id	sid	tid	token	lemma	pos
ejpam-776	1	1	3_776_mourou.dvi	3_776_mourou.dvi	NUM
ejpam-776	1	2	european	european	ADJ
ejpam-776	1	3	journal	journal	PROPN
ejpam-776	1	4	of	of	ADP
ejpam-776	1	5	pure	pure	ADJ
ejpam-776	1	6	and	and	CCONJ
ejpam-776	1	7	applied	apply	VERB
ejpam-776	1	8	mathematics	mathematic	NOUN
ejpam-776	1	9	vol	vol	NOUN
ejpam-776	1	10	.	.	PUNCT
ejpam-776	2	1	3	3	NUM
ejpam-776	2	2	,	,	PUNCT
ejpam-776	2	3	no	no	INTJ
ejpam-776	2	4	.	.	NOUN
ejpam-776	2	5	6	6	NUM
ejpam-776	2	6	,	,	PUNCT
ejpam-776	2	7	2010	2010	NUM
ejpam-776	2	8	,	,	PUNCT
ejpam-776	2	9	958	958	NUM
ejpam-776	2	10	-	-	SYM
ejpam-776	2	11	979	979	NUM
ejpam-776	2	12	issn	issn	PROPN
ejpam-776	2	13	1307	1307	NUM
ejpam-776	2	14	-	-	SYM
ejpam-776	2	15	5543	5543	NUM
ejpam-776	2	16	–	–	PUNCT
ejpam-776	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-776	2	18	special	special	ADJ
ejpam-776	2	19	issue	issue	NOUN
ejpam-776	2	20	on	on	ADP
ejpam-776	2	21	complex	complex	ADJ
ejpam-776	2	22	analysis	analysis	NOUN
ejpam-776	2	23	:	:	PUNCT
ejpam-776	2	24	theory	theory	NOUN
ejpam-776	2	25	and	and	CCONJ
ejpam-776	2	26	applications	application	NOUN
ejpam-776	2	27	dedicated	dedicate	VERB
ejpam-776	2	28	to	to	ADP
ejpam-776	2	29	professor	professor	PROPN
ejpam-776	2	30	hari	hari	PROPN
ejpam-776	2	31	m.	m.	PROPN
ejpam-776	2	32	srivastava	srivastava	PROPN
ejpam-776	2	33	,	,	PUNCT
ejpam-776	2	34	on	on	ADP
ejpam-776	2	35	the	the	DET
ejpam-776	2	36	occasion	occasion	NOUN
ejpam-776	2	37	of	of	ADP
ejpam-776	2	38	his	his	PRON
ejpam-776	2	39	70th	70th	ADJ
ejpam-776	2	40	birthday	birthday	NOUN
ejpam-776	2	41	inversion	inversion	NOUN
ejpam-776	2	42	of	of	ADP
ejpam-776	2	43	the	the	DET
ejpam-776	2	44	generalized	generalize	VERB
ejpam-776	2	45	dunkl	dunkl	NOUN
ejpam-776	2	46	intertwining	intertwine	VERB
ejpam-776	2	47	operator	operator	NOUN
ejpam-776	2	48	on	on	ADP
ejpam-776	2	49	r	r	NOUN
ejpam-776	2	50	and	and	CCONJ
ejpam-776	2	51	its	its	PRON
ejpam-776	2	52	dual	dual	ADJ
ejpam-776	2	53	using	use	VERB
ejpam-776	2	54	generalized	generalized	ADJ
ejpam-776	2	55	wavelets	wavelet	NOUN
ejpam-776	2	56	w.	w.	PROPN
ejpam-776	2	57	chabeh1	chabeh1	PROPN
ejpam-776	2	58	,	,	PUNCT
ejpam-776	2	59	m.a	m.a	PROPN
ejpam-776	2	60	.	.	PROPN
ejpam-776	2	61	mourou2,∗	mourou2,∗	VERB
ejpam-776	2	62	1	1	NUM
ejpam-776	2	63	preparatory	preparatory	NOUN
ejpam-776	2	64	institute	institute	NOUN
ejpam-776	2	65	for	for	ADP
ejpam-776	2	66	engineer	engineer	NOUN
ejpam-776	2	67	studies	study	NOUN
ejpam-776	2	68	of	of	ADP
ejpam-776	2	69	monastir	monastir	PROPN
ejpam-776	2	70	,	,	PUNCT
ejpam-776	2	71	university	university	PROPN
ejpam-776	2	72	of	of	ADP
ejpam-776	2	73	monastir	monastir	PROPN
ejpam-776	2	74	,	,	PUNCT
ejpam-776	2	75	5019	5019	NUM
ejpam-776	2	76	,	,	PUNCT
ejpam-776	2	77	monastir	monastir	PROPN
ejpam-776	2	78	,	,	PUNCT
ejpam-776	2	79	tunisia	tunisia	PROPN
ejpam-776	2	80	2	2	NUM
ejpam-776	2	81	department	department	NOUN
ejpam-776	2	82	of	of	ADP
ejpam-776	2	83	mathematics	mathematic	NOUN
ejpam-776	2	84	,	,	PUNCT
ejpam-776	2	85	college	college	NOUN
ejpam-776	2	86	of	of	ADP
ejpam-776	2	87	sciences	science	NOUN
ejpam-776	2	88	for	for	ADP
ejpam-776	2	89	girls	girl	NOUN
ejpam-776	2	90	,	,	PUNCT
ejpam-776	2	91	university	university	NOUN
ejpam-776	2	92	of	of	ADP
ejpam-776	2	93	dammam	dammam	PROPN
ejpam-776	2	94	,	,	PUNCT
ejpam-776	2	95	p.o.box	p.o.box	PROPN
ejpam-776	2	96	838	838	NUM
ejpam-776	2	97	,	,	PUNCT
ejpam-776	2	98	dammam	dammam	PROPN
ejpam-776	2	99	31113	31113	NUM
ejpam-776	2	100	,	,	PUNCT
ejpam-776	2	101	saudi	saudi	PROPN
ejpam-776	2	102	arabia	arabia	PROPN
ejpam-776	2	103	abstract	abstract	NOUN
ejpam-776	2	104	.	.	PUNCT
ejpam-776	3	1	we	we	PRON
ejpam-776	3	2	establish	establish	VERB
ejpam-776	3	3	an	an	DET
ejpam-776	3	4	inversion	inversion	NOUN
ejpam-776	3	5	formula	formula	NOUN
ejpam-776	3	6	for	for	ADP
ejpam-776	3	7	a	a	DET
ejpam-776	3	8	continuous	continuous	ADJ
ejpam-776	3	9	wavelet	wavelet	NOUN
ejpam-776	3	10	transform	transform	NOUN
ejpam-776	3	11	associated	associate	VERB
ejpam-776	3	12	with	with	ADP
ejpam-776	3	13	a	a	DET
ejpam-776	3	14	class	class	NOUN
ejpam-776	3	15	of	of	ADP
ejpam-776	3	16	singular	singular	ADJ
ejpam-776	3	17	differential	differential	ADJ
ejpam-776	3	18	-	-	PUNCT
ejpam-776	3	19	difference	difference	NOUN
ejpam-776	3	20	operators	operator	NOUN
ejpam-776	3	21	on	on	ADP
ejpam-776	3	22	r.	r.	PROPN
ejpam-776	3	23	we	we	PRON
ejpam-776	3	24	apply	apply	VERB
ejpam-776	3	25	this	this	DET
ejpam-776	3	26	result	result	NOUN
ejpam-776	3	27	to	to	PART
ejpam-776	3	28	derive	derive	VERB
ejpam-776	3	29	new	new	ADJ
ejpam-776	3	30	expressions	expression	NOUN
ejpam-776	3	31	for	for	ADP
ejpam-776	3	32	the	the	DET
ejpam-776	3	33	inverse	inverse	NOUN
ejpam-776	3	34	generalized	generalize	VERB
ejpam-776	3	35	dunkl	dunkl	NOUN
ejpam-776	3	36	intertwining	intertwine	VERB
ejpam-776	3	37	operator	operator	NOUN
ejpam-776	3	38	and	and	CCONJ
ejpam-776	3	39	its	its	PRON
ejpam-776	3	40	dual	dual	ADJ
ejpam-776	3	41	on	on	ADP
ejpam-776	3	42	r.	r.	PROPN
ejpam-776	3	43	2000	2000	NUM
ejpam-776	3	44	mathematics	mathematics	PROPN
ejpam-776	3	45	subject	subject	NOUN
ejpam-776	3	46	classifications	classification	NOUN
ejpam-776	3	47	:	:	PUNCT
ejpam-776	3	48	42b20	42b20	NUM
ejpam-776	3	49	,	,	PUNCT
ejpam-776	3	50	42c15	42c15	NUM
ejpam-776	3	51	,	,	PUNCT
ejpam-776	3	52	44a15	44a15	NUM
ejpam-776	3	53	,	,	PUNCT
ejpam-776	3	54	44a35	44a35	VERB
ejpam-776	3	55	key	key	ADJ
ejpam-776	3	56	words	word	NOUN
ejpam-776	3	57	and	and	CCONJ
ejpam-776	3	58	phrases	phrase	NOUN
ejpam-776	3	59	:	:	PUNCT
ejpam-776	3	60	differential	differential	ADJ
ejpam-776	3	61	-	-	PUNCT
ejpam-776	3	62	difference	difference	NOUN
ejpam-776	3	63	operator	operator	NOUN
ejpam-776	3	64	,	,	PUNCT
ejpam-776	3	65	generalized	generalize	VERB
ejpam-776	3	66	dunkl	dunkl	NOUN
ejpam-776	3	67	intertwining	intertwine	VERB
ejpam-776	3	68	operator	operator	NOUN
ejpam-776	3	69	,	,	PUNCT
ejpam-776	3	70	generalized	generalize	VERB
ejpam-776	3	71	continuous	continuous	ADJ
ejpam-776	3	72	wavelet	wavelet	NOUN
ejpam-776	3	73	transform	transform	NOUN
ejpam-776	3	74	.	.	PUNCT
ejpam-776	4	1	1	1	X
ejpam-776	4	2	.	.	X
ejpam-776	4	3	introduction	introduction	NOUN
ejpam-776	4	4	consider	consider	VERB
ejpam-776	4	5	the	the	DET
ejpam-776	4	6	second	second	ADJ
ejpam-776	4	7	-	-	PUNCT
ejpam-776	4	8	order	order	NOUN
ejpam-776	4	9	singular	singular	ADJ
ejpam-776	4	10	differential	differential	NOUN
ejpam-776	4	11	operator	operator	NOUN
ejpam-776	4	12	on	on	ADP
ejpam-776	4	13	the	the	DET
ejpam-776	4	14	real	real	ADJ
ejpam-776	4	15	line	line	NOUN
ejpam-776	4	16	∆=	∆=	NOUN
ejpam-776	4	17	d2	d2	PROPN
ejpam-776	4	18	d	d	PROPN
ejpam-776	4	19	x2	x2	PROPN
ejpam-776	4	20	+	+	CCONJ
ejpam-776	4	21	a′(x	a′(x	NOUN
ejpam-776	4	22	)	)	PUNCT
ejpam-776	4	23	a(x	a(x	PROPN
ejpam-776	4	24	)	)	PUNCT
ejpam-776	4	25	d	d	NOUN
ejpam-776	4	26	d	d	X
ejpam-776	4	27	x	x	X
ejpam-776	4	28	(	(	PUNCT
ejpam-776	4	29	1	1	NUM
ejpam-776	4	30	)	)	PUNCT
ejpam-776	4	31	where	where	SCONJ
ejpam-776	4	32	a(x	a(x	NOUN
ejpam-776	4	33	)	)	PUNCT
ejpam-776	4	34	=	=	PUNCT
ejpam-776	4	35	|x	|x	NOUN
ejpam-776	4	36	|2α+1	|2α+1	X
ejpam-776	4	37	b(x	b(x	NOUN
ejpam-776	4	38	)	)	PUNCT
ejpam-776	4	39	,	,	PUNCT
ejpam-776	4	40	α	α	X
ejpam-776	4	41	>	>	X
ejpam-776	4	42	−1	−1	NOUN
ejpam-776	4	43	2	2	NUM
ejpam-776	4	44	,	,	PUNCT
ejpam-776	4	45	b	b	X
ejpam-776	4	46	being	be	AUX
ejpam-776	4	47	a	a	DET
ejpam-776	4	48	positive	positive	ADJ
ejpam-776	4	49	c∞	c∞	NOUN
ejpam-776	4	50	even	even	ADV
ejpam-776	4	51	function	function	VERB
ejpam-776	4	52	on	on	ADP
ejpam-776	4	53	r.	r.	PROPN
ejpam-776	4	54	in	in	ADP
ejpam-776	4	55	addition	addition	NOUN
ejpam-776	4	56	we	we	PRON
ejpam-776	4	57	suppose	suppose	VERB
ejpam-776	4	58	that	that	SCONJ
ejpam-776	4	59	∗corresponding	∗corresponde	VERB
ejpam-776	4	60	author	author	NOUN
ejpam-776	4	61	.	.	PUNCT
ejpam-776	5	1	email	email	NOUN
ejpam-776	5	2	addresses	address	NOUN
ejpam-776	5	3	:	:	PUNCT
ejpam-776	5	4	wafa	wafa	PROPN
ejpam-776	5	5	_	_	PUNCT
ejpam-776	5	6	habbah�yahoo.fr	habbah�yahoo.fr	PROPN
ejpam-776	5	7	(	(	PUNCT
ejpam-776	5	8	w.	w.	NOUN
ejpam-776	5	9	chabeh	chabeh	PROPN
ejpam-776	5	10	)	)	PUNCT
ejpam-776	5	11	,	,	PUNCT
ejpam-776	5	12	mohamed_ali.mourou�yahoo.fr	mohamed_ali.mourou�yahoo.fr	PROPN
ejpam-776	5	13	(	(	PUNCT
ejpam-776	5	14	m.	m.	NOUN
ejpam-776	5	15	mourou	mourou	PROPN
ejpam-776	5	16	)	)	PUNCT
ejpam-776	5	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-776	6	1	958	958	NUM
ejpam-776	6	2	c	c	X
ejpam-776	6	3	©	©	PROPN
ejpam-776	6	4	2010	2010	NUM
ejpam-776	6	5	ejpam	ejpam	NOUN
ejpam-776	6	6	all	all	DET
ejpam-776	6	7	rights	right	NOUN
ejpam-776	6	8	reserved	reserve	VERB
ejpam-776	6	9	.	.	PUNCT
ejpam-776	7	1	w.	w.	PROPN
ejpam-776	7	2	chabeh	chabeh	PROPN
ejpam-776	7	3	,	,	PUNCT
ejpam-776	7	4	m.	m.	NOUN
ejpam-776	7	5	mourou	mourou	PROPN
ejpam-776	7	6	/	/	SYM
ejpam-776	7	7	eur	eur	PROPN
ejpam-776	7	8	.	.	PUNCT
ejpam-776	8	1	j.	j.	PROPN
ejpam-776	8	2	pure	pure	PROPN
ejpam-776	8	3	appl	appl	PROPN
ejpam-776	8	4	.	.	PROPN
ejpam-776	8	5	math	math	PROPN
ejpam-776	8	6	,	,	PUNCT
ejpam-776	8	7	3	3	NUM
ejpam-776	8	8	(	(	PUNCT
ejpam-776	8	9	2010	2010	NUM
ejpam-776	8	10	)	)	PUNCT
ejpam-776	8	11	,	,	PUNCT
ejpam-776	8	12	958	958	NUM
ejpam-776	8	13	-	-	SYM
ejpam-776	8	14	979	979	NUM
ejpam-776	8	15	959	959	NUM
ejpam-776	8	16	(	(	PUNCT
ejpam-776	8	17	i	i	NOUN
ejpam-776	8	18	)	)	PUNCT
ejpam-776	8	19	a	a	PRON
ejpam-776	8	20	is	be	AUX
ejpam-776	8	21	increasing	increase	VERB
ejpam-776	8	22	on	on	ADP
ejpam-776	8	23	[	[	X
ejpam-776	8	24	0,∞	0,∞	X
ejpam-776	8	25	[	[	PUNCT
ejpam-776	8	26	and	and	CCONJ
ejpam-776	8	27	limx→∞	limx→∞	PROPN
ejpam-776	8	28	a(x	a(x	PROPN
ejpam-776	8	29	)	)	PUNCT
ejpam-776	8	30	=	=	NOUN
ejpam-776	8	31	∞	∞	PROPN
ejpam-776	8	32	;	;	PUNCT
ejpam-776	8	33	(	(	PUNCT
ejpam-776	8	34	ii	ii	NOUN
ejpam-776	8	35	)	)	PUNCT
ejpam-776	8	36	a′/a	a′/a	PART
ejpam-776	8	37	is	be	AUX
ejpam-776	8	38	decreasing	decrease	VERB
ejpam-776	8	39	on	on	ADP
ejpam-776	8	40	]	]	X
ejpam-776	8	41	0,∞	0,∞	NOUN
ejpam-776	8	42	[	[	PUNCT
ejpam-776	8	43	and	and	CCONJ
ejpam-776	8	44	limx→∞	limx→∞	PROPN
ejpam-776	8	45	a′(x)/a(x	a′(x)/a(x	NOUN
ejpam-776	8	46	)	)	PUNCT
ejpam-776	8	47	=	=	SYM
ejpam-776	8	48	0	0	NUM
ejpam-776	8	49	;	;	PUNCT
ejpam-776	8	50	(	(	PUNCT
ejpam-776	8	51	iii	iii	X
ejpam-776	8	52	)	)	PUNCT
ejpam-776	8	53	there	there	PRON
ejpam-776	8	54	exists	exist	VERB
ejpam-776	8	55	a	a	DET
ejpam-776	8	56	constant	constant	ADJ
ejpam-776	8	57	δ	δ	NOUN
ejpam-776	8	58	>	>	X
ejpam-776	8	59	0	0	NUM
ejpam-776	8	60	such	such	ADJ
ejpam-776	8	61	that	that	SCONJ
ejpam-776	8	62	the	the	DET
ejpam-776	8	63	function	function	NOUN
ejpam-776	8	64	eδx	eδx	VERB
ejpam-776	8	65	b′(x)/b(x	b′(x)/b(x	NOUN
ejpam-776	8	66	)	)	PUNCT
ejpam-776	8	67	is	be	AUX
ejpam-776	8	68	bounded	bound	VERB
ejpam-776	8	69	for	for	ADP
ejpam-776	8	70	large	large	ADJ
ejpam-776	8	71	x	x	SYM
ejpam-776	8	72	∈	∈	PROPN
ejpam-776	8	73	]	]	X
ejpam-776	8	74	0,∞	0,∞	NOUN
ejpam-776	8	75	[	[	PUNCT
ejpam-776	8	76	together	together	ADV
ejpam-776	8	77	with	with	ADP
ejpam-776	8	78	its	its	PRON
ejpam-776	8	79	derivatives	derivative	NOUN
ejpam-776	8	80	.	.	PUNCT
ejpam-776	9	1	lions	lion	NOUN
ejpam-776	10	1	[	[	X
ejpam-776	10	2	5	5	NUM
ejpam-776	10	3	]	]	PUNCT
ejpam-776	10	4	has	have	AUX
ejpam-776	10	5	constructed	construct	VERB
ejpam-776	10	6	an	an	DET
ejpam-776	10	7	automorphism	automorphism	NOUN
ejpam-776	10	8	x	x	X
ejpam-776	10	9	of	of	ADP
ejpam-776	10	10	the	the	DET
ejpam-776	10	11	space	space	NOUN
ejpam-776	10	12	ee(r	ee(r	NOUN
ejpam-776	10	13	)	)	PUNCT
ejpam-776	10	14	of	of	ADP
ejpam-776	10	15	c∞	c∞	VERB
ejpam-776	10	16	even	even	ADV
ejpam-776	10	17	functions	function	NOUN
ejpam-776	10	18	on	on	ADP
ejpam-776	10	19	r	r	NOUN
ejpam-776	10	20	,	,	PUNCT
ejpam-776	10	21	which	which	PRON
ejpam-776	10	22	intertwines	intertwine	VERB
ejpam-776	10	23	∆	∆	PROPN
ejpam-776	10	24	and	and	CCONJ
ejpam-776	10	25	the	the	DET
ejpam-776	10	26	second	second	ADJ
ejpam-776	10	27	derivative	derivative	ADJ
ejpam-776	10	28	operator	operator	NOUN
ejpam-776	10	29	d2	d2	PROPN
ejpam-776	10	30	/	/	SYM
ejpam-776	10	31	d	d	PROPN
ejpam-776	10	32	x2	x2	PROPN
ejpam-776	10	33	;	;	PUNCT
ejpam-776	10	34	that	that	PRON
ejpam-776	10	35	is	is	ADV
ejpam-776	10	36	,	,	PUNCT
ejpam-776	10	37	satisfying	satisfy	VERB
ejpam-776	10	38	the	the	DET
ejpam-776	10	39	intertwining	intertwine	VERB
ejpam-776	10	40	relation	relation	NOUN
ejpam-776	10	41	x	x	PROPN
ejpam-776	10	42	d2	d2	PROPN
ejpam-776	11	1	d	d	PROPN
ejpam-776	11	2	x2	x2	PROPN
ejpam-776	11	3	f	f	PROPN
ejpam-776	11	4	=	=	PROPN
ejpam-776	11	5	∆x	∆x	PROPN
ejpam-776	11	6	f	f	PROPN
ejpam-776	11	7	,	,	PUNCT
ejpam-776	11	8	f	f	PROPN
ejpam-776	11	9	∈	∈	PROPN
ejpam-776	11	10	ee(r	ee(r	NOUN
ejpam-776	11	11	)	)	PUNCT
ejpam-776	11	12	.	.	PUNCT
ejpam-776	12	1	it	it	PRON
ejpam-776	12	2	is	be	AUX
ejpam-776	12	3	known	know	VERB
ejpam-776	12	4	[	[	X
ejpam-776	12	5	14	14	NUM
ejpam-776	12	6	]	]	PUNCT
ejpam-776	12	7	that	that	SCONJ
ejpam-776	12	8	the	the	DET
ejpam-776	12	9	lions	lion	NOUN
ejpam-776	12	10	operator	operator	NOUN
ejpam-776	12	11	x	x	PUNCT
ejpam-776	12	12	admits	admit	VERB
ejpam-776	12	13	the	the	DET
ejpam-776	12	14	integral	integral	ADJ
ejpam-776	12	15	representation	representation	NOUN
ejpam-776	13	1	x	x	X
ejpam-776	13	2	f	f	X
ejpam-776	13	3	(	(	PUNCT
ejpam-776	13	4	x	x	NOUN
ejpam-776	13	5	)	)	PUNCT
ejpam-776	13	6	=	=	SYM
ejpam-776	13	7	∫	∫	PROPN
ejpam-776	13	8	|x	|x	NOUN
ejpam-776	13	9	|	|	ADV
ejpam-776	13	10	0	0	NUM
ejpam-776	14	1	g(x	g(x	PROPN
ejpam-776	14	2	,	,	PUNCT
ejpam-776	14	3	y	y	PROPN
ejpam-776	14	4	)	)	PUNCT
ejpam-776	14	5	f	f	PROPN
ejpam-776	14	6	(	(	PUNCT
ejpam-776	14	7	y)d	y)d	PROPN
ejpam-776	14	8	y	y	PROPN
ejpam-776	14	9	,	,	PUNCT
ejpam-776	14	10	x	x	PROPN
ejpam-776	14	11	6=	6=	ADP
ejpam-776	14	12	0	0	NUM
ejpam-776	14	13	,	,	PUNCT
ejpam-776	14	14	where	where	SCONJ
ejpam-776	14	15	g(x	g(x	PROPN
ejpam-776	14	16	,	,	PUNCT
ejpam-776	14	17	·	·	PUNCT
ejpam-776	14	18	)	)	PUNCT
ejpam-776	14	19	is	be	AUX
ejpam-776	14	20	an	an	DET
ejpam-776	14	21	even	even	ADV
ejpam-776	14	22	positive	positive	ADJ
ejpam-776	14	23	function	function	NOUN
ejpam-776	14	24	on	on	ADP
ejpam-776	14	25	r	r	NOUN
ejpam-776	14	26	,	,	PUNCT
ejpam-776	14	27	continuous	continuous	ADJ
ejpam-776	14	28	on	on	ADP
ejpam-776	14	29	]	]	PUNCT
ejpam-776	14	30	−	−	PROPN
ejpam-776	14	31	|x	|x	NOUN
ejpam-776	14	32	|	|	ADV
ejpam-776	14	33	,	,	PUNCT
ejpam-776	14	34	|x	|x	NOUN
ejpam-776	14	35	|	|	ADV
ejpam-776	14	36	[	[	PUNCT
ejpam-776	14	37	and	and	CCONJ
ejpam-776	14	38	supported	support	VERB
ejpam-776	14	39	in	in	ADP
ejpam-776	14	40	[	[	X
ejpam-776	14	41	−|x	−|x	NOUN
ejpam-776	14	42	|	|	ADV
ejpam-776	14	43	,	,	PUNCT
ejpam-776	14	44	|x	|x	NOUN
ejpam-776	14	45	|	|	ADV
ejpam-776	14	46	]	]	PUNCT
ejpam-776	14	47	.	.	PUNCT
ejpam-776	15	1	furthermore	furthermore	ADV
ejpam-776	15	2	,	,	PUNCT
ejpam-776	15	3	the	the	DET
ejpam-776	15	4	dual	dual	ADJ
ejpam-776	15	5	lions	lion	NOUN
ejpam-776	15	6	operator	operator	NOUN
ejpam-776	15	7	tx	tx	PROPN
ejpam-776	15	8	f	f	PROPN
ejpam-776	15	9	(	(	PUNCT
ejpam-776	15	10	y	y	NOUN
ejpam-776	15	11	)	)	PUNCT
ejpam-776	15	12	=	=	SYM
ejpam-776	16	1	∫	∫	PROPN
ejpam-776	16	2	∞	∞	PROPN
ejpam-776	17	1	|y|	|y|	PROPN
ejpam-776	17	2	g(x	g(x	PROPN
ejpam-776	17	3	,	,	PUNCT
ejpam-776	17	4	y	y	PROPN
ejpam-776	17	5	)	)	PUNCT
ejpam-776	17	6	f	f	NOUN
ejpam-776	17	7	(	(	PUNCT
ejpam-776	17	8	x)a(x)d	x)a(x)d	PROPN
ejpam-776	17	9	x	x	SYM
ejpam-776	17	10	,	,	PUNCT
ejpam-776	17	11	y	y	PROPN
ejpam-776	17	12	∈	∈	PROPN
ejpam-776	17	13	r	r	NOUN
ejpam-776	17	14	,	,	PUNCT
ejpam-776	17	15	is	be	AUX
ejpam-776	17	16	an	an	DET
ejpam-776	17	17	automorphism	automorphism	NOUN
ejpam-776	17	18	of	of	ADP
ejpam-776	17	19	the	the	DET
ejpam-776	17	20	space	space	NOUN
ejpam-776	17	21	se(r	se(r	NOUN
ejpam-776	17	22	)	)	PUNCT
ejpam-776	17	23	of	of	ADP
ejpam-776	17	24	even	even	ADV
ejpam-776	17	25	schwartz	schwartz	PROPN
ejpam-776	17	26	functions	function	NOUN
ejpam-776	17	27	on	on	ADP
ejpam-776	17	28	r	r	NOUN
ejpam-776	17	29	,	,	PUNCT
ejpam-776	17	30	satisfying	satisfy	VERB
ejpam-776	17	31	the	the	DET
ejpam-776	17	32	intertwining	intertwine	VERB
ejpam-776	17	33	relation	relation	NOUN
ejpam-776	17	34	d2	d2	PROPN
ejpam-776	18	1	d	d	PROPN
ejpam-776	18	2	x2	x2	PROPN
ejpam-776	18	3	tx	tx	PROPN
ejpam-776	18	4	f	f	PROPN
ejpam-776	19	1	=	=	SYM
ejpam-776	19	2	tx∆	tx∆	NOUN
ejpam-776	19	3	f	f	X
ejpam-776	19	4	,	,	PUNCT
ejpam-776	19	5	f	f	PROPN
ejpam-776	19	6	∈	∈	PROPN
ejpam-776	19	7	se(r	se(r	NOUN
ejpam-776	19	8	)	)	PUNCT
ejpam-776	19	9	.	.	PUNCT
ejpam-776	20	1	in	in	ADP
ejpam-776	20	2	[	[	X
ejpam-776	20	3	8	8	NUM
ejpam-776	20	4	]	]	X
ejpam-776	20	5	the	the	DET
ejpam-776	20	6	second	second	ADJ
ejpam-776	20	7	author	author	NOUN
ejpam-776	20	8	has	have	AUX
ejpam-776	20	9	introduced	introduce	VERB
ejpam-776	20	10	on	on	ADP
ejpam-776	20	11	the	the	DET
ejpam-776	20	12	space	space	NOUN
ejpam-776	20	13	e	e	NOUN
ejpam-776	20	14	(	(	PUNCT
ejpam-776	20	15	r	r	NOUN
ejpam-776	20	16	)	)	PUNCT
ejpam-776	20	17	of	of	ADP
ejpam-776	20	18	c∞	c∞	PROPN
ejpam-776	20	19	functions	function	NOUN
ejpam-776	20	20	onr	onr	PROPN
ejpam-776	20	21	,	,	PUNCT
ejpam-776	20	22	the	the	DET
ejpam-776	20	23	following	follow	VERB
ejpam-776	20	24	operator	operator	NOUN
ejpam-776	20	25	v	v	ADP
ejpam-776	20	26	f	f	NOUN
ejpam-776	20	27	=	=	NOUN
ejpam-776	20	28	x	x	PROPN
ejpam-776	20	29	(	(	PUNCT
ejpam-776	20	30	fe	fe	NOUN
ejpam-776	20	31	)	)	PUNCT
ejpam-776	21	1	+	+	CCONJ
ejpam-776	21	2	d	d	PUNCT
ejpam-776	21	3	d	d	X
ejpam-776	21	4	x	x	X
ejpam-776	21	5	x	x	SYM
ejpam-776	21	6	i	i	PROPN
ejpam-776	21	7	(	(	PUNCT
ejpam-776	21	8	fo	fo	NOUN
ejpam-776	21	9	)	)	PUNCT
ejpam-776	21	10	,	,	PUNCT
ejpam-776	21	11	(	(	PUNCT
ejpam-776	21	12	2	2	X
ejpam-776	21	13	)	)	PUNCT
ejpam-776	21	14	where	where	SCONJ
ejpam-776	21	15	fe(x	fe(x	ADJ
ejpam-776	21	16	)	)	PUNCT
ejpam-776	21	17	=	=	SYM
ejpam-776	21	18	f	f	PROPN
ejpam-776	21	19	(	(	PUNCT
ejpam-776	21	20	x)+	x)+	PROPN
ejpam-776	21	21	f	f	PROPN
ejpam-776	21	22	(	(	PUNCT
ejpam-776	21	23	−x	−x	NOUN
ejpam-776	21	24	)	)	PUNCT
ejpam-776	21	25	2	2	NUM
ejpam-776	21	26	,	,	PUNCT
ejpam-776	21	27	fo(x	fo(x	PUNCT
ejpam-776	21	28	)	)	PUNCT
ejpam-776	22	1	=	=	SYM
ejpam-776	22	2	f	f	PROPN
ejpam-776	22	3	(	(	PUNCT
ejpam-776	22	4	x)−	x)−	PROPN
ejpam-776	22	5	f	f	PROPN
ejpam-776	22	6	(	(	PUNCT
ejpam-776	22	7	−x	−x	NOUN
ejpam-776	22	8	)	)	PUNCT
ejpam-776	22	9	2	2	NUM
ejpam-776	22	10	,	,	PUNCT
ejpam-776	22	11	(	(	PUNCT
ejpam-776	22	12	3	3	NUM
ejpam-776	22	13	)	)	PUNCT
ejpam-776	22	14	and	and	CCONJ
ejpam-776	22	15	i	i	PRON
ejpam-776	22	16	is	be	AUX
ejpam-776	22	17	the	the	DET
ejpam-776	22	18	map	map	NOUN
ejpam-776	22	19	defined	define	VERB
ejpam-776	22	20	by	by	ADP
ejpam-776	22	21	ih(x	ih(x	X
ejpam-776	22	22	)	)	PUNCT
ejpam-776	22	23	=	=	SYM
ejpam-776	23	1	∫	∫	PROPN
ejpam-776	23	2	x	x	SYM
ejpam-776	23	3	0	0	X
ejpam-776	24	1	h(t)d	h(t)d	PROPN
ejpam-776	24	2	t.	t.	NOUN
ejpam-776	24	3	mainly	mainly	ADV
ejpam-776	24	4	,	,	PUNCT
ejpam-776	24	5	he	he	PRON
ejpam-776	24	6	showed	show	VERB
ejpam-776	24	7	that	that	SCONJ
ejpam-776	24	8	v	v	NOUN
ejpam-776	24	9	is	be	AUX
ejpam-776	24	10	an	an	DET
ejpam-776	24	11	automorphism	automorphism	NOUN
ejpam-776	24	12	of	of	ADP
ejpam-776	24	13	e	e	NOUN
ejpam-776	24	14	(	(	PUNCT
ejpam-776	24	15	r	r	NOUN
ejpam-776	24	16	)	)	PUNCT
ejpam-776	24	17	satisfying	satisfy	VERB
ejpam-776	24	18	for	for	ADP
ejpam-776	24	19	all	all	DET
ejpam-776	24	20	f	f	PROPN
ejpam-776	24	21	∈	∈	PROPN
ejpam-776	24	22	e	e	X
ejpam-776	24	23	(	(	PUNCT
ejpam-776	24	24	r	r	NOUN
ejpam-776	24	25	)	)	PUNCT
ejpam-776	24	26	,	,	PUNCT
ejpam-776	25	1	v	v	X
ejpam-776	25	2	d	d	X
ejpam-776	25	3	d	d	X
ejpam-776	25	4	x	x	X
ejpam-776	25	5	f	f	PROPN
ejpam-776	25	6	=	=	X
ejpam-776	26	1	λv	λv	X
ejpam-776	26	2	f	f	PROPN
ejpam-776	26	3	,	,	PUNCT
ejpam-776	26	4	(	(	PUNCT
ejpam-776	26	5	4	4	X
ejpam-776	26	6	)	)	PUNCT
ejpam-776	26	7	where	where	SCONJ
ejpam-776	26	8	λ	λ	PROPN
ejpam-776	26	9	is	be	AUX
ejpam-776	26	10	a	a	DET
ejpam-776	26	11	first	first	ADJ
ejpam-776	26	12	-	-	PUNCT
ejpam-776	26	13	order	order	NOUN
ejpam-776	26	14	differential	differential	ADJ
ejpam-776	26	15	-	-	PUNCT
ejpam-776	26	16	difference	difference	NOUN
ejpam-776	26	17	operator	operator	NOUN
ejpam-776	26	18	on	on	ADP
ejpam-776	26	19	r	r	NOUN
ejpam-776	26	20	given	give	VERB
ejpam-776	26	21	by	by	ADP
ejpam-776	26	22	λ	λ	PROPN
ejpam-776	26	23	f	f	PROPN
ejpam-776	26	24	(	(	PUNCT
ejpam-776	26	25	x	x	NOUN
ejpam-776	26	26	)	)	PUNCT
ejpam-776	26	27	=	=	PUNCT
ejpam-776	27	1	d	d	NOUN
ejpam-776	27	2	f	f	X
ejpam-776	27	3	d	d	X
ejpam-776	27	4	x	x	PROPN
ejpam-776	27	5	+	+	CCONJ
ejpam-776	27	6	a′(x	a′(x	NOUN
ejpam-776	27	7	)	)	PUNCT
ejpam-776	27	8	a(x	a(x	PROPN
ejpam-776	27	9	)	)	PUNCT
ejpam-776	27	10	�	�	PROPN
ejpam-776	27	11	f	f	PROPN
ejpam-776	27	12	(	(	PUNCT
ejpam-776	27	13	x)−	x)−	PROPN
ejpam-776	27	14	f	f	PROPN
ejpam-776	27	15	(	(	PUNCT
ejpam-776	27	16	−x	−x	NOUN
ejpam-776	27	17	)	)	PUNCT
ejpam-776	27	18	2	2	NUM
ejpam-776	27	19	�	�	PROPN
ejpam-776	27	20	(	(	PUNCT
ejpam-776	27	21	5	5	NUM
ejpam-776	27	22	)	)	PUNCT
ejpam-776	27	23	w.	w.	NOUN
ejpam-776	27	24	chabeh	chabeh	PROPN
ejpam-776	27	25	,	,	PUNCT
ejpam-776	27	26	m.	m.	NOUN
ejpam-776	27	27	mourou	mourou	PROPN
ejpam-776	27	28	/	/	SYM
ejpam-776	27	29	eur	eur	PROPN
ejpam-776	27	30	.	.	PUNCT
ejpam-776	28	1	j.	j.	PROPN
ejpam-776	28	2	pure	pure	PROPN
ejpam-776	28	3	appl	appl	PROPN
ejpam-776	28	4	.	.	PROPN
ejpam-776	28	5	math	math	PROPN
ejpam-776	28	6	,	,	PUNCT
ejpam-776	28	7	3	3	NUM
ejpam-776	28	8	(	(	PUNCT
ejpam-776	28	9	2010	2010	NUM
ejpam-776	28	10	)	)	PUNCT
ejpam-776	28	11	,	,	PUNCT
ejpam-776	28	12	958	958	NUM
ejpam-776	28	13	-	-	SYM
ejpam-776	28	14	979	979	NUM
ejpam-776	28	15	960	960	NUM
ejpam-776	28	16	for	for	ADP
ejpam-776	28	17	a(x	a(x	NOUN
ejpam-776	28	18	)	)	PUNCT
ejpam-776	28	19	=	=	PUNCT
ejpam-776	28	20	|x	|x	NOUN
ejpam-776	28	21	|2α+1	|2α+1	NOUN
ejpam-776	28	22	,	,	PUNCT
ejpam-776	28	23	α	α	PROPN
ejpam-776	28	24	>	>	X
ejpam-776	28	25	−1/2	−1/2	PROPN
ejpam-776	28	26	,	,	PUNCT
ejpam-776	28	27	the	the	DET
ejpam-776	28	28	intertwining	intertwine	VERB
ejpam-776	28	29	operator	operator	NOUN
ejpam-776	28	30	v	v	NOUN
ejpam-776	28	31	reads	read	VERB
ejpam-776	28	32	v	v	ADP
ejpam-776	28	33	(	(	PUNCT
ejpam-776	28	34	f	f	NOUN
ejpam-776	28	35	)	)	PUNCT
ejpam-776	28	36	(	(	PUNCT
ejpam-776	28	37	x	x	X
ejpam-776	28	38	)	)	PUNCT
ejpam-776	28	39	=	=	PUNCT
ejpam-776	29	1	γ(α+	γ(α+	NUM
ejpam-776	29	2	1)p	1)p	NUM
ejpam-776	29	3	πγ(α+	πγ(α+	PROPN
ejpam-776	29	4	1/2	1/2	NUM
ejpam-776	29	5	)	)	PUNCT
ejpam-776	29	6	∫	∫	PROPN
ejpam-776	29	7	1	1	NUM
ejpam-776	29	8	−1	−1	NOUN
ejpam-776	29	9	f	f	PROPN
ejpam-776	29	10	(	(	PUNCT
ejpam-776	29	11	t	t	PROPN
ejpam-776	29	12	x)(1−	x)(1−	PROPN
ejpam-776	29	13	t2)α−1/2	t2)α−1/2	PROPN
ejpam-776	29	14	(	(	PUNCT
ejpam-776	29	15	1	1	NUM
ejpam-776	29	16	+	+	NUM
ejpam-776	29	17	t	t	NOUN
ejpam-776	29	18	)	)	PUNCT
ejpam-776	29	19	d	d	PROPN
ejpam-776	29	20	t	t	PROPN
ejpam-776	29	21	,	,	PUNCT
ejpam-776	29	22	and	and	CCONJ
ejpam-776	29	23	referred	refer	VERB
ejpam-776	29	24	to	to	ADP
ejpam-776	29	25	as	as	SCONJ
ejpam-776	29	26	the	the	DET
ejpam-776	29	27	dunkl	dunkl	NOUN
ejpam-776	29	28	intertwining	intertwine	VERB
ejpam-776	29	29	operator	operator	NOUN
ejpam-776	29	30	of	of	ADP
ejpam-776	29	31	index	index	NOUN
ejpam-776	29	32	α+	α+	PROPN
ejpam-776	29	33	1/2	1/2	NUM
ejpam-776	29	34	associated	associate	VERB
ejpam-776	29	35	with	with	ADP
ejpam-776	29	36	the	the	DET
ejpam-776	29	37	reflection	reflection	NOUN
ejpam-776	29	38	group	group	NOUN
ejpam-776	29	39	z2	z2	PROPN
ejpam-776	29	40	on	on	ADP
ejpam-776	29	41	r.	r.	PROPN
ejpam-776	29	42	the	the	DET
ejpam-776	29	43	differential	differential	ADJ
ejpam-776	29	44	-	-	PUNCT
ejpam-776	29	45	difference	difference	NOUN
ejpam-776	29	46	operator	operator	NOUN
ejpam-776	29	47	λ	λ	NOUN
ejpam-776	29	48	reduces	reduce	VERB
ejpam-776	29	49	to	to	ADP
ejpam-776	29	50	the	the	DET
ejpam-776	29	51	one	one	NUM
ejpam-776	29	52	-	-	PUNCT
ejpam-776	29	53	dimensional	dimensional	ADJ
ejpam-776	29	54	dunkl	dunkl	NOUN
ejpam-776	29	55	operator	operator	NOUN
ejpam-776	29	56	dα	dα	PART
ejpam-776	30	1	f	f	PROPN
ejpam-776	30	2	=	=	PROPN
ejpam-776	31	1	d	d	X
ejpam-776	31	2	f	f	X
ejpam-776	31	3	d	d	NOUN
ejpam-776	31	4	x	x	X
ejpam-776	32	1	+	+	CCONJ
ejpam-776	32	2	(	(	PUNCT
ejpam-776	32	3	α+	α+	NOUN
ejpam-776	32	4	1	1	NUM
ejpam-776	32	5	2	2	NUM
ejpam-776	32	6	)	)	PUNCT
ejpam-776	32	7	f	f	NOUN
ejpam-776	33	1	(	(	PUNCT
ejpam-776	33	2	x)−	x)−	PROPN
ejpam-776	33	3	f	f	PROPN
ejpam-776	33	4	(	(	PUNCT
ejpam-776	33	5	−x	−x	NOUN
ejpam-776	33	6	)	)	PUNCT
ejpam-776	33	7	x	x	X
ejpam-776	33	8	.	.	PUNCT
ejpam-776	34	1	such	such	ADJ
ejpam-776	34	2	operators	operator	NOUN
ejpam-776	34	3	have	have	AUX
ejpam-776	34	4	been	be	AUX
ejpam-776	34	5	introduced	introduce	VERB
ejpam-776	34	6	by	by	ADP
ejpam-776	34	7	dunkl	dunkl	NOUN
ejpam-776	34	8	in	in	ADP
ejpam-776	34	9	connection	connection	NOUN
ejpam-776	34	10	with	with	ADP
ejpam-776	34	11	a	a	DET
ejpam-776	34	12	generalization	generalization	NOUN
ejpam-776	34	13	of	of	ADP
ejpam-776	34	14	the	the	DET
ejpam-776	34	15	classical	classical	ADJ
ejpam-776	34	16	theory	theory	NOUN
ejpam-776	34	17	of	of	ADP
ejpam-776	34	18	spherical	spherical	ADJ
ejpam-776	34	19	harmonics	harmonic	NOUN
ejpam-776	34	20	(	(	PUNCT
ejpam-776	34	21	see	see	VERB
ejpam-776	34	22	[	[	X
ejpam-776	34	23	1	1	NUM
ejpam-776	34	24	,	,	PUNCT
ejpam-776	34	25	11	11	NUM
ejpam-776	34	26	]	]	PUNCT
ejpam-776	34	27	and	and	CCONJ
ejpam-776	34	28	the	the	DET
ejpam-776	34	29	references	reference	NOUN
ejpam-776	34	30	therein	therein	ADV
ejpam-776	34	31	)	)	PUNCT
ejpam-776	34	32	.	.	PUNCT
ejpam-776	35	1	during	during	ADP
ejpam-776	35	2	the	the	DET
ejpam-776	35	3	last	last	ADJ
ejpam-776	35	4	years	year	NOUN
ejpam-776	35	5	,	,	PUNCT
ejpam-776	35	6	the	the	DET
ejpam-776	35	7	theory	theory	NOUN
ejpam-776	35	8	of	of	ADP
ejpam-776	35	9	dunkl	dunkl	PROPN
ejpam-776	35	10	operators	operator	NOUN
ejpam-776	35	11	has	have	AUX
ejpam-776	35	12	found	find	VERB
ejpam-776	35	13	a	a	DET
ejpam-776	35	14	wide	wide	ADJ
ejpam-776	35	15	area	area	NOUN
ejpam-776	35	16	of	of	ADP
ejpam-776	35	17	applications	application	NOUN
ejpam-776	35	18	in	in	ADP
ejpam-776	35	19	mathematics	mathematic	NOUN
ejpam-776	35	20	and	and	CCONJ
ejpam-776	35	21	mathematical	mathematical	ADJ
ejpam-776	35	22	physics	physics	NOUN
ejpam-776	35	23	.	.	PUNCT
ejpam-776	36	1	in	in	ADP
ejpam-776	36	2	fact	fact	NOUN
ejpam-776	36	3	,	,	PUNCT
ejpam-776	36	4	dunkl	dunkl	PROPN
ejpam-776	36	5	operators	operator	NOUN
ejpam-776	36	6	have	have	AUX
ejpam-776	36	7	been	be	AUX
ejpam-776	36	8	used	use	VERB
ejpam-776	36	9	in	in	ADP
ejpam-776	36	10	the	the	DET
ejpam-776	36	11	study	study	NOUN
ejpam-776	36	12	of	of	ADP
ejpam-776	36	13	multivariable	multivariable	ADJ
ejpam-776	36	14	orthogonality	orthogonality	NOUN
ejpam-776	36	15	structures	structure	NOUN
ejpam-776	36	16	with	with	ADP
ejpam-776	36	17	certain	certain	ADJ
ejpam-776	36	18	reflection	reflection	NOUN
ejpam-776	36	19	symmetries	symmetry	NOUN
ejpam-776	36	20	[	[	X
ejpam-776	36	21	12	12	NUM
ejpam-776	36	22	,	,	PUNCT
ejpam-776	36	23	16	16	NUM
ejpam-776	36	24	]	]	PUNCT
ejpam-776	36	25	.	.	PUNCT
ejpam-776	37	1	moreover	moreover	ADV
ejpam-776	37	2	,	,	PUNCT
ejpam-776	37	3	they	they	PRON
ejpam-776	37	4	have	have	AUX
ejpam-776	37	5	been	be	AUX
ejpam-776	37	6	successfully	successfully	ADV
ejpam-776	37	7	involved	involve	VERB
ejpam-776	37	8	in	in	ADP
ejpam-776	37	9	the	the	DET
ejpam-776	37	10	description	description	NOUN
ejpam-776	37	11	and	and	CCONJ
ejpam-776	37	12	solution	solution	NOUN
ejpam-776	37	13	of	of	ADP
ejpam-776	37	14	calogero	calogero	PROPN
ejpam-776	37	15	-	-	PUNCT
ejpam-776	37	16	moser	moser	PROPN
ejpam-776	37	17	-	-	PUNCT
ejpam-776	37	18	sutherland	sutherland	PROPN
ejpam-776	37	19	type	type	NOUN
ejpam-776	37	20	quantum	quantum	ADJ
ejpam-776	37	21	many	many	ADJ
ejpam-776	37	22	body	body	NOUN
ejpam-776	37	23	systems	system	NOUN
ejpam-776	37	24	[	[	X
ejpam-776	37	25	4	4	NUM
ejpam-776	37	26	]	]	PUNCT
ejpam-776	37	27	.	.	PUNCT
ejpam-776	38	1	define	define	VERB
ejpam-776	38	2	the	the	DET
ejpam-776	38	3	dual	dual	ADJ
ejpam-776	38	4	operator	operator	NOUN
ejpam-776	38	5	t	t	PROPN
ejpam-776	38	6	v	v	NOUN
ejpam-776	38	7	of	of	ADP
ejpam-776	38	8	v	v	NOUN
ejpam-776	38	9	on	on	ADP
ejpam-776	38	10	the	the	DET
ejpam-776	38	11	space	space	NOUN
ejpam-776	38	12	s	s	X
ejpam-776	38	13	(	(	PUNCT
ejpam-776	38	14	r	r	NOUN
ejpam-776	38	15	)	)	PUNCT
ejpam-776	38	16	of	of	ADP
ejpam-776	38	17	schwartz	schwartz	PROPN
ejpam-776	38	18	functions	function	NOUN
ejpam-776	38	19	on	on	ADP
ejpam-776	38	20	r	r	NOUN
ejpam-776	38	21	,	,	PUNCT
ejpam-776	38	22	by	by	ADP
ejpam-776	38	23	the	the	DET
ejpam-776	38	24	relation	relation	NOUN
ejpam-776	38	25	t	t	PROPN
ejpam-776	38	26	v	v	NOUN
ejpam-776	38	27	f	f	X
ejpam-776	38	28	=	=	SYM
ejpam-776	38	29	tx	tx	PROPN
ejpam-776	38	30	(	(	PUNCT
ejpam-776	38	31	fe	fe	NOUN
ejpam-776	38	32	)	)	PUNCT
ejpam-776	38	33	+	+	CCONJ
ejpam-776	39	1	d	d	PUNCT
ejpam-776	39	2	d	d	X
ejpam-776	39	3	x	x	X
ejpam-776	39	4	tx	tx	PROPN
ejpam-776	39	5	j	j	PROPN
ejpam-776	39	6	(	(	PUNCT
ejpam-776	39	7	fo	fo	PROPN
ejpam-776	39	8	)	)	PUNCT
ejpam-776	39	9	,	,	PUNCT
ejpam-776	39	10	(	(	PUNCT
ejpam-776	39	11	6	6	NUM
ejpam-776	39	12	)	)	PUNCT
ejpam-776	39	13	where	where	SCONJ
ejpam-776	39	14	j	j	PROPN
ejpam-776	39	15	is	be	AUX
ejpam-776	39	16	the	the	DET
ejpam-776	39	17	map	map	NOUN
ejpam-776	39	18	defined	define	VERB
ejpam-776	39	19	by	by	ADP
ejpam-776	39	20	jh(x	jh(x	NOUN
ejpam-776	39	21	)	)	PUNCT
ejpam-776	40	1	=	=	SYM
ejpam-776	40	2	∫	∫	PUNCT
ejpam-776	40	3	x	x	PUNCT
ejpam-776	41	1	−∞	−∞	ADP
ejpam-776	41	2	h(y)d	h(y)d	PROPN
ejpam-776	41	3	y	y	PROPN
ejpam-776	41	4	,	,	PUNCT
ejpam-776	41	5	x	x	PROPN
ejpam-776	41	6	∈	∈	PROPN
ejpam-776	41	7	r.	r.	NOUN
ejpam-776	41	8	(	(	PUNCT
ejpam-776	41	9	7	7	NUM
ejpam-776	41	10	)	)	PUNCT
ejpam-776	41	11	in	in	ADP
ejpam-776	41	12	this	this	DET
ejpam-776	41	13	paper	paper	NOUN
ejpam-776	41	14	,	,	PUNCT
ejpam-776	41	15	it	it	PRON
ejpam-776	41	16	is	be	AUX
ejpam-776	41	17	shown	show	VERB
ejpam-776	41	18	that	that	SCONJ
ejpam-776	41	19	the	the	DET
ejpam-776	41	20	dual	dual	ADJ
ejpam-776	41	21	operator	operator	NOUN
ejpam-776	41	22	t	t	PROPN
ejpam-776	41	23	v	v	NOUN
ejpam-776	41	24	is	be	AUX
ejpam-776	41	25	an	an	DET
ejpam-776	41	26	automorphism	automorphism	NOUN
ejpam-776	41	27	of	of	ADP
ejpam-776	41	28	s	s	X
ejpam-776	41	29	(	(	PUNCT
ejpam-776	41	30	r)which	r)which	PROPN
ejpam-776	41	31	satisfies	satisfy	VERB
ejpam-776	41	32	the	the	DET
ejpam-776	41	33	intertwining	intertwine	VERB
ejpam-776	41	34	relation	relation	NOUN
ejpam-776	41	35	d	d	PROPN
ejpam-776	41	36	d	d	X
ejpam-776	41	37	x	x	SYM
ejpam-776	41	38	t	t	PROPN
ejpam-776	41	39	v	v	NOUN
ejpam-776	42	1	f	f	PROPN
ejpam-776	42	2	=	=	SYM
ejpam-776	42	3	t	t	PROPN
