id	sid	tid	token	lemma	pos
ejpam-3714	1	1	european	european	PROPN
ejpam-3714	1	2	journal	journal	PROPN
ejpam-3714	1	3	of	of	ADP
ejpam-3714	1	4	pure	pure	ADJ
ejpam-3714	1	5	and	and	CCONJ
ejpam-3714	1	6	applied	apply	VERB
ejpam-3714	1	7	mathematics	mathematic	NOUN
ejpam-3714	1	8	vol	vol	NOUN
ejpam-3714	1	9	.	.	PROPN
ejpam-3714	2	1	13	13	NUM
ejpam-3714	2	2	,	,	PUNCT
ejpam-3714	2	3	no	no	INTJ
ejpam-3714	2	4	.	.	NOUN
ejpam-3714	2	5	5	5	NUM
ejpam-3714	2	6	,	,	PUNCT
ejpam-3714	2	7	2020	2020	NUM
ejpam-3714	2	8	,	,	PUNCT
ejpam-3714	2	9	1325	1325	NUM
ejpam-3714	2	10	-	-	SYM
ejpam-3714	2	11	1336	1336	NUM
ejpam-3714	2	12	issn	issn	PROPN
ejpam-3714	2	13	1307	1307	NUM
ejpam-3714	2	14	-	-	SYM
ejpam-3714	2	15	5543	5543	NUM
ejpam-3714	2	16	–	–	PUNCT
ejpam-3714	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3714	2	18	published	publish	VERB
ejpam-3714	2	19	by	by	ADP
ejpam-3714	2	20	new	new	PROPN
ejpam-3714	2	21	york	york	PROPN
ejpam-3714	2	22	business	business	PROPN
ejpam-3714	2	23	global	global	ADJ
ejpam-3714	2	24	special	special	ADJ
ejpam-3714	2	25	issue	issue	NOUN
ejpam-3714	2	26	dedicated	dedicate	VERB
ejpam-3714	2	27	to	to	ADP
ejpam-3714	2	28	professor	professor	NOUN
ejpam-3714	2	29	hari	hari	PROPN
ejpam-3714	2	30	m.	m.	PROPN
ejpam-3714	2	31	srivastava	srivastava	PROPN
ejpam-3714	2	32	on	on	ADP
ejpam-3714	2	33	the	the	DET
ejpam-3714	2	34	occasion	occasion	NOUN
ejpam-3714	2	35	of	of	ADP
ejpam-3714	2	36	his	his	PRON
ejpam-3714	2	37	80th	80th	ADJ
ejpam-3714	2	38	birthday	birthday	NOUN
ejpam-3714	2	39	on	on	ADP
ejpam-3714	2	40	approximation	approximation	NOUN
ejpam-3714	2	41	of	of	ADP
ejpam-3714	2	42	signals	signal	NOUN
ejpam-3714	2	43	in	in	ADP
ejpam-3714	2	44	the	the	DET
ejpam-3714	2	45	generalized	generalized	ADJ
ejpam-3714	2	46	zygmund	zygmund	NOUN
ejpam-3714	2	47	class	class	NOUN
ejpam-3714	3	1	using	use	VERB
ejpam-3714	3	2	(	(	PUNCT
ejpam-3714	3	3	e	e	NOUN
ejpam-3714	3	4	,	,	PUNCT
ejpam-3714	3	5	r)(n	r)(n	PROPN
ejpam-3714	3	6	,	,	PUNCT
ejpam-3714	3	7	qn	qn	NOUN
ejpam-3714	3	8	)	)	PUNCT
ejpam-3714	3	9	mean	mean	NOUN
ejpam-3714	3	10	of	of	ADP
ejpam-3714	3	11	conjugate	conjugate	ADJ
ejpam-3714	3	12	derived	derive	VERB
ejpam-3714	3	13	fourier	fourier	NOUN
ejpam-3714	3	14	series	series	PROPN
ejpam-3714	3	15	anwesha	anwesha	PROPN
ejpam-3714	3	16	mishra1	mishra1	PROPN
ejpam-3714	3	17	,	,	PUNCT
ejpam-3714	3	18	birupakhya	birupakhya	PROPN
ejpam-3714	3	19	prasad	prasad	PROPN
ejpam-3714	3	20	padhy1,∗	padhy1,∗	PROPN
ejpam-3714	3	21	,	,	PUNCT
ejpam-3714	3	22	umakanta	umakanta	PROPN
ejpam-3714	3	23	misra3	misra3	PROPN
ejpam-3714	3	24	1	1	NUM
ejpam-3714	3	25	department	department	NOUN
ejpam-3714	3	26	of	of	ADP
ejpam-3714	3	27	mathematics	mathematic	NOUN
ejpam-3714	3	28	,	,	PUNCT
ejpam-3714	3	29	school	school	NOUN
ejpam-3714	3	30	of	of	ADP
ejpam-3714	3	31	applied	apply	VERB
ejpam-3714	3	32	sciences	science	NOUN
ejpam-3714	3	33	,	,	PUNCT
ejpam-3714	3	34	kiit	kiit	PROPN
ejpam-3714	3	35	,	,	PUNCT
ejpam-3714	3	36	deemed	deem	VERB
ejpam-3714	3	37	to	to	PART
ejpam-3714	3	38	be	be	AUX
ejpam-3714	3	39	university	university	NOUN
ejpam-3714	3	40	,	,	PUNCT
ejpam-3714	3	41	bhubaneswar	bhubaneswar	NOUN
ejpam-3714	3	42	,	,	PUNCT
ejpam-3714	3	43	odisha	odisha	PROPN
ejpam-3714	3	44	,	,	PUNCT
ejpam-3714	3	45	india	india	PROPN
ejpam-3714	3	46	2	2	NUM
ejpam-3714	3	47	department	department	NOUN
ejpam-3714	3	48	of	of	ADP
ejpam-3714	3	49	mathematics	mathematic	NOUN
ejpam-3714	3	50	,	,	PUNCT
ejpam-3714	3	51	national	national	PROPN
ejpam-3714	3	52	institute	institute	PROPN
ejpam-3714	3	53	of	of	ADP
ejpam-3714	3	54	science	science	NOUN
ejpam-3714	3	55	and	and	CCONJ
ejpam-3714	3	56	technology	technology	NOUN
ejpam-3714	3	57	,	,	PUNCT
ejpam-3714	3	58	pallur	pallur	ADJ
ejpam-3714	3	59	hills	hill	NOUN
ejpam-3714	3	60	,	,	PUNCT
ejpam-3714	3	61	berhampur	berhampur	NOUN
ejpam-3714	3	62	,	,	PUNCT
ejpam-3714	3	63	odisha	odisha	PROPN
ejpam-3714	3	64	,	,	PUNCT
ejpam-3714	3	65	india	india	PROPN
ejpam-3714	3	66	.	.	PUNCT
ejpam-3714	4	1	abstract	abstract	PROPN
ejpam-3714	4	2	.	.	PUNCT
ejpam-3714	5	1	in	in	ADP
ejpam-3714	5	2	the	the	DET
ejpam-3714	5	3	present	present	ADJ
ejpam-3714	5	4	article	article	NOUN
ejpam-3714	5	5	,	,	PUNCT
ejpam-3714	5	6	we	we	PRON
ejpam-3714	5	7	have	have	AUX
ejpam-3714	5	8	established	establish	VERB
ejpam-3714	5	9	a	a	DET
ejpam-3714	5	10	result	result	NOUN
ejpam-3714	5	11	on	on	ADP
ejpam-3714	5	12	degree	degree	NOUN
ejpam-3714	5	13	of	of	ADP
ejpam-3714	5	14	approximation	approximation	NOUN
ejpam-3714	5	15	of	of	ADP
ejpam-3714	5	16	function	function	NOUN
ejpam-3714	5	17	in	in	ADP
ejpam-3714	5	18	the	the	DET
ejpam-3714	5	19	generalized	generalized	ADJ
ejpam-3714	5	20	zygmund	zygmund	NOUN
ejpam-3714	5	21	class	class	PROPN
ejpam-3714	5	22	zl	zl	PROPN
ejpam-3714	5	23	(	(	PUNCT
ejpam-3714	5	24	m),(l	m),(l	X
ejpam-3714	5	25	≥	≥	NOUN
ejpam-3714	5	26	1	1	NUM
ejpam-3714	5	27	)	)	PUNCT
ejpam-3714	5	28	by	by	ADP
ejpam-3714	5	29	(	(	PUNCT
ejpam-3714	5	30	e	e	NOUN
ejpam-3714	5	31	,	,	PUNCT
ejpam-3714	5	32	r)(n	r)(n	PROPN
ejpam-3714	5	33	,	,	PUNCT
ejpam-3714	5	34	qn)mean	qn)mean	ADJ
ejpam-3714	5	35	of	of	ADP
ejpam-3714	5	36	conjugate	conjugate	ADJ
ejpam-3714	5	37	derived	derive	VERB
ejpam-3714	5	38	fourier	fourier	NOUN
ejpam-3714	5	39	series	series	NOUN
ejpam-3714	5	40	.	.	PUNCT
ejpam-3714	6	1	2020	2020	NUM
ejpam-3714	6	2	mathematics	mathematics	PROPN
ejpam-3714	6	3	subject	subject	NOUN
ejpam-3714	6	4	classifications	classification	NOUN
ejpam-3714	6	5	:	:	PUNCT
ejpam-3714	6	6	42a10	42a10	NUM
ejpam-3714	6	7	,	,	PUNCT
ejpam-3714	6	8	41a10	41a10	NUM
ejpam-3714	6	9	,	,	PUNCT
ejpam-3714	6	10	42b05	42b05	NUM
ejpam-3714	6	11	,	,	PUNCT
ejpam-3714	6	12	42b08	42b08	NUM
ejpam-3714	6	13	key	key	ADJ
ejpam-3714	6	14	words	word	NOUN
ejpam-3714	6	15	and	and	CCONJ
ejpam-3714	6	16	phrases	phrase	NOUN
ejpam-3714	6	17	:	:	PUNCT
ejpam-3714	6	18	degree	degree	NOUN
ejpam-3714	6	19	of	of	ADP
ejpam-3714	6	20	approximation	approximation	NOUN
ejpam-3714	6	21	,	,	PUNCT
ejpam-3714	6	22	generalized	generalized	ADJ
ejpam-3714	6	23	zygmund	zygmund	NOUN
ejpam-3714	6	24	class	class	NOUN
ejpam-3714	6	25	,	,	PUNCT
ejpam-3714	6	26	fourier	fouri	ADJ
ejpam-3714	6	27	series	series	NOUN
ejpam-3714	6	28	,	,	PUNCT
ejpam-3714	6	29	conjugate	conjugate	ADJ
ejpam-3714	6	30	fourier	fouri	ADJ
ejpam-3714	6	31	series	series	NOUN
ejpam-3714	6	32	,	,	PUNCT
ejpam-3714	6	33	conjugate	conjugate	ADJ
ejpam-3714	6	34	derived	derive	VERB
ejpam-3714	6	35	fourier	fourier	NOUN
ejpam-3714	6	36	series	series	NOUN
ejpam-3714	6	37	,	,	PUNCT
ejpam-3714	6	38	(	(	PUNCT
ejpam-3714	6	39	e	e	NOUN
ejpam-3714	6	40	,	,	PUNCT
ejpam-3714	6	41	r)-summability	r)-summability	PRON
ejpam-3714	6	42	mean	mean	VERB
ejpam-3714	6	43	,	,	PUNCT
ejpam-3714	6	44	(	(	PUNCT
ejpam-3714	6	45	n	n	CCONJ
ejpam-3714	6	46	,	,	PUNCT
ejpam-3714	6	47	qn	qn	NOUN
ejpam-3714	6	48	)	)	PUNCT
ejpam-3714	6	49	summability	summability	NOUN
ejpam-3714	6	50	mean	mean	VERB
ejpam-3714	6	51	,	,	PUNCT
ejpam-3714	6	52	(	(	PUNCT
ejpam-3714	6	53	e	e	NOUN
ejpam-3714	6	54	,	,	PUNCT
ejpam-3714	6	55	r)(n	r)(n	NOUN
ejpam-3714	6	56	,	,	PUNCT
ejpam-3714	6	57	qn)-summability	qn)-summability	NOUN
ejpam-3714	7	1	mean	mean	VERB
ejpam-3714	7	2	1	1	NUM
ejpam-3714	7	3	.	.	PUNCT
ejpam-3714	7	4	introduction	introduction	NOUN
ejpam-3714	7	5	signal	signal	NOUN
ejpam-3714	7	6	analysis	analysis	NOUN
ejpam-3714	7	7	describes	describe	VERB
ejpam-3714	7	8	the	the	DET
ejpam-3714	7	9	field	field	NOUN
ejpam-3714	7	10	of	of	ADP
ejpam-3714	7	11	study	study	NOUN
ejpam-3714	7	12	whose	whose	DET
ejpam-3714	7	13	objective	objective	NOUN
ejpam-3714	7	14	is	be	AUX
ejpam-3714	7	15	to	to	PART
ejpam-3714	7	16	collect	collect	VERB
ejpam-3714	7	17	,	,	PUNCT
ejpam-3714	7	18	understand	understand	VERB
ejpam-3714	7	19	and	and	CCONJ
ejpam-3714	7	20	deduce	deduce	ADJ
ejpam-3714	7	21	information	information	NOUN
ejpam-3714	7	22	and	and	CCONJ
ejpam-3714	7	23	intelligence	intelligence	NOUN
ejpam-3714	7	24	from	from	ADP
ejpam-3714	7	25	various	various	ADJ
ejpam-3714	7	26	signals	signal	NOUN
ejpam-3714	7	27	.	.	PUNCT
ejpam-3714	8	1	now	now	ADV
ejpam-3714	8	2	-	-	PUNCT
ejpam-3714	8	3	a	a	DET
ejpam-3714	8	4	-	-	PUNCT
ejpam-3714	8	5	days	days	NOUN
ejpam-3714	8	6	the	the	DET
ejpam-3714	8	7	analysis	analysis	NOUN
ejpam-3714	8	8	of	of	ADP
ejpam-3714	8	9	signals	signal	NOUN
ejpam-3714	8	10	is	be	AUX
ejpam-3714	8	11	a	a	DET
ejpam-3714	8	12	fundamental	fundamental	ADJ
ejpam-3714	8	13	problem	problem	NOUN
ejpam-3714	8	14	for	for	ADP
ejpam-3714	8	15	many	many	ADJ
ejpam-3714	8	16	engineers	engineer	NOUN
ejpam-3714	8	17	and	and	CCONJ
ejpam-3714	8	18	scientists	scientist	NOUN
ejpam-3714	8	19	.	.	PUNCT
ejpam-3714	9	1	in	in	ADP
ejpam-3714	9	2	the	the	DET
ejpam-3714	9	3	recent	recent	ADJ
ejpam-3714	9	4	past	past	NOUN
ejpam-3714	9	5	,	,	PUNCT
ejpam-3714	9	6	we	we	PRON
ejpam-3714	9	7	have	have	AUX
ejpam-3714	9	8	seen	see	VERB
ejpam-3714	9	9	the	the	DET
ejpam-3714	9	10	applications	application	NOUN
ejpam-3714	9	11	of	of	ADP
ejpam-3714	9	12	mathematical	mathematical	ADJ
ejpam-3714	9	13	methods	method	NOUN
ejpam-3714	9	14	such	such	ADJ
ejpam-3714	9	15	as	as	ADP
ejpam-3714	9	16	probability	probability	NOUN
ejpam-3714	9	17	theory	theory	NOUN
ejpam-3714	9	18	,	,	PUNCT
ejpam-3714	9	19	mathematical	mathematical	ADJ
ejpam-3714	9	20	statistics	statistic	NOUN
ejpam-3714	9	21	etc	etc	X
ejpam-3714	9	22	.	.	X
ejpam-3714	9	23	in	in	ADP
ejpam-3714	9	24	the	the	DET
ejpam-3714	9	25	analysis	analysis	NOUN
ejpam-3714	9	26	of	of	ADP
ejpam-3714	9	27	signals	signal	NOUN
ejpam-3714	9	28	.	.	PUNCT
ejpam-3714	10	1	very	very	ADV
ejpam-3714	10	2	recently	recently	ADV
ejpam-3714	10	3	,	,	PUNCT
ejpam-3714	10	4	approximation	approximation	NOUN
ejpam-3714	10	5	∗corresponding	∗corresponde	VERB
ejpam-3714	10	6	author	author	NOUN
ejpam-3714	10	7	.	.	PUNCT
ejpam-3714	11	1	doi	doi	NOUN
ejpam-3714	11	2	:	:	PUNCT
ejpam-3714	11	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3714	https://doi.org/10.29020/nybg.ejpam.v13i5.3714	VERB
ejpam-3714	11	4	email	email	NOUN
ejpam-3714	11	5	addresses	address	NOUN
ejpam-3714	11	6	:	:	PUNCT
ejpam-3714	11	7	m.anwesha17@gmail.com	m.anwesha17@gmail.com	X
ejpam-3714	11	8	(	(	PUNCT
ejpam-3714	11	9	a.	a.	PROPN
ejpam-3714	11	10	mishra	mishra	PROPN
ejpam-3714	11	11	)	)	PUNCT
ejpam-3714	11	12	,	,	PUNCT
ejpam-3714	11	13	birupakhya.padhyfma@kiit.ac.in	birupakhya.padhyfma@kiit.ac.in	PUNCT
ejpam-3714	11	14	(	(	PUNCT
ejpam-3714	11	15	b.	b.	PROPN
ejpam-3714	11	16	p.	p.	PROPN
ejpam-3714	11	17	padhy	padhy	PROPN
ejpam-3714	11	18	)	)	PUNCT
ejpam-3714	11	19	,	,	PUNCT
ejpam-3714	11	20	umakanta	umakanta	PROPN
ejpam-3714	12	1	misra@yahoo.com	misra@yahoo.com	PROPN
ejpam-3714	13	1	(	(	PUNCT
ejpam-3714	13	2	u.	u.	PROPN
ejpam-3714	13	3	k.	k.	PROPN
ejpam-3714	13	4	misra	misra	PROPN
ejpam-3714	13	5	)	)	PUNCT
ejpam-3714	13	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3714	13	7	1325	1325	NUM
ejpam-3714	14	1	c	c	NOUN
ejpam-3714	14	2	©	©	PROPN
ejpam-3714	14	3	2020	2020	NUM
ejpam-3714	14	4	ejpam	ejpam	VERB
ejpam-3714	14	5	all	all	DET
ejpam-3714	14	6	rights	right	NOUN
ejpam-3714	14	7	reserved	reserve	VERB
ejpam-3714	14	8	.	.	PUNCT
ejpam-3714	15	1	a.	a.	PROPN
ejpam-3714	15	2	mishra	mishra	PROPN
ejpam-3714	15	3	,	,	PUNCT
ejpam-3714	15	4	b.	b.	PROPN
ejpam-3714	15	5	p.	p.	PROPN
ejpam-3714	15	6	padhy	padhy	PROPN
ejpam-3714	15	7	,	,	PUNCT
ejpam-3714	15	8	u.	u.	PROPN
ejpam-3714	15	9	k.	k.	PROPN
ejpam-3714	15	10	misra	misra	PROPN
ejpam-3714	15	11	/	/	SYM
ejpam-3714	15	12	eur	eur	PROPN
ejpam-3714	15	13	.	.	PUNCT
ejpam-3714	16	1	j.	j.	PROPN
ejpam-3714	16	2	pure	pure	PROPN
ejpam-3714	16	3	appl	appl	PROPN
ejpam-3714	16	4	.	.	PROPN
ejpam-3714	16	5	math	math	PROPN
ejpam-3714	16	6	,	,	PUNCT
ejpam-3714	16	7	13	13	NUM
ejpam-3714	16	8	(	(	PUNCT
ejpam-3714	16	9	5	5	NUM
ejpam-3714	16	10	)	)	PUNCT
ejpam-3714	16	11	(	(	PUNCT
ejpam-3714	16	12	2020	2020	NUM
ejpam-3714	16	13	)	)	PUNCT
ejpam-3714	16	14	,	,	PUNCT
ejpam-3714	16	15	1325	1325	NUM
ejpam-3714	16	16	-	-	SYM
ejpam-3714	16	17	1336	1336	NUM
ejpam-3714	16	18	1326	1326	NUM
ejpam-3714	16	19	theory	theory	NOUN
ejpam-3714	16	20	has	have	AUX
ejpam-3714	16	21	got	get	VERB
ejpam-3714	16	22	a	a	DET
ejpam-3714	16	23	large	large	ADJ
ejpam-3714	16	24	popularity	popularity	NOUN
ejpam-3714	16	25	as	as	SCONJ
ejpam-3714	16	26	it	it	PRON
ejpam-3714	16	27	has	have	AUX
ejpam-3714	16	28	given	give	VERB
ejpam-3714	16	29	a	a	DET
ejpam-3714	16	30	new	new	ADJ
ejpam-3714	16	31	dimension	dimension	NOUN
ejpam-3714	16	32	in	in	ADP
ejpam-3714	16	33	approximating	approximate	VERB
ejpam-3714	16	34	the	the	DET
ejpam-3714	16	35	signals	signal	NOUN
ejpam-3714	16	36	.	.	PUNCT
ejpam-3714	17	1	the	the	DET
ejpam-3714	17	2	estimation	estimation	NOUN
ejpam-3714	17	3	of	of	ADP
ejpam-3714	17	4	error	error	NOUN
ejpam-3714	17	5	functions	function	NOUN
ejpam-3714	17	6	in	in	ADP
ejpam-3714	17	7	lipschitz	lipschitz	NOUN
ejpam-3714	17	8	and	and	CCONJ
ejpam-3714	17	9	zygmund	zygmund	NOUN
ejpam-3714	17	10	space	space	NOUN
ejpam-3714	17	11	using	use	VERB
ejpam-3714	17	12	different	different	ADJ
ejpam-3714	17	13	summability	summability	NOUN
ejpam-3714	17	14	techniques	technique	NOUN
ejpam-3714	17	15	of	of	ADP
ejpam-3714	17	16	fourier	fourier	ADJ
ejpam-3714	17	17	series	series	NOUN
ejpam-3714	17	18	and	and	CCONJ
ejpam-3714	17	19	conjugate	conjugate	ADJ
ejpam-3714	17	20	fourier	fourier	NOUN
ejpam-3714	17	21	series	series	NOUN
ejpam-3714	17	22	have	have	AUX
ejpam-3714	17	23	been	be	AUX
ejpam-3714	17	24	of	of	ADP
ejpam-3714	17	25	great	great	ADJ
ejpam-3714	17	26	interest	interest	NOUN
ejpam-3714	17	27	among	among	ADP
ejpam-3714	17	28	the	the	DET
ejpam-3714	17	29	researchers	researcher	NOUN
ejpam-3714	17	30	in	in	ADP
ejpam-3714	17	31	the	the	DET
ejpam-3714	17	32	last	last	ADJ
ejpam-3714	17	33	decades	decade	NOUN
ejpam-3714	17	34	.	.	PUNCT
ejpam-3714	18	1	for	for	SCONJ
ejpam-3714	18	2	details	detail	NOUN
ejpam-3714	18	3	see	see	VERB
ejpam-3714	18	4	[	[	X
ejpam-3714	18	5	3	3	NUM
ejpam-3714	18	6	,	,	PUNCT
ejpam-3714	18	7	7	7	NUM
ejpam-3714	18	8	,	,	PUNCT
ejpam-3714	18	9	9	9	NUM
ejpam-3714	18	10	,	,	PUNCT
ejpam-3714	18	11	12	12	NUM
ejpam-3714	18	12	,	,	PUNCT
ejpam-3714	18	13	13	13	NUM
ejpam-3714	18	14	]	]	PUNCT
ejpam-3714	18	15	and	and	CCONJ
ejpam-3714	18	16	[	[	X
ejpam-3714	18	17	15	15	NUM
ejpam-3714	18	18	]	]	PUNCT
ejpam-3714	18	19	to	to	ADP
ejpam-3714	18	20	[	[	X
ejpam-3714	18	21	16	16	NUM
ejpam-3714	18	22	]	]	PUNCT
ejpam-3714	18	23	.	.	PUNCT
ejpam-3714	19	1	also	also	ADV
ejpam-3714	19	2	,	,	PUNCT
ejpam-3714	19	3	the	the	DET
ejpam-3714	19	4	generalized	generalized	ADJ
ejpam-3714	19	5	zygmund	zygmund	NOUN
ejpam-3714	19	6	class	class	PROPN
ejpam-3714	19	7	zl	zl	PROPN
ejpam-3714	19	8	(	(	PUNCT
ejpam-3714	19	9	m),(l	m),(l	X
ejpam-3714	19	10	≥	≥	NOUN
ejpam-3714	19	11	1	1	NUM
ejpam-3714	19	12	)	)	PUNCT
ejpam-3714	19	13	was	be	AUX
ejpam-3714	19	14	investigated	investigate	VERB
ejpam-3714	19	15	by	by	ADP
ejpam-3714	19	16	leindler	leindler	NOUN
ejpam-3714	19	17	[	[	X
ejpam-3714	19	18	8	8	NUM
ejpam-3714	19	19	]	]	PUNCT
ejpam-3714	19	20	,	,	PUNCT
ejpam-3714	19	21	moricz	moricz	NOUN
ejpam-3714	20	1	[	[	X
ejpam-3714	20	2	4	4	NUM
ejpam-3714	20	3	]	]	PUNCT
ejpam-3714	20	4	,	,	PUNCT
ejpam-3714	20	5	moricz	moricz	NOUN
ejpam-3714	20	6	and	and	CCONJ
ejpam-3714	20	7	nemeth	nemeth	PROPN
ejpam-3714	21	1	[	[	X
ejpam-3714	21	2	6	6	NUM
ejpam-3714	21	3	]	]	PUNCT
ejpam-3714	21	4	etc	etc	X
ejpam-3714	21	5	.	.	X
ejpam-3714	21	6	very	very	ADV
ejpam-3714	21	7	recently	recently	ADV
ejpam-3714	21	8	das	das	PROPN
ejpam-3714	21	9	et	et	PROPN
ejpam-3714	21	10	al.[1	al.[1	PROPN
ejpam-3714	21	11	]	]	PUNCT
ejpam-3714	21	12	,	,	PUNCT
ejpam-3714	21	13	nigam	nigam	PROPN
ejpam-3714	22	1	[	[	X
ejpam-3714	22	2	7	7	NUM
ejpam-3714	22	3	]	]	PUNCT
ejpam-3714	22	4	,	,	PUNCT
ejpam-3714	22	5	pradhan	pradhan	PROPN
ejpam-3714	22	6	et	et	PROPN
ejpam-3714	22	7	al.[11	al.[11	PROPN
ejpam-3714	22	8	,	,	PUNCT
ejpam-3714	22	9	14	14	NUM
ejpam-3714	22	10	]	]	PUNCT
ejpam-3714	22	11	and	and	CCONJ
ejpam-3714	22	12	singh	singh	PROPN
ejpam-3714	22	13	et	et	PROPN
ejpam-3714	22	14	al.[10	al.[10	PROPN
ejpam-3714	22	15	]	]	PUNCT
ejpam-3714	22	16	proved	prove	VERB
ejpam-3714	22	17	approximation	approximation	NOUN
ejpam-3714	22	18	of	of	ADP
ejpam-3714	22	19	functions	function	NOUN
ejpam-3714	22	20	in	in	ADP
ejpam-3714	22	21	the	the	DET
ejpam-3714	22	22	generalized	generalized	ADJ
ejpam-3714	22	23	zygmund	zygmund	NOUN
ejpam-3714	22	24	class	class	NOUN
ejpam-3714	22	25	by	by	ADP
ejpam-3714	22	26	using	use	VERB
ejpam-3714	22	27	different	different	ADJ
ejpam-3714	22	28	summability	summability	NOUN
ejpam-3714	22	29	means	mean	NOUN
ejpam-3714	22	30	.	.	PUNCT
ejpam-3714	23	1	in	in	ADP
ejpam-3714	23	2	the	the	DET
ejpam-3714	23	3	present	present	ADJ
ejpam-3714	23	4	paper	paper	NOUN
ejpam-3714	23	5	,	,	PUNCT
ejpam-3714	23	6	we	we	PRON
ejpam-3714	23	7	investigate	investigate	VERB
ejpam-3714	23	8	on	on	ADP
ejpam-3714	23	9	the	the	DET
ejpam-3714	23	10	degree	degree	NOUN
ejpam-3714	23	11	of	of	ADP
ejpam-3714	23	12	approximation	approximation	NOUN
ejpam-3714	23	13	of	of	ADP
ejpam-3714	23	14	a	a	DET
ejpam-3714	23	15	function	function	NOUN
ejpam-3714	23	16	in	in	ADP
ejpam-3714	23	17	the	the	DET
ejpam-3714	23	18	generalized	generalized	ADJ
ejpam-3714	23	19	zygmund	zygmund	NOUN
ejpam-3714	23	20	class	class	PROPN
