id	sid	tid	token	lemma	pos
ejpam-3515	1	1	european	european	PROPN
ejpam-3515	1	2	journal	journal	PROPN
ejpam-3515	1	3	of	of	ADP
ejpam-3515	1	4	pure	pure	ADJ
ejpam-3515	1	5	and	and	CCONJ
ejpam-3515	1	6	applied	apply	VERB
ejpam-3515	1	7	mathematics	mathematic	NOUN
ejpam-3515	1	8	vol	vol	NOUN
ejpam-3515	1	9	.	.	PROPN
ejpam-3515	2	1	12	12	NUM
ejpam-3515	2	2	,	,	PUNCT
ejpam-3515	2	3	no	no	INTJ
ejpam-3515	2	4	.	.	NOUN
ejpam-3515	2	5	4	4	NUM
ejpam-3515	2	6	,	,	PUNCT
ejpam-3515	2	7	2019	2019	NUM
ejpam-3515	2	8	,	,	PUNCT
ejpam-3515	2	9	1441	1441	NUM
ejpam-3515	2	10	-	-	SYM
ejpam-3515	2	11	1454	1454	NUM
ejpam-3515	2	12	issn	issn	PROPN
ejpam-3515	2	13	1307	1307	NUM
ejpam-3515	2	14	-	-	SYM
ejpam-3515	2	15	5543	5543	NUM
ejpam-3515	2	16	–	–	PUNCT
ejpam-3515	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3515	2	18	published	publish	VERB
ejpam-3515	2	19	by	by	ADP
ejpam-3515	2	20	new	new	PROPN
ejpam-3515	2	21	york	york	PROPN
ejpam-3515	2	22	business	business	PROPN
ejpam-3515	2	23	global	global	PROPN
ejpam-3515	2	24	the	the	DET
ejpam-3515	2	25	smoothness	smoothness	NOUN
ejpam-3515	2	26	of	of	ADP
ejpam-3515	2	27	schrödinger	schrödinger	NOUN
ejpam-3515	2	28	operator	operator	NOUN
ejpam-3515	2	29	with	with	ADP
ejpam-3515	2	30	electromagnetic	electromagnetic	ADJ
ejpam-3515	2	31	potential	potential	ADJ
ejpam-3515	2	32	yahea	yahea	PROPN
ejpam-3515	2	33	hashem	hashem	PROPN
ejpam-3515	2	34	saleem1	saleem1	PROPN
ejpam-3515	2	35	,	,	PUNCT
ejpam-3515	2	36	hadeel	hadeel	PROPN
ejpam-3515	2	37	ali	ali	PROPN
ejpam-3515	2	38	shubber1,2,∗	shubber1,2,∗	PROPN
ejpam-3515	2	39	1	1	NUM
ejpam-3515	2	40	department	department	NOUN
ejpam-3515	2	41	of	of	ADP
ejpam-3515	2	42	mathematics	mathematic	NOUN
ejpam-3515	2	43	,	,	PUNCT
ejpam-3515	2	44	college	college	NOUN
ejpam-3515	2	45	of	of	ADP
ejpam-3515	2	46	education	education	NOUN
ejpam-3515	2	47	for	for	ADP
ejpam-3515	2	48	pure	pure	ADJ
ejpam-3515	2	49	sciences	science	NOUN
ejpam-3515	2	50	,	,	PUNCT
ejpam-3515	2	51	university	university	NOUN
ejpam-3515	2	52	of	of	ADP
ejpam-3515	2	53	basrah	basrah	PROPN
ejpam-3515	2	54	,	,	PUNCT
ejpam-3515	2	55	basrah	basrah	PROPN
ejpam-3515	2	56	,	,	PUNCT
ejpam-3515	2	57	iraq	iraq	PROPN
ejpam-3515	2	58	2	2	NUM
ejpam-3515	2	59	department	department	NOUN
ejpam-3515	2	60	of	of	ADP
ejpam-3515	2	61	mathematics	mathematic	NOUN
ejpam-3515	2	62	,	,	PUNCT
ejpam-3515	2	63	college	college	NOUN
ejpam-3515	2	64	of	of	ADP
ejpam-3515	2	65	education	education	NOUN
ejpam-3515	2	66	for	for	ADP
ejpam-3515	2	67	pure	pure	ADJ
ejpam-3515	2	68	sciences	science	NOUN
ejpam-3515	2	69	,	,	PUNCT
ejpam-3515	2	70	university	university	NOUN
ejpam-3515	2	71	of	of	ADP
ejpam-3515	2	72	thi	thi	PROPN
ejpam-3515	2	73	-	-	PUNCT
ejpam-3515	2	74	qar	qar	PROPN
ejpam-3515	2	75	,	,	PUNCT
ejpam-3515	2	76	thi	thi	PROPN
ejpam-3515	2	77	-	-	PUNCT
ejpam-3515	2	78	qar	qar	PROPN
ejpam-3515	2	79	,	,	PUNCT
ejpam-3515	2	80	iraq	iraq	PROPN
ejpam-3515	2	81	abstract	abstract	NOUN
ejpam-3515	2	82	.	.	PUNCT
ejpam-3515	3	1	in	in	ADP
ejpam-3515	3	2	this	this	DET
ejpam-3515	3	3	paper	paper	NOUN
ejpam-3515	3	4	,	,	PUNCT
ejpam-3515	3	5	we	we	PRON
ejpam-3515	3	6	prove	prove	VERB
ejpam-3515	3	7	that	that	SCONJ
ejpam-3515	3	8	the	the	DET
ejpam-3515	3	9	feynman	feynman	PROPN
ejpam-3515	3	10	-	-	PUNCT
ejpam-3515	3	11	kac	kac	PROPN
ejpam-3515	3	12	itô	itô	PROPN
ejpam-3515	3	13	formula	formula	NOUN
ejpam-3515	3	14	of	of	ADP
ejpam-3515	3	15	the	the	DET
ejpam-3515	3	16	schrödinger	schrödinger	NOUN
ejpam-3515	3	17	operator	operator	NOUN
ejpam-3515	3	18	with	with	ADP
ejpam-3515	3	19	electromagnetic	electromagnetic	ADJ
ejpam-3515	3	20	ψ(t	ψ(t	PROPN
ejpam-3515	3	21	,	,	PUNCT
ejpam-3515	3	22	x	x	NOUN
ejpam-3515	3	23	)	)	PUNCT
ejpam-3515	3	24	in	in	ADP
ejpam-3515	3	25	equation	equation	NOUN
ejpam-3515	3	26	(	(	PUNCT
ejpam-3515	3	27	1	1	NUM
ejpam-3515	3	28	)	)	PUNCT
ejpam-3515	3	29	in	in	ADP
ejpam-3515	3	30	[	[	X
ejpam-3515	3	31	8	8	NUM
ejpam-3515	3	32	]	]	PUNCT
ejpam-3515	3	33	which	which	PRON
ejpam-3515	3	34	defined	define	VERB
ejpam-3515	3	35	as	as	ADP
ejpam-3515	3	36	ψ(t	ψ(t	PROPN
ejpam-3515	3	37	,	,	PUNCT
ejpam-3515	3	38	x	x	NOUN
ejpam-3515	3	39	)	)	PUNCT
ejpam-3515	3	40	=	=	SYM
ejpam-3515	3	41	∫	∫	PROPN
ejpam-3515	3	42	dµt	dµt	ADP
ejpam-3515	3	43	x(ω)exp	x(ω)exp	PROPN
ejpam-3515	3	44	(	(	PUNCT
ejpam-3515	3	45	−i	−i	ADJ
ejpam-3515	3	46	∫	∫	PROPN
ejpam-3515	3	47	t	t	PROPN
ejpam-3515	3	48	0	0	NUM
ejpam-3515	4	1	b(ω(s))dω	b(ω(s))dω	NOUN
ejpam-3515	5	1	−	−	PROPN
ejpam-3515	6	1	i	i	PRON
ejpam-3515	6	2	2	2	NUM
ejpam-3515	6	3	∫	∫	NOUN
ejpam-3515	6	4	t	t	NOUN
ejpam-3515	6	5	0	0	NUM
ejpam-3515	6	6	divbω(s)ds−	divbω(s)ds−	NUM
ejpam-3515	6	7	∫	∫	PROPN
ejpam-3515	6	8	t	t	PROPN
ejpam-3515	6	9	0	0	NUM
ejpam-3515	6	10	v	v	PROPN
ejpam-3515	6	11	(	(	PUNCT
ejpam-3515	6	12	ω(s)ds	ω(s)ds	NUM
ejpam-3515	6	13	)	)	PUNCT
ejpam-3515	6	14	ϕ(ω(t	ϕ(ω(t	NOUN
ejpam-3515	6	15	)	)	PUNCT
ejpam-3515	6	16	)	)	PUNCT
ejpam-3515	6	17	is	be	AUX
ejpam-3515	6	18	differentiable	differentiable	ADJ
ejpam-3515	6	19	of	of	ADP
ejpam-3515	6	20	the	the	DET
ejpam-3515	6	21	variable	variable	ADJ
ejpam-3515	6	22	t	t	PROPN
ejpam-3515	6	23	,	,	PUNCT
ejpam-3515	6	24	and	and	CCONJ
ejpam-3515	6	25	so	so	ADV
ejpam-3515	6	26	establish	establish	VERB
ejpam-3515	6	27	that	that	SCONJ
ejpam-3515	6	28	the	the	DET
ejpam-3515	6	29	infinitely	infinitely	ADV
ejpam-3515	6	30	differentiable	differentiable	ADJ
ejpam-3515	6	31	in	in	ADP
ejpam-3515	6	32	a	a	DET
ejpam-3515	6	33	region	region	NOUN
ejpam-3515	6	34	,	,	PUNCT
ejpam-3515	6	35	therefore	therefore	ADV
ejpam-3515	6	36	,	,	PUNCT
ejpam-3515	6	37	investigate	investigate	VERB
ejpam-3515	6	38	smoothness	smoothness	NOUN
ejpam-3515	6	39	of	of	ADP
ejpam-3515	6	40	this	this	DET
ejpam-3515	6	41	function	function	NOUN
ejpam-3515	6	42	.	.	PUNCT
ejpam-3515	7	1	2010	2010	NUM
ejpam-3515	7	2	mathematics	mathematic	NOUN
ejpam-3515	7	3	subject	subject	NOUN
ejpam-3515	7	4	classifications	classification	NOUN
ejpam-3515	7	5	:	:	PUNCT
ejpam-3515	7	6	35j10	35j10	NUM
ejpam-3515	7	7	,	,	PUNCT
ejpam-3515	7	8	35b65	35b65	NUM
ejpam-3515	7	9	key	key	ADJ
ejpam-3515	7	10	words	word	NOUN
ejpam-3515	7	11	and	and	CCONJ
ejpam-3515	7	12	phrases	phrase	NOUN
ejpam-3515	7	13	:	:	PUNCT
ejpam-3515	7	14	schrödinger	schrödinger	NOUN
ejpam-3515	7	15	operator	operator	NOUN
ejpam-3515	7	16	,	,	PUNCT
ejpam-3515	7	17	electric	electric	ADJ
ejpam-3515	7	18	potential	potential	NOUN
ejpam-3515	7	19	,	,	PUNCT
ejpam-3515	7	20	magnetic	magnetic	ADJ
ejpam-3515	7	21	potential	potential	NOUN
ejpam-3515	7	22	,	,	PUNCT
ejpam-3515	7	23	smoothness	smoothness	ADJ
ejpam-3515	7	24	.	.	PUNCT
ejpam-3515	8	1	1	1	X
ejpam-3515	8	2	.	.	X
ejpam-3515	8	3	introduction	introduction	NOUN
ejpam-3515	8	4	the	the	DET
ejpam-3515	8	5	problem	problem	NOUN
ejpam-3515	8	6	of	of	ADP
ejpam-3515	8	7	the	the	DET
ejpam-3515	8	8	self	self	NOUN
ejpam-3515	8	9	-	-	PUNCT
ejpam-3515	8	10	adjoint	adjoint	NOUN
ejpam-3515	8	11	operator	operator	NOUN
ejpam-3515	8	12	is	be	AUX
ejpam-3515	8	13	central	central	ADJ
ejpam-3515	8	14	in	in	ADP
ejpam-3515	8	15	the	the	DET
ejpam-3515	8	16	quantum	quantum	NOUN
ejpam-3515	8	17	machine	machine	NOUN
ejpam-3515	8	18	(	(	PUNCT
ejpam-3515	8	19	the	the	DET
ejpam-3515	8	20	diracvon	diracvon	PROPN
ejpam-3515	8	21	neumann	neumann	PROPN
ejpam-3515	8	22	formulation	formulation	NOUN
ejpam-3515	8	23	of	of	ADP
ejpam-3515	8	24	quantum	quantum	ADJ
ejpam-3515	8	25	mechanics	mechanic	NOUN
ejpam-3515	8	26	,	,	PUNCT
ejpam-3515	8	27	in	in	ADP
ejpam-3515	8	28	which	which	PRON
ejpam-3515	8	29	physical	physical	ADJ
ejpam-3515	8	30	observables	observable	NOUN
ejpam-3515	8	31	such	such	ADJ
ejpam-3515	8	32	as	as	ADP
ejpam-3515	8	33	position	position	NOUN
ejpam-3515	8	34	,	,	PUNCT
ejpam-3515	8	35	momentum	momentum	NOUN
ejpam-3515	8	36	,	,	PUNCT
ejpam-3515	8	37	angular	angular	ADJ
ejpam-3515	8	38	momentum	momentum	NOUN
ejpam-3515	8	39	)	)	PUNCT
ejpam-3515	8	40	.	.	PUNCT
ejpam-3515	9	1	kato	kato	PROPN
ejpam-3515	10	1	[	[	X
ejpam-3515	10	2	5	5	NUM
ejpam-3515	10	3	]	]	PUNCT
ejpam-3515	10	4	who	who	PRON
ejpam-3515	10	5	showed	show	VERB
ejpam-3515	10	6	on	on	ADP
ejpam-3515	10	7	the	the	DET
ejpam-3515	10	8	basis	basis	NOUN
ejpam-3515	10	9	of	of	ADP
ejpam-3515	10	10	his	his	PRON
ejpam-3515	10	11	elegant	elegant	ADJ
ejpam-3515	10	12	inequality	inequality	NOUN
ejpam-3515	10	13	that	that	SCONJ
ejpam-3515	10	14	,	,	PUNCT
ejpam-3515	10	15	if	if	SCONJ
ejpam-3515	10	16	v	v	X
ejpam-3515	10	17	(	(	PUNCT
ejpam-3515	10	18	x	x	NOUN
ejpam-3515	10	19	)	)	PUNCT
ejpam-3515	10	20	≥	≥	NOUN
ejpam-3515	10	21	0	0	NUM
ejpam-3515	10	22	and	and	CCONJ
ejpam-3515	10	23	v	v	ADP
ejpam-3515	10	24	∈	∈	PROPN
ejpam-3515	10	25	l2	l2	NOUN
ejpam-3515	10	26	loc	loc	NOUN
ejpam-3515	10	27	,	,	PUNCT
ejpam-3515	10	28	then	then	ADV
ejpam-3515	10	29	the	the	DET
ejpam-3515	10	30	schrödinger	schrödinger	NOUN
ejpam-3515	10	31	operator	operator	NOUN
ejpam-3515	10	32	is	be	AUX
ejpam-3515	10	33	essentially	essentially	ADV
ejpam-3515	10	34	self	self	NOUN
ejpam-3515	10	35	-	-	PUNCT
ejpam-3515	10	36	adjoint	adjoint	NOUN
ejpam-3515	10	37	on	on	ADP
ejpam-3515	10	38	the	the	DET
ejpam-3515	10	39	set	set	NOUN
ejpam-3515	10	40	of	of	ADP
ejpam-3515	10	41	infinitely	infinitely	ADV
ejpam-3515	10	42	differentiable	differentiable	ADJ
ejpam-3515	10	43	finite	finite	ADJ
ejpam-3515	10	44	functions	function	NOUN
ejpam-3515	10	45	.	.	PUNCT
ejpam-3515	11	1	nextly	nextly	ADV
ejpam-3515	11	2	,	,	PUNCT
ejpam-3515	11	3	gaysinsky	gaysinsky	PROPN
ejpam-3515	11	4	,	,	PUNCT
ejpam-3515	11	5	goldstein	goldstein	NOUN
ejpam-3515	12	1	[	[	X
ejpam-3515	12	2	4	4	X
ejpam-3515	12	3	]	]	PUNCT
ejpam-3515	12	4	they	they	PRON
ejpam-3515	12	5	proved	prove	VERB
ejpam-3515	12	6	smoothness	smoothness	ADJ
ejpam-3515	12	7	of	of	ADP
ejpam-3515	12	8	the	the	DET
ejpam-3515	12	9	schrödinger	schrödinger	NOUN
ejpam-3515	12	10	operator	operator	NOUN
ejpam-3515	12	11	which	which	PRON
ejpam-3515	12	12	is	be	AUX
ejpam-3515	12	13	one	one	NUM
ejpam-3515	12	14	important	important	ADJ
ejpam-3515	12	15	step	step	NOUN
ejpam-3515	12	16	to	to	PART
ejpam-3515	12	17	prove	prove	VERB
ejpam-3515	12	18	self	self	NOUN
ejpam-3515	12	19	-	-	PUNCT
ejpam-3515	12	20	adjointness	adjointness	NOUN
ejpam-3515	12	21	must	must	AUX
ejpam-3515	12	22	be	be	AUX
ejpam-3515	12	23	smoothness	smoothness	ADJ
ejpam-3515	12	24	.	.	PUNCT
ejpam-3515	13	1	after	after	ADP
ejpam-3515	13	2	that	that	PRON
ejpam-3515	13	3	,	,	PUNCT
ejpam-3515	13	4	adam	adam	PROPN
ejpam-3515	13	5	ward	ward	PROPN
ejpam-3515	14	1	[	[	X
ejpam-3515	14	2	1	1	NUM
ejpam-3515	14	3	]	]	PUNCT
ejpam-3515	14	4	investigated	investigate	VERB
ejpam-3515	14	5	the	the	DET
ejpam-3515	14	6	essential	essential	ADJ
ejpam-3515	14	7	self	self	NOUN
ejpam-3515	14	8	-	-	PUNCT
ejpam-3515	14	9	adjointness	adjointness	NOUN
ejpam-3515	14	10	of	of	ADP
ejpam-3515	14	11	schrödinger	schrödinger	NOUN
ejpam-3515	14	12	operator	operator	NOUN
ejpam-3515	14	13	.	.	PUNCT
ejpam-3515	15	1	many	many	ADJ
ejpam-3515	15	2	researchers	researcher	NOUN
ejpam-3515	15	3	studied	study	VERB
ejpam-3515	15	4	self	self	NOUN
ejpam-3515	15	5	-	-	PUNCT
ejpam-3515	15	6	adjoint	adjoint	NOUN
ejpam-3515	15	7	operator	operator	NOUN
ejpam-3515	15	8	were	be	AUX
ejpam-3515	15	9	done	do	VERB
ejpam-3515	15	10	,	,	PUNCT
ejpam-3515	15	11	for	for	ADP
ejpam-3515	15	12	example	example	NOUN
ejpam-3515	16	1	[	[	X
ejpam-3515	16	2	2	2	NUM
ejpam-3515	16	3	]	]	PUNCT
ejpam-3515	16	4	,	,	PUNCT
ejpam-3515	16	5	[	[	X
ejpam-3515	16	6	6	6	NUM
ejpam-3515	16	7	]	]	PUNCT
ejpam-3515	16	8	,	,	PUNCT
ejpam-3515	16	9	[	[	X
ejpam-3515	16	10	7	7	NUM
ejpam-3515	16	11	]	]	PUNCT
ejpam-3515	16	12	,	,	PUNCT
ejpam-3515	16	13	[	[	X
ejpam-3515	16	14	9	9	NUM
ejpam-3515	16	15	]	]	PUNCT
ejpam-3515	16	16	.	.	PUNCT
ejpam-3515	17	1	∗corresponding	∗corresponde	VERB
ejpam-3515	17	2	author	author	NOUN
ejpam-3515	17	3	.	.	PUNCT
ejpam-3515	18	1	doi	doi	NOUN
ejpam-3515	18	2	:	:	PUNCT
ejpam-3515	18	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3515	https://doi.org/10.29020/nybg.ejpam.v12i4.3515	NOUN
ejpam-3515	18	4	email	email	NOUN
ejpam-3515	18	5	addresses	address	NOUN
ejpam-3515	18	6	:	:	PUNCT
ejpam-3515	18	7	yahea−h@mail.ru	yahea−h@mail.ru	INTJ
ejpam-3515	18	8	(	(	PUNCT
ejpam-3515	18	9	y.	y.	PROPN
ejpam-3515	18	10	h.	h.	PROPN
ejpam-3515	18	11	saleem	saleem	PROPN
ejpam-3515	18	12	)	)	PUNCT
ejpam-3515	18	13	,	,	PUNCT
ejpam-3515	18	14	hadeelali2007@yahoo.com	hadeelali2007@yahoo.com	X
ejpam-3515	19	1	(	(	PUNCT
ejpam-3515	19	2	h.	h.	PROPN
ejpam-3515	19	3	a.	a.	PROPN
ejpam-3515	19	4	shubber	shubber	PROPN
ejpam-3515	19	5	)	)	PUNCT
ejpam-3515	19	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3515	20	1	1441	1441	NUM
ejpam-3515	21	1	c	c	X
ejpam-3515	21	2	©	©	PROPN
ejpam-3515	21	3	2019	2019	NUM
ejpam-3515	21	4	ejpam	ejpam	NOUN
ejpam-3515	21	5	all	all	DET
ejpam-3515	21	6	rights	right	NOUN
ejpam-3515	21	7	reserved	reserve	VERB
ejpam-3515	21	8	.	.	PUNCT
ejpam-3515	22	1	y.	y.	PROPN
ejpam-3515	22	2	h.	h.	PROPN
ejpam-3515	22	3	saleem	saleem	PROPN
ejpam-3515	22	4	,	,	PUNCT
ejpam-3515	22	5	h.	h.	PROPN
ejpam-3515	22	6	a.	a.	PROPN
ejpam-3515	22	7	shubber	shubber	PROPN
ejpam-3515	22	8	/	/	SYM
ejpam-3515	22	9	eur	eur	PROPN
ejpam-3515	22	10	.	.	PUNCT
ejpam-3515	23	1	j.	j.	PROPN
ejpam-3515	23	2	pure	pure	PROPN
ejpam-3515	23	3	appl	appl	PROPN
ejpam-3515	23	4	.	.	PROPN
ejpam-3515	23	5	math	math	PROPN
ejpam-3515	23	6	,	,	PUNCT
ejpam-3515	23	7	12	12	NUM
ejpam-3515	23	8	(	(	PUNCT
ejpam-3515	23	9	4	4	NUM
ejpam-3515	23	10	)	)	PUNCT
ejpam-3515	23	11	(	(	PUNCT
ejpam-3515	23	12	2019	2019	NUM
ejpam-3515	23	13	)	)	PUNCT
ejpam-3515	23	14	,	,	PUNCT
ejpam-3515	23	15	1441	1441	NUM
ejpam-3515	23	16	-	-	SYM
ejpam-3515	23	17	1454	1454	NUM
ejpam-3515	23	18	1442	1442	NUM
ejpam-3515	23	19	we	we	PRON
ejpam-3515	23	20	consider	consider	VERB
ejpam-3515	23	21	the	the	DET
ejpam-3515	23	22	schrödinger	schrödinger	NOUN
ejpam-3515	23	23	operator	operator	NOUN
ejpam-3515	23	24	with	with	ADP
ejpam-3515	23	25	electromagnetic	electromagnetic	ADJ
ejpam-3515	23	26	potentials	potential	NOUN
ejpam-3515	23	27	h	h	NOUN
ejpam-3515	24	1	=	=	SYM
ejpam-3515	24	2	n∑	n∑	NOUN
ejpam-3515	24	3	j=1	j=1	NOUN
ejpam-3515	24	4	1	1	NUM
ejpam-3515	24	5	2	2	NUM
ejpam-3515	24	6	(	(	PUNCT
ejpam-3515	24	7	i∂j	i∂j	VERB
ejpam-3515	24	8	+	+	X
ejpam-3515	24	9	bj(x))2	bj(x))2	X
ejpam-3515	25	1	+	+	CCONJ
ejpam-3515	25	2	v	v	NOUN
ejpam-3515	25	3	(	(	PUNCT
ejpam-3515	25	4	x	x	NOUN
ejpam-3515	25	5	)	)	PUNCT
ejpam-3515	25	6	,	,	PUNCT
ejpam-3515	25	7	in	in	ADP
ejpam-3515	25	8	l2(rn	l2(rn	PROPN
ejpam-3515	25	9	)	)	PUNCT
ejpam-3515	25	10	where	where	SCONJ
ejpam-3515	25	11	,	,	PUNCT
ejpam-3515	25	12	bj(x	bj(x	X
ejpam-3515	25	13	)	)	PUNCT
ejpam-3515	25	14	,	,	PUNCT
ejpam-3515	25	15	j	j	PROPN
ejpam-3515	25	16	=	=	SYM
ejpam-3515	25	17	1	1	NUM
ejpam-3515	25	18	,	,	PUNCT
ejpam-3515	25	19	2	2	NUM
ejpam-3515	25	20	,	,	PUNCT
ejpam-3515	25	21	...	...	PUNCT
ejpam-3515	25	22	,	,	PUNCT
ejpam-3515	25	23	n	n	PROPN
ejpam-3515	25	24	and	and	CCONJ
ejpam-3515	25	25	v	v	ADP
ejpam-3515	25	26	(	(	PUNCT
ejpam-3515	25	27	x	x	NOUN
ejpam-3515	25	28	)	)	PUNCT
ejpam-3515	25	29	are	be	AUX
ejpam-3515	25	30	real	real	ADV
ejpam-3515	25	31	-	-	PUNCT
ejpam-3515	25	32	valued	value	VERB
ejpam-3515	25	33	functions	function	NOUN
ejpam-3515	25	34	on	on	ADP
ejpam-3515	25	35	rn	rn	PROPN
ejpam-3515	25	36	,	,	PUNCT
ejpam-3515	25	37	v	v	PROPN
ejpam-3515	25	38	∈	∈	PROPN
ejpam-3515	25	39	l1	l1	PROPN
ejpam-3515	25	40	loc(r	loc(r	PROPN
ejpam-3515	25	41	n	n	CCONJ
ejpam-3515	25	42	)	)	PUNCT
ejpam-3515	25	43	,	,	PUNCT
ejpam-3515	25	44	b	b	X
ejpam-3515	25	45	∈	∈	PROPN
ejpam-3515	25	46	c2(rn	c2(rn	PROPN
ejpam-3515	25	47	)	)	PUNCT
ejpam-3515	25	48	,	,	PUNCT
ejpam-3515	25	49	∂j	∂j	PROPN
ejpam-3515	25	50	=	=	SYM
ejpam-3515	25	51	∂	∂	NUM
ejpam-3515	25	52	∂xj	∂xj	NOUN
ejpam-3515	25	53	and	and	CCONJ
ejpam-3515	25	54	i	i	NOUN
ejpam-3515	25	55	=	=	NOUN
ejpam-3515	25	56	√	√	NUM
ejpam-3515	25	57	−1	−1	NOUN
ejpam-3515	25	58	.	.	PUNCT
ejpam-3515	26	1	we	we	PRON
ejpam-3515	26	2	proved	prove	VERB
ejpam-3515	26	3	in	in	ADP
ejpam-3515	26	4	[	[	X
ejpam-3515	26	5	8	8	NUM
ejpam-3515	26	6	]	]	PUNCT
ejpam-3515	26	7	the	the	DET
ejpam-3515	26	8	feynman	feynman	PROPN
ejpam-3515	26	9	-	-	PUNCT
ejpam-3515	26	10	kac	kac	PROPN
ejpam-3515	26	11	itô	itô	PROPN
ejpam-3515	26	12	formula	formula	NOUN
ejpam-3515	26	13	of	of	ADP
ejpam-3515	26	14	the	the	DET
ejpam-3515	26	15	electromagnetic	electromagnetic	ADJ
ejpam-3515	26	16	schrödinger	schrödinger	NOUN
ejpam-3515	26	17	operator	operator	NOUN
ejpam-3515	26	18	ψ(t	ψ(t	PROPN
ejpam-3515	26	19	,	,	PUNCT
ejpam-3515	26	20	x	x	X
ejpam-3515	26	21	)	)	PUNCT
ejpam-3515	26	22	which	which	PRON
ejpam-3515	26	23	define	define	VERB
ejpam-3515	26	24	as	as	ADP
ejpam-3515	26	25	the	the	DET
ejpam-3515	26	26	equation	equation	NOUN
ejpam-3515	26	27	(	(	PUNCT
ejpam-3515	26	28	1	1	NUM
ejpam-3515	26	29	)	)	PUNCT
ejpam-3515	26	30	in	in	ADP
ejpam-3515	26	31	[	[	X
ejpam-3515	26	32	8	8	NUM
ejpam-3515	26	33	]	]	PUNCT
ejpam-3515	26	34	ψ(t	ψ(t	PROPN
ejpam-3515	26	35	,	,	PUNCT
ejpam-3515	26	36	x	x	NOUN
ejpam-3515	26	37	)	)	PUNCT
ejpam-3515	26	38	=	=	SYM
ejpam-3515	26	39	∫	∫	PROPN
ejpam-3515	26	40	dµtx(ω)exp	dµtx(ω)exp	PROPN
ejpam-3515	26	41	(	(	PUNCT
ejpam-3515	26	42	−i	−i	PROPN
ejpam-3515	26	43	∫	∫	PROPN
ejpam-3515	26	44	t	t	PROPN
ejpam-3515	26	45	0	0	NUM
ejpam-3515	27	1	b(ω(s))dω	b(ω(s))dω	NOUN
ejpam-3515	27	2	−	−	PROPN
ejpam-3515	28	1	i	i	PRON
ejpam-3515	28	2	2	2	NUM
ejpam-3515	28	3	∫	∫	NOUN
ejpam-3515	28	4	t	t	NOUN
ejpam-3515	28	5	0	0	NUM
ejpam-3515	28	6	divbω(s)ds−	divbω(s)ds−	NUM
ejpam-3515	28	7	∫	∫	PROPN
ejpam-3515	28	8	t	t	PROPN
ejpam-3515	28	9	0	0	NUM
ejpam-3515	28	10	v	v	PROPN
ejpam-3515	28	11	(	(	PUNCT
ejpam-3515	28	12	ω(s)ds	ω(s)ds	NUM
ejpam-3515	28	13	)	)	PUNCT
ejpam-3515	28	14	ϕ(ω(t	ϕ(ω(t	NOUN
ejpam-3515	28	15	)	)	PUNCT
ejpam-3515	28	16	)	)	PUNCT
ejpam-3515	28	17	converges	converge	VERB
ejpam-3515	28	18	and	and	CCONJ
ejpam-3515	28	19	is	be	AUX
ejpam-3515	28	20	an	an	DET
ejpam-3515	28	21	analytic	analytic	ADJ
ejpam-3515	28	22	function	function	NOUN
ejpam-3515	28	23	of	of	ADP
ejpam-3515	28	24	the	the	DET
ejpam-3515	28	25	variable	variable	ADJ
ejpam-3515	28	26	t.	t.	NOUN
ejpam-3515	28	27	in	in	ADP
ejpam-3515	28	28	this	this	DET
ejpam-3515	28	29	work	work	NOUN
ejpam-3515	28	30	,	,	PUNCT
ejpam-3515	28	31	we	we	PRON
ejpam-3515	28	32	prove	prove	VERB
ejpam-3515	28	33	that	that	SCONJ
ejpam-3515	28	34	the	the	DET
ejpam-3515	28	35	feynman	feynman	PROPN
ejpam-3515	28	36	-	-	PUNCT
ejpam-3515	28	37	kac	kac	PROPN
ejpam-3515	28	38	itô	itô	PROPN
ejpam-3515	28	39	formula	formula	NOUN
ejpam-3515	28	40	of	of	ADP
ejpam-3515	28	41	the	the	DET
ejpam-3515	28	42	schrödinger	schrödinger	NOUN
ejpam-3515	28	43	operator	operator	NOUN
ejpam-3515	28	44	with	with	ADP
ejpam-3515	28	45	electromagnetic	electromagnetic	ADJ
ejpam-3515	28	46	potentials	potential	NOUN
ejpam-3515	28	47	ψ(t	ψ(t	PROPN
ejpam-3515	28	48	,	,	PUNCT
ejpam-3515	28	49	x	x	NOUN
ejpam-3515	28	50	)	)	PUNCT
ejpam-3515	28	51	in	in	ADP
ejpam-3515	28	52	equation	equation	NOUN
ejpam-3515	28	53	(	(	PUNCT
ejpam-3515	28	54	1	1	NUM
ejpam-3515	28	55	)	)	PUNCT
ejpam-3515	28	56	in	in	ADP
ejpam-3515	28	57	[	[	X
ejpam-3515	28	58	8	8	NUM
ejpam-3515	28	59	]	]	PUNCT
ejpam-3515	28	60	is	be	AUX
ejpam-3515	28	61	differentiable	differentiable	ADJ
ejpam-3515	28	62	of	of	ADP
ejpam-3515	28	63	the	the	DET
ejpam-3515	28	64	variable	variable	ADJ
ejpam-3515	28	65	t	t	PROPN
ejpam-3515	28	66	,	,	PUNCT
ejpam-3515	28	67	and	and	CCONJ
ejpam-3515	28	68	we	we	PRON
ejpam-3515	28	69	have	have	VERB
ejpam-3515	28	70	∂	∂	ADJ
ejpam-3515	28	71	∂tψ(t	∂tψ(t	NOUN
ejpam-3515	28	72	,	,	PUNCT
ejpam-3515	28	73	x	x	NOUN
ejpam-3515	28	74	)	)	PUNCT
ejpam-3515	29	1	=	=	SYM
ejpam-3515	29	2	−	−	PROPN
ejpam-3515	29	3	<	<	X
ejpam-3515	29	4	e−th	e−th	PROPN
ejpam-3515	29	5	,	,	PUNCT
ejpam-3515	29	6	hh	hh	PROPN
ejpam-3515	29	7	>	>	X
ejpam-3515	29	8	.	.	PUNCT
ejpam-3515	30	1	then	then	ADV
ejpam-3515	30	2	,	,	PUNCT
ejpam-3515	30	3	we	we	PRON
ejpam-3515	30	4	discuss	discuss	VERB
ejpam-3515	30	5	the	the	DET
ejpam-3515	30	6	infinite	infinite	ADJ
ejpam-3515	30	7	differentiability	differentiability	NOUN
ejpam-3515	30	8	of	of	ADP
ejpam-3515	30	9	the	the	DET
ejpam-3515	30	10	function	function	NOUN
ejpam-3515	30	11	ψ(t	ψ(t	PROPN
ejpam-3515	30	12	,	,	PUNCT
ejpam-3515	30	13	x	x	NOUN
ejpam-3515	30	14	)	)	PUNCT
ejpam-3515	30	15	in	in	ADP
ejpam-3515	30	16	rn\a	rn\a	PROPN
ejpam-3515	30	17	where	where	SCONJ
ejpam-3515	30	18	the	the	DET
ejpam-3515	30	19	potential	potential	NOUN
ejpam-3515	30	20	v	v	X
ejpam-3515	30	21	=	=	PUNCT
ejpam-3515	30	22	+	+	NUM
ejpam-3515	30	23	∞	∞	NUM
ejpam-3515	30	24	on	on	ADP
ejpam-3515	30	25	a	a	DET
ejpam-3515	30	26	set	set	NOUN
ejpam-3515	30	27	a.	a.	NOUN
ejpam-3515	30	28	finally	finally	ADV
ejpam-3515	30	29	,	,	PUNCT
ejpam-3515	30	30	we	we	PRON
ejpam-3515	30	31	investigate	investigate	VERB
ejpam-3515	30	32	the	the	DET
ejpam-3515	30	33	smoothness	smoothness	NOUN
ejpam-3515	30	34	of	of	ADP
ejpam-3515	30	35	this	this	DET
ejpam-3515	30	36	function	function	NOUN
ejpam-3515	30	37	ψ(t	ψ(t	PROPN
ejpam-3515	30	38	,	,	PUNCT
ejpam-3515	30	39	x	x	NOUN
ejpam-3515	30	40	)	)	PUNCT
ejpam-3515	30	41	.	.	PUNCT
ejpam-3515	31	1	2	2	X
ejpam-3515	31	2	.	.	X
ejpam-3515	31	3	statement	statement	NOUN
ejpam-3515	31	4	of	of	ADP
ejpam-3515	31	5	the	the	DET
ejpam-3515	31	6	problem	problem	NOUN
ejpam-3515	31	7	and	and	CCONJ
ejpam-3515	31	8	the	the	DET
ejpam-3515	31	9	main	main	ADJ
ejpam-3515	31	10	result	result	NOUN
ejpam-3515	31	11	in	in	ADP
ejpam-3515	31	12	[	[	X
ejpam-3515	31	13	8	8	NUM
ejpam-3515	31	14	]	]	PUNCT
ejpam-3515	31	15	we	we	PRON
ejpam-3515	31	16	proved	prove	VERB
ejpam-3515	31	17	that	that	SCONJ
ejpam-3515	31	18	ψ(t	ψ(t	PROPN
ejpam-3515	31	19	,	,	PUNCT
ejpam-3515	31	20	x	x	NOUN
ejpam-3515	31	21	)	)	PUNCT
ejpam-3515	31	22	converges	converge	NOUN
ejpam-3515	31	23	and	and	CCONJ
ejpam-3515	31	24	has	have	VERB
ejpam-3515	31	25	an	an	DET
ejpam-3515	31	26	analytic	analytic	ADJ
ejpam-3515	31	27	extension	extension	NOUN
ejpam-3515	31	28	for	for	ADP
ejpam-3515	31	29	a	a	DET
ejpam-3515	31	30	variable	variable	NOUN
ejpam-3515	31	31	t.	t.	NOUN
ejpam-3515	31	32	now	now	ADV
ejpam-3515	31	33	,	,	PUNCT
ejpam-3515	31	34	we	we	PRON
ejpam-3515	31	35	prove	prove	VERB
ejpam-3515	31	36	that	that	SCONJ
ejpam-3515	31	37	the	the	DET
ejpam-3515	31	38	smoothness	smoothness	NOUN
ejpam-3515	31	39	to	to	PART
ejpam-3515	31	40	achieve	achieve	VERB
ejpam-3515	31	41	this	this	DET
ejpam-3515	31	42	goal	goal	NOUN
ejpam-3515	31	43	,	,	PUNCT
ejpam-3515	31	44	we	we	PRON
ejpam-3515	31	45	will	will	AUX
ejpam-3515	31	46	follow	follow	VERB
ejpam-3515	31	47	the	the	DET
ejpam-3515	31	48	steps	step	NOUN
ejpam-3515	31	49	below	below	ADV
ejpam-3515	31	50	.	.	PUNCT
ejpam-3515	32	1	proposition	proposition	NOUN
ejpam-3515	32	2	2.1	2.1	NUM
ejpam-3515	32	3	.	.	PUNCT
ejpam-3515	33	1	if	if	SCONJ
ejpam-3515	33	2	h	h	NOUN
ejpam-3515	33	3	=	=	SYM
ejpam-3515	34	1	∑n	∑n	NUM
ejpam-3515	34	2	j=1	j=1	NOUN
ejpam-3515	34	3	1	1	NUM
ejpam-3515	34	4	2(i∂j	2(i∂j	NUM
ejpam-3515	34	5	+	+	NOUN
ejpam-3515	34	6	bj(x))2+v	bj(x))2+v	PROPN
ejpam-3515	34	7	(	(	PUNCT
ejpam-3515	34	8	x	x	X
ejpam-3515	34	9	)	)	PUNCT
ejpam-3515	34	10	is	be	AUX
ejpam-3515	34	11	the	the	DET
ejpam-3515	34	12	schrödinger	schrödinger	NOUN
ejpam-3515	34	13	operator	operator	NOUN
ejpam-3515	34	14	defined	define	VERB
ejpam-3515	34	15	on	on	ADP
ejpam-3515	34	16	the	the	DET
ejpam-3515	34	17	interval	interval	NOUN
ejpam-3515	35	1	[	[	X
ejpam-3515	35	2	α	α	NOUN
ejpam-3515	35	3	,	,	PUNCT
ejpam-3515	35	4	β]n	β]n	VERB
ejpam-3515	35	5	with	with	ADP
ejpam-3515	35	6	zero	zero	NUM
ejpam-3515	35	7	boundary	boundary	ADJ
ejpam-3515	35	8	conditions	condition	NOUN
ejpam-3515	35	9	(	(	PUNCT
ejpam-3515	35	10	v	v	NOUN
ejpam-3515	35	11	(	(	PUNCT
ejpam-3515	35	12	x	x	X
ejpam-3515	35	13	)	)	PUNCT
ejpam-3515	35	14	is	be	AUX
ejpam-3515	35	15	a	a	DET
ejpam-3515	35	16	continuous	continuous	ADJ
ejpam-3515	35	17	function	function	NOUN
ejpam-3515	35	18	defined	define	VERB
ejpam-3515	35	19	on	on	ADP
ejpam-3515	35	20	[	[	X
ejpam-3515	35	21	α	α	NOUN
ejpam-3515	35	22	,	,	PUNCT
ejpam-3515	35	23	β]n	β]n	PROPN
ejpam-3515	35	24	)	)	PUNCT
ejpam-3515	35	25	,	,	PUNCT
ejpam-3515	35	26	φ	φ	PROPN
ejpam-3515	35	27	,	,	PUNCT
ejpam-3515	35	28	h	h	PROPN
ejpam-3515	35	29	∈	∈	PROPN
ejpam-3515	35	30	c∞0	c∞0	PROPN
ejpam-3515	35	31	,	,	PUNCT
ejpam-3515	35	32	then	then	ADV
ejpam-3515	35	33	<	<	X
