id	sid	tid	token	lemma	pos
ejpam-837	1	1	5_837_mamedov.dvi	5_837_mamedov.dvi	NUM
ejpam-837	1	2	european	european	ADJ
ejpam-837	1	3	journal	journal	PROPN
ejpam-837	1	4	of	of	ADP
ejpam-837	1	5	pure	pure	ADJ
ejpam-837	1	6	and	and	CCONJ
ejpam-837	1	7	applied	apply	VERB
ejpam-837	1	8	mathematics	mathematic	NOUN
ejpam-837	1	9	vol	vol	NOUN
ejpam-837	1	10	.	.	PUNCT
ejpam-837	2	1	3	3	NUM
ejpam-837	2	2	,	,	PUNCT
ejpam-837	2	3	no	no	INTJ
ejpam-837	2	4	.	.	NOUN
ejpam-837	2	5	5	5	NUM
ejpam-837	2	6	,	,	PUNCT
ejpam-837	2	7	2010	2010	NUM
ejpam-837	2	8	,	,	PUNCT
ejpam-837	2	9	831	831	NUM
ejpam-837	2	10	-	-	SYM
ejpam-837	2	11	838	838	NUM
ejpam-837	2	12	issn	issn	PROPN
ejpam-837	2	13	1307	1307	NUM
ejpam-837	2	14	-	-	SYM
ejpam-837	2	15	5543	5543	NUM
ejpam-837	2	16	–	–	PUNCT
ejpam-837	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-837	2	18	on	on	ADP
ejpam-837	2	19	the	the	DET
ejpam-837	2	20	basis	basis	NOUN
ejpam-837	2	21	property	property	NOUN
ejpam-837	2	22	in	in	ADP
ejpam-837	2	23	lp	lp	PROPN
ejpam-837	2	24	(	(	PUNCT
ejpam-837	2	25	0	0	NUM
ejpam-837	2	26	,	,	PUNCT
ejpam-837	2	27	1	1	NUM
ejpam-837	2	28	)	)	PUNCT
ejpam-837	2	29	of	of	ADP
ejpam-837	2	30	the	the	DET
ejpam-837	2	31	root	root	NOUN
ejpam-837	2	32	functions	function	NOUN
ejpam-837	2	33	of	of	ADP
ejpam-837	2	34	a	a	DET
ejpam-837	2	35	class	class	NOUN
ejpam-837	2	36	non	non	ADJ
ejpam-837	2	37	self	self	PROPN
ejpam-837	2	38	adjoint	adjoint	PROPN
ejpam-837	2	39	sturm	sturm	PROPN
ejpam-837	2	40	-	-	PUNCT
ejpam-837	2	41	lioville	lioville	PROPN
ejpam-837	2	42	operators	operator	NOUN
ejpam-837	2	43	khanlar	khanlar	PROPN
ejpam-837	2	44	r.	r.	PROPN
ejpam-837	2	45	mamedov	mamedov	PROPN
ejpam-837	2	46	mersin	mersin	PROPN
ejpam-837	2	47	university	university	PROPN
ejpam-837	2	48	,	,	PUNCT
ejpam-837	2	49	science	science	NOUN
ejpam-837	2	50	and	and	CCONJ
ejpam-837	2	51	arts	art	NOUN
ejpam-837	2	52	faculty	faculty	NOUN
ejpam-837	2	53	,	,	PUNCT
ejpam-837	2	54	mathematics	mathematics	PROPN
ejpam-837	2	55	department	department	PROPN
ejpam-837	2	56	,	,	PUNCT
ejpam-837	2	57	33343	33343	NUM
ejpam-837	2	58	ciftlikkoy	ciftlikkoy	PROPN
ejpam-837	2	59	campus	campus	PROPN
ejpam-837	2	60	,	,	PUNCT
ejpam-837	2	61	mersin	mersin	PROPN
ejpam-837	2	62	-	-	PUNCT
ejpam-837	2	63	turkey	turkey	PROPN
ejpam-837	2	64	abstract	abstract	NOUN
ejpam-837	2	65	.	.	PUNCT
ejpam-837	3	1	in	in	ADP
ejpam-837	3	2	the	the	DET
ejpam-837	3	3	present	present	ADJ
ejpam-837	3	4	paper	paper	NOUN
ejpam-837	3	5	,	,	PUNCT
ejpam-837	3	6	we	we	PRON
ejpam-837	3	7	prove	prove	VERB
ejpam-837	3	8	the	the	DET
ejpam-837	3	9	basisness	basisness	NOUN
ejpam-837	3	10	of	of	ADP
ejpam-837	3	11	the	the	DET
ejpam-837	3	12	root	root	NOUN
ejpam-837	3	13	functions	function	NOUN
ejpam-837	3	14	of	of	ADP
ejpam-837	3	15	the	the	DET
ejpam-837	3	16	non	non	ADJ
ejpam-837	3	17	self	self	PROPN
ejpam-837	3	18	adjoint	adjoint	PROPN
ejpam-837	3	19	sturm	sturm	PROPN
ejpam-837	3	20	-	-	PUNCT
ejpam-837	3	21	liouville	liouville	NOUN
ejpam-837	3	22	operators	operator	NOUN
ejpam-837	3	23	with	with	ADP
ejpam-837	3	24	periodic	periodic	ADJ
ejpam-837	3	25	and	and	CCONJ
ejpam-837	3	26	anti	anti	ADJ
ejpam-837	3	27	-	-	ADJ
ejpam-837	3	28	periodic	periodic	ADJ
ejpam-837	3	29	boundary	boundary	ADJ
ejpam-837	3	30	conditions	condition	NOUN
ejpam-837	3	31	in	in	ADP
ejpam-837	3	32	space	space	NOUN
ejpam-837	3	33	lp(0,1	lp(0,1	NOUN
ejpam-837	3	34	)	)	PUNCT
ejpam-837	3	35	,	,	PUNCT
ejpam-837	3	36	p	p	X
ejpam-837	3	37	>	>	X
ejpam-837	3	38	1	1	NUM
ejpam-837	3	39	.	.	PUNCT
ejpam-837	4	1	here	here	ADV
ejpam-837	4	2	we	we	PRON
ejpam-837	4	3	assume	assume	VERB
ejpam-837	4	4	that	that	SCONJ
ejpam-837	4	5	the	the	DET
ejpam-837	4	6	potential	potential	NOUN
ejpam-837	4	7	is	be	AUX
ejpam-837	4	8	a	a	DET
ejpam-837	4	9	complex	complex	NOUN
ejpam-837	4	10	valued	value	VERB
ejpam-837	4	11	absolutely	absolutely	ADV
ejpam-837	4	12	continuous	continuous	ADJ
ejpam-837	4	13	function	function	NOUN
ejpam-837	4	14	in	in	ADP
ejpam-837	4	15	[	[	X
ejpam-837	4	16	0,1	0,1	NUM
ejpam-837	4	17	]	]	X
ejpam-837	4	18	.	.	PUNCT
ejpam-837	5	1	2000	2000	NUM
ejpam-837	5	2	mathematics	mathematic	NOUN
ejpam-837	5	3	subject	subject	NOUN
ejpam-837	5	4	classifications	classification	NOUN
ejpam-837	5	5	:	:	PUNCT
ejpam-837	5	6	34l10	34l10	NUM
ejpam-837	5	7	,	,	PUNCT
ejpam-837	5	8	34b24	34b24	NUM
ejpam-837	5	9	,	,	PUNCT
ejpam-837	5	10	47e05	47e05	NUM
ejpam-837	5	11	key	key	ADJ
ejpam-837	5	12	words	word	NOUN
ejpam-837	5	13	and	and	CCONJ
ejpam-837	5	14	phrases	phrase	NOUN
ejpam-837	5	15	:	:	PUNCT
ejpam-837	5	16	eigenfunctions	eigenfunction	NOUN
ejpam-837	5	17	,	,	PUNCT
ejpam-837	5	18	basis	basis	NOUN
ejpam-837	5	19	,	,	PUNCT
ejpam-837	5	20	periodic	periodic	ADJ
ejpam-837	5	21	and	and	CCONJ
ejpam-837	5	22	anti	anti	ADJ
ejpam-837	5	23	-	-	ADJ
ejpam-837	5	24	periodic	periodic	ADJ
ejpam-837	5	25	conditions	condition	NOUN
ejpam-837	5	26	,	,	PUNCT
ejpam-837	5	27	non	non	X
ejpam-837	5	28	self	self	NOUN
ejpam-837	5	29	adjoint	adjoint	PROPN
ejpam-837	5	30	sturm	sturm	PROPN
ejpam-837	5	31	-	-	PUNCT
ejpam-837	5	32	liouville	liouville	NOUN
ejpam-837	5	33	operator	operator	NOUN
ejpam-837	5	34	1	1	NUM
ejpam-837	5	35	.	.	PUNCT
ejpam-837	6	1	introduction	introduction	NOUN
ejpam-837	6	2	consider	consider	VERB
ejpam-837	6	3	the	the	DET
ejpam-837	6	4	eigenvalue	eigenvalue	NOUN
ejpam-837	6	5	problem	problem	NOUN
ejpam-837	6	6	for	for	ADP
ejpam-837	6	7	the	the	DET
ejpam-837	6	8	differential	differential	ADJ
ejpam-837	6	9	equation	equation	NOUN
ejpam-837	6	10	ℓ(u)≡	ℓ(u)≡	PROPN
ejpam-837	6	11	u′′	u′′	PROPN
ejpam-837	6	12	+	+	CCONJ
ejpam-837	6	13	q(x)u=	q(x)u=	NOUN
ejpam-837	6	14	λu	λu	X
ejpam-837	6	15	(	(	PUNCT
ejpam-837	6	16	1	1	NUM
ejpam-837	6	17	)	)	PUNCT
ejpam-837	6	18	on	on	ADP
ejpam-837	6	19	the	the	DET
ejpam-837	6	20	interval	interval	NOUN
ejpam-837	6	21	(	(	PUNCT
ejpam-837	6	22	0,1	0,1	NOUN
ejpam-837	6	23	)	)	PUNCT
ejpam-837	6	24	with	with	ADP
ejpam-837	6	25	the	the	DET
ejpam-837	6	26	periodic	periodic	ADJ
ejpam-837	6	27	u(0	u(0	NOUN
ejpam-837	6	28	)	)	PUNCT
ejpam-837	6	29	=	=	SYM
ejpam-837	7	1	u(1	u(1	PROPN
ejpam-837	7	2	)	)	PUNCT
ejpam-837	7	3	,	,	PUNCT
ejpam-837	7	4	u′(0	u′(0	PROPN
ejpam-837	7	5	)	)	PUNCT
ejpam-837	7	6	=	=	SYM
ejpam-837	7	7	u′(1	u′(1	NOUN
ejpam-837	7	8	)	)	PUNCT
ejpam-837	7	9	,	,	PUNCT
ejpam-837	7	10	(	(	PUNCT
ejpam-837	7	11	2	2	X
ejpam-837	7	12	)	)	PUNCT
ejpam-837	7	13	and	and	CCONJ
ejpam-837	7	14	antiperiodic	antiperiodic	ADJ
ejpam-837	7	15	u(0	u(0	PROPN
ejpam-837	7	16	)	)	PUNCT
ejpam-837	7	17	=	=	SYM
ejpam-837	7	18	−u(1	−u(1	NOUN
ejpam-837	7	19	)	)	PUNCT
ejpam-837	7	20	,	,	PUNCT
ejpam-837	7	21	u′(0	u′(0	PROPN
ejpam-837	7	22	)	)	PUNCT
ejpam-837	7	23	=	=	SYM
ejpam-837	7	24	−u′(1	−u′(1	PROPN
ejpam-837	7	25	)	)	PUNCT
ejpam-837	7	26	,	,	PUNCT
ejpam-837	7	27	(	(	PUNCT
ejpam-837	7	28	3	3	X
ejpam-837	7	29	)	)	PUNCT
ejpam-837	7	30	boundary	boundary	ADJ
ejpam-837	7	31	conditions	condition	NOUN
ejpam-837	7	32	,	,	PUNCT
ejpam-837	7	33	where	where	SCONJ
ejpam-837	7	34	the	the	DET
ejpam-837	7	35	potential	potential	ADJ
ejpam-837	7	36	q(x	q(x	NOUN
ejpam-837	7	37	)	)	PUNCT
ejpam-837	7	38	is	be	AUX
ejpam-837	7	39	an	an	DET
ejpam-837	7	40	arbitrary	arbitrary	ADJ
ejpam-837	7	41	complex	complex	ADJ
ejpam-837	7	42	valued	value	VERB
ejpam-837	7	43	function	function	NOUN
ejpam-837	7	44	.	.	PUNCT
ejpam-837	8	1	in	in	ADP
ejpam-837	8	2	this	this	DET
ejpam-837	8	3	paper	paper	NOUN
ejpam-837	8	4	we	we	PRON
ejpam-837	8	5	study	study	VERB
ejpam-837	8	6	the	the	DET
ejpam-837	8	7	basis	basis	NOUN
ejpam-837	8	8	property	property	NOUN
ejpam-837	8	9	of	of	ADP
ejpam-837	8	10	the	the	DET
ejpam-837	8	11	root	root	NOUN
ejpam-837	8	12	functions	function	NOUN
ejpam-837	8	13	of	of	ADP
ejpam-837	8	14	boundary	boundary	ADJ
ejpam-837	8	15	value	value	NOUN
ejpam-837	8	16	problems	problem	NOUN
ejpam-837	8	17	(	(	PUNCT
ejpam-837	8	18	1),(2	1),(2	NUM
ejpam-837	8	19	)	)	PUNCT
ejpam-837	8	20	and	and	CCONJ
ejpam-837	8	21	(	(	PUNCT
ejpam-837	8	22	1),(3	1),(3	NOUN
ejpam-837	8	23	)	)	PUNCT
ejpam-837	8	24	.	.	PUNCT
ejpam-837	9	1	this	this	DET
ejpam-837	9	2	problem	problem	NOUN
ejpam-837	9	3	is	be	AUX
ejpam-837	9	4	important	important	ADJ
ejpam-837	9	5	for	for	ADP
ejpam-837	9	6	the	the	DET
ejpam-837	9	7	study	study	NOUN
ejpam-837	9	8	of	of	ADP
ejpam-837	9	9	non	non	PROPN
ejpam-837	9	10	selfadjoint	selfadjoint	NOUN
ejpam-837	9	11	sturm	sturm	PROPN
ejpam-837	9	12	-	-	PUNCT
ejpam-837	9	13	liouville	liouville	NOUN
ejpam-837	9	14	operators	operator	NOUN
ejpam-837	9	15	.	.	PUNCT
ejpam-837	10	1	it	it	PRON
ejpam-837	10	2	is	be	AUX
ejpam-837	10	3	well	well	ADV
ejpam-837	10	4	known	know	VERB
ejpam-837	10	5	that	that	SCONJ
ejpam-837	10	6	the	the	DET
ejpam-837	10	7	basisness	basisness	NOUN
ejpam-837	10	8	of	of	ADP
ejpam-837	10	9	the	the	DET
ejpam-837	10	10	system	system	NOUN
ejpam-837	10	11	root	root	NOUN
ejpam-837	10	12	functions	function	NOUN
ejpam-837	10	13	of	of	ADP
ejpam-837	10	14	linear	linear	PROPN
ejpam-837	10	15	differential	differential	NOUN
ejpam-837	10	16	operators	operator	NOUN
ejpam-837	10	17	depends	depend	VERB
ejpam-837	10	18	on	on	ADP
ejpam-837	10	19	regularity	regularity	NOUN
ejpam-837	10	20	of	of	ADP
ejpam-837	10	21	boundary	boundary	ADJ
ejpam-837	10	22	conditions	condition	NOUN
ejpam-837	10	23	(	(	PUNCT
ejpam-837	10	24	in	in	ADP
ejpam-837	10	25	birkhoff	birkhoff	NOUN
ejpam-837	10	26	sense	sense	VERB
ejpam-837	10	27	strongly	strongly	ADV
ejpam-837	10	28	regular	regular	ADJ
ejpam-837	10	29	,	,	PUNCT
ejpam-837	10	30	see.[1	see.[1	PROPN
ejpam-837	10	31	]	]	PUNCT
ejpam-837	10	32	,	,	PUNCT
ejpam-837	10	33	p.71	p.71	PROPN
ejpam-837	10	34	)	)	PUNCT
ejpam-837	10	35	.	.	PUNCT
ejpam-837	11	1	email	email	NOUN
ejpam-837	11	2	address	address	NOUN
ejpam-837	11	3	:	:	PUNCT
ejpam-837	11	4	hanlar�mersin.edu.tr	hanlar�mersin.edu.tr	PROPN
ejpam-837	11	5	,	,	PUNCT
ejpam-837	11	6	hanlarm	hanlarm	PROPN
ejpam-837	11	7	�	�	PROPN
ejpam-837	11	8	yahoo	yahoo	PROPN
ejpam-837	11	9	.	.	PUNCT
ejpam-837	12	1	om	om	PROPN
ejpam-837	12	2	http://www.ejpam.com	http://www.ejpam.com	PROPN
ejpam-837	12	3	831	831	NUM
ejpam-837	13	1	c	c	NOUN
ejpam-837	13	2	©	©	PROPN
ejpam-837	13	3	2010	2010	NUM
ejpam-837	13	4	ejpam	ejpam	NOUN
ejpam-837	13	5	all	all	DET
ejpam-837	13	6	rights	right	NOUN
ejpam-837	13	7	reserved	reserve	VERB
ejpam-837	13	8	.	.	PUNCT
ejpam-837	14	1	k.	k.	PROPN
ejpam-837	15	1	mamedov	mamedov	PROPN
ejpam-837	16	1	/	/	SYM
ejpam-837	16	2	eur	eur	PROPN
ejpam-837	16	3	.	.	PUNCT
ejpam-837	17	1	j.	j.	PROPN
ejpam-837	17	2	pure	pure	PROPN
ejpam-837	17	3	appl	appl	PROPN
ejpam-837	17	4	.	.	PROPN
ejpam-837	17	5	math	math	PROPN
ejpam-837	17	6	,	,	PUNCT
ejpam-837	17	7	3	3	NUM
ejpam-837	17	8	(	(	PUNCT
ejpam-837	17	9	2010	2010	NUM
ejpam-837	17	10	)	)	PUNCT
ejpam-837	17	11	,	,	PUNCT
ejpam-837	17	12	831	831	NUM
ejpam-837	17	13	-	-	SYM
ejpam-837	17	14	838	838	NUM
ejpam-837	17	15	832	832	NUM
ejpam-837	17	16	in	in	ADP
ejpam-837	17	17	1962	1962	NUM
ejpam-837	17	18	mikhailov	mikhailov	NOUN
ejpam-837	18	1	[	[	X
ejpam-837	18	2	17	17	NUM
ejpam-837	18	3	]	]	PUNCT
ejpam-837	18	4	,	,	PUNCT
ejpam-837	18	5	in	in	ADP
ejpam-837	18	6	1964	1964	NUM
ejpam-837	18	7	keselman	keselman	NOUN
ejpam-837	19	1	[	[	X
ejpam-837	19	2	9	9	NUM
ejpam-837	19	3	]	]	PUNCT
ejpam-837	19	4	and	and	CCONJ
ejpam-837	19	5	in	in	ADP
ejpam-837	19	6	1971	1971	NUM
ejpam-837	19	7	dunford	dunford	NOUN
ejpam-837	19	8	and	and	CCONJ
ejpam-837	19	9	schwartz	schwartz	PROPN
ejpam-837	19	10	[	[	X
ejpam-837	19	11	4	4	X
ejpam-837	19	12	]	]	PUNCT
ejpam-837	19	13	it	it	PRON
ejpam-837	19	14	was	be	AUX
ejpam-837	19	15	showed	show	VERB
ejpam-837	19	16	the	the	DET
ejpam-837	19	17	basisness	basisness	NOUN
ejpam-837	19	18	in	in	ADP
ejpam-837	19	19	l2	l2	NOUN
ejpam-837	19	20	(	(	PUNCT
ejpam-837	19	21	0,1	0,1	NUM
ejpam-837	19	22	)	)	PUNCT
ejpam-837	19	23	of	of	ADP
ejpam-837	19	24	the	the	DET
ejpam-837	19	25	root	root	NOUN
ejpam-837	19	26	functions	function	NOUN
ejpam-837	19	27	of	of	ADP
ejpam-837	19	28	ordinary	ordinary	ADJ
ejpam-837	19	29	linear	linear	ADJ
ejpam-837	19	30	differential	differential	NOUN
ejpam-837	19	31	operator	operator	NOUN
ejpam-837	19	32	with	with	ADP
ejpam-837	19	33	regular	regular	ADJ
ejpam-837	19	34	boundary	boundary	ADJ
ejpam-837	19	35	conditions	condition	NOUN
ejpam-837	19	36	.	.	PUNCT
ejpam-837	20	1	ionkin	ionkin	NOUN
ejpam-837	21	1	[	[	X
ejpam-837	21	2	6	6	NUM
ejpam-837	21	3	]	]	PUNCT
ejpam-837	21	4	in	in	ADP
ejpam-837	21	5	1976	1976	NUM
ejpam-837	21	6	studied	study	VERB
ejpam-837	21	7	to	to	ADP
ejpam-837	21	8	following	follow	VERB
ejpam-837	21	9	boundary	boundary	ADJ
ejpam-837	21	10	value	value	NOUN
ejpam-837	21	11	problem	problem	NOUN
ejpam-837	21	12	u′′	u′′	PROPN
ejpam-837	21	13	+	+	PROPN
ejpam-837	21	14	λu	λu	X
ejpam-837	21	15	=	=	SYM
ejpam-837	21	16	0	0	PROPN
ejpam-837	21	17	,	,	PUNCT
ejpam-837	21	18	u′(0)−	u′(0)−	NOUN
ejpam-837	21	19	u′(1	u′(1	NOUN
ejpam-837	21	20	)	)	PUNCT
ejpam-837	21	21	=	=	SYM
ejpam-837	21	22	0	0	NUM
ejpam-837	21	23	,	,	PUNCT
ejpam-837	21	24	u(0	u(0	NOUN
ejpam-837	21	25	)	)	PUNCT
ejpam-837	22	1	=	=	SYM
ejpam-837	22	2	0	0	NUM
ejpam-837	23	1	whose	whose	DET
ejpam-837	23	2	boundary	boundary	ADJ
ejpam-837	23	3	conditions	condition	NOUN
ejpam-837	23	4	are	be	AUX
ejpam-837	23	5	regular	regular	ADJ
ejpam-837	23	6	,	,	PUNCT
ejpam-837	23	7	but	but	CCONJ
ejpam-837	23	8	not	not	PART
ejpam-837	23	9	strongly	strongly	ADV
ejpam-837	23	10	regular	regular	ADJ
ejpam-837	23	11	.	.	PUNCT
ejpam-837	24	1	all	all	DET
ejpam-837	24	2	the	the	DET
ejpam-837	24	3	eigenvalues	eigenvalue	NOUN
ejpam-837	24	4	of	of	ADP
ejpam-837	24	5	this	this	DET
ejpam-837	24	6	problem	problem	NOUN
ejpam-837	24	7	starting	start	VERB
ejpam-837	24	8	with	with	ADP
ejpam-837	24	9	the	the	DET
ejpam-837	24	10	second	second	ADJ
ejpam-837	24	11	one	one	NOUN
ejpam-837	24	12	are	be	AUX
ejpam-837	24	13	double	double	ADJ
ejpam-837	24	14	,	,	PUNCT
ejpam-837	24	15	the	the	DET
ejpam-837	24	16	general	general	ADJ
ejpam-837	24	17	number	number	NOUN
ejpam-837	24	18	of	of	ADP
ejpam-837	24	19	associated	associate	VERB
ejpam-837	24	20	that	that	SCONJ
ejpam-837	24	21	the	the	DET
ejpam-837	24	22	chosen	choose	VERB
ejpam-837	24	23	specially	specially	ADJ
ejpam-837	24	24	system	system	NOUN
ejpam-837	24	25	of	of	ADP
ejpam-837	24	26	root	root	NOUN
ejpam-837	24	27	functions	function	NOUN
ejpam-837	24	28	form	form	VERB
ejpam-837	24	29	an	an	DET
ejpam-837	24	30	unconditional	unconditional	ADJ
ejpam-837	24	31	basis	basis	NOUN
ejpam-837	24	32	in	in	ADP
ejpam-837	24	33	l2	l2	NOUN
ejpam-837	24	34	(	(	PUNCT
ejpam-837	24	35	0,1	0,1	NUM
ejpam-837	24	36	)	)	PUNCT
ejpam-837	24	37	.	.	PUNCT
ejpam-837	25	1	by	by	ADP
ejpam-837	25	2	shkalikov	shkalikov	PROPN
ejpam-837	25	3	[	[	X
ejpam-837	25	4	19	19	NUM
ejpam-837	25	5	]	]	PUNCT
ejpam-837	25	6	in	in	ADP
ejpam-837	25	7	1979	1979	NUM
ejpam-837	25	8	[	[	X
ejpam-837	25	9	see	see	VERB
ejpam-837	25	10	20	20	NUM
ejpam-837	25	11	]	]	PUNCT
