id	sid	tid	token	lemma	pos
ejpam-445	1	1	10_445_kumar.dvi	10_445_kumar.dvi	NUM
ejpam-445	1	2	european	european	ADJ
ejpam-445	1	3	journal	journal	NOUN
ejpam-445	1	4	of	of	ADP
ejpam-445	1	5	pure	pure	ADJ
ejpam-445	1	6	and	and	CCONJ
ejpam-445	1	7	applied	apply	VERB
ejpam-445	1	8	mathematics	mathematic	NOUN
ejpam-445	1	9	vol	vol	NOUN
ejpam-445	1	10	.	.	PUNCT
ejpam-445	2	1	3	3	NUM
ejpam-445	2	2	,	,	PUNCT
ejpam-445	2	3	no	no	INTJ
ejpam-445	2	4	.	.	NOUN
ejpam-445	2	5	4	4	NUM
ejpam-445	2	6	,	,	PUNCT
ejpam-445	2	7	2010	2010	NUM
ejpam-445	2	8	,	,	PUNCT
ejpam-445	2	9	717	717	NUM
ejpam-445	2	10	-	-	SYM
ejpam-445	2	11	724	724	NUM
ejpam-445	2	12	issn	issn	PROPN
ejpam-445	2	13	1307	1307	NUM
ejpam-445	2	14	-	-	SYM
ejpam-445	2	15	5543	5543	NUM
ejpam-445	2	16	–	–	PUNCT
ejpam-445	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-445	2	18	prolate	prolate	VERB
ejpam-445	2	19	spheroidal	spheroidal	NOUN
ejpam-445	2	20	wavelet	wavelet	NOUN
ejpam-445	2	21	coefficients	coefficient	NOUN
ejpam-445	2	22	,	,	PUNCT
ejpam-445	2	23	frames	frame	NOUN
ejpam-445	2	24	and	and	CCONJ
ejpam-445	2	25	double	double	ADJ
ejpam-445	2	26	infinite	infinite	ADJ
ejpam-445	2	27	matrices	matrix	NOUN
ejpam-445	2	28	devendra	devendra	PROPN
ejpam-445	2	29	kumar	kumar	PROPN
ejpam-445	2	30	department	department	PROPN
ejpam-445	2	31	of	of	ADP
ejpam-445	2	32	mathematics	mathematics	PROPN
ejpam-445	3	1	[	[	X
ejpam-445	3	2	research	research	NOUN
ejpam-445	3	3	and	and	CCONJ
ejpam-445	3	4	postgraduate	postgraduate	NOUN
ejpam-445	3	5	studies	study	NOUN
ejpam-445	3	6	]	]	PUNCT
ejpam-445	3	7	,	,	PUNCT
ejpam-445	3	8	m.m.h.college	m.m.h.college	PROPN
ejpam-445	3	9	,	,	PUNCT
ejpam-445	3	10	model	model	NOUN
ejpam-445	3	11	town	town	NOUN
ejpam-445	3	12	,	,	PUNCT
ejpam-445	3	13	ghaziabad201001,u.p.india	ghaziabad201001,u.p.india	PROPN
ejpam-445	3	14	abstract	abstract	NOUN
ejpam-445	3	15	.	.	PUNCT
ejpam-445	4	1	in	in	ADP
ejpam-445	4	2	this	this	DET
ejpam-445	4	3	paper	paper	NOUN
ejpam-445	4	4	we	we	PRON
ejpam-445	4	5	defined	define	VERB
ejpam-445	4	6	the	the	DET
ejpam-445	4	7	double	double	ADJ
ejpam-445	4	8	infinite	infinite	ADJ
ejpam-445	4	9	matrix	matrix	NOUN
ejpam-445	4	10	a=	a=	X
ejpam-445	4	11	a(m	a(m	PROPN
ejpam-445	4	12	,	,	PUNCT
ejpam-445	4	13	n	n	CCONJ
ejpam-445	4	14	,	,	PUNCT
ejpam-445	4	15	k)and	k)and	PROPN
ejpam-445	4	16	study	study	VERB
ejpam-445	4	17	the	the	DET
ejpam-445	4	18	action	action	NOUN
ejpam-445	4	19	of	of	ADP
ejpam-445	4	20	a	a	PRON
ejpam-445	4	21	on	on	ADP
ejpam-445	4	22	f	f	PROPN
ejpam-445	4	23	∈	∈	PROPN
ejpam-445	4	24	l2(r	l2(r	PROPN
ejpam-445	4	25	)	)	PUNCT
ejpam-445	4	26	and	and	CCONJ
ejpam-445	4	27	on	on	ADP
ejpam-445	4	28	its	its	PRON
ejpam-445	4	29	prolate	prolate	ADJ
ejpam-445	4	30	spheroidal	spheroidal	NOUN
ejpam-445	4	31	wavelet	wavelet	NOUN
ejpam-445	4	32	coefficients	coefficient	NOUN
ejpam-445	4	33	.	.	PUNCT
ejpam-445	5	1	we	we	PRON
ejpam-445	5	2	also	also	ADV
ejpam-445	5	3	find	find	VERB
ejpam-445	5	4	the	the	DET
ejpam-445	5	5	frame	frame	NOUN
ejpam-445	5	6	condition	condition	NOUN
ejpam-445	5	7	for	for	ADP
ejpam-445	5	8	a	a	DET
ejpam-445	5	9	-	-	PUNCT
ejpam-445	5	10	transform	transform	NOUN
ejpam-445	5	11	of	of	ADP
ejpam-445	5	12	f	f	PROPN
ejpam-445	5	13	∈	∈	PROPN
ejpam-445	5	14	l2(r	l2(r	PROPN
ejpam-445	5	15	)	)	PUNCT
ejpam-445	5	16	whose	whose	DET
ejpam-445	5	17	wavelet	wavelet	NOUN
ejpam-445	5	18	series	series	PROPN
ejpam-445	5	19	expansion	expansion	NOUN
ejpam-445	5	20	is	be	AUX
ejpam-445	5	21	known	know	VERB
ejpam-445	5	22	.	.	PUNCT
ejpam-445	6	1	2000	2000	NUM
ejpam-445	6	2	mathematics	mathematic	NOUN
ejpam-445	6	3	subject	subject	NOUN
ejpam-445	6	4	classifications	classification	NOUN
ejpam-445	6	5	:	:	PUNCT
ejpam-445	6	6	42c15,41a17,42c40	42c15,41a17,42c40	NUM
ejpam-445	6	7	key	key	ADJ
ejpam-445	6	8	words	word	NOUN
ejpam-445	6	9	and	and	CCONJ
ejpam-445	6	10	phrases	phrase	NOUN
ejpam-445	6	11	:	:	PUNCT
ejpam-445	6	12	prolate	prolate	ADJ
ejpam-445	6	13	spheroidal	spheroidal	NOUN
ejpam-445	6	14	wave	wave	NOUN
ejpam-445	6	15	functions	function	NOUN
ejpam-445	6	16	,	,	PUNCT
ejpam-445	6	17	double	double	ADJ
ejpam-445	6	18	infinite	infinite	NOUN
ejpam-445	6	19	matrix	matrix	NOUN
ejpam-445	6	20	and	and	CCONJ
ejpam-445	6	21	frame	frame	NOUN
ejpam-445	6	22	1	1	NUM
ejpam-445	6	23	.	.	PUNCT
ejpam-445	6	24	introduction	introduction	NOUN
ejpam-445	6	25	the	the	DET
ejpam-445	6	26	study	study	NOUN
ejpam-445	6	27	of	of	ADP
ejpam-445	6	28	continuous	continuous	ADJ
ejpam-445	6	29	prolate	prolate	ADJ
ejpam-445	6	30	spheroidal	spheroidal	NOUN
ejpam-445	6	31	wave	wave	NOUN
ejpam-445	6	32	functions	function	NOUN
ejpam-445	6	33	(	(	PUNCT
ejpam-445	6	34	pswfs	pswfs	NOUN
ejpam-445	6	35	)	)	PUNCT
ejpam-445	6	36	has	have	AUX
ejpam-445	6	37	been	be	AUX
ejpam-445	6	38	an	an	DET
ejpam-445	6	39	active	active	ADJ
ejpam-445	6	40	area	area	NOUN
ejpam-445	6	41	of	of	ADP
ejpam-445	6	42	research	research	NOUN
ejpam-445	6	43	in	in	ADP
ejpam-445	6	44	both	both	CCONJ
ejpam-445	6	45	electrical	electrical	ADJ
ejpam-445	6	46	engineering	engineering	NOUN
ejpam-445	6	47	and	and	CCONJ
ejpam-445	6	48	mathematics	mathematic	NOUN
ejpam-445	6	49	.	.	PUNCT
ejpam-445	7	1	yet	yet	ADV
ejpam-445	7	2	they	they	PRON
ejpam-445	7	3	seem	seem	VERB
ejpam-445	7	4	to	to	PART
ejpam-445	7	5	be	be	AUX
ejpam-445	7	6	an	an	DET
ejpam-445	7	7	inexhaustible	inexhaustible	ADJ
ejpam-445	7	8	and	and	CCONJ
ejpam-445	7	9	inspirational	inspirational	ADJ
ejpam-445	7	10	source	source	NOUN
ejpam-445	7	11	of	of	ADP
ejpam-445	7	12	new	new	ADJ
ejpam-445	7	13	ideas	idea	NOUN
ejpam-445	7	14	and	and	CCONJ
ejpam-445	7	15	methods	method	NOUN
ejpam-445	7	16	,	,	PUNCT
ejpam-445	7	17	both	both	CCONJ
ejpam-445	7	18	theoretical	theoretical	ADJ
ejpam-445	7	19	and	and	CCONJ
ejpam-445	7	20	applied	apply	VERB
ejpam-445	7	21	.	.	PUNCT
ejpam-445	8	1	the	the	DET
ejpam-445	8	2	pswfs	pswfs	NOUN
ejpam-445	8	3	are	be	AUX
ejpam-445	8	4	those	those	PRON
ejpam-445	8	5	that	that	PRON
ejpam-445	8	6	are	be	AUX
ejpam-445	8	7	most	most	ADV
ejpam-445	8	8	highly	highly	ADV
ejpam-445	8	9	,	,	PUNCT
ejpam-445	8	10	localized	localize	VERB
ejpam-445	8	11	simultaneously	simultaneously	ADV
ejpam-445	8	12	in	in	ADP
ejpam-445	8	13	both	both	CCONJ
ejpam-445	8	14	the	the	DET
ejpam-445	8	15	time	time	NOUN
ejpam-445	8	16	and	and	CCONJ
ejpam-445	8	17	frequency	frequency	NOUN
ejpam-445	8	18	domain	domain	NOUN
ejpam-445	8	19	.	.	PUNCT
ejpam-445	9	1	this	this	DET
ejpam-445	9	2	fact	fact	NOUN
ejpam-445	9	3	was	be	AUX
ejpam-445	9	4	discovered	discover	VERB
ejpam-445	9	5	by	by	ADP
ejpam-445	9	6	slepian	slepian	NOUN
ejpam-445	9	7	and	and	CCONJ
ejpam-445	9	8	his	his	PRON
ejpam-445	9	9	collaborators	collaborator	NOUN
ejpam-445	9	10	and	and	CCONJ
ejpam-445	9	11	was	be	AUX
ejpam-445	9	12	presented	present	VERB
ejpam-445	9	13	in	in	ADP
ejpam-445	9	14	a	a	DET
ejpam-445	9	15	series	series	NOUN
ejpam-445	9	16	of	of	ADP
ejpam-445	9	17	articles	article	NOUN
ejpam-445	9	18	[	[	X
ejpam-445	9	19	7],[8],[12]-[14	7],[8],[12]-[14	X
ejpam-445	9	20	]	]	PUNCT
ejpam-445	9	21	about	about	ADP
ejpam-445	9	22	forty	forty	NUM
ejpam-445	9	23	years	year	NOUN
ejpam-445	9	24	ago	ago	ADV
ejpam-445	9	25	.	.	PUNCT
ejpam-445	10	1	let	let	VERB
ejpam-445	10	2	us	we	PRON
ejpam-445	10	3	recall	recall	VERB
ejpam-445	10	4	the	the	DET
ejpam-445	10	5	connection	connection	NOUN
ejpam-445	10	6	between	between	ADP
ejpam-445	10	7	pswfs	pswfs	PROPN
ejpam-445	10	8	and	and	CCONJ
ejpam-445	10	9	the	the	DET
ejpam-445	10	10	shannon	shannon	PROPN
ejpam-445	10	11	sampling	sampling	NOUN
ejpam-445	10	12	theorem	theorem	NOUN
ejpam-445	10	13	(	(	PUNCT
ejpam-445	10	14	shannon[10	shannon[10	NOUN
ejpam-445	10	15	]	]	PUNCT
ejpam-445	10	16	)	)	PUNCT
ejpam-445	10	17	given	give	VERB
ejpam-445	10	18	by	by	ADP
ejpam-445	10	19	the	the	DET
ejpam-445	10	20	formula	formula	NOUN
ejpam-445	10	21	f	f	X
ejpam-445	10	22	(	(	PUNCT
ejpam-445	10	23	t	t	PROPN
ejpam-445	10	24	)	)	PUNCT
ejpam-445	10	25	=	=	SYM
ejpam-445	11	1	∞	∞	NUM
ejpam-445	11	2	∑	∑	PUNCT
ejpam-445	11	3	n=−∞	n=−∞	PROPN
ejpam-445	11	4	f	f	PROPN
ejpam-445	11	5	(	(	PUNCT
ejpam-445	11	6	n	n	CCONJ
ejpam-445	11	7	)	)	PUNCT
ejpam-445	11	8	sinπ(t	sinπ(t	NOUN
ejpam-445	11	9	−	−	PROPN
ejpam-445	11	10	n	n	CCONJ
ejpam-445	11	11	)	)	PUNCT
ejpam-445	11	12	π(t	π(t	PROPN
ejpam-445	11	13	−	−	PROPN
ejpam-445	11	14	n	n	CCONJ
ejpam-445	11	15	)	)	PUNCT
ejpam-445	11	16	.	.	PUNCT
ejpam-445	12	1	(	(	PUNCT
ejpam-445	12	2	1	1	X
ejpam-445	12	3	)	)	PUNCT
ejpam-445	12	4	the	the	DET
ejpam-445	12	5	above	above	ADJ
ejpam-445	12	6	formula	formula	NOUN
ejpam-445	12	7	(	(	PUNCT
ejpam-445	12	8	1	1	X
ejpam-445	12	9	)	)	PUNCT
ejpam-445	12	10	holds	hold	VERB
ejpam-445	12	11	for	for	ADP
ejpam-445	12	12	π	π	PROPN
ejpam-445	12	13	-	-	ADJ
ejpam-445	12	14	bandlimited	bandlimited	ADJ
ejpam-445	12	15	signals	signal	NOUN
ejpam-445	12	16	with	with	ADP
ejpam-445	12	17	finite	finite	ADJ
ejpam-445	12	18	energy	energy	NOUN
ejpam-445	12	19	,	,	PUNCT
ejpam-445	12	20	that	that	ADV
ejpam-445	12	21	is	be	AUX
ejpam-445	12	22	,	,	PUNCT
ejpam-445	12	23	for	for	ADP
ejpam-445	12	24	continuous	continuous	ADJ
ejpam-445	12	25	functions	function	NOUN
ejpam-445	12	26	in	in	ADP
ejpam-445	12	27	l2(r	l2(r	NOUN
ejpam-445	12	28	)	)	PUNCT
ejpam-445	12	29	whose	whose	DET
ejpam-445	12	30	fourier	fourier	NOUN
ejpam-445	12	31	transform	transform	NOUN
ejpam-445	12	32	has	have	VERB
ejpam-445	12	33	support	support	NOUN
ejpam-445	12	34	in	in	ADP
ejpam-445	12	35	[	[	X
ejpam-445	12	36	−π	−π	ADJ
ejpam-445	12	37	,	,	PUNCT
ejpam-445	12	38	π	π	NOUN
ejpam-445	12	39	]	]	X
ejpam-445	12	40	.	.	PUNCT
ejpam-445	13	1	this	this	DET
ejpam-445	13	2	theorem	theorem	NOUN
ejpam-445	13	3	has	have	AUX
ejpam-445	13	4	became	become	VERB
ejpam-445	13	5	a	a	DET
ejpam-445	13	6	well	well	ADV
ejpam-445	13	7	known	know	VERB
ejpam-445	13	8	part	part	NOUN
ejpam-445	13	9	of	of	ADP
ejpam-445	13	10	both	both	CCONJ
ejpam-445	13	11	the	the	DET
ejpam-445	13	12	mathematical	mathematical	ADJ
ejpam-445	13	13	and	and	CCONJ
ejpam-445	13	14	engineering	engineering	NOUN
ejpam-445	13	15	literature	literature	NOUN
ejpam-445	13	16	.	.	PUNCT
ejpam-445	14	1	the	the	DET
ejpam-445	14	2	sinc	sinc	PROPN
ejpam-445	14	3	function	function	PROPN
ejpam-445	14	4	s(t	s(t	PROPN
ejpam-445	14	5	)	)	PUNCT
ejpam-445	15	1	=	=	PUNCT
ejpam-445	15	2	sinπt	sinπt	NOUN
ejpam-445	15	3	πt	πt	ADP
ejpam-445	15	4	which	which	PRON
ejpam-445	15	5	appears	appear	VERB
ejpam-445	15	6	in	in	ADP
ejpam-445	15	7	this	this	DET
ejpam-445	15	8	formula	formula	NOUN
ejpam-445	15	9	is	be	AUX
ejpam-445	15	10	closely	closely	ADV
ejpam-445	15	11	related	relate	VERB
ejpam-445	15	12	to	to	ADP
ejpam-445	15	13	the	the	DET
ejpam-445	15	14	pswfs	pswfs	NOUN
ejpam-445	15	15	ϕn	ϕn	PROPN
ejpam-445	15	16	,	,	PUNCT
ejpam-445	15	17	σ	σ	PROPN
ejpam-445	15	18	,	,	PUNCT
ejpam-445	15	19	τ(t	τ(t	NUM
ejpam-445	15	20	)	)	PUNCT
ejpam-445	15	21	.	.	PUNCT
ejpam-445	16	1	email	email	NOUN
ejpam-445	16	2	address	address	NOUN
ejpam-445	16	3	:	:	PUNCT
ejpam-445	16	4	d_kumar001	d_kumar001	PROPN
ejpam-445	16	5	�	�	PROPN
ejpam-445	16	6	rediffmail	rediffmail	NOUN
ejpam-445	16	7	.	.	PUNCT
ejpam-445	17	1	om	om	PROPN
ejpam-445	17	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-445	18	1	717	717	NUM
ejpam-445	18	2	c	c	X
ejpam-445	18	3	©	©	PROPN
ejpam-445	18	4	2010	2010	NUM
ejpam-445	18	5	ejpam	ejpam	NOUN
ejpam-445	18	6	all	all	DET
ejpam-445	18	7	rights	right	NOUN
ejpam-445	18	8	reserved	reserve	VERB
ejpam-445	18	9	.	.	PUNCT
ejpam-445	19	1	d.	d.	PROPN
ejpam-445	19	2	kumar	kumar	PROPN
ejpam-445	19	3	/	/	SYM
ejpam-445	19	4	eur	eur	PROPN
ejpam-445	19	5	.	.	PUNCT
ejpam-445	20	1	j.	j.	PROPN
ejpam-445	20	2	pure	pure	PROPN
ejpam-445	20	3	appl	appl	PROPN
ejpam-445	20	4	.	.	PROPN
