id	sid	tid	token	lemma	pos
ejpam-4101	1	1	european	european	PROPN
ejpam-4101	1	2	journal	journal	PROPN
ejpam-4101	1	3	of	of	ADP
ejpam-4101	1	4	pure	pure	ADJ
ejpam-4101	1	5	and	and	CCONJ
ejpam-4101	1	6	applied	apply	VERB
ejpam-4101	1	7	mathematics	mathematic	NOUN
ejpam-4101	1	8	vol	vol	NOUN
ejpam-4101	1	9	.	.	PUNCT
ejpam-4101	2	1	14	14	NUM
ejpam-4101	2	2	,	,	PUNCT
ejpam-4101	2	3	no	no	INTJ
ejpam-4101	2	4	.	.	NOUN
ejpam-4101	2	5	4	4	NUM
ejpam-4101	2	6	,	,	PUNCT
ejpam-4101	2	7	2021	2021	NUM
ejpam-4101	2	8	,	,	PUNCT
ejpam-4101	2	9	1306	1306	NUM
ejpam-4101	2	10	-	-	SYM
ejpam-4101	2	11	1323	1323	NUM
ejpam-4101	2	12	issn	issn	PROPN
ejpam-4101	2	13	1307	1307	NUM
ejpam-4101	2	14	-	-	SYM
ejpam-4101	2	15	5543	5543	NUM
ejpam-4101	2	16	–	–	PUNCT
ejpam-4101	2	17	ejpam.com	ejpam.com	X
ejpam-4101	2	18	published	publish	VERB
ejpam-4101	2	19	by	by	ADP
ejpam-4101	2	20	new	new	PROPN
ejpam-4101	2	21	york	york	PROPN
ejpam-4101	2	22	business	business	PROPN
ejpam-4101	2	23	global	global	PROPN
ejpam-4101	2	24	on	on	ADP
ejpam-4101	2	25	the	the	DET
ejpam-4101	2	26	fourier	fourier	NOUN
ejpam-4101	2	27	transform	transform	NOUN
ejpam-4101	2	28	related	relate	VERB
ejpam-4101	2	29	to	to	ADP
ejpam-4101	2	30	the	the	DET
ejpam-4101	2	31	diamond	diamond	PROPN
ejpam-4101	2	32	klein	klein	PROPN
ejpam-4101	2	33	–	–	PUNCT
ejpam-4101	2	34	gordon	gordon	PROPN
ejpam-4101	2	35	kernel	kernel	PROPN
ejpam-4101	2	36	sudprathai	sudprathai	PROPN
ejpam-4101	2	37	bupasiri	bupasiri	PROPN
ejpam-4101	2	38	faculty	faculty	NOUN
ejpam-4101	2	39	of	of	ADP
ejpam-4101	2	40	education	education	NOUN
ejpam-4101	2	41	,	,	PUNCT
ejpam-4101	3	1	sakon	sakon	PROPN
ejpam-4101	3	2	nakhon	nakhon	PROPN
ejpam-4101	3	3	rajabhat	rajabhat	PROPN
ejpam-4101	3	4	university	university	PROPN
ejpam-4101	3	5	,	,	PUNCT
ejpam-4101	3	6	sakon	sakon	PROPN
ejpam-4101	3	7	nakhon	nakhon	PROPN
ejpam-4101	3	8	47000	47000	NUM
ejpam-4101	3	9	,	,	PUNCT
ejpam-4101	3	10	thailand	thailand	PROPN
ejpam-4101	3	11	abstract	abstract	NOUN
ejpam-4101	3	12	.	.	PUNCT
ejpam-4101	4	1	in	in	ADP
ejpam-4101	4	2	this	this	DET
ejpam-4101	4	3	article	article	NOUN
ejpam-4101	4	4	,	,	PUNCT
ejpam-4101	4	5	we	we	PRON
ejpam-4101	4	6	study	study	VERB
ejpam-4101	4	7	the	the	DET
ejpam-4101	4	8	fundamental	fundamental	ADJ
ejpam-4101	4	9	solution	solution	NOUN
ejpam-4101	4	10	of	of	ADP
ejpam-4101	4	11	the	the	DET
ejpam-4101	4	12	operator	operator	NOUN
ejpam-4101	4	13	(	(	PUNCT
ejpam-4101	4	14	(	(	PUNCT
ejpam-4101	4	15	♢	♢	PROPN
ejpam-4101	4	16	+	+	PROPN
ejpam-4101	4	17	m2	m2	PROPN
ejpam-4101	4	18	)	)	PUNCT
ejpam-4101	4	19	(	(	PUNCT
ejpam-4101	4	20	△	△	X
ejpam-4101	4	21	2	2	NUM
ejpam-4101	4	22	+	+	NOUN
ejpam-4101	4	23	⊡2	⊡2	PROPN
ejpam-4101	4	24	2	2	NUM
ejpam-4101	4	25	)	)	PUNCT
ejpam-4101	4	26	)	)	PUNCT
ejpam-4101	5	1	k	k	PROPN
ejpam-4101	5	2	iterated	iterate	VERB
ejpam-4101	5	3	k	k	NOUN
ejpam-4101	5	4	-	-	PUNCT
ejpam-4101	5	5	times	time	NOUN
ejpam-4101	5	6	,	,	PUNCT
ejpam-4101	5	7	which	which	PRON
ejpam-4101	5	8	is	be	AUX
ejpam-4101	5	9	defined	define	VERB
ejpam-4101	5	10	by	by	ADP
ejpam-4101	5	11	(	(	PUNCT
ejpam-4101	5	12	10	10	NUM
ejpam-4101	5	13	)	)	PUNCT
ejpam-4101	5	14	,	,	PUNCT
ejpam-4101	5	15	where	where	SCONJ
ejpam-4101	5	16	m	m	NOUN
ejpam-4101	5	17	is	be	AUX
ejpam-4101	5	18	a	a	DET
ejpam-4101	5	19	non	non	ADJ
ejpam-4101	5	20	-	-	ADJ
ejpam-4101	5	21	negative	negative	ADJ
ejpam-4101	5	22	real	real	ADJ
ejpam-4101	5	23	number	number	NOUN
ejpam-4101	5	24	,	,	PUNCT
ejpam-4101	5	25	and	and	CCONJ
ejpam-4101	5	26	k	k	PROPN
ejpam-4101	5	27	is	be	AUX
ejpam-4101	5	28	a	a	DET
ejpam-4101	5	29	nonnegative	nonnegative	ADJ
ejpam-4101	5	30	integer	integer	NOUN
ejpam-4101	5	31	.	.	PUNCT
ejpam-4101	6	1	after	after	ADP
ejpam-4101	6	2	that	that	PRON
ejpam-4101	6	3	,	,	PUNCT
ejpam-4101	6	4	we	we	PRON
ejpam-4101	6	5	study	study	VERB
ejpam-4101	6	6	the	the	DET
ejpam-4101	6	7	fourier	fourier	NOUN
ejpam-4101	6	8	transform	transform	NOUN
ejpam-4101	6	9	of	of	ADP
ejpam-4101	6	10	the	the	DET
ejpam-4101	6	11	operator	operator	NOUN
ejpam-4101	6	12	(	(	PUNCT
ejpam-4101	6	13	(	(	PUNCT
ejpam-4101	6	14	♢	♢	PROPN
ejpam-4101	6	15	+	+	PROPN
ejpam-4101	6	16	m2	m2	X
ejpam-4101	6	17	)	)	PUNCT
ejpam-4101	6	18	(	(	PUNCT
ejpam-4101	6	19	△	△	X
ejpam-4101	6	20	2+⊡2	2+⊡2	NUM
ejpam-4101	6	21	2	2	NUM
ejpam-4101	6	22	)	)	PUNCT
ejpam-4101	6	23	)	)	PUNCT
ejpam-4101	7	1	k	k	PROPN
ejpam-4101	7	2	δ	δ	PROPN
ejpam-4101	7	3	,	,	PUNCT
ejpam-4101	7	4	where	where	SCONJ
ejpam-4101	7	5	δ	δ	PROPN
ejpam-4101	7	6	is	be	AUX
ejpam-4101	7	7	the	the	DET
ejpam-4101	7	8	dirac	dirac	PROPN
ejpam-4101	7	9	delta	delta	NOUN
ejpam-4101	7	10	function	function	NOUN
ejpam-4101	7	11	.	.	PUNCT
ejpam-4101	8	1	2020	2020	NUM
ejpam-4101	8	2	mathematics	mathematic	NOUN
ejpam-4101	8	3	subject	subject	NOUN
ejpam-4101	8	4	classifications	classification	NOUN
ejpam-4101	8	5	:	:	PUNCT
ejpam-4101	8	6	46f10	46f10	NUM
ejpam-4101	8	7	key	key	ADJ
ejpam-4101	8	8	words	word	NOUN
ejpam-4101	8	9	and	and	CCONJ
ejpam-4101	8	10	phrases	phrase	NOUN
ejpam-4101	8	11	:	:	PUNCT
ejpam-4101	8	12	diamond	diamond	PROPN
ejpam-4101	8	13	klein	klein	PROPN
ejpam-4101	8	14	–	–	PUNCT
ejpam-4101	8	15	gordon	gordon	PROPN
ejpam-4101	8	16	kernel	kernel	PROPN
ejpam-4101	8	17	;	;	PUNCT
ejpam-4101	8	18	diamond	diamond	NOUN
ejpam-4101	8	19	operator	operator	NOUN
ejpam-4101	8	20	;	;	PUNCT
ejpam-4101	8	21	laplace	laplace	NOUN
ejpam-4101	8	22	operator	operator	NOUN
ejpam-4101	8	23	;	;	PUNCT
ejpam-4101	8	24	fourier	fourier	NOUN
ejpam-4101	8	25	transform	transform	NOUN
ejpam-4101	8	26	;	;	PUNCT
ejpam-4101	8	27	wave	wave	NOUN
ejpam-4101	8	28	equation	equation	NOUN
ejpam-4101	8	29	introduction	introduction	NOUN
ejpam-4101	8	30	the	the	DET
ejpam-4101	8	31	operator	operator	NOUN
ejpam-4101	8	32	⋄k	⋄k	PRON
ejpam-4101	8	33	has	have	AUX
ejpam-4101	8	34	been	be	AUX
ejpam-4101	8	35	first	first	ADV
ejpam-4101	8	36	introduced	introduce	VERB
ejpam-4101	8	37	by	by	ADP
ejpam-4101	8	38	kananthai	kananthai	PROPN
ejpam-4101	9	1	[	[	X
ejpam-4101	9	2	5	5	NUM
ejpam-4101	9	3	]	]	PUNCT
ejpam-4101	9	4	,	,	PUNCT
ejpam-4101	9	5	is	be	AUX
ejpam-4101	9	6	named	name	VERB
ejpam-4101	9	7	as	as	SCONJ
ejpam-4101	9	8	the	the	DET
ejpam-4101	9	9	diamond	diamond	NOUN
ejpam-4101	9	10	operator	operator	NOUN
ejpam-4101	9	11	iterated	iterate	VERB
ejpam-4101	9	12	k	k	NOUN
ejpam-4101	9	13	-	-	PUNCT
ejpam-4101	9	14	times	time	NOUN
ejpam-4101	9	15	,	,	PUNCT
ejpam-4101	9	16	and	and	CCONJ
ejpam-4101	9	17	is	be	AUX
ejpam-4101	9	18	defined	define	VERB
ejpam-4101	9	19	by	by	ADP
ejpam-4101	9	20	♢	♢	PROPN
ejpam-4101	9	21	k	k	PROPN
ejpam-4101	9	22	=	=	SYM
ejpam-4101	9	23			PROPN
ejpam-4101	9	24	(	(	PUNCT
ejpam-4101	9	25	p∑	p∑	NOUN
ejpam-4101	9	26	r=1	r=1	NOUN
ejpam-4101	9	27	∂2	∂2	NOUN
ejpam-4101	9	28	∂x2r	∂x2r	NOUN
ejpam-4101	9	29	)	)	PUNCT
ejpam-4101	9	30	2	2	NUM
ejpam-4101	9	31	−	−	NOUN
ejpam-4101	9	32			PROPN
ejpam-4101	9	33	p+q∑	p+q∑	PROPN
ejpam-4101	9	34	j	j	NOUN
ejpam-4101	9	35	=	=	PROPN
ejpam-4101	9	36	p+1	p+1	PROPN
ejpam-4101	9	37	∂2	∂2	PROPN
ejpam-4101	9	38	∂x2j	∂x2j	PROPN
ejpam-4101	9	39	2k	2k	PROPN
ejpam-4101	9	40	,	,	PUNCT
ejpam-4101	9	41	p+	p+	NOUN
ejpam-4101	9	42	q	q	NOUN
ejpam-4101	9	43	=	=	SYM
ejpam-4101	9	44	n	n	CCONJ
ejpam-4101	9	45	,	,	PUNCT
ejpam-4101	9	46	(	(	PUNCT
ejpam-4101	9	47	1	1	X
ejpam-4101	9	48	)	)	PUNCT
ejpam-4101	9	49	where	where	SCONJ
ejpam-4101	9	50	n	n	PRON
ejpam-4101	9	51	is	be	AUX
ejpam-4101	9	52	the	the	DET
ejpam-4101	9	53	dimension	dimension	NOUN
ejpam-4101	9	54	of	of	ADP
ejpam-4101	9	55	the	the	DET
ejpam-4101	9	56	space	space	NOUN
ejpam-4101	9	57	rn	rn	PROPN
ejpam-4101	9	58	,	,	PUNCT
ejpam-4101	9	59	for	for	ADP
ejpam-4101	9	60	x	x	SYM
ejpam-4101	9	61	=	=	SYM
ejpam-4101	9	62	(	(	PUNCT
ejpam-4101	9	63	x1	x1	PROPN
ejpam-4101	9	64	,	,	PUNCT
ejpam-4101	9	65	x2	x2	PROPN
ejpam-4101	9	66	,	,	PUNCT
ejpam-4101	9	67	.	.	PUNCT
ejpam-4101	9	68	.	.	PUNCT
ejpam-4101	10	1	.	.	PUNCT
ejpam-4101	11	1	,	,	PUNCT
ejpam-4101	11	2	xn	xn	X
ejpam-4101	11	3	)	)	PUNCT
ejpam-4101	11	4	∈	∈	PROPN
ejpam-4101	11	5	rn	rn	PROPN
ejpam-4101	11	6	and	and	CCONJ
ejpam-4101	11	7	k	k	PROPN
ejpam-4101	11	8	is	be	AUX
ejpam-4101	11	9	a	a	DET
ejpam-4101	11	10	nonnegative	nonnegative	ADJ
ejpam-4101	11	11	integer	integer	NOUN
ejpam-4101	11	12	.	.	PUNCT
ejpam-4101	12	1	the	the	DET
ejpam-4101	12	2	operator	operator	NOUN
ejpam-4101	12	3	♢	♢	PROPN
ejpam-4101	12	4	k	k	PROPN
ejpam-4101	12	5	can	can	AUX
ejpam-4101	12	6	be	be	AUX
ejpam-4101	12	7	expressed	express	VERB
ejpam-4101	12	8	in	in	ADP
ejpam-4101	12	9	the	the	DET
ejpam-4101	12	10	form	form	NOUN
ejpam-4101	12	11	♢	♢	PROPN
ejpam-4101	12	12	k	k	PROPN
ejpam-4101	12	13	=	=	SYM
ejpam-4101	12	14	⊡k	⊡k	PROPN
ejpam-4101	12	15	△	△	PROPN
ejpam-4101	12	16	k	k	X
ejpam-4101	12	17	=	=	SYM
ejpam-4101	12	18	△	△	PROPN
ejpam-4101	12	19	k⊡k	k⊡k	PROPN
ejpam-4101	12	20	,	,	PUNCT
ejpam-4101	12	21	where	where	SCONJ
ejpam-4101	12	22	the	the	DET
ejpam-4101	12	23	operator	operator	NOUN
ejpam-4101	12	24	△	△	PROPN
ejpam-4101	12	25	k	k	X
ejpam-4101	12	26	is	be	AUX
ejpam-4101	12	27	laplace	laplace	NOUN
ejpam-4101	12	28	operator	operator	NOUN
ejpam-4101	12	29	iterated	iterate	VERB
ejpam-4101	12	30	k	k	NOUN
ejpam-4101	12	31	-	-	PUNCT
ejpam-4101	12	32	times	time	NOUN
ejpam-4101	12	33	,	,	PUNCT
ejpam-4101	12	34	which	which	PRON
ejpam-4101	12	35	is	be	AUX
ejpam-4101	12	36	defined	define	VERB
ejpam-4101	12	37	by	by	ADP
ejpam-4101	12	38	△	△	NOUN
ejpam-4101	12	39	k	k	X
ejpam-4101	12	40	=	=	X
ejpam-4101	12	41	(	(	PUNCT
ejpam-4101	12	42	∂2	∂2	PROPN
ejpam-4101	12	43	∂x21	∂x21	PROPN
ejpam-4101	12	44	+	+	CCONJ
ejpam-4101	12	45	∂2	∂2	PROPN
ejpam-4101	12	46	∂x22	∂x22	PROPN
ejpam-4101	12	47	+	+	CCONJ
ejpam-4101	12	48	·	·	PUNCT
ejpam-4101	12	49	·	·	PUNCT
ejpam-4101	12	50	·	·	PUNCT
ejpam-4101	13	1	+	+	NUM
ejpam-4101	13	2	∂2	∂2	ADJ
ejpam-4101	13	3	∂x2n	∂x2n	NOUN
ejpam-4101	13	4	)	)	PUNCT
ejpam-4101	13	5	k	k	PROPN
ejpam-4101	13	6	(	(	PUNCT
ejpam-4101	13	7	2	2	NUM
ejpam-4101	13	8	)	)	PUNCT
ejpam-4101	13	9	doi	doi	NOUN
ejpam-4101	13	10	:	:	PUNCT
ejpam-4101	13	11	https://doi.org/10.29020/nybg.ejpam.v14i4.4101	https://doi.org/10.29020/nybg.ejpam.v14i4.4101	PROPN
ejpam-4101	13	12	email	email	NOUN
ejpam-4101	13	13	address	address	NOUN
ejpam-4101	13	14	:	:	PUNCT
ejpam-4101	13	15	sudprathai@gmail.com	sudprathai@gmail.com	X
ejpam-4101	13	16	(	(	PUNCT
ejpam-4101	13	17	s.	s.	PROPN
ejpam-4101	13	18	bupasiri	bupasiri	PROPN
ejpam-4101	13	19	)	)	PUNCT
ejpam-4101	13	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4101	14	1	1306	1306	NUM
ejpam-4101	15	1	©	©	PROPN
ejpam-4101	15	2	2021	2021	NUM
ejpam-4101	15	3	ejpam	ejpam	VERB
ejpam-4101	15	4	all	all	DET
ejpam-4101	15	5	rights	right	NOUN
ejpam-4101	15	6	reserved	reserve	VERB
ejpam-4101	15	7	.	.	PUNCT
ejpam-4101	16	1	s.	s.	PROPN
ejpam-4101	16	2	bupasiri	bupasiri	PROPN
ejpam-4101	16	3	/	/	SYM
ejpam-4101	16	4	eur	eur	PROPN
ejpam-4101	16	5	.	.	PUNCT
ejpam-4101	17	1	j.	j.	PROPN
ejpam-4101	17	2	pure	pure	PROPN
ejpam-4101	17	3	appl	appl	PROPN
ejpam-4101	17	4	.	.	PROPN
ejpam-4101	17	5	math	math	PROPN
ejpam-4101	17	6	,	,	PUNCT
ejpam-4101	17	7	14	14	NUM
ejpam-4101	17	8	(	(	PUNCT
ejpam-4101	17	9	4	4	NUM
ejpam-4101	17	10	)	)	PUNCT
ejpam-4101	17	11	(	(	PUNCT
ejpam-4101	17	12	2021	2021	NUM
ejpam-4101	17	13	)	)	PUNCT
ejpam-4101	17	14	,	,	PUNCT
ejpam-4101	17	15	1306	1306	NUM
ejpam-4101	17	16	-	-	SYM
ejpam-4101	17	17	1323	1323	NUM
ejpam-4101	17	18	1307	1307	NUM
ejpam-4101	17	19	and	and	CCONJ
ejpam-4101	17	20	the	the	DET
ejpam-4101	17	21	operator	operator	NOUN
ejpam-4101	17	22	⊡k	⊡k	PROPN
ejpam-4101	17	23	is	be	AUX
ejpam-4101	17	24	the	the	DET
ejpam-4101	17	25	ultra	ultra	ADJ
ejpam-4101	17	26	-	-	ADJ
ejpam-4101	17	27	hyperbolic	hyperbolic	ADJ
ejpam-4101	17	28	operator	operator	NOUN
ejpam-4101	17	29	iterated	iterate	VERB
ejpam-4101	17	30	k	k	NOUN
ejpam-4101	17	31	-	-	PUNCT
ejpam-4101	17	32	times	time	NOUN
ejpam-4101	17	33	,	,	PUNCT
ejpam-4101	17	34	which	which	PRON
ejpam-4101	17	35	is	be	AUX
ejpam-4101	17	36	defined	define	VERB
ejpam-4101	17	37	by	by	ADP
ejpam-4101	17	38	⊡k	⊡k	PROPN
ejpam-4101	17	39	=	=	SYM
ejpam-4101	17	40	(	(	PUNCT
ejpam-4101	17	41	∂2	∂2	PROPN
ejpam-4101	17	42	∂x21	∂x21	PROPN
ejpam-4101	17	43	+	+	CCONJ
ejpam-4101	17	44	∂2	∂2	PROPN
ejpam-4101	17	45	∂x22	∂x22	PROPN
ejpam-4101	17	46	+	+	CCONJ
ejpam-4101	17	47	·	·	PUNCT
ejpam-4101	17	48	·	·	PUNCT
ejpam-4101	17	49	·	·	PUNCT
ejpam-4101	18	1	+	+	NUM
ejpam-4101	18	2	∂2	∂2	NOUN
ejpam-4101	18	3	∂x2p	∂x2p	NUM
ejpam-4101	19	1	−	−	PROPN
ejpam-4101	19	2	∂2	∂2	PROPN
ejpam-4101	19	3	∂x2p+1	∂x2p+1	PROPN
ejpam-4101	19	4	−	−	PROPN
ejpam-4101	19	5	∂2	∂2	NOUN
ejpam-4101	19	6	∂x2p+2	∂x2p+2	VERB
ejpam-4101	19	7	−	−	X
ejpam-4101	19	8	·	·	PUNCT
ejpam-4101	19	9	·	·	PUNCT
ejpam-4101	19	10	·	·	PUNCT
ejpam-4101	20	1	−	−	PUNCT
ejpam-4101	20	2	∂2	∂2	NOUN
ejpam-4101	20	3	∂x2p+q	∂x2p+q	NOUN
ejpam-4101	20	4	)	)	PUNCT
ejpam-4101	21	1	k	k	X
ejpam-4101	21	2	.	.	PUNCT
ejpam-4101	22	1	(	(	PUNCT
ejpam-4101	22	2	3	3	X
ejpam-4101	22	3	)	)	PUNCT
ejpam-4101	22	4	by	by	ADP
ejpam-4101	22	5	putting	put	VERB
ejpam-4101	22	6	p	p	NOUN
ejpam-4101	22	7	=	=	NOUN
ejpam-4101	22	8	1	1	NUM
ejpam-4101	22	9	and	and	CCONJ
ejpam-4101	22	10	x1	x1	PROPN
ejpam-4101	22	11	=	=	SYM
ejpam-4101	22	12	t	t	PROPN
ejpam-4101	22	13	(	(	PUNCT
ejpam-4101	22	14	time	time	NOUN
ejpam-4101	22	15	)	)	PUNCT
ejpam-4101	22	16	in	in	ADP
ejpam-4101	22	17	(	(	PUNCT
ejpam-4101	22	18	3	3	NUM
ejpam-4101	22	19	)	)	PUNCT
ejpam-4101	22	20	,	,	PUNCT
ejpam-4101	22	21	then	then	ADV
ejpam-4101	22	22	we	we	PRON
ejpam-4101	22	23	obtain	obtain	VERB
ejpam-4101	22	24	the	the	DET
ejpam-4101	22	25	wave	wave	NOUN
ejpam-4101	22	26	operator	operator	NOUN
ejpam-4101	22	27	⊡	⊡	PUNCT
ejpam-4101	22	28	=	=	SYM
ejpam-4101	22	29	∂2	∂2	NOUN
ejpam-4101	22	30	∂t2	∂t2	NOUN
ejpam-4101	22	31	−	−	PROPN
ejpam-4101	22	32	n−1∑	n−1∑	NUM
ejpam-4101	22	33	j=1	j=1	PROPN
ejpam-4101	22	34	∂2	∂2	PROPN
ejpam-4101	22	35	∂x2j	∂x2j	PROPN
ejpam-4101	22	36	.	.	PUNCT
ejpam-4101	23	1	(	(	PUNCT
ejpam-4101	23	2	4	4	X
ejpam-4101	23	3	)	)	PUNCT
ejpam-4101	23	4	in	in	ADP
ejpam-4101	23	5	1997	1997	NUM
ejpam-4101	23	6	,	,	PUNCT
ejpam-4101	23	7	kananthai	kananthai	X
ejpam-4101	23	8	[	[	X
ejpam-4101	23	9	5	5	NUM
ejpam-4101	23	10	]	]	PUNCT
ejpam-4101	23	11	showed	show	VERB
ejpam-4101	23	12	that	that	SCONJ
ejpam-4101	23	13	the	the	DET
ejpam-4101	23	14	convolution	convolution	NOUN
ejpam-4101	23	15	(	(	PUNCT
ejpam-4101	23	16	−1)kre	−1)kre	PROPN
ejpam-4101	23	17	2k(x	2k(x	NUM
ejpam-4101	23	18	)	)	PUNCT
ejpam-4101	23	19	∗	∗	PROPN
ejpam-4101	23	20	rh	rh	PROPN
ejpam-4101	23	21	2k(x	2k(x	PROPN
ejpam-4101	23	22	)	)	PUNCT
ejpam-4101	23	23	is	be	AUX
ejpam-4101	23	24	the	the	DET
ejpam-4101	23	25	fundamental	fundamental	ADJ
ejpam-4101	23	26	solution	solution	NOUN
ejpam-4101	23	27	of	of	ADP
ejpam-4101	23	28	the	the	DET
ejpam-4101	23	29	operator	operator	NOUN
ejpam-4101	23	30	♢	♢	PROPN
ejpam-4101	23	31	k	k	PROPN
ejpam-4101	23	32	,	,	PUNCT
ejpam-4101	23	33	that	that	PRON
ejpam-4101	23	34	is	be	AUX
ejpam-4101	23	35	♢	♢	PROPN
ejpam-4101	23	36	k((−1)kre	k((−1)kre	PROPN
ejpam-4101	23	37	2k(x	2k(x	NUM
ejpam-4101	23	38	)	)	PUNCT
ejpam-4101	23	39	∗rh	∗rh	VERB
ejpam-4101	23	40	2k(x	2k(x	NUM
ejpam-4101	23	41	)	)	PUNCT
ejpam-4101	23	42	)	)	PUNCT
ejpam-4101	24	1	=	=	SYM
ejpam-4101	24	2	δ	δ	PROPN
ejpam-4101	24	3	,	,	PUNCT
ejpam-4101	24	4	(	(	PUNCT
ejpam-4101	24	5	5	5	NUM
ejpam-4101	24	6	)	)	PUNCT
ejpam-4101	24	7	where	where	SCONJ
ejpam-4101	24	8	the	the	DET
ejpam-4101	24	9	function	function	NOUN
ejpam-4101	24	10	rh	rh	PROPN
ejpam-4101	24	11	2k(x	2k(x	PROPN
ejpam-4101	24	12	)	)	PUNCT
ejpam-4101	24	13	is	be	AUX
ejpam-4101	24	14	defined	define	VERB
ejpam-4101	24	15	by	by	ADP
ejpam-4101	24	16	(	(	PUNCT
ejpam-4101	24	17	20	20	NUM
ejpam-4101	24	18	)	)	PUNCT
ejpam-4101	24	19	and	and	CCONJ
ejpam-4101	24	20	re	re	X
ejpam-4101	24	21	2k(x	2k(x	NUM
ejpam-4101	24	22	)	)	PUNCT
ejpam-4101	24	23	is	be	AUX
ejpam-4101	24	24	defined	define	VERB
ejpam-4101	24	25	by	by	ADP
ejpam-4101	24	26	(	(	PUNCT
ejpam-4101	24	27	19	19	NUM
ejpam-4101	24	28	)	)	PUNCT
ejpam-4101	24	29	.	.	PUNCT
ejpam-4101	25	1	the	the	DET
ejpam-4101	25	2	fundamental	fundamental	ADJ
ejpam-4101	25	3	solution	solution	NOUN
ejpam-4101	25	4	(	(	PUNCT
ejpam-4101	25	5	−1)kre	−1)kre	PROPN
ejpam-4101	25	6	2k(x	2k(x	NUM
ejpam-4101	25	7	)	)	PUNCT
ejpam-4101	25	8	∗	∗	PROPN
ejpam-4101	25	9	rh	rh	PROPN
ejpam-4101	25	10	2k(x	2k(x	PROPN
ejpam-4101	25	11	)	)	PUNCT
ejpam-4101	25	12	is	be	AUX
ejpam-4101	25	13	called	call	VERB
ejpam-4101	25	14	the	the	DET
ejpam-4101	25	15	diamond	diamond	NOUN
ejpam-4101	25	16	kernel	kernel	NOUN
ejpam-4101	25	17	of	of	ADP
ejpam-4101	25	18	marcel	marcel	PROPN
ejpam-4101	25	19	riesz	riesz	PROPN
ejpam-4101	25	20	.	.	PUNCT
ejpam-4101	26	1	satsanit	satsanit	VERB
ejpam-4101	27	1	[	[	X
ejpam-4101	27	2	20	20	NUM
ejpam-4101	27	3	]	]	PUNCT
ejpam-4101	27	4	showed	show	VERB
ejpam-4101	27	5	that	that	SCONJ
ejpam-4101	27	6	⊙k	⊙k	NOUN
ejpam-4101	27	7	=	=	SYM
ejpam-4101	27	8			PROPN
ejpam-4101	27	9	(	(	PUNCT
ejpam-4101	27	10	p∑	p∑	NOUN
ejpam-4101	27	11	r=1	r=1	NOUN
ejpam-4101	27	12	∂2	∂2	NOUN
ejpam-4101	27	13	∂x2r	∂x2r	NOUN
ejpam-4101	27	14	)	)	PUNCT
ejpam-4101	27	15	2	2	NUM
ejpam-4101	27	16	+	+	CCONJ
ejpam-4101	27	17			PROPN
ejpam-4101	27	18	p+q∑	p+q∑	PROPN
ejpam-4101	27	19	j	j	NOUN
ejpam-4101	27	20	=	=	PROPN
ejpam-4101	27	21	p+1	p+1	PROPN
ejpam-4101	27	22	∂2	∂2	PROPN
ejpam-4101	27	23	∂x2j	∂x2j	PUNCT
ejpam-4101	27	24	2k	2k	X
ejpam-4101	28	1	=	=	PUNCT
ejpam-4101	28	2	(	(	PUNCT
ejpam-4101	28	3	(	(	PUNCT
ejpam-4101	28	4	△	△	X
ejpam-4101	28	5	+	+	ADJ
ejpam-4101	28	6	⊡	⊡	SYM
ejpam-4101	28	7	2	2	NUM
ejpam-4101	28	8	)	)	SYM
ejpam-4101	28	9	2	2	NUM
ejpam-4101	28	10	+	+	CCONJ
ejpam-4101	28	11	(	(	PUNCT
ejpam-4101	28	12	△	△	X
ejpam-4101	28	13	−⊡	−⊡	NOUN
ejpam-4101	28	14	2	2	NUM
ejpam-4101	28	15	)	)	PUNCT
ejpam-4101	28	16	2	2	NUM
ejpam-4101	28	17	)	)	PUNCT
ejpam-4101	28	18	k	k	NOUN
ejpam-4101	28	19	=	=	PRON
ejpam-4101	28	20	(	(	PUNCT
ejpam-4101	28	21	△	△	X
ejpam-4101	28	22	2	2	NUM
ejpam-4101	28	23	+	+	NOUN
ejpam-4101	28	24	⊡2	⊡2	PROPN
ejpam-4101	28	25	2	2	NUM
ejpam-4101	28	26	)	)	PUNCT
ejpam-4101	28	27	k	k	NOUN
ejpam-4101	28	28	.	.	PUNCT
ejpam-4101	29	1	(	(	PUNCT
ejpam-4101	29	2	6	6	NUM
ejpam-4101	29	3	)	)	PUNCT
ejpam-4101	29	4	moreover	moreover	ADV
ejpam-4101	29	5	,	,	PUNCT
ejpam-4101	29	6	kananthai	kananthai	ADJ
ejpam-4101	29	7	,	,	PUNCT
ejpam-4101	29	8	suantai	suantai	VERB
ejpam-4101	29	9	and	and	CCONJ
ejpam-4101	29	10	longani	longani	NOUN
ejpam-4101	30	1	[	[	X
ejpam-4101	30	2	7	7	NUM
ejpam-4101	30	3	]	]	PUNCT
ejpam-4101	30	4	studied	study	VERB
ejpam-4101	30	5	the	the	DET
ejpam-4101	30	6	fundamental	fundamental	ADJ
ejpam-4101	30	7	solution	solution	NOUN
ejpam-4101	30	8	of	of	ADP
ejpam-4101	30	9	the	the	DET
ejpam-4101	30	10	operator	operator	NOUN
ejpam-4101	30	11	⊕k	⊕k	NOUN
ejpam-4101	30	12	and	and	CCONJ
ejpam-4101	30	13	the	the	DET
ejpam-4101	30	14	weak	weak	ADJ
ejpam-4101	30	15	solution	solution	NOUN
ejpam-4101	30	16	of	of	ADP
ejpam-4101	30	17	the	the	DET
ejpam-4101	30	18	equation	equation	NOUN
ejpam-4101	30	19	⊕ku(x	⊕ku(x	VERB
ejpam-4101	30	20	)	)	PUNCT
ejpam-4101	30	21	=	=	SYM
ejpam-4101	30	22	f(x	f(x	PROPN
ejpam-4101	30	23	)	)	PUNCT
ejpam-4101	30	24	,	,	PUNCT
ejpam-4101	30	25	where	where	SCONJ
ejpam-4101	30	26	the	the	DET
ejpam-4101	30	27	operator	operator	NOUN
ejpam-4101	30	28	⊕k	⊕k	NOUN
ejpam-4101	30	29	is	be	AUX
ejpam-4101	30	30	defined	define	VERB
ejpam-4101	30	31	by	by	ADP
ejpam-4101	30	32	⊕k	⊕k	ADJ
ejpam-4101	30	33	=	=	SYM
ejpam-4101	30	34			PROPN
ejpam-4101	30	35	(	(	PUNCT
ejpam-4101	30	36	p∑	p∑	NOUN
ejpam-4101	30	37	r=1	r=1	NOUN
ejpam-4101	30	38	∂2	∂2	NOUN
ejpam-4101	30	39	∂x2r	∂x2r	NOUN
ejpam-4101	30	40	)	)	PUNCT
ejpam-4101	30	41	4	4	NUM
ejpam-4101	30	42	−	−	NOUN
ejpam-4101	31	1			PROPN
ejpam-4101	31	2	p+q∑	p+q∑	PROPN
ejpam-4101	31	3	j	j	NOUN
ejpam-4101	31	4	=	=	PROPN
ejpam-4101	31	5	p+1	p+1	PROPN
ejpam-4101	31	6	∂2	∂2	PROPN
ejpam-4101	31	7	∂x2j	∂x2j	PROPN
ejpam-4101	31	8	4k	4k	PROPN
ejpam-4101	31	9	=	=	SYM
ejpam-4101	31	10			PROPN
ejpam-4101	31	11	(	(	PUNCT
ejpam-4101	31	12	p∑	p∑	NOUN
ejpam-4101	31	13	r=1	r=1	NOUN
ejpam-4101	31	14	∂2	∂2	NOUN
ejpam-4101	31	15	∂x2r	∂x2r	NOUN
ejpam-4101	31	16	)	)	PUNCT
ejpam-4101	31	17	2	2	NUM
ejpam-4101	31	18	−	−	NOUN
ejpam-4101	31	19			PROPN
ejpam-4101	31	20	p+q∑	p+q∑	PROPN
ejpam-4101	31	21	j	j	NOUN
ejpam-4101	31	22	=	=	PROPN
ejpam-4101	31	23	p+1	p+1	PROPN
ejpam-4101	31	24	∂2	∂2	PROPN
ejpam-4101	31	25	∂x2j	∂x2j	PROPN
ejpam-4101	31	26	2k	2k	PROPN
ejpam-4101	31	27			NOUN
ejpam-4101	31	28	(	(	PUNCT
ejpam-4101	31	29	p∑	p∑	NOUN
ejpam-4101	31	30	r=1	r=1	NOUN
ejpam-4101	31	31	∂2	∂2	NOUN
ejpam-4101	31	32	∂x2r	∂x2r	NOUN
ejpam-4101	31	33	)	)	PUNCT
ejpam-4101	31	34	2	2	NUM
ejpam-4101	31	35	+	+	CCONJ
ejpam-4101	31	36			PROPN
ejpam-4101	31	37	p+q∑	p+q∑	PROPN
ejpam-4101	31	38	j	j	NOUN
ejpam-4101	31	39	=	=	PROPN
ejpam-4101	31	40	p+1	p+1	PROPN
ejpam-4101	31	41	∂2	∂2	PROPN
ejpam-4101	31	42	∂x2j	∂x2j	PROPN
ejpam-4101	31	43	2k	2k	PUNCT
ejpam-4101	32	1	=	=	SYM
ejpam-4101	32	2	⋄klk	⋄klk	SYM
ejpam-4101	32	3	1l	1l	NUM
ejpam-4101	32	4	k	k	NOUN
ejpam-4101	32	5	2	2	NUM
ejpam-4101	32	6	=	=	SYM
ejpam-4101	32	7	⋄klk	⋄klk	X
ejpam-4101	32	8	(	(	PUNCT
ejpam-4101	32	9	7	7	NUM
ejpam-4101	32	10	)	)	PUNCT
ejpam-4101	32	11	where	where	SCONJ
ejpam-4101	32	12	p+	p+	VERB
ejpam-4101	32	13	q	q	X
ejpam-4101	32	14	=	=	SYM
ejpam-4101	32	15	n	n	X
ejpam-4101	32	16	is	be	AUX
ejpam-4101	32	17	the	the	DET
ejpam-4101	32	18	dimension	dimension	NOUN
ejpam-4101	32	19	of	of	ADP
ejpam-4101	32	20	the	the	DET
ejpam-4101	32	21	euclidean	euclidean	ADJ
ejpam-4101	32	22	space	space	PROPN
ejpam-4101	32	23	rn	rn	PROPN
ejpam-4101	32	24	,	,	PUNCT
ejpam-4101	32	25	k	k	PROPN
ejpam-4101	32	26	is	be	AUX
ejpam-4101	32	27	a	a	DET
ejpam-4101	32	28	non	non	ADJ
ejpam-4101	32	29	-	-	ADJ
ejpam-4101	32	30	negative	negative	ADJ
ejpam-4101	32	31	integer	integer	NOUN
ejpam-4101	32	32	,	,	PUNCT
ejpam-4101	32	33	and	and	CCONJ
ejpam-4101	32	34	f(x	f(x	PROPN
ejpam-4101	32	35	)	)	PUNCT
ejpam-4101	32	36	is	be	AUX
ejpam-4101	32	37	a	a	DET
ejpam-4101	32	38	generalized	generalized	ADJ
ejpam-4101	32	39	function	function	NOUN
ejpam-4101	32	40	.	.	PUNCT
ejpam-4101	33	1	s.	s.	PROPN
ejpam-4101	33	2	bupasiri	bupasiri	PROPN
ejpam-4101	33	3	/	/	SYM
ejpam-4101	33	4	eur	eur	PROPN
ejpam-4101	33	5	.	.	PUNCT
ejpam-4101	34	1	j.	j.	PROPN
ejpam-4101	34	2	pure	pure	PROPN
ejpam-4101	34	3	appl	appl	PROPN
ejpam-4101	34	4	.	.	PROPN
ejpam-4101	34	5	math	math	PROPN
ejpam-4101	34	6	,	,	PUNCT
ejpam-4101	34	7	14	14	NUM
ejpam-4101	34	8	(	(	PUNCT
ejpam-4101	34	9	4	4	NUM
ejpam-4101	34	10	)	)	PUNCT
ejpam-4101	34	11	(	(	PUNCT
ejpam-4101	34	12	2021	2021	NUM
ejpam-4101	34	13	)	)	PUNCT
ejpam-4101	34	14	,	,	PUNCT
ejpam-4101	34	15	1306	1306	NUM
ejpam-4101	34	16	-	-	SYM
ejpam-4101	34	17	1323	1323	NUM
ejpam-4101	34	18	1308	1308	NUM
ejpam-4101	34	19	next	next	ADJ
ejpam-4101	34	20	,	,	PUNCT
ejpam-4101	34	21	kananthai	kananthai	ADJ
ejpam-4101	34	22	,	,	PUNCT
ejpam-4101	34	23	suantai	suantai	VERB
ejpam-4101	34	24	and	and	CCONJ
ejpam-4101	34	25	longani	longani	NOUN
ejpam-4101	34	26	[	[	PUNCT
ejpam-4101	34	27	6	6	NUM
ejpam-4101	34	28	]	]	PUNCT
ejpam-4101	34	29	studied	study	VERB
ejpam-4101	34	30	the	the	DET
ejpam-4101	34	31	relationship	relationship	NOUN
ejpam-4101	34	32	between	between	ADP
ejpam-4101	34	33	the	the	DET
ejpam-4101	34	34	operator	operator	NOUN
ejpam-4101	34	35	⊕k	⊕k	NOUN
ejpam-4101	34	36	and	and	CCONJ
ejpam-4101	34	37	the	the	DET
ejpam-4101	34	38	wave	wave	NOUN
ejpam-4101	34	39	operator	operator	NOUN
ejpam-4101	34	40	,	,	PUNCT
ejpam-4101	34	41	and	and	CCONJ
ejpam-4101	34	42	the	the	DET
ejpam-4101	34	43	relationship	relationship	NOUN
ejpam-4101	34	44	between	between	ADP
ejpam-4101	34	45	the	the	DET
ejpam-4101	34	46	operator	operator	NOUN
ejpam-4101	34	47	⊕k	⊕k	NOUN
ejpam-4101	34	48	and	and	CCONJ
ejpam-4101	34	49	the	the	DET
ejpam-4101	34	50	laplace	laplace	NOUN
ejpam-4101	34	51	operator	operator	NOUN
ejpam-4101	34	52	.	.	PUNCT
ejpam-4101	35	1	moreover	moreover	ADV
ejpam-4101	35	2	,	,	PUNCT
ejpam-4101	35	3	they	they	PRON
ejpam-4101	35	4	studied	study	VERB
ejpam-4101	35	5	equation	equation	NOUN
ejpam-4101	35	6	⊕kk(x	⊕kk(x	VERB
ejpam-4101	35	7	)	)	PUNCT
ejpam-4101	36	1	=	=	SYM
ejpam-4101	36	2	δ	δ	PROPN
ejpam-4101	36	3	and	and	CCONJ
ejpam-4101	36	4	they	they	PRON
ejpam-4101	36	5	showed	show	VERB
ejpam-4101	36	6	that	that	SCONJ
ejpam-4101	36	7	k(x	k(x	NOUN
ejpam-4101	36	8	)	)	PUNCT
ejpam-4101	37	1	=	=	PUNCT
ejpam-4101	38	1	[	[	X
ejpam-4101	38	2	rh	rh	NUM
ejpam-4101	38	3	2k(x	2k(x	PROPN
ejpam-4101	38	4	)	)	PUNCT
ejpam-4101	38	5	∗	∗	NOUN
ejpam-4101	38	6	(	(	PUNCT
ejpam-4101	38	7	−1)kre	−1)kre	PROPN
ejpam-4101	38	8	2k(x	2k(x	NUM
ejpam-4101	38	9	)	)	PUNCT
ejpam-4101	38	10	]	]	PUNCT
ejpam-4101	38	11	∗	∗	PROPN
ejpam-4101	38	12	s2k(x	s2k(x	PROPN
ejpam-4101	38	13	)	)	PUNCT
ejpam-4101	38	14	∗	∗	PROPN
ejpam-4101	38	15	t2k(x	t2k(x	PROPN
ejpam-4101	38	16	)	)	PUNCT
ejpam-4101	38	17	is	be	AUX
ejpam-4101	38	18	the	the	DET
ejpam-4101	38	19	fundamental	fundamental	ADJ
ejpam-4101	38	20	solution	solution	NOUN
ejpam-4101	38	21	of	of	ADP
ejpam-4101	38	22	the	the	DET
ejpam-4101	38	23	operator	operator	NOUN
ejpam-4101	38	24	⊕k	⊕k	VERB
ejpam-4101	38	25	.	.	PUNCT
ejpam-4101	39	1	later	later	ADV
ejpam-4101	39	2	,	,	PUNCT
ejpam-4101	39	3	kananthai	kananthai	PROPN
ejpam-4101	39	4	[	[	X
ejpam-4101	39	5	3	3	NUM
ejpam-4101	39	6	]	]	PUNCT
ejpam-4101	39	7	studied	study	VERB
ejpam-4101	39	8	the	the	DET
ejpam-4101	39	9	inversion	inversion	NOUN
ejpam-4101	39	10	of	of	ADP
ejpam-4101	39	11	the	the	DET
ejpam-4101	39	12	kernel	kernel	NOUN
ejpam-4101	39	13	kα	kα	PROPN
ejpam-4101	39	14	,	,	PUNCT
ejpam-4101	39	15	β	β	X
ejpam-4101	39	16	,	,	PUNCT
ejpam-4101	39	17	γ	γ	X
ejpam-4101	39	18	,	,	PUNCT
ejpam-4101	39	19	ν	ν	NOUN
ejpam-4101	39	20	related	relate	VERB
ejpam-4101	39	21	to	to	ADP
ejpam-4101	39	22	the	the	DET
ejpam-4101	39	23	operator	operator	NOUN
ejpam-4101	39	24	⊕k	⊕k	VERB
ejpam-4101	39	25	.	.	PUNCT
ejpam-4101	40	1	in	in	ADP
ejpam-4101	40	2	1988	1988	NUM
ejpam-4101	40	3	,	,	PUNCT
ejpam-4101	40	4	trione	trione	NOUN
ejpam-4101	41	1	[	[	X
ejpam-4101	41	2	22	22	NUM
ejpam-4101	41	3	]	]	PUNCT
ejpam-4101	41	4	studied	study	VERB
ejpam-4101	41	5	the	the	DET
ejpam-4101	41	6	fundamental	fundamental	ADJ
ejpam-4101	41	7	solution	solution	NOUN
ejpam-4101	41	8	of	of	ADP
ejpam-4101	41	9	the	the	DET
ejpam-4101	41	10	ultra	ultra	ADJ
ejpam-4101	41	11	-	-	ADJ
ejpam-4101	41	12	hyperbolic	hyperbolic	ADJ
ejpam-4101	41	13	klein	klein	PROPN
ejpam-4101	41	14	–	–	PUNCT
ejpam-4101	41	15	gordon	gordon	PROPN
ejpam-4101	41	16	operator	operator	NOUN
ejpam-4101	41	17	iterated	iterate	VERB
ejpam-4101	41	18	k	k	NOUN
ejpam-4101	41	19	-	-	PUNCT
ejpam-4101	41	20	times	time	NOUN
ejpam-4101	41	21	,	,	PUNCT
ejpam-4101	41	22	which	which	PRON
ejpam-4101	41	23	is	be	AUX
ejpam-4101	41	24	defined	define	VERB
ejpam-4101	41	25	by	by	ADP
ejpam-4101	41	26	(	(	PUNCT
ejpam-4101	41	27	⊡+m2)k	⊡+m2)k	X
ejpam-4101	41	28	=	=	SYM
ejpam-4101	41	29	[	[	PUNCT
ejpam-4101	41	30	∂2	∂2	ADJ
ejpam-4101	41	31	∂x21	∂x21	PROPN
ejpam-4101	41	32	+	+	CCONJ
ejpam-4101	41	33	∂2	∂2	PROPN
ejpam-4101	41	34	∂x22	∂x22	PROPN
ejpam-4101	41	35	+	+	CCONJ
ejpam-4101	41	36	·	·	PUNCT
ejpam-4101	41	37	·	·	PUNCT
ejpam-4101	42	1	·	·	PUNCT
ejpam-4101	42	2	+	+	NUM
ejpam-4101	42	3	∂2	∂2	NOUN
ejpam-4101	42	4	∂x2p	∂x2p	NUM
ejpam-4101	43	1	−	−	PROPN
ejpam-4101	44	1	∂2	∂2	PROPN
ejpam-4101	44	2	∂x2p+1	∂x2p+1	PROPN
ejpam-4101	44	3	−	−	PROPN
ejpam-4101	44	4	∂2	∂2	NOUN
ejpam-4101	44	5	∂x2p+2	∂x2p+2	VERB
ejpam-4101	44	6	−	−	X
ejpam-4101	44	7	·	·	PUNCT
ejpam-4101	44	8	·	·	PUNCT
ejpam-4101	44	9	·	·	PUNCT
ejpam-4101	45	1	−	−	PUNCT
ejpam-4101	46	1	∂2	∂2	NOUN
ejpam-4101	46	2	∂x2p+q	∂x2p+q	X
ejpam-4101	46	3	+	+	CCONJ
ejpam-4101	46	4	m2	m2	PROPN
ejpam-4101	46	5	]	]	X
ejpam-4101	46	6	k	k	PROPN
ejpam-4101	46	7	.	.	PUNCT
ejpam-4101	47	1	(	(	PUNCT
ejpam-4101	47	2	8)	8)	NUM
ejpam-4101	47	3	later	later	ADV
ejpam-4101	47	4	,	,	PUNCT
ejpam-4101	47	5	lunnaree	lunnaree	ADJ
ejpam-4101	47	6	and	and	CCONJ
ejpam-4101	47	7	nonlaopon	nonlaopon	ADV
ejpam-4101	47	8	[	[	X
ejpam-4101	47	9	11	11	NUM
ejpam-4101	47	10	]	]	PUNCT
ejpam-4101	47	11	introduced	introduce	VERB
ejpam-4101	47	12	the	the	DET
ejpam-4101	47	13	operator	operator	NOUN
ejpam-4101	47	14	(	(	PUNCT
ejpam-4101	47	15	♢	♢	PROPN
ejpam-4101	47	16	+	+	PROPN
ejpam-4101	47	17	m2)k	m2)k	NOUN
ejpam-4101	47	18	,	,	PUNCT
ejpam-4101	47	19	that	that	PRON
ejpam-4101	47	20	is	be	AUX
ejpam-4101	47	21	named	name	VERB
ejpam-4101	47	22	as	as	SCONJ
ejpam-4101	47	23	the	the	DET
ejpam-4101	47	24	diamond	diamond	PROPN
ejpam-4101	47	25	klein	klein	PROPN
ejpam-4101	47	26	-	-	PUNCT
ejpam-4101	47	27	gordon	gordon	PROPN
ejpam-4101	47	28	operator	operator	NOUN
ejpam-4101	47	29	iterated	iterate	VERB
ejpam-4101	47	30	k	k	NOUN
ejpam-4101	47	31	-	-	PUNCT
ejpam-4101	47	32	times	time	NOUN
ejpam-4101	47	33	,	,	PUNCT
ejpam-4101	47	34	which	which	PRON
ejpam-4101	47	35	is	be	AUX
ejpam-4101	47	36	defined	define	VERB
ejpam-4101	47	37	by	by	ADP
ejpam-4101	47	38	(	(	PUNCT
ejpam-4101	47	39	♢	♢	PROPN
ejpam-4101	47	40	+	+	PROPN
ejpam-4101	47	41	m2)k	m2)k	NOUN
ejpam-4101	47	42	=	=	SYM
ejpam-4101	47	43			PROPN
ejpam-4101	47	44	(	(	PUNCT
ejpam-4101	47	45	p∑	p∑	NOUN
ejpam-4101	47	46	r=1	r=1	NOUN
ejpam-4101	47	47	∂2	∂2	NOUN
ejpam-4101	47	48	∂x2r	∂x2r	NOUN
ejpam-4101	47	49	)	)	PUNCT
ejpam-4101	47	50	2	2	NUM
ejpam-4101	47	51	−	−	NOUN
ejpam-4101	47	52			PROPN
ejpam-4101	47	53	p+q∑	p+q∑	PROPN
ejpam-4101	47	54	j	j	NOUN
ejpam-4101	47	55	=	=	PROPN
ejpam-4101	47	56	p+1	p+1	PROPN
ejpam-4101	47	57	∂2	∂2	PROPN
ejpam-4101	47	58	∂x2j	∂x2j	PUNCT
ejpam-4101	47	59	2	2	PROPN
ejpam-4101	48	1	+	+	PROPN
ejpam-4101	48	2	m2	m2	PROPN
ejpam-4101	48	3	k	k	PUNCT
ejpam-4101	48	4	,	,	PUNCT
ejpam-4101	48	5	(	(	PUNCT
ejpam-4101	48	6	9	9	X
ejpam-4101	48	7	)	)	PUNCT
ejpam-4101	48	8	where	where	SCONJ
ejpam-4101	48	9	p+q	p+q	NOUN
ejpam-4101	48	10	=	=	PUNCT
ejpam-4101	48	11	n	n	X
ejpam-4101	48	12	is	be	AUX
ejpam-4101	48	13	the	the	DET
ejpam-4101	48	14	dimension	dimension	NOUN
ejpam-4101	48	15	of	of	ADP
ejpam-4101	48	16	the	the	DET
ejpam-4101	48	17	space	space	NOUN
ejpam-4101	48	18	rn	rn	PROPN
ejpam-4101	48	19	,	,	PUNCT
ejpam-4101	48	20	for	for	ADP
ejpam-4101	48	21	x	x	SYM
ejpam-4101	48	22	=	=	SYM
ejpam-4101	48	23	(	(	PUNCT
ejpam-4101	48	24	x1	x1	PROPN
ejpam-4101	48	25	,	,	PUNCT
ejpam-4101	48	26	x2	x2	PROPN
ejpam-4101	48	27	,	,	PUNCT
ejpam-4101	48	28	.	.	PUNCT
ejpam-4101	48	29	.	.	PUNCT
ejpam-4101	48	30	.	.	PUNCT
ejpam-4101	49	1	,	,	PUNCT
ejpam-4101	49	2	xn	xn	X
ejpam-4101	49	3	)	)	PUNCT
ejpam-4101	49	4	∈	∈	PROPN
ejpam-4101	49	5	rn	rn	PROPN
ejpam-4101	49	6	,	,	PUNCT
ejpam-4101	49	7	m	m	VERB
ejpam-4101	49	8	is	be	AUX
ejpam-4101	49	9	a	a	DET
ejpam-4101	49	10	nonnegative	nonnegative	ADJ
ejpam-4101	49	11	real	real	ADJ
ejpam-4101	49	12	number	number	NOUN
ejpam-4101	49	13	and	and	CCONJ
ejpam-4101	49	14	k	k	PROPN
ejpam-4101	49	15	is	be	AUX
ejpam-4101	49	16	a	a	DET
ejpam-4101	49	17	non	non	ADJ
ejpam-4101	49	18	-	-	ADJ
ejpam-4101	49	19	negative	negative	ADJ
ejpam-4101	49	20	integer	integer	NOUN
ejpam-4101	49	21	,	,	PUNCT
ejpam-4101	49	22	see	see	VERB
ejpam-4101	49	23	[	[	X
ejpam-4101	49	24	9	9	NUM
ejpam-4101	49	25	,	,	PUNCT
ejpam-4101	49	26	10	10	NUM
ejpam-4101	49	27	,	,	PUNCT
ejpam-4101	49	28	17	17	NUM
ejpam-4101	49	29	,	,	PUNCT
ejpam-4101	49	30	18	18	NUM
ejpam-4101	49	31	]	]	PUNCT
ejpam-4101	49	32	for	for	ADP
ejpam-4101	49	33	more	more	ADJ
ejpam-4101	49	34	details	detail	NOUN
ejpam-4101	49	35	.	.	PUNCT
ejpam-4101	50	1	v.n	v.n	PROPN
ejpam-4101	50	2	.	.	PROPN
ejpam-4101	50	3	mishra	mishra	PROPN