ejpam-3515	35	34	e−thφ	e−thφ	PROPN
ejpam-3515	35	35	,	,	PUNCT
ejpam-3515	35	36	h	h	NOUN
ejpam-3515	35	37	>	>	X
ejpam-3515	35	38	is	be	AUX
ejpam-3515	35	39	a	a	DET
ejpam-3515	35	40	differentiable	differentiable	NOUN
ejpam-3515	35	41	.	.	PUNCT
ejpam-3515	36	1	∂	∂	PUNCT
ejpam-3515	37	1	∂t	∂t	PROPN
ejpam-3515	37	2	<	<	X
ejpam-3515	37	3	e−thϕ	e−thϕ	PROPN
ejpam-3515	37	4	,	,	PUNCT
ejpam-3515	37	5	h	h	NOUN
ejpam-3515	37	6	>	>	X
ejpam-3515	37	7	=	=	PUNCT
ejpam-3515	38	1	−	−	X
ejpam-3515	38	2	<	<	X
ejpam-3515	38	3	e−thϕ,hh	e−thϕ,hh	VERB
ejpam-3515	38	4	>	>	X
ejpam-3515	38	5	.	.	PUNCT
ejpam-3515	39	1	(	(	PUNCT
ejpam-3515	39	2	2.1	2.1	NUM
ejpam-3515	39	3	)	)	PUNCT
ejpam-3515	39	4	proof	proof	NOUN
ejpam-3515	39	5	.	.	PUNCT
ejpam-3515	40	1	let	let	VERB
ejpam-3515	40	2	f	f	PROPN
ejpam-3515	40	3	(	(	PUNCT
ejpam-3515	40	4	t	t	PROPN
ejpam-3515	40	5	,	,	PUNCT
ejpam-3515	40	6	v	v	NOUN
ejpam-3515	40	7	)	)	PUNCT
ejpam-3515	40	8	be	be	AUX
ejpam-3515	40	9	the	the	DET
ejpam-3515	40	10	analytic	analytic	ADJ
ejpam-3515	40	11	extension	extension	NOUN
ejpam-3515	40	12	defined	define	VERB
ejpam-3515	40	13	in	in	ADP
ejpam-3515	40	14	[	[	X
ejpam-3515	40	15	8	8	NUM
ejpam-3515	40	16	]	]	PUNCT
ejpam-3515	40	17	as	as	ADP
ejpam-3515	40	18	f	f	PROPN
ejpam-3515	40	19	(	(	PUNCT
ejpam-3515	40	20	t	t	PROPN
ejpam-3515	40	21	,	,	PUNCT
ejpam-3515	40	22	v	v	NOUN
ejpam-3515	40	23	)	)	PUNCT
ejpam-3515	41	1	=	=	SYM
ejpam-3515	41	2	∫	∫	PROPN
ejpam-3515	41	3	rn	rn	PROPN
ejpam-3515	41	4	ψ(t	ψ(t	PROPN
ejpam-3515	41	5	,	,	PUNCT
ejpam-3515	41	6	x)h(x)dx	x)h(x)dx	ADJ
ejpam-3515	41	7	,	,	PUNCT
ejpam-3515	41	8	(	(	PUNCT
ejpam-3515	41	9	2.2	2.2	NUM
ejpam-3515	41	10	)	)	PUNCT
ejpam-3515	41	11	and	and	CCONJ
ejpam-3515	41	12	let	let	VERB
ejpam-3515	41	13	fα	fα	ADP
ejpam-3515	41	14	,	,	PUNCT
ejpam-3515	41	15	β(t	β(t	PROPN
ejpam-3515	41	16	,	,	PUNCT
ejpam-3515	41	17	v	v	NOUN
ejpam-3515	41	18	)	)	PUNCT
ejpam-3515	41	19	=	=	SYM
ejpam-3515	42	1	∫	∫	PROPN
ejpam-3515	42	2	rn	rn	PROPN
ejpam-3515	42	3	ψα	ψα	PROPN
ejpam-3515	42	4	,	,	PUNCT
ejpam-3515	42	5	β(t	β(t	PROPN
ejpam-3515	42	6	,	,	PUNCT
ejpam-3515	42	7	x)h(x)dx	x)h(x)dx	ADJ
ejpam-3515	42	8	(	(	PUNCT
ejpam-3515	42	9	2.3	2.3	NUM
ejpam-3515	42	10	)	)	PUNCT
ejpam-3515	42	11	be	be	AUX
ejpam-3515	42	12	the	the	DET
ejpam-3515	42	13	same	same	ADJ
ejpam-3515	42	14	as	as	ADP
ejpam-3515	42	15	in	in	ADP
ejpam-3515	42	16	[	[	X
ejpam-3515	42	17	8	8	NUM
ejpam-3515	42	18	]	]	PUNCT
ejpam-3515	42	19	,	,	PUNCT
ejpam-3515	42	20	where	where	SCONJ
ejpam-3515	42	21	ψα	ψα	ADP
ejpam-3515	42	22	,	,	PUNCT
ejpam-3515	42	23	β(t	β(t	PROPN
ejpam-3515	42	24	,	,	PUNCT
ejpam-3515	42	25	x	x	X
ejpam-3515	42	26	)	)	PUNCT
ejpam-3515	43	1	=	=	SYM
ejpam-3515	43	2	∫	∫	PROPN
ejpam-3515	43	3	dy	dy	NOUN
ejpam-3515	43	4	exp(−thα	exp(−thα	PROPN
ejpam-3515	43	5	,	,	PUNCT
ejpam-3515	43	6	β	β	X
ejpam-3515	43	7	)	)	PUNCT
ejpam-3515	43	8	<	<	X
ejpam-3515	44	1	x	x	X
ejpam-3515	44	2	,	,	PUNCT
ejpam-3515	44	3	y	y	PROPN
ejpam-3515	44	4	>	>	X
ejpam-3515	44	5	,	,	PUNCT
ejpam-3515	44	6	(	(	PUNCT
ejpam-3515	44	7	2.4	2.4	NUM
ejpam-3515	44	8	)	)	PUNCT
ejpam-3515	44	9	y.	y.	PROPN
ejpam-3515	44	10	h.	h.	PROPN
ejpam-3515	44	11	saleem	saleem	PROPN
ejpam-3515	44	12	,	,	PUNCT
ejpam-3515	44	13	h.	h.	PROPN
ejpam-3515	44	14	a.	a.	PROPN
ejpam-3515	44	15	shubber	shubber	PROPN
ejpam-3515	44	16	/	/	SYM
ejpam-3515	44	17	eur	eur	PROPN
ejpam-3515	44	18	.	.	PUNCT
ejpam-3515	45	1	j.	j.	PROPN
ejpam-3515	45	2	pure	pure	PROPN
ejpam-3515	45	3	appl	appl	PROPN
ejpam-3515	45	4	.	.	PROPN
ejpam-3515	45	5	math	math	PROPN
ejpam-3515	45	6	,	,	PUNCT
ejpam-3515	45	7	12	12	NUM
ejpam-3515	45	8	(	(	PUNCT
ejpam-3515	45	9	4	4	NUM
ejpam-3515	45	10	)	)	PUNCT
ejpam-3515	45	11	(	(	PUNCT
ejpam-3515	45	12	2019	2019	NUM
ejpam-3515	45	13	)	)	PUNCT
ejpam-3515	45	14	,	,	PUNCT
ejpam-3515	45	15	1441	1441	NUM
ejpam-3515	45	16	-	-	SYM
ejpam-3515	45	17	1454	1454	NUM
ejpam-3515	45	18	1443	1443	NUM
ejpam-3515	45	19	we	we	PRON
ejpam-3515	45	20	define	define	VERB
ejpam-3515	45	21	the	the	DET
ejpam-3515	45	22	operator	operator	NOUN
ejpam-3515	45	23	h	h	NOUN
ejpam-3515	45	24	on	on	ADP
ejpam-3515	45	25	the	the	DET
ejpam-3515	45	26	interval	interval	NOUN
ejpam-3515	45	27	[	[	X
ejpam-3515	45	28	α	α	X
ejpam-3515	45	29	,	,	PUNCT
ejpam-3515	45	30	β]n	β]n	NUM
ejpam-3515	45	31	which	which	PRON
ejpam-3515	45	32	denoted	denote	VERB
ejpam-3515	45	33	by	by	ADP
ejpam-3515	45	34	hα	hα	NOUN
ejpam-3515	45	35	,	,	PUNCT
ejpam-3515	45	36	β	β	X
ejpam-3515	45	37	we	we	PRON
ejpam-3515	45	38	have	have	VERB
ejpam-3515	45	39	lim	lim	PROPN
ejpam-3515	45	40	αn→−∞	αn→−∞	PROPN
ejpam-3515	45	41	βn→+∞	βn→+∞	PROPN
ejpam-3515	45	42	‖fαn	‖fαn	PROPN
ejpam-3515	45	43	,	,	PUNCT
ejpam-3515	45	44	βn(t	βn(t	PRON
ejpam-3515	45	45	,	,	PUNCT
ejpam-3515	45	46	v	v	NOUN
ejpam-3515	45	47	)	)	PUNCT
ejpam-3515	46	1	−	−	PROPN
ejpam-3515	46	2	f	f	PROPN
ejpam-3515	46	3	(	(	PUNCT
ejpam-3515	46	4	t	t	PROPN
ejpam-3515	46	5	,	,	PUNCT
ejpam-3515	46	6	v	v	NOUN
ejpam-3515	46	7	)	)	PUNCT
ejpam-3515	46	8	‖	‖	PROPN
ejpam-3515	46	9	=	=	SYM
ejpam-3515	46	10	0	0	NUM
ejpam-3515	46	11	,	,	PUNCT
ejpam-3515	46	12	uniformly	uniformly	ADV
ejpam-3515	46	13	by	by	ADP
ejpam-3515	46	14	t	t	PROPN
ejpam-3515	46	15	∈	∈	PROPN
ejpam-3515	46	16	g	g	PROPN
ejpam-3515	46	17	,	,	PUNCT
ejpam-3515	46	18	where	where	SCONJ
ejpam-3515	46	19	g	g	PROPN
ejpam-3515	46	20	is	be	AUX
ejpam-3515	46	21	compact	compact	ADJ
ejpam-3515	46	22	subdomain	subdomain	NOUN
ejpam-3515	46	23	of	of	ADP
ejpam-3515	46	24	{	{	PUNCT
ejpam-3515	46	25	t	t	PROPN
ejpam-3515	46	26	=	=	SYM
ejpam-3515	46	27	τ	τ	PROPN
ejpam-3515	46	28	+	+	CCONJ
ejpam-3515	46	29	iθ	iθ	PROPN
ejpam-3515	46	30	,	,	PUNCT
ejpam-3515	46	31	τ	τ	PROPN
ejpam-3515	46	32	≥	≥	NOUN
ejpam-3515	46	33	τ0	τ0	PROPN
ejpam-3515	46	34	>	>	X
ejpam-3515	46	35	0	0	NUM
ejpam-3515	46	36	}	}	PUNCT
ejpam-3515	46	37	.	.	PUNCT
ejpam-3515	47	1	by	by	ADP
ejpam-3515	47	2	the	the	DET
ejpam-3515	47	3	weierstrass	weierstrass	NOUN
ejpam-3515	47	4	theorem	theorem	PROPN
ejpam-3515	47	5	lim	lim	PROPN
ejpam-3515	47	6	αn→−∞	αn→−∞	PROPN
ejpam-3515	47	7	βn→+∞	βn→+∞	PROPN
ejpam-3515	47	8	∥∥∥∥∂fαn	∥∥∥∥∂fαn	NOUN
ejpam-3515	47	9	,	,	PUNCT
ejpam-3515	47	10	βn∂t	βn∂t	NOUN
ejpam-3515	47	11	−	−	PROPN
ejpam-3515	47	12	∂f	∂f	PROPN
ejpam-3515	48	1	∂t	∂t	PROPN
ejpam-3515	48	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-3515	48	3	l2(rn	l2(rn	PROPN
ejpam-3515	48	4	,	,	PUNCT
ejpam-3515	48	5	dv	dv	PROPN
ejpam-3515	48	6	)	)	PUNCT
ejpam-3515	49	1	=	=	PUNCT
ejpam-3515	49	2	0	0	X
ejpam-3515	49	3	.	.	PUNCT
ejpam-3515	50	1	let	let	VERB
ejpam-3515	50	2	hα	hα	INTJ
ejpam-3515	50	3	,	,	PUNCT
ejpam-3515	50	4	β	β	X
ejpam-3515	50	5	as	as	ADP
ejpam-3515	50	6	above	above	ADV
ejpam-3515	50	7	then	then	ADV
ejpam-3515	50	8	by	by	ADP
ejpam-3515	50	9	equations	equation	NOUN
ejpam-3515	50	10	(	(	PUNCT
ejpam-3515	50	11	2.3	2.3	NUM
ejpam-3515	50	12	)	)	PUNCT
ejpam-3515	50	13	,	,	PUNCT
ejpam-3515	50	14	(	(	PUNCT
ejpam-3515	50	15	2.4	2.4	NUM
ejpam-3515	50	16	)	)	PUNCT
ejpam-3515	50	17	,	,	PUNCT
ejpam-3515	50	18	we	we	PRON
ejpam-3515	50	19	have	have	VERB
ejpam-3515	50	20	〈	〈	PROPN
ejpam-3515	50	21	e−thα	e−thα	ADJ
ejpam-3515	50	22	,	,	PUNCT
ejpam-3515	50	23	βϕ	βϕ	NOUN
ejpam-3515	50	24	,	,	PUNCT
ejpam-3515	50	25	h	h	NOUN
ejpam-3515	50	26	〉	〉	NOUN
ejpam-3515	50	27	=	=	SYM
ejpam-3515	50	28	fα	fα	NOUN
ejpam-3515	50	29	,	,	PUNCT
ejpam-3515	50	30	β(t	β(t	PROPN
ejpam-3515	50	31	,	,	PUNCT
ejpam-3515	50	32	v	v	NOUN
ejpam-3515	50	33	)	)	PUNCT
ejpam-3515	50	34	.	.	PUNCT
ejpam-3515	51	1	therefore	therefore	ADV
ejpam-3515	51	2	,	,	PUNCT
ejpam-3515	51	3	∂fα	∂fα	NOUN
ejpam-3515	51	4	,	,	PUNCT
ejpam-3515	51	5	β(t	β(t	PROPN
ejpam-3515	51	6	,	,	PUNCT
ejpam-3515	51	7	v	v	NOUN
ejpam-3515	51	8	)	)	PUNCT
ejpam-3515	52	1	∂t	∂t	PROPN
ejpam-3515	52	2	=	=	PUNCT
ejpam-3515	53	1	−	−	PROPN
ejpam-3515	53	2	∫	∫	PROPN
ejpam-3515	53	3	ψα	ψα	NOUN
ejpam-3515	53	4	,	,	PUNCT
ejpam-3515	53	5	β(t	β(t	PROPN
ejpam-3515	53	6	,	,	PUNCT
ejpam-3515	53	7	x)hα	x)hα	PROPN
ejpam-3515	53	8	,	,	PUNCT
ejpam-3515	53	9	βh(x)dx	βh(x)dx	VERB
ejpam-3515	53	10	,	,	PUNCT
ejpam-3515	53	11	(	(	PUNCT
ejpam-3515	53	12	2.5	2.5	NUM
ejpam-3515	53	13	)	)	PUNCT
ejpam-3515	53	14	provided	provide	VERB
ejpam-3515	53	15	suppϕ	suppϕ	NOUN
ejpam-3515	53	16	,	,	PUNCT
ejpam-3515	53	17	supph	supph	PROPN
ejpam-3515	53	18	⊂	⊂	PROPN
ejpam-3515	53	19	(	(	PUNCT
ejpam-3515	53	20	α	α	NOUN
ejpam-3515	53	21	,	,	PUNCT
ejpam-3515	53	22	β)n	β)n	ADJ
ejpam-3515	53	23	,	,	PUNCT
ejpam-3515	53	24	h(x	h(x	PROPN
ejpam-3515	53	25	)	)	PUNCT
ejpam-3515	53	26	≡	≡	PROPN
ejpam-3515	53	27	0	0	NUM
ejpam-3515	54	1	in	in	ADP
ejpam-3515	54	2	the	the	DET
ejpam-3515	54	3	neighborhood	neighborhood	NOUN
ejpam-3515	54	4	of	of	ADP
ejpam-3515	54	5	the	the	DET
ejpam-3515	54	6	center	center	NOUN
ejpam-3515	54	7	x	x	PUNCT
ejpam-3515	54	8	=	=	PUNCT
ejpam-3515	54	9	0	0	X
ejpam-3515	54	10	.	.	PUNCT
ejpam-3515	55	1	since	since	SCONJ
ejpam-3515	55	2	hα	hα	NOUN
ejpam-3515	55	3	,	,	PUNCT
ejpam-3515	55	4	βh	βh	ADP
ejpam-3515	55	5	=	=	SYM
ejpam-3515	55	6	hh	hh	PROPN
ejpam-3515	55	7	,	,	PUNCT
ejpam-3515	55	8	then	then	ADV
ejpam-3515	55	9	the	the	DET
ejpam-3515	55	10	right	right	ADJ
ejpam-3515	55	11	side	side	NOUN
ejpam-3515	55	12	of	of	ADP
ejpam-3515	55	13	(	(	PUNCT
ejpam-3515	55	14	2.5	2.5	NUM
ejpam-3515	55	15	)	)	PUNCT
ejpam-3515	55	16	represents	represent	VERB
ejpam-3515	55	17	a	a	DET
ejpam-3515	55	18	value	value	NOUN
ejpam-3515	55	19	of	of	ADP
ejpam-3515	55	20	form	form	NOUN
ejpam-3515	55	21	fα	fα	ADP
ejpam-3515	55	22	,	,	PUNCT
ejpam-3515	55	23	β(t	β(t	PROPN
ejpam-3515	55	24	,	,	PUNCT
ejpam-3515	55	25	v	v	NOUN
ejpam-3515	55	26	)	)	PUNCT
ejpam-3515	55	27	,	,	PUNCT
ejpam-3515	55	28	but	but	CCONJ
ejpam-3515	55	29	only	only	ADV
ejpam-3515	55	30	for	for	ADP
ejpam-3515	55	31	function	function	NOUN
ejpam-3515	55	32	hh	hh	PROPN
ejpam-3515	55	33	=	=	SYM
ejpam-3515	55	34	n∑	n∑	PROPN
ejpam-3515	55	35	j=1	j=1	NOUN
ejpam-3515	55	36	1	1	NUM
ejpam-3515	55	37	2	2	NUM
ejpam-3515	55	38	(	(	PUNCT
ejpam-3515	55	39	i∂j	i∂j	VERB
ejpam-3515	56	1	+	+	CCONJ
ejpam-3515	56	2	bj(x))2h+	bj(x))2h+	PROPN
ejpam-3515	56	3	v	v	X
ejpam-3515	56	4	(	(	PUNCT
ejpam-3515	56	5	x)h	x)h	PROPN
ejpam-3515	56	6	.	.	PUNCT
ejpam-3515	57	1	according	accord	VERB
ejpam-3515	57	2	to	to	ADP
ejpam-3515	57	3	the	the	DET
ejpam-3515	57	4	estimates	estimate	NOUN
ejpam-3515	57	5	for	for	ADP
ejpam-3515	57	6	such	such	ADJ
ejpam-3515	57	7	functions	function	NOUN
ejpam-3515	57	8	,	,	PUNCT
ejpam-3515	57	9	we	we	PRON
ejpam-3515	57	10	may	may	AUX
ejpam-3515	57	11	pass	pass	VERB
ejpam-3515	57	12	to	to	ADP
ejpam-3515	57	13	the	the	DET
ejpam-3515	57	14	limit	limit	NOUN
ejpam-3515	57	15	as	as	ADP
ejpam-3515	57	16	α→	α→	PROPN
ejpam-3515	57	17	−∞	−∞	PROPN
ejpam-3515	57	18	,	,	PUNCT
ejpam-3515	57	19	β	β	X
ejpam-3515	57	20	→	→	X
ejpam-3515	57	21	+	+	NOUN
ejpam-3515	57	22	∞.	∞.	PROPN
ejpam-3515	57	23	we	we	PRON
ejpam-3515	57	24	observe	observe	VERB
ejpam-3515	57	25	that	that	SCONJ
ejpam-3515	57	26	we	we	PRON
ejpam-3515	57	27	can	can	AUX
ejpam-3515	57	28	determine	determine	VERB
ejpam-3515	57	29	the	the	DET
ejpam-3515	57	30	functions	function	NOUN
ejpam-3515	57	31	ψ(t	ψ(t	PROPN
ejpam-3515	57	32	,	,	PUNCT
ejpam-3515	57	33	x	x	NOUN
ejpam-3515	57	34	)	)	PUNCT
ejpam-3515	57	35	if	if	SCONJ
ejpam-3515	57	36	the	the	DET
ejpam-3515	57	37	potentials	potential	NOUN
ejpam-3515	57	38	v	v	ADP
ejpam-3515	57	39	,	,	PUNCT
ejpam-3515	57	40	b	b	NOUN
ejpam-3515	57	41	are	be	AUX
ejpam-3515	57	42	equal	equal	ADJ
ejpam-3515	57	43	to	to	ADP
ejpam-3515	57	44	+	+	NOUN
ejpam-3515	57	45	∞	∞	PROPN
ejpam-3515	57	46	on	on	ADP
ejpam-3515	57	47	a	a	DET
ejpam-3515	57	48	set	set	NOUN
ejpam-3515	57	49	a	a	PRON
ejpam-3515	57	50	that	that	PRON
ejpam-3515	57	51	might	might	AUX
ejpam-3515	57	52	have	have	VERB
ejpam-3515	57	53	a	a	DET
ejpam-3515	57	54	positive	positive	ADJ
ejpam-3515	57	55	measure	measure	NOUN
ejpam-3515	57	56	µ	µ	X
ejpam-3515	57	57	{	{	PUNCT
ejpam-3515	57	58	s	s	NOUN
ejpam-3515	57	59	:	:	PUNCT
ejpam-3515	57	60	v	v	NOUN
ejpam-3515	57	61	(	(	PUNCT
ejpam-3515	57	62	ω(s	ω(s	NOUN
ejpam-3515	57	63	)	)	PUNCT
ejpam-3515	57	64	)	)	PUNCT
ejpam-3515	58	1	=	=	PUNCT
ejpam-3515	59	1	+	+	NUM
ejpam-3515	59	2	∞	∞	PROPN
ejpam-3515	59	3	,	,	PUNCT
ejpam-3515	59	4	b(ω(s	b(ω(s	PROPN
ejpam-3515	59	5	)	)	PUNCT
ejpam-3515	59	6	)	)	PUNCT
ejpam-3515	60	1	=	=	PUNCT
ejpam-3515	61	1	+	+	NUM
ejpam-3515	61	2	∞	∞	NOUN
ejpam-3515	61	3	}	}	PUNCT
ejpam-3515	61	4	>	>	X
ejpam-3515	61	5	0	0	NUM
ejpam-3515	61	6	,	,	PUNCT
ejpam-3515	61	7	we	we	PRON
ejpam-3515	61	8	set	set	VERB
ejpam-3515	61	9	exp	exp	NOUN
ejpam-3515	61	10	(	(	PUNCT
ejpam-3515	61	11	−	−	PROPN
ejpam-3515	61	12	∫	∫	PROPN
ejpam-3515	61	13	t	t	PROPN
ejpam-3515	61	14	0	0	NUM
ejpam-3515	61	15	v	v	NOUN
ejpam-3515	61	16	(	(	PUNCT
ejpam-3515	61	17	ω(s))ds	ω(s))ds	NUM
ejpam-3515	61	18	)	)	PUNCT
ejpam-3515	61	19	=	=	SYM
ejpam-3515	61	20	0	0	NUM
ejpam-3515	61	21	,	,	PUNCT
ejpam-3515	61	22	exp	exp	NOUN
ejpam-3515	61	23	(	(	PUNCT
ejpam-3515	61	24	−	−	PROPN
ejpam-3515	61	25	∫	∫	PROPN
ejpam-3515	61	26	t	t	PROPN
ejpam-3515	61	27	0	0	NUM
ejpam-3515	61	28	−ib(ω(s))ds	−ib(ω(s))ds	PUNCT
ejpam-3515	61	29	)	)	PUNCT
ejpam-3515	61	30	=	=	SYM
ejpam-3515	61	31	0	0	NUM
ejpam-3515	61	32	,	,	PUNCT
ejpam-3515	61	33	exp	exp	NOUN
ejpam-3515	61	34	(	(	PUNCT
ejpam-3515	61	35	−	−	PROPN
ejpam-3515	61	36	∫	∫	PROPN
ejpam-3515	61	37	t	t	PROPN
ejpam-3515	61	38	0	0	NUM
ejpam-3515	62	1	−i	−i	ADJ
ejpam-3515	62	2	2	2	NUM
ejpam-3515	62	3	divb(ω(s))ds	divb(ω(s))d	NOUN
ejpam-3515	62	4	)	)	PUNCT
ejpam-3515	63	1	=	=	SYM
ejpam-3515	63	2	0	0	X
ejpam-3515	63	3	.	.	PUNCT
ejpam-3515	64	1	then	then	ADV
ejpam-3515	64	2	the	the	DET
ejpam-3515	64	3	function	function	NOUN
ejpam-3515	64	4	ψ(t	ψ(t	PROPN
ejpam-3515	64	5	,	,	PUNCT
ejpam-3515	64	6	x	x	X
ejpam-3515	64	7	)	)	PUNCT
ejpam-3515	64	8	satisfies	satisfy	VERB
ejpam-3515	64	9	the	the	DET
ejpam-3515	64	10	equation	equation	NOUN
ejpam-3515	64	11	∂	∂	NOUN
ejpam-3515	64	12	∂t	∂t	PROPN
ejpam-3515	64	13	ψ(t	ψ(t	PROPN
ejpam-3515	64	14	,	,	PUNCT
ejpam-3515	64	15	x)ϕ	x)ϕ	PUNCT
ejpam-3515	64	16	=	=	SYM
ejpam-3515	64	17	n∑	n∑	PROPN
ejpam-3515	64	18	j=1	j=1	NOUN
ejpam-3515	64	19	1	1	NUM
ejpam-3515	64	20	2	2	NUM
ejpam-3515	64	21	(	(	PUNCT
ejpam-3515	64	22	i∂j	i∂j	VERB
ejpam-3515	64	23	+	+	CCONJ
ejpam-3515	64	24	bj(x))2ψ(t	bj(x))2ψ(t	PROPN
ejpam-3515	64	25	,	,	PUNCT
ejpam-3515	64	26	x)ϕ+	x)ϕ+	NOUN
ejpam-3515	64	27	v	v	X
ejpam-3515	64	28	(	(	PUNCT
ejpam-3515	64	29	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	64	30	,	,	PUNCT
ejpam-3515	64	31	x)ϕ.	x)ϕ.	PROPN
ejpam-3515	64	32	since	since	SCONJ
ejpam-3515	64	33	ψ(t	ψ(t	PROPN
ejpam-3515	64	34	,	,	PUNCT
ejpam-3515	64	35	x	x	PRON
ejpam-3515	64	36	)	)	PUNCT
ejpam-3515	64	37	is	be	AUX
ejpam-3515	64	38	analytical	analytical	ADJ
ejpam-3515	64	39	with	with	ADP
ejpam-3515	64	40	respect	respect	NOUN
ejpam-3515	64	41	to	to	ADP
ejpam-3515	64	42	tha	tha	NOUN
ejpam-3515	64	43	variable	variable	PROPN
ejpam-3515	64	44	t	t	PROPN
ejpam-3515	64	45	,	,	PUNCT
ejpam-3515	64	46	we	we	PRON
ejpam-3515	64	47	prove	prove	VERB
ejpam-3515	64	48	that	that	SCONJ
ejpam-3515	64	49	ψ(t	ψ(t	PROPN
ejpam-3515	64	50	,	,	PUNCT
ejpam-3515	64	51	x	x	PRON
ejpam-3515	64	52	)	)	PUNCT
ejpam-3515	64	53	is	be	AUX
ejpam-3515	64	54	a	a	DET
ejpam-3515	64	55	smooth	smooth	ADJ
ejpam-3515	64	56	function	function	NOUN
ejpam-3515	64	57	for	for	ADP
ejpam-3515	64	58	almost	almost	ADV
ejpam-3515	64	59	every	every	PRON
ejpam-3515	64	60	v	v	NOUN
ejpam-3515	64	61	,	,	PUNCT
ejpam-3515	64	62	b	b	X
ejpam-3515	64	63	where	where	SCONJ
ejpam-3515	64	64	x	x	SYM
ejpam-3515	64	65	∈	∈	PROPN
ejpam-3515	64	66	rn\a	rn\a	NOUN
ejpam-3515	64	67	.	.	PUNCT
ejpam-3515	65	1	y.	y.	PROPN
ejpam-3515	65	2	h.	h.	PROPN
ejpam-3515	65	3	saleem	saleem	PROPN
ejpam-3515	65	4	,	,	PUNCT
ejpam-3515	65	5	h.	h.	PROPN
ejpam-3515	65	6	a.	a.	PROPN
ejpam-3515	65	7	shubber	shubber	PROPN
ejpam-3515	65	8	/	/	SYM
ejpam-3515	65	9	eur	eur	PROPN
ejpam-3515	65	10	.	.	PUNCT
ejpam-3515	66	1	j.	j.	PROPN
ejpam-3515	66	2	pure	pure	PROPN
ejpam-3515	66	3	appl	appl	PROPN
ejpam-3515	66	4	.	.	PROPN
ejpam-3515	66	5	math	math	PROPN
ejpam-3515	66	6	,	,	PUNCT
ejpam-3515	66	7	12	12	NUM
ejpam-3515	66	8	(	(	PUNCT
ejpam-3515	66	9	4	4	NUM
ejpam-3515	66	10	)	)	PUNCT
ejpam-3515	66	11	(	(	PUNCT
ejpam-3515	66	12	2019	2019	NUM
ejpam-3515	66	13	)	)	PUNCT
ejpam-3515	66	14	,	,	PUNCT
ejpam-3515	66	15	1441	1441	NUM
ejpam-3515	66	16	-	-	SYM
ejpam-3515	66	17	1454	1454	NUM
ejpam-3515	66	18	1444	1444	NUM
ejpam-3515	66	19	proposition	proposition	NOUN
ejpam-3515	66	20	2.2	2.2	NUM
ejpam-3515	66	21	.	.	PUNCT
ejpam-3515	67	1	let	let	VERB
ejpam-3515	67	2	v	v	NUM
ejpam-3515	67	3	∈	∈	PROPN
ejpam-3515	67	4	l2(rn\a	l2(rn\a	NOUN
ejpam-3515	67	5	)	)	PUNCT
ejpam-3515	67	6	,	,	PUNCT
ejpam-3515	67	7	ϕ	ϕ	NOUN
ejpam-3515	67	8	,	,	PUNCT
ejpam-3515	67	9	h	h	NOUN
ejpam-3515	67	10	∈	∈	PROPN
ejpam-3515	67	11	c∞0	c∞0	PROPN
ejpam-3515	67	12	where	where	SCONJ
ejpam-3515	67	13	a	a	PRON
ejpam-3515	67	14	is	be	AUX
ejpam-3515	67	15	closed	closed	ADJ
ejpam-3515	67	16	set	set	VERB
ejpam-3515	67	17	,	,	PUNCT
ejpam-3515	67	18	v	v	NOUN
ejpam-3515	67	19	(	(	PUNCT
ejpam-3515	67	20	x	x	NOUN
ejpam-3515	67	21	)	)	PUNCT
ejpam-3515	67	22	=	=	PUNCT
ejpam-3515	68	1	+	+	NUM
ejpam-3515	68	2	∞	∞	PROPN
ejpam-3515	68	3	,	,	PUNCT
ejpam-3515	68	4	bj(x	bj(x	X
ejpam-3515	68	5	)	)	PUNCT
ejpam-3515	69	1	=	=	PUNCT
ejpam-3515	70	1	+	+	NUM
ejpam-3515	70	2	∞	∞	PROPN
ejpam-3515	70	3	,	,	PUNCT
ejpam-3515	70	4	x	x	SYM
ejpam-3515	70	5	∈	∈	PROPN
ejpam-3515	70	6	a	a	DET
ejpam-3515	70	7	such	such	ADJ
ejpam-3515	70	8	that	that	DET
ejpam-3515	70	9	suppϕ	suppϕ	NOUN
ejpam-3515	70	10	∩	∩	NOUN
ejpam-3515	70	11	a	a	DET
ejpam-3515	70	12	=	=	SYM
ejpam-3515	70	13	∅.	∅.	NOUN
ejpam-3515	70	14	then	then	ADV
ejpam-3515	70	15	ψ(t	ψ(t	PROPN
ejpam-3515	70	16	,	,	PUNCT
ejpam-3515	70	17	x	x	PRON
ejpam-3515	70	18	)	)	PUNCT
ejpam-3515	70	19	is	be	AUX
ejpam-3515	70	20	an	an	DET
ejpam-3515	70	21	infinitely	infinitely	ADV
ejpam-3515	70	22	differentiable	differentiable	ADJ
ejpam-3515	70	23	function	function	NOUN
ejpam-3515	70	24	of	of	ADP
ejpam-3515	70	25	the	the	DET
ejpam-3515	70	26	variable	variable	NOUN
ejpam-3515	70	27	x	x	PUNCT
ejpam-3515	70	28	for	for	ADP
ejpam-3515	70	29	almost	almost	ADV
ejpam-3515	70	30	every	every	PRON
ejpam-3515	70	31	v	v	NOUN
ejpam-3515	70	32	,	,	PUNCT
ejpam-3515	70	33	b	b	PROPN
ejpam-3515	70	34	for	for	ADP
ejpam-3515	70	35	ret	ret	PROPN
ejpam-3515	70	36	≥	≥	PROPN
ejpam-3515	70	37	τ0	τ0	PROPN
ejpam-3515	70	38	>	>	X
ejpam-3515	70	39	0	0	X
ejpam-3515	70	40	.	.	PUNCT
ejpam-3515	71	1	proof	proof	NOUN
ejpam-3515	71	2	.	.	PUNCT
ejpam-3515	72	1	from	from	ADP
ejpam-3515	72	2	equation	equation	NOUN
ejpam-3515	72	3	(	(	PUNCT
ejpam-3515	72	4	2.5	2.5	NUM
ejpam-3515	72	5	)	)	PUNCT
ejpam-3515	72	6	and	and	CCONJ
ejpam-3515	72	7	definition	definition	NOUN
ejpam-3515	72	8	of	of	ADP
ejpam-3515	72	9	f	f	PROPN
ejpam-3515	72	10	(	(	PUNCT
ejpam-3515	72	11	t	t	PROPN
ejpam-3515	72	12	,	,	PUNCT
ejpam-3515	72	13	v	v	NOUN
ejpam-3515	72	14	)	)	PUNCT
ejpam-3515	72	15	in	in	ADP
ejpam-3515	72	16	equation	equation	NOUN
ejpam-3515	72	17	(	(	PUNCT
ejpam-3515	72	18	2.1	2.1	NUM
ejpam-3515	72	19	)	)	PUNCT
ejpam-3515	72	20	∂	∂	NOUN
ejpam-3515	73	1	∂t	∂t	PROPN
ejpam-3515	73	2	∫	∫	PROPN
ejpam-3515	73	3	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	73	4	,	,	PUNCT
ejpam-3515	73	5	x))h(x	x))h(x	PROPN
ejpam-3515	73	6	)	)	PUNCT
ejpam-3515	73	7	=	=	PUNCT
ejpam-3515	74	1	−	−	PROPN
ejpam-3515	74	2	∫	∫	PROPN
ejpam-3515	74	3	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	74	4	,	,	PUNCT
ejpam-3515	74	5	x	x	NOUN
ejpam-3515	74	6	)	)	PUNCT
ejpam-3515	74	7	)	)	PUNCT
ejpam-3515	74	8			NOUN
ejpam-3515	75	1	n∑	n∑	INTJ
ejpam-3515	75	2	j=1	j=1	NOUN
ejpam-3515	75	3	1	1	NUM
ejpam-3515	75	4	2	2	NUM
ejpam-3515	75	5	(	(	PUNCT
ejpam-3515	75	6	i∂j	i∂j	VERB
ejpam-3515	75	7	+	+	CCONJ
ejpam-3515	75	8	bj	bj	NOUN
ejpam-3515	75	9	)	)	PUNCT
ejpam-3515	75	10	2	2	NUM
ejpam-3515	75	11	h(x	h(x	PROPN
ejpam-3515	75	12	)	)	PUNCT
ejpam-3515	76	1	+	+	NUM
ejpam-3515	76	2	v	v	X
ejpam-3515	76	3	(	(	PUNCT
ejpam-3515	76	4	x)h(x	x)h(x	PROPN
ejpam-3515	76	5	)	)	PUNCT
ejpam-3515	76	6			NOUN
ejpam-3515	76	7	dx	dx	PROPN
ejpam-3515	76	8	.	.	PUNCT
ejpam-3515	77	1	(	(	PUNCT
ejpam-3515	77	2	2.6	2.6	NUM
ejpam-3515	77	3	)	)	PUNCT
ejpam-3515	77	4	let	let	VERB
ejpam-3515	77	5	θ(v	θ(v	NOUN
ejpam-3515	77	6	)	)	PUNCT
ejpam-3515	77	7	∈	∈	PROPN
ejpam-3515	77	8	l2(rn	l2(rn	PROPN
ejpam-3515	77	9	,	,	PUNCT
ejpam-3515	77	10	dv	dv	PROPN
ejpam-3515	77	11	)	)	PUNCT
ejpam-3515	77	12	,	,	PUNCT
ejpam-3515	77	13	we	we	PRON
ejpam-3515	77	14	put	put	VERB
ejpam-3515	77	15	f(t	f(t	NOUN
ejpam-3515	77	16	)	)	PUNCT
ejpam-3515	78	1	=	=	SYM
ejpam-3515	78	2	∫	∫	PROPN
ejpam-3515	78	3	rn	rn	PROPN
ejpam-3515	78	4	e	e	PROPN
ejpam-3515	78	5	(	(	PUNCT
ejpam-3515	78	6	ψ(t	ψ(t	PROPN
ejpam-3515	78	7	,	,	PUNCT
ejpam-3515	78	8	x)θ(v	x)θ(v	NUM
ejpam-3515	78	9	)	)	PUNCT
ejpam-3515	78	10	)	)	PUNCT
ejpam-3515	78	11	h(x)dx	h(x)dx	X
ejpam-3515	78	12	=	=	SYM
ejpam-3515	78	13	e(f	e(f	PROPN
ejpam-3515	78	14	(	(	PUNCT
ejpam-3515	78	15	t	t	PROPN
ejpam-3515	78	16	,	,	PUNCT
ejpam-3515	78	17	v	v	NOUN
ejpam-3515	78	18	)	)	PUNCT
ejpam-3515	78	19	θ(v	θ(v	NOUN
ejpam-3515	78	20	)	)	PUNCT
ejpam-3515	78	21	)	)	PUNCT
ejpam-3515	78	22	.	.	PUNCT
ejpam-3515	79	1	depending	depend	VERB
ejpam-3515	79	2	on	on	ADP
ejpam-3515	79	3	above	above	ADP
ejpam-3515	79	4	that	that	DET
ejpam-3515	79	5	f(t	f(t	NOUN
ejpam-3515	79	6	)	)	PUNCT
ejpam-3515	79	7	is	be	AUX
ejpam-3515	79	8	an	an	DET
ejpam-3515	79	9	analytic	analytic	ADJ
ejpam-3515	79	10	function	function	NOUN
ejpam-3515	79	11	and	and	CCONJ
ejpam-3515	79	12	∂f	∂f	PROPN
ejpam-3515	79	13	∂t	∂t	PROPN
ejpam-3515	79	14	=	=	SYM
ejpam-3515	79	15	e	e	PROPN
ejpam-3515	79	16	(	(	PUNCT
ejpam-3515	79	17	∂f	∂f	PROPN
ejpam-3515	79	18	(	(	PUNCT
ejpam-3515	79	19	t	t	PROPN
ejpam-3515	79	20	,	,	PUNCT
ejpam-3515	79	21	x	x	NOUN
ejpam-3515	79	22	)	)	PUNCT
ejpam-3515	79	23	∂t	∂t	PROPN
ejpam-3515	79	24	θ(v	θ(v	NOUN
ejpam-3515	79	25	)	)	PUNCT
ejpam-3515	79	26	)	)	PUNCT
ejpam-3515	80	1	=	=	PUNCT
ejpam-3515	80	2	−	−	PROPN
ejpam-3515	80	3	∫	∫	PROPN
ejpam-3515	80	4	rn	rn	PROPN
ejpam-3515	80	5	e	e	PROPN
ejpam-3515	80	6	ψ(t	ψ(t	PROPN
ejpam-3515	80	7	,	,	PUNCT
ejpam-3515	80	8	x	x	X
ejpam-3515	80	9	)	)	PUNCT
ejpam-3515	80	10			NOUN
ejpam-3515	80	11	n∑	n∑	NOUN
ejpam-3515	80	12	j=1	j=1	NOUN
ejpam-3515	80	13	1	1	NUM
ejpam-3515	80	14	2	2	NUM
ejpam-3515	80	15	(	(	PUNCT
ejpam-3515	80	16	i∂j	i∂j	VERB
ejpam-3515	80	17	+	+	CCONJ
ejpam-3515	80	18	bj	bj	NOUN
ejpam-3515	80	19	)	)	PUNCT
ejpam-3515	80	20	2	2	NUM
ejpam-3515	80	21	h(x	h(x	PROPN
ejpam-3515	80	22	)	)	PUNCT
ejpam-3515	81	1	+	+	NUM
ejpam-3515	81	2	v	v	X
ejpam-3515	81	3	(	(	PUNCT
ejpam-3515	81	4	x)h(x	x)h(x	NOUN
ejpam-3515	81	5	)	)	PUNCT
ejpam-3515	81	6			NOUN
ejpam-3515	81	7	θ(v	θ(v	NOUN
ejpam-3515	81	8	)	)	PUNCT
ejpam-3515	82	1			NOUN
ejpam-3515	82	2	dx	dx	PROPN
ejpam-3515	83	1	=	=	SYM
ejpam-3515	83	2	−	−	PROPN
ejpam-3515	83	3	∫	∫	PROPN
ejpam-3515	83	4	rn	rn	PROPN
ejpam-3515	83	5	e	e	PROPN
ejpam-3515	83	6	ψ(t	ψ(t	PROPN
ejpam-3515	83	7	,	,	PUNCT
ejpam-3515	83	8	x)θ(v	x)θ(v	NUM
ejpam-3515	83	9	)	)	PUNCT
ejpam-3515	84	1	n∑	n∑	X
ejpam-3515	84	2	j=1	j=1	NOUN
ejpam-3515	84	3	1	1	NUM
ejpam-3515	84	4	2	2	NUM
ejpam-3515	84	5	(	(	PUNCT
ejpam-3515	84	6	i∂j	i∂j	VERB
ejpam-3515	84	7	+	+	CCONJ
ejpam-3515	84	8	bj	bj	NOUN
ejpam-3515	84	9	)	)	PUNCT
ejpam-3515	84	10	2	2	NUM
ejpam-3515	84	11	h(x)dx−	h(x)dx−	NOUN
ejpam-3515	84	12	∫	∫	PROPN
ejpam-3515	84	13	rn	rn	PROPN
ejpam-3515	84	14	e	e	PROPN
ejpam-3515	84	15	(	(	PUNCT
ejpam-3515	84	16	ψ(t	ψ(t	PROPN
ejpam-3515	84	17	,	,	PUNCT
ejpam-3515	84	18	x)v	x)v	PUNCT
ejpam-3515	84	19	(	(	PUNCT
ejpam-3515	84	20	x)θ(v	x)θ(v	NUM
ejpam-3515	84	21	)	)	PUNCT
ejpam-3515	84	22	)	)	PUNCT
ejpam-3515	84	23	h(x)dx	h(x)dx	PROPN
ejpam-3515	84	24	.	.	PUNCT
ejpam-3515	85	1	on	on	ADP
ejpam-3515	85	2	the	the	DET
ejpam-3515	85	3	other	other	ADJ
ejpam-3515	85	4	hand	hand	NOUN
ejpam-3515	85	5	,	,	PUNCT
ejpam-3515	85	6	f(t	f(t	PROPN
ejpam-3515	85	7	)	)	PUNCT
ejpam-3515	86	1	=	=	SYM
ejpam-3515	86	2	∫	∫	PROPN
ejpam-3515	86	3	rn	rn	PROPN
ejpam-3515	86	4	f(t	f(t	PROPN
ejpam-3515	86	5	,	,	PUNCT
ejpam-3515	86	6	x)h(x)dx	x)h(x)dx	ADJ
ejpam-3515	86	7	,	,	PUNCT
ejpam-3515	86	8	where	where	SCONJ
ejpam-3515	86	9	f(t	f(t	PROPN
ejpam-3515	86	10	,	,	PUNCT
ejpam-3515	86	11	x	x	NOUN
ejpam-3515	86	12	)	)	PUNCT
ejpam-3515	86	13	=	=	SYM
