id	sid	tid	token	lemma	pos
ejpam-3986	1	1	european	european	PROPN
ejpam-3986	1	2	journal	journal	PROPN
ejpam-3986	1	3	of	of	ADP
ejpam-3986	1	4	pure	pure	ADJ
ejpam-3986	1	5	and	and	CCONJ
ejpam-3986	1	6	applied	apply	VERB
ejpam-3986	1	7	mathematics	mathematic	NOUN
ejpam-3986	1	8	vol	vol	NOUN
ejpam-3986	1	9	.	.	PUNCT
ejpam-3986	2	1	14	14	NUM
ejpam-3986	2	2	,	,	PUNCT
ejpam-3986	2	3	no	no	INTJ
ejpam-3986	2	4	.	.	NOUN
ejpam-3986	2	5	3	3	NUM
ejpam-3986	2	6	,	,	PUNCT
ejpam-3986	2	7	2021	2021	NUM
ejpam-3986	2	8	,	,	PUNCT
ejpam-3986	2	9	783	783	NUM
ejpam-3986	2	10	-	-	SYM
ejpam-3986	2	11	787	787	NUM
ejpam-3986	2	12	issn	issn	PROPN
ejpam-3986	2	13	1307	1307	NUM
ejpam-3986	2	14	-	-	SYM
ejpam-3986	2	15	5543	5543	NUM
ejpam-3986	2	16	–	–	PUNCT
ejpam-3986	3	1	ejpam.com	ejpam.com	X
ejpam-3986	3	2	published	publish	VERB
ejpam-3986	3	3	by	by	ADP
ejpam-3986	3	4	new	new	PROPN
ejpam-3986	3	5	york	york	PROPN
ejpam-3986	3	6	business	business	PROPN
ejpam-3986	3	7	global	global	ADJ
ejpam-3986	3	8	bessel	bessel	NOUN
ejpam-3986	3	9	type	type	NOUN
ejpam-3986	3	10	transform	transform	NOUN
ejpam-3986	3	11	associated	associate	VERB
ejpam-3986	3	12	with	with	ADP
ejpam-3986	3	13	titchmarsh	titchmarsh	NOUN
ejpam-3986	3	14	’s	’s	PART
ejpam-3986	3	15	theorem	theorem	ADJ
ejpam-3986	3	16	balasaheb	balasaheb	PROPN
ejpam-3986	3	17	bhagaji	bhagaji	PROPN
ejpam-3986	3	18	waphare1,∗	waphare1,∗	PROPN
ejpam-3986	3	19	,	,	PUNCT
ejpam-3986	3	20	yashodha	yashodha	PROPN
ejpam-3986	3	21	sanjay	sanjay	PROPN
ejpam-3986	3	22	sindhe1	sindhe1	PROPN
ejpam-3986	3	23	1	1	NUM
ejpam-3986	3	24	mathematics	mathematics	PROPN
ejpam-3986	3	25	department	department	NOUN
ejpam-3986	3	26	,	,	PUNCT
ejpam-3986	3	27	maeer	maeer	PROPN
ejpam-3986	3	28	’s	’s	PART
ejpam-3986	3	29	mit	mit	PROPN
ejpam-3986	3	30	arts	art	NOUN
ejpam-3986	3	31	,	,	PUNCT
ejpam-3986	3	32	commerce	commerce	NOUN
ejpam-3986	3	33	and	and	CCONJ
ejpam-3986	3	34	science	science	PROPN
ejpam-3986	3	35	college	college	PROPN
ejpam-3986	3	36	,	,	PUNCT
ejpam-3986	3	37	alandi	alandi	NOUN
ejpam-3986	3	38	,	,	PUNCT
ejpam-3986	3	39	pune-412105,maharashtra	pune-412105,maharashtra	PROPN
ejpam-3986	3	40	,	,	PUNCT
ejpam-3986	3	41	india	india	PROPN
ejpam-3986	3	42	abstract	abstract	NOUN
ejpam-3986	3	43	.	.	PUNCT
ejpam-3986	4	1	in	in	ADP
ejpam-3986	4	2	this	this	DET
ejpam-3986	4	3	paper	paper	NOUN
ejpam-3986	4	4	we	we	PRON
ejpam-3986	4	5	have	have	VERB
ejpam-3986	4	6	extended	extend	VERB
ejpam-3986	4	7	titchmarsh	titchmarsh	NOUN
ejpam-3986	4	8	’s	’s	PART
ejpam-3986	4	9	theorem	theorem	NOUN
ejpam-3986	4	10	for	for	SCONJ
ejpam-3986	4	11	the	the	DET
ejpam-3986	4	12	bessel	bessel	NOUN
ejpam-3986	4	13	transform	transform	VERB
ejpam-3986	4	14	for	for	ADP
ejpam-3986	4	15	function	function	NOUN
ejpam-3986	4	16	on	on	ADP
ejpam-3986	4	17	half	half	ADJ
ejpam-3986	4	18	-	-	PUNCT
ejpam-3986	4	19	line	line	NOUN
ejpam-3986	4	20	[	[	X
ejpam-3986	4	21	0,∞	0,∞	NOUN
ejpam-3986	4	22	)	)	PUNCT
ejpam-3986	4	23	in	in	ADP
ejpam-3986	4	24	a	a	DET
ejpam-3986	4	25	weighted	weight	VERB
ejpam-3986	4	26	lp	lp	NOUN
ejpam-3986	4	27	metric	metric	ADJ
ejpam-3986	4	28	and	and	CCONJ
ejpam-3986	4	29	is	be	AUX
ejpam-3986	4	30	studied	study	VERB
ejpam-3986	4	31	with	with	ADP
ejpam-3986	4	32	the	the	DET
ejpam-3986	4	33	use	use	NOUN
ejpam-3986	4	34	of	of	ADP
ejpam-3986	4	35	bessel	bessel	ADJ
ejpam-3986	4	36	generalized	generalized	ADJ
ejpam-3986	4	37	translation	translation	NOUN
ejpam-3986	4	38	.	.	PUNCT
ejpam-3986	5	1	2020	2020	NUM
ejpam-3986	5	2	mathematics	mathematic	NOUN
ejpam-3986	5	3	subject	subject	NOUN
ejpam-3986	5	4	classifications	classification	NOUN
ejpam-3986	5	5	:	:	PUNCT
ejpam-3986	5	6	42a38	42a38	NUM
ejpam-3986	5	7	,	,	PUNCT
ejpam-3986	5	8	42b37	42b37	DET
ejpam-3986	5	9	key	key	ADJ
ejpam-3986	5	10	words	word	NOUN
ejpam-3986	5	11	and	and	CCONJ
ejpam-3986	5	12	phrases	phrase	NOUN
ejpam-3986	5	13	:	:	PUNCT
ejpam-3986	5	14	bessel	bessel	ADJ
ejpam-3986	5	15	operator	operator	NOUN
ejpam-3986	5	16	,	,	PUNCT
ejpam-3986	5	17	bessel	bessel	NOUN
ejpam-3986	5	18	transform	transform	NOUN
ejpam-3986	5	19	,	,	PUNCT
ejpam-3986	5	20	bessel	bessel	ADJ
ejpam-3986	5	21	generalized	generalized	ADJ
ejpam-3986	5	22	translation	translation	NOUN
ejpam-3986	5	23	1	1	NUM
ejpam-3986	5	24	.	.	PUNCT
ejpam-3986	5	25	introduction	introduction	NOUN
ejpam-3986	5	26	and	and	CCONJ
ejpam-3986	5	27	preliminaries	preliminary	NOUN
ejpam-3986	5	28	in	in	ADP
ejpam-3986	5	29	recent	recent	ADJ
ejpam-3986	5	30	past	past	NOUN
ejpam-3986	5	31	,	,	PUNCT
ejpam-3986	5	32	integral	integral	ADJ
ejpam-3986	5	33	transforms	transform	NOUN
ejpam-3986	5	34	are	be	AUX
ejpam-3986	5	35	widely	widely	ADV
ejpam-3986	5	36	used	use	VERB
ejpam-3986	5	37	to	to	PART
ejpam-3986	5	38	solve	solve	VERB
ejpam-3986	5	39	various	various	ADJ
ejpam-3986	5	40	problems	problem	NOUN
ejpam-3986	5	41	in	in	ADP
ejpam-3986	5	42	calculus	calculus	NOUN
ejpam-3986	5	43	,	,	PUNCT
ejpam-3986	5	44	mechanics	mechanic	NOUN
ejpam-3986	5	45	,	,	PUNCT
ejpam-3986	5	46	mathematical	mathematical	ADJ
ejpam-3986	5	47	physics	physics	NOUN
ejpam-3986	5	48	,	,	PUNCT
ejpam-3986	5	49	engineering	engineering	NOUN
ejpam-3986	5	50	and	and	CCONJ
ejpam-3986	5	51	computational	computational	ADJ
ejpam-3986	5	52	mathematics	mathematic	NOUN
ejpam-3986	5	53	(	(	PUNCT
ejpam-3986	5	54	see	see	VERB
ejpam-3986	5	55	[	[	X
ejpam-3986	5	56	4	4	NUM
ejpam-3986	5	57	,	,	PUNCT
ejpam-3986	5	58	6	6	NUM
ejpam-3986	5	59	]	]	PUNCT
ejpam-3986	5	60	the	the	DET
ejpam-3986	5	61	paper	paper	NOUN
ejpam-3986	5	62	by	by	ADP
ejpam-3986	5	63	r.	r.	PROPN
ejpam-3986	5	64	daher	daher	PROPN
ejpam-3986	5	65	,	,	PUNCT
ejpam-3986	5	66	m.	m.	NOUN
ejpam-3986	5	67	ei	ei	X
ejpam-3986	5	68	hamma	hamma	PROPN
ejpam-3986	5	69	and	and	CCONJ
ejpam-3986	5	70	a.	a.	NOUN
ejpam-3986	5	71	ei	ei	NOUN
ejpam-3986	5	72	houasni	houasni	PROPN
ejpam-3986	5	73	,	,	PUNCT
ejpam-3986	5	74	titehmarsh	titehmarsh	NOUN
ejpam-3986	5	75	theorem	theorem	NOUN
ejpam-3986	5	76	for	for	ADP
ejpam-3986	5	77	the	the	DET
ejpam-3986	5	78	bessel	bessel	NOUN
ejpam-3986	5	79	transform	transform	NOUN
ejpam-3986	5	80	,	,	PUNCT
ejpam-3986	5	81	matematika	matematika	NOUN
ejpam-3986	5	82	,	,	PUNCT
ejpam-3986	5	83	2012	2012	NUM
ejpam-3986	5	84	,	,	PUNCT
ejpam-3986	5	85	vol.28	vol.28	NOUN
ejpam-3986	5	86	,	,	PUNCT
ejpam-3986	5	87	no.2	no.2	PROPN
ejpam-3986	5	88	,	,	PUNCT
ejpam-3986	5	89	127	127	NUM
ejpam-3986	5	90	-	-	SYM
ejpam-3986	5	91	131	131	NUM
ejpam-3986	5	92	,	,	PUNCT
ejpam-3986	5	93	motivated	motivate	VERB
ejpam-3986	5	94	us	we	PRON
ejpam-3986	5	95	to	to	PART
ejpam-3986	5	96	prepare	prepare	VERB
ejpam-3986	5	97	this	this	DET
ejpam-3986	5	98	paper	paper	NOUN
ejpam-3986	5	99	.	.	PUNCT
ejpam-3986	6	1	titchmarsh	titchmarsh	NOUN
ejpam-3986	6	2	(	(	PUNCT
ejpam-3986	6	3	[	[	X