ejpam-4101	50	4	,	,	PUNCT
ejpam-4101	50	5	k.	k.	PROPN
ejpam-4101	50	6	khatri	khatri	PROPN
ejpam-4101	50	7	and	and	CCONJ
ejpam-4101	50	8	l.n	l.n	PROPN
ejpam-4101	50	9	.	.	PROPN
ejpam-4101	50	10	mishra	mishra	PROPN
ejpam-4101	51	1	[	[	X
ejpam-4101	51	2	15	15	NUM
ejpam-4101	51	3	]	]	PUNCT
ejpam-4101	51	4	studied	study	VERB
ejpam-4101	51	5	the	the	DET
ejpam-4101	51	6	linear	linear	PROPN
ejpam-4101	51	7	operators	operator	NOUN
ejpam-4101	51	8	to	to	PART
ejpam-4101	51	9	approximate	approximate	VERB
ejpam-4101	51	10	signals	signal	NOUN
ejpam-4101	51	11	of	of	ADP
ejpam-4101	51	12	lip	lip	NOUN
ejpam-4101	51	13	(	(	PUNCT
ejpam-4101	51	14	α	α	NOUN
ejpam-4101	51	15	,	,	PUNCT
ejpam-4101	51	16	p	p	NOUN
ejpam-4101	51	17	)	)	PUNCT
ejpam-4101	51	18	,	,	PUNCT
ejpam-4101	51	19	(	(	PUNCT
ejpam-4101	51	20	p	p	PRON
ejpam-4101	51	21	≥	≥	NOUN
ejpam-4101	51	22	1)-class	1)-class	NUM
ejpam-4101	51	23	,	,	PUNCT
ejpam-4101	51	24	see	see	VERB
ejpam-4101	51	25	[	[	X
ejpam-4101	51	26	2	2	NUM
ejpam-4101	51	27	,	,	PUNCT
ejpam-4101	51	28	12–14	12–14	NUM
ejpam-4101	51	29	,	,	PUNCT
ejpam-4101	51	30	16	16	NUM
ejpam-4101	51	31	]	]	PUNCT
ejpam-4101	51	32	for	for	ADP
ejpam-4101	51	33	more	more	ADJ
ejpam-4101	51	34	details	detail	NOUN
ejpam-4101	51	35	.	.	PUNCT
ejpam-4101	52	1	moreover	moreover	ADV
ejpam-4101	52	2	,	,	PUNCT
ejpam-4101	52	3	kananthai	kananthai	ADJ
ejpam-4101	52	4	[	[	X
ejpam-4101	52	5	4	4	X
ejpam-4101	52	6	]	]	PUNCT
ejpam-4101	52	7	studied	study	VERB
ejpam-4101	52	8	the	the	DET
ejpam-4101	52	9	fundamental	fundamental	ADJ
ejpam-4101	52	10	solution	solution	NOUN
ejpam-4101	52	11	for	for	ADP
ejpam-4101	52	12	the	the	DET
ejpam-4101	52	13	(	(	PUNCT
ejpam-4101	52	14	♢	♢	PROPN
ejpam-4101	52	15	+	+	X
ejpam-4101	52	16	m4)k	m4)k	ADJ
ejpam-4101	52	17	,	,	PUNCT
ejpam-4101	52	18	which	which	PRON
ejpam-4101	52	19	related	relate	VERB
ejpam-4101	52	20	to	to	ADP
ejpam-4101	52	21	the	the	DET
ejpam-4101	52	22	klein	klein	PROPN
ejpam-4101	52	23	-	-	PUNCT
ejpam-4101	52	24	gordon	gordon	PROPN
ejpam-4101	52	25	operator	operator	NOUN
ejpam-4101	52	26	.	.	PUNCT
ejpam-4101	53	1	from	from	ADP
ejpam-4101	53	2	(	(	PUNCT
ejpam-4101	53	3	7	7	X
ejpam-4101	53	4	)	)	PUNCT
ejpam-4101	53	5	the	the	DET
ejpam-4101	53	6	operator	operator	PROPN
ejpam-4101	53	7			PROPN
ejpam-4101	53	8	(	(	PUNCT
ejpam-4101	53	9	p∑	p∑	NOUN
ejpam-4101	53	10	r=1	r=1	NOUN
ejpam-4101	53	11	∂2	∂2	NOUN
ejpam-4101	53	12	∂x2r	∂x2r	NOUN
ejpam-4101	53	13	)	)	PUNCT
ejpam-4101	53	14	2	2	PROPN
ejpam-4101	53	15	+	+	NUM
ejpam-4101	53	16	m2	m2	PROPN
ejpam-4101	53	17	2	2	NUM
ejpam-4101	53	18	2	2	ADV
ejpam-4101	53	19	−	−	PUNCT
ejpam-4101	53	20			PROPN
ejpam-4101	53	21	p+q∑	p+q∑	PROPN
ejpam-4101	53	22	j	j	PROPN
ejpam-4101	53	23	=	=	PROPN
ejpam-4101	53	24	p+1	p+1	PROPN
ejpam-4101	53	25	∂2	∂2	PROPN
ejpam-4101	53	26	∂x2j	∂x2j	PUNCT
ejpam-4101	53	27	2	2	PROPN
ejpam-4101	53	28	−	−	PROPN
ejpam-4101	53	29	m2	m2	PROPN
ejpam-4101	53	30	2	2	NUM
ejpam-4101	53	31	2	2	ADV
ejpam-4101	53	32			NUM
ejpam-4101	53	33	k	k	NOUN
ejpam-4101	53	34	can	can	AUX
ejpam-4101	53	35	be	be	AUX
ejpam-4101	53	36	expressed	express	VERB
ejpam-4101	53	37	in	in	ADP
ejpam-4101	53	38	the	the	DET
ejpam-4101	53	39	form	form	PROPN
ejpam-4101	53	40			PROPN
ejpam-4101	53	41	(	(	PUNCT
ejpam-4101	53	42	p∑	p∑	NOUN
ejpam-4101	53	43	r=1	r=1	NOUN
ejpam-4101	53	44	∂2	∂2	NOUN
ejpam-4101	53	45	∂x2r	∂x2r	NOUN
ejpam-4101	53	46	)	)	PUNCT
ejpam-4101	53	47	2	2	PROPN
ejpam-4101	53	48	+	+	NUM
ejpam-4101	53	49	m2	m2	PROPN
ejpam-4101	53	50	2	2	NUM
ejpam-4101	53	51	2	2	ADV
ejpam-4101	53	52	−	−	PUNCT
ejpam-4101	53	53			PROPN
ejpam-4101	53	54	p+q∑	p+q∑	PROPN
ejpam-4101	53	55	j	j	PROPN
ejpam-4101	53	56	=	=	PROPN
ejpam-4101	53	57	p+1	p+1	PROPN
ejpam-4101	53	58	∂2	∂2	PROPN
ejpam-4101	53	59	∂x2j	∂x2j	PUNCT
ejpam-4101	54	1	2	2	PROPN
ejpam-4101	54	2	−	−	PROPN
ejpam-4101	54	3	m2	m2	PROPN
ejpam-4101	54	4	2	2	NUM
ejpam-4101	54	5	2	2	ADV
ejpam-4101	54	6			NUM
ejpam-4101	54	7	k	k	NOUN
ejpam-4101	54	8	=	=	SYM
ejpam-4101	54	9			PROPN
ejpam-4101	54	10	(	(	PUNCT
ejpam-4101	54	11	p∑	p∑	NOUN
ejpam-4101	54	12	r=1	r=1	NOUN
ejpam-4101	54	13	∂2	∂2	NOUN
ejpam-4101	54	14	∂x2r	∂x2r	NOUN
ejpam-4101	54	15	)	)	PUNCT
ejpam-4101	54	16	2	2	NUM
ejpam-4101	54	17	−	−	NOUN
ejpam-4101	54	18			PROPN
ejpam-4101	54	19	p+q∑	p+q∑	PROPN
ejpam-4101	54	20	j	j	NOUN
ejpam-4101	55	1	=	=	PROPN
ejpam-4101	55	2	p+1	p+1	PROPN
ejpam-4101	55	3	∂2	∂2	PROPN
ejpam-4101	55	4	∂x2j	∂x2j	PUNCT
ejpam-4101	56	1	2	2	PROPN
ejpam-4101	57	1	+	+	NUM
ejpam-4101	57	2	m2	m2	PROPN
ejpam-4101	57	3	k	k	PROPN
ejpam-4101	57	4	(	(	PUNCT
ejpam-4101	57	5	p∑	p∑	NOUN
ejpam-4101	57	6	r=1	r=1	NOUN
ejpam-4101	57	7	∂2	∂2	NOUN
ejpam-4101	57	8	∂x2r	∂x2r	NOUN
ejpam-4101	57	9	)	)	PUNCT
ejpam-4101	57	10	2	2	NUM
ejpam-4101	57	11	+	+	CCONJ
ejpam-4101	57	12			PROPN
ejpam-4101	57	13	p+q∑	p+q∑	PROPN
ejpam-4101	57	14	j	j	NOUN
ejpam-4101	57	15	=	=	PROPN
ejpam-4101	57	16	p+1	p+1	PROPN
ejpam-4101	57	17	∂2	∂2	PROPN
ejpam-4101	57	18	∂x2j	∂x2j	PUNCT
ejpam-4101	57	19	2k	2k	X
ejpam-4101	58	1	=	=	SYM
ejpam-4101	58	2	(	(	PUNCT
ejpam-4101	58	3	♢	♢	PROPN
ejpam-4101	58	4	+	+	PROPN
ejpam-4101	58	5	m2)k	m2)k	PROPN
ejpam-4101	58	6	(	(	PUNCT
ejpam-4101	58	7	△	△	X
ejpam-4101	58	8	2	2	NUM
ejpam-4101	58	9	+	+	NOUN
ejpam-4101	58	10	⊡2	⊡2	PROPN
ejpam-4101	58	11	2	2	NUM
ejpam-4101	58	12	)	)	PUNCT
ejpam-4101	58	13	k	k	PROPN
ejpam-4101	58	14	s.	s.	PROPN
ejpam-4101	58	15	bupasiri	bupasiri	PROPN
ejpam-4101	58	16	/	/	SYM
ejpam-4101	58	17	eur	eur	PROPN
ejpam-4101	58	18	.	.	PUNCT
ejpam-4101	59	1	j.	j.	PROPN
ejpam-4101	59	2	pure	pure	PROPN
ejpam-4101	59	3	appl	appl	PROPN
ejpam-4101	59	4	.	.	PROPN
ejpam-4101	59	5	math	math	PROPN
ejpam-4101	59	6	,	,	PUNCT
ejpam-4101	59	7	14	14	NUM
ejpam-4101	59	8	(	(	PUNCT
ejpam-4101	59	9	4	4	NUM
ejpam-4101	59	10	)	)	PUNCT
ejpam-4101	59	11	(	(	PUNCT
ejpam-4101	59	12	2021	2021	NUM
ejpam-4101	59	13	)	)	PUNCT
ejpam-4101	59	14	,	,	PUNCT
ejpam-4101	59	15	1306	1306	NUM
ejpam-4101	59	16	-	-	SYM
ejpam-4101	59	17	1323	1323	NUM
ejpam-4101	59	18	1309	1309	NUM
ejpam-4101	59	19	=	=	SYM
ejpam-4101	59	20	(	(	PUNCT
ejpam-4101	59	21	♢	♢	PROPN
ejpam-4101	59	22	+	+	PROPN
ejpam-4101	59	23	m2)k	m2)k	ADJ
ejpam-4101	59	24	⊙k	⊙k	NOUN
ejpam-4101	59	25	.	.	PUNCT
ejpam-4101	60	1	(	(	PUNCT
ejpam-4101	60	2	10	10	NUM
ejpam-4101	60	3	)	)	PUNCT
ejpam-4101	60	4	from	from	ADP
ejpam-4101	60	5	(	(	PUNCT
ejpam-4101	60	6	10	10	NUM
ejpam-4101	60	7	)	)	PUNCT
ejpam-4101	60	8	with	with	ADP
ejpam-4101	60	9	q	q	PROPN
ejpam-4101	61	1	=	=	PUNCT
ejpam-4101	61	2	m	m	NOUN
ejpam-4101	61	3	=	=	SYM
ejpam-4101	61	4	0	0	NUM
ejpam-4101	61	5	and	and	CCONJ
ejpam-4101	61	6	k	k	X
ejpam-4101	61	7	=	=	SYM
ejpam-4101	61	8	1	1	NUM
ejpam-4101	61	9	,	,	PUNCT
ejpam-4101	61	10	we	we	PRON
ejpam-4101	61	11	obtain	obtain	VERB
ejpam-4101	61	12	laplace	laplace	NOUN
ejpam-4101	61	13	operator	operator	NOUN
ejpam-4101	61	14	△	△	NOUN
ejpam-4101	61	15	4	4	NUM
ejpam-4101	61	16	p	p	NOUN
ejpam-4101	61	17	of	of	ADP
ejpam-4101	61	18	p	p	NOUN
ejpam-4101	61	19	-	-	PUNCT
ejpam-4101	61	20	dimension	dimension	NOUN
ejpam-4101	61	21	,	,	PUNCT
ejpam-4101	61	22	where	where	SCONJ
ejpam-4101	61	23	△	△	NOUN
ejpam-4101	61	24	p	p	NOUN
ejpam-4101	61	25	=	=	SYM
ejpam-4101	61	26	∂2	∂2	NOUN
ejpam-4101	61	27	∂x21	∂x21	PROPN
ejpam-4101	61	28	+	+	CCONJ
ejpam-4101	61	29	∂2	∂2	PROPN
ejpam-4101	61	30	∂x22	∂x22	PROPN
ejpam-4101	61	31	+	+	CCONJ
ejpam-4101	61	32	·	·	PUNCT
ejpam-4101	61	33	·	·	PUNCT
ejpam-4101	61	34	·	·	PUNCT
ejpam-4101	62	1	+	+	NUM
ejpam-4101	62	2	∂2	∂2	PROPN
ejpam-4101	62	3	∂x2p	∂x2p	INTJ
ejpam-4101	62	4	.	.	PUNCT
ejpam-4101	63	1	(	(	PUNCT
ejpam-4101	63	2	11	11	NUM
ejpam-4101	63	3	)	)	PUNCT
ejpam-4101	63	4	in	in	ADP
ejpam-4101	63	5	this	this	DET
ejpam-4101	63	6	article	article	NOUN
ejpam-4101	63	7	,	,	PUNCT
ejpam-4101	63	8	we	we	PRON
ejpam-4101	63	9	study	study	VERB
ejpam-4101	63	10	the	the	DET
ejpam-4101	63	11	fundamental	fundamental	ADJ
ejpam-4101	63	12	solution	solution	NOUN
ejpam-4101	63	13	of	of	ADP
ejpam-4101	63	14	the	the	DET
ejpam-4101	63	15	equation	equation	NOUN
ejpam-4101	63	16	of	of	ADP
ejpam-4101	63	17	the	the	DET
ejpam-4101	63	18	form	form	PROPN
ejpam-4101	63	19			PROPN
ejpam-4101	63	20	(	(	PUNCT
ejpam-4101	63	21	p∑	p∑	NOUN
ejpam-4101	63	22	r=1	r=1	NOUN
ejpam-4101	63	23	∂2	∂2	NOUN
ejpam-4101	63	24	∂x2r	∂x2r	NOUN
ejpam-4101	63	25	)	)	PUNCT
ejpam-4101	63	26	2	2	PROPN
ejpam-4101	63	27	+	+	NUM
ejpam-4101	63	28	m2	m2	PROPN
ejpam-4101	63	29	2	2	NUM
ejpam-4101	63	30	2	2	ADV
ejpam-4101	63	31	−	−	PUNCT
ejpam-4101	63	32			PROPN
ejpam-4101	63	33	p+q∑	p+q∑	PROPN
ejpam-4101	63	34	j	j	PROPN
ejpam-4101	63	35	=	=	PROPN
ejpam-4101	63	36	p+1	p+1	PROPN
ejpam-4101	63	37	∂2	∂2	PROPN
ejpam-4101	63	38	∂x2j	∂x2j	PUNCT
ejpam-4101	64	1	2	2	PROPN
ejpam-4101	64	2	−	−	PROPN
ejpam-4101	64	3	m2	m2	PROPN
ejpam-4101	64	4	2	2	NUM
ejpam-4101	64	5	2	2	PROPN
ejpam-4101	65	1			PROPN
ejpam-4101	65	2	k	k	PROPN
ejpam-4101	65	3	k(x	k(x	PROPN
ejpam-4101	65	4	,	,	PUNCT
ejpam-4101	65	5	m	m	NOUN
ejpam-4101	65	6	)	)	PUNCT
ejpam-4101	65	7	=	=	SYM
ejpam-4101	65	8	δ	δ	PROPN
ejpam-4101	65	9	,	,	PUNCT
ejpam-4101	65	10	or	or	CCONJ
ejpam-4101	65	11	(	(	PUNCT
ejpam-4101	65	12	(	(	PUNCT
ejpam-4101	65	13	♢	♢	PROPN
ejpam-4101	65	14	+	+	PROPN
ejpam-4101	65	15	m2	m2	X
ejpam-4101	65	16	)	)	PUNCT
ejpam-4101	65	17	(	(	PUNCT
ejpam-4101	65	18	△	△	X
ejpam-4101	65	19	2	2	NUM
ejpam-4101	65	20	+	+	NOUN
ejpam-4101	65	21	⊡2	⊡2	PROPN
ejpam-4101	65	22	2	2	NUM
ejpam-4101	65	23	)	)	PUNCT
ejpam-4101	65	24	)	)	PUNCT
ejpam-4101	66	1	k	k	PROPN
ejpam-4101	66	2	k(x	k(x	PROPN
ejpam-4101	66	3	,	,	PUNCT
ejpam-4101	66	4	m	m	NOUN
ejpam-4101	66	5	)	)	PUNCT
ejpam-4101	66	6	=	=	SYM
ejpam-4101	66	7	δ	δ	PROPN
ejpam-4101	66	8	,	,	PUNCT
ejpam-4101	66	9	where	where	SCONJ
ejpam-4101	66	10	k(x	k(x	PROPN
ejpam-4101	66	11	,	,	PUNCT
ejpam-4101	66	12	m	m	NOUN
ejpam-4101	66	13	)	)	PUNCT
ejpam-4101	66	14	is	be	AUX
ejpam-4101	66	15	the	the	DET
ejpam-4101	66	16	fundamental	fundamental	ADJ
ejpam-4101	66	17	solution	solution	NOUN
ejpam-4101	66	18	,	,	PUNCT
ejpam-4101	66	19	δ	δ	PROPN
ejpam-4101	66	20	is	be	AUX
ejpam-4101	66	21	the	the	DET
ejpam-4101	66	22	dirac	dirac	PROPN
ejpam-4101	66	23	delta	delta	NOUN
ejpam-4101	66	24	function	function	NOUN
ejpam-4101	66	25	,	,	PUNCT
ejpam-4101	66	26	k	k	PROPN
ejpam-4101	66	27	is	be	AUX
ejpam-4101	66	28	a	a	DET
ejpam-4101	66	29	nonnegative	nonnegative	ADJ
ejpam-4101	66	30	integer	integer	NOUN
ejpam-4101	66	31	,	,	PUNCT
ejpam-4101	66	32	and	and	CCONJ
ejpam-4101	66	33	m	m	PROPN
ejpam-4101	66	34	is	be	AUX
ejpam-4101	66	35	a	a	DET
ejpam-4101	66	36	non	non	ADJ
ejpam-4101	66	37	-	-	ADJ
ejpam-4101	66	38	negative	negative	ADJ
ejpam-4101	66	39	real	real	ADJ
ejpam-4101	66	40	number	number	NOUN
ejpam-4101	66	41	.	.	PUNCT
ejpam-4101	67	1	moreover	moreover	ADV
ejpam-4101	67	2	,	,	PUNCT
ejpam-4101	67	3	we	we	PRON
ejpam-4101	67	4	study	study	VERB
ejpam-4101	67	5	the	the	DET
ejpam-4101	67	6	fourier	fourier	NOUN
ejpam-4101	67	7	transform	transform	NOUN
ejpam-4101	67	8	of	of	ADP
ejpam-4101	67	9	the	the	DET
ejpam-4101	67	10	operator	operator	NOUN
ejpam-4101	67	11	(	(	PUNCT
ejpam-4101	67	12	(	(	PUNCT
ejpam-4101	67	13	♢	♢	PROPN
ejpam-4101	67	14	+	+	PROPN
ejpam-4101	67	15	m2	m2	X
ejpam-4101	67	16	)	)	PUNCT
ejpam-4101	67	17	(	(	PUNCT
ejpam-4101	67	18	△	△	X
ejpam-4101	67	19	2+⊡2	2+⊡2	NUM
ejpam-4101	67	20	2	2	NUM
ejpam-4101	67	21	)	)	PUNCT
ejpam-4101	67	22	)	)	PUNCT
ejpam-4101	68	1	k	k	PROPN
ejpam-4101	68	2	δ	δ	PROPN
ejpam-4101	68	3	.	.	PUNCT
ejpam-4101	69	1	preliminary	preliminary	ADJ
ejpam-4101	69	2	notes	note	NOUN
ejpam-4101	69	3	definition	definition	NOUN
ejpam-4101	69	4	1	1	X
ejpam-4101	69	5	.	.	PUNCT
ejpam-4101	70	1	let	let	VERB
ejpam-4101	70	2	x	x	PUNCT
ejpam-4101	70	3	=	=	SYM
ejpam-4101	70	4	(	(	PUNCT
ejpam-4101	70	5	x1	x1	PROPN
ejpam-4101	70	6	,	,	PUNCT
ejpam-4101	70	7	x2	x2	PROPN
ejpam-4101	70	8	,	,	PUNCT
ejpam-4101	70	9	.	.	PUNCT
ejpam-4101	70	10	.	.	PUNCT
ejpam-4101	71	1	.	.	PUNCT
ejpam-4101	72	1	,	,	PUNCT
ejpam-4101	72	2	xn	xn	X
ejpam-4101	72	3	)	)	PUNCT
ejpam-4101	72	4	be	be	VERB
ejpam-4101	72	5	a	a	DET
ejpam-4101	72	6	point	point	NOUN
ejpam-4101	72	7	of	of	ADP
ejpam-4101	72	8	the	the	DET
ejpam-4101	72	9	n	n	ADV
ejpam-4101	72	10	-	-	PUNCT
ejpam-4101	72	11	dimensional	dimensional	ADJ
ejpam-4101	72	12	space	space	NOUN
ejpam-4101	72	13	rn	rn	PROPN
ejpam-4101	72	14	,	,	PUNCT
ejpam-4101	72	15	u	u	PROPN
ejpam-4101	72	16	=	=	SYM
ejpam-4101	72	17	x21	x21	PROPN
ejpam-4101	73	1	+	+	NUM
ejpam-4101	73	2	x22	x22	NOUN
ejpam-4101	73	3	+	+	CCONJ
ejpam-4101	73	4	·	·	PUNCT
ejpam-4101	73	5	·	·	PUNCT
ejpam-4101	73	6	·	·	PUNCT
ejpam-4101	74	1	+	+	NUM
ejpam-4101	74	2	x2p	x2p	NUM
ejpam-4101	74	3	−	−	PROPN
ejpam-4101	75	1	x2p+1	x2p+1	NUM
ejpam-4101	76	1	−	−	PROPN
ejpam-4101	76	2	x2p+2	x2p+2	ADJ
ejpam-4101	77	1	−	−	PROPN
ejpam-4101	77	2	·	·	PUNCT
ejpam-4101	77	3	·	·	PUNCT
ejpam-4101	77	4	·	·	PUNCT
ejpam-4101	78	1	−	−	NOUN
ejpam-4101	78	2	x2p+q	x2p+q	NOUN
ejpam-4101	78	3	,	,	PUNCT
ejpam-4101	78	4	(	(	PUNCT
ejpam-4101	78	5	12	12	NUM
ejpam-4101	78	6	)	)	PUNCT
ejpam-4101	78	7	where	where	SCONJ
ejpam-4101	78	8	p+	p+	VERB
ejpam-4101	78	9	q	q	X
ejpam-4101	78	10	=	=	PUNCT
ejpam-4101	78	11	n.	n.	NOUN
ejpam-4101	78	12	define	define	VERB
ejpam-4101	78	13	γ+	γ+	PUNCT
ejpam-4101	78	14	=	=	SYM
ejpam-4101	78	15	{	{	PUNCT
ejpam-4101	78	16	x	x	PROPN
ejpam-4101	78	17	∈	∈	PROPN
ejpam-4101	78	18	rn	rn	PROPN
ejpam-4101	78	19	:	:	PUNCT
ejpam-4101	78	20	x1	x1	PROPN
ejpam-4101	78	21	>	>	X
ejpam-4101	78	22	0	0	PUNCT
ejpam-4101	78	23	and	and	CCONJ
ejpam-4101	78	24	u	u	X
ejpam-4101	78	25	>	>	X
ejpam-4101	78	26	0	0	NUM
ejpam-4101	78	27	}	}	PUNCT
ejpam-4101	78	28	,	,	PUNCT
ejpam-4101	78	29	which	which	PRON
ejpam-4101	78	30	designates	designate	VERB
ejpam-4101	78	31	the	the	DET
ejpam-4101	78	32	interior	interior	NOUN
ejpam-4101	78	33	of	of	ADP
ejpam-4101	78	34	the	the	DET
ejpam-4101	78	35	forward	forward	ADJ
ejpam-4101	78	36	cone	cone	NOUN
ejpam-4101	78	37	and	and	CCONJ
ejpam-4101	78	38	γ+	γ+	PRON
ejpam-4101	78	39	designates	designate	VERB
ejpam-4101	78	40	its	its	PRON
ejpam-4101	78	41	closure	closure	NOUN
ejpam-4101	78	42	and	and	CCONJ
ejpam-4101	78	43	the	the	DET
ejpam-4101	78	44	following	follow	VERB
ejpam-4101	78	45	functions	function	NOUN
ejpam-4101	78	46	introduce	introduce	VERB
ejpam-4101	78	47	by	by	ADP
ejpam-4101	78	48	nozaki	nozaki	NOUN
ejpam-4101	78	49	[	[	X
ejpam-4101	78	50	19	19	NUM
ejpam-4101	78	51	,	,	PUNCT
ejpam-4101	78	52	page	page	NOUN
ejpam-4101	78	53	72	72	NUM
ejpam-4101	78	54	]	]	PUNCT
ejpam-4101	78	55	,	,	PUNCT
ejpam-4101	78	56	that	that	SCONJ
ejpam-4101	78	57	rh	rh	PROPN
ejpam-4101	78	58	α	α	PROPN
ejpam-4101	78	59	(	(	PUNCT
ejpam-4101	78	60	x	x	NOUN
ejpam-4101	78	61	)	)	PUNCT
ejpam-4101	78	62	=	=	SYM
ejpam-4101	78	63	{	{	PUNCT
ejpam-4101	78	64	u	u	NOUN
ejpam-4101	78	65	α−n	α−n	PROPN
ejpam-4101	78	66	2	2	NUM
ejpam-4101	78	67	kn(α	kn(α	PRON
ejpam-4101	78	68	)	)	PUNCT
ejpam-4101	78	69	,	,	PUNCT
ejpam-4101	78	70	if	if	SCONJ
ejpam-4101	78	71	x	x	SYM
ejpam-4101	78	72	∈	∈	PROPN
ejpam-4101	78	73	γ+	γ+	PRON
ejpam-4101	78	74	;	;	PUNCT
ejpam-4101	78	75	0	0	NUM
ejpam-4101	78	76	,	,	PUNCT
ejpam-4101	78	77	if	if	SCONJ
ejpam-4101	78	78	x	x	PROPN
ejpam-4101	78	79	̸∈	̸∈	PROPN
ejpam-4101	78	80	γ+	γ+	PUNCT
ejpam-4101	78	81	(	(	PUNCT
ejpam-4101	78	82	13	13	NUM
ejpam-4101	78	83	)	)	PUNCT
ejpam-4101	78	84	is	be	AUX
ejpam-4101	78	85	called	call	VERB
ejpam-4101	78	86	the	the	DET
ejpam-4101	78	87	ultra	ultra	ADJ
ejpam-4101	78	88	-	-	ADJ
ejpam-4101	78	89	hyperbolic	hyperbolic	ADJ
ejpam-4101	78	90	kernel	kernel	NOUN
ejpam-4101	78	91	of	of	ADP
ejpam-4101	78	92	marcel	marcel	PROPN
ejpam-4101	78	93	riesz	riesz	PROPN
ejpam-4101	78	94	.	.	PUNCT
ejpam-4101	79	1	here	here	ADV
ejpam-4101	79	2	,	,	PUNCT
ejpam-4101	79	3	α	α	PROPN
ejpam-4101	79	4	is	be	AUX
ejpam-4101	79	5	a	a	DET
ejpam-4101	79	6	complex	complex	ADJ
ejpam-4101	79	7	parameter	parameter	NOUN
ejpam-4101	79	8	and	and	CCONJ
ejpam-4101	79	9	n	n	DET
ejpam-4101	79	10	the	the	DET
ejpam-4101	79	11	dimension	dimension	NOUN
ejpam-4101	79	12	of	of	ADP
ejpam-4101	79	13	the	the	DET
ejpam-4101	79	14	space	space	NOUN
ejpam-4101	79	15	.	.	PUNCT
ejpam-4101	80	1	the	the	DET
ejpam-4101	80	2	constant	constant	ADJ
ejpam-4101	80	3	kn(α	kn(α	PRON
ejpam-4101	80	4	)	)	PUNCT
ejpam-4101	80	5	is	be	AUX
ejpam-4101	80	6	defined	define	VERB
ejpam-4101	80	7	by	by	ADP
ejpam-4101	80	8	kn(α	kn(α	NOUN
ejpam-4101	80	9	)	)	PUNCT
ejpam-4101	80	10	=	=	PUNCT
ejpam-4101	81	1	π	π	X
ejpam-4101	81	2	n−1	n−1	PROPN
ejpam-4101	81	3	2	2	NUM
ejpam-4101	81	4	γ	γ	X
ejpam-4101	81	5	(	(	PUNCT
ejpam-4101	81	6	2+α−n	2+α−n	PROPN
ejpam-4101	81	7	2	2	NUM
ejpam-4101	81	8	)	)	PUNCT
ejpam-4101	81	9	γ	γ	X
ejpam-4101	81	10	(	(	PUNCT
ejpam-4101	81	11	1−α	1−α	NUM
ejpam-4101	81	12	2	2	NUM
ejpam-4101	81	13	)	)	PUNCT
ejpam-4101	81	14	γ(α	γ(α	PROPN
ejpam-4101	81	15	)	)	PUNCT
ejpam-4101	81	16	γ	γ	PROPN
ejpam-4101	81	17	(	(	PUNCT
ejpam-4101	81	18	2+α−p	2+α−p	NUM
ejpam-4101	81	19	2	2	NUM
ejpam-4101	81	20	)	)	PUNCT
ejpam-4101	81	21	γ	γ	X
ejpam-4101	81	22	(	(	PUNCT
ejpam-4101	81	23	p−α	p−α	NOUN
ejpam-4101	81	24	2	2	NUM
ejpam-4101	81	25	)	)	PUNCT
ejpam-4101	81	26	(	(	PUNCT
ejpam-4101	81	27	14	14	NUM
ejpam-4101	81	28	)	)	PUNCT
ejpam-4101	81	29	and	and	CCONJ
ejpam-4101	81	30	p	p	NOUN
ejpam-4101	81	31	is	be	AUX
ejpam-4101	81	32	the	the	DET
ejpam-4101	81	33	number	number	NOUN
ejpam-4101	81	34	of	of	ADP
ejpam-4101	81	35	positive	positive	ADJ
ejpam-4101	81	36	terms	term	NOUN
ejpam-4101	81	37	of	of	ADP
ejpam-4101	81	38	u	u	NOUN
ejpam-4101	81	39	=	=	SYM
ejpam-4101	81	40	x21	x21	PROPN
ejpam-4101	82	1	+	+	NUM
ejpam-4101	82	2	x22	x22	NOUN
ejpam-4101	82	3	+	+	CCONJ
ejpam-4101	82	4	·	·	PUNCT
ejpam-4101	82	5	·	·	PUNCT
ejpam-4101	82	6	·	·	PUNCT
ejpam-4101	82	7	+	+	NUM
ejpam-4101	82	8	x2p	x2p	NUM
ejpam-4101	82	9	−	−	PROPN
ejpam-4101	83	1	x2p+1	x2p+1	NUM
ejpam-4101	84	1	−	−	PROPN
ejpam-4101	84	2	x2p+2	x2p+2	ADJ
ejpam-4101	85	1	−	−	PROPN
ejpam-4101	85	2	·	·	PUNCT
ejpam-4101	85	3	·	·	PUNCT
ejpam-4101	85	4	·	·	PUNCT
ejpam-4101	86	1	−	−	NOUN
ejpam-4101	86	2	x2p+q	x2p+q	X
ejpam-4101	86	3	,	,	PUNCT
ejpam-4101	86	4	p+	p+	VERB
ejpam-4101	86	5	q	q	NOUN
ejpam-4101	86	6	=	=	SYM
ejpam-4101	86	7	n	n	PROPN
ejpam-4101	86	8	s.	s.	PROPN
ejpam-4101	86	9	bupasiri	bupasiri	PROPN
ejpam-4101	86	10	/	/	SYM
ejpam-4101	86	11	eur	eur	PROPN
ejpam-4101	86	12	.	.	PUNCT
ejpam-4101	87	1	j.	j.	PROPN
ejpam-4101	87	2	pure	pure	PROPN
ejpam-4101	87	3	appl	appl	PROPN
ejpam-4101	87	4	.	.	PROPN
ejpam-4101	87	5	math	math	PROPN
ejpam-4101	87	6	,	,	PUNCT
ejpam-4101	87	7	14	14	NUM
ejpam-4101	87	8	(	(	PUNCT
ejpam-4101	87	9	4	4	NUM
ejpam-4101	87	10	)	)	PUNCT
ejpam-4101	87	11	(	(	PUNCT
ejpam-4101	87	12	2021	2021	NUM
ejpam-4101	87	13	)	)	PUNCT
ejpam-4101	87	14	,	,	PUNCT
ejpam-4101	87	15	1306	1306	NUM
ejpam-4101	87	16	-	-	SYM
ejpam-4101	87	17	1323	1323	NUM
ejpam-4101	87	18	1310	1310	NUM
ejpam-4101	88	1	and	and	CCONJ
ejpam-4101	88	2	let	let	VERB
ejpam-4101	88	3	supp	supp	PROPN
ejpam-4101	88	4	rh	rh	PROPN
ejpam-4101	88	5	α	α	PROPN
ejpam-4101	88	6	(	(	PUNCT
ejpam-4101	88	7	x	x	X
ejpam-4101	88	8	)	)	PUNCT
ejpam-4101	88	9	⊂	⊂	PROPN
ejpam-4101	88	10	γ+	γ+	PROPN
ejpam-4101	88	11	.	.	PUNCT
ejpam-4101	89	1	now	now	ADV
ejpam-4101	89	2	,	,	PUNCT
ejpam-4101	89	3	rh	rh	PROPN
ejpam-4101	89	4	α	α	PROPN
ejpam-4101	89	5	(	(	PUNCT
ejpam-4101	89	6	x	x	X
ejpam-4101	89	7	)	)	PUNCT
ejpam-4101	89	8	is	be	AUX
ejpam-4101	89	9	an	an	DET
ejpam-4101	89	10	ordinary	ordinary	ADJ
ejpam-4101	89	11	function	function	NOUN
ejpam-4101	89	12	if	if	SCONJ
ejpam-4101	89	13	re	re	VERB
ejpam-4101	89	14	α	α	NOUN
ejpam-4101	89	15	≥	≥	NOUN
ejpam-4101	89	16	n	n	CCONJ
ejpam-4101	89	17	and	and	CCONJ
ejpam-4101	89	18	is	be	AUX
ejpam-4101	89	19	a	a	DET
ejpam-4101	89	20	distribution	distribution	NOUN
ejpam-4101	89	21	of	of	ADP
ejpam-4101	89	22	α	α	NOUN
ejpam-4101	89	23	if	if	SCONJ
ejpam-4101	89	24	re	re	ADP
ejpam-4101	89	25	α	α	X
ejpam-4101	89	26	<	<	X
ejpam-4101	89	27	n.	n.	PROPN
ejpam-4101	89	28	now	now	ADV
ejpam-4101	89	29	,	,	PUNCT
ejpam-4101	89	30	if	if	SCONJ
ejpam-4101	89	31	p	p	NOUN
ejpam-4101	89	32	=	=	NOUN
ejpam-4101	89	33	1	1	NUM
ejpam-4101	89	34	then	then	ADV
ejpam-4101	89	35	(	(	PUNCT
ejpam-4101	89	36	13	13	NUM
ejpam-4101	89	37	)	)	PUNCT
ejpam-4101	89	38	reduces	reduce	VERB
ejpam-4101	89	39	to	to	ADP
ejpam-4101	89	40	the	the	DET
ejpam-4101	89	41	function	function	NOUN
ejpam-4101	89	42	mα(u	mα(u	PROPN
ejpam-4101	89	43	)	)	PUNCT
ejpam-4101	89	44	,	,	PUNCT
ejpam-4101	89	45	and	and	CCONJ
ejpam-4101	89	46	is	be	AUX
ejpam-4101	89	47	defined	define	VERB
ejpam-4101	89	48	by	by	ADP
ejpam-4101	89	49	mα(u	mα(u	ADJ
ejpam-4101	89	50	)	)	PUNCT
ejpam-4101	90	1	=	=	PRON
ejpam-4101	90	2	{	{	PUNCT
ejpam-4101	90	3	u	u	NOUN
ejpam-4101	90	4	α−n	α−n	PROPN
ejpam-4101	90	5	2	2	NUM
ejpam-4101	90	6	hn(α	hn(α	NUM
ejpam-4101	90	7	)	)	PUNCT
ejpam-4101	90	8	,	,	PUNCT
ejpam-4101	90	9	if	if	SCONJ
ejpam-4101	90	10	x	x	PROPN
ejpam-4101	90	11	∈	∈	PROPN
ejpam-4101	90	12	γ+	γ+	PRON
ejpam-4101	90	13	;	;	PUNCT
ejpam-4101	90	14	0	0	NUM
ejpam-4101	90	15	,	,	PUNCT
ejpam-4101	90	16	if	if	SCONJ
ejpam-4101	90	17	x	x	PROPN
ejpam-4101	90	18	̸∈	̸∈	PROPN
ejpam-4101	90	19	γ+	γ+	NUM
ejpam-4101	90	20	,	,	PUNCT
ejpam-4101	90	21	(	(	PUNCT
ejpam-4101	90	22	15	15	NUM
ejpam-4101	90	23	)	)	PUNCT
ejpam-4101	90	24	where	where	SCONJ
ejpam-4101	90	25	u	u	NOUN
ejpam-4101	90	26	=	=	NOUN
ejpam-4101	90	27	x21	x21	PROPN
ejpam-4101	91	1	−	−	PROPN
ejpam-4101	91	2	x22	x22	NOUN
ejpam-4101	91	3	−	−	PROPN
ejpam-4101	91	4	·	·	PUNCT
ejpam-4101	91	5	·	·	PUNCT
ejpam-4101	91	6	·	·	PUNCT
ejpam-4101	92	1	−	−	PROPN
ejpam-4101	93	1	x2n	x2n	PROPN
ejpam-4101	93	2	and	and	CCONJ
ejpam-4101	93	3	hn(α	hn(α	PUNCT
ejpam-4101	93	4	)	)	PUNCT
ejpam-4101	93	5	=	=	SYM
ejpam-4101	93	6	π	π	X
ejpam-4101	93	7	(	(	PUNCT
ejpam-4101	93	8	n−1	n−1	PROPN
ejpam-4101	93	9	)	)	PUNCT
ejpam-4101	93	10	2	2	NUM
ejpam-4101	93	11	2α−1γ(α−n+2	2α−1γ(α−n+2	NUM
ejpam-4101	93	12	2	2	NUM
ejpam-4101	93	13	)	)	PUNCT
ejpam-4101	93	14	.	.	PUNCT
ejpam-4101	94	1	the	the	DET
ejpam-4101	94	2	function	function	NOUN
ejpam-4101	94	3	mα(u	mα(u	PROPN
ejpam-4101	94	4	)	)	PUNCT
ejpam-4101	94	5	is	be	AUX
ejpam-4101	94	6	called	call	VERB
ejpam-4101	94	7	the	the	DET
ejpam-4101	94	8	hyperbolic	hyperbolic	ADJ
ejpam-4101	94	9	kernel	kernel	NOUN
ejpam-4101	94	10	of	of	ADP
ejpam-4101	94	11	marcel	marcel	PROPN
ejpam-4101	94	12	riesz	riesz	PROPN
ejpam-4101	94	13	.	.	PUNCT
ejpam-4101	95	1	definition	definition	NOUN
ejpam-4101	95	2	2	2	NUM
ejpam-4101	95	3	.	.	PUNCT
ejpam-4101	96	1	let	let	VERB
ejpam-4101	96	2	f(x	f(x	PROPN
ejpam-4101	96	3	)	)	PUNCT
ejpam-4101	96	4	∈	∈	PROPN
ejpam-4101	96	5	l1(rn	l1(rn	PROPN
ejpam-4101	96	6	)	)	PUNCT
ejpam-4101	97	1	(	(	PUNCT
ejpam-4101	97	2	the	the	DET
ejpam-4101	97	3	space	space	NOUN
ejpam-4101	97	4	of	of	ADP
ejpam-4101	97	5	integrable	integrable	ADJ
ejpam-4101	97	6	function	function	NOUN
ejpam-4101	97	7	in	in	ADP
ejpam-4101	97	8	rn	rn	PROPN
ejpam-4101	97	9	)	)	PUNCT
ejpam-4101	97	10	.	.	PUNCT
ejpam-4101	98	1	the	the	DET
ejpam-4101	98	2	fourier	fourier	NOUN
ejpam-4101	98	3	transform	transform	NOUN
ejpam-4101	98	4	of	of	ADP
ejpam-4101	98	5	f(x	f(x	PROPN
ejpam-4101	98	6	)	)	PUNCT
ejpam-4101	98	7	is	be	AUX
ejpam-4101	98	8	defined	define	VERB
ejpam-4101	98	9	as	as	ADP
ejpam-4101	98	10	f̂(ξ	f̂(ξ	NOUN
ejpam-4101	98	11	)	)	PUNCT
ejpam-4101	98	12	=	=	SYM
ejpam-4101	98	13	1	1	NUM
ejpam-4101	98	14	(	(	PUNCT
ejpam-4101	98	15	2π)n/2	2π)n/2	NUM
ejpam-4101	98	16	∫	∫	PROPN
ejpam-4101	98	17	rn	rn	PROPN
ejpam-4101	98	18	e−iξ·xf(x)dx	e−iξ·xf(x)dx	PROPN
ejpam-4101	98	19	,	,	PUNCT
ejpam-4101	98	20	(	(	PUNCT
ejpam-4101	98	21	16	16	NUM
ejpam-4101	98	22	)	)	PUNCT
ejpam-4101	98	23	where	where	SCONJ
ejpam-4101	98	24	ξ	ξ	X
ejpam-4101	98	25	=	=	SYM
ejpam-4101	98	26	(	(	PUNCT
ejpam-4101	98	27	ξ1	ξ1	PROPN
ejpam-4101	98	28	,	,	PUNCT
ejpam-4101	98	29	ξ2	ξ2	NOUN
ejpam-4101	98	30	,	,	PUNCT
ejpam-4101	98	31	.	.	PUNCT
ejpam-4101	98	32	.	.	PUNCT
ejpam-4101	99	1	.	.	PUNCT
ejpam-4101	100	1	,	,	PUNCT
ejpam-4101	100	2	ξn	ξn	NOUN
ejpam-4101	100	3	)	)	PUNCT
ejpam-4101	100	4	,	,	PUNCT
ejpam-4101	100	5	x	x	PUNCT
ejpam-4101	100	6	=	=	PRON
ejpam-4101	100	7	(	(	PUNCT
ejpam-4101	100	8	x1	x1	PROPN
ejpam-4101	100	9	,	,	PUNCT
ejpam-4101	100	10	x2	x2	PROPN
ejpam-4101	100	11	,	,	PUNCT
ejpam-4101	100	12	.	.	PUNCT
ejpam-4101	100	13	.	.	PUNCT
ejpam-4101	101	1	.	.	PUNCT
ejpam-4101	102	1	,	,	PUNCT
ejpam-4101	102	2	xn	xn	X
ejpam-4101	102	3	)	)	PUNCT
ejpam-4101	102	4	∈	∈	PROPN
ejpam-4101	102	5	rn	rn	PROPN
ejpam-4101	102	6	,	,	PUNCT
ejpam-4101	102	7	ξ	ξ	X
ejpam-4101	102	8	·	·	PUNCT
ejpam-4101	102	9	x	x	SYM
ejpam-4101	102	10	=	=	SYM
ejpam-4101	102	11	(	(	PUNCT
ejpam-4101	102	12	ξ1x1	ξ1x1	NOUN
ejpam-4101	102	13	,	,	PUNCT
ejpam-4101	102	14	ξ2x2	ξ2x2	PROPN
ejpam-4101	102	15	,	,	PUNCT
ejpam-4101	102	16	.	.	PUNCT
ejpam-4101	102	17	.	.	PUNCT
ejpam-4101	102	18	.	.	PUNCT
ejpam-4101	103	1	,	,	PUNCT
ejpam-4101	103	2	ξnxn	ξnxn	NOUN
ejpam-4101	103	3	)	)	PUNCT
ejpam-4101	103	4	is	be	AUX
ejpam-4101	103	5	the	the	DET
ejpam-4101	103	6	usual	usual	ADJ
ejpam-4101	103	7	inner	inner	ADJ
ejpam-4101	103	8	product	product	NOUN
ejpam-4101	103	9	in	in	ADP
ejpam-4101	103	10	rn	rn	PROPN
ejpam-4101	103	11	and	and	CCONJ
ejpam-4101	103	12	dx	dx	PROPN
ejpam-4101	103	13	=	=	PROPN
ejpam-4101	103	14	dx1dx2	dx1dx2	PROPN
ejpam-4101	103	15	.	.	PUNCT
ejpam-4101	103	16	.	.	PUNCT
ejpam-4101	103	17	.	.	PUNCT
ejpam-4101	104	1	dxn	dxn	PROPN
ejpam-4101	104	2	.	.	PUNCT
ejpam-4101	105	1	the	the	DET
ejpam-4101	105	2	inverse	inverse	NOUN
ejpam-4101	105	3	of	of	ADP
ejpam-4101	105	4	the	the	DET
ejpam-4101	105	5	fourier	fourier	NOUN
ejpam-4101	105	6	transform	transform	NOUN
ejpam-4101	105	7	is	be	AUX
ejpam-4101	105	8	defined	define	VERB
ejpam-4101	105	9	by	by	ADP
ejpam-4101	105	10	f(x	f(x	PROPN
ejpam-4101	105	11	)	)	PUNCT
ejpam-4101	106	1	=	=	SYM
ejpam-4101	106	2	1	1	NUM
ejpam-4101	106	3	(	(	PUNCT
ejpam-4101	106	4	2π)n/2	2π)n/2	NUM
ejpam-4101	106	5	∫	∫	PROPN
ejpam-4101	106	6	rn	rn	PROPN
ejpam-4101	106	7	e−iξ·xf̂(ξ)dξ	e−iξ·xf̂(ξ)dξ	PROPN
ejpam-4101	106	8	.	.	PROPN
ejpam-4101	107	1	(	(	PUNCT
ejpam-4101	107	2	17	17	NUM
ejpam-4101	107	3	)	)	PUNCT
ejpam-4101	107	4	if	if	SCONJ
ejpam-4101	107	5	f	f	PROPN
ejpam-4101	107	6	is	be	AUX
ejpam-4101	107	7	a	a	DET
ejpam-4101	107	8	distribution	distribution	NOUN
ejpam-4101	107	9	with	with	ADP
ejpam-4101	107	10	compact	compact	ADJ
ejpam-4101	107	11	supports	support	NOUN
ejpam-4101	107	12	,	,	PUNCT
ejpam-4101	107	13	by	by	ADP
ejpam-4101	107	14	[	[	X
ejpam-4101	107	15	24	24	NUM
ejpam-4101	107	16	,	,	PUNCT
ejpam-4101	107	17	theorem	theorem	VERB
ejpam-4101	107	18	7.4	7.4	NUM
ejpam-4101	107	19	-	-	SYM
ejpam-4101	107	20	3	3	NUM
ejpam-4101	107	21	]	]	PUNCT
ejpam-4101	107	22	,	,	PUNCT
ejpam-4101	107	23	equation	equation	NOUN
ejpam-4101	107	24	(	(	PUNCT
ejpam-4101	107	25	17	17	NUM
ejpam-4101	107	26	)	)	PUNCT
ejpam-4101	107	27	can	can	AUX
ejpam-4101	107	28	be	be	AUX
ejpam-4101	107	29	written	write	VERB
ejpam-4101	107	30	as	as	ADP
ejpam-4101	107	31	f̂(ξ	f̂(ξ	NOUN
ejpam-4101	107	32	)	)	PUNCT
ejpam-4101	107	33	=	=	SYM
ejpam-4101	107	34	ff(x	ff(x	NOUN
ejpam-4101	107	35	)	)	PUNCT
ejpam-4101	107	36	=	=	SYM
ejpam-4101	107	37	1	1	NUM
ejpam-4101	107	38	(	(	PUNCT
ejpam-4101	107	39	2π)n/2	2π)n/2	NUM
ejpam-4101	107	40	〈	〈	PROPN
ejpam-4101	107	41	f(x	f(x	PROPN
ejpam-4101	107	42	)	)	PUNCT
ejpam-4101	107	43	,	,	PUNCT
ejpam-4101	107	44	e−iξ·x	e−iξ·x	NOUN
ejpam-4101	107	45	〉	〉	NOUN
ejpam-4101	107	46	.	.	PUNCT
ejpam-4101	108	1	(	(	PUNCT
ejpam-4101	108	2	18	18	NUM
ejpam-4101	108	3	)	)	PUNCT
ejpam-4101	108	4	lemma	lemma	PROPN
ejpam-4101	108	5	1	1	NUM
ejpam-4101	108	6	.	.	PUNCT
ejpam-4101	109	1	[	[	X
ejpam-4101	109	2	5	5	NUM
ejpam-4101	109	3	]	]	PUNCT
ejpam-4101	109	4	given	give	VERB
ejpam-4101	109	5	the	the	DET
ejpam-4101	109	6	equation	equation	NOUN
ejpam-4101	109	7	△	△	NOUN
ejpam-4101	109	8	ku(x	ku(x	X
ejpam-4101	109	9	)	)	PUNCT
ejpam-4101	109	10	=	=	SYM
ejpam-4101	109	11	δ	δ	PROPN
ejpam-4101	109	12	for	for	ADP
ejpam-4101	109	13	x	x	PROPN
ejpam-4101	109	14	∈	∈	PROPN
ejpam-4101	109	15	rn	rn	PROPN
ejpam-4101	109	16	,	,	PUNCT
ejpam-4101	109	17	where	where	SCONJ
ejpam-4101	109	18	△	△	NOUN
ejpam-4101	109	19	k	k	X
ejpam-4101	109	20	is	be	AUX
ejpam-4101	109	21	the	the	DET
ejpam-4101	109	22	laplace	laplace	NOUN
ejpam-4101	109	23	operator	operator	NOUN
ejpam-4101	109	24	iterated	iterate	VERB
ejpam-4101	109	25	k	k	NOUN
ejpam-4101	109	26	-	-	PUNCT
ejpam-4101	109	27	times	time	NOUN
ejpam-4101	109	28	,	,	PUNCT
ejpam-4101	109	29	which	which	PRON
ejpam-4101	109	30	is	be	AUX
ejpam-4101	109	31	defined	define	VERB
ejpam-4101	109	32	by	by	ADP
ejpam-4101	109	33	(	(	PUNCT
ejpam-4101	109	34	2	2	NUM
ejpam-4101	109	35	)	)	PUNCT
ejpam-4101	109	36	.	.	PUNCT
ejpam-4101	110	1	then	then	ADV
ejpam-4101	110	2	u(x	u(x	VERB
ejpam-4101	110	3	)	)	PUNCT
ejpam-4101	110	4	=	=	SYM
ejpam-4101	110	5	(	(	PUNCT
ejpam-4101	110	6	−1)kre	−1)kre	PROPN
ejpam-4101	110	7	2k(x	2k(x	NUM
ejpam-4101	110	8	)	)	PUNCT
ejpam-4101	110	9	is	be	AUX
ejpam-4101	110	10	the	the	DET
ejpam-4101	110	11	fundamental	fundamental	ADJ
ejpam-4101	110	12	solution	solution	NOUN
ejpam-4101	110	13	of	of	ADP
ejpam-4101	110	14	the	the	DET
ejpam-4101	110	15	operator	operator	NOUN
ejpam-4101	110	16	△	△	PROPN
ejpam-4101	110	17	k	k	NOUN
ejpam-4101	110	18	,	,	PUNCT
ejpam-4101	110	19	where	where	SCONJ
ejpam-4101	110	20	re	re	VERB
ejpam-4101	110	21	2k(x	2k(x	NUM
ejpam-4101	110	22	)	)	PUNCT
ejpam-4101	111	1	=	=	SYM
ejpam-4101	111	2	γ	γ	X
ejpam-4101	111	3	(	(	PUNCT
ejpam-4101	111	4	n−2k	n−2k	NOUN
ejpam-4101	111	5	2	2	X
ejpam-4101	111	6	)	)	PUNCT
ejpam-4101	111	7	22kπ	22kπ	NOUN
ejpam-4101	111	8	n	n	PRON
ejpam-4101	111	9	2	2	NUM
ejpam-4101	111	10	γ(k	γ(k	PROPN
ejpam-4101	111	11	)	)	PUNCT
ejpam-4101	111	12	|x|2k−n	|x|2k−n	PROPN
ejpam-4101	111	13	.	.	PUNCT
ejpam-4101	112	1	(	(	PUNCT
ejpam-4101	112	2	19	19	NUM
ejpam-4101	112	3	)	)	PUNCT
ejpam-4101	112	4	lemma	lemma	PROPN
ejpam-4101	112	5	2	2	NUM
ejpam-4101	112	6	.	.	PUNCT
ejpam-4101	113	1	[	[	X
ejpam-4101	113	2	22	22	NUM
ejpam-4101	113	3	]	]	PUNCT
ejpam-4101	113	4	if	if	SCONJ
ejpam-4101	113	5	⊡ku(x	⊡ku(x	NOUN
ejpam-4101	113	6	)	)	PUNCT
ejpam-4101	114	1	=	=	SYM
ejpam-4101	114	2	δ	δ	PROPN
ejpam-4101	114	3	for	for	ADP
ejpam-4101	114	4	x	x	PROPN
ejpam-4101	114	5	∈	∈	PROPN
ejpam-4101	114	6	γ+	γ+	PUNCT
ejpam-4101	114	7	=	=	SYM
ejpam-4101	114	8	{	{	PUNCT
ejpam-4101	114	9	x	x	PROPN
ejpam-4101	114	10	∈	∈	PROPN
ejpam-4101	114	11	rn	rn	PROPN
ejpam-4101	114	12	:	:	PUNCT
ejpam-4101	114	13	x1	x1	PROPN
ejpam-4101	114	14	>	>	X
ejpam-4101	114	15	0	0	PUNCT
ejpam-4101	114	16	and	and	CCONJ
ejpam-4101	114	17	u	u	X
ejpam-4101	114	18	>	>	X
ejpam-4101	114	19	0	0	NUM
ejpam-4101	114	20	}	}	PUNCT
ejpam-4101	114	21	,	,	PUNCT
ejpam-4101	114	22	where	where	SCONJ
ejpam-4101	114	23	⊡kis	⊡kis	PROPN
ejpam-4101	114	24	the	the	DET
ejpam-4101	114	25	ultra	ultra	ADJ
ejpam-4101	114	26	-	-	ADJ
ejpam-4101	114	27	hyperbolic	hyperbolic	ADJ
ejpam-4101	114	28	operator	operator	NOUN
ejpam-4101	114	29	iterated	iterate	VERB
ejpam-4101	114	30	k	k	NOUN
ejpam-4101	114	31	-	-	PUNCT
ejpam-4101	114	32	times	time	NOUN
ejpam-4101	114	33	,	,	PUNCT
ejpam-4101	114	34	which	which	PRON
ejpam-4101	114	35	is	be	AUX
ejpam-4101	114	36	defined	define	VERB
ejpam-4101	114	37	by	by	ADP
ejpam-4101	114	38	(	(	PUNCT
ejpam-4101	114	39	3	3	NUM
ejpam-4101	114	40	)	)	PUNCT
ejpam-4101	114	41	.	.	PUNCT
ejpam-4101	115	1	then	then	ADV
ejpam-4101	115	2	u(x	u(x	VERB
ejpam-4101	115	3	)	)	PUNCT
ejpam-4101	115	4	=	=	SYM
ejpam-4101	115	5	rh	rh	PROPN
ejpam-4101	115	6	2k(x	2k(x	PROPN
ejpam-4101	115	7	)	)	PUNCT
ejpam-4101	115	8	is	be	AUX
ejpam-4101	115	9	the	the	DET
ejpam-4101	115	10	unique	unique	ADJ