ejpam-837	25	12	,	,	PUNCT
ejpam-837	25	13	it	it	PRON
ejpam-837	25	14	was	be	AUX
ejpam-837	25	15	proved	prove	VERB
ejpam-837	25	16	that	that	SCONJ
ejpam-837	25	17	the	the	DET
ejpam-837	25	18	system	system	NOUN
ejpam-837	25	19	of	of	ADP
ejpam-837	25	20	root	root	NOUN
ejpam-837	25	21	functions	function	NOUN
ejpam-837	25	22	of	of	ADP
ejpam-837	25	23	a	a	DET
ejpam-837	25	24	differential	differential	ADJ
ejpam-837	25	25	operator	operator	NOUN
ejpam-837	25	26	with	with	ADP
ejpam-837	25	27	not	not	PART
ejpam-837	25	28	strongly	strongly	ADV
ejpam-837	25	29	regular	regular	ADJ
ejpam-837	25	30	boundary	boundary	ADJ
ejpam-837	25	31	conditions	condition	NOUN
ejpam-837	25	32	form	form	VERB
ejpam-837	25	33	a	a	DET
ejpam-837	25	34	riesz	riesz	ADJ
ejpam-837	25	35	basis	basis	NOUN
ejpam-837	25	36	with	with	ADP
ejpam-837	25	37	parentheses	parenthesis	NOUN
ejpam-837	25	38	.	.	PUNCT
ejpam-837	26	1	kerimov	kerimov	PROPN
ejpam-837	26	2	and	and	CCONJ
ejpam-837	26	3	mamedov	mamedov	NOUN
ejpam-837	27	1	[	[	X
ejpam-837	27	2	8	8	NUM
ejpam-837	27	3	]	]	PUNCT
ejpam-837	27	4	in	in	ADP
ejpam-837	27	5	1998	1998	NUM
ejpam-837	27	6	found	find	VERB
ejpam-837	27	7	conditions	condition	NOUN
ejpam-837	27	8	on	on	ADP
ejpam-837	27	9	the	the	DET
ejpam-837	27	10	potential	potential	ADJ
ejpam-837	27	11	q(x	q(x	NOUN
ejpam-837	27	12	)	)	PUNCT
ejpam-837	27	13	under	under	ADP
ejpam-837	27	14	which	which	PRON
ejpam-837	27	15	the	the	DET
ejpam-837	27	16	system	system	NOUN
ejpam-837	27	17	eigenfunctions	eigenfunction	NOUN
ejpam-837	27	18	of	of	ADP
ejpam-837	27	19	boundary	boundary	ADJ
ejpam-837	27	20	value	value	NOUN
ejpam-837	27	21	problems	problem	NOUN
ejpam-837	27	22	(	(	PUNCT
ejpam-837	27	23	1),(2	1),(2	NUM
ejpam-837	27	24	)	)	PUNCT
ejpam-837	27	25	and	and	CCONJ
ejpam-837	27	26	(	(	PUNCT
ejpam-837	27	27	1),(3	1),(3	NOUN
ejpam-837	27	28	)	)	PUNCT
ejpam-837	27	29	forms	form	NOUN
ejpam-837	27	30	riesz	riesz	VERB
ejpam-837	27	31	basis	basis	NOUN
ejpam-837	27	32	in	in	ADP
ejpam-837	27	33	l2	l2	NOUN
ejpam-837	27	34	(	(	PUNCT
ejpam-837	27	35	0,1	0,1	NUM
ejpam-837	27	36	)	)	PUNCT
ejpam-837	27	37	.	.	PUNCT
ejpam-837	28	1	namely	namely	ADV
ejpam-837	28	2	,	,	PUNCT
ejpam-837	28	3	they	they	PRON
ejpam-837	28	4	proved	prove	VERB
ejpam-837	28	5	the	the	DET
ejpam-837	28	6	following	follow	VERB
ejpam-837	28	7	result	result	NOUN
ejpam-837	28	8	:	:	PUNCT
ejpam-837	28	9	assume	assume	VERB
ejpam-837	28	10	that	that	SCONJ
ejpam-837	28	11	q(x	q(x	NOUN
ejpam-837	28	12	)	)	PUNCT
ejpam-837	28	13	∈	∈	PROPN
ejpam-837	28	14	c	c	NOUN
ejpam-837	28	15	(	(	PUNCT
ejpam-837	28	16	4)[0,1	4)[0,1	NOUN
ejpam-837	28	17	]	]	X
ejpam-837	28	18	is	be	AUX
ejpam-837	28	19	complexvalued	complexvalue	VERB
ejpam-837	28	20	functions	function	NOUN
ejpam-837	28	21	satisfying	satisfy	VERB
ejpam-837	28	22	the	the	DET
ejpam-837	28	23	condition	condition	NOUN
ejpam-837	28	24	q(0	q(0	PROPN
ejpam-837	28	25	)	)	PUNCT
ejpam-837	28	26	6=	6=	PROPN
ejpam-837	29	1	q(1	q(1	PROPN
ejpam-837	29	2	)	)	PUNCT
ejpam-837	29	3	,	,	PUNCT
ejpam-837	29	4	then	then	ADV
ejpam-837	29	5	the	the	DET
ejpam-837	29	6	root	root	NOUN
ejpam-837	29	7	functions	function	NOUN
ejpam-837	29	8	of	of	ADP
ejpam-837	29	9	boundary	boundary	ADJ
ejpam-837	29	10	value	value	NOUN
ejpam-837	29	11	problems	problem	NOUN
ejpam-837	29	12	(	(	PUNCT
ejpam-837	29	13	1),(2	1),(2	NUM
ejpam-837	29	14	)	)	PUNCT
ejpam-837	29	15	and	and	CCONJ
ejpam-837	29	16	(	(	PUNCT
ejpam-837	29	17	1),(3	1),(3	X
ejpam-837	29	18	)	)	PUNCT
ejpam-837	29	19	form	form	NOUN
ejpam-837	29	20	riesz	riesz	VERB
ejpam-837	29	21	basis	basis	NOUN
ejpam-837	29	22	in	in	ADP
ejpam-837	29	23	l2	l2	NOUN
ejpam-837	29	24	(	(	PUNCT
ejpam-837	29	25	0,1	0,1	NUM
ejpam-837	29	26	)	)	PUNCT
ejpam-837	29	27	.	.	PUNCT
ejpam-837	30	1	the	the	DET
ejpam-837	30	2	spectral	spectral	ADJ
ejpam-837	30	3	properties	property	NOUN
ejpam-837	30	4	of	of	ADP
ejpam-837	30	5	the	the	DET
ejpam-837	30	6	boundary	boundary	ADJ
ejpam-837	30	7	value	value	NOUN
ejpam-837	30	8	problems	problem	NOUN
ejpam-837	30	9	(	(	PUNCT
ejpam-837	30	10	1),(2	1),(2	NUM
ejpam-837	30	11	)	)	PUNCT
ejpam-837	30	12	and	and	CCONJ
ejpam-837	30	13	(	(	PUNCT
ejpam-837	30	14	1),(3	1),(3	NOUN
ejpam-837	30	15	)	)	PUNCT
ejpam-837	30	16	were	be	AUX
ejpam-837	30	17	investigated	investigate	VERB
ejpam-837	30	18	in	in	ADP
ejpam-837	30	19	[	[	X
ejpam-837	30	20	14	14	NUM
ejpam-837	30	21	]	]	SYM
ejpam-837	30	22	.	.	PUNCT
ejpam-837	31	1	dernek	dernek	ADJ
ejpam-837	31	2	and	and	CCONJ
ejpam-837	31	3	veliev	veliev	NOUN
ejpam-837	32	1	[	[	X
ejpam-837	32	2	2	2	X
ejpam-837	32	3	]	]	PUNCT
ejpam-837	32	4	in	in	ADP
ejpam-837	32	5	2005	2005	NUM
ejpam-837	32	6	established	establish	VERB
ejpam-837	32	7	conditions	condition	NOUN
ejpam-837	32	8	in	in	ADP
ejpam-837	32	9	terms	term	NOUN
ejpam-837	32	10	of	of	ADP
ejpam-837	32	11	the	the	DET
ejpam-837	32	12	fourier	fourier	NOUN
ejpam-837	32	13	coefficients	coefficient	NOUN
ejpam-837	32	14	qn	qn	NOUN
ejpam-837	32	15	=	=	X
ejpam-837	32	16	(	(	PUNCT
ejpam-837	32	17	q(x	q(x	PROPN
ejpam-837	32	18	)	)	PUNCT
ejpam-837	32	19	,	,	PUNCT
ejpam-837	32	20	exp	exp	NOUN
ejpam-837	32	21	i2nπx	i2nπx	NOUN
ejpam-837	32	22	)	)	PUNCT
ejpam-837	32	23	of	of	ADP
ejpam-837	32	24	the	the	DET
ejpam-837	32	25	potential	potential	ADJ
ejpam-837	32	26	q(x	q(x	NOUN
ejpam-837	32	27	)	)	PUNCT
ejpam-837	32	28	proved	prove	VERB
ejpam-837	32	29	the	the	DET
ejpam-837	32	30	following	follow	VERB
ejpam-837	32	31	result	result	NOUN
ejpam-837	32	32	:	:	PUNCT
ejpam-837	32	33	assume	assume	VERB
ejpam-837	32	34	that	that	SCONJ
ejpam-837	32	35	the	the	DET
ejpam-837	32	36	conditions	condition	NOUN
ejpam-837	32	37	lim	lim	PROPN
ejpam-837	32	38	n→∞	n→∞	PRON
ejpam-837	32	39	ln|n|	ln|n|	X
ejpam-837	32	40	nq2n	nq2n	PROPN
ejpam-837	32	41	=	=	SYM
ejpam-837	32	42	0	0	NUM
ejpam-837	32	43	,	,	PUNCT
ejpam-837	32	44	q2n	q2n	ADV
ejpam-837	32	45	∼	∼	NOUN
ejpam-837	32	46	q−2n	q−2n	PROPN
ejpam-837	32	47	for	for	ADP
ejpam-837	32	48	(	(	PUNCT
ejpam-837	32	49	1),(2	1),(2	PROPN
ejpam-837	32	50	)	)	PUNCT
ejpam-837	32	51	(	(	PUNCT
ejpam-837	32	52	and	and	CCONJ
ejpam-837	32	53	lim	lim	PROPN
ejpam-837	32	54	n→∞	n→∞	NUM
ejpam-837	32	55	ln|n|	ln|n|	PROPN
ejpam-837	32	56	nq2n+1	nq2n+1	X
ejpam-837	32	57	=	=	SYM
ejpam-837	32	58	0	0	PROPN
ejpam-837	32	59	,	,	PUNCT
ejpam-837	32	60	q2n+1	q2n+1	ADV
ejpam-837	32	61	∼	∼	NOUN
ejpam-837	32	62	q−2n−1	q−2n−1	INTJ
ejpam-837	32	63	for	for	ADP
ejpam-837	32	64	(	(	PUNCT
ejpam-837	32	65	1),(3	1),(3	NOUN
ejpam-837	32	66	)	)	PUNCT
ejpam-837	32	67	)	)	PUNCT
ejpam-837	32	68	hold	hold	VERB
ejpam-837	32	69	,	,	PUNCT
ejpam-837	32	70	where	where	SCONJ
ejpam-837	32	71	an	an	DET
ejpam-837	32	72	∼	∼	NOUN
ejpam-837	32	73	bn	bn	NOUN
ejpam-837	32	74	weans	wean	NOUN
ejpam-837	32	75	that	that	PRON
ejpam-837	32	76	c1	c1	PROPN
ejpam-837	32	77	�	�	PROPN
ejpam-837	32	78	�	�	PROPN
ejpam-837	32	79	bn	bn	PROPN
ejpam-837	32	80	�	�	PROPN
ejpam-837	32	81	�	�	PROPN
ejpam-837	32	82	<	<	X
ejpam-837	32	83	�	�	PROPN
ejpam-837	32	84	�	�	PROPN
ejpam-837	32	85	an	an	DET
ejpam-837	32	86	�	�	PROPN
ejpam-837	32	87	�	�	PROPN
ejpam-837	32	88	<	<	X
ejpam-837	32	89	c2	c2	PROPN
ejpam-837	32	90	�	�	PROPN
ejpam-837	32	91	�	�	PROPN
ejpam-837	32	92	bn	bn	PROPN
ejpam-837	32	93	�	�	PROPN
ejpam-837	32	94	�	�	PROPN
ejpam-837	32	95	.	.	PUNCT
ejpam-837	33	1	then	then	ADV
ejpam-837	33	2	the	the	DET
ejpam-837	33	3	root	root	NOUN
ejpam-837	33	4	functions	function	NOUN
ejpam-837	33	5	of	of	ADP
ejpam-837	33	6	the	the	DET
ejpam-837	33	7	boundary	boundary	ADJ
ejpam-837	33	8	problem	problem	NOUN
ejpam-837	33	9	(	(	PUNCT
ejpam-837	33	10	1),(2	1),(2	NUM
ejpam-837	33	11	)	)	PUNCT
ejpam-837	33	12	(	(	PUNCT
ejpam-837	33	13	and	and	CCONJ
ejpam-837	33	14	(	(	PUNCT
ejpam-837	33	15	1),(3	1),(3	NOUN
ejpam-837	33	16	)	)	PUNCT
ejpam-837	33	17	)	)	PUNCT
ejpam-837	33	18	form	form	VERB
ejpam-837	33	19	a	a	DET
ejpam-837	33	20	riesz	riesz	NOUN
ejpam-837	33	21	basis	basis	NOUN
ejpam-837	33	22	in	in	ADP
ejpam-837	33	23	l2	l2	NOUN
ejpam-837	33	24	(	(	PUNCT
ejpam-837	33	25	0,1	0,1	NUM
ejpam-837	33	26	)	)	PUNCT
ejpam-837	33	27	.	.	PUNCT
ejpam-837	34	1	makin	makin	NOUN
ejpam-837	35	1	[	[	X
ejpam-837	35	2	12	12	NUM
ejpam-837	35	3	]	]	PUNCT
ejpam-837	35	4	in	in	ADP
ejpam-837	35	5	2005	2005	NUM
ejpam-837	35	6	obtained	obtain	VERB
ejpam-837	35	7	the	the	DET
ejpam-837	35	8	following	following	ADJ
ejpam-837	35	9	result	result	NOUN
ejpam-837	35	10	:	:	PUNCT
ejpam-837	35	11	suppose	suppose	VERB
ejpam-837	35	12	that	that	SCONJ
ejpam-837	35	13	q(x	q(x	NOUN
ejpam-837	35	14	)	)	PUNCT
ejpam-837	35	15	∈w	∈w	VERB
ejpam-837	35	16	m	m	VERB
ejpam-837	35	17	1	1	NUM
ejpam-837	36	1	[	[	X
ejpam-837	36	2	0,1	0,1	NUM
ejpam-837	36	3	]	]	PUNCT
ejpam-837	36	4	,	,	PUNCT
ejpam-837	36	5	q(l)(0	q(l)(0	NUM
ejpam-837	36	6	)	)	PUNCT
ejpam-837	36	7	=	=	SYM
ejpam-837	36	8	q(l)(1	q(l)(1	NUM
ejpam-837	36	9	)	)	PUNCT
ejpam-837	36	10	,	,	PUNCT
ejpam-837	36	11	for	for	ADP
ejpam-837	36	12	all	all	DET
ejpam-837	36	13	l	l	NOUN
ejpam-837	36	14	=	=	SYM
ejpam-837	36	15	0,1	0,1	NUM
ejpam-837	36	16	,	,	PUNCT
ejpam-837	36	17	...	...	PUNCT
ejpam-837	36	18	,	,	PUNCT
ejpam-837	36	19	m	m	VERB
ejpam-837	36	20	−	−	NOUN
ejpam-837	36	21	1	1	NUM
ejpam-837	37	1	and	and	CCONJ
ejpam-837	37	2	q2n	q2n	ADV
ejpam-837	37	3	>	>	X
ejpam-837	37	4	c0n−m−1	c0n−m−1	PROPN
ejpam-837	37	5	,	,	PUNCT
ejpam-837	37	6	0	0	PUNCT
ejpam-837	37	7	<	<	X
ejpam-837	37	8	c1	c1	PROPN
ejpam-837	37	9	<	<	X
ejpam-837	37	10	|α2n|	|α2n|	NOUN
ejpam-837	37	11	|β2n|	|β2n|	VERB
ejpam-837	37	12	<	<	X
ejpam-837	37	13	c2	c2	PROPN
ejpam-837	37	14	for	for	ADP
ejpam-837	37	15	(	(	PUNCT
ejpam-837	37	16	1),(2	1),(2	PROPN
ejpam-837	37	17	)	)	PUNCT
ejpam-837	37	18	(	(	PUNCT
ejpam-837	37	19	and	and	CCONJ
ejpam-837	37	20	q2n−1	q2n−1	PROPN
ejpam-837	37	21	>	>	X
ejpam-837	37	22	c0n−m−1	c0n−m−1	PROPN
ejpam-837	37	23	,	,	PUNCT
ejpam-837	37	24	0	0	PUNCT
ejpam-837	37	25	<	<	X
ejpam-837	37	26	c1	c1	PROPN
ejpam-837	37	27	<	<	X
ejpam-837	37	28	|α2n−1|	|α2n−1|	PROPN
ejpam-837	37	29	|β2n−1|	|β2n−1|	PROPN
ejpam-837	37	30	<	<	X
ejpam-837	37	31	c2	c2	PROPN
ejpam-837	37	32	,	,	PUNCT
ejpam-837	37	33	c0	c0	PROPN
ejpam-837	37	34	>	>	X
ejpam-837	37	35	0	0	PUNCT
ejpam-837	38	1	for	for	ADP
ejpam-837	38	2	(	(	PUNCT
ejpam-837	38	3	1),(3	1),(3	NOUN
ejpam-837	38	4	)	)	PUNCT
ejpam-837	38	5	)	)	PUNCT
ejpam-837	38	6	for	for	ADP
ejpam-837	38	7	all	all	PRON
ejpam-837	38	8	n	n	PRON
ejpam-837	38	9	>	>	X
ejpam-837	38	10	n1	n1	PROPN
ejpam-837	38	11	,	,	PUNCT
ejpam-837	38	12	then	then	ADV
ejpam-837	38	13	the	the	DET
ejpam-837	38	14	root	root	NOUN
ejpam-837	38	15	functions	function	NOUN
ejpam-837	38	16	of	of	ADP
ejpam-837	38	17	boundary	boundary	ADJ
ejpam-837	38	18	value	value	NOUN
ejpam-837	38	19	problem	problem	NOUN
ejpam-837	38	20	(	(	PUNCT
ejpam-837	38	21	1),(2	1),(2	NUM
ejpam-837	38	22	)	)	PUNCT
ejpam-837	38	23	(	(	PUNCT
ejpam-837	38	24	and	and	CCONJ
ejpam-837	38	25	(	(	PUNCT
ejpam-837	38	26	1),(3	1),(3	NOUN
ejpam-837	38	27	)	)	PUNCT
ejpam-837	38	28	)	)	PUNCT
ejpam-837	38	29	form	form	VERB
ejpam-837	38	30	a	a	DET
ejpam-837	38	31	riesz	riesz	NOUN
ejpam-837	38	32	basis	basis	NOUN
ejpam-837	38	33	in	in	ADP
ejpam-837	38	34	l2	l2	NOUN
ejpam-837	38	35	(	(	PUNCT
ejpam-837	38	36	0,1	0,1	NUM
ejpam-837	38	37	)	)	PUNCT
ejpam-837	38	38	.	.	PUNCT
ejpam-837	39	1	moreover	moreover	ADV
ejpam-837	39	2	,	,	PUNCT
ejpam-837	39	3	some	some	DET
ejpam-837	39	4	theorems	theorem	NOUN
ejpam-837	39	5	for	for	ADP
ejpam-837	39	6	determining	determine	VERB
ejpam-837	39	7	whether	whether	SCONJ
ejpam-837	39	8	the	the	DET
ejpam-837	39	9	root	root	NOUN
ejpam-837	39	10	functions	function	NOUN
ejpam-837	39	11	form	form	VERB
ejpam-837	39	12	a	a	DET
ejpam-837	39	13	riesz	riesz	ADJ
ejpam-837	39	14	basis	basis	NOUN
ejpam-837	39	15	in	in	ADP
ejpam-837	39	16	l2	l2	NOUN
ejpam-837	39	17	(	(	PUNCT
ejpam-837	39	18	0,1	0,1	NOUN
ejpam-837	39	19	)	)	PUNCT
ejpam-837	39	20	or	or	CCONJ
ejpam-837	39	21	not	not	PART
ejpam-837	39	22	were	be	AUX
ejpam-837	39	23	given	give	VERB
ejpam-837	39	24	in[12	in[12	PROPN
ejpam-837	39	25	]	]	X
ejpam-837	39	26	.	.	PUNCT
ejpam-837	40	1	a	a	DET
ejpam-837	40	2	classification	classification	NOUN
ejpam-837	40	3	on	on	ADP
ejpam-837	40	4	the	the	DET
ejpam-837	40	5	boundary	boundary	ADJ
ejpam-837	40	6	conditions	condition	NOUN
ejpam-837	40	7	for	for	ADP
ejpam-837	40	8	sturmlionville	sturmlionville	NOUN
ejpam-837	40	9	operator	operator	NOUN
ejpam-837	40	10	under	under	ADP
ejpam-837	40	11	which	which	PRON
ejpam-837	40	12	the	the	DET
ejpam-837	40	13	root	root	NOUN
ejpam-837	40	14	functions	function	NOUN
ejpam-837	40	15	form	form	VERB
ejpam-837	40	16	a	a	DET
ejpam-837	40	17	riesz	riesz	ADJ
ejpam-837	40	18	basis	basis	NOUN
ejpam-837	40	19	in	in	ADP
ejpam-837	40	20	l2	l2	NOUN
ejpam-837	40	21	(	(	PUNCT
ejpam-837	40	22	0,1	0,1	NUM
ejpam-837	40	23	)	)	PUNCT
ejpam-837	40	24	is	be	AUX
ejpam-837	40	25	established	establish	VERB
ejpam-837	40	26	in	in	ADP
ejpam-837	40	27	[	[	X
ejpam-837	40	28	13	13	NUM
ejpam-837	40	29	]	]	PUNCT
ejpam-837	40	30	.	.	PUNCT
ejpam-837	41	1	shkalikov	shkalikov	PROPN
ejpam-837	41	2	and	and	CCONJ
ejpam-837	41	3	veliev	veliev	NOUN
ejpam-837	41	4	[	[	X
ejpam-837	41	5	21	21	NUM
ejpam-837	41	6	]	]	PUNCT
ejpam-837	41	7	in	in	ADP
ejpam-837	41	8	2008	2008	NUM
ejpam-837	41	9	obtained	obtain	VERB
ejpam-837	41	10	similar	similar	ADJ
ejpam-837	41	11	result	result	NOUN
ejpam-837	41	12	in	in	ADP
ejpam-837	41	13	terms	term	NOUN
ejpam-837	41	14	of	of	ADP
ejpam-837	41	15	the	the	DET
ejpam-837	41	16	fourier	fourier	NOUN
ejpam-837	41	17	coefficients	coefficient	NOUN
ejpam-837	41	18	qn	qn	INTJ
ejpam-837	41	19	on	on	ADP
ejpam-837	41	20	the	the	DET
ejpam-837	41	21	potential	potential	ADJ
ejpam-837	41	22	q(x	q(x	PROPN
ejpam-837	41	23	)	)	PUNCT
ejpam-837	41	24	∈w	∈w	VERB
ejpam-837	41	25	p	p	NOUN
ejpam-837	41	26	1	1	NUM
ejpam-837	41	27	[	[	X
ejpam-837	41	28	0,1	0,1	NUM
ejpam-837	41	29	]	]	PUNCT
ejpam-837	41	30	(	(	PUNCT
ejpam-837	41	31	q(ℓ)(0	q(ℓ)(0	NUM
ejpam-837	41	32	)	)	PUNCT
ejpam-837	41	33	=	=	SYM
ejpam-837	41	34	q(ℓ)(1	q(ℓ)(1	NOUN
ejpam-837	41	35	)	)	PUNCT
ejpam-837	41	36	=	=	NOUN
ejpam-837	41	37	0,0	0,0	NUM
ejpam-837	41	38	≤	≤	NUM
ejpam-837	41	39	ℓ	ℓ	NOUN
ejpam-837	41	40	≤	≤	NOUN
ejpam-837	41	41	s−	s−	PROPN
ejpam-837	41	42	1	1	NUM
ejpam-837	41	43	,	,	PUNCT
ejpam-837	41	44	where	where	SCONJ
ejpam-837	41	45	s	s	VERB
ejpam-837	41	46	≤	≤	PROPN
ejpam-837	41	47	p	p	NOUN
ejpam-837	41	48	)	)	PUNCT
ejpam-837	41	49	under	under	ADP
ejpam-837	41	50	which	which	PRON
ejpam-837	41	51	the	the	DET
ejpam-837	41	52	system	system	NOUN
ejpam-837	41	53	of	of	ADP
ejpam-837	41	54	root	root	NOUN
ejpam-837	41	55	functions	function	NOUN
ejpam-837	41	56	form	form	VERB
ejpam-837	41	57	a	a	DET
ejpam-837	41	58	riesz	riesz	ADJ
ejpam-837	41	59	basis	basis	NOUN
ejpam-837	41	60	in	in	ADP
ejpam-837	41	61	l2	l2	NOUN
ejpam-837	41	62	(	(	PUNCT
ejpam-837	41	63	0,1	0,1	NUM
ejpam-837	41	64	)	)	PUNCT
ejpam-837	41	65	.	.	PUNCT
ejpam-837	42	1	mamedov	mamedov	PROPN