ejpam-776	42	4	vλ	vλ	INTJ
ejpam-776	42	5	f	f	PROPN
ejpam-776	42	6	,	,	PUNCT
ejpam-776	42	7	f	f	PROPN
ejpam-776	42	8	∈	∈	PROPN
ejpam-776	42	9	s	s	X
ejpam-776	42	10	(	(	PUNCT
ejpam-776	42	11	r	r	NOUN
ejpam-776	42	12	)	)	PUNCT
ejpam-776	42	13	.	.	PUNCT
ejpam-776	43	1	moreover	moreover	ADV
ejpam-776	43	2	,	,	PUNCT
ejpam-776	43	3	the	the	DET
ejpam-776	43	4	following	follow	VERB
ejpam-776	43	5	inversion	inversion	NOUN
ejpam-776	43	6	formulas	formula	NOUN
ejpam-776	43	7	for	for	ADP
ejpam-776	43	8	v	v	NOUN
ejpam-776	43	9	and	and	CCONJ
ejpam-776	43	10	t	t	NOUN
ejpam-776	43	11	v	v	NOUN
ejpam-776	43	12	on	on	ADP
ejpam-776	43	13	certain	certain	ADJ
ejpam-776	43	14	specific	specific	ADJ
ejpam-776	43	15	subspaces	subspace	NOUN
ejpam-776	43	16	ofs	ofs	NOUN
ejpam-776	43	17	(	(	PUNCT
ejpam-776	43	18	r	r	NOUN
ejpam-776	43	19	)	)	PUNCT
ejpam-776	43	20	are	be	AUX
ejpam-776	43	21	provided	provide	VERB
ejpam-776	43	22	f	f	PROPN
ejpam-776	43	23	=	=	SYM
ejpam-776	43	24	v	v	PROPN
ejpam-776	43	25	k	k	PROPN
ejpam-776	43	26	t	t	PROPN
ejpam-776	43	27	v	v	NOUN
ejpam-776	43	28	f	f	PROPN
ejpam-776	43	29	;	;	PUNCT
ejpam-776	43	30	f	f	PROPN
ejpam-776	44	1	=	=	NOUN
ejpam-776	44	2	m	m	VERB
ejpam-776	44	3	v	v	ADP
ejpam-776	44	4	t	t	PROPN
ejpam-776	44	5	v	v	NOUN
ejpam-776	44	6	f	f	NOUN
ejpam-776	44	7	;	;	PUNCT
ejpam-776	44	8	f	f	PROPN
ejpam-776	44	9	=	=	SYM
ejpam-776	44	10	t	t	PROPN
ejpam-776	44	11	vm	vm	PROPN
ejpam-776	44	12	v	v	PROPN
ejpam-776	44	13	f	f	PROPN
ejpam-776	44	14	;	;	PUNCT
ejpam-776	44	15	f	f	PROPN
ejpam-776	44	16	=	=	PROPN
ejpam-776	44	17	k	k	PROPN
ejpam-776	44	18	t	t	PROPN
ejpam-776	44	19	v	v	X
ejpam-776	44	20	v	v	PROPN
ejpam-776	44	21	f	f	NOUN
ejpam-776	44	22	;	;	PUNCT
ejpam-776	44	23	k	k	PROPN
ejpam-776	44	24	andm	andm	PROPN
ejpam-776	44	25	being	be	AUX
ejpam-776	44	26	pseudo	pseudo	NOUN
ejpam-776	44	27	-	-	ADJ
ejpam-776	44	28	differential	differential	ADJ
ejpam-776	44	29	operators	operator	NOUN
ejpam-776	44	30	.	.	PUNCT
ejpam-776	45	1	but	but	CCONJ
ejpam-776	45	2	the	the	DET
ejpam-776	45	3	main	main	ADJ
ejpam-776	45	4	contribution	contribution	NOUN
ejpam-776	45	5	of	of	ADP
ejpam-776	45	6	this	this	DET
ejpam-776	45	7	work	work	NOUN
ejpam-776	45	8	is	be	AUX
ejpam-776	45	9	the	the	DET
ejpam-776	45	10	determination	determination	NOUN
ejpam-776	45	11	of	of	ADP
ejpam-776	45	12	the	the	DET
ejpam-776	45	13	inverse	inverse	NOUN
ejpam-776	45	14	operators	operator	NOUN
ejpam-776	45	15	v−1	v−1	PROPN
ejpam-776	45	16	and	and	CCONJ
ejpam-776	45	17	t	t	VERB
ejpam-776	45	18	v−1	v−1	PROPN
ejpam-776	45	19	through	through	ADP
ejpam-776	45	20	a	a	DET
ejpam-776	45	21	continuous	continuous	ADJ
ejpam-776	45	22	wavelet	wavelet	NOUN
ejpam-776	45	23	transform	transform	NOUN
ejpam-776	45	24	on	on	ADP
ejpam-776	45	25	r	r	NOUN
ejpam-776	45	26	associated	associate	VERB
ejpam-776	45	27	with	with	ADP
ejpam-776	45	28	the	the	DET
ejpam-776	45	29	differential	differential	ADJ
ejpam-776	45	30	-	-	PUNCT
ejpam-776	45	31	difference	difference	NOUN
ejpam-776	45	32	operator	operator	NOUN
ejpam-776	45	33	λ	λ	NOUN
ejpam-776	45	34	.	.	PROPN
ejpam-776	45	35	for	for	ADP
ejpam-776	45	36	examples	example	NOUN
ejpam-776	45	37	of	of	ADP
ejpam-776	45	38	use	use	NOUN
ejpam-776	45	39	of	of	ADP
ejpam-776	45	40	wavelet	wavelet	NOUN
ejpam-776	45	41	type	type	NOUN
ejpam-776	45	42	transforms	transform	VERB
ejpam-776	45	43	in	in	ADP
ejpam-776	45	44	inverse	inverse	NOUN
ejpam-776	45	45	problems	problem	NOUN
ejpam-776	45	46	the	the	DET
ejpam-776	45	47	reader	reader	NOUN
ejpam-776	45	48	is	be	AUX
ejpam-776	45	49	referred	refer	VERB
ejpam-776	45	50	to	to	ADP
ejpam-776	45	51	[	[	X
ejpam-776	45	52	2	2	NUM
ejpam-776	45	53	,	,	PUNCT
ejpam-776	45	54	6	6	NUM
ejpam-776	45	55	,	,	PUNCT
ejpam-776	45	56	7	7	NUM
ejpam-776	45	57	,	,	PUNCT
ejpam-776	45	58	10	10	NUM
ejpam-776	45	59	,	,	PUNCT
ejpam-776	45	60	15	15	NUM
ejpam-776	45	61	]	]	PUNCT
ejpam-776	45	62	and	and	CCONJ
ejpam-776	45	63	the	the	DET
ejpam-776	45	64	references	reference	NOUN
ejpam-776	45	65	therein	therein	ADV
ejpam-776	45	66	.	.	PUNCT
ejpam-776	46	1	the	the	DET
ejpam-776	46	2	content	content	NOUN
ejpam-776	46	3	of	of	ADP
ejpam-776	46	4	this	this	DET
ejpam-776	46	5	paper	paper	NOUN
ejpam-776	46	6	is	be	AUX
ejpam-776	46	7	as	as	SCONJ
ejpam-776	46	8	follows	follow	VERB
ejpam-776	46	9	.	.	PUNCT
ejpam-776	47	1	in	in	ADP
ejpam-776	47	2	section	section	NOUN
ejpam-776	47	3	2	2	NUM
ejpam-776	47	4	we	we	PRON
ejpam-776	47	5	provide	provide	VERB
ejpam-776	47	6	some	some	DET
ejpam-776	47	7	harmonic	harmonic	ADJ
ejpam-776	47	8	w.	w.	PROPN
ejpam-776	47	9	chabeh	chabeh	PROPN
ejpam-776	47	10	,	,	PUNCT
ejpam-776	47	11	m.	m.	NOUN
ejpam-776	47	12	mourou	mourou	PROPN
ejpam-776	47	13	/	/	SYM
ejpam-776	47	14	eur	eur	PROPN
ejpam-776	47	15	.	.	PUNCT
ejpam-776	48	1	j.	j.	PROPN
ejpam-776	48	2	pure	pure	PROPN
ejpam-776	48	3	appl	appl	PROPN
ejpam-776	48	4	.	.	PROPN
ejpam-776	48	5	math	math	PROPN
ejpam-776	48	6	,	,	PUNCT
ejpam-776	48	7	3	3	NUM
ejpam-776	48	8	(	(	PUNCT
ejpam-776	48	9	2010	2010	NUM
ejpam-776	48	10	)	)	PUNCT
ejpam-776	48	11	,	,	PUNCT
ejpam-776	48	12	958	958	NUM
ejpam-776	48	13	-	-	SYM
ejpam-776	48	14	979	979	NUM
ejpam-776	48	15	961	961	NUM
ejpam-776	48	16	analysis	analysis	NOUN
ejpam-776	48	17	results	result	NOUN
ejpam-776	48	18	related	relate	VERB
ejpam-776	48	19	to	to	ADP
ejpam-776	48	20	the	the	DET
ejpam-776	48	21	differential	differential	ADJ
ejpam-776	48	22	-	-	PUNCT
ejpam-776	48	23	difference	difference	NOUN
ejpam-776	48	24	operator	operator	NOUN
ejpam-776	48	25	λ	λ	NOUN
ejpam-776	48	26	.	.	PUNCT
ejpam-776	49	1	next	next	ADV
ejpam-776	49	2	we	we	PRON
ejpam-776	49	3	list	list	VERB
ejpam-776	49	4	some	some	DET
ejpam-776	49	5	basic	basic	ADJ
ejpam-776	49	6	properties	property	NOUN
ejpam-776	49	7	of	of	ADP
ejpam-776	49	8	the	the	DET
ejpam-776	49	9	generalized	generalize	VERB
ejpam-776	49	10	dunkl	dunkl	NOUN
ejpam-776	49	11	intertwining	intertwine	VERB
ejpam-776	49	12	operator	operator	NOUN
ejpam-776	49	13	v	v	NOUN
ejpam-776	49	14	and	and	CCONJ
ejpam-776	49	15	its	its	PRON
ejpam-776	49	16	dual	dual	ADJ
ejpam-776	49	17	t	t	NOUN
ejpam-776	49	18	v	v	NOUN
ejpam-776	49	19	.	.	PUNCT
ejpam-776	50	1	in	in	ADP
ejpam-776	50	2	section	section	NOUN
ejpam-776	50	3	3	3	NUM
ejpam-776	50	4	we	we	PRON
ejpam-776	50	5	introduce	introduce	VERB
ejpam-776	50	6	the	the	DET
ejpam-776	50	7	generalized	generalized	ADJ
ejpam-776	50	8	continuous	continuous	ADJ
ejpam-776	50	9	wavelet	wavelet	NOUN
ejpam-776	50	10	transform	transform	NOUN
ejpam-776	50	11	associated	associate	VERB
ejpam-776	50	12	with	with	ADP
ejpam-776	50	13	λ	λ	PROPN
ejpam-776	50	14	,	,	PUNCT
ejpam-776	50	15	and	and	CCONJ
ejpam-776	50	16	we	we	PRON
ejpam-776	50	17	prove	prove	VERB
ejpam-776	50	18	for	for	ADP
ejpam-776	50	19	this	this	DET
ejpam-776	50	20	transform	transform	NOUN
ejpam-776	50	21	plancherel	plancherel	NOUN
ejpam-776	50	22	and	and	CCONJ
ejpam-776	50	23	reconstruction	reconstruction	NOUN
ejpam-776	50	24	formulas	formula	NOUN
ejpam-776	50	25	.	.	PUNCT
ejpam-776	51	1	using	use	VERB
ejpam-776	51	2	generalized	generalized	ADJ
ejpam-776	51	3	wavelets	wavelet	NOUN
ejpam-776	51	4	,	,	PUNCT
ejpam-776	51	5	we	we	PRON
ejpam-776	51	6	obtain	obtain	VERB
ejpam-776	51	7	in	in	ADP
ejpam-776	51	8	section	section	NOUN
ejpam-776	51	9	4	4	NUM
ejpam-776	51	10	formulas	formula	NOUN
ejpam-776	51	11	which	which	PRON
ejpam-776	51	12	give	give	VERB
ejpam-776	51	13	the	the	DET
ejpam-776	51	14	inverse	inverse	NOUN
ejpam-776	51	15	operators	operator	NOUN
ejpam-776	52	1	v−1	v−1	PROPN
ejpam-776	52	2	and	and	CCONJ
ejpam-776	52	3	t	t	VERB
ejpam-776	52	4	v−1	v−1	PROPN
ejpam-776	52	5	on	on	ADP
ejpam-776	52	6	schwartz	schwartz	PROPN
ejpam-776	52	7	type	type	NOUN
ejpam-776	52	8	spaces	space	NOUN
ejpam-776	52	9	.	.	PUNCT
ejpam-776	53	1	2	2	X
ejpam-776	53	2	.	.	X
ejpam-776	53	3	preliminaries	preliminary	NOUN
ejpam-776	53	4	in	in	ADP
ejpam-776	53	5	this	this	DET
ejpam-776	53	6	section	section	NOUN
ejpam-776	53	7	we	we	PRON
ejpam-776	53	8	provide	provide	VERB
ejpam-776	53	9	some	some	DET
ejpam-776	53	10	facts	fact	NOUN
ejpam-776	53	11	about	about	ADP
ejpam-776	53	12	harmonic	harmonic	ADJ
ejpam-776	53	13	analysis	analysis	NOUN
ejpam-776	53	14	related	relate	VERB
ejpam-776	53	15	to	to	ADP
ejpam-776	53	16	the	the	DET
ejpam-776	53	17	differentialdifference	differentialdifference	NOUN
ejpam-776	53	18	operator	operator	NOUN
ejpam-776	53	19	λ	λ	NOUN
ejpam-776	53	20	.	.	PUNCT
ejpam-776	54	1	we	we	PRON
ejpam-776	54	2	cite	cite	VERB
ejpam-776	54	3	here	here	ADV
ejpam-776	54	4	,	,	PUNCT
ejpam-776	54	5	as	as	ADV
ejpam-776	54	6	briefly	briefly	ADV
ejpam-776	54	7	as	as	ADP
ejpam-776	54	8	possible	possible	ADJ
ejpam-776	54	9	,	,	PUNCT
ejpam-776	54	10	only	only	ADV
ejpam-776	54	11	those	those	DET
ejpam-776	54	12	properties	property	NOUN
ejpam-776	54	13	actually	actually	ADV
ejpam-776	54	14	required	require	VERB
ejpam-776	54	15	for	for	ADP
ejpam-776	54	16	the	the	DET
ejpam-776	54	17	discussion	discussion	NOUN
ejpam-776	54	18	.	.	PUNCT
ejpam-776	55	1	for	for	ADP
ejpam-776	55	2	more	more	ADJ
ejpam-776	55	3	details	detail	NOUN
ejpam-776	55	4	we	we	PRON
ejpam-776	55	5	refer	refer	VERB
ejpam-776	55	6	to	to	ADP
ejpam-776	55	7	[	[	X
ejpam-776	55	8	8	8	NUM
ejpam-776	55	9	]	]	PUNCT
ejpam-776	55	10	.	.	PUNCT
ejpam-776	56	1	notation	notation	NOUN
ejpam-776	56	2	.	.	PUNCT
ejpam-776	57	1	we	we	PRON
ejpam-776	57	2	denote	denote	VERB
ejpam-776	57	3	by	by	ADP
ejpam-776	57	4	s	s	PROPN
ejpam-776	57	5	(	(	PUNCT
ejpam-776	57	6	r	r	NOUN
ejpam-776	57	7	)	)	PUNCT
ejpam-776	57	8	the	the	DET
ejpam-776	57	9	space	space	NOUN
ejpam-776	57	10	of	of	ADP
ejpam-776	57	11	c∞	c∞	PROPN
ejpam-776	57	12	functions	function	NOUN
ejpam-776	57	13	f	f	X
ejpam-776	57	14	on	on	ADP
ejpam-776	57	15	r	r	NOUN
ejpam-776	57	16	,	,	PUNCT
ejpam-776	57	17	which	which	PRON
ejpam-776	57	18	are	be	AUX
ejpam-776	57	19	rapidly	rapidly	ADV
ejpam-776	57	20	decreasing	decrease	VERB
ejpam-776	57	21	together	together	ADV
ejpam-776	57	22	with	with	ADP
ejpam-776	57	23	their	their	PRON
ejpam-776	57	24	derivatives	derivative	NOUN
ejpam-776	57	25	,	,	PUNCT
ejpam-776	57	26	i.e.	i.e.	X
ejpam-776	57	27	,	,	PUNCT
ejpam-776	57	28	such	such	ADJ
ejpam-776	57	29	that	that	PRON
ejpam-776	57	30	for	for	ADP
ejpam-776	57	31	all	all	DET
ejpam-776	57	32	m	m	NOUN
ejpam-776	57	33	,	,	PUNCT
ejpam-776	57	34	n	n	NOUN
ejpam-776	57	35	=	=	SYM
ejpam-776	57	36	0,1	0,1	NUM
ejpam-776	57	37	,	,	PUNCT
ejpam-776	57	38	.	.	PUNCT
ejpam-776	57	39	.	.	PUNCT
ejpam-776	58	1	.	.	PUNCT
ejpam-776	58	2	,	,	PUNCT
ejpam-776	58	3	pm	pm	NOUN
ejpam-776	58	4	,	,	PUNCT
ejpam-776	58	5	n	n	CCONJ
ejpam-776	58	6	(	(	PUNCT
ejpam-776	58	7	f	f	PROPN
ejpam-776	58	8	)	)	PUNCT
ejpam-776	59	1	=	=	SYM
ejpam-776	59	2	sup	sup	NOUN
ejpam-776	59	3	x∈r	x∈r	NOUN
ejpam-776	59	4	(	(	PUNCT
ejpam-776	59	5	1	1	NUM
ejpam-776	59	6	+	+	NUM
ejpam-776	59	7	x2)m	x2)m	PROPN
ejpam-776	59	8	�	�	PROPN
ejpam-776	59	9	�	�	PROPN
ejpam-776	59	10	�	�	PROPN
ejpam-776	59	11	�	�	PROPN
ejpam-776	59	12	dn	dn	PROPN
ejpam-776	60	1	d	d	NOUN
ejpam-776	60	2	xn	xn	PROPN
ejpam-776	60	3	f	f	PROPN
ejpam-776	60	4	(	(	PUNCT
ejpam-776	60	5	x	x	NOUN
ejpam-776	60	6	)	)	PUNCT
ejpam-776	60	7	�	�	PROPN
ejpam-776	60	8	�	�	PROPN
ejpam-776	60	9	�	�	PROPN
ejpam-776	60	10	�	�	PROPN
ejpam-776	60	11	<	<	X
ejpam-776	60	12	∞.	∞.	PROPN
ejpam-776	60	13	the	the	DET
ejpam-776	60	14	topology	topology	NOUN
ejpam-776	60	15	of	of	ADP
ejpam-776	60	16	s	s	PROPN
ejpam-776	60	17	(	(	PUNCT
ejpam-776	60	18	r	r	NOUN
ejpam-776	60	19	)	)	PUNCT
ejpam-776	60	20	is	be	AUX
ejpam-776	60	21	defined	define	VERB
ejpam-776	60	22	by	by	ADP
ejpam-776	60	23	the	the	DET
ejpam-776	60	24	semi	semi	ADJ
ejpam-776	60	25	-	-	ADJ
ejpam-776	60	26	norms	norms	ADJ
ejpam-776	60	27	pm	pm	NOUN
ejpam-776	60	28	,	,	PUNCT
ejpam-776	60	29	n	n	CCONJ
ejpam-776	60	30	,	,	PUNCT
ejpam-776	60	31	m	m	PROPN
ejpam-776	60	32	,	,	PUNCT
ejpam-776	60	33	n	n	NOUN
ejpam-776	60	34	=	=	SYM
ejpam-776	60	35	0,1	0,1	NUM
ejpam-776	60	36	,	,	PUNCT
ejpam-776	60	37	.	.	PUNCT
ejpam-776	60	38	.	.	PUNCT
ejpam-776	60	39	.	.	PUNCT
ejpam-776	60	40	.	.	PUNCT
ejpam-776	61	1	se(r	se(r	PUNCT
ejpam-776	61	2	)	)	PUNCT
ejpam-776	61	3	(	(	PUNCT
ejpam-776	61	4	resp	resp	NOUN
ejpam-776	61	5	.	.	PUNCT
ejpam-776	61	6	so(r	so(r	PROPN
ejpam-776	61	7	)	)	PUNCT
ejpam-776	61	8	)	)	PUNCT
ejpam-776	62	1	the	the	DET
ejpam-776	62	2	subspace	subspace	NOUN
ejpam-776	62	3	of	of	ADP
ejpam-776	62	4	s	s	PROPN
ejpam-776	62	5	(	(	PUNCT
ejpam-776	62	6	r	r	NOUN
ejpam-776	62	7	)	)	PUNCT
ejpam-776	62	8	consisting	consist	VERB
ejpam-776	62	9	of	of	ADP
ejpam-776	62	10	even	even	ADV
ejpam-776	62	11	(	(	PUNCT
ejpam-776	62	12	rep	rep	PROPN
ejpam-776	62	13	.	.	PROPN
ejpam-776	62	14	odd	odd	ADJ
ejpam-776	62	15	)	)	PUNCT
ejpam-776	62	16	functions	function	NOUN
ejpam-776	62	17	.	.	PUNCT
ejpam-776	63	1	b(r	b(r	NOUN
ejpam-776	63	2	)	)	PUNCT
ejpam-776	63	3	the	the	DET
ejpam-776	63	4	subspace	subspace	NOUN
ejpam-776	63	5	of	of	ADP
ejpam-776	63	6	s	s	PROPN
ejpam-776	63	7	(	(	PUNCT
ejpam-776	63	8	r	r	NOUN
ejpam-776	63	9	)	)	PUNCT
ejpam-776	63	10	consisting	consist	VERB
ejpam-776	63	11	of	of	ADP
ejpam-776	63	12	functions	function	NOUN
ejpam-776	63	13	f	f	PRON
ejpam-776	63	14	such	such	ADJ
ejpam-776	63	15	that	that	PRON
ejpam-776	63	16	for	for	ADP
ejpam-776	63	17	all	all	DET
ejpam-776	63	18	n=	n=	ADJ
ejpam-776	63	19	0,1	0,1	NUM
ejpam-776	63	20	,	,	PUNCT
ejpam-776	63	21	.	.	PUNCT
ejpam-776	63	22	.	.	PUNCT
ejpam-776	64	1	.	.	PUNCT
ejpam-776	65	1	,	,	PUNCT
ejpam-776	65	2	∫	∫	PROPN
ejpam-776	65	3	r	r	NOUN
ejpam-776	65	4	f	f	PROPN
ejpam-776	65	5	(	(	PUNCT
ejpam-776	65	6	x)bn(x)a(x)d	x)bn(x)a(x)d	PROPN
ejpam-776	65	7	x	x	SYM
ejpam-776	65	8	=	=	SYM
ejpam-776	65	9	0	0	NUM
ejpam-776	65	10	,	,	PUNCT
ejpam-776	65	11	with	with	ADP
ejpam-776	65	12	bn(x	bn(x	NOUN
ejpam-776	65	13	)	)	PUNCT
ejpam-776	65	14	=	=	SYM
ejpam-776	65	15	v	v	ADP
ejpam-776	65	16	�	�	PROPN
ejpam-776	65	17	yn	yn	PROPN
ejpam-776	65	18	n	n	CCONJ
ejpam-776	65	19	!	!	PUNCT
ejpam-776	65	20	�	�	PROPN
ejpam-776	65	21	(	(	PUNCT
ejpam-776	65	22	x	x	NOUN
ejpam-776	65	23	)	)	PUNCT
ejpam-776	65	24	,	,	PUNCT
ejpam-776	65	25	v	v	ADP
ejpam-776	65	26	being	be	AUX
ejpam-776	65	27	the	the	DET
ejpam-776	65	28	generalized	generalize	VERB
ejpam-776	65	29	dunkl	dunkl	NOUN
ejpam-776	65	30	intertwining	intertwine	VERB
ejpam-776	65	31	operator	operator	NOUN
ejpam-776	65	32	given	give	VERB
ejpam-776	65	33	by	by	ADP
ejpam-776	65	34	(	(	PUNCT
ejpam-776	65	35	2	2	NUM
ejpam-776	65	36	)	)	PUNCT
ejpam-776	65	37	.	.	PUNCT
ejpam-776	66	1	w	w	NOUN
ejpam-776	66	2	(	(	PUNCT
ejpam-776	66	3	r	r	NOUN
ejpam-776	66	4	)	)	PUNCT
ejpam-776	66	5	the	the	DET
ejpam-776	66	6	subspace	subspace	NOUN
ejpam-776	66	7	of	of	ADP
ejpam-776	66	8	s	s	PROPN
ejpam-776	66	9	(	(	PUNCT
ejpam-776	66	10	r	r	NOUN
ejpam-776	66	11	)	)	PUNCT
ejpam-776	66	12	consisting	consist	VERB
ejpam-776	66	13	of	of	ADP
ejpam-776	66	14	functions	function	NOUN
ejpam-776	66	15	f	f	PRON
ejpam-776	66	16	such	such	ADJ
ejpam-776	66	17	that	that	PRON
ejpam-776	66	18	for	for	ADP
ejpam-776	66	19	all	all	DET
ejpam-776	66	20	n=	n=	ADJ
ejpam-776	66	21	0,1	0,1	NUM
ejpam-776	66	22	.	.	PUNCT
ejpam-776	66	23	.	.	PUNCT
ejpam-776	67	1	.	.	PUNCT
ejpam-776	68	1	,	,	PUNCT
ejpam-776	68	2	∫	∫	PROPN
ejpam-776	68	3	r	r	NOUN
ejpam-776	68	4	f	f	PROPN
ejpam-776	68	5	(	(	PUNCT
ejpam-776	68	6	x)xnd	x)xnd	X
ejpam-776	68	7	x	x	SYM
ejpam-776	68	8	=	=	SYM
ejpam-776	68	9	0	0	PROPN
ejpam-776	68	10	.	.	PUNCT
ejpam-776	69	1	h	h	NOUN
ejpam-776	69	2	(	(	PUNCT
ejpam-776	69	3	r	r	NOUN
ejpam-776	69	4	)	)	PUNCT
ejpam-776	69	5	the	the	DET
ejpam-776	69	6	subspace	subspace	NOUN
ejpam-776	69	7	of	of	ADP
ejpam-776	69	8	s	s	PROPN
ejpam-776	69	9	(	(	PUNCT
ejpam-776	69	10	r	r	NOUN
ejpam-776	69	11	)	)	PUNCT
ejpam-776	69	12	consisting	consist	VERB
ejpam-776	69	13	of	of	ADP
ejpam-776	69	14	functions	function	NOUN
ejpam-776	69	15	f	f	PRON
ejpam-776	69	16	such	such	ADJ
ejpam-776	69	17	that	that	PRON
ejpam-776	69	18	for	for	ADP
ejpam-776	69	19	all	all	DET
ejpam-776	69	20	n=	n=	ADJ
ejpam-776	69	21	0,1	0,1	NUM
ejpam-776	69	22	.	.	PUNCT
ejpam-776	69	23	.	.	PUNCT
ejpam-776	70	1	.	.	PUNCT
ejpam-776	71	1	,	,	PUNCT
ejpam-776	72	1	dn	dn	PROPN
ejpam-776	72	2	d	d	NOUN
ejpam-776	72	3	xn	xn	PROPN
ejpam-776	73	1	f	f	PROPN
ejpam-776	73	2	(	(	PUNCT
ejpam-776	73	3	0	0	NUM
ejpam-776	73	4	)	)	PUNCT
ejpam-776	73	5	=	=	SYM
ejpam-776	74	1	0	0	X
ejpam-776	74	2	.	.	PUNCT
ejpam-776	75	1	put	put	VERB
ejpam-776	75	2	be(r	be(r	NUM
ejpam-776	75	3	)	)	PUNCT
ejpam-776	75	4	=	=	SYM
ejpam-776	75	5	se(r)∩b(r	se(r)∩b(r	PROPN
ejpam-776	75	6	)	)	PUNCT
ejpam-776	75	7	,	,	PUNCT
ejpam-776	75	8	bo(r	bo(r	X
ejpam-776	75	9	)	)	PUNCT
ejpam-776	75	10	=	=	SYM
ejpam-776	75	11	so(r)∩b(r	so(r)∩b(r	NOUN
ejpam-776	75	12	)	)	PUNCT
ejpam-776	75	13	,	,	PUNCT
ejpam-776	75	14	we(r	we(r	NOUN
ejpam-776	75	15	)	)	PUNCT
ejpam-776	75	16	=	=	SYM
ejpam-776	76	1	se(r)∩w	se(r)∩w	ADJ
ejpam-776	76	2	(	(	PUNCT
ejpam-776	76	3	r	r	NOUN
ejpam-776	76	4	)	)	PUNCT
ejpam-776	76	5	,	,	PUNCT
ejpam-776	76	6	wo(r	wo(r	PUNCT
ejpam-776	76	7	)	)	PUNCT
ejpam-776	77	1	=	=	SYM
ejpam-776	77	2	so(r)∩w	so(r)∩w	ADJ
ejpam-776	77	3	(	(	PUNCT
ejpam-776	77	4	r	r	NOUN
ejpam-776	77	5	)	)	PUNCT
ejpam-776	77	6	,	,	PUNCT
ejpam-776	77	7	he(r	he(r	X
ejpam-776	77	8	)	)	PUNCT
ejpam-776	78	1	=	=	SYM
ejpam-776	78	2	se(r)∩h	se(r)∩h	NOUN
ejpam-776	78	3	(	(	PUNCT
ejpam-776	78	4	r	r	NOUN
ejpam-776	78	5	)	)	PUNCT
ejpam-776	78	6	,	,	PUNCT
ejpam-776	78	7	ho(r	ho(r	X
ejpam-776	78	8	)	)	PUNCT
ejpam-776	79	1	=	=	SYM
ejpam-776	79	2	so(r)∩h	so(r)∩h	PROPN
ejpam-776	79	3	(	(	PUNCT
ejpam-776	79	4	r	r	NOUN
ejpam-776	79	5	)	)	PUNCT
ejpam-776	79	6	.	.	PUNCT
ejpam-776	80	1	w.	w.	PROPN
ejpam-776	80	2	chabeh	chabeh	PROPN
ejpam-776	80	3	,	,	PUNCT
ejpam-776	80	4	m.	m.	NOUN
ejpam-776	80	5	mourou	mourou	PROPN
ejpam-776	80	6	/	/	SYM
ejpam-776	80	7	eur	eur	PROPN
ejpam-776	80	8	.	.	PUNCT
ejpam-776	81	1	j.	j.	PROPN
ejpam-776	81	2	pure	pure	PROPN
ejpam-776	81	3	appl	appl	PROPN
ejpam-776	81	4	.	.	PROPN
ejpam-776	81	5	math	math	PROPN
ejpam-776	81	6	,	,	PUNCT
ejpam-776	81	7	3	3	NUM
ejpam-776	81	8	(	(	PUNCT
ejpam-776	81	9	2010	2010	NUM
ejpam-776	81	10	)	)	PUNCT
ejpam-776	81	11	,	,	PUNCT
ejpam-776	81	12	958	958	NUM
ejpam-776	81	13	-	-	SYM
ejpam-776	81	14	979	979	NUM
ejpam-776	81	15	962	962	NUM
ejpam-776	81	16	remark	remark	NOUN
ejpam-776	81	17	1	1	NUM
ejpam-776	81	18	.	.	PUNCT
ejpam-776	82	1	(	(	PUNCT
ejpam-776	82	2	i	i	NOUN
ejpam-776	82	3	)	)	PUNCT
ejpam-776	82	4	due	due	ADP
ejpam-776	82	5	to	to	ADP
ejpam-776	82	6	our	our	PRON
ejpam-776	82	7	assumptions	assumption	NOUN
ejpam-776	82	8	on	on	ADP
ejpam-776	82	9	the	the	DET
ejpam-776	82	10	function	function	NOUN
ejpam-776	82	11	a	a	PRON
ejpam-776	82	12	there	there	PRON
ejpam-776	82	13	is	be	VERB
ejpam-776	82	14	a	a	DET
ejpam-776	82	15	positive	positive	ADJ
ejpam-776	82	16	constant	constant	ADJ
ejpam-776	82	17	k	k	NOUN
ejpam-776	82	18	such	such	ADJ
ejpam-776	82	19	that	that	SCONJ
ejpam-776	82	20	a(x)∼	a(x)∼	PROPN
ejpam-776	82	21	k	k	PROPN
ejpam-776	82	22	|x	|x	PROPN
ejpam-776	82	23	|2α+1	|2α+1	NOUN
ejpam-776	82	24	,	,	PUNCT
ejpam-776	82	25	as	as	ADP
ejpam-776	82	26	|x	|x	NOUN
ejpam-776	82	27	|	|	ADV
ejpam-776	82	28	→∞.	→∞.	PROPN
ejpam-776	82	29	(	(	PUNCT
ejpam-776	82	30	ii	ii	NOUN
ejpam-776	82	31	)	)	PUNCT
ejpam-776	82	32	it	it	PRON
ejpam-776	82	33	follows	follow	VERB
ejpam-776	82	34	from	from	ADP
ejpam-776	82	35	(	(	PUNCT
ejpam-776	82	36	4	4	NUM
ejpam-776	82	37	)	)	PUNCT
ejpam-776	82	38	that	that	PRON
ejpam-776	82	39	λbn+1	λbn+1	VERB
ejpam-776	82	40	=	=	SYM
ejpam-776	82	41	bn	bn	X
ejpam-776	82	42	(	(	PUNCT
ejpam-776	82	43	8)	8)	NUM
ejpam-776	82	44	for	for	ADP
ejpam-776	82	45	all	all	PRON
ejpam-776	82	46	n	n	PRON
ejpam-776	82	47	∈	∈	PROPN
ejpam-776	82	48	n	n	X
ejpam-776	82	49	.	.	PUNCT
ejpam-776	83	1	further	far	ADV
ejpam-776	83	2	,	,	PUNCT
ejpam-776	83	3	by	by	ADP
ejpam-776	83	4	[	[	X
ejpam-776	83	5	9	9	X
ejpam-776	83	6	]	]	PUNCT
ejpam-776	83	7	we	we	PRON
ejpam-776	83	8	have	have	VERB
ejpam-776	83	9	for	for	ADP
ejpam-776	83	10	any	any	DET
ejpam-776	83	11	n	n	ADP
ejpam-776	83	12	∈	∈	NOUN
ejpam-776	83	13	n	n	NOUN
ejpam-776	83	14	and	and	CCONJ
ejpam-776	83	15	x	x	PUNCT
ejpam-776	83	16	∈	∈	PROPN
ejpam-776	83	17	r	r	NOUN
ejpam-776	83	18	,	,	PUNCT
ejpam-776	83	19	|bn(x)|	|bn(x)|	VERB
ejpam-776	83	20	≤	≤	ADJ
ejpam-776	83	21	k	k	PROPN
ejpam-776	83	22	|x	|x	PROPN
ejpam-776	83	23	|n	|n	NOUN
ejpam-776	83	24	,	,	PUNCT
ejpam-776	84	1	k	k	X
ejpam-776	84	2	being	be	AUX
ejpam-776	84	3	a	a	DET
ejpam-776	84	4	positive	positive	ADJ
ejpam-776	84	5	constant	constant	ADJ
ejpam-776	84	6	depending	depend	VERB
ejpam-776	84	7	only	only	ADV
ejpam-776	84	8	on	on	ADP
ejpam-776	84	9	n.	n.	PROPN
ejpam-776	84	10	(	(	PUNCT
ejpam-776	84	11	iii	iii	X
ejpam-776	84	12	)	)	PUNCT
ejpam-776	84	13	it	it	PRON
ejpam-776	84	14	is	be	AUX
ejpam-776	84	15	easily	easily	ADV
ejpam-776	84	16	checked	check	VERB
ejpam-776	84	17	that	that	SCONJ
ejpam-776	84	18	the	the	DET
ejpam-776	84	19	space	space	NOUN
ejpam-776	84	20	s	s	X
ejpam-776	84	21	(	(	PUNCT
ejpam-776	84	22	r	r	NOUN
ejpam-776	84	23	)	)	PUNCT
ejpam-776	84	24	is	be	AUX
ejpam-776	84	25	invariant	invariant	ADJ
ejpam-776	84	26	under	under	ADP
ejpam-776	84	27	the	the	DET
ejpam-776	84	28	differential	differential	ADJ
ejpam-776	84	29	-	-	PUNCT
ejpam-776	84	30	difference	difference	NOUN
ejpam-776	84	31	operator	operator	NOUN
ejpam-776	84	32	λ	λ	NOUN
ejpam-776	84	33	.	.	PROPN
ejpam-776	85	1	for	for	ADP
ejpam-776	85	2	each	each	DET
ejpam-776	85	3	λ	λ	PROPN
ejpam-776	85	4	∈	∈	PROPN
ejpam-776	85	5	c	c	NOUN
ejpam-776	85	6	the	the	DET
ejpam-776	85	7	differential	differential	ADJ
ejpam-776	85	8	-	-	PUNCT
ejpam-776	85	9	difference	difference	NOUN
ejpam-776	85	10	equation	equation	NOUN
ejpam-776	85	11	λu	λu	X
ejpam-776	85	12	=	=	SYM
ejpam-776	85	13	iλu	iλu	PROPN
ejpam-776	85	14	,	,	PUNCT
ejpam-776	85	15	u(0	u(0	PROPN
ejpam-776	85	16	)	)	PUNCT
ejpam-776	85	17	=	=	SYM
ejpam-776	85	18	1	1	NUM
ejpam-776	85	19	,	,	PUNCT
ejpam-776	85	20	(	(	PUNCT
ejpam-776	85	21	9	9	X
ejpam-776	85	22	)	)	PUNCT
ejpam-776	85	23	admits	admit	VERB
ejpam-776	85	24	a	a	DET
ejpam-776	85	25	unique	unique	ADJ
ejpam-776	85	26	c∞	c∞	ADJ
ejpam-776	85	27	solution	solution	NOUN
ejpam-776	85	28	on	on	ADP
ejpam-776	85	29	r	r	NOUN
ejpam-776	85	30	,	,	PUNCT
ejpam-776	85	31	denoted	denote	VERB
ejpam-776	85	32	ψλ	ψλ	SCONJ
ejpam-776	85	33	given	give	VERB
ejpam-776	85	34	by	by	ADP
ejpam-776	85	35	ψλ(x	ψλ(x	PRON
ejpam-776	85	36	)	)	PUNCT
ejpam-776	86	1	=	=	SYM
ejpam-776	86	2	¨	¨	NOUN
ejpam-776	86	3	ϕλ(x)+	ϕλ(x)+	PROPN
ejpam-776	86	4	1	1	NUM
ejpam-776	86	5	iλ	iλ	PROPN
ejpam-776	86	6	d	d	NOUN
ejpam-776	86	7	d	d	X
ejpam-776	86	8	x	x	X
ejpam-776	86	9	ϕλ(x	ϕλ(x	PROPN
ejpam-776	86	10	)	)	PUNCT
ejpam-776	86	11	if	if	SCONJ
ejpam-776	86	12	λ	λ	PROPN
ejpam-776	86	13	6=	6=	NUM
ejpam-776	86	14	0	0	NUM
ejpam-776	86	15	,	,	PUNCT
ejpam-776	86	16	1	1	NUM
ejpam-776	86	17	if	if	SCONJ
ejpam-776	86	18	λ=	λ=	NOUN
ejpam-776	86	19	0	0	NUM
ejpam-776	86	20	,	,	PUNCT
ejpam-776	86	21	(	(	PUNCT
ejpam-776	86	22	10	10	NUM
ejpam-776	86	23	)	)	PUNCT
ejpam-776	86	24	where	where	SCONJ
ejpam-776	86	25	ϕλ	ϕλ	PROPN
ejpam-776	86	26	designates	designate	VERB
ejpam-776	86	27	the	the	DET
ejpam-776	86	28	solution	solution	NOUN
ejpam-776	86	29	of	of	ADP
ejpam-776	86	30	the	the	DET
ejpam-776	86	31	differential	differential	ADJ
ejpam-776	86	32	equation	equation	NOUN
ejpam-776	86	33	∆u=	∆u=	ADV
ejpam-776	86	34	−λ2u	−λ2u	PROPN
ejpam-776	86	35	,	,	PUNCT
ejpam-776	86	36	u(0	u(0	PROPN
ejpam-776	86	37	)	)	PUNCT
ejpam-776	86	38	=	=	SYM
ejpam-776	86	39	1	1	NUM
ejpam-776	86	40	,	,	PUNCT
ejpam-776	86	41	u′(0	u′(0	PROPN
ejpam-776	86	42	)	)	PUNCT
ejpam-776	86	43	=	=	SYM
ejpam-776	86	44	0	0	NUM
ejpam-776	86	45	,	,	PUNCT
ejpam-776	86	46	(	(	PUNCT
ejpam-776	86	47	11	11	NUM
ejpam-776	86	48	)	)	PUNCT
ejpam-776	86	49	∆	∆	PROPN
ejpam-776	86	50	being	be	AUX
ejpam-776	86	51	the	the	DET
ejpam-776	86	52	differential	differential	ADJ
ejpam-776	86	53	operator	operator	NOUN
ejpam-776	86	54	defined	define	VERB
ejpam-776	86	55	by	by	ADP
ejpam-776	86	56	(	(	PUNCT
ejpam-776	86	57	1	1	NUM
ejpam-776	86	58	)	)	PUNCT
ejpam-776	86	59	.	.	PUNCT
ejpam-776	87	1	remark	remark	PROPN
ejpam-776	87	2	2	2	NUM
ejpam-776	87	3	.	.	PUNCT
ejpam-776	88	1	(	(	PUNCT
ejpam-776	88	2	i	i	NOUN
ejpam-776	88	3	)	)	PUNCT
ejpam-776	88	4	if	if	SCONJ
ejpam-776	88	5	a(x	a(x	NOUN
ejpam-776	88	6	)	)	PUNCT
ejpam-776	88	7	=	=	PUNCT
ejpam-776	88	8	|x	|x	NOUN
ejpam-776	88	9	|2α+1	|2α+1	NOUN
ejpam-776	88	10	,	,	PUNCT
ejpam-776	88	11	α	α	PROPN
ejpam-776	88	12	>	>	X
ejpam-776	88	13	−1/2	−1/2	PROPN
ejpam-776	88	14	,	,	PUNCT
ejpam-776	88	15	then	then	ADV
ejpam-776	88	16	ψλ(x	ψλ(x	X
ejpam-776	88	17	)	)	PUNCT
ejpam-776	89	1	=	=	PUNCT
ejpam-776	89	2	jα(λx)+	jα(λx)+	ADJ
ejpam-776	89	3	iλx	iλx	ADJ
ejpam-776	89	4	2(α+	2(α+	NUM
ejpam-776	89	5	1	1	NUM
ejpam-776	89	6	)	)	PUNCT
ejpam-776	89	7	jα+1(λx	jα+1(λx	NOUN
ejpam-776	89	8	)	)	PUNCT
ejpam-776	89	9	,	,	PUNCT
ejpam-776	89	10	where	where	SCONJ
ejpam-776	89	11	jγ	jγ	NOUN
ejpam-776	89	12	(	(	PUNCT
ejpam-776	89	13	γ	γ	X
ejpam-776	89	14	>	>	X
ejpam-776	89	15	−1/2	−1/2	PROPN
ejpam-776	89	16	)	)	PUNCT
ejpam-776	89	17	stands	stand	VERB
ejpam-776	89	18	for	for	ADP
ejpam-776	89	19	the	the	DET
ejpam-776	89	20	normalized	normalize	VERB
ejpam-776	89	21	spherical	spherical	ADJ
ejpam-776	89	22	bessel	bessel	NOUN
ejpam-776	89	23	function	function	NOUN
ejpam-776	89	24	of	of	ADP
ejpam-776	89	25	index	index	NOUN
ejpam-776	89	26	γ	γ	NOUN
ejpam-776	89	27	given	give	VERB
ejpam-776	89	28	by	by	ADP
ejpam-776	89	29	jγ(z	jγ(z	PROPN
ejpam-776	89	30	)	)	PUNCT
ejpam-776	89	31	=	=	PUNCT
ejpam-776	89	32	γ(γ+	γ(γ+	PUNCT
ejpam-776	89	33	1	1	X
ejpam-776	89	34	)	)	PUNCT
ejpam-776	89	35	∞∑	∞∑	NUM
ejpam-776	89	36	n=0	n=0	NUM
ejpam-776	89	37	(	(	PUNCT
ejpam-776	89	38	−1)n	−1)n	X
ejpam-776	89	39	(	(	PUNCT
ejpam-776	89	40	z/2)2n	z/2)2n	PROPN
ejpam-776	89	41	n	n	CCONJ
ejpam-776	89	42	!	!	PUNCT
ejpam-776	89	43	γ(n+	γ(n+	NOUN
ejpam-776	89	44	γ+	γ+	PUNCT
ejpam-776	89	45	1	1	X
ejpam-776	89	46	)	)	PUNCT
ejpam-776	89	47	(	(	PUNCT
ejpam-776	89	48	z	z	NOUN
ejpam-776	89	49	∈	∈	PROPN
ejpam-776	89	50	c	c	NOUN
ejpam-776	89	51	)	)	PUNCT
ejpam-776	89	52	.	.	PUNCT
ejpam-776	90	1	w.	w.	PROPN
ejpam-776	90	2	chabeh	chabeh	PROPN
ejpam-776	90	3	,	,	PUNCT
ejpam-776	90	4	m.	m.	NOUN
ejpam-776	90	5	mourou	mourou	PROPN
ejpam-776	90	6	/	/	SYM
ejpam-776	90	7	eur	eur	PROPN
ejpam-776	90	8	.	.	PUNCT
ejpam-776	91	1	j.	j.	PROPN
ejpam-776	91	2	pure	pure	PROPN
ejpam-776	91	3	appl	appl	PROPN
ejpam-776	91	4	.	.	PROPN
ejpam-776	91	5	math	math	PROPN
ejpam-776	91	6	,	,	PUNCT
ejpam-776	91	7	3	3	NUM
ejpam-776	91	8	(	(	PUNCT
ejpam-776	91	9	2010	2010	NUM
ejpam-776	91	10	)	)	PUNCT
ejpam-776	91	11	,	,	PUNCT
ejpam-776	91	12	958	958	NUM
ejpam-776	91	13	-	-	SYM
ejpam-776	91	14	979	979	NUM
ejpam-776	91	15	963	963	NUM
ejpam-776	91	16	(	(	PUNCT
ejpam-776	91	17	ii	ii	NOUN
ejpam-776	91	18	)	)	PUNCT
ejpam-776	91	19	it	it	PRON
ejpam-776	91	20	follows	follow	VERB
ejpam-776	91	21	by	by	ADP
ejpam-776	91	22	(	(	PUNCT
ejpam-776	91	23	4	4	NUM
ejpam-776	91	24	)	)	PUNCT
ejpam-776	91	25	and	and	CCONJ
ejpam-776	91	26	(	(	PUNCT
ejpam-776	91	27	9	9	X
ejpam-776	91	28	)	)	PUNCT
ejpam-776	91	29	that	that	PRON
ejpam-776	91	30	ψλ(x	ψλ(x	PRON
ejpam-776	91	31	)	)	PUNCT
ejpam-776	91	32	=	=	SYM
ejpam-776	91	33	v	v	PRON
ejpam-776	91	34	�	�	PROPN
ejpam-776	91	35	eiλ	eiλ	NOUN
ejpam-776	91	36	·	·	SYM
ejpam-776	91	37	�	�	PROPN
ejpam-776	91	38	(	(	PUNCT
ejpam-776	91	39	x	x	NOUN
ejpam-776	91	40	)	)	PUNCT
ejpam-776	91	41	(	(	PUNCT
ejpam-776	91	42	12	12	NUM
ejpam-776	91	43	)	)	PUNCT
ejpam-776	91	44	for	for	ADP
ejpam-776	91	45	all	all	PRON
ejpam-776	91	46	x	x	SYM
ejpam-776	91	47	∈	∈	NOUN
ejpam-776	91	48	r	r	NOUN
ejpam-776	91	49	and	and	CCONJ
ejpam-776	91	50	λ	λ	PROPN
ejpam-776	91	51	∈	∈	PROPN
ejpam-776	91	52	c.	c.	NOUN
ejpam-776	92	1	the	the	DET
ejpam-776	92	2	next	next	ADJ
ejpam-776	92	3	statement	statement	NOUN
ejpam-776	92	4	provides	provide	VERB
ejpam-776	92	5	a	a	DET
ejpam-776	92	6	new	new	ADJ
ejpam-776	92	7	estimate	estimate	NOUN
ejpam-776	92	8	for	for	ADP
ejpam-776	92	9	the	the	DET
ejpam-776	92	10	eigenfunction	eigenfunction	NOUN
ejpam-776	92	11	ψλ(x	ψλ(x	NUM
ejpam-776	92	12	)	)	PUNCT
ejpam-776	92	13	.	.	PUNCT
ejpam-776	93	1	lemma	lemma	PROPN
ejpam-776	93	2	1	1	NUM
ejpam-776	93	3	.	.	PUNCT
ejpam-776	94	1	for	for	ADP
ejpam-776	94	2	all	all	DET
ejpam-776	94	3	λ	λ	PROPN
ejpam-776	94	4	,	,	PUNCT
ejpam-776	94	5	x	x	X
ejpam-776	94	6	∈	∈	PROPN
ejpam-776	94	7	r	r	NOUN
ejpam-776	94	8	,	,	PUNCT
ejpam-776	94	9	we	we	PRON
ejpam-776	94	10	have	have	VERB
ejpam-776	94	11	|ψλ(x)|	|ψλ(x)|	NOUN
ejpam-776	94	12	≤	≤	ADV
ejpam-776	94	13	1	1	NUM
ejpam-776	94	14	.	.	PUNCT
ejpam-776	95	1	proof	proof	NOUN
ejpam-776	95	2	.	.	PUNCT
ejpam-776	96	1	for	for	ADP
ejpam-776	96	2	λ	λ	PROPN
ejpam-776	96	3	=	=	SYM
ejpam-776	96	4	0	0	NUM
ejpam-776	96	5	,	,	PUNCT
ejpam-776	96	6	the	the	DET
ejpam-776	96	7	result	result	NOUN
ejpam-776	96	8	is	be	AUX
ejpam-776	96	9	obvious	obvious	ADJ
ejpam-776	96	10	.	.	PUNCT
ejpam-776	97	1	for	for	ADP
ejpam-776	97	2	λ	λ	PROPN
ejpam-776	97	3	6=	6=	ADP
ejpam-776	97	4	0	0	NUM
ejpam-776	97	5	,	,	PUNCT
ejpam-776	97	6	set	set	VERB
ejpam-776	97	7	uλ(x	uλ(x	NOUN
ejpam-776	97	8	)	)	PUNCT
ejpam-776	97	9	=	=	SYM
ejpam-776	97	10	|ψλ(x)|2	|ψλ(x)|2	PROPN
ejpam-776	97	11	=	=	SYM
ejpam-776	97	12	�	�	PROPN
ejpam-776	97	13	�	�	PROPN
ejpam-776	97	14	�	�	PROPN
ejpam-776	97	15	�	�	PROPN
ejpam-776	97	16	ϕλ(x)+	ϕλ(x)+	VERB
ejpam-776	97	17	1	1	NUM
ejpam-776	97	18	iλ	iλ	NOUN
ejpam-776	97	19	d	d	NOUN
ejpam-776	97	20	d	d	X
ejpam-776	97	21	x	x	X
ejpam-776	97	22	ϕλ(x	ϕλ(x	PROPN
ejpam-776	97	23	)	)	PUNCT
ejpam-776	97	24	�	�	PROPN
ejpam-776	97	25	�	�	PROPN
ejpam-776	97	26	�	�	PROPN
ejpam-776	97	27	�	�	PROPN
ejpam-776	97	28	2	2	NUM
ejpam-776	97	29	=	=	SYM
ejpam-776	97	30	(	(	PUNCT
ejpam-776	97	31	ϕλ(x	ϕλ(x	PROPN
ejpam-776	97	32	)	)	PUNCT
ejpam-776	97	33	)	)	PUNCT
ejpam-776	98	1	2	2	NUM
ejpam-776	98	2	+	+	SYM
ejpam-776	98	3	1	1	NUM
ejpam-776	98	4	λ2	λ2	NOUN
ejpam-776	98	5	�	�	PROPN
ejpam-776	98	6	d	d	NOUN
ejpam-776	98	7	d	d	X
ejpam-776	98	8	x	x	X
ejpam-776	98	9	ϕλ(x	ϕλ(x	PROPN
ejpam-776	98	10	)	)	PUNCT
ejpam-776	98	11	�	�	PROPN
ejpam-776	98	12	2	2	NUM
ejpam-776	98	13	.	.	PUNCT
ejpam-776	98	14	notice	notice	VERB
ejpam-776	98	15	that	that	SCONJ
ejpam-776	98	16	uλ(x	uλ(x	PUNCT
ejpam-776	98	17	)	)	PUNCT
ejpam-776	98	18	is	be	AUX
ejpam-776	98	19	even	even	ADV
ejpam-776	98	20	in	in	ADP
ejpam-776	98	21	x	x	X
ejpam-776	98	22	.	.	PUNCT
ejpam-776	99	1	by	by	ADP
ejpam-776	99	2	(	(	PUNCT
ejpam-776	99	3	11	11	NUM
ejpam-776	99	4	)	)	PUNCT
ejpam-776	99	5	,	,	PUNCT
ejpam-776	99	6	d	d	PROPN
ejpam-776	99	7	d	d	X
ejpam-776	99	8	x	x	PUNCT
ejpam-776	99	9	uλ(x	uλ(x	NUM
ejpam-776	99	10	)	)	PUNCT
ejpam-776	99	11	=	=	SYM
ejpam-776	99	12	2ϕλ(x	2ϕλ(x	NUM
ejpam-776	99	13	)	)	PUNCT
ejpam-776	99	14	d	d	NOUN
ejpam-776	100	1	d	d	X
