id	sid	tid	token	lemma	pos
ejpam-1481	1	1	7_195297_akhmedov.dvi	7_195297_akhmedov.dvi	PROPN
ejpam-1481	1	2	european	european	PROPN
ejpam-1481	1	3	journal	journal	PROPN
ejpam-1481	1	4	of	of	ADP
ejpam-1481	1	5	pure	pure	ADJ
ejpam-1481	1	6	and	and	CCONJ
ejpam-1481	1	7	applied	apply	VERB
ejpam-1481	1	8	mathematics	mathematic	NOUN
ejpam-1481	1	9	vol	vol	NOUN
ejpam-1481	1	10	.	.	PROPN
ejpam-1481	1	11	5	5	NUM
ejpam-1481	1	12	,	,	PUNCT
ejpam-1481	1	13	no	no	INTJ
ejpam-1481	1	14	.	.	NOUN
ejpam-1481	1	15	1	1	NUM
ejpam-1481	1	16	,	,	PUNCT
ejpam-1481	1	17	2012	2012	NUM
ejpam-1481	1	18	,	,	PUNCT
ejpam-1481	1	19	59	59	NUM
ejpam-1481	1	20	-	-	SYM
ejpam-1481	1	21	74	74	NUM
ejpam-1481	1	22	issn	issn	PROPN
ejpam-1481	1	23	1307	1307	NUM
ejpam-1481	1	24	-	-	SYM
ejpam-1481	1	25	5543	5543	NUM
ejpam-1481	1	26	–	–	PUNCT
ejpam-1481	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1481	1	28	special	special	ADJ
ejpam-1481	1	29	issue	issue	NOUN
ejpam-1481	1	30	for	for	ADP
ejpam-1481	1	31	the	the	DET
ejpam-1481	1	32	international	international	ADJ
ejpam-1481	1	33	conference	conference	NOUN
ejpam-1481	1	34	on	on	ADP
ejpam-1481	1	35	applied	apply	VERB
ejpam-1481	1	36	analysis	analysis	NOUN
ejpam-1481	1	37	and	and	CCONJ
ejpam-1481	1	38	algebra	algebra	NOUN
ejpam-1481	1	39	29	29	NUM
ejpam-1481	1	40	june	june	PROPN
ejpam-1481	1	41	02	02	NUM
ejpam-1481	1	42	july	july	PROPN
ejpam-1481	1	43	2011	2011	NUM
ejpam-1481	1	44	,	,	PUNCT
ejpam-1481	1	45	istanbul	istanbul	PROPN
ejpam-1481	1	46	turkey	turkey	PROPN
ejpam-1481	1	47	some	some	DET
ejpam-1481	1	48	spectral	spectral	ADJ
ejpam-1481	1	49	properties	property	NOUN
ejpam-1481	1	50	of	of	ADP
ejpam-1481	1	51	the	the	DET
ejpam-1481	1	52	generalized	generalize	VERB
ejpam-1481	1	53	difference	difference	NOUN
ejpam-1481	1	54	operator	operator	NOUN
ejpam-1481	1	55	∆v	∆v	PROPN
ejpam-1481	1	56	ali	ali	PROPN
ejpam-1481	1	57	m.	m.	PROPN
ejpam-1481	1	58	akhmedov1,∗	akhmedov1,∗	PROPN
ejpam-1481	1	59	,	,	PUNCT
ejpam-1481	1	60	saad	saad	PROPN
ejpam-1481	1	61	r.	r.	PROPN
ejpam-1481	1	62	el	el	PROPN
ejpam-1481	1	63	-	-	PUNCT
ejpam-1481	1	64	shabrawy	shabrawy	ADJ
ejpam-1481	1	65	2	2	NUM
ejpam-1481	1	66	1,2	1,2	NUM
ejpam-1481	1	67	baku	baku	PROPN
ejpam-1481	1	68	state	state	PROPN
ejpam-1481	1	69	university	university	PROPN
ejpam-1481	1	70	,	,	PUNCT
ejpam-1481	1	71	faculty	faculty	NOUN
ejpam-1481	1	72	of	of	ADP
ejpam-1481	1	73	mech	mech	NOUN
ejpam-1481	1	74	.	.	PUNCT
ejpam-1481	1	75	&	&	CCONJ
ejpam-1481	1	76	math	math	PROPN
ejpam-1481	1	77	.	.	PUNCT
ejpam-1481	1	78	,	,	PUNCT
ejpam-1481	1	79	z.	z.	PROPN
ejpam-1481	1	80	khalilov	khalilov	PROPN
ejpam-1481	1	81	str	str	PROPN
ejpam-1481	1	82	.	.	PROPN
ejpam-1481	1	83	,	,	PUNCT
ejpam-1481	1	84	23	23	NUM
ejpam-1481	1	85	,	,	PUNCT
ejpam-1481	1	86	az	az	PROPN
ejpam-1481	1	87	1148	1148	NUM
ejpam-1481	1	88	,	,	PUNCT
ejpam-1481	1	89	baku	baku	PROPN
ejpam-1481	1	90	,	,	PUNCT
ejpam-1481	1	91	azerbaijan	azerbaijan	PROPN
ejpam-1481	1	92	2	2	NUM
ejpam-1481	1	93	permanent	permanent	ADJ
ejpam-1481	1	94	address	address	NOUN
ejpam-1481	1	95	:	:	PUNCT
ejpam-1481	1	96	mansoura	mansoura	PROPN
ejpam-1481	1	97	university	university	PROPN
ejpam-1481	1	98	,	,	PUNCT
ejpam-1481	1	99	damietta	damietta	PROPN
ejpam-1481	1	100	branch	branch	NOUN
ejpam-1481	1	101	,	,	PUNCT
ejpam-1481	1	102	faculty	faculty	NOUN
ejpam-1481	1	103	of	of	ADP
ejpam-1481	1	104	science	science	NOUN
ejpam-1481	1	105	,	,	PUNCT
ejpam-1481	1	106	mathematics	mathematics	PROPN
ejpam-1481	1	107	department	department	PROPN
ejpam-1481	1	108	,	,	PUNCT
ejpam-1481	1	109	new	new	PROPN
ejpam-1481	1	110	damietta	damietta	PROPN
ejpam-1481	1	111	,	,	PUNCT
ejpam-1481	1	112	egypt	egypt	PROPN
ejpam-1481	1	113	.	.	PUNCT
ejpam-1481	2	1	abstract	abstract	PROPN
ejpam-1481	2	2	.	.	PUNCT
ejpam-1481	3	1	in	in	ADP
ejpam-1481	3	2	this	this	DET
ejpam-1481	3	3	paper	paper	NOUN
ejpam-1481	3	4	we	we	PRON
ejpam-1481	3	5	consider	consider	VERB
ejpam-1481	3	6	the	the	DET
ejpam-1481	3	7	generalized	generalized	ADJ
ejpam-1481	3	8	difference	difference	NOUN
ejpam-1481	3	9	operator	operator	NOUN
ejpam-1481	3	10	∆v	∆v	PROPN
ejpam-1481	3	11	on	on	ADP
ejpam-1481	3	12	the	the	DET
ejpam-1481	3	13	sequence	sequence	NOUN
ejpam-1481	3	14	spaces	space	VERB
ejpam-1481	3	15	l1	l1	PROPN
ejpam-1481	3	16	and	and	CCONJ
ejpam-1481	3	17	c0	c0	PROPN
ejpam-1481	3	18	.	.	PUNCT
ejpam-1481	4	1	the	the	DET
ejpam-1481	4	2	operator	operator	NOUN
ejpam-1481	4	3	∆v	∆v	PROPN
ejpam-1481	4	4	is	be	AUX
ejpam-1481	4	5	represented	represent	VERB
ejpam-1481	4	6	by	by	ADP
ejpam-1481	4	7	a	a	DET
ejpam-1481	4	8	lower	low	ADJ
ejpam-1481	4	9	triangular	triangular	NOUN
ejpam-1481	4	10	double	double	ADJ
ejpam-1481	4	11	band	band	NOUN
ejpam-1481	4	12	matrix	matrix	NOUN
ejpam-1481	4	13	whose	whose	DET
ejpam-1481	4	14	nonzero	nonzero	NOUN
ejpam-1481	4	15	entries	entry	NOUN
ejpam-1481	4	16	are	be	AUX
ejpam-1481	4	17	the	the	DET
ejpam-1481	4	18	elements	element	NOUN
ejpam-1481	4	19	of	of	ADP
ejpam-1481	4	20	a	a	DET
ejpam-1481	4	21	sequence	sequence	NOUN
ejpam-1481	4	22	(	(	PUNCT
ejpam-1481	4	23	vk	vk	PROPN
ejpam-1481	4	24	)	)	PUNCT
ejpam-1481	4	25	with	with	ADP
ejpam-1481	4	26	certain	certain	ADJ
ejpam-1481	4	27	conditions	condition	NOUN
ejpam-1481	4	28	.	.	PUNCT
ejpam-1481	5	1	we	we	PRON
ejpam-1481	5	2	mainly	mainly	ADV
ejpam-1481	5	3	review	review	VERB
ejpam-1481	5	4	several	several	ADJ
ejpam-1481	5	5	recent	recent	ADJ
ejpam-1481	5	6	results	result	NOUN
ejpam-1481	5	7	concerning	concern	VERB
ejpam-1481	5	8	the	the	DET
ejpam-1481	5	9	fine	fine	ADJ
ejpam-1481	5	10	spectrum	spectrum	NOUN
ejpam-1481	5	11	of	of	ADP
ejpam-1481	5	12	the	the	DET
ejpam-1481	5	13	operator	operator	NOUN
ejpam-1481	5	14	∆v	∆v	PROPN
ejpam-1481	5	15	over	over	ADP
ejpam-1481	5	16	the	the	DET
ejpam-1481	5	17	sequence	sequence	NOUN
ejpam-1481	5	18	spaces	space	VERB
ejpam-1481	5	19	l1	l1	PROPN
ejpam-1481	5	20	and	and	CCONJ
ejpam-1481	5	21	c0	c0	PROPN
ejpam-1481	5	22	.	.	PUNCT
ejpam-1481	6	1	also	also	ADV
ejpam-1481	6	2	,	,	PUNCT
ejpam-1481	6	3	we	we	PRON
ejpam-1481	6	4	provide	provide	VERB
ejpam-1481	6	5	some	some	DET
ejpam-1481	6	6	new	new	ADJ
ejpam-1481	6	7	results	result	NOUN
ejpam-1481	6	8	.	.	PUNCT
ejpam-1481	7	1	following	follow	VERB
ejpam-1481	7	2	that	that	SCONJ
ejpam-1481	7	3	we	we	PRON
ejpam-1481	7	4	give	give	VERB
ejpam-1481	7	5	some	some	DET
ejpam-1481	7	6	illustrative	illustrative	ADJ
ejpam-1481	7	7	examples	example	NOUN
ejpam-1481	7	8	which	which	PRON
ejpam-1481	7	9	motivate	motivate	VERB
ejpam-1481	7	10	the	the	DET
ejpam-1481	7	11	main	main	ADJ
ejpam-1481	7	12	results	result	NOUN
ejpam-1481	7	13	.	.	PUNCT
ejpam-1481	8	1	finally	finally	ADV
ejpam-1481	8	2	,	,	PUNCT
ejpam-1481	8	3	we	we	PRON
ejpam-1481	8	4	give	give	VERB
ejpam-1481	8	5	notes	note	NOUN
ejpam-1481	8	6	on	on	ADP
ejpam-1481	8	7	the	the	DET
ejpam-1481	8	8	fine	fine	ADJ
ejpam-1481	8	9	spectrum	spectrum	NOUN
ejpam-1481	8	10	of	of	ADP
ejpam-1481	8	11	the	the	DET
ejpam-1481	8	12	operator	operator	NOUN
ejpam-1481	8	13	∆v	∆v	PROPN
ejpam-1481	8	14	.	.	PUNCT
ejpam-1481	9	1	these	these	DET
ejpam-1481	9	2	notes	note	NOUN
ejpam-1481	9	3	attempt	attempt	VERB
ejpam-1481	9	4	to	to	PART
ejpam-1481	9	5	present	present	VERB
ejpam-1481	9	6	some	some	DET
ejpam-1481	9	7	ideas	idea	NOUN
ejpam-1481	9	8	about	about	ADP
ejpam-1481	9	9	changing	change	VERB
ejpam-1481	9	10	the	the	DET
ejpam-1481	9	11	conditions	condition	NOUN
ejpam-1481	9	12	on	on	ADP
ejpam-1481	9	13	the	the	DET
ejpam-1481	9	14	sequence	sequence	NOUN
ejpam-1481	9	15	(	(	PUNCT
ejpam-1481	9	16	vk	vk	PROPN
ejpam-1481	9	17	)	)	PUNCT
ejpam-1481	9	18	in	in	ADP
ejpam-1481	9	19	the	the	DET
ejpam-1481	9	20	fine	fine	ADJ
ejpam-1481	9	21	spectrum	spectrum	NOUN
ejpam-1481	9	22	of	of	ADP
ejpam-1481	9	23	the	the	DET
ejpam-1481	9	24	operator	operator	NOUN
ejpam-1481	9	25	∆v	∆v	PROPN
ejpam-1481	9	26	.	.	PUNCT
ejpam-1481	10	1	the	the	DET
ejpam-1481	10	2	new	new	ADJ
ejpam-1481	10	3	results	result	NOUN
ejpam-1481	10	4	of	of	ADP
ejpam-1481	10	5	this	this	DET
ejpam-1481	10	6	paper	paper	NOUN
ejpam-1481	10	7	generalize	generalize	VERB
ejpam-1481	10	8	and	and	CCONJ
ejpam-1481	10	9	improve	improve	VERB
ejpam-1481	10	10	some	some	DET
ejpam-1481	10	11	recent	recent	ADJ
ejpam-1481	10	12	results	result	NOUN
ejpam-1481	10	13	that	that	PRON
ejpam-1481	10	14	appeared	appear	VERB
ejpam-1481	10	15	recently	recently	ADV
ejpam-1481	10	16	in	in	ADP
ejpam-1481	10	17	the	the	DET
ejpam-1481	10	18	literature	literature	NOUN
ejpam-1481	10	19	.	.	PUNCT
ejpam-1481	11	1	key	key	ADJ
ejpam-1481	11	2	words	word	NOUN
ejpam-1481	11	3	and	and	CCONJ
ejpam-1481	11	4	phrases	phrase	NOUN
ejpam-1481	11	5	:	:	PUNCT
ejpam-1481	11	6	spectrum	spectrum	NOUN
ejpam-1481	11	7	of	of	ADP
ejpam-1481	11	8	an	an	DET
ejpam-1481	11	9	operator	operator	NOUN
ejpam-1481	11	10	;	;	PUNCT
ejpam-1481	11	11	generalized	generalized	ADJ
ejpam-1481	11	12	difference	difference	NOUN
ejpam-1481	11	13	operator	operator	NOUN
ejpam-1481	11	14	;	;	PUNCT
ejpam-1481	11	15	the	the	DET
ejpam-1481	11	16	sequence	sequence	NOUN
ejpam-1481	11	17	spaces	space	VERB
ejpam-1481	11	18	l1	l1	PROPN
ejpam-1481	11	19	and	and	CCONJ
ejpam-1481	11	20	c0	c0	PROPN
ejpam-1481	11	21	.	.	PROPN
ejpam-1481	12	1	1	1	X
ejpam-1481	12	2	.	.	X
ejpam-1481	12	3	introduction	introduction	NOUN
ejpam-1481	12	4	several	several	ADJ
ejpam-1481	12	5	authors	author	NOUN
ejpam-1481	12	6	have	have	AUX
ejpam-1481	12	7	studied	study	VERB
ejpam-1481	12	8	the	the	DET
ejpam-1481	12	9	spectrum	spectrum	NOUN
ejpam-1481	12	10	and	and	CCONJ
ejpam-1481	12	11	fine	fine	ADJ
ejpam-1481	12	12	spectrum	spectrum	NOUN
ejpam-1481	12	13	of	of	ADP
ejpam-1481	12	14	linear	linear	PROPN
ejpam-1481	12	15	operators	operator	NOUN
ejpam-1481	12	16	defined	define	VERB
ejpam-1481	12	17	by	by	ADP
ejpam-1481	12	18	some	some	DET
ejpam-1481	12	19	particular	particular	ADJ
ejpam-1481	12	20	limitation	limitation	NOUN
ejpam-1481	12	21	matrices	matrix	NOUN
ejpam-1481	12	22	over	over	ADP
ejpam-1481	12	23	some	some	DET
ejpam-1481	12	24	sequence	sequence	NOUN
ejpam-1481	12	25	spaces	space	VERB
ejpam-1481	12	26	.	.	PUNCT
ejpam-1481	13	1	we	we	PRON
ejpam-1481	13	2	summarize	summarize	VERB
ejpam-1481	13	3	the	the	DET
ejpam-1481	13	4	knowledge	knowledge	NOUN
ejpam-1481	13	5	in	in	ADP
ejpam-1481	13	6	the	the	DET
ejpam-1481	13	7	existing	exist	VERB
ejpam-1481	13	8	literature	literature	NOUN
ejpam-1481	13	9	concerning	concern	VERB
ejpam-1481	13	10	the	the	DET
ejpam-1481	13	11	spectrum	spectrum	NOUN
ejpam-1481	13	12	and	and	CCONJ
ejpam-1481	13	13	the	the	DET
ejpam-1481	13	14	fine	fine	ADJ
ejpam-1481	13	15	spectrum	spectrum	NOUN
ejpam-1481	13	16	.	.	PUNCT
ejpam-1481	14	1	the	the	DET
ejpam-1481	14	2	fine	fine	ADJ
ejpam-1481	14	3	spectrum	spectrum	NOUN
ejpam-1481	14	4	of	of	ADP
ejpam-1481	14	5	the	the	DET
ejpam-1481	14	6	difference	difference	NOUN
ejpam-1481	14	7	operator	operator	NOUN
ejpam-1481	14	8	∆	∆	PROPN
ejpam-1481	14	9	over	over	ADP
ejpam-1481	14	10	the	the	DET
ejpam-1481	14	11	sequence	sequence	NOUN
ejpam-1481	14	12	spaces	space	VERB
ejpam-1481	14	13	c0	c0	NOUN
ejpam-1481	14	14	and	and	CCONJ
ejpam-1481	14	15	c	c	PROPN
ejpam-1481	14	16	has	have	AUX
ejpam-1481	14	17	been	be	AUX
ejpam-1481	14	18	studied	study	VERB
ejpam-1481	14	19	by	by	ADP
ejpam-1481	14	20	altay	altay	NOUN
ejpam-1481	14	21	and	and	CCONJ
ejpam-1481	14	22	başar	başar	PROPN
ejpam-1481	15	1	[	[	X
ejpam-1481	15	2	9	9	NUM
ejpam-1481	15	3	]	]	PUNCT
ejpam-1481	15	4	.	.	PUNCT
ejpam-1481	16	1	akhmedov	akhmedov	VERB
ejpam-1481	16	2	and	and	CCONJ
ejpam-1481	16	3	başar	başar	PROPN
ejpam-1481	17	1	[	[	X
ejpam-1481	17	2	1	1	NUM
ejpam-1481	17	3	,	,	PUNCT
ejpam-1481	17	4	2	2	NUM
ejpam-1481	17	5	]	]	PUNCT
ejpam-1481	17	6	have	have	AUX
ejpam-1481	17	7	studied	study	VERB
ejpam-1481	17	8	the	the	DET
ejpam-1481	17	9	fine	fine	ADJ
ejpam-1481	17	10	spectrum	spectrum	NOUN
ejpam-1481	17	11	of	of	ADP
ejpam-1481	17	12	the	the	DET
ejpam-1481	17	13	difference	difference	NOUN
ejpam-1481	17	14	operator	operator	NOUN
ejpam-1481	17	15	∆	∆	PROPN
ejpam-1481	17	16	over	over	ADP
ejpam-1481	17	17	the	the	DET
ejpam-1481	17	18	sequence	sequence	NOUN
ejpam-1481	17	19	spaces	space	VERB
ejpam-1481	17	20	lp	lp	NOUN
ejpam-1481	17	21	and	and	CCONJ
ejpam-1481	17	22	bvp	bvp	NOUN
ejpam-1481	17	23	,	,	PUNCT
ejpam-1481	17	24	where	where	SCONJ
ejpam-1481	17	25	1	1	NUM
ejpam-1481	17	26	≤	≤	NOUN
ejpam-1481	17	27	p	p	NOUN
ejpam-1481	17	28	<	<	X
ejpam-1481	18	1	∞.	∞.	PROPN
ejpam-1481	18	2	note	note	VERB
ejpam-1481	18	3	that	that	SCONJ
ejpam-1481	18	4	the	the	DET
ejpam-1481	18	5	sequence	sequence	NOUN
ejpam-1481	18	6	space	space	NOUN
ejpam-1481	18	7	bvp	bvp	PROPN
ejpam-1481	18	8	was	be	AUX
ejpam-1481	18	9	studied	study	VERB
ejpam-1481	18	10	by	by	ADP
ejpam-1481	18	11	başar	başar	PROPN
ejpam-1481	18	12	and	and	CCONJ
ejpam-1481	18	13	altay	altay	NOUN
ejpam-1481	18	14	[	[	X
ejpam-1481	18	15	12	12	NUM
ejpam-1481	18	16	]	]	PUNCT
ejpam-1481	18	17	and	and	CCONJ
ejpam-1481	18	18	akhmedov	akhmedov	NOUN
ejpam-1481	18	19	and	and	CCONJ
ejpam-1481	18	20	başar	başar	PROPN
ejpam-1481	18	21	[	[	X
ejpam-1481	18	22	2	2	NUM
ejpam-1481	18	23	]	]	PUNCT
ejpam-1481	18	24	.	.	PUNCT
ejpam-1481	19	1	malafosse	malafosse	NOUN
ejpam-1481	20	1	[	[	X
ejpam-1481	20	2	22	22	NUM
ejpam-1481	20	3	]	]	PUNCT
ejpam-1481	20	4	∗corresponding	∗corresponde	VERB
ejpam-1481	20	5	author	author	NOUN
ejpam-1481	20	6	.	.	PUNCT
ejpam-1481	21	1	email	email	NOUN
ejpam-1481	21	2	addresses	address	NOUN
ejpam-1481	21	3	:	:	PUNCT
ejpam-1481	21	4	akhmedovali�rambler.ru	akhmedovali�rambler.ru	PROPN
ejpam-1481	21	5	(	(	PUNCT
ejpam-1481	21	6	a.	a.	NOUN
ejpam-1481	21	7	akhmedov	akhmedov	PROPN
ejpam-1481	21	8	)	)	PUNCT
ejpam-1481	21	9	,	,	PUNCT
ejpam-1481	21	10	srshabrawy	srshabrawy	PROPN
ejpam-1481	21	11	�	�	PROPN
ejpam-1481	21	12	yahoo	yahoo	PROPN
ejpam-1481	21	13	.	.	PUNCT
ejpam-1481	22	1	om	om	PROPN
ejpam-1481	22	2	(	(	PUNCT
ejpam-1481	22	3	s.	s.	PROPN
ejpam-1481	22	4	el	el	PROPN
ejpam-1481	22	5	-	-	PUNCT
ejpam-1481	22	6	shabrawy	shabrawy	PROPN
ejpam-1481	22	7	)	)	PUNCT
ejpam-1481	22	8	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1481	23	1	59	59	NUM
ejpam-1481	23	2	c	c	X
ejpam-1481	23	3	©	©	PROPN
ejpam-1481	23	4	2012	2012	NUM
ejpam-1481	23	5	ejpam	ejpam	VERB
ejpam-1481	23	6	all	all	DET
ejpam-1481	23	7	rights	right	NOUN
ejpam-1481	23	8	reserved	reserve	VERB
ejpam-1481	23	9	.	.	PUNCT
ejpam-1481	24	1	a.	a.	PROPN
ejpam-1481	24	2	akhmedov	akhmedov	PROPN
ejpam-1481	24	3	,	,	PUNCT
ejpam-1481	24	4	s.	s.	PROPN
ejpam-1481	24	5	el	el	PROPN
ejpam-1481	24	6	-	-	PUNCT
ejpam-1481	24	7	shabrawy	shabrawy	PROPN
ejpam-1481	24	8	/	/	SYM
ejpam-1481	24	9	eur	eur	NOUN
ejpam-1481	24	10	.	.	PUNCT
ejpam-1481	25	1	j.	j.	PROPN
ejpam-1481	25	2	pure	pure	PROPN
ejpam-1481	25	3	appl	appl	PROPN
ejpam-1481	25	4	.	.	PROPN
ejpam-1481	25	5	math	math	PROPN
ejpam-1481	25	6	,	,	PUNCT
ejpam-1481	25	7	5	5	NUM
ejpam-1481	25	8	(	(	PUNCT
ejpam-1481	25	9	2012	2012	NUM
ejpam-1481	25	10	)	)	PUNCT
ejpam-1481	25	11	,	,	PUNCT
ejpam-1481	25	12	59	59	NUM
ejpam-1481	25	13	-	-	SYM
ejpam-1481	25	14	74	74	NUM
ejpam-1481	25	15	60	60	NUM
ejpam-1481	25	16	has	have	AUX
ejpam-1481	25	17	studied	study	VERB
ejpam-1481	25	18	the	the	DET
ejpam-1481	25	19	spectrum	spectrum	NOUN
ejpam-1481	25	20	and	and	CCONJ
ejpam-1481	25	21	the	the	DET
ejpam-1481	25	22	fine	fine	ADJ
ejpam-1481	25	23	spectrum	spectrum	NOUN
ejpam-1481	25	24	of	of	ADP
ejpam-1481	25	25	the	the	DET
ejpam-1481	25	26	difference	difference	NOUN
ejpam-1481	25	27	operator	operator	NOUN
ejpam-1481	25	28	∆	∆	PROPN
ejpam-1481	25	29	over	over	ADP
ejpam-1481	25	30	the	the	DET
ejpam-1481	25	31	space	space	NOUN
ejpam-1481	25	32	sr	sr	PROPN
ejpam-1481	25	33	,	,	PUNCT
ejpam-1481	25	34	where	where	SCONJ
ejpam-1481	25	35	sr	sr	PROPN
ejpam-1481	25	36	denotes	denote	VERB
ejpam-1481	25	37	the	the	DET
ejpam-1481	25	38	banach	banach	NOUN
ejpam-1481	25	39	space	space	NOUN
ejpam-1481	25	40	of	of	ADP
ejpam-1481	25	41	all	all	DET
ejpam-1481	25	42	sequences	sequence	NOUN
ejpam-1481	25	43	x	x	PUNCT
ejpam-1481	25	44	=	=	SYM
ejpam-1481	25	45	(	(	PUNCT
ejpam-1481	25	46	xk	xk	NOUN
ejpam-1481	25	47	)	)	PUNCT
ejpam-1481	25	48	normed	norme	VERB
ejpam-1481	25	49	by	by	ADP
ejpam-1481	25	50	‖x‖sr	‖x‖sr	NOUN
ejpam-1481	25	51	=	=	NOUN
ejpam-1481	25	52	sup	sup	NOUN
ejpam-1481	25	53	k∈n	k∈n	PROPN
ejpam-1481	25	54	�	�	PROPN
ejpam-1481	25	55	�	�	PROPN
ejpam-1481	25	56	xk	xk	PROPN
ejpam-1481	25	57	�	�	PROPN
ejpam-1481	25	58	�	�	PROPN
ejpam-1481	25	59	rk	rk	PROPN
ejpam-1481	25	60	(	(	PUNCT
ejpam-1481	25	61	r	r	NOUN
ejpam-1481	25	62	>	>	X
ejpam-1481	25	63	0	0	NUM
ejpam-1481	25	64	)	)	PUNCT
ejpam-1481	25	65	.	.	PUNCT
ejpam-1481	26	1	the	the	DET
ejpam-1481	26	2	fine	fine	ADJ
ejpam-1481	26	3	spectrum	spectrum	NOUN
ejpam-1481	26	4	of	of	ADP
ejpam-1481	26	5	the	the	DET
ejpam-1481	26	6	zweier	zweier	NOUN
ejpam-1481	26	7	matrix	matrix	NOUN
ejpam-1481	26	8	operator	operator	NOUN
ejpam-1481	26	9	z	z	NOUN
ejpam-1481	26	10	s	s	PROPN
ejpam-1481	26	11	over	over	ADP
ejpam-1481	26	12	the	the	DET
ejpam-1481	26	13	sequence	sequence	NOUN
ejpam-1481	26	14	spaces	space	VERB
ejpam-1481	26	15	l1	l1	PROPN
ejpam-1481	26	16	and	and	CCONJ
ejpam-1481	26	17	bv	bv	PROPN
ejpam-1481	26	18	has	have	AUX
ejpam-1481	26	19	been	be	AUX
ejpam-1481	26	20	examined	examine	VERB
ejpam-1481	26	21	by	by	ADP
ejpam-1481	26	22	altay	altay	NOUN
ejpam-1481	26	23	and	and	CCONJ
ejpam-1481	26	24	karakuş	karakuş	NOUN
ejpam-1481	26	25	[	[	X
ejpam-1481	26	26	11	11	NUM
ejpam-1481	26	27	]	]	PUNCT
ejpam-1481	26	28	.	.	PUNCT
ejpam-1481	27	1	the	the	DET
ejpam-1481	27	2	fine	fine	ADJ
ejpam-1481	27	3	spectrum	spectrum	NOUN
ejpam-1481	27	4	of	of	ADP
ejpam-1481	27	5	the	the	DET
ejpam-1481	27	6	generalized	generalize	VERB
ejpam-1481	27	7	difference	difference	NOUN
ejpam-1481	27	8	operator	operator	NOUN
ejpam-1481	27	9	b(r	b(r	PROPN
ejpam-1481	27	10	,	,	PUNCT
ejpam-1481	27	11	s	s	NOUN
ejpam-1481	27	12	)	)	PUNCT
ejpam-1481	27	13	over	over	ADP
ejpam-1481	27	14	the	the	DET
ejpam-1481	27	15	sequence	sequence	NOUN
ejpam-1481	27	16	spaces	space	VERB
ejpam-1481	27	17	c0	c0	NOUN
ejpam-1481	27	18	and	and	CCONJ
ejpam-1481	27	19	c	c	PROPN
ejpam-1481	27	20	has	have	AUX
ejpam-1481	27	21	been	be	AUX
ejpam-1481	27	22	studied	study	VERB
ejpam-1481	27	23	by	by	ADP
ejpam-1481	27	24	altay	altay	NOUN
ejpam-1481	27	25	and	and	CCONJ
ejpam-1481	27	26	başar	başar	PROPN
ejpam-1481	28	1	[	[	X
ejpam-1481	28	2	10	10	NUM
ejpam-1481	28	3	]	]	PUNCT
ejpam-1481	28	4	.	.	PUNCT
ejpam-1481	29	1	also	also	ADV
ejpam-1481	29	2	,	,	PUNCT
ejpam-1481	29	3	the	the	DET
ejpam-1481	29	4	fine	fine	ADJ
ejpam-1481	29	5	spectrum	spectrum	NOUN
ejpam-1481	29	6	of	of	ADP
ejpam-1481	29	7	the	the	DET
ejpam-1481	29	8	operator	operator	NOUN
ejpam-1481	29	9	b(r	b(r	PROPN
ejpam-1481	29	10	,	,	PUNCT
ejpam-1481	29	11	s	s	NOUN
ejpam-1481	29	12	)	)	PUNCT
ejpam-1481	29	13	over	over	ADP
ejpam-1481	29	14	the	the	DET
ejpam-1481	29	15	sequence	sequence	NOUN
ejpam-1481	29	16	spaces	space	VERB
ejpam-1481	29	17	l1	l1	PROPN
ejpam-1481	29	18	and	and	CCONJ
ejpam-1481	29	19	bv	bv	PROPN
ejpam-1481	29	20	has	have	AUX
ejpam-1481	29	21	been	be	AUX
ejpam-1481	29	22	examined	examine	VERB
ejpam-1481	29	23	by	by	ADP
ejpam-1481	29	24	furkan	furkan	PROPN
ejpam-1481	29	25	et	et	PROPN
ejpam-1481	29	26	al	al	PROPN
ejpam-1481	29	27	.	.	PUNCT
ejpam-1481	30	1	[	[	X
ejpam-1481	30	2	18	18	NUM
ejpam-1481	30	3	]	]	PUNCT
ejpam-1481	30	4	.	.	PUNCT
ejpam-1481	31	1	the	the	DET
ejpam-1481	31	2	fine	fine	ADJ
ejpam-1481	31	3	spectrum	spectrum	NOUN
ejpam-1481	31	4	of	of	ADP
ejpam-1481	31	5	the	the	DET
ejpam-1481	31	6	operator	operator	NOUN
ejpam-1481	31	7	b(r	b(r	PROPN
ejpam-1481	31	8	,	,	PUNCT
ejpam-1481	31	9	s	s	NOUN
ejpam-1481	31	10	)	)	PUNCT
ejpam-1481	31	11	over	over	ADP
ejpam-1481	31	12	the	the	DET
ejpam-1481	31	13	sequence	sequence	NOUN
ejpam-1481	31	14	spaces	space	VERB
ejpam-1481	31	15	lp	lp	NOUN
ejpam-1481	31	16	and	and	CCONJ
ejpam-1481	31	17	bvp	bvp	NOUN
ejpam-1481	31	18	,	,	PUNCT
ejpam-1481	31	19	where	where	SCONJ
ejpam-1481	31	20	1	1	X
ejpam-1481	31	21	<	<	X
ejpam-1481	31	22	p	p	X
ejpam-1481	31	23	<	<	X
ejpam-1481	31	24	∞	∞	PROPN
ejpam-1481	31	25	has	have	AUX
ejpam-1481	31	26	been	be	AUX
ejpam-1481	31	27	determined	determine	VERB
ejpam-1481	31	28	by	by	ADP
ejpam-1481	31	29	bilgiç	bilgiç	NOUN
ejpam-1481	31	30	and	and	CCONJ
ejpam-1481	31	31	furkan	furkan	ADJ
ejpam-1481	32	1	[	[	X
ejpam-1481	32	2	13	13	NUM
ejpam-1481	32	3	]	]	PUNCT
ejpam-1481	32	4	.	.	PUNCT
ejpam-1481	33	1	the	the	DET
ejpam-1481	33	2	fine	fine	ADJ
ejpam-1481	33	3	spectrum	spectrum	NOUN
ejpam-1481	33	4	of	of	ADP
ejpam-1481	33	5	the	the	DET
ejpam-1481	33	6	operator	operator	NOUN
ejpam-1481	33	7	b(r	b(r	PROPN
ejpam-1481	33	8	,	,	PUNCT
ejpam-1481	33	9	s	s	PROPN
ejpam-1481	33	10	,	,	PUNCT
ejpam-1481	33	11	t	t	PROPN
ejpam-1481	33	12	)	)	PUNCT
ejpam-1481	33	13	over	over	ADP
ejpam-1481	33	14	the	the	DET
ejpam-1481	33	15	sequence	sequence	NOUN
ejpam-1481	33	16	spaces	space	VERB
ejpam-1481	33	17	c0	c0	NOUN
ejpam-1481	33	18	and	and	CCONJ
ejpam-1481	33	19	c	c	PROPN
ejpam-1481	33	20	has	have	AUX
ejpam-1481	33	21	been	be	AUX
ejpam-1481	33	22	studied	study	VERB
ejpam-1481	33	23	by	by	ADP
ejpam-1481	33	24	furkan	furkan	PROPN
ejpam-1481	33	25	et	et	PROPN
ejpam-1481	33	26	al	al	PROPN
ejpam-1481	33	27	.	.	PUNCT
ejpam-1481	34	1	[	[	X
ejpam-1481	34	2	16	16	NUM
ejpam-1481	34	3	]	]	PUNCT
ejpam-1481	34	4	.	.	PUNCT
ejpam-1481	35	1	also	also	ADV
ejpam-1481	35	2	,	,	PUNCT
ejpam-1481	35	3	the	the	DET
ejpam-1481	35	4	fine	fine	ADJ
ejpam-1481	35	5	spectrum	spectrum	NOUN
ejpam-1481	35	6	of	of	ADP
ejpam-1481	35	7	the	the	DET
ejpam-1481	35	8	operator	operator	NOUN
ejpam-1481	35	9	b(r	b(r	PROPN
ejpam-1481	35	10	,	,	PUNCT
ejpam-1481	35	11	s	s	PROPN
ejpam-1481	35	12	,	,	PUNCT
ejpam-1481	35	13	t	t	PROPN
ejpam-1481	35	14	)	)	PUNCT
ejpam-1481	35	15	over	over	ADP
ejpam-1481	35	16	the	the	DET
ejpam-1481	35	17	sequence	sequence	NOUN
ejpam-1481	35	18	spaces	space	VERB
ejpam-1481	35	19	lp	lp	NOUN
ejpam-1481	35	20	and	and	CCONJ
ejpam-1481	35	21	bvp	bvp	NOUN
ejpam-1481	35	22	,	,	PUNCT
ejpam-1481	35	23	where	where	SCONJ
ejpam-1481	35	24	1	1	X
ejpam-1481	35	25	<	<	X
ejpam-1481	35	26	p	p	X
ejpam-1481	35	27	<	<	X
ejpam-1481	35	28	∞	∞	PROPN
ejpam-1481	35	29	has	have	AUX
ejpam-1481	35	30	been	be	AUX
ejpam-1481	35	31	determined	determine	VERB
ejpam-1481	35	32	by	by	ADP
ejpam-1481	35	33	furkan	furkan	PROPN
ejpam-1481	35	34	et	et	PROPN
ejpam-1481	35	35	al	al	PROPN
ejpam-1481	35	36	.	.	PUNCT
ejpam-1481	36	1	[	[	X
ejpam-1481	36	2	17	17	NUM
ejpam-1481	36	3	]	]	PUNCT
ejpam-1481	36	4	.	.	PUNCT
ejpam-1481	37	1	panigrahi	panigrahi	NOUN
ejpam-1481	37	2	and	and	CCONJ
ejpam-1481	37	3	srivastava	srivastava	PROPN
ejpam-1481	38	1	[	[	X
ejpam-1481	38	2	23	23	NUM
ejpam-1481	38	3	]	]	PUNCT
ejpam-1481	38	4	have	have	AUX
ejpam-1481	38	5	studied	study	VERB
ejpam-1481	38	6	the	the	DET
ejpam-1481	38	7	fine	fine	ADJ
ejpam-1481	38	8	spectrum	spectrum	NOUN
ejpam-1481	38	9	of	of	ADP
ejpam-1481	38	10	the	the	DET
ejpam-1481	38	11	generalized	generalized	ADJ
ejpam-1481	38	12	second	second	ADJ
ejpam-1481	38	13	order	order	NOUN
ejpam-1481	38	14	difference	difference	NOUN
ejpam-1481	38	15	operator	operator	NOUN
ejpam-1481	38	16	∆2	∆2	PROPN
ejpam-1481	38	17	uv	uv	NOUN
ejpam-1481	38	18	over	over	ADP
ejpam-1481	38	19	the	the	DET
ejpam-1481	38	20	sequence	sequence	NOUN
ejpam-1481	38	21	space	space	NOUN
ejpam-1481	38	22	c0	c0	NOUN
ejpam-1481	38	23	.	.	PUNCT
ejpam-1481	39	1	the	the	DET
ejpam-1481	39	2	fine	fine	ADJ
ejpam-1481	39	3	spectrum	spectrum	NOUN
ejpam-1481	39	4	of	of	ADP
ejpam-1481	39	5	the	the	DET
ejpam-1481	39	6	generalized	generalize	VERB
ejpam-1481	39	7	difference	difference	NOUN
ejpam-1481	39	8	operator	operator	NOUN
ejpam-1481	39	9	∆a	∆a	NOUN
ejpam-1481	39	10	,	,	PUNCT
ejpam-1481	39	11	b	b	NOUN
ejpam-1481	39	12	over	over	ADP
ejpam-1481	39	13	the	the	DET
ejpam-1481	39	14	sequence	sequence	NOUN
ejpam-1481	39	15	spaces	space	VERB
ejpam-1481	39	16	c0	c0	NOUN
ejpam-1481	39	17	and	and	CCONJ
ejpam-1481	39	18	c	c	PROPN
ejpam-1481	39	19	has	have	AUX
ejpam-1481	39	20	been	be	AUX
ejpam-1481	39	21	studied	study	VERB
ejpam-1481	39	22	by	by	ADP
ejpam-1481	39	23	akhmedov	akhmedov	NOUN
ejpam-1481	39	24	and	and	CCONJ
ejpam-1481	39	25	elshabrawy	elshabrawy	VERB
ejpam-1481	39	26	[	[	X
ejpam-1481	39	27	3,5	3,5	NUM
ejpam-1481	39	28	]	]	PUNCT
ejpam-1481	39	29	.	.	PUNCT
ejpam-1481	40	1	the	the	DET
ejpam-1481	40	2	fine	fine	ADJ
ejpam-1481	40	3	spectrum	spectrum	NOUN
ejpam-1481	40	4	of	of	ADP
ejpam-1481	40	5	the	the	DET
ejpam-1481	40	6	upper	upper	ADJ
ejpam-1481	40	7	triangular	triangular	NOUN
ejpam-1481	40	8	double	double	ADJ
ejpam-1481	40	9	-	-	PUNCT
ejpam-1481	40	10	band	band	NOUN
ejpam-1481	40	11	matrices	matrix	NOUN
ejpam-1481	40	12	over	over	ADP
ejpam-1481	40	13	the	the	DET
ejpam-1481	40	14	sequence	sequence	NOUN
ejpam-1481	40	15	spaces	space	VERB
ejpam-1481	40	16	c0	c0	NOUN
ejpam-1481	40	17	and	and	CCONJ
ejpam-1481	40	18	c	c	PROPN
ejpam-1481	40	19	has	have	AUX
ejpam-1481	40	20	been	be	AUX
ejpam-1481	40	21	determined	determine	VERB
ejpam-1481	40	22	by	by	ADP
ejpam-1481	40	23	karakaya	karakaya	NOUN
ejpam-1481	40	24	and	and	CCONJ
ejpam-1481	40	25	altun	altun	NOUN
ejpam-1481	41	1	[	[	X
ejpam-1481	41	2	20	20	NUM
ejpam-1481	41	3	]	]	PUNCT
ejpam-1481	41	4	.	.	PUNCT
ejpam-1481	42	1	the	the	DET
ejpam-1481	42	2	operator	operator	NOUN
ejpam-1481	42	3	∆v	∆v	PROPN
ejpam-1481	42	4	has	have	AUX
ejpam-1481	42	5	been	be	AUX
ejpam-1481	42	6	introduced	introduce	VERB
ejpam-1481	42	7	firstly	firstly	ADV
ejpam-1481	42	8	by	by	ADP
ejpam-1481	42	9	srivastava	srivastava	PROPN
ejpam-1481	42	10	and	and	CCONJ
ejpam-1481	42	11	kumar	kumar	PROPN
ejpam-1481	42	12	[	[	X
ejpam-1481	42	13	24	24	NUM
ejpam-1481	42	14	]	]	PUNCT
ejpam-1481	42	15	.	.	PUNCT
ejpam-1481	43	1	the	the	DET
ejpam-1481	43	2	operator	operator	NOUN
ejpam-1481	43	3	∆v	∆v	PROPN
ejpam-1481	43	4	:	:	PUNCT
ejpam-1481	43	5	(	(	PUNCT
ejpam-1481	43	6	l1→	l1→	X
ejpam-1481	43	7	l1	l1	PROPN
ejpam-1481	43	8	,	,	PUNCT
ejpam-1481	43	9	c0	c0	PROPN
ejpam-1481	43	10	−→	−→	PROPN
ejpam-1481	43	11	c0	c0	PROPN
ejpam-1481	43	12	)	)	PUNCT
ejpam-1481	43	13	is	be	AUX
ejpam-1481	43	14	defined	define	VERB
ejpam-1481	43	15	as	as	SCONJ
ejpam-1481	43	16	follows	follow	VERB
ejpam-1481	43	17	:	:	PUNCT
ejpam-1481	43	18	∆v	∆v	PROPN
ejpam-1481	43	19	x	x	PUNCT
ejpam-1481	43	20	=	=	NOUN
ejpam-1481	43	21	∆v(xk	∆v(xk	X
ejpam-1481	43	22	)	)	PUNCT
ejpam-1481	43	23	=	=	SYM
ejpam-1481	43	24	(	(	PUNCT
ejpam-1481	43	25	vk	vk	INTJ
ejpam-1481	43	26	xk	xk	PROPN
ejpam-1481	43	27	−	−	PROPN
ejpam-1481	43	28	vk−1	vk−1	PROPN
ejpam-1481	43	29	xk−1	xk−1	PROPN
ejpam-1481	43	30	)	)	PUNCT
ejpam-1481	43	31	∞	∞	PROPN
ejpam-1481	43	32	k=0	k=0	PROPN
ejpam-1481	43	33	with	with	ADP
ejpam-1481	43	34	x−1	x−1	PROPN
ejpam-1481	43	35	=	=	SYM
ejpam-1481	43	36	v−1	v−1	PROPN
ejpam-1481	43	37	=	=	SYM
ejpam-1481	43	38	0	0	NUM
ejpam-1481	43	39	,	,	PUNCT
ejpam-1481	43	40	(	(	PUNCT
ejpam-1481	43	41	1	1	X
ejpam-1481	43	42	)	)	PUNCT
ejpam-1481	43	43	where	where	SCONJ
ejpam-1481	43	44	the	the	DET
ejpam-1481	43	45	sequence	sequence	NOUN
ejpam-1481	43	46	(	(	PUNCT
ejpam-1481	43	47	vk	vk	NOUN
ejpam-1481	43	48	)	)	PUNCT
ejpam-1481	43	49	is	be	AUX
ejpam-1481	43	50	assumed	assume	VERB
ejpam-1481	43	51	to	to	PART
ejpam-1481	43	52	be	be	AUX
ejpam-1481	43	53	either	either	CCONJ
ejpam-1481	43	54	constant	constant	ADJ
ejpam-1481	43	55	or	or	CCONJ
ejpam-1481	43	56	strictly	strictly	ADV
ejpam-1481	43	57	decreasing	decrease	VERB
ejpam-1481	43	58	sequence	sequence	NOUN
ejpam-1481	43	59	of	of	ADP
ejpam-1481	43	60	positive	positive	ADJ
ejpam-1481	43	61	real	real	ADJ
ejpam-1481	43	62	numbers	number	NOUN
ejpam-1481	43	63	satisfying	satisfy	VERB
ejpam-1481	43	64	lim	lim	PROPN
ejpam-1481	43	65	k→∞	k→∞	PROPN
ejpam-1481	43	66	vk	vk	PROPN
ejpam-1481	43	67	=	=	SYM
ejpam-1481	43	68	l	l	NOUN
ejpam-1481	43	69	>	>	PUNCT
ejpam-1481	43	70	0	0	PUNCT
ejpam-1481	44	1	and	and	CCONJ
ejpam-1481	44	2	sup	sup	PROPN
ejpam-1481	44	3	k	k	PROPN
ejpam-1481	44	4	vk	vk	PROPN
ejpam-1481	44	5	≤	≤	NUM
ejpam-1481	44	6	2l	2l	NUM
ejpam-1481	44	7	.	.	PUNCT
ejpam-1481	45	1	(	(	PUNCT
ejpam-1481	45	2	2	2	X
ejpam-1481	45	3	)	)	PUNCT
ejpam-1481	45	4	it	it	PRON
ejpam-1481	45	5	is	be	AUX
ejpam-1481	45	6	easy	easy	ADJ
ejpam-1481	45	7	to	to	PART
ejpam-1481	45	8	verify	verify	VERB
ejpam-1481	45	9	that	that	SCONJ
ejpam-1481	45	10	the	the	DET
ejpam-1481	45	11	operator	operator	NOUN
ejpam-1481	45	12	∆v	∆v	PROPN
ejpam-1481	45	13	is	be	AUX
ejpam-1481	45	14	represented	represent	VERB
ejpam-1481	45	15	by	by	ADP
ejpam-1481	45	16	a	a	DET
ejpam-1481	45	17	lower	low	ADJ
ejpam-1481	45	18	triangular	triangular	NOUN
ejpam-1481	45	19	double	double	ADJ
ejpam-1481	45	20	band	band	NOUN
ejpam-1481	45	21	matrix	matrix	NOUN
ejpam-1481	45	22	of	of	ADP
ejpam-1481	45	23	the	the	DET
ejpam-1481	45	24	form	form	NOUN
ejpam-1481	46	1	∆v	∆v	NOUN
ejpam-1481	46	2	=	=	PUNCT
ejpam-1481	46	3			PROPN
ejpam-1481	46	4			NOUN
ejpam-1481	46	5			NOUN
ejpam-1481	46	6			NOUN
ejpam-1481	46	7			NOUN
ejpam-1481	46	8			NOUN
ejpam-1481	46	9	v0	v0	VERB
ejpam-1481	46	10	0	0	NUM
ejpam-1481	46	11	0	0	NUM
ejpam-1481	46	12	·	·	PUNCT
ejpam-1481	46	13	·	·	PUNCT
ejpam-1481	46	14	·	·	PUNCT
ejpam-1481	47	1	−v0	−v0	INTJ
ejpam-1481	47	2	v1	v1	NOUN
ejpam-1481	47	3	0	0	NUM
ejpam-1481	47	4	·	·	PUNCT
ejpam-1481	47	5	·	·	PUNCT
ejpam-1481	47	6	·	·	PUNCT
ejpam-1481	47	7	0	0	NUM
ejpam-1481	48	1	−v1	−v1	NOUN
ejpam-1481	48	2	v2	v2	X
ejpam-1481	48	3	·	·	PUNCT
ejpam-1481	48	4	·	·	PUNCT
ejpam-1481	48	5	·	·	PUNCT
ejpam-1481	48	6	...	...	PUNCT
ejpam-1481	48	7	...	...	PUNCT
ejpam-1481	48	8	...	...	PUNCT
ejpam-1481	48	9	.	.	PUNCT
ejpam-1481	48	10	.	.	PUNCT
ejpam-1481	48	11	.	.	PUNCT
ejpam-1481	49	1			PROPN
ejpam-1481	49	2			NOUN
ejpam-1481	49	3			VERB
ejpam-1481	49	4			NOUN
ejpam-1481	49	5			NOUN
ejpam-1481	49	6			PUNCT
ejpam-1481	49	7	.	.	PUNCT
ejpam-1481	50	1	(	(	PUNCT
ejpam-1481	50	2	3	3	X
ejpam-1481	50	3	)	)	PUNCT
ejpam-1481	50	4	the	the	DET
ejpam-1481	50	5	fine	fine	ADJ
ejpam-1481	50	6	spectrum	spectrum	NOUN
ejpam-1481	50	7	of	of	ADP
ejpam-1481	50	8	the	the	DET
ejpam-1481	50	9	generalized	generalize	VERB
ejpam-1481	50	10	difference	difference	NOUN
ejpam-1481	50	11	operator	operator	NOUN
ejpam-1481	50	12	∆v	∆v	PROPN
ejpam-1481	50	13	over	over	ADP
ejpam-1481	50	14	the	the	DET
ejpam-1481	50	15	sequence	sequence	NOUN
ejpam-1481	50	16	spaces	space	VERB
ejpam-1481	50	17	c0	c0	PROPN
ejpam-1481	50	18	and	and	CCONJ
ejpam-1481	50	19	l1	l1	PROPN
ejpam-1481	50	20	was	be	AUX
ejpam-1481	50	21	investigated	investigate	VERB
ejpam-1481	50	22	by	by	ADP
ejpam-1481	50	23	srivastava	srivastava	PROPN
ejpam-1481	50	24	and	and	CCONJ
ejpam-1481	50	25	kumar	kumar	PROPN
ejpam-1481	51	1	[	[	X
ejpam-1481	51	2	24	24	NUM
ejpam-1481	51	3	,	,	PUNCT
ejpam-1481	51	4	25	25	NUM
ejpam-1481	51	5	]	]	PUNCT
ejpam-1481	51	6	.	.	PUNCT
ejpam-1481	52	1	in	in	ADP
ejpam-1481	52	2	[	[	X
ejpam-1481	52	3	7	7	NUM
ejpam-1481	52	4	,	,	PUNCT
ejpam-1481	52	5	8	8	NUM
ejpam-1481	52	6	]	]	PUNCT
ejpam-1481	52	7	,	,	PUNCT
ejpam-1481	52	8	akhmedov	akhmedov	VERB
ejpam-1481	52	9	and	and	CCONJ
ejpam-1481	52	10	elshabrawy	elshabrawy	PROPN
ejpam-1481	52	11	have	have	AUX
ejpam-1481	52	12	proved	prove	VERB
ejpam-1481	52	13	by	by	ADP
ejpam-1481	52	14	counterexamples	counterexample	NOUN
ejpam-1481	52	15	that	that	SCONJ
ejpam-1481	52	16	some	some	PRON
ejpam-1481	52	17	of	of	ADP
ejpam-1481	52	18	the	the	DET
ejpam-1481	52	19	main	main	ADJ
ejpam-1481	52	20	results	result	NOUN
ejpam-1481	52	21	in	in	ADP
ejpam-1481	52	22	[	[	X
ejpam-1481	52	23	24	24	NUM
ejpam-1481	52	24	,	,	PUNCT
ejpam-1481	52	25	25	25	NUM
ejpam-1481	52	26	]	]	PUNCT
ejpam-1481	52	27	are	be	AUX
ejpam-1481	52	28	incorrect	incorrect	ADJ
ejpam-1481	52	29	and	and	CCONJ
ejpam-1481	52	30	the	the	DET
ejpam-1481	52	31	corresponding	corresponding	ADJ
ejpam-1481	52	32	corrected	correct	VERB
ejpam-1481	52	33	results	result	NOUN
ejpam-1481	52	34	are	be	AUX
ejpam-1481	52	35	provided	provide	VERB
ejpam-1481	52	36	.	.	PUNCT
ejpam-1481	53	1	the	the	DET
ejpam-1481	53	2	fine	fine	ADJ
ejpam-1481	53	3	spectrum	spectrum	NOUN
ejpam-1481	53	4	of	of	ADP
ejpam-1481	53	5	the	the	DET
ejpam-1481	53	6	operator	operator	NOUN
ejpam-1481	53	7	∆v	∆v	PROPN
ejpam-1481	53	8	over	over	ADP
ejpam-1481	53	9	the	the	DET
ejpam-1481	53	10	sequence	sequence	NOUN
ejpam-1481	53	11	space	space	NOUN
ejpam-1481	53	12	c	c	NOUN
ejpam-1481	53	13	has	have	AUX
ejpam-1481	53	14	been	be	AUX
ejpam-1481	53	15	examined	examine	VERB
ejpam-1481	53	16	by	by	ADP
ejpam-1481	53	17	akhmedov	akhmedov	PROPN
ejpam-1481	53	18	and	and	CCONJ
ejpam-1481	53	19	el	el	NOUN
ejpam-1481	53	20	-	-	PUNCT
ejpam-1481	53	21	shabrawy	shabrawy	PROPN
ejpam-1481	54	1	[	[	X
ejpam-1481	54	2	6	6	NUM
ejpam-1481	54	3	]	]	PUNCT
ejpam-1481	54	4	.	.	PUNCT
ejpam-1481	55	1	recently	recently	ADV
ejpam-1481	55	2	,	,	PUNCT
ejpam-1481	55	3	el	el	PROPN
ejpam-1481	55	4	-	-	PUNCT
ejpam-1481	55	5	shabrawy	shabrawy	PROPN
ejpam-1481	55	6	[	[	X
ejpam-1481	55	7	15	15	NUM
ejpam-1481	55	8	]	]	PUNCT
ejpam-1481	55	9	has	have	AUX
ejpam-1481	55	10	studied	study	VERB
ejpam-1481	55	11	the	the	DET
ejpam-1481	55	12	fine	fine	ADJ
ejpam-1481	55	13	spectrum	spectrum	NOUN
ejpam-1481	55	14	of	of	ADP
ejpam-1481	55	15	the	the	DET
ejpam-1481	55	16	operator	operator	NOUN
ejpam-1481	55	17	∆v	∆v	PROPN
ejpam-1481	55	18	over	over	ADP
ejpam-1481	55	19	the	the	DET
ejpam-1481	55	20	sequence	sequence	NOUN
ejpam-1481	55	21	space	space	NOUN
ejpam-1481	55	22	lp	lp	NOUN
ejpam-1481	55	23	,	,	PUNCT
ejpam-1481	55	24	where	where	SCONJ
ejpam-1481	55	25	1	1	X
ejpam-1481	55	26	<	<	X
ejpam-1481	55	27	p	p	X
ejpam-1481	55	28	<	<	X
ejpam-1481	55	29	∞.	∞.	PROPN
ejpam-1481	55	30	akhmedov	akhmedov	PROPN
ejpam-1481	55	31	and	and	CCONJ
ejpam-1481	55	32	el	el	NOUN
ejpam-1481	55	33	-	-	PUNCT
ejpam-1481	55	34	shabrawy	shabrawy	PROPN
ejpam-1481	56	1	[	[	X
ejpam-1481	56	2	4	4	X
ejpam-1481	56	3	]	]	PUNCT
ejpam-1481	56	4	have	have	AUX
ejpam-1481	56	5	modified	modify	VERB
ejpam-1481	56	6	the	the	DET
ejpam-1481	56	7	a.	a.	NOUN
ejpam-1481	56	8	akhmedov	akhmedov	PROPN
ejpam-1481	56	9	,	,	PUNCT
ejpam-1481	56	10	s.	s.	PROPN
ejpam-1481	56	11	el	el	PROPN
ejpam-1481	56	12	-	-	PUNCT
ejpam-1481	56	13	shabrawy	shabrawy	PROPN
ejpam-1481	56	14	/	/	SYM
ejpam-1481	56	15	eur	eur	NOUN
ejpam-1481	56	16	.	.	PUNCT
ejpam-1481	57	1	j.	j.	PROPN
ejpam-1481	57	2	pure	pure	PROPN
ejpam-1481	57	3	appl	appl	PROPN
ejpam-1481	57	4	.	.	PROPN
ejpam-1481	57	5	math	math	PROPN
ejpam-1481	57	6	,	,	PUNCT
ejpam-1481	57	7	5	5	NUM
ejpam-1481	57	8	(	(	PUNCT
ejpam-1481	57	9	2012	2012	NUM
ejpam-1481	57	10	)	)	PUNCT
ejpam-1481	57	11	,	,	PUNCT
ejpam-1481	57	12	59	59	NUM
ejpam-1481	57	13	-	-	SYM
ejpam-1481	57	14	74	74	NUM
ejpam-1481	57	15	61	61	NUM
ejpam-1481	57	16	definition	definition	NOUN
ejpam-1481	57	17	of	of	ADP
ejpam-1481	57	18	the	the	DET
ejpam-1481	57	19	operator	operator	NOUN
ejpam-1481	57	20	∆v	∆v	PROPN
ejpam-1481	57	21	and	and	CCONJ
ejpam-1481	57	22	have	have	AUX
ejpam-1481	57	23	determined	determine	VERB
ejpam-1481	57	24	the	the	DET
ejpam-1481	57	25	fine	fine	ADJ
ejpam-1481	57	26	spectrum	spectrum	NOUN
ejpam-1481	57	27	of	of	ADP
ejpam-1481	57	28	the	the	DET
ejpam-1481	57	29	modified	modify	VERB
ejpam-1481	57	30	operator	operator	NOUN
ejpam-1481	57	31	∆v	∆v	PROPN
ejpam-1481	57	32	over	over	ADP
ejpam-1481	57	33	the	the	DET
ejpam-1481	57	34	sequence	sequence	NOUN
ejpam-1481	57	35	spaces	space	VERB
ejpam-1481	57	36	c	c	NOUN