ejpam-4101	115	11	fundamental	fundamental	ADJ
ejpam-4101	115	12	solution	solution	NOUN
ejpam-4101	115	13	of	of	ADP
ejpam-4101	115	14	the	the	DET
ejpam-4101	115	15	operator	operator	NOUN
ejpam-4101	115	16	⊡k	⊡k	NOUN
ejpam-4101	115	17	,	,	PUNCT
ejpam-4101	115	18	where	where	SCONJ
ejpam-4101	115	19	rh	rh	PROPN
ejpam-4101	115	20	2k(x	2k(x	PROPN
ejpam-4101	115	21	)	)	PUNCT
ejpam-4101	116	1	=	=	SYM
ejpam-4101	116	2	u	u	NOUN
ejpam-4101	116	3	(	(	PUNCT
ejpam-4101	116	4	2k−n	2k−n	NUM
ejpam-4101	116	5	2	2	NUM
ejpam-4101	116	6	)	)	PUNCT
ejpam-4101	116	7	kn(2k	kn(2k	NOUN
ejpam-4101	116	8	)	)	PUNCT
ejpam-4101	116	9	=	=	PUNCT
ejpam-4101	116	10	(	(	PUNCT
ejpam-4101	116	11	x21	x21	PROPN
ejpam-4101	116	12	+	+	NUM
ejpam-4101	116	13	x22	x22	NOUN
ejpam-4101	116	14	+	+	CCONJ
ejpam-4101	116	15	·	·	PUNCT
ejpam-4101	116	16	·	·	PUNCT
ejpam-4101	116	17	·	·	PUNCT
ejpam-4101	116	18	+	+	NUM
ejpam-4101	116	19	x2p	x2p	NUM
ejpam-4101	116	20	−	−	PROPN
ejpam-4101	117	1	x2p+1	x2p+1	INTJ
ejpam-4101	118	1	−	−	PROPN
ejpam-4101	118	2	·	·	PUNCT
ejpam-4101	118	3	·	·	PUNCT
ejpam-4101	118	4	·	·	PUNCT
ejpam-4101	119	1	−	−	NOUN
ejpam-4101	119	2	x2p+q	x2p+q	X
ejpam-4101	119	3	)	)	PUNCT
ejpam-4101	119	4	(	(	PUNCT
ejpam-4101	119	5	2k−n	2k−n	NUM
ejpam-4101	119	6	2	2	NUM
ejpam-4101	119	7	)	)	PUNCT
ejpam-4101	119	8	kn(2k	kn(2k	NOUN
ejpam-4101	119	9	)	)	PUNCT
ejpam-4101	119	10	(	(	PUNCT
ejpam-4101	119	11	20	20	NUM
ejpam-4101	119	12	)	)	PUNCT
ejpam-4101	119	13	and	and	CCONJ
ejpam-4101	119	14	kn(2k	kn(2k	NOUN
ejpam-4101	119	15	)	)	PUNCT
ejpam-4101	119	16	=	=	PUNCT
ejpam-4101	120	1	π	π	X
ejpam-4101	120	2	n−1	n−1	PROPN
ejpam-4101	120	3	2	2	NUM
ejpam-4101	120	4	γ	γ	X
ejpam-4101	120	5	(	(	PUNCT
ejpam-4101	120	6	2	2	NUM
ejpam-4101	120	7	+	+	NOUN
ejpam-4101	120	8	2k−n	2k−n	ADJ
ejpam-4101	120	9	2	2	NUM
ejpam-4101	120	10	)	)	PUNCT
ejpam-4101	120	11	γ	γ	PROPN
ejpam-4101	120	12	(	(	PUNCT
ejpam-4101	120	13	1−2k	1−2k	NUM
ejpam-4101	120	14	2	2	NUM
ejpam-4101	120	15	)	)	PUNCT
ejpam-4101	120	16	γ(2k	γ(2k	VERB
ejpam-4101	120	17	)	)	PUNCT
ejpam-4101	120	18	γ	γ	X
ejpam-4101	120	19	(	(	PUNCT
ejpam-4101	120	20	2	2	NUM
ejpam-4101	120	21	+	+	NUM
ejpam-4101	120	22	2k−p	2k−p	NUM
ejpam-4101	120	23	2	2	NUM
ejpam-4101	120	24	)	)	PUNCT
ejpam-4101	120	25	γ(p−2k	γ(p−2k	ADV
ejpam-4101	120	26	2	2	NUM
ejpam-4101	120	27	)	)	PUNCT
ejpam-4101	120	28	.	.	PUNCT
ejpam-4101	121	1	(	(	PUNCT
ejpam-4101	121	2	21	21	NUM
ejpam-4101	121	3	)	)	PUNCT
ejpam-4101	121	4	s.	s.	PROPN
ejpam-4101	121	5	bupasiri	bupasiri	PROPN
ejpam-4101	121	6	/	/	SYM
ejpam-4101	121	7	eur	eur	PROPN
ejpam-4101	121	8	.	.	PUNCT
ejpam-4101	122	1	j.	j.	PROPN
ejpam-4101	122	2	pure	pure	PROPN
ejpam-4101	122	3	appl	appl	PROPN
ejpam-4101	122	4	.	.	PROPN
ejpam-4101	122	5	math	math	PROPN
ejpam-4101	122	6	,	,	PUNCT
ejpam-4101	122	7	14	14	NUM
ejpam-4101	122	8	(	(	PUNCT
ejpam-4101	122	9	4	4	NUM
ejpam-4101	122	10	)	)	PUNCT
ejpam-4101	122	11	(	(	PUNCT
ejpam-4101	122	12	2021	2021	NUM
ejpam-4101	122	13	)	)	PUNCT
ejpam-4101	122	14	,	,	PUNCT
ejpam-4101	122	15	1306	1306	NUM
ejpam-4101	122	16	-	-	SYM
ejpam-4101	122	17	1323	1323	NUM
ejpam-4101	122	18	1311	1311	NUM
ejpam-4101	122	19	lemma	lemma	PROPN
ejpam-4101	122	20	3	3	X
ejpam-4101	122	21	.	.	PUNCT
ejpam-4101	123	1	[	[	X
ejpam-4101	123	2	5	5	NUM
ejpam-4101	123	3	]	]	PUNCT
ejpam-4101	123	4	given	give	VERB
ejpam-4101	123	5	the	the	DET
ejpam-4101	123	6	equation	equation	NOUN
ejpam-4101	123	7	♢	♢	NOUN
ejpam-4101	123	8	ku(x	ku(x	X
ejpam-4101	123	9	)	)	PUNCT
ejpam-4101	123	10	=	=	SYM
ejpam-4101	123	11	δ	δ	PROPN
ejpam-4101	123	12	for	for	ADP
ejpam-4101	123	13	x	x	PROPN
ejpam-4101	123	14	∈	∈	PROPN
ejpam-4101	123	15	rn	rn	PROPN
ejpam-4101	123	16	,	,	PUNCT
ejpam-4101	123	17	then	then	ADV
ejpam-4101	123	18	u(x	u(x	VERB
ejpam-4101	123	19	)	)	PUNCT
ejpam-4101	123	20	=	=	SYM
ejpam-4101	123	21	(	(	PUNCT
ejpam-4101	123	22	−1)kre	−1)kre	PROPN
ejpam-4101	123	23	2k(x	2k(x	NUM
ejpam-4101	123	24	)	)	PUNCT
ejpam-4101	123	25	∗	∗	PROPN
ejpam-4101	123	26	rh	rh	PROPN
ejpam-4101	123	27	2k(x	2k(x	PROPN
ejpam-4101	123	28	)	)	PUNCT
ejpam-4101	123	29	is	be	AUX
ejpam-4101	123	30	the	the	DET
ejpam-4101	123	31	unique	unique	ADJ
ejpam-4101	123	32	fundamental	fundamental	ADJ
ejpam-4101	123	33	solution	solution	NOUN
ejpam-4101	123	34	of	of	ADP
ejpam-4101	123	35	the	the	DET
ejpam-4101	123	36	operator	operator	NOUN
ejpam-4101	123	37	♢	♢	PROPN
ejpam-4101	123	38	k	k	PROPN
ejpam-4101	123	39	,	,	PUNCT
ejpam-4101	123	40	where	where	SCONJ
ejpam-4101	123	41	♢	♢	PROPN
ejpam-4101	123	42	k	k	PROPN
ejpam-4101	123	43	is	be	AUX
ejpam-4101	123	44	the	the	DET
ejpam-4101	123	45	diamond	diamond	NOUN
ejpam-4101	123	46	operator	operator	NOUN
ejpam-4101	123	47	iterated	iterate	VERB
ejpam-4101	123	48	k	k	NOUN
ejpam-4101	123	49	-	-	PUNCT
ejpam-4101	123	50	times	time	NOUN
ejpam-4101	123	51	,	,	PUNCT
ejpam-4101	123	52	which	which	PRON
ejpam-4101	123	53	is	be	AUX
ejpam-4101	123	54	defined	define	VERB
ejpam-4101	123	55	by	by	ADP
ejpam-4101	123	56	(	(	PUNCT
ejpam-4101	123	57	1	1	NUM
ejpam-4101	123	58	)	)	PUNCT
ejpam-4101	123	59	,	,	PUNCT
ejpam-4101	123	60	re	re	NOUN
ejpam-4101	123	61	2k(x	2k(x	NUM
ejpam-4101	123	62	)	)	PUNCT
ejpam-4101	123	63	and	and	CCONJ
ejpam-4101	123	64	rh	rh	PROPN
ejpam-4101	123	65	2k(x	2k(x	PROPN
ejpam-4101	123	66	)	)	PUNCT
ejpam-4101	123	67	are	be	AUX
ejpam-4101	123	68	defined	define	VERB
ejpam-4101	123	69	by	by	ADP
ejpam-4101	123	70	(	(	PUNCT
ejpam-4101	123	71	19	19	NUM
ejpam-4101	123	72	)	)	PUNCT
ejpam-4101	123	73	and	and	CCONJ
ejpam-4101	123	74	(	(	PUNCT
ejpam-4101	123	75	20	20	NUM
ejpam-4101	123	76	)	)	PUNCT
ejpam-4101	123	77	,	,	PUNCT
ejpam-4101	123	78	respectively	respectively	ADV
ejpam-4101	123	79	.	.	PUNCT
ejpam-4101	124	1	moreover	moreover	ADV
ejpam-4101	124	2	,	,	PUNCT
ejpam-4101	124	3	(	(	PUNCT
ejpam-4101	124	4	−1)kre	−1)kre	PROPN
ejpam-4101	124	5	2k(x	2k(x	NUM
ejpam-4101	124	6	)	)	PUNCT
ejpam-4101	124	7	∗rh	∗rh	VERB
ejpam-4101	124	8	2k(x	2k(x	NUM
ejpam-4101	124	9	)	)	PUNCT
ejpam-4101	124	10	is	be	AUX
ejpam-4101	124	11	a	a	DET
ejpam-4101	124	12	tempered	temper	VERB
ejpam-4101	124	13	distribution	distribution	NOUN
ejpam-4101	124	14	.	.	PUNCT
ejpam-4101	125	1	it	it	PRON
ejpam-4101	125	2	is	be	AUX
ejpam-4101	125	3	not	not	PART
ejpam-4101	125	4	difficult	difficult	ADJ
ejpam-4101	125	5	to	to	PART
ejpam-4101	125	6	show	show	VERB
ejpam-4101	125	7	that	that	SCONJ
ejpam-4101	125	8	re	re	PROPN
ejpam-4101	125	9	−2k(x	−2k(x	PROPN
ejpam-4101	125	10	)	)	PUNCT
ejpam-4101	125	11	∗rh	∗rh	DET
ejpam-4101	125	12	−2k(x	−2k(x	NOUN
ejpam-4101	125	13	)	)	PUNCT
ejpam-4101	125	14	=	=	PUNCT
ejpam-4101	125	15	(	(	PUNCT
ejpam-4101	125	16	−1)k	−1)k	PROPN
ejpam-4101	125	17	♢	♢	PROPN
ejpam-4101	125	18	kδ	kδ	PROPN
ejpam-4101	125	19	,	,	PUNCT
ejpam-4101	125	20	for	for	ADP
ejpam-4101	125	21	k	k	PROPN
ejpam-4101	125	22	is	be	AUX
ejpam-4101	125	23	a	a	DET
ejpam-4101	125	24	non	non	ADJ
ejpam-4101	125	25	-	-	ADJ
ejpam-4101	125	26	negative	negative	ADJ
ejpam-4101	125	27	integer	integer	NOUN
ejpam-4101	125	28	.	.	PUNCT
ejpam-4101	126	1	definition	definition	NOUN
ejpam-4101	126	2	3	3	X
ejpam-4101	126	3	.	.	PUNCT
ejpam-4101	127	1	let	let	VERB
ejpam-4101	127	2	x	x	PUNCT
ejpam-4101	127	3	=	=	SYM
ejpam-4101	127	4	(	(	PUNCT
ejpam-4101	127	5	x1	x1	PROPN
ejpam-4101	127	6	,	,	PUNCT
ejpam-4101	127	7	x2	x2	PROPN
ejpam-4101	127	8	,	,	PUNCT
ejpam-4101	127	9	.	.	PUNCT
ejpam-4101	127	10	.	.	PUNCT
ejpam-4101	128	1	.	.	PUNCT
ejpam-4101	129	1	,	,	PUNCT
ejpam-4101	129	2	xn	xn	X
ejpam-4101	129	3	)	)	PUNCT
ejpam-4101	129	4	be	be	VERB
ejpam-4101	129	5	a	a	DET
ejpam-4101	129	6	point	point	NOUN
ejpam-4101	129	7	of	of	ADP
ejpam-4101	129	8	rn	rn	PROPN
ejpam-4101	129	9	,	,	PUNCT
ejpam-4101	130	1	the	the	DET
ejpam-4101	130	2	function	function	NOUN
ejpam-4101	130	3	pα(x	pα(x	NOUN
ejpam-4101	130	4	,	,	PUNCT
ejpam-4101	130	5	m	m	PRON
ejpam-4101	130	6	)	)	PUNCT
ejpam-4101	130	7	is	be	AUX
ejpam-4101	130	8	defined	define	VERB
ejpam-4101	130	9	by	by	ADP
ejpam-4101	130	10	pα(x	pα(x	NOUN
ejpam-4101	130	11	,	,	PUNCT
ejpam-4101	130	12	m	m	NOUN
ejpam-4101	130	13	)	)	PUNCT
ejpam-4101	131	1	=	=	PUNCT
ejpam-4101	132	1	∞∑	∞∑	NUM
ejpam-4101	132	2	r=0	r=0	PROPN
ejpam-4101	132	3	(	(	PUNCT
ejpam-4101	132	4	−α/2	−α/2	X
ejpam-4101	132	5	r	r	NOUN
ejpam-4101	132	6	)	)	PUNCT
ejpam-4101	132	7	(	(	PUNCT
ejpam-4101	132	8	m2)r(−1)α/2+rre	m2)r(−1)α/2+rre	PROPN
ejpam-4101	132	9	α+2r(x	α+2r(x	NUM
ejpam-4101	132	10	)	)	PUNCT
ejpam-4101	132	11	∗rh	∗rh	VERB
ejpam-4101	132	12	α+2r(x	α+2r(x	NOUN
ejpam-4101	132	13	)	)	PUNCT
ejpam-4101	132	14	,	,	PUNCT
ejpam-4101	132	15	(	(	PUNCT
ejpam-4101	132	16	22	22	NUM
ejpam-4101	132	17	)	)	PUNCT
ejpam-4101	132	18	where	where	SCONJ
ejpam-4101	132	19	α	α	NOUN
ejpam-4101	132	20	is	be	AUX
ejpam-4101	132	21	a	a	DET
ejpam-4101	132	22	complex	complex	ADJ
ejpam-4101	132	23	parameter	parameter	NOUN
ejpam-4101	132	24	,	,	PUNCT
ejpam-4101	132	25	m	m	VERB
ejpam-4101	132	26	is	be	AUX
ejpam-4101	132	27	a	a	DET
ejpam-4101	132	28	non	non	ADJ
ejpam-4101	132	29	-	-	ADJ
ejpam-4101	132	30	negative	negative	ADJ
ejpam-4101	132	31	real	real	ADJ
ejpam-4101	132	32	number	number	NOUN
ejpam-4101	132	33	,	,	PUNCT
ejpam-4101	132	34	rh	rh	PROPN
ejpam-4101	132	35	α+2r(x	α+2r(x	NUM
ejpam-4101	132	36	)	)	PUNCT
ejpam-4101	132	37	and	and	CCONJ
ejpam-4101	132	38	re	re	VERB
ejpam-4101	132	39	α+2r(x	α+2r(x	NUM
ejpam-4101	132	40	)	)	PUNCT
ejpam-4101	132	41	are	be	AUX
ejpam-4101	132	42	defined	define	VERB
ejpam-4101	132	43	by	by	ADP
ejpam-4101	132	44	(	(	PUNCT
ejpam-4101	132	45	20	20	NUM
ejpam-4101	132	46	)	)	PUNCT
ejpam-4101	132	47	and	and	CCONJ
ejpam-4101	132	48	(	(	PUNCT
ejpam-4101	132	49	19	19	NUM
ejpam-4101	132	50	)	)	PUNCT
ejpam-4101	132	51	,	,	PUNCT
ejpam-4101	132	52	respectively	respectively	ADV
ejpam-4101	132	53	.	.	PUNCT
ejpam-4101	133	1	from	from	ADP
ejpam-4101	133	2	the	the	DET
ejpam-4101	133	3	definition	definition	NOUN
ejpam-4101	133	4	of	of	ADP
ejpam-4101	133	5	pα(x	pα(x	PROPN
ejpam-4101	133	6	,	,	PUNCT
ejpam-4101	133	7	m	m	NOUN
ejpam-4101	133	8	)	)	PUNCT
ejpam-4101	133	9	and	and	CCONJ
ejpam-4101	133	10	by	by	ADP
ejpam-4101	133	11	putting	put	VERB
ejpam-4101	133	12	α	α	NOUN
ejpam-4101	133	13	=	=	PUNCT
ejpam-4101	133	14	−2k	−2k	PROPN
ejpam-4101	133	15	,	,	PUNCT
ejpam-4101	133	16	we	we	PRON
ejpam-4101	133	17	have	have	VERB
ejpam-4101	133	18	p−2k(x	p−2k(x	NOUN
ejpam-4101	133	19	,	,	PUNCT
ejpam-4101	133	20	m	m	NOUN
ejpam-4101	133	21	)	)	PUNCT
ejpam-4101	133	22	=	=	PUNCT
ejpam-4101	134	1	∞∑	∞∑	NUM
ejpam-4101	134	2	r=0	r=0	PROPN
ejpam-4101	134	3	(	(	PUNCT
ejpam-4101	134	4	k	k	NOUN
ejpam-4101	134	5	r	r	NOUN
ejpam-4101	134	6	)	)	PUNCT
ejpam-4101	134	7	(	(	PUNCT
ejpam-4101	134	8	m2)r(−1)−k+rre	m2)r(−1)−k+rre	PROPN
ejpam-4101	134	9	2(−k+r)(x	2(−k+r)(x	NUM
ejpam-4101	134	10	)	)	PUNCT
ejpam-4101	134	11	∗r	∗r	PROPN
ejpam-4101	134	12	h	h	NOUN
ejpam-4101	134	13	2(−k+r)(x	2(−k+r)(x	PROPN
ejpam-4101	134	14	)	)	PUNCT
ejpam-4101	134	15	.	.	PUNCT
ejpam-4101	135	1	since	since	SCONJ
ejpam-4101	135	2	the	the	DET
ejpam-4101	135	3	operator	operator	NOUN
ejpam-4101	135	4	(	(	PUNCT
ejpam-4101	135	5	♢	♢	PROPN
ejpam-4101	135	6	+	+	PROPN
ejpam-4101	135	7	m2)k	m2)k	NOUN
ejpam-4101	135	8	defined	define	VERB
ejpam-4101	135	9	in	in	ADP
ejpam-4101	135	10	equation	equation	NOUN
ejpam-4101	135	11	(	(	PUNCT
ejpam-4101	135	12	9	9	NUM
ejpam-4101	135	13	)	)	PUNCT
ejpam-4101	135	14	is	be	AUX
ejpam-4101	135	15	a	a	DET
ejpam-4101	135	16	linearly	linearly	ADV
ejpam-4101	135	17	continuous	continuous	ADJ
ejpam-4101	135	18	and	and	CCONJ
ejpam-4101	135	19	has	have	VERB
ejpam-4101	135	20	1−1	1−1	NUM
ejpam-4101	135	21	mapping	mapping	NOUN
ejpam-4101	135	22	,	,	PUNCT
ejpam-4101	135	23	then	then	ADV
ejpam-4101	135	24	it	it	PRON
ejpam-4101	135	25	has	have	AUX
ejpam-4101	135	26	inverse	inverse	NOUN
ejpam-4101	135	27	.	.	PUNCT
ejpam-4101	136	1	from	from	ADP
ejpam-4101	136	2	lemma	lemma	PROPN
ejpam-4101	136	3	3	3	NUM
ejpam-4101	136	4	,	,	PUNCT
ejpam-4101	136	5	we	we	PRON
ejpam-4101	136	6	obtain	obtain	VERB
ejpam-4101	136	7	p−2k(x	p−2k(x	NOUN
ejpam-4101	136	8	,	,	PUNCT
ejpam-4101	136	9	m	m	NOUN
ejpam-4101	136	10	)	)	PUNCT
ejpam-4101	136	11	=	=	PUNCT
ejpam-4101	137	1	∞∑	∞∑	NUM
ejpam-4101	137	2	r=0	r=0	PROPN
ejpam-4101	137	3	(	(	PUNCT
ejpam-4101	137	4	−k	−k	NOUN
ejpam-4101	137	5	r	r	NOUN
ejpam-4101	137	6	)	)	PUNCT
ejpam-4101	137	7	(	(	PUNCT
ejpam-4101	137	8	m2)r	m2)r	PROPN
ejpam-4101	137	9	♢	♢	PROPN
ejpam-4101	137	10	−k−rδ	−k−rδ	PROPN
ejpam-4101	137	11	=	=	SYM
ejpam-4101	137	12	(	(	PUNCT
ejpam-4101	137	13	♢	♢	PROPN
ejpam-4101	137	14	+	+	PROPN
ejpam-4101	137	15	m2)kδ	m2)kδ	PROPN
ejpam-4101	137	16	.	.	PUNCT
ejpam-4101	138	1	(	(	PUNCT
ejpam-4101	138	2	23	23	NUM
ejpam-4101	138	3	)	)	PUNCT
ejpam-4101	138	4	by	by	ADP
ejpam-4101	138	5	putting	put	VERB
ejpam-4101	138	6	k	k	X
ejpam-4101	138	7	=	=	PUNCT
ejpam-4101	138	8	0	0	NUM
ejpam-4101	138	9	in	in	ADP
ejpam-4101	138	10	(	(	PUNCT
ejpam-4101	138	11	23	23	NUM
ejpam-4101	138	12	)	)	PUNCT
ejpam-4101	138	13	,	,	PUNCT
ejpam-4101	138	14	we	we	PRON
ejpam-4101	138	15	have	have	VERB
ejpam-4101	138	16	p0(x	p0(x	PROPN
ejpam-4101	138	17	,	,	PUNCT
ejpam-4101	138	18	m	m	NOUN
ejpam-4101	138	19	)	)	PUNCT
ejpam-4101	139	1	=	=	SYM
ejpam-4101	139	2	δ	δ	PROPN
ejpam-4101	139	3	.	.	PUNCT
ejpam-4101	139	4	by	by	ADP
ejpam-4101	139	5	putting	put	VERB
ejpam-4101	139	6	α	α	NOUN
ejpam-4101	139	7	=	=	PUNCT
ejpam-4101	139	8	2k	2k	NUM
ejpam-4101	139	9	into	into	ADP
ejpam-4101	139	10	(	(	PUNCT
ejpam-4101	139	11	22	22	NUM
ejpam-4101	139	12	)	)	PUNCT
ejpam-4101	139	13	,	,	PUNCT
ejpam-4101	139	14	we	we	PRON
ejpam-4101	139	15	have	have	VERB
ejpam-4101	139	16	p2k(x	p2k(x	PROPN
ejpam-4101	139	17	,	,	PUNCT
ejpam-4101	139	18	m	m	NOUN
ejpam-4101	139	19	)	)	PUNCT
ejpam-4101	139	20	=	=	SYM
ejpam-4101	139	21	(	(	PUNCT
ejpam-4101	139	22	−k	−k	NOUN
ejpam-4101	139	23	0	0	NUM
ejpam-4101	139	24	)	)	PUNCT
ejpam-4101	139	25	(	(	PUNCT
ejpam-4101	139	26	m2)0(−1)k+0re	m2)0(−1)k+0re	NOUN
ejpam-4101	139	27	2k+0(x	2k+0(x	NUM
ejpam-4101	139	28	)	)	PUNCT
ejpam-4101	139	29	∗rh	∗rh	VERB
ejpam-4101	139	30	2k+0(x	2k+0(x	NUM
ejpam-4101	139	31	)	)	PUNCT
ejpam-4101	139	32	+	+	CCONJ
ejpam-4101	139	33	∞∑	∞∑	NUM
ejpam-4101	139	34	r=1	r=1	NOUN
ejpam-4101	139	35	(	(	PUNCT
ejpam-4101	139	36	−k	−k	NOUN
ejpam-4101	139	37	r	r	NOUN
ejpam-4101	139	38	)	)	PUNCT
ejpam-4101	139	39	(	(	PUNCT
ejpam-4101	139	40	m2)r(−1)k+rre	m2)r(−1)k+rre	PROPN
ejpam-4101	139	41	2k+2r(x	2k+2r(x	NUM
ejpam-4101	139	42	)	)	PUNCT
ejpam-4101	139	43	∗rh	∗rh	ADJ
ejpam-4101	139	44	2k+2r(x	2k+2r(x	NOUN
ejpam-4101	139	45	)	)	PUNCT
ejpam-4101	139	46	.	.	PUNCT
ejpam-4101	140	1	(	(	PUNCT
ejpam-4101	140	2	24	24	NUM
ejpam-4101	140	3	)	)	PUNCT
ejpam-4101	140	4	the	the	DET
ejpam-4101	140	5	second	second	ADJ
ejpam-4101	140	6	summand	summand	NOUN
ejpam-4101	140	7	of	of	ADP
ejpam-4101	140	8	the	the	DET
ejpam-4101	140	9	right	right	ADJ
ejpam-4101	140	10	-	-	PUNCT
ejpam-4101	140	11	hand	hand	NOUN
ejpam-4101	140	12	member	member	NOUN
ejpam-4101	140	13	of	of	ADP
ejpam-4101	140	14	(	(	PUNCT
ejpam-4101	140	15	24	24	NUM
ejpam-4101	140	16	)	)	PUNCT
ejpam-4101	140	17	vanishes	vanish	VERB
ejpam-4101	140	18	for	for	ADP
ejpam-4101	140	19	m	m	PROPN
ejpam-4101	140	20	=	=	SYM
ejpam-4101	140	21	0	0	PUNCT
ejpam-4101	141	1	and	and	CCONJ
ejpam-4101	141	2	then	then	ADV
ejpam-4101	141	3	,	,	PUNCT
ejpam-4101	141	4	we	we	PRON
ejpam-4101	141	5	have	have	VERB
ejpam-4101	141	6	p2k(x	p2k(x	PROPN
ejpam-4101	141	7	,	,	PUNCT
ejpam-4101	141	8	m	m	VERB
ejpam-4101	141	9	=	=	NOUN
ejpam-4101	141	10	0	0	NUM
ejpam-4101	141	11	)	)	PUNCT
ejpam-4101	141	12	=	=	NOUN
ejpam-4101	141	13	(	(	PUNCT
ejpam-4101	141	14	−1)kre	−1)kre	PROPN
ejpam-4101	141	15	2k(x	2k(x	NUM
ejpam-4101	141	16	)	)	PUNCT
ejpam-4101	141	17	∗rh	∗rh	VERB
ejpam-4101	141	18	2k(x	2k(x	NUM
ejpam-4101	141	19	)	)	PUNCT
ejpam-4101	141	20	(	(	PUNCT
ejpam-4101	141	21	25	25	NUM
ejpam-4101	141	22	)	)	PUNCT
ejpam-4101	141	23	is	be	AUX
ejpam-4101	141	24	the	the	DET
ejpam-4101	141	25	fundamental	fundamental	ADJ
ejpam-4101	141	26	solution	solution	NOUN
ejpam-4101	141	27	of	of	ADP
ejpam-4101	141	28	the	the	DET
ejpam-4101	141	29	diamond	diamond	NOUN
ejpam-4101	141	30	operator	operator	NOUN
ejpam-4101	141	31	♢	♢	PROPN
ejpam-4101	141	32	k.	k.	PROPN
ejpam-4101	141	33	lemma	lemma	PROPN
ejpam-4101	141	34	4	4	X
ejpam-4101	141	35	.	.	PUNCT
ejpam-4101	142	1	the	the	DET
ejpam-4101	142	2	function	function	PROPN
ejpam-4101	142	3	rh	rh	PROPN
ejpam-4101	142	4	−2k(x	−2k(x	PROPN
ejpam-4101	142	5	)	)	PUNCT
ejpam-4101	142	6	and	and	CCONJ
ejpam-4101	142	7	(	(	PUNCT
ejpam-4101	142	8	−1)kre	−1)kre	PROPN
ejpam-4101	142	9	−2k(x	−2k(x	NOUN
ejpam-4101	142	10	)	)	PUNCT
ejpam-4101	142	11	are	be	AUX
ejpam-4101	142	12	the	the	DET
ejpam-4101	142	13	inverse	inverse	NOUN
ejpam-4101	142	14	in	in	ADP
ejpam-4101	142	15	the	the	DET
ejpam-4101	142	16	convolution	convolution	NOUN
ejpam-4101	142	17	algebra	algebra	NOUN
ejpam-4101	142	18	of	of	ADP
ejpam-4101	142	19	rh	rh	PROPN
ejpam-4101	142	20	2k(x	2k(x	PROPN
ejpam-4101	142	21	)	)	PUNCT
ejpam-4101	142	22	and	and	CCONJ
ejpam-4101	142	23	(	(	PUNCT
ejpam-4101	142	24	−1)kre	−1)kre	PROPN
ejpam-4101	142	25	2k(x	2k(x	NUM
ejpam-4101	142	26	)	)	PUNCT
ejpam-4101	142	27	,	,	PUNCT
ejpam-4101	142	28	respectively	respectively	ADV
ejpam-4101	142	29	.	.	PUNCT
ejpam-4101	143	1	that	that	PRON
ejpam-4101	143	2	is	is	ADV
ejpam-4101	143	3	,	,	PUNCT
ejpam-4101	143	4	rh	rh	PROPN
ejpam-4101	143	5	−2k(x	−2k(x	PROPN
ejpam-4101	143	6	)	)	PUNCT
ejpam-4101	143	7	∗rh	∗rh	VERB
ejpam-4101	143	8	2k(x	2k(x	NUM
ejpam-4101	143	9	)	)	PUNCT
ejpam-4101	144	1	=	=	SYM
ejpam-4101	144	2	rh	rh	PROPN
ejpam-4101	144	3	−2k+2k(x	−2k+2k(x	PROPN
ejpam-4101	144	4	)	)	PUNCT
ejpam-4101	145	1	=	=	SYM
ejpam-4101	145	2	rh	rh	PROPN
ejpam-4101	145	3	0	0	PUNCT
ejpam-4101	145	4	(	(	PUNCT
ejpam-4101	145	5	x	x	NOUN
ejpam-4101	145	6	)	)	PUNCT
ejpam-4101	145	7	=	=	SYM
ejpam-4101	145	8	δ	δ	PROPN
ejpam-4101	145	9	and	and	CCONJ
ejpam-4101	145	10	(	(	PUNCT
ejpam-4101	145	11	−1)kre	−1)kre	PROPN
ejpam-4101	145	12	−2k(x	−2k(x	NUM
ejpam-4101	145	13	)	)	PUNCT
ejpam-4101	145	14	∗	∗	NOUN
ejpam-4101	145	15	(	(	PUNCT
ejpam-4101	145	16	−1)kre	−1)kre	PROPN
ejpam-4101	145	17	2k(x	2k(x	NUM
ejpam-4101	145	18	)	)	PUNCT
ejpam-4101	145	19	=	=	NOUN
ejpam-4101	146	1	(	(	PUNCT
ejpam-4101	146	2	−1)2kre	−1)2kre	NOUN
ejpam-4101	146	3	−2k+2k(x	−2k+2k(x	NOUN
ejpam-4101	146	4	)	)	PUNCT
ejpam-4101	146	5	=	=	SYM
ejpam-4101	146	6	re	re	X
ejpam-4101	146	7	0(x	0(x	NOUN
ejpam-4101	146	8	)	)	PUNCT
ejpam-4101	147	1	=	=	SYM
ejpam-4101	147	2	δ	δ	PROPN
ejpam-4101	147	3	.	.	PUNCT
ejpam-4101	148	1	s.	s.	PROPN
ejpam-4101	148	2	bupasiri	bupasiri	PROPN
ejpam-4101	148	3	/	/	SYM
ejpam-4101	148	4	eur	eur	PROPN
ejpam-4101	148	5	.	.	PUNCT
ejpam-4101	149	1	j.	j.	PROPN
ejpam-4101	149	2	pure	pure	PROPN
ejpam-4101	149	3	appl	appl	PROPN
ejpam-4101	149	4	.	.	PROPN
ejpam-4101	149	5	math	math	PROPN
ejpam-4101	149	6	,	,	PUNCT
ejpam-4101	149	7	14	14	NUM
ejpam-4101	149	8	(	(	PUNCT
ejpam-4101	149	9	4	4	NUM
ejpam-4101	149	10	)	)	PUNCT
ejpam-4101	149	11	(	(	PUNCT
ejpam-4101	149	12	2021	2021	NUM
ejpam-4101	149	13	)	)	PUNCT
ejpam-4101	149	14	,	,	PUNCT
ejpam-4101	149	15	1306	1306	NUM
ejpam-4101	149	16	-	-	SYM
ejpam-4101	149	17	1323	1323	NUM
ejpam-4101	149	18	1312	1312	NUM
ejpam-4101	149	19	for	for	ADP
ejpam-4101	149	20	the	the	DET
ejpam-4101	149	21	proof	proof	NOUN
ejpam-4101	149	22	of	of	ADP
ejpam-4101	149	23	the	the	DET
ejpam-4101	149	24	this	this	DET
ejpam-4101	149	25	lemma	lemma	PROPN
ejpam-4101	149	26	is	be	AUX
ejpam-4101	149	27	given	give	VERB
ejpam-4101	149	28	in	in	ADP
ejpam-4101	149	29	[	[	X
ejpam-4101	149	30	1	1	NUM
ejpam-4101	149	31	,	,	PUNCT
ejpam-4101	149	32	21	21	NUM
ejpam-4101	149	33	,	,	PUNCT
ejpam-4101	149	34	23	23	NUM
ejpam-4101	149	35	]	]	PUNCT
ejpam-4101	149	36	.	.	PUNCT
ejpam-4101	150	1	lemma	lemma	PROPN
ejpam-4101	150	2	5	5	NUM
ejpam-4101	150	3	.	.	PUNCT
ejpam-4101	151	1	[	[	X
ejpam-4101	151	2	20](convolution	20](convolution	NUM
ejpam-4101	151	3	of	of	ADP
ejpam-4101	151	4	re	re	NOUN
ejpam-4101	151	5	α(x	α(x	NOUN
ejpam-4101	151	6	)	)	PUNCT
ejpam-4101	151	7	and	and	CCONJ
ejpam-4101	151	8	rh	rh	PROPN
ejpam-4101	151	9	α	α	PROPN
ejpam-4101	151	10	(	(	PUNCT
ejpam-4101	151	11	x	x	NOUN
ejpam-4101	151	12	)	)	PUNCT
ejpam-4101	151	13	)	)	PUNCT
ejpam-4101	151	14	.	.	PUNCT
ejpam-4101	152	1	if	if	SCONJ
ejpam-4101	152	2	re	re	VERB
ejpam-4101	152	3	α(x	α(x	NOUN
ejpam-4101	152	4	)	)	PUNCT
ejpam-4101	152	5	and	and	CCONJ
ejpam-4101	152	6	rh	rh	PROPN
ejpam-4101	152	7	α	α	PROPN
ejpam-4101	152	8	(	(	PUNCT
ejpam-4101	152	9	x	x	NOUN
ejpam-4101	152	10	)	)	PUNCT
ejpam-4101	152	11	are	be	AUX
ejpam-4101	152	12	defined	define	VERB
ejpam-4101	152	13	by	by	ADP
ejpam-4101	152	14	(	(	PUNCT
ejpam-4101	152	15	19	19	NUM
ejpam-4101	152	16	)	)	PUNCT
ejpam-4101	152	17	and	and	CCONJ
ejpam-4101	152	18	(	(	PUNCT
ejpam-4101	152	19	20	20	NUM
ejpam-4101	152	20	)	)	PUNCT
ejpam-4101	152	21	,	,	PUNCT
ejpam-4101	152	22	respectively	respectively	ADV
ejpam-4101	152	23	,	,	PUNCT
ejpam-4101	152	24	then	then	ADV
ejpam-4101	152	25	(	(	PUNCT
ejpam-4101	152	26	i	i	NOUN
ejpam-4101	152	27	)	)	PUNCT
ejpam-4101	152	28	re	re	VERB
ejpam-4101	152	29	α(x	α(x	NOUN
ejpam-4101	152	30	)	)	PUNCT
ejpam-4101	152	31	∗re	∗re	ADJ
ejpam-4101	152	32	β(x	β(x	NOUN
ejpam-4101	152	33	)	)	PUNCT
ejpam-4101	152	34	=	=	SYM
ejpam-4101	152	35	re	re	NOUN
ejpam-4101	152	36	α+β(x	α+β(x	NOUN
ejpam-4101	152	37	)	)	PUNCT
ejpam-4101	152	38	,	,	PUNCT
ejpam-4101	152	39	where	where	SCONJ
ejpam-4101	152	40	α	α	NOUN
ejpam-4101	152	41	and	and	CCONJ
ejpam-4101	152	42	β	β	X
ejpam-4101	152	43	are	be	AUX
ejpam-4101	152	44	complex	complex	ADJ
ejpam-4101	152	45	parameters	parameter	NOUN
ejpam-4101	152	46	;	;	PUNCT
ejpam-4101	152	47	(	(	PUNCT
ejpam-4101	152	48	ii	ii	X
ejpam-4101	152	49	)	)	PUNCT
ejpam-4101	152	50	rh	rh	PROPN
ejpam-4101	152	51	α	α	PROPN
ejpam-4101	152	52	(	(	PUNCT
ejpam-4101	152	53	x)∗rh	x)∗rh	PROPN
ejpam-4101	152	54	β	β	PROPN
ejpam-4101	152	55	(	(	PUNCT
ejpam-4101	152	56	x	x	NOUN
ejpam-4101	152	57	)	)	PUNCT
ejpam-4101	152	58	=	=	SYM
ejpam-4101	152	59	rh	rh	PROPN
ejpam-4101	152	60	α+β(x	α+β(x	NOUN
ejpam-4101	152	61	)	)	PUNCT
ejpam-4101	152	62	,	,	PUNCT
ejpam-4101	152	63	where	where	SCONJ
ejpam-4101	152	64	α	α	NOUN
ejpam-4101	152	65	and	and	CCONJ
ejpam-4101	152	66	β	β	X
ejpam-4101	152	67	are	be	AUX
ejpam-4101	152	68	both	both	DET
ejpam-4101	152	69	integers	integer	NOUN
ejpam-4101	152	70	and	and	CCONJ
ejpam-4101	152	71	except	except	SCONJ
ejpam-4101	152	72	only	only	ADV
ejpam-4101	152	73	the	the	DET
ejpam-4101	152	74	case	case	NOUN
ejpam-4101	152	75	both	both	CCONJ
ejpam-4101	152	76	α	α	NOUN
ejpam-4101	152	77	and	and	CCONJ
ejpam-4101	152	78	β	β	X
ejpam-4101	152	79	are	be	AUX
ejpam-4101	152	80	both	both	DET
ejpam-4101	152	81	integers	integer	NOUN
ejpam-4101	152	82	.	.	PUNCT
ejpam-4101	153	1	lemma	lemma	PROPN
ejpam-4101	153	2	6	6	NUM
ejpam-4101	153	3	.	.	PUNCT
ejpam-4101	154	1	[	[	X
ejpam-4101	154	2	11	11	NUM
ejpam-4101	154	3	]	]	PUNCT
ejpam-4101	154	4	given	give	VERB
ejpam-4101	154	5	the	the	DET
ejpam-4101	154	6	equation	equation	NOUN
ejpam-4101	154	7	(	(	PUNCT
ejpam-4101	154	8	♢	♢	PROPN
ejpam-4101	154	9	+	+	NOUN
ejpam-4101	154	10	m2)ku(x	m2)ku(x	X
ejpam-4101	154	11	)	)	PUNCT
ejpam-4101	154	12	=	=	SYM
ejpam-4101	154	13	δ	δ	PROPN
ejpam-4101	154	14	,	,	PUNCT
ejpam-4101	154	15	where	where	SCONJ
ejpam-4101	154	16	(	(	PUNCT
ejpam-4101	154	17	♢	♢	PROPN
ejpam-4101	154	18	+	+	NOUN
ejpam-4101	154	19	m2)k	m2)k	PROPN
ejpam-4101	154	20	is	be	AUX
ejpam-4101	154	21	the	the	DET
ejpam-4101	154	22	diamond	diamond	PROPN
ejpam-4101	154	23	klein	klein	PROPN
ejpam-4101	154	24	-	-	PUNCT
ejpam-4101	154	25	gordon	gordon	PROPN
ejpam-4101	154	26	operator	operator	NOUN
ejpam-4101	154	27	,	,	PUNCT
ejpam-4101	154	28	which	which	PRON
ejpam-4101	154	29	is	be	AUX
ejpam-4101	154	30	defined	define	VERB
ejpam-4101	154	31	by	by	ADP
ejpam-4101	154	32	(	(	PUNCT
ejpam-4101	154	33	♢	♢	PROPN
ejpam-4101	154	34	+	+	PROPN
ejpam-4101	154	35	m2)k	m2)k	NOUN
ejpam-4101	154	36	=	=	SYM
ejpam-4101	154	37			PROPN
ejpam-4101	154	38	(	(	PUNCT
ejpam-4101	154	39	p∑	p∑	NOUN
ejpam-4101	154	40	r=1	r=1	NOUN
ejpam-4101	154	41	∂2	∂2	NOUN
ejpam-4101	154	42	∂x2r	∂x2r	NOUN
ejpam-4101	154	43	)	)	PUNCT
ejpam-4101	154	44	2	2	NUM
ejpam-4101	154	45	−	−	NOUN
ejpam-4101	154	46			PROPN
ejpam-4101	154	47	p+q∑	p+q∑	PROPN
ejpam-4101	154	48	j	j	NOUN
ejpam-4101	154	49	=	=	PROPN
ejpam-4101	154	50	p+1	p+1	PROPN
ejpam-4101	154	51	∂2	∂2	PROPN
ejpam-4101	154	52	∂x2j	∂x2j	PUNCT
ejpam-4101	154	53	2	2	PROPN
ejpam-4101	155	1	+	+	PROPN
ejpam-4101	155	2	m2	m2	PROPN
ejpam-4101	155	3	k	k	PUNCT
ejpam-4101	155	4	,	,	PUNCT
ejpam-4101	155	5	(	(	PUNCT
ejpam-4101	155	6	26	26	NUM
ejpam-4101	155	7	)	)	PUNCT
ejpam-4101	155	8	where	where	SCONJ
ejpam-4101	155	9	x	x	SYM
ejpam-4101	155	10	=	=	PRON
ejpam-4101	155	11	(	(	PUNCT
ejpam-4101	155	12	x1	x1	PROPN
ejpam-4101	155	13	,	,	PUNCT
ejpam-4101	155	14	x2	x2	PROPN
ejpam-4101	155	15	,	,	PUNCT
ejpam-4101	155	16	.	.	PUNCT
ejpam-4101	155	17	.	.	PUNCT
ejpam-4101	156	1	.	.	PUNCT
ejpam-4101	157	1	,	,	PUNCT
ejpam-4101	157	2	xn	xn	X
ejpam-4101	157	3	)	)	PUNCT
ejpam-4101	157	4	∈	∈	PROPN
ejpam-4101	157	5	rn	rn	PROPN
ejpam-4101	157	6	,	,	PUNCT
ejpam-4101	157	7	k	k	PROPN
ejpam-4101	157	8	is	be	AUX
ejpam-4101	157	9	a	a	DET
ejpam-4101	157	10	non	non	ADJ
ejpam-4101	157	11	-	-	ADJ
ejpam-4101	157	12	negative	negative	ADJ
ejpam-4101	157	13	integer	integer	NOUN
ejpam-4101	157	14	,	,	PUNCT
ejpam-4101	157	15	m	m	VERB
ejpam-4101	157	16	is	be	AUX
ejpam-4101	157	17	a	a	DET
ejpam-4101	157	18	non	non	ADJ
ejpam-4101	157	19	-	-	ADJ
ejpam-4101	157	20	negative	negative	ADJ
ejpam-4101	157	21	real	real	ADJ
ejpam-4101	157	22	number	number	NOUN
ejpam-4101	157	23	and	and	CCONJ
ejpam-4101	157	24	δ	δ	PROPN
ejpam-4101	157	25	is	be	AUX
ejpam-4101	157	26	the	the	DET
ejpam-4101	157	27	dirac	dirac	PROPN
ejpam-4101	157	28	delta	delta	NOUN
ejpam-4101	157	29	function	function	NOUN
ejpam-4101	157	30	.	.	PUNCT
ejpam-4101	158	1	then	then	ADV
ejpam-4101	158	2	,	,	PUNCT
ejpam-4101	158	3	we	we	PRON
ejpam-4101	158	4	obtain	obtain	VERB
ejpam-4101	158	5	p2k(x	p2k(x	PROPN
ejpam-4101	158	6	,	,	PUNCT
ejpam-4101	158	7	m	m	NOUN
ejpam-4101	158	8	)	)	PUNCT
ejpam-4101	158	9	=	=	PUNCT
ejpam-4101	159	1	∞∑	∞∑	NUM
ejpam-4101	159	2	r=0	r=0	PROPN
ejpam-4101	159	3	(	(	PUNCT
ejpam-4101	159	4	−k	−k	NOUN
ejpam-4101	159	5	r	r	NOUN
ejpam-4101	159	6	)	)	PUNCT
ejpam-4101	159	7	m2r(−1)k+rre	m2r(−1)k+rre	PROPN
ejpam-4101	159	8	2k+2r(x	2k+2r(x	NUM
ejpam-4101	159	9	)	)	PUNCT
ejpam-4101	159	10	∗rh	∗rh	ADJ
ejpam-4101	159	11	2k+2r(x	2k+2r(x	NOUN
ejpam-4101	159	12	)	)	PUNCT
ejpam-4101	159	13	(	(	PUNCT
ejpam-4101	159	14	27	27	NUM
ejpam-4101	159	15	)	)	PUNCT
ejpam-4101	159	16	is	be	AUX
ejpam-4101	159	17	the	the	DET
ejpam-4101	159	18	fundamental	fundamental	ADJ
ejpam-4101	159	19	solution	solution	NOUN
ejpam-4101	159	20	of	of	ADP
ejpam-4101	159	21	the	the	DET
ejpam-4101	159	22	operator	operator	NOUN
ejpam-4101	159	23	(	(	PUNCT
ejpam-4101	159	24	♢	♢	PROPN
ejpam-4101	159	25	+	+	PROPN
ejpam-4101	159	26	m2)k	m2)k	PROPN
ejpam-4101	159	27	,	,	PUNCT
ejpam-4101	159	28	defined	define	VERB
ejpam-4101	159	29	by	by	ADP
ejpam-4101	159	30	(	(	PUNCT
ejpam-4101	159	31	9	9	NUM
ejpam-4101	159	32	)	)	PUNCT
ejpam-4101	159	33	,	,	PUNCT
ejpam-4101	159	34	where	where	SCONJ
ejpam-4101	159	35	rh	rh	PROPN
ejpam-4101	159	36	2k(x	2k(x	PROPN
ejpam-4101	159	37	)	)	PUNCT
ejpam-4101	159	38	and	and	CCONJ
ejpam-4101	159	39	re	re	X
ejpam-4101	159	40	2k(x	2k(x	NUM
ejpam-4101	159	41	)	)	PUNCT
ejpam-4101	159	42	are	be	AUX
ejpam-4101	159	43	defined	define	VERB
ejpam-4101	159	44	by	by	ADP
ejpam-4101	159	45	(	(	PUNCT
ejpam-4101	159	46	20	20	NUM
ejpam-4101	159	47	)	)	PUNCT
ejpam-4101	159	48	and	and	CCONJ
ejpam-4101	159	49	(	(	PUNCT
ejpam-4101	159	50	19	19	NUM
ejpam-4101	159	51	)	)	PUNCT
ejpam-4101	159	52	,	,	PUNCT
ejpam-4101	159	53	respectively	respectively	ADV
ejpam-4101	159	54	.	.	PUNCT
ejpam-4101	160	1	moreover	moreover	ADV
ejpam-4101	160	2	,	,	PUNCT
ejpam-4101	160	3	u(x	u(x	PROPN
ejpam-4101	160	4	)	)	PUNCT
ejpam-4101	160	5	=	=	SYM
ejpam-4101	160	6	p2k(x	p2k(x	PROPN
ejpam-4101	160	7	,	,	PUNCT
ejpam-4101	160	8	m	m	VERB
ejpam-4101	160	9	)	)	PUNCT
ejpam-4101	160	10	is	be	AUX
ejpam-4101	160	11	tempered	temper	VERB
ejpam-4101	160	12	distribution	distribution	NOUN
ejpam-4101	160	13	.	.	PUNCT
ejpam-4101	161	1	lemma	lemma	PROPN
ejpam-4101	161	2	7	7	NUM
ejpam-4101	161	3	.	.	PUNCT
ejpam-4101	162	1	[	[	X
ejpam-4101	162	2	20	20	NUM
ejpam-4101	162	3	]	]	PUNCT
ejpam-4101	162	4	given	give	VERB
ejpam-4101	162	5	the	the	DET
ejpam-4101	162	6	equation	equation	NOUN
ejpam-4101	162	7	⊙kg(x	⊙kg(x	NUM
ejpam-4101	162	8	)	)	PUNCT
ejpam-4101	162	9	=	=	SYM
ejpam-4101	162	10	δ	δ	PROPN
ejpam-4101	162	11	,	,	PUNCT
ejpam-4101	162	12	(	(	PUNCT
ejpam-4101	162	13	28	28	NUM
ejpam-4101	162	14	)	)	PUNCT
ejpam-4101	162	15	where	where	SCONJ
ejpam-4101	162	16	⊙k	⊙k	PROPN
ejpam-4101	162	17	is	be	AUX
ejpam-4101	162	18	the	the	DET
ejpam-4101	162	19	operator	operator	NOUN
ejpam-4101	162	20	iterated	iterate	VERB
ejpam-4101	162	21	k	k	NOUN
ejpam-4101	162	22	-	-	PUNCT
ejpam-4101	162	23	times	time	NOUN
ejpam-4101	162	24	is	be	AUX
ejpam-4101	162	25	defined	define	VERB
ejpam-4101	162	26	by	by	ADP
ejpam-4101	162	27	(	(	PUNCT
ejpam-4101	162	28	6	6	NUM
ejpam-4101	162	29	)	)	PUNCT
ejpam-4101	162	30	.	.	PUNCT
ejpam-4101	163	1	then	then	ADV
ejpam-4101	163	2	,	,	PUNCT
ejpam-4101	163	3	we	we	PRON
ejpam-4101	163	4	obtain	obtain	VERB
ejpam-4101	163	5	g(x	g(x	NOUN
ejpam-4101	163	6	)	)	PUNCT
ejpam-4101	163	7	is	be	AUX
ejpam-4101	163	8	the	the	DET
ejpam-4101	163	9	fundamental	fundamental	ADJ
ejpam-4101	163	10	solution	solution	NOUN
ejpam-4101	163	11	of	of	ADP
ejpam-4101	163	12	the	the	DET
ejpam-4101	163	13	equation	equation	NOUN
ejpam-4101	163	14	(	(	PUNCT
ejpam-4101	163	15	28	28	NUM
ejpam-4101	163	16	)	)	PUNCT
ejpam-4101	163	17	,	,	PUNCT
ejpam-4101	163	18	where	where	SCONJ
ejpam-4101	163	19	g(x	g(x	NOUN
ejpam-4101	163	20	)	)	PUNCT
ejpam-4101	163	21	=	=	SYM
ejpam-4101	164	1	(	(	PUNCT
ejpam-4101	164	2	rh	rh	PROPN
ejpam-4101	164	3	4k(x	4k(x	PROPN
ejpam-4101	164	4	)	)	PUNCT
ejpam-4101	165	1	∗	∗	NOUN
ejpam-4101	165	2	(	(	PUNCT
ejpam-4101	165	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	165	4	4k(x	4k(x	NOUN
ejpam-4101	165	5	)	)	PUNCT
ejpam-4101	165	6	)	)	PUNCT
ejpam-4101	166	1	∗	∗	NOUN
ejpam-4101	166	2	(	(	PUNCT
ejpam-4101	166	3	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	166	4	(	(	PUNCT
ejpam-4101	166	5	29	29	NUM
ejpam-4101	166	6	)	)	PUNCT
ejpam-4101	166	7	and	and	CCONJ
ejpam-4101	166	8	h(x	h(x	PROPN
ejpam-4101	166	9	)	)	PUNCT
ejpam-4101	166	10	=	=	SYM
ejpam-4101	166	11	1	1	NUM
ejpam-4101	166	12	2	2	NUM
ejpam-4101	166	13	rh	rh	NOUN
ejpam-4101	166	14	4	4	NUM
ejpam-4101	166	15	(	(	PUNCT
ejpam-4101	166	16	x	x	NOUN
ejpam-4101	166	17	)	)	PUNCT
ejpam-4101	166	18	+	+	CCONJ
ejpam-4101	166	19	1	1	NUM
ejpam-4101	166	20	2	2	NUM
ejpam-4101	166	21	(	(	PUNCT
ejpam-4101	166	22	−1)2re	−1)2re	NOUN
ejpam-4101	166	23	4(x	4(x	NUM
ejpam-4101	166	24	)	)	PUNCT
ejpam-4101	166	25	.	.	PUNCT
ejpam-4101	167	1	(	(	PUNCT
ejpam-4101	167	2	30	30	NUM
ejpam-4101	167	3	)	)	PUNCT
ejpam-4101	167	4	here	here	ADV
ejpam-4101	167	5	,	,	PUNCT
ejpam-4101	167	6	h∗k(x	h∗k(x	PROPN
ejpam-4101	167	7	)	)	PUNCT
ejpam-4101	167	8	denotes	denote	VERB
ejpam-4101	167	9	the	the	DET
ejpam-4101	167	10	convolution	convolution	NOUN
ejpam-4101	167	11	of	of	ADP
ejpam-4101	167	12	h(x	h(x	PROPN
ejpam-4101	167	13	)	)	PUNCT
ejpam-4101	167	14	itself	itself	PRON
ejpam-4101	168	1	k	k	NOUN
ejpam-4101	168	2	-	-	PUNCT
ejpam-4101	168	3	times	time	NOUN
ejpam-4101	168	4	,	,	PUNCT
ejpam-4101	168	5	(	(	PUNCT
