id	sid	tid	token	lemma	pos
ejpam-3329	1	1	aluthge	aluthge	ADJ
ejpam-3329	1	2	transformation	transformation	NOUN
ejpam-3329	1	3	of	of	ADP
ejpam-3329	1	4	quasi	quasi	ADJ
ejpam-3329	1	5	$	$	SYM
ejpam-3329	1	6	n$-class	n$-class	NOUN
ejpam-3329	1	7	$	$	SYM
ejpam-3329	1	8	q$	q$	NOUN
ejpam-3329	1	9	and	and	CCONJ
ejpam-3329	1	10	quasi	quasi	ADJ
ejpam-3329	1	11	$	$	SYM
ejpam-3329	1	12	n$-class	n$-class	NOUN
ejpam-3329	1	13	$	$	SYM
ejpam-3329	1	14	q^*$	q^*$	PROPN
ejpam-3329	1	15	operators	operator	NOUN
ejpam-3329	1	16	european	european	PROPN
ejpam-3329	1	17	journal	journal	PROPN
ejpam-3329	1	18	of	of	ADP
ejpam-3329	1	19	pure	pure	ADJ
ejpam-3329	1	20	and	and	CCONJ
ejpam-3329	1	21	applied	apply	VERB
ejpam-3329	1	22	mathematics	mathematic	NOUN
ejpam-3329	1	23	vol	vol	NOUN
ejpam-3329	1	24	.	.	PUNCT
ejpam-3329	2	1	11	11	NUM
ejpam-3329	2	2	,	,	PUNCT
ejpam-3329	2	3	no	no	INTJ
ejpam-3329	2	4	.	.	NOUN
ejpam-3329	2	5	4	4	NUM
ejpam-3329	2	6	,	,	PUNCT
ejpam-3329	2	7	2018	2018	NUM
ejpam-3329	2	8	,	,	PUNCT
ejpam-3329	2	9	1108	1108	NUM
ejpam-3329	2	10	-	-	SYM
ejpam-3329	2	11	1129	1129	NUM
ejpam-3329	2	12	issn	issn	PROPN
ejpam-3329	2	13	1307	1307	NUM
ejpam-3329	2	14	-	-	SYM
ejpam-3329	2	15	5543	5543	NUM
ejpam-3329	2	16	–	–	PUNCT
ejpam-3329	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3329	2	18	published	publish	VERB
ejpam-3329	2	19	by	by	ADP
ejpam-3329	2	20	new	new	PROPN
ejpam-3329	2	21	york	york	PROPN
ejpam-3329	2	22	business	business	PROPN
ejpam-3329	2	23	global	global	PROPN
ejpam-3329	2	24	aluthge	aluthge	ADJ
ejpam-3329	2	25	transformation	transformation	NOUN
ejpam-3329	2	26	of	of	ADP
ejpam-3329	2	27	quasi	quasi	ADJ
ejpam-3329	2	28	n	n	CCONJ
ejpam-3329	2	29	-	-	PUNCT
ejpam-3329	2	30	class	class	NOUN
ejpam-3329	2	31	q	q	NOUN
ejpam-3329	2	32	and	and	CCONJ
ejpam-3329	2	33	quasi	quasi	ADJ
ejpam-3329	2	34	n	n	CCONJ
ejpam-3329	2	35	-	-	PUNCT
ejpam-3329	2	36	class	class	NOUN
ejpam-3329	2	37	q∗	q∗	NOUN
ejpam-3329	2	38	operators	operator	NOUN
ejpam-3329	2	39	d.senthilkumar1	d.senthilkumar1	PROPN
ejpam-3329	2	40	,	,	PUNCT
ejpam-3329	2	41	s.	s.	PROPN
ejpam-3329	2	42	parvatham2,∗	parvatham2,∗	VERB
ejpam-3329	2	43	1	1	NUM
ejpam-3329	2	44	post	post	NOUN
ejpam-3329	2	45	graduate	graduate	NOUN
ejpam-3329	2	46	and	and	CCONJ
ejpam-3329	2	47	research	research	NOUN
ejpam-3329	2	48	department	department	PROPN
ejpam-3329	2	49	of	of	ADP
ejpam-3329	2	50	mathematics	mathematic	NOUN
ejpam-3329	2	51	,	,	PUNCT
ejpam-3329	2	52	govt	govt	NOUN
ejpam-3329	2	53	.	.	PUNCT
ejpam-3329	3	1	arts	arts	PROPN
ejpam-3329	3	2	college	college	PROPN
ejpam-3329	3	3	,	,	PUNCT
ejpam-3329	3	4	coimbatore641018	coimbatore641018	NOUN
ejpam-3329	3	5	,	,	PUNCT
ejpam-3329	3	6	tamilnadu	tamilnadu	NOUN
ejpam-3329	3	7	,	,	PUNCT
ejpam-3329	3	8	india	india	PROPN
ejpam-3329	3	9	2	2	NUM
ejpam-3329	3	10	post	post	NOUN
ejpam-3329	3	11	graduate	graduate	NOUN
ejpam-3329	3	12	and	and	CCONJ
ejpam-3329	3	13	research	research	NOUN
ejpam-3329	3	14	department	department	PROPN
ejpam-3329	3	15	of	of	ADP
ejpam-3329	3	16	mathematics	mathematic	NOUN
ejpam-3329	3	17	,	,	PUNCT
ejpam-3329	3	18	govt	govt	NOUN
ejpam-3329	3	19	.	.	PUNCT
ejpam-3329	4	1	arts	arts	PROPN
ejpam-3329	4	2	college	college	PROPN
ejpam-3329	4	3	,	,	PUNCT
ejpam-3329	4	4	coimbatore641018	coimbatore641018	NOUN
ejpam-3329	4	5	,	,	PUNCT
ejpam-3329	4	6	tamilnadu	tamilnadu	NOUN
ejpam-3329	4	7	,	,	PUNCT
ejpam-3329	4	8	india	india	PROPN
ejpam-3329	4	9	abstract	abstract	NOUN
ejpam-3329	4	10	.	.	PUNCT
ejpam-3329	5	1	in	in	ADP
ejpam-3329	5	2	this	this	DET
ejpam-3329	5	3	paper	paper	NOUN
ejpam-3329	5	4	,	,	PUNCT
ejpam-3329	5	5	a	a	DET
ejpam-3329	5	6	new	new	ADJ
ejpam-3329	5	7	class	class	NOUN
ejpam-3329	5	8	of	of	ADP
ejpam-3329	5	9	operators	operator	NOUN
ejpam-3329	5	10	called	call	VERB
ejpam-3329	5	11	quasi	quasi	ADJ
ejpam-3329	5	12	n	n	CCONJ
ejpam-3329	5	13	-	-	PUNCT
ejpam-3329	5	14	class	class	NOUN
ejpam-3329	5	15	q	q	NOUN
ejpam-3329	5	16	and	and	CCONJ
ejpam-3329	5	17	quasi	quasi	ADJ
ejpam-3329	5	18	n	n	CCONJ
ejpam-3329	5	19	-	-	PUNCT
ejpam-3329	5	20	class	class	NOUN
ejpam-3329	5	21	q∗	q∗	NOUN
ejpam-3329	5	22	operators	operator	NOUN
ejpam-3329	5	23	are	be	AUX
ejpam-3329	5	24	introduced	introduce	VERB
ejpam-3329	5	25	and	and	CCONJ
ejpam-3329	5	26	studied	study	VERB
ejpam-3329	5	27	some	some	DET
ejpam-3329	5	28	properties	property	NOUN
ejpam-3329	5	29	.	.	PUNCT
ejpam-3329	6	1	quasi	quasi	NOUN
ejpam-3329	6	2	n	n	CCONJ
ejpam-3329	6	3	-	-	PUNCT
ejpam-3329	6	4	class	class	NOUN
ejpam-3329	6	5	q	q	NOUN
ejpam-3329	6	6	and	and	CCONJ
ejpam-3329	6	7	quasi	quasi	ADJ
ejpam-3329	6	8	n	n	CCONJ
ejpam-3329	6	9	-	-	PUNCT
ejpam-3329	6	10	class	class	NOUN
ejpam-3329	6	11	q∗	q∗	NOUN
ejpam-3329	6	12	composition	composition	NOUN
ejpam-3329	6	13	and	and	CCONJ
ejpam-3329	6	14	weighted	weight	VERB
ejpam-3329	6	15	composition	composition	NOUN
ejpam-3329	6	16	operators	operator	NOUN
ejpam-3329	6	17	on	on	ADP
ejpam-3329	6	18	l2(λ	l2(λ	NOUN
ejpam-3329	6	19	)	)	PUNCT
ejpam-3329	6	20	and	and	CCONJ
ejpam-3329	6	21	h2(β	h2(β	NOUN
ejpam-3329	6	22	)	)	PUNCT
ejpam-3329	6	23	are	be	AUX
ejpam-3329	6	24	characterized	characterize	VERB
ejpam-3329	6	25	.	.	PUNCT
ejpam-3329	7	1	also	also	ADV
ejpam-3329	7	2	we	we	PRON
ejpam-3329	7	3	discuss	discuss	VERB
ejpam-3329	7	4	quasi	quasi	NOUN
ejpam-3329	7	5	n	n	CCONJ
ejpam-3329	7	6	-	-	PUNCT
ejpam-3329	7	7	class	class	NOUN
ejpam-3329	7	8	q	q	NOUN
ejpam-3329	7	9	and	and	CCONJ
ejpam-3329	7	10	quasi	quasi	ADJ
ejpam-3329	7	11	n	n	CCONJ
ejpam-3329	7	12	-	-	PUNCT
ejpam-3329	7	13	class	class	NOUN
ejpam-3329	7	14	q∗	q∗	NOUN
ejpam-3329	7	15	composite	composite	ADJ
ejpam-3329	7	16	multiplication	multiplication	NOUN
ejpam-3329	7	17	operator	operator	NOUN
ejpam-3329	7	18	on	on	ADP
ejpam-3329	7	19	l2	l2	NOUN
ejpam-3329	7	20	space	space	NOUN
ejpam-3329	7	21	and	and	CCONJ
ejpam-3329	7	22	aluthge	aluthge	ADJ
ejpam-3329	7	23	transformation	transformation	NOUN
ejpam-3329	7	24	of	of	ADP
ejpam-3329	7	25	these	these	DET
ejpam-3329	7	26	class	class	NOUN
ejpam-3329	7	27	of	of	ADP
ejpam-3329	7	28	operators	operator	NOUN
ejpam-3329	7	29	are	be	AUX
ejpam-3329	7	30	obtained	obtain	VERB
ejpam-3329	7	31	.	.	PUNCT
ejpam-3329	8	1	2010	2010	NUM
ejpam-3329	8	2	mathematics	mathematic	NOUN
ejpam-3329	8	3	subject	subject	NOUN
ejpam-3329	8	4	classifications	classification	NOUN
ejpam-3329	8	5	:	:	PUNCT
ejpam-3329	8	6	primary	primary	NOUN
ejpam-3329	8	7	47b20	47b20	NUM
ejpam-3329	8	8	;	;	PUNCT
ejpam-3329	8	9	secondary	secondary	ADJ
ejpam-3329	8	10	47b33	47b33	NUM
ejpam-3329	8	11	,	,	PUNCT
ejpam-3329	8	12	47b38	47b38	NUM
ejpam-3329	8	13	.	.	PUNCT
ejpam-3329	9	1	key	key	ADJ
ejpam-3329	9	2	words	word	NOUN
ejpam-3329	9	3	and	and	CCONJ
ejpam-3329	9	4	phrases	phrase	NOUN
ejpam-3329	9	5	:	:	PUNCT
ejpam-3329	9	6	class	class	NOUN
ejpam-3329	9	7	q	q	PROPN
ejpam-3329	9	8	operators	operator	NOUN
ejpam-3329	9	9	,	,	PUNCT
ejpam-3329	9	10	class	class	NOUN
ejpam-3329	9	11	q∗	q∗	NOUN
ejpam-3329	9	12	operators	operator	NOUN
ejpam-3329	9	13	,	,	PUNCT
ejpam-3329	9	14	composition	composition	NOUN
ejpam-3329	9	15	operators	operator	NOUN
ejpam-3329	9	16	,	,	PUNCT
ejpam-3329	9	17	weighted	weight	VERB
ejpam-3329	9	18	composition	composition	NOUN
ejpam-3329	9	19	operators	operator	NOUN
ejpam-3329	9	20	,	,	PUNCT
ejpam-3329	9	21	aluthge	aluthge	ADJ
ejpam-3329	9	22	transformation	transformation	NOUN
ejpam-3329	9	23	1	1	X
ejpam-3329	9	24	.	.	PUNCT
ejpam-3329	10	1	introduction	introduction	NOUN
ejpam-3329	10	2	let	let	VERB
ejpam-3329	10	3	h	h	PRON
ejpam-3329	10	4	be	be	AUX
ejpam-3329	10	5	an	an	DET
ejpam-3329	10	6	infinite	infinite	ADJ
ejpam-3329	10	7	dimensional	dimensional	ADJ
ejpam-3329	10	8	separable	separable	ADJ
ejpam-3329	10	9	complex	complex	ADJ
ejpam-3329	10	10	hilbert	hilbert	NOUN
ejpam-3329	10	11	space	space	NOUN
ejpam-3329	10	12	.	.	PUNCT
ejpam-3329	11	1	let	let	VERB
ejpam-3329	11	2	b(h	b(h	NOUN
ejpam-3329	11	3	)	)	PUNCT
ejpam-3329	11	4	be	be	VERB
ejpam-3329	11	5	the	the	DET
ejpam-3329	11	6	algebra	algebra	NOUN
ejpam-3329	11	7	of	of	ADP
ejpam-3329	11	8	all	all	DET
ejpam-3329	11	9	bounded	bound	VERB
ejpam-3329	11	10	linear	linear	PROPN
ejpam-3329	11	11	operators	operator	NOUN
ejpam-3329	11	12	acting	act	VERB
ejpam-3329	11	13	on	on	ADP
ejpam-3329	11	14	h.	h.	PROPN
ejpam-3329	11	15	let	let	VERB
ejpam-3329	11	16	t	t	PROPN
ejpam-3329	11	17	be	be	AUX
ejpam-3329	11	18	an	an	DET
ejpam-3329	11	19	operator	operator	NOUN
ejpam-3329	11	20	on	on	ADP
ejpam-3329	11	21	h.	h.	NOUN
ejpam-3329	11	22	every	every	DET
ejpam-3329	11	23	operator	operator	NOUN
ejpam-3329	11	24	t	t	NOUN
ejpam-3329	11	25	can	can	AUX
ejpam-3329	11	26	be	be	AUX
ejpam-3329	11	27	decomposed	decompose	VERB
ejpam-3329	11	28	into	into	ADP
ejpam-3329	11	29	t	t	NOUN
ejpam-3329	11	30	=	=	SYM
ejpam-3329	11	31	u	u	NOUN
ejpam-3329	11	32	|t	|t	VERB
ejpam-3329	11	33	|	|	ADV
ejpam-3329	11	34	with	with	ADP
ejpam-3329	11	35	a	a	DET
ejpam-3329	11	36	partial	partial	ADJ
ejpam-3329	11	37	isometry	isometry	NOUN
ejpam-3329	11	38	u	u	NOUN
ejpam-3329	11	39	,	,	PUNCT
ejpam-3329	11	40	where	where	SCONJ
ejpam-3329	11	41	|t	|t	PROPN
ejpam-3329	11	42	|	|	ADV
ejpam-3329	11	43	is	be	AUX
ejpam-3329	11	44	the	the	DET
ejpam-3329	11	45	square	square	ADJ
ejpam-3329	11	46	root	root	NOUN
ejpam-3329	11	47	of	of	ADP
ejpam-3329	11	48	(	(	PUNCT
ejpam-3329	11	49	t	t	PROPN
ejpam-3329	11	50	∗t	∗t	PROPN
ejpam-3329	11	51	)	)	PUNCT
ejpam-3329	11	52	.	.	PUNCT
ejpam-3329	12	1	if	if	SCONJ
ejpam-3329	12	2	u	u	NOUN
ejpam-3329	12	3	is	be	AUX
ejpam-3329	12	4	determined	determine	VERB
ejpam-3329	12	5	uniquely	uniquely	ADV
ejpam-3329	12	6	by	by	ADP
ejpam-3329	12	7	the	the	DET
ejpam-3329	12	8	kernel	kernel	PROPN
ejpam-3329	12	9	condition	condition	PROPN
ejpam-3329	12	10	n(u	n(u	PROPN
ejpam-3329	12	11	)	)	PUNCT
ejpam-3329	13	1	=	=	SYM
ejpam-3329	13	2	n(|t	n(|t	NOUN
ejpam-3329	13	3	|	|	ADV
ejpam-3329	13	4	)	)	PUNCT
ejpam-3329	13	5	,	,	PUNCT
ejpam-3329	13	6	then	then	ADV
ejpam-3329	13	7	this	this	DET
ejpam-3329	13	8	decomposition	decomposition	NOUN
ejpam-3329	13	9	is	be	AUX
ejpam-3329	13	10	called	call	VERB
ejpam-3329	13	11	the	the	DET
ejpam-3329	13	12	polar	polar	ADJ
ejpam-3329	13	13	decomposition	decomposition	NOUN
ejpam-3329	13	14	,	,	PUNCT
ejpam-3329	13	15	which	which	PRON
ejpam-3329	13	16	is	be	AUX
ejpam-3329	13	17	one	one	NUM
ejpam-3329	13	18	of	of	ADP
ejpam-3329	13	19	the	the	DET
ejpam-3329	13	20	most	most	ADV
ejpam-3329	13	21	important	important	ADJ
ejpam-3329	13	22	results	result	NOUN
ejpam-3329	13	23	in	in	ADP
ejpam-3329	13	24	operator	operator	NOUN
ejpam-3329	13	25	theory	theory	NOUN
ejpam-3329	13	26	.	.	PUNCT
ejpam-3329	14	1	recall	recall	VERB
ejpam-3329	14	2	that	that	SCONJ
ejpam-3329	14	3	an	an	DET
ejpam-3329	14	4	operator	operator	NOUN
ejpam-3329	14	5	t	t	NOUN
ejpam-3329	14	6	is	be	AUX
ejpam-3329	14	7	said	say	VERB
ejpam-3329	14	8	to	to	PART
ejpam-3329	14	9	be	be	AUX
ejpam-3329	14	10	paranormal	paranormal	ADJ
ejpam-3329	14	11	if	if	SCONJ
ejpam-3329	14	12	‖tx‖2	‖tx‖2	PROPN
ejpam-3329	14	13	≤	≤	ADJ
ejpam-3329	14	14	‖t	‖t	NOUN
ejpam-3329	14	15	2x‖‖x‖	2x‖‖x‖	NUM
ejpam-3329	14	16	for	for	ADP
ejpam-3329	14	17	every	every	DET
ejpam-3329	14	18	x	x	SYM
ejpam-3329	14	19	∈	∈	PROPN
ejpam-3329	14	20	h	h	NOUN
ejpam-3329	15	1	[	[	X
ejpam-3329	15	2	7	7	NUM
ejpam-3329	15	3	]	]	PUNCT
ejpam-3329	15	4	.	.	PUNCT
ejpam-3329	16	1	an	an	DET
ejpam-3329	16	2	operator	operator	NOUN
ejpam-3329	16	3	t	t	NOUN
ejpam-3329	16	4	is	be	AUX
ejpam-3329	16	5	said	say	VERB
ejpam-3329	16	6	to	to	PART
ejpam-3329	16	7	be	be	AUX
ejpam-3329	16	8	n	n	PRON
ejpam-3329	16	9	-	-	PUNCT
ejpam-3329	16	10	paranormal	paranormal	NOUN
ejpam-3329	16	11	if	if	SCONJ
ejpam-3329	16	12	‖tx‖n+1	‖tx‖n+1	ADP
ejpam-3329	16	13	≤	≤	NOUN
ejpam-3329	16	14	‖tn+1x‖‖x‖n	‖tn+1x‖‖x‖n	NOUN
ejpam-3329	16	15	for	for	ADP
ejpam-3329	16	16	every	every	DET
ejpam-3329	16	17	x	x	SYM
ejpam-3329	16	18	∈	∈	PROPN
ejpam-3329	16	19	h	h	NOUN
ejpam-3329	17	1	[	[	X
ejpam-3329	17	2	16	16	NUM
ejpam-3329	17	3	]	]	PUNCT
ejpam-3329	17	4	and	and	CCONJ
ejpam-3329	17	5	normaloid	normaloid	NOUN
ejpam-3329	17	6	if	if	SCONJ
ejpam-3329	17	7	r(t	r(t	NOUN
ejpam-3329	17	8	)	)	PUNCT
ejpam-3329	18	1	=	=	PUNCT
ejpam-3329	18	2	‖t‖	‖t‖	PROPN
ejpam-3329	18	3	,	,	PUNCT
ejpam-3329	18	4	where	where	SCONJ
ejpam-3329	18	5	r(t	r(t	NOUN
ejpam-3329	18	6	)	)	PUNCT
ejpam-3329	18	7	denotes	denote	VERB
ejpam-3329	18	8	the	the	DET
ejpam-3329	18	9	spectral	spectral	ADJ
ejpam-3329	18	10	radius	radius	NOUN
ejpam-3329	18	11	of	of	ADP
ejpam-3329	18	12	t.	t.	PROPN
ejpam-3329	18	13	an	an	DET
ejpam-3329	18	14	operator	operator	NOUN
ejpam-3329	18	15	t	t	NOUN
ejpam-3329	18	16	is	be	AUX
ejpam-3329	18	17	of	of	ADP
ejpam-3329	18	18	class	class	NOUN
ejpam-3329	18	19	q	q	NOUN
ejpam-3329	19	1	[	[	X
ejpam-3329	19	2	3	3	NUM
ejpam-3329	19	3	]	]	PUNCT
ejpam-3329	19	4	,	,	PUNCT
ejpam-3329	19	5	if	if	SCONJ
ejpam-3329	19	6	t	t	PROPN
ejpam-3329	19	7	∗2	∗2	PROPN
ejpam-3329	19	8	t	t	PROPN
ejpam-3329	19	9	2	2	NUM
ejpam-3329	19	10	−	−	PROPN
ejpam-3329	19	11	2	2	NUM
ejpam-3329	19	12	t	t	NOUN
ejpam-3329	19	13	∗t	∗t	NOUN
ejpam-3329	19	14	+	+	CCONJ
ejpam-3329	19	15	i	i	PRON
ejpam-3329	19	16	≥	≥	VERB
ejpam-3329	19	17	0	0	NUM
ejpam-3329	19	18	.	.	PUNCT
ejpam-3329	20	1	equivalently	equivalently	PROPN
ejpam-3329	20	2	t	t	PROPN
ejpam-3329	20	3	∈	∈	PROPN
ejpam-3329	20	4	q	q	PROPN
ejpam-3329	21	1	if	if	SCONJ
ejpam-3329	21	2	‖tx‖2	‖tx‖2	PROPN
ejpam-3329	21	3	≤	≤	NOUN
ejpam-3329	21	4	1	1	NUM
ejpam-3329	21	5	2	2	NUM
ejpam-3329	21	6	(	(	PUNCT
ejpam-3329	21	7	‖t	‖t	NOUN
ejpam-3329	21	8	2x‖2+‖x‖2	2x‖2+‖x‖2	NUM
ejpam-3329	21	9	)	)	PUNCT
ejpam-3329	21	10	for	for	ADP
ejpam-3329	21	11	every	every	DET
ejpam-3329	21	12	x	x	PROPN
ejpam-3329	21	13	∈	∈	PROPN
ejpam-3329	21	14	h.	h.	NOUN
ejpam-3329	21	15	class	class	PROPN
ejpam-3329	21	16	q	q	PROPN
ejpam-3329	21	17	operators	operator	NOUN
ejpam-3329	21	18	are	be	AUX
ejpam-3329	21	19	introduced	introduce	VERB
ejpam-3329	21	20	and	and	CCONJ
ejpam-3329	21	21	studied	study	VERB
ejpam-3329	21	22	by	by	ADP
ejpam-3329	21	23	b.	b.	PROPN
ejpam-3329	21	24	p.	p.	PROPN
ejpam-3329	21	25	duggal	duggal	PROPN
ejpam-3329	21	26	et	et	PROPN
ejpam-3329	21	27	al	al	PROPN
ejpam-3329	22	1	and	and	CCONJ
ejpam-3329	22	2	it	it	PRON
ejpam-3329	22	3	is	be	AUX
ejpam-3329	22	4	well	well	ADV
ejpam-3329	22	5	known	know	VERB
ejpam-3329	22	6	that	that	SCONJ
ejpam-3329	22	7	every	every	DET
ejpam-3329	22	8	class	class	NOUN
ejpam-3329	22	9	q	q	NOUN
ejpam-3329	22	10	operator	operator	NOUN
ejpam-3329	22	11	is	be	AUX
ejpam-3329	22	12	not	not	PART
ejpam-3329	22	13	necessarily	necessarily	ADV
ejpam-3329	22	14	∗corresponding	∗corresponde	VERB
ejpam-3329	22	15	author	author	NOUN
ejpam-3329	22	16	.	.	PUNCT
ejpam-3329	23	1	doi	doi	NOUN
ejpam-3329	23	2	:	:	PUNCT
ejpam-3329	23	3	https://doi.org/10.29020/nybg.ejpam.v11i4.3329	https://doi.org/10.29020/nybg.ejpam.v11i4.3329	X
ejpam-3329	23	4	email	email	NOUN
ejpam-3329	23	5	addresses	address	NOUN
ejpam-3329	23	6	:	:	PUNCT
ejpam-3329	23	7	senthilsenkumhari@gmail.com	senthilsenkumhari@gmail.com	X
ejpam-3329	23	8	(	(	PUNCT
ejpam-3329	23	9	d.senthilkumar	d.senthilkumar	PROPN
ejpam-3329	23	10	)	)	PUNCT
ejpam-3329	23	11	,	,	PUNCT
ejpam-3329	23	12	parvathasathish@gmail.com	parvathasathish@gmail.com	PROPN
ejpam-3329	23	13	(	(	PUNCT
ejpam-3329	23	14	s.	s.	PROPN
ejpam-3329	23	15	parvatham	parvatham	PROPN
ejpam-3329	23	16	)	)	PUNCT
ejpam-3329	23	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3329	24	1	1108	1108	NUM
ejpam-3329	24	2	c	c	X
ejpam-3329	24	3	©	©	PROPN
ejpam-3329	24	4	2018	2018	NUM
ejpam-3329	24	5	ejpam	ejpam	VERB
ejpam-3329	24	6	all	all	DET
ejpam-3329	24	7	rights	right	NOUN
ejpam-3329	24	8	reserved	reserve	VERB
ejpam-3329	24	9	.	.	PUNCT
ejpam-3329	25	1	d.	d.	PROPN
ejpam-3329	25	2	senthilkumar	senthilkumar	PROPN
ejpam-3329	25	3	,	,	PUNCT
ejpam-3329	25	4	s.	s.	PROPN
ejpam-3329	25	5	parvatham	parvatham	PROPN
ejpam-3329	25	6	/	/	SYM
ejpam-3329	25	7	eur	eur	PROPN
ejpam-3329	25	8	.	.	PUNCT
ejpam-3329	26	1	j.	j.	PROPN
ejpam-3329	26	2	pure	pure	PROPN
ejpam-3329	26	3	appl	appl	PROPN
ejpam-3329	26	4	.	.	PROPN
ejpam-3329	26	5	math	math	PROPN
ejpam-3329	26	6	,	,	PUNCT
ejpam-3329	26	7	11	11	NUM
ejpam-3329	26	8	(	(	PUNCT
ejpam-3329	26	9	4	4	NUM
ejpam-3329	26	10	)	)	PUNCT
ejpam-3329	26	11	(	(	PUNCT
ejpam-3329	26	12	2018	2018	NUM
ejpam-3329	26	13	)	)	PUNCT
ejpam-3329	26	14	,	,	PUNCT
ejpam-3329	26	15	1108	1108	NUM
ejpam-3329	26	16	-	-	SYM
ejpam-3329	26	17	1129	1129	NUM
ejpam-3329	26	18	1109	1109	NUM
ejpam-3329	26	19	normaloid	normaloid	NOUN
ejpam-3329	26	20	and	and	CCONJ
ejpam-3329	26	21	every	every	DET
ejpam-3329	26	22	paranormal	paranormal	ADJ
ejpam-3329	26	23	operator	operator	NOUN
ejpam-3329	26	24	is	be	AUX
ejpam-3329	26	25	a	a	DET
ejpam-3329	26	26	normaloid	normaloid	NOUN
ejpam-3329	26	27	of	of	ADP
ejpam-3329	26	28	class	class	NOUN
ejpam-3329	26	29	q.	q.	PROPN
ejpam-3329	26	30	ie	ie	X
ejpam-3329	26	31	p	p	PROPN
ejpam-3329	26	32	⊆	⊆	NUM
ejpam-3329	26	33	q∩n	q∩n	NOUN
ejpam-3329	26	34	,	,	PUNCT
ejpam-3329	26	35	where	where	SCONJ
ejpam-3329	26	36	p	p	NOUN
ejpam-3329	26	37	and	and	CCONJ
ejpam-3329	26	38	n	n	NOUN
ejpam-3329	26	39	denotes	denote	VERB
ejpam-3329	26	40	the	the	DET
ejpam-3329	26	41	class	class	NOUN
ejpam-3329	26	42	of	of	ADP
ejpam-3329	26	43	paranormal	paranormal	PROPN
ejpam-3329	26	44	and	and	CCONJ
ejpam-3329	26	45	normaloid	normaloid	ADJ
ejpam-3329	26	46	operators	operator	NOUN
ejpam-3329	26	47	respectively	respectively	ADV
ejpam-3329	26	48	.	.	PUNCT
ejpam-3329	27	1	also	also	ADV
ejpam-3329	27	2	he	he	PRON
ejpam-3329	27	3	showed	show	VERB
ejpam-3329	27	4	that	that	SCONJ
ejpam-3329	27	5	the	the	DET
ejpam-3329	27	6	restiction	restiction	NOUN
ejpam-3329	27	7	of	of	ADP
ejpam-3329	27	8	t	t	PROPN
ejpam-3329	27	9	to	to	ADP
ejpam-3329	27	10	an	an	DET
ejpam-3329	27	11	invariant	invariant	ADJ
ejpam-3329	27	12	subspace	subspace	NOUN
ejpam-3329	27	13	is	be	AUX
ejpam-3329	27	14	again	again	ADV
ejpam-3329	27	15	a	a	DET
ejpam-3329	27	16	class	class	NOUN
ejpam-3329	27	17	q	q	NOUN
ejpam-3329	27	18	operator	operator	NOUN
ejpam-3329	27	19	.	.	PUNCT
ejpam-3329	28	1	devika	devika	PROPN
ejpam-3329	28	2	,	,	PUNCT
ejpam-3329	28	3	suresh	suresh	PROPN
ejpam-3329	29	1	[	[	X
ejpam-3329	29	2	5	5	NUM
ejpam-3329	29	3	]	]	PUNCT
ejpam-3329	29	4	,	,	PUNCT
ejpam-3329	29	5	introduced	introduce	VERB
ejpam-3329	29	6	a	a	DET
ejpam-3329	29	7	new	new	ADJ
ejpam-3329	29	8	class	class	NOUN
ejpam-3329	29	9	of	of	ADP
ejpam-3329	29	10	operators	operator	NOUN
ejpam-3329	29	11	which	which	PRON
ejpam-3329	29	12	we	we	PRON
ejpam-3329	29	13	call	call	VERB
ejpam-3329	29	14	the	the	DET
ejpam-3329	29	15	quasi	quasi	ADJ
ejpam-3329	29	16	class	class	PROPN
ejpam-3329	29	17	q	q	PROPN
ejpam-3329	29	18	operators	operator	NOUN
ejpam-3329	29	19	and	and	CCONJ
ejpam-3329	29	20	it	it	PRON
ejpam-3329	29	21	is	be	AUX
ejpam-3329	29	22	defined	define	VERB
ejpam-3329	29	23	as	as	ADP
ejpam-3329	29	24	,	,	PUNCT
ejpam-3329	29	25	for	for	ADP
ejpam-3329	29	26	t	t	PROPN
ejpam-3329	29	27	∈	∈	PROPN
ejpam-3329	29	28	b(h	b(h	PROPN
ejpam-3329	29	29	)	)	PUNCT
ejpam-3329	29	30	‖t	‖t	NOUN
ejpam-3329	29	31	2x‖2	2x‖2	NUM
ejpam-3329	29	32	≤	≤	NUM
ejpam-3329	29	33	1	1	NUM
ejpam-3329	29	34	2	2	NUM
ejpam-3329	29	35	(	(	PUNCT
ejpam-3329	29	36	‖t	‖t	NOUN
ejpam-3329	29	37	3x‖2	3x‖2	NUM
ejpam-3329	29	38	+	+	CCONJ
ejpam-3329	29	39	‖tx‖2	‖tx‖2	PROPN
ejpam-3329	29	40	)	)	PUNCT
ejpam-3329	29	41	for	for	ADP
ejpam-3329	29	42	every	every	DET
ejpam-3329	29	43	x	x	SYM
ejpam-3329	29	44	∈	∈	PROPN
ejpam-3329	29	45	h	h	NOUN
ejpam-3329	29	46	in	in	ADP
ejpam-3329	29	47	[	[	X
ejpam-3329	29	48	8	8	NUM
ejpam-3329	29	49	]	]	PUNCT
ejpam-3329	29	50	,	,	PUNCT
ejpam-3329	29	51	a	a	DET
ejpam-3329	29	52	k	k	ADJ
ejpam-3329	29	53	-	-	PUNCT
ejpam-3329	29	54	quasi	quasi	ADJ
ejpam-3329	29	55	class	class	NOUN
ejpam-3329	29	56	q	q	NOUN
ejpam-3329	29	57	operator	operator	NOUN
ejpam-3329	29	58	is	be	AUX
ejpam-3329	29	59	defined	define	VERB
ejpam-3329	29	60	as	as	ADP
ejpam-3329	29	61	follows	follow	VERB
ejpam-3329	29	62	,	,	PUNCT
ejpam-3329	29	63	an	an	DET
ejpam-3329	29	64	operator	operator	NOUN
ejpam-3329	29	65	t	t	NOUN
ejpam-3329	29	66	is	be	AUX
ejpam-3329	29	67	of	of	ADP
ejpam-3329	29	68	k	k	ADJ
ejpam-3329	29	69	-	-	PUNCT
ejpam-3329	29	70	quasi	quasi	ADJ
ejpam-3329	29	71	class	class	NOUN
ejpam-3329	29	72	q	q	PROPN
ejpam-3329	29	73	if	if	SCONJ
ejpam-3329	29	74	‖t	‖t	NOUN
ejpam-3329	29	75	k+1x‖2	k+1x‖2	VERB
ejpam-3329	29	76	≤	≤	NUM
ejpam-3329	29	77	1	1	NUM
ejpam-3329	29	78	2	2	NUM
ejpam-3329	29	79	(	(	PUNCT
ejpam-3329	29	80	‖t	‖t	NOUN
ejpam-3329	29	81	k+2x‖2	k+2x‖2	PUNCT
ejpam-3329	29	82	+	+	CCONJ
ejpam-3329	29	83	‖t	‖t	ADJ
ejpam-3329	29	84	kx‖2	kx‖2	NOUN
ejpam-3329	29	85	)	)	PUNCT
ejpam-3329	29	86	for	for	ADP
ejpam-3329	29	87	every	every	DET
ejpam-3329	29	88	x	x	SYM
ejpam-3329	29	89	∈	∈	PROPN
ejpam-3329	29	90	h	h	NOUN
ejpam-3329	29	91	and	and	CCONJ
ejpam-3329	29	92	k	k	PROPN
ejpam-3329	29	93	is	be	AUX
ejpam-3329	29	94	a	a	DET
ejpam-3329	29	95	natural	natural	ADJ
ejpam-3329	29	96	number	number	NOUN
ejpam-3329	29	97	.	.	PUNCT
ejpam-3329	30	1	d.	d.	PROPN
ejpam-3329	30	2	senthil	senthil	PROPN
ejpam-3329	30	3	kumar	kumar	PROPN
ejpam-3329	30	4	,	,	PUNCT
ejpam-3329	30	5	prasad	prasad	PROPN
ejpam-3329	30	6	.	.	PUNCT
ejpam-3329	31	1	t	t	PROPN
ejpam-3329	31	2	in	in	ADP
ejpam-3329	31	3	[	[	X
ejpam-3329	31	4	11	11	NUM
ejpam-3329	31	5	]	]	PUNCT
ejpam-3329	31	6	,	,	PUNCT
ejpam-3329	31	7	has	have	AUX
ejpam-3329	31	8	defined	define	VERB
ejpam-3329	31	9	the	the	DET
ejpam-3329	31	10	new	new	ADJ
ejpam-3329	31	11	class	class	NOUN
ejpam-3329	31	12	of	of	ADP
ejpam-3329	31	13	operators	operator	NOUN
ejpam-3329	31	14	which	which	PRON
ejpam-3329	31	15	we	we	PRON
ejpam-3329	31	16	call	call	VERB
ejpam-3329	31	17	m	m	NOUN
ejpam-3329	31	18	-class	-class	PROPN
ejpam-3329	31	19	q	q	NOUN
ejpam-3329	31	20	operators	operator	NOUN
ejpam-3329	31	21	.	.	PUNCT
ejpam-3329	32	1	an	an	DET
ejpam-3329	32	2	operator	operator	NOUN
ejpam-3329	32	3	t	t	NOUN
ejpam-3329	32	4	is	be	AUX
ejpam-3329	32	5	of	of	ADP
ejpam-3329	32	6	m	m	PROPN
ejpam-3329	32	7	class	class	NOUN
ejpam-3329	32	8	q	q	PROPN
ejpam-3329	32	9	if	if	SCONJ
ejpam-3329	32	10	for	for	ADP
ejpam-3329	32	11	a	a	DET
ejpam-3329	32	12	fixed	fix	VERB
ejpam-3329	32	13	real	real	ADJ
ejpam-3329	32	14	number	number	NOUN
ejpam-3329	32	15	m	m	PROPN
ejpam-3329	32	16	≥	≥	NOUN
ejpam-3329	32	17	1	1	NUM
ejpam-3329	32	18	,	,	PUNCT
ejpam-3329	32	19	t	t	PROPN
ejpam-3329	32	20	satisfies	satisfy	VERB
ejpam-3329	32	21	m2	m2	PROPN
ejpam-3329	32	22	t	t	PROPN
ejpam-3329	32	23	∗2	∗2	PROPN
ejpam-3329	32	24	t	t	PROPN
ejpam-3329	32	25	2	2	NUM
ejpam-3329	32	26	−	−	PROPN
ejpam-3329	32	27	2	2	NUM
ejpam-3329	32	28	t	t	NOUN
ejpam-3329	32	29	∗t	∗t	NOUN
ejpam-3329	33	1	+	+	CCONJ
ejpam-3329	33	2	i	i	PRON
ejpam-3329	33	3	≥	≥	VERB
ejpam-3329	33	4	0	0	NUM
ejpam-3329	33	5	or	or	CCONJ
ejpam-3329	33	6	equivalently	equivalently	ADV
ejpam-3329	33	7	‖tx‖2	‖tx‖2	PUNCT
ejpam-3329	33	8	≤	≤	NUM
ejpam-3329	33	9	1	1	NUM
ejpam-3329	33	10	2	2	NUM
ejpam-3329	33	11	(	(	PUNCT
ejpam-3329	33	12	m2‖t	m2‖t	NOUN
ejpam-3329	33	13	2x‖2	2x‖2	NUM
ejpam-3329	33	14	+	+	CCONJ
ejpam-3329	33	15	‖x‖2	‖x‖2	ADJ
ejpam-3329	33	16	)	)	PUNCT
ejpam-3329	33	17	for	for	ADP
ejpam-3329	33	18	every	every	DET
ejpam-3329	33	19	x	x	SYM
ejpam-3329	33	20	∈	∈	PROPN
ejpam-3329	33	21	h	h	NOUN
ejpam-3329	33	22	and	and	CCONJ
ejpam-3329	33	23	a	a	DET
ejpam-3329	33	24	fixed	fix	VERB
ejpam-3329	33	25	real	real	ADJ
ejpam-3329	33	26	number	number	NOUN
ejpam-3329	33	27	m	m	PROPN
ejpam-3329	33	28	≥	≥	NOUN
ejpam-3329	33	29	1	1	NUM
ejpam-3329	33	30	.	.	PUNCT
ejpam-3329	34	1	in	in	ADP
ejpam-3329	34	2	[	[	X
ejpam-3329	34	3	15	15	NUM
ejpam-3329	34	4	]	]	PUNCT
ejpam-3329	34	5	,	,	PUNCT
ejpam-3329	34	6	youngoh	youngoh	PROPN
ejpam-3329	34	7	yang	yang	PROPN
ejpam-3329	34	8	and	and	CCONJ
ejpam-3329	34	9	cheoul	cheoul	PROPN
ejpam-3329	34	10	jun	jun	PROPN
ejpam-3329	34	11	kim	kim	PROPN
ejpam-3329	34	12	introduced	introduce	VERB
ejpam-3329	34	13	a	a	DET
ejpam-3329	34	14	class	class	NOUN
ejpam-3329	34	15	q∗	q∗	NOUN
ejpam-3329	34	16	operators	operator	NOUN
ejpam-3329	34	17	.	.	PUNCT
ejpam-3329	35	1	if	if	SCONJ
ejpam-3329	35	2	t	t	PROPN
ejpam-3329	35	3	∗2	∗2	PROPN
ejpam-3329	35	4	t	t	PROPN
ejpam-3329	35	5	2	2	NUM
ejpam-3329	35	6	−	−	NOUN
ejpam-3329	35	7	2tt	2tt	ADJ
ejpam-3329	35	8	∗	∗	NOUN
ejpam-3329	35	9	+	+	CCONJ
ejpam-3329	35	10	i	i	PRON
ejpam-3329	35	11	≥	≥	NOUN
ejpam-3329	35	12	0	0	NUM
ejpam-3329	35	13	,	,	PUNCT
ejpam-3329	35	14	then	then	ADV
ejpam-3329	35	15	t	t	PROPN
ejpam-3329	35	16	is	be	AUX
ejpam-3329	35	17	called	call	VERB
ejpam-3329	35	18	class	class	NOUN
ejpam-3329	35	19	q∗	q∗	NOUN
ejpam-3329	35	20	operators	operator	NOUN
ejpam-3329	35	21	.	.	PUNCT
ejpam-3329	36	1	he	he	PRON
ejpam-3329	36	2	also	also	ADV
ejpam-3329	36	3	proved	prove	VERB
ejpam-3329	36	4	that	that	SCONJ
ejpam-3329	36	5	if	if	SCONJ
ejpam-3329	36	6	t	t	PROPN
ejpam-3329	36	7	is	be	AUX
ejpam-3329	36	8	class	class	NOUN
ejpam-3329	36	9	q∗	q∗	NOUN
ejpam-3329	36	10	if	if	SCONJ
ejpam-3329	37	1	and	and	CCONJ
ejpam-3329	37	2	only	only	ADV
ejpam-3329	37	3	if	if	SCONJ
ejpam-3329	37	4	‖t	‖t	PUNCT
ejpam-3329	37	5	∗x‖2	∗x‖2	VERB
ejpam-3329	37	6	≤	≤	ADV
ejpam-3329	37	7	1	1	NUM
ejpam-3329	37	8	2(‖t	2(‖t	NUM
ejpam-3329	37	9	2x‖2	2x‖2	NUM
ejpam-3329	37	10	+	+	CCONJ
ejpam-3329	37	11	‖x‖2	‖x‖2	ADJ
ejpam-3329	37	12	)	)	PUNCT
ejpam-3329	37	13	for	for	ADP
ejpam-3329	37	14	every	every	DET
ejpam-3329	37	15	x	x	PROPN
ejpam-3329	37	16	∈	∈	PROPN
ejpam-3329	37	17	h.	h.	NOUN
ejpam-3329	37	18	in	in	ADP
ejpam-3329	37	19	[	[	X
ejpam-3329	37	20	4	4	NUM
ejpam-3329	37	21	]	]	PUNCT
ejpam-3329	37	22	,	,	PUNCT
ejpam-3329	37	23	d.	d.	PROPN
ejpam-3329	37	24	senthil	senthil	PROPN
ejpam-3329	37	25	kumar	kumar	PROPN
ejpam-3329	37	26	et	et	PROPN
ejpam-3329	37	27	.	.	PUNCT
ejpam-3329	38	1	al	al	PROPN
ejpam-3329	38	2	.	.	PROPN
ejpam-3329	38	3	introduced	introduce	VERB
ejpam-3329	38	4	quasi	quasi	ADJ
ejpam-3329	38	5	class	class	NOUN
ejpam-3329	38	6	q∗	q∗	NOUN
ejpam-3329	38	7	operators	operator	NOUN
ejpam-3329	38	8	.	.	PUNCT
ejpam-3329	39	1	if	if	SCONJ
ejpam-3329	39	2	t	t	PROPN
ejpam-3329	39	3	∗3	∗3	PROPN
ejpam-3329	39	4	t	t	NOUN
ejpam-3329	39	5	3	3	NUM
ejpam-3329	39	6	−	−	PROPN
ejpam-3329	39	7	2(t	2(t	NUM
ejpam-3329	39	8	∗t	∗t	ADJ
ejpam-3329	39	9	)	)	PUNCT
ejpam-3329	39	10	2	2	NUM
ejpam-3329	40	1	+	+	NUM
ejpam-3329	40	2	t	t	PROPN
ejpam-3329	40	3	∗t	∗t	PROPN
ejpam-3329	40	4	≥	≥	NUM
ejpam-3329	40	5	0	0	NUM
ejpam-3329	40	6	,	,	PUNCT
ejpam-3329	40	7	then	then	ADV
ejpam-3329	40	8	t	t	PROPN
ejpam-3329	40	9	is	be	AUX
ejpam-3329	40	10	called	call	VERB
ejpam-3329	40	11	quasi	quasi	ADJ
ejpam-3329	40	12	class	class	NOUN
ejpam-3329	40	13	q∗	q∗	NOUN
ejpam-3329	40	14	operators	operator	NOUN
ejpam-3329	40	15	.	.	PUNCT
ejpam-3329	41	1	he	he	PRON
ejpam-3329	41	2	also	also	ADV
ejpam-3329	41	3	proved	prove	VERB
ejpam-3329	41	4	that	that	SCONJ
ejpam-3329	41	5	if	if	SCONJ
ejpam-3329	41	6	t	t	PROPN
ejpam-3329	41	7	is	be	AUX
ejpam-3329	41	8	quasi	quasi	ADJ
ejpam-3329	41	9	class	class	NOUN
ejpam-3329	41	10	q∗	q∗	PROPN
ejpam-3329	41	11	if	if	SCONJ
ejpam-3329	42	1	and	and	CCONJ
ejpam-3329	42	2	only	only	ADV
ejpam-3329	42	3	if	if	SCONJ
ejpam-3329	42	4	‖t	‖t	PROPN
ejpam-3329	42	5	∗tx‖2	∗tx‖2	VERB
ejpam-3329	42	6	≤	≤	NUM
ejpam-3329	43	1	1	1	NUM
ejpam-3329	43	2	2(‖t	2(‖t	NUM
ejpam-3329	43	3	3x‖2	3x‖2	NUM
ejpam-3329	43	4	+	+	CCONJ
ejpam-3329	43	5	‖tx‖2	‖tx‖2	PROPN
ejpam-3329	43	6	)	)	PUNCT
ejpam-3329	43	7	for	for	ADP
ejpam-3329	43	8	every	every	DET
ejpam-3329	43	9	x	x	SYM
ejpam-3329	43	10	∈	∈	PROPN
ejpam-3329	43	11	h	h	NOUN
ejpam-3329	43	12	in	in	ADP
ejpam-3329	43	13	this	this	DET
ejpam-3329	43	14	paper	paper	NOUN
ejpam-3329	43	15	,	,	PUNCT
ejpam-3329	43	16	we	we	PRON
ejpam-3329	43	17	study	study	VERB
ejpam-3329	43	18	some	some	DET
ejpam-3329	43	19	properties	property	NOUN
ejpam-3329	43	20	of	of	ADP
ejpam-3329	43	21	quasi	quasi	ADJ
ejpam-3329	43	22	n	n	CCONJ
ejpam-3329	43	23	-	-	PUNCT
ejpam-3329	43	24	class	class	NOUN
ejpam-3329	43	25	q	q	NOUN
ejpam-3329	43	26	and	and	CCONJ
ejpam-3329	43	27	quasi	quasi	ADJ
ejpam-3329	43	28	n	n	CCONJ
ejpam-3329	43	29	-	-	PUNCT
ejpam-3329	43	30	class	class	NOUN
ejpam-3329	43	31	q∗	q∗	NOUN
ejpam-3329	43	32	operators	operator	NOUN
ejpam-3329	43	33	and	and	CCONJ
ejpam-3329	43	34	we	we	PRON
ejpam-3329	43	35	derive	derive	VERB
ejpam-3329	43	36	conditions	condition	NOUN
ejpam-3329	43	37	for	for	ADP
ejpam-3329	43	38	composition	composition	NOUN
ejpam-3329	43	39	and	and	CCONJ
ejpam-3329	43	40	weighted	weight	VERB
ejpam-3329	43	41	composition	composition	NOUN
ejpam-3329	43	42	operators	operator	NOUN
ejpam-3329	43	43	to	to	PART
ejpam-3329	43	44	be	be	AUX
ejpam-3329	43	45	quasi	quasi	ADJ
ejpam-3329	43	46	n	n	CCONJ
ejpam-3329	43	47	-	-	PUNCT
ejpam-3329	43	48	class	class	NOUN
ejpam-3329	43	49	q	q	NOUN
ejpam-3329	43	50	and	and	CCONJ
ejpam-3329	43	51	quasi	quasi	ADJ
ejpam-3329	43	52	n	n	CCONJ
ejpam-3329	43	53	-	-	PUNCT
ejpam-3329	43	54	class	class	NOUN
ejpam-3329	43	55	q∗.	q∗.	NOUN
ejpam-3329	43	56	aluthge	aluthge	ADJ
ejpam-3329	43	57	transformation	transformation	NOUN
ejpam-3329	43	58	of	of	ADP
ejpam-3329	43	59	quasi	quasi	ADJ
ejpam-3329	43	60	n	n	CCONJ
ejpam-3329	43	61	-	-	PUNCT
ejpam-3329	43	62	class	class	NOUN
ejpam-3329	43	63	q	q	NOUN
ejpam-3329	43	64	and	and	CCONJ
ejpam-3329	43	65	quasi	quasi	ADJ
ejpam-3329	43	66	n	n	CCONJ
ejpam-3329	43	67	-	-	PUNCT
ejpam-3329	43	68	class	class	NOUN
ejpam-3329	43	69	q∗	q∗	NOUN
ejpam-3329	43	70	operators	operator	NOUN
ejpam-3329	43	71	are	be	AUX
ejpam-3329	43	72	derived	derive	VERB
ejpam-3329	43	73	.	.	PUNCT
ejpam-3329	44	1	conditions	condition	NOUN
ejpam-3329	44	2	for	for	ADP
ejpam-3329	44	3	composite	composite	ADJ
ejpam-3329	44	4	multiplication	multiplication	NOUN
ejpam-3329	44	5	operators	operator	NOUN
ejpam-3329	44	6	to	to	PART
ejpam-3329	44	7	be	be	AUX
ejpam-3329	44	8	quasi	quasi	ADJ
ejpam-3329	44	9	n	n	CCONJ
ejpam-3329	44	10	-	-	PUNCT
ejpam-3329	44	11	class	class	NOUN
ejpam-3329	44	12	q	q	NOUN
ejpam-3329	44	13	and	and	CCONJ
ejpam-3329	44	14	quasi	quasi	ADJ
ejpam-3329	44	15	n	n	CCONJ
ejpam-3329	44	16	-	-	PUNCT
ejpam-3329	44	17	class	class	NOUN
ejpam-3329	44	18	q∗	q∗	NOUN
ejpam-3329	44	19	are	be	AUX
ejpam-3329	44	20	also	also	ADV
ejpam-3329	44	21	obtained	obtain	VERB
ejpam-3329	44	22	.	.	PUNCT
ejpam-3329	45	1	a	a	DET
ejpam-3329	45	2	characterization	characterization	NOUN
ejpam-3329	45	3	of	of	ADP
ejpam-3329	45	4	quasi	quasi	ADJ
ejpam-3329	45	5	n	n	CCONJ
ejpam-3329	45	6	-	-	PUNCT
ejpam-3329	45	7	class	class	NOUN
ejpam-3329	45	8	q	q	NOUN
ejpam-3329	45	9	and	and	CCONJ
ejpam-3329	45	10	quasi	quasi	ADJ
ejpam-3329	45	11	n	n	CCONJ
ejpam-3329	45	12	-	-	PUNCT
ejpam-3329	45	13	class	class	NOUN
ejpam-3329	45	14	q∗	q∗	NOUN
ejpam-3329	45	15	composition	composition	NOUN
ejpam-3329	45	16	and	and	CCONJ
ejpam-3329	45	17	weighted	weight	VERB
ejpam-3329	45	18	composition	composition	NOUN
ejpam-3329	45	19	operators	operator	NOUN
ejpam-3329	45	20	on	on	ADP
ejpam-3329	45	21	weighted	weight	VERB
ejpam-3329	45	22	hardy	hardy	ADJ
ejpam-3329	45	23	space	space	NOUN
ejpam-3329	45	24	are	be	AUX
ejpam-3329	45	25	obtained	obtain	VERB
ejpam-3329	45	26	.	.	PUNCT
ejpam-3329	46	1	2	2	X
ejpam-3329	46	2	.	.	PUNCT
ejpam-3329	46	3	quasi	quasi	NOUN
ejpam-3329	46	4	n	n	CCONJ
ejpam-3329	46	5	class	class	NOUN
ejpam-3329	46	6	q	q	PROPN
ejpam-3329	46	7	operators	operator	NOUN
ejpam-3329	46	8	in	in	ADP
ejpam-3329	46	9	this	this	DET
ejpam-3329	46	10	section	section	NOUN
ejpam-3329	46	11	,	,	PUNCT
ejpam-3329	46	12	we	we	PRON
ejpam-3329	46	13	define	define	VERB
ejpam-3329	46	14	new	new	ADJ
ejpam-3329	46	15	class	class	NOUN
ejpam-3329	46	16	of	of	ADP
ejpam-3329	46	17	operators	operator	NOUN
ejpam-3329	46	18	called	call	VERB
ejpam-3329	46	19	quasi	quasi	ADJ
ejpam-3329	46	20	n	n	CCONJ
ejpam-3329	46	21	-	-	PUNCT
ejpam-3329	46	22	class	class	NOUN
ejpam-3329	46	23	q	q	NOUN
ejpam-3329	46	24	,	,	PUNCT
ejpam-3329	46	25	which	which	PRON
ejpam-3329	46	26	is	be	AUX
ejpam-3329	46	27	a	a	DET
ejpam-3329	46	28	super	super	ADJ
ejpam-3329	46	29	class	class	NOUN
ejpam-3329	46	30	of	of	ADP
ejpam-3329	46	31	n	n	CCONJ
ejpam-3329	46	32	-	-	PUNCT
ejpam-3329	46	33	class	class	NOUN
ejpam-3329	46	34	q	q	NOUN
ejpam-3329	46	35	operators	operator	NOUN
ejpam-3329	46	36	and	and	CCONJ
ejpam-3329	46	37	studied	study	VERB
ejpam-3329	46	38	some	some	DET
ejpam-3329	46	39	properties	property	NOUN
ejpam-3329	46	40	of	of	ADP
ejpam-3329	46	41	this	this	DET
ejpam-3329	46	42	class	class	NOUN
ejpam-3329	46	43	of	of	ADP
ejpam-3329	46	44	operators	operator	NOUN
ejpam-3329	46	45	.	.	PUNCT
ejpam-3329	47	1	definition	definition	NOUN
ejpam-3329	47	2	1	1	NUM
ejpam-3329	47	3	.	.	PUNCT
ejpam-3329	48	1	an	an	DET
ejpam-3329	48	2	operator	operator	NOUN
ejpam-3329	48	3	t	t	PROPN
ejpam-3329	48	4	∈	∈	PROPN
ejpam-3329	48	5	b(h	b(h	PROPN
ejpam-3329	48	6	)	)	PUNCT
ejpam-3329	48	7	is	be	AUX
ejpam-3329	48	8	said	say	VERB
ejpam-3329	48	9	to	to	PART
ejpam-3329	48	10	be	be	AUX
ejpam-3329	48	11	quasi	quasi	ADJ
ejpam-3329	48	12	n	n	CCONJ
ejpam-3329	48	13	-	-	PUNCT
ejpam-3329	48	14	class	class	NOUN
ejpam-3329	48	15	q	q	NOUN
ejpam-3329	48	16	if	if	SCONJ
ejpam-3329	48	17	for	for	ADP
ejpam-3329	48	18	every	every	DET
ejpam-3329	48	19	positive	positive	ADJ
ejpam-3329	48	20	integer	integer	NOUN
ejpam-3329	48	21	n	n	NOUN
ejpam-3329	48	22	and	and	CCONJ
ejpam-3329	48	23	for	for	ADP
ejpam-3329	48	24	every	every	DET
ejpam-3329	48	25	x	x	SYM
ejpam-3329	48	26	∈	∈	PROPN
ejpam-3329	48	27	h	h	NOUN
ejpam-3329	48	28	d.	d.	PROPN
ejpam-3329	48	29	senthilkumar	senthilkumar	PROPN
ejpam-3329	48	30	,	,	PUNCT
ejpam-3329	48	31	s.	s.	PROPN
ejpam-3329	48	32	parvatham	parvatham	PROPN
ejpam-3329	48	33	/	/	SYM
ejpam-3329	48	34	eur	eur	PROPN
ejpam-3329	48	35	.	.	PUNCT
ejpam-3329	49	1	j.	j.	PROPN
ejpam-3329	49	2	pure	pure	PROPN
ejpam-3329	49	3	appl	appl	PROPN
ejpam-3329	49	4	.	.	PROPN
ejpam-3329	49	5	math	math	PROPN
ejpam-3329	49	6	,	,	PUNCT
ejpam-3329	49	7	11	11	NUM
ejpam-3329	49	8	(	(	PUNCT
ejpam-3329	49	9	4	4	NUM
ejpam-3329	49	10	)	)	PUNCT
ejpam-3329	49	11	(	(	PUNCT
ejpam-3329	49	12	2018	2018	NUM
ejpam-3329	49	13	)	)	PUNCT
ejpam-3329	49	14	,	,	PUNCT
ejpam-3329	49	15	1108	1108	NUM
ejpam-3329	49	16	-	-	SYM
ejpam-3329	49	17	1129	1129	NUM
ejpam-3329	49	18	1110	1110	NUM
ejpam-3329	49	19	‖t	‖t	PROPN
ejpam-3329	50	1	2x‖2	2x‖2	NUM
ejpam-3329	50	2	≤	≤	NUM
ejpam-3329	50	3	1	1	NUM
ejpam-3329	50	4	1	1	NUM
ejpam-3329	50	5	+	+	NUM
ejpam-3329	50	6	n	n	CCONJ
ejpam-3329	50	7	(	(	PUNCT
ejpam-3329	50	8	‖t	‖t	PROPN
ejpam-3329	50	9	2+nx‖2	2+nx‖2	PROPN
ejpam-3329	50	10	+	+	NUM
ejpam-3329	50	11	n‖tx‖2	n‖tx‖2	PROPN
ejpam-3329	50	12	)	)	PUNCT
ejpam-3329	50	13	when	when	SCONJ
ejpam-3329	50	14	n	n	PROPN
ejpam-3329	50	15	=	=	SYM
ejpam-3329	50	16	1	1	NUM
ejpam-3329	50	17	it	it	PRON
ejpam-3329	50	18	is	be	AUX
ejpam-3329	50	19	of	of	ADP
ejpam-3329	50	20	quasi	quasi	ADJ
ejpam-3329	50	21	class	class	NOUN
ejpam-3329	50	22	q	q	PROPN
ejpam-3329	50	23	operators	operator	NOUN
ejpam-3329	50	24	.	.	PUNCT
ejpam-3329	51	1	theorem	theorem	NOUN
ejpam-3329	51	2	1	1	NUM
ejpam-3329	51	3	.	.	PUNCT
ejpam-3329	52	1	an	an	DET
ejpam-3329	52	2	operator	operator	NOUN
ejpam-3329	52	3	t	t	NOUN
ejpam-3329	52	4	is	be	AUX
ejpam-3329	52	5	of	of	ADP
ejpam-3329	52	6	quasi	quasi	NOUN
ejpam-3329	52	7	n	n	CCONJ
ejpam-3329	52	8	-	-	PUNCT
ejpam-3329	52	9	class	class	NOUN
ejpam-3329	52	10	q	q	NOUN
ejpam-3329	52	11	if	if	SCONJ
ejpam-3329	53	1	and	and	CCONJ
ejpam-3329	53	2	only	only	ADV
ejpam-3329	53	3	if	if	SCONJ
ejpam-3329	53	4	t	t	PROPN
ejpam-3329	53	5	∗2+nt	∗2+nt	PROPN
ejpam-3329	53	6	2+n−(1+n)t	2+n−(1+n)t	PROPN
ejpam-3329	53	7	∗2	∗2	PROPN
ejpam-3329	53	8	t	t	PROPN
ejpam-3329	53	9	2	2	NUM
ejpam-3329	53	10	+	+	NUM
ejpam-3329	53	11	nt	not	PART
ejpam-3329	53	12	∗t	∗t	ADJ
ejpam-3329	53	13	≥	≥	NUM
ejpam-3329	53	14	0	0	NUM
ejpam-3329	53	15	for	for	ADP
ejpam-3329	53	16	every	every	DET
ejpam-3329	53	17	positive	positive	ADJ
ejpam-3329	53	18	integer	integer	NOUN
ejpam-3329	53	19	n.	n.	NOUN
ejpam-3329	53	20	proof	proof	NOUN
ejpam-3329	53	21	.	.	PUNCT
ejpam-3329	54	1	since	since	SCONJ
ejpam-3329	54	2	t	t	PROPN
ejpam-3329	54	3	is	be	AUX
ejpam-3329	54	4	quasi	quasi	NOUN
ejpam-3329	54	5	n	n	PRON
ejpam-3329	54	6	class	class	NOUN
ejpam-3329	54	7	q	q	NOUN
ejpam-3329	54	8	operator	operator	NOUN
ejpam-3329	54	9	,	,	PUNCT
ejpam-3329	54	10	we	we	PRON
ejpam-3329	54	11	have	have	VERB
ejpam-3329	54	12	‖t	‖t	NOUN
ejpam-3329	54	13	2x‖2	2x‖2	NUM
ejpam-3329	54	14	≤	≤	NUM
ejpam-3329	54	15	1	1	NUM
ejpam-3329	54	16	1	1	NUM
ejpam-3329	54	17	+	+	NUM
ejpam-3329	54	18	n	n	CCONJ
ejpam-3329	54	19	(	(	PUNCT
ejpam-3329	54	20	‖t	‖t	PROPN
ejpam-3329	54	21	2+nx‖2	2+nx‖2	PROPN
ejpam-3329	54	22	+	+	NUM
ejpam-3329	54	23	n‖tx‖2	n‖tx‖2	PROPN
ejpam-3329	54	24	)	)	PUNCT
ejpam-3329	54	25	⇔	⇔	PROPN
ejpam-3329	54	26	‖t	‖t	PROPN
ejpam-3329	55	1	2+nx‖2	2+nx‖2	ADJ
ejpam-3329	55	2	−	−	PROPN
ejpam-3329	56	1	(	(	PUNCT
ejpam-3329	56	2	1	1	NUM
ejpam-3329	56	3	+	+	CCONJ
ejpam-3329	56	4	n)‖t	n)‖t	ADJ
ejpam-3329	56	5	2x‖2	2x‖2	NUM
ejpam-3329	56	6	+	+	CCONJ
ejpam-3329	56	7	n‖tx‖2	n‖tx‖2	PROPN
ejpam-3329	56	8	)	)	PUNCT
ejpam-3329	56	9	≥	≥	NOUN
ejpam-3329	56	10	0	0	NUM
ejpam-3329	57	1	⇔	⇔	PROPN
ejpam-3329	57	2	〈	〈	PROPN
ejpam-3329	57	3	t	t	PROPN
ejpam-3329	57	4	2+nx	2+nx	NUM
ejpam-3329	57	5	,	,	PUNCT
ejpam-3329	57	6	t	t	PROPN
ejpam-3329	57	7	2+nx	2+nx	NUM
ejpam-3329	57	8	〉	〉	PROPN
ejpam-3329	57	9	−	−	PROPN
ejpam-3329	57	10	(	(	PUNCT
ejpam-3329	57	11	1	1	NUM
ejpam-3329	57	12	+	+	NUM
ejpam-3329	57	13	n)〈t	n)〈t	PROPN
ejpam-3329	57	14	2x	2x	NUM
ejpam-3329	57	15	,	,	PUNCT
ejpam-3329	57	16	t	t	PROPN
ejpam-3329	57	17	2x〉+	2x〉+	NUM
ejpam-3329	57	18	n〈tx	n〈tx	PROPN
ejpam-3329	57	19	,	,	PUNCT
ejpam-3329	57	20	tx	tx	PROPN
ejpam-3329	57	21	〉	〉	PROPN
ejpam-3329	57	22	≥	≥	NOUN
ejpam-3329	57	23	0	0	NUM
ejpam-3329	58	1	⇔	⇔	PROPN
ejpam-3329	58	2	t	t	PROPN
ejpam-3329	58	3	∗2+nt	∗2+nt	VERB
ejpam-3329	58	4	2+n	2+n	NUM
ejpam-3329	58	5	−	−	PROPN
ejpam-3329	58	6	(	(	PUNCT
ejpam-3329	58	7	1	1	NUM
ejpam-3329	58	8	+	+	CCONJ
ejpam-3329	58	9	n)t	n)t	PROPN
ejpam-3329	58	10	∗2	∗2	PROPN
ejpam-3329	58	11	t	t	PROPN
ejpam-3329	58	12	2	2	NUM
ejpam-3329	58	13	+	+	CCONJ
ejpam-3329	58	14	nt	not	PART
ejpam-3329	58	15	∗t	∗t	ADJ
ejpam-3329	58	16	≥	≥	NUM
ejpam-3329	58	17	0	0	NUM
ejpam-3329	58	18	for	for	ADP
ejpam-3329	58	19	example	example	NOUN
ejpam-3329	58	20	:	:	PUNCT
ejpam-3329	58	21	let	let	VERB
ejpam-3329	58	22	x	x	PUNCT
ejpam-3329	58	23	=	=	PRON
ejpam-3329	58	24	(	(	PUNCT
ejpam-3329	58	25	x1	x1	PROPN
ejpam-3329	58	26	,	,	PUNCT
ejpam-3329	58	27	x2	x2	PROPN
ejpam-3329	58	28	,	,	PUNCT
ejpam-3329	58	29	...	...	PUNCT
ejpam-3329	58	30	)	)	PUNCT
ejpam-3329	59	1	∈	∈	PROPN
ejpam-3329	59	2	l2	l2	NOUN
ejpam-3329	59	3	,	,	PUNCT
ejpam-3329	59	4	define	define	VERB
ejpam-3329	59	5	t	t	NOUN
ejpam-3329	59	6	:	:	PUNCT
ejpam-3329	59	7	l2	l2	NOUN
ejpam-3329	59	8	→	→	SYM
ejpam-3329	59	9	l2	l2	NOUN
ejpam-3329	59	10	by	by	ADP
ejpam-3329	59	11	t	t	PROPN
ejpam-3329	59	12	(	(	PUNCT
ejpam-3329	59	13	x	x	NOUN
ejpam-3329	59	14	)	)	PUNCT
ejpam-3329	59	15	=	=	SYM
ejpam-3329	59	16	(	(	PUNCT
ejpam-3329	59	17	0	0	NUM
ejpam-3329	59	18	,	,	PUNCT
ejpam-3329	59	19	x1	x1	PROPN
ejpam-3329	59	20	,	,	PUNCT
ejpam-3329	59	21	x2	x2	PROPN
ejpam-3329	59	22	,	,	PUNCT
ejpam-3329	59	23	...	...	PUNCT
ejpam-3329	59	24	)	)	PUNCT
ejpam-3329	59	25	,	,	PUNCT
ejpam-3329	59	26	t	t	PROPN
ejpam-3329	59	27	∗(x	∗(x	PROPN
ejpam-3329	59	28	)	)	PUNCT
ejpam-3329	59	29	=	=	SYM
ejpam-3329	59	30	(	(	PUNCT
ejpam-3329	59	31	x2	x2	PROPN
ejpam-3329	59	32	,	,	PUNCT
ejpam-3329	59	33	x3	x3	ADJ
ejpam-3329	59	34	,	,	PUNCT
ejpam-3329	59	35	...	...	PUNCT
ejpam-3329	59	36	)	)	PUNCT
ejpam-3329	59	37	.	.	PUNCT
ejpam-3329	60	1	then	then	ADV
ejpam-3329	60	2	t	t	PROPN
ejpam-3329	60	3	∗2+nt	∗2+nt	VERB
ejpam-3329	60	4	2+n	2+n	NUM
ejpam-3329	60	5	−	−	PROPN
ejpam-3329	60	6	(	(	PUNCT
ejpam-3329	60	7	1	1	NUM
ejpam-3329	60	8	+	+	CCONJ
ejpam-3329	60	9	n)t	n)t	PROPN
ejpam-3329	60	10	∗2	∗2	PROPN
ejpam-3329	60	11	t	t	PROPN
ejpam-3329	60	12	2	2	NUM
ejpam-3329	60	13	+	+	CCONJ
ejpam-3329	60	14	nt	not	PART
ejpam-3329	60	15	∗t	∗t	ADJ
ejpam-3329	60	16	≥	≥	NUM
ejpam-3329	60	17	0	0	NUM
ejpam-3329	60	18	.	.	PUNCT
ejpam-3329	61	1	ie	ie	PROPN
ejpam-3329	61	2	t	t	PROPN
ejpam-3329	61	3	is	be	AUX
ejpam-3329	61	4	quasi	quasi	ADJ
ejpam-3329	61	5	n	n	CCONJ
ejpam-3329	61	6	-	-	PUNCT
ejpam-3329	61	7	class	class	NOUN
ejpam-3329	61	8	q	q	NOUN
ejpam-3329	61	9	operators	operator	NOUN
ejpam-3329	61	10	.	.	PUNCT
ejpam-3329	62	1	from	from	ADP
ejpam-3329	62	2	the	the	DET
ejpam-3329	62	3	definition	definition	NOUN
ejpam-3329	62	4	of	of	ADP
ejpam-3329	62	5	n	n	DET
ejpam-3329	62	6	class	class	NOUN
ejpam-3329	62	7	q	q	NOUN
ejpam-3329	62	8	operator	operator	NOUN
ejpam-3329	62	9	we	we	PRON
ejpam-3329	62	10	can	can	AUX
ejpam-3329	62	11	easily	easily	ADV
ejpam-3329	62	12	say	say	VERB
ejpam-3329	62	13	that	that	SCONJ
ejpam-3329	62	14	every	every	DET
ejpam-3329	62	15	n	n	PRON
ejpam-3329	62	16	class	class	NOUN
ejpam-3329	62	17	q	q	NOUN
ejpam-3329	62	18	operator	operator	NOUN
ejpam-3329	62	19	is	be	AUX
ejpam-3329	62	20	also	also	ADV
ejpam-3329	62	21	an	an	DET
ejpam-3329	62	22	operator	operator	NOUN
ejpam-3329	62	23	of	of	ADP
ejpam-3329	62	24	quasi	quasi	NOUN
ejpam-3329	62	25	n	n	X
ejpam-3329	62	26	class	class	NOUN
ejpam-3329	62	27	q.	q.	NOUN
ejpam-3329	62	28	hence	hence	ADV
ejpam-3329	62	29	we	we	PRON
ejpam-3329	62	30	have	have	VERB
ejpam-3329	62	31	the	the	DET
ejpam-3329	62	32	following	follow	VERB
ejpam-3329	62	33	implication	implication	NOUN
ejpam-3329	62	34	class	class	NOUN
ejpam-3329	62	35	q	q	PROPN
ejpam-3329	62	36	⊂	⊂	PROPN
ejpam-3329	62	37	n	n	PRON
ejpam-3329	62	38	class	class	NOUN
ejpam-3329	62	39	q	q	X
ejpam-3329	62	40	⊂	⊂	X
ejpam-3329	62	41	quasi	quasi	PROPN
ejpam-3329	62	42	n	n	PRON
ejpam-3329	62	43	class	class	NOUN
ejpam-3329	62	44	q.	q.	PROPN
ejpam-3329	62	45	theorem	theorem	VERB
ejpam-3329	62	46	2	2	NUM
ejpam-3329	62	47	.	.	PUNCT
ejpam-3329	63	1	every	every	DET
ejpam-3329	63	2	quasi	quasi	ADJ
ejpam-3329	63	3	class	class	NOUN
ejpam-3329	63	4	q	q	NOUN
ejpam-3329	63	5	operator	operator	NOUN
ejpam-3329	63	6	is	be	AUX
ejpam-3329	63	7	quasi	quasi	NOUN
ejpam-3329	63	8	n	n	PRON
ejpam-3329	63	9	class	class	NOUN
ejpam-3329	63	10	q	q	NOUN
ejpam-3329	63	11	operator	operator	NOUN
ejpam-3329	63	12	.	.	PUNCT
ejpam-3329	64	1	proof	proof	NOUN
ejpam-3329	64	2	.	.	PUNCT
ejpam-3329	65	1	by	by	ADP
ejpam-3329	65	2	using	use	VERB
ejpam-3329	65	3	induction	induction	NOUN
ejpam-3329	65	4	principle	principle	NOUN
ejpam-3329	65	5	and	and	CCONJ
ejpam-3329	65	6	simple	simple	ADJ
ejpam-3329	65	7	calculation	calculation	NOUN
ejpam-3329	65	8	we	we	PRON
ejpam-3329	65	9	get	get	VERB
ejpam-3329	65	10	the	the	DET
ejpam-3329	65	11	result	result	NOUN
ejpam-3329	65	12	.	.	PUNCT
ejpam-3329	66	1	corollary	corollary	ADJ
ejpam-3329	66	2	1	1	NUM
ejpam-3329	66	3	.	.	PUNCT
ejpam-3329	67	1	if	if	SCONJ
ejpam-3329	67	2	t	t	PROPN
ejpam-3329	67	3	∈	∈	PROPN
ejpam-3329	67	4	b(h	b(h	PROPN
ejpam-3329	67	5	)	)	PUNCT
ejpam-3329	67	6	is	be	AUX
ejpam-3329	67	7	of	of	ADP
ejpam-3329	67	8	quasi	quasi	NOUN
ejpam-3329	67	9	n	n	CCONJ
ejpam-3329	67	10	-	-	PUNCT
ejpam-3329	67	11	class	class	NOUN
ejpam-3329	67	12	q	q	NOUN
ejpam-3329	67	13	then	then	ADV
ejpam-3329	67	14	t	t	PROPN
ejpam-3329	67	15	is	be	AUX
ejpam-3329	67	16	of	of	ADP
ejpam-3329	67	17	quasi	quasi	ADJ
ejpam-3329	67	18	n+	n+	PUNCT
ejpam-3329	67	19	1	1	NUM
ejpam-3329	67	20	-	-	PUNCT
ejpam-3329	67	21	class	class	NOUN
ejpam-3329	67	22	q	q	NOUN
ejpam-3329	67	23	operator	operator	NOUN
ejpam-3329	67	24	corollary	corollary	NOUN
ejpam-3329	67	25	2	2	NUM
ejpam-3329	67	26	.	.	PUNCT
ejpam-3329	68	1	if	if	SCONJ
ejpam-3329	68	2	t	t	PROPN
ejpam-3329	68	3	∈	∈	PROPN
ejpam-3329	68	4	b(h	b(h	PROPN
ejpam-3329	68	5	)	)	PUNCT
ejpam-3329	68	6	is	be	AUX
ejpam-3329	68	7	of	of	ADP
ejpam-3329	68	8	quasi	quasi	NOUN
ejpam-3329	68	9	n	n	CCONJ
ejpam-3329	68	10	-	-	PUNCT
ejpam-3329	68	11	class	class	NOUN
ejpam-3329	68	12	q	q	NOUN
ejpam-3329	68	13	then	then	ADV
ejpam-3329	68	14	αt	αt	PROPN
ejpam-3329	68	15	is	be	AUX
ejpam-3329	68	16	of	of	ADP
ejpam-3329	68	17	quasi	quasi	NOUN
ejpam-3329	68	18	n	n	CCONJ
ejpam-3329	68	19	-	-	PUNCT
ejpam-3329	68	20	class	class	NOUN
ejpam-3329	68	21	q	q	NOUN
ejpam-3329	68	22	operator	operator	NOUN
ejpam-3329	68	23	for	for	ADP
ejpam-3329	68	24	any	any	DET
ejpam-3329	68	25	complex	complex	ADJ
ejpam-3329	68	26	number	number	NOUN
ejpam-3329	68	27	α	α	NOUN
ejpam-3329	68	28	.	.	PUNCT
ejpam-3329	69	1	theorem	theorem	NOUN
ejpam-3329	69	2	3	3	X
ejpam-3329	69	3	.	.	PUNCT
ejpam-3329	70	1	let	let	VERB
ejpam-3329	70	2	t	t	PROPN
ejpam-3329	70	3	∈	∈	PROPN
ejpam-3329	70	4	b(h	b(h	PROPN
ejpam-3329	70	5	)	)	PUNCT
ejpam-3329	70	6	.	.	PUNCT
ejpam-3329	71	1	if	if	SCONJ
ejpam-3329	71	2	λ	λ	PROPN
ejpam-3329	71	3	−1	−1	NOUN
ejpam-3329	71	4	2	2	NUM
ejpam-3329	71	5	t	t	NOUN
ejpam-3329	71	6	is	be	AUX
ejpam-3329	71	7	an	an	DET
ejpam-3329	71	8	operator	operator	NOUN
ejpam-3329	71	9	of	of	ADP
ejpam-3329	71	10	quasi	quasi	NOUN
ejpam-3329	71	11	n	n	X
ejpam-3329	71	12	class	class	NOUN
ejpam-3329	71	13	q	q	NOUN
ejpam-3329	71	14	,	,	PUNCT
ejpam-3329	71	15	then	then	ADV
ejpam-3329	71	16	t	t	PROPN
ejpam-3329	71	17	is	be	AUX
ejpam-3329	71	18	quasi	quasi	NOUN
ejpam-3329	71	19	n	n	PRON
ejpam-3329	71	20	paranormal	paranormal	ADJ
ejpam-3329	71	21	operator	operator	NOUN
ejpam-3329	71	22	for	for	ADP
ejpam-3329	71	23	all	all	DET
ejpam-3329	71	24	λ	λ	PROPN
ejpam-3329	71	25	>	>	X
ejpam-3329	71	26	0	0	X
ejpam-3329	71	27	.	.	PUNCT
ejpam-3329	72	1	proof	proof	NOUN
ejpam-3329	72	2	.	.	PUNCT
ejpam-3329	73	1	since	since	SCONJ
ejpam-3329	73	2	λ	λ	PROPN
ejpam-3329	73	3	−1	−1	NOUN
ejpam-3329	73	4	2	2	NUM
ejpam-3329	73	5	t	t	NOUN
ejpam-3329	73	6	is	be	AUX
ejpam-3329	73	7	an	an	DET
ejpam-3329	73	8	operator	operator	NOUN
ejpam-3329	73	9	of	of	ADP
ejpam-3329	73	10	quasi	quasi	ADJ
ejpam-3329	73	11	n	n	CCONJ
ejpam-3329	73	12	-	-	PUNCT
ejpam-3329	73	13	class	class	NOUN
ejpam-3329	73	14	q	q	NOUN
ejpam-3329	73	15	,	,	PUNCT
ejpam-3329	73	16	then	then	ADV
ejpam-3329	73	17	(	(	PUNCT
ejpam-3329	73	18	λ	λ	SYM
ejpam-3329	73	19	−1	−1	NOUN
ejpam-3329	73	20	2	2	NUM
ejpam-3329	73	21	t	t	NOUN
ejpam-3329	73	22	)	)	PUNCT
ejpam-3329	73	23	∗(2+n)(λ	∗(2+n)(λ	NOUN
ejpam-3329	73	24	−1	−1	NOUN
ejpam-3329	73	25	2	2	NUM
ejpam-3329	73	26	t	t	NOUN
ejpam-3329	73	27	)	)	PUNCT
ejpam-3329	73	28	2+n	2+n	NUM
ejpam-3329	73	29	−	−	PROPN
ejpam-3329	73	30	(	(	PUNCT
ejpam-3329	73	31	1	1	NUM
ejpam-3329	73	32	+	+	NUM
ejpam-3329	73	33	n)(λ	n)(λ	PROPN
ejpam-3329	73	34	−1	−1	NOUN
ejpam-3329	73	35	2	2	NUM
ejpam-3329	73	36	t	t	NOUN
ejpam-3329	73	37	)	)	PUNCT
ejpam-3329	74	1	∗2(λ	∗2(λ	ADV
ejpam-3329	74	2	−1	−1	NOUN
ejpam-3329	74	3	2	2	NUM
ejpam-3329	74	4	t	t	NOUN
ejpam-3329	74	5	)	)	PUNCT
ejpam-3329	74	6	2	2	NUM
ejpam-3329	75	1	+	+	CCONJ
ejpam-3329	75	2	n((λ	n((λ	ADP
ejpam-3329	75	3	−1	−1	NOUN
ejpam-3329	75	4	2	2	NUM
ejpam-3329	75	5	t	t	NOUN
ejpam-3329	75	6	)	)	PUNCT
ejpam-3329	75	7	∗(λ	∗(λ	PROPN
ejpam-3329	75	8	−1	−1	NOUN
ejpam-3329	75	9	2	2	NUM
ejpam-3329	75	10	t	t	NOUN
ejpam-3329	75	11	)	)	PUNCT
ejpam-3329	75	12	)	)	PUNCT
ejpam-3329	75	13	≥	≥	NOUN
ejpam-3329	75	14	0	0	NUM
ejpam-3329	75	15	.	.	PUNCT
ejpam-3329	76	1	hence	hence	ADV
ejpam-3329	76	2	|λ	|λ	ADV
ejpam-3329	76	3	−1	−1	NOUN
ejpam-3329	76	4	2	2	NUM
ejpam-3329	76	5	|2(2+n)t	|2(2+n)t	NUM
ejpam-3329	76	6	∗2+nt	∗2+nt	ADP
ejpam-3329	76	7	2+n	2+n	NUM
ejpam-3329	76	8	−	−	PROPN
ejpam-3329	77	1	(	(	PUNCT
ejpam-3329	77	2	1	1	NUM
ejpam-3329	77	3	+	+	CCONJ
ejpam-3329	77	4	n)|λ	n)|λ	DET
ejpam-3329	77	5	−1	−1	NOUN
ejpam-3329	77	6	2	2	NUM
ejpam-3329	77	7	|4	|4	NUM
ejpam-3329	77	8	t	t	PROPN
ejpam-3329	77	9	∗2	∗2	PROPN
ejpam-3329	77	10	t	t	PROPN
ejpam-3329	77	11	2	2	NUM
ejpam-3329	77	12	+	+	NUM
ejpam-3329	77	13	n|λ	n|λ	NOUN
ejpam-3329	77	14	−1	−1	NOUN
ejpam-3329	77	15	2	2	NUM
ejpam-3329	77	16	|2	|2	NUM
ejpam-3329	77	17	t	t	NOUN
ejpam-3329	77	18	∗t	∗t	PROPN
ejpam-3329	77	19	≥	≥	NUM
ejpam-3329	77	20	0	0	NUM
ejpam-3329	77	21	.	.	PUNCT
ejpam-3329	78	1	by	by	ADP
ejpam-3329	78	2	multiplying	multiply	VERB
ejpam-3329	78	3	|λ|2+n	|λ|2+n	NOUN
ejpam-3329	78	4	and	and	CCONJ
ejpam-3329	78	5	let	let	VERB
ejpam-3329	78	6	|λ|	|λ|	PROPN
ejpam-3329	78	7	=	=	SYM
ejpam-3329	78	8	µ	µ	PROPN
ejpam-3329	78	9	,	,	PUNCT
ejpam-3329	78	10	then	then	ADV
ejpam-3329	78	11	t	t	PROPN
ejpam-3329	78	12	∗2+nt	∗2+nt	VERB
ejpam-3329	78	13	2+n	2+n	NUM
ejpam-3329	78	14	−	−	PROPN
ejpam-3329	78	15	(	(	PUNCT
ejpam-3329	78	16	1	1	NUM
ejpam-3329	78	17	+	+	CCONJ
ejpam-3329	78	18	n)µnt	n)µnt	PROPN
ejpam-3329	78	19	∗2	∗2	PROPN
ejpam-3329	78	20	t	t	NOUN
ejpam-3329	78	21	2	2	NUM
ejpam-3329	78	22	+	+	CCONJ
ejpam-3329	78	23	nµ1+nt	nµ1+nt	ADP
ejpam-3329	78	24	∗t	∗t	PROPN
ejpam-3329	78	25	≥	≥	NUM
ejpam-3329	78	26	0	0	NUM
ejpam-3329	78	27	.	.	PUNCT
ejpam-3329	79	1	hence	hence	ADV
ejpam-3329	79	2	t	t	PROPN
ejpam-3329	79	3	is	be	AUX
ejpam-3329	79	4	quasi	quasi	ADJ
ejpam-3329	79	5	n	n	CCONJ
ejpam-3329	79	6	-	-	PUNCT
ejpam-3329	79	7	paranormal	paranormal	NOUN
ejpam-3329	79	8	operator	operator	NOUN
ejpam-3329	79	9	for	for	ADP
ejpam-3329	79	10	all	all	DET
ejpam-3329	79	11	λ	λ	PROPN
ejpam-3329	79	12	>	>	X
ejpam-3329	79	13	0	0	X
ejpam-3329	79	14	.	.	PUNCT
ejpam-3329	79	15	theorem	theorem	NOUN
ejpam-3329	79	16	4	4	NUM
ejpam-3329	79	17	.	.	PUNCT
ejpam-3329	80	1	if	if	SCONJ
ejpam-3329	80	2	quasi	quasi	ADJ
ejpam-3329	80	3	n	n	CCONJ
ejpam-3329	80	4	-	-	PUNCT
ejpam-3329	80	5	class	class	NOUN
ejpam-3329	80	6	q	q	NOUN
ejpam-3329	80	7	operator	operator	NOUN
ejpam-3329	80	8	t	t	NOUN
ejpam-3329	80	9	doubly	doubly	ADV
ejpam-3329	80	10	commutes	commute	VERB
ejpam-3329	80	11	with	with	ADP
ejpam-3329	80	12	an	an	DET
ejpam-3329	80	13	isometric	isometric	ADJ
ejpam-3329	80	14	operator	operator	NOUN
ejpam-3329	80	15	s	s	PART
ejpam-3329	80	16	,	,	PUNCT
ejpam-3329	80	17	then	then	ADV
ejpam-3329	80	18	ts	ts	PROPN
ejpam-3329	80	19	is	be	AUX
ejpam-3329	80	20	an	an	DET
ejpam-3329	80	21	operator	operator	NOUN
ejpam-3329	80	22	of	of	ADP
ejpam-3329	80	23	quasi	quasi	ADJ
ejpam-3329	80	24	n	n	CCONJ
ejpam-3329	80	25	-	-	PUNCT
ejpam-3329	80	26	class	class	NOUN
ejpam-3329	80	27	q.	q.	PROPN
ejpam-3329	80	28	d.	d.	PROPN
ejpam-3329	80	29	senthilkumar	senthilkumar	PROPN
ejpam-3329	80	30	,	,	PUNCT
ejpam-3329	80	31	s.	s.	PROPN
ejpam-3329	80	32	parvatham	parvatham	PROPN
ejpam-3329	80	33	/	/	SYM
ejpam-3329	80	34	eur	eur	PROPN
ejpam-3329	80	35	.	.	PUNCT
ejpam-3329	81	1	j.	j.	PROPN
ejpam-3329	81	2	pure	pure	PROPN
ejpam-3329	81	3	appl	appl	PROPN
ejpam-3329	81	4	.	.	PROPN
ejpam-3329	81	5	math	math	PROPN
ejpam-3329	81	6	,	,	PUNCT
ejpam-3329	81	7	11	11	NUM
ejpam-3329	81	8	(	(	PUNCT
ejpam-3329	81	9	4	4	NUM
ejpam-3329	81	10	)	)	PUNCT
ejpam-3329	81	11	(	(	PUNCT
ejpam-3329	81	12	2018	2018	NUM
ejpam-3329	81	13	)	)	PUNCT
ejpam-3329	81	14	,	,	PUNCT
ejpam-3329	81	15	1108	1108	NUM
ejpam-3329	81	16	-	-	SYM
ejpam-3329	81	17	1129	1129	NUM
ejpam-3329	81	18	1111	1111	NUM
ejpam-3329	81	19	proof	proof	NOUN
ejpam-3329	81	20	.	.	PUNCT
ejpam-3329	82	1	since	since	SCONJ
ejpam-3329	82	2	t	t	PROPN
ejpam-3329	82	3	is	be	AUX
ejpam-3329	82	4	quasi	quasi	NOUN
ejpam-3329	82	5	n	n	CCONJ
ejpam-3329	82	6	-	-	PUNCT
ejpam-3329	82	7	classq	classq	NOUN
ejpam-3329	82	8	operator	operator	NOUN
ejpam-3329	82	9	,	,	PUNCT
ejpam-3329	82	10	then	then	ADV
ejpam-3329	82	11	t	t	PROPN
ejpam-3329	82	12	∗(t	∗(t	NOUN
ejpam-3329	82	13	∗1+nt	∗1+nt	VERB
ejpam-3329	82	14	1+n−(1+n)t	1+n−(1+n)t	NUM
ejpam-3329	82	15	∗t+ni)t	∗t+ni)t	PROPN
ejpam-3329	82	16	≥	≥	PROPN
ejpam-3329	82	17	0	0	NUM
ejpam-3329	82	18	.	.	PUNCT
ejpam-3329	83	1	suppose	suppose	VERB
ejpam-3329	83	2	t	t	NOUN
ejpam-3329	83	3	doubly	doubly	ADV
ejpam-3329	83	4	commutes	commute	VERB
ejpam-3329	83	5	with	with	ADP
ejpam-3329	83	6	an	an	DET
ejpam-3329	83	7	isometric	isometric	ADJ
ejpam-3329	83	8	operator	operator	NOUN
ejpam-3329	83	9	s	s	PART
ejpam-3329	83	10	,	,	PUNCT
ejpam-3329	83	11	then	then	ADV
ejpam-3329	83	12	ts	ts	ADP
ejpam-3329	83	13	=	=	PROPN
ejpam-3329	83	14	st	st	PROPN
ejpam-3329	83	15	,	,	PUNCT
ejpam-3329	83	16	s∗t	s∗t	X
ejpam-3329	83	17	=	=	SYM
ejpam-3329	83	18	ts∗	ts∗	X
ejpam-3329	83	19	and	and	CCONJ
ejpam-3329	83	20	s∗s	s∗s	ADP
ejpam-3329	83	21	=	=	PUNCT
ejpam-3329	83	22	i.	i.	NOUN
ejpam-3329	83	23	now	now	ADV
ejpam-3329	83	24	let	let	VERB
ejpam-3329	83	25	a	a	DET
ejpam-3329	83	26	=	=	NOUN
ejpam-3329	83	27	ts	ts	NOUN
ejpam-3329	83	28	.	.	PUNCT