ejpam-3714	23	21	zl	zl	PROPN
ejpam-3714	23	22	(	(	PUNCT
ejpam-3714	23	23	m),(l	m),(l	X
ejpam-3714	23	24	≥	≥	NOUN
ejpam-3714	23	25	1	1	NUM
ejpam-3714	23	26	)	)	PUNCT
ejpam-3714	23	27	by	by	ADP
ejpam-3714	23	28	(	(	PUNCT
ejpam-3714	23	29	e	e	NOUN
ejpam-3714	23	30	,	,	PUNCT
ejpam-3714	23	31	r)(n	r)(n	PROPN
ejpam-3714	23	32	,	,	PUNCT
ejpam-3714	23	33	qn	qn	NOUN
ejpam-3714	23	34	)	)	PUNCT
ejpam-3714	23	35	product	product	NOUN
ejpam-3714	23	36	mean	mean	NOUN
ejpam-3714	23	37	of	of	ADP
ejpam-3714	23	38	the	the	DET
ejpam-3714	23	39	conjugate	conjugate	ADJ
ejpam-3714	23	40	derived	derive	VERB
ejpam-3714	23	41	fourier	fourier	NOUN
ejpam-3714	23	42	series	series	NOUN
ejpam-3714	23	43	.	.	PUNCT
ejpam-3714	24	1	2	2	X
ejpam-3714	24	2	.	.	X
ejpam-3714	24	3	definitions	definition	NOUN
ejpam-3714	24	4	and	and	CCONJ
ejpam-3714	24	5	notations	notation	NOUN
ejpam-3714	24	6	let	let	VERB
ejpam-3714	24	7	h	h	PRON
ejpam-3714	24	8	be	be	AUX
ejpam-3714	24	9	a	a	DET
ejpam-3714	24	10	function	function	NOUN
ejpam-3714	24	11	,	,	PUNCT
ejpam-3714	24	12	which	which	PRON
ejpam-3714	24	13	is	be	AUX
ejpam-3714	24	14	periodic	periodic	ADJ
ejpam-3714	24	15	in	in	ADP
ejpam-3714	24	16	[	[	X
ejpam-3714	24	17	0	0	NUM
ejpam-3714	24	18	,	,	PUNCT
ejpam-3714	24	19	2π	2π	NOUN
ejpam-3714	24	20	]	]	PUNCT
ejpam-3714	24	21	such	such	ADJ
ejpam-3714	24	22	that	that	SCONJ
ejpam-3714	24	23	∫	∫	PROPN
ejpam-3714	24	24	2π	2π	PROPN
ejpam-3714	24	25	0	0	NUM
ejpam-3714	24	26	|h(x)|ldx	|h(x)|ldx	NOUN
ejpam-3714	24	27	<	<	X
ejpam-3714	24	28	∞.	∞.	PROPN
ejpam-3714	24	29	let	let	VERB
ejpam-3714	24	30	us	we	PRON
ejpam-3714	24	31	denote	denote	VERB
ejpam-3714	24	32	ll[0	ll[0	NOUN
ejpam-3714	24	33	,	,	PUNCT
ejpam-3714	24	34	2π	2π	NOUN
ejpam-3714	24	35	]	]	PUNCT
ejpam-3714	25	1	=	=	PRON
ejpam-3714	25	2	{	{	PUNCT
ejpam-3714	25	3	h	h	NOUN
ejpam-3714	25	4	:	:	PUNCT
ejpam-3714	26	1	[	[	X
ejpam-3714	26	2	0	0	NUM
ejpam-3714	26	3	,	,	PUNCT
ejpam-3714	26	4	2π]→	2π]→	NUM
ejpam-3714	26	5	r	r	NOUN
ejpam-3714	26	6	:	:	PUNCT
ejpam-3714	26	7	∫	∫	PROPN
ejpam-3714	26	8	2π	2π	PROPN
ejpam-3714	26	9	0	0	NUM
ejpam-3714	26	10	|h(x)|ldx	|h(x)|ldx	NOUN
ejpam-3714	26	11	<	<	X
ejpam-3714	26	12	∞	∞	NUM
ejpam-3714	26	13	}	}	PUNCT
ejpam-3714	26	14	,	,	PUNCT
ejpam-3714	26	15	l	l	X
ejpam-3714	26	16	≥	≥	NUM
ejpam-3714	26	17	1	1	NUM
ejpam-3714	26	18	.	.	PUNCT
ejpam-3714	27	1	the	the	DET
ejpam-3714	27	2	fourier	fourier	PROPN
ejpam-3714	27	3	series	series	NOUN
ejpam-3714	27	4	of	of	ADP
ejpam-3714	27	5	h(x	h(x	PROPN
ejpam-3714	27	6	)	)	PUNCT
ejpam-3714	27	7	is	be	AUX
ejpam-3714	27	8	given	give	VERB
ejpam-3714	27	9	by	by	ADP
ejpam-3714	27	10	∞∑	∞∑	PRON
ejpam-3714	27	11	n=0	n=0	NOUN
ejpam-3714	27	12	un(x	un(x	NOUN
ejpam-3714	27	13	)	)	PUNCT
ejpam-3714	27	14	=	=	SYM
ejpam-3714	27	15	a0	a0	NOUN
ejpam-3714	27	16	2	2	NUM
ejpam-3714	27	17	+	+	CCONJ
ejpam-3714	27	18	∞∑	∞∑	NUM
ejpam-3714	27	19	n=1	n=1	PROPN
ejpam-3714	27	20	(	(	PUNCT
ejpam-3714	27	21	ancosnx+	ancosnx+	PROPN
ejpam-3714	27	22	bnsinnx	bnsinnx	NOUN
ejpam-3714	27	23	)	)	PUNCT
ejpam-3714	27	24	(	(	PUNCT
ejpam-3714	27	25	1	1	X
ejpam-3714	27	26	)	)	PUNCT
ejpam-3714	27	27	also	also	ADV
ejpam-3714	27	28	,	,	PUNCT
ejpam-3714	27	29	the	the	DET
ejpam-3714	27	30	conjugate	conjugate	ADJ
ejpam-3714	27	31	fourier	fourier	NOUN
ejpam-3714	27	32	series	series	NOUN
ejpam-3714	27	33	and	and	CCONJ
ejpam-3714	27	34	derived	derive	VERB
ejpam-3714	27	35	conjugate	conjugate	ADJ
ejpam-3714	27	36	fourier	fourier	NOUN
ejpam-3714	27	37	series	series	NOUN
ejpam-3714	27	38	of	of	ADP
ejpam-3714	27	39	h(x	h(x	PROPN
ejpam-3714	27	40	)	)	PUNCT
ejpam-3714	27	41	are	be	AUX
ejpam-3714	27	42	respectively	respectively	ADV
ejpam-3714	27	43	∞∑	∞∑	NUM
ejpam-3714	27	44	n=1	n=1	NUM
ejpam-3714	27	45	(	(	PUNCT
ejpam-3714	27	46	bncosnx−	bncosnx−	ADV
ejpam-3714	27	47	ansinnx	ansinnx	PROPN
ejpam-3714	27	48	)	)	PUNCT
ejpam-3714	27	49	and	and	CCONJ
ejpam-3714	27	50	−	−	PROPN
ejpam-3714	27	51	∑	∑	PROPN
ejpam-3714	27	52	n	n	PRON
ejpam-3714	27	53	un(x	un(x	NOUN
ejpam-3714	27	54	)	)	PUNCT
ejpam-3714	27	55	.	.	PUNCT
ejpam-3714	28	1	let	let	VERB
ejpam-3714	28	2	us	we	PRON
ejpam-3714	28	3	define	define	VERB
ejpam-3714	28	4	‖h‖l	‖h‖l	NOUN
ejpam-3714	28	5	=	=	PUNCT
ejpam-3714	28	6	(	(	PUNCT
ejpam-3714	28	7	1	1	NUM
ejpam-3714	28	8	2π	2π	NUM
ejpam-3714	28	9	∫	∫	PROPN
ejpam-3714	28	10	2π	2π	PROPN
ejpam-3714	28	11	0	0	NUM
ejpam-3714	28	12	|h(x)|ldx	|h(x)|ldx	NOUN
ejpam-3714	28	13	)	)	PUNCT
ejpam-3714	28	14	1	1	NUM
ejpam-3714	28	15	l	l	NOUN
ejpam-3714	28	16	,	,	PUNCT
ejpam-3714	28	17	1	1	NUM
ejpam-3714	28	18	≤	≤	NUM
ejpam-3714	29	1	l	l	NOUN
ejpam-3714	29	2	<	<	X
ejpam-3714	29	3	∞	∞	NOUN
ejpam-3714	29	4	and	and	CCONJ
ejpam-3714	29	5	‖h‖l	‖h‖l	NOUN
ejpam-3714	29	6	=	=	SYM
ejpam-3714	30	1	ess	ess	PROPN
ejpam-3714	30	2	sup	sup	NOUN
ejpam-3714	30	3	0≤x≤2π	0≤x≤2π	NOUN
ejpam-3714	30	4	|h(x)|	|h(x)|	NOUN
ejpam-3714	30	5	,	,	PUNCT
ejpam-3714	30	6	l	l	NOUN
ejpam-3714	30	7	=	=	NOUN
ejpam-3714	30	8	∞	∞	NUM
ejpam-3714	30	9	let	let	VERB
ejpam-3714	30	10	s′p	s′p	PROPN
ejpam-3714	30	11	(	(	PUNCT
ejpam-3714	30	12	h;x	h;x	NOUN
ejpam-3714	30	13	)	)	PUNCT
ejpam-3714	30	14	denotes	denote	VERB
ejpam-3714	30	15	the	the	DET
ejpam-3714	30	16	p	p	PROPN
ejpam-3714	30	17	-	-	PUNCT
ejpam-3714	30	18	th	th	X
ejpam-3714	30	19	partial	partial	ADJ
ejpam-3714	30	20	sum	sum	NOUN
ejpam-3714	30	21	of	of	ADP
ejpam-3714	30	22	conjugate	conjugate	ADJ
ejpam-3714	30	23	derived	derive	VERB
ejpam-3714	30	24	fourier	fourier	NOUN
ejpam-3714	30	25	series	series	NOUN
ejpam-3714	30	26	and	and	CCONJ
ejpam-3714	30	27	is	be	AUX
ejpam-3714	30	28	given	give	VERB
ejpam-3714	30	29	by	by	ADP
ejpam-3714	30	30	s′p	s′p	PROPN
ejpam-3714	30	31	(	(	PUNCT
ejpam-3714	30	32	h;x	h;x	PROPN
ejpam-3714	30	33	)	)	PUNCT
ejpam-3714	31	1	−	−	PROPN
ejpam-3714	32	1	h′(x)−	h′(x)−	PROPN
ejpam-3714	33	1	=	=	PUNCT
ejpam-3714	34	1	−	−	PROPN
ejpam-3714	34	2	2	2	NUM
ejpam-3714	34	3	π	π	NOUN
ejpam-3714	34	4	∫	∫	PROPN
ejpam-3714	34	5	π	π	X
ejpam-3714	34	6	0	0	NUM
ejpam-3714	34	7	ψ(x	ψ(x	PROPN
ejpam-3714	34	8	;	;	PUNCT
ejpam-3714	34	9	v	v	NOUN
ejpam-3714	34	10	)	)	PUNCT
ejpam-3714	34	11	4sinv2	4sinv2	NUM
ejpam-3714	35	1	(	(	PUNCT
ejpam-3714	35	2	k	k	NOUN
ejpam-3714	35	3	+	+	CCONJ
ejpam-3714	35	4	1	1	NUM
ejpam-3714	35	5	2	2	NUM
ejpam-3714	35	6	)	)	PUNCT
ejpam-3714	35	7	sin	sin	NOUN
ejpam-3714	35	8	(	(	PUNCT
ejpam-3714	35	9	k	k	NOUN
ejpam-3714	35	10	+	+	PROPN
ejpam-3714	35	11	1	1	NUM
ejpam-3714	35	12	2	2	NUM
ejpam-3714	35	13	)	)	PUNCT
ejpam-3714	35	14	v	v	ADP
ejpam-3714	35	15	dv	dv	PROPN
ejpam-3714	35	16	−	−	PROPN
ejpam-3714	35	17	1	1	NUM
ejpam-3714	35	18	π	π	SYM
ejpam-3714	35	19	∫	∫	PROPN
ejpam-3714	35	20	π	π	X
ejpam-3714	35	21	0	0	NUM
ejpam-3714	35	22	ψ(x	ψ(x	PROPN
ejpam-3714	35	23	;	;	PUNCT
ejpam-3714	35	24	v	v	NOUN
ejpam-3714	35	25	)	)	PUNCT
ejpam-3714	35	26	4sinv2	4sinv2	NUM
ejpam-3714	36	1	sin	sin	NOUN
ejpam-3714	37	1	(	(	PUNCT
ejpam-3714	37	2	k	k	NOUN
ejpam-3714	37	3	+	+	PROPN
ejpam-3714	37	4	1	1	NUM
ejpam-3714	37	5	2	2	NUM
ejpam-3714	37	6	)	)	PUNCT
ejpam-3714	37	7	v	v	NOUN
ejpam-3714	37	8	tanv2	tanv2	NOUN
ejpam-3714	38	1	dv	dv	PROPN
ejpam-3714	38	2	a.	a.	PROPN
ejpam-3714	38	3	mishra	mishra	PROPN
ejpam-3714	38	4	,	,	PUNCT
ejpam-3714	38	5	b.	b.	PROPN
ejpam-3714	38	6	p.	p.	PROPN
ejpam-3714	38	7	padhy	padhy	PROPN
ejpam-3714	38	8	,	,	PUNCT
ejpam-3714	38	9	u.	u.	PROPN
ejpam-3714	38	10	k.	k.	PROPN
ejpam-3714	38	11	misra	misra	PROPN
ejpam-3714	38	12	/	/	SYM
ejpam-3714	38	13	eur	eur	PROPN
ejpam-3714	38	14	.	.	PUNCT
ejpam-3714	39	1	j.	j.	PROPN
ejpam-3714	39	2	pure	pure	PROPN
ejpam-3714	39	3	appl	appl	PROPN
ejpam-3714	39	4	.	.	PROPN
ejpam-3714	39	5	math	math	PROPN
ejpam-3714	39	6	,	,	PUNCT
ejpam-3714	39	7	13	13	NUM
ejpam-3714	39	8	(	(	PUNCT
ejpam-3714	39	9	5	5	NUM
ejpam-3714	39	10	)	)	PUNCT
ejpam-3714	39	11	(	(	PUNCT
ejpam-3714	39	12	2020	2020	NUM
ejpam-3714	39	13	)	)	PUNCT
ejpam-3714	39	14	,	,	PUNCT
ejpam-3714	39	15	1325	1325	NUM
ejpam-3714	39	16	-	-	SYM
ejpam-3714	39	17	1336	1336	NUM
ejpam-3714	39	18	1327	1327	NUM
ejpam-3714	39	19	where	where	SCONJ
ejpam-3714	39	20	h′	h′	PROPN
ejpam-3714	39	21	is	be	AUX
ejpam-3714	39	22	the	the	DET
ejpam-3714	39	23	conjugate	conjugate	ADJ
ejpam-3714	39	24	derived	derive	VERB
ejpam-3714	39	25	function	function	NOUN
ejpam-3714	39	26	of	of	ADP
ejpam-3714	39	27	2π	2π	PROPN
ejpam-3714	39	28	periodic	periodic	ADJ
ejpam-3714	39	29	function	function	NOUN
ejpam-3714	39	30	’	'	PUNCT
ejpam-3714	39	31	h	h	NOUN
ejpam-3714	39	32	’	'	PUNCT
ejpam-3714	39	33	,	,	PUNCT
ejpam-3714	39	34	which	which	PRON
ejpam-3714	39	35	is	be	AUX
ejpam-3714	39	36	given	give	VERB
ejpam-3714	39	37	by	by	ADP
ejpam-3714	39	38	h′(x	h′(x	NOUN
ejpam-3714	39	39	)	)	PUNCT
ejpam-3714	39	40	=	=	SYM
ejpam-3714	40	1	−	−	PROPN
ejpam-3714	40	2	1	1	NUM
ejpam-3714	40	3	π	π	NOUN
ejpam-3714	40	4	∫	∫	PROPN
ejpam-3714	40	5	π	π	X
ejpam-3714	40	6	0	0	NUM
ejpam-3714	40	7	ψ(x	ψ(x	PROPN
ejpam-3714	40	8	;	;	PUNCT
ejpam-3714	40	9	v	v	NOUN
ejpam-3714	40	10	)	)	PUNCT
ejpam-3714	40	11	cosec2	cosec2	NOUN
ejpam-3714	41	1	v	v	ADP
ejpam-3714	41	2	2	2	NUM
ejpam-3714	41	3	dv	dv	PROPN
ejpam-3714	41	4	let	let	VERB
ejpam-3714	41	5	the	the	DET
ejpam-3714	41	6	zygmund	zygmund	NOUN
ejpam-3714	41	7	modulus	modulus	NOUN
ejpam-3714	41	8	of	of	ADP
ejpam-3714	41	9	continuity	continuity	NOUN
ejpam-3714	41	10	of	of	ADP
ejpam-3714	41	11	h(x	h(x	PROPN
ejpam-3714	41	12	)	)	PUNCT
ejpam-3714	41	13	be	be	VERB
ejpam-3714	41	14	:	:	PUNCT
ejpam-3714	41	15	m(h	m(h	VERB
ejpam-3714	41	16	;	;	PUNCT
ejpam-3714	41	17	r	r	X
ejpam-3714	41	18	)	)	PUNCT
ejpam-3714	41	19	=	=	SYM
ejpam-3714	41	20	sup	sup	NOUN
ejpam-3714	41	21	0≤r	0≤r	NOUN
ejpam-3714	41	22	,	,	PUNCT
ejpam-3714	41	23	x∈r	x∈r	PROPN
ejpam-3714	41	24	|h(x+	|h(x+	PROPN
ejpam-3714	41	25	v	v	NOUN
ejpam-3714	41	26	)	)	PUNCT
ejpam-3714	42	1	+	+	SYM
ejpam-3714	42	2	h(x−	h(x−	ADP
ejpam-3714	42	3	v)|(see	v)|(see	NOUN
ejpam-3714	42	4	[	[	X
ejpam-3714	42	5	2	2	X
ejpam-3714	42	6	]	]	PUNCT
ejpam-3714	42	7	let	let	VERB
ejpam-3714	42	8	b	b	NOUN
ejpam-3714	42	9	represents	represent	VERB
ejpam-3714	42	10	the	the	DET
ejpam-3714	42	11	banach	banach	NOUN
ejpam-3714	42	12	space	space	NOUN
ejpam-3714	42	13	of	of	ADP
ejpam-3714	42	14	all	all	DET
ejpam-3714	42	15	2π	2π	NUM
ejpam-3714	42	16	periodic	periodic	ADJ
ejpam-3714	42	17	functions	function	NOUN
ejpam-3714	42	18	which	which	PRON
ejpam-3714	42	19	are	be	AUX
ejpam-3714	42	20	continuous	continuous	ADJ
ejpam-3714	42	21	and	and	CCONJ
ejpam-3714	42	22	defined	define	VERB
ejpam-3714	42	23	over	over	ADP
ejpam-3714	42	24	[	[	X
ejpam-3714	42	25	0	0	NUM
ejpam-3714	42	26	,	,	PUNCT
ejpam-3714	42	27	2π	2π	NOUN
ejpam-3714	42	28	]	]	PUNCT
ejpam-3714	42	29	under	under	ADP
ejpam-3714	42	30	the	the	DET
ejpam-3714	42	31	supremum	supremum	ADJ
ejpam-3714	42	32	norm	norm	NOUN
ejpam-3714	42	33	.	.	PUNCT
ejpam-3714	43	1	clearly	clearly	ADV
ejpam-3714	43	2	,	,	PUNCT
ejpam-3714	43	3	z(α	z(α	PROPN
ejpam-3714	43	4	)	)	PUNCT
ejpam-3714	43	5	=	=	PRON
ejpam-3714	43	6	{	{	PUNCT
ejpam-3714	43	7	h	h	NOUN
ejpam-3714	43	8	∈	∈	PROPN
ejpam-3714	43	9	b	b	PROPN
ejpam-3714	43	10	:	:	PUNCT
ejpam-3714	43	11	|h(x+	|h(x+	NOUN
ejpam-3714	43	12	v	v	NOUN
ejpam-3714	43	13	)	)	PUNCT
ejpam-3714	44	1	+	+	SYM
ejpam-3714	44	2	h(x−	h(x−	VERB
ejpam-3714	44	3	v)|	v)|	NOUN
ejpam-3714	44	4	=	=	X
ejpam-3714	44	5	o	o	X
ejpam-3714	44	6	(	(	PUNCT
ejpam-3714	44	7	|v|α	|v|α	PROPN
ejpam-3714	44	8	)	)	PUNCT
ejpam-3714	44	9	,	,	PUNCT
ejpam-3714	44	10	0	0	NUM
ejpam-3714	44	11	<	<	X
ejpam-3714	44	12	α	α	PROPN
ejpam-3714	44	13	≤	≤	NUM
ejpam-3714	44	14	1	1	NUM
ejpam-3714	44	15	}	}	PUNCT
ejpam-3714	44	16	is	be	AUX
ejpam-3714	44	17	a	a	DET
ejpam-3714	44	18	banach	banach	NOUN
ejpam-3714	44	19	space	space	NOUN
ejpam-3714	44	20	under	under	ADP
ejpam-3714	44	21	the	the	DET
ejpam-3714	44	22	norm	norm	NOUN
ejpam-3714	44	23	‖.‖(α	‖.‖(α	NOUN
ejpam-3714	44	24	)	)	PUNCT
ejpam-3714	44	25	defined	define	VERB
ejpam-3714	44	26	by	by	ADP
ejpam-3714	44	27	‖h‖(α	‖h‖(α	PRON
ejpam-3714	44	28	)	)	PUNCT
ejpam-3714	44	29	=	=	SYM
ejpam-3714	44	30	sup	sup	NOUN
ejpam-3714	44	31	0≤x≤2π	0≤x≤2π	PROPN
ejpam-3714	44	32	|h(x)|+	|h(x)|+	NOUN
ejpam-3714	44	33	sup	sup	NOUN
ejpam-3714	44	34	x	x	NOUN
ejpam-3714	44	35	,	,	PUNCT
ejpam-3714	44	36	t6=0	t6=0	PROPN
ejpam-3714	44	37	|h(x+	|h(x+	NOUN
ejpam-3714	44	38	v	v	NOUN
ejpam-3714	44	39	)	)	PUNCT
ejpam-3714	44	40	+	+	SYM
ejpam-3714	44	41	h(x−	h(x−	VERB
ejpam-3714	44	42	v)|	v)|	NOUN
ejpam-3714	44	43	|v|α	|v|α	NOUN
ejpam-3714	44	44	for	for	ADP
ejpam-3714	44	45	h	h	NOUN
ejpam-3714	44	46	∈	∈	PROPN
ejpam-3714	44	47	ll[0	ll[0	NOUN
ejpam-3714	44	48	,	,	PUNCT
ejpam-3714	44	49	2π	2π	NOUN
ejpam-3714	44	50	]	]	PUNCT
ejpam-3714	44	51	,	,	PUNCT
ejpam-3714	44	52	(	(	PUNCT
ejpam-3714	44	53	l	l	X
ejpam-3714	44	54	≥	≥	NUM
ejpam-3714	44	55	1	1	NUM
ejpam-3714	44	56	)	)	PUNCT
ejpam-3714	44	57	,	,	PUNCT
ejpam-3714	44	58	the	the	DET
ejpam-3714	44	59	integral	integral	ADJ
ejpam-3714	44	60	zygmund	zygmund	NOUN
ejpam-3714	44	61	modulus	modulus	NOUN
ejpam-3714	44	62	of	of	ADP
ejpam-3714	44	63	continuity	continuity	NOUN
ejpam-3714	44	64	is	be	AUX
ejpam-3714	44	65	defined	define	VERB
ejpam-3714	44	66	by	by	ADP
ejpam-3714	44	67	ml(h	ml(h	ADJ
ejpam-3714	44	68	;	;	PUNCT
ejpam-3714	44	69	r	r	X
ejpam-3714	44	70	)	)	PUNCT
ejpam-3714	44	71	=	=	SYM
ejpam-3714	44	72	sup	sup	NOUN
ejpam-3714	44	73	0	0	NUM
ejpam-3714	44	74	<	<	X
ejpam-3714	44	75	v≤r	v≤r	PROPN
ejpam-3714	44	76	{	{	PUNCT
ejpam-3714	44	77	1	1	NUM
ejpam-3714	44	78	2π	2π	NUM
ejpam-3714	44	79	∫	∫	PROPN
ejpam-3714	44	80	2π	2π	PROPN
ejpam-3714	44	81	0	0	NUM
ejpam-3714	44	82	|h(x+	|h(x+	NOUN
ejpam-3714	44	83	v	v	NOUN
ejpam-3714	44	84	)	)	PUNCT
ejpam-3714	44	85	+	+	NUM
ejpam-3714	44	86	h(x−	h(x−	PROPN
ejpam-3714	44	87	v)|ldx	v)|ldx	PROPN
ejpam-3714	44	88	}	}	PUNCT
ejpam-3714	44	89	1	1	NUM
ejpam-3714	44	90	l	l	NOUN
ejpam-3714	44	91	and	and	CCONJ
ejpam-3714	44	92	for	for	ADP
ejpam-3714	44	93	h	h	PROPN
ejpam-3714	44	94	∈	∈	PROPN
ejpam-3714	44	95	b	b	PROPN
ejpam-3714	44	96	,	,	PUNCT
ejpam-3714	44	97	l	l	PROPN
ejpam-3714	44	98	=	=	SYM
ejpam-3714	44	99	∞	∞	PROPN
ejpam-3714	44	100	,	,	PUNCT
ejpam-3714	44	101	m∞(h	m∞(h	NOUN
ejpam-3714	44	102	;	;	PUNCT
ejpam-3714	44	103	r	r	X
ejpam-3714	44	104	)	)	PUNCT
ejpam-3714	44	105	=	=	SYM
ejpam-3714	44	106	sup	sup	NOUN
ejpam-3714	44	107	0	0	NUM
ejpam-3714	44	108	<	<	X
ejpam-3714	44	109	v≤r	v≤r	PROPN
ejpam-3714	44	110	max	max	PROPN
ejpam-3714	44	111	x	x	X
ejpam-3714	44	112	|h(x+	|h(x+	NOUN
ejpam-3714	44	113	v	v	NOUN
ejpam-3714	44	114	)	)	PUNCT
ejpam-3714	44	115	+	+	NUM
ejpam-3714	44	116	h(x−	h(x−	NOUN
ejpam-3714	44	117	v)|	v)|	NOUN
ejpam-3714	44	118	.	.	PUNCT
ejpam-3714	45	1	clearly	clearly	ADV
ejpam-3714	45	2	,	,	PUNCT
ejpam-3714	45	3	ml(h	ml(h	NUM
ejpam-3714	45	4	;	;	PUNCT
ejpam-3714	45	5	r)→	r)→	NOUN
ejpam-3714	45	6	0	0	PUNCT
ejpam-3714	46	1	as	as	ADP
ejpam-3714	46	2	l→	l→	NOUN
ejpam-3714	46	3	0	0	NUM
ejpam-3714	46	4	.	.	PUNCT
ejpam-3714	47	1	let	let	VERB
ejpam-3714	47	2	us	we	PRON
ejpam-3714	47	3	define	define	VERB
ejpam-3714	47	4	the	the	DET
ejpam-3714	47	5	space	space	NOUN
ejpam-3714	47	6	z(α	z(α	PROPN
ejpam-3714	47	7	)	)	PUNCT
ejpam-3714	47	8	,	,	PUNCT
ejpam-3714	47	9	l	l	NOUN
ejpam-3714	47	10	=	=	PRON
ejpam-3714	47	11	{	{	PUNCT
ejpam-3714	47	12	h	h	NOUN
ejpam-3714	47	13	∈	∈	NOUN
ejpam-3714	47	14	ll[0	ll[0	NOUN
ejpam-3714	47	15	,	,	PUNCT
ejpam-3714	47	16	2π	2π	NOUN
ejpam-3714	47	17	]	]	PUNCT
ejpam-3714	47	18	:	:	PUNCT
ejpam-3714	47	19	(	(	PUNCT
ejpam-3714	47	20	∫	∫	PROPN
ejpam-3714	47	21	2π	2π	PROPN
ejpam-3714	47	22	0	0	NUM
ejpam-3714	47	23	|h(x+	|h(x+	NOUN
ejpam-3714	47	24	v	v	NOUN
ejpam-3714	47	25	)	)	PUNCT
ejpam-3714	47	26	+	+	NUM
ejpam-3714	47	27	h(x−	h(x−	PROPN
ejpam-3714	47	28	v)|ldx	v)|ldx	PROPN
ejpam-3714	47	29	)	)	PUNCT
ejpam-3714	47	30	1	1	NUM
ejpam-3714	47	31	l	l	NOUN
ejpam-3714	47	32	which	which	PRON
ejpam-3714	47	33	is	be	AUX
ejpam-3714	47	34	a	a	DET
ejpam-3714	47	35	banach	banach	NOUN
ejpam-3714	47	36	space	space	NOUN
ejpam-3714	47	37	under	under	ADP
ejpam-3714	47	38	the	the	DET
ejpam-3714	47	39	norm	norm	NOUN
ejpam-3714	47	40	‖.‖(α	‖.‖(α	PROPN
ejpam-3714	47	41	)	)	PUNCT
ejpam-3714	47	42	,	,	PUNCT
ejpam-3714	47	43	l	l	NOUN
ejpam-3714	47	44	for	for	ADP
ejpam-3714	47	45	0	0	NUM
ejpam-3714	47	46	<	<	X
ejpam-3714	47	47	α	α	PROPN
ejpam-3714	47	48	≤	≤	NUM
ejpam-3714	47	49	1	1	NUM
ejpam-3714	47	50	and	and	CCONJ
ejpam-3714	47	51	l	l	NOUN
ejpam-3714	47	52	≥	≥	NUM
ejpam-3714	47	53	1	1	NUM
ejpam-3714	47	54	.	.	PUNCT
ejpam-3714	48	1	clearly	clearly	ADV
ejpam-3714	48	2	,	,	PUNCT
ejpam-3714	48	3	‖h‖(α	‖h‖(α	NUM
ejpam-3714	48	4	)	)	PUNCT
ejpam-3714	48	5	,	,	PUNCT
ejpam-3714	48	6	l	l	NOUN
ejpam-3714	48	7	=	=	PUNCT
ejpam-3714	48	8	‖h‖l	‖h‖l	NOUN
ejpam-3714	48	9	+	+	CCONJ
ejpam-3714	48	10	sup	sup	PROPN
ejpam-3714	48	11	v	v	NUM
ejpam-3714	48	12	6=0	6=0	NUM
ejpam-3714	48	13	‖h(.+	‖h(.+	SYM
ejpam-3714	48	14	v	v	NOUN
ejpam-3714	48	15	)	)	PUNCT
ejpam-3714	49	1	+	+	CCONJ
ejpam-3714	49	2	h(.−	h(.−	ADJ
ejpam-3714	49	3	v)‖l	v)‖l	NOUN
ejpam-3714	49	4	|v|α	|v|α	PRON
ejpam-3714	49	5	let	let	VERB
ejpam-3714	49	6	z(m	z(m	NOUN
ejpam-3714	49	7	)	)	PUNCT
ejpam-3714	50	1	=	=	PRON
ejpam-3714	50	2	{	{	PUNCT
ejpam-3714	50	3	h	h	NOUN
ejpam-3714	50	4	∈	∈	PROPN
ejpam-3714	50	5	b	b	PROPN
ejpam-3714	50	6	:	:	PUNCT
ejpam-3714	50	7	|h(x+	|h(x+	NOUN
ejpam-3714	50	8	v	v	NOUN
ejpam-3714	50	9	)	)	PUNCT
ejpam-3714	50	10	+	+	SYM
ejpam-3714	50	11	h(x−	h(x−	VERB
