id	sid	tid	token	lemma	pos
ejpam-3687	1	1	european	european	PROPN
ejpam-3687	1	2	journal	journal	PROPN
ejpam-3687	1	3	of	of	ADP
ejpam-3687	1	4	pure	pure	ADJ
ejpam-3687	1	5	and	and	CCONJ
ejpam-3687	1	6	applied	apply	VERB
ejpam-3687	1	7	mathematics	mathematic	NOUN
ejpam-3687	1	8	vol	vol	NOUN
ejpam-3687	1	9	.	.	PROPN
ejpam-3687	2	1	13	13	NUM
ejpam-3687	2	2	,	,	PUNCT
ejpam-3687	2	3	no	no	INTJ
ejpam-3687	2	4	.	.	NOUN
ejpam-3687	2	5	3	3	NUM
ejpam-3687	2	6	,	,	PUNCT
ejpam-3687	2	7	2020	2020	NUM
ejpam-3687	2	8	,	,	PUNCT
ejpam-3687	2	9	390	390	NUM
ejpam-3687	2	10	-	-	SYM
ejpam-3687	2	11	402	402	NUM
ejpam-3687	2	12	issn	issn	PROPN
ejpam-3687	2	13	1307	1307	NUM
ejpam-3687	2	14	-	-	SYM
ejpam-3687	2	15	5543	5543	NUM
ejpam-3687	2	16	–	–	PUNCT
ejpam-3687	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3687	2	18	published	publish	VERB
ejpam-3687	2	19	by	by	ADP
ejpam-3687	2	20	new	new	PROPN
ejpam-3687	2	21	york	york	PROPN
ejpam-3687	2	22	business	business	PROPN
ejpam-3687	2	23	global	global	PROPN
ejpam-3687	2	24	e	e	PROPN
ejpam-3687	2	25	-	-	PROPN
ejpam-3687	2	26	j	j	PROPN
ejpam-3687	2	27	summability	summability	NOUN
ejpam-3687	2	28	of	of	ADP
ejpam-3687	2	29	orthogonal	orthogonal	ADJ
ejpam-3687	2	30	series	series	PROPN
ejpam-3687	2	31	f.	f.	PROPN
ejpam-3687	2	32	aydin	aydin	PROPN
ejpam-3687	2	33	akgun1,∗	akgun1,∗	PROPN
ejpam-3687	2	34	,	,	PUNCT
ejpam-3687	2	35	b.	b.	PROPN
ejpam-3687	2	36	e.	e.	PROPN
ejpam-3687	2	37	rhoades2	rhoades2	PROPN
ejpam-3687	3	1	1	1	NUM
ejpam-3687	3	2	department	department	NOUN
ejpam-3687	3	3	of	of	ADP
ejpam-3687	3	4	mathematical	mathematical	ADJ
ejpam-3687	3	5	engineering	engineering	NOUN
ejpam-3687	3	6	,	,	PUNCT
ejpam-3687	3	7	yildiz	yildiz	PROPN
ejpam-3687	3	8	technical	technical	PROPN
ejpam-3687	3	9	university	university	PROPN
ejpam-3687	3	10	,	,	PUNCT
ejpam-3687	3	11	34210	34210	NUM
ejpam-3687	3	12	esenler	esenler	NOUN
ejpam-3687	3	13	,	,	PUNCT
ejpam-3687	3	14	istanbul	istanbul	PROPN
ejpam-3687	3	15	,	,	PUNCT
ejpam-3687	3	16	turkey	turkey	PROPN
ejpam-3687	3	17	2	2	NUM
ejpam-3687	3	18	department	department	NOUN
ejpam-3687	3	19	of	of	ADP
ejpam-3687	3	20	mathematics	mathematics	PROPN
ejpam-3687	3	21	,	,	PUNCT
ejpam-3687	3	22	indiana	indiana	PROPN
ejpam-3687	3	23	university	university	PROPN
ejpam-3687	3	24	,	,	PUNCT
ejpam-3687	3	25	bloomington	bloomington	PROPN
ejpam-3687	3	26	,	,	PUNCT
ejpam-3687	3	27	in	in	ADP
ejpam-3687	3	28	47405	47405	NUM
ejpam-3687	3	29	-	-	SYM
ejpam-3687	3	30	7106	7106	NUM
ejpam-3687	3	31	,	,	PUNCT
ejpam-3687	3	32	u.s.a	u.s.a	PROPN
ejpam-3687	3	33	.	.	PUNCT
ejpam-3687	3	34	abstract	abstract	PROPN
ejpam-3687	3	35	.	.	PUNCT
ejpam-3687	4	1	in	in	ADP
ejpam-3687	4	2	this	this	DET
ejpam-3687	4	3	paper	paper	NOUN
ejpam-3687	4	4	we	we	PRON
ejpam-3687	4	5	obtain	obtain	VERB
ejpam-3687	4	6	a	a	DET
ejpam-3687	4	7	sufficient	sufficient	ADJ
ejpam-3687	4	8	condition	condition	NOUN
ejpam-3687	4	9	for	for	ADP
ejpam-3687	4	10	the	the	DET
ejpam-3687	4	11	e	e	PROPN
ejpam-3687	4	12	-	-	PROPN
ejpam-3687	4	13	j	j	PROPN
ejpam-3687	4	14	summability	summability	NOUN
ejpam-3687	4	15	of	of	ADP
ejpam-3687	4	16	certain	certain	ADJ
ejpam-3687	4	17	orthogonal	orthogonal	ADJ
ejpam-3687	4	18	series	series	NOUN
ejpam-3687	4	19	.	.	PUNCT
ejpam-3687	5	1	our	our	PRON
ejpam-3687	5	2	results	result	NOUN
ejpam-3687	5	3	generalize	generalize	VERB
ejpam-3687	5	4	the	the	DET
ejpam-3687	5	5	corresponding	corresponding	ADJ
ejpam-3687	5	6	theorems	theorem	NOUN
ejpam-3687	5	7	for	for	ADP
ejpam-3687	5	8	ordinary	ordinary	ADJ
ejpam-3687	5	9	hausdorff	hausdorff	NOUN
ejpam-3687	5	10	summability	summability	NOUN
ejpam-3687	5	11	obtained	obtain	VERB
ejpam-3687	5	12	by	by	ADP
ejpam-3687	5	13	kalaivana	kalaivana	NOUN
ejpam-3687	5	14	and	and	CCONJ
ejpam-3687	5	15	youvaraj	youvaraj	ADJ
ejpam-3687	5	16	.	.	PUNCT
ejpam-3687	6	1	2020	2020	NUM
ejpam-3687	6	2	mathematics	mathematic	NOUN
ejpam-3687	6	3	subject	subject	NOUN
ejpam-3687	6	4	classifications	classification	NOUN
ejpam-3687	6	5	:	:	PUNCT
ejpam-3687	6	6	40g05	40g05	NUM
ejpam-3687	6	7	key	key	ADJ
ejpam-3687	6	8	words	word	NOUN
ejpam-3687	6	9	and	and	CCONJ
ejpam-3687	6	10	phrases	phrase	NOUN
ejpam-3687	6	11	:	:	PUNCT
ejpam-3687	6	12	e	e	X
ejpam-3687	6	13	-	-	PROPN
ejpam-3687	6	14	j	j	PROPN
ejpam-3687	6	15	matrices	matrix	NOUN
ejpam-3687	6	16	,	,	PUNCT
ejpam-3687	6	17	orthogonal	orthogonal	ADJ
ejpam-3687	6	18	series	series	NOUN
ejpam-3687	6	19	1	1	NUM
ejpam-3687	6	20	.	.	PUNCT
ejpam-3687	6	21	preliminaries	preliminary	NOUN
ejpam-3687	6	22	the	the	DET
ejpam-3687	6	23	set	set	NOUN
ejpam-3687	6	24	of	of	ADP
ejpam-3687	6	25	all	all	DET
ejpam-3687	6	26	real	real	ADJ
ejpam-3687	6	27	or	or	CCONJ
ejpam-3687	6	28	complex	complex	ADJ
ejpam-3687	6	29	sequences	sequence	NOUN
ejpam-3687	6	30	{	{	PUNCT
ejpam-3687	6	31	xn	xn	NOUN
ejpam-3687	6	32	}	}	PUNCT
ejpam-3687	6	33	for	for	ADP
ejpam-3687	6	34	which	which	PRON
ejpam-3687	6	35	an(x	an(x	NUM
ejpam-3687	6	36	)	)	PUNCT
ejpam-3687	6	37	:	:	PUNCT
ejpam-3687	7	1	=	=	PUNCT
ejpam-3687	7	2	∑	∑	PUNCT
ejpam-3687	7	3	k	k	PROPN
ejpam-3687	7	4	ankxk	ankxk	PROPN
ejpam-3687	7	5	converges	converge	NOUN
ejpam-3687	7	6	is	be	AUX
ejpam-3687	7	7	called	call	VERB
ejpam-3687	7	8	the	the	DET
ejpam-3687	7	9	convergence	convergence	NOUN
ejpam-3687	7	10	domain	domain	NOUN
ejpam-3687	7	11	of	of	ADP
ejpam-3687	7	12	a	a	PRON
ejpam-3687	7	13	,	,	PUNCT
ejpam-3687	7	14	written	write	VERB
ejpam-3687	7	15	ca	ca	NOUN
ejpam-3687	7	16	,	,	PUNCT
ejpam-3687	7	17	where	where	SCONJ
ejpam-3687	7	18	a	a	PRON
ejpam-3687	7	19	is	be	AUX
ejpam-3687	7	20	an	an	DET
ejpam-3687	7	21	infinite	infinite	ADJ
ejpam-3687	7	22	matrix	matrix	NOUN
ejpam-3687	7	23	.	.	PUNCT
ejpam-3687	8	1	a	a	DET
ejpam-3687	8	2	matrix	matrix	NOUN
ejpam-3687	8	3	a	a	PRON
ejpam-3687	8	4	is	be	AUX
ejpam-3687	8	5	said	say	VERB
ejpam-3687	8	6	to	to	PART
ejpam-3687	8	7	be	be	AUX
ejpam-3687	8	8	conservative	conservative	ADJ
ejpam-3687	8	9	if	if	SCONJ
ejpam-3687	8	10	it	it	PRON
ejpam-3687	8	11	maps	map	VERB
ejpam-3687	8	12	each	each	DET
ejpam-3687	8	13	convergent	convergent	ADJ
ejpam-3687	8	14	sequence	sequence	NOUN
ejpam-3687	8	15	into	into	ADP
ejpam-3687	8	16	a	a	DET
ejpam-3687	8	17	convergent	convergent	NOUN
ejpam-3687	8	18	sequence	sequence	NOUN
ejpam-3687	8	19	,	,	PUNCT
ejpam-3687	8	20	not	not	PART
ejpam-3687	8	21	necessarily	necessarily	ADV
ejpam-3687	8	22	with	with	ADP
ejpam-3687	8	23	the	the	DET
ejpam-3687	8	24	same	same	ADJ
ejpam-3687	8	25	limit	limit	NOUN
ejpam-3687	8	26	.	.	PUNCT
ejpam-3687	9	1	if	if	SCONJ
ejpam-3687	9	2	the	the	DET
ejpam-3687	9	3	limit	limit	NOUN
ejpam-3687	9	4	is	be	AUX
ejpam-3687	9	5	also	also	ADV
ejpam-3687	9	6	preserved	preserve	VERB
ejpam-3687	9	7	,	,	PUNCT
ejpam-3687	9	8	then	then	ADV
ejpam-3687	9	9	the	the	DET
ejpam-3687	9	10	matrix	matrix	NOUN
ejpam-3687	9	11	is	be	AUX
ejpam-3687	9	12	called	call	VERB
ejpam-3687	9	13	regular	regular	ADJ
ejpam-3687	9	14	.	.	PUNCT
ejpam-3687	10	1	silverman	silverman	NOUN
ejpam-3687	10	2	and	and	CCONJ
ejpam-3687	10	3	toeplitz	toeplitz	NOUN
ejpam-3687	10	4	established	establish	VERB
ejpam-3687	10	5	necessary	necessary	ADJ
ejpam-3687	10	6	and	and	CCONJ
ejpam-3687	10	7	sufficient	sufficient	ADJ
ejpam-3687	10	8	conditions	condition	NOUN
ejpam-3687	10	9	for	for	ADP
ejpam-3687	10	10	a	a	DET
ejpam-3687	10	11	matrix	matrix	NOUN
ejpam-3687	10	12	to	to	PART
ejpam-3687	10	13	be	be	AUX
ejpam-3687	10	14	conservative[4	conservative[4	ADP
ejpam-3687	10	15	]	]	X
ejpam-3687	10	16	.	.	PUNCT
ejpam-3687	11	1	they	they	PRON
ejpam-3687	11	2	are	be	AUX
ejpam-3687	11	3	(	(	PUNCT
ejpam-3687	11	4	i	i	NOUN
ejpam-3687	11	5	)	)	PUNCT
ejpam-3687	11	6	‖a‖∞	‖a‖∞	NOUN
ejpam-3687	11	7	:	:	PUNCT
ejpam-3687	11	8	=	=	NOUN
ejpam-3687	11	9	supn	supn	NOUN
ejpam-3687	11	10	∑	∑	PUNCT
ejpam-3687	11	11	k	k	PROPN
ejpam-3687	11	12	|ank|	|ank|	PROPN
ejpam-3687	11	13	<	<	X
ejpam-3687	11	14	∞	∞	PROPN
ejpam-3687	11	15	,	,	PUNCT
ejpam-3687	11	16	(	(	PUNCT
ejpam-3687	11	17	ii	ii	NOUN
ejpam-3687	11	18	)	)	PUNCT
ejpam-3687	11	19	t	t	NOUN
ejpam-3687	11	20	:	:	PUNCT
ejpam-3687	11	21	=	=	PUNCT
ejpam-3687	11	22	limn	limn	PROPN
ejpam-3687	11	23	∑	∑	PROPN
ejpam-3687	11	24	k	k	PROPN
ejpam-3687	11	25	ank	ank	PROPN
ejpam-3687	11	26	exists	exist	VERB
ejpam-3687	11	27	,	,	PUNCT
ejpam-3687	11	28	(	(	PUNCT
ejpam-3687	11	29	iii	iii	X
ejpam-3687	11	30	)	)	PUNCT
ejpam-3687	11	31	ak	ak	NOUN
ejpam-3687	11	32	:	:	PUNCT
ejpam-3687	11	33	=	=	PROPN
ejpam-3687	11	34	limn	limn	PROPN
ejpam-3687	11	35	ank	ank	PROPN
ejpam-3687	11	36	exists	exist	VERB
ejpam-3687	11	37	for	for	ADP
ejpam-3687	11	38	each	each	DET
ejpam-3687	11	39	k.	k.	NOUN
ejpam-3687	11	40	a	a	DET
ejpam-3687	11	41	hausdorff	hausdorff	NOUN
ejpam-3687	11	42	matrix	matrix	NOUN
ejpam-3687	11	43	h	h	NOUN
ejpam-3687	12	1	=	=	SYM
ejpam-3687	12	2	(	(	PUNCT
ejpam-3687	12	3	hnk	hnk	PROPN
ejpam-3687	12	4	)	)	PUNCT
ejpam-3687	12	5	is	be	AUX
ejpam-3687	12	6	a	a	DET
ejpam-3687	12	7	lower	low	ADJ
ejpam-3687	12	8	triangular	triangular	NOUN
ejpam-3687	12	9	matrix	matrix	NOUN
ejpam-3687	12	10	with	with	ADP
ejpam-3687	12	11	nonzero	nonzero	PROPN
ejpam-3687	12	12	entries	entry	NOUN
ejpam-3687	12	13	hnk	hnk	NOUN
ejpam-3687	12	14	=	=	SYM
ejpam-3687	12	15	(	(	PUNCT
ejpam-3687	12	16	n	n	X
ejpam-3687	12	17	k	k	PROPN
ejpam-3687	12	18	)	)	PUNCT
ejpam-3687	12	19	∆n−kµk	∆n−kµk	PUNCT
ejpam-3687	12	20	,	,	PUNCT
ejpam-3687	12	21	where	where	SCONJ
ejpam-3687	12	22	{	{	PUNCT
ejpam-3687	12	23	µn	µn	NOUN
ejpam-3687	12	24	}	}	PUNCT
ejpam-3687	12	25	is	be	AUX
ejpam-3687	12	26	any	any	DET
ejpam-3687	12	27	real	real	ADJ
ejpam-3687	12	28	sequence	sequence	NOUN
ejpam-3687	12	29	and	and	CCONJ
ejpam-3687	12	30	∆	∆	PROPN
ejpam-3687	12	31	is	be	AUX
ejpam-3687	12	32	the	the	DET
ejpam-3687	12	33	forward	forward	ADJ
ejpam-3687	12	34	difference	difference	NOUN
ejpam-3687	12	35	operator	operator	NOUN
ejpam-3687	12	36	defied	defy	VERB
ejpam-3687	12	37	by	by	ADP
ejpam-3687	12	38	∆µk	∆µk	NUM
ejpam-3687	12	39	=	=	PUNCT
ejpam-3687	12	40	µk	µk	INTJ
ejpam-3687	12	41	−	−	PROPN
ejpam-3687	12	42	µk+1	µk+1	X
ejpam-3687	12	43	and	and	CCONJ
ejpam-3687	12	44	∆n+1µk	∆n+1µk	NOUN
ejpam-3687	12	45	=	=	SYM
ejpam-3687	12	46	∆(∆nµk	∆(∆nµk	NOUN
ejpam-3687	12	47	)	)	PUNCT
ejpam-3687	12	48	.	.	PUNCT
ejpam-3687	13	1	for	for	ADP
ejpam-3687	13	2	every	every	DET
ejpam-3687	13	3	hausdorff	hausdorff	NOUN
ejpam-3687	13	4	matrix	matrix	NOUN
ejpam-3687	13	5	each	each	DET
ejpam-3687	13	6	row	row	NOUN
ejpam-3687	13	7	sum	sum	NOUN
ejpam-3687	13	8	is	be	AUX
ejpam-3687	13	9	equal	equal	ADJ
ejpam-3687	13	10	to	to	ADP
ejpam-3687	13	11	µ0[3	µ0[3	X
ejpam-3687	13	12	]	]	X
ejpam-3687	13	13	.	.	PUNCT
ejpam-3687	14	1	∗corresponding	∗corresponde	VERB
ejpam-3687	14	2	author	author	NOUN
ejpam-3687	14	3	.	.	PUNCT
ejpam-3687	15	1	doi	doi	NOUN
ejpam-3687	15	2	:	:	PUNCT
ejpam-3687	15	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3687	https://doi.org/10.29020/nybg.ejpam.v13i3.3687	NOUN
ejpam-3687	15	4	email	email	NOUN
ejpam-3687	15	5	addresses	address	NOUN
ejpam-3687	15	6	:	:	PUNCT
ejpam-3687	15	7	fakgun@yildiz.edu.tr	fakgun@yildiz.edu.tr	PROPN
ejpam-3687	15	8	(	(	PUNCT
ejpam-3687	15	9	f.	f.	PROPN
ejpam-3687	15	10	aydin	aydin	PROPN
ejpam-3687	15	11	akgun	akgun	PROPN
ejpam-3687	15	12	)	)	PUNCT
ejpam-3687	15	13	,	,	PUNCT
ejpam-3687	15	14	rhoades@indiana.edu	rhoades@indiana.edu	PROPN
ejpam-3687	16	1	(	(	PUNCT
ejpam-3687	16	2	b.	b.	PROPN
ejpam-3687	16	3	e.	e.	PROPN
ejpam-3687	16	4	rhoades	rhoades	PROPN
ejpam-3687	16	5	)	)	PUNCT
ejpam-3687	16	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3687	16	7	390	390	NUM
ejpam-3687	17	1	c	c	NOUN
ejpam-3687	17	2	©	©	NOUN
ejpam-3687	17	3	2020	2020	NUM
ejpam-3687	17	4	ejpam	ejpam	VERB
ejpam-3687	17	5	all	all	DET
ejpam-3687	17	6	rights	right	NOUN
ejpam-3687	17	7	reserved	reserve	VERB
ejpam-3687	17	8	.	.	PUNCT
ejpam-3687	18	1	f.	f.	PROPN
ejpam-3687	18	2	aydin	aydin	PROPN
ejpam-3687	18	3	akgun	akgun	PROPN
ejpam-3687	18	4	,	,	PUNCT
ejpam-3687	18	5	b.	b.	PROPN
ejpam-3687	18	6	e.	e.	PROPN
ejpam-3687	18	7	rhoades	rhoades	PROPN
ejpam-3687	18	8	/	/	SYM
ejpam-3687	18	9	eur	eur	PROPN
ejpam-3687	18	10	.	.	PUNCT
ejpam-3687	19	1	j.	j.	PROPN
ejpam-3687	19	2	pure	pure	PROPN
ejpam-3687	19	3	appl	appl	PROPN
ejpam-3687	19	4	.	.	PROPN
ejpam-3687	19	5	math	math	PROPN
ejpam-3687	19	6	,	,	PUNCT
ejpam-3687	19	7	13	13	NUM
ejpam-3687	19	8	(	(	PUNCT
ejpam-3687	19	9	3	3	NUM
ejpam-3687	19	10	)	)	PUNCT
ejpam-3687	19	11	(	(	PUNCT
ejpam-3687	19	12	2020	2020	NUM
ejpam-3687	19	13	)	)	PUNCT
ejpam-3687	19	14	,	,	PUNCT
ejpam-3687	19	15	390	390	NUM
ejpam-3687	19	16	-	-	SYM
ejpam-3687	19	17	402	402	NUM
ejpam-3687	19	18	391	391	NUM
ejpam-3687	19	19	f.	f.	NOUN
ejpam-3687	19	20	hausdorff	hausdorff	NOUN
ejpam-3687	20	1	[	[	X
ejpam-3687	20	2	2	2	NUM
ejpam-3687	20	3	]	]	PUNCT
ejpam-3687	20	4	proved	prove	VERB
ejpam-3687	20	5	that	that	SCONJ
ejpam-3687	20	6	a	a	DET
ejpam-3687	20	7	hausdorff	hausdorff	NOUN
ejpam-3687	20	8	matrix	matrix	NOUN
ejpam-3687	20	9	is	be	AUX
ejpam-3687	20	10	conservative	conservative	ADJ
ejpam-3687	20	11	if	if	SCONJ
ejpam-3687	20	12	and	and	CCONJ
ejpam-3687	20	13	only	only	ADV
ejpam-3687	20	14	if	if	SCONJ
ejpam-3687	20	15	µn	µn	PROPN
ejpam-3687	20	16	=	=	SYM
ejpam-3687	20	17	∫	∫	PROPN
ejpam-3687	20	18	1	1	NUM
ejpam-3687	20	19	0	0	NUM
ejpam-3687	21	1	xndχ(x	xndχ(x	PROPN
ejpam-3687	21	2	)	)	PUNCT
ejpam-3687	21	3	,	,	PUNCT
ejpam-3687	21	4	(	(	PUNCT
ejpam-3687	21	5	1	1	X
ejpam-3687	21	6	)	)	PUNCT
ejpam-3687	21	7	where	where	SCONJ
ejpam-3687	21	8	the	the	DET
ejpam-3687	21	9	mass	mass	NOUN
ejpam-3687	21	10	function	function	VERB
ejpam-3687	21	11	χ	χ	PROPN
ejpam-3687	21	12	∈	∈	PROPN
ejpam-3687	21	13	bv	bv	PROPN
ejpam-3687	22	1	[	[	X
ejpam-3687	22	2	0	0	NUM
ejpam-3687	22	3	,	,	PUNCT
ejpam-3687	22	4	1	1	NUM
ejpam-3687	22	5	]	]	PUNCT
ejpam-3687	22	6	.	.	PUNCT
ejpam-3687	23	1	the	the	DET
ejpam-3687	23	2	e	e	PROPN
ejpam-3687	23	3	-	-	PROPN
ejpam-3687	23	4	j	j	ADJ
ejpam-3687	23	5	generalized	generalize	VERB
ejpam-3687	23	6	hausdorff	hausdorff	NOUN
ejpam-3687	23	7	matrices	matrix	NOUN
ejpam-3687	23	8	,	,	PUNCT
ejpam-3687	23	9	denoted	denote	VERB
ejpam-3687	23	10	by	by	ADP
ejpam-3687	23	11	hα	hα	ADP
ejpam-3687	23	12	µ	µ	NOUN
ejpam-3687	23	13	=	=	PUNCT
ejpam-3687	23	14	(	(	PUNCT
ejpam-3687	23	15	h	h	NOUN
ejpam-3687	23	16	(	(	PUNCT
ejpam-3687	23	17	α	α	NOUN
ejpam-3687	23	18	)	)	PUNCT
ejpam-3687	23	19	nk	nk	PROPN
ejpam-3687	23	20	)	)	PUNCT
ejpam-3687	23	21	,	,	PUNCT
ejpam-3687	23	22	were	be	AUX
ejpam-3687	23	23	defined	define	VERB
ejpam-3687	23	24	independently	independently	ADV
ejpam-3687	23	25	by	by	ADP
ejpam-3687	23	26	endl	endl	NOUN
ejpam-3687	23	27	[	[	X
ejpam-3687	23	28	1	1	NUM
ejpam-3687	23	29	]	]	PUNCT
ejpam-3687	23	30	and	and	CCONJ
ejpam-3687	23	31	jakimovski	jakimovski	VERB
ejpam-3687	24	1	[	[	X
ejpam-3687	24	2	5	5	NUM
ejpam-3687	24	3	]	]	PUNCT
ejpam-3687	24	4	,	,	PUNCT
ejpam-3687	24	5	with	with	ADP
ejpam-3687	24	6	nonzero	nonzero	PROPN
ejpam-3687	24	7	entries	entry	NOUN
ejpam-3687	24	8	h	h	NOUN
ejpam-3687	24	9	(	(	PUNCT
ejpam-3687	24	10	α	α	NOUN
ejpam-3687	24	11	)	)	PUNCT
ejpam-3687	24	12	nk	nk	PROPN
ejpam-3687	24	13	=	=	PUNCT
ejpam-3687	24	14	(	(	PUNCT
ejpam-3687	24	15	n+	n+	NUM
ejpam-3687	25	1	α	α	NUM
ejpam-3687	25	2	n−	n−	NOUN
ejpam-3687	25	3	k	k	X
ejpam-3687	25	4	)	)	PUNCT
ejpam-3687	25	5	∆n−kµ	∆n−kµ	PROPN
ejpam-3687	25	6	(	(	PUNCT
ejpam-3687	25	7	α	α	NOUN
ejpam-3687	25	8	)	)	PUNCT
ejpam-3687	25	9	k	k	NOUN
ejpam-3687	25	10	,	,	PUNCT
ejpam-3687	25	11	0	0	NUM
ejpam-3687	25	12	≤	≤	NUM
ejpam-3687	25	13	k	k	X
ejpam-3687	25	14	≤	≤	NUM
ejpam-3687	25	15	n	n	CCONJ
ejpam-3687	25	16	,	,	PUNCT
ejpam-3687	25	17	for	for	ADP
ejpam-3687	25	18	any	any	DET
ejpam-3687	25	19	α	α	DET
ejpam-3687	25	20	≥	≥	NOUN
ejpam-3687	25	21	0	0	NUM
ejpam-3687	25	22	.	.	PUNCT
ejpam-3687	26	1	for	for	ADP
ejpam-3687	26	2	α	α	NOUN
ejpam-3687	26	3	=	=	SYM
ejpam-3687	26	4	0	0	PROPN
ejpam-3687	26	5	,	,	PUNCT
ejpam-3687	26	6	the	the	DET
ejpam-3687	26	7	e	e	PROPN
ejpam-3687	26	8	-	-	PROPN
ejpam-3687	26	9	j	j	PROPN
ejpam-3687	26	10	matrices	matrix	NOUN
ejpam-3687	26	11	reduce	reduce	VERB
ejpam-3687	26	12	to	to	ADP
ejpam-3687	26	13	the	the	DET
ejpam-3687	26	14	ordinary	ordinary	ADJ
ejpam-3687	26	15	hausdorff	hausdorff	NOUN
ejpam-3687	26	16	matrices	matrix	NOUN
ejpam-3687	26	17	.	.	PUNCT
ejpam-3687	27	1	if	if	SCONJ
ejpam-3687	27	2	the	the	DET
ejpam-3687	27	3	µ	µ	X
ejpam-3687	27	4	(	(	PUNCT
ejpam-3687	27	5	α	α	NOUN
ejpam-3687	27	6	)	)	PUNCT
ejpam-3687	27	7	n	n	AUX
ejpam-3687	27	8	satisfy	satisfy	VERB
ejpam-3687	27	9	the	the	DET
ejpam-3687	27	10	condition	condition	NOUN
ejpam-3687	27	11	µ(α)n	µ(α)n	PROPN
ejpam-3687	27	12	=	=	SYM
ejpam-3687	27	13	∫	∫	PROPN
ejpam-3687	27	14	1	1	NUM
ejpam-3687	27	15	0	0	NUM
ejpam-3687	27	16	xn+αdχ(x	xn+αdχ(x	PROPN
ejpam-3687	27	17	)	)	PUNCT
ejpam-3687	27	18	,	,	PUNCT
ejpam-3687	27	19	where	where	SCONJ
ejpam-3687	27	20	χ	χ	PRON
ejpam-3687	27	21	∈	∈	PROPN
ejpam-3687	27	22	bv	bv	PROPN
ejpam-3687	28	1	[	[	X
ejpam-3687	28	2	0	0	NUM
ejpam-3687	28	3	,	,	PUNCT
ejpam-3687	28	4	1	1	NUM
ejpam-3687	28	5	]	]	PUNCT
ejpam-3687	28	6	,	,	PUNCT
ejpam-3687	28	7	then	then	ADV
ejpam-3687	28	8	the	the	DET
ejpam-3687	28	9	corresponding	corresponding	ADJ
ejpam-3687	28	10	e	e	PROPN
ejpam-3687	28	11	-	-	PROPN
ejpam-3687	28	12	j	j	ADJ
ejpam-3687	28	13	matrix	matrix	NOUN
ejpam-3687	28	14	is	be	AUX
ejpam-3687	28	15	conservative	conservative	ADJ
ejpam-3687	28	16	.	.	PUNCT
ejpam-3687	29	1	definition	definition	NOUN
ejpam-3687	29	2	1	1	NUM
ejpam-3687	29	3	.	.	PUNCT
ejpam-3687	30	1	let	let	VERB
ejpam-3687	30	2	γ	γ	X
ejpam-3687	30	3	:	:	PUNCT
ejpam-3687	31	1	[	[	X
ejpam-3687	31	2	1,∞)→	1,∞)→	NUM
ejpam-3687	31	3	[	[	X
ejpam-3687	31	4	0,∞	0,∞	NOUN
ejpam-3687	31	5	)	)	PUNCT
ejpam-3687	31	6	be	be	VERB
ejpam-3687	31	7	a	a	DET
ejpam-3687	31	8	nondecreasing	nondecrease	VERB
ejpam-3687	31	9	function	function	NOUN
ejpam-3687	31	10	,	,	PUNCT
ejpam-3687	31	11	a	a	DET
ejpam-3687	31	12	=	=	SYM
ejpam-3687	31	13	(	(	PUNCT
ejpam-3687	31	14	ank	ank	PROPN
ejpam-3687	31	15	)	)	PUNCT
ejpam-3687	31	16	an	an	DET
ejpam-3687	31	17	infinite	infinite	ADJ
ejpam-3687	31	18	matrix	matrix	NOUN
ejpam-3687	31	19	.	.	PUNCT
ejpam-3687	32	1	then	then	ADV
ejpam-3687	32	2	a	a	DET
ejpam-3687	32	3	series	series	NOUN
ejpam-3687	32	4	∑	∑	PUNCT
ejpam-3687	32	5	n	n	CCONJ
ejpam-3687	32	6	bn	bn	PROPN
ejpam-3687	32	7	is	be	AUX
