id	sid	tid	token	lemma	pos
ejpam-4006	1	1	european	european	PROPN
ejpam-4006	1	2	journal	journal	PROPN
ejpam-4006	1	3	of	of	ADP
ejpam-4006	1	4	pure	pure	ADJ
ejpam-4006	1	5	and	and	CCONJ
ejpam-4006	1	6	applied	apply	VERB
ejpam-4006	1	7	mathematics	mathematic	NOUN
ejpam-4006	1	8	vol	vol	NOUN
ejpam-4006	1	9	.	.	PUNCT
ejpam-4006	2	1	14	14	NUM
ejpam-4006	2	2	,	,	PUNCT
ejpam-4006	2	3	no	no	INTJ
ejpam-4006	2	4	.	.	NOUN
ejpam-4006	2	5	3	3	NUM
ejpam-4006	2	6	,	,	PUNCT
ejpam-4006	2	7	2021	2021	NUM
ejpam-4006	2	8	,	,	PUNCT
ejpam-4006	2	9	881	881	NUM
ejpam-4006	2	10	-	-	SYM
ejpam-4006	2	11	894	894	NUM
ejpam-4006	2	12	issn	issn	PROPN
ejpam-4006	2	13	1307	1307	NUM
ejpam-4006	2	14	-	-	SYM
ejpam-4006	2	15	5543	5543	NUM
ejpam-4006	2	16	–	–	PUNCT
ejpam-4006	3	1	ejpam.com	ejpam.com	X
ejpam-4006	3	2	published	publish	VERB
ejpam-4006	3	3	by	by	ADP
ejpam-4006	3	4	new	new	PROPN
ejpam-4006	3	5	york	york	PROPN
ejpam-4006	3	6	business	business	PROPN
ejpam-4006	3	7	global	global	PROPN
ejpam-4006	3	8	on	on	ADP
ejpam-4006	3	9	the	the	DET
ejpam-4006	3	10	operator	operator	NOUN
ejpam-4006	3	11	⊕km	⊕km	VERB
ejpam-4006	3	12	related	relate	VERB
ejpam-4006	3	13	to	to	ADP
ejpam-4006	3	14	the	the	DET
ejpam-4006	3	15	wave	wave	NOUN
ejpam-4006	3	16	equation	equation	NOUN
ejpam-4006	3	17	and	and	CCONJ
ejpam-4006	3	18	laplacian	laplacian	ADJ
ejpam-4006	3	19	sudprathai	sudprathai	NOUN
ejpam-4006	3	20	bupasiri	bupasiri	PROPN
ejpam-4006	3	21	faculty	faculty	NOUN
ejpam-4006	3	22	of	of	ADP
ejpam-4006	3	23	education	education	NOUN
ejpam-4006	3	24	,	,	PUNCT
ejpam-4006	3	25	sakon	sakon	PROPN
ejpam-4006	3	26	nakhon	nakhon	PROPN
ejpam-4006	3	27	rajabhat	rajabhat	PROPN
ejpam-4006	3	28	university	university	PROPN
ejpam-4006	3	29	,	,	PUNCT
ejpam-4006	3	30	sakon	sakon	PROPN
ejpam-4006	3	31	nakhon	nakhon	PROPN
ejpam-4006	3	32	,	,	PUNCT
ejpam-4006	3	33	thailand	thailand	PROPN
ejpam-4006	3	34	abstract	abstract	NOUN
ejpam-4006	3	35	.	.	PUNCT
ejpam-4006	4	1	in	in	ADP
ejpam-4006	4	2	this	this	DET
ejpam-4006	4	3	article	article	NOUN
ejpam-4006	4	4	,	,	PUNCT
ejpam-4006	4	5	we	we	PRON
ejpam-4006	4	6	study	study	VERB
ejpam-4006	4	7	the	the	DET
ejpam-4006	4	8	fundamental	fundamental	ADJ
ejpam-4006	4	9	solution	solution	NOUN
ejpam-4006	4	10	of	of	ADP
ejpam-4006	4	11	the	the	DET
ejpam-4006	4	12	operator	operator	NOUN
ejpam-4006	4	13	⊕k	⊕k	PROPN
ejpam-4006	4	14	m	m	PROPN
ejpam-4006	4	15	,	,	PUNCT
ejpam-4006	4	16	iterated	iterate	VERB
ejpam-4006	4	17	k	k	NOUN
ejpam-4006	4	18	-	-	PUNCT
ejpam-4006	4	19	times	time	NOUN
ejpam-4006	4	20	and	and	CCONJ
ejpam-4006	4	21	is	be	AUX
ejpam-4006	4	22	defined	define	VERB
ejpam-4006	4	23	by	by	ADP
ejpam-4006	4	24	⊕k	⊕k	ADJ
ejpam-4006	4	25	m	m	PROPN
ejpam-4006	4	26	=	=	SYM
ejpam-4006	4	27			PROPN
ejpam-4006	4	28	(	(	PUNCT
ejpam-4006	4	29	p∑	p∑	NOUN
ejpam-4006	4	30	r=1	r=1	NOUN
ejpam-4006	4	31	∂2	∂2	NOUN
ejpam-4006	4	32	∂x2r	∂x2r	ADP
ejpam-4006	4	33	+	+	NOUN
ejpam-4006	4	34	m2	m2	PROPN
ejpam-4006	4	35	)	)	PUNCT
ejpam-4006	4	36	4	4	NUM
ejpam-4006	4	37	−	−	NOUN
ejpam-4006	4	38			PROPN
ejpam-4006	4	39	p+q∑	p+q∑	PROPN
ejpam-4006	4	40	j	j	NOUN
ejpam-4006	4	41	=	=	PROPN
ejpam-4006	4	42	p+1	p+1	PROPN
ejpam-4006	4	43	∂2	∂2	NOUN
ejpam-4006	4	44	∂x2j	∂x2j	PUNCT
ejpam-4006	5	1	4	4	PROPN
ejpam-4006	6	1			NUM
ejpam-4006	6	2	k	k	NOUN
ejpam-4006	6	3	,	,	PUNCT
ejpam-4006	6	4	where	where	SCONJ
ejpam-4006	6	5	m	m	NOUN
ejpam-4006	6	6	is	be	AUX
ejpam-4006	6	7	a	a	DET
ejpam-4006	6	8	nonnegative	nonnegative	ADJ
ejpam-4006	6	9	real	real	ADJ
ejpam-4006	6	10	number	number	NOUN
ejpam-4006	6	11	,	,	PUNCT
ejpam-4006	6	12	p	p	NOUN
ejpam-4006	6	13	+	+	NOUN
ejpam-4006	6	14	q	q	NOUN
ejpam-4006	6	15	=	=	NOUN
ejpam-4006	6	16	n	n	X
ejpam-4006	6	17	is	be	AUX
ejpam-4006	6	18	the	the	DET
ejpam-4006	6	19	dimension	dimension	NOUN
ejpam-4006	6	20	of	of	ADP
ejpam-4006	6	21	the	the	DET
ejpam-4006	6	22	euclidean	euclidean	ADJ
ejpam-4006	6	23	space	space	PROPN
ejpam-4006	6	24	rn	rn	PROPN
ejpam-4006	6	25	,	,	PUNCT
ejpam-4006	6	26	x	x	PUNCT
ejpam-4006	6	27	=	=	SYM
ejpam-4006	6	28	(	(	PUNCT
ejpam-4006	6	29	x1	x1	PROPN
ejpam-4006	6	30	,	,	PUNCT
ejpam-4006	6	31	x2	x2	PROPN
ejpam-4006	6	32	,	,	PUNCT
ejpam-4006	6	33	.	.	PUNCT
ejpam-4006	6	34	.	.	PUNCT
ejpam-4006	7	1	.	.	PUNCT
ejpam-4006	8	1	,	,	PUNCT
ejpam-4006	8	2	xn	xn	X
ejpam-4006	8	3	)	)	PUNCT
ejpam-4006	8	4	∈	∈	PROPN
ejpam-4006	8	5	rn	rn	PROPN
ejpam-4006	8	6	,	,	PUNCT
ejpam-4006	8	7	k	k	PROPN
ejpam-4006	8	8	is	be	AUX
ejpam-4006	8	9	a	a	DET
ejpam-4006	8	10	nonnegative	nonnegative	ADJ
ejpam-4006	8	11	integer	integer	NOUN
ejpam-4006	8	12	.	.	PUNCT
ejpam-4006	9	1	at	at	ADP
ejpam-4006	9	2	first	first	ADV
ejpam-4006	9	3	we	we	PRON
ejpam-4006	9	4	study	study	VERB
ejpam-4006	9	5	the	the	DET
ejpam-4006	9	6	fundamental	fundamental	ADJ
ejpam-4006	9	7	solution	solution	NOUN
ejpam-4006	9	8	of	of	ADP
ejpam-4006	9	9	the	the	DET
ejpam-4006	9	10	operator	operator	NOUN
ejpam-4006	9	11	⊕k	⊕k	NOUN
ejpam-4006	9	12	m	m	PROPN
ejpam-4006	9	13	and	and	CCONJ
ejpam-4006	9	14	after	after	ADP
ejpam-4006	9	15	that	that	PRON
ejpam-4006	9	16	,	,	PUNCT
ejpam-4006	9	17	we	we	PRON
ejpam-4006	9	18	apply	apply	VERB
ejpam-4006	9	19	such	such	DET
ejpam-4006	9	20	the	the	DET
ejpam-4006	9	21	fundamental	fundamental	ADJ
ejpam-4006	9	22	solution	solution	NOUN
ejpam-4006	9	23	to	to	PART
ejpam-4006	9	24	solve	solve	VERB
ejpam-4006	9	25	for	for	ADP
ejpam-4006	9	26	the	the	DET
ejpam-4006	9	27	solution	solution	NOUN
ejpam-4006	9	28	of	of	ADP
ejpam-4006	9	29	the	the	DET
ejpam-4006	9	30	equation	equation	NOUN
ejpam-4006	9	31	⊕k	⊕k	NOUN
ejpam-4006	9	32	mu(x	mu(x	NOUN
ejpam-4006	9	33	)	)	PUNCT
ejpam-4006	10	1	=	=	SYM
ejpam-4006	10	2	f(x	f(x	PROPN
ejpam-4006	10	3	)	)	PUNCT
ejpam-4006	10	4	,	,	PUNCT
ejpam-4006	10	5	where	where	SCONJ
ejpam-4006	10	6	f(x	f(x	PROPN
ejpam-4006	10	7	)	)	PUNCT
ejpam-4006	10	8	is	be	AUX
ejpam-4006	10	9	generalized	generalize	VERB
ejpam-4006	10	10	function	function	NOUN
ejpam-4006	10	11	and	and	CCONJ
ejpam-4006	10	12	u(x	u(x	NOUN
ejpam-4006	10	13	)	)	PUNCT
ejpam-4006	10	14	is	be	AUX
ejpam-4006	10	15	unknown	unknown	ADJ
ejpam-4006	10	16	function	function	NOUN
ejpam-4006	10	17	for	for	ADP
ejpam-4006	10	18	x	x	PROPN
ejpam-4006	10	19	∈	∈	PROPN
ejpam-4006	10	20	rn	rn	PROPN
ejpam-4006	10	21	.	.	PROPN
ejpam-4006	10	22	2020	2020	NUM
ejpam-4006	10	23	mathematics	mathematic	NOUN
ejpam-4006	10	24	subject	subject	NOUN
ejpam-4006	10	25	classifications	classification	NOUN
ejpam-4006	10	26	:	:	PUNCT
ejpam-4006	10	27	46f10	46f10	NUM
ejpam-4006	10	28	key	key	ADJ
ejpam-4006	10	29	words	word	NOUN
ejpam-4006	10	30	and	and	CCONJ
ejpam-4006	10	31	phrases	phrase	NOUN
ejpam-4006	10	32	:	:	PUNCT
ejpam-4006	10	33	wave	wave	NOUN
ejpam-4006	10	34	equation	equation	NOUN
ejpam-4006	10	35	,	,	PUNCT
ejpam-4006	10	36	laplace	laplace	NOUN
ejpam-4006	10	37	operator	operator	NOUN
ejpam-4006	10	38	,	,	PUNCT
ejpam-4006	10	39	ultra	ultra	ADJ
ejpam-4006	10	40	-	-	ADJ
ejpam-4006	10	41	hyperbolic	hyperbolic	ADJ
ejpam-4006	10	42	operator	operator	NOUN
ejpam-4006	10	43	1	1	NUM
ejpam-4006	10	44	.	.	PUNCT
ejpam-4006	11	1	introduction	introduction	NOUN
ejpam-4006	11	2	we	we	PRON
ejpam-4006	11	3	have	have	AUX
ejpam-4006	11	4	observed	observe	VERB
ejpam-4006	11	5	that	that	SCONJ
ejpam-4006	11	6	an	an	DET
ejpam-4006	11	7	operational	operational	ADJ
ejpam-4006	11	8	quantity	quantity	NOUN
ejpam-4006	11	9	such	such	ADJ
ejpam-4006	11	10	as	as	ADP
ejpam-4006	11	11	δ(x	δ(x	PROPN
ejpam-4006	11	12	)	)	PUNCT
ejpam-4006	11	13	becomes	become	VERB
ejpam-4006	11	14	meaningful	meaningful	ADJ
ejpam-4006	11	15	if	if	SCONJ
ejpam-4006	11	16	it	it	PRON
ejpam-4006	11	17	is	be	AUX
ejpam-4006	11	18	first	first	ADV
ejpam-4006	11	19	multiplied	multiply	VERB
ejpam-4006	11	20	by	by	ADP
ejpam-4006	11	21	a	a	DET
ejpam-4006	11	22	sufficiently	sufficiently	ADV
ejpam-4006	11	23	smooth	smooth	ADJ
ejpam-4006	11	24	auxiliary	auxiliary	ADJ
ejpam-4006	11	25	function	function	NOUN
ejpam-4006	11	26	and	and	CCONJ
ejpam-4006	11	27	then	then	ADV
ejpam-4006	11	28	integrated	integrate	VERB
ejpam-4006	11	29	over	over	ADP
ejpam-4006	11	30	the	the	DET
ejpam-4006	11	31	entire	entire	ADJ
ejpam-4006	11	32	space	space	NOUN
ejpam-4006	11	33	.	.	PUNCT
ejpam-4006	12	1	this	this	DET
ejpam-4006	12	2	point	point	NOUN
ejpam-4006	12	3	of	of	ADP
ejpam-4006	12	4	view	view	NOUN
ejpam-4006	12	5	is	be	AUX
ejpam-4006	12	6	also	also	ADV
ejpam-4006	12	7	taken	take	VERB
ejpam-4006	12	8	as	as	ADP
ejpam-4006	12	9	the	the	DET
ejpam-4006	12	10	basis	basis	NOUN
ejpam-4006	12	11	for	for	ADP
ejpam-4006	12	12	the	the	DET
ejpam-4006	12	13	definition	definition	NOUN
ejpam-4006	12	14	of	of	ADP
ejpam-4006	12	15	an	an	DET
ejpam-4006	12	16	arbitrary	arbitrary	ADJ
ejpam-4006	12	17	generalized	generalized	ADJ
ejpam-4006	12	18	function	function	NOUN
ejpam-4006	12	19	.	.	PUNCT
ejpam-4006	13	1	accordingly	accordingly	ADV
ejpam-4006	13	2	,	,	PUNCT
ejpam-4006	13	3	consider	consider	VERB
ejpam-4006	13	4	the	the	DET
ejpam-4006	13	5	space	space	NOUN
ejpam-4006	13	6	d	d	NOUN
ejpam-4006	13	7	consisting	consist	VERB
ejpam-4006	13	8	of	of	ADP
ejpam-4006	13	9	real	real	ADV
ejpam-4006	13	10	-	-	PUNCT
ejpam-4006	13	11	valued	value	VERB
ejpam-4006	13	12	function	function	NOUN
ejpam-4006	13	13	φ(x	φ(x	NOUN
ejpam-4006	13	14	)	)	PUNCT
ejpam-4006	14	1	=	=	SYM
ejpam-4006	14	2	φ(x1	φ(x1	NOUN
ejpam-4006	14	3	,	,	PUNCT
ejpam-4006	14	4	x2	x2	PROPN
ejpam-4006	14	5	,	,	PUNCT
ejpam-4006	14	6	.	.	PUNCT
ejpam-4006	14	7	.	.	PUNCT
ejpam-4006	14	8	.	.	PUNCT
ejpam-4006	15	1	,	,	PUNCT
ejpam-4006	15	2	xn	xn	PROPN
ejpam-4006	15	3	)	)	PUNCT
ejpam-4006	15	4	,	,	PUNCT
ejpam-4006	15	5	such	such	ADJ
ejpam-4006	15	6	that	that	SCONJ
ejpam-4006	15	7	the	the	DET
ejpam-4006	15	8	following	follow	VERB
ejpam-4006	15	9	hold	hold	NOUN
ejpam-4006	15	10	:	:	PUNCT
ejpam-4006	15	11	(	(	PUNCT
ejpam-4006	15	12	1	1	X
ejpam-4006	15	13	)	)	PUNCT
ejpam-4006	15	14	φ(x	φ(x	NOUN
ejpam-4006	15	15	)	)	PUNCT
ejpam-4006	15	16	is	be	AUX
ejpam-4006	15	17	an	an	DET
ejpam-4006	15	18	infinitely	infinitely	ADV
ejpam-4006	15	19	differentiable	differentiable	ADJ
ejpam-4006	15	20	function	function	NOUN
ejpam-4006	15	21	defined	define	VERB
ejpam-4006	15	22	at	at	ADP
ejpam-4006	15	23	every	every	DET
ejpam-4006	15	24	point	point	NOUN
ejpam-4006	15	25	of	of	ADP
ejpam-4006	15	26	rn	rn	PROPN
ejpam-4006	15	27	.	.	PUNCT
ejpam-4006	16	1	this	this	DET
ejpam-4006	16	2	mean	mean	VERB
ejpam-4006	16	3	that	that	SCONJ
ejpam-4006	16	4	dkφ	dkφ	NOUN
ejpam-4006	16	5	exists	exist	VERB
ejpam-4006	16	6	for	for	ADP
ejpam-4006	16	7	all	all	DET
ejpam-4006	16	8	multi	multi	ADJ
ejpam-4006	16	9	indices	index	NOUN
ejpam-4006	16	10	k.	k.	PUNCT
ejpam-4006	17	1	such	such	DET
ejpam-4006	17	2	a	a	DET
ejpam-4006	17	3	function	function	NOUN
ejpam-4006	17	4	is	be	AUX
ejpam-4006	17	5	also	also	ADV
ejpam-4006	17	6	call	call	VERB
ejpam-4006	17	7	a	a	DET
ejpam-4006	17	8	c∞	c∞	PROPN
ejpam-4006	17	9	function	function	NOUN
ejpam-4006	17	10	.	.	PUNCT
ejpam-4006	18	1	(	(	PUNCT
ejpam-4006	18	2	2	2	X
ejpam-4006	18	3	)	)	PUNCT
ejpam-4006	18	4	there	there	PRON
ejpam-4006	18	5	exists	exist	VERB
ejpam-4006	18	6	number	number	NOUN
ejpam-4006	18	7	a	a	DET
ejpam-4006	18	8	such	such	ADJ
ejpam-4006	18	9	that	that	SCONJ
ejpam-4006	18	10	φ(x	φ(x	NOUN
ejpam-4006	18	11	)	)	PUNCT
ejpam-4006	18	12	vanishes	vanish	VERB
ejpam-4006	18	13	for	for	ADP
ejpam-4006	18	14	r	r	NOUN
ejpam-4006	18	15	>	>	PUNCT
ejpam-4006	18	16	a.	a.	NOUN
ejpam-4006	18	17	this	this	PRON
ejpam-4006	18	18	means	mean	VERB
ejpam-4006	18	19	that	that	SCONJ
ejpam-4006	18	20	φ(x	φ(x	NOUN
ejpam-4006	18	21	)	)	PUNCT
ejpam-4006	18	22	has	have	VERB
ejpam-4006	18	23	a	a	DET
ejpam-4006	18	24	compact	compact	ADJ
ejpam-4006	18	25	support	support	NOUN
ejpam-4006	18	26	.	.	PUNCT
ejpam-4006	19	1	then	then	ADV
ejpam-4006	19	2	φ(x	φ(x	NOUN
ejpam-4006	19	3	)	)	PUNCT
ejpam-4006	19	4	is	be	AUX
ejpam-4006	19	5	called	call	VERB
ejpam-4006	19	6	a	a	DET
ejpam-4006	19	7	test	test	NOUN
ejpam-4006	19	8	function	function	NOUN
ejpam-4006	19	9	.	.	PUNCT
ejpam-4006	20	1	doi	doi	NOUN
ejpam-4006	20	2	:	:	PUNCT
ejpam-4006	20	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4006	https://doi.org/10.29020/nybg.ejpam.v14i3.4006	NOUN
ejpam-4006	20	4	email	email	NOUN
ejpam-4006	20	5	address	address	NOUN
ejpam-4006	20	6	:	:	PUNCT
ejpam-4006	20	7	sudprathai@gmail.com	sudprathai@gmail.com	X
ejpam-4006	20	8	(	(	PUNCT
ejpam-4006	20	9	s.	s.	PROPN
ejpam-4006	20	10	bupasiri	bupasiri	PROPN
ejpam-4006	20	11	)	)	PUNCT
ejpam-4006	20	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4006	21	1	881	881	NUM
ejpam-4006	21	2	©	©	PROPN
ejpam-4006	21	3	2021	2021	NUM
ejpam-4006	21	4	ejpam	ejpam	VERB
ejpam-4006	21	5	all	all	DET
ejpam-4006	21	6	rights	right	NOUN
ejpam-4006	21	7	reserved	reserve	VERB
ejpam-4006	21	8	.	.	PUNCT
ejpam-4006	22	1	s.	s.	PROPN
ejpam-4006	22	2	bupasiri	bupasiri	PROPN
ejpam-4006	22	3	/	/	SYM
ejpam-4006	22	4	eur	eur	PROPN
ejpam-4006	22	5	.	.	PUNCT
ejpam-4006	23	1	j.	j.	PROPN
ejpam-4006	23	2	pure	pure	PROPN
ejpam-4006	23	3	appl	appl	PROPN
ejpam-4006	23	4	.	.	PROPN
ejpam-4006	23	5	math	math	PROPN
ejpam-4006	23	6	,	,	PUNCT
ejpam-4006	23	7	14	14	NUM
ejpam-4006	23	8	(	(	PUNCT
ejpam-4006	23	9	3	3	NUM
ejpam-4006	23	10	)	)	PUNCT
ejpam-4006	23	11	(	(	PUNCT
ejpam-4006	23	12	2021	2021	NUM
ejpam-4006	23	13	)	)	PUNCT
ejpam-4006	23	14	,	,	PUNCT
ejpam-4006	23	15	881	881	NUM
ejpam-4006	23	16	-	-	SYM
ejpam-4006	23	17	894	894	NUM
ejpam-4006	23	18	882	882	NUM
ejpam-4006	23	19	in	in	ADP
ejpam-4006	23	20	physical	physical	ADJ
ejpam-4006	23	21	problem	problem	NOUN
ejpam-4006	23	22	,	,	PUNCT
ejpam-4006	23	23	one	one	PRON
ejpam-4006	23	24	often	often	ADV
ejpam-4006	23	25	encounters	encounter	VERB
ejpam-4006	23	26	idealized	idealized	ADJ
ejpam-4006	23	27	concepts	concept	NOUN
ejpam-4006	23	28	such	such	ADJ
ejpam-4006	23	29	as	as	ADP
ejpam-4006	23	30	a	a	DET
ejpam-4006	23	31	force	force	NOUN
ejpam-4006	23	32	concentrated	concentrate	VERB
ejpam-4006	23	33	at	at	ADP
ejpam-4006	23	34	a	a	DET
ejpam-4006	23	35	point	point	NOUN
ejpam-4006	23	36	ξ	ξ	PROPN
ejpam-4006	23	37	or	or	CCONJ
ejpam-4006	23	38	an	an	DET
ejpam-4006	23	39	impulsive	impulsive	ADJ
ejpam-4006	23	40	force	force	NOUN
ejpam-4006	23	41	that	that	PRON
ejpam-4006	23	42	acts	act	VERB
ejpam-4006	23	43	instaneously	instaneously	ADV
ejpam-4006	23	44	.	.	PUNCT
ejpam-4006	24	1	these	these	DET
ejpam-4006	24	2	forces	force	NOUN
ejpam-4006	24	3	are	be	AUX
ejpam-4006	24	4	described	describe	VERB
ejpam-4006	24	5	by	by	ADP
ejpam-4006	24	6	the	the	DET
ejpam-4006	24	7	dirac	dirac	NOUN
ejpam-4006	24	8	-	-	PUNCT
ejpam-4006	24	9	delta	delta	NOUN
ejpam-4006	24	10	function	function	NOUN
ejpam-4006	24	11	δ(x−	δ(x−	NOUN
ejpam-4006	24	12	ξ	ξ	PROPN
ejpam-4006	24	13	)	)	PUNCT
ejpam-4006	24	14	,	,	PUNCT
ejpam-4006	24	15	which	which	PRON
ejpam-4006	24	16	has	have	VERB
ejpam-4006	24	17	several	several	ADJ
ejpam-4006	24	18	significant	significant	ADJ
ejpam-4006	24	19	properties	property	NOUN
ejpam-4006	24	20	:	:	PUNCT
ejpam-4006	24	21	δ(x−	δ(x−	X
ejpam-4006	24	22	ξ	ξ	PROPN
ejpam-4006	24	23	)	)	PUNCT
ejpam-4006	24	24	=	=	SYM
ejpam-4006	24	25	0	0	NUM
ejpam-4006	24	26	,	,	PUNCT
ejpam-4006	24	27	x	x	PROPN
ejpam-4006	24	28	6=	6=	NUM
ejpam-4006	24	29	ξ	ξ	PROPN
ejpam-4006	24	30	(	(	PUNCT
ejpam-4006	24	31	1)∫	1)∫	NUM
ejpam-4006	24	32	b	b	NOUN
ejpam-4006	24	33	a	a	DET
ejpam-4006	24	34	δ(x−	δ(x−	NOUN
ejpam-4006	24	35	ξ)dx	ξ)dx	PROPN
ejpam-4006	24	36	=	=	SYM
ejpam-4006	24	37	{	{	PUNCT
ejpam-4006	24	38	0	0	NUM
ejpam-4006	24	39	for	for	ADP
ejpam-4006	24	40	a	a	DET
ejpam-4006	24	41	,	,	PUNCT
ejpam-4006	24	42	b	b	X
ejpam-4006	24	43	<	<	X
ejpam-4006	24	44	ξ	ξ	PROPN
ejpam-4006	24	45	or	or	CCONJ
ejpam-4006	24	46	ξ	ξ	X
ejpam-4006	24	47	<	<	X
ejpam-4006	24	48	a	a	PROPN
ejpam-4006	24	49	,	,	PUNCT
ejpam-4006	24	50	b	b	PROPN
ejpam-4006	24	51	1	1	NUM
ejpam-4006	24	52	for	for	ADP
ejpam-4006	24	53	a	a	DET
ejpam-4006	24	54	≤	≤	NUM
ejpam-4006	24	55	ξ	ξ	PRON
ejpam-4006	24	56	≤	≤	NUM
ejpam-4006	24	57	b	b	X
ejpam-4006	24	58	(	(	PUNCT
ejpam-4006	24	59	2	2	NUM
ejpam-4006	24	60	)	)	PUNCT
ejpam-4006	24	61	and	and	CCONJ
ejpam-4006	24	62	∫	∫	PROPN
ejpam-4006	24	63	∞	∞	PROPN
ejpam-4006	24	64	−∞	−∞	ADP
ejpam-4006	25	1	δ(x−	δ(x−	NOUN
ejpam-4006	25	2	ξ)dx	ξ)dx	PROPN
ejpam-4006	25	3	=	=	SYM
ejpam-4006	25	4	1	1	X
ejpam-4006	25	5	.	.	PUNCT
ejpam-4006	25	6	(	(	PUNCT
ejpam-4006	25	7	3	3	X
ejpam-4006	25	8	)	)	PUNCT
ejpam-4006	25	9	equation	equation	NOUN
ejpam-4006	25	10	(	(	PUNCT
ejpam-4006	25	11	3	3	X
ejpam-4006	25	12	)	)	PUNCT
ejpam-4006	25	13	is	be	AUX
ejpam-4006	25	14	a	a	DET
ejpam-4006	25	15	special	special	ADJ
ejpam-4006	25	16	case	case	NOUN
ejpam-4006	25	17	of	of	ADP
ejpam-4006	25	18	the	the	DET
ejpam-4006	25	19	general	general	ADJ
ejpam-4006	25	20	formula∫	formula∫	ADJ
ejpam-4006	25	21	∞	∞	PROPN
ejpam-4006	25	22	−∞	−∞	ADP
ejpam-4006	25	23	δ(x−	δ(x−	NOUN
ejpam-4006	25	24	ξ)f(x)dx	ξ)f(x)dx	NOUN
ejpam-4006	25	25	=	=	SYM
ejpam-4006	25	26	f(ξ	f(ξ	NOUN
ejpam-4006	25	27	)	)	PUNCT
ejpam-4006	25	28	,	,	PUNCT
ejpam-4006	25	29	(	(	PUNCT
ejpam-4006	25	30	4	4	X
ejpam-4006	25	31	)	)	PUNCT
ejpam-4006	25	32	where	where	SCONJ
ejpam-4006	25	33	f(x	f(x	PROPN
ejpam-4006	25	34	)	)	PUNCT
ejpam-4006	25	35	is	be	AUX
ejpam-4006	25	36	a	a	DET
ejpam-4006	25	37	sufficiently	sufficiently	ADV
ejpam-4006	25	38	smooth	smooth	ADJ
ejpam-4006	25	39	function	function	NOUN
ejpam-4006	25	40	.	.	PUNCT
ejpam-4006	26	1	relation	relation	NOUN
ejpam-4006	26	2	(	(	PUNCT
ejpam-4006	26	3	4	4	NUM
ejpam-4006	26	4	)	)	PUNCT
ejpam-4006	26	5	is	be	AUX
ejpam-4006	26	6	called	call	VERB
ejpam-4006	26	7	the	the	DET
ejpam-4006	26	8	sifting	sift	VERB
ejpam-4006	26	9	property	property	NOUN
ejpam-4006	26	10	or	or	CCONJ
ejpam-4006	26	11	the	the	DET
ejpam-4006	26	12	reproducing	reproduce	VERB
ejpam-4006	26	13	property	property	NOUN
ejpam-4006	26	14	of	of	ADP
ejpam-4006	26	15	the	the	DET
ejpam-4006	26	16	delta	delta	NOUN
ejpam-4006	26	17	function	function	NOUN
ejpam-4006	26	18	,	,	PUNCT
ejpam-4006	26	19	and	and	CCONJ
ejpam-4006	26	20	(	(	PUNCT
ejpam-4006	26	21	3	3	X
ejpam-4006	26	22	)	)	PUNCT
ejpam-4006	26	23	is	be	AUX
ejpam-4006	26	24	obtained	obtain	VERB
ejpam-4006	26	25	from	from	ADP
ejpam-4006	26	26	it	it	PRON
ejpam-4006	26	27	by	by	ADP
ejpam-4006	26	28	putting	put	VERB
ejpam-4006	26	29	f(x	f(x	PROPN
ejpam-4006	26	30	)	)	PUNCT
ejpam-4006	26	31	=	=	SYM
ejpam-4006	27	1	1	1	X
ejpam-4006	27	2	.	.	PUNCT
ejpam-4006	27	3	moreover	moreover	ADV
ejpam-4006	27	4	,	,	PUNCT
ejpam-4006	27	5	kananthai	kananthai	PROPN
ejpam-4006	27	6	et	et	PROPN
ejpam-4006	27	7	al	al	PROPN
ejpam-4006	27	8	.	.	PUNCT
ejpam-4006	28	1	[	[	X
ejpam-4006	28	2	1	1	X
ejpam-4006	28	3	]	]	PUNCT
ejpam-4006	28	4	have	have	AUX
ejpam-4006	28	5	studied	study	VERB
ejpam-4006	28	6	the	the	DET
ejpam-4006	28	7	fundamental	fundamental	ADJ
ejpam-4006	28	8	solution	solution	NOUN
ejpam-4006	28	9	of	of	ADP
ejpam-4006	28	10	the	the	DET
ejpam-4006	28	11	operator	operator	NOUN
ejpam-4006	28	12	⊕k	⊕k	NOUN
ejpam-4006	28	13	and	and	CCONJ
ejpam-4006	28	14	the	the	DET
ejpam-4006	28	15	weak	weak	ADJ
ejpam-4006	28	16	solution	solution	NOUN
ejpam-4006	28	17	of	of	ADP
ejpam-4006	28	18	the	the	DET
ejpam-4006	28	19	equation	equation	NOUN
ejpam-4006	28	20	⊕ku(x	⊕ku(x	VERB
ejpam-4006	28	21	)	)	PUNCT
ejpam-4006	28	22	=	=	SYM
ejpam-4006	28	23	f(x	f(x	PROPN
ejpam-4006	28	24	)	)	PUNCT
ejpam-4006	28	25	,	,	PUNCT
ejpam-4006	28	26	f(x	f(x	PROPN
ejpam-4006	28	27	)	)	PUNCT
ejpam-4006	28	28	is	be	AUX
ejpam-4006	28	29	a	a	DET
ejpam-4006	28	30	generalized	generalized	ADJ
ejpam-4006	28	31	function	function	NOUN
ejpam-4006	28	32	where	where	SCONJ
ejpam-4006	28	33	the	the	DET
ejpam-4006	28	34	operator	operator	NOUN
ejpam-4006	28	35	⊕k	⊕k	NOUN
ejpam-4006	28	36	is	be	AUX
ejpam-4006	28	37	defined	define	VERB
ejpam-4006	28	38	by	by	ADP
ejpam-4006	28	39	⊕k	⊕k	ADJ
ejpam-4006	28	40	=	=	SYM
ejpam-4006	28	41			PROPN
ejpam-4006	28	42	(	(	PUNCT
ejpam-4006	28	43	p∑	p∑	NOUN
ejpam-4006	28	44	r=1	r=1	NOUN
ejpam-4006	28	45	∂2	∂2	NOUN
ejpam-4006	28	46	∂x2r	∂x2r	NOUN
ejpam-4006	28	47	)	)	PUNCT
ejpam-4006	28	48	4	4	NUM
ejpam-4006	28	49	−	−	NOUN
ejpam-4006	29	1			PROPN
ejpam-4006	29	2	p+q∑	p+q∑	PROPN
ejpam-4006	29	3	j	j	NOUN
ejpam-4006	29	4	=	=	PROPN
ejpam-4006	29	5	p+1	p+1	PROPN
ejpam-4006	29	6	∂2	∂2	PROPN
ejpam-4006	29	7	∂x2j	∂x2j	PROPN
ejpam-4006	29	8	4k	4k	PROPN
ejpam-4006	29	9	=	=	SYM
ejpam-4006	29	10			PROPN
ejpam-4006	29	11	(	(	PUNCT
ejpam-4006	29	12	p∑	p∑	NOUN
ejpam-4006	29	13	r=1	r=1	NOUN
ejpam-4006	29	14	∂2	∂2	NOUN
ejpam-4006	29	15	∂x2r	∂x2r	NOUN
ejpam-4006	29	16	)	)	PUNCT
ejpam-4006	29	17	2	2	NUM
ejpam-4006	29	18	−	−	NOUN
ejpam-4006	29	19			PROPN
ejpam-4006	29	20	p+q∑	p+q∑	PROPN
ejpam-4006	29	21	j	j	NOUN
ejpam-4006	29	22	=	=	PROPN
ejpam-4006	29	23	p+1	p+1	PROPN
ejpam-4006	29	24	∂2	∂2	PROPN
ejpam-4006	29	25	∂x2j	∂x2j	PROPN
ejpam-4006	29	26	2k	2k	PROPN
ejpam-4006	29	27			NOUN
ejpam-4006	29	28	(	(	PUNCT
ejpam-4006	29	29	p∑	p∑	NOUN
ejpam-4006	29	30	r=1	r=1	NOUN
ejpam-4006	29	31	∂2	∂2	NOUN
ejpam-4006	29	32	∂x2r	∂x2r	NOUN
ejpam-4006	29	33	)	)	PUNCT
ejpam-4006	29	34	2	2	NUM
ejpam-4006	29	35	+	+	CCONJ
ejpam-4006	29	36			PROPN
ejpam-4006	29	37	p+q∑	p+q∑	PROPN
ejpam-4006	29	38	j	j	NOUN
ejpam-4006	29	39	=	=	PROPN
ejpam-4006	29	40	p+1	p+1	PROPN
ejpam-4006	29	41	∂2	∂2	PROPN
ejpam-4006	29	42	∂x2j	∂x2j	PROPN
ejpam-4006	29	43	2k	2k	PROPN
ejpam-4006	29	44	=	=	SYM
ejpam-4006	29	45	�	�	PROPN
ejpam-4006	29	46	klk1lk2	klk1lk2	PROPN
ejpam-4006	29	47	=	=	SYM
ejpam-4006	29	48	�	�	PROPN
ejpam-4006	29	49	klk	klk	PROPN
ejpam-4006	29	50	(	(	PUNCT
ejpam-4006	29	51	5	5	NUM
ejpam-4006	29	52	)	)	PUNCT
ejpam-4006	29	53	where	where	SCONJ
ejpam-4006	29	54	p+q	p+q	NOUN
ejpam-4006	29	55	=	=	PUNCT
ejpam-4006	29	56	n	n	X
ejpam-4006	29	57	is	be	AUX
ejpam-4006	29	58	the	the	DET
ejpam-4006	29	59	dimension	dimension	NOUN
ejpam-4006	29	60	of	of	ADP
