id	sid	tid	token	lemma	pos
ejpam-2627	1	1	european	european	PROPN
ejpam-2627	1	2	journal	journal	PROPN
ejpam-2627	1	3	of	of	ADP
ejpam-2627	1	4	pure	pure	ADJ
ejpam-2627	1	5	and	and	CCONJ
ejpam-2627	1	6	applied	apply	VERB
ejpam-2627	1	7	mathematics	mathematic	NOUN
ejpam-2627	1	8	vol	vol	NOUN
ejpam-2627	1	9	.	.	PROPN
ejpam-2627	2	1	10	10	NUM
ejpam-2627	2	2	,	,	PUNCT
ejpam-2627	2	3	no	no	INTJ
ejpam-2627	2	4	.	.	NOUN
ejpam-2627	2	5	3	3	NUM
ejpam-2627	2	6	,	,	PUNCT
ejpam-2627	2	7	2017	2017	NUM
ejpam-2627	2	8	,	,	PUNCT
ejpam-2627	2	9	544	544	NUM
ejpam-2627	2	10	-	-	SYM
ejpam-2627	2	11	551	551	NUM
ejpam-2627	2	12	issn	issn	PROPN
ejpam-2627	2	13	1307	1307	NUM
ejpam-2627	2	14	-	-	SYM
ejpam-2627	2	15	5543	5543	NUM
ejpam-2627	2	16	–	–	PUNCT
ejpam-2627	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2627	2	18	published	publish	VERB
ejpam-2627	2	19	by	by	ADP
ejpam-2627	2	20	new	new	PROPN
ejpam-2627	2	21	york	york	PROPN
ejpam-2627	2	22	business	business	PROPN
ejpam-2627	2	23	global	global	ADJ
ejpam-2627	2	24	generalization	generalization	NOUN
ejpam-2627	2	25	of	of	ADP
ejpam-2627	2	26	dunkl	dunkl	PROPN
ejpam-2627	2	27	dini	dini	NOUN
ejpam-2627	2	28	lipschitz	lipschitz	PROPN
ejpam-2627	2	29	functions	function	NOUN
ejpam-2627	2	30	salah	salah	PROPN
ejpam-2627	2	31	el	el	PROPN
ejpam-2627	2	32	ouadih1,∗	ouadih1,∗	PROPN
ejpam-2627	2	33	,	,	PUNCT
ejpam-2627	2	34	radouan	radouan	PROPN
ejpam-2627	2	35	daher1	daher1	PROPN
ejpam-2627	2	36	1	1	NUM
ejpam-2627	2	37	department	department	NOUN
ejpam-2627	2	38	of	of	ADP
ejpam-2627	2	39	mathematics	mathematic	NOUN
ejpam-2627	2	40	,	,	PUNCT
ejpam-2627	2	41	faculty	faculty	NOUN
ejpam-2627	2	42	of	of	ADP
ejpam-2627	2	43	sciences	science	NOUN
ejpam-2627	2	44	aı̈n	aı̈n	NOUN
ejpam-2627	2	45	chock	chock	NOUN
ejpam-2627	2	46	,	,	PUNCT
ejpam-2627	2	47	university	university	PROPN
ejpam-2627	2	48	hassan	hassan	PROPN
ejpam-2627	2	49	ii	ii	PROPN
ejpam-2627	2	50	morocco	morocco	PROPN
ejpam-2627	2	51	abstract	abstract	PROPN
ejpam-2627	2	52	.	.	PUNCT
ejpam-2627	3	1	using	use	VERB
ejpam-2627	3	2	a	a	DET
ejpam-2627	3	3	generalized	generalized	ADJ
ejpam-2627	3	4	spherical	spherical	ADJ
ejpam-2627	3	5	mean	mean	NOUN
ejpam-2627	3	6	operator	operator	NOUN
ejpam-2627	3	7	,	,	PUNCT
ejpam-2627	3	8	we	we	PRON
ejpam-2627	3	9	obtain	obtain	VERB
ejpam-2627	3	10	a	a	DET
ejpam-2627	3	11	generalization	generalization	NOUN
ejpam-2627	3	12	of	of	ADP
ejpam-2627	3	13	younis	younis	PROPN
ejpam-2627	3	14	’s	’s	PART
ejpam-2627	3	15	theorem	theorem	VERB
ejpam-2627	3	16	5.2	5.2	NUM
ejpam-2627	3	17	in	in	ADP
ejpam-2627	3	18	[	[	X
ejpam-2627	3	19	12	12	NUM
ejpam-2627	3	20	]	]	PUNCT
ejpam-2627	3	21	for	for	ADP
ejpam-2627	3	22	the	the	DET
ejpam-2627	3	23	dunkl	dunkl	PROPN
ejpam-2627	3	24	transform	transform	NOUN
ejpam-2627	3	25	for	for	ADP
ejpam-2627	3	26	functions	function	NOUN
ejpam-2627	3	27	satisfying	satisfy	VERB
ejpam-2627	3	28	the	the	DET
ejpam-2627	3	29	d	d	PROPN
ejpam-2627	3	30	-	-	PUNCT
ejpam-2627	3	31	dunkl	dunkl	NOUN
ejpam-2627	3	32	dini	dini	NOUN
ejpam-2627	3	33	lipschitz	lipschitz	NOUN
ejpam-2627	3	34	condition	condition	NOUN
ejpam-2627	3	35	in	in	ADP
ejpam-2627	3	36	the	the	DET
ejpam-2627	3	37	space	space	NOUN
ejpam-2627	3	38	lp(rd	lp(rd	ADJ
ejpam-2627	3	39	,	,	PUNCT
ejpam-2627	3	40	wl(x)dx	wl(x)dx	NOUN
ejpam-2627	3	41	)	)	PUNCT
ejpam-2627	3	42	,	,	PUNCT
ejpam-2627	3	43	1	1	NUM
ejpam-2627	3	44	<	<	X
ejpam-2627	3	45	p	p	X
ejpam-2627	3	46	≤	≤	NOUN
ejpam-2627	3	47	2	2	NUM
ejpam-2627	3	48	,	,	PUNCT
ejpam-2627	3	49	where	where	SCONJ
ejpam-2627	3	50	wl	wl	PROPN
ejpam-2627	3	51	is	be	AUX
ejpam-2627	3	52	a	a	DET
ejpam-2627	3	53	weight	weight	NOUN
ejpam-2627	3	54	function	function	NOUN
ejpam-2627	3	55	invariant	invariant	ADJ
ejpam-2627	3	56	under	under	ADP
ejpam-2627	3	57	the	the	DET
ejpam-2627	3	58	action	action	NOUN
ejpam-2627	3	59	of	of	ADP
ejpam-2627	3	60	an	an	DET
ejpam-2627	3	61	associated	associated	ADJ
ejpam-2627	3	62	reflection	reflection	NOUN
ejpam-2627	3	63	group	group	NOUN
ejpam-2627	3	64	.	.	PUNCT
ejpam-2627	4	1	2010	2010	NUM
ejpam-2627	4	2	mathematics	mathematic	NOUN
ejpam-2627	4	3	subject	subject	NOUN
ejpam-2627	4	4	classifications	classification	NOUN
ejpam-2627	4	5	:	:	PUNCT
ejpam-2627	4	6	42b37	42b37	DET
ejpam-2627	4	7	key	key	ADJ
ejpam-2627	4	8	words	word	NOUN
ejpam-2627	4	9	and	and	CCONJ
ejpam-2627	4	10	phrases	phrase	NOUN
ejpam-2627	4	11	:	:	PUNCT
ejpam-2627	4	12	dunkl	dunkl	NOUN
ejpam-2627	4	13	transform	transform	NOUN
ejpam-2627	4	14	,	,	PUNCT
ejpam-2627	4	15	dunkl	dunkl	PROPN
ejpam-2627	4	16	kernel	kernel	PROPN
ejpam-2627	4	17	,	,	PUNCT
ejpam-2627	4	18	generalized	generalize	VERB
ejpam-2627	4	19	spherical	spherical	ADJ
ejpam-2627	4	20	mean	mean	NOUN
ejpam-2627	4	21	operator	operator	NOUN
ejpam-2627	4	22	1	1	NUM
ejpam-2627	4	23	.	.	PUNCT
ejpam-2627	4	24	introduction	introduction	NOUN
ejpam-2627	4	25	and	and	CCONJ
ejpam-2627	4	26	preliminaries	preliminary	NOUN
ejpam-2627	4	27	younis	younis	PROPN
ejpam-2627	4	28	’s	’s	PART
ejpam-2627	4	29	theorem	theorem	VERB
ejpam-2627	4	30	5.2	5.2	NUM
ejpam-2627	5	1	[	[	X
ejpam-2627	5	2	12	12	NUM
ejpam-2627	5	3	]	]	PUNCT
ejpam-2627	5	4	characterized	characterize	VERB
ejpam-2627	5	5	the	the	DET
ejpam-2627	5	6	set	set	NOUN
ejpam-2627	5	7	of	of	ADP
ejpam-2627	5	8	functions	function	NOUN
ejpam-2627	5	9	in	in	ADP
ejpam-2627	5	10	l2(r	l2(r	NOUN
ejpam-2627	5	11	)	)	PUNCT
ejpam-2627	5	12	satisfying	satisfy	VERB
ejpam-2627	5	13	the	the	DET
ejpam-2627	5	14	dini	dini	NOUN
ejpam-2627	5	15	lipschitz	lipschitz	NOUN
ejpam-2627	5	16	condition	condition	NOUN
ejpam-2627	5	17	by	by	ADP
ejpam-2627	5	18	means	mean	NOUN
ejpam-2627	5	19	of	of	ADP
ejpam-2627	5	20	an	an	DET
ejpam-2627	5	21	asymptotic	asymptotic	ADJ
ejpam-2627	5	22	estimate	estimate	NOUN
ejpam-2627	5	23	growth	growth	NOUN
ejpam-2627	5	24	of	of	ADP
ejpam-2627	5	25	the	the	DET
ejpam-2627	5	26	norm	norm	NOUN
ejpam-2627	5	27	of	of	ADP
ejpam-2627	5	28	their	their	PRON
ejpam-2627	5	29	fourier	fourier	NOUN
ejpam-2627	5	30	transforms	transform	VERB
ejpam-2627	5	31	,	,	PUNCT
ejpam-2627	5	32	namely	namely	ADV
ejpam-2627	5	33	we	we	PRON
ejpam-2627	5	34	have	have	AUX
ejpam-2627	5	35	theorem	theorem	VERB
ejpam-2627	5	36	1	1	NUM
ejpam-2627	5	37	.	.	PUNCT
ejpam-2627	6	1	[	[	X
ejpam-2627	6	2	12	12	NUM
ejpam-2627	6	3	]	]	PUNCT
ejpam-2627	6	4	let	let	VERB
ejpam-2627	6	5	f	f	PROPN
ejpam-2627	6	6	∈	∈	PROPN
ejpam-2627	6	7	l2(r	l2(r	PROPN
ejpam-2627	6	8	)	)	PUNCT
ejpam-2627	6	9	.	.	PUNCT
ejpam-2627	7	1	then	then	ADV
ejpam-2627	7	2	the	the	DET
ejpam-2627	7	3	following	follow	VERB
ejpam-2627	7	4	are	be	AUX
ejpam-2627	7	5	equivalents	equivalent	NOUN
ejpam-2627	7	6	(	(	PUNCT
ejpam-2627	7	7	i	i	NOUN
ejpam-2627	7	8	)	)	PUNCT
ejpam-2627	8	1	‖f(x+	‖f(x+	PROPN
ejpam-2627	8	2	h)−	h)−	PROPN
ejpam-2627	8	3	f(x)‖2	f(x)‖2	PROPN
ejpam-2627	9	1	=	=	PUNCT
ejpam-2627	9	2	o	o	X
ejpam-2627	9	3	(	(	PUNCT
ejpam-2627	9	4	hη	hη	PROPN
ejpam-2627	9	5	(	(	PUNCT
ejpam-2627	9	6	log	log	NOUN
ejpam-2627	9	7	1	1	NUM
ejpam-2627	9	8	h	h	NOUN
ejpam-2627	9	9	)	)	PUNCT
ejpam-2627	9	10	δ	δ	PROPN
ejpam-2627	9	11	)	)	PUNCT
ejpam-2627	9	12	,	,	PUNCT
ejpam-2627	9	13	as	as	ADP
ejpam-2627	9	14	h→	h→	NOUN
ejpam-2627	9	15	0	0	NUM
ejpam-2627	9	16	,	,	PUNCT
ejpam-2627	9	17	0	0	NUM
ejpam-2627	9	18	<	<	X
ejpam-2627	9	19	η	η	X
ejpam-2627	9	20	<	<	X
ejpam-2627	9	21	1	1	NUM
ejpam-2627	9	22	,	,	PUNCT
ejpam-2627	9	23	δ	δ	PROPN
ejpam-2627	9	24	≥	≥	X
ejpam-2627	9	25	0	0	NUM
ejpam-2627	9	26	(	(	PUNCT
ejpam-2627	9	27	ii	ii	NOUN
ejpam-2627	9	28	)	)	PUNCT
ejpam-2627	9	29	∫	∫	PROPN
ejpam-2627	9	30	|λ|≥s	|λ|≥s	PROPN
ejpam-2627	9	31	|f̂(λ)|2dλ	|f̂(λ)|2dλ	PROPN
ejpam-2627	9	32	=	=	PUNCT
ejpam-2627	9	33	o	o	X
ejpam-2627	9	34	(	(	PUNCT
ejpam-2627	9	35	s−2η	s−2η	X
ejpam-2627	9	36	(	(	PUNCT
ejpam-2627	9	37	log	log	NOUN
ejpam-2627	9	38	s)2δ	s)2δ	PROPN
ejpam-2627	9	39	)	)	PUNCT
ejpam-2627	9	40	,	,	PUNCT
ejpam-2627	9	41	as	as	ADP
ejpam-2627	9	42	s→∞	s→∞	NUM
ejpam-2627	9	43	,	,	PUNCT
ejpam-2627	9	44	where	where	SCONJ
ejpam-2627	9	45	f̂	f̂	NUM
ejpam-2627	9	46	stands	stand	VERB
ejpam-2627	9	47	for	for	ADP
ejpam-2627	9	48	the	the	DET
ejpam-2627	9	49	fourier	fourier	ADJ
ejpam-2627	9	50	transform	transform	NOUN
ejpam-2627	9	51	of	of	ADP
ejpam-2627	9	52	f	f	PROPN
ejpam-2627	9	53	.	.	PUNCT
ejpam-2627	10	1	in	in	ADP
ejpam-2627	10	2	this	this	DET
ejpam-2627	10	3	paper	paper	NOUN
ejpam-2627	10	4	,	,	PUNCT
ejpam-2627	10	5	we	we	PRON
ejpam-2627	10	6	obtain	obtain	VERB
ejpam-2627	10	7	a	a	DET
ejpam-2627	10	8	generalization	generalization	NOUN
ejpam-2627	10	9	of	of	ADP
ejpam-2627	10	10	theorem	theorem	ADJ
ejpam-2627	10	11	1.1	1.1	NUM
ejpam-2627	10	12	for	for	ADP
ejpam-2627	10	13	the	the	DET
ejpam-2627	10	14	dunkl	dunkl	PROPN
ejpam-2627	10	15	transform	transform	NOUN
ejpam-2627	10	16	on	on	ADP
ejpam-2627	10	17	rd	rd	NOUN
ejpam-2627	10	18	in	in	ADP
ejpam-2627	10	19	the	the	DET
ejpam-2627	10	20	space	space	NOUN
ejpam-2627	10	21	lp(rd	lp(rd	ADJ
ejpam-2627	10	22	,	,	PUNCT
ejpam-2627	10	23	wl(x)dx	wl(x)dx	NOUN
ejpam-2627	10	24	)	)	PUNCT
ejpam-2627	10	25	,	,	PUNCT
ejpam-2627	10	26	1	1	NUM
ejpam-2627	10	27	<	<	X
ejpam-2627	10	28	p	p	X
ejpam-2627	10	29	≤	≤	NOUN
ejpam-2627	10	30	2	2	NUM
ejpam-2627	10	31	.	.	PUNCT
ejpam-2627	11	1	for	for	ADP
ejpam-2627	11	2	this	this	DET
ejpam-2627	11	3	purpose	purpose	NOUN
ejpam-2627	11	4	,	,	PUNCT
ejpam-2627	11	5	we	we	PRON
ejpam-2627	11	6	use	use	VERB
ejpam-2627	11	7	a	a	DET
ejpam-2627	11	8	generalized	generalized	ADJ
ejpam-2627	11	9	spherical	spherical	ADJ
ejpam-2627	11	10	mean	mean	NOUN
ejpam-2627	11	11	operator	operator	NOUN
ejpam-2627	11	12	.	.	PUNCT
ejpam-2627	12	1	we	we	PRON
ejpam-2627	12	2	consider	consider	VERB
ejpam-2627	12	3	the	the	DET
ejpam-2627	12	4	dunkl	dunkl	NOUN
ejpam-2627	12	5	operators	operator	NOUN
ejpam-2627	12	6	dj	dj	X
ejpam-2627	12	7	,	,	PUNCT
ejpam-2627	12	8	1	1	NUM
ejpam-2627	12	9	≤	≤	NUM
ejpam-2627	12	10	j	j	PROPN
ejpam-2627	12	11	≤	≤	PROPN
ejpam-2627	12	12	d	d	PROPN
ejpam-2627	12	13	,	,	PUNCT
ejpam-2627	12	14	on	on	ADP
ejpam-2627	12	15	rd	rd	NOUN
ejpam-2627	12	16	which	which	PRON
ejpam-2627	12	17	are	be	AUX
ejpam-2627	12	18	the	the	DET
ejpam-2627	12	19	differentialdifference	differentialdifference	NOUN
ejpam-2627	12	20	operators	operator	NOUN
ejpam-2627	12	21	introduced	introduce	VERB
ejpam-2627	12	22	by	by	ADP
ejpam-2627	12	23	dunkl	dunkl	NOUN
ejpam-2627	12	24	in	in	ADP
ejpam-2627	12	25	[	[	X
ejpam-2627	12	26	3	3	NUM
ejpam-2627	12	27	]	]	PUNCT
ejpam-2627	12	28	.	.	PUNCT
ejpam-2627	13	1	these	these	DET
ejpam-2627	13	2	operators	operator	NOUN
ejpam-2627	13	3	are	be	AUX
ejpam-2627	13	4	very	very	ADV
ejpam-2627	13	5	important	important	ADJ
ejpam-2627	13	6	in	in	ADP
ejpam-2627	13	7	pure	pure	ADJ