ejpam-3714	50	12	v)|	v)|	NOUN
ejpam-3714	50	13	=	=	X
ejpam-3714	50	14	o	o	X
ejpam-3714	50	15	(	(	PUNCT
ejpam-3714	50	16	m(v	m(v	PROPN
ejpam-3714	50	17	)	)	PUNCT
ejpam-3714	50	18	)	)	PUNCT
ejpam-3714	50	19	}	}	PUNCT
ejpam-3714	50	20	a.	a.	PROPN
ejpam-3714	50	21	mishra	mishra	PROPN
ejpam-3714	50	22	,	,	PUNCT
ejpam-3714	50	23	b.	b.	PROPN
ejpam-3714	50	24	p.	p.	PROPN
ejpam-3714	50	25	padhy	padhy	PROPN
ejpam-3714	50	26	,	,	PUNCT
ejpam-3714	50	27	u.	u.	PROPN
ejpam-3714	50	28	k.	k.	PROPN
ejpam-3714	50	29	misra	misra	PROPN
ejpam-3714	50	30	/	/	SYM
ejpam-3714	50	31	eur	eur	PROPN
ejpam-3714	50	32	.	.	PUNCT
ejpam-3714	51	1	j.	j.	PROPN
ejpam-3714	51	2	pure	pure	PROPN
ejpam-3714	51	3	appl	appl	PROPN
ejpam-3714	51	4	.	.	PROPN
ejpam-3714	51	5	math	math	PROPN
ejpam-3714	51	6	,	,	PUNCT
ejpam-3714	51	7	13	13	NUM
ejpam-3714	51	8	(	(	PUNCT
ejpam-3714	51	9	5	5	NUM
ejpam-3714	51	10	)	)	PUNCT
ejpam-3714	51	11	(	(	PUNCT
ejpam-3714	51	12	2020	2020	NUM
ejpam-3714	51	13	)	)	PUNCT
ejpam-3714	51	14	,	,	PUNCT
ejpam-3714	51	15	1325	1325	NUM
ejpam-3714	51	16	-	-	SYM
ejpam-3714	51	17	1336	1336	NUM
ejpam-3714	51	18	1328	1328	NUM
ejpam-3714	51	19	where	where	SCONJ
ejpam-3714	51	20	m	m	PROPN
ejpam-3714	51	21	is	be	AUX
ejpam-3714	51	22	a	a	DET
ejpam-3714	51	23	zygmund	zygmund	ADJ
ejpam-3714	51	24	modulus	modulus	NOUN
ejpam-3714	51	25	of	of	ADP
ejpam-3714	51	26	continuity	continuity	NOUN
ejpam-3714	51	27	satisfying	satisfying	NOUN
ejpam-3714	51	28	(	(	PUNCT
ejpam-3714	51	29	a)m(0	a)m(0	NOUN
ejpam-3714	51	30	)	)	PUNCT
ejpam-3714	51	31	=	=	SYM
ejpam-3714	51	32	0	0	NUM
ejpam-3714	51	33	(	(	PUNCT
ejpam-3714	51	34	b)m(v1	b)m(v1	X
ejpam-3714	51	35	+	+	CCONJ
ejpam-3714	51	36	v2	v2	NOUN
ejpam-3714	51	37	)	)	PUNCT
ejpam-3714	51	38	≤	≤	NUM
ejpam-3714	51	39	m(v1	m(v1	NOUN
ejpam-3714	51	40	)	)	PUNCT
ejpam-3714	52	1	+	+	NOUN
ejpam-3714	52	2	m(v2	m(v2	NOUN
ejpam-3714	52	3	)	)	PUNCT
ejpam-3714	52	4	.	.	PUNCT
ejpam-3714	53	1	let	let	VERB
ejpam-3714	53	2	m	m	PRON
ejpam-3714	53	3	:	:	PUNCT
ejpam-3714	54	1	[	[	X
ejpam-3714	54	2	0	0	NUM
ejpam-3714	54	3	,	,	PUNCT
ejpam-3714	54	4	2π]→	2π]→	NUM
ejpam-3714	54	5	r	r	NOUN
ejpam-3714	54	6	a	a	DET
ejpam-3714	54	7	function	function	NOUN
ejpam-3714	54	8	with	with	ADP
ejpam-3714	54	9	m(v	m(v	NOUN
ejpam-3714	54	10	)	)	PUNCT
ejpam-3714	54	11	>	>	X
ejpam-3714	54	12	0	0	PUNCT
ejpam-3714	54	13	for	for	ADP
ejpam-3714	54	14	0	0	NUM
ejpam-3714	54	15	≤	≤	NUM
ejpam-3714	54	16	v	v	ADP
ejpam-3714	54	17	<	<	X
ejpam-3714	54	18	2π	2π	PROPN
ejpam-3714	54	19	and	and	CCONJ
ejpam-3714	54	20	lim	lim	PROPN
ejpam-3714	54	21	v→0	v→0	AUX
ejpam-3714	54	22	+	+	CCONJ
ejpam-3714	54	23	m(v	m(v	NUM
ejpam-3714	54	24	)	)	PUNCT
ejpam-3714	54	25	=	=	SYM
ejpam-3714	54	26	m(0	m(0	PROPN
ejpam-3714	54	27	)	)	PUNCT
ejpam-3714	54	28	=	=	SYM
ejpam-3714	54	29	0	0	X
ejpam-3714	54	30	.	.	PUNCT
ejpam-3714	54	31	define	define	VERB
ejpam-3714	54	32	z	z	PROPN
ejpam-3714	54	33	(	(	PUNCT
ejpam-3714	54	34	m	m	NOUN
ejpam-3714	54	35	)	)	PUNCT
ejpam-3714	54	36	l	l	NOUN
ejpam-3714	55	1	=	=	PRON
ejpam-3714	55	2	{	{	PUNCT
ejpam-3714	55	3	h	h	NOUN
ejpam-3714	55	4	∈	∈	PROPN
ejpam-3714	55	5	ll	ll	AUX
ejpam-3714	55	6	:	:	PUNCT
ejpam-3714	55	7	1	1	NUM
ejpam-3714	55	8	≤	≤	NUM
ejpam-3714	55	9	l	l	NOUN
ejpam-3714	55	10	<	<	X
ejpam-3714	55	11	∞	∞	PROPN
ejpam-3714	55	12	,	,	PUNCT
ejpam-3714	55	13	sup	sup	NOUN
ejpam-3714	55	14	v	v	NUM
ejpam-3714	55	15	6=0	6=0	NUM
ejpam-3714	55	16	‖h(.+	‖h(.+	SYM
ejpam-3714	55	17	v	v	NOUN
ejpam-3714	55	18	)	)	PUNCT
ejpam-3714	55	19	+	+	CCONJ
ejpam-3714	55	20	h(.−	h(.−	ADJ
ejpam-3714	55	21	v)‖l	v)‖l	NOUN
ejpam-3714	55	22	m(v	m(v	NOUN
ejpam-3714	55	23	)	)	PUNCT
ejpam-3714	55	24	<	<	X
ejpam-3714	55	25	∞	∞	NUM
ejpam-3714	55	26	}	}	PUNCT
ejpam-3714	55	27	where	where	SCONJ
ejpam-3714	55	28	‖h‖(m	‖h‖(m	NOUN
ejpam-3714	55	29	)	)	PUNCT
ejpam-3714	55	30	l	l	NOUN
ejpam-3714	55	31	=	=	PUNCT
ejpam-3714	55	32	‖h‖l	‖h‖l	NOUN
ejpam-3714	56	1	+	+	CCONJ
ejpam-3714	56	2	sup	sup	PROPN
ejpam-3714	56	3	v	v	NUM
ejpam-3714	56	4	6=0	6=0	NUM
ejpam-3714	56	5	‖h(.+	‖h(.+	SYM
ejpam-3714	56	6	v	v	NOUN
ejpam-3714	56	7	)	)	PUNCT
ejpam-3714	57	1	+	+	CCONJ
ejpam-3714	57	2	h(.−	h(.−	ADJ
ejpam-3714	57	3	v)‖l	v)‖l	NOUN
ejpam-3714	57	4	m(v	m(v	NUM
ejpam-3714	57	5	)	)	PUNCT
ejpam-3714	57	6	,	,	PUNCT
ejpam-3714	57	7	l	l	X
ejpam-3714	57	8	≥	≥	NUM
ejpam-3714	57	9	1	1	NUM
ejpam-3714	57	10	.	.	PUNCT
ejpam-3714	58	1	clearly	clearly	ADV
ejpam-3714	58	2	,	,	PUNCT
ejpam-3714	58	3	‖.‖(m	‖.‖(m	NOUN
ejpam-3714	58	4	)	)	PUNCT
ejpam-3714	58	5	l	l	NOUN
ejpam-3714	58	6	is	be	AUX
ejpam-3714	58	7	a	a	DET
ejpam-3714	58	8	norm	norm	NOUN
ejpam-3714	58	9	z	z	NOUN
ejpam-3714	58	10	(	(	PUNCT
ejpam-3714	58	11	m	m	NOUN
ejpam-3714	58	12	)	)	PUNCT
ejpam-3714	58	13	l	l	NOUN
ejpam-3714	58	14	.	.	PUNCT
ejpam-3714	59	1	also	also	ADV
ejpam-3714	59	2	,	,	PUNCT
ejpam-3714	59	3	z	z	PROPN
ejpam-3714	59	4	(	(	PUNCT
ejpam-3714	59	5	m	m	NOUN
ejpam-3714	59	6	)	)	PUNCT
ejpam-3714	59	7	l	l	NOUN
ejpam-3714	59	8	is	be	AUX
ejpam-3714	59	9	complete	complete	ADJ
ejpam-3714	59	10	since	since	SCONJ
ejpam-3714	59	11	ll	ll	PRON
ejpam-3714	59	12	,	,	PUNCT
ejpam-3714	59	13	(	(	PUNCT
ejpam-3714	59	14	l	l	X
ejpam-3714	59	15	≥	≥	NUM
ejpam-3714	59	16	1	1	NUM
ejpam-3714	59	17	)	)	PUNCT
ejpam-3714	59	18	is	be	AUX
ejpam-3714	59	19	complete	complete	ADJ
ejpam-3714	59	20	.	.	PUNCT
ejpam-3714	60	1	so	so	ADV
ejpam-3714	60	2	,	,	PUNCT
ejpam-3714	60	3	z	z	PROPN
ejpam-3714	60	4	(	(	PUNCT
ejpam-3714	60	5	m	m	NOUN
ejpam-3714	60	6	)	)	PUNCT
ejpam-3714	60	7	l	l	NOUN
ejpam-3714	60	8	is	be	AUX
ejpam-3714	60	9	a	a	DET
ejpam-3714	60	10	banach	banach	NOUN
ejpam-3714	60	11	space	space	NOUN
ejpam-3714	60	12	under	under	ADP
ejpam-3714	60	13	‖.‖(m	‖.‖(m	NOUN
ejpam-3714	60	14	)	)	PUNCT
ejpam-3714	60	15	l	l	NOUN
ejpam-3714	60	16	.	.	PUNCT
ejpam-3714	61	1	let	let	VERB
ejpam-3714	61	2	m(v	m(v	NUM
ejpam-3714	61	3	)	)	PUNCT
ejpam-3714	61	4	and	and	CCONJ
ejpam-3714	61	5	µ(v	µ(v	PROPN
ejpam-3714	61	6	)	)	PUNCT
ejpam-3714	61	7	represents	represent	VERB
ejpam-3714	61	8	the	the	DET
ejpam-3714	61	9	zygmund	zygmund	PROPN
ejpam-3714	61	10	moduli	moduli	NOUN
ejpam-3714	61	11	of	of	ADP
ejpam-3714	61	12	continuity	continuity	NOUN
ejpam-3714	61	13	such	such	ADJ
ejpam-3714	61	14	that	that	SCONJ
ejpam-3714	61	15	(	(	PUNCT
ejpam-3714	61	16	m(v	m(v	PROPN
ejpam-3714	61	17	)	)	PUNCT
ejpam-3714	61	18	µ(v	µ(v	PROPN
ejpam-3714	61	19	)	)	PUNCT
ejpam-3714	61	20	)	)	PUNCT
ejpam-3714	61	21	is	be	AUX
ejpam-3714	61	22	positive	positive	ADJ
ejpam-3714	61	23	and	and	CCONJ
ejpam-3714	61	24	non	non	ADJ
ejpam-3714	61	25	-	-	ADJ
ejpam-3714	61	26	decreasing	decrease	VERB
ejpam-3714	61	27	then	then	ADV
ejpam-3714	61	28	‖h‖(µ	‖h‖(µ	NOUN
ejpam-3714	61	29	)	)	PUNCT
ejpam-3714	61	30	l	l	NOUN
ejpam-3714	61	31	≤	≤	NUM
ejpam-3714	61	32	max	max	NOUN
ejpam-3714	61	33	.	.	PUNCT
ejpam-3714	62	1	(	(	PUNCT
ejpam-3714	62	2	1	1	NUM
ejpam-3714	62	3	,	,	PUNCT
ejpam-3714	62	4	m(2π	m(2π	NOUN
ejpam-3714	62	5	)	)	PUNCT
ejpam-3714	62	6	µ(2π	µ(2π	NUM
ejpam-3714	62	7	)	)	PUNCT
ejpam-3714	62	8	)	)	PUNCT
ejpam-3714	62	9	‖h‖(m	‖h‖(m	PROPN
ejpam-3714	62	10	)	)	PUNCT
ejpam-3714	62	11	l	l	NOUN
ejpam-3714	62	12	≤	≤	NUM
ejpam-3714	62	13	∞	∞	NUM
ejpam-3714	62	14	(	(	PUNCT
ejpam-3714	62	15	2	2	NUM
ejpam-3714	62	16	)	)	PUNCT
ejpam-3714	62	17	clearly	clearly	ADV
ejpam-3714	62	18	,	,	PUNCT
ejpam-3714	62	19	z	z	PROPN
ejpam-3714	62	20	(	(	PUNCT
ejpam-3714	62	21	m	m	NOUN
ejpam-3714	62	22	)	)	PUNCT
ejpam-3714	62	23	l	l	NOUN
ejpam-3714	62	24	⊆	⊆	NUM
ejpam-3714	62	25	z(µ	z(µ	NOUN
ejpam-3714	62	26	)	)	PUNCT
ejpam-3714	62	27	l	l	NOUN
ejpam-3714	62	28	⊆	⊆	NUM
ejpam-3714	62	29	ll	ll	NOUN
ejpam-3714	62	30	,	,	PUNCT
ejpam-3714	62	31	(	(	PUNCT
ejpam-3714	62	32	l	l	X
ejpam-3714	62	33	≥	≥	NUM
ejpam-3714	62	34	1	1	NUM
ejpam-3714	62	35	)	)	PUNCT
ejpam-3714	62	36	.	.	PUNCT
ejpam-3714	63	1	let	let	VERB
ejpam-3714	63	2	∑	∑	PROPN
ejpam-3714	63	3	un	un	PROPN
ejpam-3714	63	4	be	be	AUX
ejpam-3714	63	5	an	an	DET
ejpam-3714	63	6	infinite	infinite	ADJ
ejpam-3714	63	7	series	series	NOUN
ejpam-3714	63	8	with	with	ADP
ejpam-3714	63	9	sequence	sequence	NOUN
ejpam-3714	63	10	of	of	ADP
ejpam-3714	63	11	partial	partial	ADJ
ejpam-3714	63	12	sums	sum	NOUN
ejpam-3714	63	13	{	{	PUNCT
ejpam-3714	63	14	sn	sn	NOUN
ejpam-3714	63	15	}	}	PUNCT
ejpam-3714	63	16	.	.	PUNCT
ejpam-3714	64	1	let	let	AUX
ejpam-3714	64	2	{	{	PUNCT
ejpam-3714	64	3	qk	qk	PART
ejpam-3714	64	4	}	}	PUNCT
ejpam-3714	64	5	represents	represent	VERB
ejpam-3714	64	6	the	the	DET
ejpam-3714	64	7	sequence	sequence	NOUN
ejpam-3714	64	8	of	of	ADP
ejpam-3714	64	9	non	non	ADJ
ejpam-3714	64	10	-	-	ADJ
ejpam-3714	64	11	negative	negative	ADJ
ejpam-3714	64	12	integers	integer	NOUN
ejpam-3714	64	13	such	such	ADJ
ejpam-3714	64	14	that	that	DET
ejpam-3714	64	15	qn	qn	PROPN
ejpam-3714	64	16	=	=	PROPN
ejpam-3714	64	17	n∑	n∑	PROPN
ejpam-3714	64	18	k=0	k=0	PROPN
ejpam-3714	64	19	qk	qk	ADP
ejpam-3714	64	20	→∞	→∞	PROPN
ejpam-3714	64	21	as	as	ADP
ejpam-3714	64	22	n→∞.	n→∞.	PROPN
ejpam-3714	64	23	(	(	PUNCT
ejpam-3714	64	24	3	3	X
ejpam-3714	64	25	)	)	PUNCT
ejpam-3714	64	26	let	let	VERB
ejpam-3714	64	27	τnn	τnn	NOUN
ejpam-3714	64	28	=	=	SYM
ejpam-3714	64	29	1	1	NUM
ejpam-3714	64	30	qn	qn	NOUN
ejpam-3714	64	31	n∑	n∑	PROPN
ejpam-3714	64	32	k=0	k=0	PROPN
ejpam-3714	64	33	qn−ksk	qn−ksk	PROPN
ejpam-3714	64	34	,	,	PUNCT
ejpam-3714	64	35	n	n	NOUN
ejpam-3714	64	36	=	=	SYM
ejpam-3714	64	37	0	0	NUM
ejpam-3714	64	38	,	,	PUNCT
ejpam-3714	64	39	1	1	NUM
ejpam-3714	64	40	,	,	PUNCT
ejpam-3714	64	41	2	2	NUM
ejpam-3714	64	42	,	,	PUNCT
ejpam-3714	64	43	...	...	PUNCT
ejpam-3714	64	44	(	(	PUNCT
ejpam-3714	64	45	4	4	X
ejpam-3714	64	46	)	)	PUNCT
ejpam-3714	64	47	represents	represent	VERB
ejpam-3714	64	48	the	the	DET
ejpam-3714	64	49	(	(	PUNCT
ejpam-3714	64	50	n	n	CCONJ
ejpam-3714	64	51	,	,	PUNCT
ejpam-3714	64	52	qn	qn	NOUN
ejpam-3714	64	53	)	)	PUNCT
ejpam-3714	64	54	mean	mean	NOUN
ejpam-3714	64	55	of	of	ADP
ejpam-3714	64	56	{	{	PUNCT
ejpam-3714	64	57	sn	sn	NOUN
ejpam-3714	64	58	}	}	PUNCT
ejpam-3714	64	59	generated	generate	VERB
ejpam-3714	64	60	by	by	ADP
ejpam-3714	64	61	the	the	DET
ejpam-3714	64	62	sequence	sequence	NOUN
ejpam-3714	64	63	{	{	PUNCT
ejpam-3714	64	64	qn	qn	NOUN
ejpam-3714	64	65	}	}	PUNCT
ejpam-3714	64	66	.	.	PUNCT
ejpam-3714	65	1	by	by	ADP
ejpam-3714	65	2	(	(	PUNCT
ejpam-3714	65	3	n	n	CCONJ
ejpam-3714	65	4	,	,	PUNCT
ejpam-3714	65	5	qn	qn	NOUN
ejpam-3714	65	6	)	)	PUNCT
ejpam-3714	65	7	method	method	NOUN
ejpam-3714	65	8	,	,	PUNCT
ejpam-3714	65	9	the	the	DET
ejpam-3714	65	10	series	series	PROPN
ejpam-3714	65	11	∑	∑	PROPN
ejpam-3714	65	12	un	un	PROPN
ejpam-3714	65	13	is	be	AUX
ejpam-3714	65	14	said	say	VERB
ejpam-3714	65	15	to	to	PART
ejpam-3714	65	16	be	be	AUX
ejpam-3714	65	17	summable	summable	ADJ
ejpam-3714	65	18	to	to	ADP
ejpam-3714	65	19	′s′	′s′	NOUN
ejpam-3714	65	20	if	if	SCONJ
ejpam-3714	65	21	lim	lim	PROPN
ejpam-3714	65	22	n→∞	n→∞	NUM
ejpam-3714	65	23	τnn	τnn	PROPN
ejpam-3714	65	24	→	→	SYM
ejpam-3714	65	25	s.	s.	PROPN
ejpam-3714	65	26	a.	a.	PROPN
ejpam-3714	65	27	mishra	mishra	PROPN
ejpam-3714	65	28	,	,	PUNCT
ejpam-3714	65	29	b.	b.	PROPN
ejpam-3714	65	30	p.	p.	PROPN
ejpam-3714	65	31	padhy	padhy	PROPN
ejpam-3714	65	32	,	,	PUNCT
ejpam-3714	65	33	u.	u.	PROPN
ejpam-3714	65	34	k.	k.	PROPN
ejpam-3714	65	35	misra	misra	PROPN
ejpam-3714	65	36	/	/	SYM
ejpam-3714	65	37	eur	eur	PROPN
ejpam-3714	65	38	.	.	PUNCT
ejpam-3714	66	1	j.	j.	PROPN
ejpam-3714	66	2	pure	pure	PROPN
ejpam-3714	66	3	appl	appl	PROPN
ejpam-3714	66	4	.	.	PROPN
ejpam-3714	66	5	math	math	PROPN
ejpam-3714	66	6	,	,	PUNCT
ejpam-3714	66	7	13	13	NUM
ejpam-3714	66	8	(	(	PUNCT
ejpam-3714	66	9	5	5	NUM
ejpam-3714	66	10	)	)	PUNCT
ejpam-3714	66	11	(	(	PUNCT
ejpam-3714	66	12	2020	2020	NUM
ejpam-3714	66	13	)	)	PUNCT
ejpam-3714	66	14	,	,	PUNCT
ejpam-3714	66	15	1325	1325	NUM
ejpam-3714	66	16	-	-	SYM
ejpam-3714	66	17	1336	1336	NUM
ejpam-3714	66	18	1329	1329	NUM
ejpam-3714	66	19	we	we	PRON
ejpam-3714	66	20	know	know	VERB
ejpam-3714	66	21	,	,	PUNCT
ejpam-3714	66	22	(	(	PUNCT
ejpam-3714	66	23	n	n	CCONJ
ejpam-3714	66	24	,	,	PUNCT
ejpam-3714	66	25	qn	qn	NOUN
ejpam-3714	66	26	)	)	PUNCT
ejpam-3714	66	27	method	method	NOUN
ejpam-3714	66	28	is	be	AUX
ejpam-3714	66	29	regular	regular	ADJ
ejpam-3714	66	30	[	[	X
ejpam-3714	66	31	5	5	NUM
ejpam-3714	66	32	]	]	PUNCT
ejpam-3714	66	33	.	.	PUNCT
ejpam-3714	67	1	the	the	DET
ejpam-3714	67	2	(	(	PUNCT
ejpam-3714	67	3	e	e	NOUN
ejpam-3714	67	4	,	,	PUNCT
ejpam-3714	67	5	r	r	NOUN
ejpam-3714	67	6	)	)	PUNCT
ejpam-3714	67	7	transform	transform	NOUN
ejpam-3714	67	8	of	of	ADP
ejpam-3714	67	9	{	{	PUNCT
ejpam-3714	67	10	sn	sn	NOUN
ejpam-3714	67	11	}	}	PUNCT
ejpam-3714	67	12	is	be	AUX
ejpam-3714	67	13	given	give	VERB
ejpam-3714	67	14	by	by	ADP
ejpam-3714	67	15	ern	ern	PROPN
ejpam-3714	67	16	=	=	SYM
ejpam-3714	67	17	1	1	NUM
ejpam-3714	67	18	(	(	PUNCT
ejpam-3714	67	19	1	1	NUM
ejpam-3714	67	20	+	+	CCONJ
ejpam-3714	67	21	r)n	r)n	X
ejpam-3714	67	22	n∑	n∑	DET
ejpam-3714	67	23	k=0	k=0	PROPN
ejpam-3714	67	24	c(n	c(n	PROPN
ejpam-3714	67	25	,	,	PUNCT
ejpam-3714	67	26	k	k	NOUN
ejpam-3714	67	27	)	)	PUNCT
ejpam-3714	67	28	rn−ksk	rn−ksk	NOUN
ejpam-3714	67	29	(	(	PUNCT
ejpam-3714	67	30	5	5	NUM
ejpam-3714	67	31	)	)	PUNCT
ejpam-3714	67	32	if	if	SCONJ
ejpam-3714	67	33	ern	ern	PROPN
ejpam-3714	67	34	→	→	SYM
ejpam-3714	67	35	s	s	PROPN
ejpam-3714	67	36	as	as	ADP
ejpam-3714	67	37	n	n	PROPN
ejpam-3714	67	38	→	→	SYM
ejpam-3714	67	39	∞	∞	PROPN
ejpam-3714	67	40	then	then	ADV
ejpam-3714	67	41	∑	∑	PROPN
ejpam-3714	67	42	un	un	PROPN
ejpam-3714	67	43	is	be	AUX
ejpam-3714	67	44	summable	summable	ADJ
ejpam-3714	67	45	to	to	ADP
ejpam-3714	67	46	’s	’s	NOUN
ejpam-3714	67	47	’	'	PUNCT
ejpam-3714	67	48	by	by	ADP
ejpam-3714	67	49	(	(	PUNCT
ejpam-3714	67	50	e	e	NOUN
ejpam-3714	67	51	,	,	PUNCT
ejpam-3714	67	52	r	r	NOUN
ejpam-3714	67	53	)	)	PUNCT
ejpam-3714	67	54	summability	summability	NOUN
ejpam-3714	67	55	.	.	PUNCT
ejpam-3714	68	1	also	also	ADV
ejpam-3714	68	2	,	,	PUNCT
ejpam-3714	68	3	(	(	PUNCT
ejpam-3714	68	4	e	e	NOUN
ejpam-3714	68	5	,	,	PUNCT
ejpam-3714	68	6	r	r	NOUN
ejpam-3714	68	7	)	)	PUNCT
ejpam-3714	68	8	method	method	NOUN
ejpam-3714	68	9	is	be	AUX
ejpam-3714	68	10	regular	regular	ADJ
ejpam-3714	68	11	[	[	X
ejpam-3714	68	12	5	5	NUM
ejpam-3714	68	13	]	]	PUNCT
ejpam-3714	68	14	.	.	PUNCT
ejpam-3714	69	1	the	the	DET
ejpam-3714	69	2	(	(	PUNCT
ejpam-3714	69	3	e	e	NOUN
ejpam-3714	69	4	,	,	PUNCT
ejpam-3714	69	5	r)(n	r)(n	PROPN
ejpam-3714	69	6	,	,	PUNCT
ejpam-3714	69	7	qn	qn	NOUN
ejpam-3714	69	8	)	)	PUNCT
ejpam-3714	69	9	transform	transform	NOUN
ejpam-3714	69	10	of	of	ADP
ejpam-3714	69	11	{	{	PUNCT
ejpam-3714	69	12	sn	sn	NOUN
ejpam-3714	69	13	}	}	PUNCT
ejpam-3714	69	14	is	be	AUX
ejpam-3714	69	15	given	give	VERB
ejpam-3714	69	16	by	by	ADP
ejpam-3714	69	17	τer	τer	PROPN
ejpam-3714	69	18	,	,	PUNCT
ejpam-3714	69	19	n	n	CCONJ
ejpam-3714	69	20	n	n	NOUN
ejpam-3714	69	21	=	=	SYM
ejpam-3714	69	22	1	1	NUM
ejpam-3714	69	23	(	(	PUNCT
ejpam-3714	69	24	1	1	NUM
ejpam-3714	69	25	+	+	CCONJ
ejpam-3714	69	26	r)n	r)n	X
ejpam-3714	69	27	n∑	n∑	DET
ejpam-3714	69	28	k=0	k=0	PROPN
ejpam-3714	69	29	c(n	c(n	PROPN
ejpam-3714	69	30	,	,	PUNCT
ejpam-3714	69	31	k	k	NOUN
ejpam-3714	69	32	)	)	PUNCT
ejpam-3714	69	33	{	{	PUNCT
ejpam-3714	69	34	1	1	NUM
ejpam-3714	69	35	qk	qk	X
ejpam-3714	69	36	k∑	k∑	VERB
ejpam-3714	69	37	ν=0	ν=0	X
ejpam-3714	69	38	qk−νsν	qk−νsν	ADV
ejpam-3714	69	39	}	}	PUNCT
ejpam-3714	69	40	(	(	PUNCT
ejpam-3714	69	41	6	6	X
ejpam-3714	69	42	)	)	PUNCT
ejpam-3714	69	43	the	the	DET
ejpam-3714	69	44	series	series	PROPN
ejpam-3714	69	45	∑	∑	PROPN
ejpam-3714	69	46	un	un	PROPN
ejpam-3714	69	47	is	be	AUX
ejpam-3714	69	48	summable	summable	ADJ
ejpam-3714	69	49	to	to	ADP
ejpam-3714	69	50	s	s	PRON
ejpam-3714	69	51	by	by	ADP
ejpam-3714	69	52	the	the	DET
ejpam-3714	69	53	(	(	PUNCT
ejpam-3714	69	54	e	e	NOUN
ejpam-3714	69	55	,	,	PUNCT
ejpam-3714	69	56	r)(n	r)(n	PROPN
ejpam-3714	69	57	,	,	PUNCT
ejpam-3714	69	58	qn	qn	NOUN
ejpam-3714	69	59	)	)	PUNCT
ejpam-3714	69	60	transform	transform	NOUN
ejpam-3714	69	61	if	if	SCONJ
ejpam-3714	69	62	τer	τer	PROPN
ejpam-3714	69	63	,	,	PUNCT
ejpam-3714	69	64	n	n	CCONJ
ejpam-3714	69	65	n	n	PROPN
ejpam-3714	69	66	→	→	SYM
ejpam-3714	69	67	s	s	X
ejpam-3714	69	68	as	as	ADP
ejpam-3714	69	69	n→∞.	n→∞.	ADJ
ejpam-3714	69	70	also	also	ADV
ejpam-3714	69	71	we	we	PRON
ejpam-3714	69	72	have	have	AUX
ejpam-3714	69	73	used	use	VERB
ejpam-3714	69	74	the	the	DET
ejpam-3714	69	75	following	following	ADJ
ejpam-3714	69	76	notation	notation	NOUN
ejpam-3714	69	77	in	in	ADP
ejpam-3714	69	78	the	the	DET
ejpam-3714	69	79	rest	rest	NOUN
ejpam-3714	69	80	part	part	NOUN
ejpam-3714	69	81	of	of	ADP
ejpam-3714	69	82	our	our	PRON
ejpam-3714	69	83	paper	paper	NOUN
ejpam-3714	69	84	.	.	PUNCT
ejpam-3714	70	1	ψ(x	ψ(x	NOUN
ejpam-3714	70	2	,	,	PUNCT
ejpam-3714	70	3	v	v	NOUN
ejpam-3714	70	4	)	)	PUNCT
ejpam-3714	70	5	=	=	PUNCT
ejpam-3714	71	1	h(x+	h(x+	ADP
ejpam-3714	71	2	v	v	NOUN
ejpam-3714	71	3	)	)	PUNCT
ejpam-3714	72	1	+	+	NUM
ejpam-3714	72	2	h(x−	h(x−	ADP
ejpam-3714	72	3	v	v	NOUN
ejpam-3714	72	4	)	)	PUNCT
ejpam-3714	72	5	3	3	NUM
ejpam-3714	72	6	.	.	PUNCT
ejpam-3714	72	7	known	know	VERB
ejpam-3714	72	8	result	result	NOUN
ejpam-3714	72	9	using	use	VERB
ejpam-3714	72	10	hausdorff	hausdorff	NOUN
ejpam-3714	72	11	mean	mean	PROPN
ejpam-3714	72	12	,	,	PUNCT
ejpam-3714	72	13	nigam	nigam	PROPN
ejpam-3714	73	1	[	[	X