ejpam-3986	6	4	2	2	NUM
ejpam-3986	6	5	]	]	PUNCT
ejpam-3986	6	6	,	,	PUNCT
ejpam-3986	6	7	theorem	theorem	VERB
ejpam-3986	6	8	84	84	NUM
ejpam-3986	6	9	)	)	PUNCT
ejpam-3986	6	10	characterized	characterize	VERB
ejpam-3986	6	11	the	the	DET
ejpam-3986	6	12	set	set	NOUN
ejpam-3986	6	13	of	of	ADP
ejpam-3986	6	14	functions	function	NOUN
ejpam-3986	6	15	in	in	ADP
ejpam-3986	6	16	lp(r	lp(r	NOUN
ejpam-3986	6	17	)	)	PUNCT
ejpam-3986	6	18	satisfying	satisfy	VERB
ejpam-3986	6	19	the	the	DET
ejpam-3986	6	20	estimate	estimate	NOUN
ejpam-3986	6	21	given	give	VERB
ejpam-3986	6	22	in	in	ADP
ejpam-3986	6	23	the	the	DET
ejpam-3986	6	24	following	follow	VERB
ejpam-3986	6	25	theorem	theorem	NOUN
ejpam-3986	6	26	.	.	PUNCT
ejpam-3986	6	27	theorem	theorem	NOUN
ejpam-3986	6	28	1	1	NUM
ejpam-3986	6	29	.	.	PUNCT
ejpam-3986	7	1	let	let	VERB
ejpam-3986	7	2	f(x	f(x	PROPN
ejpam-3986	7	3	)	)	PUNCT
ejpam-3986	7	4	∈	∈	PROPN
ejpam-3986	8	1	lp(r)(1	lp(r)(1	NOUN
ejpam-3986	8	2	<	<	X
ejpam-3986	8	3	p	p	X
ejpam-3986	8	4	≤	≤	NUM
ejpam-3986	8	5	2	2	NUM
ejpam-3986	8	6	)	)	PUNCT
ejpam-3986	8	7	,	,	PUNCT
ejpam-3986	8	8	and	and	CCONJ
ejpam-3986	8	9	let∫	let∫	PROPN
ejpam-3986	8	10	∞	∞	PROPN
ejpam-3986	8	11	−∞	−∞	ADP
ejpam-3986	8	12	|f(x+	|f(x+	PROPN
ejpam-3986	9	1	h)−	h)−	PROPN
ejpam-3986	9	2	f(x−	f(x−	PROPN
ejpam-3986	9	3	h)|pdx	h)|pdx	PROPN
ejpam-3986	9	4	=	=	SYM
ejpam-3986	9	5	o	o	X
ejpam-3986	9	6	(	(	PUNCT
ejpam-3986	9	7	hαp	hαp	PROPN
ejpam-3986	9	8	)	)	PUNCT
ejpam-3986	9	9	(	(	PUNCT
ejpam-3986	9	10	0	0	NUM
ejpam-3986	9	11	<	<	X
ejpam-3986	9	12	α	α	PROPN
ejpam-3986	9	13	≤	≤	NUM
ejpam-3986	9	14	1	1	NUM
ejpam-3986	9	15	)	)	PUNCT
ejpam-3986	9	16	as	as	ADP
ejpam-3986	9	17	h→	h→	NOUN
ejpam-3986	9	18	0	0	NUM
ejpam-3986	9	19	.	.	PUNCT
ejpam-3986	10	1	then	then	ADV
ejpam-3986	10	2	f(f)(x	f(f)(x	NUM
ejpam-3986	10	3	)	)	PUNCT
ejpam-3986	10	4	∈	∈	NOUN
ejpam-3986	10	5	lβ(r	lβ(r	NOUN
ejpam-3986	10	6	)	)	PUNCT
ejpam-3986	10	7	for	for	ADP
ejpam-3986	10	8	p	p	X
ejpam-3986	10	9	p+αp−1	p+αp−1	PROPN
ejpam-3986	10	10	<	<	X
ejpam-3986	10	11	β	β	X
ejpam-3986	10	12	<	<	X
ejpam-3986	10	13	p	p	PROPN
ejpam-3986	10	14	p−1	p−1	PROPN
ejpam-3986	10	15	,	,	PUNCT
ejpam-3986	10	16	where	where	SCONJ
ejpam-3986	10	17	f(f	f(f	PROPN
ejpam-3986	10	18	)	)	PUNCT
ejpam-3986	10	19	stands	stand	VERB
ejpam-3986	10	20	for	for	ADP
ejpam-3986	10	21	the	the	DET
ejpam-3986	10	22	fourier	fourier	ADJ
ejpam-3986	10	23	transform	transform	NOUN
ejpam-3986	10	24	of	of	ADP
ejpam-3986	10	25	f.	f.	PROPN
ejpam-3986	10	26	the	the	DET
ejpam-3986	10	27	main	main	ADJ
ejpam-3986	10	28	objective	objective	NOUN
ejpam-3986	10	29	of	of	ADP
ejpam-3986	10	30	this	this	DET
ejpam-3986	10	31	paper	paper	NOUN
ejpam-3986	10	32	is	be	AUX
ejpam-3986	10	33	to	to	PART
ejpam-3986	10	34	establish	establish	VERB
ejpam-3986	10	35	an	an	DET
ejpam-3986	10	36	analog	analog	NOUN
ejpam-3986	10	37	of	of	ADP
ejpam-3986	10	38	theorem	theorem	NOUN
ejpam-3986	10	39	1	1	NUM
ejpam-3986	10	40	in	in	ADP
ejpam-3986	10	41	the	the	DET
ejpam-3986	10	42	bessel	bessel	ADJ
ejpam-3986	10	43	type	type	NOUN
ejpam-3986	10	44	operators	operator	NOUN
ejpam-3986	10	45	setting	set	VERB
ejpam-3986	10	46	by	by	ADP
ejpam-3986	10	47	means	mean	NOUN
ejpam-3986	10	48	of	of	ADP
ejpam-3986	10	49	the	the	DET
ejpam-3986	10	50	bessel	bessel	ADJ
ejpam-3986	10	51	generalized	generalized	ADJ
ejpam-3986	10	52	translation	translation	NOUN
ejpam-3986	10	53	.	.	PUNCT
ejpam-3986	11	1	let	let	VERB
ejpam-3986	11	2	∆	∆	PROPN
ejpam-3986	11	3	=	=	SYM
ejpam-3986	11	4	∆a	∆a	PROPN
ejpam-3986	11	5	,	,	PUNCT
ejpam-3986	11	6	b	b	NOUN
ejpam-3986	11	7	=	=	SYM
ejpam-3986	11	8	∗corresponding	∗corresponde	VERB
ejpam-3986	11	9	author	author	NOUN
ejpam-3986	11	10	.	.	PUNCT
ejpam-3986	12	1	doi	doi	NOUN
ejpam-3986	12	2	:	:	PUNCT
ejpam-3986	12	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3986	https://doi.org/10.29020/nybg.ejpam.v14i3.3986	PROPN
ejpam-3986	12	4	email	email	NOUN
ejpam-3986	12	5	addresses	address	NOUN
ejpam-3986	12	6	:	:	PUNCT
ejpam-3986	13	1	balasahebwaphare@gmail.com	balasahebwaphare@gmail.com	X
ejpam-3986	13	2	(	(	PUNCT
ejpam-3986	13	3	b.b.waphare	b.b.waphare	NOUN
ejpam-3986	13	4	)	)	PUNCT
ejpam-3986	13	5	,	,	PUNCT
ejpam-3986	13	6	ysindhe@gmail.com	ysindhe@gmail.com	X
ejpam-3986	13	7	(	(	PUNCT
ejpam-3986	13	8	y.s	y.s	PROPN
ejpam-3986	13	9	.	.	PROPN
ejpam-3986	13	10	sindhe	sindhe	PROPN
ejpam-3986	13	11	)	)	PUNCT
ejpam-3986	13	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3986	14	1	783	783	NUM
ejpam-3986	15	1	©	©	PROPN
ejpam-3986	15	2	2021	2021	NUM
ejpam-3986	15	3	ejpam	ejpam	VERB
ejpam-3986	15	4	all	all	DET
ejpam-3986	15	5	rights	right	NOUN
ejpam-3986	15	6	reserved	reserve	VERB
ejpam-3986	15	7	.	.	PUNCT
ejpam-3986	16	1	b.b.waphare	b.b.waphare	NOUN
ejpam-3986	16	2	,	,	PUNCT
ejpam-3986	16	3	y.s	y.s	PROPN
ejpam-3986	16	4	.	.	PROPN
ejpam-3986	16	5	sindhe	sindhe	PROPN
ejpam-3986	16	6	/	/	SYM
ejpam-3986	16	7	eur	eur	PROPN
ejpam-3986	16	8	.	.	PUNCT
ejpam-3986	17	1	j.	j.	PROPN
ejpam-3986	17	2	pure	pure	PROPN
ejpam-3986	17	3	appl	appl	PROPN
ejpam-3986	17	4	.	.	PROPN
ejpam-3986	17	5	math	math	PROPN
ejpam-3986	17	6	,	,	PUNCT
ejpam-3986	17	7	14	14	NUM
ejpam-3986	17	8	(	(	PUNCT
ejpam-3986	17	9	3	3	NUM
ejpam-3986	17	10	)	)	PUNCT
ejpam-3986	17	11	(	(	PUNCT
ejpam-3986	17	12	2021	2021	NUM
ejpam-3986	17	13	)	)	PUNCT
ejpam-3986	17	14	,	,	PUNCT
ejpam-3986	17	15	783	783	NUM
ejpam-3986	17	16	-	-	SYM
ejpam-3986	17	17	787	787	NUM
ejpam-3986	17	18	784	784	NUM
ejpam-3986	17	19	dtt	dtt	NOUN
ejpam-3986	17	20	+	+	CCONJ
ejpam-3986	17	21	a−b	a−b	PROPN
ejpam-3986	17	22	t	t	NOUN
ejpam-3986	17	23	dt	dt	NOUN
ejpam-3986	17	24	,	,	PUNCT
ejpam-3986	17	25	be	be	AUX
ejpam-3986	17	26	the	the	DET
ejpam-3986	17	27	bessel	bessel	ADJ
ejpam-3986	17	28	type	type	NOUN
ejpam-3986	17	29	differential	differential	NOUN
ejpam-3986	17	30	operator	operator	NOUN
ejpam-3986	17	31	,	,	PUNCT
ejpam-3986	17	32	where	where	SCONJ
ejpam-3986	17	33	dt	dt	NOUN
ejpam-3986	17	34	=	=	SYM
ejpam-3986	18	1	d	d	NOUN
ejpam-3986	18	2	dt	dt	X
ejpam-3986	18	3	.	.	PUNCT
ejpam-3986	19	1	by	by	ADP
ejpam-3986	19	2	ja−b−1	ja−b−1	NOUN
ejpam-3986	19	3	2	2	NUM
ejpam-3986	19	4	(	(	PUNCT
ejpam-3986	19	5	t	t	NOUN
ejpam-3986	19	6	)	)	PUNCT
ejpam-3986	19	7	denote	denote	VERB
ejpam-3986	19	8	the	the	DET
ejpam-3986	19	9	bessel	bessel	NOUN
ejpam-3986	19	10	normed	norme	VERB
ejpam-3986	19	11	function	function	NOUN
ejpam-3986	19	12	of	of	ADP
ejpam-3986	19	13	the	the	DET
ejpam-3986	19	14	first	first	ADJ
ejpam-3986	19	15	kind	kind	NOUN
ejpam-3986	19	16	.	.	PUNCT
ejpam-3986	20	1	i.e.	i.e.	X
ejpam-3986	20	2	ja−b−1	ja−b−1	NOUN
ejpam-3986	20	3	2	2	NUM
ejpam-3986	20	4	(	(	PUNCT
ejpam-3986	20	5	t	t	NOUN
ejpam-3986	20	6	)	)	PUNCT
ejpam-3986	20	7	=	=	SYM
ejpam-3986	20	8	2	2	NUM
ejpam-3986	20	9	a−b−1	a−b−1	PROPN