ejpam-445	20	5	math	math	PROPN
ejpam-445	20	6	,	,	PUNCT
ejpam-445	20	7	3	3	NUM
ejpam-445	20	8	(	(	PUNCT
ejpam-445	20	9	2010	2010	NUM
ejpam-445	20	10	)	)	PUNCT
ejpam-445	20	11	,	,	PUNCT
ejpam-445	20	12	717	717	NUM
ejpam-445	20	13	-	-	SYM
ejpam-445	20	14	724	724	NUM
ejpam-445	20	15	718	718	NUM
ejpam-445	20	16	the	the	DET
ejpam-445	20	17	pswfs	pswfs	NOUN
ejpam-445	20	18	ϕn	ϕn	PROPN
ejpam-445	20	19	,	,	PUNCT
ejpam-445	20	20	σ	σ	PROPN
ejpam-445	20	21	,	,	PUNCT
ejpam-445	20	22	τ(t	τ(t	NOUN
ejpam-445	20	23	)	)	PUNCT
ejpam-445	20	24	constitute	constitute	VERB
ejpam-445	20	25	an	an	DET
ejpam-445	20	26	orthogonal	orthogonal	ADJ
ejpam-445	20	27	basis	basis	NOUN
ejpam-445	20	28	of	of	ADP
ejpam-445	20	29	the	the	DET
ejpam-445	20	30	space	space	NOUN
ejpam-445	20	31	of	of	ADP
ejpam-445	20	32	σ	σ	PROPN
ejpam-445	20	33	-	-	PUNCT
ejpam-445	20	34	band	band	NOUN
ejpam-445	20	35	limited	limited	ADJ
ejpam-445	20	36	functions	function	NOUN
ejpam-445	20	37	on	on	ADP
ejpam-445	20	38	the	the	DET
ejpam-445	20	39	real	real	ADJ
ejpam-445	20	40	line	line	NOUN
ejpam-445	20	41	.	.	PUNCT
ejpam-445	21	1	they	they	PRON
ejpam-445	21	2	are	be	AUX
ejpam-445	21	3	maximally	maximally	ADV
ejpam-445	21	4	concentrated	concentrate	VERB
ejpam-445	21	5	on	on	ADP
ejpam-445	21	6	the	the	DET
ejpam-445	21	7	interval	interval	NOUN
ejpam-445	21	8	[	[	X
ejpam-445	21	9	−τ	−τ	NOUN
ejpam-445	21	10	,	,	PUNCT
ejpam-445	21	11	τ	τ	X
ejpam-445	21	12	]	]	PUNCT
ejpam-445	21	13	and	and	CCONJ
ejpam-445	21	14	depend	depend	VERB
ejpam-445	21	15	on	on	ADP
ejpam-445	21	16	parameters	parameter	NOUN
ejpam-445	21	17	σ	σ	PROPN
ejpam-445	21	18	and	and	CCONJ
ejpam-445	21	19	τ	τ	PROPN
ejpam-445	21	20	.	.	PROPN
ejpam-445	21	21	pswfs	pswfs	PROPN
ejpam-445	21	22	are	be	AUX
ejpam-445	21	23	characterized	characterize	VERB
ejpam-445	21	24	as	as	ADP
ejpam-445	21	25	the	the	DET
ejpam-445	21	26	eigenfunctions	eigenfunction	NOUN
ejpam-445	21	27	of	of	ADP
ejpam-445	21	28	an	an	DET
ejpam-445	21	29	integral	integral	ADJ
ejpam-445	21	30	operator	operator	NOUN
ejpam-445	21	31	with	with	ADP
ejpam-445	21	32	kernel	kernel	NOUN
ejpam-445	21	33	arising	arise	VERB
ejpam-445	21	34	from	from	ADP
ejpam-445	21	35	the	the	DET
ejpam-445	21	36	sinc	sinc	PROPN
ejpam-445	21	37	functions	function	NOUN
ejpam-445	21	38	s(t	s(t	PROPN
ejpam-445	21	39	)	)	PUNCT
ejpam-445	21	40	:	:	PUNCT
ejpam-445	22	1	σ	σ	PROPN
ejpam-445	22	2	π	π	PROPN
ejpam-445	22	3	∫	∫	PROPN
ejpam-445	22	4	τ	τ	PROPN
ejpam-445	22	5	−τ	−τ	PROPN
ejpam-445	22	6	ϕn	ϕn	PROPN
ejpam-445	22	7	,	,	PUNCT
ejpam-445	22	8	σ	σ	PROPN
ejpam-445	22	9	,	,	PUNCT
ejpam-445	22	10	τ(x)s	τ(x)s	PROPN
ejpam-445	22	11	(	(	PUNCT
ejpam-445	22	12	σ	σ	PROPN
ejpam-445	22	13	π	π	PROPN
ejpam-445	22	14	(	(	PUNCT
ejpam-445	22	15	t	t	PROPN
ejpam-445	22	16	−	−	PROPN
ejpam-445	22	17	x))d	x))d	NOUN
ejpam-445	22	18	x	x	PUNCT
ejpam-445	23	1	=	=	SYM
ejpam-445	23	2	λn	λn	PROPN
ejpam-445	23	3	,	,	PUNCT
ejpam-445	23	4	σ	σ	PROPN
ejpam-445	23	5	,	,	PUNCT
ejpam-445	23	6	τϕn	τϕn	PROPN
ejpam-445	23	7	,	,	PUNCT
ejpam-445	23	8	σ	σ	PROPN
ejpam-445	23	9	,	,	PUNCT
ejpam-445	23	10	τ(t	τ(t	NUM
ejpam-445	23	11	)	)	PUNCT
ejpam-445	23	12	,	,	PUNCT
ejpam-445	23	13	|t|	|t|	VERB
ejpam-445	23	14	≤	≤	PROPN
ejpam-445	23	15	τ	τ	X
ejpam-445	23	16	.	.	PUNCT
ejpam-445	24	1	(	(	PUNCT
ejpam-445	24	2	2	2	X
ejpam-445	24	3	)	)	PUNCT
ejpam-445	24	4	it	it	PRON
ejpam-445	24	5	is	be	AUX
ejpam-445	24	6	easy	easy	ADJ
ejpam-445	24	7	to	to	PART
ejpam-445	24	8	show	show	VERB
ejpam-445	24	9	that	that	SCONJ
ejpam-445	24	10	the	the	DET
ejpam-445	24	11	symmetrical	symmetrical	ADJ
ejpam-445	24	12	kernel	kernel	NOUN
ejpam-445	24	13	s(σ	s(σ	PROPN
ejpam-445	24	14	π	π	PROPN
ejpam-445	24	15	(	(	PUNCT
ejpam-445	24	16	t	t	PROPN
ejpam-445	24	17	−	−	PROPN
ejpam-445	24	18	x	x	NOUN
ejpam-445	24	19	)	)	PUNCT
ejpam-445	24	20	)	)	PUNCT
ejpam-445	24	21	is	be	AUX
ejpam-445	24	22	positive	positive	ADJ
ejpam-445	24	23	definite	definite	ADJ
ejpam-445	24	24	,	,	PUNCT
ejpam-445	24	25	so	so	SCONJ
ejpam-445	24	26	that	that	SCONJ
ejpam-445	24	27	from[1	from[1	SCONJ
ejpam-445	24	28	]	]	X
ejpam-445	24	29	we	we	PRON
ejpam-445	24	30	know	know	VERB
ejpam-445	24	31	that	that	SCONJ
ejpam-445	24	32	(	(	PUNCT
ejpam-445	24	33	2	2	X
ejpam-445	24	34	)	)	PUNCT
ejpam-445	24	35	has	have	VERB
ejpam-445	24	36	solutions	solution	NOUN
ejpam-445	24	37	in	in	ADP
ejpam-445	24	38	l2(−τ	l2(−τ	PROPN
ejpam-445	24	39	,	,	PUNCT
ejpam-445	24	40	τ	τ	PROPN
ejpam-445	24	41	)	)	PUNCT
ejpam-445	24	42	only	only	ADV
ejpam-445	24	43	for	for	ADP
ejpam-445	24	44	a	a	DET
ejpam-445	24	45	discrete	discrete	ADJ
ejpam-445	24	46	set	set	NOUN
ejpam-445	24	47	of	of	ADP
ejpam-445	24	48	real	real	ADJ
ejpam-445	24	49	positive	positive	ADJ
ejpam-445	24	50	values	value	NOUN
ejpam-445	24	51	of	of	ADP
ejpam-445	24	52	λn	λn	NOUN
ejpam-445	24	53	,	,	PUNCT
ejpam-445	24	54	σ	σ	PROPN
ejpam-445	24	55	,	,	PUNCT
ejpam-445	24	56	τ	τ	PROPN
ejpam-445	24	57	say	say	VERB
ejpam-445	24	58	λ0,σ	λ0,σ	PROPN
ejpam-445	24	59	,	,	PUNCT
ejpam-445	24	60	τ	τ	X
ejpam-445	24	61	≥	≥	NOUN
ejpam-445	24	62	λ1,σ	λ1,σ	PROPN
ejpam-445	24	63	,	,	PUNCT
ejpam-445	24	64	τ	τ	PROPN
ejpam-445	24	65	≥	≥	NUM
ejpam-445	24	66	.	.	PUNCT
ejpam-445	24	67	.	.	PUNCT
ejpam-445	25	1	.	.	PUNCT
ejpam-445	26	1	and	and	CCONJ
ejpam-445	26	2	that	that	SCONJ
ejpam-445	26	3	as	as	ADP
ejpam-445	26	4	n	n	PROPN
ejpam-445	26	5	→	→	SYM
ejpam-445	26	6	∞	∞	PROPN
ejpam-445	26	7	,	,	PUNCT
ejpam-445	26	8	limλn	limλn	NOUN
ejpam-445	26	9	,	,	PUNCT
ejpam-445	26	10	σ	σ	PROPN
ejpam-445	26	11	,	,	PUNCT
ejpam-445	26	12	τ	τ	PROPN
ejpam-445	26	13	=	=	SYM
ejpam-445	26	14	0	0	PROPN
ejpam-445	26	15	.	.	PUNCT
ejpam-445	27	1	the	the	DET
ejpam-445	27	2	corresponding	corresponding	ADJ
ejpam-445	27	3	solutions	solution	NOUN
ejpam-445	27	4	,	,	PUNCT
ejpam-445	27	5	or	or	CCONJ
ejpam-445	27	6	eigenfunctions,ϕ0,σ	eigenfunctions,ϕ0,σ	NOUN
ejpam-445	27	7	,	,	PUNCT
ejpam-445	27	8	τ(t),ϕ1,σ	τ(t),ϕ1,σ	NUM
ejpam-445	27	9	,	,	PUNCT
ejpam-445	27	10	τ(t	τ(t	NOUN
ejpam-445	27	11	)	)	PUNCT
ejpam-445	27	12	,	,	PUNCT
ejpam-445	27	13	.	.	PUNCT
ejpam-445	27	14	.	.	PUNCT
ejpam-445	27	15	.	.	PUNCT
ejpam-445	28	1	can	can	AUX
ejpam-445	28	2	be	be	AUX
ejpam-445	28	3	chosen	choose	VERB
ejpam-445	28	4	to	to	PART
ejpam-445	28	5	be	be	AUX
ejpam-445	28	6	the	the	DET
ejpam-445	28	7	real	real	ADJ
ejpam-445	28	8	and	and	CCONJ
ejpam-445	28	9	orthogonal	orthogonal	ADJ
ejpam-445	28	10	on	on	ADP
ejpam-445	28	11	(	(	PUNCT
ejpam-445	28	12	−τ	−τ	PROPN
ejpam-445	28	13	,	,	PUNCT
ejpam-445	28	14	τ	τ	PROPN
ejpam-445	28	15	)	)	PUNCT
ejpam-445	28	16	.	.	PUNCT
ejpam-445	29	1	the	the	DET
ejpam-445	29	2	variational	variational	ADJ
ejpam-445	29	3	problem	problem	NOUN
ejpam-445	29	4	that	that	PRON
ejpam-445	29	5	let	let	VERB
ejpam-445	29	6	to	to	PART
ejpam-445	29	7	(	(	PUNCT
ejpam-445	29	8	2	2	NUM
ejpam-445	29	9	)	)	PUNCT
ejpam-445	29	10	only	only	ADV
ejpam-445	29	11	requires	require	VERB
ejpam-445	29	12	that	that	SCONJ
ejpam-445	29	13	equation	equation	NOUN
ejpam-445	29	14	to	to	PART
ejpam-445	29	15	hold	hold	VERB
ejpam-445	29	16	for	for	ADP
ejpam-445	29	17	|t|	|t|	ADJ
ejpam-445	29	18	≤	≤	PROPN
ejpam-445	29	19	τ	τ	X
ejpam-445	29	20	.	.	PUNCT
ejpam-445	30	1	with	with	ADP
ejpam-445	30	2	ϕn	ϕn	PROPN
ejpam-445	30	3	,	,	PUNCT
ejpam-445	30	4	σ	σ	PROPN
ejpam-445	30	5	,	,	PUNCT
ejpam-445	30	6	τ(x	τ(x	NOUN
ejpam-445	30	7	)	)	PUNCT
ejpam-445	30	8	on	on	ADP
ejpam-445	30	9	the	the	DET
ejpam-445	30	10	left	left	NOUN
ejpam-445	30	11	of	of	ADP
ejpam-445	30	12	(	(	PUNCT
ejpam-445	30	13	2	2	X
ejpam-445	30	14	)	)	PUNCT
ejpam-445	30	15	gives	give	VERB
ejpam-445	30	16	for	for	ADP
ejpam-445	30	17	|x	|x	NOUN
ejpam-445	30	18	|	|	ADV
ejpam-445	30	19	≤	≤	NUM
ejpam-445	30	20	τ	τ	PROPN
ejpam-445	30	21	,	,	PUNCT
ejpam-445	30	22	however	however	ADV
ejpam-445	30	23	,	,	PUNCT
ejpam-445	30	24	the	the	DET
ejpam-445	30	25	left	left	NOUN
ejpam-445	30	26	is	be	AUX
ejpam-445	30	27	well	well	ADV
ejpam-445	30	28	defined	define	VERB
ejpam-445	30	29	for	for	ADP
ejpam-445	30	30	all	all	DET
ejpam-445	30	31	t.	t.	NOUN
ejpam-445	30	32	we	we	PRON
ejpam-445	30	33	use	use	VERB
ejpam-445	30	34	this	this	PRON
ejpam-445	30	35	to	to	PART
ejpam-445	30	36	extend	extend	VERB
ejpam-445	30	37	the	the	DET
ejpam-445	30	38	range	range	NOUN
ejpam-445	30	39	of	of	ADP
ejpam-445	30	40	definition	definition	NOUN
ejpam-445	30	41	of	of	ADP
ejpam-445	30	42	the	the	DET
ejpam-445	30	43	ϕn	ϕn	PROPN
ejpam-445	30	44	,	,	PUNCT
ejpam-445	30	45	σ	σ	PROPN
ejpam-445	30	46	,	,	PUNCT
ejpam-445	30	47	τ	τ	PROPN
ejpam-445	30	48	’s	’s	PART
ejpam-445	30	49	and	and	CCONJ
ejpam-445	30	50	so	so	ADV
ejpam-445	30	51	define	define	VERB
ejpam-445	30	52	ϕn	ϕn	PROPN
ejpam-445	30	53	,	,	PUNCT
ejpam-445	30	54	σ	σ	PROPN
ejpam-445	30	55	,	,	PUNCT
ejpam-445	30	56	τ(t	τ(t	ADJ
ejpam-445	30	57	)	)	PUNCT
ejpam-445	30	58	=	=	SYM
ejpam-445	30	59	σ	σ	PROPN
ejpam-445	30	60	πλn	πλn	PROPN
ejpam-445	30	61	,	,	PUNCT
ejpam-445	30	62	σ	σ	PROPN
ejpam-445	30	63	,	,	PUNCT
ejpam-445	30	64	τ	τ	PROPN
ejpam-445	30	65	∫	∫	PROPN
ejpam-445	30	66	τ	τ	PROPN
ejpam-445	30	67	−τ	−τ	PROPN
ejpam-445	30	68	ϕn	ϕn	PROPN
ejpam-445	30	69	,	,	PUNCT
ejpam-445	30	70	σ	σ	PROPN
ejpam-445	30	71	,	,	PUNCT
ejpam-445	30	72	τ(x)s	τ(x)s	PROPN
ejpam-445	30	73	(	(	PUNCT
ejpam-445	30	74	σ	σ	PROPN
ejpam-445	30	75	π	π	PROPN
ejpam-445	30	76	(	(	PUNCT
ejpam-445	30	77	t	t	PROPN
ejpam-445	30	78	−	−	PROPN
ejpam-445	30	79	x))d	x))d	PROPN
ejpam-445	30	80	x	x	SYM
ejpam-445	30	81	,	,	PUNCT
ejpam-445	30	82	|t|	|t|	PROPN
ejpam-445	30	83	>	>	X
ejpam-445	30	84	τ	τ	PROPN
ejpam-445	30	85	.	.	PUNCT
ejpam-445	31	1	the	the	DET
ejpam-445	31	2	eigenfunctions	eigenfunction	NOUN
ejpam-445	31	3	ϕn	ϕn	INTJ
ejpam-445	31	4	,	,	PUNCT
ejpam-445	31	5	σ	σ	PROPN
ejpam-445	31	6	,	,	PUNCT
ejpam-445	31	7	τ	τ	PROPN
ejpam-445	31	8	are	be	AUX
ejpam-445	31	9	now	now	ADV
ejpam-445	31	10	defined	define	VERB
ejpam-445	31	11	for	for	ADP
ejpam-445	31	12	all	all	DET
ejpam-445	31	13	t.	t.	NOUN
ejpam-445	31	14	in	in	ADP
ejpam-445	31	15	addition	addition	NOUN
ejpam-445	31	16	to	to	ADP
ejpam-445	31	17	the	the	DET
ejpam-445	31	18	equation	equation	NOUN
ejpam-445	31	19	(	(	PUNCT
ejpam-445	31	20	2	2	NUM
ejpam-445	31	21	)	)	PUNCT
ejpam-445	31	22	,	,	PUNCT
ejpam-445	31	23	the	the	DET
ejpam-445	31	24	{	{	PUNCT
ejpam-445	31	25	ϕn	ϕn	PROPN
ejpam-445	31	26	,	,	PUNCT
ejpam-445	31	27	σ	σ	PROPN
ejpam-445	31	28	,	,	PUNCT
ejpam-445	31	29	τ	τ	PROPN
ejpam-445	31	30	}	}	PUNCT
ejpam-445	31	31	satisfy	satisfy	VERB
ejpam-445	31	32	an	an	DET
ejpam-445	31	33	integral	integral	ADJ
ejpam-445	31	34	equation	equation	NOUN
ejpam-445	31	35	over	over	ADP
ejpam-445	31	36	(	(	PUNCT
ejpam-445	31	37	−∞,∞	−∞,∞	NOUN
ejpam-445	31	38	)	)	PUNCT
ejpam-445	31	39	σ	σ	PROPN
ejpam-445	32	1	π	π	PROPN
ejpam-445	32	2	∫	∫	PROPN
ejpam-445	32	3	∞	∞	PROPN
ejpam-445	32	4	−∞	−∞	X
ejpam-445	32	5	ϕn	ϕn	PROPN
ejpam-445	32	6	,	,	PUNCT
ejpam-445	32	7	σ	σ	PROPN
ejpam-445	32	8	,	,	PUNCT
ejpam-445	32	9	τ(x)s	τ(x)s	PROPN
ejpam-445	32	10	(	(	PUNCT
ejpam-445	32	11	σ	σ	PROPN
ejpam-445	32	12	π	π	PROPN
ejpam-445	32	13	(	(	PUNCT
ejpam-445	32	14	t	t	PROPN
ejpam-445	33	1	−	−	PROPN
ejpam-445	33	2	x))d	x))d	NOUN
ejpam-445	33	3	x	x	PUNCT
ejpam-445	34	1	=	=	PUNCT
ejpam-445	34	2	(	(	PUNCT
ejpam-445	34	3	ϕn	ϕn	INTJ
ejpam-445	34	4	,	,	PUNCT
ejpam-445	34	5	σ	σ	PROPN
ejpam-445	34	6	,	,	PUNCT
ejpam-445	34	7	τ	τ	PROPN
ejpam-445	34	8	∗	∗	NOUN
ejpam-445	34	9	sσ)(t	sσ)(t	X
ejpam-445	34	10	)	)	PUNCT
ejpam-445	34	11	=	=	SYM
ejpam-445	35	1	ϕn	ϕn	PROPN
ejpam-445	35	2	,	,	PUNCT
ejpam-445	35	3	σ	σ	PROPN
ejpam-445	35	4	,	,	PUNCT
ejpam-445	35	5	τ(t	τ(t	NUM
ejpam-445	35	6	)	)	PUNCT
ejpam-445	35	7	with	with	ADP
ejpam-445	35	8	the	the	DET
ejpam-445	35	9	same	same	ADJ
ejpam-445	35	10	kernel	kernel	NOUN