ejpam-776	100	2	x	x	X
ejpam-776	100	3	ϕλ(x)+	ϕλ(x)+	PROPN
ejpam-776	100	4	2	2	NUM
ejpam-776	100	5	λ2	λ2	NOUN
ejpam-776	100	6	d	d	NOUN
ejpam-776	100	7	d	d	X
ejpam-776	100	8	x	x	X
ejpam-776	100	9	ϕλ(x	ϕλ(x	PROPN
ejpam-776	100	10	)	)	PUNCT
ejpam-776	100	11	d2	d2	PROPN
ejpam-776	100	12	d	d	PROPN
ejpam-776	100	13	x2	x2	PROPN
ejpam-776	100	14	ϕλ(x	ϕλ(x	PROPN
ejpam-776	100	15	)	)	PUNCT
ejpam-776	101	1	=	=	SYM
ejpam-776	101	2	−	−	PROPN
ejpam-776	101	3	2	2	NUM
ejpam-776	101	4	λ2	λ2	NOUN
ejpam-776	101	5	a′(x	a′(x	NOUN
ejpam-776	101	6	)	)	PUNCT
ejpam-776	101	7	a(x	a(x	PROPN
ejpam-776	101	8	)	)	PUNCT
ejpam-776	101	9	�	�	PROPN
ejpam-776	101	10	d	d	NOUN
ejpam-776	101	11	d	d	X
ejpam-776	101	12	x	x	X
ejpam-776	101	13	ϕλ(x	ϕλ(x	PROPN
ejpam-776	101	14	)	)	PUNCT
ejpam-776	101	15	�	�	PROPN
ejpam-776	101	16	2	2	NUM
ejpam-776	101	17	.	.	PUNCT
ejpam-776	102	1	as	as	SCONJ
ejpam-776	102	2	the	the	DET
ejpam-776	102	3	function	function	NOUN
ejpam-776	102	4	a	a	PRON
ejpam-776	102	5	is	be	AUX
ejpam-776	102	6	increasing	increase	VERB
ejpam-776	102	7	on	on	ADP
ejpam-776	102	8	[	[	X
ejpam-776	102	9	0,∞	0,∞	X
ejpam-776	102	10	[	[	X
ejpam-776	102	11	,	,	PUNCT
ejpam-776	102	12	it	it	PRON
ejpam-776	102	13	follows	follow	VERB
ejpam-776	102	14	that	that	SCONJ
ejpam-776	102	15	uλ	uλ	PRON
ejpam-776	102	16	is	be	AUX
ejpam-776	102	17	decreasing	decrease	VERB
ejpam-776	102	18	on	on	ADP
ejpam-776	102	19	]	]	PUNCT
ejpam-776	102	20	0,∞	0,∞	NOUN
ejpam-776	103	1	[	[	X
ejpam-776	103	2	.	.	PUNCT
ejpam-776	104	1	as	as	ADP
ejpam-776	104	2	uλ(0	uλ(0	NOUN
ejpam-776	104	3	)	)	PUNCT
ejpam-776	104	4	=	=	SYM
ejpam-776	104	5	1	1	NUM
ejpam-776	104	6	,	,	PUNCT
ejpam-776	104	7	we	we	PRON
ejpam-776	104	8	deduce	deduce	VERB
ejpam-776	104	9	that	that	SCONJ
ejpam-776	104	10	uλ(x)≤	uλ(x)≤	PROPN
ejpam-776	104	11	1	1	NUM
ejpam-776	104	12	for	for	ADP
ejpam-776	104	13	all	all	DET
ejpam-776	104	14	x	x	PRON
ejpam-776	104	15	≥	≥	NUM
ejpam-776	104	16	0	0	NUM
ejpam-776	104	17	.	.	PUNCT
ejpam-776	105	1	this	this	PRON
ejpam-776	105	2	ends	end	VERB
ejpam-776	105	3	the	the	DET
ejpam-776	105	4	proof	proof	NOUN
ejpam-776	105	5	.	.	PUNCT
ejpam-776	106	1	notation	notation	NOUN
ejpam-776	106	2	.	.	PUNCT
ejpam-776	107	1	for	for	ADP
ejpam-776	107	2	a	a	DET
ejpam-776	107	3	positive	positive	ADJ
ejpam-776	107	4	borel	borel	NOUN
ejpam-776	107	5	measure	measure	NOUN
ejpam-776	107	6	µ	µ	X
ejpam-776	107	7	on	on	ADP
ejpam-776	107	8	r	r	NOUN
ejpam-776	107	9	,	,	PUNCT
ejpam-776	107	10	and	and	CCONJ
ejpam-776	107	11	p	p	X
ejpam-776	107	12	=	=	SYM
ejpam-776	107	13	1	1	NUM
ejpam-776	107	14	or	or	CCONJ
ejpam-776	107	15	2	2	NUM
ejpam-776	107	16	,	,	PUNCT
ejpam-776	107	17	we	we	PRON
ejpam-776	107	18	write	write	VERB
ejpam-776	107	19	lp(r	lp(r	PROPN
ejpam-776	107	20	,	,	PUNCT
ejpam-776	107	21	dµ	dµ	PROPN
ejpam-776	107	22	)	)	PUNCT
ejpam-776	107	23	for	for	ADP
ejpam-776	107	24	the	the	DET
ejpam-776	107	25	class	class	NOUN
ejpam-776	107	26	of	of	ADP
ejpam-776	107	27	measurable	measurable	ADJ
ejpam-776	107	28	functions	function	NOUN
ejpam-776	107	29	f	f	X
ejpam-776	107	30	on	on	ADP
ejpam-776	107	31	r	r	NOUN
ejpam-776	107	32	for	for	ADP
ejpam-776	107	33	which	which	PRON
ejpam-776	107	34	‖	‖	PROPN
ejpam-776	107	35	f	f	PROPN
ejpam-776	107	36	‖p,µ	‖p,µ	PROPN
ejpam-776	107	37	=	=	SYM
ejpam-776	107	38	�	�	PROPN
ejpam-776	107	39	∫	∫	PROPN
ejpam-776	107	40	r	r	NOUN
ejpam-776	107	41	|	|	NOUN
ejpam-776	107	42	f	f	PROPN
ejpam-776	107	43	(	(	PUNCT
ejpam-776	107	44	x)|pdµ(x	x)|pdµ(x	NUM
ejpam-776	107	45	)	)	PUNCT
ejpam-776	107	46	�	�	PROPN
ejpam-776	107	47	1	1	NUM
ejpam-776	107	48	/	/	SYM
ejpam-776	107	49	p	p	X
ejpam-776	107	50	<	<	X
ejpam-776	107	51	∞.	∞.	PROPN
ejpam-776	107	52	definition	definition	NOUN
ejpam-776	107	53	1	1	NUM
ejpam-776	107	54	.	.	PUNCT
ejpam-776	108	1	the	the	DET
ejpam-776	108	2	generalized	generalize	VERB
ejpam-776	108	3	fourier	fourier	NOUN
ejpam-776	108	4	transform	transform	NOUN
ejpam-776	108	5	of	of	ADP
ejpam-776	108	6	a	a	DET
ejpam-776	108	7	function	function	NOUN
ejpam-776	108	8	f	f	PROPN
ejpam-776	108	9	in	in	ADP
ejpam-776	108	10	l1(r	l1(r	PROPN
ejpam-776	108	11	,	,	PUNCT
ejpam-776	108	12	a(x)d	a(x)d	PUNCT
ejpam-776	108	13	x	x	PRON
ejpam-776	108	14	)	)	PUNCT
ejpam-776	108	15	is	be	AUX
ejpam-776	108	16	defined	define	VERB
ejpam-776	108	17	by	by	ADP
ejpam-776	108	18	fλ	fλ	PROPN
ejpam-776	108	19	(	(	PUNCT
ejpam-776	108	20	f	f	PROPN
ejpam-776	108	21	)	)	PUNCT
ejpam-776	108	22	(	(	PUNCT
ejpam-776	108	23	λ	λ	X
ejpam-776	108	24	)	)	PUNCT
ejpam-776	108	25	=	=	SYM
ejpam-776	109	1	∫	∫	PROPN
ejpam-776	109	2	r	r	NOUN
ejpam-776	109	3	f	f	X
ejpam-776	109	4	(	(	PUNCT
ejpam-776	109	5	x)ψ−λ(x)a(x)d	x)ψ−λ(x)a(x)d	PROPN
ejpam-776	109	6	x	x	X
ejpam-776	109	7	.	.	PUNCT
ejpam-776	110	1	(	(	PUNCT
ejpam-776	110	2	13	13	NUM
ejpam-776	110	3	)	)	PUNCT
ejpam-776	110	4	remark	remark	NOUN
ejpam-776	110	5	3	3	NUM
ejpam-776	110	6	.	.	PUNCT
ejpam-776	111	1	let	let	VERB
ejpam-776	111	2	f	f	PROPN
ejpam-776	111	3	∈	∈	PROPN
ejpam-776	111	4	l1(r	l1(r	PROPN
ejpam-776	111	5	,	,	PUNCT
ejpam-776	111	6	a(x)d	a(x)d	PUNCT
ejpam-776	111	7	x	x	X
ejpam-776	111	8	)	)	PUNCT
ejpam-776	111	9	.	.	PUNCT
ejpam-776	112	1	by	by	ADP
ejpam-776	112	2	lemma	lemma	PROPN
ejpam-776	112	3	1	1	NUM
ejpam-776	112	4	,	,	PUNCT
ejpam-776	112	5	it	it	PRON
ejpam-776	112	6	follows	follow	VERB
ejpam-776	112	7	that	that	SCONJ
ejpam-776	112	8	fλ	fλ	PROPN
ejpam-776	112	9	(	(	PUNCT
ejpam-776	112	10	f	f	PROPN
ejpam-776	112	11	)	)	PUNCT
ejpam-776	112	12	is	be	AUX
ejpam-776	112	13	continuous	continuous	ADJ
ejpam-776	112	14	on	on	ADP
ejpam-776	112	15	r	r	NOUN
ejpam-776	112	16	and	and	CCONJ
ejpam-776	112	17	||fλ	||fλ	NUM
ejpam-776	113	1	(	(	PUNCT
ejpam-776	113	2	f	f	NOUN
ejpam-776	113	3	)	)	PUNCT
ejpam-776	113	4	||∞	||∞	PROPN
ejpam-776	113	5	≤	≤	PROPN
ejpam-776	113	6	‖	‖	PROPN
ejpam-776	113	7	f	f	PROPN
ejpam-776	113	8	‖1,a	‖1,a	PROPN
ejpam-776	113	9	.	.	PUNCT
ejpam-776	114	1	an	an	DET
ejpam-776	114	2	outstanding	outstanding	ADJ
ejpam-776	114	3	result	result	NOUN
ejpam-776	114	4	about	about	ADP
ejpam-776	114	5	the	the	DET
ejpam-776	114	6	generalized	generalize	VERB
ejpam-776	114	7	fourier	fourier	NOUN
ejpam-776	114	8	transform	transform	NOUN
ejpam-776	114	9	f	f	NOUN
ejpam-776	114	10	is	be	AUX
ejpam-776	114	11	as	as	SCONJ
ejpam-776	114	12	follows	follow	NOUN
ejpam-776	114	13	.	.	PUNCT
ejpam-776	115	1	theorem	theorem	NOUN
ejpam-776	115	2	1	1	NUM
ejpam-776	115	3	.	.	PUNCT
ejpam-776	116	1	[	[	X
ejpam-776	116	2	8	8	NUM
ejpam-776	116	3	]	]	PUNCT
ejpam-776	116	4	(	(	PUNCT
ejpam-776	116	5	i	i	NOUN
ejpam-776	116	6	)	)	PUNCT
ejpam-776	116	7	for	for	ADP
ejpam-776	116	8	every	every	DET
ejpam-776	116	9	f	f	PROPN
ejpam-776	116	10	∈	∈	PROPN
ejpam-776	116	11	l1	l1	PROPN
ejpam-776	116	12	∩	∩	PROPN
ejpam-776	116	13	l2(r	l2(r	PROPN
ejpam-776	116	14	,	,	PUNCT
ejpam-776	116	15	a(x)d	a(x)d	PROPN
ejpam-776	116	16	x	x	PRON
ejpam-776	116	17	)	)	PUNCT
ejpam-776	116	18	we	we	PRON
ejpam-776	116	19	have	have	VERB
ejpam-776	116	20	the	the	DET
ejpam-776	116	21	plancherel	plancherel	NOUN
ejpam-776	116	22	formula	formula	NOUN
ejpam-776	116	23	∫	∫	PROPN
ejpam-776	117	1	r	r	NOUN
ejpam-776	118	1	|	|	NOUN
ejpam-776	119	1	f	f	X
ejpam-776	119	2	(	(	PUNCT
ejpam-776	119	3	x)|2a(x)d	x)|2a(x)d	X
ejpam-776	119	4	x	x	SYM
ejpam-776	119	5	=	=	SYM
ejpam-776	119	6	∫	∫	PROPN
ejpam-776	119	7	r	r	NOUN
ejpam-776	119	8	|fλ	|fλ	PROPN
ejpam-776	119	9	(	(	PUNCT
ejpam-776	119	10	f	f	NOUN
ejpam-776	119	11	)	)	PUNCT
ejpam-776	119	12	(	(	PUNCT
ejpam-776	119	13	λ)|2dσ(λ	λ)|2dσ(λ	NUM
ejpam-776	119	14	)	)	PUNCT
ejpam-776	119	15	.	.	PUNCT
ejpam-776	120	1	w.	w.	PROPN
ejpam-776	120	2	chabeh	chabeh	PROPN
ejpam-776	120	3	,	,	PUNCT
ejpam-776	120	4	m.	m.	NOUN
ejpam-776	120	5	mourou	mourou	PROPN
ejpam-776	120	6	/	/	SYM
ejpam-776	120	7	eur	eur	PROPN
ejpam-776	120	8	.	.	PUNCT
ejpam-776	121	1	j.	j.	PROPN
ejpam-776	121	2	pure	pure	PROPN
ejpam-776	121	3	appl	appl	PROPN
ejpam-776	121	4	.	.	PROPN
ejpam-776	121	5	math	math	PROPN
ejpam-776	121	6	,	,	PUNCT
ejpam-776	121	7	3	3	NUM
ejpam-776	121	8	(	(	PUNCT
ejpam-776	121	9	2010	2010	NUM
ejpam-776	121	10	)	)	PUNCT
ejpam-776	121	11	,	,	PUNCT
ejpam-776	121	12	958	958	NUM
ejpam-776	121	13	-	-	SYM
ejpam-776	121	14	979	979	NUM
ejpam-776	121	15	964	964	NUM
ejpam-776	121	16	where	where	SCONJ
ejpam-776	121	17	dσ(λ	dσ(λ	VERB
ejpam-776	121	18	)	)	PUNCT
ejpam-776	121	19	=	=	SYM
ejpam-776	121	20	dλ	dλ	NOUN
ejpam-776	121	21	|c(|λ|)|2	|c(|λ|)|2	NOUN
ejpam-776	121	22	,	,	PUNCT
ejpam-776	121	23	c(z	c(z	PROPN
ejpam-776	121	24	)	)	PUNCT
ejpam-776	121	25	being	be	AUX
ejpam-776	121	26	a	a	DET
ejpam-776	121	27	continuous	continuous	ADJ
ejpam-776	121	28	functions	function	NOUN
ejpam-776	121	29	on	on	ADP
ejpam-776	121	30	]	]	X
ejpam-776	121	31	0,∞	0,∞	NOUN
ejpam-776	121	32	[	[	PUNCT
ejpam-776	121	33	such	such	ADJ
ejpam-776	121	34	that	that	DET
ejpam-776	121	35	c(z)−1	c(z)−1	NOUN
ejpam-776	121	36	∼	∼	NOUN
ejpam-776	121	37	k1	k1	NOUN
ejpam-776	121	38	zα+	zα+	PROPN
ejpam-776	121	39	1	1	NUM
ejpam-776	121	40	2	2	NUM
ejpam-776	121	41	,	,	PUNCT
ejpam-776	121	42	as	as	ADP
ejpam-776	121	43	z→∞	z→∞	NUM
ejpam-776	121	44	,	,	PUNCT
ejpam-776	121	45	c(z)−1	c(z)−1	NOUN
ejpam-776	121	46	∼	∼	NOUN
ejpam-776	121	47	k2	k2	PROPN
ejpam-776	121	48	zα+	zα+	PROPN
ejpam-776	121	49	1	1	NUM
ejpam-776	121	50	2	2	NUM
ejpam-776	121	51	,	,	PUNCT
ejpam-776	121	52	as	as	ADP
ejpam-776	121	53	z→	z→	PROPN
ejpam-776	121	54	0	0	NUM
ejpam-776	121	55	,	,	PUNCT
ejpam-776	121	56	for	for	ADP
ejpam-776	121	57	some	some	DET
ejpam-776	121	58	k1	k1	NOUN
ejpam-776	121	59	,	,	PUNCT
ejpam-776	121	60	k2	k2	PROPN
ejpam-776	121	61	∈	∈	PROPN
ejpam-776	121	62	c.	c.	PROPN
ejpam-776	121	63	(	(	PUNCT
ejpam-776	121	64	ii	ii	PROPN
ejpam-776	121	65	)	)	PUNCT
ejpam-776	121	66	the	the	DET
ejpam-776	121	67	generalized	generalize	VERB
ejpam-776	121	68	fourier	fourier	NOUN
ejpam-776	121	69	transform	transform	NOUN
ejpam-776	121	70	fλ	fλ	PRON
ejpam-776	121	71	extends	extend	VERB
ejpam-776	121	72	uniquely	uniquely	ADV
ejpam-776	121	73	to	to	ADP
ejpam-776	121	74	a	a	DET
ejpam-776	121	75	unitary	unitary	ADJ
ejpam-776	121	76	isomorphism	isomorphism	NOUN
ejpam-776	121	77	from	from	ADP
ejpam-776	121	78	l2(r	l2(r	PROPN
ejpam-776	121	79	,	,	PUNCT
ejpam-776	121	80	a(x)d	a(x)d	PROPN
ejpam-776	121	81	x	x	X
ejpam-776	121	82	)	)	PUNCT
ejpam-776	121	83	onto	onto	ADP
ejpam-776	121	84	l2(r	l2(r	PROPN
ejpam-776	121	85	,	,	PUNCT
ejpam-776	121	86	dσ	dσ	PROPN
ejpam-776	121	87	)	)	PUNCT
ejpam-776	121	88	.	.	PUNCT
ejpam-776	122	1	the	the	DET
ejpam-776	122	2	inverse	inverse	NOUN
ejpam-776	122	3	transform	transform	NOUN
ejpam-776	122	4	is	be	AUX
ejpam-776	122	5	given	give	VERB
ejpam-776	122	6	by	by	ADP
ejpam-776	122	7	f−1	f−1	PROPN
ejpam-776	122	8	λ	λ	PROPN
ejpam-776	122	9	g(x	g(x	NOUN
ejpam-776	122	10	)	)	PUNCT
ejpam-776	123	1	=	=	SYM
ejpam-776	123	2	∫	∫	PROPN
ejpam-776	123	3	r	r	PROPN
ejpam-776	123	4	g(λ)ψλ(x)dσ(λ	g(λ)ψλ(x)dσ(λ	PROPN
ejpam-776	123	5	)	)	PUNCT
ejpam-776	123	6	where	where	SCONJ
ejpam-776	123	7	the	the	DET
ejpam-776	123	8	integral	integral	ADJ
ejpam-776	123	9	converges	converge	NOUN
ejpam-776	123	10	in	in	ADP
ejpam-776	123	11	l2(r	l2(r	NOUN
ejpam-776	123	12	,	,	PUNCT
ejpam-776	123	13	a(x)d	a(x)d	PROPN
ejpam-776	123	14	x	x	X
ejpam-776	123	15	)	)	PUNCT
ejpam-776	123	16	.	.	PUNCT
ejpam-776	124	1	remark	remark	PROPN
ejpam-776	124	2	4	4	NUM
ejpam-776	124	3	.	.	PUNCT
ejpam-776	125	1	(	(	PUNCT
ejpam-776	125	2	i	i	NOUN
ejpam-776	125	3	)	)	PUNCT
ejpam-776	125	4	the	the	DET
ejpam-776	125	5	tempered	temper	VERB
ejpam-776	125	6	measure	measure	NOUN
ejpam-776	125	7	σ	σ	PROPN
ejpam-776	125	8	is	be	AUX
ejpam-776	125	9	called	call	VERB
ejpam-776	125	10	the	the	DET
ejpam-776	125	11	spectral	spectral	ADJ
ejpam-776	125	12	measure	measure	NOUN
ejpam-776	125	13	associated	associate	VERB
ejpam-776	125	14	with	with	ADP
ejpam-776	125	15	the	the	DET
ejpam-776	125	16	differentialdifference	differentialdifference	NOUN
ejpam-776	125	17	operator	operator	NOUN
ejpam-776	125	18	λ	λ	PROPN
ejpam-776	125	19	.	.	PUNCT
ejpam-776	126	1	(	(	PUNCT
ejpam-776	126	2	ii	ii	NOUN
ejpam-776	126	3	)	)	PUNCT
ejpam-776	126	4	for	for	ADP
ejpam-776	126	5	a(x	a(x	NOUN
ejpam-776	126	6	)	)	PUNCT
ejpam-776	126	7	=	=	PUNCT
ejpam-776	126	8	|x	|x	NOUN
ejpam-776	126	9	|2α+1	|2α+1	NOUN
ejpam-776	126	10	,	,	PUNCT
ejpam-776	126	11	α	α	PROPN
ejpam-776	126	12	>	>	X
ejpam-776	126	13	−1/2	−1/2	PROPN
ejpam-776	126	14	,	,	PUNCT
ejpam-776	126	15	we	we	PRON
ejpam-776	126	16	have	have	VERB
ejpam-776	126	17	c(s	c(	NOUN
ejpam-776	126	18	)	)	PUNCT
ejpam-776	126	19	=	=	SYM
ejpam-776	127	1	2α+1	2α+1	NOUN
ejpam-776	127	2	γ(α+	γ(α+	DET
ejpam-776	127	3	1	1	NUM
ejpam-776	127	4	)	)	PUNCT
ejpam-776	127	5	sα+1/2	sα+1/2	NOUN
ejpam-776	127	6	.	.	PUNCT
ejpam-776	128	1	the	the	DET
ejpam-776	128	2	following	follow	VERB
ejpam-776	128	3	lemma	lemma	PROPN
ejpam-776	128	4	will	will	AUX
ejpam-776	128	5	play	play	VERB
ejpam-776	128	6	a	a	DET
ejpam-776	128	7	key	key	ADJ
ejpam-776	128	8	role	role	NOUN
ejpam-776	128	9	in	in	ADP
ejpam-776	128	10	the	the	DET
ejpam-776	128	11	remainder	remainder	NOUN
ejpam-776	128	12	of	of	ADP
ejpam-776	128	13	this	this	DET
ejpam-776	128	14	section	section	NOUN
ejpam-776	128	15	.	.	PUNCT
ejpam-776	129	1	lemma	lemma	PROPN
ejpam-776	129	2	2	2	NUM
ejpam-776	129	3	.	.	PUNCT
ejpam-776	130	1	the	the	DET
ejpam-776	130	2	map	map	NOUN
ejpam-776	130	3	j	j	PROPN
ejpam-776	130	4	,	,	PUNCT
ejpam-776	130	5	given	give	VERB
ejpam-776	130	6	by	by	ADP
ejpam-776	130	7	(	(	PUNCT
ejpam-776	130	8	7	7	NUM
ejpam-776	130	9	)	)	PUNCT
ejpam-776	130	10	,	,	PUNCT
ejpam-776	130	11	is	be	AUX
ejpam-776	130	12	a	a	DET
ejpam-776	130	13	topological	topological	ADJ
ejpam-776	130	14	isomorphism	isomorphism	NOUN
ejpam-776	130	15	from	from	ADP
ejpam-776	130	16	so(r	so(r	NOUN
ejpam-776	130	17	)	)	PUNCT
ejpam-776	130	18	onto	onto	ADP
ejpam-776	130	19	se(r	se(r	NOUN
ejpam-776	130	20	)	)	PUNCT
ejpam-776	130	21	;	;	PUNCT
ejpam-776	130	22	frombo(r	frombo(r	X
ejpam-776	130	23	)	)	PUNCT
ejpam-776	130	24	ontobe(r	ontobe(r	NOUN
ejpam-776	130	25	)	)	PUNCT
ejpam-776	130	26	.	.	PUNCT
ejpam-776	131	1	proof	proof	NOUN
ejpam-776	131	2	.	.	PUNCT
ejpam-776	132	1	(	(	PUNCT
ejpam-776	132	2	i	i	NOUN
ejpam-776	132	3	)	)	PUNCT
ejpam-776	132	4	it	it	PRON
ejpam-776	132	5	is	be	AUX
ejpam-776	132	6	sufficient	sufficient	ADJ
ejpam-776	132	7	to	to	PART
ejpam-776	132	8	show	show	VERB
ejpam-776	132	9	that	that	SCONJ
ejpam-776	132	10	j	j	PROPN
ejpam-776	132	11	maps	map	VERB
ejpam-776	132	12	continuously	continuously	ADV
ejpam-776	132	13	so(r	so(r	NOUN
ejpam-776	132	14	)	)	PUNCT
ejpam-776	132	15	into	into	ADP
ejpam-776	132	16	se(r	se(r	NOUN
ejpam-776	132	17	)	)	PUNCT
ejpam-776	132	18	.	.	PUNCT
ejpam-776	133	1	let	let	VERB
ejpam-776	133	2	f	f	PROPN
ejpam-776	133	3	∈	∈	PROPN
ejpam-776	133	4	so(r	so(r	PROPN
ejpam-776	133	5	)	)	PUNCT
ejpam-776	133	6	.	.	PUNCT
ejpam-776	134	1	clearly	clearly	ADV
ejpam-776	134	2	j	j	PROPN
ejpam-776	134	3	f	f	PROPN
ejpam-776	134	4	is	be	AUX
ejpam-776	134	5	a	a	DET
ejpam-776	134	6	c∞	c∞	NOUN
ejpam-776	134	7	even	even	ADV
ejpam-776	134	8	function	function	NOUN
ejpam-776	134	9	on	on	ADP
ejpam-776	134	10	r.	r.	PROPN
ejpam-776	134	11	for	for	ADP
ejpam-776	134	12	n	n	NOUN
ejpam-776	134	13	=	=	SYM
ejpam-776	134	14	1,2	1,2	NUM
ejpam-776	134	15	,	,	PUNCT
ejpam-776	134	16	.	.	PUNCT
ejpam-776	134	17	.	.	PUNCT
ejpam-776	135	1	.	.	PUNCT
ejpam-776	135	2	,	,	PUNCT
ejpam-776	135	3	pm	pm	PROPN
ejpam-776	135	4	,	,	PUNCT
ejpam-776	135	5	n(j	n(j	PROPN
ejpam-776	135	6	f	f	NOUN
ejpam-776	135	7	)	)	PUNCT
ejpam-776	136	1	=	=	SYM
ejpam-776	136	2	pm	pm	NOUN
ejpam-776	136	3	,	,	PUNCT
ejpam-776	136	4	n−1	n−1	PROPN
ejpam-776	136	5	(	(	PUNCT
ejpam-776	136	6	f	f	PROPN
ejpam-776	136	7	)	)	PUNCT
ejpam-776	136	8	.	.	PUNCT
ejpam-776	137	1	moreover	moreover	ADV
ejpam-776	137	2	,	,	PUNCT
ejpam-776	137	3	(	(	PUNCT
ejpam-776	137	4	1	1	NUM
ejpam-776	137	5	+	+	NUM
ejpam-776	137	6	x2)m	x2)m	NOUN
ejpam-776	137	7	|j	|j	NOUN
ejpam-776	137	8	f	f	X
ejpam-776	138	1	(	(	PUNCT
ejpam-776	138	2	x)|	x)|	PROPN
ejpam-776	138	3	≤	≤	PROPN
ejpam-776	138	4	(	(	PUNCT
ejpam-776	138	5	1	1	NUM
ejpam-776	138	6	+	+	NUM
ejpam-776	138	7	x2)m	x2)m	PROPN
ejpam-776	138	8	∫	∫	PROPN
ejpam-776	139	1	∞	∞	PROPN
ejpam-776	140	1	|x	|x	NOUN
ejpam-776	141	1	|	|	ADV
ejpam-776	142	1	|	|	ADV
ejpam-776	142	2	f	f	PROPN
ejpam-776	142	3	(	(	PUNCT
ejpam-776	142	4	t)|d	t)|d	PROPN
ejpam-776	142	5	t	t	PROPN
ejpam-776	142	6	w.	w.	PROPN
ejpam-776	142	7	chabeh	chabeh	PROPN
ejpam-776	142	8	,	,	PUNCT
ejpam-776	142	9	m.	m.	NOUN
ejpam-776	142	10	mourou	mourou	PROPN
ejpam-776	142	11	/	/	SYM
ejpam-776	142	12	eur	eur	PROPN
ejpam-776	142	13	.	.	PUNCT
ejpam-776	143	1	j.	j.	PROPN
ejpam-776	143	2	pure	pure	PROPN
ejpam-776	143	3	appl	appl	PROPN
ejpam-776	143	4	.	.	PROPN
ejpam-776	143	5	math	math	PROPN
ejpam-776	143	6	,	,	PUNCT
ejpam-776	143	7	3	3	NUM
ejpam-776	143	8	(	(	PUNCT
ejpam-776	143	9	2010	2010	NUM
ejpam-776	143	10	)	)	PUNCT
ejpam-776	143	11	,	,	PUNCT
ejpam-776	143	12	958	958	NUM
ejpam-776	143	13	-	-	SYM
ejpam-776	143	14	979	979	NUM
ejpam-776	143	15	965	965	NUM
ejpam-776	143	16	≤	≤	NUM
ejpam-776	143	17	∫	∫	PROPN
ejpam-776	143	18	∞	∞	PROPN
ejpam-776	143	19	|x	|x	NOUN
ejpam-776	143	20	|	|	ADV
ejpam-776	143	21	(	(	PUNCT
ejpam-776	143	22	1	1	NUM
ejpam-776	143	23	+	+	NUM
ejpam-776	143	24	t2)m	t2)m	NOUN
ejpam-776	144	1	|	|	INTJ
ejpam-776	144	2	f	f	PROPN
ejpam-776	144	3	(	(	PUNCT
ejpam-776	144	4	t)|d	t)|d	PROPN
ejpam-776	144	5	t	t	PROPN
ejpam-776	145	1	≤	≤	NOUN
ejpam-776	145	2	pm+1,0	pm+1,0	PROPN
ejpam-776	145	3	(	(	PUNCT
ejpam-776	145	4	f	f	PROPN
ejpam-776	145	5	)	)	PUNCT
ejpam-776	145	6	∫	∫	PROPN
ejpam-776	146	1	∞	∞	PROPN
ejpam-776	146	2	|x	|x	NOUN
ejpam-776	147	1	|	|	INTJ
ejpam-776	147	2	d	d	X
ejpam-776	147	3	t	t	PROPN
ejpam-776	147	4	(	(	PUNCT
ejpam-776	147	5	1	1	NUM
ejpam-776	147	6	+	+	NUM
ejpam-776	147	7	t2	t2	NOUN
ejpam-776	147	8	)	)	PUNCT
ejpam-776	147	9	hence	hence	ADV
ejpam-776	147	10	pm,0(j	pm,0(j	PROPN
ejpam-776	147	11	f	f	PROPN
ejpam-776	147	12	)	)	PUNCT
ejpam-776	147	13	≤	≤	PROPN
ejpam-776	148	1	π	π	PROPN
ejpam-776	148	2	2	2	NUM
ejpam-776	148	3	pm+1,0	pm+1,0	PROPN
ejpam-776	148	4	(	(	PUNCT
ejpam-776	148	5	f	f	PROPN
ejpam-776	148	6	)	)	PUNCT
ejpam-776	148	7	.	.	PUNCT
ejpam-776	149	1	(	(	PUNCT
ejpam-776	149	2	ii	ii	NOUN
ejpam-776	149	3	)	)	PUNCT
ejpam-776	149	4	let	let	VERB
ejpam-776	149	5	f	f	PROPN
ejpam-776	149	6	∈bo(r	∈bo(r	PROPN
ejpam-776	149	7	)	)	PUNCT
ejpam-776	149	8	.	.	PUNCT
ejpam-776	150	1	by	by	ADP
ejpam-776	150	2	using	use	VERB
ejpam-776	150	3	(	(	PUNCT
ejpam-776	150	4	8)	8)	NUM
ejpam-776	150	5	and	and	CCONJ
ejpam-776	150	6	by	by	ADP
ejpam-776	150	7	integrating	integrate	VERB
ejpam-776	150	8	by	by	ADP
ejpam-776	150	9	parts	part	NOUN
ejpam-776	150	10	we	we	PRON
ejpam-776	150	11	have	have	VERB
ejpam-776	150	12	for	for	ADP
ejpam-776	150	13	any	any	DET
ejpam-776	150	14	n=	n=	ADJ
ejpam-776	150	15	0,1	0,1	NUM
ejpam-776	150	16	,	,	PUNCT
ejpam-776	150	17	.	.	PUNCT
ejpam-776	150	18	.	.	PUNCT
ejpam-776	150	19	.	.	PUNCT
ejpam-776	151	1	,	,	PUNCT
ejpam-776	152	1	∫	∫	PROPN
ejpam-776	152	2	r	r	PROPN
ejpam-776	152	3	j	j	PROPN
ejpam-776	153	1	f	f	X
ejpam-776	153	2	(	(	PUNCT
ejpam-776	153	3	x	x	X
ejpam-776	153	4	)	)	PUNCT
ejpam-776	153	5	bn(x)a(x)d	bn(x)a(x)d	NUM
ejpam-776	153	6	x	x	PUNCT
ejpam-776	153	7	=	=	SYM
ejpam-776	153	8	∫	∫	PROPN
ejpam-776	153	9	r	r	PROPN
ejpam-776	153	10	j	j	PROPN
ejpam-776	153	11	f	f	X
ejpam-776	153	12	(	(	PUNCT
ejpam-776	153	13	x)λbn+1(x)a(x)d	x)λbn+1(x)a(x)d	NOUN
ejpam-776	153	14	x	x	X
ejpam-776	153	15	=	=	SYM
ejpam-776	154	1	−	−	NOUN
ejpam-776	154	2	∫	∫	NOUN
ejpam-776	154	3	r	r	NOUN
ejpam-776	154	4	λj	λj	PROPN
ejpam-776	154	5	f	f	X
ejpam-776	154	6	(	(	PUNCT
ejpam-776	154	7	x	x	NOUN
ejpam-776	154	8	)	)	PUNCT
ejpam-776	154	9	bn+1(x)a(x)d	bn+1(x)a(x)d	NOUN
ejpam-776	154	10	x	x	SYM
ejpam-776	154	11	=	=	PUNCT
ejpam-776	155	1	−	−	NOUN
ejpam-776	155	2	∫	∫	PROPN
ejpam-776	155	3	r	r	NOUN
ejpam-776	155	4	f	f	PROPN
ejpam-776	155	5	(	(	PUNCT
ejpam-776	155	6	x)bn+1(x)a(x)d	x)bn+1(x)a(x)d	PROPN
ejpam-776	155	7	x	x	SYM
ejpam-776	155	8	=	=	SYM
ejpam-776	155	9	0	0	NUM
ejpam-776	155	10	,	,	PUNCT
ejpam-776	155	11	which	which	PRON
ejpam-776	155	12	shows	show	VERB
ejpam-776	155	13	that	that	SCONJ
ejpam-776	155	14	j	j	PROPN
ejpam-776	155	15	f	f	PROPN
ejpam-776	155	16	∈	∈	PROPN
ejpam-776	155	17	be(r	be(r	NUM
ejpam-776	155	18	)	)	PUNCT
ejpam-776	155	19	.	.	PUNCT
ejpam-776	156	1	conversely	conversely	ADV
ejpam-776	156	2	,	,	PUNCT
ejpam-776	156	3	let	let	VERB
ejpam-776	156	4	f	f	PRON
ejpam-776	156	5	∈be(r	∈be(r	ADV
ejpam-776	156	6	)	)	PUNCT
ejpam-776	156	7	.	.	PUNCT
ejpam-776	157	1	identity	identity	NOUN
ejpam-776	157	2	(	(	PUNCT
ejpam-776	157	3	8)	8)	NUM
ejpam-776	157	4	together	together	ADV
ejpam-776	157	5	with	with	ADP
ejpam-776	157	6	an	an	DET
ejpam-776	157	7	integration	integration	NOUN
ejpam-776	157	8	by	by	ADP
ejpam-776	157	9	parts	part	NOUN
ejpam-776	157	10	yields	yield	NOUN
ejpam-776	157	11	for	for	ADP
ejpam-776	157	12	any	any	DET
ejpam-776	157	13	n=	n=	ADJ
ejpam-776	157	14	1,2	1,2	NUM
ejpam-776	157	15	,	,	PUNCT
ejpam-776	157	16	.	.	PUNCT
ejpam-776	157	17	.	.	PUNCT
ejpam-776	158	1	.	.	PUNCT
ejpam-776	159	1	,	,	PUNCT
ejpam-776	159	2	∫	∫	PROPN
ejpam-776	159	3	r	r	NOUN
ejpam-776	159	4	f	f	PROPN
ejpam-776	159	5	′(x)bn(x)a(x)d	′(x)bn(x)a(x)d	X
ejpam-776	159	6	x	x	SYM
ejpam-776	160	1	=	=	SYM
ejpam-776	160	2	∫	∫	PROPN
ejpam-776	160	3	r	r	NOUN
ejpam-776	160	4	λ	λ	X
ejpam-776	160	5	f	f	X
ejpam-776	160	6	(	(	PUNCT
ejpam-776	160	7	x)bn(x)a(x)d	x)bn(x)a(x)d	PROPN
ejpam-776	160	8	x	x	X
ejpam-776	160	9	=	=	SYM
ejpam-776	161	1	−	−	NOUN
ejpam-776	161	2	∫	∫	PROPN
ejpam-776	161	3	r	r	NOUN
ejpam-776	161	4	f	f	PROPN
ejpam-776	161	5	(	(	PUNCT
ejpam-776	161	6	x)λbn(x)a(x)d	x)λbn(x)a(x)d	PART
ejpam-776	161	7	x	x	X
ejpam-776	161	8	=	=	PUNCT
ejpam-776	162	1	−	−	NOUN
ejpam-776	162	2	∫	∫	PROPN
ejpam-776	162	3	r	r	NOUN
ejpam-776	162	4	f	f	PROPN
ejpam-776	162	5	(	(	PUNCT
ejpam-776	162	6	x)bn−1(x)a(x)d	x)bn−1(x)a(x)d	PUNCT
ejpam-776	162	7	x	x	SYM
ejpam-776	162	8	=	=	SYM
ejpam-776	162	9	0	0	NUM
ejpam-776	162	10	,	,	PUNCT
ejpam-776	162	11	which	which	PRON
ejpam-776	162	12	shows	show	VERB
ejpam-776	162	13	that	that	SCONJ
ejpam-776	162	14	f	f	PROPN
ejpam-776	162	15	′	′	NUM
ejpam-776	162	16	∈bo(r	∈bo(r	PROPN
ejpam-776	162	17	)	)	PUNCT
ejpam-776	162	18	.	.	PUNCT
ejpam-776	163	1	proposition	proposition	NOUN
ejpam-776	163	2	1	1	NUM
ejpam-776	163	3	.	.	PUNCT
ejpam-776	164	1	(	(	PUNCT
ejpam-776	164	2	i	i	NOUN
ejpam-776	164	3	)	)	PUNCT
ejpam-776	164	4	for	for	ADP
ejpam-776	164	5	all	all	DET
ejpam-776	164	6	f	f	PROPN
ejpam-776	164	7	in	in	ADP
ejpam-776	164	8	s	s	PROPN
ejpam-776	164	9	(	(	PUNCT
ejpam-776	164	10	r	r	NOUN
ejpam-776	164	11	)	)	PUNCT
ejpam-776	164	12	,	,	PUNCT
ejpam-776	164	13	we	we	PRON
ejpam-776	164	14	have	have	VERB
ejpam-776	164	15	fλ(λ	fλ(λ	NUM
ejpam-776	164	16	f	f	PROPN
ejpam-776	164	17	)	)	PUNCT
ejpam-776	164	18	(	(	PUNCT
ejpam-776	164	19	λ	λ	NOUN
ejpam-776	164	20	)	)	PUNCT
ejpam-776	164	21	=	=	SYM
ejpam-776	164	22	iλfλ	iλfλ	NOUN
ejpam-776	164	23	(	(	PUNCT
ejpam-776	164	24	f	f	NOUN
ejpam-776	164	25	)	)	PUNCT
ejpam-776	164	26	(	(	PUNCT
ejpam-776	164	27	λ	λ	NOUN
ejpam-776	164	28	)	)	PUNCT
ejpam-776	164	29	.	.	PUNCT
ejpam-776	165	1	(	(	PUNCT
ejpam-776	165	2	14	14	NUM
ejpam-776	165	3	)	)	PUNCT
ejpam-776	165	4	(	(	PUNCT
ejpam-776	165	5	ii	ii	NOUN
ejpam-776	165	6	)	)	PUNCT
ejpam-776	165	7	for	for	ADP
ejpam-776	165	8	all	all	DET
ejpam-776	165	9	f	f	PROPN
ejpam-776	165	10	in	in	ADP
ejpam-776	165	11	s	s	PROPN
ejpam-776	165	12	(	(	PUNCT
ejpam-776	165	13	r	r	NOUN
ejpam-776	165	14	)	)	PUNCT
ejpam-776	165	15	,	,	PUNCT
ejpam-776	165	16	we	we	PRON
ejpam-776	165	17	have	have	VERB
ejpam-776	165	18	fλ	fλ	PRON
ejpam-776	165	19	(	(	PUNCT
ejpam-776	165	20	f	f	NOUN
ejpam-776	165	21	)	)	PUNCT
ejpam-776	165	22	(	(	PUNCT
ejpam-776	165	23	λ	λ	NOUN
ejpam-776	165	24	)	)	PUNCT
ejpam-776	165	25	=	=	SYM
ejpam-776	165	26	f∆	f∆	NOUN
ejpam-776	165	27	(	(	PUNCT
ejpam-776	165	28	fe)(λ)+	fe)(λ)+	NOUN
ejpam-776	165	29	iλf∆(j	iλf∆(j	PUNCT
ejpam-776	165	30	fo)(λ	fo)(λ	PROPN
ejpam-776	165	31	)	)	PUNCT
ejpam-776	165	32	,	,	PUNCT
ejpam-776	165	33	(	(	PUNCT
ejpam-776	165	34	15	15	NUM
ejpam-776	165	35	)	)	PUNCT
ejpam-776	165	36	where	where	SCONJ
ejpam-776	165	37	f∆	f∆	NOUN
ejpam-776	165	38	stands	stand	VERB
ejpam-776	165	39	for	for	ADP
ejpam-776	165	40	the	the	DET
ejpam-776	165	41	fourier	fourier	NOUN
ejpam-776	165	42	transform	transform	NOUN
ejpam-776	165	43	related	relate	VERB
ejpam-776	165	44	to	to	ADP
ejpam-776	165	45	the	the	DET
ejpam-776	165	46	differential	differential	ADJ
ejpam-776	165	47	operator	operator	NOUN
ejpam-776	165	48	∆	∆	PROPN
ejpam-776	165	49	,	,	PUNCT
ejpam-776	165	50	defined	define	VERB
ejpam-776	165	51	on	on	ADP
ejpam-776	165	52	se(r	se(r	NOUN
ejpam-776	165	53	)	)	PUNCT
ejpam-776	165	54	by	by	ADP
ejpam-776	165	55	f∆(h)(λ	f∆(h)(λ	NOUN
ejpam-776	165	56	)	)	PUNCT
ejpam-776	165	57	=	=	SYM
ejpam-776	166	1	∫	∫	PROPN
ejpam-776	166	2	r	r	NOUN
ejpam-776	166	3	h(x)ϕλ(x)a(x)d	h(x)ϕλ(x)a(x)d	PROPN
ejpam-776	166	4	x	x	X
ejpam-776	166	5	,	,	PUNCT
ejpam-776	166	6	λ	λ	X
ejpam-776	166	7	∈	∈	PROPN
ejpam-776	166	8	r	r	NOUN
ejpam-776	166	9	,	,	PUNCT
ejpam-776	166	10	fe	fe	NOUN
ejpam-776	166	11	and	and	CCONJ
ejpam-776	166	12	fo	fo	ADP
ejpam-776	166	13	being	be	AUX
ejpam-776	166	14	respectively	respectively	ADV
ejpam-776	166	15	the	the	DET
ejpam-776	166	16	even	even	ADJ
ejpam-776	166	17	and	and	CCONJ
ejpam-776	166	18	odd	odd	ADJ
ejpam-776	166	19	parts	part	NOUN
ejpam-776	166	20	of	of	ADP
ejpam-776	166	21	f	f	PROPN
ejpam-776	166	22	given	give	VERB
ejpam-776	166	23	by	by	ADP
ejpam-776	166	24	(	(	PUNCT
ejpam-776	166	25	3	3	NUM
ejpam-776	166	26	)	)	PUNCT
ejpam-776	166	27	.	.	PUNCT
ejpam-776	167	1	w.	w.	PROPN
ejpam-776	167	2	chabeh	chabeh	PROPN
ejpam-776	167	3	,	,	PUNCT
ejpam-776	167	4	m.	m.	NOUN
ejpam-776	167	5	mourou	mourou	PROPN
ejpam-776	167	6	/	/	SYM
ejpam-776	167	7	eur	eur	PROPN
ejpam-776	167	8	.	.	PUNCT
ejpam-776	168	1	j.	j.	PROPN
ejpam-776	168	2	pure	pure	PROPN
ejpam-776	168	3	appl	appl	PROPN
ejpam-776	168	4	.	.	PROPN
ejpam-776	168	5	math	math	PROPN
ejpam-776	168	6	,	,	PUNCT
ejpam-776	168	7	3	3	NUM
ejpam-776	168	8	(	(	PUNCT
ejpam-776	168	9	2010	2010	NUM
ejpam-776	168	10	)	)	PUNCT
ejpam-776	168	11	,	,	PUNCT
ejpam-776	168	12	958	958	NUM
ejpam-776	168	13	-	-	SYM
ejpam-776	168	14	979	979	NUM
ejpam-776	168	15	966	966	NUM
ejpam-776	168	16	proof	proof	NOUN
ejpam-776	168	17	.	.	PUNCT
ejpam-776	169	1	(	(	PUNCT
ejpam-776	169	2	i	i	NOUN
ejpam-776	169	3	)	)	PUNCT
ejpam-776	169	4	let	let	VERB
ejpam-776	169	5	f	f	PROPN
ejpam-776	169	6	∈	∈	PROPN
ejpam-776	169	7	s	s	PART
ejpam-776	169	8	(	(	PUNCT
ejpam-776	169	9	r	r	NOUN
ejpam-776	169	10	)	)	PUNCT
ejpam-776	169	11	.	.	PUNCT
ejpam-776	170	1	by	by	ADP
ejpam-776	170	2	(	(	PUNCT
ejpam-776	170	3	5	5	NUM
ejpam-776	170	4	)	)	PUNCT
ejpam-776	170	5	,	,	PUNCT
ejpam-776	170	6	(	(	PUNCT
ejpam-776	170	7	10	10	NUM
ejpam-776	170	8	)	)	PUNCT
ejpam-776	170	9	and	and	CCONJ
ejpam-776	170	10	(	(	PUNCT
ejpam-776	170	11	13	13	NUM
ejpam-776	170	12	)	)	PUNCT
ejpam-776	170	13	,	,	PUNCT
ejpam-776	170	14	fλ(λ	fλ(λ	NUM
ejpam-776	170	15	f	f	PROPN
ejpam-776	170	16	)	)	PUNCT
ejpam-776	170	17	(	(	PUNCT
ejpam-776	170	18	λ	λ	X
ejpam-776	170	19	)	)	PUNCT
ejpam-776	170	20	=	=	SYM
ejpam-776	170	21	∫	∫	PROPN
ejpam-776	170	22	r	r	NOUN
ejpam-776	170	23	�	�	PROPN
ejpam-776	170	24	f	f	PROPN
ejpam-776	170	25	′o	′o	PROPN
ejpam-776	170	26	(	(	PUNCT
ejpam-776	170	27	x)+	x)+	PROPN
ejpam-776	170	28	a′(x	a′(x	PROPN
ejpam-776	170	29	)	)	PUNCT
ejpam-776	170	30	a(x	a(x	PROPN
ejpam-776	170	31	)	)	PUNCT
ejpam-776	170	32	fo(x	fo(x	PUNCT
ejpam-776	170	33	)	)	PUNCT
ejpam-776	170	34	�	�	PROPN
ejpam-776	170	35	ϕλ(x)a(x)d	ϕλ(x)a(x)d	X
ejpam-776	170	36	x	x	SYM
ejpam-776	170	37	−	−	PROPN
ejpam-776	170	38	1	1	NUM
ejpam-776	170	39	iλ	iλ	NOUN
ejpam-776	170	40	∫	∫	PROPN
ejpam-776	170	41	r	r	NOUN
ejpam-776	170	42	f	f	PROPN
ejpam-776	170	43	′e	′e	PROPN
ejpam-776	170	44	(	(	PUNCT
ejpam-776	170	45	x)ϕ	x)ϕ	PUNCT
ejpam-776	170	46	′	′	NUM
ejpam-776	170	47	λ(x)a(x)d	λ(x)a(x)d	PUNCT
ejpam-776	170	48	x	x	SYM
ejpam-776	170	49	=	=	SYM
ejpam-776	170	50	κ1	κ1	PROPN
ejpam-776	170	51	−	−	PROPN
ejpam-776	170	52	κ2	κ2	PROPN
ejpam-776	170	53	iλ	iλ	NOUN
ejpam-776	170	54	.	.	PUNCT
ejpam-776	171	1	by	by	ADP
ejpam-776	171	2	integrating	integrate	VERB
ejpam-776	171	3	by	by	ADP
ejpam-776	171	4	parts	part	NOUN
ejpam-776	171	5	we	we	PRON
ejpam-776	171	6	get	get	VERB
ejpam-776	171	7	κ1	κ1	NOUN
ejpam-776	171	8	=	=	SYM
ejpam-776	171	9	∫	∫	PROPN
ejpam-776	172	1	r	r	NOUN
ejpam-776	172	2	(	(	PUNCT
ejpam-776	172	3	a(x	a(x	PROPN
ejpam-776	172	4	)	)	PUNCT
ejpam-776	172	5	fo(x	fo(x	PUNCT
ejpam-776	172	6	)	)	PUNCT
ejpam-776	172	7	)	)	PUNCT
ejpam-776	172	8	′ϕλ(x)d	′ϕλ(x)d	NOUN
ejpam-776	172	9	x	x	X
ejpam-776	172	10	=	=	SYM
ejpam-776	173	1	−	−	PROPN
ejpam-776	173	2	∫	∫	NOUN
ejpam-776	173	3	r	r	NOUN
ejpam-776	173	4	fo(x)ϕ	fo(x)ϕ	PUNCT
ejpam-776	173	5	′	′	NUM
ejpam-776	173	6	λ(x)a(x)d	λ(x)a(x)d	X
ejpam-776	173	7	x	x	X
ejpam-776	173	8	and	and	CCONJ
ejpam-776	173	9	κ2	κ2	NOUN
ejpam-776	173	10	=	=	SYM
ejpam-776	173	11	∫	∫	PROPN
ejpam-776	173	12	r	r	NOUN
ejpam-776	173	13	f	f	PROPN
ejpam-776	173	14	′e	′e	PROPN
ejpam-776	173	15	(	(	PUNCT
ejpam-776	173	16	x)ϕ	x)ϕ	PUNCT
ejpam-776	173	17	′	′	NUM
ejpam-776	173	18	λ(x)a(x)d	λ(x)a(x)d	PUNCT
ejpam-776	173	19	x	x	SYM
ejpam-776	173	20	=	=	PUNCT
ejpam-776	174	1	−	−	PROPN
ejpam-776	174	2	∫	∫	NOUN
ejpam-776	174	3	r	r	NOUN
ejpam-776	174	4	fe(x)(a(x)ϕ	fe(x)(a(x)ϕ	NOUN
ejpam-776	174	5	′	′	NUM
ejpam-776	174	6	λ(x	λ(x	PROPN
ejpam-776	174	7	)	)	PUNCT
ejpam-776	174	8	)	)	PUNCT
ejpam-776	175	1	′d	′d	NOUN
ejpam-776	175	2	x	x	SYM
ejpam-776	175	3	=	=	PUNCT
ejpam-776	176	1	−	−	NOUN
ejpam-776	176	2	∫	∫	NOUN
ejpam-776	176	3	r	r	NOUN
ejpam-776	176	4	fe(x)∆ϕλ(x)a(x)d	fe(x)∆ϕλ(x)a(x)d	PROPN
ejpam-776	176	5	x	x	SYM
ejpam-776	176	6	=	=	SYM
ejpam-776	176	7	λ2	λ2	NOUN
ejpam-776	176	8	∫	∫	NOUN
ejpam-776	176	9	r	r	NOUN
ejpam-776	176	10	fe(x)ϕλ(x)a(x)d	fe(x)ϕλ(x)a(x)d	NOUN
ejpam-776	176	11	x	x	PUNCT
ejpam-776	176	12	by	by	ADP
ejpam-776	176	13	virtue	virtue	NOUN
ejpam-776	176	14	of	of	ADP
ejpam-776	176	15	(	(	PUNCT
ejpam-776	176	16	11	11	NUM
ejpam-776	176	17	)	)	PUNCT
ejpam-776	176	18	.	.	PUNCT
ejpam-776	177	1	hence	hence	ADV
ejpam-776	177	2	κ1	κ1	PROPN
ejpam-776	177	3	−	−	PROPN
ejpam-776	177	4	κ2	κ2	PROPN
ejpam-776	177	5	iλ	iλ	PROPN
ejpam-776	177	6	=	=	PUNCT
ejpam-776	177	7	iλ	iλ	PROPN
ejpam-776	177	8	∫	∫	PROPN
ejpam-776	177	9	r	r	PROPN
ejpam-776	177	10	�	�	PROPN
ejpam-776	177	11	fe(x)ϕλ(x)−	fe(x)ϕλ(x)−	PROPN
ejpam-776	177	12	fo(x	fo(x	PUNCT
ejpam-776	177	13	)	)	PUNCT
ejpam-776	177	14	ϕ′	ϕ′	PUNCT
ejpam-776	178	1	λ	λ	X
ejpam-776	178	2	(	(	PUNCT
ejpam-776	178	3	x	x	NOUN
ejpam-776	178	4	)	)	PUNCT
ejpam-776	178	5	iλ	iλ	PROPN
ejpam-776	178	6	�	�	PROPN
ejpam-776	178	7	a(x)d	a(x)d	NOUN
ejpam-776	178	8	x	x	SYM
ejpam-776	178	9	=	=	PUNCT
ejpam-776	178	10	iλ	iλ	PROPN