ejpam-1481	57	37	and	and	CCONJ
ejpam-1481	57	38	lp	lp	NOUN
ejpam-1481	57	39	,	,	PUNCT
ejpam-1481	57	40	where	where	SCONJ
ejpam-1481	57	41	1	1	NUM
ejpam-1481	57	42	<	<	X
ejpam-1481	57	43	p	p	X
ejpam-1481	57	44	<	<	X
ejpam-1481	57	45	∞.	∞.	PROPN
ejpam-1481	57	46	note	note	VERB
ejpam-1481	57	47	that	that	SCONJ
ejpam-1481	57	48	,	,	PUNCT
ejpam-1481	57	49	if	if	SCONJ
ejpam-1481	57	50	(	(	PUNCT
ejpam-1481	57	51	vk	vk	NOUN
ejpam-1481	57	52	)	)	PUNCT
ejpam-1481	57	53	is	be	AUX
ejpam-1481	57	54	a	a	DET
ejpam-1481	57	55	constant	constant	ADJ
ejpam-1481	57	56	sequence	sequence	NOUN
ejpam-1481	57	57	,	,	PUNCT
ejpam-1481	57	58	say	say	VERB
ejpam-1481	57	59	vk	vk	ADP
ejpam-1481	57	60	=	=	SYM
ejpam-1481	57	61	l	l	NOUN
ejpam-1481	58	1	6=	6=	ADP
ejpam-1481	58	2	0	0	NUM
ejpam-1481	58	3	for	for	ADP
ejpam-1481	58	4	all	all	DET
ejpam-1481	58	5	k	k	PROPN
ejpam-1481	58	6	∈	∈	PROPN
ejpam-1481	58	7	n	n	CCONJ
ejpam-1481	58	8	,	,	PUNCT
ejpam-1481	58	9	then	then	ADV
ejpam-1481	58	10	the	the	DET
ejpam-1481	58	11	operator∆v	operator∆v	NOUN
ejpam-1481	58	12	is	be	AUX
ejpam-1481	58	13	reduced	reduce	VERB
ejpam-1481	58	14	to	to	ADP
ejpam-1481	58	15	the	the	DET
ejpam-1481	58	16	operator	operator	NOUN
ejpam-1481	58	17	b(r	b(r	PROPN
ejpam-1481	58	18	,	,	PUNCT
ejpam-1481	58	19	s	s	NOUN
ejpam-1481	58	20	)	)	PUNCT
ejpam-1481	58	21	with	with	ADP
ejpam-1481	58	22	r	r	NOUN
ejpam-1481	58	23	=	=	SYM
ejpam-1481	58	24	l	l	NOUN
ejpam-1481	58	25	,	,	PUNCT
ejpam-1481	58	26	s	s	PART
ejpam-1481	58	27	=	=	NOUN
ejpam-1481	58	28	−l	−l	NOUN
ejpam-1481	58	29	and	and	CCONJ
ejpam-1481	58	30	the	the	DET
ejpam-1481	58	31	results	result	NOUN
ejpam-1481	58	32	for	for	ADP
ejpam-1481	58	33	the	the	DET
ejpam-1481	58	34	spectrum	spectrum	NOUN
ejpam-1481	58	35	and	and	CCONJ
ejpam-1481	58	36	the	the	DET
ejpam-1481	58	37	fine	fine	ADJ
ejpam-1481	58	38	spectrum	spectrum	NOUN
ejpam-1481	58	39	of	of	ADP
ejpam-1481	58	40	the	the	DET
ejpam-1481	58	41	operator	operator	NOUN
ejpam-1481	58	42	∆v	∆v	PROPN
ejpam-1481	58	43	on	on	ADP
ejpam-1481	58	44	the	the	DET
ejpam-1481	58	45	sequence	sequence	NOUN
ejpam-1481	58	46	spaces	space	VERB
ejpam-1481	58	47	l1	l1	PROPN
ejpam-1481	58	48	and	and	CCONJ
ejpam-1481	58	49	c0	c0	PROPN
ejpam-1481	58	50	follow	follow	VERB
ejpam-1481	58	51	immediately	immediately	ADV
ejpam-1481	58	52	from	from	ADP
ejpam-1481	58	53	the	the	DET
ejpam-1481	58	54	corresponding	corresponding	ADJ
ejpam-1481	58	55	results	result	NOUN
ejpam-1481	58	56	in	in	ADP
ejpam-1481	58	57	[	[	X
ejpam-1481	58	58	10	10	NUM
ejpam-1481	58	59	,	,	PUNCT
ejpam-1481	58	60	18	18	NUM
ejpam-1481	58	61	]	]	PUNCT
ejpam-1481	58	62	.	.	PUNCT
ejpam-1481	59	1	then	then	ADV
ejpam-1481	59	2	,	,	PUNCT
ejpam-1481	59	3	throughout	throughout	ADP
ejpam-1481	59	4	this	this	DET
ejpam-1481	59	5	paper	paper	NOUN
ejpam-1481	59	6	,	,	PUNCT
ejpam-1481	59	7	the	the	DET
ejpam-1481	59	8	case	case	NOUN
ejpam-1481	59	9	when	when	SCONJ
ejpam-1481	59	10	(	(	PUNCT
ejpam-1481	59	11	vk	vk	NOUN
ejpam-1481	59	12	)	)	PUNCT
ejpam-1481	59	13	is	be	AUX
ejpam-1481	59	14	a	a	DET
ejpam-1481	59	15	constant	constant	ADJ
ejpam-1481	59	16	sequence	sequence	NOUN
ejpam-1481	59	17	is	be	AUX
ejpam-1481	59	18	not	not	PART
ejpam-1481	59	19	considered	consider	VERB
ejpam-1481	59	20	.	.	PUNCT
ejpam-1481	60	1	the	the	DET
ejpam-1481	60	2	rest	rest	NOUN
ejpam-1481	60	3	of	of	ADP
ejpam-1481	60	4	the	the	DET
ejpam-1481	60	5	paper	paper	NOUN
ejpam-1481	60	6	is	be	AUX
ejpam-1481	60	7	organized	organize	VERB
ejpam-1481	60	8	as	as	SCONJ
ejpam-1481	60	9	follows	follow	VERB
ejpam-1481	60	10	.	.	PUNCT
ejpam-1481	61	1	section	section	NOUN
ejpam-1481	61	2	2	2	NUM
ejpam-1481	61	3	presents	present	VERB
ejpam-1481	61	4	some	some	DET
ejpam-1481	61	5	basic	basic	ADJ
ejpam-1481	61	6	concepts	concept	NOUN
ejpam-1481	61	7	of	of	ADP
ejpam-1481	61	8	spectral	spectral	ADJ
ejpam-1481	61	9	theory	theory	NOUN
ejpam-1481	61	10	concerning	concern	VERB
ejpam-1481	61	11	the	the	DET
ejpam-1481	61	12	spectrum	spectrum	NOUN
ejpam-1481	61	13	and	and	CCONJ
ejpam-1481	61	14	the	the	DET
ejpam-1481	61	15	fine	fine	ADJ
ejpam-1481	61	16	spectrum	spectrum	NOUN
ejpam-1481	61	17	of	of	ADP
ejpam-1481	61	18	linear	linear	PROPN
ejpam-1481	61	19	operators	operator	NOUN
ejpam-1481	61	20	.	.	PUNCT
ejpam-1481	62	1	next	next	ADV
ejpam-1481	62	2	,	,	PUNCT
ejpam-1481	62	3	in	in	ADP
ejpam-1481	62	4	section	section	NOUN
ejpam-1481	62	5	3	3	NUM
ejpam-1481	62	6	,	,	PUNCT
ejpam-1481	62	7	we	we	PRON
ejpam-1481	62	8	mainly	mainly	ADV
ejpam-1481	62	9	review	review	VERB
ejpam-1481	62	10	several	several	ADJ
ejpam-1481	62	11	recent	recent	ADJ
ejpam-1481	62	12	results	result	NOUN
ejpam-1481	62	13	concerning	concern	VERB
ejpam-1481	62	14	the	the	DET
ejpam-1481	62	15	fine	fine	ADJ
ejpam-1481	62	16	spectrum	spectrum	NOUN
ejpam-1481	62	17	of	of	ADP
ejpam-1481	62	18	operator	operator	NOUN
ejpam-1481	62	19	∆v	∆v	PROPN
ejpam-1481	62	20	over	over	ADP
ejpam-1481	62	21	the	the	DET
ejpam-1481	62	22	sequence	sequence	NOUN
ejpam-1481	62	23	spaces	space	VERB
ejpam-1481	62	24	l1	l1	PROPN
ejpam-1481	62	25	and	and	CCONJ
ejpam-1481	62	26	c0	c0	PROPN
ejpam-1481	62	27	.	.	PUNCT
ejpam-1481	63	1	also	also	ADV
ejpam-1481	63	2	,	,	PUNCT
ejpam-1481	63	3	some	some	DET
ejpam-1481	63	4	new	new	ADJ
ejpam-1481	63	5	results	result	NOUN
ejpam-1481	63	6	are	be	AUX
ejpam-1481	63	7	obtained	obtain	VERB
ejpam-1481	63	8	.	.	PUNCT
ejpam-1481	64	1	in	in	ADP
ejpam-1481	64	2	section	section	NOUN
ejpam-1481	64	3	4	4	NUM
ejpam-1481	64	4	we	we	PRON
ejpam-1481	64	5	give	give	VERB
ejpam-1481	64	6	some	some	DET
ejpam-1481	64	7	illustrative	illustrative	ADJ
ejpam-1481	64	8	examples	example	NOUN
ejpam-1481	64	9	to	to	PART
ejpam-1481	64	10	support	support	VERB
ejpam-1481	64	11	the	the	DET
ejpam-1481	64	12	main	main	ADJ
ejpam-1481	64	13	results	result	NOUN
ejpam-1481	64	14	.	.	PUNCT
ejpam-1481	65	1	in	in	ADP
ejpam-1481	65	2	section	section	NOUN
ejpam-1481	65	3	5	5	NUM
ejpam-1481	65	4	we	we	PRON
ejpam-1481	65	5	show	show	VERB
ejpam-1481	65	6	some	some	DET
ejpam-1481	65	7	ideas	idea	NOUN
ejpam-1481	65	8	about	about	ADP
ejpam-1481	65	9	changing	change	VERB
ejpam-1481	65	10	the	the	DET
ejpam-1481	65	11	conditions	condition	NOUN
ejpam-1481	65	12	on	on	ADP
ejpam-1481	65	13	the	the	DET
ejpam-1481	65	14	sequence	sequence	NOUN
ejpam-1481	65	15	(	(	PUNCT
ejpam-1481	65	16	vk	vk	PROPN
ejpam-1481	65	17	)	)	PUNCT
ejpam-1481	65	18	in	in	ADP
ejpam-1481	65	19	the	the	DET
ejpam-1481	65	20	fine	fine	ADJ
ejpam-1481	65	21	spectrum	spectrum	NOUN
ejpam-1481	65	22	of	of	ADP
ejpam-1481	65	23	the	the	DET
ejpam-1481	65	24	operator	operator	NOUN
ejpam-1481	65	25	∆v	∆v	PROPN
ejpam-1481	65	26	.	.	PROPN
ejpam-1481	66	1	2	2	NUM
ejpam-1481	66	2	.	.	X
ejpam-1481	66	3	preliminaries	preliminary	NOUN
ejpam-1481	66	4	by	by	ADP
ejpam-1481	66	5	w	w	PROPN
ejpam-1481	66	6	,	,	PUNCT
ejpam-1481	66	7	we	we	PRON
ejpam-1481	66	8	shall	shall	AUX
ejpam-1481	66	9	denote	denote	VERB
ejpam-1481	66	10	the	the	DET
ejpam-1481	66	11	space	space	NOUN
ejpam-1481	66	12	of	of	ADP
ejpam-1481	66	13	all	all	DET
ejpam-1481	66	14	real	real	ADJ
ejpam-1481	66	15	or	or	CCONJ
ejpam-1481	66	16	complex	complex	ADJ
ejpam-1481	66	17	valued	value	VERB
ejpam-1481	66	18	sequences	sequence	NOUN
ejpam-1481	66	19	.	.	PUNCT
ejpam-1481	67	1	any	any	DET
ejpam-1481	67	2	vector	vector	NOUN
ejpam-1481	67	3	subspace	subspace	NOUN
ejpam-1481	67	4	of	of	ADP
ejpam-1481	67	5	w	w	PROPN
ejpam-1481	67	6	is	be	AUX
ejpam-1481	67	7	called	call	VERB
ejpam-1481	67	8	a	a	DET
ejpam-1481	67	9	sequence	sequence	NOUN
ejpam-1481	67	10	space	space	NOUN
ejpam-1481	67	11	.	.	PUNCT
ejpam-1481	68	1	we	we	PRON
ejpam-1481	68	2	shall	shall	AUX
ejpam-1481	68	3	write	write	VERB
ejpam-1481	68	4	l∞	l∞	NOUN
ejpam-1481	68	5	,	,	PUNCT
ejpam-1481	68	6	c	c	X
ejpam-1481	68	7	,	,	PUNCT
ejpam-1481	68	8	c0	c0	NOUN
ejpam-1481	68	9	and	and	CCONJ
ejpam-1481	68	10	bv	bv	PROPN
ejpam-1481	68	11	for	for	ADP
ejpam-1481	68	12	the	the	DET
ejpam-1481	68	13	spaces	space	NOUN
ejpam-1481	68	14	of	of	ADP
ejpam-1481	68	15	all	all	DET
ejpam-1481	68	16	bounded	bounded	ADJ
ejpam-1481	68	17	,	,	PUNCT
ejpam-1481	68	18	convergent	convergent	NOUN
ejpam-1481	68	19	,	,	PUNCT
ejpam-1481	68	20	null	null	NOUN
ejpam-1481	68	21	and	and	CCONJ
ejpam-1481	68	22	bounded	bounded	ADJ
ejpam-1481	68	23	variation	variation	NOUN
ejpam-1481	68	24	sequences	sequence	NOUN
ejpam-1481	68	25	,	,	PUNCT
ejpam-1481	68	26	respectively	respectively	ADV
ejpam-1481	68	27	.	.	PUNCT
ejpam-1481	69	1	also	also	ADV
ejpam-1481	69	2	by	by	ADP
ejpam-1481	69	3	l1	l1	PROPN
ejpam-1481	69	4	,	,	PUNCT
ejpam-1481	69	5	lp	lp	NOUN
ejpam-1481	69	6	and	and	CCONJ
ejpam-1481	69	7	bvp	bvp	NOUN
ejpam-1481	69	8	we	we	PRON
ejpam-1481	69	9	denote	denote	VERB
ejpam-1481	69	10	the	the	DET
ejpam-1481	69	11	spaces	space	NOUN
ejpam-1481	69	12	of	of	ADP
ejpam-1481	69	13	all	all	DET
ejpam-1481	69	14	absolutely	absolutely	ADV
ejpam-1481	69	15	summable	summable	ADJ
ejpam-1481	69	16	sequences	sequence	NOUN
ejpam-1481	69	17	,	,	PUNCT
ejpam-1481	69	18	p	p	NOUN
ejpam-1481	69	19	-	-	PUNCT
ejpam-1481	69	20	absolutely	absolutely	ADV
ejpam-1481	69	21	summable	summable	ADJ
ejpam-1481	69	22	sequences	sequence	NOUN
ejpam-1481	69	23	and	and	CCONJ
ejpam-1481	69	24	p	p	NOUN
ejpam-1481	69	25	-	-	PUNCT
ejpam-1481	69	26	bounded	bound	VERB
ejpam-1481	69	27	variation	variation	NOUN
ejpam-1481	69	28	sequences	sequence	NOUN
ejpam-1481	69	29	,	,	PUNCT
ejpam-1481	69	30	respectively	respectively	ADV
ejpam-1481	69	31	.	.	PUNCT
ejpam-1481	70	1	a	a	DET
ejpam-1481	70	2	triangle	triangle	NOUN
ejpam-1481	70	3	is	be	AUX
ejpam-1481	70	4	a	a	DET
ejpam-1481	70	5	lower	low	ADJ
ejpam-1481	70	6	triangular	triangular	NOUN
ejpam-1481	70	7	matrix	matrix	NOUN
ejpam-1481	70	8	with	with	ADP
ejpam-1481	70	9	all	all	PRON
ejpam-1481	70	10	of	of	ADP
ejpam-1481	70	11	the	the	DET
ejpam-1481	70	12	principal	principal	ADJ
ejpam-1481	70	13	diagonal	diagonal	ADJ
ejpam-1481	70	14	elements	element	NOUN
ejpam-1481	70	15	nonzero	nonzero	X
ejpam-1481	70	16	.	.	PUNCT
ejpam-1481	71	1	let	let	VERB
ejpam-1481	71	2	λ	λ	PROPN
ejpam-1481	71	3	and	and	CCONJ
ejpam-1481	71	4	µ	µ	PRON
ejpam-1481	71	5	be	be	AUX
ejpam-1481	71	6	two	two	NUM
ejpam-1481	71	7	sequence	sequence	NOUN
ejpam-1481	71	8	spaces	space	NOUN
ejpam-1481	71	9	and	and	CCONJ
ejpam-1481	71	10	a	a	DET
ejpam-1481	71	11	=	=	SYM
ejpam-1481	71	12	(	(	PUNCT
ejpam-1481	71	13	ank	ank	PROPN
ejpam-1481	71	14	)	)	PUNCT
ejpam-1481	71	15	be	be	VERB
ejpam-1481	71	16	an	an	DET
ejpam-1481	71	17	infinite	infinite	ADJ
ejpam-1481	71	18	matrix	matrix	NOUN
ejpam-1481	71	19	of	of	ADP
ejpam-1481	71	20	real	real	ADJ
ejpam-1481	71	21	or	or	CCONJ
ejpam-1481	71	22	complex	complex	ADJ
ejpam-1481	71	23	numbers	number	NOUN
ejpam-1481	71	24	ank	ank	PROPN
ejpam-1481	71	25	,	,	PUNCT
ejpam-1481	71	26	where	where	SCONJ
ejpam-1481	71	27	n	n	X
ejpam-1481	71	28	,	,	PUNCT
ejpam-1481	71	29	k	k	PROPN
ejpam-1481	71	30	∈	∈	PROPN
ejpam-1481	71	31	n	n	NOUN
ejpam-1481	71	32	=	=	PUNCT
ejpam-1481	71	33	{	{	PUNCT
ejpam-1481	71	34	0,1,2	0,1,2	NOUN
ejpam-1481	71	35	,	,	PUNCT
ejpam-1481	71	36	.	.	PUNCT
ejpam-1481	71	37	.	.	PUNCT
ejpam-1481	72	1	.	.	PUNCT
ejpam-1481	72	2	}	}	PUNCT
ejpam-1481	72	3	.	.	PUNCT
ejpam-1481	73	1	then	then	ADV
ejpam-1481	73	2	,	,	PUNCT
ejpam-1481	73	3	we	we	PRON
ejpam-1481	73	4	say	say	VERB
ejpam-1481	73	5	that	that	SCONJ
ejpam-1481	73	6	a	a	DET
ejpam-1481	73	7	defines	define	VERB
ejpam-1481	73	8	a	a	DET
ejpam-1481	73	9	matrix	matrix	NOUN
ejpam-1481	73	10	mapping	mapping	NOUN
ejpam-1481	73	11	from	from	ADP
ejpam-1481	73	12	λ	λ	PROPN
ejpam-1481	73	13	into	into	ADP
ejpam-1481	73	14	µ	µ	NUM
ejpam-1481	73	15	,	,	PUNCT
ejpam-1481	73	16	and	and	CCONJ
ejpam-1481	73	17	we	we	PRON
ejpam-1481	73	18	denote	denote	VERB
ejpam-1481	73	19	it	it	PRON
ejpam-1481	73	20	by	by	ADP
ejpam-1481	73	21	a	a	DET
ejpam-1481	73	22	:	:	PUNCT
ejpam-1481	73	23	λ→	λ→	PUNCT
ejpam-1481	73	24	µ	µ	NOUN
ejpam-1481	73	25	if	if	SCONJ
ejpam-1481	73	26	for	for	ADP
ejpam-1481	73	27	every	every	DET
ejpam-1481	73	28	sequence	sequence	NOUN
ejpam-1481	73	29	x	x	PUNCT
ejpam-1481	73	30	=	=	SYM
ejpam-1481	73	31	(	(	PUNCT
ejpam-1481	73	32	xk	xk	NOUN
ejpam-1481	73	33	)	)	PUNCT
ejpam-1481	73	34	∈	∈	PROPN
ejpam-1481	73	35	λ	λ	PROPN
ejpam-1481	73	36	,	,	PUNCT
ejpam-1481	73	37	the	the	DET
ejpam-1481	73	38	sequence	sequence	NOUN
ejpam-1481	73	39	ax	ax	NOUN
ejpam-1481	73	40	=	=	PUNCT
ejpam-1481	73	41	{	{	PUNCT
ejpam-1481	73	42	(	(	PUNCT
ejpam-1481	73	43	ax)n	ax)n	PROPN
ejpam-1481	73	44	}	}	PUNCT
ejpam-1481	73	45	,	,	PUNCT
ejpam-1481	73	46	the	the	DET
ejpam-1481	73	47	a	a	DET
ejpam-1481	73	48	-	-	PUNCT
ejpam-1481	73	49	transform	transform	NOUN
ejpam-1481	73	50	of	of	ADP
ejpam-1481	73	51	x	x	X
ejpam-1481	73	52	,	,	PUNCT
ejpam-1481	73	53	is	be	AUX
ejpam-1481	73	54	in	in	ADP
ejpam-1481	73	55	µ	µ	NOUN
ejpam-1481	73	56	,	,	PUNCT
ejpam-1481	73	57	where	where	SCONJ
ejpam-1481	73	58	(	(	PUNCT
ejpam-1481	73	59	ax)n	ax)n	PROPN
ejpam-1481	73	60	=	=	PRON
ejpam-1481	73	61	∑	∑	PUNCT
ejpam-1481	73	62	k	k	PROPN
ejpam-1481	73	63	ank	ank	PROPN
ejpam-1481	73	64	xk	xk	PROPN
ejpam-1481	73	65	,	,	PUNCT
ejpam-1481	73	66	(	(	PUNCT
ejpam-1481	73	67	n	n	X
ejpam-1481	73	68	∈	∈	PROPN
ejpam-1481	73	69	n	n	CCONJ
ejpam-1481	73	70	)	)	PUNCT
ejpam-1481	73	71	.	.	PUNCT
ejpam-1481	74	1	(	(	PUNCT
ejpam-1481	74	2	4	4	X
ejpam-1481	74	3	)	)	PUNCT
ejpam-1481	74	4	for	for	ADP
ejpam-1481	74	5	simplicity	simplicity	NOUN
ejpam-1481	74	6	in	in	ADP
ejpam-1481	74	7	notation	notation	NOUN
ejpam-1481	74	8	,	,	PUNCT
ejpam-1481	74	9	here	here	ADV
ejpam-1481	74	10	and	and	CCONJ
ejpam-1481	74	11	in	in	ADP
ejpam-1481	74	12	what	what	PRON
ejpam-1481	74	13	follows	follow	VERB
ejpam-1481	74	14	,	,	PUNCT
ejpam-1481	74	15	the	the	DET
ejpam-1481	74	16	summation	summation	NOUN
ejpam-1481	74	17	without	without	ADP
ejpam-1481	74	18	limits	limit	NOUN
ejpam-1481	74	19	runs	run	VERB
ejpam-1481	74	20	from	from	ADP
ejpam-1481	74	21	0	0	NUM
ejpam-1481	74	22	to	to	ADP
ejpam-1481	74	23	∞.	∞.	PROPN
ejpam-1481	74	24	by	by	ADP
ejpam-1481	74	25	(	(	PUNCT
ejpam-1481	74	26	λ,µ	λ,µ	NOUN
ejpam-1481	74	27	)	)	PUNCT
ejpam-1481	74	28	,	,	PUNCT
ejpam-1481	74	29	we	we	PRON
ejpam-1481	74	30	denote	denote	VERB
ejpam-1481	74	31	the	the	DET
ejpam-1481	74	32	class	class	NOUN
ejpam-1481	74	33	of	of	ADP
ejpam-1481	74	34	all	all	DET
ejpam-1481	74	35	matrices	matrix	NOUN
ejpam-1481	74	36	a	a	DET
ejpam-1481	74	37	such	such	ADJ
ejpam-1481	74	38	that	that	SCONJ
ejpam-1481	74	39	a	a	DET
ejpam-1481	74	40	:	:	PUNCT
ejpam-1481	74	41	λ→	λ→	PUNCT
ejpam-1481	74	42	µ.	µ.	NOUN
ejpam-1481	74	43	thus	thus	ADV
ejpam-1481	74	44	,	,	PUNCT
ejpam-1481	74	45	a	a	DET
ejpam-1481	74	46	∈	∈	PROPN
ejpam-1481	74	47	(	(	PUNCT
ejpam-1481	74	48	λ,µ	λ,µ	NOUN
ejpam-1481	74	49	)	)	PUNCT
ejpam-1481	74	50	if	if	SCONJ
ejpam-1481	74	51	and	and	CCONJ
ejpam-1481	74	52	only	only	ADV
ejpam-1481	74	53	if	if	SCONJ
ejpam-1481	74	54	the	the	DET
ejpam-1481	74	55	series	series	NOUN
ejpam-1481	74	56	on	on	ADP
ejpam-1481	74	57	the	the	DET
ejpam-1481	74	58	right	right	ADJ
ejpam-1481	74	59	side	side	NOUN
ejpam-1481	74	60	of	of	ADP
ejpam-1481	74	61	(	(	PUNCT
ejpam-1481	74	62	4	4	X
ejpam-1481	74	63	)	)	PUNCT
ejpam-1481	74	64	converges	converge	NOUN
ejpam-1481	74	65	for	for	ADP
ejpam-1481	74	66	each	each	DET
ejpam-1481	74	67	n	n	PRON
ejpam-1481	74	68	∈	∈	PROPN
ejpam-1481	74	69	n	n	NOUN
ejpam-1481	74	70	and	and	CCONJ
ejpam-1481	74	71	every	every	DET
ejpam-1481	74	72	x	x	PROPN
ejpam-1481	74	73	∈	∈	PROPN
ejpam-1481	74	74	λ	λ	PROPN
ejpam-1481	74	75	,	,	PUNCT
ejpam-1481	74	76	and	and	CCONJ
ejpam-1481	74	77	we	we	PRON
ejpam-1481	74	78	have	have	VERB
ejpam-1481	74	79	ax	ax	NOUN
ejpam-1481	74	80	=	=	PUNCT
ejpam-1481	74	81	{	{	PUNCT
ejpam-1481	74	82	(	(	PUNCT
ejpam-1481	74	83	ax)n}n∈n	ax)n}n∈n	PROPN
ejpam-1481	74	84	∈	∈	PROPN
ejpam-1481	74	85	µ	µ	PROPN
ejpam-1481	74	86	for	for	ADP
ejpam-1481	74	87	all	all	DET
ejpam-1481	74	88	x	x	SYM
ejpam-1481	74	89	∈	∈	PROPN
ejpam-1481	74	90	λ	λ	NOUN
ejpam-1481	74	91	.	.	PUNCT
ejpam-1481	75	1	we	we	PRON
ejpam-1481	75	2	use	use	VERB
ejpam-1481	75	3	the	the	DET
ejpam-1481	75	4	convention	convention	NOUN
ejpam-1481	75	5	that	that	PRON
ejpam-1481	75	6	any	any	DET
ejpam-1481	75	7	term	term	NOUN
ejpam-1481	75	8	with	with	ADP
ejpam-1481	75	9	negative	negative	ADJ
ejpam-1481	75	10	subscript	subscript	NOUN
ejpam-1481	75	11	is	be	AUX
ejpam-1481	75	12	equal	equal	ADJ
ejpam-1481	75	13	to	to	AUX
ejpam-1481	75	14	naught	naught	ADJ
ejpam-1481	75	15	.	.	PUNCT
ejpam-1481	76	1	we	we	PRON
ejpam-1481	76	2	recall	recall	VERB
ejpam-1481	76	3	some	some	DET
ejpam-1481	76	4	basic	basic	ADJ
ejpam-1481	76	5	concepts	concept	NOUN
ejpam-1481	76	6	of	of	ADP
ejpam-1481	76	7	spectral	spectral	ADJ
ejpam-1481	76	8	theory	theory	NOUN
ejpam-1481	76	9	which	which	PRON
ejpam-1481	76	10	are	be	AUX
ejpam-1481	76	11	needed	need	VERB
ejpam-1481	76	12	for	for	ADP
ejpam-1481	76	13	our	our	PRON
ejpam-1481	76	14	investigation	investigation	NOUN
ejpam-1481	76	15	[	[	X
ejpam-1481	76	16	see	see	VERB
ejpam-1481	76	17	21	21	NUM
ejpam-1481	76	18	,	,	PUNCT
ejpam-1481	76	19	pp	pp	ADJ
ejpam-1481	76	20	.	.	PUNCT
ejpam-1481	77	1	370	370	NUM
ejpam-1481	77	2	-	-	SYM
ejpam-1481	77	3	372	372	NUM
ejpam-1481	77	4	]	]	PUNCT
ejpam-1481	77	5	.	.	PUNCT
ejpam-1481	78	1	let	let	VERB
ejpam-1481	78	2	x	x	PRON
ejpam-1481	78	3	be	be	AUX
ejpam-1481	78	4	a	a	DET
ejpam-1481	78	5	banach	banach	NOUN
ejpam-1481	78	6	space	space	NOUN
ejpam-1481	78	7	and	and	CCONJ
ejpam-1481	78	8	t	t	NOUN
ejpam-1481	78	9	:	:	PUNCT
ejpam-1481	78	10	x	x	X
ejpam-1481	78	11	→	→	PUNCT
ejpam-1481	78	12	x	x	PUNCT
ejpam-1481	78	13	be	be	AUX
ejpam-1481	78	14	a	a	DET
ejpam-1481	78	15	bounded	bounded	ADJ
ejpam-1481	78	16	linear	linear	ADJ
ejpam-1481	78	17	operator	operator	NOUN
ejpam-1481	78	18	.	.	PUNCT
ejpam-1481	79	1	by	by	ADP
ejpam-1481	79	2	r(t	r(t	NOUN
ejpam-1481	79	3	)	)	PUNCT
ejpam-1481	79	4	,	,	PUNCT
ejpam-1481	79	5	we	we	PRON
ejpam-1481	79	6	denote	denote	VERB
ejpam-1481	79	7	the	the	DET
ejpam-1481	79	8	range	range	NOUN
ejpam-1481	79	9	of	of	ADP
ejpam-1481	79	10	t	t	PROPN
ejpam-1481	79	11	,	,	PUNCT
ejpam-1481	79	12	i.e.	i.e.	X
ejpam-1481	79	13	,	,	PUNCT
ejpam-1481	79	14	r(t	r(t	NOUN
ejpam-1481	79	15	)	)	PUNCT
ejpam-1481	80	1	=	=	PUNCT
ejpam-1481	80	2	�	�	PROPN
ejpam-1481	80	3	y	y	PROPN
ejpam-1481	80	4	∈	∈	PROPN
ejpam-1481	80	5	x	x	X
ejpam-1481	80	6	:	:	PUNCT
ejpam-1481	80	7	y	y	PROPN
ejpam-1481	80	8	=	=	SYM
ejpam-1481	80	9	t	t	PROPN
ejpam-1481	80	10	x	x	X
ejpam-1481	80	11	,	,	PUNCT
ejpam-1481	80	12	x	x	PUNCT
ejpam-1481	80	13	∈	∈	PROPN
ejpam-1481	80	14	x	x	X
ejpam-1481	80	15	.	.	PUNCT
ejpam-1481	81	1	by	by	ADP
ejpam-1481	81	2	b(x	b(x	PROPN
ejpam-1481	81	3	)	)	PUNCT
ejpam-1481	81	4	,	,	PUNCT
ejpam-1481	81	5	we	we	PRON
ejpam-1481	81	6	denote	denote	VERB
ejpam-1481	81	7	the	the	DET
ejpam-1481	81	8	set	set	NOUN
ejpam-1481	81	9	of	of	ADP
ejpam-1481	81	10	all	all	DET
ejpam-1481	81	11	bounded	bound	VERB
ejpam-1481	81	12	linear	linear	PROPN
ejpam-1481	81	13	operators	operator	NOUN
ejpam-1481	81	14	on	on	ADP
ejpam-1481	81	15	x	x	PUNCT
ejpam-1481	81	16	into	into	ADP
ejpam-1481	81	17	itself	itself	PRON
ejpam-1481	81	18	.	.	PUNCT
ejpam-1481	82	1	if	if	SCONJ
ejpam-1481	82	2	t	t	PROPN
ejpam-1481	82	3	∈	∈	PROPN
ejpam-1481	82	4	b(x	b(x	PROPN
ejpam-1481	82	5	)	)	PUNCT
ejpam-1481	82	6	,	,	PUNCT
ejpam-1481	82	7	then	then	ADV
ejpam-1481	82	8	the	the	DET
ejpam-1481	82	9	adjoint	adjoint	PROPN
ejpam-1481	82	10	t	t	PROPN
ejpam-1481	82	11	∗	∗	NOUN
ejpam-1481	82	12	of	of	ADP
ejpam-1481	82	13	t	t	PROPN
ejpam-1481	82	14	is	be	AUX
ejpam-1481	82	15	a	a	DET
ejpam-1481	82	16	bounded	bounded	ADJ
ejpam-1481	82	17	linear	linear	ADJ
ejpam-1481	82	18	operator	operator	NOUN
ejpam-1481	82	19	on	on	ADP
ejpam-1481	82	20	the	the	DET
ejpam-1481	82	21	dual	dual	ADJ
ejpam-1481	82	22	x	x	NOUN
ejpam-1481	82	23	∗	∗	NOUN
ejpam-1481	82	24	of	of	ADP
ejpam-1481	82	25	x	x	PUNCT
ejpam-1481	82	26	defined	define	VERB
ejpam-1481	82	27	by	by	ADP
ejpam-1481	82	28	(	(	PUNCT
ejpam-1481	82	29	t	t	PROPN
ejpam-1481	82	30	∗	∗	X
ejpam-1481	82	31	f	f	PROPN
ejpam-1481	82	32	)	)	PUNCT
ejpam-1481	82	33	(	(	PUNCT
ejpam-1481	82	34	x	x	X
ejpam-1481	82	35	)	)	PUNCT
ejpam-1481	82	36	=	=	SYM
ejpam-1481	82	37	f	f	PROPN
ejpam-1481	82	38	(	(	PUNCT
ejpam-1481	82	39	t	t	NOUN
ejpam-1481	82	40	x	x	PROPN
ejpam-1481	82	41	)	)	PUNCT
ejpam-1481	82	42	for	for	ADP
ejpam-1481	82	43	all	all	DET
ejpam-1481	82	44	f	f	PROPN
ejpam-1481	82	45	∈	∈	PROPN
ejpam-1481	82	46	x	x	X
ejpam-1481	82	47	∗	∗	NOUN
ejpam-1481	82	48	and	and	CCONJ
ejpam-1481	82	49	x	x	SYM
ejpam-1481	82	50	∈	∈	PROPN
ejpam-1481	82	51	x	x	X
ejpam-1481	82	52	.	.	PUNCT
ejpam-1481	82	53	a.	a.	PROPN
ejpam-1481	82	54	akhmedov	akhmedov	PROPN
ejpam-1481	82	55	,	,	PUNCT
ejpam-1481	82	56	s.	s.	PROPN
ejpam-1481	82	57	el	el	PROPN
ejpam-1481	82	58	-	-	PUNCT
ejpam-1481	82	59	shabrawy	shabrawy	PROPN
ejpam-1481	82	60	/	/	SYM
ejpam-1481	82	61	eur	eur	NOUN
ejpam-1481	82	62	.	.	PUNCT
ejpam-1481	83	1	j.	j.	PROPN
ejpam-1481	83	2	pure	pure	PROPN
ejpam-1481	83	3	appl	appl	PROPN
ejpam-1481	83	4	.	.	PROPN
ejpam-1481	83	5	math	math	PROPN
ejpam-1481	83	6	,	,	PUNCT
ejpam-1481	83	7	5	5	NUM
ejpam-1481	83	8	(	(	PUNCT
ejpam-1481	83	9	2012	2012	NUM
ejpam-1481	83	10	)	)	PUNCT
ejpam-1481	83	11	,	,	PUNCT
ejpam-1481	83	12	59	59	NUM
ejpam-1481	83	13	-	-	SYM
ejpam-1481	83	14	74	74	NUM
ejpam-1481	83	15	62	62	NUM
ejpam-1481	83	16	if	if	SCONJ
ejpam-1481	83	17	t	t	PROPN
ejpam-1481	83	18	:	:	PUNCT
ejpam-1481	83	19	l1→	l1→	PROPN
ejpam-1481	83	20	l1	l1	PROPN
ejpam-1481	83	21	is	be	AUX
ejpam-1481	83	22	a	a	DET
ejpam-1481	83	23	bounded	bounded	ADJ
ejpam-1481	83	24	linear	linear	ADJ
ejpam-1481	83	25	operator	operator	NOUN
ejpam-1481	83	26	with	with	ADP
ejpam-1481	83	27	matrix	matrix	NOUN
ejpam-1481	83	28	a	a	PRON
ejpam-1481	83	29	,	,	PUNCT
ejpam-1481	83	30	then	then	ADV
ejpam-1481	83	31	it	it	PRON
ejpam-1481	83	32	is	be	AUX
ejpam-1481	83	33	known	know	VERB
ejpam-1481	83	34	that	that	SCONJ
ejpam-1481	83	35	the	the	DET
ejpam-1481	83	36	adjoint	adjoint	NOUN
ejpam-1481	83	37	operator	operator	NOUN
ejpam-1481	83	38	t	t	PROPN
ejpam-1481	83	39	∗	∗	NOUN
ejpam-1481	83	40	:	:	PUNCT
ejpam-1481	83	41	l∗1	l∗1	NOUN
ejpam-1481	83	42	→	→	SYM
ejpam-1481	83	43	l∗1	l∗1	NOUN
ejpam-1481	83	44	is	be	AUX
ejpam-1481	83	45	defined	define	VERB
ejpam-1481	83	46	by	by	ADP
ejpam-1481	83	47	the	the	DET
ejpam-1481	83	48	transpose	transpose	NOUN
ejpam-1481	83	49	of	of	ADP
ejpam-1481	83	50	the	the	DET
ejpam-1481	83	51	matrix	matrix	NOUN
ejpam-1481	83	52	a.	a.	NOUN
ejpam-1481	83	53	it	it	PRON
ejpam-1481	83	54	is	be	AUX
ejpam-1481	83	55	well	well	ADV
ejpam-1481	83	56	-	-	PUNCT
ejpam-1481	83	57	known	know	VERB
ejpam-1481	83	58	that	that	SCONJ
ejpam-1481	83	59	the	the	DET
ejpam-1481	83	60	dual	dual	ADJ
ejpam-1481	83	61	space	space	NOUN
ejpam-1481	83	62	l∗1	l∗1	NOUN
ejpam-1481	83	63	of	of	ADP
ejpam-1481	83	64	l1	l1	PROPN
ejpam-1481	83	65	is	be	AUX
ejpam-1481	83	66	isomorphic	isomorphic	ADJ
ejpam-1481	83	67	to	to	ADP
ejpam-1481	83	68	l∞.	l∞.	PRON
ejpam-1481	83	69	also	also	ADV
ejpam-1481	83	70	,	,	PUNCT
ejpam-1481	83	71	if	if	SCONJ
ejpam-1481	83	72	t	t	NOUN
ejpam-1481	83	73	:	:	PUNCT
ejpam-1481	83	74	c0	c0	PROPN
ejpam-1481	83	75	→	→	SYM
ejpam-1481	83	76	c0	c0	PROPN
ejpam-1481	83	77	is	be	AUX
ejpam-1481	83	78	a	a	DET
ejpam-1481	83	79	bounded	bounded	ADJ
ejpam-1481	83	80	linear	linear	ADJ
ejpam-1481	83	81	operator	operator	NOUN
ejpam-1481	83	82	with	with	ADP
ejpam-1481	83	83	matrix	matrix	NOUN
ejpam-1481	83	84	a	a	DET
ejpam-1481	83	85	then	then	ADV
ejpam-1481	83	86	the	the	DET
ejpam-1481	83	87	adjoint	adjoint	NOUN
ejpam-1481	83	88	operator	operator	NOUN
ejpam-1481	83	89	t	t	PROPN
ejpam-1481	83	90	∗	∗	NOUN
ejpam-1481	83	91	:	:	PUNCT
ejpam-1481	83	92	c∗0	c∗0	PROPN
ejpam-1481	83	93	→	→	SYM
ejpam-1481	83	94	c∗0	c∗0	NOUN
ejpam-1481	83	95	is	be	AUX
ejpam-1481	83	96	defined	define	VERB
ejpam-1481	83	97	by	by	ADP
ejpam-1481	83	98	the	the	DET
ejpam-1481	83	99	transpose	transpose	NOUN
ejpam-1481	83	100	of	of	ADP
ejpam-1481	83	101	the	the	DET
ejpam-1481	83	102	matrix	matrix	NOUN
ejpam-1481	83	103	a.	a.	NOUN
ejpam-1481	83	104	the	the	DET
ejpam-1481	83	105	dual	dual	ADJ
ejpam-1481	83	106	space	space	NOUN
ejpam-1481	83	107	c∗0	c∗0	NOUN
ejpam-1481	83	108	of	of	ADP
ejpam-1481	83	109	c0	c0	PROPN
ejpam-1481	83	110	is	be	AUX
ejpam-1481	83	111	isomorphic	isomorphic	ADJ
ejpam-1481	83	112	to	to	ADP
ejpam-1481	83	113	the	the	DET
ejpam-1481	83	114	banach	banach	NOUN
ejpam-1481	83	115	space	space	NOUN
ejpam-1481	83	116	l1	l1	PROPN
ejpam-1481	83	117	.	.	PUNCT
ejpam-1481	84	1	let	let	VERB
ejpam-1481	84	2	x	x	PRON
ejpam-1481	84	3	6=	6=	X
ejpam-1481	84	4	{	{	PUNCT
ejpam-1481	84	5	θ	θ	NOUN
ejpam-1481	84	6	}	}	PUNCT
ejpam-1481	84	7	be	be	AUX
ejpam-1481	84	8	a	a	DET
ejpam-1481	84	9	complex	complex	ADJ
ejpam-1481	84	10	normed	normed	ADJ
ejpam-1481	84	11	space	space	NOUN
ejpam-1481	84	12	and	and	CCONJ
ejpam-1481	84	13	t	t	NOUN
ejpam-1481	84	14	:	:	PUNCT
ejpam-1481	84	15	d(t	d(t	PROPN
ejpam-1481	84	16	)	)	PUNCT
ejpam-1481	84	17	→	→	PUNCT
ejpam-1481	84	18	x	x	X
ejpam-1481	84	19	be	be	AUX
ejpam-1481	84	20	a	a	DET
ejpam-1481	84	21	linear	linear	ADJ
ejpam-1481	84	22	operator	operator	NOUN
ejpam-1481	84	23	with	with	ADP
ejpam-1481	84	24	domain	domain	NOUN
ejpam-1481	84	25	d(t	d(t	PROPN
ejpam-1481	84	26	)	)	PUNCT
ejpam-1481	84	27	⊆	⊆	NUM
ejpam-1481	84	28	x	x	X
ejpam-1481	84	29	.	.	PUNCT
ejpam-1481	85	1	with	with	ADP
ejpam-1481	85	2	t	t	PROPN
ejpam-1481	85	3	we	we	PRON
ejpam-1481	85	4	associate	associate	VERB
ejpam-1481	85	5	the	the	DET
ejpam-1481	85	6	operator	operator	NOUN
ejpam-1481	85	7	tλ	tλ	ADP
ejpam-1481	85	8	=	=	SYM
ejpam-1481	85	9	t	t	PROPN
ejpam-1481	85	10	−λi	−λi	NOUN
ejpam-1481	85	11	,	,	PUNCT
ejpam-1481	85	12	(	(	PUNCT
ejpam-1481	85	13	5	5	NUM
ejpam-1481	85	14	)	)	PUNCT
ejpam-1481	85	15	where	where	SCONJ
ejpam-1481	85	16	λ	λ	PROPN
ejpam-1481	85	17	is	be	AUX
ejpam-1481	85	18	a	a	DET
ejpam-1481	85	19	complex	complex	ADJ
ejpam-1481	85	20	number	number	NOUN
ejpam-1481	86	1	and	and	CCONJ
ejpam-1481	86	2	i	i	PRON
ejpam-1481	86	3	is	be	AUX
ejpam-1481	86	4	the	the	DET
ejpam-1481	86	5	identity	identity	NOUN
ejpam-1481	86	6	operator	operator	NOUN
ejpam-1481	86	7	on	on	ADP
ejpam-1481	86	8	d(t	d(t	PROPN
ejpam-1481	86	9	)	)	PUNCT
ejpam-1481	86	10	.	.	PUNCT
ejpam-1481	87	1	if	if	SCONJ
ejpam-1481	87	2	tλ	tλ	NOUN
ejpam-1481	87	3	has	have	VERB
ejpam-1481	87	4	an	an	DET
ejpam-1481	87	5	inverse	inverse	NOUN
ejpam-1481	87	6	which	which	PRON
ejpam-1481	87	7	is	be	AUX
ejpam-1481	87	8	linear	linear	ADJ
ejpam-1481	87	9	,	,	PUNCT
ejpam-1481	87	10	we	we	PRON
ejpam-1481	87	11	denote	denote	VERB
ejpam-1481	87	12	it	it	PRON
ejpam-1481	87	13	by	by	ADP
ejpam-1481	87	14	t−1	t−1	PROPN
ejpam-1481	87	15	λ	λ	PROPN
ejpam-1481	87	16	,	,	PUNCT
ejpam-1481	87	17	that	that	PRON
ejpam-1481	87	18	is	be	AUX
ejpam-1481	87	19	t−1	t−1	PROPN
ejpam-1481	87	20	λ	λ	NOUN
ejpam-1481	87	21	=	=	SYM
ejpam-1481	87	22	(	(	PUNCT
ejpam-1481	87	23	t	t	NOUN
ejpam-1481	87	24	−λi)−1	−λi)−1	PROPN
ejpam-1481	87	25	,	,	PUNCT
ejpam-1481	87	26	(	(	PUNCT
ejpam-1481	87	27	6	6	NUM
ejpam-1481	87	28	)	)	PUNCT
ejpam-1481	87	29	and	and	CCONJ
ejpam-1481	87	30	call	call	VERB
ejpam-1481	87	31	it	it	PRON
ejpam-1481	87	32	the	the	DET
ejpam-1481	87	33	resolvent	resolvent	ADJ
ejpam-1481	87	34	operator	operator	NOUN
ejpam-1481	87	35	of	of	ADP
ejpam-1481	87	36	t	t	PROPN
ejpam-1481	87	37	.	.	PUNCT
ejpam-1481	88	1	many	many	ADJ
ejpam-1481	88	2	properties	property	NOUN
ejpam-1481	88	3	of	of	ADP
ejpam-1481	88	4	tλ	tλ	ADP
ejpam-1481	88	5	and	and	CCONJ
ejpam-1481	88	6	t−1	t−1	PROPN
ejpam-1481	88	7	λ	λ	NOUN
ejpam-1481	88	8	depend	depend	VERB
ejpam-1481	88	9	on	on	ADP
ejpam-1481	88	10	λ	λ	PROPN
ejpam-1481	88	11	,	,	PUNCT
ejpam-1481	88	12	and	and	CCONJ
ejpam-1481	88	13	spectral	spectral	ADJ
ejpam-1481	88	14	theory	theory	NOUN
ejpam-1481	88	15	is	be	AUX
ejpam-1481	88	16	concerned	concern	VERB
ejpam-1481	88	17	with	with	ADP
ejpam-1481	88	18	those	those	DET
ejpam-1481	88	19	properties	property	NOUN
ejpam-1481	88	20	.	.	PUNCT
ejpam-1481	89	1	for	for	ADP
ejpam-1481	89	2	instance	instance	NOUN
ejpam-1481	89	3	,	,	PUNCT
ejpam-1481	89	4	we	we	PRON
ejpam-1481	89	5	shall	shall	AUX
ejpam-1481	89	6	be	be	AUX
ejpam-1481	89	7	interested	interested	ADJ
ejpam-1481	89	8	in	in	ADP
ejpam-1481	89	9	the	the	DET
ejpam-1481	89	10	set	set	NOUN
ejpam-1481	89	11	of	of	ADP
ejpam-1481	89	12	all	all	DET
ejpam-1481	89	13	λ	λ	PROPN
ejpam-1481	89	14	in	in	ADP
ejpam-1481	89	15	the	the	DET
ejpam-1481	89	16	complex	complex	ADJ
ejpam-1481	89	17	plane	plane	NOUN
ejpam-1481	89	18	such	such	ADJ
ejpam-1481	89	19	that	that	SCONJ
ejpam-1481	89	20	t−1	t−1	PROPN
ejpam-1481	89	21	λ	λ	PROPN
ejpam-1481	89	22	exists	exist	VERB
ejpam-1481	89	23	.	.	PUNCT
ejpam-1481	90	1	the	the	DET
ejpam-1481	90	2	boundedness	boundedness	NOUN
ejpam-1481	90	3	of	of	ADP
ejpam-1481	90	4	t−1	t−1	PROPN
ejpam-1481	90	5	λ	λ	PROPN
ejpam-1481	90	6	is	be	AUX
ejpam-1481	90	7	another	another	DET
ejpam-1481	90	8	property	property	NOUN
ejpam-1481	90	9	that	that	PRON
ejpam-1481	90	10	will	will	AUX
ejpam-1481	90	11	be	be	AUX
ejpam-1481	90	12	essential	essential	ADJ
ejpam-1481	90	13	.	.	PUNCT
ejpam-1481	91	1	we	we	PRON
ejpam-1481	91	2	shall	shall	AUX
ejpam-1481	91	3	also	also	ADV
ejpam-1481	91	4	ask	ask	VERB
ejpam-1481	91	5	for	for	ADP
ejpam-1481	91	6	what	what	PRON
ejpam-1481	91	7	λ	λ	NOUN
ejpam-1481	91	8	’s	’	VERB
ejpam-1481	91	9	the	the	DET
ejpam-1481	91	10	domain	domain	NOUN
ejpam-1481	91	11	of	of	ADP
ejpam-1481	91	12	t−1	t−1	PROPN
ejpam-1481	91	13	λ	λ	PROPN
ejpam-1481	91	14	is	be	AUX
ejpam-1481	91	15	dense	dense	ADJ
ejpam-1481	91	16	in	in	ADP
ejpam-1481	91	17	x	x	SYM
ejpam-1481	91	18	,	,	PUNCT
ejpam-1481	91	19	to	to	PART
ejpam-1481	91	20	name	name	VERB
ejpam-1481	91	21	just	just	ADV
ejpam-1481	91	22	a	a	DET
ejpam-1481	91	23	few	few	ADJ
ejpam-1481	91	24	aspects	aspect	NOUN
ejpam-1481	91	25	.	.	PUNCT
ejpam-1481	92	1	definition	definition	NOUN
ejpam-1481	92	2	1	1	NUM
ejpam-1481	92	3	.	.	PUNCT
ejpam-1481	93	1	let	let	VERB
ejpam-1481	93	2	x	x	PRON
ejpam-1481	93	3	6=	6=	X
ejpam-1481	93	4	{	{	PUNCT
ejpam-1481	93	5	θ	θ	NOUN
ejpam-1481	93	6	}	}	PUNCT
ejpam-1481	93	7	be	be	AUX
ejpam-1481	93	8	a	a	DET
ejpam-1481	93	9	complex	complex	ADJ
ejpam-1481	93	10	normed	normed	ADJ
ejpam-1481	93	11	space	space	NOUN
ejpam-1481	93	12	and	and	CCONJ
ejpam-1481	93	13	t	t	NOUN
ejpam-1481	93	14	:	:	PUNCT
ejpam-1481	93	15	d(t	d(t	PROPN
ejpam-1481	93	16	)	)	PUNCT
ejpam-1481	93	17	→	→	SYM
ejpam-1481	93	18	x	x	X
ejpam-1481	93	19	be	be	AUX
ejpam-1481	93	20	a	a	DET
ejpam-1481	93	21	linear	linear	ADJ
ejpam-1481	93	22	operator	operator	NOUN
ejpam-1481	93	23	with	with	ADP
ejpam-1481	93	24	domain	domain	NOUN
ejpam-1481	93	25	d(t	d(t	PROPN
ejpam-1481	93	26	)	)	PUNCT
ejpam-1481	94	1	⊆	⊆	NUM
ejpam-1481	94	2	x	x	X
ejpam-1481	94	3	.	.	PUNCT
ejpam-1481	95	1	a	a	DET
ejpam-1481	95	2	regular	regular	ADJ
ejpam-1481	95	3	value	value	NOUN
ejpam-1481	95	4	λ	λ	PROPN
ejpam-1481	95	5	of	of	ADP
ejpam-1481	95	6	t	t	PROPN
ejpam-1481	95	7	is	be	AUX
ejpam-1481	95	8	a	a	DET
ejpam-1481	95	9	complex	complex	ADJ
ejpam-1481	95	10	number	number	NOUN
ejpam-1481	95	11	such	such	ADJ
ejpam-1481	95	12	that	that	SCONJ
ejpam-1481	95	13	(	(	PUNCT
ejpam-1481	95	14	r1	r1	PROPN
ejpam-1481	95	15	)	)	PUNCT
ejpam-1481	95	16	t−1	t−1	PROPN
ejpam-1481	95	17	λ	λ	PROPN
ejpam-1481	95	18	exists	exist	VERB
ejpam-1481	95	19	,	,	PUNCT
ejpam-1481	95	20	(	(	PUNCT
ejpam-1481	95	21	r2	r2	PROPN
ejpam-1481	95	22	)	)	PUNCT
ejpam-1481	96	1	t−1	t−1	PROPN
ejpam-1481	96	2	λ	λ	PROPN
ejpam-1481	96	3	is	be	AUX
ejpam-1481	96	4	bounded	bound	VERB
ejpam-1481	96	5	,	,	PUNCT
ejpam-1481	96	6	(	(	PUNCT
ejpam-1481	96	7	r3	r3	PROPN
ejpam-1481	96	8	)	)	PUNCT
ejpam-1481	96	9	t−1	t−1	PROPN
ejpam-1481	96	10	λ	λ	NOUN
ejpam-1481	96	11	is	be	AUX
ejpam-1481	96	12	defined	define	VERB
ejpam-1481	96	13	on	on	ADP
ejpam-1481	96	14	a	a	DET
ejpam-1481	96	15	set	set	NOUN
ejpam-1481	96	16	which	which	PRON
ejpam-1481	96	17	is	be	AUX
ejpam-1481	96	18	dense	dense	ADJ
ejpam-1481	96	19	in	in	ADP
ejpam-1481	96	20	x	x	X
ejpam-1481	96	21	.	.	PUNCT
ejpam-1481	97	1	the	the	DET
ejpam-1481	97	2	resolvent	resolvent	ADJ
ejpam-1481	97	3	set	set	NOUN
ejpam-1481	97	4	of	of	ADP
ejpam-1481	97	5	t	t	PROPN
ejpam-1481	97	6	,	,	PUNCT
ejpam-1481	97	7	denoted	denote	VERB
ejpam-1481	97	8	by	by	ADP
ejpam-1481	97	9	ρ(t	ρ(t	PROPN
ejpam-1481	97	10	,	,	PUNCT
ejpam-1481	97	11	x	x	PROPN
ejpam-1481	97	12	)	)	PUNCT
ejpam-1481	97	13	,	,	PUNCT
ejpam-1481	97	14	is	be	AUX
ejpam-1481	97	15	the	the	DET
ejpam-1481	97	16	set	set	NOUN
ejpam-1481	97	17	of	of	ADP
ejpam-1481	97	18	all	all	DET
ejpam-1481	97	19	regular	regular	ADJ
ejpam-1481	97	20	values	value	NOUN
ejpam-1481	97	21	λ	λ	PROPN
ejpam-1481	97	22	of	of	ADP
ejpam-1481	97	23	t	t	PROPN
ejpam-1481	97	24	.	.	PUNCT
ejpam-1481	98	1	its	its	PRON
ejpam-1481	98	2	complement	complement	NOUN
ejpam-1481	98	3	σ(t	σ(t	PROPN
ejpam-1481	98	4	,	,	PUNCT
ejpam-1481	98	5	x	x	X
ejpam-1481	98	6	)	)	PUNCT
ejpam-1481	98	7	=	=	SYM
ejpam-1481	98	8	c\ρ(t	c\ρ(t	INTJ
ejpam-1481	98	9	,	,	PUNCT
ejpam-1481	98	10	x	x	PUNCT
ejpam-1481	98	11	)	)	PUNCT
ejpam-1481	98	12	in	in	ADP
ejpam-1481	98	13	the	the	DET
ejpam-1481	98	14	complex	complex	ADJ
ejpam-1481	98	15	plane	plane	NOUN
ejpam-1481	98	16	c	c	NOUN
ejpam-1481	98	17	is	be	AUX
ejpam-1481	98	18	called	call	VERB
ejpam-1481	98	19	the	the	DET
ejpam-1481	98	20	spectrum	spectrum	NOUN
ejpam-1481	98	21	of	of	ADP
ejpam-1481	98	22	t	t	PROPN
ejpam-1481	98	23	.	.	PUNCT
ejpam-1481	99	1	furthermore	furthermore	ADV
ejpam-1481	99	2	,	,	PUNCT
ejpam-1481	99	3	the	the	DET
ejpam-1481	99	4	spectrum	spectrum	NOUN
ejpam-1481	99	5	σ(t	σ(t	PROPN
ejpam-1481	99	6	,	,	PUNCT
ejpam-1481	99	7	x	x	X
ejpam-1481	99	8	)	)	PUNCT
ejpam-1481	99	9	is	be	AUX
ejpam-1481	99	10	partitioned	partition	VERB
ejpam-1481	99	11	into	into	ADP
ejpam-1481	99	12	three	three	NUM
ejpam-1481	99	13	disjoint	disjoint	NOUN
ejpam-1481	99	14	sets	set	NOUN
ejpam-1481	99	15	as	as	SCONJ
ejpam-1481	99	16	follows	follow	VERB
ejpam-1481	99	17	:	:	PUNCT
ejpam-1481	99	18	the	the	DET
ejpam-1481	99	19	point	point	NOUN
ejpam-1481	99	20	(	(	PUNCT
ejpam-1481	99	21	discrete	discrete	NOUN
ejpam-1481	99	22	)	)	PUNCT
ejpam-1481	99	23	spectrum	spectrum	NOUN
ejpam-1481	99	24	σp(t	σp(t	NOUN
ejpam-1481	99	25	,	,	PUNCT
ejpam-1481	99	26	x	x	X
ejpam-1481	99	27	)	)	PUNCT
ejpam-1481	99	28	is	be	AUX
ejpam-1481	99	29	the	the	DET
ejpam-1481	99	30	set	set	NOUN
ejpam-1481	99	31	such	such	ADJ
ejpam-1481	99	32	that	that	SCONJ
ejpam-1481	99	33	t−1	t−1	PROPN
ejpam-1481	99	34	λ	λ	NOUN
ejpam-1481	99	35	does	do	AUX
ejpam-1481	99	36	not	not	PART
ejpam-1481	99	37	exist	exist	VERB
ejpam-1481	99	38	.	.	PUNCT
ejpam-1481	100	1	any	any	DET
ejpam-1481	100	2	such	such	ADJ
ejpam-1481	100	3	λ	λ	PROPN
ejpam-1481	100	4	∈	∈	NOUN
ejpam-1481	100	5	σp(t	σp(t	NOUN
ejpam-1481	100	6	,	,	PUNCT
ejpam-1481	100	7	x	x	X
ejpam-1481	100	8	)	)	PUNCT
ejpam-1481	100	9	is	be	AUX
ejpam-1481	100	10	called	call	VERB
ejpam-1481	100	11	an	an	DET
ejpam-1481	100	12	eigenvalue	eigenvalue	NOUN
ejpam-1481	100	13	of	of	ADP
ejpam-1481	100	14	t	t	PROPN
ejpam-1481	100	15	.	.	PUNCT
ejpam-1481	101	1	the	the	DET
ejpam-1481	101	2	continuous	continuous	ADJ
ejpam-1481	101	3	spectrum	spectrum	NOUN
ejpam-1481	101	4	σc(t	σc(t	PROPN
ejpam-1481	101	5	,	,	PUNCT
ejpam-1481	101	6	x	x	PUNCT
ejpam-1481	101	7	)	)	PUNCT
ejpam-1481	101	8	is	be	AUX
ejpam-1481	101	9	the	the	DET
ejpam-1481	101	10	set	set	NOUN
ejpam-1481	101	11	such	such	ADJ