ejpam-4006	29	61	the	the	DET
ejpam-4006	29	62	euclidean	euclidean	ADJ
ejpam-4006	29	63	space	space	PROPN
ejpam-4006	29	64	rn	rn	PROPN
ejpam-4006	29	65	and	and	CCONJ
ejpam-4006	29	66	k	k	PROPN
ejpam-4006	29	67	is	be	AUX
ejpam-4006	29	68	a	a	DET
ejpam-4006	29	69	nonnegative	nonnegative	ADJ
ejpam-4006	29	70	integer	integer	NOUN
ejpam-4006	29	71	.	.	PUNCT
ejpam-4006	30	1	next	next	ADJ
ejpam-4006	30	2	,	,	PUNCT
ejpam-4006	30	3	kananthai	kananthai	PROPN
ejpam-4006	30	4	et	et	PROPN
ejpam-4006	30	5	al	al	PROPN
ejpam-4006	30	6	.	.	PUNCT
ejpam-4006	31	1	[	[	X
ejpam-4006	31	2	2	2	X
ejpam-4006	31	3	]	]	PUNCT
ejpam-4006	31	4	have	have	AUX
ejpam-4006	31	5	studied	study	VERB
ejpam-4006	31	6	the	the	DET
ejpam-4006	31	7	relationship	relationship	NOUN
ejpam-4006	31	8	between	between	ADP
ejpam-4006	31	9	the	the	DET
ejpam-4006	31	10	operator	operator	NOUN
ejpam-4006	31	11	⊕k	⊕k	NOUN
ejpam-4006	31	12	and	and	CCONJ
ejpam-4006	31	13	the	the	DET
ejpam-4006	31	14	wave	wave	NOUN
ejpam-4006	31	15	operator	operator	NOUN
ejpam-4006	31	16	,	,	PUNCT
ejpam-4006	31	17	and	and	CCONJ
ejpam-4006	31	18	the	the	DET
ejpam-4006	31	19	relationship	relationship	NOUN
ejpam-4006	31	20	between	between	ADP
ejpam-4006	31	21	the	the	DET
ejpam-4006	31	22	operator	operator	NOUN
ejpam-4006	31	23	⊕k	⊕k	NOUN
ejpam-4006	31	24	and	and	CCONJ
ejpam-4006	31	25	the	the	DET
ejpam-4006	31	26	laplacian	laplacian	NOUN
ejpam-4006	31	27	.	.	PUNCT
ejpam-4006	32	1	moreover	moreover	ADV
ejpam-4006	32	2	,	,	PUNCT
ejpam-4006	32	3	equation	equation	NOUN
ejpam-4006	32	4	⊕kk(x	⊕kk(x	VERB
ejpam-4006	32	5	)	)	PUNCT
ejpam-4006	33	1	=	=	PUNCT
ejpam-4006	33	2	δ	δ	NOUN
ejpam-4006	33	3	we	we	PRON
ejpam-4006	33	4	have	have	VERB
ejpam-4006	33	5	k(x	k(x	PROPN
ejpam-4006	33	6	)	)	PUNCT
ejpam-4006	34	1	=	=	PUNCT
ejpam-4006	35	1	[	[	X
ejpam-4006	35	2	rh2k(x	rh2k(x	NOUN
ejpam-4006	35	3	)	)	PUNCT
ejpam-4006	35	4	∗	∗	NOUN
ejpam-4006	35	5	(	(	PUNCT
ejpam-4006	35	6	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	35	7	)	)	PUNCT
ejpam-4006	35	8	]	]	PUNCT
ejpam-4006	35	9	∗	∗	PROPN
ejpam-4006	35	10	s2k(x	s2k(x	PROPN
ejpam-4006	35	11	)	)	PUNCT
ejpam-4006	35	12	∗	∗	PROPN
ejpam-4006	35	13	t2k(x	t2k(x	PROPN
ejpam-4006	35	14	)	)	PUNCT
ejpam-4006	35	15	is	be	AUX
ejpam-4006	35	16	the	the	DET
ejpam-4006	35	17	fundamental	fundamental	ADJ
ejpam-4006	35	18	solution	solution	NOUN
ejpam-4006	35	19	of	of	ADP
ejpam-4006	35	20	the	the	DET
ejpam-4006	35	21	operator	operator	NOUN
ejpam-4006	35	22	⊕k	⊕k	VERB
ejpam-4006	35	23	.	.	PUNCT
ejpam-4006	36	1	later	later	ADV
ejpam-4006	36	2	,	,	PUNCT
ejpam-4006	36	3	kananthai	kananthai	PROPN
ejpam-4006	36	4	[	[	X
ejpam-4006	36	5	8	8	NUM
ejpam-4006	36	6	]	]	PUNCT
ejpam-4006	36	7	has	have	AUX
ejpam-4006	36	8	studied	study	VERB
ejpam-4006	36	9	the	the	DET
ejpam-4006	36	10	inversion	inversion	NOUN
ejpam-4006	36	11	of	of	ADP
ejpam-4006	36	12	the	the	DET
ejpam-4006	36	13	kernel	kernel	NOUN
ejpam-4006	36	14	kα	kα	PROPN
ejpam-4006	36	15	,	,	PUNCT
ejpam-4006	36	16	β	β	X
ejpam-4006	36	17	,	,	PUNCT
ejpam-4006	36	18	γ	γ	X
ejpam-4006	36	19	,	,	PUNCT
ejpam-4006	36	20	ν	ν	NOUN
ejpam-4006	36	21	related	relate	VERB
ejpam-4006	36	22	to	to	ADP
ejpam-4006	36	23	the	the	DET
ejpam-4006	36	24	operator	operator	NOUN
ejpam-4006	36	25	⊕k	⊕k	VERB
ejpam-4006	36	26	.	.	PUNCT
ejpam-4006	37	1	in	in	ADP
ejpam-4006	37	2	1988	1988	NUM
ejpam-4006	37	3	,	,	PUNCT
ejpam-4006	37	4	trione	trione	NOUN
ejpam-4006	38	1	[	[	X
ejpam-4006	38	2	11	11	NUM
ejpam-4006	38	3	]	]	PUNCT
ejpam-4006	38	4	has	have	AUX
ejpam-4006	38	5	studied	study	VERB
ejpam-4006	38	6	the	the	DET
ejpam-4006	38	7	fundamental	fundamental	ADJ
ejpam-4006	38	8	solution	solution	NOUN
ejpam-4006	38	9	of	of	ADP
ejpam-4006	38	10	the	the	DET
ejpam-4006	38	11	ultra	ultra	ADJ
ejpam-4006	38	12	-	-	ADJ
ejpam-4006	38	13	hyperbolic	hyperbolic	ADJ
ejpam-4006	38	14	kleingordon	kleingordon	NOUN
ejpam-4006	38	15	operator	operator	NOUN
ejpam-4006	38	16	iterated	iterate	VERB
ejpam-4006	38	17	k	k	NOUN
ejpam-4006	38	18	-	-	PUNCT
ejpam-4006	38	19	times	time	NOUN
ejpam-4006	38	20	such	such	ADJ
ejpam-4006	38	21	that	that	DET
ejpam-4006	38	22	operator	operator	NOUN
ejpam-4006	38	23	is	be	AUX
ejpam-4006	38	24	defined	define	VERB
ejpam-4006	38	25	by	by	ADP
ejpam-4006	38	26	(	(	PUNCT
ejpam-4006	38	27	�	�	PROPN
ejpam-4006	38	28	+	+	NOUN
ejpam-4006	38	29	m2)k	m2)k	NOUN
ejpam-4006	38	30	=	=	PUNCT
ejpam-4006	38	31	[	[	PUNCT
ejpam-4006	38	32	∂2	∂2	ADJ
ejpam-4006	38	33	∂x21	∂x21	PROPN
ejpam-4006	38	34	+	+	CCONJ
ejpam-4006	38	35	∂2	∂2	PROPN
ejpam-4006	38	36	∂x22	∂x22	PROPN
ejpam-4006	38	37	+	+	CCONJ
ejpam-4006	38	38	·	·	PUNCT
ejpam-4006	38	39	·	·	PUNCT
ejpam-4006	38	40	·	·	PUNCT
ejpam-4006	39	1	+	+	NUM
ejpam-4006	39	2	∂2	∂2	NOUN
ejpam-4006	39	3	∂x2p	∂x2p	NUM
ejpam-4006	40	1	−	−	PROPN
ejpam-4006	40	2	∂2	∂2	PROPN
ejpam-4006	40	3	∂x2p+1	∂x2p+1	PROPN
ejpam-4006	40	4	−	−	PROPN
ejpam-4006	40	5	∂2	∂2	NOUN
ejpam-4006	40	6	∂x2p+2	∂x2p+2	VERB
ejpam-4006	40	7	−	−	X
ejpam-4006	40	8	·	·	PUNCT
ejpam-4006	40	9	·	·	PUNCT
ejpam-4006	40	10	·	·	PUNCT
ejpam-4006	41	1	−	−	PUNCT
ejpam-4006	42	1	∂2	∂2	NOUN
ejpam-4006	42	2	∂x2p+q	∂x2p+q	X
ejpam-4006	42	3	+	+	CCONJ
ejpam-4006	42	4	m2	m2	PROPN
ejpam-4006	42	5	]	]	X
ejpam-4006	42	6	k	k	PROPN
ejpam-4006	42	7	.	.	PUNCT
ejpam-4006	43	1	(	(	PUNCT
ejpam-4006	43	2	6	6	X
ejpam-4006	43	3	)	)	PUNCT
ejpam-4006	43	4	s.	s.	PROPN
ejpam-4006	43	5	bupasiri	bupasiri	PROPN
ejpam-4006	43	6	/	/	SYM
ejpam-4006	43	7	eur	eur	PROPN
ejpam-4006	43	8	.	.	PUNCT
ejpam-4006	44	1	j.	j.	PROPN
ejpam-4006	44	2	pure	pure	PROPN
ejpam-4006	44	3	appl	appl	PROPN
ejpam-4006	44	4	.	.	PROPN
ejpam-4006	44	5	math	math	PROPN
ejpam-4006	44	6	,	,	PUNCT
ejpam-4006	44	7	14	14	NUM
ejpam-4006	44	8	(	(	PUNCT
ejpam-4006	44	9	3	3	NUM
ejpam-4006	44	10	)	)	PUNCT
ejpam-4006	44	11	(	(	PUNCT
ejpam-4006	44	12	2021	2021	NUM
ejpam-4006	44	13	)	)	PUNCT
ejpam-4006	44	14	,	,	PUNCT
ejpam-4006	44	15	881	881	NUM
ejpam-4006	44	16	-	-	SYM
ejpam-4006	44	17	894	894	NUM
ejpam-4006	44	18	883	883	NUM
ejpam-4006	44	19	later	later	ADV
ejpam-4006	44	20	,	,	PUNCT
ejpam-4006	44	21	kananthai	kananthai	PROPN
ejpam-4006	45	1	[	[	X
ejpam-4006	45	2	7	7	NUM
ejpam-4006	45	3	]	]	PUNCT
ejpam-4006	45	4	has	have	AUX
ejpam-4006	45	5	studied	study	VERB
ejpam-4006	45	6	the	the	DET
ejpam-4006	45	7	fundamental	fundamental	ADJ
ejpam-4006	45	8	solution	solution	NOUN
ejpam-4006	45	9	for	for	ADP
ejpam-4006	45	10	the	the	DET
ejpam-4006	45	11	(	(	PUNCT
ejpam-4006	45	12	♦	♦	PROPN
ejpam-4006	45	13	+	+	CCONJ
ejpam-4006	45	14	m4)k	m4)k	PROPN
ejpam-4006	45	15	which	which	PRON
ejpam-4006	45	16	related	relate	VERB
ejpam-4006	45	17	to	to	ADP
ejpam-4006	45	18	the	the	DET
ejpam-4006	45	19	klein	klein	PROPN
ejpam-4006	45	20	-	-	PUNCT
ejpam-4006	45	21	gordon	gordon	PROPN
ejpam-4006	45	22	operator	operator	NOUN
ejpam-4006	45	23	.	.	PUNCT
ejpam-4006	46	1	from	from	ADP
ejpam-4006	46	2	equation	equation	NOUN
ejpam-4006	46	3	(	(	PUNCT
ejpam-4006	46	4	5	5	NUM
ejpam-4006	46	5	)	)	PUNCT
ejpam-4006	46	6	the	the	DET
ejpam-4006	46	7	operator	operator	NOUN
ejpam-4006	46	8	⊕km	⊕km	VERB
ejpam-4006	46	9	can	can	AUX
ejpam-4006	46	10	be	be	AUX
ejpam-4006	46	11	expressed	express	VERB
ejpam-4006	46	12	in	in	ADP
ejpam-4006	46	13	the	the	DET
ejpam-4006	46	14	form	form	NOUN
ejpam-4006	46	15	⊕km	⊕km	VERB
ejpam-4006	47	1	=	=	SYM
ejpam-4006	47	2			PROPN
ejpam-4006	47	3	(	(	PUNCT
ejpam-4006	47	4	p∑	p∑	NOUN
ejpam-4006	47	5	r=1	r=1	NOUN
ejpam-4006	47	6	∂2	∂2	NOUN
ejpam-4006	47	7	∂x2r	∂x2r	ADP
ejpam-4006	47	8	+	+	NOUN
ejpam-4006	47	9	m2	m2	PROPN
ejpam-4006	47	10	)	)	PUNCT
ejpam-4006	47	11	4	4	NUM
ejpam-4006	47	12	−	−	NOUN
ejpam-4006	47	13			PROPN
ejpam-4006	47	14	p+q∑	p+q∑	PROPN
ejpam-4006	47	15	j	j	NOUN
ejpam-4006	47	16	=	=	PROPN
ejpam-4006	47	17	p+1	p+1	PROPN
ejpam-4006	47	18	∂2	∂2	PROPN
ejpam-4006	47	19	∂x2j	∂x2j	PROPN
ejpam-4006	47	20	4k	4k	PROPN
ejpam-4006	47	21	=	=	SYM
ejpam-4006	47	22			PROPN
ejpam-4006	47	23	(	(	PUNCT
ejpam-4006	47	24	p∑	p∑	NOUN
ejpam-4006	47	25	r=1	r=1	NOUN
ejpam-4006	47	26	∂2	∂2	NOUN
ejpam-4006	47	27	∂x2r	∂x2r	ADP
ejpam-4006	47	28	+	+	NOUN
ejpam-4006	47	29	m2	m2	PROPN
ejpam-4006	47	30	)	)	PUNCT
ejpam-4006	47	31	2	2	NUM
ejpam-4006	47	32	−	−	PROPN
ejpam-4006	47	33			PROPN
ejpam-4006	47	34	p+q∑	p+q∑	PROPN
ejpam-4006	47	35	j	j	NOUN
ejpam-4006	47	36	=	=	PROPN
ejpam-4006	47	37	p+1	p+1	PROPN
ejpam-4006	47	38	∂2	∂2	PROPN
ejpam-4006	47	39	∂x2j	∂x2j	PROPN
ejpam-4006	47	40	2k	2k	PROPN
ejpam-4006	47	41			NOUN
ejpam-4006	47	42	(	(	PUNCT
ejpam-4006	47	43	p∑	p∑	NOUN
ejpam-4006	47	44	r=1	r=1	NOUN
ejpam-4006	47	45	∂2	∂2	NOUN
ejpam-4006	47	46	∂x2r	∂x2r	ADP
ejpam-4006	47	47	+	+	NOUN
ejpam-4006	47	48	m2	m2	PROPN
ejpam-4006	47	49	)	)	PUNCT
ejpam-4006	47	50	2	2	NUM
ejpam-4006	47	51	+	+	CCONJ
ejpam-4006	47	52			PROPN
ejpam-4006	47	53	p+q∑	p+q∑	PROPN
ejpam-4006	47	54	j	j	NOUN
ejpam-4006	47	55	=	=	PROPN
ejpam-4006	47	56	p+1	p+1	PROPN
ejpam-4006	47	57	∂2	∂2	PROPN
ejpam-4006	47	58	∂x2j	∂x2j	PROPN
ejpam-4006	47	59	2k	2k	PROPN
ejpam-4006	47	60	=	=	SYM
ejpam-4006	47	61			CCONJ
ejpam-4006	47	62	p∑	p∑	X
ejpam-4006	47	63	r=1	r=1	NOUN
ejpam-4006	47	64	∂2	∂2	NOUN
ejpam-4006	47	65	∂x2r	∂x2r	ADP
ejpam-4006	47	66	−	−	VERB
ejpam-4006	47	67	p+q∑	p+q∑	PROPN
ejpam-4006	47	68	j	j	PROPN
ejpam-4006	47	69	=	=	PROPN
ejpam-4006	47	70	p+1	p+1	PROPN
ejpam-4006	47	71	∂2	∂2	PROPN
ejpam-4006	47	72	∂x2j	∂x2j	X
ejpam-4006	47	73	+m2	+m2	PROPN
ejpam-4006	47	74	k	k	NOUN
ejpam-4006	47	75			VERB
ejpam-4006	47	76	p∑	p∑	NOUN
ejpam-4006	48	1	r=1	r=1	NOUN
ejpam-4006	48	2	∂2	∂2	NOUN
ejpam-4006	48	3	∂x2r	∂x2r	ADP
ejpam-4006	48	4	+	+	NOUN
ejpam-4006	48	5	p+q∑	p+q∑	PROPN
ejpam-4006	48	6	j	j	NOUN
ejpam-4006	48	7	=	=	PROPN
ejpam-4006	48	8	p+1	p+1	PROPN
ejpam-4006	48	9	∂2	∂2	PROPN
ejpam-4006	48	10	∂x2j	∂x2j	X
ejpam-4006	48	11	+m2	+m2	PROPN
ejpam-4006	48	12	k	k	NOUN
ejpam-4006	48	13	×	×	NOUN
ejpam-4006	48	14			PRON
ejpam-4006	48	15	p∑	p∑	NOUN
ejpam-4006	49	1	r=1	r=1	NOUN
ejpam-4006	49	2	∂2	∂2	NOUN
ejpam-4006	49	3	∂x2r	∂x2r	ADP
ejpam-4006	49	4	+	+	CCONJ
ejpam-4006	49	5	i	i	PROPN
ejpam-4006	49	6	p+q∑	p+q∑	PROPN
ejpam-4006	49	7	j	j	X
ejpam-4006	49	8	=	=	PROPN
ejpam-4006	49	9	p+1	p+1	PROPN
ejpam-4006	49	10	∂2	∂2	PROPN
ejpam-4006	49	11	∂x2j	∂x2j	X
ejpam-4006	49	12	+m2	+m2	PROPN
ejpam-4006	49	13	k	k	NOUN
ejpam-4006	49	14			VERB
ejpam-4006	49	15	p∑	p∑	PUNCT
ejpam-4006	50	1	r=1	r=1	NOUN
ejpam-4006	50	2	∂2	∂2	NOUN
ejpam-4006	50	3	∂x2r	∂x2r	ADP
ejpam-4006	50	4	−	−	PROPN
ejpam-4006	50	5	i	i	PRON
ejpam-4006	50	6	p+q∑	p+q∑	PROPN
ejpam-4006	50	7	j	j	X
ejpam-4006	51	1	=	=	PROPN
ejpam-4006	51	2	p+1	p+1	PROPN
ejpam-4006	51	3	∂2	∂2	PROPN
ejpam-4006	51	4	∂x2j	∂x2j	X
ejpam-4006	51	5	+m2	+m2	NOUN
ejpam-4006	51	6	k	k	NOUN
ejpam-4006	51	7	,	,	PUNCT
ejpam-4006	51	8	(	(	PUNCT
ejpam-4006	51	9	7	7	NUM
ejpam-4006	51	10	)	)	PUNCT
ejpam-4006	51	11	where	where	SCONJ
ejpam-4006	51	12	i	i	PRON
ejpam-4006	51	13	=	=	VERB
ejpam-4006	51	14	√	√	NUM
ejpam-4006	51	15	−1	−1	NOUN
ejpam-4006	51	16	,	,	PUNCT
ejpam-4006	51	17	n	n	PROPN
ejpam-4006	51	18	=	=	PROPN
ejpam-4006	51	19	p+	p+	NOUN
ejpam-4006	51	20	q.	q.	NOUN
ejpam-4006	51	21	and	and	CCONJ
ejpam-4006	51	22	the	the	DET
ejpam-4006	51	23	operator	operator	PROPN
ejpam-4006	51	24	(	(	PUNCT
ejpam-4006	51	25	p∑	p∑	NOUN
ejpam-4006	51	26	r=1	r=1	NOUN
ejpam-4006	51	27	∂2	∂2	NOUN
ejpam-4006	51	28	∂x2r	∂x2r	NOUN
ejpam-4006	51	29	)	)	PUNCT
ejpam-4006	51	30	2	2	NUM
ejpam-4006	51	31	−	−	NOUN
ejpam-4006	51	32			PROPN
ejpam-4006	51	33	p+q∑	p+q∑	PROPN
ejpam-4006	51	34	j	j	NOUN
ejpam-4006	52	1	=	=	PROPN
ejpam-4006	52	2	p+1	p+1	PROPN
ejpam-4006	52	3	∂2	∂2	PROPN
ejpam-4006	52	4	∂x2j	∂x2j	PROPN
ejpam-4006	52	5	2k	2k	PROPN
ejpam-4006	52	6	is	be	AUX
ejpam-4006	52	7	introduced	introduce	VERB
ejpam-4006	52	8	by	by	ADP
ejpam-4006	52	9	kananthai	kananthai	PROPN
ejpam-4006	52	10	[	[	X
ejpam-4006	52	11	4	4	NUM
ejpam-4006	52	12	]	]	PUNCT
ejpam-4006	52	13	and	and	CCONJ
ejpam-4006	52	14	is	be	AUX
ejpam-4006	52	15	named	name	VERB
ejpam-4006	52	16	the	the	DET
ejpam-4006	52	17	diamond	diamond	NOUN
ejpam-4006	52	18	operator	operator	NOUN
ejpam-4006	52	19	which	which	PRON
ejpam-4006	52	20	is	be	AUX
ejpam-4006	52	21	defined	define	VERB
ejpam-4006	52	22	by	by	ADP
ejpam-4006	52	23	♦	♦	PROPN
ejpam-4006	52	24	k	k	PROPN
ejpam-4006	52	25	=	=	SYM
ejpam-4006	52	26			PROPN
ejpam-4006	52	27	(	(	PUNCT
ejpam-4006	52	28	p∑	p∑	NOUN
ejpam-4006	52	29	r=1	r=1	NOUN
ejpam-4006	52	30	∂2	∂2	NOUN
ejpam-4006	52	31	∂x2r	∂x2r	NOUN
ejpam-4006	52	32	)	)	PUNCT
ejpam-4006	52	33	2	2	NUM
ejpam-4006	52	34	−	−	NOUN
ejpam-4006	53	1			PROPN
ejpam-4006	53	2	p+q∑	p+q∑	PROPN
ejpam-4006	53	3	j	j	NOUN
ejpam-4006	53	4	=	=	PROPN
ejpam-4006	53	5	p+1	p+1	PROPN
ejpam-4006	53	6	∂2	∂2	PROPN
ejpam-4006	53	7	∂x2j	∂x2j	PROPN
ejpam-4006	53	8	2k	2k	PROPN
ejpam-4006	53	9	.	.	PUNCT
ejpam-4006	54	1	(	(	PUNCT
ejpam-4006	54	2	8)	8)	NUM
ejpam-4006	54	3	otherwise	otherwise	ADV
ejpam-4006	54	4	,	,	PUNCT
ejpam-4006	54	5	the	the	DET
ejpam-4006	54	6	operator	operator	NOUN
ejpam-4006	54	7	♦	♦	PROPN
ejpam-4006	54	8	k	k	PROPN
ejpam-4006	54	9	can	can	AUX
ejpam-4006	54	10	also	also	ADV
ejpam-4006	54	11	be	be	AUX
ejpam-4006	54	12	expressed	express	VERB
ejpam-4006	54	13	in	in	ADP
ejpam-4006	54	14	the	the	DET
ejpam-4006	54	15	form	form	NOUN
ejpam-4006	54	16	♦	♦	PROPN
ejpam-4006	54	17	k	k	PROPN
ejpam-4006	54	18	=	=	PROPN
ejpam-4006	54	19	�	�	PROPN
ejpam-4006	54	20	k4k	k4k	PROPN
ejpam-4006	54	21	=	=	SYM
ejpam-4006	54	22	4k	4k	X
ejpam-4006	54	23	�	�	PROPN
ejpam-4006	54	24	k	k	PROPN
ejpam-4006	54	25	,	,	PUNCT
ejpam-4006	54	26	where	where	SCONJ
ejpam-4006	54	27	�	�	NOUN
ejpam-4006	54	28	k	k	PROPN
ejpam-4006	54	29	is	be	AUX
ejpam-4006	54	30	the	the	DET
ejpam-4006	54	31	ultra	ultra	ADJ
ejpam-4006	54	32	-	-	ADJ
ejpam-4006	54	33	hyperbolic	hyperbolic	ADJ
ejpam-4006	54	34	operator	operator	NOUN
ejpam-4006	54	35	iterated	iterate	VERB
ejpam-4006	54	36	k	k	NOUN
ejpam-4006	54	37	-	-	PUNCT
ejpam-4006	54	38	times	time	NOUN
ejpam-4006	54	39	,	,	PUNCT
ejpam-4006	54	40	is	be	AUX
ejpam-4006	54	41	defined	define	VERB
ejpam-4006	54	42	by	by	ADP
ejpam-4006	54	43	�	�	NOUN
ejpam-4006	54	44	k	k	NOUN
ejpam-4006	55	1	=	=	X
ejpam-4006	55	2	[	[	PUNCT
ejpam-4006	55	3	∂2	∂2	ADJ
ejpam-4006	55	4	∂x21	∂x21	PROPN
ejpam-4006	55	5	+	+	CCONJ
ejpam-4006	55	6	∂2	∂2	PROPN
ejpam-4006	55	7	∂x22	∂x22	PROPN
ejpam-4006	55	8	+	+	CCONJ
ejpam-4006	55	9	·	·	PUNCT
ejpam-4006	55	10	·	·	PUNCT
ejpam-4006	55	11	·	·	PUNCT
ejpam-4006	56	1	+	+	NUM
ejpam-4006	56	2	∂2	∂2	NOUN
ejpam-4006	56	3	∂x2p	∂x2p	NUM
ejpam-4006	57	1	−	−	PROPN
ejpam-4006	57	2	∂2	∂2	PROPN
ejpam-4006	57	3	∂x2p+1	∂x2p+1	PROPN
ejpam-4006	57	4	−	−	PROPN
ejpam-4006	57	5	∂2	∂2	NOUN
ejpam-4006	57	6	∂x2p+2	∂x2p+2	VERB
ejpam-4006	57	7	−	−	X
ejpam-4006	57	8	·	·	PUNCT
ejpam-4006	57	9	·	·	PUNCT
ejpam-4006	57	10	·	·	PUNCT
ejpam-4006	58	1	−	−	PUNCT
ejpam-4006	59	1	∂2	∂2	NOUN
ejpam-4006	59	2	∂x2p+q	∂x2p+q	NOUN
ejpam-4006	59	3	]	]	X
ejpam-4006	59	4	k	k	X
ejpam-4006	59	5	,	,	PUNCT
ejpam-4006	59	6	(	(	PUNCT
ejpam-4006	59	7	9	9	NUM
ejpam-4006	59	8	)	)	PUNCT
ejpam-4006	59	9	and	and	CCONJ
ejpam-4006	59	10	4k	4k	PRON
ejpam-4006	59	11	is	be	AUX
ejpam-4006	59	12	the	the	DET
ejpam-4006	59	13	laplace	laplace	NOUN
ejpam-4006	59	14	operator	operator	NOUN
ejpam-4006	59	15	iterated	iterate	VERB
ejpam-4006	59	16	k	k	NOUN
ejpam-4006	59	17	-	-	PUNCT
ejpam-4006	59	18	times	time	NOUN
ejpam-4006	59	19	,	,	PUNCT
ejpam-4006	59	20	is	be	AUX
ejpam-4006	59	21	defined	define	VERB
ejpam-4006	59	22	by	by	ADP
ejpam-4006	59	23	4k	4k	X
ejpam-4006	59	24	=	=	PUNCT
ejpam-4006	59	25	[	[	PUNCT
ejpam-4006	59	26	∂2	∂2	ADJ
ejpam-4006	59	27	∂x21	∂x21	PROPN
ejpam-4006	59	28	+	+	CCONJ
ejpam-4006	59	29	∂2	∂2	PROPN
ejpam-4006	59	30	∂x22	∂x22	PROPN
ejpam-4006	59	31	+	+	CCONJ
ejpam-4006	59	32	·	·	PUNCT
ejpam-4006	59	33	·	·	PUNCT
ejpam-4006	59	34	·	·	PUNCT
ejpam-4006	60	1	+	+	NUM
ejpam-4006	60	2	∂2	∂2	NUM
ejpam-4006	60	3	∂x2n	∂x2n	NOUN
ejpam-4006	60	4	]	]	X
ejpam-4006	60	5	k	k	X
ejpam-4006	60	6	.	.	PUNCT
ejpam-4006	61	1	(	(	PUNCT
ejpam-4006	61	2	10	10	NUM
ejpam-4006	61	3	)	)	PUNCT
ejpam-4006	61	4	by	by	ADP
ejpam-4006	61	5	putting	put	VERB
ejpam-4006	61	6	p	p	NOUN
ejpam-4006	61	7	=	=	NOUN
ejpam-4006	61	8	1	1	NUM
ejpam-4006	61	9	and	and	CCONJ
ejpam-4006	61	10	x1	x1	PROPN
ejpam-4006	61	11	=	=	SYM
ejpam-4006	61	12	t	t	PROPN
ejpam-4006	61	13	(	(	PUNCT
ejpam-4006	61	14	time	time	NOUN
ejpam-4006	61	15	)	)	PUNCT
ejpam-4006	61	16	in	in	ADP
ejpam-4006	61	17	(	(	PUNCT
ejpam-4006	61	18	9	9	NUM
ejpam-4006	61	19	)	)	PUNCT
ejpam-4006	61	20	,	,	PUNCT
ejpam-4006	61	21	then	then	ADV
ejpam-4006	61	22	we	we	PRON
ejpam-4006	61	23	obtain	obtain	VERB
ejpam-4006	61	24	the	the	DET
ejpam-4006	61	25	wave	wave	NOUN
ejpam-4006	61	26	operator	operator	NOUN
ejpam-4006	61	27	�	�	PROPN
ejpam-4006	61	28	=	=	SYM
ejpam-4006	61	29	∂2	∂2	PROPN
ejpam-4006	61	30	∂t2	∂t2	NOUN
ejpam-4006	61	31	−	−	PROPN
ejpam-4006	61	32	n−1∑	n−1∑	NUM
ejpam-4006	61	33	j=1	j=1	PROPN
ejpam-4006	61	34	∂2	∂2	PROPN
ejpam-4006	61	35	∂x2j	∂x2j	PROPN
ejpam-4006	61	36	.	.	PUNCT
ejpam-4006	62	1	(	(	PUNCT
ejpam-4006	62	2	11	11	NUM
ejpam-4006	62	3	)	)	PUNCT
ejpam-4006	62	4	s.	s.	PROPN
ejpam-4006	62	5	bupasiri	bupasiri	PROPN
ejpam-4006	62	6	/	/	SYM
ejpam-4006	62	7	eur	eur	PROPN
ejpam-4006	62	8	.	.	PUNCT
ejpam-4006	63	1	j.	j.	PROPN
ejpam-4006	63	2	pure	pure	PROPN
ejpam-4006	63	3	appl	appl	PROPN
ejpam-4006	63	4	.	.	PROPN
ejpam-4006	63	5	math	math	PROPN
ejpam-4006	63	6	,	,	PUNCT
ejpam-4006	63	7	14	14	NUM
ejpam-4006	63	8	(	(	PUNCT
ejpam-4006	63	9	3	3	NUM
ejpam-4006	63	10	)	)	PUNCT
ejpam-4006	63	11	(	(	PUNCT
ejpam-4006	63	12	2021	2021	NUM
ejpam-4006	63	13	)	)	PUNCT
ejpam-4006	63	14	,	,	PUNCT
ejpam-4006	63	15	881	881	NUM
ejpam-4006	63	16	-	-	SYM
ejpam-4006	63	17	894	894	NUM
ejpam-4006	63	18	884	884	NUM
ejpam-4006	63	19	the	the	DET
ejpam-4006	63	20	operators	operator	NOUN
ejpam-4006	63	21	lk1	lk1	PROPN
ejpam-4006	63	22	and	and	CCONJ
ejpam-4006	63	23	lk2	lk2	NOUN
ejpam-4006	63	24	are	be	AUX
ejpam-4006	63	25	defined	define	VERB
ejpam-4006	63	26	by	by	ADP
ejpam-4006	63	27	lk1	lk1	NOUN
ejpam-4006	63	28	=	=	SYM
ejpam-4006	63	29			PROPN
ejpam-4006	63	30	p∑	p∑	NOUN
ejpam-4006	63	31	r=1	r=1	NOUN
ejpam-4006	63	32	∂2	∂2	NOUN
ejpam-4006	63	33	∂x2r	∂x2r	ADP
ejpam-4006	63	34	+	+	CCONJ
ejpam-4006	63	35	i	i	PROPN
ejpam-4006	63	36	p+q∑	p+q∑	PROPN
ejpam-4006	63	37	j	j	X
ejpam-4006	64	1	=	=	PROPN
ejpam-4006	64	2	p+1	p+1	PROPN
ejpam-4006	64	3	∂2	∂2	NOUN
ejpam-4006	64	4	∂x2j	∂x2j	NOUN
ejpam-4006	64	5	k	k	NOUN
ejpam-4006	64	6	(	(	PUNCT
ejpam-4006	64	7	12	12	NUM
ejpam-4006	64	8	)	)	PUNCT
ejpam-4006	64	9	and	and	CCONJ
ejpam-4006	64	10	lk2	lk2	NOUN
ejpam-4006	64	11	=	=	SYM
ejpam-4006	64	12			PROPN
ejpam-4006	64	13	p∑	p∑	NOUN
ejpam-4006	64	14	r=1	r=1	NOUN
ejpam-4006	64	15	∂2	∂2	NOUN
ejpam-4006	64	16	∂x2r	∂x2r	ADP
ejpam-4006	64	17	−	−	PROPN
ejpam-4006	64	18	i	i	PRON
ejpam-4006	64	19	p+q∑	p+q∑	PROPN
ejpam-4006	64	20	j	j	X
ejpam-4006	65	1	=	=	PROPN
ejpam-4006	65	2	p+1	p+1	PROPN
ejpam-4006	65	3	∂2	∂2	NOUN
ejpam-4006	65	4	∂x2j	∂x2j	NOUN
ejpam-4006	65	5	k	k	NOUN
ejpam-4006	65	6	,	,	PUNCT
ejpam-4006	65	7	(	(	PUNCT
ejpam-4006	65	8	13	13	NUM
ejpam-4006	65	9	)	)	PUNCT
ejpam-4006	65	10	following	follow	VERB
ejpam-4006	65	11	that	that	DET
ejpam-4006	65	12	lk	lk	PROPN
ejpam-4006	65	13	=	=	PUNCT
ejpam-4006	65	14	lk1l	lk1l	PROPN
ejpam-4006	65	15	k	k	PROPN
ejpam-4006	65	16	2	2	X
ejpam-4006	65	17	=	=	SYM
ejpam-4006	65	18	lk2l	lk2l	NOUN
ejpam-4006	65	19	k	k	NOUN
ejpam-4006	65	20	1	1	X
ejpam-4006	65	21	=	=	SYM
ejpam-4006	65	22			PROPN
ejpam-4006	65	23	(	(	PUNCT
ejpam-4006	65	24	p∑	p∑	NOUN
ejpam-4006	65	25	r=1	r=1	NOUN
ejpam-4006	65	26	∂2	∂2	NOUN
ejpam-4006	65	27	∂x2r	∂x2r	NOUN
ejpam-4006	65	28	)	)	PUNCT
ejpam-4006	65	29	2	2	NUM
ejpam-4006	65	30	+	+	CCONJ
ejpam-4006	65	31			PROPN
ejpam-4006	65	32	p+q∑	p+q∑	PROPN
ejpam-4006	65	33	j	j	NOUN
ejpam-4006	65	34	=	=	PROPN
ejpam-4006	65	35	p+1	p+1	PROPN
ejpam-4006	65	36	∂2	∂2	PROPN
ejpam-4006	65	37	∂x2j	∂x2j	PROPN
ejpam-4006	65	38	2k	2k	PROPN
ejpam-4006	65	39	.	.	PUNCT
ejpam-4006	66	1	(	(	PUNCT
ejpam-4006	66	2	14	14	NUM
ejpam-4006	66	3	)	)	PUNCT
ejpam-4006	66	4	thus	thus	ADV
ejpam-4006	66	5	,	,	PUNCT
ejpam-4006	66	6	equation	equation	NOUN
ejpam-4006	66	7	(	(	PUNCT
ejpam-4006	66	8	7	7	X
ejpam-4006	66	9	)	)	PUNCT
ejpam-4006	66	10	can	can	AUX
ejpam-4006	66	11	be	be	AUX
ejpam-4006	66	12	written	write	VERB
ejpam-4006	66	13	as	as	ADP
ejpam-4006	66	14	⊕km	⊕km	NOUN
ejpam-4006	66	15	=	=	SYM
ejpam-4006	66	16	(	(	PUNCT
ejpam-4006	66	17	�	�	PROPN
ejpam-4006	66	18	+	+	NUM
ejpam-4006	66	19	m2	m2	PROPN
ejpam-4006	66	20	)	)	PUNCT
ejpam-4006	66	21	k	k	PROPN
ejpam-4006	66	22	(	(	PUNCT
ejpam-4006	66	23	4+m2	4+m2	X
ejpam-4006	66	24	)	)	PUNCT
ejpam-4006	66	25	k	k	PROPN
ejpam-4006	66	26	(	(	PUNCT
ejpam-4006	66	27	l1	l1	PROPN
ejpam-4006	66	28	+	+	PROPN
ejpam-4006	66	29	m2	m2	PROPN
ejpam-4006	66	30	)	)	PUNCT
ejpam-4006	66	31	k	k	PROPN
ejpam-4006	66	32	(	(	PUNCT
ejpam-4006	66	33	l2	l2	NOUN
ejpam-4006	66	34	+	+	NOUN
ejpam-4006	66	35	m2	m2	PROPN
ejpam-4006	66	36	)	)	PUNCT
ejpam-4006	67	1	k	k	PROPN
ejpam-4006	67	2	=	=	PRON
ejpam-4006	67	3	(	(	PUNCT
ejpam-4006	67	4	l2	l2	NOUN
ejpam-4006	67	5	+	+	NOUN
ejpam-4006	67	6	m2	m2	PROPN
ejpam-4006	67	7	)	)	PUNCT
ejpam-4006	67	8	k	k	PROPN
ejpam-4006	67	9	(	(	PUNCT
ejpam-4006	67	10	l1	l1	PROPN
ejpam-4006	67	11	+	+	PROPN
ejpam-4006	67	12	m2	m2	PROPN
ejpam-4006	67	13	)	)	PUNCT
ejpam-4006	67	14	k	k	PROPN
ejpam-4006	67	15	(	(	PUNCT
ejpam-4006	67	16	4+m2	4+m2	X
ejpam-4006	67	17	)	)	PUNCT
ejpam-4006	68	1	k	k	PROPN
ejpam-4006	68	2	(	(	PUNCT
ejpam-4006	68	3	�	�	PROPN
ejpam-4006	68	4	+	+	NUM
ejpam-4006	68	5	m2	m2	PROPN
ejpam-4006	68	6	)	)	PUNCT
ejpam-4006	68	7	k	k	PROPN
ejpam-4006	68	8	(	(	PUNCT
ejpam-4006	68	9	15	15	NUM
ejpam-4006	68	10	)	)	PUNCT
ejpam-4006	68	11	and	and	CCONJ
ejpam-4006	68	12	from	from	ADP
ejpam-4006	68	13	(	(	PUNCT
ejpam-4006	68	14	7	7	NUM