ejpam-776	178	11	∫	∫	PROPN
ejpam-776	178	12	r	r	NOUN
ejpam-776	178	13	f	f	PROPN
ejpam-776	178	14	(	(	PUNCT
ejpam-776	178	15	x)φ−λ(x)a(x)d	x)φ−λ(x)a(x)d	PROPN
ejpam-776	178	16	x	x	X
ejpam-776	178	17	.	.	PUNCT
ejpam-776	179	1	this	this	PRON
ejpam-776	179	2	clearly	clearly	ADV
ejpam-776	179	3	yields	yield	VERB
ejpam-776	179	4	(	(	PUNCT
ejpam-776	179	5	14	14	NUM
ejpam-776	179	6	)	)	PUNCT
ejpam-776	179	7	.	.	PUNCT
ejpam-776	180	1	(	(	PUNCT
ejpam-776	180	2	ii	ii	NOUN
ejpam-776	180	3	)	)	PUNCT
ejpam-776	180	4	if	if	SCONJ
ejpam-776	180	5	f	f	PROPN
ejpam-776	180	6	∈	∈	PROPN
ejpam-776	180	7	se(r	se(r	NOUN
ejpam-776	180	8	)	)	PUNCT
ejpam-776	180	9	,	,	PUNCT
ejpam-776	180	10	identity	identity	NOUN
ejpam-776	180	11	(	(	PUNCT
ejpam-776	180	12	15	15	NUM
ejpam-776	180	13	)	)	PUNCT
ejpam-776	180	14	is	be	AUX
ejpam-776	180	15	obvious	obvious	ADJ
ejpam-776	180	16	.	.	PUNCT
ejpam-776	181	1	assume	assume	VERB
ejpam-776	181	2	f	f	PROPN
ejpam-776	181	3	∈	∈	PROPN
ejpam-776	181	4	so(r	so(r	PROPN
ejpam-776	181	5	)	)	PUNCT
ejpam-776	181	6	.	.	PUNCT
ejpam-776	182	1	by	by	ADP
ejpam-776	182	2	using	use	VERB
ejpam-776	182	3	(	(	PUNCT
ejpam-776	182	4	10	10	NUM
ejpam-776	182	5	)	)	PUNCT
ejpam-776	182	6	,	,	PUNCT
ejpam-776	182	7	(	(	PUNCT
ejpam-776	182	8	11	11	NUM
ejpam-776	182	9	)	)	PUNCT
ejpam-776	182	10	,	,	PUNCT
ejpam-776	182	11	(	(	PUNCT
ejpam-776	182	12	13	13	NUM
ejpam-776	182	13	)	)	PUNCT
ejpam-776	182	14	and	and	CCONJ
ejpam-776	182	15	by	by	ADP
ejpam-776	182	16	integrating	integrate	VERB
ejpam-776	182	17	by	by	ADP
ejpam-776	182	18	parts	part	NOUN
ejpam-776	182	19	we	we	PRON
ejpam-776	182	20	obtain	obtain	VERB
ejpam-776	182	21	fλ	fλ	PROPN
ejpam-776	182	22	(	(	PUNCT
ejpam-776	182	23	f	f	PROPN
ejpam-776	182	24	)	)	PUNCT
ejpam-776	182	25	(	(	PUNCT
ejpam-776	182	26	λ	λ	X
ejpam-776	182	27	)	)	PUNCT
ejpam-776	182	28	=	=	SYM
ejpam-776	182	29	−	−	PROPN
ejpam-776	182	30	1	1	NUM
ejpam-776	182	31	iλ	iλ	NOUN
ejpam-776	182	32	∫	∫	PROPN
ejpam-776	182	33	r	r	NOUN
ejpam-776	182	34	f	f	PROPN
ejpam-776	182	35	(	(	PUNCT
ejpam-776	182	36	x)ϕ′λ(x)a(x)d	x)ϕ′λ(x)a(x)d	NOUN
ejpam-776	182	37	x	x	X
ejpam-776	182	38	=	=	SYM
ejpam-776	182	39	1	1	NUM
ejpam-776	182	40	iλ	iλ	NOUN
ejpam-776	182	41	∫	∫	PROPN
ejpam-776	182	42	r	r	PROPN
ejpam-776	182	43	j	j	PROPN
ejpam-776	182	44	f	f	PROPN
ejpam-776	182	45	(	(	PUNCT
ejpam-776	182	46	x)(a(x)ϕ′λ(x	x)(a(x)ϕ′λ(x	PROPN
ejpam-776	182	47	)	)	PUNCT
ejpam-776	182	48	)	)	PUNCT
ejpam-776	183	1	′d	′d	INTJ
ejpam-776	183	2	x	x	SYM
ejpam-776	183	3	w.	w.	PROPN
ejpam-776	183	4	chabeh	chabeh	PROPN
ejpam-776	183	5	,	,	PUNCT
ejpam-776	183	6	m.	m.	NOUN
ejpam-776	183	7	mourou	mourou	PROPN
ejpam-776	183	8	/	/	SYM
ejpam-776	183	9	eur	eur	PROPN
ejpam-776	183	10	.	.	PUNCT
ejpam-776	184	1	j.	j.	PROPN
ejpam-776	184	2	pure	pure	PROPN
ejpam-776	184	3	appl	appl	PROPN
ejpam-776	184	4	.	.	PROPN
ejpam-776	184	5	math	math	PROPN
ejpam-776	184	6	,	,	PUNCT
ejpam-776	184	7	3	3	NUM
ejpam-776	184	8	(	(	PUNCT
ejpam-776	184	9	2010	2010	NUM
ejpam-776	184	10	)	)	PUNCT
ejpam-776	184	11	,	,	PUNCT
ejpam-776	184	12	958	958	NUM
ejpam-776	184	13	-	-	SYM
ejpam-776	184	14	979	979	NUM
ejpam-776	184	15	967	967	NUM
ejpam-776	184	16	=	=	SYM
ejpam-776	184	17	1	1	NUM
ejpam-776	184	18	iλ	iλ	NOUN
ejpam-776	184	19	∫	∫	PROPN
ejpam-776	184	20	r	r	PROPN
ejpam-776	184	21	j	j	PROPN
ejpam-776	184	22	f	f	X
ejpam-776	184	23	(	(	PUNCT
ejpam-776	184	24	x)∆ϕλ(x)a(x)d	x)∆ϕλ(x)a(x)d	NUM
ejpam-776	184	25	x	x	X
ejpam-776	184	26	=	=	PUNCT
ejpam-776	184	27	iλ	iλ	PROPN
ejpam-776	184	28	∫	∫	PROPN
ejpam-776	184	29	r	r	PROPN
ejpam-776	184	30	j	j	PROPN
ejpam-776	184	31	f	f	X
ejpam-776	184	32	(	(	PUNCT
ejpam-776	184	33	x)ϕλ(x)a(x)d	x)ϕλ(x)a(x)d	PROPN
ejpam-776	184	34	x	x	X
ejpam-776	184	35	=	=	PUNCT
ejpam-776	184	36	iλf∆j	iλf∆j	VERB
ejpam-776	184	37	f	f	PROPN
ejpam-776	184	38	(	(	PUNCT
ejpam-776	184	39	λ	λ	PROPN
ejpam-776	184	40	)	)	PUNCT
ejpam-776	184	41	,	,	PUNCT
ejpam-776	184	42	which	which	PRON
ejpam-776	184	43	completes	complete	VERB
ejpam-776	184	44	the	the	DET
ejpam-776	184	45	proof	proof	NOUN
ejpam-776	184	46	.	.	PUNCT
ejpam-776	185	1	theorem	theorem	NOUN
ejpam-776	185	2	2	2	NUM
ejpam-776	185	3	.	.	PUNCT
ejpam-776	186	1	the	the	DET
ejpam-776	186	2	generalized	generalized	ADJ
ejpam-776	186	3	fourier	fourier	NOUN
ejpam-776	186	4	transform	transform	NOUN
ejpam-776	186	5	fλ	fλ	PROPN
ejpam-776	186	6	is	be	AUX
ejpam-776	186	7	a	a	DET
ejpam-776	186	8	topological	topological	ADJ
ejpam-776	186	9	isomorphism	isomorphism	NOUN
ejpam-776	186	10	from	from	ADP
ejpam-776	186	11	s	s	PRON
ejpam-776	186	12	(	(	PUNCT
ejpam-776	186	13	r	r	NOUN
ejpam-776	186	14	)	)	PUNCT
ejpam-776	186	15	onto	onto	ADP
ejpam-776	186	16	itself	itself	PRON
ejpam-776	186	17	;	;	PUNCT
ejpam-776	186	18	fromb(r	fromb(r	X
ejpam-776	186	19	)	)	PUNCT
ejpam-776	186	20	ontoh	ontoh	NOUN
ejpam-776	186	21	(	(	PUNCT
ejpam-776	186	22	r	r	NOUN
ejpam-776	186	23	)	)	PUNCT
ejpam-776	186	24	.	.	PUNCT
ejpam-776	187	1	proof	proof	NOUN
ejpam-776	187	2	.	.	PUNCT
ejpam-776	188	1	by	by	ADP
ejpam-776	188	2	[	[	X
ejpam-776	188	3	13	13	NUM
ejpam-776	188	4	]	]	PUNCT
ejpam-776	188	5	we	we	PRON
ejpam-776	188	6	know	know	VERB
ejpam-776	188	7	that	that	SCONJ
ejpam-776	188	8	the	the	DET
ejpam-776	188	9	transform	transform	NOUN
ejpam-776	188	10	f∆	f∆	NOUN
ejpam-776	188	11	is	be	AUX
ejpam-776	188	12	a	a	DET
ejpam-776	188	13	topological	topological	ADJ
ejpam-776	188	14	isomorphism	isomorphism	NOUN
ejpam-776	188	15	from	from	ADP
ejpam-776	188	16	se(r	se(r	NOUN
ejpam-776	188	17	)	)	PUNCT
ejpam-776	188	18	onto	onto	ADP
ejpam-776	188	19	itself	itself	PRON
ejpam-776	188	20	;	;	PUNCT
ejpam-776	188	21	from	from	ADP
ejpam-776	188	22	be(r	be(r	NUM
ejpam-776	188	23	)	)	PUNCT
ejpam-776	188	24	ontohe(r	ontohe(r	NOUN
ejpam-776	188	25	)	)	PUNCT
ejpam-776	188	26	.	.	PUNCT
ejpam-776	189	1	the	the	DET
ejpam-776	189	2	result	result	NOUN
ejpam-776	189	3	follows	follow	VERB
ejpam-776	189	4	then	then	ADV
ejpam-776	189	5	from	from	ADP
ejpam-776	189	6	(	(	PUNCT
ejpam-776	189	7	15	15	NUM
ejpam-776	189	8	)	)	PUNCT
ejpam-776	189	9	,	,	PUNCT
ejpam-776	189	10	lemma	lemma	PROPN
ejpam-776	189	11	2	2	NUM
ejpam-776	189	12	and	and	CCONJ
ejpam-776	189	13	the	the	DET
ejpam-776	189	14	fact	fact	NOUN
ejpam-776	189	15	that	that	SCONJ
ejpam-776	189	16	the	the	DET
ejpam-776	189	17	operator	operator	NOUN
ejpam-776	189	18	λ	λ	NOUN
ejpam-776	189	19	7→	7→	NUM
ejpam-776	189	20	λ	λ	X
ejpam-776	189	21	f	f	PROPN
ejpam-776	189	22	is	be	AUX
ejpam-776	189	23	a	a	DET
ejpam-776	189	24	topological	topological	ADJ
ejpam-776	189	25	isomorphism	isomorphism	NOUN
ejpam-776	189	26	from	from	ADP
ejpam-776	189	27	se(r	se(r	NOUN
ejpam-776	189	28	)	)	PUNCT
ejpam-776	189	29	onto	onto	ADP
ejpam-776	189	30	so(r	so(r	NOUN
ejpam-776	189	31	)	)	PUNCT
ejpam-776	189	32	;	;	PUNCT
ejpam-776	189	33	from	from	ADP
ejpam-776	189	34	he(r	he(r	NOUN
ejpam-776	189	35	)	)	PUNCT
ejpam-776	189	36	ontoho(r	ontoho(r	NOUN
ejpam-776	189	37	)	)	PUNCT
ejpam-776	189	38	.	.	PUNCT
ejpam-776	190	1	proposition	proposition	NOUN
ejpam-776	190	2	2	2	NUM
ejpam-776	190	3	.	.	PUNCT
ejpam-776	190	4	(	(	PUNCT
ejpam-776	190	5	i	i	NOUN
ejpam-776	190	6	)	)	PUNCT
ejpam-776	190	7	for	for	ADP
ejpam-776	190	8	all	all	DET
ejpam-776	190	9	f	f	PROPN
ejpam-776	190	10	∈	∈	PROPN
ejpam-776	190	11	s	s	X
ejpam-776	190	12	(	(	PUNCT
ejpam-776	190	13	r	r	NOUN
ejpam-776	190	14	)	)	PUNCT
ejpam-776	190	15	,	,	PUNCT
ejpam-776	190	16	fλ	fλ	X
ejpam-776	190	17	(	(	PUNCT
ejpam-776	190	18	f	f	NOUN
ejpam-776	190	19	)	)	PUNCT
ejpam-776	190	20	=	=	NOUN
ejpam-776	190	21	fu	fu	NOUN
ejpam-776	190	22	◦	◦	NOUN
ejpam-776	190	23	t	t	X
ejpam-776	190	24	v	v	X
ejpam-776	190	25	(	(	PUNCT
ejpam-776	190	26	f	f	PROPN
ejpam-776	190	27	)	)	PUNCT
ejpam-776	190	28	,	,	PUNCT
ejpam-776	190	29	(	(	PUNCT
ejpam-776	190	30	16	16	NUM
ejpam-776	190	31	)	)	PUNCT
ejpam-776	190	32	where	where	SCONJ
ejpam-776	190	33	fu	fu	PROPN
ejpam-776	190	34	denotes	denote	VERB
ejpam-776	190	35	the	the	DET
ejpam-776	190	36	usual	usual	ADJ
ejpam-776	190	37	fourier	fourier	NOUN
ejpam-776	190	38	transform	transform	NOUN
ejpam-776	190	39	on	on	ADP
ejpam-776	190	40	r	r	NOUN
ejpam-776	190	41	given	give	VERB
ejpam-776	190	42	by	by	ADP
ejpam-776	190	43	fu	fu	PROPN
ejpam-776	190	44	(	(	PUNCT
ejpam-776	190	45	f	f	PROPN
ejpam-776	190	46	)	)	PUNCT
ejpam-776	190	47	(	(	PUNCT
ejpam-776	190	48	λ	λ	X
ejpam-776	190	49	)	)	PUNCT
ejpam-776	190	50	=	=	SYM
ejpam-776	191	1	∫	∫	PROPN
ejpam-776	191	2	r	r	NOUN
ejpam-776	191	3	f	f	PROPN
ejpam-776	191	4	(	(	PUNCT
ejpam-776	191	5	x)e−iλx	x)e−iλx	PROPN
ejpam-776	191	6	d	d	X
ejpam-776	191	7	x	x	PROPN
ejpam-776	191	8	.	.	PUNCT
ejpam-776	191	9	(	(	PUNCT
ejpam-776	191	10	ii	ii	NOUN
ejpam-776	191	11	)	)	PUNCT
ejpam-776	191	12	for	for	ADP
ejpam-776	191	13	all	all	DET
ejpam-776	191	14	f	f	PROPN
ejpam-776	191	15	∈	∈	PROPN
ejpam-776	191	16	s	s	X
ejpam-776	191	17	(	(	PUNCT
ejpam-776	191	18	r	r	NOUN
ejpam-776	191	19	)	)	PUNCT
ejpam-776	191	20	,	,	PUNCT
ejpam-776	192	1	d	d	PROPN
ejpam-776	192	2	d	d	X
ejpam-776	192	3	x	x	SYM
ejpam-776	192	4	t	t	PROPN
ejpam-776	192	5	v	v	NOUN
ejpam-776	192	6	f	f	PROPN
ejpam-776	192	7	=	=	SYM
ejpam-776	192	8	t	t	PROPN
ejpam-776	192	9	vλ	vλ	INTJ
ejpam-776	192	10	f	f	PROPN
ejpam-776	192	11	.	.	PUNCT
ejpam-776	193	1	(	(	PUNCT
ejpam-776	193	2	17	17	NUM
ejpam-776	193	3	)	)	PUNCT
ejpam-776	193	4	proof	proof	NOUN
ejpam-776	193	5	.	.	PUNCT
ejpam-776	194	1	assertion	assertion	NOUN
ejpam-776	194	2	(	(	PUNCT
ejpam-776	194	3	i	i	NOUN
ejpam-776	194	4	)	)	PUNCT
ejpam-776	194	5	follows	follow	VERB
ejpam-776	194	6	by	by	ADP
ejpam-776	194	7	applying	apply	VERB
ejpam-776	194	8	the	the	DET
ejpam-776	194	9	usual	usual	ADJ
ejpam-776	194	10	fourier	fourier	NOUN
ejpam-776	194	11	transform	transform	NOUN
ejpam-776	194	12	fu	fu	NOUN
ejpam-776	194	13	to	to	ADP
ejpam-776	194	14	both	both	DET
ejpam-776	194	15	sides	side	NOUN
ejpam-776	194	16	of	of	ADP
ejpam-776	194	17	(	(	PUNCT
ejpam-776	194	18	6	6	NUM
ejpam-776	194	19	)	)	PUNCT
ejpam-776	194	20	and	and	CCONJ
ejpam-776	194	21	by	by	ADP
ejpam-776	194	22	using	use	VERB
ejpam-776	194	23	the	the	DET
ejpam-776	194	24	identity	identity	NOUN
ejpam-776	194	25	f∆h(λ	f∆h(λ	NOUN
ejpam-776	194	26	)	)	PUNCT
ejpam-776	195	1	=	=	NOUN
ejpam-776	195	2	fu	fu	NOUN
ejpam-776	195	3	�	�	PROPN
ejpam-776	195	4	tx	tx	PROPN
ejpam-776	195	5	h	h	PROPN
ejpam-776	195	6	�	�	PROPN
ejpam-776	195	7	(	(	PUNCT
ejpam-776	195	8	λ	λ	PROPN
ejpam-776	195	9	)	)	PUNCT
ejpam-776	195	10	,	,	PUNCT
ejpam-776	195	11	h	h	NOUN
ejpam-776	195	12	∈	∈	PROPN
ejpam-776	195	13	se(r	se(r	NOUN
ejpam-776	195	14	)	)	PUNCT
ejpam-776	195	15	,	,	PUNCT
ejpam-776	195	16	(	(	PUNCT
ejpam-776	195	17	see	see	VERB
ejpam-776	195	18	[	[	X
ejpam-776	195	19	13	13	NUM
ejpam-776	195	20	]	]	NUM
ejpam-776	195	21	)	)	PUNCT
ejpam-776	195	22	.	.	PUNCT
ejpam-776	196	1	the	the	DET
ejpam-776	196	2	intertwining	intertwine	VERB
ejpam-776	196	3	relation	relation	NOUN
ejpam-776	196	4	(	(	PUNCT
ejpam-776	196	5	17	17	NUM
ejpam-776	196	6	)	)	PUNCT
ejpam-776	196	7	follows	follow	VERB
ejpam-776	196	8	by	by	ADP
ejpam-776	196	9	applying	apply	VERB
ejpam-776	196	10	the	the	DET
ejpam-776	196	11	usual	usual	ADJ
ejpam-776	196	12	fourier	fourier	NOUN
ejpam-776	196	13	transform	transform	NOUN
ejpam-776	196	14	fu	fu	NOUN
ejpam-776	196	15	to	to	ADP
ejpam-776	196	16	both	both	CCONJ
ejpam-776	196	17	its	its	PRON
ejpam-776	196	18	sides	side	NOUN
ejpam-776	196	19	and	and	CCONJ
ejpam-776	196	20	by	by	ADP
ejpam-776	196	21	using	use	VERB
ejpam-776	196	22	(	(	PUNCT
ejpam-776	196	23	14	14	NUM
ejpam-776	196	24	)	)	PUNCT
ejpam-776	196	25	and	and	CCONJ
ejpam-776	196	26	(	(	PUNCT
ejpam-776	196	27	16	16	NUM
ejpam-776	196	28	)	)	PUNCT
ejpam-776	196	29	.	.	PUNCT
ejpam-776	197	1	w.	w.	PROPN
ejpam-776	197	2	chabeh	chabeh	PROPN
ejpam-776	197	3	,	,	PUNCT
ejpam-776	197	4	m.	m.	NOUN
ejpam-776	197	5	mourou	mourou	PROPN
ejpam-776	197	6	/	/	SYM
ejpam-776	197	7	eur	eur	PROPN
ejpam-776	197	8	.	.	PUNCT
ejpam-776	198	1	j.	j.	PROPN
ejpam-776	198	2	pure	pure	PROPN
ejpam-776	198	3	appl	appl	PROPN
ejpam-776	198	4	.	.	PROPN
ejpam-776	198	5	math	math	PROPN
ejpam-776	198	6	,	,	PUNCT
ejpam-776	198	7	3	3	NUM
ejpam-776	198	8	(	(	PUNCT
ejpam-776	198	9	2010	2010	NUM
ejpam-776	198	10	)	)	PUNCT
ejpam-776	198	11	,	,	PUNCT
ejpam-776	198	12	958	958	NUM
ejpam-776	198	13	-	-	SYM
ejpam-776	198	14	979	979	NUM
ejpam-776	198	15	968	968	NUM
ejpam-776	198	16	theorem	theorem	NOUN
ejpam-776	198	17	3	3	NUM
ejpam-776	198	18	.	.	PUNCT
ejpam-776	199	1	the	the	DET
ejpam-776	199	2	intertwining	intertwine	VERB
ejpam-776	199	3	operator	operator	NOUN
ejpam-776	199	4	t	t	PROPN
ejpam-776	199	5	v	v	NOUN
ejpam-776	199	6	is	be	AUX
ejpam-776	199	7	a	a	DET
ejpam-776	199	8	topological	topological	ADJ
ejpam-776	199	9	isomorphism	isomorphism	NOUN
ejpam-776	199	10	from	from	ADP
ejpam-776	199	11	s	s	PRON
ejpam-776	199	12	(	(	PUNCT
ejpam-776	199	13	r	r	NOUN
ejpam-776	199	14	)	)	PUNCT
ejpam-776	199	15	onto	onto	ADP
ejpam-776	199	16	itself	itself	PRON
ejpam-776	199	17	;	;	PUNCT
ejpam-776	199	18	fromb(r	fromb(r	X
ejpam-776	199	19	)	)	PUNCT
ejpam-776	199	20	ontow	ontow	NOUN
ejpam-776	199	21	(	(	PUNCT
ejpam-776	199	22	r	r	NOUN
ejpam-776	199	23	)	)	PUNCT
ejpam-776	199	24	.	.	PUNCT
ejpam-776	200	1	proof	proof	NOUN
ejpam-776	200	2	.	.	PUNCT
ejpam-776	201	1	we	we	PRON
ejpam-776	201	2	deduce	deduce	VERB
ejpam-776	201	3	the	the	DET
ejpam-776	201	4	result	result	NOUN
ejpam-776	201	5	from	from	ADP
ejpam-776	201	6	(	(	PUNCT
ejpam-776	201	7	16	16	NUM
ejpam-776	201	8	)	)	PUNCT
ejpam-776	201	9	,	,	PUNCT
ejpam-776	201	10	theorem	theorem	VERB
ejpam-776	201	11	2	2	NUM
ejpam-776	201	12	and	and	CCONJ
ejpam-776	201	13	the	the	DET
ejpam-776	201	14	fact	fact	NOUN
ejpam-776	201	15	that	that	SCONJ
ejpam-776	201	16	the	the	DET
ejpam-776	201	17	usual	usual	ADJ
ejpam-776	201	18	fourier	fourier	NOUN
ejpam-776	201	19	transform	transform	NOUN
ejpam-776	201	20	fu	fu	NOUN
ejpam-776	201	21	is	be	AUX
ejpam-776	201	22	a	a	DET
ejpam-776	201	23	topological	topological	ADJ
ejpam-776	201	24	isomorphism	isomorphism	NOUN
ejpam-776	201	25	from	from	ADP
ejpam-776	201	26	s	s	PRON
ejpam-776	201	27	(	(	PUNCT
ejpam-776	201	28	r	r	NOUN
ejpam-776	201	29	)	)	PUNCT
ejpam-776	201	30	onto	onto	ADP
ejpam-776	201	31	itself	itself	PRON
ejpam-776	201	32	;	;	PUNCT
ejpam-776	201	33	from	from	ADP
ejpam-776	201	34	w	w	PROPN
ejpam-776	201	35	(	(	PUNCT
ejpam-776	201	36	r	r	NOUN
ejpam-776	201	37	)	)	PUNCT
ejpam-776	201	38	ontoh	ontoh	NOUN
ejpam-776	201	39	(	(	PUNCT
ejpam-776	201	40	r	r	NOUN
ejpam-776	201	41	)	)	PUNCT
ejpam-776	201	42	.	.	PUNCT
ejpam-776	202	1	definition	definition	NOUN
ejpam-776	202	2	2	2	NUM
ejpam-776	202	3	.	.	PUNCT
ejpam-776	203	1	(	(	PUNCT
ejpam-776	203	2	i	i	NOUN
ejpam-776	203	3	)	)	PUNCT
ejpam-776	203	4	the	the	DET
ejpam-776	203	5	generalized	generalize	VERB
ejpam-776	203	6	translation	translation	NOUN
ejpam-776	203	7	operators	operator	NOUN
ejpam-776	203	8	t	t	NOUN
ejpam-776	203	9	x	x	X
ejpam-776	203	10	,	,	PUNCT
ejpam-776	203	11	x	x	PUNCT
ejpam-776	203	12	∈	∈	NOUN
ejpam-776	203	13	r	r	NOUN
ejpam-776	203	14	,	,	PUNCT
ejpam-776	203	15	are	be	AUX
ejpam-776	203	16	defined	define	VERB
ejpam-776	203	17	on	on	ADP
ejpam-776	203	18	l2(r	l2(r	PROPN
ejpam-776	203	19	,	,	PUNCT
ejpam-776	203	20	a(x)d	a(x)d	PROPN
ejpam-776	203	21	x	x	X
ejpam-776	203	22	)	)	PUNCT
ejpam-776	203	23	by	by	ADP
ejpam-776	203	24	the	the	DET
ejpam-776	203	25	relation	relation	NOUN
ejpam-776	203	26	fλ(t	fλ(t	PUNCT
ejpam-776	203	27	x	x	NOUN
ejpam-776	203	28	f	f	PROPN
ejpam-776	203	29	)	)	PUNCT
ejpam-776	203	30	(	(	PUNCT
ejpam-776	203	31	λ	λ	NOUN
ejpam-776	203	32	)	)	PUNCT
ejpam-776	203	33	=	=	SYM
ejpam-776	203	34	ψλ(x)fλ	ψλ(x)fλ	PROPN
ejpam-776	203	35	(	(	PUNCT
ejpam-776	203	36	f	f	NOUN
ejpam-776	203	37	)	)	PUNCT
ejpam-776	203	38	(	(	PUNCT
ejpam-776	203	39	λ	λ	NOUN
ejpam-776	203	40	)	)	PUNCT
ejpam-776	203	41	.	.	PUNCT
ejpam-776	204	1	(	(	PUNCT
ejpam-776	204	2	18	18	NUM
ejpam-776	204	3	)	)	PUNCT
ejpam-776	204	4	(	(	PUNCT
ejpam-776	204	5	ii	ii	NOUN
ejpam-776	204	6	)	)	PUNCT
ejpam-776	204	7	the	the	DET
ejpam-776	204	8	generalized	generalize	VERB
ejpam-776	204	9	convolution	convolution	NOUN
ejpam-776	204	10	product	product	NOUN
ejpam-776	204	11	of	of	ADP
ejpam-776	204	12	two	two	NUM
ejpam-776	204	13	functions	function	NOUN
ejpam-776	204	14	f	f	NOUN
ejpam-776	204	15	and	and	CCONJ
ejpam-776	204	16	g	g	PROPN
ejpam-776	204	17	in	in	ADP
ejpam-776	204	18	l2(r	l2(r	PROPN
ejpam-776	204	19	,	,	PUNCT
ejpam-776	204	20	a(x)d	a(x)d	PROPN
ejpam-776	204	21	x	x	PRON
ejpam-776	204	22	)	)	PUNCT
ejpam-776	204	23	is	be	AUX
ejpam-776	204	24	defined	define	VERB
ejpam-776	204	25	by	by	ADP
ejpam-776	204	26	f	f	PROPN
ejpam-776	204	27	#	#	SYM
ejpam-776	204	28	g(x	g(x	NOUN
ejpam-776	204	29	)	)	PUNCT
ejpam-776	205	1	=	=	SYM
ejpam-776	206	1	∫	∫	PROPN
ejpam-776	206	2	r	r	NOUN
ejpam-776	206	3	t	t	PROPN
ejpam-776	206	4	x	x	X
ejpam-776	206	5	f	f	X
ejpam-776	206	6	(	(	PUNCT
ejpam-776	206	7	−y)g(y)a(y)d	−y)g(y)a(y)d	PROPN
ejpam-776	206	8	y.	y.	PROPN
ejpam-776	206	9	(	(	PUNCT
ejpam-776	206	10	19	19	NUM
ejpam-776	206	11	)	)	PUNCT
ejpam-776	206	12	remark	remark	NOUN
ejpam-776	206	13	5	5	NUM
ejpam-776	206	14	.	.	PUNCT
ejpam-776	207	1	let	let	VERB
ejpam-776	207	2	f	f	PROPN
ejpam-776	207	3	and	and	CCONJ
ejpam-776	207	4	g	g	PROPN
ejpam-776	207	5	be	be	VERB
ejpam-776	207	6	in	in	ADP
ejpam-776	207	7	l2(r	l2(r	NOUN
ejpam-776	207	8	,	,	PUNCT
ejpam-776	207	9	a(x)d	a(x)d	PROPN
ejpam-776	207	10	x	x	X
ejpam-776	207	11	)	)	PUNCT
ejpam-776	207	12	.	.	PUNCT
ejpam-776	208	1	then	then	ADV
ejpam-776	208	2	(	(	PUNCT
ejpam-776	208	3	i	i	NOUN
ejpam-776	208	4	)	)	PUNCT
ejpam-776	208	5	by	by	ADP
ejpam-776	208	6	(	(	PUNCT
ejpam-776	208	7	18	18	NUM
ejpam-776	208	8	)	)	PUNCT
ejpam-776	208	9	,	,	PUNCT
ejpam-776	208	10	lemma	lemma	PROPN
ejpam-776	208	11	1	1	NUM
ejpam-776	208	12	and	and	CCONJ
ejpam-776	208	13	theorem	theorem	VERB
ejpam-776	208	14	1	1	NUM
ejpam-776	208	15	,	,	PUNCT
ejpam-776	208	16	we	we	PRON
ejpam-776	208	17	deduce	deduce	VERB
ejpam-776	208	18	that	that	DET
ejpam-776	208	19	t	t	NOUN
ejpam-776	208	20	x	x	X
ejpam-776	209	1	f	f	PROPN
ejpam-776	209	2	2,a	2,a	PROPN
ejpam-776	209	3	≤	≤	PROPN
ejpam-776	210	1	f	f	X
ejpam-776	210	2	2,a	2,a	PROPN
ejpam-776	210	3	(	(	PUNCT
ejpam-776	210	4	20	20	NUM
ejpam-776	210	5	)	)	PUNCT
ejpam-776	210	6	for	for	ADP
ejpam-776	210	7	any	any	DET
ejpam-776	210	8	x	x	SYM
ejpam-776	210	9	∈	∈	PROPN
ejpam-776	210	10	r.	r.	PROPN
ejpam-776	210	11	(	(	PUNCT
ejpam-776	210	12	ii	ii	PROPN
ejpam-776	210	13	)	)	PUNCT
ejpam-776	210	14	it	it	PRON
ejpam-776	210	15	follows	follow	VERB
ejpam-776	210	16	from	from	ADP
ejpam-776	210	17	(	(	PUNCT
ejpam-776	210	18	19	19	NUM
ejpam-776	210	19	)	)	PUNCT
ejpam-776	210	20	,	,	PUNCT
ejpam-776	210	21	(	(	PUNCT
ejpam-776	210	22	20	20	NUM
ejpam-776	210	23	)	)	PUNCT
ejpam-776	210	24	and	and	CCONJ
ejpam-776	210	25	schwarz	schwarz	PROPN
ejpam-776	210	26	inequality	inequality	NOUN
ejpam-776	210	27	that	that	PRON
ejpam-776	210	28	f	f	PROPN
ejpam-776	210	29	#	#	SYM
ejpam-776	210	30	g	g	PROPN
ejpam-776	210	31	∈	∈	PROPN
ejpam-776	210	32	l∞(r	l∞(r	NOUN
ejpam-776	210	33	)	)	PUNCT
ejpam-776	210	34	and	and	CCONJ
ejpam-776	211	1	f	f	PROPN
ejpam-776	211	2	#	#	NOUN
ejpam-776	211	3	g	g	PROPN
ejpam-776	211	4	∞	∞	PROPN
ejpam-776	211	5	≤	≤	NUM
ejpam-776	212	1	f	f	PROPN
ejpam-776	213	1	2,a	2,a	NUM
ejpam-776	213	2	g	g	PROPN
ejpam-776	213	3	2,a	2,a	PROPN
ejpam-776	213	4	.	.	PUNCT
ejpam-776	214	1	(	(	PUNCT
ejpam-776	214	2	21	21	NUM
ejpam-776	214	3	)	)	PUNCT
ejpam-776	214	4	(	(	PUNCT
ejpam-776	214	5	iii	iii	NOUN
ejpam-776	214	6	)	)	PUNCT
ejpam-776	214	7	by	by	ADP
ejpam-776	214	8	virtue	virtue	NOUN
ejpam-776	214	9	of	of	ADP
ejpam-776	214	10	(	(	PUNCT
ejpam-776	214	11	18	18	NUM
ejpam-776	214	12	)	)	PUNCT
ejpam-776	214	13	,	,	PUNCT
ejpam-776	214	14	(	(	PUNCT
ejpam-776	214	15	19	19	NUM
ejpam-776	214	16	)	)	PUNCT
ejpam-776	214	17	and	and	CCONJ
ejpam-776	214	18	theorem	theorem	VERB
ejpam-776	214	19	1	1	NUM
ejpam-776	214	20	,	,	PUNCT
ejpam-776	214	21	f	f	PROPN
ejpam-776	214	22	#	#	NOUN
ejpam-776	214	23	g	g	NOUN
ejpam-776	214	24	may	may	AUX
ejpam-776	214	25	be	be	AUX
ejpam-776	214	26	rewritten	rewrite	VERB
ejpam-776	214	27	as	as	ADP
ejpam-776	214	28	f	f	PROPN
ejpam-776	214	29	#	#	SYM
ejpam-776	214	30	g(x	g(x	NOUN
ejpam-776	214	31	)	)	PUNCT
ejpam-776	215	1	=	=	SYM
ejpam-776	216	1	∫	∫	PROPN
ejpam-776	216	2	r	r	NOUN
ejpam-776	216	3	fλ	fλ	PROPN
ejpam-776	216	4	(	(	PUNCT
ejpam-776	216	5	f	f	PROPN
ejpam-776	216	6	)	)	PUNCT
ejpam-776	216	7	(	(	PUNCT
ejpam-776	216	8	λ)fλ(g)(λ)ψλ(x)dσ(λ	λ)fλ(g)(λ)ψλ(x)dσ(λ	NOUN
ejpam-776	216	9	)	)	PUNCT
ejpam-776	216	10	.	.	PUNCT
ejpam-776	217	1	(	(	PUNCT
ejpam-776	217	2	22	22	NUM
ejpam-776	217	3	)	)	PUNCT
ejpam-776	217	4	proposition	proposition	NOUN
ejpam-776	217	5	3	3	NUM
ejpam-776	217	6	.	.	PUNCT
ejpam-776	218	1	let	let	VERB
ejpam-776	218	2	f	f	PROPN
ejpam-776	218	3	∈	∈	PROPN
ejpam-776	218	4	l2(r	l2(r	PROPN
ejpam-776	218	5	,	,	PUNCT
ejpam-776	218	6	a(x)d	a(x)d	PROPN
ejpam-776	218	7	x	x	PRON
ejpam-776	218	8	)	)	PUNCT
ejpam-776	218	9	and	and	CCONJ
ejpam-776	218	10	g	g	PROPN
ejpam-776	218	11	∈	∈	PROPN
ejpam-776	218	12	l1∩l2(r	l1∩l2(r	ADJ
ejpam-776	218	13	,	,	PUNCT
ejpam-776	218	14	a(x)d	a(x)d	PROPN
ejpam-776	218	15	x	x	X
ejpam-776	218	16	)	)	PUNCT
ejpam-776	218	17	.	.	PUNCT
ejpam-776	219	1	then	then	ADV
ejpam-776	219	2	f	f	PROPN
ejpam-776	219	3	#	#	SYM
ejpam-776	219	4	g	g	PROPN
ejpam-776	219	5	∈	∈	PROPN
ejpam-776	219	6	l2(r	l2(r	NOUN
ejpam-776	219	7	,	,	PUNCT
ejpam-776	219	8	a(x)d	a(x)d	PROPN
ejpam-776	219	9	x	x	X
ejpam-776	219	10	)	)	PUNCT
ejpam-776	219	11	,	,	PUNCT
ejpam-776	220	1	f	f	PROPN
ejpam-776	220	2	#	#	SYM
ejpam-776	220	3	g	g	PROPN
ejpam-776	220	4	2,a	2,a	PROPN
ejpam-776	220	5	≤	≤	NUM
ejpam-776	221	1	f	f	NOUN
ejpam-776	222	1	2,a	2,a	NUM
ejpam-776	222	2	g	g	PROPN
ejpam-776	222	3	1,a	1,a	NUM
ejpam-776	222	4	,	,	PUNCT
ejpam-776	222	5	(	(	PUNCT
ejpam-776	222	6	23	23	NUM
ejpam-776	222	7	)	)	PUNCT
ejpam-776	222	8	and	and	CCONJ
ejpam-776	222	9	fλ	fλ	PRON
ejpam-776	222	10	(	(	PUNCT
ejpam-776	222	11	f	f	PROPN
ejpam-776	222	12	#	#	SYM
ejpam-776	222	13	g	g	NOUN
ejpam-776	222	14	)	)	PUNCT
ejpam-776	223	1	=	=	SYM
ejpam-776	223	2	fλ	fλ	X
ejpam-776	223	3	(	(	PUNCT
ejpam-776	223	4	f	f	PROPN
ejpam-776	223	5	)	)	PUNCT
ejpam-776	223	6	fλ(g	fλ(g	X
ejpam-776	223	7	)	)	PUNCT
ejpam-776	223	8	.	.	PUNCT
ejpam-776	224	1	(	(	PUNCT
ejpam-776	224	2	24	24	NUM
ejpam-776	224	3	)	)	PUNCT
ejpam-776	224	4	w.	w.	NOUN
ejpam-776	224	5	chabeh	chabeh	PROPN
ejpam-776	224	6	,	,	PUNCT
ejpam-776	224	7	m.	m.	NOUN
ejpam-776	224	8	mourou	mourou	PROPN
ejpam-776	224	9	/	/	SYM
ejpam-776	224	10	eur	eur	PROPN
ejpam-776	224	11	.	.	PUNCT
ejpam-776	225	1	j.	j.	PROPN
ejpam-776	225	2	pure	pure	PROPN
ejpam-776	225	3	appl	appl	PROPN
ejpam-776	225	4	.	.	PROPN
ejpam-776	225	5	math	math	PROPN
ejpam-776	225	6	,	,	PUNCT
ejpam-776	225	7	3	3	NUM
ejpam-776	225	8	(	(	PUNCT
ejpam-776	225	9	2010	2010	NUM
ejpam-776	225	10	)	)	PUNCT
ejpam-776	225	11	,	,	PUNCT
ejpam-776	225	12	958	958	NUM
ejpam-776	225	13	-	-	SYM
ejpam-776	225	14	979	979	NUM
ejpam-776	225	15	969	969	NUM
ejpam-776	225	16	proof	proof	NOUN
ejpam-776	225	17	.	.	PUNCT
ejpam-776	226	1	by	by	ADP
ejpam-776	226	2	schwarz	schwarz	PROPN
ejpam-776	226	3	inequality	inequality	PROPN
ejpam-776	226	4	,	,	PUNCT
ejpam-776	226	5	fλ	fλ	PRON
ejpam-776	226	6	(	(	PUNCT
ejpam-776	226	7	f	f	PROPN
ejpam-776	226	8	)	)	PUNCT
ejpam-776	226	9	fλ(g	fλ(g	X
ejpam-776	226	10	)	)	PUNCT
ejpam-776	226	11	∈	∈	PROPN
ejpam-776	226	12	l1(r	l1(r	PROPN
ejpam-776	226	13	,	,	PUNCT
ejpam-776	226	14	dσ	dσ	PROPN
ejpam-776	226	15	)	)	PUNCT
ejpam-776	226	16	.	.	PUNCT
ejpam-776	227	1	moreover	moreover	ADV
ejpam-776	227	2	,	,	PUNCT
ejpam-776	227	3	by	by	ADP
ejpam-776	227	4	remark	remark	NOUN
ejpam-776	227	5	3	3	NUM
ejpam-776	227	6	,	,	PUNCT
ejpam-776	227	7	fλ	fλ	ADJ
ejpam-776	227	8	(	(	PUNCT
ejpam-776	227	9	f	f	PROPN
ejpam-776	227	10	)	)	PUNCT
ejpam-776	227	11	fλ(g	fλ(g	X
ejpam-776	227	12	)	)	PUNCT
ejpam-776	227	13	∈	∈	PROPN
ejpam-776	227	14	l2(r	l2(r	PROPN
ejpam-776	227	15	,	,	PUNCT
ejpam-776	227	16	dσ	dσ	VERB
ejpam-776	227	17	)	)	PUNCT
ejpam-776	227	18	and	and	CCONJ
ejpam-776	227	19	fλ	fλ	PRON
ejpam-776	227	20	(	(	PUNCT
ejpam-776	227	21	f	f	PROPN
ejpam-776	227	22	)	)	PUNCT
ejpam-776	227	23	fλ(g	fλ(g	X
ejpam-776	227	24	)	)	PUNCT
ejpam-776	227	25	2,σ	2,σ	NUM
ejpam-776	227	26	≤	≤	NUM
ejpam-776	227	27	fλ	fλ	PRON
ejpam-776	227	28	(	(	PUNCT
ejpam-776	227	29	f	f	PROPN
ejpam-776	227	30	)	)	PUNCT
ejpam-776	227	31	2,σ	2,σ	NUM
ejpam-776	228	1	g	g	ADP
ejpam-776	228	2	1,a	1,a	NUM
ejpam-776	228	3	.	.	PUNCT
ejpam-776	229	1	the	the	DET
ejpam-776	229	2	result	result	NOUN
ejpam-776	229	3	follows	follow	VERB
ejpam-776	229	4	then	then	ADV
ejpam-776	229	5	by	by	ADP
ejpam-776	229	6	combining	combine	VERB
ejpam-776	229	7	(	(	PUNCT
ejpam-776	229	8	22	22	NUM
ejpam-776	229	9	)	)	PUNCT
ejpam-776	229	10	and	and	CCONJ
ejpam-776	229	11	theorem	theorem	VERB
ejpam-776	229	12	1	1	NUM
ejpam-776	229	13	.	.	PUNCT
ejpam-776	229	14	proposition	proposition	NOUN
ejpam-776	229	15	4	4	NUM
ejpam-776	229	16	.	.	PUNCT
ejpam-776	230	1	if	if	SCONJ
ejpam-776	230	2	f	f	PROPN
ejpam-776	230	3	,	,	PUNCT
ejpam-776	230	4	g	g	PROPN
ejpam-776	230	5	∈	∈	PROPN
ejpam-776	230	6	s	s	PART
ejpam-776	230	7	(	(	PUNCT
ejpam-776	230	8	r	r	NOUN
ejpam-776	230	9	)	)	PUNCT
ejpam-776	230	10	,	,	PUNCT
ejpam-776	230	11	then	then	ADV
ejpam-776	230	12	f	f	PROPN
ejpam-776	231	1	#	#	SYM
ejpam-776	231	2	g	g	PROPN
ejpam-776	231	3	∈	∈	NOUN
ejpam-776	231	4	s	s	PART
ejpam-776	231	5	(	(	PUNCT
ejpam-776	231	6	r	r	NOUN
ejpam-776	231	7	)	)	PUNCT
ejpam-776	231	8	and	and	CCONJ
ejpam-776	231	9	t	t	X
ejpam-776	231	10	v	v	X
ejpam-776	231	11	(	(	PUNCT
ejpam-776	231	12	f	f	PROPN
ejpam-776	231	13	#	#	SYM
ejpam-776	231	14	g	g	NOUN
ejpam-776	231	15	)	)	PUNCT
ejpam-776	231	16	=	=	SYM
ejpam-776	232	1	t	t	PROPN
ejpam-776	232	2	v	v	NUM
ejpam-776	232	3	f	f	PROPN
ejpam-776	232	4	∗	∗	X
ejpam-776	232	5	t	t	PROPN
ejpam-776	232	6	v	v	ADP
ejpam-776	232	7	g	g	NOUN
ejpam-776	232	8	,	,	PUNCT
ejpam-776	232	9	(	(	PUNCT
ejpam-776	232	10	25	25	NUM
ejpam-776	232	11	)	)	PUNCT
ejpam-776	232	12	where	where	SCONJ
ejpam-776	232	13	∗	∗	NOUN
ejpam-776	232	14	denotes	denote	VERB
ejpam-776	232	15	the	the	DET
ejpam-776	232	16	usual	usual	ADJ
ejpam-776	232	17	convolution	convolution	NOUN
ejpam-776	232	18	on	on	ADP
ejpam-776	232	19	r.	r.	PROPN
ejpam-776	232	20	proof	proof	NOUN
ejpam-776	232	21	.	.	PUNCT
ejpam-776	233	1	the	the	DET
ejpam-776	233	2	fact	fact	NOUN
ejpam-776	233	3	that	that	SCONJ
ejpam-776	233	4	f	f	PROPN
ejpam-776	233	5	#	#	SYM
ejpam-776	233	6	g	g	PROPN
ejpam-776	233	7	∈	∈	NOUN
ejpam-776	233	8	s	s	PART
ejpam-776	233	9	(	(	PUNCT
ejpam-776	233	10	r	r	NOUN
ejpam-776	233	11	)	)	PUNCT
ejpam-776	233	12	follows	follow	VERB
ejpam-776	233	13	from	from	ADP
ejpam-776	233	14	(	(	PUNCT
ejpam-776	233	15	24	24	NUM
ejpam-776	233	16	)	)	PUNCT
ejpam-776	233	17	and	and	CCONJ
ejpam-776	233	18	theorem	theorem	VERB
ejpam-776	233	19	2	2	NUM
ejpam-776	233	20	.	.	NOUN
ejpam-776	233	21	identity	identity	NOUN
ejpam-776	233	22	(	(	PUNCT
ejpam-776	233	23	25	25	NUM
ejpam-776	233	24	)	)	PUNCT
ejpam-776	233	25	follows	follow	VERB
ejpam-776	233	26	by	by	ADP
ejpam-776	233	27	applying	apply	VERB
ejpam-776	233	28	the	the	DET
ejpam-776	233	29	usual	usual	ADJ
ejpam-776	233	30	fourier	fourier	NOUN
ejpam-776	233	31	transform	transform	NOUN
ejpam-776	233	32	to	to	ADP
ejpam-776	233	33	both	both	DET
ejpam-776	233	34	its	its	PRON
ejpam-776	233	35	sides	side	NOUN
ejpam-776	233	36	and	and	CCONJ
ejpam-776	233	37	by	by	ADP
ejpam-776	233	38	using	use	VERB
ejpam-776	233	39	(	(	PUNCT
ejpam-776	233	40	16	16	NUM
ejpam-776	233	41	)	)	PUNCT
ejpam-776	233	42	and	and	CCONJ
ejpam-776	233	43	(	(	PUNCT
ejpam-776	233	44	24	24	NUM
ejpam-776	233	45	)	)	PUNCT
ejpam-776	233	46	.	.	PUNCT
ejpam-776	234	1	remark	remark	PROPN
ejpam-776	234	2	6	6	NUM
ejpam-776	234	3	.	.	PUNCT
ejpam-776	234	4	notice	notice	NOUN
ejpam-776	234	5	by	by	ADP
ejpam-776	234	6	(	(	PUNCT
ejpam-776	234	7	24	24	NUM
ejpam-776	234	8	)	)	PUNCT
ejpam-776	234	9	and	and	CCONJ
ejpam-776	234	10	theorem	theorem	VERB
ejpam-776	234	11	2	2	NUM
ejpam-776	234	12	thatb(r)#s	thatb(r)#	NOUN
ejpam-776	234	13	(	(	PUNCT
ejpam-776	234	14	r)⊂b(r	r)⊂b(r	NOUN
ejpam-776	234	15	)	)	PUNCT
ejpam-776	234	16	.	.	PUNCT
ejpam-776	235	1	3	3	X
ejpam-776	235	2	.	.	NUM
ejpam-776	235	3	generalized	generalize	VERB
ejpam-776	235	4	wavelets	wavelet	NOUN
ejpam-776	235	5	definition	definition	NOUN
ejpam-776	235	6	3	3	X
ejpam-776	235	7	.	.	PUNCT
ejpam-776	236	1	we	we	PRON
ejpam-776	236	2	say	say	VERB
ejpam-776	236	3	that	that	SCONJ
ejpam-776	236	4	a	a	DET
ejpam-776	236	5	function	function	NOUN
ejpam-776	236	6	g	g	PROPN
ejpam-776	236	7	∈	∈	PROPN
ejpam-776	236	8	l2(r	l2(r	PROPN
ejpam-776	236	9	,	,	PUNCT
ejpam-776	236	10	a(x)d	a(x)d	PROPN
ejpam-776	236	11	x	x	PRON
ejpam-776	236	12	)	)	PUNCT
ejpam-776	236	13	is	be	AUX
ejpam-776	236	14	a	a	DET
ejpam-776	236	15	generalized	generalized	ADJ
ejpam-776	236	16	wavelet	wavelet	NOUN
ejpam-776	236	17	if	if	SCONJ
ejpam-776	236	18	it	it	PRON
ejpam-776	236	19	satisfies	satisfy	VERB
ejpam-776	236	20	the	the	DET
ejpam-776	236	21	admissibility	admissibility	NOUN
ejpam-776	236	22	condition	condition	NOUN
ejpam-776	236	23	:	:	PUNCT
ejpam-776	236	24	0	0	PUNCT
ejpam-776	236	25	<	<	X
ejpam-776	236	26	cg	cg	NOUN
ejpam-776	236	27	=	=	SYM
ejpam-776	236	28	∫	∫	PROPN
ejpam-776	236	29	∞	∞	PROPN
ejpam-776	236	30	0	0	NUM
ejpam-776	237	1	|fλg(aλ)|2	|fλg(aλ)|2	NOUN
ejpam-776	237	2	da	da	VERB
ejpam-776	237	3	a	a	DET
ejpam-776	237	4	<	<	X
ejpam-776	237	5	∞	∞	PROPN
ejpam-776	237	6	,	,	PUNCT
ejpam-776	237	7	(	(	PUNCT
ejpam-776	237	8	26	26	NUM
ejpam-776	237	9	)	)	PUNCT
ejpam-776	237	10	for	for	ADP
ejpam-776	237	11	almost	almost	ADV
ejpam-776	237	12	all	all	PRON
ejpam-776	237	13	λ	λ	PROPN
ejpam-776	237	14	∈	∈	PROPN
ejpam-776	237	15	r.	r.	PROPN
ejpam-776	237	16	remark	remark	NOUN
ejpam-776	237	17	7	7	NUM
ejpam-776	237	18	.	.	PUNCT
ejpam-776	238	1	(	(	PUNCT
ejpam-776	238	2	i	i	NOUN
ejpam-776	238	3	)	)	PUNCT
ejpam-776	238	4	the	the	DET
ejpam-776	238	5	admissibility	admissibility	NOUN
ejpam-776	238	6	condition	condition	NOUN
ejpam-776	238	7	(	(	PUNCT
ejpam-776	238	8	26	26	NUM
ejpam-776	238	9	)	)	PUNCT
ejpam-776	238	10	can	can	AUX
ejpam-776	238	11	also	also	ADV
ejpam-776	238	12	be	be	AUX
ejpam-776	238	13	written	write	VERB
ejpam-776	238	14	as	as	ADP
ejpam-776	238	15	0	0	NUM
ejpam-776	238	16	<	<	X
ejpam-776	238	17	cg	cg	NOUN
ejpam-776	238	18	=	=	SYM
ejpam-776	238	19	∫	∫	PROPN
ejpam-776	239	1	∞	∞	PROPN
ejpam-776	239	2	0	0	NUM
ejpam-776	239	3	|fλ(g)(λ)|2	|fλ(g)(λ)|2	NOUN
ejpam-776	239	4	dλ	dλ	NOUN
ejpam-776	239	5	λ	λ	PROPN
ejpam-776	239	6	=	=	SYM
ejpam-776	239	7	∫	∫	PROPN
ejpam-776	239	8	∞	∞	PROPN
ejpam-776	239	9	0	0	NUM
ejpam-776	239	10	|fλ(g)(−λ)|2	|fλ(g)(−λ)|2	NOUN
ejpam-776	239	11	dλ	dλ	NOUN
ejpam-776	239	12	λ	λ	PROPN
ejpam-776	239	13	<	<	X