ejpam-3329	84	1	so	so	ADV
ejpam-3329	84	2	we	we	PRON
ejpam-3329	84	3	get	get	VERB
ejpam-3329	84	4	a∗(a∗(1+n)a(1+n	a∗(a∗(1+n)a(1+n	PROPN
ejpam-3329	84	5	)	)	PUNCT
ejpam-3329	85	1	−	−	PROPN
ejpam-3329	85	2	(	(	PUNCT
ejpam-3329	85	3	1	1	NUM
ejpam-3329	85	4	+	+	NUM
ejpam-3329	85	5	n)a∗a	n)a∗a	CCONJ
ejpam-3329	85	6	+	+	CCONJ
ejpam-3329	85	7	ni)a	ni)a	PROPN
ejpam-3329	85	8	≥	≥	NOUN
ejpam-3329	85	9	0	0	NUM
ejpam-3329	85	10	.	.	PUNCT
ejpam-3329	86	1	therefore	therefore	ADV
ejpam-3329	86	2	ts	ts	PROPN
ejpam-3329	86	3	is	be	AUX
ejpam-3329	86	4	a	a	DET
ejpam-3329	86	5	quasi	quasi	ADJ
ejpam-3329	86	6	n	n	CCONJ
ejpam-3329	86	7	-	-	PUNCT
ejpam-3329	86	8	class	class	NOUN
ejpam-3329	86	9	q	q	NOUN
ejpam-3329	86	10	operator	operator	NOUN
ejpam-3329	86	11	.	.	PUNCT
ejpam-3329	87	1	theorem	theorem	VERB
ejpam-3329	87	2	5	5	NUM
ejpam-3329	87	3	.	.	PUNCT
ejpam-3329	88	1	if	if	SCONJ
ejpam-3329	88	2	a	a	DET
ejpam-3329	88	3	quasi	quasi	NOUN
ejpam-3329	88	4	n	n	CCONJ
ejpam-3329	88	5	-	-	PUNCT
ejpam-3329	88	6	class	class	NOUN
ejpam-3329	88	7	q	q	NOUN
ejpam-3329	88	8	operator	operator	NOUN
ejpam-3329	88	9	t	t	PROPN
ejpam-3329	88	10	∈	∈	PROPN
ejpam-3329	88	11	b(h	b(h	PROPN
ejpam-3329	88	12	)	)	PUNCT
ejpam-3329	88	13	is	be	AUX
ejpam-3329	88	14	unitarily	unitarily	ADV
ejpam-3329	88	15	equivalent	equivalent	ADJ
ejpam-3329	88	16	to	to	PART
ejpam-3329	88	17	operator	operator	VERB
ejpam-3329	88	18	s	s	PART
ejpam-3329	88	19	,	,	PUNCT
ejpam-3329	88	20	then	then	ADV
ejpam-3329	88	21	s	s	VERB
ejpam-3329	88	22	is	be	AUX
ejpam-3329	88	23	an	an	DET
ejpam-3329	88	24	operator	operator	NOUN
ejpam-3329	88	25	of	of	ADP
ejpam-3329	88	26	quasi	quasi	ADJ
ejpam-3329	88	27	n	n	CCONJ
ejpam-3329	88	28	-	-	PUNCT
ejpam-3329	88	29	class	class	NOUN
ejpam-3329	88	30	q.	q.	NOUN
ejpam-3329	88	31	proof	proof	NOUN
ejpam-3329	88	32	.	.	PUNCT
ejpam-3329	89	1	assume	assume	VERB
ejpam-3329	89	2	t	t	PROPN
ejpam-3329	89	3	is	be	AUX
ejpam-3329	89	4	unitarily	unitarily	ADV
ejpam-3329	89	5	equivalent	equivalent	ADJ
ejpam-3329	89	6	to	to	PART
ejpam-3329	89	7	operator	operator	VERB
ejpam-3329	89	8	s.	s.	PROPN
ejpam-3329	89	9	then	then	ADV
ejpam-3329	89	10	there	there	PRON
ejpam-3329	89	11	exists	exist	VERB
ejpam-3329	89	12	an	an	DET
ejpam-3329	89	13	unitary	unitary	ADJ
ejpam-3329	89	14	operator	operator	NOUN
ejpam-3329	89	15	u	u	NOUN
ejpam-3329	89	16	such	such	ADJ
ejpam-3329	89	17	that	that	PRON
ejpam-3329	89	18	s	s	PART
ejpam-3329	89	19	=	=	VERB
ejpam-3329	89	20	u∗tu	u∗tu	PROPN
ejpam-3329	89	21	and	and	CCONJ
ejpam-3329	89	22	t	t	PROPN
ejpam-3329	89	23	is	be	AUX
ejpam-3329	89	24	quasi	quasi	ADJ
ejpam-3329	89	25	n	n	CCONJ
ejpam-3329	89	26	-	-	PUNCT
ejpam-3329	89	27	class	class	NOUN
ejpam-3329	89	28	q	q	NOUN
ejpam-3329	89	29	operator	operator	NOUN
ejpam-3329	89	30	,	,	PUNCT
ejpam-3329	89	31	then	then	ADV
ejpam-3329	89	32	s∗(s∗1+ns1+n−	s∗(s∗1+ns1+n−	PUNCT
ejpam-3329	89	33	(	(	PUNCT
ejpam-3329	89	34	1	1	NUM
ejpam-3329	89	35	+	+	NUM
ejpam-3329	89	36	n)s∗s	n)s∗s	X
ejpam-3329	89	37	+	+	X
ejpam-3329	89	38	ni)s	ni)s	NOUN
ejpam-3329	89	39	=	=	SYM
ejpam-3329	89	40	(	(	PUNCT
ejpam-3329	89	41	u∗tu)∗((u∗tu)∗1+n(u∗tu)1+n	u∗tu)∗((u∗tu)∗1+n(u∗tu)1+n	PROPN
ejpam-3329	90	1	−	−	PROPN
ejpam-3329	91	1	(	(	PUNCT
ejpam-3329	91	2	1	1	NUM
ejpam-3329	91	3	+	+	CCONJ
ejpam-3329	91	4	n)(u∗tu)∗(u∗tu	n)(u∗tu)∗(u∗tu	NOUN
ejpam-3329	91	5	)	)	PUNCT
ejpam-3329	91	6	+	+	CCONJ
ejpam-3329	91	7	ni)(u∗tu	ni)(u∗tu	PROPN
ejpam-3329	91	8	)	)	PUNCT
ejpam-3329	91	9	≥	≥	NOUN
ejpam-3329	91	10	0	0	NUM
ejpam-3329	91	11	.	.	PUNCT
ejpam-3329	92	1	therefore	therefore	ADV
ejpam-3329	92	2	s	s	VERB
ejpam-3329	92	3	is	be	AUX
ejpam-3329	92	4	quasi	quasi	ADJ
ejpam-3329	92	5	n	n	CCONJ
ejpam-3329	92	6	-	-	PUNCT
ejpam-3329	92	7	class	class	NOUN
ejpam-3329	92	8	q	q	NOUN
ejpam-3329	92	9	operator	operator	NOUN
ejpam-3329	92	10	.	.	PUNCT
ejpam-3329	93	1	theorem	theorem	VERB
ejpam-3329	93	2	6	6	NUM
ejpam-3329	93	3	.	.	PUNCT
ejpam-3329	94	1	let	let	AUX
ejpam-3329	94	2	t	t	PROPN
ejpam-3329	94	3	∈	∈	PROPN
ejpam-3329	94	4	b(h	b(h	PROPN
ejpam-3329	94	5	)	)	PUNCT
ejpam-3329	94	6	be	be	VERB
ejpam-3329	94	7	an	an	DET
ejpam-3329	94	8	invertible	invertible	ADJ
ejpam-3329	94	9	operator	operator	NOUN
ejpam-3329	94	10	and	and	CCONJ
ejpam-3329	94	11	n	n	CCONJ
ejpam-3329	94	12	be	be	VERB
ejpam-3329	94	13	an	an	DET
ejpam-3329	94	14	operator	operator	NOUN
ejpam-3329	94	15	such	such	ADJ
ejpam-3329	94	16	that	that	SCONJ
ejpam-3329	94	17	n	n	ADP
ejpam-3329	94	18	commutes	commute	NOUN
ejpam-3329	94	19	with	with	ADP
ejpam-3329	94	20	t	t	PROPN
ejpam-3329	94	21	∗t	∗t	PROPN
ejpam-3329	94	22	.	.	PUNCT
ejpam-3329	95	1	then	then	ADV
ejpam-3329	95	2	operator	operator	NOUN
ejpam-3329	95	3	n	n	X
ejpam-3329	95	4	is	be	AUX
ejpam-3329	95	5	quasi	quasi	X
ejpam-3329	95	6	n	n	X
ejpam-3329	95	7	class	class	NOUN
ejpam-3329	95	8	q	q	NOUN
ejpam-3329	95	9	if	if	SCONJ
ejpam-3329	96	1	and	and	CCONJ
ejpam-3329	96	2	only	only	ADV
ejpam-3329	96	3	if	if	SCONJ
ejpam-3329	96	4	operator	operator	NOUN
ejpam-3329	96	5	tnt−1	tnt−1	PROPN
ejpam-3329	96	6	is	be	AUX
ejpam-3329	96	7	of	of	ADP
ejpam-3329	96	8	quasi	quasi	NOUN
ejpam-3329	96	9	n	n	X
ejpam-3329	96	10	class	class	NOUN
ejpam-3329	96	11	q.	q.	NOUN
ejpam-3329	96	12	proof	proof	NOUN
ejpam-3329	96	13	.	.	PUNCT
ejpam-3329	97	1	let	let	VERB
ejpam-3329	97	2	n	n	PRON
ejpam-3329	97	3	be	be	AUX
ejpam-3329	97	4	quasi	quasi	X
ejpam-3329	97	5	n	n	PRON
ejpam-3329	97	6	class	class	NOUN
ejpam-3329	97	7	q	q	NOUN
ejpam-3329	97	8	operator	operator	NOUN
ejpam-3329	97	9	,	,	PUNCT
ejpam-3329	97	10	then	then	ADV
ejpam-3329	97	11	n∗(n∗1+nn1+n−(1+n)n∗n+ni)n	n∗(n∗1+nn1+n−(1+n)n∗n+ni)n	VERB
ejpam-3329	97	12	≥	≥	NOUN
ejpam-3329	97	13	0	0	NUM
ejpam-3329	97	14	.	.	PUNCT
ejpam-3329	98	1	since	since	SCONJ
ejpam-3329	98	2	operator	operator	NOUN
ejpam-3329	98	3	n	n	NOUN
ejpam-3329	98	4	commutes	commute	NOUN
ejpam-3329	98	5	with	with	ADP
ejpam-3329	98	6	operator	operator	NOUN
ejpam-3329	98	7	t	t	PROPN
ejpam-3329	98	8	∗t	∗t	PROPN
ejpam-3329	98	9	,	,	PUNCT
ejpam-3329	98	10	we	we	PRON
ejpam-3329	98	11	have	have	VERB
ejpam-3329	98	12	(	(	PUNCT
ejpam-3329	98	13	tnt−1)∗((tnt−1)∗1+n(tnt−1)1+n	tnt−1)∗((tnt−1)∗1+n(tnt−1)1+n	PROPN
ejpam-3329	98	14	−	−	PROPN
ejpam-3329	98	15	(	(	PUNCT
ejpam-3329	98	16	1	1	NUM
ejpam-3329	98	17	+	+	CCONJ
ejpam-3329	98	18	n)(tnt−1)∗(tnt−1	n)(tnt−1)∗(tnt−1	NOUN
ejpam-3329	98	19	)	)	PUNCT
ejpam-3329	98	20	+	+	PUNCT
ejpam-3329	98	21	ni)(tnt−1	ni)(tnt−1	NOUN
ejpam-3329	98	22	)	)	PUNCT
ejpam-3329	98	23	=	=	SYM
ejpam-3329	98	24	t	t	PROPN
ejpam-3329	98	25	(	(	PUNCT
ejpam-3329	98	26	n∗(n∗1+nn1+n	n∗(n∗1+nn1+n	NOUN
ejpam-3329	98	27	−	−	PROPN
ejpam-3329	99	1	(	(	PUNCT
ejpam-3329	99	2	1	1	NUM
ejpam-3329	99	3	+	+	CCONJ
ejpam-3329	99	4	n)n∗n	n)n∗n	X
ejpam-3329	99	5	+	+	CCONJ
ejpam-3329	99	6	ni)n)t−1	ni)n)t−1	NOUN
ejpam-3329	99	7	.	.	PUNCT
ejpam-3329	99	8	since	since	SCONJ
ejpam-3329	99	9	n	n	ADV
ejpam-3329	99	10	is	be	AUX
ejpam-3329	99	11	quasi	quasi	X
ejpam-3329	99	12	n	n	PRON
ejpam-3329	99	13	class	class	NOUN
ejpam-3329	99	14	q	q	NOUN
ejpam-3329	99	15	operator	operator	NOUN
ejpam-3329	99	16	,	,	PUNCT
ejpam-3329	99	17	then	then	ADV
ejpam-3329	99	18	t	t	PROPN
ejpam-3329	99	19	(	(	PUNCT
ejpam-3329	99	20	n∗(n∗1+nn1+n	n∗(n∗1+nn1+n	PROPN
ejpam-3329	99	21	−	−	PROPN
ejpam-3329	99	22	(	(	PUNCT
ejpam-3329	99	23	1	1	NUM
ejpam-3329	99	24	+	+	NUM
ejpam-3329	99	25	n)n∗n	n)n∗n	NOUN
ejpam-3329	100	1	+	+	CCONJ
ejpam-3329	100	2	ni)n)t	ni)n)t	NOUN
ejpam-3329	100	3	∗	∗	X
ejpam-3329	100	4	≥	≥	NOUN
ejpam-3329	100	5	0	0	NUM
ejpam-3329	100	6	.	.	PUNCT
ejpam-3329	101	1	which	which	PRON
ejpam-3329	101	2	implies	imply	VERB
ejpam-3329	101	3	(	(	PUNCT
ejpam-3329	101	4	tt	tt	PROPN
ejpam-3329	101	5	∗	∗	NOUN
ejpam-3329	101	6	)	)	PUNCT
ejpam-3329	101	7	commutes	commute	NOUN
ejpam-3329	101	8	with	with	ADP
ejpam-3329	101	9	t	t	PROPN
ejpam-3329	101	10	(	(	PUNCT
ejpam-3329	101	11	n∗(n∗1+nn1+n	n∗(n∗1+nn1+n	PROPN
ejpam-3329	101	12	−	−	PROPN
ejpam-3329	101	13	(	(	PUNCT
ejpam-3329	101	14	1	1	NUM
ejpam-3329	101	15	+	+	CCONJ
ejpam-3329	101	16	n)n∗n	n)n∗n	NOUN
ejpam-3329	102	1	+	+	CCONJ
ejpam-3329	102	2	ni)n)t	ni)n)t	NOUN
ejpam-3329	102	3	∗.	∗.	PROPN
ejpam-3329	102	4	also	also	ADV
ejpam-3329	102	5	(	(	PUNCT
ejpam-3329	102	6	tt	tt	PROPN
ejpam-3329	102	7	∗)−1	∗)−1	INTJ
ejpam-3329	102	8	is	be	AUX
ejpam-3329	102	9	also	also	ADV
ejpam-3329	102	10	commutes	commute	NOUN
ejpam-3329	102	11	with	with	ADP
ejpam-3329	102	12	tn∗((n∗1+nn1+n	tn∗((n∗1+nn1+n	PRON
ejpam-3329	102	13	−	−	PROPN
ejpam-3329	102	14	(	(	PUNCT
ejpam-3329	102	15	1	1	NUM
ejpam-3329	102	16	+	+	CCONJ
ejpam-3329	102	17	n)n∗n	n)n∗n	NOUN
ejpam-3329	103	1	+	+	CCONJ
ejpam-3329	103	2	ni)n)t	ni)n)t	NOUN
ejpam-3329	103	3	∗.	∗.	ADP
ejpam-3329	103	4	then	then	ADV
ejpam-3329	103	5	t	t	PROPN
ejpam-3329	103	6	(	(	PUNCT
ejpam-3329	103	7	n∗(n∗1+nn1+n	n∗(n∗1+nn1+n	PROPN
ejpam-3329	103	8	−	−	PROPN
ejpam-3329	104	1	(	(	PUNCT
ejpam-3329	104	2	1	1	NUM
ejpam-3329	104	3	+	+	CCONJ
ejpam-3329	104	4	n)n∗n	n)n∗n	NOUN
ejpam-3329	104	5	+	+	CCONJ
ejpam-3329	104	6	ni)n)t−1	ni)n)t−1	NOUN
ejpam-3329	104	7	≥	≥	NOUN
ejpam-3329	104	8	0	0	NUM
ejpam-3329	104	9	.	.	PUNCT
ejpam-3329	105	1	hence	hence	ADV
ejpam-3329	105	2	tnt−1	tnt−1	PROPN
ejpam-3329	105	3	is	be	AUX
ejpam-3329	105	4	quasi	quasi	NOUN
ejpam-3329	105	5	n	n	PRON
ejpam-3329	105	6	class	class	NOUN
ejpam-3329	105	7	q	q	NOUN
ejpam-3329	105	8	operator	operator	NOUN
ejpam-3329	105	9	.	.	PUNCT
ejpam-3329	106	1	conversely	conversely	ADV
ejpam-3329	106	2	suppose	suppose	VERB
ejpam-3329	106	3	that	that	SCONJ
ejpam-3329	106	4	(	(	PUNCT
ejpam-3329	106	5	tnt−1	tnt−1	NOUN
ejpam-3329	106	6	)	)	PUNCT
ejpam-3329	106	7	is	be	AUX
ejpam-3329	106	8	quasi	quasi	NOUN
ejpam-3329	106	9	n	n	PRON
ejpam-3329	106	10	class	class	NOUN
ejpam-3329	106	11	q	q	NOUN
ejpam-3329	106	12	operator	operator	NOUN
ejpam-3329	106	13	,	,	PUNCT
ejpam-3329	106	14	then	then	ADV
ejpam-3329	106	15	n∗(n∗1+nn1+n	n∗(n∗1+nn1+n	PROPN
ejpam-3329	107	1	−	−	PROPN
ejpam-3329	108	1	(	(	PUNCT
ejpam-3329	108	2	1	1	NUM
ejpam-3329	108	3	+	+	CCONJ
ejpam-3329	108	4	n)n∗n	n)n∗n	X
ejpam-3329	108	5	+	+	CCONJ
ejpam-3329	108	6	ni)n	ni)n	PROPN
ejpam-3329	108	7	≥	≥	NOUN
ejpam-3329	108	8	0	0	NUM
ejpam-3329	108	9	.	.	PUNCT
ejpam-3329	108	10	corollary	corollary	ADJ
ejpam-3329	108	11	3	3	X
ejpam-3329	108	12	.	.	PUNCT
ejpam-3329	109	1	let	let	VERB
ejpam-3329	109	2	s	s	PRON
ejpam-3329	109	3	be	be	AUX
ejpam-3329	109	4	quasi	quasi	ADJ
ejpam-3329	109	5	n	n	PRON
ejpam-3329	109	6	class	class	NOUN
ejpam-3329	109	7	q	q	NOUN
ejpam-3329	109	8	operator	operator	NOUN
ejpam-3329	109	9	and	and	CCONJ
ejpam-3329	109	10	a	a	DET
ejpam-3329	109	11	any	any	DET
ejpam-3329	109	12	positive	positive	ADJ
ejpam-3329	109	13	operator	operator	NOUN
ejpam-3329	109	14	such	such	ADJ
ejpam-3329	109	15	that	that	PRON
ejpam-3329	109	16	a−1	a−1	PROPN
ejpam-3329	109	17	=	=	SYM
ejpam-3329	109	18	a∗.	a∗.	NOUN
ejpam-3329	109	19	then	then	ADV
ejpam-3329	109	20	t	t	PROPN
ejpam-3329	109	21	=	=	SYM
ejpam-3329	109	22	a−1sa	a−1sa	NOUN
ejpam-3329	109	23	is	be	AUX
ejpam-3329	109	24	quasi	quasi	NOUN
ejpam-3329	109	25	n	n	PRON
ejpam-3329	109	26	class	class	NOUN
ejpam-3329	109	27	q	q	NOUN
ejpam-3329	109	28	operator	operator	NOUN
ejpam-3329	109	29	.	.	PUNCT
ejpam-3329	110	1	theorem	theorem	VERB
ejpam-3329	110	2	7	7	NUM
ejpam-3329	110	3	.	.	PUNCT
ejpam-3329	111	1	let	let	VERB
ejpam-3329	111	2	t	t	PROPN
ejpam-3329	111	3	be	be	AUX
ejpam-3329	111	4	quasi	quasi	ADJ
ejpam-3329	111	5	n	n	PRON
ejpam-3329	111	6	class	class	NOUN
ejpam-3329	111	7	q	q	NOUN
ejpam-3329	111	8	operator	operator	NOUN
ejpam-3329	111	9	.	.	PUNCT
ejpam-3329	112	1	then	then	ADV
ejpam-3329	112	2	the	the	DET
ejpam-3329	112	3	tensor	tensor	NOUN
ejpam-3329	112	4	product	product	NOUN
ejpam-3329	112	5	t	t	PROPN
ejpam-3329	113	1	⊗	⊗	PROPN
ejpam-3329	113	2	i	i	PRON
ejpam-3329	113	3	and	and	CCONJ
ejpam-3329	113	4	i⊗t	i⊗t	ADP
ejpam-3329	113	5	are	be	AUX
ejpam-3329	113	6	both	both	PRON
ejpam-3329	113	7	quasi	quasi	ADJ
ejpam-3329	113	8	n	n	PRON
ejpam-3329	113	9	class	class	NOUN
ejpam-3329	113	10	q	q	PROPN
ejpam-3329	113	11	operators	operator	NOUN
ejpam-3329	113	12	.	.	PUNCT
ejpam-3329	114	1	proof	proof	NOUN
ejpam-3329	114	2	.	.	PUNCT
ejpam-3329	115	1	by	by	ADP
ejpam-3329	115	2	the	the	DET
ejpam-3329	115	3	definition	definition	NOUN
ejpam-3329	115	4	of	of	ADP
ejpam-3329	115	5	quasi	quasi	NOUN
ejpam-3329	115	6	n	n	X
ejpam-3329	115	7	class	class	NOUN
ejpam-3329	115	8	q	q	NOUN
ejpam-3329	115	9	and	and	CCONJ
ejpam-3329	115	10	tensor	tensor	NOUN
ejpam-3329	115	11	product	product	NOUN
ejpam-3329	115	12	and	and	CCONJ
ejpam-3329	115	13	by	by	ADP
ejpam-3329	115	14	the	the	DET
ejpam-3329	115	15	simple	simple	ADJ
ejpam-3329	115	16	calculation	calculation	NOUN
ejpam-3329	115	17	we	we	PRON
ejpam-3329	115	18	get	get	VERB
ejpam-3329	115	19	the	the	DET
ejpam-3329	115	20	result	result	NOUN
ejpam-3329	115	21	.	.	PUNCT
ejpam-3329	116	1	theorem	theorem	ADJ
ejpam-3329	116	2	8	8	NUM
ejpam-3329	116	3	.	.	PUNCT
ejpam-3329	117	1	if	if	SCONJ
ejpam-3329	117	2	t	t	PROPN
ejpam-3329	117	3	∈	∈	PROPN
ejpam-3329	117	4	b(h	b(h	PROPN
ejpam-3329	117	5	)	)	PUNCT
ejpam-3329	117	6	is	be	AUX
ejpam-3329	117	7	a	a	DET
ejpam-3329	117	8	quasi	quasi	ADJ
ejpam-3329	117	9	n	n	CCONJ
ejpam-3329	117	10	-	-	PUNCT
ejpam-3329	117	11	class	class	NOUN
ejpam-3329	117	12	q	q	NOUN
ejpam-3329	117	13	operator	operator	NOUN
ejpam-3329	117	14	for	for	ADP
ejpam-3329	117	15	a	a	DET
ejpam-3329	117	16	positive	positive	ADJ
ejpam-3329	117	17	integer	integer	NOUN
ejpam-3329	117	18	n	n	CCONJ
ejpam-3329	117	19	,	,	PUNCT
ejpam-3329	117	20	the	the	DET
ejpam-3329	117	21	range	range	NOUN
ejpam-3329	117	22	of	of	ADP
ejpam-3329	117	23	t	t	PROPN
ejpam-3329	117	24	does	do	AUX
ejpam-3329	117	25	not	not	PART
ejpam-3329	117	26	have	have	VERB
ejpam-3329	117	27	dense	dense	ADJ
ejpam-3329	117	28	range	range	NOUN
ejpam-3329	117	29	then	then	ADV
ejpam-3329	117	30	t	t	PROPN
ejpam-3329	117	31	has	have	VERB
ejpam-3329	117	32	the	the	DET
ejpam-3329	117	33	following	following	ADJ
ejpam-3329	117	34	2×2	2×2	NUM
ejpam-3329	117	35	matrix	matrix	NOUN
ejpam-3329	117	36	representation	representation	NOUN
ejpam-3329	117	37	t	t	NOUN
ejpam-3329	117	38	=	=	SYM
ejpam-3329	117	39	(	(	PUNCT
ejpam-3329	117	40	t1	t1	PROPN
ejpam-3329	117	41	t2	t2	PROPN
ejpam-3329	117	42	0	0	NUM
ejpam-3329	117	43	t3	t3	PROPN
ejpam-3329	117	44	)	)	PUNCT
ejpam-3329	117	45	on	on	ADP
ejpam-3329	117	46	h	h	NOUN
ejpam-3329	117	47	=	=	SYM
ejpam-3329	117	48	ran(t	ran(t	PROPN
ejpam-3329	117	49	)	)	PUNCT
ejpam-3329	117	50	⊕	⊕	PROPN
ejpam-3329	117	51	kert	kert	PROPN
ejpam-3329	117	52	∗	∗	PROPN
ejpam-3329	117	53	,	,	PUNCT
ejpam-3329	117	54	if	if	SCONJ
ejpam-3329	117	55	and	and	CCONJ
ejpam-3329	117	56	only	only	ADV
ejpam-3329	117	57	if	if	SCONJ
ejpam-3329	117	58	t1	t1	NOUN
ejpam-3329	117	59	is	be	AUX
ejpam-3329	117	60	also	also	ADV
ejpam-3329	117	61	quasi	quasi	ADJ
ejpam-3329	117	62	n	n	CCONJ
ejpam-3329	117	63	-	-	PUNCT
ejpam-3329	117	64	class	class	NOUN
ejpam-3329	117	65	q	q	NOUN
ejpam-3329	117	66	operator	operator	NOUN
ejpam-3329	117	67	on	on	ADP
ejpam-3329	117	68	ran(t	ran(t	PROPN
ejpam-3329	117	69	)	)	PUNCT
ejpam-3329	117	70	and	and	CCONJ
ejpam-3329	117	71	t3	t3	NOUN
ejpam-3329	117	72	=	=	SYM
ejpam-3329	117	73	0	0	X
ejpam-3329	117	74	.	.	PUNCT
ejpam-3329	118	1	further	far	ADV
ejpam-3329	118	2	more	more	ADJ
ejpam-3329	118	3	σ(t	σ(t	NOUN
ejpam-3329	118	4	)	)	PUNCT
ejpam-3329	118	5	=	=	SYM
ejpam-3329	118	6	σ(t1)∪{0	σ(t1)∪{0	PROPN
ejpam-3329	118	7	}	}	PUNCT
ejpam-3329	118	8	where	where	SCONJ
ejpam-3329	118	9	σ(t	σ(t	PROPN
ejpam-3329	118	10	)	)	PUNCT
ejpam-3329	118	11	denotes	denote	VERB
ejpam-3329	118	12	the	the	DET
ejpam-3329	118	13	spectrum	spectrum	NOUN
ejpam-3329	118	14	of	of	ADP
ejpam-3329	118	15	t	t	PROPN
ejpam-3329	118	16	.	.	PUNCT
ejpam-3329	119	1	proof	proof	NOUN
ejpam-3329	119	2	.	.	PUNCT
ejpam-3329	120	1	let	let	VERB
ejpam-3329	120	2	p	p	PRON
ejpam-3329	120	3	be	be	AUX
ejpam-3329	120	4	an	an	DET
ejpam-3329	120	5	orthogonal	orthogonal	ADJ
ejpam-3329	120	6	projection	projection	NOUN
ejpam-3329	120	7	of	of	ADP
ejpam-3329	120	8	h	h	NOUN
ejpam-3329	120	9	onto	onto	ADP
ejpam-3329	120	10	ran(t	ran(t	PROPN
ejpam-3329	120	11	)	)	PUNCT
ejpam-3329	120	12	.	.	PUNCT
ejpam-3329	121	1	then	then	ADV
ejpam-3329	121	2	t1	t1	NOUN
ejpam-3329	121	3	=	=	PUNCT
ejpam-3329	121	4	tp	tp	PROPN
ejpam-3329	121	5	=	=	PROPN
ejpam-3329	121	6	ptp	ptp	PROPN
ejpam-3329	121	7	.	.	PUNCT
ejpam-3329	122	1	by	by	ADP
ejpam-3329	122	2	theorem	theorem	NOUN
ejpam-3329	122	3	1	1	NUM
ejpam-3329	122	4	we	we	PRON
ejpam-3329	122	5	have	have	VERB
ejpam-3329	122	6	that	that	DET
ejpam-3329	122	7	d.	d.	PROPN
ejpam-3329	122	8	senthilkumar	senthilkumar	PROPN
ejpam-3329	122	9	,	,	PUNCT
ejpam-3329	122	10	s.	s.	PROPN
ejpam-3329	122	11	parvatham	parvatham	PROPN
ejpam-3329	122	12	/	/	SYM
ejpam-3329	122	13	eur	eur	PROPN
ejpam-3329	122	14	.	.	PUNCT
ejpam-3329	123	1	j.	j.	PROPN
ejpam-3329	123	2	pure	pure	PROPN
ejpam-3329	123	3	appl	appl	PROPN
ejpam-3329	123	4	.	.	PROPN
ejpam-3329	123	5	math	math	PROPN
ejpam-3329	123	6	,	,	PUNCT
ejpam-3329	123	7	11	11	NUM
ejpam-3329	123	8	(	(	PUNCT
ejpam-3329	123	9	4	4	NUM
ejpam-3329	123	10	)	)	PUNCT
ejpam-3329	123	11	(	(	PUNCT
ejpam-3329	123	12	2018	2018	NUM
ejpam-3329	123	13	)	)	PUNCT
ejpam-3329	123	14	,	,	PUNCT
ejpam-3329	123	15	1108	1108	NUM
ejpam-3329	123	16	-	-	SYM
ejpam-3329	123	17	1129	1129	NUM
ejpam-3329	123	18	1112	1112	NUM
ejpam-3329	123	19	p	p	NOUN
ejpam-3329	123	20	(	(	PUNCT
ejpam-3329	123	21	t	t	PROPN
ejpam-3329	123	22	∗2+nt	∗2+nt	PROPN
ejpam-3329	123	23	2+n	2+n	NUM
ejpam-3329	123	24	−	−	PROPN
ejpam-3329	124	1	(	(	PUNCT
ejpam-3329	124	2	1	1	NUM
ejpam-3329	124	3	+	+	CCONJ
ejpam-3329	124	4	n)t	n)t	PROPN
ejpam-3329	124	5	∗2	∗2	PROPN
ejpam-3329	124	6	t	t	PROPN
ejpam-3329	124	7	2	2	NUM
ejpam-3329	124	8	+	+	CCONJ
ejpam-3329	124	9	nt	not	PART
ejpam-3329	124	10	∗t	∗t	ADJ
ejpam-3329	124	11	)	)	PUNCT
ejpam-3329	124	12	p	p	NOUN
ejpam-3329	124	13	≥	≥	NOUN
ejpam-3329	124	14	0	0	NUM
ejpam-3329	125	1	hence	hence	ADV
ejpam-3329	125	2	(	(	PUNCT
ejpam-3329	125	3	t	t	PROPN
ejpam-3329	125	4	∗2+n1	∗2+n1	PROPN
ejpam-3329	125	5	t	t	PROPN
ejpam-3329	125	6	2+n	2+n	NUM
ejpam-3329	125	7	1	1	NUM
ejpam-3329	125	8	−	−	PROPN
ejpam-3329	125	9	(	(	PUNCT
ejpam-3329	125	10	1	1	NUM
ejpam-3329	125	11	+	+	CCONJ
ejpam-3329	125	12	n)t	n)t	PROPN
ejpam-3329	125	13	∗21	∗21	NUM
ejpam-3329	125	14	t	t	NOUN
ejpam-3329	125	15	2	2	NUM
ejpam-3329	125	16	1	1	NUM
ejpam-3329	125	17	+	+	CCONJ
ejpam-3329	125	18	nt	not	PART
ejpam-3329	125	19	∗1	∗1	PROPN
ejpam-3329	125	20	t1	t1	NOUN
ejpam-3329	125	21	0	0	NUM
ejpam-3329	125	22	0	0	NUM
ejpam-3329	125	23	0	0	NUM
ejpam-3329	125	24	)	)	PUNCT
ejpam-3329	125	25	≥	≥	NOUN
ejpam-3329	125	26	0	0	NUM
ejpam-3329	126	1	this	this	PRON
ejpam-3329	126	2	implies	imply	VERB
ejpam-3329	126	3	t	t	PROPN
ejpam-3329	126	4	∗2+n1	∗2+n1	PROPN
ejpam-3329	126	5	t	t	PROPN
ejpam-3329	126	6	2+n	2+n	NUM
ejpam-3329	126	7	1	1	NUM
ejpam-3329	126	8	−	−	PROPN
ejpam-3329	126	9	(	(	PUNCT
ejpam-3329	126	10	1	1	NUM
ejpam-3329	126	11	+	+	CCONJ
ejpam-3329	126	12	n)t	n)t	PROPN
ejpam-3329	126	13	∗21	∗21	NUM
ejpam-3329	126	14	t	t	NOUN
ejpam-3329	126	15	2	2	NUM
ejpam-3329	126	16	1	1	NUM
ejpam-3329	126	17	+	+	CCONJ
ejpam-3329	126	18	nt	not	PART
ejpam-3329	126	19	∗1	∗1	PROPN
ejpam-3329	126	20	t1	t1	PROPN
ejpam-3329	126	21	≥	≥	NOUN
ejpam-3329	126	22	0	0	NUM
ejpam-3329	127	1	so	so	ADV
ejpam-3329	127	2	t1	t1	PROPN
ejpam-3329	127	3	is	be	AUX
ejpam-3329	127	4	quasi	quasi	ADJ
ejpam-3329	127	5	n	n	CCONJ
ejpam-3329	127	6	-	-	PUNCT
ejpam-3329	127	7	class	class	NOUN
ejpam-3329	127	8	q	q	NOUN
ejpam-3329	127	9	operator	operator	NOUN
ejpam-3329	127	10	on	on	ADP
ejpam-3329	127	11	ran(t	ran(t	PROPN
ejpam-3329	127	12	)	)	PUNCT
ejpam-3329	127	13	.	.	PUNCT
ejpam-3329	128	1	also	also	ADV
ejpam-3329	128	2	for	for	ADP
ejpam-3329	128	3	any	any	DET
ejpam-3329	128	4	x	x	SYM
ejpam-3329	128	5	=	=	SYM
ejpam-3329	128	6	(	(	PUNCT
ejpam-3329	128	7	x1	x1	PROPN
ejpam-3329	128	8	,	,	PUNCT
ejpam-3329	128	9	x2	x2	PROPN
ejpam-3329	128	10	)	)	PUNCT
ejpam-3329	128	11	∈	∈	PROPN
ejpam-3329	128	12	h	h	NOUN
ejpam-3329	128	13	,	,	PUNCT
ejpam-3329	128	14	〈	〈	PROPN
ejpam-3329	128	15	t	t	PROPN
ejpam-3329	128	16	k3	k3	VERB
ejpam-3329	128	17	x2	x2	PROPN
ejpam-3329	128	18	,	,	PUNCT
ejpam-3329	129	1	x2	x2	PROPN
ejpam-3329	129	2	〉	〉	NOUN
ejpam-3329	129	3	=	=	SYM
ejpam-3329	129	4	〈	〈	PROPN
ejpam-3329	129	5	t	t	PROPN
ejpam-3329	129	6	k(i	k(i	PROPN
ejpam-3329	129	7	−	−	PROPN
ejpam-3329	129	8	p	p	NOUN
ejpam-3329	129	9	)	)	PUNCT
ejpam-3329	129	10	x	x	NOUN
ejpam-3329	129	11	,	,	PUNCT
ejpam-3329	129	12	(	(	PUNCT
ejpam-3329	129	13	i	i	PRON
ejpam-3329	129	14	−	−	PROPN
ejpam-3329	130	1	p	p	NOUN
ejpam-3329	130	2	)	)	PUNCT
ejpam-3329	130	3	x	x	NOUN
ejpam-3329	130	4	〉	〉	NOUN
ejpam-3329	130	5	=	=	SYM
ejpam-3329	130	6	〈	〈	PROPN
ejpam-3329	130	7	(	(	PUNCT
ejpam-3329	130	8	i	i	PRON
ejpam-3329	130	9	−	−	PROPN
ejpam-3329	130	10	p	p	NOUN
ejpam-3329	130	11	)	)	PUNCT
ejpam-3329	130	12	x	x	PROPN
ejpam-3329	130	13	,	,	PUNCT
ejpam-3329	130	14	t	t	PROPN
ejpam-3329	130	15	∗k(i	∗k(i	PROPN
ejpam-3329	130	16	−	−	PROPN
ejpam-3329	130	17	p	p	NOUN
ejpam-3329	130	18	)	)	PUNCT
ejpam-3329	130	19	x	x	NOUN
ejpam-3329	130	20	〉	〉	NUM
ejpam-3329	130	21	=	=	SYM
ejpam-3329	130	22	0	0	NUM
ejpam-3329	131	1	this	this	PRON
ejpam-3329	131	2	implies	imply	VERB
ejpam-3329	131	3	t3	t3	PROPN
ejpam-3329	131	4	=	=	SYM
ejpam-3329	131	5	0	0	NUM
ejpam-3329	131	6	since	since	SCONJ
ejpam-3329	131	7	σ(t	σ(t	PROPN
ejpam-3329	131	8	)	)	PUNCT
ejpam-3329	131	9	∪	∪	ADP
ejpam-3329	131	10	τ	τ	X
ejpam-3329	131	11	=	=	SYM
ejpam-3329	131	12	σ(t1	σ(t1	NOUN
ejpam-3329	131	13	)	)	PUNCT
ejpam-3329	131	14	∪	∪	ADJ
ejpam-3329	131	15	σ(t3	σ(t3	NOUN
ejpam-3329	131	16	)	)	PUNCT
ejpam-3329	131	17	where	where	SCONJ
ejpam-3329	131	18	τ	τ	PROPN
ejpam-3329	131	19	is	be	AUX
ejpam-3329	131	20	the	the	DET
ejpam-3329	131	21	union	union	NOUN
ejpam-3329	131	22	of	of	ADP
ejpam-3329	131	23	certain	certain	ADJ
ejpam-3329	131	24	holes	hole	NOUN
ejpam-3329	131	25	in	in	ADP
ejpam-3329	131	26	σ(t	σ(t	PROPN
ejpam-3329	131	27	)	)	PUNCT
ejpam-3329	131	28	,	,	PUNCT
ejpam-3329	131	29	which	which	PRON
ejpam-3329	131	30	happens	happen	VERB
ejpam-3329	131	31	to	to	PART
ejpam-3329	131	32	be	be	AUX
ejpam-3329	131	33	a	a	DET
ejpam-3329	131	34	subset	subset	NOUN
ejpam-3329	131	35	of	of	ADP
ejpam-3329	131	36	σ(t1)∩σ(t3	σ(t1)∩σ(t3	NOUN
ejpam-3329	131	37	)	)	PUNCT
ejpam-3329	132	1	[	[	X
ejpam-3329	132	2	by	by	ADP
ejpam-3329	132	3	corollary	corollary	ADJ
ejpam-3329	132	4	7	7	NUM
ejpam-3329	132	5	,	,	PUNCT
ejpam-3329	132	6	[	[	X
ejpam-3329	132	7	10	10	NUM
ejpam-3329	132	8	]	]	SYM
ejpam-3329	132	9	]	]	PUNCT
ejpam-3329	132	10	.	.	PUNCT
ejpam-3329	132	11	σ(t3	σ(t3	PROPN
ejpam-3329	132	12	)	)	PUNCT
ejpam-3329	132	13	=	=	SYM
ejpam-3329	132	14	0	0	NUM
ejpam-3329	132	15	and	and	CCONJ
ejpam-3329	132	16	σ(t1)∩σ(t3	σ(t1)∩σ(t3	NOUN
ejpam-3329	132	17	)	)	PUNCT
ejpam-3329	132	18	has	have	VERB
ejpam-3329	132	19	no	no	DET
ejpam-3329	132	20	interior	interior	ADJ
ejpam-3329	132	21	points	point	NOUN
ejpam-3329	132	22	we	we	PRON
ejpam-3329	132	23	have	have	VERB
ejpam-3329	132	24	σ(t	σ(t	NOUN
ejpam-3329	132	25	)	)	PUNCT
ejpam-3329	133	1	=	=	SYM
ejpam-3329	133	2	σ(t1	σ(t1	X
ejpam-3329	133	3	)	)	PUNCT
ejpam-3329	133	4	∪	∪	X
ejpam-3329	133	5	{	{	PUNCT
ejpam-3329	133	6	0	0	NUM
ejpam-3329	133	7	}	}	PUNCT
ejpam-3329	133	8	.	.	PUNCT
ejpam-3329	134	1	suppose	suppose	VERB
ejpam-3329	134	2	that	that	SCONJ
ejpam-3329	134	3	t	t	NOUN
ejpam-3329	134	4	=	=	PUNCT
ejpam-3329	134	5	(	(	PUNCT
ejpam-3329	134	6	t1	t1	PROPN
ejpam-3329	134	7	t2	t2	PROPN
ejpam-3329	134	8	0	0	NUM
ejpam-3329	134	9	t3	t3	PROPN
ejpam-3329	134	10	)	)	PUNCT
ejpam-3329	134	11	on	on	ADP
ejpam-3329	134	12	h	h	NOUN
ejpam-3329	134	13	=	=	SYM
ejpam-3329	134	14	ran(t	ran(t	PROPN
ejpam-3329	135	1	)	)	PUNCT
ejpam-3329	135	2	⊕	⊕	PROPN
ejpam-3329	135	3	kert	kert	PROPN
ejpam-3329	135	4	∗	∗	PROPN
ejpam-3329	135	5	where	where	SCONJ
ejpam-3329	135	6	t1	t1	NOUN
ejpam-3329	135	7	is	be	AUX
ejpam-3329	135	8	quasi	quasi	ADJ
ejpam-3329	135	9	n	n	CCONJ
ejpam-3329	135	10	-	-	PUNCT
ejpam-3329	135	11	class	class	NOUN
ejpam-3329	135	12	q	q	NOUN
ejpam-3329	135	13	operator	operator	NOUN
ejpam-3329	135	14	on	on	ADP
ejpam-3329	135	15	ran(t	ran(t	PROPN
ejpam-3329	135	16	)	)	PUNCT
ejpam-3329	135	17	and	and	CCONJ
ejpam-3329	135	18	t3	t3	PROPN
ejpam-3329	135	19	=	=	SYM
ejpam-3329	135	20	0	0	PROPN
ejpam-3329	135	21	t	t	PROPN
ejpam-3329	135	22	2+n	2+n	NUM
ejpam-3329	135	23	=	=	SYM
ejpam-3329	135	24	(	(	PUNCT
ejpam-3329	135	25	t	t	PROPN
ejpam-3329	135	26	2+n	2+n	NUM
ejpam-3329	135	27	1	1	NUM
ejpam-3329	135	28	∑1+n	∑1+n	PROPN
ejpam-3329	135	29	j=0	j=0	PROPN
ejpam-3329	135	30	t	t	PROPN
ejpam-3329	135	31	j	j	PROPN
ejpam-3329	135	32	1t2	1t2	NUM
ejpam-3329	135	33	t	t	NOUN
ejpam-3329	135	34	n+1−j	n+1−j	PROPN
ejpam-3329	135	35	3	3	NUM
ejpam-3329	135	36	0	0	NUM
ejpam-3329	135	37	t	t	PROPN
ejpam-3329	135	38	2+n	2+n	NUM
ejpam-3329	135	39	3	3	NUM
ejpam-3329	135	40	)	)	PUNCT
ejpam-3329	135	41	and	and	CCONJ
ejpam-3329	135	42	t	t	NOUN
ejpam-3329	135	43	∗2+n	∗2+n	NOUN
ejpam-3329	135	44	=	=	SYM
ejpam-3329	135	45	(	(	PUNCT
ejpam-3329	135	46	t	t	PROPN
ejpam-3329	135	47	∗2+n1	∗2+n1	PROPN
ejpam-3329	135	48	0	0	NUM
ejpam-3329	135	49	(	(	PUNCT
ejpam-3329	135	50	∑n+1	∑n+1	NOUN
ejpam-3329	135	51	j=0	j=0	PROPN
ejpam-3329	135	52	t	t	PROPN
ejpam-3329	135	53	j	j	PROPN
ejpam-3329	135	54	1t2	1t2	NUM
ejpam-3329	135	55	t	t	NOUN
ejpam-3329	135	56	n+1−j	n+1−j	PROPN
ejpam-3329	135	57	3	3	NUM
ejpam-3329	135	58	)	)	PUNCT
ejpam-3329	135	59	∗	∗	NOUN
ejpam-3329	135	60	t	t	PROPN
ejpam-3329	135	61	∗2+n3	∗2+n3	PROPN
ejpam-3329	135	62	)	)	PUNCT
ejpam-3329	135	63	since	since	SCONJ
ejpam-3329	135	64	t3	t3	PROPN
ejpam-3329	135	65	=	=	SYM
ejpam-3329	135	66	0	0	PROPN
ejpam-3329	135	67	t	t	NOUN
ejpam-3329	135	68	∗2+nt	∗2+nt	VERB
ejpam-3329	135	69	2+n	2+n	NUM
ejpam-3329	135	70	−	−	PROPN
ejpam-3329	135	71	(	(	PUNCT
ejpam-3329	135	72	1	1	NUM
ejpam-3329	135	73	+	+	CCONJ
ejpam-3329	135	74	n)t	n)t	PROPN
ejpam-3329	135	75	∗2	∗2	PROPN
ejpam-3329	135	76	t	t	PROPN
ejpam-3329	135	77	2	2	NUM
ejpam-3329	135	78	+	+	CCONJ
ejpam-3329	135	79	nt	not	PART
ejpam-3329	135	80	∗t	∗t	PROPN
ejpam-3329	135	81	=	=	SYM
ejpam-3329	135	82	(	(	PUNCT
ejpam-3329	135	83	t	t	PROPN
ejpam-3329	135	84	∗2+n1	∗2+n1	PROPN
ejpam-3329	135	85	t	t	PROPN
ejpam-3329	135	86	2+n	2+n	NUM
ejpam-3329	135	87	1	1	NUM
ejpam-3329	135	88	−	−	PROPN
ejpam-3329	135	89	(	(	PUNCT
ejpam-3329	135	90	1	1	NUM
ejpam-3329	135	91	+	+	CCONJ
ejpam-3329	135	92	n)t	n)t	PROPN
ejpam-3329	135	93	∗21	∗21	NUM
ejpam-3329	135	94	t	t	NOUN
ejpam-3329	135	95	2	2	NUM
ejpam-3329	135	96	1	1	NUM
ejpam-3329	135	97	+	+	CCONJ
ejpam-3329	135	98	nt	not	PART
ejpam-3329	135	99	∗1	∗1	PROPN
ejpam-3329	135	100	t1	t1	NOUN
ejpam-3329	135	101	x	x	X
ejpam-3329	135	102	x∗	x∗	PROPN
ejpam-3329	135	103	y	y	PROPN
ejpam-3329	135	104	)	)	PUNCT
ejpam-3329	135	105	≥	≥	NOUN
ejpam-3329	135	106	0	0	NUM
ejpam-3329	136	1	where	where	SCONJ
ejpam-3329	136	2	x	x	X
ejpam-3329	136	3	=	=	SYM
ejpam-3329	136	4	t	t	PROPN
ejpam-3329	136	5	∗2+n1	∗2+n1	PROPN
ejpam-3329	136	6	t	t	PROPN
ejpam-3329	136	7	1+n	1+n	NUM
ejpam-3329	136	8	1	1	NUM
ejpam-3329	136	9	t2	t2	NOUN
ejpam-3329	136	10	−	−	PROPN
ejpam-3329	136	11	(	(	PUNCT
ejpam-3329	136	12	1	1	NUM
ejpam-3329	136	13	+	+	CCONJ
ejpam-3329	136	14	n)t	n)t	ADJ
ejpam-3329	136	15	∗21	∗21	NOUN
ejpam-3329	136	16	t1t2	t1t2	NOUN
ejpam-3329	136	17	+	+	CCONJ
ejpam-3329	136	18	nt	not	PART
ejpam-3329	136	19	∗1	∗1	PROPN
ejpam-3329	136	20	t2	t2	PROPN
ejpam-3329	136	21	y	y	PROPN
ejpam-3329	136	22	=	=	SYM
ejpam-3329	136	23	(	(	PUNCT
ejpam-3329	136	24	t	t	PROPN
ejpam-3329	136	25	∗2	∗2	PROPN
ejpam-3329	136	26	t	t	PROPN
ejpam-3329	136	27	∗1+n	∗1+n	PROPN
ejpam-3329	136	28	1	1	NUM
ejpam-3329	136	29	t	t	PROPN
ejpam-3329	136	30	2+n	2+n	NUM
ejpam-3329	136	31	1	1	NUM
ejpam-3329	136	32	)	)	PUNCT
ejpam-3329	136	33	(	(	PUNCT
ejpam-3329	136	34	t	t	PROPN
ejpam-3329	136	35	∗2+n1	∗2+n1	PROPN
ejpam-3329	136	36	t	t	PROPN
ejpam-3329	136	37	1+n	1+n	NUM
ejpam-3329	136	38	1	1	NUM
ejpam-3329	136	39	t2)−	t2)−	NOUN
ejpam-3329	136	40	(	(	PUNCT
ejpam-3329	136	41	1	1	NUM
ejpam-3329	136	42	+	+	CCONJ
ejpam-3329	136	43	n)t	n)t	PROPN
ejpam-3329	136	44	∗2	∗2	PROPN
ejpam-3329	136	45	t	t	NOUN
ejpam-3329	136	46	∗	∗	NOUN
ejpam-3329	136	47	1	1	NUM
ejpam-3329	136	48	t1t2	t1t2	ADP
ejpam-3329	136	49	+	+	ADJ
ejpam-3329	136	50	nt	not	PART
ejpam-3329	136	51	∗2	∗2	PROPN
ejpam-3329	136	52	t2	t2	NOUN
ejpam-3329	136	53	we	we	PRON
ejpam-3329	136	54	know	know	VERB
ejpam-3329	136	55	that	that	PRON
ejpam-3329	136	56	,	,	PUNCT
ejpam-3329	136	57	”	"	PUNCT
ejpam-3329	136	58	if	if	SCONJ
ejpam-3329	136	59	a	a	PRON
ejpam-3329	136	60	is	be	AUX
ejpam-3329	136	61	a	a	DET
ejpam-3329	136	62	matrix	matrix	NOUN
ejpam-3329	136	63	of	of	ADP
ejpam-3329	136	64	the	the	DET
ejpam-3329	136	65	form	form	NOUN
ejpam-3329	136	66	(	(	PUNCT
ejpam-3329	136	67	a	a	DET
ejpam-3329	136	68	b	b	NOUN
ejpam-3329	136	69	b∗	b∗	ADJ
ejpam-3329	136	70	c	c	NOUN
ejpam-3329	136	71	)	)	PUNCT
ejpam-3329	136	72	≥	≥	NOUN
ejpam-3329	136	73	0	0	PUNCT
ejpam-3329	137	1	if	if	SCONJ
ejpam-3329	137	2	and	and	CCONJ
ejpam-3329	137	3	only	only	ADV
ejpam-3329	137	4	if	if	SCONJ
ejpam-3329	137	5	a	a	DET
ejpam-3329	137	6	≥	≥	NOUN
ejpam-3329	137	7	0	0	NUM
ejpam-3329	137	8	,	,	PUNCT
ejpam-3329	137	9	c	c	X
ejpam-3329	137	10	≥	≥	NUM
ejpam-3329	137	11	0	0	NUM
ejpam-3329	137	12	and	and	CCONJ
ejpam-3329	137	13	b	b	X
ejpam-3329	137	14	=	=	PUNCT
ejpam-3329	137	15	a	a	DET
ejpam-3329	137	16	1	1	NUM
ejpam-3329	137	17	2wc	2wc	ADJ
ejpam-3329	137	18	1	1	NUM
ejpam-3329	137	19	2	2	NUM
ejpam-3329	137	20	for	for	ADP
ejpam-3329	137	21	some	some	DET
ejpam-3329	137	22	contraction	contraction	NOUN
ejpam-3329	137	23	w	w	INTJ
ejpam-3329	137	24	.	.	PUNCT
ejpam-3329	138	1	since	since	SCONJ
ejpam-3329	138	2	t1	t1	PROPN
ejpam-3329	138	3	is	be	AUX
ejpam-3329	138	4	quasi	quasi	ADJ
ejpam-3329	138	5	n	n	CCONJ
ejpam-3329	138	6	-	-	PUNCT
ejpam-3329	138	7	class	class	NOUN
ejpam-3329	138	8	q	q	NOUN
ejpam-3329	138	9	operator	operator	NOUN
ejpam-3329	138	10	,	,	PUNCT
ejpam-3329	138	11	then	then	ADV
ejpam-3329	138	12	we	we	PRON
ejpam-3329	138	13	have	have	AUX
ejpam-3329	138	14	t	t	X
ejpam-3329	138	15	∗2+nt	∗2+nt	VERB
ejpam-3329	138	16	2+n	2+n	NUM
ejpam-3329	138	17	−	−	PROPN
ejpam-3329	138	18	(	(	PUNCT
ejpam-3329	138	19	1	1	NUM
ejpam-3329	138	20	+	+	CCONJ
ejpam-3329	138	21	n)t	n)t	PROPN
ejpam-3329	138	22	∗2	∗2	PROPN
ejpam-3329	138	23	t	t	PROPN
ejpam-3329	138	24	2	2	NUM
ejpam-3329	138	25	+	+	CCONJ
ejpam-3329	138	26	nt	not	PART
ejpam-3329	138	27	∗t	∗t	ADJ
ejpam-3329	138	28	≥	≥	NUM
ejpam-3329	138	29	0	0	NUM
ejpam-3329	138	30	.	.	PUNCT
ejpam-3329	139	1	hence	hence	ADV
ejpam-3329	139	2	t	t	PROPN
ejpam-3329	139	3	is	be	AUX
ejpam-3329	139	4	quasi	quasi	ADJ
ejpam-3329	139	5	n	n	CCONJ
ejpam-3329	139	6	-	-	PUNCT
ejpam-3329	139	7	class	class	NOUN
ejpam-3329	139	8	q	q	NOUN
ejpam-3329	139	9	operator	operator	NOUN
ejpam-3329	139	10	.	.	PUNCT
ejpam-3329	140	1	theorem	theorem	VERB
ejpam-3329	140	2	9	9	NUM
ejpam-3329	140	3	.	.	PUNCT
ejpam-3329	141	1	let	let	VERB
ejpam-3329	141	2	m	m	PRON
ejpam-3329	141	3	be	be	AUX
ejpam-3329	141	4	a	a	DET
ejpam-3329	141	5	closed	closed	ADJ
ejpam-3329	141	6	t	t	NOUN
ejpam-3329	141	7	-invariant	-invariant	ADJ
ejpam-3329	141	8	subspace	subspace	NOUN
ejpam-3329	141	9	of	of	ADP
ejpam-3329	141	10	h.	h.	PROPN
ejpam-3329	141	11	then	then	ADV
ejpam-3329	141	12	the	the	DET
ejpam-3329	141	13	restriction	restriction	NOUN
ejpam-3329	141	14	t	t	NOUN
ejpam-3329	141	15	|m	|m	NOUN
ejpam-3329	141	16	of	of	ADP
ejpam-3329	141	17	a	a	DET
ejpam-3329	141	18	quasi	quasi	ADJ
ejpam-3329	141	19	n	n	CCONJ
ejpam-3329	141	20	-	-	PUNCT
ejpam-3329	141	21	class	class	NOUN
ejpam-3329	141	22	q	q	NOUN
ejpam-3329	141	23	operator	operator	NOUN
ejpam-3329	141	24	t	t	PROPN
ejpam-3329	141	25	to	to	ADP
ejpam-3329	141	26	m	m	PROPN
ejpam-3329	141	27	is	be	AUX
ejpam-3329	141	28	quasi	quasi	ADJ
ejpam-3329	141	29	n	n	CCONJ
ejpam-3329	141	30	-	-	PUNCT
ejpam-3329	141	31	class	class	NOUN
ejpam-3329	141	32	q	q	NOUN
ejpam-3329	141	33	operator	operator	NOUN
ejpam-3329	141	34	.	.	PUNCT
ejpam-3329	142	1	proof	proof	NOUN
ejpam-3329	142	2	.	.	PUNCT
ejpam-3329	143	1	let	let	VERB
ejpam-3329	143	2	t	t	NOUN
ejpam-3329	143	3	=	=	SYM
ejpam-3329	143	4	(	(	PUNCT
ejpam-3329	143	5	t1	t1	PROPN
ejpam-3329	143	6	t2	t2	PROPN
ejpam-3329	143	7	0	0	NUM
ejpam-3329	143	8	t3	t3	PROPN
ejpam-3329	143	9	)	)	PUNCT
ejpam-3329	143	10	on	on	ADP
ejpam-3329	143	11	h	h	NOUN
ejpam-3329	143	12	=	=	NOUN
ejpam-3329	143	13	m	m	PROPN
ejpam-3329	143	14	⊕m⊥.	⊕m⊥.	PROPN
ejpam-3329	143	15	since	since	SCONJ
ejpam-3329	143	16	t	t	PROPN
ejpam-3329	143	17	is	be	AUX
ejpam-3329	143	18	quasi	quasi	ADJ
ejpam-3329	143	19	n	n	CCONJ
ejpam-3329	143	20	-	-	PUNCT
ejpam-3329	143	21	class	class	NOUN
ejpam-3329	143	22	q	q	NOUN
ejpam-3329	143	23	operator	operator	NOUN
ejpam-3329	143	24	then	then	ADV
ejpam-3329	143	25	by	by	ADP
ejpam-3329	143	26	theorem	theorem	NOUN
ejpam-3329	143	27	8	8	NUM
ejpam-3329	143	28	,	,	PUNCT
ejpam-3329	143	29	we	we	PRON
ejpam-3329	143	30	have	have	VERB
ejpam-3329	143	31	t	t	NOUN
ejpam-3329	143	32	|m	|m	NOUN
ejpam-3329	143	33	is	be	AUX
ejpam-3329	143	34	also	also	ADV
ejpam-3329	143	35	quasi	quasi	ADJ
ejpam-3329	143	36	n	n	CCONJ
ejpam-3329	143	37	-	-	PUNCT
ejpam-3329	143	38	class	class	NOUN
ejpam-3329	143	39	q	q	NOUN
ejpam-3329	143	40	operator	operator	NOUN
ejpam-3329	143	41	.	.	PUNCT
ejpam-3329	144	1	theorem	theorem	VERB
ejpam-3329	144	2	10	10	NUM
ejpam-3329	144	3	.	.	PUNCT
ejpam-3329	145	1	let	let	VERB
ejpam-3329	145	2	t	t	NOUN
ejpam-3329	145	3	be	be	AUX
ejpam-3329	145	4	a	a	DET
ejpam-3329	145	5	regular	regular	ADJ
ejpam-3329	145	6	quasi	quasi	NOUN
ejpam-3329	145	7	n	n	PRON
ejpam-3329	145	8	class	class	NOUN
ejpam-3329	145	9	q	q	NOUN
ejpam-3329	145	10	operator	operator	NOUN
ejpam-3329	145	11	,	,	PUNCT
ejpam-3329	145	12	then	then	ADV
ejpam-3329	145	13	the	the	DET
ejpam-3329	145	14	approximate	approximate	ADJ
ejpam-3329	145	15	point	point	NOUN
ejpam-3329	145	16	spectrum	spectrum	NOUN
ejpam-3329	145	17	lies	lie	VERB
ejpam-3329	145	18	in	in	ADP
ejpam-3329	145	19	the	the	DET
ejpam-3329	145	20	disc	disc	NOUN
ejpam-3329	145	21	d.	d.	PROPN
ejpam-3329	145	22	senthilkumar	senthilkumar	PROPN
ejpam-3329	145	23	,	,	PUNCT
ejpam-3329	145	24	s.	s.	PROPN
ejpam-3329	145	25	parvatham	parvatham	PROPN
ejpam-3329	145	26	/	/	SYM
ejpam-3329	145	27	eur	eur	PROPN
ejpam-3329	145	28	.	.	PUNCT
ejpam-3329	146	1	j.	j.	PROPN
ejpam-3329	146	2	pure	pure	PROPN
ejpam-3329	146	3	appl	appl	PROPN
ejpam-3329	146	4	.	.	PROPN
ejpam-3329	146	5	math	math	PROPN
ejpam-3329	146	6	,	,	PUNCT
ejpam-3329	146	7	11	11	NUM
ejpam-3329	146	8	(	(	PUNCT
ejpam-3329	146	9	4	4	NUM
ejpam-3329	146	10	)	)	PUNCT
ejpam-3329	146	11	(	(	PUNCT
ejpam-3329	146	12	2018	2018	NUM
ejpam-3329	146	13	)	)	PUNCT
ejpam-3329	146	14	,	,	PUNCT
ejpam-3329	146	15	1108	1108	NUM
ejpam-3329	146	16	-	-	SYM
ejpam-3329	146	17	1129	1129	NUM
ejpam-3329	146	18	1113	1113	NUM
ejpam-3329	146	19	σap(t	σap(t	NOUN
ejpam-3329	146	20	)	)	PUNCT
ejpam-3329	147	1	⊆	⊆	NUM
ejpam-3329	147	2	{	{	PUNCT
ejpam-3329	147	3	λ	λ	X
ejpam-3329	147	4	∈	∈	PROPN
ejpam-3329	147	5	c	c	NOUN
ejpam-3329	147	6	:	:	PUNCT
ejpam-3329	147	7	(	(	PUNCT
ejpam-3329	147	8	1+n	1+n	NUM
ejpam-3329	147	9	)	)	PUNCT
ejpam-3329	147	10	1	1	NUM
ejpam-3329	147	11	2	2	NUM
ejpam-3329	147	12	‖t−2‖(‖t	‖t−2‖(‖t	PROPN
ejpam-3329	147	13	1+n‖2+n	1+n‖2+n	NUM
ejpam-3329	147	14	)	)	PUNCT
ejpam-3329	147	15	1	1	NUM
ejpam-3329	147	16	2	2	NUM
ejpam-3329	147	17	≤	≤	NUM
ejpam-3329	147	18	|λ|	|λ|	NOUN
ejpam-3329	147	19	≤	≤	NOUN
ejpam-3329	147	20	‖t‖	‖t‖	PROPN
ejpam-3329	147	21	proof	proof	NOUN
ejpam-3329	147	22	.	.	PUNCT
ejpam-3329	148	1	suppose	suppose	VERB
ejpam-3329	148	2	t	t	PROPN
ejpam-3329	148	3	is	be	AUX
ejpam-3329	148	4	regular	regular	ADJ
ejpam-3329	148	5	quasi	quasi	NOUN
ejpam-3329	148	6	n	n	PRON
ejpam-3329	148	7	class	class	NOUN
ejpam-3329	148	8	q	q	NOUN
ejpam-3329	148	9	operator	operator	NOUN
ejpam-3329	148	10	,	,	PUNCT
ejpam-3329	148	11	then	then	ADV
ejpam-3329	148	12	for	for	ADP
ejpam-3329	148	13	every	every	DET
ejpam-3329	148	14	unit	unit	NOUN
ejpam-3329	148	15	vector	vector	NOUN
ejpam-3329	148	16	x	x	PUNCT
ejpam-3329	148	17	in	in	ADP
ejpam-3329	148	18	h	h	NOUN
ejpam-3329	148	19	,	,	PUNCT
ejpam-3329	148	20	we	we	PRON
ejpam-3329	148	21	have	have	AUX
ejpam-3329	148	22	‖x‖2	‖x‖2	VERB
ejpam-3329	148	23	≤	≤	NUM
ejpam-3329	149	1	‖t−2‖2‖t	‖t−2‖2‖t	NUM
ejpam-3329	149	2	2x‖2	2x‖2	NUM
ejpam-3329	149	3	≤	≤	ADJ
ejpam-3329	149	4	‖t	‖t	NOUN
ejpam-3329	149	5	−2‖2	−2‖2	SYM
ejpam-3329	149	6	1+n	1+n	NUM
ejpam-3329	149	7	(	(	PUNCT
ejpam-3329	149	8	‖t	‖t	NOUN
ejpam-3329	149	9	1+n‖2‖tx‖2	1+n‖2‖tx‖2	PROPN
ejpam-3329	149	10	+	+	NUM
ejpam-3329	149	11	n‖tx‖2	n‖tx‖2	PROPN
ejpam-3329	149	12	)	)	PUNCT
ejpam-3329	149	13	.	.	PUNCT
ejpam-3329	150	1	hence	hence	ADV
ejpam-3329	150	2	‖tx‖2	‖tx‖2	X
ejpam-3329	150	3	≥	≥	NUM
ejpam-3329	150	4	(	(	PUNCT
ejpam-3329	150	5	1+n)‖x‖2	1+n)‖x‖2	PROPN
ejpam-3329	150	6	‖t−2‖2(‖t	‖t−2‖2(‖t	SYM
ejpam-3329	150	7	1+n‖2+n	1+n‖2+n	NUM
ejpam-3329	150	8	)	)	PUNCT
ejpam-3329	150	9	.	.	PUNCT
ejpam-3329	151	1	now	now	ADV
ejpam-3329	151	2	assume	assume	VERB
ejpam-3329	151	3	that	that	SCONJ
ejpam-3329	151	4	λ	λ	PROPN
ejpam-3329	151	5	∈	∈	NOUN
ejpam-3329	151	6	σap(t	σap(t	PROPN
ejpam-3329	151	7	)	)	PUNCT
ejpam-3329	151	8	.	.	PUNCT
ejpam-3329	152	1	then	then	ADV
ejpam-3329	152	2	there	there	PRON
ejpam-3329	152	3	exists	exist	VERB
ejpam-3329	152	4	a	a	DET
ejpam-3329	152	5	sequence	sequence	NOUN
ejpam-3329	152	6	{	{	PUNCT
ejpam-3329	152	7	xm	xm	PROPN
ejpam-3329	152	8	}	}	PUNCT
ejpam-3329	152	9	,	,	PUNCT
ejpam-3329	152	10	‖xm‖	‖xm‖	NOUN
ejpam-3329	152	11	=	=	NOUN
ejpam-3329	152	12	1	1	NUM
ejpam-3329	152	13	such	such	ADJ
ejpam-3329	152	14	that	that	SCONJ
ejpam-3329	152	15	‖(t	‖(t	PUNCT
ejpam-3329	153	1	−	−	PROPN
ejpam-3329	153	2	λ)xm‖	λ)xm‖	PROPN
ejpam-3329	153	3	→	→	SYM
ejpam-3329	153	4	0	0	NUM
ejpam-3329	153	5	when	when	SCONJ
ejpam-3329	153	6	m	m	PROPN
ejpam-3329	153	7	→	→	SYM
ejpam-3329	153	8	∞	∞	NUM
ejpam-3329	153	9	we	we	PRON
ejpam-3329	153	10	have	have	VERB
ejpam-3329	153	11	‖txm	‖txm	PROPN
ejpam-3329	153	12	−	−	PROPN
ejpam-3329	153	13	λxm‖	λxm‖	X
ejpam-3329	153	14	≥	≥	X
ejpam-3329	153	15	‖txm‖	‖txm‖	NUM
ejpam-3329	153	16	−	−	PROPN
ejpam-3329	153	17	|λ|‖xm‖	|λ|‖xm‖	PROPN
ejpam-3329	153	18	≥	≥	NUM
ejpam-3329	153	19	(	(	PUNCT
ejpam-3329	153	20	1+n)1/2	1+n)1/2	NUM
ejpam-3329	153	21	‖t−2‖(‖t	‖t−2‖(‖t	PROPN
ejpam-3329	153	22	1+n‖2+n)1/2	1+n‖2+n)1/2	NUM
ejpam-3329	153	23	−	−	PROPN
ejpam-3329	153	24	|λ|	|λ|	PROPN
ejpam-3329	153	25	.	.	PUNCT
ejpam-3329	154	1	now	now	ADV
ejpam-3329	154	2	,	,	PUNCT
ejpam-3329	154	3	when	when	SCONJ
ejpam-3329	154	4	m→∞	m→∞	NOUN
ejpam-3329	154	5	,	,	PUNCT
ejpam-3329	154	6	|λ|	|λ|	NOUN
ejpam-3329	154	7	≥	≥	NUM
ejpam-3329	154	8	(	(	PUNCT
ejpam-3329	154	9	1+n)1/2	1+n)1/2	NUM
ejpam-3329	154	10	‖t−2‖(‖t	‖t−2‖(‖t	PROPN
ejpam-3329	154	11	1+n‖2+n)1/2	1+n‖2+n)1/2	NUM
ejpam-3329	154	12	3	3	NUM
ejpam-3329	154	13	.	.	PUNCT
ejpam-3329	154	14	quasi	quasi	PROPN
ejpam-3329	154	15	n	n	CCONJ
ejpam-3329	154	16	-	-	PUNCT
ejpam-3329	154	17	class	class	NOUN
ejpam-3329	154	18	q∗	q∗	NOUN
ejpam-3329	154	19	operators	operator	NOUN
ejpam-3329	154	20	in	in	ADP
ejpam-3329	154	21	this	this	DET
ejpam-3329	154	22	section	section	NOUN
ejpam-3329	154	23	we	we	PRON
ejpam-3329	154	24	define	define	VERB
ejpam-3329	154	25	operators	operator	NOUN
ejpam-3329	154	26	of	of	ADP
ejpam-3329	154	27	quasi	quasi	ADJ
ejpam-3329	154	28	n	n	CCONJ
ejpam-3329	154	29	-	-	PUNCT
ejpam-3329	154	30	class	class	NOUN
ejpam-3329	154	31	q∗	q∗	NOUN
ejpam-3329	154	32	and	and	CCONJ
ejpam-3329	154	33	consider	consider	VERB
ejpam-3329	154	34	some	some	DET
ejpam-3329	154	35	basic	basic	ADJ
ejpam-3329	154	36	properties	property	NOUN
ejpam-3329	154	37	and	and	CCONJ
ejpam-3329	154	38	examples	example	NOUN
ejpam-3329	154	39	.	.	PUNCT
ejpam-3329	155	1	definition	definition	NOUN
ejpam-3329	155	2	2	2	NUM
ejpam-3329	155	3	.	.	PUNCT
ejpam-3329	156	1	an	an	DET
ejpam-3329	156	2	operator	operator	NOUN
ejpam-3329	156	3	t	t	NOUN
ejpam-3329	156	4	is	be	AUX
ejpam-3329	156	5	said	say	VERB
ejpam-3329	156	6	to	to	PART
ejpam-3329	156	7	be	be	AUX
ejpam-3329	156	8	quasi	quasi	ADJ
ejpam-3329	156	9	n	n	CCONJ
ejpam-3329	156	10	-	-	PUNCT
ejpam-3329	156	11	class	class	NOUN
ejpam-3329	156	12	q∗	q∗	NOUN
ejpam-3329	156	13	(	(	PUNCT
ejpam-3329	156	14	quasi	quasi	NOUN
ejpam-3329	156	15	*	*	ADJ
ejpam-3329	156	16	n	n	CCONJ
ejpam-3329	156	17	-	-	PUNCT
ejpam-3329	156	18	class	class	NOUN
ejpam-3329	156	19	q)if	q)if	PROPN
ejpam-3329	156	20	‖t	‖t	NOUN
ejpam-3329	156	21	∗tx‖2	∗tx‖2	VERB
ejpam-3329	156	22	≤	≤	NUM
ejpam-3329	156	23	1	1	NUM
ejpam-3329	156	24	1	1	NUM
ejpam-3329	156	25	+	+	NUM
ejpam-3329	156	26	n	n	CCONJ
ejpam-3329	156	27	(	(	PUNCT
ejpam-3329	156	28	‖t	‖t	PROPN
ejpam-3329	156	29	2+nx‖2	2+nx‖2	PROPN
ejpam-3329	156	30	+	+	NUM
ejpam-3329	156	31	n‖tx‖2	n‖tx‖2	PROPN
ejpam-3329	156	32	)	)	PUNCT
ejpam-3329	156	33	for	for	ADP
ejpam-3329	156	34	every	every	DET
ejpam-3329	156	35	x	x	SYM
ejpam-3329	156	36	∈	∈	PROPN
ejpam-3329	156	37	h	h	NOUN
ejpam-3329	156	38	and	and	CCONJ
ejpam-3329	156	39	every	every	DET
ejpam-3329	156	40	positive	positive	ADJ
ejpam-3329	156	41	integer	integer	NOUN
ejpam-3329	156	42	n.	n.	NOUN
ejpam-3329	156	43	when	when	SCONJ
ejpam-3329	156	44	n	n	PROPN
ejpam-3329	156	45	=	=	SYM
ejpam-3329	156	46	1	1	NUM
ejpam-3329	156	47	,	,	PUNCT
ejpam-3329	156	48	it	it	PRON
ejpam-3329	156	49	is	be	AUX
ejpam-3329	156	50	of	of	ADP
ejpam-3329	156	51	quasi	quasi	ADJ
ejpam-3329	156	52	class	class	NOUN
ejpam-3329	156	53	q∗	q∗	NOUN
ejpam-3329	156	54	(	(	PUNCT
ejpam-3329	156	55	quasi	quasi	NOUN
ejpam-3329	156	56	*	*	PUNCT
ejpam-3329	156	57	-class	-class	PROPN
ejpam-3329	156	58	q)operator	q)operator	NOUN
ejpam-3329	156	59	.	.	PUNCT
ejpam-3329	157	1	theorem	theorem	VERB
ejpam-3329	157	2	11	11	NUM
ejpam-3329	157	3	.	.	PUNCT
ejpam-3329	158	1	for	for	ADP
ejpam-3329	158	2	each	each	DET
ejpam-3329	158	3	positive	positive	ADJ
ejpam-3329	158	4	integer	integer	NOUN
ejpam-3329	158	5	n	n	CCONJ
ejpam-3329	158	6	,	,	PUNCT
ejpam-3329	158	7	t	t	PROPN
ejpam-3329	158	8	is	be	AUX
ejpam-3329	158	9	of	of	ADP
ejpam-3329	158	10	quasi	quasi	ADJ
ejpam-3329	158	11	n	n	CCONJ
ejpam-3329	158	12	-	-	PUNCT
ejpam-3329	158	13	class	class	NOUN
ejpam-3329	158	14	q∗	q∗	NOUN
ejpam-3329	158	15	operator	operator	NOUN
ejpam-3329	158	16	if	if	SCONJ
ejpam-3329	159	1	and	and	CCONJ
ejpam-3329	159	2	only	only	ADV
ejpam-3329	159	3	if	if	SCONJ
ejpam-3329	159	4	t	t	PROPN
ejpam-3329	159	5	∗(t	∗(t	NOUN
ejpam-3329	159	6	∗1+nt	∗1+nt	VERB
ejpam-3329	159	7	1+n	1+n	NUM
ejpam-3329	159	8	−	−	PROPN
ejpam-3329	159	9	(	(	PUNCT
ejpam-3329	159	10	1	1	NUM
ejpam-3329	159	11	+	+	CCONJ
ejpam-3329	159	12	n)tt	n)tt	ADJ
ejpam-3329	159	13	∗	∗	NOUN
ejpam-3329	159	14	+	+	CCONJ
ejpam-3329	159	15	ni)t	ni)t	PROPN
ejpam-3329	159	16	≥	≥	NOUN
ejpam-3329	159	17	0	0	NUM
ejpam-3329	159	18	.	.	PUNCT
ejpam-3329	160	1	for	for	ADP
ejpam-3329	160	2	example	example	NOUN
ejpam-3329	160	3	:	:	PUNCT
ejpam-3329	160	4	let	let	VERB
ejpam-3329	160	5	x	x	PUNCT
ejpam-3329	160	6	=	=	PRON
ejpam-3329	160	7	(	(	PUNCT
ejpam-3329	160	8	x1	x1	PROPN
ejpam-3329	160	9	,	,	PUNCT
ejpam-3329	160	10	x2	x2	PROPN
ejpam-3329	160	11	,	,	PUNCT
ejpam-3329	160	12	...	...	PUNCT
ejpam-3329	160	13	)	)	PUNCT
ejpam-3329	161	1	∈	∈	PROPN
ejpam-3329	161	2	l2	l2	NOUN
ejpam-3329	161	3	,	,	PUNCT
ejpam-3329	161	4	define	define	VERB
ejpam-3329	161	5	t	t	NOUN
ejpam-3329	161	6	:	:	PUNCT
ejpam-3329	161	7	l2	l2	NOUN
ejpam-3329	161	8	→	→	SYM
ejpam-3329	161	9	l2	l2	NOUN
ejpam-3329	161	10	by	by	ADP
ejpam-3329	161	11	t	t	PROPN
ejpam-3329	161	12	(	(	PUNCT
ejpam-3329	161	13	x	x	NOUN
ejpam-3329	161	14	)	)	PUNCT
ejpam-3329	161	15	=	=	SYM
ejpam-3329	161	16	(	(	PUNCT
ejpam-3329	161	17	0	0	NUM
ejpam-3329	161	18	,	,	PUNCT
ejpam-3329	161	19	x1	x1	PROPN
ejpam-3329	161	20	,	,	PUNCT
ejpam-3329	161	21	x2	x2	PROPN
ejpam-3329	161	22	,	,	PUNCT
ejpam-3329	161	23	...	...	PUNCT
ejpam-3329	161	24	)	)	PUNCT
ejpam-3329	161	25	,	,	PUNCT
ejpam-3329	161	26	t	t	PROPN
ejpam-3329	161	27	∗(x	∗(x	PROPN
ejpam-3329	161	28	)	)	PUNCT
ejpam-3329	161	29	=	=	SYM
ejpam-3329	161	30	(	(	PUNCT
ejpam-3329	161	31	x2	x2	PROPN
ejpam-3329	161	32	,	,	PUNCT
ejpam-3329	161	33	x3	x3	ADJ
ejpam-3329	161	34	,	,	PUNCT
ejpam-3329	161	35	...	...	PUNCT
ejpam-3329	161	36	)	)	PUNCT
ejpam-3329	161	37	.	.	PUNCT
ejpam-3329	162	1	then	then	ADV
ejpam-3329	162	2	t	t	PROPN
ejpam-3329	162	3	∗2+nt	∗2+nt	VERB
ejpam-3329	162	4	2+n	2+n	NUM
ejpam-3329	162	5	−	−	PROPN
ejpam-3329	163	1	(	(	PUNCT
ejpam-3329	163	2	1	1	NUM
ejpam-3329	163	3	+	+	CCONJ
ejpam-3329	163	4	n)(t	n)(t	PROPN
ejpam-3329	163	5	∗t	∗t	ADJ
ejpam-3329	163	6	)	)	PUNCT
ejpam-3329	163	7	2	2	NUM
ejpam-3329	163	8	+	+	CCONJ
ejpam-3329	163	9	nt	not	PART
ejpam-3329	163	10	∗t	∗t	ADJ
ejpam-3329	163	11	≥	≥	NUM
ejpam-3329	163	12	0	0	NUM
ejpam-3329	163	13	.	.	PUNCT
ejpam-3329	164	1	ie	ie	PROPN
ejpam-3329	164	2	t	t	PROPN
ejpam-3329	164	3	is	be	AUX
ejpam-3329	164	4	quasi	quasi	ADJ
ejpam-3329	164	5	n	n	CCONJ
ejpam-3329	164	6	-	-	PUNCT
ejpam-3329	164	7	class	class	NOUN
ejpam-3329	164	8	q∗.	q∗.	NOUN
ejpam-3329	164	9	from	from	ADP
ejpam-3329	164	10	the	the	DET
ejpam-3329	164	11	definition	definition	NOUN
ejpam-3329	164	12	of	of	ADP
ejpam-3329	164	13	n	n	CCONJ
ejpam-3329	164	14	-	-	PUNCT
ejpam-3329	164	15	class	class	NOUN
ejpam-3329	164	16	q∗	q∗	NOUN
ejpam-3329	164	17	operator	operator	NOUN
ejpam-3329	164	18	,	,	PUNCT
ejpam-3329	164	19	we	we	PRON
ejpam-3329	164	20	can	can	AUX
ejpam-3329	164	21	easily	easily	ADV
ejpam-3329	164	22	say	say	VERB
ejpam-3329	164	23	that	that	SCONJ
ejpam-3329	164	24	every	every	DET
ejpam-3329	164	25	operator	operator	NOUN
ejpam-3329	164	26	of	of	ADP
ejpam-3329	164	27	n	n	CCONJ
ejpam-3329	164	28	-	-	PUNCT
ejpam-3329	164	29	class	class	NOUN
ejpam-3329	164	30	q∗	q∗	NOUN
ejpam-3329	164	31	is	be	AUX
ejpam-3329	164	32	also	also	ADV
ejpam-3329	164	33	an	an	DET
ejpam-3329	164	34	operator	operator	NOUN
ejpam-3329	164	35	of	of	ADP
ejpam-3329	164	36	quasi	quasi	ADJ
ejpam-3329	164	37	n	n	CCONJ
ejpam-3329	164	38	-	-	PUNCT
ejpam-3329	164	39	class	class	NOUN
ejpam-3329	164	40	q∗.	q∗.	NOUN
ejpam-3329	164	41	hence	hence	ADV
ejpam-3329	164	42	we	we	PRON
ejpam-3329	164	43	have	have	VERB
ejpam-3329	164	44	the	the	DET
ejpam-3329	164	45	following	follow	VERB
ejpam-3329	164	46	implications	implication	NOUN
ejpam-3329	164	47	class	class	NOUN
ejpam-3329	164	48	q∗	q∗	PROPN
ejpam-3329	164	49	⊂	⊂	PROPN
ejpam-3329	164	50	n	n	CCONJ
ejpam-3329	164	51	-	-	PUNCT
ejpam-3329	164	52	class	class	NOUN
ejpam-3329	164	53	q∗	q∗	NOUN
ejpam-3329	164	54	⊂	⊂	PRON
ejpam-3329	164	55	quasi	quasi	ADJ
ejpam-3329	164	56	n	n	CCONJ
ejpam-3329	164	57	-	-	PUNCT
ejpam-3329	164	58	class	class	NOUN
ejpam-3329	164	59	q∗	q∗	NOUN
ejpam-3329	164	60	also	also	ADV
ejpam-3329	164	61	every	every	DET
ejpam-3329	164	62	quasi	quasi	ADJ
ejpam-3329	164	63	class	class	NOUN
ejpam-3329	164	64	q∗	q∗	NOUN
ejpam-3329	164	65	is	be	AUX
ejpam-3329	164	66	quasi	quasi	NOUN
ejpam-3329	164	67	n	n	CCONJ
ejpam-3329	164	68	-	-	PUNCT
ejpam-3329	164	69	class	class	NOUN
ejpam-3329	164	70	q∗	q∗	NOUN
ejpam-3329	164	71	,	,	PUNCT
ejpam-3329	164	72	but	but	CCONJ
ejpam-3329	164	73	the	the	DET
ejpam-3329	164	74	converse	converse	NOUN
ejpam-3329	164	75	is	be	AUX
ejpam-3329	164	76	not	not	PART
ejpam-3329	164	77	true	true	ADJ
ejpam-3329	164	78	and	and	CCONJ
ejpam-3329	164	79	every	every	DET
ejpam-3329	164	80	quasi	quasi	ADJ
ejpam-3329	164	81	n	n	CCONJ
ejpam-3329	164	82	-	-	PUNCT
ejpam-3329	164	83	class	class	NOUN
ejpam-3329	164	84	q∗	q∗	NOUN
ejpam-3329	164	85	is	be	AUX
ejpam-3329	164	86	quasi	quasi	NOUN
ejpam-3329	164	87	n+	n+	ADP
ejpam-3329	164	88	1	1	NUM
ejpam-3329	164	89	-	-	PUNCT
ejpam-3329	164	90	class	class	NOUN
ejpam-3329	164	91	q∗	q∗	NOUN
ejpam-3329	164	92	operator	operator	NOUN
ejpam-3329	164	93	.	.	PUNCT
ejpam-3329	165	1	again	again	ADV
ejpam-3329	165	2	,	,	PUNCT
ejpam-3329	165	3	if	if	SCONJ
ejpam-3329	165	4	t	t	PROPN
ejpam-3329	165	5	∈	∈	PROPN
ejpam-3329	165	6	b(h	b(h	PROPN
ejpam-3329	165	7	)	)	PUNCT
ejpam-3329	165	8	is	be	AUX
ejpam-3329	165	9	quasi	quasi	ADJ
ejpam-3329	165	10	n	n	CCONJ
ejpam-3329	165	11	-	-	PUNCT
ejpam-3329	165	12	class	class	NOUN
ejpam-3329	165	13	q∗	q∗	NOUN
ejpam-3329	165	14	then	then	ADV
ejpam-3329	165	15	αt	αt	NOUN
ejpam-3329	165	16	is	be	AUX
ejpam-3329	165	17	of	of	ADP
ejpam-3329	165	18	quasi	quasi	NOUN
ejpam-3329	165	19	n	n	CCONJ
ejpam-3329	165	20	-	-	PUNCT
ejpam-3329	165	21	class	class	NOUN
ejpam-3329	165	22	q∗	q∗	NOUN
ejpam-3329	165	23	operator	operator	NOUN
ejpam-3329	165	24	for	for	ADP
ejpam-3329	165	25	any	any	DET
ejpam-3329	165	26	complex	complex	ADJ
ejpam-3329	165	27	number	number	NOUN
ejpam-3329	165	28	α	α	NOUN
ejpam-3329	165	29	.	.	PUNCT
ejpam-3329	166	1	theorem	theorem	PROPN
ejpam-3329	166	2	12	12	NUM
ejpam-3329	166	3	.	.	PUNCT
ejpam-3329	167	1	let	let	VERB
ejpam-3329	167	2	t	t	PROPN
ejpam-3329	167	3	∈	∈	PROPN
ejpam-3329	167	4	b(h	b(h	PROPN
ejpam-3329	167	5	)	)	PUNCT
ejpam-3329	167	6	.	.	PUNCT
ejpam-3329	168	1	if	if	SCONJ
ejpam-3329	168	2	λ	λ	PROPN
ejpam-3329	168	3	−1	−1	NOUN
ejpam-3329	168	4	2	2	NUM
ejpam-3329	168	5	t	t	NOUN
ejpam-3329	168	6	is	be	AUX
ejpam-3329	168	7	an	an	DET
ejpam-3329	168	8	operator	operator	NOUN
ejpam-3329	168	9	of	of	ADP
ejpam-3329	168	10	quasi	quasi	ADJ
ejpam-3329	168	11	n	n	CCONJ
ejpam-3329	168	12	-	-	PUNCT
ejpam-3329	168	13	class	class	NOUN
ejpam-3329	168	14	q∗	q∗	NOUN
ejpam-3329	168	15	,	,	PUNCT
ejpam-3329	168	16	then	then	ADV
ejpam-3329	168	17	t	t	PROPN
ejpam-3329	168	18	is	be	AUX
ejpam-3329	168	19	quasi	quasi	ADJ
ejpam-3329	168	20	*	*	PUNCT
ejpam-3329	168	21	-n	-n	X
ejpam-3329	168	22	-	-	ADJ
ejpam-3329	168	23	paranormal	paranormal	ADJ
ejpam-3329	168	24	operator	operator	NOUN
ejpam-3329	168	25	for	for	ADP
ejpam-3329	168	26	all	all	DET
ejpam-3329	168	27	λ	λ	PROPN
ejpam-3329	168	28	>	>	X
ejpam-3329	168	29	0	0	X
ejpam-3329	168	30	.	.	PUNCT
ejpam-3329	169	1	proof	proof	NOUN
ejpam-3329	169	2	.	.	PUNCT
ejpam-3329	170	1	since	since	SCONJ
ejpam-3329	170	2	λ	λ	PROPN
ejpam-3329	170	3	−1	−1	NOUN
ejpam-3329	170	4	2	2	NUM
ejpam-3329	170	5	t	t	NOUN
ejpam-3329	170	6	is	be	AUX
ejpam-3329	170	7	an	an	DET
ejpam-3329	170	8	operator	operator	NOUN
ejpam-3329	170	9	of	of	ADP
ejpam-3329	170	10	quasi	quasi	ADJ
ejpam-3329	170	11	n	n	CCONJ
ejpam-3329	170	12	-	-	PUNCT
ejpam-3329	170	13	class	class	NOUN
ejpam-3329	170	14	q∗	q∗	NOUN
ejpam-3329	170	15	then	then	ADV
ejpam-3329	170	16	(	(	PUNCT
ejpam-3329	170	17	λ	λ	SYM
ejpam-3329	170	18	−1	−1	NOUN
ejpam-3329	170	19	2	2	NUM
ejpam-3329	170	20	t	t	NOUN
ejpam-3329	170	21	)	)	PUNCT
ejpam-3329	170	22	∗(2+n)(λ	∗(2+n)(λ	NOUN
ejpam-3329	170	23	−1	−1	NOUN
ejpam-3329	170	24	2	2	NUM
ejpam-3329	170	25	t	t	NOUN
ejpam-3329	170	26	)	)	PUNCT
ejpam-3329	170	27	2+n	2+n	NUM
ejpam-3329	170	28	−	−	NOUN
ejpam-3329	171	1	(	(	PUNCT
ejpam-3329	171	2	1	1	NUM
ejpam-3329	171	3	+	+	NUM
ejpam-3329	171	4	n)((λ	n)((λ	PRON
ejpam-3329	171	5	−1	−1	NOUN
ejpam-3329	171	6	2	2	NUM
ejpam-3329	171	7	t	t	NOUN
ejpam-3329	171	8	)	)	PUNCT
ejpam-3329	171	9	∗(λ	∗(λ	PROPN
ejpam-3329	171	10	−1	−1	NOUN
ejpam-3329	171	11	2	2	NUM
ejpam-3329	171	12	t	t	NOUN
ejpam-3329	171	13	)	)	PUNCT
ejpam-3329	171	14	)	)	PUNCT
ejpam-3329	171	15	2	2	NUM
ejpam-3329	172	1	+	+	NUM
ejpam-3329	172	2	n(λ	n(λ	PROPN
ejpam-3329	172	3	−1	−1	NOUN
ejpam-3329	172	4	2	2	NUM
ejpam-3329	172	5	t	t	NOUN
ejpam-3329	172	6	)	)	PUNCT
ejpam-3329	172	7	∗(λ	∗(λ	PROPN
ejpam-3329	172	8	−1	−1	NOUN
ejpam-3329	172	9	2	2	NUM
ejpam-3329	172	10	t	t	NOUN
ejpam-3329	172	11	)	)	PUNCT
ejpam-3329	172	12	≥	≥	NOUN
ejpam-3329	172	13	0	0	NUM
ejpam-3329	172	14	by	by	ADP
ejpam-3329	172	15	multiplying	multiply	VERB
ejpam-3329	172	16	|λ|2+n	|λ|2+n	NOUN
ejpam-3329	172	17	and	and	CCONJ
ejpam-3329	172	18	letting	let	VERB
ejpam-3329	172	19	|λ|	|λ|	PROPN
ejpam-3329	172	20	=	=	SYM
ejpam-3329	172	21	µ	µ	NUM
ejpam-3329	172	22	,	,	PUNCT
ejpam-3329	172	23	we	we	PRON
ejpam-3329	172	24	have	have	VERB
ejpam-3329	172	25	t	t	PROPN
ejpam-3329	172	26	is	be	AUX
ejpam-3329	172	27	quasi	quasi	ADJ
ejpam-3329	172	28	*	*	PUNCT
ejpam-3329	172	29	-n	-n	X
ejpam-3329	172	30	-	-	ADJ
ejpam-3329	172	31	paranormal	paranormal	ADJ
ejpam-3329	172	32	operator	operator	NOUN
ejpam-3329	172	33	for	for	ADP
ejpam-3329	172	34	all	all	DET
ejpam-3329	172	35	λ	λ	PROPN
