id	sid	tid	token	lemma	pos
ejpam-5735	1	1	european	european	PROPN
ejpam-5735	1	2	journal	journal	PROPN
ejpam-5735	1	3	of	of	ADP
ejpam-5735	1	4	pure	pure	ADJ
ejpam-5735	1	5	and	and	CCONJ
ejpam-5735	1	6	applied	applied	ADJ
ejpam-5735	1	7	mathematics	mathematic	NOUN
ejpam-5735	1	8	2025	2025	NUM
ejpam-5735	1	9	,	,	PUNCT
ejpam-5735	1	10	vol	vol	NOUN
ejpam-5735	1	11	.	.	PROPN
ejpam-5735	1	12	18	18	NUM
ejpam-5735	1	13	,	,	PUNCT
ejpam-5735	1	14	issue	issue	NOUN
ejpam-5735	1	15	1	1	NUM
ejpam-5735	1	16	,	,	PUNCT
ejpam-5735	1	17	article	article	NOUN
ejpam-5735	1	18	number	number	NOUN
ejpam-5735	1	19	5735	5735	NUM
ejpam-5735	1	20	issn	issn	PROPN
ejpam-5735	1	21	1307	1307	NUM
ejpam-5735	1	22	-	-	SYM
ejpam-5735	1	23	5543	5543	NUM
ejpam-5735	1	24	–	–	PUNCT
ejpam-5735	1	25	ejpam.com	ejpam.com	X
ejpam-5735	1	26	published	publish	VERB
ejpam-5735	1	27	by	by	ADP
ejpam-5735	1	28	new	new	PROPN
ejpam-5735	1	29	york	york	PROPN
ejpam-5735	1	30	business	business	PROPN
ejpam-5735	1	31	global	global	ADJ
ejpam-5735	1	32	note	note	NOUN
ejpam-5735	1	33	on	on	ADP
ejpam-5735	1	34	the	the	DET
ejpam-5735	1	35	affine	affine	NOUN
ejpam-5735	1	36	group	group	PROPN
ejpam-5735	1	37	representations	representation	VERB
ejpam-5735	1	38	amjad	amjad	PROPN
ejpam-5735	1	39	saleh	saleh	PROPN
ejpam-5735	1	40	alghamdi1,∗	alghamdi1,∗	PROPN
ejpam-5735	1	41	,	,	PUNCT
ejpam-5735	1	42	taghreed	taghreed	NOUN
ejpam-5735	1	43	alqurashi2	alqurashi2	NOUN
ejpam-5735	1	44	1	1	NUM
ejpam-5735	1	45	department	department	NOUN
ejpam-5735	1	46	of	of	ADP
ejpam-5735	1	47	mathematics	mathematic	NOUN
ejpam-5735	1	48	,	,	PUNCT
ejpam-5735	1	49	umm	umm	INTJ
ejpam-5735	1	50	al	al	PROPN
ejpam-5735	1	51	-	-	PUNCT
ejpam-5735	1	52	qura	qura	PROPN
ejpam-5735	1	53	university	university	PROPN
ejpam-5735	1	54	,	,	PUNCT
ejpam-5735	1	55	makkah	makkah	PROPN
ejpam-5735	1	56	,	,	PUNCT
ejpam-5735	1	57	saudi	saudi	PROPN
ejpam-5735	1	58	arabia	arabia	PROPN
ejpam-5735	1	59	2	2	NUM
ejpam-5735	1	60	department	department	NOUN
ejpam-5735	1	61	of	of	ADP
ejpam-5735	1	62	mathematics	mathematics	PROPN
ejpam-5735	1	63	,	,	PUNCT
ejpam-5735	1	64	al	al	PROPN
ejpam-5735	1	65	-	-	PUNCT
ejpam-5735	1	66	baha	baha	PROPN
ejpam-5735	1	67	university	university	PROPN
ejpam-5735	1	68	,	,	PUNCT
ejpam-5735	1	69	albaha	albaha	PROPN
ejpam-5735	1	70	,	,	PUNCT
ejpam-5735	1	71	saudi	saudi	PROPN
ejpam-5735	1	72	arabia	arabia	PROPN
ejpam-5735	1	73	abstract	abstract	NOUN
ejpam-5735	1	74	.	.	PUNCT
ejpam-5735	2	1	the	the	DET
ejpam-5735	2	2	representation	representation	NOUN
ejpam-5735	2	3	of	of	ADP
ejpam-5735	2	4	the	the	DET
ejpam-5735	2	5	affine	affine	NOUN
ejpam-5735	2	6	group	group	NOUN
ejpam-5735	2	7	is	be	AUX
ejpam-5735	2	8	a	a	DET
ejpam-5735	2	9	crucial	crucial	ADJ
ejpam-5735	2	10	topic	topic	NOUN
ejpam-5735	2	11	in	in	ADP
ejpam-5735	2	12	harmonic	harmonic	ADJ
ejpam-5735	2	13	analysis	analysis	NOUN
ejpam-5735	2	14	.	.	PUNCT
ejpam-5735	3	1	in	in	ADP
ejpam-5735	3	2	this	this	DET
ejpam-5735	3	3	paper	paper	NOUN
ejpam-5735	3	4	,	,	PUNCT
ejpam-5735	3	5	we	we	PRON
ejpam-5735	3	6	use	use	VERB
ejpam-5735	3	7	the	the	DET
ejpam-5735	3	8	wavelet	wavelet	NOUN
ejpam-5735	3	9	transform	transform	NOUN
ejpam-5735	3	10	to	to	PART
ejpam-5735	3	11	investigate	investigate	VERB
ejpam-5735	3	12	the	the	DET
ejpam-5735	3	13	intertwining	intertwine	VERB
ejpam-5735	3	14	operator	operator	NOUN
ejpam-5735	3	15	.	.	PUNCT
ejpam-5735	4	1	this	this	DET
ejpam-5735	4	2	approach	approach	NOUN
ejpam-5735	4	3	helps	help	VERB
ejpam-5735	4	4	to	to	PART
ejpam-5735	4	5	compare	compare	VERB
ejpam-5735	4	6	different	different	ADJ
ejpam-5735	4	7	unitary	unitary	ADJ
ejpam-5735	4	8	representations	representation	NOUN
ejpam-5735	4	9	of	of	ADP
ejpam-5735	4	10	the	the	DET
ejpam-5735	4	11	affine	affine	NOUN
ejpam-5735	4	12	group	group	NOUN
ejpam-5735	4	13	.	.	PUNCT
ejpam-5735	5	1	2020	2020	NUM
ejpam-5735	5	2	mathematics	mathematics	PROPN
ejpam-5735	5	3	subject	subject	NOUN
ejpam-5735	5	4	classifications	classification	NOUN
ejpam-5735	5	5	:	:	PUNCT
ejpam-5735	5	6	22d10	22d10	NUM
ejpam-5735	5	7	,	,	PUNCT
ejpam-5735	5	8	43a32	43a32	NUM
ejpam-5735	5	9	,	,	PUNCT
ejpam-5735	5	10	22e46	22e46	NUM
ejpam-5735	5	11	,	,	PUNCT
ejpam-5735	5	12	42c40	42c40	NUM
ejpam-5735	5	13	,	,	PUNCT
ejpam-5735	5	14	44a10	44a10	NUM
ejpam-5735	5	15	key	key	ADJ
ejpam-5735	5	16	words	word	NOUN
ejpam-5735	5	17	and	and	CCONJ
ejpam-5735	5	18	phrases	phrase	NOUN
ejpam-5735	5	19	:	:	PUNCT
ejpam-5735	5	20	affine	affine	NOUN
ejpam-5735	5	21	group	group	NOUN
ejpam-5735	5	22	,	,	PUNCT
ejpam-5735	5	23	intertwining	intertwine	VERB
ejpam-5735	5	24	operator	operator	NOUN
ejpam-5735	5	25	,	,	PUNCT
ejpam-5735	5	26	unitary	unitary	ADJ
ejpam-5735	5	27	representations	representation	NOUN
ejpam-5735	5	28	,	,	PUNCT
ejpam-5735	5	29	wavelet	wavelet	NOUN
ejpam-5735	5	30	transform	transform	NOUN
ejpam-5735	5	31	,	,	PUNCT
ejpam-5735	5	32	poisson	poisson	PROPN
ejpam-5735	5	33	integral	integral	ADJ
ejpam-5735	5	34	,	,	PUNCT
ejpam-5735	5	35	laplace	laplace	NOUN
ejpam-5735	5	36	transform	transform	VERB
ejpam-5735	5	37	1	1	NUM
ejpam-5735	5	38	.	.	PUNCT
ejpam-5735	6	1	introduction	introduction	NOUN
ejpam-5735	6	2	the	the	DET
ejpam-5735	6	3	affine	affine	NOUN
ejpam-5735	6	4	group	group	NOUN
ejpam-5735	6	5	is	be	AUX
ejpam-5735	6	6	a	a	DET
ejpam-5735	6	7	non	non	ADJ
ejpam-5735	6	8	-	-	ADJ
ejpam-5735	6	9	commutative	commutative	ADJ
ejpam-5735	6	10	,	,	PUNCT
ejpam-5735	6	11	locally	locally	ADV
ejpam-5735	6	12	compact	compact	ADJ
ejpam-5735	6	13	lie	lie	NOUN
ejpam-5735	6	14	group	group	NOUN
ejpam-5735	6	15	of	of	ADP
ejpam-5735	6	16	the	the	DET
ejpam-5735	6	17	smallest	small	ADJ
ejpam-5735	6	18	dimensionality	dimensionality	NOUN
ejpam-5735	6	19	,	,	PUNCT
ejpam-5735	6	20	and	and	CCONJ
ejpam-5735	6	21	it	it	PRON
ejpam-5735	6	22	is	be	AUX
ejpam-5735	6	23	often	often	ADV
ejpam-5735	6	24	used	use	VERB
ejpam-5735	6	25	to	to	PART
ejpam-5735	6	26	build	build	VERB
ejpam-5735	6	27	wavelets	wavelet	NOUN
ejpam-5735	6	28	.	.	PUNCT
ejpam-5735	7	1	gelfand	gelfand	PROPN
ejpam-5735	7	2	and	and	CCONJ
ejpam-5735	7	3	naimark[7	naimark[7	NOUN
ejpam-5735	7	4	]	]	PUNCT
ejpam-5735	7	5	initially	initially	ADV
ejpam-5735	7	6	introduced	introduce	VERB
ejpam-5735	7	7	the	the	DET
ejpam-5735	7	8	unitary	unitary	ADJ
ejpam-5735	7	9	representations	representation	NOUN
ejpam-5735	7	10	of	of	ADP
ejpam-5735	7	11	the	the	DET
ejpam-5735	7	12	affine	affine	NOUN
ejpam-5735	7	13	group	group	NOUN
ejpam-5735	7	14	.	.	PUNCT
ejpam-5735	8	1	the	the	DET
ejpam-5735	8	2	induced	induce	VERB
ejpam-5735	8	3	representations	representation	NOUN
ejpam-5735	8	4	of	of	ADP
ejpam-5735	8	5	the	the	DET
ejpam-5735	8	6	affine	affine	NOUN
ejpam-5735	8	7	group	group	NOUN
ejpam-5735	8	8	from	from	ADP
ejpam-5735	8	9	a	a	DET
ejpam-5735	8	10	complex	complex	ADJ
ejpam-5735	8	11	character	character	NOUN
ejpam-5735	8	12	was	be	AUX
ejpam-5735	8	13	explained	explain	VERB
ejpam-5735	8	14	in	in	ADP
ejpam-5735	8	15	[	[	X
ejpam-5735	8	16	4	4	NUM
ejpam-5735	8	17	,	,	PUNCT
ejpam-5735	8	18	5	5	NUM
ejpam-5735	8	19	]	]	PUNCT
ejpam-5735	8	20	.	.	PUNCT
ejpam-5735	9	1	moreover	moreover	ADV
ejpam-5735	9	2	,	,	PUNCT
ejpam-5735	9	3	in	in	ADP
ejpam-5735	9	4	[	[	X
ejpam-5735	9	5	4	4	X
ejpam-5735	9	6	]	]	PUNCT
ejpam-5735	9	7	they	they	PRON
ejpam-5735	9	8	described	describe	VERB
ejpam-5735	9	9	the	the	DET
ejpam-5735	9	10	intertwining	intertwine	VERB
ejpam-5735	9	11	operators	operator	NOUN
ejpam-5735	9	12	related	relate	VERB
ejpam-5735	9	13	to	to	ADP
ejpam-5735	9	14	hilbert	hilbert	NOUN
ejpam-5735	9	15	spaces	space	NOUN
ejpam-5735	9	16	in	in	ADP
ejpam-5735	9	17	terms	term	NOUN
ejpam-5735	9	18	of	of	ADP
ejpam-5735	9	19	representations	representation	NOUN
ejpam-5735	9	20	of	of	ADP
ejpam-5735	9	21	the	the	DET
ejpam-5735	9	22	affine	affine	NOUN
ejpam-5735	9	23	group	group	NOUN
ejpam-5735	9	24	.	.	PUNCT
ejpam-5735	10	1	in	in	ADP
ejpam-5735	10	2	this	this	DET
ejpam-5735	10	3	paper	paper	NOUN
ejpam-5735	10	4	,	,	PUNCT
ejpam-5735	10	5	we	we	PRON
ejpam-5735	10	6	will	will	AUX
ejpam-5735	10	7	illustrate	illustrate	VERB
ejpam-5735	10	8	the	the	DET
ejpam-5735	10	9	intertwining	intertwine	VERB
ejpam-5735	10	10	operators	operator	NOUN
ejpam-5735	10	11	between	between	ADP
ejpam-5735	10	12	all	all	DET
ejpam-5735	10	13	three	three	NUM
ejpam-5735	10	14	affine	affine	NOUN
ejpam-5735	10	15	representations	representation	NOUN
ejpam-5735	10	16	as	as	SCONJ
ejpam-5735	10	17	follows	follow	VERB
ejpam-5735	10	18	:	:	PUNCT
ejpam-5735	10	19	•	•	ADP
ejpam-5735	10	20	the	the	DET
ejpam-5735	10	21	poisson	poisson	NOUN
ejpam-5735	10	22	integral	integral	ADJ
ejpam-5735	10	23	between	between	ADP
ejpam-5735	10	24	the	the	DET
ejpam-5735	10	25	quasi	quasi	ADJ
ejpam-5735	10	26	-	-	ADJ
ejpam-5735	10	27	regular	regular	ADJ
ejpam-5735	10	28	representation	representation	NOUN
ejpam-5735	10	29	on	on	ADP
ejpam-5735	10	30	h2(r	h2(r	PROPN
ejpam-5735	10	31	)	)	PUNCT
ejpam-5735	10	32	and	and	CCONJ
ejpam-5735	10	33	the	the	DET
ejpam-5735	10	34	left	left	ADJ
ejpam-5735	10	35	regular	regular	ADJ
ejpam-5735	10	36	representation	representation	NOUN
ejpam-5735	10	37	on	on	ADP
ejpam-5735	10	38	l2(aff	l2(aff	ADJ
ejpam-5735	10	39	,	,	PUNCT
ejpam-5735	10	40	dν	dν	NOUN
ejpam-5735	10	41	)	)	PUNCT
ejpam-5735	10	42	.	.	PUNCT
ejpam-5735	11	1	•	•	NOUN
ejpam-5735	11	2	the	the	DET
ejpam-5735	11	3	laplace	laplace	NOUN
ejpam-5735	11	4	transform	transform	NOUN
ejpam-5735	11	5	between	between	ADP
ejpam-5735	11	6	the	the	DET
ejpam-5735	11	7	co	co	ADJ
ejpam-5735	11	8	-	-	ADJ
ejpam-5735	11	9	adjoint	adjoint	ADJ
ejpam-5735	11	10	representation	representation	NOUN
ejpam-5735	11	11	on	on	ADP
ejpam-5735	11	12	l2(r+	l2(r+	PROPN
ejpam-5735	11	13	)	)	PUNCT
ejpam-5735	11	14	and	and	CCONJ
ejpam-5735	11	15	the	the	DET
ejpam-5735	11	16	left	left	ADJ
ejpam-5735	11	17	regular	regular	ADJ
ejpam-5735	11	18	representation	representation	NOUN
ejpam-5735	11	19	on	on	ADP
ejpam-5735	11	20	l2(aff	l2(aff	ADJ
ejpam-5735	11	21	,	,	PUNCT
ejpam-5735	11	22	dν	dν	NOUN
ejpam-5735	11	23	)	)	PUNCT
ejpam-5735	11	24	.	.	PUNCT
ejpam-5735	12	1	•	•	NOUN
ejpam-5735	12	2	the	the	DET
ejpam-5735	12	3	fourier	fourier	NOUN
ejpam-5735	12	4	transform	transform	NOUN
ejpam-5735	12	5	between	between	ADP
ejpam-5735	12	6	the	the	DET
ejpam-5735	12	7	quasi	quasi	ADJ
ejpam-5735	12	8	-	-	ADJ
ejpam-5735	12	9	regular	regular	ADJ
ejpam-5735	12	10	representation	representation	NOUN
ejpam-5735	12	11	on	on	ADP
ejpam-5735	12	12	h2(r	h2(r	PROPN
ejpam-5735	12	13	)	)	PUNCT
ejpam-5735	12	14	and	and	CCONJ
ejpam-5735	12	15	the	the	DET
ejpam-5735	12	16	co	co	ADJ
ejpam-5735	12	17	-	-	ADJ
ejpam-5735	12	18	adjoint	adjoint	ADJ
ejpam-5735	12	19	representation	representation	NOUN
ejpam-5735	12	20	on	on	ADP
ejpam-5735	12	21	l2(r+	l2(r+	PROPN