ejpam-3986	20	10	2	2	NUM
ejpam-3986	20	11	γ	γ	X
ejpam-3986	20	12	(	(	PUNCT
ejpam-3986	20	13	a−b+1	a−b+1	ADP
ejpam-3986	20	14	2	2	NUM
ejpam-3986	20	15	)	)	PUNCT
ejpam-3986	20	16	ja−b−1	ja−b−1	NOUN
ejpam-3986	20	17	2	2	NUM
ejpam-3986	20	18	(	(	PUNCT
ejpam-3986	20	19	t	t	PROPN
ejpam-3986	20	20	)	)	PUNCT
ejpam-3986	20	21	t	t	PROPN
ejpam-3986	20	22	a−b−1	a−b−1	PROPN
ejpam-3986	20	23	2	2	NUM
ejpam-3986	20	24	,	,	PUNCT
ejpam-3986	20	25	where	where	SCONJ
ejpam-3986	20	26	jν	jν	NOUN
ejpam-3986	20	27	is	be	AUX
ejpam-3986	20	28	bessel	bessel	ADJ
ejpam-3986	20	29	function	function	NOUN
ejpam-3986	20	30	of	of	ADP
ejpam-3986	20	31	the	the	DET
ejpam-3986	20	32	first	first	ADJ
ejpam-3986	20	33	kind	kind	NOUN
ejpam-3986	20	34	with	with	ADP
ejpam-3986	20	35	ν	ν	NOUN
ejpam-3986	20	36	=	=	PUNCT
ejpam-3986	20	37	a−b−1	a−b−1	X
ejpam-3986	20	38	2	2	NUM
ejpam-3986	20	39	and	and	CCONJ
ejpam-3986	20	40	γ(x	γ(x	NOUN
ejpam-3986	20	41	)	)	PUNCT
ejpam-3986	20	42	is	be	AUX
ejpam-3986	20	43	the	the	DET
ejpam-3986	20	44	gamma	gamma	NOUN
ejpam-3986	20	45	function	function	NOUN
ejpam-3986	20	46	(	(	PUNCT
ejpam-3986	20	47	see	see	VERB
ejpam-3986	20	48	[	[	X
ejpam-3986	20	49	1	1	NUM
ejpam-3986	20	50	]	]	NUM
ejpam-3986	20	51	)	)	PUNCT
ejpam-3986	20	52	.	.	PUNCT
ejpam-3986	21	1	the	the	DET
ejpam-3986	21	2	function	function	NOUN
ejpam-3986	21	3	y	y	PROPN
ejpam-3986	21	4	=	=	NOUN
ejpam-3986	21	5	ja−b−1	ja−b−1	NOUN
ejpam-3986	21	6	2	2	NUM
ejpam-3986	21	7	(	(	PUNCT
ejpam-3986	21	8	t	t	NOUN
ejpam-3986	21	9	)	)	PUNCT
ejpam-3986	21	10	satisfies	satisfy	VERB
ejpam-3986	21	11	the	the	DET
ejpam-3986	21	12	differential	differential	ADJ
ejpam-3986	21	13	equation	equation	NOUN
ejpam-3986	21	14	∆y	∆y	NOUN
ejpam-3986	21	15	+	+	CCONJ
ejpam-3986	21	16	y	y	NOUN
ejpam-3986	21	17	=	=	NOUN
ejpam-3986	21	18	0	0	NUM
ejpam-3986	21	19	with	with	ADP
ejpam-3986	21	20	the	the	DET
ejpam-3986	21	21	initial	initial	ADJ
ejpam-3986	21	22	conditions	condition	NOUN
ejpam-3986	21	23	y(0	y(0	PROPN
ejpam-3986	21	24	)	)	PUNCT
ejpam-3986	21	25	=	=	SYM
ejpam-3986	21	26	1	1	NUM
ejpam-3986	21	27	,	,	PUNCT
ejpam-3986	21	28	y′(0	y′(0	NOUN
ejpam-3986	21	29	)	)	PUNCT
ejpam-3986	21	30	=	=	SYM
ejpam-3986	22	1	0	0	X
ejpam-3986	22	2	.	.	PUNCT
ejpam-3986	23	1	the	the	DET
ejpam-3986	23	2	function	function	NOUN
ejpam-3986	23	3	ja−b−1	ja−b−1	PROPN
ejpam-3986	23	4	2	2	NUM
ejpam-3986	23	5	(	(	PUNCT
ejpam-3986	23	6	t	t	NOUN
ejpam-3986	23	7	)	)	PUNCT
ejpam-3986	23	8	is	be	AUX
ejpam-3986	23	9	infinitely	infinitely	ADV
ejpam-3986	23	10	differentiable	differentiable	ADJ
ejpam-3986	23	11	,	,	PUNCT
ejpam-3986	23	12	entire	entire	ADJ
ejpam-3986	23	13	analytic	analytic	NOUN
ejpam-3986	23	14	.	.	PUNCT
ejpam-3986	24	1	let	let	VERB
ejpam-3986	24	2	lpa	lpa	NOUN
ejpam-3986	24	3	,	,	PUNCT
ejpam-3986	24	4	b(r+	b(r+	NOUN
ejpam-3986	24	5	)	)	PUNCT
ejpam-3986	24	6	,	,	PUNCT
ejpam-3986	24	7	(	(	PUNCT
ejpam-3986	24	8	a−	a−	PROPN
ejpam-3986	24	9	b	b	NOUN
ejpam-3986	24	10	)	)	PUNCT
ejpam-3986	24	11	>	>	X
ejpam-3986	24	12	0	0	PUNCT
ejpam-3986	25	1	and	and	CCONJ
ejpam-3986	25	2	1	1	NUM
ejpam-3986	25	3	<	<	X
ejpam-3986	25	4	p	p	X
ejpam-3986	25	5	≤	≤	ADJ
ejpam-3986	25	6	2	2	NUM
ejpam-3986	25	7	be	be	AUX
ejpam-3986	25	8	the	the	DET
ejpam-3986	25	9	banach	banach	NOUN
ejpam-3986	25	10	space	space	NOUN
ejpam-3986	25	11	of	of	ADP
ejpam-3986	25	12	measurable	measurable	ADJ
ejpam-3986	25	13	functions	function	NOUN
ejpam-3986	25	14	f(t	f(t	NOUN
ejpam-3986	25	15	)	)	PUNCT
ejpam-3986	25	16	on	on	ADP
ejpam-3986	25	17	r+	r+	NOUN
ejpam-3986	25	18	with	with	ADP
ejpam-3986	25	19	the	the	DET
ejpam-3986	25	20	finite	finite	ADJ
ejpam-3986	25	21	norm	norm	NOUN
ejpam-3986	25	22	.	.	PUNCT
ejpam-3986	26	1	‖f‖	‖f‖	NUM
ejpam-3986	26	2	=	=	PUNCT
ejpam-3986	26	3	‖f‖p	‖f‖p	NOUN
ejpam-3986	26	4	,	,	PUNCT
ejpam-3986	26	5	a	a	PRON
ejpam-3986	26	6	,	,	PUNCT
ejpam-3986	26	7	b	b	NOUN
ejpam-3986	26	8	=	=	SYM
ejpam-3986	26	9	(	(	PUNCT
ejpam-3986	26	10	∫	∫	PROPN
ejpam-3986	26	11	∞	∞	PROPN
ejpam-3986	26	12	0	0	NUM
ejpam-3986	26	13	|f(t)|pta−bdt	|f(t)|pta−bdt	PROPN
ejpam-3986	26	14	)	)	PUNCT
ejpam-3986	26	15	1	1	NUM
ejpam-3986	26	16	/	/	SYM
ejpam-3986	26	17	p	p	NOUN
ejpam-3986	26	18	.	.	PUNCT
ejpam-3986	27	1	consider	consider	VERB
ejpam-3986	27	2	the	the	DET
ejpam-3986	27	3	bessel	bessel	NOUN
ejpam-3986	27	4	generalized	generalized	ADJ
ejpam-3986	27	5	translation	translation	NOUN
ejpam-3986	27	6	th	th	X
ejpam-3986	27	7	in	in	ADP
ejpam-3986	27	8	lpa	lpa	PROPN
ejpam-3986	27	9	,	,	PUNCT
ejpam-3986	27	10	b(r+	b(r+	NOUN
ejpam-3986	27	11	)	)	PUNCT
ejpam-3986	27	12	(	(	PUNCT
ejpam-3986	27	13	see	see	VERB
ejpam-3986	27	14	[	[	X
ejpam-3986	27	15	[	[	X
ejpam-3986	27	16	4],p.121	4],p.121	NUM
ejpam-3986	27	17	]	]	PUNCT
ejpam-3986	27	18	)	)	PUNCT
ejpam-3986	27	19	thf(x	thf(x	NOUN
ejpam-3986	27	20	)	)	PUNCT
ejpam-3986	28	1	=	=	SYM
ejpam-3986	28	2	γ	γ	X
ejpam-3986	28	3	(	(	PUNCT
ejpam-3986	28	4	a−b+1	a−b+1	ADP
ejpam-3986	28	5	2	2	X
ejpam-3986	28	6	)	)	PUNCT
ejpam-3986	28	7	γ(12)γ	γ(12)γ	NOUN
ejpam-3986	28	8	(	(	PUNCT
ejpam-3986	28	9	a−b	a−b	PROPN
ejpam-3986	28	10	2	2	NUM
ejpam-3986	28	11	)	)	PUNCT
ejpam-3986	28	12	∫	∫	PROPN
ejpam-3986	29	1	π	π	NOUN
ejpam-3986	29	2	0	0	PUNCT
ejpam-3986	29	3	f	f	PROPN
ejpam-3986	29	4	(	(	PUNCT
ejpam-3986	29	5	√	√	PROPN
ejpam-3986	29	6	x2	x2	PROPN
ejpam-3986	30	1	+	+	CCONJ
ejpam-3986	30	2	h2	h2	NOUN
ejpam-3986	30	3	−	−	PROPN
ejpam-3986	30	4	2xh	2xh	NOUN
ejpam-3986	30	5	cos	cos	PROPN
ejpam-3986	30	6	t	t	PROPN
ejpam-3986	30	7	)	)	PUNCT
ejpam-3986	30	8	sina−b−1	sina−b−1	PROPN
ejpam-3986	30	9	tdt	tdt	PROPN
ejpam-3986	30	10	,	,	PUNCT
ejpam-3986	30	11	a−	a−	PROPN
ejpam-3986	30	12	b	b	PROPN
ejpam-3986	30	13	>	>	X
ejpam-3986	30	14	0	0	NUM
ejpam-3986	30	15	,	,	PUNCT
ejpam-3986	30	16	0	0	NUM
ejpam-3986	30	17	≤	≤	NUM
ejpam-3986	30	18	h	h	NOUN
ejpam-3986	30	19	<	<	X
ejpam-3986	30	20	1	1	NUM
ejpam-3986	30	21	which	which	PRON
ejpam-3986	30	22	corresponds	correspond	VERB
ejpam-3986	30	23	to	to	ADP
ejpam-3986	30	24	the	the	DET
ejpam-3986	30	25	bessel	bessel	NOUN
ejpam-3986	30	26	operator	operator	NOUN
ejpam-3986	30	27	∆a	∆a	NOUN
ejpam-3986	30	28	,	,	PUNCT
ejpam-3986	30	29	b	b	NOUN
ejpam-3986	30	30	it	it	PRON
ejpam-3986	30	31	is	be	AUX
ejpam-3986	30	32	not	not	PART
ejpam-3986	30	33	very	very	ADV
ejpam-3986	30	34	difficult	difficult	ADJ
ejpam-3986	30	35	to	to	PART
ejpam-3986	30	36	see	see	VERB
ejpam-3986	30	37	that	that	SCONJ
ejpam-3986	30	38	t0f(x	t0f(x	NOUN
ejpam-3986	30	39	)	)	PUNCT
ejpam-3986	31	1	=	=	SYM
ejpam-3986	31	2	f(x	f(x	PROPN
ejpam-3986	31	3	)	)	PUNCT
ejpam-3986	31	4	.	.	PUNCT
ejpam-3986	32	1	if	if	SCONJ
ejpam-3986	32	2	f(x	f(x	PROPN
ejpam-3986	32	3	)	)	PUNCT
ejpam-3986	32	4	has	have	VERB
ejpam-3986	32	5	a	a	DET
ejpam-3986	32	6	continuous	continuous	ADJ
ejpam-3986	32	7	first	first	ADJ