ejpam-3329	172	36	>	>	X
ejpam-3329	172	37	0	0	X
ejpam-3329	172	38	.	.	PUNCT
ejpam-3329	173	1	d.	d.	PROPN
ejpam-3329	173	2	senthilkumar	senthilkumar	PROPN
ejpam-3329	173	3	,	,	PUNCT
ejpam-3329	173	4	s.	s.	PROPN
ejpam-3329	173	5	parvatham	parvatham	PROPN
ejpam-3329	173	6	/	/	SYM
ejpam-3329	173	7	eur	eur	PROPN
ejpam-3329	173	8	.	.	PUNCT
ejpam-3329	174	1	j.	j.	PROPN
ejpam-3329	174	2	pure	pure	PROPN
ejpam-3329	174	3	appl	appl	PROPN
ejpam-3329	174	4	.	.	PROPN
ejpam-3329	174	5	math	math	PROPN
ejpam-3329	174	6	,	,	PUNCT
ejpam-3329	174	7	11	11	NUM
ejpam-3329	174	8	(	(	PUNCT
ejpam-3329	174	9	4	4	NUM
ejpam-3329	174	10	)	)	PUNCT
ejpam-3329	174	11	(	(	PUNCT
ejpam-3329	174	12	2018	2018	NUM
ejpam-3329	174	13	)	)	PUNCT
ejpam-3329	174	14	,	,	PUNCT
ejpam-3329	174	15	1108	1108	NUM
ejpam-3329	174	16	-	-	SYM
ejpam-3329	174	17	1129	1129	NUM
ejpam-3329	174	18	1114	1114	NUM
ejpam-3329	174	19	theorem	theorem	VERB
ejpam-3329	174	20	13	13	NUM
ejpam-3329	174	21	.	.	PUNCT
ejpam-3329	175	1	if	if	SCONJ
ejpam-3329	175	2	quasi	quasi	ADJ
ejpam-3329	175	3	n	n	CCONJ
ejpam-3329	175	4	-	-	PUNCT
ejpam-3329	175	5	class	class	NOUN
ejpam-3329	175	6	q∗	q∗	NOUN
ejpam-3329	175	7	operator	operator	NOUN
ejpam-3329	175	8	t	t	NOUN
ejpam-3329	175	9	doubly	doubly	ADV
ejpam-3329	175	10	commutes	commute	VERB
ejpam-3329	175	11	with	with	ADP
ejpam-3329	175	12	an	an	DET
ejpam-3329	175	13	isometric	isometric	ADJ
ejpam-3329	175	14	operator	operator	NOUN
ejpam-3329	175	15	s	s	PART
ejpam-3329	175	16	,	,	PUNCT
ejpam-3329	175	17	then	then	ADV
ejpam-3329	175	18	ts	ts	PROPN
ejpam-3329	175	19	is	be	AUX
ejpam-3329	175	20	an	an	DET
ejpam-3329	175	21	operator	operator	NOUN
ejpam-3329	175	22	of	of	ADP
ejpam-3329	175	23	quasi	quasi	ADJ
ejpam-3329	175	24	n	n	CCONJ
ejpam-3329	175	25	-	-	PUNCT
ejpam-3329	175	26	class	class	NOUN
ejpam-3329	175	27	q∗.	q∗.	NOUN
ejpam-3329	175	28	theorem	theorem	NOUN
ejpam-3329	175	29	14	14	NUM
ejpam-3329	175	30	.	.	PUNCT
ejpam-3329	176	1	if	if	SCONJ
ejpam-3329	176	2	a	a	DET
ejpam-3329	176	3	quasi	quasi	NOUN
ejpam-3329	176	4	n	n	CCONJ
ejpam-3329	176	5	-	-	PUNCT
ejpam-3329	176	6	class	class	NOUN
ejpam-3329	176	7	q∗	q∗	NOUN
ejpam-3329	176	8	operator	operator	NOUN
ejpam-3329	176	9	t	t	PROPN
ejpam-3329	176	10	∈	∈	PROPN
ejpam-3329	176	11	b(h	b(h	PROPN
ejpam-3329	176	12	)	)	PUNCT
ejpam-3329	176	13	is	be	AUX
ejpam-3329	176	14	unitarily	unitarily	ADV
ejpam-3329	176	15	equivalent	equivalent	ADJ
ejpam-3329	176	16	to	to	PART
ejpam-3329	176	17	operator	operator	VERB
ejpam-3329	176	18	s	s	PART
ejpam-3329	176	19	,	,	PUNCT
ejpam-3329	176	20	then	then	ADV
ejpam-3329	176	21	s	s	VERB
ejpam-3329	176	22	is	be	AUX
ejpam-3329	176	23	an	an	DET
ejpam-3329	176	24	operator	operator	NOUN
ejpam-3329	176	25	of	of	ADP
ejpam-3329	176	26	quasi	quasi	ADJ
ejpam-3329	176	27	n	n	CCONJ
ejpam-3329	176	28	-	-	PUNCT
ejpam-3329	176	29	class	class	NOUN
ejpam-3329	176	30	q∗.	q∗.	NOUN
ejpam-3329	176	31	theorem	theorem	NOUN
ejpam-3329	176	32	15	15	NUM
ejpam-3329	176	33	.	.	PUNCT
ejpam-3329	177	1	let	let	AUX
ejpam-3329	177	2	t	t	PROPN
ejpam-3329	177	3	∈	∈	PROPN
ejpam-3329	177	4	b(h	b(h	PROPN
ejpam-3329	177	5	)	)	PUNCT
ejpam-3329	177	6	be	be	VERB
ejpam-3329	177	7	an	an	DET
ejpam-3329	177	8	invertible	invertible	ADJ
ejpam-3329	177	9	operator	operator	NOUN
ejpam-3329	177	10	and	and	CCONJ
ejpam-3329	177	11	n	n	CCONJ
ejpam-3329	177	12	be	be	VERB
ejpam-3329	177	13	an	an	DET
ejpam-3329	177	14	operator	operator	NOUN
ejpam-3329	177	15	such	such	ADJ
ejpam-3329	177	16	that	that	SCONJ
ejpam-3329	177	17	n	n	ADP
ejpam-3329	177	18	commutes	commute	NOUN
ejpam-3329	177	19	with	with	ADP
ejpam-3329	177	20	t	t	PROPN
ejpam-3329	177	21	∗t	∗t	PROPN
ejpam-3329	177	22	.	.	PUNCT
ejpam-3329	178	1	then	then	ADV
ejpam-3329	178	2	operator	operator	NOUN
ejpam-3329	178	3	n	n	X
ejpam-3329	178	4	is	be	AUX
ejpam-3329	178	5	quasi	quasi	X
ejpam-3329	178	6	n	n	X
ejpam-3329	178	7	class	class	NOUN
ejpam-3329	178	8	q∗	q∗	NOUN
ejpam-3329	179	1	if	if	SCONJ
ejpam-3329	179	2	and	and	CCONJ
ejpam-3329	179	3	only	only	ADV
ejpam-3329	179	4	if	if	SCONJ
ejpam-3329	179	5	operator	operator	NOUN
ejpam-3329	179	6	tnt−1	tnt−1	PROPN
ejpam-3329	179	7	is	be	AUX
ejpam-3329	179	8	quasi	quasi	NOUN
ejpam-3329	179	9	of	of	ADP
ejpam-3329	179	10	n	n	PRON
ejpam-3329	179	11	class	class	NOUN
ejpam-3329	179	12	q∗.	q∗.	NOUN
ejpam-3329	179	13	corollary	corollary	ADJ
ejpam-3329	179	14	4	4	NUM
ejpam-3329	179	15	.	.	PUNCT
ejpam-3329	180	1	let	let	VERB
ejpam-3329	180	2	s	s	PRON
ejpam-3329	180	3	be	be	AUX
ejpam-3329	180	4	quasi	quasi	ADJ
ejpam-3329	180	5	n	n	PRON
ejpam-3329	180	6	class	class	NOUN
ejpam-3329	180	7	q∗	q∗	NOUN
ejpam-3329	180	8	operator	operator	NOUN
ejpam-3329	180	9	and	and	CCONJ
ejpam-3329	180	10	a	a	DET
ejpam-3329	180	11	any	any	DET
ejpam-3329	180	12	positive	positive	ADJ
ejpam-3329	180	13	operator	operator	NOUN
ejpam-3329	180	14	such	such	ADJ
ejpam-3329	180	15	that	that	PRON
ejpam-3329	180	16	a−1	a−1	PROPN
ejpam-3329	180	17	=	=	SYM
ejpam-3329	180	18	a∗.	a∗.	NOUN
ejpam-3329	180	19	then	then	ADV
ejpam-3329	180	20	t	t	PROPN
ejpam-3329	180	21	=	=	SYM
ejpam-3329	180	22	a−1sa	a−1sa	NOUN
ejpam-3329	180	23	is	be	AUX
ejpam-3329	180	24	quasi	quasi	NOUN
ejpam-3329	180	25	n	n	PRON
ejpam-3329	180	26	class	class	NOUN
ejpam-3329	180	27	q∗	q∗	NOUN
ejpam-3329	180	28	operator	operator	NOUN
ejpam-3329	180	29	.	.	PUNCT
ejpam-3329	181	1	theorem	theorem	VERB
ejpam-3329	181	2	16	16	NUM
ejpam-3329	181	3	.	.	PUNCT
ejpam-3329	182	1	let	let	VERB
ejpam-3329	182	2	t	t	PROPN
ejpam-3329	182	3	be	be	AUX
ejpam-3329	182	4	quasi	quasi	ADJ
ejpam-3329	182	5	n	n	PRON
ejpam-3329	182	6	class	class	NOUN
ejpam-3329	182	7	q∗	q∗	NOUN
ejpam-3329	182	8	operator	operator	NOUN
ejpam-3329	182	9	.	.	PUNCT
ejpam-3329	183	1	then	then	ADV
ejpam-3329	183	2	the	the	DET
ejpam-3329	183	3	tensor	tensor	NOUN
ejpam-3329	183	4	product	product	NOUN
ejpam-3329	183	5	t	t	PROPN
ejpam-3329	184	1	⊗	⊗	PROPN
ejpam-3329	184	2	i	i	PRON
ejpam-3329	185	1	and	and	CCONJ
ejpam-3329	185	2	i	i	PRON
ejpam-3329	185	3	⊗	⊗	PROPN
ejpam-3329	185	4	t	t	PROPN
ejpam-3329	185	5	are	be	AUX
ejpam-3329	185	6	both	both	PRON
ejpam-3329	185	7	quasi	quasi	ADJ
ejpam-3329	185	8	n	n	PRON
ejpam-3329	185	9	class	class	NOUN
ejpam-3329	185	10	q∗	q∗	NOUN
ejpam-3329	185	11	operators	operator	NOUN
ejpam-3329	185	12	.	.	PUNCT
ejpam-3329	186	1	theorem	theorem	VERB
ejpam-3329	186	2	17	17	NUM
ejpam-3329	186	3	.	.	PUNCT
ejpam-3329	187	1	if	if	SCONJ
ejpam-3329	187	2	t	t	PROPN
ejpam-3329	187	3	∈	∈	PROPN
ejpam-3329	187	4	b(h	b(h	PROPN
ejpam-3329	187	5	)	)	PUNCT
ejpam-3329	187	6	is	be	AUX
ejpam-3329	187	7	of	of	ADP
ejpam-3329	187	8	quasi	quasi	NOUN
ejpam-3329	187	9	n	n	PRON
ejpam-3329	187	10	class	class	NOUN
ejpam-3329	187	11	q∗	q∗	NOUN
ejpam-3329	187	12	operator	operator	NOUN
ejpam-3329	187	13	for	for	ADP
ejpam-3329	187	14	any	any	DET
ejpam-3329	187	15	positive	positive	ADJ
ejpam-3329	187	16	integer	integer	NOUN
ejpam-3329	187	17	n	n	CCONJ
ejpam-3329	187	18	,	,	PUNCT
ejpam-3329	187	19	a	a	DET
ejpam-3329	187	20	non	non	ADJ
ejpam-3329	187	21	zero	zero	NUM
ejpam-3329	187	22	complex	complex	ADJ
ejpam-3329	187	23	number	number	NOUN
ejpam-3329	187	24	λ	λ	X
ejpam-3329	187	25	∈	∈	NOUN
ejpam-3329	187	26	σp(t	σp(t	PUNCT
ejpam-3329	187	27	)	)	PUNCT
ejpam-3329	187	28	and	and	CCONJ
ejpam-3329	187	29	t	t	PROPN
ejpam-3329	187	30	is	be	AUX
ejpam-3329	187	31	of	of	ADP
ejpam-3329	187	32	the	the	DET
ejpam-3329	187	33	form	form	NOUN
ejpam-3329	187	34	t	t	NOUN
ejpam-3329	187	35	=	=	SYM
ejpam-3329	187	36	(	(	PUNCT
ejpam-3329	187	37	λ	λ	PROPN
ejpam-3329	187	38	t2	t2	PROPN
ejpam-3329	187	39	0	0	NUM
ejpam-3329	187	40	t3	t3	PROPN
ejpam-3329	187	41	)	)	PUNCT
ejpam-3329	187	42	on	on	ADP
ejpam-3329	187	43	h	h	NOUN
ejpam-3329	187	44	=	=	NOUN
ejpam-3329	187	45	ker(t	ker(t	NOUN
ejpam-3329	187	46	−	−	NOUN
ejpam-3329	187	47	λ)⊕	λ)⊕	NOUN
ejpam-3329	187	48	ran(t	ran(t	PROPN
ejpam-3329	187	49	−	−	PROPN
ejpam-3329	187	50	λ	λ	NOUN
ejpam-3329	187	51	)	)	PUNCT
ejpam-3329	187	52	∗	∗	NOUN
ejpam-3329	187	53	,	,	PUNCT
ejpam-3329	187	54	then	then	ADV
ejpam-3329	187	55	1	1	X
ejpam-3329	187	56	.	.	PUNCT
ejpam-3329	188	1	t2	t2	NOUN
ejpam-3329	188	2	=	=	SYM
ejpam-3329	188	3	0	0	NUM
ejpam-3329	188	4	and	and	CCONJ
ejpam-3329	188	5	2	2	NUM
ejpam-3329	188	6	.	.	X
ejpam-3329	189	1	t3	t3	PROPN
ejpam-3329	189	2	is	be	AUX
ejpam-3329	189	3	quasi	quasi	ADJ
ejpam-3329	189	4	n	n	CCONJ
ejpam-3329	189	5	-	-	PUNCT
ejpam-3329	189	6	class	class	NOUN
ejpam-3329	189	7	q∗	q∗	NOUN
ejpam-3329	189	8	operator	operator	NOUN
ejpam-3329	189	9	.	.	PUNCT
ejpam-3329	190	1	proof	proof	NOUN
ejpam-3329	190	2	.	.	PUNCT
ejpam-3329	191	1	let	let	VERB
ejpam-3329	191	2	t	t	NOUN
ejpam-3329	191	3	=	=	PUNCT
ejpam-3329	191	4	(	(	PUNCT
ejpam-3329	191	5	λ	λ	PROPN
ejpam-3329	191	6	t2	t2	PROPN
ejpam-3329	191	7	0	0	NUM
ejpam-3329	191	8	t3	t3	PROPN
ejpam-3329	191	9	)	)	PUNCT
ejpam-3329	191	10	onh	onh	PROPN
ejpam-3329	191	11	=	=	PUNCT
ejpam-3329	191	12	ker(t−λ)⊕ran(t	ker(t−λ)⊕ran(t	PROPN
ejpam-3329	191	13	−	−	PROPN
ejpam-3329	191	14	λ	λ	PROPN
ejpam-3329	191	15	)	)	PUNCT
ejpam-3329	191	16	∗	∗	NOUN
ejpam-3329	191	17	.	.	PUNCT
ejpam-3329	192	1	without	without	ADP
ejpam-3329	192	2	the	the	DET
ejpam-3329	192	3	loss	loss	NOUN
ejpam-3329	192	4	of	of	ADP
ejpam-3329	192	5	generality	generality	NOUN
ejpam-3329	192	6	assume	assume	VERB
ejpam-3329	192	7	that	that	SCONJ
ejpam-3329	192	8	λ	λ	NOUN
ejpam-3329	192	9	=	=	NOUN
ejpam-3329	192	10	1	1	NUM
ejpam-3329	192	11	,	,	PUNCT
ejpam-3329	192	12	then	then	ADV
ejpam-3329	192	13	by	by	ADP
ejpam-3329	192	14	theorem	theorem	NOUN
ejpam-3329	192	15	11	11	NUM
ejpam-3329	192	16	,	,	PUNCT
ejpam-3329	192	17	t	t	PROPN
ejpam-3329	192	18	∗2+nt	∗2+nt	PROPN
ejpam-3329	192	19	2+n−(1+n)(t	2+n−(1+n)(t	NUM
ejpam-3329	192	20	∗t	∗t	PROPN
ejpam-3329	192	21	)	)	PUNCT
ejpam-3329	192	22	2+nt	2+nt	PROPN
ejpam-3329	193	1	∗t	∗t	ADJ
ejpam-3329	193	2	≥	≥	NUM
ejpam-3329	193	3	0	0	NUM
ejpam-3329	193	4	.	.	PUNCT
ejpam-3329	194	1	now	now	ADV
ejpam-3329	194	2	,	,	PUNCT
ejpam-3329	194	3	t	t	PROPN
ejpam-3329	194	4	2+n	2+n	NUM
ejpam-3329	194	5	=	=	SYM
ejpam-3329	194	6	(	(	PUNCT
ejpam-3329	194	7	1	1	NUM
ejpam-3329	194	8	∑1+n	∑1+n	PROPN
ejpam-3329	194	9	j=0	j=0	PROPN
ejpam-3329	194	10	t2	t2	PROPN
ejpam-3329	194	11	t	t	PROPN
ejpam-3329	194	12	n+1−j	n+1−j	PROPN
ejpam-3329	194	13	3	3	NUM
ejpam-3329	194	14	0	0	NUM
ejpam-3329	194	15	t	t	PROPN
ejpam-3329	194	16	2+n	2+n	NUM
ejpam-3329	194	17	3	3	NUM
ejpam-3329	194	18	)	)	PUNCT
ejpam-3329	194	19	and	and	CCONJ
ejpam-3329	194	20	t	t	NOUN
ejpam-3329	194	21	∗2+n	∗2+n	NOUN
ejpam-3329	194	22	=	=	PUNCT
ejpam-3329	194	23	(	(	PUNCT
ejpam-3329	194	24	1	1	NUM
ejpam-3329	194	25	0	0	NUM
ejpam-3329	194	26	(	(	PUNCT
ejpam-3329	194	27	∑2+n	∑2+n	PROPN
ejpam-3329	194	28	j=0	j=0	PROPN
ejpam-3329	194	29	t2	t2	PROPN
ejpam-3329	194	30	t	t	PROPN
ejpam-3329	194	31	n+1−j	n+1−j	PROPN
ejpam-3329	194	32	3	3	NUM
ejpam-3329	194	33	)	)	PUNCT
ejpam-3329	194	34	∗	∗	NOUN
ejpam-3329	194	35	t	t	PROPN
ejpam-3329	194	36	∗2+n3	∗2+n3	PROPN
ejpam-3329	194	37	)	)	PUNCT
ejpam-3329	194	38	t	t	PROPN
ejpam-3329	194	39	∗2+nt	∗2+nt	PROPN
ejpam-3329	195	1	2+n	2+n	NUM
ejpam-3329	195	2	=	=	SYM
ejpam-3329	195	3	(	(	PUNCT
ejpam-3329	195	4	1	1	NUM
ejpam-3329	195	5	∑1+n	∑1+n	PROPN
ejpam-3329	195	6	j=0	j=0	PROPN
ejpam-3329	195	7	t2	t2	NOUN
ejpam-3329	195	8	t	t	PROPN
ejpam-3329	195	9	1+n−j	1+n−j	NUM
ejpam-3329	195	10	3	3	NUM
ejpam-3329	195	11	(	(	PUNCT
ejpam-3329	195	12	∑1+n	∑1+n	PROPN
ejpam-3329	195	13	j=0	j=0	PROPN
ejpam-3329	195	14	t2	t2	PROPN
ejpam-3329	195	15	t	t	PROPN
ejpam-3329	195	16	1+n−j	1+n−j	NUM
ejpam-3329	195	17	3	3	NUM
ejpam-3329	195	18	)	)	PUNCT
ejpam-3329	195	19	∗	∗	NOUN
ejpam-3329	195	20	2	2	NUM
ejpam-3329	195	21	(	(	PUNCT
ejpam-3329	195	22	∑1+n	∑1+n	PROPN
ejpam-3329	195	23	j=0	j=0	PROPN
ejpam-3329	195	24	t2	t2	PROPN
ejpam-3329	195	25	t	t	PROPN
ejpam-3329	195	26	1+n−j	1+n−j	NUM
ejpam-3329	195	27	3	3	NUM
ejpam-3329	195	28	)	)	PUNCT
ejpam-3329	195	29	∗	∗	NOUN
ejpam-3329	195	30	(	(	PUNCT
ejpam-3329	195	31	∑1+n	∑1+n	PROPN
ejpam-3329	195	32	j=0	j=0	PROPN
ejpam-3329	195	33	t2	t2	PROPN
ejpam-3329	195	34	t	t	PROPN
ejpam-3329	195	35	1+n−j	1+n−j	NUM
ejpam-3329	195	36	3	3	NUM
ejpam-3329	195	37	)	)	PUNCT
ejpam-3329	195	38	+	+	CCONJ
ejpam-3329	195	39	t	t	X
ejpam-3329	195	40	2+n	2+n	NUM
ejpam-3329	195	41	3	3	NUM
ejpam-3329	195	42	t	t	NOUN
ejpam-3329	195	43	∗1+n3	∗1+n3	NUM
ejpam-3329	195	44	)	)	PUNCT
ejpam-3329	196	1	so	so	ADV
ejpam-3329	196	2	,	,	PUNCT
ejpam-3329	196	3	t	t	PROPN
ejpam-3329	196	4	∗2+nt	∗2+nt	VERB
ejpam-3329	196	5	2+n	2+n	NUM
ejpam-3329	196	6	−	−	PROPN
ejpam-3329	197	1	(	(	PUNCT
ejpam-3329	197	2	1	1	NUM
ejpam-3329	197	3	+	+	CCONJ
ejpam-3329	197	4	n)(t	n)(t	PROPN
ejpam-3329	197	5	∗t	∗t	ADJ
ejpam-3329	197	6	)	)	PUNCT
ejpam-3329	197	7	2	2	NUM
ejpam-3329	197	8	+	+	CCONJ
ejpam-3329	197	9	nt	not	PART
ejpam-3329	197	10	∗t	∗t	ADJ
ejpam-3329	197	11	≥	≥	NUM
ejpam-3329	197	12	0	0	NUM
ejpam-3329	198	1	gives	give	VERB
ejpam-3329	198	2	(	(	PUNCT
ejpam-3329	198	3	a	a	DET
ejpam-3329	198	4	b	b	NOUN
ejpam-3329	198	5	b∗	b∗	ADJ
ejpam-3329	198	6	c	c	NOUN
ejpam-3329	198	7	)	)	PUNCT
ejpam-3329	198	8	≥	≥	NOUN
ejpam-3329	198	9	0	0	NUM
ejpam-3329	199	1	where	where	SCONJ
ejpam-3329	199	2	a	a	DET
ejpam-3329	199	3	=	=	SYM
ejpam-3329	199	4	1	1	NUM
ejpam-3329	199	5	−	−	NOUN
ejpam-3329	199	6	(	(	PUNCT
ejpam-3329	199	7	1	1	NUM
ejpam-3329	199	8	+	+	NUM
ejpam-3329	199	9	n)(1	n)(1	NOUN
ejpam-3329	199	10	+	+	CCONJ
ejpam-3329	199	11	t2	t2	PROPN
ejpam-3329	199	12	t	t	PROPN
ejpam-3329	199	13	∗	∗	X
ejpam-3329	199	14	2	2	NUM
ejpam-3329	199	15	)	)	PUNCT
ejpam-3329	199	16	+	+	SYM
ejpam-3329	199	17	n	n	CCONJ
ejpam-3329	199	18	,	,	PUNCT
ejpam-3329	199	19	b	b	X
ejpam-3329	199	20	=	=	PRON
ejpam-3329	199	21	∑1+n	∑1+n	PROPN
ejpam-3329	199	22	j=0	j=0	PROPN
ejpam-3329	199	23	t2	t2	PROPN
ejpam-3329	199	24	t	t	PROPN
ejpam-3329	199	25	1+n−j	1+n−j	NUM
ejpam-3329	199	26	3	3	NUM
ejpam-3329	199	27	−	−	PROPN
ejpam-3329	199	28	(	(	PUNCT
ejpam-3329	199	29	1	1	NUM
ejpam-3329	199	30	+	+	NUM
ejpam-3329	199	31	n)[t2	n)[t2	PROPN
ejpam-3329	199	32	+	+	CCONJ
ejpam-3329	199	33	t2(t	t2(t	PROPN
ejpam-3329	199	34	∗	∗	NOUN
ejpam-3329	199	35	2	2	NUM
ejpam-3329	199	36	t2	t2	NOUN
ejpam-3329	199	37	+	+	CCONJ
ejpam-3329	199	38	t	t	PROPN
ejpam-3329	199	39	∗3	∗3	PROPN
ejpam-3329	199	40	t3	t3	PROPN
ejpam-3329	199	41	)	)	PUNCT
ejpam-3329	199	42	]	]	PUNCT
ejpam-3329	199	43	+	+	CCONJ
ejpam-3329	199	44	nt2	nt2	NOUN
ejpam-3329	199	45	and	and	CCONJ
ejpam-3329	199	46	c	c	NOUN
ejpam-3329	199	47	=	=	SYM
ejpam-3329	199	48	(	(	PUNCT
ejpam-3329	199	49	∑1+n	∑1+n	X
ejpam-3329	199	50	j=0	j=0	PROPN
ejpam-3329	199	51	t2	t2	PROPN
ejpam-3329	199	52	t	t	PROPN
ejpam-3329	199	53	1+n−j	1+n−j	NUM
ejpam-3329	199	54	3	3	NUM
ejpam-3329	199	55	)	)	PUNCT
ejpam-3329	199	56	∗	∗	NOUN
ejpam-3329	199	57	∑1+n	∑1+n	PROPN
ejpam-3329	199	58	j=0	j=0	PROPN
ejpam-3329	199	59	t2	t2	PROPN
ejpam-3329	199	60	t	t	PROPN
ejpam-3329	199	61	1+n−j	1+n−j	NUM
ejpam-3329	199	62	3	3	NUM
ejpam-3329	199	63	+	+	NUM
ejpam-3329	199	64	t	t	PROPN
ejpam-3329	199	65	∗2+n3	∗2+n3	PROPN
ejpam-3329	199	66	t	t	PROPN
ejpam-3329	199	67	2+n	2+n	NUM
ejpam-3329	199	68	3	3	NUM
ejpam-3329	199	69	−	−	PROPN
ejpam-3329	199	70	(	(	PUNCT
ejpam-3329	199	71	1	1	NUM
ejpam-3329	199	72	+	+	CCONJ
ejpam-3329	199	73	n)t	n)t	ADJ
ejpam-3329	199	74	∗2	∗2	PROPN
ejpam-3329	199	75	t2	t2	NOUN
ejpam-3329	199	76	+	+	CCONJ
ejpam-3329	199	77	t	t	PROPN
ejpam-3329	199	78	∗2	∗2	PROPN
ejpam-3329	199	79	t2	t2	PROPN
ejpam-3329	199	80	+	+	CCONJ
ejpam-3329	199	81	t	t	PROPN
ejpam-3329	199	82	∗3	∗3	PROPN
ejpam-3329	199	83	t3	t3	PROPN
ejpam-3329	199	84	2	2	NUM
ejpam-3329	199	85	+	+	CCONJ
ejpam-3329	199	86	n(t	n(t	PROPN
ejpam-3329	199	87	∗2	∗2	PROPN
ejpam-3329	199	88	t2	t2	PROPN
ejpam-3329	199	89	+	+	CCONJ
ejpam-3329	199	90	t	t	X
ejpam-3329	199	91	∗3	∗3	PROPN
ejpam-3329	199	92	t3	t3	PROPN
ejpam-3329	199	93	)	)	PUNCT
ejpam-3329	199	94	but	but	CCONJ
ejpam-3329	199	95	,	,	PUNCT
ejpam-3329	199	96	we	we	PRON
ejpam-3329	199	97	know	know	VERB
ejpam-3329	199	98	that	that	PRON
ejpam-3329	199	99	,	,	PUNCT
ejpam-3329	199	100	”	"	PUNCT
ejpam-3329	199	101	if	if	SCONJ
ejpam-3329	199	102	a	a	PRON
ejpam-3329	199	103	is	be	AUX
ejpam-3329	199	104	a	a	DET
ejpam-3329	199	105	matrix	matrix	NOUN
ejpam-3329	199	106	of	of	ADP
ejpam-3329	199	107	the	the	DET
ejpam-3329	199	108	form	form	NOUN
ejpam-3329	199	109	(	(	PUNCT
ejpam-3329	199	110	a	a	DET
ejpam-3329	199	111	b	b	NOUN
ejpam-3329	199	112	b∗	b∗	ADJ
ejpam-3329	199	113	c	c	NOUN
ejpam-3329	199	114	)	)	PUNCT
ejpam-3329	199	115	≥	≥	NOUN
ejpam-3329	199	116	0	0	PUNCT
ejpam-3329	200	1	if	if	SCONJ
ejpam-3329	200	2	and	and	CCONJ
ejpam-3329	200	3	only	only	ADV
ejpam-3329	200	4	if	if	SCONJ
ejpam-3329	200	5	a	a	DET
ejpam-3329	200	6	≥	≥	NOUN
ejpam-3329	200	7	0	0	NUM
ejpam-3329	200	8	,	,	PUNCT
ejpam-3329	200	9	d.	d.	PROPN
ejpam-3329	200	10	senthilkumar	senthilkumar	PROPN
ejpam-3329	200	11	,	,	PUNCT
ejpam-3329	200	12	s.	s.	PROPN
ejpam-3329	200	13	parvatham	parvatham	PROPN
ejpam-3329	200	14	/	/	SYM
ejpam-3329	200	15	eur	eur	PROPN
ejpam-3329	200	16	.	.	PUNCT
ejpam-3329	201	1	j.	j.	PROPN
ejpam-3329	201	2	pure	pure	PROPN
ejpam-3329	201	3	appl	appl	PROPN
ejpam-3329	201	4	.	.	PROPN
ejpam-3329	201	5	math	math	PROPN
ejpam-3329	201	6	,	,	PUNCT
ejpam-3329	201	7	11	11	NUM
ejpam-3329	201	8	(	(	PUNCT
ejpam-3329	201	9	4	4	NUM
ejpam-3329	201	10	)	)	PUNCT
ejpam-3329	201	11	(	(	PUNCT
ejpam-3329	201	12	2018	2018	NUM
ejpam-3329	201	13	)	)	PUNCT
ejpam-3329	201	14	,	,	PUNCT
ejpam-3329	201	15	1108	1108	NUM
ejpam-3329	201	16	-	-	SYM
ejpam-3329	201	17	1129	1129	NUM
ejpam-3329	201	18	1115	1115	NUM
ejpam-3329	201	19	c	c	X
ejpam-3329	201	20	≥	≥	PROPN
ejpam-3329	201	21	0	0	NUM
ejpam-3329	201	22	and	and	CCONJ
ejpam-3329	201	23	b	b	X
ejpam-3329	201	24	=	=	PUNCT
ejpam-3329	201	25	a	a	DET
ejpam-3329	201	26	1	1	NUM
ejpam-3329	201	27	2wc	2wc	ADJ
ejpam-3329	201	28	1	1	NUM
ejpam-3329	201	29	2	2	NUM
ejpam-3329	201	30	for	for	ADP
ejpam-3329	201	31	some	some	DET
ejpam-3329	201	32	contraction	contraction	NOUN
ejpam-3329	201	33	w	w	INTJ
ejpam-3329	201	34	.	.	PUNCT
ejpam-3329	202	1	therefore	therefore	ADV
ejpam-3329	202	2	1	1	NUM
ejpam-3329	202	3	+	+	NUM
ejpam-3329	202	4	n−	n−	NOUN
ejpam-3329	202	5	(	(	PUNCT
ejpam-3329	202	6	1	1	NUM
ejpam-3329	202	7	+	+	NUM
ejpam-3329	202	8	n)(1	n)(1	NOUN
ejpam-3329	202	9	+	+	CCONJ
ejpam-3329	202	10	t2	t2	PROPN
ejpam-3329	202	11	t	t	PROPN
ejpam-3329	202	12	∗	∗	X
ejpam-3329	202	13	2	2	NUM
ejpam-3329	202	14	)	)	PUNCT
ejpam-3329	202	15	+	+	CCONJ
ejpam-3329	202	16	n	n	CCONJ
ejpam-3329	202	17	≥	≥	NOUN
ejpam-3329	202	18	0	0	NUM
ejpam-3329	202	19	,	,	PUNCT
ejpam-3329	202	20	which	which	PRON
ejpam-3329	202	21	implies	imply	VERB
ejpam-3329	202	22	that	that	SCONJ
ejpam-3329	202	23	(	(	PUNCT
ejpam-3329	202	24	1	1	NUM
ejpam-3329	202	25	+	+	CCONJ
ejpam-3329	202	26	n)(−t2	n)(−t2	PROPN
ejpam-3329	202	27	t	t	NOUN
ejpam-3329	202	28	∗2	∗2	PROPN
ejpam-3329	202	29	)	)	PUNCT
ejpam-3329	202	30	≥	≥	NOUN
ejpam-3329	202	31	0	0	NUM
ejpam-3329	202	32	.	.	PUNCT
ejpam-3329	203	1	this	this	PRON
ejpam-3329	203	2	gives	give	VERB
ejpam-3329	203	3	t2	t2	NOUN
ejpam-3329	203	4	=	=	SYM
ejpam-3329	203	5	0	0	NUM
ejpam-3329	203	6	,	,	PUNCT
ejpam-3329	203	7	since	since	SCONJ
ejpam-3329	203	8	n	n	NUM
ejpam-3329	203	9	is	be	AUX
ejpam-3329	203	10	a	a	DET
ejpam-3329	203	11	positive	positive	ADJ
ejpam-3329	203	12	integer	integer	NOUN
ejpam-3329	203	13	.	.	PUNCT
ejpam-3329	204	1	also	also	ADV
ejpam-3329	204	2	t3	t3	PROPN
ejpam-3329	204	3	is	be	AUX
ejpam-3329	204	4	quasi	quasi	ADJ
ejpam-3329	204	5	n	n	CCONJ
ejpam-3329	204	6	-	-	PUNCT
ejpam-3329	204	7	class	class	NOUN
ejpam-3329	204	8	q∗	q∗	NOUN
ejpam-3329	204	9	operator	operator	NOUN
ejpam-3329	204	10	.	.	PUNCT
ejpam-3329	205	1	corollary	corollary	ADJ
ejpam-3329	205	2	5	5	NUM
ejpam-3329	205	3	.	.	PUNCT
ejpam-3329	206	1	if	if	SCONJ
ejpam-3329	206	2	t	t	PROPN
ejpam-3329	206	3	∈	∈	PROPN
ejpam-3329	206	4	b(h	b(h	PROPN
ejpam-3329	206	5	)	)	PUNCT
ejpam-3329	206	6	is	be	AUX
ejpam-3329	206	7	of	of	ADP
ejpam-3329	206	8	quasi	quasi	NOUN
ejpam-3329	206	9	n	n	PRON
ejpam-3329	206	10	class	class	NOUN
ejpam-3329	206	11	q∗	q∗	NOUN
ejpam-3329	206	12	operator	operator	NOUN
ejpam-3329	206	13	for	for	ADP
ejpam-3329	206	14	a	a	DET
ejpam-3329	206	15	positive	positive	ADJ
ejpam-3329	206	16	integer	integer	NOUN
ejpam-3329	206	17	n	n	CCONJ
ejpam-3329	206	18	,	,	PUNCT
ejpam-3329	206	19	then	then	ADV
ejpam-3329	206	20	t	t	PROPN
ejpam-3329	206	21	is	be	AUX
ejpam-3329	206	22	of	of	ADP
ejpam-3329	206	23	the	the	DET
ejpam-3329	206	24	form	form	NOUN
ejpam-3329	206	25	t	t	NOUN
ejpam-3329	206	26	=	=	SYM
ejpam-3329	206	27	(	(	PUNCT
ejpam-3329	206	28	λ	λ	X
ejpam-3329	206	29	0	0	NUM
ejpam-3329	206	30	0	0	NUM
ejpam-3329	206	31	t3	t3	NOUN
ejpam-3329	206	32	)	)	PUNCT
ejpam-3329	206	33	on	on	ADP
ejpam-3329	206	34	h	h	NOUN
ejpam-3329	206	35	=	=	NOUN
ejpam-3329	206	36	ker(t	ker(t	NOUN
ejpam-3329	206	37	−	−	NOUN
ejpam-3329	206	38	λ)⊕	λ)⊕	NOUN
ejpam-3329	206	39	ran(t	ran(t	PROPN
ejpam-3329	206	40	−	−	PROPN
ejpam-3329	206	41	λ	λ	NOUN
ejpam-3329	206	42	)	)	PUNCT
ejpam-3329	206	43	∗	∗	NOUN
ejpam-3329	206	44	,	,	PUNCT
ejpam-3329	206	45	where	where	SCONJ
ejpam-3329	206	46	t3	t3	PROPN
ejpam-3329	206	47	is	be	AUX
ejpam-3329	206	48	quasi	quasi	ADJ
ejpam-3329	206	49	n	n	CCONJ
ejpam-3329	206	50	-	-	PUNCT
ejpam-3329	206	51	class	class	NOUN
ejpam-3329	206	52	q∗	q∗	NOUN
ejpam-3329	206	53	operator	operator	NOUN
ejpam-3329	206	54	and	and	CCONJ
ejpam-3329	206	55	ker(t	ker(t	NOUN
ejpam-3329	207	1	−	−	PROPN
ejpam-3329	207	2	λ	λ	NOUN
ejpam-3329	207	3	)	)	PUNCT
ejpam-3329	207	4	=	=	PUNCT
ejpam-3329	207	5	{	{	PUNCT
ejpam-3329	207	6	0	0	NUM
ejpam-3329	207	7	}	}	PUNCT
ejpam-3329	207	8	.	.	PUNCT
ejpam-3329	208	1	theorem	theorem	NOUN
ejpam-3329	208	2	18	18	NUM
ejpam-3329	208	3	.	.	PUNCT
ejpam-3329	209	1	if	if	SCONJ
ejpam-3329	209	2	t	t	PROPN
ejpam-3329	209	3	∈	∈	PROPN
ejpam-3329	209	4	b(h	b(h	PROPN
ejpam-3329	209	5	)	)	PUNCT
ejpam-3329	209	6	is	be	AUX
ejpam-3329	209	7	a	a	DET
ejpam-3329	209	8	quasi	quasi	ADJ
ejpam-3329	209	9	n	n	CCONJ
ejpam-3329	209	10	-	-	PUNCT
ejpam-3329	209	11	class	class	NOUN
ejpam-3329	209	12	q∗	q∗	NOUN
ejpam-3329	209	13	operator	operator	NOUN
ejpam-3329	209	14	for	for	ADP
ejpam-3329	209	15	a	a	DET
ejpam-3329	209	16	positive	positive	ADJ
ejpam-3329	209	17	integer	integer	NOUN
ejpam-3329	209	18	n	n	CCONJ
ejpam-3329	209	19	,	,	PUNCT
ejpam-3329	209	20	t	t	PROPN
ejpam-3329	209	21	does	do	AUX
ejpam-3329	209	22	not	not	PART
ejpam-3329	209	23	have	have	VERB
ejpam-3329	209	24	dense	dense	ADJ
ejpam-3329	209	25	range	range	NOUN
ejpam-3329	209	26	and	and	CCONJ
ejpam-3329	209	27	t	t	PROPN
ejpam-3329	209	28	has	have	VERB
ejpam-3329	209	29	the	the	DET
ejpam-3329	209	30	following	following	ADJ
ejpam-3329	209	31	2×	2×	NUM
ejpam-3329	209	32	2	2	NUM
ejpam-3329	209	33	matrix	matrix	NOUN
ejpam-3329	209	34	representation	representation	NOUN
ejpam-3329	209	35	t	t	NOUN
ejpam-3329	209	36	=	=	SYM
ejpam-3329	209	37	(	(	PUNCT
ejpam-3329	209	38	t1	t1	PROPN
ejpam-3329	209	39	t2	t2	PROPN
ejpam-3329	209	40	0	0	NUM
ejpam-3329	209	41	t3	t3	PROPN
ejpam-3329	209	42	)	)	PUNCT
ejpam-3329	209	43	on	on	ADP
ejpam-3329	209	44	h	h	NOUN
ejpam-3329	209	45	=	=	SYM
ejpam-3329	209	46	ran(t	ran(t	PROPN
ejpam-3329	209	47	)	)	PUNCT
ejpam-3329	209	48	⊕	⊕	PROPN
ejpam-3329	209	49	kert	kert	PROPN
ejpam-3329	209	50	∗	∗	PROPN
ejpam-3329	209	51	,	,	PUNCT
ejpam-3329	209	52	if	if	SCONJ
ejpam-3329	209	53	and	and	CCONJ
ejpam-3329	209	54	only	only	ADV
ejpam-3329	209	55	if	if	SCONJ
ejpam-3329	209	56	t	t	PROPN
ejpam-3329	209	57	∗1+n1	∗1+n1	X
ejpam-3329	209	58	t	t	PROPN
ejpam-3329	209	59	1+n	1+n	NUM
ejpam-3329	209	60	1	1	NUM
ejpam-3329	209	61	−	−	PROPN
ejpam-3329	209	62	(	(	PUNCT
ejpam-3329	209	63	1	1	NUM
ejpam-3329	209	64	+	+	NUM
ejpam-3329	209	65	n)(t1	n)(t1	PROPN
ejpam-3329	209	66	t	t	PROPN
ejpam-3329	209	67	∗	∗	NOUN
ejpam-3329	209	68	1	1	NUM
ejpam-3329	209	69	+	+	NUM
ejpam-3329	209	70	t2	t2	NOUN
ejpam-3329	209	71	t	t	PROPN
ejpam-3329	209	72	∗	∗	X
ejpam-3329	209	73	2	2	NUM
ejpam-3329	209	74	)	)	PUNCT
ejpam-3329	209	75	+	+	CCONJ
ejpam-3329	209	76	ni	ni	PROPN
ejpam-3329	209	77	≥	≥	NOUN
ejpam-3329	209	78	0	0	NUM
ejpam-3329	209	79	and	and	CCONJ
ejpam-3329	209	80	t3	t3	PROPN
ejpam-3329	209	81	=	=	PUNCT
ejpam-3329	209	82	0.further	0.further	PUNCT
ejpam-3329	209	83	more	more	ADJ
ejpam-3329	209	84	σ(t	σ(t	NOUN
ejpam-3329	209	85	)	)	PUNCT
ejpam-3329	210	1	=	=	SYM
ejpam-3329	210	2	σ(t1	σ(t1	X
ejpam-3329	210	3	)	)	PUNCT
ejpam-3329	210	4	∪	∪	ADP
ejpam-3329	210	5	{	{	PUNCT
ejpam-3329	210	6	0	0	NUM
ejpam-3329	210	7	}	}	PUNCT
ejpam-3329	210	8	where	where	SCONJ
ejpam-3329	210	9	σ(t	σ(t	PROPN
ejpam-3329	210	10	)	)	PUNCT
ejpam-3329	210	11	denotes	denote	VERB
ejpam-3329	210	12	the	the	DET
ejpam-3329	210	13	spectrum	spectrum	NOUN
ejpam-3329	210	14	of	of	ADP
ejpam-3329	210	15	t	t	PROPN
ejpam-3329	210	16	.	.	PUNCT
ejpam-3329	211	1	proof	proof	NOUN
ejpam-3329	211	2	.	.	PUNCT
ejpam-3329	212	1	let	let	AUX
ejpam-3329	212	2	t	t	PROPN
ejpam-3329	212	3	∈	∈	PROPN
ejpam-3329	212	4	b(h	b(h	PROPN
ejpam-3329	212	5	)	)	PUNCT
ejpam-3329	212	6	be	be	VERB
ejpam-3329	212	7	quasi	quasi	X
ejpam-3329	212	8	n	n	PRON
ejpam-3329	212	9	class	class	NOUN
ejpam-3329	212	10	q∗	q∗	NOUN
ejpam-3329	212	11	operator	operator	NOUN
ejpam-3329	212	12	and	and	CCONJ
ejpam-3329	212	13	p	p	NOUN
ejpam-3329	212	14	be	be	AUX
ejpam-3329	212	15	an	an	DET
ejpam-3329	212	16	orthogonal	orthogonal	ADJ
ejpam-3329	212	17	projection	projection	NOUN
ejpam-3329	212	18	onto	onto	ADP
ejpam-3329	212	19	ran(t	ran(t	PROPN
ejpam-3329	212	20	)	)	PUNCT
ejpam-3329	212	21	.	.	PUNCT
ejpam-3329	213	1	then	then	ADV
ejpam-3329	213	2	t1	t1	NOUN
ejpam-3329	213	3	=	=	PUNCT
ejpam-3329	213	4	tp	tp	PROPN
ejpam-3329	213	5	=	=	PROPN
ejpam-3329	213	6	ptp	ptp	PROPN
ejpam-3329	213	7	.	.	PUNCT
ejpam-3329	214	1	by	by	ADP
ejpam-3329	214	2	theorem	theorem	NOUN
ejpam-3329	214	3	11	11	NUM
ejpam-3329	214	4	we	we	PRON
ejpam-3329	214	5	have	have	VERB
ejpam-3329	214	6	that	that	DET
ejpam-3329	214	7	p	p	PROPN
ejpam-3329	214	8	(	(	PUNCT
ejpam-3329	214	9	t	t	PROPN
ejpam-3329	214	10	∗1+nt	∗1+nt	PROPN
ejpam-3329	214	11	1+n	1+n	NUM
ejpam-3329	214	12	−	−	PROPN
ejpam-3329	214	13	(	(	PUNCT
ejpam-3329	214	14	1	1	NUM
ejpam-3329	214	15	+	+	CCONJ
ejpam-3329	214	16	n)(tt	n)(tt	ADP
ejpam-3329	214	17	∗	∗	NOUN
ejpam-3329	214	18	)	)	PUNCT
ejpam-3329	215	1	+	+	CCONJ
ejpam-3329	215	2	ni)p	ni)p	PROPN
ejpam-3329	215	3	≥	≥	NOUN
ejpam-3329	215	4	0	0	NUM
ejpam-3329	215	5	t	t	PROPN
ejpam-3329	215	6	∗1+n1	∗1+n1	PROPN
ejpam-3329	215	7	t	t	PROPN
ejpam-3329	215	8	1+n	1+n	NUM
ejpam-3329	215	9	1	1	NUM
ejpam-3329	215	10	−	−	PROPN
ejpam-3329	215	11	(	(	PUNCT
ejpam-3329	215	12	1	1	NUM
ejpam-3329	215	13	+	+	NUM
ejpam-3329	215	14	n)(t1	n)(t1	PROPN
ejpam-3329	215	15	t	t	PROPN
ejpam-3329	215	16	∗	∗	NOUN
ejpam-3329	215	17	1	1	NUM
ejpam-3329	215	18	+	+	NUM
ejpam-3329	215	19	t2	t2	NOUN
ejpam-3329	215	20	t	t	PROPN
ejpam-3329	215	21	∗	∗	X
ejpam-3329	215	22	2	2	NUM
ejpam-3329	215	23	)	)	PUNCT
ejpam-3329	216	1	+	+	CCONJ
ejpam-3329	216	2	ni	ni	PROPN
ejpam-3329	216	3	≥	≥	NOUN
ejpam-3329	216	4	0	0	NUM
ejpam-3329	216	5	also	also	ADV
ejpam-3329	216	6	for	for	ADP
ejpam-3329	216	7	any	any	DET
ejpam-3329	216	8	x	x	SYM
ejpam-3329	216	9	=	=	SYM
ejpam-3329	216	10	(	(	PUNCT
ejpam-3329	216	11	x1	x1	PROPN
ejpam-3329	216	12	,	,	PUNCT
ejpam-3329	216	13	x2	x2	PROPN
ejpam-3329	216	14	)	)	PUNCT
ejpam-3329	216	15	∈	∈	PROPN
ejpam-3329	216	16	h	h	NOUN
ejpam-3329	216	17	,	,	PUNCT
ejpam-3329	216	18	〈	〈	PROPN
ejpam-3329	216	19	t3x2	t3x2	NOUN
ejpam-3329	216	20	,	,	PUNCT
ejpam-3329	216	21	x2	x2	PROPN
ejpam-3329	216	22	〉	〉	NOUN
ejpam-3329	216	23	=	=	SYM
ejpam-3329	216	24	〈	〈	PROPN
ejpam-3329	216	25	t	t	PROPN
ejpam-3329	216	26	(	(	PUNCT
ejpam-3329	216	27	i	i	PRON
ejpam-3329	216	28	−	−	PROPN
ejpam-3329	216	29	p	p	NOUN
ejpam-3329	216	30	)	)	PUNCT
ejpam-3329	216	31	x	x	NOUN
ejpam-3329	216	32	,	,	PUNCT
ejpam-3329	216	33	(	(	PUNCT
ejpam-3329	216	34	i	i	PRON
ejpam-3329	216	35	−	−	PROPN
ejpam-3329	216	36	p	p	NOUN
ejpam-3329	216	37	)	)	PUNCT
ejpam-3329	216	38	x	x	NOUN
ejpam-3329	216	39	〉	〉	NOUN
ejpam-3329	216	40	=	=	SYM
ejpam-3329	216	41	〈	〈	PROPN
ejpam-3329	216	42	(	(	PUNCT
ejpam-3329	216	43	i	i	PRON
ejpam-3329	216	44	−	−	PROPN
ejpam-3329	216	45	p	p	NOUN
ejpam-3329	216	46	)	)	PUNCT
ejpam-3329	216	47	x	x	PROPN
ejpam-3329	216	48	,	,	PUNCT
ejpam-3329	216	49	t	t	PROPN
ejpam-3329	216	50	∗(i	∗(i	PROPN
ejpam-3329	216	51	−	−	PROPN
ejpam-3329	216	52	p	p	NOUN
ejpam-3329	216	53	)	)	PUNCT
ejpam-3329	216	54	x	x	NOUN
ejpam-3329	216	55	〉	〉	NUM
ejpam-3329	216	56	=	=	SYM
ejpam-3329	216	57	0	0	NUM
ejpam-3329	216	58	this	this	PRON
ejpam-3329	216	59	implies	imply	VERB
ejpam-3329	216	60	t3	t3	PROPN
ejpam-3329	216	61	=	=	SYM
ejpam-3329	216	62	0	0	NUM
ejpam-3329	216	63	since	since	SCONJ
ejpam-3329	216	64	σ(t	σ(t	PROPN
ejpam-3329	216	65	)	)	PUNCT
ejpam-3329	216	66	∪τ	∪τ	PROPN
ejpam-3329	217	1	=	=	SYM
ejpam-3329	217	2	σ(t1)∪σ(t3	σ(t1)∪σ(t3	PROPN
ejpam-3329	217	3	)	)	PUNCT
ejpam-3329	217	4	where	where	SCONJ
ejpam-3329	217	5	τ	τ	PROPN
ejpam-3329	217	6	is	be	AUX
ejpam-3329	217	7	the	the	DET
ejpam-3329	217	8	union	union	NOUN
ejpam-3329	217	9	of	of	ADP
ejpam-3329	217	10	the	the	DET
ejpam-3329	217	11	holes	hole	NOUN
ejpam-3329	217	12	in	in	ADP
ejpam-3329	217	13	σ(t	σ(t	PROPN
ejpam-3329	217	14	)	)	PUNCT
ejpam-3329	217	15	,	,	PUNCT
ejpam-3329	217	16	which	which	PRON
ejpam-3329	217	17	happens	happen	VERB
ejpam-3329	217	18	to	to	PART
ejpam-3329	217	19	be	be	AUX
ejpam-3329	217	20	a	a	DET
ejpam-3329	217	21	subset	subset	NOUN
ejpam-3329	217	22	of	of	ADP
ejpam-3329	217	23	σ(t1	σ(t1	NOUN
ejpam-3329	217	24	)	)	PUNCT
ejpam-3329	217	25	∩	∩	NOUN
ejpam-3329	217	26	σ(t3	σ(t3	NOUN
ejpam-3329	217	27	)	)	PUNCT
ejpam-3329	218	1	[	[	X
ejpam-3329	218	2	by	by	ADP
ejpam-3329	218	3	corollary	corollary	ADJ
ejpam-3329	218	4	7	7	NUM
ejpam-3329	218	5	,	,	PUNCT
ejpam-3329	218	6	[	[	X
ejpam-3329	218	7	10	10	NUM
ejpam-3329	218	8	]	]	SYM
ejpam-3329	218	9	]	]	PUNCT
ejpam-3329	218	10	.	.	PUNCT
ejpam-3329	218	11	σ(t3	σ(t3	PROPN
ejpam-3329	218	12	)	)	PUNCT
ejpam-3329	218	13	=	=	SYM
ejpam-3329	218	14	0	0	NUM
ejpam-3329	218	15	and	and	CCONJ
ejpam-3329	218	16	σ(t1	σ(t1	NOUN
ejpam-3329	218	17	)	)	PUNCT
ejpam-3329	218	18	∩	∩	NOUN
ejpam-3329	218	19	σ(t3	σ(t3	NOUN
ejpam-3329	218	20	)	)	PUNCT
ejpam-3329	218	21	has	have	VERB
ejpam-3329	218	22	no	no	DET
ejpam-3329	218	23	interior	interior	ADJ
ejpam-3329	218	24	points	point	NOUN
ejpam-3329	218	25	we	we	PRON
ejpam-3329	218	26	have	have	VERB
ejpam-3329	218	27	σ(t	σ(t	NOUN
ejpam-3329	218	28	)	)	PUNCT
ejpam-3329	219	1	=	=	SYM
ejpam-3329	219	2	σ(t1	σ(t1	X
ejpam-3329	219	3	)	)	PUNCT
ejpam-3329	219	4	∪	∪	X
ejpam-3329	219	5	{	{	PUNCT
ejpam-3329	219	6	0	0	NUM
ejpam-3329	219	7	}	}	PUNCT
ejpam-3329	219	8	.	.	PUNCT
ejpam-3329	220	1	suppose	suppose	VERB
ejpam-3329	220	2	that	that	SCONJ
ejpam-3329	220	3	t	t	NOUN
ejpam-3329	220	4	=	=	PUNCT
ejpam-3329	220	5	(	(	PUNCT
ejpam-3329	220	6	t1	t1	PROPN
ejpam-3329	220	7	t2	t2	PROPN
ejpam-3329	220	8	0	0	NUM
ejpam-3329	220	9	t3	t3	PROPN
ejpam-3329	220	10	)	)	PUNCT
ejpam-3329	220	11	on	on	ADP
ejpam-3329	220	12	h	h	NOUN
ejpam-3329	220	13	=	=	SYM
ejpam-3329	220	14	ran(t	ran(t	PROPN
ejpam-3329	220	15	)	)	PUNCT
ejpam-3329	220	16	⊕	⊕	PROPN
ejpam-3329	220	17	kert	kert	PROPN
ejpam-3329	220	18	∗	∗	PROPN
ejpam-3329	220	19	,	,	PUNCT
ejpam-3329	220	20	t	t	PROPN
ejpam-3329	220	21	∗1+n1	∗1+n1	PROPN
ejpam-3329	220	22	t	t	PROPN
ejpam-3329	220	23	1+n	1+n	NUM
ejpam-3329	220	24	1	1	NUM
ejpam-3329	220	25	−	−	PROPN
ejpam-3329	220	26	(	(	PUNCT
ejpam-3329	220	27	1	1	NUM
ejpam-3329	220	28	+	+	NUM
ejpam-3329	220	29	n)(t1	n)(t1	PROPN
ejpam-3329	220	30	t	t	PROPN
ejpam-3329	220	31	∗	∗	NOUN
ejpam-3329	220	32	1	1	NUM
ejpam-3329	220	33	+	+	NUM
ejpam-3329	220	34	t2	t2	NOUN
ejpam-3329	220	35	t	t	PROPN
ejpam-3329	220	36	∗	∗	X
ejpam-3329	220	37	2	2	NUM
ejpam-3329	220	38	)	)	PUNCT
ejpam-3329	221	1	+	+	CCONJ
ejpam-3329	221	2	ni	ni	PROPN
ejpam-3329	221	3	≥	≥	NOUN
ejpam-3329	221	4	0	0	NUM
ejpam-3329	221	5	and	and	CCONJ
ejpam-3329	221	6	t3	t3	PROPN
ejpam-3329	221	7	=	=	SYM
ejpam-3329	221	8	0	0	PROPN
ejpam-3329	221	9	.	.	PUNCT
ejpam-3329	222	1	then	then	ADV
ejpam-3329	222	2	we	we	PRON
ejpam-3329	222	3	have	have	VERB
ejpam-3329	222	4	t	t	X
ejpam-3329	222	5	∗2+nt	∗2+nt	ADP
ejpam-3329	222	6	2+n−(1	2+n−(1	NUM
ejpam-3329	223	1	+	+	CCONJ
ejpam-3329	224	1	n)(t	n)(t	PROPN
ejpam-3329	224	2	∗t	∗t	ADJ
ejpam-3329	224	3	)	)	PUNCT
ejpam-3329	224	4	2	2	NUM
ejpam-3329	224	5	+	+	CCONJ
ejpam-3329	224	6	nt	not	PART
ejpam-3329	224	7	∗t	∗t	PROPN
ejpam-3329	224	8	=	=	SYM
ejpam-3329	224	9	(	(	PUNCT
ejpam-3329	224	10	t	t	PROPN
ejpam-3329	224	11	∗2+n1	∗2+n1	PROPN
ejpam-3329	224	12	0	0	NUM
ejpam-3329	224	13	(	(	PUNCT
ejpam-3329	224	14	t	t	PROPN
ejpam-3329	224	15	∗2	∗2	PROPN
ejpam-3329	224	16	t	t	PROPN
ejpam-3329	224	17	∗1+n	∗1+n	PROPN
ejpam-3329	224	18	1	1	NUM
ejpam-3329	224	19	)	)	PUNCT
ejpam-3329	224	20	0	0	NUM
ejpam-3329	224	21	)	)	PUNCT
ejpam-3329	225	1	(	(	PUNCT
ejpam-3329	225	2	t	t	PROPN
ejpam-3329	225	3	2+n	2+n	NUM
ejpam-3329	225	4	1	1	NUM
ejpam-3329	225	5	t	t	PROPN
ejpam-3329	225	6	1+n	1+n	NUM
ejpam-3329	225	7	1	1	NUM
ejpam-3329	225	8	t2	t2	NOUN
ejpam-3329	225	9	0	0	NUM
ejpam-3329	225	10	0	0	NUM
ejpam-3329	225	11	)	)	PUNCT
ejpam-3329	225	12	−	−	PROPN
ejpam-3329	226	1	(	(	PUNCT
ejpam-3329	226	2	1	1	NUM
ejpam-3329	226	3	+	+	NUM
ejpam-3329	226	4	n	n	CCONJ
ejpam-3329	226	5	)	)	PUNCT
ejpam-3329	226	6	(	(	PUNCT
ejpam-3329	226	7	(	(	PUNCT
ejpam-3329	226	8	t	t	X
ejpam-3329	226	9	∗1	∗1	PROPN
ejpam-3329	226	10	t1	t1	NOUN
ejpam-3329	226	11	)	)	PUNCT
ejpam-3329	226	12	2	2	NUM
ejpam-3329	227	1	+	+	NUM
ejpam-3329	227	2	t	t	X
ejpam-3329	227	3	∗1	∗1	PROPN
ejpam-3329	227	4	t2	t2	PROPN
ejpam-3329	227	5	t	t	PROPN
ejpam-3329	227	6	∗	∗	X
ejpam-3329	227	7	2	2	NUM
ejpam-3329	227	8	t1	t1	NOUN
ejpam-3329	227	9	t	t	PROPN
ejpam-3329	227	10	∗1	∗1	PROPN
ejpam-3329	227	11	t1	t1	PROPN
ejpam-3329	227	12	t	t	PROPN
ejpam-3329	227	13	∗	∗	NOUN
ejpam-3329	227	14	1	1	NUM
ejpam-3329	227	15	t2	t2	PROPN
ejpam-3329	227	16	+	+	CCONJ
ejpam-3329	227	17	t	t	PROPN
ejpam-3329	227	18	∗1	∗1	PROPN
ejpam-3329	227	19	t2	t2	PROPN
ejpam-3329	227	20	t	t	PROPN
ejpam-3329	227	21	∗	∗	X
ejpam-3329	227	22	2	2	NUM
ejpam-3329	227	23	t2	t2	PROPN
ejpam-3329	227	24	t	t	PROPN
ejpam-3329	227	25	∗2	∗2	PROPN
ejpam-3329	227	26	t1	t1	PROPN
ejpam-3329	227	27	t	t	PROPN
ejpam-3329	227	28	∗	∗	NOUN
ejpam-3329	227	29	1	1	NUM
ejpam-3329	227	30	t1	t1	NOUN
ejpam-3329	227	31	+	+	CCONJ
ejpam-3329	227	32	t	t	PROPN
ejpam-3329	227	33	∗2	∗2	PROPN
ejpam-3329	227	34	t2	t2	PROPN
ejpam-3329	227	35	t	t	PROPN
ejpam-3329	227	36	∗	∗	X
ejpam-3329	227	37	2	2	NUM
ejpam-3329	227	38	t1	t1	NOUN
ejpam-3329	227	39	t	t	PROPN
ejpam-3329	227	40	∗2	∗2	PROPN
ejpam-3329	227	41	t1	t1	PROPN
ejpam-3329	227	42	t	t	PROPN
ejpam-3329	227	43	∗	∗	NOUN
ejpam-3329	227	44	1	1	NUM
ejpam-3329	227	45	t2	t2	NOUN
ejpam-3329	227	46	+	+	CCONJ
ejpam-3329	227	47	(	(	PUNCT
ejpam-3329	227	48	t	t	PROPN
ejpam-3329	227	49	∗2	∗2	PROPN
ejpam-3329	227	50	t2	t2	NOUN
ejpam-3329	227	51	)	)	PUNCT
ejpam-3329	227	52	2	2	NUM
ejpam-3329	227	53	)	)	PUNCT
ejpam-3329	227	54	d.	d.	PROPN
ejpam-3329	227	55	senthilkumar	senthilkumar	PROPN
ejpam-3329	227	56	,	,	PUNCT
ejpam-3329	227	57	s.	s.	PROPN
ejpam-3329	227	58	parvatham	parvatham	PROPN
ejpam-3329	227	59	/	/	SYM
ejpam-3329	227	60	eur	eur	PROPN
ejpam-3329	227	61	.	.	PUNCT
ejpam-3329	228	1	j.	j.	PROPN
ejpam-3329	228	2	pure	pure	PROPN
ejpam-3329	228	3	appl	appl	PROPN
ejpam-3329	228	4	.	.	PROPN
ejpam-3329	228	5	math	math	PROPN
ejpam-3329	228	6	,	,	PUNCT
ejpam-3329	228	7	11	11	NUM
ejpam-3329	228	8	(	(	PUNCT
ejpam-3329	228	9	4	4	NUM
ejpam-3329	228	10	)	)	PUNCT
ejpam-3329	228	11	(	(	PUNCT
ejpam-3329	228	12	2018	2018	NUM
ejpam-3329	228	13	)	)	PUNCT
ejpam-3329	228	14	,	,	PUNCT
ejpam-3329	228	15	1108	1108	NUM
ejpam-3329	228	16	-	-	SYM
ejpam-3329	228	17	1129	1129	NUM
ejpam-3329	228	18	1116	1116	NUM
ejpam-3329	228	19	+	+	CCONJ
ejpam-3329	228	20	n	n	X
ejpam-3329	229	1	(	(	PUNCT
ejpam-3329	229	2	t	t	PROPN
ejpam-3329	229	3	∗1	∗1	PROPN
ejpam-3329	229	4	t1	t1	PROPN
ejpam-3329	229	5	t	t	PROPN
ejpam-3329	230	1	∗1	∗1	PROPN
ejpam-3329	230	2	t2	t2	PROPN
ejpam-3329	230	3	t	t	PROPN
ejpam-3329	230	4	∗2	∗2	PROPN
ejpam-3329	230	5	t1	t1	PROPN
ejpam-3329	230	6	t	t	PROPN
ejpam-3329	230	7	∗2	∗2	PROPN
ejpam-3329	230	8	t2	t2	NOUN
ejpam-3329	230	9	)	)	PUNCT
ejpam-3329	231	1	=	=	PUNCT
ejpam-3329	231	2	(	(	PUNCT
ejpam-3329	231	3	a	a	DET
ejpam-3329	231	4	b	b	NOUN
ejpam-3329	231	5	b∗	b∗	ADJ
ejpam-3329	231	6	c	c	NOUN
ejpam-3329	231	7	)	)	PUNCT
ejpam-3329	231	8	≥	≥	NOUN
ejpam-3329	231	9	0	0	NUM
ejpam-3329	231	10	where	where	SCONJ
ejpam-3329	231	11	a	a	DET
ejpam-3329	231	12	=	=	SYM
ejpam-3329	231	13	t	t	X
ejpam-3329	231	14	∗1	∗1	PROPN
ejpam-3329	231	15	(	(	PUNCT
ejpam-3329	231	16	t	t	PROPN
ejpam-3329	231	17	∗1+n1	∗1+n1	PROPN
ejpam-3329	231	18	t	t	PROPN
ejpam-3329	231	19	1+n	1+n	NUM
ejpam-3329	231	20	1	1	NUM
ejpam-3329	231	21	−	−	PROPN
ejpam-3329	231	22	(	(	PUNCT
ejpam-3329	231	23	1	1	NUM
ejpam-3329	231	24	+	+	NUM
ejpam-3329	231	25	n)(t1	n)(t1	PROPN
ejpam-3329	231	26	t	t	PROPN
ejpam-3329	231	27	∗	∗	NOUN
ejpam-3329	231	28	1	1	NUM
ejpam-3329	231	29	+	+	NUM
ejpam-3329	231	30	t2	t2	NOUN
ejpam-3329	231	31	t	t	PROPN
ejpam-3329	231	32	∗	∗	X
ejpam-3329	231	33	2	2	NUM
ejpam-3329	231	34	)	)	PUNCT
ejpam-3329	232	1	+	+	CCONJ
ejpam-3329	232	2	ni)t1	ni)t1	PROPN
ejpam-3329	232	3	b	b	PROPN
ejpam-3329	232	4	=	=	SYM
ejpam-3329	232	5	t	t	X
ejpam-3329	233	1	∗1	∗1	PROPN
ejpam-3329	233	2	(	(	PUNCT
ejpam-3329	233	3	t	t	PROPN
ejpam-3329	233	4	∗1+n1	∗1+n1	PROPN
ejpam-3329	233	5	t	t	PROPN
ejpam-3329	233	6	1+n	1+n	NUM
ejpam-3329	233	7	1	1	NUM
ejpam-3329	233	8	−	−	PROPN
ejpam-3329	233	9	(	(	PUNCT
ejpam-3329	233	10	1	1	NUM
ejpam-3329	233	11	+	+	NUM
ejpam-3329	233	12	n)(t1	n)(t1	PROPN
ejpam-3329	233	13	t	t	PROPN
ejpam-3329	233	14	∗	∗	NOUN
ejpam-3329	233	15	1	1	NUM
ejpam-3329	233	16	+	+	NUM
ejpam-3329	233	17	t2	t2	NOUN
ejpam-3329	233	18	t	t	PROPN
ejpam-3329	233	19	∗	∗	X
ejpam-3329	233	20	2	2	NUM
ejpam-3329	233	21	)	)	PUNCT
ejpam-3329	233	22	+	+	CCONJ
ejpam-3329	233	23	ni)t2	ni)t2	PROPN
ejpam-3329	233	24	c	c	PROPN
ejpam-3329	233	25	=	=	SYM
ejpam-3329	233	26	t	t	PROPN
ejpam-3329	233	27	∗2	∗2	PROPN
ejpam-3329	233	28	(	(	PUNCT
ejpam-3329	233	29	t	t	PROPN
ejpam-3329	233	30	∗1+n1	∗1+n1	PROPN
ejpam-3329	233	31	t	t	PROPN
ejpam-3329	233	32	1+n	1+n	NUM
ejpam-3329	233	33	1	1	NUM
ejpam-3329	233	34	−	−	PROPN
ejpam-3329	233	35	(	(	PUNCT
ejpam-3329	233	36	1	1	NUM
ejpam-3329	233	37	+	+	NUM
ejpam-3329	233	38	n)(t1	n)(t1	PROPN
ejpam-3329	233	39	t	t	PROPN
ejpam-3329	233	40	∗	∗	NOUN
ejpam-3329	233	41	1	1	NUM
ejpam-3329	233	42	+	+	NUM
ejpam-3329	233	43	t2	t2	NOUN
ejpam-3329	233	44	t	t	PROPN
ejpam-3329	233	45	∗	∗	X
ejpam-3329	233	46	2	2	NUM
ejpam-3329	233	47	)	)	PUNCT
ejpam-3329	233	48	+	+	CCONJ
ejpam-3329	234	1	ni)t2	ni)t2	PROPN
ejpam-3329	234	2	.	.	PUNCT
ejpam-3329	235	1	hence	hence	ADV
ejpam-3329	235	2	t	t	PROPN
ejpam-3329	235	3	is	be	AUX
ejpam-3329	235	4	quasi	quasi	NOUN
ejpam-3329	235	5	n	n	PRON
ejpam-3329	235	6	class	class	NOUN
ejpam-3329	235	7	q∗	q∗	NOUN
ejpam-3329	235	8	operator	operator	NOUN
ejpam-3329	235	9	.	.	PUNCT
ejpam-3329	236	1	theorem	theorem	PROPN
ejpam-3329	236	2	19	19	NUM
ejpam-3329	236	3	.	.	PUNCT
ejpam-3329	237	1	let	let	VERB
ejpam-3329	237	2	m	m	PRON
ejpam-3329	237	3	be	be	AUX
ejpam-3329	237	4	a	a	DET
ejpam-3329	237	5	closed	closed	ADJ
ejpam-3329	237	6	t	t	NOUN
ejpam-3329	237	7	-invariant	-invariant	ADJ
ejpam-3329	237	8	subspace	subspace	NOUN
ejpam-3329	237	9	of	of	ADP
ejpam-3329	237	10	h.	h.	PROPN
ejpam-3329	237	11	then	then	ADV
ejpam-3329	237	12	the	the	DET
ejpam-3329	237	13	restriction	restriction	NOUN
ejpam-3329	237	14	t	t	NOUN
ejpam-3329	237	15	|m	|m	NOUN
ejpam-3329	237	16	of	of	ADP
ejpam-3329	237	17	a	a	DET
ejpam-3329	237	18	quasi	quasi	NOUN
ejpam-3329	237	19	n	n	PRON
ejpam-3329	237	20	class	class	NOUN
ejpam-3329	237	21	q∗	q∗	NOUN
ejpam-3329	237	22	operator	operator	NOUN
ejpam-3329	237	23	t	t	PROPN
ejpam-3329	237	24	to	to	ADP
ejpam-3329	237	25	m	m	PROPN
ejpam-3329	237	26	is	be	AUX
ejpam-3329	237	27	quasi	quasi	ADJ
ejpam-3329	237	28	n	n	PRON
ejpam-3329	237	29	class	class	NOUN
ejpam-3329	237	30	q∗	q∗	NOUN
ejpam-3329	237	31	operator	operator	NOUN
ejpam-3329	237	32	.	.	PUNCT
ejpam-3329	238	1	proof	proof	NOUN
ejpam-3329	238	2	.	.	PUNCT
ejpam-3329	239	1	by	by	ADP
ejpam-3329	239	2	theorem	theorem	NOUN
ejpam-3329	239	3	18	18	NUM
ejpam-3329	239	4	,	,	PUNCT
ejpam-3329	239	5	t	t	PROPN
ejpam-3329	239	6	|m	|m	NOUN
ejpam-3329	239	7	is	be	AUX
ejpam-3329	239	8	also	also	ADV
ejpam-3329	239	9	quasi	quasi	ADJ
ejpam-3329	239	10	n	n	PRON
ejpam-3329	239	11	class	class	NOUN
ejpam-3329	239	12	q∗	q∗	NOUN
ejpam-3329	239	13	operator	operator	NOUN
ejpam-3329	239	14	.	.	PUNCT
ejpam-3329	240	1	theorem	theorem	VERB
ejpam-3329	240	2	20	20	NUM
ejpam-3329	240	3	.	.	PUNCT
ejpam-3329	241	1	let	let	VERB
ejpam-3329	241	2	t	t	NOUN
ejpam-3329	241	3	be	be	AUX
ejpam-3329	241	4	a	a	DET
ejpam-3329	241	5	regular	regular	ADJ
ejpam-3329	241	6	quasi	quasi	NOUN
ejpam-3329	241	7	n	n	PRON
ejpam-3329	241	8	class	class	NOUN
ejpam-3329	241	9	q∗	q∗	NOUN
ejpam-3329	241	10	operator	operator	NOUN
ejpam-3329	241	11	,	,	PUNCT
ejpam-3329	241	12	then	then	ADV
ejpam-3329	241	13	the	the	DET
ejpam-3329	241	14	approximate	approximate	ADJ
ejpam-3329	241	15	point	point	NOUN
ejpam-3329	241	16	spectrum	spectrum	NOUN
ejpam-3329	241	17	lies	lie	VERB
ejpam-3329	241	18	in	in	ADP
ejpam-3329	241	19	the	the	DET
ejpam-3329	241	20	disc	disc	NOUN
ejpam-3329	241	21	σap(t	σap(t	NOUN
ejpam-3329	241	22	)	)	PUNCT
ejpam-3329	242	1	⊆	⊆	NUM
ejpam-3329	242	2	{	{	PUNCT
ejpam-3329	242	3	λ	λ	X
ejpam-3329	242	4	∈	∈	PROPN
ejpam-3329	242	5	c	c	NOUN
ejpam-3329	242	6	:	:	PUNCT
ejpam-3329	242	7	(	(	PUNCT
ejpam-3329	242	8	1+n	1+n	NUM
ejpam-3329	242	9	)	)	PUNCT
ejpam-3329	242	10	(	(	PUNCT
ejpam-3329	242	11	1	1	NUM
ejpam-3329	242	12	2	2	NUM
ejpam-3329	242	13	)	)	PUNCT
ejpam-3329	242	14	‖t−1‖‖t	‖t−1‖‖t	NOUN
ejpam-3329	242	15	∗−1‖(‖t	∗−1‖(‖t	NOUN
ejpam-3329	242	16	1+n‖2+n	1+n‖2+n	NUM
ejpam-3329	242	17	)	)	PUNCT
ejpam-3329	242	18	1	1	NUM
ejpam-3329	242	19	2	2	NUM
ejpam-3329	242	20	≤	≤	NUM
ejpam-3329	242	21	|λ|	|λ|	NOUN
ejpam-3329	242	22	≤	≤	NOUN
ejpam-3329	242	23	‖t‖	‖t‖	PROPN
ejpam-3329	242	24	proof	proof	NOUN
ejpam-3329	242	25	.	.	PUNCT
ejpam-3329	243	1	suppose	suppose	VERB
ejpam-3329	243	2	t	t	PROPN
ejpam-3329	243	3	is	be	AUX
ejpam-3329	243	4	regular	regular	ADJ
ejpam-3329	243	5	quasi	quasi	NOUN
ejpam-3329	243	6	n	n	PRON
ejpam-3329	243	7	class	class	NOUN
ejpam-3329	243	8	q∗	q∗	NOUN
ejpam-3329	243	9	operator	operator	NOUN
ejpam-3329	243	10	,	,	PUNCT
ejpam-3329	243	11	then	then	ADV
ejpam-3329	243	12	for	for	ADP
ejpam-3329	243	13	every	every	DET
ejpam-3329	243	14	unit	unit	NOUN
ejpam-3329	243	15	vector	vector	NOUN
ejpam-3329	243	16	x	x	PUNCT
ejpam-3329	243	17	in	in	ADP
ejpam-3329	243	18	h	h	NOUN
ejpam-3329	243	19	,	,	PUNCT
ejpam-3329	243	20	we	we	PRON
ejpam-3329	243	21	have	have	VERB
ejpam-3329	243	22	‖tx‖2	‖tx‖2	PROPN
ejpam-3329	243	23	≥	≥	PUNCT
ejpam-3329	243	24	(	(	PUNCT
ejpam-3329	243	25	1	1	NUM
ejpam-3329	243	26	+	+	CCONJ
ejpam-3329	243	27	n)‖x‖2	n)‖x‖2	ADJ
ejpam-3329	243	28	‖t−1‖2‖t	‖t−1‖2‖t	ADP
ejpam-3329	243	29	∗−1‖2(‖t	∗−1‖2(‖t	PUNCT
ejpam-3329	243	30	1+n‖2	1+n‖2	PROPN
ejpam-3329	243	31	+	+	NOUN
ejpam-3329	243	32	n	n	CCONJ
ejpam-3329	243	33	)	)	PUNCT
ejpam-3329	243	34	now	now	ADV
ejpam-3329	243	35	assume	assume	VERB
ejpam-3329	243	36	that	that	SCONJ
ejpam-3329	243	37	λ	λ	PROPN
ejpam-3329	243	38	∈	∈	NOUN
ejpam-3329	243	39	σap(t	σap(t	PROPN
ejpam-3329	243	40	)	)	PUNCT
ejpam-3329	243	41	.	.	PUNCT
ejpam-3329	244	1	then	then	ADV
ejpam-3329	244	2	there	there	PRON
ejpam-3329	244	3	exists	exist	VERB
ejpam-3329	244	4	a	a	DET
ejpam-3329	244	5	sequence	sequence	NOUN
ejpam-3329	244	6	{	{	PUNCT
ejpam-3329	244	7	xm	xm	PROPN
ejpam-3329	244	8	}	}	PUNCT
ejpam-3329	244	9	,	,	PUNCT
ejpam-3329	244	10	‖xm‖	‖xm‖	NOUN
ejpam-3329	244	11	=	=	NOUN
ejpam-3329	244	12	1	1	NUM
ejpam-3329	244	13	such	such	ADJ
ejpam-3329	244	14	that	that	SCONJ
ejpam-3329	244	15	‖(t	‖(t	PUNCT
ejpam-3329	245	1	−	−	PROPN
ejpam-3329	245	2	λ)xm‖	λ)xm‖	PROPN
ejpam-3329	245	3	→	→	SYM
ejpam-3329	245	4	0	0	NUM
ejpam-3329	245	5	when	when	SCONJ
ejpam-3329	245	6	m→∞	m→∞	NOUN
ejpam-3329	245	7	we	we	PRON
ejpam-3329	245	8	have	have	VERB
ejpam-3329	245	9	‖txm	‖txm	PROPN
ejpam-3329	245	10	−	−	PROPN
ejpam-3329	245	11	λxm‖	λxm‖	X
ejpam-3329	245	12	≥	≥	X
ejpam-3329	245	13	‖txm‖	‖txm‖	NUM
ejpam-3329	245	14	−	−	PROPN
ejpam-3329	245	15	|λ|‖xm‖	|λ|‖xm‖	PROPN
ejpam-3329	245	16	≥	≥	NOUN
ejpam-3329	245	17	‖t‖	‖t‖	PROPN
ejpam-3329	245	18	−	−	PROPN
ejpam-3329	245	19	|λ|	|λ|	NOUN
ejpam-3329	245	20	≥	≥	NOUN
ejpam-3329	245	21	(	(	PUNCT
ejpam-3329	245	22	1	1	NUM
ejpam-3329	245	23	+	+	CCONJ
ejpam-3329	245	24	n)1/2	n)1/2	PROPN
ejpam-3329	245	25	‖t	‖t	NOUN
ejpam-3329	245	26	∗−1‖‖t−1‖(‖t	∗−1‖‖t−1‖(‖t	ADP
ejpam-3329	246	1	1+n‖2	1+n‖2	PROPN
ejpam-3329	247	1	+	+	NUM
ejpam-3329	247	2	n)1/2	n)1/2	NUM
ejpam-3329	247	3	−	−	PROPN
ejpam-3329	247	4	|λ|	|λ|	PROPN
ejpam-3329	247	5	now	now	ADV
ejpam-3329	247	6	when	when	SCONJ
ejpam-3329	247	7	m→∞	m→∞	NOUN
ejpam-3329	247	8	,	,	PUNCT
ejpam-3329	247	9	|λ|	|λ|	NOUN
ejpam-3329	247	10	≥	≥	NUM
ejpam-3329	247	11	(	(	PUNCT
ejpam-3329	247	12	1+n)1/2	1+n)1/2	NUM
ejpam-3329	247	13	‖t−1‖‖t	‖t−1‖‖t	NOUN
ejpam-3329	247	14	∗−1‖(‖t	∗−1‖(‖t	NOUN
ejpam-3329	247	15	1+n‖2+n)1/2	1+n‖2+n)1/2	NUM
ejpam-3329	247	16	4	4	NUM
ejpam-3329	247	17	.	.	PUNCT
ejpam-3329	247	18	quasi	quasi	PROPN
ejpam-3329	247	19	n	n	CCONJ
ejpam-3329	247	20	-	-	PUNCT
ejpam-3329	247	21	class	class	NOUN
ejpam-3329	247	22	q	q	NOUN
ejpam-3329	247	23	and	and	CCONJ
ejpam-3329	247	24	quasi	quasi	ADJ
ejpam-3329	247	25	n	n	CCONJ
ejpam-3329	247	26	-	-	PUNCT
ejpam-3329	247	27	class	class	NOUN
ejpam-3329	247	28	q∗	q∗	NOUN
ejpam-3329	247	29	composition	composition	NOUN
ejpam-3329	247	30	operators	operator	NOUN
ejpam-3329	247	31	let	let	VERB
ejpam-3329	247	32	l2(λ	l2(λ	PRON
ejpam-3329	247	33	)	)	PUNCT
ejpam-3329	247	34	=	=	SYM
ejpam-3329	247	35	l2(x	l2(x	PROPN
ejpam-3329	247	36	,	,	PUNCT
ejpam-3329	247	37	σ	σ	PROPN
ejpam-3329	247	38	,	,	PUNCT
ejpam-3329	247	39	λ	λ	PROPN
ejpam-3329	247	40	)	)	PUNCT
ejpam-3329	247	41	,	,	PUNCT
ejpam-3329	247	42	where	where	SCONJ
ejpam-3329	247	43	(	(	PUNCT
ejpam-3329	247	44	x	x	X
ejpam-3329	247	45	,	,	PUNCT
ejpam-3329	247	46	σ	σ	PROPN
ejpam-3329	247	47	,	,	PUNCT
ejpam-3329	247	48	λ	λ	PROPN
ejpam-3329	247	49	)	)	PUNCT
ejpam-3329	247	50	be	be	VERB
ejpam-3329	247	51	a	a	DET
ejpam-3329	247	52	sigma	sigma	ADJ
ejpam-3329	247	53	-	-	PUNCT
ejpam-3329	247	54	finite	finite	ADJ
ejpam-3329	247	55	measure	measure	NOUN
ejpam-3329	247	56	space	space	NOUN
ejpam-3329	247	57	.	.	PUNCT
ejpam-3329	248	1	a	a	DET
ejpam-3329	248	2	bounded	bounded	ADJ
ejpam-3329	248	3	linear	linear	ADJ
ejpam-3329	248	4	operator	operator	NOUN
ejpam-3329	248	5	ct	ct	NOUN
ejpam-3329	248	6	f	f	PROPN
ejpam-3329	249	1	=	=	SYM
ejpam-3329	249	2	f	f	PROPN
ejpam-3329	249	3	◦	◦	NOUN
ejpam-3329	249	4	t	t	X
ejpam-3329	249	5	on	on	ADP
ejpam-3329	249	6	l2(x	l2(x	PROPN
ejpam-3329	249	7	,	,	PUNCT
ejpam-3329	249	8	σ	σ	PROPN
ejpam-3329	249	9	,	,	PUNCT
ejpam-3329	249	10	λ	λ	PROPN
ejpam-3329	249	11	)	)	PUNCT
ejpam-3329	249	12	is	be	AUX
ejpam-3329	249	13	said	say	VERB
ejpam-3329	249	14	to	to	PART
ejpam-3329	249	15	be	be	AUX
ejpam-3329	249	16	a	a	DET
ejpam-3329	249	17	composition	composition	NOUN
ejpam-3329	249	18	operator	operator	NOUN
ejpam-3329	249	19	induced	induce	VERB
ejpam-3329	249	20	by	by	ADP
ejpam-3329	249	21	t	t	PROPN
ejpam-3329	249	22	,	,	PUNCT
ejpam-3329	249	23	a	a	DET
ejpam-3329	249	24	non	non	ADJ
ejpam-3329	249	25	-	-	ADJ
ejpam-3329	249	26	singular	singular	ADJ
ejpam-3329	249	27	measurable	measurable	ADJ
ejpam-3329	249	28	transformation	transformation	NOUN
ejpam-3329	249	29	from	from	ADP
ejpam-3329	249	30	x	x	PUNCT
ejpam-3329	249	31	into	into	ADP
ejpam-3329	249	32	itself	itself	PRON
ejpam-3329	249	33	,	,	PUNCT
ejpam-3329	249	34	when	when	SCONJ
ejpam-3329	249	35	the	the	DET
ejpam-3329	249	36	measure	measure	NOUN
ejpam-3329	249	37	λt−1	λt−1	NOUN
ejpam-3329	249	38	is	be	AUX
ejpam-3329	249	39	absolutely	absolutely	ADV
ejpam-3329	249	40	continuous	continuous	ADJ
ejpam-3329	249	41	with	with	ADP
ejpam-3329	249	42	respect	respect	NOUN
ejpam-3329	249	43	to	to	ADP
ejpam-3329	249	44	the	the	DET
ejpam-3329	249	45	measure	measure	NOUN
ejpam-3329	249	46	λ	λ	PROPN
ejpam-3329	249	47	and	and	CCONJ
ejpam-3329	249	48	the	the	DET
ejpam-3329	249	49	radon	radon	PROPN
ejpam-3329	249	50	-	-	PUNCT
ejpam-3329	249	51	nikodym	nikodym	PROPN
ejpam-3329	249	52	d.	d.	PROPN
ejpam-3329	249	53	senthilkumar	senthilkumar	PROPN
ejpam-3329	249	54	,	,	PUNCT
ejpam-3329	249	55	s.	s.	PROPN
ejpam-3329	249	56	parvatham	parvatham	PROPN
ejpam-3329	249	57	/	/	SYM
ejpam-3329	249	58	eur	eur	PROPN
ejpam-3329	249	59	.	.	PUNCT
ejpam-3329	250	1	j.	j.	PROPN
ejpam-3329	250	2	pure	pure	PROPN
ejpam-3329	250	3	appl	appl	PROPN
ejpam-3329	250	4	.	.	PROPN
ejpam-3329	250	5	math	math	PROPN
ejpam-3329	250	6	,	,	PUNCT
ejpam-3329	250	7	11	11	NUM
ejpam-3329	250	8	(	(	PUNCT
ejpam-3329	250	9	4	4	NUM
ejpam-3329	250	10	)	)	PUNCT
ejpam-3329	250	11	(	(	PUNCT
ejpam-3329	250	12	2018	2018	NUM
ejpam-3329	250	13	)	)	PUNCT
ejpam-3329	250	14	,	,	PUNCT
ejpam-3329	250	15	1108	1108	NUM
ejpam-3329	250	16	-	-	SYM
ejpam-3329	250	17	1129	1129	NUM
ejpam-3329	250	18	1117	1117	NUM
ejpam-3329	250	19	derivative	derivative	ADJ
ejpam-3329	250	20	dλt−1	dλt−1	PROPN
ejpam-3329	250	21	dλ	dλ	PROPN
ejpam-3329	251	1	=	=	PROPN
ejpam-3329	251	2	f0	f0	PROPN
ejpam-3329	251	3	is	be	AUX
ejpam-3329	251	4	essentially	essentially	ADV
ejpam-3329	251	5	bounded	bound	VERB
ejpam-3329	251	6	.	.	PUNCT
ejpam-3329	252	1	the	the	DET
ejpam-3329	252	2	radon	radon	PROPN
ejpam-3329	252	3	-	-	PUNCT
ejpam-3329	252	4	nikodym	nikodym	PROPN
ejpam-3329	252	5	derivative	derivative	NOUN
ejpam-3329	252	6	of	of	ADP
ejpam-3329	252	7	the	the	DET
ejpam-3329	252	8	measure	measure	NOUN
ejpam-3329	252	9	λ(t	λ(t	NOUN
ejpam-3329	252	10	k)−1	k)−1	NOUN
ejpam-3329	252	11	with	with	ADP
ejpam-3329	252	12	respect	respect	NOUN
ejpam-3329	252	13	to	to	ADP
ejpam-3329	252	14	λ	λ	PROPN
ejpam-3329	252	15	is	be	AUX
ejpam-3329	252	16	denoted	denote	VERB
ejpam-3329	252	17	by	by	ADP
ejpam-3329	252	18	f	f	PROPN
ejpam-3329	252	19	(	(	PUNCT
ejpam-3329	252	20	k	k	NOUN
ejpam-3329	252	21	)	)	PUNCT
ejpam-3329	252	22	0	0	NUM
ejpam-3329	252	23	,	,	PUNCT
ejpam-3329	252	24	where	where	SCONJ
ejpam-3329	252	25	t	t	PROPN
ejpam-3329	252	26	k	k	PROPN
ejpam-3329	252	27	is	be	AUX
ejpam-3329	252	28	obtained	obtain	VERB
ejpam-3329	252	29	by	by	ADP
ejpam-3329	252	30	composing	compose	VERB
ejpam-3329	252	31	t	t	PROPN
ejpam-3329	252	32	k	k	PROPN
ejpam-3329	252	33	times	times	PROPN
ejpam-3329	252	34	.	.	PUNCT
ejpam-3329	253	1	every	every	DET
ejpam-3329	253	2	essentially	essentially	ADV
ejpam-3329	253	3	bounded	bound	VERB
ejpam-3329	253	4	complex	complex	ADV
ejpam-3329	253	5	-	-	PUNCT
ejpam-3329	253	6	valued	value	VERB
ejpam-3329	253	7	measurable	measurable	ADJ
ejpam-3329	253	8	function	function	NOUN
ejpam-3329	253	9	f0	f0	PROPN
ejpam-3329	253	10	induces	induce	VERB
ejpam-3329	253	11	the	the	DET
ejpam-3329	253	12	bounded	bounded	ADJ
ejpam-3329	253	13	operator	operator	NOUN
ejpam-3329	253	14	mf0	mf0	NOUN
ejpam-3329	253	15	on	on	ADP
ejpam-3329	253	16	l2(λ	l2(λ	PROPN
ejpam-3329	253	17	)	)	PUNCT
ejpam-3329	253	18	,	,	PUNCT
ejpam-3329	253	19	which	which	PRON
ejpam-3329	253	20	is	be	AUX
ejpam-3329	253	21	defined	define	VERB
ejpam-3329	253	22	by	by	ADP
ejpam-3329	253	23	mf0f	mf0f	PROPN
ejpam-3329	253	24	=	=	SYM
ejpam-3329	253	25	f0f	f0f	PROPN
ejpam-3329	253	26	for	for	ADP
ejpam-3329	253	27	every	every	DET
ejpam-3329	253	28	f	f	PROPN
ejpam-3329	253	29	∈	∈	PROPN
ejpam-3329	253	30	l2(λ	l2(λ	PROPN
ejpam-3329	253	31	)	)	PUNCT
ejpam-3329	253	32	.	.	PUNCT
ejpam-3329	254	1	further	far	ADV
ejpam-3329	254	2	c∗tct	c∗tct	PUNCT
ejpam-3329	254	3	=	=	SYM
ejpam-3329	254	4	mf0	mf0	NOUN
ejpam-3329	254	5	,	,	PUNCT
ejpam-3329	254	6	c∗2	c∗2	PROPN
ejpam-3329	254	7	t	t	PROPN
ejpam-3329	254	8	c	c	PROPN
ejpam-3329	254	9	2	2	NUM
ejpam-3329	254	10	t	t	NOUN
ejpam-3329	254	11	=	=	SYM
ejpam-3329	254	12	mf0	mf0	NOUN
ejpam-3329	254	13	(	(	PUNCT
ejpam-3329	254	14	2	2	NUM
ejpam-3329	254	15	)	)	PUNCT
ejpam-3329	254	16	and	and	CCONJ
ejpam-3329	254	17	c∗1+nt	c∗1+nt	PROPN
ejpam-3329	254	18	c1+n2	c1+n2	PROPN