ejpam-445	35	11	.	.	PUNCT
ejpam-445	36	1	this	this	PRON
ejpam-445	36	2	leads	lead	VERB
ejpam-445	36	3	to	to	ADP
ejpam-445	36	4	a	a	DET
ejpam-445	36	5	dual	dual	ADJ
ejpam-445	36	6	orthogonality	orthogonality	NOUN
ejpam-445	36	7	∫	∫	PROPN
ejpam-445	36	8	τ	τ	PROPN
ejpam-445	36	9	−τ	−τ	PROPN
ejpam-445	36	10	ϕn	ϕn	PROPN
ejpam-445	36	11	,	,	PUNCT
ejpam-445	36	12	σ	σ	PROPN
ejpam-445	36	13	,	,	PUNCT
ejpam-445	36	14	τ(x)ϕm	τ(x)ϕm	NUM
ejpam-445	36	15	,	,	PUNCT
ejpam-445	36	16	σ	σ	PROPN
ejpam-445	36	17	,	,	PUNCT
ejpam-445	36	18	τ(x)d	τ(x)d	PROPN
ejpam-445	36	19	x	x	PUNCT
ejpam-445	36	20	=	=	SYM
ejpam-445	36	21	λn	λn	PROPN
ejpam-445	36	22	,	,	PUNCT
ejpam-445	36	23	σ	σ	PROPN
ejpam-445	36	24	,	,	PUNCT
ejpam-445	36	25	τδnm	τδnm	ADJ
ejpam-445	36	26	,	,	PUNCT
ejpam-445	36	27	∫	∫	PROPN
ejpam-445	36	28	∞	∞	PROPN
ejpam-445	37	1	−∞	−∞	X
ejpam-445	37	2	ϕn	ϕn	PROPN
ejpam-445	37	3	,	,	PUNCT
ejpam-445	37	4	σ	σ	PROPN
ejpam-445	37	5	,	,	PUNCT
ejpam-445	37	6	τ(x)ϕm	τ(x)ϕm	NUM
ejpam-445	37	7	,	,	PUNCT
ejpam-445	37	8	σ	σ	PROPN
ejpam-445	37	9	,	,	PUNCT
ejpam-445	37	10	τ(x)d	τ(x)d	PROPN
ejpam-445	37	11	x	x	PUNCT
ejpam-445	37	12	=	=	PUNCT
ejpam-445	37	13	δnm	δnm	NOUN
ejpam-445	37	14	and	and	CCONJ
ejpam-445	37	15	the	the	DET
ejpam-445	37	16	fact	fact	NOUN
ejpam-445	37	17	that	that	SCONJ
ejpam-445	37	18	they	they	PRON
ejpam-445	37	19	constitute	constitute	VERB
ejpam-445	37	20	an	an	DET
ejpam-445	37	21	orthogonal	orthogonal	ADJ
ejpam-445	37	22	basis	basis	NOUN
ejpam-445	37	23	of	of	ADP
ejpam-445	37	24	l2(−τ	l2(−τ	PROPN
ejpam-445	37	25	,	,	PUNCT
ejpam-445	37	26	τ	τ	PROPN
ejpam-445	37	27	)	)	PUNCT
ejpam-445	37	28	,	,	PUNCT
ejpam-445	37	29	as	as	ADV
ejpam-445	37	30	well	well	ADV
ejpam-445	37	31	as	as	ADP
ejpam-445	37	32	an	an	DET
ejpam-445	37	33	orthonormal	orthonormal	ADJ
ejpam-445	37	34	basis	basis	NOUN
ejpam-445	37	35	of	of	ADP
ejpam-445	37	36	the	the	DET
ejpam-445	37	37	subspaces	subspace	NOUN
ejpam-445	37	38	bσ	bσ	NOUN
ejpam-445	37	39	of	of	ADP
ejpam-445	37	40	l2(−∞,∞	l2(−∞,∞	PROPN
ejpam-445	37	41	)	)	PUNCT
ejpam-445	37	42	,	,	PUNCT
ejpam-445	37	43	the	the	DET
ejpam-445	37	44	paley	paley	ADJ
ejpam-445	37	45	-	-	PUNCT
ejpam-445	37	46	wiener	wiener	NOUN
ejpam-445	37	47	space	space	NOUN
ejpam-445	37	48	of	of	ADP
ejpam-445	37	49	all	all	PRON
ejpam-445	37	50	σ−bandlimited	σ−bandlimite	VERB
ejpam-445	37	51	functions	function	NOUN
ejpam-445	37	52	.	.	PUNCT
ejpam-445	38	1	we	we	PRON
ejpam-445	38	2	are	be	AUX
ejpam-445	38	3	interested	interested	ADJ
ejpam-445	38	4	mainly	mainly	ADV
ejpam-445	38	5	in	in	ADP
ejpam-445	38	6	ϕ0,σ	ϕ0,σ	PROPN
ejpam-445	38	7	,	,	PUNCT
ejpam-445	38	8	τ	τ	X
ejpam-445	38	9	whose	whose	DET
ejpam-445	38	10	concentration	concentration	NOUN
ejpam-445	38	11	on	on	ADP
ejpam-445	38	12	the	the	DET
ejpam-445	38	13	interval	interval	NOUN
ejpam-445	38	14	[	[	X
ejpam-445	38	15	−τ	−τ	NOUN
ejpam-445	38	16	,	,	PUNCT
ejpam-445	38	17	τ]is	τ]is	PROPN
ejpam-445	38	18	maximum	maximum	ADJ
ejpam-445	38	19	.	.	PUNCT
ejpam-445	39	1	since	since	SCONJ
ejpam-445	39	2	ϕk	ϕk	PROPN
ejpam-445	39	3	,	,	PUNCT
ejpam-445	39	4	σ	σ	PROPN
ejpam-445	39	5	,	,	PUNCT
ejpam-445	39	6	τ	τ	PROPN
ejpam-445	39	7	has	have	VERB
ejpam-445	39	8	exactly	exactly	ADV
ejpam-445	39	9	k	k	ADJ
ejpam-445	39	10	zeros	zero	NOUN
ejpam-445	39	11	in	in	ADP
ejpam-445	39	12	the	the	DET
ejpam-445	39	13	interval	interval	NOUN
ejpam-445	39	14	[	[	X
ejpam-445	39	15	−τ	−τ	ADJ
ejpam-445	39	16	,	,	PUNCT
ejpam-445	39	17	τ],so	τ],so	ADJ
ejpam-445	39	18	ϕ0,σ	ϕ0,σ	PROPN
ejpam-445	39	19	,	,	PUNCT
ejpam-445	39	20	τ	τ	PROPN
ejpam-445	39	21	(	(	PUNCT
ejpam-445	39	22	pswfs)are	pswfs)are	VERB
ejpam-445	39	23	entire	entire	ADJ
ejpam-445	39	24	functions	function	NOUN
ejpam-445	39	25	and	and	CCONJ
ejpam-445	39	26	therefore	therefore	ADV
ejpam-445	39	27	can	can	AUX
ejpam-445	39	28	not	not	PART
ejpam-445	39	29	vanish	vanish	VERB
ejpam-445	39	30	on	on	ADP
ejpam-445	39	31	any	any	DET
ejpam-445	39	32	interval	interval	NOUN
ejpam-445	39	33	,	,	PUNCT
ejpam-445	39	34	they	they	PRON
ejpam-445	39	35	can	can	AUX
ejpam-445	39	36	be	be	AUX
ejpam-445	39	37	made	make	VERB
ejpam-445	39	38	uniformly	uniformly	ADV
ejpam-445	39	39	small	small	ADJ
ejpam-445	39	40	outside	outside	ADV
ejpam-445	39	41	of	of	ADP
ejpam-445	39	42	[	[	X
ejpam-445	39	43	−τ	−τ	NOUN
ejpam-445	39	44	,	,	PUNCT
ejpam-445	39	45	τ	τ	X
ejpam-445	39	46	]	]	PUNCT
ejpam-445	39	47	for	for	SCONJ
ejpam-445	39	48	τ	τ	PROPN
ejpam-445	39	49	or	or	CCONJ
ejpam-445	39	50	σ	σ	PROPN
ejpam-445	39	51	sufficiently	sufficiently	ADV
ejpam-445	39	52	large	large	ADJ
ejpam-445	39	53	,	,	PUNCT
ejpam-445	39	54	so	so	SCONJ
ejpam-445	39	55	that	that	SCONJ
ejpam-445	39	56	computationally	computationally	ADV
ejpam-445	39	57	they	they	PRON
ejpam-445	39	58	behave	behave	VERB
ejpam-445	39	59	like	like	ADP
ejpam-445	39	60	functions	function	NOUN
ejpam-445	39	61	with	with	ADP
ejpam-445	39	62	compact	compact	ADJ
ejpam-445	39	63	support	support	NOUN
ejpam-445	39	64	.	.	PUNCT
ejpam-445	40	1	to	to	PART
ejpam-445	40	2	construct	construct	VERB
ejpam-445	40	3	ps	ps	PROPN
ejpam-445	40	4	wavelets	wavelet	NOUN
ejpam-445	40	5	,	,	PUNCT
ejpam-445	40	6	the	the	DET
ejpam-445	40	7	scaling	scaling	NOUN
ejpam-445	40	8	function	function	NOUN
ejpam-445	40	9	φ	φ	PROPN
ejpam-445	40	10	=	=	SYM
ejpam-445	40	11	ϕ0,π	ϕ0,π	PROPN
ejpam-445	40	12	,	,	PUNCT
ejpam-445	40	13	τ	τ	X
ejpam-445	40	14	,	,	PUNCT
ejpam-445	40	15	where	where	SCONJ
ejpam-445	40	16	τ	τ	PROPN
ejpam-445	40	17	is	be	AUX
ejpam-445	40	18	any	any	DET
ejpam-445	40	19	positive	positive	ADJ
ejpam-445	40	20	number	number	NOUN
ejpam-445	40	21	,	,	PUNCT
ejpam-445	40	22	was	be	AUX
ejpam-445	40	23	introduced	introduce	VERB
ejpam-445	40	24	by	by	ADP
ejpam-445	40	25	[	[	X
ejpam-445	40	26	15	15	NUM
ejpam-445	40	27	]	]	PUNCT
ejpam-445	40	28	and	and	CCONJ
ejpam-445	40	29	obtained	obtain	VERB
ejpam-445	40	30	a	a	DET
ejpam-445	40	31	basis	basis	NOUN
ejpam-445	40	32	composed	compose	VERB
ejpam-445	40	33	of	of	ADP
ejpam-445	40	34	a	a	DET
ejpam-445	40	35	space	space	NOUN
ejpam-445	40	36	v0	v0	NOUN
ejpam-445	40	37	⊂	⊂	X
ejpam-445	40	38	l2	l2	NOUN
ejpam-445	40	39	(	(	PUNCT
ejpam-445	40	40	r	r	NOUN
ejpam-445	40	41	)	)	PUNCT
ejpam-445	40	42	which	which	PRON
ejpam-445	40	43	turns	turn	VERB
ejpam-445	40	44	out	out	ADP
ejpam-445	40	45	to	to	PART
ejpam-445	40	46	be	be	AUX
ejpam-445	40	47	the	the	DET
ejpam-445	40	48	paley	paley	ADJ
ejpam-445	40	49	-	-	PUNCT
ejpam-445	40	50	wiener	wiener	NOUN
ejpam-445	40	51	space	space	NOUN
ejpam-445	40	52	bπ	bπ	ADP
ejpam-445	40	53	of	of	ADP
ejpam-445	40	54	π	π	PROPN
ejpam-445	40	55	bandlimited	bandlimited	ADJ
ejpam-445	40	56	functions	function	NOUN
ejpam-445	40	57	.	.	PUNCT
ejpam-445	41	1	d.	d.	PROPN
ejpam-445	41	2	kumar	kumar	PROPN
ejpam-445	41	3	/	/	SYM
ejpam-445	41	4	eur	eur	PROPN
ejpam-445	41	5	.	.	PUNCT
ejpam-445	42	1	j.	j.	PROPN
ejpam-445	42	2	pure	pure	PROPN
ejpam-445	42	3	appl	appl	PROPN
ejpam-445	42	4	.	.	PROPN
ejpam-445	42	5	math	math	PROPN
ejpam-445	42	6	,	,	PUNCT
ejpam-445	42	7	3	3	NUM
ejpam-445	42	8	(	(	PUNCT
ejpam-445	42	9	2010	2010	NUM
ejpam-445	42	10	)	)	PUNCT
ejpam-445	42	11	,	,	PUNCT
ejpam-445	42	12	717	717	NUM
ejpam-445	42	13	-	-	SYM
ejpam-445	42	14	724	724	NUM
ejpam-445	42	15	719	719	NUM
ejpam-445	42	16	a	a	DET
ejpam-445	42	17	multiresolution	multiresolution	NOUN
ejpam-445	42	18	analysis	analysis	NOUN
ejpam-445	42	19	(	(	PUNCT
ejpam-445	43	1	mra)are	mra)are	PROPN
ejpam-445	43	2	then	then	ADV
ejpam-445	43	3	based	base	VERB
ejpam-445	43	4	on	on	ADP
ejpam-445	43	5	this	this	DET
ejpam-445	43	6	construction	construction	NOUN
ejpam-445	43	7	.	.	PUNCT
ejpam-445	44	1	the	the	DET
ejpam-445	44	2	other	other	ADJ
ejpam-445	44	3	spaces	space	NOUN
ejpam-445	44	4	are	be	AUX
ejpam-445	44	5	obtained	obtain	VERB
ejpam-445	44	6	by	by	ADP
ejpam-445	44	7	dilation	dilation	NOUN
ejpam-445	44	8	by	by	ADP
ejpam-445	44	9	factors	factor	NOUN
ejpam-445	44	10	of	of	ADP
ejpam-445	44	11	two	two	NUM
ejpam-445	44	12	and	and	CCONJ
ejpam-445	44	13	consist	consist	VERB
ejpam-445	44	14	of	of	ADP
ejpam-445	44	15	the	the	DET
ejpam-445	44	16	paley	paley	ADJ
ejpam-445	44	17	-	-	PUNCT
ejpam-445	44	18	wiener	wiener	NOUN
ejpam-445	44	19	spaces	space	VERB
ejpam-445	44	20	vm	vm	NOUN
ejpam-445	44	21	=	=	PROPN
ejpam-445	44	22	b2mπ.the	b2mπ.the	PRON
ejpam-445	44	23	sinc	sinc	PROPN
ejpam-445	44	24	function	function	NOUN
ejpam-445	44	25	is	be	AUX
ejpam-445	44	26	the	the	DET
ejpam-445	44	27	standard	standard	ADJ
ejpam-445	44	28	scaling	scale	VERB
ejpam-445	44	29	function	function	NOUN
ejpam-445	44	30	of	of	ADP
ejpam-445	44	31	this	this	DET
ejpam-445	44	32	mra	mra	NOUN
ejpam-445	44	33	.	.	PUNCT
ejpam-445	45	1	it	it	PRON
ejpam-445	45	2	is	be	AUX
ejpam-445	45	3	well	well	ADV
ejpam-445	45	4	known	know	VERB
ejpam-445	45	5	that	that	SCONJ
ejpam-445	45	6	sinc	sinc	PROPN
ejpam-445	45	7	function	function	NOUN
ejpam-445	45	8	has	have	VERB
ejpam-445	45	9	very	very	ADV
ejpam-445	45	10	good	good	ADJ
ejpam-445	45	11	frequency	frequency	NOUN
ejpam-445	45	12	localization	localization	NOUN
ejpam-445	45	13	,	,	PUNCT
ejpam-445	45	14	but	but	CCONJ
ejpam-445	45	15	not	not	PART
ejpam-445	45	16	very	very	ADV
ejpam-445	45	17	good	good	ADJ
ejpam-445	45	18	time	time	NOUN
ejpam-445	45	19	localization	localization	NOUN
ejpam-445	45	20	.	.	PUNCT
ejpam-445	46	1	it	it	PRON
ejpam-445	46	2	follows	follow	VERB
ejpam-445	46	3	that	that	SCONJ
ejpam-445	46	4	this	this	DET
ejpam-445	46	5	wavelet	wavelet	NOUN
ejpam-445	46	6	basis	basis	NOUN
ejpam-445	46	7	has	have	AUX
ejpam-445	46	8	limited	limit	VERB
ejpam-445	46	9	use	use	NOUN
ejpam-445	46	10	in	in	ADP
ejpam-445	46	11	comparison	comparison	NOUN
ejpam-445	46	12	to	to	ADP
ejpam-445	46	13	the	the	DET
ejpam-445	46	14	daubechies	daubechie	NOUN
ejpam-445	46	15	wavelets	wavelet	NOUN
ejpam-445	46	16	which	which	PRON
ejpam-445	46	17	have	have	VERB
ejpam-445	46	18	compact	compact	ADJ
ejpam-445	46	19	support	support	NOUN
ejpam-445	46	20	in	in	ADP
ejpam-445	46	21	the	the	DET
ejpam-445	46	22	time	time	NOUN
ejpam-445	46	23	domain	domain	NOUN
ejpam-445	46	24	.	.	PUNCT
ejpam-445	47	1	however	however	ADV
ejpam-445	47	2	,	,	PUNCT
ejpam-445	47	3	pswfs	pswfs	PROPN
ejpam-445	47	4	are	be	AUX
ejpam-445	47	5	superior	superior	ADJ
ejpam-445	47	6	to	to	PART
ejpam-445	47	7	sinc	sinc	VERB
ejpam-445	47	8	function	function	NOUN
ejpam-445	47	9	and	and	CCONJ
ejpam-445	47	10	they	they	PRON
ejpam-445	47	11	are	be	AUX
ejpam-445	47	12	similar	similar	ADJ
ejpam-445	47	13	to	to	ADP
ejpam-445	47	14	the	the	DET
ejpam-445	47	15	daubechies	daubechie	NOUN
ejpam-445	47	16	wavelets	wavelet	VERB
ejpam-445	47	17	for	for	ADP
ejpam-445	47	18	practical	practical	ADJ
ejpam-445	47	19	computations	computation	NOUN
ejpam-445	47	20	.	.	PUNCT
ejpam-445	48	1	using	use	VERB
ejpam-445	48	2	the	the	DET
ejpam-445	48	3	standard	standard	ADJ
ejpam-445	48	4	wavelet	wavelet	NOUN
ejpam-445	48	5	approach	approach	NOUN
ejpam-445	48	6	in	in	ADP
ejpam-445	48	7	which	which	PRON
ejpam-445	48	8	dilations	dilation	NOUN
ejpam-445	48	9	of	of	ADP
ejpam-445	48	10	ϕ0,π	ϕ0,π	PROPN
ejpam-445	48	11	,	,	PUNCT
ejpam-445	48	12	τ(2	τ(2	PROPN
ejpam-445	48	13	mt	mt	PROPN
ejpam-445	48	14	)	)	PUNCT
ejpam-445	48	15	are	be	AUX
ejpam-445	48	16	used	use	VERB
ejpam-445	48	17	to	to	PART
ejpam-445	48	18	get	get	VERB
ejpam-445	48	19	the	the	DET
ejpam-445	48	20	basis	basis	NOUN
ejpam-445	48	21	{	{	PUNCT
ejpam-445	48	22	ϕ0,π	ϕ0,π	PROPN
ejpam-445	48	23	,	,	PUNCT
ejpam-445	48	24	τ(2	τ(2	PROPN
ejpam-445	48	25	mt	mt	PROPN
ejpam-445	48	26	−	−	PROPN
ejpam-445	48	27	n	n	CCONJ
ejpam-445	48	28	)	)	PUNCT
ejpam-445	48	29	}	}	PUNCT
ejpam-445	48	30	of	of	ADP
ejpam-445	48	31	vm	vm	PROPN
ejpam-445	48	32	we	we	PRON
ejpam-445	48	33	get	get	VERB
ejpam-445	48	34	φ(2	φ(2	PROPN