ejpam-1481	101	12	that	that	SCONJ
ejpam-1481	101	13	t−1	t−1	PROPN
ejpam-1481	101	14	λ	λ	PROPN
ejpam-1481	101	15	exists	exist	VERB
ejpam-1481	101	16	and	and	CCONJ
ejpam-1481	101	17	satisfies	satisfie	NOUN
ejpam-1481	101	18	(	(	PUNCT
ejpam-1481	101	19	r3	r3	PROPN
ejpam-1481	101	20	)	)	PUNCT
ejpam-1481	101	21	but	but	CCONJ
ejpam-1481	101	22	not	not	PART
ejpam-1481	101	23	(	(	PUNCT
ejpam-1481	101	24	r2	r2	PROPN
ejpam-1481	101	25	)	)	PUNCT
ejpam-1481	101	26	,	,	PUNCT
ejpam-1481	101	27	that	that	ADV
ejpam-1481	101	28	is	is	ADV
ejpam-1481	101	29	,	,	PUNCT
ejpam-1481	101	30	t−1	t−1	PROPN
ejpam-1481	101	31	λ	λ	PROPN
ejpam-1481	101	32	is	be	AUX
ejpam-1481	101	33	unbounded	unbounded	ADJ
ejpam-1481	101	34	.	.	PUNCT
ejpam-1481	102	1	the	the	DET
ejpam-1481	102	2	residual	residual	ADJ
ejpam-1481	102	3	spectrum	spectrum	NOUN
ejpam-1481	102	4	σr(t	σr(t	NOUN
ejpam-1481	102	5	,	,	PUNCT
ejpam-1481	102	6	x	x	PUNCT
ejpam-1481	102	7	)	)	PUNCT
ejpam-1481	102	8	is	be	AUX
ejpam-1481	102	9	the	the	DET
ejpam-1481	102	10	set	set	NOUN
ejpam-1481	102	11	such	such	ADJ
ejpam-1481	102	12	that	that	SCONJ
ejpam-1481	102	13	t−1	t−1	PROPN
ejpam-1481	102	14	λ	λ	PROPN
ejpam-1481	102	15	exists	exist	VERB
ejpam-1481	102	16	(	(	PUNCT
ejpam-1481	102	17	and	and	CCONJ
ejpam-1481	102	18	may	may	AUX
ejpam-1481	102	19	be	be	AUX
ejpam-1481	102	20	bounded	bound	VERB
ejpam-1481	102	21	or	or	CCONJ
ejpam-1481	102	22	not	not	PART
ejpam-1481	102	23	)	)	PUNCT
ejpam-1481	102	24	but	but	CCONJ
ejpam-1481	102	25	does	do	AUX
ejpam-1481	102	26	not	not	PART
ejpam-1481	102	27	satisfy	satisfy	VERB
ejpam-1481	102	28	(	(	PUNCT
ejpam-1481	102	29	r3	r3	PROPN
ejpam-1481	102	30	)	)	PUNCT
ejpam-1481	102	31	,	,	PUNCT
ejpam-1481	102	32	that	that	ADV
ejpam-1481	102	33	is	is	ADV
ejpam-1481	102	34	,	,	PUNCT
ejpam-1481	102	35	the	the	DET
ejpam-1481	102	36	domain	domain	NOUN
ejpam-1481	102	37	of	of	ADP
ejpam-1481	102	38	t−1	t−1	PROPN
ejpam-1481	102	39	λ	λ	PROPN
ejpam-1481	102	40	is	be	AUX
ejpam-1481	102	41	not	not	PART
ejpam-1481	102	42	dense	dense	ADJ
ejpam-1481	102	43	in	in	ADP
ejpam-1481	102	44	x	x	X
ejpam-1481	102	45	.	.	PUNCT
ejpam-1481	103	1	hence	hence	ADV
ejpam-1481	103	2	if	if	SCONJ
ejpam-1481	103	3	(	(	PUNCT
ejpam-1481	103	4	t	t	NOUN
ejpam-1481	103	5	−	−	PROPN
ejpam-1481	103	6	λi)x	λi)x	PROPN
ejpam-1481	103	7	=	=	SYM
ejpam-1481	103	8	θ	θ	PROPN
ejpam-1481	103	9	for	for	ADP
ejpam-1481	103	10	some	some	DET
ejpam-1481	103	11	x	x	PUNCT
ejpam-1481	103	12	6=	6=	NUM
ejpam-1481	103	13	θ	θ	PROPN
ejpam-1481	103	14	,	,	PUNCT
ejpam-1481	103	15	then	then	ADV
ejpam-1481	103	16	λ	λ	X
ejpam-1481	103	17	∈	∈	PROPN
ejpam-1481	103	18	σp(t	σp(t	NOUN
ejpam-1481	103	19	,	,	PUNCT
ejpam-1481	103	20	x	x	X
ejpam-1481	103	21	)	)	PUNCT
ejpam-1481	103	22	,	,	PUNCT
ejpam-1481	103	23	by	by	ADP
ejpam-1481	103	24	definition	definition	NOUN
ejpam-1481	103	25	,	,	PUNCT
ejpam-1481	103	26	that	that	ADV
ejpam-1481	103	27	is	is	ADV
ejpam-1481	103	28	,	,	PUNCT
ejpam-1481	103	29	λ	λ	X
ejpam-1481	103	30	is	be	AUX
ejpam-1481	103	31	an	an	DET
ejpam-1481	103	32	eigenvalue	eigenvalue	NOUN
ejpam-1481	103	33	of	of	ADP
ejpam-1481	103	34	t	t	PROPN
ejpam-1481	103	35	.	.	PUNCT
ejpam-1481	104	1	the	the	DET
ejpam-1481	104	2	vector	vector	NOUN
ejpam-1481	104	3	x	x	PUNCT
ejpam-1481	104	4	is	be	AUX
ejpam-1481	104	5	then	then	ADV
ejpam-1481	104	6	called	call	VERB
ejpam-1481	104	7	an	an	DET
ejpam-1481	104	8	eigenvector	eigenvector	NOUN
ejpam-1481	104	9	of	of	ADP
ejpam-1481	104	10	t	t	PROPN
ejpam-1481	104	11	corresponding	correspond	VERB
ejpam-1481	104	12	to	to	ADP
ejpam-1481	104	13	the	the	DET
ejpam-1481	104	14	eigenvalue	eigenvalue	PROPN
ejpam-1481	104	15	λ	λ	PROPN
ejpam-1481	104	16	.	.	PUNCT
ejpam-1481	105	1	now	now	ADV
ejpam-1481	105	2	,	,	PUNCT
ejpam-1481	105	3	we	we	PRON
ejpam-1481	105	4	may	may	AUX
ejpam-1481	105	5	give	give	VERB
ejpam-1481	105	6	:	:	PUNCT
ejpam-1481	105	7	lemma	lemma	PROPN
ejpam-1481	105	8	1	1	NUM
ejpam-1481	105	9	(	(	PUNCT
ejpam-1481	105	10	[	[	X
ejpam-1481	105	11	19	19	NUM
ejpam-1481	105	12	,	,	PUNCT
ejpam-1481	105	13	p.	p.	NOUN
ejpam-1481	105	14	59	59	NUM
ejpam-1481	105	15	]	]	PUNCT
ejpam-1481	105	16	)	)	PUNCT
ejpam-1481	105	17	.	.	PUNCT
ejpam-1481	106	1	t	t	PROPN
ejpam-1481	106	2	has	have	VERB
ejpam-1481	106	3	a	a	DET
ejpam-1481	106	4	dense	dense	ADJ
ejpam-1481	106	5	range	range	NOUN
ejpam-1481	106	6	if	if	SCONJ
ejpam-1481	107	1	and	and	CCONJ
ejpam-1481	107	2	only	only	ADV
ejpam-1481	107	3	if	if	SCONJ
ejpam-1481	107	4	t	t	PROPN
ejpam-1481	107	5	∗	∗	NOUN
ejpam-1481	107	6	is	be	AUX
ejpam-1481	107	7	one	one	NUM
ejpam-1481	107	8	to	to	ADP
ejpam-1481	107	9	one	one	NUM
ejpam-1481	107	10	.	.	PUNCT
ejpam-1481	108	1	a.	a.	PROPN
ejpam-1481	108	2	akhmedov	akhmedov	PROPN
ejpam-1481	108	3	,	,	PUNCT
ejpam-1481	108	4	s.	s.	PROPN
ejpam-1481	108	5	el	el	PROPN
ejpam-1481	108	6	-	-	PUNCT
ejpam-1481	108	7	shabrawy	shabrawy	PROPN
ejpam-1481	108	8	/	/	SYM
ejpam-1481	108	9	eur	eur	NOUN
ejpam-1481	108	10	.	.	PUNCT
ejpam-1481	109	1	j.	j.	PROPN
ejpam-1481	109	2	pure	pure	PROPN
ejpam-1481	109	3	appl	appl	PROPN
ejpam-1481	109	4	.	.	PROPN
ejpam-1481	109	5	math	math	PROPN
ejpam-1481	109	6	,	,	PUNCT
ejpam-1481	109	7	5	5	NUM
ejpam-1481	109	8	(	(	PUNCT
ejpam-1481	109	9	2012	2012	NUM
ejpam-1481	109	10	)	)	PUNCT
ejpam-1481	109	11	,	,	PUNCT
ejpam-1481	109	12	59	59	NUM
ejpam-1481	109	13	-	-	SYM
ejpam-1481	109	14	74	74	NUM
ejpam-1481	109	15	63	63	NUM
ejpam-1481	109	16	3	3	NUM
ejpam-1481	109	17	.	.	PUNCT
ejpam-1481	110	1	recent	recent	ADJ
ejpam-1481	110	2	and	and	CCONJ
ejpam-1481	110	3	new	new	ADJ
ejpam-1481	110	4	results	result	NOUN
ejpam-1481	110	5	on	on	ADP
ejpam-1481	110	6	the	the	DET
ejpam-1481	110	7	fine	fine	ADJ
ejpam-1481	110	8	spectrum	spectrum	NOUN
ejpam-1481	110	9	of	of	ADP
ejpam-1481	110	10	the	the	DET
ejpam-1481	110	11	operator	operator	NOUN
ejpam-1481	110	12	∆	∆	X
ejpam-1481	110	13	v	v	NOUN
ejpam-1481	110	14	on	on	ADP
ejpam-1481	110	15	l1	l1	PROPN
ejpam-1481	110	16	and	and	CCONJ
ejpam-1481	110	17	c0	c0	PROPN
ejpam-1481	110	18	in	in	ADP
ejpam-1481	110	19	this	this	DET
ejpam-1481	110	20	section	section	NOUN
ejpam-1481	110	21	we	we	PRON
ejpam-1481	110	22	mainly	mainly	ADV
ejpam-1481	110	23	review	review	VERB
ejpam-1481	110	24	several	several	ADJ
ejpam-1481	110	25	recent	recent	ADJ
ejpam-1481	110	26	results	result	NOUN
ejpam-1481	110	27	concerning	concern	VERB
ejpam-1481	110	28	the	the	DET
ejpam-1481	110	29	fine	fine	ADJ
ejpam-1481	110	30	spectrum	spectrum	NOUN
ejpam-1481	110	31	of	of	ADP
ejpam-1481	110	32	the	the	DET
ejpam-1481	110	33	operator	operator	NOUN
ejpam-1481	110	34	∆v	∆v	PROPN
ejpam-1481	110	35	on	on	ADP
ejpam-1481	110	36	the	the	DET
ejpam-1481	110	37	sequence	sequence	NOUN
ejpam-1481	110	38	spaces	space	VERB
ejpam-1481	110	39	l1	l1	PROPN
ejpam-1481	110	40	and	and	CCONJ
ejpam-1481	110	41	c0	c0	PROPN
ejpam-1481	110	42	.	.	PUNCT
ejpam-1481	111	1	also	also	ADV
ejpam-1481	111	2	,	,	PUNCT
ejpam-1481	111	3	we	we	PRON
ejpam-1481	111	4	provide	provide	VERB
ejpam-1481	111	5	some	some	DET
ejpam-1481	111	6	new	new	ADJ
ejpam-1481	111	7	results	result	NOUN
ejpam-1481	111	8	.	.	PUNCT
ejpam-1481	112	1	as	as	SCONJ
ejpam-1481	112	2	we	we	PRON
ejpam-1481	112	3	mentioned	mention	VERB
ejpam-1481	112	4	before	before	ADV
ejpam-1481	112	5	,	,	PUNCT
ejpam-1481	112	6	the	the	DET
ejpam-1481	112	7	case	case	NOUN
ejpam-1481	112	8	when	when	SCONJ
ejpam-1481	112	9	(	(	PUNCT
ejpam-1481	112	10	vk	vk	NOUN
ejpam-1481	112	11	)	)	PUNCT
ejpam-1481	112	12	is	be	AUX
ejpam-1481	112	13	a	a	DET
ejpam-1481	112	14	constant	constant	ADJ
ejpam-1481	112	15	sequence	sequence	NOUN
ejpam-1481	112	16	is	be	AUX
ejpam-1481	112	17	not	not	PART
ejpam-1481	112	18	considered	consider	VERB
ejpam-1481	112	19	here	here	ADV
ejpam-1481	112	20	.	.	PUNCT
ejpam-1481	113	1	so	so	ADV
ejpam-1481	113	2	,	,	PUNCT
ejpam-1481	113	3	throughout	throughout	ADP
ejpam-1481	113	4	this	this	DET
ejpam-1481	113	5	section	section	NOUN
ejpam-1481	113	6	,	,	PUNCT
ejpam-1481	113	7	the	the	DET
ejpam-1481	113	8	sequence	sequence	NOUN
ejpam-1481	113	9	(	(	PUNCT
ejpam-1481	113	10	vk	vk	NOUN
ejpam-1481	113	11	)	)	PUNCT
ejpam-1481	113	12	is	be	AUX
ejpam-1481	113	13	assumed	assume	VERB
ejpam-1481	113	14	to	to	PART
ejpam-1481	113	15	be	be	AUX
ejpam-1481	113	16	a	a	DET
ejpam-1481	113	17	strictly	strictly	ADV
ejpam-1481	113	18	decreasing	decrease	VERB
ejpam-1481	113	19	sequence	sequence	NOUN
ejpam-1481	113	20	of	of	ADP
ejpam-1481	113	21	positive	positive	ADJ
ejpam-1481	113	22	real	real	ADJ
ejpam-1481	113	23	numbers	number	NOUN
ejpam-1481	113	24	satisfying	satisfy	VERB
ejpam-1481	113	25	the	the	DET
ejpam-1481	113	26	conditions	condition	NOUN
ejpam-1481	113	27	(	(	PUNCT
ejpam-1481	113	28	2	2	NUM
ejpam-1481	113	29	)	)	PUNCT
ejpam-1481	113	30	.	.	PUNCT
ejpam-1481	114	1	3.1	3.1	NUM
ejpam-1481	114	2	.	.	PUNCT
ejpam-1481	115	1	the	the	DET
ejpam-1481	115	2	fine	fine	ADJ
ejpam-1481	115	3	spectrum	spectrum	NOUN
ejpam-1481	115	4	of	of	ADP
ejpam-1481	115	5	the	the	DET
ejpam-1481	115	6	operator	operator	NOUN
ejpam-1481	115	7	∆v	∆v	PROPN
ejpam-1481	115	8	on	on	ADP
ejpam-1481	115	9	l1	l1	PROPN
ejpam-1481	115	10	srivastava	srivastava	PROPN
ejpam-1481	115	11	and	and	CCONJ
ejpam-1481	115	12	kumar	kumar	PROPN
ejpam-1481	116	1	[	[	X
ejpam-1481	116	2	25	25	NUM
ejpam-1481	116	3	]	]	PUNCT
ejpam-1481	116	4	investigated	investigate	VERB
ejpam-1481	116	5	the	the	DET
ejpam-1481	116	6	fine	fine	ADJ
ejpam-1481	116	7	spectrum	spectrum	NOUN
ejpam-1481	116	8	of	of	ADP
ejpam-1481	116	9	the	the	DET
ejpam-1481	116	10	operator	operator	NOUN
ejpam-1481	116	11	∆v	∆v	PROPN
ejpam-1481	116	12	on	on	ADP
ejpam-1481	116	13	the	the	DET
ejpam-1481	116	14	sequence	sequence	NOUN
ejpam-1481	116	15	space	space	NOUN
ejpam-1481	116	16	l1	l1	PROPN
ejpam-1481	116	17	.	.	PUNCT
ejpam-1481	117	1	but	but	CCONJ
ejpam-1481	117	2	,	,	PUNCT
ejpam-1481	117	3	incorrect	incorrect	ADJ
ejpam-1481	117	4	results	result	NOUN
ejpam-1481	117	5	are	be	AUX
ejpam-1481	117	6	obtained	obtain	VERB
ejpam-1481	117	7	.	.	PUNCT
ejpam-1481	118	1	akhmedov	akhmedov	PROPN
ejpam-1481	118	2	and	and	CCONJ
ejpam-1481	118	3	el	el	NOUN
ejpam-1481	118	4	-	-	PUNCT
ejpam-1481	118	5	shabrawy	shabrawy	PROPN
ejpam-1481	119	1	[	[	X
ejpam-1481	119	2	8	8	NUM
ejpam-1481	119	3	]	]	PUNCT
ejpam-1481	119	4	have	have	AUX
ejpam-1481	119	5	proved	prove	VERB
ejpam-1481	119	6	by	by	ADP
ejpam-1481	119	7	a	a	DET
ejpam-1481	119	8	counterexample	counterexample	NOUN
ejpam-1481	119	9	that	that	SCONJ
ejpam-1481	119	10	the	the	DET
ejpam-1481	119	11	results	result	NOUN
ejpam-1481	119	12	concerning	concern	VERB
ejpam-1481	119	13	the	the	DET
ejpam-1481	119	14	point	point	NOUN
ejpam-1481	119	15	spectrum	spectrum	NOUN
ejpam-1481	119	16	and	and	CCONJ
ejpam-1481	119	17	the	the	DET
ejpam-1481	119	18	residual	residual	ADJ
ejpam-1481	119	19	spectrum	spectrum	NOUN
ejpam-1481	119	20	are	be	AUX
ejpam-1481	119	21	incorrect	incorrect	ADJ
ejpam-1481	119	22	.	.	PUNCT
ejpam-1481	120	1	in	in	ADP
ejpam-1481	120	2	this	this	DET
ejpam-1481	120	3	subsection	subsection	NOUN
ejpam-1481	120	4	we	we	PRON
ejpam-1481	120	5	summarize	summarize	VERB
ejpam-1481	120	6	the	the	DET
ejpam-1481	120	7	main	main	ADJ
ejpam-1481	120	8	results	result	NOUN
ejpam-1481	120	9	.	.	PUNCT
ejpam-1481	121	1	theorem	theorem	NOUN
ejpam-1481	121	2	1	1	NUM
ejpam-1481	121	3	.	.	PUNCT
ejpam-1481	122	1	the	the	DET
ejpam-1481	122	2	operator	operator	NOUN
ejpam-1481	122	3	∆v	∆v	PROPN
ejpam-1481	122	4	:	:	PUNCT
ejpam-1481	122	5	l1	l1	PROPN
ejpam-1481	122	6	−→	−→	PROPN
ejpam-1481	122	7	l1	l1	PROPN
ejpam-1481	122	8	is	be	AUX
ejpam-1481	122	9	a	a	DET
ejpam-1481	122	10	bounded	bounded	ADJ
ejpam-1481	122	11	linear	linear	ADJ
ejpam-1481	122	12	operator	operator	NOUN
ejpam-1481	122	13	and	and	CCONJ
ejpam-1481	122	14	(	(	PUNCT
ejpam-1481	122	15	i	i	NOUN
ejpam-1481	122	16	)	)	PUNCT
ejpam-1481	122	17	∆v	∆v	PROPN
ejpam-1481	122	18	l1	l1	PROPN
ejpam-1481	122	19	=	=	SYM
ejpam-1481	122	20	2v0	2v0	NUM
ejpam-1481	122	21	.	.	PUNCT
ejpam-1481	123	1	(	(	PUNCT
ejpam-1481	123	2	ii	ii	NOUN
ejpam-1481	123	3	)	)	PUNCT
ejpam-1481	123	4	σ(∆v	σ(∆v	NOUN
ejpam-1481	123	5	,	,	PUNCT
ejpam-1481	123	6	l1	l1	PROPN
ejpam-1481	123	7	)	)	PUNCT
ejpam-1481	123	8	=	=	PRON
ejpam-1481	124	1	{	{	PUNCT
ejpam-1481	124	2	λ	λ	X
ejpam-1481	124	3	∈	∈	PROPN
ejpam-1481	124	4	c	c	NOUN
ejpam-1481	124	5	:	:	PUNCT
ejpam-1481	124	6	|λ−	|λ−	NOUN
ejpam-1481	124	7	l|	l|	ADJ
ejpam-1481	124	8	≤	≤	ADJ
ejpam-1481	124	9	l	l	NOUN
ejpam-1481	124	10	}	}	PUNCT
ejpam-1481	124	11	.	.	PUNCT
ejpam-1481	125	1	(	(	PUNCT
ejpam-1481	125	2	iii	iii	X
ejpam-1481	125	3	)	)	PUNCT
ejpam-1481	125	4	σp(∆v	σp(∆v	PROPN
ejpam-1481	125	5	,	,	PUNCT
ejpam-1481	125	6	l1	l1	PROPN
ejpam-1481	125	7	)	)	PUNCT
ejpam-1481	125	8	=	=	SYM
ejpam-1481	126	1	φ	φ	PROPN
ejpam-1481	126	2	.	.	PUNCT
ejpam-1481	126	3	(	(	PUNCT
ejpam-1481	126	4	iv	iv	X
ejpam-1481	126	5	)	)	PUNCT
ejpam-1481	126	6	σp(∆	σp(∆	PROPN
ejpam-1481	126	7	∗	∗	NOUN
ejpam-1481	126	8	v	v	NOUN
ejpam-1481	126	9	,	,	PUNCT
ejpam-1481	126	10	l∗1	l∗1	NOUN
ejpam-1481	126	11	)	)	PUNCT
ejpam-1481	126	12	=	=	SYM
ejpam-1481	126	13	{	{	PUNCT
ejpam-1481	126	14	λ	λ	X
ejpam-1481	126	15	∈	∈	PROPN
ejpam-1481	126	16	c	c	NOUN
ejpam-1481	126	17	:	:	PUNCT
ejpam-1481	126	18	|λ−	|λ−	NOUN
ejpam-1481	126	19	l|	l|	ADJ
ejpam-1481	126	20	≤	≤	ADJ
ejpam-1481	126	21	l	l	NOUN
ejpam-1481	126	22	}	}	PUNCT
ejpam-1481	126	23	.	.	PUNCT
ejpam-1481	127	1	(	(	PUNCT
ejpam-1481	127	2	v	v	NOUN
ejpam-1481	127	3	)	)	PUNCT
ejpam-1481	127	4	σr(∆v	σr(∆v	PROPN
ejpam-1481	127	5	,	,	PUNCT
ejpam-1481	127	6	l1	l1	PROPN
ejpam-1481	127	7	)	)	PUNCT
ejpam-1481	128	1	=	=	PRON
ejpam-1481	128	2	{	{	PUNCT
ejpam-1481	128	3	λ	λ	X
ejpam-1481	128	4	∈	∈	PROPN
ejpam-1481	128	5	c	c	NOUN
ejpam-1481	128	6	:	:	PUNCT
ejpam-1481	128	7	|λ−	|λ−	NOUN
ejpam-1481	128	8	l|	l|	ADJ
ejpam-1481	128	9	≤	≤	ADJ
ejpam-1481	128	10	l	l	NOUN
ejpam-1481	128	11	}	}	PUNCT
ejpam-1481	128	12	.	.	PUNCT
ejpam-1481	129	1	(	(	PUNCT
ejpam-1481	129	2	vi	vi	NOUN
ejpam-1481	129	3	)	)	PUNCT
ejpam-1481	129	4	σc(∆v	σc(∆v	NOUN
ejpam-1481	129	5	,	,	PUNCT
ejpam-1481	129	6	l1	l1	PROPN
ejpam-1481	129	7	)	)	PUNCT
ejpam-1481	130	1	=	=	PUNCT
ejpam-1481	130	2	φ	φ	PROPN
ejpam-1481	130	3	.	.	PUNCT
ejpam-1481	131	1	the	the	DET
ejpam-1481	131	2	results	result	NOUN
ejpam-1481	131	3	(	(	PUNCT
ejpam-1481	131	4	i	i	NOUN
ejpam-1481	131	5	)	)	PUNCT
ejpam-1481	131	6	,	,	PUNCT
ejpam-1481	131	7	(	(	PUNCT
ejpam-1481	131	8	ii	ii	NOUN
ejpam-1481	131	9	)	)	PUNCT
ejpam-1481	131	10	,	,	PUNCT
ejpam-1481	131	11	(	(	PUNCT
ejpam-1481	131	12	iv	iv	X
ejpam-1481	131	13	)	)	PUNCT
ejpam-1481	131	14	and	and	CCONJ
ejpam-1481	131	15	(	(	PUNCT
ejpam-1481	131	16	vi	vi	NOUN
ejpam-1481	131	17	)	)	PUNCT
ejpam-1481	131	18	of	of	ADP
ejpam-1481	131	19	theorem	theorem	NOUN
ejpam-1481	131	20	1	1	NUM
ejpam-1481	131	21	have	have	AUX
ejpam-1481	131	22	been	be	AUX
ejpam-1481	131	23	given	give	VERB
ejpam-1481	131	24	by	by	ADP
ejpam-1481	131	25	srivastava	srivastava	PROPN
ejpam-1481	131	26	and	and	CCONJ
ejpam-1481	131	27	kumar	kumar	PROPN
ejpam-1481	132	1	[	[	X
ejpam-1481	132	2	25	25	NUM
ejpam-1481	132	3	]	]	PUNCT
ejpam-1481	132	4	and	and	CCONJ
ejpam-1481	132	5	the	the	DET
ejpam-1481	132	6	results	result	NOUN
ejpam-1481	132	7	(	(	PUNCT
ejpam-1481	132	8	iii	iii	NOUN
ejpam-1481	132	9	)	)	PUNCT
ejpam-1481	132	10	and	and	CCONJ
ejpam-1481	132	11	(	(	PUNCT
ejpam-1481	132	12	v	v	NOUN
ejpam-1481	132	13	)	)	PUNCT
ejpam-1481	132	14	of	of	ADP
ejpam-1481	132	15	theorem	theorem	NOUN
ejpam-1481	132	16	1	1	NUM
ejpam-1481	132	17	have	have	AUX
ejpam-1481	132	18	been	be	AUX
ejpam-1481	132	19	proved	prove	VERB
ejpam-1481	132	20	by	by	ADP
ejpam-1481	132	21	akhmedov	akhmedov	NOUN
ejpam-1481	132	22	and	and	CCONJ
ejpam-1481	132	23	elshabrawy	elshabrawy	VERB
ejpam-1481	132	24	[	[	X
ejpam-1481	132	25	8	8	NUM
ejpam-1481	132	26	]	]	PUNCT
ejpam-1481	132	27	.	.	PUNCT
ejpam-1481	133	1	to	to	PART
ejpam-1481	133	2	help	help	VERB
ejpam-1481	133	3	understanding	understand	VERB
ejpam-1481	133	4	we	we	PRON
ejpam-1481	133	5	give	give	VERB
ejpam-1481	133	6	the	the	DET
ejpam-1481	133	7	following	follow	VERB
ejpam-1481	133	8	example	example	NOUN
ejpam-1481	133	9	which	which	PRON
ejpam-1481	133	10	disproves	disprove	VERB
ejpam-1481	133	11	the	the	DET
ejpam-1481	133	12	statements	statement	NOUN
ejpam-1481	133	13	of	of	ADP
ejpam-1481	133	14	srivastava	srivastava	PROPN
ejpam-1481	133	15	and	and	CCONJ
ejpam-1481	133	16	kumar	kumar	PROPN
ejpam-1481	134	1	[	[	X
ejpam-1481	134	2	25	25	NUM
ejpam-1481	134	3	]	]	PUNCT
ejpam-1481	134	4	concerning	concern	VERB
ejpam-1481	134	5	the	the	DET
ejpam-1481	134	6	point	point	NOUN
ejpam-1481	134	7	spectrum	spectrum	NOUN
ejpam-1481	134	8	and	and	CCONJ
ejpam-1481	134	9	the	the	DET
ejpam-1481	134	10	residual	residual	ADJ
ejpam-1481	134	11	spectrum	spectrum	NOUN
ejpam-1481	134	12	of	of	ADP
ejpam-1481	134	13	the	the	DET
ejpam-1481	134	14	operator	operator	NOUN
ejpam-1481	134	15	∆v	∆v	PROPN
ejpam-1481	134	16	on	on	ADP
ejpam-1481	134	17	l1	l1	PROPN
ejpam-1481	134	18	.	.	PUNCT
ejpam-1481	135	1	example	example	NOUN
ejpam-1481	136	1	1	1	NUM
ejpam-1481	136	2	.	.	X
ejpam-1481	136	3	consider	consider	VERB
ejpam-1481	136	4	the	the	DET
ejpam-1481	136	5	sequence	sequence	NOUN
ejpam-1481	136	6	(	(	PUNCT
ejpam-1481	136	7	vk	vk	PROPN
ejpam-1481	136	8	)	)	PUNCT
ejpam-1481	136	9	,	,	PUNCT
ejpam-1481	136	10	where	where	SCONJ
ejpam-1481	136	11	vk	vk	X
ejpam-1481	136	12	=	=	SYM
ejpam-1481	136	13	k+2	k+2	PROPN
ejpam-1481	136	14	k+1	k+1	PROPN
ejpam-1481	136	15	,	,	PUNCT
ejpam-1481	136	16	k	k	PROPN
ejpam-1481	136	17	∈	∈	PROPN
ejpam-1481	136	18	n.	n.	NOUN
ejpam-1481	136	19	clearly	clearly	ADV
ejpam-1481	136	20	,	,	PUNCT
ejpam-1481	136	21	(	(	PUNCT
ejpam-1481	136	22	vk	vk	NOUN
ejpam-1481	136	23	)	)	PUNCT
ejpam-1481	136	24	is	be	AUX
ejpam-1481	136	25	a	a	DET
ejpam-1481	136	26	strictly	strictly	ADV
ejpam-1481	136	27	decreasing	decrease	VERB
ejpam-1481	136	28	sequence	sequence	NOUN
ejpam-1481	136	29	of	of	ADP
ejpam-1481	136	30	positive	positive	ADJ
ejpam-1481	136	31	real	real	ADJ
ejpam-1481	136	32	numbers	number	NOUN
ejpam-1481	136	33	satisfying	satisfy	VERB
ejpam-1481	136	34	the	the	DET
ejpam-1481	136	35	conditions	condition	NOUN
ejpam-1481	136	36	(	(	PUNCT
ejpam-1481	136	37	2	2	NUM
ejpam-1481	136	38	)	)	PUNCT
ejpam-1481	136	39	;	;	PUNCT
ejpam-1481	136	40	where	where	SCONJ
ejpam-1481	136	41	lim	lim	PROPN
ejpam-1481	136	42	k→∞	k→∞	NOUN
ejpam-1481	136	43	vk	vk	VERB
ejpam-1481	136	44	=	=	SYM
ejpam-1481	136	45	l	l	NOUN
ejpam-1481	136	46	=	=	SYM
ejpam-1481	136	47	1	1	NUM
ejpam-1481	136	48	,	,	PUNCT
ejpam-1481	136	49	sup	sup	NOUN
ejpam-1481	136	50	k	k	PROPN
ejpam-1481	136	51	vk	vk	PROPN
ejpam-1481	136	52	=	=	SYM
ejpam-1481	136	53	v0	v0	NOUN
ejpam-1481	136	54	=	=	PUNCT
ejpam-1481	136	55	2≤	2≤	NUM
ejpam-1481	136	56	2l	2l	NUM
ejpam-1481	136	57	.	.	PUNCT
ejpam-1481	137	1	we	we	PRON
ejpam-1481	137	2	can	can	AUX
ejpam-1481	137	3	prove	prove	VERB
ejpam-1481	137	4	that	that	DET
ejpam-1481	137	5	v0	v0	NOUN
ejpam-1481	137	6	=	=	SYM
ejpam-1481	137	7	2	2	NUM
ejpam-1481	137	8	/∈	/∈	NOUN
ejpam-1481	137	9	σp(∆v	σp(∆v	NOUN
ejpam-1481	137	10	,	,	PUNCT
ejpam-1481	137	11	l1	l1	PROPN
ejpam-1481	137	12	)	)	PUNCT
ejpam-1481	137	13	.	.	PUNCT
ejpam-1481	138	1	indeed	indeed	ADV
ejpam-1481	138	2	,	,	PUNCT
ejpam-1481	138	3	suppose	suppose	VERB
ejpam-1481	138	4	for	for	ADP
ejpam-1481	138	5	contrary	contrary	ADJ
ejpam-1481	138	6	that	that	SCONJ
ejpam-1481	138	7	there	there	PRON
ejpam-1481	138	8	exists	exist	VERB
ejpam-1481	138	9	x	x	X
ejpam-1481	138	10	=	=	SYM
ejpam-1481	138	11	(	(	PUNCT
ejpam-1481	138	12	xk	xk	PROPN
ejpam-1481	138	13	)	)	PUNCT
ejpam-1481	138	14	6=	6=	NUM
ejpam-1481	139	1	θ	θ	PROPN
ejpam-1481	139	2	in	in	ADP
ejpam-1481	139	3	l1	l1	PROPN
ejpam-1481	139	4	such	such	ADJ
ejpam-1481	139	5	that	that	DET
ejpam-1481	139	6	∆v	∆v	PROPN
ejpam-1481	139	7	x	x	PUNCT
ejpam-1481	140	1	=	=	SYM
ejpam-1481	140	2	v0	v0	PROPN
ejpam-1481	140	3	x.	x.	NOUN
ejpam-1481	140	4	then	then	ADV
ejpam-1481	140	5	(	(	PUNCT
ejpam-1481	140	6	v0	v0	NOUN
ejpam-1481	140	7	−	−	NOUN
ejpam-1481	140	8	v0)x0	v0)x0	NOUN
ejpam-1481	140	9	=	=	NOUN
ejpam-1481	140	10	0	0	NUM
ejpam-1481	140	11	and	and	CCONJ
ejpam-1481	140	12	−	−	PROPN
ejpam-1481	140	13	vk	vk	X
ejpam-1481	140	14	xk	xk	PROPN
ejpam-1481	141	1	+	+	CCONJ
ejpam-1481	141	2	(	(	PUNCT
ejpam-1481	141	3	vk+1−	vk+1−	PROPN
ejpam-1481	141	4	v0)xk+1	v0)xk+1	NOUN
ejpam-1481	141	5	=	=	SYM
ejpam-1481	141	6	0	0	NUM
ejpam-1481	141	7	,	,	PUNCT
ejpam-1481	141	8	for	for	ADP
ejpam-1481	141	9	all	all	DET
ejpam-1481	141	10	k	k	PROPN
ejpam-1481	141	11	∈	∈	PROPN
ejpam-1481	141	12	n.	n.	NOUN
ejpam-1481	141	13	if	if	SCONJ
ejpam-1481	141	14	x0	x0	PROPN
ejpam-1481	141	15	=	=	SYM
ejpam-1481	141	16	0	0	NUM
ejpam-1481	141	17	,	,	PUNCT
ejpam-1481	141	18	then	then	ADV
ejpam-1481	141	19	xk	xk	PROPN
ejpam-1481	141	20	=	=	PUNCT
ejpam-1481	141	21	0	0	PROPN
ejpam-1481	141	22	,	,	PUNCT
ejpam-1481	141	23	for	for	ADP
ejpam-1481	141	24	all	all	DET
ejpam-1481	141	25	k	k	PROPN
ejpam-1481	141	26	≥	≥	NUM
ejpam-1481	141	27	1	1	NUM
ejpam-1481	141	28	,	,	PUNCT
ejpam-1481	141	29	and	and	CCONJ
ejpam-1481	141	30	so	so	ADV
ejpam-1481	141	31	we	we	PRON
ejpam-1481	141	32	have	have	VERB
ejpam-1481	141	33	a	a	DET
ejpam-1481	141	34	contradiction	contradiction	NOUN
ejpam-1481	141	35	since	since	SCONJ
ejpam-1481	141	36	x	x	PROPN
ejpam-1481	141	37	6=	6=	NUM
ejpam-1481	141	38	θ	θ	NOUN
ejpam-1481	141	39	.	.	PUNCT
ejpam-1481	142	1	also	also	ADV
ejpam-1481	142	2	,	,	PUNCT
ejpam-1481	142	3	if	if	SCONJ
ejpam-1481	142	4	x0	x0	PROPN
ejpam-1481	142	5	6=	6=	ADP
ejpam-1481	142	6	0	0	NUM
ejpam-1481	142	7	then	then	ADV
ejpam-1481	142	8	we	we	PRON
ejpam-1481	142	9	can	can	AUX
ejpam-1481	142	10	easily	easily	ADV
ejpam-1481	142	11	see	see	VERB
ejpam-1481	142	12	that	that	SCONJ
ejpam-1481	142	13	�	�	PROPN
ejpam-1481	142	14	�	�	PROPN
ejpam-1481	142	15	xk	xk	PROPN
ejpam-1481	142	16	�	�	PROPN
ejpam-1481	142	17	�	�	PROPN
ejpam-1481	142	18	≥	≥	PROPN
ejpam-1481	142	19	�	�	PROPN
ejpam-1481	142	20	�	�	PROPN
ejpam-1481	142	21	x0	x0	PROPN
ejpam-1481	142	22	�	�	PROPN
ejpam-1481	142	23	�	�	PROPN
ejpam-1481	142	24	,	,	PUNCT
ejpam-1481	142	25	for	for	ADP
ejpam-1481	142	26	all	all	DET
ejpam-1481	142	27	k	k	PROPN
ejpam-1481	142	28	≥	≥	NUM
ejpam-1481	142	29	1	1	NUM
ejpam-1481	142	30	,	,	PUNCT
ejpam-1481	142	31	a.	a.	PROPN
ejpam-1481	142	32	akhmedov	akhmedov	PROPN
ejpam-1481	142	33	,	,	PUNCT
ejpam-1481	142	34	s.	s.	PROPN
ejpam-1481	142	35	el	el	PROPN
ejpam-1481	142	36	-	-	PUNCT
ejpam-1481	142	37	shabrawy	shabrawy	PROPN
ejpam-1481	142	38	/	/	SYM
ejpam-1481	142	39	eur	eur	NOUN
ejpam-1481	142	40	.	.	PUNCT
ejpam-1481	143	1	j.	j.	PROPN
ejpam-1481	143	2	pure	pure	PROPN
ejpam-1481	143	3	appl	appl	PROPN
ejpam-1481	143	4	.	.	PROPN
ejpam-1481	143	5	math	math	PROPN
ejpam-1481	143	6	,	,	PUNCT
ejpam-1481	143	7	5	5	NUM
ejpam-1481	143	8	(	(	PUNCT
ejpam-1481	143	9	2012	2012	NUM
ejpam-1481	143	10	)	)	PUNCT
ejpam-1481	143	11	,	,	PUNCT
ejpam-1481	143	12	59	59	NUM
ejpam-1481	143	13	-	-	SYM
ejpam-1481	143	14	74	74	NUM
ejpam-1481	143	15	64	64	NUM
ejpam-1481	144	1	and	and	CCONJ
ejpam-1481	144	2	so	so	ADV
ejpam-1481	144	3	we	we	PRON
ejpam-1481	144	4	have	have	VERB
ejpam-1481	144	5	a	a	DET
ejpam-1481	144	6	contradiction	contradiction	NOUN
ejpam-1481	144	7	since	since	SCONJ
ejpam-1481	144	8	x	x	PROPN
ejpam-1481	144	9	∈	∈	PROPN
ejpam-1481	144	10	l1	l1	PROPN
ejpam-1481	144	11	.	.	PUNCT
ejpam-1481	145	1	then	then	ADV
ejpam-1481	145	2	v0	v0	PROPN
ejpam-1481	145	3	/∈	/∈	PUNCT
ejpam-1481	146	1	σp(∆v	σp(∆v	PROPN
ejpam-1481	146	2	,	,	PUNCT
ejpam-1481	146	3	l1	l1	PROPN
ejpam-1481	146	4	)	)	PUNCT
ejpam-1481	146	5	.	.	PUNCT
ejpam-1481	147	1	similarly	similarly	ADV
ejpam-1481	147	2	,	,	PUNCT
ejpam-1481	147	3	we	we	PRON
ejpam-1481	147	4	can	can	AUX
ejpam-1481	147	5	prove	prove	VERB
ejpam-1481	147	6	that	that	DET
ejpam-1481	147	7	vk	vk	PROPN
ejpam-1481	147	8	/∈	/∈	PUNCT
ejpam-1481	147	9	σp(∆v	σp(∆v	NOUN
ejpam-1481	147	10	,	,	PUNCT
ejpam-1481	147	11	l1	l1	PROPN
ejpam-1481	147	12	)	)	PUNCT
ejpam-1481	147	13	for	for	ADP
ejpam-1481	147	14	all	all	DET
ejpam-1481	147	15	k	k	PROPN
ejpam-1481	147	16	≥	≥	NUM
ejpam-1481	147	17	1	1	NUM
ejpam-1481	147	18	.	.	PUNCT
ejpam-1481	147	19	thus	thus	ADV
ejpam-1481	147	20	σp(∆v	σp(∆v	ADP
ejpam-1481	147	21	,	,	PUNCT
ejpam-1481	147	22	l1	l1	PROPN
ejpam-1481	147	23	)	)	PUNCT
ejpam-1481	147	24	=	=	SYM
ejpam-1481	148	1	φ	φ	PROPN
ejpam-1481	148	2	.	.	PUNCT
ejpam-1481	149	1	now	now	ADV
ejpam-1481	149	2	,	,	PUNCT
ejpam-1481	149	3	the	the	DET
ejpam-1481	149	4	operator	operator	NOUN
ejpam-1481	149	5	∆v	∆v	PROPN
ejpam-1481	149	6	−	−	PROPN
ejpam-1481	149	7	v0i	v0i	VERB
ejpam-1481	149	8	on	on	ADP
ejpam-1481	149	9	l1	l1	PROPN
ejpam-1481	149	10	is	be	AUX
ejpam-1481	149	11	defined	define	VERB
ejpam-1481	149	12	by	by	ADP
ejpam-1481	149	13	(	(	PUNCT
ejpam-1481	149	14	∆v	∆v	PROPN
ejpam-1481	149	15	−	−	NOUN
ejpam-1481	149	16	v0i)x	v0i)x	NOUN
ejpam-1481	149	17	=	=	X
ejpam-1481	149	18	(	(	PUNCT
ejpam-1481	149	19	0,−v0x0	0,−v0x0	NOUN
ejpam-1481	149	20	+	+	CCONJ
ejpam-1481	149	21	(	(	PUNCT
ejpam-1481	149	22	v1−	v1−	PROPN
ejpam-1481	149	23	v0)x1,−v1	v0)x1,−v1	PROPN
ejpam-1481	149	24	x1	x1	PROPN
ejpam-1481	150	1	+	+	CCONJ
ejpam-1481	150	2	(	(	PUNCT
ejpam-1481	150	3	v2−	v2−	PROPN
ejpam-1481	150	4	v0)x2	v0)x2	NOUN
ejpam-1481	150	5	,	,	PUNCT
ejpam-1481	150	6	.	.	PUNCT
ejpam-1481	150	7	.	.	PUNCT
ejpam-1481	150	8	.	.	PUNCT
ejpam-1481	150	9	)	)	PUNCT
ejpam-1481	150	10	,	,	PUNCT
ejpam-1481	150	11	(	(	PUNCT
ejpam-1481	150	12	7	7	X
ejpam-1481	150	13	)	)	PUNCT
ejpam-1481	150	14	where	where	SCONJ
ejpam-1481	150	15	x	x	SYM
ejpam-1481	150	16	=	=	SYM
ejpam-1481	150	17	(	(	PUNCT
ejpam-1481	150	18	xk	xk	ADJ
ejpam-1481	150	19	)	)	PUNCT
ejpam-1481	150	20	∈	∈	PROPN
ejpam-1481	150	21	l1	l1	PROPN
ejpam-1481	150	22	.	.	PUNCT
ejpam-1481	151	1	the	the	DET
ejpam-1481	151	2	operator	operator	NOUN
ejpam-1481	151	3	(	(	PUNCT
ejpam-1481	151	4	∆v	∆v	PROPN
ejpam-1481	151	5	−	−	PROPN
ejpam-1481	151	6	v0	v0	NOUN
ejpam-1481	151	7	i)−1	i)−1	NOUN
ejpam-1481	151	8	exists	exist	VERB
ejpam-1481	151	9	since	since	SCONJ
ejpam-1481	151	10	v0	v0	NOUN
ejpam-1481	151	11	/∈	/∈	PUNCT
ejpam-1481	151	12	σp(∆v	σp(∆v	PROPN
ejpam-1481	151	13	,	,	PUNCT
ejpam-1481	151	14	l1	l1	PROPN
ejpam-1481	151	15	)	)	PUNCT
ejpam-1481	151	16	.	.	PUNCT
ejpam-1481	152	1	but	but	CCONJ
ejpam-1481	152	2	(	(	PUNCT
ejpam-1481	152	3	∆v	∆v	PROPN
ejpam-1481	152	4	−	−	PROPN
ejpam-1481	152	5	v0	v0	NOUN
ejpam-1481	152	6	i)−1	i)−1	NOUN
ejpam-1481	152	7	does	do	AUX
ejpam-1481	152	8	not	not	PART
ejpam-1481	152	9	satisfy	satisfy	VERB
ejpam-1481	152	10	(	(	PUNCT
ejpam-1481	152	11	r3	r3	PROPN
ejpam-1481	152	12	)	)	PUNCT
ejpam-1481	152	13	.	.	PUNCT
ejpam-1481	153	1	indeed	indeed	ADV
ejpam-1481	153	2	,	,	PUNCT
ejpam-1481	153	3	consider	consider	VERB
ejpam-1481	153	4	the	the	DET
ejpam-1481	153	5	sequence	sequence	NOUN
ejpam-1481	153	6	y	y	PROPN
ejpam-1481	153	7	=	=	SYM
ejpam-1481	153	8	(	(	PUNCT
ejpam-1481	153	9	1,0,0	1,0,0	NUM
ejpam-1481	153	10	,	,	PUNCT
ejpam-1481	153	11	.	.	PUNCT
ejpam-1481	153	12	.	.	PUNCT
ejpam-1481	153	13	.	.	PUNCT
ejpam-1481	153	14	)	)	PUNCT
ejpam-1481	154	1	in	in	ADP
ejpam-1481	154	2	l1	l1	PROPN
ejpam-1481	154	3	and	and	CCONJ
ejpam-1481	154	4	let	let	VERB
ejpam-1481	154	5	y	y	PRON
ejpam-1481	154	6	be	be	AUX
ejpam-1481	154	7	the	the	DET
ejpam-1481	154	8	center	center	NOUN
ejpam-1481	154	9	of	of	ADP
ejpam-1481	154	10	a	a	DET
ejpam-1481	154	11	small	small	ADJ
ejpam-1481	154	12	ball	ball	NOUN
ejpam-1481	154	13	,	,	PUNCT
ejpam-1481	154	14	say	say	INTJ
ejpam-1481	154	15	,	,	PUNCT
ejpam-1481	154	16	of	of	ADP
ejpam-1481	154	17	radius	radius	NOUN
ejpam-1481	154	18	1/3	1/3	NUM
ejpam-1481	154	19	.	.	PUNCT
ejpam-1481	155	1	clearly	clearly	ADV
ejpam-1481	155	2	,	,	PUNCT
ejpam-1481	155	3	by	by	ADP
ejpam-1481	155	4	(	(	PUNCT
ejpam-1481	155	5	7	7	NUM
ejpam-1481	155	6	)	)	PUNCT
ejpam-1481	155	7	,	,	PUNCT
ejpam-1481	155	8	this	this	DET
ejpam-1481	155	9	ball	ball	NOUN
ejpam-1481	155	10	does	do	AUX
ejpam-1481	155	11	not	not	PART
ejpam-1481	155	12	intersect	intersect	VERB
ejpam-1481	155	13	the	the	DET
ejpam-1481	155	14	range	range	NOUN
ejpam-1481	155	15	of	of	ADP
ejpam-1481	155	16	the	the	DET
ejpam-1481	155	17	operator	operator	NOUN
ejpam-1481	155	18	∆v	∆v	PROPN
ejpam-1481	156	1	−	−	PROPN
ejpam-1481	156	2	v0	v0	NOUN
ejpam-1481	156	3	i	i	PRON
ejpam-1481	156	4	.	.	PUNCT
ejpam-1481	157	1	then	then	ADV
ejpam-1481	157	2	,	,	PUNCT
ejpam-1481	157	3	the	the	DET
ejpam-1481	157	4	operator	operator	NOUN
ejpam-1481	157	5	∆v	∆v	PROPN
ejpam-1481	157	6	−	−	PROPN
ejpam-1481	157	7	v0	v0	NOUN
ejpam-1481	157	8	i	i	PRON
ejpam-1481	157	9	does	do	AUX
ejpam-1481	157	10	not	not	PART
ejpam-1481	157	11	have	have	VERB
ejpam-1481	157	12	a	a	DET
ejpam-1481	157	13	dense	dense	ADJ
ejpam-1481	157	14	range	range	NOUN
ejpam-1481	157	15	in	in	ADP
ejpam-1481	157	16	l1	l1	PROPN
ejpam-1481	157	17	.	.	PUNCT
ejpam-1481	158	1	hence	hence	ADV
ejpam-1481	158	2	,	,	PUNCT
ejpam-1481	158	3	by	by	ADP
ejpam-1481	158	4	definition	definition	NOUN
ejpam-1481	158	5	,	,	PUNCT
ejpam-1481	158	6	v0	v0	PROPN
ejpam-1481	158	7	∈	∈	PROPN
ejpam-1481	158	8	σr(∆v	σr(∆v	PROPN
ejpam-1481	158	9	,	,	PUNCT
ejpam-1481	158	10	l1	l1	PROPN
ejpam-1481	158	11	)	)	PUNCT
ejpam-1481	158	12	.	.	PUNCT
ejpam-1481	159	1	3.2	3.2	NUM
ejpam-1481	159	2	.	.	PUNCT
ejpam-1481	160	1	the	the	DET
ejpam-1481	160	2	fine	fine	ADJ
ejpam-1481	160	3	spectrum	spectrum	NOUN
ejpam-1481	160	4	of	of	ADP
ejpam-1481	160	5	the	the	DET
ejpam-1481	160	6	operator	operator	NOUN
ejpam-1481	160	7	∆	∆	X
ejpam-1481	160	8	v	v	NOUN
ejpam-1481	160	9	on	on	ADP
ejpam-1481	160	10	c0	c0	PROPN
ejpam-1481	160	11	srivastava	srivastava	PROPN
ejpam-1481	160	12	and	and	CCONJ
ejpam-1481	160	13	kumar	kumar	PROPN
ejpam-1481	160	14	[	[	X
ejpam-1481	160	15	24	24	NUM
ejpam-1481	160	16	]	]	PUNCT
ejpam-1481	160	17	investigated	investigate	VERB
ejpam-1481	160	18	the	the	DET
ejpam-1481	160	19	fine	fine	ADJ
ejpam-1481	160	20	spectrum	spectrum	NOUN
ejpam-1481	160	21	of	of	ADP
ejpam-1481	160	22	the	the	DET
ejpam-1481	160	23	operator	operator	NOUN
ejpam-1481	160	24	∆v	∆v	PROPN
ejpam-1481	160	25	on	on	ADP
ejpam-1481	160	26	the	the	DET
ejpam-1481	160	27	sequence	sequence	NOUN
ejpam-1481	160	28	space	space	NOUN
ejpam-1481	160	29	c0	c0	NOUN
ejpam-1481	160	30	.	.	PUNCT
ejpam-1481	161	1	but	but	CCONJ
ejpam-1481	161	2	,	,	PUNCT
ejpam-1481	161	3	incorrect	incorrect	ADJ
ejpam-1481	161	4	results	result	NOUN
ejpam-1481	161	5	are	be	AUX
ejpam-1481	161	6	also	also	ADV
ejpam-1481	161	7	obtained	obtain	VERB
ejpam-1481	161	8	.	.	PUNCT
ejpam-1481	162	1	akhmedov	akhmedov	PROPN
ejpam-1481	162	2	and	and	CCONJ
ejpam-1481	162	3	el	el	NOUN
ejpam-1481	162	4	-	-	PUNCT
ejpam-1481	162	5	shabrawy	shabrawy	PROPN
ejpam-1481	163	1	[	[	X
ejpam-1481	163	2	7	7	X
ejpam-1481	163	3	]	]	PUNCT
ejpam-1481	163	4	have	have	AUX
ejpam-1481	163	5	proved	prove	VERB
ejpam-1481	163	6	by	by	ADP
ejpam-1481	163	7	a	a	DET
ejpam-1481	163	8	counterexample	counterexample	NOUN
ejpam-1481	163	9	that	that	SCONJ
ejpam-1481	163	10	the	the	DET
ejpam-1481	163	11	results	result	NOUN
ejpam-1481	163	12	concerning	concern	VERB
ejpam-1481	163	13	the	the	DET
ejpam-1481	163	14	point	point	NOUN
ejpam-1481	163	15	spectrum	spectrum	NOUN
ejpam-1481	163	16	,	,	PUNCT
ejpam-1481	163	17	the	the	DET
ejpam-1481	163	18	residual	residual	ADJ
ejpam-1481	163	19	spectrum	spectrum	NOUN
ejpam-1481	163	20	and	and	CCONJ
ejpam-1481	163	21	the	the	DET
ejpam-1481	163	22	continuous	continuous	ADJ
ejpam-1481	163	23	spectrum	spectrum	NOUN
ejpam-1481	163	24	are	be	AUX
ejpam-1481	163	25	incorrect	incorrect	ADJ
ejpam-1481	163	26	.	.	PUNCT
ejpam-1481	164	1	in	in	ADP
ejpam-1481	164	2	this	this	DET
ejpam-1481	164	3	subsection	subsection	NOUN
ejpam-1481	164	4	we	we	PRON
ejpam-1481	164	5	summarize	summarize	VERB
ejpam-1481	164	6	the	the	DET
ejpam-1481	164	7	main	main	ADJ
ejpam-1481	164	8	results	result	NOUN
ejpam-1481	164	9	.	.	PUNCT
ejpam-1481	165	1	theorem	theorem	NOUN
ejpam-1481	165	2	2	2	NUM
ejpam-1481	165	3	.	.	PUNCT
ejpam-1481	166	1	the	the	DET
ejpam-1481	166	2	operator	operator	NOUN
ejpam-1481	166	3	∆v	∆v	PROPN
ejpam-1481	166	4	:	:	PUNCT
ejpam-1481	166	5	c0	c0	PROPN
ejpam-1481	166	6	−→	−→	PROPN
ejpam-1481	166	7	c0	c0	PROPN
ejpam-1481	166	8	is	be	AUX
ejpam-1481	166	9	a	a	DET
ejpam-1481	166	10	bounded	bounded	ADJ
ejpam-1481	166	11	linear	linear	ADJ
ejpam-1481	166	12	operator	operator	NOUN
ejpam-1481	166	13	and	and	CCONJ
ejpam-1481	166	14	(	(	PUNCT
ejpam-1481	166	15	i	i	NOUN
ejpam-1481	166	16	)	)	PUNCT
ejpam-1481	166	17	∆v	∆v	PROPN
ejpam-1481	166	18	c0	c0	NOUN
ejpam-1481	166	19	=	=	PROPN
ejpam-1481	166	20	v0	v0	PROPN
ejpam-1481	166	21	+	+	CCONJ
ejpam-1481	166	22	v1	v1	NOUN
ejpam-1481	166	23	.	.	PUNCT
ejpam-1481	167	1	(	(	PUNCT
ejpam-1481	167	2	ii	ii	NOUN
ejpam-1481	167	3	)	)	PUNCT
ejpam-1481	167	4	σ(∆v	σ(∆v	NOUN
ejpam-1481	167	5	,	,	PUNCT
ejpam-1481	167	6	c0	c0	NOUN
ejpam-1481	167	7	)	)	PUNCT
ejpam-1481	167	8	=	=	SYM
ejpam-1481	167	9	{	{	PUNCT
ejpam-1481	167	10	λ	λ	X
ejpam-1481	167	11	∈	∈	PROPN
ejpam-1481	167	12	c	c	NOUN
ejpam-1481	167	13	:	:	PUNCT
ejpam-1481	167	14	|λ−	|λ−	NOUN
ejpam-1481	167	15	l|	l|	ADJ
ejpam-1481	167	16	≤	≤	ADJ
ejpam-1481	167	17	l	l	NOUN
ejpam-1481	167	18	}	}	PUNCT
ejpam-1481	167	19	.	.	PUNCT
ejpam-1481	168	1	(	(	PUNCT
ejpam-1481	168	2	iii	iii	X
ejpam-1481	168	3	)	)	PUNCT
ejpam-1481	168	4	σp(∆v	σp(∆v	PROPN
ejpam-1481	168	5	,	,	PUNCT
ejpam-1481	168	6	c0	c0	NOUN
ejpam-1481	168	7	)	)	PUNCT
ejpam-1481	169	1	=	=	PUNCT
ejpam-1481	169	2	∅.	∅.	ADP
ejpam-1481	169	3	the	the	DET
ejpam-1481	169	4	bounded	bounded	ADJ
ejpam-1481	169	5	linearity	linearity	NOUN
ejpam-1481	169	6	of	of	ADP
ejpam-1481	169	7	the	the	DET
ejpam-1481	169	8	operator	operator	NOUN
ejpam-1481	169	9	∆v	∆v	PROPN
ejpam-1481	169	10	on	on	ADP
ejpam-1481	169	11	c0	c0	PROPN
ejpam-1481	169	12	has	have	AUX
ejpam-1481	169	13	been	be	AUX
ejpam-1481	169	14	given	give	VERB
ejpam-1481	169	15	by	by	ADP
ejpam-1481	169	16	the	the	DET
ejpam-1481	169	17	srivastava	srivastava	PROPN
ejpam-1481	169	18	and	and	CCONJ
ejpam-1481	169	19	kumar	kumar	PROPN
ejpam-1481	169	20	[	[	X
ejpam-1481	169	21	24	24	NUM
ejpam-1481	169	22	]	]	PUNCT
ejpam-1481	169	23	and	and	CCONJ
ejpam-1481	169	24	the	the	DET
ejpam-1481	169	25	norm	norm	NOUN
ejpam-1481	169	26	of	of	ADP
ejpam-1481	169	27	the	the	DET
ejpam-1481	169	28	operator	operator	NOUN
ejpam-1481	169	29	∆v	∆v	PROPN
ejpam-1481	169	30	on	on	ADP
ejpam-1481	169	31	c0	c0	PROPN
ejpam-1481	169	32	has	have	AUX
ejpam-1481	169	33	been	be	AUX
ejpam-1481	169	34	revised	revise	VERB
ejpam-1481	169	35	by	by	ADP
ejpam-1481	169	36	akhmedov	akhmedov	NOUN
ejpam-1481	169	37	and	and	CCONJ
ejpam-1481	169	38	elshabrawy	elshabrawy	VERB
ejpam-1481	169	39	[	[	X
ejpam-1481	169	40	7	7	NUM
ejpam-1481	169	41	]	]	PUNCT
ejpam-1481	169	42	.	.	PUNCT
ejpam-1481	170	1	also	also	ADV
ejpam-1481	170	2	,	,	PUNCT
ejpam-1481	170	3	the	the	DET
ejpam-1481	170	4	result	result	NOUN
ejpam-1481	170	5	(	(	PUNCT
ejpam-1481	170	6	ii	ii	NOUN
ejpam-1481	170	7	)	)	PUNCT
ejpam-1481	170	8	of	of	ADP
ejpam-1481	170	9	theorem	theorem	NOUN
ejpam-1481	170	10	2	2	NUM
ejpam-1481	170	11	has	have	AUX
ejpam-1481	170	12	been	be	AUX
ejpam-1481	170	13	proved	prove	VERB
ejpam-1481	170	14	by	by	ADP
ejpam-1481	170	15	srivastava	srivastava	PROPN
ejpam-1481	170	16	and	and	CCONJ
ejpam-1481	170	17	kumar	kumar	PROPN
ejpam-1481	171	1	[	[	X
ejpam-1481	171	2	24	24	NUM
ejpam-1481	171	3	]	]	PUNCT
ejpam-1481	171	4	and	and	CCONJ
ejpam-1481	171	5	the	the	DET