ejpam-2627	13	8	mathematics	mathematic	NOUN
ejpam-2627	13	9	and	and	CCONJ
ejpam-2627	13	10	in	in	ADP
ejpam-2627	13	11	physics	physics	NOUN
ejpam-2627	13	12	.	.	PUNCT
ejpam-2627	14	1	the	the	DET
ejpam-2627	14	2	theory	theory	NOUN
ejpam-2627	14	3	of	of	ADP
ejpam-2627	14	4	dunkl	dunkl	PROPN
ejpam-2627	14	5	operators	operator	NOUN
ejpam-2627	14	6	provides	provide	VERB
ejpam-2627	14	7	generalizations	generalization	NOUN
ejpam-2627	14	8	of	of	ADP
ejpam-2627	14	9	various	various	ADJ
ejpam-2627	14	10	multivariable	multivariable	ADJ
ejpam-2627	14	11	analytic	analytic	ADJ
ejpam-2627	14	12	structures	structure	NOUN
ejpam-2627	14	13	,	,	PUNCT
ejpam-2627	14	14	among	among	ADP
ejpam-2627	14	15	others	other	NOUN
ejpam-2627	14	16	we	we	PRON
ejpam-2627	14	17	cite	cite	VERB
ejpam-2627	14	18	the	the	DET
ejpam-2627	14	19	exponential	exponential	ADJ
ejpam-2627	14	20	function	function	NOUN
ejpam-2627	14	21	,	,	PUNCT
ejpam-2627	14	22	∗corresponding	∗corresponde	VERB
ejpam-2627	14	23	author	author	NOUN
ejpam-2627	14	24	.	.	PUNCT
ejpam-2627	15	1	email	email	NOUN
ejpam-2627	15	2	addresses	address	NOUN
ejpam-2627	15	3	:	:	PUNCT
ejpam-2627	15	4	salahwadih@gmail.com	salahwadih@gmail.com	X
ejpam-2627	15	5	(	(	PUNCT
ejpam-2627	15	6	s.	s.	PROPN
ejpam-2627	15	7	el	el	PROPN
ejpam-2627	15	8	ouadih	ouadih	PROPN
ejpam-2627	15	9	)	)	PUNCT
ejpam-2627	15	10	,	,	PUNCT
ejpam-2627	15	11	rjdaher024@gmail.com	rjdaher024@gmail.com	PROPN
ejpam-2627	15	12	(	(	PUNCT
ejpam-2627	15	13	r.	r.	PROPN
ejpam-2627	15	14	daher	daher	PROPN
ejpam-2627	15	15	)	)	PUNCT
ejpam-2627	15	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2627	16	1	544	544	NUM
ejpam-2627	16	2	c	c	NOUN
ejpam-2627	16	3	©	©	PROPN
ejpam-2627	16	4	2017	2017	NUM
ejpam-2627	16	5	ejpam	ejpam	VERB
ejpam-2627	16	6	all	all	DET
ejpam-2627	16	7	rights	right	NOUN
ejpam-2627	16	8	reserved	reserve	VERB
ejpam-2627	16	9	.	.	PUNCT
ejpam-2627	17	1	s.	s.	PROPN
ejpam-2627	17	2	el	el	PROPN
ejpam-2627	17	3	ouadih	ouadih	PROPN
ejpam-2627	17	4	,	,	PUNCT
ejpam-2627	17	5	r.	r.	PROPN
ejpam-2627	17	6	daher	daher	PROPN
ejpam-2627	17	7	/	/	SYM
ejpam-2627	17	8	eur	eur	PROPN
ejpam-2627	17	9	.	.	PUNCT
ejpam-2627	18	1	j.	j.	PROPN
ejpam-2627	18	2	pure	pure	PROPN
ejpam-2627	18	3	appl	appl	PROPN
ejpam-2627	18	4	.	.	PROPN
ejpam-2627	18	5	math	math	PROPN
ejpam-2627	18	6	,	,	PUNCT
ejpam-2627	18	7	10	10	NUM
ejpam-2627	18	8	(	(	PUNCT
ejpam-2627	18	9	3	3	NUM
ejpam-2627	18	10	)	)	PUNCT
ejpam-2627	18	11	(	(	PUNCT
ejpam-2627	18	12	2017	2017	NUM
ejpam-2627	18	13	)	)	PUNCT
ejpam-2627	18	14	,	,	PUNCT
ejpam-2627	18	15	544	544	NUM
ejpam-2627	18	16	-	-	SYM
ejpam-2627	18	17	551	551	NUM
ejpam-2627	18	18	545	545	NUM
ejpam-2627	18	19	the	the	DET
ejpam-2627	18	20	fourier	fourier	NOUN
ejpam-2627	18	21	transform	transform	NOUN
ejpam-2627	18	22	and	and	CCONJ
ejpam-2627	18	23	the	the	DET
ejpam-2627	18	24	translation	translation	NOUN
ejpam-2627	18	25	operator	operator	NOUN
ejpam-2627	18	26	.	.	PUNCT
ejpam-2627	19	1	for	for	ADP
ejpam-2627	19	2	more	more	ADJ
ejpam-2627	19	3	details	detail	NOUN
ejpam-2627	19	4	about	about	ADP
ejpam-2627	19	5	these	these	DET
ejpam-2627	19	6	operators	operator	NOUN
ejpam-2627	19	7	see	see	VERB
ejpam-2627	19	8	[	[	X
ejpam-2627	19	9	6	6	NUM
ejpam-2627	19	10	,	,	PUNCT
ejpam-2627	19	11	5	5	NUM
ejpam-2627	19	12	]	]	PUNCT
ejpam-2627	19	13	.	.	PUNCT
ejpam-2627	20	1	the	the	DET
ejpam-2627	20	2	dunkl	dunkl	PROPN
ejpam-2627	20	3	kernel	kernel	PROPN
ejpam-2627	20	4	el	el	PROPN
ejpam-2627	20	5	has	have	AUX
ejpam-2627	20	6	been	be	AUX
ejpam-2627	20	7	introduced	introduce	VERB
ejpam-2627	20	8	by	by	ADP
ejpam-2627	20	9	dunkl	dunkl	NOUN
ejpam-2627	20	10	in	in	ADP
ejpam-2627	20	11	[	[	X
ejpam-2627	20	12	4	4	NUM
ejpam-2627	20	13	]	]	PUNCT
ejpam-2627	20	14	.	.	PUNCT
ejpam-2627	21	1	this	this	DET
ejpam-2627	21	2	kernel	kernel	NOUN
ejpam-2627	21	3	is	be	AUX
ejpam-2627	21	4	used	use	VERB
ejpam-2627	21	5	to	to	PART
ejpam-2627	21	6	define	define	VERB
ejpam-2627	21	7	the	the	DET
ejpam-2627	21	8	dunkl	dunkl	NOUN
ejpam-2627	21	9	transform	transform	NOUN
ejpam-2627	21	10	.	.	PUNCT
ejpam-2627	22	1	let	let	VERB
ejpam-2627	22	2	r	r	PRON
ejpam-2627	22	3	be	be	AUX
ejpam-2627	22	4	a	a	DET
ejpam-2627	22	5	root	root	NOUN
ejpam-2627	22	6	system	system	NOUN
ejpam-2627	22	7	in	in	ADP
ejpam-2627	22	8	rd	rd	PROPN
ejpam-2627	22	9	,	,	PUNCT
ejpam-2627	22	10	w	w	ADP
ejpam-2627	22	11	the	the	DET
ejpam-2627	22	12	corresponding	corresponding	ADJ
ejpam-2627	22	13	reflection	reflection	NOUN
ejpam-2627	22	14	group	group	NOUN
ejpam-2627	22	15	,	,	PUNCT
ejpam-2627	22	16	r+	r+	VERB
ejpam-2627	22	17	a	a	DET
ejpam-2627	22	18	positive	positive	ADJ
ejpam-2627	22	19	subsystem	subsystem	NOUN
ejpam-2627	22	20	of	of	ADP
ejpam-2627	22	21	r	r	NOUN
ejpam-2627	22	22	(	(	PUNCT
ejpam-2627	22	23	see	see	VERB
ejpam-2627	22	24	[	[	X
ejpam-2627	22	25	6	6	NUM
ejpam-2627	22	26	,	,	PUNCT
ejpam-2627	22	27	5	5	NUM
ejpam-2627	22	28	,	,	PUNCT
ejpam-2627	22	29	1	1	NUM
ejpam-2627	22	30	,	,	PUNCT
ejpam-2627	22	31	8	8	NUM
ejpam-2627	22	32	,	,	PUNCT
ejpam-2627	22	33	9	9	NUM
ejpam-2627	22	34	]	]	PUNCT
ejpam-2627	22	35	)	)	PUNCT
ejpam-2627	22	36	and	and	CCONJ
ejpam-2627	22	37	l	l	NOUN
ejpam-2627	22	38	a	a	DET
ejpam-2627	22	39	non	non	ADJ
ejpam-2627	22	40	-	-	ADJ
ejpam-2627	22	41	negative	negative	ADJ
ejpam-2627	22	42	and	and	CCONJ
ejpam-2627	22	43	w	w	ADJ
ejpam-2627	22	44	-	-	PUNCT
ejpam-2627	22	45	invariant	invariant	ADJ
ejpam-2627	22	46	function	function	NOUN
ejpam-2627	22	47	defined	define	VERB
ejpam-2627	22	48	on	on	ADP
ejpam-2627	22	49	r.	r.	PROPN
ejpam-2627	22	50	the	the	DET
ejpam-2627	22	51	dunkl	dunkl	NOUN
ejpam-2627	22	52	operator	operator	NOUN
ejpam-2627	22	53	is	be	AUX
ejpam-2627	22	54	defined	define	VERB
ejpam-2627	22	55	for	for	ADP
ejpam-2627	22	56	f	f	PROPN
ejpam-2627	22	57	∈	∈	PROPN
ejpam-2627	22	58	c1(rd	c1(rd	PROPN
ejpam-2627	22	59	)	)	PUNCT
ejpam-2627	22	60	by	by	ADP
ejpam-2627	22	61	djf(x	djf(x	PROPN
ejpam-2627	22	62	)	)	PUNCT
ejpam-2627	22	63	=	=	SYM
ejpam-2627	23	1	∂f	∂f	NUM
ejpam-2627	23	2	∂xj	∂xj	NOUN
ejpam-2627	23	3	(	(	PUNCT
ejpam-2627	23	4	x	x	X
ejpam-2627	23	5	)	)	PUNCT
ejpam-2627	24	1	+	+	CCONJ
ejpam-2627	24	2	∑	∑	AUX
ejpam-2627	24	3	α∈r+	α∈r+	NOUN
ejpam-2627	24	4	l(α)αj	l(α)αj	VERB
ejpam-2627	24	5	f(x)−	f(x)−	PROPN
ejpam-2627	24	6	f(σα(x	f(σα(x	PROPN
ejpam-2627	24	7	)	)	PUNCT
ejpam-2627	24	8	)	)	PUNCT
ejpam-2627	25	1	<	<	X
ejpam-2627	25	2	α	α	X
ejpam-2627	25	3	,	,	PUNCT
ejpam-2627	25	4	x	x	X
ejpam-2627	25	5	>	>	X
ejpam-2627	25	6	,	,	PUNCT
ejpam-2627	25	7	x	x	PUNCT
ejpam-2627	25	8	∈	∈	PROPN
ejpam-2627	25	9	rd(1	rd(1	VERB
ejpam-2627	25	10	≤	≤	NUM
ejpam-2627	25	11	j	j	NOUN
ejpam-2627	26	1	≤	≤	NUM
ejpam-2627	27	1	d	d	NOUN
ejpam-2627	27	2	)	)	PUNCT
ejpam-2627	27	3	.	.	PUNCT
ejpam-2627	28	1	here	here	ADV
ejpam-2627	28	2	<	<	X
ejpam-2627	28	3	,	,	PUNCT
ejpam-2627	28	4	>	>	X
ejpam-2627	28	5	is	be	AUX
ejpam-2627	28	6	the	the	DET
ejpam-2627	28	7	usual	usual	ADJ
ejpam-2627	28	8	euclidean	euclidean	ADJ
ejpam-2627	28	9	scalar	scalar	ADJ
ejpam-2627	28	10	product	product	NOUN
ejpam-2627	28	11	on	on	ADP
ejpam-2627	28	12	rd	rd	PROPN
ejpam-2627	28	13	with	with	ADP
ejpam-2627	28	14	the	the	DET
ejpam-2627	28	15	associated	associated	ADJ
ejpam-2627	28	16	norm	norm	NOUN
ejpam-2627	28	17	|.|	|.|	NOUN
ejpam-2627	28	18	and	and	CCONJ
ejpam-2627	28	19	σα	σα	PRON
ejpam-2627	28	20	the	the	DET
ejpam-2627	28	21	reflection	reflection	NOUN
ejpam-2627	28	22	with	with	ADP
ejpam-2627	28	23	respect	respect	NOUN
ejpam-2627	28	24	to	to	ADP
ejpam-2627	28	25	the	the	DET
ejpam-2627	28	26	hyperplane	hyperplane	NOUN
ejpam-2627	28	27	hα	hα	PRON
ejpam-2627	28	28	orthogonal	orthogonal	NOUN
ejpam-2627	28	29	to	to	ADP
ejpam-2627	28	30	α	α	PRON
ejpam-2627	28	31	,	,	PUNCT
ejpam-2627	28	32	and	and	CCONJ
ejpam-2627	28	33	αj	αj	X
ejpam-2627	28	34	=	=	NOUN
ejpam-2627	28	35	<	<	X
ejpam-2627	28	36	α	α	PROPN
ejpam-2627	28	37	,	,	PUNCT
ejpam-2627	28	38	ej	ej	X
ejpam-2627	28	39	>	>	X
ejpam-2627	28	40	,	,	PUNCT
ejpam-2627	28	41	(	(	PUNCT
ejpam-2627	28	42	e1	e1	PROPN
ejpam-2627	28	43	,	,	PUNCT
ejpam-2627	28	44	e2	e2	PROPN
ejpam-2627	28	45	,	,	PUNCT
ejpam-2627	28	46	...	...	PUNCT
ejpam-2627	28	47	,	,	PUNCT
ejpam-2627	28	48	ed	ed	X
ejpam-2627	28	49	)	)	PUNCT
ejpam-2627	28	50	being	be	AUX
ejpam-2627	28	51	the	the	DET
ejpam-2627	28	52	canonical	canonical	ADJ
ejpam-2627	28	53	basis	basis	NOUN
ejpam-2627	28	54	of	of	ADP
ejpam-2627	28	55	rd	rd	PROPN
ejpam-2627	28	56	.	.	PUNCT
ejpam-2627	29	1	we	we	PRON
ejpam-2627	29	2	consider	consider	VERB
ejpam-2627	29	3	the	the	DET
ejpam-2627	29	4	weight	weight	NOUN
ejpam-2627	29	5	function	function	NOUN
ejpam-2627	29	6	wl(x	wl(x	X
ejpam-2627	29	7	)	)	PUNCT
ejpam-2627	29	8	=	=	SYM
ejpam-2627	29	9	∏	∏	PROPN
ejpam-2627	29	10	ζ∈r+	ζ∈r+	NOUN
ejpam-2627	29	11	|	|	ADV
ejpam-2627	29	12	<	<	X
ejpam-2627	29	13	ζ	ζ	NOUN
ejpam-2627	29	14	,	,	PUNCT
ejpam-2627	29	15	x	x	X
ejpam-2627	29	16	>	>	X
ejpam-2627	29	17	|2l(α	|2l(α	NUM
ejpam-2627	29	18	)	)	PUNCT
ejpam-2627	29	19	,	,	PUNCT
ejpam-2627	29	20	x	x	PROPN
ejpam-2627	29	21	∈	∈	PROPN
ejpam-2627	29	22	rd	rd	PROPN
ejpam-2627	29	23	,	,	PUNCT
ejpam-2627	29	24	where	where	SCONJ
ejpam-2627	29	25	wl	wl	PROPN
ejpam-2627	29	26	is	be	AUX
ejpam-2627	29	27	w	w	NOUN
ejpam-2627	29	28	-	-	PUNCT
ejpam-2627	29	29	invariant	invariant	ADJ
ejpam-2627	29	30	and	and	CCONJ
ejpam-2627	29	31	homogeneous	homogeneous	ADJ
ejpam-2627	29	32	of	of	ADP
ejpam-2627	29	33	degree	degree	NOUN
ejpam-2627	29	34	2γ	2γ	NOUN
ejpam-2627	29	35	where	where	SCONJ
ejpam-2627	29	36	γ	γ	X
ejpam-2627	29	37	=	=	SYM
ejpam-2627	29	38	γ(r	γ(r	PROPN
ejpam-2627	29	39	)	)	PUNCT
ejpam-2627	29	40	=	=	SYM
ejpam-2627	29	41	∑	∑	PUNCT
ejpam-2627	29	42	ζ∈r+	ζ∈r+	X
ejpam-2627	29	43	l(ζ	l(ζ	PROPN
ejpam-2627	29	44	)	)	PUNCT
ejpam-2627	29	45	≥	≥	NOUN
ejpam-2627	29	46	0	0	NUM
ejpam-2627	29	47	.	.	PUNCT
ejpam-2627	30	1	the	the	DET
ejpam-2627	30	2	dunkl	dunkl	PROPN
ejpam-2627	30	3	kernel	kernel	PROPN
ejpam-2627	30	4	el	el	PROPN
ejpam-2627	30	5	on	on	ADP
ejpam-2627	30	6	rd	rd	PROPN
ejpam-2627	30	7	×	×	PROPN
ejpam-2627	30	8	rd	rd	PROPN
ejpam-2627	30	9	has	have	AUX
ejpam-2627	30	10	been	be	AUX
ejpam-2627	30	11	introduced	introduce	VERB
ejpam-2627	30	12	by	by	ADP
ejpam-2627	30	13	c.	c.	PROPN
ejpam-2627	30	14	f.	f.	PROPN
ejpam-2627	30	15	dunkl	dunkl	PROPN
ejpam-2627	30	16	in	in	ADP
ejpam-2627	30	17	[	[	X
ejpam-2627	30	18	4	4	NUM
ejpam-2627	30	19	]	]	PUNCT
ejpam-2627	30	20	.	.	PUNCT
ejpam-2627	31	1	for	for	ADP
ejpam-2627	31	2	y	y	PROPN
ejpam-2627	31	3	∈	∈	PROPN
ejpam-2627	31	4	rd	rd	PROPN
ejpam-2627	31	5	,	,	PUNCT
ejpam-2627	31	6	the	the	DET
ejpam-2627	31	7	function	function	NOUN
ejpam-2627	31	8	x	x	SYM
ejpam-2627	31	9	7→	7→	NUM
ejpam-2627	31	10	el(x	el(x	NUM
ejpam-2627	31	11	,	,	PUNCT
ejpam-2627	31	12	y	y	NOUN