ejpam-445	48	35	m	m	NOUN
ejpam-445	48	36	t	t	PROPN
ejpam-445	48	37	)	)	PUNCT
ejpam-445	48	38	=	=	SYM
ejpam-445	48	39	ϕ0,π	ϕ0,π	PROPN
ejpam-445	48	40	,	,	PUNCT
ejpam-445	48	41	τ(2	τ(2	PROPN
ejpam-445	48	42	mt	mt	PROPN
ejpam-445	48	43	)	)	PUNCT
ejpam-445	48	44	=	=	SYM
ejpam-445	48	45	2m/2ϕ0,2mπ,2−mπτ(t	2m/2ϕ0,2mπ,2−mπτ(t	NUM
ejpam-445	48	46	)	)	PUNCT
ejpam-445	48	47	,	,	PUNCT
ejpam-445	48	48	which	which	PRON
ejpam-445	48	49	show	show	VERB
ejpam-445	48	50	that	that	SCONJ
ejpam-445	48	51	the	the	DET
ejpam-445	48	52	concentration	concentration	NOUN
ejpam-445	48	53	interval	interval	NOUN
ejpam-445	48	54	becomes	become	VERB
ejpam-445	48	55	smaller	small	ADJ
ejpam-445	48	56	as	as	ADP
ejpam-445	48	57	m	m	NOUN
ejpam-445	48	58	increases	increase	NOUN
ejpam-445	48	59	.	.	PUNCT
ejpam-445	49	1	so	so	ADV
ejpam-445	49	2	we	we	PRON
ejpam-445	49	3	have	have	VERB
ejpam-445	49	4	to	to	PART
ejpam-445	49	5	fix	fix	VERB
ejpam-445	49	6	the	the	DET
ejpam-445	49	7	concentration	concentration	NOUN
ejpam-445	49	8	interval	interval	NOUN
ejpam-445	49	9	by	by	ADP
ejpam-445	49	10	taking	take	VERB
ejpam-445	49	11	{	{	PUNCT
ejpam-445	49	12	ϕ0,2mπ	ϕ0,2mπ	NOUN
ejpam-445	49	13	,	,	PUNCT
ejpam-445	49	14	τ(t	τ(t	PROPN
ejpam-445	49	15	−	−	PROPN
ejpam-445	49	16	2−mn	2−mn	NUM
ejpam-445	49	17	)	)	PUNCT
ejpam-445	49	18	}	}	PUNCT
ejpam-445	49	19	instead	instead	ADV
ejpam-445	49	20	as	as	ADP
ejpam-445	49	21	a	a	DET
ejpam-445	49	22	possible	possible	ADJ
ejpam-445	49	23	riesz	riesz	NOUN
ejpam-445	49	24	basis	basis	NOUN
ejpam-445	49	25	of	of	ADP
ejpam-445	49	26	vm	vm	PROPN
ejpam-445	49	27	.	.	PUNCT
ejpam-445	50	1	thus	thus	ADV
ejpam-445	50	2	our	our	PRON
ejpam-445	50	3	new	new	ADJ
ejpam-445	50	4	basis	basis	NOUN
ejpam-445	50	5	for	for	ADP
ejpam-445	50	6	v0	v0	NOUN
ejpam-445	50	7	and	and	CCONJ
ejpam-445	50	8	vm	vm	PROPN
ejpam-445	50	9	are	be	AUX
ejpam-445	50	10	different	different	ADJ
ejpam-445	50	11	from	from	ADP
ejpam-445	50	12	the	the	DET
ejpam-445	50	13	standard	standard	ADJ
ejpam-445	50	14	wavelet	wavelet	NOUN
ejpam-445	50	15	basis	basis	NOUN
ejpam-445	50	16	for	for	ADP
ejpam-445	50	17	v0	v0	NOUN
ejpam-445	50	18	and	and	CCONJ
ejpam-445	50	19	vm	vm	NOUN
ejpam-445	50	20	consisting	consist	VERB
ejpam-445	50	21	of	of	ADP
ejpam-445	50	22	translates	translate	NOUN
ejpam-445	50	23	of	of	ADP
ejpam-445	50	24	the	the	DET
ejpam-445	50	25	sinc	sinc	PROPN
ejpam-445	50	26	function	function	NOUN
ejpam-445	50	27	.	.	PUNCT
ejpam-445	51	1	2	2	X
ejpam-445	51	2	.	.	NUM
ejpam-445	51	3	frames	frame	NOUN
ejpam-445	51	4	and	and	CCONJ
ejpam-445	51	5	applications	application	NOUN
ejpam-445	51	6	to	to	PART
ejpam-445	51	7	prolate	prolate	VERB
ejpam-445	51	8	spheroidal	spheroidal	NOUN
ejpam-445	51	9	wavelets	wavelet	NOUN
ejpam-445	51	10	the	the	DET
ejpam-445	51	11	notion	notion	NOUN
ejpam-445	51	12	of	of	ADP
ejpam-445	51	13	frame	frame	NOUN
ejpam-445	51	14	goes	go	VERB
ejpam-445	51	15	back	back	ADV
ejpam-445	51	16	to	to	ADP
ejpam-445	51	17	duffin	duffin	NOUN
ejpam-445	51	18	and	and	CCONJ
ejpam-445	51	19	schaeffer[6	schaeffer[6	NOUN
ejpam-445	51	20	]	]	PUNCT
ejpam-445	51	21	in	in	ADP
ejpam-445	51	22	the	the	DET
ejpam-445	51	23	early	early	ADJ
ejpam-445	51	24	1950s	1950	NOUN
ejpam-445	51	25	to	to	PART
ejpam-445	51	26	deal	deal	VERB
ejpam-445	51	27	with	with	ADP
ejpam-445	51	28	the	the	DET
ejpam-445	51	29	problems	problem	NOUN
ejpam-445	51	30	in	in	ADP
ejpam-445	51	31	nonharmonic	nonharmonic	ADJ
ejpam-445	51	32	fourier	fourier	NOUN
ejpam-445	51	33	series	series	NOUN
ejpam-445	51	34	.	.	PUNCT
ejpam-445	52	1	in	in	ADP
ejpam-445	52	2	many	many	ADJ
ejpam-445	52	3	cases	case	NOUN
ejpam-445	52	4	the	the	DET
ejpam-445	52	5	wavelet	wavelet	NOUN
ejpam-445	52	6	experts	expert	NOUN
ejpam-445	52	7	prefer	prefer	VERB
ejpam-445	52	8	to	to	PART
ejpam-445	52	9	work	work	VERB
ejpam-445	52	10	with	with	ADP
ejpam-445	52	11	frames	frame	NOUN
ejpam-445	52	12	instead	instead	ADV
ejpam-445	52	13	of	of	ADP
ejpam-445	52	14	riesz	riesz	NOUN
ejpam-445	52	15	bases	basis	NOUN
ejpam-445	52	16	.	.	PUNCT
ejpam-445	53	1	the	the	DET
ejpam-445	53	2	recent	recent	ADJ
ejpam-445	53	3	development	development	NOUN
ejpam-445	53	4	and	and	CCONJ
ejpam-445	53	5	work	work	NOUN
ejpam-445	53	6	on	on	ADP
ejpam-445	53	7	frames	frame	NOUN
ejpam-445	53	8	and	and	CCONJ
ejpam-445	53	9	related	relate	VERB
ejpam-445	53	10	topics,(see[2][3][4	topics,(see[2][3][4	PROPN
ejpam-445	53	11	]	]	PUNCT
ejpam-445	53	12	)	)	PUNCT
ejpam-445	53	13	.	.	PUNCT
ejpam-445	54	1	in	in	ADP
ejpam-445	54	2	this	this	DET
ejpam-445	54	3	paper	paper	NOUN
ejpam-445	54	4	,	,	PUNCT
ejpam-445	54	5	we	we	PRON
ejpam-445	54	6	will	will	AUX
ejpam-445	54	7	use	use	VERB
ejpam-445	54	8	the	the	DET
ejpam-445	54	9	double	double	ADJ
ejpam-445	54	10	infinite	infinite	ADJ
ejpam-445	54	11	matrices	matrix	NOUN
ejpam-445	54	12	(	(	PUNCT
ejpam-445	54	13	see	see	VERB
ejpam-445	54	14	[	[	X
ejpam-445	54	15	9][10	9][10	NUM
ejpam-445	54	16	]	]	PUNCT
ejpam-445	54	17	)	)	PUNCT
ejpam-445	54	18	to	to	PART
ejpam-445	54	19	obtain	obtain	VERB
ejpam-445	54	20	the	the	DET
ejpam-445	54	21	frame	frame	NOUN
ejpam-445	54	22	conditions	condition	NOUN
ejpam-445	54	23	and	and	CCONJ
ejpam-445	54	24	prolate	prolate	ADJ
ejpam-445	54	25	spheroidal	spheroidal	NOUN
ejpam-445	54	26	wavelet	wavelet	NOUN
ejpam-445	54	27	coefficients	coefficient	NOUN
ejpam-445	54	28	.	.	PUNCT
ejpam-445	55	1	a	a	DET
ejpam-445	55	2	sequence	sequence	NOUN
ejpam-445	55	3	{	{	PUNCT
ejpam-445	55	4	xn	xn	NUM
ejpam-445	55	5	}	}	PUNCT
ejpam-445	55	6	in	in	ADP
ejpam-445	55	7	a	a	DET
ejpam-445	55	8	hilbert	hilbert	NOUN
ejpam-445	55	9	space	space	NOUN
ejpam-445	55	10	h	h	NOUN
ejpam-445	55	11	is	be	AUX
ejpam-445	55	12	a	a	DET
ejpam-445	55	13	frame	frame	NOUN
ejpam-445	55	14	if	if	SCONJ
ejpam-445	55	15	there	there	PRON
ejpam-445	55	16	exist	exist	VERB
ejpam-445	55	17	constants	constant	NOUN
ejpam-445	55	18	c1	c1	PROPN
ejpam-445	55	19	and	and	CCONJ
ejpam-445	55	20	c2	c2	PROPN
ejpam-445	55	21	,	,	PUNCT
ejpam-445	55	22	0	0	NUM
ejpam-445	55	23	<	<	X
ejpam-445	55	24	c1	c1	PROPN
ejpam-445	55	25	≤	≤	PROPN
ejpam-445	55	26	c2	c2	PROPN
ejpam-445	55	27	<	<	X
ejpam-445	55	28	∞	∞	PROPN
ejpam-445	55	29	,	,	PUNCT
ejpam-445	55	30	such	such	ADJ
ejpam-445	55	31	that	that	DET
ejpam-445	55	32	c1||	c1||	NOUN
ejpam-445	55	33	f	f	PROPN
ejpam-445	55	34	||	||	NOUN
ejpam-445	55	35	2	2	NUM
ejpam-445	55	36	≤	≤	NOUN
ejpam-445	55	37	∑	∑	PUNCT
ejpam-445	55	38	n∈z	n∈z	VERB
ejpam-445	55	39	|	|	NOUN
ejpam-445	55	40	〈	〈	PROPN
ejpam-445	55	41	f	f	NOUN
ejpam-445	55	42	,	,	PUNCT
ejpam-445	55	43	xn〉|	xn〉|	PROPN
ejpam-445	55	44	2	2	NUM
ejpam-445	55	45	≤	≤	NOUN
ejpam-445	55	46	c2||	c2||	PROPN
ejpam-445	55	47	f	f	NOUN
ejpam-445	55	48	||	||	NOUN
ejpam-445	56	1	2	2	NUM
ejpam-445	56	2	,	,	PUNCT
ejpam-445	56	3	(	(	PUNCT
ejpam-445	56	4	3	3	X
ejpam-445	56	5	)	)	PUNCT
ejpam-445	56	6	for	for	ADP
ejpam-445	56	7	all	all	DET
ejpam-445	56	8	f	f	PROPN
ejpam-445	56	9	∈	∈	PROPN
ejpam-445	56	10	h.	h.	NOUN
ejpam-445	56	11	the	the	DET
ejpam-445	56	12	spermium	spermium	NOUN
ejpam-445	56	13	of	of	ADP
ejpam-445	56	14	all	all	DET
ejpam-445	56	15	such	such	ADJ
ejpam-445	56	16	numbers	number	NOUN
ejpam-445	56	17	c1	c1	PROPN
ejpam-445	56	18	and	and	CCONJ
ejpam-445	56	19	infimum	infimum	ADJ
ejpam-445	56	20	of	of	ADP
ejpam-445	56	21	all	all	DET
ejpam-445	56	22	such	such	ADJ
ejpam-445	56	23	numbers	number	NOUN
ejpam-445	56	24	c2	c2	PROPN
ejpam-445	56	25	are	be	AUX
ejpam-445	56	26	called	call	VERB
ejpam-445	56	27	the	the	DET
ejpam-445	56	28	frame	frame	NOUN
ejpam-445	56	29	bounds	bound	NOUN
ejpam-445	56	30	of	of	ADP
ejpam-445	56	31	the	the	DET
ejpam-445	56	32	frame	frame	NOUN
ejpam-445	56	33	.	.	PUNCT
ejpam-445	57	1	the	the	DET
ejpam-445	57	2	frame	frame	NOUN
ejpam-445	57	3	is	be	AUX
ejpam-445	57	4	called	call	VERB
ejpam-445	57	5	tight	tight	ADJ
ejpam-445	57	6	frame	frame	NOUN
ejpam-445	57	7	when	when	SCONJ
ejpam-445	57	8	c1	c1	PROPN
ejpam-445	57	9	=	=	PROPN
ejpam-445	57	10	c2	c2	PROPN
ejpam-445	57	11	and	and	CCONJ
ejpam-445	57	12	is	be	AUX
ejpam-445	57	13	called	call	VERB
ejpam-445	57	14	normalized	normalize	VERB
ejpam-445	57	15	tight	tight	ADJ
ejpam-445	57	16	frame	frame	NOUN
ejpam-445	58	1	when	when	SCONJ
ejpam-445	58	2	c1	c1	PROPN
ejpam-445	58	3	=	=	PROPN
ejpam-445	58	4	c2	c2	PROPN
ejpam-445	58	5	=	=	SYM
ejpam-445	58	6	1	1	X
ejpam-445	58	7	.	.	PUNCT
ejpam-445	59	1	any	any	DET
ejpam-445	59	2	orthonormal	orthonormal	ADJ
ejpam-445	59	3	basis	basis	NOUN
ejpam-445	59	4	in	in	ADP
ejpam-445	59	5	a	a	DET
ejpam-445	59	6	hilbert	hilbert	NOUN
ejpam-445	59	7	space	space	NOUN
ejpam-445	59	8	h	h	NOUN
ejpam-445	59	9	is	be	AUX
ejpam-445	59	10	a	a	DET
ejpam-445	59	11	normalized	normalize	VERB
ejpam-445	59	12	tight	tight	ADJ
ejpam-445	59	13	frame	frame	NOUN
ejpam-445	59	14	.	.	PUNCT
ejpam-445	60	1	in	in	ADP
ejpam-445	60	2	another	another	DET
ejpam-445	60	3	paper[5	paper[5	NOUN
ejpam-445	60	4	]	]	X
ejpam-445	60	5	we	we	PRON
ejpam-445	60	6	have	have	AUX
ejpam-445	60	7	proved	prove	VERB
ejpam-445	60	8	that	that	SCONJ
ejpam-445	60	9	a	a	DET
ejpam-445	60	10	prolate	prolate	ADJ
ejpam-445	60	11	spheroidal	spheroidal	NOUN
ejpam-445	60	12	wavelet	wavelet	NOUN
ejpam-445	60	13	function	function	NOUN
ejpam-445	60	14	φm(t	φm(t	PUNCT
ejpam-445	60	15	−	−	PROPN
ejpam-445	60	16	2−mn	2−mn	NUM
ejpam-445	60	17	)	)	PUNCT
ejpam-445	60	18	=	=	SYM
ejpam-445	61	1	ϕ0,2mπ	ϕ0,2mπ	NOUN
ejpam-445	61	2	,	,	PUNCT
ejpam-445	61	3	τ(t	τ(t	PROPN
ejpam-445	61	4	−	−	PROPN
ejpam-445	61	5	2−mn	2−mn	NUM
ejpam-445	61	6	)	)	PUNCT
ejpam-445	61	7	∈	∈	PROPN
ejpam-445	61	8	l2(r	l2(r	PROPN
ejpam-445	61	9	)	)	PUNCT
ejpam-445	61	10	,	,	PUNCT
ejpam-445	61	11	constitute	constitute	VERB
ejpam-445	61	12	a	a	DET
ejpam-445	61	13	frame	frame	NOUN
ejpam-445	61	14	with	with	ADP
ejpam-445	61	15	frame	frame	NOUN
ejpam-445	61	16	bounds	bound	NOUN
ejpam-445	61	17	c1	c1	PROPN
ejpam-445	61	18	and	and	CCONJ
ejpam-445	61	19	c2	c2	PROPN
ejpam-445	61	20	,	,	PUNCT
ejpam-445	61	21	if	if	SCONJ
ejpam-445	61	22	any	any	DET
ejpam-445	61	23	f	f	PROPN
ejpam-445	61	24	∈	∈	PROPN
ejpam-445	61	25	l2(r	l2(r	PROPN
ejpam-445	61	26	)	)	PUNCT
ejpam-445	61	27	such	such	ADJ
ejpam-445	61	28	that	that	DET
ejpam-445	61	29	c1||	c1||	PROPN
ejpam-445	61	30	f	f	PROPN
ejpam-445	61	31	||	||	NOUN
ejpam-445	61	32	2	2	NUM
ejpam-445	61	33	≤	≤	NUM
ejpam-445	61	34	∞	∞	NUM
ejpam-445	61	35	∑	∑	PROPN
ejpam-445	61	36	m	m	PROPN
ejpam-445	61	37	,	,	PUNCT
ejpam-445	61	38	n=−∞	n=−∞	X
ejpam-445	62	1	|	|	ADV
ejpam-445	62	2	〈	〈	PROPN
ejpam-445	62	3	f	f	NOUN
ejpam-445	62	4	,	,	PUNCT
ejpam-445	62	5	φm(t	φm(t	PUNCT
ejpam-445	62	6	−	−	PROPN
ejpam-445	62	7	2−mn)〉|2	2−mn)〉|2	NUM
ejpam-445	62	8	≤	≤	NOUN
ejpam-445	62	9	c2||	c2||	PROPN
ejpam-445	63	1	f	f	NOUN
ejpam-445	63	2	||	||	NOUN
ejpam-445	64	1	2	2	X
ejpam-445	64	2	.	.	PUNCT
ejpam-445	64	3	let	let	VERB
ejpam-445	64	4	a	a	DET
ejpam-445	64	5	=	=	PUNCT
ejpam-445	64	6	a(m	a(m	NOUN
ejpam-445	64	7	,	,	PUNCT
ejpam-445	64	8	n	n	CCONJ
ejpam-445	64	9	,	,	PUNCT
ejpam-445	64	10	κ	κ	NOUN
ejpam-445	64	11	)	)	PUNCT
ejpam-445	64	12	=	=	SYM
ejpam-445	64	13	∫∞	∫∞	NOUN
ejpam-445	64	14	−∞	−∞	ADP
ejpam-445	64	15	φm(t	φm(t	NOUN
ejpam-445	64	16	−	−	PROPN
ejpam-445	64	17	2−mn)φm(t	2−mn)φm(t	NUM
ejpam-445	64	18	−	−	NUM
ejpam-445	65	1	2−mκ)d	2−mκ)d	NOUN
ejpam-445	65	2	t	t	PROPN
ejpam-445	65	3	be	be	AUX
ejpam-445	65	4	a	a	DET
ejpam-445	65	5	double	double	ADJ
ejpam-445	65	6	infinite	infinite	ADJ
ejpam-445	65	7	matrix	matrix	NOUN
ejpam-445	65	8	of	of	ADP
ejpam-445	65	9	real	real	ADJ
ejpam-445	65	10	numbers	number	NOUN
ejpam-445	65	11	.	.	PUNCT
ejpam-445	66	1	then	then	ADV
ejpam-445	66	2	,	,	PUNCT
ejpam-445	66	3	a	a	DET
ejpam-445	66	4	-	-	PUNCT
ejpam-445	66	5	transform	transform	NOUN
ejpam-445	66	6	of	of	ADP