ejpam-3329	254	19	t	t	PROPN
ejpam-3329	254	20	=	=	SYM
ejpam-3329	254	21	mf0	mf0	X
ejpam-3329	254	22	(	(	PUNCT
ejpam-3329	254	23	1+n	1+n	NUM
ejpam-3329	254	24	)	)	PUNCT
ejpam-3329	254	25	.	.	PUNCT
ejpam-3329	255	1	the	the	DET
ejpam-3329	255	2	following	follow	VERB
ejpam-3329	255	3	lemma	lemma	PROPN
ejpam-3329	255	4	due	due	ADP
ejpam-3329	255	5	to	to	ADP
ejpam-3329	255	6	harrington	harrington	PROPN
ejpam-3329	255	7	and	and	CCONJ
ejpam-3329	255	8	whitley	whitley	PROPN
ejpam-3329	255	9	[	[	X
ejpam-3329	255	10	9	9	NUM
ejpam-3329	255	11	]	]	PUNCT
ejpam-3329	255	12	is	be	AUX
ejpam-3329	255	13	well	well	ADV
ejpam-3329	255	14	known	know	VERB
ejpam-3329	255	15	.	.	PUNCT
ejpam-3329	256	1	lemma	lemma	PROPN
ejpam-3329	256	2	1	1	X
ejpam-3329	256	3	.	.	PUNCT
ejpam-3329	257	1	let	let	VERB
ejpam-3329	257	2	p	p	PRON
ejpam-3329	257	3	denote	denote	VERB
ejpam-3329	257	4	the	the	DET
ejpam-3329	257	5	projection	projection	NOUN
ejpam-3329	257	6	of	of	ADP
ejpam-3329	257	7	l2	l2	NOUN
ejpam-3329	257	8	on	on	ADP
ejpam-3329	257	9	r(c	r(c	ADJ
ejpam-3329	257	10	)	)	PUNCT
ejpam-3329	257	11	(	(	PUNCT
ejpam-3329	257	12	i	i	NOUN
ejpam-3329	257	13	)	)	PUNCT
ejpam-3329	257	14	c∗tct	c∗tct	X
ejpam-3329	258	1	f	f	NOUN
ejpam-3329	259	1	=	=	SYM
ejpam-3329	259	2	f0f	f0f	PROPN
ejpam-3329	259	3	and	and	CCONJ
ejpam-3329	259	4	ctc	ctc	PROPN
ejpam-3329	259	5	∗	∗	NOUN
ejpam-3329	259	6	t	t	PROPN
ejpam-3329	259	7	f	f	PROPN
ejpam-3329	260	1	=	=	PRON
ejpam-3329	260	2	(	(	PUNCT
ejpam-3329	260	3	f0	f0	PROPN
ejpam-3329	260	4	◦	◦	NOUN
ejpam-3329	260	5	t	t	NOUN
ejpam-3329	260	6	)	)	PUNCT
ejpam-3329	260	7	pf	pf	PROPN
ejpam-3329	260	8	for	for	ADP
ejpam-3329	260	9	all	all	DET
ejpam-3329	260	10	f	f	PROPN
ejpam-3329	260	11	∈	∈	PROPN
ejpam-3329	260	12	l2	l2	NOUN
ejpam-3329	260	13	,	,	PUNCT
ejpam-3329	260	14	where	where	SCONJ
ejpam-3329	260	15	p	p	NOUN
ejpam-3329	260	16	is	be	AUX
ejpam-3329	260	17	the	the	DET
ejpam-3329	260	18	projection	projection	NOUN
ejpam-3329	260	19	of	of	ADP
ejpam-3329	260	20	l2	l2	NOUN
ejpam-3329	260	21	onto	onto	ADP
ejpam-3329	260	22	r(c	r(c	PROPN
ejpam-3329	260	23	)	)	PUNCT
ejpam-3329	260	24	.	.	PUNCT
ejpam-3329	261	1	(	(	PUNCT
ejpam-3329	261	2	ii	ii	NOUN
ejpam-3329	261	3	)	)	PUNCT
ejpam-3329	261	4	r(c	r(c	NUM
ejpam-3329	261	5	)	)	PUNCT
ejpam-3329	261	6	=	=	PRON
ejpam-3329	262	1	{	{	PUNCT
ejpam-3329	262	2	f	f	PROPN
ejpam-3329	262	3	∈	∈	PROPN
ejpam-3329	262	4	l2	l2	NOUN
ejpam-3329	262	5	:	:	PUNCT
ejpam-3329	262	6	f	f	PROPN
ejpam-3329	262	7	is	be	AUX
ejpam-3329	262	8	t−1σ	t−1σ	NOUN
ejpam-3329	262	9	measurable	measurable	ADJ
ejpam-3329	262	10	}	}	PUNCT
ejpam-3329	262	11	.	.	PUNCT
ejpam-3329	263	1	in	in	ADP
ejpam-3329	263	2	this	this	DET
ejpam-3329	263	3	section	section	NOUN
ejpam-3329	263	4	quasi	quasi	NOUN
ejpam-3329	263	5	n	n	CCONJ
ejpam-3329	263	6	-	-	PUNCT
ejpam-3329	263	7	class	class	NOUN
ejpam-3329	263	8	q	q	NOUN
ejpam-3329	263	9	and	and	CCONJ
ejpam-3329	263	10	quasi	quasi	ADJ
ejpam-3329	263	11	n	n	CCONJ
ejpam-3329	263	12	-	-	PUNCT
ejpam-3329	263	13	class	class	NOUN
ejpam-3329	263	14	q∗	q∗	NOUN
ejpam-3329	263	15	composition	composition	NOUN
ejpam-3329	263	16	operator	operator	NOUN
ejpam-3329	263	17	on	on	ADP
ejpam-3329	263	18	l2	l2	NOUN
ejpam-3329	263	19	space	space	NOUN
ejpam-3329	263	20	are	be	AUX
ejpam-3329	263	21	characterized	characterize	VERB
ejpam-3329	263	22	as	as	ADP
ejpam-3329	263	23	follows	follow	NOUN
ejpam-3329	263	24	.	.	PUNCT
ejpam-3329	264	1	theorem	theorem	NOUN
ejpam-3329	264	2	21	21	NUM
ejpam-3329	264	3	.	.	PUNCT
ejpam-3329	265	1	let	let	VERB
ejpam-3329	265	2	ct	ct	NUM
ejpam-3329	265	3	∈	∈	PROPN
ejpam-3329	265	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	265	5	)	)	PUNCT
ejpam-3329	265	6	)	)	PUNCT
ejpam-3329	265	7	.	.	PUNCT
ejpam-3329	266	1	then	then	ADV
ejpam-3329	266	2	ct	ct	PROPN
ejpam-3329	266	3	is	be	AUX
ejpam-3329	266	4	of	of	ADP
ejpam-3329	266	5	quasi	quasi	NOUN
ejpam-3329	266	6	n	n	CCONJ
ejpam-3329	266	7	-	-	PUNCT
ejpam-3329	266	8	class	class	NOUN
ejpam-3329	266	9	q	q	NOUN
ejpam-3329	266	10	if	if	SCONJ
ejpam-3329	267	1	and	and	CCONJ
ejpam-3329	267	2	only	only	ADV
ejpam-3329	267	3	if	if	SCONJ
ejpam-3329	267	4	f	f	PROPN
ejpam-3329	267	5	(	(	PUNCT
ejpam-3329	267	6	2+n	2+n	NUM
ejpam-3329	267	7	)	)	PUNCT
ejpam-3329	267	8	0	0	NUM
ejpam-3329	268	1	−	−	PROPN
ejpam-3329	268	2	(	(	PUNCT
ejpam-3329	268	3	1	1	NUM
ejpam-3329	268	4	+	+	CCONJ
ejpam-3329	268	5	n)f	n)f	NOUN
ejpam-3329	268	6	(	(	PUNCT
ejpam-3329	268	7	2	2	NUM
ejpam-3329	268	8	)	)	PUNCT
ejpam-3329	268	9	0	0	NUM
ejpam-3329	269	1	+	+	CCONJ
ejpam-3329	269	2	nf0	nf0	PROPN
ejpam-3329	269	3	≥	≥	NOUN
ejpam-3329	269	4	0	0	NUM
ejpam-3329	270	1	a.e	a.e	PROPN
ejpam-3329	270	2	.	.	PROPN
ejpam-3329	270	3	proof	proof	NOUN
ejpam-3329	270	4	.	.	PUNCT
ejpam-3329	271	1	let	let	VERB
ejpam-3329	271	2	ct	ct	PRON
ejpam-3329	271	3	∈	∈	PROPN
ejpam-3329	271	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	271	5	)	)	PUNCT
ejpam-3329	271	6	)	)	PUNCT
ejpam-3329	271	7	is	be	AUX
ejpam-3329	271	8	of	of	ADP
ejpam-3329	271	9	quasi	quasi	NOUN
ejpam-3329	271	10	n	n	CCONJ
ejpam-3329	271	11	-	-	PUNCT
ejpam-3329	271	12	class	class	NOUN
ejpam-3329	271	13	q	q	NOUN
ejpam-3329	271	14	if	if	SCONJ
ejpam-3329	272	1	and	and	CCONJ
ejpam-3329	272	2	only	only	ADV
ejpam-3329	272	3	if	if	SCONJ
ejpam-3329	272	4	c∗2+nt	c∗2+nt	PROPN
ejpam-3329	272	5	c2+n	c2+n	PROPN
ejpam-3329	272	6	t	t	PROPN
ejpam-3329	272	7	−	−	PROPN
ejpam-3329	272	8	(	(	PUNCT
ejpam-3329	272	9	1	1	NUM
ejpam-3329	272	10	+	+	NUM
ejpam-3329	272	11	n)c∗2	n)c∗2	PROPN
ejpam-3329	272	12	t	t	NOUN
ejpam-3329	272	13	c	c	NOUN
ejpam-3329	272	14	2	2	NUM
ejpam-3329	272	15	t	t	NOUN
ejpam-3329	272	16	+	+	SYM
ejpam-3329	272	17	nc∗tct	nc∗tct	PROPN
ejpam-3329	272	18	≥	≥	NOUN
ejpam-3329	272	19	0	0	NUM
ejpam-3329	272	20	.	.	PUNCT
ejpam-3329	273	1	by	by	ADP
ejpam-3329	273	2	theorem	theorem	NOUN
ejpam-3329	273	3	1	1	NUM
ejpam-3329	273	4	thus	thus	ADV
ejpam-3329	273	5	〈	〈	PROPN
ejpam-3329	273	6	(	(	PUNCT
ejpam-3329	273	7	c∗2+nt	c∗2+nt	PROPN
ejpam-3329	273	8	c2+n	c2+n	PROPN
ejpam-3329	273	9	t	t	PROPN
ejpam-3329	273	10	−	−	PROPN
ejpam-3329	274	1	(	(	PUNCT
ejpam-3329	274	2	1	1	NUM
ejpam-3329	274	3	+	+	NUM
ejpam-3329	274	4	n)c∗2	n)c∗2	PROPN
ejpam-3329	274	5	t	t	NOUN
ejpam-3329	274	6	c	c	NOUN
ejpam-3329	274	7	2	2	NUM
ejpam-3329	274	8	t	t	NOUN
ejpam-3329	274	9	+	+	CCONJ
ejpam-3329	274	10	nc∗tct	nc∗tct	NOUN
ejpam-3329	274	11	)	)	PUNCT
ejpam-3329	274	12	χe	χe	PROPN
ejpam-3329	274	13	,	,	PUNCT
ejpam-3329	274	14	χe	χe	PROPN
ejpam-3329	274	15	〉	〉	PROPN
ejpam-3329	274	16	≥	≥	NOUN
ejpam-3329	274	17	0	0	NUM
ejpam-3329	274	18	for	for	ADP
ejpam-3329	274	19	every	every	DET
ejpam-3329	274	20	characteristic	characteristic	ADJ
ejpam-3329	274	21	function	function	NOUN
ejpam-3329	274	22	χe	χe	NOUN
ejpam-3329	274	23	of	of	ADP
ejpam-3329	274	24	e	e	PROPN
ejpam-3329	274	25	in	in	ADP
ejpam-3329	274	26	σ	σ	PROPN
ejpam-3329	274	27	such	such	ADJ
ejpam-3329	274	28	that	that	SCONJ
ejpam-3329	274	29	λ(e	λ(e	PROPN
ejpam-3329	274	30	)	)	PUNCT
ejpam-3329	274	31	<	<	X
ejpam-3329	274	32	∞.	∞.	PROPN
ejpam-3329	274	33	since	since	SCONJ
ejpam-3329	274	34	c∗tct	c∗tct	NOUN
ejpam-3329	274	35	=	=	SYM
ejpam-3329	274	36	mf0	mf0	NOUN
ejpam-3329	274	37	and	and	CCONJ
ejpam-3329	274	38	c∗2+nt	c∗2+nt	PROPN
ejpam-3329	274	39	c2+n	c2+n	PROPN
ejpam-3329	274	40	t	t	NOUN
ejpam-3329	274	41	=	=	PUNCT
ejpam-3329	274	42	m	m	PROPN
ejpam-3329	274	43	f	f	X
ejpam-3329	274	44	(	(	PUNCT
ejpam-3329	274	45	2+n	2+n	NUM
ejpam-3329	274	46	)	)	PUNCT
ejpam-3329	274	47	0	0	NUM
ejpam-3329	274	48	,	,	PUNCT
ejpam-3329	274	49	then	then	ADV
ejpam-3329	274	50	〈	〈	PROPN
ejpam-3329	274	51	(	(	PUNCT
ejpam-3329	274	52	m	m	PROPN
ejpam-3329	274	53	f	f	X
ejpam-3329	274	54	(	(	PUNCT
ejpam-3329	274	55	2+n	2+n	NUM
ejpam-3329	274	56	)	)	PUNCT
ejpam-3329	274	57	0	0	NUM
ejpam-3329	275	1	−(1+n)m	−(1+n)m	X
ejpam-3329	275	2	f	f	X
ejpam-3329	275	3	(	(	PUNCT
ejpam-3329	275	4	2	2	NUM
ejpam-3329	275	5	)	)	PUNCT
ejpam-3329	275	6	0	0	PUNCT
ejpam-3329	276	1	+	+	ADJ
ejpam-3329	276	2	nmf0)χe	nmf0)χe	PROPN
ejpam-3329	276	3	,	,	PUNCT
ejpam-3329	276	4	χe	χe	PROPN
ejpam-3329	276	5	〉	〉	PROPN
ejpam-3329	276	6	≥	≥	NUM
ejpam-3329	276	7	0	0	NUM
ejpam-3329	276	8	.	.	PUNCT
ejpam-3329	277	1	hence	hence	ADV
ejpam-3329	277	2	∫	∫	PROPN
ejpam-3329	277	3	e(f	e(f	PROPN
ejpam-3329	277	4	(	(	PUNCT
ejpam-3329	277	5	2+n	2+n	NUM
ejpam-3329	277	6	)	)	PUNCT
ejpam-3329	277	7	0	0	NUM
ejpam-3329	278	1	−(1+n)f	−(1+n)f	NOUN
ejpam-3329	278	2	(	(	PUNCT
ejpam-3329	278	3	2	2	NUM
ejpam-3329	278	4	)	)	PUNCT
ejpam-3329	278	5	0	0	PUNCT
ejpam-3329	279	1	+	+	ADJ
ejpam-3329	279	2	nf0)dλ	nf0)dλ	NOUN
ejpam-3329	279	3	≥	≥	NOUN
ejpam-3329	279	4	0	0	NUM
ejpam-3329	279	5	for	for	ADP
ejpam-3329	279	6	every	every	DET
ejpam-3329	279	7	e	e	NOUN
ejpam-3329	279	8	in	in	ADP
ejpam-3329	279	9	σ	σ	PROPN
ejpam-3329	279	10	.	.	PUNCT
ejpam-3329	280	1	hence	hence	ADV
ejpam-3329	280	2	ct	ct	PROPN
ejpam-3329	280	3	is	be	AUX
ejpam-3329	280	4	of	of	ADP
ejpam-3329	280	5	quasi	quasi	NOUN
ejpam-3329	280	6	n	n	X
ejpam-3329	280	7	class	class	NOUN
ejpam-3329	280	8	q	q	NOUN
ejpam-3329	280	9	if	if	SCONJ
ejpam-3329	281	1	and	and	CCONJ
ejpam-3329	281	2	only	only	ADV
ejpam-3329	281	3	if	if	SCONJ
ejpam-3329	281	4	f	f	PROPN
ejpam-3329	281	5	(	(	PUNCT
ejpam-3329	281	6	2+n	2+n	NUM
ejpam-3329	281	7	)	)	PUNCT
ejpam-3329	281	8	0	0	NUM
ejpam-3329	282	1	−(1+n)f	−(1+n)f	NOUN
ejpam-3329	282	2	(	(	PUNCT
ejpam-3329	282	3	2	2	NUM
ejpam-3329	282	4	)	)	PUNCT
ejpam-3329	282	5	0	0	PUNCT
ejpam-3329	283	1	+	+	NUM
ejpam-3329	283	2	nf0	nf0	NOUN
ejpam-3329	283	3	≥	≥	NOUN
ejpam-3329	283	4	0	0	NUM
ejpam-3329	284	1	a.e	a.e	PROPN
ejpam-3329	284	2	.	.	PROPN
ejpam-3329	284	3	example	example	NOUN
ejpam-3329	284	4	1	1	NUM
ejpam-3329	284	5	.	.	PUNCT
ejpam-3329	285	1	let	let	VERB
ejpam-3329	285	2	x	x	SYM
ejpam-3329	285	3	=	=	SYM
ejpam-3329	285	4	n	n	PROPN
ejpam-3329	285	5	,	,	PUNCT
ejpam-3329	285	6	the	the	DET
ejpam-3329	285	7	set	set	NOUN
ejpam-3329	285	8	of	of	ADP
ejpam-3329	285	9	all	all	DET
ejpam-3329	285	10	natural	natural	ADJ
ejpam-3329	285	11	numbers	number	NOUN
ejpam-3329	285	12	and	and	CCONJ
ejpam-3329	285	13	λ	λ	NOUN
ejpam-3329	285	14	be	be	VERB
ejpam-3329	285	15	the	the	DET
ejpam-3329	285	16	counting	counting	NOUN
ejpam-3329	285	17	measure	measure	NOUN
ejpam-3329	285	18	on	on	ADP
ejpam-3329	285	19	it	it	PRON
ejpam-3329	285	20	.	.	PUNCT
ejpam-3329	286	1	define	define	VERB
ejpam-3329	286	2	t	t	PROPN
ejpam-3329	286	3	:	:	PUNCT
ejpam-3329	286	4	n	n	X
ejpam-3329	286	5	→	→	SYM
ejpam-3329	286	6	n	n	X
ejpam-3329	286	7	by	by	ADP
ejpam-3329	286	8	t	t	PROPN
ejpam-3329	286	9	(	(	PUNCT
ejpam-3329	286	10	1	1	NUM
ejpam-3329	286	11	)	)	PUNCT
ejpam-3329	286	12	=	=	SYM
ejpam-3329	286	13	1	1	NUM
ejpam-3329	286	14	,	,	PUNCT
ejpam-3329	286	15	t	t	PROPN
ejpam-3329	286	16	(	(	PUNCT
ejpam-3329	286	17	4p+	4p+	NUM
ejpam-3329	286	18	q	q	NOUN
ejpam-3329	287	1	−	−	NOUN
ejpam-3329	287	2	2	2	NUM
ejpam-3329	287	3	)	)	PUNCT
ejpam-3329	287	4	=	=	SYM
ejpam-3329	287	5	p+	p+	VERB
ejpam-3329	287	6	1	1	NUM
ejpam-3329	287	7	for	for	ADP
ejpam-3329	287	8	q	q	NOUN
ejpam-3329	287	9	=	=	SYM
ejpam-3329	287	10	0	0	NUM
ejpam-3329	287	11	,	,	PUNCT
ejpam-3329	287	12	1	1	NUM
ejpam-3329	287	13	,	,	PUNCT
ejpam-3329	287	14	2	2	NUM
ejpam-3329	287	15	,	,	PUNCT
ejpam-3329	287	16	3	3	NUM
ejpam-3329	287	17	and	and	CCONJ
ejpam-3329	287	18	p	p	NOUN
ejpam-3329	287	19	∈	∈	PROPN
ejpam-3329	287	20	n	n	CCONJ
ejpam-3329	287	21	.	.	PUNCT
ejpam-3329	288	1	we	we	PRON
ejpam-3329	288	2	have	have	VERB
ejpam-3329	288	3	f0(p	f0(p	NOUN
ejpam-3329	288	4	)	)	PUNCT
ejpam-3329	288	5	=	=	SYM
ejpam-3329	288	6	f	f	PROPN
ejpam-3329	288	7	(	(	PUNCT
ejpam-3329	288	8	2	2	NUM
ejpam-3329	288	9	)	)	PUNCT
ejpam-3329	288	10	0	0	NUM
ejpam-3329	289	1	(	(	PUNCT
ejpam-3329	289	2	p	p	NOUN
ejpam-3329	289	3	)	)	PUNCT
ejpam-3329	289	4	=	=	SYM
ejpam-3329	289	5	...	...	PUNCT
ejpam-3329	290	1	=	=	SYM
ejpam-3329	290	2	f	f	X
ejpam-3329	290	3	(	(	PUNCT
ejpam-3329	290	4	n	n	CCONJ
ejpam-3329	290	5	)	)	PUNCT
ejpam-3329	290	6	0	0	NUM
ejpam-3329	291	1	(	(	PUNCT
ejpam-3329	291	2	p	p	X
ejpam-3329	291	3	)	)	PUNCT
ejpam-3329	291	4	=	=	SYM
ejpam-3329	291	5	1	1	NUM
ejpam-3329	291	6	for	for	ADP
ejpam-3329	291	7	p	p	NOUN
ejpam-3329	291	8	=	=	NOUN
ejpam-3329	291	9	1	1	NUM
ejpam-3329	291	10	.	.	PUNCT
ejpam-3329	292	1	f0(p	f0(p	PROPN
ejpam-3329	292	2	)	)	PUNCT
ejpam-3329	292	3	=	=	SYM
ejpam-3329	292	4	4	4	NUM
ejpam-3329	292	5	,	,	PUNCT
ejpam-3329	292	6	f	f	PROPN
ejpam-3329	292	7	(	(	PUNCT
ejpam-3329	292	8	2	2	NUM
ejpam-3329	292	9	)	)	PUNCT
ejpam-3329	292	10	0	0	NUM
ejpam-3329	293	1	(	(	PUNCT
ejpam-3329	293	2	p	p	X
ejpam-3329	293	3	)	)	PUNCT
ejpam-3329	293	4	=	=	SYM
ejpam-3329	293	5	16	16	NUM
ejpam-3329	293	6	,	,	PUNCT
ejpam-3329	293	7	...	...	PUNCT
ejpam-3329	294	1	=	=	SYM
ejpam-3329	294	2	f	f	X
ejpam-3329	294	3	(	(	PUNCT
ejpam-3329	294	4	2+n	2+n	NUM
ejpam-3329	294	5	)	)	PUNCT
ejpam-3329	294	6	0	0	NUM
ejpam-3329	295	1	(	(	PUNCT
ejpam-3329	295	2	p	p	X
ejpam-3329	295	3	)	)	PUNCT
ejpam-3329	295	4	=	=	SYM
ejpam-3329	295	5	42+n	42+n	PROPN
ejpam-3329	295	6	for	for	ADP
ejpam-3329	295	7	p	p	PROPN
ejpam-3329	295	8	∈	∈	PROPN
ejpam-3329	295	9	n	n	PRON
ejpam-3329	295	10	−{1	−{1	NUM
ejpam-3329	295	11	}	}	PUNCT
ejpam-3329	295	12	.	.	PUNCT
ejpam-3329	296	1	since	since	SCONJ
ejpam-3329	296	2	f	f	PROPN
ejpam-3329	296	3	(	(	PUNCT
ejpam-3329	296	4	2+n	2+n	NUM
ejpam-3329	296	5	)	)	PUNCT
ejpam-3329	296	6	0	0	NUM
ejpam-3329	297	1	(	(	PUNCT
ejpam-3329	297	2	p)−	p)−	NOUN
ejpam-3329	297	3	(	(	PUNCT
ejpam-3329	297	4	1	1	NUM
ejpam-3329	297	5	+	+	CCONJ
ejpam-3329	297	6	n)f	n)f	NOUN
ejpam-3329	297	7	(	(	PUNCT
ejpam-3329	297	8	2	2	NUM
ejpam-3329	297	9	)	)	PUNCT
ejpam-3329	297	10	0	0	NUM
ejpam-3329	298	1	(	(	PUNCT
ejpam-3329	298	2	p	p	NOUN
ejpam-3329	298	3	)	)	PUNCT
ejpam-3329	298	4	+	+	CCONJ
ejpam-3329	298	5	nf0(p	nf0(p	PROPN
ejpam-3329	298	6	)	)	PUNCT
ejpam-3329	298	7	≥	≥	NOUN
ejpam-3329	298	8	0	0	NUM
ejpam-3329	298	9	for	for	ADP
ejpam-3329	298	10	every	every	DET
ejpam-3329	298	11	p	p	NOUN
ejpam-3329	298	12	,	,	PUNCT
ejpam-3329	298	13	hence	hence	ADV
ejpam-3329	298	14	ct	ct	PROPN
ejpam-3329	298	15	is	be	AUX
ejpam-3329	298	16	of	of	ADP
ejpam-3329	298	17	quasi	quasi	NOUN
ejpam-3329	298	18	n	n	PRON
ejpam-3329	298	19	class	class	NOUN
ejpam-3329	298	20	q	q	NOUN
ejpam-3329	298	21	operator	operator	NOUN
ejpam-3329	298	22	.	.	PUNCT
ejpam-3329	299	1	theorem	theorem	VERB
ejpam-3329	299	2	22	22	NUM
ejpam-3329	299	3	.	.	PUNCT
ejpam-3329	300	1	[	[	X
ejpam-3329	300	2	14	14	NUM
ejpam-3329	300	3	]	]	X
ejpam-3329	300	4	if	if	SCONJ
ejpam-3329	300	5	ct	ct	PROPN
ejpam-3329	300	6	∈	∈	PROPN
ejpam-3329	300	7	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	300	8	)	)	PUNCT
ejpam-3329	300	9	)	)	PUNCT
ejpam-3329	300	10	has	have	VERB
ejpam-3329	300	11	dense	dense	ADJ
ejpam-3329	300	12	range	range	NOUN
ejpam-3329	300	13	then	then	ADV
ejpam-3329	300	14	f0	f0	PROPN
ejpam-3329	300	15	=	=	PROPN
ejpam-3329	300	16	g0	g0	PROPN
ejpam-3329	300	17	◦	◦	PROPN
ejpam-3329	300	18	t	t	PROPN
ejpam-3329	300	19	a.e	a.e	PROPN
ejpam-3329	300	20	.	.	PROPN
ejpam-3329	300	21	corollary	corollary	NOUN
ejpam-3329	300	22	6	6	NUM
ejpam-3329	300	23	.	.	PUNCT
ejpam-3329	301	1	if	if	SCONJ
ejpam-3329	301	2	ct	ct	PROPN
ejpam-3329	301	3	is	be	AUX
ejpam-3329	301	4	quasi	quasi	ADJ
ejpam-3329	301	5	n	n	CCONJ
ejpam-3329	301	6	-	-	PUNCT
ejpam-3329	301	7	class	class	NOUN
ejpam-3329	301	8	q	q	NOUN
ejpam-3329	301	9	with	with	ADP
ejpam-3329	301	10	dense	dense	ADJ
ejpam-3329	301	11	range	range	NOUN
ejpam-3329	301	12	on	on	ADP
ejpam-3329	301	13	l2(λ	l2(λ	PROPN
ejpam-3329	301	14	)	)	PUNCT
ejpam-3329	301	15	then	then	ADV
ejpam-3329	301	16	(	(	PUNCT
ejpam-3329	301	17	g0	g0	PROPN
ejpam-3329	301	18	◦	◦	PROPN
ejpam-3329	301	19	t	t	PROPN
ejpam-3329	301	20	)	)	PUNCT
ejpam-3329	301	21	(	(	PUNCT
ejpam-3329	301	22	2+n	2+n	NUM
ejpam-3329	301	23	)	)	PUNCT
ejpam-3329	301	24	−	−	PROPN
ejpam-3329	302	1	(	(	PUNCT
ejpam-3329	302	2	1	1	NUM
ejpam-3329	302	3	+	+	NUM
ejpam-3329	302	4	n)(g0	n)(g0	PROPN
ejpam-3329	302	5	◦	◦	NOUN
ejpam-3329	302	6	t	t	PROPN
ejpam-3329	302	7	)	)	PUNCT
ejpam-3329	302	8	(	(	PUNCT
ejpam-3329	302	9	2	2	X
ejpam-3329	302	10	)	)	PUNCT
ejpam-3329	302	11	+	+	CCONJ
ejpam-3329	302	12	n(g0	n(g0	ADP
ejpam-3329	302	13	◦	◦	PROPN
ejpam-3329	302	14	t	t	PROPN
ejpam-3329	302	15	)	)	PUNCT
ejpam-3329	302	16	≥	≥	PROPN
ejpam-3329	302	17	0	0	NUM
ejpam-3329	303	1	a.e	a.e	PROPN
ejpam-3329	303	2	.	.	PROPN
ejpam-3329	303	3	proof	proof	NOUN
ejpam-3329	303	4	.	.	PUNCT
ejpam-3329	304	1	by	by	ADP
ejpam-3329	304	2	theorem	theorem	ADJ
ejpam-3329	304	3	21	21	NUM
ejpam-3329	304	4	and	and	CCONJ
ejpam-3329	304	5	theorem	theorem	VERB
ejpam-3329	304	6	22	22	NUM
ejpam-3329	304	7	,	,	PUNCT
ejpam-3329	304	8	we	we	PRON
ejpam-3329	304	9	obtain	obtain	VERB
ejpam-3329	304	10	the	the	DET
ejpam-3329	304	11	result	result	NOUN
ejpam-3329	304	12	.	.	PUNCT
ejpam-3329	305	1	theorem	theorem	ADJ
ejpam-3329	305	2	23	23	NUM
ejpam-3329	305	3	.	.	PUNCT
ejpam-3329	306	1	let	let	VERB
ejpam-3329	306	2	ct	ct	PRON
ejpam-3329	306	3	∈	∈	PROPN
ejpam-3329	306	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	306	5	)	)	PUNCT
ejpam-3329	306	6	)	)	PUNCT
ejpam-3329	306	7	.	.	PUNCT
ejpam-3329	307	1	then	then	ADV
ejpam-3329	307	2	c∗t	c∗t	NOUN
ejpam-3329	307	3	is	be	AUX
ejpam-3329	307	4	of	of	ADP
ejpam-3329	307	5	quasi	quasi	NOUN
ejpam-3329	307	6	n	n	CCONJ
ejpam-3329	307	7	-	-	PUNCT
ejpam-3329	307	8	class	class	NOUN
ejpam-3329	307	9	q	q	NOUN
ejpam-3329	307	10	operator	operator	NOUN
ejpam-3329	307	11	if	if	SCONJ
ejpam-3329	307	12	and	and	CCONJ
ejpam-3329	307	13	only	only	ADV
ejpam-3329	307	14	if	if	SCONJ
ejpam-3329	307	15	(	(	PUNCT
ejpam-3329	307	16	f	f	X
ejpam-3329	307	17	(	(	PUNCT
ejpam-3329	307	18	2+n	2+n	NUM
ejpam-3329	307	19	)	)	PUNCT
ejpam-3329	307	20	0	0	NUM
ejpam-3329	308	1	◦	◦	NOUN
ejpam-3329	308	2	t	t	NOUN
ejpam-3329	308	3	2+n)p2+n	2+n)p2+n	NUM
ejpam-3329	309	1	−	−	NOUN
ejpam-3329	310	1	(	(	PUNCT
ejpam-3329	310	2	1	1	NUM
ejpam-3329	310	3	+	+	NUM
ejpam-3329	310	4	n)(f	n)(f	NOUN
ejpam-3329	310	5	(	(	PUNCT
ejpam-3329	310	6	2	2	NUM
ejpam-3329	310	7	)	)	PUNCT
ejpam-3329	310	8	0	0	NUM
ejpam-3329	310	9	◦	◦	NOUN
ejpam-3329	310	10	t	t	PROPN
ejpam-3329	310	11	(	(	PUNCT
ejpam-3329	310	12	2))p2	2))p2	NUM
ejpam-3329	310	13	+	+	CCONJ
ejpam-3329	310	14	n(f0	n(f0	NOUN
ejpam-3329	310	15	◦	◦	NOUN
ejpam-3329	310	16	t	t	PROPN
ejpam-3329	310	17	)	)	PUNCT
ejpam-3329	310	18	p1	p1	NOUN
ejpam-3329	310	19	≥	≥	NOUN
ejpam-3329	310	20	0	0	NUM
ejpam-3329	311	1	a.e	a.e	PROPN
ejpam-3329	311	2	,	,	PUNCT
ejpam-3329	311	3	where	where	SCONJ
ejpam-3329	311	4	p1	p1	NOUN
ejpam-3329	311	5	,	,	PUNCT
ejpam-3329	311	6	p2	p2	NOUN
ejpam-3329	311	7	,	,	PUNCT
ejpam-3329	311	8	...	...	PUNCT
ejpam-3329	311	9	,	,	PUNCT
ejpam-3329	311	10	p2+n	p2+n	NOUN
ejpam-3329	311	11	are	be	AUX
ejpam-3329	311	12	the	the	DET
ejpam-3329	311	13	projections	projection	NOUN
ejpam-3329	311	14	of	of	ADP
ejpam-3329	311	15	l2	l2	NOUN
ejpam-3329	311	16	onto	onto	ADP
ejpam-3329	311	17	r(c	r(c	PROPN
ejpam-3329	311	18	)	)	PUNCT
ejpam-3329	311	19	,	,	PUNCT
ejpam-3329	311	20	r(c2	r(c2	VERB
ejpam-3329	311	21	)	)	PUNCT
ejpam-3329	311	22	,	,	PUNCT
ejpam-3329	311	23	...	...	PUNCT
ejpam-3329	311	24	,	,	PUNCT
ejpam-3329	311	25	r(c2+n	r(c2+n	NOUN
ejpam-3329	311	26	)	)	PUNCT
ejpam-3329	311	27	respectively	respectively	ADV
ejpam-3329	311	28	.	.	PUNCT
ejpam-3329	312	1	d.	d.	PROPN
ejpam-3329	312	2	senthilkumar	senthilkumar	PROPN
ejpam-3329	312	3	,	,	PUNCT
ejpam-3329	312	4	s.	s.	PROPN
ejpam-3329	312	5	parvatham	parvatham	PROPN
ejpam-3329	312	6	/	/	SYM
ejpam-3329	312	7	eur	eur	PROPN
ejpam-3329	312	8	.	.	PUNCT
ejpam-3329	313	1	j.	j.	PROPN
ejpam-3329	313	2	pure	pure	PROPN
ejpam-3329	313	3	appl	appl	PROPN
ejpam-3329	313	4	.	.	PROPN
ejpam-3329	313	5	math	math	PROPN
ejpam-3329	313	6	,	,	PUNCT
ejpam-3329	313	7	11	11	NUM
ejpam-3329	313	8	(	(	PUNCT
ejpam-3329	313	9	4	4	NUM
ejpam-3329	313	10	)	)	PUNCT
ejpam-3329	313	11	(	(	PUNCT
ejpam-3329	313	12	2018	2018	NUM
ejpam-3329	313	13	)	)	PUNCT
ejpam-3329	313	14	,	,	PUNCT
ejpam-3329	313	15	1108	1108	NUM
ejpam-3329	313	16	-	-	SYM
ejpam-3329	313	17	1129	1129	NUM
ejpam-3329	313	18	1118	1118	NUM
ejpam-3329	313	19	proof	proof	NOUN
ejpam-3329	313	20	.	.	PUNCT
ejpam-3329	313	21	suppose	suppose	VERB
ejpam-3329	313	22	ct	ct	NUM
ejpam-3329	313	23	∈	∈	PROPN
ejpam-3329	313	24	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	313	25	)	)	PUNCT
ejpam-3329	313	26	)	)	PUNCT
ejpam-3329	313	27	and	and	CCONJ
ejpam-3329	313	28	c∗t	c∗t	NOUN
ejpam-3329	313	29	is	be	AUX
ejpam-3329	313	30	of	of	ADP
ejpam-3329	313	31	quasi	quasi	NOUN
ejpam-3329	313	32	n	n	CCONJ
ejpam-3329	313	33	-	-	PUNCT
ejpam-3329	313	34	class	class	NOUN
ejpam-3329	313	35	q	q	NOUN
ejpam-3329	313	36	if	if	SCONJ
ejpam-3329	313	37	and	and	CCONJ
ejpam-3329	313	38	only	only	ADV
ejpam-3329	313	39	if	if	SCONJ
ejpam-3329	313	40	c2+n	c2+n	PROPN
ejpam-3329	313	41	t	t	NOUN
ejpam-3329	313	42	c∗2+nt	c∗2+nt	ADP
ejpam-3329	313	43	−	−	PROPN
ejpam-3329	313	44	(	(	PUNCT
ejpam-3329	313	45	1	1	NUM
ejpam-3329	313	46	+	+	CCONJ
ejpam-3329	314	1	n)c2	n)c2	PROPN
ejpam-3329	314	2	tc	tc	PROPN
ejpam-3329	314	3	∗2	∗2	PROPN
ejpam-3329	314	4	t	t	PROPN
ejpam-3329	314	5	+	+	NUM
ejpam-3329	314	6	nctc	nctc	ADJ
ejpam-3329	314	7	∗	∗	NOUN
ejpam-3329	314	8	t	t	PROPN
ejpam-3329	314	9	≥	≥	PROPN
ejpam-3329	314	10	0	0	NUM
ejpam-3329	314	11	.	.	PUNCT
ejpam-3329	314	12	by	by	ADP
ejpam-3329	314	13	theorem	theorem	NOUN
ejpam-3329	314	14	1	1	NUM
ejpam-3329	314	15	.	.	PUNCT
ejpam-3329	315	1	then	then	ADV
ejpam-3329	315	2	〈	〈	PROPN
ejpam-3329	315	3	(	(	PUNCT
ejpam-3329	315	4	c2+n	c2+n	NOUN
ejpam-3329	315	5	t	t	NOUN
ejpam-3329	315	6	c∗2+nt	c∗2+nt	ADP
ejpam-3329	315	7	−	−	PROPN
ejpam-3329	315	8	(	(	PUNCT
ejpam-3329	315	9	1	1	NUM
ejpam-3329	315	10	+	+	CCONJ
ejpam-3329	315	11	n)c2	n)c2	PROPN
ejpam-3329	315	12	tc	tc	PROPN
ejpam-3329	315	13	∗2	∗2	PROPN
ejpam-3329	315	14	t	t	PROPN
ejpam-3329	315	15	+	+	PUNCT
ejpam-3329	315	16	nctc	nctc	ADJ
ejpam-3329	315	17	∗	∗	NOUN
ejpam-3329	315	18	t	t	PROPN
ejpam-3329	315	19	)	)	PUNCT
ejpam-3329	315	20	f	f	X
ejpam-3329	315	21	,	,	PUNCT
ejpam-3329	315	22	f	f	PROPN
ejpam-3329	315	23	〉	〉	PROPN
ejpam-3329	315	24	≥	≥	NOUN
ejpam-3329	315	25	0	0	NUM
ejpam-3329	315	26	for	for	ADP
ejpam-3329	315	27	every	every	DET
ejpam-3329	315	28	f	f	PROPN
ejpam-3329	315	29	∈	∈	PROPN
ejpam-3329	315	30	l2(λ	l2(λ	PROPN
ejpam-3329	315	31	)	)	PUNCT
ejpam-3329	315	32	.	.	PUNCT
ejpam-3329	316	1	since	since	SCONJ
ejpam-3329	316	2	〈	〈	PROPN
ejpam-3329	316	3	cc∗f	cc∗f	VERB
ejpam-3329	316	4	,	,	PUNCT
ejpam-3329	316	5	f	f	PROPN
ejpam-3329	316	6	〉	〉	PROPN
ejpam-3329	316	7	=	=	SYM
ejpam-3329	316	8	〈	〈	PROPN
ejpam-3329	316	9	(	(	PUNCT
ejpam-3329	316	10	f0	f0	PROPN
ejpam-3329	316	11	◦	◦	NOUN
ejpam-3329	316	12	t	t	PROPN
ejpam-3329	316	13	)	)	PUNCT
ejpam-3329	316	14	p1f	p1f	PROPN
ejpam-3329	316	15	,	,	PUNCT
ejpam-3329	316	16	f	f	X
ejpam-3329	316	17	〉	〉	NUM
ejpam-3329	316	18	by	by	ADP
ejpam-3329	316	19	[	[	X
ejpam-3329	316	20	9	9	NUM
ejpam-3329	316	21	]	]	PUNCT
ejpam-3329	316	22	.	.	PUNCT
ejpam-3329	317	1	hence	hence	ADV
ejpam-3329	317	2	〈	〈	PROPN
ejpam-3329	317	3	(	(	PUNCT
ejpam-3329	317	4	f	f	PROPN
ejpam-3329	317	5	(	(	PUNCT
ejpam-3329	317	6	2+n)0	2+n)0	NUM
ejpam-3329	317	7	◦	◦	PROPN
ejpam-3329	317	8	t	t	PROPN
ejpam-3329	317	9	2+n)p2+nf	2+n)p2+nf	NUM
ejpam-3329	317	10	,	,	PUNCT
ejpam-3329	317	11	f	f	PROPN
ejpam-3329	317	12	〉	〉	NUM
ejpam-3329	317	13	−	−	PROPN
ejpam-3329	317	14	(	(	PUNCT
ejpam-3329	317	15	1	1	NUM
ejpam-3329	317	16	+	+	CCONJ
ejpam-3329	317	17	n)〈(f	n)〈(f	PROPN
ejpam-3329	317	18	(	(	PUNCT
ejpam-3329	317	19	2)0	2)0	NUM
ejpam-3329	317	20	◦	◦	NOUN
ejpam-3329	317	21	t	t	NOUN
ejpam-3329	317	22	2)p2f	2)p2f	NUM
ejpam-3329	317	23	,	,	PUNCT
ejpam-3329	317	24	f	f	PROPN
ejpam-3329	317	25	〉	〉	PROPN
ejpam-3329	317	26	+	+	NUM
ejpam-3329	317	27	n〈(f0	n〈(f0	PROPN
ejpam-3329	317	28	◦	◦	PROPN
ejpam-3329	317	29	t	t	PROPN
ejpam-3329	317	30	)	)	PUNCT
ejpam-3329	317	31	p1f	p1f	PROPN
ejpam-3329	317	32	,	,	PUNCT
ejpam-3329	317	33	f	f	PROPN
ejpam-3329	317	34	〉	〉	PROPN
ejpam-3329	317	35	≥	≥	NOUN
ejpam-3329	317	36	0	0	NUM
ejpam-3329	317	37	for	for	ADP
ejpam-3329	317	38	every	every	DET
ejpam-3329	317	39	f	f	PROPN
ejpam-3329	317	40	∈	∈	PROPN
ejpam-3329	317	41	l2(λ	l2(λ	PROPN
ejpam-3329	317	42	)	)	PUNCT
ejpam-3329	317	43	.	.	PUNCT
ejpam-3329	318	1	hence	hence	ADV
ejpam-3329	318	2	〈	〈	PROPN
ejpam-3329	318	3	(	(	PUNCT
ejpam-3329	318	4	(	(	PUNCT
ejpam-3329	318	5	f	f	X
ejpam-3329	318	6	(	(	PUNCT
ejpam-3329	318	7	2+n)0	2+n)0	NUM
ejpam-3329	318	8	◦	◦	NOUN
ejpam-3329	318	9	t	t	NOUN
ejpam-3329	318	10	2+n)p2+n	2+n)p2+n	NUM
ejpam-3329	318	11	−	−	NOUN
ejpam-3329	318	12	(	(	PUNCT
ejpam-3329	318	13	1	1	NUM
ejpam-3329	318	14	+	+	NUM
ejpam-3329	318	15	n)(f	n)(f	NOUN
ejpam-3329	318	16	(	(	PUNCT
ejpam-3329	318	17	2	2	NUM
ejpam-3329	318	18	)	)	PUNCT
ejpam-3329	318	19	0	0	NUM
ejpam-3329	319	1	◦	◦	NOUN
ejpam-3329	319	2	t	t	PROPN
ejpam-3329	319	3	2)p2	2)p2	NUM
ejpam-3329	319	4	+	+	CCONJ
ejpam-3329	319	5	n(f0	n(f0	NOUN
ejpam-3329	319	6	◦	◦	NOUN
ejpam-3329	319	7	t	t	PROPN
ejpam-3329	319	8	)	)	PUNCT
ejpam-3329	319	9	p1)f	p1)f	PROPN
ejpam-3329	319	10	,	,	PUNCT
ejpam-3329	319	11	f	f	PROPN
ejpam-3329	319	12	〉	〉	PROPN
ejpam-3329	319	13	≥	≥	NOUN
ejpam-3329	319	14	0⇔	0⇔	NOUN
ejpam-3329	319	15	(	(	PUNCT
ejpam-3329	319	16	f	f	X
ejpam-3329	319	17	(	(	PUNCT
ejpam-3329	319	18	2+n	2+n	NUM
ejpam-3329	319	19	)	)	PUNCT
ejpam-3329	319	20	0	0	NUM
ejpam-3329	320	1	◦	◦	NOUN
ejpam-3329	320	2	t	t	NOUN
ejpam-3329	320	3	2+n)p2+n	2+n)p2+n	NUM
ejpam-3329	321	1	−	−	NOUN
ejpam-3329	322	1	(	(	PUNCT
ejpam-3329	322	2	1	1	NUM
ejpam-3329	322	3	+	+	NUM
ejpam-3329	322	4	n)(f	n)(f	NOUN
ejpam-3329	322	5	(	(	PUNCT
ejpam-3329	322	6	2	2	NUM
ejpam-3329	322	7	)	)	PUNCT
ejpam-3329	322	8	0	0	NUM
ejpam-3329	322	9	◦	◦	NOUN
ejpam-3329	322	10	t	t	PROPN
ejpam-3329	322	11	2)p2	2)p2	NUM
ejpam-3329	322	12	+	+	CCONJ
ejpam-3329	322	13	n(f0	n(f0	NOUN
ejpam-3329	322	14	◦	◦	PROPN
ejpam-3329	322	15	t	t	PROPN
ejpam-3329	322	16	)	)	PUNCT
ejpam-3329	322	17	p1	p1	NOUN
ejpam-3329	322	18	≥	≥	NOUN
ejpam-3329	322	19	0	0	NUM
ejpam-3329	323	1	a.e	a.e	PROPN
ejpam-3329	323	2	.	.	PROPN
ejpam-3329	323	3	corollary	corollary	NOUN
ejpam-3329	323	4	7	7	NUM
ejpam-3329	323	5	.	.	PUNCT
ejpam-3329	324	1	let	let	VERB
ejpam-3329	324	2	ct	ct	NUM
ejpam-3329	324	3	∈	∈	PROPN
ejpam-3329	324	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	324	5	)	)	PUNCT
ejpam-3329	324	6	)	)	PUNCT
ejpam-3329	324	7	with	with	ADP
ejpam-3329	324	8	dense	dense	ADJ
ejpam-3329	324	9	range	range	NOUN
ejpam-3329	324	10	.	.	PUNCT
ejpam-3329	325	1	then	then	ADV
ejpam-3329	325	2	c∗t	c∗t	NOUN
ejpam-3329	325	3	is	be	AUX
ejpam-3329	325	4	of	of	ADP
ejpam-3329	325	5	quasi	quasi	NOUN
ejpam-3329	325	6	n	n	CCONJ
ejpam-3329	325	7	-	-	PUNCT
ejpam-3329	325	8	class	class	NOUN
ejpam-3329	325	9	q	q	NOUN
ejpam-3329	325	10	operator	operator	NOUN
ejpam-3329	325	11	if	if	SCONJ
ejpam-3329	325	12	and	and	CCONJ
ejpam-3329	325	13	only	only	ADV
ejpam-3329	325	14	if	if	SCONJ
ejpam-3329	325	15	(	(	PUNCT
ejpam-3329	325	16	f	f	X
ejpam-3329	325	17	(	(	PUNCT
ejpam-3329	325	18	2+n	2+n	NUM
ejpam-3329	325	19	)	)	PUNCT
ejpam-3329	325	20	0	0	NUM
ejpam-3329	326	1	◦	◦	NOUN
ejpam-3329	326	2	t	t	NOUN
ejpam-3329	326	3	2+n)−	2+n)−	NUM
ejpam-3329	326	4	(	(	PUNCT
ejpam-3329	326	5	1	1	NUM
ejpam-3329	326	6	+	+	NUM
ejpam-3329	326	7	n)(f	n)(f	NOUN
ejpam-3329	326	8	(	(	PUNCT
ejpam-3329	326	9	2	2	NUM
ejpam-3329	326	10	)	)	PUNCT
ejpam-3329	326	11	0	0	NUM
ejpam-3329	327	1	◦	◦	NOUN
ejpam-3329	327	2	t	t	PROPN
ejpam-3329	327	3	2	2	NUM
ejpam-3329	327	4	)	)	PUNCT
ejpam-3329	327	5	+	+	CCONJ
ejpam-3329	327	6	n(f0	n(f0	ADJ
ejpam-3329	327	7	◦	◦	NOUN
ejpam-3329	327	8	t	t	PROPN
ejpam-3329	327	9	)	)	PUNCT
ejpam-3329	327	10	≥	≥	PROPN
ejpam-3329	327	11	0	0	NUM
ejpam-3329	327	12	a.e	a.e	PROPN
ejpam-3329	327	13	.	.	PROPN
ejpam-3329	327	14	theorem	theorem	PROPN
ejpam-3329	327	15	24	24	NUM
ejpam-3329	327	16	.	.	PUNCT
ejpam-3329	328	1	let	let	VERB
ejpam-3329	328	2	ct	ct	PRON
ejpam-3329	328	3	∈	∈	PROPN
ejpam-3329	328	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	328	5	)	)	PUNCT
ejpam-3329	328	6	)	)	PUNCT
ejpam-3329	328	7	.	.	PUNCT
ejpam-3329	329	1	then	then	ADV
ejpam-3329	329	2	ct	ct	PROPN
ejpam-3329	329	3	is	be	AUX
ejpam-3329	329	4	of	of	ADP
ejpam-3329	329	5	quasi	quasi	NOUN
ejpam-3329	329	6	n	n	CCONJ
ejpam-3329	329	7	-	-	PUNCT
ejpam-3329	329	8	class	class	NOUN
ejpam-3329	329	9	q∗	q∗	NOUN
ejpam-3329	329	10	if	if	SCONJ
ejpam-3329	330	1	and	and	CCONJ
ejpam-3329	330	2	only	only	ADV
ejpam-3329	330	3	if	if	SCONJ
ejpam-3329	330	4	f	f	PROPN
ejpam-3329	330	5	(	(	PUNCT
ejpam-3329	330	6	2+n	2+n	NUM
ejpam-3329	330	7	)	)	PUNCT
ejpam-3329	330	8	0	0	NUM
ejpam-3329	331	1	−	−	PROPN
ejpam-3329	331	2	(	(	PUNCT
ejpam-3329	331	3	1	1	NUM
ejpam-3329	331	4	+	+	NUM
ejpam-3329	331	5	n)(f0	n)(f0	NOUN
ejpam-3329	331	6	)	)	PUNCT
ejpam-3329	331	7	2p	2p	NOUN
ejpam-3329	332	1	+	+	CCONJ
ejpam-3329	332	2	nf0	nf0	PROPN
ejpam-3329	332	3	≥	≥	NOUN
ejpam-3329	332	4	0	0	NUM
ejpam-3329	332	5	a.e	a.e	PROPN
ejpam-3329	332	6	.	.	PROPN
ejpam-3329	332	7	proof	proof	NOUN
ejpam-3329	332	8	.	.	PUNCT
ejpam-3329	333	1	let	let	VERB
ejpam-3329	333	2	ct	ct	PRON
ejpam-3329	333	3	∈	∈	PROPN
ejpam-3329	333	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	333	5	)	)	PUNCT
ejpam-3329	333	6	)	)	PUNCT
ejpam-3329	333	7	is	be	AUX
ejpam-3329	333	8	of	of	ADP
ejpam-3329	333	9	quasi	quasi	ADJ
ejpam-3329	333	10	n	n	CCONJ
ejpam-3329	333	11	-	-	PUNCT
ejpam-3329	333	12	class	class	NOUN
ejpam-3329	333	13	q∗	q∗	NOUN
ejpam-3329	334	1	if	if	SCONJ
ejpam-3329	334	2	and	and	CCONJ
ejpam-3329	334	3	only	only	ADV
ejpam-3329	334	4	if	if	SCONJ
ejpam-3329	334	5	c∗2+nt	c∗2+nt	PROPN
ejpam-3329	334	6	c2+n	c2+n	PROPN
ejpam-3329	334	7	t	t	PROPN
ejpam-3329	334	8	−	−	PROPN
ejpam-3329	334	9	(	(	PUNCT
ejpam-3329	334	10	1	1	NUM
ejpam-3329	334	11	+	+	CCONJ
ejpam-3329	334	12	n)(c∗tct	n)(c∗tct	NOUN
ejpam-3329	334	13	)	)	PUNCT
ejpam-3329	334	14	2	2	NUM
ejpam-3329	335	1	+	+	SYM
ejpam-3329	335	2	nc∗tct	nc∗tct	PROPN
ejpam-3329	335	3	≥	≥	NOUN
ejpam-3329	335	4	0	0	NUM
ejpam-3329	335	5	.	.	PUNCT
ejpam-3329	336	1	thus	thus	ADV
ejpam-3329	336	2	〈	〈	PROPN
ejpam-3329	336	3	(	(	PUNCT
ejpam-3329	336	4	c∗2+nt	c∗2+nt	PROPN
ejpam-3329	336	5	c2+n	c2+n	PROPN
ejpam-3329	336	6	t	t	PROPN
ejpam-3329	336	7	−	−	PROPN
ejpam-3329	336	8	(	(	PUNCT
ejpam-3329	336	9	1	1	NUM
ejpam-3329	336	10	+	+	CCONJ
ejpam-3329	336	11	n)(c∗tct	n)(c∗tct	NOUN
ejpam-3329	336	12	)	)	PUNCT
ejpam-3329	336	13	2	2	NUM
ejpam-3329	336	14	+	+	SYM
ejpam-3329	336	15	nc∗tct	nc∗tct	NOUN
ejpam-3329	336	16	)	)	PUNCT
ejpam-3329	336	17	χe	χe	PROPN
ejpam-3329	336	18	,	,	PUNCT
ejpam-3329	336	19	χe	χe	PROPN
ejpam-3329	336	20	〉	〉	PROPN
ejpam-3329	336	21	≥	≥	NOUN
ejpam-3329	336	22	0	0	NUM
ejpam-3329	336	23	for	for	ADP
ejpam-3329	336	24	every	every	DET
ejpam-3329	336	25	characteristic	characteristic	ADJ
ejpam-3329	336	26	function	function	NOUN
ejpam-3329	336	27	χe	χe	NOUN
ejpam-3329	336	28	of	of	ADP
ejpam-3329	336	29	e	e	PROPN
ejpam-3329	336	30	in	in	ADP
ejpam-3329	336	31	σ	σ	PROPN
ejpam-3329	336	32	such	such	ADJ
ejpam-3329	336	33	that	that	SCONJ
ejpam-3329	336	34	λ(e	λ(e	PROPN
ejpam-3329	336	35	)	)	PUNCT
ejpam-3329	336	36	<	<	X
ejpam-3329	336	37	∞.	∞.	PROPN
ejpam-3329	336	38	since	since	SCONJ
ejpam-3329	336	39	c∗tct	c∗tct	NOUN
ejpam-3329	336	40	=	=	SYM
ejpam-3329	336	41	mf0	mf0	NOUN
ejpam-3329	336	42	,	,	PUNCT
ejpam-3329	336	43	c∗2+nt	c∗2+nt	PROPN
ejpam-3329	336	44	c2+n	c2+n	PROPN
ejpam-3329	336	45	t	t	NOUN
ejpam-3329	336	46	=	=	PUNCT
ejpam-3329	336	47	m	m	PROPN
ejpam-3329	336	48	f	f	X
ejpam-3329	336	49	(	(	PUNCT
ejpam-3329	336	50	2+n	2+n	NUM
ejpam-3329	336	51	)	)	PUNCT
ejpam-3329	336	52	0	0	NUM
ejpam-3329	336	53	,	,	PUNCT
ejpam-3329	336	54	then	then	ADV
ejpam-3329	336	55	〈	〈	PROPN
ejpam-3329	336	56	(	(	PUNCT
ejpam-3329	336	57	m	m	PROPN
ejpam-3329	336	58	f	f	X
ejpam-3329	336	59	(	(	PUNCT
ejpam-3329	336	60	2+n	2+n	NUM
ejpam-3329	336	61	)	)	PUNCT
ejpam-3329	336	62	0	0	NUM
ejpam-3329	337	1	−	−	PROPN
ejpam-3329	337	2	(	(	PUNCT
ejpam-3329	337	3	1	1	NUM
ejpam-3329	337	4	+	+	NUM
ejpam-3329	337	5	n)(mf0)2	n)(mf0)2	NOUN
ejpam-3329	337	6	+	+	CCONJ
ejpam-3329	337	7	nmf0)χe	nmf0)χe	PROPN
ejpam-3329	337	8	,	,	PUNCT
ejpam-3329	337	9	χe	χe	PROPN
ejpam-3329	337	10	〉	〉	PROPN
ejpam-3329	337	11	≥	≥	NUM
ejpam-3329	337	12	0	0	NUM
ejpam-3329	337	13	.	.	PUNCT
ejpam-3329	338	1	hence	hence	ADV
ejpam-3329	338	2	∫	∫	PROPN
ejpam-3329	338	3	e(f	e(f	PROPN
ejpam-3329	338	4	(	(	PUNCT
ejpam-3329	338	5	2+n	2+n	NUM
ejpam-3329	338	6	)	)	PUNCT
ejpam-3329	338	7	0	0	NUM
ejpam-3329	339	1	−	−	PROPN
ejpam-3329	339	2	(	(	PUNCT
ejpam-3329	339	3	1	1	NUM
ejpam-3329	339	4	+	+	NUM
ejpam-3329	339	5	n)(f0	n)(f0	NOUN
ejpam-3329	339	6	)	)	PUNCT
ejpam-3329	339	7	2	2	NUM
ejpam-3329	340	1	+	+	CCONJ
ejpam-3329	340	2	nf0)dλ	nf0)dλ	NOUN
ejpam-3329	340	3	≥	≥	NOUN
ejpam-3329	340	4	0	0	NUM
ejpam-3329	340	5	for	for	ADP
ejpam-3329	340	6	every	every	DET
ejpam-3329	340	7	e	e	NOUN
ejpam-3329	340	8	in	in	ADP
ejpam-3329	340	9	σ	σ	PROPN
ejpam-3329	340	10	.	.	PUNCT
ejpam-3329	341	1	hence	hence	ADV
ejpam-3329	341	2	ct	ct	PROPN
ejpam-3329	341	3	is	be	AUX
ejpam-3329	341	4	quasi	quasi	NOUN
ejpam-3329	341	5	n	n	X
ejpam-3329	341	6	class	class	NOUN
ejpam-3329	341	7	q∗	q∗	NOUN
ejpam-3329	341	8	if	if	SCONJ
ejpam-3329	342	1	and	and	CCONJ
ejpam-3329	342	2	only	only	ADV
ejpam-3329	342	3	if	if	SCONJ
ejpam-3329	342	4	f	f	PROPN
ejpam-3329	342	5	(	(	PUNCT
ejpam-3329	342	6	2+n	2+n	NUM
ejpam-3329	342	7	)	)	PUNCT
ejpam-3329	342	8	0	0	NUM
ejpam-3329	343	1	−	−	PROPN
ejpam-3329	343	2	(	(	PUNCT
ejpam-3329	343	3	1	1	NUM
ejpam-3329	343	4	+	+	NUM
ejpam-3329	343	5	n)(f0	n)(f0	NOUN
ejpam-3329	343	6	)	)	PUNCT
ejpam-3329	343	7	2	2	NUM
ejpam-3329	344	1	+	+	NUM
ejpam-3329	344	2	nf0	nf0	PROPN
ejpam-3329	344	3	≥	≥	NOUN
ejpam-3329	344	4	0	0	NUM
ejpam-3329	345	1	a.e	a.e	PROPN
ejpam-3329	345	2	.	.	PROPN
ejpam-3329	345	3	example	example	NOUN
ejpam-3329	345	4	2	2	NUM
ejpam-3329	345	5	.	.	PUNCT
ejpam-3329	346	1	let	let	VERB
ejpam-3329	346	2	x	x	SYM
ejpam-3329	346	3	=	=	SYM
ejpam-3329	346	4	n	n	PROPN
ejpam-3329	346	5	,	,	PUNCT
ejpam-3329	346	6	the	the	DET
ejpam-3329	346	7	set	set	NOUN
ejpam-3329	346	8	of	of	ADP
ejpam-3329	346	9	all	all	DET
ejpam-3329	346	10	natural	natural	ADJ
ejpam-3329	346	11	numbers	number	NOUN
ejpam-3329	346	12	and	and	CCONJ
ejpam-3329	346	13	λ	λ	NOUN
ejpam-3329	346	14	be	be	VERB
ejpam-3329	346	15	the	the	DET
ejpam-3329	346	16	counting	counting	NOUN
ejpam-3329	346	17	measure	measure	NOUN
ejpam-3329	346	18	on	on	ADP
ejpam-3329	346	19	it	it	PRON
ejpam-3329	346	20	.	.	PUNCT
ejpam-3329	347	1	define	define	VERB
ejpam-3329	347	2	t	t	PROPN
ejpam-3329	347	3	:	:	PUNCT
ejpam-3329	347	4	n	n	X
ejpam-3329	347	5	→	→	SYM
ejpam-3329	347	6	n	n	X
ejpam-3329	347	7	by	by	ADP
ejpam-3329	347	8	t	t	PROPN
ejpam-3329	347	9	(	(	PUNCT
ejpam-3329	347	10	1	1	NUM
ejpam-3329	347	11	)	)	PUNCT
ejpam-3329	347	12	=	=	SYM
ejpam-3329	347	13	t	t	PROPN
ejpam-3329	347	14	(	(	PUNCT
ejpam-3329	347	15	2	2	NUM
ejpam-3329	347	16	)	)	PUNCT
ejpam-3329	347	17	=	=	SYM
ejpam-3329	347	18	t	t	PROPN
ejpam-3329	347	19	(	(	PUNCT
ejpam-3329	347	20	3	3	NUM
ejpam-3329	347	21	)	)	PUNCT
ejpam-3329	347	22	=	=	SYM
ejpam-3329	347	23	1	1	NUM
ejpam-3329	347	24	,	,	PUNCT
ejpam-3329	347	25	t	t	PROPN
ejpam-3329	347	26	(	(	PUNCT
ejpam-3329	347	27	4p+	4p+	NUM
ejpam-3329	347	28	q	q	NOUN
ejpam-3329	347	29	)	)	PUNCT
ejpam-3329	347	30	=	=	SYM
ejpam-3329	347	31	p+	p+	VERB
ejpam-3329	347	32	1	1	NUM
ejpam-3329	347	33	for	for	ADP
ejpam-3329	347	34	q	q	NOUN
ejpam-3329	347	35	=	=	SYM
ejpam-3329	347	36	0	0	NUM
ejpam-3329	347	37	,	,	PUNCT
ejpam-3329	347	38	1	1	NUM
ejpam-3329	347	39	,	,	PUNCT
ejpam-3329	347	40	2	2	NUM
ejpam-3329	347	41	,	,	PUNCT
ejpam-3329	347	42	3	3	NUM
ejpam-3329	347	43	and	and	CCONJ
ejpam-3329	347	44	p	p	NOUN
ejpam-3329	347	45	∈	∈	PROPN
ejpam-3329	347	46	n	n	ADV
ejpam-3329	347	47	.	.	PUNCT
ejpam-3329	348	1	since	since	SCONJ
ejpam-3329	348	2	f	f	PROPN
ejpam-3329	348	3	(	(	PUNCT
ejpam-3329	348	4	2+n	2+n	NUM
ejpam-3329	348	5	)	)	PUNCT
ejpam-3329	348	6	0	0	NUM
ejpam-3329	349	1	−	−	PROPN
ejpam-3329	349	2	(	(	PUNCT
ejpam-3329	349	3	1	1	NUM
ejpam-3329	349	4	+	+	NUM
ejpam-3329	349	5	n)(f0	n)(f0	NOUN
ejpam-3329	349	6	)	)	PUNCT
ejpam-3329	349	7	2	2	NUM
ejpam-3329	350	1	+	+	NUM
ejpam-3329	350	2	nf0	nf0	PROPN
ejpam-3329	350	3	≥	≥	NOUN
ejpam-3329	350	4	0	0	NUM
ejpam-3329	350	5	for	for	ADP
ejpam-3329	350	6	every	every	DET
ejpam-3329	350	7	p	p	NOUN
ejpam-3329	350	8	,	,	PUNCT
ejpam-3329	350	9	hence	hence	ADV
ejpam-3329	350	10	ct	ct	PROPN
ejpam-3329	350	11	is	be	AUX
ejpam-3329	350	12	of	of	ADP
ejpam-3329	350	13	quasi	quasi	NOUN
ejpam-3329	350	14	n	n	PRON
ejpam-3329	350	15	class	class	NOUN
ejpam-3329	350	16	q∗	q∗	NOUN
ejpam-3329	350	17	operator	operator	NOUN
ejpam-3329	350	18	.	.	PUNCT
ejpam-3329	351	1	corollary	corollary	ADJ
ejpam-3329	351	2	8	8	NUM
ejpam-3329	351	3	.	.	PUNCT
ejpam-3329	352	1	if	if	SCONJ
ejpam-3329	352	2	ct	ct	PROPN
ejpam-3329	352	3	is	be	AUX
ejpam-3329	352	4	quasi	quasi	ADJ
ejpam-3329	352	5	n	n	CCONJ
ejpam-3329	352	6	-	-	PUNCT
ejpam-3329	352	7	class	class	NOUN
ejpam-3329	352	8	q∗	q∗	NOUN
ejpam-3329	352	9	with	with	ADP
ejpam-3329	352	10	dense	dense	ADJ
ejpam-3329	352	11	range	range	NOUN
ejpam-3329	352	12	on	on	ADP
ejpam-3329	352	13	l2(λ	l2(λ	PROPN
ejpam-3329	352	14	)	)	PUNCT
ejpam-3329	352	15	if	if	SCONJ
ejpam-3329	352	16	and	and	CCONJ
ejpam-3329	352	17	only	only	ADV
ejpam-3329	353	1	if	if	SCONJ
ejpam-3329	353	2	f	f	PROPN
ejpam-3329	353	3	(	(	PUNCT
ejpam-3329	353	4	2+n	2+n	NUM
ejpam-3329	353	5	)	)	PUNCT
ejpam-3329	353	6	0	0	NUM
ejpam-3329	354	1	−	−	PROPN
ejpam-3329	354	2	(	(	PUNCT
ejpam-3329	354	3	1	1	NUM
ejpam-3329	354	4	+	+	NUM
ejpam-3329	354	5	n)(f0	n)(f0	NOUN
ejpam-3329	354	6	)	)	PUNCT
ejpam-3329	354	7	2	2	NUM
ejpam-3329	355	1	+	+	NUM
ejpam-3329	355	2	nf0	nf0	PROPN
ejpam-3329	355	3	≥	≥	NOUN
ejpam-3329	355	4	0	0	NUM
ejpam-3329	356	1	a.e	a.e	PROPN
ejpam-3329	356	2	.	.	PROPN
ejpam-3329	356	3	theorem	theorem	PROPN
ejpam-3329	356	4	25	25	NUM
ejpam-3329	356	5	.	.	PUNCT
ejpam-3329	357	1	let	let	VERB
ejpam-3329	357	2	ct	ct	NUM
ejpam-3329	357	3	∈	∈	PROPN
ejpam-3329	357	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	357	5	)	)	PUNCT
ejpam-3329	357	6	)	)	PUNCT
ejpam-3329	357	7	.	.	PUNCT
ejpam-3329	358	1	then	then	ADV
ejpam-3329	358	2	c∗t	c∗t	NOUN
ejpam-3329	358	3	is	be	AUX
ejpam-3329	358	4	quasi	quasi	ADJ
ejpam-3329	358	5	n	n	CCONJ
ejpam-3329	358	6	-	-	PUNCT
ejpam-3329	358	7	class	class	NOUN
ejpam-3329	358	8	q∗	q∗	NOUN
ejpam-3329	358	9	if	if	SCONJ
ejpam-3329	358	10	and	and	CCONJ
ejpam-3329	358	11	only	only	ADV
ejpam-3329	358	12	if	if	SCONJ
ejpam-3329	358	13	(	(	PUNCT
ejpam-3329	358	14	f	f	X
ejpam-3329	358	15	(	(	PUNCT
ejpam-3329	358	16	2+n	2+n	NUM
ejpam-3329	358	17	)	)	PUNCT
ejpam-3329	358	18	0	0	NUM
ejpam-3329	359	1	◦	◦	NOUN
ejpam-3329	359	2	t	t	NOUN
ejpam-3329	359	3	2+n)p2+n	2+n)p2+n	NUM
ejpam-3329	359	4	−	−	NOUN
ejpam-3329	360	1	(	(	PUNCT
ejpam-3329	360	2	1	1	NUM
ejpam-3329	360	3	+	+	NUM
ejpam-3329	360	4	n)(f0	n)(f0	NOUN
ejpam-3329	360	5	◦	◦	NOUN
ejpam-3329	360	6	t	t	NOUN
ejpam-3329	360	7	)	)	PUNCT
ejpam-3329	360	8	2p1	2p1	NUM
ejpam-3329	361	1	+	+	CCONJ
ejpam-3329	361	2	n(f0	n(f0	NOUN
ejpam-3329	361	3	◦	◦	NOUN
ejpam-3329	361	4	t	t	PROPN
ejpam-3329	361	5	)	)	PUNCT
ejpam-3329	361	6	p1	p1	NOUN
ejpam-3329	361	7	≥	≥	NOUN
ejpam-3329	361	8	0	0	NUM
ejpam-3329	362	1	a.e	a.e	PROPN
ejpam-3329	362	2	.	.	PROPN
ejpam-3329	362	3	where	where	SCONJ
ejpam-3329	362	4	pi	pi	NOUN
ejpam-3329	362	5	’s	’	VERB
ejpam-3329	362	6	are	be	AUX
ejpam-3329	362	7	the	the	DET
ejpam-3329	362	8	projections	projection	NOUN
ejpam-3329	362	9	of	of	ADP
ejpam-3329	362	10	l2	l2	NOUN
ejpam-3329	362	11	onto	onto	ADP
ejpam-3329	362	12	r(ci	r(ci	NOUN
ejpam-3329	362	13	)	)	PUNCT
ejpam-3329	362	14	,	,	PUNCT
ejpam-3329	362	15	respectively	respectively	ADV
ejpam-3329	362	16	.	.	PUNCT
ejpam-3329	363	1	proof	proof	NOUN
ejpam-3329	363	2	.	.	PUNCT
ejpam-3329	364	1	let	let	VERB
ejpam-3329	364	2	c∗t	c∗t	NOUN
ejpam-3329	364	3	∈	∈	PROPN
ejpam-3329	364	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	364	5	)	)	PUNCT
ejpam-3329	364	6	)	)	PUNCT
ejpam-3329	364	7	is	be	AUX
ejpam-3329	364	8	of	of	ADP
ejpam-3329	364	9	quasi	quasi	ADJ
ejpam-3329	364	10	n	n	CCONJ
ejpam-3329	364	11	-	-	PUNCT
ejpam-3329	364	12	class	class	NOUN
ejpam-3329	364	13	q∗	q∗	NOUN
ejpam-3329	365	1	if	if	SCONJ
ejpam-3329	366	1	and	and	CCONJ
ejpam-3329	366	2	only	only	ADV
ejpam-3329	366	3	if	if	SCONJ
ejpam-3329	366	4	c2+n	c2+n	PROPN
ejpam-3329	366	5	t	t	NOUN
ejpam-3329	366	6	c∗2+nt	c∗2+nt	ADP
ejpam-3329	367	1	−	−	PROPN
ejpam-3329	367	2	(	(	PUNCT
ejpam-3329	367	3	1	1	NUM
ejpam-3329	367	4	+	+	NUM
ejpam-3329	367	5	n)(ctc	n)(ctc	NOUN
ejpam-3329	367	6	∗	∗	NOUN
ejpam-3329	367	7	t	t	NOUN
ejpam-3329	367	8	)	)	PUNCT
ejpam-3329	367	9	2	2	NUM
ejpam-3329	368	1	+	+	NUM
ejpam-3329	368	2	nctc	nctc	ADJ
ejpam-3329	368	3	∗	∗	NOUN
ejpam-3329	368	4	t	t	PROPN
ejpam-3329	368	5	≥	≥	PROPN
ejpam-3329	368	6	0	0	NUM
ejpam-3329	368	7	.	.	PUNCT
ejpam-3329	369	1	thus	thus	ADV
ejpam-3329	369	2	〈	〈	PROPN
ejpam-3329	369	3	(	(	PUNCT
ejpam-3329	369	4	c2+n	c2+n	NOUN
ejpam-3329	369	5	t	t	NOUN
ejpam-3329	369	6	c∗2+nt	c∗2+nt	ADP
ejpam-3329	369	7	−	−	PROPN
ejpam-3329	369	8	(	(	PUNCT
ejpam-3329	369	9	1	1	NUM
ejpam-3329	369	10	+	+	NUM
ejpam-3329	369	11	n)(ctc	n)(ctc	NOUN
ejpam-3329	369	12	∗	∗	NOUN
ejpam-3329	369	13	t	t	NOUN
ejpam-3329	369	14	)	)	PUNCT
ejpam-3329	369	15	2	2	NUM
ejpam-3329	369	16	+	+	NUM
ejpam-3329	369	17	nctc	nctc	ADJ
ejpam-3329	369	18	∗	∗	NOUN
ejpam-3329	369	19	t	t	PROPN
ejpam-3329	369	20	)	)	PUNCT
ejpam-3329	370	1	χe	χe	PROPN
ejpam-3329	370	2	,	,	PUNCT
ejpam-3329	370	3	χe	χe	PROPN
ejpam-3329	370	4	〉	〉	PROPN
ejpam-3329	370	5	≥	≥	NOUN
ejpam-3329	370	6	0	0	NUM
ejpam-3329	370	7	for	for	ADP
ejpam-3329	370	8	every	every	DET
ejpam-3329	370	9	characteristic	characteristic	ADJ
ejpam-3329	370	10	function	function	NOUN
ejpam-3329	370	11	χe	χe	NOUN
ejpam-3329	370	12	of	of	ADP
ejpam-3329	370	13	e	e	PROPN
ejpam-3329	370	14	in	in	ADP
ejpam-3329	370	15	σ	σ	PROPN
ejpam-3329	370	16	such	such	ADJ
ejpam-3329	370	17	that	that	SCONJ
ejpam-3329	370	18	λ(e	λ(e	PROPN
ejpam-3329	370	19	)	)	PUNCT
ejpam-3329	370	20	<	<	X
ejpam-3329	370	21	∞.	∞.	PROPN
ejpam-3329	370	22	since	since	SCONJ
ejpam-3329	370	23	c∗tct	c∗tct	NOUN
ejpam-3329	370	24	=	=	SYM
ejpam-3329	370	25	mf0	mf0	PROPN
ejpam-3329	370	26	,	,	PUNCT
ejpam-3329	370	27	c∗1+nt	c∗1+nt	PROPN
ejpam-3329	370	28	c1+n	c1+n	PROPN
ejpam-3329	370	29	t	t	PROPN
ejpam-3329	371	1	=	=	PUNCT
ejpam-3329	371	2	m	m	PROPN
ejpam-3329	371	3	f	f	X
ejpam-3329	371	4	(	(	PUNCT
ejpam-3329	371	5	1+n	1+n	NUM
ejpam-3329	371	6	)	)	PUNCT
ejpam-3329	371	7	0	0	NUM
ejpam-3329	371	8	and	and	CCONJ
ejpam-3329	371	9	ctc	ctc	PROPN
ejpam-3329	371	10	∗	∗	NOUN
ejpam-3329	371	11	t	t	NOUN
ejpam-3329	371	12	=	=	SYM
ejpam-3329	371	13	(	(	PUNCT
ejpam-3329	371	14	f0	f0	PROPN
ejpam-3329	371	15	◦	◦	NOUN
ejpam-3329	371	16	t	t	NOUN
ejpam-3329	371	17	)	)	PUNCT
ejpam-3329	371	18	p	p	NOUN
ejpam-3329	371	19	,	,	PUNCT
ejpam-3329	371	20	then	then	ADV
ejpam-3329	371	21	∫	∫	INTJ
ejpam-3329	371	22	e((f	e((f	X
ejpam-3329	371	23	(	(	PUNCT
ejpam-3329	371	24	2+n	2+n	NUM
ejpam-3329	371	25	)	)	PUNCT
ejpam-3329	371	26	0	0	NUM
ejpam-3329	371	27	◦	◦	NOUN
ejpam-3329	371	28	t	t	NOUN
ejpam-3329	371	29	2+n)p2+n−(1+n)(f0	2+n)p2+n−(1+n)(f0	NUM
ejpam-3329	371	30	◦	◦	NOUN
ejpam-3329	371	31	t	t	NOUN
ejpam-3329	371	32	)	)	PUNCT
ejpam-3329	371	33	2p1+n(f0	2p1+n(f0	NUM
ejpam-3329	371	34	◦	◦	NOUN
ejpam-3329	371	35	t	t	NOUN
ejpam-3329	371	36	)	)	PUNCT
ejpam-3329	371	37	p1)dλ	p1)dλ	NOUN
ejpam-3329	371	38	≥	≥	NUM
ejpam-3329	371	39	0	0	NUM
ejpam-3329	371	40	for	for	ADP
ejpam-3329	371	41	every	every	DET
ejpam-3329	371	42	e	e	NOUN
ejpam-3329	371	43	in	in	ADP
ejpam-3329	371	44	σ	σ	PROPN
ejpam-3329	371	45	.	.	PUNCT
ejpam-3329	372	1	hence	hence	ADV
ejpam-3329	372	2	ct	ct	PROPN
ejpam-3329	372	3	is	be	AUX
ejpam-3329	372	4	of	of	ADP
ejpam-3329	372	5	quasi	quasi	NOUN
ejpam-3329	372	6	n	n	PRON
ejpam-3329	372	7	class	class	NOUN
ejpam-3329	372	8	q∗	q∗	NOUN
ejpam-3329	372	9	if	if	SCONJ
ejpam-3329	373	1	and	and	CCONJ
ejpam-3329	373	2	only	only	ADV
ejpam-3329	373	3	if	if	SCONJ
ejpam-3329	373	4	(	(	PUNCT
ejpam-3329	373	5	f	f	X
ejpam-3329	373	6	(	(	PUNCT
ejpam-3329	373	7	2+n	2+n	NUM
ejpam-3329	373	8	)	)	PUNCT
ejpam-3329	373	9	0	0	NUM
ejpam-3329	373	10	◦	◦	NOUN
ejpam-3329	373	11	t	t	NOUN
ejpam-3329	373	12	2+n)p2+n	2+n)p2+n	NUM
ejpam-3329	373	13	−	−	NOUN
ejpam-3329	373	14	(	(	PUNCT
ejpam-3329	373	15	1	1	NUM
ejpam-3329	373	16	+	+	NUM
ejpam-3329	373	17	n)(f0	n)(f0	NOUN
ejpam-3329	373	18	◦	◦	NOUN
ejpam-3329	373	19	t	t	NOUN
ejpam-3329	373	20	)	)	PUNCT
ejpam-3329	373	21	2p1	2p1	NUM
ejpam-3329	373	22	+	+	CCONJ
ejpam-3329	373	23	n(f0	n(f0	NOUN
ejpam-3329	373	24	◦	◦	NOUN
ejpam-3329	373	25	t	t	PROPN
ejpam-3329	373	26	)	)	PUNCT
ejpam-3329	373	27	p1	p1	NOUN
ejpam-3329	373	28	≥	≥	NOUN
ejpam-3329	373	29	0	0	NUM
ejpam-3329	374	1	a.e	a.e	PROPN
ejpam-3329	374	2	.	.	PROPN
ejpam-3329	374	3	corollary	corollary	NOUN
ejpam-3329	374	4	9	9	NUM
ejpam-3329	374	5	.	.	PUNCT
ejpam-3329	375	1	let	let	VERB
ejpam-3329	375	2	ct	ct	NUM
ejpam-3329	375	3	∈	∈	PROPN
ejpam-3329	375	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	375	5	)	)	PUNCT
ejpam-3329	375	6	)	)	PUNCT
ejpam-3329	375	7	with	with	ADP
ejpam-3329	375	8	dense	dense	ADJ
ejpam-3329	375	9	range	range	NOUN
ejpam-3329	375	10	.	.	PUNCT
ejpam-3329	376	1	then	then	ADV
ejpam-3329	376	2	c∗t	c∗t	NOUN
ejpam-3329	376	3	is	be	AUX
ejpam-3329	376	4	quasi	quasi	ADJ
ejpam-3329	376	5	n	n	CCONJ
ejpam-3329	376	6	-	-	PUNCT
ejpam-3329	376	7	class	class	NOUN
ejpam-3329	376	8	q∗	q∗	NOUN
ejpam-3329	376	9	if	if	SCONJ
ejpam-3329	376	10	and	and	CCONJ
ejpam-3329	376	11	only	only	ADV
ejpam-3329	376	12	if	if	SCONJ
ejpam-3329	376	13	(	(	PUNCT
ejpam-3329	376	14	f	f	X
ejpam-3329	376	15	(	(	PUNCT
ejpam-3329	376	16	2+n	2+n	NUM
ejpam-3329	376	17	)	)	PUNCT
ejpam-3329	376	18	0	0	NUM
ejpam-3329	377	1	◦	◦	NOUN
ejpam-3329	377	2	t	t	NOUN
ejpam-3329	377	3	2+n)−	2+n)−	NUM
ejpam-3329	377	4	(	(	PUNCT
ejpam-3329	377	5	1	1	NUM
ejpam-3329	377	6	+	+	NUM
ejpam-3329	377	7	n)(f0	n)(f0	NOUN
ejpam-3329	377	8	◦	◦	NOUN
ejpam-3329	377	9	t	t	NOUN
ejpam-3329	377	10	)	)	PUNCT
ejpam-3329	377	11	2	2	NUM
ejpam-3329	377	12	+	+	NUM
ejpam-3329	377	13	n(f0	n(f0	NOUN
ejpam-3329	377	14	◦	◦	NOUN
ejpam-3329	377	15	t	t	PROPN
ejpam-3329	377	16	)	)	PUNCT
ejpam-3329	377	17	≥	≥	PROPN
ejpam-3329	377	18	0	0	NUM
ejpam-3329	378	1	a.e	a.e	PROPN
ejpam-3329	378	2	.	.	PROPN
ejpam-3329	378	3	d.	d.	PROPN
ejpam-3329	378	4	senthilkumar	senthilkumar	PROPN
ejpam-3329	378	5	,	,	PUNCT
ejpam-3329	378	6	s.	s.	PROPN
ejpam-3329	378	7	parvatham	parvatham	PROPN
ejpam-3329	378	8	/	/	SYM
ejpam-3329	378	9	eur	eur	PROPN
ejpam-3329	378	10	.	.	PUNCT
ejpam-3329	379	1	j.	j.	PROPN
ejpam-3329	379	2	pure	pure	PROPN
ejpam-3329	379	3	appl	appl	PROPN
ejpam-3329	379	4	.	.	PROPN
ejpam-3329	379	5	math	math	PROPN
ejpam-3329	379	6	,	,	PUNCT
ejpam-3329	379	7	11	11	NUM
ejpam-3329	379	8	(	(	PUNCT
ejpam-3329	379	9	4	4	NUM
ejpam-3329	379	10	)	)	PUNCT
ejpam-3329	379	11	(	(	PUNCT
ejpam-3329	379	12	2018	2018	NUM
ejpam-3329	379	13	)	)	PUNCT
ejpam-3329	379	14	,	,	PUNCT
ejpam-3329	379	15	1108	1108	NUM
ejpam-3329	379	16	-	-	SYM
ejpam-3329	379	17	1129	1129	NUM
ejpam-3329	379	18	1119	1119	NUM
ejpam-3329	379	19	5	5	NUM
ejpam-3329	379	20	.	.	PUNCT
ejpam-3329	379	21	quasi	quasi	PROPN
ejpam-3329	379	22	n	n	CCONJ
ejpam-3329	379	23	-	-	PUNCT
ejpam-3329	379	24	class	class	NOUN
ejpam-3329	379	25	q	q	NOUN
ejpam-3329	379	26	and	and	CCONJ
ejpam-3329	379	27	quasi	quasi	ADJ
ejpam-3329	379	28	n	n	CCONJ
ejpam-3329	379	29	-	-	PUNCT
ejpam-3329	379	30	class	class	NOUN
ejpam-3329	379	31	q∗	q∗	NOUN
ejpam-3329	379	32	weighted	weight	VERB
ejpam-3329	379	33	composition	composition	NOUN
ejpam-3329	379	34	operators	operator	NOUN
ejpam-3329	379	35	a	a	DET
ejpam-3329	379	36	weighted	weight	VERB
ejpam-3329	379	37	composition	composition	NOUN
ejpam-3329	379	38	operator	operator	NOUN
ejpam-3329	379	39	is	be	AUX
ejpam-3329	379	40	a	a	DET
ejpam-3329	379	41	linear	linear	ADJ
ejpam-3329	379	42	transformation	transformation	NOUN
ejpam-3329	379	43	acting	act	VERB
ejpam-3329	379	44	on	on	ADP
ejpam-3329	379	45	the	the	DET
ejpam-3329	379	46	set	set	NOUN
ejpam-3329	379	47	of	of	ADP
ejpam-3329	379	48	complex	complex	ADJ
ejpam-3329	379	49	valued	value	VERB
ejpam-3329	379	50	σ	σ	PROPN
ejpam-3329	379	51	measurable	measurable	ADJ
ejpam-3329	379	52	functions	function	NOUN
ejpam-3329	379	53	f	f	PROPN
ejpam-3329	379	54	of	of	ADP
ejpam-3329	379	55	the	the	DET
ejpam-3329	379	56	form	form	NOUN
ejpam-3329	379	57	wt	wt	X
ejpam-3329	379	58	f	f	PROPN
ejpam-3329	379	59	=	=	PROPN
ejpam-3329	379	60	w(f	w(f	PROPN
ejpam-3329	379	61	◦	◦	NOUN
ejpam-3329	379	62	t	t	PROPN
ejpam-3329	379	63	)	)	PUNCT
ejpam-3329	379	64	,	,	PUNCT
ejpam-3329	379	65	where	where	SCONJ
ejpam-3329	379	66	w	w	NOUN
ejpam-3329	379	67	is	be	AUX
ejpam-3329	379	68	a	a	DET
ejpam-3329	379	69	complex	complex	ADJ
ejpam-3329	379	70	valued	value	VERB
ejpam-3329	379	71	σ	σ	NUM
ejpam-3329	379	72	measurable	measurable	ADJ
ejpam-3329	379	73	function	function	NOUN
ejpam-3329	379	74	.	.	PUNCT
ejpam-3329	380	1	in	in	ADP
ejpam-3329	380	2	the	the	DET
ejpam-3329	380	3	case	case	NOUN
ejpam-3329	380	4	that	that	SCONJ
ejpam-3329	380	5	w	w	PROPN
ejpam-3329	380	6	=	=	SYM
ejpam-3329	380	7	1	1	NUM
ejpam-3329	380	8	a.e	a.e	PROPN
ejpam-3329	380	9	.	.	PROPN
ejpam-3329	380	10	,	,	PUNCT
ejpam-3329	380	11	we	we	PRON
ejpam-3329	380	12	say	say	VERB
ejpam-3329	380	13	that	that	SCONJ
ejpam-3329	380	14	wt	wt	PROPN
ejpam-3329	380	15	is	be	AUX
ejpam-3329	380	16	a	a	DET
ejpam-3329	380	17	composition	composition	NOUN
ejpam-3329	380	18	operator	operator	NOUN
ejpam-3329	380	19	.	.	PUNCT
ejpam-3329	381	1	let	let	VERB
ejpam-3329	381	2	wk	wk	INTJ
ejpam-3329	381	3	denote	denote	VERB
ejpam-3329	381	4	w(w	w(w	PROPN
ejpam-3329	381	5	◦	◦	PROPN
ejpam-3329	381	6	t	t	PROPN
ejpam-3329	381	7	)	)	PUNCT
ejpam-3329	381	8	(	(	PUNCT
ejpam-3329	381	9	w	w	NOUN
ejpam-3329	381	10	◦	◦	NOUN
ejpam-3329	381	11	t	t	PROPN
ejpam-3329	381	12	2)	2)	NUM
ejpam-3329	381	13	...	...	PUNCT
ejpam-3329	381	14	(w	(w	INTJ
ejpam-3329	381	15	◦	◦	NOUN
ejpam-3329	381	16	t	t	PROPN
ejpam-3329	381	17	k−1	k−1	PROPN
ejpam-3329	381	18	)	)	PUNCT
ejpam-3329	382	1	so	so	SCONJ
ejpam-3329	382	2	that	that	SCONJ
ejpam-3329	382	3	w	w	PROPN
ejpam-3329	382	4	k	k	PROPN
ejpam-3329	382	5	t	t	PROPN
ejpam-3329	382	6	f	f	PROPN
ejpam-3329	383	1	=	=	PRON
ejpam-3329	384	1	wk(f	wk(f	PUNCT
ejpam-3329	385	1	◦	◦	NOUN
ejpam-3329	385	2	t	t	PROPN
ejpam-3329	385	3	)	)	PUNCT
ejpam-3329	386	1	k	k	PROPN
ejpam-3329	387	1	[	[	X
ejpam-3329	387	2	13	13	NUM
ejpam-3329	387	3	]	]	PUNCT
ejpam-3329	387	4	.	.	PUNCT
ejpam-3329	388	1	to	to	PART
ejpam-3329	388	2	examine	examine	VERB
ejpam-3329	388	3	the	the	DET
ejpam-3329	388	4	weighted	weight	VERB
ejpam-3329	388	5	composition	composition	NOUN
ejpam-3329	388	6	operators	operator	NOUN
ejpam-3329	388	7	efficiently	efficiently	ADV
ejpam-3329	388	8	,	,	PUNCT
ejpam-3329	388	9	alan	alan	PROPN
ejpam-3329	388	10	lambert	lambert	PROPN
ejpam-3329	389	1	[	[	X
ejpam-3329	389	2	12	12	NUM
ejpam-3329	389	3	]	]	PUNCT
ejpam-3329	389	4	,	,	PUNCT
ejpam-3329	389	5	associated	associate	VERB
ejpam-3329	389	6	conditional	conditional	ADJ
ejpam-3329	389	7	expectation	expectation	NOUN
ejpam-3329	389	8	operator	operator	NOUN
ejpam-3329	389	9	e	e	NOUN
ejpam-3329	389	10	with	with	ADP
ejpam-3329	389	11	each	each	DET
ejpam-3329	389	12	transformation	transformation	NOUN
ejpam-3329	389	13	t	t	PROPN
ejpam-3329	389	14	as	as	SCONJ
ejpam-3329	389	15	e(•|t	e(•|t	PROPN
ejpam-3329	389	16	1σ	1σ	NOUN
ejpam-3329	389	17	)	)	PUNCT
ejpam-3329	389	18	=	=	SYM
ejpam-3329	390	1	e(•	e(•	PROPN
ejpam-3329	390	2	)	)	PUNCT
ejpam-3329	390	3	.	.	PUNCT
ejpam-3329	391	1	e(f	e(f	PROPN
ejpam-3329	391	2	)	)	PUNCT
ejpam-3329	391	3	is	be	AUX
ejpam-3329	391	4	defined	define	VERB
ejpam-3329	391	5	for	for	ADP
ejpam-3329	391	6	each	each	DET
ejpam-3329	391	7	non	non	ADJ
ejpam-3329	391	8	-	-	ADJ
ejpam-3329	391	9	negative	negative	ADJ
ejpam-3329	391	10	measurable	measurable	ADJ
ejpam-3329	391	11	function	function	NOUN
ejpam-3329	391	12	f	f	PROPN
ejpam-3329	391	13	∈	∈	PROPN
ejpam-3329	391	14	lp(1	lp(1	PROPN
ejpam-3329	391	15	≤	≤	NOUN
ejpam-3329	391	16	p	p	X
ejpam-3329	391	17	)	)	PUNCT
ejpam-3329	391	18	and	and	CCONJ