ejpam-2627	31	13	)	)	PUNCT
ejpam-2627	31	14	is	be	AUX
ejpam-2627	31	15	the	the	DET
ejpam-2627	31	16	unique	unique	ADJ
ejpam-2627	31	17	solution	solution	NOUN
ejpam-2627	31	18	on	on	ADP
ejpam-2627	31	19	rd	rd	PROPN
ejpam-2627	31	20	of	of	ADP
ejpam-2627	31	21	the	the	DET
ejpam-2627	31	22	following	following	ADJ
ejpam-2627	31	23	initial	initial	ADJ
ejpam-2627	31	24	problem	problem	NOUN
ejpam-2627	31	25	{	{	PUNCT
ejpam-2627	31	26	dju(x	dju(x	PROPN
ejpam-2627	31	27	,	,	PUNCT
ejpam-2627	31	28	y	y	NOUN
ejpam-2627	31	29	)	)	PUNCT
ejpam-2627	32	1	=	=	SYM
ejpam-2627	32	2	yju(x	yju(x	PROPN
ejpam-2627	32	3	,	,	PUNCT
ejpam-2627	32	4	y	y	NOUN
ejpam-2627	32	5	)	)	PUNCT
ejpam-2627	32	6	si	si	NOUN
ejpam-2627	32	7	1	1	NUM
ejpam-2627	32	8	≤	≤	NUM
ejpam-2627	32	9	j	j	PROPN
ejpam-2627	32	10	≤	≤	PROPN
ejpam-2627	32	11	d	d	PROPN
ejpam-2627	32	12	u(0	u(0	PROPN
ejpam-2627	32	13	,	,	PUNCT
ejpam-2627	32	14	y	y	PROPN
ejpam-2627	32	15	)	)	PUNCT
ejpam-2627	32	16	=	=	SYM
ejpam-2627	32	17	0	0	NUM
ejpam-2627	32	18	for	for	ADP
ejpam-2627	32	19	all	all	DET
ejpam-2627	32	20	y	y	PROPN
ejpam-2627	32	21	∈	∈	PROPN
ejpam-2627	32	22	rd	rd	PROPN
ejpam-2627	32	23	el	el	PROPN
ejpam-2627	32	24	is	be	AUX
ejpam-2627	32	25	called	call	VERB
ejpam-2627	32	26	the	the	DET
ejpam-2627	32	27	dunkl	dunkl	PROPN
ejpam-2627	32	28	kernel	kernel	PROPN
ejpam-2627	32	29	.	.	PUNCT
ejpam-2627	33	1	lemma	lemma	PROPN
ejpam-2627	33	2	1	1	NUM
ejpam-2627	33	3	.	.	PUNCT
ejpam-2627	34	1	[	[	X
ejpam-2627	34	2	6	6	NUM
ejpam-2627	34	3	]	]	PUNCT
ejpam-2627	34	4	let	let	VERB
ejpam-2627	34	5	z	z	NOUN
ejpam-2627	34	6	,	,	PUNCT
ejpam-2627	34	7	w	w	PROPN
ejpam-2627	34	8	∈	∈	PROPN
ejpam-2627	34	9	cd	cd	NOUN
ejpam-2627	34	10	and	and	CCONJ
ejpam-2627	34	11	λ	λ	PROPN
ejpam-2627	34	12	∈	∈	PROPN
ejpam-2627	34	13	c	c	NOUN
ejpam-2627	34	14	1	1	NUM
ejpam-2627	34	15	.	.	PUNCT
ejpam-2627	34	16	el(z	el(z	NOUN
ejpam-2627	34	17	,	,	PUNCT
ejpam-2627	34	18	0	0	NUM
ejpam-2627	34	19	)	)	PUNCT
ejpam-2627	34	20	=	=	SYM
ejpam-2627	34	21	1	1	NUM
ejpam-2627	34	22	,	,	PUNCT
ejpam-2627	34	23	el(z	el(z	NOUN
ejpam-2627	34	24	,	,	PUNCT
ejpam-2627	34	25	w	w	NOUN
ejpam-2627	34	26	)	)	PUNCT
ejpam-2627	34	27	=	=	SYM
ejpam-2627	34	28	el(w	el(w	NOUN
ejpam-2627	34	29	,	,	PUNCT
ejpam-2627	34	30	z	z	NOUN
ejpam-2627	34	31	)	)	PUNCT
ejpam-2627	34	32	,	,	PUNCT
ejpam-2627	34	33	el(λz	el(λz	PROPN
ejpam-2627	34	34	,	,	PUNCT
ejpam-2627	34	35	w	w	NOUN
ejpam-2627	34	36	)	)	PUNCT
ejpam-2627	34	37	=	=	SYM
ejpam-2627	35	1	el(z	el(z	NOUN
ejpam-2627	35	2	,	,	PUNCT
ejpam-2627	35	3	λw	λw	NOUN
ejpam-2627	35	4	)	)	PUNCT
ejpam-2627	35	5	.	.	PUNCT
ejpam-2627	36	1	2	2	X
ejpam-2627	36	2	.	.	X
ejpam-2627	36	3	for	for	ADP
ejpam-2627	36	4	all	all	DET
ejpam-2627	36	5	ν	ν	NOUN
ejpam-2627	36	6	=	=	SYM
ejpam-2627	36	7	(	(	PUNCT
ejpam-2627	36	8	ν1	ν1	NOUN
ejpam-2627	36	9	,	,	PUNCT
ejpam-2627	36	10	...	...	PUNCT
ejpam-2627	36	11	,	,	PUNCT
ejpam-2627	36	12	νd	νd	X
ejpam-2627	36	13	)	)	PUNCT
ejpam-2627	36	14	∈	∈	PROPN
ejpam-2627	36	15	nd	nd	PRON
ejpam-2627	36	16	,	,	PUNCT
ejpam-2627	36	17	x	x	PROPN
ejpam-2627	36	18	∈	∈	PROPN
ejpam-2627	36	19	rd	rd	PROPN
ejpam-2627	36	20	,	,	PUNCT
ejpam-2627	36	21	z	z	PROPN
ejpam-2627	36	22	∈	∈	PROPN
ejpam-2627	36	23	cd	cd	PROPN
ejpam-2627	36	24	,	,	PUNCT
ejpam-2627	36	25	we	we	PRON
ejpam-2627	36	26	have	have	VERB
ejpam-2627	36	27	|∂νzel(x	|∂νzel(x	PROPN
ejpam-2627	36	28	;	;	PUNCT
ejpam-2627	36	29	z)|	z)|	ADP
ejpam-2627	36	30	≤	≤	NOUN
ejpam-2627	36	31	|x||ν|exp(|x||rez|	|x||ν|exp(|x||rez|	ADP
ejpam-2627	36	32	,	,	PUNCT
ejpam-2627	36	33	where	where	SCONJ
ejpam-2627	36	34	∂νz	∂νz	PROPN
ejpam-2627	36	35	=	=	PUNCT
ejpam-2627	36	36	∂|ν|	∂|ν|	PROPN
ejpam-2627	36	37	∂ν1z1	∂ν1z1	PROPN
ejpam-2627	36	38	....	....	PUNCT
ejpam-2627	36	39	∂	∂	NUM
ejpam-2627	37	1	ν2	ν2	PROPN
ejpam-2627	37	2	zd	zd	PROPN
ejpam-2627	37	3	,	,	PUNCT
ejpam-2627	37	4	|ν|	|ν|	PROPN
ejpam-2627	37	5	=	=	SYM
ejpam-2627	37	6	ν1	ν1	NOUN
ejpam-2627	37	7	+	+	CCONJ
ejpam-2627	37	8	....	....	PUNCT
ejpam-2627	37	9	+	+	NUM
ejpam-2627	37	10	νd	νd	NOUN
ejpam-2627	37	11	.	.	PROPN
ejpam-2627	38	1	in	in	ADP
ejpam-2627	38	2	particular	particular	ADJ
ejpam-2627	38	3	|∂νzel(ix	|∂νzel(ix	NOUN
ejpam-2627	38	4	;	;	PUNCT
ejpam-2627	38	5	z)|	z)|	ADP
ejpam-2627	38	6	≤	≤	NOUN
ejpam-2627	38	7	|x||ν|	|x||ν|	ADV
ejpam-2627	38	8	for	for	ADP
ejpam-2627	38	9	all	all	DET
ejpam-2627	38	10	x	x	NOUN
ejpam-2627	38	11	,	,	PUNCT
ejpam-2627	38	12	z	z	PROPN
ejpam-2627	38	13	∈	∈	PROPN
ejpam-2627	38	14	rd	rd	PROPN
ejpam-2627	38	15	.	.	PUNCT
ejpam-2627	39	1	we	we	PRON
ejpam-2627	39	2	denote	denote	VERB
ejpam-2627	39	3	by	by	ADP
ejpam-2627	39	4	lpl	lpl	PROPN
ejpam-2627	39	5	(	(	PUNCT
ejpam-2627	39	6	r	r	NOUN
ejpam-2627	39	7	d	d	NOUN
ejpam-2627	39	8	)	)	PUNCT
ejpam-2627	39	9	=	=	SYM
ejpam-2627	39	10	lp(rd	lp(rd	ADJ
ejpam-2627	39	11	,	,	PUNCT
ejpam-2627	39	12	wl(x)dx	wl(x)dx	NOUN
ejpam-2627	39	13	)	)	PUNCT
ejpam-2627	39	14	,	,	PUNCT
ejpam-2627	39	15	1	1	NUM
ejpam-2627	39	16	<	<	X
ejpam-2627	39	17	p	p	X
ejpam-2627	39	18	≤	≤	NOUN
ejpam-2627	39	19	2	2	NUM
ejpam-2627	39	20	,	,	PUNCT
ejpam-2627	39	21	the	the	DET
ejpam-2627	39	22	space	space	NOUN
ejpam-2627	39	23	of	of	ADP
ejpam-2627	39	24	measurable	measurable	ADJ
ejpam-2627	39	25	functions	function	NOUN
ejpam-2627	39	26	on	on	ADP
ejpam-2627	39	27	rd	rd	NOUN
ejpam-2627	39	28	with	with	ADP
ejpam-2627	39	29	the	the	DET
ejpam-2627	39	30	norm	norm	NOUN
ejpam-2627	39	31	‖f‖p	‖f‖p	NOUN
ejpam-2627	39	32	,	,	PUNCT
ejpam-2627	39	33	l	l	NOUN
ejpam-2627	39	34	=	=	SYM
ejpam-2627	39	35	(	(	PUNCT
ejpam-2627	39	36	∫	∫	PROPN
ejpam-2627	39	37	rd	rd	PROPN
ejpam-2627	39	38	|f(x)|pwl(x)dx	|f(x)|pwl(x)dx	PROPN
ejpam-2627	39	39	)	)	PUNCT
ejpam-2627	39	40	1	1	NUM
ejpam-2627	39	41	p	p	NOUN
ejpam-2627	39	42	<	<	X
ejpam-2627	39	43	∞.	∞.	PROPN
ejpam-2627	39	44	s.	s.	PROPN
ejpam-2627	39	45	el	el	PROPN
ejpam-2627	39	46	ouadih	ouadih	PROPN
ejpam-2627	39	47	,	,	PUNCT
ejpam-2627	39	48	r.	r.	PROPN
ejpam-2627	39	49	daher	daher	PROPN
ejpam-2627	39	50	/	/	SYM
ejpam-2627	39	51	eur	eur	PROPN
ejpam-2627	39	52	.	.	PUNCT
ejpam-2627	40	1	j.	j.	PROPN
ejpam-2627	40	2	pure	pure	PROPN
ejpam-2627	40	3	appl	appl	PROPN
ejpam-2627	40	4	.	.	PROPN
ejpam-2627	40	5	math	math	PROPN
ejpam-2627	40	6	,	,	PUNCT
ejpam-2627	40	7	10	10	NUM
ejpam-2627	40	8	(	(	PUNCT
ejpam-2627	40	9	3	3	NUM
ejpam-2627	40	10	)	)	PUNCT
ejpam-2627	40	11	(	(	PUNCT
ejpam-2627	40	12	2017	2017	NUM
ejpam-2627	40	13	)	)	PUNCT
ejpam-2627	40	14	,	,	PUNCT
ejpam-2627	40	15	544	544	NUM
ejpam-2627	40	16	-	-	SYM
ejpam-2627	40	17	551	551	NUM
ejpam-2627	40	18	546	546	NUM
ejpam-2627	40	19	the	the	DET
ejpam-2627	40	20	dunkl	dunkl	NOUN
ejpam-2627	40	21	transform	transform	NOUN
ejpam-2627	40	22	is	be	AUX
ejpam-2627	40	23	defined	define	VERB
ejpam-2627	40	24	for	for	ADP
ejpam-2627	40	25	f	f	PROPN
ejpam-2627	40	26	∈	∈	PROPN
ejpam-2627	40	27	l1	l1	PROPN
ejpam-2627	40	28	l	l	PROPN
ejpam-2627	40	29	(	(	PUNCT
ejpam-2627	40	30	rd	rd	NOUN
ejpam-2627	40	31	)	)	PUNCT
ejpam-2627	40	32	=	=	SYM
ejpam-2627	41	1	l1(rd	l1(rd	PROPN
ejpam-2627	41	2	,	,	PUNCT
ejpam-2627	41	3	wl(x)dx	wl(x)dx	NOUN
ejpam-2627	41	4	)	)	PUNCT
ejpam-2627	41	5	by	by	ADP
ejpam-2627	41	6	f(f)(ξ	f(f)(ξ	NOUN
ejpam-2627	41	7	)	)	PUNCT
ejpam-2627	41	8	=	=	SYM
ejpam-2627	41	9	f̂(ξ	f̂(ξ	NOUN
ejpam-2627	41	10	)	)	PUNCT
ejpam-2627	41	11	=	=	PUNCT
ejpam-2627	41	12	c−1l	c−1l	PROPN
ejpam-2627	41	13	∫	∫	PROPN
ejpam-2627	41	14	rd	rd	PROPN
ejpam-2627	41	15	f(x)el(−iξ	f(x)el(−iξ	PROPN
ejpam-2627	41	16	,	,	PUNCT
ejpam-2627	41	17	x)wl(x)dx	x)wl(x)dx	PROPN
ejpam-2627	41	18	,	,	PUNCT
ejpam-2627	41	19	where	where	SCONJ
ejpam-2627	41	20	the	the	DET
ejpam-2627	41	21	constant	constant	ADJ
ejpam-2627	41	22	cl	cl	NOUN
ejpam-2627	41	23	is	be	AUX
ejpam-2627	41	24	given	give	VERB
ejpam-2627	41	25	by	by	ADP
ejpam-2627	41	26	cl	cl	NOUN
ejpam-2627	41	27	=	=	SYM
ejpam-2627	41	28	∫	∫	PROPN
ejpam-2627	41	29	rd	rd	PROPN
ejpam-2627	41	30	e−	e−	PROPN
ejpam-2627	41	31	|z|2	|z|2	PROPN
ejpam-2627	41	32	2	2	NUM
ejpam-2627	41	33	wl(z)dz	wl(z)dz	NOUN
ejpam-2627	41	34	.	.	PUNCT
ejpam-2627	42	1	the	the	DET
ejpam-2627	42	2	dunkl	dunkl	NOUN
ejpam-2627	42	3	transform	transform	VERB
ejpam-2627	42	4	shares	share	NOUN
ejpam-2627	42	5	several	several	ADJ
ejpam-2627	42	6	properties	property	NOUN
ejpam-2627	42	7	with	with	ADP
ejpam-2627	42	8	its	its	PRON
ejpam-2627	42	9	counterpart	counterpart	NOUN
ejpam-2627	42	10	in	in	ADP
ejpam-2627	42	11	the	the	DET
ejpam-2627	42	12	classical	classical	ADJ
ejpam-2627	42	13	case	case	NOUN
ejpam-2627	42	14	,	,	PUNCT
ejpam-2627	42	15	we	we	PRON
ejpam-2627	42	16	mention	mention	VERB
ejpam-2627	42	17	here	here	ADV
ejpam-2627	42	18	in	in	ADP
ejpam-2627	42	19	particular	particular	ADJ
ejpam-2627	42	20	that	that	SCONJ
ejpam-2627	42	21	plancherel	plancherel	NOUN
ejpam-2627	42	22	’s	’s	PART
ejpam-2627	42	23	theorem	theorem	NOUN
ejpam-2627	42	24	holds	hold	VERB
ejpam-2627	42	25	in	in	ADP
ejpam-2627	42	26	l2	l2	NOUN
ejpam-2627	42	27	l	l	NOUN
ejpam-2627	42	28	(	(	PUNCT
ejpam-2627	42	29	rd	rd	NOUN
ejpam-2627	42	30	)	)	PUNCT
ejpam-2627	42	31	,	,	PUNCT
ejpam-2627	42	32	when	when	SCONJ
ejpam-2627	42	33	both	both	DET
ejpam-2627	42	34	f	f	PROPN
ejpam-2627	42	35	and	and	CCONJ
ejpam-2627	42	36	f̂	f̂	NUM
ejpam-2627	42	37	are	be	AUX
ejpam-2627	42	38	in	in	ADP
ejpam-2627	42	39	l1	l1	PROPN
ejpam-2627	42	40	l	l	PROPN
ejpam-2627	42	41	(	(	PUNCT
ejpam-2627	42	42	rd	rd	NOUN
ejpam-2627	42	43	)	)	PUNCT
ejpam-2627	42	44	,	,	PUNCT
ejpam-2627	42	45	we	we	PRON
ejpam-2627	42	46	have	have	VERB
ejpam-2627	42	47	the	the	DET
ejpam-2627	42	48	inversion	inversion	NOUN
ejpam-2627	42	49	formula	formula	NOUN
ejpam-2627	42	50	f(x	f(x	NOUN
ejpam-2627	42	51	)	)	PUNCT
ejpam-2627	43	1	=	=	SYM
ejpam-2627	43	2	∫	∫	PROPN
ejpam-2627	43	3	rd	rd	PROPN
ejpam-2627	43	4	f̂(ξ)el(ix	f̂(ξ)el(ix	PROPN
ejpam-2627	43	5	,	,	PUNCT
ejpam-2627	43	6	ξ)wl(ξ)dξ	ξ)wl(ξ)dξ	PROPN
ejpam-2627	43	7	,	,	PUNCT
ejpam-2627	43	8	x	x	PROPN
ejpam-2627	43	9	∈	∈	PROPN
ejpam-2627	43	10	rd	rd	PROPN
ejpam-2627	43	11	.	.	PUNCT
ejpam-2627	44	1	by	by	ADP
ejpam-2627	44	2	plancherel	plancherel	PROPN
ejpam-2627	44	3	’s	’s	PART
ejpam-2627	44	4	theorem	theorem	NOUN
ejpam-2627	44	5	and	and	CCONJ
ejpam-2627	44	6	the	the	DET
ejpam-2627	44	7	marcinkiewicz	marcinkiewicz	ADJ
ejpam-2627	44	8	interpolation	interpolation	NOUN
ejpam-2627	44	9	theorem	theorem	NOUN
ejpam-2627	44	10	(	(	PUNCT
ejpam-2627	44	11	see	see	VERB
ejpam-2627	44	12	[	[	X
ejpam-2627	44	13	10	10	NUM
ejpam-2627	44	14	]	]	NUM
ejpam-2627	44	15	)	)	PUNCT
ejpam-2627	44	16	,	,	PUNCT
ejpam-2627	44	17	we	we	PRON
ejpam-2627	44	18	get	get	VERB
ejpam-2627	44	19	for	for	ADP
ejpam-2627	44	20	f	f	PROPN
ejpam-2627	44	21	∈	∈	PROPN
ejpam-2627	44	22	lpl	lpl	PROPN
ejpam-2627	44	23	(	(	PUNCT