ejpam-5735	12	22	)	)	PUNCT
ejpam-5735	12	23	.	.	PUNCT
ejpam-5735	13	1	∗corresponding	∗corresponde	VERB
ejpam-5735	13	2	author	author	NOUN
ejpam-5735	13	3	.	.	PUNCT
ejpam-5735	14	1	doi	doi	NOUN
ejpam-5735	14	2	:	:	PUNCT
ejpam-5735	14	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5735	https://doi.org/10.29020/nybg.ejpam.v18i1.5735	NUM
ejpam-5735	14	4	email	email	NOUN
ejpam-5735	14	5	addresses	address	NOUN
ejpam-5735	14	6	:	:	PUNCT
ejpam-5735	14	7	asmghamdi@uqu.edu.sa	asmghamdi@uqu.edu.sa	PROPN
ejpam-5735	14	8	(	(	PUNCT
ejpam-5735	14	9	a.	a.	NOUN
ejpam-5735	14	10	alghamdi	alghamdi	PROPN
ejpam-5735	14	11	)	)	PUNCT
ejpam-5735	14	12	,	,	PUNCT
ejpam-5735	14	13	talqorashi@bu.edu.sa	talqorashi@bu.edu.sa	PROPN
ejpam-5735	14	14	(	(	PUNCT
ejpam-5735	14	15	t.	t.	PROPN
ejpam-5735	14	16	alqurashi	alqurashi	PROPN
ejpam-5735	14	17	)	)	PUNCT
ejpam-5735	14	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5735	15	1	1	1	NUM
ejpam-5735	15	2	copyright	copyright	NOUN
ejpam-5735	15	3	:	:	PUNCT
ejpam-5735	15	4	©	©	PROPN
ejpam-5735	15	5	2025	2025	NUM
ejpam-5735	15	6	the	the	DET
ejpam-5735	15	7	author(s	author(s	NOUN
ejpam-5735	15	8	)	)	PUNCT
ejpam-5735	15	9	.	.	PUNCT
ejpam-5735	16	1	(	(	PUNCT
ejpam-5735	16	2	cc	cc	NOUN
ejpam-5735	16	3	by	by	ADP
ejpam-5735	16	4	-	-	PUNCT
ejpam-5735	16	5	nc	nc	PROPN
ejpam-5735	16	6	4.0	4.0	NUM
ejpam-5735	16	7	)	)	PUNCT
ejpam-5735	16	8	a.	a.	NOUN
ejpam-5735	16	9	alghamdi	alghamdi	NOUN
ejpam-5735	16	10	,	,	PUNCT
ejpam-5735	16	11	t.	t.	PROPN
ejpam-5735	16	12	alqurashi	alqurashi	PROPN
ejpam-5735	16	13	/	/	SYM
ejpam-5735	16	14	eur	eur	PROPN
ejpam-5735	16	15	.	.	PUNCT
ejpam-5735	17	1	j.	j.	PROPN
ejpam-5735	17	2	pure	pure	PROPN
ejpam-5735	17	3	appl	appl	PROPN
ejpam-5735	17	4	.	.	PROPN
ejpam-5735	17	5	math	math	PROPN
ejpam-5735	17	6	,	,	PUNCT
ejpam-5735	17	7	18	18	NUM
ejpam-5735	17	8	(	(	PUNCT
ejpam-5735	17	9	1	1	NUM
ejpam-5735	17	10	)	)	PUNCT
ejpam-5735	17	11	(	(	PUNCT
ejpam-5735	17	12	2025	2025	NUM
ejpam-5735	17	13	)	)	PUNCT
ejpam-5735	17	14	,	,	PUNCT
ejpam-5735	17	15	5735	5735	NUM
ejpam-5735	17	16	2	2	NUM
ejpam-5735	17	17	of	of	ADP
ejpam-5735	17	18	7	7	NUM
ejpam-5735	17	19	2	2	NUM
ejpam-5735	17	20	.	.	PUNCT
ejpam-5735	18	1	the	the	DET
ejpam-5735	18	2	affine	affine	NOUN
ejpam-5735	18	3	group	group	NOUN
ejpam-5735	18	4	an	an	DET
ejpam-5735	18	5	element	element	NOUN
ejpam-5735	18	6	of	of	ADP
ejpam-5735	18	7	the	the	DET
ejpam-5735	18	8	affine	affine	NOUN
ejpam-5735	18	9	group	group	NOUN
ejpam-5735	18	10	aff	aff	PROPN
ejpam-5735	19	1	[	[	X
ejpam-5735	19	2	4	4	NUM
ejpam-5735	19	3	,	,	PUNCT
ejpam-5735	19	4	5	5	NUM
ejpam-5735	19	5	]	]	PUNCT
ejpam-5735	19	6	is	be	AUX
ejpam-5735	19	7	denoted	denote	VERB
ejpam-5735	19	8	by	by	ADP
ejpam-5735	19	9	(	(	PUNCT
ejpam-5735	19	10	a	a	DET
ejpam-5735	19	11	,	,	PUNCT
ejpam-5735	19	12	b	b	NOUN
ejpam-5735	19	13	)	)	PUNCT
ejpam-5735	19	14	,	,	PUNCT
ejpam-5735	19	15	where	where	SCONJ
ejpam-5735	19	16	a	a	DET
ejpam-5735	19	17	∈	∈	NOUN
ejpam-5735	19	18	r+	r+	NOUN
ejpam-5735	19	19	and	and	CCONJ
ejpam-5735	19	20	b	b	X
ejpam-5735	19	21	∈	∈	PROPN
ejpam-5735	19	22	r.	r.	PROPN
ejpam-5735	19	23	the	the	DET
ejpam-5735	19	24	group	group	PROPN
ejpam-5735	19	25	operation	operation	NOUN
ejpam-5735	19	26	on	on	ADP
ejpam-5735	19	27	aff	aff	PROPN
ejpam-5735	19	28	is	be	AUX
ejpam-5735	19	29	defined	define	VERB
ejpam-5735	19	30	by	by	ADP
ejpam-5735	19	31	(	(	PUNCT
ejpam-5735	19	32	a	a	DET
ejpam-5735	19	33	,	,	PUNCT
ejpam-5735	19	34	b	b	NOUN
ejpam-5735	19	35	)	)	PUNCT
ejpam-5735	19	36	∗	∗	NOUN
ejpam-5735	19	37	(	(	PUNCT
ejpam-5735	19	38	a′	a′	PROPN
ejpam-5735	19	39	,	,	PUNCT
ejpam-5735	19	40	b′	b′	NUM
ejpam-5735	19	41	)	)	PUNCT
ejpam-5735	20	1	=	=	SYM
ejpam-5735	20	2	(	(	PUNCT
ejpam-5735	20	3	aa′	aa′	INTJ
ejpam-5735	20	4	,	,	PUNCT
ejpam-5735	20	5	ab′	ab′	NOUN
ejpam-5735	20	6	+	+	CCONJ
ejpam-5735	20	7	b	b	NOUN
ejpam-5735	20	8	)	)	PUNCT
ejpam-5735	20	9	,	,	PUNCT
ejpam-5735	20	10	(	(	PUNCT
ejpam-5735	20	11	1	1	X
ejpam-5735	20	12	)	)	PUNCT
ejpam-5735	21	1	where	where	SCONJ
ejpam-5735	21	2	e	e	NOUN
ejpam-5735	21	3	=	=	SYM
ejpam-5735	21	4	(	(	PUNCT
ejpam-5735	21	5	1	1	NUM
ejpam-5735	21	6	,	,	PUNCT
ejpam-5735	21	7	0	0	NUM
ejpam-5735	21	8	)	)	PUNCT
ejpam-5735	21	9	is	be	AUX
ejpam-5735	21	10	the	the	DET
ejpam-5735	21	11	identity	identity	NOUN
ejpam-5735	21	12	element	element	NOUN
ejpam-5735	21	13	and	and	CCONJ
ejpam-5735	21	14	the	the	DET
ejpam-5735	21	15	inverse	inverse	NOUN
ejpam-5735	21	16	of	of	ADP
ejpam-5735	21	17	(	(	PUNCT
ejpam-5735	21	18	a	a	DET
ejpam-5735	21	19	,	,	PUNCT
ejpam-5735	21	20	b	b	NOUN
ejpam-5735	21	21	)	)	PUNCT
ejpam-5735	21	22	is	be	AUX
ejpam-5735	21	23	given	give	VERB
ejpam-5735	21	24	by	by	ADP
ejpam-5735	21	25	(	(	PUNCT
ejpam-5735	21	26	a	a	DET
ejpam-5735	21	27	,	,	PUNCT
ejpam-5735	21	28	b)−1	b)−1	NOUN
ejpam-5735	21	29	=	=	SYM
ejpam-5735	21	30	(	(	PUNCT
ejpam-5735	21	31	a−1,−ba−1	a−1,−ba−1	X
ejpam-5735	21	32	)	)	PUNCT
ejpam-5735	21	33	.	.	PUNCT
ejpam-5735	22	1	we	we	PRON
ejpam-5735	22	2	can	can	AUX
ejpam-5735	22	3	decompose	decompose	VERB
ejpam-5735	22	4	the	the	DET
ejpam-5735	22	5	affine	affine	NOUN
ejpam-5735	22	6	group	group	NOUN
ejpam-5735	22	7	as	as	ADP
ejpam-5735	22	8	a	a	DET
ejpam-5735	22	9	semi	semi	ADJ
ejpam-5735	22	10	-	-	ADJ
ejpam-5735	22	11	direct	direct	ADJ
ejpam-5735	22	12	product	product	NOUN
ejpam-5735	22	13	aff	aff	NOUN
ejpam-5735	22	14	=	=	SYM
ejpam-5735	22	15	a⋉n	a⋉n	PROPN
ejpam-5735	22	16	.	.	PUNCT
ejpam-5735	23	1	the	the	DET
ejpam-5735	23	2	subgroup	subgroup	NOUN
ejpam-5735	23	3	n	n	CCONJ
ejpam-5735	23	4	,	,	PUNCT
ejpam-5735	23	5	defined	define	VERB
ejpam-5735	23	6	by	by	ADP
ejpam-5735	23	7	{	{	PUNCT
ejpam-5735	23	8	(	(	PUNCT
ejpam-5735	23	9	1	1	NUM
ejpam-5735	23	10	,	,	PUNCT
ejpam-5735	23	11	b	b	NOUN
ejpam-5735	23	12	)	)	PUNCT
ejpam-5735	23	13	:	:	PUNCT
ejpam-5735	23	14	b	b	X
ejpam-5735	23	15	∈	∈	ADP
ejpam-5735	23	16	r	r	NOUN
ejpam-5735	23	17	}	}	PUNCT
ejpam-5735	23	18	,	,	PUNCT
ejpam-5735	23	19	is	be	AUX
ejpam-5735	23	20	a	a	DET
ejpam-5735	23	21	normal	normal	ADJ
ejpam-5735	23	22	subgroup	subgroup	NOUN
ejpam-5735	23	23	that	that	PRON
ejpam-5735	23	24	can	can	AUX
ejpam-5735	23	25	be	be	AUX
ejpam-5735	23	26	identified	identify	VERB
ejpam-5735	23	27	with	with	ADP
ejpam-5735	23	28	r	r	NOUN
ejpam-5735	23	29	by	by	ADP
ejpam-5735	23	30	mapping	mapping	NOUN
ejpam-5735	23	31	(	(	PUNCT
ejpam-5735	23	32	1	1	NUM
ejpam-5735	23	33	,	,	PUNCT
ejpam-5735	23	34	b	b	NOUN
ejpam-5735	23	35	)	)	PUNCT
ejpam-5735	23	36	↔	↔	PROPN
ejpam-5735	23	37	b.	b.	PROPN
ejpam-5735	23	38	moreover	moreover	ADV
ejpam-5735	23	39	,	,	PUNCT
ejpam-5735	23	40	the	the	DET
ejpam-5735	23	41	subgroup	subgroup	NOUN
ejpam-5735	23	42	a	a	X
ejpam-5735	23	43	=	=	X
ejpam-5735	23	44	{	{	PUNCT
ejpam-5735	23	45	(	(	PUNCT
ejpam-5735	23	46	a	a	PRON
ejpam-5735	23	47	,	,	PUNCT
ejpam-5735	23	48	0	0	NUM
ejpam-5735	23	49	)	)	PUNCT
ejpam-5735	23	50	:	:	PUNCT
ejpam-5735	23	51	a	a	DET
ejpam-5735	23	52	>	>	X
ejpam-5735	23	53	0	0	NUM
ejpam-5735	23	54	}	}	PUNCT
ejpam-5735	23	55	is	be	AUX
ejpam-5735	23	56	identified	identify	VERB
ejpam-5735	23	57	with	with	ADP
ejpam-5735	23	58	r+	r+	NOUN
ejpam-5735	23	59	where	where	SCONJ
ejpam-5735	23	60	(	(	PUNCT
ejpam-5735	23	61	a	a	PRON
ejpam-5735	23	62	,	,	PUNCT
ejpam-5735	23	63	0	0	NUM
ejpam-5735	23	64	)	)	PUNCT
ejpam-5735	23	65	↔	↔	PROPN
ejpam-5735	23	66	a	a	PRON
ejpam-5735	23	67	,	,	PUNCT
ejpam-5735	23	68	[	[	X
ejpam-5735	23	69	8	8	NUM
ejpam-5735	23	70	]	]	PUNCT
ejpam-5735	23	71	.	.	PUNCT
ejpam-5735	24	1	the	the	DET
ejpam-5735	24	2	affine	affine	NOUN
ejpam-5735	24	3	group	group	NOUN
ejpam-5735	24	4	is	be	AUX
ejpam-5735	24	5	locally	locally	ADV
ejpam-5735	24	6	compact	compact	ADJ
ejpam-5735	24	7	.	.	PUNCT
ejpam-5735	25	1	thus	thus	ADV
ejpam-5735	25	2	,	,	PUNCT
ejpam-5735	25	3	it	it	PRON
ejpam-5735	25	4	has	have	VERB
ejpam-5735	25	5	a	a	DET
ejpam-5735	25	6	left	left	ADJ
ejpam-5735	25	7	haar	haar	NOUN
ejpam-5735	25	8	measure	measure	NOUN
ejpam-5735	25	9	,	,	PUNCT
ejpam-5735	25	10	which	which	PRON
ejpam-5735	25	11	is	be	AUX
ejpam-5735	25	12	given	give	VERB
ejpam-5735	25	13	as	as	SCONJ
ejpam-5735	25	14	follows	follow	VERB
ejpam-5735	25	15	:	:	PUNCT
ejpam-5735	25	16	dν(a	dν(a	NUM
ejpam-5735	25	17	,	,	PUNCT
ejpam-5735	25	18	b	b	NOUN
ejpam-5735	25	19	)	)	PUNCT
ejpam-5735	25	20	=	=	VERB
ejpam-5735	25	21	a−2dadb	a−2dadb	NOUN
ejpam-5735	25	22	,	,	PUNCT
ejpam-5735	25	23	(	(	PUNCT
ejpam-5735	25	24	2	2	X
ejpam-5735	25	25	)	)	PUNCT
ejpam-5735	25	26	and	and	CCONJ
ejpam-5735	25	27	it	it	PRON
ejpam-5735	25	28	is	be	AUX
ejpam-5735	25	29	left	leave	VERB
ejpam-5735	25	30	invariant	invariant	ADJ
ejpam-5735	25	31	measure	measure	NOUN
ejpam-5735	25	32	that	that	PRON
ejpam-5735	25	33	is	be	AUX
ejpam-5735	25	34	dν((a′	dν((a′	NOUN
ejpam-5735	25	35	,	,	PUNCT
ejpam-5735	25	36	b′	b′	NUM
ejpam-5735	25	37	)	)	PUNCT
ejpam-5735	25	38	∗	∗	NOUN
ejpam-5735	25	39	(	(	PUNCT
ejpam-5735	25	40	a	a	DET
ejpam-5735	25	41	,	,	PUNCT
ejpam-5735	25	42	b	b	NOUN
ejpam-5735	25	43	)	)	PUNCT
ejpam-5735	25	44	)	)	PUNCT
ejpam-5735	26	1	=	=	SYM
ejpam-5735	26	2	dν(a	dν(a	NUM
ejpam-5735	26	3	,	,	PUNCT
ejpam-5735	26	4	b	b	NOUN
ejpam-5735	26	5	)	)	PUNCT
ejpam-5735	26	6	.	.	PUNCT
ejpam-5735	27	1	in	in	ADP
ejpam-5735	27	2	addition	addition	NOUN
ejpam-5735	27	3	,	,	PUNCT
ejpam-5735	27	4	we	we	PRON
ejpam-5735	27	5	can	can	AUX
ejpam-5735	27	6	obtain	obtain	VERB
ejpam-5735	27	7	a	a	DET
ejpam-5735	27	8	right	right	ADJ
ejpam-5735	27	9	haar	haar	NOUN
ejpam-5735	27	10	measure	measure	NOUN
ejpam-5735	27	11	dµ(a	dµ(a	PROPN
ejpam-5735	27	12	,	,	PUNCT
ejpam-5735	27	13	b	b	NOUN
ejpam-5735	27	14	)	)	PUNCT
ejpam-5735	27	15	=	=	VERB
ejpam-5735	27	16	a−1dadb	a−1dadb	NOUN
ejpam-5735	27	17	,	,	PUNCT
ejpam-5735	27	18	which	which	PRON
ejpam-5735	27	19	is	be	AUX
ejpam-5735	27	20	right	right	ADJ
ejpam-5735	27	21	invariant	invariant	ADJ
ejpam-5735	27	22	.	.	PUNCT
ejpam-5735	28	1	therefore	therefore	ADV
ejpam-5735	28	2	,	,	PUNCT
ejpam-5735	28	3	the	the	DET
ejpam-5735	28	4	affine	affine	NOUN
ejpam-5735	28	5	group	group	NOUN
ejpam-5735	28	6	is	be	AUX
ejpam-5735	28	7	non	non	ADJ
ejpam-5735	28	8	-	-	ADJ
ejpam-5735	28	9	unimodular	unimodular	ADJ
ejpam-5735	28	10	,	,	PUNCT
ejpam-5735	28	11	and	and	CCONJ
ejpam-5735	28	12	the	the	DET
ejpam-5735	28	13	modular	modular	ADJ
ejpam-5735	28	14	function	function	NOUN
ejpam-5735	28	15	of	of	ADP
ejpam-5735	28	16	the	the	DET
ejpam-5735	28	17	group	group	NOUN
ejpam-5735	28	18	is	be	AUX
ejpam-5735	28	19	given	give	VERB
ejpam-5735	28	20	by	by	ADP
ejpam-5735	28	21	△	△	PROPN
ejpam-5735	28	22	(	(	PUNCT
ejpam-5735	28	23	a	a	DET
ejpam-5735	28	24	,	,	PUNCT
ejpam-5735	28	25	b	b	NOUN
ejpam-5735	28	26	)	)	PUNCT
ejpam-5735	29	1	=	=	SYM
ejpam-5735	29	2	a−1	a−1	PROPN
ejpam-5735	30	1	[	[	X
ejpam-5735	30	2	8	8	NUM
ejpam-5735	30	3	]	]	PUNCT