ejpam-445	66	7	a	a	DET
ejpam-445	66	8	double	double	ADJ
ejpam-445	66	9	sequence	sequence	NOUN
ejpam-445	66	10	{	{	PUNCT
ejpam-445	66	11	φκm	φκm	NOUN
ejpam-445	66	12	}	}	PUNCT
ejpam-445	66	13	is	be	AUX
ejpam-445	66	14	defined	define	VERB
ejpam-445	66	15	as	as	ADP
ejpam-445	66	16	aφκm	aφκm	NOUN
ejpam-445	66	17	=	=	PUNCT
ejpam-445	66	18	∫	∫	PROPN
ejpam-445	66	19	∞	∞	PROPN
ejpam-445	66	20	−∞	−∞	X
ejpam-445	66	21	φm(t	φm(t	NOUN
ejpam-445	66	22	−	−	PROPN
ejpam-445	66	23	2−mn)φm(t	2−mn)φm(t	NUM
ejpam-445	66	24	−	−	NUM
ejpam-445	67	1	2−mκ)φκmd	2−mκ)φκmd	NUM
ejpam-445	67	2	t	t	PROPN
ejpam-445	67	3	d.	d.	PROPN
ejpam-445	67	4	kumar	kumar	PROPN
ejpam-445	67	5	/	/	SYM
ejpam-445	67	6	eur	eur	PROPN
ejpam-445	67	7	.	.	PUNCT
ejpam-445	68	1	j.	j.	PROPN
ejpam-445	68	2	pure	pure	PROPN
ejpam-445	68	3	appl	appl	PROPN
ejpam-445	68	4	.	.	PROPN
ejpam-445	68	5	math	math	PROPN
ejpam-445	68	6	,	,	PUNCT
ejpam-445	68	7	3	3	NUM
ejpam-445	68	8	(	(	PUNCT
ejpam-445	68	9	2010	2010	NUM
ejpam-445	68	10	)	)	PUNCT
ejpam-445	68	11	,	,	PUNCT
ejpam-445	68	12	717	717	NUM
ejpam-445	68	13	-	-	SYM
ejpam-445	68	14	724	724	NUM
ejpam-445	68	15	720	720	NUM
ejpam-445	68	16	which	which	PRON
ejpam-445	68	17	is	be	AUX
ejpam-445	68	18	called	call	VERB
ejpam-445	68	19	a	a	DET
ejpam-445	68	20	-	-	PUNCT
ejpam-445	68	21	means	means	NOUN
ejpam-445	68	22	of	of	ADP
ejpam-445	68	23	the	the	DET
ejpam-445	68	24	sequenceφκm	sequenceφκm	NOUN
ejpam-445	68	25	.	.	PUNCT
ejpam-445	69	1	this	this	DET
ejpam-445	69	2	definition	definition	NOUN
ejpam-445	69	3	is	be	AUX
ejpam-445	69	4	due	due	ADJ
ejpam-445	69	5	to	to	PART
ejpam-445	69	6	moricz	moricz	VERB
ejpam-445	69	7	and	and	CCONJ
ejpam-445	69	8	rhoades	rhoade	VERB
ejpam-445	69	9	[	[	X
ejpam-445	69	10	9	9	NUM
ejpam-445	69	11	]	]	PUNCT
ejpam-445	69	12	.	.	PUNCT
ejpam-445	70	1	a	a	DET
ejpam-445	70	2	double	double	ADJ
ejpam-445	70	3	matrix	matrix	NOUN
ejpam-445	70	4	a=	a=	VERB
ejpam-445	70	5	a(m	a(m	PROPN
ejpam-445	70	6	,	,	PUNCT
ejpam-445	70	7	n	n	CCONJ
ejpam-445	70	8	,	,	PUNCT
ejpam-445	70	9	κ	κ	NOUN
ejpam-445	70	10	)	)	PUNCT
ejpam-445	70	11	is	be	AUX
ejpam-445	70	12	satisfied	satisfied	ADJ
ejpam-445	70	13	the	the	DET
ejpam-445	70	14	following	follow	VERB
ejpam-445	70	15	conditions	condition	NOUN
ejpam-445	70	16	:	:	PUNCT
ejpam-445	70	17	(	(	PUNCT
ejpam-445	70	18	i	i	NOUN
ejpam-445	70	19	)	)	PUNCT
ejpam-445	70	20	limm→∞	limm→∞	PROPN
ejpam-445	70	21	a(m	a(m	NOUN
ejpam-445	70	22	,	,	PUNCT
ejpam-445	70	23	n	n	CCONJ
ejpam-445	70	24	,	,	PUNCT
ejpam-445	70	25	κ	κ	NOUN
ejpam-445	70	26	)	)	PUNCT
ejpam-445	70	27	=	=	SYM
ejpam-445	70	28	1	1	NUM
ejpam-445	70	29	,	,	PUNCT
ejpam-445	70	30	n	n	CCONJ
ejpam-445	70	31	,	,	PUNCT
ejpam-445	70	32	κ	κ	PROPN
ejpam-445	70	33	∈	∈	PROPN
ejpam-445	70	34	z	z	X
ejpam-445	70	35	(	(	PUNCT
ejpam-445	70	36	ii	ii	NOUN
ejpam-445	70	37	)	)	PUNCT
ejpam-445	70	38	||a||=	||a||=	NOUN
ejpam-445	70	39	supm>0	supm>0	PUNCT
ejpam-445	70	40	|a(m	|a(m	PROPN
ejpam-445	70	41	,	,	PUNCT
ejpam-445	70	42	n	n	CCONJ
ejpam-445	70	43	,	,	PUNCT
ejpam-445	70	44	κ)|	κ)|	NOUN
ejpam-445	70	45	<	<	X
ejpam-445	70	46	∞	∞	PROPN
ejpam-445	70	47	,	,	PUNCT
ejpam-445	70	48	n	n	CCONJ
ejpam-445	70	49	,	,	PUNCT
ejpam-445	70	50	κ	κ	PROPN
ejpam-445	70	51	∈	∈	PROPN
ejpam-445	70	52	z.	z.	PROPN
ejpam-445	71	1	the	the	DET
ejpam-445	71	2	approximation	approximation	NOUN
ejpam-445	71	3	of	of	ADP
ejpam-445	71	4	a	a	DET
ejpam-445	71	5	function	function	NOUN
ejpam-445	71	6	in	in	ADP
ejpam-445	71	7	l2(r	l2(r	NOUN
ejpam-445	71	8	)	)	PUNCT
ejpam-445	71	9	by	by	ADP
ejpam-445	71	10	function	function	NOUN
ejpam-445	71	11	in	in	ADP
ejpam-445	71	12	vm	vm	PROPN
ejpam-445	71	13	is	be	AUX
ejpam-445	71	14	given	give	VERB
ejpam-445	71	15	by	by	ADP
ejpam-445	71	16	a	a	DET
ejpam-445	71	17	series	series	NOUN
ejpam-445	71	18	of	of	ADP
ejpam-445	71	19	the	the	DET
ejpam-445	71	20	form	form	NOUN
ejpam-445	71	21	f	f	PROPN
ejpam-445	71	22	(	(	PUNCT
ejpam-445	71	23	t	t	PROPN
ejpam-445	71	24	)	)	PUNCT
ejpam-445	71	25	=	=	PUNCT
ejpam-445	72	1	∑	∑	PUNCT
ejpam-445	72	2	κ	κ	X
ejpam-445	72	3	bm	bm	PROPN
ejpam-445	72	4	κ	κ	PROPN
ejpam-445	72	5	φm(t	φm(t	PUNCT
ejpam-445	72	6	−	−	PROPN
ejpam-445	72	7	2−mκ	2−mκ	NUM
ejpam-445	72	8	)	)	PUNCT
ejpam-445	72	9	(	(	PUNCT
ejpam-445	72	10	4	4	X
ejpam-445	72	11	)	)	PUNCT
ejpam-445	72	12	where	where	SCONJ
ejpam-445	72	13	the	the	DET
ejpam-445	72	14	coefficient	coefficient	NOUN
ejpam-445	72	15	may	may	AUX
ejpam-445	72	16	be	be	AUX
ejpam-445	72	17	obtained	obtain	VERB
ejpam-445	72	18	from	from	ADP
ejpam-445	72	19	the	the	DET
ejpam-445	72	20	dual	dual	ADJ
ejpam-445	72	21	riesz	riesz	NOUN
ejpam-445	72	22	basis	basis	NOUN
ejpam-445	72	23	.	.	PUNCT
ejpam-445	73	1	in	in	ADP
ejpam-445	73	2	this	this	DET
ejpam-445	73	3	case	case	NOUN
ejpam-445	73	4	the	the	DET
ejpam-445	73	5	result	result	NOUN
ejpam-445	73	6	is	be	AUX
ejpam-445	73	7	the	the	DET
ejpam-445	73	8	projection	projection	NOUN
ejpam-445	73	9	of	of	ADP
ejpam-445	73	10	a	a	DET
ejpam-445	73	11	function	function	NOUN
ejpam-445	73	12	f	f	X
ejpam-445	73	13	onto	onto	ADP
ejpam-445	73	14	vm	vm	PROPN
ejpam-445	73	15	.	.	PUNCT
ejpam-445	74	1	the	the	DET
ejpam-445	74	2	coefficients	coefficient	NOUN
ejpam-445	74	3	for	for	ADP
ejpam-445	74	4	the	the	DET
ejpam-445	74	5	projection	projection	NOUN
ejpam-445	74	6	are	be	AUX
ejpam-445	74	7	bm	bm	PROPN
ejpam-445	74	8	κ	κ	PROPN
ejpam-445	74	9	=	=	SYM
ejpam-445	74	10	∫	∫	PROPN
ejpam-445	74	11	∞	∞	PROPN
ejpam-445	75	1	−∞	−∞	X
ejpam-445	75	2	f	f	PROPN
ejpam-445	75	3	(	(	PUNCT
ejpam-445	75	4	t)φ̃m(t	t)φ̃m(t	PROPN
ejpam-445	75	5	−	−	PROPN
ejpam-445	75	6	2−mκ)d	2−mκ)d	NUM
ejpam-445	76	1	t.	t.	NOUN
ejpam-445	76	2	the	the	DET
ejpam-445	76	3	kernel	kernel	NOUN
ejpam-445	76	4	of	of	ADP
ejpam-445	76	5	this	this	DET
ejpam-445	76	6	projection	projection	NOUN
ejpam-445	76	7	is	be	AUX
ejpam-445	76	8	given	give	VERB
ejpam-445	76	9	by	by	ADP
ejpam-445	76	10	qm(x	qm(x	NOUN
ejpam-445	76	11	,	,	PUNCT
ejpam-445	76	12	t	t	PROPN
ejpam-445	76	13	)	)	PUNCT
ejpam-445	76	14	=	=	PUNCT
ejpam-445	77	1	∑	∑	PUNCT
ejpam-445	77	2	κ	κ	X
ejpam-445	77	3	φm(x	φm(x	PUNCT
ejpam-445	77	4	−	−	PROPN
ejpam-445	77	5	2−mκ)φ̃m(t	2−mκ)φ̃m(t	NOUN
ejpam-445	77	6	−	−	NOUN
ejpam-445	77	7	2−mκ	2−mκ	NUM
ejpam-445	77	8	)	)	PUNCT
ejpam-445	77	9	,	,	PUNCT
ejpam-445	77	10	(	(	PUNCT
ejpam-445	77	11	5	5	X
ejpam-445	77	12	)	)	PUNCT
ejpam-445	77	13	here	here	ADV
ejpam-445	77	14	φ̃m	φ̃m	NOUN
ejpam-445	77	15	is	be	AUX
ejpam-445	77	16	biorthogonal	biorthogonal	ADJ
ejpam-445	77	17	to	to	PART
ejpam-445	77	18	φm	φm	VERB
ejpam-445	77	19	.	.	PROPN
ejpam-445	78	1	3	3	X
ejpam-445	78	2	.	.	X
ejpam-445	78	3	main	main	ADJ
ejpam-445	78	4	results	result	NOUN
ejpam-445	78	5	in	in	ADP
ejpam-445	78	6	this	this	DET
ejpam-445	78	7	section	section	NOUN
ejpam-445	78	8	we	we	PRON
ejpam-445	78	9	prove	prove	VERB
ejpam-445	78	10	the	the	DET
ejpam-445	78	11	following	follow	VERB
ejpam-445	78	12	theorems	theorem	NOUN
ejpam-445	78	13	.	.	PUNCT
ejpam-445	79	1	theorem	theorem	NOUN
ejpam-445	79	2	1	1	NUM
ejpam-445	79	3	.	.	PUNCT
ejpam-445	80	1	let	let	AUX
ejpam-445	80	2	a=	a=	VERB
ejpam-445	80	3	a(m	a(m	VERB
ejpam-445	80	4	,	,	PUNCT
ejpam-445	80	5	n	n	CCONJ
ejpam-445	80	6	,	,	PUNCT
ejpam-445	80	7	κ	κ	X
ejpam-445	80	8	be	be	AUX
ejpam-445	80	9	a	a	DET
ejpam-445	80	10	double	double	ADJ
ejpam-445	80	11	infinite	infinite	ADJ
ejpam-445	80	12	matrix	matrix	NOUN
ejpam-445	80	13	.	.	PUNCT
ejpam-445	81	1	if	if	SCONJ
ejpam-445	81	2	f	f	PROPN
ejpam-445	81	3	(	(	PUNCT
ejpam-445	81	4	t	t	PROPN
ejpam-445	81	5	)	)	PUNCT
ejpam-445	81	6	=	=	PUNCT
ejpam-445	81	7	∑	∑	PUNCT
ejpam-445	81	8	κ	κ	X
ejpam-445	81	9	bm	bm	PROPN
ejpam-445	81	10	κ	κ	PROPN
ejpam-445	81	11	φm(t	φm(t	PUNCT
ejpam-445	81	12	−	−	PROPN
ejpam-445	81	13	2−mκ	2−mκ	NUM
ejpam-445	81	14	)	)	PUNCT
ejpam-445	81	15	is	be	AUX
ejpam-445	81	16	a	a	DET
ejpam-445	81	17	ps	ps	NOUN
ejpam-445	81	18	wavelet	wavelet	NOUN
ejpam-445	81	19	expansion	expansion	NOUN
ejpam-445	81	20	of	of	ADP
ejpam-445	81	21	f	f	PROPN
ejpam-445	81	22	∈	∈	PROPN
ejpam-445	81	23	l2(r	l2(r	PROPN
ejpam-445	81	24	)	)	PUNCT
ejpam-445	81	25	with	with	ADP
ejpam-445	81	26	wavelet	wavelet	NOUN
ejpam-445	81	27	coefficients	coefficient	NOUN
ejpam-445	81	28	bm	bm	PROPN
ejpam-445	81	29	κ	κ	PROPN
ejpam-445	81	30	=	=	SYM
ejpam-445	81	31	∫	∫	PROPN
ejpam-445	81	32	∞	∞	PROPN
ejpam-445	82	1	−∞	−∞	X
ejpam-445	82	2	f	f	PROPN
ejpam-445	82	3	(	(	PUNCT
ejpam-445	82	4	t)φ̃m(t	t)φ̃m(t	PROPN
ejpam-445	82	5	−	−	PROPN
ejpam-445	82	6	2−mκ)d	2−mκ)d	NUM
ejpam-445	82	7	t	t	NOUN
ejpam-445	82	8	=	=	SYM
ejpam-445	82	9	〈	〈	PROPN
ejpam-445	82	10	f	f	NOUN
ejpam-445	82	11	,	,	PUNCT
ejpam-445	82	12	φ̃m(t	φ̃m(t	NOUN
ejpam-445	82	13	−	−	VERB
ejpam-445	82	14	2−mκ	2−mκ	NUM
ejpam-445	82	15	)	)	PUNCT
ejpam-445	82	16	〉	〉	NOUN
ejpam-445	82	17	,	,	PUNCT
ejpam-445	82	18	then	then	ADV
ejpam-445	82	19	the	the	DET
ejpam-445	82	20	frame	frame	NOUN
ejpam-445	82	21	condition	condition	NOUN
ejpam-445	82	22	for	for	ADP
ejpam-445	82	23	a	a	DET
ejpam-445	82	24	-	-	PUNCT
ejpam-445	82	25	transform	transform	NOUN
ejpam-445	82	26	of	of	ADP
ejpam-445	82	27	f	f	PROPN
ejpam-445	82	28	∈	∈	PROPN
ejpam-445	82	29	l2(r	l2(r	PROPN
ejpam-445	82	30	)	)	PUNCT
ejpam-445	82	31	is	be	AUX
ejpam-445	82	32	c1||	c1||	PROPN
ejpam-445	82	33	f	f	PROPN
ejpam-445	82	34	||	||	NOUN
ejpam-445	82	35	2	2	NUM
ejpam-445	82	36	2	2	NUM
ejpam-445	82	37	≤	≤	NOUN
ejpam-445	82	38	∑	∑	PUNCT
ejpam-445	82	39	κ	κ	X
ejpam-445	82	40	|〈af	|〈af	PROPN
ejpam-445	82	41	,	,	PUNCT
ejpam-445	82	42	qm(y	qm(y	NUM
ejpam-445	82	43	,	,	PUNCT
ejpam-445	83	1	t)〉|2	t)〉|2	PROPN
ejpam-445	83	2	≤	≤	PUNCT
ejpam-445	83	3	c2||	c2||	PROPN
ejpam-445	83	4	f	f	NOUN
ejpam-445	83	5	||	||	NOUN
ejpam-445	84	1	2	2	NUM
ejpam-445	84	2	2	2	NUM
ejpam-445	84	3	(	(	PUNCT
ejpam-445	84	4	6	6	NUM
ejpam-445	84	5	)	)	PUNCT
ejpam-445	84	6	where	where	SCONJ
ejpam-445	84	7	qm	qm	PROPN
ejpam-445	84	8	is	be	AUX
ejpam-445	84	9	given	give	VERB
ejpam-445	84	10	by	by	ADP
ejpam-445	84	11	(	(	PUNCT
ejpam-445	84	12	5	5	NUM
ejpam-445	84	13	)	)	PUNCT
ejpam-445	84	14	,	,	PUNCT
ejpam-445	84	15	af	af	PROPN
ejpam-445	84	16	is	be	AUX
ejpam-445	84	17	the	the	DET
ejpam-445	84	18	a	a	DET
ejpam-445	84	19	-	-	PUNCT
ejpam-445	84	20	transform	transform	NOUN
ejpam-445	84	21	of	of	ADP
ejpam-445	84	22	f	f	PROPN
ejpam-445	84	23	and	and	CCONJ
ejpam-445	84	24	0	0	NUM
ejpam-445	84	25	<	<	X
ejpam-445	84	26	c1	c1	PROPN
ejpam-445	84	27	≤	≤	PROPN
ejpam-445	84	28	c2	c2	PROPN
ejpam-445	84	29	<	<	PROPN
ejpam-445	84	30	∞.	∞.	PROPN
ejpam-445	84	31	d.	d.	PROPN
ejpam-445	84	32	kumar	kumar	PROPN
ejpam-445	84	33	/	/	SYM
ejpam-445	84	34	eur	eur	PROPN
ejpam-445	84	35	.	.	PUNCT
ejpam-445	85	1	j.	j.	PROPN
ejpam-445	85	2	pure	pure	PROPN
ejpam-445	85	3	appl	appl	PROPN
ejpam-445	85	4	.	.	PROPN
ejpam-445	85	5	math	math	PROPN
ejpam-445	85	6	,	,	PUNCT
ejpam-445	85	7	3	3	NUM
ejpam-445	85	8	(	(	PUNCT
ejpam-445	85	9	2010	2010	NUM
ejpam-445	85	10	)	)	PUNCT
ejpam-445	85	11	,	,	PUNCT
ejpam-445	85	12	717	717	NUM
ejpam-445	85	13	-	-	SYM
ejpam-445	85	14	724	724	NUM
ejpam-445	85	15	721	721	NUM
ejpam-445	85	16	proof	proof	NOUN
ejpam-445	85	17	.	.	PUNCT
ejpam-445	86	1	by	by	ADP
ejpam-445	86	2	(	(	PUNCT
ejpam-445	86	3	3	3	NUM
ejpam-445	86	4	)	)	PUNCT
ejpam-445	86	5	,	,	PUNCT
ejpam-445	86	6	we	we	PRON
ejpam-445	86	7	can	can	AUX
ejpam-445	86	8	write	write	VERB
ejpam-445	86	9	f	f	PROPN
ejpam-445	86	10	(	(	PUNCT
ejpam-445	86	11	t	t	PROPN
ejpam-445	86	12	)	)	PUNCT
ejpam-445	86	13	=	=	PUNCT
ejpam-445	87	1	∑	∑	PUNCT
ejpam-445	87	2	κ	κ	X
ejpam-445	87	3	bm	bm	PROPN
ejpam-445	87	4	κ	κ	PROPN
ejpam-445	87	5	φm(t	φm(t	PUNCT
ejpam-445	87	6	−	−	PROPN
ejpam-445	87	7	2−mκ	2−mκ	NUM
ejpam-445	87	8	)	)	PUNCT
ejpam-445	88	1	taking	take	VERB
ejpam-445	88	2	a	a	DET
ejpam-445	88	3	-	-	PUNCT
