	35	and	and	CCONJ
ejpam-4756	304	36	λ	λ	X
ejpam-4756	305	1	=	=	NOUN
ejpam-4756	305	2	2	2	NUM
ejpam-4756	305	3	then	then	ADV
ejpam-4756	305	4	from	from	ADP
ejpam-4756	305	5	theorem	theorem	NOUN
ejpam-4756	305	6	2	2	NUM
ejpam-4756	305	7	,	,	PUNCT
ejpam-4756	305	8	we	we	PRON
ejpam-4756	305	9	have	have	VERB
ejpam-4756	305	10	eν(g	eν(g	NOUN
ejpam-4756	305	11	)	)	PUNCT
ejpam-4756	306	1	=	=	PUNCT
ejpam-4756	307	1	o	o	X
ejpam-4756	308	1	[	[	X
ejpam-4756	308	2	(	(	PUNCT
ejpam-4756	308	3	(	(	PUNCT
ejpam-4756	308	4	1	1	NUM
ejpam-4756	308	5	+	+	NUM
ejpam-4756	308	6	γλ){2π(ν	γλ){2π(ν	NOUN
ejpam-4756	308	7	+	+	ADJ
ejpam-4756	309	1	1)−	1)−	NUM
ejpam-4756	309	2	1	1	NUM
ejpam-4756	309	3	}	}	PUNCT
ejpam-4756	309	4	γλ{π(ν	γλ{π(ν	PROPN
ejpam-4756	310	1	+	+	PROPN
ejpam-4756	310	2	1)−	1)−	PROPN
ejpam-4756	310	3	1	1	NUM
ejpam-4756	310	4	}	}	PUNCT
ejpam-4756	310	5	)	)	PUNCT
ejpam-4756	310	6	1	1	NUM
ejpam-4756	310	7	(	(	PUNCT
ejpam-4756	310	8	ν	ν	X
ejpam-4756	310	9	+	+	NOUN
ejpam-4756	310	10	1	1	X
ejpam-4756	310	11	)	)	PUNCT
ejpam-4756	310	12	log{(ν	log{(ν	NOUN
ejpam-4756	310	13	+	+	CCONJ
ejpam-4756	310	14	1)π	1)π	NUM
ejpam-4756	310	15	}	}	PUNCT
ejpam-4756	310	16	]	]	PUNCT
ejpam-4756	310	17	.	.	PUNCT
ejpam-4756	311	1	table	table	NOUN
ejpam-4756	311	2	1	1	NUM
ejpam-4756	311	3	:	:	PUNCT
ejpam-4756	311	4	degree	degree	NOUN
ejpam-4756	311	5	of	of	ADP
ejpam-4756	311	6	convergence	convergence	NOUN
ejpam-4756	311	7	of	of	ADP
ejpam-4756	311	8	g	g	NOUN
ejpam-4756	311	9	for	for	ADP
ejpam-4756	311	10	different	different	ADJ
ejpam-4756	311	11	ν	ν	NOUN
ejpam-4756	311	12	.	.	PUNCT
ejpam-4756	312	1	ν	ν	NOUN
ejpam-4756	312	2	degree	degree	NOUN
ejpam-4756	312	3	of	of	ADP
ejpam-4756	312	4	convergence	convergence	NOUN
ejpam-4756	312	5	of	of	ADP
ejpam-4756	312	6	g	g	PROPN
ejpam-4756	312	7	1000	1000	NUM
ejpam-4756	312	8	0.0322	0.0322	NUM
ejpam-4756	312	9	10000	10000	NUM
ejpam-4756	312	10	0.0041	0.0041	NUM
ejpam-4756	312	11	50000	50000	NUM
ejpam-4756	312	12	0.0009572	0.0009572	NUM
ejpam-4756	312	13	100000	100000	NUM
ejpam-4756	312	14	0.0005063	0.0005063	NUM
ejpam-4756	312	15	500000	500000	NUM
ejpam-4756	312	16	0.00011414	0.00011414	NUM
ejpam-4756	312	17	1000000	1000000	NUM
ejpam-4756	312	18	0.000005984	0.000005984	NUM
ejpam-4756	312	19	.	.	PUNCT
ejpam-4756	312	20	.	.	PUNCT
ejpam-4756	312	21	.	.	PUNCT
ejpam-4756	313	1	.	.	PUNCT
ejpam-4756	314	1	∞	∞	PROPN
ejpam-4756	314	2	0	0	NUM
ejpam-4756	314	3	h.	h.	PROPN
ejpam-4756	314	4	k.	k.	PROPN
ejpam-4756	314	5	nigam	nigam	PROPN
ejpam-4756	314	6	,	,	PUNCT
ejpam-4756	314	7	m.	m.	PROPN
ejpam-4756	314	8	k.	k.	PROPN
ejpam-4756	314	9	sah	sah	PROPN
ejpam-4756	314	10	/	/	SYM
ejpam-4756	314	11	eur	eur	PROPN
ejpam-4756	314	12	.	.	PUNCT
ejpam-4756	315	1	j.	j.	PROPN
ejpam-4756	315	2	pure	pure	PROPN
ejpam-4756	315	3	appl	appl	PROPN
ejpam-4756	315	4	.	.	PROPN
ejpam-4756	315	5	math	math	PROPN
ejpam-4756	315	6	,	,	PUNCT