ejpam-5735	30	4	.	.	PUNCT
ejpam-5735	31	1	the	the	DET
ejpam-5735	31	2	measure	measure	NOUN
ejpam-5735	31	3	on	on	ADP
ejpam-5735	31	4	the	the	DET
ejpam-5735	31	5	subgroup	subgroup	NOUN
ejpam-5735	31	6	a	a	PRON
ejpam-5735	31	7	is	be	AUX
ejpam-5735	31	8	the	the	DET
ejpam-5735	31	9	haar	haar	NOUN
ejpam-5735	31	10	measure	measure	NOUN
ejpam-5735	31	11	da	da	PROPN
ejpam-5735	31	12	a	a	PRON
ejpam-5735	31	13	,	,	PUNCT
ejpam-5735	31	14	and	and	CCONJ
ejpam-5735	31	15	on	on	ADP
ejpam-5735	31	16	the	the	DET
ejpam-5735	31	17	subgroup	subgroup	NOUN
ejpam-5735	31	18	n	n	NUM
ejpam-5735	31	19	is	be	AUX
ejpam-5735	31	20	the	the	DET
ejpam-5735	31	21	lebesgue	lebesgue	ADJ
ejpam-5735	31	22	measure	measure	NOUN
ejpam-5735	31	23	db	db	PROPN
ejpam-5735	31	24	.	.	PROPN
ejpam-5735	31	25	3	3	NUM
ejpam-5735	31	26	.	.	NOUN
ejpam-5735	31	27	unitary	unitary	ADJ
ejpam-5735	31	28	representations	representation	NOUN
ejpam-5735	31	29	of	of	ADP
ejpam-5735	31	30	the	the	DET
ejpam-5735	31	31	affine	affine	NOUN
ejpam-5735	31	32	group	group	NOUN
ejpam-5735	31	33	the	the	DET
ejpam-5735	31	34	affine	affine	NOUN
ejpam-5735	31	35	group	group	NOUN
ejpam-5735	31	36	has	have	VERB
ejpam-5735	31	37	three	three	NUM
ejpam-5735	31	38	unitary	unitary	ADJ
ejpam-5735	31	39	representations[4	representations[4	NOUN
ejpam-5735	31	40	,	,	PUNCT
ejpam-5735	31	41	5	5	NUM
ejpam-5735	31	42	]	]	PUNCT
ejpam-5735	31	43	given	give	VERB
ejpam-5735	31	44	in	in	ADP
ejpam-5735	31	45	the	the	DET
ejpam-5735	31	46	following	following	NOUN
ejpam-5735	31	47	:	:	PUNCT
ejpam-5735	31	48	•	•	ADP
ejpam-5735	31	49	left	leave	VERB
ejpam-5735	31	50	regular	regular	ADJ
ejpam-5735	31	51	representation	representation	NOUN
ejpam-5735	31	52	[	[	PUNCT
ejpam-5735	31	53	λ(a	λ(a	NOUN
ejpam-5735	31	54	,	,	PUNCT
ejpam-5735	31	55	b)f	b)f	X
ejpam-5735	31	56	]	]	PUNCT
ejpam-5735	31	57	(	(	PUNCT
ejpam-5735	31	58	x	x	X
ejpam-5735	31	59	,	,	PUNCT
ejpam-5735	31	60	y	y	PROPN
ejpam-5735	31	61	)	)	PUNCT
ejpam-5735	31	62	:	:	PUNCT
ejpam-5735	32	1	=	=	SYM
ejpam-5735	32	2	f	f	X
ejpam-5735	32	3	(	(	PUNCT
ejpam-5735	32	4	(	(	PUNCT
ejpam-5735	32	5	a	a	PRON
ejpam-5735	32	6	,	,	PUNCT
ejpam-5735	32	7	b)−1	b)−1	NOUN
ejpam-5735	32	8	∗	∗	NOUN
ejpam-5735	32	9	(	(	PUNCT
ejpam-5735	32	10	x	x	X
ejpam-5735	32	11	,	,	PUNCT
ejpam-5735	32	12	y	y	NOUN
ejpam-5735	32	13	)	)	PUNCT
ejpam-5735	32	14	)	)	PUNCT
ejpam-5735	33	1	=	=	SYM
ejpam-5735	33	2	f	f	X
ejpam-5735	33	3	(	(	PUNCT
ejpam-5735	33	4	x	x	X
ejpam-5735	33	5	a	a	X
ejpam-5735	33	6	,	,	PUNCT
ejpam-5735	33	7	y	y	PROPN
ejpam-5735	33	8	−	−	PROPN
ejpam-5735	33	9	b	b	PROPN
ejpam-5735	33	10	a	a	NOUN
ejpam-5735	33	11	)	)	PUNCT
ejpam-5735	33	12	,	,	PUNCT
ejpam-5735	33	13	(	(	PUNCT
ejpam-5735	33	14	3	3	X
ejpam-5735	33	15	)	)	PUNCT
ejpam-5735	33	16	where	where	SCONJ
ejpam-5735	33	17	(	(	PUNCT
ejpam-5735	33	18	x	x	NOUN
ejpam-5735	33	19	,	,	PUNCT
ejpam-5735	33	20	y	y	PROPN
ejpam-5735	33	21	)	)	PUNCT
ejpam-5735	33	22	∈	∈	PROPN
ejpam-5735	33	23	aff	aff	PROPN
ejpam-5735	33	24	.	.	PROPN
ejpam-5735	33	25	•	•	NUM
ejpam-5735	33	26	co	co	ADJ
ejpam-5735	33	27	-	-	NOUN
ejpam-5735	33	28	adjoint	adjoint	ADJ
ejpam-5735	33	29	representation	representation	NOUN
ejpam-5735	33	30	on	on	ADP
ejpam-5735	33	31	the	the	DET
ejpam-5735	33	32	half	half	ADJ
ejpam-5735	33	33	real	real	ADJ
ejpam-5735	33	34	lines	line	NOUN
ejpam-5735	34	1	[	[	X
ejpam-5735	34	2	ρ±(a	ρ±(a	PROPN
ejpam-5735	34	3	,	,	PUNCT
ejpam-5735	34	4	b)g](x	b)g](x	PROPN
ejpam-5735	34	5	)	)	PUNCT
ejpam-5735	34	6	=	=	SYM
ejpam-5735	34	7	√	√	NUM
ejpam-5735	34	8	ae2πibxg(ax	ae2πibxg(ax	NOUN
ejpam-5735	34	9	)	)	PUNCT
ejpam-5735	34	10	,	,	PUNCT
ejpam-5735	34	11	(	(	PUNCT
ejpam-5735	34	12	4	4	X
ejpam-5735	34	13	)	)	PUNCT
ejpam-5735	35	1	where	where	SCONJ
ejpam-5735	35	2	g	g	PROPN
ejpam-5735	35	3	∈	∈	PROPN
ejpam-5735	35	4	l2(r±	l2(r±	PROPN
ejpam-5735	35	5	,	,	PUNCT
ejpam-5735	35	6	da	da	NOUN
ejpam-5735	35	7	)	)	PUNCT
ejpam-5735	35	8	.	.	PUNCT
ejpam-5735	36	1	•	•	NUM
ejpam-5735	36	2	quasi	quasi	ADJ
ejpam-5735	36	3	-	-	ADJ
ejpam-5735	36	4	regular	regular	ADJ
ejpam-5735	36	5	representation	representation	NOUN
ejpam-5735	36	6	on	on	ADP
ejpam-5735	36	7	the	the	DET
ejpam-5735	36	8	real	real	ADJ
ejpam-5735	36	9	line	line	NOUN
ejpam-5735	36	10	.	.	PUNCT
ejpam-5735	37	1	the	the	DET
ejpam-5735	37	2	hilbert	hilbert	PROPN
ejpam-5735	37	3	space	space	PROPN
ejpam-5735	37	4	l2(r	l2(r	PROPN
ejpam-5735	37	5	)	)	PUNCT
ejpam-5735	37	6	with	with	ADP
ejpam-5735	37	7	respect	respect	NOUN
ejpam-5735	37	8	to	to	ADP
ejpam-5735	37	9	π	π	PROPN
ejpam-5735	37	10	contains	contain	VERB
ejpam-5735	37	11	precisely	precisely	ADV
ejpam-5735	37	12	two	two	NUM
ejpam-5735	37	13	closed	close	VERB
ejpam-5735	37	14	proper	proper	ADJ
ejpam-5735	37	15	invariant	invariant	ADJ
ejpam-5735	37	16	subspaces	subspace	NOUN
ejpam-5735	37	17	h2(r	h2(r	PRON
ejpam-5735	37	18	)	)	PUNCT
ejpam-5735	37	19	and	and	CCONJ
ejpam-5735	37	20	h⊥	h⊥	ADV
ejpam-5735	37	21	2	2	NUM
ejpam-5735	37	22	(	(	PUNCT
ejpam-5735	37	23	r	r	NOUN
ejpam-5735	37	24	)	)	PUNCT
ejpam-5735	37	25	such	such	ADJ
ejpam-5735	37	26	that	that	SCONJ
ejpam-5735	37	27	l2(r	l2(r	NOUN
ejpam-5735	37	28	)	)	PUNCT
ejpam-5735	37	29	=	=	SYM
ejpam-5735	37	30	h2(r)⊕h⊥	h2(r)⊕h⊥	PROPN
ejpam-5735	37	31	2	2	NUM
ejpam-5735	37	32	(	(	PUNCT
ejpam-5735	37	33	r	r	NOUN
ejpam-5735	37	34	)	)	PUNCT
ejpam-5735	37	35	.	.	PUNCT
ejpam-5735	38	1	a.	a.	NOUN
ejpam-5735	38	2	alghamdi	alghamdi	PROPN
ejpam-5735	38	3	,	,	PUNCT
ejpam-5735	38	4	t.	t.	PROPN
ejpam-5735	38	5	alqurashi	alqurashi	PROPN
ejpam-5735	38	6	/	/	SYM
ejpam-5735	38	7	eur	eur	PROPN
ejpam-5735	38	8	.	.	PUNCT
ejpam-5735	39	1	j.	j.	PROPN
ejpam-5735	39	2	pure	pure	PROPN
ejpam-5735	39	3	appl	appl	PROPN
ejpam-5735	39	4	.	.	PROPN
ejpam-5735	39	5	math	math	PROPN
ejpam-5735	39	6	,	,	PUNCT
ejpam-5735	39	7	18	18	NUM
ejpam-5735	39	8	(	(	PUNCT
ejpam-5735	39	9	1	1	NUM
ejpam-5735	39	10	)	)	PUNCT
ejpam-5735	39	11	(	(	PUNCT
ejpam-5735	39	12	2025	2025	NUM
ejpam-5735	39	13	)	)	PUNCT
ejpam-5735	39	14	,	,	PUNCT
ejpam-5735	39	15	5735	5735	NUM
ejpam-5735	39	16	3	3	NUM
ejpam-5735	39	17	of	of	ADP
ejpam-5735	39	18	7	7	NUM
ejpam-5735	39	19	therefore	therefore	ADV
ejpam-5735	39	20	,	,	PUNCT
ejpam-5735	39	21	the	the	DET
ejpam-5735	39	22	quasi	quasi	ADJ
ejpam-5735	39	23	-	-	ADJ
ejpam-5735	39	24	regular	regular	ADJ
ejpam-5735	39	25	representation	representation	NOUN
ejpam-5735	39	26	π	π	NOUN
ejpam-5735	39	27	is	be	AUX
ejpam-5735	39	28	decomposed	decompose	VERB
ejpam-5735	39	29	into	into	ADP
ejpam-5735	39	30	two	two	NUM
ejpam-5735	39	31	irreducible	irreducible	ADJ
ejpam-5735	39	32	representations	representation	NOUN
ejpam-5735	39	33	.	.	PUNCT
ejpam-5735	40	1	that	that	PRON
ejpam-5735	40	2	is	be	AUX
ejpam-5735	40	3	π(a	π(a	PROPN
ejpam-5735	40	4	,	,	PUNCT
ejpam-5735	40	5	b	b	NOUN
ejpam-5735	40	6	)	)	PUNCT
ejpam-5735	40	7	=	=	SYM
ejpam-5735	40	8	π+(a	π+(a	PROPN
ejpam-5735	40	9	,	,	PUNCT
ejpam-5735	40	10	b)⊕	b)⊕	ADV
ejpam-5735	40	11	π−(a	π−(a	ADV
ejpam-5735	40	12	,	,	PUNCT
ejpam-5735	40	13	b	b	NOUN
ejpam-5735	40	14	)	)	PUNCT
ejpam-5735	40	15	.	.	PUNCT
ejpam-5735	41	1	the	the	DET
ejpam-5735	41	2	operator	operator	NOUN
ejpam-5735	41	3	of	of	ADP
ejpam-5735	41	4	representation	representation	NOUN
ejpam-5735	41	5	π+	π+	PUNCT
ejpam-5735	41	6	:	:	PUNCT
ejpam-5735	41	7	h2(r	h2(r	X
ejpam-5735	41	8	)	)	PUNCT
ejpam-5735	41	9	→	→	SYM
ejpam-5735	41	10	h2(r	h2(r	PROPN
ejpam-5735	41	11	)	)	PUNCT
ejpam-5735	41	12	is	be	AUX
ejpam-5735	41	13	given	give	VERB
ejpam-5735	41	14	by	by	ADP
ejpam-5735	41	15	the	the	DET
ejpam-5735	41	16	following	following	NOUN
ejpam-5735	41	17	:	:	PUNCT
ejpam-5735	42	1	[	[	X
ejpam-5735	42	2	π+(a	π+(a	ADJ
ejpam-5735	42	3	,	,	PUNCT
ejpam-5735	42	4	b)f	b)f	X
ejpam-5735	42	5	]	]	PUNCT
ejpam-5735	42	6	(	(	PUNCT
ejpam-5735	42	7	x	x	X
ejpam-5735	42	8	)	)	PUNCT
ejpam-5735	42	9	=	=	SYM
ejpam-5735	42	10	(	(	PUNCT
ejpam-5735	42	11	1	1	NUM
ejpam-5735	42	12	a	a	X
ejpam-5735	42	13	)	)	PUNCT
ejpam-5735	42	14	−	−	PROPN
ejpam-5735	42	15	1	1	NUM
ejpam-5735	42	16	2	2	NUM
ejpam-5735	42	17	f	f	X
ejpam-5735	42	18	(	(	PUNCT
ejpam-5735	42	19	x−	x−	PROPN
ejpam-5735	42	20	b	b	PROPN
ejpam-5735	42	21	a	a	NOUN
ejpam-5735	42	22	)	)	PUNCT
ejpam-5735	42	23	,	,	PUNCT
ejpam-5735	42	24	(	(	PUNCT
ejpam-5735	42	25	5	5	X
ejpam-5735	42	26	)	)	PUNCT
ejpam-5735	42	27	where	where	SCONJ
ejpam-5735	42	28	f	f	PROPN
ejpam-5735	42	29	∈	∈	PROPN
ejpam-5735	42	30	h2(r	h2(r	PROPN
ejpam-5735	42	31	)	)	PUNCT
ejpam-5735	42	32	.	.	PUNCT
ejpam-5735	43	1	also	also	ADV
ejpam-5735	43	2	,	,	PUNCT
ejpam-5735	43	3	for	for	ADP
ejpam-5735	43	4	the	the	DET
ejpam-5735	43	5	representation	representation	NOUN
ejpam-5735	43	6	π−	π−	NOUN
ejpam-5735	43	7	:	:	PUNCT
ejpam-5735	43	8	h⊥	h⊥	ADV
ejpam-5735	43	9	2	2	NUM
ejpam-5735	43	10	(	(	PUNCT
ejpam-5735	43	11	r	r	NOUN
ejpam-5735	43	12	)	)	PUNCT
ejpam-5735	43	13	→	→	SYM
ejpam-5735	43	14	h⊥	h⊥	NOUN
ejpam-5735	43	15	2	2	NUM
ejpam-5735	43	16	(	(	PUNCT
ejpam-5735	43	17	r	r	NOUN
ejpam-5735	43	18	)	)	PUNCT
ejpam-5735	43	19	,	,	PUNCT
ejpam-5735	43	20	the	the	DET
ejpam-5735	43	21	operator	operator	NOUN
ejpam-5735	43	22	is	be	AUX
ejpam-5735	43	23	given	give	VERB
ejpam-5735	43	24	by	by	ADP
ejpam-5735	43	25	(	(	PUNCT
ejpam-5735	43	26	5	5	NUM
ejpam-5735	43	27	)	)	PUNCT
ejpam-5735	43	28	where	where	SCONJ
ejpam-5735	43	29	f	f	PROPN
ejpam-5735	43	30	∈	∈	PROPN
ejpam-5735	43	31	h⊥	h⊥	NOUN
ejpam-5735	43	32	2	2	NUM
ejpam-5735	43	33	(	(	PUNCT
ejpam-5735	43	34	r	r	NOUN
ejpam-5735	43	35	)	)	PUNCT
ejpam-5735	43	36	.	.	PUNCT
ejpam-5735	44	1	4	4	X
ejpam-5735	44	2	.	.	X
ejpam-5735	44	3	intertwining	intertwine	VERB
ejpam-5735	44	4	operators	operator	NOUN
ejpam-5735	44	5	in	in	ADP
ejpam-5735	44	6	this	this	DET
ejpam-5735	44	7	section	section	NOUN
ejpam-5735	45	1	,	,	PUNCT
ejpam-5735	45	2	we	we	PRON
ejpam-5735	45	3	study	study	VERB
ejpam-5735	45	4	the	the	DET
ejpam-5735	45	5	intertwining	intertwine	VERB
ejpam-5735	45	6	operators	operator	NOUN
ejpam-5735	45	7	between	between	ADP
ejpam-5735	45	8	the	the	DET
ejpam-5735	45	9	unitary	unitary	ADJ
ejpam-5735	45	10	representations	representation	NOUN
ejpam-5735	45	11	of	of	ADP
ejpam-5735	45	12	the	the	DET
ejpam-5735	45	13	affine	affine	NOUN
ejpam-5735	45	14	group	group	NOUN
ejpam-5735	45	15	by	by	ADP
ejpam-5735	45	16	using	use	VERB
ejpam-5735	45	17	the	the	DET
ejpam-5735	45	18	wavelet	wavelet	NOUN
ejpam-5735	45	19	transform	transform	NOUN
ejpam-5735	45	20	and	and	CCONJ
ejpam-5735	45	21	the	the	DET
ejpam-5735	45	22	induced	induced	ADJ
ejpam-5735	45	23	wavelet	wavelet	NOUN
ejpam-5735	45	24	transform	transform	NOUN
ejpam-5735	45	25	.	.	PUNCT
ejpam-5735	46	1	left	leave	VERB
ejpam-5735	46	2	regular	regular	ADJ
ejpam-5735	46	3	representation	representation	NOUN
ejpam-5735	46	4	on	on	ADP
ejpam-5735	46	5	l2(aff	l2(aff	ADJ