ejpam-837	42	2	and	and	CCONJ
ejpam-837	42	3	menken	menken	NOUN
ejpam-837	43	1	[	[	X
ejpam-837	43	2	15	15	NUM
ejpam-837	43	3	]	]	PUNCT
ejpam-837	43	4	in	in	ADP
ejpam-837	43	5	2008	2008	NUM
ejpam-837	43	6	showed	show	VERB
ejpam-837	43	7	that	that	SCONJ
ejpam-837	43	8	the	the	DET
ejpam-837	43	9	root	root	NOUN
ejpam-837	43	10	functions	function	NOUN
ejpam-837	43	11	of	of	ADP
ejpam-837	43	12	the	the	DET
ejpam-837	43	13	boundary	boundary	ADJ
ejpam-837	43	14	-	-	PUNCT
ejpam-837	43	15	value	value	NOUN
ejpam-837	43	16	problems	problem	NOUN
ejpam-837	43	17	(	(	PUNCT
ejpam-837	43	18	1),(2	1),(2	NUM
ejpam-837	43	19	)	)	PUNCT
ejpam-837	43	20	and	and	CCONJ
ejpam-837	43	21	(	(	PUNCT
ejpam-837	43	22	1),(3	1),(3	NOUN
ejpam-837	43	23	)	)	PUNCT
ejpam-837	43	24	form	form	NOUN
ejpam-837	43	25	a	a	DET
ejpam-837	43	26	riesz	riesz	NOUN
ejpam-837	43	27	basis	basis	NOUN
ejpam-837	43	28	in	in	ADP
ejpam-837	43	29	l2	l2	NOUN
ejpam-837	43	30	(	(	PUNCT
ejpam-837	43	31	0,1	0,1	NOUN
ejpam-837	43	32	)	)	PUNCT
ejpam-837	43	33	when	when	SCONJ
ejpam-837	43	34	q(x	q(x	NOUN
ejpam-837	43	35	)	)	PUNCT
ejpam-837	43	36	∈	∈	PROPN
ejpam-837	43	37	c	c	NOUN
ejpam-837	43	38	(	(	PUNCT
ejpam-837	43	39	4)[0,1	4)[0,1	NOUN
ejpam-837	43	40	]	]	X
ejpam-837	43	41	is	be	AUX
ejpam-837	43	42	complexvalued	complexvalue	VERB
ejpam-837	43	43	functions	function	NOUN
ejpam-837	43	44	satisfying	satisfy	VERB
ejpam-837	43	45	the	the	DET
ejpam-837	43	46	condition	condition	NOUN
ejpam-837	43	47	the	the	DET
ejpam-837	43	48	conditions	condition	NOUN
ejpam-837	43	49	q(0	q(0	PROPN
ejpam-837	43	50	)	)	PUNCT
ejpam-837	43	51	=	=	SYM
ejpam-837	43	52	q(1	q(1	PROPN
ejpam-837	43	53	)	)	PUNCT
ejpam-837	43	54	and	and	CCONJ
ejpam-837	43	55	q′(0	q′(0	NOUN
ejpam-837	43	56	)	)	PUNCT
ejpam-837	43	57	6=	6=	X
ejpam-837	44	1	q′(1	q′(1	PROPN
ejpam-837	44	2	)	)	PUNCT
ejpam-837	44	3	.	.	PUNCT
ejpam-837	45	1	in	in	ADP
ejpam-837	45	2	2008	2008	NUM
ejpam-837	45	3	djakov	djakov	NOUN
ejpam-837	45	4	and	and	CCONJ
ejpam-837	45	5	mitjagin	mitjagin	VERB
ejpam-837	45	6	[	[	X
ejpam-837	45	7	3	3	NUM
ejpam-837	45	8	]	]	PUNCT
ejpam-837	45	9	obtained	obtain	VERB
ejpam-837	45	10	some	some	DET
ejpam-837	45	11	result	result	NOUN
ejpam-837	45	12	on	on	ADP
ejpam-837	45	13	the	the	DET
ejpam-837	45	14	absence	absence	NOUN
ejpam-837	45	15	of	of	ADP
ejpam-837	45	16	the	the	DET
ejpam-837	45	17	riesz	riesz	PROPN
ejpam-837	45	18	basis	basis	NOUN
ejpam-837	45	19	property	property	NOUN
ejpam-837	45	20	.	.	PUNCT
ejpam-837	46	1	in	in	ADP
ejpam-837	46	2	2010	2010	NUM
ejpam-837	46	3	kıraç	kıraç	NOUN
ejpam-837	46	4	[	[	X
ejpam-837	46	5	10	10	NUM
ejpam-837	46	6	]	]	PUNCT
ejpam-837	46	7	showed	show	VERB
ejpam-837	46	8	that	that	SCONJ
ejpam-837	46	9	the	the	DET
ejpam-837	46	10	root	root	NOUN
ejpam-837	46	11	functions	function	NOUN
ejpam-837	46	12	of	of	ADP
ejpam-837	46	13	the	the	DET
ejpam-837	46	14	boundary	boundary	ADJ
ejpam-837	46	15	-	-	PUNCT
ejpam-837	46	16	value	value	NOUN
ejpam-837	46	17	problems	problem	NOUN
ejpam-837	46	18	(	(	PUNCT
ejpam-837	46	19	1),(2	1),(2	NUM
ejpam-837	46	20	)	)	PUNCT
ejpam-837	46	21	and	and	CCONJ
ejpam-837	46	22	(	(	PUNCT
ejpam-837	46	23	1),(3	1),(3	NOUN
ejpam-837	46	24	)	)	PUNCT
ejpam-837	46	25	form	form	NOUN
ejpam-837	46	26	a	a	DET
ejpam-837	46	27	riesz	riesz	NOUN
ejpam-837	46	28	basis	basis	NOUN
ejpam-837	46	29	in	in	ADP
ejpam-837	46	30	l2	l2	NOUN
ejpam-837	46	31	(	(	PUNCT
ejpam-837	46	32	0,1	0,1	NOUN
ejpam-837	46	33	)	)	PUNCT
ejpam-837	46	34	when	when	SCONJ
ejpam-837	46	35	q(x	q(x	NOUN
ejpam-837	46	36	)	)	PUNCT
ejpam-837	46	37	is	be	AUX
ejpam-837	46	38	absolutely	absolutely	ADV
ejpam-837	46	39	continuous	continuous	ADJ
ejpam-837	46	40	function	function	NOUN
ejpam-837	46	41	in	in	ADP
ejpam-837	46	42	k.	k.	PROPN
ejpam-837	46	43	mamedov	mamedov	PROPN
ejpam-837	46	44	/	/	SYM
ejpam-837	46	45	eur	eur	PROPN
ejpam-837	46	46	.	.	PUNCT
ejpam-837	47	1	j.	j.	PROPN
ejpam-837	47	2	pure	pure	PROPN
ejpam-837	47	3	appl	appl	PROPN
ejpam-837	47	4	.	.	PROPN
ejpam-837	47	5	math	math	PROPN
ejpam-837	47	6	,	,	PUNCT
ejpam-837	47	7	3	3	NUM
ejpam-837	47	8	(	(	PUNCT
ejpam-837	47	9	2010	2010	NUM
ejpam-837	47	10	)	)	PUNCT
ejpam-837	47	11	,	,	PUNCT
ejpam-837	47	12	831	831	NUM
ejpam-837	47	13	-	-	SYM
ejpam-837	47	14	838	838	NUM
ejpam-837	47	15	833	833	NUM
ejpam-837	47	16	[	[	X
ejpam-837	47	17	0,1	0,1	NUM
ejpam-837	47	18	]	]	PUNCT
ejpam-837	47	19	and	and	CCONJ
ejpam-837	47	20	q(0	q(0	PROPN
ejpam-837	47	21	)	)	PUNCT
ejpam-837	47	22	6=	6=	PROPN
ejpam-837	47	23	q(1	q(1	NOUN
ejpam-837	47	24	)	)	PUNCT
ejpam-837	47	25	.	.	PUNCT
ejpam-837	48	1	by	by	ADP
ejpam-837	48	2	kurbanov	kurbanov	PROPN
ejpam-837	48	3	[	[	X
ejpam-837	48	4	11	11	NUM
ejpam-837	48	5	]	]	PUNCT
ejpam-837	48	6	in	in	ADP
ejpam-837	48	7	2006	2006	NUM
ejpam-837	48	8	it	it	PRON
ejpam-837	48	9	was	be	AUX
ejpam-837	48	10	showed	show	VERB
ejpam-837	48	11	that	that	SCONJ
ejpam-837	48	12	the	the	DET
ejpam-837	48	13	root	root	NOUN
ejpam-837	48	14	functions	function	NOUN
ejpam-837	48	15	of	of	ADP
ejpam-837	48	16	the	the	DET
ejpam-837	48	17	boundary	boundary	ADJ
ejpam-837	48	18	value	value	NOUN
ejpam-837	48	19	problems	problem	NOUN
ejpam-837	48	20	(	(	PUNCT
ejpam-837	48	21	1),(2	1),(2	NUM
ejpam-837	48	22	)	)	PUNCT
ejpam-837	48	23	and	and	CCONJ
ejpam-837	48	24	(	(	PUNCT
ejpam-837	48	25	1),(3	1),(3	NOUN
ejpam-837	48	26	)	)	PUNCT
ejpam-837	48	27	forms	form	VERB
ejpam-837	48	28	a	a	DET
ejpam-837	48	29	basis	basis	NOUN
ejpam-837	48	30	in	in	ADP
ejpam-837	48	31	lp	lp	PROPN
ejpam-837	48	32	(	(	PUNCT
ejpam-837	48	33	0,1	0,1	NUM
ejpam-837	48	34	)	)	PUNCT
ejpam-837	48	35	,	,	PUNCT
ejpam-837	48	36	p	p	X
ejpam-837	48	37	>	>	X
ejpam-837	48	38	1	1	NUM
ejpam-837	49	1	when	when	SCONJ
ejpam-837	49	2	q(x	q(x	NOUN
ejpam-837	49	3	)	)	PUNCT
ejpam-837	49	4	∈	∈	PROPN
ejpam-837	49	5	c	c	NOUN
ejpam-837	49	6	(	(	PUNCT
ejpam-837	49	7	4)[0,1	4)[0,1	NOUN
ejpam-837	49	8	]	]	PUNCT
ejpam-837	49	9	and	and	CCONJ
ejpam-837	49	10	q(0	q(0	PROPN
ejpam-837	49	11	)	)	PUNCT
ejpam-837	49	12	6=	6=	PROPN
ejpam-837	50	1	q(1	q(1	NOUN
ejpam-837	50	2	)	)	PUNCT
ejpam-837	50	3	.	.	PUNCT
ejpam-837	51	1	in	in	ADP
ejpam-837	51	2	the	the	DET
ejpam-837	51	3	case	case	NOUN
ejpam-837	51	4	q(x	q(x	NOUN
ejpam-837	51	5	)	)	PUNCT
ejpam-837	51	6	∈	∈	PROPN
ejpam-837	51	7	c	c	NOUN
ejpam-837	51	8	(	(	PUNCT
ejpam-837	51	9	4)[0,1	4)[0,1	NOUN
ejpam-837	51	10	]	]	X
ejpam-837	51	11	,	,	PUNCT
ejpam-837	51	12	q(0	q(0	PROPN
ejpam-837	51	13	)	)	PUNCT
ejpam-837	51	14	=	=	SYM
ejpam-837	51	15	q(1	q(1	PROPN
ejpam-837	51	16	)	)	PUNCT
ejpam-837	51	17	and	and	CCONJ
ejpam-837	51	18	q′(0	q′(0	NOUN
ejpam-837	51	19	)	)	PUNCT
ejpam-837	51	20	6=	6=	X
ejpam-837	51	21	q′(1	q′(1	PROPN
ejpam-837	51	22	)	)	PUNCT
ejpam-837	51	23	menken	menken	NOUN
ejpam-837	51	24	and	and	CCONJ
ejpam-837	51	25	mamedov	mamedov	PROPN
ejpam-837	52	1	[	[	X
ejpam-837	52	2	16	16	NUM
ejpam-837	52	3	]	]	PUNCT
ejpam-837	52	4	in	in	ADP
ejpam-837	52	5	2010	2010	NUM
ejpam-837	52	6	proved	prove	VERB
ejpam-837	52	7	the	the	DET
ejpam-837	52	8	basisness	basisness	NOUN
ejpam-837	52	9	in	in	ADP
ejpam-837	52	10	lp	lp	PROPN
ejpam-837	52	11	(	(	PUNCT
ejpam-837	52	12	0,1	0,1	NUM
ejpam-837	52	13	)	)	PUNCT
ejpam-837	52	14	.	.	PUNCT
ejpam-837	53	1	the	the	DET
ejpam-837	53	2	purpose	purpose	NOUN
ejpam-837	53	3	of	of	ADP
ejpam-837	53	4	this	this	DET
ejpam-837	53	5	paper	paper	NOUN
ejpam-837	53	6	is	be	AUX
ejpam-837	53	7	to	to	PART
ejpam-837	53	8	find	find	VERB
ejpam-837	53	9	the	the	DET
ejpam-837	53	10	weaker	weak	ADJ
ejpam-837	53	11	conditions	condition	NOUN
ejpam-837	53	12	on	on	ADP
ejpam-837	53	13	the	the	DET
ejpam-837	53	14	potential	potential	ADJ
ejpam-837	53	15	q(x	q(x	NOUN
ejpam-837	53	16	)	)	PUNCT
ejpam-837	53	17	under	under	ADP
ejpam-837	53	18	which	which	PRON
ejpam-837	53	19	the	the	DET
ejpam-837	53	20	system	system	NOUN
ejpam-837	53	21	of	of	ADP
ejpam-837	53	22	root	root	NOUN
ejpam-837	53	23	functions	function	NOUN
ejpam-837	53	24	form	form	VERB
ejpam-837	53	25	basis	basis	NOUN
ejpam-837	53	26	in	in	ADP
ejpam-837	53	27	space	space	NOUN
ejpam-837	53	28	lp	lp	PROPN
ejpam-837	53	29	(	(	PUNCT
ejpam-837	53	30	0,1	0,1	NUM
ejpam-837	53	31	)	)	PUNCT
ejpam-837	53	32	,	,	PUNCT
ejpam-837	53	33	p	p	X
ejpam-837	53	34	>	>	X
ejpam-837	53	35	1	1	X
ejpam-837	53	36	.	.	PUNCT
ejpam-837	54	1	the	the	DET
ejpam-837	54	2	following	follow	VERB
ejpam-837	54	3	results	result	NOUN
ejpam-837	54	4	plays	play	VERB
ejpam-837	54	5	an	an	DET
ejpam-837	54	6	important	important	ADJ
ejpam-837	54	7	role	role	NOUN
ejpam-837	54	8	in	in	ADP
ejpam-837	54	9	the	the	DET
ejpam-837	54	10	proof	proof	NOUN
ejpam-837	54	11	of	of	ADP
ejpam-837	54	12	main	main	ADJ
ejpam-837	54	13	results	result	NOUN
ejpam-837	54	14	.	.	PUNCT
ejpam-837	55	1	theorem	theorem	NOUN
ejpam-837	55	2	1	1	NUM
ejpam-837	55	3	(	(	PUNCT
ejpam-837	55	4	[	[	X
ejpam-837	55	5	1	1	NUM
ejpam-837	55	6	,	,	PUNCT
ejpam-837	55	7	5	5	NUM
ejpam-837	55	8	]	]	NUM
ejpam-837	55	9	)	)	PUNCT
ejpam-837	55	10	.	.	PUNCT
ejpam-837	56	1	the	the	DET
ejpam-837	56	2	following	follow	VERB
ejpam-837	56	3	assertions	assertion	NOUN
ejpam-837	56	4	are	be	AUX
ejpam-837	56	5	equivalent	equivalent	ADJ
ejpam-837	56	6	:	:	PUNCT
ejpam-837	56	7	1	1	NUM
ejpam-837	56	8	)	)	PUNCT
ejpam-837	56	9	sequence	sequence	NOUN
ejpam-837	56	10	¦	¦	PROPN
ejpam-837	56	11	ϕ	ϕ	PROPN
ejpam-837	56	12	j	j	PROPN
ejpam-837	56	13	©	©	PROPN
ejpam-837	56	14	∞	∞	PROPN
ejpam-837	56	15	j=1	j=1	PROPN
ejpam-837	56	16	forms	form	VERB
ejpam-837	56	17	a	a	DET
ejpam-837	56	18	riesz	riesz	ADJ
ejpam-837	56	19	basis	basis	NOUN
ejpam-837	56	20	in	in	ADP
ejpam-837	56	21	h	h	NOUN
ejpam-837	56	22	;	;	PUNCT
ejpam-837	56	23	2	2	X
ejpam-837	56	24	)	)	PUNCT
ejpam-837	56	25	the	the	DET
ejpam-837	56	26	sequence	sequence	NOUN
ejpam-837	56	27	¦	¦	PROPN
ejpam-837	56	28	ϕ	ϕ	PROPN
ejpam-837	56	29	j	j	PROPN
ejpam-837	56	30	©	©	PROPN
ejpam-837	56	31	∞	∞	PROPN
ejpam-837	56	32	j=1	j=1	PROPN
ejpam-837	56	33	is	be	AUX
ejpam-837	56	34	complete	complete	ADJ
ejpam-837	56	35	in	in	ADP
ejpam-837	56	36	the	the	DET
ejpam-837	56	37	hilbert	hilbert	PROPN
ejpam-837	56	38	space	space	NOUN
ejpam-837	56	39	h	h	NOUN
ejpam-837	56	40	,	,	PUNCT
ejpam-837	56	41	there	there	PRON
ejpam-837	56	42	corresponds	correspond	VERB
ejpam-837	56	43	to	to	ADP
ejpam-837	56	44	it	it	PRON
ejpam-837	56	45	a	a	DET
ejpam-837	56	46	complete	complete	ADJ
ejpam-837	56	47	biorthogonal	biorthogonal	ADJ
ejpam-837	56	48	sequence	sequence	NOUN
ejpam-837	56	49	¦	¦	PROPN
ejpam-837	56	50	ψ	ψ	X
ejpam-837	56	51	j	j	PROPN
ejpam-837	56	52	©	©	PROPN
ejpam-837	56	53	∞	∞	PROPN
ejpam-837	56	54	j=1	j=1	NOUN
ejpam-837	56	55	,	,	PUNCT
ejpam-837	56	56	and	and	CCONJ
ejpam-837	56	57	for	for	ADP
ejpam-837	56	58	any	any	DET
ejpam-837	56	59	f	f	PROPN
ejpam-837	56	60	∈	∈	PROPN
ejpam-837	56	61	h	h	NOUN
ejpam-837	56	62	one	one	NOUN
ejpam-837	56	63	has	have	VERB
ejpam-837	56	64	∞	∞	PROPN
ejpam-837	56	65	∑	∑	PROPN
ejpam-837	56	66	j=1	j=1	PROPN
ejpam-837	56	67	�	�	PROPN
ejpam-837	56	68	�	�	PROPN
ejpam-837	56	69	(	(	PUNCT
ejpam-837	56	70	f	f	PROPN
ejpam-837	56	71	,	,	PUNCT
ejpam-837	56	72	ϕ	ϕ	PROPN
ejpam-837	56	73	j	j	PROPN
ejpam-837	56	74	)	)	PUNCT
ejpam-837	56	75	�	�	PROPN
ejpam-837	56	76	�	�	PROPN
ejpam-837	56	77	<	<	X
ejpam-837	56	78	∞	∞	PROPN
ejpam-837	56	79	,	,	PUNCT
ejpam-837	56	80	∞	∞	PROPN
ejpam-837	56	81	∑	∑	PROPN
ejpam-837	56	82	j=1	j=1	PROPN
ejpam-837	56	83	�	�	PROPN
ejpam-837	56	84	�	�	PROPN
ejpam-837	56	85	(	(	PUNCT
ejpam-837	56	86	f	f	PROPN
ejpam-837	56	87	,	,	PUNCT
ejpam-837	56	88	ψ	ψ	PROPN
ejpam-837	56	89	j	j	PROPN
ejpam-837	56	90	)	)	PUNCT
ejpam-837	56	91	�	�	PROPN
ejpam-837	56	92	�	�	PROPN
ejpam-837	56	93	2	2	NUM
ejpam-837	56	94	<	<	X
ejpam-837	56	95	∞.	∞.	PROPN
ejpam-837	56	96	theorem	theorem	VERB
ejpam-837	56	97	2	2	NUM
ejpam-837	56	98	(	(	PUNCT
ejpam-837	56	99	[	[	X
ejpam-837	56	100	7	7	NUM
ejpam-837	56	101	]	]	NUM
ejpam-837	56	102	)	)	PUNCT
ejpam-837	56	103	.	.	PUNCT
ejpam-837	57	1	a	a	DET
ejpam-837	57	2	system	system	NOUN
ejpam-837	57	3	¦	¦	PROPN
ejpam-837	57	4	ϕ	ϕ	PROPN
ejpam-837	57	5	j	j	PROPN
ejpam-837	57	6	©	©	PROPN
ejpam-837	57	7	∞	∞	PROPN
ejpam-837	57	8	j=1	j=1	PROPN
ejpam-837	57	9	is	be	AUX
ejpam-837	57	10	a	a	DET
ejpam-837	57	11	basis	basis	NOUN
ejpam-837	57	12	in	in	ADP
ejpam-837	57	13	the	the	DET
ejpam-837	57	14	banach	banach	NOUN
ejpam-837	57	15	space	space	NOUN
ejpam-837	57	16	x	x	INTJ
ejpam-837	57	17	if	if	SCONJ
ejpam-837	57	18	only	only	ADV
ejpam-837	57	19	if	if	SCONJ
ejpam-837	57	20	the	the	DET
ejpam-837	57	21	following	follow	VERB
ejpam-837	57	22	conditions	condition	NOUN
ejpam-837	57	23	are	be	AUX
ejpam-837	57	24	satisfied	satisfied	ADJ
ejpam-837	57	25	:	:	PUNCT
ejpam-837	57	26	a	a	X
ejpam-837	57	27	)	)	PUNCT
ejpam-837	57	28	¦	¦	PROPN
ejpam-837	57	29	ϕ	ϕ	PROPN
ejpam-837	57	30	j	j	PROPN
ejpam-837	57	31	©	©	PROPN
ejpam-837	57	32	∞	∞	PROPN
ejpam-837	57	33	j=1	j=1	PROPN
ejpam-837	57	34	is	be	AUX
ejpam-837	57	35	complete	complete	ADJ
ejpam-837	57	36	in	in	ADP
ejpam-837	57	37	x	x	SYM
ejpam-837	57	38	,	,	PUNCT
ejpam-837	57	39	b	b	X
ejpam-837	57	40	)	)	PUNCT
ejpam-837	57	41	¦	¦	PROPN
ejpam-837	57	42	ϕ	ϕ	PROPN
ejpam-837	57	43	j	j	PROPN
ejpam-837	57	44	©	©	PROPN
ejpam-837	57	45	∞	∞	PROPN
ejpam-837	57	46	j=1	j=1	PROPN
ejpam-837	57	47	is	be	AUX
ejpam-837	57	48	minimal	minimal	ADJ
ejpam-837	57	49	,	,	PUNCT
ejpam-837	57	50	c	c	X
ejpam-837	57	51	)	)	PUNCT
ejpam-837	57	52	there	there	PRON
ejpam-837	57	53	exists	exist	VERB
ejpam-837	57	54	a	a	DET
ejpam-837	57	55	number	number	NOUN
ejpam-837	57	56	m	m	VERB
ejpam-837	57	57	>	>	X
ejpam-837	57	58	0	0	NUM
ejpam-837	58	1	such	such	ADJ
ejpam-837	58	2	that	that	PRON
ejpam-837	58	3	for	for	ADP
ejpam-837	58	4	each	each	DET
ejpam-837	58	5	f	f	PROPN
ejpam-837	58	6	∈	∈	PROPN
ejpam-837	58	7	x	x	X
ejpam-837	58	8	,	,	PUNCT
ejpam-837	58	9	the	the	DET
ejpam-837	58	10	inequality	inequality	NOUN
ejpam-837	58	11	n	n	X
ejpam-837	58	12	∑	∑	PROPN
ejpam-837	58	13	j=1	j=1	PROPN
ejpam-837	58	14	(	(	PUNCT
ejpam-837	58	15	f	f	X
ejpam-837	58	16	,	,	PUNCT
ejpam-837	58	17	ψ	ψ	PROPN
ejpam-837	58	18	j)ϕ	j)ϕ	X
ejpam-837	58	19	j	j	PROPN
ejpam-837	58	20	≤	≤	NUM
ejpam-837	58	21	m	m	VERB
ejpam-837	58	22	‖x‖	‖x‖	PROPN
ejpam-837	58	23	,	,	PUNCT
ejpam-837	58	24	n	n	NOUN
ejpam-837	58	25	=	=	SYM
ejpam-837	58	26	1,2	1,2	NUM
ejpam-837	58	27	,	,	PUNCT
ejpam-837	58	28	.	.	PUNCT
ejpam-837	58	29	.	.	PUNCT
ejpam-837	58	30	.	.	PUNCT
ejpam-837	59	1	where	where	SCONJ
ejpam-837	59	2	the	the	DET
ejpam-837	59	3	sequence	sequence	NOUN
ejpam-837	59	4	¦	¦	PROPN
ejpam-837	59	5	ψ	ψ	X
ejpam-837	59	6	j	j	PROPN
ejpam-837	59	7	©	©	PROPN
ejpam-837	59	8	∞	∞	PROPN
ejpam-837	59	9	j=1	j=1	PROPN
ejpam-837	59	10	is	be	AUX
ejpam-837	59	11	the	the	DET
ejpam-837	59	12	biorthogonal	biorthogonal	ADJ
ejpam-837	59	13	adjoint	adjoint	NOUN
ejpam-837	59	14	system	system	NOUN
ejpam-837	59	15	to	to	ADP
ejpam-837	59	16	¦	¦	PROPN
ejpam-837	59	17	ϕ	ϕ	X
ejpam-837	59	18	j	j	PROPN
ejpam-837	59	19	©	©	PROPN
ejpam-837	59	20	∞	∞	PROPN
ejpam-837	59	21	j=1	j=1	NOUN