ejpam-3714	73	2	7	7	NUM
ejpam-3714	73	3	]	]	PUNCT
ejpam-3714	73	4	proved	prove	VERB
ejpam-3714	73	5	the	the	DET
ejpam-3714	73	6	following	follow	VERB
ejpam-3714	73	7	theorem	theorem	NOUN
ejpam-3714	73	8	:	:	PUNCT
ejpam-3714	73	9	theorem	theorem	ADJ
ejpam-3714	73	10	1	1	NUM
ejpam-3714	73	11	.	.	PUNCT
ejpam-3714	73	12	error	error	NOUN
ejpam-3714	73	13	approximation	approximation	NOUN
ejpam-3714	73	14	of	of	ADP
ejpam-3714	73	15	a	a	DET
ejpam-3714	73	16	conjugate	conjugate	ADJ
ejpam-3714	73	17	derived	derive	VERB
ejpam-3714	73	18	function	function	NOUN
ejpam-3714	73	19	h′	h′	NOUN
ejpam-3714	73	20	of	of	ADP
ejpam-3714	73	21	a	a	DET
ejpam-3714	73	22	2π	2π	NUM
ejpam-3714	73	23	periodic	periodic	ADJ
ejpam-3714	73	24	function	function	NOUN
ejpam-3714	73	25	h	h	NOUN
ejpam-3714	73	26	∈	∈	PROPN
ejpam-3714	73	27	z(m	z(m	PROPN
ejpam-3714	73	28	)	)	PUNCT
ejpam-3714	73	29	l	l	NOUN
ejpam-3714	73	30	,	,	PUNCT
ejpam-3714	73	31	l	l	X
ejpam-3714	73	32	≥	≥	NUM
ejpam-3714	73	33	1	1	NUM
ejpam-3714	73	34	,	,	PUNCT
ejpam-3714	73	35	using	use	VERB
ejpam-3714	73	36	h	h	NOUN
ejpam-3714	73	37	=	=	PUNCT
ejpam-3714	73	38	(	(	PUNCT
ejpam-3714	73	39	θj	θj	X
ejpam-3714	73	40	,	,	PUNCT
ejpam-3714	73	41	α	α	NOUN
ejpam-3714	73	42	)	)	PUNCT
ejpam-3714	73	43	of	of	ADP
ejpam-3714	73	44	conjugate	conjugate	ADJ
ejpam-3714	73	45	derived	derive	VERB
ejpam-3714	73	46	fourier	fourier	NOUN
ejpam-3714	73	47	series	series	NOUN
ejpam-3714	73	48	is	be	AUX
ejpam-3714	73	49	given	give	VERB
ejpam-3714	73	50	by	by	ADP
ejpam-3714	73	51	‖m	‖m	NOUN
ejpam-3714	74	1	′h	′h	PROPN
ejpam-3714	74	2	j	j	PROPN
ejpam-3714	74	3	(	(	PUNCT
ejpam-3714	74	4	h	h	NOUN
ejpam-3714	74	5	;	;	PUNCT
ejpam-3714	74	6	.)−	.)−	PROPN
ejpam-3714	74	7	h′(.)‖(m	h′(.)‖(m	PROPN
ejpam-3714	74	8	)	)	PUNCT
ejpam-3714	74	9	l	l	NOUN
ejpam-3714	75	1	=	=	PUNCT
ejpam-3714	75	2	o	o	X
ejpam-3714	75	3	(	(	PUNCT
ejpam-3714	75	4	1	1	NUM
ejpam-3714	75	5	j	j	NOUN
ejpam-3714	75	6	+	+	CCONJ
ejpam-3714	75	7	1	1	NUM
ejpam-3714	75	8	∫	∫	NOUN
ejpam-3714	75	9	π	π	NOUN
ejpam-3714	75	10	1	1	NUM
ejpam-3714	75	11	j+1	j+1	PROPN
ejpam-3714	75	12	(	(	PUNCT
ejpam-3714	75	13	v	v	NOUN
ejpam-3714	75	14	+	+	CCONJ
ejpam-3714	75	15	1)m(v	1)m(v	NUM
ejpam-3714	75	16	)	)	PUNCT
ejpam-3714	75	17	v3	v3	PROPN
ejpam-3714	75	18	µ(v	µ(v	PROPN
ejpam-3714	75	19	)	)	PUNCT
ejpam-3714	75	20	dv	dv	PROPN
ejpam-3714	75	21	)	)	PUNCT
ejpam-3714	75	22	,	,	PUNCT
ejpam-3714	75	23	where	where	SCONJ
ejpam-3714	75	24	m(v	m(v	NUM
ejpam-3714	75	25	)	)	PUNCT
ejpam-3714	75	26	and	and	CCONJ
ejpam-3714	75	27	µ(v	µ(v	PROPN
ejpam-3714	75	28	)	)	PUNCT
ejpam-3714	75	29	are	be	AUX
ejpam-3714	75	30	zygmund	zygmund	NOUN
ejpam-3714	75	31	moduli	modulus	NOUN
ejpam-3714	75	32	of	of	ADP
ejpam-3714	75	33	continuity	continuity	NOUN
ejpam-3714	75	34	,	,	PUNCT
ejpam-3714	75	35	provided∫	provided∫	VERB
ejpam-3714	75	36	π	π	PROPN
ejpam-3714	75	37	0	0	NUM
ejpam-3714	75	38	m(v	m(v	NUM
ejpam-3714	75	39	)	)	PUNCT
ejpam-3714	75	40	v2µ(v	v2µ(v	PROPN
ejpam-3714	75	41	)	)	PUNCT
ejpam-3714	75	42	dv	dv	PROPN
ejpam-3714	75	43	=	=	SYM
ejpam-3714	75	44	o	o	PROPN
ejpam-3714	75	45	(	(	PUNCT
ejpam-3714	75	46	m(η	m(η	PROPN
ejpam-3714	75	47	)	)	PUNCT
ejpam-3714	75	48	η	η	PROPN
ejpam-3714	75	49	µ(η	µ(η	NOUN
ejpam-3714	75	50	)	)	PUNCT
ejpam-3714	75	51	)	)	PUNCT
ejpam-3714	75	52	,	,	PUNCT
ejpam-3714	75	53	0	0	NUM
ejpam-3714	75	54	<	<	X
ejpam-3714	75	55	η	η	X
ejpam-3714	75	56	<	<	X
ejpam-3714	75	57	π	π	PROPN
ejpam-3714	75	58	.	.	PROPN
ejpam-3714	76	1	4	4	NUM
ejpam-3714	76	2	.	.	X
ejpam-3714	76	3	main	main	ADJ
ejpam-3714	76	4	theorem	theorem	NOUN
ejpam-3714	76	5	theorem	theorem	NOUN
ejpam-3714	76	6	2	2	NUM
ejpam-3714	76	7	.	.	PUNCT
ejpam-3714	77	1	the	the	DET
ejpam-3714	77	2	degree	degree	NOUN
ejpam-3714	77	3	of	of	ADP
ejpam-3714	77	4	approximation	approximation	NOUN
ejpam-3714	77	5	of	of	ADP
ejpam-3714	77	6	a	a	DET
ejpam-3714	77	7	conjugate	conjugate	ADJ
ejpam-3714	77	8	derived	derive	VERB
ejpam-3714	77	9	function	function	NOUN
ejpam-3714	77	10	h′	h′	NOUN
ejpam-3714	77	11	of	of	ADP
ejpam-3714	77	12	a	a	DET
ejpam-3714	77	13	2π	2π	NUM
ejpam-3714	77	14	periodic	periodic	ADJ
ejpam-3714	77	15	function	function	NOUN
ejpam-3714	77	16	h	h	NOUN
ejpam-3714	77	17	∈	∈	PROPN
ejpam-3714	77	18	z(m	z(m	PROPN
ejpam-3714	77	19	)	)	PUNCT
ejpam-3714	77	20	l	l	NOUN
ejpam-3714	77	21	,	,	PUNCT
ejpam-3714	77	22	l	l	X
ejpam-3714	77	23	≥	≥	NUM
ejpam-3714	77	24	1	1	NUM
ejpam-3714	77	25	,	,	PUNCT
ejpam-3714	77	26	using	use	VERB
ejpam-3714	77	27	(	(	PUNCT
ejpam-3714	77	28	e	e	NOUN
ejpam-3714	77	29	,	,	PUNCT
ejpam-3714	77	30	r)(n	r)(n	PROPN
ejpam-3714	77	31	,	,	PUNCT
ejpam-3714	77	32	qn)mean	qn)mean	ADJ
ejpam-3714	77	33	of	of	ADP
ejpam-3714	77	34	conjugate	conjugate	ADJ
ejpam-3714	77	35	derived	derive	VERB
ejpam-3714	77	36	fourier	fourier	NOUN
ejpam-3714	77	37	series	series	NOUN
ejpam-3714	77	38	is	be	AUX
ejpam-3714	77	39	given	give	VERB
ejpam-3714	77	40	by	by	ADP
ejpam-3714	77	41	en(h	en(h	NOUN
ejpam-3714	77	42	)	)	PUNCT
ejpam-3714	77	43	=	=	SYM
ejpam-3714	77	44	inf	inf	PROPN
ejpam-3714	77	45	n	n	PROPN
ejpam-3714	77	46	‖χn	‖χn	NUM
ejpam-3714	78	1	′	′	NUM
ejpam-3714	78	2	(	(	PUNCT
ejpam-3714	78	3	.)‖µl	.)‖µl	PUNCT
ejpam-3714	79	1	=	=	SYM
ejpam-3714	79	2	o	o	X
ejpam-3714	79	3	(	(	PUNCT
ejpam-3714	79	4	∫	∫	PROPN
ejpam-3714	79	5	π	π	PROPN
ejpam-3714	79	6	1	1	NUM
ejpam-3714	79	7	n+1	n+1	PROPN
ejpam-3714	79	8	m(v	m(v	X
ejpam-3714	79	9	)	)	PUNCT
ejpam-3714	79	10	v2	v2	PROPN
ejpam-3714	79	11	µ(v	µ(v	PROPN
ejpam-3714	79	12	)	)	PUNCT
ejpam-3714	79	13	dv	dv	PROPN
ejpam-3714	79	14	)	)	PUNCT
ejpam-3714	79	15	a.	a.	PROPN
ejpam-3714	79	16	mishra	mishra	PROPN
ejpam-3714	79	17	,	,	PUNCT
ejpam-3714	79	18	b.	b.	PROPN
ejpam-3714	79	19	p.	p.	PROPN
ejpam-3714	79	20	padhy	padhy	PROPN
ejpam-3714	79	21	,	,	PUNCT
ejpam-3714	79	22	u.	u.	PROPN
ejpam-3714	79	23	k.	k.	PROPN
ejpam-3714	79	24	misra	misra	PROPN
ejpam-3714	79	25	/	/	SYM
ejpam-3714	79	26	eur	eur	PROPN
ejpam-3714	79	27	.	.	PUNCT
ejpam-3714	80	1	j.	j.	PROPN
ejpam-3714	80	2	pure	pure	PROPN
ejpam-3714	80	3	appl	appl	PROPN
ejpam-3714	80	4	.	.	PROPN
ejpam-3714	80	5	math	math	PROPN
ejpam-3714	80	6	,	,	PUNCT
ejpam-3714	80	7	13	13	NUM
ejpam-3714	80	8	(	(	PUNCT
ejpam-3714	80	9	5	5	NUM
ejpam-3714	80	10	)	)	PUNCT
ejpam-3714	80	11	(	(	PUNCT
ejpam-3714	80	12	2020	2020	NUM
ejpam-3714	80	13	)	)	PUNCT
ejpam-3714	80	14	,	,	PUNCT
ejpam-3714	80	15	1325	1325	NUM
ejpam-3714	80	16	-	-	SYM
ejpam-3714	80	17	1336	1336	NUM
ejpam-3714	80	18	1330	1330	NUM
ejpam-3714	80	19	where	where	SCONJ
ejpam-3714	80	20	m(v	m(v	NOUN
ejpam-3714	80	21	)	)	PUNCT
ejpam-3714	80	22	and	and	CCONJ
ejpam-3714	80	23	µ(v	µ(v	PROPN
ejpam-3714	80	24	)	)	PUNCT
ejpam-3714	80	25	are	be	AUX
ejpam-3714	80	26	the	the	DET
ejpam-3714	80	27	zygmund	zygmund	PROPN
ejpam-3714	80	28	moduli	moduli	NOUN
ejpam-3714	80	29	of	of	ADP
ejpam-3714	80	30	continuity	continuity	NOUN
ejpam-3714	80	31	and	and	CCONJ
ejpam-3714	80	32	m(v	m(v	NOUN
ejpam-3714	80	33	)	)	PUNCT
ejpam-3714	80	34	v	v	ADP
ejpam-3714	80	35	µ(v	µ(v	PROPN
ejpam-3714	80	36	)	)	PUNCT
ejpam-3714	80	37	is	be	AUX
ejpam-3714	80	38	positive	positive	ADJ
ejpam-3714	80	39	and	and	CCONJ
ejpam-3714	80	40	non	non	ADJ
ejpam-3714	80	41	-	-	ADJ
ejpam-3714	80	42	decreasing	decrease	VERB
ejpam-3714	80	43	,	,	PUNCT
ejpam-3714	80	44	provided	provide	VERB
ejpam-3714	80	45	∫	∫	PROPN
ejpam-3714	80	46	η	η	PROPN
ejpam-3714	80	47	0	0	NUM
ejpam-3714	80	48	m(v	m(v	NUM
ejpam-3714	80	49	)	)	PUNCT
ejpam-3714	80	50	v	v	ADP
ejpam-3714	80	51	µ(v	µ(v	PROPN
ejpam-3714	80	52	)	)	PUNCT
ejpam-3714	80	53	dv	dv	PROPN
ejpam-3714	80	54	=	=	PROPN
ejpam-3714	80	55	o	o	PROPN
ejpam-3714	80	56	(	(	PUNCT
ejpam-3714	80	57	m(η	m(η	PROPN
ejpam-3714	80	58	)	)	PUNCT
ejpam-3714	80	59	µ(η	µ(η	NOUN
ejpam-3714	80	60	)	)	PUNCT
ejpam-3714	80	61	)	)	PUNCT
ejpam-3714	80	62	.	.	PUNCT
ejpam-3714	81	1	we	we	PRON
ejpam-3714	81	2	require	require	VERB
ejpam-3714	81	3	the	the	DET
ejpam-3714	81	4	below	below	NOUN
ejpam-3714	81	5	mentioned	mention	VERB
ejpam-3714	81	6	lemmas	lemmas	ADJ
ejpam-3714	81	7	to	to	PART
ejpam-3714	81	8	prove	prove	VERB
ejpam-3714	81	9	our	our	PRON
ejpam-3714	81	10	main	main	ADJ
ejpam-3714	81	11	theorem	theorem	NOUN
ejpam-3714	81	12	:	:	PUNCT
ejpam-3714	81	13	5	5	X
ejpam-3714	81	14	.	.	PUNCT
ejpam-3714	82	1	lemmas	lemmas	PROPN
ejpam-3714	82	2	lemma	lemma	PROPN
ejpam-3714	82	3	1	1	NUM
ejpam-3714	82	4	.	.	PUNCT
ejpam-3714	83	1	|y1	|y1	VERB
ejpam-3714	83	2	′	′	NUM
ejpam-3714	83	3	(	(	PUNCT
ejpam-3714	83	4	v)|	v)|	NOUN
ejpam-3714	83	5	=	=	SYM
ejpam-3714	83	6	o(n2	o(n2	ADV
ejpam-3714	83	7	)	)	PUNCT
ejpam-3714	83	8	for	for	ADP
ejpam-3714	83	9	0	0	NUM
ejpam-3714	83	10	<	<	X
ejpam-3714	83	11	v	v	ADJ
ejpam-3714	83	12	≤	≤	NUM
ejpam-3714	83	13	π	π	PROPN
ejpam-3714	83	14	.	.	PUNCT
ejpam-3714	84	1	lemma	lemma	PROPN
ejpam-3714	84	2	2	2	X
ejpam-3714	84	3	.	.	PUNCT
ejpam-3714	84	4	|y2	|y2	PROPN
ejpam-3714	85	1	′	′	NUM
ejpam-3714	86	1	(	(	PUNCT
ejpam-3714	86	2	v)|	v)|	NOUN
ejpam-3714	86	3	=	=	X
ejpam-3714	86	4	o	o	X
ejpam-3714	86	5	(	(	PUNCT
ejpam-3714	86	6	1	1	NUM
ejpam-3714	86	7	v2	v2	NOUN
ejpam-3714	86	8	)	)	PUNCT
ejpam-3714	86	9	for	for	ADP
ejpam-3714	86	10	0	0	NUM
ejpam-3714	86	11	<	<	X
ejpam-3714	86	12	v	v	ADJ
ejpam-3714	86	13	≤	≤	PUNCT
ejpam-3714	86	14	π	π	PROPN
ejpam-3714	86	15	.	.	PUNCT
ejpam-3714	87	1	lemma	lemma	PROPN
ejpam-3714	87	2	3	3	X
ejpam-3714	87	3	.	.	PUNCT
ejpam-3714	88	1	let	let	VERB
ejpam-3714	88	2	h	h	PRON
ejpam-3714	88	3	∈	∈	PROPN
ejpam-3714	88	4	z(m	z(m	PROPN
ejpam-3714	88	5	)	)	PUNCT
ejpam-3714	89	1	l	l	NOUN
ejpam-3714	89	2	then	then	ADV
ejpam-3714	89	3	for	for	ADP
ejpam-3714	89	4	0	0	NUM
ejpam-3714	89	5	<	<	X
ejpam-3714	89	6	v	v	ADJ
ejpam-3714	89	7	≤	≤	PUNCT
ejpam-3714	89	8	π	π	PROPN
ejpam-3714	89	9	,	,	PUNCT
ejpam-3714	89	10	(	(	PUNCT
ejpam-3714	89	11	i	i	NOUN
ejpam-3714	89	12	)	)	PUNCT
ejpam-3714	89	13	‖ψ	‖ψ	PROPN
ejpam-3714	89	14	(	(	PUNCT
ejpam-3714	89	15	.	.	PUNCT
ejpam-3714	89	16	,	,	PUNCT
ejpam-3714	89	17	v)|l	v)|l	NOUN
ejpam-3714	90	1	=	=	SYM
ejpam-3714	90	2	o	o	X
ejpam-3714	90	3	(	(	PUNCT
ejpam-3714	90	4	m(v	m(v	PROPN
ejpam-3714	90	5	)	)	PUNCT
ejpam-3714	90	6	)	)	PUNCT
ejpam-3714	91	1	(	(	PUNCT
ejpam-3714	91	2	ii	ii	NOUN
ejpam-3714	91	3	)	)	PUNCT
ejpam-3714	91	4	‖ψ(.+	‖ψ(.+	PROPN
ejpam-3714	91	5	y	y	PROPN
ejpam-3714	91	6	,	,	PUNCT
ejpam-3714	91	7	v	v	NOUN
ejpam-3714	91	8	)	)	PUNCT
ejpam-3714	91	9	+	+	CCONJ
ejpam-3714	91	10	ψ(.−	ψ(.−	VERB
ejpam-3714	91	11	y	y	PROPN
ejpam-3714	91	12	,	,	PUNCT
ejpam-3714	91	13	v)‖l	v)‖l	NOUN
ejpam-3714	91	14	=	=	NOUN
ejpam-3714	91	15	o	o	X
ejpam-3714	91	16	(	(	PUNCT
ejpam-3714	91	17	m(v	m(v	PROPN
ejpam-3714	91	18	)	)	PUNCT
ejpam-3714	91	19	)	)	PUNCT
ejpam-3714	91	20	or	or	CCONJ
ejpam-3714	91	21	o	o	X
ejpam-3714	91	22	(	(	PUNCT
ejpam-3714	91	23	m(y	m(y	NOUN
ejpam-3714	91	24	)	)	PUNCT
ejpam-3714	91	25	)	)	PUNCT
ejpam-3714	92	1	(	(	PUNCT
ejpam-3714	92	2	iii	iii	X
ejpam-3714	92	3	)	)	PUNCT
ejpam-3714	92	4	if	if	SCONJ
ejpam-3714	92	5	m(v	m(v	NOUN
ejpam-3714	92	6	)	)	PUNCT
ejpam-3714	92	7	and	and	CCONJ
ejpam-3714	92	8	µ(v	µ(v	PROPN
ejpam-3714	92	9	)	)	PUNCT
ejpam-3714	92	10	are	be	AUX
ejpam-3714	92	11	as	as	ADV
ejpam-3714	92	12	defined	define	VERB
ejpam-3714	92	13	in	in	ADP
ejpam-3714	92	14	the	the	DET
ejpam-3714	92	15	main	main	ADJ
ejpam-3714	92	16	theorem	theorem	NOUN
ejpam-3714	92	17	,	,	PUNCT
ejpam-3714	92	18	then	then	ADV
ejpam-3714	92	19	‖ψ(.+	‖ψ(.+	PUNCT
ejpam-3714	92	20	y	y	PROPN
ejpam-3714	92	21	,	,	PUNCT
ejpam-3714	92	22	v	v	NOUN
ejpam-3714	92	23	)	)	PUNCT
ejpam-3714	92	24	+	+	CCONJ
ejpam-3714	92	25	ψ(.−	ψ(.−	VERB
ejpam-3714	92	26	y	y	PROPN
ejpam-3714	92	27	,	,	PUNCT
ejpam-3714	92	28	v)‖l	v)‖l	NOUN
ejpam-3714	92	29	=	=	NOUN
ejpam-3714	92	30	o	o	X
ejpam-3714	92	31	(	(	PUNCT
ejpam-3714	92	32	µ(y	µ(y	PROPN
ejpam-3714	92	33	)	)	PUNCT
ejpam-3714	92	34	m(v	m(v	NOUN
ejpam-3714	92	35	)	)	PUNCT
ejpam-3714	92	36	µ(v	µ(v	PROPN
ejpam-3714	92	37	)	)	PUNCT
ejpam-3714	92	38	)	)	PUNCT
ejpam-3714	93	1	where	where	SCONJ
ejpam-3714	93	2	ψ(x	ψ(x	NOUN
ejpam-3714	93	3	,	,	PUNCT
ejpam-3714	93	4	v	v	NOUN
ejpam-3714	93	5	)	)	PUNCT
ejpam-3714	93	6	=	=	PUNCT
ejpam-3714	94	1	h(x+	h(x+	ADP
ejpam-3714	94	2	v	v	NOUN
ejpam-3714	94	3	)	)	PUNCT
ejpam-3714	95	1	+	+	NUM
ejpam-3714	95	2	h(x−	h(x−	ADP
ejpam-3714	95	3	v	v	NOUN
ejpam-3714	95	4	)	)	PUNCT
ejpam-3714	95	5	.	.	PUNCT
ejpam-3714	96	1	6	6	X
ejpam-3714	96	2	.	.	X
ejpam-3714	96	3	proof	proof	NOUN
ejpam-3714	96	4	of	of	ADP
ejpam-3714	96	5	the	the	DET
ejpam-3714	96	6	lemmas	lemmas	ADJ
ejpam-3714	96	7	6.1	6.1	NUM
ejpam-3714	96	8	.	.	PUNCT
ejpam-3714	97	1	proof	proof	NOUN
ejpam-3714	97	2	of	of	ADP
ejpam-3714	97	3	lemma-1	lemma-1	PROPN
ejpam-3714	97	4	for	for	ADP
ejpam-3714	97	5	v	v	NOUN
ejpam-3714	97	6	∈	∈	NOUN
ejpam-3714	97	7	(	(	PUNCT
ejpam-3714	97	8	0	0	NUM
ejpam-3714	97	9	,	,	PUNCT
ejpam-3714	97	10	1	1	NUM
ejpam-3714	97	11	n+1	n+1	X
ejpam-3714	97	12	]	]	PUNCT
ejpam-3714	97	13	and	and	CCONJ
ejpam-3714	97	14	sin	sin	VERB
ejpam-3714	97	15	nv	nv	PROPN
ejpam-3714	97	16	≤	≤	PROPN
ejpam-3714	97	17	n	n	PRON
ejpam-3714	97	18	sin	sin	NOUN
ejpam-3714	97	19	v	v	NOUN
ejpam-3714	97	20	,	,	PUNCT
ejpam-3714	97	21	we	we	PRON
ejpam-3714	97	22	have	have	AUX
ejpam-3714	97	23	|y1	|y1	VERB
ejpam-3714	97	24	′	′	NUM
ejpam-3714	97	25	(	(	PUNCT
ejpam-3714	97	26	v)|	v)|	NOUN
ejpam-3714	97	27	=	=	NOUN
ejpam-3714	97	28	∣∣∣	∣∣∣	ADJ
ejpam-3714	97	29	−2	−2	NOUN
ejpam-3714	97	30	4π(1	4π(1	NUM
ejpam-3714	97	31	+	+	NOUN
ejpam-3714	97	32	r)n	r)n	X
ejpam-3714	97	33	n∑	n∑	PRON
ejpam-3714	97	34	k=0	k=0	PROPN
ejpam-3714	97	35	k	k	PROPN
ejpam-3714	97	36	c(n	c(n	PROPN
ejpam-3714	97	37	,	,	PUNCT
ejpam-3714	97	38	k)rn−k	k)rn−k	PROPN
ejpam-3714	97	39	{	{	PUNCT
ejpam-3714	97	40	1	1	NUM
ejpam-3714	97	41	qk	qk	NOUN
ejpam-3714	97	42	k∑	k∑	VERB
ejpam-3714	97	43	ν=0	ν=0	PROPN
ejpam-3714	97	44	qk−ν	qk−ν	NOUN
ejpam-3714	97	45	sin(ν	sin(ν	NOUN
ejpam-3714	97	46	+	+	CCONJ
ejpam-3714	97	47	1	1	NUM
ejpam-3714	97	48	2)v	2)v	NUM
ejpam-3714	97	49	sinv2	sinv2	NOUN
ejpam-3714	97	50	}	}	PUNCT
ejpam-3714	97	51	∣∣∣	∣∣∣	ADJ
ejpam-3714	97	52	≤	≤	NUM
ejpam-3714	97	53	1	1	NUM
ejpam-3714	97	54	2π(1	2π(1	NUM
ejpam-3714	97	55	+	+	CCONJ
ejpam-3714	97	56	r)n	r)n	X
ejpam-3714	97	57	∣∣∣	∣∣∣	X
ejpam-3714	97	58	n∑	n∑	PROPN
ejpam-3714	97	59	k=0	k=0	PROPN
ejpam-3714	98	1	k	k	PROPN
ejpam-3714	99	1	c(n	c(n	PROPN
ejpam-3714	99	2	,	,	PUNCT
ejpam-3714	99	3	k	k	X
ejpam-3714	99	4	)	)	PUNCT
ejpam-3714	99	5	rn−k	rn−k	NOUN
ejpam-3714	99	6	{	{	PUNCT
ejpam-3714	99	7	1	1	NUM
ejpam-3714	99	8	qk	qk	NOUN
ejpam-3714	99	9	k∑	k∑	VERB
ejpam-3714	99	10	ν=0	ν=0	PROPN
ejpam-3714	99	11	qk−ν	qk−ν	NOUN
ejpam-3714	99	12	(	(	PUNCT
ejpam-3714	99	13	2ν	2ν	NOUN
ejpam-3714	99	14	+	+	CCONJ
ejpam-3714	99	15	1))sin	1))sin	NUM
ejpam-3714	99	16	(	(	PUNCT
ejpam-3714	99	17	ν	ν	X
ejpam-3714	99	18	+	+	NOUN
ejpam-3714	99	19	1	1	NUM
ejpam-3714	99	20	2	2	NUM
ejpam-3714	99	21	)	)	PUNCT
ejpam-3714	99	22	v	v	ADP
ejpam-3714	99	23	sinv2	sinv2	NOUN
ejpam-3714	99	24	}	}	PUNCT
ejpam-3714	99	25	∣∣∣	∣∣∣	ADJ
ejpam-3714	99	26	≤	≤	NUM
ejpam-3714	99	27	1	1	NUM
ejpam-3714	99	28	2π(1	2π(1	NUM
ejpam-3714	99	29	+	+	CCONJ
ejpam-3714	99	30	r)n	r)n	X
ejpam-3714	99	31	∣∣∣	∣∣∣	X
ejpam-3714	99	32	n∑	n∑	PROPN
ejpam-3714	99	33	k=0	k=0	PROPN
ejpam-3714	99	34	k	k	PROPN
ejpam-3714	100	1	c(n	c(n	PROPN
ejpam-3714	100	2	,	,	PUNCT
ejpam-3714	100	3	k	k	NOUN
ejpam-3714	100	4	)	)	PUNCT
ejpam-3714	100	5	rn−k	rn−k	NOUN
ejpam-3714	100	6	(	(	PUNCT
ejpam-3714	100	7	2k	2k	NOUN
ejpam-3714	100	8	+	+	CCONJ
ejpam-3714	100	9	1	1	X
ejpam-3714	100	10	)	)	PUNCT
ejpam-3714	100	11	{	{	PUNCT
ejpam-3714	100	12	1	1	NUM
ejpam-3714	100	13	qk	qk	NOUN
ejpam-3714	100	14	k∑	k∑	VERB
ejpam-3714	100	15	ν=0	ν=0	PROPN
ejpam-3714	100	16	qk−ν	qk−ν	ADV
ejpam-3714	100	17	}	}	PUNCT
ejpam-3714	100	18	∣∣∣	∣∣∣	PROPN
ejpam-3714	100	19	a.	a.	PROPN
ejpam-3714	100	20	mishra	mishra	PROPN
ejpam-3714	100	21	,	,	PUNCT
ejpam-3714	100	22	b.	b.	PROPN
ejpam-3714	100	23	p.	p.	PROPN
ejpam-3714	100	24	padhy	padhy	PROPN
ejpam-3714	100	25	,	,	PUNCT
ejpam-3714	100	26	u.	u.	PROPN
ejpam-3714	100	27	k.	k.	PROPN
ejpam-3714	100	28	misra	misra	PROPN
ejpam-3714	100	29	/	/	SYM
ejpam-3714	100	30	eur	eur	PROPN
ejpam-3714	100	31	.	.	PUNCT
ejpam-3714	101	1	j.	j.	PROPN
ejpam-3714	101	2	pure	pure	PROPN
ejpam-3714	101	3	appl	appl	PROPN
ejpam-3714	101	4	.	.	PROPN
ejpam-3714	101	5	math	math	PROPN
ejpam-3714	101	6	,	,	PUNCT
ejpam-3714	101	7	13	13	NUM
ejpam-3714	101	8	(	(	PUNCT
ejpam-3714	101	9	5	5	NUM
ejpam-3714	101	10	)	)	PUNCT
ejpam-3714	101	11	(	(	PUNCT
ejpam-3714	101	12	2020	2020	NUM
ejpam-3714	101	13	)	)	PUNCT
ejpam-3714	101	14	,	,	PUNCT
ejpam-3714	101	15	1325	1325	NUM
ejpam-3714	101	16	-	-	SYM
ejpam-3714	101	17	1336	1336	NUM
ejpam-3714	101	18	1331	1331	NUM
ejpam-3714	101	19	=	=	SYM
ejpam-3714	101	20	o(n2	o(n2	ADV
ejpam-3714	101	21	)	)	PUNCT
ejpam-3714	101	22	for	for	ADP
ejpam-3714	101	23	v	v	NUM
ejpam-3714	101	24	∈	∈	NOUN
ejpam-3714	101	25	[	[	PUNCT
ejpam-3714	101	26	1	1	NUM
ejpam-3714	101	27	n+1	n+1	NUM
ejpam-3714	101	28	,	,	PUNCT
ejpam-3714	101	29	π	π	X
ejpam-3714	101	30	]	]	PUNCT
ejpam-3714	101	31	,	,	PUNCT
ejpam-3714	101	32	1	1	NUM
ejpam-3714	101	33	sin	sin	NOUN
ejpam-3714	101	34	(	(	PUNCT
ejpam-3714	101	35	v	v	NOUN
ejpam-3714	101	36	2	2	NUM
ejpam-3714	101	37	)	)	PUNCT
ejpam-3714	101	38	≤	≤	NUM
ejpam-3714	102	1	π	π	PROPN
ejpam-3714	102	2	v	v	NOUN
ejpam-3714	102	3	,	,	PUNCT
ejpam-3714	102	4	sinv	sinv	ADJ
ejpam-3714	102	5	≤	≤	NUM