ejpam-4006	68	15	)	)	PUNCT
ejpam-4006	68	16	with	with	ADP
ejpam-4006	68	17	q	q	PROPN
ejpam-4006	68	18	=	=	PUNCT
ejpam-4006	68	19	m	m	NOUN
ejpam-4006	68	20	=	=	SYM
ejpam-4006	68	21	0	0	NUM
ejpam-4006	68	22	and	and	CCONJ
ejpam-4006	68	23	k	k	X
ejpam-4006	68	24	=	=	SYM
ejpam-4006	68	25	1	1	NUM
ejpam-4006	68	26	,	,	PUNCT
ejpam-4006	68	27	we	we	PRON
ejpam-4006	68	28	obtain	obtain	VERB
ejpam-4006	68	29	laplace	laplace	NOUN
ejpam-4006	68	30	operator	operator	NOUN
ejpam-4006	68	31	of	of	ADP
ejpam-4006	68	32	p	p	NOUN
ejpam-4006	68	33	-	-	PUNCT
ejpam-4006	68	34	dimension	dimension	NOUN
ejpam-4006	68	35	⊕0	⊕0	PROPN
ejpam-4006	68	36	=	=	PUNCT
ejpam-4006	68	37	44	44	NUM
ejpam-4006	68	38	p	p	NOUN
ejpam-4006	68	39	,	,	PUNCT
ejpam-4006	68	40	where	where	SCONJ
ejpam-4006	68	41	4p	4p	NOUN
ejpam-4006	68	42	=	=	SYM
ejpam-4006	68	43	∂2	∂2	NOUN
ejpam-4006	68	44	∂x21	∂x21	PROPN
ejpam-4006	68	45	+	+	CCONJ
ejpam-4006	68	46	∂2	∂2	PROPN
ejpam-4006	68	47	∂x22	∂x22	PROPN
ejpam-4006	68	48	+	+	CCONJ
ejpam-4006	68	49	·	·	PUNCT
ejpam-4006	68	50	·	·	PUNCT
ejpam-4006	68	51	·	·	PUNCT
ejpam-4006	69	1	+	+	NUM
ejpam-4006	69	2	∂2	∂2	PROPN
ejpam-4006	69	3	∂x2p	∂x2p	INTJ
ejpam-4006	69	4	.	.	PUNCT
ejpam-4006	70	1	(	(	PUNCT
ejpam-4006	70	2	16	16	NUM
ejpam-4006	70	3	)	)	PUNCT
ejpam-4006	70	4	in	in	ADP
ejpam-4006	70	5	this	this	DET
ejpam-4006	70	6	article	article	NOUN
ejpam-4006	70	7	,	,	PUNCT
ejpam-4006	70	8	we	we	PRON
ejpam-4006	70	9	further	far	ADV
ejpam-4006	70	10	study	study	VERB
ejpam-4006	70	11	the	the	DET
ejpam-4006	70	12	fundamental	fundamental	ADJ
ejpam-4006	70	13	solution	solution	NOUN
ejpam-4006	70	14	of	of	ADP
ejpam-4006	70	15	the	the	DET
ejpam-4006	70	16	operator	operator	NOUN
ejpam-4006	70	17	⊕km	⊕km	PART
ejpam-4006	70	18	,	,	PUNCT
ejpam-4006	70	19	that	that	PRON
ejpam-4006	70	20	is	be	AUX
ejpam-4006	70	21	⊕kmh(x	⊕kmh(x	NOUN
ejpam-4006	70	22	,	,	PUNCT
ejpam-4006	70	23	m	m	NOUN
ejpam-4006	70	24	)	)	PUNCT
ejpam-4006	70	25	=	=	SYM
ejpam-4006	70	26	δ	δ	PROPN
ejpam-4006	70	27	,	,	PUNCT
ejpam-4006	70	28	where	where	SCONJ
ejpam-4006	70	29	h(x	h(x	PROPN
ejpam-4006	70	30	,	,	PUNCT
ejpam-4006	70	31	m	m	PROPN
ejpam-4006	70	32	)	)	PUNCT
ejpam-4006	70	33	is	be	AUX
ejpam-4006	70	34	the	the	DET
ejpam-4006	70	35	fundamental	fundamental	ADJ
ejpam-4006	70	36	solution	solution	NOUN
ejpam-4006	70	37	,	,	PUNCT
ejpam-4006	70	38	δ	δ	PROPN
ejpam-4006	70	39	is	be	AUX
ejpam-4006	70	40	the	the	DET
ejpam-4006	70	41	dirac	dirac	NOUN
ejpam-4006	70	42	delta	delta	NOUN
ejpam-4006	70	43	distribution	distribution	NOUN
ejpam-4006	70	44	,	,	PUNCT
ejpam-4006	70	45	k	k	PROPN
ejpam-4006	70	46	is	be	AUX
ejpam-4006	70	47	a	a	DET
ejpam-4006	70	48	nonnegative	nonnegative	ADJ
ejpam-4006	70	49	integer	integer	NOUN
ejpam-4006	70	50	,	,	PUNCT
ejpam-4006	70	51	m	m	VERB
ejpam-4006	70	52	is	be	AUX
ejpam-4006	70	53	a	a	DET
ejpam-4006	70	54	nonnegative	nonnegative	ADJ
ejpam-4006	70	55	real	real	ADJ
ejpam-4006	70	56	number	number	NOUN
ejpam-4006	70	57	and	and	CCONJ
ejpam-4006	70	58	the	the	DET
ejpam-4006	70	59	operator	operator	NOUN
ejpam-4006	70	60	⊕km	⊕km	VERB
ejpam-4006	70	61	is	be	AUX
ejpam-4006	70	62	defined	define	VERB
ejpam-4006	70	63	by	by	ADP
ejpam-4006	70	64	⊕km	⊕km	NOUN
ejpam-4006	71	1	=	=	SYM
ejpam-4006	71	2			PROPN
ejpam-4006	71	3	(	(	PUNCT
ejpam-4006	71	4	p∑	p∑	NOUN
ejpam-4006	71	5	r=1	r=1	NOUN
ejpam-4006	71	6	∂2	∂2	NOUN
ejpam-4006	71	7	∂x2r	∂x2r	ADP
ejpam-4006	71	8	+	+	NOUN
ejpam-4006	71	9	m2	m2	PROPN
ejpam-4006	71	10	)	)	PUNCT
ejpam-4006	71	11	4	4	NUM
ejpam-4006	71	12	−	−	NOUN
ejpam-4006	71	13			PROPN
ejpam-4006	71	14	p+q∑	p+q∑	PROPN
ejpam-4006	71	15	j	j	NOUN
ejpam-4006	71	16	=	=	PROPN
ejpam-4006	71	17	p+1	p+1	PROPN
ejpam-4006	71	18	∂2	∂2	PROPN
ejpam-4006	71	19	∂x2j	∂x2j	PROPN
ejpam-4006	71	20	4k	4k	PROPN
ejpam-4006	71	21	.	.	PUNCT
ejpam-4006	72	1	(	(	PUNCT
ejpam-4006	72	2	17	17	NUM
ejpam-4006	72	3	)	)	PUNCT
ejpam-4006	72	4	we	we	PRON
ejpam-4006	72	5	then	then	ADV
ejpam-4006	72	6	also	also	ADV
ejpam-4006	72	7	apply	apply	VERB
ejpam-4006	72	8	such	such	DET
ejpam-4006	72	9	the	the	DET
ejpam-4006	72	10	fundamental	fundamental	ADJ
ejpam-4006	72	11	solution	solution	NOUN
ejpam-4006	72	12	to	to	PART
ejpam-4006	72	13	solve	solve	VERB
ejpam-4006	72	14	the	the	DET
ejpam-4006	72	15	solution	solution	NOUN
ejpam-4006	72	16	of	of	ADP
ejpam-4006	72	17	the	the	DET
ejpam-4006	72	18	equation	equation	NOUN
ejpam-4006	72	19	⊕kmu(x	⊕kmu(x	VERB
ejpam-4006	72	20	)	)	PUNCT
ejpam-4006	72	21	=	=	SYM
ejpam-4006	72	22	f(x	f(x	PROPN
ejpam-4006	72	23	)	)	PUNCT
ejpam-4006	72	24	,	,	PUNCT
ejpam-4006	72	25	where	where	SCONJ
ejpam-4006	72	26	f(x	f(x	PROPN
ejpam-4006	72	27	)	)	PUNCT
ejpam-4006	72	28	is	be	AUX
ejpam-4006	72	29	a	a	DET
ejpam-4006	72	30	given	give	VERB
ejpam-4006	72	31	generalized	generalized	ADJ
ejpam-4006	72	32	function	function	NOUN
ejpam-4006	72	33	and	and	CCONJ
ejpam-4006	72	34	u(x	u(x	NOUN
ejpam-4006	72	35	)	)	PUNCT
ejpam-4006	72	36	is	be	AUX
ejpam-4006	72	37	an	an	DET
ejpam-4006	72	38	unknown	unknown	ADJ
ejpam-4006	72	39	function	function	NOUN
ejpam-4006	72	40	for	for	ADP
ejpam-4006	72	41	x	x	PROPN
ejpam-4006	72	42	∈	∈	PROPN
ejpam-4006	72	43	rn	rn	PROPN
ejpam-4006	72	44	.	.	PUNCT
ejpam-4006	73	1	s.	s.	PROPN
ejpam-4006	73	2	bupasiri	bupasiri	PROPN
ejpam-4006	73	3	/	/	SYM
ejpam-4006	73	4	eur	eur	PROPN
ejpam-4006	73	5	.	.	PUNCT
ejpam-4006	74	1	j.	j.	PROPN
ejpam-4006	74	2	pure	pure	PROPN
ejpam-4006	74	3	appl	appl	PROPN
ejpam-4006	74	4	.	.	PROPN
ejpam-4006	74	5	math	math	PROPN
ejpam-4006	74	6	,	,	PUNCT
ejpam-4006	74	7	14	14	NUM
ejpam-4006	74	8	(	(	PUNCT
ejpam-4006	74	9	3	3	NUM
ejpam-4006	74	10	)	)	PUNCT
ejpam-4006	74	11	(	(	PUNCT
ejpam-4006	74	12	2021	2021	NUM
ejpam-4006	74	13	)	)	PUNCT
ejpam-4006	74	14	,	,	PUNCT
ejpam-4006	74	15	881	881	NUM
ejpam-4006	74	16	-	-	SYM
ejpam-4006	74	17	894	894	NUM
ejpam-4006	74	18	885	885	NUM
ejpam-4006	74	19	2	2	NUM
ejpam-4006	74	20	.	.	PUNCT
ejpam-4006	74	21	preliminary	preliminary	ADJ
ejpam-4006	74	22	notes	note	NOUN
ejpam-4006	74	23	in	in	ADP
ejpam-4006	74	24	this	this	DET
ejpam-4006	74	25	section	section	NOUN
ejpam-4006	75	1	,	,	PUNCT
ejpam-4006	75	2	we	we	PRON
ejpam-4006	75	3	studied	study	VERB
ejpam-4006	75	4	some	some	DET
ejpam-4006	75	5	properties	property	NOUN
ejpam-4006	75	6	of	of	ADP
ejpam-4006	75	7	the	the	DET
ejpam-4006	75	8	ultra	ultra	ADJ
ejpam-4006	75	9	-	-	ADJ
ejpam-4006	75	10	hyperbolic	hyperbolic	ADJ
ejpam-4006	75	11	kernel	kernel	NOUN
ejpam-4006	75	12	of	of	ADP
ejpam-4006	75	13	marcel	marcel	PROPN
ejpam-4006	75	14	riesz	riesz	PROPN
ejpam-4006	75	15	and	and	CCONJ
ejpam-4006	75	16	the	the	DET
ejpam-4006	75	17	fundamental	fundamental	ADJ
ejpam-4006	75	18	solution	solution	NOUN
ejpam-4006	75	19	of	of	ADP
ejpam-4006	75	20	the	the	DET
ejpam-4006	75	21	partial	partial	ADJ
ejpam-4006	75	22	differential	differential	NOUN
ejpam-4006	75	23	operators	operator	NOUN
ejpam-4006	75	24	which	which	PRON
ejpam-4006	75	25	will	will	AUX
ejpam-4006	75	26	be	be	AUX
ejpam-4006	75	27	used	use	VERB
ejpam-4006	75	28	as	as	ADP
ejpam-4006	75	29	follow	follow	NOUN
ejpam-4006	75	30	.	.	PUNCT
ejpam-4006	76	1	definition	definition	NOUN
ejpam-4006	76	2	1	1	NUM
ejpam-4006	76	3	.	.	PUNCT
ejpam-4006	77	1	let	let	VERB
ejpam-4006	77	2	x	x	PUNCT
ejpam-4006	77	3	=	=	SYM
ejpam-4006	77	4	(	(	PUNCT
ejpam-4006	77	5	x1	x1	PROPN
ejpam-4006	77	6	,	,	PUNCT
ejpam-4006	77	7	x2	x2	PROPN
ejpam-4006	77	8	,	,	PUNCT
ejpam-4006	77	9	.	.	PUNCT
ejpam-4006	77	10	.	.	PUNCT
ejpam-4006	78	1	.	.	PUNCT
ejpam-4006	79	1	,	,	PUNCT
ejpam-4006	79	2	xn	xn	X
ejpam-4006	79	3	)	)	PUNCT
ejpam-4006	79	4	be	be	VERB
ejpam-4006	79	5	a	a	DET
ejpam-4006	79	6	point	point	NOUN
ejpam-4006	79	7	of	of	ADP
ejpam-4006	79	8	the	the	DET
ejpam-4006	79	9	n	n	CCONJ
ejpam-4006	79	10	dimensional	dimensional	ADJ
ejpam-4006	79	11	space	space	NOUN
ejpam-4006	79	12	rn	rn	PROPN
ejpam-4006	79	13	,	,	PUNCT
ejpam-4006	79	14	u	u	PROPN
ejpam-4006	79	15	=	=	SYM
ejpam-4006	79	16	x21	x21	PROPN
ejpam-4006	80	1	+	+	NUM
ejpam-4006	80	2	x22	x22	NOUN
ejpam-4006	80	3	+	+	CCONJ
ejpam-4006	80	4	·	·	PUNCT
ejpam-4006	80	5	·	·	PUNCT
ejpam-4006	80	6	·	·	PUNCT
ejpam-4006	81	1	+	+	NUM
ejpam-4006	81	2	x2p	x2p	NUM
ejpam-4006	81	3	−	−	PROPN
ejpam-4006	82	1	x2p+1	x2p+1	NUM
ejpam-4006	83	1	−	−	PROPN
ejpam-4006	83	2	x2p+2	x2p+2	ADJ
ejpam-4006	84	1	−	−	PROPN
ejpam-4006	84	2	·	·	PUNCT
ejpam-4006	84	3	·	·	PUNCT
ejpam-4006	84	4	·	·	PUNCT
ejpam-4006	85	1	−	−	NOUN
ejpam-4006	85	2	x2p+q	x2p+q	NOUN
ejpam-4006	85	3	,	,	PUNCT
ejpam-4006	85	4	(	(	PUNCT
ejpam-4006	85	5	18	18	NUM
ejpam-4006	85	6	)	)	PUNCT
ejpam-4006	85	7	where	where	SCONJ
ejpam-4006	85	8	p+	p+	VERB
ejpam-4006	85	9	q	q	X
ejpam-4006	85	10	=	=	PUNCT
ejpam-4006	85	11	n.	n.	NOUN
ejpam-4006	85	12	define	define	VERB
ejpam-4006	85	13	γ+	γ+	PUNCT
ejpam-4006	85	14	=	=	SYM
ejpam-4006	85	15	{	{	PUNCT
ejpam-4006	85	16	x	x	PROPN
ejpam-4006	85	17	∈	∈	PROPN
ejpam-4006	85	18	rn	rn	PROPN
ejpam-4006	85	19	:	:	PUNCT
ejpam-4006	85	20	x1	x1	PROPN
ejpam-4006	85	21	>	>	X
ejpam-4006	85	22	0	0	PUNCT
ejpam-4006	85	23	and	and	CCONJ
ejpam-4006	85	24	u	u	X
ejpam-4006	85	25	>	>	X
ejpam-4006	85	26	0	0	NUM
ejpam-4006	85	27	}	}	PUNCT
ejpam-4006	85	28	which	which	PRON
ejpam-4006	85	29	designates	designate	VERB
ejpam-4006	85	30	the	the	DET
ejpam-4006	85	31	interior	interior	NOUN
ejpam-4006	85	32	of	of	ADP
ejpam-4006	85	33	the	the	DET
ejpam-4006	85	34	forward	forward	ADJ
ejpam-4006	85	35	cone	cone	NOUN
ejpam-4006	85	36	and	and	CCONJ
ejpam-4006	85	37	γ+	γ+	PRON
ejpam-4006	85	38	designates	designate	VERB
ejpam-4006	85	39	its	its	PRON
ejpam-4006	85	40	closure	closure	NOUN
ejpam-4006	85	41	and	and	CCONJ
ejpam-4006	85	42	the	the	DET
ejpam-4006	85	43	following	follow	VERB
ejpam-4006	85	44	functions	function	NOUN
ejpam-4006	85	45	introduce	introduce	VERB
ejpam-4006	85	46	by	by	ADP
ejpam-4006	85	47	nozaki	nozaki	NOUN
ejpam-4006	85	48	(	(	PUNCT
ejpam-4006	85	49	[	[	X
ejpam-4006	85	50	9	9	NUM
ejpam-4006	85	51	]	]	PUNCT
ejpam-4006	85	52	,	,	PUNCT
ejpam-4006	85	53	p.72	p.72	NOUN
ejpam-4006	85	54	)	)	PUNCT
ejpam-4006	85	55	that	that	PRON
ejpam-4006	85	56	rhα	rhα	ADJ
ejpam-4006	85	57	(	(	PUNCT
ejpam-4006	85	58	x	x	X
ejpam-4006	85	59	)	)	PUNCT
ejpam-4006	85	60	=	=	SYM
ejpam-4006	85	61	{	{	PUNCT
ejpam-4006	85	62	u	u	NOUN
ejpam-4006	85	63	α−n	α−n	PROPN
ejpam-4006	85	64	2	2	NUM
ejpam-4006	85	65	kn(α	kn(α	PUNCT
ejpam-4006	85	66	)	)	PUNCT
ejpam-4006	85	67	if	if	SCONJ
ejpam-4006	85	68	x	x	PUNCT
ejpam-4006	85	69	∈	∈	NOUN
ejpam-4006	85	70	γ+	γ+	PUNCT
ejpam-4006	85	71	0	0	PUNCT
ejpam-4006	86	1	if	if	SCONJ
ejpam-4006	86	2	x	x	PROPN
ejpam-4006	86	3	6∈	6∈	PROPN
ejpam-4006	86	4	γ+	γ+	PRON
ejpam-4006	86	5	,	,	PUNCT
ejpam-4006	86	6	(	(	PUNCT
ejpam-4006	86	7	19	19	NUM
ejpam-4006	86	8	)	)	PUNCT
ejpam-4006	86	9	rhα	rhα	NOUN
ejpam-4006	86	10	(	(	PUNCT
ejpam-4006	86	11	x	x	X
ejpam-4006	86	12	)	)	PUNCT
ejpam-4006	86	13	is	be	AUX
ejpam-4006	86	14	called	call	VERB
ejpam-4006	86	15	the	the	DET
ejpam-4006	86	16	ultra	ultra	ADJ
ejpam-4006	86	17	-	-	ADJ
ejpam-4006	86	18	hyperbolic	hyperbolic	ADJ
ejpam-4006	86	19	kernel	kernel	NOUN
ejpam-4006	86	20	of	of	ADP
ejpam-4006	86	21	marcel	marcel	PROPN
ejpam-4006	86	22	riesz	riesz	PROPN
ejpam-4006	86	23	.	.	PUNCT
ejpam-4006	87	1	here	here	ADV
ejpam-4006	87	2	α	α	PROPN
ejpam-4006	87	3	is	be	AUX
ejpam-4006	87	4	a	a	DET
ejpam-4006	87	5	complex	complex	ADJ
ejpam-4006	87	6	parameter	parameter	NOUN
ejpam-4006	87	7	and	and	CCONJ
ejpam-4006	87	8	n	n	DET
ejpam-4006	87	9	the	the	DET
ejpam-4006	87	10	dimension	dimension	NOUN
ejpam-4006	87	11	of	of	ADP
ejpam-4006	87	12	the	the	DET
ejpam-4006	87	13	space	space	NOUN
ejpam-4006	87	14	.	.	PUNCT
ejpam-4006	88	1	the	the	DET
ejpam-4006	88	2	constant	constant	ADJ
ejpam-4006	88	3	kn(α	kn(α	PRON
ejpam-4006	88	4	)	)	PUNCT
ejpam-4006	88	5	is	be	AUX
ejpam-4006	88	6	defined	define	VERB
ejpam-4006	88	7	by	by	ADP
ejpam-4006	88	8	kn(α	kn(α	NOUN
ejpam-4006	88	9	)	)	PUNCT
ejpam-4006	88	10	=	=	PUNCT
ejpam-4006	89	1	π	π	X
ejpam-4006	89	2	n−1	n−1	PROPN
ejpam-4006	89	3	2	2	NUM
ejpam-4006	89	4	γ	γ	X
ejpam-4006	89	5	(	(	PUNCT
ejpam-4006	89	6	2+α−n	2+α−n	PROPN
ejpam-4006	89	7	2	2	NUM
ejpam-4006	89	8	)	)	PUNCT
ejpam-4006	89	9	γ	γ	X
ejpam-4006	89	10	(	(	PUNCT
ejpam-4006	89	11	1−α	1−α	NUM
ejpam-4006	89	12	2	2	NUM
ejpam-4006	89	13	)	)	PUNCT
ejpam-4006	89	14	γ(α	γ(α	PROPN
ejpam-4006	89	15	)	)	PUNCT
ejpam-4006	89	16	γ	γ	PROPN
ejpam-4006	89	17	(	(	PUNCT
ejpam-4006	89	18	2+α−p	2+α−p	NUM
ejpam-4006	89	19	2	2	NUM
ejpam-4006	89	20	)	)	PUNCT
ejpam-4006	89	21	γ	γ	X
ejpam-4006	89	22	(	(	PUNCT
ejpam-4006	89	23	p−α	p−α	NOUN
ejpam-4006	89	24	2	2	NUM
ejpam-4006	89	25	)	)	PUNCT
ejpam-4006	89	26	(	(	PUNCT
ejpam-4006	89	27	20	20	NUM
ejpam-4006	89	28	)	)	PUNCT
ejpam-4006	89	29	and	and	CCONJ
ejpam-4006	89	30	p	p	NOUN
ejpam-4006	89	31	is	be	AUX
ejpam-4006	89	32	the	the	DET
ejpam-4006	89	33	number	number	NOUN
ejpam-4006	89	34	of	of	ADP
ejpam-4006	89	35	positive	positive	ADJ
ejpam-4006	89	36	terms	term	NOUN
ejpam-4006	89	37	of	of	ADP
ejpam-4006	89	38	u	u	NOUN
ejpam-4006	89	39	=	=	SYM
ejpam-4006	89	40	x21	x21	PROPN
ejpam-4006	90	1	+	+	NUM
ejpam-4006	90	2	x22	x22	NOUN
ejpam-4006	90	3	+	+	CCONJ
ejpam-4006	90	4	·	·	PUNCT
ejpam-4006	90	5	·	·	PUNCT
ejpam-4006	90	6	·	·	PUNCT
ejpam-4006	90	7	+	+	NUM
ejpam-4006	90	8	x2p	x2p	NUM
ejpam-4006	90	9	−	−	PROPN
ejpam-4006	91	1	x2p+1	x2p+1	NUM
ejpam-4006	92	1	−	−	PROPN
ejpam-4006	92	2	x2p+2	x2p+2	ADJ
ejpam-4006	93	1	−	−	PROPN
ejpam-4006	93	2	·	·	PUNCT
ejpam-4006	93	3	·	·	PUNCT
ejpam-4006	93	4	·	·	PUNCT
ejpam-4006	94	1	−	−	NOUN
ejpam-4006	94	2	x2p+q	x2p+q	X
ejpam-4006	94	3	,	,	PUNCT
ejpam-4006	94	4	p+	p+	VERB
ejpam-4006	94	5	q	q	NOUN
ejpam-4006	94	6	=	=	PUNCT
ejpam-4006	94	7	n	n	PROPN
ejpam-4006	94	8	and	and	CCONJ
ejpam-4006	94	9	let	let	VERB
ejpam-4006	94	10	supp	supp	PROPN
ejpam-4006	94	11	rhα	rhα	VERB
ejpam-4006	94	12	(	(	PUNCT
ejpam-4006	94	13	x	x	X
ejpam-4006	94	14	)	)	PUNCT
ejpam-4006	94	15	⊂	⊂	PROPN
ejpam-4006	94	16	γ+	γ+	PROPN
ejpam-4006	94	17	.	.	PUNCT
ejpam-4006	95	1	now	now	ADV
ejpam-4006	95	2	rhα	rhα	VERB
ejpam-4006	95	3	(	(	PUNCT
ejpam-4006	95	4	x	x	X
ejpam-4006	95	5	)	)	PUNCT
ejpam-4006	95	6	is	be	AUX
ejpam-4006	95	7	an	an	DET
ejpam-4006	95	8	ordinary	ordinary	ADJ
ejpam-4006	95	9	function	function	NOUN
ejpam-4006	95	10	if	if	SCONJ
ejpam-4006	95	11	re	re	VERB
ejpam-4006	95	12	α	α	NOUN
ejpam-4006	95	13	≥	≥	NOUN
ejpam-4006	95	14	n	n	CCONJ
ejpam-4006	95	15	and	and	CCONJ
ejpam-4006	95	16	is	be	AUX
ejpam-4006	95	17	a	a	DET
ejpam-4006	95	18	distribution	distribution	NOUN
ejpam-4006	95	19	of	of	ADP
ejpam-4006	95	20	α	α	NOUN
ejpam-4006	95	21	if	if	SCONJ
ejpam-4006	95	22	re	re	ADP
ejpam-4006	95	23	α	α	X
ejpam-4006	95	24	<	<	X
ejpam-4006	95	25	n.	n.	PROPN
ejpam-4006	95	26	now	now	ADV
ejpam-4006	95	27	,	,	PUNCT
ejpam-4006	95	28	if	if	SCONJ
ejpam-4006	95	29	p	p	NOUN
ejpam-4006	95	30	=	=	NOUN
ejpam-4006	95	31	1	1	NUM
ejpam-4006	95	32	then	then	ADV
ejpam-4006	95	33	(	(	PUNCT
ejpam-4006	95	34	19	19	NUM
ejpam-4006	95	35	)	)	PUNCT
ejpam-4006	95	36	reduces	reduce	VERB
ejpam-4006	95	37	to	to	ADP
ejpam-4006	95	38	the	the	DET
ejpam-4006	95	39	function	function	NOUN
ejpam-4006	95	40	mα(u	mα(u	PROPN
ejpam-4006	95	41	)	)	PUNCT
ejpam-4006	95	42	say	say	VERB
ejpam-4006	95	43	,	,	PUNCT
ejpam-4006	95	44	and	and	CCONJ
ejpam-4006	95	45	defined	define	VERB
ejpam-4006	95	46	by	by	ADP
ejpam-4006	95	47	mα(u	mα(u	ADJ
ejpam-4006	95	48	)	)	PUNCT
ejpam-4006	96	1	=	=	PRON
ejpam-4006	96	2	{	{	PUNCT
ejpam-4006	96	3	u	u	NOUN
ejpam-4006	96	4	α−n	α−n	PROPN
ejpam-4006	96	5	2	2	NUM
ejpam-4006	96	6	hn(α	hn(α	PUNCT
ejpam-4006	96	7	)	)	PUNCT
ejpam-4006	96	8	if	if	SCONJ
ejpam-4006	96	9	x	x	SYM
ejpam-4006	96	10	∈	∈	NOUN
ejpam-4006	96	11	γ+	γ+	PUNCT
ejpam-4006	96	12	0	0	PUNCT
ejpam-4006	97	1	if	if	SCONJ
ejpam-4006	97	2	x	x	PROPN
ejpam-4006	97	3	6∈	6∈	PROPN
ejpam-4006	97	4	γ+	γ+	PRON
ejpam-4006	97	5	,	,	PUNCT
ejpam-4006	97	6	(	(	PUNCT
ejpam-4006	97	7	21	21	NUM
ejpam-4006	97	8	)	)	PUNCT
ejpam-4006	97	9	where	where	SCONJ
ejpam-4006	97	10	u	u	NOUN
ejpam-4006	97	11	=	=	NOUN
ejpam-4006	97	12	x21	x21	PROPN
ejpam-4006	97	13	−	−	PROPN
ejpam-4006	97	14	x22	x22	NOUN
ejpam-4006	97	15	−	−	PROPN
ejpam-4006	97	16	·	·	PUNCT
ejpam-4006	97	17	·	·	PUNCT
ejpam-4006	97	18	·	·	PUNCT
ejpam-4006	98	1	−	−	PROPN
ejpam-4006	99	1	x2n	x2n	PROPN
ejpam-4006	99	2	and	and	CCONJ
ejpam-4006	99	3	hn(α	hn(α	PUNCT
ejpam-4006	99	4	)	)	PUNCT
ejpam-4006	99	5	=	=	SYM
ejpam-4006	99	6	π	π	X
ejpam-4006	99	7	(	(	PUNCT
ejpam-4006	99	8	n−1	n−1	PROPN
ejpam-4006	99	9	)	)	PUNCT
ejpam-4006	99	10	2	2	NUM
ejpam-4006	99	11	2α−1γ(α−n+2	2α−1γ(α−n+2	NUM
ejpam-4006	99	12	2	2	NUM
ejpam-4006	99	13	)	)	PUNCT
ejpam-4006	99	14	.	.	PUNCT
ejpam-4006	100	1	the	the	DET
ejpam-4006	100	2	function	function	NOUN
ejpam-4006	100	3	mα(u	mα(u	PROPN
ejpam-4006	100	4	)	)	PUNCT
ejpam-4006	100	5	is	be	AUX
ejpam-4006	100	6	called	call	VERB
ejpam-4006	100	7	the	the	DET
ejpam-4006	100	8	hyperbolic	hyperbolic	ADJ
ejpam-4006	100	9	kernel	kernel	NOUN
ejpam-4006	100	10	of	of	ADP
ejpam-4006	100	11	marcel	marcel	PROPN
ejpam-4006	100	12	riesz	riesz	PROPN
ejpam-4006	100	13	.	.	PUNCT
ejpam-4006	101	1	lemma	lemma	PROPN
ejpam-4006	101	2	1	1	NUM
ejpam-4006	101	3	.	.	PUNCT
ejpam-4006	102	1	given	give	VERB
ejpam-4006	102	2	the	the	DET
ejpam-4006	102	3	equation	equation	NOUN
ejpam-4006	102	4	4ku(x	4ku(x	AUX
ejpam-4006	102	5	)	)	PUNCT
ejpam-4006	102	6	=	=	PUNCT
ejpam-4006	102	7	δ	δ	PROPN
ejpam-4006	102	8	for	for	ADP
ejpam-4006	102	9	x	x	PROPN
ejpam-4006	102	10	∈	∈	PROPN
ejpam-4006	102	11	rn	rn	PROPN
ejpam-4006	102	12	,	,	PUNCT
ejpam-4006	102	13	where	where	SCONJ
ejpam-4006	102	14	4k	4k	PRON
ejpam-4006	102	15	is	be	AUX
ejpam-4006	102	16	the	the	DET
ejpam-4006	102	17	laplace	laplace	NOUN
ejpam-4006	102	18	operator	operator	NOUN
ejpam-4006	102	19	iterated	iterate	VERB
ejpam-4006	102	20	k	k	NOUN
ejpam-4006	102	21	-	-	PUNCT
ejpam-4006	102	22	times	time	NOUN
ejpam-4006	102	23	is	be	AUX
ejpam-4006	102	24	defined	define	VERB
ejpam-4006	102	25	by	by	ADP
ejpam-4006	102	26	(	(	PUNCT
ejpam-4006	102	27	10	10	NUM
ejpam-4006	102	28	)	)	PUNCT
ejpam-4006	102	29	.	.	PUNCT
ejpam-4006	103	1	then	then	ADV
ejpam-4006	103	2	u(x	u(x	VERB
ejpam-4006	103	3	)	)	PUNCT
ejpam-4006	103	4	=	=	SYM
ejpam-4006	103	5	(	(	PUNCT
ejpam-4006	103	6	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	103	7	)	)	PUNCT
ejpam-4006	103	8	is	be	AUX
ejpam-4006	103	9	the	the	DET
ejpam-4006	103	10	fundamental	fundamental	ADJ
ejpam-4006	103	11	solution	solution	NOUN
ejpam-4006	103	12	of	of	ADP
ejpam-4006	103	13	the	the	DET
ejpam-4006	103	14	operator	operator	NOUN
ejpam-4006	103	15	4k	4k	NUM
ejpam-4006	103	16	where	where	SCONJ
ejpam-4006	103	17	re2k(x	re2k(x	VERB
ejpam-4006	103	18	)	)	PUNCT
ejpam-4006	103	19	=	=	SYM
ejpam-4006	103	20	γ	γ	X
ejpam-4006	103	21	(	(	PUNCT
ejpam-4006	103	22	n−2k	n−2k	NOUN
ejpam-4006	103	23	2	2	X
ejpam-4006	103	24	)	)	PUNCT
ejpam-4006	103	25	22kπ	22kπ	NOUN
ejpam-4006	103	26	n	n	PRON
ejpam-4006	103	27	2	2	NUM
ejpam-4006	103	28	γ(k	γ(k	PROPN
ejpam-4006	103	29	)	)	PUNCT
ejpam-4006	103	30	|x|2k−n	|x|2k−n	PROPN
ejpam-4006	103	31	.	.	PUNCT
ejpam-4006	104	1	(	(	PUNCT
ejpam-4006	104	2	22	22	NUM
ejpam-4006	104	3	)	)	PUNCT
ejpam-4006	104	4	proof	proof	NOUN
ejpam-4006	104	5	.	.	PUNCT
ejpam-4006	105	1	see	see	VERB
ejpam-4006	105	2	[	[	X
ejpam-4006	105	3	4	4	NUM
ejpam-4006	105	4	]	]	PUNCT
ejpam-4006	105	5	.	.	PUNCT
ejpam-4006	106	1	s.	s.	PROPN
ejpam-4006	106	2	bupasiri	bupasiri	PROPN
ejpam-4006	106	3	/	/	SYM
ejpam-4006	106	4	eur	eur	PROPN
ejpam-4006	106	5	.	.	PUNCT
ejpam-4006	107	1	j.	j.	PROPN
ejpam-4006	107	2	pure	pure	PROPN
ejpam-4006	107	3	appl	appl	PROPN
ejpam-4006	107	4	.	.	PROPN
ejpam-4006	107	5	math	math	PROPN
ejpam-4006	107	6	,	,	PUNCT
ejpam-4006	107	7	14	14	NUM
ejpam-4006	107	8	(	(	PUNCT
ejpam-4006	107	9	3	3	NUM
ejpam-4006	107	10	)	)	PUNCT
ejpam-4006	107	11	(	(	PUNCT
ejpam-4006	107	12	2021	2021	NUM
ejpam-4006	107	13	)	)	PUNCT
ejpam-4006	107	14	,	,	PUNCT
ejpam-4006	107	15	881	881	NUM
ejpam-4006	107	16	-	-	SYM
ejpam-4006	107	17	894	894	NUM
ejpam-4006	107	18	886	886	NUM
ejpam-4006	107	19	lemma	lemma	PROPN
ejpam-4006	107	20	2	2	NUM
ejpam-4006	107	21	.	.	PUNCT
ejpam-4006	108	1	if	if	SCONJ
ejpam-4006	108	2	�	�	NOUN
ejpam-4006	108	3	ku(x	ku(x	X
ejpam-4006	108	4	)	)	PUNCT
ejpam-4006	108	5	=	=	SYM
ejpam-4006	108	6	δ	δ	PROPN
ejpam-4006	108	7	for	for	ADP
ejpam-4006	108	8	x	x	PROPN
ejpam-4006	108	9	∈	∈	PROPN
ejpam-4006	108	10	γ+	γ+	PUNCT
ejpam-4006	108	11	=	=	SYM
ejpam-4006	108	12	{	{	PUNCT
ejpam-4006	108	13	x	x	PROPN
ejpam-4006	108	14	∈	∈	PROPN
ejpam-4006	108	15	rn	rn	PROPN
ejpam-4006	108	16	:	:	PUNCT
ejpam-4006	108	17	x1	x1	PROPN
ejpam-4006	108	18	>	>	X
ejpam-4006	108	19	0	0	PUNCT
ejpam-4006	108	20	and	and	CCONJ
ejpam-4006	108	21	u	u	X
ejpam-4006	108	22	>	>	X
ejpam-4006	108	23	0	0	NUM
ejpam-4006	108	24	}	}	PUNCT
ejpam-4006	108	25	,	,	PUNCT
ejpam-4006	108	26	where	where	SCONJ
ejpam-4006	108	27	�	�	NOUN
ejpam-4006	108	28	kis	kis	PROPN
ejpam-4006	108	29	the	the	DET
ejpam-4006	108	30	ultra	ultra	ADJ
ejpam-4006	108	31	-	-	ADJ
ejpam-4006	108	32	hyperbolic	hyperbolic	ADJ
ejpam-4006	108	33	operator	operator	NOUN
ejpam-4006	108	34	iterated	iterate	VERB
ejpam-4006	108	35	k	k	NOUN
ejpam-4006	108	36	-	-	PUNCT
ejpam-4006	108	37	times	time	NOUN
ejpam-4006	108	38	is	be	AUX
ejpam-4006	108	39	defined	define	VERB
ejpam-4006	108	40	by	by	ADP
ejpam-4006	108	41	(	(	PUNCT
ejpam-4006	108	42	9	9	NUM
ejpam-4006	108	43	)	)	PUNCT
ejpam-4006	108	44	.	.	PUNCT
ejpam-4006	109	1	then	then	ADV
ejpam-4006	109	2	u(x	u(x	VERB
ejpam-4006	109	3	)	)	PUNCT
ejpam-4006	109	4	=	=	SYM
ejpam-4006	109	5	rh2k(x	rh2k(x	PROPN
ejpam-4006	109	6	)	)	PUNCT
ejpam-4006	109	7	is	be	AUX
ejpam-4006	109	8	the	the	DET
ejpam-4006	109	9	unique	unique	ADJ
ejpam-4006	109	10	fundamental	fundamental	ADJ
ejpam-4006	109	11	solution	solution	NOUN
ejpam-4006	109	12	of	of	ADP