ejpam-776	239	14	∞.	∞.	PROPN
ejpam-776	239	15	(	(	PUNCT
ejpam-776	239	16	ii	ii	NOUN
ejpam-776	239	17	)	)	PUNCT
ejpam-776	239	18	if	if	SCONJ
ejpam-776	239	19	g	g	PROPN
ejpam-776	239	20	is	be	AUX
ejpam-776	239	21	real	real	ADV
ejpam-776	239	22	-	-	PUNCT
ejpam-776	239	23	valued	value	VERB
ejpam-776	239	24	we	we	PRON
ejpam-776	239	25	have	have	VERB
ejpam-776	239	26	fλ(g)(−λ	fλ(g)(−λ	NOUN
ejpam-776	239	27	)	)	PUNCT
ejpam-776	240	1	=	=	NOUN
ejpam-776	240	2	fλ(g)(λ	fλ(g)(λ	NOUN
ejpam-776	240	3	)	)	PUNCT
ejpam-776	240	4	,	,	PUNCT
ejpam-776	240	5	so	so	CCONJ
ejpam-776	240	6	(	(	PUNCT
ejpam-776	240	7	26	26	NUM
ejpam-776	240	8	)	)	PUNCT
ejpam-776	240	9	reduces	reduce	VERB
ejpam-776	240	10	to	to	ADP
ejpam-776	240	11	0	0	NUM
ejpam-776	240	12	<	<	X
ejpam-776	240	13	cg	cg	NOUN
ejpam-776	240	14	=	=	SYM
ejpam-776	240	15	∫	∫	PROPN
ejpam-776	241	1	∞	∞	PROPN
ejpam-776	241	2	0	0	NUM
ejpam-776	241	3	|fλ(g)(λ)|2	|fλ(g)(λ)|2	NOUN
ejpam-776	241	4	dλ	dλ	NOUN
ejpam-776	241	5	λ	λ	X
ejpam-776	241	6	<	<	X
ejpam-776	241	7	∞.	∞.	PROPN
ejpam-776	241	8	(	(	PUNCT
ejpam-776	241	9	iii	iii	NOUN
ejpam-776	241	10	)	)	PUNCT
ejpam-776	241	11	if	if	SCONJ
ejpam-776	241	12	0	0	NUM
ejpam-776	241	13	6=	6=	NUM
ejpam-776	241	14	g	g	PROPN
ejpam-776	241	15	∈	∈	PROPN
ejpam-776	241	16	l2(r	l2(r	PROPN
ejpam-776	241	17	,	,	PUNCT
ejpam-776	241	18	a(x)d	a(x)d	PROPN
ejpam-776	241	19	x	x	PRON
ejpam-776	241	20	)	)	PUNCT
ejpam-776	241	21	is	be	AUX
ejpam-776	241	22	real	real	ADV
ejpam-776	241	23	-	-	PUNCT
ejpam-776	241	24	valued	value	VERB
ejpam-776	241	25	and	and	CCONJ
ejpam-776	241	26	satisfies	satisfy	VERB
ejpam-776	241	27	∃	∃	PROPN
ejpam-776	241	28	η	η	PROPN
ejpam-776	241	29	>	>	X
ejpam-776	241	30	0	0	NUM
ejpam-776	241	31	such	such	ADJ
ejpam-776	241	32	that	that	SCONJ
ejpam-776	241	33	fλ(g)(λ)−fλ(g)(0	fλ(g)(λ)−fλ(g)(0	ADJ
ejpam-776	241	34	)	)	PUNCT
ejpam-776	242	1	=	=	SYM
ejpam-776	242	2	o	o	X
ejpam-776	242	3	(	(	PUNCT
ejpam-776	242	4	λη	λη	NOUN
ejpam-776	242	5	)	)	PUNCT
ejpam-776	242	6	,	,	PUNCT
ejpam-776	242	7	as	as	SCONJ
ejpam-776	242	8	λ→	λ→	PROPN
ejpam-776	242	9	0	0	NUM
ejpam-776	242	10	+	+	NUM
ejpam-776	242	11	,	,	PUNCT
ejpam-776	242	12	then	then	ADV
ejpam-776	242	13	(	(	PUNCT
ejpam-776	242	14	26	26	NUM
ejpam-776	242	15	)	)	PUNCT
ejpam-776	242	16	is	be	AUX
ejpam-776	242	17	equivalent	equivalent	ADJ
ejpam-776	242	18	to	to	ADP
ejpam-776	242	19	fλ(g)(0	fλ(g)(0	ADJ
ejpam-776	242	20	)	)	PUNCT
ejpam-776	242	21	=	=	SYM
ejpam-776	243	1	0	0	X
ejpam-776	243	2	.	.	PUNCT
ejpam-776	243	3	(	(	PUNCT
ejpam-776	243	4	iv	iv	X
ejpam-776	243	5	)	)	PUNCT
ejpam-776	243	6	according	accord	VERB
ejpam-776	243	7	to	to	ADP
ejpam-776	243	8	(	(	PUNCT
ejpam-776	243	9	iii	iii	NOUN
ejpam-776	243	10	)	)	PUNCT
ejpam-776	243	11	and	and	CCONJ
ejpam-776	243	12	theorem	theorem	VERB
ejpam-776	243	13	2	2	NUM
ejpam-776	243	14	,	,	PUNCT
ejpam-776	243	15	each	each	DET
ejpam-776	243	16	real	real	ADV
ejpam-776	243	17	-	-	PUNCT
ejpam-776	243	18	valued	value	VERB
ejpam-776	243	19	function	function	NOUN
ejpam-776	243	20	g	g	NOUN
ejpam-776	243	21	in	in	ADP
ejpam-776	243	22	b(r	b(r	PROPN
ejpam-776	243	23	)	)	PUNCT
ejpam-776	243	24	is	be	AUX
ejpam-776	243	25	a	a	DET
ejpam-776	243	26	generalized	generalized	ADJ
ejpam-776	243	27	wavelet	wavelet	NOUN
ejpam-776	243	28	.	.	PUNCT
ejpam-776	244	1	w.	w.	PROPN
ejpam-776	244	2	chabeh	chabeh	PROPN
ejpam-776	244	3	,	,	PUNCT
ejpam-776	244	4	m.	m.	NOUN
ejpam-776	244	5	mourou	mourou	PROPN
ejpam-776	244	6	/	/	SYM
ejpam-776	244	7	eur	eur	PROPN
ejpam-776	244	8	.	.	PUNCT
ejpam-776	245	1	j.	j.	PROPN
ejpam-776	245	2	pure	pure	PROPN
ejpam-776	245	3	appl	appl	PROPN
ejpam-776	245	4	.	.	PROPN
ejpam-776	245	5	math	math	PROPN
ejpam-776	245	6	,	,	PUNCT
ejpam-776	245	7	3	3	NUM
ejpam-776	245	8	(	(	PUNCT
ejpam-776	245	9	2010	2010	NUM
ejpam-776	245	10	)	)	PUNCT
ejpam-776	245	11	,	,	PUNCT
ejpam-776	245	12	958	958	NUM
ejpam-776	245	13	-	-	SYM
ejpam-776	245	14	979	979	NUM
ejpam-776	245	15	970	970	NUM
ejpam-776	245	16	proposition	proposition	NOUN
ejpam-776	245	17	5	5	NUM
ejpam-776	245	18	.	.	PUNCT
ejpam-776	246	1	(	(	PUNCT
ejpam-776	246	2	i	i	NOUN
ejpam-776	246	3	)	)	PUNCT
ejpam-776	246	4	let	let	VERB
ejpam-776	246	5	h	h	NOUN
ejpam-776	246	6	∈	∈	PROPN
ejpam-776	246	7	l2(r	l2(r	PROPN
ejpam-776	246	8	,	,	PUNCT
ejpam-776	246	9	dσ	dσ	VERB
ejpam-776	246	10	)	)	PUNCT
ejpam-776	246	11	and	and	CCONJ
ejpam-776	246	12	a	a	DET
ejpam-776	246	13	>	>	X
ejpam-776	246	14	0	0	NUM
ejpam-776	246	15	.	.	PUNCT
ejpam-776	247	1	then	then	ADV
ejpam-776	247	2	the	the	DET
ejpam-776	247	3	function	function	NOUN
ejpam-776	247	4	λ	λ	X
ejpam-776	247	5	7→	7→	NUM
ejpam-776	247	6	h(aλ	h(aλ	NOUN
ejpam-776	247	7	)	)	PUNCT
ejpam-776	247	8	belongs	belong	VERB
ejpam-776	247	9	to	to	ADP
ejpam-776	247	10	l2(r	l2(r	PROPN
ejpam-776	247	11	,	,	PUNCT
ejpam-776	247	12	dσ	dσ	VERB
ejpam-776	247	13	)	)	PUNCT
ejpam-776	247	14	and	and	CCONJ
ejpam-776	247	15	we	we	PRON
ejpam-776	247	16	have	have	VERB
ejpam-776	247	17	‖h(a·)‖2,σ	‖h(a·)‖2,σ	DET
ejpam-776	247	18	≤	≤	NUM
ejpam-776	247	19	k(a)p	k(a)p	PROPN
ejpam-776	247	20	a	a	DET
ejpam-776	247	21	‖h‖2,σ	‖h‖2,σ	PROPN
ejpam-776	247	22	,	,	PUNCT
ejpam-776	247	23	where	where	SCONJ
ejpam-776	247	24	k(a	k(a	NOUN
ejpam-776	247	25	)	)	PUNCT
ejpam-776	247	26	=	=	SYM
ejpam-776	247	27	sup	sup	NOUN
ejpam-776	247	28	λ>0	λ>0	NOUN
ejpam-776	247	29	|c(λ)|	|c(λ)|	PROPN
ejpam-776	247	30	|c(λ	|c(λ	PROPN
ejpam-776	247	31	/	/	SYM
ejpam-776	247	32	a)|	a)|	PROPN
ejpam-776	247	33	.	.	PUNCT
ejpam-776	248	1	(	(	PUNCT
ejpam-776	248	2	ii	ii	NOUN
ejpam-776	248	3	)	)	PUNCT
ejpam-776	249	1	for	for	ADP
ejpam-776	249	2	every	every	DET
ejpam-776	249	3	a	a	DET
ejpam-776	249	4	>	>	X
ejpam-776	249	5	0	0	NUM
ejpam-776	249	6	,	,	PUNCT
ejpam-776	249	7	the	the	DET
ejpam-776	249	8	dilatation	dilatation	NOUN
ejpam-776	249	9	operator	operator	NOUN
ejpam-776	249	10	ha	ha	INTJ
ejpam-776	249	11	(	(	PUNCT
ejpam-776	249	12	f	f	PROPN
ejpam-776	249	13	)	)	PUNCT
ejpam-776	249	14	(	(	PUNCT
ejpam-776	249	15	x	x	X
ejpam-776	249	16	)	)	PUNCT
ejpam-776	249	17	=	=	SYM
ejpam-776	249	18	1p	1p	VERB
ejpam-776	249	19	a	a	DET
ejpam-776	249	20	f	f	PROPN
ejpam-776	249	21	�	�	PROPN
ejpam-776	249	22	x	x	PROPN
ejpam-776	249	23	a	a	DET
ejpam-776	249	24	�	�	PROPN
ejpam-776	249	25	,	,	PUNCT
ejpam-776	249	26	x	x	PUNCT
ejpam-776	249	27	∈	∈	NOUN
ejpam-776	249	28	r	r	NOUN
ejpam-776	249	29	,	,	PUNCT
ejpam-776	249	30	is	be	AUX
ejpam-776	249	31	a	a	DET
ejpam-776	249	32	topological	topological	ADJ
ejpam-776	249	33	automorphism	automorphism	NOUN
ejpam-776	249	34	of	of	ADP
ejpam-776	249	35	l2(r	l2(r	PROPN
ejpam-776	249	36	,	,	PUNCT
ejpam-776	249	37	dσ	dσ	PROPN
ejpam-776	249	38	)	)	PUNCT
ejpam-776	249	39	.	.	PUNCT
ejpam-776	250	1	proof	proof	NOUN
ejpam-776	250	2	.	.	PUNCT
ejpam-776	251	1	(	(	PUNCT
ejpam-776	251	2	i	i	NOUN
ejpam-776	251	3	)	)	PUNCT
ejpam-776	251	4	notice	notice	VERB
ejpam-776	251	5	first	first	ADV
ejpam-776	251	6	that	that	SCONJ
ejpam-776	251	7	according	accord	VERB
ejpam-776	251	8	to	to	ADP
ejpam-776	251	9	the	the	DET
ejpam-776	251	10	properties	property	NOUN
ejpam-776	251	11	of	of	ADP
ejpam-776	251	12	the	the	DET
ejpam-776	251	13	function	function	NOUN
ejpam-776	251	14	c(λ	c(λ	PROPN
ejpam-776	251	15	)	)	PUNCT
ejpam-776	251	16	given	give	VERB
ejpam-776	251	17	in	in	ADP
ejpam-776	251	18	theorem	theorem	NOUN
ejpam-776	251	19	1	1	NUM
ejpam-776	251	20	,	,	PUNCT
ejpam-776	251	21	there	there	PRON
ejpam-776	251	22	exist	exist	VERB
ejpam-776	251	23	two	two	NUM
ejpam-776	251	24	positive	positive	ADJ
ejpam-776	251	25	constants	constant	NOUN
ejpam-776	251	26	m1	m1	PROPN
ejpam-776	251	27	and	and	CCONJ
ejpam-776	251	28	m2	m2	PROPN
ejpam-776	251	29	such	such	ADJ
ejpam-776	251	30	that	that	SCONJ
ejpam-776	251	31	m1	m1	PROPN
ejpam-776	251	32	aα+1/2	aα+1/2	PROPN
ejpam-776	251	33	≤	≤	PROPN
ejpam-776	251	34	k(a)≤	k(a)≤	PART
ejpam-776	251	35	m2	m2	PROPN
ejpam-776	251	36	aα+1/2	aα+1/2	PROPN
ejpam-776	251	37	for	for	ADP
ejpam-776	251	38	all	all	DET
ejpam-776	251	39	a	a	DET
ejpam-776	251	40	>	>	X
ejpam-776	251	41	0	0	X
ejpam-776	251	42	.	.	PUNCT
ejpam-776	252	1	we	we	PRON
ejpam-776	252	2	have	have	VERB
ejpam-776	252	3	‖h(a·)‖22,σ	‖h(a·)‖22,σ	ADJ
ejpam-776	252	4	=	=	SYM
ejpam-776	252	5	∫	∫	NOUN
ejpam-776	252	6	r	r	NOUN
ejpam-776	252	7	|h(aλ)|2	|h(aλ)|2	NOUN
ejpam-776	252	8	dλ	dλ	VERB
ejpam-776	252	9	|c(|λ|)|2	|c(|λ|)|2	NOUN
ejpam-776	252	10	=	=	SYM
ejpam-776	252	11	1	1	NUM
ejpam-776	252	12	a	a	DET
ejpam-776	252	13	∫	∫	PROPN
ejpam-776	252	14	r	r	NOUN
ejpam-776	252	15	|h(s)|2	|h(s)|2	PUNCT
ejpam-776	252	16	|c(|s|)|	|c(|s|)|	PROPN
ejpam-776	252	17	2	2	NUM
ejpam-776	252	18	|c(|s|/a)|2	|c(|s|/a)|2	NOUN
ejpam-776	252	19	ds	ds	ADJ
ejpam-776	252	20	|c(|s|)|2	|c(|s|)|2	CCONJ
ejpam-776	252	21	≤	≤	PROPN
ejpam-776	252	22	k2(a	k2(a	PROPN
ejpam-776	252	23	)	)	PUNCT
ejpam-776	252	24	a	a	DET
ejpam-776	252	25	‖h‖22,σ	‖h‖22,σ	ADP
ejpam-776	252	26	(	(	PUNCT
ejpam-776	252	27	ii	ii	NOUN
ejpam-776	252	28	)	)	PUNCT
ejpam-776	252	29	we	we	PRON
ejpam-776	252	30	deduce	deduce	VERB
ejpam-776	252	31	the	the	DET
ejpam-776	252	32	result	result	NOUN
ejpam-776	252	33	from	from	ADP
ejpam-776	252	34	(	(	PUNCT
ejpam-776	252	35	i	i	NOUN
ejpam-776	252	36	)	)	PUNCT
ejpam-776	252	37	.	.	PUNCT
ejpam-776	253	1	proposition	proposition	NOUN
ejpam-776	253	2	6	6	NUM
ejpam-776	253	3	.	.	PUNCT
ejpam-776	254	1	let	let	VERB
ejpam-776	254	2	g	g	PROPN
ejpam-776	254	3	∈	∈	PROPN
ejpam-776	254	4	l2(r	l2(r	PROPN
ejpam-776	254	5	,	,	PUNCT
ejpam-776	254	6	a(x)d	a(x)d	PROPN
ejpam-776	254	7	x	x	PRON
ejpam-776	254	8	)	)	PUNCT
ejpam-776	254	9	and	and	CCONJ
ejpam-776	254	10	a	a	DET
ejpam-776	254	11	>	>	X
ejpam-776	254	12	0	0	NUM
ejpam-776	254	13	.	.	PUNCT
ejpam-776	255	1	then	then	ADV
ejpam-776	255	2	there	there	PRON
ejpam-776	255	3	exists	exist	VERB
ejpam-776	255	4	a	a	DET
ejpam-776	255	5	function	function	NOUN
ejpam-776	255	6	ga	ga	PROPN
ejpam-776	255	7	∈	∈	PROPN
ejpam-776	255	8	l2(r	l2(r	PROPN
ejpam-776	255	9	,	,	PUNCT
ejpam-776	255	10	a(x)d	a(x)d	PROPN
ejpam-776	255	11	x	x	X
ejpam-776	255	12	)	)	PUNCT
ejpam-776	255	13	(	(	PUNCT
ejpam-776	255	14	and	and	CCONJ
ejpam-776	255	15	only	only	ADV
ejpam-776	255	16	one	one	NUM
ejpam-776	255	17	)	)	PUNCT
ejpam-776	255	18	such	such	ADJ
ejpam-776	255	19	that	that	DET
ejpam-776	255	20	fλ(ga)(λ	fλ(ga)(λ	NOUN
ejpam-776	255	21	)	)	PUNCT
ejpam-776	255	22	=	=	NOUN
ejpam-776	255	23	fλ(g)(aλ	fλ(g)(aλ	NOUN
ejpam-776	255	24	)	)	PUNCT
ejpam-776	255	25	(	(	PUNCT
ejpam-776	255	26	27	27	NUM
ejpam-776	255	27	)	)	PUNCT
ejpam-776	255	28	for	for	ADP
ejpam-776	255	29	almost	almost	ADV
ejpam-776	255	30	every	every	PRON
ejpam-776	255	31	λ	λ	PROPN
ejpam-776	255	32	∈	∈	PROPN
ejpam-776	255	33	r.	r.	NOUN
ejpam-776	255	34	this	this	DET
ejpam-776	255	35	function	function	NOUN
ejpam-776	255	36	is	be	AUX
ejpam-776	255	37	given	give	VERB
ejpam-776	255	38	by	by	ADP
ejpam-776	255	39	the	the	DET
ejpam-776	255	40	relation	relation	NOUN
ejpam-776	255	41	ga	ga	PROPN
ejpam-776	256	1	=	=	PROPN
ejpam-776	256	2	1p	1p	PROPN
ejpam-776	256	3	a	a	DET
ejpam-776	256	4	f−1	f−1	PROPN
ejpam-776	257	1	λ	λ	PROPN
ejpam-776	257	2	◦	◦	PROPN
ejpam-776	257	3	ha−1	ha−1	PROPN
ejpam-776	257	4	◦	◦	NOUN
ejpam-776	257	5	fλ(g	fλ(g	NOUN
ejpam-776	257	6	)	)	PUNCT
ejpam-776	257	7	(	(	PUNCT
ejpam-776	257	8	28	28	NUM
ejpam-776	257	9	)	)	PUNCT
ejpam-776	257	10	and	and	CCONJ
ejpam-776	257	11	satisfies	satisfy	VERB
ejpam-776	257	12	ga	ga	PROPN
ejpam-776	257	13	2,a	2,a	PROPN
ejpam-776	257	14	≤	≤	PROPN
ejpam-776	257	15	k(a)p	k(a)p	PROPN
ejpam-776	257	16	a	a	DET
ejpam-776	257	17	g	g	PROPN
ejpam-776	257	18	2,a	2,a	PROPN
ejpam-776	257	19	.	.	PUNCT
ejpam-776	258	1	w.	w.	PROPN
ejpam-776	258	2	chabeh	chabeh	PROPN
ejpam-776	258	3	,	,	PUNCT
ejpam-776	258	4	m.	m.	NOUN
ejpam-776	258	5	mourou	mourou	PROPN
ejpam-776	258	6	/	/	SYM
ejpam-776	258	7	eur	eur	PROPN
ejpam-776	258	8	.	.	PUNCT
ejpam-776	259	1	j.	j.	PROPN
ejpam-776	259	2	pure	pure	PROPN
ejpam-776	259	3	appl	appl	PROPN
ejpam-776	259	4	.	.	PROPN
ejpam-776	259	5	math	math	PROPN
ejpam-776	259	6	,	,	PUNCT
ejpam-776	259	7	3	3	NUM
ejpam-776	259	8	(	(	PUNCT
ejpam-776	259	9	2010	2010	NUM
ejpam-776	259	10	)	)	PUNCT
ejpam-776	259	11	,	,	PUNCT
ejpam-776	259	12	958	958	NUM
ejpam-776	259	13	-	-	SYM
ejpam-776	259	14	979	979	NUM
ejpam-776	259	15	971	971	NUM
ejpam-776	259	16	proof	proof	NOUN
ejpam-776	259	17	.	.	PUNCT
ejpam-776	260	1	the	the	DET
ejpam-776	260	2	result	result	NOUN
ejpam-776	260	3	follows	follow	VERB
ejpam-776	260	4	by	by	ADP
ejpam-776	260	5	combining	combine	VERB
ejpam-776	260	6	theorem	theorem	ADJ
ejpam-776	260	7	1	1	NUM
ejpam-776	260	8	and	and	CCONJ
ejpam-776	260	9	proposition	proposition	NOUN
ejpam-776	260	10	5	5	NUM
ejpam-776	260	11	.	.	PUNCT
ejpam-776	260	12	remark	remark	PROPN
ejpam-776	260	13	8	8	NUM
ejpam-776	260	14	.	.	PUNCT
ejpam-776	260	15	for	for	ADP
ejpam-776	260	16	a(x	a(x	NOUN
ejpam-776	260	17	)	)	PUNCT
ejpam-776	260	18	=	=	PUNCT
ejpam-776	260	19	|x	|x	NOUN
ejpam-776	260	20	|2α+1	|2α+1	NOUN
ejpam-776	260	21	,	,	PUNCT
ejpam-776	260	22	α	α	PROPN
ejpam-776	260	23	>	>	X
ejpam-776	260	24	−1/2	−1/2	PROPN
ejpam-776	260	25	,	,	PUNCT
ejpam-776	260	26	the	the	DET
ejpam-776	260	27	function	function	PROPN
ejpam-776	260	28	ga	ga	PROPN
ejpam-776	260	29	,	,	PUNCT
ejpam-776	260	30	a	a	DET
ejpam-776	260	31	>	>	X
ejpam-776	260	32	0	0	NUM
ejpam-776	260	33	,	,	PUNCT
ejpam-776	260	34	is	be	AUX
ejpam-776	260	35	given	give	VERB
ejpam-776	260	36	by	by	ADP
ejpam-776	260	37	ga(x	ga(x	NOUN
ejpam-776	260	38	)	)	PUNCT
ejpam-776	260	39	=	=	SYM
ejpam-776	261	1	1	1	NUM
ejpam-776	261	2	a2α+2	a2α+2	PROPN
ejpam-776	261	3	g	g	ADP
ejpam-776	261	4	�	�	PROPN
ejpam-776	261	5	x	x	PUNCT
ejpam-776	261	6	a	a	DET
ejpam-776	261	7	�	�	PROPN
ejpam-776	261	8	,	,	PUNCT
ejpam-776	261	9	x	x	PROPN
ejpam-776	261	10	∈	∈	PROPN
ejpam-776	261	11	r.	r.	NOUN
ejpam-776	261	12	proposition	proposition	NOUN
ejpam-776	261	13	7	7	NUM
ejpam-776	261	14	.	.	PUNCT
ejpam-776	262	1	let	let	VERB
ejpam-776	262	2	g	g	NOUN
ejpam-776	262	3	be	be	AUX
ejpam-776	262	4	in	in	ADP
ejpam-776	262	5	s	s	PROPN
ejpam-776	262	6	(	(	PUNCT
ejpam-776	262	7	r	r	NOUN
ejpam-776	262	8	)	)	PUNCT
ejpam-776	262	9	.	.	PUNCT
ejpam-776	263	1	then	then	ADV
ejpam-776	263	2	for	for	ADP
ejpam-776	263	3	all	all	DET
ejpam-776	263	4	a	a	DET
ejpam-776	263	5	>	>	X
ejpam-776	263	6	0	0	NUM
ejpam-776	263	7	,	,	PUNCT
ejpam-776	263	8	the	the	DET
ejpam-776	263	9	function	function	NOUN
ejpam-776	263	10	ga	ga	PROPN
ejpam-776	263	11	belongs	belong	VERB
ejpam-776	263	12	to	to	ADP
ejpam-776	263	13	s	s	PROPN
ejpam-776	263	14	(	(	PUNCT
ejpam-776	263	15	r	r	NOUN
ejpam-776	263	16	)	)	PUNCT
ejpam-776	263	17	and	and	CCONJ
ejpam-776	263	18	we	we	PRON
ejpam-776	263	19	have	have	VERB
ejpam-776	263	20	the	the	DET
ejpam-776	263	21	relation	relation	NOUN
ejpam-776	263	22	ga	ga	PROPN
ejpam-776	264	1	=	=	PROPN
ejpam-776	264	2	1p	1p	PROPN
ejpam-776	264	3	a	a	DET
ejpam-776	264	4	t	t	NOUN
ejpam-776	265	1	v−1	v−1	PROPN
ejpam-776	265	2	◦	◦	NOUN
ejpam-776	265	3	ha	ha	INTJ
ejpam-776	265	4	◦	◦	NOUN
ejpam-776	265	5	t	t	X
ejpam-776	265	6	v	v	NOUN
ejpam-776	265	7	(	(	PUNCT
ejpam-776	265	8	g	g	NOUN
ejpam-776	265	9	)	)	PUNCT
ejpam-776	265	10	.	.	PUNCT
ejpam-776	266	1	(	(	PUNCT
ejpam-776	266	2	29	29	NUM
ejpam-776	266	3	)	)	PUNCT
ejpam-776	266	4	proof	proof	NOUN
ejpam-776	266	5	.	.	PUNCT
ejpam-776	267	1	the	the	DET
ejpam-776	267	2	result	result	NOUN
ejpam-776	267	3	follows	follow	VERB
ejpam-776	267	4	from	from	ADP
ejpam-776	267	5	(	(	PUNCT
ejpam-776	267	6	16	16	NUM
ejpam-776	267	7	)	)	PUNCT
ejpam-776	267	8	,	,	PUNCT
ejpam-776	267	9	(	(	PUNCT
ejpam-776	267	10	28	28	NUM
ejpam-776	267	11	)	)	PUNCT
ejpam-776	267	12	,	,	PUNCT
ejpam-776	267	13	theorem	theorem	VERB
ejpam-776	267	14	2	2	NUM
ejpam-776	267	15	,	,	PUNCT
ejpam-776	267	16	and	and	CCONJ
ejpam-776	267	17	the	the	DET
ejpam-776	267	18	fact	fact	NOUN
ejpam-776	267	19	thatfu	thatfu	NOUN
ejpam-776	267	20	◦	◦	NOUN
ejpam-776	267	21	ha	ha	NOUN
ejpam-776	267	22	=	=	ADJ
ejpam-776	267	23	ha−1	ha−1	PROPN
ejpam-776	267	24	◦	◦	NOUN
ejpam-776	267	25	fu	fu	NOUN
ejpam-776	267	26	.	.	PUNCT
ejpam-776	268	1	notation	notation	NOUN
ejpam-776	268	2	.	.	PUNCT
ejpam-776	269	1	for	for	ADP
ejpam-776	269	2	a	a	DET
ejpam-776	269	3	function	function	NOUN
ejpam-776	269	4	g	g	NOUN
ejpam-776	269	5	in	in	ADP
ejpam-776	269	6	l2(r	l2(r	PROPN
ejpam-776	269	7	,	,	PUNCT
ejpam-776	269	8	a(x)d	a(x)d	PROPN
ejpam-776	269	9	x	x	PRON
ejpam-776	269	10	)	)	PUNCT
ejpam-776	269	11	and	and	CCONJ
ejpam-776	269	12	for	for	ADP
ejpam-776	269	13	(	(	PUNCT
ejpam-776	269	14	a	a	PRON
ejpam-776	269	15	,	,	PUNCT
ejpam-776	269	16	b	b	NOUN
ejpam-776	269	17	)	)	PUNCT
ejpam-776	269	18	∈	∈	NOUN
ejpam-776	269	19	]	]	PUNCT
ejpam-776	269	20	0,∞[×r	0,∞[×r	NUM
ejpam-776	269	21	we	we	PRON
ejpam-776	269	22	write	write	VERB
ejpam-776	269	23	ga	ga	PROPN
ejpam-776	269	24	,	,	PUNCT
ejpam-776	269	25	b(x	b(x	NOUN
ejpam-776	269	26	)	)	PUNCT
ejpam-776	269	27	:	:	PUNCT
ejpam-776	270	1	=	=	X
ejpam-776	270	2	p	p	X
ejpam-776	270	3	a	a	DET
ejpam-776	270	4	t−b	t−b	NOUN
ejpam-776	270	5	ga(x	ga(x	NOUN
ejpam-776	270	6	)	)	PUNCT
ejpam-776	270	7	,	,	PUNCT
ejpam-776	270	8	(	(	PUNCT
ejpam-776	270	9	30	30	NUM
ejpam-776	270	10	)	)	PUNCT
ejpam-776	270	11	where	where	SCONJ
ejpam-776	270	12	t−b	t−b	PROPN
ejpam-776	270	13	are	be	AUX
ejpam-776	270	14	the	the	DET
ejpam-776	270	15	generalized	generalized	ADJ
ejpam-776	270	16	translation	translation	NOUN
ejpam-776	270	17	operators	operator	NOUN
ejpam-776	270	18	given	give	VERB
ejpam-776	270	19	by	by	ADP
ejpam-776	270	20	(	(	PUNCT
ejpam-776	270	21	18	18	NUM
ejpam-776	270	22	)	)	PUNCT
ejpam-776	270	23	.	.	PUNCT
ejpam-776	271	1	definition	definition	NOUN
ejpam-776	271	2	4	4	NUM
ejpam-776	271	3	.	.	PUNCT
ejpam-776	272	1	let	let	VERB
ejpam-776	272	2	g	g	PROPN
ejpam-776	272	3	∈	∈	PROPN
ejpam-776	272	4	l2(r	l2(r	PROPN
ejpam-776	272	5	,	,	PUNCT
ejpam-776	272	6	a(x)d	a(x)d	PROPN
ejpam-776	272	7	x	x	PRON
ejpam-776	272	8	)	)	PUNCT
ejpam-776	272	9	be	be	AUX
ejpam-776	272	10	a	a	DET
ejpam-776	272	11	generalized	generalized	ADJ
ejpam-776	272	12	wavelet	wavelet	NOUN
ejpam-776	272	13	.	.	PUNCT
ejpam-776	273	1	the	the	DET
ejpam-776	273	2	generalized	generalize	VERB
ejpam-776	273	3	continuous	continuous	ADJ
ejpam-776	273	4	wavelet	wavelet	NOUN
ejpam-776	273	5	transform	transform	NOUN
ejpam-776	273	6	φg	φg	NOUN
ejpam-776	273	7	is	be	AUX
ejpam-776	273	8	defined	define	VERB
ejpam-776	273	9	for	for	ADP
ejpam-776	273	10	regular	regular	ADJ
ejpam-776	273	11	functions	function	NOUN
ejpam-776	273	12	f	f	X
ejpam-776	273	13	on	on	ADP
ejpam-776	273	14	r	r	NOUN
ejpam-776	273	15	by	by	ADP
ejpam-776	273	16	:	:	PUNCT
ejpam-776	273	17	φg	φg	VERB
ejpam-776	273	18	(	(	PUNCT
ejpam-776	273	19	f	f	NOUN
ejpam-776	273	20	)	)	PUNCT
ejpam-776	273	21	(	(	PUNCT
ejpam-776	273	22	a	a	DET
ejpam-776	273	23	,	,	PUNCT
ejpam-776	273	24	b	b	NOUN
ejpam-776	273	25	)	)	PUNCT
ejpam-776	273	26	=	=	SYM
ejpam-776	274	1	∫	∫	PROPN
ejpam-776	274	2	r	r	NOUN
ejpam-776	274	3	f	f	X
ejpam-776	274	4	(	(	PUNCT
ejpam-776	274	5	x)ga	x)ga	ADV
ejpam-776	274	6	,	,	PUNCT
ejpam-776	274	7	b(x)a(x)d	b(x)a(x)d	PROPN
ejpam-776	274	8	x	x	NOUN
ejpam-776	274	9	.	.	PUNCT
ejpam-776	275	1	this	this	DET
ejpam-776	275	2	transform	transform	NOUN
ejpam-776	275	3	can	can	AUX
ejpam-776	275	4	also	also	ADV
ejpam-776	275	5	be	be	AUX
ejpam-776	275	6	written	write	VERB
ejpam-776	275	7	in	in	ADP
ejpam-776	275	8	the	the	DET
ejpam-776	275	9	form	form	NOUN
ejpam-776	275	10	φg	φg	VERB
ejpam-776	275	11	(	(	PUNCT
ejpam-776	275	12	f	f	NOUN
ejpam-776	275	13	)	)	PUNCT
ejpam-776	275	14	(	(	PUNCT
ejpam-776	275	15	a	a	DET
ejpam-776	275	16	,	,	PUNCT
ejpam-776	275	17	b	b	NOUN
ejpam-776	275	18	)	)	PUNCT
ejpam-776	275	19	=	=	PUNCT
ejpam-776	276	1	p	p	X
ejpam-776	276	2	a	a	DET
ejpam-776	276	3	f	f	NOUN
ejpam-776	276	4	#	#	SYM
ejpam-776	276	5	fga(b	fga(b	PROPN
ejpam-776	276	6	)	)	PUNCT
ejpam-776	276	7	,	,	PUNCT
ejpam-776	276	8	(	(	PUNCT
ejpam-776	276	9	31	31	NUM
ejpam-776	276	10	)	)	PUNCT
ejpam-776	276	11	where	where	SCONJ
ejpam-776	276	12	#	#	NOUN
ejpam-776	276	13	is	be	AUX
ejpam-776	276	14	the	the	DET
ejpam-776	276	15	generalized	generalized	ADJ
ejpam-776	276	16	convolution	convolution	NOUN
ejpam-776	276	17	product	product	NOUN
ejpam-776	276	18	given	give	VERB
ejpam-776	276	19	by	by	ADP
ejpam-776	276	20	(	(	PUNCT
ejpam-776	276	21	19	19	NUM
ejpam-776	276	22	)	)	PUNCT
ejpam-776	276	23	,	,	PUNCT
ejpam-776	276	24	and	and	CCONJ
ejpam-776	276	25	ega(x	ega(x	PROPN
ejpam-776	276	26	)	)	PUNCT
ejpam-776	276	27	=	=	SYM
ejpam-776	276	28	ga(−x	ga(−x	PROPN
ejpam-776	276	29	)	)	PUNCT
ejpam-776	276	30	,	,	PUNCT
ejpam-776	276	31	x	x	PROPN
ejpam-776	276	32	∈	∈	PROPN
ejpam-776	276	33	r.	r.	PROPN
ejpam-776	276	34	lemma	lemma	PROPN
ejpam-776	277	1	3	3	X
ejpam-776	277	2	.	.	PUNCT
ejpam-776	277	3	for	for	ADP
ejpam-776	277	4	all	all	DET
ejpam-776	277	5	f	f	PROPN
ejpam-776	277	6	,	,	PUNCT
ejpam-776	277	7	g	g	PROPN
ejpam-776	277	8	∈	∈	PROPN
ejpam-776	277	9	l2(r	l2(r	PROPN
ejpam-776	277	10	,	,	PUNCT
ejpam-776	277	11	a(x)d	a(x)d	PROPN
ejpam-776	277	12	x	x	PRON
ejpam-776	277	13	)	)	PUNCT
ejpam-776	277	14	and	and	CCONJ
ejpam-776	277	15	all	all	DET
ejpam-776	277	16	h	h	NOUN
ejpam-776	277	17	∈	∈	NOUN
ejpam-776	277	18	s	s	X
ejpam-776	277	19	(	(	PUNCT
ejpam-776	277	20	r	r	NOUN
ejpam-776	277	21	)	)	PUNCT
ejpam-776	277	22	we	we	PRON
ejpam-776	277	23	have	have	VERB
ejpam-776	277	24	the	the	DET
ejpam-776	277	25	identity	identity	NOUN
ejpam-776	277	26	∫	∫	NOUN
ejpam-776	277	27	r	r	NOUN
ejpam-776	277	28	f	f	PROPN
ejpam-776	277	29	#	#	NOUN
ejpam-776	277	30	g(x)f−1	g(x)f−1	PROPN
ejpam-776	277	31	λ	λ	X
ejpam-776	277	32	(	(	PUNCT
ejpam-776	277	33	h)(x)a(x)d	h)(x)a(x)d	ADJ
ejpam-776	277	34	x	x	SYM
ejpam-776	277	35	=	=	SYM
ejpam-776	277	36	∫	∫	PROPN
ejpam-776	278	1	r	r	NOUN
ejpam-776	278	2	fλ	fλ	PROPN
ejpam-776	278	3	(	(	PUNCT
ejpam-776	278	4	f	f	PROPN
ejpam-776	278	5	)	)	PUNCT
ejpam-776	278	6	(	(	PUNCT
ejpam-776	278	7	λ)fλ(g)(λ)h−(λ	λ)fλ(g)(λ)h−(λ	X
ejpam-776	278	8	)	)	PUNCT
ejpam-776	278	9	dσ(λ	dσ(λ	PUNCT
ejpam-776	278	10	)	)	PUNCT
ejpam-776	278	11	where	where	SCONJ
ejpam-776	278	12	h−(λ	h−(λ	NOUN
ejpam-776	278	13	)	)	PUNCT
ejpam-776	278	14	=	=	SYM
ejpam-776	278	15	h(−λ	h(−λ	NOUN
ejpam-776	278	16	)	)	PUNCT
ejpam-776	278	17	,	,	PUNCT
ejpam-776	278	18	λ	λ	PROPN
ejpam-776	278	19	∈	∈	PROPN
ejpam-776	278	20	r.	r.	NOUN
ejpam-776	278	21	proof	proof	NOUN
ejpam-776	278	22	.	.	PUNCT
ejpam-776	279	1	fix	fix	VERB
ejpam-776	279	2	g	g	PROPN
ejpam-776	279	3	∈	∈	PROPN
ejpam-776	279	4	l2(r	l2(r	NOUN
ejpam-776	279	5	,	,	PUNCT
ejpam-776	279	6	a(x)d	a(x)d	PROPN
ejpam-776	279	7	x	x	PRON
ejpam-776	279	8	)	)	PUNCT
ejpam-776	280	1	and	and	CCONJ
ejpam-776	280	2	h	h	NOUN
ejpam-776	280	3	∈	∈	NOUN
ejpam-776	280	4	s	s	X
ejpam-776	280	5	(	(	PUNCT
ejpam-776	280	6	r	r	NOUN
ejpam-776	280	7	)	)	PUNCT
ejpam-776	280	8	.	.	PUNCT
ejpam-776	281	1	for	for	ADP
ejpam-776	281	2	f	f	PROPN
ejpam-776	281	3	∈	∈	PROPN
ejpam-776	281	4	l2(r	l2(r	PROPN
ejpam-776	281	5	,	,	PUNCT
ejpam-776	281	6	a(x)d	a(x)d	PROPN
ejpam-776	281	7	x	x	PRON
ejpam-776	281	8	)	)	PUNCT
ejpam-776	281	9	put	put	NOUN
ejpam-776	281	10	s1	s1	NOUN
ejpam-776	281	11	(	(	PUNCT
ejpam-776	281	12	f	f	NOUN
ejpam-776	281	13	)	)	PUNCT
ejpam-776	282	1	=	=	SYM
ejpam-776	282	2	∫	∫	PUNCT
ejpam-776	282	3	r	r	NOUN
ejpam-776	282	4	f	f	PROPN
ejpam-776	282	5	#	#	NOUN
ejpam-776	282	6	g(x)f−1	g(x)f−1	PROPN
ejpam-776	282	7	λ	λ	X
ejpam-776	282	8	(	(	PUNCT
ejpam-776	282	9	h)(x)a(x)d	h)(x)a(x)d	NOUN
ejpam-776	282	10	x	x	SYM
ejpam-776	282	11	and	and	CCONJ
ejpam-776	282	12	s2	s2	PROPN
ejpam-776	282	13	(	(	PUNCT
ejpam-776	282	14	f	f	PROPN
ejpam-776	282	15	)	)	PUNCT
ejpam-776	283	1	=	=	SYM
ejpam-776	283	2	∫	∫	PROPN
ejpam-776	284	1	r	r	NOUN
ejpam-776	284	2	fλ	fλ	PROPN
ejpam-776	284	3	(	(	PUNCT
ejpam-776	284	4	f	f	PROPN
ejpam-776	284	5	)	)	PUNCT
ejpam-776	284	6	(	(	PUNCT
ejpam-776	284	7	λ)fλ(g)(λ)h−(λ)dσ(λ	λ)fλ(g)(λ)h−(λ)dσ(λ	PROPN
ejpam-776	284	8	)	)	PUNCT
ejpam-776	284	9	.	.	PUNCT
ejpam-776	285	1	w.	w.	PROPN
ejpam-776	285	2	chabeh	chabeh	PROPN
ejpam-776	285	3	,	,	PUNCT
ejpam-776	285	4	m.	m.	NOUN
ejpam-776	285	5	mourou	mourou	PROPN
ejpam-776	285	6	/	/	SYM
ejpam-776	285	7	eur	eur	PROPN
ejpam-776	285	8	.	.	PUNCT
ejpam-776	286	1	j.	j.	PROPN
ejpam-776	286	2	pure	pure	PROPN
ejpam-776	286	3	appl	appl	PROPN
ejpam-776	286	4	.	.	PROPN
ejpam-776	286	5	math	math	PROPN
ejpam-776	286	6	,	,	PUNCT
ejpam-776	286	7	3	3	NUM
ejpam-776	286	8	(	(	PUNCT
ejpam-776	286	9	2010	2010	NUM
ejpam-776	286	10	)	)	PUNCT
ejpam-776	286	11	,	,	PUNCT
ejpam-776	286	12	958	958	NUM
ejpam-776	286	13	-	-	SYM
ejpam-776	286	14	979	979	NUM
ejpam-776	286	15	972	972	NUM
ejpam-776	286	16	in	in	ADP
ejpam-776	286	17	view	view	NOUN
ejpam-776	286	18	of	of	ADP
ejpam-776	286	19	proposition	proposition	NOUN
ejpam-776	286	20	3	3	NUM
ejpam-776	286	21	and	and	CCONJ
ejpam-776	286	22	theorem	theorem	VERB
ejpam-776	286	23	1	1	NUM
ejpam-776	286	24	,	,	PUNCT
ejpam-776	286	25	we	we	PRON
ejpam-776	286	26	see	see	VERB
ejpam-776	286	27	that	that	DET
ejpam-776	286	28	s1	s1	NOUN
ejpam-776	286	29	(	(	PUNCT
ejpam-776	286	30	f	f	NOUN
ejpam-776	286	31	)	)	PUNCT
ejpam-776	286	32	=	=	SYM
ejpam-776	286	33	s2	s2	PROPN
ejpam-776	286	34	(	(	PUNCT
ejpam-776	286	35	f	f	PROPN
ejpam-776	286	36	)	)	PUNCT
ejpam-776	286	37	for	for	ADP
ejpam-776	286	38	each	each	DET
ejpam-776	286	39	f	f	PROPN
ejpam-776	286	40	∈	∈	PROPN
ejpam-776	286	41	l1	l1	PROPN
ejpam-776	286	42	∩	∩	PROPN
ejpam-776	286	43	l2(r	l2(r	PROPN
ejpam-776	286	44	,	,	PUNCT
ejpam-776	286	45	a(x)d	a(x)d	PROPN
ejpam-776	286	46	x	x	X
ejpam-776	286	47	)	)	PUNCT
ejpam-776	286	48	.	.	PUNCT
ejpam-776	287	1	moreover	moreover	ADV
ejpam-776	287	2	,	,	PUNCT
ejpam-776	287	3	by	by	ADP
ejpam-776	287	4	using	use	VERB
ejpam-776	287	5	(	(	PUNCT
ejpam-776	287	6	21	21	NUM
ejpam-776	287	7	)	)	PUNCT
ejpam-776	287	8	,	,	PUNCT
ejpam-776	287	9	schwarz	schwarz	PROPN
ejpam-776	287	10	inequality	inequality	NOUN
ejpam-776	287	11	and	and	CCONJ
ejpam-776	287	12	theorem	theorem	VERB
ejpam-776	287	13	1	1	NUM
ejpam-776	287	14	we	we	PRON
ejpam-776	287	15	get	get	VERB
ejpam-776	287	16	|s1	|s1	NOUN
ejpam-776	287	17	(	(	PUNCT
ejpam-776	287	18	f	f	X
ejpam-776	287	19	)	)	PUNCT
ejpam-776	287	20	|	|	ADV
ejpam-776	287	21	≤	≤	NUM
ejpam-776	288	1	f	f	NOUN
ejpam-776	288	2	#	#	SYM
ejpam-776	288	3	g	g	PROPN
ejpam-776	288	4	∞	∞	NUM
ejpam-776	288	5	f−1	f−1	PROPN
ejpam-776	288	6	λ	λ	NOUN
ejpam-776	288	7	(	(	PUNCT
ejpam-776	288	8	h	h	NOUN
ejpam-776	288	9	)	)	PUNCT
ejpam-776	288	10	1,a	1,a	PROPN
ejpam-776	288	11	≤	≤	NUM
ejpam-776	289	1	f	f	X
ejpam-776	290	1	2,a	2,a	NUM
ejpam-776	290	2	g	g	NOUN
ejpam-776	290	3	2,a	2,a	NUM
ejpam-776	290	4	f−1	f−1	PROPN
ejpam-776	291	1	λ	λ	PROPN
ejpam-776	291	2	(	(	PUNCT
ejpam-776	291	3	h	h	NOUN
ejpam-776	291	4	)	)	PUNCT
ejpam-776	291	5	1,a	1,a	PROPN
ejpam-776	291	6	and	and	CCONJ
ejpam-776	291	7	|s2	|s2	PROPN
ejpam-776	291	8	(	(	PUNCT
ejpam-776	291	9	f	f	NOUN
ejpam-776	291	10	)	)	PUNCT
ejpam-776	292	1	|	|	ADV
ejpam-776	292	2	≤	≤	NUM
ejpam-776	292	3	fλ	fλ	PRON
ejpam-776	292	4	(	(	PUNCT
ejpam-776	292	5	f	f	PROPN
ejpam-776	292	6	)	)	PUNCT
ejpam-776	292	7	fλ(g	fλ(g	PUNCT
ejpam-776	292	8	)	)	PUNCT
ejpam-776	293	1	1,σ	1,σ	PROPN
ejpam-776	294	1	‖h‖∞	‖h‖∞	PROPN
ejpam-776	294	2	≤	≤	NUM
ejpam-776	294	3	fλ	fλ	PROPN
ejpam-776	294	4	(	(	PUNCT
ejpam-776	294	5	f	f	PROPN
ejpam-776	294	6	)	)	PUNCT
ejpam-776	294	7	2,σ	2,σ	NUM
ejpam-776	294	8	fλ(g	fλ(g	NOUN
ejpam-776	294	9	)	)	PUNCT
ejpam-776	295	1	2,σ	2,σ	NUM
ejpam-776	296	1	‖h‖∞	‖h‖∞	PROPN
ejpam-776	296	2	≤	≤	NUM
ejpam-776	297	1	f	f	PROPN
ejpam-776	298	1	2,a	2,a	NUM
ejpam-776	298	2	g	g	PROPN
ejpam-776	298	3	2,a	2,a	PROPN
ejpam-776	298	4	‖h‖∞	‖h‖∞	PROPN
ejpam-776	298	5	,	,	PUNCT
ejpam-776	298	6	which	which	PRON
ejpam-776	298	7	shows	show	VERB
ejpam-776	298	8	that	that	SCONJ
ejpam-776	298	9	the	the	DET
ejpam-776	298	10	linear	linear	NOUN
ejpam-776	298	11	functionals	functional	VERB
ejpam-776	298	12	s1	s1	NOUN
ejpam-776	298	13	and	and	CCONJ
ejpam-776	298	14	s2	s2	PROPN
ejpam-776	298	15	are	be	AUX
ejpam-776	298	16	bounded	bound	VERB
ejpam-776	298	17	on	on	ADP
ejpam-776	298	18	l2(r	l2(r	PROPN
ejpam-776	298	19	,	,	PUNCT
ejpam-776	298	20	a(x)d	a(x)d	PROPN
ejpam-776	298	21	x	x	X
ejpam-776	298	22	)	)	PUNCT
ejpam-776	298	23	.	.	PUNCT
ejpam-776	299	1	therefore	therefore	ADV
ejpam-776	299	2	s1	s1	PROPN
ejpam-776	299	3	≡	≡	PROPN
ejpam-776	299	4	s2	s2	PROPN
ejpam-776	299	5	,	,	PUNCT
ejpam-776	299	6	and	and	CCONJ
ejpam-776	299	7	the	the	DET
ejpam-776	299	8	lemma	lemma	PROPN
ejpam-776	299	9	is	be	AUX
ejpam-776	299	10	proved	prove	VERB
ejpam-776	299	11	.	.	PUNCT
ejpam-776	300	1	lemma	lemma	PROPN
ejpam-776	300	2	4	4	X
ejpam-776	300	3	.	.	PUNCT
ejpam-776	301	1	let	let	VERB
ejpam-776	301	2	f1	f1	NOUN
ejpam-776	301	3	,	,	PUNCT
ejpam-776	301	4	f2	f2	PROPN
ejpam-776	301	5	∈	∈	PROPN
ejpam-776	301	6	l2(r	l2(r	PROPN
ejpam-776	301	7	,	,	PUNCT
ejpam-776	301	8	a(x)d	a(x)d	PROPN
ejpam-776	301	9	x	x	X
ejpam-776	301	10	)	)	PUNCT
ejpam-776	301	11	.	.	PUNCT
ejpam-776	302	1	then	then	ADV
ejpam-776	302	2	f1	f1	NOUN
ejpam-776	302	3	#	#	NOUN
ejpam-776	302	4	f2	f2	PROPN
ejpam-776	302	5	∈	∈	PROPN
ejpam-776	302	6	l2(r	l2(r	NOUN
ejpam-776	302	7	,	,	PUNCT
ejpam-776	302	8	a(x)d	a(x)d	PROPN
ejpam-776	302	9	x	x	X
ejpam-776	302	10	)	)	PUNCT
ejpam-776	302	11	if	if	SCONJ
ejpam-776	302	12	and	and	CCONJ
ejpam-776	302	13	only	only	ADV
ejpam-776	302	14	if	if	SCONJ
ejpam-776	302	15	fλ	fλ	X
ejpam-776	302	16	(	(	PUNCT
ejpam-776	302	17	f1)fλ	f1)fλ	PROPN
ejpam-776	302	18	(	(	PUNCT
ejpam-776	302	19	f2	f2	PROPN
ejpam-776	302	20	)	)	PUNCT
ejpam-776	302	21	∈	∈	PROPN
ejpam-776	302	22	l2(r	l2(r	PROPN
ejpam-776	302	23	,	,	PUNCT
ejpam-776	302	24	dσ	dσ	VERB
ejpam-776	302	25	)	)	PUNCT
ejpam-776	302	26	and	and	CCONJ
ejpam-776	302	27	we	we	PRON
ejpam-776	302	28	have	have	VERB
ejpam-776	302	29	fλ	fλ	ADJ
ejpam-776	302	30	(	(	PUNCT
ejpam-776	302	31	f1	f1	NOUN
ejpam-776	302	32	#	#	NOUN
ejpam-776	302	33	f2	f2	PROPN
ejpam-776	302	34	)	)	PUNCT
ejpam-776	302	35	=	=	SYM
ejpam-776	302	36	fλ	fλ	X
ejpam-776	302	37	(	(	PUNCT
ejpam-776	302	38	f1)fλ	f1)fλ	PROPN
ejpam-776	302	39	(	(	PUNCT
ejpam-776	302	40	f2	f2	PROPN
ejpam-776	302	41	)	)	PUNCT
ejpam-776	302	42	in	in	ADP
ejpam-776	302	43	the	the	DET
ejpam-776	302	44	l2−case	l2−case	NOUN
ejpam-776	302	45	.	.	PUNCT
ejpam-776	303	1	proof	proof	NOUN
ejpam-776	303	2	.	.	PUNCT
ejpam-776	304	1	suppose	suppose	VERB
ejpam-776	304	2	f1	f1	PROPN
ejpam-776	304	3	#	#	PROPN
ejpam-776	304	4	f2	f2	PROPN
ejpam-776	304	5	∈	∈	PROPN
ejpam-776	304	6	l2(r	l2(r	NOUN
ejpam-776	304	7	,	,	PUNCT
ejpam-776	304	8	a(x)d	a(x)d	PROPN
ejpam-776	304	9	x	x	PRON
ejpam-776	304	10	)	)	PUNCT
ejpam-776	304	11	.	.	PUNCT
ejpam-776	305	1	by	by	ADP
ejpam-776	305	2	lemma	lemma	PROPN
ejpam-776	305	3	3	3	NUM
ejpam-776	305	4	and	and	CCONJ
ejpam-776	305	5	theorem	theorem	VERB
ejpam-776	305	6	1	1	NUM
ejpam-776	305	7	,	,	PUNCT
ejpam-776	305	8	we	we	PRON
ejpam-776	305	9	have	have	VERB
ejpam-776	305	10	for	for	ADP
ejpam-776	305	11	any	any	DET