ejpam-3714	102	6	v	v	ADP
ejpam-3714	102	7	|y1	|y1	NOUN
ejpam-3714	102	8	′	′	NUM
ejpam-3714	102	9	(	(	PUNCT
ejpam-3714	102	10	v)|	v)|	NOUN
ejpam-3714	102	11	=	=	NOUN
ejpam-3714	102	12	∣∣∣	∣∣∣	ADJ
ejpam-3714	102	13	−2	−2	NOUN
ejpam-3714	102	14	4π(1	4π(1	NUM
ejpam-3714	102	15	+	+	NOUN
ejpam-3714	102	16	r)n	r)n	X
ejpam-3714	102	17	n∑	n∑	PRON
ejpam-3714	102	18	k=0	k=0	PROPN
ejpam-3714	102	19	k	k	PROPN
ejpam-3714	102	20	c(n	c(n	PROPN
ejpam-3714	102	21	,	,	PUNCT
ejpam-3714	102	22	k)rn−k	k)rn−k	PROPN
ejpam-3714	102	23	{	{	PUNCT
ejpam-3714	102	24	1	1	NUM
ejpam-3714	102	25	qk	qk	NOUN
ejpam-3714	102	26	k∑	k∑	VERB
ejpam-3714	102	27	ν=0	ν=0	PROPN
ejpam-3714	102	28	qk−ν	qk−ν	NOUN
ejpam-3714	102	29	sin(ν	sin(ν	NOUN
ejpam-3714	102	30	+	+	CCONJ
ejpam-3714	102	31	1	1	NUM
ejpam-3714	102	32	2)v	2)v	NUM
ejpam-3714	102	33	sinv2	sinv2	NOUN
ejpam-3714	102	34	}	}	PUNCT
ejpam-3714	102	35	∣∣∣	∣∣∣	ADJ
ejpam-3714	102	36	≤	≤	NUM
ejpam-3714	102	37	1	1	NUM
ejpam-3714	102	38	4π(1	4π(1	NUM
ejpam-3714	102	39	+	+	NOUN
ejpam-3714	102	40	r)n	r)n	X
ejpam-3714	102	41	∣∣∣	∣∣∣	X
ejpam-3714	102	42	n∑	n∑	PROPN
ejpam-3714	102	43	k=0	k=0	PROPN
ejpam-3714	102	44	k	k	PROPN
ejpam-3714	103	1	c(n	c(n	PROPN
ejpam-3714	103	2	,	,	PUNCT
ejpam-3714	103	3	k	k	X
ejpam-3714	103	4	)	)	PUNCT
ejpam-3714	103	5	rn−k	rn−k	NOUN
ejpam-3714	103	6	{	{	PUNCT
ejpam-3714	103	7	1	1	NUM
ejpam-3714	103	8	qk	qk	X
ejpam-3714	103	9	k∑	k∑	VERB
ejpam-3714	103	10	ν=0	ν=0	PROPN
ejpam-3714	103	11	π	π	X
ejpam-3714	103	12	v	v	NOUN
ejpam-3714	103	13	(	(	PUNCT
ejpam-3714	103	14	2ν	2ν	NUM
ejpam-3714	103	15	+	+	CCONJ
ejpam-3714	103	16	1)v	1)v	NUM
ejpam-3714	103	17	qk−ν	qk−ν	NOUN
ejpam-3714	103	18	}	}	PUNCT
ejpam-3714	103	19	∣∣∣	∣∣∣	ADJ
ejpam-3714	103	20	≤	≤	NUM
ejpam-3714	103	21	1	1	NUM
ejpam-3714	103	22	2π(1	2π(1	NUM
ejpam-3714	103	23	+	+	CCONJ
ejpam-3714	103	24	r)n	r)n	X
ejpam-3714	103	25	∣∣∣	∣∣∣	X
ejpam-3714	103	26	n∑	n∑	PROPN
ejpam-3714	103	27	k=0	k=0	PROPN
ejpam-3714	103	28	k	k	PROPN
ejpam-3714	104	1	c(n	c(n	PROPN
ejpam-3714	104	2	,	,	PUNCT
ejpam-3714	104	3	k	k	NOUN
ejpam-3714	104	4	)	)	PUNCT
ejpam-3714	104	5	rn−k	rn−k	NOUN
ejpam-3714	104	6	(	(	PUNCT
ejpam-3714	104	7	2k	2k	NOUN
ejpam-3714	104	8	+	+	CCONJ
ejpam-3714	104	9	1	1	X
ejpam-3714	104	10	)	)	PUNCT
ejpam-3714	104	11	{	{	PUNCT
ejpam-3714	104	12	1	1	NUM
ejpam-3714	104	13	qk	qk	NOUN
ejpam-3714	104	14	k∑	k∑	VERB
ejpam-3714	104	15	ν=0	ν=0	PROPN
ejpam-3714	104	16	qk−ν	qk−ν	ADV
ejpam-3714	104	17	}	}	PUNCT
ejpam-3714	104	18	∣∣∣	∣∣∣	NOUN
ejpam-3714	104	19	=	=	SYM
ejpam-3714	104	20	o(n2	o(n2	ADJ
ejpam-3714	104	21	)	)	PUNCT
ejpam-3714	104	22	6.2	6.2	NUM
ejpam-3714	104	23	.	.	PUNCT
ejpam-3714	105	1	proof	proof	NOUN
ejpam-3714	105	2	of	of	ADP
ejpam-3714	105	3	lemma-2	lemma-2	PROPN
ejpam-3714	105	4	we	we	PRON
ejpam-3714	105	5	know	know	VERB
ejpam-3714	105	6	,	,	PUNCT
ejpam-3714	105	7	1	1	NUM
ejpam-3714	105	8	sin	sin	NOUN
ejpam-3714	105	9	(	(	PUNCT
ejpam-3714	105	10	v	v	NOUN
ejpam-3714	105	11	2	2	NUM
ejpam-3714	105	12	)	)	PUNCT
ejpam-3714	105	13	≤	≤	NUM
ejpam-3714	106	1	π	π	PROPN
ejpam-3714	106	2	v	v	NOUN
ejpam-3714	106	3	,	,	PUNCT
ejpam-3714	106	4	(	(	PUNCT
ejpam-3714	106	5	0	0	NUM
ejpam-3714	106	6	<	<	X
ejpam-3714	106	7	v	v	NOUN
ejpam-3714	106	8	≤	≤	PROPN
ejpam-3714	106	9	π	π	PROPN
ejpam-3714	106	10	)	)	PUNCT
ejpam-3714	106	11	;	;	PUNCT
ejpam-3714	106	12	sin	sin	VERB
ejpam-3714	106	13	v	v	ADP
ejpam-3714	106	14	≤	≤	NUM
ejpam-3714	106	15	v	v	NOUN
ejpam-3714	106	16	,	,	PUNCT
ejpam-3714	106	17	v	v	ADP
ejpam-3714	106	18	>	>	X
ejpam-3714	106	19	0	0	NUM
ejpam-3714	106	20	;	;	PUNCT
ejpam-3714	106	21	and	and	CCONJ
ejpam-3714	106	22	|sinv|	|sinv|	ADP
ejpam-3714	106	23	≤	≤	ADV
ejpam-3714	106	24	1	1	NUM
ejpam-3714	106	25	,	,	PUNCT
ejpam-3714	106	26	|cosv|	|cosv|	PROPN
ejpam-3714	106	27	≤	≤	NOUN
ejpam-3714	106	28	1	1	NUM
ejpam-3714	106	29	for	for	ADP
ejpam-3714	106	30	all	all	DET
ejpam-3714	106	31	t.	t.	NOUN
ejpam-3714	106	32	clearly	clearly	ADV
ejpam-3714	106	33	,	,	PUNCT
ejpam-3714	106	34	for	for	ADP
ejpam-3714	106	35	v	v	ADP
ejpam-3714	106	36	∈	∈	NOUN
ejpam-3714	106	37	(	(	PUNCT
ejpam-3714	106	38	0	0	NUM
ejpam-3714	106	39	,	,	PUNCT
ejpam-3714	106	40	π	π	PROPN
ejpam-3714	106	41	]	]	X
ejpam-3714	106	42	,	,	PUNCT
ejpam-3714	106	43	|y2	|y2	ADV
ejpam-3714	106	44	′	′	VERB
ejpam-3714	107	1	(	(	PUNCT
ejpam-3714	107	2	v)|	v)|	NOUN
ejpam-3714	107	3	=	=	X
ejpam-3714	107	4	∣∣∣	∣∣∣	NOUN
ejpam-3714	107	5	−1	−1	ADP
ejpam-3714	107	6	4π(1	4π(1	NUM
ejpam-3714	107	7	+	+	PUNCT
ejpam-3714	107	8	r)n	r)n	X
ejpam-3714	107	9	n∑	n∑	DET
ejpam-3714	107	10	k=0	k=0	PROPN
ejpam-3714	107	11	c(n	c(n	PROPN
ejpam-3714	107	12	,	,	PUNCT
ejpam-3714	107	13	k	k	X
ejpam-3714	107	14	)	)	PUNCT
ejpam-3714	107	15	rn−k	rn−k	NOUN
ejpam-3714	107	16	{	{	PUNCT
ejpam-3714	107	17	1	1	NUM
ejpam-3714	107	18	qk	qk	NOUN
ejpam-3714	107	19	k∑	k∑	VERB
ejpam-3714	107	20	ν=0	ν=0	PROPN
ejpam-3714	107	21	qk−ν	qk−ν	NOUN
ejpam-3714	107	22	cos	cos	SCONJ
ejpam-3714	107	23	νv	νv	PROPN
ejpam-3714	107	24	sin2	sin2	NOUN
ejpam-3714	107	25	v	v	ADP
ejpam-3714	107	26	2	2	NUM
ejpam-3714	107	27	}	}	PUNCT
ejpam-3714	107	28	∣∣∣	∣∣∣	NOUN
ejpam-3714	107	29	=	=	SYM
ejpam-3714	107	30	o	o	X
ejpam-3714	107	31	(	(	PUNCT
ejpam-3714	107	32	1	1	NUM
ejpam-3714	107	33	v2	v2	PROPN
ejpam-3714	107	34	)	)	PUNCT
ejpam-3714	107	35	6.3	6.3	NUM
ejpam-3714	107	36	.	.	PUNCT
ejpam-3714	108	1	proof	proof	NOUN
ejpam-3714	108	2	of	of	ADP
ejpam-3714	108	3	lemma-3	lemma-3	PROPN
ejpam-3714	108	4	see	see	VERB
ejpam-3714	108	5	[	[	X
ejpam-3714	108	6	12	12	NUM
ejpam-3714	108	7	]	]	PUNCT
ejpam-3714	108	8	.	.	PUNCT
ejpam-3714	109	1	7	7	X
ejpam-3714	109	2	.	.	X
ejpam-3714	109	3	proof	proof	NOUN
ejpam-3714	109	4	of	of	ADP
ejpam-3714	109	5	the	the	DET
ejpam-3714	109	6	main	main	ADJ
ejpam-3714	109	7	theorem	theorem	NOUN
ejpam-3714	109	8	let	let	VERB
ejpam-3714	109	9	sk	sk	INTJ
ejpam-3714	109	10	′	′	NUM
ejpam-3714	109	11	(	(	PUNCT
ejpam-3714	109	12	h;x	h;x	NOUN
ejpam-3714	109	13	)	)	PUNCT
ejpam-3714	109	14	denotes	denote	VERB
ejpam-3714	109	15	the	the	DET
ejpam-3714	109	16	k	k	PROPN
ejpam-3714	109	17	-	-	PUNCT
ejpam-3714	109	18	th	th	VERB
ejpam-3714	109	19	partial	partial	ADJ
ejpam-3714	109	20	sum	sum	NOUN
ejpam-3714	109	21	of	of	ADP
ejpam-3714	109	22	the	the	DET
ejpam-3714	109	23	conjugate	conjugate	ADJ
ejpam-3714	109	24	derived	derive	VERB
ejpam-3714	109	25	fourier	fourier	NOUN
ejpam-3714	109	26	series	series	NOUN
ejpam-3714	109	27	,	,	PUNCT
ejpam-3714	109	28	we	we	PRON
ejpam-3714	109	29	have	have	VERB
ejpam-3714	109	30	sk	sk	VERB
ejpam-3714	109	31	′	′	NUM
ejpam-3714	110	1	(	(	PUNCT
ejpam-3714	110	2	h;x)−	h;x)−	PROPN
ejpam-3714	110	3	h′(x	h′(x	PROPN
ejpam-3714	110	4	)	)	PUNCT
ejpam-3714	110	5	=	=	SYM
ejpam-3714	111	1	−2	−2	NOUN
ejpam-3714	112	1	π	π	X
ejpam-3714	112	2	∫	∫	PROPN
ejpam-3714	112	3	π	π	X
ejpam-3714	112	4	0	0	NUM
ejpam-3714	112	5	ψ(x	ψ(x	PROPN
ejpam-3714	112	6	,	,	PUNCT
ejpam-3714	112	7	v	v	NOUN
ejpam-3714	112	8	)	)	PUNCT
ejpam-3714	112	9	4sinv2	4sinv2	NUM
ejpam-3714	112	10	(	(	PUNCT
ejpam-3714	112	11	k	k	NOUN
ejpam-3714	112	12	+	+	CCONJ
ejpam-3714	112	13	1	1	NUM
ejpam-3714	112	14	2	2	NUM
ejpam-3714	112	15	)	)	PUNCT
ejpam-3714	112	16	sin	sin	NOUN
ejpam-3714	112	17	(	(	PUNCT
ejpam-3714	112	18	k	k	NOUN
ejpam-3714	112	19	+	+	PROPN
ejpam-3714	112	20	1	1	NUM
ejpam-3714	112	21	2	2	NUM
ejpam-3714	112	22	)	)	PUNCT
ejpam-3714	112	23	v	v	ADP
ejpam-3714	112	24	dv	dv	PROPN
ejpam-3714	112	25	−	−	PROPN
ejpam-3714	112	26	1	1	NUM
ejpam-3714	112	27	π	π	SYM
ejpam-3714	112	28	∫	∫	PROPN
ejpam-3714	112	29	π	π	X
ejpam-3714	112	30	0	0	NUM
ejpam-3714	112	31	ψ(x	ψ(x	PROPN
ejpam-3714	112	32	,	,	PUNCT
ejpam-3714	112	33	v	v	NOUN
ejpam-3714	112	34	)	)	PUNCT
ejpam-3714	112	35	4sinv2	4sinv2	NUM
ejpam-3714	113	1	cos	cos	PROPN
ejpam-3714	113	2	(	(	PUNCT
ejpam-3714	113	3	k	k	PROPN
ejpam-3714	113	4	+	+	PROPN
ejpam-3714	113	5	1	1	NUM
ejpam-3714	113	6	2	2	NUM
ejpam-3714	113	7	)	)	PUNCT
ejpam-3714	113	8	v	v	NOUN
ejpam-3714	113	9	tanv2	tanv2	NOUN
ejpam-3714	114	1	dv	dv	PROPN
ejpam-3714	114	2	where	where	SCONJ
ejpam-3714	114	3	h′	h′	PROPN
ejpam-3714	114	4	is	be	AUX
ejpam-3714	114	5	the	the	DET
ejpam-3714	114	6	conjugate	conjugate	ADJ
ejpam-3714	114	7	derived	derive	VERB
ejpam-3714	114	8	function	function	NOUN
ejpam-3714	114	9	of	of	ADP
ejpam-3714	114	10	2π	2π	PROPN
ejpam-3714	114	11	periodic	periodic	ADJ
ejpam-3714	114	12	function	function	NOUN
ejpam-3714	114	13	h	h	NOUN
ejpam-3714	114	14	,	,	PUNCT
ejpam-3714	114	15	which	which	PRON
ejpam-3714	114	16	is	be	AUX
ejpam-3714	114	17	given	give	VERB
ejpam-3714	114	18	by	by	ADP
ejpam-3714	114	19	h′(x	h′(x	NOUN
ejpam-3714	114	20	)	)	PUNCT
ejpam-3714	114	21	=	=	SYM
ejpam-3714	114	22	1	1	NUM
ejpam-3714	115	1	4π	4π	NUM
ejpam-3714	115	2	∫	∫	PROPN
ejpam-3714	115	3	π	π	X
ejpam-3714	115	4	0	0	NUM
ejpam-3714	115	5	ψ(x	ψ(x	PROPN
ejpam-3714	115	6	;	;	PUNCT
ejpam-3714	115	7	v	v	NOUN
ejpam-3714	115	8	)	)	PUNCT
ejpam-3714	115	9	cosec2	cosec2	NOUN
ejpam-3714	116	1	v	v	ADP
ejpam-3714	116	2	2	2	NUM
ejpam-3714	116	3	dv	dv	PROPN
ejpam-3714	116	4	a.	a.	PROPN
ejpam-3714	116	5	mishra	mishra	PROPN
ejpam-3714	116	6	,	,	PUNCT
ejpam-3714	116	7	b.	b.	PROPN
ejpam-3714	116	8	p.	p.	PROPN
ejpam-3714	116	9	padhy	padhy	PROPN
ejpam-3714	116	10	,	,	PUNCT
ejpam-3714	116	11	u.	u.	PROPN
ejpam-3714	116	12	k.	k.	PROPN
ejpam-3714	116	13	misra	misra	PROPN
ejpam-3714	116	14	/	/	SYM
ejpam-3714	116	15	eur	eur	PROPN
ejpam-3714	116	16	.	.	PUNCT
ejpam-3714	117	1	j.	j.	PROPN
ejpam-3714	117	2	pure	pure	PROPN
ejpam-3714	117	3	appl	appl	PROPN
ejpam-3714	117	4	.	.	PROPN
ejpam-3714	117	5	math	math	PROPN
ejpam-3714	117	6	,	,	PUNCT
ejpam-3714	117	7	13	13	NUM
ejpam-3714	117	8	(	(	PUNCT
ejpam-3714	117	9	5	5	NUM
ejpam-3714	117	10	)	)	PUNCT
ejpam-3714	117	11	(	(	PUNCT
ejpam-3714	117	12	2020	2020	NUM
ejpam-3714	117	13	)	)	PUNCT
ejpam-3714	117	14	,	,	PUNCT
ejpam-3714	117	15	1325	1325	NUM
ejpam-3714	117	16	-	-	SYM
ejpam-3714	117	17	1336	1336	NUM
ejpam-3714	117	18	1332	1332	NUM
ejpam-3714	117	19	and	and	CCONJ
ejpam-3714	117	20	the	the	DET
ejpam-3714	117	21	(	(	PUNCT
ejpam-3714	117	22	n	n	CCONJ
ejpam-3714	117	23	,	,	PUNCT
ejpam-3714	117	24	qn	qn	NOUN
ejpam-3714	117	25	)	)	PUNCT
ejpam-3714	117	26	transform	transform	NOUN
ejpam-3714	117	27	of	of	ADP
ejpam-3714	117	28	it	it	PRON
ejpam-3714	117	29	is	be	AUX
ejpam-3714	117	30	given	give	VERB
ejpam-3714	117	31	by	by	ADP
ejpam-3714	117	32	1	1	NUM
ejpam-3714	117	33	qn	qn	PROPN
ejpam-3714	117	34	n∑	n∑	PROPN
ejpam-3714	117	35	k=0	k=0	PROPN
ejpam-3714	117	36	qn−k{sk	qn−k{sk	PROPN
ejpam-3714	117	37	′	′	NOUN
ejpam-3714	118	1	(	(	PUNCT
ejpam-3714	118	2	h;x)−	h;x)−	PROPN
ejpam-3714	118	3	h′(x	h′(x	PROPN
ejpam-3714	118	4	)	)	PUNCT
ejpam-3714	118	5	}	}	PUNCT
ejpam-3714	119	1	=	=	SYM
ejpam-3714	119	2	−2k	−2k	PROPN
ejpam-3714	119	3	π	π	PROPN
ejpam-3714	119	4	∫	∫	PROPN
ejpam-3714	119	5	π	π	X
ejpam-3714	119	6	0	0	SYM
ejpam-3714	119	7	ρ(x	ρ(x	PROPN
ejpam-3714	119	8	,	,	PUNCT
ejpam-3714	119	9	v	v	NOUN
ejpam-3714	119	10	)	)	PUNCT
ejpam-3714	119	11	1	1	NUM
ejpam-3714	119	12	qn	qn	NOUN
ejpam-3714	119	13	n∑	n∑	PROPN
ejpam-3714	119	14	k=0	k=0	PROPN
ejpam-3714	119	15	qn−ksin	qn−ksin	PROPN
ejpam-3714	119	16	(	(	PUNCT
ejpam-3714	119	17	k	k	PROPN
ejpam-3714	119	18	+	+	PROPN
ejpam-3714	119	19	1	1	NUM
ejpam-3714	119	20	2	2	NUM
ejpam-3714	119	21	)	)	PUNCT
ejpam-3714	119	22	v	v	ADP
ejpam-3714	119	23	dv	dv	PROPN
ejpam-3714	119	24	−	−	PROPN
ejpam-3714	119	25	1	1	NUM
ejpam-3714	119	26	π	π	SYM
ejpam-3714	119	27	∫	∫	PROPN
ejpam-3714	119	28	π	π	X
ejpam-3714	119	29	0	0	SYM
ejpam-3714	119	30	ρ(x	ρ(x	PROPN
ejpam-3714	119	31	,	,	PUNCT
ejpam-3714	119	32	v	v	NOUN
ejpam-3714	119	33	)	)	PUNCT
ejpam-3714	119	34	1	1	NUM
ejpam-3714	119	35	qn	qn	NOUN
ejpam-3714	119	36	n∑	n∑	PROPN
ejpam-3714	119	37	k=0	k=0	PROPN
ejpam-3714	119	38	qn−k	qn−k	PROPN
ejpam-3714	119	39	coskv	coskv	PROPN
ejpam-3714	119	40	sinv2	sinv2	PROPN
ejpam-3714	120	1	dv	dv	PROPN
ejpam-3714	120	2	where	where	SCONJ
ejpam-3714	120	3	ρ(x	ρ(x	NOUN
ejpam-3714	120	4	,	,	PUNCT
ejpam-3714	120	5	v	v	NOUN
ejpam-3714	120	6	)	)	PUNCT
ejpam-3714	120	7	=	=	PUNCT
ejpam-3714	120	8	ψ(x;v	ψ(x;v	PUNCT
ejpam-3714	120	9	)	)	PUNCT
ejpam-3714	121	1	4sin	4sin	NOUN
ejpam-3714	121	2	v	v	ADP
ejpam-3714	121	3	2	2	NUM
ejpam-3714	121	4	.	.	PUNCT
ejpam-3714	122	1	denoting	denote	VERB
ejpam-3714	122	2	the	the	DET
ejpam-3714	122	3	(	(	PUNCT
ejpam-3714	122	4	e	e	NOUN
ejpam-3714	122	5	,	,	PUNCT
ejpam-3714	122	6	r)(n	r)(n	PROPN
ejpam-3714	122	7	,	,	PUNCT
ejpam-3714	122	8	qn	qn	NOUN
ejpam-3714	122	9	)	)	PUNCT
ejpam-3714	122	10	transform	transform	NOUN
ejpam-3714	122	11	of	of	ADP
ejpam-3714	122	12	sk	sk	INTJ
ejpam-3714	122	13	′	′	NUM
ejpam-3714	122	14	(	(	PUNCT
ejpam-3714	122	15	h;x	h;x	INTJ
ejpam-3714	122	16	)	)	PUNCT
ejpam-3714	122	17	by	by	ADP
ejpam-3714	122	18	τn′	τn′	PROPN
ejpam-3714	122	19	er	er	INTJ
ejpam-3714	122	20	,	,	PUNCT
ejpam-3714	122	21	n	n	NOUN
ejpam-3714	122	22	.	.	PUNCT
ejpam-3714	123	1	then	then	ADV
ejpam-3714	123	2	,	,	PUNCT
ejpam-3714	123	3	τn′	τn′	X
ejpam-3714	123	4	er	er	INTJ
ejpam-3714	123	5	,	,	PUNCT
ejpam-3714	123	6	n	n	CCONJ
ejpam-3714	123	7	−	−	PROPN
ejpam-3714	123	8	h′(x	h′(x	NOUN
ejpam-3714	123	9	)	)	PUNCT
ejpam-3714	123	10	=	=	SYM
ejpam-3714	123	11	−2k	−2k	PROPN
ejpam-3714	123	12	π(1	π(1	NOUN
ejpam-3714	123	13	+	+	ADJ
ejpam-3714	123	14	r)n	r)n	X
ejpam-3714	123	15	∫	∫	PROPN
ejpam-3714	123	16	π	π	PROPN
ejpam-3714	123	17	0	0	SYM
ejpam-3714	123	18	ρ(x	ρ(x	NUM
ejpam-3714	123	19	,	,	PUNCT
ejpam-3714	123	20	v	v	NOUN
ejpam-3714	123	21	)	)	PUNCT
ejpam-3714	123	22	n∑	n∑	PRON
ejpam-3714	123	23	k=0	k=0	PROPN
ejpam-3714	123	24	c(n	c(n	PROPN
ejpam-3714	123	25	,	,	PUNCT
ejpam-3714	123	26	k	k	X
ejpam-3714	123	27	)	)	PUNCT
ejpam-3714	123	28	rn−k	rn−k	NOUN
ejpam-3714	123	29	{	{	PUNCT
ejpam-3714	123	30	1	1	NUM
ejpam-3714	123	31	qk	qk	NOUN
ejpam-3714	123	32	k∑	k∑	VERB
ejpam-3714	123	33	ν=0	ν=0	PRON
ejpam-3714	123	34	qk−νsin	qk−νsin	NOUN
ejpam-3714	123	35	(	(	PUNCT
ejpam-3714	123	36	ν	ν	X
ejpam-3714	123	37	+	+	NOUN
ejpam-3714	123	38	1	1	NUM
ejpam-3714	123	39	2	2	NUM
ejpam-3714	123	40	)	)	PUNCT
ejpam-3714	123	41	v	v	NOUN
ejpam-3714	123	42	}	}	PUNCT
ejpam-3714	123	43	dv	dv	PROPN
ejpam-3714	123	44	−	−	PROPN
ejpam-3714	123	45	1	1	NUM
ejpam-3714	124	1	π(1	π(1	NOUN
ejpam-3714	124	2	+	+	NUM
ejpam-3714	124	3	r)n	r)n	X
ejpam-3714	124	4	∫	∫	PROPN
ejpam-3714	124	5	π	π	PROPN
ejpam-3714	124	6	0	0	SYM
ejpam-3714	124	7	ρ(x	ρ(x	NUM
ejpam-3714	124	8	,	,	PUNCT
ejpam-3714	124	9	v	v	NOUN
ejpam-3714	124	10	)	)	PUNCT
ejpam-3714	124	11	n∑	n∑	PRON
ejpam-3714	124	12	k=0	k=0	PROPN
ejpam-3714	124	13	c(n	c(n	PROPN
ejpam-3714	124	14	,	,	PUNCT
ejpam-3714	124	15	k	k	X
ejpam-3714	124	16	)	)	PUNCT
ejpam-3714	124	17	rn−k	rn−k	NOUN
ejpam-3714	124	18	{	{	PUNCT
ejpam-3714	124	19	1	1	NUM
ejpam-3714	124	20	qk	qk	NOUN
ejpam-3714	124	21	k∑	k∑	VERB
ejpam-3714	124	22	ν=0	ν=0	PROPN
ejpam-3714	124	23	qk−ν	qk−ν	NOUN
ejpam-3714	124	24	cosνv	cosνv	NOUN
ejpam-3714	124	25	sinv2	sinv2	PROPN
ejpam-3714	124	26	}	}	PUNCT
ejpam-3714	125	1	dv	dv	PROPN
ejpam-3714	125	2	τn′	τn′	PROPN
ejpam-3714	126	1	er	er	INTJ
ejpam-3714	126	2	,	,	PUNCT
ejpam-3714	126	3	n	n	CCONJ
ejpam-3714	126	4	−	−	PROPN
ejpam-3714	126	5	h′(x	h′(x	NOUN
ejpam-3714	126	6	)	)	PUNCT
ejpam-3714	126	7	=	=	SYM
ejpam-3714	126	8	−2k	−2k	PROPN
ejpam-3714	126	9	4π(1	4π(1	NUM
ejpam-3714	126	10	+	+	PUNCT
ejpam-3714	126	11	r)n	r)n	X
ejpam-3714	126	12	∫	∫	PROPN
ejpam-3714	126	13	π	π	PROPN
ejpam-3714	126	14	0	0	NUM
ejpam-3714	126	15	ψ(x	ψ(x	PROPN
ejpam-3714	126	16	,	,	PUNCT
ejpam-3714	126	17	v	v	NOUN
ejpam-3714	126	18	)	)	PUNCT
ejpam-3714	126	19	n∑	n∑	PRON
ejpam-3714	126	20	k=0	k=0	PROPN
ejpam-3714	126	21	c(n	c(n	PROPN
ejpam-3714	126	22	,	,	PUNCT
ejpam-3714	126	23	k	k	X
ejpam-3714	126	24	)	)	PUNCT
ejpam-3714	126	25	rn−k	rn−k	NOUN
ejpam-3714	126	26	{	{	PUNCT
ejpam-3714	126	27	1	1	NUM
ejpam-3714	126	28	qk	qk	NOUN
ejpam-3714	126	29	k∑	k∑	VERB
ejpam-3714	126	30	ν=0	ν=0	DET
ejpam-3714	126	31	qk−ν	qk−ν	NOUN
ejpam-3714	126	32	sin	sin	NOUN
ejpam-3714	126	33	(	(	PUNCT
ejpam-3714	126	34	ν	ν	X
ejpam-3714	126	35	+	+	NOUN
ejpam-3714	126	36	1	1	NUM
ejpam-3714	126	37	2	2	NUM
ejpam-3714	126	38	)	)	PUNCT
ejpam-3714	126	39	v	v	ADP
ejpam-3714	126	40	sinv2	sinv2	PROPN
ejpam-3714	126	41	}	}	PUNCT
ejpam-3714	126	42	dv	dv	PROPN
ejpam-3714	126	43	−	−	PROPN
ejpam-3714	126	44	1	1	NUM
ejpam-3714	126	45	4π(1	4π(1	NUM
ejpam-3714	126	46	+	+	CCONJ
ejpam-3714	126	47	r)n	r)n	X
ejpam-3714	126	48	∫	∫	PROPN
ejpam-3714	126	49	π	π	PROPN
ejpam-3714	126	50	0	0	NUM
ejpam-3714	126	51	ψ(x	ψ(x	PROPN
ejpam-3714	126	52	,	,	PUNCT
ejpam-3714	126	53	v	v	NOUN
ejpam-3714	126	54	)	)	PUNCT
ejpam-3714	126	55	n∑	n∑	PRON
ejpam-3714	126	56	k=0	k=0	PROPN
ejpam-3714	126	57	c(n	c(n	PROPN
ejpam-3714	126	58	,	,	PUNCT
ejpam-3714	126	59	k	k	X
ejpam-3714	126	60	)	)	PUNCT
ejpam-3714	126	61	rn−k	rn−k	NOUN
ejpam-3714	126	62	{	{	PUNCT
ejpam-3714	126	63	1	1	NUM
ejpam-3714	126	64	qk	qk	NOUN
ejpam-3714	126	65	k∑	k∑	VERB
ejpam-3714	126	66	ν=0	ν=0	PROPN
ejpam-3714	126	67	qk−ν	qk−ν	NOUN
ejpam-3714	126	68	cosνv	cosνv	NOUN
ejpam-3714	126	69	sin2	sin2	NOUN
ejpam-3714	126	70	v	v	ADP
ejpam-3714	126	71	2	2	NUM
ejpam-3714	126	72	}	}	PUNCT
ejpam-3714	126	73	dv	dv	PROPN
ejpam-3714	126	74	=	=	SYM
ejpam-3714	126	75	∫	∫	PROPN
ejpam-3714	126	76	π	π	PROPN
ejpam-3714	126	77	0	0	NUM
ejpam-3714	126	78	ψ(x	ψ(x	PROPN
ejpam-3714	126	79	,	,	PUNCT
ejpam-3714	126	80	v){y	v){y	X
ejpam-3714	126	81	′1	′1	X