ejpam-4756	315	7	16	16	NUM
ejpam-4756	315	8	(	(	PUNCT
ejpam-4756	315	9	2	2	NUM
ejpam-4756	315	10	)	)	PUNCT
ejpam-4756	315	11	(	(	PUNCT
ejpam-4756	315	12	2023	2023	NUM
ejpam-4756	315	13	)	)	PUNCT
ejpam-4756	315	14	,	,	PUNCT
ejpam-4756	315	15	1302	1302	NUM
ejpam-4756	315	16	-	-	SYM
ejpam-4756	315	17	1317	1317	NUM
ejpam-4756	315	18	1315	1315	NUM
ejpam-4756	315	19	(	(	PUNCT
ejpam-4756	315	20	a	a	NOUN
ejpam-4756	315	21	)	)	PUNCT
ejpam-4756	315	22	for	for	ADP
ejpam-4756	315	23	ν	ν	NOUN
ejpam-4756	315	24	=	=	SYM
ejpam-4756	315	25	50000	50000	NUM
ejpam-4756	315	26	(	(	PUNCT
ejpam-4756	315	27	b	b	NOUN
ejpam-4756	315	28	)	)	PUNCT
ejpam-4756	315	29	for	for	ADP
ejpam-4756	315	30	ν	ν	NOUN
ejpam-4756	315	31	=	=	SYM
ejpam-4756	315	32	100000	100000	NUM
ejpam-4756	315	33	(	(	PUNCT
ejpam-4756	315	34	c	c	NOUN
ejpam-4756	315	35	)	)	PUNCT
ejpam-4756	315	36	for	for	ADP
ejpam-4756	315	37	ν	ν	X
ejpam-4756	315	38	=	=	SYM
ejpam-4756	315	39	500000	500000	NUM
ejpam-4756	315	40	(	(	PUNCT
ejpam-4756	315	41	d	d	NOUN
ejpam-4756	315	42	)	)	PUNCT
ejpam-4756	315	43	for	for	ADP
ejpam-4756	315	44	ν	ν	X
ejpam-4756	315	45	=	=	SYM
ejpam-4756	315	46	1000000	1000000	NUM
ejpam-4756	315	47	figure	figure	NOUN
ejpam-4756	315	48	1	1	NUM
ejpam-4756	315	49	:	:	PUNCT
ejpam-4756	315	50	degree	degree	NOUN
ejpam-4756	315	51	of	of	ADP
ejpam-4756	315	52	convergence	convergence	NOUN
ejpam-4756	315	53	of	of	ADP
ejpam-4756	315	54	function	function	NOUN
ejpam-4756	315	55	g.	g.	PROPN
ejpam-4756	315	56	6	6	NUM
ejpam-4756	315	57	.	.	PUNCT
ejpam-4756	316	1	conclusion	conclusion	NOUN
ejpam-4756	316	2	from	from	ADP
ejpam-4756	316	3	the	the	DET
ejpam-4756	316	4	table	table	NOUN
ejpam-4756	316	5	1	1	NUM
ejpam-4756	316	6	and	and	CCONJ
ejpam-4756	316	7	figures	figure	NOUN
ejpam-4756	316	8	1(a	1(a	NUM
ejpam-4756	316	9	)	)	PUNCT
ejpam-4756	316	10	to	to	ADP
ejpam-4756	316	11	1(d	1(d	NUM
ejpam-4756	316	12	)	)	PUNCT
ejpam-4756	316	13	,	,	PUNCT
ejpam-4756	316	14	we	we	PRON
ejpam-4756	316	15	observed	observe	VERB
ejpam-4756	316	16	that	that	SCONJ
ejpam-4756	316	17	the	the	DET
ejpam-4756	316	18	error	error	NOUN
ejpam-4756	316	19	estimation	estimation	NOUN
ejpam-4756	316	20	tends	tend	VERB
ejpam-4756	316	21	to	to	ADP
ejpam-4756	316	22	zero	zero	NUM
ejpam-4756	316	23	rapidely	rapidely	ADV
ejpam-4756	316	24	as	as	SCONJ
ejpam-4756	316	25	ν	ν	PROPN
ejpam-4756	316	26	tends	tend	VERB
ejpam-4756	316	27	to	to	PART
ejpam-4756	316	28	infinity	infinity	VERB
ejpam-4756	316	29	.	.	PUNCT
ejpam-4756	317	1	thus	thus	ADV
ejpam-4756	317	2	,	,	PUNCT
ejpam-4756	317	3	the	the	DET
ejpam-4756	317	4	results	result	NOUN
ejpam-4756	317	5	obtained	obtain	VERB
ejpam-4756	317	6	in	in	ADP
ejpam-4756	317	7	theorems	theorem	NOUN
ejpam-4756	317	8	1	1	NUM
ejpam-4756	317	9	and	and	CCONJ
ejpam-4756	317	10	2	2	NUM
ejpam-4756	317	11	provide	provide	VERB
ejpam-4756	317	12	the	the	DET
ejpam-4756	317	13	best	good	ADJ