ejpam-5735	46	6	,	,	PUNCT
ejpam-5735	46	7	dν	dν	ADJ
ejpam-5735	46	8	)	)	PUNCT
ejpam-5735	46	9	quasi	quasi	ADJ
ejpam-5735	46	10	-	-	ADJ
ejpam-5735	46	11	regular	regular	ADJ
ejpam-5735	46	12	representation	representation	NOUN
ejpam-5735	46	13	on	on	ADP
ejpam-5735	46	14	h2(r	h2(r	NOUN
ejpam-5735	46	15	)	)	PUNCT
ejpam-5735	46	16	co	co	ADJ
ejpam-5735	46	17	-	-	ADJ
ejpam-5735	46	18	adjoint	adjoint	ADJ
ejpam-5735	46	19	representation	representation	NOUN
ejpam-5735	46	20	on	on	ADP
ejpam-5735	46	21	l2(r+	l2(r+	PROPN
ejpam-5735	46	22	)	)	PUNCT
ejpam-5735	46	23	po	po	NOUN
ejpam-5735	46	24	iss	iss	PROPN
ejpam-5735	46	25	on	on	ADP
ejpam-5735	46	26	int	int	PROPN
ejpam-5735	46	27	eg	eg	PROPN
ejpam-5735	46	28	ra	ra	PROPN
ejpam-5735	46	29	l	l	NOUN
ejpam-5735	46	30	fourier	fourier	NOUN
ejpam-5735	46	31	transform	transform	VERB
ejpam-5735	46	32	fourier	fourier	NOUN
ejpam-5735	46	33	transform	transform	NOUN
ejpam-5735	46	34	laplace	laplace	NOUN
ejpam-5735	46	35	transform	transform	NOUN
ejpam-5735	46	36	figure	figure	NOUN
ejpam-5735	46	37	1	1	NUM
ejpam-5735	46	38	:	:	PUNCT
ejpam-5735	46	39	intertwining	intertwine	VERB
ejpam-5735	46	40	operators	operator	NOUN
ejpam-5735	46	41	between	between	ADP
ejpam-5735	46	42	affine	affine	NOUN
ejpam-5735	46	43	group	group	NOUN
ejpam-5735	46	44	representations	representation	VERB
ejpam-5735	46	45	4.1	4.1	NUM
ejpam-5735	46	46	.	.	PUNCT
ejpam-5735	47	1	wavelet	wavelet	NOUN
ejpam-5735	47	2	transform	transform	NOUN
ejpam-5735	47	3	definition	definition	NOUN
ejpam-5735	47	4	1	1	NUM
ejpam-5735	47	5	.	.	PUNCT
ejpam-5735	48	1	[	[	X
ejpam-5735	48	2	12	12	NUM
ejpam-5735	48	3	]	]	PUNCT
ejpam-5735	48	4	let	let	VERB
ejpam-5735	48	5	v	v	PART
ejpam-5735	48	6	be	be	AUX
ejpam-5735	48	7	a	a	DET
ejpam-5735	48	8	hilbert	hilbert	NOUN
ejpam-5735	48	9	space	space	NOUN
ejpam-5735	48	10	with	with	ADP
ejpam-5735	48	11	an	an	DET
ejpam-5735	48	12	inner	inner	ADJ
ejpam-5735	48	13	product	product	NOUN
ejpam-5735	48	14	⟨.	⟨.	NOUN
ejpam-5735	48	15	,	,	PUNCT
ejpam-5735	48	16	.⟩	.⟩	PROPN
ejpam-5735	48	17	and	and	CCONJ
ejpam-5735	48	18	ρ	ρ	PROPN
ejpam-5735	48	19	be	be	AUX
ejpam-5735	48	20	a	a	DET
ejpam-5735	48	21	unitary	unitary	ADJ
ejpam-5735	48	22	representation	representation	NOUN
ejpam-5735	48	23	of	of	ADP
ejpam-5735	48	24	a	a	DET
ejpam-5735	48	25	group	group	NOUN
ejpam-5735	48	26	g	g	NOUN
ejpam-5735	48	27	in	in	ADP
ejpam-5735	48	28	the	the	DET
ejpam-5735	48	29	space	space	NOUN
ejpam-5735	48	30	v	v	NOUN
ejpam-5735	48	31	.	.	PUNCT
ejpam-5735	49	1	let	let	VERB
ejpam-5735	49	2	f	f	NOUN
ejpam-5735	49	3	:	:	PUNCT
ejpam-5735	49	4	v	v	X
ejpam-5735	49	5	→	→	SYM
ejpam-5735	49	6	c	c	X
ejpam-5735	49	7	be	be	AUX
ejpam-5735	49	8	the	the	DET
ejpam-5735	49	9	functional	functional	ADJ
ejpam-5735	49	10	υ	υ	PROPN
ejpam-5735	49	11	7→	7→	NUM
ejpam-5735	49	12	⟨υ	⟨υ	NOUN
ejpam-5735	49	13	,	,	PUNCT
ejpam-5735	49	14	υ0⟩	υ0⟩	NOUN
ejpam-5735	49	15	defined	define	VERB
ejpam-5735	49	16	by	by	ADP
ejpam-5735	49	17	a	a	DET
ejpam-5735	49	18	vector	vector	NOUN
ejpam-5735	49	19	υ0	υ0	NOUN
ejpam-5735	49	20	∈	∈	PROPN
ejpam-5735	49	21	v	v	NOUN
ejpam-5735	49	22	.	.	PUNCT
ejpam-5735	50	1	the	the	DET
ejpam-5735	50	2	vector	vector	NOUN
ejpam-5735	50	3	υ0	υ0	NOUN
ejpam-5735	50	4	is	be	AUX
ejpam-5735	50	5	called	call	VERB
ejpam-5735	50	6	the	the	DET
ejpam-5735	50	7	mother	mother	NOUN
ejpam-5735	50	8	wavelet	wavelet	NOUN
ejpam-5735	50	9	.	.	PUNCT
ejpam-5735	51	1	we	we	PRON
ejpam-5735	51	2	define	define	VERB
ejpam-5735	51	3	a	a	DET
ejpam-5735	51	4	wavelet	wavelet	NOUN
ejpam-5735	51	5	transform	transform	NOUN
ejpam-5735	51	6	w	w	ADP
ejpam-5735	51	7	acting	act	VERB
ejpam-5735	51	8	from	from	ADP
ejpam-5735	51	9	v	v	NUM
ejpam-5735	51	10	to	to	ADP
ejpam-5735	51	11	the	the	DET
ejpam-5735	51	12	space	space	NOUN
ejpam-5735	51	13	l2(g	l2(g	NOUN
ejpam-5735	51	14	,	,	PUNCT
ejpam-5735	51	15	c	c	NOUN
ejpam-5735	51	16	)	)	PUNCT
ejpam-5735	51	17	of	of	ADP
ejpam-5735	51	18	c	c	NOUN
ejpam-5735	51	19	-	-	PUNCT
ejpam-5735	51	20	valued	value	VERB
ejpam-5735	51	21	functions	function	NOUN
ejpam-5735	51	22	on	on	ADP
ejpam-5735	51	23	g	g	NOUN
ejpam-5735	51	24	by	by	ADP
ejpam-5735	51	25	the	the	DET
ejpam-5735	51	26	formula	formula	NOUN
ejpam-5735	51	27	:	:	PUNCT
ejpam-5735	51	28	w	w	X
ejpam-5735	51	29	:	:	PUNCT
ejpam-5735	51	30	υ	υ	PROPN
ejpam-5735	51	31	7→	7→	NUM
ejpam-5735	51	32	υ̃(g	υ̃(g	NOUN
ejpam-5735	51	33	)	)	PUNCT
ejpam-5735	51	34	=	=	SYM
ejpam-5735	51	35	⟨ρ(g−1)υ	⟨ρ(g−1)υ	NOUN
ejpam-5735	51	36	,	,	PUNCT
ejpam-5735	51	37	υ0⟩	υ0⟩	NOUN
ejpam-5735	51	38	=	=	SYM
ejpam-5735	51	39	⟨υ	⟨υ	PROPN
ejpam-5735	51	40	,	,	PUNCT
ejpam-5735	51	41	ρ(g)υ0⟩	ρ(g)υ0⟩	PROPN
ejpam-5735	51	42	,	,	PUNCT
ejpam-5735	51	43	υ	υ	PROPN
ejpam-5735	51	44	∈	∈	PROPN
ejpam-5735	51	45	v	v	NOUN
ejpam-5735	51	46	,	,	PUNCT
ejpam-5735	51	47	g	g	PROPN
ejpam-5735	51	48	∈	∈	PROPN
ejpam-5735	51	49	g.	g.	NOUN
ejpam-5735	51	50	(	(	PUNCT
ejpam-5735	51	51	6	6	NUM
ejpam-5735	51	52	)	)	PUNCT
ejpam-5735	51	53	the	the	DET
ejpam-5735	51	54	collection	collection	NOUN
ejpam-5735	51	55	of	of	ADP
ejpam-5735	51	56	the	the	DET
ejpam-5735	51	57	vectors	vector	NOUN
ejpam-5735	51	58	υg	υg	X
ejpam-5735	51	59	=	=	SYM
ejpam-5735	51	60	ρ(g)υ0	ρ(g)υ0	PROPN
ejpam-5735	51	61	is	be	AUX
ejpam-5735	51	62	called	call	VERB
ejpam-5735	51	63	wavelets	wavelet	NOUN
ejpam-5735	51	64	.	.	PUNCT
ejpam-5735	52	1	a.	a.	NOUN
ejpam-5735	52	2	alghamdi	alghamdi	PROPN
ejpam-5735	52	3	,	,	PUNCT
ejpam-5735	52	4	t.	t.	PROPN
ejpam-5735	52	5	alqurashi	alqurashi	PROPN
ejpam-5735	52	6	/	/	SYM
ejpam-5735	52	7	eur	eur	PROPN
ejpam-5735	52	8	.	.	PUNCT
ejpam-5735	53	1	j.	j.	PROPN
ejpam-5735	53	2	pure	pure	PROPN
ejpam-5735	53	3	appl	appl	PROPN
ejpam-5735	53	4	.	.	PROPN
ejpam-5735	53	5	math	math	PROPN
ejpam-5735	53	6	,	,	PUNCT
ejpam-5735	53	7	18	18	NUM
ejpam-5735	53	8	(	(	PUNCT
ejpam-5735	53	9	1	1	NUM
ejpam-5735	53	10	)	)	PUNCT
ejpam-5735	53	11	(	(	PUNCT
ejpam-5735	53	12	2025	2025	NUM
ejpam-5735	53	13	)	)	PUNCT
ejpam-5735	53	14	,	,	PUNCT
ejpam-5735	53	15	5735	5735	NUM
ejpam-5735	53	16	4	4	NUM
ejpam-5735	53	17	of	of	ADP
ejpam-5735	53	18	7	7	NUM
ejpam-5735	53	19	theorem	theorem	NOUN
ejpam-5735	53	20	1	1	NUM
ejpam-5735	53	21	.	.	PUNCT
ejpam-5735	54	1	[	[	X
ejpam-5735	54	2	12	12	NUM
ejpam-5735	54	3	]	]	PUNCT
ejpam-5735	54	4	the	the	DET
ejpam-5735	54	5	wavelet	wavelet	NOUN
ejpam-5735	54	6	transform	transform	NOUN
ejpam-5735	54	7	(	(	PUNCT
ejpam-5735	54	8	6	6	NUM
ejpam-5735	54	9	)	)	PUNCT
ejpam-5735	54	10	intertwines	intertwine	VERB
ejpam-5735	54	11	the	the	DET
ejpam-5735	54	12	unitary	unitary	ADJ
ejpam-5735	54	13	representation	representation	NOUN
ejpam-5735	54	14	ρ	ρ	NOUN
ejpam-5735	54	15	and	and	CCONJ
ejpam-5735	54	16	the	the	DET
ejpam-5735	54	17	left	left	ADJ
ejpam-5735	54	18	regular	regular	ADJ
ejpam-5735	54	19	representation	representation	NOUN
ejpam-5735	54	20	on	on	ADP
ejpam-5735	54	21	l2(g	l2(g	ADP
ejpam-5735	54	22	,	,	PUNCT
ejpam-5735	54	23	c	c	NOUN
ejpam-5735	54	24	):	):	PUNCT
ejpam-5735	54	25	wρ(g	wρ(g	PUNCT
ejpam-5735	54	26	)	)	PUNCT
ejpam-5735	54	27	=	=	SYM
ejpam-5735	54	28	λ(g)w	λ(g)w	PROPN
ejpam-5735	54	29	.	.	PUNCT
ejpam-5735	54	30	corollary	corollary	ADJ
ejpam-5735	54	31	1	1	NUM
ejpam-5735	54	32	.	.	PUNCT
ejpam-5735	55	1	the	the	DET
ejpam-5735	55	2	poisson	poisson	NOUN
ejpam-5735	55	3	integral	integral	ADJ
ejpam-5735	55	4	for	for	ADP
ejpam-5735	55	5	a	a	DET
ejpam-5735	55	6	∈	∈	NOUN
ejpam-5735	55	7	r+	r+	NOUN
ejpam-5735	55	8	and	and	CCONJ
ejpam-5735	55	9	b	b	X
ejpam-5735	55	10	∈	∈	NOUN
ejpam-5735	55	11	r	r	NOUN
ejpam-5735	55	12	is	be	AUX
ejpam-5735	55	13	given	give	VERB
ejpam-5735	55	14	by	by	ADP
ejpam-5735	55	15	[	[	X
ejpam-5735	55	16	pφ](a	pφ](a	NOUN
ejpam-5735	55	17	,	,	PUNCT
ejpam-5735	55	18	b	b	NOUN
ejpam-5735	55	19	)	)	PUNCT
ejpam-5735	55	20	=	=	SYM
ejpam-5735	55	21	1	1	NUM
ejpam-5735	55	22	2	2	NUM
ejpam-5735	55	23	∫	∫	NOUN
ejpam-5735	55	24	r	r	NOUN
ejpam-5735	55	25	a	a	PROPN
ejpam-5735	55	26	(	(	PUNCT
ejpam-5735	55	27	x−	x−	PROPN
ejpam-5735	55	28	b)2	b)2	PROPN
ejpam-5735	55	29	+	+	PROPN
ejpam-5735	55	30	a2	a2	PROPN
ejpam-5735	55	31	φ(x)dx	φ(x)dx	PROPN
ejpam-5735	55	32	.	.	PUNCT
ejpam-5735	56	1	(	(	PUNCT
ejpam-5735	56	2	7	7	X
ejpam-5735	56	3	)	)	PUNCT
ejpam-5735	56	4	it	it	PRON
ejpam-5735	56	5	is	be	AUX
ejpam-5735	56	6	the	the	DET
ejpam-5735	56	7	wavelet	wavelet	NOUN
ejpam-5735	56	8	transform	transform	NOUN
ejpam-5735	56	9	that	that	PRON
ejpam-5735	56	10	intertwines	intertwine	VERB
ejpam-5735	56	11	the	the	DET
ejpam-5735	56	12	quasi	quasi	ADJ
ejpam-5735	56	13	-	-	ADJ
ejpam-5735	56	14	regular	regular	ADJ
ejpam-5735	56	15	representations	representation	NOUN
ejpam-5735	56	16	π±	π±	PUNCT
ejpam-5735	56	17	(	(	PUNCT
ejpam-5735	56	18	5	5	NUM
ejpam-5735	56	19	)	)	PUNCT
ejpam-5735	56	20	with	with	ADP
ejpam-5735	56	21	the	the	DET
ejpam-5735	56	22	left	left	ADJ
ejpam-5735	56	23	regular	regular	ADJ
ejpam-5735	56	24	representation	representation	NOUN
ejpam-5735	56	25	λ(a	λ(a	NOUN
ejpam-5735	56	26	,	,	PUNCT
ejpam-5735	56	27	b	b	NOUN
ejpam-5735	56	28	)	)	PUNCT
ejpam-5735	56	29	given	give	VERB
ejpam-5735	56	30	by	by	ADP
ejpam-5735	56	31	(	(	PUNCT
ejpam-5735	56	32	3	3	NUM
ejpam-5735	56	33	)	)	PUNCT
ejpam-5735	56	34	.	.	PUNCT
ejpam-5735	57	1	proof	proof	NOUN
ejpam-5735	57	2	.	.	PUNCT
ejpam-5735	58	1	we	we	PRON
ejpam-5735	58	2	will	will	AUX
ejpam-5735	58	3	prove	prove	VERB
ejpam-5735	58	4	it	it	PRON
ejpam-5735	58	5	for	for	ADP
ejpam-5735	58	6	the	the	DET
ejpam-5735	58	7	representation	representation	NOUN
ejpam-5735	58	8	π+	π+	PUNCT
ejpam-5735	58	9	(	(	PUNCT
ejpam-5735	58	10	5	5	NUM
ejpam-5735	58	11	)	)	PUNCT
ejpam-5735	58	12	and	and	CCONJ
ejpam-5735	58	13	the	the	DET
ejpam-5735	58	14	result	result	NOUN
ejpam-5735	58	15	is	be	AUX
ejpam-5735	58	16	valid	valid	ADJ
ejpam-5735	58	17	for	for	SCONJ
ejpam-5735	58	18	the	the	DET
ejpam-5735	58	19	representation	representation	NOUN
ejpam-5735	58	20	π−.	π−.	PROPN
ejpam-5735	58	21	let	let	VERB
ejpam-5735	58	22	the	the	DET
ejpam-5735	58	23	fiducial	fiducial	ADJ
ejpam-5735	58	24	operator	operator	NOUN
ejpam-5735	58	25	f	f	NOUN
ejpam-5735	58	26	:	:	PUNCT
ejpam-5735	58	27	h2(r	h2(r	PROPN
ejpam-5735	58	28	)	)	PUNCT
ejpam-5735	58	29	→	→	PUNCT
ejpam-5735	58	30	c	c	X
ejpam-5735	58	31	be	be	AUX
ejpam-5735	58	32	the	the	DET
ejpam-5735	58	33	functional	functional	ADJ
ejpam-5735	58	34	φ	φ	NOUN
ejpam-5735	58	35	7→	7→	NUM
ejpam-5735	58	36	⟨φ	⟨φ	NUM
ejpam-5735	58	37	,	,	PUNCT
ejpam-5735	58	38	φ0⟩	φ0⟩	ADV
ejpam-5735	58	39	,	,	PUNCT
ejpam-5735	58	40	and	and	CCONJ
ejpam-5735	58	41	the	the	DET
ejpam-5735	58	42	mother	mother	NOUN
ejpam-5735	58	43	wavelet	wavelet	NOUN
ejpam-5735	58	44	be	be	AUX
ejpam-5735	58	45	the	the	DET
ejpam-5735	58	46	conjugate	conjugate	ADJ
ejpam-5735	58	47	poisson	poisson	NOUN
ejpam-5735	58	48	kernel	kernel	PROPN