ejpam-3986	32	8	derivative	derivative	NOUN
ejpam-3986	32	9	,	,	PUNCT
ejpam-3986	32	10	then	then	ADV
ejpam-3986	32	11	∂	∂	ADV
ejpam-3986	32	12	∂h	∂h	VERB
ejpam-3986	32	13	thf(x)|h=0	thf(x)|h=0	NOUN
ejpam-3986	32	14	=	=	NOUN
ejpam-3986	32	15	0	0	X
ejpam-3986	32	16	.	.	PUNCT
ejpam-3986	33	1	if	if	SCONJ
ejpam-3986	33	2	it	it	PRON
ejpam-3986	33	3	has	have	VERB
ejpam-3986	33	4	a	a	DET
ejpam-3986	33	5	continuous	continuous	ADJ
ejpam-3986	33	6	second	second	ADJ
ejpam-3986	33	7	derivative	derivative	NOUN
ejpam-3986	33	8	,	,	PUNCT
ejpam-3986	33	9	then	then	ADV
ejpam-3986	33	10	u(x	u(x	NOUN
ejpam-3986	33	11	,	,	PUNCT
ejpam-3986	33	12	h	h	NOUN
ejpam-3986	33	13	)	)	PUNCT
ejpam-3986	33	14	=	=	SYM
ejpam-3986	33	15	thf(x	thf(x	PROPN
ejpam-3986	33	16	)	)	PUNCT
ejpam-3986	33	17	solves	solve	VERB
ejpam-3986	33	18	the	the	DET
ejpam-3986	33	19	cauchy	cauchy	PROPN
ejpam-3986	33	20	problem	problem	NOUN
ejpam-3986	33	21	∂2u	∂2u	PROPN
ejpam-3986	34	1	∂x2	∂x2	PROPN
ejpam-3986	34	2	+	+	SYM
ejpam-3986	34	3	a−	a−	PROPN
ejpam-3986	34	4	b	b	NOUN
ejpam-3986	34	5	x	x	SYM
ejpam-3986	34	6	∂u	∂u	PROPN
ejpam-3986	34	7	∂x	∂x	PROPN
ejpam-3986	34	8	=	=	PUNCT
ejpam-3986	34	9	∂2u	∂2u	ADJ
ejpam-3986	34	10	∂h2	∂h2	ADP
ejpam-3986	34	11	+	+	NUM
ejpam-3986	34	12	a−	a−	PROPN
ejpam-3986	34	13	b	b	PROPN
ejpam-3986	34	14	h	h	NOUN
ejpam-3986	35	1	∂u	∂u	PROPN
ejpam-3986	35	2	∂h	∂h	PROPN
ejpam-3986	35	3	and	and	CCONJ
ejpam-3986	35	4	u|h=0	u|h=0	PROPN
ejpam-3986	35	5	=	=	SYM
ejpam-3986	35	6	f(x	f(x	PROPN
ejpam-3986	35	7	)	)	PUNCT
ejpam-3986	35	8	,	,	PUNCT
ejpam-3986	35	9	∂u	∂u	PROPN
ejpam-3986	35	10	∂h	∂h	VERB
ejpam-3986	35	11	|h=0	|h=0	PROPN
ejpam-3986	35	12	=	=	NOUN
ejpam-3986	35	13	0	0	NUM
ejpam-3986	35	14	.	.	PUNCT
ejpam-3986	36	1	the	the	DET
ejpam-3986	36	2	operator	operator	NOUN
ejpam-3986	36	3	th	th	X
ejpam-3986	36	4	is	be	AUX
ejpam-3986	36	5	linear	linear	ADJ
ejpam-3986	36	6	,	,	PUNCT
ejpam-3986	36	7	homogeneous	homogeneous	ADJ
ejpam-3986	36	8	and	and	CCONJ
ejpam-3986	36	9	continuous	continuous	ADJ
ejpam-3986	36	10	.	.	PUNCT
ejpam-3986	37	1	below	below	ADV
ejpam-3986	37	2	are	be	AUX
ejpam-3986	37	3	some	some	DET
ejpam-3986	37	4	properties	property	NOUN
ejpam-3986	37	5	of	of	ADP
ejpam-3986	37	6	this	this	DET
ejpam-3986	37	7	operator	operator	NOUN
ejpam-3986	37	8	(	(	PUNCT
ejpam-3986	37	9	see	see	VERB
ejpam-3986	37	10	[	[	X
ejpam-3986	37	11	[	[	X
ejpam-3986	37	12	4	4	NUM
ejpam-3986	37	13	]	]	PUNCT
ejpam-3986	37	14	,	,	PUNCT
ejpam-3986	37	15	pp.124	pp.124	NOUN
ejpam-3986	37	16	-	-	SYM
ejpam-3986	37	17	125	125	NUM
ejpam-3986	37	18	]	]	PUNCT
ejpam-3986	37	19	):	):	PUNCT
ejpam-3986	37	20	(	(	PUNCT
ejpam-3986	37	21	i	i	NOUN
ejpam-3986	37	22	)	)	PUNCT
ejpam-3986	38	1	thja−b−1	thja−b−1	PROPN
ejpam-3986	38	2	2	2	NUM
ejpam-3986	38	3	(	(	PUNCT
ejpam-3986	38	4	λx	λx	NOUN
ejpam-3986	38	5	)	)	PUNCT
ejpam-3986	38	6	=	=	NOUN
ejpam-3986	38	7	ja−b−1	ja−b−1	NOUN
ejpam-3986	38	8	2	2	NUM
ejpam-3986	38	9	(	(	PUNCT
ejpam-3986	38	10	λh)ja−b−1	λh)ja−b−1	PROPN
ejpam-3986	38	11	2	2	NUM
ejpam-3986	38	12	(	(	PUNCT
ejpam-3986	38	13	λx	λx	NOUN
ejpam-3986	38	14	)	)	PUNCT
ejpam-3986	38	15	(	(	PUNCT
ejpam-3986	38	16	ii	ii	NOUN
ejpam-3986	38	17	)	)	PUNCT
ejpam-3986	38	18	th	th	X
ejpam-3986	38	19	is	be	AUX
ejpam-3986	38	20	self	self	NOUN
ejpam-3986	38	21	-	-	PUNCT
ejpam-3986	38	22	adjoint	adjoint	NOUN
ejpam-3986	38	23	.	.	PUNCT
ejpam-3986	39	1	if	if	SCONJ
ejpam-3986	39	2	f(x	f(x	PROPN
ejpam-3986	39	3	)	)	PUNCT
ejpam-3986	39	4	is	be	AUX
ejpam-3986	39	5	continuous	continuous	ADJ
ejpam-3986	39	6	function	function	NOUN
ejpam-3986	39	7	such	such	ADJ
ejpam-3986	39	8	that	that	DET
ejpam-3986	39	9	∫∞	∫∞	NOUN
ejpam-3986	39	10	0	0	NUM
ejpam-3986	39	11	xa−b|f(x)|dx	xa−b|f(x)|dx	PROPN
ejpam-3986	39	12	<	<	X
ejpam-3986	39	13	∞	∞	PROPN
ejpam-3986	39	14	,	,	PUNCT
ejpam-3986	39	15	and	and	CCONJ
ejpam-3986	39	16	g(x	g(x	NOUN
ejpam-3986	39	17	)	)	PUNCT
ejpam-3986	39	18	is	be	AUX
ejpam-3986	39	19	continuous	continuous	ADJ
ejpam-3986	39	20	and	and	CCONJ
ejpam-3986	39	21	bounded	bound	VERB
ejpam-3986	39	22	for	for	ADP
ejpam-3986	39	23	all	all	DET
ejpam-3986	39	24	x	x	PRON
ejpam-3986	39	25	≥	≥	NUM
ejpam-3986	39	26	0	0	NUM
ejpam-3986	39	27	then∫	then∫	NUM
ejpam-3986	39	28	∞	∞	NOUN
ejpam-3986	39	29	0	0	PUNCT
ejpam-3986	40	1	(	(	PUNCT
ejpam-3986	40	2	thf(x))g(x)xa−bdx	thf(x))g(x)xa−bdx	PROPN
ejpam-3986	40	3	=	=	SYM
ejpam-3986	40	4	∫	∫	PROPN
ejpam-3986	40	5	∞	∞	NUM
ejpam-3986	40	6	0	0	NUM
ejpam-3986	40	7	f(x)(thg(x))xa−bdx	f(x)(thg(x))xa−bdx	NOUN
ejpam-3986	40	8	b.b.waphare	b.b.waphare	NOUN
ejpam-3986	40	9	,	,	PUNCT
ejpam-3986	40	10	y.s	y.s	PROPN
ejpam-3986	40	11	.	.	PROPN
ejpam-3986	40	12	sindhe	sindhe	PROPN
ejpam-3986	40	13	/	/	SYM
ejpam-3986	40	14	eur	eur	PROPN
ejpam-3986	40	15	.	.	PUNCT
ejpam-3986	41	1	j.	j.	PROPN
ejpam-3986	41	2	pure	pure	PROPN
ejpam-3986	41	3	appl	appl	PROPN
ejpam-3986	41	4	.	.	PROPN
ejpam-3986	41	5	math	math	PROPN
ejpam-3986	41	6	,	,	PUNCT
ejpam-3986	41	7	14	14	NUM
ejpam-3986	41	8	(	(	PUNCT
ejpam-3986	41	9	3	3	NUM
ejpam-3986	41	10	)	)	PUNCT
ejpam-3986	41	11	(	(	PUNCT
ejpam-3986	41	12	2021	2021	NUM
ejpam-3986	41	13	)	)	PUNCT
ejpam-3986	41	14	,	,	PUNCT
ejpam-3986	41	15	783	783	NUM
ejpam-3986	41	16	-	-	SYM
ejpam-3986	41	17	787	787	NUM
ejpam-3986	41	18	785	785	NUM
ejpam-3986	41	19	(	(	PUNCT
ejpam-3986	41	20	iii	iii	NOUN
ejpam-3986	41	21	)	)	PUNCT
ejpam-3986	41	22	thf(x	thf(x	NOUN
ejpam-3986	41	23	)	)	PUNCT
ejpam-3986	41	24	=	=	SYM
ejpam-3986	41	25	txf(h	txf(h	PROPN
ejpam-3986	41	26	)	)	PUNCT
ejpam-3986	41	27	(	(	PUNCT
ejpam-3986	41	28	iv	iv	X
ejpam-3986	41	29	)	)	PUNCT
ejpam-3986	41	30	‖thf	‖thf	ADJ
ejpam-3986	41	31	−	−	ADV
ejpam-3986	41	32	f‖	f‖	ADV
ejpam-3986	41	33	→	→	SYM
ejpam-3986	41	34	0	0	PUNCT
ejpam-3986	41	35	as	as	ADP
ejpam-3986	41	36	h→	h→	NOUN
ejpam-3986	41	37	0	0	NUM
ejpam-3986	41	38	.	.	PUNCT
ejpam-3986	42	1	the	the	DET
ejpam-3986	42	2	bessel	bessel	NOUN
ejpam-3986	42	3	transform	transform	NOUN
ejpam-3986	42	4	defined	define	VERB
ejpam-3986	42	5	by	by	ADP
ejpam-3986	42	6	the	the	DET
ejpam-3986	42	7	formula	formula	NOUN
ejpam-3986	42	8	(	(	PUNCT
ejpam-3986	42	9	see	see	VERB
ejpam-3986	42	10	[	[	X
ejpam-3986	42	11	1	1	NUM
ejpam-3986	42	12	,	,	PUNCT
ejpam-3986	42	13	3	3	NUM
ejpam-3986	42	14	,	,	PUNCT
ejpam-3986	42	15	4	4	NUM
ejpam-3986	42	16	]	]	PUNCT
ejpam-3986	42	17	)	)	PUNCT
ejpam-3986	42	18	f̂(λ	f̂(λ	NOUN
ejpam-3986	42	19	)	)	PUNCT
ejpam-3986	42	20	=	=	SYM
ejpam-3986	43	1	∫	∫	PROPN
ejpam-3986	43	2	∞	∞	NUM
ejpam-3986	43	3	0	0	NUM
ejpam-3986	43	4	f(t)ja−b−1	f(t)ja−b−1	NOUN
ejpam-3986	43	5	2	2	NUM
ejpam-3986	43	6	(	(	PUNCT
ejpam-3986	43	7	λt)ta−bdt	λt)ta−bdt	X
ejpam-3986	43	8	,	,	PUNCT
ejpam-3986	43	9	λ	λ	PROPN
ejpam-3986	43	10	∈	∈	PROPN
ejpam-3986	43	11	r+	r+	NOUN
ejpam-3986	43	12	.	.	PUNCT
ejpam-3986	44	1	the	the	DET