ejpam-445	88	4	transform	transform	NOUN
ejpam-445	88	5	of	of	ADP
ejpam-445	88	6	f	f	PROPN
ejpam-445	88	7	,	,	PUNCT
ejpam-445	88	8	we	we	PRON
ejpam-445	88	9	get	get	VERB
ejpam-445	88	10	af	af	NOUN
ejpam-445	88	11	=	=	PUNCT
ejpam-445	88	12	∫	∫	PROPN
ejpam-445	88	13	∞	∞	PROPN
ejpam-445	89	1	−∞	−∞	X
ejpam-445	89	2	φm(t	φm(t	ADJ
ejpam-445	89	3	−	−	PROPN
ejpam-445	89	4	2−mn)φm(t	2−mn)φm(t	NUM
ejpam-445	89	5	−	−	NUM
ejpam-445	89	6	2−mκ)σκbm	2−mκ)σκbm	NOUN
ejpam-445	90	1	κφm(t	κφm(t	NOUN
ejpam-445	90	2	−	−	PROPN
ejpam-445	91	1	2−mκ)d	2−mκ)d	NUM
ejpam-445	91	2	t	t	NOUN
ejpam-445	91	3	=	=	PUNCT
ejpam-445	91	4	σκ	σκ	NOUN
ejpam-445	91	5	∫	∫	VERB
ejpam-445	91	6	∞	∞	PROPN
ejpam-445	91	7	−∞	−∞	X
ejpam-445	91	8	φm(t	φm(t	NOUN
ejpam-445	91	9	−	−	PROPN
ejpam-445	91	10	2−mn)φm(t	2−mn)φm(t	NUM
ejpam-445	91	11	−	−	PROPN
ejpam-445	91	12	2−mκ	2−mκ	NUM
ejpam-445	91	13	)	)	PUNCT
ejpam-445	91	14	∫	∫	PROPN
ejpam-445	92	1	∞	∞	PROPN
ejpam-445	93	1	−∞	−∞	X
ejpam-445	93	2	f	f	PROPN
ejpam-445	93	3	(	(	PUNCT
ejpam-445	93	4	y)φ̃m(y	y)φ̃m(y	PROPN
ejpam-445	93	5	−	−	PROPN
ejpam-445	93	6	2−mκ)φm(t	2−mκ)φm(t	NUM
ejpam-445	93	7	−	−	NOUN
ejpam-445	94	1	2−mκ)d	2−mκ)d	NUM
ejpam-445	94	2	yd	yd	ADP
ejpam-445	94	3	t	t	NOUN
ejpam-445	94	4	=	=	SYM
ejpam-445	94	5	σκ〈af	σκ〈af	PROPN
ejpam-445	94	6	,	,	PUNCT
ejpam-445	94	7	φ̃m(y	φ̃m(y	NOUN
ejpam-445	94	8	−	−	ADP
ejpam-445	94	9	2−mκ)〉φm(t	2−mκ)〉φm(t	NOUN
ejpam-445	95	1	−	−	ADP
ejpam-445	95	2	2−mκ	2−mκ	NUM
ejpam-445	95	3	)	)	PUNCT
ejpam-445	96	1	=	=	PUNCT
ejpam-445	96	2	〈	〈	SYM
ejpam-445	96	3	af	af	PROPN
ejpam-445	96	4	,	,	PUNCT
ejpam-445	96	5	σκφ̃m(y	σκφ̃m(y	VERB
ejpam-445	96	6	−	−	PROPN
ejpam-445	96	7	2−mκ)φm(t	2−mκ)φm(t	NOUN
ejpam-445	96	8	−	−	ADP
ejpam-445	96	9	2−mκ	2−mκ	NUM
ejpam-445	96	10	)	)	PUNCT
ejpam-445	96	11	〉	〉	NOUN
ejpam-445	96	12	=	=	PUNCT
ejpam-445	96	13	〈	〈	PROPN
ejpam-445	96	14	af	af	NOUN
ejpam-445	96	15	,	,	PUNCT
ejpam-445	96	16	qm(y	qm(y	NUM
ejpam-445	96	17	,	,	PUNCT
ejpam-445	96	18	t	t	NOUN
ejpam-445	96	19	)	)	PUNCT
ejpam-445	96	20	〉	〉	NOUN
ejpam-445	96	21	,	,	PUNCT
ejpam-445	96	22	therefore	therefore	ADV
ejpam-445	96	23	σκ|〈af	σκ|〈af	NOUN
ejpam-445	96	24	,	,	PUNCT
ejpam-445	96	25	qm(y	qm(y	NUM
ejpam-445	96	26	,	,	PUNCT
ejpam-445	96	27	t)〉|2	t)〉|2	PROPN
ejpam-445	96	28	≤	≤	ADV
ejpam-445	97	1	σκ	σκ	ADV
ejpam-445	97	2	∫	∫	VERB
ejpam-445	97	3	∞	∞	PROPN
ejpam-445	98	1	−∞	−∞	ADP
ejpam-445	98	2	|af	|af	NOUN
ejpam-445	98	3	qm(y	qm(y	PUNCT
ejpam-445	98	4	,	,	PUNCT
ejpam-445	98	5	t)|2d	t)|2d	ADP
ejpam-445	98	6	t	t	NOUN
ejpam-445	98	7	≤	≤	NUM
ejpam-445	98	8	σκ	σκ	ADV
ejpam-445	98	9	∫	∫	VERB
ejpam-445	98	10	∞	∞	PROPN
ejpam-445	98	11	−∞	−∞	X
ejpam-445	98	12	(	(	PUNCT
ejpam-445	98	13	af	af	PROPN
ejpam-445	98	14	)	)	PUNCT
ejpam-445	98	15	2d	2d	PROPN
ejpam-445	99	1	t	t	NOUN
ejpam-445	99	2	∫	∫	PROPN
ejpam-445	99	3	∞	∞	PROPN
ejpam-445	100	1	−∞	−∞	ADP
ejpam-445	100	2	[	[	X
ejpam-445	100	3	s2m(y	s2m(y	PROPN
ejpam-445	100	4	−	−	PROPN
ejpam-445	100	5	t)]2d	t)]2d	PROPN
ejpam-445	100	6	t	t	NOUN
ejpam-445	100	7	=	=	PUNCT
ejpam-445	100	8	||a||22||	||a||22||	PROPN
ejpam-445	100	9	f	f	NOUN
ejpam-445	100	10	||	||	NOUN
ejpam-445	100	11	2	2	NUM
ejpam-445	100	12	2	2	NUM
ejpam-445	100	13	(	(	PUNCT
ejpam-445	100	14	7	7	NUM
ejpam-445	100	15	)	)	PUNCT
ejpam-445	100	16	(	(	PUNCT
ejpam-445	100	17	since	since	SCONJ
ejpam-445	100	18	qm(y	qm(y	NUM
ejpam-445	100	19	,	,	PUNCT
ejpam-445	100	20	t	t	PROPN
ejpam-445	100	21	)	)	PUNCT
ejpam-445	100	22	=	=	SYM
ejpam-445	100	23	sin2mπ(y−t	sin2mπ(y−t	X
ejpam-445	100	24	)	)	PUNCT
ejpam-445	100	25	π(y−t	π(y−t	PROPN
ejpam-445	100	26	)	)	PUNCT
ejpam-445	100	27	=	=	PUNCT
ejpam-445	101	1	s2m(y	s2m(y	PROPN
ejpam-445	101	2	−	−	PROPN
ejpam-445	101	3	t	t	PROPN
ejpam-445	101	4	)	)	PUNCT
ejpam-445	101	5	)	)	PUNCT
ejpam-445	102	1	now	now	ADV
ejpam-445	102	2	,	,	PUNCT
ejpam-445	102	3	for	for	ADP
ejpam-445	102	4	any	any	DET
ejpam-445	102	5	arbitrary	arbitrary	ADJ
ejpam-445	102	6	f	f	PROPN
ejpam-445	102	7	∈	∈	PROPN
ejpam-445	102	8	l2(r	l2(r	PROPN
ejpam-445	102	9	)	)	PUNCT
ejpam-445	102	10	,	,	PUNCT
ejpam-445	102	11	define	define	VERB
ejpam-445	102	12	f̃	f̃	PROPN
ejpam-445	102	13	=	=	PUNCT
ejpam-445	103	1	[	[	X
ejpam-445	103	2	σκ|〈af	σκ|〈af	NOUN
ejpam-445	103	3	,	,	PUNCT
ejpam-445	103	4	qm(y	qm(y	NUM
ejpam-445	103	5	,	,	PUNCT
ejpam-445	103	6	t)〉|2]−1/2	t)〉|2]−1/2	PROPN
ejpam-445	103	7	f	f	X
ejpam-445	103	8	.	.	PUNCT
ejpam-445	104	1	clearly	clearly	ADV
ejpam-445	104	2	〈	〈	DET
ejpam-445	104	3	af̃	af̃	NOUN
ejpam-445	104	4	,	,	PUNCT
ejpam-445	104	5	qm(y	qm(y	NUM
ejpam-445	104	6	,	,	PUNCT
ejpam-445	104	7	t	t	NOUN
ejpam-445	104	8	)	)	PUNCT
ejpam-445	104	9	〉	〉	NOUN
ejpam-445	105	1	=	=	PUNCT
ejpam-445	106	1	[	[	X
ejpam-445	106	2	σκ|〈af	σκ|〈af	NOUN
ejpam-445	106	3	,	,	PUNCT
ejpam-445	106	4	qm(y	qm(y	NUM
ejpam-445	106	5	,	,	PUNCT
ejpam-445	106	6	t)〉|2]−1/2〈af	t)〉|2]−1/2〈af	NOUN
ejpam-445	106	7	,	,	PUNCT
ejpam-445	106	8	qm(y	qm(y	NUM
ejpam-445	106	9	,	,	PUNCT
ejpam-445	106	10	t	t	NOUN
ejpam-445	106	11	)	)	PUNCT
ejpam-445	106	12	〉	〉	NOUN
ejpam-445	106	13	then	then	ADV
ejpam-445	106	14	σκ|〈af	σκ|〈af	NOUN
ejpam-445	106	15	,	,	PUNCT
ejpam-445	106	16	qm(y	qm(y	NUM
ejpam-445	106	17	,	,	PUNCT
ejpam-445	106	18	t)〉|2	t)〉|2	PROPN
ejpam-445	106	19	≤	≤	ADV
ejpam-445	106	20	1	1	NUM
ejpam-445	106	21	.	.	PUNCT
ejpam-445	107	1	if	if	SCONJ
ejpam-445	107	2	there	there	PRON
ejpam-445	107	3	exist	exist	VERB
ejpam-445	107	4	a	a	DET
ejpam-445	107	5	positive	positive	ADJ
ejpam-445	107	6	constant	constant	ADJ
ejpam-445	107	7	α	α	NOUN
ejpam-445	107	8	,	,	PUNCT
ejpam-445	107	9	then	then	ADV
ejpam-445	107	10	||af̃	||af̃	VERB
ejpam-445	107	11	||22	||22	NOUN
ejpam-445	107	12	≤	≤	NUM
ejpam-445	107	13	α	α	NOUN
ejpam-445	107	14	,	,	PUNCT
ejpam-445	107	15	so	so	SCONJ
ejpam-445	107	16	[	[	X
ejpam-445	107	17	σκ|〈af	σκ|〈af	NOUN
ejpam-445	107	18	,	,	PUNCT
ejpam-445	107	19	qm(y	qm(y	NUM
ejpam-445	107	20	,	,	PUNCT
ejpam-445	107	21	t)〉|2]−1||af	t)〉|2]−1||af	X
ejpam-445	107	22	||22	||22	NOUN
ejpam-445	107	23	≤	≤	X
ejpam-445	107	24	α	α	NOUN
ejpam-445	107	25	or	or	CCONJ
ejpam-445	107	26	[	[	X
ejpam-445	107	27	σκ|〈af	σκ|〈af	NOUN
ejpam-445	107	28	,	,	PUNCT
ejpam-445	107	29	qm(y	qm(y	NUM
ejpam-445	107	30	,	,	PUNCT
ejpam-445	107	31	t)〉|2]−1|〈af	t)〉|2]−1|〈af	NOUN
ejpam-445	107	32	,	,	PUNCT
ejpam-445	107	33	qm(y	qm(y	NUM
ejpam-445	107	34	,	,	PUNCT
ejpam-445	107	35	t)〉|2	t)〉|2	PROPN
ejpam-445	107	36	≤	≤	PUNCT
ejpam-445	107	37	α	α	NOUN
ejpam-445	107	38	≤	≤	NOUN
ejpam-445	108	1	[	[	X
ejpam-445	108	2	σκ|〈af	σκ|〈af	NOUN
ejpam-445	108	3	,	,	PUNCT
ejpam-445	108	4	qm(y	qm(y	NUM
ejpam-445	108	5	,	,	PUNCT
ejpam-445	108	6	t)〉|2]−1||a||22||	t)〉|2]−1||a||22||	VERB
ejpam-445	108	7	f	f	NOUN
ejpam-445	108	8	||	||	NOUN
ejpam-445	108	9	2	2	NUM
ejpam-445	108	10	2	2	NUM
ejpam-445	108	11	≤	≤	NOUN
ejpam-445	108	12	α	α	PROPN
ejpam-445	108	13	d.	d.	PROPN
ejpam-445	108	14	kumar	kumar	PROPN
ejpam-445	108	15	/	/	SYM
ejpam-445	108	16	eur	eur	PROPN
ejpam-445	108	17	.	.	PUNCT
ejpam-445	109	1	j.	j.	PROPN
ejpam-445	109	2	pure	pure	PROPN
ejpam-445	109	3	appl	appl	PROPN
ejpam-445	109	4	.	.	PROPN
ejpam-445	109	5	math	math	PROPN
ejpam-445	109	6	,	,	PUNCT
ejpam-445	109	7	3	3	NUM
ejpam-445	109	8	(	(	PUNCT
ejpam-445	109	9	2010	2010	NUM
ejpam-445	109	10	)	)	PUNCT
ejpam-445	109	11	,	,	PUNCT
ejpam-445	109	12	717	717	NUM
ejpam-445	109	13	-	-	SYM
ejpam-445	109	14	724	724	NUM
ejpam-445	109	15	722	722	NUM
ejpam-445	109	16	or	or	CCONJ
ejpam-445	109	17	c1||	c1||	PROPN
ejpam-445	109	18	f	f	PROPN
ejpam-445	109	19	||	||	NOUN
ejpam-445	109	20	2	2	NUM
ejpam-445	109	21	2	2	NUM
ejpam-445	109	22	≤	≤	NUM
ejpam-445	109	23	σκ|〈af	σκ|〈af	NOUN
ejpam-445	109	24	,	,	PUNCT
ejpam-445	109	25	qm(y	qm(y	NUM
ejpam-445	109	26	,	,	PUNCT
ejpam-445	109	27	t)〉|2	t)〉|2	PROPN
ejpam-445	109	28	.	.	PUNCT
ejpam-445	110	1	(	(	PUNCT
ejpam-445	110	2	8)	8)	NUM
ejpam-445	110	3	combining	combine	VERB
ejpam-445	110	4	(	(	PUNCT
ejpam-445	110	5	7	7	NUM
ejpam-445	110	6	)	)	PUNCT
ejpam-445	110	7	and	and	CCONJ
ejpam-445	110	8	(	(	PUNCT
ejpam-445	110	9	8)	8)	NUM
ejpam-445	110	10	we	we	PRON
ejpam-445	110	11	get	get	VERB
ejpam-445	110	12	c1||	c1||	PROPN
ejpam-445	110	13	f	f	PROPN
ejpam-445	110	14	||	||	NOUN
ejpam-445	110	15	2	2	NUM
ejpam-445	110	16	2	2	NUM
ejpam-445	110	17	≤	≤	NUM
ejpam-445	110	18	σκ|〈af	σκ|〈af	NOUN
ejpam-445	110	19	,	,	PUNCT
ejpam-445	110	20	qm(y	qm(y	NUM
ejpam-445	110	21	,	,	PUNCT
ejpam-445	110	22	t)〉|2	t)〉|2	PROPN
ejpam-445	110	23	≤	≤	PUNCT
ejpam-445	110	24	c2||	c2||	PROPN
ejpam-445	110	25	f	f	NOUN
ejpam-445	110	26	||	||	NOUN
ejpam-445	111	1	2	2	NUM
ejpam-445	111	2	2	2	NUM
ejpam-445	111	3	.	.	PUNCT
ejpam-445	112	1	hence	hence	ADV
ejpam-445	112	2	the	the	DET
ejpam-445	112	3	proof	proof	NOUN
ejpam-445	112	4	is	be	AUX
ejpam-445	112	5	completed	complete	VERB
ejpam-445	112	6	.	.	PUNCT
ejpam-445	113	1	theorem	theorem	NOUN
ejpam-445	113	2	2	2	NUM
ejpam-445	113	3	.	.	PUNCT
ejpam-445	114	1	if	if	SCONJ
ejpam-445	114	2	bm	bm	PROPN
ejpam-445	114	3	κ	κ	PROPN
ejpam-445	114	4	are	be	AUX
ejpam-445	114	5	the	the	DET
ejpam-445	114	6	ps	ps	PROPN
ejpam-445	114	7	wavelet	wavelet	NOUN
ejpam-445	114	8	coefficients	coefficient	NOUN
ejpam-445	114	9	of	of	ADP
ejpam-445	114	10	f	f	PROPN
ejpam-445	114	11	∈	∈	PROPN
ejpam-445	114	12	l2(r	l2(r	PROPN
ejpam-445	114	13	)	)	PUNCT
ejpam-445	114	14	,	,	PUNCT
ejpam-445	114	15	that	that	ADV
ejpam-445	114	16	is	is	ADV
ejpam-445	114	17	,	,	PUNCT
ejpam-445	114	18	bm	bm	PROPN
ejpam-445	114	19	κ	κ	PROPN
ejpam-445	114	20	=	=	PUNCT
ejpam-445	114	21	〈	〈	PROPN
ejpam-445	114	22	f	f	PROPN
ejpam-445	114	23	,	,	PUNCT
ejpam-445	114	24	φ̃m(t	φ̃m(t	NOUN
ejpam-445	114	25	−	−	ADP
ejpam-445	114	26	2−m	2−m	NUM
ejpam-445	114	27	)	)	PUNCT
ejpam-445	114	28	〉	〉	NOUN
ejpam-445	114	29	then	then	ADV
ejpam-445	114	30	the	the	DET
ejpam-445	114	31	dm	dm	PROPN
ejpam-445	114	32	=	=	PUNCT
ejpam-445	114	33	〈	〈	PROPN
ejpam-445	114	34	f	f	PROPN
ejpam-445	114	35	,	,	PUNCT
ejpam-445	114	36	qm(y	qm(y	NUM
ejpam-445	114	37	,	,	PUNCT
ejpam-445	114	38	t	t	NOUN
ejpam-445	114	39	)	)	PUNCT
ejpam-445	114	40	〉	〉	NOUN
ejpam-445	114	41	,	,	PUNCT
ejpam-445	114	42	where	where	SCONJ
ejpam-445	114	43	{	{	PUNCT
ejpam-445	114	44	dm	dm	NOUN
ejpam-445	114	45	}	}	PUNCT
ejpam-445	114	46	is	be	AUX
ejpam-445	114	47	defined	define	VERB
ejpam-445	114	48	as	as	ADP
ejpam-445	114	49	the	the	DET
ejpam-445	114	50	a	a	DET
ejpam-445	114	51	-	-	PUNCT
ejpam-445	114	52	transform	transform	NOUN
ejpam-445	114	53	of	of	ADP
ejpam-445	114	54	{	{	PUNCT
ejpam-445	114	55	bm	bm	PROPN
ejpam-445	114	56	κ	κ	PROPN
ejpam-445	114	57	}	}	PUNCT
ejpam-445	114	58	by	by	ADP
ejpam-445	114	59	dm	dm	PROPN
ejpam-445	114	60	=	=	SYM
ejpam-445	114	61	∑	∑	PROPN
ejpam-445	114	62	n	n	CCONJ
ejpam-445	114	63	,	,	PUNCT
ejpam-445	114	64	κ	κ	X
ejpam-445	114	65	a(m	a(m	PROPN
ejpam-445	114	66	,	,	PUNCT
ejpam-445	114	67	n	n	CCONJ
ejpam-445	114	68	,	,	PUNCT
ejpam-445	114	69	κ)bm	κ)bm	PROPN
ejpam-445	114	70	κ	κ	NOUN
ejpam-445	114	71	φm(t	φm(t	NOUN
ejpam-445	114	72	−	−	PROPN
ejpam-445	114	73	2−mκ	2−mκ	NUM
ejpam-445	114	74	)	)	PUNCT
ejpam-445	114	75	.	.	PUNCT
ejpam-445	115	1	(	(	PUNCT
ejpam-445	115	2	9	9	X
ejpam-445	115	3	)	)	PUNCT
ejpam-445	115	4	proof	proof	NOUN
ejpam-445	115	5	.	.	PUNCT
ejpam-445	116	1	we	we	PRON
ejpam-445	116	2	have	have	VERB
ejpam-445	116	3	∑	∑	PROPN
ejpam-445	116	4	n	n	CCONJ
ejpam-445	116	5	,	,	PUNCT
ejpam-445	116	6	κ	κ	X
ejpam-445	116	7	a(m	a(m	PROPN
ejpam-445	116	8	,	,	PUNCT
ejpam-445	116	9	n	n	CCONJ
ejpam-445	116	10	,	,	PUNCT
ejpam-445	116	11	κ)bm	κ)bm	PROPN
ejpam-445	116	12	κ	κ	NOUN
ejpam-445	116	13	φm(t	φm(t	NOUN
ejpam-445	116	14	−	−	PROPN
ejpam-445	116	15	2−mκ	2−mκ	NUM
ejpam-445	116	16	)	)	PUNCT
ejpam-445	116	17	=	=	SYM
ejpam-445	116	18	∑	∑	PUNCT
ejpam-445	116	19	n	n	CCONJ
ejpam-445	116	20	,	,	PUNCT
