id	sid	tid	token	lemma	pos
ejpam-3175	1	1	european	european	PROPN
ejpam-3175	1	2	journal	journal	PROPN
ejpam-3175	1	3	of	of	ADP
ejpam-3175	1	4	pure	pure	ADJ
ejpam-3175	1	5	and	and	CCONJ
ejpam-3175	1	6	applied	apply	VERB
ejpam-3175	1	7	mathematics	mathematic	NOUN
ejpam-3175	1	8	vol	vol	NOUN
ejpam-3175	1	9	.	.	PUNCT
ejpam-3175	2	1	11	11	NUM
ejpam-3175	2	2	,	,	PUNCT
ejpam-3175	2	3	no	no	INTJ
ejpam-3175	2	4	.	.	NOUN
ejpam-3175	2	5	1	1	NUM
ejpam-3175	2	6	,	,	PUNCT
ejpam-3175	2	7	2018	2018	NUM
ejpam-3175	2	8	,	,	PUNCT
ejpam-3175	2	9	138	138	NUM
ejpam-3175	2	10	-	-	SYM
ejpam-3175	2	11	149	149	NUM
ejpam-3175	2	12	issn	issn	PROPN
ejpam-3175	2	13	1307	1307	NUM
ejpam-3175	2	14	-	-	SYM
ejpam-3175	2	15	5543	5543	NUM
ejpam-3175	2	16	–	–	PUNCT
ejpam-3175	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3175	2	18	published	publish	VERB
ejpam-3175	2	19	by	by	ADP
ejpam-3175	2	20	new	new	PROPN
ejpam-3175	2	21	york	york	PROPN
ejpam-3175	2	22	business	business	PROPN
ejpam-3175	2	23	global	global	PROPN
ejpam-3175	2	24	littlewood	littlewood	PROPN
ejpam-3175	2	25	-	-	PUNCT
ejpam-3175	2	26	paley	paley	PROPN
ejpam-3175	2	27	g	g	NOUN
ejpam-3175	2	28	-	-	PUNCT
ejpam-3175	2	29	function	function	NOUN
ejpam-3175	2	30	and	and	CCONJ
ejpam-3175	2	31	radon	radon	NOUN
ejpam-3175	2	32	transform	transform	NOUN
ejpam-3175	2	33	on	on	ADP
ejpam-3175	2	34	the	the	DET
ejpam-3175	2	35	heisenberg	heisenberg	PROPN
ejpam-3175	2	36	group	group	PROPN
ejpam-3175	2	37	zheng	zheng	PROPN
ejpam-3175	2	38	fang1	fang1	PROPN
ejpam-3175	2	39	,	,	PUNCT
ejpam-3175	2	40	jianxun	jianxun	PROPN
ejpam-3175	2	41	he1,∗	he1,∗	PROPN
ejpam-3175	2	42	1	1	NUM
ejpam-3175	2	43	school	school	NOUN
ejpam-3175	2	44	of	of	ADP
ejpam-3175	2	45	mathematics	mathematic	NOUN
ejpam-3175	2	46	and	and	CCONJ
ejpam-3175	2	47	information	information	NOUN
ejpam-3175	2	48	sciences	sciences	PROPN
ejpam-3175	2	49	,	,	PUNCT
ejpam-3175	2	50	guangzhou	guangzhou	PROPN
ejpam-3175	2	51	university	university	PROPN
ejpam-3175	2	52	,	,	PUNCT
ejpam-3175	2	53	guangzhou	guangzhou	PROPN
ejpam-3175	2	54	510006	510006	NUM
ejpam-3175	2	55	,	,	PUNCT
ejpam-3175	2	56	china	china	PROPN
ejpam-3175	2	57	abstract	abstract	NOUN
ejpam-3175	2	58	.	.	PUNCT
ejpam-3175	3	1	in	in	ADP
ejpam-3175	3	2	this	this	DET
ejpam-3175	3	3	paper	paper	NOUN
ejpam-3175	3	4	,	,	PUNCT
ejpam-3175	3	5	we	we	PRON
ejpam-3175	3	6	consider	consider	VERB
ejpam-3175	3	7	radon	radon	NOUN
ejpam-3175	3	8	transform	transform	NOUN
ejpam-3175	3	9	on	on	ADP
ejpam-3175	3	10	the	the	DET
ejpam-3175	3	11	heisenberg	heisenberg	PROPN
ejpam-3175	3	12	group	group	PROPN
ejpam-3175	3	13	hn	hn	PROPN
ejpam-3175	3	14	,	,	PUNCT
ejpam-3175	3	15	and	and	CCONJ
ejpam-3175	3	16	obtain	obtain	VERB
ejpam-3175	3	17	new	new	ADJ
ejpam-3175	3	18	inversion	inversion	NOUN
ejpam-3175	3	19	formulas	formula	NOUN
ejpam-3175	3	20	via	via	ADP
ejpam-3175	3	21	dual	dual	ADJ
ejpam-3175	3	22	radon	radon	NOUN
ejpam-3175	3	23	transforms	transform	VERB
ejpam-3175	3	24	and	and	CCONJ
ejpam-3175	3	25	poisson	poisson	NOUN
ejpam-3175	3	26	integrals	integral	NOUN
ejpam-3175	3	27	.	.	PUNCT
ejpam-3175	4	1	we	we	PRON
ejpam-3175	4	2	prove	prove	VERB
ejpam-3175	4	3	that	that	SCONJ
ejpam-3175	4	4	the	the	DET
ejpam-3175	4	5	radon	radon	NOUN
ejpam-3175	4	6	transform	transform	NOUN
ejpam-3175	4	7	is	be	AUX
ejpam-3175	4	8	a	a	DET
ejpam-3175	4	9	unitary	unitary	ADJ
ejpam-3175	4	10	operator	operator	NOUN
ejpam-3175	4	11	from	from	ADP
ejpam-3175	4	12	sobelov	sobelov	ADJ
ejpam-3175	4	13	space	space	NOUN
ejpam-3175	4	14	w	w	NOUN
ejpam-3175	4	15	into	into	ADP
ejpam-3175	4	16	l2(hn	l2(hn	PROPN
ejpam-3175	4	17	)	)	PUNCT
ejpam-3175	4	18	.	.	PUNCT
ejpam-3175	5	1	moreover	moreover	ADV
ejpam-3175	5	2	,	,	PUNCT
ejpam-3175	5	3	we	we	PRON
ejpam-3175	5	4	use	use	VERB
ejpam-3175	5	5	the	the	DET
ejpam-3175	5	6	radon	radon	PROPN
ejpam-3175	5	7	transform	transform	NOUN
ejpam-3175	5	8	to	to	PART
ejpam-3175	5	9	define	define	VERB
ejpam-3175	5	10	the	the	DET
ejpam-3175	5	11	littlewood	littlewood	NOUN
ejpam-3175	5	12	-	-	PUNCT
ejpam-3175	5	13	paley	paley	PROPN
ejpam-3175	5	14	g	g	NOUN
ejpam-3175	5	15	-	-	PUNCT
ejpam-3175	5	16	function	function	NOUN
ejpam-3175	5	17	on	on	ADP
ejpam-3175	5	18	a	a	DET
ejpam-3175	5	19	hyperplane	hyperplane	NOUN
ejpam-3175	5	20	and	and	CCONJ
ejpam-3175	5	21	obtain	obtain	VERB
ejpam-3175	5	22	the	the	DET
ejpam-3175	5	23	littlewoodpaley	littlewoodpaley	NOUN
ejpam-3175	5	24	theory	theory	NOUN
ejpam-3175	5	25	.	.	PUNCT
ejpam-3175	6	1	2010	2010	NUM
ejpam-3175	6	2	mathematics	mathematic	NOUN
ejpam-3175	6	3	subject	subject	NOUN
ejpam-3175	6	4	classifications	classification	NOUN
ejpam-3175	6	5	:	:	PUNCT
ejpam-3175	6	6	44a12	44a12	NUM
ejpam-3175	6	7	;	;	PUNCT
ejpam-3175	6	8	43a15	43a15	NUM
ejpam-3175	6	9	key	key	ADJ
ejpam-3175	6	10	words	word	NOUN
ejpam-3175	6	11	and	and	CCONJ
ejpam-3175	6	12	phrases	phrase	NOUN
ejpam-3175	6	13	:	:	PUNCT
ejpam-3175	6	14	heisenberg	heisenberg	PROPN
ejpam-3175	6	15	group	group	PROPN
ejpam-3175	6	16	,	,	PUNCT
ejpam-3175	6	17	little	little	ADJ
ejpam-3175	6	18	-	-	PUNCT
ejpam-3175	6	19	wood	wood	NOUN
ejpam-3175	6	20	pelay	pelay	NOUN
ejpam-3175	6	21	g	g	NOUN
ejpam-3175	6	22	-	-	PUNCT
ejpam-3175	6	23	function	function	NOUN
ejpam-3175	6	24	,	,	PUNCT
ejpam-3175	6	25	radon	radon	PROPN
ejpam-3175	6	26	transform	transform	VERB
ejpam-3175	6	27	1	1	NUM
ejpam-3175	6	28	.	.	PUNCT
ejpam-3175	7	1	introduction	introduction	NOUN
ejpam-3175	7	2	we	we	PRON
ejpam-3175	7	3	identify	identify	VERB
ejpam-3175	7	4	any	any	DET
ejpam-3175	7	5	point	point	NOUN
ejpam-3175	7	6	(	(	PUNCT
ejpam-3175	7	7	x	x	NOUN
ejpam-3175	7	8	,	,	PUNCT
ejpam-3175	7	9	y	y	NOUN
ejpam-3175	7	10	)	)	PUNCT
ejpam-3175	7	11	in	in	ADP
ejpam-3175	7	12	r2n	r2n	NOUN
ejpam-3175	7	13	with	with	ADP
ejpam-3175	7	14	the	the	DET
ejpam-3175	7	15	point	point	NOUN
ejpam-3175	8	1	z	z	NOUN
ejpam-3175	8	2	=	=	PUNCT
ejpam-3175	9	1	x	x	PROPN
ejpam-3175	9	2	+	+	NUM
ejpam-3175	9	3	iy	iy	PROPN
ejpam-3175	9	4	in	in	ADP
ejpam-3175	9	5	cn	cn	PROPN
ejpam-3175	10	1	and	and	CCONJ
ejpam-3175	10	2	denote	denote	VERB
ejpam-3175	10	3	the	the	DET
ejpam-3175	10	4	symplectic	symplectic	ADJ
ejpam-3175	10	5	form	form	NOUN
ejpam-3175	10	6	[	[	X
ejpam-3175	10	7	·	·	PUNCT
ejpam-3175	10	8	,	,	PUNCT
ejpam-3175	10	9	·	·	PUNCT
ejpam-3175	10	10	]	]	PUNCT
ejpam-3175	10	11	on	on	ADP
ejpam-3175	10	12	cn	cn	VERB
ejpam-3175	10	13	by	by	ADP
ejpam-3175	10	14	[	[	X
ejpam-3175	10	15	z	z	PROPN
ejpam-3175	10	16	,	,	PUNCT
ejpam-3175	10	17	w	w	PROPN
ejpam-3175	10	18	]	]	X
ejpam-3175	10	19	=	=	SYM
ejpam-3175	10	20	1	1	NUM
ejpam-3175	10	21	2	2	NUM
ejpam-3175	10	22	im〈z	im〈z	NOUN
ejpam-3175	10	23	,	,	PUNCT
ejpam-3175	10	24	w	w	NOUN
ejpam-3175	10	25	〉	〉	NOUN
ejpam-3175	10	26	for	for	ADP
ejpam-3175	10	27	z	z	PROPN
ejpam-3175	10	28	,	,	PUNCT
ejpam-3175	10	29	w	w	PROPN
ejpam-3175	10	30	∈	∈	PROPN
ejpam-3175	11	1	cn	cn	PROPN
ejpam-3175	11	2	.	.	PUNCT
ejpam-3175	12	1	we	we	PRON
ejpam-3175	12	2	define	define	VERB
ejpam-3175	12	3	the	the	DET
ejpam-3175	12	4	multiplication	multiplication	NOUN
ejpam-3175	12	5	on	on	ADP
ejpam-3175	12	6	cn	cn	PROPN
ejpam-3175	12	7	×	×	NOUN
ejpam-3175	12	8	r	r	NOUN
ejpam-3175	12	9	by	by	ADP
ejpam-3175	12	10	(	(	PUNCT
ejpam-3175	12	11	z	z	NOUN
ejpam-3175	12	12	,	,	PUNCT
ejpam-3175	12	13	t)(z′	t)(z′	PROPN
ejpam-3175	12	14	,	,	PUNCT
ejpam-3175	12	15	t′	t′	NUM
ejpam-3175	12	16	)	)	PUNCT
ejpam-3175	13	1	=	=	PUNCT
ejpam-3175	13	2	(	(	PUNCT
ejpam-3175	13	3	z	z	X
ejpam-3175	13	4	+	+	NOUN
ejpam-3175	13	5	z′	z′	NUM
ejpam-3175	13	6	,	,	PUNCT
ejpam-3175	13	7	t+	t+	X
ejpam-3175	13	8	t′	t′	NUM
ejpam-3175	13	9	+	+	CCONJ
ejpam-3175	13	10	1	1	NUM
ejpam-3175	13	11	2	2	NUM
ejpam-3175	13	12	im〈z	im〈z	NOUN
ejpam-3175	13	13	,	,	PUNCT
ejpam-3175	13	14	z′	z′	NOUN
ejpam-3175	13	15	〉	〉	NUM
ejpam-3175	13	16	)	)	PUNCT
ejpam-3175	13	17	(	(	PUNCT
ejpam-3175	13	18	1	1	X
ejpam-3175	13	19	)	)	PUNCT
ejpam-3175	13	20	for	for	ADP
ejpam-3175	13	21	all	all	DET
ejpam-3175	13	22	(	(	PUNCT
ejpam-3175	13	23	z	z	PROPN
ejpam-3175	13	24	,	,	PUNCT
ejpam-3175	13	25	t	t	PROPN
ejpam-3175	13	26	)	)	PUNCT
ejpam-3175	13	27	and	and	CCONJ
ejpam-3175	13	28	(	(	PUNCT
ejpam-3175	13	29	z′	z′	PROPN
ejpam-3175	13	30	,	,	PUNCT
ejpam-3175	13	31	t′	t′	NUM
ejpam-3175	13	32	)	)	PUNCT
ejpam-3175	13	33	in	in	ADP
ejpam-3175	13	34	cn	cn	PROPN
ejpam-3175	13	35	×	×	PROPN
ejpam-3175	13	36	r.	r.	PROPN
ejpam-3175	13	37	the	the	DET
ejpam-3175	13	38	group	group	NOUN
ejpam-3175	14	1	cn	cn	PROPN
ejpam-3175	14	2	×	×	NOUN
ejpam-3175	14	3	r	r	NOUN
ejpam-3175	14	4	with	with	ADP
ejpam-3175	14	5	respect	respect	NOUN
ejpam-3175	14	6	to	to	ADP
ejpam-3175	14	7	the	the	DET
ejpam-3175	14	8	multiplication	multiplication	NOUN
ejpam-3175	14	9	defined	define	VERB
ejpam-3175	14	10	by	by	ADP
ejpam-3175	14	11	(	(	PUNCT
ejpam-3175	14	12	1	1	X
ejpam-3175	14	13	)	)	PUNCT
ejpam-3175	14	14	is	be	AUX
ejpam-3175	14	15	denoted	denote	VERB
ejpam-3175	14	16	by	by	ADP
ejpam-3175	14	17	hn	hn	PROPN
ejpam-3175	14	18	and	and	CCONJ
ejpam-3175	14	19	is	be	AUX
ejpam-3175	14	20	called	call	VERB
ejpam-3175	14	21	the	the	DET
ejpam-3175	14	22	heisenberg	heisenberg	PROPN
ejpam-3175	14	23	group	group	NOUN
ejpam-3175	14	24	.	.	PUNCT
ejpam-3175	15	1	it	it	PRON
ejpam-3175	15	2	is	be	AUX
ejpam-3175	15	3	well	well	ADV
ejpam-3175	15	4	known	know	VERB
ejpam-3175	15	5	that	that	SCONJ
ejpam-3175	15	6	the	the	DET
ejpam-3175	15	7	heisenberg	heisenberg	PROPN
ejpam-3175	15	8	group	group	PROPN
ejpam-3175	15	9	plays	play	VERB
ejpam-3175	15	10	an	an	DET
ejpam-3175	15	11	important	important	ADJ
ejpam-3175	15	12	role	role	NOUN
ejpam-3175	15	13	in	in	ADP
ejpam-3175	15	14	several	several	ADJ
ejpam-3175	15	15	branches	branch	NOUN
ejpam-3175	15	16	of	of	ADP
ejpam-3175	15	17	mathematics	mathematic	NOUN
ejpam-3175	15	18	.	.	PUNCT
ejpam-3175	16	1	there	there	PRON
ejpam-3175	16	2	are	be	VERB
ejpam-3175	16	3	,	,	PUNCT
ejpam-3175	16	4	therefore	therefore	ADV
ejpam-3175	16	5	,	,	PUNCT
ejpam-3175	16	6	several	several	ADJ
ejpam-3175	16	7	ways	way	NOUN
ejpam-3175	16	8	of	of	ADP
ejpam-3175	16	9	realising	realise	VERB
ejpam-3175	16	10	the	the	DET
ejpam-3175	16	11	group	group	NOUN
ejpam-3175	16	12	due	due	ADP
ejpam-3175	16	13	to	to	ADP
ejpam-3175	16	14	the	the	DET
ejpam-3175	16	15	widely	widely	ADJ
ejpam-3175	16	16	application	application	NOUN
ejpam-3175	16	17	of	of	ADP
ejpam-3175	16	18	the	the	DET
ejpam-3175	16	19	heisenberg	heisenberg	PROPN
ejpam-3175	16	20	group	group	PROPN
ejpam-3175	16	21	(	(	PUNCT
ejpam-3175	16	22	see	see	VERB
ejpam-3175	16	23	[	[	X
ejpam-3175	16	24	2	2	NUM
ejpam-3175	16	25	,	,	PUNCT
ejpam-3175	16	26	17	17	NUM
ejpam-3175	16	27	]	]	PUNCT
ejpam-3175	16	28	)	)	PUNCT
ejpam-3175	16	29	.	.	PUNCT
ejpam-3175	17	1	in	in	ADP
ejpam-3175	17	2	1917	1917	NUM
ejpam-3175	17	3	,	,	PUNCT
ejpam-3175	17	4	radon	radon	PROPN
ejpam-3175	17	5	proved	prove	VERB
ejpam-3175	17	6	that	that	SCONJ
ejpam-3175	17	7	a	a	DET
ejpam-3175	17	8	smooth	smooth	ADJ
ejpam-3175	17	9	function	function	NOUN
ejpam-3175	17	10	in	in	ADP
ejpam-3175	17	11	r3	r3	PROPN
ejpam-3175	17	12	is	be	AUX
ejpam-3175	17	13	completely	completely	ADV
ejpam-3175	17	14	determined	determine	VERB
ejpam-3175	17	15	by	by	ADP
ejpam-3175	17	16	its	its	PRON
ejpam-3175	17	17	integrals	integral	NOUN
ejpam-3175	17	18	over	over	ADP
ejpam-3175	17	19	all	all	DET
ejpam-3175	17	20	the	the	DET
ejpam-3175	17	21	planes	plane	NOUN
ejpam-3175	17	22	.	.	PUNCT
ejpam-3175	18	1	this	this	PRON
ejpam-3175	18	2	leads	lead	VERB
ejpam-3175	18	3	in	in	ADP
ejpam-3175	18	4	a	a	DET
ejpam-3175	18	5	more	more	ADV
ejpam-3175	18	6	general	general	ADJ
ejpam-3175	18	7	setting	setting	NOUN
ejpam-3175	18	8	to	to	ADP
ejpam-3175	18	9	the	the	DET
ejpam-3175	18	10	consideration	consideration	NOUN
ejpam-3175	18	11	of	of	ADP
ejpam-3175	18	12	the	the	DET
ejpam-3175	18	13	radon	radon	PROPN
ejpam-3175	18	14	transform	transform	NOUN
ejpam-3175	18	15	.	.	PUNCT
ejpam-3175	19	1	the	the	DET
ejpam-3175	19	2	research	research	NOUN
ejpam-3175	19	3	of	of	ADP
ejpam-3175	19	4	radon	radon	PROPN
ejpam-3175	19	5	transform	transform	NOUN
ejpam-3175	19	6	has	have	AUX
ejpam-3175	19	7	made	make	VERB
ejpam-3175	19	8	important	important	ADJ
ejpam-3175	19	9	influence	influence	NOUN
ejpam-3175	19	10	due	due	ADP
ejpam-3175	19	11	to	to	ADP
ejpam-3175	19	12	its	its	PRON
ejpam-3175	19	13	wide	wide	ADJ
ejpam-3175	19	14	applications	application	NOUN
ejpam-3175	19	15	to	to	ADP
ejpam-3175	19	16	partial	partial	ADJ
ejpam-3175	19	17	differential	differential	NOUN
ejpam-3175	19	18	equations	equation	NOUN
ejpam-3175	19	19	,	,	PUNCT
ejpam-3175	19	20	x	x	NOUN
ejpam-3175	19	21	-	-	NOUN
ejpam-3175	19	22	ray	ray	NOUN
ejpam-3175	19	23	technology	technology	NOUN
ejpam-3175	19	24	,	,	PUNCT
ejpam-3175	19	25	radio	radio	NOUN
ejpam-3175	19	26	astronomy	astronomy	NOUN
ejpam-3175	19	27	and	and	CCONJ
ejpam-3175	19	28	so	so	ADV
ejpam-3175	19	29	on	on	ADV
ejpam-3175	19	30	.	.	PUNCT
ejpam-3175	20	1	the	the	DET
ejpam-3175	20	2	basic	basic	ADJ
ejpam-3175	20	3	theory	theory	NOUN
ejpam-3175	20	4	and	and	CCONJ
ejpam-3175	20	5	some	some	DET
ejpam-3175	20	6	new	new	ADJ
ejpam-3175	20	7	results	result	NOUN
ejpam-3175	20	8	can	can	AUX
ejpam-3175	20	9	be	be	AUX
ejpam-3175	20	10	found	find	VERB
ejpam-3175	20	11	in	in	ADP
ejpam-3175	20	12	[	[	X
ejpam-3175	20	13	9	9	NUM
ejpam-3175	20	14	]	]	PUNCT
ejpam-3175	20	15	.	.	PUNCT
ejpam-3175	21	1	geller	geller	PROPN
ejpam-3175	21	2	-	-	PUNCT
ejpam-3175	21	3	stein	stein	PROPN
ejpam-3175	22	1	[	[	X
ejpam-3175	22	2	5	5	NUM
ejpam-3175	22	3	]	]	PUNCT
ejpam-3175	22	4	and	and	CCONJ
ejpam-3175	22	5	strichartz	strichartz	VERB
ejpam-3175	22	6	[	[	X
ejpam-3175	22	7	16	16	NUM
ejpam-3175	22	8	]	]	PUNCT
ejpam-3175	22	9	introduced	introduce	VERB
ejpam-3175	22	10	the	the	DET
ejpam-3175	22	11	heisenberg	heisenberg	PROPN
ejpam-3175	22	12	-	-	PUNCT
ejpam-3175	22	13	radon	radon	PROPN
ejpam-3175	22	14	∗corresponding	∗corresponding	NOUN
ejpam-3175	22	15	author	author	NOUN
ejpam-3175	22	16	.	.	PUNCT
ejpam-3175	23	1	email	email	NOUN
ejpam-3175	23	2	addresses	address	NOUN
ejpam-3175	23	3	:	:	PUNCT
ejpam-3175	23	4	fangzheng@e.gzhu.edu.cn	fangzheng@e.gzhu.edu.cn	PROPN
ejpam-3175	23	5	(	(	PUNCT
ejpam-3175	23	6	z.	z.	PROPN
ejpam-3175	23	7	fang	fang	PROPN
ejpam-3175	23	8	)	)	PUNCT
ejpam-3175	23	9	,	,	PUNCT
ejpam-3175	23	10	hejianxun@gzhu.edu.cn	hejianxun@gzhu.edu.cn	PROPN
ejpam-3175	23	11	(	(	PUNCT
ejpam-3175	23	12	j.	j.	PROPN
ejpam-3175	23	13	he	he	PROPN
ejpam-3175	23	14	)	)	PUNCT
ejpam-3175	23	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3175	24	1	138	138	NUM
ejpam-3175	24	2	c	c	X
ejpam-3175	24	3	©	©	PROPN
ejpam-3175	24	4	2018	2018	NUM
ejpam-3175	24	5	ejpam	ejpam	VERB
ejpam-3175	24	6	all	all	DET
ejpam-3175	24	7	rights	right	NOUN
ejpam-3175	24	8	reserved	reserve	VERB
ejpam-3175	24	9	.	.	PUNCT
ejpam-3175	25	1	z.	z.	PROPN
ejpam-3175	25	2	fang	fang	PROPN
ejpam-3175	25	3	,	,	PUNCT
ejpam-3175	25	4	h.	h.	PROPN
ejpam-3175	25	5	jianxun	jianxun	PROPN
ejpam-3175	25	6	he	he	PRON
ejpam-3175	25	7	/	/	SYM
ejpam-3175	25	8	eur	eur	PROPN
ejpam-3175	25	9	.	.	PUNCT
ejpam-3175	26	1	j.	j.	PROPN
ejpam-3175	26	2	pure	pure	PROPN
ejpam-3175	26	3	appl	appl	PROPN
ejpam-3175	26	4	.	.	PROPN
ejpam-3175	26	5	math	math	PROPN
ejpam-3175	26	6	,	,	PUNCT
ejpam-3175	26	7	11	11	NUM
ejpam-3175	26	8	(	(	PUNCT
ejpam-3175	26	9	1	1	NUM
ejpam-3175	26	10	)	)	PUNCT
ejpam-3175	26	11	(	(	PUNCT
ejpam-3175	26	12	2018	2018	NUM
ejpam-3175	26	13	)	)	PUNCT
ejpam-3175	26	14	,	,	PUNCT
ejpam-3175	26	15	138	138	NUM
ejpam-3175	26	16	-	-	SYM
ejpam-3175	26	17	149	149	NUM
ejpam-3175	26	18	139	139	NUM
ejpam-3175	26	19	transform	transform	NOUN
ejpam-3175	26	20	on	on	ADP
ejpam-3175	26	21	hn	hn	PROPN
ejpam-3175	26	22	.	.	PUNCT
ejpam-3175	27	1	he	he	PRON
ejpam-3175	27	2	-	-	PUNCT
ejpam-3175	27	3	liu	liu	PROPN
ejpam-3175	27	4	considered	consider	VERB
ejpam-3175	27	5	inversion	inversion	NOUN
ejpam-3175	27	6	formulas	formula	NOUN
ejpam-3175	27	7	of	of	ADP
ejpam-3175	27	8	the	the	DET
ejpam-3175	27	9	radon	radon	PROPN
ejpam-3175	27	10	transform	transform	NOUN
ejpam-3175	27	11	on	on	ADP
ejpam-3175	27	12	hn	hn	PROPN
ejpam-3175	27	13	and	and	CCONJ
ejpam-3175	27	14	siegel	siegel	PROPN
ejpam-3175	27	15	type	type	PROPN
ejpam-3175	27	16	lie	lie	NOUN
ejpam-3175	27	17	group	group	NOUN
ejpam-3175	27	18	in	in	ADP
ejpam-3175	27	19	[	[	X
ejpam-3175	27	20	6	6	NUM
ejpam-3175	27	21	,	,	PUNCT
ejpam-3175	27	22	7	7	NUM
ejpam-3175	27	23	,	,	PUNCT
ejpam-3175	27	24	8	8	NUM
ejpam-3175	27	25	]	]	PUNCT
ejpam-3175	27	26	by	by	ADP
ejpam-3175	27	27	using	use	VERB
ejpam-3175	27	28	the	the	DET
ejpam-3175	27	29	continuous	continuous	ADJ
ejpam-3175	27	30	wavelet	wavelet	NOUN
ejpam-3175	27	31	transforms	transform	VERB
ejpam-3175	27	32	.	.	PUNCT
ejpam-3175	28	1	the	the	DET
ejpam-3175	28	2	combination	combination	NOUN
ejpam-3175	28	3	of	of	ADP
ejpam-3175	28	4	radon	radon	NOUN
ejpam-3175	28	5	transform	transform	NOUN
ejpam-3175	28	6	and	and	CCONJ
ejpam-3175	28	7	wavelet	wavelet	NOUN
ejpam-3175	28	8	transform	transform	NOUN
ejpam-3175	28	9	has	have	AUX
ejpam-3175	28	10	proved	prove	VERB
ejpam-3175	28	11	to	to	PART
ejpam-3175	28	12	be	be	AUX
ejpam-3175	28	13	very	very	ADV
ejpam-3175	28	14	useful	useful	ADJ
ejpam-3175	28	15	both	both	CCONJ
ejpam-3175	28	16	in	in	ADP
ejpam-3175	28	17	pure	pure	ADJ
ejpam-3175	28	18	mathematics	mathematic	NOUN
ejpam-3175	28	19	and	and	CCONJ
ejpam-3175	28	20	applied	apply	VERB
ejpam-3175	28	21	science	science	NOUN
ejpam-3175	28	22	.	.	PUNCT
ejpam-3175	29	1	therefore	therefore	ADV
ejpam-3175	29	2	,	,	PUNCT
ejpam-3175	29	3	it	it	PRON
ejpam-3175	29	4	is	be	AUX
ejpam-3175	29	5	very	very	ADV
ejpam-3175	29	6	meaningful	meaningful	ADJ
ejpam-3175	29	7	to	to	PART
ejpam-3175	29	8	give	give	VERB
ejpam-3175	29	9	the	the	DET
ejpam-3175	29	10	inversion	inversion	NOUN
ejpam-3175	29	11	formula	formula	NOUN
ejpam-3175	29	12	the	the	DET
ejpam-3175	29	13	radon	radon	PROPN
ejpam-3175	29	14	transform	transform	NOUN
ejpam-3175	29	15	by	by	ADP
ejpam-3175	29	16	using	use	VERB
ejpam-3175	29	17	various	various	ADJ
ejpam-3175	29	18	ways	way	NOUN
ejpam-3175	29	19	.	.	PUNCT
ejpam-3175	30	1	in	in	ADP
ejpam-3175	30	2	addition	addition	NOUN
ejpam-3175	30	3	,	,	PUNCT
ejpam-3175	30	4	because	because	SCONJ
ejpam-3175	30	5	of	of	ADP
ejpam-3175	30	6	great	great	ADJ