ejpam-2627	44	24	r	r	NOUN
ejpam-2627	44	25	d	d	NOUN
ejpam-2627	44	26	)	)	PUNCT
ejpam-2627	44	27	with	with	ADP
ejpam-2627	44	28	1	1	NUM
ejpam-2627	44	29	<	<	X
ejpam-2627	44	30	p	p	X
ejpam-2627	44	31	≤	≤	ADJ
ejpam-2627	44	32	2	2	NUM
ejpam-2627	44	33	and	and	CCONJ
ejpam-2627	44	34	q	q	NOUN
ejpam-2627	44	35	such	such	ADJ
ejpam-2627	44	36	that	that	SCONJ
ejpam-2627	44	37	1	1	NUM
ejpam-2627	44	38	p	p	NOUN
ejpam-2627	45	1	+	+	NOUN
ejpam-2627	45	2	1	1	NUM
ejpam-2627	45	3	q	q	NOUN
ejpam-2627	45	4	=	=	SYM
ejpam-2627	45	5	1	1	NUM
ejpam-2627	45	6	,	,	PUNCT
ejpam-2627	45	7	‖f(f)‖q	‖f(f)‖q	PROPN
ejpam-2627	45	8	,	,	PUNCT
ejpam-2627	45	9	l	l	PROPN
ejpam-2627	45	10	≤	≤	NUM
ejpam-2627	45	11	k‖f‖p	k‖f‖p	NOUN
ejpam-2627	45	12	,	,	PUNCT
ejpam-2627	45	13	l	l	NOUN
ejpam-2627	45	14	,	,	PUNCT
ejpam-2627	45	15	(	(	PUNCT
ejpam-2627	45	16	1	1	X
ejpam-2627	45	17	)	)	PUNCT
ejpam-2627	45	18	where	where	SCONJ
ejpam-2627	45	19	k	k	PROPN
ejpam-2627	45	20	is	be	AUX
ejpam-2627	45	21	a	a	DET
ejpam-2627	45	22	positive	positive	ADJ
ejpam-2627	45	23	constant	constant	NOUN
ejpam-2627	45	24	.	.	PUNCT
ejpam-2627	46	1	the	the	DET
ejpam-2627	46	2	generalized	generalized	ADJ
ejpam-2627	46	3	spherical	spherical	ADJ
ejpam-2627	46	4	mean	mean	NOUN
ejpam-2627	46	5	value	value	NOUN
ejpam-2627	46	6	of	of	ADP
ejpam-2627	46	7	f	f	PROPN
ejpam-2627	46	8	∈	∈	PROPN
ejpam-2627	46	9	lpl	lpl	PROPN
ejpam-2627	46	10	(	(	PUNCT
ejpam-2627	46	11	r	r	NOUN
ejpam-2627	46	12	d	d	PROPN
ejpam-2627	46	13	)	)	PUNCT
ejpam-2627	46	14	is	be	AUX
ejpam-2627	46	15	defined	define	VERB
ejpam-2627	46	16	by	by	ADP
ejpam-2627	46	17	mhf(x	mhf(x	PROPN
ejpam-2627	46	18	)	)	PUNCT
ejpam-2627	46	19	=	=	SYM
ejpam-2627	46	20	1	1	NUM
ejpam-2627	46	21	dl	dl	PROPN
ejpam-2627	46	22	∫	∫	PROPN
ejpam-2627	46	23	sd−1	sd−1	PROPN
ejpam-2627	46	24	τxf(hy)dµl(y	τxf(hy)dµl(y	NOUN
ejpam-2627	46	25	)	)	PUNCT
ejpam-2627	46	26	,	,	PUNCT
ejpam-2627	46	27	x	x	PROPN
ejpam-2627	46	28	∈	∈	PROPN
ejpam-2627	46	29	rd	rd	PROPN
ejpam-2627	46	30	,	,	PUNCT
ejpam-2627	46	31	h	h	PROPN
ejpam-2627	46	32	>	>	X
ejpam-2627	46	33	0	0	X
ejpam-2627	46	34	.	.	PUNCT
ejpam-2627	46	35	where	where	SCONJ
ejpam-2627	46	36	τx	τx	PART
ejpam-2627	46	37	dunkl	dunkl	VERB
ejpam-2627	46	38	translation	translation	NOUN
ejpam-2627	46	39	operator	operator	NOUN
ejpam-2627	46	40	(	(	PUNCT
ejpam-2627	46	41	see	see	VERB
ejpam-2627	46	42	[	[	X
ejpam-2627	46	43	9	9	NUM
ejpam-2627	46	44	,	,	PUNCT
ejpam-2627	46	45	11	11	NUM
ejpam-2627	46	46	]	]	NUM
ejpam-2627	46	47	)	)	PUNCT
ejpam-2627	46	48	,	,	PUNCT
ejpam-2627	46	49	µ	µ	X
ejpam-2627	46	50	be	be	AUX
ejpam-2627	46	51	the	the	DET
ejpam-2627	46	52	normalized	normalize	VERB
ejpam-2627	46	53	surface	surface	NOUN
ejpam-2627	46	54	measure	measure	NOUN
ejpam-2627	46	55	on	on	ADP
ejpam-2627	46	56	the	the	DET
ejpam-2627	46	57	unit	unit	NOUN
ejpam-2627	46	58	sphere	sphere	ADV
ejpam-2627	46	59	sd−1	sd−1	PROPN
ejpam-2627	46	60	in	in	ADP
ejpam-2627	46	61	rd	rd	NOUN
ejpam-2627	46	62	and	and	CCONJ
ejpam-2627	46	63	set	set	VERB
ejpam-2627	46	64	dµl(y	dµl(y	PROPN
ejpam-2627	46	65	)	)	PUNCT
ejpam-2627	46	66	=	=	SYM
ejpam-2627	46	67	wl(y)dµ(y	wl(y)dµ(y	PROPN
ejpam-2627	46	68	)	)	PUNCT
ejpam-2627	46	69	,	,	PUNCT
ejpam-2627	46	70	µl	µl	SCONJ
ejpam-2627	46	71	is	be	AUX
ejpam-2627	46	72	a	a	DET
ejpam-2627	46	73	w	w	ADJ
ejpam-2627	46	74	-	-	PUNCT
ejpam-2627	46	75	invariant	invariant	ADJ
ejpam-2627	46	76	measure	measure	NOUN
ejpam-2627	46	77	on	on	ADP
ejpam-2627	46	78	sd−1	sd−1	NOUN
ejpam-2627	46	79	and	and	CCONJ
ejpam-2627	46	80	dl	dl	NOUN
ejpam-2627	46	81	=	=	NOUN
ejpam-2627	46	82	µl(sd−1	µl(sd−1	NUM
ejpam-2627	46	83	)	)	PUNCT
ejpam-2627	46	84	.	.	PUNCT
ejpam-2627	47	1	we	we	PRON
ejpam-2627	47	2	see	see	VERB
ejpam-2627	47	3	that	that	DET
ejpam-2627	47	4	mhf	mhf	PROPN
ejpam-2627	47	5	∈	∈	PROPN
ejpam-2627	47	6	lpl	lpl	PROPN
ejpam-2627	47	7	(	(	PUNCT
ejpam-2627	47	8	r	r	NOUN
ejpam-2627	47	9	d	d	PROPN
ejpam-2627	47	10	)	)	PUNCT
ejpam-2627	47	11	whenever	whenever	SCONJ
ejpam-2627	47	12	f	f	PROPN
ejpam-2627	47	13	∈	∈	PROPN
ejpam-2627	47	14	lpl	lpl	PROPN
ejpam-2627	47	15	(	(	PUNCT
ejpam-2627	47	16	r	r	NOUN
ejpam-2627	47	17	d	d	PROPN
ejpam-2627	47	18	)	)	PUNCT
ejpam-2627	47	19	and	and	CCONJ
ejpam-2627	47	20	‖mhf‖p	‖mhf‖p	NOUN
ejpam-2627	47	21	,	,	PUNCT
ejpam-2627	47	22	l	l	NOUN
ejpam-2627	47	23	≤	≤	NUM
ejpam-2627	47	24	‖f‖p	‖f‖p	NOUN
ejpam-2627	47	25	,	,	PUNCT
ejpam-2627	47	26	l.	l.	NOUN
ejpam-2627	47	27	for	for	ADP
ejpam-2627	47	28	all	all	DET
ejpam-2627	47	29	h	h	NOUN
ejpam-2627	47	30	>	>	X
ejpam-2627	47	31	0	0	X
ejpam-2627	47	32	.	.	PUNCT
ejpam-2627	48	1	for	for	ADP
ejpam-2627	48	2	β	β	X
ejpam-2627	48	3	≥	≥	X
ejpam-2627	48	4	−12	−12	PRON
ejpam-2627	48	5	,	,	PUNCT
ejpam-2627	48	6	we	we	PRON
ejpam-2627	48	7	introduce	introduce	VERB
ejpam-2627	48	8	the	the	DET
ejpam-2627	48	9	bessel	bessel	NOUN
ejpam-2627	48	10	normalized	normalize	VERB
ejpam-2627	48	11	function	function	NOUN
ejpam-2627	48	12	of	of	ADP
ejpam-2627	48	13	the	the	DET
ejpam-2627	48	14	first	first	ADJ
ejpam-2627	48	15	kind	kind	NOUN
ejpam-2627	48	16	jβ	jβ	PROPN
ejpam-2627	48	17	defined	define	VERB
ejpam-2627	48	18	by	by	ADP
ejpam-2627	48	19	jβ(z	jβ(z	X
ejpam-2627	48	20	)	)	PUNCT
ejpam-2627	49	1	=	=	PUNCT
ejpam-2627	50	1	γ(β	γ(β	PROPN
ejpam-2627	50	2	+	+	CCONJ
ejpam-2627	50	3	1	1	X
ejpam-2627	50	4	)	)	PUNCT
ejpam-2627	50	5	∞∑	∞∑	NUM
ejpam-2627	50	6	n=0	n=0	NUM
ejpam-2627	50	7	(	(	PUNCT
ejpam-2627	50	8	−1)n(z/2)2n	−1)n(z/2)2n	ADJ
ejpam-2627	50	9	n!γ(n+	n!γ(n+	NOUN
ejpam-2627	50	10	β	β	X
ejpam-2627	50	11	+	+	NOUN
ejpam-2627	50	12	1	1	NUM
ejpam-2627	50	13	)	)	PUNCT
ejpam-2627	50	14	,	,	PUNCT
ejpam-2627	50	15	z	z	PROPN
ejpam-2627	50	16	∈	∈	PROPN
ejpam-2627	50	17	c.	c.	NOUN
ejpam-2627	50	18	(	(	PUNCT
ejpam-2627	50	19	2	2	X
ejpam-2627	50	20	)	)	PUNCT
ejpam-2627	50	21	lemma	lemma	PROPN
ejpam-2627	50	22	2	2	NUM
ejpam-2627	50	23	.	.	PUNCT
ejpam-2627	50	24	(	(	PUNCT
ejpam-2627	50	25	analog	analog	NOUN
ejpam-2627	50	26	of	of	ADP
ejpam-2627	50	27	lemma	lemma	PROPN
ejpam-2627	50	28	2.9	2.9	NUM
ejpam-2627	50	29	in	in	ADP
ejpam-2627	50	30	[	[	X
ejpam-2627	50	31	2	2	NUM
ejpam-2627	50	32	]	]	PUNCT
ejpam-2627	50	33	)	)	PUNCT
ejpam-2627	50	34	the	the	DET
ejpam-2627	50	35	following	follow	VERB
ejpam-2627	50	36	inequality	inequality	NOUN
ejpam-2627	50	37	is	be	AUX
ejpam-2627	50	38	true	true	ADJ
ejpam-2627	50	39	|1−	|1−	X
ejpam-2627	50	40	jβ(x)|	jβ(x)|	PUNCT
ejpam-2627	50	41	≥	≥	PROPN
ejpam-2627	50	42	c	c	NOUN
ejpam-2627	50	43	,	,	PUNCT
ejpam-2627	50	44	with	with	ADP
ejpam-2627	50	45	|x|	|x|	PROPN
ejpam-2627	50	46	≥	≥	NUM
ejpam-2627	50	47	1	1	NUM
ejpam-2627	50	48	,	,	PUNCT
ejpam-2627	50	49	where	where	SCONJ
ejpam-2627	50	50	c	c	NOUN
ejpam-2627	50	51	>	>	X
ejpam-2627	50	52	0	0	PUNCT
ejpam-2627	50	53	is	be	AUX
ejpam-2627	50	54	a	a	DET
ejpam-2627	50	55	certain	certain	ADJ
ejpam-2627	50	56	constant	constant	NOUN
ejpam-2627	50	57	which	which	PRON
ejpam-2627	50	58	depend	depend	VERB
ejpam-2627	50	59	only	only	ADV
ejpam-2627	50	60	on	on	ADP
ejpam-2627	50	61	β	β	X
ejpam-2627	50	62	.	.	PUNCT
ejpam-2627	51	1	s.	s.	PROPN
ejpam-2627	51	2	el	el	PROPN
ejpam-2627	51	3	ouadih	ouadih	PROPN
ejpam-2627	51	4	,	,	PUNCT
ejpam-2627	51	5	r.	r.	PROPN
ejpam-2627	51	6	daher	daher	PROPN
ejpam-2627	51	7	/	/	SYM
ejpam-2627	51	8	eur	eur	PROPN
ejpam-2627	51	9	.	.	PUNCT
ejpam-2627	52	1	j.	j.	PROPN
ejpam-2627	52	2	pure	pure	PROPN
ejpam-2627	52	3	appl	appl	PROPN
ejpam-2627	52	4	.	.	PROPN
ejpam-2627	52	5	math	math	PROPN
ejpam-2627	52	6	,	,	PUNCT
ejpam-2627	52	7	10	10	NUM
ejpam-2627	52	8	(	(	PUNCT
ejpam-2627	52	9	3	3	NUM
ejpam-2627	52	10	)	)	PUNCT
ejpam-2627	52	11	(	(	PUNCT
ejpam-2627	52	12	2017	2017	NUM
ejpam-2627	52	13	)	)	PUNCT
ejpam-2627	52	14	,	,	PUNCT
ejpam-2627	52	15	544	544	NUM
ejpam-2627	52	16	-	-	SYM
ejpam-2627	52	17	551	551	NUM
ejpam-2627	52	18	547	547	NUM
ejpam-2627	52	19	moreover	moreover	ADV
ejpam-2627	52	20	,	,	PUNCT
ejpam-2627	52	21	from	from	ADP
ejpam-2627	52	22	(	(	PUNCT
ejpam-2627	52	23	1	1	X
ejpam-2627	52	24	)	)	PUNCT
ejpam-2627	52	25	we	we	PRON
ejpam-2627	52	26	see	see	VERB
ejpam-2627	52	27	that	that	SCONJ
ejpam-2627	52	28	lim	lim	PROPN
ejpam-2627	52	29	z→0	z→0	PROPN
ejpam-2627	52	30	jγ+	jγ+	PROPN
ejpam-2627	53	1	d	d	PROPN
ejpam-2627	53	2	2	2	NUM
ejpam-2627	53	3	−1(z)−	−1(z)−	PROPN
ejpam-2627	53	4	1	1	NUM
ejpam-2627	53	5	z2	z2	PROPN
ejpam-2627	53	6	6=	6=	ADP
ejpam-2627	53	7	0	0	NUM
ejpam-2627	53	8	.	.	PUNCT
ejpam-2627	54	1	(	(	PUNCT
ejpam-2627	54	2	3	3	X
ejpam-2627	54	3	)	)	PUNCT
ejpam-2627	54	4	lemma	lemma	PROPN
ejpam-2627	54	5	3	3	X
ejpam-2627	54	6	.	.	PUNCT
ejpam-2627	55	1	[	[	X
ejpam-2627	55	2	7	7	X
ejpam-2627	55	3	]	]	PUNCT
ejpam-2627	55	4	let	let	VERB
ejpam-2627	55	5	f	f	PROPN
ejpam-2627	55	6	∈	∈	PROPN
ejpam-2627	55	7	lpl	lpl	PROPN
ejpam-2627	55	8	(	(	PUNCT
ejpam-2627	55	9	r	r	NOUN
ejpam-2627	55	10	d	d	PROPN
ejpam-2627	55	11	)	)	PUNCT
ejpam-2627	55	12	.	.	PUNCT
ejpam-2627	56	1	then	then	ADV
ejpam-2627	56	2	m̂hf(ξ	m̂hf(ξ	X
ejpam-2627	56	3	)	)	PUNCT
ejpam-2627	56	4	=	=	SYM
ejpam-2627	57	1	jγ+	jγ+	NOUN
ejpam-2627	57	2	d	d	PROPN
ejpam-2627	57	3	2	2	NUM
ejpam-2627	57	4	−1(h|ξ|)f̂(ξ	−1(h|ξ|)f̂(ξ	NUM
ejpam-2627	57	5	)	)	PUNCT
ejpam-2627	57	6	.	.	PUNCT
ejpam-2627	58	1	the	the	DET
ejpam-2627	58	2	first	first	ADJ
ejpam-2627	58	3	and	and	CCONJ
ejpam-2627	58	4	higher	high	ADJ
ejpam-2627	58	5	order	order	NOUN
ejpam-2627	58	6	finite	finite	VERB
ejpam-2627	58	7	differences	difference	NOUN
ejpam-2627	58	8	of	of	ADP
ejpam-2627	58	9	f	f	PROPN
ejpam-2627	58	10	(	(	PUNCT
ejpam-2627	58	11	x	x	X
ejpam-2627	58	12	)	)	PUNCT
ejpam-2627	58	13	are	be	AUX
ejpam-2627	58	14	defined	define	VERB
ejpam-2627	58	15	as	as	SCONJ
ejpam-2627	58	16	follows	follow	VERB
ejpam-2627	58	17	zhf(x	zhf(x	PROPN
ejpam-2627	58	18	)	)	PUNCT
ejpam-2627	58	19	=	=	PUNCT
ejpam-2627	59	1	(	(	PUNCT
ejpam-2627	59	2	mh	mh	PROPN
ejpam-2627	59	3	−	−	PROPN
ejpam-2627	59	4	i)f(x	i)f(x	PROPN
ejpam-2627	59	5	)	)	PUNCT
ejpam-2627	59	6	,	,	PUNCT
ejpam-2627	59	7	where	where	SCONJ
ejpam-2627	59	8	i	i	PRON
ejpam-2627	59	9	is	be	AUX
ejpam-2627	59	10	the	the	DET
ejpam-2627	59	11	identity	identity	NOUN
ejpam-2627	59	12	operator	operator	NOUN
ejpam-2627	59	13	lpl	lpl	PROPN
ejpam-2627	59	14	(	(	PUNCT
ejpam-2627	59	15	r	r	NOUN
ejpam-2627	59	16	d	d	PROPN
ejpam-2627	59	17	)	)	PUNCT
ejpam-2627	59	18	.	.	PUNCT
ejpam-2627	60	1	zkhf(x	zkhf(x	X
ejpam-2627	60	2	)	)	PUNCT
ejpam-2627	60	3	=	=	SYM
ejpam-2627	60	4	zh(zk−1h	zh(zk−1h	NUM
ejpam-2627	60	5	f(x	f(x	PROPN
ejpam-2627	60	6	)	)	PUNCT
ejpam-2627	60	7	)	)	PUNCT
ejpam-2627	61	1	=	=	PRON
ejpam-2627	61	2	(	(	PUNCT
ejpam-2627	61	3	mh	mh	PROPN
ejpam-2627	61	4	−	−	PROPN
ejpam-2627	61	5	i)kf(x	i)kf(x	PROPN
ejpam-2627	61	6	)	)	PUNCT
ejpam-2627	61	7	=	=	PUNCT
ejpam-2627	62	1	k∑	k∑	PROPN