ejpam-4101	168	6	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	168	7	denotes	denote	VERB
ejpam-4101	168	8	the	the	DET
ejpam-4101	168	9	inverse	inverse	NOUN
ejpam-4101	168	10	of	of	ADP
ejpam-4101	168	11	h∗k(x	h∗k(x	PROPN
ejpam-4101	168	12	)	)	PUNCT
ejpam-4101	168	13	in	in	ADP
ejpam-4101	168	14	the	the	DET
ejpam-4101	168	15	convolution	convolution	NOUN
ejpam-4101	168	16	algebra	algebra	NOUN
ejpam-4101	168	17	.	.	PUNCT
ejpam-4101	169	1	moreover	moreover	ADV
ejpam-4101	169	2	,	,	PUNCT
ejpam-4101	169	3	g(x	g(x	NOUN
ejpam-4101	169	4	)	)	PUNCT
ejpam-4101	169	5	is	be	AUX
ejpam-4101	169	6	a	a	DET
ejpam-4101	169	7	tempered	temper	VERB
ejpam-4101	169	8	distribution	distribution	NOUN
ejpam-4101	169	9	.	.	PUNCT
ejpam-4101	170	1	lemma	lemma	PROPN
ejpam-4101	170	2	8	8	NUM
ejpam-4101	170	3	.	.	PUNCT
ejpam-4101	171	1	(	(	PUNCT
ejpam-4101	171	2	the	the	DET
ejpam-4101	171	3	fourier	fourier	NOUN
ejpam-4101	171	4	transform	transform	NOUN
ejpam-4101	171	5	of	of	ADP
ejpam-4101	171	6	(	(	PUNCT
ejpam-4101	171	7	(	(	PUNCT
ejpam-4101	171	8	♢	♢	PROPN
ejpam-4101	171	9	+	+	PROPN
ejpam-4101	171	10	m2	m2	X
ejpam-4101	171	11	)	)	PUNCT
ejpam-4101	171	12	(	(	PUNCT
ejpam-4101	171	13	△	△	X
ejpam-4101	171	14	2+⊡2	2+⊡2	NUM
ejpam-4101	171	15	2	2	NUM
ejpam-4101	171	16	)	)	PUNCT
ejpam-4101	171	17	)	)	PUNCT
ejpam-4101	172	1	k	k	PROPN
ejpam-4101	172	2	δ	δ	PROPN
ejpam-4101	172	3	.	.	PUNCT
ejpam-4101	172	4	)	)	PUNCT
ejpam-4101	172	5	let	let	VERB
ejpam-4101	172	6	||ξ||	||ξ||	VERB
ejpam-4101	172	7	=	=	SYM
ejpam-4101	172	8	(	(	PUNCT
ejpam-4101	172	9	ξ21	ξ21	NOUN
ejpam-4101	172	10	+	+	CCONJ
ejpam-4101	172	11	ξ22	ξ22	NOUN
ejpam-4101	172	12	+	+	X
ejpam-4101	172	13	·	·	PUNCT
ejpam-4101	172	14	·	·	PUNCT
ejpam-4101	172	15	·	·	PUNCT
ejpam-4101	173	1	+	+	NUM
ejpam-4101	173	2	ξ2n	ξ2n	PROPN
ejpam-4101	173	3	)	)	PUNCT
ejpam-4101	173	4	1/2	1/2	NUM
ejpam-4101	173	5	s.	s.	PROPN
ejpam-4101	173	6	bupasiri	bupasiri	PROPN
ejpam-4101	173	7	/	/	SYM
ejpam-4101	173	8	eur	eur	PROPN
ejpam-4101	173	9	.	.	PUNCT
ejpam-4101	174	1	j.	j.	PROPN
ejpam-4101	174	2	pure	pure	PROPN
ejpam-4101	174	3	appl	appl	PROPN
ejpam-4101	174	4	.	.	PROPN
ejpam-4101	174	5	math	math	PROPN
ejpam-4101	174	6	,	,	PUNCT
ejpam-4101	174	7	14	14	NUM
ejpam-4101	174	8	(	(	PUNCT
ejpam-4101	174	9	4	4	NUM
ejpam-4101	174	10	)	)	PUNCT
ejpam-4101	174	11	(	(	PUNCT
ejpam-4101	174	12	2021	2021	NUM
ejpam-4101	174	13	)	)	PUNCT
ejpam-4101	174	14	,	,	PUNCT
ejpam-4101	174	15	1306	1306	NUM
ejpam-4101	174	16	-	-	SYM
ejpam-4101	174	17	1323	1323	NUM
ejpam-4101	174	18	1313	1313	NUM
ejpam-4101	174	19	for	for	ADP
ejpam-4101	174	20	ξ	ξ	PROPN
ejpam-4101	174	21	∈	∈	PROPN
ejpam-4101	174	22	rn	rn	PROPN
ejpam-4101	174	23	.	.	PROPN
ejpam-4101	174	24	then∣∣∣∣∣f	then∣∣∣∣∣f	NOUN
ejpam-4101	174	25	(	(	PUNCT
ejpam-4101	174	26	(	(	PUNCT
ejpam-4101	174	27	♢	♢	PROPN
ejpam-4101	174	28	+	+	PROPN
ejpam-4101	174	29	m2	m2	X
ejpam-4101	174	30	)	)	PUNCT
ejpam-4101	174	31	(	(	PUNCT
ejpam-4101	174	32	△	△	X
ejpam-4101	174	33	2	2	NUM
ejpam-4101	174	34	+	+	NOUN
ejpam-4101	174	35	⊡2	⊡2	PROPN
ejpam-4101	174	36	2	2	NUM
ejpam-4101	174	37	)	)	PUNCT
ejpam-4101	174	38	)	)	PUNCT
ejpam-4101	175	1	k	k	PROPN
ejpam-4101	175	2	δ	δ	PROPN
ejpam-4101	176	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4101	176	2	≤	≤	ADV
ejpam-4101	176	3	1	1	NUM
ejpam-4101	176	4	(	(	PUNCT
ejpam-4101	176	5	2π)n/2	2π)n/2	NUM
ejpam-4101	176	6	(	(	PUNCT
ejpam-4101	176	7	||ξ||4	||ξ||4	PROPN
ejpam-4101	176	8	+	+	NOUN
ejpam-4101	176	9	m2)k||ξ||4k	m2)k||ξ||4k	NOUN
ejpam-4101	176	10	.	.	PUNCT
ejpam-4101	177	1	that	that	PRON
ejpam-4101	177	2	is	be	AUX
ejpam-4101	177	3	,	,	PUNCT
ejpam-4101	177	4	f	f	PROPN
ejpam-4101	177	5	(	(	PUNCT
ejpam-4101	177	6	(	(	PUNCT
ejpam-4101	177	7	♢	♢	PROPN
ejpam-4101	177	8	+	+	PROPN
ejpam-4101	177	9	m2	m2	X
ejpam-4101	177	10	)	)	PUNCT
ejpam-4101	177	11	(	(	PUNCT
ejpam-4101	177	12	△	△	X
ejpam-4101	177	13	2+⊡2	2+⊡2	NUM
ejpam-4101	177	14	2	2	NUM
ejpam-4101	177	15	)	)	PUNCT
ejpam-4101	177	16	)	)	PUNCT
ejpam-4101	178	1	k	k	PROPN
ejpam-4101	178	2	δ	δ	PROPN
ejpam-4101	178	3	is	be	AUX
ejpam-4101	178	4	bounded	bound	VERB
ejpam-4101	178	5	and	and	CCONJ
ejpam-4101	178	6	continuous	continuous	ADJ
ejpam-4101	178	7	on	on	ADP
ejpam-4101	178	8	the	the	DET
ejpam-4101	178	9	space	space	NOUN
ejpam-4101	178	10	s	s	PART
ejpam-4101	178	11	′	′	NOUN
ejpam-4101	178	12	of	of	ADP
ejpam-4101	178	13	the	the	DET
ejpam-4101	178	14	tempered	temper	VERB
ejpam-4101	178	15	distribution	distribution	NOUN
ejpam-4101	178	16	.	.	PUNCT
ejpam-4101	179	1	moreover	moreover	ADV
ejpam-4101	179	2	,	,	PUNCT
ejpam-4101	179	3	by	by	ADP
ejpam-4101	179	4	the	the	DET
ejpam-4101	179	5	inverse	inverse	ADJ
ejpam-4101	179	6	fourier	fourier	NOUN
ejpam-4101	179	7	transformation	transformation	NOUN
ejpam-4101	179	8	(	(	PUNCT
ejpam-4101	179	9	(	(	PUNCT
ejpam-4101	179	10	♢	♢	PROPN
ejpam-4101	179	11	+	+	PROPN
ejpam-4101	179	12	m2	m2	X
ejpam-4101	179	13	)	)	PUNCT
ejpam-4101	179	14	(	(	PUNCT
ejpam-4101	179	15	△	△	X
ejpam-4101	179	16	2	2	NUM
ejpam-4101	179	17	+	+	NOUN
ejpam-4101	179	18	⊡2	⊡2	PROPN
ejpam-4101	179	19	2	2	NUM
ejpam-4101	179	20	)	)	PUNCT
ejpam-4101	179	21	)	)	PUNCT
ejpam-4101	180	1	k	k	PROPN
ejpam-4101	180	2	δ	δ	PROPN
ejpam-4101	180	3	=	=	SYM
ejpam-4101	180	4	f−1	f−1	PROPN
ejpam-4101	180	5	1	1	NUM
ejpam-4101	180	6	(	(	PUNCT
ejpam-4101	180	7	2π)n/2	2π)n/2	NUM
ejpam-4101	180	8	[	[	X
ejpam-4101	180	9	(	(	PUNCT
ejpam-4101	180	10	(	(	PUNCT
ejpam-4101	180	11	ξ21	ξ21	NOUN
ejpam-4101	180	12	+	+	CCONJ
ejpam-4101	180	13	ξ22	ξ22	NOUN
ejpam-4101	180	14	+	+	X
ejpam-4101	180	15	·	·	PUNCT
ejpam-4101	180	16	·	·	PUNCT
ejpam-4101	180	17	·	·	PUNCT
ejpam-4101	180	18	+	+	NUM
ejpam-4101	180	19	ξ2p	ξ2p	NUM
ejpam-4101	180	20	)	)	PUNCT
ejpam-4101	180	21	2	2	NUM
ejpam-4101	180	22	+	+	NUM
ejpam-4101	180	23	m2	m2	PROPN
ejpam-4101	180	24	2	2	NUM
ejpam-4101	180	25	)	)	SYM
ejpam-4101	180	26	2	2	NUM
ejpam-4101	180	27	−	−	NOUN
ejpam-4101	180	28	(	(	PUNCT
ejpam-4101	180	29	(	(	PUNCT
ejpam-4101	180	30	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	180	31	+	+	CCONJ
ejpam-4101	180	32	ξ2p+2	ξ2p+2	VERB
ejpam-4101	180	33	+	+	X
ejpam-4101	180	34	·	·	PUNCT
ejpam-4101	180	35	·	·	PUNCT
ejpam-4101	180	36	·	·	PUNCT
ejpam-4101	180	37	+	+	NUM
ejpam-4101	180	38	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	180	39	)	)	PUNCT
ejpam-4101	180	40	2	2	NUM
ejpam-4101	180	41	−	−	NOUN
ejpam-4101	180	42	m2	m2	PROPN
ejpam-4101	180	43	2	2	NUM
ejpam-4101	180	44	)	)	PUNCT
ejpam-4101	180	45	2	2	NUM
ejpam-4101	180	46	]	]	SYM
ejpam-4101	180	47	k	k	X
ejpam-4101	180	48	.	.	PUNCT
ejpam-4101	181	1	proof	proof	NOUN
ejpam-4101	181	2	.	.	PUNCT
ejpam-4101	182	1	from	from	ADP
ejpam-4101	182	2	the	the	DET
ejpam-4101	182	3	fourier	fourier	NOUN
ejpam-4101	182	4	transform	transform	NOUN
ejpam-4101	182	5	(	(	PUNCT
ejpam-4101	182	6	16	16	NUM
ejpam-4101	182	7	)	)	PUNCT
ejpam-4101	182	8	,	,	PUNCT
ejpam-4101	182	9	we	we	PRON
ejpam-4101	182	10	have	have	VERB
ejpam-4101	182	11	f	f	X
ejpam-4101	182	12	(	(	PUNCT
ejpam-4101	182	13	(	(	PUNCT
ejpam-4101	182	14	♢	♢	PROPN
ejpam-4101	182	15	+	+	PROPN
ejpam-4101	182	16	m2	m2	X
ejpam-4101	182	17	)	)	PUNCT
ejpam-4101	182	18	(	(	PUNCT
ejpam-4101	182	19	△	△	X
ejpam-4101	182	20	2	2	NUM
ejpam-4101	182	21	+	+	NOUN
ejpam-4101	182	22	⊡2	⊡2	PROPN
ejpam-4101	182	23	2	2	NUM
ejpam-4101	182	24	)	)	PUNCT
ejpam-4101	182	25	)	)	PUNCT
ejpam-4101	183	1	k	k	PROPN
ejpam-4101	183	2	δ	δ	PROPN
ejpam-4101	183	3	=	=	SYM
ejpam-4101	183	4	1	1	NUM
ejpam-4101	183	5	(	(	PUNCT
ejpam-4101	183	6	2π)n/2	2π)n/2	NUM
ejpam-4101	183	7	〈	〈	PROPN
ejpam-4101	183	8	δ	δ	PROPN
ejpam-4101	183	9	,	,	PUNCT
ejpam-4101	183	10	(	(	PUNCT
ejpam-4101	183	11	♢	♢	PROPN
ejpam-4101	183	12	+	+	PROPN
ejpam-4101	183	13	m2)k	m2)k	PROPN
ejpam-4101	183	14	(	(	PUNCT
ejpam-4101	183	15	△	△	X
ejpam-4101	183	16	2	2	NUM
ejpam-4101	183	17	+	+	NOUN
ejpam-4101	183	18	⊡2	⊡2	PROPN
ejpam-4101	183	19	2	2	NUM
ejpam-4101	183	20	)	)	PUNCT
ejpam-4101	183	21	k	k	NOUN
ejpam-4101	183	22	e−iξ·x	e−iξ·x	NOUN
ejpam-4101	183	23	〉	〉	NOUN
ejpam-4101	183	24	=	=	SYM
ejpam-4101	183	25	1	1	NUM
ejpam-4101	183	26	(	(	PUNCT
ejpam-4101	183	27	2π)n/2	2π)n/2	NUM
ejpam-4101	183	28	〈	〈	PROPN
ejpam-4101	183	29	δ	δ	PROPN
ejpam-4101	183	30	,	,	PUNCT
ejpam-4101	183	31	(	(	PUNCT
ejpam-4101	183	32	♢	♢	PROPN
ejpam-4101	183	33	+	+	PROPN
ejpam-4101	183	34	m2)k	m2)k	PROPN
ejpam-4101	183	35	(	(	PUNCT
ejpam-4101	183	36	−1)2k	−1)2k	PROPN
ejpam-4101	183	37	2	2	NUM
ejpam-4101	183	38	(	(	PUNCT
ejpam-4101	183	39	(	(	PUNCT
ejpam-4101	183	40	ξ21	ξ21	NOUN
ejpam-4101	183	41	+	+	CCONJ
ejpam-4101	183	42	ξ22	ξ22	NOUN
ejpam-4101	183	43	+	+	X
ejpam-4101	183	44	·	·	PUNCT
ejpam-4101	183	45	·	·	PUNCT
ejpam-4101	183	46	·	·	PUNCT
ejpam-4101	183	47	+	+	CCONJ
ejpam-4101	183	48	ξ2n	ξ2n	NUM
ejpam-4101	183	49	)	)	PUNCT
ejpam-4101	183	50	2	2	NUM
ejpam-4101	183	51	+	+	CCONJ
ejpam-4101	183	52	(	(	PUNCT
ejpam-4101	183	53	ξ21	ξ21	NOUN
ejpam-4101	183	54	+	+	CCONJ
ejpam-4101	183	55	ξ22	ξ22	NOUN
ejpam-4101	183	56	+	+	X
ejpam-4101	183	57	·	·	PUNCT
ejpam-4101	183	58	·	·	PUNCT
ejpam-4101	183	59	·	·	PUNCT
ejpam-4101	183	60	+	+	NUM
ejpam-4101	183	61	ξ2p	ξ2p	NUM
ejpam-4101	183	62	−ξ2p+1	−ξ2p+1	NOUN
ejpam-4101	183	63	−	−	PROPN
ejpam-4101	183	64	ξ2p+2	ξ2p+2	NOUN
ejpam-4101	183	65	−	−	PROPN
ejpam-4101	183	66	·	·	PUNCT
ejpam-4101	183	67	·	·	PUNCT
ejpam-4101	183	68	·	·	PUNCT
ejpam-4101	184	1	−	−	NUM
ejpam-4101	184	2	ξ2n	ξ2n	NUM
ejpam-4101	184	3	)	)	PUNCT
ejpam-4101	184	4	2	2	NUM
ejpam-4101	184	5	)	)	PUNCT
ejpam-4101	184	6	k	k	NOUN
ejpam-4101	184	7	e−iξ·x	e−iξ·x	NOUN
ejpam-4101	184	8	〉	〉	NOUN
ejpam-4101	184	9	=	=	SYM
ejpam-4101	184	10	1	1	NUM
ejpam-4101	184	11	(	(	PUNCT
ejpam-4101	184	12	2π)n/2	2π)n/2	NUM
ejpam-4101	184	13	〈	〈	PROPN
ejpam-4101	184	14	δ	δ	PROPN
ejpam-4101	184	15	,	,	PUNCT
ejpam-4101	184	16	(	(	PUNCT
ejpam-4101	184	17	−1)2k	−1)2k	PROPN
ejpam-4101	184	18	2	2	NUM
ejpam-4101	184	19	(	(	PUNCT
ejpam-4101	184	20	(	(	PUNCT
ejpam-4101	184	21	ξ21	ξ21	NOUN
ejpam-4101	184	22	+	+	CCONJ
ejpam-4101	184	23	ξ22	ξ22	NOUN
ejpam-4101	184	24	+	+	X
ejpam-4101	184	25	·	·	PUNCT
ejpam-4101	184	26	·	·	PUNCT
ejpam-4101	184	27	·	·	PUNCT
ejpam-4101	185	1	+	+	CCONJ
ejpam-4101	185	2	ξ2n	ξ2n	NUM
ejpam-4101	185	3	)	)	PUNCT
ejpam-4101	185	4	2	2	NUM
ejpam-4101	186	1	+	+	CCONJ
ejpam-4101	186	2	(	(	PUNCT
ejpam-4101	186	3	ξ21	ξ21	NOUN
ejpam-4101	186	4	+	+	CCONJ
ejpam-4101	186	5	ξ22	ξ22	NOUN
ejpam-4101	186	6	+	+	X
ejpam-4101	186	7	·	·	PUNCT
ejpam-4101	186	8	·	·	PUNCT
ejpam-4101	186	9	·	·	PUNCT
ejpam-4101	187	1	+	+	NUM
ejpam-4101	187	2	ξ2p	ξ2p	NUM
ejpam-4101	187	3	−ξ2p+1	−ξ2p+1	NOUN
ejpam-4101	187	4	−	−	PROPN
ejpam-4101	187	5	ξ2p+2	ξ2p+2	NOUN
ejpam-4101	187	6	−	−	PROPN
ejpam-4101	187	7	·	·	PUNCT
ejpam-4101	187	8	·	·	PUNCT
ejpam-4101	187	9	·	·	PUNCT
ejpam-4101	188	1	−	−	NUM
ejpam-4101	188	2	ξ2n	ξ2n	NUM
ejpam-4101	188	3	)	)	PUNCT
ejpam-4101	188	4	2	2	NUM
ejpam-4101	188	5	)	)	PUNCT
ejpam-4101	188	6	k	k	PROPN
ejpam-4101	188	7	(	(	PUNCT
ejpam-4101	188	8	♢	♢	PROPN
ejpam-4101	188	9	+	+	NOUN
ejpam-4101	188	10	m2)ke−iξ·x	m2)ke−iξ·x	NOUN
ejpam-4101	188	11	〉	〉	NOUN
ejpam-4101	188	12	=	=	SYM
ejpam-4101	188	13	1	1	NUM
ejpam-4101	188	14	(	(	PUNCT
ejpam-4101	188	15	2π)n/2	2π)n/2	NUM
ejpam-4101	188	16	〈	〈	PROPN
ejpam-4101	188	17	δ	δ	PROPN
ejpam-4101	188	18	,	,	PUNCT
ejpam-4101	188	19			PROPN
ejpam-4101	188	20	(	(	PUNCT
ejpam-4101	188	21	p∑	p∑	NOUN
ejpam-4101	188	22	i=1	i=1	PROPN
ejpam-4101	188	23	ξ2i	ξ2i	PROPN
ejpam-4101	188	24	)	)	PUNCT
ejpam-4101	188	25	2	2	NUM
ejpam-4101	189	1	+	+	CCONJ
ejpam-4101	189	2			PROPN
ejpam-4101	189	3	p+q∑	p+q∑	PROPN
ejpam-4101	189	4	j	j	NOUN
ejpam-4101	189	5	=	=	VERB
ejpam-4101	189	6	p+1	p+1	PROPN
ejpam-4101	189	7	ξ2j	ξ2j	X
ejpam-4101	189	8	2k	2k	PUNCT
ejpam-4101	189	9			NOUN
ejpam-4101	189	10	(	(	PUNCT
ejpam-4101	189	11	p∑	p∑	NOUN
ejpam-4101	189	12	i=1	i=1	PROPN
ejpam-4101	189	13	ξ2i	ξ2i	PROPN
ejpam-4101	189	14	)	)	PUNCT
ejpam-4101	189	15	2	2	NUM
ejpam-4101	189	16	−	−	PROPN
ejpam-4101	189	17			PROPN
ejpam-4101	189	18	p+q∑	p+q∑	PROPN
ejpam-4101	189	19	j	j	NOUN
ejpam-4101	189	20	=	=	VERB
ejpam-4101	189	21	p+1	p+1	PROPN
ejpam-4101	189	22	ξ2j	ξ2j	X
ejpam-4101	189	23	2	2	VERB
ejpam-4101	190	1	+	+	VERB
ejpam-4101	190	2	m2	m2	PROPN
ejpam-4101	190	3	k	k	VERB
ejpam-4101	190	4	e−iξ·x	e−iξ·x	NOUN
ejpam-4101	190	5	〉	〉	NOUN
ejpam-4101	190	6	=	=	SYM
ejpam-4101	190	7	1	1	NUM
ejpam-4101	190	8	(	(	PUNCT
ejpam-4101	190	9	2π)n/2	2π)n/2	NUM
ejpam-4101	190	10	〈	〈	PROPN
ejpam-4101	190	11	δ	δ	PROPN
ejpam-4101	190	12	,	,	PUNCT
ejpam-4101	190	13			PUNCT
ejpam-4101	191	1			PROPN
ejpam-4101	191	2	(	(	PUNCT
ejpam-4101	191	3	p∑	p∑	NOUN
ejpam-4101	191	4	i=1	i=1	PROPN
ejpam-4101	191	5	ξ2i	ξ2i	PROPN
ejpam-4101	191	6	)	)	PUNCT
ejpam-4101	191	7	2	2	PROPN
ejpam-4101	191	8	+	+	NUM
ejpam-4101	191	9	m2	m2	PROPN
ejpam-4101	191	10	2	2	NUM
ejpam-4101	191	11	2	2	ADV
ejpam-4101	191	12	−	−	PUNCT
ejpam-4101	191	13			PROPN
ejpam-4101	191	14	p+q∑	p+q∑	PROPN
ejpam-4101	191	15	j	j	X
ejpam-4101	191	16	=	=	PROPN
ejpam-4101	191	17	p+1	p+1	PROPN
ejpam-4101	191	18	ξ2j	ξ2j	X
ejpam-4101	191	19	2	2	ADJ
ejpam-4101	192	1	−	−	PUNCT
ejpam-4101	193	1	m2	m2	PROPN
ejpam-4101	194	1	2	2	NUM
ejpam-4101	195	1	2	2	ADV
ejpam-4101	195	2			NUM
ejpam-4101	195	3	k	k	NOUN
ejpam-4101	195	4	e−iξ·x	e−iξ·x	NOUN
ejpam-4101	195	5	〉	〉	NOUN
ejpam-4101	195	6	=	=	SYM
ejpam-4101	195	7	1	1	NUM
ejpam-4101	195	8	(	(	PUNCT
ejpam-4101	195	9	2π)n/2	2π)n/2	X
ejpam-4101	195	10			PUNCT
ejpam-4101	196	1			PROPN
ejpam-4101	196	2	(	(	PUNCT
ejpam-4101	196	3	p∑	p∑	NOUN
ejpam-4101	196	4	i=1	i=1	PROPN
ejpam-4101	196	5	ξ2i	ξ2i	PROPN
ejpam-4101	196	6	)	)	PUNCT
ejpam-4101	196	7	2	2	PROPN
ejpam-4101	196	8	+	+	NUM
ejpam-4101	196	9	m2	m2	PROPN
ejpam-4101	196	10	2	2	NUM
ejpam-4101	196	11	2	2	ADV
ejpam-4101	196	12	−	−	PUNCT
ejpam-4101	196	13			PROPN
ejpam-4101	196	14	p+q∑	p+q∑	PROPN
ejpam-4101	196	15	j	j	X
ejpam-4101	196	16	=	=	PROPN
ejpam-4101	196	17	p+1	p+1	PROPN
ejpam-4101	196	18	ξ2j	ξ2j	X
ejpam-4101	196	19	2	2	ADJ
ejpam-4101	197	1	−	−	PUNCT
ejpam-4101	198	1	m2	m2	PROPN
ejpam-4101	199	1	2	2	NUM
ejpam-4101	200	1	2	2	ADV
ejpam-4101	200	2			NUM
ejpam-4101	200	3	k	k	NOUN
ejpam-4101	201	1	=	=	SYM
ejpam-4101	201	2	1	1	NUM
ejpam-4101	201	3	(	(	PUNCT
ejpam-4101	201	4	2π)n/2	2π)n/2	NUM
ejpam-4101	201	5	[	[	X
ejpam-4101	201	6	(	(	PUNCT
ejpam-4101	201	7	(	(	PUNCT
ejpam-4101	201	8	ξ21	ξ21	NOUN
ejpam-4101	201	9	+	+	CCONJ
ejpam-4101	201	10	ξ22	ξ22	NOUN
ejpam-4101	201	11	+	+	X
ejpam-4101	201	12	·	·	PUNCT
ejpam-4101	201	13	·	·	PUNCT
ejpam-4101	201	14	·	·	PUNCT
ejpam-4101	201	15	+	+	NUM
ejpam-4101	201	16	ξ2p	ξ2p	NUM
ejpam-4101	201	17	)	)	PUNCT
ejpam-4101	201	18	2	2	NUM
ejpam-4101	201	19	+	+	NUM
ejpam-4101	201	20	m2	m2	PROPN
ejpam-4101	201	21	2	2	NUM
ejpam-4101	201	22	)	)	SYM
ejpam-4101	201	23	2	2	NUM
ejpam-4101	201	24	−	−	NOUN
ejpam-4101	201	25	(	(	PUNCT
ejpam-4101	201	26	(	(	PUNCT
ejpam-4101	201	27	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	201	28	+	+	CCONJ
ejpam-4101	202	1	ξ2p+2	ξ2p+2	VERB
ejpam-4101	202	2	+	+	X
ejpam-4101	202	3	·	·	PUNCT
ejpam-4101	202	4	·	·	PUNCT
ejpam-4101	202	5	·	·	PUNCT
ejpam-4101	202	6	+	+	NUM
ejpam-4101	202	7	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	202	8	)	)	PUNCT
ejpam-4101	202	9	2	2	NUM
ejpam-4101	202	10	−	−	NOUN
ejpam-4101	202	11	m2	m2	PROPN
ejpam-4101	202	12	2	2	NUM
ejpam-4101	202	13	)	)	PUNCT
ejpam-4101	202	14	2	2	NUM
ejpam-4101	202	15	]	]	SYM
ejpam-4101	202	16	k	k	X
ejpam-4101	202	17	.	.	PUNCT
ejpam-4101	203	1	s.	s.	PROPN
ejpam-4101	203	2	bupasiri	bupasiri	PROPN
ejpam-4101	203	3	/	/	SYM
ejpam-4101	203	4	eur	eur	PROPN
ejpam-4101	203	5	.	.	PUNCT
ejpam-4101	204	1	j.	j.	PROPN
ejpam-4101	204	2	pure	pure	PROPN
ejpam-4101	204	3	appl	appl	PROPN
ejpam-4101	204	4	.	.	PROPN
ejpam-4101	204	5	math	math	PROPN
ejpam-4101	204	6	,	,	PUNCT
ejpam-4101	204	7	14	14	NUM
ejpam-4101	204	8	(	(	PUNCT
ejpam-4101	204	9	4	4	NUM
ejpam-4101	204	10	)	)	PUNCT
ejpam-4101	204	11	(	(	PUNCT
ejpam-4101	204	12	2021	2021	NUM
ejpam-4101	204	13	)	)	PUNCT
ejpam-4101	204	14	,	,	PUNCT
ejpam-4101	204	15	1306	1306	NUM
ejpam-4101	204	16	-	-	SYM
ejpam-4101	204	17	1323	1323	NUM
ejpam-4101	204	18	1314	1314	NUM
ejpam-4101	204	19	next	next	ADV
ejpam-4101	204	20	,	,	PUNCT
ejpam-4101	204	21	we	we	PRON
ejpam-4101	204	22	consider	consider	VERB
ejpam-4101	204	23	the	the	DET
ejpam-4101	204	24	boundedness	boundedness	NOUN
ejpam-4101	204	25	of	of	ADP
ejpam-4101	204	26	f	f	PROPN
ejpam-4101	204	27	(	(	PUNCT
ejpam-4101	204	28	(	(	PUNCT
ejpam-4101	204	29	♢	♢	PROPN
ejpam-4101	204	30	+	+	PROPN
ejpam-4101	204	31	m2	m2	X
ejpam-4101	204	32	)	)	PUNCT
ejpam-4101	204	33	(	(	PUNCT
ejpam-4101	204	34	△	△	X
ejpam-4101	204	35	2+⊡2	2+⊡2	NUM
ejpam-4101	204	36	2	2	NUM
ejpam-4101	204	37	)	)	PUNCT
ejpam-4101	204	38	)	)	PUNCT
ejpam-4101	205	1	k	k	PROPN
ejpam-4101	205	2	δ	δ	PROPN
ejpam-4101	205	3	.	.	PUNCT
ejpam-4101	206	1	since	since	SCONJ
ejpam-4101	206	2	(	(	PUNCT
ejpam-4101	206	3	(	(	PUNCT
ejpam-4101	206	4	♢	♢	PROPN
ejpam-4101	206	5	+	+	PROPN
ejpam-4101	206	6	m2	m2	X
ejpam-4101	206	7	)	)	PUNCT
ejpam-4101	206	8	(	(	PUNCT
ejpam-4101	206	9	△	△	X
ejpam-4101	206	10	2	2	NUM
ejpam-4101	206	11	+	+	NOUN
ejpam-4101	206	12	⊡2	⊡2	PROPN
ejpam-4101	206	13	2	2	NUM
ejpam-4101	206	14	)	)	PUNCT
ejpam-4101	206	15	)	)	PUNCT
ejpam-4101	206	16	k	k	X
ejpam-4101	207	1	=	=	PUNCT
ejpam-4101	208	1	[	[	X
ejpam-4101	208	2	(	(	PUNCT
ejpam-4101	208	3	(	(	PUNCT
ejpam-4101	208	4	ξ21	ξ21	NOUN
ejpam-4101	208	5	+	+	CCONJ
ejpam-4101	208	6	ξ22	ξ22	NOUN
ejpam-4101	208	7	+	+	X
ejpam-4101	208	8	·	·	PUNCT
ejpam-4101	208	9	·	·	PUNCT
ejpam-4101	208	10	·	·	PUNCT
ejpam-4101	208	11	+	+	NUM
ejpam-4101	208	12	ξ2p	ξ2p	NUM
ejpam-4101	208	13	)	)	PUNCT
ejpam-4101	208	14	2	2	NUM
ejpam-4101	208	15	+	+	NUM
ejpam-4101	208	16	m2	m2	PROPN
ejpam-4101	208	17	2	2	NUM
ejpam-4101	208	18	)	)	SYM
ejpam-4101	208	19	2	2	NUM
ejpam-4101	208	20	−	−	NOUN
ejpam-4101	208	21	(	(	PUNCT
ejpam-4101	208	22	(	(	PUNCT
ejpam-4101	208	23	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	208	24	+	+	CCONJ
ejpam-4101	208	25	ξ2p+2	ξ2p+2	VERB
ejpam-4101	208	26	+	+	X
ejpam-4101	208	27	·	·	PUNCT
ejpam-4101	208	28	·	·	PUNCT
ejpam-4101	208	29	·	·	PUNCT
ejpam-4101	208	30	+	+	NUM
ejpam-4101	208	31	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	208	32	)	)	PUNCT
ejpam-4101	208	33	2	2	NUM
ejpam-4101	208	34	−	−	NOUN
ejpam-4101	208	35	m2	m2	PROPN
ejpam-4101	208	36	2	2	NUM
ejpam-4101	208	37	)	)	PUNCT
ejpam-4101	208	38	2	2	NUM
ejpam-4101	208	39	]	]	SYM
ejpam-4101	208	40	k	k	X
ejpam-4101	209	1	=	=	PUNCT
ejpam-4101	210	1	[	[	X
ejpam-4101	210	2	(	(	PUNCT
ejpam-4101	210	3	(	(	PUNCT
ejpam-4101	210	4	ξ21	ξ21	NOUN
ejpam-4101	210	5	+	+	CCONJ
ejpam-4101	210	6	ξ22	ξ22	NOUN
ejpam-4101	210	7	+	+	X
ejpam-4101	210	8	·	·	PUNCT
ejpam-4101	210	9	·	·	PUNCT
ejpam-4101	210	10	·	·	PUNCT
ejpam-4101	210	11	+	+	NUM
ejpam-4101	210	12	ξ2p	ξ2p	NUM
ejpam-4101	210	13	)	)	PUNCT
ejpam-4101	210	14	2	2	NUM
ejpam-4101	210	15	−	−	NOUN
ejpam-4101	210	16	(	(	PUNCT
ejpam-4101	210	17	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	210	18	+	+	CCONJ
ejpam-4101	211	1	ξ2p+2	ξ2p+2	VERB
ejpam-4101	211	2	+	+	X
ejpam-4101	211	3	·	·	PUNCT
ejpam-4101	211	4	·	·	PUNCT
ejpam-4101	211	5	·	·	PUNCT
ejpam-4101	211	6	+	+	CCONJ
ejpam-4101	211	7	ξ2n	ξ2n	NUM
ejpam-4101	211	8	)	)	PUNCT
ejpam-4101	211	9	2	2	NUM
ejpam-4101	211	10	+	+	NOUN
ejpam-4101	211	11	m2	m2	NOUN
ejpam-4101	211	12	)	)	PUNCT
ejpam-4101	211	13	k	k	PROPN
ejpam-4101	211	14	×	×	PROPN
ejpam-4101	211	15	(	(	PUNCT
ejpam-4101	211	16	(	(	PUNCT
ejpam-4101	211	17	ξ21	ξ21	NOUN
ejpam-4101	211	18	+	+	CCONJ
ejpam-4101	211	19	ξ22	ξ22	NOUN
ejpam-4101	211	20	+	+	X
ejpam-4101	211	21	·	·	PUNCT
ejpam-4101	211	22	·	·	PUNCT
ejpam-4101	211	23	·	·	PUNCT
ejpam-4101	211	24	+	+	NUM
ejpam-4101	211	25	ξ2p	ξ2p	NUM
ejpam-4101	211	26	)	)	PUNCT
ejpam-4101	211	27	2	2	NUM
ejpam-4101	211	28	+	+	CCONJ
ejpam-4101	211	29	(	(	PUNCT
ejpam-4101	211	30	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	211	31	+	+	CCONJ
ejpam-4101	212	1	ξ2p+2	ξ2p+2	VERB
ejpam-4101	212	2	+	+	X
ejpam-4101	212	3	·	·	PUNCT
ejpam-4101	212	4	·	·	PUNCT
ejpam-4101	212	5	·	·	PUNCT
ejpam-4101	212	6	+	+	CCONJ
ejpam-4101	212	7	ξ2n	ξ2n	NUM
ejpam-4101	212	8	)	)	PUNCT
ejpam-4101	212	9	2	2	NUM
ejpam-4101	213	1	)	)	PUNCT
ejpam-4101	213	2	k	k	X
ejpam-4101	213	3	]	]	X
ejpam-4101	213	4	=	=	PUNCT
ejpam-4101	214	1	[	[	X
ejpam-4101	214	2	(	(	PUNCT
ejpam-4101	214	3	(	(	PUNCT
ejpam-4101	214	4	ξ21	ξ21	NOUN
ejpam-4101	214	5	+	+	CCONJ
ejpam-4101	214	6	ξ22	ξ22	NOUN
ejpam-4101	214	7	+	+	X
ejpam-4101	214	8	·	·	PUNCT
ejpam-4101	214	9	·	·	PUNCT
ejpam-4101	214	10	·	·	PUNCT
ejpam-4101	214	11	+	+	NUM
ejpam-4101	214	12	ξ2n)(ξ	ξ2n)(ξ	PROPN
ejpam-4101	214	13	2	2	NUM
ejpam-4101	214	14	1	1	NUM
ejpam-4101	214	15	+	+	NUM
ejpam-4101	214	16	·	·	PUNCT
ejpam-4101	214	17	·	·	PUNCT
ejpam-4101	214	18	·	·	PUNCT
ejpam-4101	214	19	+	+	CCONJ
ejpam-4101	214	20	ξ2p	ξ2p	NUM
ejpam-4101	214	21	−	−	NOUN
ejpam-4101	214	22	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	214	23	−	−	PROPN
ejpam-4101	214	24	·	·	PUNCT
ejpam-4101	214	25	·	·	PUNCT
ejpam-4101	214	26	·	·	PUNCT
ejpam-4101	215	1	−	−	NUM
ejpam-4101	215	2	ξ2n	ξ2n	NUM
ejpam-4101	215	3	)	)	PUNCT
ejpam-4101	216	1	+	+	NOUN
ejpam-4101	216	2	m2	m2	PROPN
ejpam-4101	216	3	)	)	PUNCT
ejpam-4101	216	4	k	k	PROPN
ejpam-4101	216	5	×	×	PROPN
ejpam-4101	216	6	(	(	PUNCT
ejpam-4101	216	7	(	(	PUNCT
ejpam-4101	216	8	ξ21	ξ21	NOUN
ejpam-4101	216	9	+	+	CCONJ
ejpam-4101	216	10	ξ22	ξ22	NOUN
ejpam-4101	216	11	+	+	X
ejpam-4101	216	12	·	·	PUNCT
ejpam-4101	216	13	·	·	PUNCT
ejpam-4101	216	14	·	·	PUNCT
ejpam-4101	216	15	+	+	NUM
ejpam-4101	216	16	ξ2p	ξ2p	NUM
ejpam-4101	216	17	)	)	PUNCT
ejpam-4101	216	18	2	2	NUM
ejpam-4101	216	19	+	+	CCONJ
ejpam-4101	216	20	(	(	PUNCT
ejpam-4101	216	21	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	216	22	+	+	X
ejpam-4101	216	23	·	·	PUNCT
ejpam-4101	216	24	·	·	PUNCT
ejpam-4101	216	25	·	·	PUNCT
ejpam-4101	216	26	+	+	CCONJ
ejpam-4101	216	27	ξ2n	ξ2n	NUM
ejpam-4101	216	28	)	)	PUNCT
ejpam-4101	216	29	2	2	NUM
ejpam-4101	216	30	)	)	PUNCT
ejpam-4101	216	31	k	k	NOUN
ejpam-4101	216	32	]	]	PUNCT
ejpam-4101	216	33	.	.	PUNCT
ejpam-4101	217	1	thus	thus	ADV
ejpam-4101	217	2	f	f	X
ejpam-4101	217	3	(	(	PUNCT
ejpam-4101	217	4	(	(	PUNCT
ejpam-4101	217	5	♢	♢	PROPN
ejpam-4101	217	6	+	+	PROPN
ejpam-4101	217	7	m2	m2	X
ejpam-4101	217	8	)	)	PUNCT
ejpam-4101	217	9	(	(	PUNCT
ejpam-4101	217	10	△	△	X
ejpam-4101	217	11	2	2	NUM
ejpam-4101	217	12	+	+	NOUN
ejpam-4101	217	13	⊡2	⊡2	PROPN
ejpam-4101	217	14	2	2	NUM
ejpam-4101	217	15	)	)	PUNCT
ejpam-4101	217	16	)	)	PUNCT
ejpam-4101	218	1	k	k	PROPN
ejpam-4101	218	2	δ	δ	PROPN
ejpam-4101	218	3	=	=	SYM
ejpam-4101	218	4	1	1	NUM
ejpam-4101	218	5	(	(	PUNCT
ejpam-4101	218	6	2π)n/2	2π)n/2	NUM
ejpam-4101	218	7	[	[	X
ejpam-4101	218	8	(	(	PUNCT
ejpam-4101	218	9	(	(	PUNCT
ejpam-4101	218	10	ξ21	ξ21	NOUN
ejpam-4101	218	11	+	+	CCONJ
ejpam-4101	218	12	ξ22	ξ22	NOUN
ejpam-4101	218	13	+	+	X
ejpam-4101	218	14	·	·	PUNCT
ejpam-4101	218	15	·	·	PUNCT
ejpam-4101	218	16	·	·	PUNCT
ejpam-4101	218	17	+	+	NUM
ejpam-4101	218	18	ξ2n)(ξ	ξ2n)(ξ	PROPN
ejpam-4101	218	19	2	2	NUM
ejpam-4101	218	20	1	1	NUM
ejpam-4101	218	21	+	+	NUM
ejpam-4101	218	22	·	·	PUNCT
ejpam-4101	218	23	·	·	PUNCT
ejpam-4101	218	24	·	·	PUNCT
ejpam-4101	218	25	+	+	CCONJ
ejpam-4101	218	26	ξ2p	ξ2p	NUM
ejpam-4101	218	27	−	−	NOUN
ejpam-4101	218	28	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	218	29	−	−	PROPN
ejpam-4101	218	30	·	·	PUNCT
ejpam-4101	218	31	·	·	PUNCT
ejpam-4101	218	32	·	·	PUNCT
ejpam-4101	219	1	−	−	NUM
ejpam-4101	219	2	ξ2n	ξ2n	NUM
ejpam-4101	219	3	)	)	PUNCT
ejpam-4101	220	1	+	+	NOUN
ejpam-4101	220	2	m2	m2	PROPN
ejpam-4101	220	3	)	)	PUNCT
ejpam-4101	220	4	k	k	PROPN
ejpam-4101	220	5	×	×	PROPN
ejpam-4101	220	6	(	(	PUNCT
ejpam-4101	220	7	(	(	PUNCT
ejpam-4101	220	8	ξ21	ξ21	NOUN
ejpam-4101	220	9	+	+	CCONJ
ejpam-4101	220	10	ξ22	ξ22	NOUN
ejpam-4101	220	11	+	+	X
ejpam-4101	220	12	·	·	PUNCT
ejpam-4101	220	13	·	·	PUNCT
ejpam-4101	220	14	·	·	PUNCT
ejpam-4101	220	15	+	+	NUM
ejpam-4101	220	16	ξ2p	ξ2p	NUM
ejpam-4101	220	17	)	)	PUNCT
ejpam-4101	220	18	2	2	NUM
ejpam-4101	220	19	+	+	CCONJ
ejpam-4101	220	20	(	(	PUNCT
ejpam-4101	220	21	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	220	22	+	+	X
ejpam-4101	220	23	·	·	PUNCT
ejpam-4101	220	24	·	·	PUNCT
ejpam-4101	220	25	·	·	PUNCT
ejpam-4101	220	26	+	+	CCONJ
ejpam-4101	220	27	ξ2n	ξ2n	NUM
ejpam-4101	220	28	)	)	PUNCT
ejpam-4101	220	29	2	2	NUM
ejpam-4101	220	30	)	)	PUNCT
ejpam-4101	220	31	k	k	X
ejpam-4101	220	32	]	]	PUNCT
ejpam-4101	220	33	,	,	PUNCT
ejpam-4101	220	34	∣∣∣∣∣f	∣∣∣∣∣f	NOUN
ejpam-4101	220	35	(	(	PUNCT
ejpam-4101	220	36	(	(	PUNCT
ejpam-4101	220	37	♢	♢	PROPN
ejpam-4101	220	38	+	+	PROPN
ejpam-4101	220	39	m2	m2	X
ejpam-4101	220	40	)	)	PUNCT
ejpam-4101	220	41	(	(	PUNCT
ejpam-4101	220	42	△	△	X
ejpam-4101	220	43	2	2	NUM
ejpam-4101	220	44	+	+	NOUN
ejpam-4101	220	45	⊡2	⊡2	PROPN
ejpam-4101	220	46	2	2	NUM
ejpam-4101	220	47	)	)	PUNCT
ejpam-4101	220	48	)	)	PUNCT
ejpam-4101	221	1	k	k	PROPN
ejpam-4101	221	2	δ	δ	PROPN
ejpam-4101	221	3	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4101	222	1	=	=	SYM
ejpam-4101	222	2	1	1	NUM
ejpam-4101	222	3	(	(	PUNCT
ejpam-4101	222	4	2π)n/2	2π)n/2	X
ejpam-4101	222	5	(	(	PUNCT
ejpam-4101	222	6	∣∣ξ21	∣∣ξ21	PROPN
ejpam-4101	222	7	+	+	CCONJ
ejpam-4101	222	8	ξ22	ξ22	NOUN
ejpam-4101	222	9	+	+	X
ejpam-4101	222	10	·	·	PUNCT
ejpam-4101	222	11	·	·	PUNCT
ejpam-4101	222	12	·	·	PUNCT
ejpam-4101	222	13	+	+	CCONJ
ejpam-4101	222	14	ξ2n	ξ2n	PROPN
ejpam-4101	222	15	∣∣	∣∣	X
ejpam-4101	222	16	∣∣ξ21	∣∣ξ21	PROPN
ejpam-4101	222	17	+	+	CCONJ
ejpam-4101	222	18	·	·	PUNCT
ejpam-4101	222	19	·	·	PUNCT
ejpam-4101	222	20	·	·	PUNCT
ejpam-4101	222	21	+	+	CCONJ
ejpam-4101	222	22	ξ2p	ξ2p	NUM
ejpam-4101	222	23	−	−	NOUN
ejpam-4101	222	24	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	222	25	−	−	PROPN
ejpam-4101	222	26	·	·	PUNCT
ejpam-4101	222	27	·	·	PUNCT
ejpam-4101	222	28	·	·	PUNCT
ejpam-4101	223	1	−	−	NUM
ejpam-4101	224	1	ξ2n	ξ2n	PROPN
ejpam-4101	224	2	∣∣+m2	∣∣+m2	NUM
ejpam-4101	224	3	)	)	PUNCT
ejpam-4101	225	1	k	k	PROPN
ejpam-4101	225	2	×	×	NOUN
ejpam-4101	225	3	∣∣((ξ21	∣∣((ξ21	PROPN
ejpam-4101	225	4	+	+	CCONJ
ejpam-4101	225	5	ξ22	ξ22	ADJ
ejpam-4101	225	6	+	+	X
ejpam-4101	225	7	·	·	PUNCT
ejpam-4101	225	8	·	·	PUNCT
ejpam-4101	225	9	·	·	PUNCT
ejpam-4101	225	10	+	+	NUM
ejpam-4101	225	11	ξ2p	ξ2p	NUM
ejpam-4101	225	12	)	)	PUNCT
ejpam-4101	225	13	2	2	NUM
ejpam-4101	225	14	+	+	CCONJ
ejpam-4101	225	15	(	(	PUNCT
ejpam-4101	225	16	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	225	17	+	+	X
ejpam-4101	225	18	·	·	PUNCT
ejpam-4101	225	19	·	·	PUNCT
ejpam-4101	225	20	·	·	PUNCT
ejpam-4101	225	21	+	+	CCONJ
ejpam-4101	225	22	ξ2n	ξ2n	NUM
ejpam-4101	225	23	)	)	PUNCT
ejpam-4101	225	24	2	2	NUM
ejpam-4101	225	25	)	)	PUNCT
ejpam-4101	225	26	∣∣k	∣∣k	PROPN
ejpam-4101	225	27	≤	≤	NUM
ejpam-4101	225	28	1	1	NUM
ejpam-4101	225	29	(	(	PUNCT
ejpam-4101	225	30	2π)n/2	2π)n/2	X
ejpam-4101	225	31	(	(	PUNCT
ejpam-4101	225	32	∣∣ξ21	∣∣ξ21	PROPN
ejpam-4101	225	33	+	+	CCONJ
ejpam-4101	225	34	ξ22	ξ22	NOUN
ejpam-4101	225	35	+	+	X
ejpam-4101	225	36	·	·	PUNCT
ejpam-4101	225	37	·	·	PUNCT
ejpam-4101	225	38	·	·	PUNCT
ejpam-4101	225	39	+	+	NUM
ejpam-4101	225	40	ξ2n	ξ2n	PROPN
ejpam-4101	225	41	∣∣2	∣∣2	PROPN
ejpam-4101	225	42	+	+	NUM
ejpam-4101	225	43	m2	m2	PROPN
ejpam-4101	225	44	)	)	PUNCT
ejpam-4101	225	45	k	k	PROPN
ejpam-4101	225	46	∣∣ξ21	∣∣ξ21	PROPN
ejpam-4101	226	1	+	+	CCONJ
ejpam-4101	226	2	ξ22	ξ22	NOUN
ejpam-4101	226	3	+	+	X
ejpam-4101	226	4	·	·	PUNCT
ejpam-4101	226	5	·	·	PUNCT
ejpam-4101	226	6	·	·	PUNCT
ejpam-4101	226	7	+	+	CCONJ
ejpam-4101	226	8	ξ2n	ξ2n	PROPN
ejpam-4101	227	1	∣∣2k	∣∣2k	ADP
ejpam-4101	227	2	=	=	SYM
ejpam-4101	227	3	1	1	NUM
ejpam-4101	227	4	(	(	PUNCT
ejpam-4101	227	5	2π)n/2	2π)n/2	NUM
ejpam-4101	227	6	(	(	PUNCT
ejpam-4101	227	7	||ξ||4	||ξ||4	PROPN
ejpam-4101	227	8	+	+	PROPN
ejpam-4101	227	9	m2)k||ξ||4k	m2)k||ξ||4k	NOUN
ejpam-4101	227	10	,	,	PUNCT
ejpam-4101	227	11	where	where	SCONJ
ejpam-4101	227	12	||ξ||	||ξ||	VERB
ejpam-4101	227	13	=	=	SYM
ejpam-4101	227	14	(	(	PUNCT
ejpam-4101	227	15	ξ21	ξ21	NOUN
ejpam-4101	227	16	+	+	CCONJ
ejpam-4101	227	17	ξ22	ξ22	NOUN
ejpam-4101	227	18	+	+	X
ejpam-4101	227	19	·	·	PUNCT
ejpam-4101	227	20	·	·	PUNCT
ejpam-4101	227	21	·	·	PUNCT
ejpam-4101	228	1	+	+	NUM
ejpam-4101	228	2	ξ2n	ξ2n	PROPN
ejpam-4101	228	3	)	)	PUNCT
ejpam-4101	228	4	1/2	1/2	NUM
ejpam-4101	228	5	,	,	PUNCT
ejpam-4101	228	6	ξi(i	ξi(i	X
ejpam-4101	228	7	=	=	SYM
ejpam-4101	228	8	1	1	NUM
ejpam-4101	228	9	,	,	PUNCT
ejpam-4101	228	10	2	2	NUM
ejpam-4101	228	11	,	,	PUNCT
ejpam-4101	228	12	.	.	PUNCT
ejpam-4101	228	13	.	.	PUNCT
ejpam-4101	229	1	.	.	PUNCT
ejpam-4101	230	1	,	,	PUNCT
ejpam-4101	230	2	n	n	CCONJ
ejpam-4101	230	3	)	)	PUNCT
ejpam-4101	230	4	∈	∈	PROPN
ejpam-4101	230	5	r.	r.	PROPN
ejpam-4101	230	6	hence	hence	ADV
ejpam-4101	230	7	,	,	PUNCT
ejpam-4101	230	8	we	we	PRON
ejpam-4101	230	9	obtain	obtain	VERB
ejpam-4101	230	10	f	f	X
ejpam-4101	230	11	(	(	PUNCT
ejpam-4101	230	12	(	(	PUNCT
ejpam-4101	230	13	♢	♢	PROPN
ejpam-4101	230	14	+	+	PROPN
ejpam-4101	230	15	m2	m2	X
ejpam-4101	230	16	)	)	PUNCT
ejpam-4101	230	17	(	(	PUNCT
ejpam-4101	230	18	△	△	X
ejpam-4101	230	19	2	2	NUM
ejpam-4101	230	20	+	+	NOUN
ejpam-4101	230	21	⊡2	⊡2	PROPN
ejpam-4101	230	22	2	2	NUM
ejpam-4101	230	23	)	)	PUNCT
ejpam-4101	230	24	)	)	PUNCT
ejpam-4101	231	1	k	k	PROPN
ejpam-4101	231	2	δ	δ	PROPN
ejpam-4101	231	3	is	be	AUX
ejpam-4101	231	4	bounded	bound	VERB
ejpam-4101	231	5	and	and	CCONJ
ejpam-4101	231	6	continuous	continuous	ADJ
ejpam-4101	231	7	on	on	ADP
ejpam-4101	231	8	the	the	DET
ejpam-4101	231	9	space	space	NOUN
ejpam-4101	231	10	s	s	PART
ejpam-4101	231	11	′	′	NOUN
ejpam-4101	231	12	of	of	ADP
ejpam-4101	231	13	the	the	DET
ejpam-4101	231	14	tempered	temper	VERB
ejpam-4101	231	15	distribution	distribution	NOUN
ejpam-4101	231	16	.	.	PUNCT
ejpam-4101	232	1	since	since	SCONJ
ejpam-4101	232	2	f	f	PROPN
ejpam-4101	232	3	is	be	AUX
ejpam-4101	232	4	1−	1−	NUM
ejpam-4101	232	5	1	1	NUM
ejpam-4101	232	6	transformation	transformation	NOUN
ejpam-4101	232	7	from	from	ADP
ejpam-4101	232	8	the	the	DET
ejpam-4101	232	9	space	space	NOUN
ejpam-4101	232	10	s	s	PART
ejpam-4101	232	11	′	′	NOUN
ejpam-4101	232	12	of	of	ADP
ejpam-4101	232	13	the	the	DET
ejpam-4101	232	14	tempered	temper	VERB
ejpam-4101	232	15	distribution	distribution	NOUN
ejpam-4101	232	16	to	to	ADP
ejpam-4101	232	17	the	the	DET
ejpam-4101	232	18	real	real	ADJ
ejpam-4101	232	19	space	space	NOUN
ejpam-4101	232	20	r	r	NOUN
ejpam-4101	232	21	,	,	PUNCT
ejpam-4101	232	22	then	then	ADV
ejpam-4101	232	23	by	by	ADP
ejpam-4101	232	24	(	(	PUNCT
ejpam-4101	232	25	17	17	NUM
ejpam-4101	232	26	)	)	PUNCT
ejpam-4101	232	27	,	,	PUNCT
ejpam-4101	232	28	we	we	PRON
ejpam-4101	232	29	have	have	VERB
ejpam-4101	232	30	(	(	PUNCT
ejpam-4101	232	31	(	(	PUNCT
ejpam-4101	232	32	♢	♢	PROPN
ejpam-4101	232	33	+	+	PROPN
ejpam-4101	232	34	m2	m2	X
ejpam-4101	232	35	)	)	PUNCT
ejpam-4101	232	36	(	(	PUNCT
ejpam-4101	232	37	△	△	X
ejpam-4101	232	38	2	2	NUM
ejpam-4101	232	39	+	+	NOUN
ejpam-4101	232	40	⊡2	⊡2	PROPN
ejpam-4101	232	41	2	2	NUM
ejpam-4101	232	42	)	)	PUNCT
ejpam-4101	232	43	)	)	PUNCT
ejpam-4101	233	1	k	k	PROPN
ejpam-4101	233	2	δ	δ	PROPN
ejpam-4101	233	3	s.	s.	PROPN
ejpam-4101	233	4	bupasiri	bupasiri	PROPN
ejpam-4101	233	5	/	/	SYM
ejpam-4101	233	6	eur	eur	PROPN
ejpam-4101	233	7	.	.	PUNCT
ejpam-4101	234	1	j.	j.	PROPN
ejpam-4101	234	2	pure	pure	PROPN
ejpam-4101	234	3	appl	appl	PROPN
ejpam-4101	234	4	.	.	PROPN
ejpam-4101	234	5	math	math	PROPN
ejpam-4101	234	6	,	,	PUNCT
ejpam-4101	234	7	14	14	NUM
ejpam-4101	234	8	(	(	PUNCT
ejpam-4101	234	9	4	4	NUM
ejpam-4101	234	10	)	)	PUNCT
ejpam-4101	234	11	(	(	PUNCT
ejpam-4101	234	12	2021	2021	NUM