ejpam-4006	109	13	the	the	DET
ejpam-4006	109	14	operator	operator	NOUN
ejpam-4006	109	15	�	�	PROPN
ejpam-4006	109	16	k	k	PROPN
ejpam-4006	109	17	where	where	SCONJ
ejpam-4006	109	18	rh2k(x	rh2k(x	NOUN
ejpam-4006	109	19	)	)	PUNCT
ejpam-4006	109	20	=	=	SYM
ejpam-4006	109	21	u	u	NOUN
ejpam-4006	109	22	(	(	PUNCT
ejpam-4006	109	23	2k−n	2k−n	NUM
ejpam-4006	109	24	2	2	NUM
ejpam-4006	109	25	)	)	PUNCT
ejpam-4006	109	26	kn(2k	kn(2k	NOUN
ejpam-4006	109	27	)	)	PUNCT
ejpam-4006	109	28	=	=	PUNCT
ejpam-4006	109	29	(	(	PUNCT
ejpam-4006	109	30	x21	x21	PROPN
ejpam-4006	109	31	+	+	NUM
ejpam-4006	109	32	x22	x22	NOUN
ejpam-4006	110	1	+	+	CCONJ
ejpam-4006	110	2	·	·	PUNCT
ejpam-4006	110	3	·	·	PUNCT
ejpam-4006	110	4	·	·	PUNCT
ejpam-4006	110	5	+	+	NUM
ejpam-4006	110	6	x2p	x2p	NUM
ejpam-4006	110	7	−	−	PROPN
ejpam-4006	111	1	x2p+1	x2p+1	INTJ
ejpam-4006	112	1	−	−	PROPN
ejpam-4006	112	2	·	·	PUNCT
ejpam-4006	112	3	·	·	PUNCT
ejpam-4006	112	4	·	·	PUNCT
ejpam-4006	113	1	−	−	NOUN
ejpam-4006	113	2	x2p+q	x2p+q	X
ejpam-4006	113	3	)	)	PUNCT
ejpam-4006	113	4	(	(	PUNCT
ejpam-4006	113	5	2k−n	2k−n	NUM
ejpam-4006	113	6	2	2	NUM
ejpam-4006	113	7	)	)	PUNCT
ejpam-4006	113	8	kn(2k	kn(2k	NOUN
ejpam-4006	113	9	)	)	PUNCT
ejpam-4006	113	10	(	(	PUNCT
ejpam-4006	113	11	23	23	NUM
ejpam-4006	113	12	)	)	PUNCT
ejpam-4006	113	13	for	for	ADP
ejpam-4006	113	14	kn(2k	kn(2k	NOUN
ejpam-4006	113	15	)	)	PUNCT
ejpam-4006	113	16	=	=	PUNCT
ejpam-4006	114	1	π	π	X
ejpam-4006	114	2	n−1	n−1	PROPN
ejpam-4006	114	3	2	2	NUM
ejpam-4006	114	4	γ	γ	X
ejpam-4006	114	5	(	(	PUNCT
ejpam-4006	114	6	2	2	NUM
ejpam-4006	114	7	+	+	NOUN
ejpam-4006	114	8	2k−n	2k−n	ADJ
ejpam-4006	114	9	2	2	NUM
ejpam-4006	114	10	)	)	PUNCT
ejpam-4006	114	11	γ	γ	PROPN
ejpam-4006	114	12	(	(	PUNCT
ejpam-4006	114	13	1−2k	1−2k	NUM
ejpam-4006	114	14	2	2	NUM
ejpam-4006	114	15	)	)	PUNCT
ejpam-4006	114	16	γ(2k	γ(2k	VERB
ejpam-4006	114	17	)	)	PUNCT
ejpam-4006	114	18	γ	γ	X
ejpam-4006	114	19	(	(	PUNCT
ejpam-4006	114	20	2	2	NUM
ejpam-4006	114	21	+	+	NUM
ejpam-4006	114	22	2k−p	2k−p	NUM
ejpam-4006	114	23	2	2	NUM
ejpam-4006	114	24	)	)	PUNCT
ejpam-4006	114	25	γ(p−2k2	γ(p−2k2	CCONJ
ejpam-4006	114	26	)	)	PUNCT
ejpam-4006	114	27	.	.	PUNCT
ejpam-4006	115	1	(	(	PUNCT
ejpam-4006	115	2	24	24	NUM
ejpam-4006	115	3	)	)	PUNCT
ejpam-4006	115	4	proof	proof	NOUN
ejpam-4006	115	5	.	.	PUNCT
ejpam-4006	116	1	see	see	VERB
ejpam-4006	116	2	[	[	X
ejpam-4006	116	3	11	11	NUM
ejpam-4006	116	4	]	]	PUNCT
ejpam-4006	116	5	.	.	PUNCT
ejpam-4006	117	1	lemma	lemma	PROPN
ejpam-4006	117	2	3	3	X
ejpam-4006	117	3	.	.	PUNCT
ejpam-4006	117	4	given	give	VERB
ejpam-4006	117	5	the	the	DET
ejpam-4006	117	6	equation	equation	NOUN
ejpam-4006	117	7	♦	♦	PROPN
ejpam-4006	117	8	ku(x	ku(x	PRON
ejpam-4006	117	9	)	)	PUNCT
ejpam-4006	117	10	=	=	SYM
ejpam-4006	117	11	δ	δ	PROPN
ejpam-4006	117	12	for	for	ADP
ejpam-4006	117	13	x	x	PROPN
ejpam-4006	117	14	∈	∈	PROPN
ejpam-4006	117	15	rn	rn	PROPN
ejpam-4006	117	16	,	,	PUNCT
ejpam-4006	117	17	then	then	ADV
ejpam-4006	117	18	u(x	u(x	VERB
ejpam-4006	117	19	)	)	PUNCT
ejpam-4006	117	20	=	=	SYM
ejpam-4006	117	21	(	(	PUNCT
ejpam-4006	117	22	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	117	23	)	)	PUNCT
ejpam-4006	117	24	∗	∗	NOUN
ejpam-4006	117	25	rh2k(x	rh2k(x	PROPN
ejpam-4006	117	26	)	)	PUNCT
ejpam-4006	117	27	is	be	AUX
ejpam-4006	117	28	the	the	DET
ejpam-4006	117	29	unique	unique	ADJ
ejpam-4006	117	30	fundamental	fundamental	ADJ
ejpam-4006	117	31	solution	solution	NOUN
ejpam-4006	117	32	of	of	ADP
ejpam-4006	117	33	the	the	DET
ejpam-4006	117	34	operator	operator	NOUN
ejpam-4006	117	35	♦	♦	PROPN
ejpam-4006	117	36	k	k	PROPN
ejpam-4006	117	37	,	,	PUNCT
ejpam-4006	117	38	where	where	SCONJ
ejpam-4006	117	39	♦	♦	PROPN
ejpam-4006	117	40	k	k	PROPN
ejpam-4006	117	41	is	be	AUX
ejpam-4006	117	42	the	the	DET
ejpam-4006	117	43	diamond	diamond	NOUN
ejpam-4006	117	44	operator	operator	NOUN
ejpam-4006	117	45	iterated	iterate	VERB
ejpam-4006	117	46	ktimes	ktime	NOUN
ejpam-4006	117	47	is	be	AUX
ejpam-4006	117	48	defined	define	VERB
ejpam-4006	117	49	by	by	ADP
ejpam-4006	117	50	(	(	PUNCT
ejpam-4006	117	51	8)	8)	NUM
ejpam-4006	117	52	,	,	PUNCT
ejpam-4006	117	53	re2k(x	re2k(x	PROPN
ejpam-4006	117	54	)	)	PUNCT
ejpam-4006	117	55	and	and	CCONJ
ejpam-4006	117	56	rh2k(x	rh2k(x	NOUN
ejpam-4006	117	57	)	)	PUNCT
ejpam-4006	117	58	are	be	AUX
ejpam-4006	117	59	defined	define	VERB
ejpam-4006	117	60	by	by	ADP
ejpam-4006	117	61	(	(	PUNCT
ejpam-4006	117	62	22	22	NUM
ejpam-4006	117	63	)	)	PUNCT
ejpam-4006	117	64	and	and	CCONJ
ejpam-4006	117	65	(	(	PUNCT
ejpam-4006	117	66	23	23	NUM
ejpam-4006	117	67	)	)	PUNCT
ejpam-4006	117	68	,	,	PUNCT
ejpam-4006	117	69	respectively	respectively	ADV
ejpam-4006	117	70	.	.	PUNCT
ejpam-4006	118	1	moreover	moreover	ADV
ejpam-4006	118	2	,	,	PUNCT
ejpam-4006	118	3	(	(	PUNCT
ejpam-4006	118	4	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	118	5	)	)	PUNCT
ejpam-4006	118	6	∗rh2k(x	∗rh2k(x	NOUN
ejpam-4006	118	7	)	)	PUNCT
ejpam-4006	118	8	is	be	AUX
ejpam-4006	118	9	a	a	DET
ejpam-4006	118	10	tempered	temper	VERB
ejpam-4006	118	11	distribution	distribution	NOUN
ejpam-4006	118	12	.	.	PUNCT
ejpam-4006	119	1	proof	proof	NOUN
ejpam-4006	119	2	.	.	PUNCT
ejpam-4006	120	1	see	see	VERB
ejpam-4006	120	2	[	[	X
ejpam-4006	120	3	4	4	NUM
ejpam-4006	120	4	]	]	PUNCT
ejpam-4006	120	5	.	.	PUNCT
ejpam-4006	121	1	lemma	lemma	PROPN
ejpam-4006	121	2	4	4	NUM
ejpam-4006	121	3	.	.	PUNCT
ejpam-4006	122	1	given	give	VERB
ejpam-4006	122	2	the	the	DET
ejpam-4006	122	3	equation	equation	NOUN
ejpam-4006	122	4	lk1u(x	lk1u(x	AUX
ejpam-4006	122	5	)	)	PUNCT
ejpam-4006	122	6	=	=	SYM
ejpam-4006	122	7	δ	δ	PROPN
ejpam-4006	122	8	for	for	ADP
ejpam-4006	122	9	x	x	PROPN
ejpam-4006	122	10	∈	∈	PROPN
ejpam-4006	122	11	rn	rn	PROPN
ejpam-4006	122	12	,	,	PUNCT
ejpam-4006	122	13	where	where	SCONJ
ejpam-4006	122	14	lk1	lk1	NOUN
ejpam-4006	122	15	is	be	AUX
ejpam-4006	122	16	the	the	DET
ejpam-4006	122	17	operator	operator	NOUN
ejpam-4006	122	18	defined	define	VERB
ejpam-4006	122	19	by	by	ADP
ejpam-4006	122	20	(	(	PUNCT
ejpam-4006	122	21	12	12	NUM
ejpam-4006	122	22	)	)	PUNCT
ejpam-4006	122	23	,	,	PUNCT
ejpam-4006	122	24	then	then	ADV
ejpam-4006	122	25	u(x	u(x	VERB
ejpam-4006	122	26	)	)	PUNCT
ejpam-4006	122	27	=	=	SYM
ejpam-4006	122	28	(	(	PUNCT
ejpam-4006	122	29	−1)k(−i	−1)k(−i	NUM
ejpam-4006	122	30	)	)	PUNCT
ejpam-4006	122	31	q	q	NOUN
ejpam-4006	122	32	2s2k(x	2s2k(x	NOUN
ejpam-4006	122	33	)	)	PUNCT
ejpam-4006	122	34	is	be	AUX
ejpam-4006	122	35	the	the	DET
ejpam-4006	122	36	fundamental	fundamental	ADJ
ejpam-4006	122	37	solution	solution	NOUN
ejpam-4006	122	38	of	of	ADP
ejpam-4006	122	39	the	the	DET
ejpam-4006	122	40	operator	operator	NOUN
ejpam-4006	122	41	lk1	lk1	NOUN
ejpam-4006	122	42	,	,	PUNCT
ejpam-4006	122	43	where	where	SCONJ
ejpam-4006	122	44	s2k(x	s2k(x	NOUN
ejpam-4006	122	45	)	)	PUNCT
ejpam-4006	122	46	=	=	SYM
ejpam-4006	123	1	γ	γ	X
ejpam-4006	123	2	(	(	PUNCT
ejpam-4006	123	3	n−2k	n−2k	NOUN
ejpam-4006	123	4	2	2	X
ejpam-4006	123	5	)	)	PUNCT
ejpam-4006	123	6	22kπ	22kπ	NOUN
ejpam-4006	123	7	n	n	PRON
ejpam-4006	123	8	2	2	NUM
ejpam-4006	123	9	γ(k	γ(k	PROPN
ejpam-4006	123	10	)	)	PUNCT
ejpam-4006	124	1	[	[	X
ejpam-4006	124	2	x21	x21	NUM
ejpam-4006	124	3	+	+	NUM
ejpam-4006	124	4	x22	x22	NOUN
ejpam-4006	124	5	+	+	CCONJ
ejpam-4006	124	6	·	·	PUNCT
ejpam-4006	124	7	·	·	PUNCT
ejpam-4006	124	8	·	·	PUNCT
ejpam-4006	125	1	+	+	NUM
ejpam-4006	125	2	x2p	x2p	SYM
ejpam-4006	125	3	−	−	PROPN
ejpam-4006	125	4	i(x2p+1	i(x2p+1	NUM
ejpam-4006	125	5	+	+	X
ejpam-4006	125	6	·	·	PUNCT
ejpam-4006	125	7	·	·	PUNCT
ejpam-4006	125	8	·	·	PUNCT
ejpam-4006	125	9	+	+	NUM
ejpam-4006	125	10	x2p+q	x2p+q	X
ejpam-4006	125	11	)	)	PUNCT
ejpam-4006	125	12	]	]	PUNCT
ejpam-4006	126	1	(	(	PUNCT
ejpam-4006	126	2	2k−n	2k−n	NUM
ejpam-4006	126	3	2	2	NUM
ejpam-4006	126	4	)	)	PUNCT
ejpam-4006	126	5	.	.	PUNCT
ejpam-4006	127	1	(	(	PUNCT
ejpam-4006	127	2	25	25	NUM
ejpam-4006	127	3	)	)	PUNCT
ejpam-4006	127	4	lemma	lemma	PROPN
ejpam-4006	127	5	5	5	NUM
ejpam-4006	127	6	.	.	PUNCT
ejpam-4006	128	1	given	give	VERB
ejpam-4006	128	2	the	the	DET
ejpam-4006	128	3	equation	equation	NOUN
ejpam-4006	128	4	lk2u(x	lk2u(x	VERB
ejpam-4006	128	5	)	)	PUNCT
ejpam-4006	128	6	=	=	SYM
ejpam-4006	128	7	δ	δ	PROPN
ejpam-4006	128	8	for	for	ADP
ejpam-4006	128	9	x	x	PROPN
ejpam-4006	128	10	∈	∈	PROPN
ejpam-4006	128	11	rn	rn	PROPN
ejpam-4006	128	12	,	,	PUNCT
ejpam-4006	128	13	where	where	SCONJ
ejpam-4006	128	14	lk2	lk2	NOUN
ejpam-4006	128	15	is	be	AUX
ejpam-4006	128	16	the	the	DET
ejpam-4006	128	17	operator	operator	NOUN
ejpam-4006	128	18	defined	define	VERB
ejpam-4006	128	19	by	by	ADP
ejpam-4006	128	20	(	(	PUNCT
ejpam-4006	128	21	13	13	NUM
ejpam-4006	128	22	)	)	PUNCT
ejpam-4006	128	23	,	,	PUNCT
ejpam-4006	128	24	then	then	ADV
ejpam-4006	128	25	u(x	u(x	VERB
ejpam-4006	128	26	)	)	PUNCT
ejpam-4006	128	27	=	=	SYM
ejpam-4006	128	28	(	(	PUNCT
ejpam-4006	128	29	−1)k(i	−1)k(i	PROPN
ejpam-4006	128	30	)	)	PUNCT
ejpam-4006	128	31	q	q	NOUN
ejpam-4006	128	32	2t2k(x	2t2k(x	PROPN
ejpam-4006	128	33	)	)	PUNCT
ejpam-4006	128	34	is	be	AUX
ejpam-4006	128	35	the	the	DET
ejpam-4006	128	36	fundamental	fundamental	ADJ
ejpam-4006	128	37	solution	solution	NOUN
ejpam-4006	128	38	of	of	ADP
ejpam-4006	128	39	the	the	DET
ejpam-4006	128	40	operator	operator	NOUN
ejpam-4006	128	41	lk2	lk2	NOUN
ejpam-4006	128	42	,	,	PUNCT
ejpam-4006	128	43	where	where	SCONJ
ejpam-4006	128	44	t2k(x	t2k(x	NOUN
ejpam-4006	128	45	)	)	PUNCT
ejpam-4006	129	1	=	=	SYM
ejpam-4006	129	2	γ	γ	X
ejpam-4006	129	3	(	(	PUNCT
ejpam-4006	129	4	n−2k	n−2k	NOUN
ejpam-4006	129	5	2	2	X
ejpam-4006	129	6	)	)	PUNCT
ejpam-4006	129	7	22kπ	22kπ	NOUN
ejpam-4006	129	8	n	n	PRON
ejpam-4006	129	9	2	2	NUM
ejpam-4006	129	10	γ(k	γ(k	PROPN
ejpam-4006	129	11	)	)	PUNCT
ejpam-4006	130	1	[	[	X
ejpam-4006	130	2	x21	x21	NUM
ejpam-4006	130	3	+	+	NUM
ejpam-4006	130	4	x22	x22	NOUN
ejpam-4006	130	5	+	+	CCONJ
ejpam-4006	130	6	·	·	PUNCT
ejpam-4006	130	7	·	·	PUNCT
ejpam-4006	130	8	·	·	PUNCT
ejpam-4006	130	9	+	+	CCONJ
ejpam-4006	130	10	x2p	x2p	PUNCT
ejpam-4006	131	1	+	+	NUM
ejpam-4006	131	2	i(x2p+1	i(x2p+1	NUM
ejpam-4006	131	3	+	+	X
ejpam-4006	131	4	·	·	PUNCT
ejpam-4006	131	5	·	·	PUNCT
ejpam-4006	131	6	·	·	PUNCT
ejpam-4006	131	7	+	+	NUM
ejpam-4006	131	8	x2p+q	x2p+q	X
ejpam-4006	131	9	)	)	PUNCT
ejpam-4006	131	10	]	]	PUNCT
ejpam-4006	131	11	(	(	PUNCT
ejpam-4006	131	12	2k−n	2k−n	NUM
ejpam-4006	131	13	2	2	NUM
ejpam-4006	131	14	)	)	PUNCT
ejpam-4006	131	15	.	.	PUNCT
ejpam-4006	132	1	(	(	PUNCT
ejpam-4006	132	2	26	26	NUM
ejpam-4006	132	3	)	)	PUNCT
ejpam-4006	132	4	lemma	lemma	PROPN
ejpam-4006	132	5	6	6	NUM
ejpam-4006	132	6	.	.	PUNCT
ejpam-4006	133	1	given	give	VERB
ejpam-4006	133	2	the	the	DET
ejpam-4006	133	3	equation	equation	NOUN
ejpam-4006	133	4	lku(x	lku(x	VERB
ejpam-4006	133	5	)	)	PUNCT
ejpam-4006	133	6	=	=	SYM
ejpam-4006	133	7	δ	δ	PROPN
ejpam-4006	133	8	for	for	ADP
ejpam-4006	133	9	x	x	PROPN
ejpam-4006	133	10	∈	∈	PROPN
ejpam-4006	133	11	rn	rn	PROPN
ejpam-4006	133	12	,	,	PUNCT
ejpam-4006	133	13	then	then	ADV
ejpam-4006	133	14	u(x	u(x	VERB
ejpam-4006	133	15	)	)	PUNCT
ejpam-4006	133	16	=	=	SYM
ejpam-4006	133	17	s2k(x	s2k(x	PROPN
ejpam-4006	133	18	)	)	PUNCT
ejpam-4006	133	19	∗	∗	PROPN
ejpam-4006	133	20	t2k(x	t2k(x	PROPN
ejpam-4006	133	21	)	)	PUNCT
ejpam-4006	133	22	is	be	AUX
ejpam-4006	133	23	the	the	DET
ejpam-4006	133	24	fundamental	fundamental	ADJ
ejpam-4006	133	25	solution	solution	NOUN
ejpam-4006	133	26	of	of	ADP
ejpam-4006	133	27	the	the	DET
ejpam-4006	133	28	operator	operator	NOUN
ejpam-4006	133	29	lk	lk	PROPN
ejpam-4006	133	30	,	,	PUNCT
ejpam-4006	133	31	which	which	PRON
ejpam-4006	133	32	is	be	AUX
ejpam-4006	133	33	defined	define	VERB
ejpam-4006	133	34	by	by	ADP
ejpam-4006	133	35	(	(	PUNCT
ejpam-4006	133	36	14	14	NUM
ejpam-4006	133	37	)	)	PUNCT
ejpam-4006	133	38	,	,	PUNCT
ejpam-4006	133	39	s2k(x	s2k(x	PROPN
ejpam-4006	133	40	)	)	PUNCT
ejpam-4006	133	41	and	and	CCONJ
ejpam-4006	133	42	t2k(x	t2k(x	NOUN
ejpam-4006	133	43	)	)	PUNCT
ejpam-4006	133	44	are	be	AUX
ejpam-4006	133	45	defined	define	VERB
ejpam-4006	133	46	by	by	ADP
ejpam-4006	133	47	(	(	PUNCT
ejpam-4006	133	48	25	25	NUM
ejpam-4006	133	49	)	)	PUNCT
ejpam-4006	133	50	and	and	CCONJ
ejpam-4006	133	51	(	(	PUNCT
ejpam-4006	133	52	26	26	NUM
ejpam-4006	133	53	)	)	PUNCT
ejpam-4006	133	54	,	,	PUNCT
ejpam-4006	133	55	respectively	respectively	ADV
ejpam-4006	133	56	.	.	PUNCT
ejpam-4006	134	1	proof	proof	NOUN
ejpam-4006	134	2	.	.	PUNCT
ejpam-4006	135	1	the	the	DET
ejpam-4006	135	2	proof	proof	NOUN
ejpam-4006	135	3	of	of	ADP
ejpam-4006	135	4	the	the	DET
ejpam-4006	135	5	lemma	lemma	PROPN
ejpam-4006	135	6	4	4	NUM
ejpam-4006	135	7	,	,	PUNCT
ejpam-4006	135	8	lemma	lemma	PROPN
ejpam-4006	135	9	5	5	NUM
ejpam-4006	135	10	and	and	CCONJ
ejpam-4006	135	11	lemma	lemma	PROPN
ejpam-4006	135	12	6	6	NUM
ejpam-4006	135	13	are	be	AUX
ejpam-4006	135	14	given	give	VERB
ejpam-4006	135	15	in	in	ADP
ejpam-4006	135	16	[	[	X
ejpam-4006	135	17	2	2	NUM
ejpam-4006	135	18	]	]	PUNCT
ejpam-4006	135	19	.	.	PUNCT
ejpam-4006	136	1	lemma	lemma	PROPN
ejpam-4006	136	2	7	7	NUM
ejpam-4006	136	3	.	.	PUNCT
ejpam-4006	137	1	the	the	DET
ejpam-4006	137	2	function	function	NOUN
ejpam-4006	137	3	rh−2k(x	rh−2k(x	NOUN
ejpam-4006	137	4	)	)	PUNCT
ejpam-4006	137	5	and	and	CCONJ
ejpam-4006	137	6	(	(	PUNCT
ejpam-4006	137	7	−1)kre−2k(x	−1)kre−2k(x	PROPN
ejpam-4006	137	8	)	)	PUNCT
ejpam-4006	137	9	are	be	AUX
ejpam-4006	137	10	the	the	DET
ejpam-4006	137	11	inverse	inverse	NOUN
ejpam-4006	137	12	in	in	ADP
ejpam-4006	137	13	the	the	DET
ejpam-4006	137	14	convolution	convolution	NOUN
ejpam-4006	137	15	algebra	algebra	NOUN
ejpam-4006	137	16	of	of	ADP
ejpam-4006	137	17	rh2k(x	rh2k(x	PROPN
ejpam-4006	137	18	)	)	PUNCT
ejpam-4006	137	19	and	and	CCONJ
ejpam-4006	137	20	(	(	PUNCT
ejpam-4006	137	21	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	137	22	)	)	PUNCT
ejpam-4006	137	23	,	,	PUNCT
ejpam-4006	137	24	respectively	respectively	ADV
ejpam-4006	137	25	.	.	PUNCT
ejpam-4006	138	1	lemma	lemma	PROPN
ejpam-4006	138	2	8	8	NUM
ejpam-4006	138	3	.	.	PUNCT
ejpam-4006	139	1	(	(	PUNCT
ejpam-4006	139	2	1	1	X
ejpam-4006	139	3	)	)	PUNCT
ejpam-4006	139	4	the	the	DET
ejpam-4006	139	5	function	function	NOUN
ejpam-4006	139	6	s2k(x	s2k(x	PROPN
ejpam-4006	139	7	)	)	PUNCT
ejpam-4006	139	8	and	and	CCONJ
ejpam-4006	139	9	t2k(x	t2k(x	PROPN
ejpam-4006	139	10	)	)	PUNCT
ejpam-4006	139	11	are	be	AUX
ejpam-4006	139	12	the	the	DET
ejpam-4006	139	13	fundamental	fundamental	ADJ
ejpam-4006	139	14	solution	solution	NOUN
ejpam-4006	139	15	of	of	ADP
ejpam-4006	139	16	the	the	DET
ejpam-4006	139	17	operator	operator	NOUN
ejpam-4006	139	18	lk1	lk1	NOUN
ejpam-4006	139	19	and	and	CCONJ
ejpam-4006	139	20	lk2	lk2	NOUN
ejpam-4006	139	21	,	,	PUNCT
ejpam-4006	139	22	respectively	respectively	ADV
ejpam-4006	139	23	,	,	PUNCT
ejpam-4006	139	24	where	where	SCONJ
ejpam-4006	139	25	s2k(x	s2k(x	NOUN
ejpam-4006	139	26	)	)	PUNCT
ejpam-4006	139	27	and	and	CCONJ
ejpam-4006	139	28	t2k(x	t2k(x	NOUN
ejpam-4006	139	29	)	)	PUNCT
ejpam-4006	139	30	are	be	AUX
ejpam-4006	139	31	defined	define	VERB
ejpam-4006	139	32	by	by	ADP
ejpam-4006	139	33	(	(	PUNCT
ejpam-4006	139	34	25	25	NUM
ejpam-4006	139	35	)	)	PUNCT
ejpam-4006	139	36	and	and	CCONJ
ejpam-4006	139	37	(	(	PUNCT
ejpam-4006	139	38	26	26	NUM
ejpam-4006	139	39	)	)	PUNCT
ejpam-4006	139	40	,	,	PUNCT
ejpam-4006	139	41	respectively	respectively	ADV
ejpam-4006	139	42	.	.	PUNCT
ejpam-4006	140	1	s.	s.	PROPN
ejpam-4006	140	2	bupasiri	bupasiri	PROPN
ejpam-4006	140	3	/	/	SYM
ejpam-4006	140	4	eur	eur	PROPN
ejpam-4006	140	5	.	.	PUNCT
ejpam-4006	141	1	j.	j.	PROPN
ejpam-4006	141	2	pure	pure	PROPN
ejpam-4006	141	3	appl	appl	PROPN
ejpam-4006	141	4	.	.	PROPN
ejpam-4006	141	5	math	math	PROPN
ejpam-4006	141	6	,	,	PUNCT
ejpam-4006	141	7	14	14	NUM
ejpam-4006	141	8	(	(	PUNCT
ejpam-4006	141	9	3	3	NUM
ejpam-4006	141	10	)	)	PUNCT
ejpam-4006	141	11	(	(	PUNCT
ejpam-4006	141	12	2021	2021	NUM
ejpam-4006	141	13	)	)	PUNCT
ejpam-4006	141	14	,	,	PUNCT
ejpam-4006	141	15	881	881	NUM
ejpam-4006	141	16	-	-	SYM
ejpam-4006	141	17	894	894	NUM
ejpam-4006	141	18	887	887	NUM
ejpam-4006	141	19	(	(	PUNCT
ejpam-4006	141	20	2	2	NUM
ejpam-4006	141	21	)	)	PUNCT
ejpam-4006	141	22	the	the	DET
ejpam-4006	141	23	function	function	NOUN
ejpam-4006	141	24	s−2k(x	s−2k(x	PROPN
ejpam-4006	141	25	)	)	PUNCT
ejpam-4006	141	26	and	and	CCONJ
ejpam-4006	141	27	t−2k(x	t−2k(x	PROPN
ejpam-4006	141	28	)	)	PUNCT
ejpam-4006	141	29	are	be	AUX
ejpam-4006	141	30	the	the	DET
ejpam-4006	141	31	inverse	inverse	NOUN
ejpam-4006	141	32	in	in	ADP
ejpam-4006	141	33	the	the	DET
ejpam-4006	141	34	convolution	convolution	NOUN
ejpam-4006	141	35	algebra	algebra	NOUN
ejpam-4006	141	36	of	of	ADP
ejpam-4006	141	37	s2k(x	s2k(x	PROPN
ejpam-4006	141	38	)	)	PUNCT
ejpam-4006	141	39	and	and	CCONJ
ejpam-4006	141	40	t2k(x	t2k(x	NOUN
ejpam-4006	141	41	)	)	PUNCT
ejpam-4006	141	42	,	,	PUNCT
ejpam-4006	141	43	respectively	respectively	ADV
ejpam-4006	141	44	.	.	PUNCT
ejpam-4006	142	1	proof	proof	NOUN
ejpam-4006	142	2	.	.	PUNCT
ejpam-4006	143	1	the	the	DET
ejpam-4006	143	2	proof	proof	NOUN
ejpam-4006	143	3	of	of	ADP
ejpam-4006	143	4	the	the	DET
ejpam-4006	143	5	lemma	lemma	PROPN
ejpam-4006	143	6	7	7	NUM
ejpam-4006	143	7	and	and	CCONJ
ejpam-4006	143	8	lemma	lemma	PROPN
ejpam-4006	143	9	8	8	NUM
ejpam-4006	143	10	are	be	AUX
ejpam-4006	143	11	given	give	VERB
ejpam-4006	143	12	in	in	ADP
ejpam-4006	143	13	[	[	X
ejpam-4006	143	14	2	2	NUM
ejpam-4006	143	15	]	]	PUNCT
ejpam-4006	143	16	.	.	PUNCT
ejpam-4006	144	1	lemma	lemma	PROPN
ejpam-4006	144	2	9	9	NUM
ejpam-4006	144	3	.	.	PUNCT
ejpam-4006	145	1	given	give	VERB
ejpam-4006	145	2	the	the	DET
ejpam-4006	145	3	equation	equation	NOUN
ejpam-4006	145	4	(	(	PUNCT
ejpam-4006	145	5	�	�	PROPN
ejpam-4006	145	6	+	+	CCONJ
ejpam-4006	145	7	m2)ku(x	m2)ku(x	PROPN
ejpam-4006	145	8	)	)	PUNCT
ejpam-4006	145	9	=	=	SYM
ejpam-4006	145	10	δ	δ	PROPN
ejpam-4006	145	11	for	for	ADP
ejpam-4006	145	12	x	x	PROPN
ejpam-4006	145	13	∈	∈	PROPN
ejpam-4006	145	14	rn	rn	PROPN
ejpam-4006	145	15	,	,	PUNCT
ejpam-4006	145	16	where	where	SCONJ
ejpam-4006	145	17	�	�	PROPN
ejpam-4006	145	18	is	be	AUX
ejpam-4006	145	19	the	the	DET
ejpam-4006	145	20	ultrahyperbolic	ultrahyperbolic	ADJ
ejpam-4006	145	21	operator	operator	NOUN
ejpam-4006	145	22	defined	define	VERB
ejpam-4006	145	23	by	by	ADP
ejpam-4006	145	24	(	(	PUNCT
ejpam-4006	145	25	9	9	NUM
ejpam-4006	145	26	)	)	PUNCT
ejpam-4006	145	27	.	.	PUNCT
ejpam-4006	146	1	then	then	ADV
ejpam-4006	146	2	u(x	u(x	VERB
ejpam-4006	146	3	)	)	PUNCT
ejpam-4006	146	4	=	=	SYM
ejpam-4006	147	1	w2k(x	w2k(x	PROPN
ejpam-4006	147	2	,	,	PUNCT
ejpam-4006	147	3	m	m	NOUN
ejpam-4006	147	4	)	)	PUNCT
ejpam-4006	147	5	is	be	AUX
ejpam-4006	147	6	the	the	DET
ejpam-4006	147	7	fundamental	fundamental	ADJ
ejpam-4006	147	8	solution	solution	NOUN
ejpam-4006	147	9	of	of	ADP
ejpam-4006	147	10	the	the	DET
ejpam-4006	147	11	operator	operator	NOUN
ejpam-4006	147	12	(	(	PUNCT
ejpam-4006	147	13	�	�	PROPN
ejpam-4006	147	14	+	+	NOUN
ejpam-4006	147	15	m2)k	m2)k	NOUN
ejpam-4006	147	16	.	.	PUNCT
ejpam-4006	148	1	in	in	ADP
ejpam-4006	148	2	particular	particular	ADJ
ejpam-4006	148	3	,	,	PUNCT
ejpam-4006	148	4	for	for	ADP
ejpam-4006	148	5	m	m	PROPN
ejpam-4006	148	6	=	=	SYM
ejpam-4006	148	7	0	0	NUM
ejpam-4006	148	8	we	we	PRON
ejpam-4006	148	9	have	have	VERB
ejpam-4006	148	10	w2k(x	w2k(x	PROPN
ejpam-4006	148	11	,	,	PUNCT
ejpam-4006	148	12	m	m	VERB
ejpam-4006	148	13	=	=	NOUN
ejpam-4006	148	14	0	0	NUM
ejpam-4006	148	15	)	)	PUNCT
ejpam-4006	148	16	=	=	SYM
ejpam-4006	148	17	rh2k(x	rh2k(x	PROPN
ejpam-4006	148	18	)	)	PUNCT
ejpam-4006	148	19	,	,	PUNCT
ejpam-4006	149	1	where	where	SCONJ
ejpam-4006	149	2	w2k(x	w2k(x	PROPN
ejpam-4006	149	3	,	,	PUNCT
ejpam-4006	149	4	m	m	NOUN
ejpam-4006	149	5	)	)	PUNCT
ejpam-4006	149	6	=	=	PUNCT
ejpam-4006	150	1	+	+	PUNCT
ejpam-4006	150	2	∞∑	∞∑	NUM
ejpam-4006	150	3	r=0	r=0	PROPN
ejpam-4006	150	4	(	(	PUNCT
ejpam-4006	150	5	−k	−k	NOUN
ejpam-4006	150	6	r	r	NOUN
ejpam-4006	150	7	)	)	PUNCT
ejpam-4006	150	8	m2rrh2k+2r(x	m2rrh2k+2r(x	PROPN
ejpam-4006	150	9	)	)	PUNCT
ejpam-4006	150	10	,	,	PUNCT
ejpam-4006	150	11	(	(	PUNCT
ejpam-4006	150	12	27	27	NUM
ejpam-4006	150	13	)	)	PUNCT
ejpam-4006	150	14	rh2k+2r(x	rh2k+2r(x	NOUN
ejpam-4006	150	15	)	)	PUNCT
ejpam-4006	150	16	is	be	AUX
ejpam-4006	150	17	defined	define	VERB
ejpam-4006	150	18	by	by	ADP
ejpam-4006	150	19	(	(	PUNCT
ejpam-4006	150	20	23	23	NUM
ejpam-4006	150	21	)	)	PUNCT
ejpam-4006	150	22	.	.	PUNCT
ejpam-4006	151	1	proof	proof	NOUN
ejpam-4006	151	2	.	.	PUNCT
ejpam-4006	152	1	since	since	SCONJ
ejpam-4006	152	2	the	the	DET
ejpam-4006	152	3	operator	operator	NOUN
ejpam-4006	152	4	�	�	PROPN
ejpam-4006	152	5	defined	define	VERB
ejpam-4006	152	6	in	in	ADP
ejpam-4006	152	7	equation	equation	NOUN
ejpam-4006	152	8	(	(	PUNCT
ejpam-4006	152	9	9	9	NUM
ejpam-4006	152	10	)	)	PUNCT
ejpam-4006	152	11	is	be	AUX
ejpam-4006	152	12	a	a	DET
ejpam-4006	152	13	linearly	linearly	ADV
ejpam-4006	152	14	continuous	continuous	ADJ
ejpam-4006	152	15	and	and	CCONJ
ejpam-4006	152	16	have	have	VERB
ejpam-4006	152	17	1−	1−	NUM
ejpam-4006	152	18	1	1	NUM
ejpam-4006	152	19	mapping	mapping	NOUN
ejpam-4006	152	20	,	,	PUNCT
ejpam-4006	152	21	then	then	ADV
ejpam-4006	152	22	it	it	PRON
ejpam-4006	152	23	has	have	AUX
ejpam-4006	152	24	inverse	inverse	NOUN
ejpam-4006	152	25	.	.	PUNCT
ejpam-4006	153	1	from	from	ADP
ejpam-4006	153	2	lemma	lemma	PROPN
ejpam-4006	153	3	2	2	NUM
ejpam-4006	153	4	and	and	CCONJ
ejpam-4006	153	5	equation	equation	NOUN
ejpam-4006	153	6	(	(	PUNCT
ejpam-4006	153	7	27	27	NUM
ejpam-4006	153	8	)	)	PUNCT
ejpam-4006	153	9	we	we	PRON
ejpam-4006	153	10	obtain	obtain	VERB
ejpam-4006	153	11	w2k(x	w2k(x	PROPN
ejpam-4006	153	12	,	,	PUNCT
ejpam-4006	153	13	m	m	NOUN
ejpam-4006	153	14	)	)	PUNCT