ejpam-3175	30	7	application	application	NOUN
ejpam-3175	30	8	of	of	ADP
ejpam-3175	30	9	the	the	DET
ejpam-3175	30	10	heisenberg	heisenberg	PROPN
ejpam-3175	30	11	group	group	NOUN
ejpam-3175	30	12	,	,	PUNCT
ejpam-3175	30	13	many	many	ADJ
ejpam-3175	30	14	scholars	scholar	NOUN
ejpam-3175	30	15	have	have	AUX
ejpam-3175	30	16	studied	study	VERB
ejpam-3175	30	17	littlewood	littlewood	PROPN
ejpam-3175	30	18	-	-	PUNCT
ejpam-3175	30	19	paley	paley	PROPN
ejpam-3175	30	20	theory	theory	NOUN
ejpam-3175	30	21	on	on	ADP
ejpam-3175	30	22	the	the	DET
ejpam-3175	30	23	heisenberg	heisenberg	PROPN
ejpam-3175	30	24	group	group	NOUN
ejpam-3175	30	25	in	in	ADP
ejpam-3175	30	26	recent	recent	ADJ
ejpam-3175	30	27	years	year	NOUN
ejpam-3175	30	28	.	.	PUNCT
ejpam-3175	31	1	thangavelu	thangavelu	NOUN
ejpam-3175	31	2	[	[	X
ejpam-3175	31	3	17	17	NUM
ejpam-3175	31	4	]	]	PUNCT
ejpam-3175	31	5	studied	study	VERB
ejpam-3175	31	6	the	the	DET
ejpam-3175	31	7	g	g	NOUN
ejpam-3175	31	8	-	-	PUNCT
ejpam-3175	31	9	function	function	NOUN
ejpam-3175	31	10	connected	connect	VERB
ejpam-3175	31	11	with	with	ADP
ejpam-3175	31	12	the	the	DET
ejpam-3175	31	13	semigroup	semigroup	NOUN
ejpam-3175	31	14	generated	generate	VERB
ejpam-3175	31	15	by	by	ADP
ejpam-3175	31	16	the	the	DET
ejpam-3175	31	17	sub	sub	NOUN
ejpam-3175	31	18	-	-	NOUN
ejpam-3175	31	19	laplacian	laplacian	ADJ
ejpam-3175	31	20	.	.	PUNCT
ejpam-3175	32	1	liu	liu	PROPN
ejpam-3175	32	2	-	-	PUNCT
ejpam-3175	32	3	ma	ma	PROPN
ejpam-3175	33	1	[	[	X
ejpam-3175	33	2	12	12	NUM
ejpam-3175	33	3	]	]	PUNCT
ejpam-3175	33	4	investigated	investigate	VERB
ejpam-3175	33	5	the	the	DET
ejpam-3175	33	6	g	g	NOUN
ejpam-3175	33	7	-	-	PUNCT
ejpam-3175	33	8	function	function	NOUN
ejpam-3175	33	9	related	relate	VERB
ejpam-3175	33	10	to	to	ADP
ejpam-3175	33	11	a	a	DET
ejpam-3175	33	12	class	class	NOUN
ejpam-3175	33	13	of	of	ADP
ejpam-3175	33	14	radial	radial	ADJ
ejpam-3175	33	15	functions	function	NOUN
ejpam-3175	33	16	in	in	ADP
ejpam-3175	33	17	which	which	PRON
ejpam-3175	33	18	the	the	DET
ejpam-3175	33	19	characterization	characterization	NOUN
ejpam-3175	33	20	of	of	ADP
ejpam-3175	33	21	the	the	DET
ejpam-3175	33	22	lp(hn)-norm	lp(hn)-norm	NOUN
ejpam-3175	33	23	of	of	ADP
ejpam-3175	33	24	a	a	DET
ejpam-3175	33	25	function	function	NOUN
ejpam-3175	33	26	on	on	ADP
ejpam-3175	33	27	hn	hn	PROPN
ejpam-3175	33	28	was	be	AUX
ejpam-3175	33	29	obtained	obtain	VERB
ejpam-3175	33	30	.	.	PUNCT
ejpam-3175	34	1	this	this	DET
ejpam-3175	34	2	paper	paper	NOUN
ejpam-3175	34	3	is	be	AUX
ejpam-3175	34	4	organized	organize	VERB
ejpam-3175	34	5	as	as	SCONJ
ejpam-3175	34	6	follows	follow	VERB
ejpam-3175	34	7	.	.	PUNCT
ejpam-3175	35	1	in	in	ADP
ejpam-3175	35	2	section	section	NOUN
ejpam-3175	35	3	2	2	NUM
ejpam-3175	35	4	,	,	PUNCT
ejpam-3175	35	5	we	we	PRON
ejpam-3175	35	6	recall	recall	VERB
ejpam-3175	35	7	some	some	DET
ejpam-3175	35	8	notations	notation	NOUN
ejpam-3175	35	9	,	,	PUNCT
ejpam-3175	35	10	definitions	definition	NOUN
ejpam-3175	35	11	and	and	CCONJ
ejpam-3175	35	12	preliminary	preliminary	ADJ
ejpam-3175	35	13	fact	fact	NOUN
ejpam-3175	35	14	.	.	PUNCT
ejpam-3175	36	1	motivated	motivate	VERB
ejpam-3175	36	2	by	by	ADP
ejpam-3175	36	3	[	[	X
ejpam-3175	36	4	5	5	NUM
ejpam-3175	36	5	,	,	PUNCT
ejpam-3175	36	6	9	9	NUM
ejpam-3175	36	7	,	,	PUNCT
ejpam-3175	36	8	10	10	NUM
ejpam-3175	36	9	]	]	PUNCT
ejpam-3175	36	10	,	,	PUNCT
ejpam-3175	36	11	we	we	PRON
ejpam-3175	36	12	mainly	mainly	ADV
ejpam-3175	36	13	introduce	introduce	VERB
ejpam-3175	36	14	singular	singular	ADJ
ejpam-3175	36	15	convolution	convolution	NOUN
ejpam-3175	36	16	operators	operator	NOUN
ejpam-3175	36	17	on	on	ADP
ejpam-3175	36	18	hn	hn	PROPN
ejpam-3175	36	19	and	and	CCONJ
ejpam-3175	36	20	obtain	obtain	VERB
ejpam-3175	36	21	inverse	inverse	ADJ
ejpam-3175	36	22	formulas	formula	NOUN
ejpam-3175	36	23	of	of	ADP
ejpam-3175	36	24	radon	radon	NOUN
ejpam-3175	36	25	transform	transform	NOUN
ejpam-3175	36	26	in	in	ADP
ejpam-3175	36	27	section	section	NOUN
ejpam-3175	36	28	3	3	NUM
ejpam-3175	36	29	.	.	PUNCT
ejpam-3175	36	30	section	section	NOUN
ejpam-3175	36	31	4	4	NUM
ejpam-3175	36	32	is	be	AUX
ejpam-3175	36	33	to	to	PART
ejpam-3175	36	34	define	define	VERB
ejpam-3175	36	35	littlewood	littlewood	NOUN
ejpam-3175	36	36	-	-	PUNCT
ejpam-3175	36	37	paley	paley	NOUN
ejpam-3175	36	38	g	g	NOUN
ejpam-3175	36	39	-	-	PUNCT
ejpam-3175	36	40	function	function	NOUN
ejpam-3175	36	41	in	in	ADP
ejpam-3175	36	42	some	some	DET
ejpam-3175	36	43	hyperplanes	hyperplane	NOUN
ejpam-3175	36	44	and	and	CCONJ
ejpam-3175	36	45	establishes	establish	VERB
ejpam-3175	36	46	littlewoodpaley	littlewoodpaley	NOUN
ejpam-3175	36	47	theory	theory	NOUN
ejpam-3175	36	48	,	,	PUNCT
ejpam-3175	36	49	which	which	PRON
ejpam-3175	36	50	generalizes	generalize	VERB
ejpam-3175	36	51	the	the	DET
ejpam-3175	36	52	results	result	NOUN
ejpam-3175	36	53	in	in	ADP
ejpam-3175	36	54	[	[	X
ejpam-3175	36	55	12	12	NUM
ejpam-3175	36	56	]	]	PUNCT
ejpam-3175	36	57	.	.	PUNCT
ejpam-3175	37	1	at	at	ADP
ejpam-3175	37	2	last	last	ADV
ejpam-3175	37	3	,	,	PUNCT
ejpam-3175	37	4	in	in	ADP
ejpam-3175	37	5	section	section	NOUN
ejpam-3175	37	6	5	5	NUM
ejpam-3175	37	7	we	we	PRON
ejpam-3175	37	8	show	show	VERB
ejpam-3175	37	9	that	that	SCONJ
ejpam-3175	37	10	the	the	DET
ejpam-3175	37	11	radon	radon	PROPN
ejpam-3175	37	12	transform	transform	NOUN
ejpam-3175	37	13	and	and	CCONJ
ejpam-3175	37	14	the	the	DET
ejpam-3175	37	15	poisson	poisson	NOUN
ejpam-3175	37	16	integral	integral	ADJ
ejpam-3175	37	17	for	for	ADP
ejpam-3175	37	18	the	the	DET
ejpam-3175	37	19	šliov	šliov	PROPN
ejpam-3175	37	20	boundary	boundary	NOUN
ejpam-3175	37	21	are	be	AUX
ejpam-3175	37	22	equivalent	equivalent	ADJ
ejpam-3175	37	23	,	,	PUNCT
ejpam-3175	37	24	and	and	CCONJ
ejpam-3175	37	25	the	the	DET
ejpam-3175	37	26	inverse	inverse	NOUN
ejpam-3175	37	27	formula	formula	NOUN
ejpam-3175	37	28	is	be	AUX
ejpam-3175	37	29	given	give	VERB
ejpam-3175	37	30	by	by	ADP
ejpam-3175	37	31	the	the	DET
ejpam-3175	37	32	classical	classical	ADJ
ejpam-3175	37	33	schwarz	schwarz	NOUN
ejpam-3175	37	34	theorem	theorem	VERB
ejpam-3175	37	35	.	.	PROPN
ejpam-3175	37	36	2	2	X
ejpam-3175	37	37	.	.	X
ejpam-3175	37	38	preliminaries	preliminary	NOUN
ejpam-3175	37	39	we	we	PRON
ejpam-3175	37	40	denote	denote	VERB
ejpam-3175	37	41	by	by	ADP
ejpam-3175	37	42	o	o	PROPN
ejpam-3175	37	43	the	the	DET
ejpam-3175	37	44	space	space	NOUN
ejpam-3175	37	45	all	all	DET
ejpam-3175	37	46	holomorphic	holomorphic	ADJ
ejpam-3175	37	47	functions	function	NOUN
ejpam-3175	37	48	on	on	ADP
ejpam-3175	37	49	cn	cn	PROPN
ejpam-3175	37	50	,	,	PUNCT
ejpam-3175	37	51	the	the	DET
ejpam-3175	37	52	fock	fock	ADJ
ejpam-3175	37	53	space	space	NOUN
ejpam-3175	37	54	with	with	ADP
ejpam-3175	37	55	λ	λ	PROPN
ejpam-3175	37	56	∈	∈	PROPN
ejpam-3175	37	57	(	(	PUNCT
ejpam-3175	37	58	0	0	NUM
ejpam-3175	37	59	,	,	PUNCT
ejpam-3175	37	60	∞	∞	NUM
ejpam-3175	37	61	)	)	PUNCT
ejpam-3175	37	62	is	be	AUX
ejpam-3175	37	63	defined	define	VERB
ejpam-3175	37	64	by	by	ADP
ejpam-3175	37	65	hλ	hλ	NOUN
ejpam-3175	37	66	:	:	PUNCT
ejpam-3175	37	67	=	=	SYM
ejpam-3175	37	68	{	{	PUNCT
ejpam-3175	37	69	f	f	PROPN
ejpam-3175	37	70	∈	∈	PROPN
ejpam-3175	37	71	o	o	NOUN
ejpam-3175	37	72	:	:	PUNCT
ejpam-3175	37	73	‖f‖2	‖f‖2	ADJ
ejpam-3175	37	74	:	:	PUNCT
ejpam-3175	38	1	=	=	SYM
ejpam-3175	38	2	∫	∫	PROPN
ejpam-3175	38	3	cn	cn	X
ejpam-3175	38	4	|f(w)|2e−πλ|w|2λndw	|f(w)|2e−πλ|w|2λndw	PROPN
ejpam-3175	38	5	<	<	X
ejpam-3175	38	6	∞	∞	NUM
ejpam-3175	38	7	}	}	PUNCT
ejpam-3175	38	8	,	,	PUNCT
ejpam-3175	38	9	and	and	CCONJ
ejpam-3175	38	10	h−λ	h−λ	NOUN
ejpam-3175	38	11	:	:	PUNCT
ejpam-3175	38	12	=	=	X
ejpam-3175	38	13	{	{	PUNCT
ejpam-3175	38	14	f	f	X
ejpam-3175	38	15	:	:	PUNCT
ejpam-3175	38	16	f	f	X
ejpam-3175	38	17	∈hλ	∈hλ	X
ejpam-3175	38	18	}	}	PUNCT
ejpam-3175	38	19	.	.	PUNCT
ejpam-3175	39	1	the	the	DET
ejpam-3175	39	2	scalar	scalar	ADJ
ejpam-3175	39	3	product	product	NOUN
ejpam-3175	39	4	is	be	AUX
ejpam-3175	39	5	given	give	VERB
ejpam-3175	39	6	by	by	ADP
ejpam-3175	39	7	〈	〈	PROPN
ejpam-3175	39	8	f	f	PROPN
ejpam-3175	39	9	,	,	PUNCT
ejpam-3175	39	10	g	g	PROPN
ejpam-3175	39	11	〉	〉	NOUN
ejpam-3175	39	12	:	:	PUNCT
ejpam-3175	40	1	=	=	SYM
ejpam-3175	40	2	∫	∫	PROPN
ejpam-3175	40	3	cn	cn	INTJ
ejpam-3175	40	4	f(w)g(w)e−πλ|w|	f(w)g(w)e−πλ|w|	PROPN
ejpam-3175	40	5	2	2	NUM
ejpam-3175	40	6	λndw	λndw	NOUN
ejpam-3175	40	7	.	.	PUNCT
ejpam-3175	41	1	now	now	ADV
ejpam-3175	41	2	,	,	PUNCT
ejpam-3175	41	3	an	an	DET
ejpam-3175	41	4	arbitrary	arbitrary	ADJ
ejpam-3175	41	5	complete	complete	ADJ
ejpam-3175	41	6	orthonormal	orthonormal	ADJ
ejpam-3175	41	7	system	system	NOUN
ejpam-3175	41	8	of	of	ADP
ejpam-3175	41	9	functions	function	NOUN
ejpam-3175	41	10	ψλ	ψλ	ADP
ejpam-3175	41	11	,	,	PUNCT
ejpam-3175	41	12	α	α	PROPN
ejpam-3175	41	13	∈	∈	NOUN
ejpam-3175	41	14	hλ	hλ	X
ejpam-3175	41	15	on	on	ADP
ejpam-3175	41	16	cn	cn	PROPN
ejpam-3175	41	17	is	be	AUX
ejpam-3175	41	18	represented	represent	VERB
ejpam-3175	41	19	by	by	ADP
ejpam-3175	41	20	ψλ	ψλ	ADP
ejpam-3175	41	21	,	,	PUNCT
ejpam-3175	41	22	α(w	α(w	NOUN
ejpam-3175	41	23	)	)	PUNCT
ejpam-3175	42	1	=	=	SYM
ejpam-3175	42	2	λ|α|/2wα	λ|α|/2wα	NOUN
ejpam-3175	42	3	(	(	PUNCT
ejpam-3175	42	4	2|α|α!)1/2	2|α|α!)1/2	NUM
ejpam-3175	42	5	=	=	NOUN
ejpam-3175	42	6	wα1	wα1	NOUN
ejpam-3175	42	7	1	1	NUM
ejpam-3175	42	8	(	(	PUNCT
ejpam-3175	42	9	(	(	PUNCT
ejpam-3175	42	10	2	2	NUM
ejpam-3175	42	11	/	/	SYM
ejpam-3175	42	12	λ)α1α1!)1/2	λ)α1α1!)1/2	NOUN
ejpam-3175	42	13	·	·	PUNCT
ejpam-3175	42	14	·	·	PUNCT
ejpam-3175	42	15	·	·	PUNCT
ejpam-3175	42	16	wαn	wαn	VERB
ejpam-3175	42	17	n	n	INTJ
ejpam-3175	42	18	(	(	PUNCT
ejpam-3175	42	19	(	(	PUNCT
ejpam-3175	42	20	2	2	NUM
ejpam-3175	42	21	/	/	SYM
ejpam-3175	42	22	λ)αnαn!)1/2	λ)αnαn!)1/2	PROPN
ejpam-3175	42	23	(	(	PUNCT
ejpam-3175	42	24	2	2	NUM
ejpam-3175	42	25	)	)	PUNCT
ejpam-3175	42	26	which	which	PRON
ejpam-3175	42	27	satisfies	satisfy	VERB
ejpam-3175	42	28	〈	〈	PROPN
ejpam-3175	42	29	ψλ	ψλ	PROPN
ejpam-3175	42	30	,	,	PUNCT
ejpam-3175	42	31	α	α	X
ejpam-3175	42	32	,	,	PUNCT
ejpam-3175	42	33	ψλ	ψλ	ADP
ejpam-3175	42	34	,	,	PUNCT
ejpam-3175	42	35	β	β	NOUN
ejpam-3175	42	36	〉	〉	NOUN
ejpam-3175	42	37	=	=	SYM
ejpam-3175	42	38	δαβ	δαβ	NOUN
ejpam-3175	42	39	,	,	PUNCT
ejpam-3175	42	40	where	where	SCONJ
ejpam-3175	42	41	δαβ	δαβ	NOUN
ejpam-3175	42	42	denotes	denote	VERB
ejpam-3175	42	43	the	the	DET
ejpam-3175	42	44	kronecker	kronecker	NOUN
ejpam-3175	42	45	symbol	symbol	NOUN
ejpam-3175	42	46	and	and	CCONJ
ejpam-3175	42	47	α	α	NOUN
ejpam-3175	42	48	=	=	SYM
ejpam-3175	42	49	(	(	PUNCT
ejpam-3175	42	50	α1	α1	PROPN
ejpam-3175	42	51	,	,	PUNCT
ejpam-3175	42	52	...	...	PUNCT
ejpam-3175	42	53	,	,	PUNCT
ejpam-3175	42	54	αn	αn	X
ejpam-3175	42	55	)	)	PUNCT
ejpam-3175	42	56	∈	∈	PROPN
ejpam-3175	42	57	nn	nn	PROPN
ejpam-3175	42	58	.	.	PUNCT
ejpam-3175	43	1	it	it	PRON
ejpam-3175	43	2	is	be	AUX
ejpam-3175	43	3	natural	natural	ADJ
ejpam-3175	43	4	that	that	SCONJ
ejpam-3175	43	5	f	f	PROPN
ejpam-3175	43	6	∈hλ	∈hλ	PRON
ejpam-3175	43	7	is	be	AUX
ejpam-3175	43	8	represented	represent	VERB
ejpam-3175	43	9	by	by	ADP
ejpam-3175	43	10	a	a	DET
ejpam-3175	43	11	series	series	NOUN
ejpam-3175	43	12	f(w	f(w	PROPN
ejpam-3175	43	13	)	)	PUNCT
ejpam-3175	44	1	=	=	PUNCT
ejpam-3175	44	2	∑	∑	PROPN
ejpam-3175	44	3	α∈nn	α∈nn	PROPN
ejpam-3175	44	4	〈	〈	PROPN
ejpam-3175	44	5	f	f	PROPN
ejpam-3175	44	6	,	,	PUNCT
ejpam-3175	44	7	ψλ	ψλ	ADP
ejpam-3175	44	8	,	,	PUNCT
ejpam-3175	44	9	α〉ψλ	α〉ψλ	PROPN
ejpam-3175	44	10	,	,	PUNCT
ejpam-3175	44	11	α	α	NOUN
ejpam-3175	44	12	.	.	PUNCT
ejpam-3175	44	13	z.	z.	PROPN
ejpam-3175	44	14	fang	fang	PROPN
ejpam-3175	44	15	,	,	PUNCT
ejpam-3175	45	1	h.	h.	PROPN
ejpam-3175	45	2	jianxun	jianxun	PROPN
ejpam-3175	45	3	he	he	PRON
ejpam-3175	45	4	/	/	SYM
ejpam-3175	45	5	eur	eur	PROPN
ejpam-3175	45	6	.	.	PUNCT
ejpam-3175	46	1	j.	j.	PROPN
ejpam-3175	46	2	pure	pure	PROPN
ejpam-3175	46	3	appl	appl	PROPN
ejpam-3175	46	4	.	.	PROPN
ejpam-3175	46	5	math	math	PROPN
ejpam-3175	46	6	,	,	PUNCT
ejpam-3175	46	7	11	11	NUM
ejpam-3175	46	8	(	(	PUNCT
ejpam-3175	46	9	1	1	NUM
ejpam-3175	46	10	)	)	PUNCT
ejpam-3175	46	11	(	(	PUNCT
ejpam-3175	46	12	2018	2018	NUM
ejpam-3175	46	13	)	)	PUNCT
ejpam-3175	46	14	,	,	PUNCT
ejpam-3175	46	15	138	138	NUM
ejpam-3175	46	16	-	-	SYM
ejpam-3175	46	17	149	149	NUM
ejpam-3175	46	18	140	140	NUM
ejpam-3175	46	19	we	we	PRON
ejpam-3175	46	20	define	define	VERB
ejpam-3175	46	21	the	the	DET
ejpam-3175	46	22	bargmann	bargmann	NOUN
ejpam-3175	46	23	-	-	PUNCT
ejpam-3175	46	24	fock	fock	ADJ
ejpam-3175	46	25	representation	representation	NOUN
ejpam-3175	46	26	πλ	πλ	NOUN
ejpam-3175	46	27	from	from	ADP
ejpam-3175	46	28	hn	hn	PROPN
ejpam-3175	46	29	into	into	ADP
ejpam-3175	46	30	the	the	DET
ejpam-3175	46	31	group	group	NOUN
ejpam-3175	46	32	g	g	NOUN
ejpam-3175	46	33	of	of	ADP
ejpam-3175	46	34	all	all	DET
ejpam-3175	46	35	unitary	unitary	ADJ
ejpam-3175	46	36	operators	operator	NOUN
ejpam-3175	46	37	on	on	ADP
ejpam-3175	46	38	hλ	hλ	NOUN
ejpam-3175	46	39	by	by	ADV
ejpam-3175	46	40	,	,	PUNCT
ejpam-3175	46	41	for	for	ADP
ejpam-3175	46	42	any	any	DET
ejpam-3175	46	43	ψ	ψ	X
ejpam-3175	46	44	∈h±λ	∈h±λ	PROPN
ejpam-3175	46	45	and	and	CCONJ
ejpam-3175	46	46	any	any	DET
ejpam-3175	46	47	(	(	PUNCT
ejpam-3175	46	48	z	z	NOUN
ejpam-3175	46	49	,	,	PUNCT
ejpam-3175	46	50	t	t	PROPN
ejpam-3175	46	51	)	)	PUNCT
ejpam-3175	46	52	∈	∈	PROPN
ejpam-3175	46	53	hn	hn	PROPN
ejpam-3175	46	54	,	,	PUNCT
ejpam-3175	46	55	πλ(z	πλ(z	PRON
ejpam-3175	46	56	,	,	PUNCT
ejpam-3175	46	57	t)ψ(w	t)ψ(w	X
ejpam-3175	46	58	)	)	PUNCT
ejpam-3175	46	59	=	=	SYM
ejpam-3175	47	1	e−2πiλt+πλ〈w	e−2πiλt+πλ〈w	PROPN
ejpam-3175	47	2	,	,	PUNCT
ejpam-3175	47	3	z〉−πλ|z|	z〉−πλ|z|	VERB
ejpam-3175	47	4	2/2ψ(w	2/2ψ(w	NUM
ejpam-3175	47	5	−	−	PROPN
ejpam-3175	47	6	z	z	NOUN
ejpam-3175	47	7	)	)	PUNCT
ejpam-3175	47	8	,	,	PUNCT
ejpam-3175	47	9	and	and	CCONJ
ejpam-3175	47	10	π−λ(z	π−λ(z	NOUN
ejpam-3175	47	11	,	,	PUNCT
ejpam-3175	47	12	t)ψ(w	t)ψ(w	PRON
ejpam-3175	47	13	)	)	PUNCT
ejpam-3175	48	1	=	=	SYM
ejpam-3175	48	2	e2πiλt+πλ〈z	e2πiλt+πλ〈z	NOUN
ejpam-3175	48	3	,	,	PUNCT
ejpam-3175	48	4	w〉−πλ|z|	w〉−πλ|z|	VERB
ejpam-3175	49	1	2/2ψ(w	2/2ψ(w	NUM
ejpam-3175	49	2	−	−	PROPN
ejpam-3175	50	1	z	z	NOUN
ejpam-3175	50	2	)	)	PUNCT
ejpam-3175	50	3	,	,	PUNCT
ejpam-3175	50	4	for	for	ADP
ejpam-3175	50	5	any	any	DET
ejpam-3175	50	6	λ	λ	PROPN
ejpam-3175	50	7	∈	∈	PROPN
ejpam-3175	50	8	r∗	r∗	NOUN
ejpam-3175	50	9	:	:	PUNCT
ejpam-3175	51	1	=	=	SYM
ejpam-3175	51	2	r	r	NOUN
ejpam-3175	51	3	\	\	PUNCT
ejpam-3175	51	4	{	{	PUNCT
ejpam-3175	51	5	0	0	NUM
ejpam-3175	51	6	}	}	PUNCT
ejpam-3175	51	7	.	.	PUNCT
ejpam-3175	52	1	it	it	PRON
ejpam-3175	52	2	is	be	AUX
ejpam-3175	52	3	easy	easy	ADJ
ejpam-3175	52	4	to	to	PART
ejpam-3175	52	5	see	see	VERB
ejpam-3175	52	6	that	that	PRON
ejpam-3175	52	7	πλ	πλ	NOUN
ejpam-3175	52	8	:	:	PUNCT
ejpam-3175	53	1	hn	hn	PROPN
ejpam-3175	53	2	→	→	PUNCT
ejpam-3175	53	3	g	g	PROPN
ejpam-3175	53	4	is	be	AUX
ejpam-3175	53	5	a	a	DET
ejpam-3175	53	6	group	group	NOUN
ejpam-3175	53	7	homomorphism	homomorphism	NOUN
ejpam-3175	53	8	and	and	CCONJ
ejpam-3175	53	9	πλ(z	πλ(z	NOUN
ejpam-3175	53	10	,	,	PUNCT
ejpam-3175	53	11	t)ψ	t)ψ	NOUN
ejpam-3175	53	12	→	→	SYM
ejpam-3175	53	13	ψ	ψ	X
ejpam-3175	53	14	in	in	ADP
ejpam-3175	53	15	hλ	hλ	X
ejpam-3175	53	16	as	as	ADP
ejpam-3175	53	17	(	(	PUNCT
ejpam-3175	53	18	z	z	NOUN
ejpam-3175	53	19	,	,	PUNCT
ejpam-3175	53	20	t)→	t)→	PROPN
ejpam-3175	53	21	(	(	PUNCT
ejpam-3175	53	22	0	0	NUM
ejpam-3175	53	23	,	,	PUNCT
ejpam-3175	53	24	0	0	NUM
ejpam-3175	53	25	)	)	PUNCT
ejpam-3175	53	26	.	.	PUNCT
ejpam-3175	54	1	then	then	ADV
ejpam-3175	54	2	the	the	DET
ejpam-3175	54	3	unitary	unitary	ADJ
ejpam-3175	54	4	representation	representation	NOUN
ejpam-3175	54	5	πλ	πλ	NOUN
ejpam-3175	54	6	of	of	ADP
ejpam-3175	54	7	hn	hn	PROPN
ejpam-3175	54	8	on	on	ADP
ejpam-3175	54	9	hλ	hλ	INTJ
ejpam-3175	54	10	is	be	AUX
ejpam-3175	54	11	irreducible	irreducible	ADJ
ejpam-3175	54	12	in	in	ADP
ejpam-3175	54	13	the	the	DET
ejpam-3175	54	14	sense	sense	NOUN
ejpam-3175	54	15	that	that	SCONJ
ejpam-3175	54	16	the	the	DET
ejpam-3175	54	17	only	only	ADJ
ejpam-3175	54	18	closed	closed	ADJ
ejpam-3175	54	19	subspaces	subspace	NOUN
ejpam-3175	54	20	of	of	ADP
ejpam-3175	54	21	hλ	hλ	NOUN
ejpam-3175	54	22	that	that	PRON
ejpam-3175	54	23	are	be	AUX
ejpam-3175	54	24	invariant	invariant	ADJ
ejpam-3175	54	25	under	under	ADP
ejpam-3175	54	26	all	all	DET
ejpam-3175	54	27	the	the	DET
ejpam-3175	54	28	operators	operator	NOUN
ejpam-3175	54	29	πλ(z	πλ(z	PRON
ejpam-3175	54	30	,	,	PUNCT
ejpam-3175	54	31	t	t	PROPN
ejpam-3175	54	32	)	)	PUNCT
ejpam-3175	54	33	,	,	PUNCT
ejpam-3175	54	34	(	(	PUNCT
ejpam-3175	54	35	z	z	X
ejpam-3175	54	36	,	,	PUNCT
ejpam-3175	54	37	t	t	PROPN
ejpam-3175	54	38	)	)	PUNCT
ejpam-3175	54	39	∈	∈	PROPN
ejpam-3175	54	40	hn	hn	PROPN
ejpam-3175	54	41	,	,	PUNCT
ejpam-3175	54	42	are	be	AUX
ejpam-3175	54	43	{	{	PUNCT
ejpam-3175	54	44	0	0	NUM
ejpam-3175	54	45	}	}	PUNCT
ejpam-3175	54	46	and	and	CCONJ
ejpam-3175	54	47	hλ	hλ	X
ejpam-3175	54	48	.	.	PUNCT
ejpam-3175	55	1	two	two	NUM
ejpam-3175	55	2	unitary	unitary	ADJ
ejpam-3175	55	3	representations	representation	NOUN
ejpam-3175	55	4	πλ	πλ	NOUN
ejpam-3175	55	5	and	and	CCONJ
ejpam-3175	55	6	πµ	πµ	PROPN
ejpam-3175	55	7	of	of	ADP
ejpam-3175	55	8	hn	hn	PROPN
ejpam-3175	55	9	are	be	AUX
ejpam-3175	55	10	unitarily	unitarily	ADV
ejpam-3175	55	11	equivalent	equivalent	ADJ
ejpam-3175	55	12	if	if	SCONJ
ejpam-3175	56	1	and	and	CCONJ
ejpam-3175	56	2	only	only	ADV
ejpam-3175	56	3	if	if	SCONJ
ejpam-3175	56	4	λ	λ	X
ejpam-3175	56	5	=	=	VERB
ejpam-3175	56	6	µ.	µ.	NOUN
ejpam-3175	56	7	now	now	ADV
ejpam-3175	56	8	,	,	PUNCT
ejpam-3175	56	9	we	we	PRON
ejpam-3175	56	10	are	be	AUX
ejpam-3175	56	11	able	able	ADJ
ejpam-3175	56	12	to	to	PART
ejpam-3175	56	13	introduce	introduce	VERB
ejpam-3175	56	14	the	the	DET
ejpam-3175	56	15	following	following	ADJ
ejpam-3175	56	16	notion	notion	NOUN
ejpam-3175	56	17	of	of	ADP
ejpam-3175	56	18	the	the	DET
ejpam-3175	56	19	group	group	NOUN
ejpam-3175	56	20	fourier	fourier	NOUN
ejpam-3175	56	21	transform	transform	NOUN
ejpam-3175	56	22	on	on	ADP
ejpam-3175	56	23	hn	hn	PROPN
ejpam-3175	56	24	.	.	PUNCT
ejpam-3175	57	1	let	let	VERB
ejpam-3175	57	2	f	f	PROPN