ejpam-837	59	22	.	.	PUNCT
ejpam-837	60	1	assume	assume	VERB
ejpam-837	60	2	that	that	SCONJ
ejpam-837	60	3	q(x	q(x	NOUN
ejpam-837	60	4	)	)	PUNCT
ejpam-837	60	5	∈	∈	PROPN
ejpam-837	60	6	ac[0,1	ac[0,1	PROPN
ejpam-837	60	7	]	]	X
ejpam-837	60	8	(	(	PUNCT
ejpam-837	60	9	absolutely	absolutely	ADV
ejpam-837	60	10	continuous	continuous	ADJ
ejpam-837	60	11	function	function	NOUN
ejpam-837	60	12	in	in	ADP
ejpam-837	60	13	[	[	X
ejpam-837	60	14	0,1	0,1	NUM
ejpam-837	60	15	]	]	PUNCT
ejpam-837	60	16	)	)	PUNCT
ejpam-837	60	17	and	and	CCONJ
ejpam-837	60	18	q(0	q(0	PROPN
ejpam-837	60	19	)	)	PUNCT
ejpam-837	60	20	6=	6=	PROPN
ejpam-837	61	1	q(1	q(1	NOUN
ejpam-837	61	2	)	)	PUNCT
ejpam-837	61	3	.	.	PUNCT
ejpam-837	62	1	under	under	ADP
ejpam-837	62	2	these	these	DET
ejpam-837	62	3	conditions	condition	NOUN
ejpam-837	62	4	it	it	PRON
ejpam-837	62	5	is	be	AUX
ejpam-837	62	6	known	know	VERB
ejpam-837	62	7	(	(	PUNCT
ejpam-837	62	8	[	[	X
ejpam-837	62	9	10	10	NUM
ejpam-837	62	10	]	]	SYM
ejpam-837	62	11	)	)	PUNCT
ejpam-837	62	12	that	that	SCONJ
ejpam-837	62	13	:	:	PUNCT
ejpam-837	62	14	a	a	X
ejpam-837	62	15	)	)	PUNCT
ejpam-837	62	16	all	all	DET
ejpam-837	62	17	eigenvalues	eigenvalue	NOUN
ejpam-837	62	18	of	of	ADP
ejpam-837	62	19	problem	problem	NOUN
ejpam-837	62	20	(	(	PUNCT
ejpam-837	62	21	1),(2	1),(2	NUM
ejpam-837	62	22	)	)	PUNCT
ejpam-837	62	23	starting	start	VERB
ejpam-837	62	24	from	from	ADP
ejpam-837	62	25	number	number	NOUN
ejpam-837	62	26	n	n	NUM
ejpam-837	62	27	are	be	AUX
ejpam-837	62	28	simple	simple	ADJ
ejpam-837	62	29	and	and	CCONJ
ejpam-837	62	30	form	form	VERB
ejpam-837	62	31	two	two	NUM
ejpam-837	62	32	infinite	infinite	ADJ
ejpam-837	62	33	sequences	sequence	NOUN
ejpam-837	62	34	.	.	PUNCT
ejpam-837	63	1	λ2n	λ2n	NOUN
ejpam-837	63	2	=	=	PUNCT
ejpam-837	63	3	−(2nπ)2	−(2nπ)2	PROPN
ejpam-837	63	4	+	+	PROPN
ejpam-837	63	5	q(0)−	q(0)−	ADJ
ejpam-837	63	6	q(1	q(1	NOUN
ejpam-837	63	7	)	)	PUNCT
ejpam-837	63	8	4nπ	4nπ	NOUN
ejpam-837	64	1	+	+	CCONJ
ejpam-837	64	2	o	o	NOUN
ejpam-837	64	3	(	(	PUNCT
ejpam-837	64	4	1	1	NUM
ejpam-837	64	5	n	n	NOUN
ejpam-837	64	6	)	)	PUNCT
ejpam-837	64	7	,	,	PUNCT
ejpam-837	64	8	λ2n+1	λ2n+1	PROPN
ejpam-837	64	9	=	=	PROPN
ejpam-837	64	10	−(2nπ)2	−(2nπ)2	PROPN
ejpam-837	64	11	+	+	PROPN
ejpam-837	64	12	q(1)−	q(1)−	PROPN
ejpam-837	64	13	q(0	q(0	PROPN
ejpam-837	64	14	)	)	PUNCT
ejpam-837	64	15	4nπ	4nπ	NOUN
ejpam-837	65	1	+	+	CCONJ
ejpam-837	65	2	o	o	NOUN
ejpam-837	65	3	(	(	PUNCT
ejpam-837	65	4	1	1	NUM
ejpam-837	65	5	n	n	NOUN
ejpam-837	65	6	)	)	PUNCT
ejpam-837	65	7	,	,	PUNCT
ejpam-837	65	8	n=	n=	ADJ
ejpam-837	65	9	n	n	CCONJ
ejpam-837	65	10	,	,	PUNCT
ejpam-837	65	11	n	n	PROPN
ejpam-837	65	12	+	+	NOUN
ejpam-837	65	13	1	1	NUM
ejpam-837	65	14	,	,	PUNCT
ejpam-837	65	15	.	.	PUNCT
ejpam-837	66	1	.	.	PUNCT
ejpam-837	66	2	.	.	PUNCT
ejpam-837	67	1	,	,	PUNCT
ejpam-837	67	2	k.	k.	PROPN
ejpam-837	67	3	mamedov	mamedov	PROPN
ejpam-837	67	4	/	/	SYM
ejpam-837	67	5	eur	eur	PROPN
ejpam-837	67	6	.	.	PUNCT
ejpam-837	68	1	j.	j.	PROPN
ejpam-837	68	2	pure	pure	PROPN
ejpam-837	68	3	appl	appl	PROPN
ejpam-837	68	4	.	.	PROPN
ejpam-837	68	5	math	math	PROPN
ejpam-837	68	6	,	,	PUNCT
ejpam-837	68	7	3	3	NUM
ejpam-837	68	8	(	(	PUNCT
ejpam-837	68	9	2010	2010	NUM
ejpam-837	68	10	)	)	PUNCT
ejpam-837	68	11	,	,	PUNCT
ejpam-837	68	12	831	831	NUM
ejpam-837	68	13	-	-	SYM
ejpam-837	68	14	838	838	NUM
ejpam-837	68	15	834	834	NUM
ejpam-837	68	16	and	and	CCONJ
ejpam-837	68	17	the	the	DET
ejpam-837	68	18	corresponding	corresponding	ADJ
ejpam-837	68	19	eigenfunctions	eigenfunction	NOUN
ejpam-837	68	20	are	be	AUX
ejpam-837	68	21	of	of	ADP
ejpam-837	68	22	the	the	DET
ejpam-837	68	23	form	form	NOUN
ejpam-837	68	24	u2n(x	u2n(x	ADJ
ejpam-837	68	25	)	)	PUNCT
ejpam-837	68	26	=	=	PUNCT
ejpam-837	69	1	p	p	X
ejpam-837	69	2	2	2	NUM
ejpam-837	69	3	sin(2nπx	sin(2nπx	SYM
ejpam-837	69	4	−	−	PROPN
ejpam-837	69	5	π	π	PROPN
ejpam-837	69	6	4	4	NUM
ejpam-837	69	7	)	)	PUNCT
ejpam-837	70	1	+	+	NOUN
ejpam-837	70	2	o	o	NOUN
ejpam-837	70	3	(	(	PUNCT
ejpam-837	70	4	1	1	NUM
ejpam-837	70	5	n	n	NOUN
ejpam-837	70	6	)	)	PUNCT
ejpam-837	70	7	,	,	PUNCT
ejpam-837	70	8	(	(	PUNCT
ejpam-837	70	9	4	4	X
ejpam-837	70	10	)	)	PUNCT
ejpam-837	70	11	u2n+1(x	u2n+1(x	NUM
ejpam-837	70	12	)	)	PUNCT
ejpam-837	70	13	=	=	PUNCT
ejpam-837	71	1	p	p	NOUN
ejpam-837	71	2	2	2	NUM
ejpam-837	72	1	cos(2nπx	cos(2nπx	NOUN
ejpam-837	72	2	−	−	NOUN
ejpam-837	72	3	π	π	NOUN
ejpam-837	72	4	4	4	NUM
ejpam-837	72	5	)	)	PUNCT
ejpam-837	73	1	+	+	NOUN
ejpam-837	73	2	o	o	NOUN
ejpam-837	73	3	(	(	PUNCT
ejpam-837	73	4	1	1	NUM
ejpam-837	73	5	n	n	NOUN
ejpam-837	73	6	)	)	PUNCT
ejpam-837	73	7	,	,	PUNCT
ejpam-837	73	8	n=	n=	ADJ
ejpam-837	73	9	n	n	CCONJ
ejpam-837	73	10	,	,	PUNCT
ejpam-837	73	11	n	n	PROPN
ejpam-837	73	12	+	+	NOUN
ejpam-837	73	13	1	1	NUM
ejpam-837	73	14	,	,	PUNCT
ejpam-837	73	15	.	.	PUNCT
ejpam-837	73	16	.	.	PUNCT
ejpam-837	73	17	.	.	PUNCT
ejpam-837	74	1	;	;	PUNCT
ejpam-837	74	2	(	(	PUNCT
ejpam-837	74	3	5	5	X
ejpam-837	74	4	)	)	SYM
ejpam-837	74	5	b	b	NOUN
ejpam-837	74	6	)	)	PUNCT
ejpam-837	74	7	all	all	DET
ejpam-837	74	8	eigenvalues	eigenvalue	NOUN
ejpam-837	74	9	of	of	ADP
ejpam-837	74	10	the	the	DET
ejpam-837	74	11	boundary	boundary	ADJ
ejpam-837	74	12	value	value	NOUN
ejpam-837	74	13	problem	problem	NOUN
ejpam-837	74	14	(	(	PUNCT
ejpam-837	74	15	1),(3	1),(3	NOUN
ejpam-837	74	16	)	)	PUNCT
ejpam-837	74	17	starting	start	VERB
ejpam-837	74	18	from	from	ADP
ejpam-837	74	19	number	number	NOUN
ejpam-837	74	20	n	n	NUM
ejpam-837	74	21	are	be	AUX
ejpam-837	74	22	simple	simple	ADJ
ejpam-837	74	23	and	and	CCONJ
ejpam-837	74	24	form	form	VERB
ejpam-837	74	25	two	two	NUM
ejpam-837	74	26	infinite	infinite	ADJ
ejpam-837	74	27	sequences	sequence	NOUN
ejpam-837	74	28	.	.	PUNCT
ejpam-837	75	1	λ2n	λ2n	NOUN
ejpam-837	76	1	=	=	PUNCT
ejpam-837	76	2	−	−	PROPN
ejpam-837	77	1	[	[	X
ejpam-837	77	2	(	(	PUNCT
ejpam-837	77	3	2n+	2n+	NUM
ejpam-837	77	4	1)π]2	1)π]2	NUM
ejpam-837	77	5	+	+	CCONJ
ejpam-837	77	6	q(0)−	q(0)−	PROPN
ejpam-837	77	7	q(1	q(1	NOUN
ejpam-837	77	8	)	)	PUNCT
ejpam-837	77	9	4nπ	4nπ	NOUN
ejpam-837	78	1	+	+	CCONJ
ejpam-837	78	2	o	o	NOUN
ejpam-837	78	3	(	(	PUNCT
ejpam-837	78	4	1	1	NUM
ejpam-837	78	5	n	n	NOUN
ejpam-837	78	6	)	)	PUNCT
ejpam-837	78	7	,	,	PUNCT
ejpam-837	78	8	λ2n+1	λ2n+1	PUNCT
ejpam-837	78	9	=	=	SYM
ejpam-837	79	1	−	−	PROPN
ejpam-837	80	1	[	[	X
ejpam-837	80	2	(	(	PUNCT
ejpam-837	80	3	2n+	2n+	NUM
ejpam-837	80	4	1)π]2	1)π]2	NUM
ejpam-837	80	5	+	+	CCONJ
ejpam-837	80	6	q(1)−	q(1)−	PROPN
ejpam-837	80	7	q(0	q(0	PROPN
ejpam-837	80	8	)	)	PUNCT
ejpam-837	80	9	4nπ	4nπ	NOUN
ejpam-837	81	1	+	+	CCONJ
ejpam-837	81	2	o	o	NOUN
ejpam-837	81	3	(	(	PUNCT
ejpam-837	81	4	1	1	NUM
ejpam-837	81	5	n	n	NOUN
ejpam-837	81	6	)	)	PUNCT
ejpam-837	81	7	,	,	PUNCT
ejpam-837	81	8	n=	n=	ADJ
ejpam-837	81	9	n	n	CCONJ
ejpam-837	81	10	,	,	PUNCT
ejpam-837	81	11	n	n	PROPN
ejpam-837	81	12	+	+	NOUN
ejpam-837	81	13	1	1	NUM
ejpam-837	81	14	,	,	PUNCT
ejpam-837	81	15	.	.	PUNCT
ejpam-837	81	16	.	.	PUNCT
ejpam-837	82	1	.	.	PUNCT
ejpam-837	83	1	,	,	PUNCT
ejpam-837	83	2	and	and	CCONJ
ejpam-837	83	3	the	the	DET
ejpam-837	83	4	corresponding	corresponding	ADJ
ejpam-837	83	5	eigenfunctions	eigenfunction	NOUN
ejpam-837	83	6	are	be	AUX
ejpam-837	83	7	of	of	ADP
ejpam-837	83	8	the	the	DET
ejpam-837	83	9	form	form	NOUN
ejpam-837	83	10	u2n(x	u2n(x	ADJ
ejpam-837	83	11	)	)	PUNCT
ejpam-837	84	1	=	=	PUNCT
ejpam-837	85	1	p	p	X
ejpam-837	85	2	2sin((2n+	2sin((2n+	NUM
ejpam-837	86	1	1)πx	1)πx	NUM
ejpam-837	87	1	−	−	PROPN
ejpam-837	87	2	π	π	NOUN
ejpam-837	87	3	4	4	NUM
ejpam-837	87	4	)	)	PUNCT
ejpam-837	88	1	+	+	NOUN
ejpam-837	88	2	o	o	NOUN
ejpam-837	88	3	(	(	PUNCT
ejpam-837	88	4	1	1	NUM
ejpam-837	88	5	n	n	NOUN
ejpam-837	88	6	)	)	PUNCT
ejpam-837	88	7	,	,	PUNCT
ejpam-837	88	8	(	(	PUNCT
ejpam-837	88	9	6	6	NUM
ejpam-837	88	10	)	)	PUNCT
ejpam-837	88	11	u2n+1(x	u2n+1(x	NUM
ejpam-837	88	12	)	)	PUNCT
ejpam-837	88	13	=	=	PUNCT
ejpam-837	89	1	p	p	X
ejpam-837	90	1	2cos((2n+	2cos((2n+	NUM
ejpam-837	90	2	1)πx	1)πx	NUM
ejpam-837	91	1	−	−	PROPN
ejpam-837	91	2	π	π	NOUN
ejpam-837	91	3	4	4	NUM
ejpam-837	91	4	)	)	PUNCT
ejpam-837	92	1	+	+	NOUN
ejpam-837	92	2	o	o	NOUN
ejpam-837	92	3	(	(	PUNCT
ejpam-837	92	4	1	1	NUM
ejpam-837	92	5	n	n	NOUN
ejpam-837	92	6	)	)	PUNCT
ejpam-837	92	7	,	,	PUNCT
ejpam-837	92	8	n=	n=	ADJ
ejpam-837	92	9	n	n	CCONJ
ejpam-837	92	10	,	,	PUNCT
ejpam-837	92	11	n	n	PROPN
ejpam-837	92	12	+	+	NOUN
ejpam-837	92	13	1	1	NUM
ejpam-837	92	14	,	,	PUNCT
ejpam-837	92	15	.	.	PUNCT
ejpam-837	92	16	.	.	PUNCT
ejpam-837	92	17	.	.	PUNCT
ejpam-837	93	1	.	.	PUNCT
ejpam-837	94	1	(	(	PUNCT
ejpam-837	94	2	7	7	X
ejpam-837	94	3	)	)	PUNCT
ejpam-837	94	4	in	in	ADP
ejpam-837	94	5	the	the	DET
ejpam-837	94	6	present	present	ADJ
ejpam-837	94	7	paper	paper	NOUN
ejpam-837	94	8	,	,	PUNCT
ejpam-837	94	9	in	in	ADP
ejpam-837	94	10	section	section	NOUN
ejpam-837	94	11	2	2	NUM
ejpam-837	94	12	we	we	PRON
ejpam-837	94	13	using	use	VERB
ejpam-837	94	14	the	the	DET
ejpam-837	94	15	asymptotic	asymptotic	ADJ
ejpam-837	94	16	formulas	formula	NOUN
ejpam-837	94	17	(	(	PUNCT
ejpam-837	94	18	4)-(7	4)-(7	NOUN
ejpam-837	94	19	)	)	PUNCT
ejpam-837	94	20	of	of	ADP
ejpam-837	94	21	eigenfunctions	eigenfunction	NOUN
ejpam-837	94	22	of	of	ADP
ejpam-837	94	23	the	the	DET
ejpam-837	94	24	boundary	boundary	ADJ
ejpam-837	94	25	problems	problem	NOUN
ejpam-837	94	26	(	(	PUNCT
ejpam-837	94	27	1	1	NUM
ejpam-837	94	28	)	)	PUNCT
ejpam-837	94	29	,	,	PUNCT
ejpam-837	94	30	(	(	PUNCT
ejpam-837	94	31	2	2	X
ejpam-837	94	32	)	)	PUNCT
ejpam-837	94	33	and	and	CCONJ
ejpam-837	94	34	theorem	theorem	VERB
ejpam-837	94	35	1	1	NUM
ejpam-837	94	36	shown	show	VERB
ejpam-837	94	37	riesz	riesz	NOUN
ejpam-837	94	38	basisness	basisness	NOUN
ejpam-837	94	39	in	in	ADP
ejpam-837	94	40	l2	l2	NOUN
ejpam-837	94	41	(	(	PUNCT
ejpam-837	94	42	0,1	0,1	NUM
ejpam-837	94	43	)	)	PUNCT
ejpam-837	94	44	.	.	PUNCT
ejpam-837	95	1	in	in	ADP
ejpam-837	95	2	section	section	NOUN
ejpam-837	95	3	3	3	NUM
ejpam-837	95	4	,	,	PUNCT
ejpam-837	95	5	using	use	VERB
ejpam-837	95	6	theorem	theorem	ADJ
ejpam-837	95	7	2	2	NUM
ejpam-837	95	8	and	and	CCONJ
ejpam-837	95	9	f.riesz	f.riesz	ADJ
ejpam-837	95	10	theorem	theorem	NOUN
ejpam-837	95	11	(	(	PUNCT
ejpam-837	95	12	see	see	VERB
ejpam-837	95	13	[	[	X
ejpam-837	95	14	22	22	NUM
ejpam-837	95	15	]	]	PUNCT
ejpam-837	95	16	,	,	PUNCT
ejpam-837	95	17	p.154	p.154	NOUN
ejpam-837	95	18	)	)	PUNCT
ejpam-837	95	19	,	,	PUNCT
ejpam-837	95	20	we	we	PRON
ejpam-837	95	21	prove	prove	VERB
ejpam-837	95	22	the	the	DET
ejpam-837	95	23	basisness	basisness	NOUN
ejpam-837	95	24	in	in	ADP
ejpam-837	95	25	lp(0,1	lp(0,1	NOUN
ejpam-837	95	26	)	)	PUNCT
ejpam-837	95	27	of	of	ADP
ejpam-837	95	28	the	the	DET
ejpam-837	95	29	root	root	NOUN
ejpam-837	95	30	functions	function	NOUN
ejpam-837	95	31	of	of	ADP
ejpam-837	95	32	the	the	DET
ejpam-837	95	33	periodic	periodic	ADJ
ejpam-837	95	34	and	and	CCONJ
ejpam-837	95	35	anti	anti	ADJ
ejpam-837	95	36	-	-	ADJ
ejpam-837	95	37	periodic	periodic	ADJ
ejpam-837	95	38	boundary	boundary	ADJ
ejpam-837	95	39	value	value	NOUN
ejpam-837	95	40	problems	problem	NOUN
ejpam-837	95	41	.	.	PUNCT
ejpam-837	96	1	2	2	X
ejpam-837	96	2	.	.	X
ejpam-837	96	3	the	the	DET
ejpam-837	96	4	riesz	riesz	PROPN
ejpam-837	96	5	basisness	basisness	NOUN
ejpam-837	96	6	in	in	ADP
ejpam-837	96	7	l2(0	l2(0	NOUN
ejpam-837	96	8	,	,	PUNCT
ejpam-837	96	9	1	1	NUM
ejpam-837	96	10	)	)	PUNCT
ejpam-837	96	11	firstly	firstly	ADV
ejpam-837	96	12	,	,	PUNCT
ejpam-837	96	13	by	by	ADP
ejpam-837	96	14	a	a	DET
ejpam-837	96	15	different	different	ADJ
ejpam-837	96	16	method	method	NOUN
ejpam-837	96	17	,	,	PUNCT
ejpam-837	96	18	using	use	VERB
ejpam-837	96	19	the	the	DET
ejpam-837	96	20	asymptotic	asymptotic	ADJ
ejpam-837	96	21	formulas	formula	NOUN
ejpam-837	96	22	(	(	PUNCT
ejpam-837	96	23	4)-(7	4)-(7	NOUN
ejpam-837	96	24	)	)	PUNCT
ejpam-837	96	25	and	and	CCONJ
ejpam-837	96	26	the	the	DET
ejpam-837	96	27	theorem	theorem	NOUN
ejpam-837	96	28	1	1	NUM
ejpam-837	96	29	we	we	PRON
ejpam-837	96	30	will	will	AUX
ejpam-837	96	31	show	show	VERB
ejpam-837	96	32	the	the	DET
ejpam-837	96	33	riesz	riesz	NOUN
ejpam-837	96	34	basisness	basisness	NOUN
ejpam-837	96	35	in	in	ADP
ejpam-837	96	36	l2	l2	NOUN
ejpam-837	96	37	(	(	PUNCT
ejpam-837	96	38	0,1	0,1	NUM
ejpam-837	96	39	)	)	PUNCT
ejpam-837	96	40	of	of	ADP
ejpam-837	96	41	the	the	DET
ejpam-837	96	42	root	root	NOUN
ejpam-837	96	43	functions	function	NOUN
ejpam-837	96	44	of	of	ADP
ejpam-837	96	45	the	the	DET
ejpam-837	96	46	boundary	boundary	ADJ
ejpam-837	96	47	problems	problem	NOUN
ejpam-837	96	48	(	(	PUNCT
ejpam-837	96	49	1),(2	1),(2	NUM
ejpam-837	96	50	)	)	PUNCT
ejpam-837	96	51	and	and	CCONJ
ejpam-837	96	52	(	(	PUNCT
ejpam-837	96	53	1),(3	1),(3	NOUN
ejpam-837	96	54	)	)	PUNCT
ejpam-837	96	55	.	.	PUNCT
ejpam-837	97	1	theorem	theorem	NOUN
ejpam-837	97	2	3	3	X
ejpam-837	97	3	.	.	PUNCT
ejpam-837	97	4	suppose	suppose	VERB
ejpam-837	98	1	that	that	SCONJ
ejpam-837	98	2	q(x	q(x	PROPN
ejpam-837	98	3	)	)	PUNCT
ejpam-837	98	4	∈	∈	PROPN
ejpam-837	98	5	ac[0,1	ac[0,1	PROPN
ejpam-837	98	6	]	]	PUNCT
ejpam-837	98	7	and	and	CCONJ
ejpam-837	98	8	q(0	q(0	PROPN
ejpam-837	98	9	)	)	PUNCT
ejpam-837	98	10	6=	6=	PROPN
ejpam-837	98	11	q(1	q(1	NOUN
ejpam-837	98	12	)	)	PUNCT
ejpam-837	98	13	.	.	PUNCT
ejpam-837	99	1	then	then	ADV
ejpam-837	99	2	the	the	DET
ejpam-837	99	3	system	system	NOUN
ejpam-837	99	4	of	of	ADP
ejpam-837	99	5	root	root	NOUN
ejpam-837	99	6	functions	function	NOUN
ejpam-837	99	7	of	of	ADP
ejpam-837	99	8	the	the	DET
ejpam-837	99	9	boundary	boundary	ADJ
ejpam-837	99	10	value	value	NOUN
ejpam-837	99	11	problems	problem	NOUN
ejpam-837	99	12	(	(	PUNCT
ejpam-837	99	13	1),(2	1),(2	NUM
ejpam-837	99	14	)	)	PUNCT
ejpam-837	99	15	and	and	CCONJ
ejpam-837	99	16	(	(	PUNCT
ejpam-837	99	17	1),(3	1),(3	NOUN
ejpam-837	99	18	)	)	PUNCT
ejpam-837	99	19	forms	form	VERB
ejpam-837	99	20	a	a	DET
ejpam-837	99	21	riesz	riesz	ADJ
ejpam-837	99	22	basis	basis	NOUN
ejpam-837	99	23	in	in	ADP
ejpam-837	99	24	l2	l2	NOUN
ejpam-837	99	25	(	(	PUNCT
ejpam-837	99	26	0,1	0,1	NUM
ejpam-837	99	27	)	)	PUNCT
ejpam-837	99	28	.	.	PUNCT
ejpam-837	100	1	proof	proof	NOUN
ejpam-837	100	2	.	.	PUNCT
ejpam-837	101	1	it	it	PRON
ejpam-837	101	2	is	be	AUX
ejpam-837	101	3	well	well	ADV
ejpam-837	101	4	known	know	VERB
ejpam-837	101	5	that	that	SCONJ
ejpam-837	101	6	the	the	DET
ejpam-837	101	7	system	system	NOUN
ejpam-837	101	8	of	of	ADP
ejpam-837	101	9	eigenfunctions	eigenfunction	NOUN
ejpam-837	101	10	and	and	CCONJ
ejpam-837	101	11	associated	associate	VERB
ejpam-837	101	12	eigenfunctions	eigenfunction	NOUN
ejpam-837	101	13	of	of	ADP
ejpam-837	101	14	problem	problem	NOUN
ejpam-837	101	15	(	(	PUNCT
ejpam-837	101	16	1),(2	1),(2	NUM
ejpam-837	101	17	)	)	PUNCT
ejpam-837	101	18	is	be	AUX
ejpam-837	101	19	complete	complete	ADJ
ejpam-837	101	20	in	in	ADP
ejpam-837	101	21	l2(0,1	l2(0,1	ADJ
ejpam-837	101	22	)	)	PUNCT
ejpam-837	101	23	.	.	PUNCT