ejpam-4756	317	14	approximation	approximation	NOUN
ejpam-4756	317	15	of	of	ADP
ejpam-4756	317	16	the	the	DET
ejpam-4756	317	17	function	function	NOUN
ejpam-4756	317	18	g	g	NOUN
ejpam-4756	317	19	in	in	ADP
ejpam-4756	317	20	generalized	generalized	ADJ
ejpam-4756	317	21	zygmund	zygmund	NOUN
ejpam-4756	317	22	space	space	NOUN
ejpam-4756	317	23	(	(	PUNCT
ejpam-4756	317	24	z	z	NOUN
ejpam-4756	317	25	(	(	PUNCT
ejpam-4756	317	26	η	η	NOUN
ejpam-4756	317	27	)	)	PUNCT
ejpam-4756	317	28	r	r	NOUN
ejpam-4756	317	29	;	;	PUNCT
ejpam-4756	317	30	r	r	NOUN
ejpam-4756	317	31	≥	≥	NOUN
ejpam-4756	317	32	1	1	NUM
ejpam-4756	317	33	)	)	PUNCT
ejpam-4756	317	34	using	use	VERB
ejpam-4756	317	35	karamata	karamata	NOUN
ejpam-4756	317	36	-	-	PUNCT
ejpam-4756	317	37	matrix	matrix	NOUN
ejpam-4756	317	38	(	(	PUNCT
ejpam-4756	317	39	kλa	kλa	NOUN
ejpam-4756	317	40	)	)	PUNCT
ejpam-4756	317	41	product	product	NOUN
ejpam-4756	317	42	operator	operator	NOUN
ejpam-4756	317	43	.	.	PUNCT
ejpam-4756	318	1	acknowledgements	acknowledgement	NOUN
ejpam-4756	318	2	the	the	DET
ejpam-4756	318	3	first	first	ADJ
ejpam-4756	318	4	author	author	NOUN
ejpam-4756	318	5	expresses	express	VERB
ejpam-4756	318	6	his	his	PRON
ejpam-4756	318	7	gratitude	gratitude	NOUN
ejpam-4756	318	8	towards	towards	ADP
ejpam-4756	318	9	his	his	PRON
ejpam-4756	318	10	mother	mother	NOUN
ejpam-4756	318	11	for	for	ADP
ejpam-4756	318	12	her	her	PRON
ejpam-4756	318	13	blessings	blessing	NOUN
ejpam-4756	318	14	.	.	PUNCT
ejpam-4756	319	1	the	the	DET
ejpam-4756	319	2	first	first	ADJ
ejpam-4756	319	3	author	author	NOUN
ejpam-4756	319	4	also	also	ADV
ejpam-4756	319	5	expresses	express	VERB
ejpam-4756	319	6	his	his	PRON
ejpam-4756	319	7	gratitude	gratitude	NOUN
ejpam-4756	319	8	towards	towards	ADP
ejpam-4756	319	9	his	his	PRON
ejpam-4756	319	10	father	father	NOUN
ejpam-4756	319	11	in	in	ADP
ejpam-4756	319	12	heaven	heaven	PROPN
ejpam-4756	319	13	whose	whose	DET
ejpam-4756	319	14	soul	soul	NOUN
ejpam-4756	319	15	is	be	AUX
ejpam-4756	319	16	always	always	ADV
ejpam-4756	319	17	guiding	guide	VERB
ejpam-4756	319	18	and	and	CCONJ
ejpam-4756	319	19	encouraging	encourage	VERB
ejpam-4756	319	20	him	he	PRON
ejpam-4756	319	21	.	.	PUNCT
ejpam-4756	320	1	the	the	DET
ejpam-4756	320	2	second	second	ADJ
ejpam-4756	320	3	author	author	NOUN
ejpam-4756	320	4	also	also	ADV
ejpam-4756	320	5	expresses	express	VERB
ejpam-4756	320	6	his	his	PRON
ejpam-4756	320	7	gratitude	gratitude	NOUN
ejpam-4756	320	8	towards	towards	ADP
ejpam-4756	320	9	his	his	PRON
ejpam-4756	320	10	references	reference	NOUN
ejpam-4756	320	11	1316	1316	NUM
ejpam-4756	320	12	parents	parent	NOUN
ejpam-4756	320	13	for	for	ADP
ejpam-4756	320	14	their	their	PRON
ejpam-4756	320	15	blessings	blessing	NOUN
ejpam-4756	320	16	and	and	CCONJ
ejpam-4756	320	17	encouragement	encouragement	NOUN
ejpam-4756	320	18	.	.	PUNCT
ejpam-4756	321	1	both	both	CCONJ
ejpam-4756	321	2	the	the	DET