ejpam-3175	57	3	∈	∈	PROPN
ejpam-3175	57	4	l1(hn	l1(hn	PROPN
ejpam-3175	57	5	)	)	PUNCT
ejpam-3175	57	6	.	.	PUNCT
ejpam-3175	58	1	then	then	ADV
ejpam-3175	58	2	the	the	DET
ejpam-3175	58	3	group	group	NOUN
ejpam-3175	58	4	fourier	fourier	NOUN
ejpam-3175	58	5	transform	transform	VERB
ejpam-3175	58	6	πλ	πλ	NOUN
ejpam-3175	58	7	on	on	ADP
ejpam-3175	58	8	f	f	PROPN
ejpam-3175	58	9	is	be	AUX
ejpam-3175	58	10	defined	define	VERB
ejpam-3175	58	11	by	by	ADP
ejpam-3175	58	12	πλ(f	πλ(f	NOUN
ejpam-3175	58	13	)	)	PUNCT
ejpam-3175	59	1	=	=	SYM
ejpam-3175	59	2	∫	∫	PROPN
ejpam-3175	60	1	hn	hn	PROPN
ejpam-3175	60	2	f(z	f(z	PROPN
ejpam-3175	60	3	,	,	PUNCT
ejpam-3175	60	4	t)πλ(z	t)πλ(z	NOUN
ejpam-3175	60	5	,	,	PUNCT
ejpam-3175	60	6	t)dzdt	t)dzdt	X
ejpam-3175	60	7	.	.	PUNCT
ejpam-3175	61	1	(	(	PUNCT
ejpam-3175	61	2	3	3	NUM
ejpam-3175	61	3	)	)	PUNCT
ejpam-3175	61	4	thus	thus	ADV
ejpam-3175	61	5	,	,	PUNCT
ejpam-3175	61	6	the	the	DET
ejpam-3175	61	7	plancherel	plancherel	NOUN
ejpam-3175	61	8	theorem	theorem	VERB
ejpam-3175	61	9	states	state	NOUN
ejpam-3175	61	10	as	as	SCONJ
ejpam-3175	61	11	follows	follow	VERB
ejpam-3175	61	12	.	.	PUNCT
ejpam-3175	62	1	lemma	lemma	PROPN
ejpam-3175	62	2	1	1	X
ejpam-3175	62	3	.	.	PUNCT
ejpam-3175	63	1	let	let	VERB
ejpam-3175	63	2	f	f	PROPN
ejpam-3175	63	3	∈	∈	PROPN
ejpam-3175	63	4	l2(hn	l2(hn	PROPN
ejpam-3175	63	5	)	)	PUNCT
ejpam-3175	63	6	.	.	PUNCT
ejpam-3175	64	1	then	then	ADV
ejpam-3175	64	2	‖f‖2l2(hn	‖f‖2l2(hn	NUM
ejpam-3175	64	3	)	)	PUNCT
ejpam-3175	64	4	=	=	SYM
ejpam-3175	65	1	∫	∫	PROPN
ejpam-3175	65	2	r∗	r∗	PROPN
ejpam-3175	65	3	‖πλ(f)‖2hs	‖πλ(f)‖2hs	PROPN
ejpam-3175	65	4	|λ|ndλ	|λ|ndλ	NUM
ejpam-3175	65	5	.	.	PROPN
ejpam-3175	66	1	and	and	CCONJ
ejpam-3175	66	2	the	the	DET
ejpam-3175	66	3	inversion	inversion	NOUN
ejpam-3175	66	4	formula	formula	NOUN
ejpam-3175	66	5	is	be	AUX
ejpam-3175	66	6	valid	valid	ADJ
ejpam-3175	66	7	:	:	PUNCT
ejpam-3175	66	8	f(z	f(z	PROPN
ejpam-3175	66	9	,	,	PUNCT
ejpam-3175	66	10	t	t	NOUN
ejpam-3175	66	11	)	)	PUNCT
ejpam-3175	66	12	=	=	SYM
ejpam-3175	67	1	∫	∫	PROPN
ejpam-3175	67	2	r∗	r∗	PROPN
ejpam-3175	67	3	tr(π∗λ(f)πλ(z	tr(π∗λ(f)πλ(z	PROPN
ejpam-3175	67	4	,	,	PUNCT
ejpam-3175	67	5	t))|λ|ndλ	t))|λ|ndλ	PROPN
ejpam-3175	67	6	.	.	PROPN
ejpam-3175	68	1	3	3	X
ejpam-3175	68	2	.	.	X
ejpam-3175	69	1	the	the	DET
ejpam-3175	69	2	inverse	inverse	ADJ
ejpam-3175	69	3	formulas	formula	NOUN
ejpam-3175	69	4	of	of	ADP
ejpam-3175	69	5	radon	radon	PROPN
ejpam-3175	69	6	transforms	transform	VERB
ejpam-3175	69	7	in	in	ADP
ejpam-3175	69	8	this	this	DET
ejpam-3175	69	9	section	section	NOUN
ejpam-3175	69	10	,	,	PUNCT
ejpam-3175	69	11	our	our	PRON
ejpam-3175	69	12	purpose	purpose	NOUN
ejpam-3175	69	13	is	be	AUX
ejpam-3175	69	14	to	to	PART
ejpam-3175	69	15	get	get	VERB
ejpam-3175	69	16	the	the	DET
ejpam-3175	69	17	inverse	inverse	ADJ
ejpam-3175	69	18	formulas	formula	NOUN
ejpam-3175	69	19	of	of	ADP
ejpam-3175	69	20	radon	radon	NOUN
ejpam-3175	69	21	transforms	transform	VERB
ejpam-3175	69	22	.	.	PUNCT
ejpam-3175	70	1	in	in	ADP
ejpam-3175	70	2	order	order	NOUN
ejpam-3175	70	3	to	to	PART
ejpam-3175	70	4	do	do	AUX
ejpam-3175	70	5	this	this	PRON
ejpam-3175	70	6	we	we	PRON
ejpam-3175	70	7	first	first	ADV
ejpam-3175	70	8	recall	recall	VERB
ejpam-3175	70	9	the	the	DET
ejpam-3175	70	10	abel	abel	PROPN
ejpam-3175	70	11	fourier	fourier	NOUN
ejpam-3175	70	12	transform	transform	VERB
ejpam-3175	70	13	.	.	PUNCT
ejpam-3175	71	1	the	the	DET
ejpam-3175	71	2	fourier	fourier	NOUN
ejpam-3175	71	3	transform	transform	NOUN
ejpam-3175	71	4	for	for	ADP
ejpam-3175	71	5	t	t	PROPN
ejpam-3175	71	6	and	and	CCONJ
ejpam-3175	71	7	z	z	NOUN
ejpam-3175	71	8	-	-	NOUN
ejpam-3175	71	9	variable	variable	ADJ
ejpam-3175	71	10	,	,	PUNCT
ejpam-3175	71	11	respectively	respectively	ADV
ejpam-3175	71	12	,	,	PUNCT
ejpam-3175	71	13	are	be	AUX
ejpam-3175	71	14	given	give	VERB
ejpam-3175	71	15	by	by	ADP
ejpam-3175	71	16	f2f(z	f2f(z	PROPN
ejpam-3175	71	17	,	,	PUNCT
ejpam-3175	71	18	t	t	PROPN
ejpam-3175	71	19	)	)	PUNCT
ejpam-3175	71	20	=	=	SYM
ejpam-3175	72	1	∫	∫	PROPN
ejpam-3175	72	2	r	r	NOUN
ejpam-3175	72	3	f(z	f(z	PROPN
ejpam-3175	72	4	,	,	PUNCT
ejpam-3175	72	5	t′)e−2πit	t′)e−2πit	PROPN
ejpam-3175	72	6	′tdt′	′tdt′	PROPN
ejpam-3175	72	7	,	,	PUNCT
ejpam-3175	72	8	(	(	PUNCT
ejpam-3175	72	9	4	4	NUM
ejpam-3175	72	10	)	)	PUNCT
ejpam-3175	72	11	and	and	CCONJ
ejpam-3175	72	12	f1f(z	f1f(z	PROPN
ejpam-3175	72	13	,	,	PUNCT
ejpam-3175	72	14	t	t	NOUN
ejpam-3175	72	15	)	)	PUNCT
ejpam-3175	72	16	=	=	SYM
ejpam-3175	73	1	∫	∫	PROPN
ejpam-3175	73	2	cn	cn	PROPN
ejpam-3175	73	3	f(z′	f(z′	PROPN
ejpam-3175	73	4	,	,	PUNCT
ejpam-3175	73	5	t)e−2πire〈z	t)e−2πire〈z	PROPN
ejpam-3175	73	6	,	,	PUNCT
ejpam-3175	73	7	z′〉dz′.	z′〉dz′.	PROPN
ejpam-3175	73	8	the	the	DET
ejpam-3175	73	9	symplectic	symplectic	ADJ
ejpam-3175	73	10	fourier	fourier	NOUN
ejpam-3175	73	11	transform	transform	NOUN
ejpam-3175	73	12	on	on	ADP
ejpam-3175	73	13	cn	cn	PROPN
ejpam-3175	73	14	is	be	AUX
ejpam-3175	73	15	defined	define	VERB
ejpam-3175	73	16	by	by	ADP
ejpam-3175	73	17	,	,	PUNCT
ejpam-3175	73	18	for	for	ADP
ejpam-3175	73	19	any	any	DET
ejpam-3175	73	20	g	g	PROPN
ejpam-3175	73	21	∈	∈	PROPN
ejpam-3175	73	22	l2(cn	l2(cn	PROPN
ejpam-3175	73	23	)	)	PUNCT
ejpam-3175	73	24	,	,	PUNCT
ejpam-3175	73	25	fsg(z	fsg(z	PROPN
ejpam-3175	73	26	)	)	PUNCT
ejpam-3175	73	27	=	=	SYM
ejpam-3175	73	28	∫	∫	PROPN
ejpam-3175	73	29	cn	cn	PROPN
ejpam-3175	73	30	g(z′)eπiim〈z	g(z′)eπiim〈z	PROPN
ejpam-3175	73	31	,	,	PUNCT
ejpam-3175	73	32	z	z	PROPN
ejpam-3175	73	33	′〉dz′	′〉dz′	NOUN
ejpam-3175	73	34	,	,	PUNCT
ejpam-3175	73	35	(	(	PUNCT
ejpam-3175	73	36	5	5	NUM
ejpam-3175	73	37	)	)	PUNCT
ejpam-3175	73	38	z.	z.	PROPN
ejpam-3175	73	39	fang	fang	PROPN
ejpam-3175	73	40	,	,	PUNCT
ejpam-3175	73	41	h.	h.	PROPN
ejpam-3175	73	42	jianxun	jianxun	PROPN
ejpam-3175	73	43	he	he	PRON
ejpam-3175	73	44	/	/	SYM
ejpam-3175	73	45	eur	eur	PROPN
ejpam-3175	73	46	.	.	PUNCT
ejpam-3175	74	1	j.	j.	PROPN
ejpam-3175	74	2	pure	pure	PROPN
ejpam-3175	74	3	appl	appl	PROPN
ejpam-3175	74	4	.	.	PROPN
ejpam-3175	74	5	math	math	PROPN
ejpam-3175	74	6	,	,	PUNCT
ejpam-3175	74	7	11	11	NUM
ejpam-3175	74	8	(	(	PUNCT
ejpam-3175	74	9	1	1	NUM
ejpam-3175	74	10	)	)	PUNCT
ejpam-3175	74	11	(	(	PUNCT
ejpam-3175	74	12	2018	2018	NUM
ejpam-3175	74	13	)	)	PUNCT
ejpam-3175	74	14	,	,	PUNCT
ejpam-3175	74	15	138	138	NUM
ejpam-3175	74	16	-	-	SYM
ejpam-3175	74	17	149	149	NUM
ejpam-3175	74	18	141	141	NUM
ejpam-3175	74	19	and	and	CCONJ
ejpam-3175	74	20	then	then	ADV
ejpam-3175	74	21	we	we	PRON
ejpam-3175	74	22	also	also	ADV
ejpam-3175	74	23	obtain	obtain	VERB
ejpam-3175	74	24	fsg(z	fsg(z	NUM
ejpam-3175	74	25	)	)	PUNCT
ejpam-3175	74	26	=	=	SYM
ejpam-3175	74	27	f1	f1	NOUN
ejpam-3175	74	28	g	g	PROPN
ejpam-3175	74	29	(	(	PUNCT
ejpam-3175	74	30	iz/2	iz/2	PROPN
ejpam-3175	74	31	)	)	PUNCT
ejpam-3175	74	32	.	.	PUNCT
ejpam-3175	75	1	(	(	PUNCT
ejpam-3175	75	2	6	6	X
ejpam-3175	75	3	)	)	PUNCT
ejpam-3175	75	4	let	let	AUX
ejpam-3175	75	5	πλ(f	πλ(f	PUNCT
ejpam-3175	75	6	)	)	PUNCT
ejpam-3175	75	7	be	be	AUX
ejpam-3175	75	8	as	as	ADP
ejpam-3175	75	9	in	in	ADP
ejpam-3175	75	10	(	(	PUNCT
ejpam-3175	75	11	3	3	NUM
ejpam-3175	75	12	)	)	PUNCT
ejpam-3175	75	13	and	and	CCONJ
ejpam-3175	75	14	πλ(z	πλ(z	NOUN
ejpam-3175	75	15	,	,	PUNCT
ejpam-3175	75	16	0	0	NUM
ejpam-3175	75	17	)	)	PUNCT
ejpam-3175	75	18	:	:	PUNCT
ejpam-3175	76	1	=	=	NOUN
ejpam-3175	76	2	πλ(z	πλ(z	NOUN
ejpam-3175	76	3	)	)	PUNCT
ejpam-3175	76	4	.	.	PUNCT
ejpam-3175	77	1	then	then	ADV
ejpam-3175	77	2	we	we	PRON
ejpam-3175	77	3	define	define	VERB
ejpam-3175	77	4	πλ(f	πλ(f	PUNCT
ejpam-3175	77	5	)	)	PUNCT
ejpam-3175	78	1	=	=	SYM
ejpam-3175	78	2	∫	∫	PROPN
ejpam-3175	78	3	cn	cn	PROPN
ejpam-3175	78	4	f2f(z	f2f(z	PROPN
ejpam-3175	78	5	,	,	PUNCT
ejpam-3175	78	6	λ)πλ(z)dz	λ)πλ(z)dz	PROPN
ejpam-3175	78	7	.	.	PUNCT
ejpam-3175	79	1	therefore	therefore	ADV
ejpam-3175	79	2	,	,	PUNCT
ejpam-3175	79	3	the	the	DET
ejpam-3175	79	4	integral	integral	ADJ
ejpam-3175	79	5	operator	operator	NOUN
ejpam-3175	79	6	wλ	wλ	NOUN
ejpam-3175	79	7	for	for	ADP
ejpam-3175	79	8	g	g	PROPN
ejpam-3175	79	9	is	be	AUX
ejpam-3175	79	10	defined	define	VERB
ejpam-3175	79	11	by	by	ADP
ejpam-3175	79	12	wλ(g	wλ(g	NOUN
ejpam-3175	79	13	)	)	PUNCT
ejpam-3175	80	1	=	=	SYM
ejpam-3175	80	2	∫	∫	PROPN
ejpam-3175	80	3	cn	cn	PROPN
ejpam-3175	80	4	g(z)πλ(z)dz	g(z)πλ(z)dz	PROPN
ejpam-3175	80	5	,	,	PUNCT
ejpam-3175	80	6	(	(	PUNCT
ejpam-3175	80	7	7	7	NUM
ejpam-3175	80	8	)	)	PUNCT
ejpam-3175	80	9	and	and	CCONJ
ejpam-3175	80	10	plancherel	plancherel	NOUN
ejpam-3175	80	11	formula	formula	NOUN
ejpam-3175	80	12	is	be	AUX
ejpam-3175	80	13	given	give	VERB
ejpam-3175	80	14	by	by	ADP
ejpam-3175	80	15	‖wλ(g)‖2hs	‖wλ(g)‖2hs	ADP
ejpam-3175	80	16	=	=	NOUN
ejpam-3175	80	17	λ−n	λ−n	NOUN
ejpam-3175	80	18	∫	∫	X
ejpam-3175	80	19	cn	cn	X
ejpam-3175	80	20	|g(z)|2dz	|g(z)|2dz	PROPN
ejpam-3175	80	21	.	.	PUNCT
ejpam-3175	81	1	(	(	PUNCT
ejpam-3175	81	2	8)	8)	NUM
ejpam-3175	81	3	next	next	ADV
ejpam-3175	81	4	,	,	PUNCT
ejpam-3175	81	5	to	to	PART
ejpam-3175	81	6	introduce	introduce	VERB
ejpam-3175	81	7	the	the	DET
ejpam-3175	81	8	notion	notion	NOUN
ejpam-3175	81	9	of	of	ADP
ejpam-3175	81	10	the	the	DET
ejpam-3175	81	11	singular	singular	ADJ
ejpam-3175	81	12	convolution	convolution	NOUN
ejpam-3175	81	13	operator	operator	NOUN
ejpam-3175	81	14	on	on	ADP
ejpam-3175	81	15	hn	hn	PROPN
ejpam-3175	81	16	,	,	PUNCT
ejpam-3175	81	17	we	we	PRON
ejpam-3175	81	18	need	need	VERB
ejpam-3175	81	19	the	the	DET
ejpam-3175	81	20	following	follow	VERB
ejpam-3175	81	21	notation	notation	NOUN
ejpam-3175	81	22	.	.	PUNCT
ejpam-3175	82	1	let	let	VERB
ejpam-3175	82	2	tn	tn	NOUN
ejpam-3175	82	3	=	=	SYM
ejpam-3175	82	4	(	(	PUNCT
ejpam-3175	82	5	∂	∂	X
ejpam-3175	82	6	∂t	∂t	PROPN
ejpam-3175	82	7	)	)	PUNCT
ejpam-3175	83	1	n	n	CCONJ
ejpam-3175	83	2	.	.	PUNCT
ejpam-3175	84	1	we	we	PRON
ejpam-3175	84	2	consider	consider	VERB
ejpam-3175	84	3	hyperplanes	hyperplane	NOUN
ejpam-3175	84	4	e(z	e(z	PROPN
ejpam-3175	84	5	,	,	PUNCT
ejpam-3175	84	6	t	t	PROPN
ejpam-3175	84	7	)	)	PUNCT
ejpam-3175	84	8	:	:	PUNCT
ejpam-3175	84	9	=	=	SYM
ejpam-3175	84	10	{	{	PUNCT
ejpam-3175	84	11	(	(	PUNCT
ejpam-3175	84	12	z	z	NOUN
ejpam-3175	84	13	,	,	PUNCT
ejpam-3175	84	14	t+	t+	PUNCT
ejpam-3175	84	15	1	1	NUM
ejpam-3175	84	16	2	2	NUM
ejpam-3175	84	17	im〈z	im〈z	NOUN
ejpam-3175	84	18	,	,	PUNCT
ejpam-3175	84	19	z′	z′	NOUN
ejpam-3175	84	20	〉	〉	NUM
ejpam-3175	84	21	)	)	PUNCT
ejpam-3175	84	22	for	for	ADP
ejpam-3175	84	23	any	any	DET
ejpam-3175	84	24	z′	z′	NUM
ejpam-3175	84	25	∈	∈	PROPN
ejpam-3175	84	26	cn	cn	PROPN
ejpam-3175	84	27	}	}	PUNCT
ejpam-3175	84	28	and	and	CCONJ
ejpam-3175	84	29	e	e	NOUN
ejpam-3175	84	30	∗(z′,t′	∗(z′,t′	NOUN
ejpam-3175	84	31	)	)	PUNCT
ejpam-3175	84	32	:	:	PUNCT
ejpam-3175	84	33	=	=	SYM
ejpam-3175	84	34	{	{	PUNCT
ejpam-3175	84	35	(	(	PUNCT
ejpam-3175	84	36	z′	z′	PROPN
ejpam-3175	84	37	,	,	PUNCT
ejpam-3175	84	38	t′	t′	NUM
ejpam-3175	84	39	−	−	NOUN
ejpam-3175	84	40	1	1	NUM
ejpam-3175	84	41	2	2	NUM
ejpam-3175	84	42	im〈z	im〈z	NOUN
ejpam-3175	84	43	,	,	PUNCT
ejpam-3175	84	44	z′	z′	NOUN
ejpam-3175	84	45	〉	〉	NUM
ejpam-3175	84	46	)	)	PUNCT
ejpam-3175	84	47	for	for	ADP
ejpam-3175	84	48	any	any	DET
ejpam-3175	84	49	z	z	PROPN
ejpam-3175	84	50	∈	∈	PROPN
ejpam-3175	84	51	cn	cn	PROPN
ejpam-3175	84	52	}	}	PUNCT
ejpam-3175	84	53	.	.	PUNCT
ejpam-3175	85	1	as	as	SCONJ
ejpam-3175	85	2	we	we	PRON
ejpam-3175	85	3	know	know	VERB
ejpam-3175	85	4	,	,	PUNCT
ejpam-3175	85	5	tn	tn	PROPN
ejpam-3175	85	6	is	be	AUX
ejpam-3175	85	7	studied	study	VERB
ejpam-3175	85	8	in	in	ADP
ejpam-3175	85	9	fractional	fractional	ADJ
ejpam-3175	85	10	differential	differential	ADJ
ejpam-3175	85	11	equations	equation	NOUN
ejpam-3175	85	12	due	due	ADP
ejpam-3175	85	13	to	to	ADP
ejpam-3175	85	14	its	its	PRON
ejpam-3175	85	15	wide	wide	ADJ
ejpam-3175	85	16	applications	application	NOUN
ejpam-3175	85	17	(	(	PUNCT
ejpam-3175	85	18	see	see	VERB
ejpam-3175	85	19	[	[	X
ejpam-3175	85	20	1	1	NUM
ejpam-3175	85	21	,	,	PUNCT
ejpam-3175	85	22	14	14	NUM
ejpam-3175	85	23	,	,	PUNCT
ejpam-3175	85	24	15	15	NUM
ejpam-3175	85	25	]	]	NUM
ejpam-3175	85	26	)	)	PUNCT
ejpam-3175	85	27	.	.	PUNCT
ejpam-3175	86	1	in	in	ADP
ejpam-3175	86	2	this	this	DET
ejpam-3175	86	3	paper	paper	NOUN
ejpam-3175	86	4	,	,	PUNCT
ejpam-3175	86	5	combining	combine	VERB
ejpam-3175	86	6	with	with	ADP
ejpam-3175	86	7	these	these	DET
ejpam-3175	86	8	hyperplanes	hyperplane	NOUN
ejpam-3175	86	9	and	and	CCONJ
ejpam-3175	86	10	tn	tn	NOUN
ejpam-3175	86	11	we	we	PRON
ejpam-3175	86	12	have	have	VERB
ejpam-3175	86	13	the	the	DET
ejpam-3175	86	14	following	follow	VERB
ejpam-3175	86	15	definition	definition	NOUN
ejpam-3175	86	16	.	.	PUNCT
ejpam-3175	87	1	definition	definition	NOUN
ejpam-3175	87	2	1	1	NUM
ejpam-3175	87	3	.	.	PUNCT
ejpam-3175	88	1	the	the	DET
ejpam-3175	88	2	singular	singular	PROPN
ejpam-3175	88	3	convolution	convolution	NOUN
ejpam-3175	88	4	operator	operator	NOUN
ejpam-3175	88	5	rn	rn	PROPN
ejpam-3175	88	6	and	and	CCONJ
ejpam-3175	88	7	the	the	DET
ejpam-3175	88	8	dual	dual	ADJ
ejpam-3175	88	9	singular	singular	ADJ
ejpam-3175	88	10	convolution	convolution	NOUN
ejpam-3175	88	11	operator	operator	NOUN
ejpam-3175	88	12	rtn	rtn	NOUN
ejpam-3175	88	13	for	for	ADP
ejpam-3175	88	14	function	function	NOUN
ejpam-3175	88	15	f	f	PROPN
ejpam-3175	88	16	,	,	PUNCT
ejpam-3175	88	17	φ	φ	PROPN
ejpam-3175	88	18	,	,	PUNCT
ejpam-3175	88	19	respectively	respectively	ADV
ejpam-3175	88	20	,	,	PUNCT
ejpam-3175	88	21	are	be	AUX
ejpam-3175	88	22	defined	define	VERB
ejpam-3175	88	23	by	by	ADP
ejpam-3175	88	24	rn(f)(z	rn(f)(z	PROPN
ejpam-3175	88	25	,	,	PUNCT
ejpam-3175	88	26	t	t	PROPN
ejpam-3175	88	27	)	)	PUNCT
ejpam-3175	89	1	=	=	SYM
ejpam-3175	89	2	∫	∫	PROPN
ejpam-3175	89	3	cn	cn	PROPN
ejpam-3175	89	4	tnf	tnf	PROPN
ejpam-3175	89	5	(	(	PUNCT
ejpam-3175	89	6	z′	z′	PROPN
ejpam-3175	89	7	,	,	PUNCT
ejpam-3175	89	8	t+	t+	PUNCT
ejpam-3175	89	9	1	1	NUM
ejpam-3175	89	10	2	2	NUM
ejpam-3175	89	11	im〈z	im〈z	NOUN
ejpam-3175	89	12	,	,	PUNCT
ejpam-3175	89	13	z′	z′	NOUN
ejpam-3175	89	14	〉	〉	NUM
ejpam-3175	89	15	)	)	PUNCT
ejpam-3175	89	16	dz′	dz′	NOUN
ejpam-3175	89	17	(	(	PUNCT
ejpam-3175	89	18	9	9	NUM
ejpam-3175	89	19	)	)	PUNCT
ejpam-3175	89	20	and	and	CCONJ
ejpam-3175	89	21	rtnφ(z′	rtnφ(z′	NOUN
ejpam-3175	89	22	,	,	PUNCT
ejpam-3175	89	23	t′	t′	NUM
ejpam-3175	89	24	)	)	PUNCT
ejpam-3175	90	1	=	=	SYM
ejpam-3175	91	1	∫	∫	PROPN
ejpam-3175	92	1	cn	cn	PROPN
ejpam-3175	93	1	tnφ	tnφ	PROPN
ejpam-3175	94	1	(	(	PUNCT
ejpam-3175	94	2	z	z	NOUN
ejpam-3175	94	3	,	,	PUNCT
ejpam-3175	94	4	t′	t′	NUM
ejpam-3175	94	5	−	−	NOUN
ejpam-3175	94	6	1	1	NUM
ejpam-3175	94	7	2	2	NUM
ejpam-3175	94	8	im〈z	im〈z	NOUN
ejpam-3175	94	9	,	,	PUNCT
ejpam-3175	94	10	z′	z′	NOUN
ejpam-3175	94	11	〉	〉	NUM
ejpam-3175	94	12	)	)	PUNCT
ejpam-3175	94	13	dz	dz	PROPN
ejpam-3175	94	14	.	.	PUNCT
ejpam-3175	95	1	(	(	PUNCT
ejpam-3175	95	2	10	10	NUM
ejpam-3175	95	3	)	)	PUNCT
ejpam-3175	95	4	in	in	ADP
ejpam-3175	95	5	particular	particular	ADJ
ejpam-3175	95	6	,	,	PUNCT
ejpam-3175	95	7	r0	r0	NOUN
ejpam-3175	95	8	is	be	AUX
ejpam-3175	95	9	the	the	DET
ejpam-3175	95	10	heisenberg	heisenberg	PROPN
ejpam-3175	95	11	radon	radon	PROPN
ejpam-3175	95	12	transform	transform	VERB
ejpam-3175	95	13	when	when	SCONJ
ejpam-3175	95	14	n	n	X
ejpam-3175	95	15	=	=	SYM
ejpam-3175	95	16	0	0	PROPN
ejpam-3175	95	17	(	(	PUNCT
ejpam-3175	95	18	see	see	VERB
ejpam-3175	95	19	[	[	X
ejpam-3175	95	20	16	16	NUM
ejpam-3175	95	21	]	]	PUNCT
ejpam-3175	95	22	)	)	PUNCT
ejpam-3175	95	23	.	.	PUNCT
ejpam-3175	96	1	it	it	PRON
ejpam-3175	96	2	is	be	AUX
ejpam-3175	96	3	easy	easy	ADJ
ejpam-3175	96	4	to	to	PART
ejpam-3175	96	5	see	see	VERB
ejpam-3175	96	6	that	that	DET
ejpam-3175	96	7	rtnφ	rtnφ	NOUN
ejpam-3175	96	8	=	=	PRON
ejpam-3175	96	9	rnφ	rnφ	ADJ
ejpam-3175	96	10	(	(	PUNCT
ejpam-3175	96	11	also	also	ADV
ejpam-3175	96	12	see	see	VERB
ejpam-3175	96	13	[	[	X
ejpam-3175	96	14	4	4	NUM
ejpam-3175	96	15	]	]	NUM
ejpam-3175	96	16	)	)	PUNCT
ejpam-3175	96	17	.	.	PUNCT
ejpam-3175	97	1	we	we	PRON
ejpam-3175	97	2	denote	denote	VERB
ejpam-3175	97	3	by	by	ADP
ejpam-3175	97	4	s	s	PROPN
ejpam-3175	97	5	(	(	PUNCT
ejpam-3175	97	6	hn	hn	PROPN
ejpam-3175	97	7	)	)	PUNCT
ejpam-3175	97	8	the	the	DET
ejpam-3175	97	9	space	space	NOUN
ejpam-3175	97	10	all	all	DET
ejpam-3175	97	11	schwartz	schwartz	PROPN
ejpam-3175	97	12	functions	function	NOUN
ejpam-3175	97	13	on	on	ADP
ejpam-3175	97	14	hn	hn	PROPN
ejpam-3175	97	15	.	.	PUNCT
ejpam-3175	98	1	using	use	VERB
ejpam-3175	98	2	(	(	PUNCT
ejpam-3175	98	3	9	9	NUM
ejpam-3175	98	4	)	)	PUNCT
ejpam-3175	98	5	and	and	CCONJ
ejpam-3175	98	6	(	(	PUNCT
ejpam-3175	98	7	10	10	NUM
ejpam-3175	98	8	)	)	PUNCT
ejpam-3175	98	9	,	,	PUNCT
ejpam-3175	98	10	we	we	PRON
ejpam-3175	98	11	have	have	VERB
ejpam-3175	98	12	the	the	DET
ejpam-3175	98	13	following	follow	VERB
ejpam-3175	98	14	identity∫	identity∫	ADV
ejpam-3175	99	1	hn	hn	DET
ejpam-3175	99	2	f(z	f(z	PROPN
ejpam-3175	99	3	,	,	PUNCT
ejpam-3175	99	4	t)rtnφ(z	t)rtnφ(z	NOUN
ejpam-3175	99	5	,	,	PUNCT
ejpam-3175	99	6	t)dzdt	t)dzdt	PROPN
ejpam-3175	100	1	=	=	SYM
ejpam-3175	101	1	∫	∫	PROPN
ejpam-3175	102	1	hn	hn	PROPN
ejpam-3175	102	2	rnf(z	rnf(z	PROPN
ejpam-3175	102	3	,	,	PUNCT
ejpam-3175	102	4	t)φ(z	t)φ(z	PROPN
ejpam-3175	102	5	,	,	PUNCT
ejpam-3175	102	6	t)dzdt	t)dzdt	PROPN
ejpam-3175	102	7	for	for	ADP
ejpam-3175	102	8	any	any	DET
ejpam-3175	102	9	f	f	PROPN
ejpam-3175	102	10	,	,	PUNCT
ejpam-3175	102	11	φ	φ	PROPN
ejpam-3175	102	12	∈	∈	PROPN
ejpam-3175	102	13	s	s	X
ejpam-3175	102	14	(	(	PUNCT
ejpam-3175	102	15	hn	hn	PROPN
ejpam-3175	102	16	)	)	PUNCT
ejpam-3175	102	17	.	.	PUNCT
ejpam-3175	103	1	z.	z.	PROPN
ejpam-3175	103	2	fang	fang	PROPN
ejpam-3175	103	3	,	,	PUNCT
ejpam-3175	103	4	h.	h.	PROPN
ejpam-3175	103	5	jianxun	jianxun	PROPN
ejpam-3175	103	6	he	he	PRON
ejpam-3175	103	7	/	/	SYM
ejpam-3175	103	8	eur	eur	PROPN
ejpam-3175	103	9	.	.	PUNCT
ejpam-3175	104	1	j.	j.	PROPN
ejpam-3175	104	2	pure	pure	PROPN
ejpam-3175	104	3	appl	appl	PROPN
ejpam-3175	104	4	.	.	PROPN
ejpam-3175	104	5	math	math	PROPN
ejpam-3175	104	6	,	,	PUNCT
ejpam-3175	104	7	11	11	NUM
ejpam-3175	104	8	(	(	PUNCT
ejpam-3175	104	9	1	1	NUM
ejpam-3175	104	10	)	)	PUNCT
ejpam-3175	104	11	(	(	PUNCT
ejpam-3175	104	12	2018	2018	NUM