ejpam-3714	126	82	(	(	PUNCT
ejpam-3714	126	83	v	v	NOUN
ejpam-3714	126	84	)	)	PUNCT
ejpam-3714	126	85	+	+	NOUN
ejpam-3714	126	86	y	y	PROPN
ejpam-3714	126	87	′	′	NUM
ejpam-3714	126	88	2	2	NUM
ejpam-3714	126	89	(	(	PUNCT
ejpam-3714	126	90	v	v	NOUN
ejpam-3714	126	91	)	)	PUNCT
ejpam-3714	126	92	}	}	PUNCT
ejpam-3714	126	93	dv	dv	PROPN
ejpam-3714	127	1	=	=	PUNCT
ejpam-3714	127	2	χn	χn	INTJ
ejpam-3714	127	3	′	′	X
ejpam-3714	127	4	(	(	PUNCT
ejpam-3714	127	5	x	x	NOUN
ejpam-3714	127	6	)	)	PUNCT
ejpam-3714	127	7	,	,	PUNCT
ejpam-3714	127	8	(	(	PUNCT
ejpam-3714	127	9	say	say	INTJ
ejpam-3714	127	10	)	)	PUNCT
ejpam-3714	127	11	then	then	ADV
ejpam-3714	127	12	,	,	PUNCT
ejpam-3714	127	13	χn	χn	INTJ
ejpam-3714	127	14	′	′	X
ejpam-3714	127	15	(	(	PUNCT
ejpam-3714	127	16	x+	x+	PROPN
ejpam-3714	127	17	y	y	NOUN
ejpam-3714	127	18	)	)	PUNCT
ejpam-3714	128	1	+	+	CCONJ
ejpam-3714	128	2	χn	χn	INTJ
ejpam-3714	129	1	′	′	X
ejpam-3714	129	2	(	(	PUNCT
ejpam-3714	129	3	x−	x−	PROPN
ejpam-3714	129	4	y	y	PROPN
ejpam-3714	129	5	)	)	PUNCT
ejpam-3714	129	6	=	=	SYM
ejpam-3714	130	1	∫	∫	PROPN
ejpam-3714	130	2	π	π	X
ejpam-3714	130	3	0	0	PUNCT
ejpam-3714	130	4	{	{	PUNCT
ejpam-3714	130	5	ψ(x+	ψ(x+	NOUN
ejpam-3714	130	6	y	y	PROPN
ejpam-3714	130	7	,	,	PUNCT
ejpam-3714	130	8	v	v	NOUN
ejpam-3714	130	9	)	)	PUNCT
ejpam-3714	130	10	+	+	CCONJ
ejpam-3714	130	11	ψ(x−	ψ(x−	PROPN
ejpam-3714	130	12	y	y	PROPN
ejpam-3714	130	13	,	,	PUNCT
ejpam-3714	130	14	v	v	NOUN
ejpam-3714	130	15	)	)	PUNCT
ejpam-3714	130	16	}	}	PUNCT
ejpam-3714	130	17	{	{	PUNCT
ejpam-3714	130	18	y	y	PROPN
ejpam-3714	130	19	′1	′1	X
ejpam-3714	130	20	(	(	PUNCT
ejpam-3714	130	21	v	v	NOUN
ejpam-3714	130	22	)	)	PUNCT
ejpam-3714	130	23	+	+	NOUN
ejpam-3714	130	24	y	y	PROPN
ejpam-3714	130	25	′	′	NUM
ejpam-3714	130	26	2	2	NUM
ejpam-3714	130	27	(	(	PUNCT
ejpam-3714	130	28	v	v	NOUN
ejpam-3714	130	29	)	)	PUNCT
ejpam-3714	130	30	}	}	PUNCT
ejpam-3714	131	1	dv	dv	PROPN
ejpam-3714	131	2	using	use	VERB
ejpam-3714	131	3	minkowski	minkowski	PROPN
ejpam-3714	131	4	’s	’s	PART
ejpam-3714	131	5	inequality	inequality	NOUN
ejpam-3714	131	6	,	,	PUNCT
ejpam-3714	131	7	we	we	PRON
ejpam-3714	131	8	have	have	VERB
ejpam-3714	131	9	‖χn	‖χn	NUM
ejpam-3714	131	10	′	′	NUM
ejpam-3714	131	11	(	(	PUNCT
ejpam-3714	131	12	.+	.+	NOUN
ejpam-3714	131	13	y	y	X
ejpam-3714	131	14	)	)	PUNCT
ejpam-3714	132	1	+	+	CCONJ
ejpam-3714	132	2	χn	χn	INTJ
ejpam-3714	133	1	′	′	X
ejpam-3714	133	2	(	(	PUNCT
ejpam-3714	133	3	.−	.−	PUNCT
ejpam-3714	133	4	y)‖l	y)‖l	NOUN
ejpam-3714	133	5	=	=	SYM
ejpam-3714	133	6	{	{	PUNCT
ejpam-3714	133	7	1	1	NUM
ejpam-3714	133	8	2π	2π	NUM
ejpam-3714	133	9	∫	∫	PROPN
ejpam-3714	133	10	2π	2π	NOUN
ejpam-3714	133	11	0	0	NUM
ejpam-3714	133	12	|χn	|χn	NUM
ejpam-3714	133	13	′	′	NUM
ejpam-3714	133	14	(	(	PUNCT
ejpam-3714	133	15	x+	x+	PROPN
ejpam-3714	133	16	y	y	X
ejpam-3714	133	17	)	)	PUNCT
ejpam-3714	134	1	+	+	CCONJ
ejpam-3714	134	2	χn	χn	INTJ
ejpam-3714	135	1	′	′	NUM
ejpam-3714	135	2	(	(	PUNCT
ejpam-3714	135	3	x−	x−	PROPN
ejpam-3714	135	4	y)|l	y)|l	PROPN
ejpam-3714	135	5	dx	dx	PROPN
ejpam-3714	135	6	}	}	PUNCT
ejpam-3714	135	7	1	1	NUM
ejpam-3714	135	8	l	l	NOUN
ejpam-3714	135	9	≤	≤	NUM
ejpam-3714	135	10	∫	∫	PROPN
ejpam-3714	135	11	π	π	X
ejpam-3714	135	12	0	0	PUNCT
ejpam-3714	135	13	{	{	PUNCT
ejpam-3714	135	14	1	1	NUM
ejpam-3714	135	15	2π	2π	NUM
ejpam-3714	135	16	∫	∫	PROPN
ejpam-3714	135	17	2π	2π	NOUN
ejpam-3714	135	18	0	0	NUM
ejpam-3714	136	1	|ψ(x+	|ψ(x+	ADV
ejpam-3714	136	2	y	y	PROPN
ejpam-3714	136	3	,	,	PUNCT
ejpam-3714	136	4	v	v	NOUN
ejpam-3714	136	5	)	)	PUNCT
ejpam-3714	136	6	+	+	CCONJ
ejpam-3714	136	7	ψ(x−	ψ(x−	PROPN
ejpam-3714	136	8	y	y	PROPN
ejpam-3714	136	9	,	,	PUNCT
ejpam-3714	136	10	v)|ldx	v)|ldx	PROPN
ejpam-3714	136	11	}	}	PUNCT
ejpam-3714	136	12	1	1	NUM
ejpam-3714	136	13	l	l	NOUN
ejpam-3714	136	14	|y	|y	NOUN
ejpam-3714	136	15	′1	′1	X
ejpam-3714	136	16	(	(	PUNCT
ejpam-3714	136	17	v	v	NOUN
ejpam-3714	136	18	)	)	PUNCT
ejpam-3714	137	1	+	+	NOUN
ejpam-3714	137	2	y	y	PROPN
ejpam-3714	137	3	′	′	NUM
ejpam-3714	137	4	2	2	NUM
ejpam-3714	137	5	(	(	PUNCT
ejpam-3714	137	6	v)|	v)|	NOUN
ejpam-3714	137	7	dv	dv	PROPN
ejpam-3714	137	8	=	=	PROPN
ejpam-3714	137	9	∫	∫	PROPN
ejpam-3714	138	1	π	π	PROPN
ejpam-3714	138	2	0	0	PUNCT
ejpam-3714	138	3	‖ψ(.+	‖ψ(.+	SYM
ejpam-3714	138	4	y	y	PROPN
ejpam-3714	138	5	,	,	PUNCT
ejpam-3714	138	6	v	v	NOUN
ejpam-3714	138	7	)	)	PUNCT
ejpam-3714	138	8	+	+	CCONJ
ejpam-3714	138	9	ψ(.−	ψ(.−	VERB
ejpam-3714	138	10	y	y	PROPN
ejpam-3714	138	11	,	,	PUNCT
ejpam-3714	138	12	v)‖l	v)‖l	NOUN
ejpam-3714	138	13	|y	|y	NOUN
ejpam-3714	138	14	′	′	NUM
ejpam-3714	138	15	1	1	NUM
ejpam-3714	138	16	(	(	PUNCT
ejpam-3714	138	17	v	v	NOUN
ejpam-3714	138	18	)	)	PUNCT
ejpam-3714	138	19	+	+	NOUN
ejpam-3714	138	20	y	y	PROPN
ejpam-3714	138	21	′	′	NUM
ejpam-3714	138	22	2	2	NUM
ejpam-3714	138	23	(	(	PUNCT
ejpam-3714	138	24	v)|	v)|	NOUN
ejpam-3714	138	25	dv	dv	PROPN
ejpam-3714	138	26	=	=	SYM
ejpam-3714	138	27	∫	∫	PROPN
ejpam-3714	138	28	1	1	NUM
ejpam-3714	138	29	n+1	n+1	PROPN
ejpam-3714	138	30	0	0	NUM
ejpam-3714	138	31	‖ψ(.+	‖ψ(.+	X
ejpam-3714	138	32	y	y	PROPN
ejpam-3714	138	33	,	,	PUNCT
ejpam-3714	138	34	v	v	NOUN
ejpam-3714	138	35	)	)	PUNCT
ejpam-3714	138	36	+	+	CCONJ
ejpam-3714	138	37	ψ(.−	ψ(.−	VERB
ejpam-3714	138	38	y	y	PROPN
ejpam-3714	138	39	,	,	PUNCT
ejpam-3714	138	40	v)‖l	v)‖l	NOUN
ejpam-3714	138	41	|y	|y	NOUN
ejpam-3714	138	42	′	′	NUM
ejpam-3714	138	43	1	1	NUM
ejpam-3714	138	44	(	(	PUNCT
ejpam-3714	138	45	v	v	NOUN
ejpam-3714	138	46	)	)	PUNCT
ejpam-3714	138	47	+	+	NOUN
ejpam-3714	138	48	y	y	PROPN
ejpam-3714	138	49	′	′	NUM
ejpam-3714	138	50	2	2	NUM
ejpam-3714	138	51	(	(	PUNCT
ejpam-3714	138	52	v)|	v)|	PROPN
ejpam-3714	138	53	dv	dv	PROPN
ejpam-3714	138	54	+	+	CCONJ
ejpam-3714	138	55	∫	∫	PROPN
ejpam-3714	138	56	π	π	PROPN
ejpam-3714	138	57	1	1	X
ejpam-3714	138	58	n+1	n+1	PROPN
ejpam-3714	138	59	‖ψ(.+	‖ψ(.+	SYM
ejpam-3714	138	60	y	y	PROPN
ejpam-3714	138	61	,	,	PUNCT
ejpam-3714	138	62	v	v	NOUN
ejpam-3714	138	63	)	)	PUNCT
ejpam-3714	138	64	+	+	CCONJ
ejpam-3714	138	65	ψ(.−	ψ(.−	VERB
ejpam-3714	138	66	y	y	PROPN
ejpam-3714	138	67	,	,	PUNCT
ejpam-3714	138	68	v)‖l	v)‖l	NOUN
ejpam-3714	138	69	|y	|y	NOUN
ejpam-3714	138	70	′	′	NUM
ejpam-3714	138	71	1	1	NUM
ejpam-3714	138	72	(	(	PUNCT
ejpam-3714	138	73	v	v	NOUN
ejpam-3714	138	74	)	)	PUNCT
ejpam-3714	139	1	+	+	NOUN
ejpam-3714	139	2	y	y	PROPN
ejpam-3714	139	3	′	′	NUM
ejpam-3714	139	4	2	2	NUM
ejpam-3714	139	5	(	(	PUNCT
ejpam-3714	139	6	v)|	v)|	PROPN
ejpam-3714	139	7	dv	dv	PROPN
ejpam-3714	139	8	a.	a.	PROPN
ejpam-3714	139	9	mishra	mishra	PROPN
ejpam-3714	139	10	,	,	PUNCT
ejpam-3714	139	11	b.	b.	PROPN
ejpam-3714	139	12	p.	p.	PROPN
ejpam-3714	139	13	padhy	padhy	PROPN
ejpam-3714	139	14	,	,	PUNCT
ejpam-3714	139	15	u.	u.	PROPN
ejpam-3714	139	16	k.	k.	PROPN
ejpam-3714	139	17	misra	misra	PROPN
ejpam-3714	139	18	/	/	SYM
ejpam-3714	139	19	eur	eur	PROPN
ejpam-3714	139	20	.	.	PUNCT
ejpam-3714	140	1	j.	j.	PROPN
ejpam-3714	140	2	pure	pure	PROPN
ejpam-3714	140	3	appl	appl	PROPN
ejpam-3714	140	4	.	.	PROPN
ejpam-3714	140	5	math	math	PROPN
ejpam-3714	140	6	,	,	PUNCT
ejpam-3714	140	7	13	13	NUM
ejpam-3714	140	8	(	(	PUNCT
ejpam-3714	140	9	5	5	NUM
ejpam-3714	140	10	)	)	PUNCT
ejpam-3714	140	11	(	(	PUNCT
ejpam-3714	140	12	2020	2020	NUM
ejpam-3714	140	13	)	)	PUNCT
ejpam-3714	140	14	,	,	PUNCT
ejpam-3714	140	15	1325	1325	NUM
ejpam-3714	140	16	-	-	SYM
ejpam-3714	140	17	1336	1336	NUM
ejpam-3714	140	18	1333	1333	NUM
ejpam-3714	140	19	=	=	SYM
ejpam-3714	141	1	i	i	PRON
ejpam-3714	141	2	′	′	VERB
ejpam-3714	141	3	1	1	NUM
ejpam-3714	142	1	+	+	CCONJ
ejpam-3714	142	2	i	i	PRON
ejpam-3714	142	3	′	′	NOUN
ejpam-3714	142	4	2	2	NUM
ejpam-3714	142	5	,	,	PUNCT
ejpam-3714	142	6	(	(	PUNCT
ejpam-3714	142	7	say	say	INTJ
ejpam-3714	142	8	)	)	PUNCT
ejpam-3714	142	9	(	(	PUNCT
ejpam-3714	142	10	7	7	X
ejpam-3714	142	11	)	)	PUNCT
ejpam-3714	142	12	further	far	ADV
ejpam-3714	142	13	,	,	PUNCT
ejpam-3714	142	14	|ψ(x+	|ψ(x+	ADV
ejpam-3714	142	15	y	y	PROPN
ejpam-3714	142	16	;	;	PUNCT
ejpam-3714	142	17	v	v	NOUN
ejpam-3714	142	18	)	)	PUNCT
ejpam-3714	143	1	+	+	CCONJ
ejpam-3714	143	2	ψ(x−	ψ(x−	PROPN
ejpam-3714	143	3	y	y	NOUN
ejpam-3714	143	4	;	;	PUNCT
ejpam-3714	143	5	v)|	v)|	VERB
ejpam-3714	143	6	≤	≤	NOUN
ejpam-3714	143	7	‖h(x+	‖h(x+	ADP
ejpam-3714	143	8	y	y	PROPN
ejpam-3714	143	9	+	+	NOUN
ejpam-3714	143	10	v	v	NOUN
ejpam-3714	143	11	)	)	PUNCT
ejpam-3714	144	1	+	+	CCONJ
ejpam-3714	145	1	h(x+	h(x+	ADV
ejpam-3714	145	2	y	y	PROPN
ejpam-3714	145	3	−	−	PROPN
ejpam-3714	145	4	v)‖+	v)‖+	PROPN
ejpam-3714	145	5	‖h(x−	‖h(x−	PROPN
ejpam-3714	145	6	y	y	PROPN
ejpam-3714	145	7	+	+	CCONJ
ejpam-3714	145	8	v	v	NOUN
ejpam-3714	145	9	)	)	PUNCT
ejpam-3714	145	10	+	+	CCONJ
ejpam-3714	145	11	h(x−	h(x−	PROPN
ejpam-3714	145	12	y	y	PROPN
ejpam-3714	145	13	−	−	PROPN
ejpam-3714	145	14	v)‖	v)‖	NOUN
ejpam-3714	145	15	by	by	ADP
ejpam-3714	145	16	minkowski	minkowski	PROPN
ejpam-3714	145	17	’s	’s	PART
ejpam-3714	145	18	inequality	inequality	NOUN
ejpam-3714	145	19	,	,	PUNCT
ejpam-3714	145	20	we	we	PRON
ejpam-3714	145	21	have	have	VERB
ejpam-3714	145	22	|ψ(.+	|ψ(.+	PROPN
ejpam-3714	145	23	y	y	PROPN
ejpam-3714	145	24	;	;	PUNCT
ejpam-3714	145	25	v	v	NOUN
ejpam-3714	145	26	)	)	PUNCT
ejpam-3714	146	1	+	+	CCONJ
ejpam-3714	146	2	ψ(.−	ψ(.−	VERB
ejpam-3714	146	3	y	y	NOUN
ejpam-3714	146	4	;	;	PUNCT
ejpam-3714	146	5	v)|l	v)|l	VERB
ejpam-3714	146	6	≤	≤	NUM
ejpam-3714	146	7	‖h(.+	‖h(.+	NUM
ejpam-3714	146	8	y	y	PROPN
ejpam-3714	146	9	+	+	CCONJ
ejpam-3714	146	10	v	v	NOUN
ejpam-3714	146	11	)	)	PUNCT
ejpam-3714	147	1	+	+	CCONJ
ejpam-3714	147	2	h(.+	h(.+	NUM
ejpam-3714	147	3	y	y	PROPN
ejpam-3714	147	4	−	−	PROPN
ejpam-3714	147	5	v)‖l	v)‖l	NOUN
ejpam-3714	147	6	+	+	CCONJ
ejpam-3714	147	7	‖h(.−	‖h(.−	PROPN
ejpam-3714	147	8	y	y	PROPN
ejpam-3714	147	9	+	+	NOUN
ejpam-3714	147	10	v	v	NOUN
ejpam-3714	147	11	)	)	PUNCT
ejpam-3714	148	1	+	+	CCONJ
ejpam-3714	148	2	h(.−	h(.−	ADJ
ejpam-3714	148	3	y	y	PROPN
ejpam-3714	148	4	−	−	PROPN
ejpam-3714	148	5	v)‖l	v)‖l	NOUN
ejpam-3714	148	6	=	=	PUNCT
ejpam-3714	148	7	o(m(v	o(m(v	PROPN
ejpam-3714	148	8	)	)	PUNCT
ejpam-3714	148	9	)	)	PUNCT
ejpam-3714	148	10	or	or	CCONJ
ejpam-3714	148	11	o(m(y	o(m(y	PROPN
ejpam-3714	148	12	)	)	PUNCT
ejpam-3714	148	13	)	)	PUNCT
ejpam-3714	148	14	again	again	ADV
ejpam-3714	148	15	,	,	PUNCT
ejpam-3714	148	16	by	by	ADP
ejpam-3714	148	17	using	use	VERB
ejpam-3714	148	18	lemma-1	lemma-1	NUM
ejpam-3714	148	19	,	,	PUNCT
ejpam-3714	148	20	lemma-3	lemma-3	PROPN
ejpam-3714	148	21	and	and	CCONJ
ejpam-3714	148	22	monotonicity	monotonicity	NOUN
ejpam-3714	148	23	of	of	ADP
ejpam-3714	148	24	m(v	m(v	NUM
ejpam-3714	148	25	)	)	PUNCT
ejpam-3714	148	26	µ(v	µ(v	PROPN
ejpam-3714	148	27	)	)	PUNCT
ejpam-3714	148	28	,	,	PUNCT
ejpam-3714	148	29	we	we	PRON
ejpam-3714	148	30	get	get	VERB
ejpam-3714	148	31	i	i	PRON
ejpam-3714	148	32	′	′	NOUN
ejpam-3714	148	33	1	1	NUM
ejpam-3714	148	34	=	=	SYM
ejpam-3714	148	35	∫	∫	PROPN
ejpam-3714	149	1	1	1	NUM
ejpam-3714	149	2	n+1	n+1	PROPN
ejpam-3714	149	3	0	0	NUM
ejpam-3714	149	4	‖ψ(.+	‖ψ(.+	X
ejpam-3714	149	5	y	y	PROPN
ejpam-3714	149	6	,	,	PUNCT
ejpam-3714	149	7	v	v	NOUN
ejpam-3714	149	8	)	)	PUNCT
ejpam-3714	149	9	+	+	CCONJ
ejpam-3714	149	10	ψ(.−	ψ(.−	VERB
ejpam-3714	149	11	y	y	PROPN
ejpam-3714	149	12	,	,	PUNCT
ejpam-3714	149	13	v)‖l|y	v)‖l|y	NUM
ejpam-3714	149	14	′	′	NUM
ejpam-3714	149	15	1	1	NUM
ejpam-3714	149	16	(	(	PUNCT
ejpam-3714	149	17	v	v	NOUN
ejpam-3714	149	18	)	)	PUNCT
ejpam-3714	150	1	+	+	NOUN
ejpam-3714	150	2	y	y	PROPN
ejpam-3714	150	3	′	′	NUM
ejpam-3714	150	4	2	2	NUM
ejpam-3714	150	5	(	(	PUNCT
ejpam-3714	150	6	v)|	v)|	PROPN
ejpam-3714	150	7	dv	dv	PROPN
ejpam-3714	150	8	≤	≤	PROPN
ejpam-3714	150	9	o	o	PROPN
ejpam-3714	151	1	(	(	PUNCT
ejpam-3714	151	2	∫	∫	PROPN
ejpam-3714	151	3	1	1	NUM
ejpam-3714	151	4	n+1	n+1	PROPN
ejpam-3714	151	5	0	0	NUM
ejpam-3714	151	6	µ(y	µ(y	NOUN
ejpam-3714	151	7	)	)	PUNCT
ejpam-3714	151	8	m(v	m(v	NOUN
ejpam-3714	151	9	)	)	PUNCT
ejpam-3714	151	10	µ(v	µ(v	PROPN
ejpam-3714	151	11	)	)	PUNCT
ejpam-3714	151	12	n2	n2	PROPN
ejpam-3714	151	13	dv	dv	PROPN
ejpam-3714	151	14	)	)	PUNCT
ejpam-3714	152	1	+	+	NOUN
ejpam-3714	152	2	o	o	X
ejpam-3714	152	3	(	(	PUNCT
ejpam-3714	152	4	∫	∫	PROPN
ejpam-3714	152	5	1	1	NUM
ejpam-3714	152	6	n+1	n+1	PROPN
ejpam-3714	152	7	0	0	NUM
ejpam-3714	152	8	µ(y	µ(y	NOUN
ejpam-3714	152	9	)	)	PUNCT
ejpam-3714	152	10	m(v	m(v	NOUN
ejpam-3714	152	11	)	)	PUNCT
ejpam-3714	152	12	µ(v	µ(v	X
ejpam-3714	152	13	)	)	PUNCT
ejpam-3714	152	14	1	1	NUM
ejpam-3714	152	15	v2	v2	PROPN
ejpam-3714	152	16	dv	dv	PROPN
ejpam-3714	152	17	)	)	PUNCT
ejpam-3714	153	1	=	=	PUNCT
ejpam-3714	153	2	o	o	X
ejpam-3714	153	3	(	(	PUNCT
ejpam-3714	153	4	n2µ(y	n2µ(y	PROPN
ejpam-3714	153	5	)	)	PUNCT
ejpam-3714	153	6	m	m	VERB
ejpam-3714	153	7	(	(	PUNCT
ejpam-3714	153	8	1	1	NUM
ejpam-3714	153	9	n+1	n+1	X
ejpam-3714	153	10	)	)	PUNCT
ejpam-3714	153	11	µ	µ	X
ejpam-3714	153	12	(	(	PUNCT
ejpam-3714	153	13	1	1	NUM
ejpam-3714	153	14	n+1	n+1	NUM
ejpam-3714	153	15	)	)	PUNCT
ejpam-3714	153	16	)	)	PUNCT
ejpam-3714	154	1	+	+	NOUN
ejpam-3714	154	2	o	o	X
ejpam-3714	154	3	(	(	PUNCT
ejpam-3714	154	4	µ(y	µ(y	PROPN
ejpam-3714	154	5	)	)	PUNCT
ejpam-3714	154	6	∫	∫	PROPN
ejpam-3714	154	7	1	1	NUM
ejpam-3714	154	8	n+1	n+1	PROPN
ejpam-3714	154	9	0	0	NUM
ejpam-3714	154	10	m(v	m(v	NUM
ejpam-3714	154	11	)	)	PUNCT
ejpam-3714	154	12	µ(v	µ(v	X
ejpam-3714	154	13	)	)	PUNCT
ejpam-3714	154	14	1	1	NUM
ejpam-3714	154	15	v2	v2	PROPN
ejpam-3714	154	16	dv	dv	PROPN
ejpam-3714	154	17	)	)	PUNCT
ejpam-3714	154	18	(	(	PUNCT
ejpam-3714	154	19	8)	8)	NUM
ejpam-3714	154	20	similarly	similarly	ADV
ejpam-3714	154	21	,	,	PUNCT
ejpam-3714	154	22	by	by	ADP
ejpam-3714	154	23	using	use	VERB
ejpam-3714	154	24	lemma-2	lemma-2	NUM
ejpam-3714	154	25	,	,	PUNCT
ejpam-3714	154	26	lemma-3	lemma-3	PROPN
ejpam-3714	154	27	and	and	CCONJ
ejpam-3714	154	28	monotonicity	monotonicity	NOUN
ejpam-3714	154	29	of	of	ADP
ejpam-3714	154	30	m(v	m(v	NUM
ejpam-3714	154	31	)	)	PUNCT
ejpam-3714	154	32	µ(v	µ(v	PROPN
ejpam-3714	154	33	)	)	PUNCT
ejpam-3714	154	34	,	,	PUNCT
ejpam-3714	154	35	we	we	PRON
ejpam-3714	154	36	get	get	VERB
ejpam-3714	154	37	i	i	PRON
ejpam-3714	154	38	′	′	NOUN
ejpam-3714	154	39	2	2	NUM
ejpam-3714	155	1	=	=	SYM
ejpam-3714	155	2	∫	∫	PROPN
ejpam-3714	155	3	π	π	PROPN
ejpam-3714	155	4	1	1	X
ejpam-3714	155	5	n+1	n+1	PROPN
ejpam-3714	155	6	‖ψ(.+	‖ψ(.+	SYM
ejpam-3714	155	7	y	y	PROPN
ejpam-3714	155	8	,	,	PUNCT
ejpam-3714	155	9	v	v	NOUN
ejpam-3714	155	10	)	)	PUNCT
ejpam-3714	155	11	+	+	CCONJ
ejpam-3714	155	12	ψ(.−	ψ(.−	VERB
ejpam-3714	155	13	y	y	PROPN
ejpam-3714	155	14	,	,	PUNCT
ejpam-3714	155	15	v)‖l|y	v)‖l|y	NUM
ejpam-3714	155	16	′	′	NUM
ejpam-3714	155	17	1	1	NUM
ejpam-3714	155	18	(	(	PUNCT
ejpam-3714	155	19	v	v	NOUN
ejpam-3714	155	20	)	)	PUNCT
ejpam-3714	155	21	+	+	NOUN
ejpam-3714	155	22	y	y	PROPN
ejpam-3714	155	23	′	′	NUM
ejpam-3714	155	24	2	2	NUM
ejpam-3714	155	25	(	(	PUNCT
ejpam-3714	155	26	v)|	v)|	NOUN
ejpam-3714	155	27	dv	dv	PROPN
ejpam-3714	155	28	=	=	PROPN
ejpam-3714	155	29	o	o	X
ejpam-3714	155	30	(	(	PUNCT
ejpam-3714	155	31	n2µ(y	n2µ(y	PROPN
ejpam-3714	155	32	)	)	PUNCT
ejpam-3714	155	33	∫	∫	PROPN
ejpam-3714	155	34	1	1	NUM
ejpam-3714	155	35	n+1	n+1	NUM
ejpam-3714	155	36	0	0	NUM
ejpam-3714	155	37	m(v	m(v	NOUN
ejpam-3714	155	38	)	)	PUNCT
ejpam-3714	155	39	dv	dv	PROPN
ejpam-3714	155	40	µ(v	µ(v	PROPN
ejpam-3714	155	41	)	)	PUNCT
ejpam-3714	155	42	)	)	PUNCT
ejpam-3714	156	1	+	+	ADP
ejpam-3714	156	2	o	o	X
ejpam-3714	156	3	(	(	PUNCT
ejpam-3714	156	4	(	(	PUNCT
ejpam-3714	156	5	n+	n+	X
ejpam-3714	156	6	1)µ(y	1)µ(y	NUM
ejpam-3714	156	7	)	)	PUNCT
ejpam-3714	156	8	m	m	VERB
ejpam-3714	156	9	(	(	PUNCT
ejpam-3714	156	10	1	1	NUM
ejpam-3714	156	11	n+1	n+1	X
ejpam-3714	156	12	)	)	PUNCT
ejpam-3714	156	13	µ	µ	X
ejpam-3714	156	14	(	(	PUNCT
ejpam-3714	156	15	1	1	NUM
ejpam-3714	156	16	n+1	n+1	NUM
ejpam-3714	156	17	)	)	PUNCT
ejpam-3714	156	18	)	)	PUNCT
ejpam-3714	157	1	(	(	PUNCT
ejpam-3714	157	2	9	9	X
ejpam-3714	157	3	)	)	PUNCT
ejpam-3714	157	4	by	by	ADP
ejpam-3714	157	5	,	,	PUNCT
ejpam-3714	157	6	(	(	PUNCT
ejpam-3714	157	7	7	7	NUM
ejpam-3714	157	8	)	)	PUNCT
ejpam-3714	157	9	,	,	PUNCT
ejpam-3714	157	10	(	(	PUNCT
ejpam-3714	157	11	8)	8)	NUM
ejpam-3714	157	12	and	and	CCONJ
ejpam-3714	157	13	(	(	PUNCT
ejpam-3714	157	14	9	9	NUM
ejpam-3714	157	15	)	)	PUNCT
ejpam-3714	157	16	‖χn	‖χn	NOUN
ejpam-3714	157	17	′	′	NUM
ejpam-3714	157	18	(	(	PUNCT
ejpam-3714	158	1	.+	.+	NOUN
ejpam-3714	158	2	y	y	X
ejpam-3714	158	3	)	)	PUNCT
ejpam-3714	159	1	+	+	CCONJ
ejpam-3714	159	2	χn	χn	INTJ
ejpam-3714	160	1	′	′	X
ejpam-3714	160	2	(	(	PUNCT
ejpam-3714	160	3	.−	.−	PUNCT
ejpam-3714	160	4	y)|l	y)|l	PROPN
ejpam-3714	161	1	=	=	PUNCT
ejpam-3714	161	2	o	o	X
ejpam-3714	161	3	(	(	PUNCT
ejpam-3714	161	4	n2µ(y	n2µ(y	PROPN
ejpam-3714	161	5	)	)	PUNCT
ejpam-3714	161	6	m	m	VERB
ejpam-3714	161	7	(	(	PUNCT
ejpam-3714	161	8	1	1	NUM
ejpam-3714	161	9	n+1	n+1	X
ejpam-3714	161	10	)	)	PUNCT
ejpam-3714	161	11	µ	µ	X
ejpam-3714	161	12	(	(	PUNCT
ejpam-3714	161	13	1	1	NUM
ejpam-3714	161	14	n+1	n+1	NUM
ejpam-3714	161	15	)	)	PUNCT
ejpam-3714	161	16	)	)	PUNCT
ejpam-3714	162	1	+	+	NOUN
ejpam-3714	162	2	o	o	X
ejpam-3714	162	3	(	(	PUNCT
ejpam-3714	162	4	µ(y	µ(y	PROPN
ejpam-3714	162	5	)	)	PUNCT
ejpam-3714	162	6	∫	∫	PROPN
ejpam-3714	162	7	1	1	NUM
ejpam-3714	162	8	n+1	n+1	PROPN
ejpam-3714	162	9	0	0	NUM
ejpam-3714	162	10	m(v	m(v	NUM