ejpam-3687	32	8	said	say	VERB
ejpam-3687	32	9	to	to	PART
ejpam-3687	32	10	be	be	AUX
ejpam-3687	32	11	|a	|a	VERB
ejpam-3687	32	12	,	,	PUNCT
ejpam-3687	32	13	γ|k	γ|k	NOUN
ejpam-3687	32	14	summable	summable	ADJ
ejpam-3687	32	15	,	,	PUNCT
ejpam-3687	32	16	if	if	SCONJ
ejpam-3687	32	17	∞∑	∞∑	NUM
ejpam-3687	32	18	n=1	n=1	PROPN
ejpam-3687	32	19	γ(n)knk−1|σn	γ(n)knk−1|σn	VERB
ejpam-3687	32	20	−	−	PROPN
ejpam-3687	32	21	σn−1|k	σn−1|k	NOUN
ejpam-3687	32	22	converges	converge	NOUN
ejpam-3687	32	23	,	,	PUNCT
ejpam-3687	32	24	where	where	SCONJ
ejpam-3687	32	25	σn	σn	NOUN
ejpam-3687	32	26	:	:	PUNCT
ejpam-3687	32	27	∑	∑	PROPN
ejpam-3687	32	28	n	n	PRON
ejpam-3687	32	29	ankbk	ankbk	ADJ
ejpam-3687	32	30	.	.	PUNCT
ejpam-3687	33	1	definition	definition	NOUN
ejpam-3687	33	2	2	2	NUM
ejpam-3687	33	3	.	.	PUNCT
ejpam-3687	34	1	let	let	VERB
ejpam-3687	34	2	γ	γ	NOUN
ejpam-3687	34	3	:	:	PUNCT
ejpam-3687	34	4	=	=	SYM
ejpam-3687	34	5	{	{	PUNCT
ejpam-3687	34	6	γn	γn	AUX
ejpam-3687	34	7	}	}	PUNCT
ejpam-3687	34	8	be	be	AUX
ejpam-3687	34	9	a	a	DET
ejpam-3687	34	10	positive	positive	ADJ
ejpam-3687	34	11	sequence	sequence	NOUN
ejpam-3687	34	12	,	,	PUNCT
ejpam-3687	34	13	β	β	X
ejpam-3687	34	14	a	a	DET
ejpam-3687	34	15	real	real	ADJ
ejpam-3687	34	16	positive	positive	ADJ
ejpam-3687	34	17	number	number	NOUN
ejpam-3687	34	18	.	.	PUNCT
ejpam-3687	35	1	then	then	ADV
ejpam-3687	35	2	γ	γ	PROPN
ejpam-3687	35	3	is	be	AUX
ejpam-3687	35	4	called	call	VERB
ejpam-3687	35	5	quasiβ	quasiβ	NOUN
ejpam-3687	35	6	-	-	PUNCT
ejpam-3687	35	7	power	power	NOUN
ejpam-3687	35	8	monotone	monotone	NOUN
ejpam-3687	35	9	decreasing	decrease	VERB
ejpam-3687	35	10	if	if	SCONJ
ejpam-3687	35	11	there	there	PRON
ejpam-3687	35	12	exists	exist	VERB
ejpam-3687	35	13	a	a	DET
ejpam-3687	35	14	number	number	NOUN
ejpam-3687	35	15	m	m	NOUN
ejpam-3687	35	16	=	=	SYM
ejpam-3687	35	17	m(β	m(β	PROPN
ejpam-3687	35	18	,	,	PUNCT
ejpam-3687	35	19	γ	γ	PROPN
ejpam-3687	35	20	)	)	PUNCT
ejpam-3687	35	21	≥	≥	NOUN
ejpam-3687	35	22	1	1	NUM
ejpam-3687	35	23	such	such	ADJ
ejpam-3687	35	24	that	that	DET
ejpam-3687	35	25	nβγ(n	nβγ(n	PROPN
ejpam-3687	35	26	)	)	PUNCT
ejpam-3687	35	27	≤mmβγ(m	≤mmβγ(m	NOUN
ejpam-3687	35	28	)	)	PUNCT
ejpam-3687	35	29	for	for	ADP
ejpam-3687	35	30	each	each	DET
ejpam-3687	35	31	m	m	PROPN
ejpam-3687	35	32	≤	≤	ADJ
ejpam-3687	35	33	n.	n.	NOUN
ejpam-3687	35	34	for	for	ADP
ejpam-3687	35	35	any	any	DET
ejpam-3687	35	36	real	real	ADJ
ejpam-3687	35	37	number	number	NOUN
ejpam-3687	35	38	β	β	NOUN
ejpam-3687	35	39	,	,	PUNCT
ejpam-3687	35	40	γβ	γβ	PROPN
ejpam-3687	35	41	denotes	denote	VERB
ejpam-3687	35	42	the	the	DET
ejpam-3687	35	43	set	set	NOUN
ejpam-3687	35	44	of	of	ADP
ejpam-3687	35	45	all	all	DET
ejpam-3687	35	46	increasing	increase	VERB
ejpam-3687	35	47	functions	function	NOUN
ejpam-3687	35	48	γβ	γβ	NOUN
ejpam-3687	35	49	:	:	PUNCT
ejpam-3687	36	1	[	[	X
ejpam-3687	36	2	1,∞	1,∞	NUM
ejpam-3687	36	3	)	)	PUNCT
ejpam-3687	36	4	→	→	PUNCT
ejpam-3687	37	1	[	[	X
ejpam-3687	37	2	0,∞	0,∞	NUM
ejpam-3687	37	3	)	)	PUNCT
ejpam-3687	37	4	such	such	ADJ
ejpam-3687	37	5	that	that	SCONJ
ejpam-3687	37	6	each	each	PRON
ejpam-3687	37	7	{	{	PUNCT
ejpam-3687	37	8	γn	γn	NOUN
ejpam-3687	37	9	}	}	PUNCT
ejpam-3687	37	10	is	be	AUX
ejpam-3687	37	11	a	a	DET
ejpam-3687	37	12	quasi	quasi	ADJ
ejpam-3687	37	13	β	β	NOUN
ejpam-3687	37	14	-	-	ADJ
ejpam-3687	37	15	power	power	NOUN
ejpam-3687	37	16	monotone	monotone	NOUN
ejpam-3687	37	17	decreasing	decrease	VERB
ejpam-3687	37	18	sequence	sequence	NOUN
ejpam-3687	37	19	.	.	PUNCT
ejpam-3687	38	1	2	2	X
ejpam-3687	38	2	.	.	X
ejpam-3687	38	3	main	main	ADJ
ejpam-3687	38	4	results	result	NOUN
ejpam-3687	38	5	theorem	theorem	VERB
ejpam-3687	38	6	1	1	NUM
ejpam-3687	38	7	.	.	PUNCT
ejpam-3687	39	1	let	let	VERB
ejpam-3687	39	2	{	{	PUNCT
ejpam-3687	39	3	ϕn}∞n=0	ϕn}∞n=0	NUM
ejpam-3687	39	4	⊂	⊂	PROPN
ejpam-3687	39	5	l2[0	l2[0	PROPN
ejpam-3687	39	6	,	,	PUNCT
ejpam-3687	39	7	1	1	NUM
ejpam-3687	39	8	]	]	PUNCT
ejpam-3687	39	9	be	be	AUX
ejpam-3687	39	10	an	an	DET
ejpam-3687	39	11	orthonormal	orthonormal	ADJ
ejpam-3687	39	12	system	system	NOUN
ejpam-3687	39	13	,	,	PUNCT
ejpam-3687	39	14	hα	hα	ADP
ejpam-3687	39	15	µ	µ	PRON
ejpam-3687	39	16	an	an	DET
ejpam-3687	39	17	e	e	PROPN
ejpam-3687	39	18	-	-	PROPN
ejpam-3687	39	19	j	j	ADJ
ejpam-3687	39	20	hausdorff	hausdorff	NOUN
ejpam-3687	39	21	matrix	matrix	NOUN
ejpam-3687	39	22	with	with	ADP
ejpam-3687	39	23	χ	χ	DET
ejpam-3687	39	24	monotone	monotone	NOUN
ejpam-3687	39	25	decreasing	decreasing	NOUN
ejpam-3687	39	26	,	,	PUNCT
ejpam-3687	39	27	γ	γ	X
ejpam-3687	39	28	∈	∈	PROPN
ejpam-3687	39	29	γβ	γβ	NOUN
ejpam-3687	39	30	for	for	ADP
ejpam-3687	39	31	β	β	X
ejpam-3687	39	32	>	>	X
ejpam-3687	39	33	1	1	NUM
ejpam-3687	39	34	−	−	NUM
ejpam-3687	39	35	1	1	NUM
ejpam-3687	39	36	/	/	SYM
ejpam-3687	39	37	k	k	NOUN
ejpam-3687	39	38	,	,	PUNCT
ejpam-3687	39	39	1	1	NUM
ejpam-3687	39	40	≤	≤	NUM
ejpam-3687	39	41	k	k	X
ejpam-3687	39	42	≤	≤	ADJ
ejpam-3687	39	43	2	2	NUM
ejpam-3687	39	44	.	.	PUNCT
ejpam-3687	40	1	then	then	ADV
ejpam-3687	40	2	every	every	DET
ejpam-3687	40	3	orthogonal	orthogonal	ADJ
ejpam-3687	40	4	series	series	NOUN
ejpam-3687	40	5	∑∞	∑∞	NOUN
ejpam-3687	40	6	n=0	n=0	PUNCT
ejpam-3687	40	7	bnϕn	bnϕn	NOUN
ejpam-3687	40	8	is	be	AUX
ejpam-3687	40	9	|hα	|hα	NUM
ejpam-3687	40	10	,	,	PUNCT
ejpam-3687	40	11	γ|	γ|	ADJ
ejpam-3687	40	12	summable	summable	ADJ
ejpam-3687	40	13	.	.	PUNCT
ejpam-3687	41	1	the	the	DET
ejpam-3687	41	2	following	follow	VERB
ejpam-3687	41	3	lemmas	lemmas	PROPN
ejpam-3687	41	4	will	will	AUX
ejpam-3687	41	5	be	be	AUX
ejpam-3687	41	6	needed	need	VERB
ejpam-3687	41	7	in	in	ADP
ejpam-3687	41	8	the	the	DET
ejpam-3687	41	9	proof	proof	NOUN
ejpam-3687	41	10	of	of	ADP
ejpam-3687	41	11	theorem	theorem	NOUN
ejpam-3687	41	12	1	1	NUM
ejpam-3687	41	13	.	.	PUNCT
ejpam-3687	41	14	f.	f.	PROPN
ejpam-3687	41	15	aydin	aydin	PROPN
ejpam-3687	41	16	akgun	akgun	PROPN
ejpam-3687	41	17	,	,	PUNCT
ejpam-3687	41	18	b.	b.	PROPN
ejpam-3687	41	19	e.	e.	PROPN
ejpam-3687	41	20	rhoades	rhoades	PROPN
ejpam-3687	41	21	/	/	SYM
ejpam-3687	41	22	eur	eur	PROPN
ejpam-3687	41	23	.	.	PUNCT
ejpam-3687	42	1	j.	j.	PROPN
ejpam-3687	42	2	pure	pure	PROPN
ejpam-3687	42	3	appl	appl	PROPN
ejpam-3687	42	4	.	.	PROPN
ejpam-3687	42	5	math	math	PROPN
ejpam-3687	42	6	,	,	PUNCT
ejpam-3687	42	7	13	13	NUM
ejpam-3687	42	8	(	(	PUNCT
ejpam-3687	42	9	3	3	NUM
ejpam-3687	42	10	)	)	PUNCT
ejpam-3687	42	11	(	(	PUNCT
ejpam-3687	42	12	2020	2020	NUM
ejpam-3687	42	13	)	)	PUNCT
ejpam-3687	42	14	,	,	PUNCT
ejpam-3687	42	15	390	390	NUM
ejpam-3687	42	16	-	-	SYM
ejpam-3687	42	17	402	402	NUM
ejpam-3687	42	18	392	392	NUM
ejpam-3687	42	19	lemma	lemma	PROPN
ejpam-3687	42	20	1	1	NUM
ejpam-3687	42	21	.	.	PUNCT
ejpam-3687	43	1	let	let	VERB
ejpam-3687	43	2	hα	hα	PART
ejpam-3687	43	3	be	be	AUX
ejpam-3687	43	4	an	an	DET
ejpam-3687	43	5	e	e	NOUN
ejpam-3687	43	6	-	-	NOUN
ejpam-3687	43	7	j	j	ADJ
ejpam-3687	43	8	matrix	matrix	NOUN
ejpam-3687	43	9	with	with	ADP
ejpam-3687	43	10	entries	entry	NOUN
ejpam-3687	43	11	(	(	PUNCT
ejpam-3687	43	12	hnk	hnk	PROPN
ejpam-3687	43	13	)	)	PUNCT
ejpam-3687	43	14	,	,	PUNCT
ejpam-3687	43	15	where	where	SCONJ
ejpam-3687	43	16	χ	χ	NOUN
ejpam-3687	43	17	is	be	AUX
ejpam-3687	43	18	a	a	DET
ejpam-3687	43	19	monotonically	monotonically	ADV
ejpam-3687	43	20	increasing	increase	VERB
ejpam-3687	43	21	mass	mass	ADJ
ejpam-3687	43	22	function	function	NOUN
ejpam-3687	43	23	on	on	ADP
ejpam-3687	43	24	[	[	X
ejpam-3687	43	25	0	0	NUM
ejpam-3687	43	26	,	,	PUNCT
ejpam-3687	43	27	1	1	NUM
ejpam-3687	43	28	]	]	PUNCT
ejpam-3687	43	29	associated	associate	VERB
ejpam-3687	43	30	with	with	ADP
ejpam-3687	43	31	the	the	DET
ejpam-3687	43	32	µn	µn	PROPN
ejpam-3687	43	33	.	.	PUNCT
ejpam-3687	44	1	then	then	ADV
ejpam-3687	44	2	(	(	PUNCT
ejpam-3687	44	3	i	i	NOUN
ejpam-3687	44	4	)	)	PUNCT
ejpam-3687	44	5	amn	amn	PROPN
ejpam-3687	44	6	=	=	SYM
ejpam-3687	44	7	k	k	PROPN
ejpam-3687	44	8	(	(	PUNCT
ejpam-3687	44	9	n−	n−	NOUN
ejpam-3687	44	10	1	1	NUM
ejpam-3687	44	11	+	+	CCONJ
ejpam-3687	44	12	α	α	NOUN
ejpam-3687	44	13	m−	m−	PROPN
ejpam-3687	44	14	1	1	NUM
ejpam-3687	44	15	+	+	CCONJ
ejpam-3687	44	16	α	α	NOUN
ejpam-3687	44	17	)	)	PUNCT
ejpam-3687	44	18	ξm+α(1−	ξm+α(1−	NUM
ejpam-3687	44	19	ξ)n−m	ξ)n−m	NOUN
ejpam-3687	44	20	for	for	ADP
ejpam-3687	44	21	some	some	DET
ejpam-3687	44	22	ξ	ξ	PROPN
ejpam-3687	44	23	∈	∈	PROPN
ejpam-3687	44	24	(	(	PUNCT
ejpam-3687	44	25	0	0	NUM
ejpam-3687	44	26	,	,	PUNCT
ejpam-3687	44	27	1	1	NUM
ejpam-3687	44	28	)	)	PUNCT
ejpam-3687	44	29	,	,	PUNCT
ejpam-3687	44	30	(	(	PUNCT
ejpam-3687	44	31	ii	ii	NOUN
ejpam-3687	44	32	)	)	PUNCT
ejpam-3687	44	33	n∑	n∑	PROPN
ejpam-3687	44	34	m=0	m=0	PROPN
ejpam-3687	44	35	|amn|2|bm|2	|amn|2|bm|2	VERB
ejpam-3687	44	36	≤	≤	ADJ
ejpam-3687	44	37	k2	k2	PROPN
ejpam-3687	44	38	n∑	n∑	PROPN
ejpam-3687	44	39	m=0	m=0	PROPN
ejpam-3687	44	40	|bm|2	|bm|2	PUNCT
ejpam-3687	44	41	for	for	ADP
ejpam-3687	44	42	all	all	DET
ejpam-3687	44	43	bn	bn	NOUN
ejpam-3687	44	44	∈	∈	PROPN
ejpam-3687	44	45	c	c	NOUN
ejpam-3687	44	46	and	and	CCONJ
ejpam-3687	44	47	n	n	CCONJ
ejpam-3687	44	48	∈	∈	PROPN
ejpam-3687	44	49	n	n	CCONJ
ejpam-3687	44	50	,	,	PUNCT
ejpam-3687	44	51	where	where	SCONJ
ejpam-3687	44	52	k	k	PROPN
ejpam-3687	44	53	=	=	SYM
ejpam-3687	44	54	χ(1)−	χ(1)−	PROPN
ejpam-3687	44	55	χ(0	χ(0	PROPN
ejpam-3687	44	56	)	)	PUNCT
ejpam-3687	44	57	and	and	CCONJ
ejpam-3687	44	58	amn	amn	PROPN
ejpam-3687	44	59	=	=	PUNCT
ejpam-3687	45	1	∑n	∑n	PROPN
ejpam-3687	46	1	k	k	NOUN
ejpam-3687	46	2	=	=	NOUN
ejpam-3687	46	3	m	m	PROPN
ejpam-3687	46	4	|h	|h	NOUN
ejpam-3687	46	5	(	(	PUNCT
ejpam-3687	46	6	α	α	NOUN
ejpam-3687	46	7	)	)	PUNCT
ejpam-3687	46	8	nk	nk	PROPN
ejpam-3687	46	9	−	−	PROPN
ejpam-3687	47	1	h	h	NOUN
ejpam-3687	47	2	(	(	PUNCT
ejpam-3687	47	3	α	α	NOUN
ejpam-3687	47	4	)	)	PUNCT
ejpam-3687	47	5	n−1,k|	n−1,k|	NOUN
ejpam-3687	47	6	.	.	PUNCT
ejpam-3687	48	1	here	here	ADV
ejpam-3687	48	2	c	c	NOUN
ejpam-3687	48	3	=	=	SYM
ejpam-3687	48	4	complex	complex	ADJ
ejpam-3687	48	5	numbers	number	NOUN
ejpam-3687	48	6	and	and	CCONJ
ejpam-3687	48	7	n	n	CCONJ
ejpam-3687	48	8	=	=	CCONJ
ejpam-3687	48	9	natural	natural	ADJ
ejpam-3687	48	10	numbers	number	NOUN
ejpam-3687	48	11	.	.	PUNCT
ejpam-3687	49	1	proof	proof	NOUN
ejpam-3687	49	2	.	.	PUNCT
ejpam-3687	50	1	(	(	PUNCT
ejpam-3687	50	2	i	i	NOUN
ejpam-3687	50	3	)	)	PUNCT
ejpam-3687	50	4	we	we	PRON
ejpam-3687	50	5	consider	consider	VERB
ejpam-3687	50	6	h	h	NOUN
ejpam-3687	50	7	(	(	PUNCT
ejpam-3687	50	8	α	α	NOUN
ejpam-3687	50	9	)	)	PUNCT
ejpam-3687	50	10	nk	nk	PROPN
ejpam-3687	50	11	−	−	PROPN
ejpam-3687	50	12	h	h	NOUN
ejpam-3687	50	13	(	(	PUNCT
ejpam-3687	50	14	α	α	NOUN
ejpam-3687	50	15	)	)	PUNCT
ejpam-3687	50	16	n−1,k	n−1,k	PROPN
ejpam-3687	50	17	(	(	PUNCT
ejpam-3687	50	18	2	2	NUM
ejpam-3687	50	19	)	)	PUNCT
ejpam-3687	50	20	=	=	NOUN
ejpam-3687	51	1	[	[	PUNCT
ejpam-3687	51	2	∫	∫	PROPN
ejpam-3687	51	3	1	1	NUM
ejpam-3687	51	4	0	0	NUM
ejpam-3687	51	5	µk+α(1−	µk+α(1−	PROPN
ejpam-3687	51	6	µ)n−k	µ)n−k	PUNCT
ejpam-3687	51	7	(	(	PUNCT
ejpam-3687	51	8	n+	n+	ADP
ejpam-3687	51	9	α	α	X
ejpam-3687	51	10	k	k	PROPN
ejpam-3687	51	11	+	+	CCONJ
ejpam-3687	51	12	α	α	X
ejpam-3687	51	13	)	)	PUNCT
ejpam-3687	51	14	dχ(µ)−	dχ(µ)−	PROPN
ejpam-3687	51	15	∫	∫	PROPN
ejpam-3687	52	1	1	1	NUM
ejpam-3687	52	2	0	0	NUM
ejpam-3687	52	3	µk+α(1−	µk+α(1−	PRON
ejpam-3687	52	4	µ)n−1−k	µ)n−1−k	PROPN
ejpam-3687	52	5	(	(	PUNCT
ejpam-3687	52	6	n−	n−	NOUN
ejpam-3687	52	7	1	1	NUM
ejpam-3687	52	8	+	+	CCONJ
ejpam-3687	52	9	α	α	NOUN
ejpam-3687	52	10	k	k	X
ejpam-3687	53	1	+	+	CCONJ
ejpam-3687	53	2	α	α	NOUN
ejpam-3687	53	3	)	)	PUNCT
ejpam-3687	53	4	dχ(µ	dχ(µ	NOUN
ejpam-3687	53	5	)	)	PUNCT
ejpam-3687	53	6	]	]	PUNCT
ejpam-3687	54	1	=	=	PUNCT
ejpam-3687	54	2	∫	∫	PROPN
ejpam-3687	54	3	1	1	NUM
ejpam-3687	54	4	0	0	NUM
ejpam-3687	54	5	µk+α(1−	µk+α(1−	PROPN
ejpam-3687	54	6	µ)n−k	µ)n−k	PUNCT
ejpam-3687	55	1	[	[	X
ejpam-3687	55	2	(	(	PUNCT
ejpam-3687	55	3	n+	n+	NOUN
ejpam-3687	55	4	α	α	X
ejpam-3687	55	5	k	k	NOUN
ejpam-3687	56	1	+	+	CCONJ
ejpam-3687	56	2	α	α	NOUN
ejpam-3687	56	3	)	)	PUNCT
ejpam-3687	56	4	−	−	PROPN
ejpam-3687	57	1	(	(	PUNCT
ejpam-3687	57	2	n−	n−	NOUN
ejpam-3687	57	3	1	1	NUM
ejpam-3687	57	4	+	+	CCONJ
ejpam-3687	57	5	α	α	NOUN
ejpam-3687	57	6	k	k	X
ejpam-3687	58	1	+	+	CCONJ
ejpam-3687	58	2	α	α	NOUN
ejpam-3687	58	3	)	)	PUNCT
ejpam-3687	58	4	1	1	NUM
ejpam-3687	58	5	1−	1−	NUM
ejpam-3687	58	6	µ	µ	X
ejpam-3687	58	7	]	]	PUNCT
ejpam-3687	58	8	dχ(µ	dχ(µ	NOUN
ejpam-3687	58	9	)	)	PUNCT
ejpam-3687	58	10	,	,	PUNCT
ejpam-3687	58	11	where	where	SCONJ
ejpam-3687	58	12	0	0	NUM
ejpam-3687	58	13	≤	≤	NUM
ejpam-3687	58	14	k	k	X
ejpam-3687	58	15	≤	≤	PROPN
ejpam-3687	58	16	n.	n.	NOUN
ejpam-3687	58	17	since	since	SCONJ
ejpam-3687	58	18	(	(	PUNCT
ejpam-3687	58	19	n+	n+	INTJ
ejpam-3687	58	20	α	α	X
ejpam-3687	58	21	k	k	PROPN
ejpam-3687	58	22	+	+	CCONJ
ejpam-3687	58	23	α	α	NOUN
ejpam-3687	58	24	)	)	PUNCT
ejpam-3687	58	25	−	−	PROPN
ejpam-3687	58	26	(	(	PUNCT
ejpam-3687	58	27	n−	n−	NOUN
ejpam-3687	58	28	1	1	NUM
ejpam-3687	58	29	+	+	CCONJ
ejpam-3687	58	30	α	α	NOUN
ejpam-3687	58	31	k	k	X
ejpam-3687	59	1	+	+	CCONJ
ejpam-3687	59	2	α	α	NOUN
ejpam-3687	59	3	)	)	PUNCT
ejpam-3687	60	1	=	=	PUNCT
ejpam-3687	60	2	(	(	PUNCT
ejpam-3687	60	3	n−	n−	NOUN
ejpam-3687	60	4	1	1	NUM
ejpam-3687	60	5	+	+	CCONJ
ejpam-3687	60	6	α	α	NOUN
ejpam-3687	60	7	k	k	NOUN
ejpam-3687	61	1	−	−	PROPN
ejpam-3687	61	2	1	1	NUM
ejpam-3687	61	3	+	+	NUM
ejpam-3687	61	4	α	α	NOUN
ejpam-3687	61	5	)	)	PUNCT
ejpam-3687	61	6	,	,	PUNCT
ejpam-3687	61	7	from	from	ADP
ejpam-3687	61	8	(	(	PUNCT
ejpam-3687	61	9	2),∫	2),∫	NUM
ejpam-3687	61	10	1	1	NUM
ejpam-3687	61	11	0	0	NUM
ejpam-3687	61	12	µk+α(1−	µk+α(1−	PRON
ejpam-3687	61	13	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	62	1	[	[	X
ejpam-3687	62	2	(	(	PUNCT
ejpam-3687	62	3	n+	n+	ADP
ejpam-3687	62	4	α	α	X
ejpam-3687	62	5	k	k	NOUN
ejpam-3687	63	1	+	+	CCONJ
ejpam-3687	63	2	α	α	NOUN
ejpam-3687	63	3	)	)	PUNCT
ejpam-3687	63	4	(	(	PUNCT
ejpam-3687	63	5	1−	1−	NUM
ejpam-3687	64	1	µ)−	µ)−	NOUN
ejpam-3687	64	2	(	(	PUNCT
ejpam-3687	64	3	n−	n−	NOUN
ejpam-3687	64	4	1	1	NUM
ejpam-3687	64	5	+	+	CCONJ
ejpam-3687	64	6	α	α	NOUN
ejpam-3687	64	7	k	k	X
ejpam-3687	65	1	+	+	CCONJ
ejpam-3687	65	2	α	α	NOUN
ejpam-3687	65	3	)	)	PUNCT
ejpam-3687	65	4	]	]	PUNCT
ejpam-3687	65	5	dχ(µ	dχ(µ	PRON
ejpam-3687	65	6	)	)	PUNCT
ejpam-3687	66	1	=	=	SYM
ejpam-3687	66	2	∫	∫	PROPN
ejpam-3687	67	1	1	1	NUM
ejpam-3687	67	2	0	0	NUM
ejpam-3687	67	3	µk+α(1−	µk+α(1−	PRON
ejpam-3687	67	4	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	68	1	[	[	X
ejpam-3687	68	2	(	(	PUNCT
ejpam-3687	68	3	n+	n+	ADP
ejpam-3687	68	4	α	α	X
ejpam-3687	68	5	k	k	PROPN
ejpam-3687	69	1	+	+	CCONJ
ejpam-3687	69	2	α	α	NOUN
ejpam-3687	69	3	)	)	PUNCT
ejpam-3687	69	4	−	−	PROPN
ejpam-3687	70	1	(	(	PUNCT
ejpam-3687	70	2	n−	n−	NOUN
ejpam-3687	70	3	1	1	NUM
ejpam-3687	70	4	+	+	CCONJ
ejpam-3687	70	5	α	α	NOUN
ejpam-3687	70	6	k	k	X
ejpam-3687	71	1	+	+	CCONJ
ejpam-3687	71	2	α	α	NOUN
ejpam-3687	71	3	)	)	PUNCT
ejpam-3687	72	1	−	−	PROPN
ejpam-3687	72	2	µ	µ	X
ejpam-3687	72	3	(	(	PUNCT
ejpam-3687	72	4	n+	n+	ADP
ejpam-3687	72	5	α	α	X
ejpam-3687	72	6	k	k	PROPN
ejpam-3687	73	1	+	+	CCONJ
ejpam-3687	73	2	α	α	NOUN
ejpam-3687	73	3	)	)	PUNCT
ejpam-3687	73	4	]	]	PUNCT
ejpam-3687	73	5	dχ(µ	dχ(µ	PRON
ejpam-3687	73	6	)	)	PUNCT
ejpam-3687	74	1	=	=	SYM
ejpam-3687	74	2	∫	∫	PROPN
ejpam-3687	75	1	1	1	NUM
ejpam-3687	75	2	0	0	NUM
ejpam-3687	75	3	µk+α(1−	µk+α(1−	PRON
ejpam-3687	75	4	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	76	1	[	[	X
ejpam-3687	76	2	(	(	PUNCT
ejpam-3687	76	3	n−	n−	NOUN
ejpam-3687	76	4	1	1	NUM
ejpam-3687	76	5	+	+	CCONJ
ejpam-3687	76	6	α	α	NOUN
ejpam-3687	76	7	k	k	NOUN
ejpam-3687	77	1	−	−	PROPN
ejpam-3687	77	2	1	1	NUM
ejpam-3687	77	3	+	+	NUM
ejpam-3687	77	4	α	α	NOUN
ejpam-3687	77	5	)	)	PUNCT
ejpam-3687	77	6	−	−	PROPN
ejpam-3687	77	7	µ	µ	X
ejpam-3687	77	8	(	(	PUNCT
ejpam-3687	77	9	n+	n+	ADP
ejpam-3687	77	10	α	α	X
ejpam-3687	77	11	k	k	PROPN
ejpam-3687	77	12	+	+	CCONJ
ejpam-3687	77	13	α	α	NOUN
ejpam-3687	77	14	)	)	PUNCT
ejpam-3687	77	15	]	]	PUNCT
ejpam-3687	77	16	dχ(µ	dχ(µ	PRON
ejpam-3687	77	17	)	)	PUNCT
ejpam-3687	77	18	.	.	PUNCT
ejpam-3687	78	1	thus	thus	ADV
ejpam-3687	78	2	amn	amn	PROPN
ejpam-3687	78	3	=	=	SYM
ejpam-3687	78	4	n∑	n∑	PROPN
ejpam-3687	78	5	k	k	PROPN
ejpam-3687	79	1	=	=	NOUN
ejpam-3687	79	2	m	m	PROPN
ejpam-3687	79	3	(	(	PUNCT
ejpam-3687	79	4	h	h	NOUN
ejpam-3687	79	5	(	(	PUNCT
ejpam-3687	79	6	α	α	NOUN
ejpam-3687	79	7	)	)	PUNCT
ejpam-3687	79	8	nk	nk	PROPN
ejpam-3687	79	9	−	−	PROPN
ejpam-3687	79	10	h	h	NOUN
ejpam-3687	79	11	(	(	PUNCT
ejpam-3687	79	12	α	α	NOUN
ejpam-3687	79	13	)	)	PUNCT
ejpam-3687	79	14	n−1,k	n−1,k	PROPN
ejpam-3687	79	15	)	)	PUNCT
ejpam-3687	79	16	=	=	PUNCT
ejpam-3687	80	1	n∑	n∑	NOUN
ejpam-3687	80	2	k	k	PROPN
ejpam-3687	81	1	=	=	NOUN
ejpam-3687	81	2	m	m	NOUN
ejpam-3687	81	3	∫	∫	PROPN
ejpam-3687	81	4	1	1	NUM
ejpam-3687	81	5	0	0	NUM
ejpam-3687	81	6	µk+α(1−	µk+α(1−	PRON
ejpam-3687	81	7	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	82	1	[	[	X
ejpam-3687	82	2	(	(	PUNCT
ejpam-3687	82	3	n−	n−	NOUN
ejpam-3687	82	4	1	1	NUM
ejpam-3687	82	5	+	+	CCONJ
ejpam-3687	82	6	α	α	NOUN
ejpam-3687	82	7	k	k	NOUN
ejpam-3687	83	1	−	−	PROPN
ejpam-3687	83	2	1	1	NUM
ejpam-3687	83	3	+	+	NUM
ejpam-3687	83	4	α	α	NOUN
ejpam-3687	83	5	)	)	PUNCT
ejpam-3687	83	6	−	−	PROPN
ejpam-3687	83	7	µ	µ	X
ejpam-3687	83	8	(	(	PUNCT
ejpam-3687	83	9	n+	n+	ADP
ejpam-3687	83	10	α	α	X
ejpam-3687	83	11	k	k	PROPN
ejpam-3687	83	12	+	+	CCONJ
ejpam-3687	83	13	α	α	NOUN
ejpam-3687	83	14	)	)	PUNCT
ejpam-3687	83	15	]	]	PUNCT
ejpam-3687	83	16	dχ(µ	dχ(µ	PRON
ejpam-3687	83	17	)	)	PUNCT
ejpam-3687	83	18	=	=	SYM
ejpam-3687	84	1	∫	∫	PROPN
ejpam-3687	85	1	1	1	NUM
ejpam-3687	85	2	0	0	NUM
ejpam-3687	85	3	n∑	n∑	NOUN
ejpam-3687	85	4	k	k	X
ejpam-3687	86	1	=	=	NOUN
ejpam-3687	86	2	m	m	PROPN
ejpam-3687	86	3	µk+α(1−	µk+α(1−	X
ejpam-3687	86	4	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	86	5	[	[	X
ejpam-3687	86	6	(	(	PUNCT
ejpam-3687	86	7	n−	n−	NOUN
ejpam-3687	86	8	1	1	NUM
ejpam-3687	86	9	+	+	CCONJ
ejpam-3687	86	10	α	α	NOUN
ejpam-3687	86	11	k	k	NOUN
ejpam-3687	87	1	−	−	PROPN
ejpam-3687	87	2	1	1	NUM
ejpam-3687	87	3	+	+	NUM
ejpam-3687	87	4	α	α	NOUN
ejpam-3687	87	5	)	)	PUNCT
ejpam-3687	87	6	−	−	PROPN
ejpam-3687	87	7	µ	µ	X
ejpam-3687	87	8	(	(	PUNCT
ejpam-3687	87	9	n+	n+	ADP