ejpam-3175	104	13	)	)	PUNCT
ejpam-3175	104	14	,	,	PUNCT
ejpam-3175	104	15	138	138	NUM
ejpam-3175	104	16	-	-	SYM
ejpam-3175	104	17	149	149	NUM
ejpam-3175	104	18	142	142	NUM
ejpam-3175	104	19	proposition	proposition	NOUN
ejpam-3175	104	20	1	1	NUM
ejpam-3175	104	21	.	.	PUNCT
ejpam-3175	105	1	let	let	VERB
ejpam-3175	105	2	f	f	PROPN
ejpam-3175	105	3	∈	∈	PROPN
ejpam-3175	105	4	s	s	PART
ejpam-3175	105	5	(	(	PUNCT
ejpam-3175	105	6	hn	hn	PROPN
ejpam-3175	105	7	)	)	PUNCT
ejpam-3175	105	8	.	.	PUNCT
ejpam-3175	106	1	then	then	ADV
ejpam-3175	106	2	,	,	PUNCT
ejpam-3175	106	3	for	for	ADP
ejpam-3175	106	4	any	any	DET
ejpam-3175	106	5	λ	λ	PROPN
ejpam-3175	106	6	∈	∈	PROPN
ejpam-3175	106	7	r∗	r∗	PROPN
ejpam-3175	106	8	,	,	PUNCT
ejpam-3175	106	9	we	we	PRON
ejpam-3175	106	10	have	have	AUX
ejpam-3175	106	11	πλ(rnf(z	πλ(rnf(z	VERB
ejpam-3175	106	12	,	,	PUNCT
ejpam-3175	106	13	t	t	NOUN
ejpam-3175	106	14	)	)	PUNCT
ejpam-3175	106	15	)	)	PUNCT
ejpam-3175	107	1	=	=	SYM
ejpam-3175	107	2	(	(	PUNCT
ejpam-3175	107	3	2πiλ)nwλ(ff(iλz/2	2πiλ)nwλ(ff(iλz/2	PROPN
ejpam-3175	107	4	,	,	PUNCT
ejpam-3175	107	5	λ	λ	NOUN
ejpam-3175	107	6	)	)	PUNCT
ejpam-3175	107	7	)	)	PUNCT
ejpam-3175	107	8	.	.	PUNCT
ejpam-3175	108	1	proof	proof	NOUN
ejpam-3175	108	2	.	.	PUNCT
ejpam-3175	109	1	let	let	VERB
ejpam-3175	109	2	ϕλ	ϕλ	NOUN
ejpam-3175	109	3	,	,	PUNCT
ejpam-3175	109	4	α	α	PROPN
ejpam-3175	109	5	be	be	VERB
ejpam-3175	109	6	as	as	ADP
ejpam-3175	109	7	in	in	ADP
ejpam-3175	109	8	(	(	PUNCT
ejpam-3175	109	9	2	2	NUM
ejpam-3175	109	10	)	)	PUNCT
ejpam-3175	109	11	and	and	CCONJ
ejpam-3175	109	12	differential	differential	ADJ
ejpam-3175	109	13	operator	operator	NOUN
ejpam-3175	109	14	tn	tn	PROPN
ejpam-3175	109	15	.	.	PUNCT
ejpam-3175	110	1	as	as	SCONJ
ejpam-3175	110	2	we	we	PRON
ejpam-3175	110	3	know	know	VERB
ejpam-3175	110	4	,	,	PUNCT
ejpam-3175	110	5	f2(t	f2(t	PROPN
ejpam-3175	110	6	nf)(λ	nf)(λ	NOUN
ejpam-3175	110	7	)	)	PUNCT
ejpam-3175	111	1	=	=	PRON
ejpam-3175	111	2	(	(	PUNCT
ejpam-3175	111	3	2πiλ)nf2(f)(λ	2πiλ)nf2(f)(λ	NOUN
ejpam-3175	111	4	)	)	PUNCT
ejpam-3175	111	5	.	.	PUNCT
ejpam-3175	112	1	(	(	PUNCT
ejpam-3175	112	2	11	11	NUM
ejpam-3175	112	3	)	)	PUNCT
ejpam-3175	112	4	according	accord	VERB
ejpam-3175	112	5	to	to	ADP
ejpam-3175	112	6	the	the	DET
ejpam-3175	112	7	(	(	PUNCT
ejpam-3175	112	8	7	7	NUM
ejpam-3175	112	9	)	)	PUNCT
ejpam-3175	112	10	,	,	PUNCT
ejpam-3175	112	11	(	(	PUNCT
ejpam-3175	112	12	11	11	NUM
ejpam-3175	112	13	)	)	PUNCT
ejpam-3175	112	14	,	,	PUNCT
ejpam-3175	112	15	together	together	ADV
ejpam-3175	112	16	with	with	ADP
ejpam-3175	112	17	(	(	PUNCT
ejpam-3175	112	18	4	4	NUM
ejpam-3175	112	19	)	)	PUNCT
ejpam-3175	112	20	and	and	CCONJ
ejpam-3175	112	21	(	(	PUNCT
ejpam-3175	112	22	5	5	NUM
ejpam-3175	112	23	)	)	PUNCT
ejpam-3175	112	24	,	,	PUNCT
ejpam-3175	112	25	we	we	PRON
ejpam-3175	112	26	have	have	VERB
ejpam-3175	112	27	[	[	X
ejpam-3175	112	28	πλ(rnf)ϕλ	πλ(rnf)ϕλ	PROPN
ejpam-3175	112	29	,	,	PUNCT
ejpam-3175	112	30	α	α	X
ejpam-3175	112	31	]	]	X
ejpam-3175	112	32	=	=	PUNCT
ejpam-3175	113	1	[	[	X
ejpam-3175	113	2	wλf2(rnf(z	wλf2(rnf(z	ADJ
ejpam-3175	113	3	,	,	PUNCT
ejpam-3175	113	4	λ))ϕλ	λ))ϕλ	NOUN
ejpam-3175	113	5	,	,	PUNCT
ejpam-3175	113	6	α(w	α(w	NOUN
ejpam-3175	113	7	)	)	PUNCT
ejpam-3175	113	8	]	]	PUNCT
ejpam-3175	114	1	=	=	PUNCT
ejpam-3175	114	2	∫	∫	PROPN
ejpam-3175	115	1	cn	cn	PROPN
ejpam-3175	115	2	f2(rnf(z	f2(rnf(z	PROPN
ejpam-3175	115	3	,	,	PUNCT
ejpam-3175	115	4	λ))[πλ(z)ϕλ	λ))[πλ(z)ϕλ	PROPN
ejpam-3175	115	5	,	,	PUNCT
ejpam-3175	115	6	α(w)]dz	α(w)]dz	PROPN
ejpam-3175	115	7	=	=	SYM
ejpam-3175	115	8	∫	∫	PROPN
ejpam-3175	116	1	cn	cn	PROPN
ejpam-3175	116	2	∫	∫	PROPN
ejpam-3175	117	1	r	r	NOUN
ejpam-3175	117	2	rnf(z	rnf(z	PROPN
ejpam-3175	117	3	,	,	PUNCT
ejpam-3175	117	4	t)e−2πiλt[πλ(z)ϕλ	t)e−2πiλt[πλ(z)ϕλ	NOUN
ejpam-3175	117	5	,	,	PUNCT
ejpam-3175	117	6	α(w)]dzdt	α(w)]dzdt	NUM
ejpam-3175	117	7	=	=	SYM
ejpam-3175	117	8	(	(	PUNCT
ejpam-3175	117	9	2πiλ)n	2πiλ)n	NUM
ejpam-3175	117	10	∫	∫	PROPN
ejpam-3175	118	1	cn	cn	PROPN
ejpam-3175	118	2	∫	∫	PROPN
ejpam-3175	118	3	r	r	NOUN
ejpam-3175	118	4	∫	∫	PROPN
ejpam-3175	118	5	cn	cn	PROPN
ejpam-3175	118	6	f(z′	f(z′	PROPN
ejpam-3175	118	7	,	,	PUNCT
ejpam-3175	118	8	t)e−2πiλteπiλim〈z	t)e−2πiλteπiλim〈z	PROPN
ejpam-3175	118	9	,	,	PUNCT
ejpam-3175	118	10	z	z	NOUN
ejpam-3175	118	11	′〉[πλ(z)ϕλ	′〉[πλ(z)ϕλ	NOUN
ejpam-3175	118	12	,	,	PUNCT
ejpam-3175	118	13	α]dz′dzdt	α]dz′dzdt	PRON
ejpam-3175	118	14	=	=	SYM
ejpam-3175	118	15	(	(	PUNCT
ejpam-3175	118	16	2πiλ)n	2πiλ)n	NUM
ejpam-3175	118	17	∫	∫	PROPN
ejpam-3175	118	18	cn	cn	PROPN
ejpam-3175	118	19	∫	∫	PROPN
ejpam-3175	118	20	cn	cn	PROPN
ejpam-3175	118	21	f2f(z′	f2f(z′	PROPN
ejpam-3175	118	22	,	,	PUNCT
ejpam-3175	118	23	λ)eπiλim〈z	λ)eπiλim〈z	NUM
ejpam-3175	118	24	,	,	PUNCT
ejpam-3175	118	25	z	z	NOUN
ejpam-3175	118	26	′〉[πλ(z)ϕλ	′〉[πλ(z)ϕλ	NOUN
ejpam-3175	118	27	,	,	PUNCT
ejpam-3175	118	28	α(w)]dz′dz	α(w)]dz′dz	NOUN
ejpam-3175	118	29	=	=	PRON
ejpam-3175	118	30	(	(	PUNCT
ejpam-3175	118	31	2πiλ)n	2πiλ)n	NUM
ejpam-3175	118	32	∫	∫	PROPN
ejpam-3175	118	33	cn	cn	PROPN
ejpam-3175	118	34	f2fsf(λz	f2fsf(λz	PROPN
ejpam-3175	118	35	,	,	PUNCT
ejpam-3175	118	36	λ)[πλ(z)ϕλ	λ)[πλ(z)ϕλ	NOUN
ejpam-3175	118	37	,	,	PUNCT
ejpam-3175	118	38	α(w)]dz	α(w)]dz	NUM
ejpam-3175	118	39	.	.	PUNCT
ejpam-3175	119	1	in	in	ADP
ejpam-3175	119	2	addition	addition	NOUN
ejpam-3175	119	3	,	,	PUNCT
ejpam-3175	119	4	we	we	PRON
ejpam-3175	119	5	need	need	VERB
ejpam-3175	119	6	the	the	DET
ejpam-3175	119	7	full	full	ADJ
ejpam-3175	119	8	euclidean	euclidean	ADJ
ejpam-3175	119	9	fourier	fourier	NOUN
ejpam-3175	119	10	transform	transform	NOUN
ejpam-3175	119	11	ff(z	ff(z	PUNCT
ejpam-3175	119	12	,	,	PUNCT
ejpam-3175	119	13	t	t	PROPN
ejpam-3175	119	14	)	)	PUNCT
ejpam-3175	119	15	=	=	SYM
ejpam-3175	120	1	∫	∫	PROPN
ejpam-3175	120	2	r	r	NOUN
ejpam-3175	120	3	∫	∫	PROPN
ejpam-3175	120	4	cn	cn	PROPN
ejpam-3175	120	5	f(z′	f(z′	PROPN
ejpam-3175	120	6	,	,	PUNCT
ejpam-3175	120	7	t′)e−2πitt	t′)e−2πitt	PROPN
ejpam-3175	120	8	′	′	NUM
ejpam-3175	120	9	e−2πire〈z	e−2πire〈z	ADJ
ejpam-3175	120	10	,	,	PUNCT
ejpam-3175	120	11	z′〉dz′dt′.	z′〉dz′dt′.	NOUN
ejpam-3175	120	12	by	by	ADP
ejpam-3175	120	13	this	this	PRON
ejpam-3175	120	14	and	and	CCONJ
ejpam-3175	120	15	(	(	PUNCT
ejpam-3175	120	16	5	5	NUM
ejpam-3175	120	17	)	)	PUNCT
ejpam-3175	120	18	,	,	PUNCT
ejpam-3175	120	19	we	we	PRON
ejpam-3175	120	20	find	find	VERB
ejpam-3175	120	21	that	that	SCONJ
ejpam-3175	120	22	[	[	X
ejpam-3175	120	23	πλ(rnf)ϕλ	πλ(rnf)ϕλ	NOUN
ejpam-3175	120	24	,	,	PUNCT
ejpam-3175	120	25	α(w	α(w	NOUN
ejpam-3175	120	26	)	)	PUNCT
ejpam-3175	120	27	]	]	PUNCT
ejpam-3175	121	1	=	=	PUNCT
ejpam-3175	121	2	(	(	PUNCT
ejpam-3175	121	3	2πiλ)n	2πiλ)n	NUM
ejpam-3175	121	4	∫	∫	NOUN
ejpam-3175	121	5	cn	cn	INTJ
ejpam-3175	121	6	ff	ff	PROPN
ejpam-3175	121	7	(	(	PUNCT
ejpam-3175	121	8	iλz/2	iλz/2	PROPN
ejpam-3175	121	9	,	,	PUNCT
ejpam-3175	121	10	λ	λ	NOUN
ejpam-3175	121	11	)	)	PUNCT
ejpam-3175	122	1	[	[	X
ejpam-3175	122	2	πλ(z)ϕλ	πλ(z)ϕλ	NOUN
ejpam-3175	122	3	,	,	PUNCT
ejpam-3175	122	4	α(w)]dz	α(w)]dz	NUM
ejpam-3175	122	5	=	=	SYM
ejpam-3175	122	6	(	(	PUNCT
ejpam-3175	122	7	2πiλ)n	2πiλ)n	PROPN
ejpam-3175	122	8	[	[	X
ejpam-3175	122	9	wλ	wλ	X
ejpam-3175	122	10	(	(	PUNCT
ejpam-3175	122	11	ff	ff	PROPN
ejpam-3175	122	12	(	(	PUNCT
ejpam-3175	122	13	iλz/2	iλz/2	PROPN
ejpam-3175	122	14	,	,	PUNCT
ejpam-3175	122	15	λ))ϕλ	λ))ϕλ	NOUN
ejpam-3175	122	16	,	,	PUNCT
ejpam-3175	122	17	α(w	α(w	NOUN
ejpam-3175	122	18	)	)	PUNCT
ejpam-3175	122	19	]	]	PUNCT
ejpam-3175	122	20	.	.	PUNCT
ejpam-3175	123	1	the	the	DET
ejpam-3175	123	2	proof	proof	NOUN
ejpam-3175	123	3	is	be	AUX
ejpam-3175	123	4	completed	complete	VERB
ejpam-3175	123	5	.	.	PUNCT
ejpam-3175	124	1	proposition	proposition	NOUN
ejpam-3175	124	2	2	2	NUM
ejpam-3175	124	3	.	.	PUNCT
ejpam-3175	125	1	let	let	VERB
ejpam-3175	125	2	φ	φ	PROPN
ejpam-3175	125	3	∈	∈	PROPN
ejpam-3175	125	4	s	s	X
ejpam-3175	125	5	(	(	PUNCT
ejpam-3175	125	6	hn	hn	PROPN
ejpam-3175	125	7	)	)	PUNCT
ejpam-3175	125	8	.	.	PUNCT
ejpam-3175	126	1	then	then	ADV
ejpam-3175	126	2	(	(	PUNCT
ejpam-3175	126	3	8π)n(iλ)−nf2φ	8π)n(iλ)−nf2φ	NUM
ejpam-3175	126	4	(	(	PUNCT
ejpam-3175	126	5	z	z	NOUN
ejpam-3175	126	6	/	/	SYM
ejpam-3175	126	7	λ	λ	PROPN
ejpam-3175	126	8	,	,	PUNCT
ejpam-3175	126	9	λ	λ	NOUN
ejpam-3175	126	10	)	)	PUNCT
ejpam-3175	126	11	=	=	PUNCT
ejpam-3175	126	12	fsf2[r	fsf2[r	X
ejpam-3175	126	13	t	t	PROPN
ejpam-3175	126	14	nφ(z	nφ(z	PROPN
ejpam-3175	126	15	,	,	PUNCT
ejpam-3175	126	16	λ	λ	X
ejpam-3175	126	17	)	)	PUNCT
ejpam-3175	126	18	]	]	PUNCT
ejpam-3175	127	1	=	=	PUNCT
ejpam-3175	127	2	f	f	X
ejpam-3175	128	1	[	[	X
ejpam-3175	128	2	rtnφ(iz/2	rtnφ(iz/2	NOUN
ejpam-3175	128	3	,	,	PUNCT
ejpam-3175	128	4	λ	λ	NOUN
ejpam-3175	128	5	)	)	PUNCT
ejpam-3175	128	6	]	]	PUNCT
ejpam-3175	128	7	.	.	PUNCT
ejpam-3175	129	1	proof	proof	NOUN
ejpam-3175	129	2	.	.	PUNCT
ejpam-3175	130	1	let	let	VERB
ejpam-3175	130	2	φ	φ	PROPN
ejpam-3175	130	3	∈	∈	PROPN
ejpam-3175	130	4	s	s	X
ejpam-3175	130	5	(	(	PUNCT
ejpam-3175	130	6	hn	hn	PROPN
ejpam-3175	130	7	)	)	PUNCT
ejpam-3175	130	8	,	,	PUNCT
ejpam-3175	130	9	by	by	ADP
ejpam-3175	130	10	(	(	PUNCT
ejpam-3175	130	11	10	10	NUM
ejpam-3175	130	12	)	)	PUNCT
ejpam-3175	130	13	,	,	PUNCT
ejpam-3175	130	14	(	(	PUNCT
ejpam-3175	130	15	11	11	NUM
ejpam-3175	130	16	)	)	PUNCT
ejpam-3175	130	17	and	and	CCONJ
ejpam-3175	130	18	(	(	PUNCT
ejpam-3175	130	19	6	6	NUM
ejpam-3175	130	20	)	)	PUNCT
ejpam-3175	130	21	,	,	PUNCT
ejpam-3175	130	22	we	we	PRON
ejpam-3175	130	23	deduce	deduce	VERB
ejpam-3175	130	24	that	that	SCONJ
ejpam-3175	130	25	fsf2[r	fsf2[r	PROPN
ejpam-3175	130	26	t	t	PROPN
ejpam-3175	130	27	nφ(z	nφ(z	PROPN
ejpam-3175	130	28	,	,	PUNCT
ejpam-3175	130	29	λ	λ	X
ejpam-3175	130	30	)	)	PUNCT
ejpam-3175	130	31	]	]	PUNCT
ejpam-3175	131	1	=	=	SYM
ejpam-3175	131	2	(	(	PUNCT
ejpam-3175	131	3	2πiλ)n	2πiλ)n	NUM
ejpam-3175	131	4	∫	∫	PROPN
ejpam-3175	131	5	cn	cn	PROPN
ejpam-3175	131	6	∫	∫	PROPN
ejpam-3175	131	7	r	r	NOUN
ejpam-3175	131	8	∫	∫	PROPN
ejpam-3175	131	9	cn	cn	PROPN
ejpam-3175	131	10	φ	φ	PROPN
ejpam-3175	131	11	(	(	PUNCT
ejpam-3175	131	12	w	w	PROPN
ejpam-3175	131	13	,	,	PUNCT
ejpam-3175	131	14	t−	t−	PROPN
ejpam-3175	131	15	1	1	NUM
ejpam-3175	131	16	2	2	NUM
ejpam-3175	131	17	im〈w	im〈w	NOUN
ejpam-3175	131	18	,	,	PUNCT
ejpam-3175	131	19	z′	z′	NOUN
ejpam-3175	131	20	〉	〉	NUM
ejpam-3175	131	21	)	)	PUNCT
ejpam-3175	131	22	e−2πiλteπiim〈z	e−2πiλteπiim〈z	PROPN
ejpam-3175	131	23	,	,	PUNCT
ejpam-3175	131	24	z	z	NOUN
ejpam-3175	131	25	′〉dwdz′dt	′〉dwdz′dt	PUNCT
ejpam-3175	131	26	=	=	PUNCT
ejpam-3175	131	27	(	(	PUNCT
ejpam-3175	131	28	2πiλ)n	2πiλ)n	NUM
ejpam-3175	131	29	∫	∫	PROPN
ejpam-3175	131	30	cn	cn	PROPN
ejpam-3175	131	31	∫	∫	PROPN
ejpam-3175	131	32	cn	cn	PROPN
ejpam-3175	131	33	f2φ(w	f2φ(w	PROPN
ejpam-3175	131	34	,	,	PUNCT
ejpam-3175	131	35	λ)eπiim〈z	λ)eπiim〈z	PRON
ejpam-3175	131	36	,	,	PUNCT
ejpam-3175	131	37	z	z	NOUN
ejpam-3175	131	38	′〉e−πλiim〈w	′〉e−πλiim〈w	NOUN
ejpam-3175	131	39	,	,	PUNCT
ejpam-3175	131	40	z	z	NOUN
ejpam-3175	131	41	′〉dwdz′	′〉dwdz′	NUM
ejpam-3175	131	42	z.	z.	PROPN
ejpam-3175	131	43	fang	fang	PROPN
ejpam-3175	131	44	,	,	PUNCT
ejpam-3175	131	45	h.	h.	PROPN
ejpam-3175	131	46	jianxun	jianxun	PROPN
ejpam-3175	131	47	he	he	PRON
ejpam-3175	131	48	/	/	SYM
ejpam-3175	131	49	eur	eur	PROPN
ejpam-3175	131	50	.	.	PUNCT
ejpam-3175	132	1	j.	j.	PROPN
ejpam-3175	132	2	pure	pure	PROPN
ejpam-3175	132	3	appl	appl	PROPN
ejpam-3175	132	4	.	.	PROPN
ejpam-3175	132	5	math	math	PROPN
ejpam-3175	132	6	,	,	PUNCT
ejpam-3175	132	7	11	11	NUM
ejpam-3175	132	8	(	(	PUNCT
ejpam-3175	132	9	1	1	NUM
ejpam-3175	132	10	)	)	PUNCT
ejpam-3175	132	11	(	(	PUNCT
ejpam-3175	132	12	2018	2018	NUM
ejpam-3175	132	13	)	)	PUNCT
ejpam-3175	132	14	,	,	PUNCT
ejpam-3175	132	15	138	138	NUM
ejpam-3175	132	16	-	-	SYM
ejpam-3175	132	17	149	149	NUM
ejpam-3175	132	18	143	143	NUM
ejpam-3175	132	19	=	=	SYM
ejpam-3175	132	20	(	(	PUNCT
ejpam-3175	132	21	2πiλ)n	2πiλ)n	NUM
ejpam-3175	132	22	∫	∫	PROPN
ejpam-3175	132	23	cn	cn	PROPN
ejpam-3175	132	24	∫	∫	PROPN
ejpam-3175	132	25	cn	cn	PROPN
ejpam-3175	132	26	f2φ(w	f2φ(w	PROPN
ejpam-3175	132	27	,	,	PUNCT
ejpam-3175	132	28	λ)eπiim〈z	λ)eπiim〈z	PRON
ejpam-3175	132	29	,	,	PUNCT
ejpam-3175	132	30	z	z	NOUN
ejpam-3175	132	31	′〉eπλiim〈z	′〉eπλiim〈z	NOUN
ejpam-3175	132	32	′,w〉dwdz′	′,w〉dwdz′	PROPN
ejpam-3175	132	33	=	=	SYM
ejpam-3175	132	34	(	(	PUNCT
ejpam-3175	132	35	2πiλ)n	2πiλ)n	NUM
ejpam-3175	132	36	∫	∫	PROPN
ejpam-3175	132	37	cn	cn	PROPN
ejpam-3175	132	38	f2fsφ(λz′	f2fsφ(λz′	NOUN
ejpam-3175	132	39	,	,	PUNCT
ejpam-3175	132	40	λ)eπiim〈z	λ)eπiim〈z	NUM
ejpam-3175	132	41	,	,	PUNCT
ejpam-3175	132	42	z	z	NOUN
ejpam-3175	132	43	′〉dz′	′〉dz′	NOUN
ejpam-3175	132	44	=	=	SYM
ejpam-3175	132	45	(	(	PUNCT
ejpam-3175	132	46	2πiλ)n	2πiλ)n	NUM
ejpam-3175	132	47	∫	∫	PROPN
ejpam-3175	132	48	cn	cn	PROPN
ejpam-3175	132	49	f1f2φ(iλz′/2	f1f2φ(iλz′/2	PROPN
ejpam-3175	132	50	,	,	PUNCT
ejpam-3175	132	51	t)eπiim〈z	t)eπiim〈z	NUM
ejpam-3175	132	52	,	,	PUNCT
ejpam-3175	132	53	z	z	NOUN
ejpam-3175	132	54	′〉dz′	′〉dz′	NOUN
ejpam-3175	132	55	=	=	SYM
ejpam-3175	132	56	(	(	PUNCT
ejpam-3175	132	57	2πiλ)n	2πiλ)n	NUM
ejpam-3175	132	58	∫	∫	PROPN
ejpam-3175	132	59	cn	cn	PROPN
ejpam-3175	132	60	f1f2φ(iλz′/2	f1f2φ(iλz′/2	PROPN
ejpam-3175	132	61	,	,	PUNCT
ejpam-3175	132	62	λ)e2πire〈z	λ)e2πire〈z	ADJ
ejpam-3175	132	63	/	/	SYM
ejpam-3175	132	64	λ	λ	NOUN
ejpam-3175	132	65	,	,	PUNCT
ejpam-3175	132	66	iλz′/2〉dz′	iλz′/2〉dz′	ADJ
ejpam-3175	132	67	=	=	X
ejpam-3175	132	68	(	(	PUNCT
ejpam-3175	132	69	8π)n(iλ)−nf2φ	8π)n(iλ)−nf2φ	NUM
ejpam-3175	132	70	(	(	PUNCT
ejpam-3175	132	71	z	z	NOUN
ejpam-3175	132	72	/	/	SYM
ejpam-3175	132	73	λ	λ	PROPN
ejpam-3175	132	74	,	,	PUNCT
ejpam-3175	132	75	λ	λ	NOUN
ejpam-3175	132	76	)	)	PUNCT
ejpam-3175	132	77	.	.	PUNCT
ejpam-3175	133	1	this	this	PRON
ejpam-3175	133	2	finishes	finish	VERB
ejpam-3175	133	3	the	the	DET
ejpam-3175	133	4	proof	proof	NOUN
ejpam-3175	133	5	of	of	ADP
ejpam-3175	133	6	proposition	proposition	NOUN
ejpam-3175	133	7	2	2	NUM
ejpam-3175	133	8	.	.	PUNCT
ejpam-3175	133	9	theorem	theorem	NOUN
ejpam-3175	133	10	1	1	NUM
ejpam-3175	133	11	.	.	PUNCT
ejpam-3175	134	1	let	let	VERB
ejpam-3175	134	2	f	f	PROPN
ejpam-3175	134	3	∈	∈	PROPN
ejpam-3175	134	4	s	s	X
ejpam-3175	134	5	(	(	PUNCT
ejpam-3175	134	6	hn)∩l2(hn	hn)∩l2(hn	PROPN
ejpam-3175	134	7	)	)	PUNCT
ejpam-3175	134	8	and	and	CCONJ
ejpam-3175	134	9	φ(z	φ(z	PROPN
ejpam-3175	134	10	,	,	PUNCT
ejpam-3175	134	11	t	t	PROPN
ejpam-3175	134	12	)	)	PUNCT
ejpam-3175	134	13	:	:	PUNCT
ejpam-3175	135	1	=	=	SYM
ejpam-3175	135	2	rnf(z	rnf(z	PROPN
ejpam-3175	135	3	,	,	PUNCT
ejpam-3175	135	4	t	t	PROPN
ejpam-3175	135	5	)	)	PUNCT
ejpam-3175	135	6	∈	∈	PROPN
ejpam-3175	135	7	s	s	PART
ejpam-3175	135	8	(	(	PUNCT
ejpam-3175	135	9	hn	hn	PROPN
ejpam-3175	135	10	)	)	PUNCT
ejpam-3175	135	11	.	.	PUNCT
ejpam-3175	136	1	then	then	ADV
ejpam-3175	136	2	f(z	f(z	PROPN
ejpam-3175	136	3	,	,	PUNCT
ejpam-3175	136	4	t	t	NOUN
ejpam-3175	136	5	)	)	PUNCT
ejpam-3175	136	6	=	=	PUNCT
ejpam-3175	136	7	(	(	PUNCT
ejpam-3175	136	8	4π)−2nrtnφ(z	4π)−2nrtnφ(z	NUM
ejpam-3175	136	9	,	,	PUNCT
ejpam-3175	136	10	t	t	PROPN
ejpam-3175	136	11	)	)	PUNCT
ejpam-3175	136	12	holds	hold	VERB
ejpam-3175	136	13	in	in	ADP
ejpam-3175	136	14	l2(hn	l2(hn	NOUN
ejpam-3175	136	15	)	)	PUNCT
ejpam-3175	136	16	.	.	PUNCT
ejpam-3175	137	1	proof	proof	NOUN
ejpam-3175	137	2	.	.	PUNCT
ejpam-3175	138	1	according	accord	VERB
ejpam-3175	138	2	to	to	ADP
ejpam-3175	138	3	the	the	DET
ejpam-3175	138	4	inversion	inversion	NOUN
ejpam-3175	138	5	formula	formula	NOUN
ejpam-3175	138	6	in	in	ADP
ejpam-3175	138	7	lemma	lemma	PROPN
ejpam-3175	138	8	1	1	NUM
ejpam-3175	138	9	and	and	CCONJ
ejpam-3175	138	10	(	(	PUNCT
ejpam-3175	138	11	8)	8)	NUM
ejpam-3175	138	12	,	,	PUNCT
ejpam-3175	138	13	we	we	PRON
ejpam-3175	138	14	obtain∫	obtain∫	VERB
ejpam-3175	138	15	hn	hn	PROPN
ejpam-3175	138	16	|rnf(z	|rnf(z	PROPN
ejpam-3175	138	17	,	,	PUNCT
ejpam-3175	138	18	t)|2dzdt	t)|2dzdt	PUNCT
ejpam-3175	138	19	=	=	SYM
ejpam-3175	138	20	∫	∫	PROPN
ejpam-3175	138	21	r∗	r∗	PROPN
ejpam-3175	138	22	‖πλ(rnf)‖2hs	‖πλ(rnf)‖2hs	PROPN
ejpam-3175	138	23	|λ|ndλ	|λ|ndλ	PUNCT
ejpam-3175	138	24	=	=	SYM
ejpam-3175	138	25	∫	∫	PROPN
ejpam-3175	138	26	r∗	r∗	PROPN
ejpam-3175	138	27	‖(2πiλ)nwλ(ff(iλz/2	‖(2πiλ)nwλ(ff(iλz/2	PROPN
ejpam-3175	138	28	,	,	PUNCT
ejpam-3175	138	29	λ))‖2hs	λ))‖2hs	X
ejpam-3175	138	30	|λ|ndλ	|λ|ndλ	PUNCT
ejpam-3175	138	31	=	=	SYM
ejpam-3175	138	32	∫	∫	PROPN
ejpam-3175	139	1	r∗	r∗	PROPN
ejpam-3175	139	2	∫	∫	PROPN
ejpam-3175	139	3	cn	cn	PROPN
ejpam-3175	139	4	(	(	PUNCT
ejpam-3175	139	5	4π)2n(λ)−n|ff(z	4π)2n(λ)−n|ff(z	NUM
ejpam-3175	139	6	,	,	PUNCT
ejpam-3175	139	7	λ)|2dz|λ|n|dλ	λ)|2dz|λ|n|dλ	X
ejpam-3175	139	8	=	=	SYM
ejpam-3175	140	1	∫	∫	PROPN
ejpam-3175	140	2	r∗	r∗	PROPN
ejpam-3175	140	3	(	(	PUNCT
ejpam-3175	140	4	4π)2n‖wλ(ff(z	4π)2n‖wλ(ff(z	NUM
ejpam-3175	140	5	,	,	PUNCT
ejpam-3175	140	6	λ))‖2hs	λ))‖2hs	X
ejpam-3175	140	7	|λ|ndλ	|λ|ndλ	PUNCT
ejpam-3175	140	8	=	=	SYM
ejpam-3175	140	9	∫	∫	PROPN
ejpam-3175	140	10	r∗	r∗	PROPN
ejpam-3175	140	11	(	(	PUNCT
ejpam-3175	140	12	4π)2n‖πλf1f	4π)2n‖πλf1f	NOUN
ejpam-3175	140	13	(	(	PUNCT
ejpam-3175	140	14	·	·	PUNCT
ejpam-3175	140	15	,	,	PUNCT
ejpam-3175	140	16	λ)‖2hs	λ)‖2hs	NUM
ejpam-3175	140	17	|λ|ndλ	|λ|ndλ	NUM
ejpam-3175	141	1	=	=	SYM
ejpam-3175	141	2	∫	∫	PROPN
ejpam-3175	141	3	hn	hn	PROPN
ejpam-3175	141	4	(	(	PUNCT
ejpam-3175	141	5	4π)2n|f1f(z	4π)2n|f1f(z	PROPN
ejpam-3175	141	6	,	,	PUNCT
ejpam-3175	141	7	t)|2dzdt	t)|2dzdt	NUM
ejpam-3175	141	8	,	,	PUNCT
ejpam-3175	141	9	which	which	PRON
ejpam-3175	141	10	implies	imply	VERB
ejpam-3175	141	11	that	that	SCONJ
ejpam-3175	141	12	,	,	PUNCT
ejpam-3175	141	13	(	(	PUNCT
ejpam-3175	141	14	4π)nf1f(z	4π)nf1f(z	NOUN
ejpam-3175	141	15	,	,	PUNCT
ejpam-3175	141	16	t	t	PROPN
ejpam-3175	141	17	)	)	PUNCT
ejpam-3175	141	18	=	=	SYM
ejpam-3175	142	1	∫	∫	PROPN
ejpam-3175	142	2	r∗	r∗	PROPN
ejpam-3175	142	3	tr(π∗λ(rnf)πλ(z	tr(π∗λ(rnf)πλ(z	PROPN
ejpam-3175	142	4	,	,	PUNCT
ejpam-3175	142	5	t))|λ|ndλ	t))|λ|ndλ	PROPN
ejpam-3175	142	6	=	=	SYM
ejpam-3175	143	1	rnf(z	rnf(z	PROPN
ejpam-3175	143	2	,	,	PUNCT
ejpam-3175	143	3	t	t	PROPN
ejpam-3175	143	4	)	)	PUNCT
ejpam-3175	143	5	and	and	CCONJ
ejpam-3175	143	6	hence	hence	ADV