ejpam-4756	321	3	authors	author	NOUN
ejpam-4756	321	4	wish	wish	VERB
ejpam-4756	321	5	to	to	PART
ejpam-4756	321	6	thank	thank	VERB
ejpam-4756	321	7	the	the	DET
ejpam-4756	321	8	referees	referee	NOUN
ejpam-4756	321	9	for	for	ADP
ejpam-4756	321	10	their	their	PRON
ejpam-4756	321	11	insightful	insightful	ADJ
ejpam-4756	321	12	comments	comment	NOUN
ejpam-4756	321	13	and	and	CCONJ
ejpam-4756	321	14	valuable	valuable	ADJ
ejpam-4756	321	15	suggestions	suggestion	NOUN
ejpam-4756	321	16	for	for	ADP
ejpam-4756	321	17	improvement	improvement	NOUN
ejpam-4756	321	18	of	of	ADP
ejpam-4756	321	19	the	the	DET
ejpam-4756	321	20	paper	paper	NOUN
ejpam-4756	321	21	.	.	PUNCT
ejpam-4756	322	1	references	reference	NOUN
ejpam-4756	322	2	[	[	X
ejpam-4756	322	3	1	1	NUM
ejpam-4756	322	4	]	]	X
ejpam-4756	322	5	agnew	agnew	PROPN
ejpam-4756	322	6	,	,	PUNCT
ejpam-4756	322	7	r.	r.	PROPN
ejpam-4756	322	8	p.	p.	PROPN
ejpam-4756	322	9	the	the	DET
ejpam-4756	322	10	lototsky	lototsky	ADJ
ejpam-4756	322	11	method	method	NOUN
ejpam-4756	322	12	for	for	ADP
ejpam-4756	322	13	evaluation	evaluation	NOUN
ejpam-4756	322	14	of	of	ADP
ejpam-4756	322	15	series	series	NOUN
ejpam-4756	322	16	.	.	PUNCT
ejpam-4756	323	1	the	the	DET
ejpam-4756	323	2	michigan	michigan	PROPN
ejpam-4756	323	3	mathematical	mathematical	PROPN
ejpam-4756	323	4	journal	journal	PROPN
ejpam-4756	323	5	,	,	PUNCT
ejpam-4756	323	6	4(2):105–128	4(2):105–128	NUM
ejpam-4756	323	7	,	,	PUNCT
ejpam-4756	323	8	1957	1957	NUM
ejpam-4756	323	9	.	.	PUNCT
ejpam-4756	324	1	[	[	X
ejpam-4756	324	2	2	2	NUM
ejpam-4756	324	3	]	]	PUNCT
ejpam-4756	324	4	c.	c.	PROPN
ejpam-4756	324	5	k.	k.	PROPN
ejpam-4756	324	6	chui	chui	PROPN
ejpam-4756	324	7	.	.	PUNCT
ejpam-4756	325	1	an	an	DET
ejpam-4756	325	2	introduction	introduction	NOUN
ejpam-4756	325	3	to	to	ADP
ejpam-4756	325	4	wavelets	wavelet	NOUN
ejpam-4756	325	5	,	,	PUNCT
ejpam-4756	325	6	volume	volume	NOUN
ejpam-4756	325	7	1	1	NUM
ejpam-4756	325	8	.	.	PUNCT
ejpam-4756	325	9	academic	academic	ADJ
ejpam-4756	325	10	press	press	NOUN
ejpam-4756	325	11	,	,	PUNCT
ejpam-4756	325	12	1992	1992	NUM
ejpam-4756	325	13	.	.	PUNCT
ejpam-4756	326	1	[	[	X
ejpam-4756	326	2	3	3	X
ejpam-4756	326	3	]	]	X
ejpam-4756	326	4	j.	j.	PROPN
ejpam-4756	326	5	karamata	karamata	PROPN
ejpam-4756	326	6	.	.	PUNCT
ejpam-4756	327	1	théorèmes	théorèmes	PROPN
ejpam-4756	327	2	sur	sur	PROPN
ejpam-4756	327	3	la	la	PROPN
ejpam-4756	327	4	sommabilité	sommabilité	NOUN
ejpam-4756	327	5	exponentielle	exponentielle	NOUN
ejpam-4756	327	6	et	et	NOUN
ejpam-4756	327	7	d’autres	d’autre	VERB
ejpam-4756	327	8	sommabilités	sommabilités	PROPN
ejpam-4756	327	9	s’y	s’y	PROPN
ejpam-4756	327	10	rattachant	rattachant	PROPN
ejpam-4756	327	11	.	.	PUNCT
ejpam-4756	328	1	1935	1935	NUM
ejpam-4756	328	2	.	.	PUNCT
ejpam-4756	329	1	[	[	X
ejpam-4756	329	2	4	4	NUM
ejpam-4756	329	3	]	]	PUNCT
ejpam-4756	329	4	nigam	nigam	PROPN
