id	sid	tid	token	lemma	pos
ejpam-1477	1	1	3_xxx_serenbay.dvi	3_xxx_serenbay.dvi	NUM
ejpam-1477	1	2	european	european	ADJ
ejpam-1477	1	3	journal	journal	PROPN
ejpam-1477	1	4	of	of	ADP
ejpam-1477	1	5	pure	pure	ADJ
ejpam-1477	1	6	and	and	CCONJ
ejpam-1477	1	7	applied	apply	VERB
ejpam-1477	1	8	mathematics	mathematic	NOUN
ejpam-1477	1	9	vol	vol	NOUN
ejpam-1477	1	10	.	.	PROPN
ejpam-1477	1	11	5	5	NUM
ejpam-1477	1	12	,	,	PUNCT
ejpam-1477	1	13	no	no	INTJ
ejpam-1477	1	14	.	.	NOUN
ejpam-1477	1	15	1	1	NUM
ejpam-1477	1	16	,	,	PUNCT
ejpam-1477	1	17	2012	2012	NUM
ejpam-1477	1	18	,	,	PUNCT
ejpam-1477	1	19	25	25	NUM
ejpam-1477	1	20	-	-	SYM
ejpam-1477	1	21	29	29	NUM
ejpam-1477	1	22	issn	issn	PROPN
ejpam-1477	1	23	1307	1307	NUM
ejpam-1477	1	24	-	-	SYM
ejpam-1477	1	25	5543	5543	NUM
ejpam-1477	1	26	–	–	PUNCT
ejpam-1477	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1477	1	28	special	special	ADJ
ejpam-1477	1	29	issue	issue	NOUN
ejpam-1477	1	30	for	for	ADP
ejpam-1477	1	31	the	the	DET
ejpam-1477	1	32	international	international	ADJ
ejpam-1477	1	33	conference	conference	NOUN
ejpam-1477	1	34	on	on	ADP
ejpam-1477	1	35	applied	apply	VERB
ejpam-1477	1	36	analysis	analysis	NOUN
ejpam-1477	1	37	and	and	CCONJ
ejpam-1477	1	38	algebra	algebra	NOUN
ejpam-1477	1	39	29	29	NUM
ejpam-1477	1	40	june	june	PROPN
ejpam-1477	1	41	02	02	NUM
ejpam-1477	1	42	july	july	PROPN
ejpam-1477	1	43	2011	2011	NUM
ejpam-1477	1	44	,	,	PUNCT
ejpam-1477	1	45	istanbul	istanbul	PROPN
ejpam-1477	1	46	turkey	turkey	NOUN
ejpam-1477	1	47	rate	rate	NOUN
ejpam-1477	1	48	of	of	ADP
ejpam-1477	1	49	convergence	convergence	NOUN
ejpam-1477	1	50	in	in	ADP
ejpam-1477	1	51	sobolev	sobolev	PROPN
ejpam-1477	1	52	space	space	NOUN
ejpam-1477	1	53	sevilay	sevilay	PROPN
ejpam-1477	1	54	kırcı	kırcı	PROPN
ejpam-1477	1	55	serenbay	serenbay	VERB
ejpam-1477	1	56	1,∗	1,∗	PROPN
ejpam-1477	1	57	,	,	PUNCT
ejpam-1477	1	58	hande	hande	PROPN
ejpam-1477	1	59	tanberkan2	tanberkan2	PROPN
ejpam-1477	1	60	1	1	NUM
ejpam-1477	1	61	department	department	NOUN
ejpam-1477	1	62	of	of	ADP
ejpam-1477	1	63	mathematics	mathematic	NOUN
ejpam-1477	1	64	,	,	PUNCT
ejpam-1477	1	65	faculty	faculty	NOUN
ejpam-1477	1	66	of	of	ADP
ejpam-1477	1	67	education	education	NOUN
ejpam-1477	1	68	,	,	PUNCT
ejpam-1477	1	69	başkent	başkent	ADJ
ejpam-1477	1	70	university	university	NOUN
ejpam-1477	1	71	,	,	PUNCT
ejpam-1477	1	72	ankara	ankara	PROPN
ejpam-1477	1	73	,	,	PUNCT
ejpam-1477	1	74	turkey	turkey	PROPN
ejpam-1477	1	75	2	2	NUM
ejpam-1477	1	76	department	department	NOUN
ejpam-1477	1	77	of	of	ADP
ejpam-1477	1	78	mathematics	mathematic	NOUN
ejpam-1477	1	79	,	,	PUNCT
ejpam-1477	1	80	faculty	faculty	NOUN
ejpam-1477	1	81	of	of	ADP
ejpam-1477	1	82	science	science	NOUN
ejpam-1477	1	83	,	,	PUNCT
ejpam-1477	1	84	ankara	ankara	PROPN
ejpam-1477	1	85	university	university	PROPN
ejpam-1477	1	86	,	,	PUNCT
ejpam-1477	1	87	ankara	ankara	PROPN
ejpam-1477	1	88	,	,	PUNCT
ejpam-1477	1	89	turkey	turkey	PROPN
ejpam-1477	1	90	abstract	abstract	NOUN
ejpam-1477	1	91	.	.	PUNCT
ejpam-1477	2	1	in	in	ADP
ejpam-1477	2	2	this	this	DET
ejpam-1477	2	3	paper	paper	NOUN
ejpam-1477	2	4	,	,	PUNCT
ejpam-1477	2	5	a	a	DET
ejpam-1477	2	6	new	new	ADJ
ejpam-1477	2	7	theorem	theorem	NOUN
ejpam-1477	2	8	on	on	ADP
ejpam-1477	2	9	degree	degree	NOUN
ejpam-1477	2	10	of	of	ADP
ejpam-1477	2	11	approximation	approximation	NOUN
ejpam-1477	2	12	in	in	ADP
ejpam-1477	2	13	l2	l2	PROPN
ejpam-1477	2	14	p	p	PROPN
ejpam-1477	2	15	(	(	PUNCT
ejpam-1477	2	16	ω	ω	NOUN
ejpam-1477	2	17	)	)	PUNCT
ejpam-1477	2	18	sobolev	sobolev	ADJ
ejpam-1477	2	19	space	space	NOUN
ejpam-1477	2	20	of	of	ADP
ejpam-1477	2	21	integrable	integrable	ADJ
ejpam-1477	2	22	functions	function	NOUN
ejpam-1477	2	23	of	of	ADP
ejpam-1477	2	24	two	two	NUM
ejpam-1477	2	25	variables	variable	NOUN
ejpam-1477	2	26	by	by	ADP
ejpam-1477	2	27	bernstein	bernstein	PROPN
ejpam-1477	2	28	-	-	PUNCT
ejpam-1477	2	29	chlodowsky	chlodowsky	PROPN
ejpam-1477	2	30	polnomials	polnomial	NOUN
ejpam-1477	2	31	on	on	ADP
ejpam-1477	2	32	an	an	DET
ejpam-1477	2	33	unbounded	unbounded	ADJ
ejpam-1477	2	34	triangular	triangular	NOUN
ejpam-1477	2	35	domain	domain	NOUN
ejpam-1477	2	36	is	be	AUX
ejpam-1477	2	37	studied	study	VERB
ejpam-1477	2	38	.	.	PUNCT
ejpam-1477	3	1	also	also	ADV
ejpam-1477	3	2	by	by	ADP
ejpam-1477	3	3	using	use	VERB
ejpam-1477	3	4	the	the	DET
ejpam-1477	3	5	kfunctional	kfunctional	NOUN
ejpam-1477	3	6	of	of	ADP
ejpam-1477	3	7	peetre	peetre	NOUN
ejpam-1477	3	8	the	the	DET
ejpam-1477	3	9	order	order	NOUN
ejpam-1477	3	10	of	of	ADP
ejpam-1477	3	11	approximation	approximation	NOUN
ejpam-1477	3	12	are	be	AUX
ejpam-1477	3	13	established	establish	VERB
ejpam-1477	3	14	.	.	PUNCT
ejpam-1477	4	1	2000	2000	NUM
ejpam-1477	4	2	mathematics	mathematic	NOUN
ejpam-1477	4	3	subject	subject	NOUN
ejpam-1477	4	4	classifications	classification	NOUN
ejpam-1477	4	5	:	:	PUNCT
ejpam-1477	4	6	41a25	41a25	NUM
ejpam-1477	4	7	,	,	PUNCT
ejpam-1477	4	8	41a35	41a35	DET
ejpam-1477	4	9	key	key	ADJ
ejpam-1477	4	10	words	word	NOUN
ejpam-1477	4	11	and	and	CCONJ
ejpam-1477	4	12	phrases	phrase	NOUN
ejpam-1477	4	13	:	:	PUNCT
ejpam-1477	4	14	bernstein	bernstein	PROPN
ejpam-1477	4	15	-chlodowsky	-chlodowsky	PROPN
ejpam-1477	4	16	polynomials	polynomial	NOUN
ejpam-1477	4	17	,	,	PUNCT
ejpam-1477	4	18	convergence	convergence	NOUN
ejpam-1477	4	19	,	,	PUNCT
ejpam-1477	4	20	absolutely	absolutely	ADV
ejpam-1477	4	21	continuous	continuous	ADJ
ejpam-1477	4	22	function	function	NOUN
ejpam-1477	4	23	,	,	PUNCT
ejpam-1477	4	24	l2	l2	NOUN
ejpam-1477	4	25	p	p	PROPN
ejpam-1477	4	26	(	(	PUNCT
ejpam-1477	4	27	ω	ω	NOUN
ejpam-1477	4	28	)	)	PUNCT
ejpam-1477	4	29	hardy	hardy	ADJ
ejpam-1477	4	30	-	-	PUNCT
ejpam-1477	4	31	littlewood	littlewood	NOUN
ejpam-1477	4	32	majorante	majorante	NOUN
ejpam-1477	4	33	,	,	PUNCT
ejpam-1477	5	1	k	k	PROPN
ejpam-1477	5	2	functional	functional	ADJ
ejpam-1477	5	3	of	of	ADP
ejpam-1477	5	4	peetre	peetre	NOUN
ejpam-1477	5	5	1	1	NUM
ejpam-1477	5	6	.	.	PUNCT
ejpam-1477	5	7	introduction	introduction	NOUN
ejpam-1477	5	8	the	the	DET
ejpam-1477	5	9	aim	aim	NOUN
ejpam-1477	5	10	of	of	ADP
ejpam-1477	5	11	this	this	DET
ejpam-1477	5	12	paper	paper	NOUN
ejpam-1477	5	13	is	be	AUX
ejpam-1477	5	14	to	to	PART
ejpam-1477	5	15	study	study	VERB
ejpam-1477	5	16	the	the	DET
ejpam-1477	5	17	problem	problem	NOUN
ejpam-1477	5	18	on	on	ADP
ejpam-1477	5	19	degree	degree	NOUN
ejpam-1477	5	20	of	of	ADP
ejpam-1477	5	21	the	the	DET
ejpam-1477	5	22	approximation	approximation	NOUN
ejpam-1477	5	23	of	of	ADP
ejpam-1477	5	24	function	function	NOUN
ejpam-1477	5	25	of	of	ADP
ejpam-1477	5	26	two	two	NUM
ejpam-1477	5	27	variables	variable	NOUN
ejpam-1477	5	28	of	of	ADP
ejpam-1477	5	29	f	f	PROPN
ejpam-1477	5	30	∈	∈	PROPN
ejpam-1477	5	31	l2	l2	PROPN
ejpam-1477	5	32	p(ω	p(ω	PROPN
ejpam-1477	5	33	)	)	PUNCT
ejpam-1477	5	34	by	by	ADP
ejpam-1477	5	35	means	mean	NOUN
ejpam-1477	5	36	of	of	ADP
ejpam-1477	5	37	bernstein	bernstein	PROPN
ejpam-1477	5	38	chlodowsky	chlodowsky	PROPN
ejpam-1477	5	39	polynomials	polynomial	VERB
ejpam-1477	5	40	in	in	ADP
ejpam-1477	5	41	a	a	DET
ejpam-1477	5	42	triangular	triangular	NOUN
ejpam-1477	5	43	domain	domain	NOUN
ejpam-1477	5	44	extending	extending	NOUN
ejpam-1477	5	45	infinity	infinity	NOUN
ejpam-1477	5	46	,	,	PUNCT
ejpam-1477	5	47	where	where	SCONJ
ejpam-1477	5	48	ω	ω	X
ejpam-1477	5	49	=	=	SYM
ejpam-1477	5	50	limn→∞∆bn	limn→∞∆bn	PROPN
ejpam-1477	5	51	,	,	PUNCT
ejpam-1477	5	52	∆bn	∆bn	X
ejpam-1477	5	53	=	=	SYM
ejpam-1477	5	54	{	{	PUNCT
ejpam-1477	5	55	(	(	PUNCT
ejpam-1477	5	56	x	x	INTJ
ejpam-1477	5	57	,	,	PUNCT
ejpam-1477	5	58	y	y	PROPN
ejpam-1477	5	59	)	)	PUNCT
ejpam-1477	5	60	:	:	PUNCT
ejpam-1477	6	1	x	x	X
ejpam-1477	6	2	¶	¶	PROPN
ejpam-1477	6	3	0	0	NUM
ejpam-1477	6	4	,	,	PUNCT
ejpam-1477	6	5	y	y	PROPN
ejpam-1477	6	6	¾	¾	PROPN
ejpam-1477	6	7	0	0	PROPN
ejpam-1477	6	8	,	,	PUNCT
ejpam-1477	6	9	x	x	PUNCT
ejpam-1477	7	1	+	+	CCONJ
ejpam-1477	7	2	y	y	PROPN
ejpam-1477	7	3	¶	¶	PROPN
ejpam-1477	7	4	bn	bn	PROPN
ejpam-1477	7	5	}	}	PUNCT
ejpam-1477	7	6	and	and	CCONJ