ejpam-2627	63	1	i=0	i=0	ADJ
ejpam-2627	63	2	(	(	PUNCT
ejpam-2627	63	3	−1)k−i(ki	−1)k−i(ki	NOUN
ejpam-2627	63	4	)	)	PUNCT
ejpam-2627	63	5	m	m	VERB
ejpam-2627	63	6	i	i	PRON
ejpam-2627	63	7	hf(x	hf(x	NOUN
ejpam-2627	63	8	)	)	PUNCT
ejpam-2627	63	9	,	,	PUNCT
ejpam-2627	63	10	where	where	SCONJ
ejpam-2627	63	11	m0	m0	PROPN
ejpam-2627	63	12	hf(x	hf(x	PUNCT
ejpam-2627	63	13	)	)	PUNCT
ejpam-2627	63	14	=	=	SYM
ejpam-2627	63	15	f(x	f(x	PROPN
ejpam-2627	63	16	)	)	PUNCT
ejpam-2627	63	17	,	,	PUNCT
ejpam-2627	63	18	m	m	VERB
ejpam-2627	63	19	i	i	PRON
ejpam-2627	63	20	hf(x	hf(x	ADV
ejpam-2627	63	21	)	)	PUNCT
ejpam-2627	63	22	=	=	PUNCT
ejpam-2627	63	23	mh(m	mh(m	NOUN
ejpam-2627	63	24	i−1	i−1	PROPN
ejpam-2627	63	25	h	h	NOUN
ejpam-2627	63	26	f(x	f(x	PROPN
ejpam-2627	63	27	)	)	PUNCT
ejpam-2627	63	28	)	)	PUNCT
ejpam-2627	63	29	,	,	PUNCT
ejpam-2627	63	30	i	i	PRON
ejpam-2627	63	31	=	=	NOUN
ejpam-2627	63	32	1	1	NUM
ejpam-2627	63	33	,	,	PUNCT
ejpam-2627	63	34	2	2	NUM
ejpam-2627	63	35	,	,	PUNCT
ejpam-2627	63	36	..	..	PUNCT
ejpam-2627	63	37	and	and	CCONJ
ejpam-2627	63	38	k	k	X
ejpam-2627	63	39	=	=	SYM
ejpam-2627	63	40	1	1	NUM
ejpam-2627	63	41	,	,	PUNCT
ejpam-2627	63	42	2	2	NUM
ejpam-2627	63	43	,	,	PUNCT
ejpam-2627	63	44	...	...	PUNCT
ejpam-2627	63	45	from	from	ADP
ejpam-2627	63	46	lemma	lemma	PROPN
ejpam-2627	63	47	3	3	NUM
ejpam-2627	63	48	,	,	PUNCT
ejpam-2627	63	49	we	we	PRON
ejpam-2627	63	50	obtain	obtain	VERB
ejpam-2627	63	51	ẑkhf(ξ	ẑkhf(ξ	NOUN
ejpam-2627	63	52	)	)	PUNCT
ejpam-2627	63	53	=	=	PUNCT
ejpam-2627	63	54	(	(	PUNCT
ejpam-2627	63	55	jγ+	jγ+	NOUN
ejpam-2627	63	56	d	d	PROPN
ejpam-2627	63	57	2	2	NUM
ejpam-2627	63	58	−1(h|ξ|)−	−1(h|ξ|)−	PROPN
ejpam-2627	63	59	1)kf̂(ξ	1)kf̂(ξ	NUM
ejpam-2627	63	60	)	)	PUNCT
ejpam-2627	63	61	.	.	PUNCT
ejpam-2627	64	1	by	by	ADP
ejpam-2627	64	2	(	(	PUNCT
ejpam-2627	64	3	1	1	NUM
ejpam-2627	64	4	)	)	PUNCT
ejpam-2627	64	5	,	,	PUNCT
ejpam-2627	64	6	we	we	PRON
ejpam-2627	64	7	have∫	have∫	VERB
ejpam-2627	64	8	rd	rd	PROPN
ejpam-2627	64	9	|1−	|1−	PROPN
ejpam-2627	64	10	jγ+	jγ+	PROPN
ejpam-2627	65	1	d	d	PROPN
ejpam-2627	65	2	2	2	NUM
ejpam-2627	65	3	−1(h|ξ|)|	−1(h|ξ|)|	NOUN
ejpam-2627	65	4	qk|f̂(ξ)|qwl(ξ)dξ	qk|f̂(ξ)|qwl(ξ)dξ	NOUN
ejpam-2627	65	5	≤	≤	NUM
ejpam-2627	65	6	kq‖zkhf(x)‖qp	kq‖zkhf(x)‖qp	PROPN
ejpam-2627	65	7	,	,	PUNCT
ejpam-2627	65	8	l	l	NOUN
ejpam-2627	65	9	,	,	PUNCT
ejpam-2627	65	10	(	(	PUNCT
ejpam-2627	65	11	4	4	X
ejpam-2627	65	12	)	)	PUNCT
ejpam-2627	66	1	where	where	SCONJ
ejpam-2627	66	2	1	1	NUM
ejpam-2627	66	3	p	p	NOUN
ejpam-2627	66	4	+	+	NOUN
ejpam-2627	66	5	1	1	NUM
ejpam-2627	66	6	q	q	NOUN
ejpam-2627	66	7	=	=	NOUN
ejpam-2627	66	8	1	1	NUM
ejpam-2627	66	9	.	.	NOUN
ejpam-2627	66	10	2	2	NUM
ejpam-2627	66	11	.	.	X
ejpam-2627	66	12	dunkl	dunkl	NOUN
ejpam-2627	66	13	dini	dini	NOUN
ejpam-2627	66	14	lipschitz	lipschitz	PROPN
ejpam-2627	66	15	condition	condition	NOUN
ejpam-2627	66	16	definition	definition	NOUN
ejpam-2627	66	17	1	1	NUM
ejpam-2627	66	18	.	.	PUNCT
ejpam-2627	67	1	let	let	VERB
ejpam-2627	67	2	f	f	PROPN
ejpam-2627	67	3	∈	∈	PROPN
ejpam-2627	67	4	lpl	lpl	PROPN
ejpam-2627	67	5	(	(	PUNCT
ejpam-2627	67	6	r	r	NOUN
ejpam-2627	67	7	d	d	PROPN
ejpam-2627	67	8	)	)	PUNCT
ejpam-2627	67	9	,	,	PUNCT
ejpam-2627	67	10	and	and	CCONJ
ejpam-2627	67	11	define	define	VERB
ejpam-2627	67	12	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	67	13	,	,	PUNCT
ejpam-2627	67	14	l	l	PROPN
ejpam-2627	67	15	≤	≤	NUM
ejpam-2627	68	1	c	c	X
ejpam-2627	68	2	hη	hη	PROPN
ejpam-2627	68	3	(	(	PUNCT
ejpam-2627	68	4	log	log	NOUN
ejpam-2627	68	5	1	1	NUM
ejpam-2627	68	6	h)δ	h)δ	ADJ
ejpam-2627	68	7	,	,	PUNCT
ejpam-2627	68	8	δ	δ	PROPN
ejpam-2627	68	9	≥	≥	NOUN
ejpam-2627	68	10	0	0	NUM
ejpam-2627	68	11	,	,	PUNCT
ejpam-2627	68	12	i.e.	i.e.	X
ejpam-2627	68	13	,	,	PUNCT
ejpam-2627	68	14	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	68	15	,	,	PUNCT
ejpam-2627	68	16	l	l	NOUN
ejpam-2627	68	17	=	=	PUNCT
ejpam-2627	68	18	o	o	X
ejpam-2627	68	19	(	(	PUNCT
ejpam-2627	68	20	hη	hη	PROPN
ejpam-2627	68	21	(	(	PUNCT
ejpam-2627	68	22	log	log	NOUN
ejpam-2627	68	23	1	1	NUM
ejpam-2627	68	24	h)δ	h)δ	NUM
ejpam-2627	68	25	)	)	PUNCT
ejpam-2627	68	26	,	,	PUNCT
ejpam-2627	68	27	for	for	ADP
ejpam-2627	68	28	all	all	DET
ejpam-2627	68	29	x	x	NOUN
ejpam-2627	68	30	in	in	ADP
ejpam-2627	68	31	rd	rd	NOUN
ejpam-2627	68	32	and	and	CCONJ
ejpam-2627	68	33	for	for	ADP
ejpam-2627	68	34	all	all	DET
ejpam-2627	68	35	sufficiently	sufficiently	ADV
ejpam-2627	68	36	small	small	ADJ
ejpam-2627	68	37	h	h	NOUN
ejpam-2627	68	38	,	,	PUNCT
ejpam-2627	68	39	c	c	PROPN
ejpam-2627	68	40	being	be	AUX
ejpam-2627	68	41	a	a	DET
ejpam-2627	68	42	positive	positive	ADJ
ejpam-2627	68	43	constant	constant	NOUN
ejpam-2627	68	44	.	.	PUNCT
ejpam-2627	69	1	then	then	ADV
ejpam-2627	69	2	we	we	PRON
ejpam-2627	69	3	say	say	VERB
ejpam-2627	69	4	that	that	SCONJ
ejpam-2627	69	5	f	f	PROPN
ejpam-2627	69	6	satisfies	satisfy	VERB
ejpam-2627	69	7	a	a	DET
ejpam-2627	69	8	d	d	ADJ
ejpam-2627	69	9	-	-	PUNCT
ejpam-2627	69	10	dunkl	dunkl	NOUN
ejpam-2627	69	11	dini	dini	NOUN
ejpam-2627	69	12	lipschitz	lipschitz	NOUN
ejpam-2627	69	13	of	of	ADP
ejpam-2627	69	14	order	order	NOUN
ejpam-2627	69	15	η	η	PROPN
ejpam-2627	69	16	,	,	PUNCT
ejpam-2627	69	17	or	or	CCONJ
ejpam-2627	69	18	f	f	PROPN
ejpam-2627	69	19	belongs	belong	VERB
ejpam-2627	69	20	to	to	ADP
ejpam-2627	69	21	lip(η	lip(η	PROPN
ejpam-2627	69	22	,	,	PUNCT
ejpam-2627	69	23	δ	δ	PROPN
ejpam-2627	69	24	)	)	PUNCT
ejpam-2627	69	25	.	.	PUNCT
ejpam-2627	70	1	s.	s.	PROPN
ejpam-2627	70	2	el	el	PROPN
ejpam-2627	70	3	ouadih	ouadih	PROPN
ejpam-2627	70	4	,	,	PUNCT
ejpam-2627	70	5	r.	r.	PROPN
ejpam-2627	70	6	daher	daher	PROPN
ejpam-2627	70	7	/	/	SYM
ejpam-2627	70	8	eur	eur	PROPN
ejpam-2627	70	9	.	.	PUNCT
ejpam-2627	71	1	j.	j.	PROPN
ejpam-2627	71	2	pure	pure	PROPN
ejpam-2627	71	3	appl	appl	PROPN
ejpam-2627	71	4	.	.	PROPN
ejpam-2627	71	5	math	math	PROPN
ejpam-2627	71	6	,	,	PUNCT
ejpam-2627	71	7	10	10	NUM
ejpam-2627	71	8	(	(	PUNCT
ejpam-2627	71	9	3	3	NUM
ejpam-2627	71	10	)	)	PUNCT
ejpam-2627	71	11	(	(	PUNCT
ejpam-2627	71	12	2017	2017	NUM
ejpam-2627	71	13	)	)	PUNCT
ejpam-2627	71	14	,	,	PUNCT
ejpam-2627	71	15	544	544	NUM
ejpam-2627	71	16	-	-	SYM
ejpam-2627	71	17	551	551	NUM
ejpam-2627	71	18	548	548	NUM
ejpam-2627	71	19	definition	definition	NOUN
ejpam-2627	71	20	2	2	NUM
ejpam-2627	71	21	.	.	PUNCT
ejpam-2627	72	1	if	if	SCONJ
ejpam-2627	72	2	however	however	ADV
ejpam-2627	72	3	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	72	4	,	,	PUNCT
ejpam-2627	72	5	l	l	PROPN
ejpam-2627	72	6	hη	hη	PROPN
ejpam-2627	72	7	(	(	PUNCT
ejpam-2627	72	8	log	log	NOUN
ejpam-2627	72	9	1	1	NUM
ejpam-2627	72	10	h	h	NOUN
ejpam-2627	72	11	)	)	PUNCT
ejpam-2627	72	12	δ	δ	PROPN
ejpam-2627	72	13	→	→	X
ejpam-2627	72	14	0	0	NUM
ejpam-2627	72	15	,	,	PUNCT
ejpam-2627	72	16	as	as	ADP
ejpam-2627	72	17	h→	h→	NOUN
ejpam-2627	72	18	0	0	NUM
ejpam-2627	72	19	,	,	PUNCT
ejpam-2627	72	20	i.e.	i.e.	X
ejpam-2627	72	21	,	,	PUNCT
ejpam-2627	72	22	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	72	23	,	,	PUNCT
ejpam-2627	72	24	l	l	NOUN
ejpam-2627	72	25	=	=	PUNCT
ejpam-2627	72	26	o	o	X
ejpam-2627	72	27	(	(	PUNCT
ejpam-2627	72	28	hη	hη	PROPN
ejpam-2627	72	29	(	(	PUNCT
ejpam-2627	72	30	log	log	NOUN
ejpam-2627	72	31	1	1	NUM
ejpam-2627	72	32	h)δ	h)δ	NUM
ejpam-2627	72	33	)	)	PUNCT
ejpam-2627	72	34	,	,	PUNCT
ejpam-2627	72	35	as	as	ADP
ejpam-2627	72	36	h→	h→	NOUN
ejpam-2627	72	37	0	0	NUM
ejpam-2627	72	38	,	,	PUNCT
ejpam-2627	72	39	δ	δ	PROPN
ejpam-2627	72	40	≥	≥	NOUN
ejpam-2627	72	41	0	0	NUM
ejpam-2627	72	42	,	,	PUNCT
ejpam-2627	72	43	then	then	ADV
ejpam-2627	72	44	f	f	PROPN
ejpam-2627	72	45	is	be	AUX
ejpam-2627	72	46	said	say	VERB
ejpam-2627	72	47	to	to	PART
ejpam-2627	72	48	be	be	AUX
ejpam-2627	72	49	belong	belong	VERB
ejpam-2627	72	50	to	to	ADP
ejpam-2627	72	51	the	the	DET
ejpam-2627	72	52	little	little	ADJ
ejpam-2627	72	53	d	d	ADJ
ejpam-2627	72	54	-	-	PUNCT
ejpam-2627	72	55	dunkl	dunkl	NOUN
ejpam-2627	72	56	dini	dini	NOUN
ejpam-2627	72	57	lipschitz	lipschitz	PROPN
ejpam-2627	72	58	class	class	NOUN
ejpam-2627	72	59	lip(η	lip(η	PROPN
ejpam-2627	72	60	,	,	PUNCT
ejpam-2627	72	61	δ	δ	PROPN
ejpam-2627	72	62	)	)	PUNCT
ejpam-2627	72	63	.	.	PUNCT
ejpam-2627	73	1	remark	remark	PROPN
ejpam-2627	73	2	.	.	PUNCT
ejpam-2627	74	1	it	it	PRON
ejpam-2627	74	2	follows	follow	VERB
ejpam-2627	74	3	immediately	immediately	ADV
ejpam-2627	74	4	from	from	ADP
ejpam-2627	74	5	these	these	DET
ejpam-2627	74	6	definitions	definition	NOUN
ejpam-2627	74	7	that	that	SCONJ
ejpam-2627	74	8	lip(η	lip(η	NOUN
ejpam-2627	74	9	,	,	PUNCT
ejpam-2627	74	10	δ	δ	PROPN
ejpam-2627	74	11	)	)	PUNCT
ejpam-2627	74	12	⊂	⊂	PROPN
ejpam-2627	74	13	lip(η	lip(η	PROPN
ejpam-2627	74	14	,	,	PUNCT
ejpam-2627	74	15	δ	δ	PROPN
ejpam-2627	74	16	)	)	PUNCT
ejpam-2627	74	17	.	.	PUNCT
ejpam-2627	75	1	theorem	theorem	NOUN
ejpam-2627	75	2	2	2	NUM
ejpam-2627	75	3	.	.	PUNCT
ejpam-2627	76	1	let	let	VERB
ejpam-2627	76	2	η	η	PROPN
ejpam-2627	76	3	>	>	X
ejpam-2627	76	4	1	1	NUM
ejpam-2627	76	5	.	.	PUNCT
ejpam-2627	77	1	if	if	SCONJ
ejpam-2627	77	2	f	f	PROPN
ejpam-2627	77	3	∈	∈	PROPN
ejpam-2627	77	4	lip(η	lip(η	PROPN
ejpam-2627	77	5	,	,	PUNCT
ejpam-2627	77	6	δ	δ	PROPN
ejpam-2627	77	7	)	)	PUNCT
ejpam-2627	77	8	,	,	PUNCT
ejpam-2627	77	9	then	then	ADV
ejpam-2627	77	10	f	f	PROPN
ejpam-2627	77	11	∈	∈	PROPN
ejpam-2627	77	12	lip(1	lip(1	PROPN
ejpam-2627	77	13	,	,	PUNCT
ejpam-2627	77	14	δ	δ	PROPN
ejpam-2627	77	15	)	)	PUNCT
ejpam-2627	77	16	.	.	PUNCT
ejpam-2627	78	1	proof	proof	NOUN
ejpam-2627	78	2	.	.	PUNCT
ejpam-2627	79	1	for	for	ADP
ejpam-2627	79	2	x	x	PROPN
ejpam-2627	79	3	∈	∈	PROPN
ejpam-2627	79	4	rd	rd	PROPN
ejpam-2627	79	5	,	,	PUNCT
ejpam-2627	79	6	h	h	NOUN
ejpam-2627	79	7	small	small	ADJ
ejpam-2627	79	8	and	and	CCONJ
ejpam-2627	79	9	f	f	PROPN
ejpam-2627	79	10	∈	∈	PROPN
ejpam-2627	79	11	lip(η	lip(η	PROPN
ejpam-2627	79	12	,	,	PUNCT
ejpam-2627	79	13	δ	δ	PROPN
ejpam-2627	79	14	)	)	PUNCT
ejpam-2627	80	1	we	we	PRON
ejpam-2627	80	2	have	have	VERB
ejpam-2627	80	3	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	80	4	,	,	PUNCT
ejpam-2627	80	5	l	l	PROPN
ejpam-2627	80	6	≤	≤	NUM
ejpam-2627	81	1	c	c	X
ejpam-2627	81	2	hη	hη	PROPN
ejpam-2627	81	3	(	(	PUNCT
ejpam-2627	81	4	log	log	NOUN
ejpam-2627	81	5	1	1	NUM
ejpam-2627	81	6	h)δ	h)δ	ADJ
ejpam-2627	81	7	.	.	PUNCT
ejpam-2627	82	1	then	then	ADV
ejpam-2627	82	2	(	(	PUNCT
ejpam-2627	82	3	log	log	NOUN
ejpam-2627	82	4	1	1	NUM
ejpam-2627	82	5	h	h	NOUN
ejpam-2627	82	6	)	)	PUNCT
ejpam-2627	82	7	δ‖zkhf(x)‖p	δ‖zkhf(x)‖p	NOUN
ejpam-2627	82	8	,	,	PUNCT
ejpam-2627	82	9	l	l	NOUN
ejpam-2627	82	10	≤	≤	NUM
ejpam-2627	82	11	chη	chη	NOUN
ejpam-2627	82	12	.	.	PUNCT
ejpam-2627	83	1	therefore	therefore	ADV
ejpam-2627	83	2	(	(	PUNCT