ejpam-5735	58	49	φ0	φ0	PROPN
ejpam-5735	58	50	=	=	PROPN
ejpam-5735	58	51	−x	−x	NOUN
ejpam-5735	58	52	π(1+x2	π(1+x2	NOUN
ejpam-5735	58	53	)	)	PUNCT
ejpam-5735	58	54	.	.	PUNCT
ejpam-5735	59	1	then	then	ADV
ejpam-5735	59	2	,	,	PUNCT
ejpam-5735	59	3	φ̄0	φ̄0	X
ejpam-5735	59	4	=	=	SYM
ejpam-5735	59	5	1	1	NUM
ejpam-5735	59	6	π(1+x2	π(1+x2	NOUN
ejpam-5735	59	7	)	)	PUNCT
ejpam-5735	59	8	is	be	AUX
ejpam-5735	59	9	the	the	DET
ejpam-5735	59	10	poisson	poisson	PROPN
ejpam-5735	59	11	kernel	kernel	NOUN
ejpam-5735	59	12	.	.	PUNCT
ejpam-5735	60	1	hence	hence	ADV
ejpam-5735	60	2	,	,	PUNCT
ejpam-5735	60	3	the	the	DET
ejpam-5735	60	4	wavelet	wavelet	NOUN
ejpam-5735	60	5	transform	transform	NOUN
ejpam-5735	60	6	that	that	PRON
ejpam-5735	60	7	intertwines	intertwine	VERB
ejpam-5735	60	8	the	the	DET
ejpam-5735	60	9	quasi	quasi	ADJ
ejpam-5735	60	10	-	-	ADJ
ejpam-5735	60	11	regular	regular	ADJ
ejpam-5735	60	12	representation	representation	NOUN
ejpam-5735	60	13	with	with	ADP
ejpam-5735	60	14	the	the	DET
ejpam-5735	60	15	left	left	ADJ
ejpam-5735	60	16	regular	regular	ADJ
ejpam-5735	60	17	representation	representation	NOUN
ejpam-5735	60	18	is	be	AUX
ejpam-5735	60	19	given	give	VERB
ejpam-5735	60	20	as	as	SCONJ
ejpam-5735	60	21	follows	follow	VERB
ejpam-5735	60	22	:	:	PUNCT
ejpam-5735	61	1	[	[	X
ejpam-5735	61	2	wπ+(a	wπ+(a	NOUN
ejpam-5735	61	3	,	,	PUNCT
ejpam-5735	61	4	b)φ](x	b)φ](x	X
ejpam-5735	61	5	)	)	PUNCT
ejpam-5735	61	6	=	=	SYM
ejpam-5735	61	7	⟨φ	⟨φ	PROPN
ejpam-5735	61	8	,	,	PUNCT
ejpam-5735	61	9	π+(a	π+(a	PROPN
ejpam-5735	61	10	,	,	PUNCT
ejpam-5735	61	11	b)φ0⟩	b)φ0⟩	PROPN
ejpam-5735	61	12	=	=	SYM
ejpam-5735	61	13	∫	∫	PROPN
ejpam-5735	61	14	r	r	NOUN
ejpam-5735	61	15	φ(x	φ(x	PROPN
ejpam-5735	61	16	)	)	PUNCT
ejpam-5735	61	17	1√	1√	NOUN
ejpam-5735	61	18	a	a	PRON
ejpam-5735	61	19	φ̄0	φ̄0	NUM
ejpam-5735	61	20	(	(	PUNCT
ejpam-5735	61	21	x−	x−	PROPN
ejpam-5735	61	22	b	b	PROPN
ejpam-5735	61	23	a	a	PRON
ejpam-5735	61	24	)	)	PUNCT
ejpam-5735	61	25	dx	dx	PROPN
ejpam-5735	61	26	=	=	PROPN
ejpam-5735	61	27	1√	1√	PROPN
ejpam-5735	61	28	a	a	DET
ejpam-5735	61	29	∫	∫	PROPN
ejpam-5735	61	30	r	r	NOUN
ejpam-5735	61	31	φ(x	φ(x	NOUN
ejpam-5735	61	32	)	)	PUNCT
ejpam-5735	61	33	1	1	NUM
ejpam-5735	62	1	π(1	π(1	NOUN
ejpam-5735	62	2	+	+	CCONJ
ejpam-5735	62	3	(	(	PUNCT
ejpam-5735	62	4	x−ba	x−ba	PROPN
ejpam-5735	62	5	)	)	PUNCT
ejpam-5735	62	6	2	2	NUM
ejpam-5735	62	7	)	)	PUNCT
ejpam-5735	62	8	dx	dx	PROPN
ejpam-5735	62	9	=	=	SYM
ejpam-5735	62	10	1√	1√	PROPN
ejpam-5735	62	11	aπ	aπ	NOUN
ejpam-5735	62	12	∫	∫	NOUN
ejpam-5735	62	13	r	r	NOUN
ejpam-5735	62	14	φ(x	φ(x	PROPN
ejpam-5735	62	15	)	)	PUNCT
ejpam-5735	62	16	a2	a2	PROPN
ejpam-5735	62	17	a2	a2	PROPN
ejpam-5735	62	18	+	+	CCONJ
ejpam-5735	62	19	(	(	PUNCT
ejpam-5735	62	20	x−	x−	PROPN
ejpam-5735	62	21	b)2	b)2	PROPN
ejpam-5735	62	22	dx	dx	PROPN
ejpam-5735	63	1	=	=	SYM
ejpam-5735	63	2	√	√	PROPN
ejpam-5735	63	3	a	a	DET
ejpam-5735	63	4	π	π	PROPN
ejpam-5735	63	5	∫	∫	NOUN
ejpam-5735	63	6	r	r	NOUN
ejpam-5735	63	7	φ(x	φ(x	PROPN
ejpam-5735	63	8	)	)	PUNCT
ejpam-5735	63	9	a	a	DET
ejpam-5735	63	10	a2	a2	PROPN
ejpam-5735	63	11	+	+	CCONJ
ejpam-5735	63	12	(	(	PUNCT
ejpam-5735	63	13	x−	x−	PROPN
ejpam-5735	63	14	b)2	b)2	PROPN
ejpam-5735	63	15	dx	dx	PROPN
ejpam-5735	63	16	=	=	SYM
ejpam-5735	64	1	2	2	NUM
ejpam-5735	64	2	√	√	ADP
ejpam-5735	64	3	a	a	DET
ejpam-5735	64	4	π	π	PROPN
ejpam-5735	64	5	[	[	X
ejpam-5735	64	6	pφ](a	pφ](a	NOUN
ejpam-5735	64	7	,	,	PUNCT
ejpam-5735	64	8	b	b	NOUN
ejpam-5735	64	9	)	)	PUNCT
ejpam-5735	64	10	.	.	PUNCT
ejpam-5735	65	1	corollary	corollary	ADJ
ejpam-5735	65	2	2	2	NUM
ejpam-5735	65	3	.	.	PUNCT
ejpam-5735	66	1	the	the	DET
ejpam-5735	66	2	laplace	laplace	NOUN
ejpam-5735	66	3	transform	transform	NOUN
ejpam-5735	66	4	f	f	X
ejpam-5735	66	5	(	(	PUNCT
ejpam-5735	66	6	a+	a+	PUNCT
ejpam-5735	66	7	ib	ib	NOUN
ejpam-5735	66	8	)	)	PUNCT
ejpam-5735	66	9	=	=	SYM
ejpam-5735	66	10	∫	∫	PROPN
ejpam-5735	66	11	r+	r+	X
ejpam-5735	66	12	f(t)e−2π(a+ib)xdx	f(t)e−2π(a+ib)xdx	PROPN
ejpam-5735	66	13	,	,	PUNCT
ejpam-5735	66	14	a+	a+	PUNCT
ejpam-5735	66	15	ib	ib	PROPN
ejpam-5735	66	16	∈	∈	PROPN
ejpam-5735	66	17	c	c	PROPN
ejpam-5735	66	18	,	,	PUNCT
ejpam-5735	66	19	is	be	AUX
ejpam-5735	66	20	the	the	DET
ejpam-5735	66	21	wavelet	wavelet	NOUN
ejpam-5735	66	22	transform	transform	NOUN
ejpam-5735	66	23	that	that	PRON
ejpam-5735	66	24	intertwines	intertwine	VERB
ejpam-5735	66	25	the	the	DET
ejpam-5735	66	26	co	co	ADJ
ejpam-5735	66	27	-	-	ADJ
ejpam-5735	66	28	adjoint	adjoint	ADJ
ejpam-5735	66	29	representation	representation	NOUN
ejpam-5735	66	30	of	of	ADP
ejpam-5735	66	31	the	the	DET
ejpam-5735	66	32	affine	affine	NOUN
ejpam-5735	66	33	group	group	NOUN
ejpam-5735	66	34	ρ±χ	ρ±χ	PROPN
ejpam-5735	66	35	,	,	PUNCT
ejpam-5735	66	36	with	with	ADP
ejpam-5735	66	37	the	the	DET
ejpam-5735	66	38	left	left	ADJ
ejpam-5735	66	39	regular	regular	ADJ
ejpam-5735	66	40	representation	representation	NOUN
ejpam-5735	66	41	λ(a	λ(a	NOUN
ejpam-5735	66	42	,	,	PUNCT
ejpam-5735	66	43	b	b	NOUN
ejpam-5735	66	44	)	)	PUNCT
ejpam-5735	66	45	given	give	VERB
ejpam-5735	66	46	by	by	ADP
ejpam-5735	66	47	(	(	PUNCT
ejpam-5735	66	48	3	3	NUM
ejpam-5735	66	49	)	)	PUNCT
ejpam-5735	66	50	.	.	PUNCT
ejpam-5735	67	1	proof	proof	NOUN
ejpam-5735	67	2	.	.	PUNCT
ejpam-5735	68	1	it	it	PRON
ejpam-5735	68	2	is	be	AUX
ejpam-5735	68	3	enough	enough	ADJ
ejpam-5735	68	4	to	to	PART
ejpam-5735	68	5	prove	prove	VERB
ejpam-5735	68	6	the	the	DET
ejpam-5735	68	7	corollary	corollary	NOUN
ejpam-5735	68	8	for	for	ADP
ejpam-5735	68	9	the	the	DET
ejpam-5735	68	10	representation	representation	NOUN
ejpam-5735	68	11	ρ+(4	ρ+(4	NUM
ejpam-5735	68	12	)	)	PUNCT
ejpam-5735	68	13	.	.	PUNCT
ejpam-5735	69	1	the	the	DET
ejpam-5735	69	2	result	result	NOUN
ejpam-5735	69	3	works	work	VERB
ejpam-5735	69	4	for	for	ADP
ejpam-5735	69	5	ρ−.	ρ−.	NOUN
ejpam-5735	69	6	let	let	VERB
ejpam-5735	69	7	the	the	DET
ejpam-5735	69	8	fiducial	fiducial	ADJ
ejpam-5735	69	9	operator	operator	NOUN
ejpam-5735	69	10	f	f	NOUN
ejpam-5735	69	11	:	:	PUNCT
ejpam-5735	69	12	l2(r+	l2(r+	PROPN
ejpam-5735	69	13	)	)	PUNCT
ejpam-5735	69	14	→	→	PUNCT
ejpam-5735	69	15	c	c	X
ejpam-5735	69	16	be	be	AUX
ejpam-5735	69	17	the	the	DET
ejpam-5735	69	18	functional	functional	ADJ
ejpam-5735	69	19	f	f	PROPN
ejpam-5735	69	20	7→	7→	NUM
ejpam-5735	69	21	⟨f	⟨f	PUNCT
ejpam-5735	69	22	,	,	PUNCT
ejpam-5735	69	23	f0⟩	f0⟩	PROPN
ejpam-5735	69	24	,	,	PUNCT
ejpam-5735	69	25	a.	a.	NOUN
ejpam-5735	69	26	alghamdi	alghamdi	NOUN
ejpam-5735	69	27	,	,	PUNCT
ejpam-5735	69	28	t.	t.	PROPN
ejpam-5735	69	29	alqurashi	alqurashi	PROPN
ejpam-5735	69	30	/	/	SYM
ejpam-5735	69	31	eur	eur	PROPN
ejpam-5735	69	32	.	.	PUNCT
ejpam-5735	70	1	j.	j.	PROPN
ejpam-5735	70	2	pure	pure	PROPN
ejpam-5735	70	3	appl	appl	PROPN
ejpam-5735	70	4	.	.	PROPN
ejpam-5735	70	5	math	math	PROPN
ejpam-5735	70	6	,	,	PUNCT
ejpam-5735	70	7	18	18	NUM
ejpam-5735	70	8	(	(	PUNCT
ejpam-5735	70	9	1	1	NUM
ejpam-5735	70	10	)	)	PUNCT
ejpam-5735	70	11	(	(	PUNCT
ejpam-5735	70	12	2025	2025	NUM
ejpam-5735	70	13	)	)	PUNCT
ejpam-5735	70	14	,	,	PUNCT
ejpam-5735	70	15	5735	5735	NUM
ejpam-5735	70	16	5	5	NUM
ejpam-5735	70	17	of	of	ADP
ejpam-5735	70	18	7	7	NUM
ejpam-5735	70	19	and	and	CCONJ
ejpam-5735	70	20	the	the	DET
ejpam-5735	70	21	mother	mother	NOUN
ejpam-5735	70	22	wavelet	wavelet	PROPN
ejpam-5735	70	23	be	be	AUX
ejpam-5735	70	24	f0(λ	f0(λ	PROPN
ejpam-5735	70	25	)	)	PUNCT
ejpam-5735	70	26	=	=	PUNCT
ejpam-5735	71	1	e2πζ	e2πζ	X
ejpam-5735	71	2	.	.	PUNCT
ejpam-5735	72	1	then	then	ADV
ejpam-5735	72	2	,	,	PUNCT
ejpam-5735	72	3	the	the	DET
ejpam-5735	72	4	wavelet	wavelet	NOUN
ejpam-5735	72	5	transform	transform	NOUN
ejpam-5735	72	6	is	be	AUX
ejpam-5735	72	7	given	give	VERB
ejpam-5735	72	8	as	as	SCONJ
ejpam-5735	72	9	follows	follow	VERB
ejpam-5735	72	10	:	:	PUNCT
ejpam-5735	73	1	[	[	X
ejpam-5735	73	2	wf0ρ	wf0ρ	PROPN
ejpam-5735	73	3	+	+	NUM
ejpam-5735	73	4	χ	χ	X
ejpam-5735	73	5	(	(	PUNCT
ejpam-5735	73	6	a	a	PRON
ejpam-5735	73	7	,	,	PUNCT
ejpam-5735	73	8	b)f	b)f	X
ejpam-5735	73	9	]	]	X
ejpam-5735	73	10	(	(	PUNCT
ejpam-5735	73	11	ζ	ζ	NOUN
ejpam-5735	73	12	)	)	PUNCT
ejpam-5735	73	13	=	=	SYM
ejpam-5735	73	14	⟨f	⟨f	X
ejpam-5735	73	15	,	,	PUNCT
ejpam-5735	73	16	ρ+(a	ρ+(a	NUM
ejpam-5735	73	17	,	,	PUNCT
ejpam-5735	73	18	b)f0⟩	b)f0⟩	NOUN
ejpam-5735	73	19	=	=	SYM
ejpam-5735	73	20	∫	∫	PROPN
ejpam-5735	73	21	r+	r+	NOUN
ejpam-5735	73	22	f(ζ)ρ+(a	f(ζ)ρ+(a	ADV
ejpam-5735	73	23	,	,	PUNCT
ejpam-5735	73	24	b)f0(ζ)dζ	b)f0(ζ)dζ	NOUN
ejpam-5735	73	25	=	=	SYM
ejpam-5735	73	26	∫	∫	PROPN
ejpam-5735	73	27	r+	r+	PUNCT
ejpam-5735	73	28	f(ζ	f(ζ	NOUN
ejpam-5735	73	29	)	)	PUNCT
ejpam-5735	73	30	√	√	ADP
ejpam-5735	73	31	ae−2πibζf0(aζ)dζ	ae−2πibζf0(aζ)dζ	NOUN
ejpam-5735	73	32	=	=	PUNCT
ejpam-5735	73	33	√	√	NOUN
ejpam-5735	73	34	a	a	DET
ejpam-5735	73	35	∫	∫	PROPN
ejpam-5735	73	36	r+	r+	X
ejpam-5735	73	37	f(ζ)e−2iπbζe−2πaζdζ	f(ζ)e−2iπbζe−2πaζdζ	ADJ
ejpam-5735	73	38	=	=	SYM
ejpam-5735	73	39	√	√	PROPN
ejpam-5735	73	40	a	a	DET
ejpam-5735	73	41	∫	∫	PROPN
ejpam-5735	73	42	r+	r+	NOUN
ejpam-5735	73	43	f(λ)e−2π(a+ib)ζdζ	f(λ)e−2π(a+ib)ζdζ	PROPN
ejpam-5735	73	44	=	=	PUNCT
ejpam-5735	73	45	√	√	ADP
ejpam-5735	73	46	af	af	PROPN
ejpam-5735	73	47	(	(	PUNCT
ejpam-5735	73	48	a+	a+	PUNCT
ejpam-5735	73	49	ib	ib	NOUN
ejpam-5735	73	50	)	)	PUNCT
ejpam-5735	73	51	.	.	PUNCT
ejpam-5735	74	1	4.2	4.2	NUM
ejpam-5735	74	2	.	.	PUNCT
ejpam-5735	75	1	induced	induce	VERB
ejpam-5735	75	2	wavelet	wavelet	NOUN
ejpam-5735	75	3	transform	transform	NOUN
ejpam-5735	75	4	in	in	ADP
ejpam-5735	75	5	this	this	DET
ejpam-5735	75	6	subsection	subsection	NOUN
ejpam-5735	75	7	,	,	PUNCT
ejpam-5735	75	8	we	we	PRON
ejpam-5735	75	9	will	will	AUX
ejpam-5735	75	10	study	study	VERB
ejpam-5735	75	11	the	the	DET
ejpam-5735	75	12	wavelet	wavelet	NOUN
ejpam-5735	75	13	transform	transform	NOUN
ejpam-5735	75	14	that	that	PRON
ejpam-5735	75	15	produces	produce	VERB
ejpam-5735	75	16	functions	function	NOUN
ejpam-5735	75	17	on	on	ADP
ejpam-5735	75	18	a	a	DET
ejpam-5735	75	19	homogeneous	homogeneous	ADJ
ejpam-5735	75	20	space	space	NOUN
ejpam-5735	75	21	rather	rather	ADV
ejpam-5735	75	22	than	than	ADP
ejpam-5735	75	23	the	the	DET
ejpam-5735	75	24	entire	entire	ADJ
ejpam-5735	75	25	group	group	NOUN
ejpam-5735	75	26	.	.	PUNCT
ejpam-5735	76	1	definition	definition	NOUN
ejpam-5735	76	2	2	2	NUM
ejpam-5735	76	3	.	.	PUNCT
ejpam-5735	77	1	[	[	X
ejpam-5735	77	2	9	9	NUM
ejpam-5735	77	3	]	]	PUNCT
ejpam-5735	77	4	let	let	VERB
ejpam-5735	77	5	h	h	PRON
ejpam-5735	77	6	be	be	AUX
ejpam-5735	77	7	a	a	DET
ejpam-5735	77	8	closed	closed	ADJ
ejpam-5735	77	9	subgroup	subgroup	NOUN
ejpam-5735	77	10	of	of	ADP
ejpam-5735	77	11	the	the	DET
ejpam-5735	77	12	group	group	NOUN
ejpam-5735	77	13	g	g	NOUN
ejpam-5735	77	14	,	,	PUNCT
ejpam-5735	77	15	and	and	CCONJ