ejpam-3175	143	7	f(z	f(z	PROPN
ejpam-3175	143	8	,	,	PUNCT
ejpam-3175	143	9	t	t	NOUN
ejpam-3175	143	10	)	)	PUNCT
ejpam-3175	143	11	=	=	PUNCT
ejpam-3175	144	1	(	(	PUNCT
ejpam-3175	144	2	4π)−nf−11	4π)−nf−11	PROPN
ejpam-3175	144	3	rnf(z	rnf(z	PROPN
ejpam-3175	144	4	,	,	PUNCT
ejpam-3175	144	5	t	t	PROPN
ejpam-3175	144	6	)	)	PUNCT
ejpam-3175	144	7	.	.	PUNCT
ejpam-3175	145	1	(	(	PUNCT
ejpam-3175	145	2	12	12	NUM
ejpam-3175	145	3	)	)	PUNCT
ejpam-3175	145	4	from	from	ADP
ejpam-3175	145	5	(	(	PUNCT
ejpam-3175	145	6	6	6	NUM
ejpam-3175	145	7	)	)	PUNCT
ejpam-3175	145	8	,	,	PUNCT
ejpam-3175	145	9	it	it	PRON
ejpam-3175	145	10	follows	follow	VERB
ejpam-3175	145	11	that∫	that∫	NOUN
ejpam-3175	145	12	hn	hn	PROPN
ejpam-3175	145	13	|f1f2r	|f1f2r	PROPN
ejpam-3175	145	14	t	t	PROPN
ejpam-3175	145	15	nφ(iz/2	nφ(iz/2	PROPN
ejpam-3175	145	16	,	,	PUNCT
ejpam-3175	145	17	λ)|2dzdλ	λ)|2dzdλ	X
ejpam-3175	145	18	=	=	SYM
ejpam-3175	146	1	4n	4n	NUM
ejpam-3175	146	2	∫	∫	X
ejpam-3175	147	1	hn	hn	PROPN
ejpam-3175	147	2	|f1f2r	|f1f2r	PROPN
ejpam-3175	147	3	t	t	PROPN
ejpam-3175	147	4	nφ(z	nφ(z	PROPN
ejpam-3175	147	5	,	,	PUNCT
ejpam-3175	147	6	λ)|2dzdλ	λ)|2dzdλ	X
ejpam-3175	147	7	.	.	PUNCT
ejpam-3175	148	1	by	by	ADP
ejpam-3175	148	2	proposition	proposition	NOUN
ejpam-3175	148	3	2	2	NUM
ejpam-3175	148	4	,	,	PUNCT
ejpam-3175	148	5	we	we	PRON
ejpam-3175	148	6	find	find	VERB
ejpam-3175	148	7	that	that	SCONJ
ejpam-3175	148	8	4n	4n	ADJ
ejpam-3175	148	9	∫	∫	NOUN
ejpam-3175	148	10	hn	hn	PROPN
ejpam-3175	148	11	|f1f2r	|f1f2r	PROPN
ejpam-3175	148	12	t	t	PROPN
ejpam-3175	148	13	nφ(z	nφ(z	PROPN
ejpam-3175	148	14	,	,	PUNCT
ejpam-3175	148	15	λ)|2dzdλ	λ)|2dzdλ	X
ejpam-3175	149	1	=	=	SYM
ejpam-3175	150	1	(	(	PUNCT
ejpam-3175	150	2	8π)2n(iλ)−2n	8π)2n(iλ)−2n	NUM
ejpam-3175	150	3	∫	∫	NOUN
ejpam-3175	150	4	hn	hn	PROPN
ejpam-3175	150	5	|f2φ	|f2φ	NOUN
ejpam-3175	150	6	(	(	PUNCT
ejpam-3175	150	7	z	z	NOUN
ejpam-3175	150	8	/	/	SYM
ejpam-3175	150	9	λ	λ	PROPN
ejpam-3175	150	10	,	,	PUNCT
ejpam-3175	150	11	λ	λ	PROPN
ejpam-3175	150	12	)	)	PUNCT
ejpam-3175	150	13	|2dzdλ	|2dzdλ	PROPN
ejpam-3175	150	14	z.	z.	PROPN
ejpam-3175	150	15	fang	fang	PROPN
ejpam-3175	150	16	,	,	PUNCT
ejpam-3175	150	17	h.	h.	PROPN
ejpam-3175	150	18	jianxun	jianxun	PROPN
ejpam-3175	150	19	he	he	PRON
ejpam-3175	150	20	/	/	SYM
ejpam-3175	150	21	eur	eur	PROPN
ejpam-3175	150	22	.	.	PUNCT
ejpam-3175	151	1	j.	j.	PROPN
ejpam-3175	151	2	pure	pure	PROPN
ejpam-3175	151	3	appl	appl	PROPN
ejpam-3175	151	4	.	.	PROPN
ejpam-3175	151	5	math	math	PROPN
ejpam-3175	151	6	,	,	PUNCT
ejpam-3175	151	7	11	11	NUM
ejpam-3175	151	8	(	(	PUNCT
ejpam-3175	151	9	1	1	NUM
ejpam-3175	151	10	)	)	PUNCT
ejpam-3175	151	11	(	(	PUNCT
ejpam-3175	151	12	2018	2018	NUM
ejpam-3175	151	13	)	)	PUNCT
ejpam-3175	151	14	,	,	PUNCT
ejpam-3175	151	15	138	138	NUM
ejpam-3175	151	16	-	-	SYM
ejpam-3175	151	17	149	149	NUM
ejpam-3175	151	18	144	144	NUM
ejpam-3175	151	19	=	=	SYM
ejpam-3175	151	20	(	(	PUNCT
ejpam-3175	151	21	8π)2n	8π)2n	NUM
ejpam-3175	151	22	∫	∫	PROPN
ejpam-3175	151	23	hn	hn	PROPN
ejpam-3175	151	24	|f2φ(z	|f2φ(z	PROPN
ejpam-3175	151	25	,	,	PUNCT
ejpam-3175	151	26	λ)|2dzdλ	λ)|2dzdλ	X
ejpam-3175	151	27	,	,	PUNCT
ejpam-3175	151	28	which	which	PRON
ejpam-3175	151	29	implies	imply	VERB
ejpam-3175	151	30	that	that	SCONJ
ejpam-3175	151	31	,	,	PUNCT
ejpam-3175	151	32	f1f2r	f1f2r	NUM
ejpam-3175	151	33	t	t	NOUN
ejpam-3175	151	34	nφ(z	nφ(z	NUM
ejpam-3175	151	35	,	,	PUNCT
ejpam-3175	151	36	λ	λ	X
ejpam-3175	151	37	)	)	PUNCT
ejpam-3175	151	38	=	=	SYM
ejpam-3175	151	39	(	(	PUNCT
ejpam-3175	151	40	4π)nf2φ(z	4π)nf2φ(z	ADJ
ejpam-3175	151	41	,	,	PUNCT
ejpam-3175	151	42	λ	λ	NOUN
ejpam-3175	151	43	)	)	PUNCT
ejpam-3175	151	44	=	=	SYM
ejpam-3175	151	45	(	(	PUNCT
ejpam-3175	151	46	4π)nf2rnf(z	4π)nf2rnf(z	NUM
ejpam-3175	151	47	,	,	PUNCT
ejpam-3175	151	48	λ	λ	NOUN
ejpam-3175	151	49	)	)	PUNCT
ejpam-3175	151	50	(	(	PUNCT
ejpam-3175	151	51	13	13	NUM
ejpam-3175	151	52	)	)	PUNCT
ejpam-3175	151	53	holds	hold	VERB
ejpam-3175	151	54	in	in	ADP
ejpam-3175	151	55	l2(hn	l2(hn	NOUN
ejpam-3175	151	56	)	)	PUNCT
ejpam-3175	151	57	.	.	PUNCT
ejpam-3175	152	1	combining	combine	VERB
ejpam-3175	152	2	with	with	ADP
ejpam-3175	152	3	(	(	PUNCT
ejpam-3175	152	4	12	12	NUM
ejpam-3175	152	5	)	)	PUNCT
ejpam-3175	152	6	and	and	CCONJ
ejpam-3175	152	7	(	(	PUNCT
ejpam-3175	152	8	13	13	NUM
ejpam-3175	152	9	)	)	PUNCT
ejpam-3175	152	10	,	,	PUNCT
ejpam-3175	152	11	we	we	PRON
ejpam-3175	152	12	have	have	VERB
ejpam-3175	152	13	f(z	f(z	PROPN
ejpam-3175	152	14	,	,	PUNCT
ejpam-3175	152	15	t	t	NOUN
ejpam-3175	152	16	)	)	PUNCT
ejpam-3175	152	17	=	=	PUNCT
ejpam-3175	153	1	(	(	PUNCT
ejpam-3175	153	2	4π)−2nrtnφ(z	4π)−2nrtnφ(z	NUM
ejpam-3175	153	3	,	,	PUNCT
ejpam-3175	153	4	t	t	PROPN
ejpam-3175	153	5	)	)	PUNCT
ejpam-3175	153	6	.	.	PUNCT
ejpam-3175	154	1	we	we	PRON
ejpam-3175	154	2	complete	complete	VERB
ejpam-3175	154	3	the	the	DET
ejpam-3175	154	4	proof	proof	NOUN
ejpam-3175	154	5	of	of	ADP
ejpam-3175	154	6	theorem	theorem	NOUN
ejpam-3175	154	7	1	1	NUM
ejpam-3175	154	8	.	.	PUNCT
ejpam-3175	155	1	the	the	DET
ejpam-3175	155	2	sobolev	sobolev	PROPN
ejpam-3175	155	3	space	space	PROPN
ejpam-3175	155	4	w	w	PROPN
ejpam-3175	155	5	on	on	ADP
ejpam-3175	155	6	hn	hn	PROPN
ejpam-3175	155	7	is	be	AUX
ejpam-3175	155	8	defined	define	VERB
ejpam-3175	155	9	by	by	ADP
ejpam-3175	155	10	w	w	NOUN
ejpam-3175	155	11	:	:	PUNCT
ejpam-3175	155	12	=	=	X
ejpam-3175	155	13	{	{	PUNCT
ejpam-3175	155	14	f	f	PROPN
ejpam-3175	155	15	∈	∈	PROPN
ejpam-3175	155	16	l2(hn	l2(hn	PROPN
ejpam-3175	155	17	)	)	PUNCT
ejpam-3175	155	18	:	:	PUNCT
ejpam-3175	155	19	∫	∫	PROPN
ejpam-3175	155	20	hn	hn	PROPN
ejpam-3175	155	21	|tnf(z	|tnf(z	PROPN
ejpam-3175	155	22	,	,	PUNCT
ejpam-3175	155	23	t)|2dzdt	t)|2dzdt	PUNCT
ejpam-3175	155	24	<	<	X
ejpam-3175	155	25	∞	∞	NUM
ejpam-3175	155	26	}	}	PUNCT
ejpam-3175	155	27	.	.	PUNCT
ejpam-3175	156	1	theorem	theorem	NOUN
ejpam-3175	156	2	2	2	NUM
ejpam-3175	156	3	.	.	PUNCT
ejpam-3175	157	1	let	let	VERB
ejpam-3175	157	2	f	f	PROPN
ejpam-3175	157	3	∈	∈	PROPN
ejpam-3175	157	4	w	w	PROPN
ejpam-3175	157	5	.	.	PUNCT
ejpam-3175	158	1	then	then	ADV
ejpam-3175	158	2	there	there	PRON
ejpam-3175	158	3	exists	exist	VERB
ejpam-3175	158	4	a	a	DET
ejpam-3175	158	5	constant	constant	ADJ
ejpam-3175	158	6	cn	cn	NOUN
ejpam-3175	158	7	such	such	ADJ
ejpam-3175	158	8	that	that	PRON
ejpam-3175	158	9	tnrt0	tnrt0	PROPN
ejpam-3175	158	10	t	t	X
ejpam-3175	158	11	nr0f	nr0f	PROPN
ejpam-3175	158	12	=	=	SYM
ejpam-3175	158	13	cnf	cnf	PROPN
ejpam-3175	158	14	holds	hold	VERB
ejpam-3175	158	15	in	in	ADP
ejpam-3175	158	16	l2(hn	l2(hn	NOUN
ejpam-3175	158	17	)	)	PUNCT
ejpam-3175	158	18	.	.	PUNCT
ejpam-3175	159	1	proof	proof	NOUN
ejpam-3175	159	2	.	.	PUNCT
ejpam-3175	160	1	let	let	VERB
ejpam-3175	160	2	f	f	PRON
ejpam-3175	160	3	∈w	∈w	VERB
ejpam-3175	160	4	∩	∩	NOUN
ejpam-3175	160	5	l2(hn	l2(hn	NOUN
ejpam-3175	160	6	)	)	PUNCT
ejpam-3175	160	7	,	,	PUNCT
ejpam-3175	160	8	it	it	PRON
ejpam-3175	160	9	is	be	AUX
ejpam-3175	160	10	easy	easy	ADJ
ejpam-3175	160	11	to	to	PART
ejpam-3175	160	12	verify	verify	VERB
ejpam-3175	160	13	that	that	SCONJ
ejpam-3175	160	14	r0(t	r0(t	ADP
ejpam-3175	160	15	n(f	n(f	PROPN
ejpam-3175	160	16	)	)	PUNCT
ejpam-3175	160	17	)	)	PUNCT
ejpam-3175	161	1	=	=	SYM
ejpam-3175	161	2	tn(r0(f	tn(r0(f	PROPN
ejpam-3175	161	3	)	)	PUNCT
ejpam-3175	161	4	)	)	PUNCT
ejpam-3175	161	5	.	.	PUNCT
ejpam-3175	162	1	(	(	PUNCT
ejpam-3175	162	2	14	14	NUM
ejpam-3175	162	3	)	)	PUNCT
ejpam-3175	162	4	by	by	ADP
ejpam-3175	162	5	lemma	lemma	PROPN
ejpam-3175	162	6	1	1	NUM
ejpam-3175	162	7	and	and	CCONJ
ejpam-3175	162	8	the	the	DET
ejpam-3175	162	9	proof	proof	NOUN
ejpam-3175	162	10	of	of	ADP
ejpam-3175	162	11	theorem	theorem	NOUN
ejpam-3175	162	12	1	1	NUM
ejpam-3175	162	13	,	,	PUNCT
ejpam-3175	162	14	we	we	PRON
ejpam-3175	162	15	find	find	VERB
ejpam-3175	162	16	that∫	that∫	PROPN
ejpam-3175	162	17	cn	cn	PROPN
ejpam-3175	162	18	|r0	|r0	PROPN
ejpam-3175	162	19	t	t	PROPN
ejpam-3175	162	20	nf(z	nf(z	NUM
ejpam-3175	162	21	,	,	PUNCT
ejpam-3175	162	22	t)|2dzdt	t)|2dzdt	NUM
ejpam-3175	162	23	=	=	SYM
ejpam-3175	162	24	∫	∫	PROPN
ejpam-3175	162	25	r∗	r∗	PROPN
ejpam-3175	162	26	‖πλ(rn(f))‖2hs	‖πλ(rn(f))‖2hs	INTJ
ejpam-3175	162	27	|λ|ndλ	|λ|ndλ	SYM
ejpam-3175	162	28	=	=	SYM
ejpam-3175	162	29	(	(	PUNCT
ejpam-3175	162	30	4π)2n‖f‖2l2(hn	4π)2n‖f‖2l2(hn	PROPN
ejpam-3175	162	31	)	)	PUNCT
ejpam-3175	162	32	.	.	PUNCT
ejpam-3175	163	1	together	together	ADV
ejpam-3175	163	2	with	with	ADP
ejpam-3175	163	3	the	the	DET
ejpam-3175	163	4	density	density	NOUN
ejpam-3175	163	5	argument	argument	NOUN
ejpam-3175	163	6	,	,	PUNCT
ejpam-3175	163	7	we	we	PRON
ejpam-3175	163	8	obtain	obtain	VERB
ejpam-3175	163	9	that	that	SCONJ
ejpam-3175	163	10	(	(	PUNCT
ejpam-3175	163	11	14	14	NUM
ejpam-3175	163	12	)	)	PUNCT
ejpam-3175	163	13	holds	hold	VERB
ejpam-3175	163	14	in	in	ADP
ejpam-3175	163	15	w	w	PROPN
ejpam-3175	163	16	∩s	∩s	PROPN
ejpam-3175	163	17	(	(	PUNCT
ejpam-3175	163	18	hn	hn	PROPN
ejpam-3175	163	19	)	)	PUNCT
ejpam-3175	163	20	.	.	PUNCT
ejpam-3175	164	1	similarly	similarly	ADV
ejpam-3175	164	2	,	,	PUNCT
ejpam-3175	164	3	we	we	PRON
ejpam-3175	164	4	also	also	ADV
ejpam-3175	164	5	have	have	AUX
ejpam-3175	164	6	rt0	rt0	VERB
ejpam-3175	164	7	t	t	PROPN
ejpam-3175	164	8	nφ	nφ	PROPN
ejpam-3175	164	9	=	=	PROPN
ejpam-3175	164	10	tnrt0φ	tnrt0φ	PROPN
ejpam-3175	164	11	.	.	PUNCT
ejpam-3175	165	1	(	(	PUNCT
ejpam-3175	165	2	15	15	NUM
ejpam-3175	165	3	)	)	PUNCT
ejpam-3175	165	4	obviously	obviously	ADV
ejpam-3175	165	5	,	,	PUNCT
ejpam-3175	165	6	cnr0	cnr0	PROPN
ejpam-3175	165	7	t	t	PROPN
ejpam-3175	165	8	n(f	n(f	PROPN
ejpam-3175	165	9	)	)	PUNCT
ejpam-3175	165	10	=	=	PUNCT
ejpam-3175	166	1	φ	φ	PROPN
ejpam-3175	166	2	∈w	∈w	PROPN
ejpam-3175	166	3	is	be	AUX
ejpam-3175	166	4	well	well	ADV
ejpam-3175	166	5	defined	define	VERB
ejpam-3175	166	6	.	.	PUNCT
ejpam-3175	167	1	according	accord	VERB
ejpam-3175	167	2	to	to	ADP
ejpam-3175	167	3	(	(	PUNCT
ejpam-3175	167	4	15	15	NUM
ejpam-3175	167	5	)	)	PUNCT
ejpam-3175	167	6	and	and	CCONJ
ejpam-3175	167	7	(	(	PUNCT
ejpam-3175	167	8	14	14	NUM
ejpam-3175	167	9	)	)	PUNCT
ejpam-3175	167	10	,	,	PUNCT
ejpam-3175	167	11	we	we	PRON
ejpam-3175	167	12	see	see	VERB
ejpam-3175	167	13	that	that	PRON
ejpam-3175	167	14	rt0	rt0	VERB
ejpam-3175	167	15	t	t	PROPN
ejpam-3175	167	16	nφ	nφ	NOUN
ejpam-3175	167	17	=	=	PROPN
ejpam-3175	167	18	tnrt0φ	tnrt0φ	PROPN
ejpam-3175	167	19	=	=	SYM
ejpam-3175	167	20	cnt	cnt	PROPN
ejpam-3175	167	21	nrt0	nrt0	PROPN
ejpam-3175	167	22	t	t	PROPN
ejpam-3175	167	23	nr0f	nr0f	PROPN
ejpam-3175	167	24	=	=	PUNCT
ejpam-3175	167	25	cnr̃	cnr̃	NOUN
ejpam-3175	167	26	t	t	NOUN
ejpam-3175	167	27	0r0f	0r0f	PROPN
ejpam-3175	168	1	=	=	SYM
ejpam-3175	168	2	cnf	cnf	PROPN
ejpam-3175	168	3	.	.	PUNCT
ejpam-3175	169	1	we	we	PRON
ejpam-3175	169	2	remark	remark	VERB
ejpam-3175	169	3	that	that	SCONJ
ejpam-3175	169	4	the	the	DET
ejpam-3175	169	5	inverse	inverse	NOUN
ejpam-3175	169	6	formula	formula	NOUN
ejpam-3175	169	7	of	of	ADP
ejpam-3175	169	8	radon	radon	NOUN
ejpam-3175	169	9	transform	transform	NOUN
ejpam-3175	169	10	is	be	AUX
ejpam-3175	169	11	obtained	obtain	VERB
ejpam-3175	169	12	via	via	ADP
ejpam-3175	169	13	propositions	proposition	NOUN
ejpam-3175	169	14	1	1	NUM
ejpam-3175	169	15	,	,	PUNCT
ejpam-3175	169	16	2	2	NUM
ejpam-3175	169	17	and	and	CCONJ
ejpam-3175	169	18	theorems	theorem	NOUN
ejpam-3175	169	19	1	1	NUM
ejpam-3175	169	20	,	,	PUNCT
ejpam-3175	169	21	2	2	NUM
ejpam-3175	169	22	.	.	NOUN
ejpam-3175	169	23	4	4	NUM
ejpam-3175	169	24	.	.	PUNCT
ejpam-3175	169	25	littlewood	littlewood	PROPN
ejpam-3175	169	26	-	-	PUNCT
ejpam-3175	169	27	paley	paley	PROPN
ejpam-3175	169	28	g	g	NOUN
ejpam-3175	169	29	-	-	PUNCT
ejpam-3175	169	30	function	function	NOUN
ejpam-3175	169	31	let	let	VERB
ejpam-3175	169	32	xj	xj	PROPN
ejpam-3175	169	33	=	=	PROPN
ejpam-3175	169	34	∂	∂	NUM
ejpam-3175	169	35	∂xj	∂xj	NOUN
ejpam-3175	169	36	+	+	CCONJ
ejpam-3175	169	37	1	1	NUM
ejpam-3175	169	38	2yj	2yj	NOUN
ejpam-3175	169	39	∂	∂	NOUN
ejpam-3175	170	1	∂t	∂t	PROPN
ejpam-3175	170	2	,	,	PUNCT
ejpam-3175	170	3	yj	yj	PROPN
ejpam-3175	170	4	=	=	SYM
ejpam-3175	170	5	∂	∂	NUM
ejpam-3175	170	6	∂yj	∂yj	NOUN
ejpam-3175	170	7	−	−	NOUN
ejpam-3175	170	8	1	1	NUM
ejpam-3175	170	9	2xj	2xj	NOUN
ejpam-3175	170	10	∂	∂	NOUN
ejpam-3175	171	1	∂t	∂t	PROPN
ejpam-3175	171	2	,	,	PUNCT
ejpam-3175	171	3	j	j	PROPN
ejpam-3175	171	4	=	=	SYM
ejpam-3175	171	5	1	1	NUM
ejpam-3175	171	6	,	,	PUNCT
ejpam-3175	171	7	.	.	PUNCT
ejpam-3175	171	8	.	.	PUNCT
ejpam-3175	171	9	.	.	PUNCT
ejpam-3175	172	1	,	,	PUNCT
ejpam-3175	172	2	n.	n.	PROPN
ejpam-3175	172	3	xj	xj	PROPN
ejpam-3175	172	4	,	,	PUNCT
ejpam-3175	172	5	yj	yj	PROPN
ejpam-3175	172	6	be	be	AUX
ejpam-3175	172	7	left	leave	VERB
ejpam-3175	172	8	invariant	invariant	ADJ
ejpam-3175	172	9	vector	vector	NOUN
ejpam-3175	172	10	fields	field	NOUN
ejpam-3175	172	11	on	on	ADP
ejpam-3175	172	12	hn	hn	PROPN
ejpam-3175	172	13	.	.	PUNCT
ejpam-3175	173	1	the	the	DET
ejpam-3175	173	2	gradient	gradient	ADJ
ejpam-3175	173	3	operator	operator	NOUN
ejpam-3175	173	4	on	on	ADP
ejpam-3175	173	5	hn	hn	PROPN
ejpam-3175	173	6	is	be	AUX
ejpam-3175	173	7	given	give	VERB
ejpam-3175	173	8	by	by	ADP
ejpam-3175	173	9	∇	∇	X
ejpam-3175	173	10	=	=	PUNCT
ejpam-3175	173	11	(	(	PUNCT
ejpam-3175	173	12	x1	x1	PROPN
ejpam-3175	173	13	,	,	PUNCT
ejpam-3175	173	14	.	.	PUNCT
ejpam-3175	173	15	.	.	PUNCT
ejpam-3175	173	16	.	.	PUNCT
ejpam-3175	174	1	,	,	PUNCT
ejpam-3175	174	2	xn	xn	PROPN
ejpam-3175	174	3	,	,	PUNCT
ejpam-3175	174	4	y1	y1	NOUN
ejpam-3175	174	5	,	,	PUNCT
ejpam-3175	174	6	.	.	PUNCT
ejpam-3175	174	7	.	.	PUNCT
ejpam-3175	174	8	.	.	PUNCT
ejpam-3175	175	1	,	,	PUNCT
ejpam-3175	175	2	yn	yn	PROPN
ejpam-3175	175	3	)	)	PUNCT
ejpam-3175	175	4	.	.	PUNCT
ejpam-3175	176	1	z.	z.	PROPN
ejpam-3175	176	2	fang	fang	PROPN
ejpam-3175	176	3	,	,	PUNCT
ejpam-3175	176	4	h.	h.	PROPN
ejpam-3175	176	5	jianxun	jianxun	PROPN
ejpam-3175	176	6	he	he	PRON
ejpam-3175	176	7	/	/	SYM
ejpam-3175	176	8	eur	eur	PROPN
ejpam-3175	176	9	.	.	PUNCT
ejpam-3175	177	1	j.	j.	PROPN
ejpam-3175	177	2	pure	pure	PROPN
ejpam-3175	177	3	appl	appl	PROPN
ejpam-3175	177	4	.	.	PROPN
ejpam-3175	177	5	math	math	PROPN
ejpam-3175	177	6	,	,	PUNCT
ejpam-3175	177	7	11	11	NUM
ejpam-3175	177	8	(	(	PUNCT
ejpam-3175	177	9	1	1	NUM
ejpam-3175	177	10	)	)	PUNCT
ejpam-3175	177	11	(	(	PUNCT
ejpam-3175	177	12	2018	2018	NUM
ejpam-3175	177	13	)	)	PUNCT
ejpam-3175	177	14	,	,	PUNCT
ejpam-3175	177	15	138	138	NUM
ejpam-3175	177	16	-	-	SYM
ejpam-3175	177	17	149	149	NUM
ejpam-3175	177	18	145	145	NUM
ejpam-3175	177	19	the	the	DET
ejpam-3175	177	20	sub	sub	ADJ
ejpam-3175	177	21	-	-	ADJ
ejpam-3175	177	22	laplacian	laplacian	ADJ
ejpam-3175	177	23	operator	operator	NOUN
ejpam-3175	177	24	of	of	ADP
ejpam-3175	177	25	hn	hn	PROPN
ejpam-3175	177	26	is	be	AUX
ejpam-3175	177	27	defined	define	VERB
ejpam-3175	177	28	by	by	ADP
ejpam-3175	177	29	l	l	NOUN
ejpam-3175	178	1	=	=	SYM
ejpam-3175	178	2	n∑	n∑	ADJ
ejpam-3175	178	3	j=1	j=1	NOUN
ejpam-3175	178	4	(	(	PUNCT
ejpam-3175	178	5	x2	x2	INTJ
ejpam-3175	178	6	j	j	PROPN
ejpam-3175	179	1	+	+	CCONJ
ejpam-3175	179	2	y	y	PROPN
ejpam-3175	179	3	2	2	NUM
ejpam-3175	179	4	j	j	PROPN
ejpam-3175	179	5	)	)	PUNCT
ejpam-3175	179	6	.	.	PUNCT
ejpam-3175	180	1	it	it	PRON
ejpam-3175	180	2	is	be	AUX
ejpam-3175	180	3	known	know	VERB
ejpam-3175	180	4	that	that	SCONJ
ejpam-3175	180	5	πλ(l	πλ(l	NOUN
ejpam-3175	180	6	f)(λ	f)(λ	NOUN
ejpam-3175	180	7	)	)	PUNCT
ejpam-3175	180	8	=	=	SYM
ejpam-3175	180	9	πλ(f	πλ(f	X
ejpam-3175	180	10	)	)	PUNCT
ejpam-3175	180	11	∑	∑	PROPN
ejpam-3175	180	12	α∈nn	α∈nn	PROPN
ejpam-3175	180	13	(	(	PUNCT
ejpam-3175	180	14	2|α|+	2|α|+	PROPN
ejpam-3175	180	15	n)|λ|φλ	n)|λ|φλ	PROPN
ejpam-3175	180	16	,	,	PUNCT
ejpam-3175	180	17	α	α	X
ejpam-3175	180	18	.	.	PUNCT
ejpam-3175	181	1	l	l	NOUN
ejpam-3175	181	2	is	be	AUX
ejpam-3175	181	3	a	a	DET
ejpam-3175	181	4	positive	positive	ADJ
ejpam-3175	181	5	self	self	NOUN
ejpam-3175	181	6	-	-	PUNCT
ejpam-3175	181	7	adjoint	adjoint	NOUN
ejpam-3175	181	8	operator	operator	NOUN
ejpam-3175	181	9	.	.	PUNCT
ejpam-3175	182	1	for	for	ADP
ejpam-3175	182	2	a	a	DET
ejpam-3175	182	3	suitable	suitable	ADJ
ejpam-3175	182	4	function	function	NOUN
ejpam-3175	182	5	ψ	ψ	NOUN
ejpam-3175	182	6	defined	define	VERB
ejpam-3175	182	7	on	on	ADP
ejpam-3175	182	8	(	(	PUNCT
ejpam-3175	182	9	0	0	NUM
ejpam-3175	182	10	,	,	PUNCT
ejpam-3175	182	11	∞	∞	PROPN
ejpam-3175	182	12	)	)	PUNCT
ejpam-3175	182	13	,	,	PUNCT
ejpam-3175	182	14	the	the	DET
ejpam-3175	182	15	operator	operator	NOUN
ejpam-3175	182	16	ψ(l	ψ(l	PROPN
ejpam-3175	182	17	)	)	PUNCT
ejpam-3175	182	18	can	can	AUX
ejpam-3175	182	19	be	be	AUX
ejpam-3175	182	20	defined	define	VERB
ejpam-3175	182	21	in	in	ADP
ejpam-3175	182	22	terms	term	NOUN
ejpam-3175	182	23	of	of	ADP
ejpam-3175	182	24	the	the	DET
ejpam-3175	182	25	spectral	spectral	ADJ
ejpam-3175	182	26	expansion	expansion	NOUN
ejpam-3175	182	27	of	of	ADP
ejpam-3175	182	28	l	l	NOUN
ejpam-3175	182	29	.	.	PUNCT
ejpam-3175	183	1	then	then	ADV
ejpam-3175	183	2	πλ(ψ(l	πλ(ψ(l	X
ejpam-3175	183	3	)	)	PUNCT
ejpam-3175	183	4	f)(λ	f)(λ	NOUN
ejpam-3175	183	5	)	)	PUNCT
ejpam-3175	183	6	=	=	SYM
ejpam-3175	184	1	πλ(f	πλ(f	X
ejpam-3175	184	2	)	)	PUNCT
ejpam-3175	184	3	∑	∑	PUNCT
ejpam-3175	184	4	α∈nn	α∈nn	PROPN
ejpam-3175	184	5	ψ(2|α|+	ψ(2|α|+	NOUN
ejpam-3175	184	6	n)|λ|φλ	n)|λ|φλ	PROPN
ejpam-3175	184	7	,	,	PUNCT
ejpam-3175	184	8	α	α	X
ejpam-3175	184	9	.	.	PUNCT
ejpam-3175	185	1	let	let	VERB
ejpam-3175	185	2	φ	φ	PROPN
ejpam-3175	185	3	denote	denote	VERB
ejpam-3175	185	4	the	the	DET
ejpam-3175	185	5	kernel	kernel	NOUN
ejpam-3175	185	6	function	function	NOUN
ejpam-3175	185	7	of	of	ADP
ejpam-3175	185	8	ψ(l	ψ(l	PROPN
ejpam-3175	185	9	)	)	PUNCT
ejpam-3175	185	10	.	.	PUNCT
ejpam-3175	186	1	then	then	ADV
ejpam-3175	186	2	φ(λ	φ(λ	NUM
ejpam-3175	186	3	)	)	PUNCT
ejpam-3175	186	4	=	=	PUNCT
ejpam-3175	186	5	∑	∑	PUNCT
ejpam-3175	186	6	α∈nn	α∈nn	PROPN
ejpam-3175	186	7	ψ(2|α|+	ψ(2|α|+	NOUN
ejpam-3175	186	8	n)|λ|φλ	n)|λ|φλ	PROPN
ejpam-3175	186	9	,	,	PUNCT
ejpam-3175	186	10	α	α	X
ejpam-3175	186	11	.	.	PUNCT
ejpam-3175	187	1	we	we	PRON
ejpam-3175	187	2	denote	denote	VERB
ejpam-3175	187	3	by	by	ADP
ejpam-3175	187	4	r(hn	r(hn	NOUN
ejpam-3175	187	5	)	)	PUNCT