ejpam-1477	7	7	(	(	PUNCT
ejpam-1477	7	8	bn	bn	X
ejpam-1477	7	9	)	)	PUNCT
ejpam-1477	7	10	is	be	AUX
ejpam-1477	7	11	a	a	DET
ejpam-1477	7	12	sequence	sequence	NOUN
ejpam-1477	7	13	of	of	ADP
ejpam-1477	7	14	increasing	increase	VERB
ejpam-1477	7	15	positive	positive	ADJ
ejpam-1477	7	16	number	number	NOUN
ejpam-1477	7	17	,	,	PUNCT
ejpam-1477	7	18	such	such	ADJ
ejpam-1477	7	19	that	that	SCONJ
ejpam-1477	7	20	:	:	PUNCT
ejpam-1477	7	21	lim	lim	PROPN
ejpam-1477	7	22	n→∞	n→∞	X
ejpam-1477	7	23	bn	bn	PROPN
ejpam-1477	7	24	=	=	SYM
ejpam-1477	7	25	∞	∞	PROPN
ejpam-1477	7	26	,	,	PUNCT
ejpam-1477	7	27	lim	lim	PROPN
ejpam-1477	7	28	n→∞	n→∞	NUM
ejpam-1477	7	29	bn	bn	CCONJ
ejpam-1477	7	30	n	n	PROPN
ejpam-1477	7	31	=	=	SYM
ejpam-1477	7	32	0	0	PROPN
ejpam-1477	7	33	.	.	PUNCT
ejpam-1477	8	1	(	(	PUNCT
ejpam-1477	8	2	1	1	X
ejpam-1477	8	3	)	)	PUNCT
ejpam-1477	8	4	some	some	DET
ejpam-1477	8	5	properties	property	NOUN
ejpam-1477	8	6	of	of	ADP
ejpam-1477	8	7	approximation	approximation	NOUN
ejpam-1477	8	8	of	of	ADP
ejpam-1477	8	9	functions	function	NOUN
ejpam-1477	8	10	of	of	ADP
ejpam-1477	8	11	two	two	NUM
ejpam-1477	8	12	variable	variable	NOUN
ejpam-1477	8	13	by	by	ADP
ejpam-1477	8	14	bernstein	bernstein	PROPN
ejpam-1477	8	15	-chlodowsky	-chlodowsky	PROPN
ejpam-1477	8	16	polynomials	polynomial	NOUN
ejpam-1477	8	17	was	be	AUX
ejpam-1477	8	18	proven	prove	VERB
ejpam-1477	8	19	in	in	ADP
ejpam-1477	8	20	[	[	X
ejpam-1477	8	21	1]-[5	1]-[5	X
ejpam-1477	8	22	]	]	X
ejpam-1477	8	23	and	and	CCONJ
ejpam-1477	8	24	[	[	X
ejpam-1477	8	25	7	7	NUM
ejpam-1477	8	26	]	]	PUNCT
ejpam-1477	8	27	.	.	PUNCT
ejpam-1477	9	1	in	in	ADP
ejpam-1477	9	2	addition	addition	NOUN
ejpam-1477	9	3	,	,	PUNCT
ejpam-1477	9	4	convergence	convergence	NOUN
ejpam-1477	9	5	of	of	ADP
ejpam-1477	9	6	bernstein	bernstein	PROPN
ejpam-1477	9	7	-	-	PUNCT
ejpam-1477	9	8	chlodowsky	chlodowsky	PROPN
ejpam-1477	9	9	polynomials	polynomial	NOUN
ejpam-1477	9	10	of	of	ADP
ejpam-1477	9	11	two	two	NUM
ejpam-1477	9	12	variables	variable	NOUN
ejpam-1477	9	13	were	be	AUX
ejpam-1477	9	14	investigated	investigate	VERB
ejpam-1477	9	15	on	on	ADP
ejpam-1477	9	16	a	a	DET
ejpam-1477	9	17	triangular	triangular	NOUN
ejpam-1477	9	18	domain	domain	NOUN
ejpam-1477	9	19	in	in	ADP
ejpam-1477	9	20	[	[	X
ejpam-1477	9	21	6	6	NUM
ejpam-1477	9	22	]	]	PUNCT
ejpam-1477	9	23	and	and	CCONJ
ejpam-1477	9	24	[	[	X
ejpam-1477	9	25	7	7	NUM
ejpam-1477	9	26	]	]	PUNCT
ejpam-1477	9	27	.	.	PUNCT
ejpam-1477	10	1	in	in	ADP
ejpam-1477	10	2	this	this	DET
ejpam-1477	10	3	paper	paper	NOUN
ejpam-1477	10	4	we	we	PRON
ejpam-1477	10	5	will	will	AUX
ejpam-1477	10	6	use	use	VERB
ejpam-1477	10	7	bernstein	bernstein	PROPN
ejpam-1477	10	8	-	-	PUNCT
ejpam-1477	10	9	chlodowsky	chlodowsky	PROPN
ejpam-1477	10	10	polynomials	polynomial	NOUN
ejpam-1477	10	11	on	on	ADP
ejpam-1477	10	12	ω	ω	NUM
ejpam-1477	10	13	which	which	PRON
ejpam-1477	10	14	is	be	AUX
ejpam-1477	10	15	introduced	introduce	VERB
ejpam-1477	10	16	in	in	ADP
ejpam-1477	10	17	[	[	X
ejpam-1477	10	18	7	7	NUM
ejpam-1477	10	19	]	]	PUNCT
ejpam-1477	10	20	.	.	PUNCT
ejpam-1477	11	1	let	let	VERB
ejpam-1477	11	2	,	,	PUNCT
ejpam-1477	11	3	f	f	PROPN
ejpam-1477	11	4	∈	∈	PROPN
ejpam-1477	11	5	l2	l2	NOUN
ejpam-1477	11	6	p(ω	p(ω	PROPN
ejpam-1477	11	7	)	)	PUNCT
ejpam-1477	11	8	,	,	PUNCT
ejpam-1477	11	9	bn	bn	PROPN
ejpam-1477	11	10	(	(	PUNCT
ejpam-1477	11	11	f	f	X
ejpam-1477	11	12	;	;	PUNCT
ejpam-1477	11	13	x	x	X
ejpam-1477	11	14	,	,	PUNCT
ejpam-1477	11	15	y	y	PROPN
ejpam-1477	11	16	)	)	PUNCT
ejpam-1477	11	17	=	=	SYM
ejpam-1477	12	1	n∑	n∑	PROPN
ejpam-1477	12	2	k=0	k=0	PROPN
ejpam-1477	12	3	c	c	PROPN
ejpam-1477	12	4	k	k	PROPN
ejpam-1477	12	5	n	n	PROPN
ejpam-1477	12	6	(	(	PUNCT
ejpam-1477	12	7	1−	1−	NUM
ejpam-1477	12	8	x	x	X
ejpam-1477	12	9	+	+	CCONJ
ejpam-1477	12	10	y	y	PROPN
ejpam-1477	12	11	bn	bn	NOUN
ejpam-1477	12	12	)	)	PUNCT
ejpam-1477	12	13	n−k	n−k	NOUN
ejpam-1477	12	14	k∑	k∑	VERB
ejpam-1477	13	1	i=0	i=0	PROPN
ejpam-1477	13	2	f	f	X
ejpam-1477	13	3	(	(	PUNCT
ejpam-1477	13	4	k−	k−	PROPN
ejpam-1477	13	5	i	i	PRON
ejpam-1477	13	6	n	n	ADV
ejpam-1477	13	7	bn	bn	NOUN
ejpam-1477	13	8	,	,	PUNCT
ejpam-1477	13	9	i	i	PRON
ejpam-1477	13	10	n	n	VERB
ejpam-1477	13	11	bn)c	bn)c	PROPN
ejpam-1477	14	1	i	i	PRON
ejpam-1477	14	2	k	k	PROPN
ejpam-1477	15	1	(	(	PUNCT
ejpam-1477	15	2	x	x	PROPN
ejpam-1477	15	3	bn	bn	X
ejpam-1477	15	4	)	)	PUNCT
ejpam-1477	15	5	k−i	k−i	PROPN
ejpam-1477	15	6	(	(	PUNCT
ejpam-1477	15	7	y	y	PROPN
ejpam-1477	15	8	bn	bn	PROPN
ejpam-1477	15	9	)	)	PUNCT
ejpam-1477	15	10	i	i	PRON
ejpam-1477	15	11	∗corresponding	∗corresponde	VERB
ejpam-1477	15	12	author	author	NOUN
ejpam-1477	15	13	.	.	PUNCT
ejpam-1477	16	1	email	email	NOUN
ejpam-1477	16	2	addresses	address	NOUN
ejpam-1477	16	3	:	:	PUNCT
ejpam-1477	16	4	kir	kir	PROPN
ejpam-1477	16	5	i�baskent.edu.tr	i�baskent.edu.tr	ADV
ejpam-1477	16	6	(	(	PUNCT
ejpam-1477	16	7	s.	s.	PROPN
ejpam-1477	16	8	serenbay	serenbay	PROPN
ejpam-1477	16	9	)	)	PUNCT
ejpam-1477	16	10	,	,	PUNCT
ejpam-1477	16	11	handetanberkan	handetanberkan	PROPN
ejpam-1477	16	12	�	�	PROPN
ejpam-1477	16	13	hotmail	hotmail	NOUN
ejpam-1477	16	14	.	.	PUNCT
ejpam-1477	17	1	om	om	PROPN
ejpam-1477	17	2	(	(	PUNCT
ejpam-1477	17	3	h.	h.	PROPN
ejpam-1477	17	4	tanberkan	tanberkan	PROPN
ejpam-1477	17	5	)	)	PUNCT
ejpam-1477	17	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1477	18	1	25	25	NUM
ejpam-1477	18	2	c	c	X
ejpam-1477	18	3	©	©	PROPN
ejpam-1477	18	4	2012	2012	NUM
ejpam-1477	18	5	ejpam	ejpam	VERB
ejpam-1477	18	6	all	all	DET
ejpam-1477	18	7	rights	right	NOUN
ejpam-1477	18	8	reserved	reserve	VERB
ejpam-1477	18	9	.	.	PUNCT
ejpam-1477	19	1	s.	s.	PROPN
ejpam-1477	19	2	serenbay	serenbay	PROPN
ejpam-1477	19	3	,	,	PUNCT
ejpam-1477	19	4	h.	h.	PROPN
ejpam-1477	19	5	tanberkan	tanberkan	PROPN
ejpam-1477	19	6	/	/	SYM
ejpam-1477	19	7	eur	eur	PROPN
ejpam-1477	19	8	.	.	PUNCT
ejpam-1477	20	1	j.	j.	PROPN
ejpam-1477	20	2	pure	pure	PROPN
ejpam-1477	20	3	appl	appl	PROPN
ejpam-1477	20	4	.	.	PROPN
ejpam-1477	20	5	math	math	PROPN
ejpam-1477	20	6	,	,	PUNCT
ejpam-1477	20	7	5	5	NUM
ejpam-1477	20	8	(	(	PUNCT
ejpam-1477	20	9	2012	2012	NUM
ejpam-1477	20	10	)	)	PUNCT
ejpam-1477	20	11	,	,	PUNCT
ejpam-1477	20	12	25	25	NUM
ejpam-1477	20	13	-	-	SYM
ejpam-1477	20	14	29	29	NUM
ejpam-1477	20	15	26	26	NUM
ejpam-1477	20	16	for	for	ADP
ejpam-1477	20	17	(	(	PUNCT
ejpam-1477	20	18	x	x	INTJ
ejpam-1477	20	19	,	,	PUNCT
ejpam-1477	20	20	y	y	PROPN
ejpam-1477	20	21	)	)	PUNCT
ejpam-1477	20	22	∈	∈	PROPN
ejpam-1477	20	23	∆bn	∆bn	NUM
ejpam-1477	20	24	.	.	PUNCT
ejpam-1477	21	1	we	we	PRON
ejpam-1477	21	2	note	note	VERB
ejpam-1477	21	3	that	that	SCONJ
ejpam-1477	21	4	formula	formula	NOUN
ejpam-1477	21	5	(	(	PUNCT
ejpam-1477	21	6	1	1	X
ejpam-1477	21	7	)	)	PUNCT
ejpam-1477	21	8	is	be	AUX
ejpam-1477	21	9	the	the	DET
ejpam-1477	21	10	sequence	sequence	NOUN
ejpam-1477	21	11	of	of	ADP
ejpam-1477	21	12	linear	linear	ADJ
ejpam-1477	21	13	positive	positive	ADJ
ejpam-1477	21	14	operators	operator	NOUN
ejpam-1477	21	15	in	in	ADP
ejpam-1477	21	16	the	the	DET
ejpam-1477	21	17	space	space	NOUN
ejpam-1477	21	18	of	of	ADP
ejpam-1477	21	19	integrable	integrable	ADJ
ejpam-1477	21	20	functions	function	NOUN
ejpam-1477	21	21	lp	lp	NOUN
ejpam-1477	21	22	of	of	ADP
ejpam-1477	21	23	two	two	NUM
ejpam-1477	21	24	variables	variable	NOUN
ejpam-1477	21	25	,	,	PUNCT
ejpam-1477	21	26	that	that	PRON
ejpam-1477	21	27	is	be	AUX
ejpam-1477	21	28	these	these	DET
ejpam-1477	21	29	linear	linear	ADJ
ejpam-1477	21	30	positive	positive	ADJ
ejpam-1477	21	31	operators	operator	NOUN
ejpam-1477	21	32	translate	translate	VERB
ejpam-1477	21	33	a	a	DET
ejpam-1477	21	34	positive	positive	ADJ
ejpam-1477	21	35	function	function	NOUN
ejpam-1477	21	36	to	to	ADP
ejpam-1477	21	37	an	an	DET
ejpam-1477	21	38	another	another	DET
ejpam-1477	21	39	positive	positive	ADJ
ejpam-1477	21	40	one	one	NOUN
ejpam-1477	21	41	.	.	PUNCT
ejpam-1477	22	1	but	but	CCONJ
ejpam-1477	22	2	,	,	PUNCT
ejpam-1477	22	3	in	in	ADP
ejpam-1477	22	4	general	general	ADJ
ejpam-1477	22	5	,	,	PUNCT