ejpam-1481	171	6	result	result	NOUN
ejpam-1481	171	7	(	(	PUNCT
ejpam-1481	171	8	iii	iii	NOUN
ejpam-1481	171	9	)	)	PUNCT
ejpam-1481	171	10	of	of	ADP
ejpam-1481	171	11	theorem	theorem	NOUN
ejpam-1481	171	12	2	2	NUM
ejpam-1481	171	13	has	have	AUX
ejpam-1481	171	14	been	be	AUX
ejpam-1481	171	15	proved	prove	VERB
ejpam-1481	171	16	by	by	ADP
ejpam-1481	171	17	akhmedov	akhmedov	PROPN
ejpam-1481	171	18	and	and	CCONJ
ejpam-1481	171	19	el	el	NOUN
ejpam-1481	171	20	-	-	PUNCT
ejpam-1481	171	21	shabrawy	shabrawy	PROPN
ejpam-1481	172	1	[	[	X
ejpam-1481	172	2	7	7	NUM
ejpam-1481	172	3	]	]	PUNCT
ejpam-1481	172	4	.	.	PUNCT
ejpam-1481	173	1	the	the	DET
ejpam-1481	173	2	results	result	NOUN
ejpam-1481	173	3	concerning	concern	VERB
ejpam-1481	173	4	the	the	DET
ejpam-1481	173	5	point	point	NOUN
ejpam-1481	173	6	spectrum	spectrum	NOUN
ejpam-1481	173	7	of	of	ADP
ejpam-1481	173	8	the	the	DET
ejpam-1481	173	9	adjoint	adjoint	NOUN
ejpam-1481	173	10	operator	operator	NOUN
ejpam-1481	173	11	∆∗v	∆∗v	NOUN
ejpam-1481	173	12	of	of	ADP
ejpam-1481	173	13	∆v	∆v	PROPN
ejpam-1481	173	14	are	be	AUX
ejpam-1481	173	15	given	give	VERB
ejpam-1481	173	16	by	by	ADP
ejpam-1481	173	17	the	the	DET
ejpam-1481	173	18	following	follow	VERB
ejpam-1481	173	19	theorem	theorem	PROPN
ejpam-1481	173	20	.	.	PUNCT
ejpam-1481	174	1	theorem	theorem	NOUN
ejpam-1481	174	2	3	3	NUM
ejpam-1481	174	3	(	(	PUNCT
ejpam-1481	174	4	[	[	X
ejpam-1481	174	5	7	7	NUM
ejpam-1481	174	6	]	]	NUM
ejpam-1481	174	7	)	)	PUNCT
ejpam-1481	174	8	.	.	PUNCT
ejpam-1481	175	1	(	(	PUNCT
ejpam-1481	175	2	i	i	NOUN
ejpam-1481	175	3	)	)	PUNCT
ejpam-1481	175	4	{	{	PUNCT
ejpam-1481	175	5	λ	λ	X
ejpam-1481	175	6	∈	∈	PROPN
ejpam-1481	175	7	c	c	NOUN
ejpam-1481	175	8	:	:	PUNCT
ejpam-1481	175	9	|λ−	|λ−	NOUN
ejpam-1481	175	10	l|	l|	ADJ
ejpam-1481	175	11	<	<	X
ejpam-1481	175	12	l	l	NOUN
ejpam-1481	175	13	}	}	PUNCT
ejpam-1481	175	14	∪	∪	ADP
ejpam-1481	175	15	�	�	PROPN
ejpam-1481	175	16	v0	v0	NOUN
ejpam-1481	175	17	⊆	⊆	NUM
ejpam-1481	175	18	σp(∆	σp(∆	PROPN
ejpam-1481	175	19	∗	∗	NOUN
ejpam-1481	175	20	v	v	NOUN
ejpam-1481	175	21	,	,	PUNCT
ejpam-1481	175	22	c∗0	c∗0	NOUN
ejpam-1481	175	23	)	)	PUNCT
ejpam-1481	175	24	,	,	PUNCT
ejpam-1481	175	25	(	(	PUNCT
ejpam-1481	175	26	ii	ii	NOUN
ejpam-1481	175	27	)	)	PUNCT
ejpam-1481	176	1	¨	¨	NOUN
ejpam-1481	176	2	λ	λ	X
ejpam-1481	176	3	∈	∈	PROPN
ejpam-1481	176	4	c	c	NOUN
ejpam-1481	176	5	:	:	PUNCT
ejpam-1481	176	6	sup	sup	PROPN
ejpam-1481	176	7	k	k	PROPN
ejpam-1481	176	8	�	�	PROPN
ejpam-1481	176	9	�	�	PROPN
ejpam-1481	176	10	�	�	PROPN
ejpam-1481	176	11	λ−vk	λ−vk	PROPN
ejpam-1481	176	12	vk	vk	PROPN
ejpam-1481	176	13	�	�	PROPN
ejpam-1481	176	14	�	�	PROPN
ejpam-1481	176	15	�	�	PROPN
ejpam-1481	176	16	<	<	X
ejpam-1481	176	17	1	1	NUM
ejpam-1481	176	18	«	«	SYM
ejpam-1481	176	19	⊆	⊆	NUM
ejpam-1481	176	20	σp(∆	σp(∆	PROPN
ejpam-1481	176	21	∗	∗	NOUN
ejpam-1481	176	22	v	v	NOUN
ejpam-1481	176	23	,	,	PUNCT
ejpam-1481	176	24	c∗0	c∗0	NOUN
ejpam-1481	176	25	)	)	PUNCT
ejpam-1481	176	26	,	,	PUNCT
ejpam-1481	176	27	(	(	PUNCT
ejpam-1481	176	28	iii	iii	X
ejpam-1481	176	29	)	)	PUNCT
ejpam-1481	176	30	σp(∆	σp(∆	NOUN
ejpam-1481	176	31	∗	∗	NOUN
ejpam-1481	176	32	v	v	NOUN
ejpam-1481	176	33	,	,	PUNCT
ejpam-1481	176	34	c∗0)⊆	c∗0)⊆	ADJ
ejpam-1481	176	35	§	§	PROPN
ejpam-1481	176	36	λ	λ	X
ejpam-1481	176	37	∈	∈	PROPN
ejpam-1481	176	38	c	c	PROPN
ejpam-1481	176	39	:	:	PUNCT
ejpam-1481	176	40	inf	inf	PROPN
ejpam-1481	176	41	k	k	PROPN
ejpam-1481	176	42	�	�	PROPN
ejpam-1481	176	43	�	�	PROPN
ejpam-1481	176	44	�	�	PROPN
ejpam-1481	176	45	λ−vk	λ−vk	PROPN
ejpam-1481	176	46	vk	vk	PROPN
ejpam-1481	176	47	�	�	PROPN
ejpam-1481	176	48	�	�	PROPN
ejpam-1481	176	49	�	�	PROPN
ejpam-1481	176	50	<	<	X
ejpam-1481	176	51	1	1	NUM
ejpam-1481	176	52	ª	ª	X
ejpam-1481	176	53	.	.	PUNCT
ejpam-1481	177	1	we	we	PRON
ejpam-1481	177	2	give	give	VERB
ejpam-1481	177	3	the	the	DET
ejpam-1481	177	4	following	follow	VERB
ejpam-1481	177	5	example	example	NOUN
ejpam-1481	177	6	to	to	PART
ejpam-1481	177	7	support	support	VERB
ejpam-1481	177	8	the	the	DET
ejpam-1481	177	9	results	result	NOUN
ejpam-1481	177	10	in	in	ADP
ejpam-1481	177	11	theorem	theorem	NOUN
ejpam-1481	177	12	3	3	NUM
ejpam-1481	177	13	.	.	PUNCT
ejpam-1481	177	14	a.	a.	PROPN
ejpam-1481	177	15	akhmedov	akhmedov	PROPN
ejpam-1481	177	16	,	,	PUNCT
ejpam-1481	177	17	s.	s.	PROPN
ejpam-1481	177	18	el	el	PROPN
ejpam-1481	177	19	-	-	PUNCT
ejpam-1481	177	20	shabrawy	shabrawy	PROPN
ejpam-1481	177	21	/	/	SYM
ejpam-1481	177	22	eur	eur	NOUN
ejpam-1481	177	23	.	.	PUNCT
ejpam-1481	178	1	j.	j.	PROPN
ejpam-1481	178	2	pure	pure	PROPN
ejpam-1481	178	3	appl	appl	PROPN
ejpam-1481	178	4	.	.	PROPN
ejpam-1481	178	5	math	math	PROPN
ejpam-1481	178	6	,	,	PUNCT
ejpam-1481	178	7	5	5	NUM
ejpam-1481	178	8	(	(	PUNCT
ejpam-1481	178	9	2012	2012	NUM
ejpam-1481	178	10	)	)	PUNCT
ejpam-1481	178	11	,	,	PUNCT
ejpam-1481	178	12	59	59	NUM
ejpam-1481	178	13	-	-	SYM
ejpam-1481	178	14	74	74	NUM
ejpam-1481	178	15	65	65	NUM
ejpam-1481	178	16	example	example	NOUN
ejpam-1481	178	17	2	2	NUM
ejpam-1481	178	18	.	.	X
ejpam-1481	178	19	consider	consider	VERB
ejpam-1481	178	20	the	the	DET
ejpam-1481	178	21	sequence	sequence	NOUN
ejpam-1481	178	22	(	(	PUNCT
ejpam-1481	178	23	vk	vk	PROPN
ejpam-1481	178	24	)	)	PUNCT
ejpam-1481	178	25	,	,	PUNCT
ejpam-1481	178	26	where	where	SCONJ
ejpam-1481	178	27	vk	vk	VERB
ejpam-1481	178	28	=	=	SYM
ejpam-1481	178	29	(	(	PUNCT
ejpam-1481	178	30	k+3)2	k+3)2	PROPN
ejpam-1481	178	31	(	(	PUNCT
ejpam-1481	178	32	k+2)2+(k+3)2	k+2)2+(k+3)2	PROPN
ejpam-1481	178	33	,	,	PUNCT
ejpam-1481	178	34	k	k	PROPN
ejpam-1481	178	35	∈	∈	PROPN
ejpam-1481	178	36	n.	n.	NOUN
ejpam-1481	178	37	we	we	PRON
ejpam-1481	178	38	can	can	AUX
ejpam-1481	178	39	show	show	VERB
ejpam-1481	178	40	that	that	SCONJ
ejpam-1481	178	41	1	1	NUM
ejpam-1481	178	42	∈	∈	PROPN
ejpam-1481	178	43	σp(∆	σp(∆	NOUN
ejpam-1481	178	44	∗	∗	NOUN
ejpam-1481	178	45	v	v	NOUN
ejpam-1481	178	46	,	,	PUNCT
ejpam-1481	178	47	c∗0	c∗0	NOUN
ejpam-1481	178	48	)	)	PUNCT
ejpam-1481	178	49	.	.	PUNCT
ejpam-1481	179	1	but	but	CCONJ
ejpam-1481	179	2	1	1	NUM
ejpam-1481	179	3	/∈	/∈	PUNCT
ejpam-1481	179	4	{	{	PUNCT
ejpam-1481	179	5	λ	λ	X
ejpam-1481	179	6	∈	∈	PROPN
ejpam-1481	179	7	c	c	NOUN
ejpam-1481	179	8	:	:	PUNCT
ejpam-1481	179	9	|λ−	|λ−	NOUN
ejpam-1481	179	10	l|	l|	ADJ
ejpam-1481	179	11	<	<	X
ejpam-1481	179	12	l	l	NOUN
ejpam-1481	179	13	}	}	PUNCT
ejpam-1481	179	14	∪	∪	ADP
ejpam-1481	179	15	�	�	PROPN
ejpam-1481	179	16	v0	v0	NOUN
ejpam-1481	179	17	and	and	CCONJ
ejpam-1481	180	1	1	1	NUM
ejpam-1481	180	2	/∈	/∈	NOUN
ejpam-1481	180	3	�	�	PROPN
ejpam-1481	180	4	λ	λ	PROPN
ejpam-1481	180	5	∈	∈	PROPN
ejpam-1481	180	6	c	c	NOUN
ejpam-1481	180	7	:	:	PUNCT
ejpam-1481	180	8	sup	sup	NOUN
ejpam-1481	180	9	n	n	PRON
ejpam-1481	180	10	�	�	PROPN
ejpam-1481	180	11	�	�	PROPN
ejpam-1481	180	12	�	�	PROPN
ejpam-1481	180	13	λ−vk	λ−vk	PROPN
ejpam-1481	180	14	vk	vk	PROPN
ejpam-1481	180	15	�	�	PROPN
ejpam-1481	180	16	�	�	PROPN
ejpam-1481	180	17	�	�	PROPN
ejpam-1481	180	18	<	<	X
ejpam-1481	180	19	1	1	NUM
ejpam-1481	180	20	�	�	PROPN
ejpam-1481	180	21	.	.	PUNCT
ejpam-1481	181	1	on	on	ADP
ejpam-1481	181	2	the	the	DET
ejpam-1481	181	3	other	other	ADJ
ejpam-1481	181	4	hand	hand	NOUN
ejpam-1481	181	5	if	if	SCONJ
ejpam-1481	181	6	vk	vk	VERB
ejpam-1481	181	7	=	=	SYM
ejpam-1481	181	8	k+3	k+3	PROPN
ejpam-1481	181	9	2k+5	2k+5	PROPN
ejpam-1481	181	10	,	,	PUNCT
ejpam-1481	181	11	k	k	PROPN
ejpam-1481	181	12	∈	∈	PROPN
ejpam-1481	181	13	n	n	CCONJ
ejpam-1481	181	14	,	,	PUNCT
ejpam-1481	181	15	then	then	ADV
ejpam-1481	181	16	1	1	NUM
ejpam-1481	181	17	∈	∈	PROPN
ejpam-1481	181	18	§	§	PROPN
ejpam-1481	181	19	λ	λ	PROPN
ejpam-1481	181	20	∈	∈	PROPN
ejpam-1481	181	21	c	c	PROPN
ejpam-1481	181	22	:	:	PUNCT
ejpam-1481	181	23	inf	inf	PROPN
ejpam-1481	181	24	k	k	PROPN
ejpam-1481	181	25	�	�	PROPN
ejpam-1481	181	26	�	�	PROPN
ejpam-1481	181	27	�	�	PROPN
ejpam-1481	181	28	λ−vk	λ−vk	PROPN
ejpam-1481	181	29	vk	vk	PROPN
ejpam-1481	181	30	�	�	PROPN
ejpam-1481	181	31	�	�	PROPN
ejpam-1481	181	32	�	�	PROPN
ejpam-1481	181	33	<	<	X
ejpam-1481	181	34	1	1	NUM
ejpam-1481	181	35	ª	ª	NOUN
ejpam-1481	181	36	.	.	PUNCT
ejpam-1481	182	1	but	but	CCONJ
ejpam-1481	182	2	1	1	NUM
ejpam-1481	182	3	/∈	/∈	NOUN
ejpam-1481	182	4	σp(∆	σp(∆	PROPN
ejpam-1481	182	5	∗	∗	PROPN
ejpam-1481	182	6	v	v	NOUN
ejpam-1481	182	7	,	,	PUNCT
ejpam-1481	182	8	c∗0	c∗0	NOUN
ejpam-1481	182	9	)	)	PUNCT
ejpam-1481	182	10	.	.	PUNCT
ejpam-1481	183	1	the	the	DET
ejpam-1481	183	2	following	follow	VERB
ejpam-1481	183	3	theorem	theorem	NOUN
ejpam-1481	183	4	gives	give	VERB
ejpam-1481	183	5	some	some	DET
ejpam-1481	183	6	results	result	NOUN
ejpam-1481	183	7	on	on	ADP
ejpam-1481	183	8	the	the	DET
ejpam-1481	183	9	residual	residual	ADJ
ejpam-1481	183	10	spectrum	spectrum	NOUN
ejpam-1481	183	11	of	of	ADP
ejpam-1481	183	12	the	the	DET
ejpam-1481	183	13	operator	operator	NOUN
ejpam-1481	183	14	∆v	∆v	PROPN
ejpam-1481	183	15	on	on	ADP
ejpam-1481	183	16	c0	c0	PROPN
ejpam-1481	183	17	.	.	PUNCT
ejpam-1481	184	1	theorem	theorem	VERB
ejpam-1481	184	2	4	4	NUM
ejpam-1481	184	3	(	(	PUNCT
ejpam-1481	184	4	[	[	X
ejpam-1481	184	5	7	7	NUM
ejpam-1481	184	6	]	]	NUM
ejpam-1481	184	7	)	)	PUNCT
ejpam-1481	184	8	.	.	PUNCT
ejpam-1481	185	1	(	(	PUNCT
ejpam-1481	185	2	i	i	NOUN
ejpam-1481	185	3	)	)	PUNCT
ejpam-1481	185	4	{	{	PUNCT
ejpam-1481	185	5	λ	λ	X
ejpam-1481	185	6	∈	∈	PROPN
ejpam-1481	185	7	c	c	NOUN
ejpam-1481	185	8	:	:	PUNCT
ejpam-1481	185	9	|λ−	|λ−	NOUN
ejpam-1481	185	10	l|	l|	ADJ
ejpam-1481	185	11	<	<	X
ejpam-1481	185	12	l	l	NOUN
ejpam-1481	185	13	}	}	PUNCT
ejpam-1481	185	14	∪	∪	ADP
ejpam-1481	185	15	�	�	PROPN
ejpam-1481	185	16	v0	v0	PROPN
ejpam-1481	185	17	⊆	⊆	NUM
ejpam-1481	185	18	σr(∆v	σr(∆v	PROPN
ejpam-1481	185	19	,	,	PUNCT
ejpam-1481	185	20	c0	c0	NOUN
ejpam-1481	185	21	)	)	PUNCT
ejpam-1481	185	22	,	,	PUNCT
ejpam-1481	185	23	(	(	PUNCT
ejpam-1481	185	24	ii	ii	NOUN
ejpam-1481	185	25	)	)	PUNCT
ejpam-1481	185	26	¨	¨	NOUN
ejpam-1481	186	1	λ	λ	X
ejpam-1481	186	2	∈	∈	PROPN
ejpam-1481	186	3	c	c	NOUN
ejpam-1481	186	4	:	:	PUNCT
ejpam-1481	186	5	sup	sup	PROPN
ejpam-1481	186	6	k	k	PROPN
ejpam-1481	186	7	�	�	PROPN
ejpam-1481	186	8	�	�	PROPN
ejpam-1481	186	9	�	�	PROPN
ejpam-1481	186	10	λ−vk	λ−vk	PROPN
ejpam-1481	186	11	vk	vk	PROPN
ejpam-1481	186	12	�	�	PROPN
ejpam-1481	186	13	�	�	PROPN
ejpam-1481	186	14	�	�	PROPN
ejpam-1481	186	15	<	<	X
ejpam-1481	186	16	1	1	NUM
ejpam-1481	186	17	«	«	SYM
ejpam-1481	186	18	⊆	⊆	NUM
ejpam-1481	186	19	σr(∆v	σr(∆v	PROPN
ejpam-1481	186	20	,	,	PUNCT
ejpam-1481	186	21	c0	c0	NOUN
ejpam-1481	186	22	)	)	PUNCT
ejpam-1481	186	23	,	,	PUNCT
ejpam-1481	186	24	(	(	PUNCT
ejpam-1481	186	25	iii	iii	X
ejpam-1481	186	26	)	)	PUNCT
ejpam-1481	186	27	σr(∆v	σr(∆v	PROPN
ejpam-1481	186	28	,	,	PUNCT
ejpam-1481	186	29	c0)⊆	c0)⊆	PROPN
ejpam-1481	186	30	§	§	PROPN
ejpam-1481	186	31	λ	λ	PROPN
ejpam-1481	186	32	∈	∈	PROPN
ejpam-1481	186	33	c	c	PROPN
ejpam-1481	186	34	:	:	PUNCT
ejpam-1481	186	35	inf	inf	PROPN
ejpam-1481	186	36	k	k	PROPN
ejpam-1481	186	37	�	�	PROPN
ejpam-1481	186	38	�	�	PROPN
ejpam-1481	186	39	�	�	PROPN
ejpam-1481	186	40	λ−vk	λ−vk	PROPN
ejpam-1481	186	41	vk	vk	PROPN
ejpam-1481	186	42	�	�	PROPN
ejpam-1481	186	43	�	�	PROPN
ejpam-1481	186	44	�	�	PROPN
ejpam-1481	186	45	<	<	X
ejpam-1481	186	46	1	1	NUM
ejpam-1481	186	47	ª	ª	X
ejpam-1481	186	48	.	.	PUNCT
ejpam-1481	187	1	for	for	ADP
ejpam-1481	187	2	the	the	DET
ejpam-1481	187	3	continuous	continuous	ADJ
ejpam-1481	187	4	spectrum	spectrum	NOUN
ejpam-1481	187	5	of	of	ADP
ejpam-1481	187	6	the	the	DET
ejpam-1481	187	7	operator	operator	NOUN
ejpam-1481	187	8	∆v	∆v	PROPN
ejpam-1481	187	9	on	on	ADP
ejpam-1481	187	10	c0	c0	PROPN
ejpam-1481	187	11	,	,	PUNCT
ejpam-1481	187	12	we	we	PRON
ejpam-1481	187	13	have	have	VERB
ejpam-1481	187	14	the	the	DET
ejpam-1481	187	15	following	follow	VERB
ejpam-1481	187	16	theorem	theorem	VERB
ejpam-1481	187	17	.	.	PUNCT
ejpam-1481	188	1	theorem	theorem	NOUN
ejpam-1481	188	2	5	5	NUM
ejpam-1481	188	3	(	(	PUNCT
ejpam-1481	188	4	[	[	X
ejpam-1481	188	5	7	7	NUM
ejpam-1481	188	6	]	]	NUM
ejpam-1481	188	7	)	)	PUNCT
ejpam-1481	188	8	.	.	PUNCT
ejpam-1481	189	1	(	(	PUNCT
ejpam-1481	189	2	i	i	NOUN
ejpam-1481	189	3	)	)	PUNCT
ejpam-1481	189	4	σc(∆v	σc(∆v	PROPN
ejpam-1481	189	5	,	,	PUNCT
ejpam-1481	189	6	c0)⊆	c0)⊆	NOUN
ejpam-1481	189	7	{	{	PUNCT
ejpam-1481	189	8	λ	λ	X
ejpam-1481	189	9	∈	∈	PROPN
ejpam-1481	189	10	c	c	NOUN
ejpam-1481	189	11	:	:	PUNCT
ejpam-1481	189	12	|λ−	|λ−	NOUN
ejpam-1481	189	13	l|	l|	ADJ
ejpam-1481	189	14	=	=	SYM
ejpam-1481	189	15	l	l	NOUN
ejpam-1481	189	16	}	}	PUNCT
ejpam-1481	189	17	\	\	PROPN
ejpam-1481	189	18	�	�	PROPN
ejpam-1481	189	19	v0	v0	NOUN
ejpam-1481	189	20	,	,	PUNCT
ejpam-1481	189	21	(	(	PUNCT
ejpam-1481	189	22	ii	ii	NOUN
ejpam-1481	189	23	)	)	PUNCT
ejpam-1481	189	24	{	{	PUNCT
ejpam-1481	189	25	λ	λ	X
ejpam-1481	189	26	∈	∈	PROPN
ejpam-1481	189	27	c	c	NOUN
ejpam-1481	189	28	:	:	PUNCT
ejpam-1481	189	29	|λ−	|λ−	NOUN
ejpam-1481	189	30	l|	l|	ADJ
ejpam-1481	189	31	≤	≤	ADJ
ejpam-1481	189	32	l	l	NOUN
ejpam-1481	189	33	}	}	PUNCT
ejpam-1481	189	34	∩	∩	NOUN
ejpam-1481	189	35	§	§	PROPN
ejpam-1481	189	36	λ	λ	X
ejpam-1481	189	37	∈	∈	PROPN
ejpam-1481	189	38	c	c	PROPN
ejpam-1481	189	39	:	:	PUNCT
ejpam-1481	189	40	inf	inf	PROPN
ejpam-1481	189	41	k	k	PROPN
ejpam-1481	189	42	�	�	PROPN
ejpam-1481	189	43	�	�	PROPN
ejpam-1481	189	44	�	�	PROPN
ejpam-1481	189	45	λ−vk	λ−vk	PROPN
ejpam-1481	189	46	vk	vk	PROPN
ejpam-1481	189	47	�	�	PROPN
ejpam-1481	189	48	�	�	PROPN
ejpam-1481	189	49	�	�	PROPN
ejpam-1481	189	50	≥	≥	NUM
ejpam-1481	189	51	1	1	NUM
ejpam-1481	189	52	ª	ª	SYM
ejpam-1481	189	53	⊆	⊆	NUM
ejpam-1481	189	54	σc(∆v	σc(∆v	NOUN
ejpam-1481	189	55	,	,	PUNCT
ejpam-1481	189	56	c0	c0	NOUN
ejpam-1481	189	57	)	)	PUNCT
ejpam-1481	189	58	.	.	PUNCT
ejpam-1481	190	1	also	also	ADV
ejpam-1481	190	2	,	,	PUNCT
ejpam-1481	190	3	we	we	PRON
ejpam-1481	190	4	have	have	VERB
ejpam-1481	190	5	the	the	DET
ejpam-1481	190	6	following	follow	VERB
ejpam-1481	190	7	theorem	theorem	VERB
ejpam-1481	190	8	.	.	PUNCT
ejpam-1481	190	9	theorem	theorem	NOUN
ejpam-1481	190	10	6	6	NUM
ejpam-1481	190	11	(	(	PUNCT
ejpam-1481	190	12	[	[	X
ejpam-1481	190	13	7	7	NUM
ejpam-1481	190	14	]	]	NUM
ejpam-1481	190	15	)	)	PUNCT
ejpam-1481	190	16	.	.	PUNCT
ejpam-1481	191	1	(	(	PUNCT
ejpam-1481	191	2	i	i	NOUN
ejpam-1481	191	3	)	)	PUNCT
ejpam-1481	191	4	σr(∆v	σr(∆v	PROPN
ejpam-1481	191	5	,	,	PUNCT
ejpam-1481	191	6	c0	c0	NOUN
ejpam-1481	191	7	)	)	PUNCT
ejpam-1481	191	8	=	=	SYM
ejpam-1481	191	9	σp(∆	σp(∆	PROPN
ejpam-1481	191	10	∗	∗	NOUN
ejpam-1481	191	11	v	v	NOUN
ejpam-1481	191	12	,	,	PUNCT
ejpam-1481	191	13	c∗0	c∗0	NOUN
ejpam-1481	191	14	)	)	PUNCT
ejpam-1481	191	15	.	.	PUNCT
ejpam-1481	192	1	(	(	PUNCT
ejpam-1481	192	2	ii	ii	NOUN
ejpam-1481	192	3	)	)	PUNCT
ejpam-1481	192	4	σc(∆v	σc(∆v	PROPN
ejpam-1481	192	5	,	,	PUNCT
ejpam-1481	192	6	c0	c0	NOUN
ejpam-1481	192	7	)	)	PUNCT
ejpam-1481	192	8	=	=	SYM
ejpam-1481	192	9	σ(∆v	σ(∆v	NOUN
ejpam-1481	192	10	,	,	PUNCT
ejpam-1481	192	11	c0)\σp(∆	c0)\σp(∆	PROPN
ejpam-1481	192	12	∗	∗	NOUN
ejpam-1481	192	13	v	v	NOUN
ejpam-1481	192	14	,	,	PUNCT
ejpam-1481	192	15	c∗0	c∗0	NOUN
ejpam-1481	192	16	)	)	PUNCT
ejpam-1481	192	17	.	.	PUNCT
ejpam-1481	193	1	now	now	ADV
ejpam-1481	193	2	,	,	PUNCT
ejpam-1481	193	3	we	we	PRON
ejpam-1481	193	4	give	give	VERB
ejpam-1481	193	5	the	the	DET
ejpam-1481	193	6	following	follow	VERB
ejpam-1481	193	7	new	new	ADJ
ejpam-1481	193	8	results	result	NOUN
ejpam-1481	193	9	:	:	PUNCT
ejpam-1481	193	10	theorem	theorem	VERB
ejpam-1481	193	11	7	7	NUM
ejpam-1481	193	12	.	.	PUNCT
ejpam-1481	193	13	σp(∆	σp(∆	PROPN
ejpam-1481	193	14	∗	∗	PROPN
ejpam-1481	193	15	v	v	NOUN
ejpam-1481	193	16	,	,	PUNCT
ejpam-1481	193	17	c∗0	c∗0	NOUN
ejpam-1481	193	18	)	)	PUNCT
ejpam-1481	193	19	=	=	PUNCT
ejpam-1481	194	1	{	{	PUNCT
ejpam-1481	194	2	λ	λ	X
ejpam-1481	194	3	∈	∈	PROPN
ejpam-1481	194	4	c	c	NOUN
ejpam-1481	194	5	:	:	PUNCT
ejpam-1481	194	6	|λ−	|λ−	NOUN
ejpam-1481	194	7	l|	l|	ADJ
ejpam-1481	194	8	<	<	X
ejpam-1481	194	9	l	l	NOUN
ejpam-1481	194	10	}	}	PUNCT
ejpam-1481	194	11	∪h	∪h	NUM
ejpam-1481	194	12	,	,	PUNCT
ejpam-1481	194	13	where	where	SCONJ
ejpam-1481	194	14	h	h	NOUN
ejpam-1481	194	15	=	=	PUNCT
ejpam-1481	194	16	(	(	PUNCT
ejpam-1481	194	17	λ	λ	X
ejpam-1481	194	18	∈	∈	PROPN
ejpam-1481	194	19	c	c	NOUN
ejpam-1481	194	20	:	:	PUNCT
ejpam-1481	194	21	|λ−	|λ−	NOUN
ejpam-1481	194	22	l|	l|	ADJ
ejpam-1481	194	23	=	=	SYM
ejpam-1481	194	24	l	l	NOUN
ejpam-1481	194	25	,	,	PUNCT
ejpam-1481	194	26	∞	∞	PROPN
ejpam-1481	194	27	∑	∑	PROPN
ejpam-1481	194	28	k=0	k=0	PROPN
ejpam-1481	194	29	�	�	PROPN
ejpam-1481	194	30	�	�	PROPN
ejpam-1481	194	31	�	�	PROPN
ejpam-1481	194	32	�	�	PROPN
ejpam-1481	194	33	�	�	PROPN
ejpam-1481	194	34	k	k	PROPN
ejpam-1481	194	35	∏	∏	PROPN
ejpam-1481	194	36	i=0	i=0	PROPN
ejpam-1481	194	37	λ−	λ−	PROPN
ejpam-1481	194	38	vi	vi	PROPN
ejpam-1481	194	39	vi	vi	PROPN
ejpam-1481	194	40	�	�	PROPN
ejpam-1481	194	41	�	�	PROPN
ejpam-1481	194	42	�	�	PROPN
ejpam-1481	194	43	�	�	PROPN
ejpam-1481	194	44	�	�	PROPN
ejpam-1481	194	45	<	<	X
ejpam-1481	194	46	∞	∞	PROPN
ejpam-1481	194	47	)	)	PUNCT
ejpam-1481	194	48	.	.	PUNCT
ejpam-1481	195	1	proof	proof	NOUN
ejpam-1481	195	2	.	.	PUNCT
ejpam-1481	196	1	suppose	suppose	VERB
ejpam-1481	196	2	that	that	SCONJ
ejpam-1481	196	3	∆∗v	∆∗v	NOUN
ejpam-1481	196	4	f	f	X
ejpam-1481	196	5	=	=	SYM
ejpam-1481	196	6	λ	λ	X
ejpam-1481	196	7	f	f	PROPN
ejpam-1481	196	8	for	for	ADP
ejpam-1481	196	9	f	f	PROPN
ejpam-1481	196	10	=	=	SYM
ejpam-1481	196	11	(	(	PUNCT
ejpam-1481	196	12	f0	f0	PROPN
ejpam-1481	196	13	,	,	PUNCT
ejpam-1481	196	14	f1	f1	NOUN
ejpam-1481	196	15	,	,	PUNCT
ejpam-1481	196	16	f2	f2	PROPN
ejpam-1481	196	17	,	,	PUNCT
ejpam-1481	196	18	.	.	PUNCT
ejpam-1481	196	19	.	.	PUNCT
ejpam-1481	196	20	.	.	PUNCT
ejpam-1481	196	21	)	)	PUNCT
ejpam-1481	197	1	6=	6=	NUM
ejpam-1481	197	2	θ	θ	PROPN
ejpam-1481	197	3	in	in	ADP
ejpam-1481	197	4	c∗0	c∗0	NOUN
ejpam-1481	197	5	∼=	∼=	PROPN
ejpam-1481	197	6	l1	l1	PROPN
ejpam-1481	197	7	.	.	PUNCT
ejpam-1481	198	1	then	then	ADV
ejpam-1481	198	2	,	,	PUNCT
ejpam-1481	198	3	by	by	ADP
ejpam-1481	198	4	solving	solve	VERB
ejpam-1481	198	5	the	the	DET
ejpam-1481	198	6	system	system	NOUN
ejpam-1481	198	7	of	of	ADP
ejpam-1481	198	8	equations	equation	NOUN
ejpam-1481	198	9	v0	v0	VERB
ejpam-1481	198	10	f0	f0	PROPN
ejpam-1481	198	11	−	−	PROPN
ejpam-1481	198	12	v0	v0	NOUN
ejpam-1481	198	13	f1	f1	NOUN
ejpam-1481	198	14	=	=	SYM
ejpam-1481	198	15	λ	λ	PROPN
ejpam-1481	198	16	f0	f0	PROPN
ejpam-1481	198	17	,	,	PUNCT
ejpam-1481	198	18	v1	v1	NOUN
ejpam-1481	198	19	f1	f1	NOUN
ejpam-1481	198	20	−	−	PROPN
ejpam-1481	198	21	v1	v1	NOUN
ejpam-1481	198	22	f2	f2	ADJ
ejpam-1481	198	23	=	=	SYM
ejpam-1481	198	24	λ	λ	PROPN
ejpam-1481	198	25	f1	f1	NOUN
ejpam-1481	198	26	,	,	PUNCT
ejpam-1481	198	27	...	...	PUNCT
ejpam-1481	199	1	vk	vk	INTJ
ejpam-1481	199	2	fk	fk	INTJ
ejpam-1481	199	3	−	−	NOUN
ejpam-1481	199	4	vk	vk	NOUN
ejpam-1481	199	5	fk+1	fk+1	VERB
ejpam-1481	199	6	=	=	SYM
ejpam-1481	199	7	λ	λ	X
ejpam-1481	199	8	fk	fk	INTJ
ejpam-1481	199	9	,	,	PUNCT
ejpam-1481	199	10	...	...	PUNCT
ejpam-1481	199	11	a.	a.	PROPN
ejpam-1481	199	12	akhmedov	akhmedov	PROPN
ejpam-1481	199	13	,	,	PUNCT
ejpam-1481	199	14	s.	s.	PROPN
ejpam-1481	199	15	el	el	PROPN
ejpam-1481	199	16	-	-	PUNCT
ejpam-1481	199	17	shabrawy	shabrawy	PROPN
ejpam-1481	199	18	/	/	SYM
ejpam-1481	199	19	eur	eur	NOUN
ejpam-1481	199	20	.	.	PUNCT
ejpam-1481	200	1	j.	j.	PROPN
ejpam-1481	200	2	pure	pure	PROPN
ejpam-1481	200	3	appl	appl	PROPN
ejpam-1481	200	4	.	.	PROPN
ejpam-1481	200	5	math	math	PROPN
ejpam-1481	200	6	,	,	PUNCT
ejpam-1481	200	7	5	5	NUM
ejpam-1481	200	8	(	(	PUNCT
ejpam-1481	200	9	2012	2012	NUM
ejpam-1481	200	10	)	)	PUNCT
ejpam-1481	200	11	,	,	PUNCT
ejpam-1481	200	12	59	59	NUM
ejpam-1481	200	13	-	-	SYM
ejpam-1481	200	14	74	74	NUM
ejpam-1481	200	15	66	66	NUM
ejpam-1481	200	16	we	we	PRON
ejpam-1481	200	17	obtain	obtain	VERB
ejpam-1481	200	18	fk+1	fk+1	NOUN
ejpam-1481	200	19	=	=	SYM
ejpam-1481	200	20	vk	vk	NOUN
ejpam-1481	200	21	−λ	−λ	PROPN
ejpam-1481	200	22	vk	vk	PROPN
ejpam-1481	200	23	fk	fk	INTJ
ejpam-1481	200	24	,	,	PUNCT
ejpam-1481	200	25	for	for	ADP
ejpam-1481	200	26	all	all	DET
ejpam-1481	200	27	k	k	PROPN
ejpam-1481	200	28	∈	∈	PROPN
ejpam-1481	200	29	n.	n.	NOUN
ejpam-1481	200	30	then	then	ADV
ejpam-1481	200	31	we	we	PRON
ejpam-1481	200	32	must	must	AUX
ejpam-1481	200	33	take	take	VERB
ejpam-1481	200	34	f0	f0	PROPN
ejpam-1481	200	35	6=	6=	ADP
ejpam-1481	200	36	0	0	NUM
ejpam-1481	200	37	,	,	PUNCT
ejpam-1481	200	38	since	since	SCONJ
ejpam-1481	200	39	otherwise	otherwise	ADV
ejpam-1481	200	40	we	we	PRON
ejpam-1481	200	41	would	would	AUX
ejpam-1481	200	42	have	have	VERB
ejpam-1481	200	43	f	f	NOUN
ejpam-1481	200	44	=	=	SYM
ejpam-1481	200	45	θ	θ	PROPN
ejpam-1481	200	46	.	.	PUNCT
ejpam-1481	201	1	it	it	PRON
ejpam-1481	201	2	is	be	AUX
ejpam-1481	201	3	clear	clear	ADJ
ejpam-1481	201	4	that	that	SCONJ
ejpam-1481	201	5	,	,	PUNCT
ejpam-1481	201	6	for	for	ADP
ejpam-1481	201	7	all	all	DET
ejpam-1481	201	8	k	k	PROPN
ejpam-1481	201	9	∈	∈	PROPN
ejpam-1481	201	10	n	n	CCONJ
ejpam-1481	201	11	,	,	PUNCT
ejpam-1481	201	12	the	the	DET
ejpam-1481	201	13	vector	vector	NOUN
ejpam-1481	201	14	f	f	PROPN
ejpam-1481	201	15	=	=	PRON
ejpam-1481	201	16	(	(	PUNCT
ejpam-1481	201	17	f0	f0	PROPN
ejpam-1481	201	18	,	,	PUNCT
ejpam-1481	201	19	f1	f1	NOUN
ejpam-1481	201	20	,	,	PUNCT
ejpam-1481	201	21	.	.	PUNCT
ejpam-1481	201	22	.	.	PUNCT
ejpam-1481	202	1	.	.	PUNCT
ejpam-1481	203	1	,	,	PUNCT
ejpam-1481	203	2	fk	fk	INTJ
ejpam-1481	203	3	,	,	PUNCT
ejpam-1481	203	4	0,0	0,0	NOUN
ejpam-1481	203	5	,	,	PUNCT
ejpam-1481	203	6	.	.	PUNCT
ejpam-1481	203	7	.	.	PUNCT
ejpam-1481	203	8	.	.	PUNCT
ejpam-1481	203	9	)	)	PUNCT
ejpam-1481	204	1	is	be	AUX
ejpam-1481	204	2	an	an	DET
ejpam-1481	204	3	eigenvector	eigenvector	NOUN
ejpam-1481	204	4	of	of	ADP
ejpam-1481	204	5	the	the	DET
ejpam-1481	204	6	operator	operator	NOUN
ejpam-1481	204	7	∆∗v	∆∗v	NOUN
ejpam-1481	204	8	corresponding	correspond	VERB
ejpam-1481	204	9	to	to	ADP
ejpam-1481	204	10	the	the	DET
ejpam-1481	204	11	eigenvalue	eigenvalue	PROPN
ejpam-1481	204	12	λ	λ	PROPN
ejpam-1481	204	13	=	=	SYM
ejpam-1481	204	14	vk	vk	PROPN
ejpam-1481	204	15	,	,	PUNCT
ejpam-1481	204	16	where	where	SCONJ
ejpam-1481	204	17	f0	f0	PROPN
ejpam-1481	204	18	6=	6=	ADP
ejpam-1481	204	19	0	0	NUM
ejpam-1481	204	20	and	and	CCONJ
ejpam-1481	204	21	fn	fn	NOUN
ejpam-1481	204	22	=	=	ADJ
ejpam-1481	204	23	vn−1−λ	vn−1−λ	NOUN
ejpam-1481	204	24	vn−1	vn−1	ADJ
ejpam-1481	204	25	fn−1	fn−1	ADJ
ejpam-1481	204	26	for	for	ADP
ejpam-1481	204	27	all	all	DET
ejpam-1481	204	28	n	n	NOUN
ejpam-1481	204	29	=	=	NOUN
ejpam-1481	204	30	1,2,3	1,2,3	NUM
ejpam-1481	204	31	,	,	PUNCT
ejpam-1481	204	32	.	.	PUNCT
ejpam-1481	204	33	.	.	PUNCT
ejpam-1481	205	1	.	.	PUNCT
ejpam-1481	206	1	,	,	PUNCT
ejpam-1481	206	2	k.	k.	PROPN
ejpam-1481	206	3	thus	thus	ADV
ejpam-1481	206	4	�	�	PROPN
ejpam-1481	206	5	vk	vk	PROPN
ejpam-1481	206	6	:	:	PUNCT
ejpam-1481	206	7	k	k	PROPN
ejpam-1481	206	8	∈	∈	PROPN
ejpam-1481	206	9	n	n	CCONJ
ejpam-1481	206	10	⊆	⊆	NUM
ejpam-1481	206	11	σp(∆	σp(∆	NOUN
ejpam-1481	206	12	∗	∗	NOUN
ejpam-1481	206	13	v	v	NOUN
ejpam-1481	206	14	,	,	PUNCT
ejpam-1481	206	15	c∗0	c∗0	NOUN
ejpam-1481	206	16	)	)	PUNCT
ejpam-1481	206	17	.	.	PUNCT
ejpam-1481	207	1	on	on	ADP
ejpam-1481	207	2	the	the	DET
ejpam-1481	207	3	other	other	ADJ
ejpam-1481	207	4	hand	hand	NOUN
ejpam-1481	207	5	if	if	SCONJ
ejpam-1481	207	6	λ	λ	PROPN
ejpam-1481	207	7	6=	6=	SYM
ejpam-1481	207	8	vk	vk	PROPN
ejpam-1481	207	9	for	for	ADP
ejpam-1481	207	10	all	all	DET
ejpam-1481	207	11	k	k	PROPN
ejpam-1481	207	12	∈	∈	PROPN
ejpam-1481	207	13	n	n	CCONJ
ejpam-1481	207	14	,	,	PUNCT
ejpam-1481	207	15	then	then	ADV
ejpam-1481	207	16	we	we	PRON
ejpam-1481	207	17	can	can	AUX
ejpam-1481	207	18	see	see	VERB
ejpam-1481	207	19	that	that	SCONJ
ejpam-1481	207	20	∑	∑	PROPN
ejpam-1481	207	21	k	k	PROPN
ejpam-1481	207	22	�	�	PROPN
ejpam-1481	207	23	�	�	PROPN
ejpam-1481	207	24	fk	fk	INTJ
ejpam-1481	207	25	�	�	PROPN
ejpam-1481	207	26	�	�	PROPN
ejpam-1481	207	27	<	<	X
ejpam-1481	207	28	∞	∞	PROPN
ejpam-1481	207	29	if	if	SCONJ
ejpam-1481	207	30	lim	lim	PROPN
ejpam-1481	207	31	k→∞	k→∞	PROPN
ejpam-1481	207	32	�	�	PROPN
ejpam-1481	207	33	�	�	PROPN
ejpam-1481	207	34	�	�	PROPN
ejpam-1481	207	35	fk+1	fk+1	PROPN
ejpam-1481	207	36	fk	fk	PROPN
ejpam-1481	207	37	�	�	PROPN
ejpam-1481	207	38	�	�	PROPN
ejpam-1481	207	39	�	�	PROPN
ejpam-1481	207	40	=	=	SYM
ejpam-1481	207	41	�	�	PROPN
ejpam-1481	207	42	�	�	PROPN
ejpam-1481	207	43	�	�	PROPN
ejpam-1481	207	44	λ−l	λ−l	PROPN
ejpam-1481	207	45	l	l	NOUN
ejpam-1481	207	46	�	�	PROPN
ejpam-1481	207	47	�	�	PROPN
ejpam-1481	207	48	�	�	PROPN
ejpam-1481	207	49	<	<	X
ejpam-1481	207	50	1	1	NUM
ejpam-1481	207	51	.	.	PUNCT
ejpam-1481	208	1	also	also	ADV
ejpam-1481	208	2	,	,	PUNCT
ejpam-1481	208	3	it	it	PRON
ejpam-1481	208	4	can	can	AUX
ejpam-1481	208	5	be	be	AUX
ejpam-1481	208	6	proved	prove	VERB
ejpam-1481	208	7	that	that	SCONJ
ejpam-1481	208	8	h	h	NOUN
ejpam-1481	208	9	⊆	⊆	NUM
ejpam-1481	208	10	σp(∆	σp(∆	ADJ
ejpam-1481	208	11	∗	∗	NOUN
ejpam-1481	208	12	v	v	NOUN
ejpam-1481	208	13	,	,	PUNCT
ejpam-1481	208	14	c∗0	c∗0	NOUN
ejpam-1481	208	15	)	)	PUNCT
ejpam-1481	208	16	.	.	PUNCT
ejpam-1481	209	1	thus	thus	ADV
ejpam-1481	209	2	{	{	PUNCT
ejpam-1481	209	3	λ	λ	X
ejpam-1481	209	4	∈	∈	PROPN
ejpam-1481	209	5	c	c	NOUN
ejpam-1481	209	6	:	:	PUNCT
ejpam-1481	209	7	|λ−	|λ−	NOUN
ejpam-1481	209	8	l|	l|	ADJ
ejpam-1481	209	9	<	<	X
ejpam-1481	209	10	l	l	NOUN
ejpam-1481	209	11	}	}	PUNCT
ejpam-1481	209	12	∪h	∪h	NUM
ejpam-1481	209	13	⊆	⊆	NUM
ejpam-1481	209	14	σp(∆	σp(∆	NOUN
ejpam-1481	209	15	∗	∗	NOUN
ejpam-1481	209	16	v	v	NOUN
ejpam-1481	209	17	,	,	PUNCT
ejpam-1481	209	18	c∗0	c∗0	NOUN
ejpam-1481	209	19	)	)	PUNCT
ejpam-1481	209	20	.	.	PUNCT
ejpam-1481	210	1	the	the	DET
ejpam-1481	210	2	second	second	ADJ
ejpam-1481	210	3	inclusion	inclusion	NOUN
ejpam-1481	210	4	can	can	AUX
ejpam-1481	210	5	be	be	AUX
ejpam-1481	210	6	proved	prove	VERB
ejpam-1481	210	7	analogously	analogously	ADV
ejpam-1481	210	8	.	.	PUNCT
ejpam-1481	211	1	theorem	theorem	ADJ
ejpam-1481	211	2	8	8	NUM
ejpam-1481	211	3	.	.	PUNCT
ejpam-1481	212	1	σr(∆v	σr(∆v	PROPN
ejpam-1481	212	2	,	,	PUNCT
ejpam-1481	212	3	c0	c0	NOUN
ejpam-1481	212	4	)	)	PUNCT
ejpam-1481	212	5	=	=	SYM
ejpam-1481	213	1	{	{	PUNCT
ejpam-1481	213	2	λ	λ	X
ejpam-1481	213	3	∈	∈	PROPN
ejpam-1481	213	4	c	c	NOUN
ejpam-1481	213	5	:	:	PUNCT
ejpam-1481	213	6	|λ−	|λ−	NOUN
ejpam-1481	213	7	l|	l|	ADJ
ejpam-1481	213	8	<	<	X
ejpam-1481	213	9	l	l	NOUN
ejpam-1481	213	10	}	}	PUNCT
ejpam-1481	213	11	∪h	∪h	NUM
ejpam-1481	213	12	.	.	PUNCT
ejpam-1481	214	1	proof	proof	NOUN
ejpam-1481	214	2	.	.	PUNCT
ejpam-1481	215	1	the	the	DET
ejpam-1481	215	2	proof	proof	NOUN
ejpam-1481	215	3	follows	follow	VERB
ejpam-1481	215	4	immediately	immediately	ADV
ejpam-1481	215	5	from	from	ADP
ejpam-1481	215	6	theorems	theorem	NOUN
ejpam-1481	215	7	6(i	6(i	NUM
ejpam-1481	215	8	)	)	PUNCT
ejpam-1481	215	9	and	and	CCONJ
ejpam-1481	215	10	7	7	NUM
ejpam-1481	215	11	.	.	X
ejpam-1481	215	12	theorem	theorem	NOUN
ejpam-1481	215	13	9	9	NUM
ejpam-1481	215	14	.	.	PUNCT
ejpam-1481	215	15	σc(∆v	σc(∆v	PROPN
ejpam-1481	215	16	,	,	PUNCT
ejpam-1481	215	17	c0	c0	NOUN
ejpam-1481	215	18	)	)	PUNCT
ejpam-1481	215	19	=	=	SYM
ejpam-1481	215	20	{	{	PUNCT
ejpam-1481	215	21	λ	λ	X
ejpam-1481	215	22	∈	∈	PROPN
ejpam-1481	215	23	c	c	NOUN
ejpam-1481	215	24	:	:	PUNCT
ejpam-1481	215	25	|λ−	|λ−	NOUN
ejpam-1481	215	26	l|	l|	ADJ
ejpam-1481	215	27	=	=	SYM
ejpam-1481	215	28	l	l	NOUN
ejpam-1481	215	29	}	}	PUNCT
ejpam-1481	215	30	\h	\h	PROPN
ejpam-1481	215	31	.	.	PUNCT
ejpam-1481	216	1	proof	proof	NOUN
ejpam-1481	216	2	.	.	PUNCT
ejpam-1481	217	1	the	the	DET
ejpam-1481	217	2	proof	proof	NOUN
ejpam-1481	217	3	follows	follow	VERB
ejpam-1481	217	4	immediately	immediately	ADV
ejpam-1481	217	5	from	from	ADP
ejpam-1481	217	6	theorems	theorem	NOUN
ejpam-1481	217	7	2(ii	2(ii	NUM
ejpam-1481	217	8	)	)	PUNCT
ejpam-1481	217	9	,	,	PUNCT
ejpam-1481	217	10	2(iii	2(iii	NUM
ejpam-1481	217	11	)	)	PUNCT
ejpam-1481	217	12	and	and	CCONJ
ejpam-1481	217	13	8	8	NUM
ejpam-1481	217	14	.	.	NOUN
ejpam-1481	217	15	4	4	NUM
ejpam-1481	217	16	.	.	X
ejpam-1481	217	17	illustrative	illustrative	ADJ
ejpam-1481	217	18	examples	example	NOUN
ejpam-1481	217	19	in	in	ADP
ejpam-1481	217	20	this	this	DET
ejpam-1481	217	21	section	section	NOUN
ejpam-1481	217	22	we	we	PRON
ejpam-1481	217	23	give	give	VERB
ejpam-1481	217	24	some	some	DET
ejpam-1481	217	25	illustrative	illustrative	ADJ
ejpam-1481	217	26	examples	example	NOUN
ejpam-1481	217	27	on	on	ADP
ejpam-1481	217	28	the	the	DET
ejpam-1481	217	29	fine	fine	ADJ
ejpam-1481	217	30	spectrum	spectrum	NOUN
ejpam-1481	217	31	of	of	ADP
ejpam-1481	217	32	the	the	DET
ejpam-1481	217	33	operator	operator	NOUN
ejpam-1481	217	34	∆v	∆v	PROPN
ejpam-1481	217	35	on	on	ADP
ejpam-1481	217	36	the	the	DET
ejpam-1481	217	37	sequence	sequence	NOUN
ejpam-1481	217	38	spaces	space	VERB
ejpam-1481	217	39	l1	l1	PROPN
ejpam-1481	217	40	and	and	CCONJ
ejpam-1481	217	41	c0	c0	PROPN
ejpam-1481	217	42	.	.	PUNCT
ejpam-1481	218	1	in	in	ADP
ejpam-1481	218	2	the	the	DET
ejpam-1481	218	3	following	follow	VERB
ejpam-1481	218	4	example	example	NOUN
ejpam-1481	218	5	,	,	PUNCT
ejpam-1481	218	6	we	we	PRON
ejpam-1481	218	7	consider	consider	VERB
ejpam-1481	218	8	a	a	DET
ejpam-1481	218	9	strictly	strictly	ADV
ejpam-1481	218	10	decreasing	decrease	VERB
ejpam-1481	218	11	sequence	sequence	NOUN
ejpam-1481	218	12	(	(	PUNCT
ejpam-1481	218	13	vk	vk	NOUN
ejpam-1481	218	14	)	)	PUNCT
ejpam-1481	218	15	of	of	ADP
ejpam-1481	218	16	positive	positive	ADJ
ejpam-1481	218	17	real	real	ADJ
ejpam-1481	218	18	numbers	number	NOUN
ejpam-1481	218	19	satisfying	satisfy	VERB
ejpam-1481	218	20	the	the	DET
ejpam-1481	218	21	conditions	condition	NOUN
ejpam-1481	218	22	(	(	PUNCT
ejpam-1481	218	23	2	2	NUM
ejpam-1481	218	24	)	)	PUNCT
ejpam-1481	218	25	.	.	PUNCT
ejpam-1481	219	1	it	it	PRON
ejpam-1481	219	2	will	will	AUX
ejpam-1481	219	3	be	be	AUX
ejpam-1481	219	4	shown	show	VERB
ejpam-1481	219	5	that	that	SCONJ
ejpam-1481	219	6	the	the	DET
ejpam-1481	219	7	following	follow	VERB
ejpam-1481	219	8	equalities	equality	NOUN
ejpam-1481	219	9	are	be	AUX
ejpam-1481	219	10	not	not	PART
ejpam-1481	219	11	hold	hold	ADJ
ejpam-1481	219	12	;	;	PUNCT
ejpam-1481	219	13	σp(∆v	σp(∆v	NUM
ejpam-1481	219	14	,	,	PUNCT
ejpam-1481	219	15	l1	l1	PROPN
ejpam-1481	219	16	)	)	PUNCT
ejpam-1481	219	17	=	=	SYM
ejpam-1481	219	18	�	�	PROPN
ejpam-1481	219	19	v0	v0	PROPN
ejpam-1481	219	20	,	,	PUNCT
ejpam-1481	219	21	v1	v1	NOUN
ejpam-1481	219	22	,	,	PUNCT
ejpam-1481	219	23	v2	v2	NOUN
ejpam-1481	219	24	,	,	PUNCT
ejpam-1481	219	25	.	.	PUNCT
ejpam-1481	219	26	.	.	PUNCT
ejpam-1481	220	1	.	.	PUNCT
ejpam-1481	221	1	and	and	CCONJ
ejpam-1481	221	2	σr(∆v	σr(∆v	ADV
ejpam-1481	221	3	,	,	PUNCT
ejpam-1481	221	4	l1	l1	PROPN
ejpam-1481	221	5	)	)	PUNCT
ejpam-1481	221	6	=	=	PRON
ejpam-1481	222	1	{	{	PUNCT
ejpam-1481	222	2	λ	λ	X
ejpam-1481	222	3	∈	∈	PROPN
ejpam-1481	222	4	c	c	NOUN
ejpam-1481	222	5	:	:	PUNCT
ejpam-1481	222	6	|λ−	|λ−	NOUN
ejpam-1481	222	7	l|	l|	ADJ
ejpam-1481	222	8	≤	≤	PUNCT
ejpam-1481	222	9	l}\	l}\	PROPN
ejpam-1481	222	10	�	�	PROPN
ejpam-1481	222	11	v0	v0	PROPN
ejpam-1481	222	12	,	,	PUNCT
ejpam-1481	222	13	v1	v1	NOUN
ejpam-1481	222	14	,	,	PUNCT
ejpam-1481	222	15	v2	v2	NOUN
ejpam-1481	222	16	,	,	PUNCT
ejpam-1481	222	17	.	.	PUNCT
ejpam-1481	222	18	.	.	PUNCT
ejpam-1481	222	19	.	.	PUNCT
ejpam-1481	223	1	.	.	PUNCT
ejpam-1481	224	1	example	example	NOUN
ejpam-1481	225	1	3	3	NUM
ejpam-1481	225	2	(	(	PUNCT
ejpam-1481	225	3	[	[	X
ejpam-1481	225	4	8	8	NUM
ejpam-1481	225	5	]	]	PUNCT
ejpam-1481	225	6	)	)	PUNCT
ejpam-1481	225	7	.	.	PUNCT
ejpam-1481	226	1	consider	consider	VERB
ejpam-1481	226	2	the	the	DET
ejpam-1481	226	3	sequence	sequence	NOUN
ejpam-1481	226	4	(	(	PUNCT
ejpam-1481	226	5	vk	vk	PROPN
ejpam-1481	226	6	)	)	PUNCT
ejpam-1481	226	7	,	,	PUNCT
ejpam-1481	226	8	where	where	SCONJ
ejpam-1481	226	9	vk	vk	ADP
ejpam-1481	226	10	=	=	SYM
ejpam-1481	226	11	k+3	k+3	PROPN
ejpam-1481	226	12	2k+5	2k+5	PROPN
ejpam-1481	226	13	,	,	PUNCT
ejpam-1481	226	14	k	k	PROPN
ejpam-1481	226	15	∈	∈	PROPN
ejpam-1481	226	16	n.	n.	NOUN
ejpam-1481	226	17	clearly	clearly	ADV
ejpam-1481	226	18	,	,	PUNCT
ejpam-1481	226	19	(	(	PUNCT
ejpam-1481	226	20	vk	vk	NOUN
ejpam-1481	226	21	)	)	PUNCT
ejpam-1481	226	22	is	be	AUX
ejpam-1481	226	23	a	a	DET
ejpam-1481	226	24	strictly	strictly	ADV
ejpam-1481	226	25	decreasing	decrease	VERB
ejpam-1481	226	26	sequence	sequence	NOUN
ejpam-1481	226	27	of	of	ADP
ejpam-1481	226	28	positive	positive	ADJ
ejpam-1481	226	29	real	real	ADJ
ejpam-1481	226	30	numbers	number	NOUN
ejpam-1481	226	31	satisfying	satisfy	VERB
ejpam-1481	226	32	the	the	DET
ejpam-1481	226	33	conditions	condition	NOUN
ejpam-1481	226	34	(	(	PUNCT
ejpam-1481	226	35	2	2	NUM
ejpam-1481	226	36	)	)	PUNCT
ejpam-1481	226	37	;	;	PUNCT
ejpam-1481	226	38	where	where	SCONJ
ejpam-1481	226	39	lim	lim	PROPN
ejpam-1481	226	40	k→∞	k→∞	NOUN
ejpam-1481	226	41	vk	vk	VERB
ejpam-1481	226	42	=	=	SYM
ejpam-1481	226	43	l	l	NOUN
ejpam-1481	226	44	=	=	SYM
ejpam-1481	226	45	1/2	1/2	NUM
ejpam-1481	226	46	,	,	PUNCT
ejpam-1481	227	1	sup	sup	NOUN
ejpam-1481	227	2	k	k	PROPN
ejpam-1481	227	3	vk	vk	PROPN
ejpam-1481	227	4	=	=	SYM
ejpam-1481	227	5	3/5	3/5	NUM
ejpam-1481	227	6	≤	≤	NUM
ejpam-1481	227	7	1	1	NUM
ejpam-1481	227	8	=	=	SYM
ejpam-1481	227	9	2l	2l	NUM
ejpam-1481	227	10	.	.	PUNCT
ejpam-1481	228	1	we	we	PRON
ejpam-1481	228	2	can	can	AUX
ejpam-1481	228	3	prove	prove	VERB
ejpam-1481	228	4	that	that	DET
ejpam-1481	228	5	v0	v0	NOUN
ejpam-1481	228	6	=	=	NOUN
ejpam-1481	228	7	3/5	3/5	NUM
ejpam-1481	228	8	/∈	/∈	PUNCT
ejpam-1481	229	1	σp(∆v	σp(∆v	NOUN
ejpam-1481	229	2	,	,	PUNCT
ejpam-1481	229	3	l1	l1	PROPN
ejpam-1481	229	4	)	)	PUNCT
ejpam-1481	229	5	.	.	PUNCT
ejpam-1481	230	1	indeed	indeed	ADV
ejpam-1481	230	2	,	,	PUNCT
ejpam-1481	230	3	suppose	suppose	VERB
ejpam-1481	230	4	for	for	ADP
ejpam-1481	230	5	contrary	contrary	ADJ
ejpam-1481	230	6	that	that	SCONJ
ejpam-1481	230	7	there	there	PRON
ejpam-1481	230	8	exists	exist	VERB
ejpam-1481	230	9	x	x	X
ejpam-1481	230	10	=	=	SYM
ejpam-1481	230	11	(	(	PUNCT
ejpam-1481	230	12	xk	xk	PROPN
ejpam-1481	230	13	)	)	PUNCT
ejpam-1481	230	14	6=	6=	NUM
ejpam-1481	231	1	θ	θ	PROPN
ejpam-1481	231	2	in	in	ADP
ejpam-1481	231	3	l1	l1	PROPN
ejpam-1481	231	4	such	such	ADJ
ejpam-1481	231	5	that	that	DET
ejpam-1481	231	6	∆v	∆v	PROPN
ejpam-1481	231	7	x	x	PUNCT
ejpam-1481	232	1	=	=	SYM
ejpam-1481	232	2	v0	v0	PROPN
ejpam-1481	232	3	x.	x.	NOUN
ejpam-1481	232	4	then	then	ADV
ejpam-1481	232	5	(	(	PUNCT
ejpam-1481	232	6	v0	v0	NOUN
ejpam-1481	232	7	−	−	NOUN
ejpam-1481	232	8	v0)x0	v0)x0	NOUN
ejpam-1481	232	9	=	=	NOUN
ejpam-1481	232	10	0	0	NUM
ejpam-1481	232	11	and	and	CCONJ
ejpam-1481	232	12	−	−	PROPN
ejpam-1481	232	13	vk	vk	X
ejpam-1481	232	14	xk	xk	PROPN
ejpam-1481	233	1	+	+	CCONJ
ejpam-1481	233	2	(	(	PUNCT
ejpam-1481	233	3	vk+1−	vk+1−	PROPN
ejpam-1481	233	4	v0)xk+1	v0)xk+1	NOUN
ejpam-1481	233	5	=	=	SYM
ejpam-1481	233	6	0	0	NUM
ejpam-1481	233	7	,	,	PUNCT
ejpam-1481	233	8	for	for	ADP
ejpam-1481	233	9	all	all	DET
ejpam-1481	233	10	k	k	PROPN
ejpam-1481	233	11	∈	∈	PROPN
ejpam-1481	233	12	n.	n.	NOUN
ejpam-1481	233	13	if	if	SCONJ
ejpam-1481	233	14	x0	x0	PROPN
ejpam-1481	233	15	=	=	SYM
ejpam-1481	233	16	0	0	NUM
ejpam-1481	233	17	,	,	PUNCT
ejpam-1481	233	18	then	then	ADV
ejpam-1481	233	19	xk	xk	PROPN