ejpam-3687	87	10	α	α	X
ejpam-3687	87	11	k	k	PROPN
ejpam-3687	87	12	+	+	CCONJ
ejpam-3687	87	13	α	α	NOUN
ejpam-3687	87	14	)	)	PUNCT
ejpam-3687	87	15	]	]	PUNCT
ejpam-3687	87	16	dχ(µ	dχ(µ	PRON
ejpam-3687	87	17	)	)	PUNCT
ejpam-3687	87	18	.	.	PUNCT
ejpam-3687	88	1	from	from	ADP
ejpam-3687	88	2	the	the	DET
ejpam-3687	88	3	above	above	ADJ
ejpam-3687	88	4	inequality	inequality	NOUN
ejpam-3687	88	5	,	,	PUNCT
ejpam-3687	88	6	n∑	n∑	NOUN
ejpam-3687	88	7	k	k	X
ejpam-3687	88	8	=	=	NOUN
ejpam-3687	88	9	m	m	PROPN
ejpam-3687	88	10	µk+α(1−	µk+α(1−	X
ejpam-3687	88	11	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	89	1	[	[	X
ejpam-3687	89	2	(	(	PUNCT
ejpam-3687	89	3	n−	n−	NOUN
ejpam-3687	89	4	1	1	NUM
ejpam-3687	89	5	+	+	CCONJ
ejpam-3687	89	6	α	α	NOUN
ejpam-3687	89	7	k	k	NOUN
ejpam-3687	90	1	−	−	PROPN
ejpam-3687	90	2	1	1	NUM
ejpam-3687	90	3	+	+	NUM
ejpam-3687	90	4	α	α	NOUN
ejpam-3687	90	5	)	)	PUNCT
ejpam-3687	90	6	−	−	PROPN
ejpam-3687	90	7	µ	µ	X
ejpam-3687	90	8	(	(	PUNCT
ejpam-3687	90	9	n+	n+	ADP
ejpam-3687	90	10	α	α	X
ejpam-3687	90	11	k	k	PROPN
ejpam-3687	90	12	+	+	CCONJ
ejpam-3687	90	13	α	α	NOUN
ejpam-3687	90	14	)	)	PUNCT
ejpam-3687	90	15	]	]	PUNCT
ejpam-3687	91	1	f.	f.	PROPN
ejpam-3687	91	2	aydin	aydin	PROPN
ejpam-3687	91	3	akgun	akgun	PROPN
ejpam-3687	91	4	,	,	PUNCT
ejpam-3687	91	5	b.	b.	PROPN
ejpam-3687	91	6	e.	e.	PROPN
ejpam-3687	91	7	rhoades	rhoades	PROPN
ejpam-3687	91	8	/	/	SYM
ejpam-3687	91	9	eur	eur	PROPN
ejpam-3687	91	10	.	.	PUNCT
ejpam-3687	92	1	j.	j.	PROPN
ejpam-3687	92	2	pure	pure	PROPN
ejpam-3687	92	3	appl	appl	PROPN
ejpam-3687	92	4	.	.	PROPN
ejpam-3687	92	5	math	math	PROPN
ejpam-3687	92	6	,	,	PUNCT
ejpam-3687	92	7	13	13	NUM
ejpam-3687	92	8	(	(	PUNCT
ejpam-3687	92	9	3	3	NUM
ejpam-3687	92	10	)	)	PUNCT
ejpam-3687	92	11	(	(	PUNCT
ejpam-3687	92	12	2020	2020	NUM
ejpam-3687	92	13	)	)	PUNCT
ejpam-3687	92	14	,	,	PUNCT
ejpam-3687	92	15	390	390	NUM
ejpam-3687	92	16	-	-	SYM
ejpam-3687	92	17	402	402	NUM
ejpam-3687	92	18	393	393	NUM
ejpam-3687	92	19	=	=	SYM
ejpam-3687	92	20	n∑	n∑	NOUN
ejpam-3687	92	21	k	k	NOUN
ejpam-3687	93	1	=	=	NOUN
ejpam-3687	93	2	m	m	PROPN
ejpam-3687	93	3	µk+α(1−	µk+α(1−	PRON
ejpam-3687	93	4	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	93	5	(	(	PUNCT
ejpam-3687	93	6	n−	n−	NOUN
ejpam-3687	93	7	1	1	NUM
ejpam-3687	93	8	+	+	CCONJ
ejpam-3687	93	9	α	α	NOUN
ejpam-3687	93	10	k	k	NOUN
ejpam-3687	94	1	−	−	PROPN
ejpam-3687	94	2	1	1	NUM
ejpam-3687	94	3	+	+	NUM
ejpam-3687	94	4	α	α	NOUN
ejpam-3687	94	5	)	)	PUNCT
ejpam-3687	95	1	−	−	PROPN
ejpam-3687	95	2	n∑	n∑	INTJ
ejpam-3687	95	3	k	k	X
ejpam-3687	96	1	=	=	NOUN
ejpam-3687	96	2	m	m	PROPN
ejpam-3687	96	3	µk+α+1(1−	µk+α+1(1−	ADJ
ejpam-3687	96	4	µ)n−1−k	µ)n−1−k	PROPN
ejpam-3687	96	5	(	(	PUNCT
ejpam-3687	96	6	n+	n+	ADP
ejpam-3687	96	7	α	α	X
ejpam-3687	96	8	k	k	NOUN
ejpam-3687	96	9	+	+	CCONJ
ejpam-3687	96	10	α	α	NOUN
ejpam-3687	96	11	)	)	PUNCT
ejpam-3687	97	1	=	=	PUNCT
ejpam-3687	97	2	n∑	n∑	NOUN
ejpam-3687	98	1	k	k	X
ejpam-3687	99	1	=	=	NOUN
ejpam-3687	99	2	m	m	PROPN
ejpam-3687	99	3	µk+α(1−	µk+α(1−	PRON
ejpam-3687	99	4	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	99	5	(	(	PUNCT
ejpam-3687	99	6	n−	n−	NOUN
ejpam-3687	99	7	1	1	NUM
ejpam-3687	99	8	+	+	CCONJ
ejpam-3687	99	9	α	α	NOUN
ejpam-3687	99	10	k	k	NOUN
ejpam-3687	100	1	−	−	PROPN
ejpam-3687	100	2	1	1	NUM
ejpam-3687	100	3	+	+	NUM
ejpam-3687	100	4	α	α	NOUN
ejpam-3687	100	5	)	)	PUNCT
ejpam-3687	101	1	−	−	PROPN
ejpam-3687	101	2	n∑	n∑	INTJ
ejpam-3687	101	3	k	k	X
ejpam-3687	102	1	=	=	NOUN
ejpam-3687	102	2	m	m	PROPN
ejpam-3687	102	3	µk+α+1(1−	µk+α+1(1−	NOUN
ejpam-3687	102	4	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	102	5	[	[	X
ejpam-3687	102	6	(	(	PUNCT
ejpam-3687	102	7	n−	n−	NOUN
ejpam-3687	102	8	1	1	NUM
ejpam-3687	102	9	+	+	CCONJ
ejpam-3687	102	10	α	α	NOUN
ejpam-3687	102	11	k	k	NOUN
ejpam-3687	102	12	−	−	PROPN
ejpam-3687	102	13	1	1	NUM
ejpam-3687	102	14	+	+	NUM
ejpam-3687	102	15	α	α	NOUN
ejpam-3687	102	16	)	)	PUNCT
ejpam-3687	103	1	+	+	CCONJ
ejpam-3687	103	2	(	(	PUNCT
ejpam-3687	103	3	n−	n−	NOUN
ejpam-3687	103	4	1	1	NUM
ejpam-3687	103	5	+	+	CCONJ
ejpam-3687	103	6	α	α	NOUN
ejpam-3687	103	7	k	k	X
ejpam-3687	104	1	+	+	CCONJ
ejpam-3687	104	2	α	α	NOUN
ejpam-3687	104	3	)	)	PUNCT
ejpam-3687	104	4	]	]	PUNCT
ejpam-3687	105	1	=	=	PUNCT
ejpam-3687	105	2	n∑	n∑	NOUN
ejpam-3687	106	1	k	k	X
ejpam-3687	107	1	=	=	NOUN
ejpam-3687	107	2	m	m	PROPN
ejpam-3687	107	3	µk+α(1−	µk+α(1−	VERB
ejpam-3687	107	4	µ)n−k	µ)n−k	PUNCT
ejpam-3687	107	5	(	(	PUNCT
ejpam-3687	107	6	n−	n−	NOUN
ejpam-3687	107	7	1	1	NUM
ejpam-3687	108	1	+	+	CCONJ
ejpam-3687	108	2	α	α	NOUN
ejpam-3687	108	3	k	k	NOUN
ejpam-3687	109	1	−	−	PROPN
ejpam-3687	109	2	1	1	NUM
ejpam-3687	109	3	+	+	NUM
ejpam-3687	109	4	α	α	NOUN
ejpam-3687	109	5	)	)	PUNCT
ejpam-3687	110	1	−	−	PROPN
ejpam-3687	110	2	n∑	n∑	INTJ
ejpam-3687	110	3	k	k	X
ejpam-3687	111	1	=	=	NOUN
ejpam-3687	111	2	m	m	PROPN
ejpam-3687	111	3	µk+α+1(1−	µk+α+1(1−	ADJ
ejpam-3687	111	4	µ)n−1−k	µ)n−1−k	NOUN
ejpam-3687	111	5	(	(	PUNCT
ejpam-3687	111	6	n−	n−	NOUN
ejpam-3687	111	7	1	1	NUM
ejpam-3687	111	8	+	+	CCONJ
ejpam-3687	111	9	α	α	NOUN
ejpam-3687	111	10	k	k	X
ejpam-3687	112	1	+	+	CCONJ
ejpam-3687	112	2	α	α	NOUN
ejpam-3687	112	3	)	)	PUNCT
ejpam-3687	113	1	=	=	PUNCT
ejpam-3687	113	2	n∑	n∑	NOUN
ejpam-3687	114	1	k	k	X
ejpam-3687	115	1	=	=	NOUN
ejpam-3687	115	2	m	m	PROPN
ejpam-3687	115	3	µk+α(1−	µk+α(1−	VERB
ejpam-3687	115	4	µ)n−k	µ)n−k	PUNCT
ejpam-3687	116	1	(	(	PUNCT
ejpam-3687	116	2	n−	n−	NOUN
ejpam-3687	116	3	1	1	NUM
ejpam-3687	116	4	+	+	CCONJ
ejpam-3687	116	5	α	α	NOUN
ejpam-3687	116	6	k	k	NOUN
ejpam-3687	117	1	−	−	PROPN
ejpam-3687	117	2	1	1	NUM
ejpam-3687	117	3	+	+	NUM
ejpam-3687	117	4	α	α	NOUN
ejpam-3687	117	5	)	)	PUNCT
ejpam-3687	118	1	−	−	PROPN
ejpam-3687	118	2	n+1∑	n+1∑	ADV
ejpam-3687	118	3	g	g	PROPN
ejpam-3687	118	4	=	=	NOUN
ejpam-3687	118	5	m+1	m+1	PROPN
ejpam-3687	118	6	µg+α(1−	µg+α(1−	PUNCT
ejpam-3687	118	7	µ)n−g	µ)n−g	NOUN
ejpam-3687	118	8	(	(	PUNCT
ejpam-3687	118	9	n−	n−	NOUN
ejpam-3687	118	10	1	1	NUM
ejpam-3687	118	11	+	+	CCONJ
ejpam-3687	118	12	α	α	NOUN
ejpam-3687	118	13	g	g	NOUN
ejpam-3687	118	14	−	−	PROPN
ejpam-3687	118	15	1	1	NUM
ejpam-3687	118	16	+	+	NUM
ejpam-3687	118	17	α	α	NOUN
ejpam-3687	118	18	)	)	PUNCT
ejpam-3687	118	19	=	=	PUNCT
ejpam-3687	119	1	µm+α(1−	µm+α(1−	NOUN
ejpam-3687	119	2	µ)n−m	µ)n−m	PUNCT
ejpam-3687	119	3	(	(	PUNCT
ejpam-3687	119	4	n−	n−	NOUN
ejpam-3687	119	5	1	1	NUM
ejpam-3687	119	6	+	+	CCONJ
ejpam-3687	119	7	α	α	NOUN
ejpam-3687	119	8	m−	m−	PROPN
ejpam-3687	119	9	1	1	NUM
ejpam-3687	119	10	+	+	CCONJ
ejpam-3687	119	11	α	α	NOUN
ejpam-3687	119	12	)	)	PUNCT
ejpam-3687	119	13	,	,	PUNCT
ejpam-3687	119	14	and	and	CCONJ
ejpam-3687	119	15	0	0	NUM
ejpam-3687	119	16	≤	≤	NUM
ejpam-3687	119	17	amn	amn	PROPN
ejpam-3687	119	18	≤	≤	ADJ
ejpam-3687	119	19	∫	∫	PROPN
ejpam-3687	119	20	1	1	NUM
ejpam-3687	119	21	0	0	NUM
ejpam-3687	119	22	µm+α(1−	µm+α(1−	X
ejpam-3687	119	23	µ)n−m	µ)n−m	X
ejpam-3687	119	24	(	(	PUNCT
ejpam-3687	119	25	n−	n−	NOUN
ejpam-3687	119	26	1	1	NUM
ejpam-3687	119	27	+	+	CCONJ
ejpam-3687	119	28	α	α	NOUN
ejpam-3687	119	29	m−	m−	PROPN
ejpam-3687	119	30	1	1	NUM
ejpam-3687	119	31	+	+	CCONJ
ejpam-3687	119	32	α	α	NOUN
ejpam-3687	119	33	)	)	PUNCT
ejpam-3687	119	34	dχ(µ	dχ(µ	NOUN
ejpam-3687	119	35	)	)	PUNCT
ejpam-3687	119	36	.	.	PUNCT
ejpam-3687	120	1	(	(	PUNCT
ejpam-3687	120	2	3	3	X
ejpam-3687	120	3	)	)	PUNCT
ejpam-3687	120	4	using	use	VERB
ejpam-3687	120	5	the	the	DET
ejpam-3687	120	6	first	first	ADJ
ejpam-3687	120	7	mean	mean	NOUN
ejpam-3687	120	8	value	value	NOUN
ejpam-3687	120	9	theorem	theorem	NOUN
ejpam-3687	120	10	for	for	ADP
ejpam-3687	120	11	integrals	integral	NOUN
ejpam-3687	120	12	,	,	PUNCT
ejpam-3687	120	13	for	for	ADP
ejpam-3687	120	14	some	some	PRON
ejpam-3687	120	15	0	0	NUM
ejpam-3687	120	16	<	<	X
ejpam-3687	120	17	ξ	ξ	X
ejpam-3687	120	18	<	<	X
ejpam-3687	120	19	1,∫	1,∫	NUM
ejpam-3687	120	20	1	1	NUM
ejpam-3687	120	21	0	0	NUM
ejpam-3687	120	22	µm+α(1−	µm+α(1−	PUNCT
ejpam-3687	120	23	µ)n−m	µ)n−m	PUNCT
ejpam-3687	120	24	(	(	PUNCT
ejpam-3687	120	25	n−	n−	NOUN
ejpam-3687	120	26	1	1	NUM
ejpam-3687	120	27	+	+	CCONJ
ejpam-3687	120	28	α	α	NOUN
ejpam-3687	120	29	m−	m−	PROPN
ejpam-3687	120	30	1	1	NUM
ejpam-3687	120	31	+	+	CCONJ
ejpam-3687	120	32	α	α	NOUN
ejpam-3687	120	33	)	)	PUNCT
ejpam-3687	120	34	dχ(µ	dχ(µ	NOUN
ejpam-3687	120	35	)	)	PUNCT
ejpam-3687	121	1	=	=	PUNCT
ejpam-3687	122	1	ξm+α(1−	ξm+α(1−	NUM
ejpam-3687	122	2	ξ)n−m	ξ)n−m	NOUN
ejpam-3687	122	3	(	(	PUNCT
ejpam-3687	122	4	n−	n−	NOUN
ejpam-3687	122	5	1	1	NUM
ejpam-3687	122	6	+	+	CCONJ
ejpam-3687	122	7	α	α	NOUN
ejpam-3687	122	8	m−	m−	PROPN
ejpam-3687	122	9	1	1	NUM
ejpam-3687	122	10	+	+	CCONJ
ejpam-3687	122	11	α	α	NOUN
ejpam-3687	122	12	)	)	PUNCT
ejpam-3687	122	13	∫	∫	PROPN
ejpam-3687	122	14	1	1	NUM
ejpam-3687	122	15	0	0	NUM
ejpam-3687	122	16	dχ(µ	dχ(µ	NOUN
ejpam-3687	122	17	)	)	PUNCT
ejpam-3687	122	18	=	=	SYM
ejpam-3687	123	1	kξm+α(1−	kξm+α(1−	PROPN
ejpam-3687	123	2	ξ)n−m	ξ)n−m	INTJ
ejpam-3687	123	3	(	(	PUNCT
ejpam-3687	123	4	n−	n−	NOUN
ejpam-3687	123	5	1	1	NUM
ejpam-3687	123	6	+	+	CCONJ
ejpam-3687	123	7	α	α	NOUN
ejpam-3687	123	8	m−	m−	PROPN
ejpam-3687	123	9	1	1	NUM
ejpam-3687	123	10	+	+	CCONJ
ejpam-3687	123	11	α	α	NOUN
ejpam-3687	123	12	)	)	PUNCT
ejpam-3687	123	13	,	,	PUNCT
ejpam-3687	123	14	where	where	SCONJ
ejpam-3687	123	15	0	0	X
ejpam-3687	123	16	<	<	X
ejpam-3687	123	17	k	k	X
ejpam-3687	123	18	≤	≤	NUM
ejpam-3687	123	19	1	1	NUM
ejpam-3687	123	20	,	,	PUNCT
ejpam-3687	123	21	and	and	CCONJ
ejpam-3687	123	22	(	(	PUNCT
ejpam-3687	123	23	i	i	NOUN
ejpam-3687	123	24	)	)	PUNCT
ejpam-3687	123	25	is	be	AUX
ejpam-3687	123	26	satisfied	satisfied	ADJ
ejpam-3687	123	27	.	.	PUNCT
ejpam-3687	124	1	to	to	PART
ejpam-3687	124	2	prove	prove	VERB
ejpam-3687	124	3	(	(	PUNCT
ejpam-3687	124	4	ii	ii	NOUN
ejpam-3687	124	5	)	)	PUNCT
ejpam-3687	124	6	we	we	PRON
ejpam-3687	124	7	need	need	VERB
ejpam-3687	124	8	the	the	DET
ejpam-3687	124	9	following	follow	VERB
ejpam-3687	124	10	lemma	lemma	PROPN
ejpam-3687	124	11	.	.	PUNCT
ejpam-3687	125	1	lemma	lemma	PROPN
ejpam-3687	125	2	2	2	NUM
ejpam-3687	125	3	.	.	PUNCT
ejpam-3687	126	1	for	for	ADP
ejpam-3687	126	2	0	0	NUM
ejpam-3687	126	3	<	<	X
ejpam-3687	126	4	k	k	X
ejpam-3687	126	5	<	<	X
ejpam-3687	126	6	1	1	NUM
ejpam-3687	126	7	,	,	PUNCT
ejpam-3687	126	8	amn	amn	PROPN
ejpam-3687	126	9	≤	≤	ADV
ejpam-3687	126	10	1	1	NUM
ejpam-3687	126	11	.	.	PUNCT
ejpam-3687	126	12	proof	proof	NOUN
ejpam-3687	126	13	.	.	PUNCT
ejpam-3687	127	1	from	from	ADP
ejpam-3687	127	2	(	(	PUNCT
ejpam-3687	127	3	3	3	X
ejpam-3687	127	4	)	)	PUNCT
ejpam-3687	127	5	amn	amn	PROPN
ejpam-3687	127	6	=	=	SYM
ejpam-3687	127	7	k	k	PROPN
ejpam-3687	127	8	∫	∫	PROPN
ejpam-3687	127	9	1	1	NUM
ejpam-3687	127	10	0	0	NUM
ejpam-3687	127	11	µm+α(1−	µm+α(1−	X
ejpam-3687	127	12	µ)n−m	µ)n−m	X
ejpam-3687	127	13	(	(	PUNCT
ejpam-3687	127	14	n−	n−	NOUN
ejpam-3687	127	15	1	1	NUM
ejpam-3687	127	16	+	+	CCONJ
ejpam-3687	127	17	α	α	NOUN
ejpam-3687	127	18	m−	m−	PROPN
ejpam-3687	127	19	1	1	NUM
ejpam-3687	127	20	+	+	CCONJ
ejpam-3687	127	21	α	α	NOUN
ejpam-3687	127	22	)	)	PUNCT
ejpam-3687	127	23	dµ	dµ	PROPN
ejpam-3687	127	24	=	=	SYM
ejpam-3687	127	25	k	k	PROPN
ejpam-3687	127	26	(	(	PUNCT
ejpam-3687	127	27	n−	n−	NOUN
ejpam-3687	127	28	1	1	NUM
ejpam-3687	127	29	+	+	CCONJ
ejpam-3687	127	30	α	α	NOUN
ejpam-3687	127	31	m−	m−	PROPN
ejpam-3687	127	32	1	1	NUM
ejpam-3687	127	33	+	+	CCONJ
ejpam-3687	127	34	α	α	NOUN
ejpam-3687	127	35	)	)	PUNCT
ejpam-3687	127	36	∫	∫	PROPN
ejpam-3687	127	37	1	1	NUM
ejpam-3687	127	38	0	0	NUM
ejpam-3687	127	39	µm+α(1−	µm+α(1−	ADP
ejpam-3687	127	40	µ)n−mdµ	µ)n−mdµ	NOUN
ejpam-3687	127	41	=	=	SYM
ejpam-3687	127	42	k	k	X
ejpam-3687	127	43	(	(	PUNCT
ejpam-3687	127	44	n−	n−	NOUN
ejpam-3687	127	45	1	1	NUM
ejpam-3687	127	46	+	+	CCONJ
ejpam-3687	127	47	α	α	NOUN
ejpam-3687	127	48	m−	m−	PROPN
ejpam-3687	127	49	1	1	NUM
ejpam-3687	127	50	+	+	CCONJ
ejpam-3687	127	51	α	α	NOUN
ejpam-3687	127	52	)	)	PUNCT
ejpam-3687	127	53	γ(m+	γ(m+	X
ejpam-3687	128	1	α+	α+	PRON
ejpam-3687	128	2	1)γ(n−m+	1)γ(n−m+	NUM
ejpam-3687	128	3	1	1	NUM
ejpam-3687	128	4	)	)	PUNCT
ejpam-3687	128	5	γ(n+	γ(n+	NOUN
ejpam-3687	129	1	α+	α+	PRON
ejpam-3687	129	2	2	2	NUM
ejpam-3687	129	3	)	)	PUNCT
ejpam-3687	129	4	=	=	SYM
ejpam-3687	130	1	k	k	X
ejpam-3687	130	2	γ(n+	γ(n+	X
ejpam-3687	130	3	α	α	NOUN
ejpam-3687	130	4	)	)	PUNCT
ejpam-3687	130	5	γ(m+	γ(m+	X
ejpam-3687	131	1	α)γ(n−m+	α)γ(n−m+	NUM
ejpam-3687	131	2	1	1	NUM
ejpam-3687	131	3	)	)	PUNCT
ejpam-3687	131	4	γ(m+	γ(m+	X
ejpam-3687	132	1	α+	α+	PUNCT
ejpam-3687	132	2	1)γ(n−m+	1)γ(n−m+	NUM
ejpam-3687	132	3	1	1	NUM
ejpam-3687	132	4	)	)	PUNCT
ejpam-3687	132	5	γ(n+	γ(n+	NOUN
ejpam-3687	133	1	α+	α+	PRON
ejpam-3687	133	2	2	2	NUM
ejpam-3687	133	3	)	)	PUNCT
ejpam-3687	133	4	=	=	SYM
ejpam-3687	133	5	k	k	PROPN
ejpam-3687	133	6	(	(	PUNCT
ejpam-3687	133	7	m+	m+	NOUN
ejpam-3687	133	8	α	α	NOUN
ejpam-3687	133	9	)	)	PUNCT
ejpam-3687	133	10	(	(	PUNCT
ejpam-3687	133	11	n+	n+	X
ejpam-3687	133	12	α+	α+	PUNCT
ejpam-3687	133	13	1)(n+	1)(n+	NUM
ejpam-3687	133	14	α	α	NOUN
ejpam-3687	133	15	)	)	PUNCT
ejpam-3687	133	16	.	.	PUNCT
ejpam-3687	134	1	since	since	SCONJ
ejpam-3687	134	2	n	n	PROPN
ejpam-3687	134	3	≥	≥	NOUN
ejpam-3687	134	4	m	m	PROPN
ejpam-3687	134	5	,	,	PUNCT
ejpam-3687	134	6	amn	amn	PROPN
ejpam-3687	134	7	≤	≤	PUNCT
ejpam-3687	135	1	k	k	X
ejpam-3687	135	2	<	<	X
ejpam-3687	135	3	1	1	NUM
ejpam-3687	135	4	.	.	PUNCT
ejpam-3687	135	5	(	(	PUNCT
ejpam-3687	135	6	4	4	X
ejpam-3687	135	7	)	)	PUNCT
ejpam-3687	135	8	f.	f.	PROPN
ejpam-3687	135	9	aydin	aydin	PROPN
ejpam-3687	135	10	akgun	akgun	PROPN
ejpam-3687	135	11	,	,	PUNCT
ejpam-3687	135	12	b.	b.	PROPN
ejpam-3687	135	13	e.	e.	PROPN
ejpam-3687	135	14	rhoades	rhoades	PROPN
ejpam-3687	135	15	/	/	SYM
ejpam-3687	135	16	eur	eur	PROPN
ejpam-3687	135	17	.	.	PUNCT
ejpam-3687	136	1	j.	j.	PROPN
ejpam-3687	136	2	pure	pure	PROPN
ejpam-3687	136	3	appl	appl	PROPN
ejpam-3687	136	4	.	.	PROPN
ejpam-3687	136	5	math	math	PROPN
ejpam-3687	136	6	,	,	PUNCT
ejpam-3687	136	7	13	13	NUM
ejpam-3687	136	8	(	(	PUNCT
ejpam-3687	136	9	3	3	NUM
ejpam-3687	136	10	)	)	PUNCT
ejpam-3687	136	11	(	(	PUNCT
ejpam-3687	136	12	2020	2020	NUM
ejpam-3687	136	13	)	)	PUNCT
ejpam-3687	136	14	,	,	PUNCT
ejpam-3687	136	15	390	390	NUM
ejpam-3687	136	16	-	-	SYM
ejpam-3687	136	17	402	402	NUM
ejpam-3687	136	18	394	394	NUM
ejpam-3687	136	19	using	use	VERB
ejpam-3687	136	20	equation	equation	NOUN
ejpam-3687	136	21	(	(	PUNCT
ejpam-3687	136	22	4	4	X
ejpam-3687	136	23	)	)	PUNCT
ejpam-3687	136	24	we	we	PRON
ejpam-3687	136	25	can	can	AUX
ejpam-3687	136	26	write	write	VERB
ejpam-3687	136	27	n∑	n∑	PROPN
ejpam-3687	136	28	m=0	m=0	PROPN
ejpam-3687	136	29	|amn|2|bm|2	|amn|2|bm|2	VERB
ejpam-3687	136	30	≤	≤	ADJ
ejpam-3687	136	31	k2	k2	PROPN
ejpam-3687	136	32	n∑	n∑	PROPN
ejpam-3687	136	33	m=0	m=0	PROPN
ejpam-3687	136	34	|bm|2	|bm|2	PUNCT
ejpam-3687	136	35	≤	≤	PROPN
ejpam-3687	136	36	n∑	n∑	X
ejpam-3687	136	37	m=0	m=0	PROPN
ejpam-3687	136	38	|bm|2	|bm|2	PROPN
ejpam-3687	136	39	,	,	PUNCT
ejpam-3687	136	40	(	(	PUNCT
ejpam-3687	136	41	5	5	NUM
ejpam-3687	136	42	)	)	PUNCT
ejpam-3687	136	43	which	which	PRON
ejpam-3687	136	44	is	be	AUX
ejpam-3687	136	45	a	a	DET
ejpam-3687	136	46	proof	proof	NOUN
ejpam-3687	136	47	of	of	ADP
ejpam-3687	136	48	(	(	PUNCT
ejpam-3687	136	49	ii	ii	NOUN
ejpam-3687	136	50	)	)	PUNCT
ejpam-3687	136	51	.	.	PUNCT
ejpam-3687	137	1	lemma	lemma	PROPN
ejpam-3687	137	2	3	3	X
ejpam-3687	137	3	.	.	PUNCT
ejpam-3687	138	1	let	let	VERB
ejpam-3687	138	2	{	{	PUNCT
ejpam-3687	138	3	ϕn}∞n=0	ϕn}∞n=0	NUM
ejpam-3687	138	4	⊂	⊂	PROPN
ejpam-3687	138	5	l2[0	l2[0	PROPN
ejpam-3687	138	6	,	,	PUNCT
ejpam-3687	138	7	1	1	NUM
ejpam-3687	138	8	]	]	PUNCT
ejpam-3687	138	9	be	be	AUX
ejpam-3687	138	10	an	an	DET
ejpam-3687	138	11	orthonormal	orthonormal	ADJ
ejpam-3687	138	12	system	system	NOUN
ejpam-3687	138	13	,	,	PUNCT
ejpam-3687	138	14	hα	hα	AUX
ejpam-3687	138	15	µ	µ	PROPN
ejpam-3687	138	16	be	be	AUX
ejpam-3687	138	17	an	an	DET
ejpam-3687	138	18	e	e	PROPN
ejpam-3687	138	19	-	-	PROPN
ejpam-3687	138	20	j	j	ADJ
ejpam-3687	138	21	hausdorff	hausdorff	NOUN
ejpam-3687	138	22	matrix	matrix	NOUN
ejpam-3687	138	23	with	with	ADP
ejpam-3687	138	24	monotonically	monotonically	ADV
ejpam-3687	138	25	increasing	increase	VERB
ejpam-3687	138	26	function	function	NOUN
ejpam-3687	138	27	χ	χ	NOUN
ejpam-3687	138	28	on	on	ADP
ejpam-3687	138	29	[	[	X
ejpam-3687	138	30	0	0	NUM
ejpam-3687	138	31	,	,	PUNCT
ejpam-3687	138	32	1	1	NUM
ejpam-3687	138	33	]	]	PUNCT
ejpam-3687	138	34	.	.	PUNCT
ejpam-3687	139	1	then	then	ADV
ejpam-3687	139	2	,	,	PUNCT
ejpam-3687	139	3	for	for	ADP
ejpam-3687	139	4	n	n	DET
ejpam-3687	139	5	∈	∈	PROPN
ejpam-3687	139	6	n	n	NOUN
ejpam-3687	139	7	and	and	CCONJ
ejpam-3687	139	8	k	k	PROPN
ejpam-3687	139	9	=	=	SYM
ejpam-3687	139	10	∫	∫	PROPN
ejpam-3687	139	11	1	1	NUM
ejpam-3687	139	12	0	0	NUM
ejpam-3687	139	13	dχ(µ	dχ(µ	NOUN
ejpam-3687	139	14	)	)	PUNCT
ejpam-3687	139	15	,	,	PUNCT
ejpam-3687	139	16	(	(	PUNCT
ejpam-3687	139	17	i	i	NOUN
ejpam-3687	139	18	)	)	PUNCT
ejpam-3687	139	19	there	there	PRON
ejpam-3687	139	20	exists	exist	VERB
ejpam-3687	139	21	ξ	ξ	PROPN
ejpam-3687	139	22	∈	∈	PROPN
ejpam-3687	139	23	(	(	PUNCT
ejpam-3687	139	24	0	0	NUM
ejpam-3687	139	25	,	,	PUNCT
ejpam-3687	139	26	1	1	NUM
ejpam-3687	139	27	)	)	PUNCT
ejpam-3687	139	28	such	such	ADJ
ejpam-3687	139	29	that∫	that∫	NOUN
ejpam-3687	139	30	1	1	NUM
ejpam-3687	139	31	0	0	NUM
ejpam-3687	139	32	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	139	33	σn−1(x)|2	σn−1(x)|2	PROPN
ejpam-3687	139	34	=	=	SYM
ejpam-3687	139	35	k2	k2	PROPN
ejpam-3687	139	36	n∑	n∑	PROPN
ejpam-3687	139	37	m=0	m=0	PROPN
ejpam-3687	139	38	ξ2m+2α(1−	ξ2m+2α(1−	PROPN
ejpam-3687	139	39	ξ)2n−2	ξ)2n−2	PROPN
ejpam-3687	139	40	m	m	PROPN
ejpam-3687	139	41	(	(	PUNCT
ejpam-3687	139	42	n−	n−	NOUN
ejpam-3687	139	43	1	1	NUM
ejpam-3687	139	44	+	+	CCONJ
ejpam-3687	139	45	α	α	NOUN
ejpam-3687	139	46	m−	m−	PROPN
ejpam-3687	139	47	1	1	NUM
ejpam-3687	139	48	+	+	CCONJ
ejpam-3687	139	49	α	α	NOUN
ejpam-3687	139	50	)	)	PUNCT
ejpam-3687	139	51	2	2	NUM
ejpam-3687	139	52	|bm|2	|bm|2	PUNCT
ejpam-3687	139	53	and	and	CCONJ
ejpam-3687	139	54	(	(	PUNCT
ejpam-3687	139	55	ii	ii	NOUN
ejpam-3687	139	56	)	)	PUNCT
ejpam-3687	139	57	∫	∫	PROPN
ejpam-3687	140	1	1	1	NUM
ejpam-3687	140	2	0	0	X