ejpam-837	102	1	the	the	DET
ejpam-837	102	2	system	system	NOUN
ejpam-837	102	3	of	of	ADP
ejpam-837	102	4	the	the	DET
ejpam-837	102	5	root	root	NOUN
ejpam-837	102	6	functions	function	NOUN
ejpam-837	102	7	is	be	AUX
ejpam-837	102	8	minimal	minimal	ADJ
ejpam-837	102	9	in	in	ADP
ejpam-837	102	10	l2(0,1	l2(0,1	ADJ
ejpam-837	102	11	)	)	PUNCT
ejpam-837	102	12	.	.	PUNCT
ejpam-837	103	1	the	the	DET
ejpam-837	103	2	minimality	minimality	NOUN
ejpam-837	103	3	of	of	ADP
ejpam-837	103	4	this	this	DET
ejpam-837	103	5	system	system	NOUN
ejpam-837	103	6	follows	follow	VERB
ejpam-837	103	7	from	from	ADP
ejpam-837	103	8	the	the	DET
ejpam-837	103	9	fact	fact	NOUN
ejpam-837	103	10	that	that	SCONJ
ejpam-837	103	11	this	this	DET
ejpam-837	103	12	system	system	NOUN
ejpam-837	103	13	has	have	AUX
ejpam-837	103	14	a	a	DET
ejpam-837	103	15	biorthogonal	biorthogonal	ADJ
ejpam-837	103	16	system	system	NOUN
ejpam-837	103	17	consisting	consist	VERB
ejpam-837	103	18	of	of	ADP
ejpam-837	103	19	the	the	DET
ejpam-837	103	20	root	root	NOUN
ejpam-837	103	21	functions	function	NOUN
ejpam-837	103	22	of	of	ADP
ejpam-837	103	23	the	the	DET
ejpam-837	103	24	adjoint	adjoint	NOUN
ejpam-837	103	25	operator	operator	NOUN
ejpam-837	103	26	l∗(υ	l∗(υ	PROPN
ejpam-837	103	27	)	)	PUNCT
ejpam-837	103	28	=	=	PUNCT
ejpam-837	104	1	υ′′	υ′′	NOUN
ejpam-837	104	2	+	+	NUM
ejpam-837	104	3	q(x)υ	q(x)υ	NOUN
ejpam-837	104	4	,	,	PUNCT
ejpam-837	104	5	υ(1	υ(1	PROPN
ejpam-837	104	6	)	)	PUNCT
ejpam-837	104	7	=	=	SYM
ejpam-837	104	8	υ(0	υ(0	PROPN
ejpam-837	104	9	)	)	PUNCT
ejpam-837	104	10	,	,	PUNCT
ejpam-837	104	11	υ′(1	υ′(1	PROPN
ejpam-837	104	12	)	)	PUNCT
ejpam-837	104	13	=	=	SYM
ejpam-837	104	14	υ′(0	υ′(0	PROPN
ejpam-837	104	15	)	)	PUNCT
ejpam-837	104	16	.	.	PUNCT
ejpam-837	105	1	k.	k.	PROPN
ejpam-837	106	1	mamedov	mamedov	PROPN
ejpam-837	106	2	/	/	SYM
ejpam-837	106	3	eur	eur	PROPN
ejpam-837	106	4	.	.	PUNCT
ejpam-837	107	1	j.	j.	PROPN
ejpam-837	107	2	pure	pure	PROPN
ejpam-837	107	3	appl	appl	PROPN
ejpam-837	107	4	.	.	PROPN
ejpam-837	107	5	math	math	PROPN
ejpam-837	107	6	,	,	PUNCT
ejpam-837	107	7	3	3	NUM
ejpam-837	107	8	(	(	PUNCT
ejpam-837	107	9	2010	2010	NUM
ejpam-837	107	10	)	)	PUNCT
ejpam-837	107	11	,	,	PUNCT
ejpam-837	107	12	831	831	NUM
ejpam-837	107	13	-	-	SYM
ejpam-837	107	14	838	838	NUM
ejpam-837	107	15	835	835	NUM
ejpam-837	107	16	for	for	ADP
ejpam-837	107	17	any	any	DET
ejpam-837	107	18	f	f	PROPN
ejpam-837	107	19	∈	∈	PROPN
ejpam-837	107	20	l2(0,1	l2(0,1	NOUN
ejpam-837	107	21	)	)	PUNCT
ejpam-837	107	22	,	,	PUNCT
ejpam-837	107	23	with	with	ADP
ejpam-837	107	24	a	a	DET
ejpam-837	107	25	direct	direct	ADJ
ejpam-837	107	26	computation	computation	NOUN
ejpam-837	107	27	we	we	PRON
ejpam-837	107	28	have	have	VERB
ejpam-837	107	29	that	that	PRON
ejpam-837	107	30	∞	∞	PROPN
ejpam-837	107	31	∑	∑	PUNCT
ejpam-837	107	32	n	n	CCONJ
ejpam-837	107	33	=	=	NOUN
ejpam-837	107	34	n	n	PRON
ejpam-837	107	35	�	�	PROPN
ejpam-837	107	36	�	�	PROPN
ejpam-837	107	37	(	(	PUNCT
ejpam-837	107	38	f	f	PROPN
ejpam-837	107	39	,	,	PUNCT
ejpam-837	107	40	u2n	u2n	PROPN
ejpam-837	107	41	)	)	PUNCT
ejpam-837	107	42	�	�	PROPN
ejpam-837	107	43	�	�	PROPN
ejpam-837	107	44	2	2	NUM
ejpam-837	107	45	<	<	X
ejpam-837	107	46	∞	∞	PROPN
ejpam-837	107	47	,	,	PUNCT
ejpam-837	107	48	∞	∞	PROPN
ejpam-837	107	49	∑	∑	PUNCT
ejpam-837	107	50	n	n	CCONJ
ejpam-837	107	51	=	=	NOUN
ejpam-837	107	52	n	n	PRON
ejpam-837	107	53	�	�	PROPN
ejpam-837	107	54	�	�	PROPN
ejpam-837	107	55	(	(	PUNCT
ejpam-837	107	56	f	f	PROPN
ejpam-837	107	57	,	,	PUNCT
ejpam-837	107	58	u2n+1	u2n+1	PROPN
ejpam-837	107	59	)	)	PUNCT
ejpam-837	107	60	�	�	PROPN
ejpam-837	107	61	�	�	PROPN
ejpam-837	107	62	2	2	NUM
ejpam-837	107	63	<	<	X
ejpam-837	107	64	∞.	∞.	PROPN
ejpam-837	107	65	on	on	ADP
ejpam-837	107	66	the	the	DET
ejpam-837	107	67	other	other	ADJ
ejpam-837	107	68	hand	hand	NOUN
ejpam-837	107	69	,	,	PUNCT
ejpam-837	107	70	the	the	DET
ejpam-837	107	71	eigenfunctions	eigenfunction	NOUN
ejpam-837	107	72	of	of	ADP
ejpam-837	107	73	the	the	DET
ejpam-837	107	74	adjoint	adjoint	NOUN
ejpam-837	107	75	operator	operator	NOUN
ejpam-837	107	76	have	have	AUX
ejpam-837	107	77	of	of	ADP
ejpam-837	107	78	the	the	DET
ejpam-837	107	79	form	form	NOUN
ejpam-837	107	80	υ2n(x	υ2n(x	PROPN
ejpam-837	107	81	)	)	PUNCT
ejpam-837	107	82	=	=	PUNCT
ejpam-837	108	1	p	p	NOUN
ejpam-837	108	2	2	2	NUM
ejpam-837	108	3	sin((2n+	sin((2n+	NOUN
ejpam-837	109	1	1)πx	1)πx	NUM
ejpam-837	110	1	−	−	NOUN
ejpam-837	110	2	π	π	NOUN
ejpam-837	110	3	4	4	NUM
ejpam-837	110	4	)	)	PUNCT
ejpam-837	111	1	+	+	NOUN
ejpam-837	111	2	o	o	NOUN
ejpam-837	111	3	(	(	PUNCT
ejpam-837	111	4	1	1	NUM
ejpam-837	111	5	n	n	NOUN
ejpam-837	111	6	)	)	PUNCT
ejpam-837	111	7	,	,	PUNCT
ejpam-837	111	8	(	(	PUNCT
ejpam-837	111	9	8)	8)	NUM
ejpam-837	111	10	υ2n+1(x	υ2n+1(x	NOUN
ejpam-837	111	11	)	)	PUNCT
ejpam-837	111	12	=	=	PUNCT
ejpam-837	112	1	p	p	NOUN
ejpam-837	112	2	2	2	NUM
ejpam-837	112	3	cos((2n+	cos((2n+	NOUN
ejpam-837	112	4	1)πx	1)πx	NUM
ejpam-837	112	5	−	−	PUNCT
ejpam-837	113	1	π	π	NOUN
ejpam-837	113	2	4	4	NUM
ejpam-837	113	3	)	)	PUNCT
ejpam-837	114	1	+	+	NOUN
ejpam-837	114	2	o	o	NOUN
ejpam-837	114	3	(	(	PUNCT
ejpam-837	114	4	1	1	NUM
ejpam-837	114	5	n	n	NOUN
ejpam-837	114	6	)	)	PUNCT
ejpam-837	114	7	,	,	PUNCT
ejpam-837	114	8	n=	n=	ADJ
ejpam-837	114	9	n	n	CCONJ
ejpam-837	114	10	,	,	PUNCT
ejpam-837	114	11	n	n	PROPN
ejpam-837	114	12	+	+	NOUN
ejpam-837	114	13	1	1	NUM
ejpam-837	114	14	,	,	PUNCT
ejpam-837	114	15	.	.	PUNCT
ejpam-837	114	16	.	.	PUNCT
ejpam-837	114	17	.	.	PUNCT
ejpam-837	115	1	.	.	PUNCT
ejpam-837	116	1	(	(	PUNCT
ejpam-837	116	2	9	9	NUM
ejpam-837	116	3	)	)	PUNCT
ejpam-837	116	4	and	and	CCONJ
ejpam-837	116	5	the	the	DET
ejpam-837	116	6	inequalities	inequality	NOUN
ejpam-837	116	7	∞	∞	PROPN
ejpam-837	116	8	∑	∑	PROPN
ejpam-837	116	9	n	n	CCONJ
ejpam-837	116	10	=	=	NOUN
ejpam-837	116	11	n	n	PRON
ejpam-837	116	12	�	�	PROPN
ejpam-837	116	13	�	�	PROPN
ejpam-837	116	14	(	(	PUNCT
ejpam-837	116	15	f	f	PROPN
ejpam-837	116	16	,	,	PUNCT
ejpam-837	116	17	υ2n	υ2n	PROPN
ejpam-837	116	18	)	)	PUNCT
ejpam-837	116	19	�	�	PROPN
ejpam-837	116	20	�	�	PROPN
ejpam-837	116	21	2	2	NUM
ejpam-837	116	22	<	<	NOUN
ejpam-837	116	23	∞	∞	NUM
ejpam-837	116	24	and	and	CCONJ
ejpam-837	116	25	∞	∞	NUM
ejpam-837	116	26	∑	∑	CCONJ
ejpam-837	116	27	n	n	CCONJ
ejpam-837	116	28	=	=	NOUN
ejpam-837	116	29	n	n	PRON
ejpam-837	116	30	�	�	PROPN
ejpam-837	116	31	�	�	PROPN
ejpam-837	116	32	(	(	PUNCT
ejpam-837	116	33	f	f	PROPN
ejpam-837	116	34	,	,	PUNCT
ejpam-837	116	35	υ2n+1	υ2n+1	PROPN
ejpam-837	116	36	)	)	PUNCT
ejpam-837	116	37	�	�	PROPN
ejpam-837	116	38	�	�	PROPN
ejpam-837	116	39	2	2	NUM
ejpam-837	116	40	<	<	NOUN
ejpam-837	116	41	∞	∞	NUM
ejpam-837	116	42	hold	hold	NOUN
ejpam-837	116	43	.	.	PUNCT
ejpam-837	117	1	according	accord	VERB
ejpam-837	117	2	to	to	ADP
ejpam-837	117	3	theorem	theorem	NOUN
ejpam-837	117	4	1	1	NUM
ejpam-837	117	5	,	,	PUNCT
ejpam-837	117	6	the	the	DET
ejpam-837	117	7	root	root	NOUN
ejpam-837	117	8	functions	function	NOUN
ejpam-837	117	9	of	of	ADP
ejpam-837	117	10	the	the	DET
ejpam-837	117	11	boundary	boundary	ADJ
ejpam-837	117	12	problem	problem	NOUN
ejpam-837	117	13	(	(	PUNCT
ejpam-837	117	14	1),(2	1),(2	NUM
ejpam-837	117	15	)	)	PUNCT
ejpam-837	117	16	form	form	VERB
ejpam-837	117	17	a	a	DET
ejpam-837	117	18	riesz	riesz	NOUN
ejpam-837	117	19	basis	basis	NOUN
ejpam-837	117	20	in	in	ADP
ejpam-837	117	21	l2(0,1	l2(0,1	ADV
ejpam-837	117	22	)	)	PUNCT
ejpam-837	117	23	.	.	PUNCT
ejpam-837	118	1	similarly	similarly	ADV
ejpam-837	118	2	,	,	PUNCT
ejpam-837	118	3	is	be	AUX
ejpam-837	118	4	proved	prove	VERB
ejpam-837	118	5	the	the	DET
ejpam-837	118	6	basisness	basisness	NOUN
ejpam-837	118	7	in	in	ADP
ejpam-837	118	8	l2(0,1	l2(0,1	NOUN
ejpam-837	118	9	)	)	PUNCT
ejpam-837	118	10	of	of	ADP
ejpam-837	118	11	root	root	NOUN
ejpam-837	118	12	functions	function	NOUN
ejpam-837	118	13	of	of	ADP
ejpam-837	118	14	boundary	boundary	ADJ
ejpam-837	118	15	problem	problem	NOUN
ejpam-837	118	16	(	(	PUNCT
ejpam-837	118	17	1),(3	1),(3	NOUN
ejpam-837	118	18	)	)	PUNCT
ejpam-837	118	19	.	.	PUNCT
ejpam-837	119	1	this	this	PRON
ejpam-837	119	2	completes	complete	VERB
ejpam-837	119	3	the	the	DET
ejpam-837	119	4	proof	proof	NOUN
ejpam-837	119	5	.	.	PUNCT
ejpam-837	120	1	3	3	X
ejpam-837	120	2	.	.	X
ejpam-837	120	3	the	the	DET
ejpam-837	120	4	basisness	basisness	NOUN
ejpam-837	120	5	in	in	ADP
ejpam-837	120	6	lp	lp	PROPN
ejpam-837	120	7	(	(	PUNCT
ejpam-837	120	8	0	0	NUM
ejpam-837	120	9	,	,	PUNCT
ejpam-837	120	10	1	1	NUM
ejpam-837	120	11	)	)	PUNCT
ejpam-837	120	12	,	,	PUNCT
ejpam-837	120	13	p	p	X
ejpam-837	120	14	>	>	X
ejpam-837	120	15	1	1	NUM
ejpam-837	120	16	theorem	theorem	NOUN
ejpam-837	120	17	4	4	NUM
ejpam-837	120	18	.	.	PUNCT
ejpam-837	120	19	suppose	suppose	VERB
ejpam-837	120	20	that	that	SCONJ
ejpam-837	120	21	q(x	q(x	PROPN
ejpam-837	120	22	)	)	PUNCT
ejpam-837	120	23	∈	∈	PROPN
ejpam-837	121	1	ac[0,1	ac[0,1	PROPN
ejpam-837	121	2	]	]	X
ejpam-837	121	3	,	,	PUNCT
ejpam-837	121	4	q(0	q(0	PROPN
ejpam-837	121	5	)	)	PUNCT
ejpam-837	121	6	6=	6=	PROPN
ejpam-837	122	1	q(1	q(1	NOUN
ejpam-837	122	2	)	)	PUNCT
ejpam-837	122	3	.	.	PUNCT
ejpam-837	123	1	then	then	ADV
ejpam-837	123	2	the	the	DET
ejpam-837	123	3	system	system	NOUN
ejpam-837	123	4	of	of	ADP
ejpam-837	123	5	the	the	DET
ejpam-837	123	6	root	root	NOUN
ejpam-837	123	7	functions	function	NOUN
ejpam-837	123	8	of	of	ADP
ejpam-837	123	9	the	the	DET
ejpam-837	123	10	boundary	boundary	ADJ
ejpam-837	123	11	problems	problem	NOUN
ejpam-837	123	12	(	(	PUNCT
ejpam-837	123	13	1),(2	1),(2	NUM
ejpam-837	123	14	)	)	PUNCT
ejpam-837	123	15	and	and	CCONJ
ejpam-837	123	16	(	(	PUNCT
ejpam-837	123	17	1),(3	1),(3	NOUN
ejpam-837	123	18	)	)	PUNCT
ejpam-837	123	19	forms	form	VERB
ejpam-837	123	20	a	a	DET
ejpam-837	123	21	basis	basis	NOUN
ejpam-837	123	22	in	in	ADP
ejpam-837	123	23	the	the	DET
ejpam-837	123	24	space	space	NOUN
ejpam-837	123	25	lp(0,1	lp(0,1	NOUN
ejpam-837	123	26	)	)	PUNCT
ejpam-837	123	27	(	(	PUNCT
ejpam-837	124	1	1	1	NUM
ejpam-837	124	2	<	<	X
ejpam-837	124	3	p	p	X
ejpam-837	124	4	<	<	X
ejpam-837	124	5	∞	∞	NUM
ejpam-837	124	6	)	)	PUNCT
ejpam-837	124	7	.	.	PUNCT
ejpam-837	125	1	proof	proof	NOUN
ejpam-837	125	2	.	.	PUNCT
ejpam-837	126	1	let	let	VERB
ejpam-837	126	2	ψ1(x	ψ1(x	PRON
ejpam-837	126	3	)	)	PUNCT
ejpam-837	126	4	=	=	SYM
ejpam-837	126	5	1	1	NUM
ejpam-837	126	6	,	,	PUNCT
ejpam-837	126	7	ψ2n(x	ψ2n(x	PROPN
ejpam-837	126	8	)	)	PUNCT
ejpam-837	126	9	=	=	PUNCT
ejpam-837	127	1	p	p	X
ejpam-837	127	2	2	2	NUM
ejpam-837	127	3	sin(2nπx	sin(2nπx	SYM
ejpam-837	127	4	−	−	PROPN
ejpam-837	127	5	π	π	PROPN
ejpam-837	127	6	4	4	NUM
ejpam-837	127	7	)	)	PUNCT
ejpam-837	127	8	,	,	PUNCT
ejpam-837	127	9	ψ2n+1(x	ψ2n+1(x	NOUN
ejpam-837	127	10	)	)	PUNCT
ejpam-837	127	11	=	=	PUNCT
ejpam-837	128	1	p	p	NOUN
ejpam-837	128	2	2	2	NUM
ejpam-837	129	1	cos(2nπx	cos(2nπx	NOUN
ejpam-837	129	2	−	−	NOUN
ejpam-837	129	3	π	π	NOUN
ejpam-837	129	4	4	4	NUM
ejpam-837	129	5	)	)	PUNCT
ejpam-837	129	6	,	,	PUNCT
ejpam-837	129	7	n	n	NOUN
ejpam-837	129	8	=	=	SYM
ejpam-837	129	9	1,2	1,2	NUM
ejpam-837	129	10	,	,	PUNCT
ejpam-837	129	11	.	.	PUNCT
ejpam-837	129	12	.	.	PUNCT
ejpam-837	130	1	..	..	PUNCT
ejpam-837	131	1	the	the	DET
ejpam-837	131	2	systems	system	NOUN
ejpam-837	131	3	�	�	PROPN
ejpam-837	131	4	ψn(x	ψn(x	ADP
ejpam-837	131	5	)	)	PUNCT
ejpam-837	131	6	∞	∞	NUM
ejpam-837	131	7	n=1	n=1	PROPN
ejpam-837	131	8	=	=	SYM
ejpam-837	131	9	�	�	PROPN
ejpam-837	131	10	ψ1(x),ψ2n(x),ψ2n+1(x	ψ1(x),ψ2n(x),ψ2n+1(x	PROPN
ejpam-837	131	11	)	)	PUNCT
ejpam-837	131	12	∞	∞	PROPN
ejpam-837	132	1	n=1	n=1	PROPN
ejpam-837	132	2	is	be	AUX
ejpam-837	132	3	a	a	DET
ejpam-837	132	4	basis	basis	NOUN
ejpam-837	132	5	in	in	ADP
ejpam-837	132	6	the	the	DET
ejpam-837	132	7	space	space	NOUN
ejpam-837	132	8	lp	lp	NOUN
ejpam-837	132	9	(	(	PUNCT
ejpam-837	132	10	0,1	0,1	NUM
ejpam-837	132	11	)	)	PUNCT
ejpam-837	132	12	.	.	PUNCT
ejpam-837	133	1	moreover	moreover	ADV
ejpam-837	133	2	,	,	PUNCT
ejpam-837	133	3	if	if	SCONJ
ejpam-837	133	4	p	p	NOUN
ejpam-837	133	5	=	=	NOUN
ejpam-837	133	6	2	2	NUM
ejpam-837	133	7	,	,	PUNCT
ejpam-837	133	8	this	this	DET
ejpam-837	133	9	basis	basis	NOUN
ejpam-837	133	10	is	be	AUX
ejpam-837	133	11	orthonormal	orthonormal	ADJ
ejpam-837	133	12	.	.	PUNCT
ejpam-837	134	1	we	we	PRON
ejpam-837	134	2	introduce	introduce	VERB
ejpam-837	134	3	notation	notation	NOUN
ejpam-837	134	4	:	:	PUNCT
ejpam-837	134	5	�	�	PROPN
ejpam-837	134	6	un(x	un(x	NOUN
ejpam-837	134	7	)	)	PUNCT
ejpam-837	134	8	∞	∞	NUM
ejpam-837	134	9	n=1	n=1	PROPN
ejpam-837	134	10	=	=	SYM
ejpam-837	134	11	�	�	PROPN
ejpam-837	134	12	u1(x),u2n(x),u2n+1(x	u1(x),u2n(x),u2n+1(x	PROPN
ejpam-837	134	13	)	)	PUNCT
ejpam-837	134	14	∞	∞	PROPN
ejpam-837	134	15	n=1	n=1	PROPN
ejpam-837	134	16	,	,	PUNCT
ejpam-837	134	17	�	�	PROPN
ejpam-837	134	18	υn(x	υn(x	ADP
ejpam-837	134	19	)	)	PUNCT
ejpam-837	134	20	∞	∞	NUM
ejpam-837	134	21	n=1	n=1	PROPN
ejpam-837	134	22	=	=	SYM
ejpam-837	134	23	�	�	PROPN
ejpam-837	134	24	υ1(x),υ2n(x),υ2n+1(x	υ1(x),υ2n(x),υ2n+1(x	PROPN
ejpam-837	134	25	)	)	PUNCT
ejpam-837	134	26	∞	∞	PROPN
ejpam-837	134	27	n=1	n=1	PROPN
ejpam-837	134	28	.	.	PUNCT
ejpam-837	135	1	it	it	PRON
ejpam-837	135	2	follows	follow	VERB
ejpam-837	135	3	from	from	ADP
ejpam-837	135	4	the	the	DET
ejpam-837	135	5	asymptotic	asymptotic	ADJ
ejpam-837	135	6	formulas	formula	NOUN
ejpam-837	135	7	(	(	PUNCT
ejpam-837	135	8	4),(5	4),(5	NOUN
ejpam-837	135	9	)	)	PUNCT
ejpam-837	135	10	and	and	CCONJ
ejpam-837	135	11	(	(	PUNCT
ejpam-837	135	12	8),(9	8),(9	NOUN
ejpam-837	135	13	)	)	PUNCT
ejpam-837	135	14	that	that	PRON
ejpam-837	135	15	un(x	un(x	X
ejpam-837	135	16	)	)	PUNCT
ejpam-837	136	1	=	=	NOUN
ejpam-837	136	2	ψn(x)+o	ψn(x)+o	NOUN
ejpam-837	136	3	(	(	PUNCT
ejpam-837	136	4	1	1	NUM
ejpam-837	136	5	n	n	NOUN
ejpam-837	136	6	)	)	PUNCT
ejpam-837	136	7	,	,	PUNCT
ejpam-837	136	8	υn(x	υn(x	X
ejpam-837	136	9	)	)	PUNCT
ejpam-837	136	10	=	=	NOUN
ejpam-837	136	11	ψn(x)+o	ψn(x)+o	NOUN
ejpam-837	136	12	(	(	PUNCT
ejpam-837	136	13	1	1	NUM
ejpam-837	136	14	n	n	NOUN
ejpam-837	136	15	)	)	PUNCT
ejpam-837	136	16	(	(	PUNCT
ejpam-837	136	17	10	10	NUM
ejpam-837	136	18	)	)	PUNCT
ejpam-837	136	19	for	for	ADP
ejpam-837	136	20	sufficiently	sufficiently	ADV
ejpam-837	136	21	large	large	ADJ
ejpam-837	136	22	n.	n.	NOUN
ejpam-837	136	23	let	let	VERB
ejpam-837	136	24	1	1	NUM
ejpam-837	136	25	<	<	X
ejpam-837	136	26	p	p	X
ejpam-837	136	27	<	<	X
ejpam-837	136	28	2	2	NUM
ejpam-837	136	29	.	.	PUNCT
ejpam-837	136	30	by	by	ADP
ejpam-837	136	31	theorem	theorem	NOUN
ejpam-837	136	32	3	3	NUM
ejpam-837	136	33	,	,	PUNCT
ejpam-837	136	34	the	the	DET
ejpam-837	136	35	system	system	NOUN
ejpam-837	136	36	of	of	ADP
ejpam-837	136	37	the	the	DET
ejpam-837	136	38	root	root	NOUN
ejpam-837	136	39	functions	function	NOUN
ejpam-837	136	40	�	�	PROPN
ejpam-837	136	41	un(x	un(x	NOUN
ejpam-837	136	42	)	)	PUNCT
ejpam-837	136	43	∞	∞	NUM
ejpam-837	136	44	n=1	n=1	PROPN