ejpam-3714	162	11	)	)	PUNCT
ejpam-3714	162	12	µ(v	µ(v	X
ejpam-3714	162	13	)	)	PUNCT
ejpam-3714	162	14	1	1	NUM
ejpam-3714	162	15	v2	v2	PROPN
ejpam-3714	162	16	dv	dv	PROPN
ejpam-3714	162	17	)	)	PUNCT
ejpam-3714	163	1	+	+	ADP
ejpam-3714	163	2	o	o	X
ejpam-3714	163	3	(	(	PUNCT
ejpam-3714	163	4	n2µ(y	n2µ(y	PROPN
ejpam-3714	163	5	)	)	PUNCT
ejpam-3714	163	6	∫	∫	PROPN
ejpam-3714	163	7	1	1	NUM
ejpam-3714	163	8	n+1	n+1	NUM
ejpam-3714	163	9	0	0	NUM
ejpam-3714	163	10	m(v	m(v	NOUN
ejpam-3714	163	11	)	)	PUNCT
ejpam-3714	163	12	dv	dv	PROPN
ejpam-3714	163	13	µ(v	µ(v	PROPN
ejpam-3714	163	14	)	)	PUNCT
ejpam-3714	163	15	)	)	PUNCT
ejpam-3714	164	1	+	+	ADP
ejpam-3714	164	2	o	o	X
ejpam-3714	164	3	(	(	PUNCT
ejpam-3714	164	4	(	(	PUNCT
ejpam-3714	164	5	n+	n+	X
ejpam-3714	164	6	1)µ(y	1)µ(y	NUM
ejpam-3714	164	7	)	)	PUNCT
ejpam-3714	164	8	m	m	VERB
ejpam-3714	164	9	(	(	PUNCT
ejpam-3714	164	10	1	1	NUM
ejpam-3714	164	11	n+1	n+1	X
ejpam-3714	164	12	)	)	PUNCT
ejpam-3714	164	13	µ	µ	X
ejpam-3714	164	14	(	(	PUNCT
ejpam-3714	164	15	1	1	NUM
ejpam-3714	164	16	n+1	n+1	NUM
ejpam-3714	164	17	)	)	PUNCT
ejpam-3714	164	18	)	)	PUNCT
ejpam-3714	165	1	therefore	therefore	ADV
ejpam-3714	165	2	,	,	PUNCT
ejpam-3714	165	3	we	we	PRON
ejpam-3714	165	4	have	have	VERB
ejpam-3714	165	5	sup	sup	NOUN
ejpam-3714	165	6	y	y	PROPN
ejpam-3714	165	7	6=0	6=0	NUM
ejpam-3714	165	8	‖χn	‖χn	NUM
ejpam-3714	166	1	′	′	NUM
ejpam-3714	166	2	(	(	PUNCT
ejpam-3714	167	1	.+	.+	NOUN
ejpam-3714	167	2	y	y	X
ejpam-3714	167	3	)	)	PUNCT
ejpam-3714	168	1	+	+	CCONJ
ejpam-3714	168	2	χn	χn	INTJ
ejpam-3714	169	1	′	′	X
ejpam-3714	169	2	(	(	PUNCT
ejpam-3714	169	3	.−	.−	PUNCT
ejpam-3714	169	4	y)‖l	y)‖l	PROPN
ejpam-3714	169	5	µ(y	µ(y	PROPN
ejpam-3714	169	6	)	)	PUNCT
ejpam-3714	169	7	a.	a.	PROPN
ejpam-3714	169	8	mishra	mishra	PROPN
ejpam-3714	169	9	,	,	PUNCT
ejpam-3714	169	10	b.	b.	PROPN
ejpam-3714	169	11	p.	p.	PROPN
ejpam-3714	169	12	padhy	padhy	PROPN
ejpam-3714	169	13	,	,	PUNCT
ejpam-3714	170	1	u.	u.	PROPN
ejpam-3714	170	2	k.	k.	PROPN
ejpam-3714	170	3	misra	misra	PROPN
ejpam-3714	170	4	/	/	SYM
ejpam-3714	170	5	eur	eur	PROPN
ejpam-3714	170	6	.	.	PUNCT
ejpam-3714	171	1	j.	j.	PROPN
ejpam-3714	171	2	pure	pure	PROPN
ejpam-3714	171	3	appl	appl	PROPN
ejpam-3714	171	4	.	.	PROPN
ejpam-3714	171	5	math	math	PROPN
ejpam-3714	171	6	,	,	PUNCT
ejpam-3714	171	7	13	13	NUM
ejpam-3714	171	8	(	(	PUNCT
ejpam-3714	171	9	5	5	NUM
ejpam-3714	171	10	)	)	PUNCT
ejpam-3714	171	11	(	(	PUNCT
ejpam-3714	171	12	2020	2020	NUM
ejpam-3714	171	13	)	)	PUNCT
ejpam-3714	171	14	,	,	PUNCT
ejpam-3714	171	15	1325	1325	NUM
ejpam-3714	171	16	-	-	SYM
ejpam-3714	171	17	1336	1336	NUM
ejpam-3714	171	18	1334	1334	NUM
ejpam-3714	172	1	=	=	SYM
ejpam-3714	172	2	o	o	X
ejpam-3714	172	3	(	(	PUNCT
ejpam-3714	172	4	n2	n2	PROPN
ejpam-3714	172	5	m	m	PROPN
ejpam-3714	172	6	(	(	PUNCT
ejpam-3714	172	7	1	1	NUM
ejpam-3714	172	8	n+1	n+1	X
ejpam-3714	172	9	)	)	PUNCT
ejpam-3714	172	10	µ	µ	X
ejpam-3714	172	11	(	(	PUNCT
ejpam-3714	172	12	1	1	NUM
ejpam-3714	172	13	n+1	n+1	NUM
ejpam-3714	172	14	)	)	PUNCT
ejpam-3714	172	15	)	)	PUNCT
ejpam-3714	173	1	+	+	NOUN
ejpam-3714	173	2	o	o	X
ejpam-3714	173	3	(	(	PUNCT
ejpam-3714	173	4	∫	∫	PROPN
ejpam-3714	173	5	1	1	NUM
ejpam-3714	173	6	n+1	n+1	PROPN
ejpam-3714	173	7	0	0	NUM
ejpam-3714	173	8	m(v	m(v	NUM
ejpam-3714	173	9	)	)	PUNCT
ejpam-3714	173	10	µ(v	µ(v	X
ejpam-3714	173	11	)	)	PUNCT
ejpam-3714	173	12	1	1	NUM
ejpam-3714	173	13	v2	v2	PROPN
ejpam-3714	173	14	dv	dv	PROPN
ejpam-3714	173	15	)	)	PUNCT
ejpam-3714	174	1	+	+	ADP
ejpam-3714	174	2	o	o	X
ejpam-3714	174	3	(	(	PUNCT
ejpam-3714	174	4	n2	n2	ADJ
ejpam-3714	174	5	∫	∫	PROPN
ejpam-3714	174	6	1	1	NUM
ejpam-3714	174	7	n+1	n+1	PROPN
ejpam-3714	174	8	0	0	NUM
ejpam-3714	174	9	m(v	m(v	NOUN
ejpam-3714	174	10	)	)	PUNCT
ejpam-3714	174	11	dv	dv	PROPN
ejpam-3714	174	12	µ(v	µ(v	PROPN
ejpam-3714	174	13	)	)	PUNCT
ejpam-3714	174	14	)	)	PUNCT
ejpam-3714	175	1	+	+	ADP
ejpam-3714	175	2	o	o	X
ejpam-3714	175	3	(	(	PUNCT
ejpam-3714	175	4	(	(	PUNCT
ejpam-3714	175	5	n+	n+	NOUN
ejpam-3714	175	6	1	1	X
ejpam-3714	175	7	)	)	PUNCT
ejpam-3714	175	8	m	m	VERB
ejpam-3714	175	9	(	(	PUNCT
ejpam-3714	175	10	1	1	NUM
ejpam-3714	175	11	n+1	n+1	X
ejpam-3714	175	12	)	)	PUNCT
ejpam-3714	175	13	µ	µ	X
ejpam-3714	175	14	(	(	PUNCT
ejpam-3714	175	15	1	1	NUM
ejpam-3714	175	16	n+1	n+1	NUM
ejpam-3714	175	17	)	)	PUNCT
ejpam-3714	175	18	)	)	PUNCT
ejpam-3714	175	19	(	(	PUNCT
ejpam-3714	175	20	10	10	NUM
ejpam-3714	175	21	)	)	PUNCT
ejpam-3714	175	22	since	since	SCONJ
ejpam-3714	175	23	,	,	PUNCT
ejpam-3714	175	24	h	h	NOUN
ejpam-3714	175	25	∈	∈	PROPN
ejpam-3714	175	26	z(m	z(m	PROPN
ejpam-3714	175	27	)	)	PUNCT
ejpam-3714	175	28	l	l	NOUN
ejpam-3714	175	29	and	and	CCONJ
ejpam-3714	175	30	ψ(x	ψ(x	NUM
ejpam-3714	175	31	;	;	PUNCT
ejpam-3714	175	32	v	v	X
ejpam-3714	175	33	)	)	PUNCT
ejpam-3714	175	34	=	=	PUNCT
ejpam-3714	175	35	|h(x+	|h(x+	ADV
ejpam-3714	175	36	v	v	NOUN
ejpam-3714	175	37	)	)	PUNCT
ejpam-3714	175	38	+	+	NUM
ejpam-3714	175	39	h(x−	h(x−	NOUN
ejpam-3714	175	40	v)|	v)|	NOUN
ejpam-3714	175	41	,	,	PUNCT
ejpam-3714	175	42	by	by	ADP
ejpam-3714	175	43	minkowski	minkowski	PROPN
ejpam-3714	175	44	’s	’s	PART
ejpam-3714	175	45	inequality	inequality	NOUN
ejpam-3714	175	46	,	,	PUNCT
ejpam-3714	175	47	we	we	PRON
ejpam-3714	175	48	have	have	VERB
ejpam-3714	175	49	‖ψ(x	‖ψ(x	NOUN
ejpam-3714	175	50	,	,	PUNCT
ejpam-3714	175	51	v)‖l	v)‖l	NOUN
ejpam-3714	175	52	=	=	SYM
ejpam-3714	175	53	‖h(x+	‖h(x+	PROPN
ejpam-3714	175	54	v	v	NOUN
ejpam-3714	175	55	)	)	PUNCT
ejpam-3714	175	56	+	+	NUM
ejpam-3714	175	57	h(x−	h(x−	ADP
ejpam-3714	175	58	v)‖l	v)‖l	NOUN
ejpam-3714	175	59	=	=	PROPN
ejpam-3714	175	60	o	o	X
ejpam-3714	175	61	(	(	PUNCT
ejpam-3714	175	62	m(v	m(v	PROPN
ejpam-3714	175	63	)	)	PUNCT
ejpam-3714	175	64	)	)	PUNCT
ejpam-3714	175	65	therefore	therefore	ADV
ejpam-3714	175	66	,	,	PUNCT
ejpam-3714	176	1	‖χn	‖χn	PROPN
ejpam-3714	176	2	′	′	NUM
ejpam-3714	176	3	(	(	PUNCT
ejpam-3714	176	4	.)‖l	.)‖l	PROPN
ejpam-3714	176	5	≤	≤	PROPN
ejpam-3714	176	6	(	(	PUNCT
ejpam-3714	176	7	∫	∫	PROPN
ejpam-3714	176	8	1	1	NUM
ejpam-3714	176	9	n+1	n+1	PROPN
ejpam-3714	176	10	0	0	NUM
ejpam-3714	177	1	+	+	NUM
ejpam-3714	177	2	∫	∫	PROPN
ejpam-3714	177	3	π	π	PROPN
ejpam-3714	177	4	1	1	NUM
ejpam-3714	177	5	n+1	n+1	PRON
ejpam-3714	177	6	)	)	PUNCT
ejpam-3714	177	7	‖ψ	‖ψ	PROPN
ejpam-3714	177	8	(	(	PUNCT
ejpam-3714	177	9	.	.	NUM
ejpam-3714	177	10	,	,	PUNCT
ejpam-3714	177	11	v)‖l|	v)‖l|	NUM
ejpam-3714	177	12	y1	y1	NOUN
ejpam-3714	177	13	′	′	NUM
ejpam-3714	177	14	(	(	PUNCT
ejpam-3714	177	15	v	v	NOUN
ejpam-3714	177	16	)	)	PUNCT
ejpam-3714	178	1	+	+	CCONJ
ejpam-3714	178	2	y2	y2	INTJ
ejpam-3714	178	3	′	′	NOUN
ejpam-3714	178	4	(	(	PUNCT
ejpam-3714	178	5	v)|	v)|	NOUN
ejpam-3714	179	1	dv	dv	PROPN
ejpam-3714	179	2	=	=	PROPN
ejpam-3714	179	3	o	o	PROPN
ejpam-3714	180	1	(	(	PUNCT
ejpam-3714	180	2	n2	n2	PROPN
ejpam-3714	180	3	∫	∫	PROPN
ejpam-3714	180	4	1	1	NUM
ejpam-3714	180	5	n+1	n+1	PROPN
ejpam-3714	180	6	0	0	NUM
ejpam-3714	180	7	m(v	m(v	NOUN
ejpam-3714	180	8	)	)	PUNCT
ejpam-3714	180	9	dv	dv	PROPN
ejpam-3714	180	10	)	)	PUNCT
ejpam-3714	181	1	+	+	NOUN
ejpam-3714	181	2	o	o	X
ejpam-3714	181	3	(	(	PUNCT
ejpam-3714	181	4	∫	∫	PROPN
ejpam-3714	181	5	1	1	NUM
ejpam-3714	181	6	n+1	n+1	PROPN
ejpam-3714	181	7	0	0	NUM
ejpam-3714	181	8	m(v	m(v	NOUN
ejpam-3714	181	9	)	)	PUNCT
ejpam-3714	182	1	v2	v2	PROPN
ejpam-3714	182	2	dv	dv	PROPN
ejpam-3714	182	3	)	)	PUNCT
ejpam-3714	183	1	+	+	ADP
ejpam-3714	183	2	o	o	X
ejpam-3714	183	3	(	(	PUNCT
ejpam-3714	183	4	n2	n2	ADJ
ejpam-3714	183	5	∫	∫	PROPN
ejpam-3714	183	6	π	π	PROPN
ejpam-3714	183	7	1	1	NUM
ejpam-3714	183	8	n+1	n+1	PROPN
ejpam-3714	183	9	m(v	m(v	PROPN
ejpam-3714	183	10	)	)	PUNCT
ejpam-3714	183	11	dv	dv	PROPN
ejpam-3714	183	12	)	)	PUNCT
ejpam-3714	184	1	+	+	NOUN
ejpam-3714	184	2	o	o	X
ejpam-3714	184	3	(	(	PUNCT
ejpam-3714	184	4	∫	∫	PROPN
ejpam-3714	184	5	π	π	PROPN
ejpam-3714	184	6	1	1	NUM
ejpam-3714	184	7	n+1	n+1	PROPN
ejpam-3714	184	8	m(v	m(v	X
ejpam-3714	184	9	)	)	PUNCT
ejpam-3714	185	1	v2	v2	PROPN
ejpam-3714	185	2	dv	dv	PROPN
ejpam-3714	185	3	)	)	PUNCT
ejpam-3714	185	4	(	(	PUNCT
ejpam-3714	185	5	11	11	NUM
ejpam-3714	185	6	)	)	PUNCT
ejpam-3714	185	7	from	from	ADP
ejpam-3714	185	8	(	(	PUNCT
ejpam-3714	185	9	10	10	NUM
ejpam-3714	185	10	)	)	PUNCT
ejpam-3714	185	11	,	,	PUNCT
ejpam-3714	185	12	(	(	PUNCT
ejpam-3714	185	13	11	11	NUM
ejpam-3714	185	14	)	)	PUNCT
ejpam-3714	185	15	and	and	CCONJ
ejpam-3714	185	16	by	by	ADP
ejpam-3714	185	17	the	the	DET
ejpam-3714	185	18	monotonicity	monotonicity	NOUN
ejpam-3714	185	19	of	of	ADP
ejpam-3714	185	20	µ(v	µ(v	PROPN
ejpam-3714	185	21	)	)	PUNCT
ejpam-3714	185	22	we	we	PRON
ejpam-3714	185	23	have	have	VERB
ejpam-3714	185	24	‖χn	‖χn	NUM
ejpam-3714	185	25	′	′	NUM
ejpam-3714	185	26	(	(	PUNCT
ejpam-3714	185	27	.)‖µl	.)‖µl	PUNCT
ejpam-3714	185	28	=	=	SYM
ejpam-3714	186	1	‖χn	‖χn	NUM
ejpam-3714	186	2	′	′	NUM
ejpam-3714	186	3	(	(	PUNCT
ejpam-3714	186	4	.)‖l	.)‖l	PROPN
ejpam-3714	187	1	+	+	NUM
ejpam-3714	187	2	sup	sup	PROPN
ejpam-3714	187	3	y	y	PROPN
ejpam-3714	187	4	6=0	6=0	NUM
ejpam-3714	187	5	‖χn′(.+	‖χn′(.+	PROPN
ejpam-3714	187	6	y	y	PROPN
ejpam-3714	187	7	)	)	PUNCT
ejpam-3714	188	1	+	+	CCONJ
ejpam-3714	188	2	χn	χn	INTJ
ejpam-3714	189	1	′	′	X
ejpam-3714	189	2	(	(	PUNCT
ejpam-3714	189	3	.−	.−	PUNCT
ejpam-3714	189	4	y)‖l	y)‖l	PROPN
ejpam-3714	189	5	µ(y	µ(y	PROPN
ejpam-3714	189	6	)	)	PUNCT
ejpam-3714	190	1	=	=	SYM
ejpam-3714	190	2	o	o	NOUN
ejpam-3714	190	3	(	(	PUNCT
ejpam-3714	190	4	∫	∫	PROPN
ejpam-3714	190	5	π	π	PROPN
ejpam-3714	190	6	1	1	NUM
ejpam-3714	190	7	n+1	n+1	PROPN
ejpam-3714	190	8	m(v	m(v	X
ejpam-3714	190	9	)	)	PUNCT
ejpam-3714	190	10	v2	v2	PROPN
ejpam-3714	190	11	µ(v	µ(v	PROPN
ejpam-3714	190	12	)	)	PUNCT
ejpam-3714	190	13	dv	dv	PROPN
ejpam-3714	190	14	)	)	PUNCT
ejpam-3714	190	15	provided	provide	VERB
ejpam-3714	190	16	∫	∫	PROPN
ejpam-3714	190	17	η	η	PROPN
ejpam-3714	190	18	0	0	NUM
ejpam-3714	190	19	m(v	m(v	NUM
ejpam-3714	190	20	)	)	PUNCT
ejpam-3714	190	21	v	v	ADP
ejpam-3714	190	22	µ(v	µ(v	PROPN
ejpam-3714	190	23	)	)	PUNCT
ejpam-3714	190	24	dv	dv	PROPN
ejpam-3714	190	25	=	=	PROPN
ejpam-3714	190	26	o	o	PROPN
ejpam-3714	190	27	(	(	PUNCT
ejpam-3714	190	28	m(η	m(η	PROPN
ejpam-3714	190	29	)	)	PUNCT
ejpam-3714	190	30	µ(η	µ(η	NOUN
ejpam-3714	190	31	)	)	PUNCT
ejpam-3714	190	32	)	)	PUNCT
ejpam-3714	190	33	hence	hence	ADV
ejpam-3714	190	34	,	,	PUNCT
ejpam-3714	190	35	en(h	en(h	PROPN
ejpam-3714	190	36	)	)	PUNCT
ejpam-3714	190	37	=	=	SYM
ejpam-3714	190	38	inf	inf	PROPN
ejpam-3714	190	39	n	n	PROPN
ejpam-3714	190	40	‖χn	‖χn	NUM
ejpam-3714	190	41	′	′	NUM
ejpam-3714	191	1	(	(	PUNCT
ejpam-3714	191	2	.)‖µl	.)‖µl	PUNCT
ejpam-3714	191	3	=	=	SYM
ejpam-3714	191	4	o	o	X
ejpam-3714	191	5	(	(	PUNCT
ejpam-3714	191	6	∫	∫	PROPN
ejpam-3714	191	7	π	π	PROPN
ejpam-3714	191	8	1	1	NUM
ejpam-3714	191	9	n+1	n+1	PROPN
ejpam-3714	191	10	m(v	m(v	X
ejpam-3714	191	11	)	)	PUNCT
ejpam-3714	191	12	v2	v2	PROPN
ejpam-3714	191	13	µ(v	µ(v	PROPN
ejpam-3714	191	14	)	)	PUNCT
ejpam-3714	191	15	dv	dv	PROPN
ejpam-3714	191	16	)	)	PUNCT
ejpam-3714	191	17	this	this	PRON
ejpam-3714	191	18	completes	complete	VERB
ejpam-3714	191	19	the	the	DET
ejpam-3714	191	20	proof	proof	NOUN
ejpam-3714	191	21	of	of	ADP
ejpam-3714	191	22	our	our	PRON
ejpam-3714	191	23	main	main	ADJ
ejpam-3714	191	24	theorem	theorem	NOUN
ejpam-3714	191	25	.	.	PUNCT
ejpam-3714	192	1	acknowledgements	acknowledgement	NOUN
ejpam-3714	192	2	the	the	DET
ejpam-3714	192	3	authors	author	NOUN
ejpam-3714	192	4	are	be	AUX
ejpam-3714	192	5	thankful	thankful	ADJ
ejpam-3714	192	6	to	to	ADP
ejpam-3714	192	7	the	the	DET
ejpam-3714	192	8	anonymous	anonymous	ADJ
ejpam-3714	192	9	reviewers	reviewer	NOUN
ejpam-3714	192	10	for	for	ADP
ejpam-3714	192	11	their	their	PRON
ejpam-3714	192	12	constructive	constructive	ADJ
ejpam-3714	192	13	suggestions	suggestion	NOUN
ejpam-3714	192	14	to	to	PART
ejpam-3714	192	15	develop	develop	VERB
ejpam-3714	192	16	the	the	DET
ejpam-3714	192	17	article	article	NOUN
ejpam-3714	192	18	.	.	PUNCT
ejpam-3714	193	1	also	also	ADV
ejpam-3714	193	2	,	,	PUNCT
ejpam-3714	193	3	the	the	DET
ejpam-3714	193	4	authors	author	NOUN
ejpam-3714	193	5	are	be	AUX
ejpam-3714	193	6	grateful	grateful	ADJ
ejpam-3714	193	7	to	to	ADP
ejpam-3714	193	8	the	the	DET
ejpam-3714	193	9	management	management	NOUN
ejpam-3714	193	10	of	of	ADP
ejpam-3714	193	11	kiit	kiit	PROPN
ejpam-3714	193	12	,	,	PUNCT
ejpam-3714	193	13	deemed	deem	VERB
ejpam-3714	193	14	to	to	PART
ejpam-3714	193	15	be	be	AUX
ejpam-3714	193	16	university	university	NOUN
ejpam-3714	193	17	and	and	CCONJ
ejpam-3714	193	18	nist	nist	NOUN
ejpam-3714	193	19	,	,	PUNCT
ejpam-3714	193	20	berhampur	berhampur	NOUN
ejpam-3714	193	21	to	to	PART
ejpam-3714	193	22	provide	provide	VERB
ejpam-3714	193	23	the	the	DET
ejpam-3714	193	24	appropriate	appropriate	ADJ
ejpam-3714	193	25	platform	platform	NOUN
ejpam-3714	193	26	for	for	ADP
ejpam-3714	193	27	the	the	DET
ejpam-3714	193	28	collaborative	collaborative	ADJ
ejpam-3714	193	29	research	research	NOUN
ejpam-3714	193	30	.	.	PUNCT
ejpam-3714	194	1	references	reference	NOUN
ejpam-3714	194	2	1335	1335	NUM
ejpam-3714	194	3	references	reference	NOUN
ejpam-3714	194	4	[	[	X
ejpam-3714	194	5	1	1	NUM
ejpam-3714	194	6	]	]	PUNCT
ejpam-3714	194	7	a	a	DET
ejpam-3714	194	8	a	a	DET
ejpam-3714	194	9	das	das	PROPN
ejpam-3714	194	10	,	,	PUNCT
ejpam-3714	194	11	s	s	PART
ejpam-3714	194	12	k	k	NOUN
ejpam-3714	194	13	paikray	paikray	PROPN
ejpam-3714	194	14	,	,	PUNCT
ejpam-3714	194	15	t	t	PROPN
ejpam-3714	194	16	pradhan	pradhan	NOUN
ejpam-3714	194	17	,	,	PUNCT
ejpam-3714	194	18	and	and	CCONJ
ejpam-3714	194	19	h	h	PROPN
ejpam-3714	194	20	dutta	dutta	PROPN
ejpam-3714	194	21	.	.	PUNCT
ejpam-3714	195	1	approximation	approximation	NOUN
ejpam-3714	195	2	of	of	ADP
ejpam-3714	195	3	signals	signal	NOUN
ejpam-3714	195	4	in	in	ADP
ejpam-3714	195	5	the	the	DET
ejpam-3714	195	6	weighted	weight	VERB
ejpam-3714	195	7	zygmund	zygmund	PROPN
ejpam-3714	195	8	class	class	PROPN
ejpam-3714	195	9	via	via	ADP
ejpam-3714	195	10	euler	euler	NOUN
ejpam-3714	195	11	-	-	PUNCT
ejpam-3714	195	12	hausdorff	hausdorff	NOUN
ejpam-3714	195	13	product	product	NOUN
ejpam-3714	195	14	summability	summability	NOUN
ejpam-3714	195	15	mean	mean	NOUN
ejpam-3714	195	16	of	of	ADP
ejpam-3714	195	17	fourier	fourier	ADJ
ejpam-3714	195	18	series	series	NOUN
ejpam-3714	195	19	.	.	PUNCT
ejpam-3714	196	1	j.	j.	PROPN
ejpam-3714	196	2	indian	indian	PROPN
ejpam-3714	196	3	math	math	PROPN
ejpam-3714	196	4	.	.	PUNCT
ejpam-3714	197	1	soc	soc	PROPN
ejpam-3714	197	2	.	.	PUNCT
ejpam-3714	198	1	(	(	PUNCT
ejpam-3714	198	2	new	new	ADJ
ejpam-3714	198	3	ser	ser	NOUN
ejpam-3714	198	4	.	.	PUNCT
ejpam-3714	198	5	)	)	PUNCT
ejpam-3714	198	6	,	,	PUNCT
ejpam-3714	198	7	86:296–314	86:296–314	PROPN
ejpam-3714	198	8	,	,	PUNCT
ejpam-3714	198	9	2019	2019	NUM
ejpam-3714	198	10	.	.	PUNCT
ejpam-3714	199	1	[	[	X
ejpam-3714	199	2	2	2	X
ejpam-3714	199	3	]	]	PUNCT
ejpam-3714	199	4	g	g	NOUN
ejpam-3714	199	5	h	h	NOUN
ejpam-3714	199	6	hardy	hardy	ADJ
ejpam-3714	199	7	.	.	PUNCT
ejpam-3714	200	1	divergent	divergent	ADJ
ejpam-3714	200	2	series	series	NOUN
ejpam-3714	200	3	.	.	PUNCT
ejpam-3714	201	1	oxford	oxford	PROPN
ejpam-3714	201	2	university	university	PROPN
ejpam-3714	201	3	press	press	NOUN
ejpam-3714	201	4	,	,	PUNCT
ejpam-3714	201	5	1949	1949	NUM
ejpam-3714	201	6	.	.	PUNCT
ejpam-3714	202	1	[	[	X
ejpam-3714	202	2	3	3	NUM
ejpam-3714	202	3	]	]	X
ejpam-3714	202	4	s	s	X
ejpam-3714	202	5	lal	lal	PROPN
ejpam-3714	202	6	and	and	CCONJ
ejpam-3714	202	7	shreen	shreen	PROPN
ejpam-3714	202	8	.	.	PUNCT
ejpam-3714	203	1	best	good	ADJ
ejpam-3714	203	2	approximation	approximation	NOUN
ejpam-3714	203	3	of	of	ADP
ejpam-3714	203	4	functions	function	NOUN
ejpam-3714	203	5	of	of	ADP
ejpam-3714	203	6	generalized	generalized	ADJ
ejpam-3714	203	7	zygmund	zygmund	NOUN
ejpam-3714	203	8	class	class	NOUN
ejpam-3714	203	9	by	by	ADP
ejpam-3714	203	10	matrix	matrix	NOUN
ejpam-3714	203	11	-	-	PUNCT
ejpam-3714	203	12	euler	euler	NOUN
ejpam-3714	203	13	summability	summability	NOUN
ejpam-3714	203	14	mean	mean	NOUN
ejpam-3714	203	15	of	of	ADP
ejpam-3714	203	16	fourier	fourier	ADJ
ejpam-3714	203	17	series	series	NOUN
ejpam-3714	203	18	.	.	PUNCT
ejpam-3714	204	1	bull	bull	PROPN
ejpam-3714	204	2	.	.	PUNCT
ejpam-3714	205	1	math	math	NOUN
ejpam-3714	205	2	.	.	PUNCT
ejpam-3714	206	1	anal	anal	PROPN
ejpam-3714	206	2	.	.	PUNCT
ejpam-3714	206	3	appl	appl	PROPN
ejpam-3714	206	4	.	.	PROPN
ejpam-3714	206	5	,	,	PUNCT
ejpam-3714	207	1	5(4):1–13	5(4):1–13	NUM
ejpam-3714	207	2	,	,	PUNCT
ejpam-3714	207	3	2013	2013	NUM
ejpam-3714	207	4	.	.	PUNCT
ejpam-3714	208	1	[	[	X
ejpam-3714	208	2	4	4	NUM
ejpam-3714	208	3	]	]	X
ejpam-3714	208	4	l	l	NOUN
ejpam-3714	208	5	leindler	leindler	NOUN
ejpam-3714	208	6	.	.	PUNCT
ejpam-3714	209	1	strong	strong	ADJ
ejpam-3714	209	2	approximation	approximation	NOUN
ejpam-3714	209	3	and	and	CCONJ
ejpam-3714	209	4	generalized	generalized	ADJ
ejpam-3714	209	5	zygmund	zygmund	NOUN
ejpam-3714	209	6	class	class	NOUN
ejpam-3714	209	7	.	.	PUNCT
ejpam-3714	210	1	acta	acta	PROPN
ejpam-3714	210	2	.	.	PUNCT
ejpam-3714	211	1	sci	sci	PROPN
ejpam-3714	211	2	.	.	PROPN
ejpam-3714	211	3	math	math	PROPN
ejpam-3714	211	4	.	.	PUNCT
ejpam-3714	211	5	,	,	PUNCT
ejpam-3714	211	6	43:301–309	43:301–309	PROPN
ejpam-3714	211	7	,	,	PUNCT
ejpam-3714	211	8	1981	1981	NUM