ejpam-3687	140	3	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	140	4	σn−1(x)|2dx	σn−1(x)|2dx	PROPN
ejpam-3687	140	5	=	=	SYM
ejpam-3687	140	6	k2	k2	PROPN
ejpam-3687	140	7	n∑	n∑	PROPN
ejpam-3687	140	8	m=0	m=0	PROPN
ejpam-3687	140	9	|bm|2	|bm|2	PROPN
ejpam-3687	140	10	,	,	PUNCT
ejpam-3687	140	11	for	for	ADP
ejpam-3687	140	12	all	all	DET
ejpam-3687	140	13	bm	bm	PROPN
ejpam-3687	140	14	∈	∈	PROPN
ejpam-3687	140	15	c	c	X
ejpam-3687	140	16	where	where	SCONJ
ejpam-3687	140	17	,	,	PUNCT
ejpam-3687	140	18	for	for	ADP
ejpam-3687	140	19	n	n	PRON
ejpam-3687	140	20	∈	∈	PROPN
ejpam-3687	140	21	n	n	CCONJ
ejpam-3687	140	22	,	,	PUNCT
ejpam-3687	140	23	σn(x	σn(x	X
ejpam-3687	140	24	)	)	PUNCT
ejpam-3687	141	1	=	=	SYM
ejpam-3687	141	2	∑n	∑n	PROPN
ejpam-3687	141	3	k=0	k=0	PROPN
ejpam-3687	141	4	hnksk(x	hnksk(x	PROPN
ejpam-3687	141	5	)	)	PUNCT
ejpam-3687	141	6	,	,	PUNCT
ejpam-3687	141	7	where	where	SCONJ
ejpam-3687	141	8	sk	sk	AUX
ejpam-3687	141	9	denotes	denote	VERB
ejpam-3687	141	10	the	the	DET
ejpam-3687	141	11	kth	kth	PROPN
ejpam-3687	141	12	partial	partial	ADJ
ejpam-3687	141	13	sum	sum	NOUN
ejpam-3687	141	14	of	of	ADP
ejpam-3687	141	15	the	the	DET
ejpam-3687	141	16	orthogonal	orthogonal	ADJ
ejpam-3687	141	17	series	series	PROPN
ejpam-3687	141	18	∑∞	∑∞	NOUN
ejpam-3687	141	19	m=0	m=0	PROPN
ejpam-3687	141	20	bmϕm	bmϕm	VERB
ejpam-3687	141	21	.	.	PUNCT
ejpam-3687	142	1	proof	proof	NOUN
ejpam-3687	142	2	.	.	PUNCT
ejpam-3687	143	1	σn(x)−	σn(x)−	PROPN
ejpam-3687	143	2	σn−1(x	σn−1(x	PROPN
ejpam-3687	143	3	)	)	PUNCT
ejpam-3687	144	1	=	=	SYM
ejpam-3687	144	2	n∑	n∑	NOUN
ejpam-3687	144	3	k=0	k=0	PROPN
ejpam-3687	144	4	(	(	PUNCT
ejpam-3687	144	5	h	h	NOUN
ejpam-3687	144	6	(	(	PUNCT
ejpam-3687	144	7	α	α	NOUN
ejpam-3687	144	8	)	)	PUNCT
ejpam-3687	144	9	nk	nk	PROPN
ejpam-3687	144	10	−	−	PROPN
ejpam-3687	145	1	h	h	NOUN
ejpam-3687	145	2	(	(	PUNCT
ejpam-3687	145	3	α	α	NOUN
ejpam-3687	145	4	)	)	PUNCT
ejpam-3687	145	5	n−1,k)sk(x	n−1,k)sk(x	ADP
ejpam-3687	145	6	)	)	PUNCT
ejpam-3687	145	7	=	=	SYM
ejpam-3687	145	8	n∑	n∑	NOUN
ejpam-3687	145	9	k=0	k=0	PROPN
ejpam-3687	145	10	(	(	PUNCT
ejpam-3687	145	11	h	h	NOUN
ejpam-3687	145	12	(	(	PUNCT
ejpam-3687	145	13	α	α	NOUN
ejpam-3687	145	14	)	)	PUNCT
ejpam-3687	145	15	nk	nk	PROPN
ejpam-3687	145	16	−	−	PROPN
ejpam-3687	146	1	h	h	NOUN
ejpam-3687	146	2	(	(	PUNCT
ejpam-3687	146	3	α	α	NOUN
ejpam-3687	146	4	)	)	PUNCT
ejpam-3687	146	5	n−1,k	n−1,k	PROPN
ejpam-3687	146	6	)	)	PUNCT
ejpam-3687	146	7	k∑	k∑	PROPN
ejpam-3687	147	1	m=0	m=0	PROPN
ejpam-3687	147	2	bmϕm	bmϕm	PROPN
ejpam-3687	147	3	=	=	PROPN
ejpam-3687	147	4	n∑	n∑	PROPN
ejpam-3687	147	5	m=0	m=0	PROPN
ejpam-3687	147	6	n∑	n∑	PROPN
ejpam-3687	148	1	k	k	PROPN
ejpam-3687	149	1	=	=	NOUN
ejpam-3687	149	2	m	m	PROPN
ejpam-3687	149	3	(	(	PUNCT
ejpam-3687	149	4	h	h	NOUN
ejpam-3687	149	5	(	(	PUNCT
ejpam-3687	149	6	α	α	NOUN
ejpam-3687	149	7	)	)	PUNCT
ejpam-3687	149	8	nk	nk	PROPN
ejpam-3687	149	9	−	−	PROPN
ejpam-3687	149	10	h	h	NOUN
ejpam-3687	149	11	(	(	PUNCT
ejpam-3687	149	12	α	α	NOUN
ejpam-3687	149	13	)	)	PUNCT
ejpam-3687	149	14	n−1,k)bmϕm	n−1,k)bmϕm	PROPN
ejpam-3687	149	15	=	=	SYM
ejpam-3687	149	16	n∑	n∑	PROPN
ejpam-3687	149	17	m=0	m=0	PROPN
ejpam-3687	149	18	amnbmϕm	amnbmϕm	ADJ
ejpam-3687	149	19	.	.	PUNCT
ejpam-3687	150	1	since	since	SCONJ
ejpam-3687	150	2	{	{	PUNCT
ejpam-3687	150	3	ϕn}∞n=0	ϕn}∞n=0	X
ejpam-3687	150	4	is	be	AUX
ejpam-3687	150	5	an	an	DET
ejpam-3687	150	6	orthonormal	orthonormal	ADJ
ejpam-3687	150	7	system	system	NOUN
ejpam-3687	150	8	,	,	PUNCT
ejpam-3687	150	9	using	use	VERB
ejpam-3687	150	10	parseval	parseval	NOUN
ejpam-3687	150	11	’s	’s	PART
ejpam-3687	150	12	identity,∫	identity,∫	NOUN
ejpam-3687	150	13	1	1	NUM
ejpam-3687	150	14	0	0	X
ejpam-3687	150	15	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	150	16	σn−1(x)|2dx	σn−1(x)|2dx	PROPN
ejpam-3687	150	17	=	=	SYM
ejpam-3687	150	18	n∑	n∑	PROPN
ejpam-3687	150	19	m=0	m=0	PROPN
ejpam-3687	150	20	|amn|2|bm|2	|amn|2|bm|2	NOUN
ejpam-3687	150	21	=	=	SYM
ejpam-3687	150	22	k2	k2	PROPN
ejpam-3687	150	23	n∑	n∑	PROPN
ejpam-3687	150	24	m=0	m=0	PROPN
ejpam-3687	150	25	ξ2m+2α(1−	ξ2m+2α(1−	PROPN
ejpam-3687	151	1	ξ)2n−2	ξ)2n−2	PROPN
ejpam-3687	151	2	m	m	PROPN
ejpam-3687	151	3	(	(	PUNCT
ejpam-3687	151	4	n−	n−	NOUN
ejpam-3687	151	5	1	1	NUM
ejpam-3687	152	1	+	+	CCONJ
ejpam-3687	152	2	α	α	NOUN
ejpam-3687	152	3	m−	m−	PROPN
ejpam-3687	152	4	1	1	NUM
ejpam-3687	153	1	+	+	CCONJ
ejpam-3687	153	2	α	α	NOUN
ejpam-3687	153	3	)	)	PUNCT
ejpam-3687	153	4	2	2	NUM
ejpam-3687	153	5	|bm|2	|bm|2	NUM
ejpam-3687	153	6	.	.	PUNCT
ejpam-3687	153	7	f.	f.	PROPN
ejpam-3687	153	8	aydin	aydin	PROPN
ejpam-3687	153	9	akgun	akgun	PROPN
ejpam-3687	153	10	,	,	PUNCT
ejpam-3687	153	11	b.	b.	PROPN
ejpam-3687	153	12	e.	e.	PROPN
ejpam-3687	153	13	rhoades	rhoades	PROPN
ejpam-3687	153	14	/	/	SYM
ejpam-3687	153	15	eur	eur	PROPN
ejpam-3687	153	16	.	.	PUNCT
ejpam-3687	154	1	j.	j.	PROPN
ejpam-3687	154	2	pure	pure	PROPN
ejpam-3687	154	3	appl	appl	PROPN
ejpam-3687	154	4	.	.	PROPN
ejpam-3687	154	5	math	math	PROPN
ejpam-3687	154	6	,	,	PUNCT
ejpam-3687	154	7	13	13	NUM
ejpam-3687	154	8	(	(	PUNCT
ejpam-3687	154	9	3	3	NUM
ejpam-3687	154	10	)	)	PUNCT
ejpam-3687	154	11	(	(	PUNCT
ejpam-3687	154	12	2020	2020	NUM
ejpam-3687	154	13	)	)	PUNCT
ejpam-3687	154	14	,	,	PUNCT
ejpam-3687	154	15	390	390	NUM
ejpam-3687	154	16	-	-	SYM
ejpam-3687	154	17	402	402	NUM
ejpam-3687	154	18	395	395	NUM
ejpam-3687	154	19	from	from	ADP
ejpam-3687	154	20	lemma	lemma	PROPN
ejpam-3687	154	21	2,∫	2,∫	NUM
ejpam-3687	154	22	1	1	NUM
ejpam-3687	154	23	0	0	NUM
ejpam-3687	154	24	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	154	25	σn−1(x)|2dx	σn−1(x)|2dx	PROPN
ejpam-3687	154	26	=	=	SYM
ejpam-3687	154	27	n∑	n∑	PROPN
ejpam-3687	154	28	m=0	m=0	PROPN
ejpam-3687	154	29	|amn|2|bm|2	|amn|2|bm|2	VERB
ejpam-3687	154	30	≤	≤	ADJ
ejpam-3687	154	31	k2	k2	PROPN
ejpam-3687	154	32	n∑	n∑	PROPN
ejpam-3687	154	33	m=0	m=0	PROPN
ejpam-3687	154	34	|bm|2	|bm|2	PUNCT
ejpam-3687	154	35	.	.	PUNCT
ejpam-3687	155	1	proof	proof	NOUN
ejpam-3687	155	2	.	.	PUNCT
ejpam-3687	156	1	to	to	PART
ejpam-3687	156	2	prove	prove	VERB
ejpam-3687	156	3	theorem	theorem	ADJ
ejpam-3687	156	4	1	1	NUM
ejpam-3687	156	5	,	,	PUNCT
ejpam-3687	156	6	from	from	ADP
ejpam-3687	156	7	definition	definition	NOUN
ejpam-3687	156	8	1	1	NUM
ejpam-3687	156	9	we	we	PRON
ejpam-3687	156	10	need	need	VERB
ejpam-3687	156	11	to	to	PART
ejpam-3687	156	12	show	show	VERB
ejpam-3687	156	13	that	that	SCONJ
ejpam-3687	156	14	∞∑	∞∑	NUM
ejpam-3687	156	15	n=1	n=1	PROPN
ejpam-3687	156	16	γ(n)knk−1|σn	γ(n)knk−1|σn	VERB
ejpam-3687	156	17	−	−	PROPN
ejpam-3687	156	18	σn−1|k	σn−1|k	NOUN
ejpam-3687	156	19	converges	converge	VERB
ejpam-3687	156	20	for	for	ADP
ejpam-3687	156	21	1	1	NUM
ejpam-3687	156	22	≤	≤	NOUN
ejpam-3687	157	1	k	k	X
ejpam-3687	157	2	<	<	X
ejpam-3687	157	3	2	2	NUM
ejpam-3687	157	4	,	,	PUNCT
ejpam-3687	157	5	where	where	SCONJ
ejpam-3687	157	6	,	,	PUNCT
ejpam-3687	157	7	for	for	ADP
ejpam-3687	157	8	n	n	PRON
ejpam-3687	157	9	∈	∈	PROPN
ejpam-3687	157	10	n	n	CCONJ
ejpam-3687	157	11	,	,	PUNCT
ejpam-3687	157	12	σn(x	σn(x	PUNCT
ejpam-3687	157	13	)	)	PUNCT
ejpam-3687	157	14	∑n	∑n	PROPN
ejpam-3687	157	15	k=0	k=0	PROPN
ejpam-3687	157	16	h	h	PROPN
ejpam-3687	157	17	(	(	PUNCT
ejpam-3687	157	18	α	α	NOUN
ejpam-3687	157	19	)	)	PUNCT
ejpam-3687	157	20	nk	nk	PROPN
ejpam-3687	157	21	sk(x	sk(x	PROPN
ejpam-3687	157	22	)	)	PUNCT
ejpam-3687	157	23	.	.	PUNCT
ejpam-3687	158	1	using	use	VERB
ejpam-3687	158	2	lemma	lemma	PROPN
ejpam-3687	158	3	3	3	NUM
ejpam-3687	158	4	,	,	PUNCT
ejpam-3687	158	5	and	and	CCONJ
ejpam-3687	158	6	hölder	hölder	PROPN
ejpam-3687	158	7	’s	’s	PART
ejpam-3687	158	8	inequality	inequality	NOUN
ejpam-3687	158	9	with	with	ADP
ejpam-3687	158	10	p	p	NOUN
ejpam-3687	158	11	=	=	NOUN
ejpam-3687	158	12	2	2	NUM
ejpam-3687	158	13	/	/	SYM
ejpam-3687	158	14	k	k	NOUN
ejpam-3687	158	15	,	,	PUNCT
ejpam-3687	158	16	for	for	ADP
ejpam-3687	158	17	any	any	DET
ejpam-3687	158	18	1	1	NUM
ejpam-3687	158	19	≤	≤	NUM
ejpam-3687	158	20	k	k	X
ejpam-3687	158	21	≤	≤	NUM
ejpam-3687	158	22	2	2	NUM
ejpam-3687	158	23	,	,	PUNCT
ejpam-3687	158	24	and	and	CCONJ
ejpam-3687	158	25	for	for	ADP
ejpam-3687	158	26	all	all	DET
ejpam-3687	158	27	b	b	PROPN
ejpam-3687	158	28	∈	∈	PROPN
ejpam-3687	158	29	`	`	PUNCT
ejpam-3687	158	30	2(z+	2(z+	NUM
ejpam-3687	158	31	)	)	PUNCT
ejpam-3687	158	32	,	,	PUNCT
ejpam-3687	158	33	we	we	PRON
ejpam-3687	158	34	have	have	VERB
ejpam-3687	158	35	∞∑	∞∑	NUM
ejpam-3687	158	36	n=1	n=1	PROPN
ejpam-3687	158	37	γ(n)knk	γ(n)knk	ADJ
ejpam-3687	158	38	∫	∫	NOUN
ejpam-3687	158	39	n	n	CCONJ
ejpam-3687	158	40	0	0	NUM
ejpam-3687	159	1	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	159	2	σn−1(x)|kdx	σn−1(x)|kdx	X
ejpam-3687	159	3	≤	≤	NOUN
ejpam-3687	160	1	∞∑	∞∑	NUM
ejpam-3687	160	2	n=1	n=1	PROPN
ejpam-3687	160	3	γ(n)knk−1{k2‖b‖22}k/2	γ(n)knk−1{k2‖b‖22}k/2	PROPN
ejpam-3687	160	4	≤	≤	NUM
ejpam-3687	160	5	{	{	PUNCT
ejpam-3687	160	6	k‖b‖2}k	k‖b‖2}k	PROPN
ejpam-3687	160	7	∞∑	∞∑	PROPN
ejpam-3687	160	8	n=1	n=1	PROPN
ejpam-3687	160	9	γ(n)knk−1	γ(n)knk−1	PRON
ejpam-3687	160	10	.	.	PUNCT
ejpam-3687	161	1	here	here	ADV
ejpam-3687	161	2	{	{	PUNCT
ejpam-3687	161	3	γ(n	γ(n	X
ejpam-3687	161	4	)	)	PUNCT
ejpam-3687	161	5	}	}	PUNCT
ejpam-3687	161	6	is	be	AUX
ejpam-3687	161	7	a	a	DET
ejpam-3687	161	8	quasi	quasi	ADJ
ejpam-3687	161	9	β	β	NOUN
ejpam-3687	161	10	-	-	ADJ
ejpam-3687	161	11	power	power	NOUN
ejpam-3687	161	12	monotone	monotone	NOUN
ejpam-3687	161	13	decreasing	decrease	VERB
ejpam-3687	161	14	sequence	sequence	NOUN
ejpam-3687	161	15	with	with	ADP
ejpam-3687	161	16	β	β	X
ejpam-3687	161	17	>	>	X
ejpam-3687	161	18	1−1	1−1	NUM
ejpam-3687	161	19	/	/	SYM
ejpam-3687	161	20	k	k	NOUN
ejpam-3687	161	21	,	,	PUNCT
ejpam-3687	161	22	and	and	CCONJ
ejpam-3687	161	23	,	,	PUNCT
ejpam-3687	161	24	since	since	SCONJ
ejpam-3687	161	25	for	for	ADP
ejpam-3687	161	26	ε	ε	PROPN
ejpam-3687	161	27	=	=	SYM
ejpam-3687	161	28	β	β	X
ejpam-3687	161	29	−	−	NOUN
ejpam-3687	161	30	1	1	NUM
ejpam-3687	161	31	+	+	CCONJ
ejpam-3687	161	32	1	1	NUM
ejpam-3687	161	33	/	/	SYM
ejpam-3687	161	34	k	k	NOUN
ejpam-3687	161	35	,	,	PUNCT
ejpam-3687	161	36	the	the	DET
ejpam-3687	161	37	sequence	sequence	NOUN
ejpam-3687	161	38	{	{	PUNCT
ejpam-3687	161	39	nk−1γ(n)k	nk−1γ(n)k	PRON
ejpam-3687	161	40	}	}	PUNCT
ejpam-3687	161	41	is	be	AUX
ejpam-3687	161	42	quasi	quasi	ADJ
ejpam-3687	161	43	kε	kε	NOUN
ejpam-3687	161	44	-	-	PUNCT
ejpam-3687	161	45	power	power	NOUN
ejpam-3687	161	46	monotone	monotone	NOUN
ejpam-3687	161	47	decreasing	decreasing	NOUN
ejpam-3687	161	48	.	.	PUNCT
ejpam-3687	162	1	using	use	VERB
ejpam-3687	162	2	lemma	lemma	PROPN
ejpam-3687	162	3	1	1	NUM
ejpam-3687	162	4	of	of	ADP
ejpam-3687	162	5	[	[	X
ejpam-3687	162	6	6	6	NUM
ejpam-3687	162	7	]	]	PUNCT
ejpam-3687	162	8	,	,	PUNCT
ejpam-3687	162	9	we	we	PRON
ejpam-3687	162	10	have	have	VERB
ejpam-3687	162	11	≤	≤	NOUN
ejpam-3687	162	12	{	{	PUNCT
ejpam-3687	162	13	k‖b‖2}k	k‖b‖2}k	PROPN
ejpam-3687	162	14	∞∑	∞∑	PROPN
ejpam-3687	162	15	n=1	n=1	PROPN
ejpam-3687	162	16	γ(2n)k(2n)k−1	γ(2n)k(2n)k−1	PART
ejpam-3687	162	17	≤	≤	NOUN
ejpam-3687	162	18	{	{	PUNCT
ejpam-3687	162	19	k‖b‖2}kbγ(2)k(2)k−1	k‖b‖2}kbγ(2)k(2)k−1	PROPN
ejpam-3687	162	20	,	,	PUNCT
ejpam-3687	162	21	where	where	SCONJ
ejpam-3687	162	22	b	b	X
ejpam-3687	162	23	≥	≥	NUM
ejpam-3687	162	24	1	1	NUM
ejpam-3687	162	25	.	.	PUNCT
ejpam-3687	162	26	theorem	theorem	NOUN
ejpam-3687	162	27	2	2	NUM
ejpam-3687	162	28	.	.	PUNCT
ejpam-3687	163	1	let	let	VERB
ejpam-3687	163	2	{	{	PUNCT
ejpam-3687	163	3	ϕ}∞n=0	ϕ}∞n=0	PROPN
ejpam-3687	163	4	⊂	⊂	PROPN
ejpam-3687	163	5	l2[0	l2[0	PROPN
ejpam-3687	163	6	,	,	PUNCT
ejpam-3687	163	7	1	1	NUM
ejpam-3687	163	8	]	]	PUNCT
ejpam-3687	163	9	be	be	AUX
ejpam-3687	163	10	an	an	DET
ejpam-3687	163	11	orthogonal	orthogonal	ADJ
ejpam-3687	163	12	system	system	NOUN
ejpam-3687	163	13	and	and	CCONJ
ejpam-3687	163	14	hα	hα	ADP
ejpam-3687	163	15	µ	µ	X
ejpam-3687	163	16	the	the	DET
ejpam-3687	163	17	corresponding	corresponding	ADJ
ejpam-3687	163	18	e	e	PROPN
ejpam-3687	163	19	-	-	PROPN
ejpam-3687	163	20	j	j	ADJ
ejpam-3687	163	21	hausdorff	hausdorff	NOUN
ejpam-3687	163	22	matrix	matrix	NOUN
ejpam-3687	163	23	.	.	PUNCT
ejpam-3687	164	1	for	for	ADP
ejpam-3687	164	2	1	1	NUM
ejpam-3687	164	3	≤	≤	NUM
ejpam-3687	164	4	k	k	NOUN
ejpam-3687	164	5	≤	≤	NUM
ejpam-3687	164	6	2	2	NUM
ejpam-3687	164	7	and	and	CCONJ
ejpam-3687	164	8	γ	γ	PROPN
ejpam-3687	164	9	∈	∈	PROPN
ejpam-3687	164	10	γ(β	γ(β	PROPN
ejpam-3687	164	11	)	)	PUNCT
ejpam-3687	164	12	with	with	ADP
ejpam-3687	164	13	β	β	X
ejpam-3687	164	14	>	>	X
ejpam-3687	164	15	1	1	NUM
ejpam-3687	164	16	−	−	NUM
ejpam-3687	164	17	1	1	NUM
ejpam-3687	164	18	/	/	SYM
ejpam-3687	164	19	k	k	NOUN
ejpam-3687	164	20	,	,	PUNCT
ejpam-3687	164	21	every	every	DET
ejpam-3687	164	22	orthogonal	orthogonal	ADJ
ejpam-3687	164	23	series	series	NOUN
ejpam-3687	164	24	∑∞	∑∞	NOUN
ejpam-3687	164	25	n=0	n=0	PUNCT
ejpam-3687	164	26	bnϕn	bnϕn	NOUN
ejpam-3687	164	27	is	be	AUX
ejpam-3687	164	28	|hα	|hα	NUM
ejpam-3687	164	29	,	,	PUNCT
ejpam-3687	164	30	γ|k	γ|k	NOUN
ejpam-3687	164	31	summable	summable	ADJ
ejpam-3687	164	32	.	.	PUNCT
ejpam-3687	165	1	proof	proof	NOUN
ejpam-3687	165	2	.	.	PUNCT
ejpam-3687	166	1	let	let	VERB
ejpam-3687	166	2	χ	χ	PRON
ejpam-3687	166	3	∈	∈	PROPN
ejpam-3687	166	4	bv	bv	PROPN
ejpam-3687	167	1	[	[	X
ejpam-3687	167	2	0	0	NUM
ejpam-3687	167	3	,	,	PUNCT
ejpam-3687	167	4	1	1	NUM
ejpam-3687	167	5	]	]	PUNCT
ejpam-3687	167	6	be	be	AUX
ejpam-3687	167	7	the	the	DET
ejpam-3687	167	8	mass	mass	ADJ
ejpam-3687	167	9	function	function	NOUN
ejpam-3687	167	10	corresponding	correspond	VERB
ejpam-3687	167	11	to	to	ADP
ejpam-3687	167	12	the	the	DET
ejpam-3687	167	13	e	e	PROPN
ejpam-3687	167	14	-	-	PROPN
ejpam-3687	167	15	j	j	PROPN
ejpam-3687	167	16	matrix	matrix	NOUN
ejpam-3687	167	17	hα	hα	ADP
ejpam-3687	167	18	.	.	PUNCT
ejpam-3687	168	1	by	by	ADP
ejpam-3687	168	2	the	the	DET
ejpam-3687	168	3	jordan	jordan	PROPN
ejpam-3687	168	4	decomposition	decomposition	PROPN
ejpam-3687	168	5	theorem	theorem	PROPN
ejpam-3687	168	6	,	,	PUNCT
ejpam-3687	168	7	χ	χ	NOUN
ejpam-3687	168	8	=	=	SYM
ejpam-3687	168	9	χ1−χ2	χ1−χ2	NOUN
ejpam-3687	168	10	,	,	PUNCT
ejpam-3687	168	11	where	where	SCONJ
ejpam-3687	168	12	χ1	χ1	NOUN
ejpam-3687	168	13	and	and	CCONJ
ejpam-3687	168	14	χ2	χ2	PROPN
ejpam-3687	168	15	are	be	AUX
ejpam-3687	168	16	monotone	monotone	ADJ
ejpam-3687	168	17	increasing	increase	VERB
ejpam-3687	168	18	functions	function	NOUN
ejpam-3687	168	19	.	.	PUNCT
ejpam-3687	169	1	to	to	PART
ejpam-3687	169	2	prove	prove	VERB
ejpam-3687	169	3	the	the	DET
ejpam-3687	169	4	theorem	theorem	NOUN
ejpam-3687	169	5	we	we	PRON
ejpam-3687	169	6	apply	apply	VERB
ejpam-3687	169	7	theorem	theorem	VERB
ejpam-3687	169	8	1	1	NUM
ejpam-3687	169	9	to	to	ADP
ejpam-3687	169	10	χ1	χ1	NOUN
ejpam-3687	169	11	and	and	CCONJ
ejpam-3687	169	12	χ2	χ2	PROPN
ejpam-3687	169	13	.	.	PUNCT
ejpam-3687	170	1	theorems	theorems	PROPN
ejpam-3687	170	2	1	1	NUM
ejpam-3687	170	3	and	and	CCONJ
ejpam-3687	170	4	2	2	NUM
ejpam-3687	170	5	are	be	AUX
ejpam-3687	170	6	generalizations	generalization	NOUN
ejpam-3687	170	7	of	of	ADP
ejpam-3687	170	8	theorems	theorem	NOUN
ejpam-3687	170	9	1	1	NUM
ejpam-3687	170	10	and	and	CCONJ
ejpam-3687	170	11	2	2	NUM
ejpam-3687	170	12	,	,	PUNCT
ejpam-3687	170	13	respectively	respectively	ADV
ejpam-3687	170	14	,	,	PUNCT
ejpam-3687	170	15	in	in	ADP
ejpam-3687	170	16	[	[	PUNCT
ejpam-3687	170	17	6	6	NUM
ejpam-3687	170	18	]	]	PUNCT
ejpam-3687	170	19	.	.	PUNCT
ejpam-3687	171	1	theorem	theorem	NOUN
ejpam-3687	171	2	3	3	X
ejpam-3687	171	3	.	.	PUNCT
ejpam-3687	172	1	let	let	VERB
ejpam-3687	172	2	{	{	PUNCT
ejpam-3687	172	3	ϕ}∞n=0	ϕ}∞n=0	PROPN
ejpam-3687	172	4	⊂	⊂	PROPN
ejpam-3687	172	5	l2[0	l2[0	PROPN
ejpam-3687	172	6	,	,	PUNCT
ejpam-3687	172	7	1	1	NUM
ejpam-3687	172	8	]	]	PUNCT
ejpam-3687	172	9	be	be	AUX
ejpam-3687	172	10	an	an	DET
ejpam-3687	172	11	orthogonal	orthogonal	ADJ
ejpam-3687	172	12	system	system	NOUN
ejpam-3687	172	13	and	and	CCONJ
ejpam-3687	172	14	hα	hα	ADP
ejpam-3687	172	15	µ	µ	PRON
ejpam-3687	172	16	an	an	DET
ejpam-3687	172	17	e	e	PROPN
ejpam-3687	172	18	-	-	PROPN
ejpam-3687	172	19	j	j	ADJ
ejpam-3687	172	20	hausdorff	hausdorff	NOUN
ejpam-3687	172	21	matrix	matrix	NOUN
ejpam-3687	172	22	with	with	ADP
ejpam-3687	172	23	χ	χ	PROPN
ejpam-3687	172	24	∈	∈	PROPN
ejpam-3687	173	1	[	[	X
ejpam-3687	173	2	0	0	NUM
ejpam-3687	173	3	,	,	PUNCT
ejpam-3687	173	4	1	1	NUM
ejpam-3687	173	5	]	]	PUNCT
ejpam-3687	173	6	and	and	CCONJ
ejpam-3687	173	7	monotone	monotone	ADJ
ejpam-3687	173	8	increasing	increasing	NOUN
ejpam-3687	173	9	.	.	PUNCT
ejpam-3687	174	1	for	for	ADP
ejpam-3687	174	2	1	1	NUM
ejpam-3687	174	3	≤	≤	NUM
ejpam-3687	174	4	k	k	NOUN
ejpam-3687	174	5	≤	≤	NUM
ejpam-3687	174	6	2	2	NUM
ejpam-3687	174	7	and	and	CCONJ
ejpam-3687	174	8	γ	γ	PROPN
ejpam-3687	174	9	∈	∈	PROPN
ejpam-3687	174	10	γ(β	γ(β	PROPN
ejpam-3687	174	11	)	)	PUNCT
ejpam-3687	174	12	with	with	ADP
ejpam-3687	174	13	β	β	X
ejpam-3687	174	14	>	>	X
ejpam-3687	174	15	1	1	NUM
ejpam-3687	174	16	−	−	NUM
ejpam-3687	174	17	1	1	NUM
ejpam-3687	174	18	/	/	SYM
ejpam-3687	174	19	k	k	NOUN
ejpam-3687	174	20	,	,	PUNCT
ejpam-3687	174	21	a	a	DET
ejpam-3687	174	22	sufficient	sufficient	ADJ
ejpam-3687	174	23	condition	condition	NOUN
ejpam-3687	174	24	for	for	ADP
ejpam-3687	174	25	the	the	DET
ejpam-3687	174	26	orthogonal	orthogonal	ADJ
ejpam-3687	174	27	series	series	NOUN
ejpam-3687	174	28	∑∞	∑∞	NOUN
ejpam-3687	174	29	n=0	n=0	PUNCT
ejpam-3687	174	30	bnϕn	bnϕn	NOUN
ejpam-3687	174	31	to	to	PART
ejpam-3687	174	32	be	be	AUX
ejpam-3687	174	33	|hα	|hα	NUM
ejpam-3687	174	34	,	,	PUNCT
ejpam-3687	174	35	γ|k	γ|k	NOUN
ejpam-3687	174	36	summable	summable	ADJ
ejpam-3687	174	37	is	be	AUX
ejpam-3687	174	38	∞∑	∞∑	NUM
ejpam-3687	174	39	s=0	s=0	PUNCT
ejpam-3687	174	40	γ(2s)k	γ(2s)k	PROPN
ejpam-3687	174	41			PUNCT
ejpam-3687	174	42	2s+1∑	2s+1∑	NUM
ejpam-3687	174	43	m=2s+1	m=2s+1	NOUN
ejpam-3687	174	44	√	√	NUM
ejpam-3687	174	45	m+	m+	NUM
ejpam-3687	174	46	α|bm|2	α|bm|2	NOUN
ejpam-3687	174	47			PROPN
ejpam-3687	174	48	k/2	k/2	PROPN
ejpam-3687	174	49	<	<	X
ejpam-3687	174	50	∞.	∞.	PROPN
ejpam-3687	174	51	(	(	PUNCT
ejpam-3687	174	52	6	6	NUM
ejpam-3687	174	53	)	)	PUNCT
ejpam-3687	174	54	f.	f.	PROPN
ejpam-3687	174	55	aydin	aydin	PROPN
ejpam-3687	174	56	akgun	akgun	PROPN