ejpam-837	136	45	is	be	AUX
ejpam-837	136	46	basis	basis	NOUN
ejpam-837	136	47	in	in	ADP
ejpam-837	136	48	l2	l2	NOUN
ejpam-837	136	49	(	(	PUNCT
ejpam-837	136	50	0,1	0,1	NUM
ejpam-837	136	51	)	)	PUNCT
ejpam-837	136	52	and	and	CCONJ
ejpam-837	136	53	�	�	PROPN
ejpam-837	136	54	υn(x	υn(x	ADP
ejpam-837	136	55	)	)	PUNCT
ejpam-837	136	56	∞	∞	NUM
ejpam-837	136	57	n=1	n=1	PROPN
ejpam-837	136	58	is	be	AUX
ejpam-837	136	59	biorthogonal	biorthogonal	ADJ
ejpam-837	136	60	to	to	ADP
ejpam-837	136	61	the	the	DET
ejpam-837	136	62	system	system	NOUN
ejpam-837	136	63	�	�	PROPN
ejpam-837	136	64	un(x	un(x	NUM
ejpam-837	136	65	)	)	PUNCT
ejpam-837	136	66	∞	∞	PROPN
ejpam-837	136	67	n=1	n=1	PROPN
ejpam-837	136	68	.	.	PUNCT
ejpam-837	137	1	thus	thus	ADV
ejpam-837	137	2	,	,	PUNCT
ejpam-837	137	3	this	this	DET
ejpam-837	137	4	system	system	NOUN
ejpam-837	137	5	is	be	AUX
ejpam-837	137	6	complete	complete	ADJ
ejpam-837	137	7	in	in	ADP
ejpam-837	137	8	lp	lp	PROPN
ejpam-837	137	9	(	(	PUNCT
ejpam-837	137	10	0,1	0,1	NUM
ejpam-837	137	11	)	)	PUNCT
ejpam-837	137	12	.	.	PUNCT
ejpam-837	138	1	therefore	therefore	ADV
ejpam-837	138	2	,	,	PUNCT
ejpam-837	138	3	by	by	ADP
ejpam-837	138	4	theorem	theorem	NOUN
ejpam-837	138	5	2	2	NUM
ejpam-837	138	6	,	,	PUNCT
ejpam-837	138	7	to	to	PART
ejpam-837	138	8	prove	prove	VERB
ejpam-837	138	9	the	the	DET
ejpam-837	138	10	basis	basis	NOUN
ejpam-837	138	11	property	property	NOUN
ejpam-837	138	12	of	of	ADP
ejpam-837	138	13	�	�	PROPN
ejpam-837	138	14	un(x	un(x	NOUN
ejpam-837	138	15	)	)	PUNCT
ejpam-837	138	16	∞	∞	NUM
ejpam-837	138	17	n=1	n=1	PROPN
ejpam-837	138	18	in	in	ADP
ejpam-837	138	19	lp	lp	PROPN
ejpam-837	138	20	(	(	PUNCT
ejpam-837	138	21	0,1	0,1	NUM
ejpam-837	138	22	)	)	PUNCT
ejpam-837	138	23	,	,	PUNCT
ejpam-837	138	24	it	it	PRON
ejpam-837	138	25	is	be	AUX
ejpam-837	138	26	necessary	necessary	ADJ
ejpam-837	138	27	and	and	CCONJ
ejpam-837	138	28	sufficient	sufficient	ADJ
ejpam-837	138	29	to	to	PART
ejpam-837	138	30	prove	prove	VERB
ejpam-837	138	31	that	that	DET
ejpam-837	138	32	existence	existence	NOUN
ejpam-837	138	33	of	of	ADP
ejpam-837	138	34	a	a	DET
ejpam-837	138	35	constant	constant	ADJ
ejpam-837	138	36	m	m	NOUN
ejpam-837	138	37	>	>	X
ejpam-837	138	38	0	0	NUM
ejpam-837	139	1	such	such	ADJ
ejpam-837	139	2	that	that	SCONJ
ejpam-837	139	3	n	n	PROPN
ejpam-837	139	4	∑	∑	PUNCT
ejpam-837	139	5	n=1	n=1	PROPN
ejpam-837	139	6	(	(	PUNCT
ejpam-837	139	7	f	f	PROPN
ejpam-837	139	8	,	,	PUNCT
ejpam-837	139	9	υn)un	υn)un	PROPN
ejpam-837	139	10	p	p	X
ejpam-837	139	11	≤	≤	NUM
ejpam-837	139	12	m	m	NOUN
ejpam-837	139	13	f	f	PROPN
ejpam-837	139	14	p	p	NOUN
ejpam-837	139	15	,	,	PUNCT
ejpam-837	139	16	n	n	NOUN
ejpam-837	139	17	=	=	SYM
ejpam-837	139	18	1,2	1,2	NUM
ejpam-837	139	19	,	,	PUNCT
ejpam-837	139	20	.	.	PUNCT
ejpam-837	139	21	.	.	PUNCT
ejpam-837	139	22	.	.	PUNCT
ejpam-837	140	1	,	,	PUNCT
ejpam-837	140	2	(	(	PUNCT
ejpam-837	140	3	11	11	NUM
ejpam-837	140	4	)	)	PUNCT
ejpam-837	140	5	for	for	ADP
ejpam-837	140	6	all	all	DET
ejpam-837	140	7	f	f	PROPN
ejpam-837	140	8	∈	∈	PROPN
ejpam-837	140	9	lp(0,1	lp(0,1	NOUN
ejpam-837	140	10	)	)	PUNCT
ejpam-837	140	11	,	,	PUNCT
ejpam-837	140	12	where	where	SCONJ
ejpam-837	140	13	‖·‖p	‖·‖p	ADJ
ejpam-837	140	14	denotes	denote	NOUN
ejpam-837	140	15	the	the	DET
ejpam-837	140	16	norm	norm	NOUN
ejpam-837	140	17	in	in	ADP
ejpam-837	140	18	lp(0,1	lp(0,1	NOUN
ejpam-837	140	19	)	)	PUNCT
ejpam-837	140	20	.	.	PUNCT
ejpam-837	141	1	k.	k.	PROPN
ejpam-837	142	1	mamedov	mamedov	PROPN
ejpam-837	142	2	/	/	SYM
ejpam-837	142	3	eur	eur	PROPN
ejpam-837	142	4	.	.	PUNCT
ejpam-837	143	1	j.	j.	PROPN
ejpam-837	143	2	pure	pure	PROPN
ejpam-837	143	3	appl	appl	PROPN
ejpam-837	143	4	.	.	PROPN
ejpam-837	143	5	math	math	PROPN
ejpam-837	143	6	,	,	PUNCT
ejpam-837	143	7	3	3	NUM
ejpam-837	143	8	(	(	PUNCT
ejpam-837	143	9	2010	2010	NUM
ejpam-837	143	10	)	)	PUNCT
ejpam-837	143	11	,	,	PUNCT
ejpam-837	143	12	831	831	NUM
ejpam-837	143	13	-	-	SYM
ejpam-837	143	14	838	838	NUM
ejpam-837	143	15	836	836	NUM
ejpam-837	143	16	by	by	ADP
ejpam-837	143	17	(	(	PUNCT
ejpam-837	143	18	10	10	NUM
ejpam-837	143	19	)	)	PUNCT
ejpam-837	143	20	we	we	PRON
ejpam-837	143	21	obtain	obtain	VERB
ejpam-837	143	22	n	n	NOUN
ejpam-837	143	23	∑	∑	ADV
ejpam-837	143	24	n=1	n=1	PROPN
ejpam-837	143	25	(	(	PUNCT
ejpam-837	143	26	f	f	PROPN
ejpam-837	143	27	,	,	PUNCT
ejpam-837	143	28	υn)un	υn)un	PROPN
ejpam-837	143	29	p	p	NOUN
ejpam-837	143	30	≤	≤	PROPN
ejpam-837	143	31	n	n	CCONJ
ejpam-837	143	32	∑	∑	PUNCT
ejpam-837	143	33	n=1	n=1	PROPN
ejpam-837	143	34	(	(	PUNCT
ejpam-837	143	35	f	f	PROPN
ejpam-837	143	36	,	,	PUNCT
ejpam-837	143	37	ψn)ψn	ψn)ψn	PUNCT
ejpam-837	143	38	p	p	X
ejpam-837	144	1	+	+	NOUN
ejpam-837	144	2	n	n	CCONJ
ejpam-837	144	3	∑	∑	PUNCT
ejpam-837	144	4	n=1	n=1	PROPN
ejpam-837	144	5	(	(	PUNCT
ejpam-837	144	6	f	f	PROPN
ejpam-837	144	7	,	,	PUNCT
ejpam-837	144	8	ψn)o	ψn)o	PROPN
ejpam-837	144	9	(	(	PUNCT
ejpam-837	144	10	1	1	NUM
ejpam-837	144	11	n	n	NOUN
ejpam-837	144	12	)	)	PUNCT
ejpam-837	144	13	p	p	NOUN
ejpam-837	144	14	+	+	CCONJ
ejpam-837	144	15	n	n	CCONJ
ejpam-837	144	16	∑	∑	PUNCT
ejpam-837	144	17	n=1	n=1	PROPN
ejpam-837	144	18	(	(	PUNCT
ejpam-837	144	19	f	f	PROPN
ejpam-837	144	20	,	,	PUNCT
ejpam-837	144	21	o	o	X
ejpam-837	144	22	(	(	PUNCT
ejpam-837	144	23	1	1	NUM
ejpam-837	144	24	n	n	NOUN
ejpam-837	144	25	)	)	PUNCT
ejpam-837	144	26	)	)	PUNCT
ejpam-837	144	27	ψn	ψn	VERB
ejpam-837	145	1	p	p	NOUN
ejpam-837	146	1	+	+	PROPN
ejpam-837	146	2	n	n	CCONJ
ejpam-837	146	3	∑	∑	PUNCT
ejpam-837	146	4	n=1	n=1	PROPN
ejpam-837	146	5	(	(	PUNCT
ejpam-837	146	6	f	f	PROPN
ejpam-837	146	7	,	,	PUNCT
ejpam-837	146	8	o	o	X
ejpam-837	146	9	(	(	PUNCT
ejpam-837	146	10	1	1	NUM
ejpam-837	146	11	n	n	NOUN
ejpam-837	146	12	)	)	PUNCT
ejpam-837	146	13	)	)	PUNCT
ejpam-837	147	1	o	o	NOUN
ejpam-837	147	2	(	(	PUNCT
ejpam-837	147	3	1	1	NUM
ejpam-837	147	4	n	n	NOUN
ejpam-837	147	5	)	)	PUNCT
ejpam-837	147	6	p	p	NOUN
ejpam-837	147	7	.	.	PUNCT
ejpam-837	148	1	(	(	PUNCT
ejpam-837	148	2	12	12	NUM
ejpam-837	148	3	)	)	PUNCT
ejpam-837	148	4	we	we	PRON
ejpam-837	148	5	shall	shall	AUX
ejpam-837	148	6	now	now	ADV
ejpam-837	148	7	prove	prove	VERB
ejpam-837	148	8	that	that	SCONJ
ejpam-837	148	9	all	all	DET
ejpam-837	148	10	the	the	DET
ejpam-837	148	11	summands	summand	NOUN
ejpam-837	148	12	on	on	ADP
ejpam-837	148	13	the	the	DET
ejpam-837	148	14	right	right	ADJ
ejpam-837	148	15	side	side	NOUN
ejpam-837	148	16	of	of	ADP
ejpam-837	148	17	(	(	PUNCT
ejpam-837	148	18	12	12	NUM
ejpam-837	148	19	)	)	PUNCT
ejpam-837	148	20	are	be	AUX
ejpam-837	148	21	bounded	bound	VERB
ejpam-837	148	22	from	from	ADP
ejpam-837	148	23	above	above	ADV
ejpam-837	148	24	by	by	ADP
ejpam-837	148	25	constant	constant	ADJ
ejpam-837	148	26	f	f	PROPN
ejpam-837	148	27	p	p	PROPN
ejpam-837	148	28	.	.	PUNCT
ejpam-837	149	1	since	since	SCONJ
ejpam-837	149	2	the	the	DET
ejpam-837	149	3	system	system	NOUN
ejpam-837	149	4	�	�	PROPN
ejpam-837	149	5	ψn(x	ψn(x	ADP
ejpam-837	149	6	)	)	PUNCT
ejpam-837	149	7	∞	∞	PROPN
ejpam-837	149	8	n=1	n=1	PROPN
ejpam-837	149	9	is	be	AUX
ejpam-837	149	10	a	a	DET
ejpam-837	149	11	basis	basis	NOUN
ejpam-837	149	12	in	in	ADP
ejpam-837	149	13	the	the	DET
ejpam-837	149	14	space	space	NOUN
ejpam-837	149	15	lp	lp	NOUN
ejpam-837	149	16	(	(	PUNCT
ejpam-837	149	17	0,1	0,1	NOUN
ejpam-837	149	18	)	)	PUNCT
ejpam-837	149	19	,	,	PUNCT
ejpam-837	149	20	applying	apply	VERB
ejpam-837	149	21	theorem	theorem	NOUN
ejpam-837	149	22	2	2	NUM
ejpam-837	149	23	,	,	PUNCT
ejpam-837	149	24	we	we	PRON
ejpam-837	149	25	have	have	VERB
ejpam-837	149	26	n	n	NUM
ejpam-837	149	27	∑	∑	ADV
ejpam-837	149	28	n=1	n=1	PROPN
ejpam-837	149	29	(	(	PUNCT
ejpam-837	149	30	f	f	PROPN
ejpam-837	149	31	,	,	PUNCT
ejpam-837	149	32	ψn)ψn	ψn)ψn	PUNCT
ejpam-837	150	1	p	p	NOUN
ejpam-837	150	2	≤	≤	NUM
ejpam-837	150	3	c	c	NOUN
ejpam-837	150	4	f	f	PROPN
ejpam-837	150	5	p	p	NOUN
ejpam-837	150	6	,	,	PUNCT
ejpam-837	150	7	c	c	X
ejpam-837	150	8	=	=	SYM
ejpam-837	150	9	const	const	X
ejpam-837	150	10	(	(	PUNCT
ejpam-837	150	11	n	n	NOUN
ejpam-837	150	12	=	=	SYM
ejpam-837	150	13	1,2	1,2	NUM
ejpam-837	150	14	,	,	PUNCT
ejpam-837	150	15	·	·	PUNCT
ejpam-837	150	16	·	·	PUNCT
ejpam-837	150	17	·	·	PUNCT
ejpam-837	150	18	)	)	PUNCT
ejpam-837	150	19	(	(	PUNCT
ejpam-837	150	20	13	13	NUM
ejpam-837	150	21	)	)	PUNCT
ejpam-837	150	22	for	for	ADP
ejpam-837	150	23	arbitrary	arbitrary	ADJ
ejpam-837	150	24	for	for	ADP
ejpam-837	150	25	all	all	DET
ejpam-837	150	26	f	f	PROPN
ejpam-837	150	27	∈	∈	PROPN
ejpam-837	150	28	lp(0,1	lp(0,1	NOUN
ejpam-837	150	29	)	)	PUNCT
ejpam-837	150	30	.	.	PUNCT
ejpam-837	151	1	by	by	ADP
ejpam-837	151	2	f.riesz	f.riesz	ADJ
ejpam-837	151	3	theorem	theorem	NOUN
ejpam-837	151	4	(	(	PUNCT
ejpam-837	151	5	see	see	VERB
ejpam-837	151	6	[	[	X
ejpam-837	151	7	22	22	NUM
ejpam-837	151	8	]	]	PUNCT
ejpam-837	151	9	,	,	PUNCT
ejpam-837	151	10	p.154	p.154	NOUN
ejpam-837	151	11	)	)	PUNCT
ejpam-837	151	12	for	for	ADP
ejpam-837	151	13	an	an	DET
ejpam-837	151	14	arbitrary	arbitrary	ADJ
ejpam-837	151	15	function	function	NOUN
ejpam-837	151	16	f	f	PROPN
ejpam-837	151	17	∈	∈	PROPN
ejpam-837	151	18	lp(0,1	lp(0,1	NOUN
ejpam-837	151	19	)	)	PUNCT
ejpam-837	151	20	one	one	NOUN
ejpam-837	151	21	has	have	VERB
ejpam-837	151	22	the	the	DET
ejpam-837	151	23	estimate	estimate	NOUN
ejpam-837	151	24	n	n	ADP
ejpam-837	151	25	∑	∑	ADV
ejpam-837	151	26	n=1	n=1	PROPN
ejpam-837	151	27	(	(	PUNCT
ejpam-837	151	28	f	f	PROPN
ejpam-837	151	29	,	,	PUNCT
ejpam-837	151	30	ψn)o	ψn)o	PROPN
ejpam-837	151	31	(	(	PUNCT
ejpam-837	151	32	1	1	NUM
ejpam-837	151	33	n	n	NOUN
ejpam-837	151	34	)	)	PUNCT
ejpam-837	151	35	p	p	NOUN
ejpam-837	151	36	≤	≤	NUM
ejpam-837	151	37	c	c	NOUN
ejpam-837	151	38	n	n	PROPN
ejpam-837	151	39	∑	∑	PUNCT
ejpam-837	151	40	n=1	n=1	PROPN
ejpam-837	151	41	(	(	PUNCT
ejpam-837	151	42	f	f	PROPN
ejpam-837	151	43	,	,	PUNCT
ejpam-837	151	44	ψn	ψn	PROPN
ejpam-837	151	45	)	)	PUNCT
ejpam-837	151	46	1	1	NUM
ejpam-837	151	47	n	n	NUM
ejpam-837	151	48	≤	≤	NUM
ejpam-837	151	49	c	c	NOUN
ejpam-837	151	50	n	n	PROPN
ejpam-837	151	51	∑	∑	PUNCT
ejpam-837	151	52	n=1	n=1	PROPN
ejpam-837	151	53	�	�	PROPN
ejpam-837	151	54	�	�	PROPN
ejpam-837	151	55	(	(	PUNCT
ejpam-837	151	56	f	f	PROPN
ejpam-837	151	57	,	,	PUNCT
ejpam-837	151	58	ψn	ψn	PROPN
ejpam-837	151	59	)	)	PUNCT
ejpam-837	151	60	�	�	PROPN
ejpam-837	151	61	�	�	PROPN
ejpam-837	151	62	q	q	PROPN
ejpam-837	151	63	!	!	PUNCT
ejpam-837	152	1	1	1	NUM
ejpam-837	152	2	q	q	NOUN
ejpam-837	152	3	·	·	PUNCT
ejpam-837	152	4	n	n	CCONJ
ejpam-837	152	5	∑	∑	ADP
ejpam-837	152	6	n=1	n=1	PROPN
ejpam-837	152	7	1	1	NUM
ejpam-837	152	8	np	np	INTJ
ejpam-837	152	9	!	!	PUNCT
ejpam-837	153	1	1	1	NUM
ejpam-837	153	2	p	p	NOUN
ejpam-837	153	3	≤	≤	NUM
ejpam-837	153	4	c	c	NOUN
ejpam-837	154	1	f	f	PROPN
ejpam-837	154	2	p	p	X
ejpam-837	154	3	,	,	PUNCT
ejpam-837	154	4	(	(	PUNCT
ejpam-837	154	5	14	14	NUM
ejpam-837	154	6	)	)	PUNCT
ejpam-837	154	7	where	where	SCONJ
ejpam-837	154	8	1	1	NUM
ejpam-837	154	9	p	p	NOUN
ejpam-837	155	1	+	+	NOUN
ejpam-837	155	2	1	1	NUM
ejpam-837	155	3	q	q	NOUN
ejpam-837	155	4	=	=	NOUN
ejpam-837	155	5	1	1	X
ejpam-837	155	6	.	.	PUNCT
ejpam-837	155	7	using	use	VERB
ejpam-837	155	8	the	the	DET
ejpam-837	155	9	parseval	parseval	NOUN
ejpam-837	155	10	’s	’s	PART
ejpam-837	155	11	equality	equality	NOUN
ejpam-837	155	12	we	we	PRON
ejpam-837	155	13	have	have	VERB
ejpam-837	155	14	n	n	NUM
ejpam-837	155	15	∑	∑	ADV
ejpam-837	155	16	n=1	n=1	PROPN
ejpam-837	155	17	(	(	PUNCT
ejpam-837	155	18	f	f	PROPN
ejpam-837	155	19	,	,	PUNCT
ejpam-837	155	20	o	o	X
ejpam-837	155	21	(	(	PUNCT
ejpam-837	155	22	1	1	NUM
ejpam-837	155	23	n	n	NOUN
ejpam-837	155	24	)	)	PUNCT
ejpam-837	155	25	)	)	PUNCT
ejpam-837	155	26	ψn	ψn	VERB
ejpam-837	155	27	p	p	NOUN
ejpam-837	155	28	≤	≤	PROPN
ejpam-837	155	29	n	n	CCONJ
ejpam-837	155	30	∑	∑	PUNCT
ejpam-837	155	31	n=1	n=1	PROPN
ejpam-837	155	32	(	(	PUNCT
ejpam-837	155	33	f	f	PROPN
ejpam-837	155	34	,	,	PUNCT
ejpam-837	155	35	o	o	X
ejpam-837	155	36	(	(	PUNCT
ejpam-837	155	37	1	1	NUM
ejpam-837	155	38	n	n	NOUN
ejpam-837	155	39	)	)	PUNCT
ejpam-837	155	40	)	)	PUNCT
ejpam-837	155	41	ψn	ψn	ADP
ejpam-837	155	42	2	2	NUM
ejpam-837	155	43	=	=	SYM
ejpam-837	155	44	n	n	CCONJ
ejpam-837	155	45	∑	∑	PUNCT
ejpam-837	155	46	n=1	n=1	PROPN
ejpam-837	155	47	�	�	PROPN
ejpam-837	155	48	�	�	PROPN
ejpam-837	155	49	�	�	PROPN
ejpam-837	155	50	�	�	PROPN
ejpam-837	155	51	(	(	PUNCT
ejpam-837	155	52	f	f	PROPN
ejpam-837	155	53	,	,	PUNCT
ejpam-837	155	54	o	o	X
ejpam-837	155	55	(	(	PUNCT
ejpam-837	155	56	1	1	NUM
ejpam-837	155	57	n	n	NOUN
ejpam-837	155	58	)	)	PUNCT
ejpam-837	155	59	)	)	PUNCT
ejpam-837	155	60	�	�	PROPN
ejpam-837	155	61	�	�	PROPN
ejpam-837	155	62	�	�	PROPN
ejpam-837	155	63	�	�	PROPN
ejpam-837	155	64	2	2	NUM
ejpam-837	155	65	!	!	SYM
ejpam-837	155	66	1	1	NUM
ejpam-837	155	67	2	2	NUM
ejpam-837	155	68	≤	≤	NUM
ejpam-837	156	1	c	c	NOUN
ejpam-837	156	2	f	f	PROPN
ejpam-837	156	3	1	1	NUM
ejpam-837	156	4	n	n	PROPN
ejpam-837	156	5	∑	∑	ADP
ejpam-837	156	6	n=1	n=1	PROPN
ejpam-837	156	7	1	1	NUM
ejpam-837	156	8	n2	n2	NOUN
ejpam-837	156	9	!	!	PUNCT
ejpam-837	157	1	1	1	NUM
ejpam-837	157	2	2	2	NUM
ejpam-837	157	3	≤	≤	NUM
ejpam-837	157	4	c	c	NOUN
ejpam-837	157	5	f	f	PROPN
ejpam-837	157	6	p	p	X
ejpam-837	157	7	,	,	PUNCT
ejpam-837	157	8	(	(	PUNCT
ejpam-837	157	9	15	15	NUM
ejpam-837	157	10	)	)	PUNCT
ejpam-837	157	11	n	n	NOUN
ejpam-837	157	12	∑	∑	PUNCT
ejpam-837	157	13	n=1	n=1	PROPN
ejpam-837	157	14	(	(	PUNCT
ejpam-837	157	15	f	f	PROPN
ejpam-837	157	16	,	,	PUNCT
ejpam-837	157	17	o	o	X
ejpam-837	157	18	(	(	PUNCT
ejpam-837	157	19	1	1	NUM
ejpam-837	157	20	n	n	NOUN
ejpam-837	157	21	)	)	PUNCT
ejpam-837	157	22	)	)	PUNCT
ejpam-837	158	1	o	o	NOUN
ejpam-837	158	2	(	(	PUNCT
ejpam-837	158	3	1	1	NUM
ejpam-837	158	4	n	n	NOUN
ejpam-837	158	5	)	)	PUNCT
ejpam-837	159	1	p	p	NOUN
ejpam-837	159	2	≤	≤	NUM
ejpam-837	159	3	c	c	NOUN
ejpam-837	159	4	f	f	PROPN
ejpam-837	159	5	1	1	NUM
ejpam-837	159	6	n	n	PROPN
ejpam-837	159	7	∑	∑	ADP
ejpam-837	159	8	n=1	n=1	PROPN
ejpam-837	159	9	1	1	NUM
ejpam-837	159	10	n2	n2	NOUN
ejpam-837	159	11	!	!	PUNCT
ejpam-837	160	1	1	1	NUM
ejpam-837	160	2	2	2	NUM
ejpam-837	160	3	≤	≤	NUM
ejpam-837	160	4	c	c	NOUN
ejpam-837	160	5	f	f	PROPN
ejpam-837	160	6	p	p	PROPN
ejpam-837	160	7	.	.	PUNCT
ejpam-837	161	1	(	(	PUNCT
ejpam-837	161	2	16	16	NUM
ejpam-837	161	3	)	)	PUNCT
ejpam-837	161	4	using	use	VERB
ejpam-837	161	5	the	the	DET
ejpam-837	161	6	inequalities	inequality	NOUN
ejpam-837	161	7	(	(	PUNCT
ejpam-837	161	8	13)-(16	13)-(16	NOUN
ejpam-837	161	9	)	)	PUNCT
ejpam-837	161	10	in	in	ADP
ejpam-837	161	11	the	the	DET
ejpam-837	161	12	estimate	estimate	NOUN
ejpam-837	161	13	(	(	PUNCT
ejpam-837	161	14	12	12	NUM
ejpam-837	161	15	)	)	PUNCT
ejpam-837	161	16	we	we	PRON
ejpam-837	161	17	have	have	VERB
ejpam-837	161	18	(	(	PUNCT
ejpam-837	161	19	11	11	NUM
ejpam-837	161	20	)	)	PUNCT
ejpam-837	161	21	.	.	PUNCT
ejpam-837	162	1	thus	thus	ADV