ejpam-3175	187	6	the	the	DET
ejpam-3175	187	7	set	set	NOUN
ejpam-3175	187	8	of	of	ADP
ejpam-3175	187	9	all	all	DET
ejpam-3175	187	10	these	these	DET
ejpam-3175	187	11	functions	function	NOUN
ejpam-3175	187	12	φ	φ	X
ejpam-3175	187	13	.	.	PUNCT
ejpam-3175	188	1	let	let	VERB
ejpam-3175	188	2	φ	φ	PROPN
ejpam-3175	188	3	∈	∈	PROPN
ejpam-3175	188	4	r(hn	r(hn	PROPN
ejpam-3175	188	5	)	)	PUNCT
ejpam-3175	188	6	,	,	PUNCT
ejpam-3175	188	7	the	the	DET
ejpam-3175	188	8	littlewood	littlewood	NOUN
ejpam-3175	188	9	-	-	PUNCT
ejpam-3175	188	10	paley	paley	PROPN
ejpam-3175	188	11	g	g	NOUN
ejpam-3175	188	12	-	-	PUNCT
ejpam-3175	188	13	function	function	NOUN
ejpam-3175	188	14	on	on	ADP
ejpam-3175	188	15	hn	hn	PROPN
ejpam-3175	188	16	is	be	AUX
ejpam-3175	188	17	defined	define	VERB
ejpam-3175	188	18	by	by	ADP
ejpam-3175	188	19	g(rnf	g(rnf	PROPN
ejpam-3175	188	20	,	,	PUNCT
ejpam-3175	188	21	u	u	NOUN
ejpam-3175	188	22	)	)	PUNCT
ejpam-3175	188	23	=	=	PUNCT
ejpam-3175	189	1	[	[	X
ejpam-3175	189	2	∫	∫	X
ejpam-3175	189	3	∞	∞	PROPN
ejpam-3175	189	4	0	0	NUM
ejpam-3175	189	5	|rnf	|rnf	PROPN
ejpam-3175	189	6	∗	∗	NOUN
ejpam-3175	189	7	φρ(u)|2	φρ(u)|2	NOUN
ejpam-3175	189	8	dρ	dρ	PROPN
ejpam-3175	189	9	ρ	ρ	X
ejpam-3175	189	10	]	]	X
ejpam-3175	189	11	1/2	1/2	NUM
ejpam-3175	189	12	,	,	PUNCT
ejpam-3175	189	13	where	where	SCONJ
ejpam-3175	189	14	rnf	rnf	PROPN
ejpam-3175	189	15	is	be	AUX
ejpam-3175	189	16	as	as	ADP
ejpam-3175	189	17	in	in	ADP
ejpam-3175	189	18	(	(	PUNCT
ejpam-3175	189	19	9	9	NUM
ejpam-3175	189	20	)	)	PUNCT
ejpam-3175	189	21	and	and	CCONJ
ejpam-3175	189	22	φρ(u	φρ(u	NUM
ejpam-3175	189	23	)	)	PUNCT
ejpam-3175	189	24	=	=	SYM
ejpam-3175	189	25	ρ−n−1φ	ρ−n−1φ	NOUN
ejpam-3175	189	26	(	(	PUNCT
ejpam-3175	189	27	u√	u√	PROPN
ejpam-3175	189	28	ρ	ρ	NOUN
ejpam-3175	189	29	)	)	PUNCT
ejpam-3175	189	30	for	for	ADP
ejpam-3175	189	31	all	all	DET
ejpam-3175	189	32	ρ	ρ	PROPN
ejpam-3175	189	33	>	>	X
ejpam-3175	189	34	0	0	NUM
ejpam-3175	189	35	.	.	PUNCT
ejpam-3175	190	1	the	the	DET
ejpam-3175	190	2	homogeneous	homogeneous	ADJ
ejpam-3175	190	3	norm	norm	NOUN
ejpam-3175	190	4	on	on	ADP
ejpam-3175	190	5	the	the	DET
ejpam-3175	190	6	heisenberg	heisenberg	PROPN
ejpam-3175	190	7	group	group	NOUN
ejpam-3175	190	8	is	be	AUX
ejpam-3175	190	9	given	give	VERB
ejpam-3175	190	10	by	by	ADP
ejpam-3175	190	11	|u|	|u|	PROPN
ejpam-3175	190	12	=	=	SYM
ejpam-3175	190	13	|(z	|(z	PROPN
ejpam-3175	190	14	,	,	PUNCT
ejpam-3175	190	15	t)|	t)|	NOUN
ejpam-3175	190	16	=	=	SYM
ejpam-3175	190	17	(	(	PUNCT
ejpam-3175	190	18	|z|4	|z|4	VERB
ejpam-3175	190	19	+	+	NUM
ejpam-3175	190	20	t2)1/4	t2)1/4	NOUN
ejpam-3175	190	21	,	,	PUNCT
ejpam-3175	190	22	which	which	PRON
ejpam-3175	190	23	satisfies	satisfy	VERB
ejpam-3175	190	24	the	the	DET
ejpam-3175	190	25	trigonometric	trigonometric	ADJ
ejpam-3175	190	26	inequality	inequality	NOUN
ejpam-3175	190	27	|uv|	|uv|	PROPN
ejpam-3175	190	28	≤	≤	NUM
ejpam-3175	190	29	|u|+	|u|+	PROPN
ejpam-3175	190	30	|v|	|v|	NOUN
ejpam-3175	190	31	.	.	PUNCT
ejpam-3175	190	32	theorem	theorem	NOUN
ejpam-3175	190	33	3	3	NUM
ejpam-3175	190	34	.	.	PUNCT
ejpam-3175	191	1	if	if	SCONJ
ejpam-3175	191	2	φ	φ	PROPN
ejpam-3175	191	3	∈	∈	PROPN
ejpam-3175	191	4	r(hn	r(hn	NOUN
ejpam-3175	191	5	)	)	PUNCT
ejpam-3175	191	6	is	be	AUX
ejpam-3175	191	7	a	a	DET
ejpam-3175	191	8	nonzero	nonzero	NOUN
ejpam-3175	191	9	function	function	NOUN
ejpam-3175	191	10	on	on	ADP
ejpam-3175	191	11	hn	hn	PRON
ejpam-3175	191	12	such	such	ADJ
ejpam-3175	191	13	that	that	SCONJ
ejpam-3175	191	14	l	l	NOUN
ejpam-3175	191	15	−	−	PROPN
ejpam-3175	191	16	2n+2	2n+2	PROPN
ejpam-3175	191	17	4	4	NUM
ejpam-3175	191	18	φ	φ	NOUN
ejpam-3175	191	19	∈	∈	PROPN
ejpam-3175	191	20	l2(hn	l2(hn	NOUN
ejpam-3175	191	21	)	)	PUNCT
ejpam-3175	191	22	and	and	CCONJ
ejpam-3175	191	23	|∇φ(u)|	|∇φ(u)|	PROPN
ejpam-3175	191	24	≤	≤	PROPN
ejpam-3175	191	25	c(1	c(1	PROPN
ejpam-3175	191	26	+	+	CCONJ
ejpam-3175	191	27	|u|)−2n−3−ε	|u|)−2n−3−ε	PROPN
ejpam-3175	191	28	,	,	PUNCT
ejpam-3175	191	29	where	where	SCONJ
ejpam-3175	191	30	constants	constant	NOUN
ejpam-3175	191	31	c	c	VERB
ejpam-3175	191	32	,	,	PUNCT
ejpam-3175	191	33	ε	ε	PROPN
ejpam-3175	191	34	>	>	X
ejpam-3175	191	35	0	0	PROPN
ejpam-3175	191	36	,	,	PUNCT
ejpam-3175	191	37	then	then	ADV
ejpam-3175	191	38	for	for	ADP
ejpam-3175	191	39	p	p	PROPN
ejpam-3175	191	40	=	=	PROPN
ejpam-3175	191	41	2n+2	2n+2	PROPN
ejpam-3175	191	42	2n+1	2n+1	PROPN
ejpam-3175	191	43	and	and	CCONJ
ejpam-3175	191	44	q	q	NOUN
ejpam-3175	191	45	=	=	NOUN
ejpam-3175	191	46	2n+	2n+	NUM
ejpam-3175	191	47	2	2	NUM
ejpam-3175	191	48	,	,	PUNCT
ejpam-3175	191	49	there	there	PRON
ejpam-3175	191	50	exist	exist	VERB
ejpam-3175	191	51	constants	constant	NOUN
ejpam-3175	191	52	aq	aq	ADP
ejpam-3175	191	53	,	,	PUNCT
ejpam-3175	191	54	bp	bp	PROPN
ejpam-3175	191	55	>	>	X
ejpam-3175	191	56	0	0	PROPN
ejpam-3175	191	57	,	,	PUNCT
ejpam-3175	191	58	such	such	ADJ
ejpam-3175	191	59	that	that	PRON
ejpam-3175	191	60	aq‖rn(f)‖lq(hn	aq‖rn(f)‖lq(hn	NOUN
ejpam-3175	191	61	)	)	PUNCT
ejpam-3175	191	62	≤	≤	NUM
ejpam-3175	191	63	‖g(rnf)‖lq(hn	‖g(rnf)‖lq(hn	NUM
ejpam-3175	191	64	)	)	PUNCT
ejpam-3175	191	65	≤	≤	NUM
ejpam-3175	191	66	bp‖f‖lp(hn	bp‖f‖lp(hn	PROPN
ejpam-3175	191	67	)	)	PUNCT
ejpam-3175	191	68	for	for	ADP
ejpam-3175	191	69	any	any	DET
ejpam-3175	191	70	f	f	PROPN
ejpam-3175	191	71	∈	∈	PROPN
ejpam-3175	191	72	lp(hn	lp(hn	PROPN
ejpam-3175	191	73	)	)	PUNCT
ejpam-3175	191	74	.	.	PUNCT
ejpam-3175	192	1	to	to	PART
ejpam-3175	192	2	prove	prove	VERB
ejpam-3175	192	3	theorem	theorem	ADJ
ejpam-3175	192	4	3	3	NUM
ejpam-3175	192	5	,	,	PUNCT
ejpam-3175	192	6	we	we	PRON
ejpam-3175	192	7	need	need	VERB
ejpam-3175	192	8	the	the	DET
ejpam-3175	192	9	following	follow	VERB
ejpam-3175	192	10	several	several	ADJ
ejpam-3175	192	11	technique	technique	NOUN
ejpam-3175	192	12	lemmas	lemma	NOUN
ejpam-3175	192	13	.	.	PUNCT
ejpam-3175	193	1	firstly	firstly	ADV
ejpam-3175	193	2	,	,	PUNCT
ejpam-3175	193	3	we	we	PRON
ejpam-3175	193	4	consider	consider	VERB
ejpam-3175	193	5	the	the	DET
ejpam-3175	193	6	form	form	NOUN
ejpam-3175	193	7	of	of	ADP
ejpam-3175	193	8	fourier	fourier	NOUN
ejpam-3175	193	9	transform	transform	NOUN
ejpam-3175	193	10	of	of	ADP
ejpam-3175	193	11	|x|α−n	|x|α−n	NOUN
ejpam-3175	193	12	,	,	PUNCT
ejpam-3175	193	13	which	which	PRON
ejpam-3175	193	14	is	be	AUX
ejpam-3175	193	15	used	use	VERB
ejpam-3175	193	16	to	to	PART
ejpam-3175	193	17	develop	develop	VERB
ejpam-3175	193	18	the	the	DET
ejpam-3175	193	19	boundedness	boundedness	NOUN
ejpam-3175	193	20	of	of	ADP
ejpam-3175	193	21	the	the	DET
ejpam-3175	193	22	singular	singular	ADJ
ejpam-3175	193	23	convolution	convolution	NOUN
ejpam-3175	193	24	operator	operator	NOUN
ejpam-3175	193	25	from	from	ADP
ejpam-3175	193	26	lp(hn	lp(hn	PROPN
ejpam-3175	193	27	)	)	PUNCT
ejpam-3175	193	28	to	to	ADP
ejpam-3175	193	29	lq(hn	lq(hn	PROPN
ejpam-3175	193	30	)	)	PUNCT
ejpam-3175	193	31	,	,	PUNCT
ejpam-3175	193	32	where	where	SCONJ
ejpam-3175	193	33	0	0	X
ejpam-3175	193	34	<	<	X
ejpam-3175	193	35	α	α	X
ejpam-3175	193	36	<	<	X
ejpam-3175	193	37	n.	n.	PROPN
ejpam-3175	193	38	now	now	ADV
ejpam-3175	193	39	,	,	PUNCT
ejpam-3175	193	40	we	we	PRON
ejpam-3175	193	41	show	show	VERB
ejpam-3175	193	42	the	the	DET
ejpam-3175	193	43	fourier	fourier	NOUN
ejpam-3175	193	44	transform	transform	NOUN
ejpam-3175	193	45	of	of	ADP
ejpam-3175	193	46	a	a	DET
ejpam-3175	193	47	guassian	guassian	NOUN
ejpam-3175	193	48	function	function	NOUN
ejpam-3175	193	49	.	.	PUNCT
ejpam-3175	194	1	for	for	ADP
ejpam-3175	194	2	ε	ε	PROPN
ejpam-3175	194	3	>	>	X
ejpam-3175	194	4	0	0	PROPN
ejpam-3175	194	5	,	,	PUNCT
ejpam-3175	194	6	denote	denote	VERB
ejpam-3175	194	7	by	by	ADP
ejpam-3175	194	8	gε	gε	ADP
ejpam-3175	194	9	the	the	DET
ejpam-3175	194	10	gaussian	gaussian	ADJ
ejpam-3175	194	11	function	function	NOUN
ejpam-3175	194	12	on	on	ADP
ejpam-3175	194	13	rn	rn	PROPN
ejpam-3175	194	14	given	give	VERB
ejpam-3175	194	15	by	by	ADP
ejpam-3175	194	16	gε(x	gε(x	NOUN
ejpam-3175	194	17	)	)	PUNCT
ejpam-3175	194	18	=	=	SYM
ejpam-3175	195	1	exp[−π|x|2ε	exp[−π|x|2ε	PROPN
ejpam-3175	195	2	]	]	PUNCT
ejpam-3175	195	3	for	for	ADP
ejpam-3175	195	4	x	x	PROPN
ejpam-3175	195	5	∈	∈	PROPN
ejpam-3175	195	6	rn	rn	PROPN
ejpam-3175	195	7	.	.	PROPN
ejpam-3175	195	8	then	then	ADV
ejpam-3175	195	9	ĝε(k	ĝε(k	VERB
ejpam-3175	195	10	)	)	PUNCT
ejpam-3175	196	1	=	=	SYM
ejpam-3175	196	2	ε−n/2	ε−n/2	PROPN
ejpam-3175	196	3	exp[−π|k|2	exp[−π|k|2	PROPN
ejpam-3175	196	4	/	/	SYM
ejpam-3175	196	5	ε	ε	PROPN
ejpam-3175	196	6	]	]	PUNCT
ejpam-3175	196	7	.	.	PUNCT
ejpam-3175	197	1	(	(	PUNCT
ejpam-3175	197	2	16	16	NUM
ejpam-3175	197	3	)	)	PUNCT
ejpam-3175	197	4	by	by	ADP
ejpam-3175	197	5	(	(	PUNCT
ejpam-3175	197	6	16	16	NUM
ejpam-3175	197	7	)	)	PUNCT
ejpam-3175	197	8	,	,	PUNCT
ejpam-3175	197	9	we	we	PRON
ejpam-3175	197	10	obtain	obtain	VERB
ejpam-3175	197	11	the	the	DET
ejpam-3175	197	12	following	follow	VERB
ejpam-3175	197	13	lemma	lemma	PROPN
ejpam-3175	197	14	.	.	PUNCT
ejpam-3175	198	1	z.	z.	PROPN
ejpam-3175	198	2	fang	fang	PROPN
ejpam-3175	198	3	,	,	PUNCT
ejpam-3175	198	4	h.	h.	PROPN
ejpam-3175	198	5	jianxun	jianxun	PROPN
ejpam-3175	198	6	he	he	PRON
ejpam-3175	198	7	/	/	SYM
ejpam-3175	198	8	eur	eur	PROPN
ejpam-3175	198	9	.	.	PUNCT
ejpam-3175	199	1	j.	j.	PROPN
ejpam-3175	199	2	pure	pure	PROPN
ejpam-3175	199	3	appl	appl	PROPN
ejpam-3175	199	4	.	.	PROPN
ejpam-3175	199	5	math	math	PROPN
ejpam-3175	199	6	,	,	PUNCT
ejpam-3175	199	7	11	11	NUM
ejpam-3175	199	8	(	(	PUNCT
ejpam-3175	199	9	1	1	NUM
ejpam-3175	199	10	)	)	PUNCT
ejpam-3175	199	11	(	(	PUNCT
ejpam-3175	199	12	2018	2018	NUM
ejpam-3175	199	13	)	)	PUNCT
ejpam-3175	199	14	,	,	PUNCT
ejpam-3175	199	15	138	138	NUM
ejpam-3175	199	16	-	-	SYM
ejpam-3175	199	17	149	149	NUM
ejpam-3175	199	18	146	146	NUM
ejpam-3175	199	19	lemma	lemma	PROPN
ejpam-3175	199	20	2	2	NUM
ejpam-3175	199	21	.	.	PUNCT
ejpam-3175	200	1	let	let	VERB
ejpam-3175	200	2	cα	cα	VERB
ejpam-3175	200	3	:	:	PUNCT
ejpam-3175	200	4	=	=	SYM
ejpam-3175	200	5	π−α/2γ(α/2	π−α/2γ(α/2	NOUN
ejpam-3175	200	6	)	)	PUNCT
ejpam-3175	200	7	(	(	PUNCT
ejpam-3175	200	8	0	0	NUM
ejpam-3175	200	9	<	<	X
ejpam-3175	200	10	α	α	X
ejpam-3175	200	11	<	<	X
ejpam-3175	200	12	n	n	CCONJ
ejpam-3175	200	13	)	)	PUNCT
ejpam-3175	200	14	.	.	PUNCT
ejpam-3175	201	1	then	then	ADV
ejpam-3175	201	2	,	,	PUNCT
ejpam-3175	201	3	for	for	ADP
ejpam-3175	201	4	any	any	DET
ejpam-3175	201	5	s	s	PROPN
ejpam-3175	201	6	∈	∈	PROPN
ejpam-3175	201	7	rn	rn	PROPN
ejpam-3175	201	8	,	,	PUNCT
ejpam-3175	201	9	γ(α/2	γ(α/2	NOUN
ejpam-3175	201	10	)	)	PUNCT
ejpam-3175	201	11	∫	∫	PROPN
ejpam-3175	201	12	rn	rn	PROPN
ejpam-3175	201	13	|s|−αe2πiλsds	|s|−αe2πiλsds	PROPN
ejpam-3175	202	1	=	=	PUNCT
ejpam-3175	202	2	πα/2cn−α|λ|α−n	πα/2cn−α|λ|α−n	PROPN
ejpam-3175	202	3	.	.	PUNCT
ejpam-3175	203	1	(	(	PUNCT
ejpam-3175	203	2	17	17	NUM
ejpam-3175	203	3	)	)	PUNCT
ejpam-3175	203	4	proof	proof	NOUN
ejpam-3175	203	5	.	.	PUNCT
ejpam-3175	204	1	our	our	PRON
ejpam-3175	204	2	starting	starting	NOUN
ejpam-3175	204	3	point	point	NOUN
ejpam-3175	204	4	is	be	AUX
ejpam-3175	204	5	the	the	DET
ejpam-3175	204	6	elementary	elementary	ADJ
ejpam-3175	204	7	formula	formula	NOUN
ejpam-3175	204	8	cα|s|−α	cα|s|−α	PROPN
ejpam-3175	204	9	=	=	SYM
ejpam-3175	205	1	∫	∫	PROPN
ejpam-3175	205	2	∞	∞	PROPN
ejpam-3175	205	3	0	0	NUM
ejpam-3175	206	1	exp[−π|s|2ε]εα/2−1dε	exp[−π|s|2ε]εα/2−1dε	X
ejpam-3175	206	2	.	.	PUNCT
ejpam-3175	207	1	(	(	PUNCT
ejpam-3175	207	2	18	18	NUM
ejpam-3175	207	3	)	)	PUNCT
ejpam-3175	207	4	by	by	ADP
ejpam-3175	207	5	fubini	fubini	NOUN
ejpam-3175	207	6	’s	’s	PART
ejpam-3175	207	7	theorem	theorem	ADJ
ejpam-3175	207	8	,	,	PUNCT
ejpam-3175	207	9	together	together	ADV
ejpam-3175	207	10	with	with	ADP
ejpam-3175	207	11	(	(	PUNCT
ejpam-3175	207	12	18	18	NUM
ejpam-3175	207	13	)	)	PUNCT
ejpam-3175	207	14	and	and	CCONJ
ejpam-3175	207	15	(	(	PUNCT
ejpam-3175	207	16	16	16	NUM
ejpam-3175	207	17	)	)	PUNCT
ejpam-3175	207	18	,	,	PUNCT
ejpam-3175	207	19	we	we	PRON
ejpam-3175	207	20	have	have	VERB
ejpam-3175	207	21	,	,	PUNCT
ejpam-3175	207	22	γ(α/2	γ(α/2	NOUN
ejpam-3175	207	23	)	)	PUNCT
ejpam-3175	207	24	∫	∫	PROPN
ejpam-3175	208	1	r	r	NOUN
ejpam-3175	208	2	|s|−αe2πiλsds	|s|−αe2πiλsds	PROPN
ejpam-3175	208	3	=	=	PUNCT
ejpam-3175	209	1	πα/2	πα/2	NOUN
ejpam-3175	209	2	∫	∫	PROPN
ejpam-3175	210	1	∞	∞	NUM
ejpam-3175	210	2	0	0	NUM
ejpam-3175	210	3	∫	∫	PROPN
ejpam-3175	210	4	r	r	NOUN
ejpam-3175	210	5	exp[−π|s|2ε]εα/2−1e2πiλsdsdε	exp[−π|s|2ε]εα/2−1e2πiλsdsdε	NOUN
ejpam-3175	210	6	=	=	PUNCT
ejpam-3175	211	1	πα/2	πα/2	NOUN
ejpam-3175	211	2	∫	∫	PROPN
ejpam-3175	211	3	∞	∞	PROPN
ejpam-3175	211	4	0	0	NUM
ejpam-3175	211	5	εα/2−1	εα/2−1	ADP
ejpam-3175	211	6	∫	∫	PROPN
ejpam-3175	211	7	r	r	PROPN
ejpam-3175	211	8	exp[−π|s|2ε]e2πiλsdsdε	exp[−π|s|2ε]e2πiλsdsdε	PROPN
ejpam-3175	211	9	=	=	PUNCT
ejpam-3175	211	10	πα/2	πα/2	NOUN
ejpam-3175	211	11	∫	∫	PROPN
ejpam-3175	212	1	∞	∞	NUM
ejpam-3175	212	2	0	0	NUM
ejpam-3175	213	1	ε−n/2εα/2−1	ε−n/2εα/2−1	NOUN
ejpam-3175	213	2	exp[−π|λ|2	exp[−π|λ|2	NOUN
ejpam-3175	213	3	/	/	SYM
ejpam-3175	213	4	ε]dε	ε]dε	NOUN
ejpam-3175	213	5	=	=	SYM
ejpam-3175	213	6	πα/2cn−α|λ|α−n	πα/2cn−α|λ|α−n	NOUN
ejpam-3175	213	7	.	.	PUNCT
ejpam-3175	214	1	lemma	lemma	PROPN
ejpam-3175	214	2	3	3	X
ejpam-3175	214	3	.	.	PUNCT
ejpam-3175	215	1	the	the	DET
ejpam-3175	215	2	estimate	estimate	NOUN
ejpam-3175	215	3	‖rnf‖q	‖rnf‖q	PROPN
ejpam-3175	215	4	≤	≤	PROPN
ejpam-3175	215	5	c‖f‖p	c‖f‖p	VERB
ejpam-3175	215	6	holds	hold	VERB
ejpam-3175	215	7	if	if	SCONJ
ejpam-3175	215	8	and	and	CCONJ
ejpam-3175	215	9	only	only	ADV
ejpam-3175	215	10	if	if	SCONJ
ejpam-3175	215	11	p	p	X
ejpam-3175	215	12	=	=	PROPN
ejpam-3175	215	13	2n+2	2n+2	PROPN
ejpam-3175	215	14	2n+1	2n+1	PROPN
ejpam-3175	215	15	and	and	CCONJ
ejpam-3175	215	16	q	q	NOUN
ejpam-3175	216	1	=	=	NOUN
ejpam-3175	216	2	2n+	2n+	NUM
ejpam-3175	216	3	2	2	NUM
ejpam-3175	216	4	.	.	PUNCT
ejpam-3175	216	5	proof	proof	NOUN
ejpam-3175	216	6	.	.	PUNCT
ejpam-3175	217	1	to	to	PART
ejpam-3175	217	2	show	show	VERB
ejpam-3175	217	3	that	that	SCONJ
ejpam-3175	217	4	the	the	DET
ejpam-3175	217	5	estimate	estimate	NOUN
ejpam-3175	217	6	‖rnf‖q	‖rnf‖q	PROPN
ejpam-3175	217	7	≤	≤	PROPN
ejpam-3175	217	8	c‖f‖p	c‖f‖p	VERB
ejpam-3175	217	9	holds	hold	VERB
ejpam-3175	217	10	we	we	PRON
ejpam-3175	217	11	use	use	VERB
ejpam-3175	217	12	an	an	DET
ejpam-3175	217	13	analytic	analytic	ADJ
ejpam-3175	217	14	families	family	NOUN
ejpam-3175	217	15	interpolation	interpolation	NOUN
ejpam-3175	217	16	argument	argument	NOUN
ejpam-3175	217	17	.	.	PUNCT
ejpam-3175	218	1	we	we	PRON
ejpam-3175	218	2	let	let	VERB
ejpam-3175	218	3	tα	tα	PROPN
ejpam-3175	218	4	,	,	PUNCT
ejpam-3175	218	5	nf(z	nf(z	NUM
ejpam-3175	218	6	,	,	PUNCT
ejpam-3175	218	7	t	t	PROPN
ejpam-3175	218	8	)	)	PUNCT
ejpam-3175	218	9	=	=	SYM
ejpam-3175	219	1	γ(α/2	γ(α/2	X
ejpam-3175	219	2	)	)	PUNCT
ejpam-3175	219	3	∫	∫	PROPN
ejpam-3175	220	1	hn	hn	PROPN
ejpam-3175	220	2	tnf	tnf	PROPN
ejpam-3175	220	3	(	(	PUNCT
ejpam-3175	220	4	w	w	PROPN
ejpam-3175	220	5	,	,	PUNCT
ejpam-3175	220	6	t+	t+	NOUN
ejpam-3175	220	7	s+	s+	PUNCT
ejpam-3175	220	8	1	1	NUM
ejpam-3175	220	9	2	2	NUM
ejpam-3175	220	10	im〈z	im〈z	NOUN
ejpam-3175	220	11	,	,	PUNCT
ejpam-3175	220	12	w	w	NOUN
ejpam-3175	220	13	〉	〉	NOUN
ejpam-3175	220	14	)	)	PUNCT
ejpam-3175	220	15	|s|−αdsdw	|s|−αdsdw	PROPN
ejpam-3175	220	16	,	,	PUNCT
ejpam-3175	220	17	where	where	SCONJ
ejpam-3175	220	18	α	α	NOUN
ejpam-3175	220	19	is	be	AUX
ejpam-3175	220	20	complex	complex	ADJ
ejpam-3175	220	21	parameter	parameter	NOUN
ejpam-3175	220	22	in	in	ADP
ejpam-3175	220	23	the	the	DET
ejpam-3175	220	24	strip	strip	NOUN
ejpam-3175	220	25	0	0	SYM
ejpam-3175	220	26	≤	≤	NUM
ejpam-3175	220	27	reα	reα	NOUN
ejpam-3175	220	28	≤	≤	NUM
ejpam-3175	220	29	1	1	NUM
ejpam-3175	220	30	.	.	PUNCT
ejpam-3175	221	1	it	it	PRON
ejpam-3175	221	2	is	be	AUX
ejpam-3175	221	3	obvious	obvious	ADJ
ejpam-3175	221	4	that	that	SCONJ
ejpam-3175	221	5	on	on	ADP
ejpam-3175	221	6	the	the	DET
ejpam-3175	221	7	line	line	NOUN
ejpam-3175	221	8	reα	reα	NOUN
ejpam-3175	221	9	=	=	SYM
ejpam-3175	221	10	0	0	NUM
ejpam-3175	222	1	the	the	DET
ejpam-3175	222	2	operator	operator	NOUN
ejpam-3175	222	3	tα	tα	PROPN
ejpam-3175	222	4	,	,	PUNCT
ejpam-3175	222	5	n	n	PRON
ejpam-3175	222	6	is	be	AUX
ejpam-3175	222	7	bounded	bound	VERB
ejpam-3175	222	8	from	from	ADP
ejpam-3175	222	9	l1	l1	PROPN
ejpam-3175	222	10	to	to	ADP
ejpam-3175	222	11	l∞	l∞	PROPN
ejpam-3175	222	12	,	,	PUNCT
ejpam-3175	222	13	while	while	SCONJ
ejpam-3175	222	14	on	on	ADP
ejpam-3175	222	15	the	the	DET
ejpam-3175	222	16	line	line	NOUN
ejpam-3175	222	17	reα	reα	NOUN
ejpam-3175	222	18	=	=	SYM
ejpam-3175	222	19	1	1	NUM
ejpam-3175	222	20	a	a	DET
ejpam-3175	222	21	simple	simple	ADJ
ejpam-3175	222	22	computation	computation	NOUN
ejpam-3175	222	23	with	with	ADP
ejpam-3175	222	24	(	(	PUNCT
ejpam-3175	222	25	17	17	NUM
ejpam-3175	222	26	)	)	PUNCT
ejpam-3175	222	27	shows	show	VERB
ejpam-3175	222	28	f2tα	f2tα	PROPN
ejpam-3175	222	29	,	,	PUNCT
ejpam-3175	222	30	nf(z	nf(z	NUM
ejpam-3175	222	31	,	,	PUNCT
ejpam-3175	222	32	λ	λ	X
ejpam-3175	222	33	)	)	PUNCT
ejpam-3175	222	34	=	=	SYM
ejpam-3175	222	35	πα/2c1−α|λ|α−1(2πiλ)nff(iλz/2	πα/2c1−α|λ|α−1(2πiλ)nff(iλz/2	PROPN
ejpam-3175	222	36	,	,	PUNCT
ejpam-3175	222	37	λ	λ	NOUN
ejpam-3175	222	38	)	)	PUNCT
ejpam-3175	222	39	,	,	PUNCT
ejpam-3175	222	40	and	and	CCONJ
ejpam-3175	222	41	a	a	DET
ejpam-3175	222	42	modification	modification	NOUN
ejpam-3175	222	43	of	of	ADP
ejpam-3175	222	44	the	the	DET
ejpam-3175	222	45	proof	proof	NOUN
ejpam-3175	222	46	of	of	ADP
ejpam-3175	222	47	theorem	theorem	ADJ
ejpam-3175	222	48	1	1	NUM
ejpam-3175	222	49	shows	show	VERB
ejpam-3175	222	50	that	that	SCONJ
ejpam-3175	222	51	tα	tα	PROPN
ejpam-3175	222	52	,	,	PUNCT
ejpam-3175	222	53	n	n	PRON
ejpam-3175	222	54	is	be	AUX
ejpam-3175	222	55	bounded	bound	VERB
ejpam-3175	222	56	from	from	ADP
ejpam-3175	222	57	l2	l2	NOUN
ejpam-3175	222	58	to	to	AUX
ejpam-3175	222	59	l2	l2	VERB
ejpam-3175	222	60	.	.	PUNCT
ejpam-3175	223	1	the	the	DET
ejpam-3175	223	2	various	various	ADJ
ejpam-3175	223	3	γ	γ	NOUN
ejpam-3175	223	4	-	-	PUNCT
ejpam-3175	223	5	factors	factor	NOUN
ejpam-3175	223	6	are	be	AUX
ejpam-3175	223	7	innocuous	innocuous	ADJ