ejpam-3515	86	14	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	86	15	,	,	PUNCT
ejpam-3515	86	16	x)θ(v	x)θ(v	NUM
ejpam-3515	86	17	)	)	PUNCT
ejpam-3515	86	18	)	)	PUNCT
ejpam-3515	86	19	.	.	PUNCT
ejpam-3515	87	1	we	we	PRON
ejpam-3515	87	2	have	have	VERB
ejpam-3515	87	3	|f(t	|f(t	NOUN
ejpam-3515	87	4	,	,	PUNCT
ejpam-3515	87	5	x)|2	x)|2	PROPN
ejpam-3515	87	6	≤	≤	PROPN
ejpam-3515	87	7	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	87	8	,	,	PUNCT
ejpam-3515	87	9	x)2)e(θ(v	x)2)e(θ(v	NOUN
ejpam-3515	87	10	)	)	PUNCT
ejpam-3515	87	11	2	2	X
ejpam-3515	87	12	)	)	PUNCT
ejpam-3515	87	13	=	=	SYM
ejpam-3515	88	1	‖θ‖2l2(rn	‖θ‖2l2(rn	NUM
ejpam-3515	88	2	,	,	PUNCT
ejpam-3515	88	3	dv	dv	PROPN
ejpam-3515	88	4	)	)	PUNCT
ejpam-3515	88	5	×	×	PROPN
ejpam-3515	88	6	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	88	7	,	,	PUNCT
ejpam-3515	88	8	x)2	x)2	PROPN
ejpam-3515	88	9	)	)	PUNCT
ejpam-3515	88	10	.	.	PUNCT
ejpam-3515	89	1	therefore	therefore	ADV
ejpam-3515	89	2	,	,	PUNCT
ejpam-3515	89	3	∫	∫	PROPN
ejpam-3515	89	4	rn	rn	PROPN
ejpam-3515	89	5	f(t	f(t	PROPN
ejpam-3515	89	6	,	,	PUNCT
ejpam-3515	89	7	x)2dx	x)2dx	ADJ
ejpam-3515	89	8	≤	≤	NUM
ejpam-3515	89	9	const	const	NOUN
ejpam-3515	89	10	‖θ‖2l2(dv	‖θ‖2l2(dv	NUM
ejpam-3515	89	11	)	)	PUNCT
ejpam-3515	89	12	i.e.	i.e.	X
ejpam-3515	89	13	f(t	f(t	NOUN
ejpam-3515	89	14	,	,	PUNCT
ejpam-3515	89	15	x	x	X
ejpam-3515	89	16	)	)	PUNCT
ejpam-3515	89	17	∈	∈	PROPN
ejpam-3515	89	18	l2(rn	l2(rn	PROPN
ejpam-3515	89	19	,	,	PUNCT
ejpam-3515	89	20	dv	dv	PROPN
ejpam-3515	89	21	)	)	PUNCT
ejpam-3515	89	22	.	.	PUNCT
ejpam-3515	90	1	further,∣∣∣∣∫	further,∣∣∣∣∫	PROPN
ejpam-3515	90	2	rn	rn	PROPN
ejpam-3515	90	3	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	90	4	,	,	PUNCT
ejpam-3515	90	5	x)v	x)v	PUNCT
ejpam-3515	90	6	(	(	PUNCT
ejpam-3515	90	7	x)θ(v	x)θ(v	NUM
ejpam-3515	90	8	)	)	PUNCT
ejpam-3515	90	9	)	)	PUNCT
ejpam-3515	90	10	∣∣∣∣h(x)dx	∣∣∣∣h(x)dx	NOUN
ejpam-3515	90	11	≤	≤	NOUN
ejpam-3515	90	12	(	(	PUNCT
ejpam-3515	90	13	∫	∫	PROPN
ejpam-3515	90	14	rn	rn	PROPN
ejpam-3515	90	15	h(x)2dx	h(x)2dx	PROPN
ejpam-3515	90	16	)	)	PUNCT
ejpam-3515	90	17	1	1	NUM
ejpam-3515	90	18	2	2	NUM
ejpam-3515	90	19	(	(	PUNCT
ejpam-3515	90	20	∫	∫	PROPN
ejpam-3515	90	21	rn	rn	PROPN
ejpam-3515	90	22	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	90	23	,	,	PUNCT
ejpam-3515	90	24	x)v	x)v	PUNCT
ejpam-3515	90	25	(	(	PUNCT
ejpam-3515	90	26	x)θ(v	x)θ(v	NUM
ejpam-3515	90	27	)	)	PUNCT
ejpam-3515	90	28	)	)	PUNCT
ejpam-3515	91	1	2dx	2dx	X
ejpam-3515	91	2	)	)	PUNCT
ejpam-3515	91	3	1	1	NUM
ejpam-3515	91	4	2	2	NUM
ejpam-3515	91	5	≤	≤	NOUN
ejpam-3515	91	6	‖h‖l2(rn	‖h‖l2(rn	PROPN
ejpam-3515	91	7	,	,	PUNCT
ejpam-3515	91	8	dx	dx	PROPN
ejpam-3515	91	9	)	)	PUNCT
ejpam-3515	91	10	(	(	PUNCT
ejpam-3515	91	11	∫	∫	PROPN
ejpam-3515	91	12	rn	rn	PROPN
ejpam-3515	91	13	e(ψ2(t	e(ψ2(t	PROPN
ejpam-3515	91	14	,	,	PUNCT
ejpam-3515	91	15	x)v	x)v	PUNCT
ejpam-3515	91	16	2(x))e(θ2(v	2(x))e(θ2(v	NUM
ejpam-3515	91	17	(	(	PUNCT
ejpam-3515	91	18	x)))dx	x)))dx	X
ejpam-3515	91	19	)	)	PUNCT
ejpam-3515	91	20	1	1	NUM
ejpam-3515	91	21	2	2	NUM
ejpam-3515	91	22	≤	≤	NOUN
ejpam-3515	91	23	‖h‖l2(rn	‖h‖l2(rn	PROPN
ejpam-3515	91	24	,	,	PUNCT
ejpam-3515	91	25	dx	dx	PROPN
ejpam-3515	91	26	)	)	PUNCT
ejpam-3515	91	27	‖θ‖l2(rn	‖θ‖l2(rn	PROPN
ejpam-3515	91	28	,	,	PUNCT
ejpam-3515	91	29	dv	dv	PROPN
ejpam-3515	91	30	)	)	PUNCT
ejpam-3515	91	31	(	(	PUNCT
ejpam-3515	91	32	∫	∫	PROPN
ejpam-3515	91	33	rn	rn	PROPN
ejpam-3515	91	34	e(ψ2(t	e(ψ2(t	PROPN
ejpam-3515	91	35	,	,	PUNCT
ejpam-3515	91	36	x)v	x)v	X
ejpam-3515	91	37	2(x))dx	2(x))dx	X
ejpam-3515	91	38	)	)	PUNCT
ejpam-3515	91	39	1	1	NUM
ejpam-3515	91	40	2	2	NUM
ejpam-3515	91	41	y.	y.	PROPN
ejpam-3515	91	42	h.	h.	PROPN
ejpam-3515	91	43	saleem	saleem	PROPN
ejpam-3515	91	44	,	,	PUNCT
ejpam-3515	91	45	h.	h.	PROPN
ejpam-3515	91	46	a.	a.	PROPN
ejpam-3515	91	47	shubber	shubber	PROPN
ejpam-3515	91	48	/	/	SYM
ejpam-3515	91	49	eur	eur	PROPN
ejpam-3515	91	50	.	.	PUNCT
ejpam-3515	92	1	j.	j.	PROPN
ejpam-3515	92	2	pure	pure	PROPN
ejpam-3515	92	3	appl	appl	PROPN
ejpam-3515	92	4	.	.	PROPN
ejpam-3515	92	5	math	math	PROPN
ejpam-3515	92	6	,	,	PUNCT
ejpam-3515	92	7	12	12	NUM
ejpam-3515	92	8	(	(	PUNCT
ejpam-3515	92	9	4	4	NUM
ejpam-3515	92	10	)	)	PUNCT
ejpam-3515	92	11	(	(	PUNCT
ejpam-3515	92	12	2019	2019	NUM
ejpam-3515	92	13	)	)	PUNCT
ejpam-3515	92	14	,	,	PUNCT
ejpam-3515	92	15	1441	1441	NUM
ejpam-3515	92	16	-	-	SYM
ejpam-3515	92	17	1454	1454	NUM
ejpam-3515	92	18	1445	1445	NUM
ejpam-3515	92	19	≤	≤	PROPN
ejpam-3515	92	20	const	const	ADJ
ejpam-3515	92	21	‖h‖l2(rn	‖h‖l2(rn	PROPN
ejpam-3515	92	22	,	,	PUNCT
ejpam-3515	92	23	dx	dx	PROPN
ejpam-3515	92	24	)	)	PUNCT
ejpam-3515	92	25	‖θ‖l2(rn	‖θ‖l2(rn	PROPN
ejpam-3515	92	26	,	,	PUNCT
ejpam-3515	92	27	dv	dv	PROPN
ejpam-3515	92	28	)	)	PUNCT
ejpam-3515	92	29	,	,	PUNCT
ejpam-3515	92	30	where	where	SCONJ
ejpam-3515	92	31	we	we	PRON
ejpam-3515	92	32	have	have	AUX
ejpam-3515	92	33	used	use	VERB
ejpam-3515	92	34	the	the	DET
ejpam-3515	92	35	estimates∫	estimates∫	PROPN
ejpam-3515	92	36	rn	rn	PROPN
ejpam-3515	92	37	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	92	38	,	,	PUNCT
ejpam-3515	92	39	x)2	x)2	VERB
ejpam-3515	92	40	|v	|v	X
ejpam-3515	92	41	|m)dx	|m)dx	NOUN
ejpam-3515	92	42	≤	≤	NUM
ejpam-3515	92	43	const	const	NOUN
ejpam-3515	92	44	,	,	PUNCT
ejpam-3515	92	45	(	(	PUNCT
ejpam-3515	92	46	2.7	2.7	NUM
ejpam-3515	92	47	)	)	PUNCT
ejpam-3515	92	48	where	where	SCONJ
ejpam-3515	92	49	m	m	VERB
ejpam-3515	92	50	=	=	SYM
ejpam-3515	92	51	1	1	NUM
ejpam-3515	92	52	,	,	PUNCT
ejpam-3515	92	53	2	2	NUM
ejpam-3515	92	54	,	,	PUNCT
ejpam-3515	92	55	...	...	PUNCT
ejpam-3515	92	56	and	and	CCONJ
ejpam-3515	92	57	the	the	DET
ejpam-3515	92	58	constant	constant	ADJ
ejpam-3515	92	59	depends	depend	VERB
ejpam-3515	92	60	on	on	ADP
ejpam-3515	92	61	m.	m.	NOUN
ejpam-3515	92	62	we	we	PRON
ejpam-3515	92	63	estimate	estimate	VERB
ejpam-3515	92	64	the	the	DET
ejpam-3515	92	65	value	value	NOUN
ejpam-3515	92	66	∂f	∂f	PROPN
ejpam-3515	92	67	∂twith	∂twith	ADP
ejpam-3515	92	68	the	the	DET
ejpam-3515	92	69	help	help	NOUN
ejpam-3515	92	70	cauchy	cauchy	PROPN
ejpam-3515	92	71	schwartz	schwartz	PROPN
ejpam-3515	92	72	inequality	inequality	PROPN
ejpam-3515	92	73	for	for	ADP
ejpam-3515	92	74	drivatives	drivative	NOUN
ejpam-3515	92	75	of	of	ADP
ejpam-3515	92	76	analytic	analytic	ADJ
ejpam-3515	92	77	function:∣∣∣∣∂f∂t	function:∣∣∣∣∂f∂t	PROPN
ejpam-3515	92	78	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3515	92	79	≤	≤	ADJ
ejpam-3515	92	80	const.max	const.max	NOUN
ejpam-3515	92	81	|z−t|	|z−t|	PUNCT
ejpam-3515	92	82	|f(z)|	|f(z)|	PROPN
ejpam-3515	92	83	.	.	PUNCT
ejpam-3515	93	1	further	far	ADV
ejpam-3515	93	2	,	,	PUNCT
ejpam-3515	93	3	|f(z)|	|f(z)|	PROPN
ejpam-3515	93	4	=	=	SYM
ejpam-3515	93	5	|e(f	|e(f	PROPN
ejpam-3515	93	6	(	(	PUNCT
ejpam-3515	93	7	z	z	PROPN
ejpam-3515	93	8	,	,	PUNCT
ejpam-3515	93	9	v	v	NOUN
ejpam-3515	93	10	)	)	PUNCT
ejpam-3515	93	11	θ(v	θ(v	NOUN
ejpam-3515	93	12	)	)	PUNCT
ejpam-3515	93	13	)	)	PUNCT
ejpam-3515	93	14	|	|	ADV
ejpam-3515	93	15	≤	≤	NUM
ejpam-3515	93	16	‖θ‖l2(rn	‖θ‖l2(rn	PROPN
ejpam-3515	93	17	,	,	PUNCT
ejpam-3515	93	18	dv	dv	PROPN
ejpam-3515	93	19	)	)	PUNCT
ejpam-3515	93	20	e(|f	e(|f	NOUN
ejpam-3515	93	21	(	(	PUNCT
ejpam-3515	93	22	z	z	NOUN
ejpam-3515	93	23	,	,	PUNCT
ejpam-3515	93	24	v	v	NOUN
ejpam-3515	93	25	)	)	PUNCT
ejpam-3515	93	26	|2	|2	NUM
ejpam-3515	93	27	)	)	PUNCT
ejpam-3515	93	28	1	1	NUM
ejpam-3515	93	29	2	2	NUM
ejpam-3515	93	30	≤	≤	NUM
ejpam-3515	93	31	const	const	ADJ
ejpam-3515	93	32	‖θ‖l2(rn	‖θ‖l2(rn	PROPN
ejpam-3515	93	33	,	,	PUNCT
ejpam-3515	93	34	dv	dv	PROPN
ejpam-3515	93	35	)	)	PUNCT
ejpam-3515	93	36	‖h‖l2(rn	‖h‖l2(rn	PROPN
ejpam-3515	93	37	,	,	PUNCT
ejpam-3515	93	38	dx	dx	PROPN
ejpam-3515	93	39	)	)	PUNCT
ejpam-3515	93	40	.	.	PUNCT
ejpam-3515	94	1	thus,∣∣∣∣∣∣	thus,∣∣∣∣∣∣	PROPN
ejpam-3515	94	2	∫	∫	PROPN
ejpam-3515	94	3	rn	rn	PROPN
ejpam-3515	94	4	f(t	f(t	PROPN
ejpam-3515	94	5	,	,	PUNCT
ejpam-3515	94	6	x	x	X
ejpam-3515	94	7	)	)	PUNCT
ejpam-3515	94	8	n∑	n∑	PUNCT
ejpam-3515	95	1	j=1	j=1	NOUN
ejpam-3515	95	2	1	1	NUM
ejpam-3515	95	3	2	2	NUM
ejpam-3515	95	4	(	(	PUNCT
ejpam-3515	95	5	i∂j	i∂j	VERB
ejpam-3515	95	6	+	+	CCONJ
ejpam-3515	95	7	bj(x))2	bj(x))2	PROPN
ejpam-3515	95	8	h(x)dx	h(x)dx	VERB
ejpam-3515	95	9	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3515	95	10	≤	≤	NUM
ejpam-3515	95	11	const	const	ADJ
ejpam-3515	95	12	‖θ‖l2(rn	‖θ‖l2(rn	PROPN
ejpam-3515	95	13	,	,	PUNCT
ejpam-3515	95	14	dv	dv	PROPN
ejpam-3515	95	15	)	)	PUNCT
ejpam-3515	95	16	‖h‖l2(rn	‖h‖l2(rn	PROPN
ejpam-3515	95	17	,	,	PUNCT
ejpam-3515	95	18	dx	dx	PROPN
ejpam-3515	95	19	)	)	PUNCT
ejpam-3515	95	20	.	.	PUNCT
ejpam-3515	96	1	one	one	PRON
ejpam-3515	96	2	may	may	AUX
ejpam-3515	96	3	check	check	VERB
ejpam-3515	96	4	in	in	ADP
ejpam-3515	96	5	just	just	ADV
ejpam-3515	96	6	same	same	ADJ
ejpam-3515	96	7	way	way	NOUN
ejpam-3515	96	8	that	that	SCONJ
ejpam-3515	96	9	if	if	SCONJ
ejpam-3515	96	10	h1(x	h1(x	NOUN
ejpam-3515	96	11	)	)	PUNCT
ejpam-3515	96	12	,	,	PUNCT
ejpam-3515	96	13	...	...	PUNCT
ejpam-3515	96	14	,	,	PUNCT
ejpam-3515	96	15	hp(x	hp(x	PROPN
ejpam-3515	96	16	)	)	PUNCT
ejpam-3515	96	17	,	,	PUNCT
ejpam-3515	96	18	θ1(v	θ1(v	PROPN
ejpam-3515	96	19	)	)	PUNCT
ejpam-3515	96	20	,	,	PUNCT
ejpam-3515	96	21	...	...	PUNCT
ejpam-3515	96	22	,	,	PUNCT
ejpam-3515	96	23	θp(v	θp(v	PRON
ejpam-3515	96	24	)	)	PUNCT
ejpam-3515	96	25	and	and	CCONJ
ejpam-3515	96	26	constats	constat	NOUN
ejpam-3515	96	27	ck	ck	PRON
ejpam-3515	96	28	,	,	PUNCT
ejpam-3515	96	29	l	l	NOUN
ejpam-3515	96	30	,	,	PUNCT
ejpam-3515	96	31	k	k	NOUN
ejpam-3515	96	32	,	,	PUNCT
ejpam-3515	96	33	l	l	NOUN
ejpam-3515	96	34	=	=	SYM
ejpam-3515	96	35	1	1	NUM
ejpam-3515	96	36	,	,	PUNCT
ejpam-3515	96	37	...	...	PUNCT
ejpam-3515	96	38	,	,	PUNCT
ejpam-3515	96	39	p	p	NOUN
ejpam-3515	96	40	are	be	AUX
ejpam-3515	96	41	given	give	VERB
ejpam-3515	96	42	,	,	PUNCT
ejpam-3515	96	43	then∣∣∣∣∣∣e	then∣∣∣∣∣∣e	X
ejpam-3515	96	44	∫	∫	NUM
ejpam-3515	96	45	rn	rn	PROPN
ejpam-3515	96	46	ψ(t	ψ(t	PROPN
ejpam-3515	96	47	,	,	PUNCT
ejpam-3515	96	48	x	x	NOUN
ejpam-3515	96	49	)	)	PUNCT
ejpam-3515	96	50	p∑	p∑	X
ejpam-3515	97	1	k	k	NOUN
ejpam-3515	97	2	,	,	PUNCT
ejpam-3515	97	3	l=1	l=1	VERB
ejpam-3515	97	4	ck	ck	INTJ
ejpam-3515	97	5	,	,	PUNCT
ejpam-3515	97	6	l	l	PROPN
ejpam-3515	97	7	n∑	n∑	NOUN
ejpam-3515	97	8	j=1	j=1	ADJ
ejpam-3515	97	9	1	1	NUM
ejpam-3515	97	10	2	2	NUM
ejpam-3515	97	11	(	(	PUNCT
ejpam-3515	97	12	i∂j	i∂j	VERB
ejpam-3515	97	13	+	+	PUNCT
ejpam-3515	98	1	bj(x))2	bj(x))2	PROPN
ejpam-3515	98	2	hk(x)θl(v	hk(x)θl(v	X
ejpam-3515	98	3	)	)	PUNCT
ejpam-3515	98	4	dx	dx	PROPN
ejpam-3515	98	5	∣∣∣∣∣∣	∣∣∣∣∣∣	PUNCT
ejpam-3515	99	1	≤	≤	NUM
ejpam-3515	99	2	const	const	NOUN
ejpam-3515	99	3	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-3515	100	1	p∑	p∑	X
ejpam-3515	101	1	k	k	NOUN
ejpam-3515	101	2	,	,	PUNCT
ejpam-3515	101	3	l=1	l=1	VERB
ejpam-3515	101	4	ck	ck	INTJ
ejpam-3515	101	5	,	,	PUNCT
ejpam-3515	101	6	lhk(x)θl(v	lhk(x)θl(v	ADJ
ejpam-3515	101	7	)	)	PUNCT
ejpam-3515	101	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-3515	102	1	l2(rn	l2(rn	PROPN
ejpam-3515	102	2	,	,	PUNCT
ejpam-3515	102	3	dx	dx	PROPN
ejpam-3515	102	4	,	,	PUNCT
ejpam-3515	102	5	dv	dv	PROPN
ejpam-3515	102	6	)	)	PUNCT
ejpam-3515	102	7	,	,	PUNCT
ejpam-3515	102	8	the	the	DET
ejpam-3515	102	9	left	left	ADJ
ejpam-3515	102	10	side	side	NOUN
ejpam-3515	102	11	equal	equal	ADJ
ejpam-3515	102	12	to∣∣∣∣∣∣e	to∣∣∣∣∣∣e	PROPN
ejpam-3515	102	13	∫	∫	PROPN
ejpam-3515	102	14	rn	rn	PROPN
ejpam-3515	102	15	ψ(t	ψ(t	PROPN
ejpam-3515	102	16	,	,	PUNCT
ejpam-3515	102	17	x	x	NOUN
ejpam-3515	102	18	)	)	PUNCT
ejpam-3515	102	19	p∑	p∑	X
ejpam-3515	103	1	k	k	NOUN
ejpam-3515	103	2	,	,	PUNCT
ejpam-3515	103	3	l=1	l=1	VERB
ejpam-3515	103	4	ck	ck	INTJ
ejpam-3515	103	5	,	,	PUNCT
ejpam-3515	103	6	l	l	PROPN
ejpam-3515	103	7	n∑	n∑	NOUN
ejpam-3515	103	8	j=1	j=1	ADJ
ejpam-3515	103	9	1	1	NUM
ejpam-3515	103	10	2	2	NUM
ejpam-3515	103	11	(	(	PUNCT
ejpam-3515	103	12	∂2j	∂2j	PROPN
ejpam-3515	103	13	+	+	CCONJ
ejpam-3515	103	14	i∂jbj(x	i∂jbj(x	PROPN
ejpam-3515	103	15	)	)	PUNCT
ejpam-3515	104	1	+	+	CCONJ
ejpam-3515	104	2	ibj(x)∂j	ibj(x)∂j	X
ejpam-3515	104	3	+	+	CCONJ
ejpam-3515	104	4	b2j	b2j	PROPN
ejpam-3515	104	5	(	(	PUNCT
ejpam-3515	104	6	x	x	NOUN
ejpam-3515	104	7	)	)	PUNCT
ejpam-3515	104	8	)	)	PUNCT
ejpam-3515	104	9	hk(x)θl(v	hk(x)θl(v	X
ejpam-3515	104	10	)	)	PUNCT
ejpam-3515	104	11	dx	dx	PROPN
ejpam-3515	104	12	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3515	104	13	,	,	PUNCT
ejpam-3515	104	14	we	we	PRON
ejpam-3515	104	15	pass	pass	VERB
ejpam-3515	104	16	at	at	ADP
ejpam-3515	104	17	the	the	DET
ejpam-3515	104	18	left	left	ADJ
ejpam-3515	104	19	side	side	NOUN
ejpam-3515	104	20	to	to	ADP
ejpam-3515	104	21	fourier	fourier	ADJ
ejpam-3515	104	22	transformation	transformation	NOUN
ejpam-3515	104	23	by	by	ADP
ejpam-3515	104	24	the	the	DET
ejpam-3515	104	25	variable	variable	ADJ
ejpam-3515	104	26	x.	x.	NOUN
ejpam-3515	105	1	we	we	PRON
ejpam-3515	105	2	get	get	VERB
ejpam-3515	105	3	the	the	DET
ejpam-3515	105	4	following	follow	VERB
ejpam-3515	105	5	expression:-∣∣∣∣∣∣e	expression:-∣∣∣∣∣∣e	X
ejpam-3515	105	6	∫	∫	PROPN
ejpam-3515	105	7	rn	rn	PROPN
ejpam-3515	105	8	ψ̂(t	ψ̂(t	NOUN
ejpam-3515	105	9	,	,	PUNCT
ejpam-3515	105	10	q	q	NOUN
ejpam-3515	105	11	)	)	PUNCT
ejpam-3515	105	12	p∑	p∑	X
ejpam-3515	106	1	k	k	NOUN
ejpam-3515	106	2	,	,	PUNCT
ejpam-3515	106	3	l=1	l=1	VERB
ejpam-3515	106	4	ck	ck	INTJ
ejpam-3515	106	5	,	,	PUNCT
ejpam-3515	106	6	l	l	PROPN
ejpam-3515	106	7	n∑	n∑	NOUN
ejpam-3515	106	8	j=1	j=1	ADJ
ejpam-3515	106	9	1	1	NUM
ejpam-3515	106	10	2	2	NUM
ejpam-3515	106	11	(	(	PUNCT
ejpam-3515	106	12	∂2j	∂2j	PROPN
ejpam-3515	106	13	+	+	CCONJ
ejpam-3515	106	14	i∂j	i∂j	PROPN
ejpam-3515	106	15	b̂j(q	b̂j(q	NUM
ejpam-3515	106	16	)	)	PUNCT
ejpam-3515	107	1	+	+	CCONJ
ejpam-3515	107	2	ib̂j(q)∂j	ib̂j(q)∂j	X
ejpam-3515	107	3	+	+	CCONJ
ejpam-3515	107	4	b̂j	b̂j	PROPN
ejpam-3515	107	5	2	2	NUM
ejpam-3515	107	6	(	(	PUNCT
ejpam-3515	107	7	q	q	NOUN
ejpam-3515	107	8	)	)	PUNCT
ejpam-3515	107	9	)	)	PUNCT
ejpam-3515	108	1	ĥk(q)θl(v	ĥk(q)θl(v	X
ejpam-3515	108	2	)	)	PUNCT
ejpam-3515	108	3	dq	dq	ADP
ejpam-3515	108	4	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3515	108	5	,	,	PUNCT
ejpam-3515	108	6	which	which	PRON
ejpam-3515	108	7	equal	equal	ADJ
ejpam-3515	108	8	to∣∣∣∣∣∣e	to∣∣∣∣∣∣e	PROPN
ejpam-3515	108	9	∫	∫	PROPN
ejpam-3515	108	10	rn	rn	PROPN
ejpam-3515	108	11	ψ̂(t	ψ̂(t	NOUN
ejpam-3515	108	12	,	,	PUNCT
ejpam-3515	108	13	q	q	NOUN
ejpam-3515	108	14	)	)	PUNCT
ejpam-3515	108	15	p∑	p∑	X
ejpam-3515	109	1	k	k	NOUN
ejpam-3515	109	2	,	,	PUNCT
ejpam-3515	109	3	l=1	l=1	VERB
ejpam-3515	109	4	ck	ck	INTJ
ejpam-3515	109	5	,	,	PUNCT
ejpam-3515	109	6	l	l	NOUN
ejpam-3515	109	7			PROPN
ejpam-3515	109	8	n∑	n∑	PROPN
ejpam-3515	109	9	j=1	j=1	NOUN
ejpam-3515	109	10	−1	−1	NOUN
ejpam-3515	109	11	2	2	NUM
ejpam-3515	109	12	|q|2	|q|2	VERB
ejpam-3515	109	13	+	+	PROPN
ejpam-3515	110	1	n∑	n∑	ADJ
ejpam-3515	110	2	j=1	j=1	NOUN
ejpam-3515	110	3	i	i	VERB
ejpam-3515	110	4	2	2	NUM
ejpam-3515	110	5	∂j	∂j	NOUN
ejpam-3515	110	6	b̂j(q	b̂j(q	NUM
ejpam-3515	110	7	)	)	PUNCT
ejpam-3515	111	1	+	+	CCONJ
ejpam-3515	112	1	n∑	n∑	NOUN
ejpam-3515	112	2	j=1	j=1	NOUN
ejpam-3515	112	3	i	i	PRON
ejpam-3515	112	4	2	2	NUM
ejpam-3515	112	5	b̂j(q	b̂j(q	NOUN
ejpam-3515	112	6	)	)	PUNCT
ejpam-3515	112	7	|−qi|+	|−qi|+	NOUN
ejpam-3515	113	1	n∑	n∑	NOUN
ejpam-3515	113	2	j=1	j=1	NOUN
ejpam-3515	113	3	1	1	NUM
ejpam-3515	113	4	2	2	NUM
ejpam-3515	113	5	b̂j	b̂j	NOUN
ejpam-3515	113	6	2	2	NUM
ejpam-3515	113	7	(	(	PUNCT
ejpam-3515	113	8	q	q	NOUN
ejpam-3515	113	9	)	)	PUNCT
ejpam-3515	113	10			PROPN
ejpam-3515	113	11	ĥk(q)θl(v	ĥk(q)θl(v	INTJ
ejpam-3515	113	12	)	)	PUNCT
ejpam-3515	113	13	dq	dq	ADP
ejpam-3515	113	14	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3515	114	1	y.	y.	PROPN
ejpam-3515	114	2	h.	h.	PROPN
ejpam-3515	114	3	saleem	saleem	PROPN
ejpam-3515	114	4	,	,	PUNCT
ejpam-3515	114	5	h.	h.	PROPN
ejpam-3515	114	6	a.	a.	PROPN
ejpam-3515	114	7	shubber	shubber	PROPN
ejpam-3515	114	8	/	/	SYM
ejpam-3515	114	9	eur	eur	PROPN
ejpam-3515	114	10	.	.	PUNCT
ejpam-3515	115	1	j.	j.	PROPN
ejpam-3515	115	2	pure	pure	PROPN
ejpam-3515	115	3	appl	appl	PROPN
ejpam-3515	115	4	.	.	PROPN
ejpam-3515	115	5	math	math	PROPN
ejpam-3515	115	6	,	,	PUNCT
ejpam-3515	115	7	12	12	NUM
ejpam-3515	115	8	(	(	PUNCT
ejpam-3515	115	9	4	4	NUM
ejpam-3515	115	10	)	)	PUNCT
ejpam-3515	115	11	(	(	PUNCT
ejpam-3515	115	12	2019	2019	NUM
ejpam-3515	115	13	)	)	PUNCT
ejpam-3515	115	14	,	,	PUNCT
ejpam-3515	115	15	1441	1441	NUM
ejpam-3515	115	16	-	-	SYM
ejpam-3515	115	17	1454	1454	NUM
ejpam-3515	115	18	1446	1446	NUM
ejpam-3515	115	19	=	=	SYM
ejpam-3515	115	20	〈	〈	PROPN
ejpam-3515	115	21	ψ̂(t	ψ̂(t	NOUN
ejpam-3515	115	22	,	,	PUNCT
ejpam-3515	115	23	q	q	NOUN
ejpam-3515	115	24	)	)	PUNCT
ejpam-3515	115	25	,	,	PUNCT
ejpam-3515	115	26	p∑	p∑	X
ejpam-3515	116	1	k	k	NOUN
ejpam-3515	116	2	,	,	PUNCT
ejpam-3515	116	3	l=1	l=1	VERB
ejpam-3515	116	4	ck	ck	INTJ
ejpam-3515	116	5	,	,	PUNCT
ejpam-3515	116	6	l	l	NOUN
ejpam-3515	116	7			PROPN
ejpam-3515	116	8	n∑	n∑	PROPN
ejpam-3515	116	9	j=1	j=1	NOUN
ejpam-3515	116	10	−1	−1	NOUN
ejpam-3515	116	11	2	2	NUM
ejpam-3515	116	12	|q|2	|q|2	VERB
ejpam-3515	116	13	+	+	PROPN
ejpam-3515	117	1	n∑	n∑	ADJ
ejpam-3515	117	2	j=1	j=1	NOUN
ejpam-3515	117	3	i	i	VERB
ejpam-3515	117	4	2	2	NUM
ejpam-3515	117	5	∂j	∂j	NOUN
ejpam-3515	117	6	b̂j(q	b̂j(q	NUM
ejpam-3515	117	7	)	)	PUNCT
ejpam-3515	118	1	+	+	CCONJ
ejpam-3515	119	1	n∑	n∑	NOUN
ejpam-3515	119	2	j=1	j=1	NOUN
ejpam-3515	119	3	i	i	PRON
ejpam-3515	119	4	2	2	NUM
ejpam-3515	119	5	b̂j(q	b̂j(q	NOUN
ejpam-3515	119	6	)	)	PUNCT
ejpam-3515	119	7	|−qi|+	|−qi|+	NOUN
ejpam-3515	120	1	n∑	n∑	NOUN
ejpam-3515	120	2	j=1	j=1	NOUN
ejpam-3515	120	3	1	1	NUM
ejpam-3515	120	4	2	2	NUM
ejpam-3515	120	5	b̂j	b̂j	NOUN
ejpam-3515	120	6	2	2	NUM
ejpam-3515	120	7	(	(	PUNCT
ejpam-3515	120	8	q	q	NOUN
ejpam-3515	120	9	)	)	PUNCT
ejpam-3515	120	10			PROPN
ejpam-3515	120	11	ĥk(q)θl(v	ĥk(q)θl(v	ADV
ejpam-3515	120	12	)	)	PUNCT
ejpam-3515	120	13	〉	〉	NOUN
ejpam-3515	120	14	l2(rn	l2(rn	PROPN
ejpam-3515	120	15	,	,	PUNCT
ejpam-3515	120	16	dq	dq	PROPN
ejpam-3515	120	17	,	,	PUNCT
ejpam-3515	120	18	dv	dv	PROPN
ejpam-3515	120	19	)	)	PUNCT
ejpam-3515	120	20	=	=	PUNCT
ejpam-3515	120	21	〈	〈	PROPN
ejpam-3515	120	22	ψ̂(t	ψ̂(t	NOUN
ejpam-3515	120	23	,	,	PUNCT
ejpam-3515	120	24	q	q	NOUN
ejpam-3515	120	25	)	)	PUNCT
ejpam-3515	120	26	,	,	PUNCT
ejpam-3515	120	27	p∑	p∑	X
ejpam-3515	121	1	k	k	NOUN
ejpam-3515	121	2	,	,	PUNCT
ejpam-3515	121	3	l=1	l=1	VERB
ejpam-3515	121	4	ck	ck	INTJ
ejpam-3515	121	5	,	,	PUNCT
ejpam-3515	121	6	l	l	NOUN
ejpam-3515	121	7	−n	−n	ADP
ejpam-3515	121	8	2	2	NUM
ejpam-3515	121	9	|q|2	|q|2	VERB
ejpam-3515	121	10	+	+	PROPN
ejpam-3515	122	1	n∑	n∑	ADJ
ejpam-3515	122	2	j=1	j=1	NOUN
ejpam-3515	122	3	i	i	VERB
ejpam-3515	122	4	2	2	NUM
ejpam-3515	122	5	∂j	∂j	NOUN
ejpam-3515	122	6	b̂j(q	b̂j(q	NUM
ejpam-3515	122	7	)	)	PUNCT
ejpam-3515	123	1	+	+	CCONJ
ejpam-3515	124	1	n∑	n∑	NOUN
ejpam-3515	124	2	j=1	j=1	NOUN
ejpam-3515	124	3	i	i	PRON
ejpam-3515	124	4	2	2	NUM
ejpam-3515	124	5	b̂j(q	b̂j(q	NOUN
ejpam-3515	124	6	)	)	PUNCT
ejpam-3515	124	7	|q|+	|q|+	NOUN
ejpam-3515	124	8	n∑	n∑	NOUN
ejpam-3515	124	9	j=1	j=1	NOUN
ejpam-3515	124	10	1	1	NUM
ejpam-3515	124	11	2	2	NUM
ejpam-3515	124	12	b̂j	b̂j	NOUN
ejpam-3515	124	13	2	2	NUM
ejpam-3515	124	14	(	(	PUNCT
ejpam-3515	124	15	q	q	NOUN
ejpam-3515	124	16	)	)	PUNCT
ejpam-3515	124	17			PROPN
ejpam-3515	124	18	ĥk(q)θl(v	ĥk(q)θl(v	ADV
ejpam-3515	124	19	)	)	PUNCT
ejpam-3515	124	20	〉	〉	NOUN
ejpam-3515	124	21	l2(rn	l2(rn	PROPN
ejpam-3515	124	22	,	,	PUNCT
ejpam-3515	124	23	dq	dq	PROPN
ejpam-3515	124	24	,	,	PUNCT
ejpam-3515	124	25	dv	dv	PROPN
ejpam-3515	124	26	)	)	PUNCT
ejpam-3515	125	1	=	=	PUNCT
ejpam-3515	125	2	〈	〈	PROPN
ejpam-3515	125	3	ψ̂(t	ψ̂(t	NOUN
ejpam-3515	125	4	,	,	PUNCT
ejpam-3515	125	5	q	q	ADJ
ejpam-3515	125	6	)	)	PUNCT
ejpam-3515	125	7	−n	−n	ADP
ejpam-3515	125	8	2	2	NUM
ejpam-3515	125	9	|q|2	|q|2	VERB
ejpam-3515	125	10	+	+	PROPN
ejpam-3515	126	1	n∑	n∑	ADJ
ejpam-3515	126	2	j=1	j=1	NOUN
ejpam-3515	126	3	i	i	VERB
ejpam-3515	126	4	2	2	NUM
ejpam-3515	126	5	∂j	∂j	NOUN
ejpam-3515	126	6	b̂j(q	b̂j(q	NUM
ejpam-3515	126	7	)	)	PUNCT
ejpam-3515	127	1	+	+	CCONJ
ejpam-3515	128	1	n∑	n∑	NOUN
ejpam-3515	128	2	j=1	j=1	NOUN
ejpam-3515	128	3	i	i	PRON
ejpam-3515	128	4	2	2	NUM
ejpam-3515	128	5	b̂j(q	b̂j(q	NOUN
ejpam-3515	128	6	)	)	PUNCT
ejpam-3515	128	7	|q|+	|q|+	NOUN
ejpam-3515	128	8	n∑	n∑	NOUN
ejpam-3515	128	9	j=1	j=1	NOUN
ejpam-3515	128	10	1	1	NUM
ejpam-3515	128	11	2	2	NUM
ejpam-3515	128	12	b̂j	b̂j	NOUN
ejpam-3515	128	13	2	2	NUM
ejpam-3515	128	14	(	(	PUNCT
ejpam-3515	128	15	q	q	NOUN
ejpam-3515	128	16	)	)	PUNCT
ejpam-3515	128	17			PROPN
ejpam-3515	128	18	,	,	PUNCT
ejpam-3515	128	19	p∑	p∑	X
ejpam-3515	128	20	k	k	NOUN
ejpam-3515	128	21	,	,	PUNCT
ejpam-3515	128	22	l=1	l=1	NOUN
ejpam-3515	128	23	ck	ck	INTJ
ejpam-3515	128	24	,	,	PUNCT
ejpam-3515	128	25	lĥk(q)θl(v	lĥk(q)θl(v	PUNCT
ejpam-3515	128	26	)	)	PUNCT
ejpam-3515	128	27	〉	〉	NOUN
ejpam-3515	129	1	l2(rn	l2(rn	PROPN
ejpam-3515	129	2	,	,	PUNCT
ejpam-3515	129	3	dq	dq	PROPN
ejpam-3515	129	4	,	,	PUNCT
ejpam-3515	129	5	dv	dv	PROPN
ejpam-3515	129	6	)	)	PUNCT
ejpam-3515	129	7	.	.	PUNCT
ejpam-3515	130	1	the	the	DET
ejpam-3515	130	2	right	right	ADJ
ejpam-3515	130	3	side	side	NOUN
ejpam-3515	130	4	after	after	SCONJ
ejpam-3515	130	5	the	the	DET
ejpam-3515	130	6	passage	passage	NOUN
ejpam-3515	130	7	to	to	ADP
ejpam-3515	130	8	the	the	DET
ejpam-3515	130	9	fourier	fourier	NOUN
ejpam-3515	130	10	transform	transform	NOUN
ejpam-3515	130	11	gains	gain	VERB
ejpam-3515	130	12	the	the	DET
ejpam-3515	130	13	form∥∥∥∥∥∥	form∥∥∥∥∥∥	PROPN
ejpam-3515	130	14	p∑	p∑	PROPN
ejpam-3515	131	1	k	k	NOUN
ejpam-3515	131	2	,	,	PUNCT
ejpam-3515	131	3	l=1	l=1	NOUN
ejpam-3515	131	4	ck	ck	INTJ
ejpam-3515	131	5	,	,	PUNCT
ejpam-3515	131	6	lĥk(q)θl(v	lĥk(q)θl(v	PROPN
ejpam-3515	131	7	)	)	PUNCT
ejpam-3515	131	8	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-3515	132	1	l2(rn	l2(rn	PROPN
ejpam-3515	132	2	,	,	PUNCT
ejpam-3515	132	3	dq	dq	PROPN
ejpam-3515	132	4	,	,	PUNCT
ejpam-3515	132	5	dv	dv	PROPN
ejpam-3515	132	6	)	)	PUNCT
ejpam-3515	132	7	.	.	PUNCT
ejpam-3515	133	1	from	from	ADP
ejpam-3515	133	2	this	this	PRON
ejpam-3515	133	3	we	we	PRON
ejpam-3515	133	4	get∥∥∥∥∥∥	get∥∥∥∥∥∥	VERB
ejpam-3515	133	5	−n	−n	ADP
ejpam-3515	133	6	2	2	NUM
ejpam-3515	133	7	|q|2	|q|2	VERB
ejpam-3515	133	8	+	+	PROPN
ejpam-3515	134	1	n∑	n∑	ADJ
ejpam-3515	134	2	j=1	j=1	NOUN
ejpam-3515	134	3	i	i	VERB
ejpam-3515	134	4	2	2	NUM
ejpam-3515	134	5	∂j	∂j	NOUN
ejpam-3515	134	6	b̂j(q	b̂j(q	NUM
ejpam-3515	134	7	)	)	PUNCT
ejpam-3515	135	1	+	+	CCONJ
ejpam-3515	136	1	n∑	n∑	NOUN
ejpam-3515	136	2	j=1	j=1	NOUN
ejpam-3515	136	3	i	i	PRON
ejpam-3515	136	4	2	2	NUM
ejpam-3515	136	5	b̂j(q	b̂j(q	NOUN
ejpam-3515	136	6	)	)	PUNCT
ejpam-3515	136	7	|q|+	|q|+	NOUN
ejpam-3515	136	8	n∑	n∑	NOUN
ejpam-3515	136	9	j=1	j=1	NOUN
ejpam-3515	136	10	1	1	NUM
ejpam-3515	136	11	2	2	NUM
ejpam-3515	136	12	b̂j	b̂j	NOUN
ejpam-3515	136	13	2	2	NUM
ejpam-3515	136	14	(	(	PUNCT
ejpam-3515	136	15	q	q	NOUN
ejpam-3515	136	16	)	)	PUNCT
ejpam-3515	136	17			PROPN
ejpam-3515	136	18	ψ̂(t	ψ̂(t	NOUN
ejpam-3515	136	19	,	,	PUNCT
ejpam-3515	136	20	q	q	ADJ
ejpam-3515	136	21	)	)	PUNCT
ejpam-3515	136	22	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-3515	137	1	l2(rn	l2(rn	PROPN
ejpam-3515	137	2	,	,	PUNCT
ejpam-3515	137	3	dq	dq	PROPN
ejpam-3515	137	4	,	,	PUNCT
ejpam-3515	137	5	dv	dv	PROPN
ejpam-3515	137	6	)	)	PUNCT
ejpam-3515	137	7	≤	≤	NUM
ejpam-3515	137	8	const	const	NOUN
ejpam-3515	137	9	.	.	PUNCT
ejpam-3515	138	1	(	(	PUNCT
ejpam-3515	138	2	2.8	2.8	NUM
ejpam-3515	138	3	)	)	PUNCT
ejpam-3515	138	4	in	in	ADP
ejpam-3515	138	5	particular	particular	ADJ
ejpam-3515	138	6	∫	∫	PROPN
ejpam-3515	138	7	rn	rn	PROPN
ejpam-3515	138	8	−n	−n	PROPN
ejpam-3515	138	9	2	2	NUM
ejpam-3515	138	10	|q|2	|q|2	VERB
ejpam-3515	138	11	+	+	PROPN
ejpam-3515	138	12	n∑	n∑	ADJ
ejpam-3515	138	13	j=1	j=1	NOUN
ejpam-3515	138	14	i	i	VERB
ejpam-3515	138	15	2	2	NUM
ejpam-3515	138	16	∂j	∂j	NOUN
ejpam-3515	138	17	b̂j(q	b̂j(q	NUM
ejpam-3515	138	18	)	)	PUNCT
ejpam-3515	139	1	+	+	CCONJ
ejpam-3515	140	1	n∑	n∑	NOUN
ejpam-3515	140	2	j=1	j=1	NOUN
ejpam-3515	140	3	i	i	PRON
ejpam-3515	140	4	2	2	NUM
ejpam-3515	140	5	b̂j(q	b̂j(q	NOUN
ejpam-3515	140	6	)	)	PUNCT
ejpam-3515	140	7	|q|+	|q|+	NOUN
ejpam-3515	140	8	n∑	n∑	NOUN