ejpam-3329	391	19	is	be	AUX
ejpam-3329	391	20	uniquely	uniquely	ADV
ejpam-3329	391	21	determined	determine	VERB
ejpam-3329	391	22	by	by	ADP
ejpam-3329	391	23	the	the	DET
ejpam-3329	391	24	conditions	condition	NOUN
ejpam-3329	391	25	(	(	PUNCT
ejpam-3329	391	26	i	i	NOUN
ejpam-3329	391	27	)	)	PUNCT
ejpam-3329	391	28	e(f	e(f	PROPN
ejpam-3329	391	29	)	)	PUNCT
ejpam-3329	391	30	is	be	AUX
ejpam-3329	391	31	t−1σ	t−1σ	NOUN
ejpam-3329	391	32	measurable	measurable	ADJ
ejpam-3329	391	33	and	and	CCONJ
ejpam-3329	391	34	(	(	PUNCT
ejpam-3329	391	35	ii	ii	NOUN
ejpam-3329	391	36	)	)	PUNCT
ejpam-3329	391	37	if	if	SCONJ
ejpam-3329	391	38	b	b	NOUN
ejpam-3329	391	39	is	be	AUX
ejpam-3329	391	40	any	any	DET
ejpam-3329	391	41	t−1σ	t−1σ	NOUN
ejpam-3329	391	42	measurable	measurable	ADJ
ejpam-3329	391	43	set	set	NOUN
ejpam-3329	391	44	for	for	ADP
ejpam-3329	391	45	which	which	PRON
ejpam-3329	391	46	∫	∫	PROPN
ejpam-3329	391	47	b	b	NOUN
ejpam-3329	391	48	fdλ	fdλ	NOUN
ejpam-3329	391	49	converges	converge	VERB
ejpam-3329	391	50	,	,	PUNCT
ejpam-3329	391	51	then	then	ADV
ejpam-3329	391	52	we	we	PRON
ejpam-3329	391	53	have	have	VERB
ejpam-3329	391	54	∫	∫	PROPN
ejpam-3329	391	55	b	b	NOUN
ejpam-3329	391	56	fdλ	fdλ	NOUN
ejpam-3329	392	1	=	=	NOUN
ejpam-3329	392	2	∫	∫	PROPN
ejpam-3329	392	3	b	b	PROPN
ejpam-3329	392	4	e(f)dλ	e(f)dλ	PROPN
ejpam-3329	392	5	.	.	PUNCT
ejpam-3329	393	1	as	as	ADP
ejpam-3329	393	2	an	an	DET
ejpam-3329	393	3	operator	operator	NOUN
ejpam-3329	393	4	on	on	ADP
ejpam-3329	393	5	lp	lp	NOUN
ejpam-3329	393	6	,	,	PUNCT
ejpam-3329	393	7	e	e	X
ejpam-3329	393	8	is	be	AUX
ejpam-3329	393	9	the	the	DET
ejpam-3329	393	10	projection	projection	NOUN
ejpam-3329	393	11	onto	onto	ADP
ejpam-3329	393	12	the	the	DET
ejpam-3329	393	13	closure	closure	NOUN
ejpam-3329	393	14	range	range	NOUN
ejpam-3329	393	15	of	of	ADP
ejpam-3329	393	16	c.	c.	PROPN
ejpam-3329	393	17	en	en	PROPN
ejpam-3329	393	18	the	the	DET
ejpam-3329	393	19	identity	identity	NOUN
ejpam-3329	393	20	on	on	ADP
ejpam-3329	393	21	lp	lp	ADV
ejpam-3329	393	22	if	if	SCONJ
ejpam-3329	393	23	and	and	CCONJ
ejpam-3329	393	24	only	only	ADV
ejpam-3329	393	25	if	if	SCONJ
ejpam-3329	393	26	t−1σ	t−1σ	ADP
ejpam-3329	393	27	=	=	PROPN
ejpam-3329	393	28	σ	σ	PROPN
ejpam-3329	393	29	.	.	PUNCT
ejpam-3329	394	1	now	now	ADV
ejpam-3329	394	2	we	we	PRON
ejpam-3329	394	3	are	be	AUX
ejpam-3329	394	4	ready	ready	ADJ
ejpam-3329	394	5	to	to	PART
ejpam-3329	394	6	derive	derive	VERB
ejpam-3329	394	7	the	the	DET
ejpam-3329	394	8	characterization	characterization	NOUN
ejpam-3329	394	9	of	of	ADP
ejpam-3329	394	10	quasi	quasi	ADJ
ejpam-3329	394	11	n	n	CCONJ
ejpam-3329	394	12	-	-	PUNCT
ejpam-3329	394	13	class	class	NOUN
ejpam-3329	394	14	q	q	NOUN
ejpam-3329	394	15	and	and	CCONJ
ejpam-3329	394	16	quasi	quasi	ADJ
ejpam-3329	394	17	n	n	CCONJ
ejpam-3329	394	18	-	-	PUNCT
ejpam-3329	394	19	class	class	NOUN
ejpam-3329	394	20	q∗	q∗	NOUN
ejpam-3329	394	21	weighted	weight	VERB
ejpam-3329	394	22	composition	composition	NOUN
ejpam-3329	394	23	operator	operator	NOUN
ejpam-3329	394	24	as	as	SCONJ
ejpam-3329	394	25	follows	follow	VERB
ejpam-3329	394	26	.	.	PUNCT
ejpam-3329	395	1	theorem	theorem	NOUN
ejpam-3329	395	2	26	26	NUM
ejpam-3329	395	3	.	.	PUNCT
ejpam-3329	396	1	let	let	VERB
ejpam-3329	396	2	wt	wt	PART
ejpam-3329	396	3	be	be	AUX
ejpam-3329	396	4	a	a	DET
ejpam-3329	396	5	weighted	weighted	ADJ
ejpam-3329	396	6	composition	composition	NOUN
ejpam-3329	396	7	operator	operator	NOUN
ejpam-3329	396	8	on	on	ADP
ejpam-3329	396	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	396	10	)	)	PUNCT
ejpam-3329	396	11	)	)	PUNCT
ejpam-3329	396	12	.	.	PUNCT
ejpam-3329	397	1	then	then	ADV
ejpam-3329	397	2	wt	wt	PROPN
ejpam-3329	397	3	is	be	AUX
ejpam-3329	397	4	of	of	ADP
ejpam-3329	397	5	quasi	quasi	NOUN
ejpam-3329	397	6	n	n	CCONJ
ejpam-3329	397	7	-	-	PUNCT
ejpam-3329	397	8	class	class	NOUN
ejpam-3329	397	9	q	q	NOUN
ejpam-3329	397	10	if	if	SCONJ
ejpam-3329	397	11	and	and	CCONJ
ejpam-3329	397	12	only	only	ADV
ejpam-3329	397	13	if	if	SCONJ
ejpam-3329	397	14	(	(	PUNCT
ejpam-3329	397	15	f	f	X
ejpam-3329	397	16	(	(	PUNCT
ejpam-3329	397	17	2+n	2+n	NUM
ejpam-3329	397	18	)	)	PUNCT
ejpam-3329	397	19	0	0	NUM
ejpam-3329	397	20	e(w2	e(w2	NOUN
ejpam-3329	397	21	2+n	2+n	NUM
ejpam-3329	397	22	)	)	PUNCT
ejpam-3329	397	23	◦	◦	NOUN
ejpam-3329	397	24	t−(2+n))−	t−(2+n))−	PUNCT
ejpam-3329	397	25	(	(	PUNCT
ejpam-3329	397	26	1	1	NUM
ejpam-3329	397	27	+	+	NUM
ejpam-3329	397	28	n)(f	n)(f	NOUN
ejpam-3329	397	29	(	(	PUNCT
ejpam-3329	397	30	2	2	NUM
ejpam-3329	397	31	)	)	PUNCT
ejpam-3329	397	32	0	0	NUM
ejpam-3329	397	33	e(w2	e(w2	NOUN
ejpam-3329	397	34	2	2	NUM
ejpam-3329	397	35	)	)	PUNCT
ejpam-3329	397	36	◦	◦	NOUN
ejpam-3329	397	37	t−2	t−2	PROPN
ejpam-3329	397	38	)	)	PUNCT
ejpam-3329	397	39	+	+	CCONJ
ejpam-3329	397	40	nf0e(w2	nf0e(w2	NOUN
ejpam-3329	397	41	)	)	PUNCT
ejpam-3329	397	42	◦	◦	NOUN
ejpam-3329	397	43	t−1	t−1	PROPN
ejpam-3329	397	44	≥	≥	NOUN
ejpam-3329	397	45	0	0	NUM
ejpam-3329	397	46	a.e	a.e	PROPN
ejpam-3329	397	47	.	.	PROPN
ejpam-3329	397	48	proof	proof	NOUN
ejpam-3329	397	49	.	.	PUNCT
ejpam-3329	398	1	since	since	SCONJ
ejpam-3329	398	2	wt	wt	PROPN
ejpam-3329	398	3	∈	∈	PROPN
ejpam-3329	398	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	398	5	)	)	PUNCT
ejpam-3329	398	6	)	)	PUNCT
ejpam-3329	398	7	is	be	AUX
ejpam-3329	398	8	of	of	ADP
ejpam-3329	398	9	quasi	quasi	NOUN
ejpam-3329	398	10	n	n	CCONJ
ejpam-3329	398	11	-	-	PUNCT
ejpam-3329	398	12	class	class	NOUN
ejpam-3329	398	13	q	q	NOUN
ejpam-3329	398	14	if	if	SCONJ
ejpam-3329	399	1	and	and	CCONJ
ejpam-3329	399	2	only	only	ADV
ejpam-3329	399	3	if	if	SCONJ
ejpam-3329	399	4	w	w	PROPN
ejpam-3329	399	5	∗2+nt	∗2+nt	PROPN
ejpam-3329	399	6	w	w	PROPN
ejpam-3329	399	7	2+n	2+n	NUM
ejpam-3329	399	8	t	t	NOUN
ejpam-3329	399	9	−	−	PROPN
ejpam-3329	399	10	(	(	PUNCT
ejpam-3329	399	11	1	1	NUM
ejpam-3329	399	12	+	+	CCONJ
ejpam-3329	399	13	n)w	n)w	X
ejpam-3329	399	14	∗2	∗2	PROPN
ejpam-3329	399	15	t	t	PROPN
ejpam-3329	399	16	w	w	NOUN
ejpam-3329	399	17	2	2	NUM
ejpam-3329	399	18	t	t	NOUN
ejpam-3329	399	19	+	+	CCONJ
ejpam-3329	399	20	nw	nw	PROPN
ejpam-3329	399	21	∗twt	∗twt	PROPN
ejpam-3329	399	22	≥	≥	NOUN
ejpam-3329	399	23	0	0	NUM
ejpam-3329	399	24	.	.	PUNCT
ejpam-3329	400	1	by	by	ADP
ejpam-3329	400	2	theorem	theorem	NOUN
ejpam-3329	400	3	1	1	NUM
ejpam-3329	400	4	.	.	PUNCT
ejpam-3329	400	5	thus	thus	ADV
ejpam-3329	400	6	〈	〈	PROPN
ejpam-3329	400	7	(	(	PUNCT
ejpam-3329	400	8	w	w	PROPN
ejpam-3329	400	9	∗2+nt	∗2+nt	PROPN
ejpam-3329	400	10	w	w	PROPN
ejpam-3329	400	11	2+n	2+n	NUM
ejpam-3329	400	12	t	t	NOUN
ejpam-3329	400	13	−	−	PROPN
ejpam-3329	400	14	(	(	PUNCT
ejpam-3329	400	15	1	1	NUM
ejpam-3329	400	16	+	+	CCONJ
ejpam-3329	400	17	n)w	n)w	X
ejpam-3329	400	18	∗2	∗2	PROPN
ejpam-3329	400	19	t	t	PROPN
ejpam-3329	400	20	w	w	NOUN
ejpam-3329	400	21	2	2	NUM
ejpam-3329	400	22	t	t	NOUN
ejpam-3329	400	23	+	+	CCONJ
ejpam-3329	400	24	nw	nw	PROPN
ejpam-3329	400	25	∗twt	∗twt	PROPN
ejpam-3329	400	26	)	)	PUNCT
ejpam-3329	400	27	χe	χe	PROPN
ejpam-3329	400	28	,	,	PUNCT
ejpam-3329	400	29	χe	χe	PROPN
ejpam-3329	400	30	〉	〉	PROPN
ejpam-3329	400	31	≥	≥	NOUN
ejpam-3329	400	32	0	0	NUM
ejpam-3329	400	33	for	for	ADP
ejpam-3329	400	34	every	every	DET
ejpam-3329	400	35	characteristic	characteristic	ADJ
ejpam-3329	400	36	function	function	NOUN
ejpam-3329	400	37	χe	χe	NOUN
ejpam-3329	400	38	of	of	ADP
ejpam-3329	400	39	e	e	PROPN
ejpam-3329	400	40	in	in	ADP
ejpam-3329	400	41	σ	σ	PROPN
ejpam-3329	400	42	such	such	ADJ
ejpam-3329	400	43	that	that	SCONJ
ejpam-3329	400	44	λ(e	λ(e	PROPN
ejpam-3329	400	45	)	)	PUNCT
ejpam-3329	400	46	<	<	X
ejpam-3329	400	47	∞.	∞.	PROPN
ejpam-3329	400	48	since	since	SCONJ
ejpam-3329	400	49	w	w	PROPN
ejpam-3329	400	50	∗twt	∗twt	PROPN
ejpam-3329	400	51	=	=	SYM
ejpam-3329	400	52	f0e(w2	f0e(w2	NOUN
ejpam-3329	400	53	)	)	PUNCT
ejpam-3329	400	54	◦	◦	NOUN
ejpam-3329	400	55	t−1f	t−1f	PUNCT
ejpam-3329	400	56	,	,	PUNCT
ejpam-3329	400	57	w	w	PROPN
ejpam-3329	400	58	k	k	PROPN
ejpam-3329	400	59	t	t	PROPN
ejpam-3329	400	60	f	f	PROPN
ejpam-3329	400	61	=	=	PRON
ejpam-3329	400	62	wk(f	wk(f	PUNCT
ejpam-3329	400	63	◦	◦	NOUN
ejpam-3329	400	64	t	t	PROPN
ejpam-3329	400	65	)	)	PUNCT
ejpam-3329	400	66	k	k	NOUN
ejpam-3329	400	67	,	,	PUNCT
ejpam-3329	400	68	w	w	PROPN
ejpam-3329	400	69	∗kt	∗kt	SYM
ejpam-3329	400	70	f	f	X
ejpam-3329	400	71	=	=	SYM
ejpam-3329	400	72	f	f	PROPN
ejpam-3329	400	73	(	(	PUNCT
ejpam-3329	400	74	k	k	NOUN
ejpam-3329	400	75	)	)	PUNCT
ejpam-3329	400	76	0	0	NUM
ejpam-3329	400	77	e(wkf	e(wkf	X
ejpam-3329	400	78	)	)	PUNCT
ejpam-3329	400	79	◦	◦	NOUN
ejpam-3329	400	80	t−k	t−k	PROPN
ejpam-3329	400	81	and	and	CCONJ
ejpam-3329	400	82	w	w	PROPN
ejpam-3329	400	83	∗kt	∗kt	PROPN
ejpam-3329	400	84	w	w	NOUN
ejpam-3329	401	1	k	k	PROPN
ejpam-3329	401	2	t	t	PROPN
ejpam-3329	401	3	f	f	PROPN
ejpam-3329	401	4	=	=	SYM
ejpam-3329	401	5	f	f	PROPN
ejpam-3329	401	6	(	(	PUNCT
ejpam-3329	401	7	k	k	NOUN
ejpam-3329	401	8	)	)	PUNCT
ejpam-3329	401	9	0	0	NUM
ejpam-3329	401	10	e(w2	e(w2	NOUN
ejpam-3329	401	11	k	k	NOUN
ejpam-3329	401	12	)	)	PUNCT
ejpam-3329	401	13	◦	◦	NOUN
ejpam-3329	401	14	t−kf	t−kf	PROPN
ejpam-3329	401	15	.	.	PUNCT
ejpam-3329	402	1	hence	hence	ADV
ejpam-3329	402	2	〈	〈	PROPN
ejpam-3329	402	3	(	(	PUNCT
ejpam-3329	402	4	f	f	PROPN
ejpam-3329	402	5	(	(	PUNCT
ejpam-3329	402	6	2+n)0	2+n)0	PROPN
ejpam-3329	402	7	e(w2	e(w2	VERB
ejpam-3329	402	8	2+n)	2+n)	NUM
ejpam-3329	402	9	◦	◦	NOUN
ejpam-3329	402	10	t−(2+n)−(1+n)f	t−(2+n)−(1+n)f	NOUN
ejpam-3329	402	11	(	(	PUNCT
ejpam-3329	402	12	2	2	NUM
ejpam-3329	402	13	)	)	PUNCT
ejpam-3329	402	14	0	0	NUM
ejpam-3329	402	15	e(w2	e(w2	NOUN
ejpam-3329	402	16	2)	2)	VERB
ejpam-3329	402	17	◦	◦	NOUN
ejpam-3329	402	18	t−2	t−2	NOUN
ejpam-3329	402	19	+	+	NOUN
ejpam-3329	402	20	nf0e(w2)	nf0e(w2)	PROPN
ejpam-3329	402	21	◦	◦	NOUN
ejpam-3329	402	22	t−1)χe	t−1)χe	NOUN
ejpam-3329	402	23	,	,	PUNCT
ejpam-3329	402	24	χe	χe	PROPN
ejpam-3329	402	25	〉	〉	PROPN
ejpam-3329	402	26	≥	≥	NUM
ejpam-3329	402	27	0	0	NUM
ejpam-3329	402	28	.	.	PUNCT
ejpam-3329	403	1	hence∫	hence∫	PROPN
ejpam-3329	403	2	e(f	e(f	PROPN
ejpam-3329	403	3	(	(	PUNCT
ejpam-3329	403	4	2+n	2+n	NUM
ejpam-3329	403	5	)	)	PUNCT
ejpam-3329	403	6	0	0	NUM
ejpam-3329	403	7	e(w2	e(w2	NOUN
ejpam-3329	403	8	2+n)	2+n)	NUM
ejpam-3329	403	9	◦	◦	NOUN
ejpam-3329	403	10	t−(2+n)−	t−(2+n)−	NOUN
ejpam-3329	403	11	(	(	PUNCT
ejpam-3329	403	12	1	1	NUM
ejpam-3329	403	13	+	+	NOUN
ejpam-3329	403	14	n)f	n)f	NOUN
ejpam-3329	403	15	(	(	PUNCT
ejpam-3329	403	16	2	2	NUM
ejpam-3329	403	17	)	)	PUNCT
ejpam-3329	403	18	0	0	NUM
ejpam-3329	404	1	e(w2)2	e(w2)2	PROPN
ejpam-3329	404	2	◦	◦	NOUN
ejpam-3329	404	3	t−2	t−2	PROPN
ejpam-3329	404	4	+	+	NOUN
ejpam-3329	404	5	nf0e(w2)	nf0e(w2)	PROPN
ejpam-3329	404	6	◦	◦	ADJ
ejpam-3329	404	7	t−1)dλ	t−1)dλ	NOUN
ejpam-3329	404	8	≥	≥	NOUN
ejpam-3329	404	9	0	0	NUM
ejpam-3329	404	10	for	for	ADP
ejpam-3329	404	11	every	every	DET
ejpam-3329	404	12	e	e	NOUN
ejpam-3329	404	13	in	in	ADP
ejpam-3329	404	14	σ	σ	PROPN
ejpam-3329	404	15	.	.	PUNCT
ejpam-3329	405	1	hence	hence	ADV
ejpam-3329	405	2	w	w	NOUN
ejpam-3329	405	3	is	be	AUX
ejpam-3329	405	4	of	of	ADP
ejpam-3329	405	5	quasi	quasi	NOUN
ejpam-3329	405	6	n	n	X
ejpam-3329	405	7	class	class	NOUN
ejpam-3329	405	8	q	q	NOUN
ejpam-3329	405	9	if	if	SCONJ
ejpam-3329	405	10	and	and	CCONJ
ejpam-3329	405	11	only	only	ADV
ejpam-3329	405	12	if	if	SCONJ
ejpam-3329	405	13	f	f	PROPN
ejpam-3329	405	14	(	(	PUNCT
ejpam-3329	405	15	2+n	2+n	NUM
ejpam-3329	405	16	)	)	PUNCT
ejpam-3329	405	17	0	0	NUM
ejpam-3329	405	18	e(w2	e(w2	NOUN
ejpam-3329	405	19	2+n	2+n	NUM
ejpam-3329	405	20	)	)	PUNCT
ejpam-3329	405	21	◦	◦	NOUN
ejpam-3329	405	22	t−(2+n	t−(2+n	NOUN
ejpam-3329	405	23	)	)	PUNCT
ejpam-3329	405	24	−	−	PROPN
ejpam-3329	406	1	(	(	PUNCT
ejpam-3329	406	2	1	1	NUM
ejpam-3329	406	3	+	+	CCONJ
ejpam-3329	406	4	n)f	n)f	NOUN
ejpam-3329	406	5	(	(	PUNCT
ejpam-3329	406	6	2	2	NUM
ejpam-3329	406	7	)	)	PUNCT
ejpam-3329	406	8	0	0	NUM
ejpam-3329	406	9	e(w2	e(w2	NOUN
ejpam-3329	406	10	2	2	NUM
ejpam-3329	406	11	)	)	PUNCT
ejpam-3329	406	12	◦	◦	NOUN
ejpam-3329	406	13	t−2	t−2	NOUN
ejpam-3329	406	14	+	+	CCONJ
ejpam-3329	406	15	nf0e(w2	nf0e(w2	NOUN
ejpam-3329	406	16	)	)	PUNCT
ejpam-3329	406	17	◦	◦	NOUN
ejpam-3329	406	18	t−1	t−1	PROPN
ejpam-3329	406	19	≥	≥	NOUN
ejpam-3329	406	20	0	0	NUM
ejpam-3329	407	1	a.e	a.e	PROPN
ejpam-3329	407	2	.	.	PROPN
ejpam-3329	407	3	corollary	corollary	ADJ
ejpam-3329	407	4	10	10	NUM
ejpam-3329	407	5	.	.	PUNCT
ejpam-3329	408	1	let	let	VERB
ejpam-3329	408	2	wt	wt	PART
ejpam-3329	408	3	be	be	AUX
ejpam-3329	408	4	a	a	DET
ejpam-3329	408	5	weighted	weighted	ADJ
ejpam-3329	408	6	composition	composition	NOUN
ejpam-3329	408	7	operator	operator	NOUN
ejpam-3329	408	8	in	in	ADP
ejpam-3329	408	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	408	10	)	)	PUNCT
ejpam-3329	408	11	)	)	PUNCT
ejpam-3329	408	12	and	and	CCONJ
ejpam-3329	408	13	assume	assume	VERB
ejpam-3329	408	14	that	that	SCONJ
ejpam-3329	408	15	t−1σ	t−1σ	VERB
ejpam-3329	408	16	=	=	PROPN
ejpam-3329	408	17	σ	σ	PROPN
ejpam-3329	408	18	.	.	PUNCT
ejpam-3329	409	1	then	then	ADV
ejpam-3329	409	2	wt	wt	PROPN
ejpam-3329	409	3	is	be	AUX
ejpam-3329	409	4	of	of	ADP
ejpam-3329	409	5	quasi	quasi	NOUN
ejpam-3329	409	6	n	n	CCONJ
ejpam-3329	409	7	-	-	PUNCT
ejpam-3329	409	8	class	class	NOUN
ejpam-3329	409	9	q	q	NOUN
ejpam-3329	409	10	if	if	SCONJ
ejpam-3329	410	1	and	and	CCONJ
ejpam-3329	410	2	only	only	ADV
ejpam-3329	410	3	if	if	SCONJ
ejpam-3329	410	4	f	f	PROPN
ejpam-3329	410	5	(	(	PUNCT
ejpam-3329	410	6	2+n	2+n	NUM
ejpam-3329	410	7	)	)	PUNCT
ejpam-3329	410	8	0	0	NUM
ejpam-3329	410	9	w2	w2	NOUN
ejpam-3329	410	10	2+n	2+n	NUM
ejpam-3329	410	11	◦	◦	NOUN
ejpam-3329	410	12	t−(2+n	t−(2+n	NOUN
ejpam-3329	410	13	)	)	PUNCT
ejpam-3329	411	1	−	−	PROPN
ejpam-3329	412	1	(	(	PUNCT
ejpam-3329	412	2	1	1	NUM
ejpam-3329	412	3	+	+	CCONJ
ejpam-3329	412	4	n)f	n)f	NOUN
ejpam-3329	412	5	(	(	PUNCT
ejpam-3329	412	6	2	2	NUM
ejpam-3329	412	7	)	)	PUNCT
ejpam-3329	412	8	0	0	NUM
ejpam-3329	412	9	w2	w2	NOUN
ejpam-3329	412	10	2	2	NUM
ejpam-3329	412	11	◦	◦	NOUN
ejpam-3329	412	12	t−2	t−2	PROPN
ejpam-3329	412	13	+	+	CCONJ
ejpam-3329	412	14	nf0(w	nf0(w	PROPN
ejpam-3329	412	15	2	2	NUM
ejpam-3329	412	16	)	)	PUNCT
ejpam-3329	412	17	◦	◦	NOUN
ejpam-3329	412	18	t−1	t−1	PROPN
ejpam-3329	412	19	≥	≥	NOUN
ejpam-3329	412	20	0	0	NUM
ejpam-3329	413	1	a.e	a.e	PROPN
ejpam-3329	413	2	.	.	PROPN
ejpam-3329	413	3	theorem	theorem	PROPN
ejpam-3329	413	4	27	27	NUM
ejpam-3329	413	5	.	.	PUNCT
ejpam-3329	414	1	let	let	VERB
ejpam-3329	414	2	wt	wt	PART
ejpam-3329	414	3	be	be	AUX
ejpam-3329	414	4	a	a	DET
ejpam-3329	414	5	weighted	weighted	ADJ
ejpam-3329	414	6	composition	composition	NOUN
ejpam-3329	414	7	operator	operator	NOUN
ejpam-3329	414	8	in	in	ADP
ejpam-3329	414	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	414	10	)	)	PUNCT
ejpam-3329	414	11	)	)	PUNCT
ejpam-3329	414	12	.	.	PUNCT
ejpam-3329	415	1	then	then	ADV
ejpam-3329	415	2	w	w	PROPN
ejpam-3329	415	3	∗t	∗t	PROPN
ejpam-3329	415	4	is	be	AUX
ejpam-3329	415	5	of	of	ADP
ejpam-3329	415	6	quasi	quasi	NOUN
ejpam-3329	415	7	n	n	CCONJ
ejpam-3329	415	8	-	-	PUNCT
ejpam-3329	415	9	class	class	NOUN
ejpam-3329	415	10	q	q	NOUN
ejpam-3329	415	11	if	if	SCONJ
ejpam-3329	415	12	and	and	CCONJ
ejpam-3329	415	13	only	only	ADV
ejpam-3329	415	14	if	if	SCONJ
ejpam-3329	415	15	w2+n(f	w2+n(f	X
ejpam-3329	415	16	(	(	PUNCT
ejpam-3329	415	17	2+n	2+n	NUM
ejpam-3329	415	18	)	)	PUNCT
ejpam-3329	415	19	0	0	NUM
ejpam-3329	416	1	◦	◦	NOUN
ejpam-3329	416	2	t	t	X
ejpam-3329	416	3	2+n)e(w2+n)−	2+n)e(w2+n)−	NUM
ejpam-3329	416	4	(	(	PUNCT
ejpam-3329	416	5	1	1	NUM
ejpam-3329	416	6	+	+	CCONJ
ejpam-3329	416	7	n)w2(f	n)w2(f	PROPN
ejpam-3329	416	8	(	(	PUNCT
ejpam-3329	416	9	2	2	NUM
ejpam-3329	416	10	)	)	PUNCT
ejpam-3329	416	11	0	0	NUM
ejpam-3329	416	12	◦	◦	NOUN
ejpam-3329	416	13	t	t	NOUN
ejpam-3329	416	14	2)e(w2	2)e(w2	NOUN
ejpam-3329	416	15	)	)	PUNCT
ejpam-3329	417	1	+	+	CCONJ
ejpam-3329	417	2	nw(f0	nw(f0	PROPN
ejpam-3329	417	3	◦	◦	NOUN
ejpam-3329	417	4	t	t	PROPN
ejpam-3329	417	5	)	)	PUNCT
ejpam-3329	417	6	e(w	e(w	PROPN
ejpam-3329	417	7	)	)	PUNCT
ejpam-3329	417	8	≥	≥	NOUN
ejpam-3329	417	9	0	0	NUM
ejpam-3329	417	10	a.e	a.e	PROPN
ejpam-3329	417	11	.	.	PROPN
ejpam-3329	417	12	proof	proof	NOUN
ejpam-3329	417	13	.	.	PUNCT
ejpam-3329	418	1	since	since	SCONJ
ejpam-3329	418	2	w	w	PROPN
ejpam-3329	418	3	∗t	∗t	PROPN
ejpam-3329	418	4	∈	∈	PROPN
ejpam-3329	418	5	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	418	6	)	)	PUNCT
ejpam-3329	418	7	)	)	PUNCT
ejpam-3329	418	8	is	be	AUX
ejpam-3329	418	9	of	of	ADP
ejpam-3329	418	10	quasi	quasi	NOUN
ejpam-3329	418	11	n	n	CCONJ
ejpam-3329	418	12	-	-	PUNCT
ejpam-3329	418	13	class	class	NOUN
ejpam-3329	418	14	q	q	NOUN
ejpam-3329	418	15	if	if	SCONJ
ejpam-3329	419	1	and	and	CCONJ
ejpam-3329	419	2	only	only	ADV
ejpam-3329	419	3	if	if	SCONJ
ejpam-3329	419	4	d.	d.	PROPN
ejpam-3329	419	5	senthilkumar	senthilkumar	PROPN
ejpam-3329	419	6	,	,	PUNCT
ejpam-3329	419	7	s.	s.	PROPN
ejpam-3329	419	8	parvatham	parvatham	PROPN
ejpam-3329	419	9	/	/	SYM
ejpam-3329	419	10	eur	eur	PROPN
ejpam-3329	419	11	.	.	PUNCT
ejpam-3329	420	1	j.	j.	PROPN
ejpam-3329	420	2	pure	pure	PROPN
ejpam-3329	420	3	appl	appl	PROPN
ejpam-3329	420	4	.	.	PROPN
ejpam-3329	420	5	math	math	PROPN
ejpam-3329	420	6	,	,	PUNCT
ejpam-3329	420	7	11	11	NUM
ejpam-3329	420	8	(	(	PUNCT
ejpam-3329	420	9	4	4	NUM
ejpam-3329	420	10	)	)	PUNCT
ejpam-3329	420	11	(	(	PUNCT
ejpam-3329	420	12	2018	2018	NUM
ejpam-3329	420	13	)	)	PUNCT
ejpam-3329	420	14	,	,	PUNCT
ejpam-3329	420	15	1108	1108	NUM
ejpam-3329	420	16	-	-	SYM
ejpam-3329	420	17	1129	1129	NUM
ejpam-3329	420	18	1120	1120	NUM
ejpam-3329	420	19	w	w	PROPN
ejpam-3329	420	20	2+n	2+n	NUM
ejpam-3329	420	21	t	t	NOUN
ejpam-3329	420	22	w	w	PROPN
ejpam-3329	420	23	∗2+nt	∗2+nt	PROPN
ejpam-3329	421	1	−	−	PROPN
ejpam-3329	422	1	(	(	PUNCT
ejpam-3329	422	2	1	1	NUM
ejpam-3329	422	3	+	+	NUM
ejpam-3329	422	4	n)w	n)w	X
ejpam-3329	422	5	2	2	NUM
ejpam-3329	422	6	tw	tw	NOUN
ejpam-3329	422	7	∗2	∗2	PROPN
ejpam-3329	422	8	t	t	PROPN
ejpam-3329	422	9	+	+	CCONJ
ejpam-3329	422	10	nwtw	nwtw	ADJ
ejpam-3329	422	11	∗	∗	NOUN
ejpam-3329	422	12	t	t	PROPN
ejpam-3329	422	13	≥	≥	PROPN
ejpam-3329	422	14	0	0	NUM
ejpam-3329	422	15	.	.	PUNCT
ejpam-3329	423	1	by	by	ADP
ejpam-3329	423	2	theorem	theorem	NOUN
ejpam-3329	423	3	1	1	NUM
ejpam-3329	423	4	thus	thus	ADV
ejpam-3329	423	5	〈	〈	PROPN
ejpam-3329	423	6	(	(	PUNCT
ejpam-3329	423	7	w	w	PROPN
ejpam-3329	423	8	2+n	2+n	NUM
ejpam-3329	423	9	t	t	NOUN
ejpam-3329	423	10	w	w	PROPN
ejpam-3329	423	11	∗2+nt	∗2+nt	PROPN
ejpam-3329	424	1	−	−	PROPN
ejpam-3329	425	1	(	(	PUNCT
ejpam-3329	425	2	1	1	NUM
ejpam-3329	425	3	+	+	NUM
ejpam-3329	425	4	n)w	n)w	X
ejpam-3329	425	5	2	2	NUM
ejpam-3329	425	6	tw	tw	NOUN
ejpam-3329	425	7	∗2	∗2	PROPN
ejpam-3329	425	8	t	t	PROPN
ejpam-3329	425	9	+	+	CCONJ
ejpam-3329	425	10	nwtw	nwtw	ADJ
ejpam-3329	425	11	∗	∗	NOUN
ejpam-3329	425	12	t	t	PROPN
ejpam-3329	425	13	)	)	PUNCT
ejpam-3329	426	1	χe	χe	PROPN
ejpam-3329	426	2	,	,	PUNCT
ejpam-3329	426	3	χe	χe	PROPN
ejpam-3329	426	4	〉	〉	PROPN
ejpam-3329	426	5	≥	≥	NOUN
ejpam-3329	426	6	0	0	NUM
ejpam-3329	426	7	for	for	ADP
ejpam-3329	426	8	every	every	DET
ejpam-3329	426	9	characteristic	characteristic	ADJ
ejpam-3329	426	10	function	function	NOUN
ejpam-3329	426	11	χe	χe	NOUN
ejpam-3329	426	12	of	of	ADP
ejpam-3329	426	13	e	e	PROPN
ejpam-3329	426	14	in	in	ADP
ejpam-3329	426	15	σ	σ	PROPN
ejpam-3329	427	1	such	such	ADJ
ejpam-3329	427	2	that	that	SCONJ
ejpam-3329	427	3	λ(e	λ(e	PROPN
ejpam-3329	427	4	)	)	PUNCT
ejpam-3329	427	5	<	<	X
ejpam-3329	427	6	∞.	∞.	PROPN
ejpam-3329	427	7	since	since	SCONJ
ejpam-3329	427	8	wtw	wtw	PROPN
ejpam-3329	427	9	∗	∗	PROPN
ejpam-3329	427	10	t	t	PROPN
ejpam-3329	427	11	f	f	PROPN
ejpam-3329	427	12	=	=	SYM
ejpam-3329	427	13	w(f0	w(f0	NOUN
ejpam-3329	427	14	◦	◦	NOUN
ejpam-3329	427	15	t	t	NOUN
ejpam-3329	427	16	)	)	PUNCT
ejpam-3329	427	17	e(wf	e(wf	X
ejpam-3329	427	18	)	)	PUNCT
ejpam-3329	427	19	,	,	PUNCT
ejpam-3329	427	20	w	w	PROPN
ejpam-3329	427	21	k	k	PROPN
ejpam-3329	427	22	t	t	PROPN
ejpam-3329	427	23	f	f	PROPN
ejpam-3329	428	1	=	=	PRON
ejpam-3329	428	2	wk(f	wk(f	PUNCT
ejpam-3329	428	3	◦	◦	NOUN
ejpam-3329	428	4	t	t	PROPN
ejpam-3329	428	5	)	)	PUNCT
ejpam-3329	429	1	k	k	NOUN
ejpam-3329	429	2	,	,	PUNCT
ejpam-3329	429	3	w	w	PROPN
ejpam-3329	429	4	∗kt	∗kt	SYM
ejpam-3329	429	5	f	f	X
ejpam-3329	429	6	=	=	SYM
ejpam-3329	429	7	fk0e(wkf	fk0e(wkf	PROPN
ejpam-3329	429	8	)	)	PUNCT
ejpam-3329	429	9	◦	◦	VERB
ejpam-3329	429	10	t−k	t−k	PROPN
ejpam-3329	429	11	and	and	CCONJ
ejpam-3329	429	12	w	w	PROPN
ejpam-3329	429	13	k	k	PROPN
ejpam-3329	429	14	tw	tw	PROPN
ejpam-3329	429	15	∗k	∗k	NOUN
ejpam-3329	429	16	t	t	NOUN
ejpam-3329	429	17	f	f	X
ejpam-3329	429	18	=	=	PRON
ejpam-3329	429	19	wk(f	wk(f	X
ejpam-3329	429	20	(	(	PUNCT
ejpam-3329	429	21	k	k	NOUN
ejpam-3329	429	22	)	)	PUNCT
ejpam-3329	429	23	0	0	NUM
ejpam-3329	430	1	◦	◦	NOUN
ejpam-3329	430	2	t	t	PROPN
ejpam-3329	430	3	(	(	PUNCT
ejpam-3329	430	4	k))e(wkf	k))e(wkf	NOUN
ejpam-3329	430	5	)	)	PUNCT
ejpam-3329	430	6	.	.	PUNCT
ejpam-3329	431	1	then	then	ADV
ejpam-3329	431	2	〈	〈	PROPN
ejpam-3329	431	3	(	(	PUNCT
ejpam-3329	431	4	w2+n(f	w2+n(f	X
ejpam-3329	431	5	(	(	PUNCT
ejpam-3329	431	6	2+n	2+n	NUM
ejpam-3329	431	7	)	)	PUNCT
ejpam-3329	431	8	0	0	NUM
ejpam-3329	432	1	◦	◦	NOUN
ejpam-3329	432	2	t	t	X
ejpam-3329	432	3	2+n)e(w2+n)−	2+n)e(w2+n)−	NUM
ejpam-3329	432	4	(	(	PUNCT
ejpam-3329	432	5	1	1	NUM
ejpam-3329	432	6	+	+	CCONJ
ejpam-3329	432	7	n)w2(f	n)w2(f	PROPN
ejpam-3329	432	8	(	(	PUNCT
ejpam-3329	432	9	2	2	NUM
ejpam-3329	432	10	)	)	PUNCT
ejpam-3329	432	11	0	0	NUM
ejpam-3329	432	12	◦	◦	NOUN
ejpam-3329	432	13	t	t	NOUN
ejpam-3329	432	14	2)e(w2	2)e(w2	NOUN
ejpam-3329	432	15	)	)	PUNCT
ejpam-3329	433	1	+	+	CCONJ
ejpam-3329	433	2	nw(f0	nw(f0	PROPN
ejpam-3329	433	3	◦	◦	NOUN
ejpam-3329	433	4	t	t	PROPN
ejpam-3329	433	5	)	)	PUNCT
ejpam-3329	433	6	e(w))χe	e(w))χe	PROPN
ejpam-3329	433	7	,	,	PUNCT
ejpam-3329	433	8	χe	χe	PROPN
ejpam-3329	433	9	〉	〉	PROPN
ejpam-3329	433	10	≥	≥	NUM
ejpam-3329	433	11	0	0	NUM
ejpam-3329	433	12	.	.	PUNCT
ejpam-3329	433	13	which	which	PRON
ejpam-3329	433	14	gives	give	VERB
ejpam-3329	433	15	∫	∫	PROPN
ejpam-3329	433	16	e(w2+n(f	e(w2+n(f	PROPN
ejpam-3329	433	17	(	(	PUNCT
ejpam-3329	433	18	2+n	2+n	NUM
ejpam-3329	433	19	)	)	PUNCT
ejpam-3329	433	20	0	0	NUM
ejpam-3329	434	1	◦	◦	NOUN
ejpam-3329	434	2	t	t	PROPN
ejpam-3329	434	3	2+n)e(w2+n	2+n)e(w2+n	NUM
ejpam-3329	434	4	)	)	PUNCT
ejpam-3329	434	5	−	−	PROPN
ejpam-3329	435	1	(	(	PUNCT
ejpam-3329	435	2	1	1	NUM
ejpam-3329	435	3	+	+	CCONJ
ejpam-3329	435	4	n)w2(f	n)w2(f	PROPN
ejpam-3329	435	5	(	(	PUNCT
ejpam-3329	435	6	2	2	NUM
ejpam-3329	435	7	)	)	PUNCT
ejpam-3329	435	8	0	0	NUM
ejpam-3329	435	9	◦	◦	NOUN
ejpam-3329	435	10	t	t	NOUN
ejpam-3329	435	11	2)e(w2	2)e(w2	NOUN
ejpam-3329	435	12	)	)	PUNCT
ejpam-3329	436	1	+	+	CCONJ
ejpam-3329	436	2	nw(f0	nw(f0	PROPN
ejpam-3329	436	3	◦	◦	NOUN
ejpam-3329	436	4	t	t	PROPN
ejpam-3329	436	5	)	)	PUNCT
ejpam-3329	436	6	e(w))dλ	e(w))dλ	VERB
ejpam-3329	436	7	≥	≥	NOUN
ejpam-3329	436	8	0	0	NUM
ejpam-3329	436	9	for	for	ADP
ejpam-3329	436	10	every	every	DET
ejpam-3329	436	11	e	e	NOUN
ejpam-3329	436	12	in	in	ADP
ejpam-3329	436	13	σ	σ	PROPN
ejpam-3329	436	14	.	.	PUNCT
ejpam-3329	437	1	hence	hence	ADV
ejpam-3329	437	2	w	w	PROPN
ejpam-3329	437	3	∗t	∗t	PROPN
ejpam-3329	437	4	is	be	AUX
ejpam-3329	437	5	quasi	quasi	NOUN
ejpam-3329	437	6	n	n	X
ejpam-3329	437	7	class	class	NOUN
ejpam-3329	437	8	q	q	NOUN
ejpam-3329	437	9	if	if	SCONJ
ejpam-3329	438	1	and	and	CCONJ
ejpam-3329	438	2	only	only	ADV
ejpam-3329	438	3	if	if	SCONJ
ejpam-3329	438	4	(	(	PUNCT
ejpam-3329	438	5	w2+n(f	w2+n(f	X
ejpam-3329	438	6	(	(	PUNCT
ejpam-3329	438	7	2+n	2+n	NUM
ejpam-3329	438	8	)	)	PUNCT
ejpam-3329	438	9	0	0	NUM
ejpam-3329	438	10	◦	◦	NOUN
ejpam-3329	438	11	t	t	X
ejpam-3329	438	12	2+n)e(w2+n)−	2+n)e(w2+n)−	NUM
ejpam-3329	438	13	(	(	PUNCT
ejpam-3329	438	14	1	1	NUM
ejpam-3329	438	15	+	+	CCONJ
ejpam-3329	438	16	n)w2(f	n)w2(f	PROPN
ejpam-3329	438	17	(	(	PUNCT
ejpam-3329	438	18	2	2	NUM
ejpam-3329	438	19	)	)	PUNCT
ejpam-3329	438	20	0	0	NUM
ejpam-3329	438	21	◦	◦	NOUN
ejpam-3329	438	22	t	t	NOUN
ejpam-3329	438	23	2)e(w2	2)e(w2	NOUN
ejpam-3329	438	24	)	)	PUNCT
ejpam-3329	439	1	+	+	CCONJ
ejpam-3329	439	2	nw(f0	nw(f0	PROPN
ejpam-3329	439	3	◦	◦	NOUN
ejpam-3329	439	4	t	t	PROPN
ejpam-3329	439	5	)	)	PUNCT
ejpam-3329	439	6	e(w	e(w	PROPN
ejpam-3329	439	7	)	)	PUNCT
ejpam-3329	439	8	)	)	PUNCT
ejpam-3329	439	9	≥	≥	NOUN
ejpam-3329	439	10	0	0	NUM
ejpam-3329	440	1	a.e	a.e	PROPN
ejpam-3329	440	2	.	.	PROPN
ejpam-3329	440	3	corollary	corollary	ADJ
ejpam-3329	440	4	11	11	NUM
ejpam-3329	440	5	.	.	PUNCT
ejpam-3329	441	1	let	let	VERB
ejpam-3329	441	2	wt	wt	PART
ejpam-3329	441	3	be	be	AUX
ejpam-3329	441	4	a	a	DET
ejpam-3329	441	5	weighted	weighted	ADJ
ejpam-3329	441	6	composition	composition	NOUN
ejpam-3329	441	7	operator	operator	NOUN
ejpam-3329	441	8	in	in	ADP
ejpam-3329	441	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	441	10	)	)	PUNCT
ejpam-3329	441	11	)	)	PUNCT
ejpam-3329	441	12	and	and	CCONJ
ejpam-3329	441	13	t−1(σ	t−1(σ	PROPN
ejpam-3329	441	14	)	)	PUNCT
ejpam-3329	442	1	=	=	SYM
ejpam-3329	442	2	σ	σ	PROPN
ejpam-3329	442	3	.	.	PUNCT
ejpam-3329	443	1	then	then	ADV
ejpam-3329	443	2	w	w	PROPN
ejpam-3329	443	3	∗t	∗t	PROPN
ejpam-3329	443	4	is	be	AUX
ejpam-3329	443	5	of	of	ADP
ejpam-3329	443	6	n	n	CCONJ
ejpam-3329	443	7	-	-	PUNCT
ejpam-3329	443	8	class	class	NOUN
ejpam-3329	443	9	q	q	NOUN
ejpam-3329	443	10	if	if	SCONJ
ejpam-3329	444	1	and	and	CCONJ
ejpam-3329	444	2	only	only	ADV
ejpam-3329	444	3	if	if	SCONJ
ejpam-3329	444	4	w2	w2	PROPN
ejpam-3329	444	5	2+n(f	2+n(f	NUM
ejpam-3329	444	6	(	(	PUNCT
ejpam-3329	444	7	2+n	2+n	NUM
ejpam-3329	444	8	)	)	PUNCT
ejpam-3329	444	9	0	0	NUM
ejpam-3329	444	10	◦	◦	NOUN
ejpam-3329	444	11	t	t	NOUN
ejpam-3329	444	12	2+n)−	2+n)−	NUM
ejpam-3329	444	13	(	(	PUNCT
ejpam-3329	444	14	1	1	NUM
ejpam-3329	444	15	+	+	CCONJ
ejpam-3329	444	16	n)w2	n)w2	ADJ
ejpam-3329	444	17	2(f	2(f	NUM
ejpam-3329	444	18	(	(	PUNCT
ejpam-3329	444	19	2	2	NUM
ejpam-3329	444	20	)	)	PUNCT
ejpam-3329	444	21	0	0	NUM
ejpam-3329	444	22	◦	◦	NOUN
ejpam-3329	444	23	t	t	PROPN
ejpam-3329	444	24	2	2	NUM
ejpam-3329	444	25	)	)	PUNCT
ejpam-3329	444	26	+	+	CCONJ
ejpam-3329	444	27	nw2(f0	nw2(f0	NUM
ejpam-3329	444	28	◦	◦	PROPN
ejpam-3329	444	29	t	t	PROPN
ejpam-3329	444	30	)	)	PUNCT
ejpam-3329	444	31	≥	≥	PROPN
ejpam-3329	444	32	0	0	NUM
ejpam-3329	444	33	a.e	a.e	PROPN
ejpam-3329	444	34	.	.	PROPN
ejpam-3329	444	35	theorem	theorem	PROPN
ejpam-3329	444	36	28	28	NUM
ejpam-3329	444	37	.	.	PUNCT
ejpam-3329	445	1	let	let	VERB
ejpam-3329	445	2	wt	wt	PART
ejpam-3329	445	3	be	be	AUX
ejpam-3329	445	4	a	a	DET
ejpam-3329	445	5	weighted	weighted	ADJ
ejpam-3329	445	6	composition	composition	NOUN
ejpam-3329	445	7	operator	operator	NOUN
ejpam-3329	445	8	on	on	ADP
ejpam-3329	445	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	445	10	)	)	PUNCT
ejpam-3329	445	11	)	)	PUNCT
ejpam-3329	445	12	.	.	PUNCT
ejpam-3329	446	1	then	then	ADV
ejpam-3329	446	2	wt	wt	PROPN
ejpam-3329	446	3	is	be	AUX
ejpam-3329	446	4	quasi	quasi	NOUN
ejpam-3329	446	5	n	n	CCONJ
ejpam-3329	446	6	-	-	PUNCT
ejpam-3329	446	7	class	class	NOUN
ejpam-3329	446	8	q∗	q∗	NOUN
ejpam-3329	447	1	if	if	SCONJ
ejpam-3329	447	2	and	and	CCONJ
ejpam-3329	447	3	only	only	ADV
ejpam-3329	447	4	if	if	SCONJ
ejpam-3329	447	5	(	(	PUNCT
ejpam-3329	447	6	f	f	X
ejpam-3329	447	7	(	(	PUNCT
ejpam-3329	447	8	2+n	2+n	NUM
ejpam-3329	447	9	)	)	PUNCT
ejpam-3329	447	10	0	0	NUM
ejpam-3329	447	11	e(w2	e(w2	NOUN
ejpam-3329	447	12	2+n	2+n	NUM
ejpam-3329	447	13	)	)	PUNCT
ejpam-3329	447	14	◦	◦	NOUN
ejpam-3329	447	15	t−(2+n	t−(2+n	NOUN
ejpam-3329	447	16	)	)	PUNCT
ejpam-3329	447	17	)	)	PUNCT
ejpam-3329	448	1	−	−	PROPN
ejpam-3329	448	2	(	(	PUNCT
ejpam-3329	448	3	1	1	NUM
ejpam-3329	448	4	+	+	CCONJ
ejpam-3329	448	5	n)w(f0e(w2	n)w(f0e(w2	NOUN
ejpam-3329	448	6	)	)	PUNCT
ejpam-3329	448	7	◦	◦	NOUN
ejpam-3329	449	1	t−1)2	t−1)2	NUM
ejpam-3329	449	2	+	+	CCONJ
ejpam-3329	449	3	nf0e(w2	nf0e(w2	NOUN
ejpam-3329	449	4	)	)	PUNCT
ejpam-3329	449	5	◦	◦	NOUN
ejpam-3329	449	6	t−1	t−1	PROPN
ejpam-3329	449	7	≥	≥	NOUN
ejpam-3329	449	8	0	0	NUM
ejpam-3329	450	1	a.e	a.e	PROPN
ejpam-3329	450	2	.	.	PROPN
ejpam-3329	450	3	proof	proof	NOUN
ejpam-3329	450	4	.	.	PUNCT
ejpam-3329	451	1	since	since	SCONJ
ejpam-3329	451	2	wt	wt	PROPN
ejpam-3329	451	3	∈	∈	PROPN
ejpam-3329	451	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	451	5	)	)	PUNCT
ejpam-3329	451	6	)	)	PUNCT
ejpam-3329	451	7	is	be	AUX
ejpam-3329	451	8	quasi	quasi	ADJ
ejpam-3329	451	9	n	n	CCONJ
ejpam-3329	451	10	-	-	PUNCT
ejpam-3329	451	11	class	class	NOUN
ejpam-3329	451	12	q∗	q∗	NOUN
ejpam-3329	451	13	if	if	SCONJ
ejpam-3329	452	1	and	and	CCONJ
ejpam-3329	452	2	only	only	ADV
ejpam-3329	452	3	if	if	SCONJ
ejpam-3329	452	4	w	w	PROPN
ejpam-3329	452	5	∗2+nt	∗2+nt	PROPN
ejpam-3329	452	6	w	w	PROPN
ejpam-3329	452	7	2+n	2+n	NUM
ejpam-3329	452	8	t	t	NOUN
ejpam-3329	452	9	−	−	PROPN
ejpam-3329	452	10	(	(	PUNCT
ejpam-3329	452	11	1	1	NUM
ejpam-3329	452	12	+	+	NUM
ejpam-3329	452	13	n)(w	n)(w	PROPN
ejpam-3329	452	14	∗twt	∗twt	PUNCT
ejpam-3329	452	15	)	)	PUNCT
ejpam-3329	452	16	2	2	PROPN
ejpam-3329	453	1	+	+	CCONJ
ejpam-3329	453	2	nw	nw	PROPN
ejpam-3329	453	3	∗twt	∗twt	PROPN
ejpam-3329	453	4	≥	≥	NOUN
ejpam-3329	453	5	0	0	NUM
ejpam-3329	454	1	a.e	a.e	PROPN
ejpam-3329	454	2	.	.	PUNCT
ejpam-3329	455	1	thus	thus	ADV
ejpam-3329	455	2	〈	〈	PROPN
ejpam-3329	455	3	(	(	PUNCT
ejpam-3329	455	4	w	w	PROPN
ejpam-3329	455	5	∗2+nt	∗2+nt	PROPN
ejpam-3329	455	6	w	w	PROPN
ejpam-3329	455	7	2+n	2+n	NUM
ejpam-3329	455	8	t	t	NOUN
ejpam-3329	455	9	−	−	PROPN
ejpam-3329	455	10	(	(	PUNCT
ejpam-3329	455	11	1	1	NUM
ejpam-3329	455	12	+	+	NUM
ejpam-3329	455	13	n)(w	n)(w	PROPN
ejpam-3329	455	14	∗twt	∗twt	PUNCT
ejpam-3329	455	15	)	)	PUNCT
ejpam-3329	455	16	2	2	PROPN
ejpam-3329	455	17	+	+	CCONJ
ejpam-3329	455	18	nw	nw	PROPN
ejpam-3329	455	19	∗twt	∗twt	PROPN
ejpam-3329	455	20	)	)	PUNCT
ejpam-3329	456	1	χe	χe	PROPN
ejpam-3329	456	2	,	,	PUNCT
ejpam-3329	456	3	χe	χe	PROPN
ejpam-3329	456	4	〉	〉	PROPN
ejpam-3329	456	5	≥	≥	NOUN
ejpam-3329	456	6	0	0	NUM
ejpam-3329	456	7	for	for	ADP
ejpam-3329	456	8	every	every	DET
ejpam-3329	456	9	characteristic	characteristic	ADJ
ejpam-3329	456	10	function	function	NOUN
ejpam-3329	456	11	χe	χe	NOUN
ejpam-3329	456	12	of	of	ADP
ejpam-3329	456	13	e	e	PROPN
ejpam-3329	456	14	in	in	ADP
ejpam-3329	456	15	σ	σ	PROPN
ejpam-3329	456	16	such	such	ADJ
ejpam-3329	456	17	that	that	SCONJ
ejpam-3329	456	18	λ(e	λ(e	PROPN
ejpam-3329	456	19	)	)	PUNCT
ejpam-3329	456	20	<	<	X
ejpam-3329	456	21	∞.	∞.	PROPN
ejpam-3329	456	22	since	since	SCONJ
ejpam-3329	456	23	w	w	PROPN
ejpam-3329	456	24	∗twt	∗twt	PROPN
ejpam-3329	456	25	=	=	SYM
ejpam-3329	456	26	f0e(w2	f0e(w2	NOUN
ejpam-3329	456	27	)	)	PUNCT
ejpam-3329	456	28	◦	◦	NOUN
ejpam-3329	456	29	t−1f	t−1f	PUNCT
ejpam-3329	456	30	,	,	PUNCT
ejpam-3329	456	31	w	w	PROPN
ejpam-3329	456	32	k	k	PROPN
ejpam-3329	456	33	t	t	PROPN
ejpam-3329	456	34	f	f	PROPN
ejpam-3329	456	35	=	=	PRON
ejpam-3329	456	36	wk(f	wk(f	PUNCT
ejpam-3329	456	37	◦	◦	NOUN
ejpam-3329	456	38	t	t	PROPN
ejpam-3329	456	39	)	)	PUNCT
ejpam-3329	457	1	k	k	NOUN
ejpam-3329	457	2	,	,	PUNCT
ejpam-3329	457	3	w	w	PROPN
ejpam-3329	457	4	∗kt	∗kt	SYM
ejpam-3329	457	5	f	f	X
ejpam-3329	457	6	=	=	SYM
ejpam-3329	457	7	f	f	PROPN
ejpam-3329	457	8	(	(	PUNCT
ejpam-3329	457	9	k	k	NOUN
ejpam-3329	457	10	)	)	PUNCT
ejpam-3329	457	11	0	0	NUM
ejpam-3329	457	12	e(wkf	e(wkf	X
ejpam-3329	457	13	)	)	PUNCT
ejpam-3329	457	14	◦	◦	NOUN
ejpam-3329	457	15	t−k	t−k	PROPN
ejpam-3329	457	16	and	and	CCONJ
ejpam-3329	457	17	w	w	PROPN
ejpam-3329	457	18	∗kt	∗kt	PROPN
ejpam-3329	457	19	w	w	NOUN
ejpam-3329	458	1	k	k	PROPN
ejpam-3329	458	2	t	t	PROPN
ejpam-3329	458	3	f	f	PROPN
ejpam-3329	458	4	=	=	SYM
ejpam-3329	458	5	f	f	PROPN
ejpam-3329	458	6	(	(	PUNCT
ejpam-3329	458	7	k	k	NOUN
ejpam-3329	458	8	)	)	PUNCT
ejpam-3329	458	9	0	0	NUM
ejpam-3329	458	10	e(w2	e(w2	NOUN
ejpam-3329	458	11	k	k	NOUN
ejpam-3329	458	12	)	)	PUNCT
ejpam-3329	459	1	◦	◦	NOUN
ejpam-3329	459	2	t−kf	t−kf	PROPN
ejpam-3329	459	3	.	.	PUNCT
ejpam-3329	460	1	then	then	ADV
ejpam-3329	460	2	〈	〈	PROPN
ejpam-3329	460	3	(	(	PUNCT
ejpam-3329	460	4	f	f	PROPN
ejpam-3329	460	5	(	(	PUNCT
ejpam-3329	460	6	2+n)0	2+n)0	PROPN
ejpam-3329	460	7	e(w2	e(w2	VERB
ejpam-3329	460	8	2+n)	2+n)	NUM
ejpam-3329	460	9	◦	◦	NOUN
ejpam-3329	460	10	t−(2+n)−(1+n)(f0e(w2)	t−(2+n)−(1+n)(f0e(w2)	NUM
ejpam-3329	460	11	◦	◦	NOUN
ejpam-3329	460	12	t−1)2+nf0e(w2)	t−1)2+nf0e(w2)	NOUN
ejpam-3329	460	13	◦	◦	NOUN
ejpam-3329	460	14	t−1)χe	t−1)χe	NOUN
ejpam-3329	460	15	,	,	PUNCT
ejpam-3329	460	16	χe	χe	PROPN
ejpam-3329	460	17	〉	〉	PROPN
ejpam-3329	460	18	≥	≥	NUM
ejpam-3329	460	19	0	0	NUM
ejpam-3329	460	20	.	.	PUNCT
ejpam-3329	460	21	which	which	PRON
ejpam-3329	460	22	implies	imply	VERB
ejpam-3329	460	23	∫	∫	PROPN
ejpam-3329	460	24	e(f	e(f	PROPN
ejpam-3329	460	25	(	(	PUNCT
ejpam-3329	460	26	2+n	2+n	NUM
ejpam-3329	460	27	)	)	PUNCT
ejpam-3329	460	28	0	0	NUM
ejpam-3329	460	29	e(w2	e(w2	NOUN
ejpam-3329	460	30	2+n	2+n	NUM
ejpam-3329	460	31	)	)	PUNCT
ejpam-3329	460	32	◦	◦	NOUN
ejpam-3329	460	33	t−(2+n	t−(2+n	NOUN
ejpam-3329	460	34	)	)	PUNCT
ejpam-3329	460	35	−	−	PROPN
ejpam-3329	461	1	(	(	PUNCT
ejpam-3329	461	2	1	1	NUM
ejpam-3329	461	3	+	+	NUM
ejpam-3329	461	4	n)(f0e(w2	n)(f0e(w2	NOUN
ejpam-3329	461	5	)	)	PUNCT
ejpam-3329	461	6	◦	◦	NOUN
ejpam-3329	461	7	t−1)2	t−1)2	NUM
ejpam-3329	461	8	+	+	CCONJ
ejpam-3329	461	9	nf0e(w2	nf0e(w2	NOUN
ejpam-3329	461	10	)	)	PUNCT
ejpam-3329	461	11	◦	◦	NOUN
ejpam-3329	461	12	t−1)dλ	t−1)dλ	NUM
ejpam-3329	461	13	≥	≥	NOUN
ejpam-3329	461	14	0	0	NUM
ejpam-3329	461	15	for	for	ADP
ejpam-3329	461	16	every	every	DET
ejpam-3329	461	17	e	e	NOUN
ejpam-3329	461	18	in	in	ADP
ejpam-3329	461	19	σ	σ	PROPN
ejpam-3329	461	20	.	.	PUNCT
ejpam-3329	462	1	hence	hence	ADV
ejpam-3329	462	2	w	w	PROPN
ejpam-3329	462	3	is	be	AUX
ejpam-3329	462	4	quasi	quasi	NOUN
ejpam-3329	462	5	n	n	X
ejpam-3329	462	6	class	class	NOUN
ejpam-3329	462	7	q∗	q∗	NOUN
ejpam-3329	463	1	if	if	SCONJ
ejpam-3329	463	2	and	and	CCONJ
ejpam-3329	463	3	only	only	ADV
ejpam-3329	463	4	if	if	SCONJ
ejpam-3329	463	5	(	(	PUNCT
ejpam-3329	463	6	f	f	X
ejpam-3329	463	7	(	(	PUNCT
ejpam-3329	463	8	2+n	2+n	NUM
ejpam-3329	463	9	)	)	PUNCT
ejpam-3329	463	10	0	0	NUM
ejpam-3329	463	11	e(w2	e(w2	NOUN
ejpam-3329	463	12	2+n	2+n	NUM
ejpam-3329	463	13	)	)	PUNCT
ejpam-3329	463	14	◦	◦	NOUN
ejpam-3329	463	15	t−(2+n	t−(2+n	NOUN
ejpam-3329	463	16	)	)	PUNCT
ejpam-3329	463	17	−	−	PROPN
ejpam-3329	464	1	(	(	PUNCT
ejpam-3329	464	2	1	1	NUM
ejpam-3329	464	3	+	+	NUM
ejpam-3329	464	4	n)(f0e(w2	n)(f0e(w2	NOUN
ejpam-3329	464	5	)	)	PUNCT
ejpam-3329	464	6	◦	◦	NOUN
ejpam-3329	464	7	t−1)2	t−1)2	NUM
ejpam-3329	464	8	+	+	CCONJ
ejpam-3329	464	9	nf0e(w2	nf0e(w2	NOUN
ejpam-3329	464	10	)	)	PUNCT
ejpam-3329	464	11	◦	◦	NOUN
ejpam-3329	464	12	t−1	t−1	PROPN
ejpam-3329	464	13	)	)	PUNCT
ejpam-3329	464	14	≥	≥	NOUN
ejpam-3329	464	15	0	0	NUM
ejpam-3329	465	1	a.e	a.e	PROPN
ejpam-3329	465	2	.	.	PROPN
ejpam-3329	465	3	corollary	corollary	NOUN
ejpam-3329	465	4	12	12	NUM
ejpam-3329	465	5	.	.	PUNCT
ejpam-3329	466	1	let	let	VERB
ejpam-3329	466	2	wt	wt	PART
ejpam-3329	466	3	be	be	AUX
ejpam-3329	466	4	a	a	DET
ejpam-3329	466	5	weighted	weighted	ADJ
ejpam-3329	466	6	composition	composition	NOUN
ejpam-3329	466	7	operator	operator	NOUN
ejpam-3329	466	8	in	in	ADP
ejpam-3329	466	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	466	10	)	)	PUNCT
ejpam-3329	466	11	)	)	PUNCT
ejpam-3329	466	12	and	and	CCONJ
ejpam-3329	466	13	assume	assume	VERB
ejpam-3329	466	14	that	that	SCONJ
ejpam-3329	466	15	t−1σ	t−1σ	VERB
ejpam-3329	466	16	=	=	PROPN
ejpam-3329	466	17	σ	σ	PROPN
ejpam-3329	466	18	.	.	PUNCT
ejpam-3329	467	1	then	then	ADV
ejpam-3329	467	2	wt	wt	PROPN
ejpam-3329	467	3	is	be	AUX
ejpam-3329	467	4	quasi	quasi	NOUN
ejpam-3329	467	5	n	n	CCONJ
ejpam-3329	467	6	-	-	PUNCT
ejpam-3329	467	7	class	class	NOUN
ejpam-3329	467	8	q∗	q∗	NOUN
ejpam-3329	468	1	if	if	SCONJ
ejpam-3329	468	2	and	and	CCONJ
ejpam-3329	468	3	only	only	ADV
ejpam-3329	468	4	if	if	SCONJ
ejpam-3329	468	5	(	(	PUNCT
ejpam-3329	468	6	f	f	X
ejpam-3329	468	7	(	(	PUNCT
ejpam-3329	468	8	2+n	2+n	NUM
ejpam-3329	468	9	)	)	PUNCT
ejpam-3329	468	10	0	0	NUM
ejpam-3329	468	11	(	(	PUNCT
ejpam-3329	468	12	w2	w2	NOUN
ejpam-3329	468	13	2+n	2+n	NUM
ejpam-3329	468	14	)	)	PUNCT
ejpam-3329	468	15	◦	◦	NOUN
ejpam-3329	468	16	t−(2+n	t−(2+n	NOUN
ejpam-3329	468	17	)	)	PUNCT
ejpam-3329	468	18	−	−	PROPN
ejpam-3329	469	1	(	(	PUNCT
ejpam-3329	469	2	1	1	NUM
ejpam-3329	469	3	+	+	CCONJ
ejpam-3329	469	4	n)(f0(w	n)(f0(w	PROPN
ejpam-3329	469	5	2	2	NUM
ejpam-3329	469	6	)	)	PUNCT
ejpam-3329	469	7	◦	◦	NOUN
ejpam-3329	469	8	t−1)2	t−1)2	NUM
ejpam-3329	470	1	+	+	CCONJ
ejpam-3329	470	2	nf0(w	nf0(w	PROPN
ejpam-3329	470	3	2	2	NUM
ejpam-3329	470	4	)	)	PUNCT
ejpam-3329	470	5	◦	◦	NOUN
ejpam-3329	470	6	t−1	t−1	PROPN
ejpam-3329	470	7	)	)	PUNCT
ejpam-3329	470	8	≥	≥	NOUN
ejpam-3329	470	9	0	0	NUM
ejpam-3329	470	10	a.e	a.e	PROPN
ejpam-3329	470	11	.	.	PROPN
ejpam-3329	470	12	theorem	theorem	PROPN
ejpam-3329	470	13	29	29	NUM
ejpam-3329	470	14	.	.	PUNCT
ejpam-3329	471	1	let	let	VERB
ejpam-3329	471	2	wt	wt	PART
ejpam-3329	471	3	be	be	AUX
ejpam-3329	471	4	a	a	DET
ejpam-3329	471	5	weighted	weighted	ADJ
ejpam-3329	471	6	composition	composition	NOUN
ejpam-3329	471	7	operator	operator	NOUN
ejpam-3329	471	8	on	on	ADP
ejpam-3329	471	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	471	10	)	)	PUNCT
ejpam-3329	471	11	)	)	PUNCT
ejpam-3329	471	12	.	.	PUNCT
ejpam-3329	472	1	then	then	ADV
ejpam-3329	472	2	w	w	PROPN
ejpam-3329	472	3	∗t	∗t	PROPN
ejpam-3329	472	4	is	be	AUX
ejpam-3329	472	5	quasi	quasi	ADJ
ejpam-3329	472	6	n	n	CCONJ
ejpam-3329	472	7	-	-	PUNCT
ejpam-3329	472	8	class	class	NOUN
ejpam-3329	472	9	q∗	q∗	NOUN
ejpam-3329	473	1	if	if	SCONJ
ejpam-3329	473	2	and	and	CCONJ
ejpam-3329	473	3	only	only	ADV
ejpam-3329	473	4	if	if	SCONJ
ejpam-3329	473	5	w2+n(f	w2+n(f	X
ejpam-3329	473	6	(	(	PUNCT
ejpam-3329	473	7	2+n	2+n	NUM
ejpam-3329	473	8	)	)	PUNCT
ejpam-3329	473	9	0	0	NUM
ejpam-3329	474	1	◦	◦	NOUN
ejpam-3329	474	2	t	t	X
ejpam-3329	474	3	2+n)e(w2+n)−	2+n)e(w2+n)−	NUM
ejpam-3329	474	4	(	(	PUNCT
ejpam-3329	474	5	1	1	NUM
ejpam-3329	474	6	+	+	CCONJ
ejpam-3329	474	7	n)[w(f0	n)[w(f0	NOUN
ejpam-3329	474	8	◦	◦	NOUN
ejpam-3329	474	9	t	t	PROPN
ejpam-3329	474	10	)	)	PUNCT
ejpam-3329	474	11	e(w)]2	e(w)]2	PROPN
ejpam-3329	474	12	+	+	NUM
ejpam-3329	474	13	nw(f0	nw(f0	NOUN
ejpam-3329	474	14	◦	◦	NOUN
ejpam-3329	474	15	t	t	PROPN
ejpam-3329	474	16	)	)	PUNCT
ejpam-3329	474	17	e(w	e(w	PROPN
ejpam-3329	474	18	)	)	PUNCT
ejpam-3329	474	19	≥	≥	NOUN
ejpam-3329	474	20	0	0	NUM
ejpam-3329	475	1	a.e	a.e	PROPN
ejpam-3329	475	2	.	.	PROPN
ejpam-3329	475	3	corollary	corollary	ADJ
ejpam-3329	475	4	13	13	NUM
ejpam-3329	475	5	.	.	PUNCT
ejpam-3329	476	1	if	if	SCONJ
ejpam-3329	476	2	wt	wt	PROPN
ejpam-3329	476	3	is	be	AUX
ejpam-3329	476	4	a	a	DET
ejpam-3329	476	5	weighted	weighted	ADJ
ejpam-3329	476	6	composition	composition	NOUN
ejpam-3329	476	7	operator	operator	NOUN
ejpam-3329	476	8	in	in	ADP
ejpam-3329	476	9	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	476	10	)	)	PUNCT
ejpam-3329	476	11	)	)	PUNCT
ejpam-3329	476	12	and	and	CCONJ
ejpam-3329	476	13	assume	assume	VERB
ejpam-3329	476	14	that	that	SCONJ
ejpam-3329	476	15	t−1σ	t−1σ	VERB
ejpam-3329	476	16	=	=	PROPN
ejpam-3329	476	17	σ	σ	PROPN
ejpam-3329	476	18	.	.	PUNCT
ejpam-3329	477	1	then	then	ADV
ejpam-3329	477	2	w	w	PROPN
ejpam-3329	477	3	∗t	∗t	PROPN
ejpam-3329	477	4	is	be	AUX
ejpam-3329	477	5	quasi	quasi	ADJ
ejpam-3329	477	6	n	n	CCONJ
ejpam-3329	477	7	-	-	PUNCT
ejpam-3329	477	8	class	class	NOUN
ejpam-3329	477	9	q∗	q∗	NOUN
ejpam-3329	478	1	if	if	SCONJ
ejpam-3329	478	2	and	and	CCONJ
ejpam-3329	478	3	only	only	ADV
ejpam-3329	478	4	if	if	SCONJ
ejpam-3329	478	5	w2	w2	PROPN
ejpam-3329	478	6	2+n(f	2+n(f	NUM
ejpam-3329	478	7	(	(	PUNCT
ejpam-3329	478	8	2+n	2+n	NUM
ejpam-3329	478	9	)	)	PUNCT
ejpam-3329	478	10	0	0	NUM
ejpam-3329	478	11	◦	◦	NOUN
ejpam-3329	478	12	t	t	NOUN
ejpam-3329	478	13	2+n)−	2+n)−	NUM
ejpam-3329	478	14	(	(	PUNCT
ejpam-3329	478	15	1	1	NUM
ejpam-3329	478	16	+	+	NUM
ejpam-3329	478	17	n)w4(f0	n)w4(f0	VERB
ejpam-3329	478	18	◦	◦	NOUN
ejpam-3329	478	19	t	t	NOUN
ejpam-3329	478	20	)	)	PUNCT
ejpam-3329	478	21	2	2	NUM
ejpam-3329	478	22	+	+	CCONJ
ejpam-3329	478	23	nw2f0	nw2f0	PROPN
ejpam-3329	478	24	◦	◦	NOUN
ejpam-3329	478	25	t	t	X
ejpam-3329	478	26	≥	≥	NOUN
ejpam-3329	478	27	0	0	NUM
ejpam-3329	479	1	a.e	a.e	PROPN
ejpam-3329	479	2	.	.	PROPN
ejpam-3329	479	3	d.	d.	PROPN
ejpam-3329	479	4	senthilkumar	senthilkumar	PROPN
ejpam-3329	479	5	,	,	PUNCT
ejpam-3329	479	6	s.	s.	PROPN
ejpam-3329	479	7	parvatham	parvatham	PROPN
ejpam-3329	479	8	/	/	SYM
ejpam-3329	479	9	eur	eur	PROPN
ejpam-3329	479	10	.	.	PUNCT
ejpam-3329	480	1	j.	j.	PROPN
ejpam-3329	480	2	pure	pure	PROPN
ejpam-3329	480	3	appl	appl	PROPN
ejpam-3329	480	4	.	.	PROPN
ejpam-3329	480	5	math	math	PROPN
ejpam-3329	480	6	,	,	PUNCT
ejpam-3329	480	7	11	11	NUM
ejpam-3329	480	8	(	(	PUNCT
ejpam-3329	480	9	4	4	NUM
ejpam-3329	480	10	)	)	PUNCT
ejpam-3329	480	11	(	(	PUNCT
ejpam-3329	480	12	2018	2018	NUM
ejpam-3329	480	13	)	)	PUNCT
ejpam-3329	480	14	,	,	PUNCT
ejpam-3329	480	15	1108	1108	NUM
ejpam-3329	480	16	-	-	SYM
ejpam-3329	480	17	1129	1129	NUM
ejpam-3329	480	18	1121	1121	NUM
ejpam-3329	480	19	the	the	DET
ejpam-3329	480	20	aluthge	aluthge	ADJ
ejpam-3329	480	21	transform	transform	NOUN
ejpam-3329	480	22	of	of	ADP
ejpam-3329	480	23	t	t	PROPN
ejpam-3329	480	24	is	be	AUX
ejpam-3329	480	25	the	the	DET
ejpam-3329	480	26	operator	operator	NOUN
ejpam-3329	480	27	t̃	t̃	PROPN
ejpam-3329	480	28	given	give	VERB
ejpam-3329	480	29	by	by	ADP
ejpam-3329	480	30	t̃	t̃	PROPN
ejpam-3329	480	31	=	=	PUNCT
ejpam-3329	480	32	|t	|t	NOUN
ejpam-3329	481	1	|	|	ADV
ejpam-3329	481	2	1	1	NUM
ejpam-3329	481	3	2u	2u	NOUN
ejpam-3329	481	4	|t	|t	VERB
ejpam-3329	481	5	|	|	ADV
ejpam-3329	481	6	1	1	NUM
ejpam-3329	481	7	2	2	NUM
ejpam-3329	481	8	was	be	AUX
ejpam-3329	481	9	introduced	introduce	VERB
ejpam-3329	481	10	in	in	ADP
ejpam-3329	481	11	[	[	X
ejpam-3329	481	12	1	1	NUM
ejpam-3329	481	13	]	]	PUNCT
ejpam-3329	481	14	by	by	ADP
ejpam-3329	481	15	aluthge	aluthge	PROPN
ejpam-3329	481	16	.	.	PUNCT
ejpam-3329	482	1	the	the	DET
ejpam-3329	482	2	idea	idea	NOUN
ejpam-3329	482	3	behind	behind	ADP
ejpam-3329	482	4	the	the	DET
ejpam-3329	482	5	aluthge	aluthge	ADJ
ejpam-3329	482	6	transform	transform	NOUN
ejpam-3329	482	7	is	be	AUX
ejpam-3329	482	8	to	to	PART
ejpam-3329	482	9	convert	convert	VERB
ejpam-3329	482	10	an	an	DET
ejpam-3329	482	11	operator	operator	NOUN
ejpam-3329	482	12	into	into	ADP
ejpam-3329	482	13	another	another	DET
ejpam-3329	482	14	operator	operator	NOUN
ejpam-3329	482	15	which	which	PRON
ejpam-3329	482	16	shares	share	VERB
ejpam-3329	482	17	with	with	ADP
ejpam-3329	482	18	the	the	DET
ejpam-3329	482	19	first	first	ADJ
ejpam-3329	482	20	one	one	NUM
ejpam-3329	482	21	some	some	DET
ejpam-3329	482	22	spectral	spectral	ADJ
ejpam-3329	482	23	properties	property	NOUN
ejpam-3329	482	24	but	but	CCONJ
ejpam-3329	482	25	it	it	PRON
ejpam-3329	482	26	is	be	AUX
ejpam-3329	482	27	closed	close	VERB
ejpam-3329	482	28	to	to	ADP
ejpam-3329	482	29	being	be	AUX
ejpam-3329	482	30	a	a	DET
ejpam-3329	482	31	normal	normal	ADJ
ejpam-3329	482	32	operator	operator	NOUN
ejpam-3329	482	33	.	.	PUNCT
ejpam-3329	483	1	more	more	ADV
ejpam-3329	483	2	generally	generally	ADV
ejpam-3329	483	3	we	we	PRON
ejpam-3329	483	4	may	may	AUX
ejpam-3329	483	5	form	form	VERB
ejpam-3329	483	6	the	the	DET
ejpam-3329	483	7	family	family	NOUN
ejpam-3329	483	8	of	of	ADP
ejpam-3329	483	9	operators	operator	NOUN
ejpam-3329	483	10	tr	tr	VERB
ejpam-3329	483	11	:	:	PUNCT
ejpam-3329	483	12	0	0	NUM
ejpam-3329	483	13	<	<	X
ejpam-3329	483	14	r	r	NOUN
ejpam-3329	483	15	≤	≤	NOUN
ejpam-3329	483	16	1	1	NUM
ejpam-3329	483	17	where	where	SCONJ
ejpam-3329	483	18	tr	tr	VERB
ejpam-3329	483	19	=	=	SYM
ejpam-3329	483	20	|t	|t	NOUN
ejpam-3329	483	21	|ru	|ru	NUM
ejpam-3329	483	22	|t	|t	VERB
ejpam-3329	483	23	|1−r	|1−r	PRON
ejpam-3329	484	1	[	[	X
ejpam-3329	484	2	2	2	NUM
ejpam-3329	484	3	]	]	PUNCT
ejpam-3329	484	4	.	.	PUNCT
ejpam-3329	485	1	for	for	ADP
ejpam-3329	485	2	a	a	DET
ejpam-3329	485	3	composition	composition	NOUN
ejpam-3329	485	4	operator	operator	NOUN
ejpam-3329	485	5	c	c	NOUN
ejpam-3329	485	6	,	,	PUNCT
ejpam-3329	485	7	the	the	DET
ejpam-3329	485	8	polar	polar	ADJ
ejpam-3329	485	9	decomposition	decomposition	NOUN
ejpam-3329	485	10	is	be	AUX
ejpam-3329	485	11	given	give	VERB
ejpam-3329	485	12	by	by	ADP
ejpam-3329	485	13	c	c	NOUN
ejpam-3329	485	14	=	=	SYM
ejpam-3329	485	15	u	u	PROPN
ejpam-3329	485	16	|c|	|c|	PROPN
ejpam-3329	485	17	where	where	SCONJ
ejpam-3329	485	18	|c|f	|c|f	PROPN
ejpam-3329	485	19	=	=	SYM
ejpam-3329	485	20	√	√	PROPN
ejpam-3329	485	21	f0f	f0f	NOUN
ejpam-3329	485	22	and	and	CCONJ
ejpam-3329	485	23	uf	uf	NOUN
ejpam-3329	485	24	=	=	PROPN
ejpam-3329	485	25	1√	1√	PROPN
ejpam-3329	485	26	f0	f0	PROPN
ejpam-3329	485	27	◦	◦	PROPN
ejpam-3329	485	28	t	t	NOUN
ejpam-3329	485	29	f	f	PROPN
ejpam-3329	485	30	◦	◦	NOUN
ejpam-3329	485	31	t	t	PROPN
ejpam-3329	485	32	.	.	PUNCT
ejpam-3329	486	1	in	in	ADP
ejpam-3329	486	2	[	[	X
ejpam-3329	486	3	12	12	NUM
ejpam-3329	486	4	]	]	X
ejpam-3329	486	5	lambert	lambert	PROPN
ejpam-3329	486	6	has	have	AUX
ejpam-3329	486	7	given	give	VERB
ejpam-3329	486	8	more	more	ADJ
ejpam-3329	486	9	general	general	ADJ
ejpam-3329	486	10	aluthge	aluthge	ADJ
ejpam-3329	486	11	transformation	transformation	NOUN
ejpam-3329	486	12	for	for	ADP
ejpam-3329	486	13	composition	composition	NOUN
ejpam-3329	486	14	operators	operator	NOUN
ejpam-3329	486	15	as	as	ADP
ejpam-3329	486	16	cr	cr	PROPN
ejpam-3329	486	17	=	=	PROPN
ejpam-3329	486	18	|c|ru	|c|ru	PROPN
ejpam-3329	486	19	|c|1−r	|c|1−r	NUM
ejpam-3329	486	20	and	and	CCONJ
ejpam-3329	486	21	crf	crf	NUM
ejpam-3329	486	22	=	=	SYM
ejpam-3329	486	23	(	(	PUNCT
ejpam-3329	486	24	f0	f0	PROPN
ejpam-3329	486	25	f0	f0	PROPN
ejpam-3329	486	26	◦	◦	PROPN
ejpam-3329	486	27	t	t	NOUN
ejpam-3329	486	28	)	)	PUNCT
ejpam-3329	487	1	r	r	NOUN
ejpam-3329	487	2	2	2	NUM
ejpam-3329	487	3	f	f	NOUN
ejpam-3329	487	4	◦	◦	NOUN
ejpam-3329	487	5	t	t	PROPN
ejpam-3329	487	6	.	.	PUNCT
ejpam-3329	488	1	that	that	PRON
ejpam-3329	488	2	is	be	AUX
ejpam-3329	488	3	cr	cr	PROPN
ejpam-3329	488	4	is	be	AUX
ejpam-3329	488	5	weighted	weight	VERB
ejpam-3329	488	6	composition	composition	NOUN
ejpam-3329	488	7	operator	operator	NOUN
ejpam-3329	488	8	with	with	ADP
ejpam-3329	488	9	weight	weight	NOUN
ejpam-3329	488	10	π	π	PROPN
ejpam-3329	488	11	=	=	SYM
ejpam-3329	488	12	(	(	PUNCT
ejpam-3329	488	13	f0	f0	PROPN
ejpam-3329	488	14	f0	f0	PROPN
ejpam-3329	488	15	◦	◦	PROPN
ejpam-3329	488	16	t	t	NOUN
ejpam-3329	488	17	)	)	PUNCT
ejpam-3329	489	1	r	r	NOUN
ejpam-3329	489	2	2	2	NUM
ejpam-3329	489	3	where	where	SCONJ
ejpam-3329	489	4	0	0	NUM
ejpam-3329	489	5	<	<	X
ejpam-3329	489	6	r	r	X
ejpam-3329	489	7	<	<	X
ejpam-3329	489	8	1	1	NUM
ejpam-3329	489	9	.	.	PUNCT
ejpam-3329	489	10	since	since	SCONJ
ejpam-3329	489	11	cr	cr	PROPN
ejpam-3329	489	12	is	be	AUX
ejpam-3329	489	13	a	a	DET
ejpam-3329	489	14	weighted	weighted	ADJ
ejpam-3329	489	15	composition	composition	NOUN
ejpam-3329	489	16	operator	operator	NOUN
ejpam-3329	489	17	it	it	PRON
ejpam-3329	489	18	is	be	AUX
ejpam-3329	489	19	easy	easy	ADJ
ejpam-3329	489	20	to	to	PART
ejpam-3329	489	21	show	show	VERB
ejpam-3329	489	22	that	that	SCONJ
ejpam-3329	489	23	|cr|f	|cr|f	NOUN
ejpam-3329	489	24	=	=	SYM
ejpam-3329	489	25	√	√	NUM
ejpam-3329	489	26	f0(e(π)2	f0(e(π)2	PROPN
ejpam-3329	489	27	◦	◦	NOUN
ejpam-3329	489	28	t−1)f	t−1)f	NUM
ejpam-3329	489	29	and	and	CCONJ
ejpam-3329	489	30	|c∗r	|c∗r	NOUN
ejpam-3329	489	31	|f	|f	PUNCT
ejpam-3329	490	1	=	=	SYM
ejpam-3329	490	2	ve(vf	ve(vf	PROPN
ejpam-3329	490	3	)	)	PUNCT
ejpam-3329	490	4	where	where	SCONJ
ejpam-3329	490	5	v	v	NOUN
ejpam-3329	490	6	=	=	SYM
ejpam-3329	490	7	π	π	NOUN
ejpam-3329	490	8	√	√	NUM
ejpam-3329	490	9	f0	f0	PROPN
ejpam-3329	490	10	◦	◦	NOUN
ejpam-3329	490	11	t	t	NOUN
ejpam-3329	490	12	(	(	PUNCT
ejpam-3329	490	13	e(π	e(π	PROPN
ejpam-3329	490	14	√	√	NUM
ejpam-3329	490	15	f0	f0	PROPN
ejpam-3329	490	16	◦	◦	NOUN
ejpam-3329	490	17	t	t	NOUN
ejpam-3329	490	18	)	)	PUNCT
ejpam-3329	490	19	2	2	NUM
ejpam-3329	490	20	)	)	PUNCT
ejpam-3329	490	21	1	1	NUM
ejpam-3329	490	22	4	4	NUM
ejpam-3329	490	23	.	.	PUNCT
ejpam-3329	491	1	also	also	ADV
ejpam-3329	491	2	we	we	PRON
ejpam-3329	491	3	have	have	VERB
ejpam-3329	491	4	ckr	ckr	PROPN
ejpam-3329	491	5	f	f	PROPN
ejpam-3329	491	6	=	=	PUNCT
ejpam-3329	491	7	πk(f	πk(f	PUNCT
ejpam-3329	491	8	◦	◦	NOUN
ejpam-3329	491	9	t	t	NOUN
ejpam-3329	491	10	)	)	PUNCT
ejpam-3329	492	1	k	k	PROPN
ejpam-3329	492	2	c∗kr	c∗kr	PROPN
ejpam-3329	492	3	f	f	NOUN
ejpam-3329	492	4	=	=	PUNCT
ejpam-3329	492	5	fk0e(πkf	fk0e(πkf	NOUN
ejpam-3329	492	6	)	)	PUNCT
ejpam-3329	492	7	◦	◦	NOUN
ejpam-3329	492	8	t−k	t−k	NOUN
ejpam-3329	492	9	c∗kr	c∗kr	NOUN
ejpam-3329	492	10	c	c	AUX
ejpam-3329	492	11	k	k	NOUN
ejpam-3329	492	12	r	r	NOUN
ejpam-3329	492	13	f	f	PROPN
ejpam-3329	492	14	=	=	SYM
ejpam-3329	492	15	fk0e(π2k	fk0e(π2k	PROPN
ejpam-3329	492	16	)	)	PUNCT
ejpam-3329	492	17	◦	◦	NOUN
ejpam-3329	492	18	t−kf	t−kf	NOUN
ejpam-3329	492	19	theorem	theorem	NOUN
ejpam-3329	492	20	30	30	NUM
ejpam-3329	492	21	.	.	PUNCT
ejpam-3329	493	1	let	let	VERB
ejpam-3329	493	2	cr	cr	PROPN
ejpam-3329	493	3	∈	∈	VERB
ejpam-3329	493	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	493	5	)	)	PUNCT
ejpam-3329	493	6	)	)	PUNCT
ejpam-3329	493	7	.	.	PUNCT
ejpam-3329	494	1	then	then	ADV
ejpam-3329	494	2	cr	cr	PROPN
ejpam-3329	494	3	is	be	AUX
ejpam-3329	494	4	of	of	ADP
ejpam-3329	494	5	quasi	quasi	NOUN
ejpam-3329	494	6	n	n	CCONJ
ejpam-3329	494	7	-	-	PUNCT
ejpam-3329	494	8	class	class	NOUN
ejpam-3329	494	9	q	q	NOUN
ejpam-3329	494	10	if	if	SCONJ
ejpam-3329	494	11	and	and	CCONJ
ejpam-3329	494	12	only	only	ADV
ejpam-3329	494	13	if	if	SCONJ
ejpam-3329	494	14	(	(	PUNCT
ejpam-3329	494	15	f	f	X
ejpam-3329	494	16	(	(	PUNCT
ejpam-3329	494	17	2+n	2+n	NUM
ejpam-3329	494	18	)	)	PUNCT
ejpam-3329	494	19	0	0	NUM
ejpam-3329	495	1	e(π22+n	e(π22+n	NOUN
ejpam-3329	495	2	)	)	PUNCT
ejpam-3329	496	1	◦	◦	NOUN
ejpam-3329	496	2	t−(2+n))−	t−(2+n))−	NOUN
ejpam-3329	496	3	(	(	PUNCT
ejpam-3329	496	4	1	1	NUM
ejpam-3329	496	5	+	+	NUM
ejpam-3329	496	6	n)(f	n)(f	NOUN
ejpam-3329	496	7	(	(	PUNCT
ejpam-3329	496	8	2	2	NUM
ejpam-3329	496	9	)	)	PUNCT
ejpam-3329	496	10	0	0	NUM
ejpam-3329	496	11	e(π22	e(π22	NOUN
ejpam-3329	496	12	)	)	PUNCT
ejpam-3329	496	13	◦	◦	NOUN
ejpam-3329	496	14	t−2	t−2	PROPN
ejpam-3329	496	15	)	)	PUNCT
ejpam-3329	496	16	+	+	CCONJ
ejpam-3329	496	17	n(f0e(π2	n(f0e(π2	ADJ
ejpam-3329	496	18	)	)	PUNCT
ejpam-3329	496	19	◦	◦	NOUN
ejpam-3329	496	20	t−1	t−1	PROPN
ejpam-3329	496	21	)	)	PUNCT
ejpam-3329	496	22	≥	≥	NOUN
ejpam-3329	496	23	0	0	NUM
ejpam-3329	497	1	a.e	a.e	PROPN
ejpam-3329	497	2	.	.	PROPN
ejpam-3329	497	3	proof	proof	NOUN
ejpam-3329	497	4	.	.	PUNCT
ejpam-3329	498	1	since	since	SCONJ
ejpam-3329	498	2	cr	cr	PROPN
ejpam-3329	498	3	is	be	AUX
ejpam-3329	498	4	a	a	DET
ejpam-3329	498	5	weighted	weighted	ADJ
ejpam-3329	498	6	composition	composition	NOUN
ejpam-3329	498	7	operator	operator	NOUN
ejpam-3329	498	8	with	with	ADP
ejpam-3329	498	9	weight	weight	NOUN
ejpam-3329	498	10	π	π	PROPN
ejpam-3329	498	11	=	=	SYM
ejpam-3329	498	12	(	(	PUNCT
ejpam-3329	498	13	f0	f0	PROPN
ejpam-3329	498	14	f0	f0	PROPN
ejpam-3329	498	15	◦	◦	PROPN
ejpam-3329	498	16	t	t	NOUN
ejpam-3329	498	17	)	)	PUNCT
ejpam-3329	498	18	r	r	NOUN
ejpam-3329	498	19	2	2	NUM
ejpam-3329	498	20	,	,	PUNCT
ejpam-3329	498	21	it	it	PRON
ejpam-3329	498	22	follows	follow	VERB
ejpam-3329	498	23	from	from	ADP
ejpam-3329	498	24	theorem	theorem	ADJ
ejpam-3329	498	25	26	26	NUM
ejpam-3329	498	26	that	that	SCONJ
ejpam-3329	498	27	cr	cr	PROPN
ejpam-3329	498	28	is	be	AUX
ejpam-3329	498	29	quasi	quasi	ADJ
ejpam-3329	498	30	n	n	CCONJ
ejpam-3329	498	31	-	-	PUNCT
ejpam-3329	498	32	class	class	NOUN
ejpam-3329	498	33	q	q	NOUN
ejpam-3329	498	34	if	if	SCONJ
ejpam-3329	498	35	and	and	CCONJ
ejpam-3329	498	36	only	only	ADV
ejpam-3329	498	37	if	if	SCONJ
ejpam-3329	498	38	(	(	PUNCT
ejpam-3329	498	39	f	f	X
ejpam-3329	498	40	(	(	PUNCT