ejpam-837	162	2	the	the	DET
ejpam-837	162	3	proof	proof	NOUN
ejpam-837	162	4	of	of	ADP
ejpam-837	162	5	assertion	assertion	NOUN
ejpam-837	162	6	(	(	PUNCT
ejpam-837	162	7	11	11	NUM
ejpam-837	162	8	)	)	PUNCT
ejpam-837	162	9	is	be	AUX
ejpam-837	162	10	complete	complete	ADJ
ejpam-837	162	11	.	.	PUNCT
ejpam-837	163	1	consequently	consequently	ADV
ejpam-837	163	2	,	,	PUNCT
ejpam-837	163	3	the	the	DET
ejpam-837	163	4	system	system	NOUN
ejpam-837	163	5	�	�	PROPN
ejpam-837	163	6	un(x	un(x	NUM
ejpam-837	163	7	)	)	PUNCT
ejpam-837	163	8	∞	∞	NUM
ejpam-837	163	9	n=1	n=1	PROPN
ejpam-837	163	10	is	be	AUX
ejpam-837	163	11	a	a	DET
ejpam-837	163	12	basis	basis	NOUN
ejpam-837	163	13	in	in	ADP
ejpam-837	163	14	the	the	DET
ejpam-837	163	15	space	space	NOUN
ejpam-837	163	16	lp	lp	NOUN
ejpam-837	163	17	(	(	PUNCT
ejpam-837	163	18	0,1	0,1	NUM
ejpam-837	163	19	)	)	PUNCT
ejpam-837	163	20	,	,	PUNCT
ejpam-837	163	21	1	1	NUM
ejpam-837	163	22	<	<	X
ejpam-837	163	23	p	p	X
ejpam-837	163	24	<	<	X
ejpam-837	163	25	2	2	NUM
ejpam-837	163	26	.	.	PUNCT
ejpam-837	163	27	now	now	ADV
ejpam-837	163	28	assume	assume	VERB
ejpam-837	163	29	that	that	SCONJ
ejpam-837	163	30	2	2	NUM
ejpam-837	163	31	<	<	X
ejpam-837	163	32	p	p	X
ejpam-837	163	33	<	<	X
ejpam-837	163	34	∞.	∞.	PROPN
ejpam-837	163	35	it	it	PRON
ejpam-837	163	36	is	be	AUX
ejpam-837	163	37	clear	clear	ADJ
ejpam-837	163	38	that	that	SCONJ
ejpam-837	163	39	the	the	DET
ejpam-837	163	40	system	system	NOUN
ejpam-837	163	41	�	�	PROPN
ejpam-837	163	42	un(x	un(x	NUM
ejpam-837	163	43	)	)	PUNCT
ejpam-837	163	44	∞	∞	NUM
ejpam-837	163	45	n=1	n=1	PROPN
ejpam-837	163	46	is	be	AUX
ejpam-837	163	47	a	a	DET
ejpam-837	163	48	basis	basis	NOUN
ejpam-837	163	49	in	in	ADP
ejpam-837	163	50	lq	lq	X
ejpam-837	163	51	(	(	PUNCT
ejpam-837	163	52	0,1	0,1	NOUN
ejpam-837	163	53	)	)	PUNCT
ejpam-837	163	54	.	.	PUNCT
ejpam-837	164	1	by	by	ADP
ejpam-837	164	2	corollary	corollary	ADJ
ejpam-837	164	3	2	2	NUM
ejpam-837	164	4	in	in	ADP
ejpam-837	164	5	[	[	X
ejpam-837	164	6	7	7	NUM
ejpam-837	164	7	]	]	PUNCT
ejpam-837	164	8	(	(	PUNCT
ejpam-837	164	9	in	in	ADP
ejpam-837	164	10	section	section	NOUN
ejpam-837	164	11	i	i	NOUN
ejpam-837	164	12	)	)	PUNCT
ejpam-837	165	1	it	it	PRON
ejpam-837	165	2	follows	follow	VERB
ejpam-837	165	3	that	that	SCONJ
ejpam-837	165	4	the	the	DET
ejpam-837	165	5	system	system	NOUN
ejpam-837	165	6	�	�	PROPN
ejpam-837	165	7	υn(x	υn(x	ADP
ejpam-837	165	8	)	)	PUNCT
ejpam-837	165	9	∞	∞	NUM
ejpam-837	165	10	n=1	n=1	PROPN
ejpam-837	165	11	is	be	AUX
ejpam-837	165	12	a	a	DET
ejpam-837	165	13	basis	basis	NOUN
ejpam-837	165	14	in	in	ADP
ejpam-837	165	15	the	the	DET
ejpam-837	165	16	references	reference	NOUN
ejpam-837	165	17	837	837	NUM
ejpam-837	165	18	space	space	NOUN
ejpam-837	165	19	lp	lp	NOUN
ejpam-837	165	20	(	(	PUNCT
ejpam-837	165	21	0,1	0,1	NUM
ejpam-837	165	22	)	)	PUNCT
ejpam-837	165	23	,	,	PUNCT
ejpam-837	165	24	where	where	SCONJ
ejpam-837	165	25	1	1	NUM
ejpam-837	165	26	p	p	NOUN
ejpam-837	166	1	+	+	NOUN
ejpam-837	166	2	1	1	NUM
ejpam-837	166	3	q	q	NOUN
ejpam-837	166	4	=	=	SYM
ejpam-837	166	5	1	1	X
ejpam-837	166	6	.	.	X
ejpam-837	166	7	note	note	VERB
ejpam-837	166	8	that	that	SCONJ
ejpam-837	166	9	1	1	NUM
ejpam-837	166	10	<	<	X
ejpam-837	166	11	q	q	X
ejpam-837	166	12	<	<	X
ejpam-837	166	13	2	2	NUM
ejpam-837	166	14	.	.	PUNCT
ejpam-837	166	15	using	use	VERB
ejpam-837	166	16	the	the	DET
ejpam-837	166	17	discussions	discussion	NOUN
ejpam-837	166	18	introduced	introduce	VERB
ejpam-837	166	19	above	above	ADP
ejpam-837	166	20	entirely	entirely	ADV
ejpam-837	166	21	analogously	analogously	ADV
ejpam-837	166	22	it	it	PRON
ejpam-837	166	23	is	be	AUX
ejpam-837	166	24	proved	prove	VERB
ejpam-837	166	25	that	that	SCONJ
ejpam-837	166	26	the	the	DET
ejpam-837	166	27	system	system	NOUN
ejpam-837	166	28	�	�	PROPN
ejpam-837	166	29	υn(x	υn(x	ADP
ejpam-837	166	30	)	)	PUNCT
ejpam-837	166	31	∞	∞	NUM
ejpam-837	166	32	n=1	n=1	PROPN
ejpam-837	166	33	is	be	AUX
ejpam-837	166	34	a	a	DET
ejpam-837	166	35	basis	basis	NOUN
ejpam-837	166	36	in	in	ADP
ejpam-837	166	37	lq	lq	X
ejpam-837	166	38	(	(	PUNCT
ejpam-837	166	39	0,1	0,1	NUM
ejpam-837	166	40	)	)	PUNCT
ejpam-837	166	41	.	.	PUNCT
ejpam-837	167	1	it	it	PRON
ejpam-837	167	2	follows	follow	VERB
ejpam-837	167	3	that	that	SCONJ
ejpam-837	167	4	�	�	PROPN
ejpam-837	167	5	un(x	un(x	NOUN
ejpam-837	167	6	)	)	PUNCT
ejpam-837	167	7	∞	∞	NUM
ejpam-837	167	8	n=1	n=1	PROPN
ejpam-837	167	9	is	be	AUX
ejpam-837	167	10	a	a	DET
ejpam-837	167	11	basis	basis	NOUN
ejpam-837	167	12	in	in	ADP
ejpam-837	167	13	the	the	DET
ejpam-837	167	14	space	space	NOUN
ejpam-837	167	15	lp	lp	NOUN
ejpam-837	167	16	(	(	PUNCT
ejpam-837	167	17	0,1	0,1	NUM
ejpam-837	167	18	)	)	PUNCT
ejpam-837	167	19	,	,	PUNCT
ejpam-837	167	20	p	p	X
ejpam-837	167	21	>	>	X
ejpam-837	167	22	2	2	X
ejpam-837	167	23	.	.	PUNCT
ejpam-837	167	24	entirely	entirely	ADV
ejpam-837	167	25	analogously	analogously	ADV
ejpam-837	167	26	it	it	PRON
ejpam-837	167	27	is	be	AUX
ejpam-837	167	28	not	not	PART
ejpam-837	167	29	difficult	difficult	ADJ
ejpam-837	167	30	to	to	PART
ejpam-837	167	31	prove	prove	VERB
ejpam-837	167	32	that	that	SCONJ
ejpam-837	167	33	the	the	DET
ejpam-837	167	34	system	system	NOUN
ejpam-837	167	35	of	of	ADP
ejpam-837	167	36	the	the	DET
ejpam-837	167	37	root	root	NOUN
ejpam-837	167	38	functions	function	NOUN
ejpam-837	167	39	of	of	ADP
ejpam-837	167	40	the	the	DET
ejpam-837	167	41	boundary	boundary	ADJ
ejpam-837	167	42	problem	problem	NOUN
ejpam-837	167	43	(	(	PUNCT
ejpam-837	167	44	1),(3	1),(3	NOUN
ejpam-837	167	45	)	)	PUNCT
ejpam-837	167	46	form	form	NOUN
ejpam-837	167	47	a	a	DET
ejpam-837	167	48	basis	basis	NOUN
ejpam-837	167	49	in	in	ADP
ejpam-837	167	50	the	the	DET
ejpam-837	167	51	space	space	NOUN
ejpam-837	167	52	lp(0,1	lp(0,1	NOUN
ejpam-837	167	53	)	)	PUNCT
ejpam-837	167	54	(	(	PUNCT
ejpam-837	167	55	1	1	NUM
ejpam-837	167	56	<	<	X
ejpam-837	167	57	p	p	X
ejpam-837	167	58	<	<	X
ejpam-837	167	59	∞	∞	PROPN
ejpam-837	167	60	)	)	PUNCT
ejpam-837	167	61	.	.	PUNCT
ejpam-837	168	1	the	the	DET
ejpam-837	168	2	proof	proof	NOUN
ejpam-837	168	3	of	of	ADP
ejpam-837	168	4	the	the	DET
ejpam-837	168	5	theorem	theorem	NOUN
ejpam-837	168	6	is	be	AUX
ejpam-837	168	7	complete	complete	ADJ
ejpam-837	168	8	.	.	PUNCT
ejpam-837	169	1	references	reference	NOUN
ejpam-837	169	2	[	[	X
ejpam-837	169	3	1	1	NUM
ejpam-837	169	4	]	]	PUNCT
ejpam-837	169	5	n	n	PRON
ejpam-837	169	6	k	k	PROPN
ejpam-837	169	7	bari	bari	PROPN
ejpam-837	169	8	.	.	PUNCT
ejpam-837	170	1	biorthogonal	biorthogonal	PROPN
ejpam-837	170	2	systems	system	NOUN
ejpam-837	170	3	and	and	CCONJ
ejpam-837	170	4	bases	basis	NOUN
ejpam-837	170	5	in	in	ADP
ejpam-837	170	6	hilbert	hilbert	PROPN
ejpam-837	170	7	spaces	space	NOUN
ejpam-837	170	8	.	.	PUNCT
ejpam-837	171	1	uchen	uchen	NOUN
ejpam-837	171	2	.	.	PUNCT
ejpam-837	172	1	zap	zap	PROPN
ejpam-837	172	2	.	.	PUNCT
ejpam-837	172	3	moskov	moskov	PROPN
ejpam-837	172	4	.	.	PUNCT
ejpam-837	173	1	gos	gos	PROPN
ejpam-837	173	2	.	.	PUNCT
ejpam-837	174	1	univ	univ	PROPN
ejpam-837	174	2	.	.	PUNCT
ejpam-837	175	1	148(4):68	148(4):68	NUM
ejpam-837	175	2	-	-	SYM
ejpam-837	175	3	107	107	NUM
ejpam-837	175	4	,	,	PUNCT
ejpam-837	175	5	1951	1951	NUM
ejpam-837	175	6	(	(	PUNCT
ejpam-837	175	7	russian	russian	ADJ
ejpam-837	175	8	)	)	PUNCT
ejpam-837	175	9	.	.	PUNCT
ejpam-837	176	1	[	[	X
ejpam-837	176	2	2	2	NUM
ejpam-837	176	3	]	]	PUNCT
ejpam-837	176	4	n	n	CCONJ
ejpam-837	176	5	dernek	dernek	ADJ
ejpam-837	176	6	and	and	CCONJ
ejpam-837	176	7	o	o	X
ejpam-837	176	8	a	a	DET
ejpam-837	176	9	veliev	veliev	NOUN
ejpam-837	176	10	.	.	PUNCT
ejpam-837	177	1	on	on	ADP
ejpam-837	177	2	the	the	DET
ejpam-837	177	3	riesz	riesz	NOUN
ejpam-837	177	4	basisness	basisness	NOUN
ejpam-837	177	5	of	of	ADP
ejpam-837	177	6	the	the	DET
ejpam-837	177	7	root	root	NOUN
ejpam-837	177	8	functions	function	NOUN
ejpam-837	177	9	of	of	ADP
ejpam-837	177	10	the	the	DET
ejpam-837	177	11	nonselfadjoint	nonselfadjoint	NOUN
ejpam-837	177	12	sturm	sturm	NOUN
ejpam-837	177	13	-	-	PUNCT
ejpam-837	177	14	liouville	liouville	NOUN
ejpam-837	177	15	operators	operator	NOUN
ejpam-837	177	16	.	.	PUNCT
ejpam-837	178	1	israel	israel	PROPN
ejpam-837	178	2	journal	journal	PROPN
ejpam-837	178	3	of	of	ADP
ejpam-837	178	4	mathematics	mathematic	NOUN
ejpam-837	178	5	,	,	PUNCT
ejpam-837	178	6	145:113	145:113	PROPN
ejpam-837	178	7	-	-	SYM
ejpam-837	178	8	123	123	NUM
ejpam-837	178	9	,	,	PUNCT
ejpam-837	178	10	2005	2005	NUM
ejpam-837	178	11	.	.	PUNCT
ejpam-837	179	1	[	[	X
ejpam-837	179	2	3	3	X
ejpam-837	179	3	]	]	X
ejpam-837	179	4	p	p	NOUN
ejpam-837	179	5	djakov	djakov	NOUN
ejpam-837	179	6	and	and	CCONJ
ejpam-837	179	7	b	b	NOUN
ejpam-837	179	8	s	s	NOUN
ejpam-837	179	9	mitjagin	mitjagin	NOUN
ejpam-837	179	10	.	.	PUNCT
ejpam-837	180	1	instability	instability	NOUN
ejpam-837	180	2	zones	zone	NOUN
ejpam-837	180	3	of	of	ADP
ejpam-837	180	4	periodic	periodic	ADJ
ejpam-837	180	5	1	1	NUM
ejpam-837	180	6	-	-	PUNCT
ejpam-837	180	7	dimensional	dimensional	ADJ
ejpam-837	180	8	schrodinger	schrodinger	NOUN
ejpam-837	180	9	and	and	CCONJ
ejpam-837	180	10	dirac	dirac	NOUN
ejpam-837	180	11	operators	operator	NOUN
ejpam-837	180	12	.	.	PUNCT
ejpam-837	181	1	uspekhi	uspekhi	PROPN
ejpam-837	181	2	mat	mat	PROPN
ejpam-837	181	3	.	.	PUNCT
ejpam-837	182	1	nauk	nauk	PROPN
ejpam-837	182	2	,	,	PUNCT
ejpam-837	182	3	61:4	61:4	NUM
ejpam-837	182	4	,	,	PUNCT
ejpam-837	182	5	77	77	NUM
ejpam-837	182	6	-	-	SYM
ejpam-837	182	7	182	182	NUM
ejpam-837	182	8	,	,	PUNCT
ejpam-837	182	9	2006	2006	NUM
ejpam-837	182	10	.	.	PUNCT
ejpam-837	183	1	english	english	PROPN
ejpam-837	183	2	transl	transl	PROPN
ejpam-837	183	3	.	.	PUNCT
ejpam-837	184	1	in	in	ADP
ejpam-837	184	2	russian	russian	ADJ
ejpam-837	184	3	math	math	NOUN
ejpam-837	184	4	.	.	PUNCT
ejpam-837	185	1	surves	surf	NOUN
ejpam-837	185	2	,	,	PUNCT
ejpam-837	185	3	61:4	61:4	NUM
ejpam-837	185	4	,	,	PUNCT
ejpam-837	185	5	663	663	NUM
ejpam-837	185	6	-	-	SYM
ejpam-837	185	7	776	776	NUM
ejpam-837	185	8	,	,	PUNCT
ejpam-837	185	9	2006	2006	NUM
ejpam-837	185	10	.	.	PUNCT
ejpam-837	186	1	[	[	X
ejpam-837	186	2	4	4	X
ejpam-837	186	3	]	]	PUNCT
ejpam-837	186	4	n	n	PRON
ejpam-837	186	5	dunford	dunford	NOUN
ejpam-837	186	6	and	and	CCONJ
ejpam-837	186	7	j	j	PROPN
ejpam-837	186	8	t	t	PROPN
ejpam-837	186	9	schwartz	schwartz	PROPN
ejpam-837	186	10	.	.	PUNCT
ejpam-837	187	1	linear	linear	PROPN
ejpam-837	187	2	operators	operator	NOUN
ejpam-837	187	3	,	,	PUNCT
ejpam-837	187	4	prt.3	prt.3	PROPN
ejpam-837	187	5	spectral	spectral	ADJ
ejpam-837	187	6	operators	operator	NOUN
ejpam-837	187	7	.	.	PUNCT
ejpam-837	188	1	wiley	wiley	PROPN
ejpam-837	188	2	,	,	PUNCT
ejpam-837	188	3	new	new	PROPN
ejpam-837	188	4	york	york	PROPN
ejpam-837	188	5	,	,	PUNCT
ejpam-837	188	6	1970	1970	NUM
ejpam-837	188	7	.	.	PUNCT
ejpam-837	189	1	[	[	X
ejpam-837	189	2	5	5	X
ejpam-837	189	3	]	]	PUNCT
ejpam-837	189	4	i	i	PRON
ejpam-837	189	5	c	c	PROPN
ejpam-837	189	6	gohberg	gohberg	PROPN
ejpam-837	189	7	and	and	CCONJ
ejpam-837	189	8	m	m	VERB
ejpam-837	189	9	g	g	PROPN
ejpam-837	189	10	krein	krein	NOUN
ejpam-837	189	11	.	.	PUNCT
ejpam-837	190	1	introduction	introduction	NOUN
ejpam-837	190	2	to	to	ADP
ejpam-837	190	3	the	the	DET
ejpam-837	190	4	theory	theory	NOUN
ejpam-837	190	5	of	of	ADP
ejpam-837	190	6	linear	linear	PROPN
ejpam-837	190	7	nonselfadjoint	nonselfadjoint	NOUN
ejpam-837	190	8	operators	operator	NOUN
ejpam-837	190	9	.	.	PUNCT
ejpam-837	191	1	american	american	ADJ
ejpam-837	191	2	math	math	PROPN
ejpam-837	191	3	.	.	PUNCT
ejpam-837	192	1	soc	soc	PROPN
ejpam-837	192	2	.	.	PUNCT
ejpam-837	192	3	,	,	PUNCT
ejpam-837	192	4	providence	providence	NOUN
ejpam-837	192	5	,	,	PUNCT
ejpam-837	192	6	rhode	rhode	NOUN
ejpam-837	192	7	island	island	NOUN
ejpam-837	192	8	,	,	PUNCT
ejpam-837	192	9	1969	1969	NUM
ejpam-837	192	10	.	.	PUNCT
ejpam-837	193	1	[	[	X
ejpam-837	193	2	6	6	NUM
ejpam-837	193	3	]	]	PUNCT
ejpam-837	193	4	n	n	NOUN
ejpam-837	193	5	i	i	PRON
ejpam-837	193	6	ionkin	ionkin	VERB
ejpam-837	193	7	.	.	PUNCT
ejpam-837	194	1	the	the	DET
ejpam-837	194	2	solution	solution	NOUN
ejpam-837	194	3	of	of	ADP
ejpam-837	194	4	a	a	DET
ejpam-837	194	5	boundary	boundary	ADJ
ejpam-837	194	6	-	-	PUNCT
ejpam-837	194	7	value	value	NOUN
ejpam-837	194	8	problem	problem	NOUN
ejpam-837	194	9	in	in	ADP
ejpam-837	194	10	heat	heat	NOUN
ejpam-837	194	11	conduction	conduction	NOUN
ejpam-837	194	12	with	with	ADP
ejpam-837	194	13	a	a	DET
ejpam-837	194	14	nonclassical	nonclassical	ADJ
ejpam-837	194	15	boundary	boundary	ADJ
ejpam-837	194	16	condition	condition	NOUN
ejpam-837	194	17	.	.	PUNCT
ejpam-837	195	1	differ	differ	VERB
ejpam-837	195	2	.	.	PUNCT
ejpam-837	196	1	equations	equation	NOUN
ejpam-837	196	2	,	,	PUNCT
ejpam-837	196	3	13(2	13(2	PROPN
ejpam-837	196	4	):	):	PUNCT
ejpam-837	196	5	294	294	NUM
ejpam-837	196	6	-	-	SYM
ejpam-837	196	7	304	304	NUM
ejpam-837	196	8	,	,	PUNCT
ejpam-837	196	9	1977	1977	NUM
ejpam-837	196	10	.	.	PUNCT
ejpam-837	197	1	[	[	X
ejpam-837	197	2	7	7	NUM
ejpam-837	197	3	]	]	SYM
ejpam-837	197	4	b	b	PROPN
ejpam-837	197	5	s	s	PART
ejpam-837	197	6	kashin	kashin	NOUN
ejpam-837	197	7	and	and	CCONJ
ejpam-837	197	8	a	a	DET
ejpam-837	197	9	a	a	DET
ejpam-837	197	10	saakyan	saakyan	NOUN
ejpam-837	197	11	.	.	PUNCT
ejpam-837	198	1	orthogonal	orthogonal	ADJ
ejpam-837	198	2	series	series	PROPN
ejpam-837	198	3	.	.	PUNCT
ejpam-837	199	1	american	american	PROPN
ejpam-837	199	2	mathematical	mathematical	PROPN
ejpam-837	199	3	society	society	NOUN
ejpam-837	199	4	,	,	PUNCT
ejpam-837	199	5	1989	1989	NUM
ejpam-837	199	6	.	.	PUNCT
ejpam-837	200	1	[	[	X
ejpam-837	200	2	8	8	NUM
ejpam-837	200	3	]	]	SYM
ejpam-837	200	4	n	n	PROPN
ejpam-837	200	5	b	b	PROPN
ejpam-837	200	6	kerimov	kerimov	PROPN
ejpam-837	200	7	and	and	CCONJ
ejpam-837	200	8	kh	kh	PROPN
ejpam-837	200	9	r	r	PROPN
ejpam-837	200	10	mamedov	mamedov	PROPN
ejpam-837	200	11	.	.	PUNCT
ejpam-837	201	1	on	on	ADP
ejpam-837	201	2	the	the	DET
ejpam-837	201	3	riesz	riesz	PROPN
ejpam-837	201	4	basis	basis	NOUN
ejpam-837	201	5	property	property	NOUN
ejpam-837	201	6	of	of	ADP
ejpam-837	201	7	the	the	DET
ejpam-837	201	8	root	root	NOUN
ejpam-837	201	9	functions	function	NOUN
ejpam-837	201	10	in	in	ADP
ejpam-837	201	11	certain	certain	ADJ
ejpam-837	201	12	regular	regular	ADJ
ejpam-837	201	13	boundary	boundary	ADJ
ejpam-837	201	14	value	value	NOUN
ejpam-837	201	15	problems	problem	NOUN
ejpam-837	201	16	.	.	PUNCT
ejpam-837	202	1	math	math	NOUN
ejpam-837	202	2	.	.	PUNCT
ejpam-837	203	1	notes	note	NOUN
ejpam-837	203	2	,	,	PUNCT
ejpam-837	203	3	64(4	64(4	NOUN
ejpam-837	203	4	):	):	PUNCT
ejpam-837	203	5	483	483	NUM
ejpam-837	203	6	-	-	SYM
ejpam-837	203	7	487	487	NUM
ejpam-837	203	8	,	,	PUNCT
ejpam-837	203	9	1998	1998	NUM
ejpam-837	203	10	.	.	PUNCT
ejpam-837	204	1	[	[	X
ejpam-837	204	2	9	9	NUM
ejpam-837	204	3	]	]	SYM
ejpam-837	204	4	g	g	PROPN
ejpam-837	204	5	m	m	PROPN
ejpam-837	204	6	kesel’man	kesel’man	NOUN