ejpam-4006	153	15	=	=	PUNCT
ejpam-4006	154	1	+	+	PUNCT
ejpam-4006	154	2	∞∑	∞∑	NUM
ejpam-4006	154	3	r=0	r=0	PROPN
ejpam-4006	154	4	(	(	PUNCT
ejpam-4006	154	5	−k	−k	NOUN
ejpam-4006	154	6	r	r	NOUN
ejpam-4006	154	7	)	)	PUNCT
ejpam-4006	154	8	(	(	PUNCT
ejpam-4006	154	9	m2)r	m2)r	PROPN
ejpam-4006	154	10	�	�	PROPN
ejpam-4006	154	11	−k−rδ	−k−rδ	NOUN
ejpam-4006	154	12	=	=	SYM
ejpam-4006	154	13	(	(	PUNCT
ejpam-4006	154	14	�	�	PROPN
ejpam-4006	154	15	+	+	NOUN
ejpam-4006	154	16	m2)−kδ	m2)−kδ	NOUN
ejpam-4006	154	17	.	.	PUNCT
ejpam-4006	155	1	(	(	PUNCT
ejpam-4006	155	2	28	28	NUM
ejpam-4006	155	3	)	)	PUNCT
ejpam-4006	155	4	by	by	ADP
ejpam-4006	155	5	applying	apply	VERB
ejpam-4006	155	6	the	the	DET
ejpam-4006	155	7	operator	operator	NOUN
ejpam-4006	155	8	(	(	PUNCT
ejpam-4006	155	9	�	�	PROPN
ejpam-4006	155	10	+	+	NOUN
ejpam-4006	155	11	m2)k	m2)k	NOUN
ejpam-4006	155	12	to	to	ADP
ejpam-4006	155	13	both	both	DET
ejpam-4006	155	14	sides	side	NOUN
ejpam-4006	155	15	of	of	ADP
ejpam-4006	155	16	equation	equation	NOUN
ejpam-4006	155	17	(	(	PUNCT
ejpam-4006	155	18	28	28	NUM
ejpam-4006	155	19	)	)	PUNCT
ejpam-4006	155	20	,	,	PUNCT
ejpam-4006	155	21	we	we	PRON
ejpam-4006	155	22	obtain	obtain	VERB
ejpam-4006	155	23	(	(	PUNCT
ejpam-4006	155	24	�	�	PROPN
ejpam-4006	156	1	+	+	NOUN
ejpam-4006	156	2	m2)kw2k(x	m2)kw2k(x	PROPN
ejpam-4006	156	3	,	,	PUNCT
ejpam-4006	156	4	m	m	NOUN
ejpam-4006	156	5	)	)	PUNCT
ejpam-4006	157	1	=	=	SYM
ejpam-4006	157	2	(	(	PUNCT
ejpam-4006	157	3	�	�	PROPN
ejpam-4006	157	4	+	+	PROPN
ejpam-4006	157	5	m2)k	m2)k	PROPN
ejpam-4006	157	6	·	·	PUNCT
ejpam-4006	157	7	(	(	PUNCT
ejpam-4006	157	8	�	�	PROPN
ejpam-4006	157	9	+	+	NOUN
ejpam-4006	157	10	m2)−kδ	m2)−kδ	NOUN
ejpam-4006	157	11	.	.	PUNCT
ejpam-4006	158	1	therefore	therefore	ADV
ejpam-4006	158	2	,	,	PUNCT
ejpam-4006	158	3	(	(	PUNCT
ejpam-4006	158	4	�	�	PROPN
ejpam-4006	158	5	+	+	SYM
ejpam-4006	158	6	m2)kw2k(x	m2)kw2k(x	PROPN
ejpam-4006	158	7	,	,	PUNCT
ejpam-4006	158	8	m	m	NOUN
ejpam-4006	158	9	)	)	PUNCT
ejpam-4006	158	10	=	=	SYM
ejpam-4006	158	11	δ	δ	PROPN
ejpam-4006	158	12	.	.	PUNCT
ejpam-4006	159	1	since	since	SCONJ
ejpam-4006	159	2	w2k(x	w2k(x	PROPN
ejpam-4006	159	3	,	,	PUNCT
ejpam-4006	159	4	m	m	NOUN
ejpam-4006	159	5	)	)	PUNCT
ejpam-4006	159	6	=	=	SYM
ejpam-4006	159	7	(	(	PUNCT
ejpam-4006	159	8	−k	−k	NOUN
ejpam-4006	159	9	0	0	NUM
ejpam-4006	159	10	)	)	PUNCT
ejpam-4006	159	11	m2(0)rh2k+2(0)(x	m2(0)rh2k+2(0)(x	NOUN
ejpam-4006	159	12	)	)	PUNCT
ejpam-4006	160	1	+	+	PUNCT
ejpam-4006	161	1	+	+	ADJ
ejpam-4006	161	2	∞∑	∞∑	NUM
ejpam-4006	161	3	r=1	r=1	NOUN
ejpam-4006	161	4	(	(	PUNCT
ejpam-4006	161	5	−k	−k	NOUN
ejpam-4006	161	6	r	r	NOUN
ejpam-4006	161	7	)	)	PUNCT
ejpam-4006	161	8	m2rrh2k+2r(x	m2rrh2k+2r(x	PROPN
ejpam-4006	161	9	)	)	PUNCT
ejpam-4006	161	10	.	.	PUNCT
ejpam-4006	162	1	(	(	PUNCT
ejpam-4006	162	2	29	29	NUM
ejpam-4006	162	3	)	)	PUNCT
ejpam-4006	162	4	the	the	DET
ejpam-4006	162	5	second	second	ADJ
ejpam-4006	162	6	summand	summand	NOUN
ejpam-4006	162	7	of	of	ADP
ejpam-4006	162	8	the	the	DET
ejpam-4006	162	9	right	right	ADJ
ejpam-4006	162	10	-	-	PUNCT
ejpam-4006	162	11	hand	hand	NOUN
ejpam-4006	162	12	member	member	NOUN
ejpam-4006	162	13	of	of	ADP
ejpam-4006	162	14	(	(	PUNCT
ejpam-4006	162	15	29	29	NUM
ejpam-4006	162	16	)	)	PUNCT
ejpam-4006	162	17	vanishes	vanish	VERB
ejpam-4006	162	18	for	for	ADP
ejpam-4006	162	19	m	m	PROPN
ejpam-4006	162	20	=	=	SYM
ejpam-4006	162	21	0	0	PUNCT
ejpam-4006	163	1	and	and	CCONJ
ejpam-4006	163	2	then	then	ADV
ejpam-4006	163	3	,	,	PUNCT
ejpam-4006	163	4	we	we	PRON
ejpam-4006	163	5	have	have	VERB
ejpam-4006	163	6	w2k(x	w2k(x	PROPN
ejpam-4006	163	7	,	,	PUNCT
ejpam-4006	163	8	m	m	VERB
ejpam-4006	163	9	=	=	NOUN
ejpam-4006	163	10	0	0	NUM
ejpam-4006	163	11	)	)	PUNCT
ejpam-4006	163	12	=	=	SYM
ejpam-4006	163	13	rh2k(x	rh2k(x	PROPN
ejpam-4006	163	14	)	)	PUNCT
ejpam-4006	163	15	which	which	PRON
ejpam-4006	163	16	is	be	AUX
ejpam-4006	163	17	the	the	DET
ejpam-4006	163	18	fundamental	fundamental	ADJ
ejpam-4006	163	19	solution	solution	NOUN
ejpam-4006	163	20	of	of	ADP
ejpam-4006	163	21	the	the	DET
ejpam-4006	163	22	ultra	ultra	ADJ
ejpam-4006	163	23	hyperbolic	hyperbolic	ADJ
ejpam-4006	163	24	operator	operator	NOUN
ejpam-4006	163	25	�	�	PROPN
ejpam-4006	163	26	k	k	PROPN
ejpam-4006	163	27	.	.	PUNCT
ejpam-4006	164	1	lemma	lemma	PROPN
ejpam-4006	164	2	10	10	NUM
ejpam-4006	164	3	.	.	PUNCT
ejpam-4006	165	1	given	give	VERB
ejpam-4006	165	2	the	the	DET
ejpam-4006	165	3	equation	equation	NOUN
ejpam-4006	165	4	(	(	PUNCT
ejpam-4006	165	5	4+m2)ku(x	4+m2)ku(x	NUM
ejpam-4006	165	6	)	)	PUNCT
ejpam-4006	165	7	=	=	SYM
ejpam-4006	165	8	δ	δ	PROPN
ejpam-4006	165	9	for	for	ADP
ejpam-4006	165	10	x	x	PROPN
ejpam-4006	165	11	∈	∈	PROPN
ejpam-4006	165	12	rn	rn	PROPN
ejpam-4006	165	13	,	,	PUNCT
ejpam-4006	165	14	where	where	SCONJ
ejpam-4006	165	15	4	4	NUM
ejpam-4006	165	16	is	be	AUX
ejpam-4006	165	17	laplace	laplace	NOUN
ejpam-4006	165	18	operator	operator	NOUN
ejpam-4006	165	19	defined	define	VERB
ejpam-4006	165	20	by	by	ADP
ejpam-4006	165	21	(	(	PUNCT
ejpam-4006	165	22	10	10	NUM
ejpam-4006	165	23	)	)	PUNCT
ejpam-4006	165	24	.	.	PUNCT
ejpam-4006	166	1	then	then	ADV
ejpam-4006	166	2	u(x	u(x	VERB
ejpam-4006	166	3	)	)	PUNCT
ejpam-4006	166	4	=	=	SYM
ejpam-4006	166	5	y2k(x	y2k(x	PROPN
ejpam-4006	166	6	,	,	PUNCT
ejpam-4006	166	7	m	m	VERB
ejpam-4006	166	8	)	)	PUNCT
ejpam-4006	166	9	is	be	AUX
ejpam-4006	166	10	the	the	DET
ejpam-4006	166	11	fundamental	fundamental	ADJ
ejpam-4006	166	12	solution	solution	NOUN
ejpam-4006	166	13	of	of	ADP
ejpam-4006	166	14	the	the	DET
ejpam-4006	166	15	operator	operator	NOUN
ejpam-4006	166	16	(	(	PUNCT
ejpam-4006	166	17	4+m2)k	4+m2)k	NOUN
ejpam-4006	166	18	.	.	PUNCT
ejpam-4006	167	1	in	in	ADP
ejpam-4006	167	2	particular	particular	ADJ
ejpam-4006	167	3	,	,	PUNCT
ejpam-4006	167	4	for	for	ADP
ejpam-4006	167	5	m	m	PROPN
ejpam-4006	167	6	=	=	SYM
ejpam-4006	167	7	0	0	NUM
ejpam-4006	167	8	we	we	PRON
ejpam-4006	167	9	have	have	VERB
ejpam-4006	167	10	y2k(x	y2k(x	PROPN
ejpam-4006	167	11	,	,	PUNCT
ejpam-4006	167	12	m	m	VERB
ejpam-4006	167	13	=	=	NOUN
ejpam-4006	167	14	0	0	NUM
ejpam-4006	167	15	)	)	PUNCT
ejpam-4006	167	16	=	=	PRON
ejpam-4006	167	17	(	(	PUNCT
ejpam-4006	167	18	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	167	19	)	)	PUNCT
ejpam-4006	167	20	,	,	PUNCT
ejpam-4006	167	21	where	where	SCONJ
ejpam-4006	167	22	y2k(x	y2k(x	PROPN
ejpam-4006	167	23	,	,	PUNCT
ejpam-4006	167	24	m	m	NOUN
ejpam-4006	167	25	)	)	PUNCT
ejpam-4006	168	1	=	=	PUNCT
ejpam-4006	169	1	+	+	PUNCT
ejpam-4006	169	2	∞∑	∞∑	NUM
ejpam-4006	169	3	r=0	r=0	PROPN
ejpam-4006	169	4	(	(	PUNCT
ejpam-4006	169	5	−k	−k	NOUN
ejpam-4006	169	6	r	r	NOUN
ejpam-4006	169	7	)	)	PUNCT
ejpam-4006	169	8	m2r(−1)k+rre2k+2r(x	m2r(−1)k+rre2k+2r(x	PROPN
ejpam-4006	169	9	)	)	PUNCT
ejpam-4006	169	10	,	,	PUNCT
ejpam-4006	169	11	(	(	PUNCT
ejpam-4006	169	12	30	30	X
ejpam-4006	169	13	)	)	PUNCT
ejpam-4006	169	14	re2k+2r(x	re2k+2r(x	PROPN
ejpam-4006	169	15	)	)	PUNCT
ejpam-4006	169	16	is	be	AUX
ejpam-4006	169	17	defined	define	VERB
ejpam-4006	169	18	by	by	ADP
ejpam-4006	169	19	(	(	PUNCT
ejpam-4006	169	20	22	22	NUM
ejpam-4006	169	21	)	)	PUNCT
ejpam-4006	169	22	.	.	PUNCT
ejpam-4006	170	1	s.	s.	PROPN
ejpam-4006	170	2	bupasiri	bupasiri	PROPN
ejpam-4006	170	3	/	/	SYM
ejpam-4006	170	4	eur	eur	PROPN
ejpam-4006	170	5	.	.	PUNCT
ejpam-4006	171	1	j.	j.	PROPN
ejpam-4006	171	2	pure	pure	PROPN
ejpam-4006	171	3	appl	appl	PROPN
ejpam-4006	171	4	.	.	PROPN
ejpam-4006	171	5	math	math	PROPN
ejpam-4006	171	6	,	,	PUNCT
ejpam-4006	171	7	14	14	NUM
ejpam-4006	171	8	(	(	PUNCT
ejpam-4006	171	9	3	3	NUM
ejpam-4006	171	10	)	)	PUNCT
ejpam-4006	171	11	(	(	PUNCT
ejpam-4006	171	12	2021	2021	NUM
ejpam-4006	171	13	)	)	PUNCT
ejpam-4006	171	14	,	,	PUNCT
ejpam-4006	171	15	881	881	NUM
ejpam-4006	171	16	-	-	SYM
ejpam-4006	171	17	894	894	NUM
ejpam-4006	171	18	888	888	NUM
ejpam-4006	171	19	proof	proof	NOUN
ejpam-4006	171	20	.	.	PUNCT
ejpam-4006	172	1	since	since	SCONJ
ejpam-4006	172	2	the	the	DET
ejpam-4006	172	3	operator	operator	NOUN
ejpam-4006	172	4	4	4	NUM
ejpam-4006	172	5	defined	define	VERB
ejpam-4006	172	6	by	by	ADP
ejpam-4006	172	7	equation	equation	NOUN
ejpam-4006	172	8	(	(	PUNCT
ejpam-4006	172	9	10	10	NUM
ejpam-4006	172	10	)	)	PUNCT
ejpam-4006	172	11	is	be	AUX
ejpam-4006	172	12	a	a	DET
ejpam-4006	172	13	linearly	linearly	ADV
ejpam-4006	172	14	continuous	continuous	ADJ
ejpam-4006	172	15	and	and	CCONJ
ejpam-4006	172	16	have	have	VERB
ejpam-4006	172	17	1−	1−	NUM
ejpam-4006	172	18	1	1	NUM
ejpam-4006	172	19	mapping	mapping	NOUN
ejpam-4006	172	20	,	,	PUNCT
ejpam-4006	172	21	then	then	ADV
ejpam-4006	172	22	it	it	PRON
ejpam-4006	172	23	has	have	AUX
ejpam-4006	172	24	inverse	inverse	NOUN
ejpam-4006	172	25	.	.	PUNCT
ejpam-4006	173	1	from	from	ADP
ejpam-4006	173	2	lemma	lemma	PROPN
ejpam-4006	173	3	1	1	NUM
ejpam-4006	173	4	and	and	CCONJ
ejpam-4006	173	5	equation	equation	NOUN
ejpam-4006	173	6	(	(	PUNCT
ejpam-4006	173	7	30	30	NUM
ejpam-4006	173	8	)	)	PUNCT
ejpam-4006	173	9	,	,	PUNCT
ejpam-4006	173	10	we	we	PRON
ejpam-4006	173	11	obtain	obtain	VERB
ejpam-4006	173	12	y2k(x	y2k(x	PROPN
ejpam-4006	173	13	,	,	PUNCT
ejpam-4006	173	14	m	m	NOUN
ejpam-4006	173	15	)	)	PUNCT
ejpam-4006	173	16	=	=	PUNCT
ejpam-4006	174	1	+	+	PUNCT
ejpam-4006	174	2	∞∑	∞∑	NUM
ejpam-4006	174	3	r=0	r=0	PROPN
ejpam-4006	174	4	(	(	PUNCT
ejpam-4006	174	5	−k	−k	NOUN
ejpam-4006	174	6	r	r	NOUN
ejpam-4006	174	7	)	)	PUNCT
ejpam-4006	174	8	(	(	PUNCT
ejpam-4006	174	9	m2)r	m2)r	INTJ
ejpam-4006	174	10	4−k−r	4−k−r	VERB
ejpam-4006	174	11	δ	δ	PROPN
ejpam-4006	174	12	=	=	PUNCT
ejpam-4006	174	13	(	(	PUNCT
ejpam-4006	174	14	4+m2)−kδ	4+m2)−kδ	NOUN
ejpam-4006	174	15	.	.	PUNCT
ejpam-4006	175	1	(	(	PUNCT
ejpam-4006	175	2	31	31	NUM
ejpam-4006	175	3	)	)	PUNCT
ejpam-4006	175	4	by	by	ADP
ejpam-4006	175	5	applying	apply	VERB
ejpam-4006	175	6	the	the	DET
ejpam-4006	175	7	operator	operator	NOUN
ejpam-4006	175	8	(	(	PUNCT
ejpam-4006	175	9	4+m2)k	4+m2)k	NUM
ejpam-4006	175	10	to	to	ADP
ejpam-4006	175	11	both	both	DET
ejpam-4006	175	12	sides	side	NOUN
ejpam-4006	175	13	of	of	ADP
ejpam-4006	175	14	equation	equation	NOUN
ejpam-4006	175	15	(	(	PUNCT
ejpam-4006	175	16	31	31	NUM
ejpam-4006	175	17	)	)	PUNCT
ejpam-4006	175	18	,	,	PUNCT
ejpam-4006	175	19	we	we	PRON
ejpam-4006	175	20	obtain	obtain	VERB
ejpam-4006	175	21	(	(	PUNCT
ejpam-4006	175	22	4+m2)ky2k(x	4+m2)ky2k(x	NUM
ejpam-4006	175	23	,	,	PUNCT
ejpam-4006	175	24	m	m	NOUN
ejpam-4006	175	25	)	)	PUNCT
ejpam-4006	175	26	=	=	SYM
ejpam-4006	175	27	(	(	PUNCT
ejpam-4006	175	28	4+m2)k	4+m2)k	X
ejpam-4006	175	29	·	·	PUNCT
ejpam-4006	175	30	(	(	PUNCT
ejpam-4006	175	31	4+m2)−kδ	4+m2)−kδ	NOUN
ejpam-4006	175	32	.	.	PUNCT
ejpam-4006	176	1	therefore	therefore	ADV
ejpam-4006	176	2	,	,	PUNCT
ejpam-4006	176	3	(	(	PUNCT
ejpam-4006	176	4	4+m2)ky2k(x	4+m2)ky2k(x	NUM
ejpam-4006	176	5	,	,	PUNCT
ejpam-4006	176	6	m	m	NOUN
ejpam-4006	176	7	)	)	PUNCT
ejpam-4006	176	8	=	=	SYM
ejpam-4006	176	9	δ	δ	PROPN
ejpam-4006	176	10	.	.	PUNCT
ejpam-4006	176	11	since	since	SCONJ
ejpam-4006	176	12	y2k(x	y2k(x	PROPN
ejpam-4006	176	13	,	,	PUNCT
ejpam-4006	176	14	m	m	NOUN
ejpam-4006	176	15	)	)	PUNCT
ejpam-4006	176	16	=	=	SYM
ejpam-4006	176	17	(	(	PUNCT
ejpam-4006	176	18	−k	−k	NOUN
ejpam-4006	176	19	0	0	NUM
ejpam-4006	176	20	)	)	PUNCT
ejpam-4006	176	21	m2(0)(−1)kre2k+2(0)(x	m2(0)(−1)kre2k+2(0)(x	NOUN
ejpam-4006	176	22	)	)	PUNCT
ejpam-4006	177	1	+	+	PUNCT
ejpam-4006	178	1	+	+	ADJ
ejpam-4006	178	2	∞∑	∞∑	NUM
ejpam-4006	178	3	r=1	r=1	NOUN
ejpam-4006	178	4	(	(	PUNCT
ejpam-4006	178	5	−k	−k	NOUN
ejpam-4006	178	6	r	r	NOUN
ejpam-4006	178	7	)	)	PUNCT
ejpam-4006	178	8	m2r(−1)kre2k+2r(x	m2r(−1)kre2k+2r(x	NOUN
ejpam-4006	178	9	)	)	PUNCT
ejpam-4006	178	10	.	.	PUNCT
ejpam-4006	179	1	(	(	PUNCT
ejpam-4006	179	2	32	32	NUM
ejpam-4006	179	3	)	)	PUNCT
ejpam-4006	179	4	the	the	DET
ejpam-4006	179	5	second	second	ADJ
ejpam-4006	179	6	summand	summand	NOUN
ejpam-4006	179	7	of	of	ADP
ejpam-4006	179	8	the	the	DET
ejpam-4006	179	9	right	right	ADJ
ejpam-4006	179	10	-	-	PUNCT
ejpam-4006	179	11	hand	hand	NOUN
ejpam-4006	179	12	member	member	NOUN
ejpam-4006	179	13	of	of	ADP
ejpam-4006	179	14	(	(	PUNCT
ejpam-4006	179	15	32	32	NUM
ejpam-4006	179	16	)	)	PUNCT
ejpam-4006	179	17	vanishes	vanish	VERB
ejpam-4006	179	18	for	for	ADP
ejpam-4006	179	19	m	m	PROPN
ejpam-4006	179	20	=	=	SYM
ejpam-4006	179	21	0	0	PUNCT
ejpam-4006	180	1	and	and	CCONJ
ejpam-4006	180	2	then	then	ADV
ejpam-4006	180	3	,	,	PUNCT
ejpam-4006	180	4	we	we	PRON
ejpam-4006	180	5	have	have	VERB
ejpam-4006	180	6	y2k(x	y2k(x	PROPN
ejpam-4006	180	7	,	,	PUNCT
ejpam-4006	180	8	m	m	VERB
ejpam-4006	180	9	=	=	NOUN
ejpam-4006	180	10	0	0	NUM
ejpam-4006	180	11	)	)	PUNCT
ejpam-4006	180	12	=	=	PRON
ejpam-4006	180	13	(	(	PUNCT
ejpam-4006	180	14	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	180	15	)	)	PUNCT
ejpam-4006	180	16	which	which	PRON
ejpam-4006	180	17	is	be	AUX
ejpam-4006	180	18	the	the	DET
ejpam-4006	180	19	fundamental	fundamental	ADJ
ejpam-4006	180	20	solution	solution	NOUN
ejpam-4006	180	21	of	of	ADP
ejpam-4006	180	22	the	the	DET
ejpam-4006	180	23	laplace	laplace	NOUN
ejpam-4006	180	24	operator	operator	NOUN
ejpam-4006	180	25	4k	4k	NOUN
ejpam-4006	180	26	.	.	PUNCT
ejpam-4006	181	1	lemma	lemma	PROPN
ejpam-4006	181	2	11	11	NUM
ejpam-4006	181	3	.	.	PUNCT
ejpam-4006	182	1	given	give	VERB
ejpam-4006	182	2	the	the	DET
ejpam-4006	182	3	equation	equation	NOUN
ejpam-4006	182	4	(	(	PUNCT
ejpam-4006	182	5	l1	l1	PROPN
ejpam-4006	182	6	+	+	X
ejpam-4006	182	7	m2)ku(x	m2)ku(x	X
ejpam-4006	182	8	)	)	PUNCT
ejpam-4006	182	9	=	=	SYM
ejpam-4006	182	10	δ	δ	PROPN
ejpam-4006	182	11	for	for	ADP
ejpam-4006	182	12	x	x	PROPN
ejpam-4006	182	13	∈	∈	PROPN
ejpam-4006	182	14	rn	rn	PROPN
ejpam-4006	182	15	,	,	PUNCT
ejpam-4006	182	16	where	where	SCONJ
ejpam-4006	182	17	l1	l1	PROPN
ejpam-4006	182	18	is	be	AUX
ejpam-4006	182	19	the	the	DET
ejpam-4006	182	20	operator	operator	NOUN
ejpam-4006	182	21	defined	define	VERB
ejpam-4006	182	22	by	by	ADP
ejpam-4006	182	23	(	(	PUNCT
ejpam-4006	182	24	12	12	NUM
ejpam-4006	182	25	)	)	PUNCT
ejpam-4006	182	26	.	.	PUNCT
ejpam-4006	183	1	then	then	ADV
ejpam-4006	183	2	u(x	u(x	VERB
ejpam-4006	183	3	)	)	PUNCT
ejpam-4006	183	4	=	=	SYM
ejpam-4006	183	5	m2k(x	m2k(x	PROPN
ejpam-4006	183	6	,	,	PUNCT
ejpam-4006	183	7	m	m	PROPN
ejpam-4006	183	8	)	)	PUNCT
ejpam-4006	183	9	is	be	AUX
ejpam-4006	183	10	the	the	DET
ejpam-4006	183	11	fundamental	fundamental	ADJ
ejpam-4006	183	12	solution	solution	NOUN
ejpam-4006	183	13	of	of	ADP
ejpam-4006	183	14	the	the	DET
ejpam-4006	183	15	operator	operator	NOUN
ejpam-4006	183	16	(	(	PUNCT
ejpam-4006	183	17	l1	l1	PROPN
ejpam-4006	183	18	+	+	PROPN
ejpam-4006	183	19	m2)k	m2)k	PROPN
ejpam-4006	183	20	.	.	PUNCT
ejpam-4006	184	1	in	in	ADP
ejpam-4006	184	2	particular	particular	ADJ
ejpam-4006	184	3	,	,	PUNCT
ejpam-4006	184	4	for	for	ADP
ejpam-4006	184	5	m	m	PROPN
ejpam-4006	184	6	=	=	SYM
ejpam-4006	184	7	0	0	NUM
ejpam-4006	184	8	we	we	PRON
ejpam-4006	184	9	have	have	VERB
ejpam-4006	184	10	m2k(x	m2k(x	PROPN
ejpam-4006	184	11	,	,	PUNCT
ejpam-4006	184	12	m	m	VERB
ejpam-4006	184	13	=	=	NOUN
ejpam-4006	184	14	0	0	NUM
ejpam-4006	184	15	)	)	PUNCT
ejpam-4006	184	16	=	=	PRON
ejpam-4006	184	17	(	(	PUNCT
ejpam-4006	184	18	−1)k(−i	−1)k(−i	NOUN
ejpam-4006	184	19	)	)	PUNCT
ejpam-4006	184	20	q	q	NOUN
ejpam-4006	184	21	2s2k(x	2s2k(x	NOUN
ejpam-4006	184	22	)	)	PUNCT
ejpam-4006	185	1	where	where	SCONJ
ejpam-4006	185	2	m2k(x	m2k(x	PROPN
ejpam-4006	185	3	,	,	PUNCT
ejpam-4006	185	4	m	m	NOUN
ejpam-4006	185	5	)	)	PUNCT
ejpam-4006	186	1	=	=	PUNCT
ejpam-4006	187	1	+	+	PUNCT
ejpam-4006	187	2	∞∑	∞∑	NUM
ejpam-4006	187	3	r=0	r=0	PROPN
ejpam-4006	187	4	(	(	PUNCT
ejpam-4006	187	5	−k	−k	NOUN
ejpam-4006	187	6	r	r	NOUN
ejpam-4006	187	7	)	)	PUNCT
ejpam-4006	187	8	m2r(−1)k+r(−i	m2r(−1)k+r(−i	NOUN
ejpam-4006	187	9	)	)	PUNCT
ejpam-4006	187	10	q	q	PROPN
ejpam-4006	187	11	2s2k+2r(x	2s2k+2r(x	PROPN
ejpam-4006	187	12	)	)	PUNCT
ejpam-4006	187	13	,	,	PUNCT
ejpam-4006	187	14	(	(	PUNCT
ejpam-4006	187	15	33	33	NUM
ejpam-4006	187	16	)	)	PUNCT
ejpam-4006	187	17	s2k+2r(x	s2k+2r(x	NOUN
ejpam-4006	187	18	)	)	PUNCT
ejpam-4006	187	19	is	be	AUX
ejpam-4006	187	20	defined	define	VERB
ejpam-4006	187	21	by	by	ADP
ejpam-4006	187	22	(	(	PUNCT
ejpam-4006	187	23	25	25	NUM
ejpam-4006	187	24	)	)	PUNCT
ejpam-4006	187	25	.	.	PUNCT
ejpam-4006	188	1	proof	proof	NOUN
ejpam-4006	188	2	.	.	PUNCT
ejpam-4006	189	1	since	since	SCONJ
ejpam-4006	189	2	the	the	DET
ejpam-4006	189	3	operator	operator	NOUN
ejpam-4006	189	4	l1	l1	PROPN
ejpam-4006	189	5	defined	define	VERB
ejpam-4006	189	6	in	in	ADP
ejpam-4006	189	7	equation	equation	NOUN
ejpam-4006	189	8	(	(	PUNCT
ejpam-4006	189	9	12	12	NUM
ejpam-4006	189	10	)	)	PUNCT
ejpam-4006	189	11	is	be	AUX
ejpam-4006	189	12	a	a	DET
ejpam-4006	189	13	linearly	linearly	ADV
ejpam-4006	189	14	continuous	continuous	ADJ
ejpam-4006	189	15	and	and	CCONJ
ejpam-4006	189	16	have	have	VERB
ejpam-4006	189	17	1−	1−	NUM
ejpam-4006	189	18	1	1	NUM
ejpam-4006	189	19	mapping	mapping	NOUN
ejpam-4006	189	20	,	,	PUNCT
ejpam-4006	189	21	then	then	ADV
ejpam-4006	189	22	it	it	PRON
ejpam-4006	189	23	has	have	AUX
ejpam-4006	189	24	inverse	inverse	NOUN
ejpam-4006	189	25	.	.	PUNCT
ejpam-4006	190	1	from	from	ADP
ejpam-4006	190	2	lemma	lemma	PROPN
ejpam-4006	190	3	4	4	NUM
ejpam-4006	190	4	and	and	CCONJ
ejpam-4006	190	5	equation	equation	NOUN
ejpam-4006	190	6	(	(	PUNCT
ejpam-4006	190	7	33	33	NUM
ejpam-4006	190	8	)	)	PUNCT
ejpam-4006	190	9	,	,	PUNCT
ejpam-4006	190	10	we	we	PRON
ejpam-4006	190	11	obtain	obtain	VERB
ejpam-4006	190	12	m2k(x	m2k(x	PROPN
ejpam-4006	190	13	,	,	PUNCT
ejpam-4006	190	14	m	m	NOUN
ejpam-4006	190	15	)	)	PUNCT
ejpam-4006	190	16	=	=	PUNCT
ejpam-4006	191	1	+	+	PUNCT
ejpam-4006	191	2	∞∑	∞∑	NUM
ejpam-4006	191	3	r=0	r=0	PROPN
ejpam-4006	191	4	(	(	PUNCT
ejpam-4006	191	5	−k	−k	NOUN
ejpam-4006	191	6	r	r	NOUN
ejpam-4006	191	7	)	)	PUNCT
ejpam-4006	191	8	(	(	PUNCT
ejpam-4006	191	9	m2)rl−k−r1	m2)rl−k−r1	PROPN
ejpam-4006	191	10	δ	δ	PROPN
ejpam-4006	191	11	=	=	PUNCT
ejpam-4006	191	12	(	(	PUNCT
ejpam-4006	191	13	l1	l1	PROPN
ejpam-4006	191	14	+	+	PROPN
ejpam-4006	191	15	m2)−kδ	m2)−kδ	PROPN
ejpam-4006	191	16	.	.	PUNCT
ejpam-4006	192	1	(	(	PUNCT
ejpam-4006	192	2	34	34	NUM
ejpam-4006	192	3	)	)	PUNCT
ejpam-4006	192	4	by	by	ADP
ejpam-4006	192	5	applying	apply	VERB
ejpam-4006	192	6	the	the	DET
ejpam-4006	192	7	operator	operator	NOUN
ejpam-4006	192	8	(	(	PUNCT
ejpam-4006	192	9	l1	l1	PROPN
ejpam-4006	192	10	+	+	PROPN
ejpam-4006	192	11	m2)k	m2)k	PROPN
ejpam-4006	192	12	to	to	ADP
ejpam-4006	192	13	both	both	DET
ejpam-4006	192	14	sides	side	NOUN
ejpam-4006	192	15	of	of	ADP
ejpam-4006	192	16	equation	equation	NOUN
ejpam-4006	192	17	(	(	PUNCT
ejpam-4006	192	18	34	34	NUM
ejpam-4006	192	19	)	)	PUNCT
ejpam-4006	192	20	,	,	PUNCT
ejpam-4006	192	21	we	we	PRON
ejpam-4006	192	22	obtain	obtain	VERB
ejpam-4006	192	23	(	(	PUNCT
ejpam-4006	192	24	l1	l1	PROPN
ejpam-4006	192	25	+	+	PROPN
ejpam-4006	192	26	m2)km2k(x	m2)km2k(x	PROPN
ejpam-4006	192	27	,	,	PUNCT
ejpam-4006	192	28	m	m	NOUN
ejpam-4006	192	29	)	)	PUNCT
ejpam-4006	192	30	=	=	SYM
ejpam-4006	192	31	(	(	PUNCT
ejpam-4006	192	32	l1	l1	PROPN
ejpam-4006	192	33	+	+	PROPN
ejpam-4006	192	34	m2)k	m2)k	PROPN
ejpam-4006	192	35	·	·	PUNCT
ejpam-4006	192	36	(	(	PUNCT
ejpam-4006	192	37	l1	l1	PROPN
ejpam-4006	192	38	+	+	PROPN
ejpam-4006	192	39	m2)−kδ	m2)−kδ	PROPN
ejpam-4006	192	40	.	.	PUNCT
ejpam-4006	193	1	therefore	therefore	ADV
ejpam-4006	193	2	,	,	PUNCT
ejpam-4006	193	3	(	(	PUNCT
ejpam-4006	193	4	l1	l1	PROPN
ejpam-4006	193	5	+	+	PROPN
ejpam-4006	193	6	m2)km2k(x	m2)km2k(x	PROPN
ejpam-4006	193	7	,	,	PUNCT
ejpam-4006	193	8	m	m	NOUN
ejpam-4006	193	9	)	)	PUNCT
ejpam-4006	193	10	=	=	SYM
ejpam-4006	193	11	δ	δ	PROPN
ejpam-4006	193	12	.	.	PUNCT
ejpam-4006	193	13	s.	s.	PROPN
ejpam-4006	193	14	bupasiri	bupasiri	PROPN
ejpam-4006	193	15	/	/	SYM
ejpam-4006	193	16	eur	eur	PROPN
ejpam-4006	193	17	.	.	PUNCT
ejpam-4006	194	1	j.	j.	PROPN
ejpam-4006	194	2	pure	pure	PROPN
ejpam-4006	194	3	appl	appl	PROPN
ejpam-4006	194	4	.	.	PROPN
ejpam-4006	194	5	math	math	PROPN
ejpam-4006	194	6	,	,	PUNCT
ejpam-4006	194	7	14	14	NUM
ejpam-4006	194	8	(	(	PUNCT
ejpam-4006	194	9	3	3	NUM
ejpam-4006	194	10	)	)	PUNCT
ejpam-4006	194	11	(	(	PUNCT
ejpam-4006	194	12	2021	2021	NUM
ejpam-4006	194	13	)	)	PUNCT
ejpam-4006	194	14	,	,	PUNCT
ejpam-4006	194	15	881	881	NUM
ejpam-4006	194	16	-	-	SYM
ejpam-4006	194	17	894	894	NUM
ejpam-4006	194	18	889	889	NUM
ejpam-4006	194	19	since	since	SCONJ
ejpam-4006	194	20	m2k(x	m2k(x	PROPN
ejpam-4006	194	21	,	,	PUNCT
ejpam-4006	194	22	m	m	NOUN
ejpam-4006	194	23	)	)	PUNCT
ejpam-4006	194	24	=	=	SYM
ejpam-4006	194	25	(	(	PUNCT
ejpam-4006	194	26	−k	−k	NOUN
ejpam-4006	194	27	0	0	NUM
ejpam-4006	194	28	)	)	PUNCT
ejpam-4006	194	29	m2(0)(−1)k+0(−i	m2(0)(−1)k+0(−i	PROPN
ejpam-4006	194	30	)	)	PUNCT
ejpam-4006	194	31	q	q	NOUN
ejpam-4006	194	32	2s2k+2(0)(x	2s2k+2(0)(x	NUM
ejpam-4006	194	33	)	)	PUNCT
ejpam-4006	195	1	+	+	PUNCT
ejpam-4006	196	1	+	+	PUNCT
ejpam-4006	196	2	∞∑	∞∑	NUM
ejpam-4006	196	3	r=1	r=1	NOUN
ejpam-4006	196	4	(	(	PUNCT
ejpam-4006	196	5	−k	−k	NOUN
ejpam-4006	196	6	r	r	NOUN
ejpam-4006	196	7	)	)	PUNCT
ejpam-4006	196	8	m2r(−1)k+r(−i	m2r(−1)k+r(−i	NOUN
ejpam-4006	196	9	)	)	PUNCT
ejpam-4006	196	10	q	q	PROPN
ejpam-4006	196	11	2s2k+2r(x	2s2k+2r(x	PROPN
ejpam-4006	196	12	)	)	PUNCT
ejpam-4006	196	13	.	.	PUNCT
ejpam-4006	197	1	(	(	PUNCT
ejpam-4006	197	2	35	35	NUM
ejpam-4006	197	3	)	)	PUNCT
ejpam-4006	197	4	the	the	DET
ejpam-4006	197	5	second	second	ADJ
ejpam-4006	197	6	summand	summand	NOUN
ejpam-4006	197	7	of	of	ADP
ejpam-4006	197	8	the	the	DET
ejpam-4006	197	9	right	right	ADJ
ejpam-4006	197	10	-	-	PUNCT
ejpam-4006	197	11	hand	hand	NOUN
ejpam-4006	197	12	member	member	NOUN
ejpam-4006	197	13	of	of	ADP