ejpam-2627	83	3	log	log	NOUN
ejpam-2627	83	4	1	1	NUM
ejpam-2627	83	5	h)δ	h)δ	NOUN
ejpam-2627	83	6	h	h	NOUN
ejpam-2627	83	7	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	83	8	,	,	PUNCT
ejpam-2627	83	9	l	l	PROPN
ejpam-2627	83	10	≤	≤	PROPN
ejpam-2627	83	11	chη−1	chη−1	PROPN
ejpam-2627	83	12	,	,	PUNCT
ejpam-2627	83	13	which	which	PRON
ejpam-2627	83	14	tends	tend	VERB
ejpam-2627	83	15	to	to	ADP
ejpam-2627	83	16	zero	zero	NUM
ejpam-2627	83	17	with	with	ADP
ejpam-2627	83	18	h→	h→	PROPN
ejpam-2627	83	19	0	0	NUM
ejpam-2627	83	20	.	.	PUNCT
ejpam-2627	84	1	thus	thus	ADV
ejpam-2627	84	2	(	(	PUNCT
ejpam-2627	84	3	log	log	NOUN
ejpam-2627	84	4	1	1	NUM
ejpam-2627	84	5	h)δ	h)δ	NOUN
ejpam-2627	84	6	h	h	NOUN
ejpam-2627	84	7	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	84	8	,	,	PUNCT
ejpam-2627	84	9	l	l	PROPN
ejpam-2627	84	10	→	→	SYM
ejpam-2627	84	11	0	0	NUM
ejpam-2627	84	12	,	,	PUNCT
ejpam-2627	84	13	h→	h→	NOUN
ejpam-2627	84	14	0	0	NUM
ejpam-2627	84	15	.	.	PUNCT
ejpam-2627	85	1	then	then	ADV
ejpam-2627	85	2	f	f	PROPN
ejpam-2627	85	3	∈	∈	PROPN
ejpam-2627	85	4	lip(1	lip(1	PROPN
ejpam-2627	85	5	,	,	PUNCT
ejpam-2627	85	6	δ	δ	PROPN
ejpam-2627	85	7	)	)	PUNCT
ejpam-2627	85	8	.	.	PUNCT
ejpam-2627	86	1	theorem	theorem	NOUN
ejpam-2627	86	2	3	3	NUM
ejpam-2627	86	3	.	.	PUNCT
ejpam-2627	87	1	if	if	SCONJ
ejpam-2627	87	2	η	η	PROPN
ejpam-2627	87	3	<	<	X
ejpam-2627	87	4	ν	ν	PROPN
ejpam-2627	87	5	,	,	PUNCT
ejpam-2627	87	6	then	then	ADV
ejpam-2627	87	7	lip(η	lip(η	PROPN
ejpam-2627	87	8	,	,	PUNCT
ejpam-2627	87	9	0	0	NUM
ejpam-2627	87	10	)	)	PUNCT
ejpam-2627	87	11	⊃	⊃	PROPN
ejpam-2627	87	12	lip(ν	lip(ν	PROPN
ejpam-2627	87	13	,	,	PUNCT
ejpam-2627	87	14	0	0	NUM
ejpam-2627	87	15	)	)	PUNCT
ejpam-2627	87	16	and	and	CCONJ
ejpam-2627	87	17	lip(η	lip(η	PROPN
ejpam-2627	87	18	,	,	PUNCT
ejpam-2627	87	19	0	0	NUM
ejpam-2627	87	20	)	)	PUNCT
ejpam-2627	87	21	⊃	⊃	PROPN
ejpam-2627	87	22	lip(ν	lip(ν	PROPN
ejpam-2627	87	23	,	,	PUNCT
ejpam-2627	87	24	0	0	NUM
ejpam-2627	87	25	)	)	PUNCT
ejpam-2627	87	26	.	.	PUNCT
ejpam-2627	88	1	proof	proof	NOUN
ejpam-2627	88	2	.	.	PUNCT
ejpam-2627	89	1	we	we	PRON
ejpam-2627	89	2	have	have	VERB
ejpam-2627	89	3	0	0	NUM
ejpam-2627	89	4	≤	≤	NUM
ejpam-2627	89	5	h	h	NOUN
ejpam-2627	89	6	≤	≤	NOUN
ejpam-2627	89	7	1	1	NUM
ejpam-2627	89	8	and	and	CCONJ
ejpam-2627	89	9	η	η	NOUN
ejpam-2627	89	10	<	<	X
ejpam-2627	89	11	ν	ν	PROPN
ejpam-2627	89	12	,	,	PUNCT
ejpam-2627	89	13	then	then	ADV
ejpam-2627	89	14	hν	hν	VERB
ejpam-2627	89	15	≤	≤	NUM
ejpam-2627	89	16	hη	hη	PRON
ejpam-2627	89	17	.	.	PUNCT
ejpam-2627	90	1	then	then	ADV
ejpam-2627	90	2	the	the	DET
ejpam-2627	90	3	proof	proof	NOUN
ejpam-2627	90	4	of	of	ADP
ejpam-2627	90	5	the	the	DET
ejpam-2627	90	6	theorem	theorem	NOUN
ejpam-2627	90	7	is	be	AUX
ejpam-2627	90	8	immediate	immediate	ADJ
ejpam-2627	90	9	.	.	PUNCT
ejpam-2627	91	1	3	3	X
ejpam-2627	91	2	.	.	X
ejpam-2627	91	3	new	new	ADJ
ejpam-2627	91	4	results	result	NOUN
ejpam-2627	91	5	on	on	ADP
ejpam-2627	91	6	dunkl	dunkl	NOUN
ejpam-2627	91	7	dini	dini	NOUN
ejpam-2627	91	8	lipschitz	lipschitz	PROPN
ejpam-2627	91	9	class	class	NOUN
ejpam-2627	91	10	theorem	theorem	NOUN
ejpam-2627	91	11	4	4	NUM
ejpam-2627	91	12	.	.	PUNCT
ejpam-2627	92	1	let	let	VERB
ejpam-2627	92	2	η	η	PROPN
ejpam-2627	92	3	>	>	X
ejpam-2627	92	4	2k	2k	PROPN
ejpam-2627	92	5	.	.	PUNCT
ejpam-2627	93	1	if	if	SCONJ
ejpam-2627	93	2	f	f	PROPN
ejpam-2627	93	3	belong	belong	VERB
ejpam-2627	93	4	to	to	ADP
ejpam-2627	93	5	the	the	DET
ejpam-2627	93	6	d	d	PROPN
ejpam-2627	93	7	-	-	PUNCT
ejpam-2627	93	8	dunkl	dunkl	NOUN
ejpam-2627	93	9	dini	dini	NOUN
ejpam-2627	93	10	lipschitz	lipschitz	PROPN
ejpam-2627	93	11	class	class	NOUN
ejpam-2627	93	12	,	,	PUNCT
ejpam-2627	93	13	i.e.	i.e.	X
ejpam-2627	93	14	,	,	PUNCT
ejpam-2627	93	15	f	f	PROPN
ejpam-2627	93	16	∈	∈	PROPN
ejpam-2627	93	17	lip(η	lip(η	PROPN
ejpam-2627	93	18	,	,	PUNCT
ejpam-2627	93	19	δ	δ	PROPN
ejpam-2627	93	20	)	)	PUNCT
ejpam-2627	93	21	,	,	PUNCT
ejpam-2627	93	22	η	η	PROPN
ejpam-2627	93	23	>	>	X
ejpam-2627	93	24	2k	2k	PROPN
ejpam-2627	93	25	,	,	PUNCT
ejpam-2627	93	26	δ	δ	PROPN
ejpam-2627	93	27	≥	≥	NOUN
ejpam-2627	93	28	0	0	NUM
ejpam-2627	93	29	.	.	PUNCT
ejpam-2627	94	1	then	then	ADV
ejpam-2627	94	2	f	f	PROPN
ejpam-2627	94	3	is	be	AUX
ejpam-2627	94	4	equal	equal	ADJ
ejpam-2627	94	5	to	to	ADP
ejpam-2627	94	6	the	the	DET
ejpam-2627	94	7	null	null	ADJ
ejpam-2627	94	8	function	function	NOUN
ejpam-2627	94	9	in	in	ADP
ejpam-2627	94	10	rd	rd	PROPN
ejpam-2627	94	11	.	.	PUNCT
ejpam-2627	95	1	s.	s.	PROPN
ejpam-2627	95	2	el	el	PROPN
ejpam-2627	95	3	ouadih	ouadih	PROPN
ejpam-2627	95	4	,	,	PUNCT
ejpam-2627	95	5	r.	r.	PROPN
ejpam-2627	95	6	daher	daher	PROPN
ejpam-2627	95	7	/	/	SYM
ejpam-2627	95	8	eur	eur	PROPN
ejpam-2627	95	9	.	.	PUNCT
ejpam-2627	96	1	j.	j.	PROPN
ejpam-2627	96	2	pure	pure	PROPN
ejpam-2627	96	3	appl	appl	PROPN
ejpam-2627	96	4	.	.	PROPN
ejpam-2627	96	5	math	math	PROPN
ejpam-2627	96	6	,	,	PUNCT
ejpam-2627	96	7	10	10	NUM
ejpam-2627	96	8	(	(	PUNCT
ejpam-2627	96	9	3	3	NUM
ejpam-2627	96	10	)	)	PUNCT
ejpam-2627	96	11	(	(	PUNCT
ejpam-2627	96	12	2017	2017	NUM
ejpam-2627	96	13	)	)	PUNCT
ejpam-2627	96	14	,	,	PUNCT
ejpam-2627	96	15	544	544	NUM
ejpam-2627	96	16	-	-	SYM
ejpam-2627	96	17	551	551	NUM
ejpam-2627	96	18	549	549	NUM
ejpam-2627	96	19	proof	proof	NOUN
ejpam-2627	96	20	.	.	PUNCT
ejpam-2627	97	1	assume	assume	VERB
ejpam-2627	97	2	that	that	SCONJ
ejpam-2627	97	3	f	f	PROPN
ejpam-2627	97	4	∈	∈	PROPN
ejpam-2627	97	5	lip(η	lip(η	PROPN
ejpam-2627	97	6	,	,	PUNCT
ejpam-2627	97	7	δ	δ	PROPN
ejpam-2627	97	8	)	)	PUNCT
ejpam-2627	97	9	.	.	PUNCT
ejpam-2627	98	1	then	then	ADV
ejpam-2627	98	2	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	98	3	,	,	PUNCT
ejpam-2627	98	4	l	l	PROPN
ejpam-2627	98	5	≤	≤	NUM
ejpam-2627	98	6	c	c	X
ejpam-2627	98	7	hη	hη	PROPN
ejpam-2627	98	8	(	(	PUNCT
ejpam-2627	98	9	log	log	NOUN
ejpam-2627	98	10	1	1	NUM
ejpam-2627	98	11	h)δ	h)δ	NOUN
ejpam-2627	98	12	.	.	PUNCT
ejpam-2627	99	1	from	from	ADP
ejpam-2627	99	2	(	(	PUNCT
ejpam-2627	99	3	4	4	NUM
ejpam-2627	99	4	)	)	PUNCT
ejpam-2627	99	5	,	,	PUNCT
ejpam-2627	99	6	we	we	PRON
ejpam-2627	99	7	have∫	have∫	VERB
ejpam-2627	99	8	rd	rd	PROPN
ejpam-2627	99	9	|1−	|1−	PROPN
ejpam-2627	99	10	jγ+	jγ+	PROPN
ejpam-2627	100	1	d	d	PROPN
ejpam-2627	100	2	2	2	NUM
ejpam-2627	100	3	−1(h|ξ|)|	−1(h|ξ|)|	NOUN
ejpam-2627	100	4	qk|f̂(ξ)|qwl(ξ)dξ	qk|f̂(ξ)|qwl(ξ)dξ	NOUN
ejpam-2627	100	5	≤	≤	NUM
ejpam-2627	100	6	kqcq	kqcq	NOUN
ejpam-2627	100	7	hqη	hqη	PROPN
ejpam-2627	100	8	(	(	PUNCT
ejpam-2627	100	9	log	log	NOUN
ejpam-2627	100	10	1	1	NUM
ejpam-2627	100	11	h)qδ	h)qδ	PROPN
ejpam-2627	100	12	.	.	PUNCT
ejpam-2627	101	1	then	then	ADV
ejpam-2627	101	2	∫	∫	PROPN
ejpam-2627	101	3	rd	rd	PROPN
ejpam-2627	101	4	|1−	|1−	PROPN
ejpam-2627	101	5	jγ+	jγ+	PROPN
ejpam-2627	102	1	d	d	PROPN
ejpam-2627	102	2	2	2	NUM
ejpam-2627	102	3	−1(h|ξ|)|	−1(h|ξ|)|	NOUN
ejpam-2627	102	4	qk|f̂(ξ)|qwl(ξ)dξ	qk|f̂(ξ)|qwl(ξ)dξ	NOUN
ejpam-2627	102	5	h2qk	h2qk	PUNCT
ejpam-2627	103	1	≤	≤	NUM
ejpam-2627	103	2	kqcq	kqcq	NOUN
ejpam-2627	103	3	hqη−2qk	hqη−2qk	PROPN
ejpam-2627	103	4	(	(	PUNCT
ejpam-2627	103	5	log	log	VERB
ejpam-2627	103	6	1	1	NUM
ejpam-2627	103	7	h)qδ	h)qδ	PROPN
ejpam-2627	103	8	,	,	PUNCT
ejpam-2627	103	9	since	since	SCONJ
ejpam-2627	103	10	η	η	PROPN
ejpam-2627	103	11	>	>	X
ejpam-2627	103	12	2k	2k	PROPN
ejpam-2627	103	13	we	we	PRON
ejpam-2627	103	14	have	have	VERB
ejpam-2627	103	15	lim	lim	PROPN
ejpam-2627	103	16	h→0	h→0	PROPN
ejpam-2627	103	17	hqη−2qk	hqη−2qk	PROPN
ejpam-2627	103	18	(	(	PUNCT
ejpam-2627	103	19	log	log	VERB
ejpam-2627	103	20	1	1	NUM
ejpam-2627	103	21	h)qδ	h)qδ	PROPN
ejpam-2627	103	22	=	=	SYM
ejpam-2627	103	23	0	0	NUM
ejpam-2627	103	24	.	.	PUNCT
ejpam-2627	104	1	thus	thus	ADV
ejpam-2627	104	2	lim	lim	PROPN
ejpam-2627	104	3	h→0	h→0	PROPN
ejpam-2627	104	4	∫	∫	PROPN
ejpam-2627	104	5	rd	rd	PROPN
ejpam-2627	104	6	(	(	PUNCT
ejpam-2627	104	7	|1−	|1−	INTJ
ejpam-2627	104	8	jγ+	jγ+	NOUN
ejpam-2627	104	9	d	d	PROPN
ejpam-2627	104	10	2	2	NUM
ejpam-2627	104	11	−1(h|ξ|)|	−1(h|ξ|)|	X
ejpam-2627	104	12	|ξ|2h2	|ξ|2h2	X
ejpam-2627	104	13	)	)	PUNCT
ejpam-2627	104	14	qk	qk	ADP
ejpam-2627	104	15	|ξ|2qk|f̂(ξ)|qwl(ξ)dξ	|ξ|2qk|f̂(ξ)|qwl(ξ)dξ	NOUN
ejpam-2627	104	16	=	=	SYM
ejpam-2627	104	17	0	0	NUM
ejpam-2627	104	18	.	.	PUNCT
ejpam-2627	105	1	and	and	CCONJ
ejpam-2627	105	2	also	also	ADV
ejpam-2627	105	3	from	from	ADP
ejpam-2627	105	4	the	the	DET
ejpam-2627	105	5	formula	formula	NOUN
ejpam-2627	105	6	(	(	PUNCT
ejpam-2627	105	7	3	3	NUM
ejpam-2627	105	8	)	)	PUNCT
ejpam-2627	105	9	and	and	CCONJ
ejpam-2627	105	10	fatou	fatou	NOUN
ejpam-2627	105	11	’s	’s	PART
ejpam-2627	105	12	theorem	theorem	PROPN
ejpam-2627	105	13	,	,	PUNCT
ejpam-2627	105	14	we	we	PRON
ejpam-2627	105	15	obtain∫	obtain∫	VERB
ejpam-2627	105	16	rd	rd	NOUN
ejpam-2627	105	17	|ξ|2qk|f̂(ξ)|qwl(ξ)dξ	|ξ|2qk|f̂(ξ)|qwl(ξ)dξ	PROPN
ejpam-2627	106	1	=	=	SYM
ejpam-2627	107	1	0	0	X
ejpam-2627	107	2	.	.	PUNCT
ejpam-2627	107	3	hence	hence	ADV
ejpam-2627	107	4	|ξ|2kf̂(ξ	|ξ|2kf̂(ξ	NUM
ejpam-2627	107	5	)	)	PUNCT
ejpam-2627	108	1	=	=	SYM
ejpam-2627	108	2	0	0	NUM
ejpam-2627	109	1	for	for	ADP
ejpam-2627	109	2	all	all	DET
ejpam-2627	109	3	ξ	ξ	PROPN
ejpam-2627	109	4	∈	∈	PROPN
ejpam-2627	109	5	rd	rd	PROPN
ejpam-2627	109	6	,	,	PUNCT
ejpam-2627	109	7	then	then	ADV
ejpam-2627	109	8	f(x	f(x	PROPN
ejpam-2627	109	9	)	)	PUNCT
ejpam-2627	109	10	is	be	AUX
ejpam-2627	109	11	the	the	DET
ejpam-2627	109	12	null	null	ADJ
ejpam-2627	109	13	function	function	NOUN
ejpam-2627	109	14	.	.	PUNCT
ejpam-2627	110	1	analog	analog	NOUN
ejpam-2627	110	2	of	of	ADP
ejpam-2627	110	3	the	the	DET
ejpam-2627	110	4	theorem	theorem	NOUN
ejpam-2627	110	5	4	4	NUM
ejpam-2627	110	6	,	,	PUNCT
ejpam-2627	110	7	we	we	PRON
ejpam-2627	110	8	obtain	obtain	VERB
ejpam-2627	110	9	this	this	DET
ejpam-2627	110	10	theorem	theorem	VERB
ejpam-2627	110	11	.	.	PUNCT
ejpam-2627	111	1	theorem	theorem	NOUN
ejpam-2627	111	2	5	5	NUM
ejpam-2627	111	3	.	.	PUNCT
ejpam-2627	112	1	let	let	VERB
ejpam-2627	112	2	f	f	PROPN
ejpam-2627	112	3	∈	∈	PROPN
ejpam-2627	112	4	lpl	lpl	PROPN
ejpam-2627	112	5	(	(	PUNCT
ejpam-2627	112	6	r	r	NOUN
ejpam-2627	112	7	d	d	PROPN
ejpam-2627	112	8	)	)	PUNCT
ejpam-2627	112	9	.	.	PUNCT
ejpam-2627	113	1	if	if	SCONJ
ejpam-2627	113	2	f	f	PROPN
ejpam-2627	113	3	belong	belong	VERB
ejpam-2627	113	4	to	to	ADP
ejpam-2627	113	5	lip(2	lip(2	PROPN
ejpam-2627	113	6	,	,	PUNCT
ejpam-2627	113	7	0	0	NUM
ejpam-2627	113	8	)	)	PUNCT
ejpam-2627	113	9	,	,	PUNCT
ejpam-2627	113	10	i.e.	i.e.	X
ejpam-2627	113	11	,	,	PUNCT
ejpam-2627	113	12	‖zkhf(x)‖p	‖zkhf(x)‖p	PROPN
ejpam-2627	113	13	,	,	PUNCT
ejpam-2627	113	14	l	l	NOUN
ejpam-2627	113	15	=	=	SYM
ejpam-2627	113	16	o(h2	o(h2	NOUN
ejpam-2627	113	17	)	)	PUNCT