ejpam-1477	22	6	the	the	DET
ejpam-1477	22	7	function	function	NOUN
ejpam-1477	22	8	is	be	AUX
ejpam-1477	22	9	not	not	PART
ejpam-1477	22	10	necessarily	necessarily	ADV
ejpam-1477	22	11	a	a	DET
ejpam-1477	22	12	continuous	continuous	ADJ
ejpam-1477	22	13	one	one	NUM
ejpam-1477	22	14	in	in	ADP
ejpam-1477	22	15	lp	lp	ADJ
ejpam-1477	22	16	space	space	NOUN
ejpam-1477	22	17	.	.	PUNCT
ejpam-1477	23	1	we	we	PRON
ejpam-1477	23	2	can	can	AUX
ejpam-1477	23	3	not	not	PART
ejpam-1477	23	4	use	use	VERB
ejpam-1477	23	5	korovkin	korovkin	PROPN
ejpam-1477	23	6	’s	’s	PART
ejpam-1477	23	7	theorem	theorem	PROPN
ejpam-1477	23	8	.	.	PUNCT
ejpam-1477	24	1	first	first	ADV
ejpam-1477	24	2	,	,	PUNCT
ejpam-1477	24	3	we	we	PRON
ejpam-1477	24	4	give	give	VERB
ejpam-1477	24	5	certain	certain	ADJ
ejpam-1477	24	6	results	result	NOUN
ejpam-1477	24	7	which	which	PRON
ejpam-1477	24	8	are	be	AUX
ejpam-1477	24	9	necessary	necessary	ADJ
ejpam-1477	24	10	to	to	PART
ejpam-1477	24	11	prove	prove	VERB
ejpam-1477	24	12	the	the	DET
ejpam-1477	24	13	main	main	ADJ
ejpam-1477	24	14	results	result	NOUN
ejpam-1477	24	15	.	.	PUNCT
ejpam-1477	25	1	lemma	lemma	PROPN
ejpam-1477	25	2	1	1	NUM
ejpam-1477	25	3	.	.	PUNCT
ejpam-1477	25	4	suppose	suppose	VERB
ejpam-1477	25	5	that	that	SCONJ
ejpam-1477	25	6	ek	ek	PROPN
ejpam-1477	25	7	,	,	PUNCT
ejpam-1477	25	8	m(t	m(t	NOUN
ejpam-1477	25	9	,	,	PUNCT
ejpam-1477	25	10	)	)	PUNCT
ejpam-1477	25	11	=	=	SYM
ejpam-1477	25	12	tkm	tkm	PROPN
ejpam-1477	25	13	then	then	ADV
ejpam-1477	25	14	bn(e0,0	bn(e0,0	NOUN
ejpam-1477	25	15	;	;	PUNCT
ejpam-1477	25	16	x	x	SYM
ejpam-1477	25	17	,	,	PUNCT
ejpam-1477	25	18	y	y	PROPN
ejpam-1477	25	19	)	)	PUNCT
ejpam-1477	25	20	=	=	SYM
ejpam-1477	26	1	1	1	NUM
ejpam-1477	26	2	bn(e1,0	bn(e1,0	INTJ
ejpam-1477	26	3	;	;	PUNCT
ejpam-1477	26	4	x	x	X
ejpam-1477	26	5	,	,	PUNCT
ejpam-1477	26	6	y	y	PROPN
ejpam-1477	26	7	)	)	PUNCT
ejpam-1477	26	8	=	=	SYM
ejpam-1477	27	1	x	x	PUNCT
ejpam-1477	27	2	bn(e0,1	bn(e0,1	NOUN
ejpam-1477	27	3	;	;	PUNCT
ejpam-1477	27	4	x	x	X
ejpam-1477	27	5	,	,	PUNCT
ejpam-1477	27	6	y	y	PROPN
ejpam-1477	27	7	)	)	PUNCT
ejpam-1477	28	1	=	=	SYM
ejpam-1477	28	2	y	y	PROPN
ejpam-1477	28	3	bn(e2,0	bn(e2,0	PROPN
ejpam-1477	28	4	;	;	PUNCT
ejpam-1477	28	5	x	x	X
ejpam-1477	28	6	,	,	PUNCT
ejpam-1477	28	7	y	y	PROPN
ejpam-1477	28	8	)	)	PUNCT
ejpam-1477	28	9	=	=	SYM
ejpam-1477	29	1	x2	x2	PROPN
ejpam-1477	29	2	+	+	X
ejpam-1477	29	3	x(bn−	x(bn−	NUM
ejpam-1477	29	4	x	x	X
ejpam-1477	29	5	)	)	PUNCT
ejpam-1477	29	6	n	n	PRON
ejpam-1477	29	7	bn(e0,2	bn(e0,2	NOUN
ejpam-1477	29	8	;	;	PUNCT
ejpam-1477	29	9	x	x	X
ejpam-1477	29	10	,	,	PUNCT
ejpam-1477	29	11	y	y	PROPN
ejpam-1477	29	12	)	)	PUNCT
ejpam-1477	29	13	=	=	PUNCT
ejpam-1477	30	1	y2	y2	PROPN
ejpam-1477	31	1	+	+	CCONJ
ejpam-1477	32	1	y(bn	y(bn	PROPN
ejpam-1477	32	2	−	−	PROPN
ejpam-1477	32	3	y	y	PROPN
ejpam-1477	32	4	)	)	PUNCT
ejpam-1477	32	5	n	n	PRON
ejpam-1477	32	6	simple	simple	ADJ
ejpam-1477	32	7	calculations	calculation	NOUN
ejpam-1477	32	8	can	can	AUX
ejpam-1477	32	9	be	be	AUX
ejpam-1477	32	10	calculated	calculate	VERB
ejpam-1477	32	11	above	above	ADP
ejpam-1477	32	12	lemma	lemma	PROPN
ejpam-1477	32	13	.	.	PUNCT
ejpam-1477	33	1	theorem	theorem	NOUN
ejpam-1477	33	2	1	1	NUM
ejpam-1477	33	3	(	(	PUNCT
ejpam-1477	33	4	[	[	X
ejpam-1477	33	5	7	7	NUM
ejpam-1477	33	6	]	]	NUM
ejpam-1477	33	7	)	)	PUNCT
ejpam-1477	33	8	.	.	PUNCT
ejpam-1477	34	1	let	let	VERB
ejpam-1477	34	2	f	f	PROPN
ejpam-1477	34	3	∈	∈	PROPN
ejpam-1477	34	4	lp(ω	lp(ω	PROPN
ejpam-1477	34	5	)	)	PUNCT
ejpam-1477	34	6	and	and	CCONJ
ejpam-1477	34	7	a	a	DET
ejpam-1477	34	8	be	be	AUX
ejpam-1477	34	9	a	a	DET
ejpam-1477	34	10	fixed	fix	VERB
ejpam-1477	34	11	point	point	NOUN
ejpam-1477	34	12	in	in	ADP
ejpam-1477	34	13	(	(	PUNCT
ejpam-1477	34	14	0	0	NUM
ejpam-1477	34	15	,	,	PUNCT
ejpam-1477	34	16	bn	bn	NOUN
ejpam-1477	34	17	)	)	PUNCT
ejpam-1477	34	18	.	.	PUNCT
ejpam-1477	35	1	if	if	SCONJ
ejpam-1477	35	2	,	,	PUNCT
ejpam-1477	35	3	for	for	ADP
ejpam-1477	35	4	every	every	DET
ejpam-1477	35	5	(	(	PUNCT
ejpam-1477	35	6	x	x	INTJ
ejpam-1477	35	7	,	,	PUNCT
ejpam-1477	35	8	y	y	PROPN
ejpam-1477	35	9	)	)	PUNCT
ejpam-1477	35	10	∈∆a	∈∆a	NOUN
ejpam-1477	35	11	and	and	CCONJ
ejpam-1477	35	12	(	(	PUNCT
ejpam-1477	35	13	t	t	PROPN
ejpam-1477	35	14	,	,	PUNCT
ejpam-1477	35	15	s	s	PART
ejpam-1477	35	16	)	)	PUNCT
ejpam-1477	35	17	∈∆bn	∈∆bn	PROPN
ejpam-1477	35	18	|	|	INTJ
ejpam-1477	35	19	f	f	PROPN
ejpam-1477	35	20	(	(	PUNCT
ejpam-1477	35	21	t	t	PROPN
ejpam-1477	35	22	,	,	PUNCT
ejpam-1477	35	23	s)−	s)−	PROPN
ejpam-1477	35	24	f	f	PROPN
ejpam-1477	36	1	(	(	PUNCT
ejpam-1477	36	2	x	x	INTJ
ejpam-1477	36	3	,	,	PUNCT
ejpam-1477	36	4	y)|	y)|	PROPN
ejpam-1477	36	5	|(t	|(t	PROPN
ejpam-1477	36	6	,	,	PUNCT
ejpam-1477	36	7	s)−	s)−	PROPN
ejpam-1477	36	8	(	(	PUNCT
ejpam-1477	36	9	x	x	X
ejpam-1477	36	10	,	,	PUNCT
ejpam-1477	36	11	y)|	y)|	PROPN
ejpam-1477	36	12	¶	¶	PROPN
ejpam-1477	36	13	m	m	VERB
ejpam-1477	36	14	(	(	PUNCT
ejpam-1477	36	15	2	2	X
ejpam-1477	36	16	)	)	PUNCT
ejpam-1477	36	17	hold	hold	VERB
ejpam-1477	36	18	with	with	ADP
ejpam-1477	36	19	the	the	DET
ejpam-1477	36	20	constant	constant	ADJ
ejpam-1477	36	21	m	m	NOUN
ejpam-1477	36	22	,	,	PUNCT
ejpam-1477	36	23	then	then	ADV
ejpam-1477	36	24	‖bn	‖bn	PROPN
ejpam-1477	36	25	(	(	PUNCT
ejpam-1477	36	26	f	f	PROPN
ejpam-1477	36	27	)	)	PUNCT
ejpam-1477	36	28	−	−	PROPN
ejpam-1477	37	1	f	f	PROPN
ejpam-1477	37	2	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	37	3	)	)	PUNCT
ejpam-1477	37	4	→	→	SYM
ejpam-1477	37	5	0	0	NUM
ejpam-1477	37	6	,	,	PUNCT
ejpam-1477	37	7	n→∞.	n→∞.	PUNCT
ejpam-1477	37	8	where	where	SCONJ
ejpam-1477	37	9	a	a	DET
ejpam-1477	37	10	>	>	X
ejpam-1477	37	11	0	0	NUM
ejpam-1477	37	12	.	.	NOUN
ejpam-1477	38	1	2	2	NUM
ejpam-1477	38	2	.	.	X
ejpam-1477	38	3	main	main	ADJ
ejpam-1477	38	4	theorems	theorem	NOUN
ejpam-1477	38	5	to	to	PART
ejpam-1477	38	6	simplify	simplify	VERB
ejpam-1477	38	7	notation	notation	NOUN
ejpam-1477	38	8	,	,	PUNCT
ejpam-1477	38	9	we	we	PRON
ejpam-1477	38	10	need	need	VERB
ejpam-1477	38	11	the	the	DET
ejpam-1477	38	12	following	following	NOUN
ejpam-1477	38	13	.	.	PUNCT
ejpam-1477	39	1	l2	l2	VERB
ejpam-1477	39	2	p(ω1	p(ω1	ADJ
ejpam-1477	39	3	)	)	PUNCT
ejpam-1477	39	4	=	=	NOUN
ejpam-1477	39	5	{	{	PUNCT
ejpam-1477	39	6	f	f	PROPN
ejpam-1477	39	7	∈	∈	PROPN
ejpam-1477	39	8	lp(ω1	lp(ω1	VERB
ejpam-1477	39	9	)	)	PUNCT
ejpam-1477	39	10	:	:	PUNCT
ejpam-1477	39	11	∆|α|	∆|α|	VERB
ejpam-1477	39	12	f	f	PROPN
ejpam-1477	39	13	∈	∈	PROPN
ejpam-1477	39	14	lp(∆a	lp(∆a	PROPN
ejpam-1477	39	15	)	)	PUNCT
ejpam-1477	39	16	,	,	PUNCT
ejpam-1477	39	17	|α|	|α|	PROPN
ejpam-1477	39	18	=	=	SYM
ejpam-1477	40	1	2},ω1	2},ω1	NUM
ejpam-1477	40	2	⊂	⊂	PROPN
ejpam-1477	41	1	[	[	X
ejpam-1477	41	2	0	0	NUM
ejpam-1477	41	3	,	,	PUNCT
ejpam-1477	41	4	bn)×	bn)×	PUNCT
ejpam-1477	42	1	[	[	X
ejpam-1477	42	2	0	0	NUM
ejpam-1477	42	3	,	,	PUNCT
ejpam-1477	42	4	bn	bn	NOUN
ejpam-1477	42	5	)	)	PUNCT
ejpam-1477	42	6	.	.	PUNCT
ejpam-1477	43	1	we	we	PRON
ejpam-1477	43	2	consider	consider	VERB
ejpam-1477	43	3	also	also	ADV
ejpam-1477	43	4	the	the	DET
ejpam-1477	43	5	following	follow	VERB
ejpam-1477	43	6	k	k	ADJ
ejpam-1477	43	7	-	-	ADJ
ejpam-1477	43	8	functional	functional	ADJ
ejpam-1477	43	9	of	of	ADP
ejpam-1477	43	10	peetre	peetre	NOUN
ejpam-1477	43	11	;	;	PUNCT
ejpam-1477	43	12	kp	kp	X
ejpam-1477	43	13	(	(	PUNCT
ejpam-1477	43	14	f	f	PROPN
ejpam-1477	43	15	;	;	PUNCT
ejpam-1477	43	16	δ	δ	PROPN
ejpam-1477	43	17	)	)	PUNCT
ejpam-1477	43	18	=	=	PROPN
ejpam-1477	43	19	inf	inf	ADJ
ejpam-1477	43	20	g∈l2	g∈l2	ADJ
ejpam-1477	43	21	p(∆a	p(∆a	NOUN
ejpam-1477	43	22	)	)	PUNCT
ejpam-1477	44	1	[	[	X
ejpam-1477	44	2	‖	‖	PROPN
ejpam-1477	44	3	f	f	PROPN
ejpam-1477	44	4	−	−	PROPN
ejpam-1477	44	5	g‖lp(∆a	g‖lp(∆a	PROPN
ejpam-1477	44	6	)	)	PUNCT
ejpam-1477	44	7	+	+	NUM
ejpam-1477	44	8	δ(‖g‖l2	δ(‖g‖l2	NOUN
ejpam-1477	44	9	p(∆a	p(∆a	NOUN
ejpam-1477	44	10	)	)	PUNCT
ejpam-1477	44	11	)	)	PUNCT
ejpam-1477	44	12	]	]	PUNCT
ejpam-1477	44	13	,	,	PUNCT
ejpam-1477	44	14	δ	δ	PROPN
ejpam-1477	44	15	¾	¾	PROPN