ejpam-3515	140	9	j=1	j=1	NOUN
ejpam-3515	140	10	1	1	NUM
ejpam-3515	140	11	2	2	NUM
ejpam-3515	140	12	b̂j	b̂j	NOUN
ejpam-3515	140	13	2	2	NUM
ejpam-3515	140	14	(	(	PUNCT
ejpam-3515	140	15	q	q	NOUN
ejpam-3515	140	16	)	)	PUNCT
ejpam-3515	140	17	2	2	PRON
ejpam-3515	140	18	∣∣∣ψ̂(t	∣∣∣ψ̂(t	NOUN
ejpam-3515	140	19	,	,	PUNCT
ejpam-3515	140	20	q	q	NOUN
ejpam-3515	140	21	)	)	PUNCT
ejpam-3515	140	22	∣∣∣2	∣∣∣2	NOUN
ejpam-3515	140	23	dq	dq	ADP
ejpam-3515	140	24	<	<	X
ejpam-3515	140	25	+	+	NOUN
ejpam-3515	140	26	∞	∞	PROPN
ejpam-3515	140	27	,	,	PUNCT
ejpam-3515	140	28	(	(	PUNCT
ejpam-3515	140	29	2.9	2.9	NUM
ejpam-3515	140	30	)	)	PUNCT
ejpam-3515	140	31	for	for	ADP
ejpam-3515	140	32	almost	almost	ADV
ejpam-3515	140	33	every	every	PRON
ejpam-3515	140	34	v	v	NOUN
ejpam-3515	140	35	and	and	CCONJ
ejpam-3515	140	36	b	b	NOUN
ejpam-3515	140	37	,	,	PUNCT
ejpam-3515	140	38	i.e.	i.e.	X
ejpam-3515	140	39	ψ(t	ψ(t	PROPN
ejpam-3515	140	40	,	,	PUNCT
ejpam-3515	140	41	x	x	X
ejpam-3515	140	42	)	)	PUNCT
ejpam-3515	140	43	∈	∈	PROPN
ejpam-3515	140	44	w1	w1	NOUN
ejpam-3515	140	45	for	for	ADP
ejpam-3515	140	46	almost	almost	ADV
ejpam-3515	140	47	every	every	PRON
ejpam-3515	140	48	v	v	NOUN
ejpam-3515	140	49	and	and	CCONJ
ejpam-3515	140	50	b.	b.	PROPN
ejpam-3515	140	51	besides	besides	PROPN
ejpam-3515	140	52	,	,	PUNCT
ejpam-3515	140	53	‖ψ‖2w1	‖ψ‖2w1	PROPN
ejpam-3515	140	54	is	be	AUX
ejpam-3515	140	55	an	an	DET
ejpam-3515	140	56	integrable	integrable	ADJ
ejpam-3515	140	57	function	function	NOUN
ejpam-3515	140	58	of	of	ADP
ejpam-3515	140	59	v.	v.	CCONJ
ejpam-3515	140	60	further	far	ADV
ejpam-3515	140	61	,	,	PUNCT
ejpam-3515	140	62	in	in	ADP
ejpam-3515	140	63	just	just	ADV
ejpam-3515	140	64	the	the	DET
ejpam-3515	140	65	same	same	ADJ
ejpam-3515	140	66	way	way	NOUN
ejpam-3515	140	67	as	as	SCONJ
ejpam-3515	140	68	it	it	PRON
ejpam-3515	140	69	was	be	AUX
ejpam-3515	140	70	as	as	ADV
ejpam-3515	140	71	done	do	VERB
ejpam-3515	140	72	while	while	SCONJ
ejpam-3515	140	73	deducing	deduce	VERB
ejpam-3515	140	74	(	(	PUNCT
ejpam-3515	140	75	2.6	2.6	NUM
ejpam-3515	140	76	)	)	PUNCT
ejpam-3515	140	77	one	one	NOUN
ejpam-3515	140	78	can	can	AUX
ejpam-3515	140	79	show	show	VERB
ejpam-3515	140	80	that	that	SCONJ
ejpam-3515	140	81	∂2	∂2	ADJ
ejpam-3515	140	82	∂t2	∂t2	PROPN
ejpam-3515	140	83	∫	∫	PROPN
ejpam-3515	140	84	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	140	85	,	,	PUNCT
ejpam-3515	140	86	x))h(x)dx	x))h(x)dx	NOUN
ejpam-3515	140	87	=	=	SYM
ejpam-3515	140	88	∫	∫	PROPN
ejpam-3515	140	89	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	140	90	,	,	PUNCT
ejpam-3515	140	91	x	x	NOUN
ejpam-3515	140	92	)	)	PUNCT
ejpam-3515	140	93	)	)	PUNCT
ejpam-3515	141	1			VERB
ejpam-3515	141	2	n∑	n∑	NOUN
ejpam-3515	142	1	j=1	j=1	NOUN
ejpam-3515	142	2	1	1	NUM
ejpam-3515	142	3	2	2	NUM
ejpam-3515	142	4	(	(	PUNCT
ejpam-3515	142	5	i∂j	i∂j	VERB
ejpam-3515	142	6	+	+	X
ejpam-3515	142	7	bj(x))2	bj(x))2	X
ejpam-3515	143	1	+	+	CCONJ
ejpam-3515	143	2	v	v	NOUN
ejpam-3515	143	3	(	(	PUNCT
ejpam-3515	143	4	x	x	X
ejpam-3515	143	5	)	)	PUNCT
ejpam-3515	143	6	2	2	ADJ
ejpam-3515	143	7	h(x	h(x	PROPN
ejpam-3515	143	8	)	)	PUNCT
ejpam-3515	143	9			NOUN
ejpam-3515	143	10	dx	dx	PROPN
ejpam-3515	143	11	.	.	PROPN
ejpam-3515	143	12	∂2	∂2	PROPN
ejpam-3515	143	13	∂t2	∂t2	PROPN
ejpam-3515	143	14	∫	∫	PROPN
ejpam-3515	143	15	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	143	16	,	,	PUNCT
ejpam-3515	143	17	x))h(x)dx	x))h(x)dx	NOUN
ejpam-3515	143	18	=	=	SYM
ejpam-3515	143	19	∫	∫	PROPN
ejpam-3515	143	20	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	143	21	,	,	PUNCT
ejpam-3515	143	22	x	x	NOUN
ejpam-3515	143	23	)	)	PUNCT
ejpam-3515	143	24	)	)	PUNCT
ejpam-3515	144	1	[	[	PUNCT
ejpam-3515	144	2			PROPN
ejpam-3515	144	3	n∑	n∑	NOUN
ejpam-3515	144	4	j=1	j=1	NOUN
ejpam-3515	144	5	1	1	NUM
ejpam-3515	144	6	2	2	NUM
ejpam-3515	144	7	(	(	PUNCT
ejpam-3515	144	8	i∂j	i∂j	VERB
ejpam-3515	144	9	+	+	CCONJ
ejpam-3515	144	10	bj(x))2	bj(x))2	PROPN
ejpam-3515	144	11	2	2	ADJ
ejpam-3515	144	12	h(x	h(x	PROPN
ejpam-3515	144	13	)	)	PUNCT
ejpam-3515	145	1	+	+	PUNCT
ejpam-3515	145	2	n∑	n∑	PUNCT
ejpam-3515	145	3	j=1	j=1	NOUN
ejpam-3515	145	4	1	1	NUM
ejpam-3515	145	5	2	2	NUM
ejpam-3515	145	6	(	(	PUNCT
ejpam-3515	145	7	i∂j	i∂j	VERB
ejpam-3515	145	8	+	+	CCONJ
ejpam-3515	145	9	bj(x))2	bj(x))2	PROPN
ejpam-3515	145	10	v	v	X
ejpam-3515	145	11	(	(	PUNCT
ejpam-3515	145	12	x)h(x	x)h(x	PROPN
ejpam-3515	145	13	)	)	PUNCT
ejpam-3515	146	1	+	+	CCONJ
ejpam-3515	146	2	v	v	X
ejpam-3515	146	3	(	(	PUNCT
ejpam-3515	146	4	x	x	NOUN
ejpam-3515	146	5	)	)	PUNCT
ejpam-3515	146	6	n∑	n∑	NOUN
ejpam-3515	146	7	j=1	j=1	NOUN
ejpam-3515	146	8	1	1	NUM
ejpam-3515	146	9	2	2	NUM
ejpam-3515	146	10	(	(	PUNCT
ejpam-3515	146	11	i∂j	i∂j	VERB
ejpam-3515	146	12	+	+	CCONJ
ejpam-3515	146	13	bj(x))2	bj(x))2	PROPN
ejpam-3515	146	14	h(x	h(x	PROPN
ejpam-3515	146	15	)	)	PUNCT
ejpam-3515	147	1	+	+	CCONJ
ejpam-3515	147	2	v	v	NUM
ejpam-3515	147	3	2(x)h(x)]dx	2(x)h(x)]dx	NUM
ejpam-3515	147	4	.	.	PUNCT
ejpam-3515	148	1	y.	y.	PROPN
ejpam-3515	148	2	h.	h.	PROPN
ejpam-3515	148	3	saleem	saleem	PROPN
ejpam-3515	148	4	,	,	PUNCT
ejpam-3515	148	5	h.	h.	PROPN
ejpam-3515	148	6	a.	a.	PROPN
ejpam-3515	148	7	shubber	shubber	PROPN
ejpam-3515	148	8	/	/	SYM
ejpam-3515	148	9	eur	eur	PROPN
ejpam-3515	148	10	.	.	PUNCT
ejpam-3515	149	1	j.	j.	PROPN
ejpam-3515	149	2	pure	pure	PROPN
ejpam-3515	149	3	appl	appl	PROPN
ejpam-3515	149	4	.	.	PROPN
ejpam-3515	149	5	math	math	PROPN
ejpam-3515	149	6	,	,	PUNCT
ejpam-3515	149	7	12	12	NUM
ejpam-3515	149	8	(	(	PUNCT
ejpam-3515	149	9	4	4	NUM
ejpam-3515	149	10	)	)	PUNCT
ejpam-3515	149	11	(	(	PUNCT
ejpam-3515	149	12	2019	2019	NUM
ejpam-3515	149	13	)	)	PUNCT
ejpam-3515	149	14	,	,	PUNCT
ejpam-3515	149	15	1441	1441	NUM
ejpam-3515	149	16	-	-	SYM
ejpam-3515	149	17	1454	1454	NUM
ejpam-3515	149	18	1447	1447	NUM
ejpam-3515	149	19	let	let	VERB
ejpam-3515	149	20	us	we	PRON
ejpam-3515	149	21	multiply	multiply	VERB
ejpam-3515	149	22	the	the	DET
ejpam-3515	149	23	above	above	ADJ
ejpam-3515	149	24	equation	equation	NOUN
ejpam-3515	149	25	by	by	ADP
ejpam-3515	149	26	θ(v	θ(v	NOUN
ejpam-3515	149	27	)	)	PUNCT
ejpam-3515	149	28	and	and	CCONJ
ejpam-3515	149	29	integrate	integrate	VERB
ejpam-3515	149	30	over	over	ADP
ejpam-3515	149	31	dv	dv	PROPN
ejpam-3515	149	32	,	,	PUNCT
ejpam-3515	149	33	extract	extract	VERB
ejpam-3515	149	34	the	the	DET
ejpam-3515	149	35	expression	expression	NOUN
ejpam-3515	149	36	containing	contain	VERB
ejpam-3515	149	37	(	(	PUNCT
ejpam-3515	149	38	∑n	∑n	PROPN
ejpam-3515	149	39	j=1	j=1	NOUN
ejpam-3515	149	40	1	1	NUM
ejpam-3515	149	41	2	2	NUM
ejpam-3515	149	42	(	(	PUNCT
ejpam-3515	149	43	i∂j	i∂j	VERB
ejpam-3515	149	44	+	+	CCONJ
ejpam-3515	149	45	bj(x))2	bj(x))2	PROPN
ejpam-3515	149	46	)	)	PUNCT
ejpam-3515	149	47	2	2	NUM
ejpam-3515	149	48	h(x	h(x	PROPN
ejpam-3515	149	49	)	)	PUNCT
ejpam-3515	149	50	and	and	CCONJ
ejpam-3515	149	51	estimate	estimate	VERB
ejpam-3515	149	52	the	the	DET
ejpam-3515	149	53	other	other	ADJ
ejpam-3515	149	54	terms	term	NOUN
ejpam-3515	149	55	in	in	ADP
ejpam-3515	149	56	this	this	DET
ejpam-3515	149	57	equation	equation	NOUN
ejpam-3515	149	58	.	.	PUNCT
ejpam-3515	150	1	the	the	DET
ejpam-3515	150	2	term	term	NOUN
ejpam-3515	150	3	∂2	∂2	PROPN
ejpam-3515	150	4	∂t2	∂t2	PROPN
ejpam-3515	150	5	∫	∫	PROPN
ejpam-3515	150	6	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	150	7	,	,	PUNCT
ejpam-3515	150	8	x))h(x)θ(v	x))h(x)θ(v	PROPN
ejpam-3515	150	9	)	)	PUNCT
ejpam-3515	150	10	dx	dx	PROPN
ejpam-3515	150	11	is	be	AUX
ejpam-3515	150	12	estimated	estimate	VERB
ejpam-3515	150	13	in	in	ADP
ejpam-3515	150	14	just	just	ADV
ejpam-3515	150	15	the	the	DET
ejpam-3515	150	16	same	same	ADJ
ejpam-3515	150	17	way	way	NOUN
ejpam-3515	150	18	as	as	ADP
ejpam-3515	150	19	in	in	ADP
ejpam-3515	150	20	the	the	DET
ejpam-3515	150	21	case	case	NOUN
ejpam-3515	150	22	of	of	ADP
ejpam-3515	150	23	the	the	DET
ejpam-3515	150	24	first	first	ADJ
ejpam-3515	150	25	derivative	derivative	NOUN
ejpam-3515	150	26	,	,	PUNCT
ejpam-3515	150	27	i.e.	i.e.	X
ejpam-3515	150	28	with	with	ADP
ejpam-3515	150	29	the	the	DET
ejpam-3515	150	30	help	help	NOUN
ejpam-3515	150	31	of	of	ADP
ejpam-3515	150	32	the	the	DET
ejpam-3515	150	33	cauchy	cauchy	ADJ
ejpam-3515	150	34	integral	integral	ADJ
ejpam-3515	150	35	formula	formula	NOUN
ejpam-3515	150	36	.	.	PUNCT
ejpam-3515	151	1	the	the	DET
ejpam-3515	151	2	term	term	NOUN
ejpam-3515	151	3	∫	∫	PROPN
ejpam-3515	151	4	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	151	5	,	,	PUNCT
ejpam-3515	151	6	x)h(x)v	x)h(x)v	PROPN
ejpam-3515	151	7	2(x))dx	2(x))dx	NUM
ejpam-3515	151	8	admits	admit	VERB
ejpam-3515	151	9	application	application	NOUN
ejpam-3515	151	10	of	of	ADP
ejpam-3515	151	11	the	the	DET
ejpam-3515	151	12	estimates	estimate	NOUN
ejpam-3515	151	13	see	see	VERB
ejpam-3515	151	14	equation	equation	NOUN
ejpam-3515	151	15	(	(	PUNCT
ejpam-3515	151	16	2.7	2.7	NUM
ejpam-3515	151	17	)	)	PUNCT
ejpam-3515	151	18	.	.	PUNCT
ejpam-3515	152	1	let	let	VERB
ejpam-3515	152	2	us	we	PRON
ejpam-3515	152	3	write	write	VERB
ejpam-3515	152	4	n∑	n∑	PROPN
ejpam-3515	152	5	j=1	j=1	NOUN
ejpam-3515	152	6	1	1	NUM
ejpam-3515	152	7	2	2	NUM
ejpam-3515	152	8	(	(	PUNCT
ejpam-3515	152	9	i∂j	i∂j	VERB
ejpam-3515	153	1	+	+	CCONJ
ejpam-3515	154	1	bj(x))2	bj(x))2	PROPN
ejpam-3515	154	2	v	v	X
ejpam-3515	154	3	(	(	PUNCT
ejpam-3515	154	4	x)h(x	x)h(x	PROPN
ejpam-3515	154	5	)	)	PUNCT
ejpam-3515	155	1	+	+	CCONJ
ejpam-3515	155	2	v	v	X
ejpam-3515	155	3	(	(	PUNCT
ejpam-3515	155	4	x	x	NOUN
ejpam-3515	155	5	)	)	PUNCT
ejpam-3515	155	6	n∑	n∑	NOUN
ejpam-3515	155	7	j=1	j=1	NOUN
ejpam-3515	155	8	1	1	NUM
ejpam-3515	155	9	2	2	NUM
ejpam-3515	155	10	(	(	PUNCT
ejpam-3515	155	11	i∂j	i∂j	VERB
ejpam-3515	155	12	+	+	CCONJ
ejpam-3515	155	13	bj(x))2	bj(x))2	PROPN
ejpam-3515	155	14	h(x	h(x	PROPN
ejpam-3515	155	15	)	)	PUNCT
ejpam-3515	155	16	=	=	PUNCT
ejpam-3515	156	1	n∑	n∑	NOUN
ejpam-3515	156	2	j=1	j=1	PROPN
ejpam-3515	156	3	−1	−1	NOUN
ejpam-3515	156	4	2	2	NUM
ejpam-3515	156	5	∂2j	∂2j	PROPN
ejpam-3515	156	6	(	(	PUNCT
ejpam-3515	156	7	v	v	NOUN
ejpam-3515	156	8	(	(	PUNCT
ejpam-3515	156	9	x)h(x))+	x)h(x))+	PROPN
ejpam-3515	156	10	n∑	n∑	NOUN
ejpam-3515	157	1	j=1	j=1	NOUN
ejpam-3515	157	2	i	i	PRON
ejpam-3515	157	3	2	2	X
ejpam-3515	157	4	∂jbj(x)(v	∂jbj(x)(v	NOUN
ejpam-3515	157	5	(	(	PUNCT
ejpam-3515	157	6	x)h(x))+	x)h(x))+	PROPN
ejpam-3515	157	7	n∑	n∑	INTJ
ejpam-3515	158	1	j=1	j=1	NOUN
ejpam-3515	158	2	i	i	PRON
ejpam-3515	158	3	2	2	NUM
ejpam-3515	158	4	bj(x)∂j(v	bj(x)∂j(v	ADJ
ejpam-3515	158	5	(	(	PUNCT
ejpam-3515	158	6	x)h(x))+	x)h(x))+	PROPN
ejpam-3515	158	7	n∑	n∑	NOUN
ejpam-3515	158	8	j=1	j=1	ADJ
ejpam-3515	158	9	1	1	NUM
ejpam-3515	158	10	2	2	NUM
ejpam-3515	158	11	b2j	b2j	X
ejpam-3515	158	12	(	(	PUNCT
ejpam-3515	158	13	x)(v	x)(v	X
ejpam-3515	158	14	(	(	PUNCT
ejpam-3515	158	15	x)h(x	x)h(x	PROPN
ejpam-3515	158	16	)	)	PUNCT
ejpam-3515	158	17	)	)	PUNCT
ejpam-3515	159	1	+	+	X
ejpam-3515	159	2	v	v	NOUN
ejpam-3515	159	3	(	(	PUNCT
ejpam-3515	159	4	x	x	NOUN
ejpam-3515	159	5	)	)	PUNCT
ejpam-3515	159	6	n∑	n∑	NOUN
ejpam-3515	159	7	j=1	j=1	ADJ
ejpam-3515	159	8	−1	−1	NOUN
ejpam-3515	159	9	2	2	NUM
ejpam-3515	159	10	∂2j	∂2j	PROPN
ejpam-3515	159	11	(	(	PUNCT
ejpam-3515	159	12	h(x))+v	h(x))+v	PROPN
ejpam-3515	159	13	(	(	PUNCT
ejpam-3515	159	14	x	x	NOUN
ejpam-3515	159	15	)	)	PUNCT
ejpam-3515	159	16	n∑	n∑	PUNCT
ejpam-3515	160	1	j=1	j=1	NOUN
ejpam-3515	160	2	i	i	PRON
ejpam-3515	160	3	2	2	NUM
ejpam-3515	160	4	∂jbj(x)(h(x))+v	∂jbj(x)(h(x))+v	NOUN
ejpam-3515	160	5	(	(	PUNCT
ejpam-3515	160	6	x	x	NOUN
ejpam-3515	160	7	)	)	PUNCT
ejpam-3515	160	8	n∑	n∑	PUNCT
ejpam-3515	161	1	j=1	j=1	NOUN
ejpam-3515	161	2	i	i	PRON
ejpam-3515	161	3	2	2	NUM
ejpam-3515	161	4	bj(x)∂j(h(x))+v	bj(x)∂j(h(x))+v	PROPN
ejpam-3515	161	5	(	(	PUNCT
ejpam-3515	161	6	x	x	X
ejpam-3515	161	7	)	)	PUNCT
ejpam-3515	161	8	n∑	n∑	NOUN
ejpam-3515	162	1	j=1	j=1	NOUN
ejpam-3515	162	2	1	1	NUM
ejpam-3515	162	3	2	2	NUM
ejpam-3515	162	4	b2j	b2j	X
ejpam-3515	162	5	(	(	PUNCT
ejpam-3515	162	6	x)(h(x	x)(h(x	NOUN
ejpam-3515	162	7	)	)	PUNCT
ejpam-3515	162	8	)	)	PUNCT
ejpam-3515	163	1	=	=	PUNCT
ejpam-3515	163	2	n∑	n∑	NOUN
ejpam-3515	163	3	j=1	j=1	PROPN
ejpam-3515	163	4	−1	−1	NOUN
ejpam-3515	163	5	2	2	NUM
ejpam-3515	163	6	∂2j	∂2j	PROPN
ejpam-3515	163	7	(	(	PUNCT
ejpam-3515	163	8	v	v	PROPN
ejpam-3515	163	9	(	(	PUNCT
ejpam-3515	163	10	x))h(x	x))h(x	PROPN
ejpam-3515	163	11	)	)	PUNCT
ejpam-3515	164	1	+	+	PUNCT
ejpam-3515	164	2	n∑	n∑	ADJ
ejpam-3515	164	3	j=1	j=1	ADJ
ejpam-3515	164	4	−1	−1	NOUN
ejpam-3515	164	5	2	2	NUM
ejpam-3515	164	6	v	v	NOUN
ejpam-3515	164	7	(	(	PUNCT
ejpam-3515	164	8	x)∂2j	x)∂2j	PROPN
ejpam-3515	164	9	(	(	PUNCT
ejpam-3515	164	10	h(x	h(x	PROPN
ejpam-3515	164	11	)	)	PUNCT
ejpam-3515	164	12	)	)	PUNCT
ejpam-3515	165	1	+	+	CCONJ
ejpam-3515	165	2	2	2	NUM
ejpam-3515	165	3	n∑	n∑	NOUN
ejpam-3515	165	4	j=1	j=1	NOUN
ejpam-3515	165	5	(	(	PUNCT
ejpam-3515	165	6	−1	−1	NOUN
ejpam-3515	165	7	2	2	NUM
ejpam-3515	165	8	∂(j)(v	∂(j)(v	NOUN
ejpam-3515	165	9	(	(	PUNCT
ejpam-3515	165	10	x	x	NOUN
ejpam-3515	165	11	)	)	PUNCT
ejpam-3515	165	12	)	)	PUNCT
ejpam-3515	165	13	)	)	PUNCT
ejpam-3515	165	14	(	(	PUNCT
ejpam-3515	165	15	−1	−1	NOUN
ejpam-3515	165	16	2	2	NUM
ejpam-3515	165	17	∂(j)(h(x	∂(j)(h(x	NOUN
ejpam-3515	165	18	)	)	PUNCT
ejpam-3515	165	19	)	)	PUNCT
ejpam-3515	165	20	)	)	PUNCT
ejpam-3515	166	1	+	+	PUNCT
ejpam-3515	166	2	n∑	n∑	INTJ
ejpam-3515	166	3	j=1	j=1	NOUN
ejpam-3515	166	4	i	i	PRON
ejpam-3515	166	5	2	2	X
ejpam-3515	166	6	∂jbj(x)(v	∂jbj(x)(v	NOUN
ejpam-3515	166	7	(	(	PUNCT
ejpam-3515	166	8	x)h(x))+	x)h(x))+	PROPN
ejpam-3515	166	9	n∑	n∑	INTJ
ejpam-3515	167	1	j=1	j=1	NOUN
ejpam-3515	168	1	i	i	PRON
ejpam-3515	168	2	2	2	NUM
ejpam-3515	168	3	bj(x)∂j(v	bj(x)∂j(v	ADJ
ejpam-3515	168	4	(	(	PUNCT
ejpam-3515	168	5	x))h(x)+	x))h(x)+	PROPN
ejpam-3515	168	6	n∑	n∑	NOUN
ejpam-3515	168	7	j=1	j=1	NOUN
ejpam-3515	168	8	i	i	PRON
ejpam-3515	168	9	2	2	X
ejpam-3515	168	10	bj(x)v	bj(x)v	PUNCT
ejpam-3515	168	11	(	(	PUNCT
ejpam-3515	168	12	x)∂j(h(x))+	x)∂j(h(x))+	PROPN
ejpam-3515	168	13	n∑	n∑	X
ejpam-3515	168	14	j=1	j=1	ADJ
ejpam-3515	168	15	1	1	NUM
ejpam-3515	168	16	2	2	NUM
ejpam-3515	168	17	b2j	b2j	X
ejpam-3515	168	18	(	(	PUNCT
ejpam-3515	168	19	x)(v	x)(v	X
ejpam-3515	168	20	(	(	PUNCT
ejpam-3515	168	21	x)h(x	x)h(x	PROPN
ejpam-3515	168	22	)	)	PUNCT
ejpam-3515	168	23	)	)	PUNCT
ejpam-3515	169	1	+	+	X
ejpam-3515	169	2	v	v	NOUN
ejpam-3515	169	3	(	(	PUNCT
ejpam-3515	169	4	x	x	NOUN
ejpam-3515	169	5	)	)	PUNCT
ejpam-3515	169	6	n∑	n∑	NOUN
ejpam-3515	169	7	j=1	j=1	ADJ
ejpam-3515	169	8	−1	−1	NOUN
ejpam-3515	169	9	2	2	NUM
ejpam-3515	169	10	∂2j	∂2j	PROPN
ejpam-3515	169	11	(	(	PUNCT
ejpam-3515	169	12	h(x))+v	h(x))+v	PROPN
ejpam-3515	169	13	(	(	PUNCT
ejpam-3515	169	14	x	x	NOUN
ejpam-3515	169	15	)	)	PUNCT
ejpam-3515	169	16	n∑	n∑	PUNCT
ejpam-3515	170	1	j=1	j=1	NOUN
ejpam-3515	170	2	i	i	PRON
ejpam-3515	170	3	2	2	NUM
ejpam-3515	170	4	∂jbj(x)(h(x))+v	∂jbj(x)(h(x))+v	NOUN
ejpam-3515	170	5	(	(	PUNCT
ejpam-3515	170	6	x	x	NOUN
ejpam-3515	170	7	)	)	PUNCT
ejpam-3515	170	8	n∑	n∑	PUNCT
ejpam-3515	171	1	j=1	j=1	NOUN
ejpam-3515	171	2	i	i	PRON
ejpam-3515	171	3	2	2	NUM
ejpam-3515	171	4	bj(x)∂j(h(x))+v	bj(x)∂j(h(x))+v	PROPN
ejpam-3515	171	5	(	(	PUNCT
ejpam-3515	171	6	x	x	X
ejpam-3515	171	7	)	)	PUNCT
ejpam-3515	171	8	n∑	n∑	NOUN
ejpam-3515	172	1	j=1	j=1	NOUN
ejpam-3515	172	2	1	1	NUM
ejpam-3515	172	3	2	2	NUM
ejpam-3515	172	4	b2j	b2j	X
ejpam-3515	172	5	(	(	PUNCT
ejpam-3515	172	6	x)(h(x	x)(h(x	NOUN
ejpam-3515	172	7	)	)	PUNCT
ejpam-3515	172	8	)	)	PUNCT
ejpam-3515	173	1	=	=	PUNCT
ejpam-3515	173	2	n∑	n∑	NOUN
ejpam-3515	173	3	j=1	j=1	PROPN
ejpam-3515	173	4	−1	−1	NOUN
ejpam-3515	173	5	2	2	NUM
ejpam-3515	173	6	∂2j	∂2j	PROPN
ejpam-3515	173	7	(	(	PUNCT
ejpam-3515	173	8	v	v	PROPN
ejpam-3515	173	9	(	(	PUNCT
ejpam-3515	173	10	x))h(x	x))h(x	PROPN
ejpam-3515	173	11	)	)	PUNCT
ejpam-3515	174	1	+	+	PUNCT
ejpam-3515	174	2	n∑	n∑	ADJ
ejpam-3515	174	3	j=1	j=1	ADJ
ejpam-3515	174	4	−v	−v	NOUN
ejpam-3515	174	5	(	(	PUNCT
ejpam-3515	174	6	x)∂2j	x)∂2j	PROPN
ejpam-3515	174	7	(	(	PUNCT
ejpam-3515	174	8	h(x	h(x	PROPN
ejpam-3515	174	9	)	)	PUNCT
ejpam-3515	174	10	)	)	PUNCT
ejpam-3515	175	1	+	+	CCONJ
ejpam-3515	175	2	2	2	NUM
ejpam-3515	175	3	n∑	n∑	NOUN
ejpam-3515	175	4	j=1	j=1	NOUN
ejpam-3515	175	5	(	(	PUNCT
ejpam-3515	175	6	−1	−1	NOUN
ejpam-3515	175	7	2	2	NUM
ejpam-3515	175	8	∂(j)(v	∂(j)(v	NOUN
ejpam-3515	175	9	(	(	PUNCT
ejpam-3515	175	10	x	x	NOUN
ejpam-3515	175	11	)	)	PUNCT
ejpam-3515	175	12	)	)	PUNCT
ejpam-3515	175	13	)	)	PUNCT
ejpam-3515	175	14	(	(	PUNCT
ejpam-3515	175	15	−1	−1	NOUN
ejpam-3515	175	16	2	2	NUM
ejpam-3515	175	17	∂(j)(h(x	∂(j)(h(x	NOUN
ejpam-3515	175	18	)	)	PUNCT
ejpam-3515	175	19	)	)	PUNCT
ejpam-3515	175	20	)	)	PUNCT
ejpam-3515	176	1	+	+	CCONJ
ejpam-3515	176	2	n∑	n∑	PROPN
ejpam-3515	176	3	j=1	j=1	ADJ
ejpam-3515	176	4	i∂jbj(x)(v	i∂jbj(x)(v	X
ejpam-3515	176	5	(	(	PUNCT
ejpam-3515	176	6	x)h(x))+	x)h(x))+	NOUN
ejpam-3515	176	7	n∑	n∑	INTJ
ejpam-3515	177	1	j=1	j=1	NOUN
ejpam-3515	177	2	i	i	PRON
ejpam-3515	177	3	2	2	NUM
ejpam-3515	177	4	bj(x)∂j(v	bj(x)∂j(v	ADJ
ejpam-3515	177	5	(	(	PUNCT
ejpam-3515	177	6	x))h(x)+	x))h(x)+	PROPN
ejpam-3515	177	7	n∑	n∑	NOUN
ejpam-3515	177	8	j=1	j=1	PROPN
ejpam-3515	177	9	ibj(x)v	ibj(x)v	PROPN
ejpam-3515	177	10	(	(	PUNCT
ejpam-3515	177	11	x)∂j(h(x))+	x)∂j(h(x))+	PROPN
ejpam-3515	177	12	n∑	n∑	X
ejpam-3515	177	13	j=1	j=1	ADJ
ejpam-3515	177	14	b2j	b2j	PROPN
ejpam-3515	177	15	(	(	PUNCT
ejpam-3515	177	16	x)(v	x)(v	X
ejpam-3515	177	17	(	(	PUNCT
ejpam-3515	177	18	x)h(x	x)h(x	PROPN
ejpam-3515	177	19	)	)	PUNCT
ejpam-3515	177	20	)	)	PUNCT
ejpam-3515	177	21	.	.	PUNCT
ejpam-3515	178	1	according	accord	VERB
ejpam-3515	178	2	to	to	ADP
ejpam-3515	178	3	the	the	DET
ejpam-3515	178	4	definition	definition	NOUN
ejpam-3515	178	5	of	of	ADP
ejpam-3515	178	6	the	the	DET
ejpam-3515	178	7	potential	potential	ADJ
ejpam-3515	178	8	v	v	X
ejpam-3515	178	9	(	(	PUNCT
ejpam-3515	178	10	x	x	NOUN
ejpam-3515	178	11	)	)	PUNCT
ejpam-3515	178	12	,	,	PUNCT
ejpam-3515	178	13	n∑	n∑	NOUN
ejpam-3515	178	14	j=1	j=1	NOUN
ejpam-3515	178	15	1	1	NUM
ejpam-3515	178	16	2	2	NUM
ejpam-3515	178	17	(	(	PUNCT
ejpam-3515	178	18	i∂j	i∂j	VERB
ejpam-3515	178	19	+	+	CCONJ
ejpam-3515	178	20	bj(x))2	bj(x))2	PROPN
ejpam-3515	178	21	v	v	X
ejpam-3515	178	22	(	(	PUNCT
ejpam-3515	178	23	x	x	NOUN
ejpam-3515	178	24	)	)	PUNCT
ejpam-3515	178	25	=	=	SYM
ejpam-3515	178	26	ξj−1,m	ξj−1,m	NOUN
ejpam-3515	178	27	n∑	n∑	NOUN
ejpam-3515	179	1	j=1	j=1	NOUN
ejpam-3515	179	2	1	1	NUM
ejpam-3515	179	3	2	2	NUM
ejpam-3515	179	4	(	(	PUNCT
ejpam-3515	179	5	i∂j	i∂j	VERB
ejpam-3515	179	6	+	+	CCONJ
ejpam-3515	179	7	bj(x))2	bj(x))2	PROPN
ejpam-3515	179	8	vj−1,m	vj−1,m	NOUN
ejpam-3515	179	9	(	(	PUNCT
ejpam-3515	179	10	x−	x−	PROPN
ejpam-3515	179	11	(	(	PUNCT
ejpam-3515	179	12	aj−1,m1	aj−1,m1	PROPN
ejpam-3515	179	13	,	,	PUNCT
ejpam-3515	179	14	aj−1,m2	aj−1,m2	PROPN
ejpam-3515	179	15	,	,	PUNCT
ejpam-3515	179	16	...	...	PUNCT
ejpam-3515	179	17	,	,	PUNCT
ejpam-3515	179	18	aj−1,mn	aj−1,mn	PROPN
ejpam-3515	179	19	)	)	PUNCT
ejpam-3515	179	20	)	)	PUNCT
ejpam-3515	180	1	y.	y.	PROPN
ejpam-3515	180	2	h.	h.	PROPN
ejpam-3515	180	3	saleem	saleem	PROPN
ejpam-3515	180	4	,	,	PUNCT
ejpam-3515	180	5	h.	h.	PROPN
ejpam-3515	180	6	a.	a.	PROPN
ejpam-3515	180	7	shubber	shubber	PROPN
ejpam-3515	180	8	/	/	SYM
ejpam-3515	180	9	eur	eur	PROPN
ejpam-3515	180	10	.	.	PUNCT
ejpam-3515	181	1	j.	j.	PROPN
ejpam-3515	181	2	pure	pure	PROPN
ejpam-3515	181	3	appl	appl	PROPN
ejpam-3515	181	4	.	.	PROPN
ejpam-3515	181	5	math	math	PROPN
ejpam-3515	181	6	,	,	PUNCT
ejpam-3515	181	7	12	12	NUM
ejpam-3515	181	8	(	(	PUNCT
ejpam-3515	181	9	4	4	NUM
ejpam-3515	181	10	)	)	PUNCT
ejpam-3515	181	11	(	(	PUNCT
ejpam-3515	181	12	2019	2019	NUM
ejpam-3515	181	13	)	)	PUNCT
ejpam-3515	181	14	,	,	PUNCT
ejpam-3515	181	15	1441	1441	NUM
ejpam-3515	181	16	-	-	SYM
ejpam-3515	181	17	1454	1454	NUM
ejpam-3515	181	18	1448	1448	NUM
ejpam-3515	181	19	+	+	CCONJ
ejpam-3515	181	20	ξj	ξj	NOUN
ejpam-3515	181	21	,	,	PUNCT
ejpam-3515	181	22	m	m	PROPN
ejpam-3515	181	23	n∑	n∑	NOUN
ejpam-3515	181	24	j=1	j=1	NOUN
ejpam-3515	181	25	1	1	NUM
ejpam-3515	181	26	2	2	NUM
ejpam-3515	181	27	(	(	PUNCT
ejpam-3515	181	28	i∂j	i∂j	VERB
ejpam-3515	181	29	+	+	CCONJ
ejpam-3515	181	30	bj(x))2	bj(x))2	PROPN
ejpam-3515	181	31	vj	vj	PROPN
ejpam-3515	181	32	,	,	PUNCT
ejpam-3515	181	33	m	m	PROPN
ejpam-3515	181	34	(	(	PUNCT
ejpam-3515	181	35	x−	x−	PROPN
ejpam-3515	181	36	(	(	PUNCT
ejpam-3515	181	37	aj	aj	PROPN
ejpam-3515	181	38	,	,	PUNCT
ejpam-3515	181	39	m1	m1	PROPN
ejpam-3515	181	40	,	,	PUNCT
ejpam-3515	181	41	aj	aj	PROPN
ejpam-3515	181	42	,	,	PUNCT
ejpam-3515	181	43	m2	m2	PROPN
ejpam-3515	181	44	,	,	PUNCT
ejpam-3515	181	45	...	...	PUNCT
ejpam-3515	181	46	,	,	PUNCT
ejpam-3515	181	47	aj	aj	PROPN
ejpam-3515	181	48	,	,	PUNCT
ejpam-3515	181	49	mn	mn	PROPN
ejpam-3515	181	50	)	)	PUNCT
ejpam-3515	181	51	)	)	PUNCT
ejpam-3515	181	52	for	for	ADP
ejpam-3515	181	53	x	x	SYM
ejpam-3515	181	54	∈	∈	PROPN
ejpam-3515	181	55	πn	πn	X
ejpam-3515	181	56	d=1[aj	d=1[aj	PROPN
ejpam-3515	181	57	,	,	PUNCT
ejpam-3515	181	58	md	md	PROPN
ejpam-3515	181	59	,	,	PUNCT
ejpam-3515	181	60	aj−1,md	aj−1,md	NUM
ejpam-3515	181	61	)	)	PUNCT
ejpam-3515	181	62	hence	hence	ADV
ejpam-3515	181	63	the	the	DET
ejpam-3515	181	64	term∫	term∫	ADJ
ejpam-3515	181	65	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	181	66	,	,	PUNCT
ejpam-3515	181	67	x)θ(v	x)θ(v	NUM
ejpam-3515	181	68	)	)	PUNCT
ejpam-3515	181	69	h(x	h(x	PROPN
ejpam-3515	181	70	)	)	PUNCT
ejpam-3515	182	1	n∑	n∑	NOUN
ejpam-3515	182	2	j=1	j=1	NOUN
ejpam-3515	182	3	1	1	NUM
ejpam-3515	182	4	2	2	NUM
ejpam-3515	182	5	(	(	PUNCT
ejpam-3515	182	6	i∂j	i∂j	VERB
ejpam-3515	182	7	+	+	CCONJ
ejpam-3515	182	8	bj(x))2	bj(x))2	PROPN
ejpam-3515	182	9	v	v	NOUN
ejpam-3515	182	10	(	(	PUNCT
ejpam-3515	182	11	x))dx	x))dx	NOUN
ejpam-3515	182	12	also	also	ADV
ejpam-3515	182	13	admits	admit	VERB
ejpam-3515	182	14	application	application	NOUN
ejpam-3515	182	15	of	of	ADP
ejpam-3515	182	16	the	the	DET
ejpam-3515	182	17	estimates	estimate	NOUN
ejpam-3515	182	18	see	see	VERB
ejpam-3515	182	19	equation	equation	NOUN
ejpam-3515	182	20	(	(	PUNCT
ejpam-3515	182	21	2.7	2.7	NUM
ejpam-3515	182	22	)	)	PUNCT
ejpam-3515	182	23	.	.	PUNCT
ejpam-3515	183	1	let	let	VERB
ejpam-3515	183	2	us	we	PRON
ejpam-3515	183	3	pass	pass	VERB
ejpam-3515	183	4	in	in	ADP
ejpam-3515	183	5	the	the	DET
ejpam-3515	183	6	expression∫	expression∫	NOUN
ejpam-3515	183	7	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	183	8	,	,	PUNCT
ejpam-3515	183	9	x)v	x)v	PUNCT
ejpam-3515	183	10	(	(	PUNCT
ejpam-3515	183	11	x)θ(v	x)θ(v	NUM
ejpam-3515	183	12	)	)	PUNCT
ejpam-3515	184	1	n∑	n∑	NOUN
ejpam-3515	184	2	j=1	j=1	NOUN
ejpam-3515	184	3	1	1	NUM
ejpam-3515	184	4	2	2	NUM
ejpam-3515	184	5	(	(	PUNCT
ejpam-3515	184	6	i∂j	i∂j	VERB
ejpam-3515	184	7	+	+	CCONJ
ejpam-3515	184	8	bj(x))2	bj(x))2	PROPN
ejpam-3515	184	9	h(x))dx	h(x))dx	PROPN
ejpam-3515	184	10	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	184	11	,	,	PUNCT
ejpam-3515	184	12	x	x	NOUN
ejpam-3515	184	13	)	)	PUNCT
ejpam-3515	184	14	n∑	n∑	NOUN
ejpam-3515	185	1	j=1	j=1	ADJ
ejpam-3515	185	2	−1	−1	NOUN
ejpam-3515	185	3	2	2	NUM
ejpam-3515	185	4	∂j(v	∂j(v	NOUN
ejpam-3515	185	5	(	(	PUNCT
ejpam-3515	185	6	x))θ(v	x))θ(v	PROPN
ejpam-3515	185	7	)	)	PUNCT
ejpam-3515	186	1	n∑	n∑	NOUN
ejpam-3515	186	2	j=1	j=1	NOUN
ejpam-3515	186	3	−1	−1	NOUN
ejpam-3515	186	4	2	2	NUM
ejpam-3515	186	5	∂j(h(x)))dx	∂j(h(x)))dx	VERB
ejpam-3515	186	6	to	to	ADP
ejpam-3515	186	7	the	the	DET
ejpam-3515	186	8	fourier	fourier	NOUN
ejpam-3515	186	9	transform	transform	NOUN
ejpam-3515	186	10	over	over	ADP
ejpam-3515	186	11	the	the	DET
ejpam-3515	186	12	variable	variable	NOUN
ejpam-3515	186	13	x.	x.	NOUN
ejpam-3515	186	14	consider	consider	VERB
ejpam-3515	186	15	,	,	PUNCT
ejpam-3515	186	16	for	for	ADP
ejpam-3515	186	17	example	example	NOUN
ejpam-3515	186	18	,	,	PUNCT
ejpam-3515	186	19	the	the	DET
ejpam-3515	186	20	second	second	ADJ
ejpam-3515	186	21	one	one	NUM
ejpam-3515	186	22	.	.	PUNCT
ejpam-3515	187	1	it	it	PRON
ejpam-3515	187	2	will	will	AUX
ejpam-3515	187	3	have	have	VERB
ejpam-3515	187	4	the	the	DET
ejpam-3515	187	5	following	follow	VERB
ejpam-3515	187	6	form	form	NOUN
ejpam-3515	187	7	:	:	PUNCT
ejpam-3515	187	8	e	e	X
ejpam-3515	187	9	∫	∫	PROPN
ejpam-3515	187	10	rn	rn	PROPN
ejpam-3515	187	11	ψ̂(t	ψ̂(t	NOUN
ejpam-3515	187	12	,	,	PUNCT