ejpam-4101	234	13	)	)	PUNCT
ejpam-4101	234	14	,	,	PUNCT
ejpam-4101	234	15	1306	1306	NUM
ejpam-4101	234	16	-	-	SYM
ejpam-4101	234	17	1323	1323	NUM
ejpam-4101	234	18	1315	1315	NUM
ejpam-4101	234	19	=	=	SYM
ejpam-4101	234	20	1	1	NUM
ejpam-4101	234	21	(	(	PUNCT
ejpam-4101	234	22	2π)n/2	2π)n/2	NUM
ejpam-4101	234	23	f−1	f−1	PROPN
ejpam-4101	235	1	[	[	X
ejpam-4101	235	2	(	(	PUNCT
ejpam-4101	235	3	(	(	PUNCT
ejpam-4101	235	4	ξ21	ξ21	NOUN
ejpam-4101	235	5	+	+	CCONJ
ejpam-4101	235	6	ξ22	ξ22	NOUN
ejpam-4101	235	7	+	+	X
ejpam-4101	235	8	·	·	PUNCT
ejpam-4101	235	9	·	·	PUNCT
ejpam-4101	235	10	·	·	PUNCT
ejpam-4101	235	11	+	+	NUM
ejpam-4101	235	12	ξ2p	ξ2p	NUM
ejpam-4101	235	13	)	)	PUNCT
ejpam-4101	235	14	2	2	NUM
ejpam-4101	235	15	+	+	NUM
ejpam-4101	235	16	m2	m2	PROPN
ejpam-4101	235	17	2	2	NUM
ejpam-4101	235	18	)	)	SYM
ejpam-4101	235	19	2	2	NUM
ejpam-4101	235	20	−	−	NOUN
ejpam-4101	235	21	(	(	PUNCT
ejpam-4101	235	22	(	(	PUNCT
ejpam-4101	235	23	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	235	24	+	+	CCONJ
ejpam-4101	235	25	ξ2p+2	ξ2p+2	VERB
ejpam-4101	235	26	+	+	X
ejpam-4101	235	27	·	·	PUNCT
ejpam-4101	235	28	·	·	PUNCT
ejpam-4101	235	29	·	·	PUNCT
ejpam-4101	235	30	+	+	NUM
ejpam-4101	235	31	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	235	32	)	)	PUNCT
ejpam-4101	235	33	2	2	NUM
ejpam-4101	235	34	−	−	NOUN
ejpam-4101	235	35	m2	m2	PROPN
ejpam-4101	235	36	2	2	NUM
ejpam-4101	235	37	)	)	PUNCT
ejpam-4101	235	38	2	2	NUM
ejpam-4101	235	39	]	]	SYM
ejpam-4101	235	40	k	k	X
ejpam-4101	235	41	.	.	PUNCT
ejpam-4101	236	1	main	main	ADJ
ejpam-4101	236	2	results	result	NOUN
ejpam-4101	236	3	theorem	theorem	VERB
ejpam-4101	236	4	1	1	NUM
ejpam-4101	236	5	.	.	PUNCT
ejpam-4101	237	1	(	(	PUNCT
ejpam-4101	237	2	the	the	DET
ejpam-4101	237	3	fundamental	fundamental	ADJ
ejpam-4101	237	4	solution	solution	NOUN
ejpam-4101	237	5	of	of	ADP
ejpam-4101	237	6	(	(	PUNCT
ejpam-4101	237	7	(	(	PUNCT
ejpam-4101	237	8	♢	♢	PROPN
ejpam-4101	237	9	+	+	PROPN
ejpam-4101	237	10	m2	m2	X
ejpam-4101	237	11	)	)	PUNCT
ejpam-4101	237	12	(	(	PUNCT
ejpam-4101	237	13	△	△	X
ejpam-4101	237	14	2+⊡2	2+⊡2	NUM
ejpam-4101	237	15	2	2	NUM
ejpam-4101	237	16	)	)	PUNCT
ejpam-4101	237	17	)	)	PUNCT
ejpam-4101	238	1	k	k	X
ejpam-4101	238	2	)	)	PUNCT
ejpam-4101	238	3	.	.	PUNCT
ejpam-4101	239	1	given	give	VERB
ejpam-4101	239	2	the	the	DET
ejpam-4101	239	3	equation	equation	NOUN
ejpam-4101	239	4	(	(	PUNCT
ejpam-4101	239	5	(	(	PUNCT
ejpam-4101	239	6	♢	♢	PROPN
ejpam-4101	239	7	+	+	PROPN
ejpam-4101	239	8	m2	m2	X
ejpam-4101	239	9	)	)	PUNCT
ejpam-4101	239	10	(	(	PUNCT
ejpam-4101	239	11	△	△	X
ejpam-4101	239	12	2	2	NUM
ejpam-4101	239	13	+	+	NOUN
ejpam-4101	239	14	⊡2	⊡2	PROPN
ejpam-4101	239	15	2	2	NUM
ejpam-4101	239	16	)	)	PUNCT
ejpam-4101	239	17	)	)	PUNCT
ejpam-4101	240	1	k	k	PROPN
ejpam-4101	240	2	k(x	k(x	PROPN
ejpam-4101	240	3	,	,	PUNCT
ejpam-4101	240	4	m	m	NOUN
ejpam-4101	240	5	)	)	PUNCT
ejpam-4101	240	6	=	=	SYM
ejpam-4101	240	7	δ	δ	PROPN
ejpam-4101	240	8	,	,	PUNCT
ejpam-4101	240	9	(	(	PUNCT
ejpam-4101	240	10	31	31	NUM
ejpam-4101	240	11	)	)	PUNCT
ejpam-4101	240	12	where	where	SCONJ
ejpam-4101	240	13	(	(	PUNCT
ejpam-4101	240	14	(	(	PUNCT
ejpam-4101	240	15	♢	♢	PROPN
ejpam-4101	240	16	+	+	PROPN
ejpam-4101	240	17	m2	m2	X
ejpam-4101	240	18	)	)	PUNCT
ejpam-4101	240	19	(	(	PUNCT
ejpam-4101	240	20	△	△	X
ejpam-4101	240	21	2+⊡2	2+⊡2	NUM
ejpam-4101	240	22	2	2	NUM
ejpam-4101	240	23	)	)	PUNCT
ejpam-4101	240	24	)	)	PUNCT
ejpam-4101	241	1	k	k	PROPN
ejpam-4101	241	2	is	be	AUX
ejpam-4101	241	3	the	the	DET
ejpam-4101	241	4	operator	operator	NOUN
ejpam-4101	241	5	iterated	iterate	VERB
ejpam-4101	241	6	k	k	NOUN
ejpam-4101	241	7	-	-	PUNCT
ejpam-4101	241	8	times	time	NOUN
ejpam-4101	241	9	,	,	PUNCT
ejpam-4101	241	10	which	which	PRON
ejpam-4101	241	11	is	be	AUX
ejpam-4101	241	12	defined	define	VERB
ejpam-4101	241	13	by	by	ADP
ejpam-4101	241	14	(	(	PUNCT
ejpam-4101	241	15	10	10	NUM
ejpam-4101	241	16	)	)	PUNCT
ejpam-4101	241	17	,	,	PUNCT
ejpam-4101	241	18	δ	δ	PROPN
ejpam-4101	241	19	is	be	AUX
ejpam-4101	241	20	the	the	DET
ejpam-4101	241	21	dirac	dirac	NOUN
ejpam-4101	241	22	-	-	PUNCT
ejpam-4101	241	23	delta	delta	NOUN
ejpam-4101	241	24	function	function	NOUN
ejpam-4101	241	25	,	,	PUNCT
ejpam-4101	241	26	x	x	PROPN
ejpam-4101	241	27	∈	∈	PROPN
ejpam-4101	241	28	rn	rn	PROPN
ejpam-4101	241	29	,	,	PUNCT
ejpam-4101	241	30	m	m	VERB
ejpam-4101	241	31	is	be	AUX
ejpam-4101	241	32	a	a	DET
ejpam-4101	241	33	non	non	ADJ
ejpam-4101	241	34	-	-	ADJ
ejpam-4101	241	35	negative	negative	ADJ
ejpam-4101	241	36	real	real	ADJ
ejpam-4101	241	37	number	number	NOUN
ejpam-4101	241	38	and	and	CCONJ
ejpam-4101	241	39	k	k	PROPN
ejpam-4101	241	40	is	be	AUX
ejpam-4101	241	41	a	a	DET
ejpam-4101	241	42	non	non	ADJ
ejpam-4101	241	43	-	-	ADJ
ejpam-4101	241	44	negative	negative	ADJ
ejpam-4101	241	45	integer	integer	NOUN
ejpam-4101	241	46	.	.	PUNCT
ejpam-4101	242	1	then	then	ADV
ejpam-4101	242	2	,	,	PUNCT
ejpam-4101	242	3	we	we	PRON
ejpam-4101	242	4	obtain	obtain	VERB
ejpam-4101	242	5	k(x	k(x	PROPN
ejpam-4101	242	6	,	,	PUNCT
ejpam-4101	242	7	m	m	NOUN
ejpam-4101	242	8	)	)	PUNCT
ejpam-4101	242	9	=	=	SYM
ejpam-4101	242	10	(	(	PUNCT
ejpam-4101	242	11	rh	rh	PROPN
ejpam-4101	242	12	4k(x	4k(x	PROPN
ejpam-4101	242	13	)	)	PUNCT
ejpam-4101	243	1	∗	∗	NOUN
ejpam-4101	243	2	(	(	PUNCT
ejpam-4101	243	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	243	4	4k(x	4k(x	PROPN
ejpam-4101	243	5	)	)	PUNCT
ejpam-4101	243	6	∗	∗	NOUN
ejpam-4101	243	7	(	(	PUNCT
ejpam-4101	243	8	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	243	9	)	)	PUNCT
ejpam-4101	243	10	∗	∗	NOUN
ejpam-4101	243	11	p2k(x	p2k(x	PROPN
ejpam-4101	243	12	,	,	PUNCT
ejpam-4101	243	13	m	m	PROPN
ejpam-4101	243	14	)	)	PUNCT
ejpam-4101	243	15	(	(	PUNCT
ejpam-4101	243	16	32	32	NUM
ejpam-4101	243	17	)	)	PUNCT
ejpam-4101	243	18	is	be	AUX
ejpam-4101	243	19	the	the	DET
ejpam-4101	243	20	fundamental	fundamental	ADJ
ejpam-4101	243	21	solution	solution	NOUN
ejpam-4101	243	22	for	for	ADP
ejpam-4101	243	23	the	the	DET
ejpam-4101	243	24	operator	operator	NOUN
ejpam-4101	243	25	iterated	iterate	VERB
ejpam-4101	243	26	k	k	NOUN
ejpam-4101	243	27	-	-	PUNCT
ejpam-4101	243	28	times	time	NOUN
ejpam-4101	243	29	,	,	PUNCT
ejpam-4101	243	30	which	which	PRON
ejpam-4101	243	31	is	be	AUX
ejpam-4101	243	32	defined	define	VERB
ejpam-4101	243	33	by	by	ADP
ejpam-4101	243	34	(	(	PUNCT
ejpam-4101	243	35	10	10	NUM
ejpam-4101	243	36	)	)	PUNCT
ejpam-4101	243	37	.	.	PUNCT
ejpam-4101	244	1	in	in	ADP
ejpam-4101	244	2	particular	particular	ADJ
ejpam-4101	244	3	,	,	PUNCT
ejpam-4101	244	4	for	for	ADP
ejpam-4101	244	5	m	m	PROPN
ejpam-4101	244	6	=	=	SYM
ejpam-4101	244	7	0	0	NUM
ejpam-4101	244	8	then	then	ADV
ejpam-4101	244	9	(	(	PUNCT
ejpam-4101	244	10	31	31	NUM
ejpam-4101	244	11	)	)	PUNCT
ejpam-4101	244	12	becomes	become	VERB
ejpam-4101	244	13	⊕kk(x	⊕kk(x	PROPN
ejpam-4101	244	14	,	,	PUNCT
ejpam-4101	244	15	0	0	NUM
ejpam-4101	244	16	)	)	PUNCT
ejpam-4101	244	17	=	=	SYM
ejpam-4101	244	18	δ	δ	PROPN
ejpam-4101	244	19	,	,	PUNCT
ejpam-4101	244	20	(	(	PUNCT
ejpam-4101	244	21	33	33	NUM
ejpam-4101	244	22	)	)	PUNCT
ejpam-4101	244	23	and	and	CCONJ
ejpam-4101	244	24	we	we	PRON
ejpam-4101	244	25	obtain	obtain	VERB
ejpam-4101	244	26	k(x	k(x	PROPN
ejpam-4101	244	27	,	,	PUNCT
ejpam-4101	244	28	0	0	NUM
ejpam-4101	244	29	)	)	PUNCT
ejpam-4101	244	30	=	=	NOUN
ejpam-4101	245	1	(	(	PUNCT
ejpam-4101	245	2	rh	rh	PROPN
ejpam-4101	245	3	6k(x	6k(x	PROPN
ejpam-4101	245	4	)	)	PUNCT
ejpam-4101	246	1	∗	∗	NOUN
ejpam-4101	246	2	(	(	PUNCT
ejpam-4101	246	3	−1)3kre	−1)3kre	PROPN
ejpam-4101	246	4	6k(x	6k(x	NUM
ejpam-4101	246	5	)	)	PUNCT
ejpam-4101	246	6	)	)	PUNCT
ejpam-4101	247	1	∗	∗	NOUN
ejpam-4101	247	2	(	(	PUNCT
ejpam-4101	247	3	(	(	PUNCT
ejpam-4101	247	4	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	247	5	)	)	PUNCT
ejpam-4101	247	6	(	(	PUNCT
ejpam-4101	247	7	34	34	NUM
ejpam-4101	247	8	)	)	PUNCT
ejpam-4101	247	9	is	be	AUX
ejpam-4101	247	10	the	the	DET
ejpam-4101	247	11	fundamental	fundamental	ADJ
ejpam-4101	247	12	solution	solution	NOUN
ejpam-4101	247	13	of	of	ADP
ejpam-4101	247	14	the	the	DET
ejpam-4101	247	15	o	o	ADJ
ejpam-4101	247	16	-	-	ADJ
ejpam-4101	247	17	plus	plus	ADJ
ejpam-4101	247	18	operator	operator	NOUN
ejpam-4101	247	19	⊕k	⊕k	NOUN
ejpam-4101	247	20	,	,	PUNCT
ejpam-4101	247	21	for	for	ADP
ejpam-4101	247	22	q	q	NOUN
ejpam-4101	247	23	=	=	NOUN
ejpam-4101	247	24	m	m	NOUN
ejpam-4101	247	25	=	=	NOUN
ejpam-4101	247	26	0	0	PUNCT
ejpam-4101	247	27	then	then	ADV
ejpam-4101	247	28	(	(	PUNCT
ejpam-4101	247	29	31	31	NUM
ejpam-4101	247	30	)	)	PUNCT
ejpam-4101	247	31	becomes	become	VERB
ejpam-4101	247	32	△	△	NOUN
ejpam-4101	247	33	4k	4k	NOUN
ejpam-4101	247	34	p	p	ADJ
ejpam-4101	247	35	k(x	k(x	PROPN
ejpam-4101	247	36	,	,	PUNCT
ejpam-4101	247	37	0	0	NUM
ejpam-4101	247	38	)	)	PUNCT
ejpam-4101	247	39	=	=	SYM
ejpam-4101	247	40	δ	δ	PROPN
ejpam-4101	247	41	,	,	PUNCT
ejpam-4101	247	42	(	(	PUNCT
ejpam-4101	247	43	35	35	NUM
ejpam-4101	247	44	)	)	PUNCT
ejpam-4101	247	45	and	and	CCONJ
ejpam-4101	247	46	we	we	PRON
ejpam-4101	247	47	obtain	obtain	VERB
ejpam-4101	247	48	k(x	k(x	PROPN
ejpam-4101	247	49	,	,	PUNCT
ejpam-4101	247	50	0	0	NUM
ejpam-4101	247	51	)	)	PUNCT
ejpam-4101	247	52	=	=	SYM
ejpam-4101	247	53	re	re	NOUN
ejpam-4101	247	54	8k(x	8k(x	NUM
ejpam-4101	247	55	)	)	PUNCT
ejpam-4101	247	56	(	(	PUNCT
ejpam-4101	247	57	36	36	NUM
ejpam-4101	247	58	)	)	PUNCT
ejpam-4101	247	59	is	be	AUX
ejpam-4101	247	60	the	the	DET
ejpam-4101	247	61	fundamental	fundamental	ADJ
ejpam-4101	247	62	solution	solution	NOUN
ejpam-4101	247	63	of	of	ADP
ejpam-4101	247	64	(	(	PUNCT
ejpam-4101	247	65	35	35	NUM
ejpam-4101	247	66	)	)	PUNCT
ejpam-4101	247	67	,	,	PUNCT
ejpam-4101	247	68	where	where	SCONJ
ejpam-4101	247	69	△	△	NOUN
ejpam-4101	247	70	4k	4k	NOUN
ejpam-4101	247	71	p	p	NOUN
ejpam-4101	247	72	is	be	AUX
ejpam-4101	247	73	the	the	DET
ejpam-4101	247	74	laplace	laplace	NOUN
ejpam-4101	247	75	operator	operator	NOUN
ejpam-4101	247	76	of	of	ADP
ejpam-4101	247	77	p	p	NOUN
ejpam-4101	247	78	-	-	PUNCT
ejpam-4101	247	79	dimension	dimension	NOUN
ejpam-4101	247	80	,	,	PUNCT
ejpam-4101	247	81	iterated	iterate	VERB
ejpam-4101	247	82	4k	4k	NOUN
ejpam-4101	247	83	-	-	NOUN
ejpam-4101	247	84	times	time	NOUN
ejpam-4101	247	85	which	which	PRON
ejpam-4101	247	86	is	be	AUX
ejpam-4101	247	87	defined	define	VERB
ejpam-4101	247	88	by	by	ADP
ejpam-4101	247	89	(	(	PUNCT
ejpam-4101	247	90	11	11	NUM
ejpam-4101	247	91	)	)	PUNCT
ejpam-4101	247	92	.	.	PUNCT
ejpam-4101	248	1	moreover	moreover	ADV
ejpam-4101	248	2	,	,	PUNCT
ejpam-4101	248	3	from	from	ADP
ejpam-4101	248	4	(	(	PUNCT
ejpam-4101	248	5	34	34	NUM
ejpam-4101	248	6	)	)	PUNCT
ejpam-4101	248	7	,	,	PUNCT
ejpam-4101	248	8	we	we	PRON
ejpam-4101	248	9	obtain	obtain	VERB
ejpam-4101	248	10	(	(	PUNCT
ejpam-4101	248	11	rh	rh	PROPN
ejpam-4101	248	12	−4k(x	−4k(x	PROPN
ejpam-4101	248	13	)	)	PUNCT
ejpam-4101	248	14	∗	∗	NOUN
ejpam-4101	248	15	(	(	PUNCT
ejpam-4101	248	16	−1)3kre	−1)3kre	PROPN
ejpam-4101	248	17	−6k(x	−6k(x	NUM
ejpam-4101	248	18	)	)	PUNCT
ejpam-4101	248	19	)	)	PUNCT
ejpam-4101	249	1	∗	∗	NOUN
ejpam-4101	249	2	(	(	PUNCT
ejpam-4101	249	3	h∗k(x	h∗k(x	PROPN
ejpam-4101	249	4	)	)	PUNCT
ejpam-4101	249	5	)	)	PUNCT
ejpam-4101	250	1	∗k(x	∗k(x	PROPN
ejpam-4101	250	2	,	,	PUNCT
ejpam-4101	250	3	0	0	NUM
ejpam-4101	250	4	)	)	PUNCT
ejpam-4101	250	5	=	=	SYM
ejpam-4101	250	6	rh	rh	PROPN
ejpam-4101	250	7	2k(x	2k(x	PROPN
ejpam-4101	250	8	)	)	PUNCT
ejpam-4101	250	9	(	(	PUNCT
ejpam-4101	250	10	37	37	NUM
ejpam-4101	250	11	)	)	PUNCT
ejpam-4101	250	12	is	be	AUX
ejpam-4101	250	13	the	the	DET
ejpam-4101	250	14	fundamental	fundamental	ADJ
ejpam-4101	250	15	solution	solution	NOUN
ejpam-4101	250	16	of	of	ADP
ejpam-4101	250	17	the	the	DET
ejpam-4101	250	18	ultra	ultra	ADJ
ejpam-4101	250	19	-	-	ADJ
ejpam-4101	250	20	hyperbolic	hyperbolic	ADJ
ejpam-4101	250	21	operator	operator	NOUN
ejpam-4101	250	22	⊡k	⊡k	NOUN
ejpam-4101	250	23	iterated	iterate	VERB
ejpam-4101	250	24	k	k	NOUN
ejpam-4101	250	25	-	-	PUNCT
ejpam-4101	250	26	times	time	NOUN
ejpam-4101	250	27	,	,	PUNCT
ejpam-4101	250	28	which	which	PRON
ejpam-4101	250	29	defined	define	VERB
ejpam-4101	250	30	by	by	ADP
ejpam-4101	250	31	(	(	PUNCT
ejpam-4101	250	32	3	3	NUM
ejpam-4101	250	33	)	)	PUNCT
ejpam-4101	250	34	,	,	PUNCT
ejpam-4101	250	35	where	where	SCONJ
ejpam-4101	250	36	re	re	X
ejpam-4101	250	37	−6k(x	−6k(x	NUM
ejpam-4101	250	38	)	)	PUNCT
ejpam-4101	250	39	and	and	CCONJ
ejpam-4101	250	40	rh	rh	PROPN
ejpam-4101	250	41	−4k(x	−4k(x	PROPN
ejpam-4101	250	42	)	)	PUNCT
ejpam-4101	250	43	are	be	AUX
ejpam-4101	250	44	inverse	inverse	NOUN
ejpam-4101	250	45	of	of	ADP
ejpam-4101	250	46	re	re	PROPN
ejpam-4101	250	47	6k(x	6k(x	NUM
ejpam-4101	250	48	)	)	PUNCT
ejpam-4101	250	49	and	and	CCONJ
ejpam-4101	250	50	rh	rh	PROPN
ejpam-4101	250	51	4k(x	4k(x	PROPN
ejpam-4101	250	52	)	)	PUNCT
ejpam-4101	250	53	,	,	PUNCT
ejpam-4101	250	54	respectively	respectively	ADV
ejpam-4101	250	55	.	.	PUNCT
ejpam-4101	251	1	s.	s.	PROPN
ejpam-4101	251	2	bupasiri	bupasiri	PROPN
ejpam-4101	251	3	/	/	SYM
ejpam-4101	251	4	eur	eur	PROPN
ejpam-4101	251	5	.	.	PUNCT
ejpam-4101	252	1	j.	j.	PROPN
ejpam-4101	252	2	pure	pure	PROPN
ejpam-4101	252	3	appl	appl	PROPN
ejpam-4101	252	4	.	.	PROPN
ejpam-4101	252	5	math	math	PROPN
ejpam-4101	252	6	,	,	PUNCT
ejpam-4101	252	7	14	14	NUM
ejpam-4101	252	8	(	(	PUNCT
ejpam-4101	252	9	4	4	NUM
ejpam-4101	252	10	)	)	PUNCT
ejpam-4101	252	11	(	(	PUNCT
ejpam-4101	252	12	2021	2021	NUM
ejpam-4101	252	13	)	)	PUNCT
ejpam-4101	252	14	,	,	PUNCT
ejpam-4101	252	15	1306	1306	NUM
ejpam-4101	252	16	-	-	SYM
ejpam-4101	252	17	1323	1323	NUM
ejpam-4101	252	18	1316	1316	NUM
ejpam-4101	252	19	from	from	ADP
ejpam-4101	252	20	(	(	PUNCT
ejpam-4101	252	21	34	34	NUM
ejpam-4101	252	22	)	)	PUNCT
ejpam-4101	252	23	and	and	CCONJ
ejpam-4101	252	24	(	(	PUNCT
ejpam-4101	252	25	37	37	NUM
ejpam-4101	252	26	)	)	PUNCT
ejpam-4101	252	27	with	with	ADP
ejpam-4101	252	28	p	p	NOUN
ejpam-4101	252	29	=	=	SYM
ejpam-4101	252	30	1	1	NUM
ejpam-4101	252	31	,	,	PUNCT
ejpam-4101	252	32	q	q	NOUN
ejpam-4101	253	1	=	=	PUNCT
ejpam-4101	253	2	n−	n−	NOUN
ejpam-4101	253	3	1	1	NUM
ejpam-4101	253	4	,	,	PUNCT
ejpam-4101	253	5	k	k	NOUN
ejpam-4101	253	6	=	=	SYM
ejpam-4101	254	1	1,m	1,m	PROPN
ejpam-4101	254	2	=	=	SYM
ejpam-4101	254	3	0	0	NUM
ejpam-4101	255	1	and	and	CCONJ
ejpam-4101	255	2	x1	x1	PROPN
ejpam-4101	255	3	=	=	SYM
ejpam-4101	255	4	t	t	PROPN
ejpam-4101	255	5	(	(	PUNCT
ejpam-4101	255	6	time	time	NOUN
ejpam-4101	255	7	)	)	PUNCT
ejpam-4101	255	8	,	,	PUNCT
ejpam-4101	255	9	we	we	PRON
ejpam-4101	255	10	obtain	obtain	VERB
ejpam-4101	255	11	(	(	PUNCT
ejpam-4101	255	12	(	(	PUNCT
ejpam-4101	255	13	−1)3	−1)3	NOUN
ejpam-4101	255	14	2	2	NUM
ejpam-4101	255	15	re	re	NOUN
ejpam-4101	255	16	−6(x	−6(x	NOUN
ejpam-4101	255	17	)	)	PUNCT
ejpam-4101	255	18	+	+	PROPN
ejpam-4101	255	19	mh	mh	PROPN
ejpam-4101	255	20	−4(u	−4(u	NOUN
ejpam-4101	255	21	)	)	PUNCT
ejpam-4101	255	22	∗	∗	NOUN
ejpam-4101	255	23	(	(	PUNCT
ejpam-4101	255	24	−1)5	−1)5	NOUN
ejpam-4101	255	25	2	2	NUM
ejpam-4101	255	26	re	re	NOUN
ejpam-4101	255	27	−2(x	−2(x	NOUN
ejpam-4101	255	28	)	)	PUNCT
ejpam-4101	255	29	)	)	PUNCT
ejpam-4101	256	1	∗k(x	∗k(x	PROPN
ejpam-4101	256	2	,	,	PUNCT
ejpam-4101	256	3	0	0	NUM
ejpam-4101	256	4	)	)	PUNCT
ejpam-4101	256	5	=	=	SYM
ejpam-4101	256	6	mh	mh	PROPN
ejpam-4101	256	7	2	2	NUM
ejpam-4101	256	8	(	(	PUNCT
ejpam-4101	256	9	u	u	NOUN
ejpam-4101	256	10	)	)	PUNCT
ejpam-4101	256	11	(	(	PUNCT
ejpam-4101	256	12	38	38	NUM
ejpam-4101	256	13	)	)	PUNCT
ejpam-4101	256	14	or	or	CCONJ
ejpam-4101	256	15	(	(	PUNCT
ejpam-4101	256	16	(	(	PUNCT
ejpam-4101	256	17	−1	−1	NOUN
ejpam-4101	256	18	2	2	NUM
ejpam-4101	256	19	re	re	NOUN
ejpam-4101	256	20	−6(x	−6(x	NOUN
ejpam-4101	256	21	)	)	PUNCT
ejpam-4101	256	22	)	)	PUNCT
ejpam-4101	257	1	+	+	ADP
ejpam-4101	257	2	mh	mh	PROPN
ejpam-4101	257	3	−4(u	−4(u	NOUN
ejpam-4101	257	4	)	)	PUNCT
ejpam-4101	257	5	∗	∗	NOUN
ejpam-4101	257	6	(	(	PUNCT
ejpam-4101	257	7	−1	−1	NOUN
ejpam-4101	257	8	2	2	NUM
ejpam-4101	257	9	re	re	NOUN
ejpam-4101	257	10	−2(x	−2(x	NOUN
ejpam-4101	257	11	)	)	PUNCT
ejpam-4101	257	12	)	)	PUNCT
ejpam-4101	257	13	)	)	PUNCT
ejpam-4101	258	1	∗k(x	∗k(x	NOUN
ejpam-4101	258	2	,	,	PUNCT
ejpam-4101	258	3	0	0	NUM
ejpam-4101	258	4	)	)	PUNCT
ejpam-4101	258	5	=	=	SYM
ejpam-4101	258	6	mh	mh	PROPN
ejpam-4101	258	7	2	2	NUM
ejpam-4101	258	8	(	(	PUNCT
ejpam-4101	258	9	u	u	NOUN
ejpam-4101	258	10	)	)	PUNCT
ejpam-4101	258	11	(	(	PUNCT
ejpam-4101	258	12	39	39	NUM
ejpam-4101	258	13	)	)	PUNCT
ejpam-4101	258	14	is	be	AUX
ejpam-4101	258	15	the	the	DET
ejpam-4101	258	16	fundamental	fundamental	ADJ
ejpam-4101	258	17	solution	solution	NOUN
ejpam-4101	258	18	of	of	ADP
ejpam-4101	258	19	the	the	DET
ejpam-4101	258	20	wave	wave	NOUN
ejpam-4101	258	21	operator	operator	NOUN
ejpam-4101	258	22	is	be	AUX
ejpam-4101	258	23	defined	define	VERB
ejpam-4101	258	24	by	by	ADP
ejpam-4101	258	25	(	(	PUNCT
ejpam-4101	258	26	4	4	NUM
ejpam-4101	258	27	)	)	PUNCT
ejpam-4101	258	28	,	,	PUNCT
ejpam-4101	258	29	where	where	SCONJ
ejpam-4101	258	30	m2(u	m2(u	X
ejpam-4101	258	31	)	)	PUNCT
ejpam-4101	258	32	is	be	AUX
ejpam-4101	258	33	defined	define	VERB
ejpam-4101	258	34	by	by	ADP
ejpam-4101	258	35	(	(	PUNCT
ejpam-4101	258	36	15	15	NUM
ejpam-4101	258	37	)	)	PUNCT
ejpam-4101	258	38	with	with	ADP
ejpam-4101	258	39	α	α	NOUN
ejpam-4101	258	40	=	=	SYM
ejpam-4101	258	41	2	2	NUM
ejpam-4101	258	42	.	.	PUNCT
ejpam-4101	258	43	proof	proof	NOUN
ejpam-4101	258	44	.	.	PUNCT
ejpam-4101	259	1	from	from	ADP
ejpam-4101	259	2	(	(	PUNCT
ejpam-4101	259	3	10	10	NUM
ejpam-4101	259	4	)	)	PUNCT
ejpam-4101	259	5	and	and	CCONJ
ejpam-4101	259	6	(	(	PUNCT
ejpam-4101	259	7	31	31	NUM
ejpam-4101	259	8	)	)	PUNCT
ejpam-4101	259	9	,	,	PUNCT
ejpam-4101	259	10	we	we	PRON
ejpam-4101	259	11	have	have	VERB
ejpam-4101	259	12	(	(	PUNCT
ejpam-4101	259	13	(	(	PUNCT
ejpam-4101	259	14	♢	♢	PROPN
ejpam-4101	259	15	+	+	PROPN
ejpam-4101	259	16	m2	m2	X
ejpam-4101	259	17	)	)	PUNCT
ejpam-4101	259	18	(	(	PUNCT
ejpam-4101	259	19	△	△	X
ejpam-4101	259	20	2	2	NUM
ejpam-4101	259	21	+	+	NOUN
ejpam-4101	259	22	⊡2	⊡2	PROPN
ejpam-4101	259	23	2	2	NUM
ejpam-4101	259	24	)	)	PUNCT
ejpam-4101	259	25	)	)	PUNCT
ejpam-4101	260	1	k	k	PROPN
ejpam-4101	260	2	k(x	k(x	PROPN
ejpam-4101	260	3	,	,	PUNCT
ejpam-4101	260	4	m	m	NOUN
ejpam-4101	260	5	)	)	PUNCT
ejpam-4101	260	6	=	=	SYM
ejpam-4101	260	7	(	(	PUNCT
ejpam-4101	260	8	♢	♢	PROPN
ejpam-4101	260	9	+	+	PROPN
ejpam-4101	260	10	m2)k	m2)k	PROPN
ejpam-4101	260	11	(	(	PUNCT
ejpam-4101	260	12	△	△	X
ejpam-4101	260	13	2	2	NUM
ejpam-4101	260	14	+	+	NOUN
ejpam-4101	260	15	⊡2	⊡2	PROPN
ejpam-4101	260	16	2	2	NUM
ejpam-4101	260	17	)	)	PUNCT
ejpam-4101	260	18	k	k	PROPN
ejpam-4101	260	19	k(x	k(x	PROPN
ejpam-4101	260	20	,	,	PUNCT
ejpam-4101	260	21	m	m	NOUN
ejpam-4101	260	22	)	)	PUNCT
ejpam-4101	260	23	=	=	SYM
ejpam-4101	260	24	δ	δ	PROPN
ejpam-4101	260	25	.	.	PUNCT
ejpam-4101	261	1	(	(	PUNCT
ejpam-4101	261	2	40	40	NUM
ejpam-4101	261	3	)	)	PUNCT
ejpam-4101	261	4	convolving	convolve	VERB
ejpam-4101	261	5	both	both	DET
ejpam-4101	261	6	sides	side	NOUN
ejpam-4101	261	7	of	of	ADP
ejpam-4101	261	8	(	(	PUNCT
ejpam-4101	261	9	40	40	NUM
ejpam-4101	261	10	)	)	PUNCT
ejpam-4101	261	11	by	by	ADP
ejpam-4101	261	12	(	(	PUNCT
ejpam-4101	261	13	rh	rh	PROPN
ejpam-4101	261	14	4k(x	4k(x	PROPN
ejpam-4101	261	15	)	)	PUNCT
ejpam-4101	261	16	∗	∗	NOUN
ejpam-4101	261	17	(	(	PUNCT
ejpam-4101	261	18	−1)2kre	−1)2kre	PROPN
ejpam-4101	261	19	4k(x	4k(x	PROPN
ejpam-4101	261	20	)	)	PUNCT
ejpam-4101	261	21	∗	∗	NOUN
ejpam-4101	261	22	(	(	PUNCT
ejpam-4101	261	23	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	261	24	)	)	PUNCT
ejpam-4101	261	25	∗	∗	NOUN
ejpam-4101	261	26	p2k(x	p2k(x	PROPN
ejpam-4101	261	27	,	,	PUNCT
ejpam-4101	261	28	m	m	PROPN
ejpam-4101	261	29	)	)	PUNCT
ejpam-4101	261	30	,	,	PUNCT
ejpam-4101	261	31	we	we	PRON
ejpam-4101	261	32	obtain	obtain	VERB
ejpam-4101	261	33	[	[	X
ejpam-4101	261	34	(	(	PUNCT
ejpam-4101	261	35	rh	rh	PROPN
ejpam-4101	261	36	4k(x	4k(x	PROPN
ejpam-4101	261	37	)	)	PUNCT
ejpam-4101	262	1	∗	∗	NOUN
ejpam-4101	262	2	(	(	PUNCT
ejpam-4101	262	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	262	4	4k(x	4k(x	PROPN
ejpam-4101	262	5	)	)	PUNCT
ejpam-4101	262	6	∗	∗	NOUN
ejpam-4101	262	7	(	(	PUNCT
ejpam-4101	262	8	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	262	9	)	)	PUNCT
ejpam-4101	262	10	∗	∗	NOUN
ejpam-4101	262	11	p2k(x	p2k(x	PROPN
ejpam-4101	262	12	,	,	PUNCT
ejpam-4101	262	13	m	m	PROPN
ejpam-4101	262	14	)	)	PUNCT
ejpam-4101	262	15	]	]	PUNCT
ejpam-4101	263	1	∗	∗	NOUN
ejpam-4101	263	2	(	(	PUNCT
ejpam-4101	263	3	♢	♢	PROPN
ejpam-4101	263	4	+	+	PROPN
ejpam-4101	263	5	m2)k	m2)k	PROPN
ejpam-4101	263	6	(	(	PUNCT
ejpam-4101	263	7	△	△	X
ejpam-4101	263	8	2	2	NUM
ejpam-4101	263	9	+	+	NOUN
ejpam-4101	263	10	⊡2	⊡2	PROPN
ejpam-4101	263	11	2	2	NUM
ejpam-4101	263	12	)	)	PUNCT
ejpam-4101	263	13	k	k	PROPN
ejpam-4101	263	14	k(x	k(x	PROPN
ejpam-4101	263	15	,	,	PUNCT
ejpam-4101	263	16	m	m	NOUN
ejpam-4101	263	17	)	)	PUNCT
ejpam-4101	263	18	=	=	PUNCT
ejpam-4101	264	1	[	[	X
ejpam-4101	264	2	(	(	PUNCT
ejpam-4101	264	3	rh	rh	PROPN
ejpam-4101	264	4	4k(x	4k(x	PROPN
ejpam-4101	264	5	)	)	PUNCT
ejpam-4101	264	6	∗	∗	NOUN
ejpam-4101	264	7	(	(	PUNCT
ejpam-4101	264	8	−1)2kre	−1)2kre	PROPN
ejpam-4101	264	9	4k(x	4k(x	PROPN
ejpam-4101	264	10	)	)	PUNCT
ejpam-4101	264	11	∗	∗	NOUN
ejpam-4101	264	12	(	(	PUNCT
ejpam-4101	264	13	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	264	14	)	)	PUNCT
ejpam-4101	264	15	∗	∗	NOUN
ejpam-4101	264	16	p2k(x	p2k(x	PROPN
ejpam-4101	264	17	,	,	PUNCT
ejpam-4101	264	18	m	m	PROPN
ejpam-4101	264	19	)	)	PUNCT
ejpam-4101	264	20	]	]	PUNCT
ejpam-4101	264	21	∗	∗	PROPN
ejpam-4101	264	22	δ	δ	PROPN
ejpam-4101	264	23	.	.	PUNCT
ejpam-4101	265	1	by	by	ADP
ejpam-4101	265	2	properties	property	NOUN
ejpam-4101	265	3	of	of	ADP
ejpam-4101	265	4	the	the	DET
ejpam-4101	265	5	convolution	convolution	NOUN
ejpam-4101	265	6	,	,	PUNCT
ejpam-4101	265	7	we	we	PRON
ejpam-4101	265	8	have	have	VERB
ejpam-4101	265	9	(	(	PUNCT
ejpam-4101	265	10	♢	♢	PROPN
ejpam-4101	265	11	+	+	PROPN
ejpam-4101	265	12	m2)k(p2k(x	m2)k(p2k(x	PROPN
ejpam-4101	265	13	,	,	PUNCT
ejpam-4101	265	14	m	m	NOUN
ejpam-4101	265	15	)	)	PUNCT
ejpam-4101	265	16	)	)	PUNCT
ejpam-4101	266	1	∗	∗	NOUN
ejpam-4101	266	2	(	(	PUNCT
ejpam-4101	266	3	△	△	X
ejpam-4101	266	4	2	2	NUM
ejpam-4101	266	5	+	+	NOUN
ejpam-4101	266	6	⊡2	⊡2	PROPN
ejpam-4101	266	7	2	2	NUM
ejpam-4101	266	8	)	)	PUNCT
ejpam-4101	266	9	k	k	NOUN
ejpam-4101	266	10	(	(	PUNCT
ejpam-4101	266	11	(	(	PUNCT
ejpam-4101	266	12	rh	rh	PROPN
ejpam-4101	266	13	4k(x	4k(x	PROPN
ejpam-4101	266	14	)	)	PUNCT
ejpam-4101	266	15	∗	∗	NOUN
ejpam-4101	266	16	(	(	PUNCT
ejpam-4101	266	17	−1)2kre	−1)2kre	PROPN
ejpam-4101	266	18	4k(x	4k(x	PROPN
ejpam-4101	266	19	)	)	PUNCT
ejpam-4101	266	20	∗	∗	NOUN
ejpam-4101	266	21	(	(	PUNCT
ejpam-4101	266	22	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	266	23	)	)	PUNCT
ejpam-4101	266	24	)	)	PUNCT
ejpam-4101	267	1	∗k(x	∗k(x	PROPN
ejpam-4101	267	2	,	,	PUNCT
ejpam-4101	267	3	m	m	NOUN
ejpam-4101	267	4	)	)	PUNCT
ejpam-4101	267	5	=	=	SYM
ejpam-4101	268	1	(	(	PUNCT
ejpam-4101	268	2	rh	rh	PROPN
ejpam-4101	268	3	4k(x	4k(x	PROPN
ejpam-4101	268	4	)	)	PUNCT
ejpam-4101	269	1	∗	∗	NOUN
ejpam-4101	269	2	(	(	PUNCT
ejpam-4101	269	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	269	4	4k(x	4k(x	PROPN
ejpam-4101	269	5	)	)	PUNCT
ejpam-4101	269	6	∗	∗	NOUN
ejpam-4101	269	7	(	(	PUNCT
ejpam-4101	269	8	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	269	9	)	)	PUNCT
ejpam-4101	269	10	∗	∗	NOUN
ejpam-4101	269	11	p2k(x	p2k(x	PROPN
ejpam-4101	269	12	,	,	PUNCT
ejpam-4101	269	13	m	m	NOUN
ejpam-4101	269	14	)	)	PUNCT
ejpam-4101	269	15	.	.	PUNCT
ejpam-4101	270	1	by	by	ADP
ejpam-4101	270	2	lemma	lemma	PROPN
ejpam-4101	270	3	6	6	NUM
ejpam-4101	270	4	and	and	CCONJ
ejpam-4101	270	5	lemma	lemma	PROPN
ejpam-4101	270	6	7	7	NUM
ejpam-4101	270	7	,	,	PUNCT
ejpam-4101	270	8	we	we	PRON
ejpam-4101	270	9	obtain	obtain	VERB
ejpam-4101	270	10	,	,	PUNCT
ejpam-4101	271	1	δ	δ	PROPN
ejpam-4101	271	2	∗	∗	NOUN
ejpam-4101	271	3	δ	δ	PROPN
ejpam-4101	271	4	∗k(x	∗k(x	PROPN
ejpam-4101	271	5	,	,	PUNCT
ejpam-4101	271	6	m	m	NOUN
ejpam-4101	271	7	)	)	PUNCT
ejpam-4101	272	1	=	=	SYM
ejpam-4101	272	2	k(x	k(x	PROPN
ejpam-4101	272	3	,	,	PUNCT
ejpam-4101	272	4	m	m	NOUN
ejpam-4101	272	5	)	)	PUNCT
ejpam-4101	272	6	=	=	SYM
ejpam-4101	272	7	(	(	PUNCT
ejpam-4101	272	8	rh	rh	PROPN
ejpam-4101	272	9	4k(x	4k(x	PROPN
ejpam-4101	272	10	)	)	PUNCT
ejpam-4101	272	11	∗	∗	NOUN
ejpam-4101	272	12	(	(	PUNCT
ejpam-4101	272	13	−1)2kre	−1)2kre	PROPN
ejpam-4101	272	14	4k(x	4k(x	PROPN
ejpam-4101	272	15	)	)	PUNCT
ejpam-4101	272	16	∗	∗	NOUN
ejpam-4101	272	17	(	(	PUNCT
ejpam-4101	272	18	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	272	19	)	)	PUNCT
ejpam-4101	272	20	∗	∗	NOUN
ejpam-4101	272	21	p2k(x	p2k(x	PROPN
ejpam-4101	272	22	,	,	PUNCT
ejpam-4101	272	23	m	m	PROPN
ejpam-4101	272	24	)	)	PUNCT
ejpam-4101	272	25	(	(	PUNCT
ejpam-4101	272	26	41	41	NUM
ejpam-4101	272	27	)	)	PUNCT
ejpam-4101	272	28	is	be	AUX
ejpam-4101	272	29	the	the	DET
ejpam-4101	272	30	fundamental	fundamental	ADJ
ejpam-4101	272	31	solution	solution	NOUN
ejpam-4101	272	32	of	of	ADP
ejpam-4101	272	33	(	(	PUNCT
ejpam-4101	272	34	(	(	PUNCT
ejpam-4101	272	35	♢	♢	PROPN
ejpam-4101	272	36	+	+	PROPN
ejpam-4101	272	37	m2	m2	X
ejpam-4101	272	38	)	)	PUNCT
ejpam-4101	272	39	(	(	PUNCT
ejpam-4101	272	40	△	△	X
ejpam-4101	272	41	2+⊡2	2+⊡2	NUM
ejpam-4101	272	42	2	2	NUM
ejpam-4101	272	43	)	)	PUNCT
ejpam-4101	272	44	)	)	PUNCT
ejpam-4101	273	1	k	k	NOUN
ejpam-4101	273	2	operator	operator	NOUN
ejpam-4101	273	3	.	.	PUNCT
ejpam-4101	274	1	in	in	ADP
ejpam-4101	274	2	particular	particular	ADJ
ejpam-4101	274	3	,	,	PUNCT
ejpam-4101	274	4	for	for	ADP
ejpam-4101	274	5	m	m	PROPN
ejpam-4101	274	6	=	=	SYM
ejpam-4101	274	7	0	0	NUM
ejpam-4101	274	8	then	then	ADV
ejpam-4101	274	9	(	(	PUNCT
ejpam-4101	274	10	31	31	NUM
ejpam-4101	274	11	)	)	PUNCT
ejpam-4101	274	12	becomes	become	VERB
ejpam-4101	274	13	⊕kk(x	⊕kk(x	PROPN
ejpam-4101	274	14	,	,	PUNCT
ejpam-4101	274	15	0	0	NUM
ejpam-4101	274	16	)	)	PUNCT
ejpam-4101	274	17	=	=	SYM
ejpam-4101	274	18	δ	δ	PROPN
ejpam-4101	274	19	.	.	PUNCT
ejpam-4101	275	1	(	(	PUNCT
ejpam-4101	275	2	42	42	NUM
ejpam-4101	275	3	)	)	PUNCT
ejpam-4101	275	4	from	from	ADP
ejpam-4101	275	5	lemma	lemma	PROPN
ejpam-4101	275	6	5	5	NUM
ejpam-4101	275	7	,	,	PUNCT
ejpam-4101	275	8	(	(	PUNCT
ejpam-4101	275	9	22	22	NUM
ejpam-4101	275	10	)	)	PUNCT
ejpam-4101	275	11	and	and	CCONJ
ejpam-4101	275	12	(	(	PUNCT
ejpam-4101	275	13	41	41	NUM
ejpam-4101	275	14	)	)	PUNCT
ejpam-4101	275	15	,	,	PUNCT
ejpam-4101	275	16	we	we	PRON
ejpam-4101	275	17	obtain	obtain	VERB
ejpam-4101	275	18	k(x	k(x	PROPN
ejpam-4101	275	19	,	,	PUNCT
ejpam-4101	275	20	0	0	NUM
ejpam-4101	275	21	)	)	PUNCT
ejpam-4101	275	22	=	=	NOUN
ejpam-4101	276	1	(	(	PUNCT
ejpam-4101	276	2	rh	rh	PROPN
ejpam-4101	276	3	4k(x	4k(x	PROPN
ejpam-4101	276	4	)	)	PUNCT
ejpam-4101	277	1	∗	∗	NOUN
ejpam-4101	277	2	(	(	PUNCT
ejpam-4101	277	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	277	4	4k(x	4k(x	PROPN
ejpam-4101	277	5	)	)	PUNCT
ejpam-4101	277	6	∗	∗	NOUN
ejpam-4101	277	7	(	(	PUNCT
ejpam-4101	277	8	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	277	9	)	)	PUNCT
ejpam-4101	277	10	∗	∗	NOUN
ejpam-4101	277	11	p2k(x	p2k(x	PROPN
ejpam-4101	277	12	,	,	PUNCT
ejpam-4101	277	13	0	0	NUM
ejpam-4101	277	14	)	)	PUNCT
ejpam-4101	277	15	=	=	NOUN
ejpam-4101	278	1	(	(	PUNCT
ejpam-4101	278	2	rh	rh	PROPN
ejpam-4101	278	3	4k(x	4k(x	PROPN
ejpam-4101	278	4	)	)	PUNCT
ejpam-4101	279	1	∗	∗	NOUN
ejpam-4101	279	2	(	(	PUNCT
ejpam-4101	279	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	279	4	4k(x	4k(x	PROPN
ejpam-4101	279	5	)	)	PUNCT
ejpam-4101	279	6	∗	∗	NOUN
ejpam-4101	279	7	(	(	PUNCT
ejpam-4101	279	8	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	279	9	)	)	PUNCT
ejpam-4101	279	10	∗	∗	NOUN
ejpam-4101	279	11	(	(	PUNCT
ejpam-4101	279	12	(	(	PUNCT
ejpam-4101	279	13	−1)kre	−1)kre	PROPN
ejpam-4101	279	14	2k(x	2k(x	NUM
ejpam-4101	279	15	)	)	PUNCT
ejpam-4101	279	16	∗rh	∗rh	VERB
ejpam-4101	279	17	2k(x	2k(x	NUM
ejpam-4101	279	18	)	)	PUNCT
ejpam-4101	279	19	)	)	PUNCT
ejpam-4101	280	1	s.	s.	PROPN
ejpam-4101	280	2	bupasiri	bupasiri	PROPN
ejpam-4101	280	3	/	/	SYM
ejpam-4101	280	4	eur	eur	PROPN
ejpam-4101	280	5	.	.	PUNCT
ejpam-4101	281	1	j.	j.	PROPN
ejpam-4101	281	2	pure	pure	PROPN
ejpam-4101	281	3	appl	appl	PROPN
ejpam-4101	281	4	.	.	PROPN
ejpam-4101	281	5	math	math	PROPN
ejpam-4101	281	6	,	,	PUNCT
ejpam-4101	281	7	14	14	NUM
ejpam-4101	281	8	(	(	PUNCT
ejpam-4101	281	9	4	4	NUM
ejpam-4101	281	10	)	)	PUNCT
ejpam-4101	281	11	(	(	PUNCT
ejpam-4101	281	12	2021	2021	NUM
ejpam-4101	281	13	)	)	PUNCT
ejpam-4101	281	14	,	,	PUNCT
ejpam-4101	281	15	1306	1306	NUM
ejpam-4101	281	16	-	-	SYM
ejpam-4101	281	17	1323	1323	NUM
ejpam-4101	281	18	1317	1317	NUM
ejpam-4101	281	19	=	=	SYM
ejpam-4101	281	20	(	(	PUNCT
ejpam-4101	281	21	rh	rh	PROPN
ejpam-4101	281	22	6k(x	6k(x	PROPN
ejpam-4101	281	23	)	)	PUNCT
ejpam-4101	281	24	∗	∗	NOUN
ejpam-4101	281	25	(	(	PUNCT
ejpam-4101	281	26	−1)3kre	−1)3kre	PROPN
ejpam-4101	281	27	6k(x	6k(x	NUM
ejpam-4101	281	28	)	)	PUNCT
ejpam-4101	281	29	)	)	PUNCT
ejpam-4101	282	1	∗	∗	NOUN
ejpam-4101	282	2	(	(	PUNCT
ejpam-4101	282	3	(	(	PUNCT
ejpam-4101	282	4	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	282	5	)	)	PUNCT
ejpam-4101	282	6	(	(	PUNCT
ejpam-4101	282	7	43	43	NUM
ejpam-4101	282	8	)	)	PUNCT
ejpam-4101	282	9	is	be	AUX
ejpam-4101	282	10	the	the	DET
ejpam-4101	282	11	fundamental	fundamental	ADJ
ejpam-4101	282	12	solution	solution	NOUN
ejpam-4101	282	13	of	of	ADP
ejpam-4101	282	14	the	the	DET
ejpam-4101	282	15	o	o	ADJ
ejpam-4101	282	16	-	-	ADJ
ejpam-4101	282	17	plus	plus	ADJ
ejpam-4101	282	18	operator	operator	NOUN
ejpam-4101	282	19	⊕k	⊕k	NOUN
ejpam-4101	282	20	.	.	PUNCT
ejpam-4101	283	1	putting	put	VERB
ejpam-4101	283	2	q	q	NOUN
ejpam-4101	283	3	=	=	NOUN
ejpam-4101	283	4	m	m	NOUN
ejpam-4101	283	5	=	=	SYM
ejpam-4101	283	6	0	0	NUM
ejpam-4101	283	7	,	,	PUNCT
ejpam-4101	283	8	then	then	ADV
ejpam-4101	283	9	(	(	PUNCT
ejpam-4101	283	10	31	31	NUM
ejpam-4101	283	11	)	)	PUNCT
ejpam-4101	283	12	becomes	become	VERB
ejpam-4101	283	13	△	△	NOUN
ejpam-4101	283	14	4k	4k	NOUN
ejpam-4101	283	15	p	p	ADJ
ejpam-4101	283	16	k(x	k(x	PROPN
ejpam-4101	283	17	,	,	PUNCT
ejpam-4101	283	18	0	0	NUM
ejpam-4101	283	19	)	)	PUNCT
ejpam-4101	283	20	=	=	SYM
ejpam-4101	283	21	δ	δ	PROPN
ejpam-4101	283	22	,	,	PUNCT
ejpam-4101	283	23	(	(	PUNCT
ejpam-4101	283	24	44	44	NUM
ejpam-4101	283	25	)	)	PUNCT
ejpam-4101	283	26	where	where	SCONJ
ejpam-4101	283	27	△	△	NOUN
ejpam-4101	283	28	4k	4k	NOUN
ejpam-4101	283	29	p	p	NOUN
ejpam-4101	283	30	is	be	AUX
ejpam-4101	283	31	laplace	laplace	NOUN
ejpam-4101	283	32	operator	operator	NOUN
ejpam-4101	283	33	of	of	ADP
ejpam-4101	283	34	p	p	NOUN
ejpam-4101	283	35	-	-	PUNCT
ejpam-4101	283	36	dimension	dimension	NOUN
ejpam-4101	283	37	iterated	iterated	ADJ
ejpam-4101	283	38	4k	4k	NOUN
ejpam-4101	283	39	-	-	NOUN
ejpam-4101	283	40	times	time	NOUN
ejpam-4101	283	41	.	.	PUNCT
ejpam-4101	284	1	by	by	ADP
ejpam-4101	284	2	lemma	lemma	PROPN
ejpam-4101	284	3	1	1	NUM
ejpam-4101	284	4	,	,	PUNCT
ejpam-4101	284	5	we	we	PRON
ejpam-4101	284	6	have	have	VERB
ejpam-4101	284	7	k(x	k(x	PROPN
ejpam-4101	284	8	,	,	PUNCT
ejpam-4101	284	9	0	0	NUM
ejpam-4101	284	10	)	)	PUNCT
ejpam-4101	284	11	=	=	NOUN
ejpam-4101	285	1	(	(	PUNCT
ejpam-4101	285	2	−1)4kre	−1)4kre	NOUN
ejpam-4101	285	3	8k(x	8k(x	NUM
ejpam-4101	285	4	)	)	PUNCT
ejpam-4101	286	1	=	=	SYM