ejpam-1477	44	16	0	0	NUM
ejpam-1477	44	17	.	.	PUNCT
ejpam-1477	45	1	for	for	ADP
ejpam-1477	45	2	f	f	PROPN
ejpam-1477	45	3	∈	∈	PROPN
ejpam-1477	45	4	lp(∆a	lp(∆a	PROPN
ejpam-1477	45	5	)	)	PUNCT
ejpam-1477	45	6	,	,	PUNCT
ejpam-1477	45	7	we	we	PRON
ejpam-1477	45	8	have	have	VERB
ejpam-1477	45	9	limδ→0	limδ→0	PROPN
ejpam-1477	45	10	k	k	X
ejpam-1477	45	11	(	(	PUNCT
ejpam-1477	45	12	f	f	PROPN
ejpam-1477	45	13	;	;	PUNCT
ejpam-1477	45	14	δ	δ	PROPN
ejpam-1477	45	15	)	)	PUNCT
ejpam-1477	46	1	=	=	PUNCT
ejpam-1477	46	2	0	0	X
ejpam-1477	46	3	.	.	PUNCT
ejpam-1477	47	1	therefore	therefore	ADV
ejpam-1477	47	2	the	the	DET
ejpam-1477	47	3	k	k	ADJ
ejpam-1477	47	4	-	-	ADJ
ejpam-1477	47	5	functional	functional	ADJ
ejpam-1477	47	6	gives	give	VERB
ejpam-1477	47	7	the	the	DET
ejpam-1477	47	8	degree	degree	NOUN
ejpam-1477	47	9	of	of	ADP
ejpam-1477	47	10	approximation	approximation	NOUN
ejpam-1477	47	11	of	of	ADP
ejpam-1477	47	12	a	a	DET
ejpam-1477	47	13	function	function	NOUN
ejpam-1477	47	14	f	f	PROPN
ejpam-1477	47	15	∈	∈	PROPN
ejpam-1477	47	16	lp(∆a	lp(∆a	PROPN
ejpam-1477	47	17	)	)	PUNCT
ejpam-1477	47	18	by	by	ADP
ejpam-1477	47	19	smoother	smooth	ADJ
ejpam-1477	47	20	functions	function	NOUN
ejpam-1477	47	21	g	g	PROPN
ejpam-1477	47	22	∈	∈	PROPN
ejpam-1477	47	23	l2	l2	NOUN
ejpam-1477	47	24	p(∆a	p(∆a	NOUN
ejpam-1477	47	25	)	)	PUNCT
ejpam-1477	47	26	.	.	PUNCT
ejpam-1477	48	1	remember	remember	VERB
ejpam-1477	48	2	that	that	SCONJ
ejpam-1477	48	3	the	the	DET
ejpam-1477	48	4	second	second	ADJ
ejpam-1477	48	5	order	order	NOUN
ejpam-1477	48	6	integral	integral	ADJ
ejpam-1477	48	7	modulus	modulus	NOUN
ejpam-1477	48	8	of	of	ADP
ejpam-1477	48	9	smoothness	smoothness	NOUN
ejpam-1477	48	10	is	be	AUX
ejpam-1477	48	11	given	give	VERB
ejpam-1477	48	12	by	by	ADP
ejpam-1477	48	13	ω2,p	ω2,p	PROPN
ejpam-1477	48	14	(	(	PUNCT
ejpam-1477	48	15	f	f	PROPN
ejpam-1477	48	16	;	;	PUNCT
ejpam-1477	48	17	δ	δ	PROPN
ejpam-1477	48	18	)	)	PUNCT
ejpam-1477	49	1	=	=	SYM
ejpam-1477	49	2	sup	sup	NOUN
ejpam-1477	49	3	0¶h¶δ	0¶h¶δ	PROPN
ejpam-1477	49	4	‖	‖	PROPN
ejpam-1477	49	5	f	f	PROPN
ejpam-1477	49	6	(	(	PUNCT
ejpam-1477	49	7	x	x	PROPN
ejpam-1477	49	8	+	+	NUM
ejpam-1477	49	9	h)−	h)−	PROPN
ejpam-1477	49	10	2	2	NUM
ejpam-1477	49	11	f	f	NOUN
ejpam-1477	49	12	(	(	PUNCT
ejpam-1477	49	13	x)+	x)+	PROPN
ejpam-1477	49	14	f	f	PROPN
ejpam-1477	49	15	(	(	PUNCT
ejpam-1477	49	16	x	x	X
ejpam-1477	49	17	−	−	PROPN
ejpam-1477	49	18	h)‖lp(∆a	h)‖lp(∆a	PROPN
ejpam-1477	49	19	)	)	PUNCT
ejpam-1477	49	20	(	(	PUNCT
ejpam-1477	49	21	ih	ih	X
ejpam-1477	49	22	)	)	PUNCT
ejpam-1477	49	23	s.	s.	PROPN
ejpam-1477	49	24	serenbay	serenbay	PROPN
ejpam-1477	49	25	,	,	PUNCT
ejpam-1477	49	26	h.	h.	PROPN
ejpam-1477	49	27	tanberkan	tanberkan	PROPN
ejpam-1477	49	28	/	/	SYM
ejpam-1477	49	29	eur	eur	PROPN
ejpam-1477	49	30	.	.	PUNCT
ejpam-1477	50	1	j.	j.	PROPN
ejpam-1477	50	2	pure	pure	PROPN
ejpam-1477	50	3	appl	appl	PROPN
ejpam-1477	50	4	.	.	PROPN
ejpam-1477	50	5	math	math	PROPN
ejpam-1477	50	6	,	,	PUNCT
ejpam-1477	50	7	5	5	NUM
ejpam-1477	50	8	(	(	PUNCT
ejpam-1477	50	9	2012	2012	NUM
ejpam-1477	50	10	)	)	PUNCT
ejpam-1477	50	11	,	,	PUNCT
ejpam-1477	50	12	25	25	NUM
ejpam-1477	50	13	-	-	SYM
ejpam-1477	50	14	29	29	NUM
ejpam-1477	50	15	27	27	NUM
ejpam-1477	50	16	for	for	ADP
ejpam-1477	50	17	an	an	DET
ejpam-1477	50	18	f	f	PROPN
ejpam-1477	50	19	∈	∈	PROPN
ejpam-1477	50	20	lp(∆a	lp(∆a	PROPN
ejpam-1477	50	21	)	)	PUNCT
ejpam-1477	50	22	,	,	PUNCT
ejpam-1477	50	23	where	where	SCONJ
ejpam-1477	50	24	ih	ih	PRON
ejpam-1477	50	25	indicates	indicate	VERB
ejpam-1477	50	26	that	that	SCONJ
ejpam-1477	50	27	the	the	DET
ejpam-1477	50	28	lp	lp	NOUN
ejpam-1477	50	29	-	-	PUNCT
ejpam-1477	50	30	norm	norm	NOUN
ejpam-1477	50	31	is	be	AUX
ejpam-1477	50	32	taken	take	VERB
ejpam-1477	50	33	over	over	ADP
ejpam-1477	50	34	the	the	DET
ejpam-1477	50	35	interval	interval	NOUN
ejpam-1477	50	36	[	[	X
ejpam-1477	50	37	h	h	X
ejpam-1477	50	38	,	,	PUNCT
ejpam-1477	50	39	bn	bn	ADP
ejpam-1477	50	40	−	−	PROPN
ejpam-1477	50	41	h	h	NOUN
ejpam-1477	50	42	]	]	X
ejpam-1477	50	43	.	.	PUNCT
ejpam-1477	51	1	it	it	PRON
ejpam-1477	51	2	is	be	AUX
ejpam-1477	51	3	also	also	ADV
ejpam-1477	51	4	know	know	VERB
ejpam-1477	51	5	that	that	SCONJ
ejpam-1477	51	6	there	there	PRON
ejpam-1477	51	7	are	be	VERB
ejpam-1477	51	8	constants	constant	NOUN
ejpam-1477	51	9	a1	a1	NOUN
ejpam-1477	51	10	>	>	X
ejpam-1477	51	11	0	0	PROPN
ejpam-1477	51	12	,	,	PUNCT
ejpam-1477	51	13	a2	a2	PROPN
ejpam-1477	51	14	>	>	X
ejpam-1477	51	15	0	0	PROPN
ejpam-1477	51	16	,	,	PUNCT
ejpam-1477	51	17	independent	independent	ADJ
ejpam-1477	51	18	of	of	ADP
ejpam-1477	51	19	f	f	PROPN
ejpam-1477	51	20	and	and	CCONJ
ejpam-1477	51	21	p	p	NOUN
ejpam-1477	51	22	such	such	ADJ
ejpam-1477	51	23	that	that	DET
ejpam-1477	51	24	a1ω2,p	a1ω2,p	PROPN
ejpam-1477	51	25	(	(	PUNCT
ejpam-1477	51	26	f	f	NOUN
ejpam-1477	51	27	;	;	PUNCT
ejpam-1477	51	28	δ1/2)¶	δ1/2)¶	X
ejpam-1477	51	29	kp	kp	X
ejpam-1477	51	30	(	(	PUNCT
ejpam-1477	51	31	f	f	PROPN
ejpam-1477	51	32	;	;	PUNCT
ejpam-1477	51	33	δ)¶min(1,δ)‖	δ)¶min(1,δ)‖	PROPN
ejpam-1477	51	34	f	f	PROPN
ejpam-1477	51	35	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	51	36	)	)	PUNCT
ejpam-1477	51	37	+2a2ω2,p	+2a2ω2,p	PROPN
ejpam-1477	51	38	(	(	PUNCT
ejpam-1477	51	39	f	f	NOUN
ejpam-1477	51	40	;	;	PUNCT
ejpam-1477	51	41	δ1/2	δ1/2	PROPN
ejpam-1477	51	42	)	)	PUNCT
ejpam-1477	51	43	(	(	PUNCT
ejpam-1477	51	44	3	3	X
ejpam-1477	51	45	)	)	PUNCT
ejpam-1477	51	46	we	we	PRON
ejpam-1477	51	47	prove	prove	VERB
ejpam-1477	51	48	the	the	DET
ejpam-1477	51	49	following	follow	VERB
ejpam-1477	51	50	theorems	theorem	NOUN
ejpam-1477	51	51	:	:	PUNCT
ejpam-1477	51	52	theorem	theorem	NOUN
ejpam-1477	51	53	2	2	NUM
ejpam-1477	51	54	.	.	PUNCT
ejpam-1477	52	1	let	let	VERB
ejpam-1477	52	2	f	f	PROPN
ejpam-1477	52	3	∈	∈	PROPN
ejpam-1477	52	4	l2	l2	NOUN
ejpam-1477	52	5	p(ω1	p(ω1	ADJ
ejpam-1477	52	6	)	)	PUNCT
ejpam-1477	52	7	,	,	PUNCT
ejpam-1477	52	8	1¶	1¶	NOUN
ejpam-1477	52	9	p	p	X
ejpam-1477	53	1	<	<	X
ejpam-1477	53	2	∞	∞	PROPN
ejpam-1477	53	3	and	and	CCONJ
ejpam-1477	53	4	a	a	PRON
ejpam-1477	53	5	,	,	PUNCT
ejpam-1477	53	6	m	m	PROPN
ejpam-1477	53	7	are	be	AUX
ejpam-1477	53	8	constants	constant	NOUN
ejpam-1477	53	9	,	,	PUNCT
ejpam-1477	53	10	if	if	SCONJ
ejpam-1477	53	11	the	the	DET
ejpam-1477	53	12	condition	condition	NOUN
ejpam-1477	53	13	,	,	PUNCT
ejpam-1477	54	1	|	|	ADV
ejpam-1477	54	2	f	f	X
ejpam-1477	54	3	(	(	PUNCT
ejpam-1477	54	4	t	t	PROPN
ejpam-1477	54	5	,	,	PUNCT
ejpam-1477	54	6	s)−	s)−	PROPN
ejpam-1477	54	7	f	f	PROPN
ejpam-1477	54	8	(	(	PUNCT
ejpam-1477	54	9	x	x	INTJ
ejpam-1477	54	10	,	,	PUNCT
ejpam-1477	54	11	y)|	y)|	PROPN
ejpam-1477	54	12	|(t	|(t	PROPN
ejpam-1477	54	13	,	,	PUNCT
ejpam-1477	54	14	s)−	s)−	PROPN
ejpam-1477	54	15	(	(	PUNCT
ejpam-1477	54	16	x	x	X
ejpam-1477	54	17	,	,	PUNCT
ejpam-1477	54	18	y)|	y)|	PROPN
ejpam-1477	54	19	¶	¶	PROPN
ejpam-1477	54	20	m	m	PROPN
ejpam-1477	54	21	,	,	PUNCT
ejpam-1477	54	22	t	t	PROPN
ejpam-1477	54	23	∈	∈	PROPN
ejpam-1477	54	24	(	(	PUNCT
ejpam-1477	54	25	a	a	PRON
ejpam-1477	54	26	,	,	PUNCT
ejpam-1477	54	27	bn	bn	NOUN
ejpam-1477	54	28	]	]	PUNCT
ejpam-1477	54	29	,	,	PUNCT
ejpam-1477	54	30	s	s	PROPN
ejpam-1477	54	31	∈	∈	PROPN
ejpam-1477	54	32	(	(	PUNCT
ejpam-1477	54	33	a	a	PRON
ejpam-1477	54	34	,	,	PUNCT
ejpam-1477	54	35	bn	bn	NOUN
ejpam-1477	54	36	]	]	PUNCT
ejpam-1477	54	37	,	,	PUNCT
ejpam-1477	54	38	(	(	PUNCT
ejpam-1477	54	39	x	x	X
ejpam-1477	54	40	,	,	PUNCT
ejpam-1477	54	41	y	y	PROPN
ejpam-1477	54	42	)	)	PUNCT
ejpam-1477	54	43	∈∆a	∈∆a	NOUN
ejpam-1477	54	44	is	be	AUX
ejpam-1477	54	45	satisfied	satisfied	ADJ
ejpam-1477	54	46	,	,	PUNCT
ejpam-1477	54	47	then	then	ADV
ejpam-1477	54	48	‖bn	‖bn	PROPN
ejpam-1477	54	49	(	(	PUNCT
ejpam-1477	54	50	f	f	PROPN
ejpam-1477	54	51	)	)	PUNCT
ejpam-1477	54	52	−	−	PROPN
ejpam-1477	55	1	f	f	PROPN
ejpam-1477	55	2	‖l2	‖l2	VERB
ejpam-1477	55	3	p(∆a	p(∆a	NOUN
ejpam-1477	55	4	)	)	PUNCT
ejpam-1477	55	5	¶	¶	NOUN
ejpam-1477	55	6	cp(‖	cp(‖	X
ejpam-1477	55	7	f	f	PROPN
ejpam-1477	55	8	‖l2	‖l2	VERB