ejpam-1481	233	20	=	=	PUNCT
ejpam-1481	233	21	0	0	PROPN
ejpam-1481	233	22	,	,	PUNCT
ejpam-1481	233	23	for	for	ADP
ejpam-1481	233	24	all	all	DET
ejpam-1481	233	25	k	k	PROPN
ejpam-1481	233	26	≥	≥	NUM
ejpam-1481	233	27	1	1	NUM
ejpam-1481	233	28	,	,	PUNCT
ejpam-1481	233	29	and	and	CCONJ
ejpam-1481	233	30	so	so	ADV
ejpam-1481	233	31	we	we	PRON
ejpam-1481	233	32	have	have	VERB
ejpam-1481	233	33	a	a	DET
ejpam-1481	233	34	contradiction	contradiction	NOUN
ejpam-1481	233	35	since	since	SCONJ
ejpam-1481	233	36	x	x	PROPN
ejpam-1481	233	37	6=	6=	NUM
ejpam-1481	233	38	θ	θ	NOUN
ejpam-1481	233	39	.	.	PUNCT
ejpam-1481	234	1	also	also	ADV
ejpam-1481	234	2	,	,	PUNCT
ejpam-1481	234	3	if	if	SCONJ
ejpam-1481	234	4	x0	x0	PROPN
ejpam-1481	234	5	6=	6=	ADP
ejpam-1481	234	6	0	0	NUM
ejpam-1481	234	7	then	then	ADV
ejpam-1481	234	8	lim	lim	PROPN
ejpam-1481	234	9	k→∞	k→∞	NOUN
ejpam-1481	234	10	�	�	PROPN
ejpam-1481	234	11	�	�	PROPN
ejpam-1481	234	12	�	�	PROPN
ejpam-1481	234	13	�	�	PROPN
ejpam-1481	234	14	xk+1	xk+1	PROPN
ejpam-1481	234	15	xk	xk	PROPN
ejpam-1481	234	16	�	�	PROPN
ejpam-1481	234	17	�	�	PROPN
ejpam-1481	234	18	�	�	PROPN
ejpam-1481	234	19	�	�	PROPN
ejpam-1481	234	20	=	=	SYM
ejpam-1481	234	21	�	�	PROPN
ejpam-1481	234	22	�	�	PROPN
ejpam-1481	234	23	�	�	PROPN
ejpam-1481	234	24	�	�	PROPN
ejpam-1481	234	25	l	l	PROPN
ejpam-1481	234	26	l	l	NOUN
ejpam-1481	234	27	−	−	PROPN
ejpam-1481	234	28	vo	vo	X
ejpam-1481	234	29	�	�	PROPN
ejpam-1481	234	30	�	�	PROPN
ejpam-1481	234	31	�	�	PROPN
ejpam-1481	234	32	�	�	PROPN
ejpam-1481	234	33	=	=	PROPN
ejpam-1481	234	34	5	5	PROPN
ejpam-1481	234	35	>	>	SYM
ejpam-1481	234	36	1	1	NUM
ejpam-1481	234	37	,	,	PUNCT
ejpam-1481	234	38	a.	a.	NOUN
ejpam-1481	234	39	akhmedov	akhmedov	PROPN
ejpam-1481	234	40	,	,	PUNCT
ejpam-1481	234	41	s.	s.	PROPN
ejpam-1481	234	42	el	el	PROPN
ejpam-1481	234	43	-	-	PUNCT
ejpam-1481	234	44	shabrawy	shabrawy	PROPN
ejpam-1481	234	45	/	/	SYM
ejpam-1481	234	46	eur	eur	NOUN
ejpam-1481	234	47	.	.	PUNCT
ejpam-1481	235	1	j.	j.	PROPN
ejpam-1481	235	2	pure	pure	PROPN
ejpam-1481	235	3	appl	appl	PROPN
ejpam-1481	235	4	.	.	PROPN
ejpam-1481	235	5	math	math	PROPN
ejpam-1481	235	6	,	,	PUNCT
ejpam-1481	235	7	5	5	NUM
ejpam-1481	235	8	(	(	PUNCT
ejpam-1481	235	9	2012	2012	NUM
ejpam-1481	235	10	)	)	PUNCT
ejpam-1481	235	11	,	,	PUNCT
ejpam-1481	235	12	59	59	NUM
ejpam-1481	235	13	-	-	SYM
ejpam-1481	235	14	74	74	NUM
ejpam-1481	235	15	67	67	NUM
ejpam-1481	236	1	and	and	CCONJ
ejpam-1481	236	2	so	so	ADV
ejpam-1481	236	3	we	we	PRON
ejpam-1481	236	4	have	have	VERB
ejpam-1481	236	5	a	a	DET
ejpam-1481	236	6	contradiction	contradiction	NOUN
ejpam-1481	236	7	since	since	SCONJ
ejpam-1481	236	8	x	x	PROPN
ejpam-1481	236	9	∈	∈	PROPN
ejpam-1481	236	10	l1	l1	PROPN
ejpam-1481	236	11	.	.	PUNCT
ejpam-1481	237	1	then	then	ADV
ejpam-1481	237	2	v0	v0	PROPN
ejpam-1481	237	3	/∈	/∈	PUNCT
ejpam-1481	238	1	σp(∆v	σp(∆v	PROPN
ejpam-1481	238	2	,	,	PUNCT
ejpam-1481	238	3	l1	l1	PROPN
ejpam-1481	238	4	)	)	PUNCT
ejpam-1481	238	5	.	.	PUNCT
ejpam-1481	239	1	similarly	similarly	ADV
ejpam-1481	239	2	,	,	PUNCT
ejpam-1481	239	3	we	we	PRON
ejpam-1481	239	4	can	can	AUX
ejpam-1481	239	5	prove	prove	VERB
ejpam-1481	239	6	that	that	DET
ejpam-1481	239	7	vk	vk	PROPN
ejpam-1481	239	8	/∈	/∈	PUNCT
ejpam-1481	239	9	σp(∆v	σp(∆v	NOUN
ejpam-1481	239	10	,	,	PUNCT
ejpam-1481	239	11	l1	l1	PROPN
ejpam-1481	239	12	)	)	PUNCT
ejpam-1481	239	13	for	for	ADP
ejpam-1481	239	14	all	all	DET
ejpam-1481	239	15	k	k	PROPN
ejpam-1481	239	16	≥	≥	NUM
ejpam-1481	239	17	1	1	NUM
ejpam-1481	239	18	,	,	PUNCT
ejpam-1481	239	19	and	and	CCONJ
ejpam-1481	239	20	so	so	ADV
ejpam-1481	239	21	σp(∆v	σp(∆v	PROPN
ejpam-1481	239	22	,	,	PUNCT
ejpam-1481	239	23	l1	l1	PROPN
ejpam-1481	239	24	)	)	PUNCT
ejpam-1481	239	25	=	=	SYM
ejpam-1481	240	1	φ	φ	PROPN
ejpam-1481	240	2	.	.	PUNCT
ejpam-1481	241	1	now	now	ADV
ejpam-1481	241	2	,	,	PUNCT
ejpam-1481	241	3	the	the	DET
ejpam-1481	241	4	operator	operator	NOUN
ejpam-1481	241	5	∆v	∆v	PROPN
ejpam-1481	241	6	−	−	PROPN
ejpam-1481	241	7	v0i	v0i	VERB
ejpam-1481	241	8	on	on	ADP
ejpam-1481	241	9	l1	l1	PROPN
ejpam-1481	241	10	is	be	AUX
ejpam-1481	241	11	defined	define	VERB
ejpam-1481	241	12	by	by	ADP
ejpam-1481	241	13	(	(	PUNCT
ejpam-1481	241	14	∆v	∆v	PROPN
ejpam-1481	241	15	−	−	NOUN
ejpam-1481	241	16	v0i)x	v0i)x	NOUN
ejpam-1481	242	1	=	=	X
ejpam-1481	242	2	(	(	PUNCT
ejpam-1481	242	3	0,−v0	0,−v0	NUM
ejpam-1481	242	4	x0	x0	PROPN
ejpam-1481	243	1	+	+	CCONJ
ejpam-1481	243	2	(	(	PUNCT
ejpam-1481	243	3	v1−	v1−	PROPN
ejpam-1481	243	4	v0)x1	v0)x1	NOUN
ejpam-1481	243	5	,	,	PUNCT
ejpam-1481	243	6	−v1	−v1	PROPN
ejpam-1481	243	7	x1	x1	PROPN
ejpam-1481	244	1	+	+	CCONJ
ejpam-1481	244	2	(	(	PUNCT
ejpam-1481	244	3	v2	v2	PROPN
ejpam-1481	244	4	−	−	PROPN
ejpam-1481	244	5	v0)x2	v0)x2	NOUN
ejpam-1481	244	6	,	,	PUNCT
ejpam-1481	244	7	.	.	PUNCT
ejpam-1481	244	8	.	.	PUNCT
ejpam-1481	245	1	.	.	PUNCT
ejpam-1481	245	2	)	)	PUNCT
ejpam-1481	246	1	,	,	PUNCT
ejpam-1481	246	2	(	(	PUNCT
ejpam-1481	246	3	8)	8)	NUM
ejpam-1481	246	4	where	where	SCONJ
ejpam-1481	246	5	x	x	SYM
ejpam-1481	246	6	=	=	SYM
ejpam-1481	246	7	(	(	PUNCT
ejpam-1481	246	8	xk	xk	ADJ
ejpam-1481	246	9	)	)	PUNCT
ejpam-1481	246	10	∈	∈	PROPN
ejpam-1481	246	11	l1	l1	PROPN
ejpam-1481	246	12	.	.	PUNCT
ejpam-1481	247	1	the	the	DET
ejpam-1481	247	2	operator	operator	NOUN
ejpam-1481	247	3	(	(	PUNCT
ejpam-1481	247	4	∆v	∆v	PROPN
ejpam-1481	247	5	−	−	PROPN
ejpam-1481	247	6	v0	v0	NOUN
ejpam-1481	247	7	i)−1	i)−1	NOUN
ejpam-1481	247	8	exists	exist	VERB
ejpam-1481	247	9	since	since	SCONJ
ejpam-1481	247	10	v0	v0	NOUN
ejpam-1481	247	11	/∈	/∈	PUNCT
ejpam-1481	247	12	σp(∆v	σp(∆v	PROPN
ejpam-1481	247	13	,	,	PUNCT
ejpam-1481	247	14	l1	l1	PROPN
ejpam-1481	247	15	)	)	PUNCT
ejpam-1481	247	16	.	.	PUNCT
ejpam-1481	248	1	but	but	CCONJ
ejpam-1481	248	2	(	(	PUNCT
ejpam-1481	248	3	∆v	∆v	PROPN
ejpam-1481	248	4	−	−	PROPN
ejpam-1481	248	5	v0	v0	NOUN
ejpam-1481	248	6	i)−1	i)−1	NOUN
ejpam-1481	248	7	does	do	AUX
ejpam-1481	248	8	not	not	PART
ejpam-1481	248	9	satisfy	satisfy	VERB
ejpam-1481	248	10	(	(	PUNCT
ejpam-1481	248	11	r3	r3	PROPN
ejpam-1481	248	12	)	)	PUNCT
ejpam-1481	248	13	.	.	PUNCT
ejpam-1481	249	1	indeed	indeed	ADV
ejpam-1481	249	2	,	,	PUNCT
ejpam-1481	249	3	consider	consider	VERB
ejpam-1481	249	4	the	the	DET
ejpam-1481	249	5	sequence	sequence	NOUN
ejpam-1481	249	6	y	y	PROPN
ejpam-1481	249	7	=	=	SYM
ejpam-1481	249	8	(	(	PUNCT
ejpam-1481	249	9	1,0,0	1,0,0	NUM
ejpam-1481	249	10	,	,	PUNCT
ejpam-1481	249	11	.	.	PUNCT
ejpam-1481	249	12	.	.	PUNCT
ejpam-1481	249	13	.	.	PUNCT
ejpam-1481	249	14	)	)	PUNCT
ejpam-1481	250	1	in	in	ADP
ejpam-1481	250	2	l1	l1	PROPN
ejpam-1481	250	3	and	and	CCONJ
ejpam-1481	250	4	let	let	VERB
ejpam-1481	250	5	y	y	PRON
ejpam-1481	250	6	be	be	AUX
ejpam-1481	250	7	the	the	DET
ejpam-1481	250	8	center	center	NOUN
ejpam-1481	250	9	of	of	ADP
ejpam-1481	250	10	a	a	DET
ejpam-1481	250	11	small	small	ADJ
ejpam-1481	250	12	ball	ball	NOUN
ejpam-1481	250	13	,	,	PUNCT
ejpam-1481	250	14	say	say	INTJ
ejpam-1481	250	15	,	,	PUNCT
ejpam-1481	250	16	of	of	ADP
ejpam-1481	250	17	radius	radius	NOUN
ejpam-1481	250	18	1/3	1/3	NUM
ejpam-1481	250	19	.	.	PUNCT
ejpam-1481	251	1	clearly	clearly	ADV
ejpam-1481	251	2	,	,	PUNCT
ejpam-1481	251	3	by	by	ADP
ejpam-1481	251	4	(	(	PUNCT
ejpam-1481	251	5	8)	8)	NUM
ejpam-1481	251	6	,	,	PUNCT
ejpam-1481	251	7	this	this	DET
ejpam-1481	251	8	ball	ball	NOUN
ejpam-1481	251	9	does	do	AUX
ejpam-1481	251	10	not	not	PART
ejpam-1481	251	11	intersect	intersect	VERB
ejpam-1481	251	12	the	the	DET
ejpam-1481	251	13	range	range	NOUN
ejpam-1481	251	14	of	of	ADP
ejpam-1481	251	15	the	the	DET
ejpam-1481	251	16	operator	operator	NOUN
ejpam-1481	251	17	∆v	∆v	PROPN
ejpam-1481	252	1	−	−	PROPN
ejpam-1481	252	2	v0	v0	NOUN
ejpam-1481	252	3	i	i	PRON
ejpam-1481	252	4	.	.	PUNCT
ejpam-1481	253	1	then	then	ADV
ejpam-1481	253	2	,	,	PUNCT
ejpam-1481	253	3	the	the	DET
ejpam-1481	253	4	operator	operator	NOUN
ejpam-1481	253	5	∆v	∆v	PROPN
ejpam-1481	253	6	−	−	PROPN
ejpam-1481	253	7	v0	v0	NOUN
ejpam-1481	253	8	i	i	PRON
ejpam-1481	253	9	does	do	AUX
ejpam-1481	253	10	not	not	PART
ejpam-1481	253	11	have	have	VERB
ejpam-1481	253	12	a	a	DET
ejpam-1481	253	13	dense	dense	ADJ
ejpam-1481	253	14	range	range	NOUN
ejpam-1481	253	15	in	in	ADP
ejpam-1481	253	16	l1	l1	PROPN
ejpam-1481	253	17	.	.	PUNCT
ejpam-1481	254	1	hence	hence	ADV
ejpam-1481	254	2	,	,	PUNCT
ejpam-1481	254	3	by	by	ADP
ejpam-1481	254	4	definition	definition	NOUN
ejpam-1481	254	5	,	,	PUNCT
ejpam-1481	254	6	v0	v0	PROPN
ejpam-1481	254	7	∈	∈	PROPN
ejpam-1481	254	8	σr(∆v	σr(∆v	PROPN
ejpam-1481	254	9	,	,	PUNCT
ejpam-1481	254	10	l1	l1	PROPN
ejpam-1481	254	11	)	)	PUNCT
ejpam-1481	254	12	.	.	PUNCT
ejpam-1481	255	1	the	the	DET
ejpam-1481	255	2	following	follow	VERB
ejpam-1481	255	3	example	example	NOUN
ejpam-1481	255	4	disproves	disprove	VERB
ejpam-1481	255	5	the	the	DET
ejpam-1481	255	6	statements	statement	NOUN
ejpam-1481	255	7	of	of	ADP
ejpam-1481	255	8	srivastava	srivastava	PROPN
ejpam-1481	255	9	and	and	CCONJ
ejpam-1481	255	10	kumar	kumar	PROPN
ejpam-1481	256	1	[	[	X
ejpam-1481	256	2	24	24	NUM
ejpam-1481	256	3	]	]	PUNCT
ejpam-1481	256	4	concerning	concern	VERB
ejpam-1481	256	5	the	the	DET
ejpam-1481	256	6	point	point	NOUN
ejpam-1481	256	7	spectrum	spectrum	NOUN
ejpam-1481	256	8	,	,	PUNCT
ejpam-1481	256	9	the	the	DET
ejpam-1481	256	10	residual	residual	ADJ
ejpam-1481	256	11	spectrum	spectrum	NOUN
ejpam-1481	256	12	and	and	CCONJ
ejpam-1481	256	13	the	the	DET
ejpam-1481	256	14	continuous	continuous	ADJ
ejpam-1481	256	15	spectrum	spectrum	NOUN
ejpam-1481	256	16	of	of	ADP
ejpam-1481	256	17	the	the	DET
ejpam-1481	256	18	operator	operator	NOUN
ejpam-1481	256	19	∆v	∆v	PROPN
ejpam-1481	256	20	on	on	ADP
ejpam-1481	256	21	c0	c0	NOUN
ejpam-1481	256	22	.	.	PUNCT
ejpam-1481	257	1	more	more	ADV
ejpam-1481	257	2	precisely	precisely	ADV
ejpam-1481	257	3	,	,	PUNCT
ejpam-1481	257	4	we	we	PRON
ejpam-1481	257	5	consider	consider	VERB
ejpam-1481	257	6	a	a	DET
ejpam-1481	257	7	strictly	strictly	ADV
ejpam-1481	257	8	decreasing	decrease	VERB
ejpam-1481	257	9	sequence	sequence	NOUN
ejpam-1481	257	10	(	(	PUNCT
ejpam-1481	257	11	vk	vk	NOUN
ejpam-1481	257	12	)	)	PUNCT
ejpam-1481	257	13	of	of	ADP
ejpam-1481	257	14	positive	positive	ADJ
ejpam-1481	257	15	real	real	ADJ
ejpam-1481	257	16	numbers	number	NOUN
ejpam-1481	257	17	satisfying	satisfy	VERB
ejpam-1481	257	18	the	the	DET
ejpam-1481	257	19	conditions	condition	NOUN
ejpam-1481	257	20	(	(	PUNCT
ejpam-1481	257	21	2	2	NUM
ejpam-1481	257	22	)	)	PUNCT
ejpam-1481	257	23	and	and	CCONJ
ejpam-1481	257	24	it	it	PRON
ejpam-1481	257	25	will	will	AUX
ejpam-1481	257	26	be	be	AUX
ejpam-1481	257	27	shown	show	VERB
ejpam-1481	257	28	that	that	SCONJ
ejpam-1481	257	29	the	the	DET
ejpam-1481	257	30	following	follow	VERB
ejpam-1481	257	31	equalities	equality	NOUN
ejpam-1481	257	32	are	be	AUX
ejpam-1481	257	33	not	not	PART
ejpam-1481	257	34	hold	hold	ADJ
ejpam-1481	257	35	;	;	PUNCT
ejpam-1481	257	36	σp(∆v	σp(∆v	NUM
ejpam-1481	257	37	,	,	PUNCT
ejpam-1481	257	38	c0	c0	NOUN
ejpam-1481	257	39	)	)	PUNCT
ejpam-1481	257	40	=	=	SYM
ejpam-1481	257	41	�	�	PROPN
ejpam-1481	257	42	v0	v0	PROPN
ejpam-1481	257	43	,	,	PUNCT
ejpam-1481	257	44	v1	v1	NOUN
ejpam-1481	257	45	,	,	PUNCT
ejpam-1481	257	46	v2	v2	NOUN
ejpam-1481	257	47	,	,	PUNCT
ejpam-1481	257	48	.	.	PUNCT
ejpam-1481	257	49	.	.	PUNCT
ejpam-1481	257	50	.	.	PUNCT
ejpam-1481	258	1	,	,	PUNCT
ejpam-1481	258	2	σr(∆v	σr(∆v	ADV
ejpam-1481	258	3	,	,	PUNCT
ejpam-1481	258	4	c0	c0	NOUN
ejpam-1481	258	5	)	)	PUNCT
ejpam-1481	258	6	=	=	SYM
ejpam-1481	259	1	{	{	PUNCT
ejpam-1481	259	2	λ	λ	X
ejpam-1481	259	3	∈	∈	PROPN
ejpam-1481	259	4	c	c	NOUN
ejpam-1481	259	5	:	:	PUNCT
ejpam-1481	259	6	|λ−	|λ−	NOUN
ejpam-1481	259	7	l|	l|	ADJ
ejpam-1481	259	8	<	<	X
ejpam-1481	259	9	l	l	NOUN
ejpam-1481	259	10	}	}	PUNCT
ejpam-1481	259	11	\	\	PROPN
ejpam-1481	259	12	�	�	PROPN
ejpam-1481	259	13	v0	v0	PROPN
ejpam-1481	259	14	,	,	PUNCT
ejpam-1481	259	15	v1	v1	NOUN
ejpam-1481	259	16	,	,	PUNCT
ejpam-1481	259	17	v2	v2	NOUN
ejpam-1481	259	18	,	,	PUNCT
ejpam-1481	259	19	.	.	PUNCT
ejpam-1481	259	20	.	.	PUNCT
ejpam-1481	260	1	.	.	PUNCT
ejpam-1481	261	1	,	,	PUNCT
ejpam-1481	261	2	σp(∆	σp(∆	PROPN
ejpam-1481	261	3	∗	∗	NOUN
ejpam-1481	261	4	v	v	NOUN
ejpam-1481	261	5	,	,	PUNCT
ejpam-1481	261	6	c∗0	c∗0	NOUN
ejpam-1481	261	7	)	)	PUNCT
ejpam-1481	261	8	=	=	PUNCT
ejpam-1481	262	1	{	{	PUNCT
ejpam-1481	262	2	λ	λ	X
ejpam-1481	262	3	∈	∈	PROPN
ejpam-1481	262	4	c	c	NOUN
ejpam-1481	262	5	:	:	PUNCT
ejpam-1481	262	6	|λ−	|λ−	NOUN
ejpam-1481	262	7	l|	l|	ADJ
ejpam-1481	262	8	<	<	X
ejpam-1481	262	9	l	l	NOUN
ejpam-1481	262	10	}	}	PUNCT
ejpam-1481	262	11	,	,	PUNCT
ejpam-1481	262	12	σc(∆v	σc(∆v	PROPN
ejpam-1481	262	13	,	,	PUNCT
ejpam-1481	262	14	c0	c0	NOUN
ejpam-1481	262	15	)	)	PUNCT
ejpam-1481	262	16	=	=	SYM
ejpam-1481	262	17	{	{	PUNCT
ejpam-1481	262	18	λ	λ	X
ejpam-1481	262	19	∈	∈	PROPN
ejpam-1481	262	20	c	c	NOUN
ejpam-1481	262	21	:	:	PUNCT
ejpam-1481	262	22	|λ−	|λ−	NOUN
ejpam-1481	262	23	l|	l|	ADJ
ejpam-1481	262	24	=	=	SYM
ejpam-1481	262	25	l}\	l}\	PROPN
ejpam-1481	262	26	�	�	PROPN
ejpam-1481	262	27	v0	v0	NOUN
ejpam-1481	262	28	.	.	PUNCT
ejpam-1481	263	1	example	example	NOUN
ejpam-1481	263	2	4	4	NUM
ejpam-1481	263	3	(	(	PUNCT
ejpam-1481	263	4	[	[	X
ejpam-1481	263	5	7	7	NUM
ejpam-1481	263	6	]	]	NUM
ejpam-1481	263	7	)	)	PUNCT
ejpam-1481	263	8	.	.	PUNCT
ejpam-1481	264	1	consider	consider	VERB
ejpam-1481	264	2	the	the	DET
ejpam-1481	264	3	sequence	sequence	NOUN
ejpam-1481	264	4	(	(	PUNCT
ejpam-1481	264	5	vk	vk	PROPN
ejpam-1481	264	6	)	)	PUNCT
ejpam-1481	264	7	,	,	PUNCT
ejpam-1481	264	8	where	where	SCONJ
ejpam-1481	264	9	vk	vk	VERB
ejpam-1481	264	10	=	=	SYM
ejpam-1481	264	11	(	(	PUNCT
ejpam-1481	264	12	k+3)2	k+3)2	PROPN
ejpam-1481	264	13	(	(	PUNCT
ejpam-1481	264	14	k+2)2+(k+3)2	k+2)2+(k+3)2	PROPN
ejpam-1481	264	15	,	,	PUNCT
ejpam-1481	264	16	k	k	PROPN
ejpam-1481	264	17	∈	∈	PROPN
ejpam-1481	264	18	n.	n.	NOUN
ejpam-1481	264	19	the	the	DET
ejpam-1481	264	20	sequence	sequence	NOUN
ejpam-1481	264	21	(	(	PUNCT
ejpam-1481	264	22	vk	vk	PROPN
ejpam-1481	264	23	)	)	PUNCT
ejpam-1481	264	24	is	be	AUX
ejpam-1481	264	25	a	a	DET
ejpam-1481	264	26	strictly	strictly	ADV
ejpam-1481	264	27	decreasing	decrease	VERB
ejpam-1481	264	28	sequence	sequence	NOUN
ejpam-1481	264	29	of	of	ADP
ejpam-1481	264	30	positive	positive	ADJ
ejpam-1481	264	31	real	real	ADJ
ejpam-1481	264	32	numbers	number	NOUN
ejpam-1481	264	33	satisfying	satisfy	VERB
ejpam-1481	264	34	the	the	DET
ejpam-1481	264	35	conditions	condition	NOUN
ejpam-1481	264	36	(	(	PUNCT
ejpam-1481	264	37	2	2	NUM
ejpam-1481	264	38	)	)	PUNCT
ejpam-1481	264	39	;	;	PUNCT
ejpam-1481	264	40	where	where	SCONJ
ejpam-1481	264	41	lim	lim	PROPN
ejpam-1481	264	42	k→∞	k→∞	NOUN
ejpam-1481	264	43	vk	vk	VERB
ejpam-1481	264	44	=	=	SYM
ejpam-1481	264	45	l	l	NOUN
ejpam-1481	264	46	=	=	SYM
ejpam-1481	264	47	1/2	1/2	NUM
ejpam-1481	264	48	,	,	PUNCT
ejpam-1481	264	49	sup	sup	NOUN
ejpam-1481	264	50	k	k	PROPN
ejpam-1481	264	51	vk	vk	PROPN
ejpam-1481	264	52	=	=	SYM
ejpam-1481	264	53	9/13≤	9/13≤	NOUN
ejpam-1481	264	54	1=	1=	NUM
ejpam-1481	264	55	2l	2l	NUM
ejpam-1481	264	56	.	.	PUNCT
ejpam-1481	265	1	we	we	PRON
ejpam-1481	265	2	can	can	AUX
ejpam-1481	265	3	prove	prove	VERB
ejpam-1481	265	4	,	,	PUNCT
ejpam-1481	265	5	as	as	ADP
ejpam-1481	265	6	in	in	ADP
ejpam-1481	265	7	example	example	NOUN
ejpam-1481	265	8	3	3	NUM
ejpam-1481	265	9	,	,	PUNCT
ejpam-1481	265	10	that	that	PRON
ejpam-1481	265	11	vk	vk	NOUN
ejpam-1481	265	12	/∈	/∈	PUNCT
ejpam-1481	265	13	σp(∆v	σp(∆v	NOUN
ejpam-1481	265	14	,	,	PUNCT
ejpam-1481	265	15	c0	c0	NOUN
ejpam-1481	265	16	)	)	PUNCT
ejpam-1481	265	17	for	for	ADP
ejpam-1481	265	18	all	all	DET
ejpam-1481	265	19	k	k	PROPN
ejpam-1481	265	20	∈	∈	PROPN
ejpam-1481	265	21	n.	n.	NOUN
ejpam-1481	265	22	also	also	ADV
ejpam-1481	265	23	,	,	PUNCT
ejpam-1481	265	24	we	we	PRON
ejpam-1481	265	25	can	can	AUX
ejpam-1481	265	26	prove	prove	VERB
ejpam-1481	265	27	that	that	SCONJ
ejpam-1481	265	28	v0	v0	PROPN
ejpam-1481	265	29	∈	∈	PROPN
ejpam-1481	265	30	σr(∆v	σr(∆v	PROPN
ejpam-1481	265	31	,	,	PUNCT
ejpam-1481	265	32	c0	c0	NOUN
ejpam-1481	265	33	)	)	PUNCT
ejpam-1481	265	34	.	.	PUNCT
ejpam-1481	266	1	on	on	ADP
ejpam-1481	266	2	the	the	DET
ejpam-1481	266	3	other	other	ADJ
ejpam-1481	266	4	hand	hand	NOUN
ejpam-1481	266	5	,	,	PUNCT
ejpam-1481	266	6	for	for	ADP
ejpam-1481	266	7	λ	λ	PROPN
ejpam-1481	266	8	=	=	SYM
ejpam-1481	266	9	1	1	NUM
ejpam-1481	266	10	,	,	PUNCT
ejpam-1481	266	11	we	we	PRON
ejpam-1481	266	12	have	have	VERB
ejpam-1481	266	13	λ−	λ−	PROPN
ejpam-1481	266	14	vk	vk	PROPN
ejpam-1481	266	15	vk	vk	NOUN
ejpam-1481	267	1	=	=	SYM
ejpam-1481	268	1	1−	1−	NUM
ejpam-1481	268	2	vk	vk	PROPN
ejpam-1481	268	3	vk	vk	NOUN
ejpam-1481	268	4	=	=	SYM
ejpam-1481	268	5	�	�	PROPN
ejpam-1481	268	6	k+	k+	NOUN
ejpam-1481	268	7	2	2	NUM
ejpam-1481	268	8	k+	k+	X
ejpam-1481	268	9	3	3	NUM
ejpam-1481	268	10	�	�	NOUN
ejpam-1481	268	11	2	2	NUM
ejpam-1481	268	12	.	.	PUNCT
ejpam-1481	269	1	if	if	SCONJ
ejpam-1481	269	2	we	we	PRON
ejpam-1481	269	3	suppose	suppose	VERB
ejpam-1481	269	4	that	that	SCONJ
ejpam-1481	269	5	∆∗v	∆∗v	NOUN
ejpam-1481	269	6	f	f	X
ejpam-1481	269	7	=	=	PUNCT
ejpam-1481	269	8	(	(	PUNCT
ejpam-1481	269	9	1	1	X
ejpam-1481	269	10	)	)	PUNCT
ejpam-1481	269	11	f	f	NOUN
ejpam-1481	269	12	for	for	ADP
ejpam-1481	269	13	some	some	DET
ejpam-1481	269	14	f	f	NOUN
ejpam-1481	269	15	=	=	PRON
ejpam-1481	269	16	(	(	PUNCT
ejpam-1481	269	17	f0	f0	PROPN
ejpam-1481	269	18	,	,	PUNCT
ejpam-1481	269	19	f1	f1	NOUN
ejpam-1481	269	20	,	,	PUNCT
ejpam-1481	269	21	f2	f2	PROPN
ejpam-1481	269	22	,	,	PUNCT
ejpam-1481	269	23	.	.	PUNCT
ejpam-1481	269	24	.	.	PUNCT
ejpam-1481	270	1	.	.	PUNCT
ejpam-1481	270	2	)	)	PUNCT
ejpam-1481	271	1	6=	6=	NUM
ejpam-1481	271	2	θ	θ	PROPN
ejpam-1481	271	3	in	in	ADP
ejpam-1481	271	4	c∗0	c∗0	NOUN
ejpam-1481	271	5	∼=	∼=	PROPN
ejpam-1481	271	6	l1	l1	NOUN
ejpam-1481	271	7	,	,	PUNCT
ejpam-1481	271	8	then	then	ADV
ejpam-1481	271	9	we	we	PRON
ejpam-1481	271	10	obtain	obtain	VERB
ejpam-1481	271	11	that	that	DET
ejpam-1481	271	12	fk	fk	INTJ
ejpam-1481	271	13	=	=	NUM
ejpam-1481	271	14	vk−1−1	vk−1−1	VERB
ejpam-1481	271	15	vk−1	vk−1	NOUN
ejpam-1481	271	16	fk−1	fk−1	NOUN
ejpam-1481	271	17	,	,	PUNCT
ejpam-1481	271	18	k	k	X
ejpam-1481	271	19	≥	≥	NUM
ejpam-1481	271	20	1	1	NUM
ejpam-1481	271	21	.	.	PUNCT
ejpam-1481	272	1	if	if	SCONJ
ejpam-1481	272	2	we	we	PRON
ejpam-1481	272	3	take	take	VERB
ejpam-1481	272	4	f0	f0	PROPN
ejpam-1481	272	5	=	=	SYM
ejpam-1481	272	6	0	0	NUM
ejpam-1481	272	7	,	,	PUNCT
ejpam-1481	272	8	then	then	ADV
ejpam-1481	272	9	f	f	PROPN
ejpam-1481	272	10	=	=	SYM
ejpam-1481	272	11	θ	θ	PROPN
ejpam-1481	272	12	and	and	CCONJ
ejpam-1481	272	13	we	we	PRON
ejpam-1481	272	14	have	have	VERB
ejpam-1481	272	15	a	a	DET
ejpam-1481	272	16	contradiction	contradiction	NOUN
ejpam-1481	272	17	since	since	SCONJ
ejpam-1481	272	18	f	f	PROPN
ejpam-1481	272	19	6=	6=	PROPN
ejpam-1481	272	20	θ	θ	PROPN
ejpam-1481	272	21	.	.	PUNCT
ejpam-1481	273	1	if	if	SCONJ
ejpam-1481	273	2	f0	f0	PROPN
ejpam-1481	273	3	6=	6=	PROPN
ejpam-1481	273	4	0	0	NUM
ejpam-1481	273	5	,	,	PUNCT
ejpam-1481	273	6	then	then	ADV
ejpam-1481	273	7	∞	∞	PROPN
ejpam-1481	273	8	∑	∑	PROPN
ejpam-1481	273	9	k=0	k=0	PROPN
ejpam-1481	273	10	�	�	PROPN
ejpam-1481	273	11	�	�	PROPN
ejpam-1481	273	12	fk	fk	INTJ
ejpam-1481	273	13	�	�	PROPN
ejpam-1481	273	14	�	�	PROPN
ejpam-1481	273	15	=	=	SYM
ejpam-1481	273	16	�	�	PROPN
ejpam-1481	273	17	�	�	PROPN
ejpam-1481	273	18	f0	f0	PROPN
ejpam-1481	273	19	�	�	PROPN
ejpam-1481	273	20	�	�	PROPN
ejpam-1481	273	21	+	+	PROPN
ejpam-1481	273	22	�	�	PROPN
ejpam-1481	273	23	�	�	PROPN
ejpam-1481	273	24	f0	f0	PROPN
ejpam-1481	273	25	�	�	PROPN
ejpam-1481	273	26	�	�	PROPN
ejpam-1481	273	27	∞	∞	PROPN
ejpam-1481	273	28	∑	∑	PROPN
ejpam-1481	273	29	k=1	k=1	PROPN
ejpam-1481	273	30	�	�	PROPN
ejpam-1481	273	31	�	�	PROPN
ejpam-1481	273	32	�	�	PROPN
ejpam-1481	273	33	�	�	PROPN
ejpam-1481	273	34	1−	1−	NUM
ejpam-1481	273	35	v0	v0	PROPN
ejpam-1481	273	36	v0	v0	PROPN
ejpam-1481	273	37	�	�	PROPN
ejpam-1481	273	38	�	�	PROPN
ejpam-1481	273	39	�	�	PROPN
ejpam-1481	273	40	�	�	PROPN
ejpam-1481	273	41	�	�	PROPN
ejpam-1481	273	42	�	�	PROPN
ejpam-1481	273	43	�	�	PROPN
ejpam-1481	273	44	�	�	PROPN
ejpam-1481	273	45	1−	1−	NUM
ejpam-1481	273	46	v1	v1	PROPN
ejpam-1481	273	47	v1	v1	PROPN
ejpam-1481	273	48	�	�	PROPN
ejpam-1481	273	49	�	�	PROPN
ejpam-1481	273	50	�	�	PROPN
ejpam-1481	273	51	�	�	PROPN
ejpam-1481	273	52	.	.	PUNCT
ejpam-1481	273	53	.	.	PUNCT
ejpam-1481	273	54	.	.	PUNCT
ejpam-1481	274	1	�	�	PROPN
ejpam-1481	274	2	�	�	PROPN
ejpam-1481	274	3	�	�	PROPN
ejpam-1481	274	4	�	�	PROPN
ejpam-1481	274	5	1−	1−	NUM
ejpam-1481	274	6	vk−1	vk−1	PROPN
ejpam-1481	274	7	vk−1	vk−1	PROPN
ejpam-1481	274	8	�	�	PROPN
ejpam-1481	274	9	�	�	PROPN
ejpam-1481	274	10	�	�	PROPN
ejpam-1481	274	11	�	�	PROPN
ejpam-1481	274	12	=	=	SYM
ejpam-1481	274	13	�	�	PROPN
ejpam-1481	274	14	�	�	PROPN
ejpam-1481	274	15	f0	f0	PROPN
ejpam-1481	274	16	�	�	PROPN
ejpam-1481	274	17	�	�	PROPN
ejpam-1481	274	18	+	+	CCONJ
ejpam-1481	274	19	4	4	NUM
ejpam-1481	274	20	�	�	PROPN
ejpam-1481	274	21	�	�	PROPN
ejpam-1481	274	22	f0	f0	PROPN
ejpam-1481	274	23	�	�	PROPN
ejpam-1481	274	24	�	�	PROPN
ejpam-1481	274	25	∞	∞	PROPN
ejpam-1481	274	26	∑	∑	PROPN
ejpam-1481	274	27	k=1	k=1	PROPN
ejpam-1481	274	28	�	�	PROPN
ejpam-1481	274	29	1	1	NUM
ejpam-1481	274	30	k+	k+	X
ejpam-1481	274	31	2	2	NUM
ejpam-1481	274	32	�	�	NOUN
ejpam-1481	274	33	2	2	NUM
ejpam-1481	274	34	<	<	ADP
ejpam-1481	274	35	∞.	∞.	PROPN
ejpam-1481	274	36	then	then	ADV
ejpam-1481	274	37	1	1	NUM
ejpam-1481	274	38	∈	∈	PROPN
ejpam-1481	274	39	σp(∆	σp(∆	NOUN
ejpam-1481	274	40	∗	∗	PROPN
ejpam-1481	274	41	v	v	NOUN
ejpam-1481	274	42	,	,	PUNCT
ejpam-1481	274	43	c∗0	c∗0	NOUN
ejpam-1481	274	44	)	)	PUNCT
ejpam-1481	274	45	,	,	PUNCT
ejpam-1481	274	46	and	and	CCONJ
ejpam-1481	274	47	consequently	consequently	ADV
ejpam-1481	274	48	1	1	NUM
ejpam-1481	274	49	/∈	/∈	SYM
ejpam-1481	274	50	σc(∆v	σc(∆v	NOUN
ejpam-1481	274	51	,	,	PUNCT
ejpam-1481	274	52	c0	c0	NOUN
ejpam-1481	274	53	)	)	PUNCT
ejpam-1481	274	54	.	.	PUNCT
ejpam-1481	275	1	in	in	ADP
ejpam-1481	275	2	the	the	DET
ejpam-1481	275	3	following	follow	VERB
ejpam-1481	275	4	example	example	NOUN
ejpam-1481	275	5	,	,	PUNCT
ejpam-1481	275	6	we	we	PRON
ejpam-1481	275	7	consider	consider	VERB
ejpam-1481	275	8	a	a	DET
ejpam-1481	275	9	sequence	sequence	NOUN
ejpam-1481	275	10	of	of	ADP
ejpam-1481	275	11	positive	positive	ADJ
ejpam-1481	275	12	real	real	ADJ
ejpam-1481	275	13	numbers	number	NOUN
ejpam-1481	275	14	(	(	PUNCT
ejpam-1481	275	15	not	not	PART
ejpam-1481	275	16	necessarily	necessarily	ADV
ejpam-1481	275	17	strictly	strictly	ADV
ejpam-1481	275	18	decreasing	decrease	VERB
ejpam-1481	275	19	)	)	PUNCT
ejpam-1481	275	20	satisfying	satisfy	VERB
ejpam-1481	275	21	the	the	DET
ejpam-1481	275	22	conditions	condition	NOUN
ejpam-1481	275	23	(	(	PUNCT
ejpam-1481	275	24	2	2	NUM
ejpam-1481	275	25	)	)	PUNCT
ejpam-1481	275	26	and	and	CCONJ
ejpam-1481	275	27	we	we	PRON
ejpam-1481	275	28	calculate	calculate	VERB
ejpam-1481	275	29	the	the	DET
ejpam-1481	275	30	spectrum	spectrum	NOUN
ejpam-1481	275	31	,	,	PUNCT
ejpam-1481	275	32	the	the	DET
ejpam-1481	275	33	point	point	NOUN
ejpam-1481	275	34	spectrum	spectrum	NOUN
ejpam-1481	275	35	,	,	PUNCT
ejpam-1481	275	36	the	the	DET
ejpam-1481	275	37	residual	residual	ADJ
ejpam-1481	275	38	spectrum	spectrum	NOUN
ejpam-1481	275	39	and	and	CCONJ
ejpam-1481	275	40	the	the	DET
ejpam-1481	275	41	continuous	continuous	ADJ
ejpam-1481	275	42	spectrum	spectrum	NOUN
ejpam-1481	275	43	of	of	ADP
ejpam-1481	275	44	the	the	DET
ejpam-1481	275	45	operator	operator	NOUN
ejpam-1481	275	46	∆v	∆v	PROPN
ejpam-1481	275	47	on	on	ADP
ejpam-1481	275	48	c0	c0	PROPN
ejpam-1481	275	49	.	.	PUNCT
ejpam-1481	276	1	a.	a.	PROPN
ejpam-1481	276	2	akhmedov	akhmedov	PROPN
ejpam-1481	276	3	,	,	PUNCT
ejpam-1481	276	4	s.	s.	PROPN
ejpam-1481	276	5	el	el	PROPN
ejpam-1481	276	6	-	-	PUNCT
ejpam-1481	276	7	shabrawy	shabrawy	PROPN
ejpam-1481	276	8	/	/	SYM
ejpam-1481	276	9	eur	eur	NOUN
ejpam-1481	276	10	.	.	PUNCT
ejpam-1481	277	1	j.	j.	PROPN
ejpam-1481	277	2	pure	pure	PROPN
ejpam-1481	277	3	appl	appl	PROPN
ejpam-1481	277	4	.	.	PROPN
ejpam-1481	277	5	math	math	PROPN
ejpam-1481	277	6	,	,	PUNCT
ejpam-1481	277	7	5	5	NUM
ejpam-1481	277	8	(	(	PUNCT
ejpam-1481	277	9	2012	2012	NUM
ejpam-1481	277	10	)	)	PUNCT
ejpam-1481	277	11	,	,	PUNCT
ejpam-1481	277	12	59	59	NUM
ejpam-1481	277	13	-	-	SYM
ejpam-1481	277	14	74	74	NUM
ejpam-1481	277	15	68	68	NUM
ejpam-1481	277	16	example	example	NOUN
ejpam-1481	277	17	5	5	NUM
ejpam-1481	277	18	.	.	X
ejpam-1481	277	19	consider	consider	VERB
ejpam-1481	277	20	the	the	DET
ejpam-1481	277	21	sequence	sequence	NOUN
ejpam-1481	277	22	(	(	PUNCT
ejpam-1481	277	23	vk	vk	PROPN
ejpam-1481	277	24	)	)	PUNCT
ejpam-1481	277	25	,	,	PUNCT
ejpam-1481	277	26	where	where	SCONJ
ejpam-1481	277	27	vk	vk	VERB
ejpam-1481	277	28	=	=	SYM
ejpam-1481	277	29	(	(	PUNCT
ejpam-1481	277	30	k+2)2	k+2)2	PROPN
ejpam-1481	277	31	(	(	PUNCT
ejpam-1481	277	32	k+2)2+(k+3)2	k+2)2+(k+3)2	INTJ
ejpam-1481	277	33	,	,	PUNCT
ejpam-1481	277	34	k	k	PROPN
ejpam-1481	277	35	∈	∈	PROPN
ejpam-1481	277	36	n.	n.	NOUN
ejpam-1481	277	37	we	we	PRON
ejpam-1481	277	38	can	can	AUX
ejpam-1481	277	39	prove	prove	VERB
ejpam-1481	277	40	that	that	SCONJ
ejpam-1481	277	41	the	the	DET
ejpam-1481	277	42	operator	operator	NOUN
ejpam-1481	277	43	∆v	∆v	PROPN
ejpam-1481	277	44	:	:	PUNCT
ejpam-1481	277	45	c0	c0	PROPN
ejpam-1481	277	46	−→	−→	PROPN
ejpam-1481	277	47	c0	c0	PROPN
ejpam-1481	277	48	is	be	AUX
ejpam-1481	277	49	a	a	DET
ejpam-1481	277	50	bounded	bounded	ADJ
ejpam-1481	277	51	linear	linear	ADJ
ejpam-1481	277	52	operator	operator	NOUN
ejpam-1481	277	53	with	with	ADP
ejpam-1481	277	54	the	the	DET
ejpam-1481	277	55	norm	norm	NOUN
ejpam-1481	277	56	∆v	∆v	PROPN
ejpam-1481	277	57	c0	c0	NOUN
ejpam-1481	277	58	=	=	PROPN
ejpam-1481	277	59	1	1	NUM
ejpam-1481	277	60	and	and	CCONJ
ejpam-1481	277	61	σ(∆v	σ(∆v	NOUN
ejpam-1481	277	62	,	,	PUNCT
ejpam-1481	277	63	c0	c0	NOUN
ejpam-1481	277	64	)	)	PUNCT
ejpam-1481	277	65	=	=	PUNCT
ejpam-1481	278	1	¨	¨	X
ejpam-1481	278	2	λ	λ	X
ejpam-1481	278	3	∈	∈	PROPN
ejpam-1481	278	4	c	c	NOUN
ejpam-1481	278	5	:	:	PUNCT
ejpam-1481	278	6	�	�	PROPN
ejpam-1481	278	7	�	�	PROPN
ejpam-1481	278	8	�	�	PROPN
ejpam-1481	278	9	�	�	PROPN
ejpam-1481	278	10	λ−	λ−	PROPN
ejpam-1481	278	11	1	1	NUM
ejpam-1481	278	12	2	2	NUM
ejpam-1481	278	13	�	�	PROPN
ejpam-1481	278	14	�	�	PROPN
ejpam-1481	278	15	�	�	PROPN
ejpam-1481	278	16	�	�	PROPN
ejpam-1481	278	17	≤	≤	PROPN
ejpam-1481	278	18	1	1	NUM
ejpam-1481	278	19	2	2	NUM
ejpam-1481	278	20	«	«	PUNCT
ejpam-1481	278	21	,	,	PUNCT
ejpam-1481	278	22	σp(∆v	σp(∆v	PROPN
ejpam-1481	278	23	,	,	PUNCT
ejpam-1481	278	24	c0	c0	NOUN
ejpam-1481	278	25	)	)	PUNCT
ejpam-1481	278	26	=	=	PUNCT
ejpam-1481	278	27	∅.	∅.	PROPN
ejpam-1481	278	28	σp(∆	σp(∆	PROPN
ejpam-1481	278	29	∗	∗	NOUN
ejpam-1481	278	30	v	v	NOUN
ejpam-1481	278	31	,	,	PUNCT
ejpam-1481	278	32	c∗0	c∗0	NOUN
ejpam-1481	278	33	)	)	PUNCT
ejpam-1481	278	34	=	=	PUNCT
ejpam-1481	279	1	¨	¨	X
ejpam-1481	279	2	λ	λ	X
ejpam-1481	279	3	∈	∈	PROPN
ejpam-1481	279	4	c	c	NOUN
ejpam-1481	279	5	:	:	PUNCT
ejpam-1481	279	6	�	�	PROPN
ejpam-1481	279	7	�	�	PROPN
ejpam-1481	279	8	�	�	PROPN
ejpam-1481	279	9	�	�	PROPN
ejpam-1481	279	10	λ−	λ−	PROPN
ejpam-1481	279	11	1	1	NUM
ejpam-1481	279	12	2	2	NUM
ejpam-1481	279	13	�	�	PROPN
ejpam-1481	279	14	�	�	PROPN
ejpam-1481	279	15	�	�	PROPN
ejpam-1481	279	16	�	�	PROPN
ejpam-1481	279	17	<	<	X
ejpam-1481	279	18	1	1	NUM
ejpam-1481	279	19	2	2	NUM
ejpam-1481	279	20	«	«	PUNCT
ejpam-1481	279	21	,	,	PUNCT
ejpam-1481	279	22	σr(∆v	σr(∆v	PROPN
ejpam-1481	279	23	,	,	PUNCT
ejpam-1481	279	24	c0	c0	NOUN
ejpam-1481	279	25	)	)	PUNCT
ejpam-1481	279	26	=	=	PUNCT
ejpam-1481	279	27	¨	¨	X
ejpam-1481	279	28	λ	λ	X
ejpam-1481	279	29	∈	∈	PROPN
ejpam-1481	279	30	c	c	NOUN
ejpam-1481	279	31	:	:	PUNCT
ejpam-1481	279	32	�	�	PROPN
ejpam-1481	279	33	�	�	PROPN
ejpam-1481	279	34	�	�	PROPN
ejpam-1481	279	35	�	�	PROPN
ejpam-1481	279	36	λ−	λ−	PROPN
ejpam-1481	279	37	1	1	NUM
ejpam-1481	279	38	2	2	NUM
ejpam-1481	279	39	�	�	PROPN
ejpam-1481	279	40	�	�	PROPN
ejpam-1481	279	41	�	�	PROPN
ejpam-1481	279	42	�	�	PROPN
ejpam-1481	279	43	<	<	X
ejpam-1481	279	44	1	1	NUM
ejpam-1481	279	45	2	2	NUM
ejpam-1481	279	46	«	«	PUNCT
ejpam-1481	279	47	,	,	PUNCT
ejpam-1481	279	48	σc(∆v	σc(∆v	PROPN
ejpam-1481	279	49	,	,	PUNCT
ejpam-1481	279	50	c0	c0	NOUN
ejpam-1481	279	51	)	)	PUNCT
ejpam-1481	279	52	=	=	PUNCT
ejpam-1481	279	53	¨	¨	X
ejpam-1481	279	54	λ	λ	X
ejpam-1481	279	55	∈	∈	PROPN
ejpam-1481	279	56	c	c	NOUN
ejpam-1481	279	57	:	:	PUNCT
ejpam-1481	279	58	�	�	PROPN
ejpam-1481	279	59	�	�	PROPN
ejpam-1481	279	60	�	�	PROPN
ejpam-1481	279	61	�	�	PROPN
ejpam-1481	279	62	λ−	λ−	PROPN
ejpam-1481	279	63	1	1	NUM
ejpam-1481	279	64	2	2	NUM
ejpam-1481	279	65	�	�	PROPN
ejpam-1481	279	66	�	�	PROPN
ejpam-1481	279	67	�	�	PROPN
ejpam-1481	279	68	�	�	PROPN
ejpam-1481	279	69	=	=	NOUN
ejpam-1481	279	70	1	1	NUM
ejpam-1481	279	71	2	2	NUM
ejpam-1481	279	72	«	«	PUNCT
ejpam-1481	279	73	.	.	PUNCT
ejpam-1481	280	1	in	in	ADP
ejpam-1481	280	2	example	example	NOUN
ejpam-1481	280	3	5	5	NUM
ejpam-1481	280	4	,	,	PUNCT
ejpam-1481	280	5	we	we	PRON
ejpam-1481	280	6	see	see	VERB
ejpam-1481	280	7	that	that	SCONJ
ejpam-1481	280	8	although	although	SCONJ
ejpam-1481	280	9	the	the	DET
ejpam-1481	280	10	sequence	sequence	NOUN
ejpam-1481	280	11	(	(	PUNCT
ejpam-1481	280	12	vk	vk	NOUN
ejpam-1481	280	13	)	)	PUNCT
ejpam-1481	280	14	is	be	AUX
ejpam-1481	280	15	not	not	PART
ejpam-1481	280	16	strictly	strictly	ADV
ejpam-1481	280	17	decreasing	decrease	VERB
ejpam-1481	280	18	,	,	PUNCT
ejpam-1481	280	19	the	the	DET
ejpam-1481	280	20	residual	residual	ADJ
ejpam-1481	280	21	spectrum	spectrum	NOUN
ejpam-1481	280	22	and	and	CCONJ
ejpam-1481	280	23	the	the	DET
ejpam-1481	280	24	continuous	continuous	ADJ
ejpam-1481	280	25	spectrum	spectrum	NOUN
ejpam-1481	280	26	in	in	ADP
ejpam-1481	280	27	addition	addition	NOUN
ejpam-1481	280	28	to	to	ADP
ejpam-1481	280	29	the	the	DET
ejpam-1481	280	30	spectrum	spectrum	NOUN
ejpam-1481	280	31	and	and	CCONJ
ejpam-1481	280	32	the	the	DET
ejpam-1481	280	33	point	point	NOUN
ejpam-1481	280	34	spectrum	spectrum	NOUN
ejpam-1481	280	35	of	of	ADP
ejpam-1481	280	36	the	the	DET
ejpam-1481	280	37	operator	operator	NOUN
ejpam-1481	280	38	∆v	∆v	PROPN
ejpam-1481	280	39	are	be	AUX
ejpam-1481	280	40	completely	completely	ADV
ejpam-1481	280	41	determined	determine	VERB
ejpam-1481	280	42	.	.	PUNCT
ejpam-1481	281	1	in	in	ADP
ejpam-1481	281	2	fact	fact	NOUN
ejpam-1481	281	3	,	,	PUNCT
ejpam-1481	281	4	if	if	SCONJ
ejpam-1481	281	5	(	(	PUNCT
ejpam-1481	281	6	vk	vk	NOUN
ejpam-1481	281	7	)	)	PUNCT
ejpam-1481	281	8	is	be	AUX
ejpam-1481	281	9	assumed	assume	VERB
ejpam-1481	281	10	to	to	PART
ejpam-1481	281	11	be	be	AUX
ejpam-1481	281	12	a	a	DET
ejpam-1481	281	13	sequence	sequence	NOUN
ejpam-1481	281	14	of	of	ADP
ejpam-1481	281	15	positive	positive	ADJ
ejpam-1481	281	16	real	real	ADJ
ejpam-1481	281	17	numbers	number	NOUN
ejpam-1481	281	18	(	(	PUNCT
ejpam-1481	281	19	not	not	PART
ejpam-1481	281	20	necessarily	necessarily	ADV
ejpam-1481	281	21	strictly	strictly	ADV
ejpam-1481	281	22	decreasing	decrease	VERB
ejpam-1481	281	23	)	)	PUNCT
ejpam-1481	281	24	satisfying	satisfy	VERB
ejpam-1481	281	25	the	the	DET
ejpam-1481	281	26	conditions	condition	NOUN
ejpam-1481	281	27	(	(	PUNCT
ejpam-1481	281	28	2	2	NUM
ejpam-1481	281	29	)	)	PUNCT
ejpam-1481	281	30	,	,	PUNCT
ejpam-1481	281	31	then	then	ADV
ejpam-1481	281	32	we	we	PRON
ejpam-1481	281	33	can	can	AUX
ejpam-1481	281	34	have	have	VERB
ejpam-1481	281	35	results	result	NOUN
ejpam-1481	281	36	similar	similar	ADJ
ejpam-1481	281	37	to	to	ADP
ejpam-1481	281	38	those	those	PRON
ejpam-1481	281	39	in	in	ADP
ejpam-1481	281	40	section	section	NOUN
ejpam-1481	281	41	3.2	3.2	NUM
ejpam-1481	281	42	.	.	PUNCT
ejpam-1481	282	1	this	this	PRON
ejpam-1481	282	2	means	mean	VERB
ejpam-1481	282	3	that	that	SCONJ
ejpam-1481	282	4	the	the	DET
ejpam-1481	282	5	condition	condition	NOUN
ejpam-1481	282	6	that	that	SCONJ
ejpam-1481	282	7	(	(	PUNCT
ejpam-1481	282	8	vk	vk	NOUN
ejpam-1481	282	9	)	)	PUNCT
ejpam-1481	282	10	is	be	AUX
ejpam-1481	282	11	a	a	DET
ejpam-1481	282	12	strictly	strictly	ADV
ejpam-1481	282	13	decreasing	decrease	VERB
ejpam-1481	282	14	is	be	AUX
ejpam-1481	282	15	not	not	PART
ejpam-1481	282	16	an	an	DET
ejpam-1481	282	17	effective	effective	ADJ
ejpam-1481	282	18	condition	condition	NOUN
ejpam-1481	282	19	.	.	PUNCT
ejpam-1481	283	1	in	in	ADP
ejpam-1481	283	2	the	the	DET
ejpam-1481	283	3	next	next	ADJ
ejpam-1481	283	4	section	section	NOUN
ejpam-1481	283	5	we	we	PRON
ejpam-1481	283	6	modify	modify	VERB
ejpam-1481	283	7	the	the	DET
ejpam-1481	283	8	definition	definition	NOUN
ejpam-1481	283	9	of	of	ADP
ejpam-1481	283	10	the	the	DET
ejpam-1481	283	11	operator	operator	NOUN
ejpam-1481	283	12	∆v	∆v	PROPN
ejpam-1481	283	13	in	in	ADP
ejpam-1481	283	14	two	two	NUM
ejpam-1481	283	15	ways	way	NOUN
ejpam-1481	283	16	by	by	ADP
ejpam-1481	283	17	dropping	drop	VERB
ejpam-1481	283	18	the	the	DET
ejpam-1481	283	19	condition	condition	NOUN
ejpam-1481	283	20	that	that	SCONJ
ejpam-1481	283	21	(	(	PUNCT
ejpam-1481	283	22	vk	vk	NOUN
ejpam-1481	283	23	)	)	PUNCT
ejpam-1481	283	24	is	be	AUX
ejpam-1481	283	25	strictly	strictly	ADV
ejpam-1481	283	26	decreasing	decrease	VERB
ejpam-1481	283	27	sequence	sequence	NOUN
ejpam-1481	283	28	of	of	ADP
ejpam-1481	283	29	positive	positive	ADJ
ejpam-1481	283	30	real	real	ADJ
ejpam-1481	283	31	numbers	number	NOUN
ejpam-1481	283	32	and	and	CCONJ
ejpam-1481	283	33	replacing	replace	VERB
ejpam-1481	283	34	the	the	DET
ejpam-1481	283	35	conditions	condition	NOUN
ejpam-1481	283	36	(	(	PUNCT
ejpam-1481	283	37	2	2	NUM
ejpam-1481	283	38	)	)	PUNCT
ejpam-1481	283	39	by	by	ADP
ejpam-1481	283	40	another	another	DET
ejpam-1481	283	41	conditions	condition	NOUN
ejpam-1481	283	42	.	.	PUNCT
ejpam-1481	284	1	5	5	X
ejpam-1481	284	2	.	.	X
ejpam-1481	284	3	notes	note	NOUN
ejpam-1481	284	4	on	on	ADP
ejpam-1481	284	5	the	the	DET
ejpam-1481	284	6	fine	fine	ADJ
ejpam-1481	284	7	spectrum	spectrum	NOUN
ejpam-1481	284	8	of	of	ADP
ejpam-1481	284	9	the	the	DET
ejpam-1481	284	10	operator	operator	NOUN
ejpam-1481	284	11	∆	∆	X
ejpam-1481	284	12	v	v	NOUN
ejpam-1481	284	13	on	on	ADP
ejpam-1481	284	14	c0	c0	PROPN
ejpam-1481	284	15	and	and	CCONJ
ejpam-1481	284	16	l1	l1	PROPN
ejpam-1481	284	17	in	in	ADP
ejpam-1481	284	18	this	this	DET
ejpam-1481	284	19	section	section	NOUN
ejpam-1481	284	20	we	we	PRON
ejpam-1481	284	21	are	be	AUX
ejpam-1481	284	22	going	go	VERB
ejpam-1481	284	23	to	to	PART
ejpam-1481	284	24	show	show	VERB
ejpam-1481	284	25	some	some	DET
ejpam-1481	284	26	ideas	idea	NOUN
ejpam-1481	284	27	about	about	ADP
ejpam-1481	284	28	changing	change	VERB
ejpam-1481	284	29	the	the	DET
ejpam-1481	284	30	conditions	condition	NOUN
ejpam-1481	284	31	on	on	ADP
ejpam-1481	284	32	the	the	DET
ejpam-1481	284	33	sequence	sequence	NOUN
ejpam-1481	284	34	(	(	PUNCT
ejpam-1481	284	35	vk	vk	PROPN
ejpam-1481	284	36	)	)	PUNCT
ejpam-1481	284	37	in	in	ADP
ejpam-1481	284	38	the	the	DET
ejpam-1481	284	39	fine	fine	ADJ
ejpam-1481	284	40	spectrum	spectrum	NOUN
ejpam-1481	284	41	of	of	ADP
ejpam-1481	284	42	the	the	DET
ejpam-1481	284	43	operator	operator	NOUN
ejpam-1481	284	44	∆v	∆v	PROPN
ejpam-1481	284	45	.	.	PUNCT
ejpam-1481	285	1	we	we	PRON