ejpam-5735	77	16	h	h	NOUN
ejpam-5735	77	17	is	be	AUX
ejpam-5735	77	18	a	a	DET
ejpam-5735	77	19	hilbert	hilbert	NOUN
ejpam-5735	77	20	space	space	NOUN
ejpam-5735	77	21	.	.	PUNCT
ejpam-5735	78	1	for	for	ADP
ejpam-5735	78	2	some	some	DET
ejpam-5735	78	3	character	character	NOUN
ejpam-5735	78	4	χ	χ	NOUN
ejpam-5735	78	5	of	of	ADP
ejpam-5735	78	6	h	h	PRON
ejpam-5735	78	7	where	where	SCONJ
ejpam-5735	78	8	h	h	NOUN
ejpam-5735	78	9	∈	∈	PROPN
ejpam-5735	78	10	h	h	NOUN
ejpam-5735	78	11	and	and	CCONJ
ejpam-5735	78	12	ρ	ρ	PROPN
ejpam-5735	78	13	is	be	AUX
ejpam-5735	78	14	a	a	DET
ejpam-5735	78	15	unitary	unitary	ADJ
ejpam-5735	78	16	representation	representation	NOUN
ejpam-5735	78	17	of	of	ADP
ejpam-5735	78	18	the	the	DET
ejpam-5735	78	19	group	group	NOUN
ejpam-5735	78	20	g	g	PROPN
ejpam-5735	78	21	in	in	ADP
ejpam-5735	78	22	the	the	DET
ejpam-5735	78	23	space	space	NOUN
ejpam-5735	78	24	h	h	NOUN
ejpam-5735	78	25	there	there	PRON
ejpam-5735	78	26	is	be	VERB
ejpam-5735	78	27	a	a	DET
ejpam-5735	78	28	mother	mother	NOUN
ejpam-5735	78	29	wavelet	wavelet	NOUN
ejpam-5735	78	30	υ0	υ0	PROPN
ejpam-5735	78	31	∈	∈	PROPN
ejpam-5735	78	32	h	h	NOUN
ejpam-5735	78	33	such	such	ADJ
ejpam-5735	78	34	that	that	SCONJ
ejpam-5735	78	35	:	:	PUNCT
ejpam-5735	78	36	ρ(h)υ0	ρ(h)υ0	ADJ
ejpam-5735	78	37	=	=	PUNCT
ejpam-5735	78	38	χ(h)υ0	χ(h)υ0	ADJ
ejpam-5735	78	39	.	.	PUNCT
ejpam-5735	79	1	(	(	PUNCT
ejpam-5735	79	2	8)	8)	NUM
ejpam-5735	79	3	then	then	ADV
ejpam-5735	79	4	,	,	PUNCT
ejpam-5735	79	5	for	for	ADP
ejpam-5735	79	6	any	any	DET
ejpam-5735	79	7	continuous	continuous	ADJ
ejpam-5735	79	8	section	section	NOUN
ejpam-5735	79	9	s	s	PART
ejpam-5735	79	10	:	:	PUNCT
ejpam-5735	79	11	g	g	NOUN
ejpam-5735	79	12	/	/	SYM
ejpam-5735	79	13	h	h	NOUN
ejpam-5735	79	14	→	→	SYM
ejpam-5735	79	15	g	g	X
ejpam-5735	79	16	the	the	DET
ejpam-5735	79	17	induced	induced	ADJ
ejpam-5735	79	18	wavelet	wavelet	NOUN
ejpam-5735	79	19	transform	transform	NOUN
ejpam-5735	79	20	is	be	AUX
ejpam-5735	79	21	given	give	VERB
ejpam-5735	79	22	as	as	SCONJ
ejpam-5735	79	23	follows	follow	VERB
ejpam-5735	79	24	:	:	PUNCT
ejpam-5735	79	25	wυ0	wυ0	NOUN
ejpam-5735	79	26	:	:	PUNCT
ejpam-5735	79	27	υ	υ	PROPN
ejpam-5735	79	28	7→	7→	PROPN
ejpam-5735	79	29	υ̃(x	υ̃(x	PROPN
ejpam-5735	79	30	)	)	PUNCT
ejpam-5735	79	31	=	=	SYM
ejpam-5735	79	32	⟨υ	⟨υ	PROPN
ejpam-5735	79	33	,	,	PUNCT
ejpam-5735	79	34	ρ(s(x))υ0⟩	ρ(s(x))υ0⟩	PROPN
ejpam-5735	79	35	,	,	PUNCT
ejpam-5735	79	36	where	where	SCONJ
ejpam-5735	79	37	x	x	PUNCT
ejpam-5735	79	38	∈	∈	PROPN
ejpam-5735	79	39	g	g	PROPN
ejpam-5735	79	40	/	/	SYM
ejpam-5735	79	41	h	h	NOUN
ejpam-5735	79	42	(	(	PUNCT
ejpam-5735	79	43	9	9	NUM
ejpam-5735	79	44	)	)	PUNCT
ejpam-5735	79	45	intertwines	intertwine	VERB
ejpam-5735	79	46	ρ	ρ	NOUN
ejpam-5735	79	47	with	with	ADP
ejpam-5735	79	48	the	the	DET
ejpam-5735	79	49	representation	representation	NOUN
ejpam-5735	79	50	ρχ	ρχ	INTJ
ejpam-5735	79	51	in	in	ADP
ejpam-5735	79	52	a	a	DET
ejpam-5735	79	53	certain	certain	ADJ
ejpam-5735	79	54	function	function	NOUN
ejpam-5735	79	55	space	space	NOUN
ejpam-5735	79	56	on	on	ADP
ejpam-5735	79	57	the	the	DET
ejpam-5735	79	58	homogeneous	homogeneous	ADJ
ejpam-5735	79	59	space	space	NOUN
ejpam-5735	79	60	g	g	NOUN
ejpam-5735	79	61	/	/	SYM
ejpam-5735	79	62	h	h	NOUN
ejpam-5735	79	63	induced	induce	VERB
ejpam-5735	79	64	by	by	ADP
ejpam-5735	79	65	the	the	DET
ejpam-5735	79	66	character	character	NOUN
ejpam-5735	79	67	χ	χ	PROPN
ejpam-5735	79	68	of	of	ADP
ejpam-5735	79	69	h.	h.	PROPN
ejpam-5735	79	70	corollary	corollary	PROPN
ejpam-5735	79	71	3	3	PROPN
ejpam-5735	79	72	.	.	PUNCT
ejpam-5735	80	1	the	the	DET
ejpam-5735	80	2	induced	induce	VERB
ejpam-5735	80	3	wavelet	wavelet	NOUN
ejpam-5735	80	4	transform	transform	NOUN
ejpam-5735	80	5	that	that	PRON
ejpam-5735	80	6	intertwines	intertwine	VERB
ejpam-5735	80	7	respectively	respectively	ADV
ejpam-5735	80	8	the	the	DET
ejpam-5735	80	9	quasi	quasi	ADJ
ejpam-5735	80	10	-	-	ADJ
ejpam-5735	80	11	regular	regular	ADJ
ejpam-5735	80	12	representations	representation	NOUN
ejpam-5735	80	13	π+	π+	PUNCT
ejpam-5735	80	14	and	and	CCONJ
ejpam-5735	80	15	π−(5	π−(5	PROPN
ejpam-5735	80	16	)	)	PUNCT
ejpam-5735	80	17	with	with	ADP
ejpam-5735	80	18	the	the	DET
ejpam-5735	80	19	co	co	ADJ
ejpam-5735	80	20	-	-	ADJ
ejpam-5735	80	21	adjoint	adjoint	ADJ
ejpam-5735	80	22	representation	representation	NOUN
ejpam-5735	80	23	ρ+	ρ+	NOUN
ejpam-5735	80	24	and	and	CCONJ
ejpam-5735	80	25	ρ−	ρ−	NOUN
ejpam-5735	80	26	(	(	PUNCT
ejpam-5735	80	27	4	4	X
ejpam-5735	80	28	)	)	PUNCT
ejpam-5735	80	29	is	be	AUX
ejpam-5735	80	30	the	the	DET
ejpam-5735	80	31	fourier	fourier	NOUN
ejpam-5735	80	32	transform	transform	NOUN
ejpam-5735	81	1	[	[	X
ejpam-5735	81	2	ff	ff	X
ejpam-5735	81	3	]	]	PUNCT
ejpam-5735	81	4	(	(	PUNCT
ejpam-5735	81	5	λ	λ	NOUN
ejpam-5735	81	6	)	)	PUNCT
ejpam-5735	81	7	=	=	SYM
ejpam-5735	81	8	f̂(λ	f̂(λ	NOUN
ejpam-5735	81	9	)	)	PUNCT
ejpam-5735	81	10	=	=	SYM
ejpam-5735	82	1	∫	∫	PROPN
ejpam-5735	82	2	∞	∞	PROPN
ejpam-5735	82	3	−∞	−∞	ADP
ejpam-5735	82	4	f(x)e−2πixλdx	f(x)e−2πixλdx	NOUN
ejpam-5735	82	5	,	,	PUNCT
ejpam-5735	82	6	λ	λ	PROPN
ejpam-5735	82	7	∈	∈	PROPN
ejpam-5735	82	8	r.	r.	PROPN
ejpam-5735	82	9	(	(	PUNCT
ejpam-5735	82	10	10	10	NUM
ejpam-5735	82	11	)	)	PUNCT
ejpam-5735	82	12	proof	proof	NOUN
ejpam-5735	82	13	.	.	PUNCT
ejpam-5735	83	1	for	for	ADP
ejpam-5735	83	2	simplicity	simplicity	NOUN
ejpam-5735	83	3	,	,	PUNCT
ejpam-5735	83	4	it	it	PRON
ejpam-5735	83	5	suffices	suffice	VERB
ejpam-5735	83	6	to	to	PART
ejpam-5735	83	7	prove	prove	VERB
ejpam-5735	83	8	the	the	DET
ejpam-5735	83	9	corollary	corollary	NOUN
ejpam-5735	83	10	for	for	ADP
ejpam-5735	83	11	the	the	DET
ejpam-5735	83	12	representation	representation	NOUN
ejpam-5735	83	13	π+(5	π+(5	NOUN
ejpam-5735	83	14	)	)	PUNCT
ejpam-5735	83	15	.	.	PUNCT
ejpam-5735	84	1	the	the	DET
ejpam-5735	84	2	same	same	ADJ
ejpam-5735	84	3	argument	argument	NOUN
ejpam-5735	84	4	is	be	AUX
ejpam-5735	84	5	valid	valid	ADJ
ejpam-5735	84	6	for	for	ADP
ejpam-5735	84	7	π−.	π−.	ADJ
ejpam-5735	84	8	let	let	VERB
ejpam-5735	84	9	the	the	DET
ejpam-5735	84	10	mother	mother	NOUN
ejpam-5735	84	11	wavelet	wavelet	NOUN
ejpam-5735	84	12	be	be	AUX
ejpam-5735	84	13	ψ0(x	ψ0(x	NUM
ejpam-5735	84	14	)	)	PUNCT
ejpam-5735	84	15	=	=	PUNCT
ejpam-5735	85	1	e2πix	e2πix	PROPN
ejpam-5735	85	2	.	.	PUNCT
ejpam-5735	86	1	it	it	PRON
ejpam-5735	86	2	is	be	AUX
ejpam-5735	86	3	clear	clear	ADJ
ejpam-5735	86	4	that	that	SCONJ
ejpam-5735	86	5	ψ0	ψ0	ADV
ejpam-5735	86	6	satisfies	satisfy	VERB
ejpam-5735	86	7	the	the	DET
ejpam-5735	86	8	following	follow	VERB
ejpam-5735	86	9	condition	condition	NOUN
ejpam-5735	86	10	:	:	PUNCT
ejpam-5735	86	11	π+(1	π+(1	NOUN
ejpam-5735	86	12	,	,	PUNCT
ejpam-5735	86	13	b)ψ0	b)ψ0	PROPN
ejpam-5735	86	14	=	=	SYM
ejpam-5735	86	15	χ(1	χ(1	PROPN
ejpam-5735	86	16	,	,	PUNCT
ejpam-5735	86	17	b)ψ0	b)ψ0	PROPN
ejpam-5735	86	18	,	,	PUNCT
ejpam-5735	86	19	a.	a.	NOUN
ejpam-5735	86	20	alghamdi	alghamdi	NOUN
ejpam-5735	86	21	,	,	PUNCT
ejpam-5735	86	22	t.	t.	PROPN
ejpam-5735	86	23	alqurashi	alqurashi	PROPN
ejpam-5735	86	24	/	/	SYM
ejpam-5735	86	25	eur	eur	PROPN
ejpam-5735	86	26	.	.	PUNCT
ejpam-5735	87	1	j.	j.	PROPN
ejpam-5735	87	2	pure	pure	PROPN
ejpam-5735	87	3	appl	appl	PROPN
ejpam-5735	87	4	.	.	PROPN
ejpam-5735	87	5	math	math	PROPN
ejpam-5735	87	6	,	,	PUNCT
ejpam-5735	87	7	18	18	NUM
ejpam-5735	87	8	(	(	PUNCT
ejpam-5735	87	9	1	1	NUM
ejpam-5735	87	10	)	)	PUNCT
ejpam-5735	87	11	(	(	PUNCT
ejpam-5735	87	12	2025	2025	NUM
ejpam-5735	87	13	)	)	PUNCT
ejpam-5735	87	14	,	,	PUNCT
ejpam-5735	87	15	5735	5735	NUM
ejpam-5735	87	16	6	6	NUM
ejpam-5735	87	17	of	of	ADP
ejpam-5735	87	18	7	7	NUM
ejpam-5735	87	19	where	where	SCONJ
ejpam-5735	87	20	χ(1	χ(1	PROPN
ejpam-5735	87	21	,	,	PUNCT
ejpam-5735	87	22	b	b	NOUN
ejpam-5735	87	23	)	)	PUNCT
ejpam-5735	87	24	=	=	SYM
ejpam-5735	87	25	e2πib	e2πib	PROPN
ejpam-5735	87	26	is	be	AUX
ejpam-5735	87	27	the	the	DET
ejpam-5735	87	28	character	character	NOUN
ejpam-5735	87	29	of	of	ADP
ejpam-5735	87	30	the	the	DET
ejpam-5735	87	31	subgroup	subgroup	NOUN
ejpam-5735	87	32	n	n	NOUN
ejpam-5735	87	33	.	.	PUNCT
ejpam-5735	88	1	let	let	VERB
ejpam-5735	88	2	s	s	PRON
ejpam-5735	88	3	:	:	PUNCT
ejpam-5735	88	4	r+	r+	NOUN
ejpam-5735	88	5	→	→	PUNCT
ejpam-5735	88	6	aff	aff	PROPN
ejpam-5735	88	7	be	be	AUX
ejpam-5735	88	8	the	the	DET
ejpam-5735	88	9	continuous	continuous	ADJ
ejpam-5735	88	10	section	section	NOUN
ejpam-5735	88	11	defined	define	VERB
ejpam-5735	88	12	as	as	ADP
ejpam-5735	88	13	s(a	s(a	NOUN
ejpam-5735	88	14	)	)	PUNCT
ejpam-5735	88	15	=	=	PUNCT
ejpam-5735	89	1	(	(	PUNCT
ejpam-5735	89	2	a	a	PRON
ejpam-5735	89	3	,	,	PUNCT
ejpam-5735	89	4	0	0	NUM
ejpam-5735	89	5	)	)	PUNCT
ejpam-5735	89	6	where	where	SCONJ
ejpam-5735	89	7	a	a	DET
ejpam-5735	89	8	∈	∈	NOUN
ejpam-5735	89	9	r+	r+	NOUN
ejpam-5735	89	10	.	.	PUNCT
ejpam-5735	90	1	then	then	ADV
ejpam-5735	90	2	,	,	PUNCT
ejpam-5735	90	3	for	for	ADP
ejpam-5735	90	4	f	f	PROPN
ejpam-5735	90	5	∈	∈	PROPN
ejpam-5735	90	6	h2(r	h2(r	PROPN
ejpam-5735	90	7	)	)	PUNCT
ejpam-5735	90	8	,	,	PUNCT
ejpam-5735	90	9	we	we	PRON
ejpam-5735	90	10	calculate	calculate	VERB
ejpam-5735	90	11	the	the	DET
ejpam-5735	90	12	induced	induced	ADJ
ejpam-5735	90	13	wavelet	wavelet	NOUN
ejpam-5735	90	14	transform	transform	NOUN
ejpam-5735	90	15	as	as	SCONJ
ejpam-5735	90	16	follows	follow	VERB
ejpam-5735	90	17	:	:	PUNCT
ejpam-5735	91	1	[	[	X
ejpam-5735	91	2	wψ0f	wψ0f	X
ejpam-5735	91	3	]	]	X
ejpam-5735	91	4	(	(	PUNCT
ejpam-5735	91	5	λ	λ	NOUN
ejpam-5735	91	6	)	)	PUNCT
ejpam-5735	91	7	=	=	SYM
ejpam-5735	91	8	⟨f	⟨f	X
ejpam-5735	91	9	,	,	PUNCT
ejpam-5735	91	10	π+(s(λ))ψ0⟩	π+(s(λ))ψ0⟩	PROPN
ejpam-5735	91	11	=	=	SYM
ejpam-5735	91	12	⟨f	⟨f	X
ejpam-5735	91	13	,	,	PUNCT
ejpam-5735	91	14	π+(λ	π+(λ	CCONJ
ejpam-5735	91	15	,	,	PUNCT
ejpam-5735	91	16	0)ψ0⟩	0)ψ0⟩	NOUN
ejpam-5735	91	17	=	=	SYM
ejpam-5735	91	18	∫	∫	PROPN
ejpam-5735	91	19	r	r	NOUN
ejpam-5735	91	20	f(x)π+(λ	f(x)π+(λ	NOUN
ejpam-5735	91	21	,	,	PUNCT
ejpam-5735	91	22	0)ψ0(x)dx	0)ψ0(x)dx	NOUN
ejpam-5735	91	23	=	=	SYM
ejpam-5735	91	24	1√	1√	PROPN
ejpam-5735	91	25	λ	λ	PROPN
ejpam-5735	91	26	∫	∫	NOUN
ejpam-5735	91	27	r	r	NOUN
ejpam-5735	91	28	f(x)ψ0	f(x)ψ0	PROPN
ejpam-5735	91	29	(	(	PUNCT
ejpam-5735	91	30	x	x	PART
ejpam-5735	91	31	λ	λ	X
ejpam-5735	91	32	)	)	PUNCT
ejpam-5735	91	33	dx	dx	PROPN
ejpam-5735	92	1	=	=	SYM
ejpam-5735	92	2	1√	1√	PROPN
ejpam-5735	92	3	λ	λ	PROPN
ejpam-5735	92	4	∫	∫	PROPN
ejpam-5735	92	5	r	r	NOUN
ejpam-5735	92	6	f(x)e−2πi	f(x)e−2πi	NOUN
ejpam-5735	92	7	x	x	NOUN
ejpam-5735	92	8	λdx	λdx	ADJ
ejpam-5735	92	9	=	=	SYM
ejpam-5735	92	10	1√	1√	PROPN
ejpam-5735	92	11	λ	λ	PROPN
ejpam-5735	92	12	f̂	f̂	X
ejpam-5735	92	13	(	(	PUNCT
ejpam-5735	92	14	1	1	NUM
ejpam-5735	92	15	λ	λ	NOUN
ejpam-5735	92	16	)	)	PUNCT