ejpam-4756	329	5	hare	hare	PROPN
ejpam-4756	329	6	krishna	krishna	PROPN
ejpam-4756	329	7	.	.	PUNCT
ejpam-4756	330	1	trigonometric	trigonometric	ADJ
ejpam-4756	330	2	approximation	approximation	NOUN
ejpam-4756	330	3	of	of	ADP
ejpam-4756	330	4	functions	function	NOUN
ejpam-4756	330	5	by	by	ADP
ejpam-4756	330	6	hausdorff	hausdorff	NOUN
ejpam-4756	330	7	-	-	PUNCT
ejpam-4756	330	8	matrix	matrix	NOUN
ejpam-4756	330	9	product	product	NOUN
ejpam-4756	330	10	operators	operator	NOUN
ejpam-4756	330	11	.	.	PUNCT
ejpam-4756	331	1	nonlinear	nonlinear	ADJ
ejpam-4756	331	2	functional	functional	ADJ
ejpam-4756	331	3	analysis	analysis	NOUN
ejpam-4756	331	4	and	and	CCONJ
ejpam-4756	331	5	applications	application	NOUN
ejpam-4756	331	6	,	,	PUNCT
ejpam-4756	331	7	24(4):675–689	24(4):675–689	PROPN
ejpam-4756	331	8	,	,	PUNCT
ejpam-4756	331	9	2019	2019	NUM
ejpam-4756	331	10	.	.	PUNCT
ejpam-4756	332	1	[	[	X
ejpam-4756	332	2	5	5	X
ejpam-4756	332	3	]	]	X
ejpam-4756	332	4	shyam	shyam	PROPN
ejpam-4756	332	5	lal	lal	PROPN
ejpam-4756	332	6	.	.	PUNCT
ejpam-4756	333	1	approximation	approximation	NOUN
ejpam-4756	333	2	of	of	ADP
ejpam-4756	333	3	functions	function	NOUN
ejpam-4756	333	4	belonging	belong	VERB
ejpam-4756	333	5	to	to	ADP
ejpam-4756	333	6	the	the	DET
ejpam-4756	333	7	generalized	generalize	VERB
ejpam-4756	333	8	lipschitz	lipschitz	NOUN
ejpam-4756	333	9	class	class	NOUN
ejpam-4756	333	10	by	by	ADP
ejpam-4756	333	11	c1npsummability	c1npsummability	NOUN
ejpam-4756	333	12	method	method	NOUN
ejpam-4756	333	13	of	of	ADP
ejpam-4756	333	14	fourier	fourier	ADJ
ejpam-4756	333	15	series	series	NOUN
ejpam-4756	333	16	.	.	PUNCT
ejpam-4756	334	1	applied	apply	VERB
ejpam-4756	334	2	mathematics	mathematic	NOUN
ejpam-4756	334	3	and	and	CCONJ
ejpam-4756	334	4	computation	computation	NOUN
ejpam-4756	334	5	,	,	PUNCT
ejpam-4756	334	6	209(2):346–350	209(2):346–350	NUM
ejpam-4756	334	7	,	,	PUNCT
ejpam-4756	334	8	2009	2009	NUM
ejpam-4756	334	9	.	.	PUNCT
ejpam-4756	335	1	[	[	X
ejpam-4756	335	2	6	6	NUM
ejpam-4756	335	3	]	]	X
ejpam-4756	335	4	shyam	shyam	PROPN
ejpam-4756	335	5	lal	lal	PROPN
ejpam-4756	335	6	and	and	CCONJ
ejpam-4756	335	7	abhishek	abhishek	PROPN
ejpam-4756	335	8	mishra	mishra	PROPN
ejpam-4756	335	9	.	.	PUNCT
ejpam-4756	336	1	the	the	DET
ejpam-4756	336	2	method	method	NOUN
ejpam-4756	336	3	of	of	ADP
ejpam-4756	336	4	summation	summation	NOUN
ejpam-4756	336	5	(	(	PUNCT
ejpam-4756	336	6	e	e	NOUN
ejpam-4756	336	7	,	,	PUNCT
ejpam-4756	336	8	1)(n	1)(n	NUM
ejpam-4756	336	9	,	,	PUNCT
ejpam-4756	336	10	pn	pn	NOUN
ejpam-4756	336	11	)	)	PUNCT
ejpam-4756	336	12	and	and	CCONJ
ejpam-4756	336	13	trigonometric	trigonometric	ADJ
ejpam-4756	336	14	approximation	approximation	NOUN
ejpam-4756	336	15	of	of	ADP
ejpam-4756	336	16	functions	function	NOUN
ejpam-4756	336	17	in	in	ADP
ejpam-4756	336	18	generalized	generalized	ADJ
ejpam-4756	336	19	holder	holder	NOUN