ejpam-3515	187	13	q)ĥ(q)v̂	q)ĥ(q)v̂	NOUN
ejpam-3515	187	14	(	(	PUNCT
ejpam-3515	187	15	q	q	X
ejpam-3515	187	16	)	)	PUNCT
ejpam-3515	187	17			PROPN
ejpam-3515	187	18	n∑	n∑	PROPN
ejpam-3515	187	19	j=1	j=1	NOUN
ejpam-3515	187	20	−1	−1	NOUN
ejpam-3515	187	21	2	2	NUM
ejpam-3515	188	1	|q|2	|q|2	VERB
ejpam-3515	188	2	+	+	CCONJ
ejpam-3515	189	1	1	1	NUM
ejpam-3515	189	2	2	2	NUM
ejpam-3515	189	3	n∑	n∑	NOUN
ejpam-3515	189	4	j=1	j=1	PROPN
ejpam-3515	189	5	i∂j	i∂j	VERB
ejpam-3515	189	6	b̂j(q	b̂j(q	NUM
ejpam-3515	189	7	)	)	PUNCT
ejpam-3515	190	1	+	+	CCONJ
ejpam-3515	190	2	1	1	NUM
ejpam-3515	190	3	2	2	NUM
ejpam-3515	190	4	n∑	n∑	NOUN
ejpam-3515	190	5	j=1	j=1	NOUN
ejpam-3515	190	6	ib̂j(q)|	ib̂j(q)|	PUNCT
ejpam-3515	191	1	−	−	PROPN
ejpam-3515	191	2	iq|+	iq|+	NOUN
ejpam-3515	191	3	1	1	NUM
ejpam-3515	191	4	2	2	NUM
ejpam-3515	191	5	n∑	n∑	NOUN
ejpam-3515	191	6	j=1	j=1	NOUN
ejpam-3515	191	7	b̂2j	b̂2j	ADJ
ejpam-3515	191	8	(	(	PUNCT
ejpam-3515	191	9	q	q	X
ejpam-3515	191	10	)	)	PUNCT
ejpam-3515	191	11			PROPN
ejpam-3515	191	12	dqθ(v	dqθ(v	X
ejpam-3515	191	13	)	)	PUNCT
ejpam-3515	191	14			PROPN
ejpam-3515	191	15	and	and	CCONJ
ejpam-3515	191	16	its	its	PRON
ejpam-3515	191	17	absolute	absolute	ADJ
ejpam-3515	191	18	value	value	NOUN
ejpam-3515	191	19	is	be	AUX
ejpam-3515	191	20	less	less	ADV
ejpam-3515	191	21	or	or	CCONJ
ejpam-3515	191	22	equal	equal	ADJ
ejpam-3515	191	23	to	to	ADP
ejpam-3515	191	24	the	the	DET
ejpam-3515	191	25	expression	expression	NOUN
ejpam-3515	191	26	const	const	NOUN
ejpam-3515	191	27	e	e	PROPN
ejpam-3515	191	28	(	(	PUNCT
ejpam-3515	191	29	∫	∫	PROPN
ejpam-3515	191	30	rn	rn	PROPN
ejpam-3515	191	31	|ψ̂(t	|ψ̂(t	PROPN
ejpam-3515	191	32	,	,	PUNCT
ejpam-3515	191	33	q)|2	q)|2	NOUN
ejpam-3515	191	34	)	)	PUNCT
ejpam-3515	191	35	×	×	PROPN
ejpam-3515	191	36			PROPN
ejpam-3515	191	37	n∑	n∑	PROPN
ejpam-3515	191	38	j=1	j=1	NOUN
ejpam-3515	191	39	−1	−1	NOUN
ejpam-3515	191	40	2	2	NUM
ejpam-3515	192	1	|q|2	|q|2	VERB
ejpam-3515	192	2	+	+	CCONJ
ejpam-3515	193	1	1	1	NUM
ejpam-3515	193	2	2	2	NUM
ejpam-3515	193	3	n∑	n∑	NOUN
ejpam-3515	193	4	j=1	j=1	PROPN
ejpam-3515	193	5	i∂j	i∂j	VERB
ejpam-3515	193	6	b̂j(q	b̂j(q	NUM
ejpam-3515	193	7	)	)	PUNCT
ejpam-3515	194	1	+	+	CCONJ
ejpam-3515	194	2	1	1	NUM
ejpam-3515	194	3	2	2	NUM
ejpam-3515	194	4	n∑	n∑	NOUN
ejpam-3515	194	5	j=1	j=1	NOUN
ejpam-3515	194	6	ib̂j(q)|	ib̂j(q)|	PUNCT
ejpam-3515	195	1	−	−	PROPN
ejpam-3515	195	2	iq|+	iq|+	NOUN
ejpam-3515	195	3	1	1	NUM
ejpam-3515	195	4	2	2	NUM
ejpam-3515	195	5	n∑	n∑	NOUN
ejpam-3515	195	6	j=1	j=1	NOUN
ejpam-3515	195	7	b̂2j	b̂2j	ADJ
ejpam-3515	195	8	(	(	PUNCT
ejpam-3515	195	9	q	q	X
ejpam-3515	195	10	)	)	PUNCT
ejpam-3515	195	11	2	2	ADV
ejpam-3515	195	12	dq	dq	NOUN
ejpam-3515	195	13			NOUN
ejpam-3515	195	14	∥∥∥ĥ(q	∥∥∥ĥ(q	NUM
ejpam-3515	195	15	)	)	PUNCT
ejpam-3515	195	16	∥∥∥	∥∥∥	PROPN
ejpam-3515	195	17	l2(dx	l2(dx	NUM
ejpam-3515	195	18	)	)	PUNCT
ejpam-3515	195	19	‖θ(v	‖θ(v	NUM
ejpam-3515	195	20	)	)	PUNCT
ejpam-3515	195	21	‖l2(dv	‖l2(dv	NUM
ejpam-3515	195	22	)	)	PUNCT
ejpam-3515	195	23	.	.	PUNCT
ejpam-3515	196	1	now	now	ADV
ejpam-3515	196	2	we	we	PRON
ejpam-3515	196	3	get	get	VERB
ejpam-3515	196	4	from	from	ADP
ejpam-3515	196	5	the	the	DET
ejpam-3515	196	6	above	above	ADJ
ejpam-3515	196	7	estimate	estimate	NOUN
ejpam-3515	196	8	,	,	PUNCT
ejpam-3515	196	9	∫	∫	PROPN
ejpam-3515	196	10	rn	rn	PROPN
ejpam-3515	196	11	e	e	PROPN
ejpam-3515	196	12	ψ(t	ψ(t	PROPN
ejpam-3515	196	13	,	,	PUNCT
ejpam-3515	196	14	x	x	NOUN
ejpam-3515	196	15	)	)	PUNCT
ejpam-3515	196	16			PROPN
ejpam-3515	196	17	n∑	n∑	NOUN
ejpam-3515	196	18	j=1	j=1	NOUN
ejpam-3515	196	19	1	1	NUM
ejpam-3515	196	20	2	2	NUM
ejpam-3515	196	21	(	(	PUNCT
ejpam-3515	196	22	i∂j	i∂j	VERB
ejpam-3515	197	1	+	+	CCONJ
ejpam-3515	197	2	bj(x))2	bj(x))2	PROPN
ejpam-3515	197	3	2	2	X
ejpam-3515	197	4	h(x)θ(v	h(x)θ(v	NOUN
ejpam-3515	197	5	)	)	PUNCT
ejpam-3515	198	1			PROPN
ejpam-3515	198	2	dx	dx	PROPN
ejpam-3515	198	3	≤	≤	NUM
ejpam-3515	198	4	const	const	VERB
ejpam-3515	198	5	‖h‖l2(rn	‖h‖l2(rn	PROPN
ejpam-3515	198	6	,	,	PUNCT
ejpam-3515	198	7	dx	dx	PROPN
ejpam-3515	198	8	)	)	PUNCT
ejpam-3515	198	9	‖θ‖l2(rn	‖θ‖l2(rn	PROPN
ejpam-3515	198	10	,	,	PUNCT
ejpam-3515	198	11	dv	dv	PROPN
ejpam-3515	198	12	)	)	PUNCT
ejpam-3515	198	13	.	.	PUNCT
ejpam-3515	199	1	we	we	PRON
ejpam-3515	199	2	apply	apply	VERB
ejpam-3515	199	3	also	also	ADV
ejpam-3515	199	4	calculations	calculation	NOUN
ejpam-3515	199	5	to	to	ADP
ejpam-3515	199	6	a	a	DET
ejpam-3515	199	7	random	random	ADJ
ejpam-3515	199	8	variable	variable	NOUN
ejpam-3515	199	9	of	of	ADP
ejpam-3515	199	10	the	the	DET
ejpam-3515	199	11	form	form	NOUN
ejpam-3515	199	12	∑p	∑p	PROPN
ejpam-3515	199	13	k	k	NOUN
ejpam-3515	199	14	,	,	PUNCT
ejpam-3515	199	15	l=1ck	l=1ck	NOUN
ejpam-3515	199	16	,	,	PUNCT
ejpam-3515	199	17	lhk(x)θl(v	lhk(x)θl(v	ADJ
ejpam-3515	199	18	)	)	PUNCT
ejpam-3515	199	19	.	.	PUNCT
ejpam-3515	200	1	we	we	PRON
ejpam-3515	200	2	get	get	VERB
ejpam-3515	200	3	the	the	DET
ejpam-3515	200	4	estimate	estimate	NOUN
ejpam-3515	200	5	of	of	ADP
ejpam-3515	200	6	the	the	DET
ejpam-3515	200	7	form	form	NOUN
ejpam-3515	200	8	(	(	PUNCT
ejpam-3515	200	9	2.7	2.7	NUM
ejpam-3515	200	10	)	)	PUNCT
ejpam-3515	200	11	where	where	SCONJ
ejpam-3515	200	12	∑n	∑n	PROPN
ejpam-3515	200	13	j=1	j=1	NOUN
ejpam-3515	200	14	1	1	NUM
ejpam-3515	200	15	2	2	NUM
ejpam-3515	200	16	(	(	PUNCT
ejpam-3515	200	17	i∂j	i∂j	VERB
ejpam-3515	200	18	+	+	CCONJ
ejpam-3515	200	19	bj(x))2	bj(x))2	PROPN
ejpam-3515	200	20	hk(x	hk(x	NOUN
ejpam-3515	200	21	)	)	PUNCT
ejpam-3515	200	22	is	be	AUX
ejpam-3515	200	23	replaced	replace	VERB
ejpam-3515	200	24	by(∑n	by(∑n	PROPN
ejpam-3515	200	25	j=1	j=1	NOUN
ejpam-3515	200	26	1	1	NUM
ejpam-3515	200	27	2	2	NUM
ejpam-3515	200	28	(	(	PUNCT
ejpam-3515	200	29	i∂j	i∂j	VERB
ejpam-3515	200	30	+	+	CCONJ
ejpam-3515	200	31	bj(x))2	bj(x))2	PROPN
ejpam-3515	200	32	)	)	PUNCT
ejpam-3515	200	33	2	2	NUM
ejpam-3515	200	34	hk(x	hk(x	NOUN
ejpam-3515	200	35	)	)	PUNCT
ejpam-3515	200	36	.	.	PUNCT
ejpam-3515	201	1	from	from	ADP
ejpam-3515	201	2	this	this	PRON
ejpam-3515	201	3	,	,	PUNCT
ejpam-3515	201	4	we	we	PRON
ejpam-3515	201	5	get	get	VERB
ejpam-3515	201	6	the	the	DET
ejpam-3515	201	7	estimates	estimate	NOUN
ejpam-3515	201	8	(	(	PUNCT
ejpam-3515	201	9	2.8	2.8	NUM
ejpam-3515	201	10	)	)	PUNCT
ejpam-3515	201	11	and	and	CCONJ
ejpam-3515	201	12	(	(	PUNCT
ejpam-3515	201	13	2.9	2.9	NUM
ejpam-3515	201	14	)	)	PUNCT
ejpam-3515	201	15	where	where	SCONJ
ejpam-3515	201	16	q	q	NOUN
ejpam-3515	201	17	is	be	AUX
ejpam-3515	201	18	replaced	replace	VERB
ejpam-3515	201	19	by	by	ADP
ejpam-3515	201	20	q2	q2	NOUN
ejpam-3515	201	21	.	.	PUNCT
ejpam-3515	202	1	thus	thus	ADV
ejpam-3515	202	2	ψ(t	ψ(t	PROPN
ejpam-3515	202	3	,	,	PUNCT
ejpam-3515	202	4	x	x	NOUN
ejpam-3515	202	5	)	)	PUNCT
ejpam-3515	202	6	∈	∈	PROPN
ejpam-3515	202	7	w2	w2	NOUN
ejpam-3515	202	8	for	for	ADP
ejpam-3515	202	9	almost	almost	ADV
ejpam-3515	202	10	every	every	PRON
ejpam-3515	202	11	v	v	NOUN
ejpam-3515	202	12	,	,	PUNCT
ejpam-3515	202	13	b.	b.	PROPN
ejpam-3515	202	14	besides	besides	PROPN
ejpam-3515	202	15	,	,	PUNCT
ejpam-3515	202	16	‖ψ‖2w2	‖ψ‖2w2	ADJ
ejpam-3515	202	17	is	be	AUX
ejpam-3515	202	18	an	an	DET
ejpam-3515	202	19	integrable	integrable	ADJ
ejpam-3515	202	20	function	function	NOUN
ejpam-3515	202	21	of	of	ADP
ejpam-3515	202	22	v.	v.	PROPN
ejpam-3515	202	23	y.	y.	PROPN
ejpam-3515	202	24	h.	h.	PROPN
ejpam-3515	202	25	saleem	saleem	PROPN
ejpam-3515	202	26	,	,	PUNCT
ejpam-3515	202	27	h.	h.	PROPN
ejpam-3515	202	28	a.	a.	PROPN
ejpam-3515	202	29	shubber	shubber	PROPN
ejpam-3515	202	30	/	/	SYM
ejpam-3515	202	31	eur	eur	PROPN
ejpam-3515	202	32	.	.	PUNCT
ejpam-3515	203	1	j.	j.	PROPN
ejpam-3515	203	2	pure	pure	PROPN
ejpam-3515	203	3	appl	appl	PROPN
ejpam-3515	203	4	.	.	PROPN
ejpam-3515	203	5	math	math	PROPN
ejpam-3515	203	6	,	,	PUNCT
ejpam-3515	203	7	12	12	NUM
ejpam-3515	203	8	(	(	PUNCT
ejpam-3515	203	9	4	4	NUM
ejpam-3515	203	10	)	)	PUNCT
ejpam-3515	203	11	(	(	PUNCT
ejpam-3515	203	12	2019	2019	NUM
ejpam-3515	203	13	)	)	PUNCT
ejpam-3515	203	14	,	,	PUNCT
ejpam-3515	203	15	1441	1441	NUM
ejpam-3515	203	16	-	-	SYM
ejpam-3515	203	17	1454	1454	NUM
ejpam-3515	203	18	1449	1449	NUM
ejpam-3515	204	1	we	we	PRON
ejpam-3515	204	2	can	can	AUX
ejpam-3515	204	3	continue	continue	VERB
ejpam-3515	204	4	this	this	DET
ejpam-3515	204	5	arguments	argument	NOUN
ejpam-3515	204	6	.	.	PUNCT
ejpam-3515	205	1	as	as	ADP
ejpam-3515	205	2	a	a	DET
ejpam-3515	205	3	result	result	NOUN
ejpam-3515	205	4	,	,	PUNCT
ejpam-3515	205	5	we	we	PRON
ejpam-3515	205	6	get	get	VERB
ejpam-3515	205	7	that	that	PRON
ejpam-3515	205	8	ψ(t	ψ(t	PROPN
ejpam-3515	205	9	,	,	PUNCT
ejpam-3515	205	10	x	x	X
ejpam-3515	205	11	)	)	PUNCT
ejpam-3515	205	12	∈	∈	PROPN
ejpam-3515	205	13	wm	wm	PROPN
ejpam-3515	205	14	for	for	ADP
ejpam-3515	205	15	all	all	DET
ejpam-3515	205	16	m	m	NOUN
ejpam-3515	205	17	=	=	NOUN
ejpam-3515	205	18	1	1	NUM
ejpam-3515	205	19	,	,	PUNCT
ejpam-3515	205	20	2	2	NUM
ejpam-3515	205	21	,	,	PUNCT
ejpam-3515	205	22	...	...	PUNCT
ejpam-3515	205	23	,	,	PUNCT
ejpam-3515	205	24	and	and	CCONJ
ejpam-3515	205	25	for	for	ADP
ejpam-3515	205	26	almost	almost	ADV
ejpam-3515	205	27	every	every	PRON
ejpam-3515	205	28	v	v	NOUN
ejpam-3515	205	29	and	and	CCONJ
ejpam-3515	205	30	‖ψ‖2wm	‖ψ‖2wm	NOUN
ejpam-3515	205	31	is	be	AUX
ejpam-3515	205	32	an	an	DET
ejpam-3515	205	33	integrable	integrable	ADJ
ejpam-3515	205	34	function	function	NOUN
ejpam-3515	205	35	of	of	ADP
ejpam-3515	205	36	v.	v.	CCONJ
ejpam-3515	205	37	therefore	therefore	ADV
ejpam-3515	205	38	,	,	PUNCT
ejpam-3515	205	39	ψ(t	ψ(t	PROPN
ejpam-3515	205	40	,	,	PUNCT
ejpam-3515	205	41	x	x	PRON
ejpam-3515	205	42	)	)	PUNCT
ejpam-3515	205	43	is	be	AUX
ejpam-3515	205	44	an	an	DET
ejpam-3515	205	45	infinitely	infinitely	ADV
ejpam-3515	205	46	differentiable	differentiable	ADJ
ejpam-3515	205	47	function	function	NOUN
ejpam-3515	205	48	of	of	ADP
ejpam-3515	205	49	the	the	DET
ejpam-3515	205	50	variable	variable	NOUN
ejpam-3515	205	51	x	x	PUNCT
ejpam-3515	205	52	for	for	ADP
ejpam-3515	205	53	almost	almost	ADV
ejpam-3515	205	54	every	every	PRON
ejpam-3515	205	55	v.	v.	NOUN
ejpam-3515	205	56	in	in	ADP
ejpam-3515	205	57	addition	addition	NOUN
ejpam-3515	205	58	,	,	PUNCT
ejpam-3515	205	59	the	the	DET
ejpam-3515	205	60	function	function	NOUN
ejpam-3515	205	61	ψ	ψ	X
ejpam-3515	205	62	satisfies	satisfie	NOUN
ejpam-3515	205	63	,	,	PUNCT
ejpam-3515	205	64	in	in	ADP
ejpam-3515	205	65	the	the	DET
ejpam-3515	205	66	classical	classical	ADJ
ejpam-3515	205	67	sense	sense	NOUN
ejpam-3515	205	68	,	,	PUNCT
ejpam-3515	205	69	the	the	DET
ejpam-3515	205	70	following	follow	VERB
ejpam-3515	205	71	differential	differential	ADJ
ejpam-3515	205	72	equation	equation	NOUN
ejpam-3515	205	73	∂ψ	∂ψ	PROPN
ejpam-3515	205	74	∂t	∂t	PROPN
ejpam-3515	205	75	=	=	PUNCT
ejpam-3515	205	76	n∑	n∑	PROPN
ejpam-3515	205	77	j=1	j=1	NOUN
ejpam-3515	205	78	1	1	NUM
ejpam-3515	205	79	2	2	NUM
ejpam-3515	205	80	(	(	PUNCT
ejpam-3515	205	81	i∂j	i∂j	VERB
ejpam-3515	205	82	+	+	CCONJ
ejpam-3515	205	83	bj(x))2	bj(x))2	PROPN
ejpam-3515	205	84	ψ(t	ψ(t	PROPN
ejpam-3515	205	85	,	,	PUNCT
ejpam-3515	205	86	x)−	x)−	PROPN
ejpam-3515	205	87	v	v	NOUN
ejpam-3515	205	88	(	(	PUNCT
ejpam-3515	205	89	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	205	90	,	,	PUNCT
ejpam-3515	205	91	x	x	NOUN
ejpam-3515	205	92	)	)	PUNCT
ejpam-3515	205	93	for	for	ADP
ejpam-3515	205	94	almost	almost	ADV
ejpam-3515	205	95	every	every	PRON
ejpam-3515	205	96	v.	v.	NOUN
ejpam-3515	205	97	let	let	VERB
ejpam-3515	205	98	us	we	PRON
ejpam-3515	205	99	consider	consider	VERB
ejpam-3515	205	100	an	an	DET
ejpam-3515	205	101	initial	initial	ADJ
ejpam-3515	205	102	condition	condition	NOUN
ejpam-3515	205	103	which	which	PRON
ejpam-3515	205	104	is	be	AUX
ejpam-3515	205	105	satisfied	satisfied	ADJ
ejpam-3515	205	106	by	by	ADP
ejpam-3515	205	107	the	the	DET
ejpam-3515	205	108	function	function	NOUN
ejpam-3515	205	109	ψ	ψ	NOUN
ejpam-3515	205	110	.	.	PUNCT
ejpam-3515	206	1	since	since	SCONJ
ejpam-3515	206	2	ψ(t	ψ(t	PROPN
ejpam-3515	206	3	,	,	PUNCT
ejpam-3515	206	4	x	x	PRON
ejpam-3515	206	5	)	)	PUNCT
ejpam-3515	206	6	is	be	AUX
ejpam-3515	206	7	defined	define	VERB
ejpam-3515	206	8	for	for	ADP
ejpam-3515	206	9	t	t	PROPN
ejpam-3515	206	10	>	>	X
ejpam-3515	206	11	0	0	PROPN
ejpam-3515	206	12	,	,	PUNCT
ejpam-3515	206	13	we	we	PRON
ejpam-3515	206	14	have	have	VERB
ejpam-3515	206	15	to	to	PART
ejpam-3515	206	16	find	find	VERB
ejpam-3515	206	17	limt→0ψ(t	limt→0ψ(t	PROPN
ejpam-3515	206	18	,	,	PUNCT
ejpam-3515	206	19	x	x	NOUN
ejpam-3515	206	20	)	)	PUNCT
ejpam-3515	206	21	.	.	PUNCT
ejpam-3515	207	1	we	we	PRON
ejpam-3515	207	2	record	record	VERB
ejpam-3515	207	3	ψ(t	ψ(t	PROPN
ejpam-3515	207	4	,	,	PUNCT
ejpam-3515	207	5	x	x	NOUN
ejpam-3515	207	6	)	)	PUNCT
ejpam-3515	207	7	=	=	SYM
ejpam-3515	207	8	∫	∫	PROPN
ejpam-3515	207	9	rn	rn	PROPN
ejpam-3515	207	10	dy	dy	PROPN
ejpam-3515	207	11	(	(	PUNCT
ejpam-3515	207	12	∫	∫	PROPN
ejpam-3515	207	13	dµtx(ω	dµtx(ω	NOUN
ejpam-3515	207	14	)	)	PUNCT
ejpam-3515	207	15	exp	exp	NOUN
ejpam-3515	207	16	(	(	PUNCT
ejpam-3515	207	17	−i	−i	PROPN
ejpam-3515	207	18	∫	∫	PROPN
ejpam-3515	207	19	t	t	PROPN
ejpam-3515	207	20	0	0	NUM
ejpam-3515	207	21	b(ω(s))dω	b(ω(s))dω	NOUN
ejpam-3515	208	1	−	−	PROPN
ejpam-3515	209	1	i	i	PRON
ejpam-3515	209	2	2	2	NUM
ejpam-3515	209	3	∫	∫	NOUN
ejpam-3515	209	4	t	t	NOUN
ejpam-3515	209	5	0	0	NUM
ejpam-3515	210	1	divb(ω(s))ds−	divb(ω(s))ds−	CCONJ
ejpam-3515	210	2	∫	∫	PROPN
ejpam-3515	210	3	t	t	PROPN
ejpam-3515	210	4	0	0	NUM
ejpam-3515	210	5	v	v	NOUN
ejpam-3515	210	6	(	(	PUNCT
ejpam-3515	210	7	ω(s))ds	ω(s))ds	NUM
ejpam-3515	210	8	)	)	PUNCT
ejpam-3515	210	9	)	)	PUNCT
ejpam-3515	211	1	ϕ(y	ϕ(y	PROPN
ejpam-3515	211	2	)	)	PUNCT
ejpam-3515	211	3	,	,	PUNCT
ejpam-3515	211	4	where	where	SCONJ
ejpam-3515	211	5	the	the	DET
ejpam-3515	211	6	integral	integral	ADJ
ejpam-3515	211	7	converges	converge	NOUN
ejpam-3515	211	8	for	for	ADP
ejpam-3515	211	9	almost	almost	ADV
ejpam-3515	211	10	every	every	PRON
ejpam-3515	211	11	v	v	NOUN
ejpam-3515	211	12	,	,	PUNCT
ejpam-3515	211	13	b	b	NOUN
ejpam-3515	211	14	,	,	PUNCT
ejpam-3515	211	15	x.∫	x.∫	PROPN
ejpam-3515	211	16	rn	rn	PROPN
ejpam-3515	211	17	e	e	PROPN
ejpam-3515	211	18	(	(	PUNCT
ejpam-3515	211	19	ψ(t	ψ(t	PROPN
ejpam-3515	211	20	,	,	PUNCT
ejpam-3515	211	21	x)−	x)−	PROPN
ejpam-3515	211	22	ϕ(x))2	ϕ(x))2	PROPN
ejpam-3515	211	23	dx	dx	PROPN
ejpam-3515	211	24	=	=	SYM
ejpam-3515	211	25	∫	∫	PROPN
ejpam-3515	211	26	rn	rn	PROPN
ejpam-3515	211	27	dxe	dxe	PROPN
ejpam-3515	211	28	(	(	PUNCT
ejpam-3515	211	29	∫	∫	PROPN
ejpam-3515	211	30	rn	rn	PROPN
ejpam-3515	211	31	dy	dy	PROPN
ejpam-3515	211	32	(	(	PUNCT
ejpam-3515	211	33	∫	∫	PROPN
ejpam-3515	211	34	dµtx(ω	dµtx(ω	ADJ
ejpam-3515	211	35	)	)	PUNCT
ejpam-3515	211	36	exp(−i	exp(−i	PROPN
ejpam-3515	211	37	∫	∫	PROPN
ejpam-3515	211	38	t	t	PROPN
ejpam-3515	211	39	0	0	NUM
ejpam-3515	211	40	b(ω(s))dω−	b(ω(s))dω−	NOUN
ejpam-3515	211	41	i	i	PRON
ejpam-3515	211	42	2	2	NUM
ejpam-3515	211	43	∫	∫	NOUN
ejpam-3515	211	44	t	t	NOUN
ejpam-3515	211	45	0	0	NUM
ejpam-3515	212	1	divb(ω(s))ds−	divb(ω(s))ds−	CCONJ
ejpam-3515	212	2	∫	∫	PROPN
ejpam-3515	212	3	t	t	PROPN
ejpam-3515	212	4	0	0	NUM
ejpam-3515	212	5	v	v	NOUN
ejpam-3515	212	6	(	(	PUNCT
ejpam-3515	212	7	ω(s))ds))φ(ω(t))−	ω(s))ds))φ(ω(t))−	NOUN
ejpam-3515	212	8	∫	∫	NOUN
ejpam-3515	212	9	p(x	p(x	PROPN
ejpam-3515	212	10	,	,	PUNCT
ejpam-3515	212	11	y	y	PROPN
ejpam-3515	212	12	,	,	PUNCT
ejpam-3515	212	13	t)ϕ(x)dy)2	t)ϕ(x)dy)2	PROPN
ejpam-3515	212	14	=	=	SYM
ejpam-3515	212	15	∫	∫	PROPN
ejpam-3515	213	1	rn	rn	PROPN
ejpam-3515	213	2	dx	dx	PROPN
ejpam-3515	213	3	∫	∫	PROPN
ejpam-3515	213	4	rn	rn	PROPN
ejpam-3515	213	5	∫	∫	PROPN
ejpam-3515	213	6	rn	rn	PROPN
ejpam-3515	213	7	dydz	dydz	PROPN
ejpam-3515	213	8	∫	∫	PROPN
ejpam-3515	213	9	∫	∫	PROPN
ejpam-3515	213	10	dµtx	dµtx	PROPN
ejpam-3515	213	11	,	,	PUNCT
ejpam-3515	213	12	y(ω)dµtx	y(ω)dµtx	NUM
ejpam-3515	213	13	,	,	PUNCT
ejpam-3515	213	14	z(η))e(exp(−i	z(η))e(exp(−i	VERB
ejpam-3515	213	15	∫	∫	PROPN
ejpam-3515	213	16	t	t	PROPN
ejpam-3515	213	17	0	0	NUM
ejpam-3515	213	18	b(ω(s))dω−	b(ω(s))dω−	NOUN
ejpam-3515	214	1	i	i	PRON
ejpam-3515	214	2	2	2	NUM
ejpam-3515	214	3	∫	∫	NOUN
ejpam-3515	214	4	t	t	NOUN
ejpam-3515	214	5	0	0	NUM
ejpam-3515	215	1	divb(ω(s))ds−	divb(ω(s))ds−	CCONJ
ejpam-3515	215	2	∫	∫	PROPN
ejpam-3515	215	3	t	t	PROPN
ejpam-3515	215	4	0	0	NUM
ejpam-3515	215	5	v	v	NOUN
ejpam-3515	215	6	(	(	PUNCT
ejpam-3515	215	7	ω(s))ds))ϕ(y)−ϕ(x)(exp(−i	ω(s))ds))ϕ(y)−ϕ(x)(exp(−i	NOUN
ejpam-3515	215	8	∫	∫	PROPN
ejpam-3515	215	9	t	t	PROPN
ejpam-3515	215	10	0	0	NUM
ejpam-3515	216	1	b(η(s))dη−	b(η(s))dη−	ADJ
ejpam-3515	217	1	i	i	PRON
ejpam-3515	218	1	2	2	NUM
ejpam-3515	218	2	∫	∫	NOUN
ejpam-3515	218	3	t	t	NOUN
ejpam-3515	218	4	0	0	NUM
ejpam-3515	219	1	divb(η(s))ds−	divb(η(s))ds−	X
ejpam-3515	219	2	∫	∫	PROPN
ejpam-3515	219	3	t	t	PROPN
ejpam-3515	219	4	0	0	NUM
ejpam-3515	219	5	v	v	NOUN
ejpam-3515	219	6	(	(	PUNCT
ejpam-3515	219	7	η(s))ds)ϕ(z)−ϕ(x	η(s))ds)ϕ(z)−ϕ(x	PROPN
ejpam-3515	219	8	)	)	PUNCT
ejpam-3515	219	9	)	)	PUNCT
ejpam-3515	219	10	,	,	PUNCT
ejpam-3515	219	11	now	now	ADV
ejpam-3515	219	12	exp	exp	X
ejpam-3515	219	13	(	(	PUNCT
ejpam-3515	219	14	−i	−i	PROPN
ejpam-3515	219	15	∫	∫	PROPN
ejpam-3515	219	16	t	t	PROPN
ejpam-3515	219	17	0	0	NUM
ejpam-3515	219	18	b(γ(s))dγ	b(γ(s))dγ	NOUN
ejpam-3515	220	1	−	−	PROPN
ejpam-3515	220	2	i	i	PRON
ejpam-3515	220	3	2	2	NUM
ejpam-3515	220	4	∫	∫	NOUN
ejpam-3515	220	5	t	t	NOUN
ejpam-3515	220	6	0	0	NUM
ejpam-3515	220	7	divb(γ(s))ds−	divb(γ(s))ds−	NOUN
ejpam-3515	220	8	∫	∫	PROPN
ejpam-3515	220	9	t	t	PROPN
ejpam-3515	220	10	0	0	NUM
ejpam-3515	220	11	v	v	NOUN
ejpam-3515	220	12	(	(	PUNCT
ejpam-3515	220	13	γ(s))ds	γ(s))ds	PROPN
ejpam-3515	220	14	)	)	PUNCT
ejpam-3515	220	15	=	=	SYM
ejpam-3515	221	1	1−	1−	NUM
ejpam-3515	221	2	∫	∫	NOUN
ejpam-3515	221	3	1	1	NUM
ejpam-3515	221	4	0	0	NUM
ejpam-3515	221	5	(	(	PUNCT
ejpam-3515	221	6	−i	−i	ADJ
ejpam-3515	221	7	∫	∫	PROPN
ejpam-3515	221	8	t	t	PROPN
ejpam-3515	221	9	0	0	NUM
ejpam-3515	221	10	b(γ(s))dγ	b(γ(s))dγ	NOUN
ejpam-3515	222	1	−	−	PROPN
ejpam-3515	222	2	i	i	PRON
ejpam-3515	222	3	2	2	NUM
ejpam-3515	222	4	∫	∫	NOUN
ejpam-3515	222	5	t	t	NOUN
ejpam-3515	222	6	0	0	NUM
ejpam-3515	222	7	divb(γ(s))ds−	divb(γ(s))ds−	NOUN
ejpam-3515	222	8	∫	∫	PROPN
ejpam-3515	222	9	t	t	PROPN
ejpam-3515	222	10	0	0	NUM
ejpam-3515	222	11	v	v	NOUN
ejpam-3515	222	12	(	(	PUNCT
ejpam-3515	222	13	γ(s))ds	γ(s))ds	PROPN
ejpam-3515	222	14	)	)	PUNCT
ejpam-3515	222	15	.	.	PUNCT
ejpam-3515	223	1	expα	expα	PROPN
ejpam-3515	223	2	(	(	PUNCT
ejpam-3515	223	3	−i	−i	ADJ
ejpam-3515	223	4	∫	∫	PROPN
ejpam-3515	223	5	t	t	PROPN
ejpam-3515	223	6	0	0	NUM
ejpam-3515	223	7	b(γ(s))dγ	b(γ(s))dγ	NOUN
ejpam-3515	224	1	−	−	PROPN
ejpam-3515	224	2	i	i	PRON
ejpam-3515	224	3	2	2	NUM
ejpam-3515	224	4	∫	∫	NOUN
ejpam-3515	224	5	t	t	NOUN
ejpam-3515	224	6	0	0	NUM
ejpam-3515	224	7	divb(γ(s))ds−	divb(γ(s))ds−	NOUN
ejpam-3515	224	8	∫	∫	PROPN
ejpam-3515	224	9	t	t	PROPN
ejpam-3515	224	10	0	0	NUM
ejpam-3515	224	11	v	v	NOUN
ejpam-3515	224	12	(	(	PUNCT
ejpam-3515	224	13	γ(s))ds	γ(s))ds	PROPN
ejpam-3515	224	14	)	)	PUNCT
ejpam-3515	224	15	dα	dα	PROPN
ejpam-3515	224	16	(	(	PUNCT
ejpam-3515	224	17	2.10	2.10	NUM
ejpam-3515	224	18	)	)	PUNCT
ejpam-3515	224	19	we	we	PRON
ejpam-3515	224	20	get	get	VERB
ejpam-3515	224	21	from	from	ADP
ejpam-3515	224	22	(	(	PUNCT
ejpam-3515	224	23	2.10	2.10	NUM
ejpam-3515	224	24	)	)	PUNCT
ejpam-3515	224	25	and	and	CCONJ
ejpam-3515	224	26	from	from	ADP
ejpam-3515	224	27	the	the	DET
ejpam-3515	224	28	estimates	estimate	NOUN
ejpam-3515	224	29	in	in	ADP
ejpam-3515	224	30	(	(	PUNCT
ejpam-3515	224	31	proposition	proposition	NOUN
ejpam-3515	224	32	2.1	2.1	NUM
ejpam-3515	224	33	in	in	ADP
ejpam-3515	224	34	[	[	X
ejpam-3515	224	35	8	8	NUM
ejpam-3515	224	36	]	]	NUM
ejpam-3515	224	37	)	)	PUNCT
ejpam-3515	224	38	.	.	PUNCT
ejpam-3515	225	1	|e	|e	PROPN
ejpam-3515	225	2	[	[	PUNCT
ejpam-3515	225	3	∫	∫	PROPN
ejpam-3515	225	4	dy	dy	PROPN
ejpam-3515	225	5	∫	∫	PROPN
ejpam-3515	225	6	dµtx	dµtx	PROPN
ejpam-3515	225	7	,	,	PUNCT
ejpam-3515	225	8	y(ω	y(ω	PROPN
ejpam-3515	225	9	)	)	PUNCT
ejpam-3515	225	10	[	[	PUNCT
ejpam-3515	225	11	exp	exp	NOUN
ejpam-3515	225	12	(	(	PUNCT
ejpam-3515	225	13	−i	−i	PROPN
ejpam-3515	225	14	∫	∫	PROPN
ejpam-3515	225	15	t	t	PROPN
ejpam-3515	225	16	0	0	NUM
ejpam-3515	225	17	b(ω(s))dω	b(ω(s))dω	NOUN
ejpam-3515	226	1	−	−	PROPN
ejpam-3515	227	1	i	i	PRON
ejpam-3515	227	2	2	2	NUM
ejpam-3515	227	3	∫	∫	NOUN
ejpam-3515	227	4	t	t	NOUN
ejpam-3515	227	5	0	0	NUM
ejpam-3515	228	1	divb(ω(s))ds−	divb(ω(s))ds−	CCONJ
ejpam-3515	228	2	∫	∫	PROPN
ejpam-3515	228	3	t	t	PROPN
ejpam-3515	228	4	0	0	NUM
ejpam-3515	228	5	v	v	NOUN
ejpam-3515	228	6	(	(	PUNCT
ejpam-3515	228	7	ω(s))ds	ω(s))ds	NUM
ejpam-3515	228	8	)	)	PUNCT
ejpam-3515	228	9	(	(	PUNCT
ejpam-3515	228	10	ϕ(y)−	ϕ(y)−	PROPN
ejpam-3515	228	11	ϕ(x	ϕ(x	PROPN
ejpam-3515	228	12	)	)	PUNCT
ejpam-3515	228	13	)	)	PUNCT
ejpam-3515	228	14	]	]	PUNCT
ejpam-3515	229	1	y.	y.	PROPN
ejpam-3515	229	2	h.	h.	PROPN
ejpam-3515	229	3	saleem	saleem	PROPN
ejpam-3515	229	4	,	,	PUNCT
ejpam-3515	229	5	h.	h.	PROPN
ejpam-3515	229	6	a.	a.	PROPN
ejpam-3515	229	7	shubber	shubber	PROPN
ejpam-3515	229	8	/	/	SYM
ejpam-3515	229	9	eur	eur	PROPN
ejpam-3515	229	10	.	.	PUNCT
ejpam-3515	230	1	j.	j.	PROPN
ejpam-3515	230	2	pure	pure	PROPN
ejpam-3515	230	3	appl	appl	PROPN
ejpam-3515	230	4	.	.	PROPN
ejpam-3515	230	5	math	math	PROPN
ejpam-3515	230	6	,	,	PUNCT
ejpam-3515	230	7	12	12	NUM
ejpam-3515	230	8	(	(	PUNCT
ejpam-3515	230	9	4	4	NUM
ejpam-3515	230	10	)	)	PUNCT
ejpam-3515	230	11	(	(	PUNCT
ejpam-3515	230	12	2019	2019	NUM
ejpam-3515	230	13	)	)	PUNCT
ejpam-3515	230	14	,	,	PUNCT
ejpam-3515	230	15	1441	1441	NUM
ejpam-3515	230	16	-	-	SYM
ejpam-3515	230	17	1454	1454	NUM
ejpam-3515	230	18	1450	1450	NUM
ejpam-3515	230	19	.	.	PUNCT
ejpam-3515	231	1	[	[	PUNCT
ejpam-3515	231	2	∫	∫	X
ejpam-3515	231	3	dz	dz	PROPN
ejpam-3515	231	4	∫	∫	PROPN
ejpam-3515	231	5	dµtx	dµtx	PROPN
ejpam-3515	231	6	,	,	PUNCT
ejpam-3515	231	7	z(ω	z(ω	PROPN
ejpam-3515	231	8	)	)	PUNCT
ejpam-3515	231	9	[	[	PUNCT
ejpam-3515	231	10	exp	exp	NOUN
ejpam-3515	231	11	(	(	PUNCT
ejpam-3515	231	12	−i	−i	PROPN
ejpam-3515	231	13	∫	∫	PROPN
ejpam-3515	231	14	t	t	PROPN
ejpam-3515	231	15	0	0	NUM
ejpam-3515	231	16	b(ω(s))dω	b(ω(s))dω	NOUN
ejpam-3515	232	1	−	−	PROPN
ejpam-3515	233	1	i	i	PRON
ejpam-3515	233	2	2	2	NUM
ejpam-3515	233	3	∫	∫	NOUN
ejpam-3515	233	4	t	t	NOUN
ejpam-3515	233	5	0	0	NUM
ejpam-3515	234	1	divb(ω(s))ds−	divb(ω(s))ds−	CCONJ
ejpam-3515	234	2	∫	∫	PROPN
ejpam-3515	234	3	t	t	PROPN
ejpam-3515	234	4	0	0	NUM
ejpam-3515	234	5	v	v	NOUN
ejpam-3515	234	6	(	(	PUNCT
ejpam-3515	234	7	ω(s))ds	ω(s))ds	NUM
ejpam-3515	234	8	)	)	PUNCT
ejpam-3515	234	9	(	(	PUNCT
ejpam-3515	234	10	ϕ(z)−	ϕ(z)−	PROPN
ejpam-3515	234	11	ϕ(x	ϕ(x	PROPN
ejpam-3515	234	12	)	)	PUNCT
ejpam-3515	234	13	)	)	PUNCT
ejpam-3515	234	14	]	]	PUNCT
ejpam-3515	235	1	|	|	ADV
ejpam-3515	235	2	≤	≤	NUM
ejpam-3515	235	3	(	(	PUNCT
ejpam-3515	235	4	∫	∫	PROPN
ejpam-3515	235	5	p(x	p(x	PROPN
ejpam-3515	235	6	,	,	PUNCT
ejpam-3515	235	7	y	y	PROPN
ejpam-3515	235	8	,	,	PUNCT
ejpam-3515	235	9	t)ϕ(y)dy−ϕ(x	t)ϕ(y)dy−ϕ(x	PROPN
ejpam-3515	235	10	)	)	PUNCT
ejpam-3515	235	11	)	)	PUNCT
ejpam-3515	236	1	(	(	PUNCT
ejpam-3515	236	2	∫	∫	PROPN
ejpam-3515	236	3	p(x	p(x	PROPN
ejpam-3515	236	4	,	,	PUNCT
ejpam-3515	236	5	z	z	NOUN
ejpam-3515	236	6	,	,	PUNCT
ejpam-3515	236	7	t)ϕ(z)dz−ϕ(x))+const|	t)ϕ(z)dz−ϕ(x))+const|	PRON
ejpam-3515	236	8	∫	∫	PROPN
ejpam-3515	236	9	p(x	p(x	PROPN
ejpam-3515	236	10	,	,	PUNCT
ejpam-3515	236	11	y	y	PROPN
ejpam-3515	236	12	,	,	PUNCT
ejpam-3515	236	13	t)ϕ(y)dy−ϕ(x)|t	t)ϕ(y)dy−ϕ(x)|t	PROPN
ejpam-3515	236	14	+	+	PROPN
ejpam-3515	236	15	const|	const|	PROPN
ejpam-3515	236	16	(	(	PUNCT
ejpam-3515	236	17	∫	∫	PROPN
ejpam-3515	236	18	p(x	p(x	PROPN
ejpam-3515	236	19	,	,	PUNCT
ejpam-3515	236	20	z	z	PROPN
ejpam-3515	236	21	,	,	PUNCT
ejpam-3515	236	22	t)ϕ(z)dz	t)ϕ(z)dz	NOUN
ejpam-3515	236	23	−	−	PROPN
ejpam-3515	236	24	ϕ(x))|t+	ϕ(x))|t+	PROPN
ejpam-3515	236	25	const.t2	const.t2	VERB
ejpam-3515	236	26	since	since	SCONJ
ejpam-3515	236	27	ϕ(x	ϕ(x	PROPN
ejpam-3515	236	28	)	)	PUNCT
ejpam-3515	236	29	∈	∈	PROPN
ejpam-3515	236	30	c∞0	c∞0	PROPN
ejpam-3515	236	31	,	,	PUNCT
ejpam-3515	236	32	we	we	PRON
ejpam-3515	236	33	have	have	VERB
ejpam-3515	236	34	∫	∫	PROPN
ejpam-3515	236	35	rn	rn	PROPN
ejpam-3515	236	36	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	236	37	,	,	PUNCT