ejpam-5735	92	17	,	,	PUNCT
ejpam-5735	92	18	λ	λ	PROPN
ejpam-5735	92	19	∈	∈	PROPN
ejpam-5735	92	20	r+	r+	X
ejpam-5735	92	21	.	.	PUNCT
ejpam-5735	93	1	this	this	PRON
ejpam-5735	93	2	is	be	AUX
ejpam-5735	93	3	the	the	DET
ejpam-5735	93	4	fourier	fourier	NOUN
ejpam-5735	93	5	transform	transform	NOUN
ejpam-5735	93	6	.	.	PUNCT
ejpam-5735	94	1	next	next	ADV
ejpam-5735	94	2	,	,	PUNCT
ejpam-5735	94	3	for	for	ADP
ejpam-5735	94	4	the	the	DET
ejpam-5735	94	5	co	co	ADJ
ejpam-5735	94	6	-	-	ADJ
ejpam-5735	94	7	adjoint	adjoint	ADJ
ejpam-5735	94	8	representation	representation	NOUN
ejpam-5735	94	9	ρ+	ρ+	NOUN
ejpam-5735	94	10	,	,	PUNCT
ejpam-5735	94	11	the	the	DET
ejpam-5735	94	12	mother	mother	NOUN
ejpam-5735	94	13	wavelet	wavelet	NOUN
ejpam-5735	94	14	ψ0(x	ψ0(x	NOUN
ejpam-5735	94	15	)	)	PUNCT
ejpam-5735	94	16	=	=	SYM
ejpam-5735	94	17	1	1	NUM
ejpam-5735	94	18	satisfies	satisfy	VERB
ejpam-5735	94	19	the	the	DET
ejpam-5735	94	20	condition	condition	NOUN
ejpam-5735	94	21	ρ+(a	ρ+(a	NUM
ejpam-5735	94	22	,	,	PUNCT
ejpam-5735	94	23	0)ψ0	0)ψ0	PROPN
ejpam-5735	94	24	=	=	SYM
ejpam-5735	95	1	χ(a	χ(a	NOUN
ejpam-5735	95	2	,	,	PUNCT
ejpam-5735	95	3	0)ψ0	0)ψ0	PROPN
ejpam-5735	95	4	,	,	PUNCT
ejpam-5735	95	5	where	where	SCONJ
ejpam-5735	95	6	χ(a	χ(a	NOUN
ejpam-5735	95	7	,	,	PUNCT
ejpam-5735	95	8	0	0	NUM
ejpam-5735	95	9	)	)	PUNCT
ejpam-5735	95	10	=	=	PUNCT
ejpam-5735	95	11	a	a	DET
ejpam-5735	95	12	1	1	NUM
ejpam-5735	95	13	2	2	NUM
ejpam-5735	95	14	is	be	AUX
ejpam-5735	95	15	the	the	DET
ejpam-5735	95	16	character	character	NOUN
ejpam-5735	95	17	of	of	ADP
ejpam-5735	95	18	the	the	DET
ejpam-5735	95	19	subgroup	subgroup	PROPN
ejpam-5735	95	20	a.	a.	NOUN
ejpam-5735	95	21	let	let	VERB
ejpam-5735	95	22	s	s	PRON
ejpam-5735	95	23	:	:	PUNCT
ejpam-5735	95	24	r	r	X
ejpam-5735	95	25	→	→	PUNCT
ejpam-5735	95	26	aff	aff	X
ejpam-5735	95	27	be	be	AUX
ejpam-5735	95	28	the	the	DET
ejpam-5735	95	29	continuous	continuous	ADJ
ejpam-5735	95	30	section	section	NOUN
ejpam-5735	95	31	defined	define	VERB
ejpam-5735	95	32	as	as	ADP
ejpam-5735	95	33	s(b	s(b	NOUN
ejpam-5735	95	34	)	)	PUNCT
ejpam-5735	95	35	=	=	PUNCT
ejpam-5735	95	36	(	(	PUNCT
ejpam-5735	95	37	1	1	NUM
ejpam-5735	95	38	,	,	PUNCT
ejpam-5735	95	39	b	b	NOUN
ejpam-5735	95	40	)	)	PUNCT
ejpam-5735	95	41	,	,	PUNCT
ejpam-5735	95	42	where	where	SCONJ
ejpam-5735	95	43	b	b	PROPN
ejpam-5735	95	44	∈	∈	PROPN
ejpam-5735	95	45	r.	r.	PROPN
ejpam-5735	95	46	then	then	ADV
ejpam-5735	95	47	,	,	PUNCT
ejpam-5735	95	48	for	for	ADP
ejpam-5735	95	49	g	g	PROPN
ejpam-5735	95	50	∈	∈	PROPN
ejpam-5735	95	51	l2(r+	l2(r+	PROPN
ejpam-5735	95	52	)	)	PUNCT
ejpam-5735	95	53	the	the	DET
ejpam-5735	95	54	induced	induce	VERB
ejpam-5735	95	55	wavelet	wavelet	NOUN
ejpam-5735	95	56	transform	transform	NOUN
ejpam-5735	95	57	[	[	X
ejpam-5735	95	58	wψ0g](ξ	wψ0g](ξ	NOUN
ejpam-5735	95	59	)	)	PUNCT
ejpam-5735	96	1	=	=	SYM
ejpam-5735	96	2	⟨g	⟨g	NOUN
ejpam-5735	96	3	,	,	PUNCT
ejpam-5735	96	4	ρ+(s(ξ))ψ0⟩	ρ+(s(ξ))ψ0⟩	NUM
ejpam-5735	96	5	where	where	SCONJ
ejpam-5735	96	6	ξ	ξ	PROPN
ejpam-5735	96	7	∈	∈	PROPN
ejpam-5735	96	8	r	r	NOUN
ejpam-5735	96	9	,	,	PUNCT
ejpam-5735	96	10	is	be	AUX
ejpam-5735	96	11	the	the	DET
ejpam-5735	96	12	fourier	fourier	NOUN
ejpam-5735	96	13	transform	transform	NOUN
ejpam-5735	96	14	.	.	PUNCT
ejpam-5735	97	1	5	5	X
ejpam-5735	97	2	.	.	X
ejpam-5735	97	3	conclusion	conclusion	NOUN
ejpam-5735	97	4	we	we	PRON
ejpam-5735	97	5	demonstrated	demonstrate	VERB
ejpam-5735	97	6	the	the	DET
ejpam-5735	97	7	intertwining	intertwine	VERB
ejpam-5735	97	8	operator	operator	NOUN
ejpam-5735	97	9	of	of	ADP
ejpam-5735	97	10	the	the	DET
ejpam-5735	97	11	affine	affine	NOUN
ejpam-5735	97	12	group	group	NOUN
ejpam-5735	97	13	,	,	PUNCT
ejpam-5735	97	14	which	which	PRON
ejpam-5735	97	15	allows	allow	VERB
ejpam-5735	97	16	a	a	DET
ejpam-5735	97	17	connection	connection	NOUN
ejpam-5735	97	18	between	between	ADP
ejpam-5735	97	19	the	the	DET
ejpam-5735	97	20	representations	representation	NOUN
ejpam-5735	97	21	while	while	SCONJ
ejpam-5735	97	22	preserving	preserve	VERB
ejpam-5735	97	23	the	the	DET
ejpam-5735	97	24	action	action	NOUN
ejpam-5735	97	25	of	of	ADP
ejpam-5735	97	26	the	the	DET
ejpam-5735	97	27	affine	affine	NOUN
ejpam-5735	97	28	group	group	NOUN
ejpam-5735	97	29	.	.	PUNCT
ejpam-5735	98	1	we	we	PRON
ejpam-5735	98	2	find	find	VERB
ejpam-5735	98	3	that	that	SCONJ
ejpam-5735	98	4	the	the	DET
ejpam-5735	98	5	laplace	laplace	NOUN
ejpam-5735	98	6	transform	transform	NOUN
ejpam-5735	98	7	intertwines	intertwine	VERB
ejpam-5735	98	8	the	the	DET
ejpam-5735	98	9	co	co	ADJ
ejpam-5735	98	10	-	-	ADJ
ejpam-5735	98	11	adjoint	adjoint	ADJ
ejpam-5735	98	12	representation	representation	NOUN
ejpam-5735	98	13	with	with	ADP
ejpam-5735	98	14	the	the	DET
ejpam-5735	98	15	left	leave	VERB
ejpam-5735	98	16	-	-	PUNCT
ejpam-5735	98	17	regular	regular	ADJ
ejpam-5735	98	18	representation	representation	NOUN
ejpam-5735	98	19	of	of	ADP
ejpam-5735	98	20	the	the	DET
ejpam-5735	98	21	affine	affine	NOUN
ejpam-5735	98	22	group	group	NOUN
ejpam-5735	98	23	.	.	PUNCT
ejpam-5735	99	1	moreover	moreover	ADV
ejpam-5735	99	2	,	,	PUNCT
ejpam-5735	99	3	the	the	DET
ejpam-5735	99	4	poisson	poisson	NOUN
ejpam-5735	99	5	integral	integral	ADJ
ejpam-5735	99	6	is	be	AUX
ejpam-5735	99	7	the	the	DET
ejpam-5735	99	8	intertwining	intertwine	VERB
ejpam-5735	99	9	operator	operator	NOUN
ejpam-5735	99	10	between	between	ADP
ejpam-5735	99	11	the	the	DET
ejpam-5735	99	12	quasi	quasi	NOUN
ejpam-5735	99	13	-	-	ADJ
ejpam-5735	99	14	regular	regular	ADJ
ejpam-5735	99	15	and	and	CCONJ
ejpam-5735	99	16	left	left	ADJ
ejpam-5735	99	17	-	-	PUNCT
ejpam-5735	99	18	regular	regular	ADJ
ejpam-5735	99	19	representations	representation	NOUN
ejpam-5735	99	20	.	.	PUNCT
ejpam-5735	100	1	finally	finally	ADV
ejpam-5735	100	2	,	,	PUNCT
ejpam-5735	100	3	the	the	DET
ejpam-5735	100	4	fourier	fourier	NOUN
ejpam-5735	100	5	transform	transform	NOUN
ejpam-5735	100	6	intertwines	intertwine	VERB
ejpam-5735	100	7	the	the	DET
ejpam-5735	100	8	co	co	NOUN
ejpam-5735	100	9	-	-	NOUN
ejpam-5735	100	10	adjoint	adjoint	ADJ
ejpam-5735	100	11	with	with	ADP
ejpam-5735	100	12	the	the	DET
ejpam-5735	100	13	quasi	quasi	ADJ
ejpam-5735	100	14	-	-	ADJ
ejpam-5735	100	15	regular	regular	ADJ
ejpam-5735	100	16	representation	representation	NOUN
ejpam-5735	100	17	.	.	PUNCT
ejpam-5735	101	1	references	reference	NOUN
ejpam-5735	101	2	[	[	X
ejpam-5735	101	3	1	1	NUM
ejpam-5735	101	4	]	]	PUNCT
ejpam-5735	101	5	syed	syed	PROPN
ejpam-5735	101	6	ali	ali	PROPN
ejpam-5735	101	7	,	,	PUNCT
ejpam-5735	101	8	jean	jean	PROPN
ejpam-5735	101	9	-	-	PUNCT
ejpam-5735	101	10	pierre	pierre	PROPN
ejpam-5735	101	11	antoine	antoine	PROPN
ejpam-5735	101	12	,	,	PUNCT
ejpam-5735	101	13	and	and	CCONJ
ejpam-5735	101	14	jean	jean	PROPN
ejpam-5735	101	15	-	-	PUNCT
ejpam-5735	101	16	pierre	pierre	PROPN
ejpam-5735	101	17	gazeau	gazeau	NOUN
ejpam-5735	101	18	.	.	PUNCT
ejpam-5735	102	1	coherent	coherent	ADJ
ejpam-5735	102	2	states	state	NOUN
ejpam-5735	102	3	,	,	PUNCT
ejpam-5735	102	4	wavelets	wavelet	NOUN
ejpam-5735	102	5	,	,	PUNCT
ejpam-5735	102	6	and	and	CCONJ
ejpam-5735	102	7	their	their	PRON
ejpam-5735	102	8	generalizations	generalization	NOUN
ejpam-5735	102	9	.	.	PUNCT
ejpam-5735	103	1	2nd	2nd	ADJ
ejpam-5735	103	2	updated	update	VERB
ejpam-5735	103	3	ed	ed	NOUN
ejpam-5735	103	4	.	.	PUNCT
ejpam-5735	103	5	springer	springer	PROPN
ejpam-5735	103	6	new	new	PROPN
ejpam-5735	103	7	york	york	PROPN
ejpam-5735	103	8	,	,	PUNCT
ejpam-5735	103	9	ny	ny	PROPN
ejpam-5735	103	10	,	,	PUNCT
ejpam-5735	103	11	01	01	NUM
ejpam-5735	103	12	2014	2014	NUM
ejpam-5735	103	13	.	.	PUNCT
ejpam-5735	104	1	[	[	X
ejpam-5735	104	2	2	2	NUM
ejpam-5735	104	3	]	]	PUNCT
ejpam-5735	104	4	taghreed	taghreed	NOUN
ejpam-5735	104	5	alqurashi	alqurashi	NOUN
ejpam-5735	104	6	and	and	CCONJ
ejpam-5735	104	7	vladimir	vladimir	PROPN
ejpam-5735	104	8	v.	v.	PROPN
ejpam-5735	104	9	kisil	kisil	PROPN
ejpam-5735	104	10	.	.	PUNCT
ejpam-5735	105	1	metamorphism	metamorphism	PROPN
ejpam-5735	105	2	as	as	ADP
ejpam-5735	105	3	a	a	DET
ejpam-5735	105	4	covariant	covariant	ADJ
ejpam-5735	105	5	transform	transform	NOUN
ejpam-5735	105	6	for	for	ADP
ejpam-5735	105	7	the	the	DET
ejpam-5735	105	8	ssr	ssr	PROPN
ejpam-5735	105	9	group	group	NOUN
ejpam-5735	105	10	.	.	PUNCT
ejpam-5735	106	1	bolet́ın	bolet́ın	PROPN
ejpam-5735	106	2	de	de	X
ejpam-5735	106	3	la	la	PROPN
ejpam-5735	106	4	sociedad	sociedad	PROPN
ejpam-5735	106	5	matemática	matemática	PROPN
ejpam-5735	106	6	mexicana	mexicana	PROPN
ejpam-5735	106	7	,	,	PUNCT
ejpam-5735	106	8	29(2	29(2	NUM
ejpam-5735	106	9	)	)	PUNCT
ejpam-5735	106	10	,	,	PUNCT
ejpam-5735	106	11	may	may	AUX
ejpam-5735	106	12	2023	2023	NUM
ejpam-5735	106	13	.	.	PUNCT
ejpam-5735	107	1	[	[	X
ejpam-5735	107	2	3	3	X
ejpam-5735	107	3	]	]	PUNCT
ejpam-5735	107	4	ingrid	ingrid	PROPN
ejpam-5735	107	5	daubechies	daubechies	PROPN
ejpam-5735	107	6	.	.	PUNCT
ejpam-5735	108	1	ten	ten	NUM
ejpam-5735	108	2	lectures	lecture	NOUN
ejpam-5735	108	3	on	on	ADP
ejpam-5735	108	4	wavelets	wavelet	NOUN
ejpam-5735	108	5	,	,	PUNCT
ejpam-5735	108	6	volume	volume	NOUN
ejpam-5735	108	7	61	61	NUM
ejpam-5735	108	8	of	of	ADP
ejpam-5735	108	9	cbms	cbms	ADJ
ejpam-5735	108	10	-	-	PUNCT
ejpam-5735	108	11	nsf	nsf	ADJ
ejpam-5735	108	12	regional	regional	ADJ
ejpam-5735	108	13	conference	conference	NOUN
ejpam-5735	108	14	series	series	NOUN
ejpam-5735	108	15	in	in	ADP
ejpam-5735	108	16	applied	applied	ADJ
ejpam-5735	108	17	mathematics	mathematic	NOUN
ejpam-5735	108	18	.	.	PUNCT
ejpam-5735	109	1	society	society	NOUN
ejpam-5735	109	2	for	for	ADP
ejpam-5735	109	3	industrial	industrial	ADJ
ejpam-5735	109	4	and	and	CCONJ
ejpam-5735	109	5	applied	applied	ADJ
ejpam-5735	109	6	mathematics	mathematic	NOUN
ejpam-5735	109	7	(	(	PUNCT
ejpam-5735	109	8	siam	siam	NOUN
ejpam-5735	109	9	)	)	PUNCT
ejpam-5735	109	10	,	,	PUNCT
ejpam-5735	109	11	philadelphia	philadelphia	PROPN
ejpam-5735	109	12	,	,	PUNCT
ejpam-5735	109	13	pa	pa	PROPN
ejpam-5735	109	14	,	,	PUNCT
ejpam-5735	109	15	1992	1992	NUM
ejpam-5735	109	16	.	.	PUNCT
ejpam-5735	110	1	[	[	X
ejpam-5735	110	2	4	4	X
ejpam-5735	110	3	]	]	X
ejpam-5735	110	4	abdelhamid	abdelhamid	PROPN
ejpam-5735	110	5	s.	s.	PROPN
ejpam-5735	110	6	elmabrok	elmabrok	PROPN
ejpam-5735	110	7	and	and	CCONJ
ejpam-5735	110	8	ondrej	ondrej	VERB
ejpam-5735	110	9	hutńık	hutńık	ADV
ejpam-5735	110	10	.	.	PUNCT
ejpam-5735	111	1	induced	induce	VERB
ejpam-5735	111	2	representations	representation	NOUN
ejpam-5735	111	3	of	of	ADP
ejpam-5735	111	4	the	the	DET
ejpam-5735	111	5	affine	affine	NOUN
ejpam-5735	111	6	group	group	NOUN
ejpam-5735	111	7	and	and	CCONJ
ejpam-5735	111	8	intertwining	intertwine	VERB
ejpam-5735	111	9	operators	operator	NOUN
ejpam-5735	111	10	:	:	PUNCT