ejpam-776	305	12	h	h	NOUN
ejpam-776	305	13	∈	∈	NOUN
ejpam-776	305	14	s	s	X
ejpam-776	305	15	(	(	PUNCT
ejpam-776	305	16	r	r	NOUN
ejpam-776	305	17	)	)	PUNCT
ejpam-776	305	18	,	,	PUNCT
ejpam-776	305	19	∫	∫	PROPN
ejpam-776	305	20	r	r	NOUN
ejpam-776	305	21	fλ	fλ	PROPN
ejpam-776	305	22	(	(	PUNCT
ejpam-776	305	23	f1)(λ)fλ	f1)(λ)fλ	PROPN
ejpam-776	305	24	(	(	PUNCT
ejpam-776	305	25	f2)(λ)h(λ	f2)(λ)h(λ	NOUN
ejpam-776	305	26	)	)	PUNCT
ejpam-776	305	27	dσ(λ	dσ(λ	PUNCT
ejpam-776	305	28	)	)	PUNCT
ejpam-776	306	1	=	=	SYM
ejpam-776	306	2	∫	∫	PROPN
ejpam-776	306	3	r	r	NOUN
ejpam-776	306	4	f1	f1	NOUN
ejpam-776	306	5	#	#	NOUN
ejpam-776	306	6	f2(x)f−1	f2(x)f−1	X
ejpam-776	306	7	λ	λ	PROPN
ejpam-776	306	8	(	(	PUNCT
ejpam-776	306	9	h	h	PROPN
ejpam-776	306	10	−)(x	−)(x	PROPN
ejpam-776	306	11	)	)	PUNCT
ejpam-776	306	12	a(x)d	a(x)d	VERB
ejpam-776	306	13	x	x	PUNCT
ejpam-776	307	1	=	=	SYM
ejpam-776	307	2	∫	∫	PROPN
ejpam-776	307	3	r	r	NOUN
ejpam-776	307	4	f1	f1	NOUN
ejpam-776	307	5	#	#	NOUN
ejpam-776	307	6	f2(x)f−1	f2(x)f−1	VERB
ejpam-776	307	7	λ	λ	PROPN
ejpam-776	307	8	�	�	PROPN
ejpam-776	307	9	h	h	PROPN
ejpam-776	307	10	�	�	PROPN
ejpam-776	307	11	(	(	PUNCT
ejpam-776	307	12	x)a(x)d	x)a(x)d	PROPN
ejpam-776	307	13	x	x	X
ejpam-776	307	14	=	=	SYM
ejpam-776	307	15	∫	∫	PROPN
ejpam-776	307	16	r	r	NOUN
ejpam-776	307	17	fλ	fλ	PROPN
ejpam-776	307	18	(	(	PUNCT
ejpam-776	307	19	f1	f1	NOUN
ejpam-776	307	20	#	#	NOUN
ejpam-776	307	21	f2)(λ)h(λ	f2)(λ)h(λ	NOUN
ejpam-776	307	22	)	)	PUNCT
ejpam-776	307	23	dσ(λ	dσ(λ	NUM
ejpam-776	307	24	)	)	PUNCT
ejpam-776	307	25	,	,	PUNCT
ejpam-776	307	26	which	which	PRON
ejpam-776	307	27	shows	show	VERB
ejpam-776	307	28	that	that	SCONJ
ejpam-776	307	29	fλ	fλ	PROPN
ejpam-776	307	30	(	(	PUNCT
ejpam-776	307	31	f1)fλ	f1)fλ	PROPN
ejpam-776	307	32	(	(	PUNCT
ejpam-776	307	33	f2	f2	PROPN
ejpam-776	307	34	)	)	PUNCT
ejpam-776	307	35	=	=	SYM
ejpam-776	307	36	fλ	fλ	X
ejpam-776	307	37	(	(	PUNCT
ejpam-776	307	38	f1	f1	NOUN
ejpam-776	307	39	#	#	NOUN
ejpam-776	307	40	f2	f2	PROPN
ejpam-776	307	41	)	)	PUNCT
ejpam-776	307	42	.	.	PUNCT
ejpam-776	308	1	conversely	conversely	ADV
ejpam-776	308	2	,	,	PUNCT
ejpam-776	308	3	if	if	SCONJ
ejpam-776	308	4	fλ	fλ	X
ejpam-776	308	5	(	(	PUNCT
ejpam-776	308	6	f1)fλ	f1)fλ	PROPN
ejpam-776	308	7	(	(	PUNCT
ejpam-776	308	8	f2	f2	PROPN
ejpam-776	308	9	)	)	PUNCT
ejpam-776	308	10	∈	∈	PROPN
ejpam-776	308	11	l2(r	l2(r	PROPN
ejpam-776	308	12	,	,	PUNCT
ejpam-776	308	13	dσ	dσ	PROPN
ejpam-776	308	14	)	)	PUNCT
ejpam-776	308	15	,	,	PUNCT
ejpam-776	308	16	then	then	ADV
ejpam-776	308	17	by	by	ADP
ejpam-776	308	18	lemma	lemma	PROPN
ejpam-776	308	19	3	3	NUM
ejpam-776	308	20	and	and	CCONJ
ejpam-776	308	21	theorem	theorem	VERB
ejpam-776	308	22	1	1	NUM
ejpam-776	308	23	,	,	PUNCT
ejpam-776	308	24	we	we	PRON
ejpam-776	308	25	have	have	VERB
ejpam-776	308	26	for	for	ADP
ejpam-776	308	27	any	any	DET
ejpam-776	308	28	h	h	NOUN
ejpam-776	308	29	∈	∈	NOUN
ejpam-776	308	30	s	s	X
ejpam-776	308	31	(	(	PUNCT
ejpam-776	308	32	r	r	NOUN
ejpam-776	308	33	)	)	PUNCT
ejpam-776	308	34	,	,	PUNCT
ejpam-776	308	35	∫	∫	PROPN
ejpam-776	308	36	r	r	NOUN
ejpam-776	308	37	f1	f1	NOUN
ejpam-776	308	38	#	#	NOUN
ejpam-776	308	39	f2(x)f−1	f2(x)f−1	VERB
ejpam-776	308	40	λ	λ	X
ejpam-776	308	41	(	(	PUNCT
ejpam-776	308	42	h)(x)a(x)d	h)(x)a(x)d	NOUN
ejpam-776	308	43	x	x	SYM
ejpam-776	308	44	=	=	SYM
ejpam-776	308	45	∫	∫	PROPN
ejpam-776	309	1	r	r	NOUN
ejpam-776	309	2	fλ	fλ	PROPN
ejpam-776	309	3	(	(	PUNCT
ejpam-776	309	4	f1)(λ)fλ	f1)(λ)fλ	PROPN
ejpam-776	309	5	(	(	PUNCT
ejpam-776	309	6	f2)(λ)eh(λ	f2)(λ)eh(λ	PROPN
ejpam-776	309	7	)	)	PUNCT
ejpam-776	309	8	dσ(λ	dσ(λ	PUNCT
ejpam-776	309	9	)	)	PUNCT
ejpam-776	309	10	=	=	SYM
ejpam-776	309	11	∫	∫	PROPN
ejpam-776	309	12	r	r	NOUN
ejpam-776	309	13	f−1	f−1	PROPN
ejpam-776	309	14	λ	λ	PROPN
ejpam-776	309	15	[	[	X
ejpam-776	309	16	fλ	fλ	X
ejpam-776	309	17	(	(	PUNCT
ejpam-776	309	18	f1)fλ	f1)fλ	PROPN
ejpam-776	309	19	(	(	PUNCT
ejpam-776	309	20	f2)](x)f−1	f2)](x)f−1	PROPN
ejpam-776	309	21	λ	λ	PROPN
ejpam-776	309	22	(	(	PUNCT
ejpam-776	309	23	h)(x)a(x)d	h)(x)a(x)d	NOUN
ejpam-776	309	24	x	x	SYM
ejpam-776	309	25	,	,	PUNCT
ejpam-776	309	26	which	which	PRON
ejpam-776	309	27	shows	show	VERB
ejpam-776	309	28	,	,	PUNCT
ejpam-776	309	29	in	in	ADP
ejpam-776	309	30	view	view	NOUN
ejpam-776	309	31	of	of	ADP
ejpam-776	309	32	theorem	theorem	NOUN
ejpam-776	309	33	2	2	NUM
ejpam-776	309	34	,	,	PUNCT
ejpam-776	309	35	that	that	DET
ejpam-776	309	36	f1	f1	NOUN
ejpam-776	309	37	#	#	NOUN
ejpam-776	309	38	f2	f2	NOUN
ejpam-776	309	39	=	=	SYM
ejpam-776	309	40	f−1	f−1	PROPN
ejpam-776	309	41	λ	λ	X
ejpam-776	309	42	[	[	X
ejpam-776	309	43	fλ	fλ	X
ejpam-776	309	44	(	(	PUNCT
ejpam-776	309	45	f1)fλ	f1)fλ	PROPN
ejpam-776	309	46	(	(	PUNCT
ejpam-776	309	47	f2	f2	PROPN
ejpam-776	309	48	)	)	PUNCT
ejpam-776	309	49	]	]	PUNCT
ejpam-776	309	50	.	.	PUNCT
ejpam-776	310	1	this	this	PRON
ejpam-776	310	2	achieves	achieve	VERB
ejpam-776	310	3	the	the	DET
ejpam-776	310	4	proof	proof	NOUN
ejpam-776	310	5	.	.	PUNCT
ejpam-776	311	1	a	a	DET
ejpam-776	311	2	combination	combination	NOUN
ejpam-776	311	3	of	of	ADP
ejpam-776	311	4	lemma	lemma	PROPN
ejpam-776	311	5	4	4	NUM
ejpam-776	311	6	and	and	CCONJ
ejpam-776	311	7	theorem	theorem	VERB
ejpam-776	311	8	1	1	NUM
ejpam-776	311	9	gives	give	VERB
ejpam-776	311	10	us	we	PRON
ejpam-776	311	11	the	the	DET
ejpam-776	311	12	following	following	NOUN
ejpam-776	311	13	.	.	PUNCT
ejpam-776	312	1	w.	w.	PROPN
ejpam-776	312	2	chabeh	chabeh	PROPN
ejpam-776	312	3	,	,	PUNCT
ejpam-776	312	4	m.	m.	NOUN
ejpam-776	312	5	mourou	mourou	PROPN
ejpam-776	312	6	/	/	SYM
ejpam-776	312	7	eur	eur	PROPN
ejpam-776	312	8	.	.	PUNCT
ejpam-776	313	1	j.	j.	PROPN
ejpam-776	313	2	pure	pure	PROPN
ejpam-776	313	3	appl	appl	PROPN
ejpam-776	313	4	.	.	PROPN
ejpam-776	313	5	math	math	PROPN
ejpam-776	313	6	,	,	PUNCT
ejpam-776	313	7	3	3	NUM
ejpam-776	313	8	(	(	PUNCT
ejpam-776	313	9	2010	2010	NUM
ejpam-776	313	10	)	)	PUNCT
ejpam-776	313	11	,	,	PUNCT
ejpam-776	313	12	958	958	NUM
ejpam-776	313	13	-	-	SYM
ejpam-776	313	14	979	979	NUM
ejpam-776	313	15	973	973	NUM
ejpam-776	313	16	lemma	lemma	PROPN
ejpam-776	313	17	5	5	NUM
ejpam-776	313	18	.	.	PUNCT
ejpam-776	314	1	let	let	VERB
ejpam-776	314	2	f1	f1	NOUN
ejpam-776	314	3	,	,	PUNCT
ejpam-776	314	4	f2	f2	PROPN
ejpam-776	314	5	∈	∈	PROPN
ejpam-776	314	6	l2(r	l2(r	PROPN
ejpam-776	314	7	,	,	PUNCT
ejpam-776	314	8	a(x)d	a(x)d	PROPN
ejpam-776	314	9	x	x	X
ejpam-776	314	10	)	)	PUNCT
ejpam-776	314	11	.	.	PUNCT
ejpam-776	315	1	then	then	ADV
ejpam-776	315	2	∫	∫	PROPN
ejpam-776	315	3	r	r	NOUN
ejpam-776	315	4	|	|	NOUN
ejpam-776	315	5	f1	f1	NOUN
ejpam-776	315	6	#	#	NOUN
ejpam-776	315	7	f2(x)|2a(x)d	f2(x)|2a(x)d	NUM
ejpam-776	315	8	x	x	SYM
ejpam-776	315	9	=	=	SYM
ejpam-776	315	10	∫	∫	PROPN
ejpam-776	315	11	r	r	NOUN
ejpam-776	315	12	|fλ	|fλ	PROPN
ejpam-776	315	13	(	(	PUNCT
ejpam-776	315	14	f1)(λ)|2|fλ	f1)(λ)|2|fλ	NOUN
ejpam-776	315	15	(	(	PUNCT
ejpam-776	315	16	f2)(λ)|2dσ(λ	f2)(λ)|2dσ(λ	NOUN
ejpam-776	315	17	)	)	PUNCT
ejpam-776	315	18	where	where	SCONJ
ejpam-776	315	19	both	both	DET
ejpam-776	315	20	sides	side	NOUN
ejpam-776	315	21	are	be	AUX
ejpam-776	315	22	finite	finite	ADJ
ejpam-776	315	23	or	or	CCONJ
ejpam-776	315	24	infinite	infinite	NOUN
ejpam-776	315	25	.	.	PUNCT
ejpam-776	315	26	theorem	theorem	NOUN
ejpam-776	315	27	4	4	NUM
ejpam-776	315	28	.	.	PUNCT
ejpam-776	316	1	let	let	VERB
ejpam-776	316	2	g	g	PROPN
ejpam-776	316	3	∈	∈	PROPN
ejpam-776	316	4	l2(r	l2(r	PROPN
ejpam-776	316	5	,	,	PUNCT
ejpam-776	316	6	a(x)d	a(x)d	PROPN
ejpam-776	316	7	x	x	PRON
ejpam-776	316	8	)	)	PUNCT
ejpam-776	316	9	be	be	AUX
ejpam-776	316	10	a	a	DET
ejpam-776	316	11	generalized	generalized	ADJ
ejpam-776	316	12	wavelet	wavelet	NOUN
ejpam-776	316	13	.	.	PUNCT
ejpam-776	317	1	then	then	ADV
ejpam-776	317	2	for	for	ADP
ejpam-776	317	3	all	all	DET
ejpam-776	317	4	f	f	PROPN
ejpam-776	317	5	∈	∈	PROPN
ejpam-776	317	6	l2(r	l2(r	PROPN
ejpam-776	317	7	,	,	PUNCT
ejpam-776	317	8	a(x)d	a(x)d	PROPN
ejpam-776	317	9	x	x	PRON
ejpam-776	317	10	)	)	PUNCT
ejpam-776	317	11	,	,	PUNCT
ejpam-776	317	12	we	we	PRON
ejpam-776	317	13	have	have	VERB
ejpam-776	317	14	the	the	DET
ejpam-776	317	15	plancherel	plancherel	NOUN
ejpam-776	317	16	formula	formula	NOUN
ejpam-776	317	17	∫	∫	PROPN
ejpam-776	318	1	r	r	NOUN
ejpam-776	319	1	|	|	NOUN
ejpam-776	320	1	f	f	X
ejpam-776	320	2	(	(	PUNCT
ejpam-776	320	3	x)|2a(x)d	x)|2a(x)d	X
ejpam-776	320	4	x	x	SYM
ejpam-776	320	5	=	=	SYM
ejpam-776	320	6	1	1	NUM
ejpam-776	320	7	cg	cg	NOUN
ejpam-776	320	8	∫	∫	PROPN
ejpam-776	320	9	∞	∞	PROPN
ejpam-776	320	10	0	0	NUM
ejpam-776	320	11	∫	∫	PROPN
ejpam-776	320	12	r	r	NOUN
ejpam-776	320	13	|φg	|φg	PROPN
ejpam-776	320	14	(	(	PUNCT
ejpam-776	320	15	f	f	PROPN
ejpam-776	320	16	)	)	PUNCT
ejpam-776	320	17	(	(	PUNCT
ejpam-776	320	18	a	a	PRON
ejpam-776	320	19	,	,	PUNCT
ejpam-776	320	20	b)|2a(b)d	b)|2a(b)d	PROPN
ejpam-776	320	21	b	b	PROPN
ejpam-776	320	22	da	da	PROPN
ejpam-776	320	23	a2	a2	PROPN
ejpam-776	320	24	.	.	PUNCT
ejpam-776	321	1	proof	proof	NOUN
ejpam-776	321	2	.	.	PUNCT
ejpam-776	322	1	using	use	VERB
ejpam-776	322	2	(	(	PUNCT
ejpam-776	322	3	26	26	NUM
ejpam-776	322	4	)	)	PUNCT
ejpam-776	322	5	,	,	PUNCT
ejpam-776	322	6	(	(	PUNCT
ejpam-776	322	7	27	27	NUM
ejpam-776	322	8	)	)	PUNCT
ejpam-776	322	9	,	,	PUNCT
ejpam-776	322	10	(	(	PUNCT
ejpam-776	322	11	31	31	NUM
ejpam-776	322	12	)	)	PUNCT
ejpam-776	322	13	,	,	PUNCT
ejpam-776	322	14	fubini	fubini	NOUN
ejpam-776	322	15	’s	’s	PART
ejpam-776	322	16	theorem	theorem	NOUN
ejpam-776	322	17	and	and	CCONJ
ejpam-776	322	18	lemma	lemma	PROPN
ejpam-776	322	19	5	5	NUM
ejpam-776	322	20	,	,	PUNCT
ejpam-776	322	21	we	we	PRON
ejpam-776	322	22	have	have	VERB
ejpam-776	322	23	1	1	NUM
ejpam-776	322	24	cg	cg	NOUN
ejpam-776	322	25	∫	∫	PROPN
ejpam-776	322	26	∞	∞	PROPN
ejpam-776	322	27	0	0	NUM
ejpam-776	323	1	∫	∫	PROPN
ejpam-776	323	2	r	r	NOUN
ejpam-776	323	3	|φg	|φg	PROPN
ejpam-776	323	4	(	(	PUNCT
ejpam-776	323	5	f	f	PROPN
ejpam-776	323	6	)	)	PUNCT
ejpam-776	323	7	(	(	PUNCT
ejpam-776	323	8	a	a	DET
ejpam-776	323	9	,	,	PUNCT
ejpam-776	323	10	b)|2a(b)d	b)|2a(b)d	PROPN
ejpam-776	323	11	b	b	PROPN
ejpam-776	323	12	da	da	PROPN
ejpam-776	323	13	a2	a2	PROPN
ejpam-776	323	14	=	=	PUNCT
ejpam-776	323	15	=	=	SYM
ejpam-776	323	16	1	1	NUM
ejpam-776	323	17	cg	cg	NOUN
ejpam-776	323	18	∫	∫	PROPN
ejpam-776	323	19	∞	∞	PROPN
ejpam-776	323	20	0	0	NUM
ejpam-776	323	21	�	�	PROPN
ejpam-776	323	22	∫	∫	PROPN
ejpam-776	323	23	r	r	NOUN
ejpam-776	324	1	|	|	NOUN
ejpam-776	324	2	f	f	NOUN
ejpam-776	324	3	#	#	NOUN
ejpam-776	324	4	ega(b)|2a(b)d	ega(b)|2a(b)d	PROPN
ejpam-776	324	5	b	b	PROPN
ejpam-776	324	6	�	�	PROPN
ejpam-776	324	7	da	da	PROPN
ejpam-776	324	8	a	a	PRON
ejpam-776	324	9	=	=	SYM
ejpam-776	324	10	1	1	NUM
ejpam-776	324	11	cg	cg	NOUN
ejpam-776	324	12	∫	∫	PROPN
ejpam-776	324	13	∞	∞	PROPN
ejpam-776	324	14	0	0	NUM
ejpam-776	324	15	�	�	PROPN
ejpam-776	324	16	∫	∫	PROPN
ejpam-776	324	17	r	r	NOUN
ejpam-776	324	18	|fλ	|fλ	PROPN
ejpam-776	324	19	(	(	PUNCT
ejpam-776	324	20	f	f	NOUN
ejpam-776	324	21	)	)	PUNCT
ejpam-776	324	22	(	(	PUNCT
ejpam-776	324	23	λ)|2|fλ(g)(aλ)|2dσ(λ	λ)|2|fλ(g)(aλ)|2dσ(λ	NOUN
ejpam-776	324	24	)	)	PUNCT
ejpam-776	324	25	�	�	PROPN
ejpam-776	324	26	da	da	PROPN
ejpam-776	324	27	a	a	PRON
ejpam-776	324	28	=	=	X
ejpam-776	324	29	∫	∫	NOUN
ejpam-776	324	30	r	r	NOUN
ejpam-776	324	31	|fλ	|fλ	PROPN
ejpam-776	324	32	(	(	PUNCT
ejpam-776	324	33	f	f	NOUN
ejpam-776	324	34	)	)	PUNCT
ejpam-776	325	1	(	(	PUNCT
ejpam-776	325	2	λ)|2	λ)|2	PROPN
ejpam-776	325	3	�	�	PROPN
ejpam-776	325	4	1	1	NUM
ejpam-776	325	5	cg	cg	NOUN
ejpam-776	325	6	∫	∫	PROPN
ejpam-776	325	7	∞	∞	NOUN
ejpam-776	325	8	0	0	NUM
ejpam-776	325	9	|fλ(g)(aλ)|2	|fλ(g)(aλ)|2	PROPN
ejpam-776	325	10	da	da	PROPN
ejpam-776	325	11	a	a	DET
ejpam-776	325	12	�	�	PROPN
ejpam-776	325	13	dσ(λ	dσ(λ	PUNCT
ejpam-776	325	14	)	)	PUNCT
ejpam-776	325	15	=	=	SYM
ejpam-776	326	1	∫	∫	PROPN
ejpam-776	326	2	r	r	NOUN
ejpam-776	326	3	|fλ	|fλ	PROPN
ejpam-776	326	4	(	(	PUNCT
ejpam-776	326	5	f	f	NOUN
ejpam-776	326	6	)	)	PUNCT
ejpam-776	326	7	(	(	PUNCT
ejpam-776	326	8	λ)|2dσ(λ	λ)|2dσ(λ	X
ejpam-776	326	9	)	)	PUNCT
ejpam-776	326	10	the	the	DET
ejpam-776	326	11	result	result	NOUN
ejpam-776	326	12	is	be	AUX
ejpam-776	326	13	now	now	ADV
ejpam-776	326	14	a	a	DET
ejpam-776	326	15	direct	direct	ADJ
ejpam-776	326	16	consequence	consequence	NOUN
ejpam-776	326	17	of	of	ADP
ejpam-776	326	18	theorem	theorem	NOUN
ejpam-776	326	19	1	1	NUM
ejpam-776	326	20	.	.	PUNCT
ejpam-776	326	21	theorem	theorem	NOUN
ejpam-776	326	22	5	5	NUM
ejpam-776	326	23	.	.	PUNCT
ejpam-776	327	1	let	let	VERB
ejpam-776	327	2	g	g	PROPN
ejpam-776	327	3	∈	∈	PROPN
ejpam-776	327	4	l2(r	l2(r	PROPN
ejpam-776	327	5	,	,	PUNCT
ejpam-776	327	6	a(x)d	a(x)d	PROPN
ejpam-776	327	7	x	x	PRON
ejpam-776	327	8	)	)	PUNCT
ejpam-776	327	9	be	be	AUX
ejpam-776	327	10	a	a	DET
ejpam-776	327	11	generalized	generalized	ADJ
ejpam-776	327	12	wavelet	wavelet	NOUN
ejpam-776	327	13	.	.	PUNCT
ejpam-776	328	1	then	then	ADV
ejpam-776	328	2	for	for	ADP
ejpam-776	328	3	f	f	PROPN
ejpam-776	328	4	∈	∈	PROPN
ejpam-776	328	5	l1	l1	PROPN
ejpam-776	328	6	∩	∩	PROPN
ejpam-776	328	7	l2(r	l2(r	PROPN
ejpam-776	328	8	,	,	PUNCT
ejpam-776	328	9	a(x)d	a(x)d	PROPN
ejpam-776	328	10	x	x	X
ejpam-776	328	11	)	)	PUNCT
ejpam-776	328	12	such	such	ADJ
ejpam-776	328	13	that	that	SCONJ
ejpam-776	328	14	fλ	fλ	PROPN
ejpam-776	328	15	(	(	PUNCT
ejpam-776	328	16	f	f	X
ejpam-776	328	17	)	)	PUNCT
ejpam-776	328	18	∈	∈	PROPN
ejpam-776	328	19	l1(r	l1(r	PROPN
ejpam-776	328	20	,	,	PUNCT
ejpam-776	328	21	dσ	dσ	PROPN
ejpam-776	328	22	)	)	PUNCT
ejpam-776	328	23	,	,	PUNCT
ejpam-776	328	24	we	we	PRON
ejpam-776	328	25	have	have	VERB
ejpam-776	328	26	f	f	PROPN
ejpam-776	328	27	(	(	PUNCT
ejpam-776	328	28	x	x	NOUN
ejpam-776	328	29	)	)	PUNCT
ejpam-776	328	30	=	=	SYM
ejpam-776	329	1	1	1	NUM
ejpam-776	329	2	cg	cg	NOUN
ejpam-776	329	3	∫	∫	PROPN
ejpam-776	329	4	∞	∞	PROPN
ejpam-776	329	5	0	0	NUM
ejpam-776	329	6	�	�	PROPN
ejpam-776	329	7	∫	∫	PROPN
ejpam-776	329	8	r	r	NOUN
ejpam-776	329	9	φg	φg	PROPN
ejpam-776	329	10	(	(	PUNCT
ejpam-776	329	11	f	f	NOUN
ejpam-776	329	12	)	)	PUNCT
ejpam-776	329	13	(	(	PUNCT
ejpam-776	329	14	a	a	DET
ejpam-776	329	15	,	,	PUNCT
ejpam-776	329	16	b)ga	b)ga	PROPN
ejpam-776	329	17	,	,	PUNCT
ejpam-776	329	18	b(x)a(b)d	b(x)a(b)d	PROPN
ejpam-776	329	19	b	b	PROPN
ejpam-776	329	20	�	�	PROPN
ejpam-776	329	21	da	da	PROPN
ejpam-776	329	22	a2	a2	PROPN
ejpam-776	329	23	,	,	PUNCT
ejpam-776	329	24	a.e	a.e	PROPN
ejpam-776	329	25	.	.	PROPN
ejpam-776	329	26	,	,	PUNCT
ejpam-776	329	27	where	where	SCONJ
ejpam-776	329	28	,	,	PUNCT
ejpam-776	329	29	for	for	ADP
ejpam-776	329	30	each	each	DET
ejpam-776	329	31	x	x	SYM
ejpam-776	329	32	∈	∈	PROPN
ejpam-776	329	33	r	r	NOUN
ejpam-776	329	34	,	,	PUNCT
ejpam-776	329	35	both	both	CCONJ
ejpam-776	329	36	the	the	DET
ejpam-776	329	37	inner	inner	ADJ
ejpam-776	329	38	integral	integral	ADJ
ejpam-776	329	39	and	and	CCONJ
ejpam-776	329	40	the	the	DET
ejpam-776	329	41	outer	outer	ADJ
ejpam-776	329	42	integral	integral	ADJ
ejpam-776	329	43	are	be	AUX
ejpam-776	329	44	absolutely	absolutely	ADV
ejpam-776	329	45	convergent	convergent	ADJ
ejpam-776	329	46	,	,	PUNCT
ejpam-776	329	47	but	but	CCONJ
ejpam-776	329	48	possibly	possibly	ADV
ejpam-776	329	49	not	not	PART
ejpam-776	329	50	the	the	DET
ejpam-776	329	51	double	double	ADJ
ejpam-776	329	52	integral	integral	ADJ
ejpam-776	329	53	.	.	PUNCT
ejpam-776	330	1	proof	proof	NOUN
ejpam-776	330	2	.	.	PUNCT
ejpam-776	331	1	put	put	VERB
ejpam-776	331	2	i	i	PRON
ejpam-776	331	3	(	(	PUNCT
ejpam-776	331	4	a	a	PRON
ejpam-776	331	5	,	,	PUNCT
ejpam-776	331	6	x	x	NOUN
ejpam-776	331	7	)	)	PUNCT
ejpam-776	331	8	=	=	SYM
ejpam-776	332	1	∫	∫	PROPN
ejpam-776	332	2	r	r	NOUN
ejpam-776	332	3	φg	φg	PROPN
ejpam-776	332	4	(	(	PUNCT
ejpam-776	332	5	f	f	NOUN
ejpam-776	332	6	)	)	PUNCT
ejpam-776	332	7	(	(	PUNCT
ejpam-776	332	8	a	a	PRON
ejpam-776	332	9	,	,	PUNCT
ejpam-776	332	10	b)ga	b)ga	PROPN
ejpam-776	332	11	,	,	PUNCT
ejpam-776	332	12	b(x)a(b)d	b(x)a(b)d	PROPN
ejpam-776	332	13	b	b	PROPN
ejpam-776	332	14	and	and	CCONJ
ejpam-776	332	15	j	j	PROPN
ejpam-776	332	16	(	(	PUNCT
ejpam-776	332	17	x	x	X
ejpam-776	332	18	)	)	PUNCT
ejpam-776	332	19	=	=	SYM
ejpam-776	332	20	1	1	NUM
ejpam-776	332	21	cg	cg	NOUN
ejpam-776	332	22	∫	∫	PROPN
ejpam-776	332	23	∞	∞	PROPN
ejpam-776	332	24	0	0	NUM
ejpam-776	333	1	i	i	PRON
ejpam-776	333	2	(	(	PUNCT
ejpam-776	333	3	a	a	PRON
ejpam-776	333	4	,	,	PUNCT
ejpam-776	333	5	x	x	NOUN
ejpam-776	333	6	)	)	PUNCT
ejpam-776	333	7	da	da	PROPN
ejpam-776	333	8	a2	a2	PROPN
ejpam-776	333	9	.	.	PUNCT
ejpam-776	334	1	w.	w.	PROPN
ejpam-776	334	2	chabeh	chabeh	PROPN
ejpam-776	334	3	,	,	PUNCT
ejpam-776	334	4	m.	m.	NOUN
ejpam-776	334	5	mourou	mourou	PROPN
ejpam-776	334	6	/	/	SYM
ejpam-776	334	7	eur	eur	PROPN
ejpam-776	334	8	.	.	PUNCT
ejpam-776	335	1	j.	j.	PROPN
ejpam-776	335	2	pure	pure	PROPN
ejpam-776	335	3	appl	appl	PROPN
ejpam-776	335	4	.	.	PROPN
ejpam-776	335	5	math	math	PROPN
ejpam-776	335	6	,	,	PUNCT
ejpam-776	335	7	3	3	NUM
ejpam-776	335	8	(	(	PUNCT
ejpam-776	335	9	2010	2010	NUM
ejpam-776	335	10	)	)	PUNCT
ejpam-776	335	11	,	,	PUNCT
ejpam-776	335	12	958	958	NUM
ejpam-776	335	13	-	-	SYM
ejpam-776	335	14	979	979	NUM
ejpam-776	335	15	974	974	NUM
ejpam-776	335	16	by	by	ADP
ejpam-776	335	17	(	(	PUNCT
ejpam-776	335	18	30	30	NUM
ejpam-776	335	19	)	)	PUNCT
ejpam-776	335	20	and	and	CCONJ
ejpam-776	335	21	(	(	PUNCT
ejpam-776	335	22	31	31	NUM
ejpam-776	335	23	)	)	PUNCT
ejpam-776	335	24	we	we	PRON
ejpam-776	335	25	have	have	VERB
ejpam-776	335	26	i	i	PRON
ejpam-776	335	27	(	(	PUNCT
ejpam-776	335	28	a	a	PRON
ejpam-776	335	29	,	,	PUNCT
ejpam-776	335	30	x	x	NOUN
ejpam-776	335	31	)	)	PUNCT
ejpam-776	335	32	=	=	PUNCT
ejpam-776	336	1	a	a	DET
ejpam-776	336	2	∫	∫	PROPN
ejpam-776	336	3	r	r	NOUN
ejpam-776	336	4	f	f	NOUN
ejpam-776	336	5	#	#	NOUN
ejpam-776	336	6	g̃a(b	g̃a(b	PROPN
ejpam-776	336	7	)	)	PUNCT
ejpam-776	336	8	t	t	PROPN
ejpam-776	336	9	−x	−x	NOUN
ejpam-776	336	10	ega(b)a(b)d	ega(b)a(b)d	PROPN
ejpam-776	336	11	b.	b.	PROPN
ejpam-776	336	12	from	from	ADP
ejpam-776	336	13	(	(	PUNCT
ejpam-776	336	14	20	20	NUM
ejpam-776	336	15	)	)	PUNCT
ejpam-776	336	16	,	,	PUNCT
ejpam-776	336	17	(	(	PUNCT
ejpam-776	336	18	23	23	NUM
ejpam-776	336	19	)	)	PUNCT
ejpam-776	336	20	and	and	CCONJ
ejpam-776	336	21	schwarz	schwarz	PROPN
ejpam-776	336	22	inequality	inequality	NOUN
ejpam-776	336	23	we	we	PRON
ejpam-776	336	24	deduce	deduce	VERB
ejpam-776	336	25	that	that	SCONJ
ejpam-776	336	26	the	the	DET
ejpam-776	336	27	integral	integral	ADJ
ejpam-776	336	28	i	i	X
ejpam-776	336	29	(	(	PUNCT
ejpam-776	336	30	a	a	DET
ejpam-776	336	31	,	,	PUNCT
ejpam-776	336	32	x	x	X
ejpam-776	336	33	)	)	PUNCT
ejpam-776	336	34	is	be	AUX
ejpam-776	336	35	absolutely	absolutely	ADV
ejpam-776	336	36	convergent	convergent	ADJ
ejpam-776	336	37	.	.	PUNCT
ejpam-776	337	1	on	on	ADP
ejpam-776	337	2	the	the	DET
ejpam-776	337	3	other	other	ADJ
ejpam-776	337	4	hand	hand	NOUN
ejpam-776	337	5	,	,	PUNCT
ejpam-776	337	6	by	by	ADP
ejpam-776	337	7	(	(	PUNCT
ejpam-776	337	8	18	18	NUM
ejpam-776	337	9	)	)	PUNCT
ejpam-776	337	10	,	,	PUNCT
ejpam-776	337	11	(	(	PUNCT
ejpam-776	337	12	24	24	NUM
ejpam-776	337	13	)	)	PUNCT
ejpam-776	337	14	and	and	CCONJ
ejpam-776	337	15	(	(	PUNCT
ejpam-776	337	16	27	27	NUM
ejpam-776	337	17	)	)	PUNCT
ejpam-776	337	18	,	,	PUNCT
ejpam-776	337	19	fλ	fλ	X
ejpam-776	337	20	(	(	PUNCT
ejpam-776	337	21	f	f	PROPN
ejpam-776	337	22	#	#	SYM
ejpam-776	337	23	ega)(λ	ega)(λ	NOUN
ejpam-776	337	24	)	)	PUNCT
ejpam-776	337	25	=	=	SYM
ejpam-776	337	26	fλ	fλ	X
ejpam-776	337	27	(	(	PUNCT
ejpam-776	337	28	f	f	PROPN
ejpam-776	337	29	)	)	PUNCT
ejpam-776	337	30	(	(	PUNCT
ejpam-776	337	31	λ)fλ(g)(aλ	λ)fλ(g)(aλ	PROPN
ejpam-776	337	32	)	)	PUNCT
ejpam-776	337	33	and	and	CCONJ
ejpam-776	337	34	fλ(t−x	fλ(t−x	PROPN
ejpam-776	337	35	g̃a)(λ	g̃a)(λ	NOUN
ejpam-776	337	36	)	)	PUNCT
ejpam-776	337	37	=	=	SYM
ejpam-776	337	38	ψλ(−x)fλ(g)(aλ	ψλ(−x)fλ(g)(aλ	NOUN
ejpam-776	337	39	)	)	PUNCT
ejpam-776	337	40	.	.	PUNCT
ejpam-776	338	1	so	so	ADV
ejpam-776	338	2	using	use	VERB
ejpam-776	338	3	theorem	theorem	NOUN
ejpam-776	338	4	1	1	NUM
ejpam-776	338	5	we	we	PRON
ejpam-776	338	6	obtain	obtain	VERB
ejpam-776	338	7	i	i	PRON
ejpam-776	338	8	(	(	PUNCT
ejpam-776	338	9	a	a	PRON
ejpam-776	338	10	,	,	PUNCT
ejpam-776	338	11	x	x	NOUN
ejpam-776	338	12	)	)	PUNCT
ejpam-776	338	13	=	=	PUNCT
ejpam-776	338	14	a	a	DET
ejpam-776	338	15	∫	∫	PROPN
ejpam-776	338	16	r	r	NOUN
ejpam-776	338	17	fλ	fλ	PROPN
ejpam-776	338	18	(	(	PUNCT
ejpam-776	338	19	f	f	PROPN
ejpam-776	338	20	)	)	PUNCT
ejpam-776	338	21	(	(	PUNCT
ejpam-776	338	22	λ)ψλ(x)|fλ(g)(aλ)|2dσ(λ	λ)ψλ(x)|fλ(g)(aλ)|2dσ(λ	NUM
ejpam-776	338	23	)	)	PUNCT
ejpam-776	338	24	.	.	PUNCT
ejpam-776	339	1	in	in	ADP
ejpam-776	339	2	particular	particular	ADJ
ejpam-776	339	3	,	,	PUNCT
ejpam-776	339	4	this	this	PRON
ejpam-776	339	5	implies	imply	VERB
ejpam-776	339	6	that	that	SCONJ
ejpam-776	339	7	1	1	NUM
ejpam-776	339	8	cg	cg	NOUN
ejpam-776	339	9	∫	∫	PROPN
ejpam-776	339	10	∞	∞	PROPN
ejpam-776	339	11	0	0	PROPN
ejpam-776	339	12	|i	|i	X
ejpam-776	339	13	(	(	PUNCT
ejpam-776	339	14	a	a	PRON
ejpam-776	339	15	,	,	PUNCT
ejpam-776	339	16	x)|	x)|	PROPN
ejpam-776	339	17	da	da	PROPN
ejpam-776	339	18	a2	a2	PROPN
ejpam-776	339	19	≤	≤	PROPN
ejpam-776	339	20	∫	∫	PROPN
ejpam-776	340	1	r	r	NOUN
ejpam-776	340	2	|fλ	|fλ	PROPN
ejpam-776	340	3	(	(	PUNCT
ejpam-776	340	4	f	f	NOUN
ejpam-776	340	5	)	)	PUNCT
ejpam-776	340	6	(	(	PUNCT
ejpam-776	340	7	λ)|	λ)|	PROPN
ejpam-776	340	8	�	�	PROPN
ejpam-776	340	9	1	1	NUM
ejpam-776	340	10	cg	cg	NOUN
ejpam-776	340	11	∫	∫	PROPN
ejpam-776	340	12	∞	∞	NOUN
ejpam-776	340	13	0	0	NUM
ejpam-776	341	1	|fλ(g)(aλ)|2	|fλ(g)(aλ)|2	PROPN
ejpam-776	341	2	da	da	PROPN
ejpam-776	341	3	a	a	DET
ejpam-776	341	4	�	�	PROPN
ejpam-776	341	5	dσ(λ	dσ(λ	PUNCT
ejpam-776	341	6	)	)	PUNCT
ejpam-776	341	7	=	=	SYM
ejpam-776	341	8	fλ	fλ	X
ejpam-776	341	9	(	(	PUNCT
ejpam-776	341	10	f	f	PROPN
ejpam-776	341	11	)	)	PUNCT
ejpam-776	341	12	1,σ	1,σ	PROPN
ejpam-776	341	13	<	<	X
ejpam-776	341	14	∞	∞	PROPN
ejpam-776	341	15	,	,	PUNCT
ejpam-776	341	16	that	that	ADV
ejpam-776	341	17	is	is	ADV
ejpam-776	341	18	,	,	PUNCT
ejpam-776	341	19	the	the	DET
ejpam-776	341	20	integral	integral	ADJ
ejpam-776	341	21	j	j	PROPN
ejpam-776	341	22	(	(	PUNCT
ejpam-776	341	23	x	x	X
ejpam-776	341	24	)	)	PUNCT
ejpam-776	341	25	is	be	AUX
ejpam-776	341	26	absolutely	absolutely	ADV
ejpam-776	341	27	convergent	convergent	ADJ
ejpam-776	341	28	.	.	PUNCT
ejpam-776	342	1	finally	finally	ADV
ejpam-776	342	2	,	,	PUNCT
ejpam-776	342	3	using	use	VERB
ejpam-776	342	4	fubini	fubini	NOUN
ejpam-776	342	5	’s	’s	PART
ejpam-776	342	6	theorem	theorem	NOUN
ejpam-776	342	7	we	we	PRON
ejpam-776	342	8	get	get	VERB
ejpam-776	342	9	j	j	PROPN
ejpam-776	342	10	(	(	PUNCT
ejpam-776	342	11	x	x	NOUN
ejpam-776	342	12	)	)	PUNCT
ejpam-776	342	13	=	=	SYM
ejpam-776	342	14	1	1	NUM
ejpam-776	342	15	cg	cg	NOUN
ejpam-776	342	16	∫	∫	PROPN
ejpam-776	342	17	∞	∞	PROPN
ejpam-776	342	18	0	0	NUM
ejpam-776	342	19	�	�	PROPN
ejpam-776	342	20	∫	∫	PROPN
ejpam-776	342	21	r	r	NOUN
ejpam-776	342	22	fλ	fλ	PROPN
ejpam-776	342	23	(	(	PUNCT
ejpam-776	342	24	f	f	PROPN
ejpam-776	342	25	)	)	PUNCT
ejpam-776	342	26	(	(	PUNCT
ejpam-776	342	27	λ)|fλ(g)(aλ)|2ψλ(x)dσ(λ	λ)|fλ(g)(aλ)|2ψλ(x)dσ(λ	X
ejpam-776	342	28	)	)	PUNCT
ejpam-776	342	29	�	�	PROPN
ejpam-776	342	30	da	da	PROPN
ejpam-776	342	31	a	a	PROPN
ejpam-776	342	32	=	=	X
ejpam-776	342	33	∫	∫	PROPN
ejpam-776	343	1	r	r	NOUN
ejpam-776	343	2	fλ	fλ	PROPN
ejpam-776	343	3	(	(	PUNCT
ejpam-776	343	4	f	f	PROPN
ejpam-776	343	5	)	)	PUNCT
ejpam-776	343	6	(	(	PUNCT
ejpam-776	343	7	λ	λ	NOUN
ejpam-776	343	8	)	)	PUNCT
ejpam-776	343	9	�	�	PROPN
ejpam-776	343	10	1	1	NUM
ejpam-776	343	11	cg	cg	NOUN
ejpam-776	343	12	∫	∫	PROPN
ejpam-776	343	13	∞	∞	NOUN
ejpam-776	343	14	0	0	NUM
ejpam-776	344	1	|fλ(g)(aλ)|2	|fλ(g)(aλ)|2	PROPN
ejpam-776	344	2	da	da	PROPN
ejpam-776	344	3	a	a	DET
ejpam-776	344	4	�	�	PROPN
ejpam-776	344	5	ψλ(x)dσ(λ	ψλ(x)dσ(λ	PROPN
ejpam-776	344	6	)	)	PUNCT
ejpam-776	345	1	=	=	SYM
ejpam-776	346	1	∫	∫	PROPN
ejpam-776	346	2	r	r	NOUN
ejpam-776	346	3	fλ	fλ	PROPN
ejpam-776	346	4	(	(	PUNCT
ejpam-776	346	5	f	f	PROPN
ejpam-776	346	6	)	)	PUNCT
ejpam-776	346	7	(	(	PUNCT
ejpam-776	346	8	λ)ψλ(x)dσ(λ	λ)ψλ(x)dσ(λ	X
ejpam-776	346	9	)	)	PUNCT
ejpam-776	346	10	,	,	PUNCT
ejpam-776	346	11	which	which	PRON
ejpam-776	346	12	ends	end	VERB
ejpam-776	346	13	the	the	DET
ejpam-776	346	14	proof	proof	NOUN
ejpam-776	346	15	in	in	ADP
ejpam-776	346	16	view	view	NOUN
ejpam-776	346	17	of	of	ADP
ejpam-776	346	18	theorem	theorem	NOUN
ejpam-776	346	19	1	1	NUM
ejpam-776	346	20	.	.	NOUN
ejpam-776	346	21	4	4	NUM
ejpam-776	346	22	.	.	X
ejpam-776	347	1	inversion	inversion	NOUN
ejpam-776	347	2	of	of	ADP
ejpam-776	347	3	the	the	DET
ejpam-776	347	4	intertwining	intertwine	VERB
ejpam-776	347	5	operators	operator	NOUN
ejpam-776	347	6	using	use	VERB
ejpam-776	347	7	generalized	generalized	ADJ
ejpam-776	347	8	wavelets	wavelet	NOUN
ejpam-776	347	9	in	in	ADP
ejpam-776	347	10	this	this	DET
ejpam-776	347	11	section	section	NOUN
ejpam-776	347	12	we	we	PRON
ejpam-776	347	13	suppose	suppose	VERB
ejpam-776	347	14	that	that	SCONJ
ejpam-776	347	15	the	the	DET
ejpam-776	347	16	function	function	NOUN
ejpam-776	347	17	|c(λ)|−2	|c(λ)|−2	NOUN
ejpam-776	347	18	is	be	AUX
ejpam-776	347	19	c∞	c∞	ADJ
ejpam-776	347	20	on	on	ADP
ejpam-776	347	21	]	]	PUNCT
ejpam-776	347	22	0,∞	0,∞	NOUN
ejpam-776	347	23	[	[	X
ejpam-776	347	24	,	,	PUNCT
ejpam-776	347	25	and	and	CCONJ
ejpam-776	347	26	for	for	ADP
ejpam-776	347	27	all	all	PRON
ejpam-776	347	28	n	n	PRON
ejpam-776	347	29	∈	∈	NOUN
ejpam-776	347	30	n	n	NOUN
ejpam-776	347	31	:	:	PUNCT
ejpam-776	347	32	(	(	PUNCT
ejpam-776	347	33	i	i	NOUN
ejpam-776	347	34	)	)	PUNCT
ejpam-776	347	35	dn	dn	PROPN
ejpam-776	347	36	/	/	SYM
ejpam-776	347	37	dλn|c(λ)|−2	dλn|c(λ)|−2	NOUN
ejpam-776	347	38	6=	6=	ADV
ejpam-776	347	39	0	0	NUM
ejpam-776	347	40	on	on	ADP
ejpam-776	347	41	]	]	PUNCT
ejpam-776	347	42	0,∞	0,∞	NOUN
ejpam-776	347	43	[	[	X
ejpam-776	347	44	;	;	PUNCT
ejpam-776	347	45	(	(	PUNCT
ejpam-776	347	46	ii	ii	NOUN
ejpam-776	347	47	)	)	PUNCT
ejpam-776	347	48	∃	∃	PROPN
ejpam-776	347	49	pn	pn	PROPN
ejpam-776	347	50	∈	∈	PROPN
ejpam-776	347	51	n	n	PROPN
ejpam-776	347	52	and	and	CCONJ
ejpam-776	347	53	kn	kn	PROPN
ejpam-776	347	54	>	>	X
ejpam-776	347	55	0	0	NUM
ejpam-776	347	56	such	such	ADJ
ejpam-776	347	57	that	that	DET
ejpam-776	347	58	dn	dn	PROPN
ejpam-776	347	59	/	/	SYM
ejpam-776	347	60	dλn|c(λ)|−2	dλn|c(λ)|−2	NOUN
ejpam-776	347	61	≤	≤	PROPN
ejpam-776	347	62	knλ	knλ	PROPN
ejpam-776	347	63	pn	pn	PROPN
ejpam-776	347	64	for	for	ADP
ejpam-776	347	65	λ	λ	PROPN
ejpam-776	347	66	≥	≥	NOUN
ejpam-776	347	67	1	1	NUM
ejpam-776	347	68	;	;	PUNCT
ejpam-776	347	69	(	(	PUNCT
ejpam-776	347	70	iii	iii	NOUN
ejpam-776	347	71	)	)	PUNCT
ejpam-776	347	72	dn	dn	ADJ
ejpam-776	347	73	/	/	SYM
ejpam-776	347	74	dλn|c(λ)|−2	dλn|c(λ)|−2	NOUN
ejpam-776	347	75	∼0	∼0	NOUN
ejpam-776	347	76	+	+	SYM
ejpam-776	347	77	anλ	anλ	NOUN
ejpam-776	347	78	qn	qn	NOUN
ejpam-776	347	79	,	,	PUNCT
ejpam-776	347	80	where	where	SCONJ
ejpam-776	347	81	an	an	DET
ejpam-776	347	82	∈	∈	PROPN
ejpam-776	347	83	r	r	NOUN
ejpam-776	347	84	and	and	CCONJ
ejpam-776	347	85	qn	qn	NOUN
ejpam-776	347	86	∈	∈	PROPN
ejpam-776	347	87	z.	z.	PROPN
ejpam-776	347	88	w.	w.	PROPN
ejpam-776	347	89	chabeh	chabeh	PROPN
ejpam-776	347	90	,	,	PUNCT
ejpam-776	347	91	m.	m.	NOUN
ejpam-776	347	92	mourou	mourou	PROPN
ejpam-776	347	93	/	/	SYM
ejpam-776	347	94	eur	eur	PROPN
ejpam-776	347	95	.	.	PUNCT
ejpam-776	348	1	j.	j.	PROPN
ejpam-776	348	2	pure	pure	PROPN
ejpam-776	348	3	appl	appl	PROPN
ejpam-776	348	4	.	.	PROPN
ejpam-776	348	5	math	math	PROPN
ejpam-776	348	6	,	,	PUNCT
ejpam-776	348	7	3	3	NUM
ejpam-776	348	8	(	(	PUNCT
ejpam-776	348	9	2010	2010	NUM
ejpam-776	348	10	)	)	PUNCT
ejpam-776	348	11	,	,	PUNCT
ejpam-776	348	12	958	958	NUM
ejpam-776	348	13	-	-	SYM
ejpam-776	348	14	979	979	NUM
ejpam-776	348	15	975	975	NUM
ejpam-776	348	16	remark	remark	NOUN
ejpam-776	348	17	9	9	NUM
ejpam-776	348	18	.	.	PUNCT
ejpam-776	349	1	these	these	DET
ejpam-776	349	2	conditions	condition	NOUN
ejpam-776	349	3	are	be	AUX
ejpam-776	349	4	satisfied	satisfied	ADJ
ejpam-776	349	5	in	in	ADP
ejpam-776	349	6	the	the	DET
ejpam-776	349	7	dunkl	dunkl	NOUN
ejpam-776	349	8	operator	operator	NOUN
ejpam-776	349	9	case	case	NOUN
ejpam-776	349	10	.	.	PUNCT
ejpam-776	350	1	proposition	proposition	NOUN
ejpam-776	350	2	8	8	NUM
ejpam-776	350	3	.	.	PUNCT
ejpam-776	351	1	the	the	DET
ejpam-776	351	2	operatork	operatork	NOUN
ejpam-776	351	3	(	(	PUNCT
ejpam-776	351	4	resp.m	resp.m	NOUN
ejpam-776	351	5	)	)	PUNCT
ejpam-776	351	6	defined	define	VERB
ejpam-776	351	7	by	by	ADP
ejpam-776	351	8	k	k	PROPN
ejpam-776	351	9	(	(	PUNCT
ejpam-776	351	10	f	f	X
ejpam-776	351	11	)	)	PUNCT
ejpam-776	352	1	=	=	SYM
ejpam-776	352	2	f−1	f−1	NUM
ejpam-776	352	3	u	u	PROPN
ejpam-776	352	4	�	�	PROPN
ejpam-776	352	5	2π	2π	PROPN
ejpam-776	352	6	|c(|λ|)|−2fu	|c(|λ|)|−2fu	VERB
ejpam-776	352	7	(	(	PUNCT
ejpam-776	352	8	f	f	PROPN
ejpam-776	352	9	)	)	PUNCT
ejpam-776	352	10	�	�	PROPN
ejpam-776	352	11	(	(	PUNCT
ejpam-776	352	12	32	32	NUM
ejpam-776	352	13	)	)	PUNCT
ejpam-776	352	14	�	�	PROPN
ejpam-776	352	15	resp.m	resp.m	PROPN
ejpam-776	352	16	(	(	PUNCT
ejpam-776	352	17	f	f	X
ejpam-776	352	18	)	)	PUNCT
ejpam-776	353	1	=	=	NOUN
ejpam-776	353	2	f−1	f−1	PROPN
ejpam-776	353	3	λ	λ	PROPN
ejpam-776	353	4	�	�	PROPN
ejpam-776	353	5	2π	2π	PROPN
ejpam-776	353	6	|c(|λ|)|−2fλ	|c(|λ|)|−2fλ	VERB
ejpam-776	353	7	(	(	PUNCT
ejpam-776	353	8	f	f	PROPN
ejpam-776	353	9	)	)	PUNCT
ejpam-776	353	10	�	�	PROPN
ejpam-776	353	11	�	�	PROPN
ejpam-776	353	12	(	(	PUNCT
ejpam-776	353	13	33	33	NUM
ejpam-776	353	14	)	)	PUNCT
ejpam-776	353	15	is	be	AUX
ejpam-776	353	16	a	a	DET
ejpam-776	353	17	topological	topological	ADJ
ejpam-776	353	18	automorphism	automorphism	NOUN
ejpam-776	353	19	of	of	ADP
ejpam-776	353	20	w	w	PROPN
ejpam-776	353	21	(	(	PUNCT
ejpam-776	353	22	r	r	NOUN
ejpam-776	353	23	)	)	PUNCT
ejpam-776	353	24	(	(	PUNCT
ejpam-776	353	25	resp	resp	NOUN
ejpam-776	353	26	.	.	PUNCT
ejpam-776	354	1	b(r	b(r	NOUN
ejpam-776	354	2	)	)	PUNCT
ejpam-776	354	3	)	)	PUNCT
ejpam-776	354	4	.	.	PUNCT
ejpam-776	355	1	proof	proof	NOUN
ejpam-776	355	2	.	.	PUNCT
ejpam-776	356	1	clearly	clearly	ADV
ejpam-776	356	2	,	,	PUNCT
ejpam-776	356	3	the	the	DET
ejpam-776	356	4	mapping	mapping	NOUN
ejpam-776	356	5	f	f	PROPN
ejpam-776	356	6	7→	7→	NUM
ejpam-776	356	7	2π	2π	PROPN
ejpam-776	356	8	|c(λ)|−2	|c(λ)|−2	PROPN
ejpam-776	356	9	f	f	PROPN
ejpam-776	356	10	is	be	AUX
ejpam-776	356	11	a	a	DET
ejpam-776	356	12	topological	topological	ADJ
ejpam-776	356	13	automorphism	automorphism	NOUN
ejpam-776	356	14	of	of	ADP
ejpam-776	356	15	h	h	NOUN
ejpam-776	356	16	(	(	PUNCT
ejpam-776	356	17	r	r	NOUN
ejpam-776	356	18	)	)	PUNCT
ejpam-776	356	19	,	,	PUNCT
ejpam-776	356	20	and	and	CCONJ