ejpam-3986	44	2	inverse	inverse	ADJ
ejpam-3986	44	3	bessel	bessel	NOUN
ejpam-3986	44	4	transform	transform	NOUN
ejpam-3986	44	5	is	be	AUX
ejpam-3986	44	6	given	give	VERB
ejpam-3986	44	7	by	by	ADP
ejpam-3986	44	8	the	the	DET
ejpam-3986	44	9	formula	formula	NOUN
ejpam-3986	44	10	f(t	f(t	NOUN
ejpam-3986	44	11	)	)	PUNCT
ejpam-3986	44	12	=	=	SYM
ejpam-3986	44	13	(	(	PUNCT
ejpam-3986	44	14	2	2	NUM
ejpam-3986	44	15	a−b−1	a−b−1	NOUN
ejpam-3986	44	16	2	2	NUM
ejpam-3986	44	17	γ	γ	X
ejpam-3986	44	18	(	(	PUNCT
ejpam-3986	44	19	a−	a−	PROPN
ejpam-3986	44	20	b+	b+	VERB
ejpam-3986	44	21	1	1	NUM
ejpam-3986	44	22	2	2	NUM
ejpam-3986	44	23	)	)	PUNCT
ejpam-3986	44	24	)	)	PUNCT
ejpam-3986	45	1	−2	−2	NOUN
ejpam-3986	46	1	∫	∫	PROPN
ejpam-3986	46	2	∞	∞	NOUN
ejpam-3986	46	3	0	0	NUM
ejpam-3986	47	1	f̂(λ)ja−b−1	f̂(λ)ja−b−1	NOUN
ejpam-3986	47	2	2	2	NUM
ejpam-3986	47	3	(	(	PUNCT
ejpam-3986	47	4	λt)λa−bdλ	λt)λa−bdλ	PROPN
ejpam-3986	47	5	.	.	PUNCT
ejpam-3986	48	1	the	the	DET
ejpam-3986	48	2	following	follow	VERB
ejpam-3986	48	3	relation	relation	NOUN
ejpam-3986	48	4	connect	connect	VERB
ejpam-3986	48	5	the	the	DET
ejpam-3986	48	6	bessel	bessel	ADJ
ejpam-3986	48	7	generalized	generalized	ADJ
ejpam-3986	48	8	translation	translation	NOUN
ejpam-3986	48	9	,	,	PUNCT
ejpam-3986	48	10	and	and	CCONJ
ejpam-3986	48	11	the	the	DET
ejpam-3986	48	12	bessel	bessel	NOUN
ejpam-3986	48	13	transform	transform	VERB
ejpam-3986	48	14	in	in	ADP
ejpam-3986	48	15	[	[	X
ejpam-3986	48	16	5	5	NUM
ejpam-3986	48	17	]	]	PUNCT
ejpam-3986	48	18	,	,	PUNCT
ejpam-3986	48	19	we	we	PRON
ejpam-3986	48	20	have	have	VERB
ejpam-3986	48	21	(	(	PUNCT
ejpam-3986	48	22	t̂hf	t̂hf	PROPN
ejpam-3986	48	23	)	)	PUNCT
ejpam-3986	48	24	(	(	PUNCT
ejpam-3986	48	25	λ	λ	NOUN
ejpam-3986	48	26	)	)	PUNCT
ejpam-3986	48	27	=	=	NOUN
ejpam-3986	48	28	ja−b−1	ja−b−1	NOUN
ejpam-3986	48	29	2	2	NUM
ejpam-3986	48	30	(	(	PUNCT
ejpam-3986	48	31	λh)f̂(λ	λh)f̂(λ	PROPN
ejpam-3986	48	32	)	)	PUNCT
ejpam-3986	48	33	.	.	PUNCT
ejpam-3986	49	1	(	(	PUNCT
ejpam-3986	49	2	1	1	X
ejpam-3986	49	3	)	)	PUNCT
ejpam-3986	49	4	for	for	ADP
ejpam-3986	49	5	(	(	PUNCT
ejpam-3986	49	6	a	a	DET
ejpam-3986	49	7	−	−	PROPN
ejpam-3986	49	8	b	b	NOUN
ejpam-3986	49	9	)	)	PUNCT
ejpam-3986	49	10	>	>	X
ejpam-3986	49	11	0	0	PUNCT
ejpam-3986	49	12	,	,	PUNCT
ejpam-3986	49	13	we	we	PRON
ejpam-3986	49	14	introduce	introduce	VERB
ejpam-3986	49	15	the	the	DET
ejpam-3986	49	16	bessel	bessel	NOUN
ejpam-3986	49	17	normalized	normalize	VERB
ejpam-3986	49	18	function	function	NOUN
ejpam-3986	49	19	of	of	ADP
ejpam-3986	49	20	the	the	DET
ejpam-3986	49	21	first	first	ADJ
ejpam-3986	49	22	kind	kind	NOUN
ejpam-3986	49	23	ja−b−1	ja−b−1	NOUN
ejpam-3986	49	24	2	2	NUM
ejpam-3986	49	25	defined	define	VERB
ejpam-3986	49	26	by	by	ADP
ejpam-3986	49	27	ja−b−1	ja−b−1	NOUN
ejpam-3986	49	28	2	2	NUM
ejpam-3986	49	29	(	(	PUNCT
ejpam-3986	49	30	x	x	NOUN
ejpam-3986	49	31	)	)	PUNCT
ejpam-3986	49	32	=	=	SYM
ejpam-3986	49	33	γ	γ	X
ejpam-3986	49	34	(	(	PUNCT
ejpam-3986	49	35	a−	a−	PROPN
ejpam-3986	49	36	b+	b+	ADJ
ejpam-3986	49	37	1	1	NUM
ejpam-3986	49	38	2	2	NUM
ejpam-3986	49	39	)	)	PUNCT
ejpam-3986	49	40	∞∑	∞∑	PRON
ejpam-3986	49	41	n=0	n=0	NUM
ejpam-3986	49	42	(	(	PUNCT
ejpam-3986	49	43	−1)n(x/2)2n	−1)n(x/2)2n	NOUN
ejpam-3986	49	44	n!γ	n!γ	PROPN
ejpam-3986	49	45	(	(	PUNCT
ejpam-3986	49	46	n+	n+	X
ejpam-3986	49	47	a−b+1	a−b+1	ADP
ejpam-3986	49	48	2	2	NUM
ejpam-3986	49	49	)	)	PUNCT
ejpam-3986	49	50	.	.	PUNCT
ejpam-3986	50	1	(	(	PUNCT
ejpam-3986	50	2	2	2	X
ejpam-3986	50	3	)	)	PUNCT
ejpam-3986	50	4	therefore	therefore	ADV
ejpam-3986	50	5	from	from	ADP
ejpam-3986	50	6	(	(	PUNCT
ejpam-3986	50	7	2	2	NUM
ejpam-3986	50	8	)	)	PUNCT
ejpam-3986	50	9	,	,	PUNCT
ejpam-3986	50	10	we	we	PRON
ejpam-3986	50	11	have	have	VERB
ejpam-3986	50	12	lim	lim	PROPN
ejpam-3986	50	13	x→0	x→0	PUNCT
ejpam-3986	51	1	(	(	PUNCT
ejpam-3986	51	2	ja−b−1	ja−b−1	NOUN
ejpam-3986	51	3	2	2	NUM
ejpam-3986	51	4	(	(	PUNCT
ejpam-3986	51	5	x)−	x)−	PROPN
ejpam-3986	51	6	1	1	NUM
ejpam-3986	51	7	)	)	PUNCT
ejpam-3986	51	8	x2	x2	PROPN
ejpam-3986	51	9	6=	6=	ADP
ejpam-3986	51	10	0	0	NUM
ejpam-3986	51	11	.	.	PUNCT
ejpam-3986	52	1	by	by	ADP
ejpam-3986	52	2	consequence	consequence	NOUN
ejpam-3986	52	3	,	,	PUNCT
ejpam-3986	52	4	there	there	PRON
ejpam-3986	52	5	exist	exist	VERB
ejpam-3986	52	6	c	c	PROPN
ejpam-3986	52	7	>	>	X
ejpam-3986	52	8	0	0	PROPN
ejpam-3986	52	9	and	and	CCONJ
ejpam-3986	52	10	η	η	PROPN
ejpam-3986	52	11	>	>	X
ejpam-3986	52	12	0	0	PUNCT
ejpam-3986	52	13	satisfying	satisfy	VERB
ejpam-3986	52	14	|x|	|x|	PROPN
ejpam-3986	52	15	≤	≤	PROPN
ejpam-3986	52	16	η	η	PROPN
ejpam-3986	52	17	⇒	⇒	NOUN
ejpam-3986	52	18	|ja−b−1	|ja−b−1	NOUN
ejpam-3986	52	19	2	2	NUM
ejpam-3986	52	20	(	(	PUNCT
ejpam-3986	52	21	x)−	x)−	PROPN
ejpam-3986	52	22	1|	1|	NUM
ejpam-3986	52	23	≥	≥	NOUN
ejpam-3986	52	24	c|x|2	c|x|2	ADJ
ejpam-3986	52	25	.	.	PUNCT
ejpam-3986	53	1	(	(	PUNCT
ejpam-3986	53	2	3	3	X
ejpam-3986	53	3	)	)	PUNCT
ejpam-3986	53	4	2	2	NUM
ejpam-3986	53	5	.	.	PUNCT
ejpam-3986	54	1	an	an	DET
ejpam-3986	54	2	analog	analog	NOUN
ejpam-3986	54	3	of	of	ADP
ejpam-3986	54	4	titchmarsh	titchmarsh	NOUN
ejpam-3986	54	5	’s	’s	PART
ejpam-3986	54	6	theorem	theorem	NOUN
ejpam-3986	54	7	in	in	ADP
ejpam-3986	54	8	this	this	DET
ejpam-3986	54	9	section	section	NOUN
ejpam-3986	54	10	we	we	PRON
ejpam-3986	54	11	give	give	VERB
ejpam-3986	54	12	an	an	DET
ejpam-3986	54	13	analog	analog	NOUN
ejpam-3986	54	14	of	of	ADP
ejpam-3986	54	15	titchmarsh	titchmarsh	NOUN
ejpam-3986	54	16	’s	’s	PART
ejpam-3986	54	17	theorem	theorem	NOUN
ejpam-3986	54	18	1	1	NUM
ejpam-3986	54	19	(	(	PUNCT
ejpam-3986	54	20	see	see	VERB
ejpam-3986	54	21	[	[	X
ejpam-3986	54	22	[	[	X
ejpam-3986	54	23	2	2	NUM
ejpam-3986	54	24	]	]	PUNCT
ejpam-3986	54	25	,	,	PUNCT
ejpam-3986	54	26	theorem	theorem	VERB
ejpam-3986	54	27	84	84	NUM
ejpam-3986	54	28	]	]	PUNCT
ejpam-3986	54	29	)	)	PUNCT
ejpam-3986	54	30	for	for	ADP
ejpam-3986	54	31	the	the	DET
ejpam-3986	54	32	bessel	bessel	NOUN
ejpam-3986	54	33	transform	transform	NOUN
ejpam-3986	54	34	.	.	PUNCT
ejpam-3986	55	1	theorem	theorem	NOUN
ejpam-3986	55	2	2	2	NUM
ejpam-3986	55	3	.	.	PUNCT
ejpam-3986	56	1	let	let	VERB
ejpam-3986	56	2	f(x	f(x	PROPN
ejpam-3986	56	3	)	)	PUNCT
ejpam-3986	56	4	∈	∈	PROPN
ejpam-3986	56	5	lpa	lpa	PROPN
ejpam-3986	56	6	,	,	PUNCT
ejpam-3986	56	7	b(r+	b(r+	NOUN
ejpam-3986	56	8	)	)	PUNCT
ejpam-3986	56	9	,	,	PUNCT
ejpam-3986	56	10	(	(	PUNCT
ejpam-3986	56	11	1	1	NUM
ejpam-3986	56	12	<	<	X
ejpam-3986	56	13	p	p	X
ejpam-3986	56	14	≤	≤	NUM
ejpam-3986	56	15	2	2	NUM
ejpam-3986	56	16	)	)	PUNCT
ejpam-3986	56	17	,	,	PUNCT
ejpam-3986	56	18	and	and	CCONJ
ejpam-3986	56	19	let∫	let∫	PROPN
ejpam-3986	56	20	∞	∞	PROPN
ejpam-3986	56	21	0	0	PROPN
ejpam-3986	56	22	|thf(x)−	|thf(x)−	PROPN