ejpam-5735	111	11	i.	i.	PROPN
ejpam-5735	111	12	analytical	analytical	ADJ
ejpam-5735	111	13	approach	approach	NOUN
ejpam-5735	111	14	.	.	PUNCT
ejpam-5735	112	1	j.	j.	PROPN
ejpam-5735	112	2	phys	phys	PROPN
ejpam-5735	112	3	.	.	PUNCT
ejpam-5735	113	1	a	a	DET
ejpam-5735	113	2	,	,	PUNCT
ejpam-5735	113	3	45(24):244017	45(24):244017	NUM
ejpam-5735	113	4	,	,	PUNCT
ejpam-5735	113	5	15	15	NUM
ejpam-5735	113	6	,	,	PUNCT
ejpam-5735	113	7	2012	2012	NUM
ejpam-5735	113	8	.	.	PUNCT
ejpam-5735	113	9	a.	a.	NOUN
ejpam-5735	113	10	alghamdi	alghamdi	PROPN
ejpam-5735	113	11	,	,	PUNCT
ejpam-5735	113	12	t.	t.	PROPN
ejpam-5735	113	13	alqurashi	alqurashi	PROPN
ejpam-5735	113	14	/	/	SYM
ejpam-5735	113	15	eur	eur	PROPN
ejpam-5735	113	16	.	.	PUNCT
ejpam-5735	114	1	j.	j.	PROPN
ejpam-5735	114	2	pure	pure	PROPN
ejpam-5735	114	3	appl	appl	PROPN
ejpam-5735	114	4	.	.	PROPN
ejpam-5735	114	5	math	math	PROPN
ejpam-5735	114	6	,	,	PUNCT
ejpam-5735	114	7	18	18	NUM
ejpam-5735	114	8	(	(	PUNCT
ejpam-5735	114	9	1	1	NUM
ejpam-5735	114	10	)	)	PUNCT
ejpam-5735	114	11	(	(	PUNCT
ejpam-5735	114	12	2025	2025	NUM
ejpam-5735	114	13	)	)	PUNCT
ejpam-5735	114	14	,	,	PUNCT
ejpam-5735	114	15	5735	5735	NUM
ejpam-5735	114	16	7	7	NUM
ejpam-5735	114	17	of	of	ADP
ejpam-5735	114	18	7	7	NUM
ejpam-5735	114	19	[	[	SYM
ejpam-5735	114	20	5	5	NUM
ejpam-5735	114	21	]	]	X
ejpam-5735	114	22	g.b	g.b	PROPN
ejpam-5735	114	23	.	.	PROPN
ejpam-5735	114	24	folland	folland	PROPN
ejpam-5735	114	25	.	.	PUNCT
ejpam-5735	115	1	a	a	DET
ejpam-5735	115	2	course	course	NOUN
ejpam-5735	115	3	in	in	ADP
ejpam-5735	115	4	abstract	abstract	ADJ
ejpam-5735	115	5	harmonic	harmonic	ADJ
ejpam-5735	115	6	analysis	analysis	NOUN
ejpam-5735	115	7	,	,	PUNCT
ejpam-5735	115	8	second	second	ADJ
ejpam-5735	115	9	edition	edition	NOUN
ejpam-5735	115	10	.	.	PUNCT
ejpam-5735	116	1	chapman	chapman	PROPN
ejpam-5735	116	2	and	and	CCONJ
ejpam-5735	116	3	hall	hall	PROPN
ejpam-5735	116	4	/	/	SYM
ejpam-5735	116	5	crc	crc	PROPN
ejpam-5735	116	6	,	,	PUNCT
ejpam-5735	116	7	02	02	NUM
ejpam-5735	116	8	2015	2015	NUM
ejpam-5735	116	9	.	.	PUNCT
ejpam-5735	117	1	[	[	X
ejpam-5735	117	2	6	6	NUM
ejpam-5735	117	3	]	]	X
ejpam-5735	117	4	jason	jason	PROPN
ejpam-5735	117	5	fulman	fulman	PROPN
ejpam-5735	117	6	and	and	CCONJ
ejpam-5735	117	7	robert	robert	PROPN
ejpam-5735	117	8	m.	m.	PROPN
ejpam-5735	117	9	guralnick	guralnick	PROPN
ejpam-5735	117	10	.	.	PUNCT
ejpam-5735	118	1	enumeration	enumeration	NOUN
ejpam-5735	118	2	of	of	ADP
ejpam-5735	118	3	conjugacy	conjugacy	PROPN
ejpam-5735	118	4	classes	class	NOUN
ejpam-5735	118	5	in	in	ADP
ejpam-5735	118	6	affine	affine	NOUN
ejpam-5735	118	7	groups	group	NOUN
ejpam-5735	118	8	.	.	PUNCT
ejpam-5735	119	1	algebra	algebra	NOUN
ejpam-5735	119	2	number	number	NOUN
ejpam-5735	119	3	theory	theory	NOUN
ejpam-5735	119	4	,	,	PUNCT
ejpam-5735	119	5	18(6):1189–1219	18(6):1189–1219	NUM
ejpam-5735	119	6	,	,	PUNCT
ejpam-5735	119	7	2024	2024	NUM
ejpam-5735	119	8	.	.	PUNCT
ejpam-5735	120	1	[	[	X
ejpam-5735	120	2	7	7	NUM
ejpam-5735	120	3	]	]	X
ejpam-5735	120	4	i.	i.	PROPN
ejpam-5735	120	5	m.	m.	PROPN
ejpam-5735	120	6	gelfand	gelfand	PROPN
ejpam-5735	120	7	and	and	CCONJ
ejpam-5735	120	8	m.	m.	PROPN
ejpam-5735	120	9	a.	a.	PROPN
ejpam-5735	120	10	naimark	naimark	PROPN
ejpam-5735	120	11	.	.	PUNCT
ejpam-5735	121	1	unitary	unitary	ADJ
ejpam-5735	121	2	representations	representation	NOUN
ejpam-5735	121	3	of	of	ADP
ejpam-5735	121	4	the	the	DET
ejpam-5735	121	5	group	group	NOUN
ejpam-5735	121	6	of	of	ADP
ejpam-5735	121	7	linear	linear	ADJ
ejpam-5735	121	8	transformations	transformation	NOUN
ejpam-5735	121	9	of	of	ADP
ejpam-5735	121	10	the	the	DET
ejpam-5735	121	11	straight	straight	ADJ
ejpam-5735	121	12	line	line	NOUN
ejpam-5735	121	13	.	.	PUNCT
ejpam-5735	122	1	dokl	dokl	NOUN
ejpam-5735	122	2	.	.	PUNCT
ejpam-5735	123	1	akad	akad	PROPN
ejpam-5735	123	2	.	.	PUNCT
ejpam-5735	124	1	nauk	nauk	PROPN
ejpam-5735	124	2	sssr	sssr	NOUN
ejpam-5735	124	3	55	55	NUM
ejpam-5735	124	4	,	,	PUNCT
ejpam-5735	124	5	567–570	567–570	NUM
ejpam-5735	124	6	.	.	PUNCT
ejpam-5735	125	1	also	also	ADV
ejpam-5735	125	2	p.	p.	NOUN
ejpam-5735	125	3	18–21	18–21	NUM
ejpam-5735	125	4	in	in	ADP
ejpam-5735	125	5	gelfand	gelfand	PROPN
ejpam-5735	125	6	’s	’s	PART
ejpam-5735	125	7	collected	collect	VERB
ejpam-5735	125	8	papers	paper	NOUN
ejpam-5735	125	9	,	,	PUNCT
ejpam-5735	125	10	vol	vol	NOUN
ejpam-5735	125	11	ii	ii	PROPN
ejpam-5735	125	12	,	,	PUNCT
ejpam-5735	125	13	springer	springer	NOUN
ejpam-5735	125	14	-	-	PUNCT
ejpam-5735	125	15	verlag	verlag	PROPN
ejpam-5735	125	16	,	,	PUNCT
ejpam-5735	125	17	berlin	berlin	PROPN
ejpam-5735	125	18	,	,	PUNCT
ejpam-5735	125	19	1988	1988	NUM
ejpam-5735	125	20	,	,	PUNCT
ejpam-5735	125	21	1947	1947	NUM
ejpam-5735	125	22	.	.	PUNCT
ejpam-5735	126	1	[	[	X
ejpam-5735	126	2	8	8	X
ejpam-5735	126	3	]	]	X
ejpam-5735	126	4	eberhard	eberhard	NOUN
ejpam-5735	126	5	kaniuth	kaniuth	NOUN
ejpam-5735	126	6	and	and	CCONJ
ejpam-5735	126	7	keith	keith	PROPN
ejpam-5735	126	8	f	f	PROPN
ejpam-5735	126	9	taylor	taylor	PROPN
ejpam-5735	126	10	.	.	PUNCT
ejpam-5735	127	1	induced	induce	VERB
ejpam-5735	127	2	representations	representation	NOUN
ejpam-5735	127	3	of	of	ADP
ejpam-5735	127	4	locally	locally	ADV
ejpam-5735	127	5	compact	compact	ADJ
ejpam-5735	127	6	groups	group	NOUN
ejpam-5735	127	7	,	,	PUNCT
ejpam-5735	127	8	volume	volume	NOUN
ejpam-5735	127	9	197	197	NUM
ejpam-5735	127	10	.	.	PUNCT
ejpam-5735	128	1	cambridge	cambridge	PROPN
ejpam-5735	128	2	university	university	PROPN
ejpam-5735	128	3	press	press	NOUN
ejpam-5735	128	4	,	,	PUNCT
ejpam-5735	128	5	2013	2013	NUM
ejpam-5735	128	6	.	.	PUNCT
ejpam-5735	129	1	[	[	X
ejpam-5735	129	2	9	9	NUM
ejpam-5735	129	3	]	]	X
ejpam-5735	129	4	v.v	v.v	PROPN
ejpam-5735	129	5	.	.	PROPN
ejpam-5735	129	6	kisil	kisil	PROPN
ejpam-5735	129	7	.	.	PROPN
ejpam-5735	129	8	symmetry	symmetry	PROPN
ejpam-5735	129	9	,	,	PUNCT
ejpam-5735	129	10	geometry	geometry	NOUN
ejpam-5735	129	11	and	and	CCONJ
ejpam-5735	129	12	quantization	quantization	NOUN
ejpam-5735	129	13	with	with	ADP
ejpam-5735	129	14	hypercomplex	hypercomplex	ADJ
ejpam-5735	129	15	numbers	number	NOUN
ejpam-5735	129	16	,	,	PUNCT
ejpam-5735	129	17	pages	page	NOUN
ejpam-5735	129	18	11–76	11–76	NUM
ejpam-5735	129	19	.	.	PUNCT
ejpam-5735	129	20	bulgar	bulgar	NOUN
ejpam-5735	129	21	.	.	PUNCT
ejpam-5735	130	1	acad	acad	PROPN
ejpam-5735	130	2	.	.	PUNCT
ejpam-5735	131	1	sci	sci	PROPN
ejpam-5735	131	2	.	.	PROPN
ejpam-5735	131	3	,	,	PUNCT
ejpam-5735	131	4	sofia	sofia	PROPN
ejpam-5735	131	5	,	,	PUNCT
ejpam-5735	131	6	2017	2017	NUM
ejpam-5735	131	7	.	.	PUNCT
ejpam-5735	132	1	[	[	X
ejpam-5735	132	2	10	10	NUM
ejpam-5735	132	3	]	]	X
ejpam-5735	132	4	giorgis	giorgis	NOUN
ejpam-5735	132	5	petridis	petridis	PROPN
ejpam-5735	132	6	,	,	PUNCT
ejpam-5735	132	7	oliver	oliver	PROPN
ejpam-5735	132	8	roche	roche	PROPN
ejpam-5735	132	9	-	-	PUNCT
ejpam-5735	132	10	newton	newton	PROPN
ejpam-5735	132	11	,	,	PUNCT
ejpam-5735	132	12	misha	misha	PROPN
ejpam-5735	132	13	rudnev	rudnev	PROPN
ejpam-5735	132	14	,	,	PUNCT
ejpam-5735	132	15	and	and	CCONJ
ejpam-5735	132	16	audie	audie	PROPN
ejpam-5735	132	17	warren	warren	PROPN
ejpam-5735	132	18	.	.	PUNCT
ejpam-5735	133	1	an	an	DET
ejpam-5735	133	2	energy	energy	NOUN
ejpam-5735	133	3	bound	bind	VERB
ejpam-5735	133	4	in	in	ADP
ejpam-5735	133	5	the	the	DET
ejpam-5735	133	6	affine	affine	NOUN
ejpam-5735	133	7	group	group	NOUN
ejpam-5735	133	8	.	.	PUNCT
ejpam-5735	134	1	international	international	ADJ
ejpam-5735	134	2	mathematics	mathematics	PROPN
ejpam-5735	134	3	research	research	NOUN
ejpam-5735	134	4	notices	notice	NOUN
ejpam-5735	134	5	,	,	PUNCT
ejpam-5735	134	6	2022(2):1154–1172	2022(2):1154–1172	NUM
ejpam-5735	134	7	,	,	PUNCT
ejpam-5735	134	8	2020	2020	NUM
ejpam-5735	134	9	.	.	PUNCT
ejpam-5735	135	1	[	[	X
ejpam-5735	135	2	11	11	NUM
ejpam-5735	135	3	]	]	PUNCT
ejpam-5735	135	4	rendra	rendra	PROPN
ejpam-5735	135	5	soekarta	soekarta	PROPN
ejpam-5735	135	6	and	and	CCONJ
ejpam-5735	135	7	miftah	miftah	PROPN
ejpam-5735	135	8	sigit	sigit	PROPN
ejpam-5735	135	9	.	.	PUNCT
ejpam-5735	136	1	implementation	implementation	NOUN
ejpam-5735	136	2	of	of	ADP
ejpam-5735	136	3	affine	affine	NOUN
ejpam-5735	136	4	group	group	NOUN
ejpam-5735	136	5	algebra	algebra	PROPN
ejpam-5735	136	6	on	on	ADP
ejpam-5735	136	7	digital	digital	ADJ
ejpam-5735	136	8	image	image	NOUN
ejpam-5735	136	9	security	security	NOUN
ejpam-5735	136	10	.	.	PUNCT
ejpam-5735	137	1	mobile	mobile	ADJ
ejpam-5735	137	2	and	and	CCONJ
ejpam-5735	137	3	forensics	forensic	NOUN
ejpam-5735	137	4	,	,	PUNCT
ejpam-5735	137	5	4:137–146	4:137–146	NUM
ejpam-5735	137	6	,	,	PUNCT
ejpam-5735	137	7	2023	2023	NUM
ejpam-5735	137	8	.	.	PUNCT
ejpam-5735	138	1	[	[	X
ejpam-5735	138	2	12	12	NUM
ejpam-5735	138	3	]	]	PUNCT
ejpam-5735	138	4	v.v.kisil	v.v.kisil	NOUN
ejpam-5735	138	5	.	.	PUNCT
ejpam-5735	139	1	the	the	DET
ejpam-5735	139	2	real	real	ADJ
ejpam-5735	139	3	and	and	CCONJ
ejpam-5735	139	4	complex	complex	ADJ
ejpam-5735	139	5	techniques	technique	NOUN
ejpam-5735	139	6	in	in	ADP
ejpam-5735	139	7	harmonic	harmonic	ADJ
ejpam-5735	139	8	analysis	analysis	NOUN
ejpam-5735	139	9	from	from	ADP
ejpam-5735	139	10	the	the	DET
ejpam-5735	139	11	point	point	NOUN
ejpam-5735	139	12	of	of	ADP
ejpam-5735	139	13	view	view	NOUN
ejpam-5735	139	14	of	of	ADP
ejpam-5735	139	15	covariant	covariant	ADJ
ejpam-5735	139	16	transform	transform	NOUN
ejpam-5735	139	17	.	.	PUNCT
ejpam-5735	140	1	eurasian	eurasian	ADJ
ejpam-5735	140	2	math	math	NOUN
ejpam-5735	140	3	.	.	PUNCT
ejpam-5735	141	1	j.5,95	j.5,95	X
ejpam-5735	141	2	-	-	SYM
ejpam-5735	141	3	121	121	NUM
ejpam-5735	141	4	,	,	PUNCT
ejpam-5735	141	5	2014	2014	NUM
ejpam-5735	141	6	.	.	PUNCT
ejpam-5735	142	1	[	[	X
ejpam-5735	142	2	13	13	NUM
ejpam-5735	142	3	]	]	PUNCT
ejpam-5735	142	4	m.	m.	PROPN
ejpam-5735	142	5	w.	w.	PROPN
ejpam-5735	142	6	wong	wong	PROPN
ejpam-5735	142	7	.	.	PROPN
ejpam-5735	142	8	wavelet	wavelet	PROPN
ejpam-5735	142	9	transforms	transform	VERB
ejpam-5735	142	10	and	and	CCONJ
ejpam-5735	142	11	localization	localization	NOUN
ejpam-5735	142	12	operators	operator	NOUN
ejpam-5735	142	13	,	,	PUNCT
ejpam-5735	142	14	volume	volume	NOUN
ejpam-5735	142	15	136	136	NUM
ejpam-5735	142	16	of	of	ADP
ejpam-5735	142	17	operator	operator	NOUN
ejpam-5735	142	18	theory	theory	NOUN
ejpam-5735	142	19	:	:	PUNCT
ejpam-5735	142	20	advances	advance	NOUN
ejpam-5735	142	21	and	and	CCONJ
ejpam-5735	142	22	applications	application	NOUN
ejpam-5735	142	23	.	.	PUNCT
ejpam-5735	143	1	birkhäuser	birkhäuser	X
ejpam-5735	143	2	verlag	verlag	PROPN
ejpam-5735	143	3	,	,	PUNCT
ejpam-5735	143	4	basel	basel	PROPN
ejpam-5735	143	5	,	,	PUNCT
ejpam-5735	143	6	2002	2002	NUM
ejpam-5735	143	7	.	.	PUNCT