ejpam-1477	55	9	p(∆a	p(∆a	NOUN
ejpam-1477	55	10	)	)	PUNCT
ejpam-1477	55	11	)	)	PUNCT
ejpam-1477	55	12	δn	δn	NOUN
ejpam-1477	55	13	,	,	PUNCT
ejpam-1477	55	14	δn	δn	NOUN
ejpam-1477	55	15	=	=	PUNCT
ejpam-1477	55	16	a(bn	a(bn	PROPN
ejpam-1477	55	17	+	+	CCONJ
ejpam-1477	55	18	a	a	X
ejpam-1477	55	19	)	)	PUNCT
ejpam-1477	55	20	n	n	NOUN
ejpam-1477	55	21	cp	cp	INTJ
ejpam-1477	55	22	=	=	PUNCT
ejpam-1477	55	23			PROPN
ejpam-1477	55	24			VERB
ejpam-1477	55	25			NOUN
ejpam-1477	55	26	p	p	PROPN
ejpam-1477	55	27	>	>	X
ejpam-1477	55	28	1,2	1,2	NUM
ejpam-1477	55	29	(	(	PUNCT
ejpam-1477	55	30	p	p	PROPN
ejpam-1477	55	31	p+	p+	NOUN
ejpam-1477	55	32	1	1	NUM
ejpam-1477	55	33	)	)	PUNCT
ejpam-1477	55	34	p	p	X
ejpam-1477	55	35	p	p	X
ejpam-1477	55	36	=	=	SYM
ejpam-1477	55	37	1	1	NUM
ejpam-1477	55	38	,	,	PUNCT
ejpam-1477	55	39	a2	a2	NOUN
ejpam-1477	55	40	proof	proof	NOUN
ejpam-1477	55	41	.	.	PUNCT
ejpam-1477	56	1	for	for	ADP
ejpam-1477	56	2	f	f	PROPN
ejpam-1477	56	3	∈	∈	PROPN
ejpam-1477	56	4	l2	l2	NOUN
ejpam-1477	56	5	p(ω1	p(ω1	ADJ
ejpam-1477	56	6	)	)	PUNCT
ejpam-1477	56	7	we	we	PRON
ejpam-1477	56	8	can	can	AUX
ejpam-1477	56	9	write	write	VERB
ejpam-1477	56	10	that	that	PRON
ejpam-1477	56	11	,	,	PUNCT
ejpam-1477	56	12	bn	bn	PROPN
ejpam-1477	56	13	(	(	PUNCT
ejpam-1477	56	14	f	f	PROPN
ejpam-1477	56	15	(	(	PUNCT
ejpam-1477	56	16	t	t	PROPN
ejpam-1477	56	17	,	,	PUNCT
ejpam-1477	56	18	s)−	s)−	PROPN
ejpam-1477	56	19	f	f	PROPN
ejpam-1477	56	20	(	(	PUNCT
ejpam-1477	56	21	x	x	INTJ
ejpam-1477	56	22	,	,	PUNCT
ejpam-1477	56	23	y	y	PROPN
ejpam-1477	56	24	)	)	PUNCT
ejpam-1477	56	25	;	;	PUNCT
ejpam-1477	56	26	x	x	X
ejpam-1477	56	27	,	,	PUNCT
ejpam-1477	56	28	y	y	PROPN
ejpam-1477	56	29	)	)	PUNCT
ejpam-1477	57	1	=	=	SYM
ejpam-1477	57	2	fx	fx	NOUN
ejpam-1477	57	3	(	(	PUNCT
ejpam-1477	57	4	x	x	INTJ
ejpam-1477	57	5	,	,	PUNCT
ejpam-1477	57	6	y)bn((t	y)bn((t	PROPN
ejpam-1477	57	7	−	−	PROPN
ejpam-1477	57	8	x	x	X
ejpam-1477	57	9	)	)	PUNCT
ejpam-1477	57	10	;	;	PUNCT
ejpam-1477	57	11	x	x	X
ejpam-1477	57	12	,	,	PUNCT
ejpam-1477	57	13	y)+	y)+	NOUN
ejpam-1477	57	14	f	f	NOUN
ejpam-1477	57	15	y	y	PROPN
ejpam-1477	57	16	(	(	PUNCT
ejpam-1477	57	17	x	x	INTJ
ejpam-1477	57	18	,	,	PUNCT
ejpam-1477	57	19	y)bn((s−	y)bn((s−	PROPN
ejpam-1477	57	20	y	y	NOUN
ejpam-1477	57	21	)	)	PUNCT
ejpam-1477	57	22	;	;	PUNCT
ejpam-1477	57	23	x	x	X
ejpam-1477	57	24	,	,	PUNCT
ejpam-1477	57	25	y	y	PROPN
ejpam-1477	57	26	)	)	PUNCT
ejpam-1477	58	1	+	+	CCONJ
ejpam-1477	58	2	bn	bn	X
ejpam-1477	58	3	(	(	PUNCT
ejpam-1477	58	4	∫	∫	PROPN
ejpam-1477	58	5	t	t	PROPN
ejpam-1477	58	6	x	x	SYM
ejpam-1477	58	7	fuu(u	fuu(u	PROPN
ejpam-1477	58	8	,	,	PUNCT
ejpam-1477	58	9	y)(u−	y)(u−	PROPN
ejpam-1477	58	10	t)du	t)du	PROPN
ejpam-1477	58	11	;	;	PUNCT
ejpam-1477	58	12	x	x	X
ejpam-1477	58	13	,	,	PUNCT
ejpam-1477	58	14	y	y	PROPN
ejpam-1477	58	15	)	)	PUNCT
ejpam-1477	58	16	+	+	CCONJ
ejpam-1477	58	17	bn	bn	X
ejpam-1477	58	18	(	(	PUNCT
ejpam-1477	58	19	∫	∫	PROPN
ejpam-1477	58	20	s	s	PROPN
ejpam-1477	58	21	y	y	PROPN
ejpam-1477	58	22	fkk(x	fkk(x	PROPN
ejpam-1477	58	23	,	,	PUNCT
ejpam-1477	58	24	k)(k−	k)(k−	PROPN
ejpam-1477	58	25	s)dk	s)dk	PROPN
ejpam-1477	58	26	;	;	PUNCT
ejpam-1477	58	27	x	x	X
ejpam-1477	58	28	,	,	PUNCT
ejpam-1477	58	29	y	y	PROPN
ejpam-1477	58	30	)	)	PUNCT
ejpam-1477	58	31	+	+	CCONJ
ejpam-1477	58	32	bn	bn	X
ejpam-1477	58	33	(	(	PUNCT
ejpam-1477	58	34	∫	∫	PROPN
ejpam-1477	58	35	t	t	PROPN
ejpam-1477	58	36	x	x	SYM
ejpam-1477	58	37	∫	∫	PROPN
ejpam-1477	58	38	s	s	PART
ejpam-1477	58	39	y	y	PROPN
ejpam-1477	58	40	fts(t	fts(t	PROPN
ejpam-1477	58	41	,	,	PUNCT
ejpam-1477	58	42	s)dsd	s)dsd	ADJ
ejpam-1477	58	43	t	t	NOUN
ejpam-1477	58	44	;	;	PUNCT
ejpam-1477	58	45	x	x	X
ejpam-1477	58	46	,	,	PUNCT
ejpam-1477	58	47	y	y	PROPN
ejpam-1477	58	48	)	)	PUNCT
ejpam-1477	58	49	now	now	ADV
ejpam-1477	58	50	,	,	PUNCT
ejpam-1477	58	51	we	we	PRON
ejpam-1477	58	52	need	need	VERB
ejpam-1477	58	53	the	the	DET
ejpam-1477	58	54	hardy	hardy	ADJ
ejpam-1477	58	55	-	-	PUNCT
ejpam-1477	58	56	littlewood	littlewood	NOUN
ejpam-1477	58	57	majorante	majorante	NOUN
ejpam-1477	58	58	of	of	ADP
ejpam-1477	58	59	fx	fx	PROPN
ejpam-1477	58	60	x	x	PUNCT
ejpam-1477	58	61	at	at	ADP
ejpam-1477	58	62	x	x	X
ejpam-1477	58	63	,	,	PUNCT
ejpam-1477	58	64	which	which	PRON
ejpam-1477	58	65	is	be	AUX
ejpam-1477	58	66	defined	define	VERB
ejpam-1477	58	67	as	as	ADP
ejpam-1477	58	68	following	follow	VERB
ejpam-1477	58	69	:	:	PUNCT
ejpam-1477	58	70	ϕ	ϕ	PROPN
ejpam-1477	58	71	fx	fx	PROPN
ejpam-1477	58	72	x(x	x(x	PROPN
ejpam-1477	58	73	,	,	PUNCT
ejpam-1477	58	74	y	y	PROPN
ejpam-1477	58	75	)	)	PUNCT
ejpam-1477	58	76	=	=	SYM
ejpam-1477	58	77	sup	sup	NOUN
ejpam-1477	58	78	0¶t¶x	0¶t¶x	NUM
ejpam-1477	58	79	,	,	PUNCT
ejpam-1477	58	80	t	t	PROPN
ejpam-1477	58	81	6	6	NUM
ejpam-1477	58	82	=	=	NOUN
ejpam-1477	58	83	x	x	X
ejpam-1477	58	84	(	(	PUNCT
ejpam-1477	58	85	1	1	NUM
ejpam-1477	58	86	t	t	NOUN
ejpam-1477	58	87	−	−	NOUN
ejpam-1477	58	88	x	x	SYM
ejpam-1477	58	89	)	)	PUNCT
ejpam-1477	59	1	∫	∫	PROPN
ejpam-1477	59	2	t	t	NOUN
ejpam-1477	59	3	x	x	PUNCT
ejpam-1477	59	4	fuu(u	fuu(u	PROPN
ejpam-1477	59	5	,	,	PUNCT
ejpam-1477	59	6	y)du	y)du	PROPN
ejpam-1477	59	7	and	and	CCONJ
ejpam-1477	59	8	using	use	VERB
ejpam-1477	59	9	following	follow	VERB
ejpam-1477	59	10	inequality	inequality	NOUN
ejpam-1477	59	11	∫	∫	PROPN
ejpam-1477	59	12	ω	ω	PROPN
ejpam-1477	59	13	|ϕ	|ϕ	PROPN
ejpam-1477	59	14	fx	fx	PROPN
ejpam-1477	59	15	y(x	y(x	PROPN
ejpam-1477	59	16	,	,	PUNCT
ejpam-1477	59	17	y)|	y)|	PROPN
ejpam-1477	59	18	pd	pd	INTJ
ejpam-1477	60	1	xd	xd	INTJ
ejpam-1477	60	2	y	y	PROPN
ejpam-1477	60	3	¶	¶	PROPN
ejpam-1477	60	4	2	2	NUM
ejpam-1477	60	5	(	(	PUNCT
ejpam-1477	60	6	p	p	PROPN
ejpam-1477	60	7	p+	p+	NOUN
ejpam-1477	60	8	1	1	NUM
ejpam-1477	60	9	)	)	PUNCT
ejpam-1477	60	10	p	p	NOUN
ejpam-1477	60	11	∫	∫	PROPN
ejpam-1477	61	1	a	a	DET
ejpam-1477	61	2	0	0	NUM
ejpam-1477	61	3	∫	∫	NOUN
ejpam-1477	61	4	a	a	DET
ejpam-1477	61	5	0	0	NUM
ejpam-1477	62	1	|	|	ADV
ejpam-1477	62	2	fts(t	fts(t	PROPN
ejpam-1477	62	3	,	,	PUNCT
ejpam-1477	62	4	s)|	s)|	NOUN
ejpam-1477	62	5	pdsd	pdsd	NOUN
ejpam-1477	62	6	t	t	PROPN
ejpam-1477	62	7	using	use	VERB
ejpam-1477	62	8	lp	lp	NOUN
ejpam-1477	62	9	-	-	PUNCT
ejpam-1477	62	10	norm	norm	NOUN
ejpam-1477	62	11	,	,	PUNCT
ejpam-1477	62	12	we	we	PRON
ejpam-1477	62	13	get	get	VERB
ejpam-1477	62	14	|b1(x	|b1(x	NUM
ejpam-1477	62	15	,	,	PUNCT
ejpam-1477	62	16	y)|+	y)|+	NOUN
ejpam-1477	62	17	|b2(x	|b2(x	NOUN
ejpam-1477	62	18	,	,	PUNCT
ejpam-1477	62	19	y)|+	y)|+	NOUN
ejpam-1477	62	20	|b3(x	|b3(x	PROPN
ejpam-1477	62	21	,	,	PUNCT
ejpam-1477	62	22	y)|	y)|	PROPN
ejpam-1477	62	23	¶	¶	PROPN
ejpam-1477	62	24	ϕ	ϕ	PROPN
ejpam-1477	62	25	fx	fx	PROPN
ejpam-1477	62	26	x(x	x(x	PROPN
ejpam-1477	62	27	,	,	PUNCT
ejpam-1477	62	28	y)δn	y)δn	PROPN
ejpam-1477	63	1	+	+	PROPN
ejpam-1477	63	2	ϕ	ϕ	PROPN
ejpam-1477	63	3	f	f	X
ejpam-1477	63	4	y	y	PROPN
ejpam-1477	63	5	y(x	y(x	PROPN
ejpam-1477	63	6	,	,	PUNCT
ejpam-1477	63	7	y)δn+ϕ	y)δn+ϕ	PROPN
ejpam-1477	63	8	f	f	PROPN
ejpam-1477	63	9	x	x	X
ejpam-1477	63	10	y(x	y(x	PROPN
ejpam-1477	63	11	,	,	PUNCT
ejpam-1477	63	12	y	y	NOUN
ejpam-1477	63	13	)	)	PUNCT
ejpam-1477	63	14	p	p	NOUN
ejpam-1477	63	15	δn	δn	PROPN
ejpam-1477	63	16	s.	s.	PROPN
ejpam-1477	63	17	serenbay	serenbay	PROPN
ejpam-1477	63	18	,	,	PUNCT
ejpam-1477	63	19	h.	h.	PROPN
ejpam-1477	63	20	tanberkan	tanberkan	PROPN
ejpam-1477	63	21	/	/	SYM
ejpam-1477	63	22	eur	eur	PROPN
ejpam-1477	63	23	.	.	PUNCT
ejpam-1477	64	1	j.	j.	PROPN
ejpam-1477	64	2	pure	pure	PROPN
ejpam-1477	64	3	appl	appl	PROPN
ejpam-1477	64	4	.	.	PROPN
ejpam-1477	64	5	math	math	PROPN
ejpam-1477	64	6	,	,	PUNCT
ejpam-1477	64	7	5	5	NUM
ejpam-1477	64	8	(	(	PUNCT
ejpam-1477	64	9	2012	2012	NUM
ejpam-1477	64	10	)	)	PUNCT
ejpam-1477	64	11	,	,	PUNCT
ejpam-1477	64	12	25	25	NUM
ejpam-1477	64	13	-	-	SYM
ejpam-1477	64	14	29	29	NUM
ejpam-1477	64	15	28	28	NUM
ejpam-1477	64	16	|b1|lp(∆a	|b1|lp(∆a	NOUN
ejpam-1477	64	17	)	)	PUNCT
ejpam-1477	65	1	+	+	CCONJ
ejpam-1477	65	2	|b2|lp(∆a	|b2|lp(∆a	X
ejpam-1477	65	3	)	)	PUNCT
ejpam-1477	65	4	+	+	CCONJ