ejpam-3986	56	23	f(x)|pxa−bdx	f(x)|pxa−bdx	PROPN
ejpam-3986	56	24	=	=	SYM
ejpam-3986	56	25	o(hγp)(0	o(hγp)(0	ADJ
ejpam-3986	56	26	≤	≤	PUNCT
ejpam-3986	56	27	γ	γ	X
ejpam-3986	56	28	≤	≤	NOUN
ejpam-3986	56	29	2	2	NUM
ejpam-3986	56	30	)	)	PUNCT
ejpam-3986	56	31	as	as	ADP
ejpam-3986	56	32	h→	h→	NOUN
ejpam-3986	56	33	0	0	NUM
ejpam-3986	56	34	.	.	PUNCT
ejpam-3986	57	1	then	then	ADV
ejpam-3986	57	2	f̂(x	f̂(x	NOUN
ejpam-3986	57	3	)	)	PUNCT
ejpam-3986	57	4	∈	∈	PROPN
ejpam-3986	57	5	lβa	lβa	NOUN
ejpam-3986	57	6	,	,	PUNCT
ejpam-3986	57	7	b(r+	b(r+	NOUN
ejpam-3986	57	8	)	)	PUNCT
ejpam-3986	57	9	,	,	PUNCT
ejpam-3986	57	10	for	for	ADP
ejpam-3986	57	11	p(a−b+1	p(a−b+1	NUM
ejpam-3986	57	12	)	)	PUNCT
ejpam-3986	57	13	(	(	PUNCT
ejpam-3986	57	14	a−b+1)(p−1)+γp	a−b+1)(p−1)+γp	X
ejpam-3986	57	15	<	<	X
ejpam-3986	57	16	β	β	X
ejpam-3986	57	17	≤	≤	NOUN
ejpam-3986	57	18	p	p	PROPN
ejpam-3986	57	19	p−1	p−1	PROPN
ejpam-3986	57	20	,	,	PUNCT
ejpam-3986	57	21	where	where	SCONJ
ejpam-3986	57	22	0	0	X
ejpam-3986	57	23	<	<	X
ejpam-3986	57	24	γ	γ	X
ejpam-3986	57	25	<	<	X
ejpam-3986	57	26	1	1	NUM
ejpam-3986	57	27	proof	proof	NOUN
ejpam-3986	57	28	.	.	PUNCT
ejpam-3986	58	1	for	for	ADP
ejpam-3986	58	2	a	a	DET
ejpam-3986	58	3	fixed	fix	VERB
ejpam-3986	58	4	h	h	NOUN
ejpam-3986	58	5	the	the	DET
ejpam-3986	58	6	bessel	bessel	NOUN
ejpam-3986	58	7	transform	transform	NOUN
ejpam-3986	58	8	of	of	ADP
ejpam-3986	58	9	thf(x	thf(x	NOUN
ejpam-3986	58	10	)	)	PUNCT
ejpam-3986	58	11	is	be	AUX
ejpam-3986	58	12	ja−b−1	ja−b−1	NOUN
ejpam-3986	58	13	2	2	NUM
ejpam-3986	58	14	(	(	PUNCT
ejpam-3986	58	15	hx)f̂(x	hx)f̂(x	NOUN
ejpam-3986	58	16	)	)	PUNCT
ejpam-3986	58	17	.	.	PUNCT
ejpam-3986	59	1	hence	hence	ADV
ejpam-3986	59	2	the	the	DET
ejpam-3986	59	3	bessel	bessel	NOUN
ejpam-3986	59	4	transform	transform	NOUN
ejpam-3986	59	5	of	of	ADP
ejpam-3986	59	6	thf(x)−	thf(x)−	PROPN
ejpam-3986	59	7	f(x	f(x	PROPN
ejpam-3986	59	8	)	)	PUNCT
ejpam-3986	59	9	,	,	PUNCT
ejpam-3986	59	10	as	as	ADP
ejpam-3986	59	11	a	a	DET
ejpam-3986	59	12	function	function	NOUN
ejpam-3986	59	13	of	of	ADP
ejpam-3986	59	14	x	x	PUNCT
ejpam-3986	59	15	is	be	AUX
ejpam-3986	59	16	(	(	PUNCT
ejpam-3986	59	17	ja−b−1	ja−b−1	NOUN
ejpam-3986	59	18	2	2	NUM
ejpam-3986	59	19	(	(	PUNCT
ejpam-3986	59	20	hx)−	hx)−	PROPN
ejpam-3986	59	21	1)f̂(x	1)f̂(x	NUM
ejpam-3986	59	22	)	)	PUNCT
ejpam-3986	59	23	.	.	PUNCT
ejpam-3986	60	1	thus∫	thus∫	NOUN
ejpam-3986	60	2	∞	∞	NOUN
ejpam-3986	60	3	0	0	NUM
ejpam-3986	61	1	|ja−b−1	|ja−b−1	NOUN
ejpam-3986	61	2	2	2	NUM
ejpam-3986	61	3	(	(	PUNCT
ejpam-3986	61	4	hx)−1|p′	hx)−1|p′	NOUN
ejpam-3986	61	5	|f̂(x)|p′xa−bdx	|f̂(x)|p′xa−bdx	PROPN
ejpam-3986	61	6	<	<	X
ejpam-3986	61	7	k(p	k(p	PROPN
ejpam-3986	61	8	)	)	PUNCT
ejpam-3986	61	9	(	(	PUNCT
ejpam-3986	61	10	∫	∫	PROPN
ejpam-3986	61	11	∞	∞	PROPN
ejpam-3986	61	12	0	0	PROPN
ejpam-3986	61	13	|thf(x)−	|thf(x)−	PROPN
ejpam-3986	61	14	f(x)|pxa−bdx	f(x)|pxa−bdx	PROPN
ejpam-3986	61	15	)	)	PUNCT
ejpam-3986	61	16	1/(p−1	1/(p−1	NUM
ejpam-3986	61	17	)	)	PUNCT
ejpam-3986	61	18	<	<	X
ejpam-3986	61	19	k(p)hγp	k(p)hγp	PROPN
ejpam-3986	61	20	′	′	NUM
ejpam-3986	61	21	b.b.waphare	b.b.waphare	NOUN
ejpam-3986	61	22	,	,	PUNCT
ejpam-3986	61	23	y.s	y.s	PROPN
ejpam-3986	61	24	.	.	PROPN
ejpam-3986	61	25	sindhe	sindhe	PROPN
ejpam-3986	61	26	/	/	SYM
ejpam-3986	61	27	eur	eur	PROPN
ejpam-3986	61	28	.	.	PUNCT
ejpam-3986	62	1	j.	j.	PROPN
ejpam-3986	62	2	pure	pure	PROPN
ejpam-3986	62	3	appl	appl	PROPN
ejpam-3986	62	4	.	.	PROPN
ejpam-3986	62	5	math	math	PROPN
ejpam-3986	62	6	,	,	PUNCT
ejpam-3986	62	7	14	14	NUM
ejpam-3986	62	8	(	(	PUNCT
ejpam-3986	62	9	3	3	NUM
ejpam-3986	62	10	)	)	PUNCT
ejpam-3986	62	11	(	(	PUNCT
ejpam-3986	62	12	2021	2021	NUM
ejpam-3986	62	13	)	)	PUNCT
ejpam-3986	62	14	,	,	PUNCT
ejpam-3986	62	15	783	783	NUM
ejpam-3986	62	16	-	-	SYM
ejpam-3986	62	17	787	787	NUM
ejpam-3986	62	18	786	786	NUM
ejpam-3986	62	19	now	now	ADV
ejpam-3986	62	20	from	from	ADP
ejpam-3986	62	21	(	(	PUNCT
ejpam-3986	62	22	3	3	NUM
ejpam-3986	62	23	)	)	PUNCT
ejpam-3986	62	24	,	,	PUNCT
ejpam-3986	62	25	we	we	PRON
ejpam-3986	62	26	have∫	have∫	VERB
ejpam-3986	62	27	η	η	PROPN
ejpam-3986	62	28	/	/	SYM
ejpam-3986	62	29	h	h	NOUN
ejpam-3986	62	30	0	0	NUM
ejpam-3986	62	31	|hx|2p′	|hx|2p′	NOUN
ejpam-3986	62	32	|f̂(x)|p′xa−bdx	|f̂(x)|p′xa−bdx	PROPN
ejpam-3986	62	33	<	<	X
ejpam-3986	62	34	k(p)hγp	k(p)hγp	PROPN
ejpam-3986	62	35	′	′	NOUN
ejpam-3986	62	36	,	,	PUNCT
ejpam-3986	63	1	where	where	SCONJ
ejpam-3986	63	2	p′	p′	NOUN
ejpam-3986	63	3	=	=	PUNCT
ejpam-3986	64	1	p	p	X
ejpam-3986	64	2	p−	p−	NOUN
ejpam-3986	64	3	1	1	NUM
ejpam-3986	64	4	then	then	ADV
ejpam-3986	64	5	∫	∫	PROPN
ejpam-3986	64	6	η	η	PROPN
ejpam-3986	64	7	/	/	PROPN
ejpam-3986	64	8	h	h	PROPN
ejpam-3986	64	9	0	0	PUNCT
ejpam-3986	65	1	x2p	x2p	NUM
ejpam-3986	65	2	′	′	NUM
ejpam-3986	66	1	|f̂(x)|p′xa−bdx	|f̂(x)|p′xa−bdx	ADV
ejpam-3986	66	2	<	<	X
ejpam-3986	66	3	k(p)h(γ−2)p	k(p)h(γ−2)p	VERB
ejpam-3986	66	4	′	′	NOUN
ejpam-3986	66	5	,	,	PUNCT
ejpam-3986	66	6	let	let	VERB
ejpam-3986	66	7	ϕ(ξ	ϕ(ξ	PROPN
ejpam-3986	66	8	)	)	PUNCT
ejpam-3986	67	1	=	=	PUNCT
ejpam-3986	67	2	∫	∫	PUNCT
ejpam-3986	68	1	ξ	ξ	PROPN
ejpam-3986	68	2	1	1	NUM
ejpam-3986	68	3	|x2f̂(x)|βx(a−b)p′/βdx	|x2f̂(x)|βx(a−b)p′/βdx	PROPN
ejpam-3986	68	4	.	.	PUNCT
ejpam-3986	69	1	then	then	ADV
ejpam-3986	69	2	,	,	PUNCT
ejpam-3986	69	3	if	if	SCONJ
ejpam-3986	69	4	β	β	X
ejpam-3986	69	5	<	<	X
ejpam-3986	69	6	p′	p′	PROPN
ejpam-3986	69	7	ϕ(ξ	ϕ(ξ	PROPN
ejpam-3986	69	8	)	)	PUNCT
ejpam-3986	69	9	≤	≤	NOUN
ejpam-3986	69	10	(	(	PUNCT
ejpam-3986	69	11	∫	∫	PROPN
ejpam-3986	69	12	ξ	ξ	PROPN
ejpam-3986	69	13	1	1	NUM
ejpam-3986	69	14	|x2f̂(x)|p′xa−bdx	|x2f̂(x)|p′xa−bdx	ADJ
ejpam-3986	69	15	)	)	PUNCT
ejpam-3986	69	16	β	β	X
ejpam-3986	69	17	/	/	SYM
ejpam-3986	69	18	p′	p′	PROPN
ejpam-3986	69	19	(	(	PUNCT
ejpam-3986	69	20	∫	∫	PROPN
ejpam-3986	69	21	ξ	ξ	PROPN
ejpam-3986	69	22	1	1	NUM
ejpam-3986	69	23	dx	dx	PROPN
ejpam-3986	69	24	)	)	PUNCT
ejpam-3986	69	25	1−β	1−β	NUM
ejpam-3986	69	26	/	/	SYM
ejpam-3986	69	27	p′	p′	NOUN
ejpam-3986	69	28	=	=	SYM
ejpam-3986	69	29	o	o	X
ejpam-3986	69	30	(	(	PUNCT
ejpam-3986	69	31	ξ	ξ	PROPN
ejpam-3986	69	32	(	(	PUNCT
ejpam-3986	69	33	2−γ)p′	2−γ)p′	NUM
ejpam-3986	69	34	β	β	X
ejpam-3986	69	35	p′	p′	X
ejpam-3986	69	36	ξ	ξ	PROPN
ejpam-3986	69	37	1−	1−	NUM
ejpam-3986	69	38	β	β	X
ejpam-3986	69	39	p′	p′	NOUN
ejpam-3986	69	40	)	)	PUNCT
ejpam-3986	70	1	=	=	PUNCT
ejpam-3986	70	2	o	o	X
ejpam-3986	70	3	(	(	PUNCT
ejpam-3986	70	4	ξ	ξ	PROPN
ejpam-3986	70	5	2β−γβ+1−	2β−γβ+1−	PROPN
ejpam-3986	70	6	β	β	X
ejpam-3986	70	7	p′	p′	NOUN
ejpam-3986	70	8	)	)	PUNCT
ejpam-3986	70	9	hence∫	hence∫	VERB
ejpam-3986	71	1	ξ	ξ	SYM
ejpam-3986	71	2	1	1	NUM
ejpam-3986	71	3	|f̂(ξ)|βxa−bdx	|f̂(ξ)|βxa−bdx	PROPN
ejpam-3986	71	4	=	=	SYM
ejpam-3986	72	1	∫	∫	PROPN
ejpam-3986	72	2	ξ	ξ	PROPN