ejpam-3687	174	57	,	,	PUNCT
ejpam-3687	174	58	b.	b.	PROPN
ejpam-3687	174	59	e.	e.	PROPN
ejpam-3687	174	60	rhoades	rhoades	PROPN
ejpam-3687	174	61	/	/	SYM
ejpam-3687	174	62	eur	eur	PROPN
ejpam-3687	174	63	.	.	PUNCT
ejpam-3687	175	1	j.	j.	PROPN
ejpam-3687	175	2	pure	pure	PROPN
ejpam-3687	175	3	appl	appl	PROPN
ejpam-3687	175	4	.	.	PROPN
ejpam-3687	175	5	math	math	PROPN
ejpam-3687	175	6	,	,	PUNCT
ejpam-3687	175	7	13	13	NUM
ejpam-3687	175	8	(	(	PUNCT
ejpam-3687	175	9	3	3	NUM
ejpam-3687	175	10	)	)	PUNCT
ejpam-3687	175	11	(	(	PUNCT
ejpam-3687	175	12	2020	2020	NUM
ejpam-3687	175	13	)	)	PUNCT
ejpam-3687	175	14	,	,	PUNCT
ejpam-3687	175	15	390	390	NUM
ejpam-3687	175	16	-	-	SYM
ejpam-3687	175	17	402	402	NUM
ejpam-3687	175	18	396	396	NUM
ejpam-3687	175	19	proof	proof	NOUN
ejpam-3687	175	20	.	.	PUNCT
ejpam-3687	176	1	let	let	VERB
ejpam-3687	176	2	χ	χ	PRON
ejpam-3687	176	3	∈	∈	PROPN
ejpam-3687	176	4	bv	bv	PROPN
ejpam-3687	177	1	[	[	X
ejpam-3687	177	2	0	0	NUM
ejpam-3687	177	3	,	,	PUNCT
ejpam-3687	177	4	1	1	NUM
ejpam-3687	177	5	]	]	PUNCT
ejpam-3687	177	6	and	and	CCONJ
ejpam-3687	177	7	monotonically	monotonically	ADV
ejpam-3687	177	8	increasing	increase	VERB
ejpam-3687	177	9	on	on	ADP
ejpam-3687	177	10	[	[	X
ejpam-3687	177	11	0	0	NUM
ejpam-3687	177	12	,	,	PUNCT
ejpam-3687	177	13	1	1	NUM
ejpam-3687	177	14	]	]	PUNCT
ejpam-3687	177	15	.	.	PUNCT
ejpam-3687	178	1	by	by	ADP
ejpam-3687	178	2	lemma	lemma	PROPN
ejpam-3687	178	3	1(i	1(i	NUM
ejpam-3687	178	4	)	)	PUNCT
ejpam-3687	178	5	there	there	PRON
ejpam-3687	178	6	exists	exist	VERB
ejpam-3687	178	7	a	a	DET
ejpam-3687	178	8	ξ	ξ	PROPN
ejpam-3687	178	9	∈	∈	PROPN
ejpam-3687	178	10	(	(	PUNCT
ejpam-3687	178	11	0	0	NUM
ejpam-3687	178	12	,	,	PUNCT
ejpam-3687	178	13	1	1	NUM
ejpam-3687	178	14	)	)	PUNCT
ejpam-3687	178	15	such	such	ADJ
ejpam-3687	178	16	that∫	that∫	NOUN
ejpam-3687	178	17	1	1	NUM
ejpam-3687	178	18	0	0	NUM
ejpam-3687	178	19	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	178	20	σn−1(x)|dx	σn−1(x)|dx	NOUN
ejpam-3687	178	21	≤	≤	PROPN
ejpam-3687	178	22	k2	k2	PROPN
ejpam-3687	178	23	n∑	n∑	PROPN
ejpam-3687	178	24	m=0	m=0	PROPN
ejpam-3687	179	1	(	(	PUNCT
ejpam-3687	179	2	n+	n+	X
ejpam-3687	179	3	α−	α−	ADP
ejpam-3687	179	4	1	1	NUM
ejpam-3687	179	5	m+	m+	NUM
ejpam-3687	179	6	α−	α−	ADP
ejpam-3687	179	7	1	1	NUM
ejpam-3687	179	8	)	)	SYM
ejpam-3687	179	9	2	2	NUM
ejpam-3687	179	10	ξ2m+2α(1−	ξ2m+2α(1−	ADJ
ejpam-3687	179	11	ξ)2n−2m|bm|2	ξ)2n−2m|bm|2	NOUN
ejpam-3687	179	12	,	,	PUNCT
ejpam-3687	179	13	(	(	PUNCT
ejpam-3687	179	14	7	7	X
ejpam-3687	179	15	)	)	PUNCT
ejpam-3687	179	16	where	where	SCONJ
ejpam-3687	179	17	σn(x	σn(x	X
ejpam-3687	179	18	)	)	PUNCT
ejpam-3687	179	19	=	=	SYM
ejpam-3687	179	20	n∑	n∑	PROPN
ejpam-3687	179	21	k=0	k=0	PROPN
ejpam-3687	179	22	h	h	PROPN
ejpam-3687	179	23	(	(	PUNCT
ejpam-3687	179	24	α	α	NOUN
ejpam-3687	179	25	)	)	PUNCT
ejpam-3687	179	26	nk	nk	PROPN
ejpam-3687	179	27	sk	sk	PROPN
ejpam-3687	179	28	.	.	PUNCT
ejpam-3687	180	1	for	for	ADP
ejpam-3687	180	2	1	1	NUM
ejpam-3687	180	3	≤	≤	NUM
ejpam-3687	180	4	k	k	X
ejpam-3687	180	5	≤	≤	NUM
ejpam-3687	180	6	2	2	NUM
ejpam-3687	180	7	,	,	PUNCT
ejpam-3687	180	8	by	by	ADP
ejpam-3687	180	9	using	use	VERB
ejpam-3687	180	10	hölder	hölder	PROPN
ejpam-3687	180	11	’s	’s	PART
ejpam-3687	180	12	inequality	inequality	NOUN
ejpam-3687	180	13	and	and	CCONJ
ejpam-3687	180	14	equation	equation	NOUN
ejpam-3687	180	15	(	(	PUNCT
ejpam-3687	180	16	1	1	NUM
ejpam-3687	180	17	)	)	PUNCT
ejpam-3687	180	18	,	,	PUNCT
ejpam-3687	180	19	∞∑	∞∑	PROPN
ejpam-3687	180	20	n=2	n=2	PRON
ejpam-3687	180	21	γ(n)knk−1	γ(n)knk−1	PROPN
ejpam-3687	180	22	{	{	PUNCT
ejpam-3687	180	23	∫	∫	PROPN
ejpam-3687	180	24	1	1	NUM
ejpam-3687	180	25	0	0	NUM
ejpam-3687	180	26	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	180	27	σn−1(x)|dx	σn−1(x)|dx	NOUN
ejpam-3687	180	28	}	}	PUNCT
ejpam-3687	180	29	k	k	NOUN
ejpam-3687	180	30	≤	≤	NOUN
ejpam-3687	180	31	∞∑	∞∑	NUM
ejpam-3687	180	32	n=2	n=2	PRON
ejpam-3687	180	33	γ(n)knk−1	γ(n)knk−1	NOUN
ejpam-3687	180	34	{	{	PUNCT
ejpam-3687	180	35	k2	k2	PROPN
ejpam-3687	180	36	n∑	n∑	PROPN
ejpam-3687	180	37	m=0	m=0	PROPN
ejpam-3687	181	1	(	(	PUNCT
ejpam-3687	181	2	n+	n+	X
ejpam-3687	181	3	α−	α−	ADP
ejpam-3687	181	4	1	1	NUM
ejpam-3687	181	5	m+	m+	NUM
ejpam-3687	181	6	α−	α−	ADP
ejpam-3687	181	7	1	1	NUM
ejpam-3687	181	8	)	)	PUNCT
ejpam-3687	181	9	2	2	NUM
ejpam-3687	181	10	ξ2m+2α(1−	ξ2m+2α(1−	ADJ
ejpam-3687	181	11	ξ)2n−2m|bm|2	ξ)2n−2m|bm|2	PROPN
ejpam-3687	181	12	}	}	PUNCT
ejpam-3687	181	13	k/2	k/2	PROPN
ejpam-3687	181	14	.	.	PUNCT
ejpam-3687	182	1	(	(	PUNCT
ejpam-3687	182	2	8)	8)	NUM
ejpam-3687	182	3	replacing	replace	VERB
ejpam-3687	182	4	ξ	ξ	PROPN
ejpam-3687	182	5	by	by	ADP
ejpam-3687	182	6	1/(1	1/(1	PROPN
ejpam-3687	182	7	+	+	CCONJ
ejpam-3687	182	8	q	q	X
ejpam-3687	182	9	)	)	PUNCT
ejpam-3687	182	10	in	in	ADP
ejpam-3687	182	11	(	(	PUNCT
ejpam-3687	182	12	8)	8)	NUM
ejpam-3687	182	13	,	,	PUNCT
ejpam-3687	182	14	we	we	PRON
ejpam-3687	182	15	obtain	obtain	VERB
ejpam-3687	182	16	=	=	SYM
ejpam-3687	182	17	kk	kk	PROPN
ejpam-3687	183	1	∞∑	∞∑	PROPN
ejpam-3687	183	2	r=0	r=0	PROPN
ejpam-3687	183	3	2r+1∑	2r+1∑	NUM
ejpam-3687	184	1	n=2r+1	n=2r+1	PROPN
ejpam-3687	184	2	γ(n)knk−1	γ(n)knk−1	NOUN
ejpam-3687	184	3	{	{	PUNCT
ejpam-3687	184	4	n∑	n∑	NOUN
ejpam-3687	184	5	n=0	n=0	NUM
ejpam-3687	184	6	(	(	PUNCT
ejpam-3687	184	7	n+	n+	ADP
ejpam-3687	184	8	α	α	PRON
ejpam-3687	184	9	m+	m+	NUM
ejpam-3687	184	10	α	α	NOUN
ejpam-3687	184	11	)	)	PUNCT
ejpam-3687	184	12	2(m+	2(m+	PROPN
ejpam-3687	185	1	α	α	NOUN
ejpam-3687	185	2	n+	n+	PUNCT
ejpam-3687	185	3	α	α	NOUN
ejpam-3687	185	4	)	)	PUNCT
ejpam-3687	185	5	2	2	NUM
ejpam-3687	185	6	q2n−2m(1	q2n−2m(1	NOUN
ejpam-3687	185	7	+	+	CCONJ
ejpam-3687	185	8	q)−2n−2α|bm|2	q)−2n−2α|bm|2	NOUN
ejpam-3687	185	9	}	}	PUNCT
ejpam-3687	185	10	k/2	k/2	PROPN
ejpam-3687	185	11	.	.	PUNCT
ejpam-3687	186	1	(	(	PUNCT
ejpam-3687	186	2	9	9	X
ejpam-3687	186	3	)	)	PUNCT
ejpam-3687	186	4	o.a	o.a	PROPN
ejpam-3687	186	5	.	.	PROPN
ejpam-3687	186	6	ziza	ziza	PROPN
ejpam-3687	187	1	[	[	X
ejpam-3687	187	2	7	7	NUM
ejpam-3687	187	3	]	]	PUNCT
ejpam-3687	187	4	proved	prove	VERB
ejpam-3687	187	5	that	that	SCONJ
ejpam-3687	187	6	,	,	PUNCT
ejpam-3687	187	7	for	for	ADP
ejpam-3687	187	8	q	q	PROPN
ejpam-3687	187	9	>	>	X
ejpam-3687	187	10	0	0	NUM
ejpam-3687	187	11	,	,	PUNCT
ejpam-3687	187	12	there	there	PRON
ejpam-3687	187	13	exists	exist	VERB
ejpam-3687	187	14	a	a	DET
ejpam-3687	187	15	constant	constant	ADJ
ejpam-3687	187	16	cq	cq	NOUN
ejpam-3687	187	17	>	>	X
ejpam-3687	187	18	0	0	NUM
ejpam-3687	188	1	such	such	ADJ
ejpam-3687	188	2	that	that	SCONJ
ejpam-3687	188	3	max	max	PROPN
ejpam-3687	188	4	0≤k≤n	0≤k≤n	PROPN
ejpam-3687	188	5	(	(	PUNCT
ejpam-3687	188	6	n	n	X
ejpam-3687	188	7	k	k	NOUN
ejpam-3687	188	8	)	)	PUNCT
ejpam-3687	188	9	qk	qk	ADP
ejpam-3687	188	10	≤	≤	PROPN
ejpam-3687	188	11	cq	cq	NOUN
ejpam-3687	189	1	(	(	PUNCT
ejpam-3687	189	2	1	1	NUM
ejpam-3687	189	3	+	+	NUM
ejpam-3687	189	4	q)n√	q)n√	NOUN
ejpam-3687	189	5	n	n	NOUN
ejpam-3687	189	6	,	,	PUNCT
ejpam-3687	189	7	n	n	NOUN
ejpam-3687	189	8	=	=	SYM
ejpam-3687	189	9	1	1	NUM
ejpam-3687	189	10	,	,	PUNCT
ejpam-3687	189	11	2	2	NUM
ejpam-3687	189	12	,	,	PUNCT
ejpam-3687	189	13	...	...	PUNCT
ejpam-3687	189	14	.	.	PUNCT
ejpam-3687	190	1	we	we	PRON
ejpam-3687	190	2	shall	shall	AUX
ejpam-3687	190	3	generalize	generalize	VERB
ejpam-3687	190	4	this	this	DET
ejpam-3687	190	5	lemma	lemma	PROPN
ejpam-3687	190	6	for	for	ADP
ejpam-3687	190	7	e	e	PROPN
ejpam-3687	190	8	-	-	PROPN
ejpam-3687	190	9	j	j	PROPN
ejpam-3687	190	10	matrices	matrix	NOUN
ejpam-3687	190	11	.	.	PUNCT
ejpam-3687	191	1	lemma	lemma	PROPN
ejpam-3687	191	2	4	4	NUM
ejpam-3687	191	3	.	.	X
ejpam-3687	192	1	for	for	ADP
ejpam-3687	192	2	q	q	PROPN
ejpam-3687	192	3	>	>	X
ejpam-3687	192	4	0	0	PUNCT
ejpam-3687	192	5	there	there	PRON
ejpam-3687	192	6	exists	exist	VERB
ejpam-3687	192	7	a	a	DET
ejpam-3687	192	8	cq	cq	NOUN
ejpam-3687	192	9	>	>	X
ejpam-3687	192	10	0	0	NUM
ejpam-3687	193	1	such	such	ADJ
ejpam-3687	193	2	that	that	SCONJ
ejpam-3687	193	3	max	max	PROPN
ejpam-3687	193	4	0≤k≤n	0≤k≤n	PROPN
ejpam-3687	193	5	(	(	PUNCT
ejpam-3687	193	6	n+	n+	ADP
ejpam-3687	193	7	α	α	X
ejpam-3687	193	8	k	k	PROPN
ejpam-3687	194	1	+	+	CCONJ
ejpam-3687	194	2	α	α	NOUN
ejpam-3687	194	3	)	)	PUNCT
ejpam-3687	194	4	qk+α	qk+α	PROPN
ejpam-3687	194	5	≤	≤	PROPN
ejpam-3687	194	6	cq	cq	NOUN
ejpam-3687	194	7	(	(	PUNCT
ejpam-3687	194	8	1	1	NUM
ejpam-3687	194	9	+	+	CCONJ
ejpam-3687	194	10	q)n+α√	q)n+α√	NOUN
ejpam-3687	194	11	n+	n+	NUM
ejpam-3687	194	12	α	α	NOUN
ejpam-3687	194	13	,	,	PUNCT
ejpam-3687	194	14	n	n	NOUN
ejpam-3687	194	15	=	=	SYM
ejpam-3687	194	16	1	1	NUM
ejpam-3687	194	17	,	,	PUNCT
ejpam-3687	194	18	2	2	NUM
ejpam-3687	194	19	,	,	PUNCT
ejpam-3687	194	20	...	...	PUNCT
ejpam-3687	195	1	proof	proof	NOUN
ejpam-3687	195	2	.	.	PUNCT
ejpam-3687	196	1	(	(	PUNCT
ejpam-3687	196	2	n+α+1	n+α+1	ADV
ejpam-3687	196	3	k+α	k+α	PROPN
ejpam-3687	196	4	)	)	PUNCT
ejpam-3687	196	5	(	(	PUNCT
ejpam-3687	196	6	n+α	n+α	X
ejpam-3687	196	7	k+α−1	k+α−1	X
ejpam-3687	196	8	)	)	PUNCT
ejpam-3687	196	9	=	=	SYM
ejpam-3687	196	10	n+	n+	X
ejpam-3687	196	11	α+	α+	PRON
ejpam-3687	196	12	1	1	NUM
ejpam-3687	196	13	k	k	NOUN
ejpam-3687	196	14	+	+	CCONJ
ejpam-3687	196	15	α	α	NOUN
ejpam-3687	196	16	.	.	PUNCT
ejpam-3687	197	1	let	let	VERB
ejpam-3687	197	2	dk	dk	NOUN
ejpam-3687	197	3	=	=	X
ejpam-3687	197	4	(	(	PUNCT
ejpam-3687	197	5	n+	n+	X
ejpam-3687	197	6	α+	α+	PUNCT
ejpam-3687	197	7	1	1	NUM
ejpam-3687	197	8	k	k	NOUN
ejpam-3687	197	9	+	+	CCONJ
ejpam-3687	197	10	α	α	NOUN
ejpam-3687	197	11	−	−	NOUN
ejpam-3687	197	12	1	1	NUM
ejpam-3687	197	13	)	)	PUNCT
ejpam-3687	197	14	q.	q.	NOUN
ejpam-3687	197	15	the	the	DET
ejpam-3687	197	16	dn	dn	PROPN
ejpam-3687	197	17	are	be	AUX
ejpam-3687	197	18	decreasing	decrease	VERB
ejpam-3687	197	19	in	in	ADP
ejpam-3687	197	20	k.	k.	PROPN
ejpam-3687	197	21	let	let	VERB
ejpam-3687	197	22	kn	kn	PROPN
ejpam-3687	197	23	denote	denote	VERB
ejpam-3687	197	24	the	the	DET
ejpam-3687	197	25	largest	large	ADJ
ejpam-3687	197	26	value	value	NOUN
ejpam-3687	197	27	of	of	ADP
ejpam-3687	197	28	k	k	PROPN
ejpam-3687	198	1	+	+	CCONJ
ejpam-3687	198	2	α	α	PROPN
ejpam-3687	198	3	for	for	ADP
ejpam-3687	198	4	which	which	PRON
ejpam-3687	198	5	dkn	dkn	NOUN
ejpam-3687	198	6	≥	≥	NOUN
ejpam-3687	198	7	1	1	NUM
ejpam-3687	198	8	.	.	PUNCT
ejpam-3687	198	9	then	then	ADV
ejpam-3687	198	10	dkn+1	dkn+1	VERB
ejpam-3687	198	11	<	<	X
ejpam-3687	198	12	1	1	NUM
ejpam-3687	198	13	,	,	PUNCT
ejpam-3687	198	14	and	and	CCONJ
ejpam-3687	198	15	max	max	PROPN
ejpam-3687	198	16	0≤k≤n	0≤k≤n	PROPN
ejpam-3687	198	17	(	(	PUNCT
ejpam-3687	198	18	n+	n+	ADP
ejpam-3687	198	19	α	α	X
ejpam-3687	198	20	k	k	PROPN
ejpam-3687	199	1	+	+	CCONJ
ejpam-3687	199	2	α	α	NOUN
ejpam-3687	199	3	)	)	PUNCT
ejpam-3687	199	4	qk+α	qk+α	NOUN
ejpam-3687	199	5	=	=	SYM
ejpam-3687	199	6	(	(	PUNCT
ejpam-3687	199	7	n+	n+	NUM
ejpam-3687	199	8	α	α	PROPN
ejpam-3687	199	9	kn	kn	PROPN
ejpam-3687	199	10	)	)	PUNCT
ejpam-3687	199	11	qkn	qkn	PROPN
ejpam-3687	199	12	.	.	PUNCT
ejpam-3687	200	1	f.	f.	PROPN
ejpam-3687	200	2	aydin	aydin	PROPN
ejpam-3687	200	3	akgun	akgun	PROPN
ejpam-3687	200	4	,	,	PUNCT
ejpam-3687	200	5	b.	b.	PROPN
ejpam-3687	200	6	e.	e.	PROPN
ejpam-3687	200	7	rhoades	rhoades	PROPN
ejpam-3687	200	8	/	/	SYM
ejpam-3687	200	9	eur	eur	PROPN
ejpam-3687	200	10	.	.	PUNCT
ejpam-3687	201	1	j.	j.	PROPN
ejpam-3687	201	2	pure	pure	PROPN
ejpam-3687	201	3	appl	appl	PROPN
ejpam-3687	201	4	.	.	PROPN
ejpam-3687	201	5	math	math	PROPN
ejpam-3687	201	6	,	,	PUNCT
ejpam-3687	201	7	13	13	NUM
ejpam-3687	201	8	(	(	PUNCT
ejpam-3687	201	9	3	3	NUM
ejpam-3687	201	10	)	)	PUNCT
ejpam-3687	201	11	(	(	PUNCT
ejpam-3687	201	12	2020	2020	NUM
ejpam-3687	201	13	)	)	PUNCT
ejpam-3687	201	14	,	,	PUNCT
ejpam-3687	201	15	390	390	NUM
ejpam-3687	201	16	-	-	SYM
ejpam-3687	201	17	402	402	NUM
ejpam-3687	201	18	397	397	NUM
ejpam-3687	201	19	it	it	PRON
ejpam-3687	201	20	then	then	ADV
ejpam-3687	201	21	follows	follow	VERB
ejpam-3687	201	22	that	that	SCONJ
ejpam-3687	201	23	one	one	PRON
ejpam-3687	201	24	can	can	AUX
ejpam-3687	201	25	write	write	VERB
ejpam-3687	201	26	kn	kn	PROPN
ejpam-3687	201	27	=	=	PUNCT
ejpam-3687	201	28	q	q	PROPN
ejpam-3687	201	29	1	1	NUM
ejpam-3687	202	1	+	+	CCONJ
ejpam-3687	202	2	q	q	X
ejpam-3687	202	3	(	(	PUNCT
ejpam-3687	202	4	n+	n+	NOUN
ejpam-3687	202	5	α	α	NOUN
ejpam-3687	202	6	)	)	PUNCT
ejpam-3687	202	7	+	+	CCONJ
ejpam-3687	203	1	νn	νn	PRON
ejpam-3687	203	2	,	,	PUNCT
ejpam-3687	203	3	where	where	SCONJ
ejpam-3687	203	4	0	0	X
ejpam-3687	203	5	<	<	X
ejpam-3687	203	6	νn	νn	X
ejpam-3687	203	7	<	<	X
ejpam-3687	203	8	1	1	NUM
ejpam-3687	203	9	.	.	PUNCT
ejpam-3687	204	1	then	then	ADV
ejpam-3687	204	2	(	(	PUNCT
ejpam-3687	204	3	n+	n+	NUM
ejpam-3687	204	4	α	α	PROPN
ejpam-3687	204	5	kn	kn	PROPN
ejpam-3687	204	6	)	)	PUNCT
ejpam-3687	204	7	≤	≤	PROPN
ejpam-3687	204	8	c1	c1	PROPN
ejpam-3687	204	9	(	(	PUNCT
ejpam-3687	204	10	n+	n+	NOUN
ejpam-3687	204	11	α	α	NOUN
ejpam-3687	204	12	)	)	PUNCT
ejpam-3687	204	13	!	!	PUNCT
ejpam-3687	205	1	kn!(n+	kn!(n+	PROPN
ejpam-3687	205	2	α−	α−	PROPN
ejpam-3687	205	3	kn	kn	PROPN
ejpam-3687	205	4	)	)	PUNCT
ejpam-3687	205	5	!	!	PUNCT
ejpam-3687	206	1	=	=	PUNCT
ejpam-3687	207	1	(	(	PUNCT
ejpam-3687	207	2	n+	n+	NUM
ejpam-3687	207	3	α)n+αe−(n+α	α)n+αe−(n+α	NOUN
ejpam-3687	207	4	)	)	PUNCT
ejpam-3687	207	5	√	√	PROPN
ejpam-3687	207	6	n+	n+	PUNCT
ejpam-3687	208	1	α	α	PROPN
ejpam-3687	208	2	(	(	PUNCT
ejpam-3687	208	3	kn)kne−(kn	kn)kne−(kn	PROPN
ejpam-3687	208	4	)	)	PUNCT
ejpam-3687	208	5	√	√	ADP
ejpam-3687	208	6	kn(n+	kn(n+	PROPN
ejpam-3687	208	7	α−	α−	ADP
ejpam-3687	208	8	kn)(n+α−kn)e−(n+α−kn	kn)(n+α−kn)e−(n+α−kn	PROPN
ejpam-3687	208	9	)	)	PUNCT
ejpam-3687	209	1	√	√	PROPN
ejpam-3687	209	2	n+	n+	PUNCT
ejpam-3687	210	1	α−	α−	ADP
ejpam-3687	210	2	kn	kn	PROPN
ejpam-3687	210	3	.	.	PUNCT
ejpam-3687	211	1	(	(	PUNCT
ejpam-3687	211	2	10	10	NUM
ejpam-3687	211	3	)	)	PUNCT
ejpam-3687	211	4	with	with	ADP
ejpam-3687	211	5	p	p	NOUN
ejpam-3687	211	6	=	=	PUNCT
ejpam-3687	211	7	q/(1	q/(1	PROPN
ejpam-3687	211	8	+	+	CCONJ
ejpam-3687	211	9	q	q	X
ejpam-3687	211	10	)	)	PUNCT
ejpam-3687	211	11	,	,	PUNCT
ejpam-3687	211	12	the	the	DET
ejpam-3687	211	13	right	right	ADJ
ejpam-3687	211	14	hand	hand	NOUN
ejpam-3687	211	15	side	side	NOUN
ejpam-3687	211	16	of	of	ADP
ejpam-3687	211	17	(	(	PUNCT
ejpam-3687	211	18	10	10	NUM
ejpam-3687	211	19	)	)	PUNCT
ejpam-3687	211	20	equals	equal	VERB
ejpam-3687	211	21	(	(	PUNCT
ejpam-3687	211	22	n+	n+	NUM
ejpam-3687	211	23	α)(n+α)e−(n+α	α)(n+α)e−(n+α	NUM
ejpam-3687	211	24	)	)	PUNCT
ejpam-3687	211	25	√	√	NUM
ejpam-3687	211	26	n+	n+	PUNCT
ejpam-3687	212	1	α	α	PROPN
ejpam-3687	212	2	(	(	PUNCT
ejpam-3687	212	3	p(n+	p(n+	NOUN
ejpam-3687	212	4	α	α	NUM
ejpam-3687	212	5	)	)	PUNCT
ejpam-3687	212	6	+	+	CCONJ
ejpam-3687	212	7	νn)(p(n+α)+νn)e−(p(n+α)+νn	νn)(p(n+α)+νn)e−(p(n+α)+νn	PROPN
ejpam-3687	212	8	)	)	PUNCT
ejpam-3687	212	9	√	√	PROPN
ejpam-3687	212	10	(	(	PUNCT
ejpam-3687	212	11	p(n+	p(n+	NOUN
ejpam-3687	212	12	α	α	X
ejpam-3687	212	13	)	)	PUNCT
ejpam-3687	212	14	+	+	CCONJ
ejpam-3687	212	15	νn	νn	X
ejpam-3687	212	16	)	)	PUNCT
ejpam-3687	212	17	×	×	NOUN
ejpam-3687	212	18	1	1	NUM
ejpam-3687	212	19	(	(	PUNCT
ejpam-3687	212	20	n+	n+	X
ejpam-3687	212	21	α−	α−	PART
ejpam-3687	212	22	p(n+	p(n+	NOUN
ejpam-3687	212	23	α)−	α)−	VERB
ejpam-3687	212	24	νn)(n+α−p(n+α)−νn)e−(n+α−p(n+α)−νn	νn)(n+α−p(n+α)−νn)e−(n+α−p(n+α)−νn	NOUN
ejpam-3687	212	25	)	)	PUNCT
ejpam-3687	212	26	√	√	PROPN
ejpam-3687	212	27	(	(	PUNCT
ejpam-3687	212	28	n+	n+	X
ejpam-3687	212	29	α−	α−	PART
ejpam-3687	212	30	p(n+	p(n+	NOUN
ejpam-3687	212	31	α)−	α)−	VERB
ejpam-3687	212	32	νn	νn	NOUN
ejpam-3687	212	33	)	)	PUNCT
ejpam-3687	212	34	=	=	SYM
ejpam-3687	212	35	(	(	PUNCT
ejpam-3687	212	36	n+	n+	INTJ
ejpam-3687	212	37	α)p(n+α)+νn	α)p(n+α)+νn	INTJ
ejpam-3687	212	38	(	(	PUNCT
ejpam-3687	212	39	p(n+	p(n+	NOUN
ejpam-3687	212	40	α	α	X
ejpam-3687	212	41	)	)	PUNCT
ejpam-3687	212	42	+	+	NUM
ejpam-3687	212	43	νn)(p(n+α)+νn	νn)(p(n+α)+νn	PROPN
ejpam-3687	212	44	)	)	PUNCT
ejpam-3687	212	45	×	×	NOUN
ejpam-3687	212	46	(	(	PUNCT
ejpam-3687	212	47	n+	n+	NUM
ejpam-3687	212	48	α)n+α−p(n+α)−νn	α)n+α−p(n+α)−νn	X
ejpam-3687	212	49	(	(	PUNCT
ejpam-3687	212	50	n+	n+	X
ejpam-3687	212	51	α−	α−	PART
ejpam-3687	212	52	p(n+	p(n+	NOUN
ejpam-3687	212	53	α)−	α)−	VERB
ejpam-3687	212	54	νn)n+α−p(n+α)−νn	νn)n+α−p(n+α)−νn	NOUN
ejpam-3687	212	55	(	(	PUNCT
ejpam-3687	212	56	11	11	NUM
ejpam-3687	212	57	)	)	PUNCT
ejpam-3687	212	58	×	×	NOUN
ejpam-3687	212	59	√	√	NUM
ejpam-3687	212	60	n+	n+	ADP
ejpam-3687	212	61	α√	α√	PROPN
ejpam-3687	212	62	(	(	PUNCT
ejpam-3687	212	63	p(n+	p(n+	NOUN
ejpam-3687	212	64	α	α	NUM
ejpam-3687	212	65	)	)	PUNCT
ejpam-3687	212	66	+	+	CCONJ
ejpam-3687	212	67	νn)(n+	νn)(n+	PROPN
ejpam-3687	212	68	α−	α−	AUX
ejpam-3687	212	69	p(n+	p(n+	NOUN
ejpam-3687	212	70	α)−	α)−	VERB
ejpam-3687	212	71	νn	νn	NOUN
ejpam-3687	212	72	)	)	PUNCT
ejpam-3687	212	73	.	.	PUNCT
ejpam-3687	213	1	note	note	VERB
ejpam-3687	213	2	that	that	SCONJ
ejpam-3687	213	3	(	(	PUNCT
ejpam-3687	213	4	n+	n+	X
ejpam-3687	213	5	α	α	NOUN
ejpam-3687	213	6	)	)	PUNCT
ejpam-3687	213	7	(	(	PUNCT
ejpam-3687	213	8	p(n+	p(n+	NOUN
ejpam-3687	213	9	α	α	X
ejpam-3687	213	10	)	)	PUNCT
ejpam-3687	214	1	+	+	CCONJ
ejpam-3687	214	2	νn)(n+	νn)(n+	PROPN
ejpam-3687	214	3	α−	α−	AUX
ejpam-3687	214	4	p(n+	p(n+	NOUN
ejpam-3687	214	5	α)−	α)−	VERB
ejpam-3687	214	6	νn	νn	PRON
ejpam-3687	214	7	)	)	PUNCT
ejpam-3687	214	8	=	=	SYM
ejpam-3687	214	9	(	(	PUNCT
ejpam-3687	214	10	n+	n+	NOUN
ejpam-3687	214	11	α	α	NOUN
ejpam-3687	214	12	)	)	PUNCT
ejpam-3687	214	13	(	(	PUNCT
ejpam-3687	214	14	n+	n+	NUM
ejpam-3687	214	15	α)2(p+	α)2(p+	PROPN
ejpam-3687	214	16	νn	νn	NOUN
ejpam-3687	214	17	n+α)(1−	n+α)(1−	NUM
ejpam-3687	214	18	(	(	PUNCT
ejpam-3687	214	19	p+	p+	X
ejpam-3687	214	20	νn	νn	NOUN
ejpam-3687	214	21	n+α	n+α	NUM
ejpam-3687	214	22	)	)	PUNCT
ejpam-3687	214	23	)	)	PUNCT
ejpam-3687	214	24	.	.	PUNCT
ejpam-3687	215	1	set	set	VERB
ejpam-3687	215	2	a	a	DET
ejpam-3687	215	3	=	=	X
ejpam-3687	215	4	p	p	NOUN
ejpam-3687	215	5	+	+	NOUN
ejpam-3687	215	6	νn/(n	νn/(n	NOUN
ejpam-3687	215	7	+	+	NOUN
ejpam-3687	215	8	α	α	NOUN
ejpam-3687	215	9	)	)	PUNCT
ejpam-3687	215	10	and	and	CCONJ
ejpam-3687	215	11	define	define	VERB
ejpam-3687	215	12	a	a	DET