ejpam-4101	286	2	re	re	VERB
ejpam-4101	286	3	8k(x	8k(x	NUM
ejpam-4101	286	4	)	)	PUNCT
ejpam-4101	286	5	is	be	AUX
ejpam-4101	286	6	the	the	DET
ejpam-4101	286	7	fundamental	fundamental	ADJ
ejpam-4101	286	8	solution	solution	NOUN
ejpam-4101	286	9	of	of	ADP
ejpam-4101	286	10	(	(	PUNCT
ejpam-4101	286	11	44	44	NUM
ejpam-4101	286	12	)	)	PUNCT
ejpam-4101	286	13	.	.	PUNCT
ejpam-4101	287	1	on	on	ADP
ejpam-4101	287	2	the	the	DET
ejpam-4101	287	3	other	other	ADJ
ejpam-4101	287	4	hand	hand	NOUN
ejpam-4101	287	5	,	,	PUNCT
ejpam-4101	287	6	we	we	PRON
ejpam-4101	287	7	can	can	AUX
ejpam-4101	287	8	also	also	ADV
ejpam-4101	287	9	find	find	VERB
ejpam-4101	287	10	k(x	k(x	PROPN
ejpam-4101	287	11	,	,	PUNCT
ejpam-4101	287	12	m	m	NOUN
ejpam-4101	287	13	)	)	PUNCT
ejpam-4101	287	14	from	from	ADP
ejpam-4101	287	15	(	(	PUNCT
ejpam-4101	287	16	41	41	NUM
ejpam-4101	287	17	)	)	PUNCT
ejpam-4101	287	18	.	.	PUNCT
ejpam-4101	288	1	since	since	SCONJ
ejpam-4101	288	2	q	q	PROPN
ejpam-4101	288	3	=	=	SYM
ejpam-4101	288	4	0	0	NUM
ejpam-4101	288	5	,	,	PUNCT
ejpam-4101	288	6	we	we	PRON
ejpam-4101	288	7	have	have	VERB
ejpam-4101	288	8	rh	rh	PROPN
ejpam-4101	288	9	2k(x	2k(x	NUM
ejpam-4101	288	10	)	)	PUNCT
ejpam-4101	288	11	reduces	reduce	VERB
ejpam-4101	288	12	to	to	PART
ejpam-4101	288	13	(	(	PUNCT
ejpam-4101	288	14	−1)kre	−1)kre	PROPN
ejpam-4101	288	15	2k(x	2k(x	NUM
ejpam-4101	288	16	)	)	PUNCT
ejpam-4101	288	17	.	.	PUNCT
ejpam-4101	289	1	thus	thus	ADV
ejpam-4101	289	2	,	,	PUNCT
ejpam-4101	289	3	by	by	ADP
ejpam-4101	289	4	(	(	PUNCT
ejpam-4101	289	5	41	41	NUM
ejpam-4101	289	6	)	)	PUNCT
ejpam-4101	289	7	for	for	ADP
ejpam-4101	289	8	q	q	NOUN
ejpam-4101	289	9	=	=	NOUN
ejpam-4101	289	10	m	m	NOUN
ejpam-4101	289	11	=	=	SYM
ejpam-4101	289	12	0	0	NUM
ejpam-4101	289	13	,	,	PUNCT
ejpam-4101	289	14	we	we	PRON
ejpam-4101	289	15	obtain	obtain	VERB
ejpam-4101	289	16	k(x	k(x	PROPN
ejpam-4101	289	17	,	,	PUNCT
ejpam-4101	289	18	0	0	NUM
ejpam-4101	289	19	)	)	PUNCT
ejpam-4101	290	1	=	=	PRON
ejpam-4101	291	1	(	(	PUNCT
ejpam-4101	291	2	(	(	PUNCT
ejpam-4101	291	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	291	4	4k(x	4k(x	PROPN
ejpam-4101	291	5	)	)	PUNCT
ejpam-4101	291	6	∗	∗	NOUN
ejpam-4101	291	7	(	(	PUNCT
ejpam-4101	291	8	−1)2kre	−1)2kre	PROPN
ejpam-4101	291	9	4k(x	4k(x	PROPN
ejpam-4101	291	10	)	)	PUNCT
ejpam-4101	291	11	)	)	PUNCT
ejpam-4101	292	1	∗	∗	NOUN
ejpam-4101	292	2	(	(	PUNCT
ejpam-4101	292	3	(	(	PUNCT
ejpam-4101	292	4	−1)2kre	−1)2kre	PROPN
ejpam-4101	292	5	4k(x	4k(x	PROPN
ejpam-4101	292	6	)	)	PUNCT
ejpam-4101	292	7	)	)	PUNCT
ejpam-4101	293	1	∗−1	∗−1	PROPN
ejpam-4101	293	2	∗	∗	PROPN
ejpam-4101	293	3	p2k(x	p2k(x	PROPN
ejpam-4101	293	4	,	,	PUNCT
ejpam-4101	293	5	0	0	NUM
ejpam-4101	293	6	)	)	PUNCT
ejpam-4101	293	7	=	=	NOUN
ejpam-4101	293	8	(	(	PUNCT
ejpam-4101	293	9	−1)4kre	−1)4kre	NOUN
ejpam-4101	293	10	4k+4k(x	4k+4k(x	NOUN
ejpam-4101	293	11	)	)	PUNCT
ejpam-4101	293	12	∗	∗	NOUN
ejpam-4101	293	13	(	(	PUNCT
ejpam-4101	293	14	(	(	PUNCT
ejpam-4101	293	15	−1)2kre	−1)2kre	PROPN
ejpam-4101	293	16	4k(x	4k(x	PROPN
ejpam-4101	293	17	)	)	PUNCT
ejpam-4101	293	18	)	)	PUNCT
ejpam-4101	294	1	∗−1	∗−1	PROPN
ejpam-4101	294	2	∗	∗	NOUN
ejpam-4101	294	3	(	(	PUNCT
ejpam-4101	294	4	(	(	PUNCT
ejpam-4101	294	5	−1)kre	−1)kre	PROPN
ejpam-4101	294	6	2k(x	2k(x	NUM
ejpam-4101	294	7	)	)	PUNCT
ejpam-4101	294	8	∗	∗	NOUN
ejpam-4101	294	9	(	(	PUNCT
ejpam-4101	294	10	−1)kre	−1)kre	PROPN
ejpam-4101	294	11	2k(x	2k(x	NUM
ejpam-4101	294	12	)	)	PUNCT
ejpam-4101	294	13	)	)	PUNCT
ejpam-4101	295	1	=	=	SYM
ejpam-4101	295	2	(	(	PUNCT
ejpam-4101	295	3	−1)8kre	−1)8kre	PROPN
ejpam-4101	295	4	8k(x	8k(x	NUM
ejpam-4101	295	5	)	)	PUNCT
ejpam-4101	295	6	=	=	SYM
ejpam-4101	295	7	re	re	VERB
ejpam-4101	295	8	8k(x	8k(x	NUM
ejpam-4101	295	9	)	)	PUNCT
ejpam-4101	295	10	,	,	PUNCT
ejpam-4101	295	11	where	where	SCONJ
ejpam-4101	295	12	(	(	PUNCT
ejpam-4101	295	13	re	re	NOUN
ejpam-4101	295	14	4k(x	4k(x	NUM
ejpam-4101	295	15	)	)	PUNCT
ejpam-4101	295	16	)	)	PUNCT
ejpam-4101	296	1	∗−1	∗−1	NOUN
ejpam-4101	296	2	is	be	AUX
ejpam-4101	296	3	the	the	DET
ejpam-4101	296	4	inverse	inverse	NOUN
ejpam-4101	296	5	of	of	ADP
ejpam-4101	296	6	re	re	PROPN
ejpam-4101	296	7	4k(x	4k(x	PROPN
ejpam-4101	296	8	)	)	PUNCT
ejpam-4101	296	9	in	in	ADP
ejpam-4101	296	10	the	the	DET
ejpam-4101	296	11	convolution	convolution	NOUN
ejpam-4101	296	12	algebra	algebra	NOUN
ejpam-4101	296	13	.	.	PUNCT
ejpam-4101	297	1	from	from	ADP
ejpam-4101	297	2	(	(	PUNCT
ejpam-4101	297	3	41	41	NUM
ejpam-4101	297	4	)	)	PUNCT
ejpam-4101	297	5	,	,	PUNCT
ejpam-4101	297	6	we	we	PRON
ejpam-4101	297	7	have	have	VERB
ejpam-4101	297	8	k(x	k(x	PROPN
ejpam-4101	297	9	,	,	PUNCT
ejpam-4101	297	10	0	0	NUM
ejpam-4101	297	11	)	)	PUNCT
ejpam-4101	297	12	=	=	NOUN
ejpam-4101	298	1	(	(	PUNCT
ejpam-4101	298	2	rh	rh	PROPN
ejpam-4101	298	3	4k(x	4k(x	PROPN
ejpam-4101	298	4	)	)	PUNCT
ejpam-4101	299	1	∗	∗	NOUN
ejpam-4101	299	2	(	(	PUNCT
ejpam-4101	299	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	299	4	4k(x	4k(x	PROPN
ejpam-4101	299	5	)	)	PUNCT
ejpam-4101	299	6	)	)	PUNCT
ejpam-4101	300	1	∗	∗	NOUN
ejpam-4101	300	2	(	(	PUNCT
ejpam-4101	300	3	h∗k(x	h∗k(x	PROPN
ejpam-4101	300	4	)	)	PUNCT
ejpam-4101	300	5	)	)	PUNCT
ejpam-4101	300	6	∗−1	∗−1	PROPN
ejpam-4101	300	7	∗	∗	PROPN
ejpam-4101	300	8	p2k(x	p2k(x	PROPN
ejpam-4101	300	9	,	,	PUNCT
ejpam-4101	300	10	0	0	NUM
ejpam-4101	300	11	)	)	PUNCT
ejpam-4101	300	12	.	.	PUNCT
ejpam-4101	301	1	convolving	convolve	VERB
ejpam-4101	301	2	the	the	DET
ejpam-4101	301	3	above	above	ADJ
ejpam-4101	301	4	equation	equation	NOUN
ejpam-4101	301	5	by	by	ADP
ejpam-4101	301	6	(	(	PUNCT
ejpam-4101	301	7	rh	rh	PROPN
ejpam-4101	301	8	−4k(x	−4k(x	PROPN
ejpam-4101	301	9	)	)	PUNCT
ejpam-4101	301	10	∗	∗	NOUN
ejpam-4101	301	11	(	(	PUNCT
ejpam-4101	301	12	−1)3kre	−1)3kre	PROPN
ejpam-4101	301	13	−6k(x	−6k(x	NUM
ejpam-4101	301	14	)	)	PUNCT
ejpam-4101	301	15	)	)	PUNCT
ejpam-4101	301	16	∗	∗	NOUN
ejpam-4101	301	17	(	(	PUNCT
ejpam-4101	301	18	h∗k(x	h∗k(x	PROPN
ejpam-4101	301	19	)	)	PUNCT
ejpam-4101	301	20	)	)	PUNCT
ejpam-4101	301	21	.	.	PUNCT
ejpam-4101	302	1	by	by	ADP
ejpam-4101	302	2	lemma	lemma	PROPN
ejpam-4101	302	3	4	4	NUM
ejpam-4101	302	4	,	,	PUNCT
ejpam-4101	302	5	lemma	lemma	PROPN
ejpam-4101	302	6	5	5	NUM
ejpam-4101	302	7	,	,	PUNCT
ejpam-4101	302	8	and	and	CCONJ
ejpam-4101	302	9	(	(	PUNCT
ejpam-4101	302	10	25	25	NUM
ejpam-4101	302	11	)	)	PUNCT
ejpam-4101	302	12	,	,	PUNCT
ejpam-4101	302	13	we	we	PRON
ejpam-4101	302	14	obtain	obtain	VERB
ejpam-4101	302	15	(	(	PUNCT
ejpam-4101	302	16	rh	rh	PROPN
ejpam-4101	302	17	−4k(x	−4k(x	PROPN
ejpam-4101	302	18	)	)	PUNCT
ejpam-4101	302	19	∗	∗	NOUN
ejpam-4101	302	20	(	(	PUNCT
ejpam-4101	302	21	−1)3kre	−1)3kre	PROPN
ejpam-4101	302	22	−6k(x	−6k(x	NUM
ejpam-4101	302	23	)	)	PUNCT
ejpam-4101	302	24	)	)	PUNCT
ejpam-4101	303	1	∗	∗	NOUN
ejpam-4101	303	2	(	(	PUNCT
ejpam-4101	303	3	h∗k(x	h∗k(x	PROPN
ejpam-4101	303	4	)	)	PUNCT
ejpam-4101	303	5	)	)	PUNCT
ejpam-4101	304	1	∗k(x	∗k(x	PROPN
ejpam-4101	304	2	,	,	PUNCT
ejpam-4101	304	3	0	0	NUM
ejpam-4101	304	4	)	)	PUNCT
ejpam-4101	304	5	=	=	NOUN
ejpam-4101	304	6	(	(	PUNCT
ejpam-4101	304	7	rh	rh	PROPN
ejpam-4101	304	8	4k(x	4k(x	PROPN
ejpam-4101	304	9	)	)	PUNCT
ejpam-4101	304	10	∗rh	∗rh	VERB
ejpam-4101	304	11	−4k(x	−4k(x	PROPN
ejpam-4101	304	12	)	)	PUNCT
ejpam-4101	304	13	)	)	PUNCT
ejpam-4101	305	1	∗	∗	NOUN
ejpam-4101	305	2	(	(	PUNCT
ejpam-4101	305	3	(	(	PUNCT
ejpam-4101	305	4	−1)2kre	−1)2kre	PROPN
ejpam-4101	305	5	4k(x	4k(x	PROPN
ejpam-4101	305	6	)	)	PUNCT
ejpam-4101	305	7	∗	∗	NOUN
ejpam-4101	305	8	(	(	PUNCT
ejpam-4101	305	9	−1)3kre	−1)3kre	PROPN
ejpam-4101	305	10	−6k(x	−6k(x	NUM
ejpam-4101	305	11	)	)	PUNCT
ejpam-4101	305	12	)	)	PUNCT
ejpam-4101	305	13	)	)	PUNCT
ejpam-4101	306	1	∗	∗	NOUN
ejpam-4101	306	2	(	(	PUNCT
ejpam-4101	306	3	(	(	PUNCT
ejpam-4101	306	4	h∗k(x	h∗k(x	PROPN
ejpam-4101	306	5	)	)	PUNCT
ejpam-4101	306	6	)	)	PUNCT
ejpam-4101	307	1	∗	∗	NOUN
ejpam-4101	307	2	(	(	PUNCT
ejpam-4101	307	3	h∗k(x	h∗k(x	PROPN
ejpam-4101	307	4	)	)	PUNCT
ejpam-4101	307	5	)	)	PUNCT
ejpam-4101	307	6	∗−1	∗−1	NOUN
ejpam-4101	307	7	)	)	PUNCT
ejpam-4101	307	8	∗	∗	NOUN
ejpam-4101	307	9	p2k(x	p2k(x	PROPN
ejpam-4101	307	10	,	,	PUNCT
ejpam-4101	307	11	0	0	NUM
ejpam-4101	307	12	)	)	PUNCT
ejpam-4101	307	13	or	or	CCONJ
ejpam-4101	307	14	(	(	PUNCT
ejpam-4101	307	15	rh	rh	PROPN
ejpam-4101	307	16	−4k(x	−4k(x	PROPN
ejpam-4101	307	17	)	)	PUNCT
ejpam-4101	307	18	∗	∗	NOUN
ejpam-4101	307	19	(	(	PUNCT
ejpam-4101	307	20	−1)3kre	−1)3kre	PROPN
ejpam-4101	307	21	−6k(x	−6k(x	NUM
ejpam-4101	307	22	)	)	PUNCT
ejpam-4101	307	23	)	)	PUNCT
ejpam-4101	308	1	∗	∗	NOUN
ejpam-4101	308	2	(	(	PUNCT
ejpam-4101	308	3	h∗k(x	h∗k(x	PROPN
ejpam-4101	308	4	)	)	PUNCT
ejpam-4101	308	5	)	)	PUNCT
ejpam-4101	309	1	∗k(x	∗k(x	PROPN
ejpam-4101	309	2	,	,	PUNCT
ejpam-4101	309	3	0	0	NUM
ejpam-4101	309	4	)	)	PUNCT
ejpam-4101	309	5	=	=	SYM
ejpam-4101	310	1	δ(x	δ(x	ADJ
ejpam-4101	310	2	)	)	PUNCT
ejpam-4101	310	3	∗	∗	NOUN
ejpam-4101	310	4	(	(	PUNCT
ejpam-4101	310	5	−1)5kre	−1)5kre	PROPN
ejpam-4101	310	6	−2k(x	−2k(x	NOUN
ejpam-4101	310	7	)	)	PUNCT
ejpam-4101	310	8	∗	∗	NOUN
ejpam-4101	310	9	δ(x	δ(x	PROPN
ejpam-4101	310	10	)	)	PUNCT
ejpam-4101	310	11	∗	∗	NOUN
ejpam-4101	310	12	p2k(x	p2k(x	PROPN
ejpam-4101	310	13	,	,	PUNCT
ejpam-4101	310	14	0	0	NUM
ejpam-4101	310	15	)	)	PUNCT
ejpam-4101	310	16	=	=	SYM
ejpam-4101	310	17	δ(x	δ(x	ADJ
ejpam-4101	310	18	)	)	PUNCT
ejpam-4101	310	19	∗	∗	NOUN
ejpam-4101	310	20	(	(	PUNCT
ejpam-4101	310	21	−1)5kre	−1)5kre	PROPN
ejpam-4101	310	22	−2k(x	−2k(x	NOUN
ejpam-4101	310	23	)	)	PUNCT
ejpam-4101	310	24	∗	∗	NOUN
ejpam-4101	310	25	δ(x	δ(x	PROPN
ejpam-4101	310	26	)	)	PUNCT
ejpam-4101	310	27	∗	∗	NOUN
ejpam-4101	310	28	(	(	PUNCT
ejpam-4101	310	29	(	(	PUNCT
ejpam-4101	310	30	−1)kre	−1)kre	PROPN
ejpam-4101	310	31	2k(x	2k(x	NUM
ejpam-4101	310	32	)	)	PUNCT
ejpam-4101	310	33	∗rh	∗rh	VERB
ejpam-4101	310	34	2k(x	2k(x	NUM
ejpam-4101	310	35	)	)	PUNCT
ejpam-4101	310	36	)	)	PUNCT
ejpam-4101	311	1	=	=	SYM
ejpam-4101	311	2	δ(x	δ(x	ADJ
ejpam-4101	311	3	)	)	PUNCT
ejpam-4101	311	4	∗	∗	NOUN
ejpam-4101	311	5	δ(x	δ(x	PROPN
ejpam-4101	311	6	)	)	PUNCT
ejpam-4101	311	7	∗	∗	NOUN
ejpam-4101	311	8	δ(x	δ(x	PROPN
ejpam-4101	311	9	)	)	PUNCT
ejpam-4101	311	10	∗rh	∗rh	VERB
ejpam-4101	311	11	2k(x	2k(x	NUM
ejpam-4101	311	12	)	)	PUNCT
ejpam-4101	311	13	=	=	SYM
ejpam-4101	311	14	rh	rh	PROPN
ejpam-4101	311	15	2k(x	2k(x	NUM
ejpam-4101	311	16	)	)	PUNCT
ejpam-4101	311	17	.	.	PUNCT
ejpam-4101	312	1	it	it	PRON
ejpam-4101	312	2	follows	follow	VERB
ejpam-4101	312	3	that	that	SCONJ
ejpam-4101	312	4	(	(	PUNCT
ejpam-4101	312	5	rh	rh	PROPN
ejpam-4101	312	6	−4k(x	−4k(x	PROPN
ejpam-4101	312	7	)	)	PUNCT
ejpam-4101	312	8	∗	∗	NOUN
ejpam-4101	312	9	(	(	PUNCT
ejpam-4101	312	10	−1)3kre	−1)3kre	PROPN
ejpam-4101	312	11	−6k(x	−6k(x	NUM
ejpam-4101	312	12	)	)	PUNCT
ejpam-4101	312	13	)	)	PUNCT
ejpam-4101	312	14	∗	∗	NOUN
ejpam-4101	312	15	(	(	PUNCT
ejpam-4101	312	16	h∗k(x	h∗k(x	PROPN
ejpam-4101	312	17	)	)	PUNCT
ejpam-4101	312	18	)	)	PUNCT
ejpam-4101	313	1	∗k(x	∗k(x	PROPN
ejpam-4101	313	2	,	,	PUNCT
ejpam-4101	313	3	0	0	NUM
ejpam-4101	313	4	)	)	PUNCT
ejpam-4101	313	5	=	=	SYM
ejpam-4101	313	6	rh	rh	PROPN
ejpam-4101	313	7	2k(x	2k(x	PROPN
ejpam-4101	313	8	)	)	PUNCT
ejpam-4101	313	9	(	(	PUNCT
ejpam-4101	313	10	45	45	NUM
ejpam-4101	313	11	)	)	PUNCT
ejpam-4101	313	12	s.	s.	PROPN
ejpam-4101	313	13	bupasiri	bupasiri	PROPN
ejpam-4101	313	14	/	/	SYM
ejpam-4101	313	15	eur	eur	PROPN
ejpam-4101	313	16	.	.	PUNCT
ejpam-4101	314	1	j.	j.	PROPN
ejpam-4101	314	2	pure	pure	PROPN
ejpam-4101	314	3	appl	appl	PROPN
ejpam-4101	314	4	.	.	PROPN
ejpam-4101	314	5	math	math	PROPN
ejpam-4101	314	6	,	,	PUNCT
ejpam-4101	314	7	14	14	NUM
ejpam-4101	314	8	(	(	PUNCT
ejpam-4101	314	9	4	4	NUM
ejpam-4101	314	10	)	)	PUNCT
ejpam-4101	314	11	(	(	PUNCT
ejpam-4101	314	12	2021	2021	NUM
ejpam-4101	314	13	)	)	PUNCT
ejpam-4101	314	14	,	,	PUNCT
ejpam-4101	314	15	1306	1306	NUM
ejpam-4101	314	16	-	-	SYM
ejpam-4101	314	17	1323	1323	NUM
ejpam-4101	314	18	1318	1318	NUM
ejpam-4101	314	19	as	as	ADP
ejpam-4101	314	20	the	the	DET
ejpam-4101	314	21	fundamental	fundamental	ADJ
ejpam-4101	314	22	solution	solution	NOUN
ejpam-4101	314	23	of	of	ADP
ejpam-4101	314	24	the	the	DET
ejpam-4101	314	25	ultra	ultra	ADJ
ejpam-4101	314	26	-	-	ADJ
ejpam-4101	314	27	hyperbolic	hyperbolic	ADJ
ejpam-4101	314	28	operator	operator	NOUN
ejpam-4101	314	29	iterated	iterate	VERB
ejpam-4101	314	30	k	k	NOUN
ejpam-4101	314	31	-	-	PUNCT
ejpam-4101	314	32	times	time	NOUN
ejpam-4101	314	33	defined	define	VERB
ejpam-4101	314	34	by	by	ADP
ejpam-4101	314	35	(	(	PUNCT
ejpam-4101	314	36	3	3	NUM
ejpam-4101	314	37	)	)	PUNCT
ejpam-4101	314	38	.	.	PUNCT
ejpam-4101	315	1	in	in	ADP
ejpam-4101	315	2	particular	particular	ADJ
ejpam-4101	315	3	,	,	PUNCT
ejpam-4101	315	4	if	if	SCONJ
ejpam-4101	315	5	we	we	PRON
ejpam-4101	315	6	put	put	VERB
ejpam-4101	315	7	p	p	NOUN
ejpam-4101	315	8	=	=	NOUN
ejpam-4101	315	9	1	1	NUM
ejpam-4101	315	10	,	,	PUNCT
ejpam-4101	315	11	q	q	NOUN
ejpam-4101	316	1	=	=	SYM
ejpam-4101	316	2	n	n	CCONJ
ejpam-4101	316	3	−	−	PROPN
ejpam-4101	316	4	1	1	NUM
ejpam-4101	316	5	,	,	PUNCT
ejpam-4101	316	6	k	k	NOUN
ejpam-4101	316	7	=	=	SYM
ejpam-4101	317	1	1,m	1,m	PROPN
ejpam-4101	317	2	=	=	SYM
ejpam-4101	317	3	0	0	NUM
ejpam-4101	318	1	and	and	CCONJ
ejpam-4101	318	2	x1	x1	PROPN
ejpam-4101	318	3	=	=	SYM
ejpam-4101	318	4	t	t	PROPN
ejpam-4101	318	5	(	(	PUNCT
ejpam-4101	318	6	time	time	NOUN
ejpam-4101	318	7	)	)	PUNCT
ejpam-4101	318	8	in	in	ADP
ejpam-4101	318	9	(	(	PUNCT
ejpam-4101	318	10	41	41	NUM
ejpam-4101	318	11	)	)	PUNCT
ejpam-4101	318	12	then	then	ADV
ejpam-4101	318	13	rh	rh	PROPN
ejpam-4101	318	14	−4(x	−4(x	PROPN
ejpam-4101	318	15	)	)	PUNCT
ejpam-4101	318	16	reduces	reduce	VERB
ejpam-4101	318	17	to	to	ADP
ejpam-4101	318	18	mh	mh	PROPN
ejpam-4101	318	19	−4(u	−4(u	PROPN
ejpam-4101	318	20	)	)	PUNCT
ejpam-4101	318	21	and	and	CCONJ
ejpam-4101	318	22	rh	rh	PROPN
ejpam-4101	318	23	2	2	NUM
ejpam-4101	318	24	(	(	PUNCT
ejpam-4101	318	25	x	x	X
ejpam-4101	318	26	)	)	PUNCT
ejpam-4101	318	27	reduce	reduce	VERB
ejpam-4101	318	28	to	to	ADP
ejpam-4101	318	29	mh	mh	PROPN
ejpam-4101	318	30	2	2	NUM
ejpam-4101	318	31	(	(	PUNCT
ejpam-4101	318	32	u	u	NOUN
ejpam-4101	318	33	)	)	PUNCT
ejpam-4101	318	34	,	,	PUNCT
ejpam-4101	318	35	where	where	SCONJ
ejpam-4101	318	36	mh	mh	PROPN
ejpam-4101	318	37	4	4	NUM
ejpam-4101	318	38	(	(	PUNCT
ejpam-4101	318	39	u	u	NOUN
ejpam-4101	318	40	)	)	PUNCT
ejpam-4101	318	41	and	and	CCONJ
ejpam-4101	318	42	mh	mh	PROPN
ejpam-4101	318	43	2	2	NUM
ejpam-4101	318	44	(	(	PUNCT
ejpam-4101	318	45	u	u	NOUN
ejpam-4101	318	46	)	)	PUNCT
ejpam-4101	318	47	are	be	AUX
ejpam-4101	318	48	defined	define	VERB
ejpam-4101	318	49	by	by	ADP
ejpam-4101	318	50	(	(	PUNCT
ejpam-4101	318	51	15	15	NUM
ejpam-4101	318	52	)	)	PUNCT
ejpam-4101	318	53	with	with	ADP
ejpam-4101	318	54	α	α	PROPN
ejpam-4101	318	55	=	=	SYM
ejpam-4101	318	56	−4	−4	PROPN
ejpam-4101	318	57	,	,	PUNCT
ejpam-4101	318	58	α	α	NOUN
ejpam-4101	318	59	=	=	SYM
ejpam-4101	318	60	2	2	NUM
ejpam-4101	318	61	,	,	PUNCT
ejpam-4101	318	62	respectively	respectively	ADV
ejpam-4101	318	63	.	.	PUNCT
ejpam-4101	319	1	thus	thus	ADV
ejpam-4101	319	2	,	,	PUNCT
ejpam-4101	319	3	(	(	PUNCT
ejpam-4101	319	4	45	45	NUM
ejpam-4101	319	5	)	)	PUNCT
ejpam-4101	319	6	becomes	become	VERB
ejpam-4101	319	7	(	(	PUNCT
ejpam-4101	319	8	mh	mh	PROPN
ejpam-4101	319	9	−4(u	−4(u	PROPN
ejpam-4101	319	10	)	)	PUNCT
ejpam-4101	319	11	∗	∗	NOUN
ejpam-4101	319	12	(	(	PUNCT
ejpam-4101	319	13	−1)3re	−1)3re	NOUN
ejpam-4101	319	14	−6(x	−6(x	NOUN
ejpam-4101	319	15	)	)	PUNCT
ejpam-4101	319	16	)	)	PUNCT
ejpam-4101	319	17	∗	∗	NOUN
ejpam-4101	319	18	(	(	PUNCT
ejpam-4101	319	19	1	1	NUM
ejpam-4101	319	20	2	2	NUM
ejpam-4101	319	21	mh	mh	NOUN
ejpam-4101	319	22	4	4	NUM
ejpam-4101	319	23	(	(	PUNCT
ejpam-4101	319	24	x	x	NOUN
ejpam-4101	319	25	)	)	PUNCT
ejpam-4101	320	1	+	+	CCONJ
ejpam-4101	320	2	(	(	PUNCT
ejpam-4101	320	3	−1)2	−1)2	X
ejpam-4101	320	4	2	2	NUM
ejpam-4101	320	5	re	re	NOUN
ejpam-4101	320	6	4(x	4(x	NUM
ejpam-4101	320	7	)	)	PUNCT
ejpam-4101	320	8	)	)	PUNCT
ejpam-4101	321	1	∗k(x	∗k(x	PROPN
ejpam-4101	321	2	,	,	PUNCT
ejpam-4101	321	3	0	0	NUM
ejpam-4101	321	4	)	)	PUNCT
ejpam-4101	321	5	=	=	SYM
ejpam-4101	321	6	mh	mh	PROPN
ejpam-4101	321	7	2	2	NUM
ejpam-4101	321	8	(	(	PUNCT
ejpam-4101	321	9	u	u	NOUN
ejpam-4101	321	10	)	)	PUNCT
ejpam-4101	321	11	.	.	PUNCT
ejpam-4101	322	1	(	(	PUNCT
ejpam-4101	322	2	46	46	NUM
ejpam-4101	322	3	)	)	PUNCT
ejpam-4101	322	4	by	by	ADP
ejpam-4101	322	5	lemma	lemma	PROPN
ejpam-4101	322	6	7	7	NUM
ejpam-4101	322	7	,	,	PUNCT
ejpam-4101	322	8	we	we	PRON
ejpam-4101	322	9	obtain	obtain	VERB
ejpam-4101	322	10	(	(	PUNCT
ejpam-4101	322	11	(	(	PUNCT
ejpam-4101	322	12	−1)3	−1)3	NOUN
ejpam-4101	322	13	2	2	NUM
ejpam-4101	322	14	re	re	NOUN
ejpam-4101	322	15	−6(x	−6(x	NOUN
ejpam-4101	322	16	)	)	PUNCT
ejpam-4101	323	1	+	+	PROPN
ejpam-4101	323	2	mh	mh	PROPN
ejpam-4101	323	3	−4(u	−4(u	NOUN
ejpam-4101	323	4	)	)	PUNCT
ejpam-4101	323	5	∗	∗	NOUN
ejpam-4101	323	6	(	(	PUNCT
ejpam-4101	323	7	−1)5	−1)5	NOUN
ejpam-4101	323	8	2	2	NUM
ejpam-4101	323	9	re	re	NOUN
ejpam-4101	323	10	−2(x	−2(x	NOUN
ejpam-4101	323	11	)	)	PUNCT
ejpam-4101	323	12	)	)	PUNCT
ejpam-4101	324	1	∗k(x	∗k(x	PROPN
ejpam-4101	324	2	,	,	PUNCT
ejpam-4101	324	3	0	0	NUM
ejpam-4101	324	4	)	)	PUNCT
ejpam-4101	324	5	=	=	SYM
ejpam-4101	324	6	mh	mh	PROPN
ejpam-4101	324	7	2	2	NUM
ejpam-4101	324	8	(	(	PUNCT
ejpam-4101	324	9	u	u	NOUN
ejpam-4101	324	10	)	)	PUNCT
ejpam-4101	324	11	(	(	PUNCT
ejpam-4101	324	12	47	47	NUM
ejpam-4101	324	13	)	)	PUNCT
ejpam-4101	324	14	or	or	CCONJ
ejpam-4101	324	15	(	(	PUNCT
ejpam-4101	324	16	(	(	PUNCT
ejpam-4101	324	17	−1	−1	NOUN
ejpam-4101	324	18	2	2	NUM
ejpam-4101	324	19	re	re	NOUN
ejpam-4101	324	20	−6(x	−6(x	NOUN
ejpam-4101	324	21	)	)	PUNCT
ejpam-4101	324	22	)	)	PUNCT
ejpam-4101	325	1	+	+	ADP
ejpam-4101	325	2	mh	mh	PROPN
ejpam-4101	325	3	−4(u	−4(u	NOUN
ejpam-4101	325	4	)	)	PUNCT
ejpam-4101	325	5	∗	∗	NOUN
ejpam-4101	325	6	(	(	PUNCT
ejpam-4101	325	7	−1	−1	NOUN
ejpam-4101	325	8	2	2	NUM
ejpam-4101	325	9	re	re	NOUN
ejpam-4101	325	10	−2(x	−2(x	NOUN
ejpam-4101	325	11	)	)	PUNCT
ejpam-4101	325	12	)	)	PUNCT
ejpam-4101	325	13	)	)	PUNCT
ejpam-4101	326	1	∗k(x	∗k(x	NOUN
ejpam-4101	326	2	,	,	PUNCT
ejpam-4101	326	3	0	0	NUM
ejpam-4101	326	4	)	)	PUNCT
ejpam-4101	326	5	=	=	SYM
ejpam-4101	326	6	mh	mh	PROPN
ejpam-4101	326	7	2	2	NUM
ejpam-4101	326	8	(	(	PUNCT
ejpam-4101	326	9	u	u	NOUN
ejpam-4101	326	10	)	)	PUNCT
ejpam-4101	326	11	(	(	PUNCT
ejpam-4101	326	12	48	48	NUM
ejpam-4101	326	13	)	)	PUNCT
ejpam-4101	326	14	as	as	ADP
ejpam-4101	326	15	the	the	DET
ejpam-4101	326	16	fundamental	fundamental	ADJ
ejpam-4101	326	17	solution	solution	NOUN
ejpam-4101	326	18	of	of	ADP
ejpam-4101	326	19	the	the	DET
ejpam-4101	326	20	wave	wave	NOUN
ejpam-4101	326	21	operator	operator	NOUN
ejpam-4101	326	22	defined	define	VERB
ejpam-4101	326	23	by	by	ADP
ejpam-4101	326	24	⊡	⊡	PUNCT
ejpam-4101	326	25	=	=	SYM
ejpam-4101	326	26	∂2	∂2	NOUN
ejpam-4101	326	27	∂t2	∂t2	NOUN
ejpam-4101	326	28	−	−	PROPN
ejpam-4101	326	29	n−1∑	n−1∑	NUM
ejpam-4101	326	30	j=1	j=1	PROPN
ejpam-4101	326	31	∂2	∂2	PROPN
ejpam-4101	326	32	∂x2j	∂x2j	PROPN
ejpam-4101	326	33	,	,	PUNCT
ejpam-4101	326	34	(	(	PUNCT
ejpam-4101	326	35	49	49	NUM
ejpam-4101	326	36	)	)	PUNCT
ejpam-4101	326	37	where	where	SCONJ
ejpam-4101	326	38	re	re	X
ejpam-4101	326	39	−6(x	−6(x	NOUN
ejpam-4101	326	40	)	)	PUNCT
ejpam-4101	326	41	defined	define	VERB
ejpam-4101	326	42	by	by	ADP
ejpam-4101	326	43	(	(	PUNCT
ejpam-4101	326	44	19	19	NUM
ejpam-4101	326	45	)	)	PUNCT
ejpam-4101	326	46	.	.	PUNCT
ejpam-4101	327	1	this	this	PRON
ejpam-4101	327	2	completes	complete	VERB
ejpam-4101	327	3	the	the	DET
ejpam-4101	327	4	proof	proof	NOUN
ejpam-4101	327	5	.	.	PUNCT
ejpam-4101	328	1	theorem	theorem	NOUN
ejpam-4101	328	2	2	2	NUM
ejpam-4101	328	3	.	.	PUNCT
ejpam-4101	328	4	f	f	X
ejpam-4101	329	1	[	[	X
ejpam-4101	329	2	(	(	PUNCT
ejpam-4101	329	3	rh	rh	PROPN
ejpam-4101	329	4	4k(x	4k(x	PROPN
ejpam-4101	329	5	)	)	PUNCT
ejpam-4101	329	6	∗	∗	NOUN
ejpam-4101	329	7	(	(	PUNCT
ejpam-4101	329	8	−1)2kre	−1)2kre	PROPN
ejpam-4101	329	9	4k(x	4k(x	PROPN
ejpam-4101	329	10	)	)	PUNCT
ejpam-4101	329	11	∗	∗	NOUN
ejpam-4101	329	12	(	(	PUNCT
ejpam-4101	329	13	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	329	14	)	)	PUNCT
ejpam-4101	329	15	∗	∗	NOUN
ejpam-4101	329	16	p2k(x	p2k(x	PROPN
ejpam-4101	329	17	,	,	PUNCT
ejpam-4101	329	18	m	m	NOUN
ejpam-4101	329	19	)	)	PUNCT
ejpam-4101	329	20	]	]	PUNCT
ejpam-4101	330	1	=	=	SYM
ejpam-4101	330	2	1	1	X
ejpam-4101	330	3	(	(	PUNCT
ejpam-4101	330	4	2π)n/2	2π)n/2	NUM
ejpam-4101	330	5	[	[	X
ejpam-4101	330	6	(	(	PUNCT
ejpam-4101	330	7	(	(	PUNCT
ejpam-4101	330	8	ξ21	ξ21	NOUN
ejpam-4101	330	9	+	+	CCONJ
ejpam-4101	330	10	ξ22	ξ22	NOUN
ejpam-4101	330	11	+	+	X
ejpam-4101	330	12	·	·	PUNCT
ejpam-4101	330	13	·	·	PUNCT
ejpam-4101	330	14	·	·	PUNCT
ejpam-4101	330	15	+	+	NUM
ejpam-4101	330	16	ξ2p	ξ2p	NUM
ejpam-4101	330	17	)	)	PUNCT
ejpam-4101	330	18	2	2	NUM
ejpam-4101	330	19	+	+	NUM
ejpam-4101	330	20	m2	m2	PROPN
ejpam-4101	330	21	2	2	NUM
ejpam-4101	330	22	)	)	SYM
ejpam-4101	330	23	2	2	NUM
ejpam-4101	330	24	−	−	NOUN
ejpam-4101	330	25	(	(	PUNCT
ejpam-4101	330	26	(	(	PUNCT
ejpam-4101	330	27	ξ21	ξ21	NOUN
ejpam-4101	330	28	+	+	CCONJ
ejpam-4101	330	29	ξ22	ξ22	NOUN
ejpam-4101	330	30	+	+	X
ejpam-4101	330	31	·	·	PUNCT
ejpam-4101	330	32	·	·	PUNCT
ejpam-4101	330	33	·	·	PUNCT
ejpam-4101	330	34	+	+	NUM
ejpam-4101	330	35	ξ2p	ξ2p	NUM
ejpam-4101	330	36	)	)	PUNCT
ejpam-4101	330	37	2	2	NUM
ejpam-4101	330	38	−	−	NOUN
ejpam-4101	330	39	m2	m2	PROPN
ejpam-4101	330	40	2	2	NUM
ejpam-4101	330	41	)	)	PUNCT
ejpam-4101	330	42	2]k	2]k	NUM
ejpam-4101	330	43	=	=	PUNCT
ejpam-4101	331	1	∣∣∣f	∣∣∣f	PROPN
ejpam-4101	332	1	[	[	X
ejpam-4101	332	2	(	(	PUNCT
ejpam-4101	332	3	rh	rh	PROPN
ejpam-4101	332	4	4k(x	4k(x	PROPN
ejpam-4101	332	5	)	)	PUNCT
ejpam-4101	332	6	∗	∗	NOUN
ejpam-4101	332	7	(	(	PUNCT
ejpam-4101	332	8	−1)2kre	−1)2kre	PROPN
ejpam-4101	332	9	4k(x	4k(x	PROPN
ejpam-4101	332	10	)	)	PUNCT
ejpam-4101	332	11	∗	∗	NOUN
ejpam-4101	332	12	(	(	PUNCT
ejpam-4101	332	13	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	332	14	)	)	PUNCT
ejpam-4101	332	15	∗	∗	NOUN
ejpam-4101	332	16	p2k(x	p2k(x	PROPN
ejpam-4101	332	17	,	,	PUNCT
ejpam-4101	332	18	m	m	PROPN
ejpam-4101	332	19	)	)	PUNCT
ejpam-4101	332	20	]	]	PUNCT
ejpam-4101	332	21	∣∣∣	∣∣∣	ADJ
ejpam-4101	332	22	≤	≤	NUM
ejpam-4101	332	23	1	1	NUM
ejpam-4101	332	24	(	(	PUNCT
ejpam-4101	332	25	2π	2π	NOUN
ejpam-4101	332	26	)	)	PUNCT
ejpam-4101	332	27	n	n	PRON
ejpam-4101	332	28	2	2	NUM
ejpam-4101	332	29	m	m	NOUN
ejpam-4101	332	30	(	(	PUNCT
ejpam-4101	332	31	50	50	NUM
ejpam-4101	332	32	)	)	PUNCT
ejpam-4101	332	33	for	for	ADP
ejpam-4101	332	34	a	a	DET
ejpam-4101	332	35	large	large	ADJ
ejpam-4101	332	36	ξi	ξi	NOUN
ejpam-4101	332	37	∈	∈	NOUN
ejpam-4101	332	38	r	r	NOUN
ejpam-4101	332	39	,	,	PUNCT
ejpam-4101	332	40	where	where	SCONJ
ejpam-4101	332	41	m	m	NOUN
ejpam-4101	332	42	is	be	AUX
ejpam-4101	332	43	a	a	DET
ejpam-4101	332	44	non	non	ADJ
ejpam-4101	332	45	-	-	ADJ
ejpam-4101	332	46	negative	negative	ADJ
ejpam-4101	332	47	real	real	ADJ
ejpam-4101	332	48	number	number	NOUN
ejpam-4101	332	49	and	and	CCONJ
ejpam-4101	332	50	m	m	NOUN
ejpam-4101	332	51	is	be	AUX
ejpam-4101	332	52	a	a	DET
ejpam-4101	332	53	constant	constant	ADJ
ejpam-4101	332	54	.	.	PUNCT
ejpam-4101	333	1	that	that	PRON
ejpam-4101	333	2	is	is	ADV
ejpam-4101	333	3	,	,	PUNCT
ejpam-4101	333	4	f	f	PROPN
ejpam-4101	333	5	is	be	AUX
ejpam-4101	333	6	bounded	bound	VERB
ejpam-4101	333	7	and	and	CCONJ
ejpam-4101	333	8	continuous	continuous	ADJ
ejpam-4101	333	9	on	on	ADP
ejpam-4101	333	10	the	the	DET
ejpam-4101	333	11	space	space	NOUN
ejpam-4101	333	12	s	s	PART
ejpam-4101	333	13	′	′	NOUN
ejpam-4101	333	14	of	of	ADP
ejpam-4101	333	15	the	the	DET
ejpam-4101	333	16	tempered	temper	VERB
ejpam-4101	333	17	distributions	distribution	NOUN
ejpam-4101	333	18	.	.	PUNCT
ejpam-4101	334	1	proof	proof	NOUN
ejpam-4101	334	2	.	.	PUNCT
ejpam-4101	335	1	by	by	ADP
ejpam-4101	335	2	theorem	theorem	NOUN
ejpam-4101	335	3	1	1	NUM
ejpam-4101	335	4	,	,	PUNCT
ejpam-4101	335	5	we	we	PRON
ejpam-4101	335	6	obtain	obtain	VERB
ejpam-4101	335	7	(	(	PUNCT
ejpam-4101	335	8	(	(	PUNCT
ejpam-4101	335	9	♢	♢	PROPN
ejpam-4101	335	10	+	+	PROPN
ejpam-4101	335	11	m2	m2	X
ejpam-4101	335	12	)	)	PUNCT
ejpam-4101	335	13	(	(	PUNCT
ejpam-4101	335	14	△	△	X
ejpam-4101	335	15	2	2	NUM
ejpam-4101	335	16	+	+	NOUN
ejpam-4101	335	17	⊡2	⊡2	PROPN
ejpam-4101	335	18	2	2	NUM
ejpam-4101	335	19	)	)	PUNCT
ejpam-4101	335	20	)	)	PUNCT
ejpam-4101	336	1	k	k	X
ejpam-4101	336	2	(	(	PUNCT
ejpam-4101	336	3	(	(	PUNCT
ejpam-4101	336	4	rh	rh	PROPN
ejpam-4101	336	5	4k(x	4k(x	PROPN
ejpam-4101	336	6	)	)	PUNCT
ejpam-4101	336	7	∗	∗	NOUN
ejpam-4101	336	8	(	(	PUNCT
ejpam-4101	336	9	−1)2kre	−1)2kre	PROPN
ejpam-4101	336	10	4k(x	4k(x	PROPN
ejpam-4101	336	11	)	)	PUNCT
ejpam-4101	336	12	∗	∗	NOUN
ejpam-4101	336	13	(	(	PUNCT
ejpam-4101	336	14	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	336	15	)	)	PUNCT
ejpam-4101	336	16	∗	∗	NOUN
ejpam-4101	336	17	p2k(x	p2k(x	PROPN
ejpam-4101	336	18	,	,	PUNCT
ejpam-4101	336	19	m	m	NOUN
ejpam-4101	336	20	)	)	PUNCT
ejpam-4101	336	21	)	)	PUNCT
ejpam-4101	337	1	=	=	PUNCT
ejpam-4101	337	2	δ	δ	PROPN
ejpam-4101	337	3	or	or	CCONJ
ejpam-4101	337	4	(	(	PUNCT
ejpam-4101	337	5	(	(	PUNCT
ejpam-4101	337	6	(	(	PUNCT
ejpam-4101	337	7	♢	♢	PROPN
ejpam-4101	337	8	+	+	PROPN
ejpam-4101	337	9	m2	m2	X
ejpam-4101	337	10	)	)	PUNCT
ejpam-4101	337	11	(	(	PUNCT
ejpam-4101	337	12	△	△	X
ejpam-4101	337	13	2	2	NUM
ejpam-4101	337	14	+	+	NOUN
ejpam-4101	337	15	⊡2	⊡2	PROPN
ejpam-4101	337	16	2	2	NUM
ejpam-4101	337	17	)	)	PUNCT
ejpam-4101	337	18	)	)	PUNCT
ejpam-4101	338	1	k	k	PROPN
ejpam-4101	338	2	δ	δ	PROPN
ejpam-4101	338	3	)	)	PUNCT
ejpam-4101	338	4	∗	∗	NOUN
ejpam-4101	338	5	(	(	PUNCT
ejpam-4101	338	6	(	(	PUNCT
ejpam-4101	338	7	rh	rh	PROPN
ejpam-4101	338	8	4k(x	4k(x	PROPN
ejpam-4101	338	9	)	)	PUNCT
ejpam-4101	338	10	∗	∗	NOUN
ejpam-4101	338	11	(	(	PUNCT
ejpam-4101	338	12	−1)2kre	−1)2kre	PROPN
ejpam-4101	338	13	4k(x	4k(x	PROPN
ejpam-4101	338	14	)	)	PUNCT
ejpam-4101	338	15	∗	∗	NOUN
ejpam-4101	338	16	(	(	PUNCT
ejpam-4101	338	17	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	338	18	)	)	PUNCT
ejpam-4101	338	19	∗	∗	NOUN
ejpam-4101	338	20	p2k(x	p2k(x	PROPN
ejpam-4101	338	21	,	,	PUNCT
ejpam-4101	338	22	m	m	NOUN
ejpam-4101	338	23	)	)	PUNCT
ejpam-4101	338	24	)	)	PUNCT
ejpam-4101	339	1	=	=	SYM
ejpam-4101	339	2	δ	δ	PROPN
ejpam-4101	339	3	.	.	PUNCT
ejpam-4101	340	1	s.	s.	PROPN
ejpam-4101	340	2	bupasiri	bupasiri	PROPN
ejpam-4101	340	3	/	/	SYM
ejpam-4101	340	4	eur	eur	PROPN
ejpam-4101	340	5	.	.	PUNCT
ejpam-4101	341	1	j.	j.	PROPN
ejpam-4101	341	2	pure	pure	PROPN
ejpam-4101	341	3	appl	appl	PROPN
ejpam-4101	341	4	.	.	PROPN
ejpam-4101	341	5	math	math	PROPN
ejpam-4101	341	6	,	,	PUNCT
ejpam-4101	341	7	14	14	NUM
ejpam-4101	341	8	(	(	PUNCT
ejpam-4101	341	9	4	4	NUM
ejpam-4101	341	10	)	)	PUNCT
ejpam-4101	341	11	(	(	PUNCT
ejpam-4101	341	12	2021	2021	NUM
ejpam-4101	341	13	)	)	PUNCT
ejpam-4101	341	14	,	,	PUNCT
ejpam-4101	341	15	1306	1306	NUM
ejpam-4101	341	16	-	-	SYM
ejpam-4101	341	17	1323	1323	NUM
ejpam-4101	341	18	1319	1319	NUM
ejpam-4101	341	19	taking	take	VERB
ejpam-4101	341	20	the	the	DET
ejpam-4101	341	21	fourier	fourier	NOUN
ejpam-4101	341	22	transform	transform	NOUN
ejpam-4101	341	23	on	on	ADP
ejpam-4101	341	24	both	both	DET
ejpam-4101	341	25	sides	side	NOUN
ejpam-4101	341	26	of	of	ADP
ejpam-4101	341	27	the	the	DET
ejpam-4101	341	28	above	above	ADJ
ejpam-4101	341	29	equation	equation	NOUN
ejpam-4101	341	30	,	,	PUNCT
ejpam-4101	341	31	we	we	PRON
ejpam-4101	341	32	obtain	obtain	VERB
ejpam-4101	341	33	f	f	X
ejpam-4101	341	34	(	(	PUNCT
ejpam-4101	341	35	(	(	PUNCT
ejpam-4101	341	36	(	(	PUNCT
ejpam-4101	341	37	(	(	PUNCT
ejpam-4101	341	38	♢	♢	PROPN
ejpam-4101	341	39	+	+	PROPN
ejpam-4101	341	40	m2	m2	X
ejpam-4101	341	41	)	)	PUNCT
ejpam-4101	341	42	(	(	PUNCT
ejpam-4101	341	43	△	△	X
ejpam-4101	341	44	2	2	NUM
ejpam-4101	341	45	+	+	NOUN
ejpam-4101	341	46	⊡2	⊡2	PROPN
ejpam-4101	341	47	2	2	NUM
ejpam-4101	341	48	)	)	PUNCT
ejpam-4101	341	49	)	)	PUNCT
ejpam-4101	342	1	k	k	PROPN
ejpam-4101	342	2	δ	δ	PROPN
ejpam-4101	342	3	)	)	PUNCT
ejpam-4101	342	4	∗	∗	NOUN
ejpam-4101	342	5	(	(	PUNCT
ejpam-4101	342	6	(	(	PUNCT
ejpam-4101	342	7	rh	rh	PROPN
ejpam-4101	342	8	4k(x	4k(x	PROPN
ejpam-4101	342	9	)	)	PUNCT
ejpam-4101	342	10	∗	∗	NOUN
ejpam-4101	342	11	(	(	PUNCT
ejpam-4101	342	12	−1)2kre	−1)2kre	PROPN
ejpam-4101	342	13	4k(x	4k(x	PROPN
ejpam-4101	342	14	)	)	PUNCT
ejpam-4101	342	15	∗	∗	NOUN
ejpam-4101	342	16	(	(	PUNCT
ejpam-4101	342	17	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	342	18	)	)	PUNCT
ejpam-4101	342	19	∗p2k(x	∗p2k(x	NOUN
ejpam-4101	342	20	,	,	PUNCT
ejpam-4101	342	21	m	m	NOUN
ejpam-4101	342	22	)	)	PUNCT
ejpam-4101	342	23	)	)	PUNCT
ejpam-4101	342	24	)	)	PUNCT
ejpam-4101	343	1	=	=	PRON
ejpam-4101	343	2	fδ	fδ	NOUN
ejpam-4101	343	3	=	=	SYM
ejpam-4101	343	4	1	1	NUM
ejpam-4101	343	5	(	(	PUNCT
ejpam-4101	343	6	2π)n/2	2π)n/2	NOUN
ejpam-4101	343	7	.	.	PUNCT
ejpam-4101	344	1	by	by	ADP
ejpam-4101	344	2	(	(	PUNCT
ejpam-4101	344	3	18	18	NUM
ejpam-4101	344	4	)	)	PUNCT
ejpam-4101	344	5	,	,	PUNCT
ejpam-4101	344	6	we	we	PRON
ejpam-4101	344	7	have	have	VERB
ejpam-4101	344	8	1	1	NUM
ejpam-4101	344	9	(	(	PUNCT
ejpam-4101	344	10	2π)n/2	2π)n/2	NUM
ejpam-4101	344	11	〈	〈	PROPN
ejpam-4101	344	12	(	(	PUNCT
ejpam-4101	344	13	(	(	PUNCT
ejpam-4101	344	14	(	(	PUNCT
ejpam-4101	344	15	♢	♢	PROPN
ejpam-4101	344	16	+	+	PROPN
ejpam-4101	344	17	m2	m2	X
ejpam-4101	344	18	)	)	PUNCT
ejpam-4101	344	19	(	(	PUNCT
ejpam-4101	344	20	△	△	X
ejpam-4101	344	21	2	2	NUM
ejpam-4101	344	22	+	+	NOUN
ejpam-4101	344	23	⊡2	⊡2	PROPN
ejpam-4101	344	24	2	2	NUM
ejpam-4101	344	25	)	)	PUNCT
ejpam-4101	344	26	)	)	PUNCT
ejpam-4101	345	1	k	k	PROPN
ejpam-4101	345	2	δ	δ	PROPN
ejpam-4101	345	3	)	)	PUNCT
ejpam-4101	345	4	∗	∗	NOUN
ejpam-4101	345	5	(	(	PUNCT
ejpam-4101	345	6	(	(	PUNCT
ejpam-4101	345	7	rh	rh	PROPN
ejpam-4101	345	8	4k(x	4k(x	PROPN
ejpam-4101	345	9	)	)	PUNCT
ejpam-4101	345	10	∗	∗	NOUN
ejpam-4101	345	11	(	(	PUNCT
ejpam-4101	345	12	−1)2kre	−1)2kre	PROPN
ejpam-4101	345	13	4k(x	4k(x	PROPN
ejpam-4101	345	14	)	)	PUNCT
ejpam-4101	345	15	∗	∗	NOUN
ejpam-4101	345	16	(	(	PUNCT
ejpam-4101	345	17	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	345	18	)	)	PUNCT
ejpam-4101	345	19	∗p2k(x	∗p2k(x	NOUN
ejpam-4101	345	20	,	,	PUNCT
ejpam-4101	345	21	m	m	NOUN
ejpam-4101	345	22	)	)	PUNCT
ejpam-4101	345	23	)	)	PUNCT
ejpam-4101	345	24	,	,	PUNCT
ejpam-4101	345	25	e−i(ξ·x	e−i(ξ·x	NOUN
ejpam-4101	345	26	)	)	PUNCT
ejpam-4101	345	27	〉	〉	NOUN
ejpam-4101	345	28	=	=	SYM
ejpam-4101	345	29	1	1	NUM
ejpam-4101	345	30	(	(	PUNCT
ejpam-4101	345	31	2π)n/2	2π)n/2	NOUN
ejpam-4101	345	32	.	.	PUNCT
ejpam-4101	346	1	by	by	ADP
ejpam-4101	346	2	the	the	DET
ejpam-4101	346	3	definition	definition	NOUN
ejpam-4101	346	4	of	of	ADP
ejpam-4101	346	5	convolution	convolution	NOUN
ejpam-4101	346	6	1	1	NUM
ejpam-4101	346	7	(	(	PUNCT
ejpam-4101	346	8	2π)n/2	2π)n/2	NUM
ejpam-4101	346	9	〈	〈	PROPN
ejpam-4101	346	10	(	(	PUNCT
ejpam-4101	346	11	(	(	PUNCT
ejpam-4101	346	12	(	(	PUNCT
ejpam-4101	346	13	♢	♢	PROPN
ejpam-4101	346	14	+	+	PROPN
ejpam-4101	346	15	m2	m2	X
ejpam-4101	346	16	)	)	PUNCT
ejpam-4101	346	17	(	(	PUNCT
ejpam-4101	346	18	△	△	X
ejpam-4101	346	19	2	2	NUM
ejpam-4101	346	20	+	+	NOUN
ejpam-4101	346	21	⊡2	⊡2	PROPN
ejpam-4101	346	22	2	2	NUM
ejpam-4101	346	23	)	)	PUNCT
ejpam-4101	346	24	)	)	PUNCT
ejpam-4101	347	1	k	k	PROPN