ejpam-3515	236	38	x)−	x)−	PROPN
ejpam-3515	236	39	ϕ(x))2dx→	ϕ(x))2dx→	PROPN
ejpam-3515	236	40	0	0	NUM
ejpam-3515	236	41	.	.	PUNCT
ejpam-3515	237	1	thus	thus	ADV
ejpam-3515	237	2	ψ(t	ψ(t	PROPN
ejpam-3515	237	3	,	,	PUNCT
ejpam-3515	237	4	x	x	X
ejpam-3515	237	5	)	)	PUNCT
ejpam-3515	237	6	satisfies	satisfy	VERB
ejpam-3515	237	7	the	the	DET
ejpam-3515	237	8	equation	equation	NOUN
ejpam-3515	237	9	∂ψ	∂ψ	VERB
ejpam-3515	238	1	∂t	∂t	PROPN
ejpam-3515	238	2	=	=	PUNCT
ejpam-3515	238	3	∑n	∑n	PROPN
ejpam-3515	238	4	j=1	j=1	NOUN
ejpam-3515	238	5	1	1	NUM
ejpam-3515	238	6	2	2	NUM
ejpam-3515	238	7	(	(	PUNCT
ejpam-3515	238	8	i∂j	i∂j	VERB
ejpam-3515	238	9	+	+	CCONJ
ejpam-3515	238	10	bj(x))2	bj(x))2	PROPN
ejpam-3515	238	11	ψ(t	ψ(t	PROPN
ejpam-3515	238	12	,	,	PUNCT
ejpam-3515	238	13	x	x	NOUN
ejpam-3515	238	14	)	)	PUNCT
ejpam-3515	238	15	−	−	PROPN
ejpam-3515	238	16	v	v	NOUN
ejpam-3515	238	17	(	(	PUNCT
ejpam-3515	238	18	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	238	19	,	,	PUNCT
ejpam-3515	238	20	x	x	NOUN
ejpam-3515	238	21	)	)	PUNCT
ejpam-3515	238	22	with	with	ADP
ejpam-3515	238	23	the	the	DET
ejpam-3515	238	24	initial	initial	ADJ
ejpam-3515	238	25	condition	condition	NOUN
ejpam-3515	238	26	ψ(t	ψ(t	PROPN
ejpam-3515	238	27	,	,	PUNCT
ejpam-3515	238	28	x	x	NOUN
ejpam-3515	238	29	)	)	PUNCT
ejpam-3515	238	30	→	→	SYM
ejpam-3515	238	31	ϕ(x	ϕ(x	X
ejpam-3515	238	32	)	)	PUNCT
ejpam-3515	238	33	in	in	ADP
ejpam-3515	238	34	l2(rn	l2(rn	PROPN
ejpam-3515	238	35	,	,	PUNCT
ejpam-3515	238	36	dx	dx	PROPN
ejpam-3515	238	37	,	,	PUNCT
ejpam-3515	238	38	dv	dv	PROPN
ejpam-3515	238	39	)	)	PUNCT
ejpam-3515	238	40	as	as	ADP
ejpam-3515	238	41	t	t	PROPN
ejpam-3515	238	42	→	→	SYM
ejpam-3515	238	43	0	0	X
ejpam-3515	238	44	.	.	PUNCT
ejpam-3515	239	1	repeating	repeat	VERB
ejpam-3515	239	2	the	the	DET
ejpam-3515	239	3	same	same	ADJ
ejpam-3515	239	4	estimates	estimate	NOUN
ejpam-3515	239	5	,	,	PUNCT
ejpam-3515	239	6	we	we	PRON
ejpam-3515	239	7	can	can	AUX
ejpam-3515	239	8	show	show	VERB
ejpam-3515	239	9	that	that	SCONJ
ejpam-3515	239	10	ψ̃1(t	ψ̃1(t	VERB
ejpam-3515	239	11	,	,	PUNCT
ejpam-3515	239	12	x	x	X
ejpam-3515	239	13	)	)	PUNCT
ejpam-3515	239	14	→	→	SYM
ejpam-3515	239	15	hϕ(x	hϕ(x	NUM
ejpam-3515	239	16	)	)	PUNCT
ejpam-3515	239	17	in	in	ADP
ejpam-3515	239	18	l2(rn	l2(rn	PROPN
ejpam-3515	239	19	,	,	PUNCT
ejpam-3515	239	20	dx	dx	PROPN
ejpam-3515	239	21	,	,	PUNCT
ejpam-3515	239	22	dv	dv	PROPN
ejpam-3515	239	23	)	)	PUNCT
ejpam-3515	239	24	as	as	ADP
ejpam-3515	239	25	t	t	PROPN
ejpam-3515	239	26	→	→	SYM
ejpam-3515	239	27	0	0	NUM
ejpam-3515	239	28	where	where	SCONJ
ejpam-3515	239	29	ψ̃	ψ̃	PROPN
ejpam-3515	239	30	corresponds	correspond	VERB
ejpam-3515	239	31	hϕ(x	hϕ(x	NOUN
ejpam-3515	239	32	)	)	PUNCT
ejpam-3515	239	33	,	,	PUNCT
ejpam-3515	239	34	and	and	CCONJ
ejpam-3515	239	35	also	also	ADV
ejpam-3515	239	36	ψ̃m(t	ψ̃m(t	PROPN
ejpam-3515	239	37	,	,	PUNCT
ejpam-3515	239	38	x	x	X
ejpam-3515	239	39	)	)	PUNCT
ejpam-3515	239	40	→	→	SYM
ejpam-3515	239	41	hmϕ(x	hmϕ(x	PROPN
ejpam-3515	239	42	)	)	PUNCT
ejpam-3515	239	43	in	in	ADP
ejpam-3515	239	44	l2(rn	l2(rn	PROPN
ejpam-3515	239	45	,	,	PUNCT
ejpam-3515	239	46	dx	dx	PROPN
ejpam-3515	239	47	,	,	PUNCT
ejpam-3515	239	48	dv	dv	PROPN
ejpam-3515	239	49	)	)	PUNCT
ejpam-3515	239	50	as	as	ADP
ejpam-3515	239	51	t	t	PROPN
ejpam-3515	239	52	→	→	SYM
ejpam-3515	239	53	0	0	NUM
ejpam-3515	239	54	where	where	SCONJ
ejpam-3515	239	55	ψ̃	ψ̃	PROPN
ejpam-3515	239	56	corresponds	correspond	VERB
ejpam-3515	239	57	hmϕ(x	hmϕ(x	PROPN
ejpam-3515	239	58	)	)	PUNCT
ejpam-3515	239	59	.	.	PUNCT
ejpam-3515	240	1	first	first	ADV
ejpam-3515	240	2	,	,	PUNCT
ejpam-3515	240	3	we	we	PRON
ejpam-3515	240	4	note	note	VERB
ejpam-3515	240	5	that	that	SCONJ
ejpam-3515	240	6	since	since	SCONJ
ejpam-3515	240	7	the	the	DET
ejpam-3515	240	8	function	function	NOUN
ejpam-3515	240	9	ψ(t	ψ(t	PROPN
ejpam-3515	240	10	,	,	PUNCT
ejpam-3515	240	11	x	x	X
ejpam-3515	240	12	)	)	PUNCT
ejpam-3515	240	13	satisfies	satisfy	VERB
ejpam-3515	240	14	the	the	DET
ejpam-3515	240	15	estimates	estimate	NOUN
ejpam-3515	240	16	equation	equation	NOUN
ejpam-3515	240	17	(	(	PUNCT
ejpam-3515	240	18	2.7	2.7	NUM
ejpam-3515	240	19	)	)	PUNCT
ejpam-3515	240	20	and	and	CCONJ
ejpam-3515	240	21	,	,	PUNCT
ejpam-3515	240	22	by	by	ADP
ejpam-3515	240	23	lemma	lemma	PROPN
ejpam-3515	240	24	(	(	PUNCT
ejpam-3515	240	25	3.1	3.1	NUM
ejpam-3515	240	26	)	)	PUNCT
ejpam-3515	240	27	in	in	ADP
ejpam-3515	240	28	[	[	X
ejpam-3515	240	29	8	8	NUM
ejpam-3515	240	30	]	]	PUNCT
ejpam-3515	240	31	,	,	PUNCT
ejpam-3515	240	32	may	may	AUX
ejpam-3515	240	33	be	be	AUX
ejpam-3515	240	34	analytically	analytically	ADV
ejpam-3515	240	35	extended	extend	VERB
ejpam-3515	240	36	into	into	ADP
ejpam-3515	240	37	the	the	DET
ejpam-3515	240	38	mentioned	mention	VERB
ejpam-3515	240	39	band	band	NOUN
ejpam-3515	240	40	,	,	PUNCT
ejpam-3515	240	41	then	then	ADV
ejpam-3515	240	42	we	we	PRON
ejpam-3515	240	43	can	can	AUX
ejpam-3515	240	44	repeat	repeat	VERB
ejpam-3515	240	45	literally	literally	ADV
ejpam-3515	240	46	all	all	DET
ejpam-3515	240	47	the	the	DET
ejpam-3515	240	48	arguments	argument	NOUN
ejpam-3515	240	49	of	of	ADP
ejpam-3515	240	50	this	this	DET
ejpam-3515	240	51	section	section	NOUN
ejpam-3515	240	52	for	for	ADP
ejpam-3515	240	53	x	x	PROPN
ejpam-3515	240	54	∈	∈	PROPN
ejpam-3515	240	55	rn\a	rn\a	PUNCT
ejpam-3515	240	56	and	and	CCONJ
ejpam-3515	240	57	show	show	VERB
ejpam-3515	240	58	that	that	SCONJ
ejpam-3515	240	59	the	the	DET
ejpam-3515	240	60	function	function	NOUN
ejpam-3515	240	61	ψ(t	ψ(t	PROPN
ejpam-3515	240	62	,	,	PUNCT
ejpam-3515	240	63	x	x	PRON
ejpam-3515	240	64	)	)	PUNCT
ejpam-3515	240	65	is	be	AUX
ejpam-3515	240	66	infinitely	infinitely	ADV
ejpam-3515	240	67	differentiable	differentiable	ADJ
ejpam-3515	240	68	if	if	SCONJ
ejpam-3515	240	69	x	x	X
ejpam-3515	240	70	∈	∈	PROPN
ejpam-3515	240	71	rn\a	rn\a	NOUN
ejpam-3515	240	72	.	.	PUNCT
ejpam-3515	241	1	we	we	PRON
ejpam-3515	241	2	now	now	ADV
ejpam-3515	241	3	consider	consider	VERB
ejpam-3515	241	4	the	the	DET
ejpam-3515	241	5	case	case	NOUN
ejpam-3515	241	6	x	x	X
ejpam-3515	241	7	∈	∈	NOUN
ejpam-3515	241	8	a.	a.	NOUN
ejpam-3515	241	9	we	we	PRON
ejpam-3515	241	10	assume	assume	VERB
ejpam-3515	241	11	,	,	PUNCT
ejpam-3515	241	12	that	that	SCONJ
ejpam-3515	241	13	the	the	DET
ejpam-3515	241	14	function	function	NOUN
ejpam-3515	241	15	v	v	NOUN
ejpam-3515	241	16	(	(	PUNCT
ejpam-3515	241	17	x	x	X
ejpam-3515	241	18	)	)	PUNCT
ejpam-3515	241	19	in	in	ADP
ejpam-3515	241	20	a	a	DET
ejpam-3515	241	21	neighborhood	neighborhood	NOUN
ejpam-3515	241	22	of	of	ADP
ejpam-3515	241	23	x	x	PUNCT
ejpam-3515	241	24	∈	∈	PROPN
ejpam-3515	241	25	a	a	DET
ejpam-3515	241	26	satisfies	satisfie	NOUN
ejpam-3515	241	27	the	the	DET
ejpam-3515	241	28	following	follow	VERB
ejpam-3515	241	29	requirements	requirement	NOUN
ejpam-3515	241	30	considered	consider	VERB
ejpam-3515	241	31	in	in	ADP
ejpam-3515	241	32	the	the	DET
ejpam-3515	241	33	work	work	NOUN
ejpam-3515	241	34	of	of	ADP
ejpam-3515	241	35	m.d	m.d	PROPN
ejpam-3515	241	36	.	.	PROPN
ejpam-3515	241	37	gaysinsky	gaysinsky	PROPN
ejpam-3515	241	38	(	(	PUNCT
ejpam-3515	241	39	see[3],p.23	see[3],p.23	PROPN
ejpam-3515	241	40	):	):	PUNCT
ejpam-3515	241	41	(	(	PUNCT
ejpam-3515	241	42	i	i	NOUN
ejpam-3515	241	43	)	)	PUNCT
ejpam-3515	241	44	there	there	PRON
ejpam-3515	241	45	exists	exist	VERB
ejpam-3515	241	46	ε	ε	PROPN
ejpam-3515	241	47	>	>	X
ejpam-3515	241	48	0	0	PROPN
ejpam-3515	241	49	,	,	PUNCT
ejpam-3515	241	50	δ	δ	PROPN
ejpam-3515	241	51	>	>	X
ejpam-3515	241	52	0	0	PROPN
ejpam-3515	241	53	,	,	PUNCT
ejpam-3515	241	54	k	k	NOUN
ejpam-3515	241	55	,	,	PUNCT
ejpam-3515	241	56	n	n	PRON
ejpam-3515	241	57	are	be	AUX
ejpam-3515	241	58	some	some	PRON
ejpam-3515	241	59	constant	constant	ADJ
ejpam-3515	241	60	such	such	ADJ
ejpam-3515	241	61	that	that	SCONJ
ejpam-3515	241	62	0	0	NUM
ejpam-3515	241	63	<	<	X
ejpam-3515	241	64	v	v	X
ejpam-3515	241	65	(	(	PUNCT
ejpam-3515	241	66	x)−	x)−	PROPN
ejpam-3515	241	67	d(x	d(x	PROPN
ejpam-3515	241	68	,	,	PUNCT
ejpam-3515	241	69	a)−2−ε	a)−2−ε	PROPN
ejpam-3515	241	70	<	<	X
ejpam-3515	241	71	kd(x	kd(x	PROPN
ejpam-3515	241	72	,	,	PUNCT
ejpam-3515	241	73	a)−n	a)−n	PROPN
ejpam-3515	241	74	,	,	PUNCT
ejpam-3515	241	75	if	if	SCONJ
ejpam-3515	241	76	0	0	NUM
ejpam-3515	241	77	<	<	X
ejpam-3515	241	78	d(x	d(x	PROPN
ejpam-3515	241	79	,	,	PUNCT
ejpam-3515	241	80	a	a	PRON
ejpam-3515	241	81	)	)	PUNCT
ejpam-3515	241	82	<	<	X
ejpam-3515	241	83	δ	δ	PROPN
ejpam-3515	241	84	;	;	PUNCT
ejpam-3515	241	85	where	where	SCONJ
ejpam-3515	241	86	x	x	X
ejpam-3515	241	87	∈	∈	PROPN
ejpam-3515	241	88	rn\a	rn\a	NOUN
ejpam-3515	241	89	,	,	PUNCT
ejpam-3515	241	90	d(x	d(x	PROPN
ejpam-3515	241	91	,	,	PUNCT
ejpam-3515	241	92	a	a	PRON
ejpam-3515	241	93	)	)	PUNCT
ejpam-3515	241	94	is	be	AUX
ejpam-3515	241	95	the	the	DET
ejpam-3515	241	96	distance	distance	NOUN
ejpam-3515	241	97	between	between	ADP
ejpam-3515	241	98	x	x	PUNCT
ejpam-3515	241	99	and	and	CCONJ
ejpam-3515	241	100	closed	close	VERB
ejpam-3515	241	101	set	set	ADJ
ejpam-3515	241	102	a.	a.	NOUN
ejpam-3515	241	103	(	(	PUNCT
ejpam-3515	241	104	ii	ii	NOUN
ejpam-3515	241	105	)	)	PUNCT
ejpam-3515	241	106	for	for	ADP
ejpam-3515	241	107	each	each	DET
ejpam-3515	241	108	α	α	NOUN
ejpam-3515	241	109	=	=	SYM
ejpam-3515	241	110	(	(	PUNCT
ejpam-3515	241	111	α1	α1	PROPN
ejpam-3515	241	112	,	,	PUNCT
ejpam-3515	241	113	α2	α2	ADJ
ejpam-3515	241	114	,	,	PUNCT
ejpam-3515	241	115	,	,	PUNCT
ejpam-3515	241	116	αn	αn	X
ejpam-3515	241	117	)	)	PUNCT
ejpam-3515	241	118	there	there	PRON
ejpam-3515	241	119	exists	exist	VERB
ejpam-3515	241	120	δα	δα	PRON
ejpam-3515	241	121	>	>	X
ejpam-3515	241	122	0	0	NUM
ejpam-3515	241	123	such	such	ADJ
ejpam-3515	241	124	that	that	SCONJ
ejpam-3515	241	125	|	|	INTJ
ejpam-3515	242	1	∂α∂xαv	∂α∂xαv	INTJ
ejpam-3515	243	1	(	(	PUNCT
ejpam-3515	243	2	x)|	x)|	NOUN
ejpam-3515	243	3	=	=	PUNCT
ejpam-3515	243	4	o(d(x	o(d(x	PROPN
ejpam-3515	243	5	,	,	PUNCT
ejpam-3515	243	6	a)−kα	a)−kα	NOUN
ejpam-3515	243	7	,	,	PUNCT
ejpam-3515	243	8	if	if	SCONJ
ejpam-3515	243	9	0	0	NUM
ejpam-3515	243	10	<	<	X
ejpam-3515	243	11	d(x	d(x	PROPN
ejpam-3515	243	12	,	,	PUNCT
ejpam-3515	243	13	a	a	PRON
ejpam-3515	243	14	)	)	PUNCT
ejpam-3515	243	15	<	<	X
ejpam-3515	243	16	δα	δα	PRON
ejpam-3515	243	17	where	where	SCONJ
ejpam-3515	243	18	kα	kα	PRON
ejpam-3515	243	19	are	be	AUX
ejpam-3515	243	20	some	some	DET
ejpam-3515	243	21	constants	constant	NOUN
ejpam-3515	243	22	.	.	PUNCT
ejpam-3515	244	1	we	we	PRON
ejpam-3515	244	2	will	will	AUX
ejpam-3515	244	3	show	show	VERB
ejpam-3515	244	4	now	now	ADV
ejpam-3515	244	5	that	that	SCONJ
ejpam-3515	244	6	,	,	PUNCT
ejpam-3515	244	7	in	in	ADP
ejpam-3515	244	8	this	this	DET
ejpam-3515	244	9	case	case	NOUN
ejpam-3515	244	10	,	,	PUNCT
ejpam-3515	244	11	ψ(t	ψ(t	PROPN
ejpam-3515	244	12	,	,	PUNCT
ejpam-3515	244	13	x	x	PRON
ejpam-3515	244	14	)	)	PUNCT
ejpam-3515	244	15	is	be	AUX
ejpam-3515	244	16	infinitely	infinitely	ADV
ejpam-3515	244	17	differentiable	differentiable	ADJ
ejpam-3515	244	18	at	at	ADP
ejpam-3515	244	19	zero	zero	NUM
ejpam-3515	244	20	for	for	ADP
ejpam-3515	244	21	almost	almost	ADV
ejpam-3515	244	22	every	every	PRON
ejpam-3515	244	23	v	v	NOUN
ejpam-3515	244	24	,	,	PUNCT
ejpam-3515	244	25	b	b	NOUN
ejpam-3515	244	26	,	,	PUNCT
ejpam-3515	244	27	and	and	CCONJ
ejpam-3515	244	28	also	also	ADV
ejpam-3515	244	29	estimate	estimate	VERB
ejpam-3515	244	30	the	the	DET
ejpam-3515	244	31	derivations	derivation	NOUN
ejpam-3515	244	32	of	of	ADP
ejpam-3515	244	33	ψ(t	ψ(t	PROPN
ejpam-3515	244	34	,	,	PUNCT
ejpam-3515	244	35	x	x	NOUN
ejpam-3515	244	36	)	)	PUNCT
ejpam-3515	244	37	in	in	ADP
ejpam-3515	244	38	a	a	DET
ejpam-3515	244	39	neighborhood	neighborhood	NOUN
ejpam-3515	244	40	of	of	ADP
ejpam-3515	244	41	x	x	SYM
ejpam-3515	244	42	∈	∈	PROPN
ejpam-3515	244	43	a	a	PRON
ejpam-3515	244	44	if	if	SCONJ
ejpam-3515	244	45	the	the	DET
ejpam-3515	244	46	support	support	NOUN
ejpam-3515	244	47	of	of	ADP
ejpam-3515	244	48	the	the	DET
ejpam-3515	244	49	function	function	NOUN
ejpam-3515	244	50	ϕ(x	ϕ(x	NOUN
ejpam-3515	244	51	)	)	PUNCT
ejpam-3515	244	52	is	be	AUX
ejpam-3515	244	53	disjoint	disjoint	ADJ
ejpam-3515	244	54	with	with	ADP
ejpam-3515	244	55	the	the	DET
ejpam-3515	244	56	closed	closed	ADJ
ejpam-3515	244	57	set	set	NOUN
ejpam-3515	244	58	a.	a.	NOUN
ejpam-3515	244	59	first	first	ADV
ejpam-3515	244	60	,	,	PUNCT
ejpam-3515	244	61	we	we	PRON
ejpam-3515	244	62	show	show	VERB
ejpam-3515	244	63	that	that	SCONJ
ejpam-3515	244	64	ψ(t	ψ(t	PROPN
ejpam-3515	244	65	,	,	PUNCT
ejpam-3515	244	66	x	x	X
ejpam-3515	244	67	)	)	PUNCT
ejpam-3515	244	68	fast	fast	ADJ
ejpam-3515	244	69	decreases	decrease	NOUN
ejpam-3515	244	70	as	as	ADP
ejpam-3515	244	71	x	x	SYM
ejpam-3515	244	72	approach	approach	NOUN
ejpam-3515	244	73	to	to	ADP
ejpam-3515	244	74	the	the	DET
ejpam-3515	244	75	set	set	NOUN
ejpam-3515	244	76	a.	a.	NOUN
ejpam-3515	244	77	proposition	proposition	NOUN
ejpam-3515	244	78	2.3	2.3	NUM
ejpam-3515	244	79	.	.	PUNCT
ejpam-3515	245	1	let	let	VERB
ejpam-3515	245	2	v	v	NUM
ejpam-3515	245	3	∈	∈	PROPN
ejpam-3515	245	4	l2(rn\a	l2(rn\a	NOUN
ejpam-3515	245	5	)	)	PUNCT
ejpam-3515	245	6	,	,	PUNCT
ejpam-3515	245	7	ϕ	ϕ	NOUN
ejpam-3515	245	8	,	,	PUNCT
ejpam-3515	245	9	h	h	NOUN
ejpam-3515	245	10	∈	∈	PROPN
ejpam-3515	245	11	c∞0	c∞0	PROPN
ejpam-3515	245	12	where	where	SCONJ
ejpam-3515	245	13	a	a	PRON
ejpam-3515	245	14	is	be	AUX
ejpam-3515	245	15	closed	closed	ADJ
ejpam-3515	245	16	set	set	VERB
ejpam-3515	245	17	,	,	PUNCT
ejpam-3515	245	18	v	v	NOUN
ejpam-3515	245	19	(	(	PUNCT
ejpam-3515	245	20	x	x	NOUN
ejpam-3515	245	21	)	)	PUNCT
ejpam-3515	245	22	=	=	PUNCT
ejpam-3515	246	1	+	+	NUM
ejpam-3515	246	2	∞	∞	PROPN
ejpam-3515	246	3	,	,	PUNCT
ejpam-3515	246	4	bj(x	bj(x	X
ejpam-3515	246	5	)	)	PUNCT
ejpam-3515	247	1	=	=	PUNCT
ejpam-3515	248	1	+	+	NUM
ejpam-3515	248	2	∞	∞	NOUN
ejpam-3515	248	3	,	,	PUNCT
ejpam-3515	248	4	if	if	SCONJ
ejpam-3515	248	5	x	x	PROPN
ejpam-3515	248	6	∈	∈	PROPN
ejpam-3515	248	7	a	a	X
ejpam-3515	248	8	,	,	PUNCT
ejpam-3515	248	9	0	0	NUM
ejpam-3515	248	10	<	<	X
ejpam-3515	248	11	v	v	NOUN
ejpam-3515	248	12	(	(	PUNCT
ejpam-3515	248	13	x)−d(x	x)−d(x	PROPN
ejpam-3515	248	14	,	,	PUNCT
ejpam-3515	248	15	a)−2−ε	a)−2−ε	PROPN
ejpam-3515	248	16	<	<	X
ejpam-3515	248	17	kd(x	kd(x	PROPN
ejpam-3515	248	18	,	,	PUNCT
ejpam-3515	248	19	a)−n	a)−n	PROPN
ejpam-3515	248	20	,	,	PUNCT
ejpam-3515	248	21	if	if	SCONJ
ejpam-3515	248	22	0	0	NUM
ejpam-3515	248	23	<	<	X
ejpam-3515	248	24	d(x	d(x	PROPN
ejpam-3515	248	25	,	,	PUNCT
ejpam-3515	248	26	a	a	PRON
ejpam-3515	248	27	)	)	PUNCT
ejpam-3515	248	28	<	<	X
ejpam-3515	248	29	δ	δ	PROPN
ejpam-3515	248	30	;	;	PUNCT
ejpam-3515	248	31	where	where	SCONJ
ejpam-3515	248	32	x	x	X
ejpam-3515	248	33	∈	∈	PROPN
ejpam-3515	248	34	rn\a	rn\a	NOUN
ejpam-3515	248	35	,	,	PUNCT
ejpam-3515	248	36	d(x	d(x	PROPN
ejpam-3515	248	37	,	,	PUNCT
ejpam-3515	248	38	a	a	PRON
ejpam-3515	248	39	)	)	PUNCT
ejpam-3515	248	40	is	be	AUX
ejpam-3515	248	41	the	the	DET
ejpam-3515	248	42	distance	distance	NOUN
ejpam-3515	248	43	between	between	ADP
ejpam-3515	248	44	x	x	PUNCT
ejpam-3515	248	45	and	and	CCONJ
ejpam-3515	248	46	closed	close	VERB
ejpam-3515	248	47	set	set	VERB
ejpam-3515	248	48	a	a	PRON
ejpam-3515	248	49	,	,	PUNCT
ejpam-3515	248	50	ε	ε	PROPN
ejpam-3515	248	51	>	>	X
ejpam-3515	248	52	0	0	PROPN
ejpam-3515	248	53	,	,	PUNCT
ejpam-3515	248	54	δ	δ	PROPN
ejpam-3515	248	55	>	>	X
ejpam-3515	248	56	0	0	PROPN
ejpam-3515	248	57	,	,	PUNCT
ejpam-3515	248	58	k	k	NOUN
ejpam-3515	248	59	,	,	PUNCT
ejpam-3515	248	60	n	n	PRON
ejpam-3515	248	61	are	be	AUX
ejpam-3515	248	62	some	some	PRON
ejpam-3515	248	63	constant	constant	ADJ
ejpam-3515	248	64	,	,	PUNCT
ejpam-3515	248	65	and	and	CCONJ
ejpam-3515	248	66	let	let	VERB
ejpam-3515	248	67	for	for	ADP
ejpam-3515	248	68	each	each	DET
ejpam-3515	248	69	α	α	NOUN
ejpam-3515	248	70	=	=	SYM
ejpam-3515	248	71	(	(	PUNCT
ejpam-3515	248	72	α1	α1	PROPN
ejpam-3515	248	73	,	,	PUNCT
ejpam-3515	248	74	α2	α2	ADJ
ejpam-3515	248	75	,	,	PUNCT
ejpam-3515	248	76	,	,	PUNCT
ejpam-3515	248	77	αn	αn	X
ejpam-3515	248	78	)	)	PUNCT
ejpam-3515	248	79	there	there	PRON
ejpam-3515	248	80	exists	exist	VERB
ejpam-3515	248	81	δα	δα	PRON
ejpam-3515	248	82	>	>	X
ejpam-3515	248	83	0	0	NUM
ejpam-3515	249	1	such	such	ADJ
ejpam-3515	249	2	that	that	SCONJ
ejpam-3515	249	3	|	|	INTJ
ejpam-3515	250	1	∂α∂xαv	∂α∂xαv	INTJ
ejpam-3515	251	1	(	(	PUNCT
ejpam-3515	251	2	x)|	x)|	NOUN
ejpam-3515	251	3	=	=	PUNCT
ejpam-3515	251	4	o(d(x	o(d(x	PROPN
ejpam-3515	251	5	,	,	PUNCT
ejpam-3515	251	6	a)−kα	a)−kα	NOUN
ejpam-3515	251	7	,	,	PUNCT
ejpam-3515	251	8	if	if	SCONJ
ejpam-3515	251	9	0	0	NUM
ejpam-3515	251	10	<	<	X
ejpam-3515	251	11	d(x	d(x	PROPN
ejpam-3515	251	12	,	,	PUNCT
ejpam-3515	251	13	a	a	PRON
ejpam-3515	251	14	)	)	PUNCT
ejpam-3515	251	15	<	<	X
ejpam-3515	251	16	δα	δα	PRON
ejpam-3515	251	17	where	where	SCONJ
ejpam-3515	251	18	kα	kα	PRON
ejpam-3515	251	19	are	be	AUX
ejpam-3515	251	20	some	some	DET
ejpam-3515	251	21	constants	constant	NOUN
ejpam-3515	251	22	.	.	PUNCT
ejpam-3515	252	1	let	let	VERB
ejpam-3515	252	2	ϕ	ϕ	PROPN
ejpam-3515	252	3	∈	∈	PROPN
ejpam-3515	252	4	c∞0	c∞0	PROPN
ejpam-3515	252	5	such	such	ADJ
ejpam-3515	252	6	that	that	DET
ejpam-3515	252	7	suppϕ	suppϕ	NOUN
ejpam-3515	253	1	∩a	∩a	PROPN
ejpam-3515	253	2	=	=	PUNCT
ejpam-3515	253	3	∅.	∅.	X
ejpam-3515	253	4	then	then	ADV
ejpam-3515	253	5	ψ(t	ψ(t	PROPN
ejpam-3515	253	6	,	,	PUNCT
ejpam-3515	253	7	x	x	PRON
ejpam-3515	253	8	)	)	PUNCT
ejpam-3515	253	9	is	be	AUX
ejpam-3515	253	10	an	an	DET
ejpam-3515	253	11	infinitely	infinitely	ADV
ejpam-3515	253	12	differentable	differentable	ADJ
ejpam-3515	253	13	function	function	NOUN
ejpam-3515	253	14	.	.	PUNCT
ejpam-3515	254	1	y.	y.	PROPN
ejpam-3515	254	2	h.	h.	PROPN
ejpam-3515	254	3	saleem	saleem	PROPN
ejpam-3515	254	4	,	,	PUNCT
ejpam-3515	254	5	h.	h.	PROPN
ejpam-3515	254	6	a.	a.	PROPN
ejpam-3515	254	7	shubber	shubber	PROPN
ejpam-3515	254	8	/	/	SYM
ejpam-3515	254	9	eur	eur	PROPN
ejpam-3515	254	10	.	.	PUNCT
ejpam-3515	255	1	j.	j.	PROPN
ejpam-3515	255	2	pure	pure	PROPN
ejpam-3515	255	3	appl	appl	PROPN
ejpam-3515	255	4	.	.	PROPN
ejpam-3515	255	5	math	math	PROPN
ejpam-3515	255	6	,	,	PUNCT
ejpam-3515	255	7	12	12	NUM
ejpam-3515	255	8	(	(	PUNCT
ejpam-3515	255	9	4	4	NUM
ejpam-3515	255	10	)	)	PUNCT
ejpam-3515	255	11	(	(	PUNCT
ejpam-3515	255	12	2019	2019	NUM
ejpam-3515	255	13	)	)	PUNCT
ejpam-3515	255	14	,	,	PUNCT
ejpam-3515	255	15	1441	1441	NUM
ejpam-3515	255	16	-	-	SYM
ejpam-3515	255	17	1454	1454	NUM
ejpam-3515	255	18	1451	1451	NUM
ejpam-3515	255	19	proof	proof	NOUN
ejpam-3515	255	20	.	.	PUNCT
ejpam-3515	256	1	following	follow	VERB
ejpam-3515	256	2	the	the	DET
ejpam-3515	256	3	works	work	NOUN
ejpam-3515	256	4	of	of	ADP
ejpam-3515	256	5	m.d	m.d	PROPN
ejpam-3515	256	6	.	.	PROPN
ejpam-3515	256	7	gaysinsky	gaysinsky	PROPN
ejpam-3515	256	8	[	[	X
ejpam-3515	256	9	3	3	NUM
ejpam-3515	256	10	]	]	PUNCT
ejpam-3515	256	11	,	,	PUNCT
ejpam-3515	256	12	we	we	PRON
ejpam-3515	256	13	will	will	AUX
ejpam-3515	256	14	say	say	VERB
ejpam-3515	256	15	that	that	SCONJ
ejpam-3515	256	16	a	a	DET
ejpam-3515	256	17	random	random	ADJ
ejpam-3515	256	18	variable	variable	ADJ
ejpam-3515	256	19	ṽ	ṽ	PROPN
ejpam-3515	256	20	(	(	PUNCT
ejpam-3515	256	21	x	x	X
ejpam-3515	256	22	)	)	PUNCT
ejpam-3515	256	23	has	have	VERB
ejpam-3515	256	24	a−property	a−property	X
ejpam-3515	256	25	if	if	SCONJ
ejpam-3515	256	26	e|	e|	PROPN
ejpam-3515	256	27	∂	∂	NOUN
ejpam-3515	256	28	m	m	PROPN
ejpam-3515	256	29	∂xm	∂xm	PROPN
ejpam-3515	256	30	ṽ	ṽ	PROPN
ejpam-3515	256	31	(	(	PUNCT
ejpam-3515	256	32	x)|r	x)|r	PROPN
ejpam-3515	256	33	≤	≤	ADV
ejpam-3515	256	34	o(d(x	o(d(x	PROPN
ejpam-3515	256	35	,	,	PUNCT
ejpam-3515	256	36	a)−km	a)−km	PROPN
ejpam-3515	256	37	,	,	PUNCT
ejpam-3515	256	38	r	r	NOUN
ejpam-3515	256	39	,	,	PUNCT
ejpam-3515	256	40	for	for	ADP
ejpam-3515	256	41	d(x	d(x	PROPN
ejpam-3515	256	42	,	,	PUNCT
ejpam-3515	256	43	a	a	PRON
ejpam-3515	256	44	)	)	PUNCT
ejpam-3515	256	45	<	<	X
ejpam-3515	256	46	δm	δm	PROPN
ejpam-3515	256	47	,	,	PUNCT
ejpam-3515	256	48	r	r	NOUN
ejpam-3515	256	49	where	where	SCONJ
ejpam-3515	256	50	δm	δm	X
ejpam-3515	256	51	,	,	PUNCT
ejpam-3515	256	52	r	r	NOUN
ejpam-3515	256	53	,	,	PUNCT
ejpam-3515	256	54	km	km	PROPN
ejpam-3515	256	55	,	,	PUNCT
ejpam-3515	256	56	r	r	NOUN
ejpam-3515	256	57	>	>	X
ejpam-3515	256	58	0	0	NUM
ejpam-3515	256	59	are	be	AUX
ejpam-3515	256	60	constant	constant	ADJ
ejpam-3515	256	61	,	,	PUNCT
ejpam-3515	256	62	m	m	VERB
ejpam-3515	256	63	=	=	NOUN
ejpam-3515	256	64	1	1	NUM
ejpam-3515	256	65	,	,	PUNCT
ejpam-3515	256	66	2	2	NUM
ejpam-3515	256	67	,	,	PUNCT
ejpam-3515	256	68	...	...	PUNCT
ejpam-3515	257	1	e|	e|	PROPN
ejpam-3515	257	2	∂	∂	NOUN
ejpam-3515	257	3	m	m	PROPN
ejpam-3515	257	4	∂xm	∂xm	PROPN
ejpam-3515	257	5	ṽ	ṽ	PROPN
ejpam-3515	257	6	(	(	PUNCT
ejpam-3515	257	7	x)|r	x)|r	PROPN
ejpam-3515	257	8	≤	≤	PROPN
ejpam-3515	257	9	exp(cm	exp(cm	NOUN
ejpam-3515	257	10	,	,	PUNCT
ejpam-3515	257	11	rx	rx	VERB
ejpam-3515	257	12	2	2	NUM
ejpam-3515	257	13	)	)	PUNCT
ejpam-3515	257	14	,	,	PUNCT
ejpam-3515	257	15	where	where	SCONJ
ejpam-3515	257	16	cm	cm	NOUN
ejpam-3515	257	17	,	,	PUNCT
ejpam-3515	257	18	r	r	NOUN
ejpam-3515	257	19	>	>	X
ejpam-3515	257	20	0	0	NUM
ejpam-3515	257	21	is	be	AUX
ejpam-3515	257	22	some	some	DET
ejpam-3515	257	23	constant	constant	ADJ
ejpam-3515	257	24	,	,	PUNCT
ejpam-3515	257	25	m	m	VERB
ejpam-3515	257	26	=	=	NOUN
ejpam-3515	257	27	0	0	NUM
ejpam-3515	257	28	,	,	PUNCT
ejpam-3515	257	29	1	1	NUM
ejpam-3515	257	30	,	,	PUNCT
ejpam-3515	257	31	2	2	NUM
ejpam-3515	257	32	,	,	PUNCT
ejpam-3515	257	33	...	...	PUNCT
ejpam-3515	257	34	.	.	PUNCT
ejpam-3515	258	1	it	it	PRON
ejpam-3515	258	2	is	be	AUX
ejpam-3515	258	3	evident	evident	ADJ
ejpam-3515	258	4	that	that	SCONJ
ejpam-3515	258	5	the	the	DET
ejpam-3515	258	6	derivations	derivation	NOUN
ejpam-3515	258	7	of	of	ADP
ejpam-3515	258	8	a	a	DET
ejpam-3515	258	9	function	function	NOUN
ejpam-3515	258	10	(	(	PUNCT
ejpam-3515	258	11	ṽ	ṽ	PROPN
ejpam-3515	258	12	(	(	PUNCT
ejpam-3515	258	13	x	x	NOUN
ejpam-3515	258	14	)	)	PUNCT
ejpam-3515	258	15	)	)	PUNCT
ejpam-3515	258	16	,	,	PUNCT
ejpam-3515	258	17	having	have	VERB
ejpam-3515	258	18	the	the	DET
ejpam-3515	258	19	a−property	a−property	NOUN
ejpam-3515	258	20	,	,	PUNCT
ejpam-3515	258	21	also	also	ADV
ejpam-3515	258	22	have	have	VERB
ejpam-3515	258	23	the	the	DET
ejpam-3515	258	24	a−property	a−property	NOUN
ejpam-3515	258	25	;	;	PUNCT
ejpam-3515	258	26	the	the	DET
ejpam-3515	258	27	product	product	NOUN
ejpam-3515	258	28	of	of	ADP
ejpam-3515	258	29	functions	function	NOUN
ejpam-3515	258	30	,	,	PUNCT
ejpam-3515	258	31	having	have	VERB
ejpam-3515	258	32	the	the	DET
ejpam-3515	258	33	a−property	a−property	NOUN
ejpam-3515	258	34	,	,	PUNCT
ejpam-3515	258	35	also	also	ADV
ejpam-3515	258	36	has	have	VERB
ejpam-3515	258	37	the	the	DET
ejpam-3515	258	38	a−property	a−property	NOUN
ejpam-3515	258	39	.	.	PUNCT
ejpam-3515	259	1	we	we	PRON
ejpam-3515	259	2	prove	prove	VERB
ejpam-3515	259	3	,	,	PUNCT
ejpam-3515	259	4	by	by	ADP
ejpam-3515	259	5	induction	induction	NOUN
ejpam-3515	259	6	,	,	PUNCT
ejpam-3515	259	7	that	that	SCONJ
ejpam-3515	259	8	for	for	ADP
ejpam-3515	259	9	any	any	DET
ejpam-3515	259	10	random	random	ADJ
ejpam-3515	259	11	function	function	NOUN
ejpam-3515	259	12	ṽ	ṽ	PROPN
ejpam-3515	259	13	with	with	ADP
ejpam-3515	259	14	a−property	a−property	NOUN
ejpam-3515	259	15	of	of	ADP
ejpam-3515	259	16	the	the	DET
ejpam-3515	259	17	function	function	NOUN
ejpam-3515	259	18	ṽ	ṽ	PROPN
ejpam-3515	259	19	ψ(t	ψ(t	PROPN
ejpam-3515	259	20	,	,	PUNCT
ejpam-3515	259	21	x	x	PRON
ejpam-3515	259	22	)	)	PUNCT
ejpam-3515	259	23	belongs	belong	VERB
ejpam-3515	259	24	to	to	ADP
ejpam-3515	259	25	the	the	DET
ejpam-3515	259	26	sobolev	sobolev	PROPN
ejpam-3515	259	27	space	space	PROPN
ejpam-3515	259	28	wm	wm	PROPN
ejpam-3515	259	29	,	,	PUNCT
ejpam-3515	259	30	m	m	VERB
ejpam-3515	259	31	=	=	NOUN
ejpam-3515	259	32	0	0	NUM
ejpam-3515	259	33	,	,	PUNCT
ejpam-3515	259	34	1	1	NUM
ejpam-3515	259	35	,	,	PUNCT
ejpam-3515	259	36	2	2	NUM
ejpam-3515	259	37	,	,	PUNCT
ejpam-3515	259	38	...	...	PUNCT
ejpam-3515	259	39	,	,	PUNCT
ejpam-3515	259	40	for	for	ADP
ejpam-3515	259	41	almost	almost	ADV
ejpam-3515	259	42	every	every	PRON
ejpam-3515	259	43	v	v	NOUN
ejpam-3515	259	44	,	,	PUNCT
ejpam-3515	259	45	b.	b.	PROPN