ejpam-3687	215	13	function	function	NOUN
ejpam-3687	215	14	f	f	NOUN
ejpam-3687	215	15	by	by	ADP
ejpam-3687	215	16	f(a	f(a	PROPN
ejpam-3687	215	17	)	)	PUNCT
ejpam-3687	215	18	=	=	PUNCT
ejpam-3687	216	1	a(1	a(1	PROPN
ejpam-3687	216	2	−	−	PROPN
ejpam-3687	216	3	a	a	X
ejpam-3687	216	4	)	)	PUNCT
ejpam-3687	216	5	.	.	PUNCT
ejpam-3687	217	1	then	then	ADV
ejpam-3687	217	2	f(a	f(a	PROPN
ejpam-3687	217	3	)	)	PUNCT
ejpam-3687	217	4	has	have	VERB
ejpam-3687	217	5	a	a	DET
ejpam-3687	217	6	minimum	minimum	ADJ
ejpam-3687	217	7	value	value	NOUN
ejpam-3687	217	8	of	of	ADP
ejpam-3687	217	9	1/4	1/4	NUM
ejpam-3687	217	10	at	at	ADP
ejpam-3687	217	11	a	a	DET
ejpam-3687	217	12	=	=	SYM
ejpam-3687	217	13	1/2	1/2	NUM
ejpam-3687	217	14	.	.	PUNCT
ejpam-3687	218	1	therefore	therefore	ADV
ejpam-3687	218	2	1/	1/	NUM
ejpam-3687	218	3	√	√	NUM
ejpam-3687	218	4	f(a	f(a	NOUN
ejpam-3687	218	5	)	)	PUNCT
ejpam-3687	218	6	≤	≤	NOUN
ejpam-3687	218	7	2	2	NUM
ejpam-3687	218	8	.	.	PUNCT
ejpam-3687	218	9	from	from	ADP
ejpam-3687	218	10	(	(	PUNCT
ejpam-3687	218	11	11	11	NUM
ejpam-3687	218	12	)	)	PUNCT
ejpam-3687	218	13	(	(	PUNCT
ejpam-3687	218	14	n+	n+	NUM
ejpam-3687	218	15	α	α	PROPN
ejpam-3687	218	16	kn	kn	PROPN
ejpam-3687	218	17	)	)	PUNCT
ejpam-3687	218	18	≤	≤	ADV
ejpam-3687	218	19	2	2	NUM
ejpam-3687	218	20	1	1	NUM
ejpam-3687	218	21	(	(	PUNCT
ejpam-3687	218	22	p+	p+	NOUN
ejpam-3687	218	23	νn	νn	X
ejpam-3687	218	24	n+α	n+α	NUM
ejpam-3687	218	25	)	)	PUNCT
ejpam-3687	218	26	p(n+α)+νn	p(n+α)+νn	PROPN
ejpam-3687	218	27	×	×	NOUN
ejpam-3687	218	28	1	1	NUM
ejpam-3687	218	29	(	(	PUNCT
ejpam-3687	218	30	1−	1−	NUM
ejpam-3687	218	31	p−	p−	NOUN
ejpam-3687	218	32	νn	νn	ADJ
ejpam-3687	218	33	n+α	n+α	NUM
ejpam-3687	218	34	)	)	PUNCT
ejpam-3687	218	35	(	(	PUNCT
ejpam-3687	218	36	1−p)(n+α)−νn	1−p)(n+α)−νn	NUM
ejpam-3687	218	37	×	×	PROPN
ejpam-3687	218	38	1√	1√	PROPN
ejpam-3687	218	39	n+	n+	NUM
ejpam-3687	218	40	α	α	NOUN
ejpam-3687	218	41	=	=	SYM
ejpam-3687	218	42	2	2	NUM
ejpam-3687	218	43	1	1	NUM
ejpam-3687	218	44	pp(n+α)+νn	pp(n+α)+νn	ADP
ejpam-3687	218	45	(	(	PUNCT
ejpam-3687	218	46	1	1	NUM
ejpam-3687	218	47	+	+	CCONJ
ejpam-3687	218	48	νn	νn	NOUN
ejpam-3687	218	49	p(n+α	p(n+α	NUM
ejpam-3687	218	50	)	)	PUNCT
ejpam-3687	218	51	)	)	PUNCT
ejpam-3687	219	1	p(n+α)+νn	p(n+α)+νn	NOUN
ejpam-3687	219	2	×	×	NOUN
ejpam-3687	219	3	1	1	NUM
ejpam-3687	219	4	(	(	PUNCT
ejpam-3687	219	5	1−	1−	NUM
ejpam-3687	219	6	p)(1−p)(n+α)−νn	p)(1−p)(n+α)−νn	PROPN
ejpam-3687	219	7	(	(	PUNCT
ejpam-3687	219	8	1−	1−	NUM
ejpam-3687	219	9	νn	νn	PROPN
ejpam-3687	219	10	(	(	PUNCT
ejpam-3687	219	11	1−p)(n+α	1−p)(n+α	NUM
ejpam-3687	219	12	)	)	PUNCT
ejpam-3687	219	13	)	)	PUNCT
ejpam-3687	219	14	(	(	PUNCT
ejpam-3687	219	15	1−p)(n+α)−νn	1−p)(n+α)−νn	NUM
ejpam-3687	219	16	×	×	PROPN
ejpam-3687	219	17	1√	1√	PROPN
ejpam-3687	219	18	n+	n+	NUM
ejpam-3687	219	19	α	α	PROPN
ejpam-3687	219	20	.	.	PUNCT
ejpam-3687	220	1	since	since	SCONJ
ejpam-3687	220	2	(	(	PUNCT
ejpam-3687	220	3	1−p)/p	1−p)/p	NUM
ejpam-3687	220	4	=	=	SYM
ejpam-3687	220	5	(	(	PUNCT
ejpam-3687	220	6	1	1	NUM
ejpam-3687	220	7	/	/	SYM
ejpam-3687	220	8	p)−1	p)−1	NOUN
ejpam-3687	220	9	and	and	CCONJ
ejpam-3687	220	10	p	p	NOUN
ejpam-3687	220	11	is	be	AUX
ejpam-3687	220	12	a	a	DET
ejpam-3687	220	13	fixed	fix	VERB
ejpam-3687	220	14	positive	positive	ADJ
ejpam-3687	220	15	constant	constant	NOUN
ejpam-3687	220	16	between	between	ADP
ejpam-3687	220	17	0	0	NUM
ejpam-3687	220	18	and	and	CCONJ
ejpam-3687	220	19	1	1	NUM
ejpam-3687	220	20	,	,	PUNCT
ejpam-3687	220	21	(	(	PUNCT
ejpam-3687	220	22	p/(1−p))−νn	p/(1−p))−νn	NOUN
ejpam-3687	220	23	is	be	AUX
ejpam-3687	220	24	clearly	clearly	ADV
ejpam-3687	220	25	bounded	bound	VERB
ejpam-3687	220	26	.	.	PUNCT
ejpam-3687	221	1	so	so	ADV
ejpam-3687	221	2	also	also	ADV
ejpam-3687	221	3	is	be	AUX
ejpam-3687	221	4	(	(	PUNCT
ejpam-3687	221	5	1	1	NUM
ejpam-3687	221	6	+	+	NUM
ejpam-3687	221	7	νn/(p(n+	νn/(p(n+	X
ejpam-3687	221	8	α)))−p(n+α)−νn	α)))−p(n+α)−νn	PROPN
ejpam-3687	221	9	.	.	PUNCT
ejpam-3687	222	1	let	let	VERB
ejpam-3687	222	2	g(p	g(p	NOUN
ejpam-3687	222	3	)	)	PUNCT
ejpam-3687	223	1	=	=	SYM
ejpam-3687	223	2	1−	1−	NUM
ejpam-3687	223	3	νn/(1−	νn/(1−	VERB
ejpam-3687	223	4	p)(n+	p)(n+	PROPN
ejpam-3687	223	5	α	α	NOUN
ejpam-3687	223	6	)	)	PUNCT
ejpam-3687	223	7	.	.	PUNCT
ejpam-3687	224	1	then	then	ADV
ejpam-3687	224	2	g′(p	g′(p	X
ejpam-3687	224	3	)	)	PUNCT
ejpam-3687	224	4	=	=	SYM
ejpam-3687	225	1	νn	νn	X
ejpam-3687	225	2	(	(	PUNCT
ejpam-3687	225	3	1−	1−	NUM
ejpam-3687	225	4	p)2(n+	p)2(n+	NOUN
ejpam-3687	225	5	α	α	NOUN
ejpam-3687	225	6	)	)	PUNCT
ejpam-3687	225	7	,	,	PUNCT
ejpam-3687	225	8	f.	f.	PROPN
ejpam-3687	225	9	aydin	aydin	PROPN
ejpam-3687	225	10	akgun	akgun	PROPN
ejpam-3687	225	11	,	,	PUNCT
ejpam-3687	225	12	b.	b.	PROPN
ejpam-3687	225	13	e.	e.	PROPN
ejpam-3687	225	14	rhoades	rhoades	PROPN
ejpam-3687	225	15	/	/	SYM
ejpam-3687	225	16	eur	eur	PROPN
ejpam-3687	225	17	.	.	PUNCT
ejpam-3687	226	1	j.	j.	PROPN
ejpam-3687	226	2	pure	pure	PROPN
ejpam-3687	226	3	appl	appl	PROPN
ejpam-3687	226	4	.	.	PROPN
ejpam-3687	226	5	math	math	PROPN
ejpam-3687	226	6	,	,	PUNCT
ejpam-3687	226	7	13	13	NUM
ejpam-3687	226	8	(	(	PUNCT
ejpam-3687	226	9	3	3	NUM
ejpam-3687	226	10	)	)	PUNCT
ejpam-3687	226	11	(	(	PUNCT
ejpam-3687	226	12	2020	2020	NUM
ejpam-3687	226	13	)	)	PUNCT
ejpam-3687	226	14	,	,	PUNCT
ejpam-3687	226	15	390	390	NUM
ejpam-3687	226	16	-	-	SYM
ejpam-3687	226	17	402	402	NUM
ejpam-3687	226	18	398	398	NUM
ejpam-3687	226	19	and	and	CCONJ
ejpam-3687	226	20	g	g	PROPN
ejpam-3687	226	21	is	be	AUX
ejpam-3687	226	22	decreasing	decrease	VERB
ejpam-3687	226	23	in	in	ADP
ejpam-3687	226	24	p.	p.	NOUN
ejpam-3687	226	25	since	since	SCONJ
ejpam-3687	226	26	0	0	NUM
ejpam-3687	226	27	<	<	X
ejpam-3687	226	28	p	p	X
ejpam-3687	226	29	<	<	X
ejpam-3687	226	30	1	1	NUM
ejpam-3687	226	31	and	and	CCONJ
ejpam-3687	226	32	fixed	fix	VERB
ejpam-3687	226	33	,	,	PUNCT
ejpam-3687	226	34	g(p	g(p	PROPN
ejpam-3687	226	35	)	)	PUNCT
ejpam-3687	226	36	is	be	AUX
ejpam-3687	226	37	bounded	bound	VERB
ejpam-3687	226	38	,	,	PUNCT
ejpam-3687	226	39	using	use	VERB
ejpam-3687	226	40	the	the	DET
ejpam-3687	226	41	above	above	ADJ
ejpam-3687	226	42	facts	fact	NOUN
ejpam-3687	226	43	,	,	PUNCT
ejpam-3687	226	44	(	(	PUNCT
ejpam-3687	226	45	1−	1−	NUM
ejpam-3687	226	46	p	p	NOUN
ejpam-3687	226	47	p	p	PROPN
ejpam-3687	226	48	)	)	PUNCT
ejpam-3687	226	49	−νn	−νn	PROPN
ejpam-3687	226	50	and	and	CCONJ
ejpam-3687	226	51	(	(	PUNCT
ejpam-3687	226	52	p	p	PROPN
ejpam-3687	226	53	1−	1−	NUM
ejpam-3687	226	54	p	p	NOUN
ejpam-3687	226	55	)	)	PUNCT
ejpam-3687	226	56	−νn	−νn	PROPN
ejpam-3687	226	57	(	(	PUNCT
ejpam-3687	226	58	1	1	NUM
ejpam-3687	226	59	+	+	CCONJ
ejpam-3687	226	60	νn	νn	VERB
ejpam-3687	226	61	p(n+	p(n+	ADJ
ejpam-3687	226	62	α	α	NOUN
ejpam-3687	226	63	)	)	PUNCT
ejpam-3687	226	64	)	)	PUNCT
ejpam-3687	227	1	−(p(n+α))+νn	−(p(n+α))+νn	NOUN
ejpam-3687	227	2	(	(	PUNCT
ejpam-3687	227	3	1−	1−	NUM
ejpam-3687	227	4	νn	νn	X
ejpam-3687	227	5	(	(	PUNCT
ejpam-3687	227	6	1−	1−	NUM
ejpam-3687	227	7	p)n+	p)n+	NUM
ejpam-3687	227	8	α	α	NOUN
ejpam-3687	227	9	)	)	PUNCT
ejpam-3687	227	10	−((1−p)(n+α)+νn	−((1−p)(n+α)+νn	NOUN
ejpam-3687	227	11	)	)	PUNCT
ejpam-3687	227	12	are	be	AUX
ejpam-3687	227	13	bounded	bound	VERB
ejpam-3687	227	14	.	.	PUNCT
ejpam-3687	228	1	also	also	ADV
ejpam-3687	228	2	,	,	PUNCT
ejpam-3687	228	3	(	(	PUNCT
ejpam-3687	228	4	n+	n+	ADP
ejpam-3687	228	5	α	α	PROPN
ejpam-3687	228	6	kn	kn	NOUN
ejpam-3687	228	7	)	)	PUNCT
ejpam-3687	228	8	≤	≤	PUNCT
ejpam-3687	229	1	c3	c3	PROPN
ejpam-3687	229	2	1	1	NUM
ejpam-3687	229	3	pp(n+α	pp(n+α	NOUN
ejpam-3687	229	4	)	)	PUNCT
ejpam-3687	229	5	×	×	NOUN
ejpam-3687	229	6	1	1	NUM
ejpam-3687	229	7	(	(	PUNCT
ejpam-3687	229	8	1−	1−	NUM
ejpam-3687	229	9	p)(1−p)(n+α	p)(1−p)(n+α	NOUN
ejpam-3687	229	10	)	)	PUNCT
ejpam-3687	229	11	×	×	PROPN
ejpam-3687	229	12	1√	1√	PROPN
ejpam-3687	229	13	n+	n+	NUM
ejpam-3687	229	14	α	α	NOUN
ejpam-3687	229	15	.	.	PUNCT
ejpam-3687	230	1	(	(	PUNCT
ejpam-3687	230	2	12	12	NUM
ejpam-3687	230	3	)	)	PUNCT
ejpam-3687	230	4	we	we	PRON
ejpam-3687	230	5	can	can	AUX
ejpam-3687	230	6	write	write	VERB
ejpam-3687	230	7	(	(	PUNCT
ejpam-3687	230	8	12	12	NUM
ejpam-3687	230	9	)	)	PUNCT
ejpam-3687	230	10	as	as	ADP
ejpam-3687	230	11	(	(	PUNCT
ejpam-3687	230	12	n+	n+	ADP
ejpam-3687	230	13	α	α	PROPN
ejpam-3687	230	14	kn	kn	NOUN
ejpam-3687	230	15	)	)	PUNCT
ejpam-3687	230	16	≤	≤	PUNCT
ejpam-3687	230	17	c3	c3	X
ejpam-3687	230	18	1	1	NUM
ejpam-3687	230	19	q	q	PROPN
ejpam-3687	230	20	1+q	1+q	NUM
ejpam-3687	230	21	(	(	PUNCT
ejpam-3687	230	22	q	q	PROPN
ejpam-3687	230	23	1+q	1+q	NUM
ejpam-3687	230	24	)	)	PUNCT
ejpam-3687	230	25	(	(	PUNCT
ejpam-3687	230	26	n+α	n+α	NUM
ejpam-3687	230	27	)	)	PUNCT
ejpam-3687	230	28	×	×	NOUN
ejpam-3687	230	29	1	1	NUM
ejpam-3687	230	30	(	(	PUNCT
ejpam-3687	230	31	1	1	NUM
ejpam-3687	230	32	1+q	1+q	NUM
ejpam-3687	230	33	)	)	PUNCT
ejpam-3687	230	34	(	(	PUNCT
ejpam-3687	230	35	1	1	NUM
ejpam-3687	230	36	1+q	1+q	NUM
ejpam-3687	230	37	)	)	PUNCT
ejpam-3687	230	38	(	(	PUNCT
ejpam-3687	230	39	n+α	n+α	NUM
ejpam-3687	230	40	)	)	PUNCT
ejpam-3687	230	41	×	×	PROPN
ejpam-3687	230	42	1√	1√	NOUN
ejpam-3687	230	43	n+	n+	NUM
ejpam-3687	230	44	α	α	NOUN
ejpam-3687	230	45	.	.	PUNCT
ejpam-3687	231	1	(	(	PUNCT
ejpam-3687	231	2	13	13	NUM
ejpam-3687	231	3	)	)	PUNCT
ejpam-3687	231	4	from	from	ADP
ejpam-3687	231	5	(	(	PUNCT
ejpam-3687	231	6	13	13	NUM
ejpam-3687	231	7	)	)	PUNCT
ejpam-3687	231	8	(	(	PUNCT
ejpam-3687	231	9	n+	n+	ADP
ejpam-3687	231	10	α	α	PROPN
ejpam-3687	231	11	kn	kn	PROPN
ejpam-3687	231	12	)	)	PUNCT
ejpam-3687	231	13	qkn	qkn	PROPN
ejpam-3687	231	14	≤	≤	PUNCT
ejpam-3687	231	15	c3	c3	X
ejpam-3687	231	16	1	1	NUM
ejpam-3687	231	17	(	(	PUNCT
ejpam-3687	231	18	q	q	PROPN
ejpam-3687	231	19	1+q	1+q	NUM
ejpam-3687	231	20	)	)	PUNCT
ejpam-3687	231	21	(	(	PUNCT
ejpam-3687	231	22	q	q	PROPN
ejpam-3687	231	23	1+q	1+q	NUM
ejpam-3687	231	24	)	)	PUNCT
ejpam-3687	231	25	(	(	PUNCT
ejpam-3687	231	26	n+α	n+α	NUM
ejpam-3687	231	27	)	)	PUNCT
ejpam-3687	231	28	×	×	NOUN
ejpam-3687	231	29	1	1	NUM
ejpam-3687	231	30	(	(	PUNCT
ejpam-3687	231	31	1	1	NUM
ejpam-3687	231	32	1+q	1+q	NUM
ejpam-3687	231	33	)	)	PUNCT
ejpam-3687	231	34	(	(	PUNCT
ejpam-3687	231	35	1	1	NUM
ejpam-3687	231	36	1+q	1+q	NUM
ejpam-3687	231	37	)	)	PUNCT
ejpam-3687	231	38	(	(	PUNCT
ejpam-3687	231	39	n+α	n+α	NUM
ejpam-3687	231	40	)	)	PUNCT
ejpam-3687	231	41	×	×	PROPN
ejpam-3687	231	42	1√	1√	NOUN
ejpam-3687	231	43	n+	n+	NUM
ejpam-3687	231	44	α	α	PROPN
ejpam-3687	231	45	qkn	qkn	NOUN
ejpam-3687	231	46	=	=	PUNCT
ejpam-3687	231	47	c3	c3	NOUN
ejpam-3687	231	48	1	1	NUM
ejpam-3687	231	49	(	(	PUNCT
ejpam-3687	231	50	q	q	PROPN
ejpam-3687	231	51	1+q	1+q	NUM
ejpam-3687	231	52	)	)	PUNCT
ejpam-3687	231	53	(	(	PUNCT
ejpam-3687	231	54	q	q	PROPN
ejpam-3687	231	55	1+q	1+q	NUM
ejpam-3687	231	56	)	)	PUNCT
ejpam-3687	231	57	(	(	PUNCT
ejpam-3687	231	58	n+α	n+α	NUM
ejpam-3687	231	59	)	)	PUNCT
ejpam-3687	231	60	×	×	NOUN
ejpam-3687	231	61	1	1	NUM
ejpam-3687	231	62	(	(	PUNCT
ejpam-3687	231	63	1	1	NUM
ejpam-3687	231	64	1+q	1+q	NUM
ejpam-3687	231	65	)	)	PUNCT
ejpam-3687	231	66	(	(	PUNCT
ejpam-3687	231	67	1	1	NUM
ejpam-3687	231	68	1+q	1+q	NUM
ejpam-3687	231	69	)	)	PUNCT
ejpam-3687	231	70	(	(	PUNCT
ejpam-3687	231	71	n+α	n+α	NUM
ejpam-3687	231	72	)	)	PUNCT
ejpam-3687	231	73	×	×	PROPN
ejpam-3687	231	74	1√	1√	NOUN
ejpam-3687	231	75	n+	n+	PUNCT
ejpam-3687	232	1	α	α	PRON
ejpam-3687	232	2	q	q	NOUN
ejpam-3687	232	3	(	(	PUNCT
ejpam-3687	232	4	1	1	NUM
ejpam-3687	232	5	1+q	1+q	NUM
ejpam-3687	232	6	)	)	PUNCT
ejpam-3687	232	7	(	(	PUNCT
ejpam-3687	232	8	n+α)+νn	n+α)+νn	NOUN
ejpam-3687	232	9	=	=	SYM
ejpam-3687	232	10	c3	c3	PROPN
ejpam-3687	232	11	(	(	PUNCT
ejpam-3687	232	12	1	1	NUM
ejpam-3687	232	13	+	+	CCONJ
ejpam-3687	232	14	q)n+α√	q)n+α√	NOUN
ejpam-3687	232	15	n+	n+	NUM
ejpam-3687	232	16	α	α	NOUN
ejpam-3687	232	17	qνn	qνn	NOUN
ejpam-3687	233	1	≤	≤	PROPN
ejpam-3687	233	2	cq	cq	PROPN
ejpam-3687	233	3	(	(	PUNCT
ejpam-3687	233	4	1	1	NUM
ejpam-3687	233	5	+	+	CCONJ
ejpam-3687	233	6	q)n+α√	q)n+α√	NOUN
ejpam-3687	233	7	n+	n+	NUM
ejpam-3687	233	8	α	α	NOUN
ejpam-3687	233	9	.	.	PUNCT
ejpam-3687	234	1	thus	thus	ADV
ejpam-3687	234	2	max	max	PROPN
ejpam-3687	234	3	0≤k≤n	0≤k≤n	PROPN
ejpam-3687	234	4	(	(	PUNCT
ejpam-3687	234	5	n+	n+	ADP
ejpam-3687	234	6	α	α	X
ejpam-3687	234	7	k	k	PROPN
ejpam-3687	235	1	+	+	CCONJ
ejpam-3687	235	2	α	α	NOUN
ejpam-3687	235	3	)	)	PUNCT
ejpam-3687	235	4	qk+α	qk+α	PROPN
ejpam-3687	235	5	≤	≤	PROPN
ejpam-3687	235	6	cq	cq	NOUN
ejpam-3687	235	7	(	(	PUNCT
ejpam-3687	235	8	1	1	NUM
ejpam-3687	235	9	+	+	CCONJ
ejpam-3687	235	10	q)n+α√	q)n+α√	NOUN
ejpam-3687	235	11	n+	n+	NUM
ejpam-3687	235	12	α	α	NOUN
ejpam-3687	235	13	.	.	PUNCT
ejpam-3687	236	1	from	from	ADP
ejpam-3687	236	2	(	(	PUNCT
ejpam-3687	236	3	9	9	X
ejpam-3687	236	4	)	)	PUNCT
ejpam-3687	236	5	kk	kk	NOUN
ejpam-3687	237	1	∞∑	∞∑	NUM
ejpam-3687	237	2	r=0	r=0	PROPN
ejpam-3687	237	3	2r+1∑	2r+1∑	NUM
ejpam-3687	237	4	n=2r+1	n=2r+1	PROPN
ejpam-3687	237	5	γ(n)knk−1	γ(n)knk−1	NOUN
ejpam-3687	237	6	{	{	PUNCT
ejpam-3687	237	7	n∑	n∑	PROPN
ejpam-3687	237	8	m=0	m=0	PROPN
ejpam-3687	237	9	(	(	PUNCT
ejpam-3687	237	10	n+	n+	ADP
ejpam-3687	237	11	α	α	PRON
ejpam-3687	237	12	m+	m+	NUM
ejpam-3687	237	13	α	α	NOUN
ejpam-3687	237	14	)	)	PUNCT
ejpam-3687	237	15	2(m+	2(m+	PROPN
ejpam-3687	238	1	α	α	NOUN
ejpam-3687	238	2	n+	n+	PUNCT
ejpam-3687	238	3	α	α	NOUN
ejpam-3687	238	4	)	)	PUNCT
ejpam-3687	238	5	2	2	NUM
ejpam-3687	238	6	q2n−2m(1	q2n−2m(1	NOUN
ejpam-3687	238	7	+	+	CCONJ
ejpam-3687	238	8	q)−2n−2α|bm|2	q)−2n−2α|bm|2	NOUN
ejpam-3687	238	9	}	}	PUNCT
ejpam-3687	238	10	k/2	k/2	PROPN
ejpam-3687	238	11	=	=	PUNCT
ejpam-3687	239	1	kk	kk	PROPN
ejpam-3687	240	1	∞∑	∞∑	PROPN
ejpam-3687	240	2	r=0	r=0	PROPN
ejpam-3687	240	3	2r+1∑	2r+1∑	NUM
ejpam-3687	241	1	n=2r+1	n=2r+1	PROPN
ejpam-3687	241	2	γ(n)knk−1	γ(n)knk−1	NOUN
ejpam-3687	241	3	{	{	PUNCT
ejpam-3687	241	4	n∑	n∑	PROPN
ejpam-3687	241	5	m=0	m=0	PROPN
ejpam-3687	241	6	(	(	PUNCT
ejpam-3687	241	7	n+	n+	ADP
ejpam-3687	241	8	α	α	PRON
ejpam-3687	241	9	m+	m+	NUM
ejpam-3687	241	10	α	α	NOUN
ejpam-3687	241	11	)	)	PUNCT
ejpam-3687	241	12	(	(	PUNCT
ejpam-3687	241	13	m+	m+	NUM
ejpam-3687	241	14	α	α	NOUN
ejpam-3687	241	15	n+	n+	PUNCT
ejpam-3687	241	16	α	α	NOUN
ejpam-3687	241	17	)	)	PUNCT
ejpam-3687	241	18	2(n+	2(n+	NOUN
ejpam-3687	242	1	α	α	NOUN
ejpam-3687	242	2	n−m	n−m	PROPN
ejpam-3687	242	3	)	)	PUNCT
ejpam-3687	242	4	qn−mqn−m(1	qn−mqn−m(1	NOUN
ejpam-3687	242	5	+	+	X
ejpam-3687	242	6	q)−2n−2α|bm|2	q)−2n−2α|bm|2	NOUN
ejpam-3687	242	7	}	}	PUNCT
ejpam-3687	242	8	k/2	k/2	PROPN
ejpam-3687	242	9	.	.	PUNCT
ejpam-3687	243	1	(	(	PUNCT
ejpam-3687	243	2	14	14	NUM
ejpam-3687	243	3	)	)	PUNCT
ejpam-3687	243	4	using	use	VERB
ejpam-3687	243	5	lemma	lemma	PROPN
ejpam-3687	243	6	4	4	NUM
ejpam-3687	243	7	,	,	PUNCT
ejpam-3687	243	8	equation	equation	NOUN
ejpam-3687	243	9	(	(	PUNCT
ejpam-3687	243	10	14	14	NUM
ejpam-3687	243	11	)	)	PUNCT
ejpam-3687	243	12	can	can	AUX
ejpam-3687	243	13	be	be	AUX
ejpam-3687	243	14	written	write	VERB
ejpam-3687	243	15	as	as	SCONJ
ejpam-3687	243	16	≤	≤	NUM
ejpam-3687	243	17	kkck/2q	kkck/2q	VERB
ejpam-3687	243	18	∞∑	∞∑	NUM
ejpam-3687	243	19	r=0	r=0	PROPN
ejpam-3687	243	20	2r+1∑	2r+1∑	NUM
ejpam-3687	243	21	n=2r+1	n=2r+1	PROPN
ejpam-3687	243	22	γ(n)knk−1	γ(n)knk−1	NOUN
ejpam-3687	243	23	{	{	PUNCT
ejpam-3687	243	24	n∑	n∑	PROPN
ejpam-3687	243	25	m=0	m=0	PROPN
ejpam-3687	243	26	(	(	PUNCT
ejpam-3687	243	27	n+	n+	ADP
ejpam-3687	243	28	α	α	PRON
ejpam-3687	243	29	m+	m+	NUM
ejpam-3687	243	30	α	α	NOUN
ejpam-3687	243	31	)	)	PUNCT
ejpam-3687	243	32	(	(	PUNCT
ejpam-3687	243	33	m+	m+	NUM
ejpam-3687	243	34	α	α	NOUN
ejpam-3687	243	35	n+	n+	PUNCT
ejpam-3687	243	36	α	α	NOUN
ejpam-3687	243	37	)	)	PUNCT
ejpam-3687	243	38	2	2	NUM
ejpam-3687	243	39	1√	1√	NUM
ejpam-3687	243	40	n+	n+	ADP
ejpam-3687	243	41	α	α	NOUN
ejpam-3687	243	42	qn−m(1	qn−m(1	NOUN
ejpam-3687	243	43	+	+	X
ejpam-3687	243	44	q)−2n−2α|bm|2	q)−2n−2α|bm|2	NOUN
ejpam-3687	243	45	}	}	PUNCT
ejpam-3687	243	46	k/2	k/2	PROPN
ejpam-3687	243	47	f.	f.	PROPN
ejpam-3687	243	48	aydin	aydin	PROPN
ejpam-3687	243	49	akgun	akgun	PROPN
ejpam-3687	243	50	,	,	PUNCT
ejpam-3687	243	51	b.	b.	PROPN
ejpam-3687	243	52	e.	e.	PROPN
ejpam-3687	243	53	rhoades	rhoades	PROPN
ejpam-3687	243	54	/	/	SYM
ejpam-3687	243	55	eur	eur	PROPN
ejpam-3687	243	56	.	.	PUNCT
ejpam-3687	244	1	j.	j.	PROPN
ejpam-3687	244	2	pure	pure	PROPN
ejpam-3687	244	3	appl	appl	PROPN
ejpam-3687	244	4	.	.	PROPN
ejpam-3687	244	5	math	math	PROPN
ejpam-3687	244	6	,	,	PUNCT
ejpam-3687	244	7	13	13	NUM
ejpam-3687	244	8	(	(	PUNCT
ejpam-3687	244	9	3	3	NUM
ejpam-3687	244	10	)	)	PUNCT
ejpam-3687	244	11	(	(	PUNCT
ejpam-3687	244	12	2020	2020	NUM
ejpam-3687	244	13	)	)	PUNCT
ejpam-3687	244	14	,	,	PUNCT
ejpam-3687	244	15	390	390	NUM
ejpam-3687	244	16	-	-	SYM
ejpam-3687	244	17	402	402	NUM
ejpam-3687	244	18	399	399	NUM
ejpam-3687	244	19	=	=	PUNCT
ejpam-3687	244	20	kkck/2q	kkck/2q	VERB
ejpam-3687	244	21	∞∑	∞∑	NUM
ejpam-3687	244	22	r=0	r=0	PROPN
ejpam-3687	244	23	2r+1∑	2r+1∑	NUM
ejpam-3687	245	1	n=2r+1	n=2r+1	PROPN
ejpam-3687	245	2	γ(n)knk−1	γ(n)knk−1	NOUN
ejpam-3687	245	3	{	{	PUNCT
ejpam-3687	245	4	n∑	n∑	PROPN
ejpam-3687	245	5	m=0	m=0	PROPN
ejpam-3687	245	6	(	(	PUNCT
ejpam-3687	245	7	n+	n+	ADP
ejpam-3687	245	8	α	α	PRON
ejpam-3687	245	9	m+	m+	NUM
ejpam-3687	245	10	α	α	NOUN
ejpam-3687	245	11	)	)	PUNCT
ejpam-3687	245	12	(	(	PUNCT
ejpam-3687	245	13	m+	m+	NUM
ejpam-3687	245	14	α)2	α)2	NOUN
ejpam-3687	245	15	1	1	NUM
ejpam-3687	245	16	(	(	PUNCT
ejpam-3687	245	17	n+	n+	ADP
ejpam-3687	245	18	α)5/2	α)5/2	NUM
ejpam-3687	245	19	qn−m(1	qn−m(1	NOUN
ejpam-3687	245	20	+	+	X
ejpam-3687	245	21	q)−2n−2α|bm|2	q)−2n−2α|bm|2	NOUN
ejpam-3687	245	22	}	}	PUNCT
ejpam-3687	245	23	k/2	k/2	PROPN
ejpam-3687	245	24	.	.	PUNCT
ejpam-3687	246	1	(	(	PUNCT
ejpam-3687	246	2	15	15	NUM
ejpam-3687	246	3	)	)	PUNCT
ejpam-3687	246	4	for	for	ADP
ejpam-3687	246	5	k	k	PROPN
ejpam-3687	246	6	=	=	SYM
ejpam-3687	246	7	2	2	NUM
ejpam-3687	246	8	,	,	PUNCT
ejpam-3687	246	9	the	the	DET
ejpam-3687	246	10	above	above	ADJ
ejpam-3687	246	11	inequality	inequality	NOUN
ejpam-3687	246	12	becomes	become	VERB
ejpam-3687	246	13	ω	ω	PROPN
ejpam-3687	246	14	≤	≤	NUM
ejpam-3687	246	15	k2cq	k2cq	VERB
ejpam-3687	247	1	∞∑	∞∑	NUM
ejpam-3687	247	2	r=0	r=0	PROPN
ejpam-3687	247	3	2r+1∑	2r+1∑	NUM