ejpam-4101	347	2	δ	δ	PROPN
ejpam-4101	347	3	)	)	PUNCT
ejpam-4101	347	4	∗	∗	NOUN
ejpam-4101	347	5	(	(	PUNCT
ejpam-4101	347	6	(	(	PUNCT
ejpam-4101	347	7	rh	rh	PROPN
ejpam-4101	347	8	4k(x	4k(x	PROPN
ejpam-4101	347	9	)	)	PUNCT
ejpam-4101	347	10	∗	∗	NOUN
ejpam-4101	347	11	(	(	PUNCT
ejpam-4101	347	12	−1)2kre	−1)2kre	PROPN
ejpam-4101	347	13	4k(x	4k(x	PROPN
ejpam-4101	347	14	)	)	PUNCT
ejpam-4101	347	15	∗	∗	NOUN
ejpam-4101	347	16	(	(	PUNCT
ejpam-4101	347	17	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	347	18	)	)	PUNCT
ejpam-4101	347	19	∗p2k(x	∗p2k(x	NOUN
ejpam-4101	347	20	,	,	PUNCT
ejpam-4101	347	21	m	m	NOUN
ejpam-4101	347	22	)	)	PUNCT
ejpam-4101	347	23	)	)	PUNCT
ejpam-4101	347	24	,	,	PUNCT
ejpam-4101	347	25	e−iξ·(x+r	e−iξ·(x+r	PROPN
ejpam-4101	347	26	)	)	PUNCT
ejpam-4101	347	27	〉	〉	NOUN
ejpam-4101	347	28	=	=	SYM
ejpam-4101	347	29	1	1	NUM
ejpam-4101	347	30	(	(	PUNCT
ejpam-4101	347	31	2π)n/2	2π)n/2	NUM
ejpam-4101	347	32	,	,	PUNCT
ejpam-4101	347	33	1	1	NUM
ejpam-4101	347	34	(	(	PUNCT
ejpam-4101	347	35	2π)n/2	2π)n/2	NUM
ejpam-4101	347	36	〈	〈	PROPN
ejpam-4101	347	37	(	(	PUNCT
ejpam-4101	347	38	rh	rh	PROPN
ejpam-4101	347	39	4k(x	4k(x	PROPN
ejpam-4101	347	40	)	)	PUNCT
ejpam-4101	347	41	∗	∗	NOUN
ejpam-4101	347	42	(	(	PUNCT
ejpam-4101	347	43	−1)2kre	−1)2kre	PROPN
ejpam-4101	347	44	4k(x	4k(x	PROPN
ejpam-4101	347	45	)	)	PUNCT
ejpam-4101	347	46	∗	∗	NOUN
ejpam-4101	347	47	(	(	PUNCT
ejpam-4101	347	48	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	347	49	)	)	PUNCT
ejpam-4101	347	50	∗	∗	NOUN
ejpam-4101	347	51	p2k(x	p2k(x	PROPN
ejpam-4101	347	52	,	,	PUNCT
ejpam-4101	347	53	m	m	NOUN
ejpam-4101	347	54	)	)	PUNCT
ejpam-4101	347	55	,	,	PUNCT
ejpam-4101	347	56	e−i(ξ·r	e−i(ξ·r	NUM
ejpam-4101	347	57	)	)	PUNCT
ejpam-4101	347	58	〉	〉	NOUN
ejpam-4101	347	59	×	×	NOUN
ejpam-4101	347	60	〈	〈	PROPN
ejpam-4101	347	61	(	(	PUNCT
ejpam-4101	347	62	(	(	PUNCT
ejpam-4101	347	63	♢	♢	PROPN
ejpam-4101	347	64	+	+	PROPN
ejpam-4101	347	65	m2	m2	X
ejpam-4101	347	66	)	)	PUNCT
ejpam-4101	347	67	(	(	PUNCT
ejpam-4101	347	68	△	△	X
ejpam-4101	347	69	2	2	NUM
ejpam-4101	347	70	+	+	NOUN
ejpam-4101	347	71	⊡2	⊡2	PROPN
ejpam-4101	347	72	2	2	NUM
ejpam-4101	347	73	)	)	PUNCT
ejpam-4101	347	74	)	)	PUNCT
ejpam-4101	347	75	k	k	PROPN
ejpam-4101	347	76	δ	δ	PROPN
ejpam-4101	347	77	,	,	PUNCT
ejpam-4101	347	78	e−i(ξ·x	e−i(ξ·x	NOUN
ejpam-4101	347	79	)	)	PUNCT
ejpam-4101	347	80	〉	〉	NOUN
ejpam-4101	347	81	=	=	SYM
ejpam-4101	347	82	1	1	NUM
ejpam-4101	347	83	(	(	PUNCT
ejpam-4101	347	84	2π)n/2	2π)n/2	NUM
ejpam-4101	347	85	,	,	PUNCT
ejpam-4101	347	86	f((rh	f((rh	PROPN
ejpam-4101	347	87	4k(x	4k(x	PROPN
ejpam-4101	347	88	)	)	PUNCT
ejpam-4101	347	89	∗	∗	NOUN
ejpam-4101	347	90	(	(	PUNCT
ejpam-4101	347	91	−1)2kre	−1)2kre	PROPN
ejpam-4101	347	92	4k(x	4k(x	PROPN
ejpam-4101	347	93	)	)	PUNCT
ejpam-4101	347	94	∗	∗	NOUN
ejpam-4101	347	95	(	(	PUNCT
ejpam-4101	347	96	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	347	97	)	)	PUNCT
ejpam-4101	347	98	∗	∗	NOUN
ejpam-4101	347	99	p2k(x	p2k(x	PROPN
ejpam-4101	347	100	,	,	PUNCT
ejpam-4101	347	101	m))(2π	m))(2π	PROPN
ejpam-4101	347	102	)	)	PUNCT
ejpam-4101	347	103	n	n	PRON
ejpam-4101	347	104	2	2	NUM
ejpam-4101	347	105	f	f	NOUN
ejpam-4101	347	106	(	(	PUNCT
ejpam-4101	347	107	(	(	PUNCT
ejpam-4101	347	108	(	(	PUNCT
ejpam-4101	347	109	♢	♢	PROPN
ejpam-4101	347	110	+	+	PROPN
ejpam-4101	347	111	m2	m2	X
ejpam-4101	347	112	)	)	PUNCT
ejpam-4101	347	113	(	(	PUNCT
ejpam-4101	347	114	△	△	X
ejpam-4101	347	115	2	2	NUM
ejpam-4101	347	116	+	+	NOUN
ejpam-4101	347	117	⊡2	⊡2	PROPN
ejpam-4101	347	118	2	2	NUM
ejpam-4101	347	119	)	)	PUNCT
ejpam-4101	347	120	)	)	PUNCT
ejpam-4101	347	121	k	k	PROPN
ejpam-4101	347	122	δ	δ	PROPN
ejpam-4101	347	123	)	)	PUNCT
ejpam-4101	347	124	=	=	SYM
ejpam-4101	348	1	1	1	NUM
ejpam-4101	348	2	(	(	PUNCT
ejpam-4101	348	3	2π)n/2	2π)n/2	NOUN
ejpam-4101	348	4	.	.	PUNCT
ejpam-4101	349	1	by	by	ADP
ejpam-4101	349	2	lemma	lemma	PROPN
ejpam-4101	349	3	8	8	NUM
ejpam-4101	349	4	,	,	PUNCT
ejpam-4101	349	5	we	we	PRON
ejpam-4101	349	6	obtain	obtain	VERB
ejpam-4101	349	7	f((rh	f((rh	ADP
ejpam-4101	349	8	4k(x	4k(x	PROPN
ejpam-4101	349	9	)	)	PUNCT
ejpam-4101	349	10	∗	∗	NOUN
ejpam-4101	349	11	(	(	PUNCT
ejpam-4101	349	12	−1)2kre	−1)2kre	PROPN
ejpam-4101	349	13	4k(x	4k(x	PROPN
ejpam-4101	349	14	)	)	PUNCT
ejpam-4101	349	15	∗	∗	NOUN
ejpam-4101	349	16	(	(	PUNCT
ejpam-4101	349	17	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	349	18	)	)	PUNCT
ejpam-4101	349	19	∗	∗	NOUN
ejpam-4101	349	20	p2k(x	p2k(x	PROPN
ejpam-4101	349	21	,	,	PUNCT
ejpam-4101	349	22	m	m	NOUN
ejpam-4101	349	23	)	)	PUNCT
ejpam-4101	349	24	)	)	PUNCT
ejpam-4101	350	1	×	×	NOUN
ejpam-4101	351	1	[	[	X
ejpam-4101	351	2	(	(	PUNCT
ejpam-4101	351	3	(	(	PUNCT
ejpam-4101	351	4	ξ21	ξ21	NOUN
ejpam-4101	351	5	+	+	CCONJ
ejpam-4101	351	6	ξ22	ξ22	NOUN
ejpam-4101	351	7	+	+	X
ejpam-4101	351	8	·	·	PUNCT
ejpam-4101	351	9	·	·	PUNCT
ejpam-4101	351	10	·	·	PUNCT
ejpam-4101	351	11	+	+	NUM
ejpam-4101	351	12	ξ2p	ξ2p	NUM
ejpam-4101	351	13	)	)	PUNCT
ejpam-4101	351	14	2	2	NUM
ejpam-4101	351	15	+	+	NUM
ejpam-4101	351	16	m2	m2	PROPN
ejpam-4101	351	17	2	2	NUM
ejpam-4101	351	18	)	)	SYM
ejpam-4101	351	19	2	2	NUM
ejpam-4101	351	20	−	−	NOUN
ejpam-4101	351	21	(	(	PUNCT
ejpam-4101	351	22	(	(	PUNCT
ejpam-4101	351	23	ξ21	ξ21	NOUN
ejpam-4101	351	24	+	+	CCONJ
ejpam-4101	351	25	ξ22	ξ22	NOUN
ejpam-4101	351	26	+	+	X
ejpam-4101	351	27	·	·	PUNCT
ejpam-4101	351	28	·	·	PUNCT
ejpam-4101	351	29	·	·	PUNCT
ejpam-4101	351	30	+	+	NUM
ejpam-4101	351	31	ξ2p	ξ2p	NUM
ejpam-4101	351	32	)	)	PUNCT
ejpam-4101	351	33	2	2	NUM
ejpam-4101	351	34	−	−	NOUN
ejpam-4101	351	35	m2	m2	PROPN
ejpam-4101	351	36	2	2	NUM
ejpam-4101	351	37	)	)	PUNCT
ejpam-4101	351	38	2	2	NUM
ejpam-4101	351	39	]	]	SYM
ejpam-4101	351	40	k	k	X
ejpam-4101	351	41	=	=	SYM
ejpam-4101	351	42	1	1	NUM
ejpam-4101	351	43	(	(	PUNCT
ejpam-4101	351	44	2π)n/2	2π)n/2	NOUN
ejpam-4101	351	45	.	.	PUNCT
ejpam-4101	352	1	it	it	PRON
ejpam-4101	352	2	follows	follow	VERB
ejpam-4101	352	3	that	that	SCONJ
ejpam-4101	352	4	f((rh	f((rh	PROPN
ejpam-4101	352	5	4k(x	4k(x	PROPN
ejpam-4101	352	6	)	)	PUNCT
ejpam-4101	352	7	∗	∗	NOUN
ejpam-4101	352	8	(	(	PUNCT
ejpam-4101	352	9	−1)2kre	−1)2kre	PROPN
ejpam-4101	352	10	4k(x	4k(x	PROPN
ejpam-4101	352	11	)	)	PUNCT
ejpam-4101	352	12	∗	∗	NOUN
ejpam-4101	352	13	(	(	PUNCT
ejpam-4101	352	14	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	352	15	)	)	PUNCT
ejpam-4101	352	16	∗	∗	NOUN
ejpam-4101	352	17	p2k(x	p2k(x	PROPN
ejpam-4101	352	18	,	,	PUNCT
ejpam-4101	352	19	m	m	NOUN
ejpam-4101	352	20	)	)	PUNCT
ejpam-4101	352	21	)	)	PUNCT
ejpam-4101	353	1	s.	s.	PROPN
ejpam-4101	353	2	bupasiri	bupasiri	PROPN
ejpam-4101	353	3	/	/	SYM
ejpam-4101	353	4	eur	eur	PROPN
ejpam-4101	353	5	.	.	PUNCT
ejpam-4101	354	1	j.	j.	PROPN
ejpam-4101	354	2	pure	pure	PROPN
ejpam-4101	354	3	appl	appl	PROPN
ejpam-4101	354	4	.	.	PROPN
ejpam-4101	354	5	math	math	PROPN
ejpam-4101	354	6	,	,	PUNCT
ejpam-4101	354	7	14	14	NUM
ejpam-4101	354	8	(	(	PUNCT
ejpam-4101	354	9	4	4	NUM
ejpam-4101	354	10	)	)	PUNCT
ejpam-4101	354	11	(	(	PUNCT
ejpam-4101	354	12	2021	2021	NUM
ejpam-4101	354	13	)	)	PUNCT
ejpam-4101	354	14	,	,	PUNCT
ejpam-4101	354	15	1306	1306	NUM
ejpam-4101	354	16	-	-	SYM
ejpam-4101	354	17	1323	1323	NUM
ejpam-4101	354	18	1320	1320	NUM
ejpam-4101	354	19	=	=	SYM
ejpam-4101	354	20	1	1	NUM
ejpam-4101	354	21	(	(	PUNCT
ejpam-4101	354	22	2π)n/2	2π)n/2	NUM
ejpam-4101	354	23	[	[	X
ejpam-4101	354	24	(	(	PUNCT
ejpam-4101	354	25	(	(	PUNCT
ejpam-4101	354	26	ξ21	ξ21	NOUN
ejpam-4101	354	27	+	+	CCONJ
ejpam-4101	354	28	ξ22	ξ22	NOUN
ejpam-4101	354	29	+	+	X
ejpam-4101	354	30	·	·	PUNCT
ejpam-4101	354	31	·	·	PUNCT
ejpam-4101	354	32	·	·	PUNCT
ejpam-4101	354	33	+	+	NUM
ejpam-4101	354	34	ξ2p	ξ2p	NUM
ejpam-4101	354	35	)	)	PUNCT
ejpam-4101	354	36	2	2	NUM
ejpam-4101	354	37	+	+	NUM
ejpam-4101	354	38	m2	m2	PROPN
ejpam-4101	354	39	2	2	NUM
ejpam-4101	354	40	)	)	SYM
ejpam-4101	354	41	2	2	NUM
ejpam-4101	354	42	−	−	NOUN
ejpam-4101	354	43	(	(	PUNCT
ejpam-4101	354	44	(	(	PUNCT
ejpam-4101	354	45	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	354	46	+	+	CCONJ
ejpam-4101	355	1	ξ2p+2	ξ2p+2	VERB
ejpam-4101	355	2	+	+	X
ejpam-4101	355	3	·	·	PUNCT
ejpam-4101	355	4	·	·	PUNCT
ejpam-4101	355	5	·	·	PUNCT
ejpam-4101	355	6	+	+	NUM
ejpam-4101	355	7	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	355	8	)	)	PUNCT
ejpam-4101	355	9	2	2	NUM
ejpam-4101	355	10	−	−	NOUN
ejpam-4101	355	11	m2	m2	PROPN
ejpam-4101	355	12	2	2	NUM
ejpam-4101	355	13	)	)	PUNCT
ejpam-4101	355	14	2]k	2]k	NUM
ejpam-4101	355	15	.	.	PUNCT
ejpam-4101	356	1	since	since	SCONJ
ejpam-4101	356	2	1	1	NUM
ejpam-4101	356	3	[	[	X
ejpam-4101	356	4	(	(	PUNCT
ejpam-4101	356	5	(	(	PUNCT
ejpam-4101	356	6	ξ21	ξ21	NOUN
ejpam-4101	356	7	+	+	CCONJ
ejpam-4101	356	8	ξ22	ξ22	NOUN
ejpam-4101	356	9	+	+	X
ejpam-4101	356	10	·	·	PUNCT
ejpam-4101	356	11	·	·	PUNCT
ejpam-4101	356	12	·	·	PUNCT
ejpam-4101	356	13	+	+	NUM
ejpam-4101	356	14	ξ2p	ξ2p	NUM
ejpam-4101	356	15	)	)	PUNCT
ejpam-4101	356	16	2	2	NUM
ejpam-4101	356	17	+	+	NUM
ejpam-4101	356	18	m2	m2	PROPN
ejpam-4101	356	19	2	2	NUM
ejpam-4101	356	20	)	)	SYM
ejpam-4101	356	21	2	2	NUM
ejpam-4101	356	22	−	−	NOUN
ejpam-4101	356	23	(	(	PUNCT
ejpam-4101	356	24	(	(	PUNCT
ejpam-4101	356	25	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	356	26	+	+	CCONJ
ejpam-4101	356	27	ξ2p+2	ξ2p+2	VERB
ejpam-4101	356	28	+	+	X
ejpam-4101	356	29	·	·	PUNCT
ejpam-4101	356	30	·	·	PUNCT
ejpam-4101	356	31	·	·	PUNCT
ejpam-4101	356	32	+	+	NUM
ejpam-4101	356	33	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	356	34	)	)	PUNCT
ejpam-4101	356	35	2	2	NUM
ejpam-4101	356	36	−	−	NOUN
ejpam-4101	356	37	m2	m2	PROPN
ejpam-4101	356	38	2	2	NUM
ejpam-4101	356	39	)	)	PUNCT
ejpam-4101	356	40	2	2	NUM
ejpam-4101	356	41	]	]	PUNCT
ejpam-4101	356	42	=	=	SYM
ejpam-4101	356	43	1	1	NUM
ejpam-4101	356	44	[	[	PUNCT
ejpam-4101	356	45	(	(	PUNCT
ejpam-4101	356	46	ξ21	ξ21	NOUN
ejpam-4101	356	47	+	+	CCONJ
ejpam-4101	356	48	ξ22	ξ22	NOUN
ejpam-4101	356	49	+	+	X
ejpam-4101	356	50	·	·	PUNCT
ejpam-4101	356	51	·	·	PUNCT
ejpam-4101	356	52	·	·	PUNCT
ejpam-4101	356	53	+	+	NUM
ejpam-4101	356	54	ξ2p	ξ2p	NUM
ejpam-4101	356	55	)	)	PUNCT
ejpam-4101	356	56	2	2	NUM
ejpam-4101	356	57	+	+	CCONJ
ejpam-4101	356	58	(	(	PUNCT
ejpam-4101	356	59	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	356	60	+	+	CCONJ
ejpam-4101	356	61	ξ2p+2	ξ2p+2	VERB
ejpam-4101	356	62	+	+	X
ejpam-4101	356	63	·	·	PUNCT
ejpam-4101	356	64	·	·	PUNCT
ejpam-4101	356	65	·	·	PUNCT
ejpam-4101	356	66	+	+	NUM
ejpam-4101	356	67	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	356	68	)	)	PUNCT
ejpam-4101	356	69	2	2	NUM
ejpam-4101	356	70	]	]	SYM
ejpam-4101	356	71	×	×	NOUN
ejpam-4101	356	72	1	1	NUM
ejpam-4101	356	73	[	[	PUNCT
ejpam-4101	356	74	(	(	PUNCT
ejpam-4101	356	75	ξ21	ξ21	NOUN
ejpam-4101	356	76	+	+	CCONJ
ejpam-4101	356	77	ξ22	ξ22	NOUN
ejpam-4101	356	78	+	+	X
ejpam-4101	356	79	·	·	PUNCT
ejpam-4101	356	80	·	·	PUNCT
ejpam-4101	356	81	·	·	PUNCT
ejpam-4101	357	1	+	+	NUM
ejpam-4101	357	2	ξ2n)(ξ	ξ2n)(ξ	PROPN
ejpam-4101	357	3	2	2	NUM
ejpam-4101	357	4	1	1	NUM
ejpam-4101	357	5	+	+	NUM
ejpam-4101	357	6	ξ22	ξ22	NOUN
ejpam-4101	357	7	+	+	X
ejpam-4101	357	8	·	·	PUNCT
ejpam-4101	357	9	·	·	PUNCT
ejpam-4101	357	10	·	·	PUNCT
ejpam-4101	357	11	+	+	CCONJ
ejpam-4101	357	12	ξ2p	ξ2p	NUM
ejpam-4101	357	13	−	−	NOUN
ejpam-4101	357	14	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	357	15	−	−	PROPN
ejpam-4101	357	16	·	·	PUNCT
ejpam-4101	357	17	·	·	PUNCT
ejpam-4101	357	18	·	·	PUNCT
ejpam-4101	358	1	−	−	NUM
ejpam-4101	358	2	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	358	3	)	)	PUNCT
ejpam-4101	359	1	+	+	NOUN
ejpam-4101	359	2	m2	m2	X
ejpam-4101	359	3	]	]	PUNCT
ejpam-4101	359	4	.	.	PUNCT
ejpam-4101	360	1	(	(	PUNCT
ejpam-4101	360	2	51	51	NUM
ejpam-4101	360	3	)	)	PUNCT
ejpam-4101	360	4	let	let	VERB
ejpam-4101	360	5	ξ	ξ	X
ejpam-4101	360	6	=	=	SYM
ejpam-4101	360	7	(	(	PUNCT
ejpam-4101	360	8	ξ1	ξ1	PROPN
ejpam-4101	360	9	,	,	PUNCT
ejpam-4101	360	10	ξ2	ξ2	NOUN
ejpam-4101	360	11	,	,	PUNCT
ejpam-4101	360	12	.	.	PUNCT
ejpam-4101	360	13	.	.	PUNCT
ejpam-4101	361	1	.	.	PUNCT
ejpam-4101	362	1	,	,	PUNCT
ejpam-4101	362	2	ξn	ξn	NOUN
ejpam-4101	362	3	)	)	PUNCT
ejpam-4101	362	4	∈	∈	PROPN
ejpam-4101	362	5	γ+	γ+	PUNCT
ejpam-4101	362	6	with	with	ADP
ejpam-4101	362	7	γ+	γ+	NUM
ejpam-4101	362	8	defined	define	VERB
ejpam-4101	362	9	by	by	ADP
ejpam-4101	362	10	definition	definition	NOUN
ejpam-4101	362	11	1	1	NUM
ejpam-4101	362	12	.	.	PUNCT
ejpam-4101	363	1	then	then	ADV
ejpam-4101	363	2	(	(	PUNCT
ejpam-4101	363	3	ξ21	ξ21	NOUN
ejpam-4101	363	4	+	+	CCONJ
ejpam-4101	363	5	ξ22	ξ22	NOUN
ejpam-4101	363	6	+	+	X
ejpam-4101	363	7	·	·	PUNCT
ejpam-4101	363	8	·	·	PUNCT
ejpam-4101	363	9	·	·	PUNCT
ejpam-4101	364	1	+	+	CCONJ
ejpam-4101	364	2	ξ2p	ξ2p	PRON
ejpam-4101	364	3	+	+	NUM
ejpam-4101	364	4	ξ2p+1	ξ2p+1	NOUN
ejpam-4101	364	5	+	+	CCONJ
ejpam-4101	364	6	ξ2p+2	ξ2p+2	VERB
ejpam-4101	364	7	+	+	X
ejpam-4101	364	8	·	·	PUNCT
ejpam-4101	364	9	·	·	PUNCT
ejpam-4101	364	10	·	·	PUNCT
ejpam-4101	364	11	+	+	NUM
ejpam-4101	364	12	ξ2p+q	ξ2p+q	NOUN
ejpam-4101	364	13	)	)	PUNCT
ejpam-4101	364	14	>	>	X
ejpam-4101	364	15	0	0	PUNCT
ejpam-4101	364	16	and	and	CCONJ
ejpam-4101	364	17	for	for	ADP
ejpam-4101	364	18	a	a	DET
ejpam-4101	364	19	large	large	ADJ
ejpam-4101	364	20	k	k	NOUN
ejpam-4101	364	21	,	,	PUNCT
ejpam-4101	364	22	the	the	DET
ejpam-4101	364	23	right	right	ADJ
ejpam-4101	364	24	-	-	PUNCT
ejpam-4101	364	25	hand	hand	NOUN
ejpam-4101	364	26	side	side	NOUN
ejpam-4101	364	27	of	of	ADP
ejpam-4101	364	28	(	(	PUNCT
ejpam-4101	364	29	51	51	NUM
ejpam-4101	364	30	)	)	PUNCT
ejpam-4101	364	31	tend	tend	VERB
ejpam-4101	364	32	to	to	ADP
ejpam-4101	364	33	zero	zero	NUM
ejpam-4101	364	34	.	.	PUNCT
ejpam-4101	365	1	it	it	PRON
ejpam-4101	365	2	follows	follow	VERB
ejpam-4101	365	3	that	that	SCONJ
ejpam-4101	365	4	it	it	PRON
ejpam-4101	365	5	is	be	AUX
ejpam-4101	365	6	bounded	bound	VERB
ejpam-4101	365	7	by	by	ADP
ejpam-4101	365	8	a	a	DET
ejpam-4101	365	9	positive	positive	ADJ
ejpam-4101	365	10	constant	constant	ADJ
ejpam-4101	365	11	m	m	NOUN
ejpam-4101	365	12	say	say	VERB
ejpam-4101	365	13	,	,	PUNCT
ejpam-4101	365	14	that	that	PRON
ejpam-4101	365	15	is	be	AUX
ejpam-4101	365	16	we	we	PRON
ejpam-4101	365	17	obtain	obtain	VERB
ejpam-4101	365	18	(	(	PUNCT
ejpam-4101	365	19	50	50	NUM
ejpam-4101	365	20	)	)	PUNCT
ejpam-4101	365	21	as	as	SCONJ
ejpam-4101	365	22	required	require	VERB
ejpam-4101	365	23	and	and	CCONJ
ejpam-4101	365	24	also	also	ADV
ejpam-4101	365	25	by	by	ADP
ejpam-4101	365	26	(	(	PUNCT
ejpam-4101	365	27	50	50	NUM
ejpam-4101	365	28	)	)	PUNCT
ejpam-4101	365	29	f	f	PROPN
ejpam-4101	365	30	is	be	AUX
ejpam-4101	365	31	continuous	continuous	ADJ
ejpam-4101	365	32	on	on	ADP
ejpam-4101	365	33	the	the	DET
ejpam-4101	365	34	space	space	NOUN
ejpam-4101	365	35	s	s	PART
ejpam-4101	365	36	′	′	NOUN
ejpam-4101	365	37	of	of	ADP
ejpam-4101	365	38	the	the	DET
ejpam-4101	365	39	tempered	temper	VERB
ejpam-4101	365	40	distribution	distribution	NOUN
ejpam-4101	365	41	.	.	PUNCT
ejpam-4101	366	1	theorem	theorem	NOUN
ejpam-4101	366	2	3	3	NUM
ejpam-4101	366	3	.	.	PUNCT
ejpam-4101	367	1	f	f	PROPN
ejpam-4101	367	2	(	(	PUNCT
ejpam-4101	367	3	[	[	X
ejpam-4101	367	4	(	(	PUNCT
ejpam-4101	367	5	rh	rh	PROPN
ejpam-4101	367	6	4k(x	4k(x	PROPN
ejpam-4101	367	7	)	)	PUNCT
ejpam-4101	367	8	∗	∗	NOUN
ejpam-4101	367	9	(	(	PUNCT
ejpam-4101	367	10	−1)2kre	−1)2kre	PROPN
ejpam-4101	367	11	4k(x	4k(x	PROPN
ejpam-4101	367	12	)	)	PUNCT
ejpam-4101	367	13	∗	∗	NOUN
ejpam-4101	367	14	(	(	PUNCT
ejpam-4101	367	15	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	367	16	)	)	PUNCT
ejpam-4101	367	17	∗	∗	NOUN
ejpam-4101	367	18	p2k(x	p2k(x	PROPN
ejpam-4101	367	19	,	,	PUNCT
ejpam-4101	367	20	m	m	PROPN
ejpam-4101	367	21	)	)	PUNCT
ejpam-4101	367	22	]	]	PUNCT
ejpam-4101	368	1	∗	∗	NOUN
ejpam-4101	368	2	[	[	X
ejpam-4101	368	3	(	(	PUNCT
ejpam-4101	368	4	rh	rh	PROPN
ejpam-4101	368	5	4l	4l	NOUN
ejpam-4101	368	6	(	(	PUNCT
ejpam-4101	368	7	x	x	NOUN
ejpam-4101	368	8	)	)	PUNCT
ejpam-4101	368	9	∗	∗	NOUN
ejpam-4101	368	10	(	(	PUNCT
ejpam-4101	368	11	−1)2lre	−1)2lre	NOUN
ejpam-4101	368	12	4l(x	4l(x	NUM
ejpam-4101	368	13	)	)	PUNCT
ejpam-4101	368	14	∗	∗	NOUN
ejpam-4101	368	15	(	(	PUNCT
ejpam-4101	368	16	h∗l(x))∗−1	h∗l(x))∗−1	NOUN
ejpam-4101	368	17	)	)	PUNCT
ejpam-4101	368	18	∗	∗	NOUN
ejpam-4101	368	19	p2l(x	p2l(x	PROPN
ejpam-4101	368	20	,	,	PUNCT
ejpam-4101	368	21	m	m	NOUN
ejpam-4101	368	22	)	)	PUNCT
ejpam-4101	368	23	]	]	PUNCT
ejpam-4101	368	24	)	)	PUNCT
ejpam-4101	369	1	=	=	SYM
ejpam-4101	369	2	(	(	PUNCT
ejpam-4101	369	3	2π)n/2f	2π)n/2f	NUM
ejpam-4101	369	4	[	[	X
ejpam-4101	369	5	(	(	PUNCT
ejpam-4101	369	6	rh	rh	PROPN
ejpam-4101	369	7	4k(x	4k(x	PROPN
ejpam-4101	369	8	)	)	PUNCT
ejpam-4101	369	9	∗	∗	NOUN
ejpam-4101	369	10	(	(	PUNCT
ejpam-4101	369	11	−1)2kre	−1)2kre	PROPN
ejpam-4101	369	12	4k(x	4k(x	PROPN
ejpam-4101	369	13	)	)	PUNCT
ejpam-4101	369	14	∗	∗	NOUN
ejpam-4101	369	15	(	(	PUNCT
ejpam-4101	369	16	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	369	17	)	)	PUNCT
ejpam-4101	369	18	∗	∗	NOUN
ejpam-4101	369	19	p2k(x	p2k(x	PROPN
ejpam-4101	369	20	,	,	PUNCT
ejpam-4101	369	21	m	m	PROPN
ejpam-4101	369	22	)	)	PUNCT
ejpam-4101	369	23	]	]	PUNCT
ejpam-4101	370	1	×f	×f	PROPN
ejpam-4101	370	2	[	[	X
ejpam-4101	370	3	(	(	PUNCT
ejpam-4101	370	4	rh	rh	PROPN
ejpam-4101	370	5	4l	4l	NOUN
ejpam-4101	370	6	(	(	PUNCT
ejpam-4101	370	7	x	x	NOUN
ejpam-4101	370	8	)	)	PUNCT
ejpam-4101	370	9	∗	∗	NOUN
ejpam-4101	370	10	(	(	PUNCT
ejpam-4101	370	11	−1)2lre	−1)2lre	NOUN
ejpam-4101	370	12	4l(x	4l(x	NUM
ejpam-4101	370	13	)	)	PUNCT
ejpam-4101	370	14	∗	∗	NOUN
ejpam-4101	370	15	(	(	PUNCT
ejpam-4101	370	16	h∗l(x))∗−1	h∗l(x))∗−1	NOUN
ejpam-4101	370	17	)	)	PUNCT
ejpam-4101	370	18	∗	∗	NOUN
ejpam-4101	370	19	p2l(x	p2l(x	PROPN
ejpam-4101	370	20	,	,	PUNCT
ejpam-4101	370	21	m	m	NOUN
ejpam-4101	370	22	)	)	PUNCT
ejpam-4101	370	23	]	]	PUNCT
ejpam-4101	371	1	=	=	SYM
ejpam-4101	371	2	1	1	X
ejpam-4101	371	3	(	(	PUNCT
ejpam-4101	371	4	2π)n/2	2π)n/2	NUM
ejpam-4101	371	5	[	[	X
ejpam-4101	371	6	(	(	PUNCT
ejpam-4101	371	7	(	(	PUNCT
ejpam-4101	371	8	ξ21	ξ21	NOUN
ejpam-4101	371	9	+	+	CCONJ
ejpam-4101	371	10	ξ22	ξ22	NOUN
ejpam-4101	371	11	+	+	X
ejpam-4101	371	12	·	·	PUNCT
ejpam-4101	371	13	·	·	PUNCT
ejpam-4101	371	14	·	·	PUNCT
ejpam-4101	371	15	+	+	NUM
ejpam-4101	371	16	ξ2p	ξ2p	NUM
ejpam-4101	371	17	)	)	PUNCT
ejpam-4101	371	18	2	2	NUM
ejpam-4101	371	19	+	+	NUM
ejpam-4101	371	20	m2	m2	PROPN
ejpam-4101	371	21	2	2	NUM
ejpam-4101	371	22	)	)	SYM
ejpam-4101	371	23	2	2	NUM
ejpam-4101	371	24	−	−	NOUN
ejpam-4101	371	25	(	(	PUNCT
ejpam-4101	371	26	(	(	PUNCT
ejpam-4101	371	27	ξ21	ξ21	NOUN
ejpam-4101	371	28	+	+	CCONJ
ejpam-4101	371	29	ξ22	ξ22	NOUN
ejpam-4101	371	30	+	+	X
ejpam-4101	371	31	·	·	PUNCT
ejpam-4101	371	32	·	·	PUNCT
ejpam-4101	371	33	·	·	PUNCT
ejpam-4101	371	34	+	+	NUM
ejpam-4101	371	35	ξ2p	ξ2p	NUM
ejpam-4101	371	36	)	)	PUNCT
ejpam-4101	371	37	2	2	NUM
ejpam-4101	371	38	−	−	NOUN
ejpam-4101	371	39	m2	m2	PROPN
ejpam-4101	371	40	2	2	NUM
ejpam-4101	371	41	)	)	PUNCT
ejpam-4101	371	42	2]k+l	2]k+l	NOUN
ejpam-4101	371	43	,	,	PUNCT
ejpam-4101	371	44	where	where	SCONJ
ejpam-4101	371	45	k	k	PROPN
ejpam-4101	371	46	and	and	CCONJ
ejpam-4101	371	47	l	l	NOUN
ejpam-4101	371	48	are	be	AUX
ejpam-4101	371	49	non	non	ADJ
ejpam-4101	371	50	-	-	ADJ
ejpam-4101	371	51	negative	negative	ADJ
ejpam-4101	371	52	integers	integer	NOUN
ejpam-4101	371	53	and	and	CCONJ
ejpam-4101	371	54	f	f	PROPN
ejpam-4101	371	55	is	be	AUX
ejpam-4101	371	56	bounded	bound	VERB
ejpam-4101	371	57	and	and	CCONJ
ejpam-4101	371	58	continuous	continuous	ADJ
ejpam-4101	371	59	on	on	ADP
ejpam-4101	371	60	the	the	DET
ejpam-4101	371	61	space	space	NOUN
ejpam-4101	371	62	s	s	PART
ejpam-4101	371	63	′	′	NOUN
ejpam-4101	371	64	of	of	ADP
ejpam-4101	371	65	tempered	temper	VERB
ejpam-4101	371	66	distribution	distribution	NOUN
ejpam-4101	371	67	.	.	PUNCT
ejpam-4101	372	1	proof	proof	NOUN
ejpam-4101	372	2	.	.	PUNCT
ejpam-4101	373	1	since	since	SCONJ
ejpam-4101	373	2	rh	rh	PROPN
ejpam-4101	373	3	4k(x	4k(x	PROPN
ejpam-4101	373	4	)	)	PUNCT
ejpam-4101	373	5	,	,	PUNCT
ejpam-4101	373	6	r	r	NOUN
ejpam-4101	373	7	e	e	NOUN
ejpam-4101	373	8	4k(x	4k(x	NUM
ejpam-4101	373	9	)	)	PUNCT
ejpam-4101	373	10	and	and	CCONJ
ejpam-4101	373	11	p2k(x	p2k(x	PROPN
ejpam-4101	373	12	,	,	PUNCT
ejpam-4101	373	13	m	m	VERB
ejpam-4101	373	14	)	)	PUNCT
ejpam-4101	373	15	are	be	AUX
ejpam-4101	373	16	tempered	temper	VERB
ejpam-4101	373	17	distribution	distribution	NOUN
ejpam-4101	373	18	with	with	ADP
ejpam-4101	373	19	compact	compact	ADJ
ejpam-4101	373	20	support	support	NOUN
ejpam-4101	373	21	,	,	PUNCT
ejpam-4101	373	22	(	(	PUNCT
ejpam-4101	373	23	[	[	X
ejpam-4101	373	24	(	(	PUNCT
ejpam-4101	373	25	rh	rh	PROPN
ejpam-4101	373	26	4k(x	4k(x	PROPN
ejpam-4101	373	27	)	)	PUNCT
ejpam-4101	373	28	∗	∗	NOUN
ejpam-4101	373	29	(	(	PUNCT
ejpam-4101	373	30	−1)2kre	−1)2kre	PROPN
ejpam-4101	373	31	4k(x	4k(x	PROPN
ejpam-4101	373	32	)	)	PUNCT
ejpam-4101	373	33	∗	∗	NOUN
ejpam-4101	373	34	(	(	PUNCT
ejpam-4101	373	35	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	373	36	)	)	PUNCT
ejpam-4101	373	37	∗	∗	NOUN
ejpam-4101	373	38	p2k(x	p2k(x	PROPN
ejpam-4101	373	39	,	,	PUNCT
ejpam-4101	373	40	m	m	PROPN
ejpam-4101	373	41	)	)	PUNCT
ejpam-4101	373	42	]	]	PUNCT
ejpam-4101	374	1	∗	∗	NOUN
ejpam-4101	374	2	[	[	X
ejpam-4101	374	3	(	(	PUNCT
ejpam-4101	374	4	rh	rh	PROPN
ejpam-4101	374	5	4l	4l	NOUN
ejpam-4101	374	6	(	(	PUNCT
ejpam-4101	374	7	x	x	NOUN
ejpam-4101	374	8	)	)	PUNCT
ejpam-4101	374	9	∗	∗	NOUN
ejpam-4101	374	10	(	(	PUNCT
ejpam-4101	374	11	−1)2lre	−1)2lre	NOUN
ejpam-4101	374	12	4l(x	4l(x	NUM
ejpam-4101	374	13	)	)	PUNCT
ejpam-4101	374	14	∗	∗	NOUN
ejpam-4101	374	15	(	(	PUNCT
ejpam-4101	374	16	h∗l(x))∗−1	h∗l(x))∗−1	NOUN
ejpam-4101	374	17	)	)	PUNCT
ejpam-4101	374	18	∗	∗	NOUN
ejpam-4101	374	19	p2l(x	p2l(x	PROPN
ejpam-4101	374	20	,	,	PUNCT
ejpam-4101	374	21	m	m	NOUN
ejpam-4101	374	22	)	)	PUNCT
ejpam-4101	374	23	]	]	PUNCT
ejpam-4101	374	24	)	)	PUNCT
ejpam-4101	375	1	=	=	PUNCT
ejpam-4101	375	2	[	[	PUNCT
ejpam-4101	375	3	rh	rh	PROPN
ejpam-4101	375	4	4k(x	4k(x	PROPN
ejpam-4101	375	5	)	)	PUNCT
ejpam-4101	375	6	∗rh	∗rh	VERB
ejpam-4101	375	7	4l	4l	NOUN
ejpam-4101	375	8	(	(	PUNCT
ejpam-4101	375	9	x	x	X
ejpam-4101	375	10	)	)	PUNCT
ejpam-4101	375	11	]	]	PUNCT
ejpam-4101	376	1	∗	∗	NOUN
ejpam-4101	376	2	[	[	PUNCT
ejpam-4101	376	3	(	(	PUNCT
ejpam-4101	376	4	−1)2k+2lre	−1)2k+2lre	PROPN
ejpam-4101	376	5	4k(x	4k(x	PROPN
ejpam-4101	376	6	)	)	PUNCT
ejpam-4101	376	7	∗re	∗re	ADJ
ejpam-4101	376	8	4l(x	4l(x	NUM
ejpam-4101	376	9	)	)	PUNCT
ejpam-4101	376	10	]	]	PUNCT
ejpam-4101	377	1	∗	∗	NOUN
ejpam-4101	377	2	[	[	PUNCT
ejpam-4101	377	3	(	(	PUNCT
ejpam-4101	377	4	h∗k(x))∗−1(h∗l(x))∗−1	h∗k(x))∗−1(h∗l(x))∗−1	PROPN
ejpam-4101	377	5	]	]	X
ejpam-4101	377	6	∗	∗	NOUN
ejpam-4101	378	1	[	[	X
ejpam-4101	378	2	p2k(x	p2k(x	PROPN
ejpam-4101	378	3	,	,	PUNCT
ejpam-4101	378	4	m	m	NOUN
ejpam-4101	378	5	)	)	PUNCT
ejpam-4101	378	6	∗	∗	NOUN
ejpam-4101	378	7	p2l(x	p2l(x	PROPN
ejpam-4101	378	8	,	,	PUNCT
ejpam-4101	378	9	m	m	NOUN
ejpam-4101	378	10	)	)	PUNCT
ejpam-4101	378	11	]	]	PUNCT
ejpam-4101	378	12	references	reference	VERB
ejpam-4101	378	13	1321	1321	NUM
ejpam-4101	378	14	=	=	SYM
ejpam-4101	378	15	[	[	PUNCT
ejpam-4101	378	16	rh	rh	PROPN
ejpam-4101	378	17	4(k+l)(x	4(k+l)(x	PROPN
ejpam-4101	378	18	)	)	PUNCT
ejpam-4101	378	19	]	]	PUNCT
ejpam-4101	379	1	∗	∗	NOUN
ejpam-4101	379	2	[	[	PUNCT
ejpam-4101	379	3	(	(	PUNCT
ejpam-4101	379	4	−1)2(k+l)re	−1)2(k+l)re	NOUN
ejpam-4101	379	5	4(k+l)(x	4(k+l)(x	NOUN
ejpam-4101	379	6	)	)	PUNCT
ejpam-4101	379	7	]	]	PUNCT
ejpam-4101	380	1	∗	∗	NOUN
ejpam-4101	380	2	[	[	PUNCT
ejpam-4101	380	3	(	(	PUNCT
ejpam-4101	380	4	h∗(k+l)(x))∗−1	h∗(k+l)(x))∗−1	NOUN
ejpam-4101	380	5	]	]	PUNCT
ejpam-4101	380	6	∗	∗	NOUN
ejpam-4101	380	7	[	[	PUNCT
ejpam-4101	380	8	p2(k+l)(x	p2(k+l)(x	NOUN
ejpam-4101	380	9	,	,	PUNCT
ejpam-4101	380	10	m	m	NOUN
ejpam-4101	380	11	)	)	PUNCT
ejpam-4101	380	12	]	]	PUNCT
ejpam-4101	380	13	by	by	ADP
ejpam-4101	380	14	[	[	X
ejpam-4101	380	15	8	8	NUM
ejpam-4101	380	16	,	,	PUNCT
ejpam-4101	380	17	pages	page	NOUN
ejpam-4101	380	18	156–159	156–159	NUM
ejpam-4101	380	19	]	]	PUNCT
ejpam-4101	380	20	and	and	CCONJ
ejpam-4101	380	21	[	[	X
ejpam-4101	380	22	21	21	NUM
ejpam-4101	380	23	,	,	PUNCT
ejpam-4101	380	24	lemma	lemma	PROPN
ejpam-4101	380	25	2.45	2.45	NUM
ejpam-4101	380	26	]	]	PUNCT
ejpam-4101	380	27	.	.	PUNCT
ejpam-4101	381	1	taking	take	VERB
ejpam-4101	381	2	the	the	DET
ejpam-4101	381	3	fourier	fourier	NOUN
ejpam-4101	381	4	transform	transform	NOUN
ejpam-4101	381	5	on	on	ADP
ejpam-4101	381	6	both	both	DET
ejpam-4101	381	7	sides	side	NOUN
ejpam-4101	381	8	and	and	CCONJ
ejpam-4101	381	9	using	use	VERB
ejpam-4101	381	10	theorem	theorem	NOUN
ejpam-4101	381	11	2	2	NUM
ejpam-4101	381	12	,	,	PUNCT
ejpam-4101	381	13	we	we	PRON
ejpam-4101	381	14	obtain	obtain	VERB
ejpam-4101	381	15	f	f	X
ejpam-4101	381	16	(	(	PUNCT
ejpam-4101	381	17	[	[	X
ejpam-4101	381	18	(	(	PUNCT
ejpam-4101	381	19	rh	rh	PROPN
ejpam-4101	381	20	4k(x	4k(x	PROPN
ejpam-4101	381	21	)	)	PUNCT
ejpam-4101	382	1	∗	∗	NOUN
ejpam-4101	382	2	(	(	PUNCT
ejpam-4101	382	3	−1)2kre	−1)2kre	PROPN
ejpam-4101	382	4	4k(x	4k(x	PROPN
ejpam-4101	382	5	)	)	PUNCT
ejpam-4101	382	6	∗	∗	NOUN
ejpam-4101	382	7	(	(	PUNCT
ejpam-4101	382	8	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	382	9	)	)	PUNCT
ejpam-4101	382	10	∗	∗	NOUN
ejpam-4101	382	11	p2k(x	p2k(x	PROPN
ejpam-4101	382	12	,	,	PUNCT
ejpam-4101	382	13	m	m	PROPN
ejpam-4101	382	14	)	)	PUNCT
ejpam-4101	382	15	]	]	PUNCT
ejpam-4101	383	1	∗	∗	NOUN
ejpam-4101	383	2	[	[	X
ejpam-4101	383	3	(	(	PUNCT
ejpam-4101	383	4	rh	rh	PROPN
ejpam-4101	383	5	4l	4l	NOUN
ejpam-4101	383	6	(	(	PUNCT
ejpam-4101	383	7	x	x	NOUN
ejpam-4101	383	8	)	)	PUNCT
ejpam-4101	383	9	∗	∗	NOUN
ejpam-4101	383	10	(	(	PUNCT
ejpam-4101	383	11	−1)2lre	−1)2lre	NOUN
ejpam-4101	383	12	4l(x	4l(x	NUM
ejpam-4101	383	13	)	)	PUNCT
ejpam-4101	383	14	∗	∗	NOUN
ejpam-4101	383	15	(	(	PUNCT
ejpam-4101	383	16	h∗l(x))∗−1	h∗l(x))∗−1	NOUN
ejpam-4101	383	17	)	)	PUNCT
ejpam-4101	383	18	∗	∗	NOUN
ejpam-4101	383	19	p2l(x	p2l(x	PROPN
ejpam-4101	383	20	,	,	PUNCT
ejpam-4101	383	21	m	m	NOUN
ejpam-4101	383	22	)	)	PUNCT
ejpam-4101	383	23	]	]	PUNCT
ejpam-4101	383	24	)	)	PUNCT
ejpam-4101	384	1	=	=	SYM
ejpam-4101	384	2	1	1	NUM
ejpam-4101	384	3	(	(	PUNCT
ejpam-4101	384	4	2π)n/2	2π)n/2	NUM
ejpam-4101	384	5	[	[	X
ejpam-4101	384	6	(	(	PUNCT
ejpam-4101	384	7	(	(	PUNCT
ejpam-4101	384	8	ξ21	ξ21	NOUN
ejpam-4101	384	9	+	+	CCONJ
ejpam-4101	384	10	ξ22	ξ22	NOUN
ejpam-4101	384	11	+	+	X
ejpam-4101	384	12	·	·	PUNCT
ejpam-4101	384	13	·	·	PUNCT
ejpam-4101	384	14	·	·	PUNCT
ejpam-4101	384	15	+	+	NUM
ejpam-4101	384	16	ξ2p	ξ2p	NUM
ejpam-4101	384	17	)	)	PUNCT
ejpam-4101	384	18	2	2	NUM
ejpam-4101	384	19	+	+	NUM
ejpam-4101	384	20	m2	m2	PROPN
ejpam-4101	384	21	2	2	NUM
ejpam-4101	384	22	)	)	SYM
ejpam-4101	384	23	2	2	NUM
ejpam-4101	384	24	−	−	NOUN
ejpam-4101	384	25	(	(	PUNCT
ejpam-4101	384	26	(	(	PUNCT
ejpam-4101	384	27	ξ21	ξ21	NOUN
ejpam-4101	384	28	+	+	CCONJ
ejpam-4101	384	29	ξ22	ξ22	NOUN
ejpam-4101	384	30	+	+	X
ejpam-4101	384	31	·	·	PUNCT
ejpam-4101	384	32	·	·	PUNCT
ejpam-4101	384	33	·	·	PUNCT
ejpam-4101	384	34	+	+	NUM
ejpam-4101	384	35	ξ2p	ξ2p	NUM
ejpam-4101	384	36	)	)	PUNCT
ejpam-4101	384	37	2	2	NUM
ejpam-4101	384	38	−	−	NOUN
ejpam-4101	384	39	m2	m2	PROPN
ejpam-4101	384	40	2	2	NUM
ejpam-4101	384	41	)	)	PUNCT
ejpam-4101	384	42	2]k+l	2]k+l	NOUN
ejpam-4101	384	43	=	=	SYM
ejpam-4101	384	44	1	1	NUM
ejpam-4101	384	45	(	(	PUNCT
ejpam-4101	384	46	2π)n/2	2π)n/2	NUM
ejpam-4101	384	47	[	[	X
ejpam-4101	384	48	(	(	PUNCT
ejpam-4101	384	49	(	(	PUNCT
ejpam-4101	384	50	ξ21	ξ21	NOUN
ejpam-4101	384	51	+	+	CCONJ
ejpam-4101	384	52	ξ22	ξ22	NOUN
ejpam-4101	384	53	+	+	X
ejpam-4101	384	54	·	·	PUNCT
ejpam-4101	384	55	·	·	PUNCT
ejpam-4101	384	56	·	·	PUNCT
ejpam-4101	384	57	+	+	NUM
ejpam-4101	384	58	ξ2p	ξ2p	NUM
ejpam-4101	384	59	)	)	PUNCT
ejpam-4101	384	60	2	2	NUM
ejpam-4101	384	61	+	+	NUM
ejpam-4101	384	62	m2	m2	PROPN
ejpam-4101	384	63	2	2	NUM
ejpam-4101	384	64	)	)	SYM
ejpam-4101	384	65	2	2	NUM
ejpam-4101	384	66	−	−	NOUN
ejpam-4101	384	67	(	(	PUNCT
ejpam-4101	384	68	(	(	PUNCT
ejpam-4101	384	69	ξ21	ξ21	NOUN
ejpam-4101	384	70	+	+	CCONJ
ejpam-4101	384	71	ξ22	ξ22	NOUN
ejpam-4101	384	72	+	+	X
ejpam-4101	384	73	·	·	PUNCT
ejpam-4101	384	74	·	·	PUNCT
ejpam-4101	384	75	·	·	PUNCT
ejpam-4101	384	76	+	+	NUM
ejpam-4101	384	77	ξ2p	ξ2p	NUM
ejpam-4101	384	78	)	)	PUNCT
ejpam-4101	384	79	2	2	NUM
ejpam-4101	384	80	−	−	NOUN
ejpam-4101	384	81	m2	m2	PROPN
ejpam-4101	384	82	2	2	NUM
ejpam-4101	384	83	)	)	PUNCT
ejpam-4101	384	84	2]k	2]k	NUM
ejpam-4101	384	85	×	×	NOUN
ejpam-4101	384	86	(	(	PUNCT
ejpam-4101	384	87	2π)n/2	2π)n/2	NUM
ejpam-4101	384	88	(	(	PUNCT
ejpam-4101	384	89	2π)n/2	2π)n/2	NUM
ejpam-4101	384	90	[	[	X
ejpam-4101	384	91	(	(	PUNCT
ejpam-4101	384	92	(	(	PUNCT
ejpam-4101	384	93	ξ21	ξ21	NOUN
ejpam-4101	384	94	+	+	CCONJ
ejpam-4101	384	95	ξ22	ξ22	NOUN
ejpam-4101	384	96	+	+	X
ejpam-4101	384	97	·	·	PUNCT
ejpam-4101	384	98	·	·	PUNCT
ejpam-4101	384	99	·	·	PUNCT
ejpam-4101	384	100	+	+	NUM
ejpam-4101	384	101	ξ2p	ξ2p	NUM
ejpam-4101	384	102	)	)	PUNCT
ejpam-4101	384	103	2	2	NUM
ejpam-4101	384	104	+	+	NUM
ejpam-4101	384	105	m2	m2	PROPN
ejpam-4101	384	106	2	2	NUM
ejpam-4101	384	107	)	)	SYM
ejpam-4101	384	108	2	2	NUM
ejpam-4101	384	109	−	−	NOUN
ejpam-4101	384	110	(	(	PUNCT
ejpam-4101	384	111	(	(	PUNCT
ejpam-4101	384	112	ξ21	ξ21	NOUN
ejpam-4101	384	113	+	+	CCONJ
ejpam-4101	384	114	ξ22	ξ22	NOUN
ejpam-4101	384	115	+	+	X
ejpam-4101	384	116	·	·	PUNCT
ejpam-4101	384	117	·	·	PUNCT
ejpam-4101	384	118	·	·	PUNCT
ejpam-4101	384	119	+	+	NUM
ejpam-4101	384	120	ξ2p	ξ2p	NUM
ejpam-4101	384	121	)	)	PUNCT
ejpam-4101	384	122	2	2	NUM
ejpam-4101	384	123	−	−	NOUN
ejpam-4101	384	124	m2	m2	PROPN
ejpam-4101	384	125	2	2	NUM
ejpam-4101	384	126	)	)	PUNCT
ejpam-4101	384	127	2]l	2]l	NUM
ejpam-4101	384	128	=	=	SYM
ejpam-4101	384	129	(	(	PUNCT
ejpam-4101	384	130	2π)n/2f	2π)n/2f	NUM
ejpam-4101	384	131	[	[	X
ejpam-4101	384	132	(	(	PUNCT
ejpam-4101	384	133	rh	rh	PROPN
ejpam-4101	384	134	4k(x	4k(x	PROPN
ejpam-4101	384	135	)	)	PUNCT
ejpam-4101	384	136	∗	∗	NOUN
ejpam-4101	384	137	(	(	PUNCT
ejpam-4101	384	138	−1)2kre	−1)2kre	PROPN
ejpam-4101	384	139	4k(x	4k(x	PROPN
ejpam-4101	384	140	)	)	PUNCT
ejpam-4101	384	141	∗	∗	NOUN
ejpam-4101	384	142	(	(	PUNCT
ejpam-4101	384	143	h∗k(x))∗−1	h∗k(x))∗−1	NOUN
ejpam-4101	384	144	)	)	PUNCT
ejpam-4101	384	145	∗	∗	NOUN
ejpam-4101	384	146	p2k(x	p2k(x	PROPN
ejpam-4101	384	147	,	,	PUNCT
ejpam-4101	384	148	m	m	PROPN
ejpam-4101	384	149	)	)	PUNCT
ejpam-4101	384	150	]	]	PUNCT
ejpam-4101	385	1	×f	×f	PROPN
ejpam-4101	385	2	[	[	X
ejpam-4101	385	3	(	(	PUNCT
ejpam-4101	385	4	rh	rh	PROPN
ejpam-4101	385	5	4l	4l	NOUN
ejpam-4101	385	6	(	(	PUNCT
ejpam-4101	385	7	x	x	NOUN
ejpam-4101	385	8	)	)	PUNCT
ejpam-4101	385	9	∗	∗	NOUN
ejpam-4101	385	10	(	(	PUNCT
ejpam-4101	385	11	−1)2lre	−1)2lre	NOUN
ejpam-4101	385	12	4l(x	4l(x	NUM
ejpam-4101	385	13	)	)	PUNCT
ejpam-4101	385	14	∗	∗	NOUN
ejpam-4101	385	15	(	(	PUNCT
ejpam-4101	385	16	h∗l(x))∗−1	h∗l(x))∗−1	NOUN
ejpam-4101	385	17	)	)	PUNCT
ejpam-4101	385	18	∗	∗	NOUN
ejpam-4101	385	19	p2l(x	p2l(x	PROPN
ejpam-4101	385	20	,	,	PUNCT
ejpam-4101	385	21	m	m	PROPN
ejpam-4101	385	22	)	)	PUNCT
ejpam-4101	385	23	]	]	PUNCT
ejpam-4101	385	24	.	.	PUNCT
ejpam-4101	386	1	since	since	SCONJ
ejpam-4101	386	2	(	(	PUNCT
ejpam-4101	386	3	rh	rh	PROPN
ejpam-4101	386	4	4(k+l)(x	4(k+l)(x	PROPN
ejpam-4101	386	5	)	)	PUNCT
ejpam-4101	386	6	∗	∗	NOUN
ejpam-4101	386	7	(	(	PUNCT