ejpam-3175	223	8	,	,	PUNCT
ejpam-3175	223	9	so	so	SCONJ
ejpam-3175	223	10	the	the	DET
ejpam-3175	223	11	stein	stein	PROPN
ejpam-3175	223	12	interpolation	interpolation	PROPN
ejpam-3175	223	13	theorem	theorem	VERB
ejpam-3175	223	14	yields	yield	VERB
ejpam-3175	223	15	the	the	DET
ejpam-3175	223	16	boundedness	boundedness	NOUN
ejpam-3175	223	17	of	of	ADP
ejpam-3175	223	18	rn	rn	PROPN
ejpam-3175	223	19	from	from	ADP
ejpam-3175	223	20	lp	lp	NOUN
ejpam-3175	223	21	to	to	ADP
ejpam-3175	223	22	lq	lq	NOUN
ejpam-3175	223	23	for	for	ADP
ejpam-3175	223	24	exactly	exactly	ADV
ejpam-3175	223	25	p	p	NOUN
ejpam-3175	223	26	=	=	PROPN
ejpam-3175	223	27	2n+2	2n+2	PROPN
ejpam-3175	223	28	2n+1	2n+1	PROPN
ejpam-3175	223	29	,	,	PUNCT
ejpam-3175	223	30	q	q	X
ejpam-3175	224	1	=	=	SYM
ejpam-3175	224	2	2n+	2n+	NUM
ejpam-3175	224	3	2	2	NUM
ejpam-3175	224	4	.	.	PUNCT
ejpam-3175	225	1	the	the	DET
ejpam-3175	225	2	necessity	necessity	NOUN
ejpam-3175	225	3	of	of	ADP
ejpam-3175	225	4	proof	proof	NOUN
ejpam-3175	225	5	is	be	AUX
ejpam-3175	225	6	similar	similar	ADJ
ejpam-3175	225	7	to	to	ADP
ejpam-3175	225	8	that	that	PRON
ejpam-3175	225	9	of	of	ADP
ejpam-3175	225	10	[	[	X
ejpam-3175	225	11	16	16	NUM
ejpam-3175	225	12	,	,	PUNCT
ejpam-3175	225	13	p.	p.	NOUN
ejpam-3175	225	14	387	387	NUM
ejpam-3175	225	15	]	]	PUNCT
ejpam-3175	225	16	,	,	PUNCT
ejpam-3175	225	17	the	the	DET
ejpam-3175	225	18	details	detail	NOUN
ejpam-3175	225	19	being	be	AUX
ejpam-3175	225	20	omitted	omit	VERB
ejpam-3175	225	21	.	.	PUNCT
ejpam-3175	226	1	the	the	DET
ejpam-3175	226	2	following	follow	VERB
ejpam-3175	226	3	lemma	lemma	PROPN
ejpam-3175	226	4	is	be	AUX
ejpam-3175	226	5	just	just	ADV
ejpam-3175	226	6	[	[	X
ejpam-3175	226	7	12	12	NUM
ejpam-3175	226	8	]	]	PUNCT
ejpam-3175	226	9	.	.	PUNCT
ejpam-3175	227	1	lemma	lemma	PROPN
ejpam-3175	227	2	4	4	X
ejpam-3175	227	3	.	.	PUNCT
ejpam-3175	228	1	if	if	SCONJ
ejpam-3175	228	2	φ	φ	PROPN
ejpam-3175	228	3	∈	∈	PROPN
ejpam-3175	228	4	s	s	X
ejpam-3175	228	5	(	(	PUNCT
ejpam-3175	228	6	hn	hn	NOUN
ejpam-3175	228	7	)	)	PUNCT
ejpam-3175	228	8	is	be	AUX
ejpam-3175	228	9	a	a	DET
ejpam-3175	228	10	nonzero	nonzero	NOUN
ejpam-3175	228	11	function	function	NOUN
ejpam-3175	228	12	on	on	ADP
ejpam-3175	228	13	hn	hn	PRON
ejpam-3175	228	14	such	such	ADJ
ejpam-3175	228	15	that	that	SCONJ
ejpam-3175	228	16	l	l	NOUN
ejpam-3175	228	17	−	−	PROPN
ejpam-3175	228	18	2n+2	2n+2	PROPN
ejpam-3175	228	19	4	4	NUM
ejpam-3175	228	20	φ	φ	NOUN
ejpam-3175	228	21	∈	∈	PROPN
ejpam-3175	228	22	l2(hn	l2(hn	NOUN
ejpam-3175	228	23	)	)	PUNCT
ejpam-3175	228	24	and	and	CCONJ
ejpam-3175	228	25	|∇φ(u)|	|∇φ(u)|	PROPN
ejpam-3175	228	26	≤	≤	PROPN
ejpam-3175	228	27	c(1	c(1	PROPN
ejpam-3175	228	28	+	+	CCONJ
ejpam-3175	228	29	|u|)−2n−3−ε	|u|)−2n−3−ε	PROPN
ejpam-3175	228	30	,	,	PUNCT
ejpam-3175	228	31	where	where	SCONJ
ejpam-3175	228	32	constants	constant	NOUN
ejpam-3175	228	33	c	c	VERB
ejpam-3175	228	34	,	,	PUNCT
ejpam-3175	228	35	ε	ε	PROPN
ejpam-3175	228	36	>	>	X
ejpam-3175	228	37	0	0	PROPN
ejpam-3175	228	38	,	,	PUNCT
ejpam-3175	228	39	there	there	PRON
ejpam-3175	228	40	exist	exist	VERB
ejpam-3175	228	41	constants	constant	NOUN
ejpam-3175	228	42	ap	ap	PROPN
ejpam-3175	228	43	,	,	PUNCT
ejpam-3175	228	44	bp	bp	PROPN
ejpam-3175	228	45	>	>	X
ejpam-3175	228	46	0	0	PROPN
ejpam-3175	228	47	,	,	PUNCT
ejpam-3175	228	48	such	such	ADJ
ejpam-3175	228	49	that	that	PRON
ejpam-3175	228	50	ap‖f‖lp(hn	ap‖f‖lp(hn	PROPN
ejpam-3175	228	51	)	)	PUNCT
ejpam-3175	228	52	≤	≤	NUM
ejpam-3175	228	53	‖g(f)‖lp(hn	‖g(f)‖lp(hn	NOUN
ejpam-3175	228	54	)	)	PUNCT
ejpam-3175	228	55	≤	≤	NUM
ejpam-3175	228	56	bp‖f‖lp(hn	bp‖f‖lp(hn	PROPN
ejpam-3175	228	57	)	)	PUNCT
ejpam-3175	228	58	for	for	ADP
ejpam-3175	228	59	any	any	DET
ejpam-3175	228	60	f	f	PROPN
ejpam-3175	228	61	∈	∈	PROPN
ejpam-3175	228	62	lp(hn	lp(hn	PROPN
ejpam-3175	228	63	)	)	PUNCT
ejpam-3175	228	64	.	.	PUNCT
ejpam-3175	229	1	z.	z.	PROPN
ejpam-3175	229	2	fang	fang	PROPN
ejpam-3175	229	3	,	,	PUNCT
ejpam-3175	229	4	h.	h.	PROPN
ejpam-3175	229	5	jianxun	jianxun	PROPN
ejpam-3175	229	6	he	he	PRON
ejpam-3175	229	7	/	/	SYM
ejpam-3175	229	8	eur	eur	PROPN
ejpam-3175	229	9	.	.	PUNCT
ejpam-3175	230	1	j.	j.	PROPN
ejpam-3175	230	2	pure	pure	PROPN
ejpam-3175	230	3	appl	appl	PROPN
ejpam-3175	230	4	.	.	PROPN
ejpam-3175	230	5	math	math	PROPN
ejpam-3175	230	6	,	,	PUNCT
ejpam-3175	230	7	11	11	NUM
ejpam-3175	230	8	(	(	PUNCT
ejpam-3175	230	9	1	1	NUM
ejpam-3175	230	10	)	)	PUNCT
ejpam-3175	230	11	(	(	PUNCT
ejpam-3175	230	12	2018	2018	NUM
ejpam-3175	230	13	)	)	PUNCT
ejpam-3175	230	14	,	,	PUNCT
ejpam-3175	230	15	138	138	NUM
ejpam-3175	230	16	-	-	SYM
ejpam-3175	230	17	149	149	NUM
ejpam-3175	230	18	147	147	NUM
ejpam-3175	230	19	proof	proof	NOUN
ejpam-3175	230	20	.	.	PUNCT
ejpam-3175	231	1	[	[	X
ejpam-3175	231	2	proof	proof	NOUN
ejpam-3175	231	3	of	of	ADP
ejpam-3175	231	4	theorem	theorem	ADJ
ejpam-3175	231	5	3	3	NUM
ejpam-3175	231	6	]	]	PUNCT
ejpam-3175	231	7	let	let	VERB
ejpam-3175	231	8	f	f	PROPN
ejpam-3175	231	9	∈	∈	PROPN
ejpam-3175	231	10	lp(hn	lp(hn	PROPN
ejpam-3175	231	11	)	)	PUNCT
ejpam-3175	231	12	.	.	PUNCT
ejpam-3175	232	1	for	for	ADP
ejpam-3175	232	2	p	p	PROPN
ejpam-3175	232	3	=	=	PROPN
ejpam-3175	232	4	2n+2	2n+2	PROPN
ejpam-3175	232	5	2n+1	2n+1	PROPN
ejpam-3175	232	6	and	and	CCONJ
ejpam-3175	232	7	q	q	NOUN
ejpam-3175	232	8	=	=	SYM
ejpam-3175	232	9	2n+2	2n+2	PROPN
ejpam-3175	232	10	,	,	PUNCT
ejpam-3175	232	11	by	by	ADP
ejpam-3175	232	12	lemma	lemma	PROPN
ejpam-3175	232	13	3	3	NUM
ejpam-3175	232	14	,	,	PUNCT
ejpam-3175	232	15	we	we	PRON
ejpam-3175	232	16	know	know	VERB
ejpam-3175	232	17	that	that	PRON
ejpam-3175	232	18	‖rnf‖lq(hn	‖rnf‖lq(hn	NUM
ejpam-3175	232	19	)	)	PUNCT
ejpam-3175	232	20	≤	≤	NUM
ejpam-3175	232	21	c‖f‖lp(hn	c‖f‖lp(hn	NOUN
ejpam-3175	232	22	)	)	PUNCT
ejpam-3175	232	23	.	.	PUNCT
ejpam-3175	233	1	from	from	ADP
ejpam-3175	233	2	lemma	lemma	PROPN
ejpam-3175	233	3	4	4	NUM
ejpam-3175	233	4	,	,	PUNCT
ejpam-3175	233	5	it	it	PRON
ejpam-3175	233	6	follows	follow	VERB
ejpam-3175	233	7	that	that	SCONJ
ejpam-3175	233	8	aq‖rnf‖lq(hn	aq‖rnf‖lq(hn	NOUN
ejpam-3175	233	9	)	)	PUNCT
ejpam-3175	233	10	≤	≤	NOUN
ejpam-3175	233	11	‖g(rnf)‖lq(hn	‖g(rnf)‖lq(hn	NUM
ejpam-3175	233	12	)	)	PUNCT
ejpam-3175	233	13	≤	≤	NUM
ejpam-3175	233	14	b̃q‖rnf‖lq(hn	b̃q‖rnf‖lq(hn	NOUN
ejpam-3175	233	15	)	)	PUNCT
ejpam-3175	233	16	≤	≤	NUM
ejpam-3175	233	17	bp‖f‖lp(hn	bp‖f‖lp(hn	PROPN
ejpam-3175	233	18	)	)	PUNCT
ejpam-3175	233	19	.	.	PUNCT
ejpam-3175	234	1	the	the	DET
ejpam-3175	234	2	proof	proof	NOUN
ejpam-3175	234	3	is	be	AUX
ejpam-3175	234	4	completed	complete	VERB
ejpam-3175	234	5	.	.	PUNCT
ejpam-3175	235	1	5	5	X
ejpam-3175	235	2	.	.	X
ejpam-3175	235	3	the	the	DET
ejpam-3175	235	4	poisson	poisson	NOUN
ejpam-3175	235	5	integral	integral	ADJ
ejpam-3175	235	6	as	as	ADP
ejpam-3175	235	7	a	a	DET
ejpam-3175	235	8	radon	radon	NOUN
ejpam-3175	235	9	transform	transform	NOUN
ejpam-3175	235	10	on	on	ADP
ejpam-3175	235	11	šilov	šilov	PROPN
ejpam-3175	235	12	boundary	boundary	ADJ
ejpam-3175	235	13	∂un+1	∂un+1	NOUN
ejpam-3175	235	14	let	let	VERB
ejpam-3175	235	15	un+1	un+1	ADV
ejpam-3175	235	16	be	be	AUX
ejpam-3175	235	17	the	the	DET
ejpam-3175	235	18	generalized	generalized	ADJ
ejpam-3175	235	19	upper	upper	ADJ
ejpam-3175	235	20	half	half	ADJ
ejpam-3175	235	21	-	-	PUNCT
ejpam-3175	235	22	plane	plane	NOUN
ejpam-3175	235	23	in	in	ADP
ejpam-3175	235	24	cn+1	cn+1	NUM
ejpam-3175	235	25	,	,	PUNCT
ejpam-3175	235	26	un+1	un+1	NOUN
ejpam-3175	235	27	=	=	SYM
ejpam-3175	235	28	{	{	PUNCT
ejpam-3175	235	29	(	(	PUNCT
ejpam-3175	235	30	z1	z1	PROPN
ejpam-3175	235	31	,	,	PUNCT
ejpam-3175	235	32	z̃	z̃	PROPN
ejpam-3175	235	33	)	)	PUNCT
ejpam-3175	235	34	∈	∈	NOUN
ejpam-3175	235	35	cn+1	cn+1	NOUN
ejpam-3175	235	36	:	:	PUNCT
ejpam-3175	235	37	imz1	imz1	PROPN
ejpam-3175	235	38	>	>	X
ejpam-3175	235	39	|z̃|2	|z̃|2	PROPN
ejpam-3175	235	40	}	}	PUNCT
ejpam-3175	235	41	,	,	PUNCT
ejpam-3175	236	1	where	where	SCONJ
ejpam-3175	236	2	z̃	z̃	PROPN
ejpam-3175	236	3	=	=	SYM
ejpam-3175	236	4	(	(	PUNCT
ejpam-3175	236	5	z2	z2	PROPN
ejpam-3175	236	6	,	,	PUNCT
ejpam-3175	236	7	·	·	PUNCT
ejpam-3175	236	8	·	·	PUNCT
ejpam-3175	236	9	·	·	PUNCT
ejpam-3175	236	10	,	,	PUNCT
ejpam-3175	236	11	zn+1	zn+1	X
ejpam-3175	236	12	)	)	PUNCT
ejpam-3175	236	13	∈	∈	PROPN
ejpam-3175	236	14	cn	cn	PROPN
ejpam-3175	236	15	,	,	PUNCT
ejpam-3175	236	16	|z̃|2	|z̃|2	PROPN
ejpam-3175	236	17	=	=	SYM
ejpam-3175	237	1	n+1∑	n+1∑	PROPN
ejpam-3175	237	2	j=2	j=2	PROPN
ejpam-3175	237	3	|zj	|zj	ADP
ejpam-3175	237	4	|2	|2	NUM
ejpam-3175	237	5	;	;	PUNCT
ejpam-3175	237	6	see	see	VERB
ejpam-3175	237	7	,	,	PUNCT
ejpam-3175	237	8	for	for	ADP
ejpam-3175	237	9	example	example	NOUN
ejpam-3175	237	10	,	,	PUNCT
ejpam-3175	237	11	[	[	X
ejpam-3175	237	12	13	13	NUM
ejpam-3175	237	13	]	]	PUNCT
ejpam-3175	237	14	.	.	PUNCT
ejpam-3175	238	1	for	for	ADP
ejpam-3175	238	2	any	any	DET
ejpam-3175	238	3	α	α	NOUN
ejpam-3175	238	4	=	=	SYM
ejpam-3175	238	5	(	(	PUNCT
ejpam-3175	238	6	α1	α1	PROPN
ejpam-3175	238	7	,	,	PUNCT
ejpam-3175	238	8	α̃	α̃	PROPN
ejpam-3175	238	9	)	)	PUNCT
ejpam-3175	238	10	,	,	PUNCT
ejpam-3175	238	11	β	β	X
ejpam-3175	238	12	=	=	SYM
ejpam-3175	238	13	(	(	PUNCT
ejpam-3175	238	14	β1	β1	PROPN
ejpam-3175	238	15	,	,	PUNCT
ejpam-3175	238	16	β̃	β̃	PROPN
ejpam-3175	238	17	)	)	PUNCT
ejpam-3175	238	18	∈	∈	PROPN
ejpam-3175	238	19	un+1	un+1	PROPN
ejpam-3175	238	20	,	,	PUNCT
ejpam-3175	238	21	we	we	PRON
ejpam-3175	238	22	consider	consider	VERB
ejpam-3175	238	23	the	the	DET
ejpam-3175	238	24	almost	almost	ADV
ejpam-3175	238	25	analytic	analytic	ADJ
ejpam-3175	238	26	extension	extension	NOUN
ejpam-3175	238	27	of	of	ADP
ejpam-3175	238	28	ρ(α	ρ(α	NOUN
ejpam-3175	238	29	,	,	PUNCT
ejpam-3175	238	30	β	β	X
ejpam-3175	238	31	)	)	PUNCT
ejpam-3175	239	1	=	=	SYM
ejpam-3175	239	2	i	i	PRON
ejpam-3175	239	3	2	2	X
ejpam-3175	239	4	(	(	PUNCT
ejpam-3175	239	5	β1	β1	PROPN
ejpam-3175	239	6	−	−	PROPN
ejpam-3175	239	7	α1)−	α1)−	PROPN
ejpam-3175	239	8	n+1∑	n+1∑	PROPN
ejpam-3175	239	9	k=2	k=2	PROPN
ejpam-3175	239	10	αkβk	αkβk	NOUN
ejpam-3175	239	11	.	.	PUNCT
ejpam-3175	240	1	in	in	ADP
ejpam-3175	240	2	particular	particular	ADJ
ejpam-3175	240	3	,	,	PUNCT
ejpam-3175	240	4	when	when	SCONJ
ejpam-3175	240	5	α	α	PROPN
ejpam-3175	240	6	=	=	SYM
ejpam-3175	240	7	β	β	X
ejpam-3175	240	8	,	,	PUNCT
ejpam-3175	240	9	ρ(α	ρ(α	NOUN
ejpam-3175	240	10	,	,	PUNCT
ejpam-3175	240	11	α	α	NOUN
ejpam-3175	240	12	)	)	PUNCT
ejpam-3175	240	13	=	=	SYM
ejpam-3175	240	14	ρ(α	ρ(α	NOUN
ejpam-3175	240	15	)	)	PUNCT
ejpam-3175	240	16	=	=	SYM
ejpam-3175	240	17	imα1	imα1	PROPN
ejpam-3175	240	18	−	−	PROPN
ejpam-3175	240	19	|α̃|2	|α̃|2	PROPN
ejpam-3175	240	20	.	.	PUNCT
ejpam-3175	241	1	for	for	ADP
ejpam-3175	241	2	f	f	PROPN
ejpam-3175	241	3	holomorphic	holomorphic	PROPN
ejpam-3175	241	4	on	on	ADP
ejpam-3175	241	5	the	the	DET
ejpam-3175	241	6	siegel	siegel	NOUN
ejpam-3175	241	7	upper	upper	ADJ
ejpam-3175	241	8	half	half	ADJ
ejpam-3175	241	9	-	-	PUNCT
ejpam-3175	241	10	space	space	NOUN
ejpam-3175	241	11	un+1	un+1	NOUN
ejpam-3175	241	12	,	,	PUNCT
ejpam-3175	241	13	we	we	PRON
ejpam-3175	241	14	define	define	VERB
ejpam-3175	241	15	‖f‖h2	‖f‖h2	NUM
ejpam-3175	241	16	=	=	NOUN
ejpam-3175	241	17	sup	sup	NOUN
ejpam-3175	241	18	ρ>0	ρ>0	NOUN
ejpam-3175	241	19	(	(	PUNCT
ejpam-3175	241	20	∫	∫	PROPN
ejpam-3175	241	21	∫	∫	PROPN
ejpam-3175	241	22	|f(z̃	|f(z̃	PROPN
ejpam-3175	241	23	,	,	PUNCT
ejpam-3175	241	24	z1	z1	NOUN
ejpam-3175	241	25	+	+	CCONJ
ejpam-3175	241	26	i|z̃|2	i|z̃|2	NOUN
ejpam-3175	241	27	+	+	CCONJ
ejpam-3175	241	28	iρ)|2d|z̃|d|z1|	iρ)|2d|z̃|d|z1|	NUM
ejpam-3175	241	29	)	)	PUNCT
ejpam-3175	241	30	1	1	NUM
ejpam-3175	241	31	2	2	NUM
ejpam-3175	241	32	.	.	PUNCT
ejpam-3175	242	1	then	then	ADV
ejpam-3175	242	2	we	we	PRON
ejpam-3175	242	3	set	set	VERB
ejpam-3175	242	4	h2(un+1	h2(un+1	NOUN
ejpam-3175	242	5	)	)	PUNCT
ejpam-3175	242	6	=	=	PRON
ejpam-3175	243	1	{	{	PUNCT
ejpam-3175	243	2	f	f	X
ejpam-3175	243	3	:	:	PUNCT
ejpam-3175	243	4	f	f	PROPN
ejpam-3175	243	5	is	be	AUX
ejpam-3175	243	6	holomorphic	holomorphic	ADJ
ejpam-3175	243	7	on	on	ADP
ejpam-3175	243	8	un+1	un+1	PROPN
ejpam-3175	243	9	,	,	PUNCT
ejpam-3175	243	10	‖f‖h2	‖f‖h2	VERB
ejpam-3175	243	11	<	<	X
ejpam-3175	243	12	∞	∞	NUM
ejpam-3175	243	13	}	}	PUNCT
ejpam-3175	243	14	,	,	PUNCT
ejpam-3175	243	15	where	where	SCONJ
ejpam-3175	243	16	ρ	ρ	PROPN
ejpam-3175	243	17	is	be	AUX
ejpam-3175	243	18	introduced	introduce	VERB
ejpam-3175	243	19	on	on	ADP
ejpam-3175	243	20	un+1	un+1	PROPN
ejpam-3175	243	21	.	.	PUNCT
ejpam-3175	244	1	for	for	ADP
ejpam-3175	244	2	f	f	PROPN
ejpam-3175	244	3	∈	∈	PROPN
ejpam-3175	244	4	h2(un+1	h2(un+1	NOUN
ejpam-3175	244	5	)	)	PUNCT
ejpam-3175	244	6	,	,	PUNCT
ejpam-3175	244	7	we	we	PRON
ejpam-3175	244	8	let	let	VERB
ejpam-3175	244	9	fρ(α̃	fρ(α̃	NOUN
ejpam-3175	244	10	,	,	PUNCT
ejpam-3175	244	11	t	t	PROPN
ejpam-3175	244	12	)	)	PUNCT
ejpam-3175	244	13	=	=	SYM
ejpam-3175	244	14	f	f	PROPN
ejpam-3175	244	15	(	(	PUNCT
ejpam-3175	244	16	α̃	α̃	PROPN
ejpam-3175	244	17	,	,	PUNCT
ejpam-3175	244	18	t+	t+	NOUN
ejpam-3175	244	19	i|α̃|2	i|α̃|2	NOUN
ejpam-3175	244	20	+	+	CCONJ
ejpam-3175	244	21	iρ	iρ	NOUN
ejpam-3175	244	22	)	)	PUNCT
ejpam-3175	244	23	.	.	PUNCT
ejpam-3175	245	1	(	(	PUNCT
ejpam-3175	245	2	19	19	NUM
ejpam-3175	245	3	)	)	PUNCT
ejpam-3175	245	4	definition	definition	NOUN
ejpam-3175	245	5	2	2	NUM
ejpam-3175	245	6	.	.	PUNCT
ejpam-3175	246	1	the	the	DET
ejpam-3175	246	2	poisson	poisson	PROPN
ejpam-3175	246	3	-	-	ADJ
ejpam-3175	246	4	szegö	szegö	ADJ
ejpam-3175	246	5	kernel	kernel	PROPN
ejpam-3175	246	6	p	p	NOUN
ejpam-3175	246	7	is	be	AUX
ejpam-3175	246	8	defined	define	VERB
ejpam-3175	246	9	by	by	ADP
ejpam-3175	246	10	p	p	PROPN
ejpam-3175	246	11	(	(	PUNCT
ejpam-3175	246	12	α	α	NOUN
ejpam-3175	246	13	,	,	PUNCT
ejpam-3175	246	14	β	β	NOUN
ejpam-3175	246	15	)	)	PUNCT
ejpam-3175	246	16	:	:	PUNCT
ejpam-3175	247	1	=	=	SYM
ejpam-3175	247	2	|s(α	|s(α	ADJ
ejpam-3175	247	3	,	,	PUNCT
ejpam-3175	247	4	β)|2	β)|2	PROPN
ejpam-3175	247	5	s(α	s(α	NOUN
ejpam-3175	247	6	,	,	PUNCT
ejpam-3175	247	7	α	α	NOUN
ejpam-3175	247	8	)	)	PUNCT
ejpam-3175	247	9	,	,	PUNCT
ejpam-3175	247	10	(	(	PUNCT
ejpam-3175	247	11	20	20	NUM
ejpam-3175	247	12	)	)	PUNCT
ejpam-3175	247	13	where	where	SCONJ
ejpam-3175	247	14	s(α	s(α	NOUN
ejpam-3175	247	15	,	,	PUNCT
ejpam-3175	247	16	β	β	X
ejpam-3175	247	17	)	)	PUNCT
ejpam-3175	247	18	=	=	SYM
ejpam-3175	247	19	(	(	PUNCT
ejpam-3175	247	20	n+1	n+1	NOUN
ejpam-3175	247	21	)	)	PUNCT
ejpam-3175	247	22	!	!	PUNCT
ejpam-3175	248	1	4πn+1	4πn+1	NOUN
ejpam-3175	248	2	·	·	SYM
ejpam-3175	248	3	1	1	NUM
ejpam-3175	248	4	ρ(α	ρ(α	NOUN
ejpam-3175	248	5	,	,	PUNCT
ejpam-3175	248	6	β)n+1	β)n+1	NOUN
ejpam-3175	248	7	is	be	AUX
ejpam-3175	248	8	szegö	szegö	ADJ
ejpam-3175	248	9	kernel	kernel	PROPN
ejpam-3175	248	10	.	.	PUNCT
ejpam-3175	249	1	references	reference	NOUN
ejpam-3175	249	2	148	148	NUM
ejpam-3175	249	3	let	let	VERB
ejpam-3175	249	4	the	the	DET
ejpam-3175	249	5	poisson	poisson	PROPN
ejpam-3175	249	6	kernel	kernel	PROPN
ejpam-3175	249	7	p	p	PROPN
ejpam-3175	249	8	be	be	AUX
ejpam-3175	249	9	as	as	ADP
ejpam-3175	249	10	in	in	ADP
ejpam-3175	249	11	(	(	PUNCT
ejpam-3175	249	12	20	20	NUM
ejpam-3175	249	13	)	)	PUNCT
ejpam-3175	249	14	.	.	PUNCT
ejpam-3175	250	1	then	then	ADV
ejpam-3175	250	2	,	,	PUNCT
ejpam-3175	250	3	for	for	ADP
ejpam-3175	250	4	any	any	DET
ejpam-3175	250	5	f	f	PROPN
ejpam-3175	250	6	∈	∈	PROPN
ejpam-3175	250	7	l2(∂un+1	l2(∂un+1	PROPN
ejpam-3175	250	8	)	)	PUNCT
ejpam-3175	250	9	,	,	PUNCT
ejpam-3175	250	10	we	we	PRON
ejpam-3175	250	11	have	have	VERB
ejpam-3175	250	12	f	f	PROPN
ejpam-3175	250	13	(	(	PUNCT
ejpam-3175	250	14	α	α	NOUN
ejpam-3175	250	15	)	)	PUNCT
ejpam-3175	250	16	=	=	SYM
ejpam-3175	251	1	∫	∫	PROPN
ejpam-3175	251	2	∂un+1	∂un+1	INTJ
ejpam-3175	251	3	f(β)p	f(β)p	PROPN
ejpam-3175	251	4	(	(	PUNCT
ejpam-3175	251	5	α	α	NOUN
ejpam-3175	251	6	,	,	PUNCT
ejpam-3175	251	7	β)dσ(β	β)dσ(β	NOUN
ejpam-3175	251	8	)	)	PUNCT
ejpam-3175	251	9	,	,	PUNCT
ejpam-3175	251	10	(	(	PUNCT
ejpam-3175	251	11	21	21	NUM
ejpam-3175	251	12	)	)	PUNCT
ejpam-3175	251	13	where	where	SCONJ
ejpam-3175	251	14	dσ	dσ	PROPN
ejpam-3175	251	15	is	be	AUX
ejpam-3175	251	16	a	a	DET
ejpam-3175	251	17	measure	measure	NOUN
ejpam-3175	251	18	element	element	NOUN
ejpam-3175	251	19	of	of	ADP
ejpam-3175	251	20	∂un+1	∂un+1	NOUN
ejpam-3175	251	21	(	(	PUNCT
ejpam-3175	251	22	see	see	VERB
ejpam-3175	251	23	[	[	X
ejpam-3175	251	24	11	11	NUM
ejpam-3175	251	25	]	]	NUM
ejpam-3175	251	26	)	)	PUNCT
ejpam-3175	251	27	.	.	PUNCT
ejpam-3175	252	1	on	on	ADP
ejpam-3175	252	2	the	the	DET
ejpam-3175	252	3	disk	disk	NOUN
ejpam-3175	252	4	d	d	NOUN
ejpam-3175	252	5	:	:	PUNCT
ejpam-3175	252	6	|z|	|z|	NOUN
ejpam-3175	252	7	<	<	X
ejpam-3175	252	8	1	1	NUM
ejpam-3175	252	9	,	,	PUNCT
ejpam-3175	252	10	helgason	helgason	NOUN
ejpam-3175	253	1	[	[	X
ejpam-3175	253	2	9	9	NUM
ejpam-3175	253	3	]	]	PUNCT
ejpam-3175	253	4	proved	prove	VERB
ejpam-3175	253	5	that	that	SCONJ
ejpam-3175	253	6	the	the	DET
ejpam-3175	253	7	poisson	poisson	NOUN
ejpam-3175	253	8	integral	integral	ADJ
ejpam-3175	253	9	and	and	CCONJ
ejpam-3175	253	10	radon	radon	NOUN
ejpam-3175	253	11	transforms	transform	NOUN
ejpam-3175	253	12	are	be	AUX
ejpam-3175	253	13	equivalent	equivalent	ADJ
ejpam-3175	253	14	.	.	PUNCT
ejpam-3175	254	1	by	by	ADP
ejpam-3175	254	2	[	[	X
ejpam-3175	254	3	10	10	NUM
ejpam-3175	254	4	,	,	PUNCT
ejpam-3175	254	5	proposition	proposition	NOUN
ejpam-3175	254	6	2.5	2.5	NUM
ejpam-3175	254	7	and	and	CCONJ
ejpam-3175	254	8	2.6	2.6	NUM
ejpam-3175	254	9	]	]	PUNCT
ejpam-3175	254	10	,	,	PUNCT
ejpam-3175	254	11	we	we	PRON
ejpam-3175	254	12	can	can	AUX
ejpam-3175	254	13	obtain	obtain	VERB
ejpam-3175	254	14	the	the	DET
ejpam-3175	254	15	following	follow	VERB
ejpam-3175	254	16	proposition	proposition	NOUN
ejpam-3175	254	17	.	.	PUNCT
ejpam-3175	255	1	proposition	proposition	NOUN
ejpam-3175	255	2	3	3	X
ejpam-3175	255	3	.	.	PUNCT
ejpam-3175	256	1	let	let	VERB
ejpam-3175	256	2	fρ	fρ	AUX
ejpam-3175	256	3	be	be	AUX
ejpam-3175	256	4	as	as	ADP
ejpam-3175	256	5	in	in	ADP
ejpam-3175	256	6	(	(	PUNCT
ejpam-3175	256	7	19	19	NUM
ejpam-3175	256	8	)	)	PUNCT
ejpam-3175	256	9	.	.	PUNCT
ejpam-3175	257	1	we	we	PRON
ejpam-3175	257	2	assume	assume	VERB