ejpam-3687	247	4	n=2r+1	n=2r+1	PROPN
ejpam-3687	247	5	γ(n)2n(n+α)−5/2	γ(n)2n(n+α)−5/2	PROPN
ejpam-3687	247	6	{	{	PUNCT
ejpam-3687	247	7	n∑	n∑	NOUN
ejpam-3687	247	8	m=0	m=0	PROPN
ejpam-3687	247	9	(	(	PUNCT
ejpam-3687	247	10	n+	n+	ADP
ejpam-3687	247	11	α	α	PRON
ejpam-3687	247	12	m+	m+	NUM
ejpam-3687	247	13	α	α	NOUN
ejpam-3687	247	14	)	)	PUNCT
ejpam-3687	247	15	(	(	PUNCT
ejpam-3687	247	16	m+	m+	NOUN
ejpam-3687	247	17	α)2qn−m(1	α)2qn−m(1	NUM
ejpam-3687	247	18	+	+	PUNCT
ejpam-3687	247	19	q)−2n−2α|bm|2	q)−2n−2α|bm|2	NOUN
ejpam-3687	247	20	}	}	PUNCT
ejpam-3687	247	21	5/2	5/2	NUM
ejpam-3687	247	22	.	.	PUNCT
ejpam-3687	248	1	(	(	PUNCT
ejpam-3687	248	2	16	16	NUM
ejpam-3687	248	3	)	)	PUNCT
ejpam-3687	248	4	lemma	lemma	PROPN
ejpam-3687	248	5	5	5	NUM
ejpam-3687	248	6	.	.	PUNCT
ejpam-3687	249	1	there	there	PRON
ejpam-3687	249	2	exists	exist	VERB
ejpam-3687	249	3	a	a	DET
ejpam-3687	249	4	dq	dq	NOUN
ejpam-3687	249	5	>	>	X
ejpam-3687	249	6	0	0	NUM
ejpam-3687	250	1	such	such	ADJ
ejpam-3687	250	2	that	that	SCONJ
ejpam-3687	250	3	∞∑	∞∑	NUM
ejpam-3687	250	4	n	n	NOUN
ejpam-3687	250	5	=	=	NOUN
ejpam-3687	250	6	m	m	PROPN
ejpam-3687	250	7	(	(	PUNCT
ejpam-3687	250	8	n+	n+	ADP
ejpam-3687	250	9	α	α	PRON
ejpam-3687	250	10	m+	m+	NUM
ejpam-3687	250	11	α	α	NOUN
ejpam-3687	250	12	)	)	PUNCT
ejpam-3687	250	13	qn−m(1	qn−m(1	NOUN
ejpam-3687	250	14	+	+	CCONJ
ejpam-3687	250	15	q)−n−α	q)−n−α	CCONJ
ejpam-3687	250	16	≤	≤	NUM
ejpam-3687	250	17	dq	dq	NOUN
ejpam-3687	250	18	for	for	ADP
ejpam-3687	250	19	all	all	DET
ejpam-3687	250	20	m	m	NOUN
ejpam-3687	250	21	∈	∈	NOUN
ejpam-3687	250	22	z+	z+	NUM
ejpam-3687	250	23	and	and	CCONJ
ejpam-3687	250	24	1	1	NUM
ejpam-3687	250	25	≤	≤	NUM
ejpam-3687	250	26	k	k	X
ejpam-3687	250	27	≤	≤	NUM
ejpam-3687	250	28	2	2	NUM
ejpam-3687	250	29	.	.	PUNCT
ejpam-3687	251	1	proof	proof	NOUN
ejpam-3687	251	2	.	.	PUNCT
ejpam-3687	252	1	the	the	DET
ejpam-3687	252	2	proof	proof	NOUN
ejpam-3687	252	3	of	of	ADP
ejpam-3687	252	4	the	the	DET
ejpam-3687	252	5	lemma	lemma	PROPN
ejpam-3687	252	6	is	be	AUX
ejpam-3687	252	7	easy	easy	ADJ
ejpam-3687	252	8	to	to	PART
ejpam-3687	252	9	verify	verify	VERB
ejpam-3687	252	10	and	and	CCONJ
ejpam-3687	252	11	it	it	PRON
ejpam-3687	252	12	is	be	AUX
ejpam-3687	252	13	a	a	DET
ejpam-3687	252	14	generalization	generalization	NOUN
ejpam-3687	252	15	of	of	ADP
ejpam-3687	252	16	theorem	theorem	PROPN
ejpam-3687	252	17	b	b	PROPN
ejpam-3687	252	18	of	of	ADP
ejpam-3687	252	19	[	[	X
ejpam-3687	252	20	6	6	NUM
ejpam-3687	252	21	]	]	PUNCT
ejpam-3687	252	22	to	to	ADP
ejpam-3687	252	23	e	e	PROPN
ejpam-3687	252	24	-	-	PROPN
ejpam-3687	252	25	j	j	NOUN
ejpam-3687	252	26	matrices	matrix	NOUN
ejpam-3687	252	27	.	.	PUNCT
ejpam-3687	253	1	using	use	VERB
ejpam-3687	253	2	theorem	theorem	ADJ
ejpam-3687	253	3	b	b	PROPN
ejpam-3687	253	4	of	of	ADP
ejpam-3687	253	5	[	[	X
ejpam-3687	253	6	6	6	NUM
ejpam-3687	253	7	]	]	PUNCT
ejpam-3687	253	8	,	,	PUNCT
ejpam-3687	253	9	we	we	PRON
ejpam-3687	253	10	can	can	AUX
ejpam-3687	253	11	write	write	VERB
ejpam-3687	253	12	(	(	PUNCT
ejpam-3687	253	13	16	16	NUM
ejpam-3687	253	14	)	)	PUNCT
ejpam-3687	253	15	as	as	ADP
ejpam-3687	253	16	ω	ω	NUM
ejpam-3687	253	17	≤	≤	NUM
ejpam-3687	253	18	k2cqdq	k2cqdq	NOUN
ejpam-3687	253	19	∞∑	∞∑	PROPN
ejpam-3687	253	20	r=0	r=0	PROPN
ejpam-3687	253	21	γ(2r+1)22r(2r	γ(2r+1)22r(2r	X
ejpam-3687	254	1	+	+	CCONJ
ejpam-3687	254	2	α)−5/2	α)−5/2	PROPN
ejpam-3687	254	3	2r+1∑	2r+1∑	PROPN
ejpam-3687	254	4	m=0	m=0	PROPN
ejpam-3687	254	5	(	(	PUNCT
ejpam-3687	254	6	m+	m+	NOUN
ejpam-3687	254	7	α)2|bm|2	α)2|bm|2	X
ejpam-3687	254	8	≤	≤	NUM
ejpam-3687	254	9	k2cqdq	k2cqdq	NOUN
ejpam-3687	254	10	∞∑	∞∑	PROPN
ejpam-3687	254	11	r=0	r=0	PROPN
ejpam-3687	254	12	γ(2r+1)2(2r	γ(2r+1)2(2r	PRON
ejpam-3687	255	1	+	+	CCONJ
ejpam-3687	255	2	α)−3/2	α)−3/2	PROPN
ejpam-3687	255	3	2r+1∑	2r+1∑	NUM
ejpam-3687	255	4	m=0	m=0	PROPN
ejpam-3687	255	5	(	(	PUNCT
ejpam-3687	255	6	m+	m+	NUM
ejpam-3687	255	7	α)2|bm|2	α)2|bm|2	NOUN
ejpam-3687	255	8	,	,	PUNCT
ejpam-3687	255	9	α	α	NOUN
ejpam-3687	255	10	>	>	X
ejpam-3687	255	11	0	0	X
ejpam-3687	255	12	.	.	PUNCT
ejpam-3687	256	1	let	let	VERB
ejpam-3687	256	2	p	p	NOUN
ejpam-3687	256	3	=	=	ADJ
ejpam-3687	256	4	2	2	NUM
ejpam-3687	256	5	/	/	SYM
ejpam-3687	256	6	k.	k.	NOUN
ejpam-3687	256	7	by	by	ADP
ejpam-3687	256	8	hölder	hölder	PROPN
ejpam-3687	256	9	’s	’s	PART
ejpam-3687	256	10	inequality	inequality	NOUN
ejpam-3687	256	11	,	,	PUNCT
ejpam-3687	256	12	for	for	ADP
ejpam-3687	256	13	α	α	PROPN
ejpam-3687	256	14	>	>	X
ejpam-3687	256	15	0	0	NUM
ejpam-3687	256	16	and	and	CCONJ
ejpam-3687	256	17	1	1	NUM
ejpam-3687	256	18	≤	≤	NUM
ejpam-3687	256	19	k	k	X
ejpam-3687	256	20	≤	≤	NUM
ejpam-3687	256	21	2	2	NUM
ejpam-3687	256	22	,	,	PUNCT
ejpam-3687	256	23	ω	ω	NOUN
ejpam-3687	256	24	=	=	PUNCT
ejpam-3687	256	25	kkck/2q	kkck/2q	PROPN
ejpam-3687	256	26	∞∑	∞∑	PROPN
ejpam-3687	256	27	r=0	r=0	PROPN
ejpam-3687	256	28	(	(	PUNCT
ejpam-3687	256	29	2r+1∑	2r+1∑	NUM
ejpam-3687	256	30	n=2r+1	n=2r+1	PROPN
ejpam-3687	256	31	γ(n)kqnq	γ(n)kqnq	NOUN
ejpam-3687	256	32	(	(	PUNCT
ejpam-3687	256	33	−k	−k	PROPN
ejpam-3687	256	34	4	4	NUM
ejpam-3687	256	35	−1	−1	NOUN
ejpam-3687	256	36	)	)	PUNCT
ejpam-3687	256	37	)	)	PUNCT
ejpam-3687	257	1	1	1	X
ejpam-3687	257	2	/	/	SYM
ejpam-3687	257	3	q	q	NOUN
ejpam-3687	257	4	{	{	PUNCT
ejpam-3687	257	5	2r+1∑	2r+1∑	NUM
ejpam-3687	257	6	n=2r+1	n=2r+1	PROPN
ejpam-3687	257	7	n∑	n∑	PROPN
ejpam-3687	257	8	m=0	m=0	PROPN
ejpam-3687	257	9	(	(	PUNCT
ejpam-3687	257	10	n+	n+	ADP
ejpam-3687	257	11	α	α	PRON
ejpam-3687	257	12	m+	m+	NUM
ejpam-3687	257	13	α	α	NOUN
ejpam-3687	257	14	)	)	PUNCT
ejpam-3687	257	15	(	(	PUNCT
ejpam-3687	257	16	m+α)2qn−m(1+q)−n−α|bm|2	m+α)2qn−m(1+q)−n−α|bm|2	X
ejpam-3687	257	17	}	}	PUNCT
ejpam-3687	257	18	.	.	PUNCT
ejpam-3687	258	1	(	(	PUNCT
ejpam-3687	258	2	17	17	NUM
ejpam-3687	258	3	)	)	PUNCT
ejpam-3687	258	4	since	since	SCONJ
ejpam-3687	258	5	γ	γ	PROPN
ejpam-3687	258	6	∈	∈	PROPN
ejpam-3687	258	7	γ(β	γ(β	PROPN
ejpam-3687	258	8	)	)	PUNCT
ejpam-3687	258	9	and	and	CCONJ
ejpam-3687	258	10	,	,	PUNCT
ejpam-3687	258	11	for	for	ADP
ejpam-3687	258	12	β	β	X
ejpam-3687	258	13	∈	∈	PROPN
ejpam-3687	258	14	r	r	NOUN
ejpam-3687	258	15	,	,	PUNCT
ejpam-3687	258	16	by	by	ADP
ejpam-3687	258	17	theorem	theorem	NOUN
ejpam-3687	258	18	a	a	PRON
ejpam-3687	258	19	in	in	ADP
ejpam-3687	258	20	[	[	X
ejpam-3687	258	21	6	6	NUM
ejpam-3687	258	22	]	]	PUNCT
ejpam-3687	258	23	,	,	PUNCT
ejpam-3687	258	24	we	we	PRON
ejpam-3687	258	25	can	can	AUX
ejpam-3687	258	26	write	write	VERB
ejpam-3687	258	27	the	the	DET
ejpam-3687	258	28	expression	expression	NOUN
ejpam-3687	258	29	in	in	ADP
ejpam-3687	258	30	the	the	DET
ejpam-3687	258	31	first	first	ADJ
ejpam-3687	258	32	bracket	bracket	NOUN
ejpam-3687	258	33	in	in	ADP
ejpam-3687	258	34	(	(	PUNCT
ejpam-3687	258	35	17	17	NUM
ejpam-3687	258	36	)	)	PUNCT
ejpam-3687	258	37	as	as	PROPN
ejpam-3687	258	38	2r+1∑	2r+1∑	PROPN
ejpam-3687	258	39	n=2r+1	n=2r+1	PROPN
ejpam-3687	258	40	γ(n)kqnq	γ(n)kqnq	NOUN
ejpam-3687	258	41	(	(	PUNCT
ejpam-3687	258	42	−k	−k	PROPN
ejpam-3687	258	43	4	4	NUM
ejpam-3687	258	44	−1	−1	NOUN
ejpam-3687	258	45	)	)	PUNCT
ejpam-3687	258	46	1	1	NOUN
ejpam-3687	258	47	/	/	SYM
ejpam-3687	258	48	q	q	NOUN
ejpam-3687	258	49	≤	≤	NUM
ejpam-3687	258	50	k1	k1	NOUN
ejpam-3687	258	51	/	/	SYM
ejpam-3687	258	52	qγ(2r	qγ(2r	PROPN
ejpam-3687	258	53	+	+	X
ejpam-3687	258	54	1)k(2r	1)k(2r	NOUN
ejpam-3687	259	1	+	+	CCONJ
ejpam-3687	259	2	1)(−	1)(−	NUM
ejpam-3687	259	3	k	k	NOUN
ejpam-3687	259	4	4	4	NUM
ejpam-3687	259	5	−1	−1	NOUN
ejpam-3687	259	6	)	)	PUNCT
ejpam-3687	259	7	≤	≤	NUM
ejpam-3687	259	8	k1	k1	NOUN
ejpam-3687	259	9	/	/	SYM
ejpam-3687	259	10	qγ(2r	qγ(2r	PROPN
ejpam-3687	259	11	+	+	X
ejpam-3687	259	12	1)k(2r)(−	1)k(2r)(−	NUM
ejpam-3687	259	13	k	k	NOUN
ejpam-3687	259	14	4	4	NUM
ejpam-3687	259	15	−1	−1	NOUN
ejpam-3687	259	16	)	)	PUNCT
ejpam-3687	259	17	.	.	PUNCT
ejpam-3687	260	1	thus	thus	ADV
ejpam-3687	260	2	,	,	PUNCT
ejpam-3687	260	3	from	from	ADP
ejpam-3687	260	4	(	(	PUNCT
ejpam-3687	260	5	17	17	NUM
ejpam-3687	260	6	)	)	PUNCT
ejpam-3687	260	7	,	,	PUNCT
ejpam-3687	260	8	ω	ω	PROPN
ejpam-3687	260	9	≤	≤	X
ejpam-3687	260	10	kk+	kk+	NOUN
ejpam-3687	260	11	1	1	NUM
ejpam-3687	260	12	qck/2q	qck/2q	NOUN
ejpam-3687	260	13	∞∑	∞∑	PROPN
ejpam-3687	260	14	r=0	r=0	PROPN
ejpam-3687	260	15	γ(2r+1)k(2r	γ(2r+1)k(2r	NOUN
ejpam-3687	260	16	)	)	PUNCT
ejpam-3687	260	17	(	(	PUNCT
ejpam-3687	260	18	−k	−k	PROPN
ejpam-3687	260	19	4	4	NUM
ejpam-3687	260	20	−1	−1	NOUN
ejpam-3687	260	21	)	)	PUNCT
ejpam-3687	260	22			PROPN
ejpam-3687	260	23	2r+1∑	2r+1∑	NUM
ejpam-3687	260	24	n=2r+1	n=2r+1	PROPN
ejpam-3687	260	25	n∑	n∑	PROPN
ejpam-3687	260	26	m=0	m=0	PROPN
ejpam-3687	260	27	(	(	PUNCT
ejpam-3687	260	28	n+	n+	ADP
ejpam-3687	260	29	α	α	PRON
ejpam-3687	260	30	m+	m+	NUM
ejpam-3687	260	31	α	α	NOUN
ejpam-3687	260	32	)	)	PUNCT
ejpam-3687	260	33	(	(	PUNCT
ejpam-3687	260	34	m+	m+	NOUN
ejpam-3687	260	35	α)2qn−m(1	α)2qn−m(1	NUM
ejpam-3687	260	36	+	+	CCONJ
ejpam-3687	260	37	q)−n−α|bm|2	q)−n−α|bm|2	X
ejpam-3687	260	38			PROPN
ejpam-3687	260	39	k/2	k/2	PROPN
ejpam-3687	260	40	.	.	PUNCT
ejpam-3687	261	1	(	(	PUNCT
ejpam-3687	261	2	18	18	NUM
ejpam-3687	261	3	)	)	PUNCT
ejpam-3687	261	4	f.	f.	PROPN
ejpam-3687	261	5	aydin	aydin	PROPN
ejpam-3687	261	6	akgun	akgun	PROPN
ejpam-3687	261	7	,	,	PUNCT
ejpam-3687	261	8	b.	b.	PROPN
ejpam-3687	261	9	e.	e.	PROPN
ejpam-3687	261	10	rhoades	rhoades	PROPN
ejpam-3687	261	11	/	/	SYM
ejpam-3687	261	12	eur	eur	PROPN
ejpam-3687	261	13	.	.	PUNCT
ejpam-3687	262	1	j.	j.	PROPN
ejpam-3687	262	2	pure	pure	PROPN
ejpam-3687	262	3	appl	appl	PROPN
ejpam-3687	262	4	.	.	PROPN
ejpam-3687	262	5	math	math	PROPN
ejpam-3687	262	6	,	,	PUNCT
ejpam-3687	262	7	13	13	NUM
ejpam-3687	262	8	(	(	PUNCT
ejpam-3687	262	9	3	3	NUM
ejpam-3687	262	10	)	)	PUNCT
ejpam-3687	262	11	(	(	PUNCT
ejpam-3687	262	12	2020	2020	NUM
ejpam-3687	262	13	)	)	PUNCT
ejpam-3687	262	14	,	,	PUNCT
ejpam-3687	262	15	390	390	NUM
ejpam-3687	262	16	-	-	SYM
ejpam-3687	262	17	402	402	NUM
ejpam-3687	262	18	400	400	NUM
ejpam-3687	262	19	changing	change	VERB
ejpam-3687	262	20	the	the	DET
ejpam-3687	262	21	order	order	NOUN
ejpam-3687	262	22	of	of	ADP
ejpam-3687	262	23	summation	summation	NOUN
ejpam-3687	262	24	inside	inside	ADP
ejpam-3687	262	25	the	the	DET
ejpam-3687	262	26	brackets	bracket	NOUN
ejpam-3687	262	27	in	in	ADP
ejpam-3687	262	28	the	the	DET
ejpam-3687	262	29	above	above	ADJ
ejpam-3687	262	30	inequality	inequality	NOUN
ejpam-3687	262	31	,	,	PUNCT
ejpam-3687	262	32	(	(	PUNCT
ejpam-3687	262	33	18	18	NUM
ejpam-3687	262	34	)	)	PUNCT
ejpam-3687	262	35	is	be	AUX
ejpam-3687	262	36	equal	equal	ADJ
ejpam-3687	262	37	to	to	ADP
ejpam-3687	262	38	=	=	SYM
ejpam-3687	262	39	k	k	X
ejpam-3687	262	40	k+	k+	NOUN
ejpam-3687	262	41	1	1	NUM
ejpam-3687	262	42	qck/2q	qck/2q	NOUN
ejpam-3687	262	43	∞∑	∞∑	PROPN
ejpam-3687	262	44	r=0	r=0	PROPN
ejpam-3687	262	45	{	{	PUNCT
ejpam-3687	262	46	γ(2r+1)kq(2r)q(−	γ(2r+1)kq(2r)q(−	PROPN
ejpam-3687	262	47	k	k	PROPN
ejpam-3687	262	48	4	4	NUM
ejpam-3687	262	49	−1	−1	NOUN
ejpam-3687	262	50	)	)	PUNCT
ejpam-3687	262	51	}	}	PUNCT
ejpam-3687	263	1	1	1	NUM
ejpam-3687	263	2	q	q	NOUN
ejpam-3687	263	3			PUNCT
ejpam-3687	263	4	2r+1∑	2r+1∑	NUM
ejpam-3687	263	5	m=0	m=0	PROPN
ejpam-3687	263	6	2r+1∑	2r+1∑	PROPN
ejpam-3687	263	7	n=2r+1	n=2r+1	PROPN
ejpam-3687	263	8	(	(	PUNCT
ejpam-3687	263	9	n+	n+	ADP
ejpam-3687	263	10	α	α	PROPN
ejpam-3687	263	11	m+	m+	NUM
ejpam-3687	263	12	α	α	NOUN
ejpam-3687	263	13	)	)	PUNCT
ejpam-3687	263	14	(	(	PUNCT
ejpam-3687	263	15	m+	m+	NOUN
ejpam-3687	263	16	α)2qn−m(1	α)2qn−m(1	NUM
ejpam-3687	263	17	+	+	CCONJ
ejpam-3687	263	18	q)−n−α|bm|2	q)−n−α|bm|2	X
ejpam-3687	263	19			PROPN
ejpam-3687	263	20	k/2	k/2	PROPN
ejpam-3687	263	21	≤	≤	PROPN
ejpam-3687	263	22	kk+	kk+	NOUN
ejpam-3687	263	23	1	1	NUM
ejpam-3687	263	24	qck/2q	qck/2q	NOUN
ejpam-3687	263	25	∞∑	∞∑	PROPN
ejpam-3687	263	26	r=0	r=0	PROPN
ejpam-3687	263	27	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	263	28	k	k	PROPN
ejpam-3687	263	29	4	4	NUM
ejpam-3687	263	30	−1	−1	NOUN
ejpam-3687	263	31	)	)	PUNCT
ejpam-3687	263	32			PUNCT
ejpam-3687	263	33	2r+1∑	2r+1∑	NUM
ejpam-3687	263	34	m=0	m=0	PROPN
ejpam-3687	263	35	2r+1∑	2r+1∑	PROPN
ejpam-3687	264	1	n=2r+1	n=2r+1	PROPN
ejpam-3687	264	2	(	(	PUNCT
ejpam-3687	264	3	n+	n+	ADP
ejpam-3687	264	4	α	α	PROPN
ejpam-3687	264	5	m+	m+	NUM
ejpam-3687	264	6	α	α	NOUN
ejpam-3687	264	7	)	)	PUNCT
ejpam-3687	264	8	(	(	PUNCT
ejpam-3687	264	9	m+	m+	NOUN
ejpam-3687	264	10	α)2qn−m(1	α)2qn−m(1	NUM
ejpam-3687	264	11	+	+	CCONJ
ejpam-3687	264	12	q)−n−α|bm|2	q)−n−α|bm|2	X
ejpam-3687	264	13			PROPN
ejpam-3687	264	14	k/2	k/2	PROPN
ejpam-3687	264	15	+	+	PROPN
ejpam-3687	264	16	k	k	PROPN
ejpam-3687	264	17	k+	k+	NOUN
ejpam-3687	264	18	1	1	NUM
ejpam-3687	264	19	qck/2q	qck/2q	NOUN
ejpam-3687	264	20	∞∑	∞∑	PROPN
ejpam-3687	264	21	r=0	r=0	PROPN
ejpam-3687	264	22	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	264	23	k	k	PROPN
ejpam-3687	264	24	4	4	NUM
ejpam-3687	264	25	−1	−1	NOUN
ejpam-3687	264	26	)	)	PUNCT
ejpam-3687	264	27			PUNCT
ejpam-3687	265	1	2r+1∑	2r+1∑	NUM
ejpam-3687	265	2	m=2r+1	m=2r+1	PROPN
ejpam-3687	265	3	2r+1∑	2r+1∑	PROPN
ejpam-3687	266	1	n=2r+1	n=2r+1	PROPN
ejpam-3687	266	2	(	(	PUNCT
ejpam-3687	266	3	n+	n+	ADP
ejpam-3687	266	4	α	α	PROPN
ejpam-3687	266	5	m+	m+	NUM
ejpam-3687	266	6	α	α	NOUN
ejpam-3687	266	7	)	)	PUNCT
ejpam-3687	266	8	(	(	PUNCT
ejpam-3687	266	9	m+	m+	NOUN
ejpam-3687	266	10	α)2qn−m(1	α)2qn−m(1	NUM
ejpam-3687	266	11	+	+	CCONJ
ejpam-3687	266	12	q)−n−α|bm|2	q)−n−α|bm|2	X
ejpam-3687	266	13			PROPN
ejpam-3687	266	14	k/2	k/2	PROPN
ejpam-3687	266	15	.	.	PUNCT
ejpam-3687	267	1	using	use	VERB
ejpam-3687	267	2	lemma	lemma	PROPN
ejpam-3687	267	3	5	5	NUM
ejpam-3687	267	4	,	,	PUNCT
ejpam-3687	267	5	ω	ω	NUM
ejpam-3687	267	6	≤	≤	X
ejpam-3687	267	7	kk+	kk+	NOUN
ejpam-3687	267	8	1	1	NUM
ejpam-3687	267	9	qck/2q	qck/2q	NOUN
ejpam-3687	267	10	∞∑	∞∑	PROPN
ejpam-3687	267	11	r=0	r=0	PROPN
ejpam-3687	267	12	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	267	13	k	k	PROPN
ejpam-3687	267	14	4	4	NUM
ejpam-3687	267	15	−1	−1	NOUN
ejpam-3687	267	16	)	)	PUNCT
ejpam-3687	267	17	{	{	PUNCT
ejpam-3687	267	18	2r+1∑	2r+1∑	NUM
ejpam-3687	267	19	m=0	m=0	PROPN
ejpam-3687	267	20	dq(m+	dq(m+	NOUN
ejpam-3687	267	21	α)2|bm|2	α)2|bm|2	NUM
ejpam-3687	267	22	}	}	PUNCT
ejpam-3687	267	23	k/2	k/2	PROPN
ejpam-3687	267	24	+	+	PROPN
ejpam-3687	267	25	k	k	PROPN
ejpam-3687	267	26	k+	k+	NOUN
ejpam-3687	267	27	1	1	NUM
ejpam-3687	267	28	qck/2q	qck/2q	NOUN
ejpam-3687	267	29	∞∑	∞∑	PROPN
ejpam-3687	267	30	r=0	r=0	PROPN
ejpam-3687	267	31	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	267	32	k	k	PROPN
ejpam-3687	267	33	4	4	NUM
ejpam-3687	267	34	−1	−1	NOUN
ejpam-3687	267	35	)	)	PUNCT
ejpam-3687	267	36			NUM
ejpam-3687	267	37	2r+1∑	2r+1∑	NUM
ejpam-3687	267	38	m=2r+1	m=2r+1	PROPN
ejpam-3687	267	39	dq(m+	dq(m+	NOUN
ejpam-3687	267	40	α)2|bm|2	α)2|bm|2	NUM
ejpam-3687	267	41			PROPN
ejpam-3687	267	42	k/2	k/2	PROPN
ejpam-3687	267	43	≤	≤	PROPN
ejpam-3687	267	44	kk+	kk+	NOUN
ejpam-3687	267	45	1	1	NUM
ejpam-3687	267	46	qck/2q	qck/2q	NOUN
ejpam-3687	267	47	∞∑	∞∑	PROPN
ejpam-3687	267	48	r=0	r=0	PROPN
ejpam-3687	267	49	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	267	50	k	k	PROPN
ejpam-3687	267	51	4	4	NUM
ejpam-3687	267	52	−1	−1	NOUN
ejpam-3687	267	53	)	)	PUNCT
ejpam-3687	267	54			PUNCT
ejpam-3687	267	55	2r+1∑	2r+1∑	NUM
ejpam-3687	267	56	m=0	m=0	PROPN
ejpam-3687	267	57	dq(m+	dq(m+	NOUN
ejpam-3687	267	58	α)2|bm|2	α)2|bm|2	NUM
ejpam-3687	267	59			PROPN
ejpam-3687	267	60	k/2	k/2	PROPN
ejpam-3687	267	61	≤	≤	PROPN
ejpam-3687	267	62	kk+	kk+	NOUN
ejpam-3687	267	63	1	1	NUM
ejpam-3687	267	64	qck/2q	qck/2q	NOUN
ejpam-3687	267	65	∞∑	∞∑	PROPN
ejpam-3687	267	66	r=0	r=0	PROPN
ejpam-3687	267	67	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	267	68	3k	3k	X
ejpam-3687	267	69	4	4	NUM
ejpam-3687	267	70	)	)	PUNCT
ejpam-3687	267	71			PUNCT
ejpam-3687	267	72	2r+1∑	2r+1∑	NUM
ejpam-3687	267	73	m=0	m=0	PROPN
ejpam-3687	267	74	dq(m+	dq(m+	NOUN
ejpam-3687	267	75	α)2|bm|2	α)2|bm|2	NUM
ejpam-3687	267	76			PROPN
ejpam-3687	267	77	k/2	k/2	PROPN
ejpam-3687	267	78	≤	≤	PROPN
ejpam-3687	267	79	kk+	kk+	NOUN
ejpam-3687	267	80	1	1	NUM
ejpam-3687	267	81	qck/2q	qck/2q	NOUN
ejpam-3687	267	82	dk/2	dk/2	VERB
ejpam-3687	267	83	q	q	NOUN
ejpam-3687	267	84	∞∑	∞∑	PROPN
ejpam-3687	267	85	r=0	r=0	PROPN
ejpam-3687	267	86	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	NOUN
ejpam-3687	267	87	3k	3k	X
ejpam-3687	267	88	4	4	NUM
ejpam-3687	267	89	)	)	PUNCT
ejpam-3687	267	90			PUNCT
ejpam-3687	267	91	2r+1∑	2r+1∑	NUM
ejpam-3687	267	92	m=0	m=0	PROPN
ejpam-3687	267	93	(	(	PUNCT
ejpam-3687	267	94	m+	m+	NOUN
ejpam-3687	267	95	α)2|bm|2	α)2|bm|2	X
ejpam-3687	267	96			PROPN
ejpam-3687	267	97	k/2	k/2	PROPN
ejpam-3687	267	98	.	.	PUNCT
ejpam-3687	268	1	for	for	ADP
ejpam-3687	268	2	1	1	NUM
ejpam-3687	268	3	≤	≤	NUM
ejpam-3687	268	4	k	k	X
ejpam-3687	268	5	≤	≤	NUM
ejpam-3687	268	6	2	2	NUM
ejpam-3687	268	7	,	,	PUNCT
ejpam-3687	268	8	ω	ω	NUM
ejpam-3687	268	9	≤	≤	NOUN
ejpam-3687	268	10	l	l	NOUN
ejpam-3687	268	11	∞∑	∞∑	PROPN
ejpam-3687	268	12	r=0	r=0	PROPN
ejpam-3687	268	13	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	NOUN
ejpam-3687	268	14	3k	3k	X
ejpam-3687	268	15	4	4	NUM
ejpam-3687	268	16	)	)	PUNCT
ejpam-3687	268	17	{	{	PUNCT
ejpam-3687	268	18	2r+1∑	2r+1∑	NUM
ejpam-3687	268	19	m=0	m=0	PROPN
ejpam-3687	268	20	(	(	PUNCT
ejpam-3687	268	21	m+	m+	NOUN
ejpam-3687	268	22	α)2|bm|2	α)2|bm|2	PROPN
ejpam-3687	268	23	}	}	PUNCT
ejpam-3687	268	24	k/2	k/2	PROPN
ejpam-3687	268	25	,	,	PUNCT
ejpam-3687	268	26	(	(	PUNCT
ejpam-3687	268	27	19	19	NUM
ejpam-3687	268	28	)	)	PUNCT
ejpam-3687	268	29	where	where	SCONJ
ejpam-3687	268	30	l	l	NOUN
ejpam-3687	268	31	=	=	SYM
ejpam-3687	268	32	k	k	PROPN
ejpam-3687	268	33	k+	k+	PROPN
ejpam-3687	268	34	1	1	NUM
ejpam-3687	268	35	qc	qc	PROPN
ejpam-3687	268	36	k/2	k/2	PROPN
ejpam-3687	268	37	q	q	PROPN
ejpam-3687	268	38	d	d	PROPN
ejpam-3687	268	39	k/2	k/2	PROPN
ejpam-3687	268	40	q	q	NOUN
ejpam-3687	268	41	.	.	PUNCT
ejpam-3687	269	1	from	from	ADP
ejpam-3687	269	2	(	(	PUNCT
ejpam-3687	269	3	19	19	NUM
ejpam-3687	269	4	)	)	PUNCT
ejpam-3687	269	5	,	,	PUNCT
ejpam-3687	269	6	ω	ω	NUM
ejpam-3687	269	7	≤	≤	NUM
ejpam-3687	269	8	l	l	NOUN
ejpam-3687	269	9	∞∑	∞∑	PROPN
ejpam-3687	269	10	r=0	r=0	PROPN