ejpam-4101	386	8	−1)2(k+l)re	−1)2(k+l)re	NOUN
ejpam-4101	386	9	4(k+l)(x	4(k+l)(x	NOUN
ejpam-4101	386	10	)	)	PUNCT
ejpam-4101	386	11	∗	∗	NOUN
ejpam-4101	386	12	(	(	PUNCT
ejpam-4101	386	13	h	h	NOUN
ejpam-4101	386	14	∗(k+l)(x))∗−1	∗(k+l)(x))∗−1	PROPN
ejpam-4101	386	15	)	)	PUNCT
ejpam-4101	386	16	∗	∗	NOUN
ejpam-4101	386	17	(	(	PUNCT
ejpam-4101	386	18	p2(k+l)(x	p2(k+l)(x	NOUN
ejpam-4101	386	19	,	,	PUNCT
ejpam-4101	386	20	m	m	NOUN
ejpam-4101	386	21	)	)	PUNCT
ejpam-4101	386	22	)	)	PUNCT
ejpam-4101	387	1	∈	∈	PROPN
ejpam-4101	387	2	s	s	VERB
ejpam-4101	387	3	′	′	NOUN
ejpam-4101	387	4	,	,	PUNCT
ejpam-4101	387	5	the	the	DET
ejpam-4101	387	6	space	space	NOUN
ejpam-4101	387	7	of	of	ADP
ejpam-4101	387	8	tempered	temper	VERB
ejpam-4101	387	9	distribution	distribution	NOUN
ejpam-4101	387	10	and	and	CCONJ
ejpam-4101	387	11	by	by	ADP
ejpam-4101	387	12	theorem	theorem	NOUN
ejpam-4101	387	13	2	2	NUM
ejpam-4101	387	14	,	,	PUNCT
ejpam-4101	387	15	we	we	PRON
ejpam-4101	387	16	obtain	obtain	VERB
ejpam-4101	387	17	that	that	SCONJ
ejpam-4101	387	18	f	f	PROPN
ejpam-4101	387	19	is	be	AUX
ejpam-4101	387	20	bounded	bound	VERB
ejpam-4101	387	21	and	and	CCONJ
ejpam-4101	387	22	continuous	continuous	ADJ
ejpam-4101	387	23	on	on	ADP
ejpam-4101	387	24	s	s	NOUN
ejpam-4101	387	25	′	′	NUM
ejpam-4101	387	26	.	.	PUNCT
ejpam-4101	388	1	acknowledgements	acknowledgement	NOUN
ejpam-4101	388	2	the	the	DET
ejpam-4101	388	3	author	author	NOUN
ejpam-4101	388	4	would	would	AUX
ejpam-4101	388	5	like	like	VERB
ejpam-4101	388	6	to	to	PART
ejpam-4101	388	7	thank	thank	VERB
ejpam-4101	388	8	the	the	DET
ejpam-4101	388	9	referees	referee	NOUN
ejpam-4101	388	10	for	for	ADP
ejpam-4101	388	11	their	their	PRON
ejpam-4101	388	12	suggestions	suggestion	NOUN
ejpam-4101	388	13	which	which	PRON
ejpam-4101	388	14	enhanced	enhance	VERB
ejpam-4101	388	15	the	the	DET
ejpam-4101	388	16	presentation	presentation	NOUN
ejpam-4101	388	17	of	of	ADP
ejpam-4101	388	18	the	the	DET
ejpam-4101	388	19	paper	paper	NOUN
ejpam-4101	388	20	.	.	PUNCT
ejpam-4101	389	1	the	the	DET
ejpam-4101	389	2	author	author	NOUN
ejpam-4101	389	3	was	be	AUX
ejpam-4101	389	4	supported	support	VERB
ejpam-4101	389	5	by	by	ADP
ejpam-4101	389	6	sakon	sakon	PROPN
ejpam-4101	389	7	nakhon	nakhon	PROPN
ejpam-4101	389	8	rajabhat	rajabhat	PROPN
ejpam-4101	389	9	university	university	PROPN
ejpam-4101	389	10	,	,	PUNCT
ejpam-4101	389	11	thailand	thailand	PROPN
ejpam-4101	389	12	.	.	PUNCT
ejpam-4101	390	1	references	reference	NOUN
ejpam-4101	390	2	[	[	X
ejpam-4101	390	3	1	1	NUM
ejpam-4101	390	4	]	]	X
ejpam-4101	390	5	w.f	w.f	PROPN
ejpam-4101	390	6	.	.	PROPN
ejpam-4101	390	7	donoghue	donoghue	PROPN
ejpam-4101	390	8	,	,	PUNCT
ejpam-4101	390	9	distribution	distribution	NOUN
ejpam-4101	390	10	and	and	CCONJ
ejpam-4101	390	11	fourier	fourier	NOUN
ejpam-4101	390	12	transform	transform	NOUN
ejpam-4101	390	13	.	.	PUNCT
ejpam-4101	391	1	academic	academic	ADJ
ejpam-4101	391	2	press	press	NOUN
ejpam-4101	391	3	,	,	PUNCT
ejpam-4101	391	4	new	new	PROPN
ejpam-4101	391	5	york	york	PROPN
ejpam-4101	391	6	,	,	PUNCT
ejpam-4101	391	7	1969	1969	NUM
ejpam-4101	391	8	.	.	PUNCT
ejpam-4101	392	1	[	[	X
ejpam-4101	392	2	2	2	NUM
ejpam-4101	392	3	]	]	X
ejpam-4101	392	4	deepmala	deepmala	PROPN
ejpam-4101	392	5	,	,	PUNCT
ejpam-4101	392	6	l.n	l.n	PROPN
ejpam-4101	392	7	.	.	PROPN
ejpam-4101	392	8	mishra	mishra	PROPN
ejpam-4101	392	9	and	and	CCONJ
ejpam-4101	392	10	v.n	v.n	PROPN
ejpam-4101	392	11	.	.	PUNCT
ejpam-4101	393	1	mishra	mishra	PROPN
ejpam-4101	393	2	.	.	PROPN
ejpam-4101	394	1	trigonometric	trigonometric	ADJ
ejpam-4101	394	2	approximation	approximation	NOUN
ejpam-4101	394	3	of	of	ADP
ejpam-4101	394	4	signals	signal	NOUN
ejpam-4101	394	5	(	(	PUNCT
ejpam-4101	394	6	functions	function	NOUN
ejpam-4101	394	7	)	)	PUNCT
ejpam-4101	394	8	belonging	belong	VERB
ejpam-4101	394	9	to	to	ADP
ejpam-4101	394	10	the	the	DET
ejpam-4101	394	11	w	w	PROPN
ejpam-4101	394	12	(	(	PUNCT
ejpam-4101	394	13	lr	lr	INTJ
ejpam-4101	394	14	,	,	PUNCT
ejpam-4101	394	15	ξ(t	ξ(t	NOUN
ejpam-4101	394	16	)	)	PUNCT
ejpam-4101	394	17	)	)	PUNCT
ejpam-4101	394	18	,	,	PUNCT
ejpam-4101	394	19	(	(	PUNCT
ejpam-4101	394	20	r	r	NOUN
ejpam-4101	394	21	≥	≥	NOUN
ejpam-4101	394	22	1)class	1)class	NUM
ejpam-4101	394	23	by	by	ADP
ejpam-4101	394	24	(	(	PUNCT
ejpam-4101	394	25	e	e	NOUN
ejpam-4101	394	26	,	,	PUNCT
ejpam-4101	394	27	q)(q	q)(q	X
ejpam-4101	394	28	>	>	X
ejpam-4101	394	29	0)-means	0)-mean	NOUN
ejpam-4101	394	30	of	of	ADP
ejpam-4101	394	31	the	the	DET
ejpam-4101	394	32	conjugate	conjugate	ADJ
ejpam-4101	394	33	series	series	NOUN
ejpam-4101	394	34	of	of	ADP
ejpam-4101	394	35	its	its	PRON
ejpam-4101	394	36	fourier	fourier	NOUN
ejpam-4101	394	37	series	series	NOUN
ejpam-4101	394	38	.	.	PUNCT
ejpam-4101	395	1	gjms	gjms	PROPN
ejpam-4101	395	2	special	special	ADJ
ejpam-4101	395	3	issue	issue	NOUN
ejpam-4101	395	4	for	for	ADP
ejpam-4101	395	5	recent	recent	ADJ
ejpam-4101	395	6	advances	advance	NOUN
ejpam-4101	395	7	in	in	ADP
ejpam-4101	395	8	references	reference	NOUN
ejpam-4101	395	9	1322	1322	NUM
ejpam-4101	395	10	mathematical	mathematical	ADJ
ejpam-4101	395	11	sciences	sciences	PROPN
ejpam-4101	395	12	and	and	CCONJ
ejpam-4101	395	13	applications-13	applications-13	PROPN
ejpam-4101	395	14	,	,	PUNCT
ejpam-4101	395	15	global	global	ADJ
ejpam-4101	395	16	journal	journal	NOUN
ejpam-4101	395	17	of	of	ADP
ejpam-4101	395	18	mathematical	mathematical	ADJ
ejpam-4101	395	19	sciences	science	NOUN
ejpam-4101	395	20	,	,	PUNCT
ejpam-4101	395	21	2:61	2:61	NUM
ejpam-4101	395	22	-	-	SYM
ejpam-4101	395	23	69	69	NUM
ejpam-4101	395	24	,	,	PUNCT
ejpam-4101	395	25	2014	2014	NUM
ejpam-4101	395	26	.	.	PUNCT
ejpam-4101	396	1	[	[	X
ejpam-4101	396	2	3	3	NUM
ejpam-4101	396	3	]	]	PUNCT
ejpam-4101	396	4	a.	a.	NOUN
ejpam-4101	396	5	kananthai	kananthai	PROPN
ejpam-4101	396	6	,	,	PUNCT
ejpam-4101	396	7	on	on	ADP
ejpam-4101	396	8	the	the	DET
ejpam-4101	396	9	inversion	inversion	NOUN
ejpam-4101	396	10	of	of	ADP
ejpam-4101	396	11	the	the	DET
ejpam-4101	396	12	kernel	kernel	NOUN
ejpam-4101	396	13	kα	kα	PROPN
ejpam-4101	396	14	,	,	PUNCT
ejpam-4101	396	15	β	β	X
ejpam-4101	396	16	,	,	PUNCT
ejpam-4101	396	17	γ	γ	X
ejpam-4101	396	18	,	,	PUNCT
ejpam-4101	396	19	ν	ν	NOUN
ejpam-4101	396	20	related	relate	VERB
ejpam-4101	396	21	to	to	ADP
ejpam-4101	396	22	the	the	DET
ejpam-4101	396	23	operator	operator	NOUN
ejpam-4101	396	24	⊕k	⊕k	NOUN
ejpam-4101	396	25	.	.	PUNCT
ejpam-4101	397	1	indian	indian	PROPN
ejpam-4101	397	2	journal	journal	PROPN
ejpam-4101	397	3	of	of	ADP
ejpam-4101	397	4	pure	pure	ADJ
ejpam-4101	397	5	and	and	CCONJ
ejpam-4101	397	6	applied	applied	ADJ
ejpam-4101	397	7	mathematics	mathematic	NOUN
ejpam-4101	397	8	,	,	PUNCT
ejpam-4101	397	9	34:1419	34:1419	NUM
ejpam-4101	397	10	-	-	SYM
ejpam-4101	397	11	1429	1429	NUM
ejpam-4101	397	12	,	,	PUNCT
ejpam-4101	397	13	2003	2003	NUM
ejpam-4101	397	14	.	.	PUNCT
ejpam-4101	398	1	[	[	X
ejpam-4101	398	2	4	4	NUM
ejpam-4101	398	3	]	]	PUNCT
ejpam-4101	398	4	a.	a.	NOUN
ejpam-4101	398	5	kananthai	kananthai	PROPN
ejpam-4101	398	6	.	.	PUNCT
ejpam-4101	399	1	on	on	ADP
ejpam-4101	399	2	the	the	DET
ejpam-4101	399	3	green	green	ADJ
ejpam-4101	399	4	function	function	NOUN
ejpam-4101	399	5	of	of	ADP
ejpam-4101	399	6	the	the	DET
ejpam-4101	399	7	diamond	diamond	NOUN
ejpam-4101	399	8	operator	operator	NOUN
ejpam-4101	399	9	related	relate	VERB
ejpam-4101	399	10	to	to	ADP
ejpam-4101	399	11	the	the	DET
ejpam-4101	399	12	kleingordon	kleingordon	NOUN
ejpam-4101	399	13	operator	operator	NOUN
ejpam-4101	399	14	.	.	PUNCT
ejpam-4101	400	1	bulletin	bulletin	NOUN
ejpam-4101	400	2	of	of	ADP
ejpam-4101	400	3	the	the	DET
ejpam-4101	400	4	calcutta	calcutta	PROPN
ejpam-4101	400	5	mathematical	mathematical	ADJ
ejpam-4101	400	6	society	society	NOUN
ejpam-4101	400	7	,	,	PUNCT
ejpam-4101	400	8	93:353	93:353	NUM
ejpam-4101	400	9	-	-	SYM
ejpam-4101	400	10	360	360	NUM
ejpam-4101	400	11	,	,	PUNCT
ejpam-4101	400	12	2001	2001	NUM
ejpam-4101	400	13	.	.	PUNCT
ejpam-4101	401	1	[	[	X
ejpam-4101	401	2	5	5	NUM
ejpam-4101	401	3	]	]	PUNCT
ejpam-4101	401	4	a.	a.	NOUN
ejpam-4101	401	5	kananthai	kananthai	PROPN
ejpam-4101	401	6	.	.	PUNCT
ejpam-4101	402	1	on	on	ADP
ejpam-4101	402	2	the	the	DET
ejpam-4101	402	3	solutions	solution	NOUN
ejpam-4101	402	4	of	of	ADP
ejpam-4101	402	5	the	the	DET
ejpam-4101	402	6	n	n	ADV
ejpam-4101	402	7	-	-	PUNCT
ejpam-4101	402	8	dimensional	dimensional	ADJ
ejpam-4101	402	9	diamond	diamond	NOUN
ejpam-4101	402	10	operator	operator	NOUN
ejpam-4101	402	11	.	.	PUNCT
ejpam-4101	403	1	applied	apply	VERB
ejpam-4101	403	2	mathematics	mathematic	NOUN
ejpam-4101	403	3	and	and	CCONJ
ejpam-4101	403	4	computation	computation	NOUN
ejpam-4101	403	5	,	,	PUNCT
ejpam-4101	403	6	88:27	88:27	NUM
ejpam-4101	403	7	-	-	SYM
ejpam-4101	403	8	37	37	NUM
ejpam-4101	403	9	,	,	PUNCT
ejpam-4101	403	10	1997	1997	NUM
ejpam-4101	403	11	.	.	PUNCT
ejpam-4101	404	1	[	[	X
ejpam-4101	404	2	6	6	NUM
ejpam-4101	404	3	]	]	PUNCT
ejpam-4101	404	4	a.	a.	NOUN
ejpam-4101	404	5	kananthai	kananthai	PROPN
ejpam-4101	404	6	,	,	PUNCT
ejpam-4101	404	7	s.	s.	PROPN
ejpam-4101	404	8	suantai	suantai	VERB
ejpam-4101	404	9	and	and	CCONJ
ejpam-4101	404	10	v.	v.	ADP
ejpam-4101	404	11	longani	longani	PROPN
ejpam-4101	404	12	.	.	PUNCT
ejpam-4101	405	1	on	on	ADP
ejpam-4101	405	2	the	the	DET
ejpam-4101	405	3	operator	operator	NOUN
ejpam-4101	405	4	⊕k	⊕k	NOUN
ejpam-4101	405	5	related	relate	VERB
ejpam-4101	405	6	to	to	ADP
ejpam-4101	405	7	the	the	DET
ejpam-4101	405	8	wave	wave	NOUN
ejpam-4101	405	9	equation	equation	NOUN
ejpam-4101	405	10	and	and	CCONJ
ejpam-4101	405	11	laplacian	laplacian	PROPN
ejpam-4101	405	12	.	.	PUNCT
ejpam-4101	405	13	applied	apply	VERB
ejpam-4101	405	14	mathematics	mathematic	NOUN
ejpam-4101	405	15	and	and	CCONJ
ejpam-4101	405	16	computation	computation	NOUN
ejpam-4101	405	17	,	,	PUNCT
ejpam-4101	405	18	132:219	132:219	NOUN
ejpam-4101	405	19	-	-	SYM
ejpam-4101	405	20	229	229	NUM
ejpam-4101	405	21	,	,	PUNCT
ejpam-4101	405	22	2002	2002	NUM
ejpam-4101	405	23	.	.	PUNCT
ejpam-4101	406	1	[	[	X
ejpam-4101	406	2	7	7	X
ejpam-4101	406	3	]	]	PUNCT
ejpam-4101	406	4	a.	a.	NOUN
ejpam-4101	406	5	kananthai	kananthai	PROPN
ejpam-4101	406	6	,	,	PUNCT
ejpam-4101	406	7	s.	s.	PROPN
ejpam-4101	406	8	suantai	suantai	VERB
ejpam-4101	406	9	and	and	CCONJ
ejpam-4101	406	10	v.	v.	ADP
ejpam-4101	406	11	longani	longani	PROPN
ejpam-4101	406	12	.	.	PUNCT
ejpam-4101	407	1	on	on	ADP
ejpam-4101	407	2	the	the	DET
ejpam-4101	407	3	weak	weak	ADJ
ejpam-4101	407	4	solution	solution	NOUN
ejpam-4101	407	5	of	of	ADP
ejpam-4101	407	6	the	the	DET
ejpam-4101	407	7	equation	equation	NOUN
ejpam-4101	407	8	related	relate	VERB
ejpam-4101	407	9	to	to	ADP
ejpam-4101	407	10	the	the	DET
ejpam-4101	407	11	diamond	diamond	NOUN
ejpam-4101	407	12	operator	operator	NOUN
ejpam-4101	407	13	.	.	PUNCT
ejpam-4101	408	1	computational	computational	ADJ
ejpam-4101	408	2	technologies	technology	NOUN
ejpam-4101	408	3	,	,	PUNCT
ejpam-4101	408	4	5:42	5:42	NUM
ejpam-4101	408	5	-	-	SYM
ejpam-4101	408	6	48	48	NUM
ejpam-4101	408	7	,	,	PUNCT
ejpam-4101	408	8	2000	2000	NUM
ejpam-4101	408	9	.	.	PUNCT
ejpam-4101	409	1	[	[	X
ejpam-4101	409	2	8	8	NUM
ejpam-4101	409	3	]	]	PUNCT
ejpam-4101	409	4	a.	a.	NOUN
ejpam-4101	409	5	kananthai	kananthai	PROPN
ejpam-4101	409	6	.	.	PUNCT
ejpam-4101	410	1	on	on	ADP
ejpam-4101	410	2	the	the	DET
ejpam-4101	410	3	distribution	distribution	NOUN
ejpam-4101	410	4	related	relate	VERB
ejpam-4101	410	5	to	to	ADP
ejpam-4101	410	6	the	the	DET
ejpam-4101	410	7	ultra	ultra	ADJ
ejpam-4101	410	8	-	-	ADJ
ejpam-4101	410	9	hyperbolic	hyperbolic	ADJ
ejpam-4101	410	10	equation	equation	NOUN
ejpam-4101	410	11	.	.	PUNCT
ejpam-4101	411	1	journal	journal	NOUN
ejpam-4101	411	2	of	of	ADP
ejpam-4101	411	3	computational	computational	ADJ
ejpam-4101	411	4	and	and	CCONJ
ejpam-4101	411	5	applied	applied	ADJ
ejpam-4101	411	6	mathematics	mathematic	NOUN
ejpam-4101	411	7	,	,	PUNCT
ejpam-4101	411	8	84:101	84:101	NUM
ejpam-4101	411	9	-	-	SYM
ejpam-4101	411	10	106	106	NUM
ejpam-4101	411	11	,	,	PUNCT
ejpam-4101	411	12	1997	1997	NUM
ejpam-4101	411	13	.	.	PUNCT
ejpam-4101	412	1	[	[	X
ejpam-4101	412	2	9	9	NUM
ejpam-4101	412	3	]	]	PUNCT
ejpam-4101	412	4	a.	a.	NOUN
ejpam-4101	412	5	liangprom	liangprom	NOUN
ejpam-4101	412	6	and	and	CCONJ
ejpam-4101	412	7	k.	k.	X
ejpam-4101	412	8	nonlaopon	nonlaopon	PROPN
ejpam-4101	412	9	.	.	PUNCT
ejpam-4101	413	1	on	on	ADP
ejpam-4101	413	2	the	the	DET
ejpam-4101	413	3	convolution	convolution	NOUN
ejpam-4101	413	4	equation	equation	NOUN
ejpam-4101	413	5	related	relate	VERB
ejpam-4101	413	6	to	to	ADP
ejpam-4101	413	7	the	the	DET
ejpam-4101	413	8	kleingordon	kleingordon	NOUN
ejpam-4101	413	9	operator	operator	NOUN
ejpam-4101	413	10	,	,	PUNCT
ejpam-4101	413	11	international	international	ADJ
ejpam-4101	413	12	journal	journal	NOUN
ejpam-4101	413	13	of	of	ADP
ejpam-4101	413	14	pure	pure	ADJ
ejpam-4101	413	15	and	and	CCONJ
ejpam-4101	413	16	applied	applied	ADJ
ejpam-4101	413	17	mathematics	mathematic	NOUN
ejpam-4101	413	18	,	,	PUNCT
ejpam-4101	413	19	71:67	71:67	NUM
ejpam-4101	413	20	-	-	SYM
ejpam-4101	413	21	82	82	NUM
ejpam-4101	413	22	,	,	PUNCT
ejpam-4101	413	23	2011	2011	NUM
ejpam-4101	413	24	.	.	PUNCT
ejpam-4101	414	1	[	[	X
ejpam-4101	414	2	10	10	NUM
ejpam-4101	414	3	]	]	PUNCT
ejpam-4101	414	4	a.	a.	NOUN
ejpam-4101	414	5	liangprom	liangprom	NOUN
ejpam-4101	414	6	and	and	CCONJ
ejpam-4101	414	7	k.	k.	X
ejpam-4101	414	8	nonlaopon	nonlaopon	PROPN
ejpam-4101	414	9	.	.	PUNCT
ejpam-4101	415	1	on	on	ADP
ejpam-4101	415	2	the	the	DET
ejpam-4101	415	3	convolution	convolution	NOUN
ejpam-4101	415	4	equation	equation	NOUN
ejpam-4101	415	5	related	relate	VERB
ejpam-4101	415	6	to	to	ADP
ejpam-4101	415	7	the	the	DET
ejpam-4101	415	8	diamond	diamond	PROPN
ejpam-4101	415	9	klein	klein	PROPN
ejpam-4101	415	10	-	-	PUNCT
ejpam-4101	415	11	gordon	gordon	PROPN
ejpam-4101	415	12	operator	operator	NOUN
ejpam-4101	415	13	,	,	PUNCT
ejpam-4101	415	14	abstract	abstract	ADJ
ejpam-4101	415	15	and	and	CCONJ
ejpam-4101	415	16	applied	apply	VERB
ejpam-4101	415	17	analysis	analysis	NOUN
ejpam-4101	415	18	,	,	PUNCT
ejpam-4101	415	19	2011:1	2011:1	NUM
ejpam-4101	415	20	-	-	SYM
ejpam-4101	415	21	14	14	NUM
ejpam-4101	415	22	,	,	PUNCT
ejpam-4101	415	23	2011	2011	NUM
ejpam-4101	415	24	.	.	PUNCT
ejpam-4101	416	1	[	[	X
ejpam-4101	416	2	11	11	NUM
ejpam-4101	416	3	]	]	PUNCT
ejpam-4101	416	4	a.	a.	NOUN
ejpam-4101	416	5	lunnaree	lunnaree	NOUN
ejpam-4101	416	6	and	and	CCONJ
ejpam-4101	416	7	k.	k.	X
ejpam-4101	416	8	nonlaopon	nonlaopon	NOUN
ejpam-4101	416	9	.	.	PUNCT
ejpam-4101	417	1	on	on	ADP
ejpam-4101	417	2	the	the	DET
ejpam-4101	417	3	fourier	fourier	NOUN
ejpam-4101	417	4	transform	transform	NOUN
ejpam-4101	417	5	of	of	ADP
ejpam-4101	417	6	the	the	DET
ejpam-4101	417	7	diamond	diamond	NOUN
ejpam-4101	417	8	kleingordon	kleingordon	PROPN
ejpam-4101	417	9	kernel	kernel	PROPN
ejpam-4101	417	10	.	.	PUNCT
ejpam-4101	418	1	international	international	ADJ
ejpam-4101	418	2	journal	journal	NOUN
ejpam-4101	418	3	of	of	ADP
ejpam-4101	418	4	pure	pure	ADJ
ejpam-4101	418	5	and	and	CCONJ
ejpam-4101	418	6	applied	applied	ADJ
ejpam-4101	418	7	mathematics	mathematic	NOUN
ejpam-4101	418	8	,	,	PUNCT
ejpam-4101	418	9	68:85	68:85	NUM
ejpam-4101	418	10	-	-	SYM
ejpam-4101	418	11	97	97	NUM
ejpam-4101	418	12	,	,	PUNCT
ejpam-4101	418	13	2011	2011	NUM
ejpam-4101	418	14	.	.	PUNCT
ejpam-4101	419	1	[	[	X
ejpam-4101	419	2	12	12	NUM
ejpam-4101	419	3	]	]	X
ejpam-4101	419	4	v.n	v.n	PROPN
ejpam-4101	419	5	.	.	PROPN
ejpam-4101	419	6	mishra	mishra	PROPN
ejpam-4101	419	7	and	and	CCONJ
ejpam-4101	419	8	l.n	l.n	PROPN
ejpam-4101	419	9	.	.	PROPN
ejpam-4101	419	10	mishra	mishra	PROPN
ejpam-4101	419	11	.	.	PROPN
ejpam-4101	419	12	trigonometric	trigonometric	ADJ
ejpam-4101	419	13	approximation	approximation	NOUN
ejpam-4101	419	14	of	of	ADP
ejpam-4101	419	15	signals	signal	NOUN
ejpam-4101	419	16	(	(	PUNCT
ejpam-4101	419	17	functions	function	NOUN
ejpam-4101	419	18	)	)	PUNCT
ejpam-4101	419	19	in	in	ADP
ejpam-4101	419	20	lp	lp	ADJ
ejpam-4101	419	21	-	-	PUNCT
ejpam-4101	419	22	norm	norm	NOUN
ejpam-4101	419	23	.	.	PUNCT
ejpam-4101	420	1	international	international	ADJ
ejpam-4101	420	2	journal	journal	PROPN
ejpam-4101	420	3	of	of	ADP
ejpam-4101	420	4	contemporary	contemporary	PROPN
ejpam-4101	420	5	mathematical	mathematical	PROPN
ejpam-4101	420	6	sciences	sciences	PROPN
ejpam-4101	420	7	,	,	PUNCT
ejpam-4101	420	8	7:909	7:909	NUM
ejpam-4101	420	9	-	-	SYM
ejpam-4101	420	10	918	918	NUM
ejpam-4101	420	11	,	,	PUNCT
ejpam-4101	420	12	2012	2012	NUM
ejpam-4101	420	13	.	.	PUNCT
ejpam-4101	421	1	[	[	X
ejpam-4101	421	2	13	13	NUM
ejpam-4101	421	3	]	]	X
ejpam-4101	421	4	l.n	l.n	PROPN
ejpam-4101	421	5	.	.	PROPN
ejpam-4101	421	6	mishra	mishra	PROPN
ejpam-4101	421	7	,	,	PUNCT
ejpam-4101	421	8	v.n	v.n	PROPN
ejpam-4101	421	9	.	.	PROPN
ejpam-4101	421	10	mishra	mishra	PROPN
ejpam-4101	421	11	,	,	PUNCT
ejpam-4101	421	12	k.	k.	PROPN
ejpam-4101	421	13	khatri	khatri	PROPN
ejpam-4101	421	14	and	and	CCONJ
ejpam-4101	421	15	deepmala	deepmala	PROPN
ejpam-4101	421	16	.	.	PUNCT
ejpam-4101	422	1	on	on	ADP
ejpam-4101	422	2	the	the	DET
ejpam-4101	422	3	trigonometric	trigonometric	ADJ
ejpam-4101	422	4	approximation	approximation	NOUN
ejpam-4101	422	5	of	of	ADP
ejpam-4101	422	6	signals	signal	NOUN
ejpam-4101	422	7	belonging	belong	VERB
ejpam-4101	422	8	to	to	ADP
ejpam-4101	422	9	generalized	generalize	VERB
ejpam-4101	422	10	weighted	weight	VERB
ejpam-4101	422	11	lipschitz	lipschitz	PROPN
ejpam-4101	422	12	w	w	PROPN
ejpam-4101	422	13	(	(	PUNCT
ejpam-4101	422	14	lr	lr	INTJ
ejpam-4101	422	15	,	,	PUNCT
ejpam-4101	422	16	ξ(t))(r	ξ(t))(r	PROPN
ejpam-4101	422	17	≥	≥	NOUN
ejpam-4101	422	18	1)class	1)class	NUM
ejpam-4101	422	19	by	by	ADP
ejpam-4101	422	20	matrix	matrix	NOUN
ejpam-4101	422	21	(	(	PUNCT
ejpam-4101	422	22	c1.np	c1.np	NOUN
ejpam-4101	422	23	)	)	PUNCT
ejpam-4101	422	24	operator	operator	NOUN
ejpam-4101	422	25	of	of	ADP
ejpam-4101	422	26	conjugate	conjugate	ADJ
ejpam-4101	422	27	series	series	NOUN
ejpam-4101	422	28	of	of	ADP
ejpam-4101	422	29	its	its	PRON
ejpam-4101	422	30	fourier	fourier	NOUN
ejpam-4101	422	31	series	series	NOUN
ejpam-4101	422	32	.	.	PUNCT
ejpam-4101	423	1	applied	apply	VERB
ejpam-4101	423	2	mathematics	mathematic	NOUN
ejpam-4101	423	3	and	and	CCONJ
ejpam-4101	423	4	computation	computation	NOUN
ejpam-4101	423	5	,	,	PUNCT
ejpam-4101	423	6	273:252	273:252	NOUN
ejpam-4101	423	7	-	-	SYM
ejpam-4101	423	8	263	263	NUM
ejpam-4101	423	9	,	,	PUNCT
ejpam-4101	423	10	2014	2014	NUM
ejpam-4101	423	11	.	.	PUNCT
ejpam-4101	424	1	[	[	X
ejpam-4101	424	2	14	14	NUM
ejpam-4101	424	3	]	]	X
ejpam-4101	424	4	v.n	v.n	PROPN
ejpam-4101	424	5	.	.	PROPN
ejpam-4101	424	6	mishra	mishra	PROPN
ejpam-4101	424	7	,	,	PUNCT
ejpam-4101	424	8	k.	k.	PROPN
ejpam-4101	424	9	khatri	khatri	PROPN
ejpam-4101	424	10	,	,	PUNCT
ejpam-4101	424	11	l.n	l.n	PROPN
ejpam-4101	424	12	.	.	PROPN
ejpam-4101	424	13	mishra	mishra	PROPN
ejpam-4101	424	14	,	,	PUNCT
ejpam-4101	424	15	and	and	CCONJ
ejpam-4101	424	16	deepmala	deepmala	NOUN
ejpam-4101	424	17	.	.	PUNCT
ejpam-4101	425	1	trigonometric	trigonometric	ADJ
ejpam-4101	425	2	approximation	approximation	NOUN
ejpam-4101	425	3	of	of	ADP
ejpam-4101	425	4	periodic	periodic	ADJ
ejpam-4101	425	5	signals	signal	NOUN
ejpam-4101	425	6	belonging	belong	VERB
ejpam-4101	425	7	to	to	ADP
ejpam-4101	425	8	generalized	generalize	VERB
ejpam-4101	425	9	weighted	weight	VERB
ejpam-4101	425	10	lipschitz	lipschitz	NOUN
ejpam-4101	425	11	w	w	PROPN
ejpam-4101	425	12	′	′	NUM
ejpam-4101	425	13	(	(	PUNCT
ejpam-4101	425	14	lr	lr	INTJ
ejpam-4101	425	15	,	,	PUNCT
ejpam-4101	425	16	ξ(t	ξ(t	NOUN
ejpam-4101	425	17	)	)	PUNCT
ejpam-4101	425	18	)	)	PUNCT
ejpam-4101	425	19	,	,	PUNCT
ejpam-4101	425	20	(	(	PUNCT
ejpam-4101	425	21	r	r	NOUN
ejpam-4101	425	22	≥	≥	NOUN
ejpam-4101	425	23	1)class	1)class	NUM
ejpam-4101	425	24	by	by	ADP
ejpam-4101	425	25	nörlund	nörlund	NOUN
ejpam-4101	425	26	-	-	PUNCT
ejpam-4101	425	27	euler	euler	NOUN
ejpam-4101	425	28	(	(	PUNCT
ejpam-4101	425	29	n	n	X
ejpam-4101	425	30	,	,	PUNCT
ejpam-4101	425	31	pn)(e	pn)(e	PROPN
ejpam-4101	425	32	,	,	PUNCT
ejpam-4101	425	33	q	q	NOUN
ejpam-4101	425	34	)	)	PUNCT
ejpam-4101	425	35	operator	operator	NOUN
ejpam-4101	425	36	of	of	ADP
ejpam-4101	425	37	conjugate	conjugate	ADJ
ejpam-4101	425	38	series	series	NOUN
ejpam-4101	425	39	of	of	ADP
ejpam-4101	425	40	its	its	PRON
ejpam-4101	425	41	fourier	fourier	NOUN
ejpam-4101	425	42	series	series	NOUN
ejpam-4101	425	43	.	.	PUNCT
ejpam-4101	426	1	journal	journal	PROPN
ejpam-4101	426	2	of	of	ADP
ejpam-4101	426	3	classical	classical	ADJ
ejpam-4101	426	4	analysis	analysis	NOUN
ejpam-4101	426	5	,	,	PUNCT
ejpam-4101	426	6	5:91	5:91	NUM
ejpam-4101	426	7	-	-	SYM
ejpam-4101	426	8	105	105	NUM
ejpam-4101	426	9	,	,	PUNCT
ejpam-4101	426	10	2014	2014	NUM
ejpam-4101	426	11	.	.	PUNCT
ejpam-4101	427	1	[	[	X
ejpam-4101	427	2	15	15	NUM
ejpam-4101	427	3	]	]	X
ejpam-4101	427	4	v.n	v.n	PROPN
ejpam-4101	427	5	.	.	PROPN
ejpam-4101	427	6	mishra	mishra	PROPN
ejpam-4101	427	7	,	,	PUNCT
ejpam-4101	427	8	k.	k.	PROPN
ejpam-4101	427	9	khatri	khatri	PROPN
ejpam-4101	427	10	and	and	CCONJ
ejpam-4101	427	11	l.n	l.n	PROPN
ejpam-4101	427	12	.	.	PROPN
ejpam-4101	427	13	mishra	mishra	PROPN
ejpam-4101	427	14	.	.	PROPN
ejpam-4101	427	15	using	use	VERB
ejpam-4101	427	16	linear	linear	PROPN
ejpam-4101	427	17	operators	operator	NOUN
ejpam-4101	427	18	to	to	PART
ejpam-4101	427	19	approximate	approximate	VERB
ejpam-4101	427	20	signals	signal	NOUN
ejpam-4101	427	21	of	of	ADP
ejpam-4101	427	22	lip	lip	NOUN
ejpam-4101	427	23	(	(	PUNCT
ejpam-4101	427	24	α	α	NOUN
ejpam-4101	427	25	,	,	PUNCT
ejpam-4101	427	26	p	p	NOUN
ejpam-4101	427	27	)	)	PUNCT
ejpam-4101	427	28	,	,	PUNCT
ejpam-4101	427	29	(	(	PUNCT
ejpam-4101	427	30	p	p	PRON
ejpam-4101	427	31	≥	≥	PROPN
ejpam-4101	427	32	1)-class	1)-class	NUM
ejpam-4101	427	33	.	.	PUNCT
ejpam-4101	427	34	filomat	filomat	PROPN
ejpam-4101	427	35	,	,	PUNCT
ejpam-4101	427	36	27:353	27:353	NUM
ejpam-4101	427	37	-	-	SYM
ejpam-4101	427	38	363	363	NUM
ejpam-4101	427	39	,	,	PUNCT
ejpam-4101	427	40	2013	2013	NUM
ejpam-4101	427	41	.	.	PUNCT
ejpam-4101	428	1	references	reference	NOUN
ejpam-4101	428	2	1323	1323	NUM
ejpam-4101	429	1	[	[	X
ejpam-4101	429	2	16	16	NUM
ejpam-4101	429	3	]	]	X
ejpam-4101	429	4	l.n	l.n	PROPN
ejpam-4101	429	5	.	.	PROPN
ejpam-4101	429	6	mishra	mishra	PROPN
ejpam-4101	429	7	,	,	PUNCT
ejpam-4101	429	8	v.n	v.n	PROPN
ejpam-4101	429	9	.	.	PROPN
ejpam-4101	429	10	mishra	mishra	PROPN
ejpam-4101	429	11	and	and	CCONJ
ejpam-4101	429	12	v.	v.	ADP
ejpam-4101	429	13	sonavane	sonavane	NOUN
ejpam-4101	429	14	.	.	PUNCT
ejpam-4101	430	1	trigonometric	trigonometric	ADJ
ejpam-4101	430	2	approximation	approximation	NOUN
ejpam-4101	430	3	of	of	ADP
ejpam-4101	430	4	functions	function	NOUN
ejpam-4101	430	5	belonging	belong	VERB
ejpam-4101	430	6	to	to	ADP
ejpam-4101	430	7	lipschitz	lipschitz	VERB
ejpam-4101	430	8	class	class	NOUN
ejpam-4101	430	9	by	by	ADP
ejpam-4101	430	10	matrix	matrix	NOUN
ejpam-4101	430	11	(	(	PUNCT
ejpam-4101	430	12	c1.np	c1.np	NOUN
ejpam-4101	430	13	)	)	PUNCT
ejpam-4101	430	14	operator	operator	NOUN
ejpam-4101	430	15	of	of	ADP
ejpam-4101	430	16	conjugate	conjugate	ADJ
ejpam-4101	430	17	series	series	NOUN
ejpam-4101	430	18	of	of	ADP
ejpam-4101	430	19	fourier	fourier	PROPN
ejpam-4101	430	20	series	series	PROPN
ejpam-4101	430	21	.	.	PUNCT
ejpam-4101	431	1	advances	advance	NOUN
ejpam-4101	431	2	in	in	ADP
ejpam-4101	431	3	difference	difference	NOUN
ejpam-4101	431	4	equations	equation	NOUN
ejpam-4101	431	5	,	,	PUNCT
ejpam-4101	431	6	127	127	NUM
ejpam-4101	431	7	:	:	SYM
ejpam-4101	431	8	2013	2013	NUM
ejpam-4101	431	9	.	.	PUNCT
ejpam-4101	432	1	[	[	X
ejpam-4101	432	2	17	17	NUM
ejpam-4101	432	3	]	]	PUNCT
ejpam-4101	432	4	k.	k.	NOUN
ejpam-4101	432	5	nonlaopon	nonlaopon	PROPN
ejpam-4101	432	6	.	.	PUNCT
ejpam-4101	433	1	on	on	ADP
ejpam-4101	433	2	the	the	DET
ejpam-4101	433	3	inverse	inverse	NOUN
ejpam-4101	433	4	ultrahyperbolic	ultrahyperbolic	PROPN
ejpam-4101	433	5	klein	klein	PROPN
ejpam-4101	433	6	-	-	PUNCT
ejpam-4101	433	7	gordon	gordon	PROPN
ejpam-4101	433	8	kernel	kernel	PROPN
ejpam-4101	433	9	,	,	PUNCT
ejpam-4101	433	10	mathematics	mathematic	NOUN
ejpam-4101	433	11	,	,	PUNCT
ejpam-4101	433	12	7:534	7:534	NUM
ejpam-4101	433	13	,	,	PUNCT
ejpam-4101	433	14	2019	2019	NUM
ejpam-4101	433	15	.	.	PUNCT
ejpam-4101	434	1	[	[	X
ejpam-4101	434	2	18	18	NUM
ejpam-4101	434	3	]	]	PUNCT
ejpam-4101	434	4	k.	k.	NOUN
ejpam-4101	434	5	nonlaopon	nonlaopon	PROPN
ejpam-4101	434	6	,	,	PUNCT
ejpam-4101	434	7	a.	a.	NOUN
ejpam-4101	434	8	lunnaree	lunnaree	NOUN
ejpam-4101	434	9	and	and	CCONJ
ejpam-4101	434	10	a.	a.	NOUN
ejpam-4101	434	11	kananthai	kananthai	PROPN
ejpam-4101	434	12	.	.	PUNCT
ejpam-4101	435	1	on	on	ADP
ejpam-4101	435	2	the	the	DET
ejpam-4101	435	3	solution	solution	NOUN
ejpam-4101	435	4	of	of	ADP
ejpam-4101	435	5	the	the	DET
ejpam-4101	435	6	n	n	ADV
ejpam-4101	435	7	-	-	PUNCT
ejpam-4101	435	8	dimensional	dimensional	ADJ
ejpam-4101	435	9	diamond	diamond	NOUN
ejpam-4101	435	10	klein	klein	PROPN
ejpam-4101	435	11	-	-	PUNCT
ejpam-4101	435	12	gordon	gordon	PROPN
ejpam-4101	435	13	operator	operator	NOUN
ejpam-4101	435	14	and	and	CCONJ
ejpam-4101	435	15	its	its	PRON
ejpam-4101	435	16	convolution	convolution	NOUN
ejpam-4101	435	17	,	,	PUNCT
ejpam-4101	435	18	far	far	ADV
ejpam-4101	435	19	east	east	PROPN
ejpam-4101	435	20	journal	journal	PROPN
ejpam-4101	435	21	of	of	ADP
ejpam-4101	435	22	mathematical	mathematical	ADJ
ejpam-4101	435	23	sciences	science	NOUN
ejpam-4101	435	24	,	,	PUNCT
ejpam-4101	435	25	63:203	63:203	NUM
ejpam-4101	435	26	-	-	SYM
ejpam-4101	435	27	220	220	NUM
ejpam-4101	435	28	,	,	PUNCT
ejpam-4101	435	29	2012	2012	NUM
ejpam-4101	435	30	.	.	PUNCT
ejpam-4101	436	1	[	[	X
ejpam-4101	436	2	19	19	NUM
ejpam-4101	436	3	]	]	X
ejpam-4101	436	4	y.	y.	PROPN
ejpam-4101	436	5	nozaki	nozaki	PROPN
ejpam-4101	436	6	.	.	PUNCT
ejpam-4101	437	1	on	on	ADP
ejpam-4101	437	2	riemann	riemann	PROPN
ejpam-4101	437	3	-	-	PUNCT
ejpam-4101	437	4	liouville	liouville	VERB
ejpam-4101	437	5	integral	integral	ADJ
ejpam-4101	437	6	of	of	ADP
ejpam-4101	437	7	ultra	ultra	ADJ
ejpam-4101	437	8	-	-	ADJ
ejpam-4101	437	9	hyperbolic	hyperbolic	ADJ
ejpam-4101	437	10	type	type	NOUN
ejpam-4101	437	11	.	.	PUNCT
ejpam-4101	438	1	kodai	kodai	PROPN
ejpam-4101	438	2	mathematical	mathematical	ADJ
ejpam-4101	438	3	seminar	seminar	NOUN
ejpam-4101	438	4	reports	report	NOUN
ejpam-4101	438	5	,	,	PUNCT
ejpam-4101	438	6	6:69	6:69	NUM
ejpam-4101	438	7	-	-	SYM
ejpam-4101	438	8	87	87	NUM
ejpam-4101	438	9	,	,	PUNCT
ejpam-4101	438	10	1964	1964	NUM
ejpam-4101	438	11	.	.	PUNCT
ejpam-4101	439	1	[	[	X
ejpam-4101	439	2	20	20	NUM
ejpam-4101	439	3	]	]	X
ejpam-4101	439	4	w.	w.	PROPN
ejpam-4101	439	5	satsanit	satsanit	PROPN
ejpam-4101	439	6	.	.	PUNCT
ejpam-4101	440	1	green	green	ADJ
ejpam-4101	440	2	function	function	NOUN
ejpam-4101	440	3	and	and	CCONJ
ejpam-4101	440	4	fourier	fourier	NOUN
ejpam-4101	440	5	transform	transform	NOUN
ejpam-4101	440	6	for	for	ADP
ejpam-4101	440	7	o	o	NOUN
ejpam-4101	440	8	-	-	ADJ
ejpam-4101	440	9	plus	plus	CCONJ
ejpam-4101	440	10	operator	operator	NOUN
ejpam-4101	440	11	.	.	PUNCT
ejpam-4101	441	1	electronic	electronic	ADJ
ejpam-4101	441	2	journal	journal	NOUN
ejpam-4101	441	3	of	of	ADP
ejpam-4101	441	4	differential	differential	ADJ
ejpam-4101	441	5	equation	equation	NOUN
ejpam-4101	441	6	,	,	PUNCT
ejpam-4101	441	7	2010:1	2010:1	NUM
ejpam-4101	441	8	-	-	SYM
ejpam-4101	441	9	14	14	NUM
ejpam-4101	441	10	,	,	PUNCT
ejpam-4101	441	11	2010	2010	NUM
ejpam-4101	441	12	.	.	PUNCT
ejpam-4101	442	1	[	[	X
ejpam-4101	442	2	21	21	NUM
ejpam-4101	442	3	]	]	X
ejpam-4101	442	4	m.a	m.a	PROPN
ejpam-4101	442	5	.	.	PROPN
ejpam-4101	442	6	tellez	tellez	PROPN
ejpam-4101	442	7	and	and	CCONJ
ejpam-4101	442	8	s.e	s.e	PROPN
ejpam-4101	442	9	.	.	PROPN
ejpam-4101	442	10	trione	trione	NOUN
ejpam-4101	442	11	.	.	PUNCT
ejpam-4101	443	1	the	the	DET
ejpam-4101	443	2	distributional	distributional	ADJ
ejpam-4101	443	3	convolution	convolution	NOUN
ejpam-4101	443	4	products	product	NOUN
ejpam-4101	443	5	of	of	ADP
ejpam-4101	443	6	marcel	marcel	PROPN
ejpam-4101	443	7	riesz	riesz	PROPN
ejpam-4101	443	8	’s	’s	PART
ejpam-4101	443	9	ultra	ultra	ADJ
ejpam-4101	443	10	-	-	ADJ
ejpam-4101	443	11	hyperbolic	hyperbolic	ADJ
ejpam-4101	443	12	kernel	kernel	NOUN
ejpam-4101	443	13	.	.	PUNCT
ejpam-4101	444	1	ravista	ravista	PROPN
ejpam-4101	444	2	de	de	PROPN
ejpam-4101	444	3	la	la	PROPN
ejpam-4101	444	4	union	union	PROPN
ejpam-4101	444	5	mathematica	mathematica	PROPN
ejpam-4101	444	6	argentina	argentina	PROPN
ejpam-4101	444	7	,	,	PUNCT
ejpam-4101	444	8	39:115	39:115	PROPN
ejpam-4101	444	9	-	-	SYM
ejpam-4101	444	10	124	124	NUM
ejpam-4101	444	11	,	,	PUNCT
ejpam-4101	444	12	1995	1995	NUM
ejpam-4101	444	13	.	.	PUNCT
ejpam-4101	445	1	[	[	X
ejpam-4101	445	2	22	22	NUM
ejpam-4101	445	3	]	]	X
ejpam-4101	445	4	s.e	s.e	PROPN
ejpam-4101	445	5	.	.	PROPN
ejpam-4101	445	6	trione	trione	PROPN
ejpam-4101	445	7	,	,	PUNCT
ejpam-4101	445	8	on	on	ADP
ejpam-4101	445	9	the	the	DET
ejpam-4101	445	10	elementary	elementary	NOUN
ejpam-4101	445	11	related	relate	VERB
ejpam-4101	445	12	,	,	PUNCT
ejpam-4101	445	13	ultra	ultra	ADJ
ejpam-4101	445	14	-	-	ADJ
ejpam-4101	445	15	hyperbolic	hyperbolic	ADJ
ejpam-4101	445	16	solution	solution	NOUN
ejpam-4101	445	17	of	of	ADP
ejpam-4101	445	18	the	the	DET
ejpam-4101	445	19	klein	klein	PROPN
ejpam-4101	445	20	-	-	PUNCT
ejpam-4101	445	21	gordon	gordon	PROPN
ejpam-4101	445	22	operator	operator	NOUN
ejpam-4101	445	23	iterated	iterate	VERB
ejpam-4101	445	24	k	k	NOUN
ejpam-4101	445	25	-	-	PUNCT
ejpam-4101	445	26	times	time	NOUN
ejpam-4101	445	27	.	.	PUNCT
ejpam-4101	446	1	studies	study	NOUN
ejpam-4101	446	2	in	in	ADP
ejpam-4101	446	3	applied	applied	ADJ
ejpam-4101	446	4	mathematics	mathematic	NOUN
ejpam-4101	446	5	,	,	PUNCT
ejpam-4101	446	6	89:121	89:121	NUM
ejpam-4101	446	7	-	-	SYM
ejpam-4101	446	8	141	141	NUM
ejpam-4101	446	9	,	,	PUNCT
ejpam-4101	446	10	1988	1988	NUM
ejpam-4101	446	11	.	.	PUNCT
ejpam-4101	447	1	[	[	X
ejpam-4101	447	2	23	23	NUM
ejpam-4101	447	3	]	]	X
ejpam-4101	447	4	s.e	s.e	PROPN
ejpam-4101	447	5	.	.	PROPN
ejpam-4101	447	6	trione	trione	NOUN
ejpam-4101	447	7	.	.	PUNCT
ejpam-4101	448	1	on	on	ADP
ejpam-4101	448	2	the	the	DET
ejpam-4101	448	3	ultra	ultra	ADJ
ejpam-4101	448	4	-	-	ADJ
ejpam-4101	448	5	hyperbolic	hyperbolic	ADJ
ejpam-4101	448	6	kernel	kernel	NOUN
ejpam-4101	448	7	.	.	PUNCT
ejpam-4101	448	8	trabajos	trabajos	PROPN
ejpam-4101	448	9	de	de	PROPN
ejpam-4101	448	10	mathematica	mathematica	PROPN
ejpam-4101	448	11	,	,	PUNCT
ejpam-4101	448	12	116	116	NUM
ejpam-4101	448	13	,	,	PUNCT
ejpam-4101	448	14	1987	1987	NUM
ejpam-4101	448	15	.	.	PUNCT
ejpam-4101	449	1	[	[	X
ejpam-4101	449	2	24	24	NUM
ejpam-4101	449	3	]	]	PUNCT
ejpam-4101	449	4	a.	a.	NOUN
ejpam-4101	449	5	h.	h.	PROPN
ejpam-4101	449	6	zemanian	zemanian	PROPN
ejpam-4101	449	7	.	.	PUNCT
ejpam-4101	449	8	distribution	distribution	NOUN
ejpam-4101	449	9	theory	theory	NOUN
ejpam-4101	449	10	and	and	CCONJ
ejpam-4101	449	11	transform	transform	VERB
ejpam-4101	449	12	analysis	analysis	NOUN
ejpam-4101	449	13	.	.	PUNCT
ejpam-4101	450	1	mcgraw	mcgraw	PROPN
ejpam-4101	450	2	-	-	PUNCT
ejpam-4101	450	3	hill	hill	PROPN
ejpam-4101	450	4	,	,	PUNCT
ejpam-4101	450	5	new	new	PROPN
ejpam-4101	450	6	york	york	PROPN
ejpam-4101	450	7	,	,	PUNCT
ejpam-4101	450	8	1965	1965	NUM
ejpam-4101	450	9	.	.	PUNCT