ejpam-3329	498	41	2+n	2+n	NUM
ejpam-3329	498	42	)	)	PUNCT
ejpam-3329	498	43	0	0	NUM
ejpam-3329	498	44	e(π22+n	e(π22+n	NOUN
ejpam-3329	498	45	)	)	PUNCT
ejpam-3329	498	46	◦	◦	NOUN
ejpam-3329	498	47	t−(2+n	t−(2+n	NOUN
ejpam-3329	498	48	)	)	PUNCT
ejpam-3329	498	49	)	)	PUNCT
ejpam-3329	499	1	−	−	PROPN
ejpam-3329	499	2	(	(	PUNCT
ejpam-3329	499	3	1	1	NUM
ejpam-3329	499	4	+	+	NUM
ejpam-3329	499	5	n)(f	n)(f	NOUN
ejpam-3329	499	6	(	(	PUNCT
ejpam-3329	499	7	2	2	NUM
ejpam-3329	499	8	)	)	PUNCT
ejpam-3329	499	9	0	0	NUM
ejpam-3329	499	10	e(π22	e(π22	NOUN
ejpam-3329	499	11	)	)	PUNCT
ejpam-3329	499	12	◦	◦	NOUN
ejpam-3329	499	13	t−2	t−2	PROPN
ejpam-3329	499	14	)	)	PUNCT
ejpam-3329	499	15	+	+	CCONJ
ejpam-3329	499	16	n(f0e(π2	n(f0e(π2	ADJ
ejpam-3329	499	17	)	)	PUNCT
ejpam-3329	499	18	◦	◦	NOUN
ejpam-3329	499	19	t−1	t−1	PROPN
ejpam-3329	499	20	)	)	PUNCT
ejpam-3329	499	21	≥	≥	NOUN
ejpam-3329	499	22	0	0	NUM
ejpam-3329	500	1	a.e	a.e	PROPN
ejpam-3329	500	2	.	.	PROPN
ejpam-3329	500	3	corollary	corollary	ADJ
ejpam-3329	500	4	14	14	NUM
ejpam-3329	500	5	.	.	PUNCT
ejpam-3329	501	1	if	if	SCONJ
ejpam-3329	501	2	t−1σ	t−1σ	ADP
ejpam-3329	501	3	=	=	PROPN
ejpam-3329	501	4	σ	σ	PROPN
ejpam-3329	501	5	and	and	CCONJ
ejpam-3329	501	6	cr	cr	PROPN
ejpam-3329	501	7	∈	∈	PROPN
ejpam-3329	501	8	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	501	9	)	)	PUNCT
ejpam-3329	501	10	)	)	PUNCT
ejpam-3329	501	11	.	.	PUNCT
ejpam-3329	502	1	then	then	ADV
ejpam-3329	502	2	cr	cr	PROPN
ejpam-3329	502	3	is	be	AUX
ejpam-3329	502	4	of	of	ADP
ejpam-3329	502	5	quasi	quasi	NOUN
ejpam-3329	502	6	n	n	CCONJ
ejpam-3329	502	7	-	-	PUNCT
ejpam-3329	502	8	class	class	NOUN
ejpam-3329	502	9	q	q	NOUN
ejpam-3329	502	10	if	if	SCONJ
ejpam-3329	502	11	and	and	CCONJ
ejpam-3329	502	12	only	only	ADV
ejpam-3329	502	13	if	if	SCONJ
ejpam-3329	502	14	(	(	PUNCT
ejpam-3329	502	15	f	f	X
ejpam-3329	502	16	(	(	PUNCT
ejpam-3329	502	17	2+n	2+n	NUM
ejpam-3329	502	18	)	)	PUNCT
ejpam-3329	502	19	0	0	NUM
ejpam-3329	502	20	(	(	PUNCT
ejpam-3329	502	21	π22+n	π22+n	NOUN
ejpam-3329	502	22	)	)	PUNCT
ejpam-3329	502	23	◦	◦	NOUN
ejpam-3329	502	24	t−(2+n))−	t−(2+n))−	NOUN
ejpam-3329	502	25	(	(	PUNCT
ejpam-3329	502	26	1	1	NUM
ejpam-3329	502	27	+	+	NUM
ejpam-3329	502	28	n)(f	n)(f	NOUN
ejpam-3329	502	29	(	(	PUNCT
ejpam-3329	502	30	2	2	NUM
ejpam-3329	502	31	)	)	PUNCT
ejpam-3329	502	32	0	0	NUM
ejpam-3329	503	1	(	(	PUNCT
ejpam-3329	503	2	π22	π22	NOUN
ejpam-3329	503	3	)	)	PUNCT
ejpam-3329	503	4	◦	◦	NOUN
ejpam-3329	503	5	t−2	t−2	PROPN
ejpam-3329	503	6	)	)	PUNCT
ejpam-3329	504	1	+	+	CCONJ
ejpam-3329	504	2	n(f0(π	n(f0(π	PROPN
ejpam-3329	504	3	2	2	NUM
ejpam-3329	504	4	)	)	PUNCT
ejpam-3329	504	5	◦	◦	NOUN
ejpam-3329	504	6	t−1	t−1	PROPN
ejpam-3329	504	7	)	)	PUNCT
ejpam-3329	504	8	≥	≥	NOUN
ejpam-3329	504	9	0	0	NUM
ejpam-3329	505	1	a.e	a.e	PROPN
ejpam-3329	505	2	.	.	PROPN
ejpam-3329	505	3	theorem	theorem	PROPN
ejpam-3329	505	4	31	31	NUM
ejpam-3329	505	5	.	.	PUNCT
ejpam-3329	506	1	let	let	VERB
ejpam-3329	506	2	cr	cr	PROPN
ejpam-3329	506	3	∈	∈	VERB
ejpam-3329	506	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	506	5	)	)	PUNCT
ejpam-3329	506	6	)	)	PUNCT
ejpam-3329	506	7	.	.	PUNCT
ejpam-3329	507	1	then	then	ADV
ejpam-3329	507	2	c∗r	c∗r	X
ejpam-3329	507	3	is	be	AUX
ejpam-3329	507	4	of	of	ADP
ejpam-3329	507	5	quasi	quasi	NOUN
ejpam-3329	507	6	n	n	CCONJ
ejpam-3329	507	7	-	-	PUNCT
ejpam-3329	507	8	class	class	NOUN
ejpam-3329	507	9	q	q	NOUN
ejpam-3329	507	10	if	if	SCONJ
ejpam-3329	508	1	and	and	CCONJ
ejpam-3329	508	2	only	only	ADV
ejpam-3329	508	3	if	if	SCONJ
ejpam-3329	508	4	π2+n(f	π2+n(f	X
ejpam-3329	508	5	(	(	PUNCT
ejpam-3329	508	6	2+n	2+n	NUM
ejpam-3329	508	7	)	)	PUNCT
ejpam-3329	508	8	0	0	NUM
ejpam-3329	509	1	◦	◦	NOUN
ejpam-3329	509	2	t	t	X
ejpam-3329	509	3	2+n)e(π2+n)−	2+n)e(π2+n)−	NUM
ejpam-3329	509	4	(	(	PUNCT
ejpam-3329	509	5	1	1	NUM
ejpam-3329	509	6	+	+	CCONJ
ejpam-3329	509	7	n)π2(f	n)π2(f	PRON
ejpam-3329	509	8	(	(	PUNCT
ejpam-3329	509	9	2	2	NUM
ejpam-3329	509	10	)	)	PUNCT
ejpam-3329	509	11	0	0	NUM
ejpam-3329	510	1	◦	◦	NOUN
ejpam-3329	510	2	t	t	NOUN
ejpam-3329	510	3	2)e(π2	2)e(π2	AUX
ejpam-3329	510	4	)	)	PUNCT
ejpam-3329	511	1	+	+	CCONJ
ejpam-3329	511	2	nπ(f0	nπ(f0	NOUN
ejpam-3329	511	3	◦	◦	NOUN
ejpam-3329	511	4	t	t	NOUN
ejpam-3329	511	5	)	)	PUNCT
ejpam-3329	511	6	e(π	e(π	PROPN
ejpam-3329	511	7	)	)	PUNCT
ejpam-3329	511	8	≥	≥	NOUN
ejpam-3329	511	9	0	0	NUM
ejpam-3329	512	1	a.e	a.e	PROPN
ejpam-3329	512	2	.	.	PROPN
ejpam-3329	512	3	proof	proof	NOUN
ejpam-3329	512	4	.	.	PUNCT
ejpam-3329	513	1	since	since	SCONJ
ejpam-3329	513	2	c∗r	c∗r	PRON
ejpam-3329	513	3	is	be	AUX
ejpam-3329	513	4	a	a	DET
ejpam-3329	513	5	weighted	weighted	ADJ
ejpam-3329	513	6	composition	composition	NOUN
ejpam-3329	513	7	operator	operator	NOUN
ejpam-3329	513	8	with	with	ADP
ejpam-3329	513	9	weight	weight	NOUN
ejpam-3329	513	10	π	π	PROPN
ejpam-3329	513	11	=	=	SYM
ejpam-3329	513	12	(	(	PUNCT
ejpam-3329	513	13	f0	f0	PROPN
ejpam-3329	513	14	f0	f0	PROPN
ejpam-3329	513	15	◦	◦	PROPN
ejpam-3329	513	16	t	t	NOUN
ejpam-3329	513	17	)	)	PUNCT
ejpam-3329	513	18	r	r	NOUN
ejpam-3329	513	19	2	2	NUM
ejpam-3329	513	20	,	,	PUNCT
ejpam-3329	513	21	it	it	PRON
ejpam-3329	513	22	follows	follow	VERB
ejpam-3329	513	23	from	from	ADP
ejpam-3329	513	24	theorem	theorem	ADJ
ejpam-3329	513	25	27	27	NUM
ejpam-3329	513	26	that	that	SCONJ
ejpam-3329	513	27	c∗r	c∗r	PRON
ejpam-3329	513	28	is	be	AUX
ejpam-3329	513	29	of	of	ADP
ejpam-3329	513	30	quasi	quasi	NOUN
ejpam-3329	513	31	n	n	CCONJ
ejpam-3329	513	32	-	-	PUNCT
ejpam-3329	513	33	class	class	NOUN
ejpam-3329	513	34	q	q	NOUN
ejpam-3329	513	35	if	if	SCONJ
ejpam-3329	513	36	and	and	CCONJ
ejpam-3329	513	37	only	only	ADV
ejpam-3329	513	38	if	if	SCONJ
ejpam-3329	513	39	π2+n(f	π2+n(f	X
ejpam-3329	513	40	(	(	PUNCT
ejpam-3329	513	41	2+n	2+n	NUM
ejpam-3329	513	42	)	)	PUNCT
ejpam-3329	513	43	0	0	NUM
ejpam-3329	514	1	◦	◦	NOUN
ejpam-3329	514	2	t	t	NOUN
ejpam-3329	514	3	2+n)e(π2+n)−	2+n)e(π2+n)−	NUM
ejpam-3329	514	4	(	(	PUNCT
ejpam-3329	514	5	1	1	NUM
ejpam-3329	514	6	+	+	CCONJ
ejpam-3329	514	7	n)π2(f	n)π2(f	PRON
ejpam-3329	514	8	(	(	PUNCT
ejpam-3329	514	9	2	2	NUM
ejpam-3329	514	10	)	)	PUNCT
ejpam-3329	514	11	0	0	NUM
ejpam-3329	515	1	◦	◦	NOUN
ejpam-3329	515	2	t	t	NOUN
ejpam-3329	515	3	2)e(π2	2)e(π2	AUX
ejpam-3329	515	4	)	)	PUNCT
ejpam-3329	516	1	+	+	CCONJ
ejpam-3329	516	2	nπ(f0	nπ(f0	NOUN
ejpam-3329	516	3	◦	◦	NOUN
ejpam-3329	516	4	t	t	NOUN
ejpam-3329	516	5	)	)	PUNCT
ejpam-3329	516	6	e(π	e(π	PROPN
ejpam-3329	516	7	)	)	PUNCT
ejpam-3329	516	8	≥	≥	NOUN
ejpam-3329	516	9	0	0	NUM
ejpam-3329	517	1	a.e	a.e	PROPN
ejpam-3329	517	2	.	.	PROPN
ejpam-3329	517	3	corollary	corollary	NOUN
ejpam-3329	517	4	15	15	NUM
ejpam-3329	517	5	.	.	PUNCT
ejpam-3329	518	1	let	let	VERB
ejpam-3329	518	2	cr	cr	PROPN
ejpam-3329	518	3	∈	∈	PROPN
ejpam-3329	518	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	518	5	)	)	PUNCT
ejpam-3329	518	6	)	)	PUNCT
ejpam-3329	518	7	and	and	CCONJ
ejpam-3329	518	8	t−1σ	t−1σ	X
ejpam-3329	518	9	=	=	PROPN
ejpam-3329	519	1	σ	σ	PROPN
ejpam-3329	519	2	.	.	PUNCT
ejpam-3329	520	1	then	then	ADV
ejpam-3329	520	2	c∗r	c∗r	X
ejpam-3329	520	3	is	be	AUX
ejpam-3329	520	4	of	of	ADP
ejpam-3329	520	5	quasi	quasi	NOUN
ejpam-3329	520	6	n	n	CCONJ
ejpam-3329	520	7	-	-	PUNCT
ejpam-3329	520	8	class	class	NOUN
ejpam-3329	520	9	q	q	NOUN
ejpam-3329	520	10	if	if	SCONJ
ejpam-3329	521	1	and	and	CCONJ
ejpam-3329	521	2	only	only	ADV
ejpam-3329	521	3	if	if	SCONJ
ejpam-3329	521	4	π22+n(f	π22+n(f	X
ejpam-3329	521	5	(	(	PUNCT
ejpam-3329	521	6	2+n	2+n	NUM
ejpam-3329	521	7	)	)	PUNCT
ejpam-3329	521	8	0	0	NUM
ejpam-3329	522	1	◦	◦	NOUN
ejpam-3329	522	2	t	t	NOUN
ejpam-3329	522	3	2+n)−	2+n)−	NUM
ejpam-3329	522	4	(	(	PUNCT
ejpam-3329	522	5	1	1	NUM
ejpam-3329	522	6	+	+	CCONJ
ejpam-3329	522	7	n)π22(f	n)π22(f	PROPN
ejpam-3329	522	8	(	(	PUNCT
ejpam-3329	522	9	2	2	NUM
ejpam-3329	522	10	)	)	PUNCT
ejpam-3329	522	11	0	0	NUM
ejpam-3329	523	1	◦	◦	NOUN
ejpam-3329	523	2	t	t	PROPN
ejpam-3329	523	3	2	2	NUM
ejpam-3329	523	4	)	)	PUNCT
ejpam-3329	523	5	+	+	NUM
ejpam-3329	523	6	nπ2(f0	nπ2(f0	NOUN
ejpam-3329	523	7	◦	◦	NOUN
ejpam-3329	523	8	t	t	PROPN
ejpam-3329	523	9	)	)	PUNCT
ejpam-3329	523	10	≥	≥	PROPN
ejpam-3329	523	11	0	0	NUM
ejpam-3329	523	12	a.e	a.e	PROPN
ejpam-3329	523	13	.	.	PROPN
ejpam-3329	523	14	theorem	theorem	PROPN
ejpam-3329	523	15	32	32	NUM
ejpam-3329	523	16	.	.	PUNCT
ejpam-3329	524	1	let	let	VERB
ejpam-3329	524	2	cr	cr	PROPN
ejpam-3329	524	3	∈	∈	VERB
ejpam-3329	524	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	524	5	)	)	PUNCT
ejpam-3329	524	6	)	)	PUNCT
ejpam-3329	524	7	.	.	PUNCT
ejpam-3329	525	1	then	then	ADV
ejpam-3329	525	2	cr	cr	PROPN
ejpam-3329	525	3	is	be	AUX
ejpam-3329	525	4	of	of	ADP
ejpam-3329	525	5	quasi	quasi	ADJ
ejpam-3329	525	6	n	n	CCONJ
ejpam-3329	525	7	-	-	PUNCT
ejpam-3329	525	8	class	class	NOUN
ejpam-3329	525	9	q∗	q∗	NOUN
ejpam-3329	525	10	if	if	SCONJ
ejpam-3329	526	1	and	and	CCONJ
ejpam-3329	526	2	only	only	ADV
ejpam-3329	526	3	if	if	SCONJ
ejpam-3329	526	4	(	(	PUNCT
ejpam-3329	526	5	f	f	X
ejpam-3329	526	6	(	(	PUNCT
ejpam-3329	526	7	2+n	2+n	NUM
ejpam-3329	526	8	)	)	PUNCT
ejpam-3329	526	9	0	0	NUM
ejpam-3329	526	10	e(π21+n	e(π21+n	PRON
ejpam-3329	526	11	)	)	PUNCT
ejpam-3329	526	12	◦	◦	NOUN
ejpam-3329	526	13	t−(2+n))−	t−(2+n))−	PUNCT
ejpam-3329	526	14	(	(	PUNCT
ejpam-3329	526	15	1	1	NUM
ejpam-3329	526	16	+	+	NUM
ejpam-3329	526	17	n)(f0e(π2	n)(f0e(π2	PROPN
ejpam-3329	526	18	)	)	PUNCT
ejpam-3329	526	19	◦	◦	NOUN
ejpam-3329	526	20	t−1)2	t−1)2	NUM
ejpam-3329	526	21	+	+	CCONJ
ejpam-3329	526	22	n(f0e(π2	n(f0e(π2	ADJ
ejpam-3329	526	23	)	)	PUNCT
ejpam-3329	526	24	◦	◦	NOUN
ejpam-3329	526	25	t−1	t−1	PROPN
ejpam-3329	526	26	)	)	PUNCT
ejpam-3329	526	27	≥	≥	NOUN
ejpam-3329	526	28	0	0	NUM
ejpam-3329	527	1	a.e	a.e	PROPN
ejpam-3329	527	2	.	.	PROPN
ejpam-3329	527	3	proof	proof	NOUN
ejpam-3329	527	4	.	.	PUNCT
ejpam-3329	528	1	since	since	SCONJ
ejpam-3329	528	2	cr	cr	PROPN
ejpam-3329	528	3	is	be	AUX
ejpam-3329	528	4	a	a	DET
ejpam-3329	528	5	weighted	weighted	ADJ
ejpam-3329	528	6	composition	composition	NOUN
ejpam-3329	528	7	operator	operator	NOUN
ejpam-3329	528	8	with	with	ADP
ejpam-3329	528	9	weight	weight	NOUN
ejpam-3329	528	10	π	π	PROPN
ejpam-3329	528	11	=	=	SYM
ejpam-3329	528	12	(	(	PUNCT
ejpam-3329	528	13	f0	f0	PROPN
ejpam-3329	528	14	f0	f0	PROPN
ejpam-3329	528	15	◦	◦	PROPN
ejpam-3329	528	16	t	t	NOUN
ejpam-3329	528	17	)	)	PUNCT
ejpam-3329	528	18	r	r	NOUN
ejpam-3329	528	19	2	2	NUM
ejpam-3329	528	20	,	,	PUNCT
ejpam-3329	528	21	it	it	PRON
ejpam-3329	528	22	follows	follow	VERB
ejpam-3329	528	23	from	from	ADP
ejpam-3329	528	24	theorem	theorem	ADJ
ejpam-3329	528	25	46	46	NUM
ejpam-3329	528	26	that	that	SCONJ
ejpam-3329	528	27	cr	cr	PROPN
ejpam-3329	528	28	is	be	AUX
ejpam-3329	528	29	of	of	ADP
ejpam-3329	528	30	quasi	quasi	ADJ
ejpam-3329	528	31	n	n	CCONJ
ejpam-3329	528	32	-	-	PUNCT
ejpam-3329	528	33	class	class	NOUN
ejpam-3329	528	34	q∗	q∗	NOUN
ejpam-3329	529	1	if	if	SCONJ
ejpam-3329	530	1	and	and	CCONJ
ejpam-3329	530	2	only	only	ADV
ejpam-3329	530	3	if	if	SCONJ
ejpam-3329	530	4	(	(	PUNCT
ejpam-3329	530	5	f	f	X
ejpam-3329	530	6	(	(	PUNCT
ejpam-3329	530	7	2+n	2+n	NUM
ejpam-3329	530	8	)	)	PUNCT
ejpam-3329	530	9	0	0	NUM
ejpam-3329	530	10	e(π21+n	e(π21+n	NUM
ejpam-3329	530	11	)	)	PUNCT
ejpam-3329	530	12	◦	◦	NOUN
ejpam-3329	530	13	t−(2+n))−	t−(2+n))−	PROPN
ejpam-3329	530	14	(	(	PUNCT
ejpam-3329	530	15	1	1	NUM
ejpam-3329	530	16	+	+	NUM
ejpam-3329	530	17	n)(f0e(π2	n)(f0e(π2	PROPN
ejpam-3329	530	18	)	)	PUNCT
ejpam-3329	530	19	◦	◦	NOUN
ejpam-3329	530	20	t−1)2	t−1)2	NUM
ejpam-3329	530	21	+	+	CCONJ
ejpam-3329	530	22	n(f0e(π2	n(f0e(π2	ADJ
ejpam-3329	530	23	)	)	PUNCT
ejpam-3329	530	24	◦	◦	NOUN
ejpam-3329	530	25	t−1	t−1	PROPN
ejpam-3329	530	26	)	)	PUNCT
ejpam-3329	530	27	≥	≥	NOUN
ejpam-3329	530	28	0	0	NUM
ejpam-3329	531	1	a.e	a.e	PROPN
ejpam-3329	531	2	.	.	PROPN
ejpam-3329	531	3	d.	d.	PROPN
ejpam-3329	531	4	senthilkumar	senthilkumar	PROPN
ejpam-3329	531	5	,	,	PUNCT
ejpam-3329	531	6	s.	s.	PROPN
ejpam-3329	531	7	parvatham	parvatham	PROPN
ejpam-3329	531	8	/	/	SYM
ejpam-3329	531	9	eur	eur	PROPN
ejpam-3329	531	10	.	.	PUNCT
ejpam-3329	532	1	j.	j.	PROPN
ejpam-3329	532	2	pure	pure	PROPN
ejpam-3329	532	3	appl	appl	PROPN
ejpam-3329	532	4	.	.	PROPN
ejpam-3329	532	5	math	math	PROPN
ejpam-3329	532	6	,	,	PUNCT
ejpam-3329	532	7	11	11	NUM
ejpam-3329	532	8	(	(	PUNCT
ejpam-3329	532	9	4	4	NUM
ejpam-3329	532	10	)	)	PUNCT
ejpam-3329	532	11	(	(	PUNCT
ejpam-3329	532	12	2018	2018	NUM
ejpam-3329	532	13	)	)	PUNCT
ejpam-3329	532	14	,	,	PUNCT
ejpam-3329	532	15	1108	1108	NUM
ejpam-3329	532	16	-	-	SYM
ejpam-3329	532	17	1129	1129	NUM
ejpam-3329	532	18	1122	1122	NUM
ejpam-3329	532	19	corollary	corollary	NOUN
ejpam-3329	532	20	16	16	NUM
ejpam-3329	532	21	.	.	PUNCT
ejpam-3329	533	1	if	if	SCONJ
ejpam-3329	533	2	t−1σ	t−1σ	ADP
ejpam-3329	533	3	=	=	PROPN
ejpam-3329	533	4	σ	σ	PROPN
ejpam-3329	533	5	and	and	CCONJ
ejpam-3329	533	6	cr	cr	PROPN
ejpam-3329	533	7	∈	∈	PROPN
ejpam-3329	533	8	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	533	9	)	)	PUNCT
ejpam-3329	533	10	)	)	PUNCT
ejpam-3329	533	11	.	.	PUNCT
ejpam-3329	534	1	then	then	ADV
ejpam-3329	534	2	cr	cr	PROPN
ejpam-3329	534	3	is	be	AUX
ejpam-3329	534	4	of	of	ADP
ejpam-3329	534	5	quasi	quasi	ADJ
ejpam-3329	534	6	n	n	CCONJ
ejpam-3329	534	7	-	-	PUNCT
ejpam-3329	534	8	class	class	NOUN
ejpam-3329	534	9	q∗	q∗	NOUN
ejpam-3329	534	10	if	if	SCONJ
ejpam-3329	535	1	and	and	CCONJ
ejpam-3329	535	2	only	only	ADV
ejpam-3329	535	3	if	if	SCONJ
ejpam-3329	535	4	(	(	PUNCT
ejpam-3329	535	5	f	f	X
ejpam-3329	535	6	(	(	PUNCT
ejpam-3329	535	7	2+n	2+n	NUM
ejpam-3329	535	8	)	)	PUNCT
ejpam-3329	535	9	0	0	NUM
ejpam-3329	535	10	(	(	PUNCT
ejpam-3329	535	11	π21+n	π21+n	NOUN
ejpam-3329	535	12	)	)	PUNCT
ejpam-3329	535	13	◦	◦	NOUN
ejpam-3329	535	14	t−(2+n))−	t−(2+n))−	NOUN
ejpam-3329	535	15	(	(	PUNCT
ejpam-3329	535	16	1	1	NUM
ejpam-3329	535	17	+	+	NUM
ejpam-3329	535	18	n)(f0(π	n)(f0(π	NOUN
ejpam-3329	535	19	2	2	NUM
ejpam-3329	535	20	)	)	PUNCT
ejpam-3329	535	21	◦	◦	VERB
ejpam-3329	535	22	t−1)2	t−1)2	NUM
ejpam-3329	535	23	+	+	CCONJ
ejpam-3329	535	24	n(f0(π	n(f0(π	PROPN
ejpam-3329	535	25	2	2	NUM
ejpam-3329	535	26	)	)	PUNCT
ejpam-3329	535	27	◦	◦	NOUN
ejpam-3329	535	28	t−1	t−1	PROPN
ejpam-3329	535	29	)	)	PUNCT
ejpam-3329	535	30	≥	≥	NOUN
ejpam-3329	535	31	0	0	NUM
ejpam-3329	536	1	a.e	a.e	PROPN
ejpam-3329	536	2	.	.	PROPN
ejpam-3329	536	3	theorem	theorem	PROPN
ejpam-3329	536	4	33	33	NUM
ejpam-3329	536	5	.	.	PUNCT
ejpam-3329	537	1	let	let	VERB
ejpam-3329	537	2	cr	cr	PROPN
ejpam-3329	537	3	∈	∈	VERB
ejpam-3329	537	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	537	5	)	)	PUNCT
ejpam-3329	537	6	)	)	PUNCT
ejpam-3329	537	7	.	.	PUNCT
ejpam-3329	538	1	then	then	ADV
ejpam-3329	538	2	c∗r	c∗r	X
ejpam-3329	538	3	is	be	AUX
ejpam-3329	538	4	of	of	ADP
ejpam-3329	538	5	quasi	quasi	ADJ
ejpam-3329	538	6	n	n	CCONJ
ejpam-3329	538	7	-	-	PUNCT
ejpam-3329	538	8	class	class	NOUN
ejpam-3329	538	9	q∗	q∗	NOUN
ejpam-3329	538	10	if	if	SCONJ
ejpam-3329	539	1	and	and	CCONJ
ejpam-3329	539	2	only	only	ADV
ejpam-3329	539	3	if	if	SCONJ
ejpam-3329	539	4	π2+n(f	π2+n(f	X
ejpam-3329	539	5	(	(	PUNCT
ejpam-3329	539	6	2+n	2+n	NUM
ejpam-3329	539	7	)	)	PUNCT
ejpam-3329	539	8	0	0	NUM
ejpam-3329	540	1	◦	◦	NOUN
ejpam-3329	540	2	t	t	X
ejpam-3329	540	3	2+n)e(π2+n)−	2+n)e(π2+n)−	NUM
ejpam-3329	540	4	(	(	PUNCT
ejpam-3329	540	5	1	1	NUM
ejpam-3329	540	6	+	+	NUM
ejpam-3329	540	7	n)(π(f0	n)(π(f0	PROPN
ejpam-3329	540	8	◦	◦	NOUN
ejpam-3329	540	9	t	t	PROPN
ejpam-3329	540	10	)	)	PUNCT
ejpam-3329	541	1	e(π))2	e(π))2	PROPN
ejpam-3329	541	2	+	+	CCONJ
ejpam-3329	541	3	nπ(f0	nπ(f0	NOUN
ejpam-3329	541	4	◦	◦	NOUN
ejpam-3329	541	5	t	t	NOUN
ejpam-3329	541	6	)	)	PUNCT
ejpam-3329	541	7	e(π	e(π	PROPN
ejpam-3329	541	8	)	)	PUNCT
ejpam-3329	541	9	≥	≥	NOUN
ejpam-3329	541	10	0	0	NUM
ejpam-3329	542	1	a.e	a.e	PROPN
ejpam-3329	542	2	.	.	PROPN
ejpam-3329	542	3	corollary	corollary	NOUN
ejpam-3329	542	4	17	17	NUM
ejpam-3329	542	5	.	.	PUNCT
ejpam-3329	543	1	if	if	SCONJ
ejpam-3329	543	2	t−1σ	t−1σ	NOUN
ejpam-3329	543	3	=	=	PROPN
ejpam-3329	543	4	σ	σ	PROPN
ejpam-3329	543	5	and	and	CCONJ
ejpam-3329	543	6	c∗r	c∗r	ADJ
ejpam-3329	543	7	∈	∈	PROPN
ejpam-3329	543	8	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	543	9	)	)	PUNCT
ejpam-3329	543	10	)	)	PUNCT
ejpam-3329	543	11	is	be	AUX
ejpam-3329	543	12	quasi	quasi	ADJ
ejpam-3329	543	13	n	n	CCONJ
ejpam-3329	543	14	-	-	PUNCT
ejpam-3329	543	15	class	class	NOUN
ejpam-3329	543	16	q∗	q∗	NOUN
ejpam-3329	543	17	if	if	SCONJ
ejpam-3329	544	1	and	and	CCONJ
ejpam-3329	544	2	only	only	ADV
ejpam-3329	544	3	if	if	SCONJ
ejpam-3329	544	4	π22+n(f	π22+n(f	X
ejpam-3329	544	5	(	(	PUNCT
ejpam-3329	544	6	2+n	2+n	NUM
ejpam-3329	544	7	)	)	PUNCT
ejpam-3329	544	8	0	0	NUM
ejpam-3329	545	1	◦	◦	NOUN
ejpam-3329	545	2	t	t	NOUN
ejpam-3329	545	3	2+n)−	2+n)−	NUM
ejpam-3329	545	4	(	(	PUNCT
ejpam-3329	545	5	1	1	NUM
ejpam-3329	545	6	+	+	NOUN
ejpam-3329	545	7	n)(π2(f0	n)(π2(f0	NOUN
ejpam-3329	545	8	◦	◦	NOUN
ejpam-3329	545	9	t	t	PROPN
ejpam-3329	545	10	)	)	PUNCT
ejpam-3329	545	11	)	)	PUNCT
ejpam-3329	545	12	2	2	NUM
ejpam-3329	546	1	+	+	NUM
ejpam-3329	546	2	nπ2(f0	nπ2(f0	NOUN
ejpam-3329	546	3	◦	◦	NOUN
ejpam-3329	546	4	t	t	PROPN
ejpam-3329	546	5	)	)	PUNCT
ejpam-3329	546	6	≥	≥	PROPN
ejpam-3329	546	7	0	0	NUM
ejpam-3329	547	1	a.e	a.e	PROPN
ejpam-3329	547	2	.	.	PROPN
ejpam-3329	547	3	b.	b.	PROPN
ejpam-3329	548	1	p	p	PROPN
ejpam-3329	548	2	duggal	duggal	PROPN
ejpam-3329	548	3	[	[	X
ejpam-3329	548	4	6	6	NUM
ejpam-3329	548	5	]	]	PUNCT
ejpam-3329	548	6	described	describe	VERB
ejpam-3329	548	7	the	the	DET
ejpam-3329	548	8	second	second	ADJ
ejpam-3329	548	9	aluthge	aluthge	ADJ
ejpam-3329	548	10	transformation	transformation	NOUN
ejpam-3329	548	11	of	of	ADP
ejpam-3329	548	12	t	t	PROPN
ejpam-3329	548	13	by	by	ADP
ejpam-3329	548	14	t̃	t̃	PROPN
ejpam-3329	548	15	=	=	SYM
ejpam-3329	548	16	|t̂	|t̂	VERB
ejpam-3329	548	17	|	|	ADV
ejpam-3329	548	18	1	1	NUM
ejpam-3329	548	19	2v	2v	NUM
ejpam-3329	548	20	|t̂	|t̂	VERB
ejpam-3329	548	21	|	|	ADV
ejpam-3329	548	22	1	1	NUM
ejpam-3329	548	23	2	2	NUM
ejpam-3329	548	24	,	,	PUNCT
ejpam-3329	548	25	where	where	SCONJ
ejpam-3329	548	26	t̂	t̂	ADP
ejpam-3329	548	27	=	=	SYM
ejpam-3329	548	28	v	v	NOUN
ejpam-3329	548	29	|t̂	|t̂	ADJ
ejpam-3329	548	30	|	|	ADV
ejpam-3329	548	31	is	be	AUX
ejpam-3329	548	32	the	the	DET
ejpam-3329	548	33	polar	polar	ADJ
ejpam-3329	548	34	decomposition	decomposition	NOUN
ejpam-3329	548	35	of	of	ADP
ejpam-3329	548	36	t̂	t̂	PROPN
ejpam-3329	548	37	.	.	PUNCT
ejpam-3329	549	1	now	now	ADV
ejpam-3329	549	2	we	we	PRON
ejpam-3329	549	3	consider	consider	VERB
ejpam-3329	549	4	c̃	c̃	PROPN
ejpam-3329	549	5	=	=	SYM
ejpam-3329	549	6	|cr|	|cr|	PROPN
ejpam-3329	549	7	1	1	NUM
ejpam-3329	549	8	2v	2v	PROPN
ejpam-3329	549	9	|cr|	|cr|	VERB
ejpam-3329	549	10	1	1	NUM
ejpam-3329	549	11	2	2	NUM
ejpam-3329	549	12	,	,	PUNCT
ejpam-3329	549	13	where	where	SCONJ
ejpam-3329	549	14	cr	cr	PROPN
ejpam-3329	549	15	=	=	SYM
ejpam-3329	549	16	v	v	PROPN
ejpam-3329	549	17	|cr|	|cr|	PROPN
ejpam-3329	549	18	is	be	AUX
ejpam-3329	549	19	the	the	DET
ejpam-3329	549	20	polar	polar	ADJ
ejpam-3329	549	21	decomposition	decomposition	NOUN
ejpam-3329	549	22	of	of	ADP
ejpam-3329	549	23	the	the	DET
ejpam-3329	549	24	generalized	generalize	VERB
ejpam-3329	549	25	aluthge	aluthge	ADJ
ejpam-3329	549	26	transformation	transformation	NOUN
ejpam-3329	549	27	cr	cr	PROPN
ejpam-3329	549	28	:	:	PUNCT
ejpam-3329	549	29	0	0	PUNCT
ejpam-3329	550	1	<	<	X
ejpam-3329	550	2	r	r	X
ejpam-3329	550	3	<	<	X
ejpam-3329	550	4	1	1	NUM
ejpam-3329	550	5	.	.	PUNCT
ejpam-3329	551	1	we	we	PRON
ejpam-3329	551	2	have	have	VERB
ejpam-3329	551	3	|cr|f	|cr|f	NOUN
ejpam-3329	551	4	=	=	SYM
ejpam-3329	551	5	√	√	PROPN
ejpam-3329	551	6	jf	jf	INTJ
ejpam-3329	551	7	,	,	PUNCT
ejpam-3329	551	8	where	where	SCONJ
ejpam-3329	551	9	j	j	PROPN
ejpam-3329	551	10	=	=	SYM
ejpam-3329	551	11	f0e(π2	f0e(π2	NOUN
ejpam-3329	551	12	)	)	PUNCT
ejpam-3329	551	13	◦	◦	NOUN
ejpam-3329	551	14	t−1	t−1	PROPN
ejpam-3329	551	15	.	.	PUNCT
ejpam-3329	552	1	c̃	c̃	PROPN
ejpam-3329	552	2	=	=	SYM
ejpam-3329	552	3	|cr|	|cr|	PROPN
ejpam-3329	552	4	1	1	NUM
ejpam-3329	552	5	2v	2v	PROPN
ejpam-3329	552	6	|cr|	|cr|	VERB
ejpam-3329	552	7	1	1	NUM
ejpam-3329	552	8	2	2	NUM
ejpam-3329	552	9	=	=	SYM
ejpam-3329	552	10	√	√	NUM
ejpam-3329	552	11	j	j	NOUN
ejpam-3329	552	12	1	1	NUM
ejpam-3329	552	13	2v	2v	PROPN
ejpam-3329	552	14	(	(	PUNCT
ejpam-3329	552	15	√	√	NUM
ejpam-3329	552	16	j	j	NOUN
ejpam-3329	552	17	1	1	NUM
ejpam-3329	552	18	2	2	NUM
ejpam-3329	552	19	f)|=	f)|=	NUM
ejpam-3329	552	20	√	√	NUM
ejpam-3329	552	21	j	j	NOUN
ejpam-3329	552	22	1	1	NUM
ejpam-3329	552	23	2π	2π	NOUN
ejpam-3329	552	24	(	(	PUNCT
ejpam-3329	552	25	χsupj√	χsupj√	NOUN
ejpam-3329	552	26	j	j	PROPN
ejpam-3329	552	27	j	j	PROPN
ejpam-3329	552	28	1	1	NUM
ejpam-3329	552	29	4	4	NUM
ejpam-3329	552	30	f)	f)	SYM
ejpam-3329	552	31	◦	◦	NOUN
ejpam-3329	552	32	t	t	NOUN
ejpam-3329	552	33	=	=	SYM
ejpam-3329	552	34	j	j	PROPN
ejpam-3329	552	35	1	1	NUM
ejpam-3329	552	36	4π	4π	NUM
ejpam-3329	552	37	(	(	PUNCT
ejpam-3329	552	38	(	(	PUNCT
ejpam-3329	552	39	χsupj	χsupj	INTJ
ejpam-3329	552	40	j	j	PROPN
ejpam-3329	552	41	1	1	NUM
ejpam-3329	552	42	4	4	NUM
ejpam-3329	552	43	)	)	PUNCT
ejpam-3329	552	44	◦	◦	NOUN
ejpam-3329	552	45	t	t	NOUN
ejpam-3329	552	46	)	)	PUNCT
ejpam-3329	552	47	(	(	PUNCT
ejpam-3329	552	48	f	f	PROPN
ejpam-3329	552	49	◦	◦	NOUN
ejpam-3329	552	50	t	t	PROPN
ejpam-3329	552	51	)	)	PUNCT
ejpam-3329	552	52	.	.	PUNCT
ejpam-3329	553	1	we	we	PRON
ejpam-3329	553	2	see	see	VERB
ejpam-3329	553	3	then	then	ADV
ejpam-3329	553	4	that	that	SCONJ
ejpam-3329	553	5	c̃	c̃	PROPN
ejpam-3329	553	6	is	be	AUX
ejpam-3329	553	7	a	a	DET
ejpam-3329	553	8	weighted	weighted	ADJ
ejpam-3329	553	9	composition	composition	NOUN
ejpam-3329	553	10	operator	operator	NOUN
ejpam-3329	553	11	with	with	ADP
ejpam-3329	553	12	weight	weight	NOUN
ejpam-3329	553	13	w′	w′	NOUN
ejpam-3329	554	1	=	=	PUNCT
ejpam-3329	555	1	j	j	PROPN
ejpam-3329	555	2	1	1	NUM
ejpam-3329	555	3	4π	4π	NUM
ejpam-3329	555	4	(	(	PUNCT
ejpam-3329	555	5	(	(	PUNCT
ejpam-3329	555	6	χsupj	χsupj	INTJ
ejpam-3329	555	7	j	j	PROPN
ejpam-3329	555	8	1	1	NUM
ejpam-3329	555	9	4	4	NUM
ejpam-3329	555	10	)	)	PUNCT
ejpam-3329	555	11	◦	◦	NOUN
ejpam-3329	555	12	t	t	NOUN
ejpam-3329	555	13	)	)	PUNCT
ejpam-3329	555	14	.	.	PUNCT
ejpam-3329	556	1	theorem	theorem	VERB
ejpam-3329	556	2	34	34	NUM
ejpam-3329	556	3	.	.	PUNCT
ejpam-3329	557	1	if	if	SCONJ
ejpam-3329	557	2	c̃	c̃	PROPN
ejpam-3329	557	3	is	be	AUX
ejpam-3329	557	4	of	of	ADP
ejpam-3329	557	5	quasi	quasi	NOUN
ejpam-3329	557	6	n	n	CCONJ
ejpam-3329	557	7	-	-	PUNCT
ejpam-3329	557	8	class	class	NOUN
ejpam-3329	557	9	q	q	NOUN
ejpam-3329	557	10	if	if	SCONJ
ejpam-3329	557	11	and	and	CCONJ
ejpam-3329	557	12	only	only	ADV
ejpam-3329	558	1	if	if	SCONJ
ejpam-3329	558	2	f	f	PROPN
ejpam-3329	558	3	(	(	PUNCT
ejpam-3329	558	4	2+n	2+n	NUM
ejpam-3329	558	5	)	)	PUNCT
ejpam-3329	558	6	0	0	NUM
ejpam-3329	558	7	e(w	e(w	PROPN
ejpam-3329	558	8	′2	′2	VERB
ejpam-3329	558	9	2+n	2+n	NUM
ejpam-3329	558	10	)	)	PUNCT
ejpam-3329	558	11	◦	◦	NOUN
ejpam-3329	558	12	t−(2+n	t−(2+n	NOUN
ejpam-3329	558	13	)	)	PUNCT
ejpam-3329	558	14	−	−	PROPN
ejpam-3329	559	1	(	(	PUNCT
ejpam-3329	559	2	1	1	NUM
ejpam-3329	559	3	+	+	NUM
ejpam-3329	559	4	n)(f	n)(f	NOUN
ejpam-3329	559	5	(	(	PUNCT
ejpam-3329	559	6	2	2	NUM
ejpam-3329	559	7	)	)	PUNCT
ejpam-3329	559	8	0	0	NUM
ejpam-3329	560	1	e(w	e(w	PROPN
ejpam-3329	560	2	′2	′2	X
ejpam-3329	560	3	2	2	NUM
ejpam-3329	560	4	)	)	PUNCT
ejpam-3329	560	5	◦	◦	NOUN
ejpam-3329	560	6	t−2	t−2	PROPN
ejpam-3329	560	7	)	)	PUNCT
ejpam-3329	560	8	+	+	CCONJ
ejpam-3329	560	9	n(f0e(w′2	n(f0e(w′2	PROPN
ejpam-3329	560	10	)	)	PUNCT
ejpam-3329	560	11	◦	◦	PROPN
ejpam-3329	560	12	t−1	t−1	PROPN
ejpam-3329	560	13	)	)	PUNCT
ejpam-3329	560	14	≥	≥	NOUN
ejpam-3329	560	15	0	0	NUM
ejpam-3329	561	1	a.e	a.e	PROPN
ejpam-3329	561	2	.	.	PROPN
ejpam-3329	561	3	proof	proof	NOUN
ejpam-3329	561	4	.	.	PUNCT
ejpam-3329	562	1	since	since	SCONJ
ejpam-3329	562	2	c̃	c̃	PROPN
ejpam-3329	562	3	is	be	AUX
ejpam-3329	562	4	a	a	DET
ejpam-3329	562	5	weighted	weighted	ADJ
ejpam-3329	562	6	composition	composition	NOUN
ejpam-3329	562	7	operator	operator	NOUN
ejpam-3329	562	8	with	with	ADP
ejpam-3329	562	9	weight	weight	NOUN
ejpam-3329	562	10	w′	w′	NOUN
ejpam-3329	562	11	=	=	PUNCT
ejpam-3329	562	12	j	j	PROPN
ejpam-3329	562	13	1	1	NUM
ejpam-3329	562	14	4π	4π	NUM
ejpam-3329	562	15	(	(	PUNCT
ejpam-3329	562	16	(	(	PUNCT
ejpam-3329	562	17	χsupj	χsupj	INTJ
ejpam-3329	562	18	j	j	PROPN
ejpam-3329	562	19	1	1	NUM
ejpam-3329	562	20	4	4	NUM
ejpam-3329	562	21	)	)	PUNCT
ejpam-3329	562	22	◦	◦	NOUN
ejpam-3329	562	23	t	t	NOUN
ejpam-3329	562	24	)	)	PUNCT
ejpam-3329	562	25	,	,	PUNCT
ejpam-3329	562	26	then	then	ADV
ejpam-3329	562	27	by	by	ADP
ejpam-3329	562	28	theorem	theorem	NOUN
ejpam-3329	562	29	26	26	NUM
ejpam-3329	562	30	we	we	PRON
ejpam-3329	562	31	obtain	obtain	VERB
ejpam-3329	562	32	the	the	DET
ejpam-3329	562	33	result	result	NOUN
ejpam-3329	562	34	.	.	PUNCT
ejpam-3329	563	1	corollary	corollary	ADJ
ejpam-3329	563	2	18	18	NUM
ejpam-3329	563	3	.	.	PUNCT
ejpam-3329	564	1	if	if	SCONJ
ejpam-3329	564	2	t−1σ	t−1σ	ADP
ejpam-3329	564	3	=	=	PROPN
ejpam-3329	564	4	σ	σ	PROPN
ejpam-3329	564	5	and	and	CCONJ
ejpam-3329	564	6	c̃	c̃	PROPN
ejpam-3329	564	7	∈	∈	PROPN
ejpam-3329	564	8	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	564	9	)	)	PUNCT
ejpam-3329	564	10	)	)	PUNCT
ejpam-3329	564	11	is	be	AUX
ejpam-3329	564	12	of	of	ADP
ejpam-3329	564	13	quasi	quasi	NOUN
ejpam-3329	564	14	n	n	CCONJ
ejpam-3329	564	15	-	-	PUNCT
ejpam-3329	564	16	class	class	NOUN
ejpam-3329	564	17	q	q	NOUN
ejpam-3329	564	18	if	if	SCONJ
ejpam-3329	565	1	and	and	CCONJ
ejpam-3329	565	2	only	only	ADV
ejpam-3329	565	3	if	if	SCONJ
ejpam-3329	565	4	f	f	PROPN
ejpam-3329	565	5	(	(	PUNCT
ejpam-3329	565	6	2+n	2+n	NUM
ejpam-3329	565	7	)	)	PUNCT
ejpam-3329	565	8	0	0	NUM
ejpam-3329	565	9	(	(	PUNCT
ejpam-3329	565	10	w	w	NOUN
ejpam-3329	565	11	′2	′2	PROPN
ejpam-3329	565	12	2+n	2+n	NUM
ejpam-3329	565	13	)	)	PUNCT
ejpam-3329	565	14	◦	◦	NOUN
ejpam-3329	565	15	t−(2+n	t−(2+n	NOUN
ejpam-3329	565	16	)	)	PUNCT
ejpam-3329	565	17	−	−	PROPN
ejpam-3329	566	1	(	(	PUNCT
ejpam-3329	566	2	1	1	NUM
ejpam-3329	566	3	+	+	NUM
ejpam-3329	566	4	n)(f	n)(f	NOUN
ejpam-3329	566	5	(	(	PUNCT
ejpam-3329	566	6	2	2	NUM
ejpam-3329	566	7	)	)	PUNCT
ejpam-3329	566	8	0	0	NUM
ejpam-3329	567	1	(	(	PUNCT
ejpam-3329	567	2	w	w	NOUN
ejpam-3329	567	3	′2	′2	PROPN
ejpam-3329	567	4	2	2	NUM
ejpam-3329	567	5	)	)	PUNCT
ejpam-3329	567	6	◦	◦	NOUN
ejpam-3329	567	7	t−2	t−2	PROPN
ejpam-3329	567	8	)	)	PUNCT
ejpam-3329	568	1	+	+	CCONJ
ejpam-3329	568	2	n(f0(w	n(f0(w	NOUN
ejpam-3329	568	3	′2	′2	NOUN
ejpam-3329	568	4	)	)	PUNCT
ejpam-3329	568	5	◦	◦	NOUN
ejpam-3329	568	6	t−1	t−1	PROPN
ejpam-3329	568	7	)	)	PUNCT
ejpam-3329	568	8	≥	≥	NOUN
ejpam-3329	568	9	0	0	NUM
ejpam-3329	569	1	a.e	a.e	PROPN
ejpam-3329	569	2	.	.	PROPN
ejpam-3329	569	3	theorem	theorem	PROPN
ejpam-3329	569	4	35	35	NUM
ejpam-3329	569	5	.	.	PUNCT
ejpam-3329	570	1	let	let	VERB
ejpam-3329	570	2	c̃	c̃	PROPN
ejpam-3329	570	3	∈	∈	PROPN
ejpam-3329	570	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	570	5	)	)	PUNCT
ejpam-3329	570	6	)	)	PUNCT
ejpam-3329	570	7	.	.	PUNCT
ejpam-3329	571	1	then	then	ADV
ejpam-3329	571	2	c̃∗	c̃∗	PROPN
ejpam-3329	571	3	is	be	AUX
ejpam-3329	571	4	of	of	ADP
ejpam-3329	571	5	quasi	quasi	NOUN
ejpam-3329	571	6	n	n	CCONJ
ejpam-3329	571	7	-	-	PUNCT
ejpam-3329	571	8	class	class	NOUN
ejpam-3329	571	9	q	q	NOUN
ejpam-3329	571	10	if	if	SCONJ
ejpam-3329	572	1	and	and	CCONJ
ejpam-3329	572	2	only	only	ADV
ejpam-3329	572	3	if	if	SCONJ
ejpam-3329	572	4	w′2+n(f	w′2+n(f	PROPN
ejpam-3329	572	5	(	(	PUNCT
ejpam-3329	572	6	2+n	2+n	NUM
ejpam-3329	572	7	)	)	PUNCT
ejpam-3329	572	8	0	0	NUM
ejpam-3329	573	1	◦	◦	NOUN
ejpam-3329	573	2	t	t	PROPN
ejpam-3329	573	3	2+n)e(w′2+n)−	2+n)e(w′2+n)−	PROPN
ejpam-3329	573	4	(	(	PUNCT
ejpam-3329	573	5	1	1	NUM
ejpam-3329	573	6	+	+	CCONJ
ejpam-3329	573	7	n)w′2(f	n)w′2(f	ADJ
ejpam-3329	573	8	(	(	PUNCT
ejpam-3329	573	9	2	2	NUM
ejpam-3329	573	10	)	)	PUNCT
ejpam-3329	573	11	0	0	NUM
ejpam-3329	574	1	◦	◦	NOUN
ejpam-3329	574	2	t	t	NOUN
ejpam-3329	574	3	2)e(w′2	2)e(w′2	NUM
ejpam-3329	574	4	)	)	PUNCT
ejpam-3329	575	1	+	+	CCONJ
ejpam-3329	575	2	nw′(f0	nw′(f0	PROPN
ejpam-3329	575	3	◦	◦	NOUN
ejpam-3329	575	4	t	t	PROPN
ejpam-3329	575	5	)	)	PUNCT
ejpam-3329	575	6	e(w′	e(w′	PROPN
ejpam-3329	575	7	)	)	PUNCT
ejpam-3329	575	8	≥	≥	NOUN
ejpam-3329	575	9	0	0	NUM
ejpam-3329	576	1	a.e	a.e	PROPN
ejpam-3329	576	2	.	.	PROPN
ejpam-3329	576	3	proof	proof	NOUN
ejpam-3329	576	4	.	.	PUNCT
ejpam-3329	577	1	since	since	SCONJ
ejpam-3329	577	2	c̃∗	c̃∗	PROPN
ejpam-3329	577	3	is	be	AUX
ejpam-3329	577	4	a	a	DET
ejpam-3329	577	5	weighted	weighted	ADJ
ejpam-3329	577	6	composition	composition	NOUN
ejpam-3329	577	7	operator	operator	NOUN
ejpam-3329	577	8	with	with	ADP
ejpam-3329	577	9	weight	weight	NOUN
ejpam-3329	577	10	w′	w′	NOUN
ejpam-3329	577	11	=	=	PUNCT
ejpam-3329	577	12	j	j	PROPN
ejpam-3329	577	13	1	1	NUM
ejpam-3329	577	14	4π	4π	NUM
ejpam-3329	577	15	(	(	PUNCT
ejpam-3329	577	16	(	(	PUNCT
ejpam-3329	577	17	χsupj	χsupj	INTJ
ejpam-3329	577	18	j	j	PROPN
ejpam-3329	577	19	1	1	NUM
ejpam-3329	577	20	4	4	NUM
ejpam-3329	577	21	)	)	PUNCT
ejpam-3329	577	22	◦	◦	NOUN
ejpam-3329	577	23	t	t	NOUN
ejpam-3329	577	24	)	)	PUNCT
ejpam-3329	577	25	,	,	PUNCT
ejpam-3329	577	26	then	then	ADV
ejpam-3329	577	27	by	by	ADP
ejpam-3329	577	28	from	from	ADP
ejpam-3329	577	29	theorem	theorem	ADJ
ejpam-3329	577	30	27	27	NUM
ejpam-3329	577	31	we	we	PRON
ejpam-3329	577	32	obtain	obtain	VERB
ejpam-3329	577	33	the	the	DET
ejpam-3329	577	34	result	result	NOUN
ejpam-3329	577	35	.	.	PUNCT
ejpam-3329	578	1	corollary	corollary	ADJ
ejpam-3329	578	2	19	19	NUM
ejpam-3329	578	3	.	.	PUNCT
ejpam-3329	579	1	let	let	VERB
ejpam-3329	579	2	c̃	c̃	PROPN
ejpam-3329	579	3	∈	∈	PROPN
ejpam-3329	579	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	579	5	)	)	PUNCT
ejpam-3329	579	6	)	)	PUNCT
ejpam-3329	579	7	and	and	CCONJ
ejpam-3329	579	8	t−1σ	t−1σ	X
ejpam-3329	579	9	=	=	PROPN
ejpam-3329	580	1	σ	σ	PROPN
ejpam-3329	580	2	.	.	PUNCT
ejpam-3329	581	1	then	then	ADV
ejpam-3329	581	2	c̃∗	c̃∗	PROPN
ejpam-3329	581	3	is	be	AUX
ejpam-3329	581	4	quasi	quasi	ADJ
ejpam-3329	581	5	n	n	CCONJ
ejpam-3329	581	6	-	-	PUNCT
ejpam-3329	581	7	class	class	NOUN
ejpam-3329	581	8	q	q	NOUN
ejpam-3329	581	9	if	if	SCONJ
ejpam-3329	582	1	and	and	CCONJ
ejpam-3329	582	2	only	only	ADV
ejpam-3329	582	3	if	if	SCONJ
ejpam-3329	582	4	w	w	PROPN
ejpam-3329	582	5	′2	′2	PROPN
ejpam-3329	582	6	2+n(f	2+n(f	PUNCT
ejpam-3329	582	7	(	(	PUNCT
ejpam-3329	582	8	2+n	2+n	NUM
ejpam-3329	582	9	)	)	PUNCT
ejpam-3329	582	10	0	0	NUM
ejpam-3329	583	1	◦	◦	NOUN
ejpam-3329	583	2	t	t	NOUN
ejpam-3329	583	3	2+n)−	2+n)−	NUM
ejpam-3329	583	4	(	(	PUNCT
ejpam-3329	583	5	1	1	NUM
ejpam-3329	583	6	+	+	CCONJ
ejpam-3329	583	7	n)w	n)w	X
ejpam-3329	583	8	′2	′2	X
ejpam-3329	583	9	2	2	NUM
ejpam-3329	583	10	(	(	PUNCT
ejpam-3329	583	11	f	f	X
ejpam-3329	583	12	(	(	PUNCT
ejpam-3329	583	13	2	2	NUM
ejpam-3329	583	14	)	)	PUNCT
ejpam-3329	583	15	0	0	NUM
ejpam-3329	584	1	◦	◦	NOUN
ejpam-3329	584	2	t	t	PROPN
ejpam-3329	584	3	2	2	NUM
ejpam-3329	584	4	)	)	PUNCT
ejpam-3329	585	1	+	+	CCONJ
ejpam-3329	585	2	nw	nw	PRON
ejpam-3329	585	3	′2(f0	′2(f0	NOUN
ejpam-3329	585	4	◦	◦	PROPN
ejpam-3329	585	5	t	t	PROPN
ejpam-3329	585	6	)	)	PUNCT
ejpam-3329	585	7	≥	≥	PROPN
ejpam-3329	585	8	0	0	NUM
ejpam-3329	586	1	a.e	a.e	PROPN
ejpam-3329	586	2	.	.	PROPN
ejpam-3329	586	3	theorem	theorem	VERB
ejpam-3329	586	4	36	36	NUM
ejpam-3329	586	5	.	.	PUNCT
ejpam-3329	587	1	if	if	SCONJ
ejpam-3329	587	2	c̃	c̃	PROPN
ejpam-3329	587	3	is	be	AUX
ejpam-3329	587	4	quasi	quasi	ADJ
ejpam-3329	587	5	n	n	CCONJ
ejpam-3329	587	6	-	-	PUNCT
ejpam-3329	587	7	class	class	NOUN
ejpam-3329	587	8	q∗	q∗	NOUN
ejpam-3329	587	9	if	if	SCONJ
ejpam-3329	587	10	and	and	CCONJ
ejpam-3329	587	11	only	only	ADV
ejpam-3329	587	12	if	if	SCONJ
ejpam-3329	587	13	f	f	PROPN
ejpam-3329	587	14	(	(	PUNCT
ejpam-3329	587	15	2+n	2+n	NUM
ejpam-3329	587	16	)	)	PUNCT
ejpam-3329	587	17	0	0	NUM
ejpam-3329	588	1	e(w	e(w	PROPN
ejpam-3329	588	2	′2	′2	VERB
ejpam-3329	588	3	2+n	2+n	NUM
ejpam-3329	588	4	)	)	PUNCT
ejpam-3329	588	5	◦	◦	NOUN
ejpam-3329	588	6	t−(2+n	t−(2+n	NOUN
ejpam-3329	588	7	)	)	PUNCT
ejpam-3329	588	8	−	−	PROPN
ejpam-3329	589	1	(	(	PUNCT
ejpam-3329	589	2	1	1	NUM
ejpam-3329	589	3	+	+	CCONJ
ejpam-3329	589	4	n)(f0e(w	n)(f0e(w	ADJ
ejpam-3329	589	5	′2	′2	NOUN
ejpam-3329	589	6	)	)	PUNCT
ejpam-3329	589	7	◦	◦	NOUN
ejpam-3329	589	8	t−1)2	t−1)2	NUM
ejpam-3329	589	9	+	+	CCONJ
ejpam-3329	589	10	n(f0e(w	n(f0e(w	ADJ
ejpam-3329	589	11	′2	′2	NOUN
ejpam-3329	589	12	)	)	PUNCT
ejpam-3329	589	13	◦	◦	NOUN
ejpam-3329	589	14	t−1	t−1	PROPN
ejpam-3329	589	15	)	)	PUNCT
ejpam-3329	589	16	≥	≥	NOUN
ejpam-3329	589	17	0	0	NUM
ejpam-3329	590	1	a.e	a.e	PROPN
ejpam-3329	590	2	.	.	PROPN
ejpam-3329	590	3	corollary	corollary	NOUN
ejpam-3329	590	4	20	20	NUM
ejpam-3329	590	5	.	.	PUNCT
ejpam-3329	591	1	if	if	SCONJ
ejpam-3329	591	2	t−1σ	t−1σ	NOUN
ejpam-3329	591	3	=	=	PROPN
ejpam-3329	591	4	σ	σ	PROPN
ejpam-3329	591	5	and	and	CCONJ
ejpam-3329	591	6	c̃	c̃	PROPN
ejpam-3329	591	7	∈	∈	PROPN
ejpam-3329	591	8	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	591	9	)	)	PUNCT
ejpam-3329	591	10	)	)	PUNCT
ejpam-3329	591	11	is	be	AUX
ejpam-3329	591	12	of	of	ADP
ejpam-3329	591	13	n	n	CCONJ
ejpam-3329	591	14	-	-	PUNCT
ejpam-3329	591	15	class	class	NOUN
ejpam-3329	591	16	q∗	q∗	NOUN
ejpam-3329	591	17	if	if	SCONJ
ejpam-3329	592	1	and	and	CCONJ
ejpam-3329	592	2	only	only	ADV
ejpam-3329	592	3	if	if	SCONJ
ejpam-3329	592	4	f	f	PROPN
ejpam-3329	592	5	(	(	PUNCT
ejpam-3329	592	6	2+n	2+n	NUM
ejpam-3329	592	7	)	)	PUNCT
ejpam-3329	592	8	0	0	NUM
ejpam-3329	592	9	(	(	PUNCT
ejpam-3329	592	10	w	w	NOUN
ejpam-3329	592	11	′2	′2	NOUN
ejpam-3329	592	12	2+n	2+n	NUM
ejpam-3329	592	13	)	)	PUNCT
ejpam-3329	592	14	◦	◦	NOUN
ejpam-3329	592	15	t−(2+n	t−(2+n	NOUN
ejpam-3329	592	16	)	)	PUNCT
ejpam-3329	592	17	−	−	PROPN
ejpam-3329	593	1	(	(	PUNCT
ejpam-3329	593	2	1	1	NUM
ejpam-3329	593	3	+	+	CCONJ
ejpam-3329	593	4	n)(f0(w	n)(f0(w	ADJ
ejpam-3329	593	5	′2	′2	NOUN
ejpam-3329	593	6	)	)	PUNCT
ejpam-3329	593	7	◦	◦	NOUN
ejpam-3329	593	8	t−1)2	t−1)2	NUM
ejpam-3329	593	9	+	+	CCONJ
ejpam-3329	593	10	n(f0(w	n(f0(w	NOUN
ejpam-3329	593	11	′2	′2	NOUN
ejpam-3329	593	12	)	)	PUNCT
ejpam-3329	593	13	◦	◦	NOUN
ejpam-3329	593	14	t−1	t−1	PROPN
ejpam-3329	593	15	)	)	PUNCT
ejpam-3329	593	16	≥	≥	NOUN
ejpam-3329	593	17	0	0	NUM
ejpam-3329	594	1	a.e	a.e	PROPN
ejpam-3329	594	2	.	.	PROPN
ejpam-3329	594	3	theorem	theorem	VERB
ejpam-3329	594	4	37	37	NUM
ejpam-3329	594	5	.	.	PUNCT
ejpam-3329	595	1	let	let	VERB
ejpam-3329	595	2	c̃	c̃	PROPN
ejpam-3329	595	3	∈	∈	PROPN
ejpam-3329	595	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	595	5	)	)	PUNCT
ejpam-3329	595	6	)	)	PUNCT
ejpam-3329	595	7	.	.	PUNCT
ejpam-3329	596	1	then	then	ADV
ejpam-3329	596	2	c̃∗	c̃∗	PROPN
ejpam-3329	596	3	is	be	AUX
ejpam-3329	596	4	of	of	ADP
ejpam-3329	596	5	quasi	quasi	ADJ
ejpam-3329	596	6	n	n	CCONJ
ejpam-3329	596	7	-	-	PUNCT
ejpam-3329	596	8	class	class	NOUN
ejpam-3329	596	9	q∗	q∗	NOUN
ejpam-3329	596	10	if	if	SCONJ
ejpam-3329	597	1	and	and	CCONJ
ejpam-3329	597	2	only	only	ADV
ejpam-3329	597	3	if	if	SCONJ
ejpam-3329	597	4	w′2+n(f	w′2+n(f	PROPN
ejpam-3329	597	5	(	(	PUNCT
ejpam-3329	597	6	2+n	2+n	NUM
ejpam-3329	597	7	)	)	PUNCT
ejpam-3329	597	8	0	0	NUM
ejpam-3329	598	1	◦	◦	NOUN
ejpam-3329	598	2	t	t	PROPN
ejpam-3329	598	3	2+n)e(w′2+n)−	2+n)e(w′2+n)−	PROPN
ejpam-3329	598	4	(	(	PUNCT
ejpam-3329	598	5	1	1	NUM
ejpam-3329	598	6	+	+	NUM
ejpam-3329	598	7	n)(w′(f0	n)(w′(f0	ADV
ejpam-3329	598	8	◦	◦	NOUN
ejpam-3329	598	9	t	t	NOUN
ejpam-3329	598	10	)	)	PUNCT
ejpam-3329	598	11	e(w′))2	e(w′))2	NOUN
ejpam-3329	599	1	+	+	CCONJ
ejpam-3329	599	2	n(w′(f0	n(w′(f0	NOUN
ejpam-3329	599	3	◦	◦	NOUN
ejpam-3329	599	4	t	t	NOUN
ejpam-3329	599	5	)	)	PUNCT
ejpam-3329	599	6	e(w′	e(w′	PROPN
ejpam-3329	599	7	)	)	PUNCT
ejpam-3329	599	8	)	)	PUNCT
ejpam-3329	600	1	≥	≥	NOUN
ejpam-3329	600	2	0	0	NUM
ejpam-3329	601	1	a.e	a.e	PROPN
ejpam-3329	601	2	.	.	PROPN
ejpam-3329	601	3	corollary	corollary	NOUN
ejpam-3329	601	4	21	21	NUM
ejpam-3329	601	5	.	.	PUNCT
ejpam-3329	602	1	let	let	VERB
ejpam-3329	602	2	c̃	c̃	PROPN
ejpam-3329	602	3	∈	∈	PROPN
ejpam-3329	602	4	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	602	5	)	)	PUNCT
ejpam-3329	602	6	)	)	PUNCT
ejpam-3329	602	7	and	and	CCONJ
ejpam-3329	602	8	t−1σ	t−1σ	X
ejpam-3329	602	9	=	=	PROPN
ejpam-3329	603	1	σ	σ	PROPN
ejpam-3329	603	2	.	.	PUNCT
ejpam-3329	604	1	then	then	ADV
ejpam-3329	604	2	c̃∗	c̃∗	PROPN
ejpam-3329	604	3	is	be	AUX
ejpam-3329	604	4	of	of	ADP
ejpam-3329	604	5	n	n	CCONJ
ejpam-3329	604	6	-	-	PUNCT
ejpam-3329	604	7	class	class	NOUN
ejpam-3329	604	8	q∗	q∗	NOUN
ejpam-3329	605	1	if	if	SCONJ
ejpam-3329	606	1	and	and	CCONJ
ejpam-3329	606	2	only	only	ADV
ejpam-3329	606	3	if	if	SCONJ
ejpam-3329	606	4	w	w	PROPN
ejpam-3329	606	5	′2	′2	PROPN
ejpam-3329	606	6	2+n(f	2+n(f	PUNCT
ejpam-3329	606	7	(	(	PUNCT
ejpam-3329	606	8	2+n	2+n	NUM
ejpam-3329	606	9	)	)	PUNCT
ejpam-3329	606	10	0	0	NUM
ejpam-3329	607	1	◦	◦	NOUN
ejpam-3329	607	2	t	t	NOUN
ejpam-3329	607	3	2+n)−	2+n)−	NUM
ejpam-3329	607	4	(	(	PUNCT
ejpam-3329	607	5	1	1	NUM
ejpam-3329	607	6	+	+	CCONJ
ejpam-3329	607	7	n)(w	n)(w	PROPN
ejpam-3329	607	8	′2(f0	′2(f0	NUM
ejpam-3329	607	9	◦	◦	NOUN
ejpam-3329	607	10	t	t	PROPN
ejpam-3329	607	11	)	)	PUNCT
ejpam-3329	607	12	)	)	PUNCT
ejpam-3329	607	13	2	2	NUM
ejpam-3329	608	1	+	+	NUM
ejpam-3329	608	2	n(w	n(w	ADJ
ejpam-3329	608	3	′2(f0	′2(f0	NOUN
ejpam-3329	608	4	◦	◦	PROPN
ejpam-3329	608	5	t	t	PROPN
ejpam-3329	608	6	)	)	PUNCT
ejpam-3329	608	7	)	)	PUNCT
ejpam-3329	609	1	≥	≥	NOUN
ejpam-3329	609	2	0	0	NUM
ejpam-3329	610	1	a.e	a.e	PROPN
ejpam-3329	610	2	.	.	PROPN
ejpam-3329	610	3	d.	d.	PROPN
ejpam-3329	610	4	senthilkumar	senthilkumar	PROPN
ejpam-3329	610	5	,	,	PUNCT
ejpam-3329	610	6	s.	s.	PROPN
ejpam-3329	610	7	parvatham	parvatham	PROPN
ejpam-3329	610	8	/	/	SYM
ejpam-3329	610	9	eur	eur	PROPN
ejpam-3329	610	10	.	.	PUNCT
ejpam-3329	611	1	j.	j.	PROPN
ejpam-3329	611	2	pure	pure	PROPN
ejpam-3329	611	3	appl	appl	PROPN
ejpam-3329	611	4	.	.	PROPN
ejpam-3329	611	5	math	math	PROPN
ejpam-3329	611	6	,	,	PUNCT
ejpam-3329	611	7	11	11	NUM
ejpam-3329	611	8	(	(	PUNCT
ejpam-3329	611	9	4	4	NUM
ejpam-3329	611	10	)	)	PUNCT
ejpam-3329	611	11	(	(	PUNCT
ejpam-3329	611	12	2018	2018	NUM
ejpam-3329	611	13	)	)	PUNCT
ejpam-3329	611	14	,	,	PUNCT
ejpam-3329	611	15	1108	1108	NUM
ejpam-3329	611	16	-	-	SYM
ejpam-3329	611	17	1129	1129	NUM
ejpam-3329	611	18	1123	1123	NUM
ejpam-3329	611	19	6	6	NUM
ejpam-3329	611	20	.	.	PUNCT
ejpam-3329	612	1	quasi	quasi	PROPN
ejpam-3329	612	2	n	n	CCONJ
ejpam-3329	612	3	-	-	PUNCT
ejpam-3329	612	4	class	class	NOUN
ejpam-3329	612	5	q	q	NOUN
ejpam-3329	612	6	and	and	CCONJ
ejpam-3329	612	7	quasi	quasi	ADJ
ejpam-3329	612	8	n	n	CCONJ
ejpam-3329	612	9	-	-	PUNCT
ejpam-3329	612	10	class	class	NOUN
ejpam-3329	612	11	q∗	q∗	NOUN
ejpam-3329	612	12	weighted	weight	VERB
ejpam-3329	612	13	composition	composition	NOUN
ejpam-3329	612	14	operators	operator	NOUN
ejpam-3329	612	15	on	on	ADP
ejpam-3329	612	16	weighted	weight	VERB
ejpam-3329	612	17	hardy	hardy	ADJ
ejpam-3329	612	18	space	space	NOUN
ejpam-3329	612	19	the	the	DET
ejpam-3329	612	20	set	set	NOUN
ejpam-3329	612	21	h2(β	h2(β	PRON
ejpam-3329	612	22	)	)	PUNCT
ejpam-3329	612	23	of	of	ADP
ejpam-3329	612	24	formal	formal	ADJ
ejpam-3329	612	25	complex	complex	ADJ
ejpam-3329	612	26	power	power	NOUN
ejpam-3329	612	27	series	series	NOUN
ejpam-3329	612	28	f(z	f(z	PROPN
ejpam-3329	612	29	)	)	PUNCT
ejpam-3329	612	30	=	=	PUNCT
ejpam-3329	612	31	∑∞	∑∞	X
ejpam-3329	612	32	m=0	m=0	PROPN
ejpam-3329	612	33	amz	amz	PROPN
ejpam-3329	612	34	m	m	VERB
ejpam-3329	612	35	such	such	ADJ
ejpam-3329	612	36	that	that	SCONJ
ejpam-3329	612	37	‖f‖2β	‖f‖2β	PROPN
ejpam-3329	612	38	=	=	NOUN
ejpam-3329	612	39	∑∞	∑∞	NOUN
ejpam-3329	612	40	m=0|am|2β2	m=0|am|2β2	VERB
ejpam-3329	612	41	m	m	NOUN
ejpam-3329	612	42	<	<	X
ejpam-3329	612	43	∞	∞	PROPN
ejpam-3329	612	44	is	be	AUX
ejpam-3329	612	45	a	a	DET
ejpam-3329	612	46	hilbert	hilbert	NOUN
ejpam-3329	612	47	space	space	NOUN
ejpam-3329	612	48	of	of	ADP
ejpam-3329	612	49	functions	function	NOUN
ejpam-3329	612	50	analytic	analytic	ADJ
ejpam-3329	612	51	in	in	ADP
ejpam-3329	612	52	the	the	DET
ejpam-3329	612	53	unit	unit	NOUN
ejpam-3329	612	54	disc	disc	VERB
ejpam-3329	612	55	with	with	ADP
ejpam-3329	612	56	the	the	DET
ejpam-3329	612	57	inner	inner	ADJ
ejpam-3329	612	58	product	product	NOUN
ejpam-3329	612	59	.	.	PUNCT
ejpam-3329	613	1	〈	〈	PROPN
ejpam-3329	613	2	f	f	PROPN
ejpam-3329	613	3	,	,	PUNCT
ejpam-3329	613	4	g〉β	g〉β	NOUN
ejpam-3329	613	5	=	=	PUNCT
ejpam-3329	613	6	∑∞	∑∞	X
ejpam-3329	613	7	m=0	m=0	PUNCT
ejpam-3329	613	8	ambmβ	ambmβ	VERB
ejpam-3329	613	9	2	2	NUM
ejpam-3329	613	10	m	m	NOUN
ejpam-3329	613	11	for	for	ADP
ejpam-3329	613	12	an	an	DET
ejpam-3329	613	13	analytic	analytic	ADJ
ejpam-3329	613	14	map	map	NOUN
ejpam-3329	613	15	f	f	PROPN
ejpam-3329	613	16	on	on	ADP
ejpam-3329	613	17	the	the	DET
ejpam-3329	613	18	open	open	ADJ
ejpam-3329	613	19	unit	unit	NOUN
ejpam-3329	613	20	disc	disc	NOUN
ejpam-3329	613	21	d	d	PROPN
ejpam-3329	613	22	and	and	CCONJ
ejpam-3329	613	23	g(z	g(z	ADJ
ejpam-3329	613	24	)	)	PUNCT
ejpam-3329	614	1	=	=	NOUN
ejpam-3329	614	2	∑∞	∑∞	NOUN
ejpam-3329	614	3	m=0	m=0	PROPN
ejpam-3329	614	4	bmz	bmz	NOUN
ejpam-3329	614	5	m.	m.	NOUN
ejpam-3329	614	6	let	let	VERB
ejpam-3329	614	7	φ	φ	NOUN
ejpam-3329	614	8	:	:	PUNCT
ejpam-3329	615	1	d	d	X
ejpam-3329	615	2	→	→	PUNCT
ejpam-3329	615	3	d	d	X
ejpam-3329	615	4	be	be	AUX
ejpam-3329	615	5	an	an	DET
ejpam-3329	615	6	analytic	analytic	ADJ
ejpam-3329	615	7	self	self	NOUN
ejpam-3329	615	8	map	map	NOUN
ejpam-3329	615	9	of	of	ADP
ejpam-3329	615	10	the	the	DET
ejpam-3329	615	11	unit	unit	NOUN
ejpam-3329	615	12	disc	disc	NOUN
ejpam-3329	615	13	and	and	CCONJ
ejpam-3329	615	14	consider	consider	VERB
ejpam-3329	615	15	the	the	DET
ejpam-3329	615	16	corresponding	corresponding	ADJ
ejpam-3329	615	17	composition	composition	NOUN
ejpam-3329	615	18	operator	operator	NOUN
ejpam-3329	615	19	cφ	cφ	NOUN
ejpam-3329	615	20	acting	act	VERB
ejpam-3329	615	21	on	on	ADP
ejpam-3329	615	22	h2(β	h2(β	PROPN
ejpam-3329	615	23	)	)	PUNCT
ejpam-3329	615	24	.	.	PUNCT
ejpam-3329	616	1	that	that	PRON
ejpam-3329	616	2	is	be	AUX
ejpam-3329	616	3	cφ(f	cφ(f	PUNCT
ejpam-3329	616	4	)	)	PUNCT
ejpam-3329	617	1	=	=	SYM
ejpam-3329	617	2	f	f	PROPN
ejpam-3329	617	3	◦	◦	NOUN
ejpam-3329	617	4	φ	φ	PROPN
ejpam-3329	617	5	for	for	ADP
ejpam-3329	617	6	f	f	PROPN
ejpam-3329	617	7	∈	∈	PROPN
ejpam-3329	617	8	h2(β	h2(β	PROPN
ejpam-3329	617	9	)	)	PUNCT
ejpam-3329	617	10	.	.	PUNCT
ejpam-3329	618	1	the	the	DET
ejpam-3329	618	2	operators	operator	NOUN
ejpam-3329	618	3	cφ	cφ	NOUN
ejpam-3329	618	4	are	be	AUX
ejpam-3329	618	5	not	not	PART
ejpam-3329	618	6	necessarily	necessarily	ADV
ejpam-3329	618	7	defined	define	VERB
ejpam-3329	618	8	on	on	ADP
ejpam-3329	618	9	all	all	PRON
ejpam-3329	618	10	of	of	ADP
ejpam-3329	618	11	h2(β	h2(β	PROPN
ejpam-3329	618	12	)	)	PUNCT
ejpam-3329	618	13	.	.	PUNCT
ejpam-3329	619	1	they	they	PRON
ejpam-3329	619	2	are	be	AUX
ejpam-3329	619	3	everywhere	everywhere	ADV
ejpam-3329	619	4	defined	define	VERB
ejpam-3329	619	5	in	in	ADP
ejpam-3329	619	6	some	some	DET
ejpam-3329	619	7	special	special	ADJ
ejpam-3329	619	8	cases	case	NOUN
ejpam-3329	619	9	on	on	ADP
ejpam-3329	619	10	the	the	DET
ejpam-3329	619	11	classical	classical	ADJ
ejpam-3329	619	12	hardy	hardy	ADJ
ejpam-3329	619	13	space	space	NOUN
ejpam-3329	619	14	h2	h2	NOUN
ejpam-3329	619	15	(	(	PUNCT
ejpam-3329	619	16	the	the	DET
ejpam-3329	619	17	case	case	NOUN
ejpam-3329	619	18	when	when	SCONJ
ejpam-3329	619	19	βn	βn	VERB
ejpam-3329	619	20	=	=	SYM
ejpam-3329	619	21	1	1	NUM
ejpam-3329	619	22	for	for	ADP
ejpam-3329	619	23	all	all	DET
ejpam-3329	619	24	n	n	CCONJ
ejpam-3329	619	25	)	)	PUNCT
ejpam-3329	619	26	and	and	CCONJ
ejpam-3329	619	27	on	on	ADP
ejpam-3329	619	28	a	a	DET
ejpam-3329	619	29	general	general	ADJ
ejpam-3329	619	30	space	space	NOUN
ejpam-3329	619	31	h2(β	h2(β	PROPN
ejpam-3329	619	32	)	)	PUNCT
ejpam-3329	619	33	if	if	SCONJ
ejpam-3329	619	34	the	the	DET
ejpam-3329	619	35	function	function	NOUN
ejpam-3329	619	36	φ	φ	PROPN
ejpam-3329	619	37	is	be	AUX
ejpam-3329	619	38	analytic	analytic	ADJ
ejpam-3329	619	39	on	on	ADP
ejpam-3329	619	40	some	some	DET
ejpam-3329	619	41	open	open	ADJ
ejpam-3329	619	42	set	set	NOUN
ejpam-3329	619	43	containing	contain	VERB
ejpam-3329	619	44	the	the	DET
ejpam-3329	619	45	closed	closed	ADJ
ejpam-3329	619	46	unit	unit	NOUN
ejpam-3329	619	47	disc	disc	NOUN
ejpam-3329	619	48	having	have	VERB
ejpam-3329	619	49	supremum	supremum	ADJ
ejpam-3329	619	50	norm	norm	NOUN
ejpam-3329	619	51	strictly	strictly	ADV
ejpam-3329	619	52	smaller	small	ADJ
ejpam-3329	619	53	than	than	ADP
ejpam-3329	619	54	one	one	NUM
ejpam-3329	619	55	.	.	PUNCT
ejpam-3329	620	1	the	the	DET
ejpam-3329	620	2	weighted	weight	VERB
ejpam-3329	620	3	composition	composition	NOUN
ejpam-3329	620	4	operator	operator	NOUN
ejpam-3329	620	5	wφ	wφ	NOUN
ejpam-3329	620	6	is	be	AUX
ejpam-3329	620	7	defined	define	VERB
ejpam-3329	620	8	as	as	ADP
ejpam-3329	620	9	(	(	PUNCT
ejpam-3329	620	10	wφf)(z	wφf)(z	X
ejpam-3329	620	11	)	)	PUNCT
ejpam-3329	620	12	=	=	SYM
ejpam-3329	620	13	πf(φ(z	πf(φ(z	PUNCT
ejpam-3329	620	14	)	)	PUNCT
ejpam-3329	620	15	)	)	PUNCT
ejpam-3329	621	1	and	and	CCONJ
ejpam-3329	621	2	(	(	PUNCT
ejpam-3329	621	3	w	w	NOUN
ejpam-3329	621	4	∗φf)(z	∗φf)(z	NUM
ejpam-3329	621	5	)	)	PUNCT
ejpam-3329	621	6	=	=	SYM
ejpam-3329	621	7	π̄f(φ(z	π̄f(φ(z	NOUN
ejpam-3329	621	8	)	)	PUNCT
ejpam-3329	621	9	)	)	PUNCT
ejpam-3329	622	1	for	for	ADP
ejpam-3329	622	2	every	every	DET
ejpam-3329	622	3	z	z	NOUN
ejpam-3329	622	4	∈	∈	PROPN
ejpam-3329	622	5	d	d	NOUN
ejpam-3329	622	6	let	let	VERB
ejpam-3329	622	7	w	w	NOUN
ejpam-3329	622	8	be	be	AUX
ejpam-3329	622	9	a	a	DET
ejpam-3329	622	10	point	point	NOUN
ejpam-3329	622	11	on	on	ADP
ejpam-3329	622	12	the	the	DET
ejpam-3329	622	13	open	open	ADJ
ejpam-3329	622	14	disc	disc	NOUN
ejpam-3329	622	15	.	.	PUNCT
ejpam-3329	623	1	define	define	VERB
ejpam-3329	623	2	kβw(z	kβw(z	NOUN
ejpam-3329	623	3	)	)	PUNCT
ejpam-3329	623	4	=	=	PUNCT
ejpam-3329	623	5	∑∞	∑∞	X
ejpam-3329	623	6	m=0	m=0	PROPN
ejpam-3329	623	7	zmw−m	zmw−m	PROPN
ejpam-3329	623	8	β2	β2	VERB
ejpam-3329	623	9	m	m	PROPN
ejpam-3329	623	10	.	.	PUNCT
ejpam-3329	624	1	then	then	ADV
ejpam-3329	624	2	the	the	DET
ejpam-3329	624	3	function	function	NOUN
ejpam-3329	624	4	kβw	kβw	PROPN
ejpam-3329	624	5	is	be	AUX
ejpam-3329	624	6	a	a	DET
ejpam-3329	624	7	point	point	NOUN
ejpam-3329	624	8	evaluation	evaluation	NOUN
ejpam-3329	624	9	for	for	ADP
ejpam-3329	624	10	h2(β).then	h2(β).then	ADJ
ejpam-3329	624	11	kβw	kβw	PROPN
ejpam-3329	624	12	is	be	AUX
ejpam-3329	624	13	in	in	ADP
ejpam-3329	624	14	h2(β	h2(β	PRON
ejpam-3329	624	15	)	)	PUNCT
ejpam-3329	624	16	and	and	CCONJ
ejpam-3329	624	17	‖kβw‖2	‖kβw‖2	ADV
ejpam-3329	624	18	=	=	PUNCT
ejpam-3329	624	19	∑∞	∑∞	X
ejpam-3329	624	20	m=0	m=0	PROPN
ejpam-3329	624	21	|w|2	|w|2	PROPN
ejpam-3329	624	22	m	m	VERB
ejpam-3329	624	23	β2	β2	NOUN
ejpam-3329	624	24	m	m	PROPN
ejpam-3329	624	25	.	.	PUNCT
ejpam-3329	625	1	thus	thus	ADV
ejpam-3329	625	2	‖kw‖	‖kw‖	NOUN
ejpam-3329	625	3	is	be	AUX
ejpam-3329	625	4	an	an	DET
ejpam-3329	625	5	increasing	increase	VERB
ejpam-3329	625	6	function	function	NOUN
ejpam-3329	625	7	of	of	ADP
ejpam-3329	625	8	|w|	|w|	PROPN
ejpam-3329	625	9	.	.	PUNCT
ejpam-3329	626	1	if	if	SCONJ
ejpam-3329	626	2	f(z	f(z	NUM
ejpam-3329	626	3	)	)	PUNCT
ejpam-3329	626	4	=	=	PUNCT
ejpam-3329	626	5	∑∞	∑∞	X
ejpam-3329	627	1	m=0	m=0	PROPN
ejpam-3329	627	2	amz	amz	PROPN
ejpam-3329	627	3	m	m	VERB
ejpam-3329	627	4	then	then	ADV
ejpam-3329	627	5	〈	〈	PROPN
ejpam-3329	627	6	f	f	PROPN
ejpam-3329	627	7	,	,	PUNCT
ejpam-3329	627	8	kβw	kβw	PROPN
ejpam-3329	627	9	〉	〉	PROPN
ejpam-3329	627	10	=	=	SYM
ejpam-3329	627	11	f(w	f(w	PROPN
ejpam-3329	627	12	)	)	PUNCT
ejpam-3329	627	13	for	for	ADP
ejpam-3329	627	14	all	all	DET
ejpam-3329	627	15	f	f	PROPN
ejpam-3329	627	16	and	and	CCONJ
ejpam-3329	627	17	kβw	kβw	PROPN
ejpam-3329	627	18	.	.	PUNCT
ejpam-3329	628	1	hence	hence	ADV
ejpam-3329	628	2	we	we	PRON
ejpam-3329	628	3	can	can	AUX
ejpam-3329	628	4	easily	easily	ADV
ejpam-3329	628	5	seen	see	VERB
ejpam-3329	628	6	that	that	SCONJ
ejpam-3329	628	7	c∗φk	c∗φk	PROPN
ejpam-3329	628	8	β	β	X
ejpam-3329	628	9	w	w	PROPN
ejpam-3329	628	10	=	=	SYM
ejpam-3329	628	11	kβφ(w	kβφ(w	PROPN
ejpam-3329	628	12	)	)	PUNCT
ejpam-3329	628	13	,	,	PUNCT
ejpam-3329	628	14	w	w	NOUN
ejpam-3329	628	15	∗	∗	NOUN
ejpam-3329	628	16	φk	φk	ADP
ejpam-3329	628	17	β	β	PROPN
ejpam-3329	628	18	w	w	PROPN
ejpam-3329	628	19	=	=	PUNCT
ejpam-3329	628	20	π̄kβφ(w	π̄kβφ(w	ADJ
ejpam-3329	628	21	)	)	PUNCT
ejpam-3329	628	22	and	and	CCONJ
ejpam-3329	628	23	kβ0	kβ0	NOUN
ejpam-3329	628	24	=	=	SYM
ejpam-3329	628	25	1	1	NUM
ejpam-3329	628	26	(	(	PUNCT
ejpam-3329	628	27	the	the	DET
ejpam-3329	628	28	function	function	NOUN
ejpam-3329	628	29	identically	identically	ADV
ejpam-3329	628	30	equal	equal	ADJ
ejpam-3329	628	31	to	to	ADP
ejpam-3329	628	32	1	1	NUM
ejpam-3329	628	33	)	)	PUNCT
ejpam-3329	628	34	.	.	PUNCT
ejpam-3329	629	1	now	now	ADV
ejpam-3329	629	2	we	we	PRON
ejpam-3329	629	3	characterize	characterize	VERB
ejpam-3329	629	4	quasi	quasi	NOUN
ejpam-3329	629	5	n	n	PRON
ejpam-3329	629	6	class	class	NOUN
ejpam-3329	629	7	q	q	NOUN
ejpam-3329	629	8	and	and	CCONJ
ejpam-3329	629	9	quasi	quasi	ADJ
ejpam-3329	629	10	n	n	CCONJ
ejpam-3329	629	11	-	-	PUNCT
ejpam-3329	629	12	class	class	NOUN
ejpam-3329	629	13	q∗	q∗	NOUN
ejpam-3329	629	14	composition	composition	NOUN
ejpam-3329	629	15	operators	operator	NOUN
ejpam-3329	629	16	on	on	ADP
ejpam-3329	629	17	this	this	DET
ejpam-3329	629	18	space	space	NOUN
ejpam-3329	629	19	as	as	SCONJ
ejpam-3329	629	20	follows	follow	VERB
ejpam-3329	629	21	.	.	PUNCT
ejpam-3329	630	1	theorem	theorem	VERB
ejpam-3329	630	2	38	38	NUM
ejpam-3329	630	3	.	.	PUNCT
ejpam-3329	631	1	if	if	SCONJ
ejpam-3329	631	2	cφ	cφ	PROPN
ejpam-3329	631	3	is	be	AUX
ejpam-3329	631	4	of	of	ADP
ejpam-3329	631	5	quasi	quasi	NOUN
ejpam-3329	631	6	n	n	CCONJ
ejpam-3329	631	7	-	-	PUNCT
ejpam-3329	631	8	class	class	NOUN
ejpam-3329	631	9	q	q	NOUN
ejpam-3329	631	10	operator	operator	NOUN
ejpam-3329	631	11	in	in	ADP
ejpam-3329	631	12	h2(β	h2(β	PROPN
ejpam-3329	631	13	)	)	PUNCT
ejpam-3329	631	14	,	,	PUNCT
ejpam-3329	631	15	then	then	ADV
ejpam-3329	631	16	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	631	17	c2+n	c2+n	PROPN
ejpam-3329	631	18	φ	φ	PROPN
ejpam-3329	631	19	−	−	PROPN
ejpam-3329	631	20	(	(	PUNCT
ejpam-3329	631	21	1	1	NUM
ejpam-3329	631	22	+	+	NUM
ejpam-3329	631	23	n)c∗2φ	n)c∗2φ	PROPN
ejpam-3329	631	24	c	c	NOUN
ejpam-3329	631	25	2	2	NUM
ejpam-3329	631	26	φ	φ	NOUN
ejpam-3329	631	27	+	+	CCONJ
ejpam-3329	631	28	nc∗φcφ	nc∗φcφ	PROPN
ejpam-3329	631	29	≥	≥	NOUN
ejpam-3329	631	30	0	0	NUM
ejpam-3329	631	31	proof	proof	NOUN
ejpam-3329	631	32	.	.	PUNCT
ejpam-3329	632	1	for	for	ADP
ejpam-3329	632	2	f	f	PROPN
ejpam-3329	632	3	∈	∈	PROPN
ejpam-3329	632	4	h2(β	h2(β	PROPN
ejpam-3329	632	5	)	)	PUNCT
ejpam-3329	632	6	,	,	PUNCT
ejpam-3329	632	7	consider	consider	VERB
ejpam-3329	632	8	〈	〈	PROPN
ejpam-3329	632	9	(	(	PUNCT
ejpam-3329	632	10	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	632	11	c2+n	c2+n	PROPN
ejpam-3329	632	12	φ	φ	PROPN
ejpam-3329	632	13	−(1	−(1	PROPN
ejpam-3329	633	1	+	+	CCONJ
ejpam-3329	633	2	n)c∗2φ	n)c∗2φ	PROPN
ejpam-3329	633	3	c	c	NOUN
ejpam-3329	633	4	2	2	NUM
ejpam-3329	633	5	φ	φ	NOUN
ejpam-3329	633	6	+	+	CCONJ
ejpam-3329	633	7	nc∗φcφ)f	nc∗φcφ)f	NUM
ejpam-3329	633	8	,	,	PUNCT
ejpam-3329	633	9	f	f	PROPN
ejpam-3329	633	10	〉	〉	NUM
ejpam-3329	633	11	=	=	SYM
ejpam-3329	634	1	〈	〈	PROPN
ejpam-3329	634	2	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	634	3	c2+n	c2+n	PROPN
ejpam-3329	634	4	φ	φ	PROPN
ejpam-3329	634	5	f	f	PROPN
ejpam-3329	634	6	,	,	PUNCT
ejpam-3329	634	7	f	f	PROPN
ejpam-3329	634	8	〉	〉	NUM
ejpam-3329	634	9	−	−	PROPN
ejpam-3329	635	1	(	(	PUNCT
ejpam-3329	635	2	1	1	NUM
ejpam-3329	635	3	+	+	NUM
ejpam-3329	635	4	n)〈c∗2φ	n)〈c∗2φ	NOUN
ejpam-3329	635	5	c2	c2	PROPN
ejpam-3329	635	6	φf	φf	PRON
ejpam-3329	635	7	,	,	PUNCT