ejpam-1477	65	5	|b3|lp(a	|b3|lp(a	NOUN
ejpam-1477	65	6	)	)	PUNCT
ejpam-1477	65	7	¶	¶	NOUN
ejpam-1477	65	8	cp(‖	cp(‖	NOUN
ejpam-1477	65	9	fx	fx	PROPN
ejpam-1477	65	10	x‖lp(∆a	x‖lp(∆a	PROPN
ejpam-1477	65	11	)	)	PUNCT
ejpam-1477	66	1	+	+	CCONJ
ejpam-1477	66	2	‖	‖	PROPN
ejpam-1477	66	3	f	f	PROPN
ejpam-1477	66	4	y	y	PROPN
ejpam-1477	66	5	y‖lp(∆a	y‖lp(∆a	PROPN
ejpam-1477	66	6	)	)	PUNCT
ejpam-1477	67	1	+	+	CCONJ
ejpam-1477	67	2	‖	‖	PROPN
ejpam-1477	67	3	fx	fx	PROPN
ejpam-1477	67	4	y‖lp(∆a	y‖lp(∆a	PROPN
ejpam-1477	67	5	)	)	PUNCT
ejpam-1477	67	6	)	)	PUNCT
ejpam-1477	68	1	δn	δn	ADP
ejpam-1477	68	2	<	<	X
ejpam-1477	68	3	cp(‖	cp(‖	X
ejpam-1477	68	4	f	f	PROPN
ejpam-1477	68	5	‖l2	‖l2	VERB
ejpam-1477	68	6	p(∆a	p(∆a	NOUN
ejpam-1477	68	7	)	)	PUNCT
ejpam-1477	68	8	)	)	PUNCT
ejpam-1477	68	9	δn	δn	PROPN
ejpam-1477	68	10	‖bn	‖bn	PROPN
ejpam-1477	68	11	f	f	PROPN
ejpam-1477	68	12	−	−	PROPN
ejpam-1477	68	13	f	f	PROPN
ejpam-1477	68	14	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	68	15	)	)	PUNCT
ejpam-1477	68	16	¶	¶	NOUN
ejpam-1477	68	17	cp(‖	cp(‖	X
ejpam-1477	69	1	f	f	PROPN
ejpam-1477	69	2	‖l2	‖l2	VERB
ejpam-1477	69	3	p(∆a	p(∆a	NOUN
ejpam-1477	69	4	)	)	PUNCT
ejpam-1477	69	5	)	)	PUNCT
ejpam-1477	70	1	δn	δn	NOUN
ejpam-1477	70	2	where	where	SCONJ
ejpam-1477	70	3	cp	cp	PROPN
ejpam-1477	70	4	=	=	NOUN
ejpam-1477	70	5	21	21	NUM
ejpam-1477	70	6	/	/	SYM
ejpam-1477	70	7	p	p	X
ejpam-1477	70	8	(	(	PUNCT
ejpam-1477	70	9	p	p	NOUN
ejpam-1477	70	10	p−	p−	NOUN
ejpam-1477	70	11	1	1	NUM
ejpam-1477	70	12	)	)	PUNCT
ejpam-1477	70	13	,	,	PUNCT
ejpam-1477	70	14	(	(	PUNCT
ejpam-1477	70	15	1	1	NUM
ejpam-1477	70	16	<	<	X
ejpam-1477	70	17	p	p	X
ejpam-1477	70	18	<	<	X
ejpam-1477	70	19	∞	∞	NOUN
ejpam-1477	70	20	)	)	PUNCT
ejpam-1477	70	21	if	if	SCONJ
ejpam-1477	70	22	p	p	NOUN
ejpam-1477	70	23	=	=	NOUN
ejpam-1477	70	24	1	1	NUM
ejpam-1477	70	25	,	,	PUNCT
ejpam-1477	70	26	∫	∫	PROPN
ejpam-1477	70	27	(	(	PUNCT
ejpam-1477	70	28	∆a	∆a	PROPN
ejpam-1477	70	29	)	)	PUNCT
ejpam-1477	70	30	|b1(x	|b1(x	NUM
ejpam-1477	70	31	,	,	PUNCT
ejpam-1477	70	32	y)|d	y)|d	NOUN
ejpam-1477	70	33	xd	xd	INTJ
ejpam-1477	71	1	y	y	PROPN
ejpam-1477	71	2	¶	¶	PROPN
ejpam-1477	71	3	∫	∫	PROPN
ejpam-1477	72	1	a	a	DET
ejpam-1477	72	2	0	0	NUM
ejpam-1477	72	3	∫	∫	NOUN
ejpam-1477	72	4	a	a	DET
ejpam-1477	72	5	0	0	NUM
ejpam-1477	72	6	|bn	|bn	NOUN
ejpam-1477	73	1	(	(	PUNCT
ejpam-1477	73	2	∫	∫	PROPN
ejpam-1477	73	3	t	t	PROPN
ejpam-1477	73	4	x	x	SYM
ejpam-1477	73	5	fuu(u	fuu(u	PROPN
ejpam-1477	73	6	,	,	PUNCT
ejpam-1477	73	7	y)(u−	y)(u−	PROPN
ejpam-1477	73	8	t)du	t)du	PROPN
ejpam-1477	73	9	;	;	PUNCT
ejpam-1477	73	10	x	x	X
ejpam-1477	73	11	,	,	PUNCT
ejpam-1477	73	12	y)|d	y)|d	NOUN
ejpam-1477	73	13	xd	xd	INTJ
ejpam-1477	73	14	y	y	PROPN
ejpam-1477	74	1	¶	¶	PROPN
ejpam-1477	74	2	∫	∫	PROPN
ejpam-1477	74	3	a	a	DET
ejpam-1477	74	4	0	0	NUM
ejpam-1477	74	5	∫	∫	NOUN
ejpam-1477	74	6	a	a	DET
ejpam-1477	74	7	0	0	PUNCT
ejpam-1477	74	8	bn(|t	bn(|t	VERB
ejpam-1477	75	1	−	−	PROPN
ejpam-1477	75	2	x	x	SYM
ejpam-1477	76	1	|	|	ADV
ejpam-1477	76	2	∫	∫	PROPN
ejpam-1477	76	3	t	t	NOUN
ejpam-1477	76	4	x	x	PUNCT
ejpam-1477	76	5	fuu(u	fuu(u	PROPN
ejpam-1477	76	6	,	,	PUNCT
ejpam-1477	76	7	y)du	y)du	PROPN
ejpam-1477	76	8	;	;	PUNCT
ejpam-1477	76	9	x	x	SYM
ejpam-1477	76	10	,	,	PUNCT
ejpam-1477	76	11	y)d	y)d	PROPN
ejpam-1477	76	12	xd	xd	INTJ
ejpam-1477	77	1	y	y	PROPN
ejpam-1477	77	2	=	=	SYM
ejpam-1477	77	3	‖	‖	PROPN
ejpam-1477	77	4	fx	fx	PROPN
ejpam-1477	77	5	x‖l1(∆a	x‖l1(∆a	PROPN
ejpam-1477	77	6	)	)	PUNCT
ejpam-1477	77	7	a2δn	a2δn	NOUN
ejpam-1477	77	8	.	.	PUNCT
ejpam-1477	78	1	∫	∫	PROPN
ejpam-1477	78	2	(	(	PUNCT
ejpam-1477	78	3	∆a	∆a	PROPN
ejpam-1477	78	4	)	)	PUNCT
ejpam-1477	78	5	|b2(x	|b2(x	NOUN
ejpam-1477	78	6	,	,	PUNCT
ejpam-1477	78	7	y)|d	y)|d	NOUN
ejpam-1477	79	1	xd	xd	INTJ
ejpam-1477	79	2	y	y	PROPN
ejpam-1477	79	3	¶	¶	PROPN
ejpam-1477	79	4	∫	∫	PROPN
ejpam-1477	80	1	a	a	DET
ejpam-1477	80	2	0	0	NUM
ejpam-1477	80	3	∫	∫	NOUN
ejpam-1477	80	4	a	a	DET
ejpam-1477	80	5	0	0	NUM
ejpam-1477	80	6	bn(|s−	bn(|s−	PROPN
ejpam-1477	80	7	y|	y|	NOUN
ejpam-1477	80	8	∫	∫	PROPN
ejpam-1477	80	9	t	t	PROPN
ejpam-1477	80	10	x	x	PROPN
ejpam-1477	80	11	fkk(x	fkk(x	PROPN
ejpam-1477	80	12	,	,	PUNCT
ejpam-1477	80	13	k)dk	k)dk	PROPN
ejpam-1477	80	14	;	;	PUNCT
ejpam-1477	80	15	x	x	SYM
ejpam-1477	80	16	,	,	PUNCT
ejpam-1477	80	17	y)d	y)d	PROPN
ejpam-1477	81	1	xd	xd	INTJ
ejpam-1477	81	2	y	y	PROPN
ejpam-1477	81	3	=	=	PUNCT
ejpam-1477	81	4	‖	‖	PROPN
ejpam-1477	81	5	f	f	PROPN
ejpam-1477	81	6	y	y	PROPN
ejpam-1477	81	7	y‖l1(∆a	y‖l1(∆a	PROPN
ejpam-1477	81	8	)	)	PUNCT
ejpam-1477	81	9	a2δn	a2δn	NOUN
ejpam-1477	81	10	.	.	PROPN
ejpam-1477	81	11	∫	∫	PROPN
ejpam-1477	82	1	(	(	PUNCT
ejpam-1477	82	2	∆a	∆a	PROPN
ejpam-1477	82	3	)	)	PUNCT
ejpam-1477	82	4	|b3(x	|b3(x	PROPN
ejpam-1477	82	5	,	,	PUNCT
ejpam-1477	82	6	y)|d	y)|d	NOUN
ejpam-1477	83	1	xd	xd	INTJ
ejpam-1477	83	2	y	y	PROPN
ejpam-1477	83	3	¶	¶	PROPN
ejpam-1477	83	4	∫	∫	PROPN
ejpam-1477	84	1	a	a	DET
ejpam-1477	84	2	0	0	NUM
ejpam-1477	84	3	∫	∫	NOUN
ejpam-1477	84	4	a	a	DET
ejpam-1477	84	5	0	0	NUM
ejpam-1477	84	6	|bn	|bn	NOUN
ejpam-1477	85	1	(	(	PUNCT
ejpam-1477	85	2	∫	∫	PROPN
ejpam-1477	85	3	t	t	PROPN
ejpam-1477	85	4	x	x	SYM
ejpam-1477	85	5	∫	∫	PROPN
ejpam-1477	85	6	s	s	PART
ejpam-1477	85	7	y	y	PROPN
ejpam-1477	85	8	fts(t	fts(t	PROPN
ejpam-1477	85	9	,	,	PUNCT
ejpam-1477	85	10	s)dsd	s)dsd	ADJ
ejpam-1477	85	11	t	t	NOUN
ejpam-1477	85	12	;	;	PUNCT
ejpam-1477	85	13	x	x	X
ejpam-1477	85	14	,	,	PUNCT
ejpam-1477	85	15	y)|d	y)|d	NOUN
ejpam-1477	85	16	xd	xd	INTJ
ejpam-1477	85	17	y	y	PROPN
ejpam-1477	85	18	=	=	SYM
ejpam-1477	85	19	‖	‖	PROPN
ejpam-1477	85	20	fx	fx	PROPN
ejpam-1477	85	21	y‖l1(∆a	y‖l1(∆a	PROPN
ejpam-1477	85	22	)	)	PUNCT
ejpam-1477	85	23	a2δn	a2δn	NOUN
ejpam-1477	85	24	.	.	PUNCT
ejpam-1477	86	1	then	then	ADV
ejpam-1477	86	2	‖b1‖lp(∆a	‖b1‖lp(∆a	PRON
ejpam-1477	86	3	)	)	PUNCT
ejpam-1477	86	4	+	+	CCONJ
ejpam-1477	86	5	‖b2‖lp(∆a	‖b2‖lp(∆a	X
ejpam-1477	86	6	)	)	PUNCT
ejpam-1477	86	7	+	+	NUM
ejpam-1477	86	8	‖b3‖lp(a	‖b3‖lp(a	NOUN
ejpam-1477	86	9	)	)	PUNCT
ejpam-1477	86	10	¶	¶	NOUN
ejpam-1477	86	11	a2(‖	a2(‖	VERB
ejpam-1477	86	12	fx	fx	PROPN
ejpam-1477	86	13	x‖lp(∆a	x‖lp(∆a	PROPN
ejpam-1477	86	14	)	)	PUNCT
ejpam-1477	87	1	+	+	CCONJ
ejpam-1477	87	2	‖	‖	PROPN
ejpam-1477	87	3	f	f	PROPN
ejpam-1477	87	4	y	y	PROPN
ejpam-1477	87	5	y‖lp(∆a	y‖lp(∆a	PROPN
ejpam-1477	87	6	)	)	PUNCT
ejpam-1477	88	1	+	+	CCONJ
ejpam-1477	89	1	‖	‖	PROPN
ejpam-1477	89	2	fx	fx	PROPN
ejpam-1477	89	3	y‖lp(∆a	y‖lp(∆a	PROPN
ejpam-1477	89	4	)	)	PUNCT
ejpam-1477	89	5	)	)	PUNCT
ejpam-1477	90	1	δn	δn	ADP
ejpam-1477	90	2	‖bn	‖bn	PROPN
ejpam-1477	90	3	f	f	PROPN
ejpam-1477	90	4	−	−	PROPN
ejpam-1477	90	5	f	f	PROPN
ejpam-1477	90	6	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	90	7	)	)	PUNCT
ejpam-1477	90	8	¶	¶	PROPN
ejpam-1477	90	9	a2‖	a2‖	PROPN
ejpam-1477	91	1	f	f	PROPN
ejpam-1477	91	2	‖l2	‖l2	VERB
ejpam-1477	91	3	p(∆a	p(∆a	NOUN
ejpam-1477	91	4	)	)	PUNCT
ejpam-1477	91	5	δn	δn	NOUN
ejpam-1477	91	6	.	.	PUNCT
ejpam-1477	92	1	thus	thus	ADV
ejpam-1477	92	2	,	,	PUNCT
ejpam-1477	92	3	the	the	DET
ejpam-1477	92	4	proof	proof	NOUN
ejpam-1477	92	5	is	be	AUX
ejpam-1477	92	6	completed	complete	VERB
ejpam-1477	92	7	.	.	PUNCT
ejpam-1477	93	1	theorem	theorem	NOUN
ejpam-1477	93	2	3	3	X
ejpam-1477	93	3	.	.	PUNCT
ejpam-1477	94	1	let	let	VERB
ejpam-1477	94	2	f	f	PROPN
ejpam-1477	94	3	∈	∈	PROPN
ejpam-1477	94	4	l2	l2	NOUN
ejpam-1477	94	5	p(ω	p(ω	PROPN
ejpam-1477	94	6	1	1	NUM
ejpam-1477	94	7	)	)	PUNCT
ejpam-1477	94	8	,	,	PUNCT
ejpam-1477	94	9	1	1	NUM
ejpam-1477	94	10	≤	≤	NOUN
ejpam-1477	94	11	p	p	X
ejpam-1477	94	12	<	<	X
ejpam-1477	94	13	∞	∞	PROPN
ejpam-1477	94	14	and	and	CCONJ
ejpam-1477	94	15	f	f	PROPN
ejpam-1477	94	16	satisfies	satisfy	VERB
ejpam-1477	94	17	the	the	DET
ejpam-1477	94	18	condition	condition	NOUN
ejpam-1477	94	19	(	(	PUNCT
ejpam-1477	94	20	2	2	NUM
ejpam-1477	94	21	)	)	PUNCT
ejpam-1477	94	22	then	then	ADV
ejpam-1477	94	23	the	the	DET
ejpam-1477	94	24	following	follow	VERB
ejpam-1477	94	25	inequality	inequality	NOUN