ejpam-776	356	21	its	its	PRON
ejpam-776	356	22	inverse	inverse	NOUN
ejpam-776	356	23	is	be	AUX
ejpam-776	356	24	given	give	VERB
ejpam-776	356	25	by	by	ADP
ejpam-776	356	26	f	f	PROPN
ejpam-776	356	27	7−→	7−→	PROPN
ejpam-776	356	28	1	1	NUM
ejpam-776	356	29	2π	2π	PROPN
ejpam-776	356	30	|c(|λ|)|2	|c(|λ|)|2	VERB
ejpam-776	356	31	f	f	NOUN
ejpam-776	356	32	.	.	PUNCT
ejpam-776	357	1	we	we	PRON
ejpam-776	357	2	deduce	deduce	VERB
ejpam-776	357	3	the	the	DET
ejpam-776	357	4	result	result	NOUN
ejpam-776	357	5	from	from	ADP
ejpam-776	357	6	theorem	theorem	ADJ
ejpam-776	357	7	2	2	NUM
ejpam-776	357	8	and	and	CCONJ
ejpam-776	357	9	the	the	DET
ejpam-776	357	10	fact	fact	NOUN
ejpam-776	357	11	that	that	SCONJ
ejpam-776	357	12	the	the	DET
ejpam-776	357	13	usual	usual	ADJ
ejpam-776	357	14	fourier	fourier	NOUN
ejpam-776	357	15	transform	transform	NOUN
ejpam-776	357	16	fu	fu	NOUN
ejpam-776	357	17	is	be	AUX
ejpam-776	357	18	a	a	DET
ejpam-776	357	19	topological	topological	ADJ
ejpam-776	357	20	isomorphism	isomorphism	NOUN
ejpam-776	357	21	fromw	fromw	PROPN
ejpam-776	357	22	(	(	PUNCT
ejpam-776	357	23	r	r	NOUN
ejpam-776	357	24	)	)	PUNCT
ejpam-776	357	25	ontoh	ontoh	NOUN
ejpam-776	357	26	(	(	PUNCT
ejpam-776	357	27	r	r	NOUN
ejpam-776	357	28	)	)	PUNCT
ejpam-776	357	29	.	.	PUNCT
ejpam-776	358	1	proposition	proposition	NOUN
ejpam-776	358	2	9	9	NUM
ejpam-776	358	3	.	.	PUNCT
ejpam-776	358	4	for	for	ADP
ejpam-776	358	5	f	f	PROPN
ejpam-776	358	6	inb(r	inb(r	PROPN
ejpam-776	358	7	)	)	PUNCT
ejpam-776	358	8	,	,	PUNCT
ejpam-776	358	9	we	we	PRON
ejpam-776	358	10	have	have	VERB
ejpam-776	358	11	m	m	PROPN
ejpam-776	358	12	(	(	PUNCT
ejpam-776	358	13	f	f	PROPN
ejpam-776	358	14	)	)	PUNCT
ejpam-776	359	1	=	=	SYM
ejpam-776	359	2	t	t	PROPN
ejpam-776	359	3	v	v	NUM
ejpam-776	359	4	−1	−1	NOUN
ejpam-776	359	5	◦	◦	NOUN
ejpam-776	359	6	k	k	NOUN
ejpam-776	359	7	◦	◦	NOUN
ejpam-776	359	8	t	t	X
ejpam-776	359	9	v	v	X
ejpam-776	359	10	(	(	PUNCT
ejpam-776	359	11	f	f	PROPN
ejpam-776	359	12	)	)	PUNCT
ejpam-776	359	13	.	.	PUNCT
ejpam-776	360	1	(	(	PUNCT
ejpam-776	360	2	34	34	NUM
ejpam-776	360	3	)	)	PUNCT
ejpam-776	360	4	proof	proof	NOUN
ejpam-776	360	5	.	.	PUNCT
ejpam-776	361	1	by	by	ADP
ejpam-776	361	2	(	(	PUNCT
ejpam-776	361	3	16	16	NUM
ejpam-776	361	4	)	)	PUNCT
ejpam-776	361	5	,	,	PUNCT
ejpam-776	361	6	(	(	PUNCT
ejpam-776	361	7	32	32	NUM
ejpam-776	361	8	)	)	PUNCT
ejpam-776	361	9	and	and	CCONJ
ejpam-776	361	10	(	(	PUNCT
ejpam-776	361	11	33	33	NUM
ejpam-776	361	12	)	)	PUNCT
ejpam-776	361	13	,	,	PUNCT
ejpam-776	361	14	m	m	VERB
ejpam-776	361	15	(	(	PUNCT
ejpam-776	361	16	f	f	X
ejpam-776	361	17	)	)	PUNCT
ejpam-776	362	1	=	=	SYM
ejpam-776	362	2	f−1	f−1	PROPN
ejpam-776	362	3	λ	λ	PROPN
ejpam-776	362	4	�	�	PROPN
ejpam-776	362	5	2π	2π	PROPN
ejpam-776	362	6	|c(|λ|)|−2fλ	|c(|λ|)|−2fλ	VERB
ejpam-776	362	7	(	(	PUNCT
ejpam-776	362	8	f	f	PROPN
ejpam-776	362	9	)	)	PUNCT
ejpam-776	362	10	�	�	PROPN
ejpam-776	362	11	=	=	SYM
ejpam-776	362	12	t	t	PROPN
ejpam-776	362	13	v	v	NUM
ejpam-776	362	14	−1	−1	NOUN
ejpam-776	362	15	◦	◦	NOUN
ejpam-776	362	16	f−1	f−1	PROPN
ejpam-776	362	17	u	u	PROPN
ejpam-776	362	18	�	�	PROPN
ejpam-776	362	19	2π	2π	NOUN
ejpam-776	362	20	|c(|λ|)|−2fu	|c(|λ|)|−2fu	VERB
ejpam-776	362	21	◦	◦	NOUN
ejpam-776	362	22	t	t	NOUN
ejpam-776	362	23	v	v	NOUN
ejpam-776	362	24	(	(	PUNCT
ejpam-776	362	25	f	f	PROPN
ejpam-776	362	26	)	)	PUNCT
ejpam-776	362	27	�	�	PROPN
ejpam-776	362	28	=	=	SYM
ejpam-776	363	1	t	t	PROPN
ejpam-776	363	2	v	v	NUM
ejpam-776	363	3	−1	−1	NOUN
ejpam-776	363	4	◦	◦	NOUN
ejpam-776	363	5	k	k	NOUN
ejpam-776	363	6	◦	◦	NOUN
ejpam-776	363	7	t	t	X
ejpam-776	363	8	v	v	X
ejpam-776	363	9	(	(	PUNCT
ejpam-776	363	10	f	f	PROPN
ejpam-776	363	11	)	)	PUNCT
ejpam-776	363	12	.	.	PUNCT
ejpam-776	364	1	proposition	proposition	NOUN
ejpam-776	364	2	10	10	NUM
ejpam-776	364	3	.	.	PUNCT
ejpam-776	365	1	(	(	PUNCT
ejpam-776	365	2	i	i	NOUN
ejpam-776	365	3	)	)	PUNCT
ejpam-776	365	4	for	for	ADP
ejpam-776	365	5	all	all	DET
ejpam-776	365	6	f	f	PROPN
ejpam-776	365	7	in	in	ADP
ejpam-776	365	8	w	w	PROPN
ejpam-776	365	9	(	(	PUNCT
ejpam-776	365	10	r	r	NOUN
ejpam-776	365	11	)	)	PUNCT
ejpam-776	365	12	and	and	CCONJ
ejpam-776	365	13	g	g	NOUN
ejpam-776	365	14	in	in	ADP
ejpam-776	365	15	s	s	PROPN
ejpam-776	365	16	(	(	PUNCT
ejpam-776	365	17	r	r	NOUN
ejpam-776	365	18	)	)	PUNCT
ejpam-776	365	19	,	,	PUNCT
ejpam-776	365	20	we	we	PRON
ejpam-776	365	21	have	have	VERB
ejpam-776	365	22	k	k	PROPN
ejpam-776	365	23	(	(	PUNCT
ejpam-776	365	24	f	f	PROPN
ejpam-776	365	25	∗	∗	VERB
ejpam-776	365	26	g	g	NOUN
ejpam-776	365	27	)	)	PUNCT
ejpam-776	366	1	=	=	NOUN
ejpam-776	366	2	k	k	X
ejpam-776	366	3	(	(	PUNCT
ejpam-776	366	4	f	f	PROPN
ejpam-776	366	5	)	)	PUNCT
ejpam-776	366	6	∗	∗	NOUN
ejpam-776	366	7	g	g	NOUN
ejpam-776	366	8	.	.	PUNCT
ejpam-776	367	1	(	(	PUNCT
ejpam-776	367	2	ii	ii	NOUN
ejpam-776	367	3	)	)	PUNCT
ejpam-776	367	4	for	for	ADP
ejpam-776	367	5	all	all	DET
ejpam-776	367	6	f	f	PROPN
ejpam-776	367	7	inb(r	inb(r	PROPN
ejpam-776	367	8	)	)	PUNCT
ejpam-776	367	9	and	and	CCONJ
ejpam-776	367	10	g	g	NOUN
ejpam-776	367	11	in	in	ADP
ejpam-776	367	12	s	s	PROPN
ejpam-776	367	13	(	(	PUNCT
ejpam-776	367	14	r	r	NOUN
ejpam-776	367	15	)	)	PUNCT
ejpam-776	367	16	,	,	PUNCT
ejpam-776	367	17	we	we	PRON
ejpam-776	367	18	have	have	VERB
ejpam-776	367	19	m	m	PROPN
ejpam-776	367	20	(	(	PUNCT
ejpam-776	367	21	f	f	PROPN
ejpam-776	367	22	#	#	SYM
ejpam-776	367	23	g	g	NOUN
ejpam-776	367	24	)	)	PUNCT
ejpam-776	368	1	=	=	VERB
ejpam-776	368	2	m	m	PROPN
ejpam-776	368	3	(	(	PUNCT
ejpam-776	368	4	f	f	NOUN
ejpam-776	368	5	)	)	PUNCT
ejpam-776	368	6	#	#	SYM
ejpam-776	368	7	g	g	NOUN
ejpam-776	368	8	.	.	PUNCT
ejpam-776	369	1	proof	proof	NOUN
ejpam-776	369	2	.	.	PUNCT
ejpam-776	370	1	we	we	PRON
ejpam-776	370	2	have	have	VERB
ejpam-776	370	3	k	k	PROPN
ejpam-776	370	4	(	(	PUNCT
ejpam-776	370	5	f	f	PROPN
ejpam-776	370	6	∗	∗	VERB
ejpam-776	370	7	g	g	NOUN
ejpam-776	370	8	)	)	PUNCT
ejpam-776	371	1	=	=	SYM
ejpam-776	371	2	f−1	f−1	PROPN
ejpam-776	371	3	u	u	PROPN
ejpam-776	371	4	�	�	PROPN
ejpam-776	371	5	2π	2π	PROPN
ejpam-776	371	6	|c(|λ|)|−2fu	|c(|λ|)|−2fu	VERB
ejpam-776	371	7	(	(	PUNCT
ejpam-776	371	8	f	f	PROPN
ejpam-776	371	9	∗	∗	PUNCT
ejpam-776	371	10	g	g	NOUN
ejpam-776	371	11	)	)	PUNCT
ejpam-776	371	12	�	�	PROPN
ejpam-776	371	13	=	=	SYM
ejpam-776	371	14	f−1	f−1	PROPN
ejpam-776	371	15	u	u	PROPN
ejpam-776	371	16	�	�	PROPN
ejpam-776	371	17	2π	2π	PROPN
ejpam-776	371	18	|c(|λ|)|−2fu	|c(|λ|)|−2fu	VERB
ejpam-776	371	19	(	(	PUNCT
ejpam-776	371	20	f	f	NOUN
ejpam-776	371	21	)	)	PUNCT
ejpam-776	371	22	fu(g	fu(g	NUM
ejpam-776	371	23	)	)	PUNCT
ejpam-776	371	24	�	�	PROPN
ejpam-776	372	1	=	=	SYM
ejpam-776	372	2	¦	¦	PROPN
ejpam-776	372	3	f−1	f−1	PROPN
ejpam-776	372	4	u	u	PROPN
ejpam-776	372	5	�	�	PROPN
ejpam-776	372	6	2π	2π	PROPN
ejpam-776	372	7	|c(|λ|)|−2fu	|c(|λ|)|−2fu	VERB
ejpam-776	372	8	(	(	PUNCT
ejpam-776	372	9	f	f	X
ejpam-776	372	10	)	)	PUNCT
ejpam-776	372	11	�	�	PROPN
ejpam-776	373	1	©	©	NOUN
ejpam-776	373	2	∗	∗	NOUN
ejpam-776	373	3	g	g	PROPN
ejpam-776	374	1	=	=	SYM
ejpam-776	374	2	k	k	PROPN
ejpam-776	374	3	(	(	PUNCT
ejpam-776	374	4	f	f	PROPN
ejpam-776	374	5	)	)	PUNCT
ejpam-776	374	6	∗	∗	NOUN
ejpam-776	374	7	g	g	NOUN
ejpam-776	374	8	and	and	CCONJ
ejpam-776	374	9	m	m	PROPN
ejpam-776	374	10	(	(	PUNCT
ejpam-776	374	11	f	f	PROPN
ejpam-776	374	12	#	#	SYM
ejpam-776	374	13	g	g	NOUN
ejpam-776	374	14	)	)	PUNCT
ejpam-776	374	15	=	=	SYM
ejpam-776	374	16	f−1	f−1	PROPN
ejpam-776	374	17	λ	λ	PROPN
ejpam-776	374	18	�	�	PROPN
ejpam-776	374	19	2π	2π	PROPN
ejpam-776	374	20	|c(|λ|)|−2fλ	|c(|λ|)|−2fλ	VERB
ejpam-776	374	21	(	(	PUNCT
ejpam-776	374	22	f	f	PROPN
ejpam-776	374	23	#	#	SYM
ejpam-776	374	24	g	g	NOUN
ejpam-776	374	25	)	)	PUNCT
ejpam-776	374	26	�	�	PROPN
ejpam-776	374	27	w.	w.	PROPN
ejpam-776	374	28	chabeh	chabeh	PROPN
ejpam-776	374	29	,	,	PUNCT
ejpam-776	374	30	m.	m.	NOUN
ejpam-776	374	31	mourou	mourou	PROPN
ejpam-776	374	32	/	/	SYM
ejpam-776	374	33	eur	eur	PROPN
ejpam-776	374	34	.	.	PUNCT
ejpam-776	375	1	j.	j.	PROPN
ejpam-776	375	2	pure	pure	PROPN
ejpam-776	375	3	appl	appl	PROPN
ejpam-776	375	4	.	.	PROPN
ejpam-776	375	5	math	math	PROPN
ejpam-776	375	6	,	,	PUNCT
ejpam-776	375	7	3	3	NUM
ejpam-776	375	8	(	(	PUNCT
ejpam-776	375	9	2010	2010	NUM
ejpam-776	375	10	)	)	PUNCT
ejpam-776	375	11	,	,	PUNCT
ejpam-776	375	12	958	958	NUM
ejpam-776	375	13	-	-	SYM
ejpam-776	375	14	979	979	NUM
ejpam-776	375	15	976	976	NUM
ejpam-776	375	16	=	=	SYM
ejpam-776	375	17	f−1	f−1	PROPN
ejpam-776	375	18	λ	λ	PROPN
ejpam-776	375	19	�	�	PROPN
ejpam-776	375	20	2π	2π	PROPN
ejpam-776	375	21	|c(|λ|)|−2fλ	|c(|λ|)|−2fλ	VERB
ejpam-776	375	22	(	(	PUNCT
ejpam-776	375	23	f	f	PROPN
ejpam-776	375	24	)	)	PUNCT
ejpam-776	375	25	fλ(g	fλ(g	X
ejpam-776	375	26	)	)	PUNCT
ejpam-776	375	27	�	�	PROPN
ejpam-776	375	28	=	=	SYM
ejpam-776	376	1	¦	¦	PROPN
ejpam-776	376	2	f−1	f−1	PROPN
ejpam-776	376	3	λ	λ	PROPN
ejpam-776	376	4	�	�	PROPN
ejpam-776	376	5	2π	2π	PROPN
ejpam-776	376	6	|c(|λ|)|−2fλ	|c(|λ|)|−2fλ	VERB
ejpam-776	376	7	(	(	PUNCT
ejpam-776	376	8	f	f	PROPN
ejpam-776	376	9	)	)	PUNCT
ejpam-776	376	10	�	�	PROPN
ejpam-776	377	1	©	©	NOUN
ejpam-776	377	2	#	#	SYM
ejpam-776	377	3	g	g	NOUN
ejpam-776	377	4	=	=	NOUN
ejpam-776	377	5	m	m	PROPN
ejpam-776	377	6	(	(	PUNCT
ejpam-776	377	7	f	f	NOUN
ejpam-776	377	8	)	)	PUNCT
ejpam-776	377	9	#	#	SYM
ejpam-776	377	10	g	g	NOUN
ejpam-776	377	11	,	,	PUNCT
ejpam-776	377	12	which	which	PRON
ejpam-776	377	13	ends	end	VERB
ejpam-776	377	14	the	the	DET
ejpam-776	377	15	proof	proof	NOUN
ejpam-776	377	16	.	.	PUNCT
ejpam-776	378	1	theorem	theorem	VERB
ejpam-776	378	2	6	6	NUM
ejpam-776	378	3	.	.	NOUN
ejpam-776	378	4	1	1	NUM
ejpam-776	378	5	.	.	X
ejpam-776	379	1	the	the	DET
ejpam-776	379	2	intertwining	intertwine	VERB
ejpam-776	379	3	operator	operator	NOUN
ejpam-776	379	4	v	v	NOUN
ejpam-776	379	5	is	be	AUX
ejpam-776	379	6	a	a	DET
ejpam-776	379	7	topological	topological	ADJ
ejpam-776	379	8	isomorphism	isomorphism	NOUN
ejpam-776	379	9	from	from	ADP
ejpam-776	379	10	w	w	PROPN
ejpam-776	379	11	(	(	PUNCT
ejpam-776	379	12	r	r	NOUN
ejpam-776	379	13	)	)	PUNCT
ejpam-776	379	14	onto	onto	ADP
ejpam-776	379	15	b(r	b(r	NOUN
ejpam-776	379	16	)	)	PUNCT
ejpam-776	379	17	.	.	PUNCT
ejpam-776	380	1	2	2	X
ejpam-776	380	2	.	.	X
ejpam-776	380	3	we	we	PRON
ejpam-776	380	4	have	have	VERB
ejpam-776	380	5	the	the	DET
ejpam-776	380	6	following	follow	VERB
ejpam-776	380	7	inverse	inverse	NOUN
ejpam-776	380	8	formulas	formula	NOUN
ejpam-776	380	9	for	for	ADP
ejpam-776	380	10	v	v	NOUN
ejpam-776	380	11	and	and	CCONJ
ejpam-776	380	12	t	t	NOUN
ejpam-776	380	13	v	v	NOUN
ejpam-776	380	14	:	:	PUNCT
ejpam-776	380	15	(	(	PUNCT
ejpam-776	380	16	a	a	X
ejpam-776	380	17	)	)	PUNCT
ejpam-776	380	18	for	for	ADP
ejpam-776	380	19	f	f	PROPN
ejpam-776	380	20	∈b(r	∈b(r	PROPN
ejpam-776	380	21	)	)	PUNCT
ejpam-776	380	22	,	,	PUNCT
ejpam-776	380	23	f	f	PROPN
ejpam-776	380	24	=	=	SYM
ejpam-776	380	25	v	v	PROPN
ejpam-776	381	1	k	k	PROPN
ejpam-776	381	2	t	t	PROPN
ejpam-776	381	3	v	v	PROPN
ejpam-776	381	4	(	(	PUNCT
ejpam-776	381	5	f	f	PROPN
ejpam-776	381	6	)	)	PUNCT
ejpam-776	381	7	;	;	PUNCT
ejpam-776	381	8	(	(	PUNCT
ejpam-776	381	9	35	35	NUM
ejpam-776	381	10	)	)	PUNCT
ejpam-776	381	11	f	f	NOUN
ejpam-776	382	1	=	=	NOUN
ejpam-776	382	2	m	m	PROPN
ejpam-776	382	3	v	v	ADP
ejpam-776	382	4	t	t	X
ejpam-776	382	5	v	v	NOUN
ejpam-776	382	6	(	(	PUNCT
ejpam-776	382	7	f	f	PROPN
ejpam-776	382	8	)	)	PUNCT
ejpam-776	382	9	.	.	PUNCT
ejpam-776	383	1	(	(	PUNCT
ejpam-776	383	2	36	36	NUM
ejpam-776	383	3	)	)	PUNCT
ejpam-776	383	4	(	(	PUNCT
ejpam-776	383	5	b	b	NOUN
ejpam-776	383	6	)	)	PUNCT
ejpam-776	383	7	for	for	ADP
ejpam-776	383	8	f	f	PROPN
ejpam-776	383	9	∈w	∈w	PROPN
ejpam-776	383	10	(	(	PUNCT
ejpam-776	383	11	r	r	NOUN
ejpam-776	383	12	)	)	PUNCT
ejpam-776	383	13	,	,	PUNCT
ejpam-776	383	14	f	f	PROPN
ejpam-776	383	15	=	=	PROPN
ejpam-776	383	16	k	k	PROPN
ejpam-776	383	17	t	t	PROPN
ejpam-776	383	18	v	v	X
ejpam-776	383	19	v	v	NOUN
ejpam-776	383	20	(	(	PUNCT
ejpam-776	383	21	f	f	PROPN
ejpam-776	383	22	)	)	PUNCT
ejpam-776	383	23	;	;	PUNCT
ejpam-776	383	24	(	(	PUNCT
ejpam-776	383	25	37	37	NUM
ejpam-776	383	26	)	)	PUNCT
ejpam-776	383	27	f	f	NOUN
ejpam-776	384	1	=	=	SYM
ejpam-776	384	2	t	t	PROPN
ejpam-776	384	3	vm	vm	PROPN
ejpam-776	384	4	v	v	PROPN
ejpam-776	384	5	(	(	PUNCT
ejpam-776	384	6	f	f	PROPN
ejpam-776	384	7	)	)	PUNCT
ejpam-776	384	8	.	.	PUNCT
ejpam-776	385	1	(	(	PUNCT
ejpam-776	385	2	38	38	NUM
ejpam-776	385	3	)	)	PUNCT
ejpam-776	385	4	proof	proof	NOUN
ejpam-776	385	5	.	.	PUNCT
ejpam-776	386	1	let	let	VERB
ejpam-776	386	2	f	f	PROPN
ejpam-776	386	3	∈b(r	∈b(r	PROPN
ejpam-776	386	4	)	)	PUNCT
ejpam-776	386	5	.	.	PUNCT
ejpam-776	387	1	from	from	ADP
ejpam-776	387	2	(	(	PUNCT
ejpam-776	387	3	12	12	NUM
ejpam-776	387	4	)	)	PUNCT
ejpam-776	387	5	,	,	PUNCT
ejpam-776	387	6	(	(	PUNCT
ejpam-776	387	7	16	16	NUM
ejpam-776	387	8	)	)	PUNCT
ejpam-776	387	9	and	and	CCONJ
ejpam-776	387	10	theorem	theorem	VERB
ejpam-776	387	11	1	1	NUM
ejpam-776	387	12	we	we	PRON
ejpam-776	387	13	have	have	VERB
ejpam-776	387	14	for	for	ADP
ejpam-776	387	15	all	all	DET
ejpam-776	387	16	x	x	SYM
ejpam-776	387	17	∈	∈	PROPN
ejpam-776	387	18	r	r	NOUN
ejpam-776	387	19	,	,	PUNCT
ejpam-776	387	20	f	f	PROPN
ejpam-776	387	21	(	(	PUNCT
ejpam-776	387	22	x	x	X
ejpam-776	387	23	)	)	PUNCT
ejpam-776	387	24	=	=	SYM
ejpam-776	387	25	∫	∫	PROPN
ejpam-776	387	26	r	r	NOUN
ejpam-776	387	27	fλ	fλ	PROPN
ejpam-776	387	28	(	(	PUNCT
ejpam-776	387	29	f	f	PROPN
ejpam-776	387	30	)	)	PUNCT
ejpam-776	387	31	(	(	PUNCT
ejpam-776	387	32	λ)ψλ(x	λ)ψλ(x	NOUN
ejpam-776	387	33	)	)	PUNCT
ejpam-776	387	34	dλ	dλ	NOUN
ejpam-776	387	35	|c(|λ|)|2	|c(|λ|)|2	NOUN
ejpam-776	387	36	=	=	SYM
ejpam-776	387	37	v	v	ADP
ejpam-776	387	38	�	�	PROPN
ejpam-776	387	39	∫	∫	PROPN
ejpam-776	387	40	r	r	NOUN
ejpam-776	387	41	fλ	fλ	PROPN
ejpam-776	387	42	(	(	PUNCT
ejpam-776	387	43	f	f	PROPN
ejpam-776	387	44	)	)	PUNCT
ejpam-776	387	45	(	(	PUNCT
ejpam-776	387	46	λ	λ	NOUN
ejpam-776	387	47	)	)	PUNCT
ejpam-776	387	48	eiλ	eiλ	NOUN
ejpam-776	387	49	·	·	PUNCT
ejpam-776	387	50	dλ	dλ	PROPN
ejpam-776	387	51	|c(|λ|)|2	|c(|λ|)|2	PROPN
ejpam-776	387	52	�	�	PROPN
ejpam-776	387	53	(	(	PUNCT
ejpam-776	387	54	x	x	NOUN
ejpam-776	387	55	)	)	PUNCT
ejpam-776	387	56	=	=	SYM
ejpam-776	387	57	v	v	NUM
ejpam-776	387	58	�	�	PROPN
ejpam-776	387	59	1	1	NUM
ejpam-776	387	60	2π	2π	PROPN
ejpam-776	387	61	∫	∫	NOUN
ejpam-776	387	62	r	r	PROPN
ejpam-776	387	63	�	�	PROPN
ejpam-776	387	64	2π	2π	NOUN
ejpam-776	387	65	|c(|λ|)|−2fu	|c(|λ|)|−2fu	VERB
ejpam-776	387	66	◦	◦	NOUN
ejpam-776	387	67	t	t	NOUN
ejpam-776	387	68	v	v	NOUN
ejpam-776	387	69	(	(	PUNCT
ejpam-776	387	70	f	f	PROPN
ejpam-776	387	71	)	)	PUNCT
ejpam-776	387	72	�	�	PROPN
ejpam-776	387	73	eiλ·dλ	eiλ·dλ	PROPN
ejpam-776	387	74	�	�	PROPN
ejpam-776	387	75	(	(	PUNCT
ejpam-776	387	76	x	x	NOUN
ejpam-776	387	77	)	)	PUNCT
ejpam-776	387	78	=	=	SYM
ejpam-776	387	79	vk	vk	ADP
ejpam-776	387	80	t	t	PROPN
ejpam-776	387	81	v	v	PROPN
ejpam-776	387	82	(	(	PUNCT
ejpam-776	387	83	f	f	PROPN
ejpam-776	387	84	)	)	PUNCT
ejpam-776	387	85	(	(	PUNCT
ejpam-776	387	86	x	x	NOUN
ejpam-776	387	87	)	)	PUNCT
ejpam-776	387	88	.	.	PUNCT
ejpam-776	388	1	this	this	PRON
ejpam-776	388	2	when	when	SCONJ
ejpam-776	388	3	combined	combine	VERB
ejpam-776	388	4	with	with	ADP
ejpam-776	388	5	(	(	PUNCT
ejpam-776	388	6	34	34	NUM
ejpam-776	388	7	)	)	PUNCT
ejpam-776	388	8	yields	yield	NOUN
ejpam-776	388	9	formula	formula	NOUN
ejpam-776	388	10	(	(	PUNCT
ejpam-776	388	11	36	36	NUM
ejpam-776	388	12	)	)	PUNCT
ejpam-776	388	13	.	.	PUNCT
ejpam-776	389	1	by	by	ADP
ejpam-776	389	2	replacing	replace	VERB
ejpam-776	389	3	f	f	PROPN
ejpam-776	389	4	respectively	respectively	ADV
ejpam-776	389	5	by	by	ADP
ejpam-776	389	6	v	v	NUM
ejpam-776	389	7	f	f	NOUN
ejpam-776	389	8	and	and	CCONJ
ejpam-776	389	9	t	t	PROPN
ejpam-776	389	10	v−1	v−1	PROPN
ejpam-776	389	11	f	f	PROPN
ejpam-776	389	12	into	into	ADP
ejpam-776	389	13	formulas	formula	NOUN
ejpam-776	389	14	(	(	PUNCT
ejpam-776	389	15	35	35	NUM
ejpam-776	389	16	)	)	PUNCT
ejpam-776	389	17	and	and	CCONJ
ejpam-776	389	18	(	(	PUNCT
ejpam-776	389	19	36	36	NUM
ejpam-776	389	20	)	)	PUNCT
ejpam-776	389	21	,	,	PUNCT
ejpam-776	389	22	we	we	PRON
ejpam-776	389	23	regain	regain	VERB
ejpam-776	389	24	identities	identity	NOUN
ejpam-776	389	25	(	(	PUNCT
ejpam-776	389	26	37	37	NUM
ejpam-776	389	27	)	)	PUNCT
ejpam-776	389	28	and	and	CCONJ
ejpam-776	389	29	(	(	PUNCT
ejpam-776	389	30	38	38	NUM
ejpam-776	389	31	)	)	PUNCT
ejpam-776	389	32	.	.	PUNCT
ejpam-776	390	1	from	from	ADP
ejpam-776	390	2	(	(	PUNCT
ejpam-776	390	3	35	35	NUM
ejpam-776	390	4	)	)	PUNCT
ejpam-776	390	5	,	,	PUNCT
ejpam-776	390	6	proposition	proposition	NOUN
ejpam-776	390	7	8	8	NUM
ejpam-776	390	8	and	and	CCONJ
ejpam-776	390	9	theorem	theorem	VERB
ejpam-776	390	10	3	3	NUM
ejpam-776	390	11	,	,	PUNCT
ejpam-776	390	12	we	we	PRON
ejpam-776	390	13	deduce	deduce	VERB
ejpam-776	390	14	that	that	PRON
ejpam-776	390	15	v	v	NOUN
ejpam-776	390	16	is	be	AUX
ejpam-776	390	17	a	a	DET
ejpam-776	390	18	topological	topological	ADJ
ejpam-776	390	19	isomorphism	isomorphism	NOUN
ejpam-776	390	20	from	from	ADP
ejpam-776	390	21	w	w	PROPN
ejpam-776	390	22	(	(	PUNCT
ejpam-776	390	23	r	r	NOUN
ejpam-776	390	24	)	)	PUNCT
ejpam-776	390	25	onto	onto	ADP
ejpam-776	390	26	b(r	b(r	NOUN
ejpam-776	390	27	)	)	PUNCT
ejpam-776	390	28	.	.	PUNCT
ejpam-776	391	1	in	in	ADP
ejpam-776	391	2	order	order	NOUN
ejpam-776	391	3	to	to	PART
ejpam-776	391	4	invert	invert	VERB
ejpam-776	391	5	the	the	DET
ejpam-776	391	6	intertwining	intertwine	VERB
ejpam-776	391	7	operators	operator	NOUN
ejpam-776	391	8	v	v	ADP
ejpam-776	391	9	and	and	CCONJ
ejpam-776	391	10	t	t	PROPN
ejpam-776	391	11	v	v	NOUN
ejpam-776	391	12	we	we	PRON
ejpam-776	391	13	shall	shall	AUX
ejpam-776	391	14	need	need	VERB
ejpam-776	391	15	some	some	DET
ejpam-776	391	16	technical	technical	ADJ
ejpam-776	391	17	lemmas	lemma	NOUN
ejpam-776	391	18	.	.	PUNCT
ejpam-776	392	1	lemma	lemma	PROPN
ejpam-776	392	2	6	6	NUM
ejpam-776	392	3	.	.	PUNCT
ejpam-776	393	1	for	for	ADP
ejpam-776	393	2	all	all	DET
ejpam-776	393	3	f	f	PROPN
ejpam-776	393	4	in	in	ADP
ejpam-776	393	5	w	w	PROPN
ejpam-776	393	6	(	(	PUNCT
ejpam-776	393	7	r	r	NOUN
ejpam-776	393	8	)	)	PUNCT
ejpam-776	393	9	and	and	CCONJ
ejpam-776	393	10	g	g	NOUN
ejpam-776	393	11	in	in	ADP
ejpam-776	393	12	s	s	PROPN
ejpam-776	393	13	(	(	PUNCT
ejpam-776	393	14	r	r	NOUN
ejpam-776	393	15	)	)	PUNCT
ejpam-776	393	16	,	,	PUNCT
ejpam-776	393	17	we	we	PRON
ejpam-776	393	18	have	have	VERB
ejpam-776	393	19	v	v	NUM
ejpam-776	393	20	(	(	PUNCT
ejpam-776	393	21	f	f	PROPN
ejpam-776	393	22	∗	∗	NOUN
ejpam-776	393	23	g	g	NOUN
ejpam-776	393	24	)	)	PUNCT
ejpam-776	394	1	=	=	SYM
ejpam-776	394	2	v	v	X
ejpam-776	394	3	(	(	PUNCT
ejpam-776	394	4	f	f	NOUN
ejpam-776	394	5	)	)	PUNCT
ejpam-776	394	6	#	#	NOUN
ejpam-776	394	7	t	t	NOUN
ejpam-776	394	8	v	v	NOUN
ejpam-776	394	9	−1	−1	NOUN
ejpam-776	394	10	(	(	PUNCT
ejpam-776	394	11	g	g	NOUN
ejpam-776	394	12	)	)	PUNCT
ejpam-776	394	13	.	.	PUNCT
ejpam-776	395	1	(	(	PUNCT
ejpam-776	395	2	39	39	NUM
ejpam-776	395	3	)	)	PUNCT
ejpam-776	395	4	proof	proof	NOUN
ejpam-776	395	5	.	.	PUNCT
ejpam-776	396	1	by	by	ADP
ejpam-776	396	2	using	use	VERB
ejpam-776	396	3	relations	relation	NOUN
ejpam-776	396	4	(	(	PUNCT
ejpam-776	396	5	25	25	NUM
ejpam-776	396	6	)	)	PUNCT
ejpam-776	396	7	,	,	PUNCT
ejpam-776	396	8	(	(	PUNCT
ejpam-776	396	9	35	35	NUM
ejpam-776	396	10	)	)	PUNCT
ejpam-776	396	11	,	,	PUNCT
ejpam-776	396	12	(	(	PUNCT
ejpam-776	396	13	37	37	NUM
ejpam-776	396	14	)	)	PUNCT
ejpam-776	396	15	and	and	CCONJ
ejpam-776	396	16	proposition	proposition	NOUN
ejpam-776	396	17	10(i	10(i	NUM
ejpam-776	396	18	)	)	PUNCT
ejpam-776	396	19	we	we	PRON
ejpam-776	396	20	have	have	VERB
ejpam-776	396	21	v−1	v−1	PROPN
ejpam-776	396	22	�	�	PROPN
ejpam-776	396	23	v	v	PROPN
ejpam-776	396	24	(	(	PUNCT
ejpam-776	396	25	f	f	NOUN
ejpam-776	396	26	)	)	PUNCT
ejpam-776	396	27	#	#	NOUN
ejpam-776	396	28	t	t	PROPN
ejpam-776	396	29	v−1(g	v−1(g	PROPN
ejpam-776	396	30	)	)	PUNCT
ejpam-776	396	31	�	�	PROPN
ejpam-776	397	1	=	=	PUNCT
ejpam-776	397	2	k	k	PROPN
ejpam-776	397	3	t	t	PROPN
ejpam-776	397	4	v	v	PROPN
ejpam-776	397	5	�	�	PROPN
ejpam-776	397	6	v	v	PROPN
ejpam-776	397	7	(	(	PUNCT
ejpam-776	397	8	f	f	NOUN
ejpam-776	397	9	)	)	PUNCT
ejpam-776	397	10	#	#	NOUN
ejpam-776	397	11	t	t	PROPN
ejpam-776	397	12	v−1(g	v−1(g	PROPN
ejpam-776	397	13	)	)	PUNCT
ejpam-776	397	14	�	�	PROPN
ejpam-776	397	15	=	=	SYM
ejpam-776	397	16	k	k	PROPN
ejpam-776	397	17	�	�	PROPN
ejpam-776	397	18	t	t	PROPN
ejpam-776	397	19	v	v	NUM
ejpam-776	397	20	v	v	NOUN
ejpam-776	397	21	(	(	PUNCT
ejpam-776	397	22	f	f	PROPN
ejpam-776	397	23	)	)	PUNCT
ejpam-776	397	24	∗	∗	NOUN
ejpam-776	397	25	g	g	PROPN
ejpam-776	397	26	�	�	PROPN
ejpam-776	397	27	=	=	SYM
ejpam-776	397	28	�	�	PROPN
ejpam-776	397	29	k	k	PROPN
ejpam-776	397	30	t	t	PROPN
ejpam-776	397	31	v	v	PROPN
ejpam-776	397	32	v	v	NOUN
ejpam-776	397	33	(	(	PUNCT
ejpam-776	397	34	f	f	PROPN
ejpam-776	397	35	)	)	PUNCT
ejpam-776	397	36	�	�	PROPN
ejpam-776	397	37	∗	∗	VERB
ejpam-776	397	38	g	g	NOUN
ejpam-776	397	39	=	=	SYM
ejpam-776	397	40	f	f	PROPN
ejpam-776	397	41	∗	∗	NOUN
ejpam-776	397	42	g.	g.	PROPN
ejpam-776	397	43	w.	w.	PROPN
ejpam-776	397	44	chabeh	chabeh	PROPN
ejpam-776	397	45	,	,	PUNCT
ejpam-776	397	46	m.	m.	NOUN
ejpam-776	397	47	mourou	mourou	PROPN
ejpam-776	397	48	/	/	SYM
ejpam-776	397	49	eur	eur	PROPN
ejpam-776	397	50	.	.	PUNCT
ejpam-776	398	1	j.	j.	PROPN
ejpam-776	398	2	pure	pure	PROPN
ejpam-776	398	3	appl	appl	PROPN
ejpam-776	398	4	.	.	PROPN
ejpam-776	398	5	math	math	PROPN
ejpam-776	398	6	,	,	PUNCT
ejpam-776	398	7	3	3	NUM
ejpam-776	398	8	(	(	PUNCT
ejpam-776	398	9	2010	2010	NUM
ejpam-776	398	10	)	)	PUNCT
ejpam-776	398	11	,	,	PUNCT
ejpam-776	398	12	958	958	NUM
ejpam-776	398	13	-	-	SYM
ejpam-776	398	14	979	979	NUM
ejpam-776	398	15	977	977	NUM
ejpam-776	398	16	definition	definition	NOUN
ejpam-776	398	17	5	5	NUM
ejpam-776	398	18	.	.	PUNCT
ejpam-776	399	1	the	the	DET
ejpam-776	399	2	classical	classical	ADJ
ejpam-776	399	3	continuous	continuous	ADJ
ejpam-776	399	4	wavelet	wavelet	NOUN
ejpam-776	399	5	transform	transform	NOUN
ejpam-776	399	6	on	on	ADP
ejpam-776	399	7	r	r	NOUN
ejpam-776	399	8	is	be	AUX
ejpam-776	399	9	defined	define	VERB
ejpam-776	399	10	for	for	ADP
ejpam-776	399	11	regular	regular	ADJ
ejpam-776	399	12	functions	function	NOUN
ejpam-776	399	13	by	by	ADP
ejpam-776	399	14	sg	sg	PROPN
ejpam-776	399	15	(	(	PUNCT
ejpam-776	399	16	f	f	PROPN
ejpam-776	399	17	)	)	PUNCT
ejpam-776	399	18	(	(	PUNCT
ejpam-776	399	19	a	a	DET
ejpam-776	399	20	,	,	PUNCT
ejpam-776	399	21	b	b	NOUN
ejpam-776	399	22	)	)	PUNCT
ejpam-776	399	23	=	=	SYM
ejpam-776	400	1	∫	∫	PROPN
ejpam-776	400	2	r	r	NOUN
ejpam-776	400	3	f	f	PROPN
ejpam-776	400	4	(	(	PUNCT
ejpam-776	400	5	x	x	NOUN
ejpam-776	400	6	)	)	PUNCT
ejpam-776	400	7	g0	g0	NOUN
ejpam-776	400	8	a	a	PROPN
ejpam-776	400	9	,	,	PUNCT
ejpam-776	400	10	b	b	PROPN
ejpam-776	400	11	(	(	PUNCT
ejpam-776	400	12	x)d	x)d	X
ejpam-776	400	13	x	x	X
ejpam-776	400	14	,	,	PUNCT
ejpam-776	400	15	a	a	PRON
ejpam-776	400	16	>	>	X
ejpam-776	400	17	0	0	NUM
ejpam-776	400	18	,	,	PUNCT
ejpam-776	400	19	b	b	X
ejpam-776	400	20	∈	∈	PROPN
ejpam-776	400	21	r	r	NOUN
ejpam-776	400	22	,	,	PUNCT
ejpam-776	400	23	where	where	SCONJ
ejpam-776	400	24	g0	g0	PROPN
ejpam-776	400	25	a	a	PRON
ejpam-776	400	26	,	,	PUNCT
ejpam-776	400	27	b	b	PROPN
ejpam-776	400	28	(	(	PUNCT
ejpam-776	400	29	x	x	NOUN
ejpam-776	400	30	)	)	PUNCT
ejpam-776	400	31	:	:	PUNCT
ejpam-776	401	1	=	=	SYM
ejpam-776	401	2	1p	1p	VERB
ejpam-776	401	3	a	a	DET
ejpam-776	401	4	g	g	PROPN
ejpam-776	401	5	�	�	PROPN
ejpam-776	401	6	x	x	PUNCT
ejpam-776	401	7	−	−	PROPN
ejpam-776	401	8	b	b	PROPN
ejpam-776	401	9	a	a	DET
ejpam-776	401	10	�	�	PROPN
ejpam-776	401	11	the	the	DET
ejpam-776	401	12	function	function	NOUN
ejpam-776	401	13	g	g	PROPN
ejpam-776	401	14	is	be	AUX
ejpam-776	401	15	a	a	DET
ejpam-776	401	16	classical	classical	ADJ
ejpam-776	401	17	wavelet	wavelet	NOUN
ejpam-776	401	18	on	on	ADP
ejpam-776	401	19	r	r	NOUN
ejpam-776	401	20	,	,	PUNCT
ejpam-776	401	21	i.e.	i.e.	X
ejpam-776	401	22	,	,	PUNCT
ejpam-776	401	23	a	a	DET
ejpam-776	401	24	function	function	NOUN
ejpam-776	401	25	in	in	ADP
ejpam-776	401	26	l2(r	l2(r	PROPN
ejpam-776	401	27	,	,	PUNCT
ejpam-776	401	28	d	d	NOUN
ejpam-776	401	29	x	x	X
ejpam-776	401	30	)	)	PUNCT
ejpam-776	401	31	satisfying	satisfy	VERB
ejpam-776	401	32	the	the	DET
ejpam-776	401	33	admissibility	admissibility	NOUN
ejpam-776	401	34	condition	condition	NOUN
ejpam-776	401	35	:	:	PUNCT
ejpam-776	401	36	0	0	NUM
ejpam-776	401	37	<	<	X
ejpam-776	401	38	c0	c0	X
ejpam-776	401	39	g	g	PROPN
ejpam-776	401	40	=	=	SYM
ejpam-776	401	41	∫	∫	PROPN
ejpam-776	402	1	∞	∞	PROPN
ejpam-776	402	2	0	0	NUM
ejpam-776	403	1	|fu(g)(aλ)|2	|fu(g)(aλ)|2	NOUN
ejpam-776	403	2	da	da	NOUN
ejpam-776	403	3	a	a	DET
ejpam-776	403	4	<	<	X
ejpam-776	403	5	∞	∞	PROPN
ejpam-776	403	6	,	,	PUNCT
ejpam-776	403	7	for	for	ADP
ejpam-776	403	8	almost	almost	ADV
ejpam-776	403	9	all	all	PRON
ejpam-776	403	10	λ	λ	PROPN
ejpam-776	403	11	∈	∈	PROPN
ejpam-776	403	12	r.	r.	NOUN
ejpam-776	403	13	a	a	DET
ejpam-776	403	14	more	more	ADV
ejpam-776	403	15	complete	complete	ADJ
ejpam-776	403	16	and	and	CCONJ
ejpam-776	403	17	detailed	detailed	ADJ
ejpam-776	403	18	discussion	discussion	NOUN
ejpam-776	403	19	of	of	ADP
ejpam-776	403	20	the	the	DET
ejpam-776	403	21	properties	property	NOUN
ejpam-776	403	22	of	of	ADP
ejpam-776	403	23	the	the	DET
ejpam-776	403	24	classical	classical	ADJ
ejpam-776	403	25	wavelet	wavelet	NOUN
ejpam-776	403	26	transform	transform	NOUN
ejpam-776	403	27	on	on	ADP
ejpam-776	403	28	r	r	NOUN
ejpam-776	403	29	can	can	AUX
ejpam-776	403	30	be	be	AUX
ejpam-776	403	31	found	find	VERB
ejpam-776	403	32	in	in	ADP
ejpam-776	403	33	[	[	X
ejpam-776	403	34	3	3	NUM
ejpam-776	403	35	]	]	PUNCT
ejpam-776	403	36	,	,	PUNCT
ejpam-776	403	37	from	from	ADP
ejpam-776	403	38	which	which	PRON
ejpam-776	403	39	we	we	PRON
ejpam-776	403	40	have	have	VERB
ejpam-776	403	41	the	the	DET
ejpam-776	403	42	following	follow	VERB
ejpam-776	403	43	inversion	inversion	NOUN
ejpam-776	403	44	formula	formula	NOUN
ejpam-776	403	45	.	.	PUNCT
ejpam-776	404	1	theorem	theorem	VERB
ejpam-776	404	2	7	7	NUM
ejpam-776	404	3	.	.	PUNCT
ejpam-776	405	1	let	let	VERB
ejpam-776	405	2	g	g	PROPN
ejpam-776	405	3	∈	∈	PROPN
ejpam-776	405	4	l2(r	l2(r	PROPN
ejpam-776	405	5	,	,	PUNCT
ejpam-776	405	6	d	d	NOUN
ejpam-776	405	7	x	x	X
ejpam-776	405	8	)	)	PUNCT
ejpam-776	405	9	be	be	VERB
ejpam-776	405	10	a	a	DET
ejpam-776	405	11	classical	classical	ADJ
ejpam-776	405	12	wavelet	wavelet	NOUN
ejpam-776	405	13	.	.	PUNCT
ejpam-776	406	1	if	if	SCONJ
ejpam-776	406	2	both	both	PRON
ejpam-776	406	3	f	f	PROPN
ejpam-776	406	4	and	and	CCONJ
ejpam-776	406	5	fu	fu	PROPN
ejpam-776	406	6	(	(	PUNCT
ejpam-776	406	7	f	f	PROPN
ejpam-776	406	8	)	)	PUNCT
ejpam-776	406	9	are	be	AUX
ejpam-776	406	10	in	in	ADP
ejpam-776	406	11	l1(r	l1(r	PROPN
ejpam-776	406	12	,	,	PUNCT
ejpam-776	406	13	d	d	NOUN
ejpam-776	406	14	x	x	X
ejpam-776	406	15	)	)	PUNCT
ejpam-776	406	16	then	then	ADV
ejpam-776	406	17	we	we	PRON
ejpam-776	406	18	have	have	VERB
ejpam-776	406	19	f	f	PROPN
ejpam-776	406	20	(	(	PUNCT
ejpam-776	406	21	x	x	NOUN
ejpam-776	406	22	)	)	PUNCT
ejpam-776	406	23	=	=	SYM
ejpam-776	406	24	1	1	NUM
ejpam-776	406	25	c0	c0	NOUN
ejpam-776	406	26	g	g	PROPN
ejpam-776	406	27	∫	∫	PROPN
ejpam-776	406	28	∞	∞	PROPN
ejpam-776	406	29	0	0	NUM
ejpam-776	406	30	�	�	PROPN
ejpam-776	406	31	∫	∫	PROPN
ejpam-776	406	32	r	r	NOUN
ejpam-776	406	33	sg	sg	PROPN
ejpam-776	406	34	(	(	PUNCT
ejpam-776	406	35	f	f	PROPN
ejpam-776	406	36	)	)	PUNCT
ejpam-776	406	37	(	(	PUNCT
ejpam-776	406	38	a	a	X
ejpam-776	406	39	,	,	PUNCT
ejpam-776	406	40	b)g0	b)g0	PROPN
ejpam-776	406	41	a	a	PRON
ejpam-776	406	42	,	,	PUNCT
ejpam-776	406	43	b(x)d	b(x)d	PROPN
ejpam-776	406	44	b	b	PROPN
ejpam-776	406	45	�	�	PROPN
ejpam-776	406	46	da	da	PROPN
ejpam-776	406	47	a2	a2	PROPN
ejpam-776	406	48	for	for	ADP
ejpam-776	406	49	almost	almost	ADV
ejpam-776	406	50	every	every	PRON
ejpam-776	406	51	x	x	PROPN
ejpam-776	406	52	∈	∈	PROPN
ejpam-776	406	53	r.	r.	PROPN
ejpam-776	406	54	remark	remark	NOUN
ejpam-776	406	55	10	10	NUM
ejpam-776	406	56	.	.	PUNCT
ejpam-776	407	1	according	accord	VERB
ejpam-776	407	2	to	to	ADP
ejpam-776	407	3	(	(	PUNCT
ejpam-776	407	4	16	16	NUM
ejpam-776	407	5	)	)	PUNCT
ejpam-776	407	6	and	and	CCONJ
ejpam-776	407	7	definitions	definition	NOUN
ejpam-776	407	8	3	3	NUM
ejpam-776	407	9	,	,	PUNCT
ejpam-776	407	10	5	5	NUM
ejpam-776	407	11	,	,	PUNCT
ejpam-776	407	12	g	g	PROPN
ejpam-776	407	13	∈	∈	PROPN
ejpam-776	407	14	s	s	PART
ejpam-776	407	15	(	(	PUNCT
ejpam-776	407	16	r	r	NOUN
ejpam-776	407	17	)	)	PUNCT
ejpam-776	407	18	is	be	AUX
ejpam-776	407	19	a	a	DET
ejpam-776	407	20	generalized	generalized	ADJ
ejpam-776	407	21	wavelet	wavelet	NOUN
ejpam-776	407	22	,	,	PUNCT
ejpam-776	407	23	if	if	SCONJ
ejpam-776	407	24	and	and	CCONJ
ejpam-776	407	25	only	only	ADV
ejpam-776	407	26	if	if	SCONJ
ejpam-776	407	27	,	,	PUNCT
ejpam-776	407	28	t	t	PROPN
ejpam-776	407	29	v	v	PROPN
ejpam-776	407	30	(	(	PUNCT
ejpam-776	407	31	g	g	NOUN
ejpam-776	407	32	)	)	PUNCT
ejpam-776	407	33	is	be	AUX
ejpam-776	407	34	a	a	DET
ejpam-776	407	35	classical	classical	ADJ
ejpam-776	407	36	wavelet	wavelet	NOUN
ejpam-776	407	37	and	and	CCONJ
ejpam-776	407	38	we	we	PRON
ejpam-776	407	39	have	have	VERB
ejpam-776	407	40	:	:	PUNCT
ejpam-776	407	41	c0	c0	PROPN
ejpam-776	407	42	t	t	PROPN
ejpam-776	407	43	v(g	v(g	PROPN
ejpam-776	407	44	)	)	PUNCT
ejpam-776	407	45	=	=	SYM
ejpam-776	407	46	cg	cg	NOUN
ejpam-776	407	47	.	.	PUNCT
ejpam-776	408	1	(	(	PUNCT
ejpam-776	408	2	40	40	NUM
ejpam-776	408	3	)	)	PUNCT
ejpam-776	408	4	lemma	lemma	PROPN
ejpam-776	408	5	7	7	X
ejpam-776	408	6	.	.	PUNCT
ejpam-776	409	1	let	let	VERB
ejpam-776	409	2	g	g	PROPN
ejpam-776	409	3	∈w	∈w	PROPN
ejpam-776	409	4	(	(	PUNCT
ejpam-776	409	5	r	r	AUX
ejpam-776	409	6	)	)	PUNCT
ejpam-776	409	7	be	be	AUX
ejpam-776	409	8	real	real	ADV
ejpam-776	409	9	-	-	PUNCT
ejpam-776	409	10	valued	value	VERB
ejpam-776	409	11	.	.	PUNCT
ejpam-776	410	1	then	then	ADV
ejpam-776	410	2	for	for	ADP
ejpam-776	410	3	all	all	DET
ejpam-776	410	4	f	f	PROPN
ejpam-776	410	5	∈	∈	PROPN
ejpam-776	410	6	s	s	X
ejpam-776	410	7	(	(	PUNCT
ejpam-776	410	8	r	r	NOUN
ejpam-776	410	9	)	)	PUNCT
ejpam-776	410	10	we	we	PRON
ejpam-776	410	11	have	have	VERB
ejpam-776	410	12	φvk	φvk	ADJ
ejpam-776	410	13	g	g	PROPN
ejpam-776	410	14	(	(	PUNCT
ejpam-776	410	15	f	f	PROPN
ejpam-776	410	16	)	)	PUNCT
ejpam-776	410	17	(	(	PUNCT
ejpam-776	410	18	a	a	DET
ejpam-776	410	19	,	,	PUNCT
ejpam-776	410	20	b	b	NOUN
ejpam-776	410	21	)	)	PUNCT
ejpam-776	411	1	=	=	NOUN
ejpam-776	411	2	mv	mv	PROPN
ejpam-776	411	3	�	�	PROPN
ejpam-776	411	4	sg	sg	ADP
ejpam-776	411	5	�	�	PROPN
ejpam-776	411	6	t	t	PROPN
ejpam-776	411	7	v	v	PROPN
ejpam-776	411	8	f	f	PROPN