ejpam-3515	259	46	consider	consider	VERB
ejpam-3515	259	47	a	a	DET
ejpam-3515	259	48	sequence	sequence	NOUN
ejpam-3515	259	49	of	of	ADP
ejpam-3515	259	50	smooth	smooth	ADJ
ejpam-3515	259	51	function	function	NOUN
ejpam-3515	259	52	λν(x	λν(x	NOUN
ejpam-3515	259	53	)	)	PUNCT
ejpam-3515	259	54	such	such	ADJ
ejpam-3515	259	55	that	that	SCONJ
ejpam-3515	259	56	(	(	PUNCT
ejpam-3515	259	57	a	a	NOUN
ejpam-3515	259	58	)	)	PUNCT
ejpam-3515	259	59	λν(x	λν(x	PUNCT
ejpam-3515	259	60	)	)	PUNCT
ejpam-3515	259	61	=	=	SYM
ejpam-3515	259	62	0	0	PUNCT
ejpam-3515	260	1	if	if	SCONJ
ejpam-3515	260	2	d(x	d(x	PROPN
ejpam-3515	260	3	,	,	PUNCT
ejpam-3515	260	4	a	a	PRON
ejpam-3515	260	5	)	)	PUNCT
ejpam-3515	260	6	<	<	X
ejpam-3515	260	7	1	1	NUM
ejpam-3515	260	8	ν	ν	NOUN
ejpam-3515	260	9	or	or	CCONJ
ejpam-3515	260	10	d(x	d(x	PROPN
ejpam-3515	260	11	,	,	PUNCT
ejpam-3515	260	12	a	a	PRON
ejpam-3515	260	13	)	)	PUNCT
ejpam-3515	260	14	>	>	X
ejpam-3515	261	1	ν	ν	X
ejpam-3515	261	2	(	(	PUNCT
ejpam-3515	261	3	b	b	NOUN
ejpam-3515	261	4	)	)	PUNCT
ejpam-3515	261	5	λν(x	λν(x	PUNCT
ejpam-3515	261	6	)	)	PUNCT
ejpam-3515	261	7	=	=	SYM
ejpam-3515	261	8	1	1	NUM
ejpam-3515	261	9	if	if	SCONJ
ejpam-3515	261	10	2	2	NUM
ejpam-3515	261	11	ν	ν	NOUN
ejpam-3515	261	12	<	<	X
ejpam-3515	261	13	d(x	d(x	PROPN
ejpam-3515	261	14	,	,	PUNCT
ejpam-3515	261	15	a	a	PRON
ejpam-3515	261	16	)	)	PUNCT
ejpam-3515	261	17	<	<	X
ejpam-3515	261	18	ν	ν	X
ejpam-3515	261	19	−	−	PROPN
ejpam-3515	261	20	1	1	NUM
ejpam-3515	261	21	(	(	PUNCT
ejpam-3515	261	22	c	c	NOUN
ejpam-3515	261	23	)	)	PUNCT
ejpam-3515	261	24	max|α|≤2	max|α|≤2	NOUN
ejpam-3515	261	25	∣∣	∣∣	X
ejpam-3515	261	26	∂α	∂α	PROPN
ejpam-3515	261	27	∂xαλν(x	∂xαλν(x	X
ejpam-3515	261	28	)	)	PUNCT
ejpam-3515	261	29	∣∣	∣∣	NUM
ejpam-3515	261	30	≤mνs	≤mνs	PROPN
ejpam-3515	261	31	,	,	PUNCT
ejpam-3515	261	32	where	where	SCONJ
ejpam-3515	261	33	m	m	VERB
ejpam-3515	261	34	,	,	PUNCT
ejpam-3515	261	35	s	s	VERB
ejpam-3515	261	36	are	be	AUX
ejpam-3515	261	37	constant	constant	ADJ
ejpam-3515	261	38	.	.	PUNCT
ejpam-3515	262	1	let	let	VERB
ejpam-3515	262	2	m	m	VERB
ejpam-3515	262	3	=	=	NOUN
ejpam-3515	262	4	0	0	X
ejpam-3515	262	5	.	.	PUNCT
ejpam-3515	263	1	we	we	PRON
ejpam-3515	263	2	record	record	VERB
ejpam-3515	263	3	e|ψ(t	e|ψ(t	PROPN
ejpam-3515	263	4	,	,	PUNCT
ejpam-3515	263	5	x)ṽ	x)ṽ	NUM
ejpam-3515	263	6	(	(	PUNCT
ejpam-3515	263	7	x)|2	x)|2	PROPN
ejpam-3515	263	8	≤	≤	PROPN
ejpam-3515	263	9	(	(	PUNCT
ejpam-3515	263	10	e(ψ(t	e(ψ(t	PROPN
ejpam-3515	263	11	,	,	PUNCT
ejpam-3515	263	12	x))4	x))4	PROPN
ejpam-3515	263	13	)	)	PUNCT
ejpam-3515	263	14	1	1	NUM
ejpam-3515	263	15	2	2	NUM
ejpam-3515	263	16	(	(	PUNCT
ejpam-3515	263	17	e(ṽ	e(ṽ	PROPN
ejpam-3515	263	18	(	(	PUNCT
ejpam-3515	263	19	x))4	x))4	PROPN
ejpam-3515	263	20	)	)	PUNCT
ejpam-3515	263	21	1	1	NUM
ejpam-3515	263	22	2	2	NUM
ejpam-3515	263	23	≤	≤	NUM
ejpam-3515	263	24	β̃0	β̃0	NOUN
ejpam-3515	263	25	,	,	PUNCT
ejpam-3515	263	26	(	(	PUNCT
ejpam-3515	263	27	2.11	2.11	NUM
ejpam-3515	263	28	)	)	PUNCT
ejpam-3515	263	29	where	where	SCONJ
ejpam-3515	263	30	β̃0	β̃0	NOUN
ejpam-3515	263	31	is	be	AUX
ejpam-3515	263	32	some	some	PRON
ejpam-3515	263	33	constant	constant	ADJ
ejpam-3515	263	34	.	.	PUNCT
ejpam-3515	264	1	now	now	ADV
ejpam-3515	264	2	,	,	PUNCT
ejpam-3515	264	3	it	it	PRON
ejpam-3515	264	4	follows	follow	VERB
ejpam-3515	264	5	from	from	ADP
ejpam-3515	264	6	(	(	PUNCT
ejpam-3515	264	7	2.11	2.11	NUM
ejpam-3515	264	8	)	)	PUNCT
ejpam-3515	264	9	and	and	CCONJ
ejpam-3515	264	10	corollary(2.2)in	corollary(2.2)in	X
ejpam-3515	265	1	[	[	X
ejpam-3515	265	2	8	8	NUM
ejpam-3515	265	3	]	]	PUNCT
ejpam-3515	265	4	that	that	SCONJ
ejpam-3515	265	5	e	e	PROPN
ejpam-3515	265	6	(	(	PUNCT
ejpam-3515	265	7	∫	∫	PROPN
ejpam-3515	265	8	rn	rn	PROPN
ejpam-3515	265	9	|ψ(t	|ψ(t	PROPN
ejpam-3515	265	10	,	,	PUNCT
ejpam-3515	265	11	x)ṽ	x)ṽ	PROPN
ejpam-3515	265	12	(	(	PUNCT
ejpam-3515	265	13	x)|2	x)|2	PROPN
ejpam-3515	265	14	)	)	PUNCT
ejpam-3515	265	15	dx	dx	PROPN
ejpam-3515	265	16	≤	≤	PROPN
ejpam-3515	265	17	β0	β0	PROPN
ejpam-3515	265	18	,	,	PUNCT
ejpam-3515	265	19	where	where	SCONJ
ejpam-3515	265	20	β0	β0	PROPN
ejpam-3515	265	21	is	be	AUX
ejpam-3515	265	22	a	a	DET
ejpam-3515	265	23	constant	constant	ADJ
ejpam-3515	265	24	.	.	PUNCT
ejpam-3515	266	1	we	we	PRON
ejpam-3515	266	2	can	can	AUX
ejpam-3515	266	3	write	write	VERB
ejpam-3515	266	4	for	for	ADP
ejpam-3515	266	5	any	any	DET
ejpam-3515	266	6	h(x	h(x	PROPN
ejpam-3515	266	7	)	)	PUNCT
ejpam-3515	266	8	,	,	PUNCT
ejpam-3515	266	9	θ(v	θ(v	NOUN
ejpam-3515	266	10	)	)	PUNCT
ejpam-3515	266	11	e	e	NOUN
ejpam-3515	266	12	∫	∫	NUM
ejpam-3515	266	13	ṽ	ṽ	PROPN
ejpam-3515	266	14	(	(	PUNCT
ejpam-3515	266	15	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	266	16	,	,	PUNCT
ejpam-3515	266	17	x	x	X
ejpam-3515	266	18	)	)	PUNCT
ejpam-3515	266	19			PROPN
ejpam-3515	266	20	n∑	n∑	NOUN
ejpam-3515	266	21	j=1	j=1	NOUN
ejpam-3515	266	22	1	1	NUM
ejpam-3515	266	23	2	2	NUM
ejpam-3515	266	24	(	(	PUNCT
ejpam-3515	266	25	i∂j	i∂j	VERB
ejpam-3515	266	26	+	+	CCONJ
ejpam-3515	266	27	bj	bj	NOUN
ejpam-3515	266	28	)	)	PUNCT
ejpam-3515	266	29	2	2	NUM
ejpam-3515	266	30	h(x)θ(v	h(x)θ(v	PROPN
ejpam-3515	266	31	)	)	PUNCT
ejpam-3515	266	32			PROPN
ejpam-3515	266	33	dx	dx	PROPN
ejpam-3515	266	34	=	=	SYM
ejpam-3515	266	35	lim	lim	PROPN
ejpam-3515	266	36	ν→∞	ν→∞	NUM
ejpam-3515	266	37	∫	∫	NUM
ejpam-3515	266	38	ṽ	ṽ	PROPN
ejpam-3515	266	39	(	(	PUNCT
ejpam-3515	266	40	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	266	41	,	,	PUNCT
ejpam-3515	266	42	x	x	X
ejpam-3515	266	43	)	)	PUNCT
ejpam-3515	266	44			PROPN
ejpam-3515	266	45	n∑	n∑	NOUN
ejpam-3515	266	46	j=1	j=1	NOUN
ejpam-3515	266	47	1	1	NUM
ejpam-3515	266	48	2	2	NUM
ejpam-3515	266	49	(	(	PUNCT
ejpam-3515	266	50	i∂j	i∂j	VERB
ejpam-3515	266	51	+	+	CCONJ
ejpam-3515	266	52	bj	bj	NOUN
ejpam-3515	266	53	)	)	PUNCT
ejpam-3515	266	54	2	2	NUM
ejpam-3515	266	55	λνh(x)θ(v	λνh(x)θ(v	NOUN
ejpam-3515	266	56	)	)	PUNCT
ejpam-3515	267	1			PROPN
ejpam-3515	267	2	dx	dx	PROPN
ejpam-3515	267	3	=	=	SYM
ejpam-3515	267	4	lim	lim	PROPN
ejpam-3515	267	5	ν→∞	ν→∞	X
ejpam-3515	267	6	(	(	PUNCT
ejpam-3515	267	7	∫	∫	PROPN
ejpam-3515	267	8	ṽ	ṽ	PROPN
ejpam-3515	267	9	(	(	PUNCT
ejpam-3515	267	10	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	267	11	,	,	PUNCT
ejpam-3515	267	12	x	x	X
ejpam-3515	267	13	)	)	PUNCT
ejpam-3515	267	14			VERB
ejpam-3515	267	15	n∑	n∑	NOUN
ejpam-3515	268	1	j=1	j=1	NOUN
ejpam-3515	268	2	1	1	NUM
ejpam-3515	268	3	2	2	NUM
ejpam-3515	268	4	(	(	PUNCT
ejpam-3515	268	5	i∂j	i∂j	VERB
ejpam-3515	268	6	+	+	CCONJ
ejpam-3515	268	7	bj	bj	NOUN
ejpam-3515	268	8	)	)	PUNCT
ejpam-3515	268	9	2	2	NUM
ejpam-3515	268	10			PROPN
ejpam-3515	268	11	(	(	PUNCT
ejpam-3515	268	12	ṽ	ṽ	PROPN
ejpam-3515	268	13	λνh(x	λνh(x	PROPN
ejpam-3515	268	14	)	)	PUNCT
ejpam-3515	268	15	)	)	PUNCT
ejpam-3515	269	1	+	+	CCONJ
ejpam-3515	269	2	v	v	AUX
ejpam-3515	269	3	ṽ	ṽ	PROPN
ejpam-3515	269	4	λνh(x	λνh(x	PROPN
ejpam-3515	269	5	)	)	PUNCT
ejpam-3515	269	6	−	−	X
ejpam-3515	269	7	v	v	ADP
ejpam-3515	269	8	ṽ	ṽ	PROPN
ejpam-3515	269	9	ψ(t	ψ(t	PROPN
ejpam-3515	269	10	,	,	PUNCT
ejpam-3515	269	11	x)λνh(x	x)λνh(x	PROPN
ejpam-3515	269	12	)	)	PUNCT
ejpam-3515	270	1	y.	y.	PROPN
ejpam-3515	270	2	h.	h.	PROPN
ejpam-3515	270	3	saleem	saleem	PROPN
ejpam-3515	270	4	,	,	PUNCT
ejpam-3515	270	5	h.	h.	PROPN
ejpam-3515	270	6	a.	a.	PROPN
ejpam-3515	270	7	shubber	shubber	PROPN
ejpam-3515	270	8	/	/	SYM
ejpam-3515	270	9	eur	eur	PROPN
ejpam-3515	270	10	.	.	PUNCT
ejpam-3515	271	1	j.	j.	PROPN
ejpam-3515	271	2	pure	pure	PROPN
ejpam-3515	271	3	appl	appl	PROPN
ejpam-3515	271	4	.	.	PROPN
ejpam-3515	271	5	math	math	PROPN
ejpam-3515	271	6	,	,	PUNCT
ejpam-3515	271	7	12	12	NUM
ejpam-3515	271	8	(	(	PUNCT
ejpam-3515	271	9	4	4	NUM
ejpam-3515	271	10	)	)	PUNCT
ejpam-3515	271	11	(	(	PUNCT
ejpam-3515	271	12	2019	2019	NUM
ejpam-3515	271	13	)	)	PUNCT
ejpam-3515	271	14	,	,	PUNCT
ejpam-3515	271	15	1441	1441	NUM
ejpam-3515	271	16	-	-	SYM
ejpam-3515	271	17	1454	1454	NUM
ejpam-3515	271	18	1452	1452	NUM
ejpam-3515	271	19	−ψ(t	−ψ(t	PROPN
ejpam-3515	271	20	,	,	PUNCT
ejpam-3515	271	21	x)λνh(x	x)λνh(x	NUM
ejpam-3515	271	22	)	)	PUNCT
ejpam-3515	272	1			PROPN
ejpam-3515	272	2	n∑	n∑	NOUN
ejpam-3515	272	3	j=1	j=1	NOUN
ejpam-3515	272	4	1	1	NUM
ejpam-3515	272	5	2	2	NUM
ejpam-3515	272	6	(	(	PUNCT
ejpam-3515	272	7	i∂j	i∂j	VERB
ejpam-3515	272	8	+	+	CCONJ
ejpam-3515	272	9	bj	bj	NOUN
ejpam-3515	272	10	)	)	PUNCT
ejpam-3515	272	11	2	2	NUM
ejpam-3515	272	12			PROPN
ejpam-3515	272	13	ṽ−2ψ(t	ṽ−2ψ(t	NUM
ejpam-3515	272	14	,	,	PUNCT
ejpam-3515	272	15	x	x	NOUN
ejpam-3515	272	16	)	)	PUNCT
ejpam-3515	272	17			PROPN
ejpam-3515	272	18	n∑	n∑	PROPN
ejpam-3515	272	19	j=1	j=1	NOUN
ejpam-3515	272	20	−1	−1	NOUN
ejpam-3515	272	21	2	2	NUM
ejpam-3515	272	22	∂j(ṽ	∂j(ṽ	ADV
ejpam-3515	272	23	)	)	PUNCT
ejpam-3515	272	24			PUNCT
ejpam-3515	273	1	n∑	n∑	PUNCT
ejpam-3515	273	2	j=1	j=1	ADJ
ejpam-3515	273	3	−1	−1	NOUN
ejpam-3515	273	4	2	2	NUM
ejpam-3515	273	5	∂j(λνh	∂j(λνh	NOUN
ejpam-3515	273	6	)	)	PUNCT
ejpam-3515	273	7	)θ(v	)θ(v	NOUN
ejpam-3515	273	8	)	)	PUNCT
ejpam-3515	273	9	dx	dx	PROPN
ejpam-3515	273	10	.	.	PUNCT
ejpam-3515	274	1	since	since	SCONJ
ejpam-3515	274	2	the	the	DET
ejpam-3515	274	3	support	support	NOUN
ejpam-3515	274	4	of	of	ADP
ejpam-3515	274	5	the	the	DET
ejpam-3515	274	6	functions	function	NOUN
ejpam-3515	274	7	h̃(x	h̃(x	PROPN
ejpam-3515	274	8	)	)	PUNCT
ejpam-3515	274	9	=	=	PROPN
ejpam-3515	274	10	ṽ	ṽ	PROPN
ejpam-3515	274	11	(	(	PUNCT
ejpam-3515	274	12	x)λνh(x	x)λνh(x	PROPN
ejpam-3515	274	13	)	)	PUNCT
ejpam-3515	274	14	is	be	AUX
ejpam-3515	274	15	disjoint	disjoint	ADJ
ejpam-3515	274	16	with	with	ADP
ejpam-3515	274	17	the	the	DET
ejpam-3515	274	18	neighborhood	neighborhood	NOUN
ejpam-3515	274	19	of	of	ADP
ejpam-3515	274	20	the	the	DET
ejpam-3515	274	21	point	point	NOUN
ejpam-3515	274	22	x	x	X
ejpam-3515	274	23	∈	∈	PROPN
ejpam-3515	274	24	a	a	X
ejpam-3515	274	25	,	,	PUNCT
ejpam-3515	274	26	we	we	PRON
ejpam-3515	274	27	can	can	AUX
ejpam-3515	274	28	repeat	repeat	VERB
ejpam-3515	274	29	literally	literally	ADV
ejpam-3515	274	30	for	for	ADP
ejpam-3515	274	31	h̃(x)θ(v	h̃(x)θ(v	NOUN
ejpam-3515	274	32	)	)	PUNCT
ejpam-3515	274	33	all	all	DET
ejpam-3515	274	34	the	the	DET
ejpam-3515	274	35	arguments	argument	NOUN
ejpam-3515	274	36	which	which	PRON
ejpam-3515	274	37	we	we	PRON
ejpam-3515	274	38	have	have	AUX
ejpam-3515	274	39	stated	state	VERB
ejpam-3515	274	40	in	in	ADP
ejpam-3515	274	41	the	the	DET
ejpam-3515	274	42	case	case	NOUN
ejpam-3515	274	43	when	when	SCONJ
ejpam-3515	274	44	v	v	X
ejpam-3515	274	45	(	(	PUNCT
ejpam-3515	274	46	x	x	X
ejpam-3515	274	47	)	)	PUNCT
ejpam-3515	274	48	has	have	VERB
ejpam-3515	274	49	no	no	DET
ejpam-3515	274	50	singular	singular	ADJ
ejpam-3515	274	51	points	point	NOUN
ejpam-3515	274	52	.	.	PUNCT
ejpam-3515	275	1	we	we	PRON
ejpam-3515	275	2	have	have	VERB
ejpam-3515	275	3	then	then	ADV
ejpam-3515	275	4	e	e	X
ejpam-3515	275	5	(	(	PUNCT
ejpam-3515	275	6	∫	∫	PROPN
ejpam-3515	275	7	ψ(t	ψ(t	PROPN
ejpam-3515	275	8	,	,	PUNCT
ejpam-3515	275	9	x)hh̃(x)θ(v	x)hh̃(x)θ(v	NUM
ejpam-3515	275	10	)	)	PUNCT
ejpam-3515	275	11	)	)	PUNCT
ejpam-3515	275	12	dx	dx	PROPN
ejpam-3515	276	1	=	=	SYM
ejpam-3515	276	2	e	e	PROPN
ejpam-3515	276	3	(	(	PUNCT
ejpam-3515	276	4	∫	∫	PROPN
ejpam-3515	276	5	ψ	ψ	X
ejpam-3515	276	6	(	(	PUNCT
ejpam-3515	276	7	1)(t	1)(t	NUM
ejpam-3515	276	8	,	,	PUNCT
ejpam-3515	276	9	x)h̃(x)θ(v	x)h̃(x)θ(v	PROPN
ejpam-3515	276	10	)	)	PUNCT
ejpam-3515	276	11	)	)	PUNCT
ejpam-3515	277	1	dx	dx	PROPN
ejpam-3515	277	2	,	,	PUNCT
ejpam-3515	277	3	where	where	SCONJ
ejpam-3515	277	4	ψ1(t	ψ1(t	ADP
ejpam-3515	277	5	,	,	PUNCT
ejpam-3515	277	6	x	x	X
ejpam-3515	277	7	)	)	PUNCT
ejpam-3515	277	8	corresponds	correspond	VERB
ejpam-3515	277	9	to	to	ADP
ejpam-3515	277	10	the	the	DET
ejpam-3515	277	11	function	function	NOUN
ejpam-3515	277	12	ϕ(1)(x	ϕ(1)(x	NOUN
ejpam-3515	277	13	)	)	PUNCT
ejpam-3515	277	14	=	=	SYM
ejpam-3515	277	15	hϕ(x	hϕ(x	NUM
ejpam-3515	277	16	)	)	PUNCT
ejpam-3515	277	17	.	.	PUNCT
ejpam-3515	278	1	thus	thus	ADV
ejpam-3515	278	2	,	,	PUNCT
ejpam-3515	278	3	we	we	PRON
ejpam-3515	278	4	have	have	VERB
ejpam-3515	278	5	lim	lim	PROPN
ejpam-3515	278	6	ν→∞	ν→∞	NUM
ejpam-3515	278	7	e	e	PART
ejpam-3515	278	8	∫	∫	NUM
ejpam-3515	278	9	ψ(t	ψ(t	PROPN
ejpam-3515	278	10	,	,	PUNCT
ejpam-3515	278	11	x	x	NOUN
ejpam-3515	278	12	)	)	PUNCT
ejpam-3515	278	13			VERB
ejpam-3515	279	1	n∑	n∑	NOUN
ejpam-3515	280	1	j=1	j=1	NOUN
ejpam-3515	280	2	1	1	NUM
ejpam-3515	280	3	2	2	NUM
ejpam-3515	280	4	(	(	PUNCT
ejpam-3515	280	5	i∂j	i∂j	VERB
ejpam-3515	280	6	+	+	CCONJ
ejpam-3515	280	7	bj	bj	NOUN
ejpam-3515	280	8	)	)	PUNCT
ejpam-3515	280	9	2	2	NUM
ejpam-3515	280	10			PROPN
ejpam-3515	280	11	(	(	PUNCT
ejpam-3515	280	12	ṽ	ṽ	PROPN
ejpam-3515	280	13	λνh(x	λνh(x	PROPN
ejpam-3515	280	14	)	)	PUNCT
ejpam-3515	280	15	)	)	PUNCT
ejpam-3515	281	1	+	+	CCONJ
ejpam-3515	281	2	v	v	AUX
ejpam-3515	281	3	ṽ	ṽ	PROPN
ejpam-3515	281	4	λνh(x	λνh(x	PROPN
ejpam-3515	281	5	)	)	PUNCT
ejpam-3515	281	6			NOUN
ejpam-3515	281	7	θ(v	θ(v	NOUN
ejpam-3515	281	8	)	)	PUNCT
ejpam-3515	282	1			PROPN
ejpam-3515	282	2	dx	dx	PROPN
ejpam-3515	282	3	=	=	SYM
ejpam-3515	282	4	lim	lim	PROPN
ejpam-3515	282	5	ν→∞	ν→∞	NUM
ejpam-3515	282	6	e	e	X
ejpam-3515	282	7	(	(	PUNCT
ejpam-3515	282	8	∫	∫	PROPN
ejpam-3515	282	9	ψ	ψ	X
ejpam-3515	282	10	(	(	PUNCT
ejpam-3515	282	11	1)(t	1)(t	NUM
ejpam-3515	282	12	,	,	PUNCT
ejpam-3515	282	13	x)(ṽ	x)(ṽ	PROPN
ejpam-3515	282	14	λνh(x))θ(v	λνh(x))θ(v	NOUN
ejpam-3515	282	15	)	)	PUNCT
ejpam-3515	282	16	)	)	PUNCT
ejpam-3515	283	1	dx	dx	PROPN
ejpam-3515	283	2	.	.	PUNCT
ejpam-3515	284	1	in	in	ADP
ejpam-3515	284	2	addition	addition	NOUN
ejpam-3515	284	3	,	,	PUNCT
ejpam-3515	284	4	|e	|e	PROPN
ejpam-3515	284	5	(	(	PUNCT
ejpam-3515	284	6	∫	∫	PROPN
ejpam-3515	284	7	v	v	NUM
ejpam-3515	284	8	ṽ	ṽ	PROPN
ejpam-3515	284	9	ψ(t	ψ(t	PROPN
ejpam-3515	284	10	,	,	PUNCT
ejpam-3515	284	11	x)h(x)θ(v	x)h(x)θ(v	NUM
ejpam-3515	284	12	)	)	PUNCT
ejpam-3515	284	13	)	)	PUNCT
ejpam-3515	284	14	dx|	dx|	PROPN
ejpam-3515	284	15	≤	≤	PROPN
ejpam-3515	284	16	const	const	X
ejpam-3515	284	17	∫	∫	PROPN
ejpam-3515	284	18	e(v	e(v	PROPN
ejpam-3515	284	19	(	(	PUNCT
ejpam-3515	284	20	x)2|ψ(t	x)2|ψ(t	PROPN
ejpam-3515	284	21	,	,	PUNCT
ejpam-3515	284	22	x)|	x)|	PROPN
ejpam-3515	284	23	)	)	PUNCT
ejpam-3515	284	24	1	1	NUM
ejpam-3515	284	25	2e(ṽ	2e(ṽ	NUM
ejpam-3515	284	26	(	(	PUNCT
ejpam-3515	284	27	x)2|ψ(t	x)2|ψ(t	PROPN
ejpam-3515	284	28	,	,	PUNCT
ejpam-3515	284	29	x)|	x)|	PROPN
ejpam-3515	284	30	)	)	PUNCT
ejpam-3515	284	31	1	1	NUM
ejpam-3515	284	32	2dx	2dx	NOUN
ejpam-3515	284	33	;	;	PUNCT
ejpam-3515	285	1	e(ṽ	e(ṽ	PROPN
ejpam-3515	285	2	(	(	PUNCT
ejpam-3515	285	3	x)2|ψ(t	x)2|ψ(t	PROPN
ejpam-3515	285	4	,	,	PUNCT
ejpam-3515	285	5	x)|	x)|	PROPN
ejpam-3515	285	6	)	)	PUNCT
ejpam-3515	285	7	≤	≤	PROPN
ejpam-3515	285	8	e(ṽ	e(ṽ	PROPN
ejpam-3515	285	9	(	(	PUNCT
ejpam-3515	285	10	x)4	x)4	PROPN
ejpam-3515	285	11	)	)	PUNCT
ejpam-3515	285	12	1	1	NUM
ejpam-3515	285	13	2e(ψ(t	2e(ψ(t	NUM
ejpam-3515	285	14	,	,	PUNCT
ejpam-3515	285	15	x))2	x))2	PROPN
ejpam-3515	285	16	)	)	PUNCT
ejpam-3515	285	17	1	1	NUM
ejpam-3515	285	18	2	2	NUM
ejpam-3515	285	19	≤	≤	NUM
ejpam-3515	285	20	const	const	NOUN
ejpam-3515	285	21	exp	exp	NOUN
ejpam-3515	285	22	(	(	PUNCT
ejpam-3515	285	23	−	−	PROPN
ejpam-3515	285	24	l−1∑	l−1∑	ADJ
ejpam-3515	285	25	k=0	k=0	PROPN
ejpam-3515	285	26	(	(	PUNCT
ejpam-3515	285	27	tk+1	tk+1	NUM
ejpam-3515	285	28	−	−	PROPN
ejpam-3515	285	29	tk)(bk)2	tk)(bk)2	PRON
ejpam-3515	285	30	)	)	PUNCT
ejpam-3515	285	31	exp	exp	NOUN
ejpam-3515	285	32	(	(	PUNCT
ejpam-3515	285	33	−(x−	−(x−	NOUN
ejpam-3515	285	34	α)2	α)2	NOUN
ejpam-3515	285	35	ct	ct	PROPN
ejpam-3515	285	36	)	)	PUNCT
ejpam-3515	285	37	,	,	PUNCT
ejpam-3515	285	38	where	where	SCONJ
ejpam-3515	285	39	c	c	X
ejpam-3515	285	40	>	>	X
ejpam-3515	285	41	0	0	PROPN
ejpam-3515	285	42	is	be	AUX
ejpam-3515	285	43	constants	constant	NOUN
ejpam-3515	285	44	.	.	PUNCT
ejpam-3515	286	1	the	the	DET
ejpam-3515	286	2	similar	similar	ADJ
ejpam-3515	286	3	estimate	estimate	NOUN
ejpam-3515	286	4	is	be	AUX
ejpam-3515	286	5	true	true	ADJ
ejpam-3515	286	6	if	if	SCONJ
ejpam-3515	286	7	we	we	PRON
ejpam-3515	286	8	replace	replace	VERB
ejpam-3515	286	9	ṽ	ṽ	PROPN
ejpam-3515	286	10	by	by	ADP
ejpam-3515	286	11	∑n	∑n	PROPN
ejpam-3515	286	12	j=1	j=1	PROPN
ejpam-3515	286	13	1	1	NUM
ejpam-3515	286	14	2∂j	2∂j	NUM
ejpam-3515	286	15	ṽ	ṽ	PROPN
ejpam-3515	286	16	or(∑n	or(∑n	PROPN
ejpam-3515	286	17	j=1	j=1	PROPN
ejpam-3515	286	18	1	1	NUM
ejpam-3515	286	19	2(i∂j	2(i∂j	NUM
ejpam-3515	286	20	+	+	CCONJ
ejpam-3515	286	21	bj	bj	NOUN
ejpam-3515	286	22	)	)	PUNCT
ejpam-3515	286	23	2	2	NUM
ejpam-3515	286	24	)	)	PUNCT
ejpam-3515	286	25	(	(	PUNCT
ejpam-3515	286	26	ṽ	ṽ	PROPN
ejpam-3515	286	27	)	)	PUNCT
ejpam-3515	286	28	(	(	PUNCT
ejpam-3515	286	29	we	we	PRON
ejpam-3515	286	30	use	use	VERB
ejpam-3515	286	31	the	the	DET
ejpam-3515	286	32	a−property	a−property	NOUN
ejpam-3515	286	33	)	)	PUNCT
ejpam-3515	286	34	.	.	PUNCT
ejpam-3515	287	1	since	since	SCONJ
ejpam-3515	287	2	λν(x	λν(x	NOUN
ejpam-3515	287	3	)	)	PUNCT
ejpam-3515	287	4	is	be	AUX
ejpam-3515	287	5	bounded	bound	VERB
ejpam-3515	287	6	and	and	CCONJ
ejpam-3515	287	7	λν(x	λν(x	PRON
ejpam-3515	287	8	)	)	PUNCT
ejpam-3515	287	9	6=	6=	ADP
ejpam-3515	287	10	1	1	NUM
ejpam-3515	287	11	whenever	whenever	SCONJ
ejpam-3515	287	12	d(x	d(x	PROPN
ejpam-3515	287	13	,	,	PUNCT
ejpam-3515	287	14	a	a	PRON
ejpam-3515	287	15	)	)	PUNCT
ejpam-3515	287	16	<	<	X
ejpam-3515	287	17	2	2	NUM
ejpam-3515	287	18	ν	ν	NOUN
ejpam-3515	287	19	or	or	CCONJ
ejpam-3515	287	20	d(x	d(x	PROPN
ejpam-3515	287	21	,	,	PUNCT
ejpam-3515	287	22	a	a	PRON
ejpam-3515	287	23	)	)	PUNCT
ejpam-3515	287	24	>	>	PUNCT
ejpam-3515	288	1	ν	ν	X
ejpam-3515	288	2	−	−	NOUN
ejpam-3515	288	3	1	1	NUM
ejpam-3515	288	4	,	,	PUNCT
ejpam-3515	288	5	we	we	PRON
ejpam-3515	288	6	have	have	VERB
ejpam-3515	288	7	e	e	NOUN
ejpam-3515	288	8	(	(	PUNCT
ejpam-3515	288	9	∫	∫	PROPN
ejpam-3515	288	10	−v	−v	PROPN
ejpam-3515	288	11	ṽ	ṽ	PROPN
ejpam-3515	288	12	ψ(t	ψ(t	PROPN
ejpam-3515	288	13	,	,	PUNCT
ejpam-3515	288	14	x)λνh(x)−ψ(t	x)λνh(x)−ψ(t	PROPN
ejpam-3515	288	15	,	,	PUNCT
ejpam-3515	288	16	x)λνh(x	x)λνh(x	NUM
ejpam-3515	288	17	)	)	PUNCT
ejpam-3515	289	1			PROPN
ejpam-3515	289	2	n∑	n∑	NOUN
ejpam-3515	289	3	j=1	j=1	NOUN
ejpam-3515	289	4	1	1	NUM
ejpam-3515	289	5	2	2	NUM
ejpam-3515	289	6	(	(	PUNCT
ejpam-3515	289	7	i∂j	i∂j	VERB
ejpam-3515	289	8	+	+	CCONJ
ejpam-3515	289	9	bj	bj	NOUN
ejpam-3515	289	10	)	)	PUNCT
ejpam-3515	289	11	2	2	NUM
ejpam-3515	289	12			PROPN
ejpam-3515	289	13	ṽ	ṽ	PROPN
ejpam-3515	289	14	−2ψ(t	−2ψ(t	PROPN
ejpam-3515	289	15	,	,	PUNCT
ejpam-3515	289	16	x	x	NOUN
ejpam-3515	289	17	)	)	PUNCT
ejpam-3515	289	18			PROPN
ejpam-3515	289	19	n∑	n∑	PROPN
ejpam-3515	289	20	j=1	j=1	NOUN
ejpam-3515	289	21	−1	−1	NOUN
ejpam-3515	289	22	2	2	NUM
ejpam-3515	289	23	∂j(ṽ	∂j(ṽ	NOUN
ejpam-3515	289	24	)	)	PUNCT
ejpam-3515	290	1			PROPN
ejpam-3515	290	2			PROPN
ejpam-3515	290	3	n∑	n∑	PROPN
ejpam-3515	290	4	j=1	j=1	NOUN
ejpam-3515	290	5	−1	−1	NOUN
ejpam-3515	290	6	2	2	NUM
ejpam-3515	290	7	∂j(λνh	∂j(λνh	NOUN
ejpam-3515	290	8	)	)	PUNCT
ejpam-3515	290	9	)θ(v	)θ(v	NOUN
ejpam-3515	290	10	)	)	PUNCT
ejpam-3515	290	11	dx−	dx−	X
ejpam-3515	291	1	e	e	X
ejpam-3515	291	2	(	(	PUNCT
ejpam-3515	291	3	∫	∫	PROPN
ejpam-3515	291	4	v	v	NUM
ejpam-3515	291	5	ṽ	ṽ	PROPN
ejpam-3515	291	6	ψ(t	ψ(t	PROPN
ejpam-3515	291	7	,	,	PUNCT
ejpam-3515	291	8	x)h(x)−	x)h(x)−	PROPN
ejpam-3515	291	9	ψ(t	ψ(t	PROPN
ejpam-3515	291	10	,	,	PUNCT
ejpam-3515	291	11	x)h(x	x)h(x	PUNCT
ejpam-3515	291	12	)	)	PUNCT
ejpam-3515	292	1			PROPN
ejpam-3515	292	2	n∑	n∑	NOUN
ejpam-3515	292	3	j=1	j=1	NOUN
ejpam-3515	292	4	1	1	NUM
ejpam-3515	292	5	2	2	NUM
ejpam-3515	292	6	(	(	PUNCT
ejpam-3515	292	7	i∂j	i∂j	VERB
ejpam-3515	292	8	+	+	CCONJ
ejpam-3515	292	9	bj	bj	NOUN
ejpam-3515	292	10	)	)	PUNCT
ejpam-3515	292	11	2	2	NUM
ejpam-3515	292	12			PROPN
ejpam-3515	292	13	ṽ	ṽ	PROPN
ejpam-3515	292	14	−2ψ(t	−2ψ(t	PROPN
ejpam-3515	292	15	,	,	PUNCT
ejpam-3515	292	16	x	x	NOUN
ejpam-3515	292	17	)	)	PUNCT
ejpam-3515	292	18			PROPN
ejpam-3515	292	19	n∑	n∑	PROPN
ejpam-3515	292	20	j=1	j=1	NOUN
ejpam-3515	292	21	−1	−1	NOUN
ejpam-3515	292	22	2	2	NUM
ejpam-3515	292	23	∂j(ṽ	∂j(ṽ	ADV
ejpam-3515	292	24	)	)	PUNCT
ejpam-3515	292	25			PUNCT
ejpam-3515	293	1	n∑	n∑	PUNCT
ejpam-3515	293	2	j=1	j=1	ADJ
ejpam-3515	293	3	−1	−1	NOUN
ejpam-3515	293	4	2	2	NUM
ejpam-3515	293	5	∂jh	∂jh	PROPN
ejpam-3515	293	6	)θ(v	)θ(v	NOUN
ejpam-3515	293	7	)	)	PUNCT
ejpam-3515	293	8	dx	dx	PROPN
ejpam-3515	293	9	≤	≤	PROPN
ejpam-3515	293	10	const	const	X
ejpam-3515	293	11	∫	∫	PROPN
ejpam-3515	293	12	{	{	PUNCT
ejpam-3515	293	13	d(x	d(x	PROPN
ejpam-3515	293	14	,	,	PUNCT
ejpam-3515	293	15	a	a	PRON
ejpam-3515	293	16	)	)	PUNCT
ejpam-3515	293	17	<	<	X
ejpam-3515	293	18	2	2	NUM
ejpam-3515	293	19	ν	ν	NOUN
ejpam-3515	293	20	}	}	PUNCT
ejpam-3515	293	21	∪{d(x	∪{d(x	PROPN
ejpam-3515	293	22	,	,	PUNCT
ejpam-3515	293	23	a)>ν−1	a)>ν−1	ADV
ejpam-3515	293	24	}	}	PUNCT
ejpam-3515	293	25	exp	exp	NOUN
ejpam-3515	293	26	(	(	PUNCT
ejpam-3515	293	27	−	−	PROPN
ejpam-3515	293	28	l−1∑	l−1∑	ADJ
ejpam-3515	293	29	k=0	k=0	PROPN
ejpam-3515	293	30	(	(	PUNCT
ejpam-3515	293	31	tk+1	tk+1	NUM
ejpam-3515	293	32	−	−	PROPN
ejpam-3515	293	33	tk)(bk)2	tk)(bk)2	PRON
ejpam-3515	293	34	)	)	PUNCT
ejpam-3515	293	35	exp	exp	NOUN
ejpam-3515	293	36	(	(	PUNCT
ejpam-3515	293	37	−(x−	−(x−	NOUN
ejpam-3515	293	38	α)2	α)2	NOUN
ejpam-3515	293	39	ct	ct	PROPN
ejpam-3515	293	40	)	)	PUNCT
ejpam-3515	293	41	dx	dx	PROPN
ejpam-3515	293	42	,	,	PUNCT
ejpam-3515	293	43	y.	y.	PROPN
ejpam-3515	293	44	h.	h.	PROPN
ejpam-3515	293	45	saleem	saleem	PROPN
ejpam-3515	293	46	,	,	PUNCT
ejpam-3515	293	47	h.	h.	PROPN
ejpam-3515	293	48	a.	a.	PROPN
ejpam-3515	293	49	shubber	shubber	PROPN
ejpam-3515	293	50	/	/	SYM
ejpam-3515	293	51	eur	eur	PROPN
ejpam-3515	293	52	.	.	PUNCT
ejpam-3515	294	1	j.	j.	PROPN
ejpam-3515	294	2	pure	pure	PROPN
ejpam-3515	294	3	appl	appl	PROPN
ejpam-3515	294	4	.	.	PROPN
ejpam-3515	294	5	math	math	PROPN
ejpam-3515	294	6	,	,	PUNCT
ejpam-3515	294	7	12	12	NUM
ejpam-3515	294	8	(	(	PUNCT
ejpam-3515	294	9	4	4	NUM
ejpam-3515	294	10	)	)	PUNCT
ejpam-3515	294	11	(	(	PUNCT
ejpam-3515	294	12	2019	2019	NUM
ejpam-3515	294	13	)	)	PUNCT
ejpam-3515	294	14	,	,	PUNCT
ejpam-3515	294	15	1441	1441	NUM
ejpam-3515	294	16	-	-	SYM
ejpam-3515	294	17	1454	1454	NUM
ejpam-3515	294	18	1453	1453	NUM
ejpam-3515	294	19	where	where	SCONJ
ejpam-3515	294	20	c	c	AUX
ejpam-3515	294	21	>	>	X
ejpam-3515	294	22	0	0	PROPN
ejpam-3515	294	23	is	be	AUX
ejpam-3515	294	24	constants	constant	NOUN
ejpam-3515	294	25	.	.	PUNCT
ejpam-3515	295	1	therefore	therefore	ADV
ejpam-3515	295	2	,	,	PUNCT
ejpam-3515	295	3	e	e	PROPN
ejpam-3515	295	4	∫	∫	NUM
ejpam-3515	295	5	ṽ	ṽ	PROPN
ejpam-3515	295	6	(	(	PUNCT
ejpam-3515	295	7	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	295	8	,	,	PUNCT
ejpam-3515	295	9	x	x	X
ejpam-3515	295	10	)	)	PUNCT
ejpam-3515	295	11			PROPN
ejpam-3515	295	12	n∑	n∑	NOUN
ejpam-3515	295	13	j=1	j=1	NOUN
ejpam-3515	295	14	1	1	NUM
ejpam-3515	295	15	2	2	NUM
ejpam-3515	295	16	(	(	PUNCT
ejpam-3515	295	17	i∂j	i∂j	VERB
ejpam-3515	295	18	+	+	CCONJ
ejpam-3515	295	19	bj(x))2	bj(x))2	PROPN
ejpam-3515	295	20	h(x)θ(v	h(x)θ(v	NOUN
ejpam-3515	295	21	)	)	PUNCT
ejpam-3515	295	22			PROPN
ejpam-3515	295	23	dx	dx	PROPN
ejpam-3515	295	24	=	=	SYM
ejpam-3515	295	25	e	e	PROPN
ejpam-3515	295	26	(	(	PUNCT
ejpam-3515	295	27	∫	∫	PROPN
ejpam-3515	295	28	ψ	ψ	X
ejpam-3515	295	29	(	(	PUNCT
ejpam-3515	295	30	1)(t	1)(t	NUM
ejpam-3515	295	31	,	,	PUNCT
ejpam-3515	295	32	x)ṽ	x)ṽ	NUM
ejpam-3515	295	33	(	(	PUNCT
ejpam-3515	295	34	x)h(x)θ(v	x)h(x)θ(v	NUM
ejpam-3515	295	35	)	)	PUNCT
ejpam-3515	295	36	)	)	PUNCT
ejpam-3515	295	37	dx	dx	PROPN
ejpam-3515	296	1	+	+	NOUN
ejpam-3515	296	2	e	e	PROPN
ejpam-3515	296	3	(	(	PUNCT
ejpam-3515	296	4	∫	∫	PROPN
ejpam-3515	297	1	[	[	X
ejpam-3515	297	2	v	v	X
ejpam-3515	297	3	(	(	PUNCT
ejpam-3515	297	4	x)ṽ	x)ṽ	X
ejpam-3515	297	5	(	(	PUNCT
ejpam-3515	297	6	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	297	7	,	,	PUNCT
ejpam-3515	297	8	x)h(x)−ψ(t	x)h(x)−ψ(t	PROPN
ejpam-3515	297	9	,	,	PUNCT
ejpam-3515	297	10	x)h(x	x)h(x	PROPN
ejpam-3515	297	11	)	)	PUNCT
ejpam-3515	298	1			PROPN
ejpam-3515	298	2	n∑	n∑	NOUN
ejpam-3515	298	3	j=1	j=1	NOUN
ejpam-3515	298	4	1	1	NUM
ejpam-3515	298	5	2	2	NUM
ejpam-3515	298	6	(	(	PUNCT
ejpam-3515	298	7	i∂j	i∂j	VERB
ejpam-3515	298	8	+	+	CCONJ