ejpam-3714	211	9	.	.	PUNCT
ejpam-3714	212	1	[	[	X
ejpam-3714	212	2	5	5	NUM
ejpam-3714	212	3	]	]	SYM
ejpam-3714	212	4	l	l	NOUN
ejpam-3714	212	5	n	n	X
ejpam-3714	212	6	mishra	mishra	PROPN
ejpam-3714	212	7	,	,	PUNCT
ejpam-3714	212	8	v	v	ADP
ejpam-3714	212	9	n	n	PRON
ejpam-3714	212	10	mishra	mishra	PROPN
ejpam-3714	212	11	,	,	PUNCT
ejpam-3714	212	12	k	k	PROPN
ejpam-3714	212	13	khatri	khatri	PROPN
ejpam-3714	212	14	,	,	PUNCT
ejpam-3714	212	15	and	and	CCONJ
ejpam-3714	212	16	deepmala	deepmala	NOUN
ejpam-3714	212	17	.	.	PUNCT
ejpam-3714	213	1	on	on	ADP
ejpam-3714	213	2	the	the	DET
ejpam-3714	213	3	trigonometric	trigonometric	ADJ
ejpam-3714	213	4	approximation	approximation	NOUN
ejpam-3714	213	5	of	of	ADP
ejpam-3714	213	6	signals	signal	NOUN
ejpam-3714	213	7	belonging	belong	VERB
ejpam-3714	213	8	to	to	ADP
ejpam-3714	213	9	generalized	generalize	VERB
ejpam-3714	213	10	weighted	weight	VERB
ejpam-3714	213	11	lipschitz	lipschitz	NOUN
ejpam-3714	213	12	class	class	NOUN
ejpam-3714	213	13	w	w	PROPN
ejpam-3714	213	14	(	(	PUNCT
ejpam-3714	213	15	lr	lr	INTJ
ejpam-3714	213	16	,	,	PUNCT
ejpam-3714	213	17	ξ(t	ξ(t	NOUN
ejpam-3714	213	18	)	)	PUNCT
ejpam-3714	213	19	)	)	PUNCT
ejpam-3714	213	20	,	,	PUNCT
ejpam-3714	213	21	(	(	PUNCT
ejpam-3714	213	22	r	r	NOUN
ejpam-3714	213	23	≥	≥	NOUN
ejpam-3714	213	24	1)class	1)class	NUM
ejpam-3714	213	25	by	by	ADP
ejpam-3714	213	26	matrix	matrix	NOUN
ejpam-3714	213	27	(	(	PUNCT
ejpam-3714	213	28	c1	c1	PROPN
ejpam-3714	213	29	,	,	PUNCT
ejpam-3714	213	30	np	np	NOUN
ejpam-3714	213	31	)	)	PUNCT
ejpam-3714	213	32	operator	operator	NOUN
ejpam-3714	213	33	of	of	ADP
ejpam-3714	213	34	conjugate	conjugate	ADJ
ejpam-3714	213	35	series	series	NOUN
ejpam-3714	213	36	of	of	ADP
ejpam-3714	213	37	its	its	PRON
ejpam-3714	213	38	fourier	fourier	NOUN
ejpam-3714	213	39	series	series	NOUN
ejpam-3714	213	40	.	.	PUNCT
ejpam-3714	214	1	appl	appl	PROPN
ejpam-3714	214	2	.	.	PROPN
ejpam-3714	214	3	math	math	PROPN
ejpam-3714	214	4	.	.	PUNCT
ejpam-3714	215	1	comput	comput	NOUN
ejpam-3714	215	2	.	.	PUNCT
ejpam-3714	215	3	,	,	PUNCT
ejpam-3714	215	4	237:252–263	237:252–263	NUM
ejpam-3714	215	5	,	,	PUNCT
ejpam-3714	215	6	2014	2014	NUM
ejpam-3714	215	7	.	.	PUNCT
ejpam-3714	216	1	[	[	X
ejpam-3714	216	2	6	6	NUM
ejpam-3714	216	3	]	]	SYM
ejpam-3714	216	4	v	v	NOUN
ejpam-3714	216	5	n	n	X
ejpam-3714	216	6	mishra	mishra	PROPN
ejpam-3714	216	7	,	,	PUNCT
ejpam-3714	216	8	k	k	PROPN
ejpam-3714	216	9	khatri	khatri	PROPN
ejpam-3714	216	10	,	,	PUNCT
ejpam-3714	216	11	and	and	CCONJ
ejpam-3714	216	12	l	l	PROPN
ejpam-3714	216	13	n	n	X
ejpam-3714	216	14	mishra	mishra	PROPN
ejpam-3714	216	15	.	.	PROPN
ejpam-3714	216	16	approximation	approximation	NOUN
ejpam-3714	216	17	of	of	ADP
ejpam-3714	216	18	functions	function	NOUN
ejpam-3714	216	19	belonging	belong	VERB
ejpam-3714	216	20	to	to	ADP
ejpam-3714	216	21	lip	lip	NOUN
ejpam-3714	216	22	(	(	PUNCT
ejpam-3714	216	23	ξ(t	ξ(t	NOUN
ejpam-3714	216	24	)	)	PUNCT
ejpam-3714	216	25	,	,	PUNCT
ejpam-3714	216	26	r	r	NOUN
ejpam-3714	216	27	)	)	PUNCT
ejpam-3714	216	28	class	class	NOUN
ejpam-3714	216	29	by	by	ADP
ejpam-3714	216	30	(	(	PUNCT
ejpam-3714	216	31	n	n	CCONJ
ejpam-3714	216	32	,	,	PUNCT
ejpam-3714	216	33	pn)(e	pn)(e	PROPN
ejpam-3714	216	34	,	,	PUNCT
ejpam-3714	216	35	q)-summability	q)-summability	NOUN
ejpam-3714	216	36	of	of	ADP
ejpam-3714	216	37	conjugate	conjugate	ADJ
ejpam-3714	216	38	series	series	NOUN
ejpam-3714	216	39	of	of	ADP
ejpam-3714	216	40	fourier	fourier	PROPN
ejpam-3714	216	41	series	series	PROPN
ejpam-3714	216	42	.	.	PUNCT
ejpam-3714	217	1	j.	j.	PROPN
ejpam-3714	217	2	ineqal	ineqal	PROPN
ejpam-3714	217	3	.	.	PUNCT
ejpam-3714	218	1	appl	appl	PROPN
ejpam-3714	218	2	.	.	PROPN
ejpam-3714	218	3	,	,	PUNCT
ejpam-3714	218	4	article	article	PROPN
ejpam-3714	218	5	id-296	id-296	PROPN
ejpam-3714	218	6	,	,	PUNCT
ejpam-3714	218	7	2012	2012	NUM
ejpam-3714	218	8	.	.	PUNCT
ejpam-3714	219	1	[	[	X
ejpam-3714	219	2	7	7	NUM
ejpam-3714	219	3	]	]	SYM
ejpam-3714	219	4	v	v	NOUN
ejpam-3714	219	5	n	n	X
ejpam-3714	219	6	mishra	mishra	PROPN
ejpam-3714	219	7	,	,	PUNCT
ejpam-3714	219	8	k	k	PROPN
ejpam-3714	219	9	khatri	khatri	PROPN
ejpam-3714	219	10	,	,	PUNCT
ejpam-3714	219	11	and	and	CCONJ
ejpam-3714	219	12	l	l	PROPN
ejpam-3714	219	13	n	n	X
ejpam-3714	219	14	mishra	mishra	PROPN
ejpam-3714	219	15	.	.	PROPN
ejpam-3714	219	16	product	product	PROPN
ejpam-3714	219	17	(	(	PUNCT
ejpam-3714	219	18	n	n	CCONJ
ejpam-3714	219	19	,	,	PUNCT
ejpam-3714	219	20	pn)(c	pn)(c	PROPN
ejpam-3714	219	21	,	,	PUNCT
ejpam-3714	219	22	1)-summability	1)-summability	NUM
ejpam-3714	219	23	of	of	ADP
ejpam-3714	219	24	a	a	DET
ejpam-3714	219	25	sequence	sequence	NOUN
ejpam-3714	219	26	of	of	ADP
ejpam-3714	219	27	fourier	fourier	ADJ
ejpam-3714	219	28	coefficients	coefficient	NOUN
ejpam-3714	219	29	.	.	PUNCT
ejpam-3714	220	1	math	math	NOUN
ejpam-3714	220	2	.	.	PUNCT
ejpam-3714	221	1	sci	sci	PROPN
ejpam-3714	221	2	.	.	PROPN
ejpam-3714	221	3	,	,	PUNCT
ejpam-3714	221	4	doi	doi	PROPN
ejpam-3714	221	5	:	:	PUNCT
ejpam-3714	221	6	10.1186/2251	10.1186/2251	NUM
ejpam-3714	221	7	-	-	SYM
ejpam-3714	221	8	7456	7456	NUM
ejpam-3714	221	9	-	-	PUNCT
ejpam-3714	221	10	6	6	NUM
ejpam-3714	221	11	-	-	SYM
ejpam-3714	221	12	38	38	NUM
ejpam-3714	221	13	,	,	PUNCT
ejpam-3714	221	14	2012	2012	NUM
ejpam-3714	221	15	.	.	PUNCT
ejpam-3714	222	1	[	[	X
ejpam-3714	222	2	8	8	NUM
ejpam-3714	222	3	]	]	SYM
ejpam-3714	222	4	v	v	NOUN
ejpam-3714	222	5	n	n	X
ejpam-3714	222	6	mishra	mishra	PROPN
ejpam-3714	222	7	,	,	PUNCT
ejpam-3714	222	8	k	k	PROPN
ejpam-3714	222	9	khatri	khatri	PROPN
ejpam-3714	222	10	,	,	PUNCT
ejpam-3714	222	11	l	l	PROPN
ejpam-3714	222	12	n	n	X
ejpam-3714	222	13	mishra	mishra	PROPN
ejpam-3714	222	14	,	,	PUNCT
ejpam-3714	222	15	and	and	CCONJ
ejpam-3714	222	16	deepmala	deepmala	NOUN
ejpam-3714	222	17	.	.	PUNCT
ejpam-3714	223	1	trigonometric	trigonometric	ADJ
ejpam-3714	223	2	approximation	approximation	NOUN
ejpam-3714	223	3	of	of	ADP
ejpam-3714	223	4	periodic	periodic	ADJ
ejpam-3714	223	5	signals	signal	NOUN
ejpam-3714	223	6	belonging	belong	VERB
ejpam-3714	223	7	to	to	ADP
ejpam-3714	223	8	generalized	generalize	VERB
ejpam-3714	223	9	weighted	weight	VERB
ejpam-3714	223	10	lipschitz	lipschitz	PROPN
ejpam-3714	223	11	w	w	PROPN
ejpam-3714	223	12	(	(	PUNCT
ejpam-3714	223	13	lr	lr	INTJ
ejpam-3714	223	14	,	,	PUNCT
ejpam-3714	223	15	ξ(t	ξ(t	NOUN
ejpam-3714	223	16	)	)	PUNCT
ejpam-3714	223	17	)	)	PUNCT
ejpam-3714	223	18	,	,	PUNCT
ejpam-3714	223	19	(	(	PUNCT
ejpam-3714	223	20	r	r	NOUN
ejpam-3714	223	21	≥	≥	NOUN
ejpam-3714	223	22	1)class	1)class	NUM
ejpam-3714	223	23	by	by	ADP
ejpam-3714	223	24	norlund	norlund	PROPN
ejpam-3714	223	25	euler	euler	PROPN
ejpam-3714	223	26	(	(	PUNCT
ejpam-3714	223	27	n	n	X
ejpam-3714	223	28	,	,	PUNCT
ejpam-3714	223	29	pn)(e	pn)(e	PROPN
ejpam-3714	223	30	,	,	PUNCT
ejpam-3714	223	31	q	q	NOUN
ejpam-3714	223	32	)	)	PUNCT
ejpam-3714	223	33	operator	operator	NOUN
ejpam-3714	223	34	of	of	ADP
ejpam-3714	223	35	conjugate	conjugate	ADJ
ejpam-3714	223	36	series	series	NOUN
ejpam-3714	223	37	of	of	ADP
ejpam-3714	223	38	its	its	PRON
ejpam-3714	223	39	fourier	fourier	NOUN
ejpam-3714	223	40	series	series	NOUN
ejpam-3714	223	41	.	.	PUNCT
ejpam-3714	224	1	j.	j.	PROPN
ejpam-3714	224	2	class	class	PROPN
ejpam-3714	224	3	.	.	PUNCT
ejpam-3714	225	1	anal	anal	PROPN
ejpam-3714	225	2	.	.	PROPN
ejpam-3714	225	3	,	,	PUNCT
ejpam-3714	225	4	5:91–105	5:91–105	NUM
ejpam-3714	225	5	,	,	PUNCT
ejpam-3714	225	6	2014	2014	NUM
ejpam-3714	225	7	.	.	PUNCT
ejpam-3714	226	1	[	[	X
ejpam-3714	226	2	9	9	NUM
ejpam-3714	226	3	]	]	SYM
ejpam-3714	226	4	v	v	NOUN
ejpam-3714	226	5	n	n	X
ejpam-3714	226	6	mishra	mishra	PROPN
ejpam-3714	226	7	and	and	CCONJ
ejpam-3714	226	8	l	l	PROPN
ejpam-3714	226	9	n	n	X
ejpam-3714	226	10	mishra	mishra	PROPN
ejpam-3714	226	11	.	.	PUNCT
ejpam-3714	227	1	trigonometric	trigonometric	ADJ
ejpam-3714	227	2	approximation	approximation	NOUN
ejpam-3714	227	3	of	of	ADP
ejpam-3714	227	4	signals	signal	NOUN
ejpam-3714	227	5	(	(	PUNCT
ejpam-3714	227	6	functions	function	NOUN
ejpam-3714	227	7	)	)	PUNCT
ejpam-3714	227	8	in	in	ADP
ejpam-3714	227	9	lp	lp	NOUN
ejpam-3714	227	10	,	,	PUNCT
ejpam-3714	227	11	(	(	PUNCT
ejpam-3714	227	12	p	p	NOUN
ejpam-3714	227	13	≥	≥	PROPN
ejpam-3714	227	14	1)-norm	1)-norm	NUM
ejpam-3714	227	15	.	.	PUNCT
ejpam-3714	227	16	international	international	ADJ
ejpam-3714	227	17	j.	j.	PROPN
ejpam-3714	227	18	contemp	contemp	PROPN
ejpam-3714	227	19	.	.	PUNCT
ejpam-3714	228	1	math	math	NOUN
ejpam-3714	228	2	.	.	PUNCT
ejpam-3714	229	1	sci	sci	PROPN
ejpam-3714	229	2	.	.	PROPN
ejpam-3714	229	3	,	,	PUNCT
ejpam-3714	229	4	7:909–918	7:909–918	NUM
ejpam-3714	229	5	,	,	PUNCT
ejpam-3714	229	6	2012	2012	NUM
ejpam-3714	229	7	.	.	PUNCT
ejpam-3714	230	1	[	[	X
ejpam-3714	230	2	10	10	NUM
ejpam-3714	230	3	]	]	X
ejpam-3714	230	4	f	f	PROPN
ejpam-3714	230	5	moricz	moricz	PROPN
ejpam-3714	230	6	.	.	PUNCT
ejpam-3714	231	1	enlarged	enlarge	VERB
ejpam-3714	231	2	lipschitz	lipschitz	NOUN
ejpam-3714	231	3	and	and	CCONJ
ejpam-3714	231	4	zygmund	zygmund	NOUN
ejpam-3714	231	5	classes	class	NOUN
ejpam-3714	231	6	of	of	ADP
ejpam-3714	231	7	functions	function	NOUN
ejpam-3714	231	8	and	and	CCONJ
ejpam-3714	231	9	fourier	fourier	NOUN
ejpam-3714	231	10	transforms	transform	VERB
ejpam-3714	231	11	.	.	PUNCT
ejpam-3714	232	1	east	east	PROPN
ejpam-3714	232	2	.	.	PUNCT
ejpam-3714	233	1	j.	j.	PROPN
ejpam-3714	233	2	approx	approx	PROPN
ejpam-3714	233	3	.	.	PUNCT
ejpam-3714	233	4	,	,	PUNCT
ejpam-3714	233	5	16(3):259–271	16(3):259–271	PROPN
ejpam-3714	233	6	,	,	PUNCT
ejpam-3714	233	7	2010	2010	NUM
ejpam-3714	233	8	.	.	PUNCT
ejpam-3714	234	1	[	[	X
ejpam-3714	234	2	11	11	NUM
ejpam-3714	234	3	]	]	X
ejpam-3714	234	4	f	f	PROPN
ejpam-3714	234	5	moricz	moricz	NOUN
ejpam-3714	234	6	and	and	CCONJ
ejpam-3714	234	7	j	j	PROPN
ejpam-3714	234	8	nemeth	nemeth	PROPN
ejpam-3714	234	9	.	.	PROPN
ejpam-3714	235	1	generalized	generalized	ADJ
ejpam-3714	235	2	zygmund	zygmund	PROPN
ejpam-3714	235	3	classes	class	NOUN
ejpam-3714	235	4	of	of	ADP
ejpam-3714	235	5	functions	function	NOUN
ejpam-3714	235	6	and	and	CCONJ
ejpam-3714	235	7	strong	strong	ADJ
ejpam-3714	235	8	approximation	approximation	NOUN
ejpam-3714	235	9	of	of	ADP
ejpam-3714	235	10	fourier	fourier	ADJ
ejpam-3714	235	11	series	series	NOUN
ejpam-3714	235	12	.	.	PUNCT
ejpam-3714	236	1	acta	acta	PROPN
ejpam-3714	236	2	.	.	PUNCT
ejpam-3714	237	1	sci	sci	PROPN
ejpam-3714	237	2	.	.	PUNCT
ejpam-3714	237	3	math	math	PROPN
ejpam-3714	237	4	.	.	PUNCT
ejpam-3714	237	5	,	,	PUNCT
ejpam-3714	238	1	73:637–647	73:637–647	NUM
ejpam-3714	238	2	,	,	PUNCT
ejpam-3714	238	3	2007	2007	NUM
ejpam-3714	238	4	.	.	PUNCT
ejpam-3714	239	1	[	[	X
ejpam-3714	239	2	12	12	NUM
ejpam-3714	239	3	]	]	X
ejpam-3714	239	4	h	h	NOUN
ejpam-3714	239	5	k	k	PROPN
ejpam-3714	239	6	nigam	nigam	PROPN
ejpam-3714	239	7	.	.	PUNCT
ejpam-3714	240	1	on	on	ADP
ejpam-3714	240	2	approximation	approximation	NOUN
ejpam-3714	240	3	in	in	ADP
ejpam-3714	240	4	generalized	generalized	ADJ
ejpam-3714	240	5	zygmund	zygmund	NOUN
ejpam-3714	240	6	class	class	NOUN
ejpam-3714	240	7	.	.	PUNCT
ejpam-3714	241	1	demonstr	demonstr	PROPN
ejpam-3714	241	2	.	.	PUNCT
ejpam-3714	242	1	math	math	NOUN
ejpam-3714	242	2	.	.	PUNCT
ejpam-3714	243	1	(	(	PUNCT
ejpam-3714	243	2	de	de	X
ejpam-3714	243	3	gruyter	gruyter	NOUN
ejpam-3714	243	4	)	)	PUNCT
ejpam-3714	243	5	,	,	PUNCT
ejpam-3714	243	6	52:370–387	52:370–387	PROPN
ejpam-3714	243	7	,	,	PUNCT
ejpam-3714	243	8	2019	2019	NUM
ejpam-3714	243	9	.	.	PUNCT
ejpam-3714	244	1	[	[	X
ejpam-3714	244	2	13	13	NUM
ejpam-3714	244	3	]	]	SYM
ejpam-3714	244	4	b	b	NOUN
ejpam-3714	244	5	p	p	X
ejpam-3714	244	6	padhy	padhy	NOUN
ejpam-3714	244	7	,	,	PUNCT
ejpam-3714	244	8	p	p	PROPN
ejpam-3714	244	9	k	k	PROPN
ejpam-3714	244	10	das	das	PROPN
ejpam-3714	244	11	,	,	PUNCT
ejpam-3714	244	12	m	m	VERB
ejpam-3714	244	13	misra	misra	ADJ
ejpam-3714	244	14	,	,	PUNCT
ejpam-3714	244	15	p.	p.	PROPN
ejpam-3714	244	16	samanta	samanta	PROPN
ejpam-3714	244	17	,	,	PUNCT
ejpam-3714	244	18	and	and	CCONJ
ejpam-3714	244	19	u	u	X
ejpam-3714	244	20	k	k	PROPN
ejpam-3714	244	21	misra	misra	ADJ
ejpam-3714	244	22	.	.	PUNCT
ejpam-3714	245	1	trigonometric	trigonometric	ADJ
ejpam-3714	245	2	fourier	fourier	NOUN
ejpam-3714	245	3	approximation	approximation	NOUN
ejpam-3714	245	4	of	of	ADP
ejpam-3714	245	5	the	the	DET
ejpam-3714	245	6	conjugate	conjugate	ADJ
ejpam-3714	245	7	series	series	NOUN
ejpam-3714	245	8	of	of	ADP
ejpam-3714	245	9	a	a	DET
ejpam-3714	245	10	function	function	NOUN
ejpam-3714	245	11	of	of	ADP
ejpam-3714	245	12	generalized	generalized	ADJ
ejpam-3714	245	13	lipschitz	lipschitz	NOUN
ejpam-3714	245	14	class	class	NOUN
ejpam-3714	245	15	by	by	ADP
ejpam-3714	245	16	references	reference	NOUN
ejpam-3714	245	17	1336	1336	NUM
ejpam-3714	245	18	product	product	NOUN
ejpam-3714	245	19	summability	summability	NOUN
ejpam-3714	245	20	.	.	PUNCT
ejpam-3714	246	1	computational	computational	ADJ
ejpam-3714	246	2	intelligence	intelligence	NOUN
ejpam-3714	246	3	in	in	ADP
ejpam-3714	246	4	data	datum	NOUN
ejpam-3714	246	5	mining	mining	NOUN
ejpam-3714	246	6	,	,	PUNCT
ejpam-3714	246	7	10.1007/978	10.1007/978	PROPN
ejpam-3714	246	8	-	-	SYM
ejpam-3714	246	9	81322	81322	NUM
ejpam-3714	246	10	-	-	SYM
ejpam-3714	246	11	2734	2734	NUM
ejpam-3714	246	12	-	-	PUNCT
ejpam-3714	246	13	2	2	NUM
ejpam-3714	246	14	-	-	SYM
ejpam-3714	246	15	19	19	NUM
ejpam-3714	246	16	,	,	PUNCT
ejpam-3714	246	17	2016	2016	NUM
ejpam-3714	246	18	.	.	PUNCT
ejpam-3714	247	1	[	[	X
ejpam-3714	247	2	14	14	NUM
ejpam-3714	247	3	]	]	PUNCT
ejpam-3714	247	4	t	t	PROPN
ejpam-3714	247	5	pradhan	pradhan	PROPN
ejpam-3714	247	6	,	,	PUNCT
ejpam-3714	247	7	b.	b.	PROPN
ejpam-3714	247	8	b.	b.	PROPN
ejpam-3714	247	9	jena	jena	PROPN
ejpam-3714	247	10	,	,	PUNCT
ejpam-3714	247	11	s.	s.	PROPN
ejpam-3714	247	12	k.	k.	PROPN
ejpam-3714	247	13	paikray	paikray	PROPN
ejpam-3714	247	14	,	,	PUNCT
ejpam-3714	247	15	h.	h.	PROPN
ejpam-3714	247	16	dutta	dutta	PROPN
ejpam-3714	247	17	,	,	PUNCT
ejpam-3714	247	18	and	and	CCONJ
ejpam-3714	247	19	u	u	X
ejpam-3714	247	20	k	k	PROPN
ejpam-3714	247	21	misra	misra	ADJ
ejpam-3714	247	22	.	.	PUNCT
ejpam-3714	248	1	on	on	ADP
ejpam-3714	248	2	approximation	approximation	NOUN
ejpam-3714	248	3	of	of	ADP
ejpam-3714	248	4	the	the	DET
ejpam-3714	248	5	rate	rate	NOUN
ejpam-3714	248	6	of	of	ADP
ejpam-3714	248	7	convergence	convergence	NOUN
ejpam-3714	248	8	of	of	ADP
ejpam-3714	248	9	fourier	fourier	ADJ
ejpam-3714	248	10	series	series	NOUN
ejpam-3714	248	11	in	in	ADP
ejpam-3714	248	12	the	the	DET
ejpam-3714	248	13	generalized	generalized	ADJ
ejpam-3714	248	14	holder	holder	NOUN
ejpam-3714	248	15	metric	metric	ADJ
ejpam-3714	248	16	by	by	ADP
ejpam-3714	248	17	deferred	defer	VERB
ejpam-3714	248	18	norlund	norlund	ADV
ejpam-3714	248	19	mean	mean	NOUN
ejpam-3714	248	20	.	.	PUNCT
ejpam-3714	249	1	afrika	afrika	PROPN
ejpam-3714	249	2	mat	mat	PROPN
ejpam-3714	249	3	.	.	PROPN
ejpam-3714	249	4	,	,	PUNCT
ejpam-3714	249	5	30:1119–1131	30:1119–1131	PROPN
ejpam-3714	249	6	,	,	PUNCT
ejpam-3714	249	7	2019	2019	NUM
ejpam-3714	249	8	.	.	PUNCT
ejpam-3714	250	1	[	[	X
ejpam-3714	250	2	15	15	NUM
ejpam-3714	250	3	]	]	PUNCT
ejpam-3714	250	4	t	t	PROPN
ejpam-3714	250	5	pradhan	pradhan	PROPN
ejpam-3714	250	6	,	,	PUNCT
ejpam-3714	250	7	s.	s.	PROPN
ejpam-3714	250	8	k.	k.	PROPN
ejpam-3714	250	9	paikray	paikray	PROPN
ejpam-3714	250	10	,	,	PUNCT
ejpam-3714	250	11	a	a	DET
ejpam-3714	250	12	a	a	DET
ejpam-3714	250	13	das	das	PROPN
ejpam-3714	250	14	,	,	PUNCT
ejpam-3714	250	15	and	and	CCONJ
ejpam-3714	250	16	h.	h.	PROPN
ejpam-3714	250	17	dutta	dutta	PROPN
ejpam-3714	250	18	.	.	PUNCT
ejpam-3714	251	1	on	on	ADP
ejpam-3714	251	2	approximation	approximation	NOUN
ejpam-3714	251	3	of	of	ADP
ejpam-3714	251	4	signals	signal	NOUN
ejpam-3714	251	5	in	in	ADP
ejpam-3714	251	6	the	the	DET
ejpam-3714	251	7	generalized	generalized	ADJ
ejpam-3714	251	8	zygmund	zygmund	NOUN
ejpam-3714	251	9	class	class	NOUN
ejpam-3714	251	10	via	via	ADP
ejpam-3714	251	11	(	(	PUNCT
ejpam-3714	251	12	e	e	NOUN
ejpam-3714	251	13	;	;	PUNCT
ejpam-3714	251	14	1)(n	1)(n	NUM
ejpam-3714	251	15	;	;	PUNCT
ejpam-3714	251	16	pn	pn	PROPN
ejpam-3714	251	17	)	)	PUNCT
ejpam-3714	251	18	summability	summability	NOUN
ejpam-3714	251	19	means	mean	NOUN
ejpam-3714	251	20	of	of	ADP
ejpam-3714	251	21	conjugate	conjugate	ADJ
ejpam-3714	251	22	fourier	fourier	NOUN
ejpam-3714	251	23	series	series	NOUN
ejpam-3714	251	24	.	.	PUNCT
ejpam-3714	252	1	proyecciones	proyecciones	PROPN
ejpam-3714	252	2	j.	j.	PROPN
ejpam-3714	252	3	math	math	PROPN
ejpam-3714	252	4	.	.	PUNCT
ejpam-3714	252	5	,	,	PUNCT
ejpam-3714	252	6	38:1015–1033	38:1015–1033	NUM
ejpam-3714	252	7	,	,	PUNCT
ejpam-3714	252	8	2019	2019	NUM
ejpam-3714	252	9	.	.	PUNCT
ejpam-3714	253	1	[	[	X
ejpam-3714	253	2	16	16	NUM
ejpam-3714	253	3	]	]	PUNCT
ejpam-3714	253	4	a	a	DET
ejpam-3714	253	5	zygmund	zygmund	NOUN
ejpam-3714	253	6	.	.	PUNCT
ejpam-3714	254	1	trigonometric	trigonometric	PROPN
ejpam-3714	254	2	series(2nd	series(2nd	PROPN
ejpam-3714	254	3	edition	edition	PROPN
ejpam-3714	254	4	.	.	PUNCT
ejpam-3714	255	1	cambridge	cambridge	PROPN
ejpam-3714	255	2	university	university	PROPN
ejpam-3714	255	3	press	press	NOUN
ejpam-3714	255	4	,	,	PUNCT
ejpam-3714	255	5	1959	1959	NUM
ejpam-3714	255	6	.	.	PUNCT