ejpam-1477	94	26	‖bn	‖bn	PROPN
ejpam-1477	94	27	f	f	PROPN
ejpam-1477	94	28	−	−	PROPN
ejpam-1477	94	29	f	f	PROPN
ejpam-1477	94	30	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	94	31	)	)	PUNCT
ejpam-1477	94	32	¶	¶	PROPN
ejpam-1477	94	33	mp[‖	mp[‖	PROPN
ejpam-1477	95	1	f	f	PROPN
ejpam-1477	95	2	‖l2	‖l2	VERB
ejpam-1477	95	3	p(∆a	p(∆a	NOUN
ejpam-1477	95	4	)	)	PUNCT
ejpam-1477	95	5	δn+ω2,p	δn+ω2,p	PROPN
ejpam-1477	95	6	(	(	PUNCT
ejpam-1477	95	7	f	f	PROPN
ejpam-1477	95	8	;	;	PUNCT
ejpam-1477	95	9	δ(1/2	δ(1/2	PROPN
ejpam-1477	95	10	)	)	PUNCT
ejpam-1477	95	11	)	)	PUNCT
ejpam-1477	95	12	]	]	PUNCT
ejpam-1477	96	1	(	(	PUNCT
ejpam-1477	96	2	4	4	X
ejpam-1477	96	3	)	)	PUNCT
ejpam-1477	96	4	holds	hold	NOUN
ejpam-1477	96	5	.	.	PUNCT
ejpam-1477	97	1	where	where	SCONJ
ejpam-1477	97	2	a	a	X
ejpam-1477	97	3	,	,	PUNCT
ejpam-1477	97	4	m	m	VERB
ejpam-1477	97	5	are	be	AUX
ejpam-1477	97	6	constants	constant	NOUN
ejpam-1477	97	7	.	.	PUNCT
ejpam-1477	98	1	proof	proof	NOUN
ejpam-1477	98	2	.	.	PUNCT
ejpam-1477	99	1	for	for	ADP
ejpam-1477	99	2	all	all	DET
ejpam-1477	99	3	sufficiently	sufficiently	ADV
ejpam-1477	99	4	large	large	ADJ
ejpam-1477	99	5	n	n	CCONJ
ejpam-1477	99	6	,	,	PUNCT
ejpam-1477	99	7	from	from	ADP
ejpam-1477	99	8	theorem	theorem	NOUN
ejpam-1477	99	9	2	2	NUM
ejpam-1477	99	10	we	we	PRON
ejpam-1477	99	11	can	can	AUX
ejpam-1477	99	12	write	write	VERB
ejpam-1477	99	13	‖bnh−	‖bnh−	PROPN
ejpam-1477	99	14	h‖lp∆a	h‖lp∆a	PROPN
ejpam-1477	99	15	¶	¶	PROPN
ejpam-1477	99	16	¨	¨	X
ejpam-1477	99	17	(	(	PUNCT
ejpam-1477	99	18	ǫ+mδna)‖h‖lp(∆a	ǫ+mδna)‖h‖lp(∆a	NUM
ejpam-1477	99	19	)	)	PUNCT
ejpam-1477	99	20	,	,	PUNCT
ejpam-1477	99	21	h	h	NOUN
ejpam-1477	99	22	∈	∈	PROPN
ejpam-1477	99	23	lp(∆a	lp(∆a	PROPN
ejpam-1477	99	24	)	)	PUNCT
ejpam-1477	99	25	cp‖	cp‖	PROPN
ejpam-1477	99	26	f	f	PROPN
ejpam-1477	99	27	‖lp	‖lp	PROPN
ejpam-1477	99	28	(	(	PUNCT
ejpam-1477	99	29	∆a	∆a	NOUN
ejpam-1477	99	30	)	)	PUNCT
ejpam-1477	99	31	δn	δn	NOUN
ejpam-1477	99	32	,	,	PUNCT
ejpam-1477	99	33	h	h	NOUN
ejpam-1477	99	34	∈	∈	PROPN
ejpam-1477	99	35	l2	l2	NOUN
ejpam-1477	99	36	p(∆a	p(∆a	NOUN
ejpam-1477	99	37	)	)	PUNCT
ejpam-1477	99	38	where	where	SCONJ
ejpam-1477	99	39	cp	cp	PROPN
ejpam-1477	99	40	is	be	AUX
ejpam-1477	99	41	positive	positive	ADJ
ejpam-1477	99	42	constant	constant	ADJ
ejpam-1477	99	43	which	which	DET
ejpam-1477	99	44	independent	independent	NOUN
ejpam-1477	99	45	of	of	ADP
ejpam-1477	99	46	h	h	NOUN
ejpam-1477	99	47	,	,	PUNCT
ejpam-1477	99	48	n	n	PROPN
ejpam-1477	99	49	and	and	CCONJ
ejpam-1477	99	50	where	where	SCONJ
ejpam-1477	99	51	h	h	NOUN
ejpam-1477	99	52	satisfies	satisfie	NOUN
ejpam-1477	99	53	(	(	PUNCT
ejpam-1477	99	54	2	2	NUM
ejpam-1477	99	55	)	)	PUNCT
ejpam-1477	99	56	.	.	PUNCT
ejpam-1477	100	1	when	when	SCONJ
ejpam-1477	100	2	f	f	X
ejpam-1477	100	3	l2	l2	VERB
ejpam-1477	100	4	p(ω1	p(ω1	ADJ
ejpam-1477	100	5	)	)	PUNCT
ejpam-1477	100	6	and	and	CCONJ
ejpam-1477	100	7	g	g	PROPN
ejpam-1477	100	8	∈	∈	PROPN
ejpam-1477	100	9	l2	l2	NOUN
ejpam-1477	100	10	p(∆a	p(∆a	NOUN
ejpam-1477	100	11	)	)	PUNCT
ejpam-1477	100	12	the	the	DET
ejpam-1477	100	13	condition	condition	NOUN
ejpam-1477	100	14	(	(	PUNCT
ejpam-1477	100	15	2	2	X
ejpam-1477	100	16	)	)	PUNCT
ejpam-1477	100	17	is	be	AUX
ejpam-1477	100	18	satisfied	satisfied	ADJ
ejpam-1477	100	19	then	then	ADV
ejpam-1477	100	20	‖bn	‖bn	PROPN
ejpam-1477	100	21	f	f	PROPN
ejpam-1477	100	22	−	−	PROPN
ejpam-1477	100	23	f	f	PROPN
ejpam-1477	100	24	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	100	25	)	)	PUNCT
ejpam-1477	100	26	¶	¶	PROPN
ejpam-1477	100	27	‖bn	‖bn	PROPN
ejpam-1477	100	28	(	(	PUNCT
ejpam-1477	101	1	f	f	PROPN
ejpam-1477	101	2	−	−	PROPN
ejpam-1477	101	3	g)−	g)−	PROPN
ejpam-1477	101	4	(	(	PUNCT
ejpam-1477	101	5	f	f	PROPN
ejpam-1477	101	6	−	−	PROPN
ejpam-1477	101	7	g)‖lp(∆a	g)‖lp(∆a	PROPN
ejpam-1477	101	8	)	)	PUNCT
ejpam-1477	101	9	+	+	NUM
ejpam-1477	101	10	‖bn	‖bn	NUM
ejpam-1477	101	11	g	g	NOUN
ejpam-1477	101	12	−	−	PROPN
ejpam-1477	101	13	g‖lp(∆a	g‖lp(∆a	PROPN
ejpam-1477	101	14	)	)	PUNCT
ejpam-1477	101	15	references	reference	NOUN
ejpam-1477	101	16	29	29	NUM
ejpam-1477	101	17	¶	¶	NOUN
ejpam-1477	101	18	(	(	PUNCT
ejpam-1477	102	1	ǫ+mδna)‖	ǫ+mδna)‖	PROPN
ejpam-1477	102	2	f	f	NOUN
ejpam-1477	102	3	−	−	PROPN
ejpam-1477	102	4	g‖lp(∆a	g‖lp(∆a	PROPN
ejpam-1477	102	5	+	+	CCONJ
ejpam-1477	102	6	cp‖g‖l2	cp‖g‖l2	PROPN
ejpam-1477	102	7	p(∆a	p(∆a	NOUN
ejpam-1477	102	8	δn	δn	NOUN
ejpam-1477	102	9	¶	¶	PROPN
ejpam-1477	102	10	em[‖	em[‖	PROPN
ejpam-1477	103	1	f	f	X
ejpam-1477	104	1	−	−	PROPN
ejpam-1477	105	1	g‖lp(∆a	g‖lp(∆a	NOUN
ejpam-1477	105	2	+	+	NUM
ejpam-1477	105	3	‖g‖l2	‖g‖l2	NUM
ejpam-1477	105	4	p(∆a	p(∆a	NOUN
ejpam-1477	105	5	δn	δn	NOUN
ejpam-1477	105	6	]	]	PUNCT
ejpam-1477	105	7	where	where	SCONJ
ejpam-1477	105	8	em	em	PRON
ejpam-1477	105	9	=	=	AUX
ejpam-1477	105	10	max{ǫ	max{ǫ	X
ejpam-1477	105	11	+	+	NOUN
ejpam-1477	105	12	mδna	mδna	ADJ
ejpam-1477	105	13	,	,	PUNCT
ejpam-1477	105	14	cp	cp	NOUN
ejpam-1477	105	15	}	}	PUNCT
ejpam-1477	105	16	.	.	PUNCT
ejpam-1477	106	1	using	use	VERB
ejpam-1477	106	2	the	the	DET
ejpam-1477	106	3	k	k	ADJ
ejpam-1477	106	4	-	-	ADJ
ejpam-1477	106	5	functional	functional	ADJ
ejpam-1477	106	6	we	we	PRON
ejpam-1477	106	7	get	get	VERB
ejpam-1477	106	8	,	,	PUNCT
ejpam-1477	106	9	‖bn	‖bn	PROPN
ejpam-1477	106	10	f	f	PROPN
ejpam-1477	106	11	−	−	PROPN
ejpam-1477	106	12	f	f	PROPN
ejpam-1477	106	13	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	106	14	)	)	PUNCT
ejpam-1477	106	15	¶	¶	NOUN
ejpam-1477	106	16	em	em	PRON
ejpam-1477	106	17	sup	sup	NOUN
ejpam-1477	106	18	g∈l2	g∈l2	ADJ
ejpam-1477	106	19	p(∆a	p(∆a	NOUN
ejpam-1477	106	20	)	)	PUNCT
ejpam-1477	107	1	[	[	X
ejpam-1477	107	2	‖	‖	NOUN
ejpam-1477	107	3	f	f	X
ejpam-1477	107	4	−	−	X
ejpam-1477	107	5	g‖lp(∆a	g‖lp(∆a	NOUN
ejpam-1477	107	6	+	+	CCONJ
ejpam-1477	107	7	‖g‖l2	‖g‖l2	NUM
ejpam-1477	107	8	p(∆a	p(∆a	NOUN
ejpam-1477	107	9	)	)	PUNCT
ejpam-1477	107	10	δn	δn	NOUN
ejpam-1477	107	11	]	]	PUNCT
ejpam-1477	107	12	since	since	SCONJ
ejpam-1477	107	13	,	,	PUNCT
ejpam-1477	107	14	for	for	ADP
ejpam-1477	107	15	a	a	DET
ejpam-1477	107	16	sufficiently	sufficiently	ADV
ejpam-1477	107	17	large	large	ADJ
ejpam-1477	107	18	n	n	CCONJ
ejpam-1477	107	19	,	,	PUNCT
ejpam-1477	107	20	δn	δn	NOUN
ejpam-1477	107	21	and	and	CCONJ
ejpam-1477	107	22	from	from	ADP
ejpam-1477	107	23	(	(	PUNCT
ejpam-1477	107	24	3	3	NUM
ejpam-1477	107	25	)	)	PUNCT
ejpam-1477	107	26	,	,	PUNCT
ejpam-1477	107	27	kp	kp	PROPN
ejpam-1477	107	28	(	(	PUNCT
ejpam-1477	107	29	f	f	PROPN
ejpam-1477	107	30	;	;	PUNCT
ejpam-1477	107	31	δ	δ	PROPN
ejpam-1477	107	32	)	)	PUNCT
ejpam-1477	107	33	¶	¶	INTJ
ejpam-1477	107	34	δn‖	δn‖	PROPN
ejpam-1477	107	35	f	f	PROPN
ejpam-1477	107	36	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	107	37	)	)	PUNCT
ejpam-1477	108	1	+	+	CCONJ
ejpam-1477	109	1	2a1ω2,p	2a1ω2,p	NUM
ejpam-1477	109	2	(	(	PUNCT
ejpam-1477	109	3	f	f	PROPN
ejpam-1477	109	4	;	;	PUNCT
ejpam-1477	109	5	δ(1/2	δ(1/2	NUM
ejpam-1477	109	6	)	)	PUNCT
ejpam-1477	109	7	)	)	PUNCT
ejpam-1477	109	8	emkp	emkp	VERB
ejpam-1477	109	9	(	(	PUNCT
ejpam-1477	109	10	f	f	PROPN
ejpam-1477	109	11	;	;	PUNCT
ejpam-1477	109	12	δ	δ	PROPN
ejpam-1477	109	13	)	)	PUNCT
ejpam-1477	109	14	¶	¶	PROPN
ejpam-1477	110	1	em[δn‖	em[δn‖	PROPN
ejpam-1477	110	2	f	f	PROPN
ejpam-1477	110	3	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	110	4	)	)	PUNCT
ejpam-1477	111	1	+	+	CCONJ
ejpam-1477	111	2	2a1ω2,p	2a1ω2,p	NUM
ejpam-1477	111	3	(	(	PUNCT
ejpam-1477	111	4	f	f	PROPN
ejpam-1477	111	5	;	;	PUNCT
ejpam-1477	111	6	δ(1/2	δ(1/2	PROPN
ejpam-1477	111	7	)	)	PUNCT
ejpam-1477	111	8	)	)	PUNCT
ejpam-1477	111	9	]	]	PUNCT
ejpam-1477	112	1	we	we	PRON
ejpam-1477	112	2	obtain	obtain	VERB
ejpam-1477	112	3	(	(	PUNCT
ejpam-1477	112	4	4	4	NUM
ejpam-1477	112	5	)	)	PUNCT
ejpam-1477	112	6	,	,	PUNCT
ejpam-1477	112	7	‖bn	‖bn	PROPN
ejpam-1477	112	8	f	f	PROPN
ejpam-1477	112	9	−	−	PROPN
ejpam-1477	112	10	f	f	PROPN
ejpam-1477	112	11	‖lp(∆a	‖lp(∆a	PROPN
ejpam-1477	112	12	)	)	PUNCT
ejpam-1477	112	13	¶	¶	PROPN
ejpam-1477	112	14	mp[‖	mp[‖	PROPN