ejpam-4006	197	14	(	(	PUNCT
ejpam-4006	197	15	35	35	NUM
ejpam-4006	197	16	)	)	PUNCT
ejpam-4006	197	17	vanishes	vanish	VERB
ejpam-4006	197	18	for	for	ADP
ejpam-4006	197	19	m	m	PROPN
ejpam-4006	197	20	=	=	SYM
ejpam-4006	197	21	0	0	PUNCT
ejpam-4006	198	1	and	and	CCONJ
ejpam-4006	198	2	then	then	ADV
ejpam-4006	198	3	,	,	PUNCT
ejpam-4006	198	4	we	we	PRON
ejpam-4006	198	5	have	have	VERB
ejpam-4006	198	6	m2k(x	m2k(x	PROPN
ejpam-4006	198	7	,	,	PUNCT
ejpam-4006	198	8	m	m	VERB
ejpam-4006	198	9	=	=	NOUN
ejpam-4006	198	10	0	0	NUM
ejpam-4006	198	11	)	)	PUNCT
ejpam-4006	198	12	=	=	PRON
ejpam-4006	198	13	(	(	PUNCT
ejpam-4006	198	14	−1)k(−i	−1)k(−i	NOUN
ejpam-4006	198	15	)	)	PUNCT
ejpam-4006	198	16	q	q	NOUN
ejpam-4006	198	17	2s2k(x	2s2k(x	NOUN
ejpam-4006	198	18	)	)	PUNCT
ejpam-4006	198	19	which	which	PRON
ejpam-4006	198	20	is	be	AUX
ejpam-4006	198	21	the	the	DET
ejpam-4006	198	22	fundamental	fundamental	ADJ
ejpam-4006	198	23	solution	solution	NOUN
ejpam-4006	198	24	of	of	ADP
ejpam-4006	198	25	the	the	DET
ejpam-4006	198	26	operator	operator	NOUN
ejpam-4006	198	27	lk1	lk1	NOUN
ejpam-4006	198	28	.	.	PUNCT
ejpam-4006	199	1	lemma	lemma	PROPN
ejpam-4006	199	2	12	12	NUM
ejpam-4006	199	3	.	.	PUNCT
ejpam-4006	200	1	given	give	VERB
ejpam-4006	200	2	the	the	DET
ejpam-4006	200	3	equation	equation	NOUN
ejpam-4006	200	4	(	(	PUNCT
ejpam-4006	200	5	l2	l2	VERB
ejpam-4006	200	6	+	+	CCONJ
ejpam-4006	200	7	m2)ku(x	m2)ku(x	X
ejpam-4006	200	8	)	)	PUNCT
ejpam-4006	200	9	=	=	SYM
ejpam-4006	200	10	δ	δ	PROPN
ejpam-4006	200	11	for	for	ADP
ejpam-4006	200	12	x	x	PROPN
ejpam-4006	200	13	∈	∈	PROPN
ejpam-4006	200	14	rn	rn	PROPN
ejpam-4006	200	15	,	,	PUNCT
ejpam-4006	200	16	where	where	SCONJ
ejpam-4006	200	17	l2	l2	NOUN
ejpam-4006	200	18	is	be	AUX
ejpam-4006	200	19	the	the	DET
ejpam-4006	200	20	operator	operator	NOUN
ejpam-4006	200	21	defined	define	VERB
ejpam-4006	200	22	by	by	ADP
ejpam-4006	200	23	(	(	PUNCT
ejpam-4006	200	24	13	13	NUM
ejpam-4006	200	25	)	)	PUNCT
ejpam-4006	200	26	.	.	PUNCT
ejpam-4006	201	1	then	then	ADV
ejpam-4006	201	2	u(x	u(x	VERB
ejpam-4006	201	3	)	)	PUNCT
ejpam-4006	201	4	=	=	SYM
ejpam-4006	201	5	n2k(x	n2k(x	PROPN
ejpam-4006	201	6	,	,	PUNCT
ejpam-4006	201	7	m	m	NOUN
ejpam-4006	201	8	)	)	PUNCT
ejpam-4006	201	9	is	be	AUX
ejpam-4006	201	10	the	the	DET
ejpam-4006	201	11	fundamental	fundamental	ADJ
ejpam-4006	201	12	solution	solution	NOUN
ejpam-4006	201	13	of	of	ADP
ejpam-4006	201	14	the	the	DET
ejpam-4006	201	15	operator	operator	NOUN
ejpam-4006	201	16	(	(	PUNCT
ejpam-4006	201	17	l2	l2	NOUN
ejpam-4006	201	18	+	+	NOUN
ejpam-4006	201	19	m2)k	m2)k	NOUN
ejpam-4006	201	20	.	.	PUNCT
ejpam-4006	202	1	in	in	ADP
ejpam-4006	202	2	particular	particular	ADJ
ejpam-4006	202	3	,	,	PUNCT
ejpam-4006	202	4	for	for	ADP
ejpam-4006	202	5	m	m	PROPN
ejpam-4006	202	6	=	=	SYM
ejpam-4006	202	7	0	0	NUM
ejpam-4006	202	8	we	we	PRON
ejpam-4006	202	9	have	have	VERB
ejpam-4006	202	10	n2k(x	n2k(x	NOUN
ejpam-4006	202	11	,	,	PUNCT
ejpam-4006	202	12	m	m	VERB
ejpam-4006	202	13	=	=	NOUN
ejpam-4006	202	14	0	0	NUM
ejpam-4006	202	15	)	)	PUNCT
ejpam-4006	202	16	=	=	PRON
ejpam-4006	202	17	(	(	PUNCT
ejpam-4006	202	18	−1)k(i	−1)k(i	PROPN
ejpam-4006	202	19	)	)	PUNCT
ejpam-4006	202	20	q	q	NOUN
ejpam-4006	202	21	2t2k(x	2t2k(x	PROPN
ejpam-4006	202	22	)	)	PUNCT
ejpam-4006	202	23	,	,	PUNCT
ejpam-4006	202	24	where	where	SCONJ
ejpam-4006	202	25	n2k(x	n2k(x	PROPN
ejpam-4006	202	26	,	,	PUNCT
ejpam-4006	202	27	m	m	NOUN
ejpam-4006	202	28	)	)	PUNCT
ejpam-4006	203	1	=	=	PUNCT
ejpam-4006	204	1	+	+	PUNCT
ejpam-4006	204	2	∞∑	∞∑	NUM
ejpam-4006	204	3	r=0	r=0	PROPN
ejpam-4006	204	4	(	(	PUNCT
ejpam-4006	204	5	−k	−k	NOUN
ejpam-4006	204	6	r	r	NOUN
ejpam-4006	204	7	)	)	PUNCT
ejpam-4006	204	8	m2r(−1)k+r(i	m2r(−1)k+r(i	PROPN
ejpam-4006	204	9	)	)	PUNCT
ejpam-4006	204	10	q	q	PROPN
ejpam-4006	204	11	2t2k+2r(x	2t2k+2r(x	NUM
ejpam-4006	204	12	)	)	PUNCT
ejpam-4006	204	13	,	,	PUNCT
ejpam-4006	204	14	(	(	PUNCT
ejpam-4006	204	15	36	36	NUM
ejpam-4006	204	16	)	)	PUNCT
ejpam-4006	204	17	t2k+2r(x	t2k+2r(x	VERB
ejpam-4006	204	18	)	)	PUNCT
ejpam-4006	204	19	is	be	AUX
ejpam-4006	204	20	defined	define	VERB
ejpam-4006	204	21	by	by	ADP
ejpam-4006	204	22	(	(	PUNCT
ejpam-4006	204	23	26	26	NUM
ejpam-4006	204	24	)	)	PUNCT
ejpam-4006	204	25	.	.	PUNCT
ejpam-4006	205	1	proof	proof	NOUN
ejpam-4006	205	2	.	.	PUNCT
ejpam-4006	206	1	since	since	SCONJ
ejpam-4006	206	2	the	the	DET
ejpam-4006	206	3	operator	operator	NOUN
ejpam-4006	206	4	l2	l2	NOUN
ejpam-4006	206	5	defined	define	VERB
ejpam-4006	206	6	in	in	ADP
ejpam-4006	206	7	equation	equation	NOUN
ejpam-4006	206	8	(	(	PUNCT
ejpam-4006	206	9	13	13	NUM
ejpam-4006	206	10	)	)	PUNCT
ejpam-4006	206	11	is	be	AUX
ejpam-4006	206	12	a	a	DET
ejpam-4006	206	13	linearly	linearly	ADV
ejpam-4006	206	14	continuous	continuous	ADJ
ejpam-4006	206	15	and	and	CCONJ
ejpam-4006	206	16	have	have	VERB
ejpam-4006	206	17	1−	1−	NUM
ejpam-4006	206	18	1	1	NUM
ejpam-4006	206	19	mapping	mapping	NOUN
ejpam-4006	206	20	,	,	PUNCT
ejpam-4006	206	21	then	then	ADV
ejpam-4006	206	22	it	it	PRON
ejpam-4006	206	23	has	have	AUX
ejpam-4006	206	24	inverse	inverse	NOUN
ejpam-4006	206	25	.	.	PUNCT
ejpam-4006	207	1	from	from	ADP
ejpam-4006	207	2	lemma	lemma	PROPN
ejpam-4006	207	3	5	5	NUM
ejpam-4006	207	4	and	and	CCONJ
ejpam-4006	207	5	equation	equation	NOUN
ejpam-4006	207	6	(	(	PUNCT
ejpam-4006	207	7	36	36	NUM
ejpam-4006	207	8	)	)	PUNCT
ejpam-4006	207	9	,	,	PUNCT
ejpam-4006	207	10	we	we	PRON
ejpam-4006	207	11	obtain	obtain	VERB
ejpam-4006	207	12	n2k(x	n2k(x	PROPN
ejpam-4006	207	13	,	,	PUNCT
ejpam-4006	207	14	m	m	NOUN
ejpam-4006	207	15	)	)	PUNCT
ejpam-4006	207	16	=	=	PUNCT
ejpam-4006	208	1	+	+	PUNCT
ejpam-4006	208	2	∞∑	∞∑	NUM
ejpam-4006	208	3	r=0	r=0	PROPN
ejpam-4006	208	4	(	(	PUNCT
ejpam-4006	208	5	−k	−k	NOUN
ejpam-4006	208	6	r	r	NOUN
ejpam-4006	208	7	)	)	PUNCT
ejpam-4006	208	8	(	(	PUNCT
ejpam-4006	208	9	m2)rl−k−r2	m2)rl−k−r2	PROPN
ejpam-4006	208	10	δ	δ	PROPN
ejpam-4006	208	11	=	=	PUNCT
ejpam-4006	208	12	(	(	PUNCT
ejpam-4006	208	13	l2	l2	NOUN
ejpam-4006	208	14	+	+	NOUN
ejpam-4006	208	15	m2)−kδ	m2)−kδ	ADJ
ejpam-4006	208	16	.	.	PUNCT
ejpam-4006	209	1	(	(	PUNCT
ejpam-4006	209	2	37	37	NUM
ejpam-4006	209	3	)	)	PUNCT
ejpam-4006	209	4	by	by	ADP
ejpam-4006	209	5	applying	apply	VERB
ejpam-4006	209	6	the	the	DET
ejpam-4006	209	7	operator	operator	NOUN
ejpam-4006	209	8	(	(	PUNCT
ejpam-4006	209	9	l2	l2	NOUN
ejpam-4006	209	10	+	+	CCONJ
ejpam-4006	209	11	m2)k	m2)k	NOUN
ejpam-4006	209	12	to	to	ADP
ejpam-4006	209	13	both	both	DET
ejpam-4006	209	14	sides	side	NOUN
ejpam-4006	209	15	of	of	ADP
ejpam-4006	209	16	equation	equation	NOUN
ejpam-4006	209	17	(	(	PUNCT
ejpam-4006	209	18	37	37	NUM
ejpam-4006	209	19	)	)	PUNCT
ejpam-4006	209	20	,	,	PUNCT
ejpam-4006	209	21	we	we	PRON
ejpam-4006	209	22	obtain	obtain	VERB
ejpam-4006	209	23	(	(	PUNCT
ejpam-4006	209	24	l2	l2	NOUN
ejpam-4006	209	25	+	+	SYM
ejpam-4006	209	26	m2)kn2k(x	m2)kn2k(x	NOUN
ejpam-4006	209	27	,	,	PUNCT
ejpam-4006	209	28	m	m	NOUN
ejpam-4006	209	29	)	)	PUNCT
ejpam-4006	210	1	=	=	PRON
ejpam-4006	210	2	(	(	PUNCT
ejpam-4006	210	3	l2	l2	NOUN
ejpam-4006	210	4	+	+	NOUN
ejpam-4006	210	5	m2)k	m2)k	NOUN
ejpam-4006	210	6	·	·	PUNCT
ejpam-4006	210	7	(	(	PUNCT
ejpam-4006	210	8	l2	l2	NOUN
ejpam-4006	210	9	+	+	NOUN
ejpam-4006	210	10	m2)−kδ	m2)−kδ	ADJ
ejpam-4006	210	11	.	.	PUNCT
ejpam-4006	211	1	therefore	therefore	ADV
ejpam-4006	211	2	,	,	PUNCT
ejpam-4006	211	3	(	(	PUNCT
ejpam-4006	211	4	l2	l2	NOUN
ejpam-4006	211	5	+	+	SYM
ejpam-4006	211	6	m2)kn2k(x	m2)kn2k(x	NOUN
ejpam-4006	211	7	,	,	PUNCT
ejpam-4006	211	8	m	m	NOUN
ejpam-4006	211	9	)	)	PUNCT
ejpam-4006	211	10	=	=	SYM
ejpam-4006	211	11	δ	δ	PROPN
ejpam-4006	211	12	.	.	PUNCT
ejpam-4006	212	1	since	since	SCONJ
ejpam-4006	212	2	n2k(x	n2k(x	PROPN
ejpam-4006	212	3	,	,	PUNCT
ejpam-4006	212	4	m	m	NOUN
ejpam-4006	212	5	)	)	PUNCT
ejpam-4006	213	1	=	=	SYM
ejpam-4006	213	2	(	(	PUNCT
ejpam-4006	213	3	−k	−k	NOUN
ejpam-4006	213	4	0	0	NUM
ejpam-4006	213	5	)	)	PUNCT
ejpam-4006	213	6	m2(0)(−1)k+0(i	m2(0)(−1)k+0(i	PROPN
ejpam-4006	213	7	)	)	PUNCT
ejpam-4006	213	8	q	q	PROPN
ejpam-4006	213	9	2t2k+2(0)(x	2t2k+2(0)(x	NUM
ejpam-4006	213	10	)	)	PUNCT
ejpam-4006	213	11	+	+	CCONJ
ejpam-4006	214	1	+	+	PUNCT
ejpam-4006	214	2	∞∑	∞∑	NUM
ejpam-4006	214	3	r=1	r=1	NOUN
ejpam-4006	214	4	(	(	PUNCT
ejpam-4006	214	5	−k	−k	NOUN
ejpam-4006	214	6	r	r	NOUN
ejpam-4006	214	7	)	)	PUNCT
ejpam-4006	214	8	m2r(−1)k+r(i	m2r(−1)k+r(i	PROPN
ejpam-4006	214	9	)	)	PUNCT
ejpam-4006	214	10	q	q	PROPN
ejpam-4006	214	11	2t2k+2r(x	2t2k+2r(x	NUM
ejpam-4006	214	12	)	)	PUNCT
ejpam-4006	214	13	.	.	PUNCT
ejpam-4006	215	1	(	(	PUNCT
ejpam-4006	215	2	38	38	NUM
ejpam-4006	215	3	)	)	PUNCT
ejpam-4006	215	4	the	the	DET
ejpam-4006	215	5	second	second	ADJ
ejpam-4006	215	6	summand	summand	NOUN
ejpam-4006	215	7	of	of	ADP
ejpam-4006	215	8	the	the	DET
ejpam-4006	215	9	right	right	ADJ
ejpam-4006	215	10	-	-	PUNCT
ejpam-4006	215	11	hand	hand	NOUN
ejpam-4006	215	12	member	member	NOUN
ejpam-4006	215	13	of	of	ADP
ejpam-4006	215	14	(	(	PUNCT
ejpam-4006	215	15	38	38	NUM
ejpam-4006	215	16	)	)	PUNCT
ejpam-4006	215	17	vanishes	vanish	VERB
ejpam-4006	215	18	for	for	ADP
ejpam-4006	215	19	m	m	PROPN
ejpam-4006	215	20	=	=	SYM
ejpam-4006	215	21	0	0	PUNCT
ejpam-4006	216	1	and	and	CCONJ
ejpam-4006	216	2	then	then	ADV
ejpam-4006	216	3	,	,	PUNCT
ejpam-4006	216	4	we	we	PRON
ejpam-4006	216	5	have	have	VERB
ejpam-4006	216	6	n2k(x	n2k(x	NOUN
ejpam-4006	216	7	,	,	PUNCT
ejpam-4006	216	8	m	m	VERB
ejpam-4006	216	9	=	=	NOUN
ejpam-4006	216	10	0	0	NUM
ejpam-4006	216	11	)	)	PUNCT
ejpam-4006	216	12	=	=	PRON
ejpam-4006	216	13	(	(	PUNCT
ejpam-4006	216	14	−1)k(i	−1)k(i	PROPN
ejpam-4006	216	15	)	)	PUNCT
ejpam-4006	216	16	q	q	NOUN
ejpam-4006	216	17	2t2k(x	2t2k(x	PROPN
ejpam-4006	216	18	)	)	PUNCT
ejpam-4006	216	19	which	which	PRON
ejpam-4006	216	20	is	be	AUX
ejpam-4006	216	21	the	the	DET
ejpam-4006	216	22	fundamental	fundamental	ADJ
ejpam-4006	216	23	solution	solution	NOUN
ejpam-4006	216	24	of	of	ADP
ejpam-4006	216	25	the	the	DET
ejpam-4006	216	26	operator	operator	NOUN
ejpam-4006	216	27	lk2	lk2	NOUN
ejpam-4006	216	28	.	.	PUNCT
ejpam-4006	217	1	s.	s.	PROPN
ejpam-4006	217	2	bupasiri	bupasiri	PROPN
ejpam-4006	217	3	/	/	SYM
ejpam-4006	217	4	eur	eur	PROPN
ejpam-4006	217	5	.	.	PUNCT
ejpam-4006	218	1	j.	j.	PROPN
ejpam-4006	218	2	pure	pure	PROPN
ejpam-4006	218	3	appl	appl	PROPN
ejpam-4006	218	4	.	.	PROPN
ejpam-4006	218	5	math	math	PROPN
ejpam-4006	218	6	,	,	PUNCT
ejpam-4006	218	7	14	14	NUM
ejpam-4006	218	8	(	(	PUNCT
ejpam-4006	218	9	3	3	NUM
ejpam-4006	218	10	)	)	PUNCT
ejpam-4006	218	11	(	(	PUNCT
ejpam-4006	218	12	2021	2021	NUM
ejpam-4006	218	13	)	)	PUNCT
ejpam-4006	218	14	,	,	PUNCT
ejpam-4006	218	15	881	881	NUM
ejpam-4006	218	16	-	-	SYM
ejpam-4006	218	17	894	894	NUM
ejpam-4006	218	18	890	890	NUM
ejpam-4006	218	19	lemma	lemma	PROPN
ejpam-4006	218	20	13	13	NUM
ejpam-4006	218	21	.	.	PUNCT
ejpam-4006	219	1	the	the	DET
ejpam-4006	219	2	convolution	convolution	NOUN
ejpam-4006	219	3	w2k(x	w2k(x	PROPN
ejpam-4006	219	4	,	,	PUNCT
ejpam-4006	219	5	m	m	NOUN
ejpam-4006	219	6	)	)	PUNCT
ejpam-4006	219	7	∗	∗	NOUN
ejpam-4006	219	8	y2k(x	y2k(x	PROPN
ejpam-4006	219	9	,	,	PUNCT
ejpam-4006	219	10	m	m	NOUN
ejpam-4006	219	11	)	)	PUNCT
ejpam-4006	219	12	exists	exist	VERB
ejpam-4006	219	13	and	and	CCONJ
ejpam-4006	219	14	is	be	AUX
ejpam-4006	219	15	a	a	DET
ejpam-4006	219	16	tempered	temper	VERB
ejpam-4006	219	17	distribution	distribution	NOUN
ejpam-4006	219	18	where	where	SCONJ
ejpam-4006	219	19	w2k(x	w2k(x	PROPN
ejpam-4006	219	20	,	,	PUNCT
ejpam-4006	219	21	m	m	NOUN
ejpam-4006	219	22	)	)	PUNCT
ejpam-4006	219	23	and	and	CCONJ
ejpam-4006	219	24	y2k(x	y2k(x	PROPN
ejpam-4006	219	25	,	,	PUNCT
ejpam-4006	219	26	m	m	VERB
ejpam-4006	219	27	)	)	PUNCT
ejpam-4006	219	28	are	be	AUX
ejpam-4006	219	29	defined	define	VERB
ejpam-4006	219	30	by	by	ADP
ejpam-4006	219	31	(	(	PUNCT
ejpam-4006	219	32	27	27	NUM
ejpam-4006	219	33	)	)	PUNCT
ejpam-4006	219	34	and	and	CCONJ
ejpam-4006	219	35	(	(	PUNCT
ejpam-4006	219	36	30	30	NUM
ejpam-4006	219	37	)	)	PUNCT
ejpam-4006	219	38	,	,	PUNCT
ejpam-4006	219	39	respectively	respectively	ADV
ejpam-4006	219	40	.	.	PUNCT
ejpam-4006	220	1	proof	proof	NOUN
ejpam-4006	220	2	.	.	PUNCT
ejpam-4006	221	1	see	see	VERB
ejpam-4006	221	2	[	[	X
ejpam-4006	221	3	7	7	NUM
ejpam-4006	221	4	]	]	PUNCT
ejpam-4006	221	5	.	.	PUNCT
ejpam-4006	222	1	lemma	lemma	PROPN
ejpam-4006	222	2	14	14	NUM
ejpam-4006	222	3	.	.	PUNCT
ejpam-4006	223	1	the	the	DET
ejpam-4006	223	2	convolution	convolution	NOUN
ejpam-4006	223	3	m2k(x	m2k(x	PROPN
ejpam-4006	223	4	,	,	PUNCT
ejpam-4006	223	5	m	m	NOUN
ejpam-4006	223	6	)	)	PUNCT
ejpam-4006	223	7	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	223	8	,	,	PUNCT
ejpam-4006	223	9	m	m	NOUN
ejpam-4006	223	10	)	)	PUNCT
ejpam-4006	223	11	exists	exist	VERB
ejpam-4006	223	12	and	and	CCONJ
ejpam-4006	223	13	is	be	AUX
ejpam-4006	223	14	a	a	DET
ejpam-4006	223	15	tempered	temper	VERB
ejpam-4006	223	16	distribution	distribution	NOUN
ejpam-4006	223	17	where	where	SCONJ
ejpam-4006	223	18	m2k(x	m2k(x	PROPN
ejpam-4006	223	19	,	,	PUNCT
ejpam-4006	223	20	m	m	PROPN
ejpam-4006	223	21	)	)	PUNCT
ejpam-4006	223	22	and	and	CCONJ
ejpam-4006	223	23	n2k(x	n2k(x	PROPN
ejpam-4006	223	24	,	,	PUNCT
ejpam-4006	223	25	m	m	VERB
ejpam-4006	223	26	)	)	PUNCT
ejpam-4006	223	27	are	be	AUX
ejpam-4006	223	28	defined	define	VERB
ejpam-4006	223	29	by	by	ADP
ejpam-4006	223	30	(	(	PUNCT
ejpam-4006	223	31	33	33	NUM
ejpam-4006	223	32	)	)	PUNCT
ejpam-4006	223	33	and	and	CCONJ
ejpam-4006	223	34	(	(	PUNCT
ejpam-4006	223	35	36	36	NUM
ejpam-4006	223	36	)	)	PUNCT
ejpam-4006	223	37	,	,	PUNCT
ejpam-4006	223	38	respectively	respectively	ADV
ejpam-4006	223	39	.	.	PUNCT
ejpam-4006	224	1	proof	proof	NOUN
ejpam-4006	224	2	.	.	PUNCT
ejpam-4006	225	1	from	from	ADP
ejpam-4006	225	2	(	(	PUNCT
ejpam-4006	225	3	33	33	NUM
ejpam-4006	225	4	)	)	PUNCT
ejpam-4006	225	5	and	and	CCONJ
ejpam-4006	225	6	(	(	PUNCT
ejpam-4006	225	7	36	36	NUM
ejpam-4006	225	8	)	)	PUNCT
ejpam-4006	225	9	,	,	PUNCT
ejpam-4006	225	10	we	we	PRON
ejpam-4006	225	11	have	have	VERB
ejpam-4006	225	12	m2k(x	m2k(x	PROPN
ejpam-4006	225	13	,	,	PUNCT
ejpam-4006	225	14	m	m	NOUN
ejpam-4006	225	15	)	)	PUNCT
ejpam-4006	225	16	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	225	17	,	,	PUNCT
ejpam-4006	225	18	m	m	NOUN
ejpam-4006	225	19	)	)	PUNCT
ejpam-4006	225	20	=	=	SYM
ejpam-4006	226	1	(	(	PUNCT
ejpam-4006	226	2	+	+	ADJ
ejpam-4006	226	3	∞∑	∞∑	NUM
ejpam-4006	226	4	r=0	r=0	VERB
ejpam-4006	226	5	(	(	PUNCT
ejpam-4006	226	6	−k	−k	NOUN
ejpam-4006	226	7	r	r	NOUN
ejpam-4006	226	8	)	)	PUNCT
ejpam-4006	226	9	m2r(−1)k+r(−i	m2r(−1)k+r(−i	NOUN
ejpam-4006	226	10	)	)	PUNCT
ejpam-4006	226	11	q	q	PROPN
ejpam-4006	226	12	2s2k+2r(x	2s2k+2r(x	PROPN
ejpam-4006	226	13	)	)	PUNCT
ejpam-4006	226	14	)	)	PUNCT
ejpam-4006	227	1	∗	∗	NOUN
ejpam-4006	227	2	(	(	PUNCT
ejpam-4006	227	3	+	+	PROPN
ejpam-4006	227	4	∞∑	∞∑	NUM
ejpam-4006	227	5	r=0	r=0	VERB
ejpam-4006	227	6	(	(	PUNCT
ejpam-4006	227	7	−k	−k	NOUN
ejpam-4006	227	8	r	r	NOUN
ejpam-4006	227	9	)	)	PUNCT
ejpam-4006	227	10	m2r(−1)k+r(i	m2r(−1)k+r(i	PROPN
ejpam-4006	227	11	)	)	PUNCT
ejpam-4006	227	12	q	q	PROPN
ejpam-4006	227	13	2t2k+2r(x	2t2k+2r(x	NUM
ejpam-4006	227	14	)	)	PUNCT
ejpam-4006	227	15	)	)	PUNCT
ejpam-4006	228	1	=	=	PUNCT
ejpam-4006	229	1	+	+	PUNCT
ejpam-4006	229	2	∞∑	∞∑	NUM
ejpam-4006	229	3	r=0	r=0	NUM
ejpam-4006	229	4	+	+	NOUN
ejpam-4006	229	5	∞∑	∞∑	PROPN
ejpam-4006	229	6	s=0	s=0	PUNCT
ejpam-4006	229	7	(	(	PUNCT
ejpam-4006	229	8	−k	−k	NOUN
ejpam-4006	229	9	r	r	NOUN
ejpam-4006	229	10	)	)	PUNCT
ejpam-4006	229	11	(	(	PUNCT
ejpam-4006	229	12	−k	−k	PROPN
ejpam-4006	229	13	s	s	PART
ejpam-4006	229	14	)	)	PUNCT
ejpam-4006	229	15	m2r+2ss2k+2r(x	m2r+2ss2k+2r(x	PROPN
ejpam-4006	229	16	)	)	PUNCT
ejpam-4006	229	17	∗	∗	NOUN
ejpam-4006	229	18	t2k+2r(x	t2k+2r(x	VERB
ejpam-4006	229	19	)	)	PUNCT
ejpam-4006	229	20	.	.	PUNCT
ejpam-4006	230	1	since	since	SCONJ
ejpam-4006	230	2	the	the	DET
ejpam-4006	230	3	function	function	NOUN
ejpam-4006	230	4	s2k+2r(x	s2k+2r(x	NOUN
ejpam-4006	230	5	)	)	PUNCT
ejpam-4006	230	6	and	and	CCONJ
ejpam-4006	230	7	t2k+2r(x	t2k+2r(x	VERB
ejpam-4006	230	8	)	)	PUNCT
ejpam-4006	230	9	are	be	AUX
ejpam-4006	230	10	tempered	temper	VERB
ejpam-4006	230	11	distributions	distribution	NOUN
ejpam-4006	230	12	,	,	PUNCT
ejpam-4006	230	13	see	see	VERB
ejpam-4006	230	14	(	(	PUNCT
ejpam-4006	230	15	[	[	X
ejpam-4006	230	16	5],p.34	5],p.34	NOUN
ejpam-4006	230	17	,	,	PUNCT
ejpam-4006	230	18	[	[	X
ejpam-4006	230	19	2	2	NUM
ejpam-4006	230	20	]	]	PUNCT
ejpam-4006	230	21	,	,	PUNCT
ejpam-4006	230	22	p.302	p.302	NOUN
ejpam-4006	230	23	and	and	CCONJ
ejpam-4006	230	24	[	[	X
ejpam-4006	230	25	6	6	NUM
ejpam-4006	230	26	]	]	PUNCT
ejpam-4006	230	27	,	,	PUNCT
ejpam-4006	230	28	p.97	p.97	NOUN
ejpam-4006	230	29	)	)	PUNCT
ejpam-4006	230	30	and	and	CCONJ
ejpam-4006	230	31	the	the	DET
ejpam-4006	230	32	convolution	convolution	NOUN
ejpam-4006	230	33	of	of	ADP
ejpam-4006	230	34	functions	function	NOUN
ejpam-4006	230	35	s2k+2r(x	s2k+2r(x	NOUN
ejpam-4006	230	36	)	)	PUNCT
ejpam-4006	230	37	∗	∗	NOUN
ejpam-4006	230	38	t2k+2r(x	t2k+2r(x	VERB
ejpam-4006	230	39	)	)	PUNCT
ejpam-4006	230	40	exists	exist	VERB
ejpam-4006	230	41	and	and	CCONJ
ejpam-4006	230	42	is	be	AUX
ejpam-4006	230	43	also	also	ADV
ejpam-4006	230	44	a	a	DET
ejpam-4006	230	45	tempered	temper	VERB
ejpam-4006	230	46	distribution	distribution	NOUN
ejpam-4006	230	47	,	,	PUNCT
ejpam-4006	230	48	see	see	VERB
ejpam-4006	230	49	(	(	PUNCT
ejpam-4006	230	50	[	[	X
ejpam-4006	230	51	3	3	NUM
ejpam-4006	230	52	]	]	PUNCT
ejpam-4006	230	53	,	,	PUNCT
ejpam-4006	230	54	p.152	p.152	NUM
ejpam-4006	230	55	)	)	PUNCT
ejpam-4006	230	56	.	.	PUNCT
ejpam-4006	231	1	thus	thus	ADV
ejpam-4006	231	2	,	,	PUNCT
ejpam-4006	231	3	m2k(x	m2k(x	PROPN
ejpam-4006	231	4	,	,	PUNCT
ejpam-4006	231	5	m	m	NOUN
ejpam-4006	231	6	)	)	PUNCT
ejpam-4006	231	7	∗	∗	NOUN
ejpam-4006	231	8	n2k(x	n2k(x	PROPN
ejpam-4006	231	9	,	,	PUNCT
ejpam-4006	231	10	m	m	NOUN
ejpam-4006	231	11	)	)	PUNCT
ejpam-4006	231	12	exists	exist	VERB
ejpam-4006	231	13	and	and	CCONJ
ejpam-4006	231	14	also	also	ADV
ejpam-4006	231	15	is	be	AUX
ejpam-4006	231	16	a	a	DET
ejpam-4006	231	17	tempered	temper	VERB
ejpam-4006	231	18	distribution	distribution	NOUN
ejpam-4006	231	19	.	.	PUNCT
ejpam-4006	232	1	lemma	lemma	PROPN
ejpam-4006	232	2	15	15	NUM
ejpam-4006	232	3	.	.	PUNCT
ejpam-4006	233	1	(	(	PUNCT
ejpam-4006	233	2	the	the	DET
ejpam-4006	233	3	convolution	convolution	NOUN
ejpam-4006	233	4	w2k(x	w2k(x	PROPN
ejpam-4006	233	5	,	,	PUNCT
ejpam-4006	233	6	m	m	NOUN
ejpam-4006	233	7	)	)	PUNCT
ejpam-4006	233	8	∗	∗	NOUN
ejpam-4006	233	9	y2k(x	y2k(x	PROPN
ejpam-4006	233	10	,	,	PUNCT
ejpam-4006	233	11	m	m	NOUN
ejpam-4006	233	12	)	)	PUNCT
ejpam-4006	233	13	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	233	14	,	,	PUNCT
ejpam-4006	233	15	m	m	NOUN
ejpam-4006	233	16	)	)	PUNCT
ejpam-4006	233	17	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	233	18	,	,	PUNCT
ejpam-4006	233	19	m	m	NOUN
ejpam-4006	233	20	)	)	PUNCT
ejpam-4006	233	21	)	)	PUNCT
ejpam-4006	233	22	.	.	PUNCT
ejpam-4006	234	1	the	the	DET
ejpam-4006	234	2	function	function	NOUN
ejpam-4006	234	3	w2k(x	w2k(x	PROPN
ejpam-4006	234	4	,	,	PUNCT
ejpam-4006	234	5	m	m	NOUN
ejpam-4006	234	6	)	)	PUNCT
ejpam-4006	234	7	∗y2k(x	∗y2k(x	VERB
ejpam-4006	234	8	,	,	PUNCT
ejpam-4006	234	9	m	m	NOUN
ejpam-4006	234	10	)	)	PUNCT
ejpam-4006	234	11	and	and	CCONJ
ejpam-4006	234	12	m2k(x	m2k(x	PROPN
ejpam-4006	234	13	,	,	PUNCT
ejpam-4006	234	14	m	m	NOUN
ejpam-4006	234	15	)	)	PUNCT
ejpam-4006	234	16	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	234	17	,	,	PUNCT
ejpam-4006	234	18	m	m	VERB
ejpam-4006	234	19	)	)	PUNCT
ejpam-4006	234	20	are	be	AUX
ejpam-4006	234	21	tempered	temper	VERB
ejpam-4006	234	22	distributions	distribution	NOUN
ejpam-4006	234	23	.	.	PUNCT
ejpam-4006	235	1	the	the	DET
ejpam-4006	235	2	convolution	convolution	NOUN
ejpam-4006	235	3	w2k(x	w2k(x	PROPN
ejpam-4006	235	4	,	,	PUNCT
ejpam-4006	235	5	m	m	NOUN
ejpam-4006	235	6	)	)	PUNCT
ejpam-4006	235	7	∗	∗	NOUN
ejpam-4006	235	8	y2k(x	y2k(x	PROPN
ejpam-4006	235	9	,	,	PUNCT
ejpam-4006	235	10	m	m	NOUN
ejpam-4006	235	11	)	)	PUNCT
ejpam-4006	235	12	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	235	13	,	,	PUNCT
ejpam-4006	235	14	m	m	NOUN
ejpam-4006	235	15	)	)	PUNCT
ejpam-4006	235	16	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	235	17	,	,	PUNCT
ejpam-4006	235	18	m	m	NOUN
ejpam-4006	235	19	)	)	PUNCT
ejpam-4006	235	20	exists	exist	VERB
ejpam-4006	235	21	and	and	CCONJ
ejpam-4006	235	22	also	also	ADV
ejpam-4006	235	23	a	a	DET
ejpam-4006	235	24	tempered	temper	VERB
ejpam-4006	235	25	distribution	distribution	NOUN
ejpam-4006	235	26	.	.	PUNCT
ejpam-4006	236	1	proof	proof	NOUN
ejpam-4006	236	2	.	.	PUNCT
ejpam-4006	237	1	see	see	VERB
ejpam-4006	237	2	[	[	X
ejpam-4006	237	3	10	10	NUM
ejpam-4006	237	4	]	]	PUNCT
ejpam-4006	237	5	.	.	PUNCT
ejpam-4006	238	1	3	3	X
ejpam-4006	238	2	.	.	X
ejpam-4006	238	3	main	main	ADJ
ejpam-4006	238	4	results	result	NOUN
ejpam-4006	238	5	in	in	ADP
ejpam-4006	238	6	this	this	DET
ejpam-4006	238	7	main	main	ADJ
ejpam-4006	238	8	results	result	NOUN
ejpam-4006	238	9	,	,	PUNCT
ejpam-4006	238	10	we	we	PRON
ejpam-4006	238	11	obtained	obtain	VERB
ejpam-4006	238	12	two	two	NUM
ejpam-4006	238	13	theorems	theorem	NOUN
ejpam-4006	238	14	and	and	CCONJ
ejpam-4006	238	15	such	such	DET
ejpam-4006	238	16	a	a	DET
ejpam-4006	238	17	solution	solution	NOUN
ejpam-4006	238	18	h(x	h(x	PROPN
ejpam-4006	238	19	,	,	PUNCT
ejpam-4006	238	20	m	m	NOUN
ejpam-4006	238	21	)	)	PUNCT
ejpam-4006	238	22	related	relate	VERB
ejpam-4006	238	23	to	to	ADP
ejpam-4006	238	24	the	the	DET
ejpam-4006	238	25	partial	partial	ADJ
ejpam-4006	238	26	differential	differential	NOUN