ejpam-3986	72	3	1	1	NUM
ejpam-3986	72	4	x	x	SYM
ejpam-3986	72	5	−2β−(a−b	−2β−(a−b	NOUN
ejpam-3986	72	6	)	)	PUNCT
ejpam-3986	72	7	β	β	NOUN
ejpam-3986	72	8	p′	p′	NOUN
ejpam-3986	72	9	ϕ′(x)xa−bdx	ϕ′(x)xa−bdx	NOUN
ejpam-3986	72	10	=	=	PUNCT
ejpam-3986	72	11	ξ	ξ	PRON
ejpam-3986	72	12	−2β−(a−b	−2β−(a−b	NOUN
ejpam-3986	72	13	)	)	PUNCT
ejpam-3986	72	14	β	β	NOUN
ejpam-3986	72	15	p′	p′	NOUN
ejpam-3986	72	16	ξa−bϕ(ξ	ξa−bϕ(ξ	PROPN
ejpam-3986	72	17	)	)	PUNCT
ejpam-3986	73	1	+	+	CCONJ
ejpam-3986	73	2	(	(	PUNCT
ejpam-3986	73	3	2β	2β	NOUN
ejpam-3986	73	4	+	+	CCONJ
ejpam-3986	73	5	a−	a−	PROPN
ejpam-3986	73	6	b	b	NOUN
ejpam-3986	73	7	)	)	PUNCT
ejpam-3986	73	8	β	β	NOUN
ejpam-3986	73	9	p′	p′	NOUN
ejpam-3986	73	10	−	−	PROPN
ejpam-3986	73	11	(	(	PUNCT
ejpam-3986	73	12	a−	a−	PROPN
ejpam-3986	73	13	b	b	PROPN
ejpam-3986	73	14	)	)	PUNCT
ejpam-3986	73	15	∫	∫	PROPN
ejpam-3986	74	1	ξ	ξ	PROPN
ejpam-3986	74	2	1	1	NUM
ejpam-3986	74	3	x	x	SYM
ejpam-3986	74	4	−2β−(a−b	−2β−(a−b	NOUN
ejpam-3986	74	5	)	)	PUNCT
ejpam-3986	74	6	β	β	NOUN
ejpam-3986	74	7	p′+(a−b−1	p′+(a−b−1	NOUN
ejpam-3986	74	8	)	)	PUNCT
ejpam-3986	74	9	ϕ(x)dx	ϕ(x)dx	VERB
ejpam-3986	75	1	=	=	SYM
ejpam-3986	75	2	o	o	X
ejpam-3986	75	3	(	(	PUNCT
ejpam-3986	75	4	ξ	ξ	X
ejpam-3986	75	5	−2β−(a−b	−2β−(a−b	NOUN
ejpam-3986	75	6	)	)	PUNCT
ejpam-3986	75	7	β	β	NOUN
ejpam-3986	75	8	p′+a−b+1−γβ+β	p′+a−b+1−γβ+β	PROPN
ejpam-3986	75	9	(	(	PUNCT
ejpam-3986	75	10	p+1	p+1	NOUN
ejpam-3986	75	11	p	p	NOUN
ejpam-3986	75	12	)	)	PUNCT
ejpam-3986	75	13	)	)	PUNCT
ejpam-3986	76	1	+	+	NOUN
ejpam-3986	76	2	o	o	X
ejpam-3986	76	3	(	(	PUNCT
ejpam-3986	76	4	∫	∫	PROPN
ejpam-3986	76	5	∞	∞	NUM
ejpam-3986	76	6	1	1	NUM
ejpam-3986	76	7	x	x	SYM
ejpam-3986	76	8	−2β−(a−b	−2β−(a−b	NOUN
ejpam-3986	76	9	)	)	PUNCT
ejpam-3986	76	10	β	β	NOUN
ejpam-3986	76	11	p′+(a−b−1	p′+(a−b−1	NOUN
ejpam-3986	76	12	)	)	PUNCT
ejpam-3986	76	13	x	x	SYM
ejpam-3986	76	14	1−γβ+β	1−γβ+β	NUM
ejpam-3986	76	15	(	(	PUNCT
ejpam-3986	76	16	p+1	p+1	PROPN
ejpam-3986	76	17	p	p	X
ejpam-3986	76	18	)	)	PUNCT
ejpam-3986	76	19	dx	dx	PROPN
ejpam-3986	76	20	)	)	PUNCT
ejpam-3986	77	1	=	=	PUNCT
ejpam-3986	77	2	o	o	X
ejpam-3986	77	3	(	(	PUNCT
ejpam-3986	77	4	ξ	ξ	X
ejpam-3986	77	5	−2β−(a−b	−2β−(a−b	NOUN
ejpam-3986	77	6	)	)	PUNCT
ejpam-3986	77	7	β	β	NOUN
ejpam-3986	77	8	p′+a−b+1−γβ+β	p′+a−b+1−γβ+β	PROPN
ejpam-3986	77	9	(	(	PUNCT
ejpam-3986	77	10	p+1	p+1	NOUN
ejpam-3986	77	11	p	p	NOUN
ejpam-3986	77	12	)	)	PUNCT
ejpam-3986	77	13	)	)	PUNCT
ejpam-3986	77	14	and	and	CCONJ
ejpam-3986	77	15	this	this	PRON
ejpam-3986	77	16	is	be	AUX
ejpam-3986	77	17	bounded	bound	VERB
ejpam-3986	77	18	as	as	ADP
ejpam-3986	77	19	ξ	ξ	X
ejpam-3986	77	20	→∞	→∞	PROPN
ejpam-3986	77	21	if	if	SCONJ
ejpam-3986	77	22	−2β	−2β	PROPN
ejpam-3986	77	23	−	−	PROPN
ejpam-3986	77	24	(	(	PUNCT
ejpam-3986	77	25	a−	a−	PROPN
ejpam-3986	77	26	b	b	PROPN
ejpam-3986	77	27	)	)	PUNCT
ejpam-3986	77	28	βp′	βp′	PUNCT
ejpam-3986	78	1	+	+	CCONJ
ejpam-3986	78	2	a−	a−	PROPN
ejpam-3986	78	3	b+	b+	X
ejpam-3986	78	4	1−	1−	NUM
ejpam-3986	78	5	γβ	γβ	NOUN
ejpam-3986	78	6	+	+	X
ejpam-3986	78	7	β	β	X
ejpam-3986	78	8	(	(	PUNCT
ejpam-3986	78	9	p+1	p+1	NOUN
ejpam-3986	78	10	p	p	PROPN
ejpam-3986	78	11	)	)	PUNCT
ejpam-3986	78	12	<	<	X
ejpam-3986	78	13	0	0	PUNCT
ejpam-3986	78	14	i.e.	i.e.	X
ejpam-3986	78	15	if	if	SCONJ
ejpam-3986	78	16	β	β	X
ejpam-3986	78	17	>	>	X
ejpam-3986	78	18	p(a−	p(a−	PROPN
ejpam-3986	78	19	b+	b+	ADP
ejpam-3986	78	20	1	1	NUM
ejpam-3986	78	21	)	)	PUNCT
ejpam-3986	78	22	(	(	PUNCT
ejpam-3986	78	23	a−	a−	PROPN
ejpam-3986	78	24	b+	b+	VERB
ejpam-3986	78	25	1)(p−	1)(p−	NUM
ejpam-3986	78	26	1	1	NUM
ejpam-3986	78	27	)	)	PUNCT
ejpam-3986	78	28	+	+	CCONJ
ejpam-3986	78	29	γp	γp	X
ejpam-3986	78	30	.	.	PUNCT
ejpam-3986	79	1	thus	thus	ADV
ejpam-3986	79	2	theorem	theorem	VERB
ejpam-3986	79	3	is	be	AUX
ejpam-3986	79	4	proved	prove	VERB
ejpam-3986	79	5	.	.	PUNCT
ejpam-3986	80	1	3	3	X
ejpam-3986	80	2	.	.	X
ejpam-3986	80	3	conclusion	conclusion	NOUN
ejpam-3986	80	4	there	there	PRON
ejpam-3986	80	5	are	be	VERB
ejpam-3986	80	6	many	many	ADJ
ejpam-3986	80	7	theorems	theorem	NOUN
ejpam-3986	80	8	known	know	VERB
ejpam-3986	80	9	about	about	ADP
ejpam-3986	80	10	to	to	ADP
ejpam-3986	80	11	classical	classical	ADJ
ejpam-3986	80	12	fourier	fourier	NOUN
ejpam-3986	80	13	transform	transform	NOUN
ejpam-3986	80	14	can	can	AUX
ejpam-3986	80	15	be	be	AUX
ejpam-3986	80	16	generalized	generalize	VERB
ejpam-3986	80	17	for	for	ADP
ejpam-3986	80	18	the	the	DET
ejpam-3986	80	19	bessel	bessel	ADJ
ejpam-3986	80	20	type	type	NOUN
ejpam-3986	80	21	transform	transform	NOUN
ejpam-3986	80	22	,	,	PUNCT
ejpam-3986	80	23	among	among	ADP
ejpam-3986	80	24	them	they	PRON
ejpam-3986	80	25	is	be	AUX
ejpam-3986	80	26	titchmarsh	titchmarsh	ADJ
ejpam-3986	80	27	’s	’s	PART
ejpam-3986	80	28	theorem	theorem	NOUN
ejpam-3986	80	29	.	.	PUNCT
ejpam-3986	81	1	we	we	PRON
ejpam-3986	81	2	have	have	AUX
ejpam-3986	81	3	succussfully	succussfully	ADV
ejpam-3986	81	4	generelised	generelise	VERB
ejpam-3986	81	5	this	this	DET
ejpam-3986	81	6	titchmarsh	titchmarsh	NOUN
ejpam-3986	81	7	’s	’s	PART
ejpam-3986	81	8	theorem	theorem	NOUN
ejpam-3986	81	9	for	for	ADP
ejpam-3986	81	10	the	the	DET
ejpam-3986	81	11	bessel	bessel	NOUN
ejpam-3986	81	12	transform	transform	NOUN
ejpam-3986	81	13	in	in	ADP
ejpam-3986	81	14	this	this	DET
ejpam-3986	81	15	space	space	NOUN
ejpam-3986	81	16	lpa	lpa	NOUN
ejpam-3986	81	17	,	,	PUNCT
ejpam-3986	81	18	br+	br+	ADJ
ejpam-3986	81	19	remarks	remark	NOUN
ejpam-3986	81	20	:	:	PUNCT
ejpam-3986	81	21	references	reference	NOUN
ejpam-3986	81	22	787	787	NUM
ejpam-3986	81	23	1	1	NUM
ejpam-3986	81	24	.	.	PUNCT
ejpam-3986	82	1	if	if	SCONJ
ejpam-3986	82	2	we	we	PRON
ejpam-3986	82	3	take	take	VERB
ejpam-3986	82	4	a	a	DET
ejpam-3986	82	5	=	=	X
ejpam-3986	82	6	α+	α+	PROPN
ejpam-3986	82	7	3	3	NUM
ejpam-3986	82	8	4	4	NUM
ejpam-3986	82	9	,	,	PUNCT
ejpam-3986	82	10	b	b	X
ejpam-3986	82	11	=	=	NOUN
ejpam-3986	82	12	−α−	−α−	VERB
ejpam-3986	82	13	1	1	NUM
ejpam-3986	82	14	4	4	NUM
ejpam-3986	82	15	throughout	throughout	ADP
ejpam-3986	82	16	this	this	DET
ejpam-3986	82	17	paper	paper	NOUN
ejpam-3986	82	18	then	then	ADV
ejpam-3986	82	19	we	we	PRON
ejpam-3986	82	20	obtain	obtain	VERB
ejpam-3986	82	21	the	the	DET
ejpam-3986	82	22	results	result	NOUN
ejpam-3986	82	23	studied	study	VERB
ejpam-3986	82	24	by	by	ADP
ejpam-3986	82	25	r.	r.	PROPN
ejpam-3986	82	26	daher	daher	PROPN
ejpam-3986	82	27	,	,	PUNCT
ejpam-3986	82	28	m.	m.	NOUN
ejpam-3986	82	29	ei	ei	X
ejpam-3986	82	30	hamma	hamma	PROPN
ejpam-3986	82	31	and	and	CCONJ
ejpam-3986	82	32	a.ei	a.ei	PROPN
ejpam-3986	82	33	houashi	houashi	PROPN
ejpam-3986	82	34	,	,	PUNCT
ejpam-3986	82	35	published	publish	VERB
ejpam-3986	82	36	in	in	ADP
ejpam-3986	82	37	matematika	matematika	NOUN
ejpam-3986	82	38	,	,	PUNCT