ejpam-837	204	7	.	.	PUNCT
ejpam-837	205	1	on	on	ADP
ejpam-837	205	2	the	the	DET
ejpam-837	205	3	unconditional	unconditional	ADJ
ejpam-837	205	4	convergence	convergence	NOUN
ejpam-837	205	5	of	of	ADP
ejpam-837	205	6	expansions	expansion	NOUN
ejpam-837	205	7	in	in	ADP
ejpam-837	205	8	the	the	DET
ejpam-837	205	9	eigenfunctions	eigenfunction	NOUN
ejpam-837	205	10	of	of	ADP
ejpam-837	205	11	some	some	DET
ejpam-837	205	12	differential	differential	ADJ
ejpam-837	205	13	operators	operator	NOUN
ejpam-837	205	14	,	,	PUNCT
ejpam-837	205	15	izv	izv	PROPN
ejpam-837	205	16	.	.	PROPN
ejpam-837	205	17	vyssh	vyssh	PROPN
ejpam-837	205	18	.	.	PUNCT
ejpam-837	206	1	uchebn	uchebn	NOUN
ejpam-837	206	2	.	.	PUNCT
ejpam-837	207	1	zaved	zave	VERB
ejpam-837	207	2	.	.	PUNCT
ejpam-837	208	1	mat	mat	NOUN
ejpam-837	208	2	.	.	PUNCT
ejpam-837	209	1	[	[	X
ejpam-837	209	2	soviet	soviet	ADJ
ejpam-837	209	3	math	math	NOUN
ejpam-837	209	4	.	.	PUNCT
ejpam-837	210	1	(	(	PUNCT
ejpam-837	210	2	iz	iz	INTJ
ejpam-837	210	3	.	.	PUNCT
ejpam-837	210	4	vuz	vuz	PROPN
ejpam-837	210	5	)	)	PUNCT
ejpam-837	210	6	]	]	X
ejpam-837	210	7	,	,	PUNCT
ejpam-837	210	8	2	2	NUM
ejpam-837	210	9	:	:	SYM
ejpam-837	210	10	82	82	NUM
ejpam-837	210	11	-	-	SYM
ejpam-837	210	12	93	93	NUM
ejpam-837	210	13	,	,	PUNCT
ejpam-837	210	14	1964	1964	NUM
ejpam-837	210	15	.	.	PUNCT
ejpam-837	211	1	[	[	X
ejpam-837	211	2	10	10	NUM
ejpam-837	211	3	]	]	X
ejpam-837	211	4	a	a	DET
ejpam-837	211	5	a	a	DET
ejpam-837	211	6	kıraç	kıraç	ADJ
ejpam-837	211	7	.	.	PUNCT
ejpam-837	212	1	riesz	riesz	VERB
ejpam-837	212	2	basis	basis	NOUN
ejpam-837	212	3	property	property	NOUN
ejpam-837	212	4	of	of	ADP
ejpam-837	212	5	the	the	DET
ejpam-837	212	6	root	root	NOUN
ejpam-837	212	7	functions	function	NOUN
ejpam-837	212	8	of	of	ADP
ejpam-837	212	9	non	non	ADJ
ejpam-837	212	10	-	-	ADJ
ejpam-837	212	11	selfadjoint	selfadjoint	ADJ
ejpam-837	212	12	operators	operator	NOUN
ejpam-837	212	13	wit	wit	ADP
ejpam-837	212	14	regular	regular	ADJ
ejpam-837	212	15	boundary	boundary	ADJ
ejpam-837	212	16	conditions	condition	NOUN
ejpam-837	212	17	,	,	PUNCT
ejpam-837	212	18	int.journal	int.journal	ADJ
ejpam-837	212	19	of	of	ADP
ejpam-837	212	20	math.analysis	math.analysis	NOUN
ejpam-837	212	21	.	.	PUNCT
ejpam-837	213	1	3(22):1101	3(22):1101	NUM
ejpam-837	213	2	-	-	PUNCT
ejpam-837	213	3	1109	1109	NUM
ejpam-837	213	4	,	,	PUNCT
ejpam-837	213	5	2009	2009	NUM
ejpam-837	213	6	.	.	PUNCT
ejpam-837	214	1	[	[	X
ejpam-837	214	2	11	11	NUM
ejpam-837	214	3	]	]	SYM
ejpam-837	214	4	v	v	PROPN
ejpam-837	214	5	m	m	PROPN
ejpam-837	214	6	kurbanov	kurbanov	PROPN
ejpam-837	214	7	.	.	PUNCT
ejpam-837	215	1	a	a	DET
ejpam-837	215	2	theorem	theorem	NOUN
ejpam-837	215	3	on	on	ADP
ejpam-837	215	4	equivalent	equivalent	ADJ
ejpam-837	215	5	bases	basis	NOUN
ejpam-837	215	6	for	for	ADP
ejpam-837	215	7	a	a	DET
ejpam-837	215	8	differential	differential	ADJ
ejpam-837	215	9	operator	operator	NOUN
ejpam-837	215	10	.	.	PUNCT
ejpam-837	216	1	dokl	dokl	NOUN
ejpam-837	216	2	.	.	PUNCT
ejpam-837	217	1	akad	akad	PROPN
ejpam-837	217	2	.	.	PUNCT
ejpam-837	218	1	nauk	nauk	PROPN
ejpam-837	218	2	,	,	PUNCT
ejpam-837	218	3	406(1):17	406(1):17	PROPN
ejpam-837	218	4	-	-	PUNCT
ejpam-837	218	5	20	20	NUM
ejpam-837	218	6	,	,	PUNCT
ejpam-837	218	7	2006	2006	NUM
ejpam-837	218	8	.	.	PUNCT
ejpam-837	219	1	[	[	X
ejpam-837	219	2	12	12	NUM
ejpam-837	219	3	]	]	PUNCT
ejpam-837	219	4	a	a	PRON
ejpam-837	219	5	s	s	X
ejpam-837	219	6	makin	makin	NOUN
ejpam-837	219	7	.	.	PUNCT
ejpam-837	220	1	convergence	convergence	NOUN
ejpam-837	220	2	of	of	ADP
ejpam-837	220	3	expansions	expansion	NOUN
ejpam-837	220	4	in	in	ADP
ejpam-837	220	5	the	the	DET
ejpam-837	220	6	root	root	NOUN
ejpam-837	220	7	functions	function	NOUN
ejpam-837	220	8	of	of	ADP
ejpam-837	220	9	periodic	periodic	ADJ
ejpam-837	220	10	boundary	boundary	ADJ
ejpam-837	220	11	value	value	NOUN
ejpam-837	220	12	problems	problem	NOUN
ejpam-837	220	13	.	.	PUNCT
ejpam-837	221	1	doklady	doklady	PROPN
ejpam-837	221	2	math	math	NOUN
ejpam-837	221	3	.	.	PUNCT
ejpam-837	222	1	,	,	PUNCT
ejpam-837	222	2	73(1):71	73(1):71	NUM
ejpam-837	222	3	-	-	SYM
ejpam-837	222	4	76	76	NUM
ejpam-837	222	5	,	,	PUNCT
ejpam-837	222	6	2006	2006	NUM
ejpam-837	222	7	.	.	PUNCT
ejpam-837	223	1	references	reference	NOUN
ejpam-837	223	2	838	838	NUM
ejpam-837	224	1	[	[	X
ejpam-837	224	2	13	13	NUM
ejpam-837	224	3	]	]	PUNCT
ejpam-837	224	4	a	a	PRON
ejpam-837	224	5	s	s	X
ejpam-837	224	6	makin	makin	NOUN
ejpam-837	224	7	.	.	PUNCT
ejpam-837	225	1	on	on	ADP
ejpam-837	225	2	spectral	spectral	ADJ
ejpam-837	225	3	decompositions	decomposition	NOUN
ejpam-837	225	4	corresponding	correspond	VERB
ejpam-837	225	5	to	to	ADP
ejpam-837	225	6	non	non	ADJ
ejpam-837	225	7	-	-	ADJ
ejpam-837	225	8	self	self	NOUN
ejpam-837	225	9	-	-	PUNCT
ejpam-837	225	10	adjoint	adjoint	NOUN
ejpam-837	225	11	sturm	sturm	PROPN
ejpam-837	225	12	-	-	PUNCT
ejpam-837	225	13	lioville	lioville	PROPN
ejpam-837	225	14	operators	operator	NOUN
ejpam-837	225	15	.	.	PUNCT
ejpam-837	226	1	doklady	doklady	PROPN
ejpam-837	226	2	math	math	NOUN
ejpam-837	226	3	.	.	PUNCT
ejpam-837	227	1	,	,	PUNCT
ejpam-837	228	1	73(1):15	73(1):15	NOUN
ejpam-837	228	2	-	-	SYM
ejpam-837	228	3	18	18	NUM
ejpam-837	228	4	,	,	PUNCT
ejpam-837	228	5	2006	2006	NUM
ejpam-837	228	6	.	.	PUNCT
ejpam-837	229	1	[	[	X
ejpam-837	229	2	14	14	NUM
ejpam-837	229	3	]	]	X
ejpam-837	229	4	kh	kh	PROPN
ejpam-837	229	5	r	r	PROPN
ejpam-837	229	6	mamedov	mamedov	PROPN
ejpam-837	229	7	.	.	PUNCT
ejpam-837	230	1	on	on	ADP
ejpam-837	230	2	spectrally	spectrally	ADV
ejpam-837	230	3	of	of	ADP
ejpam-837	230	4	differential	differential	ADJ
ejpam-837	230	5	operator	operator	NOUN
ejpam-837	230	6	of	of	ADP
ejpam-837	230	7	second	second	ADJ
ejpam-837	230	8	order	order	NOUN
ejpam-837	230	9	.	.	PUNCT
ejpam-837	231	1	proceeding	proceed	VERB
ejpam-837	231	2	of	of	ADP
ejpam-837	231	3	institute	institute	PROPN
ejpam-837	231	4	of	of	ADP
ejpam-837	231	5	mathematics	mathematics	PROPN
ejpam-837	231	6	and	and	CCONJ
ejpam-837	231	7	mechanics	mechanic	NOUN
ejpam-837	231	8	,	,	PUNCT
ejpam-837	231	9	acad	acad	PROPN
ejpam-837	231	10	,	,	PUNCT
ejpam-837	231	11	sci	sci	PROPN
ejpam-837	231	12	.	.	PUNCT
ejpam-837	231	13	azer	azer	PROPN
ejpam-837	231	14	.	.	PUNCT
ejpam-837	232	1	repub	repub	NOUN
ejpam-837	232	2	.	.	PUNCT
ejpam-837	233	1	5:179	5:179	NUM
ejpam-837	233	2	-	-	SYM
ejpam-837	233	3	181	181	NUM
ejpam-837	233	4	,	,	PUNCT
ejpam-837	233	5	1996	1996	NUM
ejpam-837	233	6	.	.	PUNCT
ejpam-837	234	1	[	[	X
ejpam-837	234	2	15	15	NUM
ejpam-837	234	3	]	]	X
ejpam-837	234	4	kh	kh	PROPN
ejpam-837	234	5	r	r	PROPN
ejpam-837	234	6	mamedov	mamedov	PROPN
ejpam-837	234	7	and	and	CCONJ
ejpam-837	234	8	h	h	PROPN
ejpam-837	234	9	menken	menken	PROPN
ejpam-837	234	10	.	.	PUNCT
ejpam-837	235	1	on	on	ADP
ejpam-837	235	2	the	the	DET
ejpam-837	235	3	basisness	basisness	NOUN
ejpam-837	235	4	in	in	ADP
ejpam-837	235	5	l2(0,1	l2(0,1	NOUN
ejpam-837	235	6	)	)	PUNCT
ejpam-837	235	7	of	of	ADP
ejpam-837	235	8	the	the	DET
ejpam-837	235	9	root	root	NOUN
ejpam-837	235	10	functions	function	NOUN
ejpam-837	235	11	in	in	ADP
ejpam-837	235	12	not	not	PART
ejpam-837	235	13	strongly	strongly	ADV
ejpam-837	235	14	regular	regular	ADJ
ejpam-837	235	15	boundary	boundary	ADJ
ejpam-837	235	16	value	value	NOUN
ejpam-837	235	17	problems	problem	NOUN
ejpam-837	235	18	.	.	PUNCT
ejpam-837	236	1	european	european	ADJ
ejpam-837	236	2	journal	journal	PROPN
ejpam-837	236	3	of	of	ADP
ejpam-837	236	4	pure	pure	ADJ
ejpam-837	236	5	and	and	CCONJ
ejpam-837	236	6	applied	applied	ADJ
ejpam-837	236	7	math	math	NOUN
ejpam-837	236	8	.	.	PUNCT
ejpam-837	237	1	,1(2):51	,1(2):51	PUNCT
ejpam-837	237	2	-	-	PUNCT
ejpam-837	237	3	60	60	NUM
ejpam-837	237	4	,	,	PUNCT
ejpam-837	237	5	2008	2008	NUM
ejpam-837	237	6	.	.	PUNCT
ejpam-837	238	1	[	[	X
ejpam-837	238	2	16	16	NUM
ejpam-837	238	3	]	]	X
ejpam-837	238	4	h	h	PROPN
ejpam-837	238	5	menken	menken	PROPN
ejpam-837	238	6	and	and	CCONJ
ejpam-837	238	7	kh	kh	PROPN
ejpam-837	238	8	r	r	PROPN
ejpam-837	238	9	mamedov	mamedov	PROPN
ejpam-837	238	10	.	.	PUNCT
ejpam-837	239	1	basis	basis	NOUN
ejpam-837	239	2	property	property	NOUN
ejpam-837	239	3	in	in	ADP
ejpam-837	239	4	lp(0,1	lp(0,1	NOUN
ejpam-837	239	5	)	)	PUNCT
ejpam-837	239	6	of	of	ADP
ejpam-837	239	7	the	the	DET
ejpam-837	239	8	root	root	NOUN
ejpam-837	239	9	functıons	functıon	NOUN
ejpam-837	239	10	correspondıng	correspondıng	VERB
ejpam-837	239	11	to	to	ADP
ejpam-837	239	12	a	a	DET
ejpam-837	239	13	boundary	boundary	ADJ
ejpam-837	239	14	-	-	PUNCT
ejpam-837	239	15	value	value	NOUN
ejpam-837	239	16	problem	problem	NOUN
ejpam-837	239	17	.	.	PUNCT
ejpam-837	240	1	journal	journal	NOUN
ejpam-837	240	2	of	of	ADP
ejpam-837	240	3	applied	apply	VERB
ejpam-837	240	4	functional	functional	ADJ
ejpam-837	240	5	analysis	analysis	NOUN
ejpam-837	240	6	,	,	PUNCT
ejpam-837	240	7	5(4):351356	5(4):351356	NUM
ejpam-837	240	8	,	,	PUNCT
ejpam-837	240	9	2010	2010	NUM
ejpam-837	240	10	.	.	PUNCT
ejpam-837	241	1	[	[	X
ejpam-837	241	2	17	17	NUM
ejpam-837	241	3	]	]	SYM
ejpam-837	241	4	v	v	ADP
ejpam-837	241	5	p	p	PROPN
ejpam-837	241	6	mikhailov	mikhailov	PROPN
ejpam-837	241	7	.	.	PUNCT
ejpam-837	242	1	on	on	ADP
ejpam-837	242	2	the	the	DET
ejpam-837	242	3	bases	basis	NOUN
ejpam-837	242	4	in	in	ADP
ejpam-837	242	5	l2(0,1	l2(0,1	ADV
ejpam-837	242	6	)	)	PUNCT
ejpam-837	242	7	.	.	PUNCT
ejpam-837	243	1	dokl	dokl	NOUN
ejpam-837	243	2	.	.	PUNCT
ejpam-837	243	3	akad	akad	PROPN
ejpam-837	243	4	.	.	PUNCT
ejpam-837	244	1	nauk	nauk	NOUN
ejpam-837	244	2	sssr	sssr	NOUN
ejpam-837	245	1	[	[	X
ejpam-837	245	2	soviet	soviet	ADJ
ejpam-837	245	3	math	math	NOUN
ejpam-837	245	4	.	.	PUNCT
ejpam-837	246	1	dokl	dokl	NOUN
ejpam-837	246	2	.	.	PUNCT
ejpam-837	247	1	]	]	X
ejpam-837	247	2	,	,	PUNCT
ejpam-837	247	3	144(5	144(5	NUM
ejpam-837	247	4	):	):	PUNCT
ejpam-837	247	5	981	981	NUM
ejpam-837	247	6	-	-	SYM
ejpam-837	247	7	984	984	NUM
ejpam-837	247	8	,	,	PUNCT
ejpam-837	247	9	1962	1962	NUM
ejpam-837	247	10	.	.	PUNCT
ejpam-837	248	1	[	[	X
ejpam-837	248	2	18	18	NUM
ejpam-837	248	3	]	]	X
ejpam-837	248	4	m	m	VERB
ejpam-837	248	5	a	a	DET
ejpam-837	248	6	naimark	naimark	NOUN
ejpam-837	248	7	.	.	PUNCT
ejpam-837	249	1	linear	linear	ADJ
ejpam-837	249	2	differential	differential	PROPN
ejpam-837	249	3	operators	operator	NOUN
ejpam-837	249	4	,	,	PUNCT
ejpam-837	249	5	part	part	PROPN
ejpam-837	249	6	i.	i.	PROPN
ejpam-837	249	7	frederick	frederick	PROPN
ejpam-837	249	8	ungar	ungar	PROPN
ejpam-837	249	9	pub	pub	PROPN
ejpam-837	249	10	.	.	PUNCT
ejpam-837	250	1	co.	co.	PROPN
ejpam-837	250	2	,	,	PUNCT
ejpam-837	250	3	new	new	PROPN
ejpam-837	250	4	york	york	PROPN
ejpam-837	250	5	,	,	PUNCT
ejpam-837	250	6	1967	1967	NUM
ejpam-837	250	7	.	.	PUNCT
ejpam-837	251	1	[	[	X
ejpam-837	251	2	19	19	NUM
ejpam-837	251	3	]	]	X
ejpam-837	251	4	a	a	DET
ejpam-837	251	5	a	a	DET
ejpam-837	251	6	shkalikov	shkalikov	NOUN
ejpam-837	251	7	.	.	PUNCT
ejpam-837	252	1	on	on	ADP
ejpam-837	252	2	the	the	DET
ejpam-837	252	3	riesz	riesz	PROPN
ejpam-837	252	4	basis	basis	NOUN
ejpam-837	252	5	property	property	NOUN
ejpam-837	252	6	of	of	ADP
ejpam-837	252	7	the	the	DET
ejpam-837	252	8	root	root	NOUN
ejpam-837	252	9	vectors	vector	NOUN
ejpam-837	252	10	of	of	ADP
ejpam-837	252	11	ordinary	ordinary	ADJ
ejpam-837	252	12	differential	differential	ADJ
ejpam-837	252	13	operators	operator	NOUN
ejpam-837	252	14	.	.	PUNCT
ejpam-837	253	1	russian	russian	ADJ
ejpam-837	253	2	math	math	PROPN
ejpam-837	253	3	.	.	PUNCT
ejpam-837	254	1	surveys	survey	NOUN
ejpam-837	254	2	,	,	PUNCT
ejpam-837	254	3	34(5):249	34(5):249	PROPN
ejpam-837	254	4	-	-	SYM
ejpam-837	254	5	250	250	NUM
ejpam-837	254	6	,	,	PUNCT
ejpam-837	254	7	1979	1979	NUM
ejpam-837	254	8	.	.	PUNCT
ejpam-837	255	1	[	[	X
ejpam-837	255	2	20	20	NUM
ejpam-837	255	3	]	]	PUNCT
ejpam-837	255	4	a	a	DET
ejpam-837	255	5	a	a	DET
ejpam-837	255	6	shkalikov	shkalikov	NOUN
ejpam-837	255	7	.	.	PUNCT
ejpam-837	256	1	on	on	ADP
ejpam-837	256	2	the	the	DET
ejpam-837	256	3	basis	basis	NOUN
ejpam-837	256	4	property	property	NOUN
ejpam-837	256	5	of	of	ADP
ejpam-837	256	6	the	the	DET
ejpam-837	256	7	eigenfunctions	eigenfunction	NOUN
ejpam-837	256	8	of	of	ADP
ejpam-837	256	9	ordinary	ordinary	ADJ
ejpam-837	256	10	differential	differential	ADJ
ejpam-837	256	11	operators	operator	NOUN
ejpam-837	256	12	with	with	ADP
ejpam-837	256	13	integral	integral	ADJ
ejpam-837	256	14	boundary	boundary	ADJ
ejpam-837	256	15	conditions	condition	NOUN
ejpam-837	256	16	.	.	PUNCT
ejpam-837	257	1	vestnik	vestnik	PROPN
ejpam-837	257	2	moscow	moscow	PROPN
ejpam-837	257	3	university	university	PROPN
ejpam-837	257	4	,	,	PUNCT
ejpam-837	257	5	ser	ser	PROPN
ejpam-837	257	6	.	.	PROPN
ejpam-837	257	7	mat	mat	PROPN
ejpam-837	257	8	.	.	PROPN
ejpam-837	257	9	mekh	mekh	PROPN
ejpam-837	257	10	.	.	PROPN
ejpam-837	257	11	,	,	PUNCT
ejpam-837	257	12	37(6):12	37(6):12	NUM
ejpam-837	257	13	-	-	SYM
ejpam-837	257	14	21	21	NUM
ejpam-837	257	15	,	,	PUNCT
ejpam-837	257	16	1982	1982	NUM
ejpam-837	257	17	.	.	PUNCT
ejpam-837	258	1	[	[	X
ejpam-837	258	2	21	21	NUM
ejpam-837	258	3	]	]	X
ejpam-837	258	4	o	o	X
ejpam-837	258	5	a	a	DET
ejpam-837	258	6	veliev	veliev	NOUN
ejpam-837	258	7	and	and	CCONJ
ejpam-837	258	8	a	a	DET
ejpam-837	258	9	a	a	DET
ejpam-837	258	10	shkalikov	shkalikov	NOUN
ejpam-837	258	11	.	.	PUNCT
ejpam-837	259	1	on	on	ADP
ejpam-837	259	2	the	the	DET
ejpam-837	259	3	riesz	riesz	PROPN
ejpam-837	259	4	basis	basis	NOUN
ejpam-837	259	5	property	property	NOUN
ejpam-837	259	6	of	of	ADP
ejpam-837	259	7	the	the	DET
ejpam-837	259	8	eigenand	eigenand	NOUN
ejpam-837	259	9	associated	associate	VERB
ejpam-837	259	10	functions	function	NOUN
ejpam-837	259	11	of	of	ADP
ejpam-837	259	12	periodic	periodic	ADJ
ejpam-837	259	13	and	and	CCONJ
ejpam-837	259	14	antiperiodic	antiperiodic	ADJ
ejpam-837	259	15	sturm	sturm	PROPN
ejpam-837	259	16	–	–	PUNCT
ejpam-837	259	17	liouville	liouville	NOUN
ejpam-837	259	18	problems	problem	NOUN
ejpam-837	259	19	.	.	PUNCT
ejpam-837	260	1	mat	mat	NOUN
ejpam-837	260	2	.	.	PUNCT
ejpam-837	260	3	zametki	zametki	NOUN
ejpam-837	260	4	,	,	PUNCT
ejpam-837	260	5	85(5):671–686	85(5):671–686	PROPN
ejpam-837	260	6	,	,	PUNCT
ejpam-837	260	7	2009	2009	NUM
ejpam-837	260	8	.	.	PUNCT
ejpam-837	261	1	[	[	X
ejpam-837	261	2	22	22	NUM
ejpam-837	261	3	]	]	PUNCT
ejpam-837	261	4	a	a	DET
ejpam-837	261	5	zygmund	zygmund	NOUN
ejpam-837	261	6	.	.	PUNCT
ejpam-837	262	1	trigonometric	trigonometric	PROPN
ejpam-837	262	2	series	series	PROPN
ejpam-837	262	3	,	,	PUNCT
ejpam-837	262	4	vol	vol	NOUN
ejpam-837	262	5	.	.	PROPN
ejpam-837	262	6	2	2	NUM
ejpam-837	262	7	.	.	X
ejpam-837	262	8	cambridge	cambridge	PROPN
ejpam-837	262	9	univ	univ	PROPN
ejpam-837	262	10	.	.	PUNCT
ejpam-837	263	1	press	press	PROPN
ejpam-837	263	2	,	,	PUNCT
ejpam-837	263	3	cambridge	cambridge	PROPN
ejpam-837	263	4	,	,	PUNCT
ejpam-837	263	5	1959	1959	NUM
ejpam-837	263	6	.	.	PUNCT