ejpam-4006	238	27	operator	operator	NOUN
ejpam-4006	238	28	depends	depend	VERB
ejpam-4006	238	29	on	on	ADP
ejpam-4006	238	30	the	the	DET
ejpam-4006	238	31	condition	condition	NOUN
ejpam-4006	238	32	of	of	ADP
ejpam-4006	238	33	p	p	X
ejpam-4006	238	34	,	,	PUNCT
ejpam-4006	238	35	q	q	X
ejpam-4006	238	36	,	,	PUNCT
ejpam-4006	238	37	k	k	PROPN
ejpam-4006	238	38	and	and	CCONJ
ejpam-4006	238	39	m.	m.	NOUN
ejpam-4006	238	40	theorem	theorem	NOUN
ejpam-4006	238	41	1	1	NUM
ejpam-4006	238	42	.	.	PUNCT
ejpam-4006	238	43	given	give	VERB
ejpam-4006	238	44	the	the	DET
ejpam-4006	238	45	equation	equation	NOUN
ejpam-4006	238	46	⊕kmh(x	⊕kmh(x	NOUN
ejpam-4006	238	47	,	,	PUNCT
ejpam-4006	238	48	m	m	NOUN
ejpam-4006	238	49	)	)	PUNCT
ejpam-4006	239	1	=	=	SYM
ejpam-4006	239	2	δ	δ	PROPN
ejpam-4006	239	3	,	,	PUNCT
ejpam-4006	239	4	(	(	PUNCT
ejpam-4006	239	5	39	39	NUM
ejpam-4006	239	6	)	)	PUNCT
ejpam-4006	239	7	where	where	SCONJ
ejpam-4006	239	8	⊕km	⊕km	VERB
ejpam-4006	239	9	is	be	AUX
ejpam-4006	239	10	the	the	DET
ejpam-4006	239	11	operator	operator	NOUN
ejpam-4006	239	12	iterated	iterate	VERB
ejpam-4006	239	13	ktimes	ktime	NOUN
ejpam-4006	239	14	defined	define	VERB
ejpam-4006	239	15	by	by	ADP
ejpam-4006	239	16	(	(	PUNCT
ejpam-4006	239	17	7	7	NUM
ejpam-4006	239	18	)	)	PUNCT
ejpam-4006	239	19	,	,	PUNCT
ejpam-4006	239	20	δ	δ	PROPN
ejpam-4006	239	21	is	be	AUX
ejpam-4006	239	22	the	the	DET
ejpam-4006	239	23	dirac	dirac	NOUN
ejpam-4006	239	24	delta	delta	NOUN
ejpam-4006	239	25	distribution	distribution	NOUN
ejpam-4006	239	26	,	,	PUNCT
ejpam-4006	239	27	x	x	SYM
ejpam-4006	239	28	=	=	SYM
ejpam-4006	239	29	(	(	PUNCT
ejpam-4006	239	30	x1	x1	PROPN
ejpam-4006	239	31	,	,	PUNCT
ejpam-4006	239	32	x2	x2	PROPN
ejpam-4006	239	33	,	,	PUNCT
ejpam-4006	239	34	.	.	PUNCT
ejpam-4006	239	35	.	.	PUNCT
ejpam-4006	239	36	.	.	PUNCT
ejpam-4006	240	1	,	,	PUNCT
ejpam-4006	240	2	xn	xn	X
ejpam-4006	240	3	)	)	PUNCT
ejpam-4006	240	4	∈	∈	PROPN
ejpam-4006	240	5	rn	rn	PROPN
ejpam-4006	240	6	,	,	PUNCT
ejpam-4006	240	7	k	k	PROPN
ejpam-4006	240	8	is	be	AUX
ejpam-4006	240	9	a	a	DET
ejpam-4006	240	10	nonnegative	nonnegative	ADJ
ejpam-4006	240	11	integer	integer	NOUN
ejpam-4006	240	12	and	and	CCONJ
ejpam-4006	240	13	m	m	NOUN
ejpam-4006	240	14	is	be	AUX
ejpam-4006	240	15	a	a	DET
ejpam-4006	240	16	nonnegative	nonnegative	ADJ
ejpam-4006	240	17	real	real	ADJ
ejpam-4006	240	18	number	number	NOUN
ejpam-4006	240	19	.	.	PUNCT
ejpam-4006	241	1	then	then	ADV
ejpam-4006	241	2	we	we	PRON
ejpam-4006	241	3	obtain	obtain	VERB
ejpam-4006	241	4	h(x	h(x	PROPN
ejpam-4006	241	5	,	,	PUNCT
ejpam-4006	241	6	m	m	NOUN
ejpam-4006	241	7	)	)	PUNCT
ejpam-4006	241	8	=	=	SYM
ejpam-4006	242	1	w2k(x	w2k(x	PROPN
ejpam-4006	242	2	,	,	PUNCT
ejpam-4006	242	3	m	m	NOUN
ejpam-4006	242	4	)	)	PUNCT
ejpam-4006	242	5	∗	∗	NOUN
ejpam-4006	242	6	y2k(x	y2k(x	PROPN
ejpam-4006	242	7	,	,	PUNCT
ejpam-4006	242	8	m	m	NOUN
ejpam-4006	242	9	)	)	PUNCT
ejpam-4006	242	10	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	242	11	,	,	PUNCT
ejpam-4006	242	12	m	m	NOUN
ejpam-4006	242	13	)	)	PUNCT
ejpam-4006	242	14	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	242	15	,	,	PUNCT
ejpam-4006	242	16	m	m	NOUN
ejpam-4006	242	17	)	)	PUNCT
ejpam-4006	242	18	(	(	PUNCT
ejpam-4006	242	19	40	40	NUM
ejpam-4006	242	20	)	)	PUNCT
ejpam-4006	242	21	s.	s.	PROPN
ejpam-4006	242	22	bupasiri	bupasiri	PROPN
ejpam-4006	242	23	/	/	SYM
ejpam-4006	242	24	eur	eur	PROPN
ejpam-4006	242	25	.	.	PUNCT
ejpam-4006	243	1	j.	j.	PROPN
ejpam-4006	243	2	pure	pure	PROPN
ejpam-4006	243	3	appl	appl	PROPN
ejpam-4006	243	4	.	.	PROPN
ejpam-4006	243	5	math	math	PROPN
ejpam-4006	243	6	,	,	PUNCT
ejpam-4006	243	7	14	14	NUM
ejpam-4006	243	8	(	(	PUNCT
ejpam-4006	243	9	3	3	NUM
ejpam-4006	243	10	)	)	PUNCT
ejpam-4006	243	11	(	(	PUNCT
ejpam-4006	243	12	2021	2021	NUM
ejpam-4006	243	13	)	)	PUNCT
ejpam-4006	243	14	,	,	PUNCT
ejpam-4006	243	15	881	881	NUM
ejpam-4006	243	16	-	-	SYM
ejpam-4006	243	17	894	894	NUM
ejpam-4006	243	18	891	891	NUM
ejpam-4006	243	19	is	be	AUX
ejpam-4006	243	20	the	the	DET
ejpam-4006	243	21	fundamental	fundamental	ADJ
ejpam-4006	243	22	solution	solution	NOUN
ejpam-4006	243	23	for	for	ADP
ejpam-4006	243	24	the	the	DET
ejpam-4006	243	25	operator	operator	NOUN
ejpam-4006	243	26	⊕km	⊕km	PART
ejpam-4006	243	27	iterated	iterated	ADJ
ejpam-4006	243	28	k	k	NOUN
ejpam-4006	243	29	-	-	PUNCT
ejpam-4006	243	30	times	time	NOUN
ejpam-4006	243	31	,	,	PUNCT
ejpam-4006	243	32	where	where	SCONJ
ejpam-4006	243	33	⊕km	⊕km	VERB
ejpam-4006	243	34	is	be	AUX
ejpam-4006	243	35	defined	define	VERB
ejpam-4006	243	36	by	by	ADP
ejpam-4006	243	37	(	(	PUNCT
ejpam-4006	243	38	7	7	NUM
ejpam-4006	243	39	)	)	PUNCT
ejpam-4006	243	40	.	.	PUNCT
ejpam-4006	244	1	in	in	ADP
ejpam-4006	244	2	particular	particular	ADJ
ejpam-4006	244	3	,	,	PUNCT
ejpam-4006	244	4	for	for	ADP
ejpam-4006	244	5	q	q	NOUN
ejpam-4006	244	6	=	=	NOUN
ejpam-4006	244	7	m	m	NOUN
ejpam-4006	244	8	=	=	NOUN
ejpam-4006	244	9	0	0	PUNCT
ejpam-4006	244	10	then	then	ADV
ejpam-4006	244	11	(	(	PUNCT
ejpam-4006	244	12	39	39	NUM
ejpam-4006	244	13	)	)	PUNCT
ejpam-4006	244	14	becomes	become	VERB
ejpam-4006	244	15	44k	44k	PROPN
ejpam-4006	244	16	p	p	ADJ
ejpam-4006	244	17	h(x	h(x	PROPN
ejpam-4006	244	18	,	,	PUNCT
ejpam-4006	244	19	0	0	NUM
ejpam-4006	244	20	)	)	PUNCT
ejpam-4006	244	21	=	=	SYM
ejpam-4006	244	22	δ	δ	PROPN
ejpam-4006	244	23	,	,	PUNCT
ejpam-4006	244	24	(	(	PUNCT
ejpam-4006	244	25	41	41	NUM
ejpam-4006	244	26	)	)	PUNCT
ejpam-4006	244	27	we	we	PRON
ejpam-4006	244	28	obtain	obtain	VERB
ejpam-4006	244	29	h(x	h(x	PROPN
ejpam-4006	244	30	,	,	PUNCT
ejpam-4006	244	31	0	0	NUM
ejpam-4006	244	32	)	)	PUNCT
ejpam-4006	244	33	=	=	SYM
ejpam-4006	244	34	y8k(x	y8k(x	PROPN
ejpam-4006	244	35	,	,	PUNCT
ejpam-4006	244	36	0	0	NUM
ejpam-4006	244	37	)	)	PUNCT
ejpam-4006	244	38	=	=	SYM
ejpam-4006	244	39	re8k(x	re8k(x	PROPN
ejpam-4006	244	40	)	)	PUNCT
ejpam-4006	244	41	(	(	PUNCT
ejpam-4006	244	42	42	42	NUM
ejpam-4006	244	43	)	)	PUNCT
ejpam-4006	244	44	is	be	AUX
ejpam-4006	244	45	the	the	DET
ejpam-4006	244	46	fundamental	fundamental	ADJ
ejpam-4006	244	47	solution	solution	NOUN
ejpam-4006	244	48	of	of	ADP
ejpam-4006	244	49	(	(	PUNCT
ejpam-4006	244	50	41	41	NUM
ejpam-4006	244	51	)	)	PUNCT
ejpam-4006	244	52	,	,	PUNCT
ejpam-4006	244	53	where	where	SCONJ
ejpam-4006	244	54	44k	44k	PROPN
ejpam-4006	244	55	p	p	PROPN
ejpam-4006	244	56	is	be	AUX
ejpam-4006	244	57	the	the	DET
ejpam-4006	244	58	laplace	laplace	NOUN
ejpam-4006	244	59	operator	operator	NOUN
ejpam-4006	244	60	of	of	ADP
ejpam-4006	244	61	p	p	NOUN
ejpam-4006	244	62	-	-	PUNCT
ejpam-4006	244	63	dimension	dimension	NOUN
ejpam-4006	244	64	,	,	PUNCT
ejpam-4006	244	65	iterated	iterate	VERB
ejpam-4006	244	66	4k	4k	NOUN
ejpam-4006	244	67	-	-	NOUN
ejpam-4006	244	68	times	time	NOUN
ejpam-4006	244	69	which	which	PRON
ejpam-4006	244	70	is	be	AUX
ejpam-4006	244	71	defined	define	VERB
ejpam-4006	244	72	by	by	ADP
ejpam-4006	244	73	(	(	PUNCT
ejpam-4006	244	74	16	16	NUM
ejpam-4006	244	75	)	)	PUNCT
ejpam-4006	244	76	.	.	PUNCT
ejpam-4006	245	1	moreover	moreover	ADV
ejpam-4006	245	2	,	,	PUNCT
ejpam-4006	245	3	from	from	ADP
ejpam-4006	245	4	(	(	PUNCT
ejpam-4006	245	5	40	40	NUM
ejpam-4006	245	6	)	)	PUNCT
ejpam-4006	245	7	h(x	h(x	PROPN
ejpam-4006	245	8	,	,	PUNCT
ejpam-4006	245	9	0	0	NUM
ejpam-4006	245	10	)	)	PUNCT
ejpam-4006	245	11	=	=	NOUN
ejpam-4006	245	12	[	[	PUNCT
ejpam-4006	245	13	rh2k(x	rh2k(x	PROPN
ejpam-4006	245	14	)	)	PUNCT
ejpam-4006	245	15	∗	∗	NOUN
ejpam-4006	245	16	(	(	PUNCT
ejpam-4006	245	17	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	245	18	)	)	PUNCT
ejpam-4006	245	19	]	]	PUNCT
ejpam-4006	245	20	∗	∗	PROPN
ejpam-4006	245	21	s2k(x	s2k(x	PROPN
ejpam-4006	245	22	)	)	PUNCT
ejpam-4006	245	23	∗	∗	PROPN
ejpam-4006	245	24	t2k(x	t2k(x	PROPN
ejpam-4006	245	25	)	)	PUNCT
ejpam-4006	245	26	(	(	PUNCT
ejpam-4006	245	27	43	43	NUM
ejpam-4006	245	28	)	)	PUNCT
ejpam-4006	245	29	is	be	AUX
ejpam-4006	245	30	the	the	DET
ejpam-4006	245	31	fundamental	fundamental	ADJ
ejpam-4006	245	32	solution	solution	NOUN
ejpam-4006	245	33	of	of	ADP
ejpam-4006	245	34	o	o	ADJ
ejpam-4006	245	35	-	-	ADJ
ejpam-4006	245	36	plus	plus	ADJ
ejpam-4006	245	37	operator	operator	NOUN
ejpam-4006	245	38	⊕k	⊕k	NOUN
ejpam-4006	245	39	and	and	CCONJ
ejpam-4006	245	40	from	from	ADP
ejpam-4006	245	41	(	(	PUNCT
ejpam-4006	245	42	43	43	NUM
ejpam-4006	245	43	)	)	PUNCT
ejpam-4006	245	44	we	we	PRON
ejpam-4006	245	45	obtain	obtain	VERB
ejpam-4006	245	46	[	[	X
ejpam-4006	245	47	(	(	PUNCT
ejpam-4006	245	48	−1)kre−2k(x	−1)kre−2k(x	NOUN
ejpam-4006	245	49	)	)	PUNCT
ejpam-4006	245	50	∗	∗	PROPN
ejpam-4006	245	51	s−2k(x	s−2k(x	PROPN
ejpam-4006	245	52	)	)	PUNCT
ejpam-4006	245	53	∗	∗	NOUN
ejpam-4006	245	54	t−2k(x	t−2k(x	NOUN
ejpam-4006	245	55	)	)	PUNCT
ejpam-4006	245	56	]	]	PUNCT
ejpam-4006	246	1	∗h(x	∗h(x	PROPN
ejpam-4006	246	2	,	,	PUNCT
ejpam-4006	246	3	0	0	NUM
ejpam-4006	246	4	)	)	PUNCT
ejpam-4006	246	5	=	=	SYM
ejpam-4006	246	6	rh2k(x	rh2k(x	PROPN
ejpam-4006	246	7	)	)	PUNCT
ejpam-4006	246	8	(	(	PUNCT
ejpam-4006	246	9	44	44	NUM
ejpam-4006	246	10	)	)	PUNCT
ejpam-4006	246	11	is	be	AUX
ejpam-4006	246	12	the	the	DET
ejpam-4006	246	13	fundamental	fundamental	ADJ
ejpam-4006	246	14	solution	solution	NOUN
ejpam-4006	246	15	of	of	ADP
ejpam-4006	246	16	the	the	DET
ejpam-4006	246	17	ultra	ultra	ADJ
ejpam-4006	246	18	-	-	ADJ
ejpam-4006	246	19	hyperbolic	hyperbolic	ADJ
ejpam-4006	246	20	operator	operator	NOUN
ejpam-4006	246	21	�	�	PROPN
ejpam-4006	246	22	k	k	PROPN
ejpam-4006	246	23	iterated	iterate	VERB
ejpam-4006	246	24	k	k	NOUN
ejpam-4006	246	25	-	-	PUNCT
ejpam-4006	246	26	times	time	NOUN
ejpam-4006	246	27	defined	define	VERB
ejpam-4006	246	28	by	by	ADP
ejpam-4006	246	29	(	(	PUNCT
ejpam-4006	246	30	9	9	NUM
ejpam-4006	246	31	)	)	PUNCT
ejpam-4006	246	32	,	,	PUNCT
ejpam-4006	246	33	where	where	SCONJ
ejpam-4006	246	34	re−2k(x	re−2k(x	NOUN
ejpam-4006	246	35	)	)	PUNCT
ejpam-4006	246	36	,	,	PUNCT
ejpam-4006	246	37	s−2k(x	s−2k(x	PROPN
ejpam-4006	246	38	)	)	PUNCT
ejpam-4006	246	39	and	and	CCONJ
ejpam-4006	246	40	t−2k(x	t−2k(x	PROPN
ejpam-4006	246	41	)	)	PUNCT
ejpam-4006	246	42	are	be	AUX
ejpam-4006	246	43	inverse	inverse	NOUN
ejpam-4006	246	44	of	of	ADP
ejpam-4006	246	45	re2k(x	re2k(x	PROPN
ejpam-4006	246	46	)	)	PUNCT
ejpam-4006	246	47	,	,	PUNCT
ejpam-4006	246	48	s2k(x	s2k(x	PROPN
ejpam-4006	246	49	)	)	PUNCT
ejpam-4006	246	50	and	and	CCONJ
ejpam-4006	246	51	t2k(x	t2k(x	NOUN
ejpam-4006	246	52	)	)	PUNCT
ejpam-4006	246	53	respectively	respectively	ADV
ejpam-4006	246	54	.	.	PUNCT
ejpam-4006	247	1	from	from	ADP
ejpam-4006	247	2	(	(	PUNCT
ejpam-4006	247	3	43	43	NUM
ejpam-4006	247	4	)	)	PUNCT
ejpam-4006	247	5	and	and	CCONJ
ejpam-4006	247	6	(	(	PUNCT
ejpam-4006	247	7	44	44	NUM
ejpam-4006	247	8	)	)	PUNCT
ejpam-4006	247	9	with	with	ADP
ejpam-4006	247	10	p	p	NOUN
ejpam-4006	247	11	=	=	SYM
ejpam-4006	247	12	1	1	NUM
ejpam-4006	247	13	,	,	PUNCT
ejpam-4006	247	14	q	q	NOUN
ejpam-4006	247	15	=	=	PUNCT
ejpam-4006	247	16	n−	n−	NOUN
ejpam-4006	247	17	1	1	NUM
ejpam-4006	247	18	,	,	PUNCT
ejpam-4006	247	19	k	k	NOUN
ejpam-4006	247	20	=	=	SYM
ejpam-4006	247	21	1	1	NUM
ejpam-4006	247	22	and	and	CCONJ
ejpam-4006	247	23	x1	x1	PROPN
ejpam-4006	247	24	=	=	SYM
ejpam-4006	247	25	t	t	PROPN
ejpam-4006	247	26	,	,	PUNCT
ejpam-4006	247	27	we	we	PRON
ejpam-4006	247	28	obtain	obtain	VERB
ejpam-4006	247	29	[	[	X
ejpam-4006	247	30	(	(	PUNCT
ejpam-4006	247	31	−1)kre−2(x	−1)kre−2(x	NOUN
ejpam-4006	247	32	)	)	PUNCT
ejpam-4006	247	33	∗	∗	NOUN
ejpam-4006	247	34	s−2(x	s−2(x	PROPN
ejpam-4006	247	35	)	)	PUNCT
ejpam-4006	247	36	∗	∗	PROPN
ejpam-4006	247	37	t−2(x	t−2(x	PROPN
ejpam-4006	247	38	)	)	PUNCT
ejpam-4006	247	39	]	]	PUNCT
ejpam-4006	248	1	∗h(x	∗h(x	PROPN
ejpam-4006	248	2	,	,	PUNCT
ejpam-4006	248	3	0	0	NUM
ejpam-4006	248	4	)	)	PUNCT
ejpam-4006	248	5	=	=	SYM
ejpam-4006	248	6	m2(u	m2(u	PROPN
ejpam-4006	248	7	)	)	PUNCT
ejpam-4006	248	8	(	(	PUNCT
ejpam-4006	248	9	45	45	NUM
ejpam-4006	248	10	)	)	PUNCT
ejpam-4006	248	11	is	be	AUX
ejpam-4006	248	12	the	the	DET
ejpam-4006	248	13	fundamental	fundamental	ADJ
ejpam-4006	248	14	solution	solution	NOUN
ejpam-4006	248	15	of	of	ADP
ejpam-4006	248	16	the	the	DET
ejpam-4006	248	17	wave	wave	NOUN
ejpam-4006	248	18	operator	operator	NOUN
ejpam-4006	248	19	is	be	AUX
ejpam-4006	248	20	defined	define	VERB
ejpam-4006	248	21	by	by	ADP
ejpam-4006	248	22	(	(	PUNCT
ejpam-4006	248	23	11	11	NUM
ejpam-4006	248	24	)	)	PUNCT
ejpam-4006	248	25	where	where	SCONJ
ejpam-4006	248	26	m2(u	m2(u	X
ejpam-4006	248	27	)	)	PUNCT
ejpam-4006	248	28	is	be	AUX
ejpam-4006	248	29	defined	define	VERB
ejpam-4006	248	30	by	by	ADP
ejpam-4006	248	31	(	(	PUNCT
ejpam-4006	248	32	21	21	NUM
ejpam-4006	248	33	)	)	PUNCT
ejpam-4006	248	34	with	with	ADP
ejpam-4006	248	35	α	α	NOUN
ejpam-4006	248	36	=	=	SYM
ejpam-4006	248	37	2	2	NUM
ejpam-4006	248	38	.	.	PUNCT
ejpam-4006	248	39	proof	proof	NOUN
ejpam-4006	248	40	.	.	PUNCT
ejpam-4006	249	1	from	from	ADP
ejpam-4006	249	2	(	(	PUNCT
ejpam-4006	249	3	15	15	NUM
ejpam-4006	249	4	)	)	PUNCT
ejpam-4006	249	5	and	and	CCONJ
ejpam-4006	249	6	(	(	PUNCT
ejpam-4006	249	7	39	39	NUM
ejpam-4006	249	8	)	)	PUNCT
ejpam-4006	249	9	we	we	PRON
ejpam-4006	249	10	have	have	VERB
ejpam-4006	249	11	⊕kmh(x	⊕kmh(x	NOUN
ejpam-4006	249	12	,	,	PUNCT
ejpam-4006	249	13	m	m	NOUN
ejpam-4006	249	14	)	)	PUNCT
ejpam-4006	249	15	=	=	SYM
ejpam-4006	250	1	(	(	PUNCT
ejpam-4006	250	2	(	(	PUNCT
ejpam-4006	250	3	�	�	PROPN
ejpam-4006	250	4	+	+	NUM
ejpam-4006	250	5	m2	m2	PROPN
ejpam-4006	250	6	)	)	PUNCT
ejpam-4006	250	7	k	k	PROPN
ejpam-4006	251	1	(	(	PUNCT
ejpam-4006	251	2	4+m2	4+m2	X
ejpam-4006	251	3	)	)	PUNCT
ejpam-4006	251	4	k	k	PROPN
ejpam-4006	252	1	(	(	PUNCT
ejpam-4006	252	2	l1	l1	PROPN
ejpam-4006	252	3	+	+	PROPN
ejpam-4006	252	4	m2	m2	PROPN
ejpam-4006	252	5	)	)	PUNCT
ejpam-4006	252	6	k	k	PROPN
ejpam-4006	252	7	(	(	PUNCT
ejpam-4006	252	8	l2	l2	NOUN
ejpam-4006	252	9	+	+	NOUN
ejpam-4006	252	10	m2	m2	PROPN
ejpam-4006	252	11	)	)	PUNCT
ejpam-4006	252	12	k	k	PROPN
ejpam-4006	252	13	)	)	PUNCT
ejpam-4006	252	14	h(x	h(x	PROPN
ejpam-4006	252	15	,	,	PUNCT
ejpam-4006	252	16	m	m	NOUN
ejpam-4006	252	17	)	)	PUNCT
ejpam-4006	252	18	=	=	SYM
ejpam-4006	252	19	δ	δ	PROPN
ejpam-4006	252	20	.	.	PUNCT
ejpam-4006	253	1	convolving	convolve	VERB
ejpam-4006	253	2	both	both	DET
ejpam-4006	253	3	sides	side	NOUN
ejpam-4006	253	4	of	of	ADP
ejpam-4006	253	5	the	the	DET
ejpam-4006	253	6	above	above	ADJ
ejpam-4006	253	7	equation	equation	NOUN
ejpam-4006	253	8	by	by	ADP
ejpam-4006	253	9	the	the	DET
ejpam-4006	253	10	convolution	convolution	NOUN
ejpam-4006	253	11	w2k(x	w2k(x	PROPN
ejpam-4006	253	12	,	,	PUNCT
ejpam-4006	253	13	m	m	NOUN
ejpam-4006	253	14	)	)	PUNCT
ejpam-4006	253	15	∗	∗	NOUN
ejpam-4006	253	16	y2k(x	y2k(x	PROPN
ejpam-4006	253	17	,	,	PUNCT
ejpam-4006	253	18	m	m	NOUN
ejpam-4006	253	19	)	)	PUNCT
ejpam-4006	253	20	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	253	21	,	,	PUNCT
ejpam-4006	253	22	m	m	NOUN
ejpam-4006	253	23	)	)	PUNCT
ejpam-4006	253	24	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	253	25	,	,	PUNCT
ejpam-4006	253	26	m	m	NOUN
ejpam-4006	253	27	)	)	PUNCT
ejpam-4006	253	28	and	and	CCONJ
ejpam-4006	253	29	the	the	DET
ejpam-4006	253	30	properties	property	NOUN
ejpam-4006	253	31	of	of	ADP
ejpam-4006	253	32	convolution	convolution	NOUN
ejpam-4006	253	33	with	with	ADP
ejpam-4006	253	34	derivatives	derivative	NOUN
ejpam-4006	253	35	,	,	PUNCT
ejpam-4006	253	36	we	we	PRON
ejpam-4006	253	37	obtain	obtain	VERB
ejpam-4006	253	38	(	(	PUNCT
ejpam-4006	253	39	�	�	PROPN
ejpam-4006	253	40	+	+	NOUN
ejpam-4006	253	41	m2	m2	PROPN
ejpam-4006	253	42	)	)	PUNCT
ejpam-4006	253	43	k	k	PROPN
ejpam-4006	254	1	w2k(x	w2k(x	PROPN
ejpam-4006	254	2	,	,	PUNCT
ejpam-4006	254	3	m	m	NOUN
ejpam-4006	254	4	)	)	PUNCT
ejpam-4006	254	5	∗	∗	NOUN
ejpam-4006	254	6	(	(	PUNCT
ejpam-4006	254	7	4+m2	4+m2	NOUN
ejpam-4006	254	8	)	)	PUNCT
ejpam-4006	254	9	k	k	PROPN
ejpam-4006	254	10	y2k(x	y2k(x	PROPN
ejpam-4006	254	11	,	,	PUNCT
ejpam-4006	254	12	m	m	NOUN
ejpam-4006	254	13	)	)	PUNCT
ejpam-4006	254	14	∗	∗	NOUN
ejpam-4006	254	15	(	(	PUNCT
ejpam-4006	254	16	l1	l1	PROPN
ejpam-4006	254	17	+	+	PROPN
ejpam-4006	254	18	m2	m2	PROPN
ejpam-4006	254	19	)	)	PUNCT
ejpam-4006	254	20	k	k	PROPN
ejpam-4006	254	21	m2k(x	m2k(x	PROPN
ejpam-4006	254	22	,	,	PUNCT
ejpam-4006	254	23	m	m	NOUN
ejpam-4006	254	24	)	)	PUNCT
ejpam-4006	254	25	∗	∗	NOUN
ejpam-4006	254	26	(	(	PUNCT
ejpam-4006	254	27	l2	l2	NOUN
ejpam-4006	254	28	+	+	NOUN
ejpam-4006	254	29	m2	m2	PROPN
ejpam-4006	254	30	)	)	PUNCT
ejpam-4006	254	31	k	k	PROPN
ejpam-4006	254	32	n2k(x	n2k(x	PROPN
ejpam-4006	254	33	,	,	PUNCT
ejpam-4006	254	34	m	m	NOUN
ejpam-4006	254	35	)	)	PUNCT
ejpam-4006	254	36	∗h(x	∗h(x	PROPN
ejpam-4006	254	37	,	,	PUNCT
ejpam-4006	254	38	m	m	NOUN
ejpam-4006	254	39	)	)	PUNCT
ejpam-4006	254	40	=	=	SYM
ejpam-4006	254	41	y2k(x	y2k(x	PROPN
ejpam-4006	254	42	,	,	PUNCT
ejpam-4006	254	43	m	m	NOUN
ejpam-4006	254	44	)	)	PUNCT
ejpam-4006	254	45	∗w2k(x	∗w2k(x	PROPN
ejpam-4006	254	46	,	,	PUNCT
ejpam-4006	254	47	m	m	NOUN
ejpam-4006	254	48	)	)	PUNCT
ejpam-4006	254	49	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	254	50	,	,	PUNCT
ejpam-4006	254	51	m	m	NOUN
ejpam-4006	254	52	)	)	PUNCT
ejpam-4006	254	53	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	254	54	,	,	PUNCT
ejpam-4006	254	55	m	m	NOUN
ejpam-4006	254	56	)	)	PUNCT
ejpam-4006	254	57	∗	∗	PROPN
ejpam-4006	254	58	δ	δ	PROPN
ejpam-4006	254	59	.	.	PUNCT
ejpam-4006	255	1	(	(	PUNCT
ejpam-4006	255	2	46	46	NUM
ejpam-4006	255	3	)	)	PUNCT
ejpam-4006	255	4	thus	thus	ADV
ejpam-4006	255	5	h(x	h(x	PROPN
ejpam-4006	255	6	,	,	PUNCT
ejpam-4006	255	7	m	m	NOUN
ejpam-4006	255	8	)	)	PUNCT
ejpam-4006	256	1	=	=	SYM
ejpam-4006	256	2	δ	δ	PROPN
ejpam-4006	256	3	∗	∗	NOUN
ejpam-4006	256	4	δ	δ	PROPN
ejpam-4006	256	5	∗	∗	NOUN
ejpam-4006	256	6	δ	δ	PROPN
ejpam-4006	256	7	∗	∗	NOUN
ejpam-4006	256	8	δ	δ	PROPN
ejpam-4006	256	9	∗h(x	∗h(x	PROPN
ejpam-4006	256	10	,	,	PUNCT
ejpam-4006	256	11	m	m	NOUN
ejpam-4006	256	12	)	)	PUNCT
ejpam-4006	256	13	=	=	SYM
ejpam-4006	257	1	w2k(x	w2k(x	PROPN
ejpam-4006	257	2	,	,	PUNCT
ejpam-4006	257	3	m	m	NOUN
ejpam-4006	257	4	)	)	PUNCT
ejpam-4006	257	5	∗	∗	NOUN
ejpam-4006	257	6	y2k(x	y2k(x	PROPN
ejpam-4006	257	7	,	,	PUNCT
ejpam-4006	257	8	m	m	NOUN
ejpam-4006	257	9	)	)	PUNCT
ejpam-4006	257	10	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	257	11	,	,	PUNCT
ejpam-4006	257	12	m	m	NOUN
ejpam-4006	257	13	)	)	PUNCT
ejpam-4006	257	14	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	257	15	,	,	PUNCT
ejpam-4006	257	16	m	m	NOUN
ejpam-4006	257	17	)	)	PUNCT
ejpam-4006	257	18	(	(	PUNCT
ejpam-4006	257	19	47	47	NUM
ejpam-4006	257	20	)	)	PUNCT
ejpam-4006	257	21	by	by	ADP
ejpam-4006	257	22	lemma	lemma	PROPN
ejpam-4006	257	23	9	9	NUM
ejpam-4006	257	24	,	,	PUNCT
ejpam-4006	257	25	lemma	lemma	PROPN
ejpam-4006	257	26	10	10	NUM
ejpam-4006	257	27	,	,	PUNCT
ejpam-4006	257	28	lemma	lemma	PROPN
ejpam-4006	257	29	11	11	NUM
ejpam-4006	257	30	and	and	CCONJ
ejpam-4006	257	31	lemma	lemma	PROPN
ejpam-4006	257	32	12	12	NUM
ejpam-4006	257	33	.	.	PUNCT
ejpam-4006	258	1	thus	thus	ADV
ejpam-4006	258	2	we	we	PRON
ejpam-4006	258	3	obtain	obtain	VERB
ejpam-4006	258	4	(	(	PUNCT
ejpam-4006	258	5	40	40	NUM
ejpam-4006	258	6	)	)	PUNCT
ejpam-4006	258	7	as	as	SCONJ
ejpam-4006	258	8	required	require	VERB
ejpam-4006	258	9	.	.	PUNCT
ejpam-4006	259	1	in	in	ADP
ejpam-4006	259	2	particular	particular	ADJ
ejpam-4006	259	3	,	,	PUNCT
ejpam-4006	259	4	for	for	ADP
ejpam-4006	259	5	q	q	NOUN
ejpam-4006	259	6	=	=	NOUN
ejpam-4006	259	7	m	m	NOUN
ejpam-4006	259	8	=	=	NOUN
ejpam-4006	259	9	0	0	PUNCT
ejpam-4006	259	10	then	then	ADV
ejpam-4006	259	11	(	(	PUNCT
ejpam-4006	259	12	39	39	NUM
ejpam-4006	259	13	)	)	PUNCT
ejpam-4006	259	14	becomes	become	VERB
ejpam-4006	259	15	44k	44k	PROPN
ejpam-4006	259	16	p	p	ADJ
ejpam-4006	259	17	h(x	h(x	PROPN
ejpam-4006	259	18	,	,	PUNCT
ejpam-4006	259	19	0	0	NUM
ejpam-4006	259	20	)	)	PUNCT
ejpam-4006	259	21	=	=	SYM
ejpam-4006	259	22	δ	δ	PROPN
ejpam-4006	259	23	s.	s.	PROPN
ejpam-4006	259	24	bupasiri	bupasiri	PROPN
ejpam-4006	259	25	/	/	SYM
ejpam-4006	259	26	eur	eur	PROPN
ejpam-4006	259	27	.	.	PUNCT
ejpam-4006	260	1	j.	j.	PROPN
ejpam-4006	260	2	pure	pure	PROPN
ejpam-4006	260	3	appl	appl	PROPN
ejpam-4006	260	4	.	.	PROPN
ejpam-4006	260	5	math	math	PROPN
ejpam-4006	260	6	,	,	PUNCT
ejpam-4006	260	7	14	14	NUM
ejpam-4006	260	8	(	(	PUNCT
ejpam-4006	260	9	3	3	NUM
ejpam-4006	260	10	)	)	PUNCT
ejpam-4006	260	11	(	(	PUNCT
ejpam-4006	260	12	2021	2021	NUM
ejpam-4006	260	13	)	)	PUNCT
ejpam-4006	260	14	,	,	PUNCT
ejpam-4006	260	15	881	881	NUM
ejpam-4006	260	16	-	-	SYM
ejpam-4006	260	17	894	894	NUM
ejpam-4006	260	18	892	892	NUM
ejpam-4006	260	19	where	where	SCONJ
ejpam-4006	260	20	44k	44k	PROPN
ejpam-4006	260	21	p	p	PROPN
ejpam-4006	260	22	is	be	AUX
ejpam-4006	260	23	the	the	DET
ejpam-4006	260	24	laplace	laplace	NOUN
ejpam-4006	260	25	operator	operator	NOUN
ejpam-4006	260	26	of	of	ADP
ejpam-4006	260	27	p	p	NOUN
ejpam-4006	260	28	-	-	PUNCT
ejpam-4006	260	29	dimension	dimension	NOUN
ejpam-4006	260	30	iterated	iterated	ADJ
ejpam-4006	260	31	4k	4k	NOUN
ejpam-4006	260	32	-	-	NOUN
ejpam-4006	260	33	times	time	NOUN
ejpam-4006	260	34	.	.	PUNCT
ejpam-4006	261	1	by	by	ADP
ejpam-4006	261	2	lemma	lemma	PROPN
ejpam-4006	261	3	10	10	NUM
ejpam-4006	261	4	,	,	PUNCT
ejpam-4006	261	5	we	we	PRON
ejpam-4006	261	6	have	have	VERB
ejpam-4006	261	7	h(x	h(x	PROPN
ejpam-4006	261	8	,	,	PUNCT
ejpam-4006	261	9	0	0	NUM
ejpam-4006	261	10	)	)	PUNCT
ejpam-4006	261	11	=	=	SYM
ejpam-4006	261	12	y8k(x	y8k(x	PROPN
ejpam-4006	261	13	,	,	PUNCT
ejpam-4006	261	14	0	0	NUM
ejpam-4006	261	15	)	)	PUNCT
ejpam-4006	261	16	=	=	SYM
ejpam-4006	261	17	re8k(x	re8k(x	PROPN
ejpam-4006	261	18	)	)	PUNCT
ejpam-4006	261	19	(	(	PUNCT