ejpam-1481	285	2	consider	consider	VERB
ejpam-1481	285	3	two	two	NUM
ejpam-1481	285	4	modifications	modification	NOUN
ejpam-1481	285	5	of	of	ADP
ejpam-1481	285	6	the	the	DET
ejpam-1481	285	7	operator	operator	NOUN
ejpam-1481	285	8	∆v	∆v	PROPN
ejpam-1481	285	9	.	.	PUNCT
ejpam-1481	286	1	more	more	ADV
ejpam-1481	286	2	precisely	precisely	ADV
ejpam-1481	286	3	,	,	PUNCT
ejpam-1481	286	4	we	we	PRON
ejpam-1481	286	5	modify	modify	VERB
ejpam-1481	286	6	the	the	DET
ejpam-1481	286	7	definition	definition	NOUN
ejpam-1481	286	8	of	of	ADP
ejpam-1481	286	9	the	the	DET
ejpam-1481	286	10	operator	operator	NOUN
ejpam-1481	286	11	∆v	∆v	PROPN
ejpam-1481	286	12	by	by	ADP
ejpam-1481	286	13	changing	change	VERB
ejpam-1481	286	14	the	the	DET
ejpam-1481	286	15	conditions	condition	NOUN
ejpam-1481	286	16	on	on	ADP
ejpam-1481	286	17	the	the	DET
ejpam-1481	286	18	sequence	sequence	NOUN
ejpam-1481	286	19	(	(	PUNCT
ejpam-1481	286	20	vk	vk	PROPN
ejpam-1481	286	21	)	)	PUNCT
ejpam-1481	286	22	in	in	ADP
ejpam-1481	286	23	two	two	NUM
ejpam-1481	286	24	ways	way	NOUN
ejpam-1481	286	25	.	.	PUNCT
ejpam-1481	287	1	first	first	ADV
ejpam-1481	287	2	,	,	PUNCT
ejpam-1481	287	3	we	we	PRON
ejpam-1481	287	4	consider	consider	VERB
ejpam-1481	287	5	the	the	DET
ejpam-1481	287	6	sequence	sequence	NOUN
ejpam-1481	287	7	(	(	PUNCT
ejpam-1481	287	8	vk	vk	NOUN
ejpam-1481	287	9	)	)	PUNCT
ejpam-1481	287	10	of	of	ADP
ejpam-1481	287	11	nonzero	nonzero	NOUN
ejpam-1481	287	12	real	real	ADJ
ejpam-1481	287	13	numbers	number	NOUN
ejpam-1481	287	14	such	such	ADJ
ejpam-1481	287	15	that	that	SCONJ
ejpam-1481	287	16	lim	lim	PROPN
ejpam-1481	287	17	k→∞	k→∞	NOUN
ejpam-1481	287	18	vk	vk	PROPN
ejpam-1481	287	19	=	=	SYM
ejpam-1481	287	20	l	l	NOUN
ejpam-1481	287	21	>	>	PUNCT
ejpam-1481	287	22	0	0	PUNCT
ejpam-1481	287	23	and	and	CCONJ
ejpam-1481	287	24	sup	sup	PROPN
ejpam-1481	287	25	k	k	PROPN
ejpam-1481	287	26	vk	vk	PROPN
ejpam-1481	287	27	≤	≤	NUM
ejpam-1481	287	28	l	l	NOUN
ejpam-1481	287	29	,	,	PUNCT
ejpam-1481	287	30	(	(	PUNCT
ejpam-1481	287	31	9	9	NUM
ejpam-1481	287	32	)	)	PUNCT
ejpam-1481	287	33	and	and	CCONJ
ejpam-1481	287	34	we	we	PRON
ejpam-1481	287	35	study	study	VERB
ejpam-1481	287	36	the	the	DET
ejpam-1481	287	37	fine	fine	ADJ
ejpam-1481	287	38	spectrum	spectrum	NOUN
ejpam-1481	287	39	of	of	ADP
ejpam-1481	287	40	the	the	DET
ejpam-1481	287	41	modified	modify	VERB
ejpam-1481	287	42	operator	operator	NOUN
ejpam-1481	287	43	∆v	∆v	PROPN
ejpam-1481	287	44	on	on	ADP
ejpam-1481	287	45	c0	c0	PROPN
ejpam-1481	287	46	.	.	PUNCT
ejpam-1481	288	1	second	second	ADJ
ejpam-1481	288	2	,	,	PUNCT
ejpam-1481	288	3	we	we	PRON
ejpam-1481	288	4	consider	consider	VERB
ejpam-1481	288	5	the	the	DET
ejpam-1481	288	6	sequence	sequence	NOUN
ejpam-1481	288	7	(	(	PUNCT
ejpam-1481	288	8	vk	vk	NOUN
ejpam-1481	288	9	)	)	PUNCT
ejpam-1481	288	10	of	of	ADP
ejpam-1481	288	11	nonzero	nonzero	NOUN
ejpam-1481	288	12	real	real	ADJ
ejpam-1481	288	13	numbers	number	NOUN
ejpam-1481	288	14	such	such	ADJ
ejpam-1481	288	15	that	that	SCONJ
ejpam-1481	288	16	lim	lim	PROPN
ejpam-1481	288	17	k→∞	k→∞	NOUN
ejpam-1481	288	18	vk	vk	PROPN
ejpam-1481	288	19	=	=	SYM
ejpam-1481	288	20	l	l	NOUN
ejpam-1481	288	21	>	>	X
ejpam-1481	288	22	0	0	NUM
ejpam-1481	288	23	,	,	PUNCT
ejpam-1481	288	24	vk	vk	ADP
ejpam-1481	288	25	≥	≥	NOUN
ejpam-1481	288	26	l	l	NOUN
ejpam-1481	288	27	and	and	CCONJ
ejpam-1481	288	28	vk	vk	PROPN
ejpam-1481	288	29	6=	6=	NUM
ejpam-1481	288	30	2l	2l	NUM
ejpam-1481	288	31	,	,	PUNCT
ejpam-1481	288	32	for	for	ADP
ejpam-1481	288	33	all	all	DET
ejpam-1481	288	34	k	k	PROPN
ejpam-1481	288	35	∈	∈	PROPN
ejpam-1481	288	36	n	n	CCONJ
ejpam-1481	288	37	,	,	PUNCT
ejpam-1481	288	38	(	(	PUNCT
ejpam-1481	288	39	10	10	NUM
ejpam-1481	288	40	)	)	PUNCT
ejpam-1481	288	41	and	and	CCONJ
ejpam-1481	288	42	we	we	PRON
ejpam-1481	288	43	study	study	VERB
ejpam-1481	288	44	the	the	DET
ejpam-1481	288	45	fine	fine	ADJ
ejpam-1481	288	46	spectrum	spectrum	NOUN
ejpam-1481	288	47	of	of	ADP
ejpam-1481	288	48	the	the	DET
ejpam-1481	288	49	modified	modify	VERB
ejpam-1481	288	50	operator	operator	NOUN
ejpam-1481	288	51	∆v	∆v	PROPN
ejpam-1481	288	52	on	on	ADP
ejpam-1481	288	53	l1	l1	PROPN
ejpam-1481	288	54	.	.	PUNCT
ejpam-1481	289	1	we	we	PRON
ejpam-1481	289	2	should	should	AUX
ejpam-1481	289	3	indicate	indicate	VERB
ejpam-1481	289	4	the	the	DET
ejpam-1481	289	5	reader	reader	NOUN
ejpam-1481	289	6	that	that	SCONJ
ejpam-1481	289	7	we	we	PRON
ejpam-1481	289	8	use	use	VERB
ejpam-1481	289	9	the	the	DET
ejpam-1481	289	10	same	same	ADJ
ejpam-1481	289	11	symbol	symbol	NOUN
ejpam-1481	289	12	for	for	ADP
ejpam-1481	289	13	the	the	DET
ejpam-1481	289	14	operator	operator	NOUN
ejpam-1481	289	15	∆v	∆v	PROPN
ejpam-1481	289	16	and	and	CCONJ
ejpam-1481	289	17	its	its	PRON
ejpam-1481	289	18	modifications	modification	NOUN
ejpam-1481	289	19	here	here	ADV
ejpam-1481	289	20	,	,	PUNCT
ejpam-1481	289	21	since	since	SCONJ
ejpam-1481	289	22	they	they	PRON
ejpam-1481	289	23	have	have	VERB
ejpam-1481	289	24	the	the	DET
ejpam-1481	289	25	same	same	ADJ
ejpam-1481	289	26	matrix	matrix	NOUN
ejpam-1481	289	27	representation	representation	NOUN
ejpam-1481	289	28	and	and	CCONJ
ejpam-1481	289	29	the	the	DET
ejpam-1481	289	30	difference	difference	NOUN
ejpam-1481	289	31	between	between	ADP
ejpam-1481	289	32	them	they	PRON
ejpam-1481	289	33	lies	lie	VERB
ejpam-1481	289	34	in	in	ADP
ejpam-1481	289	35	the	the	DET
ejpam-1481	289	36	conditions	condition	NOUN
ejpam-1481	289	37	on	on	ADP
ejpam-1481	289	38	the	the	DET
ejpam-1481	289	39	sequence	sequence	NOUN
ejpam-1481	289	40	(	(	PUNCT
ejpam-1481	289	41	vk	vk	PROPN
ejpam-1481	289	42	)	)	PUNCT
ejpam-1481	289	43	.	.	PUNCT
ejpam-1481	290	1	a.	a.	PROPN
ejpam-1481	290	2	akhmedov	akhmedov	PROPN
ejpam-1481	290	3	,	,	PUNCT
ejpam-1481	290	4	s.	s.	PROPN
ejpam-1481	290	5	el	el	PROPN
ejpam-1481	290	6	-	-	PUNCT
ejpam-1481	290	7	shabrawy	shabrawy	PROPN
ejpam-1481	290	8	/	/	SYM
ejpam-1481	290	9	eur	eur	NOUN
ejpam-1481	290	10	.	.	PUNCT
ejpam-1481	291	1	j.	j.	PROPN
ejpam-1481	291	2	pure	pure	PROPN
ejpam-1481	291	3	appl	appl	PROPN
ejpam-1481	291	4	.	.	PROPN
ejpam-1481	291	5	math	math	PROPN
ejpam-1481	291	6	,	,	PUNCT
ejpam-1481	291	7	5	5	NUM
ejpam-1481	291	8	(	(	PUNCT
ejpam-1481	291	9	2012	2012	NUM
ejpam-1481	291	10	)	)	PUNCT
ejpam-1481	291	11	,	,	PUNCT
ejpam-1481	291	12	59	59	NUM
ejpam-1481	291	13	-	-	SYM
ejpam-1481	291	14	74	74	NUM
ejpam-1481	291	15	69	69	NUM
ejpam-1481	291	16	5.1	5.1	NUM
ejpam-1481	291	17	.	.	PUNCT
ejpam-1481	292	1	the	the	DET
ejpam-1481	292	2	fine	fine	ADJ
ejpam-1481	292	3	spectrum	spectrum	NOUN
ejpam-1481	292	4	of	of	ADP
ejpam-1481	292	5	the	the	DET
ejpam-1481	292	6	modified	modify	VERB
ejpam-1481	292	7	operator	operator	NOUN
ejpam-1481	292	8	∆	∆	X
ejpam-1481	292	9	v	v	NOUN
ejpam-1481	292	10	on	on	ADP
ejpam-1481	292	11	c0	c0	PROPN
ejpam-1481	292	12	in	in	ADP
ejpam-1481	292	13	this	this	DET
ejpam-1481	292	14	subsection	subsection	NOUN
ejpam-1481	292	15	we	we	PRON
ejpam-1481	292	16	calculate	calculate	VERB
ejpam-1481	292	17	the	the	DET
ejpam-1481	292	18	fine	fine	ADJ
ejpam-1481	292	19	spectrum	spectrum	NOUN
ejpam-1481	292	20	of	of	ADP
ejpam-1481	292	21	the	the	DET
ejpam-1481	292	22	modified	modify	VERB
ejpam-1481	292	23	operator	operator	NOUN
ejpam-1481	292	24	∆v	∆v	PROPN
ejpam-1481	292	25	,	,	PUNCT
ejpam-1481	292	26	which	which	PRON
ejpam-1481	292	27	is	be	AUX
ejpam-1481	292	28	represented	represent	VERB
ejpam-1481	292	29	by	by	ADP
ejpam-1481	292	30	the	the	DET
ejpam-1481	292	31	matrix	matrix	NOUN
ejpam-1481	292	32	in	in	ADP
ejpam-1481	292	33	(	(	PUNCT
ejpam-1481	292	34	3	3	X
ejpam-1481	292	35	)	)	PUNCT
ejpam-1481	292	36	such	such	ADJ
ejpam-1481	292	37	that	that	SCONJ
ejpam-1481	292	38	the	the	DET
ejpam-1481	292	39	conditions	condition	NOUN
ejpam-1481	292	40	(	(	PUNCT
ejpam-1481	292	41	9	9	X
ejpam-1481	292	42	)	)	PUNCT
ejpam-1481	292	43	are	be	AUX
ejpam-1481	292	44	satisfied	satisfied	ADJ
ejpam-1481	292	45	,	,	PUNCT
ejpam-1481	292	46	on	on	ADP
ejpam-1481	292	47	the	the	DET
ejpam-1481	292	48	sequence	sequence	NOUN
ejpam-1481	292	49	space	space	NOUN
ejpam-1481	292	50	c0	c0	NOUN
ejpam-1481	292	51	.	.	PUNCT
ejpam-1481	293	1	the	the	DET
ejpam-1481	293	2	modified	modify	VERB
ejpam-1481	293	3	operator	operator	NOUN
ejpam-1481	293	4	∆v	∆v	PROPN
ejpam-1481	293	5	of	of	ADP
ejpam-1481	293	6	this	this	DET
ejpam-1481	293	7	form	form	NOUN
ejpam-1481	293	8	has	have	AUX
ejpam-1481	293	9	been	be	AUX
ejpam-1481	293	10	introduced	introduce	VERB
ejpam-1481	293	11	and	and	CCONJ
ejpam-1481	293	12	studied	study	VERB
ejpam-1481	293	13	by	by	ADP
ejpam-1481	293	14	akhmedov	akhmedov	PROPN
ejpam-1481	293	15	and	and	CCONJ
ejpam-1481	293	16	el	el	NOUN
ejpam-1481	293	17	-	-	PUNCT
ejpam-1481	293	18	shabrawy	shabrawy	PROPN
ejpam-1481	294	1	[	[	X
ejpam-1481	294	2	4	4	X
ejpam-1481	294	3	]	]	PUNCT
ejpam-1481	294	4	over	over	ADP
ejpam-1481	294	5	the	the	DET
ejpam-1481	294	6	sequence	sequence	NOUN
ejpam-1481	294	7	spaces	space	VERB
ejpam-1481	294	8	c	c	NOUN
ejpam-1481	294	9	and	and	CCONJ
ejpam-1481	294	10	lp	lp	NOUN
ejpam-1481	294	11	,	,	PUNCT
ejpam-1481	294	12	where	where	SCONJ
ejpam-1481	294	13	1	1	NUM
ejpam-1481	294	14	<	<	X
ejpam-1481	294	15	p	p	X
ejpam-1481	294	16	<	<	X
ejpam-1481	294	17	∞.	∞.	PROPN
ejpam-1481	294	18	the	the	DET
ejpam-1481	294	19	results	result	NOUN
ejpam-1481	294	20	of	of	ADP
ejpam-1481	294	21	this	this	DET
ejpam-1481	294	22	section	section	NOUN
ejpam-1481	294	23	improve	improve	VERB
ejpam-1481	294	24	the	the	DET
ejpam-1481	294	25	corresponding	corresponding	ADJ
ejpam-1481	294	26	results	result	NOUN
ejpam-1481	294	27	in	in	ADP
ejpam-1481	294	28	section	section	NOUN
ejpam-1481	294	29	3.2	3.2	NUM
ejpam-1481	294	30	.	.	PUNCT
ejpam-1481	295	1	we	we	PRON
ejpam-1481	295	2	begin	begin	VERB
ejpam-1481	295	3	by	by	ADP
ejpam-1481	295	4	determining	determine	VERB
ejpam-1481	295	5	when	when	SCONJ
ejpam-1481	295	6	a	a	DET
ejpam-1481	295	7	matrix	matrix	NOUN
ejpam-1481	295	8	a	a	DET
ejpam-1481	295	9	induces	induce	VERB
ejpam-1481	295	10	a	a	DET
ejpam-1481	295	11	bounded	bounded	ADJ
ejpam-1481	295	12	linear	linear	ADJ
ejpam-1481	295	13	operator	operator	NOUN
ejpam-1481	295	14	from	from	ADP
ejpam-1481	295	15	c0	c0	NOUN
ejpam-1481	295	16	to	to	ADP
ejpam-1481	295	17	itself	itself	PRON
ejpam-1481	295	18	.	.	PUNCT
ejpam-1481	296	1	lemma	lemma	PROPN
ejpam-1481	296	2	2	2	NUM
ejpam-1481	296	3	(	(	PUNCT
ejpam-1481	296	4	[	[	X
ejpam-1481	296	5	26	26	NUM
ejpam-1481	296	6	,	,	PUNCT
ejpam-1481	296	7	p.	p.	NOUN
ejpam-1481	296	8	129	129	NUM
ejpam-1481	296	9	]	]	PUNCT
ejpam-1481	296	10	)	)	PUNCT
ejpam-1481	296	11	.	.	PUNCT
ejpam-1481	297	1	the	the	DET
ejpam-1481	297	2	matrix	matrix	NOUN
ejpam-1481	297	3	a	a	DET
ejpam-1481	297	4	=	=	SYM
ejpam-1481	297	5	�	�	PROPN
ejpam-1481	297	6	ank	ank	PROPN
ejpam-1481	297	7	�	�	PROPN
ejpam-1481	297	8	gives	give	VERB
ejpam-1481	297	9	rise	rise	NOUN
ejpam-1481	297	10	to	to	ADP
ejpam-1481	297	11	a	a	DET
ejpam-1481	297	12	bounded	bounded	ADJ
ejpam-1481	297	13	linear	linear	ADJ
ejpam-1481	297	14	operator	operator	NOUN
ejpam-1481	297	15	t	t	PROPN
ejpam-1481	297	16	∈	∈	PROPN
ejpam-1481	297	17	b	b	PROPN
ejpam-1481	297	18	�	�	PROPN
ejpam-1481	297	19	c0	c0	PROPN
ejpam-1481	297	20	�	�	PROPN
ejpam-1481	297	21	from	from	ADP
ejpam-1481	297	22	c0	c0	PROPN
ejpam-1481	297	23	to	to	ADP
ejpam-1481	297	24	itself	itself	PRON
ejpam-1481	297	25	if	if	SCONJ
ejpam-1481	297	26	and	and	CCONJ
ejpam-1481	297	27	only	only	ADV
ejpam-1481	297	28	if	if	SCONJ
ejpam-1481	297	29	(	(	PUNCT
ejpam-1481	297	30	i	i	NOUN
ejpam-1481	297	31	)	)	PUNCT
ejpam-1481	297	32	the	the	DET
ejpam-1481	297	33	rows	row	NOUN
ejpam-1481	297	34	of	of	ADP
ejpam-1481	297	35	a	a	PRON
ejpam-1481	297	36	are	be	AUX
ejpam-1481	297	37	in	in	ADP
ejpam-1481	297	38	l1	l1	PROPN
ejpam-1481	297	39	and	and	CCONJ
ejpam-1481	297	40	their	their	PRON
ejpam-1481	297	41	l1	l1	PROPN
ejpam-1481	297	42	norms	norm	NOUN
ejpam-1481	297	43	are	be	AUX
ejpam-1481	297	44	bounded	bound	VERB
ejpam-1481	297	45	,	,	PUNCT
ejpam-1481	297	46	(	(	PUNCT
ejpam-1481	297	47	ii	ii	NOUN
ejpam-1481	297	48	)	)	PUNCT
ejpam-1481	297	49	the	the	DET
ejpam-1481	297	50	columns	column	NOUN
ejpam-1481	297	51	of	of	ADP
ejpam-1481	297	52	a	a	PRON
ejpam-1481	297	53	are	be	AUX
ejpam-1481	297	54	in	in	ADP
ejpam-1481	297	55	c0	c0	NOUN
ejpam-1481	297	56	.	.	PUNCT
ejpam-1481	298	1	the	the	DET
ejpam-1481	298	2	operator	operator	NOUN
ejpam-1481	298	3	norm	norm	NOUN
ejpam-1481	298	4	of	of	ADP
ejpam-1481	298	5	t	t	PROPN
ejpam-1481	298	6	is	be	AUX
ejpam-1481	298	7	the	the	DET
ejpam-1481	298	8	supremum	supremum	NOUN
ejpam-1481	298	9	of	of	ADP
ejpam-1481	298	10	the	the	DET
ejpam-1481	298	11	l1	l1	PROPN
ejpam-1481	298	12	norms	norm	NOUN
ejpam-1481	298	13	of	of	ADP
ejpam-1481	298	14	the	the	DET
ejpam-1481	298	15	rows	row	NOUN
ejpam-1481	298	16	.	.	PUNCT
ejpam-1481	299	1	corollary	corollary	ADJ
ejpam-1481	299	2	1	1	NUM
ejpam-1481	299	3	.	.	PUNCT
ejpam-1481	300	1	the	the	DET
ejpam-1481	300	2	modified	modify	VERB
ejpam-1481	300	3	operator	operator	NOUN
ejpam-1481	300	4	∆v	∆v	PROPN
ejpam-1481	300	5	:	:	PUNCT
ejpam-1481	300	6	c0	c0	PROPN
ejpam-1481	300	7	→	→	SYM
ejpam-1481	300	8	c0	c0	PROPN
ejpam-1481	300	9	is	be	AUX
ejpam-1481	300	10	a	a	DET
ejpam-1481	300	11	bounded	bounded	ADJ
ejpam-1481	300	12	linear	linear	ADJ
ejpam-1481	300	13	operator	operator	NOUN
ejpam-1481	300	14	with	with	ADP
ejpam-1481	300	15	the	the	DET
ejpam-1481	300	16	norm	norm	NOUN
ejpam-1481	300	17	∆v	∆v	PROPN
ejpam-1481	300	18	c0	c0	NOUN
ejpam-1481	300	19	=	=	PROPN
ejpam-1481	301	1	sup	sup	PROPN
ejpam-1481	301	2	k	k	PROPN
ejpam-1481	301	3	(	(	PUNCT
ejpam-1481	301	4	�	�	PROPN
ejpam-1481	301	5	�	�	PROPN
ejpam-1481	301	6	vk	vk	PROPN
ejpam-1481	301	7	�	�	PROPN
ejpam-1481	301	8	�	�	PROPN
ejpam-1481	301	9	+	+	PROPN
ejpam-1481	301	10	�	�	PROPN
ejpam-1481	301	11	�	�	PROPN
ejpam-1481	301	12	vk−1	vk−1	PROPN
ejpam-1481	301	13	�	�	PROPN
ejpam-1481	301	14	�	�	PROPN
ejpam-1481	301	15	)	)	PUNCT
ejpam-1481	301	16	.	.	PUNCT
ejpam-1481	302	1	theorem	theorem	ADJ
ejpam-1481	302	2	10	10	NUM
ejpam-1481	302	3	.	.	PUNCT
ejpam-1481	303	1	let	let	VERB
ejpam-1481	303	2	d	d	NOUN
ejpam-1481	303	3	=	=	SYM
ejpam-1481	303	4	{	{	PUNCT
ejpam-1481	303	5	λ	λ	X
ejpam-1481	303	6	∈	∈	PROPN
ejpam-1481	303	7	c	c	NOUN
ejpam-1481	303	8	:	:	PUNCT
ejpam-1481	303	9	|λ−	|λ−	NOUN
ejpam-1481	303	10	l|	l|	ADJ
ejpam-1481	303	11	≤	≤	ADJ
ejpam-1481	303	12	l	l	NOUN
ejpam-1481	303	13	}	}	PUNCT
ejpam-1481	303	14	and	and	CCONJ
ejpam-1481	303	15	e	e	NOUN
ejpam-1481	303	16	=	=	SYM
ejpam-1481	303	17	¦	¦	PROPN
ejpam-1481	303	18	vk	vk	NOUN
ejpam-1481	303	19	:	:	PUNCT
ejpam-1481	303	20	k	k	PROPN
ejpam-1481	303	21	∈	∈	PROPN
ejpam-1481	303	22	n	n	CCONJ
ejpam-1481	303	23	,	,	PUNCT
ejpam-1481	303	24	�	�	PROPN
ejpam-1481	303	25	�	�	PROPN
ejpam-1481	303	26	vk	vk	ADP
ejpam-1481	303	27	−	−	PROPN
ejpam-1481	303	28	l	l	X
ejpam-1481	303	29	�	�	PROPN
ejpam-1481	303	30	�	�	PROPN
ejpam-1481	303	31	>	>	PUNCT
ejpam-1481	303	32	l	l	PROPN
ejpam-1481	304	1	©	©	PROPN
ejpam-1481	304	2	.	.	PUNCT
ejpam-1481	305	1	then	then	ADV
ejpam-1481	305	2	σ(∆v	σ(∆v	NOUN
ejpam-1481	305	3	,	,	PUNCT
ejpam-1481	305	4	c0	c0	NOUN
ejpam-1481	305	5	)	)	PUNCT
ejpam-1481	305	6	=	=	PUNCT
ejpam-1481	306	1	d	d	X
ejpam-1481	306	2	∪	∪	ADP
ejpam-1481	306	3	e.	e.	PROPN
ejpam-1481	306	4	proof	proof	NOUN
ejpam-1481	306	5	.	.	PUNCT
ejpam-1481	307	1	first	first	ADV
ejpam-1481	307	2	,	,	PUNCT
ejpam-1481	307	3	we	we	PRON
ejpam-1481	307	4	prove	prove	VERB
ejpam-1481	307	5	that	that	SCONJ
ejpam-1481	307	6	(	(	PUNCT
ejpam-1481	307	7	∆v	∆v	NOUN
ejpam-1481	307	8	−	−	NOUN
ejpam-1481	308	1	λi)−1	λi)−1	ADP
ejpam-1481	308	2	exists	exist	VERB
ejpam-1481	308	3	and	and	CCONJ
ejpam-1481	308	4	is	be	AUX
ejpam-1481	308	5	in	in	ADP
ejpam-1481	308	6	b(c0	b(c0	NOUN
ejpam-1481	308	7	)	)	PUNCT
ejpam-1481	308	8	for	for	ADP
ejpam-1481	308	9	λ	λ	PROPN
ejpam-1481	308	10	/∈	/∈	PUNCT
ejpam-1481	309	1	d	d	X
ejpam-1481	309	2	∪	∪	NOUN
ejpam-1481	309	3	e	e	NOUN
ejpam-1481	309	4	and	and	CCONJ
ejpam-1481	309	5	then	then	ADV
ejpam-1481	309	6	the	the	DET
ejpam-1481	309	7	operator	operator	NOUN
ejpam-1481	309	8	∆v	∆v	PROPN
ejpam-1481	309	9	−λi	−λi	ADV
ejpam-1481	309	10	is	be	AUX
ejpam-1481	309	11	not	not	PART
ejpam-1481	309	12	invertible	invertible	ADJ
ejpam-1481	309	13	for	for	SCONJ
ejpam-1481	309	14	λ	λ	PROPN
ejpam-1481	309	15	∈	∈	PROPN
ejpam-1481	309	16	d	d	X
ejpam-1481	309	17	∪	∪	PROPN
ejpam-1481	309	18	e.	e.	PROPN
ejpam-1481	309	19	let	let	VERB
ejpam-1481	310	1	λ	λ	PROPN
ejpam-1481	310	2	/∈	/∈	PUNCT
ejpam-1481	311	1	d	d	AUX
ejpam-1481	311	2	∪	∪	ADP
ejpam-1481	311	3	e.	e.	PROPN
ejpam-1481	311	4	then	then	ADV
ejpam-1481	311	5	,	,	PUNCT
ejpam-1481	311	6	|λ−	|λ−	PUNCT
ejpam-1481	311	7	l|	l|	PROPN
ejpam-1481	311	8	>	>	X
ejpam-1481	311	9	l	l	NOUN
ejpam-1481	311	10	and	and	CCONJ
ejpam-1481	311	11	λ	λ	PROPN
ejpam-1481	311	12	6=	6=	PROPN
ejpam-1481	311	13	vk	vk	PROPN
ejpam-1481	311	14	for	for	ADP
ejpam-1481	311	15	all	all	DET
ejpam-1481	311	16	k	k	PROPN
ejpam-1481	311	17	∈	∈	PROPN
ejpam-1481	311	18	n.	n.	NOUN
ejpam-1481	312	1	so	so	ADV
ejpam-1481	312	2	,	,	PUNCT
ejpam-1481	312	3	∆v	∆v	PROPN
ejpam-1481	312	4	−	−	PROPN
ejpam-1481	312	5	λi	λi	ADP
ejpam-1481	312	6	is	be	AUX
ejpam-1481	312	7	triangle	triangle	NOUN
ejpam-1481	312	8	,	,	PUNCT
ejpam-1481	312	9	and	and	CCONJ
ejpam-1481	312	10	hence	hence	ADV
ejpam-1481	312	11	(	(	PUNCT
ejpam-1481	312	12	∆v	∆v	PROPN
ejpam-1481	312	13	−λi)−1	−λi)−1	NOUN
ejpam-1481	312	14	exists	exist	VERB
ejpam-1481	312	15	.	.	PUNCT
ejpam-1481	313	1	we	we	PRON
ejpam-1481	313	2	can	can	AUX
ejpam-1481	313	3	calculate	calculate	VERB
ejpam-1481	313	4	that	that	PRON
ejpam-1481	313	5	(	(	PUNCT
ejpam-1481	313	6	∆v	∆v	PROPN
ejpam-1481	313	7	−λi)−1	−λi)−1	NUM
ejpam-1481	313	8	=	=	SYM
ejpam-1481	313	9			PROPN
ejpam-1481	313	10			NOUN
ejpam-1481	313	11			NOUN
ejpam-1481	313	12			NOUN
ejpam-1481	313	13			NOUN
ejpam-1481	313	14			NOUN
ejpam-1481	313	15			NOUN
ejpam-1481	313	16	1	1	NUM
ejpam-1481	313	17	(	(	PUNCT
ejpam-1481	313	18	v0−λ	v0−λ	PROPN
ejpam-1481	313	19	)	)	PUNCT
ejpam-1481	313	20	0	0	NUM
ejpam-1481	313	21	0	0	NUM
ejpam-1481	313	22	·	·	PUNCT
ejpam-1481	313	23	·	·	PUNCT
ejpam-1481	313	24	·	·	PUNCT
ejpam-1481	313	25	v0	v0	NOUN
ejpam-1481	313	26	(	(	PUNCT
ejpam-1481	313	27	v0−λ)(v1−λ	v0−λ)(v1−λ	PROPN
ejpam-1481	313	28	)	)	PUNCT
ejpam-1481	313	29	1	1	NUM
ejpam-1481	313	30	(	(	PUNCT
ejpam-1481	313	31	v1−λ	v1−λ	PROPN
ejpam-1481	313	32	)	)	PUNCT
ejpam-1481	313	33	0	0	NUM
ejpam-1481	313	34	·	·	PUNCT
ejpam-1481	313	35	·	·	PUNCT
ejpam-1481	313	36	·	·	PUNCT
ejpam-1481	314	1	v0v1	v0v1	X
ejpam-1481	314	2	(	(	PUNCT
ejpam-1481	314	3	v0−λ)(v1−λ)(v2−λ	v0−λ)(v1−λ)(v2−λ	NOUN
ejpam-1481	314	4	)	)	PUNCT
ejpam-1481	314	5	v1	v1	PROPN
ejpam-1481	314	6	(	(	PUNCT
ejpam-1481	314	7	v1−λ)(v2−λ	v1−λ)(v2−λ	NOUN
ejpam-1481	314	8	)	)	PUNCT
ejpam-1481	314	9	1	1	NUM
ejpam-1481	314	10	(	(	PUNCT
ejpam-1481	314	11	v2−λ	v2−λ	PROPN
ejpam-1481	314	12	)	)	PUNCT
ejpam-1481	314	13	·	·	PUNCT
ejpam-1481	314	14	·	·	PUNCT
ejpam-1481	314	15	·	·	PUNCT
ejpam-1481	314	16	...	...	PUNCT
ejpam-1481	314	17	...	...	PUNCT
ejpam-1481	314	18	...	...	PUNCT
ejpam-1481	314	19	.	.	PUNCT
ejpam-1481	314	20	.	.	PUNCT
ejpam-1481	314	21	.	.	PUNCT
ejpam-1481	315	1			PROPN
ejpam-1481	315	2			NOUN
ejpam-1481	315	3			VERB
ejpam-1481	315	4			NOUN
ejpam-1481	315	5			NOUN
ejpam-1481	315	6			NOUN
ejpam-1481	315	7			PUNCT
ejpam-1481	315	8	.	.	PUNCT
ejpam-1481	316	1	then	then	ADV
ejpam-1481	316	2	,	,	PUNCT
ejpam-1481	316	3	the	the	DET
ejpam-1481	316	4	rows	row	NOUN
ejpam-1481	316	5	of	of	ADP
ejpam-1481	316	6	(	(	PUNCT
ejpam-1481	316	7	∆v	∆v	PROPN
ejpam-1481	316	8	−	−	PROPN
ejpam-1481	316	9	λi)−1	λi)−1	ADP
ejpam-1481	316	10	are	be	AUX
ejpam-1481	316	11	in	in	ADP
ejpam-1481	316	12	l1	l1	PROPN
ejpam-1481	316	13	and	and	CCONJ
ejpam-1481	316	14	the	the	DET
ejpam-1481	316	15	supremum	supremum	NOUN
ejpam-1481	316	16	of	of	ADP
ejpam-1481	316	17	the	the	DET
ejpam-1481	316	18	l1	l1	PROPN
ejpam-1481	316	19	norms	norm	NOUN
ejpam-1481	316	20	of	of	ADP
ejpam-1481	316	21	the	the	DET
ejpam-1481	316	22	rows	row	NOUN
ejpam-1481	316	23	of	of	ADP
ejpam-1481	316	24	(	(	PUNCT
ejpam-1481	316	25	∆v	∆v	PROPN
ejpam-1481	316	26	−λi)−1	−λi)−1	ADJ
ejpam-1481	316	27	is	be	AUX
ejpam-1481	316	28	sup	sup	NOUN
ejpam-1481	316	29	k	k	NOUN
ejpam-1481	316	30	sk	sk	NOUN
ejpam-1481	316	31	,	,	PUNCT
ejpam-1481	316	32	where	where	SCONJ
ejpam-1481	316	33	sk	sk	PROPN
ejpam-1481	316	34	=	=	PUNCT
ejpam-1481	316	35			PROPN
ejpam-1481	316	36			NUM
ejpam-1481	316	37	1	1	NUM
ejpam-1481	316	38	�	�	PROPN
ejpam-1481	316	39	�	�	PROPN
ejpam-1481	316	40	vk	vk	PROPN
ejpam-1481	316	41	−λ	−λ	PROPN
ejpam-1481	316	42	�	�	PROPN
ejpam-1481	316	43	�	�	PROPN
ejpam-1481	316	44	+	+	CCONJ
ejpam-1481	316	45	�	�	PROPN
ejpam-1481	316	46	�	�	PROPN
ejpam-1481	316	47	vk−1	vk−1	PROPN
ejpam-1481	316	48	�	�	PROPN
ejpam-1481	316	49	�	�	PROPN
ejpam-1481	316	50	�	�	PROPN
ejpam-1481	316	51	�	�	PROPN
ejpam-1481	316	52	vk	vk	PROPN
ejpam-1481	316	53	−λ	−λ	PROPN
ejpam-1481	316	54	�	�	PROPN
ejpam-1481	316	55	�	�	PROPN
ejpam-1481	316	56	�	�	PROPN
ejpam-1481	316	57	�	�	PROPN
ejpam-1481	316	58	vk−1−λ	vk−1−λ	PROPN
ejpam-1481	316	59	�	�	PROPN
ejpam-1481	316	60	�	�	PROPN
ejpam-1481	316	61	+	+	CCONJ
ejpam-1481	316	62	.	.	PUNCT
ejpam-1481	316	63	.	.	PUNCT
ejpam-1481	316	64	.	.	PUNCT
ejpam-1481	317	1	.+	.+	PROPN
ejpam-1481	317	2	�	�	PROPN
ejpam-1481	317	3	�	�	PROPN
ejpam-1481	317	4	vk−1	vk−1	PROPN
ejpam-1481	317	5	�	�	PROPN
ejpam-1481	317	6	�	�	PROPN
ejpam-1481	317	7	�	�	PROPN
ejpam-1481	317	8	�	�	PROPN
ejpam-1481	317	9	vk−2	vk−2	PROPN
ejpam-1481	317	10	�	�	PROPN
ejpam-1481	317	11	�	�	PROPN
ejpam-1481	317	12	.	.	PUNCT
ejpam-1481	317	13	.	.	PUNCT
ejpam-1481	317	14	.	.	PUNCT
ejpam-1481	318	1	�	�	PROPN
ejpam-1481	318	2	�	�	PROPN
ejpam-1481	318	3	v0	v0	PROPN
ejpam-1481	318	4	�	�	PROPN
ejpam-1481	318	5	�	�	PROPN
ejpam-1481	318	6	�	�	PROPN
ejpam-1481	318	7	�	�	PROPN
ejpam-1481	318	8	vk	vk	PROPN
ejpam-1481	318	9	−λ	−λ	PROPN
ejpam-1481	318	10	�	�	PROPN
ejpam-1481	318	11	�	�	PROPN
ejpam-1481	318	12	�	�	PROPN
ejpam-1481	318	13	�	�	PROPN
ejpam-1481	318	14	vk−1−λ	vk−1−λ	PROPN
ejpam-1481	318	15	�	�	PROPN
ejpam-1481	318	16	�	�	PROPN
ejpam-1481	318	17	.	.	PUNCT
ejpam-1481	318	18	.	.	PUNCT
ejpam-1481	318	19	.	.	PUNCT
ejpam-1481	319	1	�	�	PROPN
ejpam-1481	319	2	�	�	PROPN
ejpam-1481	319	3	v0−λ	v0−λ	PROPN
ejpam-1481	319	4	�	�	PROPN
ejpam-1481	319	5	�	�	PROPN
ejpam-1481	319	6			PROPN
ejpam-1481	319	7			PROPN
ejpam-1481	319	8	,	,	PUNCT
ejpam-1481	319	9	k	k	PROPN
ejpam-1481	319	10	∈	∈	PROPN
ejpam-1481	319	11	n.	n.	NOUN
ejpam-1481	319	12	then	then	ADV
ejpam-1481	319	13	,	,	PUNCT
ejpam-1481	319	14	we	we	PRON
ejpam-1481	319	15	can	can	AUX
ejpam-1481	319	16	easily	easily	ADV
ejpam-1481	319	17	prove	prove	VERB
ejpam-1481	319	18	that	that	SCONJ
ejpam-1481	319	19	sup	sup	NOUN
ejpam-1481	319	20	k	k	PROPN
ejpam-1481	319	21	sk	sk	NOUN
ejpam-1481	319	22	<	<	X
ejpam-1481	319	23	∞.	∞.	PROPN
ejpam-1481	319	24	also	also	ADV
ejpam-1481	319	25	,	,	PUNCT
ejpam-1481	319	26	it	it	PRON
ejpam-1481	319	27	is	be	AUX
ejpam-1481	319	28	clear	clear	ADJ
ejpam-1481	319	29	that	that	SCONJ
ejpam-1481	319	30	the	the	DET
ejpam-1481	319	31	columns	column	NOUN
ejpam-1481	319	32	of	of	ADP
ejpam-1481	319	33	(	(	PUNCT
ejpam-1481	319	34	∆v	∆v	PROPN
ejpam-1481	319	35	−	−	PROPN
ejpam-1481	319	36	λi)−1	λi)−1	ADP
ejpam-1481	319	37	are	be	AUX
ejpam-1481	319	38	in	in	ADP
ejpam-1481	319	39	c0	c0	PROPN
ejpam-1481	319	40	.	.	PUNCT
ejpam-1481	320	1	from	from	ADP
ejpam-1481	320	2	lemma	lemma	PROPN
ejpam-1481	320	3	2	2	NUM
ejpam-1481	320	4	,	,	PUNCT
ejpam-1481	320	5	(	(	PUNCT
ejpam-1481	320	6	∆v	∆v	PROPN
ejpam-1481	320	7	−λi)−1	−λi)−1	NUM
ejpam-1481	320	8	∈	∈	PROPN
ejpam-1481	320	9	(	(	PUNCT
ejpam-1481	320	10	c0	c0	NOUN
ejpam-1481	320	11	,	,	PUNCT
ejpam-1481	320	12	c0	c0	NOUN
ejpam-1481	320	13	)	)	PUNCT
ejpam-1481	320	14	.	.	PUNCT
ejpam-1481	321	1	thus	thus	ADV
ejpam-1481	321	2	σ(∆v	σ(∆v	VERB
ejpam-1481	321	3	,	,	PUNCT
ejpam-1481	321	4	c0)⊆	c0)⊆	NOUN
ejpam-1481	321	5	d	d	X
ejpam-1481	321	6	∪	∪	PROPN
ejpam-1481	321	7	e.	e.	PROPN
ejpam-1481	321	8	a.	a.	PROPN
ejpam-1481	321	9	akhmedov	akhmedov	PROPN
ejpam-1481	321	10	,	,	PUNCT
ejpam-1481	321	11	s.	s.	PROPN
ejpam-1481	321	12	el	el	PROPN
ejpam-1481	321	13	-	-	PUNCT
ejpam-1481	321	14	shabrawy	shabrawy	PROPN
ejpam-1481	321	15	/	/	SYM
ejpam-1481	321	16	eur	eur	NOUN
ejpam-1481	321	17	.	.	PUNCT
ejpam-1481	322	1	j.	j.	PROPN
ejpam-1481	322	2	pure	pure	PROPN
ejpam-1481	322	3	appl	appl	PROPN
ejpam-1481	322	4	.	.	PROPN
ejpam-1481	322	5	math	math	PROPN
ejpam-1481	322	6	,	,	PUNCT
ejpam-1481	322	7	5	5	NUM
ejpam-1481	322	8	(	(	PUNCT
ejpam-1481	322	9	2012	2012	NUM
ejpam-1481	322	10	)	)	PUNCT
ejpam-1481	322	11	,	,	PUNCT
ejpam-1481	322	12	59	59	NUM
ejpam-1481	322	13	-	-	SYM
ejpam-1481	322	14	74	74	NUM
ejpam-1481	322	15	70	70	NUM
ejpam-1481	322	16	conversely	conversely	ADV
ejpam-1481	322	17	,	,	PUNCT
ejpam-1481	322	18	suppose	suppose	VERB
ejpam-1481	322	19	that	that	SCONJ
ejpam-1481	322	20	λ	λ	PROPN
ejpam-1481	322	21	/∈	/∈	PUNCT
ejpam-1481	322	22	σ(∆v	σ(∆v	NOUN
ejpam-1481	322	23	,	,	PUNCT
ejpam-1481	322	24	c0	c0	NOUN
ejpam-1481	322	25	)	)	PUNCT
ejpam-1481	322	26	.	.	PUNCT
ejpam-1481	323	1	then	then	ADV
ejpam-1481	323	2	(	(	PUNCT
ejpam-1481	323	3	∆v	∆v	PROPN
ejpam-1481	323	4	−	−	NOUN
ejpam-1481	323	5	λi)−1	λi)−1	NOUN
ejpam-1481	323	6	∈	∈	NOUN
ejpam-1481	323	7	b(c0	b(c0	NOUN
ejpam-1481	323	8	)	)	PUNCT
ejpam-1481	323	9	.	.	PUNCT
ejpam-1481	324	1	since	since	SCONJ
ejpam-1481	324	2	(	(	PUNCT
ejpam-1481	324	3	∆v	∆v	PROPN
ejpam-1481	324	4	−	−	PROPN
ejpam-1481	324	5	λi)−1transform	λi)−1transform	NOUN
ejpam-1481	324	6	of	of	ADP
ejpam-1481	324	7	the	the	DET
ejpam-1481	324	8	unit	unit	NOUN
ejpam-1481	324	9	sequence	sequence	NOUN
ejpam-1481	324	10	e	e	NOUN
ejpam-1481	324	11	=	=	PUNCT
ejpam-1481	324	12	(	(	PUNCT
ejpam-1481	324	13	1,0,0	1,0,0	NUM
ejpam-1481	324	14	,	,	PUNCT
ejpam-1481	324	15	.	.	PUNCT
ejpam-1481	324	16	.	.	PUNCT
ejpam-1481	324	17	.	.	PUNCT
ejpam-1481	324	18	)	)	PUNCT
ejpam-1481	325	1	is	be	AUX
ejpam-1481	325	2	in	in	ADP
ejpam-1481	325	3	c0	c0	NOUN
ejpam-1481	325	4	,	,	PUNCT
ejpam-1481	325	5	we	we	PRON
ejpam-1481	325	6	have	have	VERB
ejpam-1481	325	7	lim	lim	PROPN
ejpam-1481	325	8	k→∞	k→∞	PROPN
ejpam-1481	325	9	�	�	PROPN
ejpam-1481	325	10	�	�	PROPN
ejpam-1481	325	11	�	�	PROPN
ejpam-1481	325	12	vk	vk	PROPN
ejpam-1481	325	13	vk+1−λ	vk+1−λ	NOUN
ejpam-1481	325	14	�	�	PROPN
ejpam-1481	325	15	�	�	PROPN
ejpam-1481	325	16	�	�	PROPN
ejpam-1481	325	17	=	=	SYM
ejpam-1481	325	18	�	�	PROPN
ejpam-1481	325	19	�	�	PROPN
ejpam-1481	325	20	�	�	PROPN
ejpam-1481	325	21	l	l	PROPN
ejpam-1481	325	22	l−λ	l−λ	PROPN
ejpam-1481	325	23	�	�	PROPN
ejpam-1481	325	24	�	�	PROPN
ejpam-1481	325	25	�	�	PROPN
ejpam-1481	325	26	≤	≤	PROPN
ejpam-1481	325	27	1	1	NUM
ejpam-1481	325	28	and	and	CCONJ
ejpam-1481	325	29	λ	λ	PROPN
ejpam-1481	325	30	6=	6=	PROPN
ejpam-1481	325	31	vk	vk	PROPN
ejpam-1481	325	32	for	for	ADP
ejpam-1481	325	33	all	all	DET
ejpam-1481	325	34	k	k	PROPN
ejpam-1481	325	35	∈	∈	PROPN
ejpam-1481	325	36	n.	n.	NOUN
ejpam-1481	325	37	then	then	ADV
ejpam-1481	326	1	{	{	PUNCT
ejpam-1481	326	2	λ	λ	X
ejpam-1481	326	3	∈	∈	PROPN
ejpam-1481	326	4	c	c	NOUN
ejpam-1481	326	5	:	:	PUNCT
ejpam-1481	326	6	|λ−	|λ−	NOUN
ejpam-1481	326	7	l|	l|	ADJ
ejpam-1481	326	8	<	<	X
ejpam-1481	326	9	l	l	NOUN
ejpam-1481	326	10	}	}	PUNCT
ejpam-1481	326	11	⊆	⊆	NUM
ejpam-1481	326	12	σ(∆v	σ(∆v	NOUN
ejpam-1481	326	13	,	,	PUNCT
ejpam-1481	326	14	c0	c0	NOUN
ejpam-1481	326	15	)	)	PUNCT
ejpam-1481	326	16	and	and	CCONJ
ejpam-1481	326	17	�	�	PROPN
ejpam-1481	326	18	vk	vk	NOUN
ejpam-1481	326	19	:	:	PUNCT
ejpam-1481	326	20	k	k	PROPN
ejpam-1481	326	21	∈	∈	PROPN
ejpam-1481	326	22	n	n	PRON
ejpam-1481	326	23	⊆	⊆	NUM
ejpam-1481	326	24	σ(∆v	σ(∆v	NOUN
ejpam-1481	326	25	,	,	PUNCT
ejpam-1481	326	26	c0	c0	NOUN
ejpam-1481	326	27	)	)	PUNCT
ejpam-1481	326	28	.	.	PUNCT
ejpam-1481	327	1	but	but	CCONJ
ejpam-1481	327	2	σ(∆v	σ(∆v	NOUN
ejpam-1481	327	3	,	,	PUNCT
ejpam-1481	327	4	c0	c0	NOUN
ejpam-1481	327	5	)	)	PUNCT
ejpam-1481	327	6	is	be	AUX
ejpam-1481	327	7	compact	compact	ADJ
ejpam-1481	327	8	set	set	NOUN
ejpam-1481	327	9	,	,	PUNCT
ejpam-1481	327	10	and	and	CCONJ
ejpam-1481	327	11	so	so	ADV
ejpam-1481	327	12	it	it	PRON
ejpam-1481	327	13	is	be	AUX
ejpam-1481	327	14	closed	closed	ADJ
ejpam-1481	327	15	.	.	PUNCT
ejpam-1481	328	1	then	then	ADV
ejpam-1481	328	2	d	d	X
ejpam-1481	328	3	=	=	PUNCT
ejpam-1481	328	4	{	{	PUNCT
ejpam-1481	328	5	λ	λ	X
ejpam-1481	328	6	∈	∈	PROPN
ejpam-1481	328	7	c	c	NOUN
ejpam-1481	328	8	:	:	PUNCT
ejpam-1481	328	9	|λ−	|λ−	NOUN
ejpam-1481	328	10	l|	l|	ADJ
ejpam-1481	328	11	≤	≤	ADJ
ejpam-1481	328	12	l	l	NOUN
ejpam-1481	328	13	}	}	PUNCT
ejpam-1481	328	14	⊆	⊆	NUM
ejpam-1481	328	15	σ(∆v	σ(∆v	NOUN
ejpam-1481	328	16	,	,	PUNCT
ejpam-1481	328	17	c0	c0	NOUN
ejpam-1481	328	18	)	)	PUNCT
ejpam-1481	328	19	and	and	CCONJ
ejpam-1481	328	20	e	e	X
ejpam-1481	328	21	=	=	SYM
ejpam-1481	328	22	¦	¦	PROPN
ejpam-1481	328	23	vk	vk	NOUN
ejpam-1481	328	24	:	:	PUNCT
ejpam-1481	328	25	k	k	PROPN
ejpam-1481	328	26	∈	∈	PROPN
ejpam-1481	328	27	n	n	CCONJ
ejpam-1481	328	28	,	,	PUNCT
ejpam-1481	328	29	�	�	PROPN
ejpam-1481	328	30	�	�	PROPN
ejpam-1481	328	31	vk	vk	ADP
ejpam-1481	328	32	−	−	PROPN
ejpam-1481	328	33	l	l	X
ejpam-1481	328	34	�	�	PROPN
ejpam-1481	328	35	�	�	PROPN
ejpam-1481	328	36	>	>	X
ejpam-1481	328	37	l	l	NOUN
ejpam-1481	329	1	©	©	PROPN
ejpam-1481	329	2	⊆	⊆	NUM
ejpam-1481	329	3	σ(∆v	σ(∆v	NOUN
ejpam-1481	329	4	,	,	PUNCT
ejpam-1481	329	5	c0	c0	NOUN
ejpam-1481	329	6	)	)	PUNCT
ejpam-1481	329	7	.	.	PUNCT
ejpam-1481	330	1	this	this	PRON
ejpam-1481	330	2	completes	complete	VERB
ejpam-1481	330	3	the	the	DET
ejpam-1481	330	4	proof	proof	NOUN
ejpam-1481	330	5	.	.	PUNCT
ejpam-1481	331	1	the	the	DET
ejpam-1481	331	2	point	point	NOUN
ejpam-1481	331	3	spectrum	spectrum	NOUN
ejpam-1481	331	4	of	of	ADP
ejpam-1481	331	5	the	the	DET
ejpam-1481	331	6	operator	operator	NOUN
ejpam-1481	331	7	∆v	∆v	PROPN
ejpam-1481	331	8	on	on	ADP
ejpam-1481	331	9	c0	c0	PROPN
ejpam-1481	331	10	is	be	AUX
ejpam-1481	331	11	given	give	VERB
ejpam-1481	331	12	by	by	ADP
ejpam-1481	331	13	the	the	DET
ejpam-1481	331	14	following	follow	VERB
ejpam-1481	331	15	theorem	theorem	PROPN
ejpam-1481	331	16	.	.	PUNCT
ejpam-1481	332	1	theorem	theorem	PROPN
ejpam-1481	332	2	11	11	NUM
ejpam-1481	332	3	.	.	PUNCT
ejpam-1481	333	1	σp(∆v	σp(∆v	NOUN
ejpam-1481	333	2	,	,	PUNCT
ejpam-1481	333	3	c0	c0	NOUN
ejpam-1481	333	4	)	)	PUNCT
ejpam-1481	334	1	=	=	SYM
ejpam-1481	334	2	e.	e.	PROPN
ejpam-1481	334	3	proof	proof	PROPN
ejpam-1481	334	4	.	.	PUNCT
ejpam-1481	335	1	suppose	suppose	VERB
ejpam-1481	336	1	∆v	∆v	NOUN
ejpam-1481	336	2	x	x	PUNCT
ejpam-1481	336	3	=	=	PUNCT
ejpam-1481	336	4	λx	λx	PROPN
ejpam-1481	336	5	for	for	ADP
ejpam-1481	336	6	x	x	PROPN
ejpam-1481	336	7	6=	6=	ADP
ejpam-1481	336	8	θ	θ	X
ejpam-1481	336	9	=	=	SYM
ejpam-1481	336	10	(	(	PUNCT
ejpam-1481	336	11	0,0,0	0,0,0	NOUN
ejpam-1481	336	12	,	,	PUNCT
ejpam-1481	336	13	.	.	PUNCT
ejpam-1481	336	14	.	.	PUNCT
ejpam-1481	336	15	.	.	PUNCT
ejpam-1481	336	16	)	)	PUNCT
ejpam-1481	337	1	in	in	ADP
ejpam-1481	337	2	c0	c0	PROPN
ejpam-1481	337	3	.	.	PUNCT
ejpam-1481	338	1	then	then	ADV
ejpam-1481	338	2	by	by	ADP
ejpam-1481	338	3	solving	solve	VERB
ejpam-1481	338	4	the	the	DET
ejpam-1481	338	5	system	system	NOUN
ejpam-1481	338	6	of	of	ADP
ejpam-1481	338	7	equations	equation	NOUN
ejpam-1481	338	8	v0	v0	VERB
ejpam-1481	338	9	x0	x0	PROPN
ejpam-1481	339	1	=	=	PUNCT
ejpam-1481	340	1	λx0	λx0	NOUN
ejpam-1481	340	2	−v0	−v0	VERB
ejpam-1481	340	3	x0	x0	PROPN
ejpam-1481	341	1	+	+	CCONJ
ejpam-1481	342	1	v1	v1	VERB
ejpam-1481	342	2	x1	x1	NOUN
ejpam-1481	342	3	=	=	PUNCT
ejpam-1481	343	1	λx1	λx1	X
ejpam-1481	343	2	−v1	−v1	X
ejpam-1481	343	3	x1	x1	PROPN
ejpam-1481	344	1	+	+	X
ejpam-1481	344	2	v2	v2	NOUN
ejpam-1481	344	3	x2	x2	NOUN
ejpam-1481	345	1	=	=	PUNCT
ejpam-1481	346	1	λx2	λx2	NOUN
ejpam-1481	346	2	...	...	PUNCT
ejpam-1481	347	1			PROPN
ejpam-1481	347	2			PROPN
ejpam-1481	348	1			PROPN
ejpam-1481	348	2			ADJ
ejpam-1481	348	3			NOUN
ejpam-1481	348	4	we	we	PRON
ejpam-1481	348	5	obtain	obtain	VERB
ejpam-1481	348	6	(	(	PUNCT
ejpam-1481	348	7	v0	v0	NOUN
ejpam-1481	348	8	−λ)x0	−λ)x0	NOUN
ejpam-1481	349	1	=	=	SYM
ejpam-1481	349	2	0	0	NUM
ejpam-1481	349	3	and	and	CCONJ
ejpam-1481	349	4	−	−	PROPN
ejpam-1481	349	5	vk	vk	X
ejpam-1481	349	6	xk	xk	PROPN
ejpam-1481	350	1	+	+	CCONJ
ejpam-1481	350	2	(	(	PUNCT
ejpam-1481	350	3	vk+1−λ)xk+1	vk+1−λ)xk+1	NOUN
ejpam-1481	350	4	=	=	SYM
ejpam-1481	350	5	0	0	NUM
ejpam-1481	350	6	,	,	PUNCT
ejpam-1481	350	7	for	for	ADP
ejpam-1481	350	8	all	all	DET
ejpam-1481	350	9	k	k	PROPN
ejpam-1481	350	10	∈	∈	PROPN
ejpam-1481	350	11	n.	n.	NOUN
ejpam-1481	350	12	hence	hence	ADV
ejpam-1481	350	13	,	,	PUNCT
ejpam-1481	350	14	for	for	ADP
ejpam-1481	350	15	all	all	DET
ejpam-1481	350	16	λ	λ	PROPN
ejpam-1481	350	17	/∈	/∈	PROPN
ejpam-1481	350	18	�	�	PROPN
ejpam-1481	350	19	vk	vk	NOUN
ejpam-1481	350	20	:	:	PUNCT
ejpam-1481	350	21	k	k	PROPN
ejpam-1481	350	22	∈	∈	PROPN
ejpam-1481	350	23	n	n	X
ejpam-1481	350	24	,	,	PUNCT
ejpam-1481	350	25	we	we	PRON
ejpam-1481	350	26	have	have	VERB
ejpam-1481	350	27	xk	xk	PROPN
ejpam-1481	350	28	=	=	PUNCT
ejpam-1481	350	29	0	0	PROPN
ejpam-1481	350	30	for	for	ADP
ejpam-1481	350	31	all	all	DET
ejpam-1481	350	32	k	k	PROPN
ejpam-1481	350	33	∈	∈	PROPN
ejpam-1481	350	34	n	n	CCONJ
ejpam-1481	350	35	,	,	PUNCT
ejpam-1481	350	36	which	which	PRON
ejpam-1481	350	37	contradicts	contradict	VERB
ejpam-1481	350	38	our	our	PRON
ejpam-1481	350	39	assumption	assumption	NOUN
ejpam-1481	350	40	.	.	PUNCT
ejpam-1481	351	1	this	this	PRON
ejpam-1481	351	2	shows	show	VERB
ejpam-1481	351	3	that	that	SCONJ
ejpam-1481	351	4	σp(∆v	σp(∆v	NOUN
ejpam-1481	351	5	,	,	PUNCT
ejpam-1481	351	6	c0	c0	NOUN
ejpam-1481	351	7	)	)	PUNCT
ejpam-1481	351	8	⊆	⊆	NUM
ejpam-1481	351	9	�	�	PROPN
ejpam-1481	351	10	vk	vk	PROPN
ejpam-1481	351	11	:	:	PUNCT
ejpam-1481	351	12	k	k	PROPN
ejpam-1481	351	13	∈	∈	PROPN
ejpam-1481	351	14	n	n	INTJ
ejpam-1481	351	15	.	.	PUNCT
ejpam-1481	352	1	also	also	ADV
ejpam-1481	352	2	,	,	PUNCT
ejpam-1481	352	3	if	if	SCONJ
ejpam-1481	352	4	λ	λ	X
ejpam-1481	352	5	=	=	SYM
ejpam-1481	352	6	l	l	NOUN
ejpam-1481	352	7	,	,	PUNCT
ejpam-1481	352	8	then	then	ADV
ejpam-1481	352	9	we	we	PRON
ejpam-1481	352	10	can	can	AUX
ejpam-1481	352	11	easily	easily	ADV
ejpam-1481	352	12	prove	prove	VERB
ejpam-1481	352	13	that	that	SCONJ
ejpam-1481	352	14	λ	λ	PROPN
ejpam-1481	352	15	/∈	/∈	PUNCT
ejpam-1481	352	16	σp(∆v	σp(∆v	NOUN
ejpam-1481	352	17	,	,	PUNCT
ejpam-1481	352	18	c0	c0	NOUN
ejpam-1481	352	19	)	)	PUNCT
ejpam-1481	352	20	.	.	PUNCT
ejpam-1481	353	1	thus	thus	ADV
ejpam-1481	353	2	σp(∆v	σp(∆v	NUM
ejpam-1481	353	3	,	,	PUNCT
ejpam-1481	353	4	c0)⊆	c0)⊆	PROPN
ejpam-1481	353	5	�	�	PROPN
ejpam-1481	353	6	vk	vk	PROPN
ejpam-1481	353	7	:	:	PUNCT
ejpam-1481	353	8	k	k	PROPN
ejpam-1481	353	9	∈	∈	PROPN
ejpam-1481	353	10	n	n	PRON
ejpam-1481	353	11	\{l	\{l	VERB
ejpam-1481	353	12	}	}	PUNCT
ejpam-1481	353	13	.	.	PUNCT
ejpam-1481	354	1	now	now	ADV
ejpam-1481	354	2	,	,	PUNCT
ejpam-1481	354	3	we	we	PRON
ejpam-1481	354	4	will	will	AUX
ejpam-1481	354	5	prove	prove	VERB
ejpam-1481	354	6	that	that	SCONJ
ejpam-1481	354	7	λ	λ	PROPN
ejpam-1481	354	8	∈	∈	NOUN
ejpam-1481	354	9	σp(∆v	σp(∆v	NOUN
ejpam-1481	354	10	,	,	PUNCT
ejpam-1481	354	11	c0	c0	NOUN
ejpam-1481	354	12	)	)	PUNCT
ejpam-1481	354	13	if	if	SCONJ