ejpam-2627	113	18	,	,	PUNCT
ejpam-2627	113	19	as	as	ADP
ejpam-2627	113	20	h→	h→	NOUN
ejpam-2627	113	21	0	0	NUM
ejpam-2627	113	22	.	.	PUNCT
ejpam-2627	114	1	then	then	ADV
ejpam-2627	114	2	f	f	PROPN
ejpam-2627	114	3	is	be	AUX
ejpam-2627	114	4	equal	equal	ADJ
ejpam-2627	114	5	to	to	ADP
ejpam-2627	114	6	null	null	ADJ
ejpam-2627	114	7	function	function	NOUN
ejpam-2627	114	8	in	in	ADP
ejpam-2627	114	9	rd	rd	PROPN
ejpam-2627	114	10	.	.	PUNCT
ejpam-2627	115	1	now	now	ADV
ejpam-2627	115	2	,	,	PUNCT
ejpam-2627	115	3	we	we	PRON
ejpam-2627	115	4	give	give	VERB
ejpam-2627	115	5	another	another	PRON
ejpam-2627	115	6	the	the	DET
ejpam-2627	115	7	main	main	ADJ
ejpam-2627	115	8	result	result	NOUN
ejpam-2627	115	9	of	of	ADP
ejpam-2627	115	10	this	this	DET
ejpam-2627	115	11	paper	paper	NOUN
ejpam-2627	115	12	analog	analog	NOUN
ejpam-2627	115	13	of	of	ADP
ejpam-2627	115	14	theorem	theorem	NOUN
ejpam-2627	115	15	1	1	NUM
ejpam-2627	115	16	.	.	PUNCT
ejpam-2627	115	17	theorem	theorem	NOUN
ejpam-2627	115	18	6	6	NUM
ejpam-2627	115	19	.	.	PUNCT
ejpam-2627	116	1	let	let	VERB
ejpam-2627	116	2	f	f	PROPN
ejpam-2627	116	3	∈	∈	PROPN
ejpam-2627	116	4	lpl	lpl	PROPN
ejpam-2627	116	5	(	(	PUNCT
ejpam-2627	116	6	r	r	NOUN
ejpam-2627	116	7	d	d	PROPN
ejpam-2627	116	8	)	)	PUNCT
ejpam-2627	116	9	.	.	PUNCT
ejpam-2627	117	1	if	if	SCONJ
ejpam-2627	117	2	f(x	f(x	PROPN
ejpam-2627	117	3	)	)	PUNCT
ejpam-2627	117	4	belong	belong	VERB
ejpam-2627	117	5	to	to	ADP
ejpam-2627	117	6	lip(η	lip(η	PROPN
ejpam-2627	117	7	,	,	PUNCT
ejpam-2627	117	8	δ	δ	PROPN
ejpam-2627	117	9	)	)	PUNCT
ejpam-2627	117	10	,	,	PUNCT
ejpam-2627	117	11	then∫	then∫	NOUN
ejpam-2627	117	12	|ξ|≥s	|ξ|≥s	NOUN
ejpam-2627	117	13	|f̂(ξ)|qwl(ξ)dξ	|f̂(ξ)|qwl(ξ)dξ	ADJ
ejpam-2627	117	14	=	=	SYM
ejpam-2627	117	15	o	o	X
ejpam-2627	117	16	(	(	PUNCT
ejpam-2627	117	17	s−qη	s−qη	PROPN
ejpam-2627	117	18	(	(	PUNCT
ejpam-2627	117	19	log	log	PROPN
ejpam-2627	117	20	s)qδ	s)qδ	PROPN
ejpam-2627	117	21	)	)	PUNCT
ejpam-2627	117	22	,	,	PUNCT
ejpam-2627	117	23	s→∞	s→∞	NOUN
ejpam-2627	117	24	,	,	PUNCT
ejpam-2627	117	25	where	where	SCONJ
ejpam-2627	117	26	1	1	NUM
ejpam-2627	117	27	p	p	NOUN
ejpam-2627	118	1	+	+	NOUN
ejpam-2627	118	2	1	1	NUM
ejpam-2627	118	3	q	q	NOUN
ejpam-2627	118	4	=	=	ADJ
ejpam-2627	118	5	1	1	X
ejpam-2627	118	6	.	.	PUNCT
ejpam-2627	119	1	s.	s.	PROPN
ejpam-2627	119	2	el	el	PROPN
ejpam-2627	119	3	ouadih	ouadih	PROPN
ejpam-2627	119	4	,	,	PUNCT
ejpam-2627	119	5	r.	r.	PROPN
ejpam-2627	119	6	daher	daher	PROPN
ejpam-2627	119	7	/	/	SYM
ejpam-2627	119	8	eur	eur	PROPN
ejpam-2627	119	9	.	.	PUNCT
ejpam-2627	120	1	j.	j.	PROPN
ejpam-2627	120	2	pure	pure	PROPN
ejpam-2627	120	3	appl	appl	PROPN
ejpam-2627	120	4	.	.	PROPN
ejpam-2627	120	5	math	math	PROPN
ejpam-2627	120	6	,	,	PUNCT
ejpam-2627	120	7	10	10	NUM
ejpam-2627	120	8	(	(	PUNCT
ejpam-2627	120	9	3	3	NUM
ejpam-2627	120	10	)	)	PUNCT
ejpam-2627	120	11	(	(	PUNCT
ejpam-2627	120	12	2017	2017	NUM
ejpam-2627	120	13	)	)	PUNCT
ejpam-2627	120	14	,	,	PUNCT
ejpam-2627	120	15	544	544	NUM
ejpam-2627	120	16	-	-	SYM
ejpam-2627	120	17	551	551	NUM
ejpam-2627	120	18	550	550	NUM
ejpam-2627	120	19	proof	proof	NOUN
ejpam-2627	120	20	.	.	PUNCT
ejpam-2627	120	21	suppose	suppose	VERB
ejpam-2627	120	22	that	that	SCONJ
ejpam-2627	120	23	f	f	PROPN
ejpam-2627	120	24	∈	∈	PROPN
ejpam-2627	120	25	lip(η	lip(η	PROPN
ejpam-2627	120	26	,	,	PUNCT
ejpam-2627	120	27	δ	δ	PROPN
ejpam-2627	120	28	)	)	PUNCT
ejpam-2627	120	29	.	.	PUNCT
ejpam-2627	121	1	then	then	ADV
ejpam-2627	121	2	‖zkhf(x)‖p	‖zkhf(x)‖p	NOUN
ejpam-2627	121	3	,	,	PUNCT
ejpam-2627	121	4	l	l	NOUN
ejpam-2627	121	5	=	=	PUNCT
ejpam-2627	121	6	o	o	X
ejpam-2627	121	7	(	(	PUNCT
ejpam-2627	121	8	hη	hη	PROPN
ejpam-2627	121	9	(	(	PUNCT
ejpam-2627	121	10	log	log	NOUN
ejpam-2627	121	11	1	1	NUM
ejpam-2627	121	12	h)δ	h)δ	NUM
ejpam-2627	121	13	)	)	PUNCT
ejpam-2627	121	14	,	,	PUNCT
ejpam-2627	121	15	h→	h→	NOUN
ejpam-2627	121	16	0	0	NUM
ejpam-2627	121	17	.	.	PUNCT
ejpam-2627	122	1	from	from	ADP
ejpam-2627	122	2	(	(	PUNCT
ejpam-2627	122	3	4	4	NUM
ejpam-2627	122	4	)	)	PUNCT
ejpam-2627	122	5	,	,	PUNCT
ejpam-2627	122	6	we	we	PRON
ejpam-2627	122	7	have∫	have∫	VERB
ejpam-2627	122	8	rd	rd	PROPN
ejpam-2627	122	9	|1−	|1−	PROPN
ejpam-2627	122	10	jγ+	jγ+	PROPN
ejpam-2627	123	1	d	d	PROPN
ejpam-2627	123	2	2	2	NUM
ejpam-2627	123	3	−1(h|ξ|)|	−1(h|ξ|)|	NOUN
ejpam-2627	123	4	qk|f̂(ξ)|qwl(ξ)dξ	qk|f̂(ξ)|qwl(ξ)dξ	NOUN
ejpam-2627	123	5	≤	≤	NUM
ejpam-2627	123	6	kq‖zkhf(x)‖qp	kq‖zkhf(x)‖qp	PROPN
ejpam-2627	123	7	,	,	PUNCT
ejpam-2627	123	8	l.	l.	NOUN
ejpam-2627	124	1	if	if	SCONJ
ejpam-2627	124	2	|ξ|	|ξ|	PROPN
ejpam-2627	124	3	∈	∈	PROPN
ejpam-2627	124	4	[	[	PUNCT
ejpam-2627	124	5	1h	1h	NUM
ejpam-2627	124	6	,	,	PUNCT
ejpam-2627	124	7	2	2	NUM
ejpam-2627	124	8	h	h	NOUN
ejpam-2627	124	9	]	]	PUNCT
ejpam-2627	124	10	then	then	ADV
ejpam-2627	124	11	h|ξ|	h|ξ|	NOUN
ejpam-2627	124	12	≥	≥	NUM
ejpam-2627	124	13	1	1	NUM
ejpam-2627	124	14	and	and	CCONJ
ejpam-2627	124	15	lemma	lemma	PROPN
ejpam-2627	124	16	2	2	NUM
ejpam-2627	124	17	implies	imply	VERB
ejpam-2627	124	18	that	that	SCONJ
ejpam-2627	124	19	1	1	NUM
ejpam-2627	124	20	≤	≤	NUM
ejpam-2627	124	21	1	1	NUM
ejpam-2627	124	22	cqk	cqk	NOUN
ejpam-2627	124	23	|1−	|1−	VERB
ejpam-2627	124	24	jγ+	jγ+	NOUN
ejpam-2627	124	25	d	d	PROPN
ejpam-2627	124	26	2	2	NUM
ejpam-2627	124	27	−1(h|ξ|)|	−1(h|ξ|)|	X
ejpam-2627	124	28	qk	qk	NOUN
ejpam-2627	124	29	.	.	PUNCT
ejpam-2627	125	1	then	then	ADV
ejpam-2627	125	2	∫	∫	PROPN
ejpam-2627	125	3	1	1	NUM
ejpam-2627	125	4	h	h	NOUN
ejpam-2627	125	5	≤|ξ|≤	≤|ξ|≤	PROPN
ejpam-2627	125	6	2	2	NUM
ejpam-2627	125	7	h	h	NOUN
ejpam-2627	125	8	|f̂(ξ)|qwl(ξ)dξ	|f̂(ξ)|qwl(ξ)dξ	ADP
ejpam-2627	125	9	≤	≤	NUM
ejpam-2627	125	10	1	1	NUM
ejpam-2627	125	11	cqk	cqk	NOUN
ejpam-2627	125	12	∫	∫	PROPN
ejpam-2627	125	13	1	1	NUM
ejpam-2627	125	14	h	h	NOUN
ejpam-2627	125	15	≤|ξ|≤	≤|ξ|≤	PROPN
ejpam-2627	125	16	2	2	NUM
ejpam-2627	125	17	h	h	NOUN
ejpam-2627	125	18	|1−	|1−	NOUN
ejpam-2627	125	19	jγ+	jγ+	NOUN
ejpam-2627	125	20	d	d	PROPN
ejpam-2627	125	21	2	2	NUM
ejpam-2627	125	22	−1(h|ξ|)|	−1(h|ξ|)|	NOUN
ejpam-2627	125	23	qk|f̂(ξ)|qwl(ξ)dξ	qk|f̂(ξ)|qwl(ξ)dξ	NOUN
ejpam-2627	125	24	≤	≤	NUM
ejpam-2627	125	25	1	1	NUM
ejpam-2627	125	26	cqk	cqk	NOUN
ejpam-2627	125	27	∫	∫	PROPN
ejpam-2627	125	28	rd	rd	PROPN
ejpam-2627	125	29	|1−	|1−	PROPN
ejpam-2627	125	30	jγ+	jγ+	PROPN
ejpam-2627	126	1	d	d	PROPN
ejpam-2627	126	2	2	2	NUM
ejpam-2627	126	3	−1(h|ξ|)|	−1(h|ξ|)|	NOUN
ejpam-2627	126	4	qk|f̂(ξ)|qwl(ξ)dξ	qk|f̂(ξ)|qwl(ξ)dξ	NOUN
ejpam-2627	126	5	≤	≤	NUM
ejpam-2627	126	6	kq	kq	PROPN
ejpam-2627	127	1	cqk	cqk	NOUN
ejpam-2627	127	2	‖zkhf(x)‖qp	‖zkhf(x)‖qp	PROPN
ejpam-2627	127	3	,	,	PUNCT
ejpam-2627	127	4	l	l	PROPN
ejpam-2627	127	5	=	=	PUNCT
ejpam-2627	127	6	o	o	X
ejpam-2627	127	7	(	(	PUNCT
ejpam-2627	127	8	hqη	hqη	PROPN
ejpam-2627	127	9	(	(	PUNCT
ejpam-2627	127	10	log	log	NOUN
ejpam-2627	127	11	1	1	NUM
ejpam-2627	127	12	h)qδ	h)qδ	PROPN
ejpam-2627	127	13	)	)	PUNCT
ejpam-2627	127	14	.	.	PUNCT
ejpam-2627	128	1	so	so	ADV
ejpam-2627	128	2	we	we	PRON
ejpam-2627	128	3	obtain	obtain	VERB
ejpam-2627	128	4	∫	∫	PROPN
ejpam-2627	128	5	s≤|ξ|≤2s	s≤|ξ|≤2s	PROPN
ejpam-2627	128	6	|f̂(ξ)|qwl(ξ)dξ	|f̂(ξ)|qwl(ξ)dξ	ADP
ejpam-2627	128	7	≤	≤	PUNCT
ejpam-2627	128	8	c	c	NOUN
ejpam-2627	128	9	′	′	NOUN
ejpam-2627	129	1	s−qη	s−qη	PROPN
ejpam-2627	129	2	(	(	PUNCT
ejpam-2627	129	3	log	log	PROPN
ejpam-2627	129	4	s)qδ	s)qδ	PROPN
ejpam-2627	129	5	,	,	PUNCT
ejpam-2627	129	6	where	where	SCONJ
ejpam-2627	129	7	c	c	NOUN
ejpam-2627	129	8	′	′	NOUN
ejpam-2627	129	9	is	be	AUX
ejpam-2627	129	10	a	a	DET
ejpam-2627	129	11	positive	positive	ADJ
ejpam-2627	129	12	constant	constant	NOUN
ejpam-2627	129	13	.	.	PUNCT
ejpam-2627	130	1	now	now	ADV
ejpam-2627	130	2	,	,	PUNCT
ejpam-2627	130	3	we	we	PRON
ejpam-2627	130	4	have∫	have∫	VERB
ejpam-2627	130	5	|ξ|≥s	|ξ|≥s	NOUN
ejpam-2627	130	6	|f̂(ξ)|qwl(ξ)dξ	|f̂(ξ)|qwl(ξ)dξ	ADJ
ejpam-2627	130	7	=	=	SYM
ejpam-2627	130	8	∞∑	∞∑	NUM
ejpam-2627	130	9	i=0	i=0	ADJ
ejpam-2627	130	10	∫	∫	NOUN
ejpam-2627	130	11	2i+1s	2i+1s	NUM
ejpam-2627	130	12	2is	2is	NOUN
ejpam-2627	130	13	|f̂(ξ)|qwl(ξ)dξ	|f̂(ξ)|qwl(ξ)dξ	ADP
ejpam-2627	130	14	≤	≤	NUM
ejpam-2627	130	15	c	c	NOUN
ejpam-2627	130	16	′	′	NUM
ejpam-2627	130	17	(	(	PUNCT
ejpam-2627	130	18	s−qη	s−qη	PROPN
ejpam-2627	130	19	(	(	PUNCT
ejpam-2627	130	20	log	log	VERB
ejpam-2627	130	21	s)qδ	s)qδ	PROPN
ejpam-2627	130	22	+	+	CCONJ
ejpam-2627	130	23	(	(	PUNCT
ejpam-2627	130	24	2s)−qη	2s)−qη	NUM
ejpam-2627	130	25	(	(	PUNCT
ejpam-2627	130	26	log	log	VERB
ejpam-2627	130	27	2s)qδ	2s)qδ	NUM
ejpam-2627	131	1	+	+	CCONJ
ejpam-2627	132	1	(	(	PUNCT
ejpam-2627	132	2	4s)−qη	4s)−qη	NOUN
ejpam-2627	132	3	(	(	PUNCT
ejpam-2627	132	4	log	log	VERB
ejpam-2627	132	5	4s)qδ	4s)qδ	NUM
ejpam-2627	132	6	+	+	CCONJ
ejpam-2627	132	7	·	·	PUNCT
ejpam-2627	132	8	·	·	PUNCT
ejpam-2627	132	9	·	·	PUNCT
ejpam-2627	132	10	)	)	PUNCT
ejpam-2627	133	1	≤	≤	NUM
ejpam-2627	134	1	c	c	NOUN
ejpam-2627	134	2	′	′	NOUN
ejpam-2627	135	1	s−qη	s−qη	PROPN
ejpam-2627	135	2	(	(	PUNCT
ejpam-2627	135	3	log	log	PROPN
ejpam-2627	135	4	s)qδ	s)qδ	PROPN
ejpam-2627	135	5	(	(	PUNCT
ejpam-2627	135	6	1	1	NUM
ejpam-2627	135	7	+	+	NUM
ejpam-2627	135	8	2−qη	2−qη	NUM
ejpam-2627	135	9	+	+	CCONJ
ejpam-2627	135	10	(	(	PUNCT
ejpam-2627	135	11	2−qη)2	2−qη)2	NUM
ejpam-2627	135	12	+	+	CCONJ
ejpam-2627	135	13	(	(	PUNCT
ejpam-2627	135	14	2−qη)3	2−qη)3	NUM
ejpam-2627	135	15	+	+	NUM
ejpam-2627	135	16	·	·	PUNCT
ejpam-2627	135	17	·	·	PUNCT
ejpam-2627	135	18	·	·	PUNCT
ejpam-2627	135	19	)	)	PUNCT
ejpam-2627	135	20	≤	≤	NOUN
ejpam-2627	136	1	kη	kη	PROPN
ejpam-2627	136	2	s−qη	s−qη	PROPN
ejpam-2627	136	3	(	(	PUNCT
ejpam-2627	136	4	log	log	PROPN
ejpam-2627	136	5	s)qδ	s)qδ	PROPN
ejpam-2627	136	6	,	,	PUNCT
ejpam-2627	136	7	where	where	SCONJ
ejpam-2627	136	8	kη	kη	PROPN
ejpam-2627	136	9	=	=	SYM
ejpam-2627	136	10	c	c	PROPN
ejpam-2627	136	11	′(1−	′(1−	NOUN
ejpam-2627	136	12	2−qη)−1	2−qη)−1	NUM
ejpam-2627	136	13	since	since	SCONJ
ejpam-2627	136	14	2−qη	2−qη	PROPN
ejpam-2627	136	15	<	<	X
ejpam-2627	136	16	1	1	NUM
ejpam-2627	136	17	.	.	PUNCT
ejpam-2627	136	18	consequently	consequently	ADV
ejpam-2627	136	19	∫	∫	X
ejpam-2627	136	20	|ξ|≥s	|ξ|≥s	NOUN
ejpam-2627	136	21	|f̂(ξ)|qwl(ξ)dξ	|f̂(ξ)|qwl(ξ)dξ	ADJ
ejpam-2627	136	22	=	=	SYM
ejpam-2627	136	23	o	o	X
ejpam-2627	136	24	(	(	PUNCT
ejpam-2627	136	25	s−qη	s−qη	PROPN
ejpam-2627	136	26	(	(	PUNCT
ejpam-2627	136	27	log	log	PROPN
ejpam-2627	136	28	s)qδ	s)qδ	PROPN
ejpam-2627	136	29	)	)	PUNCT
ejpam-2627	136	30	,	,	PUNCT
ejpam-2627	136	31	as	as	SCONJ
ejpam-2627	136	32	s→∞.	s→∞.	VERB
ejpam-2627	136	33	references	reference	NOUN
ejpam-2627	136	34	551	551	NUM
ejpam-2627	136	35	references	reference	NOUN
ejpam-2627	136	36	[	[	X
ejpam-2627	136	37	1	1	NUM