ejpam-3986	82	39	2012	2012	NUM
ejpam-3986	82	40	,	,	PUNCT
ejpam-3986	82	41	vol	vol	NOUN
ejpam-3986	82	42	.	.	PROPN
ejpam-3986	82	43	28	28	NUM
ejpam-3986	82	44	,	,	PUNCT
ejpam-3986	82	45	no.2	no.2	PROPN
ejpam-3986	82	46	,	,	PUNCT
ejpam-3986	82	47	127	127	NUM
ejpam-3986	82	48	-	-	SYM
ejpam-3986	82	49	131	131	NUM
ejpam-3986	82	50	.	.	NOUN
ejpam-3986	83	1	2	2	X
ejpam-3986	83	2	.	.	X
ejpam-3986	83	3	authors	author	NOUN
ejpam-3986	83	4	claim	claim	VERB
ejpam-3986	83	5	that	that	SCONJ
ejpam-3986	83	6	results	result	NOUN
ejpam-3986	83	7	studied	study	VERB
ejpam-3986	83	8	in	in	ADP
ejpam-3986	83	9	this	this	DET
ejpam-3986	83	10	paper	paper	NOUN
ejpam-3986	83	11	are	be	AUX
ejpam-3986	83	12	stronger	strong	ADJ
ejpam-3986	83	13	than	than	ADP
ejpam-3986	83	14	that	that	PRON
ejpam-3986	83	15	of	of	ADP
ejpam-3986	83	16	r.	r.	PROPN
ejpam-3986	83	17	daher	daher	PROPN
ejpam-3986	83	18	,	,	PUNCT
ejpam-3986	83	19	m.ei	m.ei	PROPN
ejpam-3986	83	20	hamma	hamma	NOUN
ejpam-3986	83	21	and	and	CCONJ
ejpam-3986	83	22	a.ei	a.ei	PROPN
ejpam-3986	83	23	houasni	houasni	NOUN
ejpam-3986	83	24	.	.	PUNCT
ejpam-3986	84	1	references	reference	NOUN
ejpam-3986	84	2	[	[	X
ejpam-3986	84	3	1	1	NUM
ejpam-3986	84	4	]	]	X
ejpam-3986	84	5	levitan	levitan	PROPN
ejpam-3986	84	6	b.m	b.m	PROPN
ejpam-3986	84	7	.	.	PROPN
ejpam-3986	84	8	expansion	expansion	NOUN
ejpam-3986	84	9	in	in	ADP
ejpam-3986	84	10	fourier	fourier	ADJ
ejpam-3986	84	11	series	series	NOUN
ejpam-3986	84	12	and	and	CCONJ
ejpam-3986	84	13	integrals	integral	NOUN
ejpam-3986	84	14	over	over	ADP
ejpam-3986	84	15	bessel	bessel	NOUN
ejpam-3986	84	16	functions	function	NOUN
ejpam-3986	84	17	.	.	PUNCT
ejpam-3986	85	1	usperchi	usperchi	NOUN
ejpam-3986	85	2	.	.	PUNCT
ejpam-3986	86	1	mat	mat	NOUN
ejpam-3986	86	2	.	.	PUNCT
ejpam-3986	86	3	nauk	nauk	PROPN
ejpam-3986	86	4	.	.	PROPN
ejpam-3986	86	5	,	,	PUNCT
ejpam-3986	86	6	1951	1951	NUM
ejpam-3986	86	7	.	.	PUNCT
ejpam-3986	87	1	[	[	X
ejpam-3986	87	2	2	2	NUM
ejpam-3986	87	3	]	]	PUNCT
ejpam-3986	87	4	titchmarsh	titchmarsh	ADJ
ejpam-3986	87	5	e.c.(2005	e.c.(2005	NOUN
ejpam-3986	87	6	)	)	PUNCT
ejpam-3986	87	7	.	.	PUNCT
ejpam-3986	88	1	introduction	introduction	NOUN
ejpam-3986	88	2	to	to	ADP
ejpam-3986	88	3	the	the	DET
ejpam-3986	88	4	theory	theory	NOUN
ejpam-3986	88	5	of	of	ADP
ejpam-3986	88	6	fourier	fourier	ADJ
ejpam-3986	88	7	integrals	integral	NOUN
ejpam-3986	88	8	.	.	PUNCT
ejpam-3986	89	1	moscow	moscow	PROPN
ejpam-3986	89	2	:	:	PUNCT
ejpam-3986	90	1	clarendon	clarendon	PROPN
ejpam-3986	90	2	.	.	PUNCT
ejpam-3986	91	1	oxford	oxford	PROPN
ejpam-3986	91	2	,	,	PUNCT
ejpam-3986	91	3	kormkniga	kormkniga	PROPN
ejpam-3986	91	4	,	,	PUNCT
ejpam-3986	91	5	moscow	moscow	PROPN
ejpam-3986	91	6	.	.	PUNCT
ejpam-3986	91	7	,	,	PUNCT
ejpam-3986	91	8	1948	1948	NUM
ejpam-3986	91	9	.	.	PUNCT
ejpam-3986	92	1	[	[	X
ejpam-3986	92	2	3	3	NUM
ejpam-3986	92	3	]	]	PUNCT
ejpam-3986	92	4	trimeche	trimeche	NOUN
ejpam-3986	92	5	k.	k.	PROPN
ejpam-3986	92	6	generalized	generalize	VERB
ejpam-3986	92	7	harmonic	harmonic	ADJ
ejpam-3986	92	8	analysis	analysis	NOUN
ejpam-3986	92	9	and	and	CCONJ
ejpam-3986	92	10	wavelet	wavelet	NOUN
ejpam-3986	92	11	packets	packet	NOUN
ejpam-3986	92	12	.	.	PUNCT
ejpam-3986	93	1	amsterdam	amsterdam	PROPN
ejpam-3986	93	2	:	:	PUNCT
ejpam-3986	93	3	gordon	gordon	PROPN
ejpam-3986	93	4	and	and	CCONJ
ejpam-3986	93	5	breach	breach	VERB
ejpam-3986	93	6	science	science	NOUN
ejpam-3986	93	7	publ	publ	NOUN
ejpam-3986	93	8	.	.	PUNCT
ejpam-3986	94	1	amsterdam	amsterdam	PROPN
ejpam-3986	94	2	:	:	PUNCT
ejpam-3986	94	3	gordon	gordon	PROPN
ejpam-3986	94	4	and	and	CCONJ
ejpam-3986	94	5	breach	breach	VERB
ejpam-3986	94	6	science	science	NOUN
ejpam-3986	94	7	publ	publ	NOUN
ejpam-3986	94	8	.	.	PUNCT
ejpam-3986	94	9	,	,	PUNCT
ejpam-3986	94	10	2000	2000	NUM
ejpam-3986	94	11	.	.	PUNCT
ejpam-3986	95	1	[	[	X
ejpam-3986	95	2	4	4	X
ejpam-3986	95	3	]	]	X
ejpam-3986	95	4	kipriyanov	kipriyanov	NOUN
ejpam-3986	95	5	i.	i.	PROPN
ejpam-3986	95	6	v.	v.	PROPN
ejpam-3986	95	7	singular	singular	PROPN
ejpam-3986	95	8	elliptic	elliptic	ADJ
ejpam-3986	95	9	boundary	boundary	ADJ
ejpam-3986	95	10	value	value	NOUN
ejpam-3986	95	11	problems	problem	NOUN
ejpam-3986	95	12	.	.	PUNCT
ejpam-3986	96	1	moscow	moscow	PROPN
ejpam-3986	96	2	:	:	PUNCT
ejpam-3986	96	3	nauka	nauka	PROPN
ejpam-3986	96	4	.	.	PROPN
ejpam-3986	96	5	,	,	PUNCT
ejpam-3986	96	6	1997	1997	NUM
ejpam-3986	96	7	.	.	PUNCT
ejpam-3986	97	1	[	[	X
ejpam-3986	97	2	5	5	NUM
ejpam-3986	97	3	]	]	PUNCT
ejpam-3986	97	4	abilov	abilov	NOUN
ejpam-3986	97	5	v.a	v.a	PROPN
ejpam-3986	97	6	.	.	PROPN
ejpam-3986	97	7	,	,	PUNCT
ejpam-3986	97	8	abilova	abilova	PROPN
ejpam-3986	97	9	f.v	f.v	PROPN
ejpam-3986	97	10	.	.	PROPN
ejpam-3986	97	11	,	,	PUNCT
ejpam-3986	97	12	and	and	CCONJ
ejpam-3986	97	13	kerimov	kerimov	PROPN
ejpam-3986	97	14	m.k	m.k	PROPN
ejpam-3986	97	15	.	.	PROPN
ejpam-3986	97	16	estimates	estimate	NOUN
ejpam-3986	97	17	for	for	ADP
ejpam-3986	97	18	the	the	DET
ejpam-3986	97	19	fourierbessel	fourierbessel	ADJ
ejpam-3986	97	20	integral	integral	ADJ
ejpam-3986	97	21	transform	transform	NOUN
ejpam-3986	97	22	in	in	ADP
ejpam-3986	97	23	the	the	DET
ejpam-3986	97	24	l2(r+	l2(r+	PROPN
ejpam-3986	97	25	)	)	PUNCT
ejpam-3986	97	26	..	..	PUNCT
ejpam-3986	98	1	zh	zh	X
ejpam-3986	98	2	.	.	PUNCT
ejpam-3986	99	1	vychis	vychis	PROPN
ejpam-3986	99	2	.	.	PUNCT
ejpam-3986	99	3	mat	mat	PROPN
ejpam-3986	99	4	.	.	PUNCT
ejpam-3986	99	5	mat	mat	PROPN
ejpam-3986	99	6	.	.	PUNCT
ejpam-3986	100	1	fiz	fiz	PROPN
ejpam-3986	100	2	,	,	PUNCT
ejpam-3986	100	3	49(7):1158–1166	49(7):1158–1166	NUM
ejpam-3986	100	4	,	,	PUNCT
ejpam-3986	100	5	2009	2009	NUM
ejpam-3986	100	6	.	.	PUNCT
ejpam-3986	101	1	[	[	X
ejpam-3986	101	2	6	6	NUM
ejpam-3986	101	3	]	]	PUNCT
ejpam-3986	101	4	zhitomirskii	zhitomirskii	PROPN
ejpam-3986	101	5	y.a	y.a	PROPN
ejpam-3986	101	6	.	.	PROPN
ejpam-3986	101	7	cauchy	cauchy	PROPN
ejpam-3986	101	8	’s	’s	PART
ejpam-3986	101	9	problem	problem	NOUN
ejpam-3986	101	10	for	for	ADP
ejpam-3986	101	11	systems	system	NOUN
ejpam-3986	101	12	of	of	ADP
ejpam-3986	101	13	linear	linear	ADJ
ejpam-3986	101	14	partial	partial	ADJ
ejpam-3986	101	15	differential	differential	NOUN
ejpam-3986	101	16	equations	equation	NOUN
ejpam-3986	101	17	with	with	ADP
ejpam-3986	101	18	differential	differential	ADJ
ejpam-3986	101	19	operators	operator	NOUN
ejpam-3986	101	20	of	of	ADP
ejpam-3986	101	21	bessel	bessel	ADJ
ejpam-3986	101	22	type	type	NOUN
ejpam-3986	101	23	.	.	PUNCT
ejpam-3986	102	1	mat	mat	PROPN
ejpam-3986	102	2	.	.	PUNCT
ejpam-3986	102	3	sb	sb	PROPN
ejpam-3986	102	4	.	.	PROPN
ejpam-3986	102	5	,	,	PUNCT
ejpam-3986	102	6	36(2):299–310	36(2):299–310	PROPN
ejpam-3986	102	7	,	,	PUNCT
ejpam-3986	102	8	1955	1955	NUM
ejpam-3986	102	9	.	.	PUNCT