ejpam-3329	635	8	f〉+	f〉+	PROPN
ejpam-3329	635	9	n〈c∗φcφf	n〈c∗φcφf	PROPN
ejpam-3329	635	10	,	,	PUNCT
ejpam-3329	635	11	f	f	PROPN
ejpam-3329	635	12	〉	〉	NUM
ejpam-3329	635	13	=	=	SYM
ejpam-3329	635	14	〈	〈	PROPN
ejpam-3329	635	15	c2+n	c2+n	PROPN
ejpam-3329	635	16	φ	φ	PROPN
ejpam-3329	635	17	f	f	PROPN
ejpam-3329	635	18	,	,	PUNCT
ejpam-3329	635	19	c2+n	c2+n	PROPN
ejpam-3329	635	20	φ	φ	NOUN
ejpam-3329	635	21	f	f	PROPN
ejpam-3329	635	22	〉	〉	PROPN
ejpam-3329	635	23	−	−	PROPN
ejpam-3329	635	24	(	(	PUNCT
ejpam-3329	635	25	1	1	NUM
ejpam-3329	635	26	+	+	NUM
ejpam-3329	635	27	n)〈c2	n)〈c2	PROPN
ejpam-3329	635	28	φf	φf	NOUN
ejpam-3329	635	29	,	,	PUNCT
ejpam-3329	635	30	c	c	PROPN
ejpam-3329	635	31	2	2	NUM
ejpam-3329	635	32	φf〉+	φf〉+	PROPN
ejpam-3329	635	33	n〈cφf	n〈cφf	PROPN
ejpam-3329	635	34	,	,	PUNCT
ejpam-3329	635	35	cφf	cφf	PROPN
ejpam-3329	635	36	〉	〉	PROPN
ejpam-3329	635	37	=	=	SYM
ejpam-3329	635	38	‖c2+n	‖c2+n	PROPN
ejpam-3329	635	39	φ	φ	NUM
ejpam-3329	635	40	f‖2	f‖2	X
ejpam-3329	636	1	−	−	X
ejpam-3329	636	2	(	(	PUNCT
ejpam-3329	636	3	1	1	NUM
ejpam-3329	636	4	+	+	CCONJ
ejpam-3329	636	5	n)‖c2	n)‖c2	ADJ
ejpam-3329	636	6	φf‖2	φf‖2	NOUN
ejpam-3329	636	7	+	+	CCONJ
ejpam-3329	636	8	n‖cφf‖2	n‖cφf‖2	PRON
ejpam-3329	636	9	let	let	VERB
ejpam-3329	636	10	f	f	NOUN
ejpam-3329	636	11	=	=	PUNCT
ejpam-3329	636	12	kβ0	kβ0	ADV
ejpam-3329	636	13	then	then	ADV
ejpam-3329	636	14	〈	〈	PROPN
ejpam-3329	636	15	(	(	PUNCT
ejpam-3329	636	16	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	636	17	c2+n	c2+n	PROPN
ejpam-3329	636	18	φ	φ	PROPN
ejpam-3329	636	19	−	−	PROPN
ejpam-3329	636	20	(	(	PUNCT
ejpam-3329	636	21	1	1	NUM
ejpam-3329	636	22	+	+	NUM
ejpam-3329	636	23	n)c∗2φ	n)c∗2φ	PROPN
ejpam-3329	636	24	c	c	NOUN
ejpam-3329	636	25	2	2	NUM
ejpam-3329	636	26	φ	φ	NOUN
ejpam-3329	636	27	+	+	CCONJ
ejpam-3329	636	28	nc∗φcφ)f	nc∗φcφ)f	NUM
ejpam-3329	636	29	,	,	PUNCT
ejpam-3329	636	30	f	f	PROPN
ejpam-3329	636	31	〉	〉	NUM
ejpam-3329	636	32	=	=	SYM
ejpam-3329	636	33	‖c2+n	‖c2+n	PROPN
ejpam-3329	636	34	φ	φ	NUM
ejpam-3329	636	35	kβ0	kβ0	ADV
ejpam-3329	636	36	‖	‖	PROPN
ejpam-3329	636	37	2	2	NUM
ejpam-3329	636	38	−	−	NOUN
ejpam-3329	636	39	(	(	PUNCT
ejpam-3329	636	40	1	1	NUM
ejpam-3329	636	41	+	+	CCONJ
ejpam-3329	636	42	n)‖c2	n)‖c2	ADJ
ejpam-3329	636	43	φk	φk	ADP
ejpam-3329	636	44	β	β	PROPN
ejpam-3329	636	45	0	0	PUNCT
ejpam-3329	636	46	‖	‖	PROPN
ejpam-3329	636	47	2	2	NUM
ejpam-3329	636	48	+	+	CCONJ
ejpam-3329	636	49	n‖cφkβ0	n‖cφkβ0	ADV
ejpam-3329	636	50	‖	‖	ADJ
ejpam-3329	636	51	2	2	X
ejpam-3329	636	52	=	=	SYM
ejpam-3329	636	53	‖kβ0	‖kβ0	ADJ
ejpam-3329	636	54	‖	‖	ADJ
ejpam-3329	636	55	2	2	NUM
ejpam-3329	636	56	−	−	NOUN
ejpam-3329	636	57	(	(	PUNCT
ejpam-3329	636	58	1	1	NUM
ejpam-3329	636	59	+	+	NUM
ejpam-3329	636	60	n)‖kβ0	n)‖kβ0	VERB
ejpam-3329	636	61	‖	‖	ADJ
ejpam-3329	636	62	2	2	NUM
ejpam-3329	636	63	+	+	PUNCT
ejpam-3329	636	64	n‖kβ0	n‖kβ0	NUM
ejpam-3329	636	65	‖	‖	PROPN
ejpam-3329	636	66	2	2	NUM
ejpam-3329	636	67	=	=	SYM
ejpam-3329	636	68	0	0	PUNCT
ejpam-3329	637	1	hence	hence	ADV
ejpam-3329	637	2	cφ	cφ	PROPN
ejpam-3329	637	3	is	be	AUX
ejpam-3329	637	4	quasi	quasi	ADJ
ejpam-3329	637	5	n	n	CCONJ
ejpam-3329	637	6	-	-	PUNCT
ejpam-3329	637	7	class	class	NOUN
ejpam-3329	637	8	q	q	NOUN
ejpam-3329	637	9	operator	operator	NOUN
ejpam-3329	637	10	.	.	PUNCT
ejpam-3329	638	1	d.	d.	PROPN
ejpam-3329	638	2	senthilkumar	senthilkumar	PROPN
ejpam-3329	638	3	,	,	PUNCT
ejpam-3329	638	4	s.	s.	PROPN
ejpam-3329	638	5	parvatham	parvatham	PROPN
ejpam-3329	638	6	/	/	SYM
ejpam-3329	638	7	eur	eur	PROPN
ejpam-3329	638	8	.	.	PUNCT
ejpam-3329	639	1	j.	j.	PROPN
ejpam-3329	639	2	pure	pure	PROPN
ejpam-3329	639	3	appl	appl	PROPN
ejpam-3329	639	4	.	.	PROPN
ejpam-3329	639	5	math	math	PROPN
ejpam-3329	639	6	,	,	PUNCT
ejpam-3329	639	7	11	11	NUM
ejpam-3329	639	8	(	(	PUNCT
ejpam-3329	639	9	4	4	NUM
ejpam-3329	639	10	)	)	PUNCT
ejpam-3329	639	11	(	(	PUNCT
ejpam-3329	639	12	2018	2018	NUM
ejpam-3329	639	13	)	)	PUNCT
ejpam-3329	639	14	,	,	PUNCT
ejpam-3329	639	15	1108	1108	NUM
ejpam-3329	639	16	-	-	SYM
ejpam-3329	639	17	1129	1129	NUM
ejpam-3329	639	18	1124	1124	NUM
ejpam-3329	639	19	theorem	theorem	VERB
ejpam-3329	639	20	39	39	NUM
ejpam-3329	639	21	.	.	PUNCT
ejpam-3329	640	1	if	if	SCONJ
ejpam-3329	640	2	c∗φ	c∗φ	NOUN
ejpam-3329	640	3	is	be	AUX
ejpam-3329	640	4	quasi	quasi	ADJ
ejpam-3329	640	5	n	n	CCONJ
ejpam-3329	640	6	-	-	PUNCT
ejpam-3329	640	7	class	class	NOUN
ejpam-3329	640	8	q	q	NOUN
ejpam-3329	640	9	operator	operator	NOUN
ejpam-3329	640	10	in	in	ADP
ejpam-3329	640	11	h2(β	h2(β	PROPN
ejpam-3329	640	12	)	)	PUNCT
ejpam-3329	640	13	,	,	PUNCT
ejpam-3329	640	14	then	then	ADV
ejpam-3329	640	15	c2+n	c2+n	PROPN
ejpam-3329	640	16	φ	φ	PROPN
ejpam-3329	640	17	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	640	18	−	−	PROPN
ejpam-3329	641	1	(	(	PUNCT
ejpam-3329	641	2	1	1	NUM
ejpam-3329	641	3	+	+	CCONJ
ejpam-3329	641	4	n)c2	n)c2	PROPN
ejpam-3329	641	5	φc	φc	PROPN
ejpam-3329	641	6	∗2	∗2	PROPN
ejpam-3329	641	7	φ	φ	X
ejpam-3329	641	8	+	+	PROPN
ejpam-3329	641	9	ncφc	ncφc	PROPN
ejpam-3329	641	10	∗	∗	PROPN
ejpam-3329	641	11	φ	φ	PROPN
ejpam-3329	641	12	≥	≥	PROPN
ejpam-3329	641	13	0	0	NUM
ejpam-3329	641	14	proof	proof	NOUN
ejpam-3329	641	15	.	.	PUNCT
ejpam-3329	642	1	for	for	ADP
ejpam-3329	642	2	f	f	PROPN
ejpam-3329	642	3	∈	∈	PROPN
ejpam-3329	642	4	h2(β	h2(β	PROPN
ejpam-3329	642	5	)	)	PUNCT
ejpam-3329	642	6	,	,	PUNCT
ejpam-3329	642	7	consider	consider	VERB
ejpam-3329	642	8	〈	〈	PROPN
ejpam-3329	642	9	(	(	PUNCT
ejpam-3329	642	10	c2+n	c2+n	PROPN
ejpam-3329	642	11	φ	φ	NOUN
ejpam-3329	642	12	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	642	13	−(1	−(1	PROPN
ejpam-3329	642	14	+	+	CCONJ
ejpam-3329	642	15	n)c2	n)c2	PROPN
ejpam-3329	642	16	φc	φc	PROPN
ejpam-3329	642	17	∗2	∗2	PROPN
ejpam-3329	642	18	φ	φ	X
ejpam-3329	642	19	+	+	PROPN
ejpam-3329	642	20	ncφc	ncφc	NOUN
ejpam-3329	642	21	∗	∗	NOUN
ejpam-3329	642	22	φ)f	φ)f	NOUN
ejpam-3329	642	23	,	,	PUNCT
ejpam-3329	642	24	f	f	PROPN
ejpam-3329	642	25	〉	〉	NUM
ejpam-3329	642	26	=	=	SYM
ejpam-3329	642	27	〈	〈	PROPN
ejpam-3329	642	28	c2+n	c2+n	PROPN
ejpam-3329	642	29	φ	φ	NOUN
ejpam-3329	642	30	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	642	31	f	f	PROPN
ejpam-3329	642	32	,	,	PUNCT
ejpam-3329	642	33	f	f	PROPN
ejpam-3329	642	34	〉	〉	NUM
ejpam-3329	643	1	−	−	PROPN
ejpam-3329	643	2	(	(	PUNCT
ejpam-3329	643	3	1	1	NUM
ejpam-3329	643	4	+	+	NUM
ejpam-3329	643	5	n)〈c2	n)〈c2	PROPN
ejpam-3329	643	6	φc	φc	NOUN
ejpam-3329	643	7	∗2	∗2	PROPN
ejpam-3329	643	8	φ	φ	PROPN
ejpam-3329	643	9	f	f	PROPN
ejpam-3329	643	10	,	,	PUNCT
ejpam-3329	643	11	f〉+	f〉+	PROPN
ejpam-3329	643	12	n〈cφc∗φf	n〈cφc∗φf	PROPN
ejpam-3329	643	13	,	,	PUNCT
ejpam-3329	643	14	f	f	PROPN
ejpam-3329	643	15	〉	〉	NUM
ejpam-3329	643	16	=	=	SYM
ejpam-3329	644	1	〈	〈	PROPN
ejpam-3329	644	2	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	644	3	f	f	PROPN
ejpam-3329	644	4	,	,	PUNCT
ejpam-3329	644	5	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	644	6	f	f	PROPN
ejpam-3329	644	7	〉	〉	PROPN
ejpam-3329	644	8	−	−	PROPN
ejpam-3329	644	9	(	(	PUNCT
ejpam-3329	644	10	1	1	NUM
ejpam-3329	644	11	+	+	NUM
ejpam-3329	644	12	n)〈c∗2φ	n)〈c∗2φ	NOUN
ejpam-3329	644	13	f	f	NOUN
ejpam-3329	644	14	,	,	PUNCT
ejpam-3329	644	15	c∗2φ	c∗2φ	PROPN
ejpam-3329	644	16	f〉+	f〉+	PROPN
ejpam-3329	644	17	n〈c∗φf	n〈c∗φf	PROPN
ejpam-3329	644	18	,	,	PUNCT
ejpam-3329	644	19	c∗φf	c∗φf	PROPN
ejpam-3329	644	20	〉	〉	NUM
ejpam-3329	644	21	=	=	SYM
ejpam-3329	645	1	‖c∗2+nφ	‖c∗2+nφ	PUNCT
ejpam-3329	645	2	f‖2	f‖2	X
ejpam-3329	646	1	−	−	X
ejpam-3329	646	2	(	(	PUNCT
ejpam-3329	646	3	1	1	NUM
ejpam-3329	646	4	+	+	NUM
ejpam-3329	646	5	n)‖c∗2φ	n)‖c∗2φ	PROPN
ejpam-3329	646	6	f‖2	f‖2	X
ejpam-3329	647	1	+	+	CCONJ
ejpam-3329	647	2	n‖c∗φf‖2	n‖c∗φf‖2	NUM
ejpam-3329	647	3	let	let	VERB
ejpam-3329	647	4	f	f	NOUN
ejpam-3329	647	5	=	=	PUNCT
ejpam-3329	647	6	kβ0	kβ0	ADV
ejpam-3329	647	7	and	and	CCONJ
ejpam-3329	647	8	φ(0	φ(0	ADJ
ejpam-3329	647	9	)	)	PUNCT
ejpam-3329	648	1	=	=	SYM
ejpam-3329	649	1	0	0	PUNCT
ejpam-3329	650	1	then	then	ADV
ejpam-3329	650	2	we	we	PRON
ejpam-3329	650	3	have	have	VERB
ejpam-3329	650	4	〈	〈	PROPN
ejpam-3329	650	5	(	(	PUNCT
ejpam-3329	650	6	c2+n	c2+n	PROPN
ejpam-3329	650	7	φ	φ	NOUN
ejpam-3329	650	8	c∗2+nφ	c∗2+nφ	PROPN
ejpam-3329	650	9	−(1	−(1	PROPN
ejpam-3329	650	10	+	+	CCONJ
ejpam-3329	650	11	n)c2	n)c2	PROPN
ejpam-3329	650	12	φc	φc	PROPN
ejpam-3329	650	13	∗2	∗2	PROPN
ejpam-3329	650	14	φ	φ	X
ejpam-3329	650	15	+	+	PROPN
ejpam-3329	650	16	ncφc	ncφc	NOUN
ejpam-3329	650	17	∗	∗	NOUN
ejpam-3329	650	18	φ)f	φ)f	NOUN
ejpam-3329	650	19	,	,	PUNCT
ejpam-3329	650	20	f	f	PROPN
ejpam-3329	650	21	〉	〉	NUM
ejpam-3329	650	22	=	=	SYM
ejpam-3329	651	1	‖c∗2+nφ	‖c∗2+nφ	SYM
ejpam-3329	651	2	kβ0	kβ0	ADV
ejpam-3329	651	3	‖	‖	ADJ
ejpam-3329	651	4	2	2	NUM
ejpam-3329	651	5	−	−	NOUN
ejpam-3329	651	6	(	(	PUNCT
ejpam-3329	651	7	1	1	NUM
ejpam-3329	651	8	+	+	NUM
ejpam-3329	651	9	n)‖c∗2φ	n)‖c∗2φ	PROPN
ejpam-3329	651	10	k	k	PROPN
ejpam-3329	651	11	β	β	X
ejpam-3329	651	12	0	0	PUNCT
ejpam-3329	651	13	‖	‖	PROPN
ejpam-3329	651	14	2	2	NUM
ejpam-3329	651	15	+	+	CCONJ
ejpam-3329	651	16	n‖c∗φk	n‖c∗φk	NOUN
ejpam-3329	651	17	β	β	X
ejpam-3329	651	18	0	0	SYM
ejpam-3329	651	19	‖	‖	PROPN
ejpam-3329	651	20	2	2	NUM
ejpam-3329	651	21	=	=	SYM
ejpam-3329	651	22	‖kβ0	‖kβ0	ADJ
ejpam-3329	651	23	‖	‖	ADJ
ejpam-3329	651	24	2	2	NUM
ejpam-3329	651	25	−	−	NOUN
ejpam-3329	651	26	(	(	PUNCT
ejpam-3329	651	27	1	1	NUM
ejpam-3329	651	28	+	+	NUM
ejpam-3329	651	29	n)‖kβ0	n)‖kβ0	VERB
ejpam-3329	651	30	‖	‖	ADJ
ejpam-3329	651	31	2	2	NUM
ejpam-3329	651	32	+	+	PUNCT
ejpam-3329	651	33	n‖kβ0	n‖kβ0	NUM
ejpam-3329	651	34	‖	‖	PROPN
ejpam-3329	651	35	2	2	NUM
ejpam-3329	651	36	=	=	SYM
ejpam-3329	651	37	0	0	NUM
ejpam-3329	652	1	hence	hence	ADV
ejpam-3329	652	2	c∗φ	c∗φ	NUM
ejpam-3329	652	3	is	be	AUX
ejpam-3329	652	4	quasi	quasi	NOUN
ejpam-3329	652	5	n	n	CCONJ
ejpam-3329	652	6	-	-	PUNCT
ejpam-3329	652	7	class	class	NOUN
ejpam-3329	652	8	q	q	NOUN
ejpam-3329	652	9	operator	operator	NOUN
ejpam-3329	652	10	.	.	PUNCT
ejpam-3329	653	1	theorem	theorem	VERB
ejpam-3329	653	2	40	40	NUM
ejpam-3329	653	3	.	.	PUNCT
ejpam-3329	654	1	if	if	SCONJ
ejpam-3329	654	2	cφ	cφ	PROPN
ejpam-3329	654	3	is	be	AUX
ejpam-3329	654	4	quasi	quasi	ADJ
ejpam-3329	654	5	n	n	CCONJ
ejpam-3329	654	6	-	-	PUNCT
ejpam-3329	654	7	class	class	NOUN
ejpam-3329	654	8	q∗	q∗	NOUN
ejpam-3329	654	9	operator	operator	NOUN
ejpam-3329	654	10	in	in	ADP
ejpam-3329	654	11	h2(β	h2(β	PROPN
ejpam-3329	654	12	)	)	PUNCT
ejpam-3329	655	1	if	if	SCONJ
ejpam-3329	655	2	and	and	CCONJ
ejpam-3329	655	3	only	only	ADV
ejpam-3329	655	4	if	if	SCONJ
ejpam-3329	655	5	‖kβ0	‖kβ0	ADJ
ejpam-3329	655	6	‖2	‖2	NOUN
ejpam-3329	655	7	≥	≥	NOUN
ejpam-3329	655	8	‖k	‖k	NOUN
ejpam-3329	655	9	β	β	X
ejpam-3329	655	10	φ(0)‖	φ(0)‖	NOUN
ejpam-3329	655	11	2	2	NUM
ejpam-3329	655	12	.	.	PUNCT
ejpam-3329	655	13	theorem	theorem	VERB
ejpam-3329	655	14	41	41	NUM
ejpam-3329	655	15	.	.	PUNCT
ejpam-3329	656	1	if	if	SCONJ
ejpam-3329	656	2	c∗φ	c∗φ	NUM
ejpam-3329	656	3	is	be	AUX
ejpam-3329	656	4	of	of	ADP
ejpam-3329	656	5	quasi	quasi	NOUN
ejpam-3329	656	6	n	n	CCONJ
ejpam-3329	656	7	-	-	PUNCT
ejpam-3329	656	8	class	class	NOUN
ejpam-3329	656	9	q∗	q∗	NOUN
ejpam-3329	656	10	operator	operator	NOUN
ejpam-3329	656	11	in	in	ADP
ejpam-3329	656	12	h2(β	h2(β	PROPN
ejpam-3329	656	13	)	)	PUNCT
ejpam-3329	656	14	if	if	SCONJ
ejpam-3329	656	15	and	and	CCONJ
ejpam-3329	656	16	only	only	ADV
ejpam-3329	656	17	if	if	SCONJ
ejpam-3329	656	18	‖kβ	‖kβ	NUM
ejpam-3329	656	19	φ2+n(0	φ2+n(0	NOUN
ejpam-3329	656	20	)	)	PUNCT
ejpam-3329	656	21	‖2	‖2	NOUN
ejpam-3329	656	22	≥	≥	NOUN
ejpam-3329	657	1	‖kβφ(0)‖	‖kβφ(0)‖	NUM
ejpam-3329	657	2	2	2	NUM
ejpam-3329	657	3	.	.	PUNCT
ejpam-3329	658	1	next	next	ADV
ejpam-3329	658	2	we	we	PRON
ejpam-3329	658	3	characterize	characterize	VERB
ejpam-3329	658	4	the	the	DET
ejpam-3329	658	5	quasi	quasi	NOUN
ejpam-3329	658	6	n	n	PRON
ejpam-3329	658	7	class	class	NOUN
ejpam-3329	658	8	q	q	NOUN
ejpam-3329	658	9	and	and	CCONJ
ejpam-3329	658	10	quasi	quasi	ADJ
ejpam-3329	658	11	n	n	PRON
ejpam-3329	658	12	class	class	NOUN
ejpam-3329	658	13	q∗	q∗	NOUN
ejpam-3329	658	14	weighted	weight	VERB
ejpam-3329	658	15	composition	composition	NOUN
ejpam-3329	658	16	operator	operator	NOUN
ejpam-3329	658	17	on	on	ADP
ejpam-3329	658	18	weighted	weight	VERB
ejpam-3329	658	19	hardy	hardy	ADJ
ejpam-3329	658	20	space	space	NOUN
ejpam-3329	658	21	as	as	SCONJ
ejpam-3329	658	22	follows	follow	VERB
ejpam-3329	658	23	theorem	theorem	VERB
ejpam-3329	658	24	42	42	NUM
ejpam-3329	658	25	.	.	PUNCT
ejpam-3329	659	1	an	an	DET
ejpam-3329	659	2	operator	operator	NOUN
ejpam-3329	659	3	wφ	wφ	ADP
ejpam-3329	659	4	∈	∈	PROPN
ejpam-3329	659	5	h2(β	h2(β	PROPN
ejpam-3329	659	6	)	)	PUNCT
ejpam-3329	659	7	is	be	AUX
ejpam-3329	659	8	quasi	quasi	NOUN
ejpam-3329	659	9	n	n	X
ejpam-3329	659	10	class	class	NOUN
ejpam-3329	659	11	q	q	NOUN
ejpam-3329	659	12	if	if	SCONJ
ejpam-3329	660	1	and	and	CCONJ
ejpam-3329	660	2	only	only	ADV
ejpam-3329	660	3	if	if	SCONJ
ejpam-3329	660	4	‖π2+n‖2	‖π2+n‖2	ADJ
ejpam-3329	660	5	−	−	PROPN
ejpam-3329	660	6	(	(	PUNCT
ejpam-3329	660	7	1	1	NUM
ejpam-3329	660	8	+	+	NUM
ejpam-3329	660	9	n)‖π2‖2	n)‖π2‖2	NUM
ejpam-3329	660	10	+	+	CCONJ
ejpam-3329	660	11	n‖π‖2	n‖π‖2	PROPN
ejpam-3329	660	12	≥	≥	NUM
ejpam-3329	660	13	0	0	NUM
ejpam-3329	660	14	.	.	PUNCT
ejpam-3329	661	1	proof	proof	NOUN
ejpam-3329	661	2	.	.	PUNCT
ejpam-3329	662	1	since	since	SCONJ
ejpam-3329	662	2	wφ	wφ	NOUN
ejpam-3329	662	3	is	be	AUX
ejpam-3329	662	4	quasi	quasi	NOUN
ejpam-3329	662	5	n	n	PRON
ejpam-3329	662	6	class	class	NOUN
ejpam-3329	662	7	q	q	NOUN
ejpam-3329	662	8	operator	operator	NOUN
ejpam-3329	662	9	,	,	PUNCT
ejpam-3329	662	10	then	then	ADV
ejpam-3329	662	11	for	for	ADP
ejpam-3329	662	12	any	any	DET
ejpam-3329	662	13	f	f	PROPN
ejpam-3329	662	14	∈	∈	PROPN
ejpam-3329	662	15	h2(β	h2(β	PROPN
ejpam-3329	662	16	)	)	PUNCT
ejpam-3329	662	17	,	,	PUNCT
ejpam-3329	662	18	we	we	PRON
ejpam-3329	662	19	have	have	VERB
ejpam-3329	662	20	〈	〈	PROPN
ejpam-3329	662	21	(	(	PUNCT
ejpam-3329	662	22	w	w	PROPN
ejpam-3329	662	23	∗2+nφ	∗2+nφ	PROPN
ejpam-3329	662	24	w	w	PROPN
ejpam-3329	662	25	2+n	2+n	NUM
ejpam-3329	662	26	φ	φ	NUM
ejpam-3329	662	27	−	−	PROPN
ejpam-3329	663	1	(	(	PUNCT
ejpam-3329	663	2	1	1	NUM
ejpam-3329	663	3	+	+	CCONJ
ejpam-3329	663	4	n)w	n)w	X
ejpam-3329	663	5	∗2φ	∗2φ	PROPN
ejpam-3329	663	6	w	w	PROPN
ejpam-3329	663	7	2	2	NUM
ejpam-3329	663	8	φ	φ	NOUN
ejpam-3329	663	9	+	+	CCONJ
ejpam-3329	663	10	nw	nw	PROPN
ejpam-3329	663	11	∗φwφ)f	∗φwφ)f	NOUN
ejpam-3329	663	12	,	,	PUNCT
ejpam-3329	663	13	f	f	PROPN
ejpam-3329	663	14	〉	〉	PROPN
ejpam-3329	663	15	≥	≥	NOUN
ejpam-3329	663	16	0	0	NUM
ejpam-3329	663	17	⇔	⇔	X
ejpam-3329	663	18	‖w	‖w	PROPN
ejpam-3329	663	19	2+n	2+n	NUM
ejpam-3329	663	20	φ	φ	NUM
ejpam-3329	663	21	f‖2	f‖2	X
ejpam-3329	664	1	−	−	X
ejpam-3329	664	2	(	(	PUNCT
ejpam-3329	664	3	1	1	NUM
ejpam-3329	664	4	+	+	CCONJ
ejpam-3329	664	5	n)‖w	n)‖w	PROPN
ejpam-3329	664	6	2	2	NUM
ejpam-3329	664	7	φf‖2	φf‖2	NOUN
ejpam-3329	664	8	+	+	CCONJ
ejpam-3329	664	9	n‖wφf‖2	n‖wφf‖2	X
ejpam-3329	664	10	≥	≥	NOUN
ejpam-3329	664	11	0	0	NUM
ejpam-3329	664	12	⇔	⇔	X
ejpam-3329	664	13	‖w	‖w	PROPN
ejpam-3329	664	14	2+n	2+n	NUM
ejpam-3329	664	15	φ	φ	NUM
ejpam-3329	664	16	kβ0	kβ0	ADV
ejpam-3329	664	17	‖	‖	PROPN
ejpam-3329	664	18	2	2	NUM
ejpam-3329	664	19	−	−	NOUN
ejpam-3329	664	20	(	(	PUNCT
ejpam-3329	664	21	1	1	NUM
ejpam-3329	664	22	+	+	CCONJ
ejpam-3329	664	23	n)‖w	n)‖w	PROPN
ejpam-3329	664	24	2	2	NUM
ejpam-3329	664	25	φk	φk	ADP
ejpam-3329	664	26	β	β	X
ejpam-3329	664	27	0	0	PUNCT
ejpam-3329	664	28	‖	‖	PROPN
ejpam-3329	664	29	2	2	NUM
ejpam-3329	664	30	+	+	CCONJ
ejpam-3329	664	31	n‖wφk	n‖wφk	NUM
ejpam-3329	664	32	β	β	X
ejpam-3329	664	33	0	0	NUM
ejpam-3329	664	34	‖	‖	PROPN
ejpam-3329	664	35	2	2	NUM
ejpam-3329	664	36	≥	≥	NOUN
ejpam-3329	664	37	0	0	NUM
ejpam-3329	664	38	when	when	SCONJ
ejpam-3329	664	39	f	f	X
ejpam-3329	664	40	=	=	PUNCT
ejpam-3329	664	41	kβ0	kβ0	PROPN
ejpam-3329	664	42	⇔	⇔	X
ejpam-3329	664	43	‖π2+nkβ0	‖π2+nkβ0	ADJ
ejpam-3329	664	44	‖	‖	PROPN
ejpam-3329	664	45	2	2	NUM
ejpam-3329	664	46	−	−	NOUN
ejpam-3329	664	47	(	(	PUNCT
ejpam-3329	664	48	1	1	NUM
ejpam-3329	664	49	+	+	NUM
ejpam-3329	664	50	n)‖π2kβ0	n)‖π2kβ0	ADJ
ejpam-3329	664	51	‖	‖	ADJ
ejpam-3329	664	52	2	2	NUM
ejpam-3329	664	53	+	+	CCONJ
ejpam-3329	664	54	n‖πkβ0	n‖πkβ0	NOUN
ejpam-3329	664	55	‖	‖	ADJ
ejpam-3329	664	56	2	2	NUM
ejpam-3329	664	57	≥	≥	NOUN
ejpam-3329	664	58	0	0	NUM
ejpam-3329	664	59	⇔	⇔	X
ejpam-3329	664	60	‖π2+n‖2‖kβ0	‖π2+n‖2‖kβ0	X
ejpam-3329	664	61	‖	‖	ADJ
ejpam-3329	664	62	2	2	NUM
ejpam-3329	664	63	−	−	NOUN
ejpam-3329	664	64	(	(	PUNCT
ejpam-3329	664	65	1	1	NUM
ejpam-3329	664	66	+	+	CCONJ
ejpam-3329	664	67	n)‖π2‖2‖kβ0	n)‖π2‖2‖kβ0	ADJ
ejpam-3329	664	68	‖	‖	ADJ
ejpam-3329	664	69	2	2	NUM
ejpam-3329	664	70	+	+	CCONJ
ejpam-3329	664	71	n‖π‖2‖kβ0	n‖π‖2‖kβ0	NOUN
ejpam-3329	664	72	‖	‖	ADJ
ejpam-3329	664	73	2	2	NUM
ejpam-3329	664	74	≥	≥	NOUN
ejpam-3329	664	75	0	0	NUM
ejpam-3329	664	76	⇔	⇔	X
ejpam-3329	664	77	‖π2+n‖2	‖π2+n‖2	PUNCT
ejpam-3329	664	78	−	−	PROPN
ejpam-3329	664	79	(	(	PUNCT
ejpam-3329	664	80	1	1	NUM
ejpam-3329	664	81	+	+	NUM
ejpam-3329	664	82	n)‖π2‖2	n)‖π2‖2	NUM
ejpam-3329	664	83	+	+	CCONJ
ejpam-3329	664	84	n‖π‖2	n‖π‖2	PROPN
ejpam-3329	664	85	≥	≥	NUM
ejpam-3329	664	86	0	0	NUM
ejpam-3329	664	87	theorem	theorem	VERB
ejpam-3329	664	88	43	43	NUM
ejpam-3329	664	89	.	.	PUNCT
ejpam-3329	665	1	an	an	DET
ejpam-3329	665	2	operator	operator	NOUN
ejpam-3329	665	3	w	w	ADP
ejpam-3329	665	4	∗φ	∗φ	PROPN
ejpam-3329	665	5	∈	∈	PROPN
ejpam-3329	665	6	h2(β	h2(β	PROPN
ejpam-3329	665	7	)	)	PUNCT
ejpam-3329	665	8	is	be	AUX
ejpam-3329	665	9	quasi	quasi	NOUN
ejpam-3329	665	10	n	n	X
ejpam-3329	665	11	class	class	NOUN
ejpam-3329	665	12	q	q	NOUN
ejpam-3329	665	13	if	if	SCONJ
ejpam-3329	666	1	and	and	CCONJ
ejpam-3329	666	2	only	only	ADV
ejpam-3329	666	3	if	if	SCONJ
ejpam-3329	666	4	‖π2+n‖2	‖π2+n‖2	ADJ
ejpam-3329	666	5	−	−	PROPN
ejpam-3329	666	6	(	(	PUNCT
ejpam-3329	666	7	1	1	NUM
ejpam-3329	666	8	+	+	NUM
ejpam-3329	666	9	n)‖π2‖2	n)‖π2‖2	NUM
ejpam-3329	666	10	+	+	CCONJ
ejpam-3329	666	11	n‖π‖2	n‖π‖2	PROPN
ejpam-3329	666	12	≥	≥	NOUN
ejpam-3329	666	13	0	0	NUM
ejpam-3329	666	14	.	.	PUNCT
ejpam-3329	667	1	d.	d.	PROPN
ejpam-3329	667	2	senthilkumar	senthilkumar	PROPN
ejpam-3329	667	3	,	,	PUNCT
ejpam-3329	667	4	s.	s.	PROPN
ejpam-3329	667	5	parvatham	parvatham	PROPN
ejpam-3329	667	6	/	/	SYM
ejpam-3329	667	7	eur	eur	PROPN
ejpam-3329	667	8	.	.	PUNCT
ejpam-3329	668	1	j.	j.	PROPN
ejpam-3329	668	2	pure	pure	PROPN
ejpam-3329	668	3	appl	appl	PROPN
ejpam-3329	668	4	.	.	PROPN
ejpam-3329	668	5	math	math	PROPN
ejpam-3329	668	6	,	,	PUNCT
ejpam-3329	668	7	11	11	NUM
ejpam-3329	668	8	(	(	PUNCT
ejpam-3329	668	9	4	4	NUM
ejpam-3329	668	10	)	)	PUNCT
ejpam-3329	668	11	(	(	PUNCT
ejpam-3329	668	12	2018	2018	NUM
ejpam-3329	668	13	)	)	PUNCT
ejpam-3329	668	14	,	,	PUNCT
ejpam-3329	668	15	1108	1108	NUM
ejpam-3329	668	16	-	-	SYM
ejpam-3329	668	17	1129	1129	NUM
ejpam-3329	668	18	1125	1125	NUM
ejpam-3329	668	19	proof	proof	NOUN
ejpam-3329	668	20	.	.	PUNCT
ejpam-3329	669	1	since	since	SCONJ
ejpam-3329	669	2	w	w	PROPN
ejpam-3329	669	3	∗φ	∗φ	PROPN
ejpam-3329	669	4	is	be	AUX
ejpam-3329	669	5	quasi	quasi	NOUN
ejpam-3329	669	6	n	n	PRON
ejpam-3329	669	7	class	class	NOUN
ejpam-3329	669	8	q	q	NOUN
ejpam-3329	669	9	operator	operator	NOUN
ejpam-3329	669	10	,	,	PUNCT
ejpam-3329	669	11	we	we	PRON
ejpam-3329	669	12	have	have	VERB
ejpam-3329	669	13	〈	〈	PROPN
ejpam-3329	669	14	(	(	PUNCT
ejpam-3329	669	15	w	w	PROPN
ejpam-3329	669	16	2+n	2+n	NUM
ejpam-3329	669	17	φ	φ	PROPN
ejpam-3329	669	18	w	w	PROPN
ejpam-3329	669	19	∗2+nφ	∗2+nφ	PROPN
ejpam-3329	669	20	−	−	PROPN
ejpam-3329	669	21	(	(	PUNCT
ejpam-3329	669	22	1	1	NUM
ejpam-3329	669	23	+	+	CCONJ
ejpam-3329	669	24	n)(wφw	n)(wφw	ADJ
ejpam-3329	669	25	∗	∗	X
ejpam-3329	669	26	φ)2	φ)2	PROPN
ejpam-3329	669	27	+	+	CCONJ
ejpam-3329	669	28	nwφw	nwφw	NOUN
ejpam-3329	669	29	∗	∗	NOUN
ejpam-3329	669	30	φ)f	φ)f	NOUN
ejpam-3329	669	31	,	,	PUNCT
ejpam-3329	669	32	f	f	PROPN
ejpam-3329	669	33	〉	〉	PROPN
ejpam-3329	669	34	≥	≥	NOUN
ejpam-3329	669	35	0	0	NUM
ejpam-3329	669	36	for	for	ADP
ejpam-3329	669	37	any	any	DET
ejpam-3329	669	38	f	f	PROPN
ejpam-3329	669	39	∈	∈	PROPN
ejpam-3329	669	40	h2(β	h2(β	NOUN
ejpam-3329	669	41	)	)	PUNCT
ejpam-3329	669	42	〈	〈	PROPN
ejpam-3329	669	43	(	(	PUNCT
ejpam-3329	669	44	w	w	PROPN
ejpam-3329	669	45	2+n	2+n	NUM
ejpam-3329	669	46	φ	φ	PROPN
ejpam-3329	669	47	w	w	PROPN
ejpam-3329	669	48	∗2+nφ	∗2+nφ	PROPN
ejpam-3329	669	49	−	−	PROPN
ejpam-3329	669	50	(	(	PUNCT
ejpam-3329	669	51	1	1	NUM
ejpam-3329	669	52	+	+	CCONJ
ejpam-3329	669	53	n)(wφw	n)(wφw	ADJ
ejpam-3329	669	54	∗	∗	X
ejpam-3329	669	55	φ)2	φ)2	PROPN
ejpam-3329	669	56	+	+	CCONJ
ejpam-3329	669	57	nwφw	nwφw	NOUN
ejpam-3329	669	58	∗	∗	NOUN
ejpam-3329	669	59	φ)f	φ)f	NOUN
ejpam-3329	669	60	,	,	PUNCT
ejpam-3329	670	1	f	f	PROPN
ejpam-3329	670	2	〉	〉	PROPN
ejpam-3329	670	3	≥	≥	NOUN
ejpam-3329	670	4	0	0	NUM
ejpam-3329	670	5	⇔	⇔	PROPN
ejpam-3329	670	6	‖w	‖w	PROPN
ejpam-3329	670	7	∗2+nφ	∗2+nφ	PROPN
ejpam-3329	670	8	f‖2	f‖2	PROPN
ejpam-3329	670	9	−	−	X
ejpam-3329	670	10	(	(	PUNCT
ejpam-3329	670	11	1	1	NUM
ejpam-3329	670	12	+	+	CCONJ
ejpam-3329	670	13	n)‖w	n)‖w	PROPN
ejpam-3329	670	14	∗2φ	∗2φ	PROPN
ejpam-3329	670	15	f‖2	f‖2	VERB
ejpam-3329	671	1	+	+	CCONJ
ejpam-3329	671	2	n‖w	n‖w	NOUN
ejpam-3329	671	3	∗φf‖2	∗φf‖2	PROPN
ejpam-3329	671	4	≥	≥	PROPN
ejpam-3329	671	5	0	0	NUM
ejpam-3329	671	6	⇔	⇔	X
ejpam-3329	671	7	‖π2+nkβ0	‖π2+nkβ0	PROPN
ejpam-3329	671	8	‖	‖	PROPN
ejpam-3329	671	9	2	2	NUM
ejpam-3329	671	10	−	−	NOUN
ejpam-3329	671	11	(	(	PUNCT
ejpam-3329	671	12	1	1	NUM
ejpam-3329	671	13	+	+	NUM
ejpam-3329	671	14	n)‖π2kβ0	n)‖π2kβ0	ADJ
ejpam-3329	671	15	‖	‖	ADJ
ejpam-3329	671	16	2	2	NUM
ejpam-3329	671	17	+	+	CCONJ
ejpam-3329	671	18	n‖πkβ0	n‖πkβ0	NOUN
ejpam-3329	671	19	‖	‖	ADJ
ejpam-3329	671	20	2	2	NUM
ejpam-3329	671	21	≥	≥	NOUN
ejpam-3329	671	22	0	0	NUM
ejpam-3329	671	23	for	for	ADP
ejpam-3329	671	24	f	f	NOUN
ejpam-3329	671	25	=	=	PUNCT
ejpam-3329	671	26	kβ0	kβ0	ADJ
ejpam-3329	671	27	andφ(0	andφ(0	NOUN
ejpam-3329	671	28	)	)	PUNCT
ejpam-3329	671	29	=	=	SYM
ejpam-3329	671	30	0	0	NUM
ejpam-3329	671	31	⇔	⇔	NOUN
ejpam-3329	671	32	‖π2+n‖2	‖π2+n‖2	PUNCT
ejpam-3329	671	33	−	−	PROPN
ejpam-3329	671	34	(	(	PUNCT
ejpam-3329	671	35	1	1	NUM
ejpam-3329	671	36	+	+	NUM
ejpam-3329	671	37	n)‖π2‖2	n)‖π2‖2	NUM
ejpam-3329	671	38	+	+	CCONJ
ejpam-3329	671	39	n‖π‖2	n‖π‖2	PROPN
ejpam-3329	671	40	≥	≥	NOUN
ejpam-3329	671	41	0	0	NUM
ejpam-3329	671	42	hence	hence	ADV
ejpam-3329	671	43	the	the	DET
ejpam-3329	671	44	theorem	theorem	PROPN
ejpam-3329	671	45	.	.	PUNCT
ejpam-3329	671	46	theorem	theorem	VERB
ejpam-3329	671	47	44	44	NUM
ejpam-3329	671	48	.	.	PUNCT
ejpam-3329	672	1	an	an	DET
ejpam-3329	672	2	operator	operator	NOUN
ejpam-3329	672	3	wφ	wφ	NOUN
ejpam-3329	672	4	is	be	AUX
ejpam-3329	672	5	of	of	ADP
ejpam-3329	672	6	quasi	quasi	ADJ
ejpam-3329	672	7	n	n	CCONJ
ejpam-3329	672	8	-	-	PUNCT
ejpam-3329	672	9	class	class	NOUN
ejpam-3329	672	10	q∗	q∗	NOUN
ejpam-3329	672	11	operator	operator	NOUN
ejpam-3329	672	12	in	in	ADP
ejpam-3329	672	13	h2(β	h2(β	PROPN
ejpam-3329	672	14	)	)	PUNCT
ejpam-3329	673	1	if	if	SCONJ
ejpam-3329	673	2	and	and	CCONJ
ejpam-3329	673	3	only	only	ADV
ejpam-3329	673	4	if	if	SCONJ
ejpam-3329	673	5	(	(	PUNCT
ejpam-3329	673	6	‖π2+n‖2	‖π2+n‖2	DET
ejpam-3329	673	7	+	+	NUM
ejpam-3329	673	8	n‖π‖2)‖kβ0	n‖π‖2)‖kβ0	ADJ
ejpam-3329	673	9	‖2	‖2	NOUN
ejpam-3329	673	10	≥	≥	NOUN
ejpam-3329	673	11	(	(	PUNCT
ejpam-3329	673	12	1	1	NUM
ejpam-3329	673	13	+	+	NUM
ejpam-3329	673	14	n)|π|2‖kβφ(0)‖	n)|π|2‖kβφ(0)‖	NOUN
ejpam-3329	673	15	2	2	NUM
ejpam-3329	673	16	.	.	PUNCT
ejpam-3329	673	17	theorem	theorem	VERB
ejpam-3329	673	18	45	45	NUM
ejpam-3329	673	19	.	.	PUNCT
ejpam-3329	674	1	an	an	DET
ejpam-3329	674	2	operator	operator	NOUN
ejpam-3329	674	3	w	w	ADP
ejpam-3329	674	4	∗φ	∗φ	PROPN
ejpam-3329	674	5	∈	∈	PROPN
ejpam-3329	674	6	h2(β	h2(β	NOUN
ejpam-3329	674	7	)	)	PUNCT
ejpam-3329	674	8	is	be	AUX
ejpam-3329	674	9	of	of	ADP
ejpam-3329	674	10	quasi	quasi	ADJ
ejpam-3329	674	11	n	n	CCONJ
ejpam-3329	674	12	-	-	PUNCT
ejpam-3329	674	13	class	class	NOUN
ejpam-3329	674	14	q∗	q∗	NOUN
ejpam-3329	674	15	if	if	SCONJ
ejpam-3329	675	1	and	and	CCONJ
ejpam-3329	675	2	only	only	ADV
ejpam-3329	675	3	if	if	SCONJ
ejpam-3329	675	4	‖π2+n‖2	‖π2+n‖2	PRON
ejpam-3329	675	5	≥	≥	X
ejpam-3329	675	6	(	(	PUNCT
ejpam-3329	675	7	1	1	NUM
ejpam-3329	675	8	+	+	NUM
ejpam-3329	675	9	n)|π|2	n)|π|2	PROPN
ejpam-3329	675	10	−	−	NOUN
ejpam-3329	675	11	n‖π‖2	n‖π‖2	NOUN
ejpam-3329	675	12	.	.	NOUN
ejpam-3329	675	13	7	7	X
ejpam-3329	675	14	.	.	PUNCT
ejpam-3329	675	15	quasi	quasi	NOUN
ejpam-3329	675	16	n	n	CCONJ
ejpam-3329	675	17	-	-	PUNCT
ejpam-3329	675	18	class	class	NOUN
ejpam-3329	675	19	q	q	NOUN
ejpam-3329	675	20	and	and	CCONJ
ejpam-3329	675	21	quasi	quasi	ADJ
ejpam-3329	675	22	n	n	CCONJ
ejpam-3329	675	23	-	-	PUNCT
ejpam-3329	675	24	class	class	NOUN
ejpam-3329	675	25	q∗	q∗	NOUN
ejpam-3329	675	26	composite	composite	ADJ
ejpam-3329	675	27	multiplication	multiplication	NOUN
ejpam-3329	675	28	operator	operator	NOUN
ejpam-3329	675	29	as	as	ADP
ejpam-3329	675	30	composite	composite	ADJ
ejpam-3329	675	31	multiplication	multiplication	NOUN
ejpam-3329	675	32	operator	operator	NOUN
ejpam-3329	675	33	to	to	ADP
ejpam-3329	675	34	a	a	DET
ejpam-3329	675	35	linear	linear	ADJ
ejpam-3329	675	36	transformation	transformation	NOUN
ejpam-3329	675	37	acting	act	VERB
ejpam-3329	675	38	on	on	ADP
ejpam-3329	675	39	a	a	DET
ejpam-3329	675	40	set	set	NOUN
ejpam-3329	675	41	of	of	ADP
ejpam-3329	675	42	complex	complex	ADJ
ejpam-3329	675	43	value	value	NOUN
ejpam-3329	675	44	σ	σ	X
ejpam-3329	675	45	measurable	measurable	ADJ
ejpam-3329	675	46	functions	function	NOUN
ejpam-3329	675	47	f	f	PROPN
ejpam-3329	675	48	of	of	ADP
ejpam-3329	675	49	the	the	DET
ejpam-3329	675	50	form	form	NOUN
ejpam-3329	675	51	mu	mu	PROPN
ejpam-3329	675	52	,	,	PUNCT
ejpam-3329	675	53	t	t	PROPN
ejpam-3329	675	54	(	(	PUNCT
ejpam-3329	675	55	f	f	X
ejpam-3329	675	56	)	)	PUNCT
ejpam-3329	675	57	=	=	SYM
ejpam-3329	675	58	ctmuf	ctmuf	NOUN
ejpam-3329	675	59	=	=	PUNCT
ejpam-3329	675	60	u	u	NOUN
ejpam-3329	675	61	◦	◦	NOUN
ejpam-3329	675	62	tf	tf	INTJ
ejpam-3329	675	63	◦	◦	NOUN
ejpam-3329	675	64	t	t	NOUN
ejpam-3329	675	65	where	where	SCONJ
ejpam-3329	675	66	u	u	NOUN
ejpam-3329	675	67	is	be	AUX
ejpam-3329	675	68	a	a	DET
ejpam-3329	675	69	complex	complex	ADJ
ejpam-3329	675	70	valued	value	VERB
ejpam-3329	675	71	σ	σ	NUM
ejpam-3329	675	72	measurable	measurable	ADJ
ejpam-3329	675	73	function	function	NOUN
ejpam-3329	675	74	.	.	PUNCT
ejpam-3329	676	1	in	in	ADP
ejpam-3329	676	2	the	the	DET
ejpam-3329	676	3	case	case	NOUN
ejpam-3329	676	4	u	u	NOUN
ejpam-3329	676	5	=	=	SYM
ejpam-3329	676	6	1	1	NUM
ejpam-3329	676	7	a.e	a.e	PROPN
ejpam-3329	676	8	,	,	PUNCT
ejpam-3329	676	9	mu	mu	PROPN
ejpam-3329	676	10	,	,	PUNCT
ejpam-3329	676	11	t	t	PROPN
ejpam-3329	676	12	becomes	become	VERB
ejpam-3329	676	13	a	a	DET
ejpam-3329	676	14	composition	composition	NOUN
ejpam-3329	676	15	operator	operator	NOUN
ejpam-3329	676	16	denoted	denote	VERB
ejpam-3329	676	17	by	by	ADP
ejpam-3329	676	18	ct	ct	PROPN
ejpam-3329	676	19	.	.	PUNCT
ejpam-3329	677	1	proposition	proposition	NOUN
ejpam-3329	677	2	1	1	NUM
ejpam-3329	677	3	.	.	PUNCT
ejpam-3329	678	1	let	let	VERB
ejpam-3329	678	2	the	the	DET
ejpam-3329	678	3	composite	composite	ADJ
ejpam-3329	678	4	multiplication	multiplication	NOUN
ejpam-3329	678	5	operator	operator	NOUN
ejpam-3329	678	6	mu	mu	NOUN
ejpam-3329	678	7	,	,	PUNCT
ejpam-3329	678	8	t	t	PROPN
ejpam-3329	678	9	(	(	PUNCT
ejpam-3329	678	10	f	f	X
ejpam-3329	678	11	)	)	PUNCT
ejpam-3329	678	12	∈	∈	PROPN
ejpam-3329	678	13	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	678	14	)	)	PUNCT
ejpam-3329	678	15	)	)	PUNCT
ejpam-3329	678	16	then	then	ADV
ejpam-3329	678	17	for	for	SCONJ
ejpam-3329	678	18	u	u	PROPN
ejpam-3329	678	19	≥	≥	NUM
ejpam-3329	678	20	0	0	NUM
ejpam-3329	678	21	(	(	PUNCT
ejpam-3329	678	22	i	i	NOUN
ejpam-3329	678	23	)	)	PUNCT
ejpam-3329	678	24	m∗u	m∗u	PROPN
ejpam-3329	678	25	,	,	PUNCT
ejpam-3329	678	26	tmu	tmu	PROPN
ejpam-3329	678	27	,	,	PUNCT
ejpam-3329	678	28	t	t	PROPN
ejpam-3329	678	29	f	f	PROPN
ejpam-3329	678	30	=	=	PUNCT
ejpam-3329	678	31	u2f0f	u2f0f	NUM
ejpam-3329	678	32	.	.	PUNCT
ejpam-3329	679	1	(	(	PUNCT
ejpam-3329	679	2	ii	ii	X
ejpam-3329	679	3	)	)	PUNCT
ejpam-3329	679	4	mu	mu	PROPN
ejpam-3329	679	5	,	,	PUNCT
ejpam-3329	679	6	tm	tm	PROPN
ejpam-3329	679	7	∗	∗	NOUN
ejpam-3329	679	8	u	u	PROPN
ejpam-3329	679	9	,	,	PUNCT
ejpam-3329	679	10	t	t	PROPN
ejpam-3329	679	11	f	f	PROPN
ejpam-3329	680	1	=	=	PRON
ejpam-3329	681	1	(	(	PUNCT
ejpam-3329	681	2	u2	u2	PROPN
ejpam-3329	681	3	◦	◦	PROPN
ejpam-3329	681	4	t	t	PROPN
ejpam-3329	681	5	)	)	PUNCT
ejpam-3329	681	6	(	(	PUNCT
ejpam-3329	681	7	f0	f0	PROPN
ejpam-3329	681	8	◦	◦	PROPN
ejpam-3329	681	9	t	t	PROPN
ejpam-3329	681	10	)	)	PUNCT
ejpam-3329	681	11	.e(f	.e(f	PROPN
ejpam-3329	681	12	)	)	PUNCT
ejpam-3329	681	13	.	.	PUNCT
ejpam-3329	682	1	since	since	SCONJ
ejpam-3329	682	2	mu	mu	PROPN
ejpam-3329	682	3	,	,	PUNCT
ejpam-3329	682	4	t	t	PROPN
ejpam-3329	682	5	(	(	PUNCT
ejpam-3329	682	6	f	f	X
ejpam-3329	682	7	)	)	PUNCT
ejpam-3329	682	8	=	=	SYM
ejpam-3329	682	9	ctmuf	ctmuf	NOUN
ejpam-3329	682	10	=	=	PUNCT
ejpam-3329	682	11	u	u	NOUN
ejpam-3329	682	12	◦	◦	NOUN
ejpam-3329	682	13	tf	tf	NOUN
ejpam-3329	682	14	◦	◦	NOUN
ejpam-3329	682	15	t	t	PROPN
ejpam-3329	682	16	mn	mn	PROPN
ejpam-3329	682	17	u	u	PROPN
ejpam-3329	682	18	,	,	PUNCT
ejpam-3329	682	19	t	t	PROPN
ejpam-3329	682	20	(	(	PUNCT
ejpam-3329	682	21	f	f	X
ejpam-3329	682	22	)	)	PUNCT
ejpam-3329	682	23	=	=	SYM
ejpam-3329	682	24	(	(	PUNCT
ejpam-3329	682	25	ctmu)n(f	ctmu)n(f	PROPN
ejpam-3329	682	26	)	)	PUNCT
ejpam-3329	682	27	=	=	SYM
ejpam-3329	682	28	un(f	un(f	PUNCT
ejpam-3329	682	29	◦	◦	NOUN
ejpam-3329	682	30	t	t	NOUN
ejpam-3329	682	31	)	)	PUNCT
ejpam-3329	682	32	2	2	NUM
ejpam-3329	682	33	and	and	CCONJ
ejpam-3329	682	34	m∗u	m∗u	NUM
ejpam-3329	682	35	,	,	PUNCT
ejpam-3329	682	36	t	t	PROPN
ejpam-3329	682	37	(	(	PUNCT
ejpam-3329	682	38	f	f	X
ejpam-3329	682	39	)	)	PUNCT
ejpam-3329	682	40	=	=	SYM
ejpam-3329	682	41	uf0.e(f	uf0.e(f	PROPN
ejpam-3329	682	42	)	)	PUNCT
ejpam-3329	682	43	◦	◦	NOUN
ejpam-3329	682	44	t−1	t−1	PROPN
ejpam-3329	682	45	m∗nu	m∗nu	PROPN
ejpam-3329	682	46	,	,	PUNCT
ejpam-3329	682	47	t	t	PROPN
ejpam-3329	682	48	(	(	PUNCT
ejpam-3329	682	49	f	f	X
ejpam-3329	682	50	)	)	PUNCT
ejpam-3329	682	51	=	=	PUNCT
ejpam-3329	682	52	uf0.e(uf0	uf0.e(uf0	ADJ
ejpam-3329	682	53	)	)	PUNCT
ejpam-3329	682	54	◦	◦	NOUN
ejpam-3329	682	55	t−(n−1).e(f	t−(n−1).e(f	NUM
ejpam-3329	682	56	)	)	PUNCT
ejpam-3329	682	57	◦	◦	NOUN
ejpam-3329	682	58	t−n	t−n	NOUN
ejpam-3329	682	59	where	where	SCONJ
ejpam-3329	682	60	e(uf0	e(uf0	NOUN
ejpam-3329	682	61	)	)	PUNCT
ejpam-3329	682	62	◦	◦	NOUN
ejpam-3329	682	63	t−(n−1	t−(n−1	ADJ
ejpam-3329	682	64	)	)	PUNCT
ejpam-3329	682	65	=	=	SYM
ejpam-3329	682	66	e(uf0	e(uf0	X
ejpam-3329	682	67	)	)	PUNCT
ejpam-3329	682	68	◦	◦	PROPN
ejpam-3329	682	69	t−1	t−1	PROPN
ejpam-3329	682	70	,	,	PUNCT
ejpam-3329	682	71	e(uf0	e(uf0	ADJ
ejpam-3329	682	72	)	)	PUNCT
ejpam-3329	682	73	◦	◦	NOUN
ejpam-3329	682	74	t−2	t−2	PROPN
ejpam-3329	682	75	,	,	PUNCT
ejpam-3329	682	76	...	...	PUNCT
ejpam-3329	682	77	,	,	PUNCT
ejpam-3329	682	78	e(uf0	e(uf0	X
ejpam-3329	682	79	)	)	PUNCT
ejpam-3329	682	80	◦	◦	NOUN
ejpam-3329	682	81	t−(n−1	t−(n−1	ADJ
ejpam-3329	682	82	)	)	PUNCT
ejpam-3329	682	83	e(uf0	e(uf0	ADJ
ejpam-3329	682	84	)	)	PUNCT
ejpam-3329	682	85	◦	◦	VERB
ejpam-3329	682	86	tn−1	tn−1	PROPN
ejpam-3329	682	87	=	=	SYM
ejpam-3329	682	88	e(uf0	e(uf0	ADJ
ejpam-3329	682	89	)	)	PUNCT
ejpam-3329	682	90	◦	◦	NOUN
ejpam-3329	682	91	t	t	PROPN
ejpam-3329	682	92	1	1	NUM
ejpam-3329	682	93	,	,	PUNCT
ejpam-3329	682	94	e(uf0	e(uf0	ADJ
ejpam-3329	682	95	)	)	PUNCT
ejpam-3329	682	96	◦	◦	NOUN
ejpam-3329	682	97	t	t	PROPN
ejpam-3329	682	98	2	2	NUM
ejpam-3329	682	99	,	,	PUNCT
ejpam-3329	682	100	...	...	PUNCT
ejpam-3329	682	101	,	,	PUNCT
ejpam-3329	682	102	e(uf0	e(uf0	X
ejpam-3329	682	103	)	)	PUNCT
ejpam-3329	682	104	◦	◦	VERB
ejpam-3329	682	105	tn−1	tn−1	ADJ
ejpam-3329	682	106	in	in	ADP
ejpam-3329	682	107	this	this	DET
ejpam-3329	682	108	section	section	NOUN
ejpam-3329	682	109	,	,	PUNCT
ejpam-3329	682	110	we	we	PRON
ejpam-3329	682	111	study	study	VERB
ejpam-3329	682	112	quasi	quasi	NOUN
ejpam-3329	682	113	n	n	CCONJ
ejpam-3329	682	114	-	-	PUNCT
ejpam-3329	682	115	class	class	NOUN
ejpam-3329	682	116	q	q	NOUN
ejpam-3329	682	117	and	and	CCONJ
ejpam-3329	682	118	quasi	quasi	ADJ
ejpam-3329	682	119	n	n	CCONJ
ejpam-3329	682	120	-	-	PUNCT
ejpam-3329	682	121	class	class	NOUN
ejpam-3329	682	122	q∗	q∗	NOUN
ejpam-3329	682	123	composite	composite	ADJ
ejpam-3329	682	124	multiplication	multiplication	NOUN
ejpam-3329	682	125	operator	operator	NOUN
ejpam-3329	682	126	as	as	SCONJ
ejpam-3329	682	127	follows	follow	VERB
ejpam-3329	682	128	.	.	PUNCT
ejpam-3329	683	1	theorem	theorem	ADJ
ejpam-3329	683	2	46	46	NUM
ejpam-3329	683	3	.	.	PUNCT
ejpam-3329	684	1	let	let	VERB
ejpam-3329	684	2	the	the	DET
ejpam-3329	684	3	composite	composite	ADJ
ejpam-3329	684	4	multiplication	multiplication	NOUN
ejpam-3329	684	5	operator	operator	NOUN
ejpam-3329	684	6	mu	mu	NOUN
ejpam-3329	684	7	,	,	PUNCT
ejpam-3329	684	8	t	t	PROPN
ejpam-3329	684	9	∈	∈	PROPN
ejpam-3329	684	10	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	684	11	)	)	PUNCT
ejpam-3329	684	12	)	)	PUNCT
ejpam-3329	684	13	.	.	PUNCT
ejpam-3329	685	1	then	then	ADV
ejpam-3329	685	2	mu	mu	PROPN
ejpam-3329	685	3	,	,	PUNCT
ejpam-3329	685	4	t	t	PROPN
ejpam-3329	685	5	is	be	AUX
ejpam-3329	685	6	quasi	quasi	NOUN
ejpam-3329	685	7	n	n	X
ejpam-3329	685	8	class	class	NOUN
ejpam-3329	685	9	q	q	NOUN
ejpam-3329	685	10	if	if	SCONJ
ejpam-3329	686	1	and	and	CCONJ
ejpam-3329	686	2	only	only	ADV
ejpam-3329	686	3	if	if	SCONJ
ejpam-3329	686	4	uf0.e(uf0)	uf0.e(uf0)	PROPN
ejpam-3329	686	5	◦	◦	NOUN
ejpam-3329	686	6	t−(1+n).e(u2+n)	t−(1+n).e(u2+n)	ADJ
ejpam-3329	686	7	◦	◦	NOUN
ejpam-3329	686	8	t−(2+n)−(1+n)uf0.e(uf0	t−(2+n)−(1+n)uf0.e(uf0	NUM
ejpam-3329	686	9	)	)	PUNCT
ejpam-3329	686	10	◦	◦	NOUN
ejpam-3329	686	11	t−1.e(u2	t−1.e(u2	PROPN
ejpam-3329	686	12	)	)	PUNCT
ejpam-3329	686	13	◦	◦	NOUN
ejpam-3329	686	14	t−2	t−2	NOUN
ejpam-3329	686	15	+	+	CCONJ
ejpam-3329	686	16	nu2f0	nu2f0	PROPN
ejpam-3329	686	17	≥	≥	NOUN
ejpam-3329	686	18	0	0	NUM
ejpam-3329	686	19	.	.	PUNCT
ejpam-3329	687	1	a.e	a.e	PROPN
ejpam-3329	687	2	.	.	PROPN
ejpam-3329	687	3	d.	d.	PROPN
ejpam-3329	687	4	senthilkumar	senthilkumar	PROPN
ejpam-3329	687	5	,	,	PUNCT
ejpam-3329	687	6	s.	s.	PROPN
ejpam-3329	687	7	parvatham	parvatham	PROPN
ejpam-3329	687	8	/	/	SYM
ejpam-3329	687	9	eur	eur	PROPN
ejpam-3329	687	10	.	.	PUNCT
ejpam-3329	688	1	j.	j.	PROPN
ejpam-3329	688	2	pure	pure	PROPN
ejpam-3329	688	3	appl	appl	PROPN
ejpam-3329	688	4	.	.	PROPN
ejpam-3329	688	5	math	math	PROPN
ejpam-3329	688	6	,	,	PUNCT
ejpam-3329	688	7	11	11	NUM
ejpam-3329	688	8	(	(	PUNCT
ejpam-3329	688	9	4	4	NUM
ejpam-3329	688	10	)	)	PUNCT
ejpam-3329	688	11	(	(	PUNCT
ejpam-3329	688	12	2018	2018	NUM
ejpam-3329	688	13	)	)	PUNCT
ejpam-3329	688	14	,	,	PUNCT
ejpam-3329	688	15	1108	1108	NUM
ejpam-3329	688	16	-	-	SYM
ejpam-3329	688	17	1129	1129	NUM
ejpam-3329	688	18	1126	1126	NUM
ejpam-3329	688	19	proof	proof	NOUN
ejpam-3329	688	20	.	.	PUNCT
ejpam-3329	689	1	suppose	suppose	VERB
ejpam-3329	689	2	mu	mu	PROPN
ejpam-3329	689	3	,	,	PUNCT
ejpam-3329	689	4	t	t	PROPN
ejpam-3329	689	5	is	be	AUX
ejpam-3329	689	6	quasi	quasi	NOUN
ejpam-3329	689	7	n	n	PRON
ejpam-3329	689	8	class	class	NOUN
ejpam-3329	689	9	q	q	NOUN
ejpam-3329	689	10	operator	operator	NOUN
ejpam-3329	689	11	,	,	PUNCT
ejpam-3329	689	12	then	then	ADV
ejpam-3329	689	13	m∗2+nu	m∗2+nu	PROPN
ejpam-3329	689	14	,	,	PUNCT
ejpam-3329	689	15	t	t	PROPN
ejpam-3329	689	16	m2+n	m2+n	PROPN
ejpam-3329	689	17	u	u	PROPN
ejpam-3329	689	18	,	,	PUNCT
ejpam-3329	689	19	t	t	PROPN
ejpam-3329	690	1	−	−	PROPN
ejpam-3329	690	2	(	(	PUNCT
ejpam-3329	690	3	1	1	NUM
ejpam-3329	690	4	+	+	CCONJ
ejpam-3329	690	5	n)m∗2u	n)m∗2u	PROPN
ejpam-3329	690	6	,	,	PUNCT
ejpam-3329	690	7	tm	tm	PRON
ejpam-3329	690	8	2	2	NUM
ejpam-3329	690	9	u	u	NOUN
ejpam-3329	690	10	,	,	PUNCT
ejpam-3329	690	11	t	t	PROPN
ejpam-3329	690	12	+	+	CCONJ
ejpam-3329	690	13	nm∗u	nm∗u	PROPN
ejpam-3329	690	14	,	,	PUNCT
ejpam-3329	690	15	tmu	tmu	PROPN
ejpam-3329	690	16	,	,	PUNCT
ejpam-3329	690	17	t	t	PROPN
ejpam-3329	690	18	≥	≥	NOUN
ejpam-3329	690	19	0	0	PUNCT
ejpam-3329	690	20	then	then	ADV
ejpam-3329	690	21	for	for	ADP
ejpam-3329	690	22	any	any	DET
ejpam-3329	690	23	f	f	PROPN
ejpam-3329	690	24	∈	∈	PROPN
ejpam-3329	690	25	l2(λ	l2(λ	PROPN
ejpam-3329	690	26	)	)	PUNCT
ejpam-3329	690	27	,	,	PUNCT
ejpam-3329	690	28	we	we	PRON
ejpam-3329	690	29	have	have	VERB
ejpam-3329	690	30	〈	〈	PROPN
ejpam-3329	690	31	(	(	PUNCT
ejpam-3329	690	32	m∗2+nu	m∗2+nu	PROPN
ejpam-3329	690	33	,	,	PUNCT
ejpam-3329	690	34	t	t	PROPN
ejpam-3329	690	35	m2+n	m2+n	PROPN
ejpam-3329	690	36	u	u	PROPN
ejpam-3329	690	37	,	,	PUNCT
ejpam-3329	690	38	t	t	PROPN
ejpam-3329	690	39	−	−	PROPN
ejpam-3329	691	1	(	(	PUNCT
ejpam-3329	691	2	1	1	NUM
ejpam-3329	691	3	+	+	CCONJ
ejpam-3329	691	4	n)m∗2u	n)m∗2u	PROPN
ejpam-3329	691	5	,	,	PUNCT
ejpam-3329	691	6	tm	tm	PRON
ejpam-3329	691	7	2	2	NUM
ejpam-3329	691	8	u	u	NOUN
ejpam-3329	691	9	,	,	PUNCT
ejpam-3329	691	10	t	t	PROPN
ejpam-3329	691	11	+	+	CCONJ
ejpam-3329	691	12	nm∗u	nm∗u	PROPN
ejpam-3329	691	13	,	,	PUNCT
ejpam-3329	691	14	tmu	tmu	PROPN
ejpam-3329	691	15	,	,	PUNCT
ejpam-3329	691	16	t	t	PROPN
ejpam-3329	691	17	)	)	PUNCT
ejpam-3329	692	1	f	f	X
ejpam-3329	692	2	,	,	PUNCT
ejpam-3329	692	3	f	f	PROPN
ejpam-3329	692	4	〉	〉	PROPN
ejpam-3329	692	5	≥	≥	NOUN
ejpam-3329	692	6	0	0	NUM
ejpam-3329	693	1	〈	〈	PROPN
ejpam-3329	693	2	m∗2+nu	m∗2+nu	PROPN
ejpam-3329	693	3	,	,	PUNCT
ejpam-3329	693	4	t	t	PROPN
ejpam-3329	693	5	m2+n	m2+n	PROPN
ejpam-3329	693	6	u	u	PROPN
ejpam-3329	693	7	,	,	PUNCT
ejpam-3329	693	8	t	t	PROPN
ejpam-3329	693	9	f	f	NUM
ejpam-3329	693	10	,	,	PUNCT
ejpam-3329	693	11	f	f	PROPN
ejpam-3329	693	12	〉	〉	NUM
ejpam-3329	693	13	−	−	PROPN
ejpam-3329	693	14	(	(	PUNCT
ejpam-3329	693	15	1	1	NUM
ejpam-3329	693	16	+	+	NUM
ejpam-3329	693	17	n)〈m∗2u	n)〈m∗2u	ADJ
ejpam-3329	693	18	,	,	PUNCT
ejpam-3329	693	19	tm2	tm2	ADJ
ejpam-3329	693	20	u	u	NOUN
ejpam-3329	693	21	,	,	PUNCT
ejpam-3329	693	22	t	t	PROPN
ejpam-3329	693	23	f	f	NUM
ejpam-3329	693	24	,	,	PUNCT
ejpam-3329	693	25	f〉+	f〉+	PROPN
ejpam-3329	693	26	n〈m∗u	n〈m∗u	ADJ
ejpam-3329	693	27	,	,	PUNCT
ejpam-3329	693	28	tmu	tmu	PROPN
ejpam-3329	693	29	,	,	PUNCT
ejpam-3329	693	30	t	t	PROPN
ejpam-3329	693	31	f	f	PROPN
ejpam-3329	693	32	,	,	PUNCT
ejpam-3329	693	33	f	f	PROPN
ejpam-3329	693	34	〉	〉	PROPN
ejpam-3329	693	35	≥	≥	NOUN
ejpam-3329	693	36	0	0	NUM
ejpam-3329	693	37	since	since	SCONJ
ejpam-3329	693	38	m∗ku	m∗ku	NOUN
ejpam-3329	693	39	,	,	PUNCT
ejpam-3329	693	40	tm	tm	PROPN
ejpam-3329	693	41	k	k	PROPN
ejpam-3329	693	42	u	u	PROPN
ejpam-3329	693	43	,	,	PUNCT
ejpam-3329	693	44	t	t	PROPN
ejpam-3329	693	45	=	=	SYM
ejpam-3329	693	46	uf0.e(uf0	uf0.e(uf0	ADJ
ejpam-3329	693	47	)	)	PUNCT
ejpam-3329	693	48	◦	◦	NOUN
ejpam-3329	693	49	t−(k−1).e(f	t−(k−1).e(f	NUM
ejpam-3329	693	50	)	)	PUNCT
ejpam-3329	693	51	◦	◦	NOUN
ejpam-3329	693	52	t−n	t−n	PROPN
ejpam-3329	693	53	mk	mk	PROPN
ejpam-3329	693	54	u	u	PROPN
ejpam-3329	693	55	,	,	PUNCT
ejpam-3329	693	56	tm	tm	PROPN
ejpam-3329	693	57	∗k	∗k	PROPN
ejpam-3329	693	58	u	u	PROPN
ejpam-3329	693	59	,	,	PUNCT
ejpam-3329	693	60	t	t	NOUN
ejpam-3329	693	61	=	=	PUNCT
ejpam-3329	693	62	uk.u	uk.u	NOUN
ejpam-3329	693	63	◦	◦	PROPN
ejpam-3329	693	64	t	t	PROPN
ejpam-3329	693	65	k.f0	k.f0	NOUN
ejpam-3329	693	66	◦	◦	PROPN
ejpam-3329	693	67	t	t	PROPN
ejpam-3329	693	68	k.e(uf0	k.e(uf0	PROPN
ejpam-3329	693	69	)	)	PUNCT
ejpam-3329	693	70	◦	◦	NOUN
ejpam-3329	693	71	t	t	PROPN
ejpam-3329	693	72	k−1.e(f	k−1.e(f	PROPN
ejpam-3329	693	73	)	)	PUNCT
ejpam-3329	693	74	where	where	SCONJ
ejpam-3329	693	75	uk	uk	PROPN
ejpam-3329	693	76	=	=	SYM
ejpam-3329	693	77	u	u	PROPN
ejpam-3329	693	78	◦	◦	NOUN
ejpam-3329	693	79	t.u	t.u	PROPN
ejpam-3329	693	80	◦	◦	NOUN
ejpam-3329	693	81	t	t	PROPN
ejpam-3329	693	82	2	2	NUM
ejpam-3329	693	83	...	...	SYM
ejpam-3329	693	84	u	u	NOUN
ejpam-3329	693	85	◦	◦	NOUN
ejpam-3329	693	86	t	t	X
ejpam-3329	693	87	k	k	PROPN
ejpam-3329	693	88	⇔	⇔	PROPN
ejpam-3329	693	89	〈	〈	PROPN
ejpam-3329	693	90	(	(	PUNCT
ejpam-3329	693	91	uf0.e(uf0	uf0.e(uf0	NOUN
ejpam-3329	693	92	)	)	PUNCT
ejpam-3329	693	93	◦	◦	NOUN
ejpam-3329	693	94	t−(1+n).e(u2+n	t−(1+n).e(u2+n	NOUN
ejpam-3329	693	95	)	)	PUNCT
ejpam-3329	693	96	◦	◦	NOUN
ejpam-3329	693	97	t−(2+n))f	t−(2+n))f	NOUN
ejpam-3329	693	98	,	,	PUNCT
ejpam-3329	693	99	f〉−	f〉−	NOUN
ejpam-3329	693	100	(	(	PUNCT
ejpam-3329	693	101	1	1	NUM
ejpam-3329	693	102	+	+	CCONJ
ejpam-3329	693	103	n)〈(uf0.e(uf0	n)〈(uf0.e(uf0	PROPN
ejpam-3329	693	104	)	)	PUNCT
ejpam-3329	693	105	◦	◦	NOUN
ejpam-3329	693	106	t−1.e(u2	t−1.e(u2	PROPN
ejpam-3329	693	107	)	)	PUNCT
ejpam-3329	693	108	◦	◦	NOUN
ejpam-3329	693	109	t−2)f	t−2)f	PROPN
ejpam-3329	693	110	,	,	PUNCT
ejpam-3329	693	111	f〉+	f〉+	PROPN
ejpam-3329	693	112	n〈(u2f0)f	n〈(u2f0)f	NUM
ejpam-3329	693	113	,	,	PUNCT
ejpam-3329	693	114	f	f	PROPN
ejpam-3329	693	115	〉	〉	PROPN
ejpam-3329	693	116	≥	≥	NOUN
ejpam-3329	693	117	0	0	NUM
ejpam-3329	693	118	⇔	⇔	NUM
ejpam-3329	693	119	∫	∫	PROPN
ejpam-3329	693	120	e	e	PROPN
ejpam-3329	693	121	(	(	PUNCT
ejpam-3329	693	122	uf0.e(uf0	uf0.e(uf0	ADJ
ejpam-3329	693	123	)	)	PUNCT
ejpam-3329	693	124	◦	◦	NOUN
ejpam-3329	693	125	t−(1+n).e(u2+n	t−(1+n).e(u2+n	NOUN
ejpam-3329	693	126	)	)	PUNCT
ejpam-3329	693	127	◦	◦	NOUN
ejpam-3329	693	128	t−(2+n	t−(2+n	NOUN
ejpam-3329	693	129	)	)	PUNCT
ejpam-3329	694	1	−	−	PROPN
ejpam-3329	694	2	(	(	PUNCT
ejpam-3329	694	3	1	1	NUM
ejpam-3329	694	4	+	+	CCONJ
ejpam-3329	694	5	n)uf0.e(uf0	n)uf0.e(uf0	NOUN
ejpam-3329	694	6	)	)	PUNCT
ejpam-3329	694	7	◦	◦	NOUN
ejpam-3329	694	8	t−1	t−1	PROPN
ejpam-3329	694	9	.e(u2	.e(u2	PUNCT
ejpam-3329	694	10	)	)	PUNCT
ejpam-3329	695	1	◦	◦	NOUN
ejpam-3329	695	2	t−2	t−2	NOUN
ejpam-3329	695	3	+	+	CCONJ
ejpam-3329	695	4	nu2f0)dλ	nu2f0)dλ	PROPN
ejpam-3329	695	5	≥	≥	NOUN
ejpam-3329	695	6	0	0	NUM
ejpam-3329	695	7	⇔	⇔	X
ejpam-3329	695	8	uf0.e(uf0	uf0.e(uf0	NOUN
ejpam-3329	695	9	)	)	PUNCT
ejpam-3329	695	10	◦	◦	NOUN
ejpam-3329	695	11	t−(1+n).e(u2+n	t−(1+n).e(u2+n	NOUN
ejpam-3329	695	12	)	)	PUNCT
ejpam-3329	695	13	◦	◦	NOUN
ejpam-3329	695	14	t−(2+n	t−(2+n	NOUN
ejpam-3329	695	15	)	)	PUNCT
ejpam-3329	695	16	−	−	PROPN
ejpam-3329	696	1	(	(	PUNCT
ejpam-3329	696	2	1	1	NUM
ejpam-3329	696	3	+	+	CCONJ
ejpam-3329	696	4	n)uf0.e(uf0	n)uf0.e(uf0	NOUN
ejpam-3329	696	5	)	)	PUNCT
ejpam-3329	696	6	◦	◦	NOUN
ejpam-3329	696	7	t−1	t−1	PROPN
ejpam-3329	696	8	.e(u2	.e(u2	PUNCT
ejpam-3329	696	9	)	)	PUNCT
ejpam-3329	697	1	◦	◦	NOUN
ejpam-3329	697	2	t−2	t−2	NOUN
ejpam-3329	697	3	+	+	CCONJ
ejpam-3329	697	4	nu2f0	nu2f0	ADJ
ejpam-3329	697	5	≥	≥	NUM
ejpam-3329	697	6	0	0	NUM
ejpam-3329	697	7	a.e	a.e	NOUN
ejpam-3329	697	8	corollary	corollary	NOUN
ejpam-3329	697	9	22	22	NUM
ejpam-3329	697	10	.	.	PUNCT
ejpam-3329	698	1	if	if	SCONJ
ejpam-3329	698	2	the	the	DET
ejpam-3329	698	3	composition	composition	NOUN
ejpam-3329	698	4	operator	operator	NOUN
ejpam-3329	698	5	ct	ct	PROPN
ejpam-3329	698	6	∈	∈	PROPN
ejpam-3329	698	7	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	698	8	)	)	PUNCT
ejpam-3329	698	9	)	)	PUNCT
ejpam-3329	698	10	then	then	ADV
ejpam-3329	698	11	ct	ct	PROPN
ejpam-3329	698	12	is	be	AUX
ejpam-3329	698	13	quasi	quasi	NOUN
ejpam-3329	698	14	n	n	X
ejpam-3329	698	15	class	class	NOUN
ejpam-3329	698	16	q	q	NOUN
ejpam-3329	698	17	if	if	SCONJ
ejpam-3329	699	1	and	and	CCONJ
ejpam-3329	699	2	only	only	ADV
ejpam-3329	699	3	if	if	SCONJ
ejpam-3329	699	4	f0.e(f0	f0.e(f0	ADJ
ejpam-3329	699	5	)	)	PUNCT
ejpam-3329	699	6	◦	◦	NOUN
ejpam-3329	699	7	t−(1+n	t−(1+n	NOUN
ejpam-3329	699	8	)	)	PUNCT
ejpam-3329	700	1	−	−	PROPN
ejpam-3329	700	2	(	(	PUNCT
ejpam-3329	700	3	1	1	NUM
ejpam-3329	700	4	+	+	NUM
ejpam-3329	700	5	n)f0.e(f0	n)f0.e(f0	NOUN
ejpam-3329	700	6	)	)	PUNCT
ejpam-3329	700	7	◦	◦	NOUN
ejpam-3329	700	8	t−1	t−1	PROPN
ejpam-3329	701	1	+	+	CCONJ
ejpam-3329	701	2	nf0	nf0	PROPN
ejpam-3329	701	3	≥	≥	NOUN
ejpam-3329	701	4	0	0	NUM
ejpam-3329	701	5	.	.	PUNCT
ejpam-3329	702	1	a.e	a.e	PROPN
ejpam-3329	702	2	.	.	PROPN
ejpam-3329	702	3	proof	proof	NOUN
ejpam-3329	702	4	.	.	PUNCT
ejpam-3329	703	1	by	by	ADP
ejpam-3329	703	2	putting	put	VERB
ejpam-3329	703	3	u	u	NOUN
ejpam-3329	703	4	=	=	NOUN
ejpam-3329	703	5	1	1	NUM
ejpam-3329	703	6	in	in	ADP
ejpam-3329	703	7	theorem	theorem	NOUN
ejpam-3329	703	8	46	46	NUM
ejpam-3329	703	9	,	,	PUNCT
ejpam-3329	703	10	we	we	PRON
ejpam-3329	703	11	get	get	VERB
ejpam-3329	703	12	the	the	DET
ejpam-3329	703	13	result	result	NOUN
ejpam-3329	703	14	.	.	PUNCT
ejpam-3329	704	1	theorem	theorem	VERB
ejpam-3329	704	2	47	47	NUM
ejpam-3329	704	3	.	.	PUNCT
ejpam-3329	705	1	let	let	VERB
ejpam-3329	705	2	the	the	DET
ejpam-3329	705	3	composite	composite	ADJ
ejpam-3329	705	4	multiplication	multiplication	NOUN
ejpam-3329	705	5	operator	operator	NOUN
ejpam-3329	705	6	mu	mu	NOUN
ejpam-3329	705	7	,	,	PUNCT
ejpam-3329	705	8	t	t	PROPN
ejpam-3329	705	9	∈	∈	PROPN
ejpam-3329	705	10	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	705	11	)	)	PUNCT
ejpam-3329	705	12	)	)	PUNCT
ejpam-3329	705	13	.	.	PUNCT
ejpam-3329	706	1	then	then	ADV
ejpam-3329	706	2	m∗u	m∗u	NUM
ejpam-3329	706	3	,	,	PUNCT
ejpam-3329	706	4	t	t	PROPN
ejpam-3329	706	5	is	be	AUX
ejpam-3329	706	6	quasi	quasi	NOUN
ejpam-3329	706	7	n	n	X
ejpam-3329	706	8	class	class	NOUN
ejpam-3329	706	9	q	q	NOUN
ejpam-3329	707	1	if	if	SCONJ
ejpam-3329	708	1	and	and	CCONJ
ejpam-3329	708	2	only	only	ADV
ejpam-3329	708	3	if	if	SCONJ
ejpam-3329	708	4	u2+n.u	u2+n.u	PROPN
ejpam-3329	708	5	◦	◦	NOUN
ejpam-3329	708	6	t	t	NOUN
ejpam-3329	708	7	2+n.f0	2+n.f0	NUM
ejpam-3329	708	8	◦	◦	NOUN
ejpam-3329	708	9	t	t	X
ejpam-3329	708	10	2+n.e(uf0	2+n.e(uf0	NUM
ejpam-3329	708	11	)	)	PUNCT
ejpam-3329	708	12	◦	◦	NOUN
ejpam-3329	708	13	t	t	NOUN
ejpam-3329	708	14	1+n.e(f)−	1+n.e(f)−	NUM
ejpam-3329	708	15	(	(	PUNCT
ejpam-3329	708	16	1	1	NUM
ejpam-3329	708	17	+	+	NOUN
ejpam-3329	708	18	n)u2(u	n)u2(u	NOUN
ejpam-3329	708	19	◦	◦	NOUN
ejpam-3329	708	20	t	t	PROPN
ejpam-3329	708	21	2)(f0	2)(f0	NUM
ejpam-3329	708	22	◦	◦	NOUN
ejpam-3329	708	23	t	t	PROPN
ejpam-3329	708	24	2).e(uf0	2).e(uf0	NUM
ejpam-3329	708	25	)	)	PUNCT
ejpam-3329	708	26	◦	◦	NOUN
ejpam-3329	708	27	te(f	te(f	PUNCT
ejpam-3329	708	28	)	)	PUNCT
ejpam-3329	709	1	+	+	CCONJ
ejpam-3329	709	2	n(u2	n(u2	PROPN
ejpam-3329	709	3	◦	◦	NOUN
ejpam-3329	709	4	t	t	PROPN
ejpam-3329	709	5	)	)	PUNCT
ejpam-3329	709	6	(	(	PUNCT
ejpam-3329	709	7	f0	f0	PROPN
ejpam-3329	709	8	◦	◦	PROPN
ejpam-3329	709	9	t	t	PROPN
ejpam-3329	709	10	)	)	PUNCT
ejpam-3329	709	11	.e(f	.e(f	PROPN
ejpam-3329	709	12	)	)	PUNCT
ejpam-3329	709	13	≥	≥	NOUN
ejpam-3329	709	14	0	0	NUM
ejpam-3329	709	15	.	.	PUNCT
ejpam-3329	710	1	a.e	a.e	PROPN
ejpam-3329	710	2	.	.	PROPN
ejpam-3329	710	3	proof	proof	NOUN
ejpam-3329	710	4	.	.	PUNCT
ejpam-3329	711	1	supposem∗u	supposem∗u	PROPN
ejpam-3329	711	2	,	,	PUNCT
ejpam-3329	711	3	t	t	PROPN
ejpam-3329	711	4	is	be	AUX
ejpam-3329	711	5	quasi	quasi	NOUN
ejpam-3329	711	6	n	n	X
ejpam-3329	711	7	classq	classq	NOUN
ejpam-3329	711	8	operator	operator	NOUN
ejpam-3329	711	9	,	,	PUNCT
ejpam-3329	711	10	thenm2+n	thenm2+n	PUNCT
ejpam-3329	711	11	u	u	PROPN
ejpam-3329	711	12	,	,	PUNCT
ejpam-3329	711	13	t	t	PROPN
ejpam-3329	711	14	m∗2+nu	m∗2+nu	PROPN
ejpam-3329	711	15	,	,	PUNCT
ejpam-3329	711	16	t	t	PROPN
ejpam-3329	711	17	−(1+n)m2	−(1+n)m2	PROPN
ejpam-3329	711	18	u	u	NOUN
ejpam-3329	711	19	,	,	PUNCT
ejpam-3329	711	20	tm	tm	PROPN
ejpam-3329	711	21	∗2	∗2	PROPN
ejpam-3329	711	22	u	u	PROPN
ejpam-3329	711	23	,	,	PUNCT
ejpam-3329	711	24	t+	t+	NOUN
ejpam-3329	711	25	nmu	nmu	NOUN
ejpam-3329	711	26	,	,	PUNCT
ejpam-3329	711	27	tm	tm	PROPN
ejpam-3329	711	28	∗	∗	NOUN
ejpam-3329	711	29	u	u	PROPN
ejpam-3329	711	30	,	,	PUNCT
ejpam-3329	711	31	t	t	PROPN
ejpam-3329	711	32	≥	≥	NOUN
ejpam-3329	711	33	0	0	PUNCT
ejpam-3329	712	1	then	then	ADV
ejpam-3329	712	2	for	for	ADP
ejpam-3329	712	3	any	any	DET
ejpam-3329	712	4	f	f	PROPN
ejpam-3329	712	5	∈	∈	PROPN
ejpam-3329	712	6	l2(λ	l2(λ	PROPN
ejpam-3329	712	7	)	)	PUNCT
ejpam-3329	712	8	,	,	PUNCT
ejpam-3329	712	9	we	we	PRON
ejpam-3329	712	10	have	have	VERB
ejpam-3329	712	11	〈	〈	PROPN
ejpam-3329	712	12	(	(	PUNCT
ejpam-3329	712	13	m2+n	m2+n	NOUN
ejpam-3329	712	14	u	u	PROPN
ejpam-3329	712	15	,	,	PUNCT
ejpam-3329	712	16	t	t	PROPN
ejpam-3329	712	17	m∗2+nu	m∗2+nu	PROPN
ejpam-3329	712	18	,	,	PUNCT
ejpam-3329	712	19	t	t	PROPN
ejpam-3329	712	20	−	−	PROPN
ejpam-3329	713	1	(	(	PUNCT
ejpam-3329	713	2	1	1	NUM
ejpam-3329	713	3	+	+	CCONJ
ejpam-3329	713	4	n)m2	n)m2	PROPN
ejpam-3329	713	5	u	u	NOUN
ejpam-3329	713	6	,	,	PUNCT
ejpam-3329	713	7	tm	tm	PROPN
ejpam-3329	713	8	∗2	∗2	PROPN
ejpam-3329	713	9	u	u	PROPN
ejpam-3329	713	10	,	,	PUNCT
ejpam-3329	713	11	t	t	PROPN
ejpam-3329	713	12	+	+	CCONJ
ejpam-3329	713	13	nmu	nmu	NOUN
ejpam-3329	713	14	,	,	PUNCT
ejpam-3329	713	15	tm	tm	PROPN
ejpam-3329	713	16	∗	∗	NOUN
ejpam-3329	713	17	u	u	PROPN
ejpam-3329	713	18	,	,	PUNCT
ejpam-3329	713	19	t	t	NOUN
ejpam-3329	713	20	)	)	PUNCT
ejpam-3329	714	1	f	f	X
ejpam-3329	714	2	,	,	PUNCT
ejpam-3329	714	3	f	f	PROPN
ejpam-3329	714	4	〉	〉	PROPN
ejpam-3329	714	5	≥	≥	NOUN
ejpam-3329	714	6	0	0	NUM
ejpam-3329	714	7	⇔	⇔	NUM
ejpam-3329	714	8	∫	∫	PROPN
ejpam-3329	714	9	e	e	PROPN
ejpam-3329	714	10	(	(	PUNCT
ejpam-3329	714	11	u2+n.u	u2+n.u	PROPN
ejpam-3329	714	12	◦	◦	NOUN
ejpam-3329	714	13	t	t	NOUN
ejpam-3329	714	14	2+n.f0	2+n.f0	NUM
ejpam-3329	714	15	◦	◦	NOUN
ejpam-3329	714	16	t	t	X
ejpam-3329	714	17	2+n.e(uf0	2+n.e(uf0	NUM
ejpam-3329	714	18	)	)	PUNCT
ejpam-3329	714	19	◦	◦	NOUN
ejpam-3329	714	20	t	t	NOUN
ejpam-3329	714	21	1+n.e(f)−	1+n.e(f)−	NUM
ejpam-3329	714	22	(	(	PUNCT
ejpam-3329	714	23	1	1	NUM
ejpam-3329	714	24	+	+	NUM
ejpam-3329	714	25	n	n	CCONJ
ejpam-3329	714	26	)	)	PUNCT
ejpam-3329	714	27	u2(u	u2(u	VERB
ejpam-3329	714	28	◦	◦	NOUN
ejpam-3329	714	29	t	t	PROPN
ejpam-3329	714	30	2)(f0	2)(f0	NUM
ejpam-3329	714	31	◦	◦	NOUN
ejpam-3329	714	32	t	t	PROPN
ejpam-3329	714	33	2).e(uf0	2).e(uf0	NUM
ejpam-3329	714	34	)	)	PUNCT
ejpam-3329	714	35	◦	◦	NOUN
ejpam-3329	714	36	te(f	te(f	PUNCT
ejpam-3329	714	37	)	)	PUNCT
ejpam-3329	715	1	+	+	CCONJ
ejpam-3329	715	2	n(u2	n(u2	PROPN
ejpam-3329	715	3	◦	◦	NOUN
ejpam-3329	715	4	t	t	PROPN
ejpam-3329	715	5	)	)	PUNCT
ejpam-3329	715	6	(	(	PUNCT
ejpam-3329	715	7	f0	f0	PROPN
ejpam-3329	715	8	◦	◦	NOUN
ejpam-3329	715	9	t	t	PROPN
ejpam-3329	715	10	)	)	PUNCT
ejpam-3329	715	11	.e(f))dλ	.e(f))dλ	PROPN
ejpam-3329	715	12	≥	≥	PROPN
ejpam-3329	715	13	0	0	NUM
ejpam-3329	715	14	⇔	⇔	X
ejpam-3329	715	15	u2+n.u	u2+n.u	PROPN
ejpam-3329	715	16	◦	◦	PROPN
ejpam-3329	715	17	t	t	PROPN
ejpam-3329	715	18	2+n.f0	2+n.f0	NUM
ejpam-3329	715	19	◦	◦	NOUN
ejpam-3329	715	20	t	t	X
ejpam-3329	715	21	2+n.e(uf0	2+n.e(uf0	NUM
ejpam-3329	715	22	)	)	PUNCT
ejpam-3329	715	23	◦	◦	NOUN
ejpam-3329	715	24	t	t	NOUN
ejpam-3329	715	25	1+n.e(f)−	1+n.e(f)−	NUM
ejpam-3329	715	26	(	(	PUNCT
ejpam-3329	715	27	1	1	NUM
ejpam-3329	715	28	+	+	NUM
ejpam-3329	715	29	n	n	CCONJ
ejpam-3329	715	30	)	)	PUNCT
ejpam-3329	715	31	u2(u	u2(u	VERB
ejpam-3329	715	32	◦	◦	NOUN
ejpam-3329	715	33	t	t	PROPN
ejpam-3329	715	34	2)(f0	2)(f0	NUM
ejpam-3329	715	35	◦	◦	NOUN
ejpam-3329	715	36	t	t	PROPN
ejpam-3329	715	37	2).e(uf0	2).e(uf0	NUM
ejpam-3329	715	38	)	)	PUNCT
ejpam-3329	715	39	◦	◦	NOUN
ejpam-3329	715	40	te(f	te(f	PUNCT
ejpam-3329	715	41	)	)	PUNCT
ejpam-3329	716	1	+	+	CCONJ
ejpam-3329	716	2	n(u2	n(u2	PROPN
ejpam-3329	716	3	◦	◦	NOUN
ejpam-3329	716	4	t	t	PROPN
ejpam-3329	716	5	)	)	PUNCT
ejpam-3329	716	6	(	(	PUNCT
ejpam-3329	716	7	f0	f0	PROPN
ejpam-3329	716	8	◦	◦	PROPN
ejpam-3329	716	9	t	t	PROPN
ejpam-3329	716	10	)	)	PUNCT
ejpam-3329	716	11	.e(f	.e(f	PROPN
ejpam-3329	716	12	)	)	PUNCT
ejpam-3329	716	13	≥	≥	NOUN
ejpam-3329	716	14	0	0	NUM
ejpam-3329	717	1	a.e	a.e	NOUN
ejpam-3329	717	2	corollary	corollary	NOUN
ejpam-3329	717	3	23	23	NUM
ejpam-3329	717	4	.	.	PUNCT
ejpam-3329	718	1	if	if	SCONJ
ejpam-3329	718	2	the	the	DET
ejpam-3329	718	3	composition	composition	NOUN
ejpam-3329	718	4	operator	operator	NOUN
ejpam-3329	718	5	ct	ct	PROPN