ejpam-4756	336	20	metric	metric	NOUN
ejpam-4756	336	21	.	.	PUNCT
ejpam-4756	337	1	journal	journal	PROPN
ejpam-4756	337	2	of	of	ADP
ejpam-4756	337	3	the	the	DET
ejpam-4756	337	4	indian	indian	PROPN
ejpam-4756	337	5	mathematical	mathematical	ADJ
ejpam-4756	337	6	society	society	NOUN
ejpam-4756	337	7	,	,	PUNCT
ejpam-4756	337	8	80:87–98	80:87–98	NUM
ejpam-4756	337	9	,	,	PUNCT
ejpam-4756	337	10	2013	2013	NUM
ejpam-4756	337	11	.	.	PUNCT
ejpam-4756	338	1	[	[	X
ejpam-4756	338	2	7	7	X
ejpam-4756	338	3	]	]	X
ejpam-4756	338	4	b.	b.	PROPN
ejpam-4756	338	5	a.	a.	PROPN
ejpam-4756	338	6	landon	landon	PROPN
ejpam-4756	338	7	.	.	PUNCT
ejpam-4756	338	8	degree	degree	NOUN
ejpam-4756	338	9	of	of	ADP
ejpam-4756	338	10	approximation	approximation	NOUN
ejpam-4756	338	11	of	of	ADP
ejpam-4756	338	12	hölder	hölder	NOUN
ejpam-4756	338	13	continuous	continuous	ADJ
ejpam-4756	338	14	functions	function	NOUN
ejpam-4756	338	15	.	.	PUNCT
ejpam-4756	339	1	university	university	NOUN
ejpam-4756	339	2	of	of	ADP
ejpam-4756	339	3	central	central	PROPN
ejpam-4756	339	4	florida	florida	PROPN
ejpam-4756	339	5	,	,	PUNCT
ejpam-4756	339	6	2008	2008	NUM
ejpam-4756	339	7	.	.	PUNCT
ejpam-4756	340	1	[	[	X
ejpam-4756	340	2	8	8	NUM
ejpam-4756	340	3	]	]	X
ejpam-4756	340	4	a.	a.	NOUN
ejpam-4756	340	5	v.	v.	ADP
ejpam-4756	340	6	lototsky	lototsky	PROPN
ejpam-4756	340	7	.	.	PUNCT
ejpam-4756	341	1	on	on	ADP
ejpam-4756	341	2	a	a	DET
ejpam-4756	341	3	linear	linear	ADJ
ejpam-4756	341	4	transformation	transformation	NOUN
ejpam-4756	341	5	of	of	ADP
ejpam-4756	341	6	sequences	sequence	NOUN
ejpam-4756	341	7	and	and	CCONJ
ejpam-4756	341	8	series	series	NOUN
ejpam-4756	341	9	.	.	PUNCT
ejpam-4756	342	1	ped	ped	PROPN
ejpam-4756	342	2	.	.	PROPN
ejpam-4756	342	3	inst	inst	PROPN
ejpam-4756	342	4	.	.	PUNCT
ejpam-4756	343	1	uch	uch	PROPN
ejpam-4756	343	2	.	.	PUNCT
ejpam-4756	343	3	zap	zap	PROPN
ejpam-4756	343	4	.	.	PUNCT
ejpam-4756	344	1	fix	fix	NOUN
ejpam-4756	344	2	-	-	PUNCT
ejpam-4756	344	3	mat	mat	NOUN
ejpam-4756	344	4	.	.	PROPN
ejpam-4756	344	5	nauki	nauki	PROPN
ejpam-4756	344	6	,	,	PUNCT
ejpam-4756	344	7	4:61–91	4:61–91	NUM
ejpam-4756	344	8	,	,	PUNCT
ejpam-4756	344	9	1953	1953	NUM
ejpam-4756	344	10	.	.	PUNCT
ejpam-4756	345	1	[	[	X
ejpam-4756	345	2	9	9	NUM
ejpam-4756	345	3	]	]	PUNCT
ejpam-4756	345	4	h.	h.	PROPN
ejpam-4756	345	5	k.	k.	PROPN
ejpam-4756	345	6	nigam	nigam	PROPN
ejpam-4756	345	7	.	.	PUNCT
ejpam-4756	345	8	degree	degree	NOUN
ejpam-4756	345	9	of	of	ADP
ejpam-4756	345	10	approximation	approximation	NOUN
ejpam-4756	345	11	of	of	ADP
ejpam-4756	345	12	a	a	DET
ejpam-4756	345	13	function	function	NOUN
ejpam-4756	345	14	belonging	belong	VERB
ejpam-4756	345	15	to	to	ADP
ejpam-4756	345	16	weighted	weight	VERB
ejpam-4756	345	17	(	(	PUNCT
ejpam-4756	345	18	lr	lr	INTJ
ejpam-4756	345	19	,	,	PUNCT
ejpam-4756	345	20	ξ(t	ξ(t	NOUN
ejpam-4756	345	21	)	)	PUNCT
ejpam-4756	345	22	)	)	PUNCT