ejpam-3175	257	3	that	that	SCONJ
ejpam-3175	257	4	the	the	DET
ejpam-3175	257	5	radon	radon	NOUN
ejpam-3175	257	6	transform	transform	NOUN
ejpam-3175	257	7	is	be	AUX
ejpam-3175	257	8	the	the	DET
ejpam-3175	257	9	classical	classical	ADJ
ejpam-3175	257	10	poisson	poisson	NOUN
ejpam-3175	257	11	integral	integral	ADJ
ejpam-3175	257	12	as	as	ADP
ejpam-3175	257	13	in	in	ADP
ejpam-3175	257	14	(	(	PUNCT
ejpam-3175	257	15	21	21	NUM
ejpam-3175	257	16	)	)	PUNCT
ejpam-3175	257	17	.	.	PUNCT
ejpam-3175	258	1	then	then	ADV
ejpam-3175	258	2	the	the	DET
ejpam-3175	258	3	inverse	inverse	NOUN
ejpam-3175	258	4	formula	formula	NOUN
ejpam-3175	258	5	is	be	AUX
ejpam-3175	258	6	given	give	VERB
ejpam-3175	258	7	by	by	ADP
ejpam-3175	258	8	f(z̃	f(z̃	PROPN
ejpam-3175	258	9	,	,	PUNCT
ejpam-3175	258	10	t	t	PROPN
ejpam-3175	258	11	)	)	PUNCT
ejpam-3175	258	12	=	=	PROPN
ejpam-3175	258	13	lim	lim	PROPN
ejpam-3175	258	14	ρ→0	ρ→0	PUNCT
ejpam-3175	258	15	fρ(z̃	fρ(z̃	PROPN
ejpam-3175	258	16	,	,	PUNCT
ejpam-3175	258	17	t	t	PROPN
ejpam-3175	258	18	)	)	PUNCT
ejpam-3175	258	19	,	,	PUNCT
ejpam-3175	258	20	where	where	SCONJ
ejpam-3175	258	21	f(z̃	f(z̃	PROPN
ejpam-3175	258	22	,	,	PUNCT
ejpam-3175	258	23	t	t	PROPN
ejpam-3175	258	24	)	)	PUNCT
ejpam-3175	258	25	∈	∈	PROPN
ejpam-3175	258	26	l2(∂un+1	l2(∂un+1	PROPN
ejpam-3175	258	27	)	)	PUNCT
ejpam-3175	258	28	.	.	PUNCT
ejpam-3175	259	1	acknowledgements	acknowledgement	VERB
ejpam-3175	259	2	the	the	DET
ejpam-3175	259	3	authors	author	NOUN
ejpam-3175	259	4	thank	thank	VERB
ejpam-3175	259	5	the	the	DET
ejpam-3175	259	6	anonymous	anonymous	ADJ
ejpam-3175	259	7	referee	referee	NOUN
ejpam-3175	259	8	for	for	ADP
ejpam-3175	259	9	some	some	DET
ejpam-3175	259	10	expert	expert	ADJ
ejpam-3175	259	11	comments	comment	NOUN
ejpam-3175	259	12	and	and	CCONJ
ejpam-3175	259	13	suggestions	suggestion	NOUN
ejpam-3175	259	14	.	.	PUNCT
ejpam-3175	260	1	the	the	DET
ejpam-3175	260	2	research	research	NOUN
ejpam-3175	260	3	of	of	ADP
ejpam-3175	260	4	the	the	DET
ejpam-3175	260	5	second	second	ADJ
ejpam-3175	260	6	author	author	NOUN
ejpam-3175	260	7	was	be	AUX
ejpam-3175	260	8	supported	support	VERB
ejpam-3175	260	9	by	by	ADP
ejpam-3175	260	10	national	national	ADJ
ejpam-3175	260	11	natural	natural	PROPN
ejpam-3175	260	12	science	science	PROPN
ejpam-3175	260	13	foundation	foundation	PROPN
ejpam-3175	260	14	of	of	ADP
ejpam-3175	260	15	china	china	PROPN
ejpam-3175	260	16	(	(	PUNCT
ejpam-3175	260	17	grant	grant	PROPN
ejpam-3175	260	18	nos	nos	PROPN
ejpam-3175	260	19	.	.	PROPN
ejpam-3175	260	20	11471040	11471040	NUM
ejpam-3175	260	21	,	,	PUNCT
ejpam-3175	260	22	11671414	11671414	NUM
ejpam-3175	260	23	)	)	PUNCT
ejpam-3175	260	24	.	.	PUNCT
ejpam-3175	261	1	references	reference	NOUN
ejpam-3175	261	2	[	[	X
ejpam-3175	261	3	1	1	NUM
ejpam-3175	261	4	]	]	PUNCT
ejpam-3175	261	5	h	h	NOUN
ejpam-3175	261	6	afshari	afshari	NOUN
ejpam-3175	261	7	,	,	PUNCT
ejpam-3175	261	8	h	h	NOUN
ejpam-3175	261	9	marasi	marasi	NOUN
ejpam-3175	261	10	and	and	CCONJ
ejpam-3175	261	11	h	h	NOUN
ejpam-3175	261	12	aydi	aydi	ADJ
ejpam-3175	261	13	,	,	PUNCT
ejpam-3175	261	14	existence	existence	NOUN
ejpam-3175	261	15	and	and	CCONJ
ejpam-3175	261	16	uniqueness	uniqueness	NOUN
ejpam-3175	261	17	of	of	ADP
ejpam-3175	261	18	positive	positive	ADJ
ejpam-3175	261	19	solutions	solution	NOUN
ejpam-3175	261	20	for	for	ADP
ejpam-3175	261	21	boundary	boundary	ADJ
ejpam-3175	261	22	value	value	NOUN
ejpam-3175	261	23	problems	problem	NOUN
ejpam-3175	261	24	of	of	ADP
ejpam-3175	261	25	fractional	fractional	ADJ
ejpam-3175	261	26	differential	differential	ADJ
ejpam-3175	261	27	equations	equation	NOUN
ejpam-3175	261	28	,	,	PUNCT
ejpam-3175	261	29	filomat	filomat	PROPN
ejpam-3175	261	30	31(2017	31(2017	NUM
ejpam-3175	261	31	)	)	PUNCT
ejpam-3175	261	32	,	,	PUNCT
ejpam-3175	261	33	26752682	26752682	NUM
ejpam-3175	261	34	.	.	PUNCT
ejpam-3175	262	1	[	[	X
ejpam-3175	262	2	2	2	NUM
ejpam-3175	262	3	]	]	X
ejpam-3175	262	4	s	s	PART
ejpam-3175	262	5	barker	barker	PROPN
ejpam-3175	262	6	and	and	CCONJ
ejpam-3175	262	7	s	s	PROPN
ejpam-3175	262	8	salamon	salamon	PROPN
ejpam-3175	262	9	,	,	PUNCT
ejpam-3175	262	10	analysis	analysis	NOUN
ejpam-3175	262	11	on	on	ADP
ejpam-3175	262	12	a	a	DET
ejpam-3175	262	13	generalized	generalized	ADJ
ejpam-3175	262	14	heisenberg	heisenberg	PROPN
ejpam-3175	262	15	group	group	NOUN
ejpam-3175	262	16	,	,	PUNCT
ejpam-3175	262	17	j.	j.	PROPN
ejpam-3175	262	18	london	london	PROPN
ejpam-3175	262	19	math	math	PROPN
ejpam-3175	262	20	.	.	PUNCT
ejpam-3175	263	1	soc	soc	PROPN
ejpam-3175	263	2	.	.	PUNCT
ejpam-3175	264	1	28(1983	28(1983	NUM
ejpam-3175	264	2	)	)	PUNCT
ejpam-3175	264	3	184	184	NUM
ejpam-3175	264	4	-	-	SYM
ejpam-3175	264	5	192	192	NUM
ejpam-3175	264	6	.	.	PUNCT
ejpam-3175	265	1	[	[	X
ejpam-3175	265	2	3	3	X
ejpam-3175	265	3	]	]	X
ejpam-3175	265	4	h	h	PROPN
ejpam-3175	265	5	elliott	elliott	PROPN
ejpam-3175	265	6	and	and	CCONJ
ejpam-3175	265	7	l	l	PROPN
ejpam-3175	265	8	michael	michael	PROPN
ejpam-3175	265	9	,	,	PUNCT
ejpam-3175	265	10	analysis	analysis	NOUN
ejpam-3175	265	11	(	(	PUNCT
ejpam-3175	265	12	second	second	ADJ
ejpam-3175	265	13	edition	edition	NOUN
ejpam-3175	265	14	)	)	PUNCT
ejpam-3175	265	15	,	,	PUNCT
ejpam-3175	265	16	mathematical	mathematical	ADJ
ejpam-3175	265	17	gazette	gazette	PROPN
ejpam-3175	265	18	(	(	PUNCT
ejpam-3175	265	19	1999	1999	NUM
ejpam-3175	265	20	)	)	PUNCT
ejpam-3175	265	21	.	.	PUNCT
ejpam-3175	266	1	[	[	X
ejpam-3175	266	2	4	4	NUM
ejpam-3175	266	3	]	]	X
ejpam-3175	266	4	r	r	NOUN
ejpam-3175	266	5	felix	felix	NOUN
ejpam-3175	266	6	,	,	PUNCT
ejpam-3175	266	7	radon	radon	NOUN
ejpam-3175	266	8	-	-	PUNCT
ejpam-3175	266	9	transformation	transformation	NOUN
ejpam-3175	266	10	auf	auf	PROPN
ejpam-3175	266	11	nilpotenten	nilpotenten	ADV
ejpam-3175	266	12	lie	lie	VERB
ejpam-3175	266	13	-	-	PUNCT
ejpam-3175	266	14	gruppen	gruppen	ADJ
ejpam-3175	266	15	,	,	PUNCT
ejpam-3175	266	16	invent	invent	NOUN
ejpam-3175	266	17	.	.	PUNCT
ejpam-3175	267	1	math	math	NOUN
ejpam-3175	267	2	.	.	PUNCT
ejpam-3175	268	1	112(1993	112(1993	X
ejpam-3175	268	2	)	)	PUNCT
ejpam-3175	268	3	413	413	NUM
ejpam-3175	268	4	-	-	SYM
ejpam-3175	268	5	443	443	NUM
ejpam-3175	268	6	.	.	PUNCT
ejpam-3175	269	1	[	[	X
ejpam-3175	269	2	5	5	NUM
ejpam-3175	269	3	]	]	X
ejpam-3175	269	4	d	d	X
ejpam-3175	269	5	geller	geller	PROPN
ejpam-3175	269	6	and	and	CCONJ
ejpam-3175	269	7	e	e	PROPN
ejpam-3175	269	8	m	m	PROPN
ejpam-3175	269	9	stein	stein	PROPN
ejpam-3175	269	10	,	,	PUNCT
ejpam-3175	269	11	estimates	estimate	VERB
ejpam-3175	269	12	convolution	convolution	NOUN
ejpam-3175	269	13	operators	operator	NOUN
ejpam-3175	269	14	on	on	ADP
ejpam-3175	269	15	the	the	DET
ejpam-3175	269	16	heisenberg	heisenberg	PROPN
ejpam-3175	269	17	group	group	PROPN
ejpam-3175	269	18	,	,	PUNCT
ejpam-3175	269	19	bull	bull	PROPN
ejpam-3175	269	20	.	.	PUNCT
ejpam-3175	270	1	amer	amer	PROPN
ejpam-3175	270	2	.	.	PUNCT
ejpam-3175	270	3	math	math	PROPN
ejpam-3175	270	4	.	.	PUNCT
ejpam-3175	271	1	soc	soc	PROPN
ejpam-3175	271	2	.	.	PUNCT
ejpam-3175	272	1	267(1984	267(1984	NUM
ejpam-3175	272	2	)	)	PUNCT
ejpam-3175	272	3	99	99	NUM
ejpam-3175	272	4	-	-	SYM
ejpam-3175	272	5	103	103	NUM
ejpam-3175	272	6	.	.	PUNCT
ejpam-3175	273	1	[	[	X
ejpam-3175	273	2	6	6	NUM
ejpam-3175	273	3	]	]	PUNCT
ejpam-3175	273	4	j	j	PROPN
ejpam-3175	273	5	he	he	PRON
ejpam-3175	273	6	,	,	PUNCT
ejpam-3175	273	7	an	an	DET
ejpam-3175	273	8	inversion	inversion	NOUN
ejpam-3175	273	9	formula	formula	NOUN
ejpam-3175	273	10	of	of	ADP
ejpam-3175	273	11	the	the	DET
ejpam-3175	273	12	radon	radon	PROPN
ejpam-3175	273	13	transform	transform	NOUN
ejpam-3175	273	14	on	on	ADP
ejpam-3175	273	15	the	the	DET
ejpam-3175	273	16	heisenberg	heisenberg	PROPN
ejpam-3175	273	17	group	group	PROPN
ejpam-3175	273	18	,	,	PUNCT
ejpam-3175	273	19	canad	canad	PROPN
ejpam-3175	273	20	.	.	PUNCT
ejpam-3175	274	1	math	math	NOUN
ejpam-3175	274	2	.	.	PUNCT
ejpam-3175	275	1	bull	bull	NOUN
ejpam-3175	275	2	.	.	PUNCT
ejpam-3175	276	1	47(2004	47(2004	X
ejpam-3175	276	2	)	)	PUNCT
ejpam-3175	276	3	389	389	NUM
ejpam-3175	276	4	-	-	SYM
ejpam-3175	276	5	397	397	NUM
ejpam-3175	276	6	.	.	PUNCT
ejpam-3175	277	1	[	[	X
ejpam-3175	277	2	7	7	X
ejpam-3175	277	3	]	]	X
ejpam-3175	277	4	j	j	PROPN
ejpam-3175	277	5	he	he	PRON
ejpam-3175	277	6	and	and	CCONJ
ejpam-3175	277	7	h	h	PROPN
ejpam-3175	277	8	liu	liu	PROPN
ejpam-3175	277	9	,	,	PUNCT
ejpam-3175	277	10	inversion	inversion	NOUN
ejpam-3175	277	11	of	of	ADP
ejpam-3175	277	12	the	the	DET
ejpam-3175	277	13	radon	radon	PROPN
ejpam-3175	277	14	transform	transform	NOUN
ejpam-3175	277	15	associated	associate	VERB
ejpam-3175	277	16	with	with	ADP
ejpam-3175	277	17	the	the	DET
ejpam-3175	277	18	classical	classical	ADJ
ejpam-3175	277	19	domain	domain	NOUN
ejpam-3175	277	20	of	of	ADP
ejpam-3175	277	21	type	type	NOUN
ejpam-3175	277	22	one	one	NUM
ejpam-3175	277	23	,	,	PUNCT
ejpam-3175	277	24	intern	intern	NOUN
ejpam-3175	277	25	.	.	PUNCT
ejpam-3175	278	1	j.	j.	PROPN
ejpam-3175	278	2	math	math	PROPN
ejpam-3175	278	3	.	.	PUNCT
ejpam-3175	279	1	16(2005	16(2005	NUM
ejpam-3175	279	2	)	)	PUNCT
ejpam-3175	279	3	875	875	NUM
ejpam-3175	279	4	-	-	SYM
ejpam-3175	279	5	887	887	NUM
ejpam-3175	279	6	.	.	PUNCT
ejpam-3175	280	1	references	reference	NOUN
ejpam-3175	280	2	149	149	NUM
ejpam-3175	281	1	[	[	X
ejpam-3175	281	2	8	8	NUM
ejpam-3175	281	3	]	]	X
ejpam-3175	281	4	j	j	PROPN
ejpam-3175	282	1	he	he	PRON
ejpam-3175	282	2	and	and	CCONJ
ejpam-3175	282	3	h	h	PROPN
ejpam-3175	282	4	liu	liu	PROPN
ejpam-3175	282	5	,	,	PUNCT
ejpam-3175	282	6	admissible	admissible	ADJ
ejpam-3175	282	7	wavelets	wavelet	NOUN
ejpam-3175	282	8	and	and	CCONJ
ejpam-3175	282	9	inverse	inverse	ADJ
ejpam-3175	282	10	radon	radon	NOUN
ejpam-3175	282	11	transform	transform	NOUN
ejpam-3175	282	12	associated	associate	VERB
ejpam-3175	282	13	with	with	ADP
ejpam-3175	282	14	the	the	DET
ejpam-3175	282	15	affine	affine	ADJ
ejpam-3175	282	16	homogenous	homogenous	ADJ
ejpam-3175	282	17	siegel	siegel	NOUN
ejpam-3175	282	18	domain	domain	NOUN
ejpam-3175	282	19	of	of	ADP
ejpam-3175	282	20	type	type	NOUN
ejpam-3175	282	21	two	two	NUM
ejpam-3175	282	22	,	,	PUNCT
ejpam-3175	282	23	commun	commun	PROPN
ejpam-3175	282	24	.	.	PUNCT
ejpam-3175	283	1	anal	anal	PROPN
ejpam-3175	283	2	.	.	PUNCT
ejpam-3175	284	1	geom	geom	PROPN
ejpam-3175	284	2	.	.	PUNCT
ejpam-3175	285	1	15(2007	15(2007	NUM
ejpam-3175	285	2	)	)	PUNCT
ejpam-3175	285	3	1	1	NUM
ejpam-3175	285	4	-	-	SYM
ejpam-3175	285	5	28	28	NUM
ejpam-3175	285	6	.	.	PUNCT
ejpam-3175	286	1	[	[	X
ejpam-3175	286	2	9	9	NUM
ejpam-3175	286	3	]	]	SYM
ejpam-3175	286	4	s	s	PART
ejpam-3175	286	5	helgason	helgason	NOUN
ejpam-3175	286	6	,	,	PUNCT
ejpam-3175	286	7	integral	integral	ADJ
ejpam-3175	286	8	geometry	geometry	NOUN
ejpam-3175	286	9	and	and	CCONJ
ejpam-3175	286	10	radon	radon	NOUN
ejpam-3175	286	11	transforms	transform	VERB
ejpam-3175	286	12	,	,	PUNCT
ejpam-3175	286	13	springer	springer	NOUN
ejpam-3175	286	14	new	new	PROPN
ejpam-3175	286	15	york	york	PROPN
ejpam-3175	286	16	(	(	PUNCT
ejpam-3175	286	17	2011	2011	NUM
ejpam-3175	286	18	)	)	PUNCT
ejpam-3175	286	19	.	.	PUNCT
ejpam-3175	287	1	[	[	X
ejpam-3175	287	2	10	10	NUM
ejpam-3175	287	3	]	]	X
ejpam-3175	287	4	a	a	DET
ejpam-3175	287	5	korányi	korányi	NOUN
ejpam-3175	287	6	,	,	PUNCT
ejpam-3175	287	7	the	the	DET
ejpam-3175	287	8	poisson	poisson	NOUN
ejpam-3175	287	9	integral	integral	ADJ
ejpam-3175	287	10	for	for	ADP
ejpam-3175	287	11	generalized	generalized	ADJ
ejpam-3175	287	12	half	half	ADJ
ejpam-3175	287	13	-	-	PUNCT
ejpam-3175	287	14	planes	plane	NOUN
ejpam-3175	287	15	and	and	CCONJ
ejpam-3175	287	16	bounded	bound	VERB
ejpam-3175	287	17	symmetric	symmetric	ADJ
ejpam-3175	287	18	domains	domain	NOUN
ejpam-3175	287	19	,	,	PUNCT
ejpam-3175	287	20	ann	ann	PROPN
ejpam-3175	287	21	.	.	PROPN
ejpam-3175	287	22	of	of	ADP
ejpam-3175	287	23	math	math	NOUN
ejpam-3175	287	24	.	.	PUNCT
ejpam-3175	288	1	2(1965	2(1965	X
ejpam-3175	288	2	)	)	PUNCT
ejpam-3175	288	3	332	332	NUM
ejpam-3175	288	4	-	-	SYM
ejpam-3175	288	5	350	350	NUM
ejpam-3175	288	6	.	.	PUNCT
ejpam-3175	289	1	[	[	X
ejpam-3175	289	2	11	11	NUM
ejpam-3175	289	3	]	]	X
ejpam-3175	289	4	p	p	X
ejpam-3175	289	5	krantz	krantz	PROPN
ejpam-3175	289	6	,	,	PUNCT
ejpam-3175	289	7	explorations	exploration	NOUN
ejpam-3175	289	8	in	in	ADP
ejpam-3175	289	9	harmonic	harmonic	ADJ
ejpam-3175	289	10	analysis	analysis	NOUN
ejpam-3175	289	11	,	,	PUNCT
ejpam-3175	289	12	birkhäuser	birkhäuser	X
ejpam-3175	289	13	boston	boston	PROPN
ejpam-3175	289	14	(	(	PUNCT
ejpam-3175	289	15	2009	2009	NUM
ejpam-3175	289	16	)	)	PUNCT
ejpam-3175	289	17	.	.	PUNCT
ejpam-3175	290	1	[	[	X
ejpam-3175	290	2	12	12	NUM
ejpam-3175	290	3	]	]	X
ejpam-3175	290	4	h	h	NOUN
ejpam-3175	290	5	liu	liu	PROPN
ejpam-3175	290	6	and	and	CCONJ
ejpam-3175	290	7	r	r	PROPN
ejpam-3175	290	8	ma	ma	PROPN
ejpam-3175	290	9	,	,	PUNCT
ejpam-3175	290	10	littlewood	littlewood	NOUN
ejpam-3175	290	11	-	-	PUNCT
ejpam-3175	290	12	paley	paley	PROPN
ejpam-3175	290	13	g	g	NOUN
ejpam-3175	290	14	-	-	PUNCT
ejpam-3175	290	15	function	function	NOUN
ejpam-3175	290	16	on	on	ADP
ejpam-3175	290	17	the	the	DET
ejpam-3175	290	18	heisenberg	heisenberg	PROPN
ejpam-3175	290	19	group	group	PROPN
ejpam-3175	290	20	,	,	PUNCT
ejpam-3175	290	21	acta	acta	PROPN
ejpam-3175	290	22	math	math	PROPN
ejpam-3175	290	23	.	.	PUNCT
ejpam-3175	291	1	sinica	sinica	PROPN
ejpam-3175	291	2	,	,	PUNCT
ejpam-3175	291	3	english	english	ADJ
ejpam-3175	291	4	series	series	NOUN
ejpam-3175	291	5	.	.	PUNCT
ejpam-3175	292	1	22(2006	22(2006	NUM
ejpam-3175	292	2	)	)	PUNCT
ejpam-3175	292	3	95	95	NUM
ejpam-3175	292	4	-	-	SYM
ejpam-3175	292	5	100	100	NUM
ejpam-3175	292	6	.	.	PUNCT
ejpam-3175	293	1	[	[	X
ejpam-3175	293	2	13	13	NUM
ejpam-3175	293	3	]	]	X
ejpam-3175	293	4	h	h	NOUN
ejpam-3175	293	5	liu	liu	PROPN
ejpam-3175	293	6	and	and	CCONJ
ejpam-3175	293	7	l	l	PROPN
ejpam-3175	293	8	peng	peng	PROPN
ejpam-3175	293	9	,	,	PUNCT
ejpam-3175	293	10	admissible	admissible	ADJ
ejpam-3175	293	11	wavelets	wavelet	NOUN
ejpam-3175	293	12	associated	associate	VERB
ejpam-3175	293	13	with	with	ADP
ejpam-3175	293	14	the	the	DET
ejpam-3175	293	15	heisenberg	heisenberg	PROPN
ejpam-3175	293	16	group	group	PROPN
ejpam-3175	293	17	,	,	PUNCT
ejpam-3175	293	18	pac	pac	PROPN
ejpam-3175	293	19	.	.	PROPN
ejpam-3175	293	20	j.	j.	PROPN
ejpam-3175	293	21	math	math	PROPN
ejpam-3175	293	22	.	.	PUNCT
ejpam-3175	294	1	180(1997	180(1997	NUM
ejpam-3175	294	2	)	)	PUNCT
ejpam-3175	294	3	101	101	NUM
ejpam-3175	294	4	-	-	SYM
ejpam-3175	294	5	123	123	NUM
ejpam-3175	294	6	.	.	PUNCT
ejpam-3175	295	1	[	[	X
ejpam-3175	295	2	14	14	NUM
ejpam-3175	295	3	]	]	X
ejpam-3175	295	4	h	h	NOUN
ejpam-3175	295	5	marasi	marasi	PROPN
ejpam-3175	295	6	h	h	NOUN
ejpam-3175	295	7	piri	piri	NOUN
ejpam-3175	295	8	and	and	CCONJ
ejpam-3175	295	9	h	h	NOUN
ejpam-3175	295	10	aydi	aydi	ADJ
ejpam-3175	295	11	,	,	PUNCT
ejpam-3175	295	12	existence	existence	NOUN
ejpam-3175	295	13	and	and	CCONJ
ejpam-3175	295	14	multiplicity	multiplicity	NOUN
ejpam-3175	295	15	of	of	ADP
ejpam-3175	295	16	solutions	solution	NOUN
ejpam-3175	295	17	for	for	ADP
ejpam-3175	295	18	nonlinear	nonlinear	ADJ
ejpam-3175	295	19	fractional	fractional	ADJ
ejpam-3175	295	20	differential	differential	NOUN
ejpam-3175	295	21	equations	equation	NOUN
ejpam-3175	295	22	,	,	PUNCT
ejpam-3175	295	23	j.	j.	PROPN
ejpam-3175	295	24	nonlinear	nonlinear	PROPN
ejpam-3175	295	25	sci	sci	PROPN
ejpam-3175	295	26	.	.	PUNCT
ejpam-3175	295	27	appl	appl	PROPN
ejpam-3175	295	28	.	.	PUNCT
ejpam-3175	296	1	9(2016	9(2016	NUM
ejpam-3175	296	2	)	)	PUNCT
ejpam-3175	296	3	,	,	PUNCT
ejpam-3175	296	4	4639	4639	NUM
ejpam-3175	296	5	-	-	SYM
ejpam-3175	296	6	4646	4646	NUM
ejpam-3175	296	7	.	.	PUNCT
ejpam-3175	297	1	[	[	X
ejpam-3175	297	2	15	15	NUM
ejpam-3175	297	3	]	]	X
ejpam-3175	297	4	h	h	NOUN
ejpam-3175	297	5	marasi	marasi	NOUN
ejpam-3175	297	6	,	,	PUNCT
ejpam-3175	297	7	a	a	DET
ejpam-3175	297	8	solution	solution	NOUN
ejpam-3175	297	9	of	of	ADP
ejpam-3175	297	10	the	the	DET
ejpam-3175	297	11	new	new	PROPN
ejpam-3175	297	12	caputo	caputo	PROPN
ejpam-3175	297	13	-	-	PUNCT
ejpam-3175	297	14	fabrizio	fabrizio	PROPN
ejpam-3175	297	15	fractonal	fractonal	ADJ
ejpam-3175	297	16	kdv	kdv	NOUN
ejpam-3175	297	17	equation	equation	NOUN
ejpam-3175	297	18	via	via	ADP
ejpam-3175	297	19	stability	stability	NOUN
ejpam-3175	297	20	,	,	PUNCT
ejpam-3175	297	21	j.	j.	PROPN
ejpam-3175	297	22	math	math	PROPN
ejpam-3175	297	23	.	.	PUNCT
ejpam-3175	298	1	anal	anal	PROPN
ejpam-3175	298	2	.	.	PUNCT
ejpam-3175	299	1	4(2017	4(2017	NUM
ejpam-3175	299	2	)	)	PUNCT
ejpam-3175	299	3	,	,	PUNCT
ejpam-3175	299	4	147	147	NUM
ejpam-3175	299	5	-	-	SYM
ejpam-3175	299	6	155	155	NUM
ejpam-3175	299	7	.	.	PUNCT
ejpam-3175	300	1	[	[	X
ejpam-3175	300	2	16	16	NUM
ejpam-3175	300	3	]	]	X
ejpam-3175	300	4	r	r	NOUN
ejpam-3175	300	5	strichartz	strichartz	NOUN
ejpam-3175	300	6	,	,	PUNCT
ejpam-3175	300	7	lp	lp	PROPN
ejpam-3175	300	8	harmonic	harmonic	ADJ
ejpam-3175	300	9	analysis	analysis	NOUN
ejpam-3175	300	10	and	and	CCONJ
ejpam-3175	300	11	radon	radon	NOUN
ejpam-3175	300	12	transforms	transform	VERB
ejpam-3175	300	13	on	on	ADP
ejpam-3175	300	14	the	the	DET
ejpam-3175	300	15	heisenberg	heisenberg	PROPN
ejpam-3175	300	16	group	group	PROPN
ejpam-3175	300	17	,	,	PUNCT
ejpam-3175	300	18	j.	j.	PROPN
ejpam-3175	300	19	funct	funct	PROPN
ejpam-3175	300	20	.	.	PUNCT
ejpam-3175	301	1	anal	anal	PROPN
ejpam-3175	301	2	.	.	PUNCT
ejpam-3175	302	1	96(1991	96(1991	NUM
ejpam-3175	302	2	)	)	PUNCT
ejpam-3175	302	3	350	350	NUM
ejpam-3175	302	4	-	-	SYM
ejpam-3175	302	5	406	406	NUM
ejpam-3175	302	6	.	.	PUNCT
ejpam-3175	303	1	[	[	X
ejpam-3175	303	2	17	17	NUM
ejpam-3175	303	3	]	]	X
ejpam-3175	303	4	s	s	PART
ejpam-3175	303	5	thangavelu	thangavelu	NOUN
ejpam-3175	303	6	,	,	PUNCT
ejpam-3175	303	7	harmonic	harmonic	VERB
ejpam-3175	303	8	analysis	analysis	NOUN
ejpam-3175	303	9	on	on	ADP
ejpam-3175	303	10	the	the	DET
ejpam-3175	303	11	heisenberg	heisenberg	PROPN
ejpam-3175	303	12	group	group	NOUN
ejpam-3175	303	13	,	,	PUNCT
ejpam-3175	303	14	birkhauser	birkhauser	NOUN
ejpam-3175	303	15	(	(	PUNCT
ejpam-3175	303	16	1998	1998	NUM
ejpam-3175	303	17	)	)	PUNCT
ejpam-3175	303	18	.	.	PUNCT