ejpam-1477	113	1	f	f	PROPN
ejpam-1477	113	2	‖l2	‖l2	VERB
ejpam-1477	113	3	p(∆a	p(∆a	NOUN
ejpam-1477	113	4	)	)	PUNCT
ejpam-1477	113	5	δn	δn	ADP
ejpam-1477	114	1	+	+	SYM
ejpam-1477	114	2	ω2,p	ω2,p	PROPN
ejpam-1477	114	3	(	(	PUNCT
ejpam-1477	114	4	f	f	PROPN
ejpam-1477	114	5	;	;	PUNCT
ejpam-1477	114	6	δ(1/2	δ(1/2	PROPN
ejpam-1477	114	7	)	)	PUNCT
ejpam-1477	114	8	)	)	PUNCT
ejpam-1477	114	9	]	]	PUNCT
ejpam-1477	114	10	.	.	PUNCT
ejpam-1477	115	1	thus	thus	ADV
ejpam-1477	115	2	,	,	PUNCT
ejpam-1477	115	3	the	the	DET
ejpam-1477	115	4	proof	proof	NOUN
ejpam-1477	115	5	is	be	AUX
ejpam-1477	115	6	completed	complete	VERB
ejpam-1477	115	7	.	.	PUNCT
ejpam-1477	116	1	references	reference	NOUN
ejpam-1477	116	2	[	[	X
ejpam-1477	116	3	1	1	X
ejpam-1477	116	4	]	]	PUNCT
ejpam-1477	116	5	a	a	DET
ejpam-1477	116	6	gadjiev	gadjiev	NOUN
ejpam-1477	116	7	,	,	PUNCT
ejpam-1477	116	8	r	r	NOUN
ejpam-1477	116	9	efendiev	efendiev	NOUN
ejpam-1477	116	10	and	and	CCONJ
ejpam-1477	116	11	e	e	NOUN
ejpam-1477	116	12	ibikli	ibikli	NOUN
ejpam-1477	116	13	,	,	PUNCT
ejpam-1477	116	14	generalized	generalized	ADJ
ejpam-1477	116	15	bernstein	bernstein	PROPN
ejpam-1477	116	16	-chlodowsky	-chlodowsky	PROPN
ejpam-1477	116	17	polynomials	polynomial	NOUN
ejpam-1477	116	18	.	.	PUNCT
ejpam-1477	117	1	rocky	rocky	ADJ
ejpam-1477	117	2	mountain	mountain	PROPN
ejpam-1477	117	3	journal	journal	NOUN
ejpam-1477	117	4	of	of	ADP
ejpam-1477	117	5	mathematics	mathematic	NOUN
ejpam-1477	117	6	,	,	PUNCT
ejpam-1477	117	7	issue	issue	NOUN
ejpam-1477	117	8	2	2	NUM
ejpam-1477	117	9	-	-	SYM
ejpam-1477	117	10	3	3	NUM
ejpam-1477	117	11	,	,	PUNCT
ejpam-1477	117	12	1998	1998	NUM
ejpam-1477	117	13	.	.	PUNCT
ejpam-1477	118	1	[	[	X
ejpam-1477	118	2	2	2	X
ejpam-1477	118	3	]	]	PUNCT
ejpam-1477	118	4	a	a	DET
ejpam-1477	118	5	izgi	izgi	ADJ
ejpam-1477	118	6	,	,	PUNCT
ejpam-1477	118	7	order	order	NOUN
ejpam-1477	118	8	of	of	ADP
ejpam-1477	118	9	approximation	approximation	NOUN
ejpam-1477	118	10	of	of	ADP
ejpam-1477	118	11	functions	function	NOUN
ejpam-1477	118	12	of	of	ADP
ejpam-1477	118	13	two	two	NUM
ejpam-1477	118	14	variable	variable	NOUN
ejpam-1477	118	15	by	by	ADP
ejpam-1477	118	16	new	new	ADJ
ejpam-1477	118	17	type	type	NOUN
ejpam-1477	118	18	gamma	gamma	NOUN
ejpam-1477	118	19	operators	operator	NOUN
ejpam-1477	118	20	.	.	PUNCT
ejpam-1477	119	1	general	general	ADJ
ejpam-1477	119	2	mathematics	mathematic	NOUN
ejpam-1477	119	3	.	.	PUNCT
ejpam-1477	120	1	vol.17	vol.17	ADJ
ejpam-1477	120	2	,	,	PUNCT
ejpam-1477	120	3	no	no	INTJ
ejpam-1477	120	4	:	:	SYM
ejpam-1477	120	5	1	1	NUM
ejpam-1477	120	6	23	23	NUM
ejpam-1477	120	7	-	-	SYM
ejpam-1477	120	8	32	32	NUM
ejpam-1477	120	9	(	(	PUNCT
ejpam-1477	120	10	2009	2009	NUM
ejpam-1477	120	11	)	)	PUNCT
ejpam-1477	120	12	.	.	PUNCT
ejpam-1477	121	1	[	[	X
ejpam-1477	121	2	3	3	NUM
ejpam-1477	121	3	]	]	X
ejpam-1477	121	4	e	e	X
ejpam-1477	121	5	gadjieva	gadjieva	PROPN
ejpam-1477	121	6	and	and	CCONJ
ejpam-1477	121	7	e	e	NOUN
ejpam-1477	121	8	ibikli	ibikli	NOUN
ejpam-1477	121	9	,	,	PUNCT
ejpam-1477	121	10	on	on	ADP
ejpam-1477	121	11	generalization	generalization	NOUN
ejpam-1477	121	12	of	of	ADP
ejpam-1477	121	13	bernstein	bernstein	PROPN
ejpam-1477	121	14	–	–	PUNCT
ejpam-1477	121	15	chlodowsky	chlodowsky	PROPN
ejpam-1477	121	16	polynomials	polynomial	NOUN
ejpam-1477	121	17	,	,	PUNCT
ejpam-1477	121	18	hacettepe	hacettepe	ADJ
ejpam-1477	121	19	bulletin	bulletin	NOUN
ejpam-1477	121	20	of	of	ADP
ejpam-1477	121	21	natural	natural	ADJ
ejpam-1477	121	22	sciences	science	NOUN
ejpam-1477	121	23	and	and	CCONJ
ejpam-1477	121	24	engineering	engineering	NOUN
ejpam-1477	121	25	volume	volume	NOUN
ejpam-1477	121	26	24	24	NUM
ejpam-1477	121	27	/	/	SYM
ejpam-1477	121	28	p.p.31	p.p.31	PROPN
ejpam-1477	121	29	-	-	PUNCT
ejpam-1477	121	30	40	40	NUM
ejpam-1477	121	31	1995	1995	NUM
ejpam-1477	121	32	.	.	PUNCT
ejpam-1477	122	1	[	[	X
ejpam-1477	122	2	4	4	NUM
ejpam-1477	122	3	]	]	X
ejpam-1477	122	4	e	e	X
ejpam-1477	122	5	ibikli	ibikli	NOUN
ejpam-1477	122	6	and	and	CCONJ
ejpam-1477	122	7	e	e	PROPN
ejpam-1477	122	8	gadjieva	gadjieva	PROPN
ejpam-1477	122	9	,	,	PUNCT
ejpam-1477	122	10	the	the	DET
ejpam-1477	122	11	order	order	NOUN
ejpam-1477	122	12	of	of	ADP
ejpam-1477	122	13	approximation	approximation	NOUN
ejpam-1477	122	14	of	of	ADP
ejpam-1477	122	15	some	some	DET
ejpam-1477	122	16	un	un	PROPN
ejpam-1477	122	17	bounded	bounded	PROPN
ejpam-1477	122	18	functions	function	NOUN
ejpam-1477	122	19	by	by	ADP
ejpam-1477	122	20	the	the	DET
ejpam-1477	122	21	sequence	sequence	NOUN
ejpam-1477	122	22	of	of	ADP
ejpam-1477	122	23	positive	positive	ADJ
ejpam-1477	122	24	linear	linear	PROPN
ejpam-1477	122	25	operators	operator	NOUN
ejpam-1477	122	26	,	,	PUNCT
ejpam-1477	122	27	turkish	turkish	ADJ
ejpam-1477	122	28	j.of	j.of	PROPN
ejpam-1477	122	29	math	math	NOUN
ejpam-1477	122	30	.	.	PUNCT
ejpam-1477	123	1	v19	v19	PROPN
ejpam-1477	123	2	no.3	no.3	PROPN
ejpam-1477	123	3	1995	1995	NUM
ejpam-1477	123	4	.	.	PUNCT
ejpam-1477	124	1	[	[	X
ejpam-1477	124	2	5	5	NUM
ejpam-1477	124	3	]	]	PUNCT
ejpam-1477	124	4	e	e	X
ejpam-1477	124	5	ibikli	ibikli	NOUN
ejpam-1477	124	6	,	,	PUNCT
ejpam-1477	124	7	on	on	ADP
ejpam-1477	124	8	approximation	approximation	NOUN
ejpam-1477	124	9	of	of	ADP
ejpam-1477	124	10	lp	lp	DET
ejpam-1477	124	11	locally	locally	ADV
ejpam-1477	124	12	integrable	integrable	ADJ
ejpam-1477	124	13	functions	function	NOUN
ejpam-1477	124	14	by	by	ADP
ejpam-1477	124	15	the	the	DET
ejpam-1477	124	16	sequences	sequence	NOUN
ejpam-1477	124	17	of	of	ADP
ejpam-1477	124	18	linear	linear	ADJ
ejpam-1477	124	19	positive	positive	ADJ
ejpam-1477	124	20	operators	operator	NOUN
ejpam-1477	124	21	.	.	PUNCT
ejpam-1477	125	1	dokl	dokl	NOUN
ejpam-1477	125	2	.	.	PUNCT
ejpam-1477	126	1	nats	nat	NOUN
ejpam-1477	126	2	.	.	PUNCT
ejpam-1477	127	1	akad	akad	NOUN
ejpam-1477	127	2	.	.	PUNCT
ejpam-1477	128	1	nauk	nauk	PROPN
ejpam-1477	128	2	azerb	azerb	PROPN
ejpam-1477	128	3	.	.	PUNCT
ejpam-1477	129	1	59	59	NUM
ejpam-1477	129	2	.	.	NUM
ejpam-1477	129	3	2003	2003	NUM
ejpam-1477	129	4	.	.	PUNCT
ejpam-1477	130	1	[	[	X
ejpam-1477	130	2	6	6	NUM
ejpam-1477	130	3	]	]	PUNCT
ejpam-1477	130	4	e	e	X
ejpam-1477	130	5	ibikli	ibikli	NOUN
ejpam-1477	130	6	,	,	PUNCT
ejpam-1477	130	7	on	on	ADP
ejpam-1477	130	8	approximation	approximation	NOUN
ejpam-1477	130	9	for	for	ADP
ejpam-1477	130	10	functions	function	NOUN
ejpam-1477	130	11	of	of	ADP
ejpam-1477	130	12	two	two	NUM
ejpam-1477	130	13	variables	variable	NOUN
ejpam-1477	130	14	on	on	ADP
ejpam-1477	130	15	a	a	DET
ejpam-1477	130	16	triangular	triangular	NOUN
ejpam-1477	130	17	domain	domain	NOUN
ejpam-1477	130	18	.	.	PUNCT
ejpam-1477	131	1	rocky	rocky	ADJ
ejpam-1477	131	2	mountain	mountain	PROPN
ejpam-1477	131	3	j.	j.	PROPN
ejpam-1477	131	4	math	math	PROPN
ejpam-1477	131	5	.	.	PUNCT
ejpam-1477	132	1	35	35	NUM
ejpam-1477	132	2	.	.	X
ejpam-1477	132	3	1523	1523	NUM
ejpam-1477	132	4	-	-	SYM
ejpam-1477	132	5	1531	1531	NUM
ejpam-1477	132	6	,	,	PUNCT
ejpam-1477	132	7	2005	2005	NUM
ejpam-1477	132	8	.	.	PUNCT
ejpam-1477	133	1	[	[	X
ejpam-1477	133	2	7	7	NUM
ejpam-1477	133	3	]	]	X
ejpam-1477	133	4	s	s	VERB
ejpam-1477	133	5	serenbay	serenbay	NOUN
ejpam-1477	133	6	,	,	PUNCT
ejpam-1477	133	7	e	e	X
ejpam-1477	133	8	ibikli	ibikli	NOUN
ejpam-1477	133	9	and	and	CCONJ
ejpam-1477	133	10	i	i	PROPN
ejpam-1477	133	11	büyükyazıcı	büyükyazıcı	NOUN
ejpam-1477	133	12	,	,	PUNCT
ejpam-1477	133	13	approximation	approximation	NOUN
ejpam-1477	133	14	of	of	ADP
ejpam-1477	133	15	functions	function	NOUN
ejpam-1477	133	16	with	with	ADP
ejpam-1477	133	17	two	two	NUM
ejpam-1477	133	18	variables	variable	NOUN
ejpam-1477	133	19	in	in	ADP
ejpam-1477	133	20	sobolev	sobolev	NOUN
ejpam-1477	133	21	space.journal	space.journal	PROPN
ejpam-1477	133	22	of	of	ADP
ejpam-1477	133	23	classical	classical	ADJ
ejpam-1477	133	24	analysis	analysis	NOUN
ejpam-1477	133	25	(	(	PUNCT
ejpam-1477	133	26	is	be	AUX
ejpam-1477	133	27	submitted	submit	VERB
ejpam-1477	133	28	)	)	PUNCT
ejpam-1477	133	29	.	.	PUNCT