ejpam-1481	354	14	and	and	CCONJ
ejpam-1481	354	15	only	only	ADV
ejpam-1481	354	16	if	if	SCONJ
ejpam-1481	354	17	λ	λ	PROPN
ejpam-1481	354	18	∈	∈	PROPN
ejpam-1481	354	19	e.	e.	PROPN
ejpam-1481	355	1	if	if	SCONJ
ejpam-1481	355	2	λ	λ	PROPN
ejpam-1481	355	3	∈	∈	NOUN
ejpam-1481	355	4	σp(∆v	σp(∆v	NOUN
ejpam-1481	355	5	,	,	PUNCT
ejpam-1481	355	6	c0	c0	NOUN
ejpam-1481	355	7	)	)	PUNCT
ejpam-1481	355	8	,	,	PUNCT
ejpam-1481	355	9	then	then	ADV
ejpam-1481	355	10	λ	λ	X
ejpam-1481	355	11	=	=	PROPN
ejpam-1481	355	12	v	v	PROPN
ejpam-1481	355	13	j	j	PROPN
ejpam-1481	355	14	6=	6=	PROPN
ejpam-1481	355	15	l	l	PROPN
ejpam-1481	355	16	for	for	ADP
ejpam-1481	355	17	some	some	DET
ejpam-1481	355	18	j	j	PROPN
ejpam-1481	355	19	∈	∈	PROPN
ejpam-1481	355	20	n	n	ADV
ejpam-1481	355	21	and	and	CCONJ
ejpam-1481	355	22	there	there	PRON
ejpam-1481	355	23	exists	exist	VERB
ejpam-1481	355	24	x	x	X
ejpam-1481	355	25	∈	∈	PROPN
ejpam-1481	355	26	c0	c0	NOUN
ejpam-1481	355	27	,	,	PUNCT
ejpam-1481	355	28	x	x	PROPN
ejpam-1481	355	29	6=	6=	NUM
ejpam-1481	355	30	θ	θ	NUM
ejpam-1481	355	31	such	such	ADJ
ejpam-1481	355	32	that	that	DET
ejpam-1481	355	33	∆v	∆v	NOUN
ejpam-1481	355	34	x	x	PUNCT
ejpam-1481	356	1	=	=	PUNCT
ejpam-1481	356	2	v	v	NUM
ejpam-1481	356	3	j	j	PROPN
ejpam-1481	356	4	x	x	INTJ
ejpam-1481	356	5	.	.	PUNCT
ejpam-1481	357	1	then	then	ADV
ejpam-1481	357	2	lim	lim	PROPN
ejpam-1481	357	3	k→∞	k→∞	PROPN
ejpam-1481	357	4	�	�	PROPN
ejpam-1481	357	5	�	�	PROPN
ejpam-1481	357	6	�	�	PROPN
ejpam-1481	357	7	�	�	PROPN
ejpam-1481	357	8	xk+1	xk+1	PROPN
ejpam-1481	357	9	xk	xk	PROPN
ejpam-1481	357	10	�	�	PROPN
ejpam-1481	357	11	�	�	PROPN
ejpam-1481	357	12	�	�	PROPN
ejpam-1481	357	13	�	�	PROPN
ejpam-1481	357	14	=	=	SYM
ejpam-1481	357	15	�	�	PROPN
ejpam-1481	357	16	�	�	PROPN
ejpam-1481	357	17	�	�	PROPN
ejpam-1481	357	18	�	�	PROPN
ejpam-1481	357	19	�	�	PROPN
ejpam-1481	357	20	l	l	PROPN
ejpam-1481	357	21	l	l	NOUN
ejpam-1481	358	1	−	−	NOUN
ejpam-1481	358	2	v	v	PART
ejpam-1481	358	3	j	j	PROPN
ejpam-1481	358	4	�	�	PROPN
ejpam-1481	358	5	�	�	PROPN
ejpam-1481	358	6	�	�	PROPN
ejpam-1481	358	7	�	�	PROPN
ejpam-1481	358	8	�	�	PROPN
ejpam-1481	358	9	≤	≤	PROPN
ejpam-1481	358	10	1	1	NUM
ejpam-1481	358	11	.	.	PUNCT
ejpam-1481	359	1	but	but	CCONJ
ejpam-1481	359	2	�	�	PROPN
ejpam-1481	359	3	�	�	PROPN
ejpam-1481	359	4	�	�	PROPN
ejpam-1481	359	5	l	l	PROPN
ejpam-1481	359	6	l−v	l−v	ADV
ejpam-1481	359	7	j	j	PROPN
ejpam-1481	359	8	�	�	PROPN
ejpam-1481	359	9	�	�	PROPN
ejpam-1481	359	10	�	�	PROPN
ejpam-1481	359	11	6=	6=	ADP
ejpam-1481	359	12	1	1	NUM
ejpam-1481	359	13	.	.	PUNCT
ejpam-1481	360	1	then	then	ADV
ejpam-1481	360	2	λ=	λ=	VERB
ejpam-1481	360	3	v	v	NUM
ejpam-1481	360	4	j	j	PROPN
ejpam-1481	360	5	∈	∈	PROPN
ejpam-1481	360	6	¦	¦	PROPN
ejpam-1481	360	7	vk	vk	NOUN
ejpam-1481	360	8	:	:	PUNCT
ejpam-1481	360	9	k	k	PROPN
ejpam-1481	360	10	∈	∈	PROPN
ejpam-1481	360	11	n	n	CCONJ
ejpam-1481	360	12	,	,	PUNCT
ejpam-1481	360	13	�	�	PROPN
ejpam-1481	360	14	�	�	PROPN
ejpam-1481	360	15	vk	vk	ADP
ejpam-1481	360	16	−	−	PROPN
ejpam-1481	360	17	l	l	X
ejpam-1481	360	18	�	�	PROPN
ejpam-1481	360	19	�	�	PROPN
ejpam-1481	360	20	>	>	PUNCT
ejpam-1481	360	21	l	l	PUNCT
ejpam-1481	361	1	©	©	PROPN
ejpam-1481	361	2	=	=	PUNCT
ejpam-1481	361	3	e.	e.	PROPN
ejpam-1481	361	4	thus	thus	ADV
ejpam-1481	361	5	σp(∆v	σp(∆v	PROPN
ejpam-1481	361	6	,	,	PUNCT
ejpam-1481	361	7	c0)⊆	c0)⊆	PROPN
ejpam-1481	361	8	e.	e.	PROPN
ejpam-1481	361	9	conversely	conversely	ADV
ejpam-1481	361	10	,	,	PUNCT
ejpam-1481	361	11	let	let	VERB
ejpam-1481	361	12	λ	λ	X
ejpam-1481	361	13	∈	∈	PROPN
ejpam-1481	361	14	e.	e.	PROPN
ejpam-1481	361	15	then	then	ADV
ejpam-1481	361	16	there	there	PRON
ejpam-1481	361	17	exists	exist	VERB
ejpam-1481	361	18	i	i	PRON
ejpam-1481	361	19	∈	∈	PROPN
ejpam-1481	361	20	n	n	PRON
ejpam-1481	361	21	such	such	ADJ
ejpam-1481	361	22	that	that	SCONJ
ejpam-1481	361	23	λ	λ	PROPN
ejpam-1481	361	24	=	=	SYM
ejpam-1481	361	25	vi	vi	PROPN
ejpam-1481	361	26	6=	6=	ADP
ejpam-1481	361	27	l	l	NOUN
ejpam-1481	361	28	and	and	CCONJ
ejpam-1481	361	29	so	so	ADV
ejpam-1481	361	30	we	we	PRON
ejpam-1481	361	31	can	can	AUX
ejpam-1481	361	32	take	take	VERB
ejpam-1481	361	33	x	x	PUNCT
ejpam-1481	361	34	6=	6=	ADP
ejpam-1481	361	35	θ	θ	NUM
ejpam-1481	361	36	such	such	ADJ
ejpam-1481	361	37	that	that	DET
ejpam-1481	361	38	∆v	∆v	NOUN
ejpam-1481	361	39	x	x	PUNCT
ejpam-1481	361	40	=	=	SYM
ejpam-1481	361	41	vi	vi	PROPN
ejpam-1481	361	42	x	x	X
ejpam-1481	361	43	and	and	CCONJ
ejpam-1481	361	44	lim	lim	PROPN
ejpam-1481	361	45	k→∞	k→∞	PROPN
ejpam-1481	361	46	�	�	PROPN
ejpam-1481	361	47	�	�	PROPN
ejpam-1481	361	48	�	�	PROPN
ejpam-1481	361	49	�	�	PROPN
ejpam-1481	361	50	xk+1	xk+1	PROPN
ejpam-1481	361	51	xk	xk	PROPN
ejpam-1481	361	52	�	�	PROPN
ejpam-1481	361	53	�	�	PROPN
ejpam-1481	361	54	�	�	PROPN
ejpam-1481	361	55	�	�	PROPN
ejpam-1481	361	56	=	=	SYM
ejpam-1481	361	57	�	�	PROPN
ejpam-1481	361	58	�	�	PROPN
ejpam-1481	361	59	�	�	PROPN
ejpam-1481	361	60	�	�	PROPN
ejpam-1481	361	61	l	l	PROPN
ejpam-1481	361	62	l	l	NOUN
ejpam-1481	361	63	−	−	PROPN
ejpam-1481	361	64	vi	vi	PROPN
ejpam-1481	361	65	�	�	PROPN
ejpam-1481	361	66	�	�	PROPN
ejpam-1481	361	67	�	�	PROPN
ejpam-1481	361	68	�	�	PROPN
ejpam-1481	361	69	<	<	X
ejpam-1481	361	70	1	1	NUM
ejpam-1481	361	71	,	,	PUNCT
ejpam-1481	361	72	that	that	ADV
ejpam-1481	361	73	is	is	ADV
ejpam-1481	361	74	,	,	PUNCT
ejpam-1481	361	75	x	x	PROPN
ejpam-1481	361	76	∈	∈	PROPN
ejpam-1481	361	77	c0	c0	NOUN
ejpam-1481	361	78	.	.	PUNCT
ejpam-1481	362	1	thus	thus	ADV
ejpam-1481	362	2	e	e	X
ejpam-1481	362	3	⊆	⊆	NUM
ejpam-1481	362	4	σp(∆v	σp(∆v	NOUN
ejpam-1481	362	5	,	,	PUNCT
ejpam-1481	362	6	c0	c0	NOUN
ejpam-1481	362	7	)	)	PUNCT
ejpam-1481	362	8	.	.	PUNCT
ejpam-1481	363	1	this	this	PRON
ejpam-1481	363	2	completes	complete	VERB
ejpam-1481	363	3	the	the	DET
ejpam-1481	363	4	proof	proof	NOUN
ejpam-1481	363	5	.	.	PUNCT
ejpam-1481	364	1	we	we	PRON
ejpam-1481	364	2	give	give	VERB
ejpam-1481	364	3	the	the	DET
ejpam-1481	364	4	following	follow	VERB
ejpam-1481	364	5	lemma	lemma	PROPN
ejpam-1481	364	6	which	which	PRON
ejpam-1481	364	7	is	be	AUX
ejpam-1481	364	8	required	require	VERB
ejpam-1481	364	9	in	in	ADP
ejpam-1481	364	10	the	the	DET
ejpam-1481	364	11	proof	proof	NOUN
ejpam-1481	364	12	of	of	ADP
ejpam-1481	364	13	the	the	DET
ejpam-1481	364	14	next	next	ADJ
ejpam-1481	364	15	theorem	theorem	NOUN
ejpam-1481	364	16	.	.	PUNCT
ejpam-1481	365	1	lemma	lemma	PROPN
ejpam-1481	365	2	3	3	X
ejpam-1481	365	3	.	.	PUNCT
ejpam-1481	366	1	let	let	VERB
ejpam-1481	366	2	λ	λ	X
ejpam-1481	366	3	∈	∈	PROPN
ejpam-1481	366	4	{	{	PUNCT
ejpam-1481	366	5	λ	λ	X
ejpam-1481	366	6	∈	∈	PROPN
ejpam-1481	366	7	c	c	NOUN
ejpam-1481	366	8	:	:	PUNCT
ejpam-1481	366	9	|λ−	|λ−	NOUN
ejpam-1481	366	10	l|	l|	ADJ
ejpam-1481	366	11	=	=	SYM
ejpam-1481	366	12	l	l	NOUN
ejpam-1481	366	13	}	}	PUNCT
ejpam-1481	366	14	.	.	PUNCT
ejpam-1481	367	1	then	then	ADV
ejpam-1481	367	2	the	the	DET
ejpam-1481	367	3	series	series	NOUN
ejpam-1481	367	4	∑	∑	PROPN
ejpam-1481	367	5	k	k	PROPN
ejpam-1481	367	6	�	�	PROPN
ejpam-1481	367	7	�	�	PROPN
ejpam-1481	367	8	�	�	PROPN
ejpam-1481	367	9	�	�	PROPN
ejpam-1481	367	10	(	(	PUNCT
ejpam-1481	367	11	v0	v0	NOUN
ejpam-1481	367	12	−λ)(v1−λ	−λ)(v1−λ	NUM
ejpam-1481	367	13	)	)	PUNCT
ejpam-1481	367	14	.	.	PUNCT
ejpam-1481	367	15	.	.	PUNCT
ejpam-1481	367	16	.	.	PUNCT
ejpam-1481	368	1	(	(	PUNCT
ejpam-1481	368	2	vk	vk	NOUN
ejpam-1481	368	3	−λ	−λ	VERB
ejpam-1481	368	4	)	)	PUNCT
ejpam-1481	368	5	v0v1	v0v1	X
ejpam-1481	368	6	.	.	PUNCT
ejpam-1481	368	7	.	.	PUNCT
ejpam-1481	368	8	.	.	PUNCT
ejpam-1481	369	1	vk	vk	PROPN
ejpam-1481	369	2	�	�	PROPN
ejpam-1481	369	3	�	�	PROPN
ejpam-1481	369	4	�	�	PROPN
ejpam-1481	369	5	�	�	PROPN
ejpam-1481	369	6	,	,	PUNCT
ejpam-1481	369	7	is	be	AUX
ejpam-1481	369	8	not	not	PART
ejpam-1481	369	9	a	a	DET
ejpam-1481	369	10	convergent	convergent	NOUN
ejpam-1481	369	11	series	series	NOUN
ejpam-1481	369	12	.	.	PUNCT
ejpam-1481	370	1	a.	a.	PROPN
ejpam-1481	370	2	akhmedov	akhmedov	PROPN
ejpam-1481	370	3	,	,	PUNCT
ejpam-1481	370	4	s.	s.	PROPN
ejpam-1481	370	5	el	el	PROPN
ejpam-1481	370	6	-	-	PUNCT
ejpam-1481	370	7	shabrawy	shabrawy	PROPN
ejpam-1481	370	8	/	/	SYM
ejpam-1481	370	9	eur	eur	NOUN
ejpam-1481	370	10	.	.	PUNCT
ejpam-1481	371	1	j.	j.	PROPN
ejpam-1481	371	2	pure	pure	PROPN
ejpam-1481	371	3	appl	appl	PROPN
ejpam-1481	371	4	.	.	PROPN
ejpam-1481	371	5	math	math	PROPN
ejpam-1481	371	6	,	,	PUNCT
ejpam-1481	371	7	5	5	NUM
ejpam-1481	371	8	(	(	PUNCT
ejpam-1481	371	9	2012	2012	NUM
ejpam-1481	371	10	)	)	PUNCT
ejpam-1481	371	11	,	,	PUNCT
ejpam-1481	371	12	59	59	NUM
ejpam-1481	371	13	-	-	SYM
ejpam-1481	371	14	74	74	NUM
ejpam-1481	371	15	71	71	NUM
ejpam-1481	371	16	proof	proof	NOUN
ejpam-1481	371	17	.	.	PUNCT
ejpam-1481	372	1	let	let	VERB
ejpam-1481	372	2	λ=	λ=	NOUN
ejpam-1481	372	3	λ1	λ1	ADJ
ejpam-1481	372	4	+	+	CCONJ
ejpam-1481	372	5	iλ2	iλ2	NOUN
ejpam-1481	372	6	∈	∈	PROPN
ejpam-1481	372	7	c	c	NOUN
ejpam-1481	372	8	such	such	ADJ
ejpam-1481	372	9	that	that	DET
ejpam-1481	372	10	|λ−	|λ−	NOUN
ejpam-1481	372	11	l|	l|	PROPN
ejpam-1481	372	12	=	=	PUNCT
ejpam-1481	372	13	l.	l.	NOUN
ejpam-1481	372	14	then	then	ADV
ejpam-1481	372	15	|λ|2	|λ|2	PROPN
ejpam-1481	372	16	=	=	SYM
ejpam-1481	372	17	λ2	λ2	NOUN
ejpam-1481	372	18	1	1	NUM
ejpam-1481	372	19	+	+	NOUN
ejpam-1481	372	20	λ	λ	X
ejpam-1481	372	21	2	2	NUM
ejpam-1481	372	22	2	2	NUM
ejpam-1481	372	23	=	=	SYM
ejpam-1481	372	24	2λ1	2λ1	NUM
ejpam-1481	372	25	l.	l.	NOUN
ejpam-1481	372	26	also	also	ADV
ejpam-1481	372	27	,	,	PUNCT
ejpam-1481	372	28	�	�	PROPN
ejpam-1481	372	29	�	�	PROPN
ejpam-1481	372	30	vk	vk	PROPN
ejpam-1481	372	31	−λ	−λ	PROPN
ejpam-1481	372	32	�	�	PROPN
ejpam-1481	372	33	�	�	PROPN
ejpam-1481	372	34	2	2	NUM
ejpam-1481	372	35	=	=	SYM
ejpam-1481	372	36	v2	v2	NOUN
ejpam-1481	372	37	k	k	NOUN
ejpam-1481	373	1	+	+	CCONJ
ejpam-1481	373	2	(	(	PUNCT
ejpam-1481	373	3	λ2	λ2	NOUN
ejpam-1481	373	4	1	1	NUM
ejpam-1481	373	5	+	+	NOUN
ejpam-1481	373	6	λ	λ	PROPN
ejpam-1481	373	7	2	2	NUM
ejpam-1481	373	8	2)−	2)−	NUM
ejpam-1481	373	9	2λ1vk	2λ1vk	NUM
ejpam-1481	373	10	=	=	SYM
ejpam-1481	373	11	v2	v2	PROPN
ejpam-1481	373	12	k	k	NOUN
ejpam-1481	374	1	−	−	PROPN
ejpam-1481	374	2	2λ1(vk	2λ1(vk	NUM
ejpam-1481	375	1	−	−	PROPN
ejpam-1481	375	2	l	l	NOUN
ejpam-1481	375	3	)	)	PUNCT
ejpam-1481	376	1	≥	≥	NOUN
ejpam-1481	376	2	v2	v2	PROPN
ejpam-1481	376	3	k	k	X
ejpam-1481	376	4	.	.	PUNCT
ejpam-1481	377	1	therefore	therefore	ADV
ejpam-1481	377	2	�	�	PROPN
ejpam-1481	377	3	�	�	PROPN
ejpam-1481	377	4	�	�	PROPN
ejpam-1481	377	5	�	�	PROPN
ejpam-1481	377	6	vk	vk	VERB
ejpam-1481	377	7	−λ	−λ	PROPN
ejpam-1481	377	8	vk	vk	PROPN
ejpam-1481	377	9	�	�	PROPN
ejpam-1481	377	10	�	�	PROPN
ejpam-1481	377	11	�	�	PROPN
ejpam-1481	377	12	�	�	PROPN
ejpam-1481	377	13	≥	≥	NUM
ejpam-1481	377	14	1	1	NUM
ejpam-1481	377	15	,	,	PUNCT
ejpam-1481	377	16	for	for	ADP
ejpam-1481	377	17	all	all	DET
ejpam-1481	377	18	k	k	PROPN
ejpam-1481	377	19	∈	∈	PROPN
ejpam-1481	377	20	n.	n.	NOUN
ejpam-1481	377	21	this	this	PRON
ejpam-1481	377	22	completes	complete	VERB
ejpam-1481	377	23	the	the	DET
ejpam-1481	377	24	proof	proof	NOUN
ejpam-1481	377	25	.	.	PUNCT
ejpam-1481	378	1	theorem	theorem	ADJ
ejpam-1481	378	2	12	12	NUM
ejpam-1481	378	3	.	.	PUNCT
ejpam-1481	379	1	σp(∆	σp(∆	PROPN
ejpam-1481	379	2	∗	∗	PROPN
ejpam-1481	379	3	v	v	NOUN
ejpam-1481	379	4	,	,	PUNCT
ejpam-1481	379	5	c∗0	c∗0	NOUN
ejpam-1481	379	6	)	)	PUNCT
ejpam-1481	379	7	=	=	PUNCT
ejpam-1481	380	1	{	{	PUNCT
ejpam-1481	380	2	λ	λ	X
ejpam-1481	380	3	∈	∈	PROPN
ejpam-1481	380	4	c	c	NOUN
ejpam-1481	380	5	:	:	PUNCT
ejpam-1481	380	6	|λ−	|λ−	NOUN
ejpam-1481	380	7	l|	l|	ADJ
ejpam-1481	380	8	<	<	X
ejpam-1481	380	9	l	l	NOUN
ejpam-1481	380	10	}	}	PUNCT
ejpam-1481	380	11	∪	∪	ADJ
ejpam-1481	380	12	e.	e.	PROPN
ejpam-1481	380	13	proof	proof	PROPN
ejpam-1481	380	14	.	.	PUNCT
ejpam-1481	381	1	suppose	suppose	VERB
ejpam-1481	381	2	that	that	SCONJ
ejpam-1481	381	3	∆∗v	∆∗v	NOUN
ejpam-1481	381	4	f	f	X
ejpam-1481	381	5	=	=	SYM
ejpam-1481	381	6	λ	λ	X
ejpam-1481	381	7	f	f	PROPN
ejpam-1481	381	8	for	for	ADP
ejpam-1481	381	9	f	f	PROPN
ejpam-1481	381	10	=	=	SYM
ejpam-1481	381	11	(	(	PUNCT
ejpam-1481	381	12	f0	f0	PROPN
ejpam-1481	381	13	,	,	PUNCT
ejpam-1481	381	14	f1	f1	NOUN
ejpam-1481	381	15	,	,	PUNCT
ejpam-1481	381	16	f2	f2	PROPN
ejpam-1481	381	17	,	,	PUNCT
ejpam-1481	381	18	.	.	PUNCT
ejpam-1481	381	19	.	.	PUNCT
ejpam-1481	381	20	.	.	PUNCT
ejpam-1481	381	21	)	)	PUNCT
ejpam-1481	382	1	6=	6=	NUM
ejpam-1481	382	2	θ	θ	PROPN
ejpam-1481	382	3	in	in	ADP
ejpam-1481	382	4	c∗0	c∗0	NOUN
ejpam-1481	382	5	∼=	∼=	PROPN
ejpam-1481	382	6	l1	l1	PROPN
ejpam-1481	382	7	.	.	PUNCT
ejpam-1481	383	1	then	then	ADV
ejpam-1481	383	2	,	,	PUNCT
ejpam-1481	383	3	by	by	ADP
ejpam-1481	383	4	solving	solve	VERB
ejpam-1481	383	5	the	the	DET
ejpam-1481	383	6	system	system	NOUN
ejpam-1481	383	7	of	of	ADP
ejpam-1481	383	8	equations	equation	NOUN
ejpam-1481	383	9	v0	v0	VERB
ejpam-1481	383	10	f0	f0	PROPN
ejpam-1481	383	11	−	−	PROPN
ejpam-1481	383	12	v0	v0	NOUN
ejpam-1481	383	13	f1	f1	NOUN
ejpam-1481	383	14	=	=	SYM
ejpam-1481	383	15	λ	λ	PROPN
ejpam-1481	383	16	f0	f0	NOUN
ejpam-1481	383	17	v1	v1	NOUN
ejpam-1481	383	18	f1	f1	NOUN
ejpam-1481	383	19	−	−	PROPN
ejpam-1481	383	20	v1	v1	NOUN
ejpam-1481	383	21	f2	f2	ADV
ejpam-1481	383	22	=	=	SYM
ejpam-1481	383	23	λ	λ	PROPN
ejpam-1481	383	24	f1	f1	NOUN
ejpam-1481	383	25	...	...	PUNCT
ejpam-1481	384	1	vk	vk	INTJ
ejpam-1481	384	2	fk	fk	INTJ
ejpam-1481	384	3	−	−	NOUN
ejpam-1481	384	4	vk	vk	NOUN
ejpam-1481	384	5	fk+1	fk+1	VERB
ejpam-1481	384	6	=	=	SYM
ejpam-1481	384	7	λ	λ	X
ejpam-1481	384	8	fk	fk	INTJ
ejpam-1481	384	9	,	,	PUNCT
ejpam-1481	384	10	...	...	PUNCT
ejpam-1481	385	1	we	we	PRON
ejpam-1481	385	2	obtain	obtain	VERB
ejpam-1481	385	3	fk+1	fk+1	NOUN
ejpam-1481	385	4	=	=	SYM
ejpam-1481	385	5	vk	vk	NOUN
ejpam-1481	385	6	−λ	−λ	PROPN
ejpam-1481	385	7	vk	vk	PROPN
ejpam-1481	385	8	fk	fk	INTJ
ejpam-1481	385	9	,	,	PUNCT
ejpam-1481	385	10	k	k	PROPN
ejpam-1481	385	11	∈	∈	PROPN
ejpam-1481	385	12	n.	n.	PROPN
ejpam-1481	385	13	therefore	therefore	ADV
ejpam-1481	385	14	,	,	PUNCT
ejpam-1481	385	15	we	we	PRON
ejpam-1481	385	16	must	must	AUX
ejpam-1481	385	17	take	take	VERB
ejpam-1481	385	18	f0	f0	PROPN
ejpam-1481	385	19	6=	6=	ADP
ejpam-1481	385	20	0	0	NUM
ejpam-1481	385	21	,	,	PUNCT
ejpam-1481	385	22	since	since	SCONJ
ejpam-1481	385	23	otherwise	otherwise	ADV
ejpam-1481	385	24	we	we	PRON
ejpam-1481	385	25	would	would	AUX
ejpam-1481	385	26	have	have	VERB
ejpam-1481	385	27	f	f	NOUN
ejpam-1481	385	28	=	=	SYM
ejpam-1481	385	29	θ	θ	PROPN
ejpam-1481	385	30	.	.	PUNCT
ejpam-1481	386	1	it	it	PRON
ejpam-1481	386	2	is	be	AUX
ejpam-1481	386	3	clear	clear	ADJ
ejpam-1481	386	4	that	that	SCONJ
ejpam-1481	386	5	,	,	PUNCT
ejpam-1481	386	6	for	for	ADP
ejpam-1481	386	7	all	all	DET
ejpam-1481	386	8	k	k	PROPN
ejpam-1481	386	9	∈	∈	PROPN
ejpam-1481	386	10	n	n	CCONJ
ejpam-1481	386	11	,	,	PUNCT
ejpam-1481	386	12	the	the	DET
ejpam-1481	386	13	vector	vector	NOUN
ejpam-1481	386	14	f	f	PROPN
ejpam-1481	386	15	=	=	PRON
ejpam-1481	386	16	(	(	PUNCT
ejpam-1481	386	17	f0	f0	PROPN
ejpam-1481	386	18	,	,	PUNCT
ejpam-1481	386	19	f1	f1	NOUN
ejpam-1481	386	20	,	,	PUNCT
ejpam-1481	386	21	.	.	PUNCT
ejpam-1481	386	22	.	.	PUNCT
ejpam-1481	387	1	.	.	PUNCT
ejpam-1481	388	1	,	,	PUNCT
ejpam-1481	388	2	fk	fk	INTJ
ejpam-1481	388	3	,	,	PUNCT
ejpam-1481	388	4	0,0	0,0	NOUN
ejpam-1481	388	5	,	,	PUNCT
ejpam-1481	388	6	.	.	PUNCT
ejpam-1481	388	7	.	.	PUNCT
ejpam-1481	388	8	.	.	PUNCT
ejpam-1481	388	9	)	)	PUNCT
ejpam-1481	389	1	is	be	AUX
ejpam-1481	389	2	an	an	DET
ejpam-1481	389	3	eigenvector	eigenvector	NOUN
ejpam-1481	389	4	of	of	ADP
ejpam-1481	389	5	the	the	DET
ejpam-1481	389	6	operator	operator	NOUN
ejpam-1481	389	7	∆∗v	∆∗v	NOUN
ejpam-1481	389	8	corresponding	correspond	VERB
ejpam-1481	389	9	to	to	ADP
ejpam-1481	389	10	the	the	DET
ejpam-1481	389	11	eigenvalue	eigenvalue	PROPN
ejpam-1481	389	12	λ	λ	PROPN
ejpam-1481	389	13	=	=	SYM
ejpam-1481	389	14	vk	vk	PROPN
ejpam-1481	389	15	,	,	PUNCT
ejpam-1481	389	16	where	where	SCONJ
ejpam-1481	389	17	f0	f0	PROPN
ejpam-1481	389	18	6=	6=	ADP
ejpam-1481	389	19	0	0	NUM
ejpam-1481	389	20	and	and	CCONJ
ejpam-1481	389	21	fn	fn	NOUN
ejpam-1481	389	22	=	=	ADJ
ejpam-1481	389	23	vn−1−λ	vn−1−λ	NOUN
ejpam-1481	389	24	vn−1	vn−1	PROPN
ejpam-1481	389	25	fn−1	fn−1	PROPN
ejpam-1481	389	26	,	,	PUNCT
ejpam-1481	389	27	for	for	ADP
ejpam-1481	389	28	all	all	DET
ejpam-1481	389	29	n	n	PRON
ejpam-1481	389	30	=	=	SYM
ejpam-1481	389	31	1,2	1,2	NUM
ejpam-1481	389	32	,	,	PUNCT
ejpam-1481	389	33	.	.	PUNCT
ejpam-1481	389	34	.	.	PUNCT
ejpam-1481	390	1	.	.	PUNCT
ejpam-1481	391	1	,	,	PUNCT
ejpam-1481	391	2	k.	k.	PROPN
ejpam-1481	391	3	thus	thus	ADV
ejpam-1481	391	4	�	�	PROPN
ejpam-1481	391	5	vk	vk	PROPN
ejpam-1481	391	6	:	:	PUNCT
ejpam-1481	391	7	k	k	PROPN
ejpam-1481	391	8	∈	∈	PROPN
ejpam-1481	391	9	n	n	CCONJ
ejpam-1481	391	10	⊆	⊆	NUM
ejpam-1481	391	11	σp(∆	σp(∆	NOUN
ejpam-1481	391	12	∗	∗	NOUN
ejpam-1481	391	13	v	v	NOUN
ejpam-1481	391	14	,	,	PUNCT
ejpam-1481	391	15	c∗0	c∗0	NOUN
ejpam-1481	391	16	)	)	PUNCT
ejpam-1481	391	17	.	.	PUNCT
ejpam-1481	392	1	also	also	ADV
ejpam-1481	392	2	,	,	PUNCT
ejpam-1481	392	3	if	if	SCONJ
ejpam-1481	392	4	λ	λ	PROPN
ejpam-1481	392	5	6=	6=	SYM
ejpam-1481	392	6	vk	vk	PROPN
ejpam-1481	392	7	for	for	ADP
ejpam-1481	392	8	all	all	DET
ejpam-1481	392	9	k	k	PROPN
ejpam-1481	392	10	∈	∈	PROPN
ejpam-1481	392	11	n	n	CCONJ
ejpam-1481	392	12	,	,	PUNCT
ejpam-1481	392	13	then	then	ADV
ejpam-1481	392	14	fk	fk	INTJ
ejpam-1481	392	15	6=	6=	ADP
ejpam-1481	392	16	0	0	NUM
ejpam-1481	392	17	for	for	ADP
ejpam-1481	392	18	all	all	DET
ejpam-1481	392	19	k	k	PROPN
ejpam-1481	392	20	∈	∈	PROPN
ejpam-1481	392	21	n	n	CCONJ
ejpam-1481	392	22	,	,	PUNCT
ejpam-1481	392	23	and	and	CCONJ
ejpam-1481	392	24	so	so	ADV
ejpam-1481	392	25	,	,	PUNCT
ejpam-1481	392	26	∑	∑	PROPN
ejpam-1481	392	27	k	k	PROPN
ejpam-1481	392	28	�	�	PROPN
ejpam-1481	392	29	�	�	PROPN
ejpam-1481	392	30	fk	fk	INTJ
ejpam-1481	392	31	�	�	PROPN
ejpam-1481	392	32	�	�	PROPN
ejpam-1481	392	33	<	<	X
ejpam-1481	392	34	∞	∞	PROPN
ejpam-1481	392	35	if	if	SCONJ
ejpam-1481	392	36	lim	lim	PROPN
ejpam-1481	392	37	k→∞	k→∞	PROPN
ejpam-1481	392	38	�	�	PROPN
ejpam-1481	392	39	�	�	PROPN
ejpam-1481	392	40	�	�	PROPN
ejpam-1481	392	41	fk+1	fk+1	PROPN
ejpam-1481	392	42	fk	fk	X
ejpam-1481	392	43	�	�	PROPN
ejpam-1481	392	44	�	�	PROPN
ejpam-1481	392	45	�	�	PROPN
ejpam-1481	392	46	=	=	SYM
ejpam-1481	392	47	�	�	PROPN
ejpam-1481	392	48	�	�	PROPN
ejpam-1481	392	49	�	�	PROPN
ejpam-1481	392	50	λ−l	λ−l	PROPN
ejpam-1481	392	51	l	l	NOUN
ejpam-1481	392	52	�	�	PROPN
ejpam-1481	392	53	�	�	PROPN
ejpam-1481	392	54	�	�	PROPN
ejpam-1481	392	55	<	<	X
ejpam-1481	392	56	1	1	NUM
ejpam-1481	392	57	.	.	PUNCT
ejpam-1481	393	1	thus	thus	ADV
ejpam-1481	393	2	{	{	PUNCT
ejpam-1481	393	3	λ	λ	X
ejpam-1481	393	4	∈	∈	PROPN
ejpam-1481	393	5	c	c	NOUN
ejpam-1481	393	6	:	:	PUNCT
ejpam-1481	393	7	|λ−	|λ−	NOUN
ejpam-1481	393	8	l|	l|	ADJ
ejpam-1481	393	9	<	<	X
ejpam-1481	393	10	l	l	NOUN
ejpam-1481	393	11	}	}	PUNCT
ejpam-1481	393	12	∪	∪	ADP
ejpam-1481	393	13	e	e	NOUN
ejpam-1481	393	14	⊆	⊆	NUM
ejpam-1481	393	15	σp(∆	σp(∆	ADJ
ejpam-1481	393	16	∗	∗	NOUN
ejpam-1481	393	17	v	v	NOUN
ejpam-1481	393	18	,	,	PUNCT
ejpam-1481	393	19	c∗0	c∗0	NOUN
ejpam-1481	393	20	)	)	PUNCT
ejpam-1481	393	21	.	.	PUNCT
ejpam-1481	394	1	conversely	conversely	ADV
ejpam-1481	394	2	,	,	PUNCT
ejpam-1481	394	3	if	if	SCONJ
ejpam-1481	394	4	λ	λ	PROPN
ejpam-1481	394	5	∈	∈	PROPN
ejpam-1481	394	6	σp(∆	σp(∆	PROPN
ejpam-1481	394	7	∗	∗	PROPN
ejpam-1481	394	8	v	v	NOUN
ejpam-1481	394	9	,	,	PUNCT
ejpam-1481	394	10	c∗0	c∗0	NOUN
ejpam-1481	394	11	)	)	PUNCT
ejpam-1481	394	12	,	,	PUNCT
ejpam-1481	394	13	then	then	ADV
ejpam-1481	394	14	there	there	PRON
ejpam-1481	394	15	exists	exist	VERB
ejpam-1481	394	16	f	f	PROPN
ejpam-1481	394	17	=	=	PRON
ejpam-1481	394	18	(	(	PUNCT
ejpam-1481	394	19	f0	f0	PROPN
ejpam-1481	394	20	,	,	PUNCT
ejpam-1481	394	21	f1	f1	NOUN
ejpam-1481	394	22	,	,	PUNCT
ejpam-1481	394	23	f2	f2	PROPN
ejpam-1481	394	24	,	,	PUNCT
ejpam-1481	394	25	.	.	PUNCT
ejpam-1481	394	26	.	.	PUNCT
ejpam-1481	394	27	.	.	PUNCT
ejpam-1481	394	28	)	)	PUNCT
ejpam-1481	395	1	6=	6=	NUM
ejpam-1481	395	2	θ	θ	PROPN
ejpam-1481	395	3	in	in	ADP
ejpam-1481	395	4	c∗0	c∗0	NOUN
ejpam-1481	395	5	∼=	∼=	PROPN
ejpam-1481	395	6	l1	l1	PROPN
ejpam-1481	395	7	,	,	PUNCT
ejpam-1481	395	8	∆∗v	∆∗v	NOUN
ejpam-1481	395	9	f	f	X
ejpam-1481	395	10	=	=	SYM
ejpam-1481	395	11	λ	λ	X
ejpam-1481	395	12	f	f	PROPN
ejpam-1481	395	13	.	.	PUNCT
ejpam-1481	396	1	then	then	ADV
ejpam-1481	396	2	,	,	PUNCT
ejpam-1481	396	3	fk+1	fk+1	NOUN
ejpam-1481	396	4	=	=	SYM
ejpam-1481	396	5	vk−λ	vk−λ	PROPN
ejpam-1481	396	6	vk	vk	X
ejpam-1481	396	7	fk	fk	INTJ
ejpam-1481	396	8	,	,	PUNCT
ejpam-1481	396	9	k	k	PROPN
ejpam-1481	396	10	∈	∈	PROPN
ejpam-1481	396	11	n	n	PRON
ejpam-1481	396	12	and	and	CCONJ
ejpam-1481	396	13	∑	∑	PROPN
ejpam-1481	396	14	k	k	PROPN
ejpam-1481	396	15	�	�	PROPN
ejpam-1481	396	16	�	�	PROPN
ejpam-1481	396	17	fk	fk	INTJ
ejpam-1481	396	18	�	�	PROPN
ejpam-1481	396	19	�	�	PROPN
ejpam-1481	396	20	<	<	X
ejpam-1481	396	21	∞.	∞.	PROPN
ejpam-1481	396	22	therefore	therefore	ADV
ejpam-1481	396	23	lim	lim	PROPN
ejpam-1481	396	24	k→∞	k→∞	PROPN
ejpam-1481	396	25	�	�	PROPN
ejpam-1481	396	26	�	�	PROPN
ejpam-1481	396	27	�	�	PROPN
ejpam-1481	396	28	fk+1	fk+1	PROPN
ejpam-1481	396	29	fk	fk	X
ejpam-1481	396	30	�	�	PROPN
ejpam-1481	396	31	�	�	PROPN
ejpam-1481	396	32	�	�	PROPN
ejpam-1481	396	33	=	=	SYM
ejpam-1481	396	34	�	�	PROPN
ejpam-1481	396	35	�	�	PROPN
ejpam-1481	396	36	�	�	PROPN
ejpam-1481	396	37	λ−l	λ−l	PROPN
ejpam-1481	396	38	l	l	NOUN
ejpam-1481	396	39	�	�	PROPN
ejpam-1481	396	40	�	�	PROPN
ejpam-1481	396	41	�	�	PROPN
ejpam-1481	396	42	<	<	X
ejpam-1481	396	43	1	1	NUM
ejpam-1481	396	44	or	or	CCONJ
ejpam-1481	396	45	λ	λ	PROPN
ejpam-1481	396	46	∈	∈	PROPN
ejpam-1481	396	47	�	�	PROPN
ejpam-1481	396	48	vk	vk	NOUN
ejpam-1481	396	49	:	:	PUNCT
ejpam-1481	396	50	k	k	PROPN
ejpam-1481	396	51	∈	∈	PROPN
ejpam-1481	396	52	n	n	CCONJ
ejpam-1481	396	53	(	(	PUNCT
ejpam-1481	396	54	note	note	VERB
ejpam-1481	396	55	that	that	SCONJ
ejpam-1481	396	56	|λ−	|λ−	NOUN
ejpam-1481	396	57	l|	l|	NOUN
ejpam-1481	396	58	=	=	SYM
ejpam-1481	396	59	l	l	NOUN
ejpam-1481	396	60	contradicts	contradict	VERB
ejpam-1481	396	61	with	with	ADP
ejpam-1481	396	62	∑	∑	PROPN
ejpam-1481	396	63	k	k	PROPN
ejpam-1481	396	64	�	�	PROPN
ejpam-1481	396	65	�	�	PROPN
ejpam-1481	396	66	fk	fk	INTJ
ejpam-1481	396	67	�	�	PROPN
ejpam-1481	396	68	�	�	PROPN
ejpam-1481	396	69	<	<	X
ejpam-1481	396	70	∞	∞	PROPN
ejpam-1481	396	71	,	,	PUNCT
ejpam-1481	396	72	by	by	ADP
ejpam-1481	396	73	using	use	VERB
ejpam-1481	396	74	lemma	lemma	PROPN
ejpam-1481	396	75	3	3	NUM
ejpam-1481	396	76	.	.	PUNCT
ejpam-1481	397	1	this	this	PRON
ejpam-1481	397	2	completes	complete	VERB
ejpam-1481	397	3	the	the	DET
ejpam-1481	397	4	proof	proof	NOUN
ejpam-1481	397	5	.	.	PUNCT
ejpam-1481	398	1	theorem	theorem	VERB
ejpam-1481	398	2	13	13	NUM
ejpam-1481	398	3	.	.	PUNCT
ejpam-1481	399	1	σr(∆v	σr(∆v	ADV
ejpam-1481	399	2	,	,	PUNCT
ejpam-1481	399	3	c0	c0	NOUN
ejpam-1481	399	4	)	)	PUNCT
ejpam-1481	399	5	=	=	SYM
ejpam-1481	399	6	σp(∆	σp(∆	PROPN
ejpam-1481	399	7	∗	∗	NOUN
ejpam-1481	399	8	v	v	NOUN
ejpam-1481	399	9	,	,	PUNCT
ejpam-1481	399	10	c∗0)\σp(∆v	c∗0)\σp(∆v	NOUN
ejpam-1481	399	11	,	,	PUNCT
ejpam-1481	399	12	c0	c0	NOUN
ejpam-1481	399	13	)	)	PUNCT
ejpam-1481	399	14	.	.	PUNCT
ejpam-1481	400	1	a.	a.	PROPN
ejpam-1481	400	2	akhmedov	akhmedov	PROPN
ejpam-1481	400	3	,	,	PUNCT
ejpam-1481	400	4	s.	s.	PROPN
ejpam-1481	400	5	el	el	PROPN
ejpam-1481	400	6	-	-	PUNCT
ejpam-1481	400	7	shabrawy	shabrawy	PROPN
ejpam-1481	400	8	/	/	SYM
ejpam-1481	400	9	eur	eur	NOUN
ejpam-1481	400	10	.	.	PUNCT
ejpam-1481	401	1	j.	j.	PROPN
ejpam-1481	401	2	pure	pure	PROPN
ejpam-1481	401	3	appl	appl	PROPN
ejpam-1481	401	4	.	.	PROPN
ejpam-1481	401	5	math	math	PROPN
ejpam-1481	401	6	,	,	PUNCT
ejpam-1481	401	7	5	5	NUM
ejpam-1481	401	8	(	(	PUNCT
ejpam-1481	401	9	2012	2012	NUM
ejpam-1481	401	10	)	)	PUNCT
ejpam-1481	401	11	,	,	PUNCT
ejpam-1481	401	12	59	59	NUM
ejpam-1481	401	13	-	-	SYM
ejpam-1481	401	14	74	74	NUM
ejpam-1481	401	15	72	72	NUM
ejpam-1481	401	16	proof	proof	NOUN
ejpam-1481	401	17	.	.	PUNCT
ejpam-1481	402	1	the	the	DET
ejpam-1481	402	2	proof	proof	NOUN
ejpam-1481	402	3	follows	follow	VERB
ejpam-1481	402	4	immediately	immediately	ADV
ejpam-1481	402	5	from	from	ADP
ejpam-1481	402	6	the	the	DET
ejpam-1481	402	7	definition	definition	NOUN
ejpam-1481	402	8	of	of	ADP
ejpam-1481	402	9	the	the	DET
ejpam-1481	402	10	residual	residual	ADJ
ejpam-1481	402	11	spectrum	spectrum	NOUN
ejpam-1481	402	12	and	and	CCONJ
ejpam-1481	402	13	lemma	lemma	PROPN
ejpam-1481	402	14	1	1	NUM
ejpam-1481	402	15	.	.	PUNCT
ejpam-1481	402	16	theorem	theorem	VERB
ejpam-1481	402	17	14	14	NUM
ejpam-1481	402	18	.	.	PUNCT
ejpam-1481	403	1	σr(∆v	σr(∆v	ADV
ejpam-1481	403	2	,	,	PUNCT
ejpam-1481	403	3	c0	c0	NOUN
ejpam-1481	403	4	)	)	PUNCT
ejpam-1481	403	5	=	=	SYM
ejpam-1481	404	1	{	{	PUNCT
ejpam-1481	404	2	λ	λ	X
ejpam-1481	404	3	∈	∈	PROPN
ejpam-1481	404	4	c	c	NOUN
ejpam-1481	404	5	:	:	PUNCT
ejpam-1481	404	6	|λ−	|λ−	NOUN
ejpam-1481	404	7	l|	l|	ADJ
ejpam-1481	404	8	<	<	X
ejpam-1481	404	9	l	l	NOUN
ejpam-1481	404	10	}	}	PUNCT
ejpam-1481	404	11	.	.	PUNCT
ejpam-1481	405	1	proof	proof	NOUN
ejpam-1481	405	2	.	.	PUNCT
ejpam-1481	406	1	the	the	DET
ejpam-1481	406	2	proof	proof	NOUN
ejpam-1481	406	3	follows	follow	VERB
ejpam-1481	406	4	immediately	immediately	ADV
ejpam-1481	406	5	from	from	ADP
ejpam-1481	406	6	theorems	theorem	NOUN
ejpam-1481	406	7	11	11	NUM
ejpam-1481	406	8	,	,	PUNCT
ejpam-1481	406	9	12	12	NUM
ejpam-1481	406	10	and	and	CCONJ
ejpam-1481	406	11	13	13	NUM
ejpam-1481	406	12	.	.	PUNCT
ejpam-1481	407	1	theorem	theorem	VERB
ejpam-1481	407	2	15	15	NUM
ejpam-1481	407	3	.	.	PUNCT
ejpam-1481	408	1	σc(∆v	σc(∆v	PROPN
ejpam-1481	408	2	,	,	PUNCT
ejpam-1481	408	3	c0	c0	NOUN
ejpam-1481	408	4	)	)	PUNCT
ejpam-1481	408	5	=	=	SYM
ejpam-1481	408	6	σ(∆v	σ(∆v	NOUN
ejpam-1481	408	7	,	,	PUNCT
ejpam-1481	408	8	c0)\σp(∆	c0)\σp(∆	PROPN
ejpam-1481	408	9	∗	∗	NOUN
ejpam-1481	408	10	v	v	NOUN
ejpam-1481	408	11	,	,	PUNCT
ejpam-1481	408	12	c∗0	c∗0	NOUN
ejpam-1481	408	13	)	)	PUNCT
ejpam-1481	408	14	.	.	PUNCT
ejpam-1481	409	1	proof	proof	NOUN
ejpam-1481	409	2	.	.	PUNCT
ejpam-1481	410	1	the	the	DET
ejpam-1481	410	2	proof	proof	NOUN
ejpam-1481	410	3	follows	follow	VERB
ejpam-1481	410	4	immediately	immediately	ADV
ejpam-1481	410	5	from	from	ADP
ejpam-1481	410	6	theorems	theorem	NOUN
ejpam-1481	410	7	11	11	NUM
ejpam-1481	410	8	,	,	PUNCT
ejpam-1481	410	9	12	12	NUM
ejpam-1481	410	10	and	and	CCONJ
ejpam-1481	410	11	13	13	NUM
ejpam-1481	410	12	.	.	PUNCT
ejpam-1481	411	1	theorem	theorem	VERB
ejpam-1481	411	2	16	16	NUM
ejpam-1481	411	3	.	.	PUNCT
ejpam-1481	412	1	σc(∆v	σc(∆v	PROPN
ejpam-1481	412	2	,	,	PUNCT
ejpam-1481	412	3	c0	c0	NOUN
ejpam-1481	412	4	)	)	PUNCT
ejpam-1481	412	5	=	=	SYM
ejpam-1481	412	6	{	{	PUNCT
ejpam-1481	412	7	λ	λ	X
ejpam-1481	412	8	∈	∈	PROPN
ejpam-1481	412	9	c	c	NOUN
ejpam-1481	412	10	:	:	PUNCT
ejpam-1481	412	11	|λ−	|λ−	NOUN
ejpam-1481	412	12	l|	l|	ADJ
ejpam-1481	412	13	=	=	SYM
ejpam-1481	412	14	l	l	NOUN
ejpam-1481	412	15	}	}	PUNCT
ejpam-1481	412	16	.	.	PUNCT
ejpam-1481	413	1	proof	proof	NOUN
ejpam-1481	413	2	.	.	PUNCT
ejpam-1481	414	1	the	the	DET
ejpam-1481	414	2	proof	proof	NOUN
ejpam-1481	414	3	follows	follow	VERB
ejpam-1481	414	4	immediately	immediately	ADV
ejpam-1481	414	5	from	from	ADP
ejpam-1481	414	6	theorems	theorem	NOUN
ejpam-1481	414	7	10	10	NUM
ejpam-1481	414	8	,	,	PUNCT
ejpam-1481	414	9	12	12	NUM
ejpam-1481	414	10	and	and	CCONJ
ejpam-1481	414	11	15	15	NUM
ejpam-1481	414	12	.	.	X
ejpam-1481	415	1	5.2	5.2	NUM
ejpam-1481	415	2	.	.	PUNCT
ejpam-1481	416	1	the	the	DET
ejpam-1481	416	2	fine	fine	ADJ
ejpam-1481	416	3	spectrum	spectrum	NOUN
ejpam-1481	416	4	of	of	ADP
ejpam-1481	416	5	the	the	DET
ejpam-1481	416	6	modified	modify	VERB
ejpam-1481	416	7	operator	operator	NOUN
ejpam-1481	416	8	∆v	∆v	PROPN
ejpam-1481	416	9	on	on	ADP
ejpam-1481	416	10	l1	l1	PROPN
ejpam-1481	416	11	in	in	ADP
ejpam-1481	416	12	this	this	DET
ejpam-1481	416	13	subsection	subsection	NOUN
ejpam-1481	416	14	we	we	PRON
ejpam-1481	416	15	calculate	calculate	VERB
ejpam-1481	416	16	the	the	DET
ejpam-1481	416	17	fine	fine	ADJ
ejpam-1481	416	18	spectrum	spectrum	NOUN
ejpam-1481	416	19	of	of	ADP
ejpam-1481	416	20	the	the	DET
ejpam-1481	416	21	operator	operator	NOUN
ejpam-1481	416	22	∆v	∆v	PROPN
ejpam-1481	416	23	,	,	PUNCT
ejpam-1481	416	24	which	which	PRON
ejpam-1481	416	25	is	be	AUX
ejpam-1481	416	26	represented	represent	VERB
ejpam-1481	416	27	by	by	ADP
ejpam-1481	416	28	the	the	DET
ejpam-1481	416	29	matrix	matrix	NOUN
ejpam-1481	416	30	in	in	ADP
ejpam-1481	416	31	(	(	PUNCT
ejpam-1481	416	32	3	3	X
ejpam-1481	416	33	)	)	PUNCT
ejpam-1481	416	34	such	such	ADJ
ejpam-1481	416	35	that	that	SCONJ
ejpam-1481	416	36	the	the	DET
ejpam-1481	416	37	conditions	condition	NOUN
ejpam-1481	416	38	(	(	PUNCT
ejpam-1481	416	39	10	10	NUM
ejpam-1481	416	40	)	)	PUNCT
ejpam-1481	416	41	are	be	AUX
ejpam-1481	416	42	satisfied	satisfied	ADJ
ejpam-1481	416	43	,	,	PUNCT
ejpam-1481	416	44	on	on	ADP
ejpam-1481	416	45	the	the	DET
ejpam-1481	416	46	sequence	sequence	NOUN
ejpam-1481	416	47	space	space	NOUN
ejpam-1481	416	48	l1	l1	PROPN
ejpam-1481	416	49	.	.	PUNCT
ejpam-1481	417	1	the	the	DET
ejpam-1481	417	2	results	result	NOUN
ejpam-1481	417	3	of	of	ADP
ejpam-1481	417	4	this	this	DET
ejpam-1481	417	5	section	section	NOUN
ejpam-1481	417	6	generalize	generalize	VERB
ejpam-1481	417	7	the	the	DET
ejpam-1481	417	8	corresponding	corresponding	ADJ
ejpam-1481	417	9	results	result	NOUN
ejpam-1481	417	10	in	in	ADP
ejpam-1481	417	11	section	section	NOUN
ejpam-1481	417	12	3.1	3.1	NUM
ejpam-1481	417	13	.	.	PUNCT
ejpam-1481	418	1	we	we	PRON
ejpam-1481	418	2	begin	begin	VERB
ejpam-1481	418	3	by	by	ADP
ejpam-1481	418	4	determining	determine	VERB
ejpam-1481	418	5	when	when	SCONJ
ejpam-1481	418	6	a	a	DET
ejpam-1481	418	7	matrix	matrix	NOUN
ejpam-1481	418	8	a	a	DET
ejpam-1481	418	9	induces	induce	VERB
ejpam-1481	418	10	a	a	DET
ejpam-1481	418	11	bounded	bounded	ADJ
ejpam-1481	418	12	linear	linear	ADJ
ejpam-1481	418	13	operator	operator	NOUN
ejpam-1481	418	14	from	from	ADP
ejpam-1481	418	15	l1	l1	PROPN
ejpam-1481	418	16	to	to	ADP
ejpam-1481	418	17	itself	itself	PRON
ejpam-1481	418	18	.	.	PUNCT
ejpam-1481	419	1	lemma	lemma	PROPN
ejpam-1481	419	2	4	4	NUM
ejpam-1481	419	3	(	(	PUNCT
ejpam-1481	419	4	[	[	NOUN
ejpam-1481	419	5	14	14	NUM
ejpam-1481	419	6	,	,	PUNCT
ejpam-1481	419	7	p.	p.	NOUN
ejpam-1481	419	8	253	253	NUM
ejpam-1481	419	9	,	,	PUNCT
ejpam-1481	419	10	theorem	theorem	VERB
ejpam-1481	419	11	34.16	34.16	NUM
ejpam-1481	419	12	]	]	PUNCT
ejpam-1481	419	13	)	)	PUNCT
ejpam-1481	419	14	.	.	PUNCT
ejpam-1481	420	1	the	the	DET
ejpam-1481	420	2	matrix	matrix	NOUN
ejpam-1481	420	3	a=	a=	X
ejpam-1481	420	4	(	(	PUNCT
ejpam-1481	420	5	ank	ank	PROPN
ejpam-1481	420	6	)	)	PUNCT
ejpam-1481	420	7	gives	give	VERB
ejpam-1481	420	8	rise	rise	NOUN
ejpam-1481	420	9	to	to	ADP
ejpam-1481	420	10	a	a	DET
ejpam-1481	420	11	bounded	bounded	ADJ
ejpam-1481	420	12	linear	linear	ADJ
ejpam-1481	420	13	operator	operator	NOUN
ejpam-1481	420	14	t	t	PROPN
ejpam-1481	420	15	∈	∈	PROPN
ejpam-1481	420	16	b(l1	b(l1	PROPN
ejpam-1481	420	17	)	)	PUNCT
ejpam-1481	420	18	from	from	ADP
ejpam-1481	420	19	l1	l1	PROPN
ejpam-1481	420	20	to	to	ADP
ejpam-1481	420	21	itself	itself	PRON
ejpam-1481	420	22	if	if	SCONJ
ejpam-1481	420	23	and	and	CCONJ
ejpam-1481	420	24	only	only	ADV
ejpam-1481	420	25	if	if	SCONJ
ejpam-1481	420	26	the	the	DET
ejpam-1481	420	27	supremum	supremum	NOUN
ejpam-1481	420	28	of	of	ADP
ejpam-1481	420	29	l1	l1	PROPN
ejpam-1481	420	30	norms	norm	NOUN
ejpam-1481	420	31	of	of	ADP
ejpam-1481	420	32	the	the	DET
ejpam-1481	420	33	columns	column	NOUN
ejpam-1481	420	34	of	of	ADP
ejpam-1481	420	35	a	a	PRON
ejpam-1481	420	36	is	be	AUX
ejpam-1481	420	37	bounded	bound	VERB
ejpam-1481	420	38	.	.	PUNCT
ejpam-1481	421	1	corollary	corollary	ADJ
ejpam-1481	421	2	2	2	NUM
ejpam-1481	421	3	.	.	PUNCT
ejpam-1481	422	1	the	the	DET
ejpam-1481	422	2	operator	operator	NOUN
ejpam-1481	422	3	∆v	∆v	PROPN
ejpam-1481	422	4	:	:	PUNCT
ejpam-1481	422	5	l1→	l1→	PROPN
ejpam-1481	422	6	l1	l1	PROPN
ejpam-1481	422	7	is	be	AUX
ejpam-1481	422	8	a	a	DET
ejpam-1481	422	9	bounded	bounded	ADJ
ejpam-1481	422	10	linear	linear	ADJ
ejpam-1481	422	11	operator	operator	NOUN
ejpam-1481	422	12	with	with	ADP
ejpam-1481	422	13	the	the	DET
ejpam-1481	422	14	norm	norm	NOUN
ejpam-1481	422	15	∆v	∆v	PROPN
ejpam-1481	422	16	l1	l1	PROPN
ejpam-1481	422	17	=	=	SYM
ejpam-1481	422	18	2	2	NUM
ejpam-1481	422	19	sup	sup	NOUN
ejpam-1481	422	20	k	k	PROPN
ejpam-1481	422	21	vk	vk	PROPN
ejpam-1481	422	22	.	.	PUNCT
ejpam-1481	423	1	by	by	ADP
ejpam-1481	423	2	using	use	VERB
ejpam-1481	423	3	arguments	argument	NOUN
ejpam-1481	423	4	similar	similar	ADJ
ejpam-1481	423	5	to	to	ADP
ejpam-1481	423	6	those	those	PRON
ejpam-1481	423	7	used	use	VERB
ejpam-1481	423	8	in	in	ADP
ejpam-1481	423	9	section	section	NOUN
ejpam-1481	423	10	5.1	5.1	NUM
ejpam-1481	423	11	,	,	PUNCT
ejpam-1481	423	12	we	we	PRON
ejpam-1481	423	13	can	can	AUX
ejpam-1481	423	14	prove	prove	VERB
ejpam-1481	423	15	the	the	DET
ejpam-1481	423	16	following	follow	VERB
ejpam-1481	423	17	main	main	ADJ
ejpam-1481	423	18	theorem	theorem	NOUN
ejpam-1481	423	19	.	.	PUNCT
ejpam-1481	423	20	theorem	theorem	PROPN
ejpam-1481	423	21	17	17	NUM
ejpam-1481	423	22	.	.	PUNCT
ejpam-1481	424	1	(	(	PUNCT
ejpam-1481	424	2	i	i	NOUN
ejpam-1481	424	3	)	)	PUNCT
ejpam-1481	424	4	σ(∆v	σ(∆v	NOUN
ejpam-1481	424	5	,	,	PUNCT
ejpam-1481	424	6	l1	l1	PROPN
ejpam-1481	424	7	)	)	PUNCT
ejpam-1481	425	1	=	=	PUNCT
ejpam-1481	426	1	d	d	X
ejpam-1481	426	2	∪	∪	X
ejpam-1481	426	3	e.	e.	PROPN
ejpam-1481	426	4	(	(	PUNCT
ejpam-1481	426	5	ii	ii	PROPN
ejpam-1481	426	6	)	)	PUNCT
ejpam-1481	426	7	σp(∆v	σp(∆v	PROPN
ejpam-1481	426	8	,	,	PUNCT
ejpam-1481	426	9	l1	l1	PROPN
ejpam-1481	426	10	)	)	PUNCT
ejpam-1481	426	11	=	=	SYM
ejpam-1481	426	12	e.	e.	PROPN
ejpam-1481	426	13	(	(	PUNCT
ejpam-1481	426	14	iii	iii	NOUN
ejpam-1481	426	15	)	)	PUNCT
ejpam-1481	426	16	σp(∆	σp(∆	NOUN
ejpam-1481	426	17	∗	∗	NOUN
ejpam-1481	426	18	v	v	NOUN
ejpam-1481	426	19	,	,	PUNCT
ejpam-1481	426	20	l∗1	l∗1	NOUN
ejpam-1481	426	21	)	)	PUNCT
ejpam-1481	426	22	=	=	PUNCT
ejpam-1481	427	1	d	d	X
ejpam-1481	427	2	∪	∪	X
ejpam-1481	427	3	e.	e.	PROPN
ejpam-1481	427	4	(	(	PUNCT
ejpam-1481	427	5	iv	iv	X
ejpam-1481	427	6	)	)	PUNCT
ejpam-1481	427	7	σr(∆v	σr(∆v	PROPN
ejpam-1481	427	8	,	,	PUNCT
ejpam-1481	427	9	l1	l1	PROPN
ejpam-1481	427	10	)	)	PUNCT
ejpam-1481	427	11	=	=	SYM
ejpam-1481	427	12	d.	d.	PROPN
ejpam-1481	427	13	(	(	PUNCT
ejpam-1481	427	14	v	v	NOUN
ejpam-1481	427	15	)	)	PUNCT
ejpam-1481	427	16	σc(∆v	σc(∆v	PROPN
ejpam-1481	427	17	,	,	PUNCT
ejpam-1481	427	18	l1	l1	PROPN
ejpam-1481	427	19	)	)	PUNCT
ejpam-1481	427	20	=	=	SYM
ejpam-1481	428	1	φ	φ	PROPN
ejpam-1481	428	2	.	.	PUNCT
ejpam-1481	429	1	references	reference	NOUN
ejpam-1481	429	2	73	73	NUM
ejpam-1481	429	3	6	6	NUM
ejpam-1481	429	4	.	.	PUNCT
ejpam-1481	430	1	conclusion	conclusion	NOUN
ejpam-1481	430	2	in	in	ADP
ejpam-1481	430	3	this	this	DET
ejpam-1481	430	4	paper	paper	NOUN
ejpam-1481	430	5	,	,	PUNCT
ejpam-1481	430	6	the	the	DET
ejpam-1481	430	7	fine	fine	ADJ
ejpam-1481	430	8	spectrum	spectrum	NOUN
ejpam-1481	430	9	of	of	ADP
ejpam-1481	430	10	the	the	DET