ejpam-3329	718	6	∈	∈	PROPN
ejpam-3329	718	7	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	718	8	)	)	PUNCT
ejpam-3329	718	9	)	)	PUNCT
ejpam-3329	718	10	then	then	ADV
ejpam-3329	718	11	c∗t	c∗t	NOUN
ejpam-3329	718	12	is	be	AUX
ejpam-3329	718	13	quasi	quasi	NOUN
ejpam-3329	718	14	n	n	X
ejpam-3329	718	15	class	class	NOUN
ejpam-3329	718	16	q	q	NOUN
ejpam-3329	718	17	if	if	SCONJ
ejpam-3329	719	1	and	and	CCONJ
ejpam-3329	719	2	only	only	ADV
ejpam-3329	719	3	if	if	SCONJ
ejpam-3329	719	4	f0	f0	PROPN
ejpam-3329	719	5	◦	◦	PROPN
ejpam-3329	719	6	t	t	NOUN
ejpam-3329	719	7	2+n.e(f0)	2+n.e(f0)	NUM
ejpam-3329	719	8	◦	◦	PROPN
ejpam-3329	719	9	t	t	NOUN
ejpam-3329	719	10	1+n.e(f)−(1+n)(f0	1+n.e(f)−(1+n)(f0	NUM
ejpam-3329	719	11	◦	◦	NOUN
ejpam-3329	719	12	t	t	NOUN
ejpam-3329	719	13	2).e(f0)	2).e(f0)	NUM
ejpam-3329	719	14	◦	◦	NOUN
ejpam-3329	719	15	te(f)+n(f0	te(f)+n(f0	NOUN
ejpam-3329	719	16	◦	◦	NOUN
ejpam-3329	719	17	t	t	NOUN
ejpam-3329	719	18	)	)	PUNCT
ejpam-3329	719	19	.e(f	.e(f	PROPN
ejpam-3329	719	20	)	)	PUNCT
ejpam-3329	719	21	≥	≥	NOUN
ejpam-3329	719	22	0	0	NUM
ejpam-3329	719	23	.	.	PUNCT
ejpam-3329	720	1	a.e	a.e	PROPN
ejpam-3329	720	2	.	.	PROPN
ejpam-3329	720	3	d.	d.	PROPN
ejpam-3329	720	4	senthilkumar	senthilkumar	PROPN
ejpam-3329	720	5	,	,	PUNCT
ejpam-3329	720	6	s.	s.	PROPN
ejpam-3329	720	7	parvatham	parvatham	PROPN
ejpam-3329	720	8	/	/	SYM
ejpam-3329	720	9	eur	eur	PROPN
ejpam-3329	720	10	.	.	PUNCT
ejpam-3329	721	1	j.	j.	PROPN
ejpam-3329	721	2	pure	pure	PROPN
ejpam-3329	721	3	appl	appl	PROPN
ejpam-3329	721	4	.	.	PROPN
ejpam-3329	721	5	math	math	PROPN
ejpam-3329	721	6	,	,	PUNCT
ejpam-3329	721	7	11	11	NUM
ejpam-3329	721	8	(	(	PUNCT
ejpam-3329	721	9	4	4	NUM
ejpam-3329	721	10	)	)	PUNCT
ejpam-3329	721	11	(	(	PUNCT
ejpam-3329	721	12	2018	2018	NUM
ejpam-3329	721	13	)	)	PUNCT
ejpam-3329	721	14	,	,	PUNCT
ejpam-3329	721	15	1108	1108	NUM
ejpam-3329	721	16	-	-	SYM
ejpam-3329	721	17	1129	1129	NUM
ejpam-3329	721	18	1127	1127	NUM
ejpam-3329	721	19	theorem	theorem	VERB
ejpam-3329	721	20	48	48	NUM
ejpam-3329	721	21	.	.	PUNCT
ejpam-3329	722	1	let	let	VERB
ejpam-3329	722	2	the	the	DET
ejpam-3329	722	3	composite	composite	ADJ
ejpam-3329	722	4	multiplication	multiplication	NOUN
ejpam-3329	722	5	operator	operator	NOUN
ejpam-3329	722	6	mu	mu	NOUN
ejpam-3329	722	7	,	,	PUNCT
ejpam-3329	722	8	t	t	PROPN
ejpam-3329	722	9	∈	∈	PROPN
ejpam-3329	722	10	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	722	11	)	)	PUNCT
ejpam-3329	722	12	)	)	PUNCT
ejpam-3329	722	13	.	.	PUNCT
ejpam-3329	723	1	then	then	ADV
ejpam-3329	723	2	mu	mu	PROPN
ejpam-3329	723	3	,	,	PUNCT
ejpam-3329	723	4	t	t	PROPN
ejpam-3329	723	5	is	be	AUX
ejpam-3329	723	6	quasi	quasi	NOUN
ejpam-3329	723	7	n	n	PRON
ejpam-3329	723	8	class	class	NOUN
ejpam-3329	723	9	q∗	q∗	NOUN
ejpam-3329	724	1	if	if	SCONJ
ejpam-3329	724	2	and	and	CCONJ
ejpam-3329	724	3	only	only	ADV
ejpam-3329	724	4	if	if	SCONJ
ejpam-3329	724	5	uf0.e(uf0)	uf0.e(uf0)	PRON
ejpam-3329	724	6	◦	◦	NOUN
ejpam-3329	724	7	t−(1+n).e(u2+n)	t−(1+n).e(u2+n)	ADJ
ejpam-3329	724	8	◦	◦	NOUN
ejpam-3329	724	9	t−(2+n)−	t−(2+n)−	NOUN
ejpam-3329	724	10	(	(	PUNCT
ejpam-3329	724	11	1+n)(u4)(f20	1+n)(u4)(f20	NUM
ejpam-3329	724	12	)	)	PUNCT
ejpam-3329	724	13	+	+	NUM
ejpam-3329	724	14	n(u2)(f0	n(u2)(f0	NUM
ejpam-3329	724	15	)	)	PUNCT
ejpam-3329	724	16	≥	≥	NOUN
ejpam-3329	724	17	0	0	NUM
ejpam-3329	724	18	.	.	PUNCT
ejpam-3329	725	1	a.e	a.e	PROPN
ejpam-3329	725	2	.	.	PROPN
ejpam-3329	725	3	corollary	corollary	NOUN
ejpam-3329	725	4	24	24	NUM
ejpam-3329	725	5	.	.	PUNCT
ejpam-3329	726	1	if	if	SCONJ
ejpam-3329	726	2	the	the	DET
ejpam-3329	726	3	composition	composition	NOUN
ejpam-3329	726	4	operator	operator	NOUN
ejpam-3329	726	5	ct	ct	PROPN
ejpam-3329	726	6	∈	∈	PROPN
ejpam-3329	726	7	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	726	8	)	)	PUNCT
ejpam-3329	726	9	)	)	PUNCT
ejpam-3329	726	10	.	.	PUNCT
ejpam-3329	727	1	then	then	ADV
ejpam-3329	727	2	ct	ct	PROPN
ejpam-3329	727	3	is	be	AUX
ejpam-3329	727	4	quasi	quasi	NOUN
ejpam-3329	727	5	n	n	X
ejpam-3329	727	6	class	class	NOUN
ejpam-3329	727	7	q∗	q∗	NOUN
ejpam-3329	727	8	if	if	SCONJ
ejpam-3329	727	9	and	and	CCONJ
ejpam-3329	727	10	only	only	ADV
ejpam-3329	727	11	if	if	SCONJ
ejpam-3329	727	12	f0.e(f0	f0.e(f0	ADJ
ejpam-3329	727	13	)	)	PUNCT
ejpam-3329	727	14	◦	◦	NOUN
ejpam-3329	727	15	t−(1+n	t−(1+n	NOUN
ejpam-3329	727	16	)	)	PUNCT
ejpam-3329	727	17	−	−	PROPN
ejpam-3329	728	1	(	(	PUNCT
ejpam-3329	728	2	1	1	NUM
ejpam-3329	728	3	+	+	CCONJ
ejpam-3329	728	4	n)(f20	n)(f20	NOUN
ejpam-3329	728	5	)	)	PUNCT
ejpam-3329	729	1	+	+	CCONJ
ejpam-3329	729	2	n(f0	n(f0	NOUN
ejpam-3329	729	3	)	)	PUNCT
ejpam-3329	729	4	≥	≥	NOUN
ejpam-3329	729	5	0	0	NUM
ejpam-3329	729	6	.	.	PUNCT
ejpam-3329	730	1	a.e	a.e	PROPN
ejpam-3329	730	2	.	.	PROPN
ejpam-3329	730	3	theorem	theorem	VERB
ejpam-3329	730	4	49	49	NUM
ejpam-3329	730	5	.	.	PUNCT
ejpam-3329	731	1	let	let	VERB
ejpam-3329	731	2	the	the	DET
ejpam-3329	731	3	composite	composite	ADJ
ejpam-3329	731	4	multiplication	multiplication	NOUN
ejpam-3329	731	5	operator	operator	NOUN
ejpam-3329	731	6	mu	mu	NOUN
ejpam-3329	731	7	,	,	PUNCT
ejpam-3329	731	8	t	t	PROPN
ejpam-3329	731	9	∈	∈	PROPN
ejpam-3329	731	10	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	731	11	)	)	PUNCT
ejpam-3329	731	12	)	)	PUNCT
ejpam-3329	731	13	.	.	PUNCT
ejpam-3329	732	1	then	then	ADV
ejpam-3329	732	2	m∗u	m∗u	NUM
ejpam-3329	732	3	,	,	PUNCT
ejpam-3329	732	4	t	t	PROPN
ejpam-3329	732	5	is	be	AUX
ejpam-3329	732	6	quasi	quasi	NOUN
ejpam-3329	732	7	n	n	PRON
ejpam-3329	732	8	class	class	NOUN
ejpam-3329	732	9	q∗	q∗	NOUN
ejpam-3329	733	1	if	if	SCONJ
ejpam-3329	733	2	and	and	CCONJ
ejpam-3329	733	3	only	only	ADV
ejpam-3329	733	4	if	if	SCONJ
ejpam-3329	733	5	u2+nu	u2+nu	ADP
ejpam-3329	733	6	◦	◦	NOUN
ejpam-3329	733	7	t	t	X
ejpam-3329	733	8	2+nf0	2+nf0	NOUN
ejpam-3329	733	9	◦	◦	PROPN
ejpam-3329	733	10	t	t	X
ejpam-3329	733	11	2+n.e(uf0	2+n.e(uf0	NUM
ejpam-3329	733	12	)	)	PUNCT
ejpam-3329	733	13	◦	◦	NOUN
ejpam-3329	733	14	t	t	NOUN
ejpam-3329	733	15	1+n.e(f)−	1+n.e(f)−	NUM
ejpam-3329	733	16	(	(	PUNCT
ejpam-3329	733	17	1	1	NUM
ejpam-3329	733	18	+	+	NOUN
ejpam-3329	733	19	n)(u2f0	n)(u2f0	NOUN
ejpam-3329	733	20	◦	◦	NOUN
ejpam-3329	733	21	te(f))2	te(f))2	PRON
ejpam-3329	734	1	+	+	CCONJ
ejpam-3329	734	2	n(u2f0	n(u2f0	NUM
ejpam-3329	734	3	◦	◦	NOUN
ejpam-3329	734	4	t	t	NOUN
ejpam-3329	734	5	)	)	PUNCT
ejpam-3329	734	6	e(f	e(f	PROPN
ejpam-3329	734	7	)	)	PUNCT
ejpam-3329	734	8	≥	≥	NOUN
ejpam-3329	734	9	0	0	NUM
ejpam-3329	734	10	.	.	PUNCT
ejpam-3329	735	1	a.e	a.e	PROPN
ejpam-3329	735	2	.	.	PROPN
ejpam-3329	735	3	corollary	corollary	NOUN
ejpam-3329	735	4	25	25	NUM
ejpam-3329	735	5	.	.	PUNCT
ejpam-3329	736	1	if	if	SCONJ
ejpam-3329	736	2	the	the	DET
ejpam-3329	736	3	composition	composition	NOUN
ejpam-3329	736	4	operator	operator	NOUN
ejpam-3329	736	5	ct	ct	PROPN
ejpam-3329	736	6	∈	∈	PROPN
ejpam-3329	736	7	b(l2(λ	b(l2(λ	PROPN
ejpam-3329	736	8	)	)	PUNCT
ejpam-3329	736	9	)	)	PUNCT
ejpam-3329	736	10	.	.	PUNCT
ejpam-3329	737	1	then	then	ADV
ejpam-3329	737	2	c∗t	c∗t	NOUN
ejpam-3329	737	3	is	be	AUX
ejpam-3329	737	4	quasi	quasi	NOUN
ejpam-3329	737	5	n	n	PRON
ejpam-3329	737	6	class	class	NOUN
ejpam-3329	737	7	q∗	q∗	NOUN
ejpam-3329	737	8	if	if	SCONJ
ejpam-3329	738	1	and	and	CCONJ
ejpam-3329	738	2	only	only	ADV
ejpam-3329	738	3	if	if	SCONJ
ejpam-3329	738	4	f0	f0	PROPN
ejpam-3329	738	5	◦	◦	NOUN
ejpam-3329	738	6	t	t	NOUN
ejpam-3329	738	7	2+n.e(f0	2+n.e(f0	NUM
ejpam-3329	738	8	)	)	PUNCT
ejpam-3329	738	9	◦	◦	NOUN
ejpam-3329	738	10	t	t	PROPN
ejpam-3329	738	11	1+n.e(f	1+n.e(f	PROPN
ejpam-3329	738	12	)	)	PUNCT
ejpam-3329	739	1	−	−	PROPN
ejpam-3329	739	2	(	(	PUNCT
ejpam-3329	739	3	1	1	NUM
ejpam-3329	739	4	+	+	NUM
ejpam-3329	739	5	n)(f0	n)(f0	NOUN
ejpam-3329	739	6	◦	◦	VERB
ejpam-3329	739	7	te(f))2	te(f))2	PRON
ejpam-3329	740	1	+	+	CCONJ
ejpam-3329	740	2	n(f0	n(f0	NOUN
ejpam-3329	740	3	◦	◦	NOUN
ejpam-3329	740	4	t	t	PROPN
ejpam-3329	740	5	)	)	PUNCT
ejpam-3329	740	6	e(f	e(f	PROPN
ejpam-3329	740	7	)	)	PUNCT
ejpam-3329	740	8	≥	≥	NOUN
ejpam-3329	740	9	0	0	NUM
ejpam-3329	740	10	.	.	PUNCT
ejpam-3329	741	1	a.e	a.e	PROPN
ejpam-3329	741	2	.	.	PROPN
ejpam-3329	741	3	8	8	NUM
ejpam-3329	741	4	.	.	PUNCT
ejpam-3329	741	5	aluthge	aluthge	ADJ
ejpam-3329	741	6	transformation	transformation	NOUN
ejpam-3329	741	7	of	of	ADP
ejpam-3329	741	8	quasi	quasi	ADJ
ejpam-3329	741	9	n	n	CCONJ
ejpam-3329	741	10	-	-	PUNCT
ejpam-3329	741	11	class	class	NOUN
ejpam-3329	741	12	q	q	NOUN
ejpam-3329	741	13	and	and	CCONJ
ejpam-3329	741	14	quasi	quasi	ADJ
ejpam-3329	741	15	n	n	DET
ejpam-3329	741	16	class	class	NOUN
ejpam-3329	741	17	q∗	q∗	NOUN
ejpam-3329	741	18	operator	operator	NOUN
ejpam-3329	741	19	let	let	VERB
ejpam-3329	741	20	t	t	NOUN
ejpam-3329	741	21	=	=	SYM
ejpam-3329	741	22	u	u	NOUN
ejpam-3329	741	23	|t	|t	VERB
ejpam-3329	741	24	|	|	ADV
ejpam-3329	741	25	be	be	AUX
ejpam-3329	741	26	the	the	DET
ejpam-3329	741	27	polar	polar	ADJ
ejpam-3329	741	28	decomposition	decomposition	NOUN
ejpam-3329	741	29	of	of	ADP
ejpam-3329	741	30	t.	t.	PROPN
ejpam-3329	741	31	then	then	ADV
ejpam-3329	742	1	the	the	DET
ejpam-3329	742	2	aluthge	aluthge	ADJ
ejpam-3329	742	3	transformation	transformation	NOUN
ejpam-3329	742	4	t̃	t̃	PROPN
ejpam-3329	742	5	=	=	PUNCT
ejpam-3329	742	6	|t	|t	NOUN
ejpam-3329	742	7	|	|	ADV
ejpam-3329	742	8	1	1	NUM
ejpam-3329	742	9	2u	2u	NOUN
ejpam-3329	742	10	|t	|t	VERB
ejpam-3329	742	11	|	|	ADV
ejpam-3329	742	12	1	1	NUM
ejpam-3329	742	13	2	2	NUM
ejpam-3329	742	14	was	be	AUX
ejpam-3329	742	15	introduced	introduce	VERB
ejpam-3329	742	16	by	by	ADP
ejpam-3329	742	17	aluthge[1	aluthge[1	PROPN
ejpam-3329	742	18	]	]	X
ejpam-3329	742	19	.	.	PUNCT
ejpam-3329	743	1	an	an	DET
ejpam-3329	743	2	operator	operator	NOUN
ejpam-3329	743	3	t	t	NOUN
ejpam-3329	743	4	is	be	AUX
ejpam-3329	743	5	called	call	VERB
ejpam-3329	743	6	w	w	PROPN
ejpam-3329	743	7	hyponormal	hyponormal	ADJ
ejpam-3329	743	8	if	if	SCONJ
ejpam-3329	743	9	|t̃	|t̃	PROPN
ejpam-3329	744	1	|	|	ADV
ejpam-3329	744	2	≥	≥	NOUN
ejpam-3329	744	3	|t	|t	INTJ
ejpam-3329	744	4	|	|	ADV
ejpam-3329	744	5	≥	≥	NOUN
ejpam-3329	744	6	|t̃	|t̃	PUNCT
ejpam-3329	745	1	∗|	∗|	NOUN
ejpam-3329	745	2	and	and	CCONJ
ejpam-3329	745	3	he	he	PRON
ejpam-3329	745	4	defined	define	VERB
ejpam-3329	745	5	˜̃t	˜̃t	NOUN
ejpam-3329	745	6	=	=	PUNCT
ejpam-3329	746	1	|t̃	|t̃	NOUN
ejpam-3329	746	2	|	|	ADV
ejpam-3329	746	3	1	1	NUM
ejpam-3329	746	4	2	2	NUM
ejpam-3329	746	5	t̃	t̃	PROPN
ejpam-3329	746	6	|t̃	|t̃	PUNCT
ejpam-3329	747	1	|	|	ADV
ejpam-3329	747	2	1	1	NUM
ejpam-3329	747	3	2	2	NUM
ejpam-3329	747	4	where	where	SCONJ
ejpam-3329	747	5	t̃	t̃	PROPN
ejpam-3329	747	6	=	=	SYM
ejpam-3329	747	7	ũ	ũ	PROPN
ejpam-3329	747	8	|t̃	|t̃	NOUN
ejpam-3329	747	9	|	|	NOUN
ejpam-3329	747	10	.	.	PUNCT
ejpam-3329	748	1	also	also	ADV
ejpam-3329	748	2	the	the	DET
ejpam-3329	748	3	adjoint	adjoint	NOUN
ejpam-3329	748	4	of	of	ADP
ejpam-3329	748	5	aluthge	aluthge	ADJ
ejpam-3329	748	6	transformation	transformation	NOUN
ejpam-3329	748	7	is	be	AUX
ejpam-3329	748	8	defined	define	VERB
ejpam-3329	748	9	as	as	ADP
ejpam-3329	748	10	t̃	t̃	PROPN
ejpam-3329	748	11	∗	∗	NOUN
ejpam-3329	748	12	=	=	PUNCT
ejpam-3329	749	1	|t	|t	NOUN
ejpam-3329	750	1	|	|	ADV
ejpam-3329	750	2	1	1	NUM
ejpam-3329	751	1	2u∗|t	2u∗|t	NOUN
ejpam-3329	751	2	|	|	NOUN
ejpam-3329	751	3	1	1	NUM
ejpam-3329	751	4	2	2	NUM
ejpam-3329	751	5	,	,	PUNCT
ejpam-3329	751	6	*	*	PUNCT
ejpam-3329	751	7	-aluthge	-aluthge	ADJ
ejpam-3329	751	8	transformation	transformation	NOUN
ejpam-3329	751	9	is	be	AUX
ejpam-3329	751	10	t̃	t̃	PROPN
ejpam-3329	751	11	∗	∗	NOUN
ejpam-3329	751	12	=	=	PUNCT
ejpam-3329	751	13	|t	|t	NOUN
ejpam-3329	752	1	∗|	∗|	NOUN
ejpam-3329	752	2	1	1	NUM
ejpam-3329	752	3	2u	2u	NOUN
ejpam-3329	752	4	|t	|t	VERB
ejpam-3329	753	1	∗|	∗|	NOUN
ejpam-3329	753	2	1	1	NUM
ejpam-3329	753	3	2	2	NUM
ejpam-3329	753	4	and	and	CCONJ
ejpam-3329	753	5	adjoint	adjoint	NOUN
ejpam-3329	753	6	of	of	ADP
ejpam-3329	753	7	*	*	PUNCT
ejpam-3329	753	8	-aluthge	-aluthge	ADJ
ejpam-3329	753	9	transformation	transformation	NOUN
ejpam-3329	753	10	is	be	AUX
ejpam-3329	753	11	given	give	VERB
ejpam-3329	753	12	by	by	ADP
ejpam-3329	753	13	t̃	t̃	PROPN
ejpam-3329	753	14	∗	∗	NOUN
ejpam-3329	753	15	∗	∗	NOUN
ejpam-3329	753	16	=	=	PUNCT
ejpam-3329	753	17	|t	|t	NOUN
ejpam-3329	754	1	∗|	∗|	NOUN
ejpam-3329	754	2	1	1	NUM
ejpam-3329	754	3	2u∗|t	2u∗|t	PROPN
ejpam-3329	754	4	∗|	∗|	NOUN
ejpam-3329	754	5	1	1	NUM
ejpam-3329	754	6	2	2	NUM
ejpam-3329	754	7	.	.	PUNCT
ejpam-3329	755	1	theorem	theorem	VERB
ejpam-3329	755	2	50	50	NUM
ejpam-3329	755	3	.	.	PUNCT
ejpam-3329	756	1	an	an	DET
ejpam-3329	756	2	operator	operator	NOUN
ejpam-3329	756	3	t	t	NOUN
ejpam-3329	756	4	is	be	AUX
ejpam-3329	756	5	quasi	quasi	NOUN
ejpam-3329	756	6	n	n	X
ejpam-3329	756	7	class	class	NOUN
ejpam-3329	756	8	q	q	NOUN
ejpam-3329	756	9	if	if	SCONJ
ejpam-3329	757	1	and	and	CCONJ
ejpam-3329	757	2	only	only	ADV
ejpam-3329	757	3	if	if	SCONJ
ejpam-3329	757	4	(	(	PUNCT
ejpam-3329	757	5	1+n)t	1+n)t	NUM
ejpam-3329	757	6	∗|t	∗|t	NOUN
ejpam-3329	757	7	|2	|2	NUM
ejpam-3329	757	8	t	t	NOUN
ejpam-3329	757	9	≤	≤	NOUN
ejpam-3329	757	10	t	t	PROPN
ejpam-3329	757	11	∗|t	∗|t	PROPN
ejpam-3329	757	12	(	(	PUNCT
ejpam-3329	757	13	1+n)|2t+	1+n)|2t+	NUM
ejpam-3329	757	14	nt	not	PART
ejpam-3329	757	15	∗t	∗t	ADJ
ejpam-3329	757	16	for	for	ADP
ejpam-3329	757	17	all	all	DET
ejpam-3329	757	18	x	x	SYM
ejpam-3329	757	19	∈	∈	PROPN
ejpam-3329	757	20	h	h	NOUN
ejpam-3329	757	21	and	and	CCONJ
ejpam-3329	757	22	for	for	ADP
ejpam-3329	757	23	every	every	DET
ejpam-3329	757	24	positive	positive	ADJ
ejpam-3329	757	25	integer	integer	NOUN
ejpam-3329	757	26	n.	n.	NOUN
ejpam-3329	757	27	proof	proof	NOUN
ejpam-3329	757	28	.	.	PUNCT
ejpam-3329	758	1	since	since	SCONJ
ejpam-3329	758	2	t	t	PROPN
ejpam-3329	758	3	is	be	AUX
ejpam-3329	758	4	quasi	quasi	NOUN
ejpam-3329	758	5	n	n	PRON
ejpam-3329	758	6	class	class	NOUN
ejpam-3329	758	7	q	q	NOUN
ejpam-3329	758	8	operator	operator	NOUN
ejpam-3329	758	9	,	,	PUNCT
ejpam-3329	758	10	then	then	ADV
ejpam-3329	758	11	t	t	PROPN
ejpam-3329	758	12	∗(t	∗(t	NOUN
ejpam-3329	758	13	∗1+nt	∗1+nt	VERB
ejpam-3329	758	14	1+n−(1+n)t	1+n−(1+n)t	NUM
ejpam-3329	758	15	∗t+ni)t	∗t+ni)t	PROPN
ejpam-3329	758	16	≥	≥	NOUN
ejpam-3329	758	17	0	0	NUM
ejpam-3329	758	18	for	for	ADP
ejpam-3329	758	19	every	every	DET
ejpam-3329	758	20	positive	positive	ADJ
ejpam-3329	758	21	integer	integer	NOUN
ejpam-3329	758	22	n.	n.	NOUN
ejpam-3329	758	23	by	by	ADP
ejpam-3329	758	24	simple	simple	ADJ
ejpam-3329	758	25	calculation	calculation	NOUN
ejpam-3329	758	26	we	we	PRON
ejpam-3329	758	27	get	get	VERB
ejpam-3329	758	28	the	the	DET
ejpam-3329	758	29	result	result	NOUN
ejpam-3329	758	30	.	.	PUNCT
ejpam-3329	759	1	theorem	theorem	VERB
ejpam-3329	759	2	51	51	NUM
ejpam-3329	759	3	.	.	PUNCT
ejpam-3329	760	1	if	if	SCONJ
ejpam-3329	760	2	t	t	PROPN
ejpam-3329	760	3	=	=	SYM
ejpam-3329	760	4	u	u	SYM
ejpam-3329	760	5	|t	|t	NOUN
ejpam-3329	761	1	|	|	ADV
ejpam-3329	761	2	is	be	AUX
ejpam-3329	761	3	the	the	DET
ejpam-3329	761	4	polar	polar	ADJ
ejpam-3329	761	5	decomposition	decomposition	NOUN
ejpam-3329	761	6	of	of	ADP
ejpam-3329	761	7	quasi	quasi	NOUN
ejpam-3329	761	8	n	n	PRON
ejpam-3329	761	9	class	class	NOUN
ejpam-3329	761	10	q	q	NOUN
ejpam-3329	761	11	operator	operator	NOUN
ejpam-3329	761	12	t	t	NOUN
ejpam-3329	761	13	,	,	PUNCT
ejpam-3329	761	14	then	then	ADV
ejpam-3329	761	15	t	t	PROPN
ejpam-3329	761	16	is	be	AUX
ejpam-3329	761	17	quasi	quasi	NOUN
ejpam-3329	761	18	n	n	PRON
ejpam-3329	761	19	class	class	NOUN
ejpam-3329	761	20	q	q	NOUN
ejpam-3329	761	21	operator	operator	NOUN
ejpam-3329	761	22	.	.	PUNCT
ejpam-3329	762	1	theorem	theorem	VERB
ejpam-3329	762	2	52	52	NUM
ejpam-3329	762	3	.	.	PUNCT
ejpam-3329	763	1	if	if	SCONJ
ejpam-3329	763	2	t	t	PROPN
ejpam-3329	763	3	is	be	AUX
ejpam-3329	763	4	quasi	quasi	NOUN
ejpam-3329	763	5	n	n	PRON
ejpam-3329	763	6	class	class	NOUN
ejpam-3329	763	7	q	q	NOUN
ejpam-3329	763	8	operator	operator	NOUN
ejpam-3329	763	9	t	t	PROPN
ejpam-3329	763	10	and	and	CCONJ
ejpam-3329	763	11	s	s	VERB
ejpam-3329	763	12	is	be	AUX
ejpam-3329	763	13	unitary	unitary	ADJ
ejpam-3329	764	1	such	such	ADJ
ejpam-3329	764	2	that	that	PRON
ejpam-3329	764	3	ts	ts	ADP
ejpam-3329	764	4	=	=	PROPN
ejpam-3329	764	5	st	st	PROPN
ejpam-3329	764	6	then	then	ADV
ejpam-3329	764	7	a	a	DET
ejpam-3329	764	8	=	=	X
ejpam-3329	764	9	ts	ts	NOUN
ejpam-3329	764	10	is	be	AUX
ejpam-3329	764	11	also	also	ADV
ejpam-3329	764	12	quasi	quasi	ADJ
ejpam-3329	764	13	n	n	PRON
ejpam-3329	764	14	class	class	NOUN
ejpam-3329	764	15	q	q	NOUN
ejpam-3329	764	16	operator	operator	NOUN
ejpam-3329	764	17	.	.	PUNCT
ejpam-3329	765	1	theorem	theorem	VERB
ejpam-3329	765	2	53	53	NUM
ejpam-3329	765	3	.	.	PUNCT
ejpam-3329	766	1	let	let	AUX
ejpam-3329	766	2	t	t	NOUN
ejpam-3329	766	3	=	=	SYM
ejpam-3329	766	4	u	u	NOUN
ejpam-3329	766	5	|t	|t	VERB
ejpam-3329	766	6	|	|	ADV
ejpam-3329	766	7	be	be	AUX
ejpam-3329	766	8	the	the	DET
ejpam-3329	766	9	polar	polar	ADJ
ejpam-3329	766	10	decomposition	decomposition	NOUN
ejpam-3329	766	11	of	of	ADP
ejpam-3329	766	12	quasi	quasi	NOUN
ejpam-3329	766	13	n	n	PRON
ejpam-3329	766	14	class	class	NOUN
ejpam-3329	766	15	q	q	NOUN
ejpam-3329	766	16	operator	operator	NOUN
ejpam-3329	766	17	t	t	NOUN
ejpam-3329	766	18	,	,	PUNCT
ejpam-3329	766	19	where	where	SCONJ
ejpam-3329	766	20	u	u	NOUN
ejpam-3329	766	21	is	be	AUX
ejpam-3329	766	22	unitary	unitary	ADJ
ejpam-3329	766	23	if	if	SCONJ
ejpam-3329	766	24	and	and	CCONJ
ejpam-3329	766	25	only	only	ADV
ejpam-3329	766	26	if	if	SCONJ
ejpam-3329	766	27	t̃	t̃	PROPN
ejpam-3329	766	28	is	be	AUX
ejpam-3329	766	29	quasi	quasi	NOUN
ejpam-3329	766	30	n	n	PRON
ejpam-3329	766	31	class	class	NOUN
ejpam-3329	766	32	q	q	NOUN
ejpam-3329	766	33	operator	operator	NOUN
ejpam-3329	766	34	.	.	PUNCT
ejpam-3329	767	1	proof	proof	NOUN
ejpam-3329	767	2	.	.	PUNCT
ejpam-3329	768	1	suppose	suppose	VERB
ejpam-3329	768	2	we	we	PRON
ejpam-3329	768	3	assume	assume	VERB
ejpam-3329	768	4	that	that	SCONJ
ejpam-3329	768	5	t	t	PROPN
ejpam-3329	768	6	is	be	AUX
ejpam-3329	768	7	quasi	quasi	NOUN
ejpam-3329	768	8	n	n	PRON
ejpam-3329	768	9	class	class	NOUN
ejpam-3329	768	10	q	q	NOUN
ejpam-3329	768	11	operator	operator	NOUN
ejpam-3329	768	12	and	and	CCONJ
ejpam-3329	768	13	t	t	NOUN
ejpam-3329	768	14	=	=	SYM
ejpam-3329	768	15	u	u	NOUN
ejpam-3329	769	1	|t	|t	NOUN
ejpam-3329	769	2	|	|	ADV
ejpam-3329	769	3	is	be	AUX
ejpam-3329	769	4	the	the	DET
ejpam-3329	769	5	polar	polar	ADJ
ejpam-3329	769	6	decomposition	decomposition	NOUN
ejpam-3329	769	7	of	of	ADP
ejpam-3329	769	8	t	t	PROPN
ejpam-3329	769	9	,	,	PUNCT
ejpam-3329	769	10	then	then	ADV
ejpam-3329	769	11	we	we	PRON
ejpam-3329	769	12	have	have	VERB
ejpam-3329	769	13	that	that	DET
ejpam-3329	769	14	t	t	PROPN
ejpam-3329	769	15	∗(t	∗(t	PROPN
ejpam-3329	769	16	∗1+nt	∗1+nt	VERB
ejpam-3329	769	17	1+n	1+n	NUM
ejpam-3329	769	18	−	−	PROPN
ejpam-3329	769	19	(	(	PUNCT
ejpam-3329	769	20	1	1	NUM
ejpam-3329	769	21	+	+	CCONJ
ejpam-3329	769	22	n)t	n)t	ADJ
ejpam-3329	769	23	∗t	∗t	ADJ
ejpam-3329	769	24	+	+	CCONJ
ejpam-3329	769	25	ni)t	ni)t	PROPN
ejpam-3329	769	26	≥	≥	NOUN
ejpam-3329	769	27	0	0	NUM
ejpam-3329	769	28	for	for	ADP
ejpam-3329	769	29	every	every	DET
ejpam-3329	769	30	positive	positive	ADJ
ejpam-3329	769	31	integer	integer	NOUN
ejpam-3329	769	32	n.	n.	PROPN
ejpam-3329	769	33	⇔	⇔	PROPN
ejpam-3329	769	34	(	(	PUNCT
ejpam-3329	769	35	u	u	NOUN
ejpam-3329	769	36	|t	|t	PROPN
ejpam-3329	769	37	|)∗((u	|)∗((u	NOUN
ejpam-3329	769	38	|t	|t	VERB
ejpam-3329	769	39	|)∗1+n(u	|)∗1+n(u	PROPN
ejpam-3329	769	40	|t	|t	PROPN
ejpam-3329	769	41	|)1+n	|)1+n	PROPN
ejpam-3329	770	1	−	−	PROPN
ejpam-3329	770	2	(	(	PUNCT
ejpam-3329	770	3	1	1	NUM
ejpam-3329	770	4	+	+	CCONJ
ejpam-3329	770	5	n)(u	n)(u	ADJ
ejpam-3329	770	6	|t	|t	ADJ
ejpam-3329	770	7	|)∗(u	|)∗(u	NOUN
ejpam-3329	770	8	|t	|t	PROPN
ejpam-3329	770	9	|	|	ADV
ejpam-3329	770	10	)	)	PUNCT
ejpam-3329	771	1	+	+	CCONJ
ejpam-3329	771	2	ni)(u	ni)(u	PROPN
ejpam-3329	771	3	|t	|t	VERB
ejpam-3329	771	4	|	|	ADV
ejpam-3329	771	5	)	)	PUNCT
ejpam-3329	771	6	≥	≥	NOUN
ejpam-3329	771	7	0	0	NUM
ejpam-3329	771	8	.	.	PUNCT
ejpam-3329	772	1	⇔	⇔	PROPN
ejpam-3329	772	2	|t	|t	PROPN
ejpam-3329	773	1	|	|	ADV
ejpam-3329	773	2	1	1	NUM
ejpam-3329	774	1	2u∗|t	2u∗|t	NOUN
ejpam-3329	774	2	|	|	NOUN
ejpam-3329	774	3	1	1	NUM
ejpam-3329	774	4	2	2	NUM
ejpam-3329	774	5	(	(	PUNCT
ejpam-3329	774	6	|t	|t	PROPN
ejpam-3329	774	7	(	(	PUNCT
ejpam-3329	774	8	1+n)|	1+n)|	NUM
ejpam-3329	774	9	1	1	NUM
ejpam-3329	774	10	2u∗(1+n)|t	2u∗(1+n)|t	NUM
ejpam-3329	774	11	∗(1+n)|u	∗(1+n)|u	PROPN
ejpam-3329	774	12	(	(	PUNCT
ejpam-3329	774	13	1+n)|t	1+n)|t	NUM
ejpam-3329	774	14	(	(	PUNCT
ejpam-3329	774	15	1+n)|	1+n)|	NUM
ejpam-3329	774	16	1	1	NUM
ejpam-3329	774	17	2	2	NUM
ejpam-3329	774	18	−	−	NOUN
ejpam-3329	774	19	(	(	PUNCT
ejpam-3329	774	20	1	1	NUM
ejpam-3329	774	21	+	+	NUM
ejpam-3329	774	22	n	n	CCONJ
ejpam-3329	774	23	)	)	PUNCT
ejpam-3329	774	24	d.	d.	PROPN
ejpam-3329	774	25	senthilkumar	senthilkumar	PROPN
ejpam-3329	774	26	,	,	PUNCT
ejpam-3329	774	27	s.	s.	PROPN
ejpam-3329	774	28	parvatham	parvatham	PROPN
ejpam-3329	774	29	/	/	SYM
ejpam-3329	774	30	eur	eur	PROPN
ejpam-3329	774	31	.	.	PUNCT
ejpam-3329	775	1	j.	j.	PROPN
ejpam-3329	775	2	pure	pure	PROPN
ejpam-3329	775	3	appl	appl	PROPN
ejpam-3329	775	4	.	.	PROPN
ejpam-3329	775	5	math	math	PROPN
ejpam-3329	775	6	,	,	PUNCT
ejpam-3329	775	7	11	11	NUM
ejpam-3329	775	8	(	(	PUNCT
ejpam-3329	775	9	4	4	NUM
ejpam-3329	775	10	)	)	PUNCT
ejpam-3329	775	11	(	(	PUNCT
ejpam-3329	775	12	2018	2018	NUM
ejpam-3329	775	13	)	)	PUNCT
ejpam-3329	775	14	,	,	PUNCT
ejpam-3329	775	15	1108	1108	NUM
ejpam-3329	775	16	-	-	SYM
ejpam-3329	775	17	1129	1129	NUM
ejpam-3329	775	18	1128	1128	NUM
ejpam-3329	775	19	|t	|t	VERB
ejpam-3329	776	1	|	|	ADV
ejpam-3329	776	2	1	1	NUM
ejpam-3329	776	3	2u∗|t	2u∗|t	PROPN
ejpam-3329	776	4	∗|u	∗|u	NOUN
ejpam-3329	776	5	|t	|t	VERB
ejpam-3329	777	1	|	|	ADV
ejpam-3329	777	2	1	1	NUM
ejpam-3329	777	3	2	2	NUM
ejpam-3329	777	4	+	+	CCONJ
ejpam-3329	777	5	ni)|t	ni)|t	ADJ
ejpam-3329	777	6	|	|	ADV
ejpam-3329	777	7	1	1	NUM
ejpam-3329	777	8	2u	2u	NOUN
ejpam-3329	777	9	|t	|t	VERB
ejpam-3329	777	10	|	|	ADV
ejpam-3329	777	11	1	1	NUM
ejpam-3329	777	12	2	2	NUM
ejpam-3329	777	13	≥	≥	NOUN
ejpam-3329	777	14	0	0	NUM
ejpam-3329	777	15	.	.	PUNCT
ejpam-3329	778	1	⇔	⇔	PROPN
ejpam-3329	778	2	t̃	t̃	PROPN
ejpam-3329	778	3	∗(t̃	∗(t̃	NUM
ejpam-3329	778	4	∗1+nt̃	∗1+nt̃	NOUN
ejpam-3329	778	5	1+n	1+n	NUM
ejpam-3329	778	6	−	−	PROPN
ejpam-3329	778	7	(	(	PUNCT
ejpam-3329	778	8	1	1	NUM
ejpam-3329	778	9	+	+	CCONJ
ejpam-3329	778	10	n)t̃	n)t̃	NUM
ejpam-3329	778	11	∗t̃	∗t̃	NOUN
ejpam-3329	778	12	+	+	CCONJ
ejpam-3329	778	13	ni)t̃	ni)t̃	ADP
ejpam-3329	778	14	≥	≥	NOUN
ejpam-3329	778	15	0	0	NUM
ejpam-3329	778	16	for	for	ADP
ejpam-3329	778	17	every	every	DET
ejpam-3329	778	18	positive	positive	ADJ
ejpam-3329	778	19	integer	integer	NOUN
ejpam-3329	778	20	n.	n.	NOUN
ejpam-3329	778	21	hence	hence	ADV
ejpam-3329	778	22	t̃	t̃	PROPN
ejpam-3329	778	23	is	be	AUX
ejpam-3329	778	24	quasi	quasi	NOUN
ejpam-3329	778	25	n	n	PRON
ejpam-3329	778	26	class	class	NOUN
ejpam-3329	778	27	q	q	NOUN
ejpam-3329	778	28	operator	operator	NOUN
ejpam-3329	778	29	.	.	PUNCT
ejpam-3329	779	1	theorem	theorem	VERB
ejpam-3329	779	2	54	54	NUM
ejpam-3329	779	3	.	.	PUNCT
ejpam-3329	780	1	let	let	AUX
ejpam-3329	780	2	t	t	NOUN
ejpam-3329	780	3	=	=	SYM
ejpam-3329	780	4	u	u	NOUN
ejpam-3329	780	5	|t	|t	VERB
ejpam-3329	780	6	|	|	ADV
ejpam-3329	780	7	be	be	AUX
ejpam-3329	780	8	the	the	DET
ejpam-3329	780	9	polar	polar	ADJ
ejpam-3329	780	10	decomposition	decomposition	NOUN
ejpam-3329	780	11	of	of	ADP
ejpam-3329	780	12	quasi	quasi	NOUN
ejpam-3329	780	13	n	n	PRON
ejpam-3329	780	14	class	class	NOUN
ejpam-3329	780	15	q	q	NOUN
ejpam-3329	780	16	operator	operator	NOUN
ejpam-3329	780	17	t	t	PROPN
ejpam-3329	780	18	and	and	CCONJ
ejpam-3329	780	19	u	u	NOUN
ejpam-3329	780	20	is	be	AUX
ejpam-3329	780	21	unitary	unitary	ADJ
ejpam-3329	780	22	,	,	PUNCT
ejpam-3329	780	23	then	then	ADV
ejpam-3329	780	24	t	t	PROPN
ejpam-3329	780	25	is	be	AUX
ejpam-3329	780	26	quasi	quasi	NOUN
ejpam-3329	780	27	n	n	X
ejpam-3329	780	28	class	class	NOUN
ejpam-3329	780	29	q	q	NOUN
ejpam-3329	780	30	if	if	SCONJ
ejpam-3329	781	1	and	and	CCONJ
ejpam-3329	781	2	only	only	ADV
ejpam-3329	781	3	if	if	SCONJ
ejpam-3329	781	4	t̃	t̃	PROPN
ejpam-3329	781	5	∗	∗	NOUN
ejpam-3329	781	6	is	be	AUX
ejpam-3329	781	7	quasi	quasi	NOUN
ejpam-3329	781	8	n	n	PRON
ejpam-3329	781	9	class	class	NOUN
ejpam-3329	781	10	q	q	NOUN
ejpam-3329	781	11	operator	operator	NOUN
ejpam-3329	781	12	.	.	PUNCT
ejpam-3329	782	1	proof	proof	NOUN
ejpam-3329	782	2	.	.	PUNCT
ejpam-3329	783	1	suppose	suppose	VERB
ejpam-3329	783	2	we	we	PRON
ejpam-3329	783	3	assume	assume	VERB
ejpam-3329	783	4	that	that	SCONJ
ejpam-3329	783	5	t	t	PROPN
ejpam-3329	783	6	is	be	AUX
ejpam-3329	783	7	quasi	quasi	NOUN
ejpam-3329	783	8	n	n	PRON
ejpam-3329	783	9	class	class	NOUN
ejpam-3329	783	10	q	q	NOUN
ejpam-3329	783	11	operator	operator	NOUN
ejpam-3329	783	12	and	and	CCONJ
ejpam-3329	783	13	t	t	NOUN
ejpam-3329	783	14	=	=	SYM
ejpam-3329	783	15	u	u	NOUN
ejpam-3329	784	1	|t	|t	NOUN
ejpam-3329	784	2	|	|	ADV
ejpam-3329	784	3	is	be	AUX
ejpam-3329	784	4	the	the	DET
ejpam-3329	784	5	polar	polar	ADJ
ejpam-3329	784	6	decomposition	decomposition	NOUN
ejpam-3329	784	7	of	of	ADP
ejpam-3329	784	8	t	t	PROPN
ejpam-3329	784	9	,	,	PUNCT
ejpam-3329	784	10	then	then	ADV
ejpam-3329	784	11	we	we	PRON
ejpam-3329	784	12	have	have	VERB
ejpam-3329	784	13	that	that	DET
ejpam-3329	784	14	t	t	PROPN
ejpam-3329	784	15	∗(t	∗(t	PROPN
ejpam-3329	784	16	∗1+nt	∗1+nt	VERB
ejpam-3329	784	17	1+n	1+n	NUM
ejpam-3329	784	18	−	−	PROPN
ejpam-3329	784	19	(	(	PUNCT
ejpam-3329	784	20	1	1	NUM
ejpam-3329	784	21	+	+	CCONJ
ejpam-3329	784	22	n)t	n)t	ADJ
ejpam-3329	784	23	∗t	∗t	ADJ
ejpam-3329	784	24	+	+	CCONJ
ejpam-3329	784	25	ni)t	ni)t	PROPN
ejpam-3329	784	26	≥	≥	NOUN
ejpam-3329	784	27	0	0	NUM
ejpam-3329	784	28	for	for	ADP
ejpam-3329	784	29	every	every	DET
ejpam-3329	784	30	positive	positive	ADJ
ejpam-3329	784	31	integer	integer	NOUN
ejpam-3329	784	32	n.	n.	PROPN
ejpam-3329	784	33	⇔	⇔	PROPN
ejpam-3329	784	34	(	(	PUNCT
ejpam-3329	784	35	u	u	NOUN
ejpam-3329	784	36	|t	|t	NOUN
ejpam-3329	784	37	|)∗[(u	|)∗[(u	PROPN
ejpam-3329	784	38	|t	|t	VERB
ejpam-3329	784	39	|)∗1+n(u	|)∗1+n(u	PROPN
ejpam-3329	784	40	|t	|t	PROPN
ejpam-3329	784	41	|)1+n	|)1+n	PROPN
ejpam-3329	784	42	−	−	PROPN
ejpam-3329	785	1	(	(	PUNCT
ejpam-3329	785	2	1	1	NUM
ejpam-3329	785	3	+	+	CCONJ
ejpam-3329	785	4	n)(u	n)(u	ADJ
ejpam-3329	785	5	|t	|t	ADJ
ejpam-3329	785	6	|)∗(u	|)∗(u	NOUN
ejpam-3329	785	7	|t	|t	PROPN
ejpam-3329	785	8	|	|	ADV
ejpam-3329	785	9	)	)	PUNCT
ejpam-3329	786	1	+	+	CCONJ
ejpam-3329	786	2	ni](u	ni](u	ADV
ejpam-3329	786	3	|t	|t	NOUN
ejpam-3329	786	4	|	|	ADV
ejpam-3329	786	5	)	)	PUNCT
ejpam-3329	786	6	≥	≥	NOUN
ejpam-3329	786	7	0	0	NUM
ejpam-3329	786	8	.	.	PUNCT
ejpam-3329	787	1	⇔	⇔	PROPN
ejpam-3329	787	2	|t	|t	PROPN
ejpam-3329	788	1	|	|	ADV
ejpam-3329	788	2	1	1	NUM
ejpam-3329	789	1	2u∗|t	2u∗|t	NOUN
ejpam-3329	789	2	|	|	NOUN
ejpam-3329	789	3	1	1	NUM
ejpam-3329	789	4	2	2	NUM
ejpam-3329	789	5	(	(	PUNCT
ejpam-3329	789	6	|t	|t	PROPN
ejpam-3329	789	7	(	(	PUNCT
ejpam-3329	789	8	1+n)|	1+n)|	NUM
ejpam-3329	789	9	1	1	NUM
ejpam-3329	789	10	2u	2u	NOUN
ejpam-3329	789	11	(	(	PUNCT
ejpam-3329	789	12	1+n)|t	1+n)|t	NUM
ejpam-3329	789	13	∗(1+n)|u∗(1+n)|t	∗(1+n)|u∗(1+n)|t	X
ejpam-3329	789	14	(	(	PUNCT
ejpam-3329	789	15	1+n)|	1+n)|	NUM
ejpam-3329	789	16	1	1	NUM
ejpam-3329	789	17	2	2	NUM
ejpam-3329	789	18	−	−	NOUN
ejpam-3329	789	19	(	(	PUNCT
ejpam-3329	789	20	1	1	NUM
ejpam-3329	789	21	+	+	NUM
ejpam-3329	789	22	n	n	CCONJ
ejpam-3329	789	23	)	)	PUNCT
ejpam-3329	789	24	|t	|t	VERB
ejpam-3329	790	1	|	|	ADV
ejpam-3329	790	2	1	1	NUM
ejpam-3329	790	3	2u	2u	NOUN
ejpam-3329	790	4	|t	|t	VERB
ejpam-3329	790	5	∗|u∗|t	∗|u∗|t	NOUN
ejpam-3329	791	1	|	|	ADV
ejpam-3329	791	2	1	1	NUM
ejpam-3329	791	3	2	2	NUM
ejpam-3329	791	4	+	+	CCONJ
ejpam-3329	791	5	ni)|t	ni)|t	ADJ
ejpam-3329	791	6	|	|	ADV
ejpam-3329	791	7	1	1	NUM
ejpam-3329	791	8	2u	2u	NOUN
ejpam-3329	791	9	|t	|t	VERB
ejpam-3329	791	10	|	|	ADV
ejpam-3329	791	11	1	1	NUM
ejpam-3329	791	12	2	2	NUM
ejpam-3329	791	13	≥	≥	NOUN
ejpam-3329	791	14	0	0	NUM
ejpam-3329	791	15	.	.	PUNCT
ejpam-3329	792	1	⇔	⇔	PROPN
ejpam-3329	792	2	t̃	t̃	PROPN
ejpam-3329	792	3	∗(t̃	∗(t̃	NUM
ejpam-3329	792	4	1+nt̃	1+nt̃	NUM
ejpam-3329	792	5	∗1+n	∗1+n	NOUN
ejpam-3329	792	6	−	−	PROPN
ejpam-3329	793	1	(	(	PUNCT
ejpam-3329	793	2	1	1	NUM
ejpam-3329	793	3	+	+	CCONJ
ejpam-3329	793	4	n)t̃	n)t̃	ADJ
ejpam-3329	793	5	t̃	t̃	PROPN
ejpam-3329	793	6	∗	∗	NOUN
ejpam-3329	793	7	+	+	CCONJ
ejpam-3329	793	8	ni)t̃	ni)t̃	ADP
ejpam-3329	793	9	≥	≥	NOUN
ejpam-3329	793	10	0	0	NUM
ejpam-3329	793	11	for	for	ADP
ejpam-3329	793	12	every	every	DET
ejpam-3329	793	13	positive	positive	ADJ
ejpam-3329	793	14	integer	integer	NOUN
ejpam-3329	793	15	n.	n.	NOUN
ejpam-3329	793	16	hence	hence	ADV
ejpam-3329	793	17	t̃	t̃	PROPN
ejpam-3329	793	18	∗	∗	NOUN
ejpam-3329	793	19	is	be	AUX
ejpam-3329	793	20	quasi	quasi	NOUN
ejpam-3329	793	21	n	n	PRON
ejpam-3329	793	22	class	class	NOUN
ejpam-3329	793	23	q	q	NOUN
ejpam-3329	793	24	operator	operator	NOUN
ejpam-3329	793	25	.	.	PUNCT
ejpam-3329	794	1	corollary	corollary	ADJ
ejpam-3329	794	2	26	26	NUM
ejpam-3329	794	3	.	.	PUNCT
ejpam-3329	795	1	if	if	SCONJ
ejpam-3329	795	2	t̃	t̃	PROPN
ejpam-3329	795	3	is	be	AUX
ejpam-3329	795	4	quasi	quasi	NOUN
ejpam-3329	795	5	n	n	PRON
ejpam-3329	795	6	class	class	NOUN
ejpam-3329	795	7	q	q	NOUN
ejpam-3329	795	8	if	if	SCONJ
ejpam-3329	795	9	and	and	CCONJ
ejpam-3329	795	10	only	only	ADV
ejpam-3329	795	11	if	if	SCONJ
ejpam-3329	795	12	t̃	t̃	PROPN
ejpam-3329	795	13	∗	∗	NOUN
ejpam-3329	795	14	is	be	AUX
ejpam-3329	795	15	quasi	quasi	NOUN
ejpam-3329	795	16	n	n	PRON
ejpam-3329	795	17	class	class	NOUN
ejpam-3329	795	18	q	q	NOUN
ejpam-3329	795	19	operator	operator	NOUN
ejpam-3329	795	20	.	.	PUNCT
ejpam-3329	796	1	theorem	theorem	VERB
ejpam-3329	796	2	55	55	NUM
ejpam-3329	796	3	.	.	PUNCT
ejpam-3329	797	1	let	let	AUX
ejpam-3329	797	2	t	t	NOUN
ejpam-3329	797	3	=	=	SYM
ejpam-3329	797	4	u	u	NOUN
ejpam-3329	797	5	|t	|t	VERB
ejpam-3329	797	6	|	|	ADV
ejpam-3329	797	7	be	be	AUX
ejpam-3329	797	8	the	the	DET
ejpam-3329	797	9	polar	polar	ADJ
ejpam-3329	797	10	decomposition	decomposition	NOUN
ejpam-3329	797	11	of	of	ADP
ejpam-3329	797	12	quasi	quasi	NOUN
ejpam-3329	797	13	n	n	PRON
ejpam-3329	797	14	class	class	NOUN
ejpam-3329	797	15	q	q	NOUN
ejpam-3329	797	16	operator	operator	NOUN
ejpam-3329	797	17	t	t	PROPN
ejpam-3329	797	18	and	and	CCONJ
ejpam-3329	797	19	u	u	NOUN
ejpam-3329	797	20	is	be	AUX
ejpam-3329	797	21	unitary	unitary	ADJ
ejpam-3329	797	22	,	,	PUNCT
ejpam-3329	797	23	then	then	ADV
ejpam-3329	797	24	t	t	PROPN
ejpam-3329	797	25	is	be	AUX
ejpam-3329	797	26	quasi	quasi	NOUN
ejpam-3329	797	27	n	n	X
ejpam-3329	797	28	class	class	NOUN
ejpam-3329	797	29	q	q	NOUN
ejpam-3329	797	30	if	if	SCONJ
ejpam-3329	798	1	and	and	CCONJ
ejpam-3329	798	2	only	only	ADV
ejpam-3329	798	3	if	if	SCONJ
ejpam-3329	798	4	t̃	t̃	PROPN
ejpam-3329	798	5	∗	∗	NOUN
ejpam-3329	798	6	∗	∗	NOUN
ejpam-3329	798	7	is	be	AUX
ejpam-3329	798	8	quasi	quasi	NOUN
ejpam-3329	798	9	n	n	PRON
ejpam-3329	798	10	class	class	NOUN
ejpam-3329	798	11	q	q	NOUN
ejpam-3329	798	12	operator	operator	NOUN
ejpam-3329	798	13	.	.	PUNCT
ejpam-3329	799	1	theorem	theorem	VERB
ejpam-3329	799	2	56	56	NUM
ejpam-3329	799	3	.	.	PUNCT
ejpam-3329	800	1	let	let	AUX
ejpam-3329	800	2	t	t	NOUN
ejpam-3329	800	3	=	=	SYM
ejpam-3329	800	4	u	u	NOUN
ejpam-3329	800	5	|t	|t	VERB
ejpam-3329	800	6	|	|	ADV
ejpam-3329	800	7	be	be	AUX
ejpam-3329	800	8	the	the	DET
ejpam-3329	800	9	polar	polar	ADJ
ejpam-3329	800	10	decomposition	decomposition	NOUN
ejpam-3329	800	11	of	of	ADP
ejpam-3329	800	12	quasi	quasi	NOUN
ejpam-3329	800	13	n	n	PRON
ejpam-3329	800	14	class	class	NOUN
ejpam-3329	800	15	q	q	NOUN
ejpam-3329	800	16	operator	operator	NOUN
ejpam-3329	800	17	t	t	PROPN
ejpam-3329	800	18	and	and	CCONJ
ejpam-3329	800	19	u	u	NOUN
ejpam-3329	800	20	is	be	AUX
ejpam-3329	800	21	unitary	unitary	ADJ
ejpam-3329	800	22	,	,	PUNCT
ejpam-3329	800	23	then	then	ADV
ejpam-3329	800	24	t̃	t̃	PROPN
ejpam-3329	800	25	∗	∗	NOUN
ejpam-3329	800	26	is	be	AUX
ejpam-3329	800	27	quasi	quasi	NOUN
ejpam-3329	800	28	n	n	X
ejpam-3329	800	29	class	class	NOUN
ejpam-3329	800	30	q	q	NOUN
ejpam-3329	800	31	if	if	SCONJ
ejpam-3329	801	1	and	and	CCONJ
ejpam-3329	801	2	only	only	ADV
ejpam-3329	801	3	if	if	SCONJ
ejpam-3329	801	4	t̃	t̃	PROPN
ejpam-3329	801	5	∗	∗	NOUN
ejpam-3329	801	6	∗	∗	NOUN
ejpam-3329	801	7	is	be	AUX
ejpam-3329	801	8	quasi	quasi	NOUN
ejpam-3329	801	9	n	n	PRON
ejpam-3329	801	10	class	class	NOUN
ejpam-3329	801	11	q	q	NOUN
ejpam-3329	801	12	operator	operator	NOUN
ejpam-3329	801	13	.	.	PUNCT
ejpam-3329	802	1	theorem	theorem	VERB
ejpam-3329	802	2	57	57	NUM
ejpam-3329	802	3	.	.	PUNCT
ejpam-3329	803	1	an	an	DET
ejpam-3329	803	2	operator	operator	NOUN
ejpam-3329	803	3	t	t	NOUN
ejpam-3329	803	4	is	be	AUX
ejpam-3329	803	5	quasi	quasi	NOUN
ejpam-3329	803	6	n	n	PRON
ejpam-3329	803	7	class	class	NOUN
ejpam-3329	803	8	q∗	q∗	NOUN
ejpam-3329	804	1	if	if	SCONJ
ejpam-3329	804	2	and	and	CCONJ
ejpam-3329	804	3	only	only	ADV
ejpam-3329	804	4	if	if	SCONJ
ejpam-3329	804	5	(	(	PUNCT
ejpam-3329	804	6	1	1	NUM
ejpam-3329	804	7	+	+	CCONJ
ejpam-3329	804	8	n)t	n)t	ADJ
ejpam-3329	804	9	∗|t	∗|t	NUM
ejpam-3329	804	10	∗|2	∗|2	PROPN
ejpam-3329	804	11	t	t	PROPN
ejpam-3329	804	12	≤	≤	X
ejpam-3329	804	13	t	t	PROPN
ejpam-3329	804	14	∗|t	∗|t	PROPN
ejpam-3329	804	15	(	(	PUNCT
ejpam-3329	804	16	1+n)|2	1+n)|2	NUM
ejpam-3329	804	17	t	t	NOUN
ejpam-3329	804	18	+	+	CCONJ
ejpam-3329	804	19	nt	not	PART
ejpam-3329	804	20	∗t	∗t	ADJ
ejpam-3329	804	21	for	for	ADP
ejpam-3329	804	22	all	all	DET
ejpam-3329	804	23	x	x	SYM
ejpam-3329	804	24	∈	∈	PROPN
ejpam-3329	804	25	h	h	NOUN
ejpam-3329	804	26	and	and	CCONJ
ejpam-3329	804	27	for	for	ADP
ejpam-3329	804	28	every	every	DET
ejpam-3329	804	29	positive	positive	ADJ
ejpam-3329	804	30	integer	integer	NOUN
ejpam-3329	804	31	n.	n.	NOUN
ejpam-3329	804	32	theorem	theorem	VERB
ejpam-3329	804	33	58	58	NUM
ejpam-3329	804	34	.	.	PUNCT
ejpam-3329	805	1	if	if	SCONJ
ejpam-3329	805	2	t	t	PROPN
ejpam-3329	805	3	=	=	SYM
ejpam-3329	805	4	u	u	SYM
ejpam-3329	805	5	|t	|t	NOUN
ejpam-3329	805	6	|	|	ADV
ejpam-3329	805	7	is	be	AUX
ejpam-3329	805	8	the	the	DET
ejpam-3329	805	9	polar	polar	ADJ
ejpam-3329	805	10	decomposition	decomposition	NOUN
ejpam-3329	805	11	of	of	ADP
ejpam-3329	805	12	quasi	quasi	NOUN
ejpam-3329	805	13	n	n	PRON
ejpam-3329	805	14	class	class	NOUN
ejpam-3329	805	15	q∗	q∗	NOUN
ejpam-3329	805	16	operator	operator	NOUN
ejpam-3329	805	17	t	t	NOUN
ejpam-3329	805	18	,	,	PUNCT
ejpam-3329	805	19	then	then	ADV
ejpam-3329	805	20	t	t	PROPN
ejpam-3329	805	21	is	be	AUX
ejpam-3329	805	22	quasi	quasi	NOUN
ejpam-3329	805	23	n	n	PRON
ejpam-3329	805	24	class	class	NOUN
ejpam-3329	805	25	q∗	q∗	NOUN
ejpam-3329	805	26	operator	operator	NOUN
ejpam-3329	805	27	.	.	PUNCT
ejpam-3329	806	1	theorem	theorem	VERB
ejpam-3329	806	2	59	59	NUM
ejpam-3329	806	3	.	.	PUNCT
ejpam-3329	807	1	if	if	SCONJ
ejpam-3329	807	2	t	t	PROPN
ejpam-3329	807	3	is	be	AUX
ejpam-3329	807	4	quasi	quasi	NOUN
ejpam-3329	807	5	n	n	PRON
ejpam-3329	807	6	class	class	NOUN
ejpam-3329	807	7	q∗	q∗	NOUN
ejpam-3329	807	8	operator	operator	NOUN
ejpam-3329	807	9	t	t	NOUN
ejpam-3329	807	10	and	and	CCONJ
ejpam-3329	807	11	s	s	VERB
ejpam-3329	807	12	is	be	AUX
ejpam-3329	807	13	unitary	unitary	ADJ
ejpam-3329	808	1	such	such	ADJ
ejpam-3329	808	2	that	that	PRON
ejpam-3329	808	3	ts	ts	ADP
ejpam-3329	808	4	=	=	PROPN
ejpam-3329	808	5	st	st	PROPN
ejpam-3329	808	6	then	then	ADV
ejpam-3329	808	7	a	a	DET
ejpam-3329	808	8	=	=	X
ejpam-3329	808	9	ts	ts	NOUN
ejpam-3329	808	10	is	be	AUX
ejpam-3329	808	11	also	also	ADV
ejpam-3329	808	12	quasi	quasi	ADJ
ejpam-3329	808	13	n	n	PRON
ejpam-3329	808	14	class	class	NOUN
ejpam-3329	808	15	q∗	q∗	NOUN
ejpam-3329	808	16	operator	operator	NOUN
ejpam-3329	808	17	.	.	PUNCT
ejpam-3329	809	1	theorem	theorem	VERB
ejpam-3329	809	2	60	60	NUM
ejpam-3329	809	3	.	.	PUNCT
ejpam-3329	810	1	if	if	SCONJ
ejpam-3329	810	2	t̃	t̃	PROPN
ejpam-3329	810	3	is	be	AUX
ejpam-3329	810	4	quasi	quasi	NOUN
ejpam-3329	810	5	n	n	PRON
ejpam-3329	810	6	class	class	NOUN
ejpam-3329	810	7	q∗	q∗	NOUN
ejpam-3329	810	8	if	if	SCONJ
ejpam-3329	810	9	and	and	CCONJ
ejpam-3329	810	10	only	only	ADV
ejpam-3329	810	11	if	if	SCONJ
ejpam-3329	810	12	t̃	t̃	PROPN
ejpam-3329	810	13	∗	∗	NOUN
ejpam-3329	810	14	is	be	AUX
ejpam-3329	810	15	quasi	quasi	NOUN
ejpam-3329	810	16	n	n	PRON
ejpam-3329	810	17	class	class	NOUN
ejpam-3329	810	18	q∗	q∗	NOUN
ejpam-3329	810	19	operator	operator	NOUN
ejpam-3329	810	20	.	.	PUNCT
ejpam-3329	811	1	theorem	theorem	VERB
ejpam-3329	811	2	61	61	NUM
ejpam-3329	811	3	.	.	PUNCT
ejpam-3329	812	1	if	if	SCONJ
ejpam-3329	812	2	t̃	t̃	PROPN
ejpam-3329	812	3	∗	∗	NOUN
ejpam-3329	812	4	is	be	AUX
ejpam-3329	812	5	quasi	quasi	NOUN
ejpam-3329	812	6	n	n	PRON
ejpam-3329	812	7	class	class	NOUN
ejpam-3329	812	8	q∗	q∗	NOUN
ejpam-3329	812	9	if	if	SCONJ
ejpam-3329	812	10	and	and	CCONJ
ejpam-3329	812	11	only	only	ADV
ejpam-3329	812	12	if	if	SCONJ
ejpam-3329	812	13	t̃	t̃	PROPN
ejpam-3329	812	14	∗	∗	NOUN
ejpam-3329	812	15	∗	∗	NOUN
ejpam-3329	812	16	is	be	AUX
ejpam-3329	812	17	quasi	quasi	NOUN
ejpam-3329	812	18	n	n	PRON
ejpam-3329	812	19	class	class	NOUN
ejpam-3329	812	20	q∗	q∗	NOUN
ejpam-3329	812	21	operator	operator	NOUN
ejpam-3329	812	22	.	.	PUNCT
ejpam-3329	813	1	references	reference	NOUN
ejpam-3329	813	2	1129	1129	NUM
ejpam-3329	813	3	references	reference	NOUN
ejpam-3329	813	4	[	[	X
ejpam-3329	813	5	1	1	NUM
ejpam-3329	813	6	]	]	PUNCT
ejpam-3329	813	7	a.	a.	NOUN
ejpam-3329	813	8	aluthge	aluthge	PROPN
ejpam-3329	813	9	.	.	PUNCT
ejpam-3329	814	1	on	on	ADP
ejpam-3329	814	2	p	p	PROPN
ejpam-3329	814	3	-	-	PUNCT
ejpam-3329	814	4	hyponormal	hyponormal	ADJ
ejpam-3329	814	5	operators	operator	NOUN
ejpam-3329	814	6	for	for	ADP
ejpam-3329	814	7	0	0	NUM
ejpam-3329	814	8	<	<	X
ejpam-3329	814	9	p	p	X
ejpam-3329	814	10	<	<	X
ejpam-3329	814	11	1	1	NUM
ejpam-3329	814	12	.	.	PUNCT
ejpam-3329	814	13	integr	integr	NOUN
ejpam-3329	814	14	.	.	PUNCT
ejpam-3329	815	1	equat	equat	PROPN
ejpam-3329	815	2	.	.	PUNCT
ejpam-3329	816	1	oper	oper	PROPN
ejpam-3329	816	2	.	.	PUNCT
ejpam-3329	817	1	th	th	PROPN
ejpam-3329	817	2	.	.	PROPN
ejpam-3329	817	3	,	,	PUNCT
ejpam-3329	817	4	13:307–315	13:307–315	NUM
ejpam-3329	817	5	,	,	PUNCT
ejpam-3329	817	6	1990	1990	NUM
ejpam-3329	817	7	.	.	PUNCT
ejpam-3329	818	1	[	[	X
ejpam-3329	818	2	2	2	NUM
ejpam-3329	818	3	]	]	PUNCT
ejpam-3329	818	4	a.	a.	NOUN
ejpam-3329	818	5	aluthge	aluthge	PROPN
ejpam-3329	818	6	.	.	PUNCT
ejpam-3329	819	1	some	some	DET
ejpam-3329	819	2	generalized	generalized	ADJ
ejpam-3329	819	3	theorems	theorem	NOUN
ejpam-3329	819	4	on	on	ADP
ejpam-3329	819	5	p	p	ADJ
ejpam-3329	819	6	-	-	PUNCT
ejpam-3329	819	7	hyponormal	hyponormal	ADJ
ejpam-3329	819	8	operators	operator	NOUN
ejpam-3329	819	9	for	for	ADP
ejpam-3329	819	10	0	0	NUM
ejpam-3329	819	11	<	<	X
ejpam-3329	819	12	p	p	X
ejpam-3329	819	13	<	<	X
ejpam-3329	819	14	1	1	NUM
ejpam-3329	819	15	.	.	PUNCT
ejpam-3329	819	16	integr	integr	NOUN
ejpam-3329	819	17	.	.	PUNCT
ejpam-3329	820	1	equat	equat	PROPN
ejpam-3329	820	2	.	.	PUNCT
ejpam-3329	821	1	oper	oper	PROPN
ejpam-3329	821	2	.	.	PUNCT
ejpam-3329	822	1	th	th	PROPN
ejpam-3329	822	2	.	.	PROPN
ejpam-3329	822	3	,	,	PUNCT
ejpam-3329	822	4	24:497	24:497	NUM
ejpam-3329	822	5	–	–	PUNCT
ejpam-3329	822	6	502	502	NUM
ejpam-3329	822	7	,	,	PUNCT
ejpam-3329	822	8	1996	1996	NUM
ejpam-3329	822	9	.	.	PUNCT
ejpam-3329	823	1	[	[	X
ejpam-3329	823	2	3	3	X
ejpam-3329	823	3	]	]	X
ejpam-3329	823	4	c.	c.	PROPN
ejpam-3329	823	5	s	s	PROPN
ejpam-3329	823	6	kubrusly	kubrusly	PROPN
ejpam-3329	823	7	b.p	b.p	PROPN
ejpam-3329	823	8	.	.	PROPN
ejpam-3329	823	9	duggal	duggal	PROPN
ejpam-3329	823	10	and	and	CCONJ
ejpam-3329	823	11	n.	n.	PROPN
ejpam-3329	823	12	levan	levan	PROPN
ejpam-3329	823	13	.	.	PUNCT
ejpam-3329	824	1	contractions	contraction	NOUN
ejpam-3329	824	2	of	of	ADP
ejpam-3329	824	3	class	class	NOUN
ejpam-3329	824	4	q	q	NOUN
ejpam-3329	824	5	and	and	CCONJ
ejpam-3329	824	6	invariant	invariant	ADJ
ejpam-3329	824	7	subspaces	subspace	NOUN
ejpam-3329	824	8	.	.	PUNCT
ejpam-3329	825	1	bull	bull	NOUN
ejpam-3329	825	2	.	.	PUNCT
ejpam-3329	826	1	korean	korean	PROPN
ejpam-3329	826	2	mathematical	mathematical	ADJ
ejpam-3329	826	3	society	society	NOUN
ejpam-3329	826	4	,	,	PUNCT
ejpam-3329	826	5	42:169–177	42:169–177	NUM
ejpam-3329	826	6	,	,	PUNCT
ejpam-3329	826	7	2005	2005	NUM
ejpam-3329	826	8	.	.	PUNCT
ejpam-3329	827	1	[	[	X
ejpam-3329	827	2	4	4	X
ejpam-3329	827	3	]	]	PUNCT
ejpam-3329	827	4	p.	p.	NOUN
ejpam-3329	827	5	maheswari	maheswari	PROPN
ejpam-3329	827	6	naik	naik	PROPN
ejpam-3329	827	7	d.	d.	PROPN
ejpam-3329	827	8	senthilkumar	senthilkumar	PROPN
ejpam-3329	827	9	and	and	CCONJ
ejpam-3329	827	10	d.	d.	PROPN
ejpam-3329	827	11	kiruthika	kiruthika	PROPN
ejpam-3329	827	12	.	.	PUNCT
ejpam-3329	827	13	quasi	quasi	PROPN
ejpam-3329	827	14	class	class	PROPN
ejpam-3329	827	15	q	q	NOUN
ejpam-3329	827	16	*	*	NOUN
ejpam-3329	827	17	composition	composition	NOUN
ejpam-3329	827	18	operators	operator	NOUN
ejpam-3329	827	19	.	.	PUNCT
ejpam-3329	828	1	international	international	ADJ
ejpam-3329	828	2	j.	j.	PROPN
ejpam-3329	828	3	of	of	ADP
ejpam-3329	828	4	math	math	PROPN
ejpam-3329	828	5	.	.	PUNCT
ejpam-3329	829	1	sci	sci	PROPN
ejpam-3329	829	2	.	.	PROPN
ejpam-3329	829	3	and	and	CCONJ
ejpam-3329	829	4	engg	engg	PROPN
ejpam-3329	829	5	.	.	PUNCT
ejpam-3329	830	1	appls	appls	PROPN
ejpam-3329	830	2	.	.	PUNCT
ejpam-3329	831	1	(	(	PUNCT
ejpam-3329	831	2	ijmsea	ijmsea	NOUN
ejpam-3329	831	3	)	)	PUNCT
ejpam-3329	831	4	,	,	PUNCT
ejpam-3329	831	5	4:1–9	4:1–9	NUM
ejpam-3329	831	6	,	,	PUNCT
ejpam-3329	831	7	2011	2011	NUM
ejpam-3329	831	8	.	.	PUNCT
ejpam-3329	832	1	[	[	X
ejpam-3329	832	2	5	5	NUM
ejpam-3329	832	3	]	]	PUNCT
ejpam-3329	832	4	a.	a.	NOUN
ejpam-3329	832	5	devika	devika	PROPN
ejpam-3329	832	6	and	and	CCONJ
ejpam-3329	832	7	g.	g.	PROPN
ejpam-3329	832	8	suresh	suresh	PROPN
ejpam-3329	832	9	.	.	PUNCT
ejpam-3329	833	1	some	some	DET
ejpam-3329	833	2	properties	property	NOUN
ejpam-3329	833	3	of	of	ADP
ejpam-3329	833	4	quasi	quasi	ADJ
ejpam-3329	833	5	class	class	PROPN
ejpam-3329	833	6	q	q	PROPN
ejpam-3329	833	7	operators	operator	NOUN
ejpam-3329	833	8	.	.	PUNCT
ejpam-3329	834	1	international	international	ADJ
ejpam-3329	834	2	journal	journal	PROPN
ejpam-3329	834	3	of	of	ADP
ejpam-3329	834	4	applied	apply	VERB
ejpam-3329	834	5	mathematics	mathematic	NOUN
ejpam-3329	834	6	and	and	CCONJ
ejpam-3329	834	7	statistical	statistical	ADJ
ejpam-3329	834	8	sciences	science	NOUN
ejpam-3329	834	9	(	(	PUNCT
ejpam-3329	834	10	ijamss	ijamss	NOUN
ejpam-3329	834	11	)	)	PUNCT
ejpam-3329	834	12	,	,	PUNCT
ejpam-3329	834	13	1:63–68	1:63–68	NUM
ejpam-3329	834	14	,	,	PUNCT
ejpam-3329	834	15	2013	2013	NUM
ejpam-3329	834	16	.	.	PUNCT
ejpam-3329	835	1	[	[	X
ejpam-3329	835	2	6	6	NUM
ejpam-3329	835	3	]	]	X
ejpam-3329	835	4	b.p	b.p	PROPN
ejpam-3329	835	5	.	.	PROPN
ejpam-3329	835	6	duggal	duggal	PROPN
ejpam-3329	835	7	.	.	PUNCT
ejpam-3329	836	1	quasi	quasi	PROPN
ejpam-3329	836	2	similar	similar	ADJ
ejpam-3329	836	3	p	p	PROPN
ejpam-3329	836	4	hyponormal	hyponormal	ADJ
ejpam-3329	836	5	operators	operator	NOUN
ejpam-3329	836	6	.	.	PUNCT
ejpam-3329	837	1	integr	integr	PROPN
ejpam-3329	837	2	.	.	PUNCT
ejpam-3329	838	1	equat.oper	equat.oper	NOUN
ejpam-3329	838	2	,	,	PUNCT
ejpam-3329	838	3	26:338–345	26:338–345	PROPN
ejpam-3329	838	4	,	,	PUNCT
ejpam-3329	838	5	1996	1996	NUM
ejpam-3329	838	6	.	.	PUNCT
ejpam-3329	839	1	[	[	X
ejpam-3329	839	2	7	7	X
ejpam-3329	839	3	]	]	PUNCT
ejpam-3329	839	4	t.	t.	PROPN
ejpam-3329	839	5	furuta	furuta	PROPN
ejpam-3329	839	6	.	.	PUNCT
ejpam-3329	840	1	on	on	ADP
ejpam-3329	840	2	the	the	DET
ejpam-3329	840	3	class	class	NOUN
ejpam-3329	840	4	of	of	ADP
ejpam-3329	840	5	paranormal	paranormal	ADJ
ejpam-3329	840	6	operators	operator	NOUN
ejpam-3329	840	7	.	.	PUNCT
ejpam-3329	841	1	proc	proc	PROPN
ejpam-3329	841	2	.	.	PUNCT
ejpam-3329	842	1	japan	japan	PROPN
ejpam-3329	842	2	.	.	PUNCT
ejpam-3329	843	1	acad	acad	PROPN
ejpam-3329	843	2	.	.	PROPN
ejpam-3329	843	3	,	,	PUNCT
ejpam-3329	843	4	43:594–598	43:594–598	PROPN
ejpam-3329	843	5	,	,	PUNCT
ejpam-3329	843	6	1967	1967	NUM
ejpam-3329	843	7	.	.	PUNCT
ejpam-3329	844	1	[	[	X
ejpam-3329	844	2	8	8	NUM
ejpam-3329	844	3	]	]	SYM
ejpam-3329	844	4	v.r	v.r	PROPN
ejpam-3329	844	5	.	.	PROPN
ejpam-3329	844	6	hamiti	hamiti	PROPN
ejpam-3329	844	7	.	.	PUNCT
ejpam-3329	845	1	on	on	ADP
ejpam-3329	845	2	k	k	ADJ
ejpam-3329	845	3	-	-	PUNCT
ejpam-3329	845	4	quasi	quasi	ADJ
ejpam-3329	845	5	class	class	NOUN
ejpam-3329	845	6	q	q	PROPN
ejpam-3329	845	7	operators	operator	NOUN
ejpam-3329	845	8	.	.	PUNCT
ejpam-3329	846	1	bulletin	bulletin	NOUN
ejpam-3329	846	2	of	of	ADP
ejpam-3329	846	3	mathematical	mathematical	ADJ
ejpam-3329	846	4	analysis	analysis	NOUN
ejpam-3329	846	5	and	and	CCONJ
ejpam-3329	846	6	applications	application	NOUN
ejpam-3329	846	7	,	,	PUNCT
ejpam-3329	846	8	6:31–37	6:31–37	NOUN
ejpam-3329	846	9	,	,	PUNCT
ejpam-3329	846	10	2014	2014	NUM
ejpam-3329	846	11	.	.	PUNCT
ejpam-3329	847	1	[	[	X
ejpam-3329	847	2	9	9	NUM
ejpam-3329	847	3	]	]	X
ejpam-3329	847	4	d.	d.	PROPN
ejpam-3329	847	5	j.	j.	PROPN
ejpam-3329	847	6	harrington	harrington	PROPN
ejpam-3329	847	7	and	and	CCONJ
ejpam-3329	847	8	r.	r.	PROPN
ejpam-3329	847	9	whitley	whitley	PROPN
ejpam-3329	847	10	.	.	PUNCT
ejpam-3329	848	1	seminormal	seminormal	ADJ
ejpam-3329	848	2	composition	composition	NOUN
ejpam-3329	848	3	operators	operator	NOUN
ejpam-3329	848	4	.	.	PUNCT
ejpam-3329	849	1	j.	j.	PROPN
ejpam-3329	849	2	operator	operator	PROPN
ejpam-3329	849	3	theory	theory	NOUN
ejpam-3329	849	4	.	.	PUNCT
ejpam-3329	849	5	,	,	PUNCT
ejpam-3329	849	6	11:125–135	11:125–135	NUM
ejpam-3329	849	7	,	,	PUNCT
ejpam-3329	849	8	1984	1984	NUM
ejpam-3329	849	9	.	.	PUNCT
ejpam-3329	850	1	[	[	X
ejpam-3329	850	2	10	10	NUM
ejpam-3329	850	3	]	]	X
ejpam-3329	850	4	h.	h.	PROPN
ejpam-3329	850	5	y.	y.	PROPN
ejpam-3329	850	6	lee	lee	PROPN
ejpam-3329	850	7	j.	j.	PROPN
ejpam-3329	850	8	k.	k.	PROPN
ejpam-3329	850	9	han	han	PROPN
ejpam-3329	850	10	and	and	CCONJ
ejpam-3329	850	11	w.	w.	PROPN
ejpam-3329	850	12	y.	y.	PROPN
ejpam-3329	850	13	lee	lee	PROPN
ejpam-3329	850	14	.	.	PUNCT
ejpam-3329	851	1	invertible	invertible	ADJ
ejpam-3329	851	2	completions	completion	NOUN
ejpam-3329	851	3	of	of	ADP
ejpam-3329	851	4	2×	2×	NUM
ejpam-3329	851	5	2	2	NUM
ejpam-3329	851	6	upper	upper	ADJ
ejpam-3329	851	7	triangular	triangular	NOUN
ejpam-3329	851	8	operator	operator	NOUN
ejpam-3329	851	9	matrices	matrix	NOUN
ejpam-3329	851	10	.	.	PUNCT
ejpam-3329	852	1	proc	proc	PROPN
ejpam-3329	852	2	.	.	PUNCT
ejpam-3329	853	1	amer	amer	PROPN
ejpam-3329	853	2	.	.	PUNCT
ejpam-3329	853	3	math	math	PROPN
ejpam-3329	853	4	.	.	PUNCT
ejpam-3329	854	1	soc	soc	PROPN
ejpam-3329	854	2	.	.	PUNCT
ejpam-3329	854	3	,	,	PUNCT
ejpam-3329	854	4	128:119–123	128:119–123	NUM
ejpam-3329	854	5	,	,	PUNCT
ejpam-3329	854	6	2000	2000	NUM
ejpam-3329	854	7	.	.	PUNCT
ejpam-3329	855	1	[	[	X
ejpam-3329	855	2	11	11	NUM
ejpam-3329	855	3	]	]	X
ejpam-3329	855	4	d.	d.	PROPN
ejpam-3329	855	5	senthil	senthil	PROPN
ejpam-3329	855	6	kumar	kumar	PROPN
ejpam-3329	855	7	and	and	CCONJ
ejpam-3329	855	8	t.	t.	PROPN
ejpam-3329	855	9	prasad	prasad	PROPN
ejpam-3329	855	10	.	.	PUNCT
ejpam-3329	856	1	m	m	PROPN
ejpam-3329	856	2	class	class	NOUN
ejpam-3329	856	3	q	q	NOUN
ejpam-3329	856	4	composition	composition	NOUN
ejpam-3329	856	5	operators	operator	NOUN
ejpam-3329	856	6	.	.	PUNCT
ejpam-3329	857	1	scientia	scientia	PROPN
ejpam-3329	857	2	magna	magna	PROPN
ejpam-3329	857	3	.	.	PROPN
ejpam-3329	857	4	,	,	PUNCT
ejpam-3329	857	5	6:25–30	6:25–30	NUM
ejpam-3329	857	6	,	,	PUNCT
ejpam-3329	857	7	2010	2010	NUM
ejpam-3329	857	8	.	.	PUNCT
ejpam-3329	858	1	[	[	X
ejpam-3329	858	2	12	12	NUM
ejpam-3329	858	3	]	]	PUNCT
ejpam-3329	858	4	a	a	DET
ejpam-3329	858	5	lambert	lambert	PROPN
ejpam-3329	858	6	.	.	PUNCT
ejpam-3329	858	7	hyponormal	hyponormal	ADJ
ejpam-3329	858	8	composition	composition	NOUN
ejpam-3329	858	9	operators	operator	NOUN
ejpam-3329	858	10	.	.	PUNCT
ejpam-3329	859	1	bull	bull	NOUN
ejpam-3329	859	2	.	.	PUNCT
ejpam-3329	860	1	london	london	PROPN
ejpam-3329	860	2	.	.	PUNCT
ejpam-3329	861	1	math	math	PROPN
ejpam-3329	861	2	.	.	PUNCT
ejpam-3329	862	1	soc	soc	PROPN
ejpam-3329	862	2	.	.	PUNCT
ejpam-3329	862	3	,	,	PUNCT
ejpam-3329	862	4	18:395	18:395	NUM
ejpam-3329	862	5	–	–	PUNCT
ejpam-3329	862	6	400	400	NUM
ejpam-3329	862	7	,	,	PUNCT
ejpam-3329	862	8	1986	1986	NUM
ejpam-3329	862	9	.	.	PUNCT
ejpam-3329	863	1	[	[	X
ejpam-3329	863	2	13	13	NUM
ejpam-3329	863	3	]	]	PUNCT
ejpam-3329	863	4	s.	s.	PROPN
ejpam-3329	863	5	panayappan	panayappan	PROPN
ejpam-3329	863	6	.	.	PUNCT
ejpam-3329	864	1	non	non	ADJ
ejpam-3329	864	2	-	-	ADJ
ejpam-3329	864	3	hyponormal	hyponormal	ADJ
ejpam-3329	864	4	weighted	weight	VERB
ejpam-3329	864	5	composition	composition	NOUN
ejpam-3329	864	6	operators	operator	NOUN
ejpam-3329	864	7	.	.	PUNCT
ejpam-3329	865	1	indian	indian	PROPN
ejpam-3329	865	2	j.	j.	PROPN
ejpam-3329	865	3	pure	pure	PROPN
ejpam-3329	865	4	appl	appl	PROPN
ejpam-3329	865	5	.	.	PUNCT
ejpam-3329	865	6	math	math	PROPN
ejpam-3329	865	7	.	.	PUNCT
ejpam-3329	865	8	,	,	PUNCT
ejpam-3329	865	9	27:979–983	27:979–983	NUM
ejpam-3329	865	10	,	,	PUNCT
ejpam-3329	865	11	1996	1996	NUM
ejpam-3329	865	12	.	.	PUNCT
ejpam-3329	866	1	[	[	X
ejpam-3329	866	2	14	14	NUM
ejpam-3329	866	3	]	]	PUNCT
ejpam-3329	866	4	t.	t.	NOUN
ejpam-3329	866	5	veluchamy	veluchamy	NOUN
ejpam-3329	866	6	and	and	CCONJ
ejpam-3329	866	7	s.panayappan	s.panayappan	ADJ
ejpam-3329	866	8	.	.	PUNCT
ejpam-3329	867	1	paranormal	paranormal	ADJ
ejpam-3329	867	2	composition	composition	NOUN
ejpam-3329	867	3	operators	operator	NOUN
ejpam-3329	867	4	.	.	PUNCT
ejpam-3329	868	1	indian	indian	ADJ
ejpam-3329	868	2	journal	journal	PROPN
ejpam-3329	868	3	of	of	ADP
ejpam-3329	868	4	pure	pure	ADJ
ejpam-3329	868	5	and	and	CCONJ
ejpam-3329	868	6	applied	applied	ADJ
ejpam-3329	868	7	math	math	NOUN
ejpam-3329	868	8	.	.	PUNCT
ejpam-3329	868	9	,	,	PUNCT
ejpam-3329	868	10	24:257–262	24:257–262	NUM
ejpam-3329	868	11	,	,	PUNCT
ejpam-3329	868	12	1993	1993	NUM
ejpam-3329	868	13	.	.	PUNCT
ejpam-3329	869	1	[	[	X
ejpam-3329	869	2	15	15	NUM
ejpam-3329	869	3	]	]	X
ejpam-3329	869	4	y.	y.	PROPN
ejpam-3329	869	5	yang	yang	PROPN
ejpam-3329	869	6	and	and	CCONJ
ejpam-3329	869	7	cheoul	cheoul	PROPN
ejpam-3329	869	8	jun	jun	PROPN
ejpam-3329	869	9	kim	kim	PROPN
ejpam-3329	869	10	.	.	PUNCT
ejpam-3329	870	1	contractions	contraction	NOUN
ejpam-3329	870	2	of	of	ADP
ejpam-3329	870	3	class	class	NOUN
ejpam-3329	870	4	q	q	PROPN
ejpam-3329	870	5	*	*	NOUN
ejpam-3329	870	6	.	.	PUNCT
ejpam-3329	871	1	far	far	PROPN
ejpam-3329	871	2	east	east	NOUN
ejpam-3329	871	3	.	.	PUNCT
ejpam-3329	872	1	j.math.sci.(fjms	j.math.sci.(fjms	ADJ
ejpam-3329	872	2	)	)	PUNCT
ejpam-3329	872	3	,	,	PUNCT
ejpam-3329	872	4	27:649–657	27:649–657	NUM
ejpam-3329	872	5	,	,	PUNCT
ejpam-3329	872	6	2007	2007	NUM
ejpam-3329	872	7	.	.	PUNCT
ejpam-3329	873	1	[	[	X
ejpam-3329	873	2	16	16	NUM
ejpam-3329	873	3	]	]	X
ejpam-3329	873	4	j.	j.	PROPN
ejpam-3329	873	5	yuan	yuan	PROPN
ejpam-3329	873	6	and	and	CCONJ
ejpam-3329	873	7	z.	z.	PROPN
ejpam-3329	873	8	gao	gao	PROPN
ejpam-3329	873	9	.	.	PUNCT
ejpam-3329	874	1	weyl	weyl	PROPN
ejpam-3329	874	2	spectrum	spectrum	NOUN
ejpam-3329	874	3	of	of	ADP
ejpam-3329	874	4	class	class	NOUN
ejpam-3329	874	5	a(n	a(n	ADV
ejpam-3329	874	6	)	)	PUNCT
ejpam-3329	874	7	and	and	CCONJ
ejpam-3329	874	8	n	n	CCONJ
ejpam-3329	874	9	-	-	PUNCT
ejpam-3329	874	10	paranormal	paranormal	ADJ
ejpam-3329	874	11	operators	operator	NOUN
ejpam-3329	874	12	.	.	PUNCT
ejpam-3329	875	1	integr	integr	PROPN
ejpam-3329	875	2	.	.	PUNCT
ejpam-3329	876	1	equ	equ	PROPN
ejpam-3329	876	2	.	.	PUNCT
ejpam-3329	876	3	oper	oper	PROPN
ejpam-3329	876	4	.	.	PUNCT
ejpam-3329	876	5	theory	theory	NOUN
ejpam-3329	876	6	.	.	PUNCT
ejpam-3329	876	7	,	,	PUNCT
ejpam-3329	877	1	60:289–298	60:289–298	NUM
ejpam-3329	877	2	,	,	PUNCT
ejpam-3329	877	3	2008	2008	NUM
ejpam-3329	877	4	.	.	PUNCT