ejpam-4756	345	23	class	class	NOUN
ejpam-4756	345	24	by	by	ADP
ejpam-4756	345	25	(	(	PUNCT
ejpam-4756	345	26	c	c	NOUN
ejpam-4756	345	27	,	,	PUNCT
ejpam-4756	345	28	1)(e	1)(e	NUM
ejpam-4756	345	29	,	,	PUNCT
ejpam-4756	345	30	q	q	NOUN
ejpam-4756	345	31	)	)	PUNCT
ejpam-4756	345	32	means	mean	NOUN
ejpam-4756	345	33	.	.	PUNCT
ejpam-4756	346	1	tamkang	tamkang	PROPN
ejpam-4756	346	2	journal	journal	PROPN
ejpam-4756	346	3	of	of	ADP
ejpam-4756	346	4	mathematics	mathematic	NOUN
ejpam-4756	346	5	,	,	PUNCT
ejpam-4756	346	6	42(1):31–37	42(1):31–37	NOUN
ejpam-4756	346	7	,	,	PUNCT
ejpam-4756	346	8	2011	2011	NUM
ejpam-4756	346	9	.	.	PUNCT
ejpam-4756	347	1	[	[	X
ejpam-4756	347	2	10	10	NUM
ejpam-4756	347	3	]	]	X
ejpam-4756	347	4	h.	h.	PROPN
ejpam-4756	347	5	k.	k.	PROPN
ejpam-4756	347	6	nigam	nigam	PROPN
ejpam-4756	347	7	and	and	CCONJ
ejpam-4756	347	8	md	md	PROPN
ejpam-4756	347	9	.	.	PROPN
ejpam-4756	347	10	hadish	hadish	PROPN
ejpam-4756	347	11	.	.	PUNCT
ejpam-4756	348	1	best	good	ADJ
ejpam-4756	348	2	approximation	approximation	NOUN
ejpam-4756	348	3	of	of	ADP
ejpam-4756	348	4	functions	function	NOUN
ejpam-4756	348	5	in	in	ADP
ejpam-4756	348	6	generalized	generalized	ADJ
ejpam-4756	348	7	hölder	hölder	NOUN
ejpam-4756	348	8	class	class	NOUN
ejpam-4756	348	9	.	.	PUNCT
ejpam-4756	349	1	journal	journal	PROPN
ejpam-4756	349	2	of	of	ADP
ejpam-4756	349	3	inequalities	inequality	NOUN
ejpam-4756	349	4	and	and	CCONJ
ejpam-4756	349	5	applications	application	NOUN
ejpam-4756	349	6	,	,	PUNCT
ejpam-4756	349	7	2018(1):1–15	2018(1):1–15	NOUN
ejpam-4756	349	8	,	,	PUNCT
ejpam-4756	349	9	2018	2018	NUM
ejpam-4756	349	10	.	.	PUNCT
ejpam-4756	350	1	[	[	X
ejpam-4756	350	2	11	11	NUM
ejpam-4756	350	3	]	]	X
ejpam-4756	350	4	hk	hk	PROPN
ejpam-4756	350	5	nigam	nigam	PROPN
ejpam-4756	350	6	and	and	CCONJ
ejpam-4756	350	7	md	md	PROPN
ejpam-4756	350	8	hadish	hadish	PROPN
ejpam-4756	350	9	.	.	PUNCT
ejpam-4756	351	1	approximation	approximation	NOUN
ejpam-4756	351	2	of	of	ADP
ejpam-4756	351	3	a	a	DET
ejpam-4756	351	4	function	function	NOUN
ejpam-4756	351	5	in	in	ADP
ejpam-4756	351	6	holder	holder	NOUN
ejpam-4756	351	7	class	class	NOUN
ejpam-4756	351	8	using	use	VERB
ejpam-4756	351	9	double	double	ADJ
ejpam-4756	351	10	karamata	karamata	NOUN
ejpam-4756	351	11	(	(	PUNCT
ejpam-4756	351	12	kλ,µ	kλ,µ	NOUN
ejpam-4756	351	13	)	)	PUNCT
ejpam-4756	351	14	method	method	NOUN
ejpam-4756	351	15	.	.	PUNCT
ejpam-4756	352	1	european	european	PROPN
ejpam-4756	352	2	journal	journal	PROPN
ejpam-4756	352	3	of	of	ADP
ejpam-4756	352	4	pure	pure	ADJ
ejpam-4756	352	5	and	and	CCONJ
ejpam-4756	352	6	applied	applied	ADJ
ejpam-4756	352	7	mathematics	mathematic	NOUN
ejpam-4756	352	8	,	,	PUNCT
ejpam-4756	352	9	13(3):567–578	13(3):567–578	PROPN
ejpam-4756	352	10	,	,	PUNCT
ejpam-4756	352	11	2020	2020	NUM
ejpam-4756	352	12	.	.	PUNCT
ejpam-4756	353	1	[	[	X
ejpam-4756	353	2	12	12	NUM
ejpam-4756	353	3	]	]	PUNCT