ejpam-445	116	21	κ	κ	PROPN
ejpam-445	116	22	〈	〈	NOUN
ejpam-445	116	23	φm(t	φm(t	PUNCT
ejpam-445	116	24	−	−	PROPN
ejpam-445	116	25	2−mn),φm(t	2−mn),φm(t	NUM
ejpam-445	116	26	−	−	NOUN
ejpam-445	116	27	2−mκ	2−mκ	NUM
ejpam-445	116	28	)	)	PUNCT
ejpam-445	116	29	〉	〉	NOUN
ejpam-445	116	30	〈	〈	PROPN
ejpam-445	116	31	f	f	NOUN
ejpam-445	116	32	,	,	PUNCT
ejpam-445	116	33	φ̃m(t	φ̃m(t	NOUN
ejpam-445	116	34	−	−	NOUN
ejpam-445	116	35	2−mn)〉φm(t	2−mn)〉φm(t	NUM
ejpam-445	116	36	−	−	NOUN
ejpam-445	116	37	2−mn	2−mn	NUM
ejpam-445	116	38	)	)	PUNCT
ejpam-445	117	1	=	=	SYM
ejpam-445	117	2	∫	∫	PROPN
ejpam-445	118	1	∞	∞	PROPN
ejpam-445	118	2	−∞	−∞	ADP
ejpam-445	118	3	∑	∑	PROPN
ejpam-445	118	4	n	n	CCONJ
ejpam-445	118	5	,	,	PUNCT
ejpam-445	118	6	κ	κ	NOUN
ejpam-445	118	7	φm(t	φm(t	ADJ
ejpam-445	118	8	−	−	PROPN
ejpam-445	118	9	2−mn)φm(t	2−mn)φm(t	NUM
ejpam-445	118	10	−	−	NUM
ejpam-445	118	11	2−mκ)d	2−mκ)d	NUM
ejpam-445	118	12	t	t	NOUN
ejpam-445	118	13	×	×	NOUN
ejpam-445	118	14	(	(	PUNCT
ejpam-445	118	15	∫	∫	PROPN
ejpam-445	118	16	∞	∞	PROPN
ejpam-445	119	1	−∞	−∞	X
ejpam-445	119	2	f	f	PROPN
ejpam-445	119	3	(	(	PUNCT
ejpam-445	119	4	y)φ̃m(y	y)φ̃m(y	PROPN
ejpam-445	119	5	−	−	NOUN
ejpam-445	120	1	2−mκ)d	2−mκ)d	NOUN
ejpam-445	120	2	y)φm(t	y)φm(t	NOUN
ejpam-445	120	3	−	−	PROPN
ejpam-445	120	4	2−mκ	2−mκ	NUM
ejpam-445	120	5	)	)	PUNCT
ejpam-445	121	1	=	=	SYM
ejpam-445	121	2	∫	∫	PROPN
ejpam-445	122	1	∞	∞	PROPN
ejpam-445	122	2	−∞	−∞	ADP
ejpam-445	122	3	∑	∑	PROPN
ejpam-445	122	4	n	n	CCONJ
ejpam-445	122	5	,	,	PUNCT
ejpam-445	122	6	κ	κ	NOUN
ejpam-445	122	7	φm(t	φm(t	PUNCT
ejpam-445	122	8	−	−	PROPN
ejpam-445	123	1	2−mn)φ̃m(y	2−mn)φ̃m(y	NUM
ejpam-445	124	1	−	−	NOUN
ejpam-445	124	2	2−mκ)(φm(t	2−mκ)(φm(t	NUM
ejpam-445	125	1	−	−	ADP
ejpam-445	125	2	2−mn))2d	2−mn))2d	NUM
ejpam-445	125	3	t	t	NOUN
ejpam-445	125	4	∫	∫	NOUN
ejpam-445	125	5	∞	∞	PROPN
ejpam-445	126	1	−∞	−∞	X
ejpam-445	126	2	f	f	PROPN
ejpam-445	126	3	(	(	PUNCT
ejpam-445	126	4	y)d	y)d	NOUN
ejpam-445	126	5	y	y	PROPN
ejpam-445	127	1	=	=	SYM
ejpam-445	127	2	∫	∫	PROPN
ejpam-445	127	3	∞	∞	PROPN
ejpam-445	128	1	−∞	−∞	X
ejpam-445	128	2	qm(y	qm(y	NUM
ejpam-445	128	3	,	,	PUNCT
ejpam-445	128	4	t	t	PROPN
ejpam-445	128	5	)	)	PUNCT
ejpam-445	128	6	f	f	PROPN
ejpam-445	129	1	(	(	PUNCT
ejpam-445	129	2	y)d	y)d	PROPN
ejpam-445	129	3	y	y	PROPN
ejpam-445	129	4	∫	∫	PROPN
ejpam-445	129	5	∞	∞	PROPN
ejpam-445	129	6	−∞	−∞	ADP
ejpam-445	130	1	[	[	X
ejpam-445	130	2	φm(t	φm(t	PUNCT
ejpam-445	130	3	−	−	PROPN
ejpam-445	130	4	2−mn)]2d	2−mn)]2d	PROPN
ejpam-445	130	5	t	t	NOUN
ejpam-445	130	6	=	=	SYM
ejpam-445	130	7	〈	〈	PROPN
ejpam-445	130	8	f	f	PROPN
ejpam-445	130	9	,	,	PUNCT
ejpam-445	130	10	qm(y	qm(y	NUM
ejpam-445	130	11	,	,	PUNCT
ejpam-445	130	12	t	t	NOUN
ejpam-445	130	13	)	)	PUNCT
ejpam-445	130	14	〉	〉	NOUN
ejpam-445	130	15	.	.	PUNCT
ejpam-445	131	1	hence	hence	ADV
ejpam-445	131	2	the	the	DET
ejpam-445	131	3	proof	proof	NOUN
ejpam-445	131	4	is	be	AUX
ejpam-445	131	5	completed	complete	VERB
ejpam-445	131	6	.	.	PUNCT
ejpam-445	132	1	theorem	theorem	NOUN
ejpam-445	132	2	3	3	X
ejpam-445	132	3	.	.	PUNCT
ejpam-445	132	4	let	let	AUX
ejpam-445	132	5	a=	a=	VERB
ejpam-445	132	6	a(m	a(m	VERB
ejpam-445	132	7	,	,	PUNCT
ejpam-445	132	8	n	n	CCONJ
ejpam-445	132	9	,	,	PUNCT
ejpam-445	132	10	κ	κ	NOUN
ejpam-445	132	11	)	)	PUNCT
ejpam-445	132	12	be	be	VERB
ejpam-445	132	13	a	a	DET
ejpam-445	132	14	double	double	ADJ
ejpam-445	132	15	nonnegative	nonnegative	ADJ
ejpam-445	132	16	infinite	infinite	ADJ
ejpam-445	132	17	matrix	matrix	NOUN
ejpam-445	132	18	then	then	ADV
ejpam-445	132	19	{	{	PUNCT
ejpam-445	132	20	qm(y	qm(y	NUM
ejpam-445	132	21	,	,	PUNCT
ejpam-445	132	22	t	t	PROPN
ejpam-445	132	23	)	)	PUNCT
ejpam-445	132	24	}	}	PUNCT
ejpam-445	132	25	constitute	constitute	VERB
ejpam-445	132	26	a	a	DET
ejpam-445	132	27	frame	frame	NOUN
ejpam-445	132	28	of	of	ADP
ejpam-445	132	29	l2(r	l2(r	NOUN
ejpam-445	132	30	)	)	PUNCT
ejpam-445	132	31	.	.	PUNCT
ejpam-445	133	1	proof	proof	NOUN
ejpam-445	133	2	.	.	PUNCT
ejpam-445	134	1	we	we	PRON
ejpam-445	134	2	have	have	VERB
ejpam-445	134	3	∑	∑	ADV
ejpam-445	134	4	m	m	PUNCT
ejpam-445	134	5	|dm|	|dm|	VERB
ejpam-445	134	6	2	2	NUM
ejpam-445	134	7	=	=	SYM
ejpam-445	134	8	∑	∑	NOUN
ejpam-445	134	9	m	m	VERB
ejpam-445	134	10	|	|	ADV
ejpam-445	134	11	〈	〈	PROPN
ejpam-445	134	12	f	f	PROPN
ejpam-445	134	13	,	,	PUNCT
ejpam-445	134	14	qm(y	qm(y	NUM
ejpam-445	134	15	,	,	PUNCT
ejpam-445	134	16	t)〉|2	t)〉|2	PROPN
ejpam-445	134	17	=	=	PUNCT
ejpam-445	134	18	1	1	NUM
ejpam-445	134	19	2π	2π	NOUN
ejpam-445	134	20	∑	∑	PUNCT
ejpam-445	134	21	m	m	VERB
ejpam-445	134	22	|	|	ADV
ejpam-445	134	23	〈	〈	PROPN
ejpam-445	134	24	f̂	f̂	PROPN
ejpam-445	134	25	,	,	PUNCT
ejpam-445	134	26	q̂m(y	q̂m(y	PROPN
ejpam-445	134	27	,	,	PUNCT
ejpam-445	134	28	t)〉|2	t)〉|2	PROPN
ejpam-445	134	29	references	reference	VERB
ejpam-445	134	30	723	723	NUM
ejpam-445	134	31	=	=	SYM
ejpam-445	134	32	1	1	NUM
ejpam-445	134	33	2π	2π	NOUN
ejpam-445	134	34	∑	∑	PUNCT
ejpam-445	134	35	m	m	VERB
ejpam-445	134	36	∫	∫	NOUN
ejpam-445	134	37	∞	∞	PROPN
ejpam-445	135	1	−∞	−∞	PUNCT
ejpam-445	135	2	|	|	ADV
ejpam-445	135	3	1	1	NUM
ejpam-445	135	4	2π	2π	NUM
ejpam-445	135	5	∫	∫	NOUN
ejpam-445	135	6	∞	∞	PROPN
ejpam-445	135	7	−∞	−∞	ADP
ejpam-445	135	8	f̂	f̂	PROPN
ejpam-445	135	9	(	(	PUNCT
ejpam-445	135	10	ξ	ξ	NOUN
ejpam-445	135	11	)	)	PUNCT
ejpam-445	135	12	,	,	PUNCT
ejpam-445	135	13	q̂m(w	q̂m(w	PROPN
ejpam-445	135	14	,	,	PUNCT
ejpam-445	135	15	ξ)dξ|2dw	ξ)dξ|2dw	NUM
ejpam-445	135	16	=	=	SYM
ejpam-445	135	17	1	1	NUM
ejpam-445	135	18	2π	2π	NOUN
ejpam-445	135	19	∑	∑	PUNCT
ejpam-445	135	20	m	m	PROPN
ejpam-445	135	21	∫	∫	PROPN
ejpam-445	135	22	∞	∞	PROPN
ejpam-445	135	23	−∞	−∞	ADP
ejpam-445	135	24	|χ2mπ(w	|χ2mπ(w	NOUN
ejpam-445	135	25	)	)	PUNCT
ejpam-445	135	26	f̂	f̂	PROPN
ejpam-445	135	27	(	(	PUNCT
ejpam-445	135	28	w)|	w)|	VERB
ejpam-445	135	29	2dw	2dw	ADJ
ejpam-445	135	30	=	=	SYM
ejpam-445	135	31	1	1	NUM
ejpam-445	135	32	2π	2π	NOUN
ejpam-445	135	33	∑	∑	PUNCT
ejpam-445	135	34	m	m	PROPN
ejpam-445	135	35	∫	∫	PROPN
ejpam-445	135	36	2mπ	2mπ	ADJ
ejpam-445	135	37	−2mπ	−2mπ	PROPN
ejpam-445	135	38	|	|	ADV
ejpam-445	135	39	f̂	f̂	X
ejpam-445	135	40	(	(	PUNCT
ejpam-445	135	41	w)|2dw	w)|2dw	PROPN
ejpam-445	135	42	=	=	SYM
ejpam-445	135	43	1	1	NUM
ejpam-445	135	44	2π	2π	NUM
ejpam-445	135	45	∫	∫	NOUN
ejpam-445	135	46	∞	∞	PROPN
ejpam-445	136	1	−∞	−∞	ADP
ejpam-445	136	2	|	|	ADV
ejpam-445	136	3	f̂	f̂	X
ejpam-445	136	4	(	(	PUNCT
ejpam-445	136	5	w)|2dw	w)|2dw	PROPN
ejpam-445	136	6	=	=	SYM
ejpam-445	136	7	||	||	NOUN
ejpam-445	137	1	f	f	NOUN
ejpam-445	137	2	||22	||22	NOUN
ejpam-445	137	3	that	that	PRON
ejpam-445	137	4	is	be	AUX
ejpam-445	137	5	,	,	PUNCT
ejpam-445	137	6	∑	∑	ADP
ejpam-445	137	7	m	m	VERB
ejpam-445	137	8	|dm|	|dm|	VERB
ejpam-445	137	9	2	2	NUM
ejpam-445	137	10	=	=	SYM
ejpam-445	137	11	||	||	NOUN
ejpam-445	137	12	f	f	PROPN
ejpam-445	137	13	||22	||22	NOUN
ejpam-445	137	14	,	,	PUNCT
ejpam-445	137	15	f	f	PROPN
ejpam-445	137	16	∈	∈	PROPN
ejpam-445	137	17	l2(r	l2(r	PROPN
ejpam-445	137	18	)	)	PUNCT
ejpam-445	137	19	.	.	PUNCT
ejpam-445	138	1	therefore	therefore	ADV
ejpam-445	138	2	,	,	PUNCT
ejpam-445	138	3	for	for	ADP
ejpam-445	138	4	matrix	matrix	NOUN
ejpam-445	138	5	a	a	DET
ejpam-445	138	6	=	=	NOUN
ejpam-445	138	7	a(m	a(m	NOUN
ejpam-445	138	8	,	,	PUNCT
ejpam-445	138	9	n	n	CCONJ
ejpam-445	138	10	,	,	PUNCT
ejpam-445	138	11	κ	κ	NOUN
ejpam-445	138	12	)	)	PUNCT
ejpam-445	138	13	,	,	PUNCT
ejpam-445	138	14	we	we	PRON
ejpam-445	138	15	have	have	VERB
ejpam-445	138	16	c1||	c1||	PROPN
ejpam-445	138	17	f	f	PROPN
ejpam-445	138	18	||	||	NOUN
ejpam-445	138	19	2	2	NUM
ejpam-445	138	20	2	2	NUM
ejpam-445	138	21	≤	≤	NOUN
ejpam-445	138	22	∑	∑	PUNCT
ejpam-445	138	23	m	m	PUNCT
ejpam-445	138	24	|dm|	|dm|	VERB
ejpam-445	138	25	2	2	NUM
ejpam-445	138	26	≤	≤	NOUN
ejpam-445	138	27	c2||	c2||	PROPN
ejpam-445	138	28	f	f	NOUN
ejpam-445	138	29	||	||	NOUN
ejpam-445	138	30	2	2	NUM
ejpam-445	138	31	2	2	NUM
ejpam-445	138	32	,	,	PUNCT
ejpam-445	138	33	where	where	SCONJ
ejpam-445	138	34	0≤	0≤	NUM
ejpam-445	138	35	c1	c1	NOUN
ejpam-445	138	36	,	,	PUNCT
ejpam-445	138	37	c2	c2	PROPN
ejpam-445	138	38	<	<	PROPN
ejpam-445	138	39	∞.	∞.	PROPN
ejpam-445	138	40	this	this	PRON
ejpam-445	138	41	completes	complete	VERB
ejpam-445	138	42	the	the	DET
ejpam-445	138	43	proof	proof	NOUN
ejpam-445	138	44	of	of	ADP
ejpam-445	138	45	the	the	DET
ejpam-445	138	46	theorem	theorem	PROPN
ejpam-445	138	47	.	.	PUNCT
ejpam-445	138	48	references	reference	NOUN
ejpam-445	139	1	[	[	X
ejpam-445	139	2	1	1	NUM
ejpam-445	139	3	]	]	PUNCT
ejpam-445	139	4	r.	r.	X
ejpam-445	139	5	courant	courant	PROPN
ejpam-445	139	6	and	and	CCONJ
ejpam-445	139	7	d.	d.	PROPN
ejpam-445	139	8	hilbert	hilbert	PROPN
ejpam-445	139	9	,	,	PUNCT
ejpam-445	139	10	methods	method	NOUN
ejpam-445	139	11	of	of	ADP
ejpam-445	139	12	mathematical	mathematical	ADJ
ejpam-445	139	13	physics	physics	NOUN
ejpam-445	139	14	,	,	PUNCT
ejpam-445	139	15	vol	vol	NOUN
ejpam-445	139	16	1	1	NUM
ejpam-445	139	17	,	,	PUNCT
ejpam-445	139	18	interscience	interscience	NOUN
ejpam-445	139	19	publishers	publisher	NOUN
ejpam-445	139	20	,	,	PUNCT
ejpam-445	139	21	new	new	PROPN
ejpam-445	139	22	york	york	PROPN
ejpam-445	139	23	,	,	PUNCT
ejpam-445	139	24	pp	pp	ADP
ejpam-445	139	25	122	122	NUM
ejpam-445	139	26	-	-	SYM
ejpam-445	139	27	134	134	NUM
ejpam-445	139	28	.	.	PUNCT
ejpam-445	139	29	1955	1955	NUM
ejpam-445	139	30	.	.	PUNCT
ejpam-445	140	1	[	[	X
ejpam-445	140	2	2	2	NUM
ejpam-445	140	3	]	]	PUNCT
ejpam-445	140	4	i.	i.	NOUN
ejpam-445	140	5	daubechies	daubechies	PROPN
ejpam-445	140	6	,	,	PUNCT
ejpam-445	140	7	orthonormal	orthonormal	ADJ
ejpam-445	140	8	bases	basis	NOUN
ejpam-445	140	9	of	of	ADP
ejpam-445	140	10	compactly	compactly	ADV
ejpam-445	140	11	supported	support	VERB
ejpam-445	140	12	wavelets	wavelet	NOUN
ejpam-445	140	13	,	,	PUNCT
ejpam-445	140	14	comm	comm	NOUN
ejpam-445	140	15	.	.	PUNCT
ejpam-445	141	1	pure	pure	ADJ
ejpam-445	141	2	appl	appl	PROPN
ejpam-445	141	3	.	.	PUNCT
ejpam-445	141	4	math	math	PROPN
ejpam-445	141	5	.	.	PUNCT
ejpam-445	142	1	41	41	NUM
ejpam-445	142	2	,	,	PUNCT
ejpam-445	142	3	no	no	DET
ejpam-445	142	4	-7	-7	NOUN
ejpam-445	142	5	,	,	PUNCT
ejpam-445	142	6	909	909	NUM
ejpam-445	142	7	-	-	SYM
ejpam-445	142	8	996	996	NUM
ejpam-445	142	9	.	.	PUNCT
ejpam-445	143	1	1988	1988	NUM
ejpam-445	143	2	.	.	PUNCT
ejpam-445	144	1	[	[	X
ejpam-445	144	2	3	3	NUM
ejpam-445	144	3	]	]	X
ejpam-445	144	4	i.	i.	NOUN
ejpam-445	144	5	daubechies	daubechies	PROPN
ejpam-445	144	6	,	,	PUNCT
ejpam-445	144	7	the	the	DET
ejpam-445	144	8	wavelet	wavelet	NOUN
ejpam-445	144	9	transform	transform	NOUN
ejpam-445	144	10	,	,	PUNCT
ejpam-445	144	11	time	time	NOUN
ejpam-445	144	12	frequency	frequency	NOUN
ejpam-445	144	13	localization	localization	NOUN
ejpam-445	144	14	and	and	CCONJ
ejpam-445	144	15	signal	signal	VERB
ejpam-445	144	16	analysis	analysis	NOUN
ejpam-445	144	17	,	,	PUNCT
ejpam-445	144	18	ieee	ieee	NOUN
ejpam-445	144	19	trans	tran	NOUN
ejpam-445	144	20	.	.	PUNCT
ejpam-445	145	1	inform	inform	NOUN
ejpam-445	145	2	.	.	PUNCT
ejpam-445	146	1	theory	theory	NOUN
ejpam-445	146	2	36	36	NUM
ejpam-445	146	3	,	,	PUNCT
ejpam-445	146	4	no5	no5	PROPN
ejpam-445	146	5	,	,	PUNCT
ejpam-445	146	6	961	961	NUM
ejpam-445	146	7	-	-	PUNCT
ejpam-445	146	8	1005	1005	NUM
ejpam-445	146	9	.	.	PUNCT
ejpam-445	147	1	1990	1990	NUM
ejpam-445	147	2	.	.	PUNCT
ejpam-445	148	1	[	[	X
ejpam-445	148	2	4	4	NUM
ejpam-445	148	3	]	]	X
ejpam-445	148	4	i.	i.	NOUN
ejpam-445	148	5	daubechies	daubechies	PROPN
ejpam-445	148	6	,	,	PUNCT
ejpam-445	148	7	ten	ten	NUM
ejpam-445	148	8	lectures	lecture	NOUN
ejpam-445	148	9	on	on	ADP
ejpam-445	148	10	wavelets	wavelet	NOUN
ejpam-445	148	11	,	,	PUNCT