ejpam-2627	136	38	]	]	PUNCT
ejpam-2627	136	39	c.	c.	PROPN
ejpam-2627	136	40	f	f	PROPN
ejpam-2627	136	41	dunkl	dunkl	PROPN
ejpam-2627	136	42	ana	ana	PROPN
ejpam-2627	136	43	y	y	PROPN
ejpam-2627	136	44	xu	xu	PROPN
ejpam-2627	136	45	.	.	PUNCT
ejpam-2627	137	1	orthogonal	orthogonal	ADJ
ejpam-2627	137	2	polynomials	polynomial	NOUN
ejpam-2627	137	3	of	of	ADP
ejpam-2627	137	4	several	several	ADJ
ejpam-2627	137	5	variables	variable	NOUN
ejpam-2627	137	6	.	.	PUNCT
ejpam-2627	138	1	iencyclopedia	iencyclopedia	NOUN
ejpam-2627	138	2	of	of	ADP
ejpam-2627	138	3	mathematics	mathematic	NOUN
ejpam-2627	138	4	and	and	CCONJ
ejpam-2627	138	5	its	its	PRON
ejpam-2627	138	6	applications	application	NOUN
ejpam-2627	138	7	.	.	PUNCT
ejpam-2627	139	1	cambridge	cambridge	PROPN
ejpam-2627	139	2	university	university	PROPN
ejpam-2627	139	3	press	press	PROPN
ejpam-2627	139	4	,	,	PUNCT
ejpam-2627	139	5	cambridge	cambridge	PROPN
ejpam-2627	139	6	,	,	PUNCT
ejpam-2627	139	7	2nd	2nd	PROPN
ejpam-2627	139	8	edition	edition	NOUN
ejpam-2627	139	9	,	,	PUNCT
ejpam-2627	139	10	2001	2001	NUM
ejpam-2627	139	11	.	.	PUNCT
ejpam-2627	140	1	[	[	X
ejpam-2627	140	2	2	2	X
ejpam-2627	140	3	]	]	PUNCT
ejpam-2627	140	4	e.	e.	PROPN
ejpam-2627	140	5	s	s	PROPN
ejpam-2627	140	6	belkina	belkina	NOUN
ejpam-2627	140	7	and	and	CCONJ
ejpam-2627	140	8	s.	s.	PROPN
ejpam-2627	140	9	s	s	PART
ejpam-2627	140	10	platonov	platonov	NOUN
ejpam-2627	140	11	.	.	PUNCT
ejpam-2627	141	1	equivalence	equivalence	NOUN
ejpam-2627	141	2	of	of	ADP
ejpam-2627	141	3	k	k	NOUN
ejpam-2627	141	4	-	-	PUNCT
ejpam-2627	141	5	functionals	functional	NOUN
ejpam-2627	141	6	and	and	CCONJ
ejpam-2627	141	7	modulus	modulus	NOUN
ejpam-2627	141	8	of	of	ADP
ejpam-2627	141	9	smoothness	smoothness	NOUN
ejpam-2627	141	10	constructed	construct	VERB
ejpam-2627	141	11	by	by	ADP
ejpam-2627	141	12	generalized	generalized	ADJ
ejpam-2627	141	13	dunkl	dunkl	NOUN
ejpam-2627	141	14	translations	translation	NOUN
ejpam-2627	141	15	.	.	PUNCT
ejpam-2627	142	1	izv	izv	PROPN
ejpam-2627	142	2	.	.	PROPN
ejpam-2627	142	3	vyssh	vyssh	PROPN
ejpam-2627	142	4	.	.	PUNCT
ejpam-2627	143	1	uchebn	uchebn	NOUN
ejpam-2627	143	2	.	.	PUNCT
ejpam-2627	144	1	zaved	zave	VERB
ejpam-2627	144	2	.	.	PUNCT
ejpam-2627	145	1	mat	mat	NOUN
ejpam-2627	145	2	,	,	PUNCT
ejpam-2627	145	3	52(8):1–11	52(8):1–11	NOUN
ejpam-2627	145	4	,	,	PUNCT
ejpam-2627	145	5	2008	2008	NUM
ejpam-2627	145	6	.	.	PUNCT
ejpam-2627	146	1	[	[	X
ejpam-2627	146	2	3	3	X
ejpam-2627	146	3	]	]	X
ejpam-2627	146	4	c.	c.	PROPN
ejpam-2627	146	5	f	f	PROPN
ejpam-2627	146	6	dunkl	dunkl	PROPN
ejpam-2627	146	7	.	.	PUNCT
ejpam-2627	147	1	differentialdifference	differentialdifference	NOUN
ejpam-2627	147	2	operators	operator	NOUN
ejpam-2627	147	3	associated	associate	VERB
ejpam-2627	147	4	to	to	ADP
ejpam-2627	147	5	reflection	reflection	NOUN
ejpam-2627	147	6	groups	group	NOUN
ejpam-2627	147	7	.	.	PUNCT
ejpam-2627	148	1	trans	trans	AUX
ejpam-2627	148	2	.	.	PROPN
ejpam-2627	148	3	am	be	AUX
ejpam-2627	148	4	.	.	PUNCT
ejpam-2627	149	1	math	math	PROPN
ejpam-2627	149	2	soc	soc	PROPN
ejpam-2627	149	3	.	.	PUNCT
ejpam-2627	149	4	,	,	PUNCT
ejpam-2627	149	5	313(1):167–183	313(1):167–183	NUM
ejpam-2627	149	6	,	,	PUNCT
ejpam-2627	149	7	1989	1989	NUM
ejpam-2627	149	8	.	.	PUNCT
ejpam-2627	150	1	[	[	X
ejpam-2627	150	2	4	4	NUM
ejpam-2627	150	3	]	]	X
ejpam-2627	150	4	c.	c.	PROPN
ejpam-2627	150	5	f	f	PROPN
ejpam-2627	150	6	dunkl	dunkl	PROPN
ejpam-2627	150	7	.	.	PUNCT
ejpam-2627	151	1	integral	integral	ADJ
ejpam-2627	151	2	kernels	kernel	NOUN
ejpam-2627	151	3	with	with	ADP
ejpam-2627	151	4	reflection	reflection	NOUN
ejpam-2627	151	5	group	group	NOUN
ejpam-2627	151	6	invariance	invariance	NOUN
ejpam-2627	151	7	.	.	PUNCT
ejpam-2627	152	1	canad	canad	PROPN
ejpam-2627	152	2	.	.	PUNCT
ejpam-2627	153	1	j.	j.	PROPN
ejpam-2627	153	2	math	math	PROPN
ejpam-2627	153	3	.	.	PUNCT
ejpam-2627	153	4	,	,	PUNCT
ejpam-2627	154	1	43(6):1213–1227	43(6):1213–1227	NUM
ejpam-2627	154	2	,	,	PUNCT
ejpam-2627	154	3	1991	1991	NUM
ejpam-2627	154	4	.	.	PUNCT
ejpam-2627	155	1	[	[	X
ejpam-2627	155	2	5	5	X
ejpam-2627	155	3	]	]	PUNCT
ejpam-2627	155	4	c.	c.	PROPN
ejpam-2627	155	5	f	f	PROPN
ejpam-2627	155	6	dunkl	dunkl	PROPN
ejpam-2627	155	7	.	.	PUNCT
ejpam-2627	156	1	hankel	hankel	NOUN
ejpam-2627	156	2	transforms	transform	VERB
ejpam-2627	156	3	associated	associate	VERB
ejpam-2627	156	4	to	to	ADP
ejpam-2627	156	5	finite	finite	VERB
ejpam-2627	156	6	reflection	reflection	NOUN
ejpam-2627	156	7	groups	group	NOUN
ejpam-2627	156	8	.	.	PUNCT
ejpam-2627	157	1	contemp	contemp	NOUN
ejpam-2627	157	2	.	.	PUNCT
ejpam-2627	158	1	math	math	NOUN
ejpam-2627	158	2	.	.	PUNCT
ejpam-2627	158	3	,	,	PUNCT
ejpam-2627	158	4	138(1):123–138	138(1):123–138	NUM
ejpam-2627	158	5	,	,	PUNCT
ejpam-2627	158	6	1992	1992	NUM
ejpam-2627	158	7	.	.	PUNCT
ejpam-2627	159	1	[	[	X
ejpam-2627	159	2	6	6	NUM
ejpam-2627	159	3	]	]	PUNCT
ejpam-2627	159	4	m.	m.	NOUN
ejpam-2627	159	5	f	f	PROPN
ejpam-2627	159	6	de	de	X
ejpam-2627	159	7	jeu	jeu	PROPN
ejpam-2627	159	8	.	.	PUNCT
ejpam-2627	160	1	the	the	DET
ejpam-2627	160	2	dunkl	dunkl	PROPN
ejpam-2627	160	3	transform	transform	NOUN
ejpam-2627	160	4	.	.	PUNCT
ejpam-2627	161	1	inv	inv	PROPN
ejpam-2627	161	2	.	.	PUNCT
ejpam-2627	161	3	math	math	NOUN
ejpam-2627	161	4	.	.	PUNCT
ejpam-2627	161	5	,	,	PUNCT
ejpam-2627	162	1	113(1):147–162	113(1):147–162	NUM
ejpam-2627	162	2	,	,	PUNCT
ejpam-2627	162	3	1993	1993	NUM
ejpam-2627	162	4	.	.	PUNCT
ejpam-2627	163	1	[	[	X
ejpam-2627	163	2	7	7	NUM
ejpam-2627	163	3	]	]	X
ejpam-2627	163	4	m	m	VERB
ejpam-2627	163	5	maslouhi	maslouhi	NOUN
ejpam-2627	163	6	.	.	PUNCT
ejpam-2627	164	1	an	an	DET
ejpam-2627	164	2	analog	analog	NOUN
ejpam-2627	164	3	of	of	ADP
ejpam-2627	164	4	titchmarshs	titchmarshs	PROPN
ejpam-2627	164	5	theorem	theorem	NOUN
ejpam-2627	164	6	for	for	ADP
ejpam-2627	164	7	the	the	DET
ejpam-2627	164	8	dunkl	dunkl	NOUN
ejpam-2627	164	9	transform	transform	NOUN
ejpam-2627	164	10	.	.	PUNCT
ejpam-2627	164	11	integral	integral	ADJ
ejpam-2627	164	12	transform	transform	NOUN
ejpam-2627	164	13	spec	spec	NOUN
ejpam-2627	164	14	.	.	PUNCT
ejpam-2627	165	1	funct	funct	PROPN
ejpam-2627	165	2	.	.	PROPN
ejpam-2627	165	3	,	,	PUNCT
ejpam-2627	166	1	21(10):771–778	21(10):771–778	NUM
ejpam-2627	166	2	,	,	PUNCT
ejpam-2627	166	3	2010	2010	NUM
ejpam-2627	166	4	.	.	PUNCT
ejpam-2627	167	1	[	[	X
ejpam-2627	167	2	8	8	NUM
ejpam-2627	167	3	]	]	X
ejpam-2627	167	4	m	m	NOUN
ejpam-2627	167	5	rsler	rsler	NOUN
ejpam-2627	167	6	and	and	CCONJ
ejpam-2627	167	7	m	m	PROPN
ejpam-2627	167	8	voit	voit	NOUN
ejpam-2627	167	9	.	.	PUNCT
ejpam-2627	168	1	markov	markov	NOUN
ejpam-2627	168	2	processes	process	NOUN
ejpam-2627	168	3	with	with	ADP
ejpam-2627	168	4	dunkl	dunkl	NOUN
ejpam-2627	168	5	operators	operator	NOUN
ejpam-2627	168	6	.	.	PUNCT
ejpam-2627	169	1	adv	adv	PROPN
ejpam-2627	169	2	.	.	PUNCT
ejpam-2627	169	3	appl	appl	PROPN
ejpam-2627	169	4	.	.	PROPN
ejpam-2627	169	5	math	math	PROPN
ejpam-2627	169	6	.	.	PUNCT
ejpam-2627	169	7	,	,	PUNCT
ejpam-2627	170	1	21(4):575–643	21(4):575–643	PROPN
ejpam-2627	170	2	,	,	PUNCT
ejpam-2627	170	3	1998	1998	NUM
ejpam-2627	170	4	.	.	PUNCT
ejpam-2627	171	1	[	[	X
ejpam-2627	171	2	9	9	NUM
ejpam-2627	171	3	]	]	SYM
ejpam-2627	171	4	s	s	PART
ejpam-2627	171	5	thangavelu	thangavelu	NOUN
ejpam-2627	171	6	and	and	CCONJ
ejpam-2627	171	7	y	y	PROPN
ejpam-2627	171	8	xu	xu	PROPN
ejpam-2627	171	9	.	.	PUNCT
ejpam-2627	172	1	convolution	convolution	NOUN
ejpam-2627	172	2	operator	operator	NOUN
ejpam-2627	172	3	and	and	CCONJ
ejpam-2627	172	4	maximal	maximal	ADJ
ejpam-2627	172	5	function	function	NOUN
ejpam-2627	172	6	for	for	ADP
ejpam-2627	172	7	dunkl	dunkl	NOUN
ejpam-2627	172	8	transform	transform	NOUN
ejpam-2627	172	9	.	.	PUNCT
ejpam-2627	173	1	j.	j.	PROPN
ejpam-2627	173	2	anal	anal	PROPN
ejpam-2627	173	3	.	.	PUNCT
ejpam-2627	173	4	math	math	PROPN
ejpam-2627	173	5	.	.	PUNCT
ejpam-2627	173	6	,	,	PUNCT
ejpam-2627	173	7	97(1):25–56	97(1):25–56	NUM
ejpam-2627	173	8	,	,	PUNCT
ejpam-2627	173	9	2005	2005	NUM
ejpam-2627	173	10	.	.	PUNCT
ejpam-2627	174	1	[	[	X
ejpam-2627	174	2	10	10	NUM
ejpam-2627	174	3	]	]	X
ejpam-2627	174	4	e.	e.	PROPN
ejpam-2627	174	5	c	c	PROPN
ejpam-2627	174	6	titchmarsh	titchmarsh	NOUN
ejpam-2627	174	7	.	.	PUNCT
ejpam-2627	175	1	introduction	introduction	NOUN
ejpam-2627	175	2	to	to	ADP
ejpam-2627	175	3	the	the	DET
ejpam-2627	175	4	theory	theory	NOUN
ejpam-2627	175	5	of	of	ADP
ejpam-2627	175	6	fourier	fourier	ADJ
ejpam-2627	175	7	integrals	integral	NOUN
ejpam-2627	175	8	.	.	PUNCT
ejpam-2627	176	1	clarendon	clarendon	PROPN
ejpam-2627	176	2	press	press	PROPN
ejpam-2627	176	3	,	,	PUNCT
ejpam-2627	176	4	oxford	oxford	PROPN
ejpam-2627	176	5	,	,	PUNCT
ejpam-2627	176	6	1937	1937	NUM
ejpam-2627	176	7	.	.	PUNCT
ejpam-2627	177	1	[	[	X
ejpam-2627	177	2	11	11	NUM
ejpam-2627	177	3	]	]	X
ejpam-2627	177	4	k	k	PROPN
ejpam-2627	177	5	trimèche	trimèche	PROPN
ejpam-2627	177	6	.	.	PROPN
ejpam-2627	177	7	paley	paley	PROPN
ejpam-2627	177	8	-	-	PUNCT
ejpam-2627	177	9	wiener	wiener	NOUN
ejpam-2627	177	10	theorems	theorem	NOUN
ejpam-2627	177	11	for	for	ADP
ejpam-2627	177	12	the	the	DET
ejpam-2627	177	13	dunkl	dunkl	PROPN
ejpam-2627	177	14	transform	transform	NOUN
ejpam-2627	177	15	and	and	CCONJ
ejpam-2627	177	16	dunkl	dunkl	VERB
ejpam-2627	177	17	transform	transform	VERB
ejpam-2627	177	18	operators	operator	NOUN
ejpam-2627	177	19	.	.	PUNCT
ejpam-2627	178	1	integral	integral	ADJ
ejpam-2627	178	2	transf	transf	NOUN
ejpam-2627	178	3	.	.	PUNCT
ejpam-2627	179	1	spec	spec	PROPN
ejpam-2627	179	2	.	.	PUNCT
ejpam-2627	180	1	funct	funct	PROPN
ejpam-2627	180	2	.	.	PUNCT
ejpam-2627	180	3	,	,	PUNCT
ejpam-2627	180	4	13(1):17–38	13(1):17–38	NUM
ejpam-2627	180	5	,	,	PUNCT
ejpam-2627	180	6	2002	2002	NUM
ejpam-2627	180	7	.	.	PUNCT
ejpam-2627	181	1	[	[	X
ejpam-2627	181	2	12	12	NUM
ejpam-2627	181	3	]	]	PUNCT
ejpam-2627	181	4	m.	m.	NOUN
ejpam-2627	181	5	s	s	PROPN
ejpam-2627	181	6	younis	younis	PROPN
ejpam-2627	181	7	.	.	PUNCT
ejpam-2627	182	1	fourier	fourier	PROPN
ejpam-2627	182	2	transforms	transform	VERB
ejpam-2627	182	3	of	of	ADP
ejpam-2627	182	4	dini	dini	NOUN
ejpam-2627	182	5	-	-	PUNCT
ejpam-2627	182	6	lipschitz	lipschitz	NOUN
ejpam-2627	182	7	functions	function	NOUN
ejpam-2627	182	8	.	.	PUNCT
ejpam-2627	183	1	int	int	NOUN
ejpam-2627	183	2	.	.	PUNCT
ejpam-2627	184	1	j.	j.	PROPN
ejpam-2627	184	2	math	math	PROPN
ejpam-2627	184	3	.	.	PUNCT
ejpam-2627	185	1	math	math	NOUN
ejpam-2627	185	2	.	.	PUNCT
ejpam-2627	186	1	sci	sci	PROPN
ejpam-2627	186	2	.	.	PROPN
ejpam-2627	186	3	,	,	PUNCT
ejpam-2627	186	4	9(2):301–312	9(2):301–312	NUM
ejpam-2627	186	5	,	,	PUNCT
ejpam-2627	186	6	1986	1986	NUM
ejpam-2627	186	7	.	.	PUNCT