ejpam-3687	269	11	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	269	12	3k	3k	X
ejpam-3687	269	13	4	4	NUM
ejpam-3687	269	14	)	)	PUNCT
ejpam-3687	269	15	α2|b0|2	α2|b0|2	NOUN
ejpam-3687	269	16	+	+	CCONJ
ejpam-3687	269	17	r∑	r∑	ADJ
ejpam-3687	269	18	s=0	s=0	X
ejpam-3687	269	19	2s+1∑	2s+1∑	NUM
ejpam-3687	269	20	m=2s+1	m=2s+1	PROPN
ejpam-3687	269	21	(	(	PUNCT
ejpam-3687	269	22	m+	m+	NOUN
ejpam-3687	269	23	α)2|bm|2	α)2|bm|2	X
ejpam-3687	269	24			PROPN
ejpam-3687	269	25	k/2	k/2	PROPN
ejpam-3687	269	26	f.	f.	PROPN
ejpam-3687	269	27	aydin	aydin	PROPN
ejpam-3687	269	28	akgun	akgun	PROPN
ejpam-3687	269	29	,	,	PUNCT
ejpam-3687	269	30	b.	b.	PROPN
ejpam-3687	269	31	e.	e.	PROPN
ejpam-3687	269	32	rhoades	rhoades	PROPN
ejpam-3687	269	33	/	/	SYM
ejpam-3687	269	34	eur	eur	PROPN
ejpam-3687	269	35	.	.	PUNCT
ejpam-3687	270	1	j.	j.	PROPN
ejpam-3687	270	2	pure	pure	PROPN
ejpam-3687	270	3	appl	appl	PROPN
ejpam-3687	270	4	.	.	PROPN
ejpam-3687	270	5	math	math	PROPN
ejpam-3687	270	6	,	,	PUNCT
ejpam-3687	270	7	13	13	NUM
ejpam-3687	270	8	(	(	PUNCT
ejpam-3687	270	9	3	3	NUM
ejpam-3687	270	10	)	)	PUNCT
ejpam-3687	270	11	(	(	PUNCT
ejpam-3687	270	12	2020	2020	NUM
ejpam-3687	270	13	)	)	PUNCT
ejpam-3687	270	14	,	,	PUNCT
ejpam-3687	270	15	390	390	NUM
ejpam-3687	270	16	-	-	SYM
ejpam-3687	270	17	402	402	NUM
ejpam-3687	270	18	401	401	NUM
ejpam-3687	270	19	≤	≤	NOUN
ejpam-3687	270	20	l	l	NOUN
ejpam-3687	270	21	∞∑	∞∑	PROPN
ejpam-3687	270	22	s=0	s=0	NOUN
ejpam-3687	271	1	∞∑	∞∑	NUM
ejpam-3687	271	2	r	r	NOUN
ejpam-3687	271	3	=	=	SYM
ejpam-3687	271	4	s	s	PART
ejpam-3687	271	5	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	NOUN
ejpam-3687	271	6	3k	3k	NOUN
ejpam-3687	271	7	4	4	NUM
ejpam-3687	271	8	)	)	PUNCT
ejpam-3687	271	9			PUNCT
ejpam-3687	271	10	2s+1∑	2s+1∑	NUM
ejpam-3687	271	11	m=2s+1	m=2s+1	PROPN
ejpam-3687	271	12	(	(	PUNCT
ejpam-3687	271	13	m+	m+	NOUN
ejpam-3687	271	14	α)2|bm|2	α)2|bm|2	X
ejpam-3687	271	15			PROPN
ejpam-3687	271	16	k/2	k/2	PROPN
ejpam-3687	271	17	+	+	NOUN
ejpam-3687	271	18	l	l	NOUN
ejpam-3687	271	19	∞∑	∞∑	PROPN
ejpam-3687	271	20	r=0	r=0	PROPN
ejpam-3687	271	21	γ(2r+1)k(2r)(−	γ(2r+1)k(2r)(−	PROPN
ejpam-3687	271	22	3k	3k	X
ejpam-3687	271	23	4	4	NUM
ejpam-3687	271	24	)	)	PUNCT
ejpam-3687	271	25	αk|b0|k	αk|b0|k	NOUN
ejpam-3687	271	26	.	.	PUNCT
ejpam-3687	271	27	here	here	ADV
ejpam-3687	271	28	{	{	PUNCT
ejpam-3687	271	29	γ(n	γ(n	X
ejpam-3687	271	30	)	)	PUNCT
ejpam-3687	271	31	}	}	PUNCT
ejpam-3687	271	32	is	be	AUX
ejpam-3687	271	33	quasi	quasi	ADJ
ejpam-3687	271	34	β	β	NOUN
ejpam-3687	271	35	-	-	ADJ
ejpam-3687	271	36	power	power	NOUN
ejpam-3687	271	37	monotone	monotone	NOUN
ejpam-3687	271	38	decreasing	decrease	VERB
ejpam-3687	271	39	and	and	CCONJ
ejpam-3687	271	40	{	{	PUNCT
ejpam-3687	271	41	n−3/4γ(n	n−3/4γ(n	NUM
ejpam-3687	271	42	)	)	PUNCT
ejpam-3687	271	43	}	}	PUNCT
ejpam-3687	271	44	is	be	AUX
ejpam-3687	271	45	quasi	quasi	ADJ
ejpam-3687	271	46	ε	ε	PROPN
ejpam-3687	271	47	-	-	PUNCT
ejpam-3687	271	48	power	power	NOUN
ejpam-3687	271	49	monotone	monotone	NOUN
ejpam-3687	271	50	decreasing	decreasing	NOUN
ejpam-3687	271	51	,	,	PUNCT
ejpam-3687	271	52	where	where	SCONJ
ejpam-3687	271	53	β	β	X
ejpam-3687	271	54	>	>	X
ejpam-3687	271	55	3/4	3/4	NUM
ejpam-3687	271	56	and	and	CCONJ
ejpam-3687	271	57	ε	ε	PROPN
ejpam-3687	271	58	=	=	SYM
ejpam-3687	271	59	β	β	X
ejpam-3687	271	60	+	+	NOUN
ejpam-3687	271	61	3/4	3/4	NUM
ejpam-3687	271	62	.	.	PUNCT
ejpam-3687	272	1	thus	thus	ADV
ejpam-3687	272	2	,	,	PUNCT
ejpam-3687	272	3	by	by	ADP
ejpam-3687	272	4	using	use	VERB
ejpam-3687	272	5	lemma	lemma	PROPN
ejpam-3687	272	6	1	1	NUM
ejpam-3687	272	7	of	of	ADP
ejpam-3687	272	8	[	[	X
ejpam-3687	272	9	6	6	NUM
ejpam-3687	272	10	]	]	PUNCT
ejpam-3687	272	11	,	,	PUNCT
ejpam-3687	272	12	∞∑	∞∑	PROPN
ejpam-3687	272	13	n	n	CCONJ
ejpam-3687	272	14	=	=	NOUN
ejpam-3687	272	15	m	m	NOUN
ejpam-3687	272	16	γ(2n)k(2n)−3k/4	γ(2n)k(2n)−3k/4	PROPN
ejpam-3687	272	17	≤mγ(2m)k(2m)−3k/4,m	≤mγ(2m)k(2m)−3k/4,m	X
ejpam-3687	272	18	∈	∈	PROPN
ejpam-3687	272	19	z+	z+	PUNCT
ejpam-3687	272	20	.	.	PUNCT
ejpam-3687	273	1	therefore	therefore	ADV
ejpam-3687	273	2	ω	ω	NUM
ejpam-3687	273	3	≤	≤	PUNCT
ejpam-3687	273	4	l	l	NOUN
ejpam-3687	273	5	∞∑	∞∑	PROPN
ejpam-3687	273	6	s=0	s=0	SYM
ejpam-3687	273	7	γ(2s+1)k(2s)(−3k/4	γ(2s+1)k(2s)(−3k/4	PROPN
ejpam-3687	273	8	)	)	PUNCT
ejpam-3687	273	9			PUNCT
ejpam-3687	273	10	2s+1∑	2s+1∑	NUM
ejpam-3687	273	11	m=2s+1	m=2s+1	PROPN
ejpam-3687	273	12	(	(	PUNCT
ejpam-3687	273	13	m+	m+	NOUN
ejpam-3687	273	14	α)2|bm|2	α)2|bm|2	X
ejpam-3687	273	15			PROPN
ejpam-3687	273	16	k/2	k/2	PROPN
ejpam-3687	273	17	+	+	CCONJ
ejpam-3687	273	18	lγ(2)kαk|b0|k	lγ(2)kαk|b0|k	PROPN
ejpam-3687	273	19	≤	≤	NUM
ejpam-3687	273	20	2kl	2kl	NOUN
ejpam-3687	273	21	∞∑	∞∑	PRON
ejpam-3687	273	22	s=0	s=0	SYM
ejpam-3687	273	23	γ(2s)k(2s)(−3k/4	γ(2s)k(2s)(−3k/4	PROPN
ejpam-3687	273	24	)	)	PUNCT
ejpam-3687	273	25			PUNCT
ejpam-3687	273	26	2s+1∑	2s+1∑	NUM
ejpam-3687	273	27	m=2s+1	m=2s+1	PROPN
ejpam-3687	273	28	(	(	PUNCT
ejpam-3687	273	29	m+	m+	NOUN
ejpam-3687	273	30	α)2|bm|2	α)2|bm|2	X
ejpam-3687	273	31			PROPN
ejpam-3687	273	32	k/2	k/2	PROPN
ejpam-3687	273	33	+	+	CCONJ
ejpam-3687	273	34	lγ(2)kαk|b0|k	lγ(2)kαk|b0|k	PROPN
ejpam-3687	273	35	≤	≤	NUM
ejpam-3687	273	36	2kl	2kl	NOUN
ejpam-3687	273	37	∞∑	∞∑	PROPN
ejpam-3687	273	38	s=0	s=0	NOUN
ejpam-3687	273	39	γ(2s)k	γ(2s)k	PROPN
ejpam-3687	273	40			PUNCT
ejpam-3687	273	41	2s+1∑	2s+1∑	NUM
ejpam-3687	273	42	m=2s+1	m=2s+1	PROPN
ejpam-3687	273	43	(	(	PUNCT
ejpam-3687	273	44	m+	m+	NOUN
ejpam-3687	273	45	α)2|bm|2	α)2|bm|2	X
ejpam-3687	273	46			PROPN
ejpam-3687	273	47	k/2	k/2	PROPN
ejpam-3687	273	48	+	+	CCONJ
ejpam-3687	273	49	lγ(2)kαk|b0|k	lγ(2)kαk|b0|k	NOUN
ejpam-3687	273	50	and	and	CCONJ
ejpam-3687	273	51	thus	thus	ADV
ejpam-3687	273	52	∞∑	∞∑	NUM
ejpam-3687	273	53	n=2	n=2	PRON
ejpam-3687	273	54	γ(n)knk−1	γ(n)knk−1	NUM
ejpam-3687	273	55	∫	∫	NOUN
ejpam-3687	273	56	1	1	NUM
ejpam-3687	273	57	0	0	NUM
ejpam-3687	273	58	|σn(x)−	|σn(x)−	PROPN
ejpam-3687	273	59	σn−1(x)|kdx	σn−1(x)|kdx	X
ejpam-3687	273	60	≤	≤	ADV
ejpam-3687	273	61	2(−	2(−	NUM
ejpam-3687	273	62	3k	3k	NOUN
ejpam-3687	273	63	4	4	NUM
ejpam-3687	273	64	)	)	PUNCT
ejpam-3687	273	65	l	l	NOUN
ejpam-3687	274	1	∞∑	∞∑	NUM
ejpam-3687	274	2	s=0	s=0	NOUN
ejpam-3687	274	3	γ(2s)k	γ(2s)k	PROPN
ejpam-3687	274	4			PUNCT
ejpam-3687	274	5	2s+1∑	2s+1∑	NUM
ejpam-3687	274	6	m=2s+1	m=2s+1	PROPN
ejpam-3687	274	7	(	(	PUNCT
ejpam-3687	274	8	m+	m+	NOUN
ejpam-3687	274	9	α)2|bm|2	α)2|bm|2	X
ejpam-3687	274	10			PROPN
ejpam-3687	274	11	k/2	k/2	PROPN
ejpam-3687	274	12	+	+	CCONJ
ejpam-3687	274	13	lγ(2)kαk|b0|k	lγ(2)kαk|b0|k	PROPN
ejpam-3687	274	14	.	.	PUNCT
ejpam-3687	275	1	the	the	DET
ejpam-3687	275	2	following	follow	VERB
ejpam-3687	275	3	corollaries	corollary	NOUN
ejpam-3687	275	4	can	can	AUX
ejpam-3687	275	5	be	be	AUX
ejpam-3687	275	6	verified	verify	VERB
ejpam-3687	275	7	by	by	ADP
ejpam-3687	275	8	taking	take	VERB
ejpam-3687	275	9	α	α	NOUN
ejpam-3687	275	10	=	=	NOUN
ejpam-3687	275	11	0	0	NUM
ejpam-3687	275	12	in	in	ADP
ejpam-3687	275	13	the	the	DET
ejpam-3687	275	14	above	above	ADJ
ejpam-3687	275	15	theorems	theorem	NOUN
ejpam-3687	275	16	.	.	PUNCT
ejpam-3687	276	1	corollary	corollary	ADJ
ejpam-3687	276	2	1	1	NUM
ejpam-3687	276	3	.	.	PUNCT
ejpam-3687	277	1	every	every	DET
ejpam-3687	277	2	orthogonal	orthogonal	ADJ
ejpam-3687	277	3	series	series	NOUN
ejpam-3687	277	4	∑∞	∑∞	PROPN
ejpam-3687	277	5	n=0	n=0	PUNCT
ejpam-3687	277	6	cnψn	cnψn	NOUN
ejpam-3687	277	7	,	,	PUNCT
ejpam-3687	277	8	cn	cn	PROPN
ejpam-3687	277	9	∈	∈	PROPN
ejpam-3687	277	10	`	`	PUNCT
ejpam-3687	277	11	2(z+	2(z+	NUM
ejpam-3687	277	12	)	)	PUNCT
ejpam-3687	277	13	is	be	AUX
ejpam-3687	277	14	|h	|h	NOUN
ejpam-3687	277	15	,	,	PUNCT
ejpam-3687	277	16	ψ|k	ψ|k	NOUN
ejpam-3687	277	17	summable	summable	ADJ
ejpam-3687	277	18	for	for	ADP
ejpam-3687	277	19	1	1	NUM
ejpam-3687	277	20	≤	≤	NUM
ejpam-3687	277	21	k	k	NOUN
ejpam-3687	277	22	≤	≤	NUM
ejpam-3687	277	23	2	2	NUM
ejpam-3687	277	24	and	and	CCONJ
ejpam-3687	277	25	γ	γ	X
ejpam-3687	277	26	∈	∈	PROPN
ejpam-3687	277	27	γβ	γβ	NOUN
ejpam-3687	277	28	with	with	ADP
ejpam-3687	277	29	β	β	X
ejpam-3687	277	30	>	>	X
ejpam-3687	277	31	1	1	NUM
ejpam-3687	277	32	−	−	PROPN
ejpam-3687	277	33	l	l	NOUN
ejpam-3687	277	34	/	/	SYM
ejpam-3687	277	35	k	k	NOUN
ejpam-3687	277	36	,	,	PUNCT
ejpam-3687	277	37	where	where	SCONJ
ejpam-3687	277	38	{	{	PUNCT
ejpam-3687	277	39	ψn}∞n=0	ψn}∞n=0	X
ejpam-3687	277	40	⊂	⊂	PROPN
ejpam-3687	277	41	l2[0	l2[0	PROPN
ejpam-3687	277	42	,	,	PUNCT
ejpam-3687	277	43	1	1	NUM
ejpam-3687	277	44	]	]	PUNCT
ejpam-3687	277	45	and	and	CCONJ
ejpam-3687	277	46	h	h	NOUN
ejpam-3687	277	47	is	be	AUX
ejpam-3687	277	48	a	a	DET
ejpam-3687	277	49	hausdorff	hausdorff	NOUN
ejpam-3687	277	50	matrix	matrix	NOUN
ejpam-3687	277	51	with	with	ADP
ejpam-3687	277	52	entries	entry	NOUN
ejpam-3687	277	53	(	(	PUNCT
ejpam-3687	277	54	hnk)n	hnk)n	PROPN
ejpam-3687	277	55	,	,	PUNCT
ejpam-3687	277	56	k	k	PROPN
ejpam-3687	277	57	∈	∈	PROPN
ejpam-3687	277	58	z+	z+	PUNCT
ejpam-3687	277	59	.	.	PUNCT
ejpam-3687	278	1	this	this	PRON
ejpam-3687	278	2	is	be	AUX
ejpam-3687	278	3	theorem	theorem	VERB
ejpam-3687	278	4	2	2	NUM
ejpam-3687	278	5	of	of	ADP
ejpam-3687	278	6	[	[	X
ejpam-3687	278	7	6	6	NUM
ejpam-3687	278	8	]	]	PUNCT
ejpam-3687	278	9	.	.	PUNCT
ejpam-3687	279	1	corollary	corollary	ADJ
ejpam-3687	279	2	2	2	NUM
ejpam-3687	279	3	.	.	PUNCT
ejpam-3687	280	1	let	let	VERB
ejpam-3687	280	2	1	1	NUM
ejpam-3687	280	3	≤	≤	NOUN
ejpam-3687	280	4	k	k	NOUN
ejpam-3687	280	5	≤	≤	NUM
ejpam-3687	280	6	2	2	NUM
ejpam-3687	280	7	and	and	CCONJ
ejpam-3687	280	8	γ	γ	X
ejpam-3687	280	9	∈	∈	PROPN
ejpam-3687	280	10	γβ	γβ	NOUN
ejpam-3687	280	11	with	with	ADP
ejpam-3687	280	12	β	β	X
ejpam-3687	280	13	>	>	X
ejpam-3687	280	14	−3/4	−3/4	NOUN
ejpam-3687	280	15	,	,	PUNCT
ejpam-3687	280	16	where	where	SCONJ
ejpam-3687	280	17	{	{	PUNCT
ejpam-3687	280	18	φn}∞n=0	φn}∞n=0	X
ejpam-3687	280	19	⊂	⊂	PROPN
ejpam-3687	280	20	l2[0	l2[0	PROPN
ejpam-3687	280	21	,	,	PUNCT
ejpam-3687	280	22	1	1	NUM
ejpam-3687	280	23	]	]	PUNCT
ejpam-3687	280	24	and	and	CCONJ
ejpam-3687	280	25	h	h	NOUN
ejpam-3687	280	26	is	be	AUX
ejpam-3687	280	27	a	a	DET
ejpam-3687	280	28	hausdorff	hausdorff	NOUN
ejpam-3687	280	29	matrix	matrix	NOUN
ejpam-3687	280	30	.	.	PUNCT
ejpam-3687	281	1	then	then	ADV
ejpam-3687	281	2	,	,	PUNCT
ejpam-3687	281	3	for	for	ADP
ejpam-3687	281	4	any	any	DET
ejpam-3687	281	5	cn	cn	PROPN
ejpam-3687	281	6	∈	∈	PROPN
ejpam-3687	281	7	`	`	PUNCT
ejpam-3687	281	8	2(z+	2(z+	NUM
ejpam-3687	281	9	)	)	PUNCT
ejpam-3687	281	10	,	,	PUNCT
ejpam-3687	281	11	a	a	DET
ejpam-3687	281	12	sufficient	sufficient	ADJ
ejpam-3687	281	13	condition	condition	NOUN
ejpam-3687	281	14	for	for	ADP
ejpam-3687	281	15	the	the	DET
ejpam-3687	281	16	orthogonal	orthogonal	ADJ
ejpam-3687	281	17	series	series	NOUN
ejpam-3687	281	18	∑∞	∑∞	PROPN
ejpam-3687	281	19	n=0	n=0	PUNCT
ejpam-3687	281	20	cnψn	cnψn	NOUN
ejpam-3687	281	21	to	to	PART
ejpam-3687	281	22	be	be	AUX
ejpam-3687	281	23	|h	|h	NOUN
ejpam-3687	281	24	,	,	PUNCT
ejpam-3687	281	25	γ|k	γ|k	NOUN
ejpam-3687	281	26	summable	summable	ADJ
ejpam-3687	281	27	is	be	AUX
ejpam-3687	281	28	∞∑	∞∑	NUM
ejpam-3687	281	29	m=0	m=0	PROPN
ejpam-3687	281	30	γ(2m)k	γ(2m)k	NOUN
ejpam-3687	281	31	{	{	PUNCT
ejpam-3687	281	32	2m+1∑	2m+1∑	NUM
ejpam-3687	281	33	n=2m+1	n=2m+1	PROPN
ejpam-3687	281	34	√	√	ADJ
ejpam-3687	281	35	n|cn|2	n|cn|2	PROPN
ejpam-3687	281	36	}	}	PUNCT
ejpam-3687	281	37	k/2	k/2	PROPN
ejpam-3687	281	38	<	<	X
ejpam-3687	281	39	∞.	∞.	PROPN
ejpam-3687	281	40	(	(	PUNCT
ejpam-3687	281	41	20	20	NUM
ejpam-3687	281	42	)	)	PUNCT
ejpam-3687	281	43	this	this	PRON
ejpam-3687	281	44	includes	include	VERB
ejpam-3687	281	45	the	the	DET
ejpam-3687	281	46	results	result	NOUN
ejpam-3687	281	47	of	of	ADP
ejpam-3687	281	48	theorem	theorem	ADJ
ejpam-3687	281	49	3	3	NUM
ejpam-3687	281	50	of	of	ADP
ejpam-3687	281	51	[	[	X
ejpam-3687	281	52	6	6	NUM
ejpam-3687	281	53	]	]	PUNCT
ejpam-3687	281	54	.	.	PUNCT
ejpam-3687	282	1	references	reference	NOUN
ejpam-3687	282	2	402	402	NUM
ejpam-3687	282	3	references	reference	NOUN
ejpam-3687	282	4	[	[	X
ejpam-3687	282	5	1	1	NUM
ejpam-3687	282	6	]	]	X
ejpam-3687	282	7	k	k	PROPN
ejpam-3687	282	8	endl	endl	PROPN
ejpam-3687	282	9	.	.	PUNCT
ejpam-3687	283	1	abstracts	abstract	NOUN
ejpam-3687	283	2	of	of	ADP
ejpam-3687	283	3	short	short	ADJ
ejpam-3687	283	4	communications	communication	NOUN
ejpam-3687	283	5	and	and	CCONJ
ejpam-3687	283	6	scientific	scientific	ADJ
ejpam-3687	283	7	program	program	NOUN
ejpam-3687	283	8	.	.	PUNCT
ejpam-3687	284	1	int	int	NOUN
ejpam-3687	284	2	.	.	PUNCT
ejpam-3687	285	1	congress	congress	PROPN
ejpam-3687	285	2	of	of	ADP
ejpam-3687	285	3	math	math	NOUN
ejpam-3687	285	4	.	.	PUNCT
ejpam-3687	285	5	,	,	PUNCT
ejpam-3687	285	6	page	page	NOUN
ejpam-3687	285	7	46	46	NUM
ejpam-3687	285	8	,	,	PUNCT
ejpam-3687	285	9	1960	1960	NUM
ejpam-3687	285	10	.	.	PUNCT
ejpam-3687	286	1	[	[	X
ejpam-3687	286	2	2	2	NUM
ejpam-3687	286	3	]	]	SYM
ejpam-3687	286	4	f	f	PROPN
ejpam-3687	286	5	hausdorff	hausdorff	PROPN
ejpam-3687	286	6	.	.	PUNCT
ejpam-3687	287	1	summationmethoden	summationmethoden	PROPN
ejpam-3687	287	2	und	und	PROPN
ejpam-3687	287	3	momentfolgen	momentfolgen	PROPN
ejpam-3687	288	1	i	i	PROPN
ejpam-3687	288	2	..	..	PUNCT
ejpam-3687	288	3	math	math	PROPN
ejpam-3687	288	4	.	.	PUNCT
ejpam-3687	289	1	z.	z.	PROPN
ejpam-3687	289	2	,	,	PUNCT
ejpam-3687	289	3	9:74–109	9:74–109	NUM
ejpam-3687	289	4	,	,	PUNCT
ejpam-3687	289	5	1921	1921	NUM
ejpam-3687	289	6	.	.	PUNCT
ejpam-3687	290	1	[	[	X
ejpam-3687	290	2	3	3	X
ejpam-3687	290	3	]	]	X
ejpam-3687	290	4	f	f	PROPN
ejpam-3687	290	5	hausdorff	hausdorff	PROPN
ejpam-3687	290	6	.	.	PUNCT
ejpam-3687	290	7	summationmethoden	summationmethoden	PROPN
ejpam-3687	290	8	und	und	PROPN
ejpam-3687	290	9	momentfolgen	momentfolgen	PROPN
ejpam-3687	290	10	ii	ii	PROPN
ejpam-3687	290	11	..	..	PROPN
ejpam-3687	290	12	math	math	PROPN
ejpam-3687	290	13	.	.	PUNCT
ejpam-3687	291	1	z.	z.	PROPN
ejpam-3687	291	2	,	,	PUNCT
ejpam-3687	291	3	9:280–299	9:280–299	NOUN
ejpam-3687	291	4	,	,	PUNCT
ejpam-3687	291	5	1921	1921	NUM
ejpam-3687	291	6	.	.	PUNCT
ejpam-3687	292	1	[	[	X
ejpam-3687	292	2	4	4	X
ejpam-3687	292	3	]	]	X
ejpam-3687	292	4	w	w	ADP
ejpam-3687	292	5	a	a	DET
ejpam-3687	292	6	hurwitz	hurwitz	PROPN
ejpam-3687	292	7	and	and	CCONJ
ejpam-3687	292	8	l	l	PROPN
ejpam-3687	292	9	l	l	X
ejpam-3687	292	10	silverman	silverman	NOUN
ejpam-3687	292	11	.	.	PUNCT
ejpam-3687	293	1	on	on	ADP
ejpam-3687	293	2	the	the	DET
ejpam-3687	293	3	consistency	consistency	NOUN
ejpam-3687	293	4	and	and	CCONJ
ejpam-3687	293	5	equivalence	equivalence	NOUN
ejpam-3687	293	6	of	of	ADP
ejpam-3687	293	7	certain	certain	ADJ
ejpam-3687	293	8	definitions	definition	NOUN
ejpam-3687	293	9	of	of	ADP
ejpam-3687	293	10	summability	summability	NOUN
ejpam-3687	293	11	.	.	PUNCT
ejpam-3687	294	1	trans	trans	PROPN
ejpam-3687	294	2	.	.	PUNCT
ejpam-3687	295	1	amer	amer	PROPN
ejpam-3687	295	2	.	.	PUNCT
ejpam-3687	295	3	math	math	PROPN
ejpam-3687	295	4	.	.	PUNCT
ejpam-3687	296	1	soc	soc	PROPN
ejpam-3687	296	2	.	.	PUNCT
ejpam-3687	296	3	,	,	PUNCT
ejpam-3687	296	4	18:1–20	18:1–20	NUM
ejpam-3687	296	5	,	,	PUNCT
ejpam-3687	296	6	1917	1917	NUM
ejpam-3687	296	7	.	.	PUNCT
ejpam-3687	297	1	[	[	X
ejpam-3687	297	2	5	5	NUM
ejpam-3687	297	3	]	]	PUNCT
ejpam-3687	297	4	a	a	DET
ejpam-3687	297	5	jakimovski	jakimovski	NOUN
ejpam-3687	297	6	.	.	PUNCT
ejpam-3687	298	1	the	the	DET
ejpam-3687	298	2	product	product	NOUN
ejpam-3687	298	3	of	of	ADP
ejpam-3687	298	4	summability	summability	NOUN
ejpam-3687	298	5	methods	method	NOUN
ejpam-3687	298	6	;	;	PUNCT
ejpam-3687	298	7	new	new	ADJ
ejpam-3687	298	8	classes	class	NOUN
ejpam-3687	298	9	of	of	ADP
ejpam-3687	298	10	transformations	transformation	NOUN
ejpam-3687	298	11	and	and	CCONJ
ejpam-3687	298	12	their	their	PRON
ejpam-3687	298	13	properties	property	NOUN
ejpam-3687	298	14	,	,	PUNCT
ejpam-3687	298	15	i	i	PRON
ejpam-3687	298	16	,	,	PUNCT
ejpam-3687	298	17	ii	ii	PROPN
ejpam-3687	298	18	..	..	PUNCT
ejpam-3687	298	19	contract	contract	NOUN
ejpam-3687	298	20	no	no	INTJ
ejpam-3687	298	21	.	.	PUNCT
ejpam-3687	299	1	af61(052)-187	af61(052)-187	ADJ
ejpam-3687	299	2	,	,	PUNCT
ejpam-3687	299	3	technical	technical	ADJ
ejpam-3687	299	4	(	(	PUNCT
ejpam-3687	299	5	scientific	scientific	ADJ
ejpam-3687	299	6	)	)	PUNCT
ejpam-3687	299	7	note	note	NOUN
ejpam-3687	299	8	no	no	INTJ
ejpam-3687	299	9	.	.	NOUN
ejpam-3687	299	10	2	2	NUM
ejpam-3687	299	11	,	,	PUNCT
ejpam-3687	299	12	1959	1959	NUM
ejpam-3687	299	13	.	.	PUNCT
ejpam-3687	300	1	[	[	X
ejpam-3687	300	2	6	6	NUM
ejpam-3687	300	3	]	]	X
ejpam-3687	300	4	k	k	PROPN
ejpam-3687	300	5	kalaivana	kalaivana	PROPN
ejpam-3687	300	6	and	and	CCONJ
ejpam-3687	300	7	g	g	PROPN
ejpam-3687	300	8	p	p	PROPN
ejpam-3687	300	9	youvaraj	youvaraj	VERB
ejpam-3687	300	10	.	.	PUNCT
ejpam-3687	301	1	generalized	generalize	VERB
ejpam-3687	301	2	absolute	absolute	ADJ
ejpam-3687	301	3	hausdorff	hausdorff	NOUN
ejpam-3687	301	4	summability	summability	NOUN
ejpam-3687	301	5	of	of	ADP
ejpam-3687	301	6	orthogonal	orthogonal	ADJ
ejpam-3687	301	7	series	series	NOUN
ejpam-3687	301	8	.	.	PUNCT
ejpam-3687	302	1	acta	acta	PROPN
ejpam-3687	302	2	.	.	PUNCT
ejpam-3687	303	1	math	math	PROPN
ejpam-3687	303	2	hungarica	hungarica	PROPN
ejpam-3687	303	3	,	,	PUNCT
ejpam-3687	303	4	140:169–186	140:169–186	NUM
ejpam-3687	303	5	,	,	PUNCT
ejpam-3687	303	6	2013	2013	NUM
ejpam-3687	303	7	.	.	PUNCT
ejpam-3687	304	1	[	[	X
ejpam-3687	304	2	7	7	X
ejpam-3687	304	3	]	]	X
ejpam-3687	304	4	o	o	NOUN
ejpam-3687	304	5	a	a	DET
ejpam-3687	304	6	ziza	ziza	NOUN
ejpam-3687	304	7	.	.	PUNCT
ejpam-3687	305	1	on	on	ADP
ejpam-3687	305	2	the	the	DET
ejpam-3687	305	3	summation	summation	NOUN
ejpam-3687	305	4	of	of	ADP
ejpam-3687	305	5	orthogonal	orthogonal	ADJ
ejpam-3687	305	6	series	series	NOUN
ejpam-3687	305	7	by	by	ADP
ejpam-3687	305	8	euler	euler	PROPN
ejpam-3687	305	9	’s	’s	PART
ejpam-3687	305	10	method	method	NOUN
ejpam-3687	305	11	.	.	PUNCT
ejpam-3687	306	1	matem	matem	NOUN
ejpam-3687	306	2	.	.	PUNCT
ejpam-3687	307	1	sb	sb	PROPN
ejpam-3687	307	2	.	.	PROPN
ejpam-3687	307	3	,	,	PUNCT
ejpam-3687	307	4	66:354–377	66:354–377	NUM
ejpam-3687	307	5	,	,	PUNCT
ejpam-3687	307	6	1965	1965	NUM
ejpam-3687	307	7	.	.	PUNCT