ejpam-776	411	9	�	�	PROPN
ejpam-776	411	10	(	(	PUNCT
ejpam-776	411	11	a	a	PRON
ejpam-776	411	12	,	,	PUNCT
ejpam-776	411	13	·	·	SYM
ejpam-776	411	14	)	)	PUNCT
ejpam-776	411	15	�	�	PROPN
ejpam-776	411	16	(	(	PUNCT
ejpam-776	411	17	b	b	NOUN
ejpam-776	411	18	)	)	PUNCT
ejpam-776	411	19	.	.	PUNCT
ejpam-776	412	1	proof	proof	NOUN
ejpam-776	412	2	.	.	PUNCT
ejpam-776	413	1	notice	notice	VERB
ejpam-776	413	2	that	that	SCONJ
ejpam-776	413	3	vk	vk	VERB
ejpam-776	413	4	g	g	NOUN
ejpam-776	413	5	=	=	SYM
ejpam-776	413	6	t	t	PROPN
ejpam-776	413	7	v−1	v−1	PROPN
ejpam-776	413	8	g	g	NOUN
ejpam-776	413	9	by	by	ADP
ejpam-776	413	10	virtue	virtue	NOUN
ejpam-776	413	11	of	of	ADP
ejpam-776	413	12	(	(	PUNCT
ejpam-776	413	13	35	35	NUM
ejpam-776	413	14	)	)	PUNCT
ejpam-776	413	15	.	.	PUNCT
ejpam-776	414	1	further	far	ADV
ejpam-776	414	2	,	,	PUNCT
ejpam-776	414	3	g	g	PROPN
ejpam-776	414	4	is	be	AUX
ejpam-776	414	5	a	a	DET
ejpam-776	414	6	classical	classical	ADJ
ejpam-776	414	7	wavelet	wavelet	NOUN
ejpam-776	414	8	according	accord	VERB
ejpam-776	414	9	to	to	ADP
ejpam-776	414	10	[	[	X
ejpam-776	414	11	3	3	NUM
ejpam-776	414	12	]	]	PUNCT
ejpam-776	414	13	.	.	PUNCT
ejpam-776	415	1	so	so	ADV
ejpam-776	415	2	it	it	PRON
ejpam-776	415	3	follows	follow	VERB
ejpam-776	415	4	from	from	ADP
ejpam-776	415	5	remark	remark	NOUN
ejpam-776	415	6	10	10	NUM
ejpam-776	415	7	that	that	PRON
ejpam-776	415	8	vk	vk	VERB
ejpam-776	415	9	g	g	PROPN
ejpam-776	415	10	∈	∈	PROPN
ejpam-776	415	11	b(r	b(r	PROPN
ejpam-776	415	12	)	)	PUNCT
ejpam-776	415	13	is	be	AUX
ejpam-776	415	14	a	a	DET
ejpam-776	415	15	generalized	generalized	ADJ
ejpam-776	415	16	wavelet	wavelet	NOUN
ejpam-776	415	17	and	and	CCONJ
ejpam-776	415	18	cvk	cvk	ADJ
ejpam-776	415	19	g	g	PROPN
ejpam-776	415	20	=	=	PROPN
ejpam-776	415	21	c0	c0	PROPN
ejpam-776	415	22	g	g	PROPN
ejpam-776	415	23	.	.	PUNCT
ejpam-776	416	1	(	(	PUNCT
ejpam-776	416	2	41	41	NUM
ejpam-776	416	3	)	)	PUNCT
ejpam-776	416	4	due	due	ADP
ejpam-776	416	5	to	to	ADP
ejpam-776	416	6	(	(	PUNCT
ejpam-776	416	7	25	25	NUM
ejpam-776	416	8	)	)	PUNCT
ejpam-776	416	9	,	,	PUNCT
ejpam-776	416	10	(	(	PUNCT
ejpam-776	416	11	29	29	NUM
ejpam-776	416	12	)	)	PUNCT
ejpam-776	416	13	,	,	PUNCT
ejpam-776	416	14	(	(	PUNCT
ejpam-776	416	15	31	31	NUM
ejpam-776	416	16	)	)	PUNCT
ejpam-776	416	17	,	,	PUNCT
ejpam-776	416	18	(	(	PUNCT
ejpam-776	416	19	35	35	NUM
ejpam-776	416	20	)	)	PUNCT
ejpam-776	416	21	,	,	PUNCT
ejpam-776	416	22	(	(	PUNCT
ejpam-776	416	23	38	38	NUM
ejpam-776	416	24	)	)	PUNCT
ejpam-776	416	25	and	and	CCONJ
ejpam-776	416	26	definition	definition	NOUN
ejpam-776	416	27	5	5	NUM
ejpam-776	416	28	we	we	PRON
ejpam-776	416	29	have	have	VERB
ejpam-776	416	30	φvk	φvk	ADJ
ejpam-776	416	31	g	g	PROPN
ejpam-776	416	32	(	(	PUNCT
ejpam-776	416	33	f	f	PROPN
ejpam-776	416	34	)	)	PUNCT
ejpam-776	416	35	(	(	PUNCT
ejpam-776	416	36	a	a	DET
ejpam-776	416	37	,	,	PUNCT
ejpam-776	416	38	b	b	NOUN
ejpam-776	416	39	)	)	PUNCT
ejpam-776	416	40	=	=	PUNCT
ejpam-776	417	1	p	p	X
ejpam-776	417	2	a	a	DET
ejpam-776	417	3	f	f	NOUN
ejpam-776	417	4	#	#	SYM
ejpam-776	417	5	(	(	PUNCT
ejpam-776	417	6	vk	vk	ADP
ejpam-776	417	7	g)ea(b	g)ea(b	NUM
ejpam-776	417	8	)	)	PUNCT
ejpam-776	418	1	=	=	SYM
ejpam-776	419	1	p	p	X
ejpam-776	419	2	a	a	DET
ejpam-776	419	3	t	t	NOUN
ejpam-776	419	4	v−1	v−1	PROPN
ejpam-776	419	5	�	�	PROPN
ejpam-776	419	6	t	t	PROPN
ejpam-776	419	7	v	v	PROPN
ejpam-776	419	8	f	f	PROPN
ejpam-776	419	9	∗	∗	NOUN
ejpam-776	419	10	t	t	PROPN
ejpam-776	419	11	v	v	NOUN
ejpam-776	419	12	(	(	PUNCT
ejpam-776	419	13	vk	vk	PROPN
ejpam-776	419	14	g)ea	g)ea	PROPN
ejpam-776	419	15	�	�	PROPN
ejpam-776	419	16	(	(	PUNCT
ejpam-776	419	17	b	b	NOUN
ejpam-776	419	18	)	)	PUNCT
ejpam-776	419	19	=	=	SYM
ejpam-776	419	20	t	t	PROPN
ejpam-776	419	21	v−1	v−1	PROPN
ejpam-776	419	22	�	�	PROPN
ejpam-776	419	23	t	t	PROPN
ejpam-776	419	24	v	v	NOUN
ejpam-776	419	25	f	f	PROPN
ejpam-776	419	26	∗ha	∗ha	PUNCT
ejpam-776	419	27	�	�	PROPN
ejpam-776	419	28	t	t	PROPN
ejpam-776	419	29	v	v	NOUN
ejpam-776	419	30	vk	vk	ADP
ejpam-776	419	31	eg	eg	PROPN
ejpam-776	419	32	�	�	PROPN
ejpam-776	419	33	�	�	PROPN
ejpam-776	419	34	(	(	PUNCT
ejpam-776	419	35	b	b	NOUN
ejpam-776	419	36	)	)	PUNCT
ejpam-776	419	37	=	=	SYM
ejpam-776	419	38	mv	mv	PROPN
ejpam-776	419	39	�	�	PROPN
ejpam-776	419	40	t	t	PROPN
ejpam-776	419	41	v	v	NUM
ejpam-776	419	42	f	f	PROPN
ejpam-776	419	43	∗ha(eg	∗ha(eg	NUM
ejpam-776	419	44	)	)	PUNCT
ejpam-776	419	45	�	�	PROPN
ejpam-776	419	46	(	(	PUNCT
ejpam-776	419	47	b	b	NOUN
ejpam-776	419	48	)	)	PUNCT
ejpam-776	419	49	=	=	SYM
ejpam-776	419	50	mv	mv	PROPN
ejpam-776	419	51	�	�	PROPN
ejpam-776	419	52	sg	sg	PROPN
ejpam-776	419	53	�	�	PROPN
ejpam-776	419	54	t	t	PROPN
ejpam-776	419	55	v	v	PROPN
ejpam-776	419	56	f	f	PROPN
ejpam-776	419	57	�	�	PROPN
ejpam-776	419	58	(	(	PUNCT
ejpam-776	419	59	a	a	PRON
ejpam-776	419	60	,	,	PUNCT
ejpam-776	419	61	·	·	SYM
ejpam-776	419	62	)	)	PUNCT
ejpam-776	419	63	�	�	PROPN
ejpam-776	419	64	(	(	PUNCT
ejpam-776	419	65	b	b	NOUN
ejpam-776	419	66	)	)	PUNCT
ejpam-776	419	67	.	.	PUNCT
ejpam-776	420	1	references	reference	NOUN
ejpam-776	420	2	978	978	NUM
ejpam-776	420	3	lemma	lemma	PROPN
ejpam-776	420	4	8	8	NUM
ejpam-776	420	5	.	.	PUNCT
ejpam-776	421	1	let	let	AUX
ejpam-776	421	2	g	g	PROPN
ejpam-776	421	3	∈b(r	∈b(r	PROPN
ejpam-776	421	4	)	)	PUNCT
ejpam-776	421	5	be	be	AUX
ejpam-776	421	6	real	real	ADV
ejpam-776	421	7	-	-	PUNCT
ejpam-776	421	8	valued	value	VERB
ejpam-776	421	9	.	.	PUNCT
ejpam-776	422	1	then	then	ADV
ejpam-776	422	2	for	for	ADP
ejpam-776	422	3	all	all	DET
ejpam-776	422	4	f	f	PROPN
ejpam-776	422	5	∈w	∈w	PROPN
ejpam-776	422	6	(	(	PUNCT
ejpam-776	422	7	r	r	NOUN
ejpam-776	422	8	)	)	PUNCT
ejpam-776	422	9	,	,	PUNCT
ejpam-776	422	10	we	we	PRON
ejpam-776	422	11	have	have	VERB
ejpam-776	422	12	s	s	PROPN
ejpam-776	422	13	t	t	NOUN
ejpam-776	422	14	v	v	ADP
ejpam-776	422	15	g	g	PROPN
ejpam-776	422	16	(	(	PUNCT
ejpam-776	422	17	f	f	PROPN
ejpam-776	422	18	)	)	PUNCT
ejpam-776	422	19	(	(	PUNCT
ejpam-776	422	20	a	a	DET
ejpam-776	422	21	,	,	PUNCT
ejpam-776	422	22	b	b	NOUN
ejpam-776	422	23	)	)	PUNCT
ejpam-776	423	1	=	=	NOUN
ejpam-776	423	2	k	k	PROPN
ejpam-776	423	3	t	t	PROPN
ejpam-776	423	4	v	v	PROPN
ejpam-776	423	5	�	�	PROPN
ejpam-776	423	6	φg(v	φg(v	DET
ejpam-776	423	7	f	f	PROPN
ejpam-776	423	8	)	)	PUNCT
ejpam-776	423	9	(	(	PUNCT
ejpam-776	423	10	a	a	PRON
ejpam-776	423	11	,	,	PUNCT
ejpam-776	423	12	·	·	SYM
ejpam-776	423	13	)	)	PUNCT
ejpam-776	423	14	�	�	PROPN
ejpam-776	423	15	(	(	PUNCT
ejpam-776	423	16	b	b	NOUN
ejpam-776	423	17	)	)	PUNCT
ejpam-776	423	18	.	.	PUNCT
ejpam-776	424	1	proof	proof	NOUN
ejpam-776	424	2	.	.	PUNCT
ejpam-776	425	1	observe	observe	VERB
ejpam-776	425	2	that	that	SCONJ
ejpam-776	425	3	by	by	ADP
ejpam-776	425	4	remarks	remark	NOUN
ejpam-776	425	5	7(iv	7(iv	NUM
ejpam-776	425	6	)	)	PUNCT
ejpam-776	425	7	and	and	CCONJ
ejpam-776	425	8	10	10	NUM
ejpam-776	425	9	,	,	PUNCT
ejpam-776	425	10	t	t	PROPN
ejpam-776	425	11	v	v	NOUN
ejpam-776	425	12	g	g	PROPN
ejpam-776	425	13	is	be	AUX
ejpam-776	425	14	a	a	DET
ejpam-776	425	15	classical	classical	ADJ
ejpam-776	425	16	wavelet	wavelet	NOUN
ejpam-776	425	17	.	.	PUNCT
ejpam-776	426	1	using	use	VERB
ejpam-776	426	2	(	(	PUNCT
ejpam-776	426	3	29	29	NUM
ejpam-776	426	4	)	)	PUNCT
ejpam-776	426	5	,	,	PUNCT
ejpam-776	426	6	(	(	PUNCT
ejpam-776	426	7	31	31	NUM
ejpam-776	426	8	)	)	PUNCT
ejpam-776	426	9	,	,	PUNCT
ejpam-776	426	10	(	(	PUNCT
ejpam-776	426	11	39	39	NUM
ejpam-776	426	12	)	)	PUNCT
ejpam-776	426	13	and	and	CCONJ
ejpam-776	426	14	definition	definition	NOUN
ejpam-776	426	15	5	5	NUM
ejpam-776	426	16	we	we	PRON
ejpam-776	426	17	have	have	VERB
ejpam-776	426	18	v	v	ADP
ejpam-776	426	19	�	�	PROPN
ejpam-776	426	20	s	s	PART
ejpam-776	426	21	t	t	NOUN
ejpam-776	426	22	v	v	NOUN
ejpam-776	426	23	g	g	PROPN
ejpam-776	426	24	(	(	PUNCT
ejpam-776	426	25	f	f	PROPN
ejpam-776	426	26	)	)	PUNCT
ejpam-776	426	27	(	(	PUNCT
ejpam-776	426	28	a	a	PRON
ejpam-776	426	29	,	,	PUNCT
ejpam-776	426	30	·	·	SYM
ejpam-776	426	31	)	)	PUNCT
ejpam-776	426	32	�	�	PROPN
ejpam-776	426	33	(	(	PUNCT
ejpam-776	426	34	b	b	NOUN
ejpam-776	426	35	)	)	PUNCT
ejpam-776	426	36	=	=	SYM
ejpam-776	427	1	v	v	NUM
ejpam-776	427	2	�	�	PROPN
ejpam-776	427	3	f	f	PROPN
ejpam-776	427	4	∗	∗	PROPN
ejpam-776	427	5	ha	ha	INTJ
ejpam-776	427	6	�	�	PROPN
ejpam-776	427	7	t	t	PROPN
ejpam-776	427	8	v	v	NUM
ejpam-776	427	9	eg	eg	PROPN
ejpam-776	427	10	�	�	PROPN
ejpam-776	427	11	�	�	PROPN
ejpam-776	427	12	(	(	PUNCT
ejpam-776	427	13	b	b	NOUN
ejpam-776	427	14	)	)	PUNCT
ejpam-776	427	15	=	=	PUNCT
ejpam-776	428	1	p	p	X
ejpam-776	428	2	a	a	DET
ejpam-776	428	3	v	v	X
ejpam-776	428	4	�	�	PROPN
ejpam-776	428	5	f	f	PROPN
ejpam-776	428	6	∗	∗	NOUN
ejpam-776	428	7	t	t	PROPN
ejpam-776	428	8	v	v	PROPN
ejpam-776	428	9	(	(	PUNCT
ejpam-776	428	10	ega	ega	PROPN
ejpam-776	428	11	)	)	PUNCT
ejpam-776	428	12	�	�	PROPN
ejpam-776	428	13	(	(	PUNCT
ejpam-776	428	14	b	b	NOUN
ejpam-776	428	15	)	)	PUNCT
ejpam-776	428	16	=	=	PUNCT
ejpam-776	429	1	p	p	X
ejpam-776	429	2	a	a	DET
ejpam-776	429	3	v	v	NOUN
ejpam-776	429	4	(	(	PUNCT
ejpam-776	429	5	f	f	NOUN
ejpam-776	429	6	)	)	PUNCT
ejpam-776	429	7	#	#	NOUN
ejpam-776	429	8	ega(b	ega(b	PROPN
ejpam-776	429	9	)	)	PUNCT
ejpam-776	429	10	=	=	SYM
ejpam-776	429	11	φg(v	φg(v	DET
ejpam-776	429	12	f	f	PROPN
ejpam-776	429	13	)	)	PUNCT
ejpam-776	429	14	(	(	PUNCT
ejpam-776	429	15	a	a	DET
ejpam-776	429	16	,	,	PUNCT
ejpam-776	429	17	b	b	NOUN
ejpam-776	429	18	)	)	PUNCT
ejpam-776	429	19	.	.	PUNCT
ejpam-776	430	1	thus	thus	ADV
ejpam-776	430	2	s	s	VERB
ejpam-776	430	3	t	t	NOUN
ejpam-776	430	4	v	v	ADP
ejpam-776	430	5	g	g	PROPN
ejpam-776	430	6	(	(	PUNCT
ejpam-776	430	7	f	f	PROPN
ejpam-776	430	8	)	)	PUNCT
ejpam-776	430	9	(	(	PUNCT
ejpam-776	430	10	a	a	DET
ejpam-776	430	11	,	,	PUNCT
ejpam-776	430	12	b	b	NOUN
ejpam-776	430	13	)	)	PUNCT
ejpam-776	430	14	=	=	SYM
ejpam-776	431	1	v−1	v−1	PROPN
ejpam-776	431	2	[	[	X
ejpam-776	431	3	φg(v	φg(v	X
ejpam-776	431	4	f	f	PROPN
ejpam-776	431	5	)	)	PUNCT
ejpam-776	431	6	(	(	PUNCT
ejpam-776	431	7	a	a	PRON
ejpam-776	431	8	,	,	PUNCT
ejpam-776	431	9	·	·	PUNCT
ejpam-776	431	10	)	)	PUNCT
ejpam-776	431	11	]	]	PUNCT
ejpam-776	431	12	(	(	PUNCT
ejpam-776	431	13	b	b	X
ejpam-776	431	14	)	)	PUNCT
ejpam-776	431	15	=	=	SYM
ejpam-776	432	1	k	k	PROPN
ejpam-776	432	2	t	t	PROPN
ejpam-776	432	3	v[φg(v	v[φg(v	PROPN
ejpam-776	432	4	f	f	PROPN
ejpam-776	432	5	)	)	PUNCT
ejpam-776	432	6	(	(	PUNCT
ejpam-776	432	7	a	a	PRON
ejpam-776	432	8	,	,	PUNCT
ejpam-776	432	9	·	·	PUNCT
ejpam-776	432	10	)	)	PUNCT
ejpam-776	432	11	]	]	PUNCT
ejpam-776	432	12	(	(	PUNCT
ejpam-776	432	13	b	b	NOUN
ejpam-776	432	14	)	)	PUNCT
ejpam-776	432	15	by	by	ADP
ejpam-776	432	16	virtue	virtue	NOUN
ejpam-776	432	17	of	of	ADP
ejpam-776	432	18	(	(	PUNCT
ejpam-776	432	19	35	35	NUM
ejpam-776	432	20	)	)	PUNCT
ejpam-776	432	21	.	.	PUNCT
ejpam-776	433	1	we	we	PRON
ejpam-776	433	2	can	can	AUX
ejpam-776	433	3	now	now	ADV
ejpam-776	433	4	state	state	VERB
ejpam-776	433	5	our	our	PRON
ejpam-776	433	6	main	main	ADJ
ejpam-776	433	7	result	result	NOUN
ejpam-776	433	8	.	.	PUNCT
ejpam-776	434	1	theorem	theorem	ADJ
ejpam-776	434	2	8	8	NUM
ejpam-776	434	3	.	.	PUNCT
ejpam-776	435	1	(	(	PUNCT
ejpam-776	435	2	i	i	NOUN
ejpam-776	435	3	)	)	PUNCT
ejpam-776	435	4	let	let	VERB
ejpam-776	435	5	g	g	PROPN
ejpam-776	435	6	∈w	∈w	PROPN
ejpam-776	435	7	(	(	PUNCT
ejpam-776	435	8	r	r	AUX
ejpam-776	435	9	)	)	PUNCT
ejpam-776	435	10	be	be	AUX
ejpam-776	435	11	real	real	ADV
ejpam-776	435	12	-	-	PUNCT
ejpam-776	435	13	valued	value	VERB
ejpam-776	435	14	.	.	PUNCT
ejpam-776	436	1	then	then	ADV
ejpam-776	436	2	for	for	ADP
ejpam-776	436	3	all	all	DET
ejpam-776	436	4	f	f	PROPN
ejpam-776	436	5	∈	∈	PROPN
ejpam-776	436	6	s	s	X
ejpam-776	436	7	(	(	PUNCT
ejpam-776	436	8	r	r	NOUN
ejpam-776	436	9	)	)	PUNCT
ejpam-776	436	10	we	we	PRON
ejpam-776	436	11	have	have	VERB
ejpam-776	436	12	t	t	PROPN
ejpam-776	436	13	v	v	NUM
ejpam-776	436	14	−1	−1	NOUN
ejpam-776	436	15	f	f	X
ejpam-776	436	16	(	(	PUNCT
ejpam-776	436	17	x	x	X
ejpam-776	436	18	)	)	PUNCT
ejpam-776	436	19	=	=	SYM
ejpam-776	436	20	1	1	NUM
ejpam-776	436	21	c0	c0	NOUN
ejpam-776	436	22	g	g	PROPN
ejpam-776	436	23	∫	∫	PROPN
ejpam-776	436	24	∞	∞	PROPN
ejpam-776	436	25	0	0	NUM
ejpam-776	436	26	�	�	PROPN
ejpam-776	436	27	∫	∫	PROPN
ejpam-776	437	1	r	r	NOUN
ejpam-776	437	2	mv	mv	PROPN
ejpam-776	438	1	[	[	X
ejpam-776	438	2	sg	sg	X
ejpam-776	438	3	(	(	PUNCT
ejpam-776	438	4	f	f	PROPN
ejpam-776	438	5	)	)	PUNCT
ejpam-776	438	6	(	(	PUNCT
ejpam-776	438	7	a	a	PRON
ejpam-776	438	8	,	,	PUNCT
ejpam-776	438	9	·	·	PUNCT
ejpam-776	438	10	)	)	PUNCT
ejpam-776	438	11	]	]	PUNCT
ejpam-776	438	12	(	(	PUNCT
ejpam-776	438	13	b	b	NOUN
ejpam-776	438	14	)	)	PUNCT
ejpam-776	438	15	(	(	PUNCT
ejpam-776	438	16	vk	vk	NOUN
ejpam-776	438	17	g)a	g)a	NOUN
ejpam-776	438	18	,	,	PUNCT
ejpam-776	438	19	b(x)a(b)d	b(x)a(b)d	PROPN
ejpam-776	438	20	b	b	PROPN
ejpam-776	438	21	�	�	PROPN
ejpam-776	438	22	da	da	PROPN
ejpam-776	438	23	a2	a2	PROPN
ejpam-776	438	24	.	.	PUNCT
ejpam-776	439	1	(	(	PUNCT
ejpam-776	439	2	ii	ii	NOUN
ejpam-776	439	3	)	)	PUNCT
ejpam-776	439	4	let	let	VERB
ejpam-776	439	5	g	g	PROPN
ejpam-776	439	6	∈b(r	∈b(r	PROPN
ejpam-776	439	7	)	)	PUNCT
ejpam-776	439	8	be	be	AUX
ejpam-776	439	9	real	real	ADV
ejpam-776	439	10	-	-	PUNCT
ejpam-776	439	11	valued	value	VERB
ejpam-776	439	12	.	.	PUNCT
ejpam-776	440	1	then	then	ADV
ejpam-776	440	2	for	for	ADP
ejpam-776	440	3	all	all	DET
ejpam-776	440	4	f	f	PROPN
ejpam-776	440	5	∈b(r	∈b(r	PROPN
ejpam-776	440	6	)	)	PUNCT
ejpam-776	440	7	we	we	PRON
ejpam-776	440	8	have	have	VERB
ejpam-776	440	9	v−1	v−1	PROPN
ejpam-776	440	10	f	f	X
ejpam-776	440	11	(	(	PUNCT
ejpam-776	440	12	x	x	X
ejpam-776	440	13	)	)	PUNCT
ejpam-776	440	14	=	=	SYM
ejpam-776	440	15	1	1	NUM
ejpam-776	440	16	cg	cg	NOUN
ejpam-776	440	17	∫	∫	PROPN
ejpam-776	440	18	∞	∞	PROPN
ejpam-776	440	19	0	0	NUM
ejpam-776	440	20	�	�	PROPN
ejpam-776	440	21	∫	∫	PROPN
ejpam-776	440	22	r	r	PROPN
ejpam-776	440	23	k	k	PROPN
ejpam-776	440	24	t	t	PROPN
ejpam-776	440	25	v[φg	v[φg	PROPN
ejpam-776	440	26	(	(	PUNCT
ejpam-776	440	27	f	f	PROPN
ejpam-776	440	28	)	)	PUNCT
ejpam-776	440	29	(	(	PUNCT
ejpam-776	440	30	a	a	PRON
ejpam-776	440	31	,	,	PUNCT
ejpam-776	440	32	·	·	PUNCT
ejpam-776	440	33	)	)	PUNCT
ejpam-776	440	34	]	]	PUNCT
ejpam-776	440	35	(	(	PUNCT
ejpam-776	440	36	b	b	X
ejpam-776	440	37	)	)	PUNCT
ejpam-776	440	38	�	�	PROPN
ejpam-776	440	39	t	t	PROPN
ejpam-776	440	40	v	v	NOUN
ejpam-776	440	41	g	g	PROPN
ejpam-776	440	42	�	�	PROPN
ejpam-776	440	43	0	0	NUM
ejpam-776	440	44	a	a	DET
ejpam-776	440	45	,	,	PUNCT
ejpam-776	440	46	b	b	NOUN
ejpam-776	440	47	(	(	PUNCT
ejpam-776	440	48	x)d	x)d	PROPN
ejpam-776	440	49	b	b	X
ejpam-776	440	50	�	�	PROPN
ejpam-776	440	51	da	da	PROPN
ejpam-776	440	52	a2	a2	PROPN
ejpam-776	440	53	.	.	PUNCT
ejpam-776	441	1	proof	proof	NOUN
ejpam-776	441	2	.	.	PUNCT
ejpam-776	442	1	the	the	DET
ejpam-776	442	2	result	result	NOUN
ejpam-776	442	3	follows	follow	VERB
ejpam-776	442	4	by	by	ADP
ejpam-776	442	5	combining	combine	VERB
ejpam-776	442	6	theorems	theorem	NOUN
ejpam-776	442	7	5	5	NUM
ejpam-776	442	8	,	,	PUNCT
ejpam-776	442	9	7	7	NUM
ejpam-776	442	10	,	,	PUNCT
ejpam-776	442	11	lemmas	lemma	VERB
ejpam-776	442	12	7	7	NUM
ejpam-776	442	13	,	,	PUNCT
ejpam-776	442	14	8	8	NUM
ejpam-776	442	15	and	and	CCONJ
ejpam-776	442	16	identities	identity	NOUN
ejpam-776	442	17	(	(	PUNCT
ejpam-776	442	18	40	40	NUM
ejpam-776	442	19	)	)	PUNCT
ejpam-776	442	20	,	,	PUNCT
ejpam-776	442	21	(	(	PUNCT
ejpam-776	442	22	41	41	NUM
ejpam-776	442	23	)	)	PUNCT
ejpam-776	442	24	.	.	PUNCT
ejpam-776	443	1	references	reference	NOUN
ejpam-776	443	2	[	[	X
ejpam-776	443	3	1	1	NUM
ejpam-776	443	4	]	]	X
ejpam-776	443	5	mfe	mfe	PROPN
ejpam-776	443	6	de	de	X
ejpam-776	443	7	jeu	jeu	PROPN
ejpam-776	443	8	.	.	PUNCT
ejpam-776	444	1	the	the	DET
ejpam-776	444	2	dunkl	dunkl	PROPN
ejpam-776	444	3	transform	transform	NOUN
ejpam-776	444	4	.	.	PUNCT
ejpam-776	445	1	invent	invent	NOUN
ejpam-776	445	2	.	.	PUNCT
ejpam-776	446	1	math	math	NOUN
ejpam-776	446	2	,	,	PUNCT
ejpam-776	446	3	133:147	133:147	NOUN
ejpam-776	446	4	-	-	PUNCT
ejpam-776	446	5	162	162	NUM
ejpam-776	446	6	,	,	PUNCT
ejpam-776	446	7	1993	1993	NUM
ejpam-776	446	8	.	.	PUNCT
ejpam-776	447	1	[	[	X
ejpam-776	447	2	2	2	NUM
ejpam-776	447	3	]	]	PUNCT
ejpam-776	447	4	m	m	VERB
ejpam-776	447	5	holschneider	holschneider	ADV
ejpam-776	447	6	.	.	PUNCT
ejpam-776	448	1	inverse	inverse	PROPN
ejpam-776	448	2	radon	radon	PROPN
ejpam-776	448	3	transform	transform	VERB
ejpam-776	448	4	through	through	ADP
ejpam-776	448	5	inverse	inverse	NOUN
ejpam-776	448	6	wavelet	wavelet	NOUN
ejpam-776	448	7	transform	transform	NOUN
ejpam-776	448	8	.	.	PUNCT
ejpam-776	449	1	inverse	inverse	NOUN
ejpam-776	449	2	problems	problem	NOUN
ejpam-776	449	3	,	,	PUNCT
ejpam-776	449	4	7:853	7:853	NUM
ejpam-776	449	5	-	-	SYM
ejpam-776	449	6	861	861	NUM
ejpam-776	449	7	,	,	PUNCT
ejpam-776	449	8	1991	1991	NUM
ejpam-776	449	9	.	.	PUNCT
ejpam-776	450	1	references	reference	NOUN
ejpam-776	450	2	979	979	NUM
ejpam-776	450	3	[	[	X
ejpam-776	450	4	3	3	NUM
ejpam-776	450	5	]	]	PUNCT
ejpam-776	450	6	th	th	NUM
ejpam-776	450	7	koornwinder	koornwinder	NOUN
ejpam-776	450	8	.	.	PUNCT
ejpam-776	451	1	the	the	DET
ejpam-776	451	2	continuous	continuous	ADJ
ejpam-776	451	3	wavelet	wavelet	NOUN
ejpam-776	451	4	transform	transform	NOUN
ejpam-776	451	5	.	.	PUNCT
ejpam-776	452	1	wavelets	wavelet	NOUN
ejpam-776	452	2	:	:	PUNCT
ejpam-776	452	3	an	an	DET
ejpam-776	452	4	elementary	elementary	ADJ
ejpam-776	452	5	treatement	treatement	NOUN
ejpam-776	452	6	of	of	ADP
ejpam-776	452	7	theory	theory	NOUN
ejpam-776	452	8	and	and	CCONJ
ejpam-776	452	9	applications	application	NOUN
ejpam-776	452	10	.	.	PUNCT
ejpam-776	453	1	edited	edit	VERB
ejpam-776	453	2	by	by	ADP
ejpam-776	453	3	t.h	t.h	PROPN
ejpam-776	453	4	.	.	PROPN
ejpam-776	453	5	koornwinder	koornwinder	NOUN
ejpam-776	453	6	,	,	PUNCT
ejpam-776	453	7	world	world	NOUN
ejpam-776	453	8	scientific	scientific	ADJ
ejpam-776	453	9	,	,	PUNCT
ejpam-776	453	10	pages	page	NOUN
ejpam-776	453	11	27	27	NUM
ejpam-776	453	12	-	-	SYM
ejpam-776	453	13	48	48	NUM
ejpam-776	453	14	,	,	PUNCT
ejpam-776	453	15	1993	1993	NUM
ejpam-776	453	16	.	.	PUNCT
ejpam-776	454	1	[	[	X
ejpam-776	454	2	4	4	NUM
ejpam-776	454	3	]	]	X
ejpam-776	454	4	l	l	NOUN
ejpam-776	454	5	lapointe	lapointe	NOUN
ejpam-776	454	6	and	and	CCONJ
ejpam-776	454	7	l	l	PROPN
ejpam-776	454	8	vinet	vinet	PROPN
ejpam-776	454	9	.	.	PUNCT
ejpam-776	455	1	exact	exact	ADJ
ejpam-776	455	2	operator	operator	NOUN
ejpam-776	455	3	solution	solution	NOUN
ejpam-776	455	4	of	of	ADP
ejpam-776	455	5	the	the	DET
ejpam-776	455	6	calogero	calogero	PROPN
ejpam-776	455	7	-	-	PUNCT
ejpam-776	455	8	sutherland	sutherland	PROPN
ejpam-776	455	9	model	model	NOUN
ejpam-776	455	10	.	.	PUNCT
ejpam-776	456	1	comm	comm	NOUN
ejpam-776	456	2	.	.	PUNCT
ejpam-776	456	3	math	math	NOUN
ejpam-776	456	4	.	.	PUNCT
ejpam-776	457	1	phys	phy	NOUN
ejpam-776	457	2	.	.	PUNCT
ejpam-776	457	3	,	,	PUNCT
ejpam-776	457	4	178:425	178:425	PROPN
ejpam-776	457	5	-	-	PUNCT
ejpam-776	457	6	452	452	NUM
ejpam-776	457	7	,	,	PUNCT
ejpam-776	457	8	1996	1996	NUM
ejpam-776	457	9	.	.	PUNCT
ejpam-776	458	1	[	[	X
ejpam-776	458	2	5	5	X
ejpam-776	458	3	]	]	PUNCT
ejpam-776	458	4	jl	jl	PROPN
ejpam-776	458	5	lions	lion	NOUN
ejpam-776	458	6	.	.	PUNCT
ejpam-776	459	1	equations	equation	NOUN
ejpam-776	459	2	différentielles	différentielle	VERB
ejpam-776	459	3	opérationnelles	opérationnelle	NOUN
ejpam-776	459	4	et	et	PROPN
ejpam-776	459	5	problèmes	problème	NOUN
ejpam-776	459	6	aux	aux	PROPN
ejpam-776	459	7	limites	limites	PROPN
ejpam-776	459	8	.	.	PROPN
ejpam-776	459	9	springerverlag	springerverlag	PROPN
ejpam-776	459	10	,	,	PUNCT
ejpam-776	459	11	berlin	berlin	PROPN
ejpam-776	459	12	,	,	PUNCT
ejpam-776	459	13	1961	1961	NUM
ejpam-776	459	14	.	.	PUNCT
ejpam-776	460	1	[	[	X
ejpam-776	460	2	6	6	NUM
ejpam-776	460	3	]	]	SYM
ejpam-776	460	4	ma	ma	PROPN
ejpam-776	460	5	mourou	mourou	PROPN
ejpam-776	460	6	and	and	CCONJ
ejpam-776	460	7	k	k	PROPN
ejpam-776	460	8	trimèche	trimèche	NOUN
ejpam-776	460	9	.	.	PUNCT
ejpam-776	461	1	inversion	inversion	NOUN
ejpam-776	461	2	of	of	ADP
ejpam-776	461	3	the	the	DET
ejpam-776	461	4	weyl	weyl	VERB
ejpam-776	461	5	integral	integral	ADJ
ejpam-776	461	6	transform	transform	NOUN
ejpam-776	461	7	and	and	CCONJ
ejpam-776	461	8	the	the	DET
ejpam-776	461	9	radon	radon	PROPN
ejpam-776	461	10	transform	transform	NOUN
ejpam-776	461	11	on	on	ADP
ejpam-776	461	12	rn	rn	NOUN
ejpam-776	461	13	using	use	VERB
ejpam-776	461	14	generalized	generalized	ADJ
ejpam-776	461	15	wavelets	wavelet	NOUN
ejpam-776	461	16	.	.	PUNCT
ejpam-776	462	1	monatshefte	monatshefte	PROPN
ejpam-776	462	2	für	für	PROPN
ejpam-776	462	3	mathematik	mathematik	PROPN
ejpam-776	462	4	,	,	PUNCT
ejpam-776	462	5	126:73	126:73	PROPN
ejpam-776	462	6	-	-	SYM
ejpam-776	462	7	83	83	NUM
ejpam-776	462	8	,	,	PUNCT
ejpam-776	462	9	1998	1998	NUM
ejpam-776	462	10	.	.	PUNCT
ejpam-776	463	1	[	[	X
ejpam-776	463	2	7	7	X
ejpam-776	463	3	]	]	X
ejpam-776	463	4	ma	ma	PROPN
ejpam-776	463	5	mourou	mourou	PROPN
ejpam-776	463	6	and	and	CCONJ
ejpam-776	463	7	k	k	PROPN
ejpam-776	463	8	trimèche	trimèche	PROPN
ejpam-776	463	9	.	.	PUNCT
ejpam-776	464	1	calderon	calderon	PROPN
ejpam-776	464	2	’s	’s	PART
ejpam-776	464	3	formula	formula	NOUN
ejpam-776	464	4	associated	associate	VERB
ejpam-776	464	5	with	with	ADP
ejpam-776	464	6	a	a	DET
ejpam-776	464	7	differential	differential	ADJ
ejpam-776	464	8	operator	operator	NOUN
ejpam-776	464	9	on	on	ADP
ejpam-776	464	10	(	(	PUNCT
ejpam-776	464	11	0,∞	0,∞	NOUN
ejpam-776	464	12	)	)	PUNCT
ejpam-776	464	13	and	and	CCONJ
ejpam-776	464	14	inversion	inversion	NOUN
ejpam-776	464	15	of	of	ADP
ejpam-776	464	16	the	the	DET
ejpam-776	464	17	generalized	generalized	ADJ
ejpam-776	464	18	abel	abel	PROPN
ejpam-776	464	19	transform	transform	NOUN
ejpam-776	464	20	.	.	PUNCT
ejpam-776	465	1	journal	journal	PROPN
ejpam-776	465	2	of	of	ADP
ejpam-776	465	3	fourier	fourier	ADJ
ejpam-776	465	4	analysis	analysis	NOUN
ejpam-776	465	5	and	and	CCONJ
ejpam-776	465	6	applications	application	NOUN
ejpam-776	465	7	,	,	PUNCT
ejpam-776	465	8	4:229	4:229	NOUN
ejpam-776	465	9	-	-	SYM
ejpam-776	465	10	245	245	NUM
ejpam-776	465	11	,	,	PUNCT
ejpam-776	465	12	1998	1998	NUM
ejpam-776	465	13	.	.	PUNCT
ejpam-776	466	1	[	[	X
ejpam-776	466	2	8	8	NUM
ejpam-776	466	3	]	]	X
ejpam-776	466	4	ma	ma	PROPN
ejpam-776	466	5	mourou	mourou	PROPN
ejpam-776	466	6	and	and	CCONJ
ejpam-776	466	7	k	k	PROPN
ejpam-776	466	8	trimèche	trimèche	PROPN
ejpam-776	466	9	.	.	PUNCT
ejpam-776	467	1	transmutation	transmutation	NOUN
ejpam-776	467	2	operators	operator	NOUN
ejpam-776	467	3	and	and	CCONJ
ejpam-776	467	4	paley	paley	ADJ
ejpam-776	467	5	-	-	PUNCT
ejpam-776	467	6	wiener	wiener	NOUN
ejpam-776	467	7	theorem	theorem	NOUN
ejpam-776	467	8	associated	associate	VERB
ejpam-776	467	9	with	with	ADP
ejpam-776	467	10	a	a	DET
ejpam-776	467	11	singular	singular	ADJ
ejpam-776	467	12	differential	differential	ADJ
ejpam-776	467	13	-	-	PUNCT
ejpam-776	467	14	difference	difference	NOUN
ejpam-776	467	15	operator	operator	NOUN
ejpam-776	467	16	on	on	ADP
ejpam-776	467	17	the	the	DET
ejpam-776	467	18	real	real	ADJ
ejpam-776	467	19	line	line	NOUN
ejpam-776	467	20	.	.	PUNCT
ejpam-776	468	1	analysis	analysis	NOUN
ejpam-776	468	2	and	and	CCONJ
ejpam-776	468	3	applications	application	NOUN
ejpam-776	468	4	,	,	PUNCT
ejpam-776	468	5	1:43	1:43	PROPN
ejpam-776	468	6	-	-	SYM
ejpam-776	468	7	69	69	NUM
ejpam-776	468	8	,	,	PUNCT
ejpam-776	468	9	2003	2003	NUM
ejpam-776	468	10	.	.	PUNCT
ejpam-776	469	1	[	[	X
ejpam-776	469	2	9	9	NUM
ejpam-776	469	3	]	]	X
ejpam-776	469	4	ma	ma	PROPN
ejpam-776	469	5	mourou	mourou	PROPN
ejpam-776	469	6	.	.	PUNCT
ejpam-776	470	1	taylor	taylor	PROPN
ejpam-776	470	2	series	series	PROPN
ejpam-776	470	3	associated	associate	VERB
ejpam-776	470	4	with	with	ADP
ejpam-776	470	5	a	a	DET
ejpam-776	470	6	differential	differential	ADJ
ejpam-776	470	7	-	-	PUNCT
ejpam-776	470	8	difference	difference	NOUN
ejpam-776	470	9	operator	operator	NOUN
ejpam-776	470	10	on	on	ADP
ejpam-776	470	11	the	the	DET
ejpam-776	470	12	real	real	ADJ
ejpam-776	470	13	line	line	NOUN
ejpam-776	470	14	.	.	PUNCT
ejpam-776	471	1	journal	journal	NOUN
ejpam-776	471	2	of	of	ADP
ejpam-776	471	3	computational	computational	ADJ
ejpam-776	471	4	and	and	CCONJ
ejpam-776	471	5	applied	applied	ADJ
ejpam-776	471	6	mathematics	mathematic	NOUN
ejpam-776	471	7	,	,	PUNCT
ejpam-776	471	8	153:343	153:343	NOUN
ejpam-776	471	9	-	-	PUNCT
ejpam-776	471	10	354	354	NUM
ejpam-776	471	11	,	,	PUNCT
ejpam-776	471	12	2003	2003	NUM
ejpam-776	471	13	.	.	PUNCT
ejpam-776	472	1	[	[	X
ejpam-776	472	2	10	10	NUM
ejpam-776	472	3	]	]	X
ejpam-776	472	4	ma	ma	PROPN
ejpam-776	472	5	mourou	mourou	PROPN
ejpam-776	472	6	.	.	PUNCT
ejpam-776	473	1	inversion	inversion	NOUN
ejpam-776	473	2	of	of	ADP
ejpam-776	473	3	the	the	DET
ejpam-776	473	4	dual	dual	ADJ
ejpam-776	473	5	dunkl	dunkl	PROPN
ejpam-776	473	6	-	-	PUNCT
ejpam-776	473	7	sonine	sonine	NOUN
ejpam-776	473	8	integral	integral	ADJ
ejpam-776	473	9	transform	transform	NOUN
ejpam-776	473	10	on	on	ADP
ejpam-776	473	11	r	r	NOUN
ejpam-776	473	12	using	use	VERB
ejpam-776	473	13	dunkl	dunkl	NOUN
ejpam-776	473	14	wavelets	wavelet	NOUN
ejpam-776	473	15	.	.	PUNCT
ejpam-776	474	1	sigma	sigma	PROPN
ejpam-776	474	2	,	,	PUNCT
ejpam-776	474	3	5:1	5:1	NUM
ejpam-776	474	4	-	-	SYM
ejpam-776	474	5	12	12	NUM
ejpam-776	474	6	,	,	PUNCT
ejpam-776	474	7	2009	2009	NUM
ejpam-776	474	8	.	.	PUNCT
ejpam-776	475	1	[	[	X
ejpam-776	475	2	11	11	NUM
ejpam-776	475	3	]	]	PUNCT
ejpam-776	475	4	m	m	NOUN
ejpam-776	475	5	rösler	rösler	NOUN
ejpam-776	475	6	.	.	PUNCT
ejpam-776	476	1	positivity	positivity	NOUN
ejpam-776	476	2	of	of	ADP
ejpam-776	476	3	dunkl	dunkl	PROPN
ejpam-776	476	4	’s	’s	PART
ejpam-776	476	5	intertwining	intertwine	VERB
ejpam-776	476	6	operator	operator	NOUN
ejpam-776	476	7	.	.	PUNCT
ejpam-776	477	1	duke	duke	PROPN
ejpam-776	477	2	math	math	PROPN
ejpam-776	477	3	.	.	PUNCT
ejpam-776	478	1	j.	j.	PROPN
ejpam-776	478	2	,	,	PUNCT
ejpam-776	478	3	98:445	98:445	NUM
ejpam-776	478	4	-	-	SYM
ejpam-776	478	5	463	463	NUM
ejpam-776	478	6	,	,	PUNCT
ejpam-776	478	7	1999	1999	NUM
ejpam-776	478	8	.	.	PUNCT
ejpam-776	479	1	[	[	X
ejpam-776	479	2	12	12	NUM
ejpam-776	479	3	]	]	X
ejpam-776	479	4	m	m	NOUN
ejpam-776	479	5	rösler	rösler	NOUN
ejpam-776	479	6	.	.	PUNCT
ejpam-776	480	1	generalized	generalize	VERB
ejpam-776	480	2	hermite	hermite	ADJ
ejpam-776	480	3	polynomials	polynomial	NOUN
ejpam-776	480	4	and	and	CCONJ
ejpam-776	480	5	the	the	DET
ejpam-776	480	6	heat	heat	NOUN
ejpam-776	480	7	equation	equation	NOUN
ejpam-776	480	8	for	for	ADP
ejpam-776	480	9	dunkl	dunkl	PROPN
ejpam-776	480	10	operators	operator	NOUN
ejpam-776	480	11	.	.	PUNCT
ejpam-776	481	1	comm	comm	NOUN
ejpam-776	481	2	.	.	PUNCT
ejpam-776	481	3	math	math	NOUN
ejpam-776	481	4	.	.	PUNCT
ejpam-776	482	1	phys	phy	NOUN
ejpam-776	482	2	.	.	PUNCT
ejpam-776	482	3	,	,	PUNCT
ejpam-776	482	4	192:519	192:519	PROPN
ejpam-776	482	5	-	-	SYM
ejpam-776	482	6	542	542	NUM
ejpam-776	482	7	,	,	PUNCT
ejpam-776	482	8	1998	1998	NUM
ejpam-776	482	9	.	.	PUNCT
ejpam-776	483	1	[	[	X
ejpam-776	483	2	13	13	NUM
ejpam-776	483	3	]	]	X
ejpam-776	483	4	k	k	PROPN
ejpam-776	483	5	trimèche	trimèche	NOUN
ejpam-776	483	6	.	.	PUNCT
ejpam-776	484	1	inversion	inversion	NOUN
ejpam-776	484	2	of	of	ADP
ejpam-776	484	3	the	the	DET
ejpam-776	484	4	lions	lion	NOUN
ejpam-776	484	5	transmutation	transmutation	NOUN
ejpam-776	484	6	operators	operator	NOUN
ejpam-776	484	7	using	use	VERB
ejpam-776	484	8	generalized	generalized	ADJ
ejpam-776	484	9	wavelets	wavelet	NOUN
ejpam-776	484	10	.	.	PUNCT
ejpam-776	485	1	appl	appl	PROPN
ejpam-776	485	2	.	.	PUNCT
ejpam-776	486	1	and	and	CCONJ
ejpam-776	486	2	comput	comput	NOUN
ejpam-776	486	3	.	.	PUNCT
ejpam-776	487	1	harm	harm	NOUN
ejpam-776	487	2	.	.	PUNCT
ejpam-776	488	1	anal	anal	ADJ
ejpam-776	488	2	.	.	PROPN
ejpam-776	488	3	,	,	PUNCT
ejpam-776	488	4	4:97	4:97	NUM
ejpam-776	488	5	-	-	SYM
ejpam-776	488	6	112	112	NUM
ejpam-776	488	7	,	,	PUNCT
ejpam-776	488	8	1997	1997	NUM
ejpam-776	488	9	.	.	PUNCT
ejpam-776	489	1	[	[	X
ejpam-776	489	2	14	14	NUM
ejpam-776	489	3	]	]	X
ejpam-776	489	4	k	k	PROPN
ejpam-776	489	5	trimèche	trimèche	PROPN
ejpam-776	489	6	.	.	PUNCT
ejpam-776	490	1	transformation	transformation	NOUN
ejpam-776	490	2	intégrale	intégrale	PROPN
ejpam-776	490	3	de	de	X
ejpam-776	490	4	weyl	weyl	X
ejpam-776	490	5	et	et	PROPN
ejpam-776	490	6	théorème	théorème	PROPN
ejpam-776	490	7	de	de	X
ejpam-776	490	8	paley	paley	PROPN
ejpam-776	490	9	-	-	PUNCT
ejpam-776	490	10	wiener	wiener	NOUN
ejpam-776	490	11	associés	associé	NOUN
ejpam-776	490	12	àun	àun	VERB
ejpam-776	490	13	opérateur	opérateur	PROPN
ejpam-776	490	14	différentiel	différentiel	PROPN
ejpam-776	490	15	singulier	singulier	PROPN
ejpam-776	490	16	sur	sur	PROPN
ejpam-776	491	1	[	[	X
ejpam-776	491	2	0,+∞	0,+∞	PROPN
ejpam-776	491	3	[	[	X
ejpam-776	491	4	.	.	PUNCT
ejpam-776	491	5	j.	j.	PROPN
ejpam-776	491	6	math	math	PROPN
ejpam-776	491	7	.	.	PUNCT
ejpam-776	492	1	pures	pure	NOUN
ejpam-776	492	2	appl	appl	PROPN
ejpam-776	492	3	.	.	PROPN
ejpam-776	492	4	,	,	PUNCT
ejpam-776	492	5	60:51	60:51	NUM
ejpam-776	492	6	-	-	SYM
ejpam-776	492	7	98	98	NUM
ejpam-776	492	8	,	,	PUNCT
ejpam-776	492	9	1981	1981	NUM
ejpam-776	492	10	.	.	PUNCT
ejpam-776	493	1	[	[	X
ejpam-776	493	2	15	15	NUM
ejpam-776	493	3	]	]	X
ejpam-776	493	4	k	k	PROPN
ejpam-776	493	5	trimèche	trimèche	PROPN
ejpam-776	493	6	.	.	PUNCT
ejpam-776	494	1	generalized	generalized	ADJ
ejpam-776	494	2	wavelets	wavelet	NOUN
ejpam-776	494	3	and	and	CCONJ
ejpam-776	494	4	hypergroups	hypergroup	NOUN
ejpam-776	494	5	.	.	PUNCT
ejpam-776	495	1	gordon	gordon	PROPN
ejpam-776	495	2	and	and	CCONJ
ejpam-776	495	3	breach	breach	VERB
ejpam-776	495	4	publishing	publishing	NOUN
ejpam-776	495	5	group	group	NOUN
ejpam-776	495	6	,	,	PUNCT
ejpam-776	495	7	1997	1997	NUM
ejpam-776	495	8	.	.	PUNCT
ejpam-776	496	1	[	[	X
ejpam-776	496	2	16	16	NUM
ejpam-776	496	3	]	]	X
ejpam-776	496	4	y	y	PROPN
ejpam-776	496	5	xu	xu	PROPN
ejpam-776	496	6	.	.	PUNCT
ejpam-776	497	1	intertwining	intertwine	VERB
ejpam-776	497	2	operator	operator	NOUN
ejpam-776	497	3	and	and	CCONJ
ejpam-776	497	4	h	h	NOUN
ejpam-776	497	5	-	-	PUNCT
ejpam-776	497	6	harmonics	harmonic	NOUN
ejpam-776	497	7	associated	associate	VERB
ejpam-776	497	8	with	with	ADP
ejpam-776	497	9	reflection	reflection	NOUN
ejpam-776	497	10	groups	group	NOUN
ejpam-776	497	11	.	.	PUNCT
ejpam-776	498	1	canad	canad	PROPN
ejpam-776	498	2	.	.	PUNCT
ejpam-776	499	1	j.	j.	PROPN
ejpam-776	499	2	math	math	PROPN
ejpam-776	499	3	.	.	PROPN
ejpam-776	499	4	,	,	PUNCT
ejpam-776	499	5	50:193	50:193	NUM
ejpam-776	499	6	-	-	SYM
ejpam-776	499	7	209	209	NUM
ejpam-776	499	8	,	,	PUNCT
ejpam-776	499	9	1998	1998	NUM
ejpam-776	499	10	.	.	PUNCT