ejpam-1481	430	11	generalized	generalize	VERB
ejpam-1481	430	12	difference	difference	NOUN
ejpam-1481	430	13	operator	operator	NOUN
ejpam-1481	430	14	∆v	∆v	PROPN
ejpam-1481	430	15	on	on	ADP
ejpam-1481	430	16	the	the	DET
ejpam-1481	430	17	sequence	sequence	NOUN
ejpam-1481	430	18	spaces	space	VERB
ejpam-1481	430	19	c0	c0	PROPN
ejpam-1481	430	20	and	and	CCONJ
ejpam-1481	430	21	l1	l1	PROPN
ejpam-1481	430	22	is	be	AUX
ejpam-1481	430	23	commented	comment	VERB
ejpam-1481	430	24	on	on	ADP
ejpam-1481	430	25	,	,	PUNCT
ejpam-1481	430	26	and	and	CCONJ
ejpam-1481	430	27	some	some	DET
ejpam-1481	430	28	new	new	ADJ
ejpam-1481	430	29	results	result	NOUN
ejpam-1481	430	30	are	be	AUX
ejpam-1481	430	31	obtained	obtain	VERB
ejpam-1481	430	32	.	.	PUNCT
ejpam-1481	431	1	illustrative	illustrative	ADJ
ejpam-1481	431	2	examples	example	NOUN
ejpam-1481	431	3	are	be	AUX
ejpam-1481	431	4	given	give	VERB
ejpam-1481	431	5	as	as	ADV
ejpam-1481	431	6	well	well	ADV
ejpam-1481	431	7	.	.	PUNCT
ejpam-1481	432	1	these	these	DET
ejpam-1481	432	2	examples	example	NOUN
ejpam-1481	432	3	are	be	AUX
ejpam-1481	432	4	used	use	VERB
ejpam-1481	432	5	not	not	PART
ejpam-1481	432	6	only	only	ADV
ejpam-1481	432	7	to	to	PART
ejpam-1481	432	8	apply	apply	VERB
ejpam-1481	432	9	new	new	ADJ
ejpam-1481	432	10	results	result	NOUN
ejpam-1481	432	11	but	but	CCONJ
ejpam-1481	432	12	also	also	ADV
ejpam-1481	432	13	to	to	PART
ejpam-1481	432	14	disprove	disprove	VERB
ejpam-1481	432	15	some	some	DET
ejpam-1481	432	16	recent	recent	ADJ
ejpam-1481	432	17	results	result	NOUN
ejpam-1481	432	18	.	.	PUNCT
ejpam-1481	433	1	finally	finally	ADV
ejpam-1481	433	2	,	,	PUNCT
ejpam-1481	433	3	two	two	NUM
ejpam-1481	433	4	modifications	modification	NOUN
ejpam-1481	433	5	of	of	ADP
ejpam-1481	433	6	the	the	DET
ejpam-1481	433	7	operator	operator	NOUN
ejpam-1481	433	8	∆v	∆v	PROPN
ejpam-1481	433	9	are	be	AUX
ejpam-1481	433	10	introduced	introduce	VERB
ejpam-1481	433	11	.	.	PUNCT
ejpam-1481	434	1	the	the	DET
ejpam-1481	434	2	new	new	ADJ
ejpam-1481	434	3	results	result	NOUN
ejpam-1481	434	4	of	of	ADP
ejpam-1481	434	5	this	this	DET
ejpam-1481	434	6	paper	paper	NOUN
ejpam-1481	434	7	generalize	generalize	VERB
ejpam-1481	434	8	and	and	CCONJ
ejpam-1481	434	9	improve	improve	VERB
ejpam-1481	434	10	some	some	DET
ejpam-1481	434	11	recent	recent	ADJ
ejpam-1481	434	12	results	result	NOUN
ejpam-1481	434	13	that	that	PRON
ejpam-1481	434	14	appeared	appear	VERB
ejpam-1481	434	15	in	in	ADP
ejpam-1481	434	16	the	the	DET
ejpam-1481	434	17	literature	literature	NOUN
ejpam-1481	434	18	.	.	PUNCT
ejpam-1481	435	1	references	reference	NOUN
ejpam-1481	435	2	[	[	X
ejpam-1481	435	3	1	1	X
ejpam-1481	435	4	]	]	PUNCT
ejpam-1481	435	5	a	a	DET
ejpam-1481	435	6	akhmedov	akhmedov	NOUN
ejpam-1481	435	7	and	and	CCONJ
ejpam-1481	435	8	f	f	PROPN
ejpam-1481	435	9	başar	başar	PROPN
ejpam-1481	435	10	,	,	PUNCT
ejpam-1481	435	11	on	on	ADP
ejpam-1481	435	12	the	the	DET
ejpam-1481	435	13	fine	fine	ADJ
ejpam-1481	435	14	spectra	spectra	NOUN
ejpam-1481	435	15	of	of	ADP
ejpam-1481	435	16	the	the	DET
ejpam-1481	435	17	difference	difference	NOUN
ejpam-1481	435	18	operator	operator	NOUN
ejpam-1481	435	19	∆	∆	PROPN
ejpam-1481	435	20	over	over	ADP
ejpam-1481	435	21	the	the	DET
ejpam-1481	435	22	sequence	sequence	NOUN
ejpam-1481	435	23	space	space	NOUN
ejpam-1481	435	24	lp	lp	NOUN
ejpam-1481	435	25	,	,	PUNCT
ejpam-1481	435	26	(	(	PUNCT
ejpam-1481	435	27	1≤	1≤	NUM
ejpam-1481	435	28	p	p	X
ejpam-1481	435	29	<	<	PROPN
ejpam-1481	435	30	∞	∞	PROPN
ejpam-1481	435	31	)	)	PUNCT
ejpam-1481	435	32	,	,	PUNCT
ejpam-1481	435	33	demonstratio	demonstratio	PROPN
ejpam-1481	435	34	math	math	PROPN
ejpam-1481	435	35	.	.	PUNCT
ejpam-1481	436	1	39	39	NUM
ejpam-1481	436	2	(	(	PUNCT
ejpam-1481	436	3	3	3	NUM
ejpam-1481	436	4	)	)	PUNCT
ejpam-1481	436	5	.	.	PUNCT
ejpam-1481	437	1	585	585	NUM
ejpam-1481	437	2	-	-	SYM
ejpam-1481	437	3	595	595	NUM
ejpam-1481	437	4	.	.	PUNCT
ejpam-1481	438	1	2006	2006	NUM
ejpam-1481	438	2	.	.	PUNCT
ejpam-1481	439	1	[	[	X
ejpam-1481	439	2	2	2	X
ejpam-1481	439	3	]	]	PUNCT
ejpam-1481	439	4	a	a	DET
ejpam-1481	439	5	akhmedov	akhmedov	NOUN
ejpam-1481	439	6	and	and	CCONJ
ejpam-1481	439	7	f	f	PROPN
ejpam-1481	439	8	başar	başar	PROPN
ejpam-1481	439	9	,	,	PUNCT
ejpam-1481	439	10	the	the	DET
ejpam-1481	439	11	fine	fine	ADJ
ejpam-1481	439	12	spectra	spectra	NOUN
ejpam-1481	439	13	of	of	ADP
ejpam-1481	439	14	the	the	DET
ejpam-1481	439	15	difference	difference	NOUN
ejpam-1481	439	16	operator∆	operator∆	PROPN
ejpam-1481	439	17	over	over	ADP
ejpam-1481	439	18	the	the	DET
ejpam-1481	439	19	sequence	sequence	NOUN
ejpam-1481	439	20	space	space	NOUN
ejpam-1481	439	21	bvp	bvp	NOUN
ejpam-1481	439	22	,	,	PUNCT
ejpam-1481	439	23	(	(	PUNCT
ejpam-1481	439	24	1≤	1≤	NUM
ejpam-1481	439	25	p	p	X
ejpam-1481	439	26	<	<	PROPN
ejpam-1481	439	27	∞	∞	PROPN
ejpam-1481	439	28	)	)	PUNCT
ejpam-1481	439	29	,	,	PUNCT
ejpam-1481	439	30	acta	acta	PROPN
ejpam-1481	439	31	math	math	PROPN
ejpam-1481	439	32	.	.	PUNCT
ejpam-1481	440	1	sin	sin	NOUN
ejpam-1481	440	2	.	.	PUNCT
ejpam-1481	441	1	(	(	PUNCT
ejpam-1481	441	2	engl	engl	PROPN
ejpam-1481	441	3	.	.	PUNCT
ejpam-1481	441	4	ser	ser	PROPN
ejpam-1481	441	5	.	.	PUNCT
ejpam-1481	441	6	)	)	PUNCT
ejpam-1481	442	1	23	23	NUM
ejpam-1481	442	2	(	(	PUNCT
ejpam-1481	442	3	10	10	NUM
ejpam-1481	442	4	)	)	PUNCT
ejpam-1481	442	5	.	.	PUNCT
ejpam-1481	443	1	1757	1757	NUM
ejpam-1481	443	2	-	-	SYM
ejpam-1481	443	3	1768	1768	NUM
ejpam-1481	443	4	.	.	PUNCT
ejpam-1481	444	1	2007	2007	NUM
ejpam-1481	444	2	.	.	PUNCT
ejpam-1481	445	1	[	[	X
ejpam-1481	445	2	3	3	X
ejpam-1481	445	3	]	]	X
ejpam-1481	445	4	a	a	DET
ejpam-1481	445	5	akhmedov	akhmedov	NOUN
ejpam-1481	445	6	and	and	CCONJ
ejpam-1481	445	7	s	s	PROPN
ejpam-1481	445	8	el	el	NOUN
ejpam-1481	445	9	-	-	PUNCT
ejpam-1481	445	10	shabrawy	shabrawy	PROPN
ejpam-1481	445	11	,	,	PUNCT
ejpam-1481	445	12	on	on	ADP
ejpam-1481	445	13	the	the	DET
ejpam-1481	445	14	fine	fine	ADJ
ejpam-1481	445	15	spectrum	spectrum	NOUN
ejpam-1481	445	16	of	of	ADP
ejpam-1481	445	17	the	the	DET
ejpam-1481	445	18	operator	operator	NOUN
ejpam-1481	445	19	∆a	∆a	PROPN
ejpam-1481	445	20	,	,	PUNCT
ejpam-1481	445	21	b	b	NOUN
ejpam-1481	445	22	over	over	ADP
ejpam-1481	445	23	the	the	DET
ejpam-1481	445	24	sequence	sequence	NOUN
ejpam-1481	445	25	space	space	NOUN
ejpam-1481	445	26	c	c	NOUN
ejpam-1481	445	27	,	,	PUNCT
ejpam-1481	445	28	comput	comput	NOUN
ejpam-1481	445	29	.	.	PUNCT
ejpam-1481	446	1	math	math	NOUN
ejpam-1481	446	2	.	.	PUNCT
ejpam-1481	447	1	appl	appl	PROPN
ejpam-1481	447	2	.	.	PROPN
ejpam-1481	448	1	61	61	NUM
ejpam-1481	448	2	.	.	X
ejpam-1481	448	3	2994	2994	NUM
ejpam-1481	448	4	-	-	SYM
ejpam-1481	448	5	3002	3002	NUM
ejpam-1481	448	6	.	.	PUNCT
ejpam-1481	449	1	2011	2011	NUM
ejpam-1481	449	2	.	.	PUNCT
ejpam-1481	450	1	[	[	X
ejpam-1481	450	2	4	4	X
ejpam-1481	450	3	]	]	X
ejpam-1481	450	4	a	a	DET
ejpam-1481	450	5	akhmedov	akhmedov	NOUN
ejpam-1481	450	6	and	and	CCONJ
ejpam-1481	450	7	s	s	PROPN
ejpam-1481	450	8	el	el	NOUN
ejpam-1481	450	9	-	-	PUNCT
ejpam-1481	450	10	shabrawy	shabrawy	PROPN
ejpam-1481	450	11	,	,	PUNCT
ejpam-1481	450	12	on	on	ADP
ejpam-1481	450	13	the	the	DET
ejpam-1481	450	14	fine	fine	ADJ
ejpam-1481	450	15	spectrum	spectrum	NOUN
ejpam-1481	450	16	of	of	ADP
ejpam-1481	450	17	the	the	DET
ejpam-1481	450	18	operator	operator	NOUN
ejpam-1481	450	19	∆v	∆v	PROPN
ejpam-1481	450	20	over	over	ADP
ejpam-1481	450	21	the	the	DET
ejpam-1481	450	22	sequence	sequence	NOUN
ejpam-1481	450	23	spaces	space	VERB
ejpam-1481	450	24	c	c	NOUN
ejpam-1481	450	25	and	and	CCONJ
ejpam-1481	450	26	lp	lp	NOUN
ejpam-1481	450	27	,	,	PUNCT
ejpam-1481	450	28	(	(	PUNCT
ejpam-1481	450	29	1	1	NUM
ejpam-1481	450	30	<	<	X
ejpam-1481	450	31	p	p	X
ejpam-1481	450	32	<	<	X
ejpam-1481	450	33	∞	∞	NUM
ejpam-1481	450	34	)	)	PUNCT
ejpam-1481	450	35	,	,	PUNCT
ejpam-1481	451	1	appl	appl	PROPN
ejpam-1481	451	2	.	.	PROPN
ejpam-1481	451	3	math	math	PROPN
ejpam-1481	451	4	.	.	PUNCT
ejpam-1481	452	1	inf	inf	PROPN
ejpam-1481	452	2	.	.	PUNCT
ejpam-1481	453	1	sci	sci	PROPN
ejpam-1481	453	2	.	.	PROPN
ejpam-1481	453	3	5	5	NUM
ejpam-1481	453	4	(	(	PUNCT
ejpam-1481	453	5	3	3	NUM
ejpam-1481	453	6	)	)	PUNCT
ejpam-1481	453	7	.	.	PUNCT
ejpam-1481	454	1	635	635	NUM
ejpam-1481	454	2	-	-	SYM
ejpam-1481	454	3	654	654	NUM
ejpam-1481	454	4	.	.	PUNCT
ejpam-1481	455	1	2011	2011	NUM
ejpam-1481	455	2	.	.	PUNCT
ejpam-1481	456	1	[	[	X
ejpam-1481	456	2	5	5	NUM
ejpam-1481	456	3	]	]	PUNCT
ejpam-1481	456	4	a	a	DET
ejpam-1481	456	5	akhmedov	akhmedov	NOUN
ejpam-1481	456	6	and	and	CCONJ
ejpam-1481	456	7	s	s	PROPN
ejpam-1481	456	8	el	el	NOUN
ejpam-1481	456	9	-	-	PUNCT
ejpam-1481	456	10	shabrawy	shabrawy	PROPN
ejpam-1481	456	11	,	,	PUNCT
ejpam-1481	456	12	on	on	ADP
ejpam-1481	456	13	the	the	DET
ejpam-1481	456	14	spectrum	spectrum	NOUN
ejpam-1481	456	15	of	of	ADP
ejpam-1481	456	16	the	the	DET
ejpam-1481	456	17	generalized	generalize	VERB
ejpam-1481	456	18	difference	difference	NOUN
ejpam-1481	456	19	operator	operator	NOUN
ejpam-1481	456	20	∆a	∆a	NOUN
ejpam-1481	456	21	,	,	PUNCT
ejpam-1481	456	22	b	b	NOUN
ejpam-1481	456	23	over	over	ADP
ejpam-1481	456	24	the	the	DET
ejpam-1481	456	25	sequence	sequence	NOUN
ejpam-1481	456	26	space	space	NOUN
ejpam-1481	456	27	c0	c0	PROPN
ejpam-1481	456	28	,	,	PUNCT
ejpam-1481	456	29	baku	baku	PROPN
ejpam-1481	456	30	univ	univ	PROPN
ejpam-1481	456	31	.	.	PUNCT
ejpam-1481	457	1	news	news	PROPN
ejpam-1481	457	2	j.	j.	PROPN
ejpam-1481	457	3	,	,	PUNCT
ejpam-1481	457	4	phys	phys	PROPN
ejpam-1481	457	5	.	.	PUNCT
ejpam-1481	457	6	math	math	NOUN
ejpam-1481	457	7	.	.	PUNCT
ejpam-1481	458	1	sci	sci	PROPN
ejpam-1481	458	2	.	.	PUNCT
ejpam-1481	458	3	ser	ser	PROPN
ejpam-1481	458	4	.	.	PROPN
ejpam-1481	459	1	4	4	NUM
ejpam-1481	459	2	.	.	X
ejpam-1481	459	3	12	12	NUM
ejpam-1481	459	4	-	-	SYM
ejpam-1481	459	5	21	21	NUM
ejpam-1481	459	6	.	.	PUNCT
ejpam-1481	459	7	2010	2010	NUM
ejpam-1481	459	8	.	.	PUNCT
ejpam-1481	460	1	[	[	X
ejpam-1481	460	2	6	6	NUM
ejpam-1481	460	3	]	]	PUNCT
ejpam-1481	460	4	a	a	DET
ejpam-1481	460	5	akhmedov	akhmedov	NOUN
ejpam-1481	460	6	and	and	CCONJ
ejpam-1481	460	7	s	s	PROPN
ejpam-1481	460	8	el	el	NOUN
ejpam-1481	460	9	-	-	PUNCT
ejpam-1481	460	10	shabrawy	shabrawy	PROPN
ejpam-1481	460	11	,	,	PUNCT
ejpam-1481	460	12	the	the	DET
ejpam-1481	460	13	spectrum	spectrum	NOUN
ejpam-1481	460	14	of	of	ADP
ejpam-1481	460	15	the	the	DET
ejpam-1481	460	16	generalized	generalize	VERB
ejpam-1481	460	17	lower	low	ADJ
ejpam-1481	460	18	triangle	triangle	NOUN
ejpam-1481	460	19	doubleband	doubleband	NOUN
ejpam-1481	460	20	matrix	matrix	NOUN
ejpam-1481	460	21	∆a	∆a	VERB
ejpam-1481	460	22	over	over	ADP
ejpam-1481	460	23	the	the	DET
ejpam-1481	460	24	sequence	sequence	NOUN
ejpam-1481	460	25	space	space	NOUN
ejpam-1481	460	26	c	c	NOUN
ejpam-1481	460	27	,	,	PUNCT
ejpam-1481	460	28	al	al	PROPN
ejpam-1481	460	29	-	-	PUNCT
ejpam-1481	460	30	azhar	azhar	PROPN
ejpam-1481	460	31	univ	univ	PROPN
ejpam-1481	460	32	.	.	PUNCT
ejpam-1481	461	1	eng	eng	PROPN
ejpam-1481	461	2	.	.	PUNCT
ejpam-1481	462	1	j.	j.	PROPN
ejpam-1481	462	2	,	,	PUNCT
ejpam-1481	462	3	jaues	jaue	NOUN
ejpam-1481	462	4	(	(	PUNCT
ejpam-1481	462	5	special	special	ADJ
ejpam-1481	462	6	issue	issue	NOUN
ejpam-1481	462	7	)	)	PUNCT
ejpam-1481	462	8	,	,	PUNCT
ejpam-1481	462	9	5	5	NUM
ejpam-1481	462	10	(	(	PUNCT
ejpam-1481	462	11	9	9	NUM
ejpam-1481	462	12	)	)	PUNCT
ejpam-1481	462	13	,	,	PUNCT
ejpam-1481	462	14	54	54	NUM
ejpam-1481	462	15	-	-	SYM
ejpam-1481	462	16	63	63	NUM
ejpam-1481	462	17	.	.	PUNCT
ejpam-1481	462	18	2010	2010	NUM
ejpam-1481	462	19	.	.	PUNCT
ejpam-1481	463	1	[	[	X
ejpam-1481	463	2	7	7	X
ejpam-1481	463	3	]	]	X
ejpam-1481	463	4	a	a	DET
ejpam-1481	463	5	akhmedov	akhmedov	NOUN
ejpam-1481	463	6	and	and	CCONJ
ejpam-1481	463	7	s	s	PROPN
ejpam-1481	463	8	el	el	NOUN
ejpam-1481	463	9	-	-	PUNCT
ejpam-1481	463	10	shabrawy	shabrawy	PROPN
ejpam-1481	463	11	,	,	PUNCT
ejpam-1481	463	12	comments	comment	NOUN
ejpam-1481	463	13	on	on	ADP
ejpam-1481	463	14	“	"	PUNCT
ejpam-1481	463	15	on	on	ADP
ejpam-1481	463	16	the	the	DET
ejpam-1481	463	17	fine	fine	ADJ
ejpam-1481	463	18	spectrum	spectrum	NOUN
ejpam-1481	463	19	of	of	ADP
ejpam-1481	463	20	the	the	DET
ejpam-1481	463	21	generalized	generalize	VERB
ejpam-1481	463	22	difference	difference	NOUN
ejpam-1481	463	23	operator	operator	NOUN
ejpam-1481	463	24	∆v	∆v	PROPN
ejpam-1481	463	25	over	over	ADP
ejpam-1481	463	26	the	the	DET
ejpam-1481	463	27	sequence	sequence	NOUN
ejpam-1481	463	28	space	space	NOUN
ejpam-1481	463	29	c0	c0	PROPN
ejpam-1481	463	30	”	"	PUNCT
ejpam-1481	463	31	,	,	PUNCT
ejpam-1481	463	32	submitted	submit	VERB
ejpam-1481	463	33	for	for	ADP
ejpam-1481	463	34	publication	publication	NOUN
ejpam-1481	463	35	.	.	PUNCT
ejpam-1481	464	1	[	[	X
ejpam-1481	464	2	8	8	NUM
ejpam-1481	464	3	]	]	X
ejpam-1481	464	4	a	a	DET
ejpam-1481	464	5	akhmedov	akhmedov	PROPN
ejpam-1481	464	6	and	and	CCONJ
ejpam-1481	464	7	s	s	PROPN
ejpam-1481	464	8	el	el	NOUN
ejpam-1481	464	9	-	-	PUNCT
ejpam-1481	464	10	shabrawy	shabrawy	PROPN
ejpam-1481	464	11	,	,	PUNCT
ejpam-1481	464	12	notes	note	NOUN
ejpam-1481	464	13	on	on	ADP
ejpam-1481	464	14	the	the	DET
ejpam-1481	464	15	spectrum	spectrum	NOUN
ejpam-1481	464	16	of	of	ADP
ejpam-1481	464	17	lower	low	ADJ
ejpam-1481	464	18	triangular	triangular	NOUN
ejpam-1481	464	19	double	double	ADJ
ejpam-1481	464	20	-	-	PUNCT
ejpam-1481	464	21	band	band	NOUN
ejpam-1481	464	22	matrices	matrix	NOUN
ejpam-1481	464	23	,	,	PUNCT
ejpam-1481	464	24	submitted	submit	VERB
ejpam-1481	464	25	for	for	ADP
ejpam-1481	464	26	publication	publication	NOUN
ejpam-1481	464	27	.	.	PUNCT
ejpam-1481	465	1	[	[	X
ejpam-1481	465	2	9	9	NUM
ejpam-1481	465	3	]	]	SYM
ejpam-1481	465	4	b	b	NOUN
ejpam-1481	465	5	altay	altay	NOUN
ejpam-1481	465	6	and	and	CCONJ
ejpam-1481	465	7	f	f	PROPN
ejpam-1481	465	8	başar	başar	PROPN
ejpam-1481	465	9	,	,	PUNCT
ejpam-1481	465	10	on	on	ADP
ejpam-1481	465	11	the	the	DET
ejpam-1481	465	12	fine	fine	ADJ
ejpam-1481	465	13	spectrum	spectrum	NOUN
ejpam-1481	465	14	of	of	ADP
ejpam-1481	465	15	the	the	DET
ejpam-1481	465	16	difference	difference	NOUN
ejpam-1481	465	17	operator	operator	NOUN
ejpam-1481	465	18	∆	∆	PROPN
ejpam-1481	465	19	on	on	ADP
ejpam-1481	465	20	c0	c0	PROPN
ejpam-1481	465	21	and	and	CCONJ
ejpam-1481	465	22	c	c	NOUN
ejpam-1481	465	23	,	,	PUNCT
ejpam-1481	465	24	inform	inform	NOUN
ejpam-1481	465	25	.	.	PUNCT
ejpam-1481	466	1	sci	sci	PROPN
ejpam-1481	466	2	.	.	PROPN
ejpam-1481	466	3	168	168	NUM
ejpam-1481	466	4	.	.	PUNCT
ejpam-1481	467	1	217	217	NUM
ejpam-1481	467	2	-	-	SYM
ejpam-1481	467	3	224	224	NUM
ejpam-1481	467	4	.	.	PUNCT
ejpam-1481	468	1	2004	2004	NUM
ejpam-1481	468	2	.	.	PUNCT
ejpam-1481	469	1	[	[	X
ejpam-1481	469	2	10	10	NUM
ejpam-1481	469	3	]	]	SYM
ejpam-1481	469	4	b	b	NOUN
ejpam-1481	469	5	altay	altay	NOUN
ejpam-1481	469	6	and	and	CCONJ
ejpam-1481	469	7	f	f	PROPN
ejpam-1481	469	8	başar	başar	PROPN
ejpam-1481	469	9	,	,	PUNCT
ejpam-1481	469	10	on	on	ADP
ejpam-1481	469	11	the	the	DET
ejpam-1481	469	12	fine	fine	ADJ
ejpam-1481	469	13	spectrum	spectrum	NOUN
ejpam-1481	469	14	of	of	ADP
ejpam-1481	469	15	the	the	DET
ejpam-1481	469	16	generalized	generalize	VERB
ejpam-1481	469	17	difference	difference	NOUN
ejpam-1481	469	18	operator	operator	NOUN
ejpam-1481	469	19	b(r	b(r	PROPN
ejpam-1481	469	20	,	,	PUNCT
ejpam-1481	469	21	s	s	NOUN
ejpam-1481	469	22	)	)	PUNCT
ejpam-1481	469	23	over	over	ADP
ejpam-1481	469	24	the	the	DET
ejpam-1481	469	25	sequence	sequence	NOUN
ejpam-1481	469	26	spaces	space	VERB
ejpam-1481	469	27	c0	c0	NOUN
ejpam-1481	469	28	and	and	CCONJ
ejpam-1481	469	29	c	c	NOUN
ejpam-1481	469	30	,	,	PUNCT
ejpam-1481	469	31	int	int	NOUN
ejpam-1481	469	32	.	.	PUNCT
ejpam-1481	470	1	j.	j.	PROPN
ejpam-1481	470	2	math	math	PROPN
ejpam-1481	470	3	.	.	PUNCT
ejpam-1481	471	1	math	math	NOUN
ejpam-1481	471	2	.	.	PUNCT
ejpam-1481	472	1	sci	sci	PROPN
ejpam-1481	472	2	.	.	PROPN
ejpam-1481	473	1	18	18	NUM
ejpam-1481	473	2	.	.	X
ejpam-1481	473	3	3005	3005	NUM
ejpam-1481	473	4	-	-	SYM
ejpam-1481	473	5	3013	3013	NUM
ejpam-1481	473	6	.	.	PUNCT
ejpam-1481	474	1	2005	2005	NUM
ejpam-1481	474	2	.	.	PUNCT
ejpam-1481	475	1	[	[	X
ejpam-1481	475	2	11	11	NUM
ejpam-1481	475	3	]	]	SYM
ejpam-1481	475	4	b	b	NOUN
ejpam-1481	475	5	altay	altay	NOUN
ejpam-1481	475	6	and	and	CCONJ
ejpam-1481	475	7	m	m	PROPN
ejpam-1481	475	8	karakuş	karakuş	NOUN
ejpam-1481	475	9	,	,	PUNCT
ejpam-1481	475	10	on	on	ADP
ejpam-1481	475	11	the	the	DET
ejpam-1481	475	12	spectrum	spectrum	NOUN
ejpam-1481	475	13	and	and	CCONJ
ejpam-1481	475	14	the	the	DET
ejpam-1481	475	15	fine	fine	ADJ
ejpam-1481	475	16	spectrum	spectrum	NOUN
ejpam-1481	475	17	of	of	ADP
ejpam-1481	475	18	the	the	DET
ejpam-1481	475	19	zweier	zweier	NOUN
ejpam-1481	475	20	matrix	matrix	NOUN
ejpam-1481	475	21	as	as	ADP
ejpam-1481	475	22	an	an	DET
ejpam-1481	475	23	operator	operator	NOUN
ejpam-1481	475	24	on	on	ADP
ejpam-1481	475	25	some	some	DET
ejpam-1481	475	26	sequence	sequence	NOUN
ejpam-1481	475	27	spaces	space	NOUN
ejpam-1481	475	28	,	,	PUNCT
ejpam-1481	475	29	thai	thai	PROPN
ejpam-1481	475	30	j.	j.	PROPN
ejpam-1481	475	31	math	math	PROPN
ejpam-1481	475	32	.	.	PUNCT
ejpam-1481	476	1	3(2	3(2	NUM
ejpam-1481	476	2	)	)	PUNCT
ejpam-1481	476	3	.	.	PUNCT
ejpam-1481	477	1	153	153	NUM
ejpam-1481	477	2	-	-	SYM
ejpam-1481	477	3	162	162	NUM
ejpam-1481	477	4	.	.	PUNCT
ejpam-1481	478	1	2005	2005	NUM
ejpam-1481	478	2	.	.	PUNCT
ejpam-1481	479	1	references	reference	NOUN
ejpam-1481	479	2	74	74	NUM
ejpam-1481	479	3	[	[	X
ejpam-1481	479	4	12	12	NUM
ejpam-1481	479	5	]	]	X
ejpam-1481	479	6	f	f	PROPN
ejpam-1481	479	7	başar	başar	PROPN
ejpam-1481	479	8	and	and	CCONJ
ejpam-1481	479	9	b	b	NOUN
ejpam-1481	479	10	altay	altay	NOUN
ejpam-1481	479	11	,	,	PUNCT
ejpam-1481	479	12	on	on	ADP
ejpam-1481	479	13	the	the	DET
ejpam-1481	479	14	space	space	NOUN
ejpam-1481	479	15	of	of	ADP
ejpam-1481	479	16	sequences	sequence	NOUN
ejpam-1481	479	17	of	of	ADP
ejpam-1481	479	18	p	p	NOUN
ejpam-1481	479	19	-	-	PUNCT
ejpam-1481	479	20	bounded	bound	VERB
ejpam-1481	479	21	variation	variation	NOUN
ejpam-1481	479	22	and	and	CCONJ
ejpam-1481	479	23	related	relate	VERB
ejpam-1481	479	24	matrix	matrix	NOUN
ejpam-1481	479	25	mappings	mapping	NOUN
ejpam-1481	479	26	,	,	PUNCT
ejpam-1481	479	27	ukrainian	ukrainian	ADJ
ejpam-1481	479	28	math	math	NOUN
ejpam-1481	479	29	.	.	PUNCT
ejpam-1481	480	1	j.	j.	PROPN
ejpam-1481	480	2	55	55	NUM
ejpam-1481	480	3	(	(	PUNCT
ejpam-1481	480	4	1	1	NUM
ejpam-1481	480	5	)	)	PUNCT
ejpam-1481	480	6	.	.	PUNCT
ejpam-1481	481	1	136	136	NUM
ejpam-1481	481	2	-	-	SYM
ejpam-1481	481	3	147	147	NUM
ejpam-1481	481	4	.	.	PUNCT
ejpam-1481	481	5	2003	2003	NUM
ejpam-1481	481	6	.	.	PUNCT
ejpam-1481	482	1	[	[	X
ejpam-1481	482	2	13	13	NUM
ejpam-1481	482	3	]	]	PUNCT
ejpam-1481	482	4	h	h	NOUN
ejpam-1481	482	5	bilgiç	bilgiç	NOUN
ejpam-1481	482	6	and	and	CCONJ
ejpam-1481	482	7	h	h	PROPN
ejpam-1481	482	8	furkan	furkan	PROPN
ejpam-1481	482	9	,	,	PUNCT
ejpam-1481	482	10	on	on	ADP
ejpam-1481	482	11	the	the	DET
ejpam-1481	482	12	fine	fine	ADJ
ejpam-1481	482	13	spectrum	spectrum	NOUN
ejpam-1481	482	14	of	of	ADP
ejpam-1481	482	15	the	the	DET
ejpam-1481	482	16	generalized	generalize	VERB
ejpam-1481	482	17	difference	difference	NOUN
ejpam-1481	482	18	operator	operator	NOUN
ejpam-1481	482	19	b(r	b(r	PROPN
ejpam-1481	482	20	,	,	PUNCT
ejpam-1481	482	21	s	s	NOUN
ejpam-1481	482	22	)	)	PUNCT
ejpam-1481	482	23	over	over	ADP
ejpam-1481	482	24	the	the	DET
ejpam-1481	482	25	sequence	sequence	NOUN
ejpam-1481	482	26	spaces	space	VERB
ejpam-1481	482	27	lp	lp	NOUN
ejpam-1481	482	28	and	and	CCONJ
ejpam-1481	482	29	bvp	bvp	NOUN
ejpam-1481	482	30	,	,	PUNCT
ejpam-1481	482	31	(	(	PUNCT
ejpam-1481	482	32	1	1	NUM
ejpam-1481	482	33	<	<	X
ejpam-1481	482	34	p	p	X
ejpam-1481	482	35	<	<	X
ejpam-1481	482	36	∞	∞	NUM
ejpam-1481	482	37	)	)	PUNCT
ejpam-1481	482	38	,	,	PUNCT
ejpam-1481	482	39	nonlinear	nonlinear	ADJ
ejpam-1481	482	40	anal	anal	NOUN
ejpam-1481	482	41	.	.	PUNCT
ejpam-1481	483	1	68	68	NUM
ejpam-1481	483	2	.	.	X
ejpam-1481	483	3	499	499	NUM
ejpam-1481	483	4	-	-	SYM
ejpam-1481	483	5	506	506	NUM
ejpam-1481	483	6	.	.	NUM
ejpam-1481	483	7	2008	2008	NUM
ejpam-1481	483	8	.	.	PUNCT
ejpam-1481	484	1	[	[	X
ejpam-1481	484	2	14	14	NUM
ejpam-1481	484	3	]	]	SYM
ejpam-1481	484	4	b	b	X
ejpam-1481	484	5	choudhary	choudhary	PROPN
ejpam-1481	484	6	and	and	CCONJ
ejpam-1481	484	7	s	s	PROPN
ejpam-1481	484	8	nanda	nanda	ADJ
ejpam-1481	484	9	,	,	PUNCT
ejpam-1481	484	10	functional	functional	ADJ
ejpam-1481	484	11	analysis	analysis	NOUN
ejpam-1481	484	12	with	with	ADP
ejpam-1481	484	13	applications	application	NOUN
ejpam-1481	484	14	,	,	PUNCT
ejpam-1481	484	15	john	john	PROPN
ejpam-1481	484	16	wiley	wiley	PROPN
ejpam-1481	484	17	&	&	CCONJ
ejpam-1481	484	18	sons	sons	PROPN
ejpam-1481	484	19	inc	inc	PROPN
ejpam-1481	484	20	.	.	PROPN
ejpam-1481	484	21	,	,	PUNCT
ejpam-1481	484	22	new	new	PROPN
ejpam-1481	484	23	york	york	PROPN
ejpam-1481	484	24	.	.	PUNCT
ejpam-1481	484	25	1989	1989	NUM
ejpam-1481	484	26	.	.	PUNCT
ejpam-1481	485	1	[	[	X
ejpam-1481	485	2	15	15	NUM
ejpam-1481	485	3	]	]	X
ejpam-1481	485	4	s	s	PART
ejpam-1481	485	5	el	el	PROPN
ejpam-1481	485	6	-	-	PUNCT
ejpam-1481	485	7	shabrawy	shabrawy	PROPN
ejpam-1481	485	8	,	,	PUNCT
ejpam-1481	485	9	on	on	ADP
ejpam-1481	485	10	the	the	DET
ejpam-1481	485	11	spectrum	spectrum	NOUN
ejpam-1481	485	12	of	of	ADP
ejpam-1481	485	13	the	the	DET
ejpam-1481	485	14	operator	operator	NOUN
ejpam-1481	485	15	∆v	∆v	PROPN
ejpam-1481	485	16	over	over	ADP
ejpam-1481	485	17	the	the	DET
ejpam-1481	485	18	space	space	NOUN
ejpam-1481	485	19	lp	lp	NOUN
ejpam-1481	485	20	,	,	PUNCT
ejpam-1481	485	21	(	(	PUNCT
ejpam-1481	485	22	1	1	NUM
ejpam-1481	485	23	<	<	X
ejpam-1481	485	24	p	p	X
ejpam-1481	485	25	<	<	X
ejpam-1481	485	26	∞	∞	PROPN
ejpam-1481	485	27	)	)	PUNCT
ejpam-1481	485	28	,	,	PUNCT
ejpam-1481	485	29	baku	baku	PROPN
ejpam-1481	485	30	univ	univ	PROPN
ejpam-1481	485	31	.	.	PUNCT
ejpam-1481	486	1	news	news	PROPN
ejpam-1481	486	2	j.	j.	PROPN
ejpam-1481	486	3	,	,	PUNCT
ejpam-1481	486	4	phys	phys	PROPN
ejpam-1481	486	5	.	.	PUNCT
ejpam-1481	486	6	math	math	NOUN
ejpam-1481	486	7	.	.	PUNCT
ejpam-1481	487	1	sci	sci	PROPN
ejpam-1481	487	2	.	.	PUNCT
ejpam-1481	487	3	ser	ser	PROPN
ejpam-1481	487	4	.	.	PROPN
ejpam-1481	487	5	,	,	PUNCT
ejpam-1481	487	6	to	to	PART
ejpam-1481	487	7	appear	appear	VERB
ejpam-1481	487	8	.	.	PUNCT
ejpam-1481	488	1	[	[	X
ejpam-1481	488	2	16	16	NUM
ejpam-1481	488	3	]	]	X
ejpam-1481	488	4	h	h	NOUN
ejpam-1481	488	5	furkan	furkan	PROPN
ejpam-1481	488	6	,	,	PUNCT
ejpam-1481	488	7	h	h	NOUN
ejpam-1481	488	8	bilgiç	bilgiç	NOUN
ejpam-1481	488	9	and	and	CCONJ
ejpam-1481	488	10	b	b	NOUN
ejpam-1481	488	11	altay	altay	NOUN
ejpam-1481	488	12	,	,	PUNCT
ejpam-1481	488	13	on	on	ADP
ejpam-1481	488	14	the	the	DET
ejpam-1481	488	15	fine	fine	ADJ
ejpam-1481	488	16	spectrum	spectrum	NOUN
ejpam-1481	488	17	of	of	ADP
ejpam-1481	488	18	the	the	DET
ejpam-1481	488	19	operator	operator	NOUN
ejpam-1481	488	20	b(r	b(r	PROPN
ejpam-1481	488	21	,	,	PUNCT
ejpam-1481	488	22	s	s	PROPN
ejpam-1481	488	23	,	,	PUNCT
ejpam-1481	488	24	t	t	PROPN
ejpam-1481	488	25	)	)	PUNCT
ejpam-1481	488	26	over	over	ADP
ejpam-1481	488	27	c0	c0	PROPN
ejpam-1481	488	28	and	and	CCONJ
ejpam-1481	488	29	c	c	NOUN
ejpam-1481	488	30	,	,	PUNCT
ejpam-1481	488	31	comput	comput	NOUN
ejpam-1481	488	32	.	.	PUNCT
ejpam-1481	489	1	math	math	NOUN
ejpam-1481	489	2	.	.	PUNCT
ejpam-1481	490	1	appl	appl	PROPN
ejpam-1481	490	2	.	.	PUNCT
ejpam-1481	491	1	53	53	NUM
ejpam-1481	491	2	.	.	X
ejpam-1481	491	3	989	989	NUM
ejpam-1481	491	4	-	-	SYM
ejpam-1481	491	5	998	998	NUM
ejpam-1481	491	6	.	.	PUNCT
ejpam-1481	492	1	2007	2007	NUM
ejpam-1481	492	2	.	.	PUNCT
ejpam-1481	493	1	[	[	X
ejpam-1481	493	2	17	17	NUM
ejpam-1481	493	3	]	]	X
ejpam-1481	493	4	h	h	NOUN
ejpam-1481	493	5	furkan	furkan	PROPN
ejpam-1481	493	6	,	,	PUNCT
ejpam-1481	493	7	h	h	NOUN
ejpam-1481	493	8	bilgiç	bilgiç	NOUN
ejpam-1481	493	9	and	and	CCONJ
ejpam-1481	493	10	f	f	PROPN
ejpam-1481	493	11	başar	başar	PROPN
ejpam-1481	493	12	,	,	PUNCT
ejpam-1481	493	13	on	on	ADP
ejpam-1481	493	14	the	the	DET
ejpam-1481	493	15	fine	fine	ADJ
ejpam-1481	493	16	spectrum	spectrum	NOUN
ejpam-1481	493	17	of	of	ADP
ejpam-1481	493	18	the	the	DET
ejpam-1481	493	19	operator	operator	NOUN
ejpam-1481	493	20	b(r	b(r	PROPN
ejpam-1481	493	21	,	,	PUNCT
ejpam-1481	493	22	s	s	PROPN
ejpam-1481	493	23	,	,	PUNCT
ejpam-1481	493	24	t	t	PROPN
ejpam-1481	493	25	)	)	PUNCT
ejpam-1481	493	26	over	over	ADP
ejpam-1481	493	27	the	the	DET
ejpam-1481	493	28	sequence	sequence	NOUN
ejpam-1481	493	29	spaces	space	VERB
ejpam-1481	493	30	lp	lp	NOUN
ejpam-1481	493	31	and	and	CCONJ
ejpam-1481	493	32	bvp	bvp	NOUN
ejpam-1481	493	33	,	,	PUNCT
ejpam-1481	493	34	(	(	PUNCT
ejpam-1481	493	35	1	1	NUM
ejpam-1481	493	36	<	<	X
ejpam-1481	493	37	p	p	X
ejpam-1481	493	38	<	<	X
ejpam-1481	493	39	∞	∞	NUM
ejpam-1481	493	40	)	)	PUNCT
ejpam-1481	493	41	,	,	PUNCT
ejpam-1481	493	42	comput	comput	NOUN
ejpam-1481	493	43	.	.	PUNCT
ejpam-1481	494	1	math	math	NOUN
ejpam-1481	494	2	.	.	PUNCT
ejpam-1481	495	1	appl	appl	PROPN
ejpam-1481	495	2	.	.	PROPN
ejpam-1481	496	1	60	60	NUM
ejpam-1481	496	2	.	.	X
ejpam-1481	497	1	2141	2141	NUM
ejpam-1481	497	2	-	-	SYM
ejpam-1481	497	3	2152	2152	NUM
ejpam-1481	497	4	.	.	PUNCT
ejpam-1481	498	1	2010	2010	NUM
ejpam-1481	498	2	.	.	PUNCT
ejpam-1481	499	1	[	[	X
ejpam-1481	499	2	18	18	NUM
ejpam-1481	499	3	]	]	X
ejpam-1481	499	4	h	h	NOUN
ejpam-1481	499	5	furkan	furkan	PROPN
ejpam-1481	499	6	,	,	PUNCT
ejpam-1481	499	7	h	h	NOUN
ejpam-1481	499	8	bilgiç	bilgiç	NOUN
ejpam-1481	499	9	and	and	CCONJ
ejpam-1481	499	10	k	k	PROPN
ejpam-1481	499	11	kayaduman	kayaduman	PROPN
ejpam-1481	499	12	,	,	PUNCT
ejpam-1481	499	13	on	on	ADP
ejpam-1481	499	14	the	the	DET
ejpam-1481	499	15	fine	fine	ADJ
ejpam-1481	499	16	spectrum	spectrum	NOUN
ejpam-1481	499	17	of	of	ADP
ejpam-1481	499	18	the	the	DET
ejpam-1481	499	19	generalized	generalize	VERB
ejpam-1481	499	20	difference	difference	NOUN
ejpam-1481	499	21	operator	operator	NOUN
ejpam-1481	499	22	b(r	b(r	PROPN
ejpam-1481	499	23	,	,	PUNCT
ejpam-1481	499	24	s	s	NOUN
ejpam-1481	499	25	)	)	PUNCT
ejpam-1481	499	26	over	over	ADP
ejpam-1481	499	27	the	the	DET
ejpam-1481	499	28	sequence	sequence	NOUN
ejpam-1481	499	29	spaces	space	VERB
ejpam-1481	499	30	l1	l1	PROPN
ejpam-1481	499	31	and	and	CCONJ
ejpam-1481	499	32	bv	bv	PROPN
ejpam-1481	499	33	,	,	PUNCT
ejpam-1481	499	34	hokkaido	hokkaido	PROPN
ejpam-1481	499	35	math	math	PROPN
ejpam-1481	499	36	.	.	PUNCT
ejpam-1481	500	1	j.	j.	PROPN
ejpam-1481	500	2	35	35	NUM
ejpam-1481	500	3	.	.	PUNCT
ejpam-1481	500	4	893	893	NUM
ejpam-1481	500	5	-	-	SYM
ejpam-1481	500	6	904	904	NUM
ejpam-1481	500	7	.	.	PUNCT
ejpam-1481	500	8	2006	2006	NUM
ejpam-1481	500	9	.	.	PUNCT
ejpam-1481	501	1	[	[	X
ejpam-1481	501	2	19	19	NUM
ejpam-1481	501	3	]	]	X
ejpam-1481	501	4	s	s	PROPN
ejpam-1481	501	5	goldberg	goldberg	PROPN
ejpam-1481	501	6	,	,	PUNCT
ejpam-1481	501	7	unbounded	unbounded	ADJ
ejpam-1481	501	8	linear	linear	PROPN
ejpam-1481	501	9	operators	operator	NOUN
ejpam-1481	501	10	:	:	PUNCT
ejpam-1481	501	11	theory	theory	NOUN
ejpam-1481	501	12	and	and	CCONJ
ejpam-1481	501	13	applications	application	NOUN
ejpam-1481	501	14	,	,	PUNCT
ejpam-1481	501	15	mcgraw	mcgraw	PROPN
ejpam-1481	501	16	-	-	PUNCT
ejpam-1481	501	17	hill	hill	PROPN
ejpam-1481	501	18	,	,	PUNCT
ejpam-1481	501	19	inc	inc	PROPN
ejpam-1481	501	20	.	.	PROPN
ejpam-1481	501	21	,	,	PUNCT
ejpam-1481	501	22	new	new	PROPN
ejpam-1481	501	23	york	york	PROPN
ejpam-1481	501	24	,	,	PUNCT
ejpam-1481	501	25	1966	1966	NUM
ejpam-1481	501	26	.	.	PUNCT
ejpam-1481	502	1	[	[	X
ejpam-1481	502	2	20	20	NUM
ejpam-1481	502	3	]	]	SYM
ejpam-1481	502	4	v	v	NUM
ejpam-1481	502	5	karakaya	karakaya	NOUN
ejpam-1481	502	6	and	and	CCONJ
ejpam-1481	502	7	m	m	NOUN
ejpam-1481	502	8	altun	altun	NOUN
ejpam-1481	502	9	,	,	PUNCT
ejpam-1481	502	10	fine	fine	ADJ
ejpam-1481	502	11	spectra	spectra	NOUN
ejpam-1481	502	12	of	of	ADP
ejpam-1481	502	13	upper	upper	ADJ
ejpam-1481	502	14	triangular	triangular	NOUN
ejpam-1481	502	15	double	double	ADJ
ejpam-1481	502	16	-	-	PUNCT
ejpam-1481	502	17	band	band	NOUN
ejpam-1481	502	18	matrices	matrix	NOUN
ejpam-1481	502	19	,	,	PUNCT
ejpam-1481	502	20	j.	j.	PROPN
ejpam-1481	502	21	comput	comput	PROPN
ejpam-1481	502	22	.	.	PUNCT
ejpam-1481	503	1	appl	appl	PROPN
ejpam-1481	503	2	.	.	PROPN
ejpam-1481	503	3	math	math	PROPN
ejpam-1481	503	4	.	.	PUNCT
ejpam-1481	504	1	234	234	NUM
ejpam-1481	504	2	.	.	X
ejpam-1481	504	3	1387	1387	NUM
ejpam-1481	504	4	-	-	SYM
ejpam-1481	504	5	1394	1394	NUM
ejpam-1481	504	6	.	.	PUNCT
ejpam-1481	505	1	2010	2010	NUM
ejpam-1481	505	2	.	.	PUNCT
ejpam-1481	506	1	[	[	X
ejpam-1481	506	2	21	21	NUM
ejpam-1481	506	3	]	]	X
ejpam-1481	506	4	e	e	X
ejpam-1481	506	5	kreyszig	kreyszig	PROPN
ejpam-1481	506	6	,	,	PUNCT
ejpam-1481	506	7	introductory	introductory	ADJ
ejpam-1481	506	8	functional	functional	ADJ
ejpam-1481	506	9	analysis	analysis	NOUN
ejpam-1481	506	10	with	with	ADP
ejpam-1481	506	11	applications	application	NOUN
ejpam-1481	506	12	,	,	PUNCT
ejpam-1481	506	13	john	john	PROPN
ejpam-1481	506	14	wiley	wiley	PROPN
ejpam-1481	506	15	&	&	CCONJ
ejpam-1481	506	16	sons	sons	PROPN
ejpam-1481	506	17	inc	inc	PROPN
ejpam-1481	506	18	.	.	PROPN
ejpam-1481	506	19	,	,	PUNCT
ejpam-1481	506	20	new	new	PROPN
ejpam-1481	506	21	york	york	PROPN
ejpam-1481	506	22	.	.	PUNCT
ejpam-1481	506	23	1978	1978	NUM
ejpam-1481	506	24	.	.	PUNCT
ejpam-1481	507	1	[	[	X
ejpam-1481	507	2	22	22	NUM
ejpam-1481	507	3	]	]	X
ejpam-1481	507	4	b	b	PROPN
ejpam-1481	507	5	de	de	X
ejpam-1481	507	6	malafosse	malafosse	PROPN
ejpam-1481	507	7	,	,	PUNCT
ejpam-1481	507	8	properties	property	NOUN
ejpam-1481	507	9	of	of	ADP
ejpam-1481	507	10	some	some	DET
ejpam-1481	507	11	sets	set	NOUN
ejpam-1481	507	12	of	of	ADP
ejpam-1481	507	13	sequences	sequence	NOUN
ejpam-1481	507	14	and	and	CCONJ
ejpam-1481	507	15	application	application	NOUN
ejpam-1481	507	16	to	to	ADP
ejpam-1481	507	17	the	the	DET
ejpam-1481	507	18	spaces	space	NOUN
ejpam-1481	507	19	of	of	ADP
ejpam-1481	507	20	bounded	bounded	ADJ
ejpam-1481	507	21	difference	difference	NOUN
ejpam-1481	507	22	sequences	sequence	NOUN
ejpam-1481	507	23	of	of	ADP
ejpam-1481	507	24	order	order	NOUN
ejpam-1481	507	25	µ	µ	X
ejpam-1481	507	26	,	,	PUNCT
ejpam-1481	507	27	hokkaido	hokkaido	PROPN
ejpam-1481	507	28	math	math	PROPN
ejpam-1481	507	29	.	.	PUNCT
ejpam-1481	508	1	j.	j.	PROPN
ejpam-1481	508	2	31	31	NUM
ejpam-1481	508	3	.	.	PUNCT
ejpam-1481	509	1	283–299	283–299	NUM
ejpam-1481	509	2	.	.	PUNCT
ejpam-1481	509	3	2002	2002	NUM
ejpam-1481	509	4	.	.	PUNCT
ejpam-1481	510	1	[	[	X
ejpam-1481	510	2	23	23	NUM
ejpam-1481	510	3	]	]	SYM
ejpam-1481	510	4	b	b	X
ejpam-1481	510	5	panigrahi	panigrahi	NOUN
ejpam-1481	510	6	and	and	CCONJ
ejpam-1481	510	7	p	p	PROPN
ejpam-1481	510	8	srivastava	srivastava	PROPN
ejpam-1481	510	9	,	,	PUNCT
ejpam-1481	510	10	spectrum	spectrum	NOUN
ejpam-1481	510	11	and	and	CCONJ
ejpam-1481	510	12	fine	fine	ADJ
ejpam-1481	510	13	spectrum	spectrum	NOUN
ejpam-1481	510	14	of	of	ADP
ejpam-1481	510	15	generalized	generalized	ADJ
ejpam-1481	510	16	second	second	ADJ
ejpam-1481	510	17	order	order	NOUN
ejpam-1481	510	18	difference	difference	NOUN
ejpam-1481	510	19	operator	operator	NOUN
ejpam-1481	510	20	∆2	∆2	PROPN
ejpam-1481	510	21	uv	uv	NOUN
ejpam-1481	510	22	on	on	ADP
ejpam-1481	510	23	sequence	sequence	NOUN
ejpam-1481	510	24	space	space	NOUN
ejpam-1481	510	25	c0	c0	PROPN
ejpam-1481	510	26	,	,	PUNCT
ejpam-1481	510	27	thai	thai	PROPN
ejpam-1481	510	28	j.	j.	PROPN
ejpam-1481	510	29	math	math	PROPN
ejpam-1481	510	30	.	.	PUNCT
ejpam-1481	511	1	9	9	NUM
ejpam-1481	511	2	(	(	PUNCT
ejpam-1481	511	3	1	1	NUM
ejpam-1481	511	4	)	)	PUNCT
ejpam-1481	511	5	.	.	PUNCT
ejpam-1481	512	1	57–74	57–74	NUM
ejpam-1481	512	2	.	.	PUNCT
ejpam-1481	512	3	2011	2011	NUM
ejpam-1481	512	4	.	.	PUNCT
ejpam-1481	513	1	[	[	X
ejpam-1481	513	2	24	24	NUM
ejpam-1481	513	3	]	]	X
ejpam-1481	513	4	p	p	PROPN
ejpam-1481	513	5	srivastava	srivastava	PROPN
ejpam-1481	513	6	and	and	CCONJ
ejpam-1481	513	7	s	s	PROPN
ejpam-1481	513	8	kumar	kumar	PROPN
ejpam-1481	513	9	,	,	PUNCT
ejpam-1481	513	10	on	on	ADP
ejpam-1481	513	11	the	the	DET
ejpam-1481	513	12	fine	fine	ADJ
ejpam-1481	513	13	spectrum	spectrum	NOUN
ejpam-1481	513	14	of	of	ADP
ejpam-1481	513	15	the	the	DET
ejpam-1481	513	16	generalized	generalize	VERB
ejpam-1481	513	17	difference	difference	NOUN
ejpam-1481	513	18	operator	operator	NOUN
ejpam-1481	513	19	∆v	∆v	PROPN
ejpam-1481	513	20	over	over	ADP
ejpam-1481	513	21	the	the	DET
ejpam-1481	513	22	sequence	sequence	NOUN
ejpam-1481	513	23	space	space	NOUN
ejpam-1481	513	24	c0	c0	PROPN
ejpam-1481	513	25	,	,	PUNCT
ejpam-1481	513	26	commun	commun	PROPN
ejpam-1481	513	27	.	.	PUNCT
ejpam-1481	513	28	math	math	PROPN
ejpam-1481	513	29	.	.	PUNCT
ejpam-1481	514	1	anal	anal	ADJ
ejpam-1481	514	2	.	.	PUNCT
ejpam-1481	515	1	6	6	NUM
ejpam-1481	515	2	(	(	PUNCT
ejpam-1481	515	3	1	1	NUM
ejpam-1481	515	4	)	)	PUNCT
ejpam-1481	515	5	.	.	PUNCT
ejpam-1481	516	1	8	8	NUM
ejpam-1481	516	2	-	-	SYM
ejpam-1481	516	3	21	21	NUM
ejpam-1481	516	4	.	.	PUNCT
ejpam-1481	516	5	2009	2009	NUM
ejpam-1481	516	6	.	.	PUNCT
ejpam-1481	517	1	[	[	X
ejpam-1481	517	2	25	25	NUM
ejpam-1481	517	3	]	]	X
ejpam-1481	517	4	p	p	X
ejpam-1481	517	5	srivastava	srivastava	PROPN
ejpam-1481	517	6	and	and	CCONJ
ejpam-1481	517	7	s	s	PROPN
ejpam-1481	517	8	kumar	kumar	PROPN
ejpam-1481	517	9	,	,	PUNCT
ejpam-1481	517	10	fine	fine	ADJ
ejpam-1481	517	11	spectrum	spectrum	NOUN
ejpam-1481	517	12	of	of	ADP
ejpam-1481	517	13	the	the	DET
ejpam-1481	517	14	generalized	generalize	VERB
ejpam-1481	517	15	difference	difference	NOUN
ejpam-1481	517	16	operator	operator	NOUN
ejpam-1481	517	17	∆v	∆v	PROPN
ejpam-1481	517	18	on	on	ADP
ejpam-1481	517	19	sequence	sequence	NOUN
ejpam-1481	517	20	space	space	NOUN
ejpam-1481	517	21	l1	l1	PROPN
ejpam-1481	517	22	,	,	PUNCT
ejpam-1481	517	23	thai	thai	PROPN
ejpam-1481	517	24	j.	j.	PROPN
ejpam-1481	517	25	math	math	PROPN
ejpam-1481	517	26	.	.	PUNCT
ejpam-1481	518	1	8	8	NUM
ejpam-1481	518	2	(	(	PUNCT
ejpam-1481	518	3	2	2	NUM
ejpam-1481	518	4	)	)	PUNCT
ejpam-1481	518	5	.	.	PUNCT
ejpam-1481	519	1	221–233	221–233	NUM
ejpam-1481	519	2	.	.	PUNCT
ejpam-1481	519	3	2010	2010	NUM
ejpam-1481	519	4	.	.	PUNCT
ejpam-1481	520	1	[	[	X
ejpam-1481	520	2	26	26	NUM
ejpam-1481	520	3	]	]	PUNCT
ejpam-1481	520	4	a	a	DET
ejpam-1481	520	5	wilansky	wilansky	ADJ
ejpam-1481	520	6	,	,	PUNCT
ejpam-1481	520	7	summability	summability	NOUN
ejpam-1481	520	8	through	through	ADP
ejpam-1481	520	9	functional	functional	ADJ
ejpam-1481	520	10	analysis	analysis	NOUN
ejpam-1481	520	11	,	,	PUNCT
ejpam-1481	520	12	in	in	ADP
ejpam-1481	520	13	:	:	PUNCT
ejpam-1481	520	14	north	north	NOUN
ejpam-1481	520	15	-	-	PUNCT
ejpam-1481	520	16	holland	holland	PROPN
ejpam-1481	520	17	mathematics	mathematics	PROPN
ejpam-1481	520	18	studies	study	NOUN
ejpam-1481	520	19	,	,	PUNCT
ejpam-1481	520	20	vol	vol	NOUN
ejpam-1481	520	21	.	.	PROPN
ejpam-1481	520	22	85	85	NUM
ejpam-1481	520	23	,	,	PUNCT
ejpam-1481	520	24	north	north	NOUN
ejpam-1481	520	25	-	-	PUNCT
ejpam-1481	520	26	holland	holland	PROPN
ejpam-1481	520	27	,	,	PUNCT
ejpam-1481	520	28	amsterdam	amsterdam	PROPN
ejpam-1481	520	29	,	,	PUNCT
ejpam-1481	520	30	1984	1984	NUM
ejpam-1481	520	31	.	.	PUNCT