ejpam-445	148	12	cbms	cbms	PROPN
ejpam-445	148	13	nsf	nsf	PROPN
ejpam-445	148	14	regional	regional	PROPN
ejpam-445	148	15	conference	conference	NOUN
ejpam-445	148	16	series	series	NOUN
ejpam-445	148	17	in	in	ADP
ejpam-445	148	18	applied	apply	VERB
ejpam-445	148	19	mathematics	mathematic	NOUN
ejpam-445	148	20	,	,	PUNCT
ejpam-445	148	21	vol	vol	NOUN
ejpam-445	148	22	61	61	NUM
ejpam-445	148	23	,	,	PUNCT
ejpam-445	148	24	society	society	NOUN
ejpam-445	148	25	for	for	ADP
ejpam-445	148	26	industrial	industrial	ADJ
ejpam-445	148	27	and	and	CCONJ
ejpam-445	148	28	applied	applied	ADJ
ejpam-445	148	29	mathematics	mathematic	NOUN
ejpam-445	148	30	(	(	PUNCT
ejpam-445	148	31	siam	siam	PROPN
ejpam-445	148	32	)	)	PUNCT
ejpam-445	148	33	pennsylvania	pennsylvania	PROPN
ejpam-445	148	34	,	,	PUNCT
ejpam-445	148	35	1992	1992	NUM
ejpam-445	148	36	.	.	PUNCT
ejpam-445	149	1	[	[	X
ejpam-445	149	2	5	5	X
ejpam-445	149	3	]	]	PUNCT
ejpam-445	149	4	devendra	devendra	PROPN
ejpam-445	149	5	kumar	kumar	PROPN
ejpam-445	149	6	,	,	PUNCT
ejpam-445	149	7	convergence	convergence	NOUN
ejpam-445	149	8	of	of	ADP
ejpam-445	149	9	prolate	prolate	ADJ
ejpam-445	149	10	spheroidal	spheroidal	NOUN
ejpam-445	149	11	wavelets	wavelet	NOUN
ejpam-445	149	12	in	in	ADP
ejpam-445	149	13	a	a	DET
ejpam-445	149	14	generalized	generalized	ADJ
ejpam-445	149	15	sobolev	sobolev	NOUN
ejpam-445	149	16	space	space	NOUN
ejpam-445	149	17	and	and	CCONJ
ejpam-445	149	18	frames	frame	NOUN
ejpam-445	149	19	,	,	PUNCT
ejpam-445	149	20	submitted	submit	VERB
ejpam-445	149	21	for	for	ADP
ejpam-445	149	22	publication	publication	NOUN
ejpam-445	149	23	in	in	ADP
ejpam-445	149	24	indian	indian	ADJ
ejpam-445	149	25	journal	journal	PROPN
ejpam-445	149	26	of	of	ADP
ejpam-445	149	27	industrial	industrial	ADJ
ejpam-445	149	28	and	and	CCONJ
ejpam-445	149	29	applied	apply	VERB
ejpam-445	149	30	mathematics	mathematic	NOUN
ejpam-445	149	31	.	.	PUNCT
ejpam-445	150	1	[	[	X
ejpam-445	150	2	6	6	NUM
ejpam-445	150	3	]	]	X
ejpam-445	150	4	r.j	r.j	PROPN
ejpam-445	150	5	.	.	PROPN
ejpam-445	150	6	duffin	duffin	PROPN
ejpam-445	150	7	and	and	CCONJ
ejpam-445	150	8	a.c	a.c	PROPN
ejpam-445	150	9	.	.	PROPN
ejpam-445	150	10	schaeffer	schaeffer	PROPN
ejpam-445	150	11	,	,	PUNCT
ejpam-445	150	12	a	a	DET
ejpam-445	150	13	calss	calss	PROPN
ejpam-445	150	14	of	of	ADP
ejpam-445	150	15	nonharmonic	nonharmonic	ADJ
ejpam-445	150	16	fourir	fourir	NOUN
ejpam-445	150	17	series	series	PROPN
ejpam-445	150	18	,	,	PUNCT
ejpam-445	150	19	trans	trans	PROPN
ejpam-445	150	20	.	.	PROPN
ejpam-445	150	21	amer	amer	PROPN
ejpam-445	150	22	.	.	PUNCT
ejpam-445	150	23	math	math	PROPN
ejpam-445	150	24	.	.	PUNCT
ejpam-445	151	1	soc	soc	PROPN
ejpam-445	151	2	.	.	PUNCT
ejpam-445	152	1	72	72	NUM
ejpam-445	152	2	,	,	PUNCT
ejpam-445	152	3	341	341	NUM
ejpam-445	152	4	-	-	SYM
ejpam-445	152	5	366	366	NUM
ejpam-445	152	6	.	.	PUNCT
ejpam-445	153	1	1952	1952	NUM
ejpam-445	153	2	.	.	PUNCT
ejpam-445	154	1	references	reference	NOUN
ejpam-445	154	2	724	724	NUM
ejpam-445	154	3	[	[	X
ejpam-445	154	4	7	7	X
ejpam-445	154	5	]	]	X
ejpam-445	154	6	h.j	h.j	PROPN
ejpam-445	154	7	.	.	PROPN
ejpam-445	154	8	landau	landau	NOUN
ejpam-445	154	9	and	and	CCONJ
ejpam-445	154	10	h.o	h.o	PROPN
ejpam-445	154	11	.	.	PUNCT
ejpam-445	154	12	pollak	pollak	PROPN
ejpam-445	154	13	,	,	PUNCT
ejpam-445	154	14	prolate	prolate	ADJ
ejpam-445	154	15	sheroidal	sheroidal	ADJ
ejpam-445	154	16	wave	wave	NOUN
ejpam-445	154	17	functions	function	NOUN
ejpam-445	154	18	,	,	PUNCT
ejpam-445	154	19	fourier	fourier	ADJ
ejpam-445	154	20	analysis	analysis	NOUN
ejpam-445	154	21	and	and	CCONJ
ejpam-445	154	22	uncertainity	uncertainity	NOUN
ejpam-445	154	23	,	,	PUNCT
ejpam-445	154	24	ii	ii	PROPN
ejpam-445	154	25	,	,	PUNCT
ejpam-445	154	26	bell	bell	NOUN
ejpam-445	154	27	system	system	NOUN
ejpam-445	154	28	tech	tech	NOUN
ejpam-445	154	29	.	.	PUNCT
ejpam-445	155	1	j.	j.	PROPN
ejpam-445	155	2	40	40	NUM
ejpam-445	155	3	.	.	PUNCT
ejpam-445	156	1	65	65	NUM
ejpam-445	156	2	-	-	SYM
ejpam-445	156	3	84	84	NUM
ejpam-445	156	4	.	.	PUNCT
ejpam-445	157	1	1961	1961	NUM
ejpam-445	157	2	.	.	PUNCT
ejpam-445	158	1	[	[	X
ejpam-445	158	2	8	8	NUM
ejpam-445	158	3	]	]	X
ejpam-445	158	4	h.j	h.j	PROPN
ejpam-445	158	5	.	.	PROPN
ejpam-445	158	6	landau	landau	NOUN
ejpam-445	158	7	and	and	CCONJ
ejpam-445	158	8	h.o	h.o	PROPN
ejpam-445	158	9	.	.	PUNCT
ejpam-445	158	10	pollak	pollak	PROPN
ejpam-445	158	11	,	,	PUNCT
ejpam-445	158	12	prolate	prolate	ADJ
ejpam-445	158	13	sheroidal	sheroidal	ADJ
ejpam-445	158	14	wave	wave	NOUN
ejpam-445	158	15	functions	function	NOUN
ejpam-445	158	16	,	,	PUNCT
ejpam-445	158	17	fourier	fourier	ADJ
ejpam-445	158	18	analysis	analysis	NOUN
ejpam-445	158	19	and	and	CCONJ
ejpam-445	158	20	uncertainity	uncertainity	NOUN
ejpam-445	158	21	,	,	PUNCT
ejpam-445	158	22	iii	iii	PROPN
ejpam-445	158	23	,	,	PUNCT
ejpam-445	158	24	bell	bell	NOUN
ejpam-445	158	25	system	system	NOUN
ejpam-445	158	26	tech	tech	NOUN
ejpam-445	158	27	.	.	PUNCT
ejpam-445	159	1	j.	j.	PROPN
ejpam-445	159	2	41	41	PROPN
ejpam-445	159	3	.	.	PUNCT
ejpam-445	160	1	1295	1295	NUM
ejpam-445	160	2	-	-	SYM
ejpam-445	160	3	1336	1336	NUM
ejpam-445	160	4	.	.	PUNCT
ejpam-445	161	1	1982	1982	NUM
ejpam-445	161	2	.	.	PUNCT
ejpam-445	162	1	[	[	X
ejpam-445	162	2	9	9	NUM
ejpam-445	162	3	]	]	PUNCT
ejpam-445	162	4	f.	f.	NOUN
ejpam-445	162	5	moricz	moricz	PROPN
ejpam-445	162	6	and	and	CCONJ
ejpam-445	162	7	b.e	b.e	PROPN
ejpam-445	162	8	.	.	PROPN
ejpam-445	162	9	rhaodes	rhaode	NOUN
ejpam-445	162	10	,	,	PUNCT
ejpam-445	162	11	comparison	comparison	NOUN
ejpam-445	162	12	theorems	theorem	NOUN
ejpam-445	162	13	for	for	ADP
ejpam-445	162	14	double	double	ADJ
ejpam-445	162	15	summability	summability	NOUN
ejpam-445	162	16	methods	method	NOUN
ejpam-445	162	17	,	,	PUNCT
ejpam-445	162	18	publ	publ	NOUN
ejpam-445	162	19	.	.	PUNCT
ejpam-445	163	1	math	math	NOUN
ejpam-445	163	2	.	.	PUNCT
ejpam-445	164	1	debrecen	debrecen	PROPN
ejpam-445	164	2	36	36	NUM
ejpam-445	164	3	,	,	PUNCT
ejpam-445	164	4	no	no	DET
ejpam-445	164	5	1	1	NUM
ejpam-445	164	6	-	-	SYM
ejpam-445	164	7	4	4	NUM
ejpam-445	164	8	,	,	PUNCT
ejpam-445	164	9	207220	207220	NUM
ejpam-445	164	10	.	.	PUNCT
ejpam-445	164	11	1989	1989	NUM
ejpam-445	164	12	.	.	PUNCT
ejpam-445	165	1	[	[	X
ejpam-445	165	2	10	10	NUM
ejpam-445	165	3	]	]	X
ejpam-445	165	4	g.m	g.m	PROPN
ejpam-445	165	5	.	.	PROPN
ejpam-445	165	6	robinson	robinson	PROPN
ejpam-445	165	7	,	,	PUNCT
ejpam-445	165	8	divergent	divergent	ADJ
ejpam-445	165	9	double	double	ADJ
ejpam-445	165	10	sequences	sequence	NOUN
ejpam-445	165	11	and	and	CCONJ
ejpam-445	165	12	series	series	NOUN
ejpam-445	165	13	,	,	PUNCT
ejpam-445	165	14	trans	trans	PROPN
ejpam-445	165	15	.	.	PROPN
ejpam-445	165	16	amer	amer	PROPN
ejpam-445	165	17	.	.	PUNCT
ejpam-445	165	18	math	math	PROPN
ejpam-445	165	19	.	.	PUNCT
ejpam-445	166	1	soc	soc	PROPN
ejpam-445	166	2	.	.	PUNCT
ejpam-445	167	1	28	28	NUM
ejpam-445	167	2	,	,	PUNCT
ejpam-445	167	3	5073	5073	NUM
ejpam-445	167	4	.	.	PUNCT
ejpam-445	168	1	1926	1926	NUM
ejpam-445	168	2	.	.	PUNCT
ejpam-445	169	1	[	[	X
ejpam-445	169	2	11	11	NUM
ejpam-445	169	3	]	]	X
ejpam-445	169	4	c.e	c.e	PROPN
ejpam-445	169	5	.	.	PROPN
ejpam-445	169	6	shannon	shannon	PROPN
ejpam-445	169	7	,	,	PUNCT
ejpam-445	169	8	communication	communication	NOUN
ejpam-445	169	9	in	in	ADP
ejpam-445	169	10	the	the	DET
ejpam-445	169	11	presence	presence	NOUN
ejpam-445	169	12	of	of	ADP
ejpam-445	169	13	noise	noise	NOUN
ejpam-445	169	14	,	,	PUNCT
ejpam-445	169	15	proc	proc	NOUN
ejpam-445	169	16	.	.	PUNCT
ejpam-445	169	17	ire	ire	VERB
ejpam-445	169	18	37	37	NUM
ejpam-445	169	19	,	,	PUNCT
ejpam-445	169	20	10	10	NUM
ejpam-445	169	21	-	-	SYM
ejpam-445	169	22	21	21	NUM
ejpam-445	169	23	.	.	PUNCT
ejpam-445	169	24	1949	1949	NUM
ejpam-445	169	25	.	.	PUNCT
ejpam-445	170	1	[	[	X
ejpam-445	170	2	12	12	NUM
ejpam-445	170	3	]	]	X
ejpam-445	170	4	d.	d.	PROPN
ejpam-445	170	5	slepian	slepian	PROPN
ejpam-445	170	6	and	and	CCONJ
ejpam-445	170	7	h.o	h.o	PROPN
ejpam-445	170	8	.	.	PUNCT
ejpam-445	170	9	pollak	pollak	PROPN
ejpam-445	170	10	,	,	PUNCT
ejpam-445	170	11	prolate	prolate	ADJ
ejpam-445	170	12	spheroidal	spheroidal	NOUN
ejpam-445	170	13	wave	wave	NOUN
ejpam-445	170	14	functions	function	NOUN
ejpam-445	170	15	,	,	PUNCT
ejpam-445	170	16	fourier	fourier	ADJ
ejpam-445	170	17	analysis	analysis	NOUN
ejpam-445	170	18	and	and	CCONJ
ejpam-445	170	19	uncertainity	uncertainity	NOUN
ejpam-445	170	20	,	,	PUNCT
ejpam-445	170	21	i.	i.	PROPN
ejpam-445	170	22	bell	bell	PROPN
ejpam-445	170	23	system	system	NOUN
ejpam-445	170	24	tech	tech	NOUN
ejpam-445	170	25	.	.	PUNCT
ejpam-445	171	1	j.	j.	PROPN
ejpam-445	171	2	40	40	NUM
ejpam-445	171	3	,	,	PUNCT
ejpam-445	171	4	43	43	NUM
ejpam-445	171	5	-	-	SYM
ejpam-445	171	6	64	64	NUM
ejpam-445	171	7	.	.	PUNCT
ejpam-445	172	1	1961	1961	NUM
ejpam-445	172	2	[	[	X
ejpam-445	172	3	13	13	NUM
ejpam-445	172	4	]	]	X
ejpam-445	172	5	d.	d.	PROPN
ejpam-445	172	6	slepian	slepian	PROPN
ejpam-445	172	7	,	,	PUNCT
ejpam-445	172	8	prolate	prolate	ADJ
ejpam-445	172	9	spheroidal	spheroidal	NOUN
ejpam-445	172	10	wave	wave	NOUN
ejpam-445	172	11	functions	function	NOUN
ejpam-445	172	12	,	,	PUNCT
ejpam-445	172	13	fourier	fourier	ADJ
ejpam-445	172	14	analysis	analysis	NOUN
ejpam-445	172	15	and	and	CCONJ
ejpam-445	172	16	uncertainity	uncertainity	NOUN
ejpam-445	172	17	,	,	PUNCT
ejpam-445	172	18	iv	iv	NUM
ejpam-445	172	19	bell	bell	NOUN
ejpam-445	172	20	system	system	NOUN
ejpam-445	172	21	tech	tech	NOUN
ejpam-445	172	22	.	.	PUNCT
ejpam-445	173	1	j.	j.	PROPN
ejpam-445	173	2	43	43	NUM
ejpam-445	173	3	,	,	PUNCT
ejpam-445	173	4	3009	3009	NUM
ejpam-445	173	5	-	-	SYM
ejpam-445	173	6	3058	3058	NUM
ejpam-445	173	7	.	.	PUNCT
ejpam-445	173	8	1964	1964	NUM
ejpam-445	173	9	.	.	PUNCT
ejpam-445	174	1	[	[	X
ejpam-445	174	2	14	14	NUM
ejpam-445	174	3	]	]	X
ejpam-445	174	4	d.	d.	PROPN
ejpam-445	174	5	slepian	slepian	PROPN
ejpam-445	174	6	,	,	PUNCT
ejpam-445	174	7	some	some	DET
ejpam-445	174	8	comments	comment	NOUN
ejpam-445	174	9	on	on	ADP
ejpam-445	174	10	fourier	fourier	ADJ
ejpam-445	174	11	analysis	analysis	NOUN
ejpam-445	174	12	,	,	PUNCT
ejpam-445	174	13	uncertainity	uncertainity	NOUN
ejpam-445	174	14	and	and	CCONJ
ejpam-445	174	15	modeling	modeling	NOUN
ejpam-445	174	16	,	,	PUNCT
ejpam-445	174	17	siam	siam	PROPN
ejpam-445	174	18	review	review	NOUN
ejpam-445	174	19	,	,	PUNCT
ejpam-445	174	20	25	25	NUM
ejpam-445	174	21	,	,	PUNCT
ejpam-445	174	22	379	379	NUM
ejpam-445	174	23	-	-	SYM
ejpam-445	174	24	393	393	NUM
ejpam-445	174	25	.	.	PUNCT
ejpam-445	174	26	1983	1983	NUM
ejpam-445	174	27	.	.	PUNCT
ejpam-445	175	1	[	[	X
ejpam-445	175	2	15	15	NUM
ejpam-445	175	3	]	]	X
ejpam-445	175	4	g.g	g.g	PROPN
ejpam-445	175	5	.	.	PROPN
ejpam-445	175	6	walter	walter	PROPN
ejpam-445	175	7	and	and	CCONJ
ejpam-445	175	8	xiaoping	xiaoping	PROPN
ejpam-445	175	9	shen	shen	PROPN
ejpam-445	175	10	,	,	PUNCT
ejpam-445	175	11	wavelet	wavelet	NOUN
ejpam-445	175	12	based	base	VERB
ejpam-445	175	13	on	on	ADP
ejpam-445	175	14	prolate	prolate	ADJ
ejpam-445	175	15	spheroidal	spheroidal	NOUN
ejpam-445	175	16	wave	wave	NOUN
ejpam-445	175	17	functions	function	NOUN
ejpam-445	175	18	,	,	PUNCT
ejpam-445	175	19	the	the	DET
ejpam-445	175	20	j.fourier	j.fourier	NOUN
ejpam-445	175	21	analysis	analysis	NOUN
ejpam-445	175	22	and	and	CCONJ
ejpam-445	175	23	applications	application	NOUN
ejpam-445	175	24	10	10	NUM
ejpam-445	175	25	,	,	PUNCT
ejpam-445	175	26	issue	issue	NOUN
ejpam-445	175	27	1	1	NUM
ejpam-445	175	28	,	,	PUNCT
ejpam-445	175	29	1	1	NUM
ejpam-445	175	30	-	-	SYM
ejpam-445	175	31	26	26	NUM
ejpam-445	175	32	.	.	PUNCT
ejpam-445	175	33	2004	2004	NUM
ejpam-445	175	34	.	.	PUNCT