ejpam-3515	298	9	bj(x))2	bj(x))2	PROPN
ejpam-3515	298	10			PROPN
ejpam-3515	298	11	ṽ	ṽ	PROPN
ejpam-3515	298	12	(	(	PUNCT
ejpam-3515	298	13	x)−2ψ(t	x)−2ψ(t	PROPN
ejpam-3515	298	14	,	,	PUNCT
ejpam-3515	298	15	x	x	X
ejpam-3515	298	16	)	)	PUNCT
ejpam-3515	298	17			PROPN
ejpam-3515	298	18	n∑	n∑	PROPN
ejpam-3515	298	19	j=1	j=1	NOUN
ejpam-3515	298	20	−1	−1	NOUN
ejpam-3515	298	21	2	2	NUM
ejpam-3515	298	22	∂j(ṽ	∂j(ṽ	NOUN
ejpam-3515	298	23	)	)	PUNCT
ejpam-3515	299	1			PROPN
ejpam-3515	299	2			PROPN
ejpam-3515	299	3	n∑	n∑	PROPN
ejpam-3515	299	4	j=1	j=1	NOUN
ejpam-3515	299	5	−1	−1	NOUN
ejpam-3515	299	6	2	2	NUM
ejpam-3515	299	7	∂jh	∂jh	NOUN
ejpam-3515	299	8			PROPN
ejpam-3515	299	9	θ(v	θ(v	NOUN
ejpam-3515	299	10	)	)	PUNCT
ejpam-3515	299	11	]	]	PUNCT
ejpam-3515	299	12	)	)	PUNCT
ejpam-3515	299	13	dx	dx	PROPN
ejpam-3515	299	14	.	.	PUNCT
ejpam-3515	300	1	now	now	ADV
ejpam-3515	300	2	,	,	PUNCT
ejpam-3515	300	3	we	we	PRON
ejpam-3515	300	4	act	act	VERB
ejpam-3515	300	5	in	in	ADP
ejpam-3515	300	6	just	just	ADV
ejpam-3515	300	7	the	the	DET
ejpam-3515	300	8	same	same	ADJ
ejpam-3515	300	9	way	way	NOUN
ejpam-3515	300	10	as	as	ADP
ejpam-3515	300	11	in	in	ADP
ejpam-3515	300	12	the	the	DET
ejpam-3515	300	13	case	case	NOUN
ejpam-3515	300	14	of	of	ADP
ejpam-3515	300	15	the	the	DET
ejpam-3515	300	16	potential	potential	NOUN
ejpam-3515	300	17	without	without	ADP
ejpam-3515	300	18	singularities	singularity	NOUN
ejpam-3515	300	19	.	.	PUNCT
ejpam-3515	301	1	namely	namely	ADV
ejpam-3515	301	2	,	,	PUNCT
ejpam-3515	301	3	we	we	PRON
ejpam-3515	301	4	make	make	VERB
ejpam-3515	301	5	the	the	DET
ejpam-3515	301	6	fourier	fourier	ADJ
ejpam-3515	301	7	transform	transform	NOUN
ejpam-3515	301	8	by	by	ADP
ejpam-3515	301	9	the	the	DET
ejpam-3515	301	10	variable	variable	NOUN
ejpam-3515	301	11	x	x	NOUN
ejpam-3515	301	12	at	at	ADP
ejpam-3515	301	13	the	the	DET
ejpam-3515	301	14	left	left	ADJ
ejpam-3515	301	15	side	side	NOUN
ejpam-3515	301	16	.	.	PUNCT
ejpam-3515	302	1	we	we	PRON
ejpam-3515	302	2	get	get	VERB
ejpam-3515	302	3	the	the	DET
ejpam-3515	302	4	following	follow	VERB
ejpam-3515	302	5	expression	expression	NOUN
ejpam-3515	302	6	:	:	PUNCT
ejpam-3515	303	1	e	e	X
ejpam-3515	303	2	(	(	PUNCT
ejpam-3515	303	3	∫	∫	PROPN
ejpam-3515	303	4	̂(ṽ	̂(ṽ	PROPN
ejpam-3515	303	5	(	(	PUNCT
ejpam-3515	303	6	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	303	7	,	,	PUNCT
ejpam-3515	303	8	x))(k	x))(k	NOUN
ejpam-3515	303	9	)	)	PUNCT
ejpam-3515	304	1			PROPN
ejpam-3515	304	2	n∑	n∑	PROPN
ejpam-3515	304	3	j=1	j=1	NOUN
ejpam-3515	304	4	−1	−1	NOUN
ejpam-3515	304	5	2	2	NUM
ejpam-3515	304	6	|k|2	|k|2	NOUN
ejpam-3515	304	7	+	+	CCONJ
ejpam-3515	304	8	1	1	NUM
ejpam-3515	304	9	2	2	NUM
ejpam-3515	304	10	n∑	n∑	NOUN
ejpam-3515	304	11	j=1	j=1	PROPN
ejpam-3515	304	12	i∂j	i∂j	VERB
ejpam-3515	304	13	b̂j(k	b̂j(k	PROPN
ejpam-3515	304	14	)	)	PUNCT
ejpam-3515	305	1	+	+	CCONJ
ejpam-3515	305	2	1	1	NUM
ejpam-3515	305	3	2	2	NUM
ejpam-3515	305	4	n∑	n∑	NOUN
ejpam-3515	305	5	j=1	j=1	NOUN
ejpam-3515	305	6	ib̂j(k)|	ib̂j(k)|	VERB
ejpam-3515	306	1	−	−	VERB
ejpam-3515	306	2	ki|+	ki|+	NOUN
ejpam-3515	306	3	1	1	NUM
ejpam-3515	306	4	2	2	NUM
ejpam-3515	306	5	n∑	n∑	NOUN
ejpam-3515	306	6	j=1	j=1	ADJ
ejpam-3515	306	7	ib̂2j	ib̂2j	VERB
ejpam-3515	306	8	(	(	PUNCT
ejpam-3515	306	9	k	k	NOUN
ejpam-3515	306	10	)	)	PUNCT
ejpam-3515	306	11			PROPN
ejpam-3515	306	12	h̃(k)θ(v	h̃(k)θ(v	X
ejpam-3515	306	13	)	)	PUNCT
ejpam-3515	307	1	dk	dk	PROPN
ejpam-3515	307	2	.	.	PUNCT
ejpam-3515	307	3	(	(	PUNCT
ejpam-3515	307	4	2.12	2.12	NUM
ejpam-3515	307	5	)	)	PUNCT
ejpam-3515	307	6	since	since	SCONJ
ejpam-3515	307	7	v	v	NOUN
ejpam-3515	307	8	(	(	PUNCT
ejpam-3515	307	9	x)ṽ	x)ṽ	X
ejpam-3515	307	10	(	(	PUNCT
ejpam-3515	307	11	x	x	NOUN
ejpam-3515	307	12	)	)	PUNCT
ejpam-3515	307	13	and	and	CCONJ
ejpam-3515	307	14	(	(	PUNCT
ejpam-3515	307	15	∑n	∑n	PROPN
ejpam-3515	307	16	j=1	j=1	NOUN
ejpam-3515	307	17	1	1	NUM
ejpam-3515	307	18	2(i∂j	2(i∂j	NUM
ejpam-3515	307	19	+	+	CCONJ
ejpam-3515	307	20	bj(x))2	bj(x))2	PROPN
ejpam-3515	307	21	)	)	PUNCT
ejpam-3515	307	22	have	have	VERB
ejpam-3515	307	23	the	the	DET
ejpam-3515	307	24	a−property	a−property	NOUN
ejpam-3515	307	25	,	,	PUNCT
ejpam-3515	307	26	we	we	PRON
ejpam-3515	307	27	have∣∣∣e	have∣∣∣e	PROPN
ejpam-3515	307	28	(	(	PUNCT
ejpam-3515	307	29	v	v	NOUN
ejpam-3515	307	30	(	(	PUNCT
ejpam-3515	307	31	x)ṽ	x)ṽ	X
ejpam-3515	307	32	(	(	PUNCT
ejpam-3515	307	33	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	307	34	,	,	PUNCT
ejpam-3515	307	35	x)h(x)θ(v	x)h(x)θ(v	NUM
ejpam-3515	307	36	)	)	PUNCT
ejpam-3515	307	37	)	)	PUNCT
ejpam-3515	307	38	dx	dx	PROPN
ejpam-3515	307	39	∣∣∣	∣∣∣	PROPN
ejpam-3515	307	40	≤	≤	X
ejpam-3515	307	41	const	const	ADJ
ejpam-3515	307	42	‖h(x)θ(v	‖h(x)θ(v	PROPN
ejpam-3515	307	43	)	)	PUNCT
ejpam-3515	307	44	‖l2((rn,,dx	‖l2((rn,,dx	PROPN
ejpam-3515	307	45	,	,	PUNCT
ejpam-3515	307	46	dv	dv	PROPN
ejpam-3515	307	47	)	)	PUNCT
ejpam-3515	307	48	;	;	PUNCT
ejpam-3515	307	49	(	(	PUNCT
ejpam-3515	307	50	2.13	2.13	NUM
ejpam-3515	307	51	)	)	PUNCT
ejpam-3515	307	52	∣∣∣∣∣∣e	∣∣∣∣∣∣e	NOUN
ejpam-3515	307	53	∫	∫	PUNCT
ejpam-3515	307	54	ψ(t	ψ(t	PROPN
ejpam-3515	307	55	,	,	PUNCT
ejpam-3515	307	56	x	x	NOUN
ejpam-3515	307	57	)	)	PUNCT
ejpam-3515	307	58			PROPN
ejpam-3515	307	59	n∑	n∑	NOUN
ejpam-3515	307	60	j=1	j=1	NOUN
ejpam-3515	307	61	1	1	NUM
ejpam-3515	307	62	2	2	NUM
ejpam-3515	307	63	(	(	PUNCT
ejpam-3515	307	64	i∂j	i∂j	VERB
ejpam-3515	307	65	+	+	CCONJ
ejpam-3515	307	66	bj(x))2	bj(x))2	PROPN
ejpam-3515	307	67			PROPN
ejpam-3515	307	68	ṽ	ṽ	PROPN
ejpam-3515	307	69	(	(	PUNCT
ejpam-3515	307	70	x)h(x)θ(v	x)h(x)θ(v	NUM
ejpam-3515	307	71	)	)	PUNCT
ejpam-3515	308	1			PROPN
ejpam-3515	308	2	dx	dx	PROPN
ejpam-3515	308	3	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3515	308	4	≤	≤	PROPN
ejpam-3515	308	5	const	const	X
ejpam-3515	308	6	‖h(x)θ(v	‖h(x)θ(v	PROPN
ejpam-3515	308	7	)	)	PUNCT
ejpam-3515	308	8	‖l2((rn,,dx	‖l2((rn,,dx	PROPN
ejpam-3515	308	9	,	,	PUNCT
ejpam-3515	308	10	dv	dv	PROPN
ejpam-3515	308	11	)	)	PUNCT
ejpam-3515	308	12	.	.	PUNCT
ejpam-3515	309	1	(	(	PUNCT
ejpam-3515	309	2	2.14	2.14	NUM
ejpam-3515	309	3	)	)	PUNCT
ejpam-3515	309	4	in	in	ADP
ejpam-3515	309	5	the	the	DET
ejpam-3515	309	6	last	last	ADJ
ejpam-3515	309	7	term	term	NOUN
ejpam-3515	309	8	we	we	PRON
ejpam-3515	309	9	also	also	ADV
ejpam-3515	309	10	make	make	VERB
ejpam-3515	309	11	the	the	DET
ejpam-3515	309	12	fourier	fourier	NOUN
ejpam-3515	309	13	transform	transform	NOUN
ejpam-3515	309	14	by	by	ADP
ejpam-3515	309	15	x.	x.	NOUN
ejpam-3515	309	16	we	we	PRON
ejpam-3515	309	17	get	get	VERB
ejpam-3515	309	18	the	the	DET
ejpam-3515	309	19	following	follow	VERB
ejpam-3515	309	20	expression	expression	NOUN
ejpam-3515	309	21	:	:	PUNCT
ejpam-3515	309	22	2ie	2ie	ADJ
ejpam-3515	309	23	∫	∫	NOUN
ejpam-3515	309	24	ψ(t	ψ(t	VERB
ejpam-3515	309	25	,	,	PUNCT
ejpam-3515	309	26	x	x	NOUN
ejpam-3515	309	27	)	)	PUNCT
ejpam-3515	309	28			PROPN
ejpam-3515	309	29	̂n∑	̂n∑	PROPN
ejpam-3515	309	30	j=1	j=1	NOUN
ejpam-3515	309	31	−1	−1	NOUN
ejpam-3515	309	32	2	2	NUM
ejpam-3515	309	33	∂j	∂j	PROPN
ejpam-3515	309	34	(	(	PUNCT
ejpam-3515	309	35	˜(v	˜(v	PROPN
ejpam-3515	309	36	)	)	PUNCT
ejpam-3515	309	37	)	)	PUNCT
ejpam-3515	310	1			PROPN
ejpam-3515	310	2	(	(	PUNCT
ejpam-3515	310	3	k)h̃(k	k)h̃(k	PROPN
ejpam-3515	310	4	)	)	PUNCT
ejpam-3515	310	5	(	(	PUNCT
ejpam-3515	310	6	−nk	−nk	NOUN
ejpam-3515	310	7	2	2	NUM
ejpam-3515	310	8	)	)	PUNCT
ejpam-3515	310	9	θ(v	θ(v	NOUN
ejpam-3515	310	10	)	)	PUNCT
ejpam-3515	310	11			PROPN
ejpam-3515	310	12	dk	dk	PROPN
ejpam-3515	310	13	.	.	PUNCT
ejpam-3515	310	14	(	(	PUNCT
ejpam-3515	310	15	2.15	2.15	NUM
ejpam-3515	310	16	)	)	PUNCT
ejpam-3515	310	17	now	now	ADV
ejpam-3515	310	18	,	,	PUNCT
ejpam-3515	310	19	it	it	PRON
ejpam-3515	310	20	follows	follow	VERB
ejpam-3515	310	21	from	from	ADP
ejpam-3515	310	22	(	(	PUNCT
ejpam-3515	310	23	2.12)-(2.15	2.12)-(2.15	NUM
ejpam-3515	310	24	)	)	PUNCT
ejpam-3515	310	25	that	that	DET
ejpam-3515	310	26	|e	|e	PROPN
ejpam-3515	310	27	(	(	PUNCT
ejpam-3515	310	28	∫	∫	PROPN
ejpam-3515	310	29	̂(ṽ	̂(ṽ	PROPN
ejpam-3515	310	30	(	(	PUNCT
ejpam-3515	310	31	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	310	32	,	,	PUNCT
ejpam-3515	310	33	x))(k	x))(k	NOUN
ejpam-3515	310	34	)	)	PUNCT
ejpam-3515	311	1	∑n	∑n	PROPN
ejpam-3515	311	2	j=1	j=1	NOUN
ejpam-3515	311	3	−|k|2	−|k|2	ADP
ejpam-3515	311	4	2	2	NUM
ejpam-3515	312	1	+	+	CCONJ
ejpam-3515	312	2	i	i	PRON
ejpam-3515	312	3	2	2	NUM
ejpam-3515	312	4	∑n	∑n	PROPN
ejpam-3515	312	5	j=1	j=1	PROPN
ejpam-3515	312	6	∂j	∂j	PROPN
ejpam-3515	312	7	b̂j(k	b̂j(k	PROPN
ejpam-3515	312	8	)	)	PUNCT
ejpam-3515	313	1	+	+	CCONJ
ejpam-3515	313	2	i	i	PRON
ejpam-3515	313	3	2	2	NUM
ejpam-3515	314	1	∑n	∑n	PROPN
ejpam-3515	314	2	j=1	j=1	NOUN
ejpam-3515	314	3	b̂j(k)|	b̂j(k)|	PROPN
ejpam-3515	315	1	−	−	NOUN
ejpam-3515	315	2	ki|+	ki|+	VERB
ejpam-3515	315	3	i	i	NOUN
ejpam-3515	315	4	2	2	NUM
ejpam-3515	315	5	∑n	∑n	PROPN
ejpam-3515	315	6	j=1	j=1	NOUN
ejpam-3515	315	7	b̂	b̂	NOUN
ejpam-3515	315	8	2	2	NUM
ejpam-3515	315	9	j	j	PROPN
ejpam-3515	315	10	(	(	PUNCT
ejpam-3515	315	11	k	k	NOUN
ejpam-3515	315	12	)	)	PUNCT
ejpam-3515	315	13	1	1	NUM
ejpam-3515	316	1	+	+	NUM
ejpam-3515	316	2	|−nk2	|−nk2	NOUN
ejpam-3515	316	3	|	|	NOUN
ejpam-3515	316	4	h̃(k)θ(v	h̃(k)θ(v	NUM
ejpam-3515	316	5	)	)	PUNCT
ejpam-3515	317	1	dk|	dk|	VERB
ejpam-3515	317	2	references	reference	NOUN
ejpam-3515	317	3	1454	1454	NUM
ejpam-3515	317	4	≤	≤	NUM
ejpam-3515	317	5	const‖h(x)θ(v	const‖h(x)θ(v	NOUN
ejpam-3515	317	6	)	)	PUNCT
ejpam-3515	317	7	‖l2(rn	‖l2(rn	PROPN
ejpam-3515	317	8	,	,	PUNCT
ejpam-3515	317	9	dx	dx	PROPN
ejpam-3515	317	10	,	,	PUNCT
ejpam-3515	317	11	dv	dv	PROPN
ejpam-3515	317	12	)	)	PUNCT
ejpam-3515	317	13	.	.	PUNCT
ejpam-3515	318	1	(	(	PUNCT
ejpam-3515	318	2	2.16	2.16	NUM
ejpam-3515	318	3	)	)	PUNCT
ejpam-3515	318	4	further	far	ADV
ejpam-3515	318	5	the	the	DET
ejpam-3515	318	6	estimate	estimate	NOUN
ejpam-3515	318	7	(	(	PUNCT
ejpam-3515	318	8	2.16	2.16	NUM
ejpam-3515	318	9	)	)	PUNCT
ejpam-3515	318	10	is	be	AUX
ejpam-3515	318	11	literally	literally	ADV
ejpam-3515	318	12	transferred	transfer	VERB
ejpam-3515	318	13	onto	onto	ADP
ejpam-3515	318	14	functions	function	NOUN
ejpam-3515	318	15	of	of	ADP
ejpam-3515	318	16	the	the	DET
ejpam-3515	318	17	form	form	NOUN
ejpam-3515	318	18	∑	∑	PUNCT
ejpam-3515	318	19	ck	ck	INTJ
ejpam-3515	318	20	,	,	PUNCT
ejpam-3515	318	21	lhk(x)θl(v	lhk(x)θl(v	ADJ
ejpam-3515	318	22	)	)	PUNCT
ejpam-3515	318	23	.	.	PUNCT
ejpam-3515	319	1	therefore	therefore	ADV
ejpam-3515	319	2	,	,	PUNCT
ejpam-3515	319	3	ṽ	ṽ	PROPN
ejpam-3515	319	4	(	(	PUNCT
ejpam-3515	319	5	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	319	6	,	,	PUNCT
ejpam-3515	319	7	x	x	X
ejpam-3515	319	8	)	)	PUNCT
ejpam-3515	319	9	∈w1	∈w1	ADV
ejpam-3515	319	10	for	for	ADP
ejpam-3515	319	11	almost	almost	ADV
ejpam-3515	319	12	every	every	PRON
ejpam-3515	319	13	v	v	NOUN
ejpam-3515	319	14	,	,	PUNCT
ejpam-3515	319	15	b	b	PROPN
ejpam-3515	319	16	‖ṽ	‖ṽ	PROPN
ejpam-3515	319	17	(	(	PUNCT
ejpam-3515	319	18	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	319	19	,	,	PUNCT
ejpam-3515	319	20	x)‖2w1	x)‖2w1	PROPN
ejpam-3515	319	21	≤	≤	PROPN
ejpam-3515	319	22	β1(v	β1(v	PUNCT
ejpam-3515	319	23	)	)	PUNCT
ejpam-3515	319	24	,	,	PUNCT
ejpam-3515	319	25	where	where	SCONJ
ejpam-3515	319	26	e(β1(v	e(β1(v	PROPN
ejpam-3515	319	27	)	)	PUNCT
ejpam-3515	319	28	)	)	PUNCT
ejpam-3515	320	1	<	<	X
ejpam-3515	320	2	+	+	X
ejpam-3515	320	3	∞.	∞.	PROPN
ejpam-3515	320	4	continuting	continute	VERB
ejpam-3515	320	5	these	these	DET
ejpam-3515	320	6	arguments	argument	NOUN
ejpam-3515	320	7	of	of	ADP
ejpam-3515	320	8	induction	induction	NOUN
ejpam-3515	320	9	,	,	PUNCT
ejpam-3515	320	10	we	we	PRON
ejpam-3515	320	11	get	get	VERB
ejpam-3515	320	12	ṽ	ṽ	PROPN
ejpam-3515	320	13	(	(	PUNCT
ejpam-3515	320	14	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	320	15	,	,	PUNCT
ejpam-3515	320	16	x	x	X
ejpam-3515	320	17	)	)	PUNCT
ejpam-3515	320	18	∈	∈	PROPN
ejpam-3515	320	19	wm	wm	PROPN
ejpam-3515	320	20	for	for	ADP
ejpam-3515	320	21	almost	almost	ADV
ejpam-3515	320	22	every	every	PRON
ejpam-3515	320	23	v	v	NOUN
ejpam-3515	320	24	,	,	PUNCT
ejpam-3515	320	25	b	b	PROPN
ejpam-3515	320	26	‖ṽ	‖ṽ	PROPN
ejpam-3515	320	27	(	(	PUNCT
ejpam-3515	320	28	x)ψ(t	x)ψ(t	PROPN
ejpam-3515	320	29	,	,	PUNCT
ejpam-3515	320	30	x)‖2wm	x)‖2wm	X
ejpam-3515	320	31	≤	≤	NOUN
ejpam-3515	320	32	βm(v	βm(v	PUNCT
ejpam-3515	320	33	)	)	PUNCT
ejpam-3515	320	34	,	,	PUNCT
ejpam-3515	320	35	(	(	PUNCT
ejpam-3515	320	36	2.17	2.17	NUM
ejpam-3515	320	37	)	)	PUNCT
ejpam-3515	320	38	where	where	SCONJ
ejpam-3515	320	39	e(βm(v	e(βm(v	PRON
ejpam-3515	320	40	)	)	PUNCT
ejpam-3515	320	41	)	)	PUNCT
ejpam-3515	320	42	<	<	X
ejpam-3515	321	1	+	+	PUNCT
ejpam-3515	321	2	∞.	∞.	PROPN
ejpam-3515	321	3	thus	thus	ADV
ejpam-3515	321	4	,	,	PUNCT
ejpam-3515	321	5	we	we	PRON
ejpam-3515	321	6	have	have	AUX
ejpam-3515	321	7	proved	prove	VERB
ejpam-3515	321	8	that	that	SCONJ
ejpam-3515	321	9	the	the	DET
ejpam-3515	321	10	function	function	NOUN
ejpam-3515	321	11	ψ(t	ψ(t	PROPN
ejpam-3515	321	12	,	,	PUNCT
ejpam-3515	321	13	x	x	NOUN
ejpam-3515	321	14	)	)	PUNCT
ejpam-3515	321	15	for	for	ADP
ejpam-3515	321	16	almost	almost	ADV
ejpam-3515	321	17	every	every	PRON
ejpam-3515	321	18	v	v	NOUN
ejpam-3515	321	19	,	,	PUNCT
ejpam-3515	321	20	b	b	PROPN
ejpam-3515	321	21	is	be	AUX
ejpam-3515	321	22	infinitely	infinitely	ADV
ejpam-3515	321	23	differentiable	differentiable	ADJ
ejpam-3515	321	24	for	for	ADP
ejpam-3515	321	25	all	all	DET
ejpam-3515	321	26	x	x	NOUN
ejpam-3515	321	27	,	,	PUNCT
ejpam-3515	321	28	in	in	ADP
ejpam-3515	321	29	particular	particular	ADJ
ejpam-3515	321	30	,	,	PUNCT
ejpam-3515	321	31	at	at	ADP
ejpam-3515	321	32	the	the	DET
ejpam-3515	321	33	point	point	NOUN
ejpam-3515	321	34	x	x	X
ejpam-3515	321	35	∈	∈	NOUN
ejpam-3515	321	36	a.	a.	NOUN
ejpam-3515	321	37	besides	besides	SCONJ
ejpam-3515	321	38	,	,	PUNCT
ejpam-3515	321	39	for	for	ADP
ejpam-3515	321	40	any	any	DET
ejpam-3515	321	41	function	function	NOUN
ejpam-3515	321	42	with	with	ADP
ejpam-3515	321	43	the	the	DET
ejpam-3515	321	44	a	a	DET
ejpam-3515	321	45	-	-	PUNCT
ejpam-3515	321	46	property	property	NOUN
ejpam-3515	321	47	,	,	PUNCT
ejpam-3515	321	48	the	the	DET
ejpam-3515	321	49	estimates	estimate	NOUN
ejpam-3515	321	50	of	of	ADP
ejpam-3515	321	51	the	the	DET
ejpam-3515	321	52	form	form	NOUN
ejpam-3515	321	53	(	(	PUNCT
ejpam-3515	321	54	2.17	2.17	NUM
ejpam-3515	321	55	)	)	PUNCT
ejpam-3515	321	56	take	take	VERB
ejpam-3515	321	57	place	place	NOUN
ejpam-3515	321	58	.	.	PUNCT
ejpam-3515	322	1	references	reference	NOUN
ejpam-3515	322	2	[	[	X
ejpam-3515	322	3	1	1	NUM
ejpam-3515	322	4	]	]	X
ejpam-3515	322	5	d.w	d.w	PROPN
ejpam-3515	322	6	.	.	PUNCT
ejpam-3515	322	7	adam	adam	PROPN
ejpam-3515	322	8	the	the	DET
ejpam-3515	322	9	essential	essential	ADJ
ejpam-3515	322	10	self	self	NOUN
ejpam-3515	322	11	-	-	PUNCT
ejpam-3515	322	12	adjointness	adjointness	NOUN
ejpam-3515	322	13	of	of	ADP
ejpam-3515	322	14	schrödinger	schrödinger	NOUN
ejpam-3515	322	15	operator	operator	NOUN
ejpam-3515	322	16	with	with	ADP
ejpam-3515	322	17	oscillating	oscillate	VERB
ejpam-3515	322	18	potential	potential	NOUN
ejpam-3515	322	19	,	,	PUNCT
ejpam-3515	322	20	new	new	PROPN
ejpam-3515	322	21	zealand	zealand	PROPN
ejpam-3515	322	22	j.	j.	PROPN
ejpam-3515	322	23	of	of	ADP
ejpam-3515	322	24	math	math	PROPN
ejpam-3515	322	25	.	.	PUNCT
ejpam-3515	323	1	,	,	PUNCT
ejpam-3515	323	2	vol	vol	NOUN
ejpam-3515	323	3	.	.	PROPN
ejpam-3515	323	4	46	46	NUM
ejpam-3515	323	5	,	,	PUNCT
ejpam-3515	323	6	2016	2016	NUM
ejpam-3515	323	7	,	,	PUNCT
ejpam-3515	323	8	p.	p.	NOUN
ejpam-3515	323	9	65	65	NUM
ejpam-3515	323	10	-	-	SYM
ejpam-3515	323	11	72	72	NUM
ejpam-3515	323	12	.	.	PUNCT
ejpam-3515	324	1	[	[	X
ejpam-3515	324	2	2	2	NUM
ejpam-3515	324	3	]	]	PUNCT
ejpam-3515	324	4	t.o.bonafos	t.o.bonafos	NOUN
ejpam-3515	324	5	,	,	PUNCT
ejpam-3515	324	6	l.vega	l.vega	NOUN
ejpam-3515	324	7	,	,	PUNCT
ejpam-3515	324	8	a	a	DET
ejpam-3515	324	9	strategy	strategy	NOUN
ejpam-3515	324	10	for	for	ADP
ejpam-3515	324	11	self	self	NOUN
ejpam-3515	324	12	-	-	PUNCT
ejpam-3515	324	13	adjointness	adjointness	NOUN
ejpam-3515	324	14	of	of	ADP
ejpam-3515	324	15	dirac	dirac	NOUN
ejpam-3515	324	16	operators	operator	NOUN
ejpam-3515	324	17	:	:	PUNCT
ejpam-3515	324	18	applications	application	NOUN
ejpam-3515	324	19	to	to	ADP
ejpam-3515	324	20	the	the	DET
ejpam-3515	324	21	mit	mit	PROPN
ejpam-3515	324	22	bag	bag	NOUN
ejpam-3515	324	23	model	model	NOUN
ejpam-3515	324	24	and	and	CCONJ
ejpam-3515	324	25	δ−shell	δ−shell	NOUN
ejpam-3515	324	26	interactions	interaction	NOUN
ejpam-3515	324	27	,	,	PUNCT
ejpam-3515	324	28	publ	publ	NOUN
ejpam-3515	324	29	.	.	PUNCT
ejpam-3515	325	1	mat	mat	NOUN
ejpam-3515	325	2	.	.	NOUN
ejpam-3515	325	3	62	62	NUM
ejpam-3515	325	4	,	,	PUNCT
ejpam-3515	325	5	2018	2018	NUM
ejpam-3515	325	6	,	,	PUNCT
ejpam-3515	325	7	p.	p.	NOUN
ejpam-3515	325	8	397437	397437	NUM
ejpam-3515	325	9	.	.	PUNCT
ejpam-3515	326	1	[	[	X
ejpam-3515	326	2	3	3	X
ejpam-3515	326	3	]	]	X
ejpam-3515	326	4	m.d	m.d	PROPN
ejpam-3515	326	5	.	.	PROPN
ejpam-3515	326	6	gaysinsky	gaysinsky	PROPN
ejpam-3515	326	7	,	,	PUNCT
ejpam-3515	326	8	investigation	investigation	NOUN
ejpam-3515	326	9	of	of	ADP
ejpam-3515	326	10	self	self	NOUN
ejpam-3515	326	11	-	-	PUNCT
ejpam-3515	326	12	adjointness	adjointness	NOUN
ejpam-3515	326	13	of	of	ADP
ejpam-3515	326	14	schrödinger	schrödinger	NOUN
ejpam-3515	326	15	operator	operator	NOUN
ejpam-3515	326	16	and	and	CCONJ
ejpam-3515	326	17	its	its	PRON
ejpam-3515	326	18	powers	power	NOUN
ejpam-3515	326	19	with	with	ADP
ejpam-3515	326	20	the	the	DET
ejpam-3515	326	21	help	help	NOUN
ejpam-3515	326	22	of	of	ADP
ejpam-3515	326	23	integrals	integral	NOUN
ejpam-3515	326	24	along	along	ADP
ejpam-3515	326	25	trajectories	trajectory	NOUN
ejpam-3515	326	26	,	,	PUNCT
ejpam-3515	326	27	dissertation	dissertation	NOUN
ejpam-3515	326	28	for	for	ADP
ejpam-3515	326	29	the	the	DET
ejpam-3515	326	30	candidate	candidate	NOUN
ejpam-3515	326	31	degree	degree	NOUN
ejpam-3515	326	32	.	.	PUNCT
ejpam-3515	327	1	tashkent	tashkent	ADJ
ejpam-3515	327	2	,	,	PUNCT
ejpam-3515	327	3	1990[russian	1990[russian	NUM
ejpam-3515	327	4	]	]	PUNCT
ejpam-3515	327	5	.	.	PUNCT
ejpam-3515	328	1	[	[	X
ejpam-3515	328	2	4	4	NUM
ejpam-3515	328	3	]	]	X
ejpam-3515	328	4	m.d	m.d	PROPN
ejpam-3515	328	5	.	.	PROPN
ejpam-3515	328	6	gaysinsky	gaysinsky	PROPN
ejpam-3515	328	7	,	,	PUNCT
ejpam-3515	328	8	m.s	m.s	PROPN
ejpam-3515	328	9	.	.	PROPN
ejpam-3515	328	10	goldstein	goldstein	PROPN
ejpam-3515	328	11	self	self	NOUN
ejpam-3515	328	12	-adjointness	-adjointness	NOUN
ejpam-3515	328	13	of	of	ADP
ejpam-3515	328	14	schrödinger	schrödinger	NOUN
ejpam-3515	328	15	operator	operator	NOUN
ejpam-3515	328	16	and	and	CCONJ
ejpam-3515	328	17	wiener	wiener	NOUN
ejpam-3515	328	18	integral	integral	ADJ
ejpam-3515	328	19	integr.equat.opera.th	integr.equat.opera.th	NOUN
ejpam-3515	328	20	.	.	PUNCT
ejpam-3515	328	21	,	,	PUNCT
ejpam-3515	328	22	vol	vol	NOUN
ejpam-3515	328	23	.	.	PROPN
ejpam-3515	328	24	15	15	NUM
ejpam-3515	328	25	,	,	PUNCT
ejpam-3515	328	26	1992	1992	NUM
ejpam-3515	328	27	,	,	PUNCT
ejpam-3515	328	28	p.973	p.973	NOUN
ejpam-3515	328	29	-	-	SYM
ejpam-3515	328	30	990	990	NUM
ejpam-3515	328	31	.	.	PUNCT
ejpam-3515	329	1	[	[	X
ejpam-3515	329	2	5	5	X
ejpam-3515	329	3	]	]	PUNCT
ejpam-3515	329	4	t.	t.	PROPN
ejpam-3515	329	5	kato	kato	PROPN
ejpam-3515	329	6	,	,	PUNCT
ejpam-3515	329	7	schrödinger	schrödinger	NOUN
ejpam-3515	329	8	operators	operator	NOUN
ejpam-3515	329	9	with	with	ADP
ejpam-3515	329	10	singular	singular	PROPN
ejpam-3515	329	11	potentials	potential	NOUN
ejpam-3515	329	12	.	.	PUNCT
ejpam-3515	330	1	israel	israel	PROPN
ejpam-3515	330	2	j.	j.	PROPN
ejpam-3515	330	3	math	math	PROPN
ejpam-3515	330	4	.	.	PUNCT
ejpam-3515	330	5	,	,	PUNCT
ejpam-3515	330	6	13	13	NUM
ejpam-3515	330	7	,	,	PUNCT
ejpam-3515	330	8	1973	1973	NUM
ejpam-3515	330	9	,	,	PUNCT
ejpam-3515	330	10	p.	p.	NOUN
ejpam-3515	330	11	135	135	NUM
ejpam-3515	330	12	-	-	SYM
ejpam-3515	330	13	148	148	NUM
ejpam-3515	330	14	.	.	PUNCT
ejpam-3515	331	1	[	[	X
ejpam-3515	331	2	6	6	NUM
ejpam-3515	331	3	]	]	X
ejpam-3515	331	4	e.s	e.s	PROPN
ejpam-3515	331	5	.	.	PROPN
ejpam-3515	331	6	nathanson	nathanson	PROPN
ejpam-3515	331	7	et	et	PROPN
ejpam-3515	331	8	al	al	PROPN
ejpam-3515	331	9	,	,	PUNCT
ejpam-3515	331	10	trotters	trotter	NOUN
ejpam-3515	331	11	limit	limit	VERB
ejpam-3515	331	12	formula	formula	NOUN
ejpam-3515	331	13	for	for	ADP
ejpam-3515	331	14	the	the	DET
ejpam-3515	331	15	schrödinger	schrödinger	NOUN
ejpam-3515	331	16	equation	equation	NOUN
ejpam-3515	331	17	with	with	ADP
ejpam-3515	331	18	singular	singular	PROPN
ejpam-3515	331	19	potential	potential	NOUN
ejpam-3515	331	20	,	,	PUNCT
ejpam-3515	331	21	j.	j.	PROPN
ejpam-3515	331	22	of	of	ADP
ejpam-3515	331	23	math	math	PROPN
ejpam-3515	331	24	.	.	PUNCT
ejpam-3515	332	1	phy	phy	PROPN
ejpam-3515	332	2	.	.	PROPN
ejpam-3515	333	1	58	58	NUM
ejpam-3515	333	2	,	,	PUNCT
ejpam-3515	333	3	122101	122101	NUM
ejpam-3515	333	4	,	,	PUNCT
ejpam-3515	333	5	2017	2017	NUM
ejpam-3515	333	6	.	.	PUNCT
ejpam-3515	334	1	[	[	X
ejpam-3515	334	2	7	7	X
ejpam-3515	334	3	]	]	PUNCT
ejpam-3515	334	4	l.m.nieto	l.m.nieto	VERB
ejpam-3515	334	5	et	et	PROPN
ejpam-3515	334	6	al	al	PROPN
ejpam-3515	334	7	,	,	PUNCT
ejpam-3515	334	8	towards	towards	ADP
ejpam-3515	334	9	modelling	model	VERB
ejpam-3515	334	10	qft	qft	NOUN
ejpam-3515	334	11	in	in	ADP
ejpam-3515	334	12	real	real	ADJ
ejpam-3515	334	13	metamaterials	metamaterial	NOUN
ejpam-3515	334	14	:	:	PUNCT
ejpam-3515	334	15	singular	singular	PROPN
ejpam-3515	334	16	potentials	potential	NOUN
ejpam-3515	334	17	and	and	CCONJ
ejpam-3515	334	18	self	self	NOUN
ejpam-3515	334	19	-	-	PUNCT
ejpam-3515	334	20	adjoint	adjoint	NOUN
ejpam-3515	334	21	extensions	extension	NOUN
ejpam-3515	334	22	,	,	PUNCT
ejpam-3515	334	23	j.	j.	PROPN
ejpam-3515	334	24	phys	phys	PROPN
ejpam-3515	334	25	.	.	PUNCT
ejpam-3515	334	26	:	:	PUNCT
ejpam-3515	335	1	conf	conf	PROPN
ejpam-3515	335	2	.	.	PUNCT
ejpam-3515	335	3	ser	ser	PROPN
ejpam-3515	335	4	.	.	PROPN
ejpam-3515	335	5	839	839	NUM
ejpam-3515	335	6	012007	012007	NUM
ejpam-3515	335	7	,	,	PUNCT
ejpam-3515	335	8	2017	2017	NUM
ejpam-3515	335	9	.	.	PUNCT
ejpam-3515	336	1	[	[	X
ejpam-3515	336	2	8	8	NUM
ejpam-3515	336	3	]	]	X
ejpam-3515	336	4	y.h	y.h	PROPN
ejpam-3515	336	5	.	.	PROPN
ejpam-3515	336	6	saleem	saleem	PROPN
ejpam-3515	336	7	,	,	PUNCT
ejpam-3515	336	8	h.a	h.a	PROPN
ejpam-3515	336	9	.	.	PROPN
ejpam-3515	336	10	hassen	hassen	PROPN
ejpam-3515	336	11	,	,	PUNCT
ejpam-3515	336	12	convergence	convergence	NOUN
ejpam-3515	336	13	of	of	ADP
ejpam-3515	336	14	schrödinger	schrödinger	NOUN
ejpam-3515	336	15	operator	operator	NOUN
ejpam-3515	336	16	with	with	ADP
ejpam-3515	336	17	electromagnetic	electromagnetic	ADJ
ejpam-3515	336	18	potential	potential	NOUN
ejpam-3515	336	19	,	,	PUNCT
ejpam-3515	336	20	sci.int.lahore	sci.int.lahore	PRON
ejpam-3515	336	21	,	,	PUNCT
ejpam-3515	336	22	vol.31	vol.31	ADJ
ejpam-3515	336	23	,	,	PUNCT
ejpam-3515	336	24	2	2	NUM
ejpam-3515	336	25	,	,	PUNCT
ejpam-3515	336	26	2019	2019	NUM
ejpam-3515	336	27	,	,	PUNCT
ejpam-3515	336	28	p.303	p.303	NOUN
ejpam-3515	336	29	-	-	SYM
ejpam-3515	336	30	308	308	NUM
ejpam-3515	336	31	.	.	PUNCT
ejpam-3515	337	1	[	[	X
ejpam-3515	337	2	9	9	NUM
ejpam-3515	337	3	]	]	X
ejpam-3515	337	4	x.c	x.c	PROPN
ejpam-3515	337	5	.	.	PUNCT
ejpam-3515	337	6	xu	xu	PROPN
ejpam-3515	337	7	et	et	PROPN
ejpam-3515	337	8	al	al	PROPN
ejpam-3515	337	9	,	,	PUNCT
ejpam-3515	337	10	determination	determination	NOUN
ejpam-3515	337	11	of	of	ADP
ejpam-3515	337	12	the	the	DET
ejpam-3515	337	13	self	self	NOUN
ejpam-3515	337	14	-	-	PUNCT
ejpam-3515	337	15	adjoint	adjoint	NOUN
ejpam-3515	337	16	matrix	matrix	NOUN
ejpam-3515	337	17	schrödinger	schrödinger	NOUN
ejpam-3515	337	18	operators	operator	NOUN
ejpam-3515	337	19	without	without	ADP
ejpam-3515	337	20	the	the	DET
ejpam-3515	337	21	bound	bound	ADJ
ejpam-3515	337	22	state	state	NOUN
ejpam-3515	337	23	data	datum	NOUN
ejpam-3515	337	24	,	,	PUNCT
ejpam-3515	337	25	inverse	inverse	NOUN
ejpam-3515	337	26	problems	problem	NOUN
ejpam-3515	337	27	,	,	PUNCT
ejpam-3515	337	28	vol.34	vol.34	PROPN
ejpam-3515	337	29	,	,	PUNCT
ejpam-3515	337	30	6	6	NUM
ejpam-3515	337	31	,	,	PUNCT
ejpam-3515	337	32	2018	2018	NUM
ejpam-3515	337	33	.	.	PUNCT