ejpam-4756	353	4	supriya	supriya	PROPN
ejpam-4756	353	5	rani	rani	PROPN
ejpam-4756	353	6	and	and	CCONJ
ejpam-4756	353	7	hk	hk	PROPN
ejpam-4756	353	8	nigam	nigam	PROPN
ejpam-4756	353	9	.	.	PUNCT
ejpam-4756	354	1	approximation	approximation	NOUN
ejpam-4756	354	2	of	of	ADP
ejpam-4756	354	3	function	function	NOUN
ejpam-4756	354	4	in	in	ADP
ejpam-4756	354	5	generalized	generalized	ADJ
ejpam-4756	354	6	holder	holder	NOUN
ejpam-4756	354	7	class	class	NOUN
ejpam-4756	354	8	.	.	PUNCT
ejpam-4756	355	1	european	european	PROPN
ejpam-4756	355	2	journal	journal	PROPN
ejpam-4756	355	3	of	of	ADP
ejpam-4756	355	4	pure	pure	ADJ
ejpam-4756	355	5	and	and	CCONJ
ejpam-4756	355	6	applied	applied	ADJ
ejpam-4756	355	7	mathematics	mathematic	NOUN
ejpam-4756	355	8	,	,	PUNCT
ejpam-4756	355	9	13(2):351–368	13(2):351–368	PROPN
ejpam-4756	355	10	,	,	PUNCT
ejpam-4756	355	11	2020	2020	NUM
ejpam-4756	355	12	.	.	PUNCT
ejpam-4756	356	1	[	[	X
ejpam-4756	356	2	13	13	NUM
ejpam-4756	356	3	]	]	PUNCT
ejpam-4756	356	4	titchmarsh	titchmarsh	NOUN
ejpam-4756	356	5	,	,	PUNCT
ejpam-4756	356	6	e.	e.	PROPN
ejpam-4756	356	7	c.	c.	PROPN
ejpam-4756	356	8	.	.	PUNCT
ejpam-4756	357	1	the	the	DET
ejpam-4756	357	2	theory	theory	NOUN
ejpam-4756	357	3	of	of	ADP
ejpam-4756	357	4	functions	function	NOUN
ejpam-4756	357	5	.	.	PUNCT
ejpam-4756	358	1	oxford	oxford	PROPN
ejpam-4756	358	2	university	university	PROPN
ejpam-4756	358	3	press	press	PROPN
ejpam-4756	358	4	,	,	PUNCT
ejpam-4756	358	5	london	london	PROPN
ejpam-4756	358	6	,	,	PUNCT
ejpam-4756	358	7	1939	1939	NUM
ejpam-4756	358	8	.	.	PUNCT
ejpam-4756	359	1	references	reference	NOUN
ejpam-4756	359	2	1317	1317	NUM
ejpam-4756	359	3	[	[	X
ejpam-4756	359	4	14	14	NUM
ejpam-4756	359	5	]	]	PUNCT
ejpam-4756	359	6	toeplitz	toeplitz	NOUN
ejpam-4756	359	7	,	,	PUNCT
ejpam-4756	359	8	o.	o.	PROPN
ejpam-4756	359	9	über	über	PROPN
ejpam-4756	359	10	allgemeine	allgemeine	PROPN
ejpam-4756	359	11	lineare	lineare	PROPN
ejpam-4756	359	12	mittelbildungen	mittelbildungen	NOUN
ejpam-4756	359	13	.	.	PUNCT
ejpam-4756	360	1	prace	prace	PROPN
ejpam-4756	360	2	matematycznofizyczne	matematycznofizyczne	PROPN
ejpam-4756	360	3	,	,	PUNCT
ejpam-4756	360	4	22(1):113–119	22(1):113–119	PROPN
ejpam-4756	360	5	,	,	PUNCT
ejpam-4756	360	6	1911	1911	NUM
ejpam-4756	360	7	.	.	PUNCT
ejpam-4756	361	1	[	[	X
ejpam-4756	361	2	15	15	NUM
ejpam-4756	361	3	]	]	PUNCT
ejpam-4756	361	4	a.	a.	NOUN
ejpam-4756	361	5	zygmund	zygmund	PROPN
ejpam-4756	361	6	.	.	PUNCT
ejpam-4756	362	1	trigonometric	trigonometric	PROPN
ejpam-4756	362	2	series	series	NOUN
ejpam-4756	362	3	,	,	PUNCT
ejpam-4756	362	4	volume	volume	NOUN
ejpam-4756	362	5	1	1	NUM
ejpam-4756	362	6	.	.	PUNCT
ejpam-4756	362	7	cambridge	cambridge	PROPN
ejpam-4756	362	8	university	university	PROPN
ejpam-4756	362	9	press	press	NOUN
ejpam-4756	362	10	,	,	PUNCT
ejpam-4756	362	11	2002	2002	NUM
ejpam-4756	362	12	.	.	PUNCT