ejpam-4006	261	20	48	48	NUM
ejpam-4006	261	21	)	)	PUNCT
ejpam-4006	261	22	is	be	AUX
ejpam-4006	261	23	the	the	DET
ejpam-4006	261	24	fundamental	fundamental	ADJ
ejpam-4006	261	25	solution	solution	NOUN
ejpam-4006	261	26	of	of	ADP
ejpam-4006	261	27	(	(	PUNCT
ejpam-4006	261	28	41	41	NUM
ejpam-4006	261	29	)	)	PUNCT
ejpam-4006	261	30	.	.	PUNCT
ejpam-4006	262	1	from	from	ADP
ejpam-4006	262	2	lemma	lemma	PROPN
ejpam-4006	262	3	9	9	NUM
ejpam-4006	262	4	,	,	PUNCT
ejpam-4006	262	5	lemma	lemma	PROPN
ejpam-4006	262	6	10	10	NUM
ejpam-4006	262	7	,	,	PUNCT
ejpam-4006	262	8	lemma	lemma	PROPN
ejpam-4006	262	9	11	11	NUM
ejpam-4006	262	10	and	and	CCONJ
ejpam-4006	262	11	lemma	lemma	PROPN
ejpam-4006	262	12	12	12	NUM
ejpam-4006	262	13	,	,	PUNCT
ejpam-4006	262	14	we	we	PRON
ejpam-4006	262	15	have	have	VERB
ejpam-4006	262	16	h(x	h(x	PROPN
ejpam-4006	262	17	,	,	PUNCT
ejpam-4006	262	18	m	m	VERB
ejpam-4006	262	19	=	=	NOUN
ejpam-4006	262	20	0	0	NUM
ejpam-4006	262	21	)	)	PUNCT
ejpam-4006	262	22	=	=	SYM
ejpam-4006	263	1	w2k(x	w2k(x	PROPN
ejpam-4006	263	2	,	,	PUNCT
ejpam-4006	263	3	0	0	NUM
ejpam-4006	263	4	)	)	PUNCT
ejpam-4006	263	5	∗	∗	NOUN
ejpam-4006	263	6	y2k(x	y2k(x	PROPN
ejpam-4006	263	7	,	,	PUNCT
ejpam-4006	263	8	0	0	NUM
ejpam-4006	263	9	)	)	PUNCT
ejpam-4006	263	10	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	263	11	,	,	PUNCT
ejpam-4006	263	12	0	0	NUM
ejpam-4006	263	13	)	)	PUNCT
ejpam-4006	263	14	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	263	15	,	,	PUNCT
ejpam-4006	263	16	0	0	NUM
ejpam-4006	263	17	)	)	PUNCT
ejpam-4006	263	18	=	=	NOUN
ejpam-4006	263	19	[	[	PUNCT
ejpam-4006	263	20	rh2k(x	rh2k(x	PROPN
ejpam-4006	263	21	)	)	PUNCT
ejpam-4006	263	22	∗	∗	NOUN
ejpam-4006	263	23	(	(	PUNCT
ejpam-4006	263	24	−1)kre2k(x	−1)kre2k(x	PROPN
ejpam-4006	263	25	)	)	PUNCT
ejpam-4006	263	26	]	]	PUNCT
ejpam-4006	263	27	∗	∗	PROPN
ejpam-4006	263	28	s2k(x	s2k(x	PROPN
ejpam-4006	263	29	)	)	PUNCT
ejpam-4006	263	30	∗	∗	PROPN
ejpam-4006	263	31	t2k(x	t2k(x	PROPN
ejpam-4006	263	32	)	)	PUNCT
ejpam-4006	263	33	(	(	PUNCT
ejpam-4006	263	34	49	49	NUM
ejpam-4006	263	35	)	)	PUNCT
ejpam-4006	263	36	is	be	AUX
ejpam-4006	263	37	the	the	DET
ejpam-4006	263	38	fundamental	fundamental	ADJ
ejpam-4006	263	39	solution	solution	NOUN
ejpam-4006	263	40	of	of	ADP
ejpam-4006	263	41	the	the	DET
ejpam-4006	263	42	o	o	NOUN
ejpam-4006	263	43	-	-	ADJ
ejpam-4006	263	44	plus	plus	ADJ
ejpam-4006	263	45	operator	operator	NOUN
ejpam-4006	263	46	⊕k	⊕k	NOUN
ejpam-4006	263	47	in	in	ADP
ejpam-4006	263	48	[	[	X
ejpam-4006	263	49	2	2	NUM
ejpam-4006	263	50	]	]	PUNCT
ejpam-4006	263	51	.	.	PUNCT
ejpam-4006	264	1	now	now	ADV
ejpam-4006	264	2	we	we	PRON
ejpam-4006	264	3	will	will	AUX
ejpam-4006	264	4	relate	relate	VERB
ejpam-4006	264	5	the	the	DET
ejpam-4006	264	6	fundamental	fundamental	ADJ
ejpam-4006	264	7	solution	solution	NOUN
ejpam-4006	264	8	h(x	h(x	PROPN
ejpam-4006	264	9	,	,	PUNCT
ejpam-4006	264	10	m	m	VERB
ejpam-4006	264	11	=	=	NOUN
ejpam-4006	264	12	0	0	NUM
ejpam-4006	264	13	)	)	PUNCT
ejpam-4006	264	14	given	give	VERB
ejpam-4006	264	15	by	by	ADP
ejpam-4006	264	16	(	(	PUNCT
ejpam-4006	264	17	43	43	NUM
ejpam-4006	264	18	)	)	PUNCT
ejpam-4006	264	19	to	to	ADP
ejpam-4006	264	20	the	the	DET
ejpam-4006	264	21	fundamental	fundamental	ADJ
ejpam-4006	264	22	solution	solution	NOUN
ejpam-4006	264	23	of	of	ADP
ejpam-4006	264	24	the	the	DET
ejpam-4006	264	25	wave	wave	NOUN
ejpam-4006	264	26	equation	equation	NOUN
ejpam-4006	264	27	is	be	AUX
ejpam-4006	264	28	defined	define	VERB
ejpam-4006	264	29	by	by	ADP
ejpam-4006	264	30	(	(	PUNCT
ejpam-4006	264	31	11	11	NUM
ejpam-4006	264	32	)	)	PUNCT
ejpam-4006	264	33	.	.	PUNCT
ejpam-4006	265	1	now	now	ADV
ejpam-4006	265	2	from	from	ADP
ejpam-4006	265	3	(	(	PUNCT
ejpam-4006	265	4	43	43	NUM
ejpam-4006	265	5	)	)	PUNCT
ejpam-4006	265	6	and	and	CCONJ
ejpam-4006	265	7	by	by	ADP
ejpam-4006	265	8	lemma	lemma	PROPN
ejpam-4006	265	9	7	7	NUM
ejpam-4006	265	10	and	and	CCONJ
ejpam-4006	265	11	lemma	lemma	PROPN
ejpam-4006	265	12	8(2	8(2	NUM
ejpam-4006	265	13	)	)	PUNCT
ejpam-4006	265	14	and	and	CCONJ
ejpam-4006	265	15	the	the	DET
ejpam-4006	265	16	properties	property	NOUN
ejpam-4006	265	17	of	of	ADP
ejpam-4006	265	18	inverses	inverse	NOUN
ejpam-4006	265	19	in	in	ADP
ejpam-4006	265	20	convolution	convolution	NOUN
ejpam-4006	265	21	algebra	algebra	NOUN
ejpam-4006	265	22	,	,	PUNCT
ejpam-4006	265	23	we	we	PRON
ejpam-4006	265	24	obtain	obtain	VERB
ejpam-4006	265	25	[	[	X
ejpam-4006	265	26	(	(	PUNCT
ejpam-4006	265	27	−1)kre−2k(x	−1)kre−2k(x	NOUN
ejpam-4006	265	28	)	)	PUNCT
ejpam-4006	265	29	∗	∗	PROPN
ejpam-4006	265	30	s−2k(x	s−2k(x	PROPN
ejpam-4006	265	31	)	)	PUNCT
ejpam-4006	265	32	∗	∗	NOUN
ejpam-4006	265	33	t−2k(x	t−2k(x	NOUN
ejpam-4006	265	34	)	)	PUNCT
ejpam-4006	265	35	]	]	PUNCT
ejpam-4006	266	1	∗h(x	∗h(x	PROPN
ejpam-4006	266	2	,	,	PUNCT
ejpam-4006	266	3	m	m	NOUN
ejpam-4006	266	4	=	=	NOUN
ejpam-4006	266	5	0	0	NUM
ejpam-4006	266	6	)	)	PUNCT
ejpam-4006	266	7	=	=	SYM
ejpam-4006	267	1	δ	δ	PROPN
ejpam-4006	267	2	∗	∗	NOUN
ejpam-4006	267	3	δ	δ	PROPN
ejpam-4006	267	4	∗	∗	PROPN
ejpam-4006	267	5	δ	δ	PROPN
ejpam-4006	267	6	∗rh2k(x	∗rh2k(x	VERB
ejpam-4006	267	7	)	)	PUNCT
ejpam-4006	267	8	=	=	SYM
ejpam-4006	268	1	rh2k(x	rh2k(x	PROPN
ejpam-4006	268	2	)	)	PUNCT
ejpam-4006	268	3	.	.	PUNCT
ejpam-4006	269	1	actually	actually	ADV
ejpam-4006	269	2	,	,	PUNCT
ejpam-4006	269	3	by	by	ADP
ejpam-4006	269	4	lemma	lemma	PROPN
ejpam-4006	269	5	2	2	NUM
ejpam-4006	269	6	rh2k(x	rh2k(x	PROPN
ejpam-4006	269	7	)	)	PUNCT
ejpam-4006	269	8	is	be	AUX
ejpam-4006	269	9	the	the	DET
ejpam-4006	269	10	fundamental	fundamental	ADJ
ejpam-4006	269	11	solution	solution	NOUN
ejpam-4006	269	12	of	of	ADP
ejpam-4006	269	13	the	the	DET
ejpam-4006	269	14	ultra	ultra	ADJ
ejpam-4006	269	15	-	-	ADJ
ejpam-4006	269	16	hyperbolic	hyperbolic	ADJ
ejpam-4006	269	17	operator	operator	NOUN
ejpam-4006	269	18	�	�	PROPN
ejpam-4006	269	19	k	k	PROPN
ejpam-4006	269	20	iterated	iterate	VERB
ejpam-4006	269	21	k	k	NOUN
ejpam-4006	269	22	-	-	PUNCT
ejpam-4006	269	23	times	time	NOUN
ejpam-4006	269	24	is	be	AUX
ejpam-4006	269	25	defined	define	VERB
ejpam-4006	269	26	by	by	ADP
ejpam-4006	269	27	(	(	PUNCT
ejpam-4006	269	28	9	9	NUM
ejpam-4006	269	29	)	)	PUNCT
ejpam-4006	269	30	.	.	PUNCT
ejpam-4006	270	1	in	in	ADP
ejpam-4006	270	2	particular	particular	ADJ
ejpam-4006	270	3	,	,	PUNCT
ejpam-4006	270	4	by	by	ADP
ejpam-4006	270	5	putting	put	VERB
ejpam-4006	270	6	p	p	NOUN
ejpam-4006	270	7	=	=	NOUN
ejpam-4006	270	8	1	1	NUM
ejpam-4006	270	9	,	,	PUNCT
ejpam-4006	270	10	q	q	NOUN
ejpam-4006	270	11	=	=	PUNCT
ejpam-4006	270	12	n−	n−	NOUN
ejpam-4006	270	13	1	1	NUM
ejpam-4006	270	14	,	,	PUNCT
ejpam-4006	270	15	k	k	NOUN
ejpam-4006	270	16	=	=	SYM
ejpam-4006	270	17	1	1	NUM
ejpam-4006	270	18	and	and	CCONJ
ejpam-4006	270	19	x1	x1	PROPN
ejpam-4006	270	20	=	=	SYM
ejpam-4006	270	21	t	t	PROPN
ejpam-4006	270	22	in	in	ADP
ejpam-4006	270	23	(	(	PUNCT
ejpam-4006	270	24	43	43	NUM
ejpam-4006	270	25	)	)	PUNCT
ejpam-4006	270	26	and	and	CCONJ
ejpam-4006	270	27	(	(	PUNCT
ejpam-4006	270	28	44	44	NUM
ejpam-4006	270	29	)	)	PUNCT
ejpam-4006	270	30	then	then	ADV
ejpam-4006	270	31	rh2	rh2	INTJ
ejpam-4006	270	32	(	(	PUNCT
ejpam-4006	270	33	x	x	X
ejpam-4006	270	34	)	)	PUNCT
ejpam-4006	270	35	reduce	reduce	VERB
ejpam-4006	270	36	to	to	ADP
ejpam-4006	270	37	m2(u	m2(u	NUM
ejpam-4006	270	38	)	)	PUNCT
ejpam-4006	270	39	is	be	AUX
ejpam-4006	270	40	defined	define	VERB
ejpam-4006	270	41	by	by	ADP
ejpam-4006	270	42	(	(	PUNCT
ejpam-4006	270	43	21	21	NUM
ejpam-4006	270	44	)	)	PUNCT
ejpam-4006	270	45	with	with	ADP
ejpam-4006	270	46	α	α	NOUN
ejpam-4006	270	47	=	=	SYM
ejpam-4006	270	48	2	2	NUM
ejpam-4006	270	49	.	.	PUNCT
ejpam-4006	270	50	thus	thus	ADV
ejpam-4006	270	51	we	we	PRON
ejpam-4006	270	52	obtain	obtain	VERB
ejpam-4006	270	53	[	[	X
ejpam-4006	270	54	(	(	PUNCT
ejpam-4006	270	55	−1)kre−2(x	−1)kre−2(x	NOUN
ejpam-4006	270	56	)	)	PUNCT
ejpam-4006	270	57	∗	∗	NOUN
ejpam-4006	270	58	s−2(x	s−2(x	PROPN
ejpam-4006	270	59	)	)	PUNCT
ejpam-4006	270	60	∗	∗	PROPN
ejpam-4006	270	61	t−2(x	t−2(x	PROPN
ejpam-4006	270	62	)	)	PUNCT
ejpam-4006	270	63	]	]	PUNCT
ejpam-4006	271	1	∗h(x	∗h(x	PROPN
ejpam-4006	271	2	,	,	PUNCT
ejpam-4006	271	3	m	m	NOUN
ejpam-4006	271	4	=	=	NOUN
ejpam-4006	271	5	0	0	NUM
ejpam-4006	271	6	)	)	PUNCT
ejpam-4006	271	7	=	=	SYM
ejpam-4006	271	8	m2(u	m2(u	PROPN
ejpam-4006	271	9	)	)	PUNCT
ejpam-4006	271	10	is	be	AUX
ejpam-4006	271	11	the	the	DET
ejpam-4006	271	12	fundamental	fundamental	ADJ
ejpam-4006	271	13	solution	solution	NOUN
ejpam-4006	271	14	of	of	ADP
ejpam-4006	271	15	the	the	DET
ejpam-4006	271	16	wave	wave	NOUN
ejpam-4006	271	17	operator	operator	NOUN
ejpam-4006	271	18	is	be	AUX
ejpam-4006	271	19	defined	define	VERB
ejpam-4006	271	20	by	by	ADP
ejpam-4006	271	21	(	(	PUNCT
ejpam-4006	271	22	11	11	NUM
ejpam-4006	271	23	)	)	PUNCT
ejpam-4006	271	24	where	where	SCONJ
ejpam-4006	271	25	u	u	NOUN
ejpam-4006	271	26	=	=	PROPN
ejpam-4006	271	27	t2	t2	PROPN
ejpam-4006	271	28	−	−	PROPN
ejpam-4006	272	1	x21	x21	NUM
ejpam-4006	272	2	−	−	PROPN
ejpam-4006	272	3	x22	x22	NOUN
ejpam-4006	272	4	−	−	PROPN
ejpam-4006	272	5	·	·	PUNCT
ejpam-4006	272	6	·	·	PUNCT
ejpam-4006	272	7	·	·	PUNCT
ejpam-4006	273	1	−	−	PROPN
ejpam-4006	274	1	x2n−1	x2n−1	PROPN
ejpam-4006	274	2	.	.	PUNCT
ejpam-4006	275	1	theorem	theorem	VERB
ejpam-4006	275	2	2	2	NUM
ejpam-4006	275	3	.	.	PUNCT
ejpam-4006	275	4	given	give	VERB
ejpam-4006	275	5	the	the	DET
ejpam-4006	275	6	equation	equation	NOUN
ejpam-4006	275	7	⊕kmu(x	⊕kmu(x	VERB
ejpam-4006	275	8	)	)	PUNCT
ejpam-4006	275	9	=	=	SYM
ejpam-4006	275	10	f(x	f(x	PROPN
ejpam-4006	275	11	)	)	PUNCT
ejpam-4006	275	12	,	,	PUNCT
ejpam-4006	275	13	(	(	PUNCT
ejpam-4006	275	14	50	50	NUM
ejpam-4006	275	15	)	)	PUNCT
ejpam-4006	275	16	where	where	SCONJ
ejpam-4006	275	17	f(x	f(x	PROPN
ejpam-4006	275	18	)	)	PUNCT
ejpam-4006	275	19	is	be	AUX
ejpam-4006	275	20	a	a	DET
ejpam-4006	275	21	given	give	VERB
ejpam-4006	275	22	generalized	generalized	ADJ
ejpam-4006	275	23	function	function	NOUN
ejpam-4006	275	24	and	and	CCONJ
ejpam-4006	275	25	u(x	u(x	NOUN
ejpam-4006	275	26	)	)	PUNCT
ejpam-4006	275	27	is	be	AUX
ejpam-4006	275	28	an	an	DET
ejpam-4006	275	29	unknown	unknown	ADJ
ejpam-4006	275	30	function	function	NOUN
ejpam-4006	275	31	,	,	PUNCT
ejpam-4006	275	32	we	we	PRON
ejpam-4006	275	33	obtain	obtain	VERB
ejpam-4006	275	34	u(x	u(x	NOUN
ejpam-4006	275	35	)	)	PUNCT
ejpam-4006	276	1	=	=	SYM
ejpam-4006	276	2	h(x	h(x	PROPN
ejpam-4006	276	3	,	,	PUNCT
ejpam-4006	276	4	m	m	NOUN
ejpam-4006	276	5	)	)	PUNCT
ejpam-4006	276	6	∗	∗	NOUN
ejpam-4006	276	7	f(x	f(x	PROPN
ejpam-4006	276	8	)	)	PUNCT
ejpam-4006	276	9	(	(	PUNCT
ejpam-4006	276	10	51	51	NUM
ejpam-4006	276	11	)	)	PUNCT
ejpam-4006	276	12	is	be	AUX
ejpam-4006	276	13	a	a	DET
ejpam-4006	276	14	solution	solution	NOUN
ejpam-4006	276	15	of	of	ADP
ejpam-4006	276	16	the	the	DET
ejpam-4006	276	17	equation	equation	NOUN
ejpam-4006	276	18	(	(	PUNCT
ejpam-4006	276	19	50	50	NUM
ejpam-4006	276	20	)	)	PUNCT
ejpam-4006	276	21	,	,	PUNCT
ejpam-4006	276	22	where	where	SCONJ
ejpam-4006	276	23	h(x	h(x	PROPN
ejpam-4006	276	24	,	,	PUNCT
ejpam-4006	276	25	m	m	PROPN
ejpam-4006	276	26	)	)	PUNCT
ejpam-4006	276	27	is	be	AUX
ejpam-4006	276	28	the	the	DET
ejpam-4006	276	29	fundamental	fundamental	ADJ
ejpam-4006	276	30	solution	solution	NOUN
ejpam-4006	276	31	of	of	ADP
ejpam-4006	276	32	equation	equation	NOUN
ejpam-4006	276	33	(	(	PUNCT
ejpam-4006	276	34	39	39	NUM
ejpam-4006	276	35	)	)	PUNCT
ejpam-4006	276	36	.	.	PUNCT
ejpam-4006	277	1	proof	proof	NOUN
ejpam-4006	277	2	.	.	PUNCT
ejpam-4006	278	1	convolving	convolve	VERB
ejpam-4006	278	2	both	both	DET
ejpam-4006	278	3	sides	side	NOUN
ejpam-4006	278	4	of	of	ADP
ejpam-4006	278	5	(	(	PUNCT
ejpam-4006	278	6	50	50	NUM
ejpam-4006	278	7	)	)	PUNCT
ejpam-4006	278	8	by	by	ADP
ejpam-4006	278	9	h(x	h(x	PROPN
ejpam-4006	278	10	,	,	PUNCT
ejpam-4006	278	11	m	m	PROPN
ejpam-4006	278	12	)	)	PUNCT
ejpam-4006	278	13	,	,	PUNCT
ejpam-4006	278	14	where	where	SCONJ
ejpam-4006	278	15	h(x	h(x	PROPN
ejpam-4006	278	16	,	,	PUNCT
ejpam-4006	278	17	m	m	PROPN
ejpam-4006	278	18	)	)	PUNCT
ejpam-4006	278	19	is	be	AUX
ejpam-4006	278	20	the	the	DET
ejpam-4006	278	21	fundamental	fundamental	ADJ
ejpam-4006	278	22	solution	solution	NOUN
ejpam-4006	278	23	for	for	ADP
ejpam-4006	278	24	⊕km	⊕km	NOUN
ejpam-4006	278	25	in	in	ADP
ejpam-4006	278	26	theorem	theorem	NOUN
ejpam-4006	278	27	1	1	NUM
ejpam-4006	278	28	,	,	PUNCT
ejpam-4006	278	29	we	we	PRON
ejpam-4006	278	30	obtain	obtain	VERB
ejpam-4006	278	31	h(x	h(x	PROPN
ejpam-4006	278	32	,	,	PUNCT
ejpam-4006	278	33	m	m	NOUN
ejpam-4006	278	34	)	)	PUNCT
ejpam-4006	278	35	∗	∗	NOUN
ejpam-4006	278	36	⊕kmu(x	⊕kmu(x	NOUN
ejpam-4006	278	37	)	)	PUNCT
ejpam-4006	278	38	=	=	SYM
ejpam-4006	278	39	h(x	h(x	PROPN
ejpam-4006	278	40	,	,	PUNCT
ejpam-4006	278	41	m	m	NOUN
ejpam-4006	278	42	)	)	PUNCT
ejpam-4006	278	43	∗	∗	NOUN
ejpam-4006	278	44	f(x	f(x	PROPN
ejpam-4006	278	45	)	)	PUNCT
ejpam-4006	278	46	or	or	CCONJ
ejpam-4006	278	47	,	,	PUNCT
ejpam-4006	278	48	⊕kmh(x	⊕kmh(x	NOUN
ejpam-4006	278	49	,	,	PUNCT
ejpam-4006	278	50	m	m	NOUN
ejpam-4006	278	51	)	)	PUNCT
ejpam-4006	278	52	∗	∗	NOUN
ejpam-4006	278	53	u(x	u(x	PROPN
ejpam-4006	278	54	)	)	PUNCT
ejpam-4006	279	1	=	=	SYM
ejpam-4006	279	2	h(x	h(x	PROPN
ejpam-4006	279	3	,	,	PUNCT
ejpam-4006	279	4	m	m	NOUN
ejpam-4006	279	5	)	)	PUNCT
ejpam-4006	279	6	∗	∗	NOUN
ejpam-4006	279	7	f(x	f(x	PROPN
ejpam-4006	279	8	)	)	PUNCT
ejpam-4006	279	9	s.	s.	PROPN
ejpam-4006	279	10	bupasiri	bupasiri	PROPN
ejpam-4006	279	11	/	/	SYM
ejpam-4006	279	12	eur	eur	PROPN
ejpam-4006	279	13	.	.	PUNCT
ejpam-4006	280	1	j.	j.	PROPN
ejpam-4006	280	2	pure	pure	PROPN
ejpam-4006	280	3	appl	appl	PROPN
ejpam-4006	280	4	.	.	PROPN
ejpam-4006	280	5	math	math	PROPN
ejpam-4006	280	6	,	,	PUNCT
ejpam-4006	280	7	14	14	NUM
ejpam-4006	280	8	(	(	PUNCT
ejpam-4006	280	9	3	3	NUM
ejpam-4006	280	10	)	)	PUNCT
ejpam-4006	280	11	(	(	PUNCT
ejpam-4006	280	12	2021	2021	NUM
ejpam-4006	280	13	)	)	PUNCT
ejpam-4006	280	14	,	,	PUNCT
ejpam-4006	280	15	881	881	NUM
ejpam-4006	280	16	-	-	SYM
ejpam-4006	280	17	894	894	NUM
ejpam-4006	280	18	893	893	NUM
ejpam-4006	280	19	applying	apply	VERB
ejpam-4006	280	20	the	the	DET
ejpam-4006	280	21	theorem	theorem	NOUN
ejpam-4006	280	22	1	1	NUM
ejpam-4006	280	23	,	,	PUNCT
ejpam-4006	280	24	we	we	PRON
ejpam-4006	280	25	have	have	VERB
ejpam-4006	280	26	δ	δ	PROPN
ejpam-4006	280	27	∗	∗	X
ejpam-4006	280	28	u(x	u(x	NOUN
ejpam-4006	280	29	)	)	PUNCT
ejpam-4006	281	1	=	=	SYM
ejpam-4006	281	2	h(x	h(x	PROPN
ejpam-4006	281	3	,	,	PUNCT
ejpam-4006	281	4	m	m	NOUN
ejpam-4006	281	5	)	)	PUNCT
ejpam-4006	281	6	∗	∗	NOUN
ejpam-4006	281	7	f(x	f(x	PROPN
ejpam-4006	281	8	)	)	PUNCT
ejpam-4006	281	9	.	.	PUNCT
ejpam-4006	282	1	therefore	therefore	ADV
ejpam-4006	282	2	,	,	PUNCT
ejpam-4006	282	3	u(x	u(x	PROPN
ejpam-4006	282	4	)	)	PUNCT
ejpam-4006	282	5	=	=	SYM
ejpam-4006	283	1	h(x	h(x	PROPN
ejpam-4006	283	2	,	,	PUNCT
ejpam-4006	283	3	m	m	NOUN
ejpam-4006	283	4	)	)	PUNCT
ejpam-4006	283	5	∗	∗	NOUN
ejpam-4006	283	6	f(x	f(x	PROPN
ejpam-4006	283	7	)	)	PUNCT
ejpam-4006	283	8	.	.	PUNCT
ejpam-4006	284	1	example	example	NOUN
ejpam-4006	285	1	1	1	X
ejpam-4006	285	2	.	.	X
ejpam-4006	285	3	consider	consider	VERB
ejpam-4006	285	4	the	the	DET
ejpam-4006	285	5	equation	equation	NOUN
ejpam-4006	285	6	(	(	PUNCT
ejpam-4006	285	7	m4	m4	PROPN
ejpam-4006	285	8	+42)k(m4	+42)k(m4	NOUN
ejpam-4006	285	9	−42)ku(x	−42)ku(x	NOUN
ejpam-4006	285	10	)	)	PUNCT
ejpam-4006	285	11	=	=	SYM
ejpam-4006	285	12	f(x	f(x	PROPN
ejpam-4006	285	13	)	)	PUNCT
ejpam-4006	285	14	,	,	PUNCT
ejpam-4006	285	15	(	(	PUNCT
ejpam-4006	285	16	52	52	NUM
ejpam-4006	285	17	)	)	PUNCT
ejpam-4006	285	18	where	where	SCONJ
ejpam-4006	285	19	42	42	NUM
ejpam-4006	285	20	is	be	AUX
ejpam-4006	285	21	the	the	DET
ejpam-4006	285	22	biharmonic	biharmonic	NOUN
ejpam-4006	285	23	operator	operator	NOUN
ejpam-4006	285	24	defined	define	VERB
ejpam-4006	285	25	by	by	ADP
ejpam-4006	285	26	42	42	NUM
ejpam-4006	285	27	=	=	SYM
ejpam-4006	285	28	(	(	PUNCT
ejpam-4006	285	29	∂2	∂2	PROPN
ejpam-4006	285	30	∂x21	∂x21	PROPN
ejpam-4006	285	31	+	+	CCONJ
ejpam-4006	285	32	∂2	∂2	PROPN
ejpam-4006	285	33	∂x22	∂x22	PROPN
ejpam-4006	285	34	+	+	CCONJ
ejpam-4006	285	35	·	·	PUNCT
ejpam-4006	285	36	·	·	PUNCT
ejpam-4006	285	37	·	·	PUNCT
ejpam-4006	286	1	+	+	NUM
ejpam-4006	286	2	∂2	∂2	ADJ
ejpam-4006	286	3	∂x2n	∂x2n	NOUN
ejpam-4006	286	4	)	)	PUNCT
ejpam-4006	286	5	2	2	NUM
ejpam-4006	286	6	,	,	PUNCT
ejpam-4006	286	7	(	(	PUNCT
ejpam-4006	286	8	53	53	NUM
ejpam-4006	286	9	)	)	PUNCT
ejpam-4006	286	10	x	x	SYM
ejpam-4006	286	11	∈	∈	PROPN
ejpam-4006	286	12	rn	rn	PROPN
ejpam-4006	286	13	,	,	PUNCT
ejpam-4006	286	14	f(x	f(x	PROPN
ejpam-4006	286	15	)	)	PUNCT
ejpam-4006	286	16	is	be	AUX
ejpam-4006	286	17	a	a	DET
ejpam-4006	286	18	given	give	VERB
ejpam-4006	286	19	generalized	generalized	ADJ
ejpam-4006	286	20	function	function	NOUN
ejpam-4006	286	21	and	and	CCONJ
ejpam-4006	286	22	u(x	u(x	NOUN
ejpam-4006	286	23	)	)	PUNCT
ejpam-4006	286	24	is	be	AUX
ejpam-4006	286	25	an	an	DET
ejpam-4006	286	26	unknown	unknown	ADJ
ejpam-4006	286	27	function	function	NOUN
ejpam-4006	286	28	.	.	PUNCT
ejpam-4006	287	1	for	for	ADP
ejpam-4006	287	2	solving	solve	VERB
ejpam-4006	287	3	the	the	DET
ejpam-4006	287	4	product	product	NOUN
ejpam-4006	287	5	of	of	ADP
ejpam-4006	287	6	biharmonic	biharmonic	NOUN
ejpam-4006	287	7	operators	operator	NOUN
ejpam-4006	287	8	,	,	PUNCT
ejpam-4006	287	9	we	we	PRON
ejpam-4006	287	10	can	can	AUX
ejpam-4006	287	11	rewrite	rewrite	VERB
ejpam-4006	287	12	the	the	DET
ejpam-4006	287	13	equation	equation	NOUN
ejpam-4006	287	14	(	(	PUNCT
ejpam-4006	287	15	52	52	NUM
ejpam-4006	287	16	)	)	PUNCT
ejpam-4006	287	17	as	as	ADP
ejpam-4006	287	18	(	(	PUNCT
ejpam-4006	287	19	m8	m8	PROPN
ejpam-4006	287	20	−44)ku(x	−44)ku(x	PROPN
ejpam-4006	287	21	)	)	PUNCT
ejpam-4006	287	22	=	=	SYM
ejpam-4006	287	23	f(x	f(x	PROPN
ejpam-4006	287	24	)	)	PUNCT
ejpam-4006	287	25	(	(	PUNCT
ejpam-4006	287	26	54	54	NUM
ejpam-4006	287	27	)	)	PUNCT
ejpam-4006	287	28	and	and	CCONJ
ejpam-4006	287	29	we	we	PRON
ejpam-4006	287	30	know	know	VERB
ejpam-4006	287	31	that	that	SCONJ
ejpam-4006	287	32	the	the	DET
ejpam-4006	287	33	operator	operator	NOUN
ejpam-4006	287	34	in	in	ADP
ejpam-4006	287	35	the	the	DET
ejpam-4006	287	36	equation	equation	NOUN
ejpam-4006	287	37	(	(	PUNCT
ejpam-4006	287	38	54	54	NUM
ejpam-4006	287	39	)	)	PUNCT
ejpam-4006	287	40	is	be	AUX
ejpam-4006	287	41	the	the	DET
ejpam-4006	287	42	operator	operator	NOUN
ejpam-4006	287	43	⊕km	⊕km	VERB
ejpam-4006	287	44	with	with	ADP
ejpam-4006	287	45	p	p	NOUN
ejpam-4006	287	46	=	=	SYM
ejpam-4006	287	47	0	0	NUM
ejpam-4006	287	48	and	and	CCONJ
ejpam-4006	287	49	n	n	NOUN
ejpam-4006	287	50	=	=	SYM
ejpam-4006	288	1	q	q	NOUN
ejpam-4006	288	2	,	,	PUNCT
ejpam-4006	288	3	we	we	PRON
ejpam-4006	288	4	obtain	obtain	VERB
ejpam-4006	288	5	the	the	DET
ejpam-4006	288	6	function	function	NOUN
ejpam-4006	288	7	h(x	h(x	PROPN
ejpam-4006	288	8	,	,	PUNCT
ejpam-4006	288	9	m	m	NOUN
ejpam-4006	288	10	)	)	PUNCT
ejpam-4006	288	11	=	=	SYM
ejpam-4006	288	12	w2k(x	w2k(x	PROPN
ejpam-4006	288	13	,	,	PUNCT
ejpam-4006	288	14	m	m	NOUN
ejpam-4006	288	15	)	)	PUNCT
ejpam-4006	288	16	∗	∗	NOUN
ejpam-4006	288	17	y2k(x	y2k(x	PROPN
ejpam-4006	288	18	,	,	PUNCT
ejpam-4006	288	19	m	m	NOUN
ejpam-4006	288	20	)	)	PUNCT
ejpam-4006	288	21	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	288	22	,	,	PUNCT
ejpam-4006	288	23	m	m	NOUN
ejpam-4006	288	24	)	)	PUNCT
ejpam-4006	288	25	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	288	26	,	,	PUNCT
ejpam-4006	288	27	m	m	NOUN
ejpam-4006	288	28	)	)	PUNCT
ejpam-4006	288	29	,	,	PUNCT
ejpam-4006	288	30	where	where	SCONJ
ejpam-4006	288	31	w2k(x	w2k(x	PROPN
ejpam-4006	288	32	,	,	PUNCT
ejpam-4006	288	33	m	m	NOUN
ejpam-4006	288	34	)	)	PUNCT
ejpam-4006	288	35	,	,	PUNCT
ejpam-4006	288	36	y2k(x	y2k(x	PROPN
ejpam-4006	288	37	,	,	PUNCT
ejpam-4006	288	38	m),m2k(x	m),m2k(x	NOUN
ejpam-4006	288	39	,	,	PUNCT
ejpam-4006	288	40	m	m	NOUN
ejpam-4006	288	41	)	)	PUNCT
ejpam-4006	288	42	and	and	CCONJ
ejpam-4006	288	43	n2k(x	n2k(x	PROPN
ejpam-4006	288	44	,	,	PUNCT
ejpam-4006	288	45	m	m	VERB
ejpam-4006	288	46	)	)	PUNCT
ejpam-4006	288	47	are	be	AUX
ejpam-4006	288	48	defined	define	VERB
ejpam-4006	288	49	by	by	ADP
ejpam-4006	288	50	(	(	PUNCT
ejpam-4006	288	51	27	27	NUM
ejpam-4006	288	52	)	)	PUNCT
ejpam-4006	288	53	,	,	PUNCT
ejpam-4006	288	54	(	(	PUNCT
ejpam-4006	288	55	30	30	NUM
ejpam-4006	288	56	)	)	PUNCT
ejpam-4006	288	57	,	,	PUNCT
ejpam-4006	288	58	(	(	PUNCT
ejpam-4006	288	59	33	33	NUM
ejpam-4006	288	60	)	)	PUNCT
ejpam-4006	288	61	and	and	CCONJ
ejpam-4006	288	62	(	(	PUNCT
ejpam-4006	288	63	36	36	NUM
ejpam-4006	288	64	)	)	PUNCT
ejpam-4006	288	65	,	,	PUNCT
ejpam-4006	288	66	respectively	respectively	ADV
ejpam-4006	288	67	,	,	PUNCT
ejpam-4006	288	68	and	and	CCONJ
ejpam-4006	288	69	re2k(x	re2k(x	PROPN
ejpam-4006	288	70	)	)	PUNCT
ejpam-4006	288	71	=	=	SYM
ejpam-4006	288	72	γ	γ	X
ejpam-4006	288	73	(	(	PUNCT
ejpam-4006	288	74	n−2k	n−2k	NOUN
ejpam-4006	288	75	2	2	X
ejpam-4006	288	76	)	)	PUNCT
ejpam-4006	288	77	22kπ	22kπ	NOUN
ejpam-4006	288	78	n	n	PRON
ejpam-4006	288	79	2	2	NUM
ejpam-4006	288	80	γ(k	γ(k	PROPN
ejpam-4006	288	81	)	)	PUNCT
ejpam-4006	288	82	(	(	PUNCT
ejpam-4006	288	83	x21	x21	NUM
ejpam-4006	288	84	+	+	CCONJ
ejpam-4006	288	85	·	·	PUNCT
ejpam-4006	288	86	·	·	PUNCT
ejpam-4006	288	87	·	·	PUNCT
ejpam-4006	288	88	+	+	NUM
ejpam-4006	288	89	x2n	x2n	NOUN
ejpam-4006	288	90	)	)	PUNCT
ejpam-4006	288	91	(	(	PUNCT
ejpam-4006	288	92	2k−n	2k−n	NUM
ejpam-4006	288	93	2	2	NUM
ejpam-4006	288	94	)	)	PUNCT
ejpam-4006	288	95	,	,	PUNCT
ejpam-4006	288	96	n	n	PROPN
ejpam-4006	288	97	=	=	SYM
ejpam-4006	288	98	p+	p+	PROPN
ejpam-4006	288	99	q	q	X
ejpam-4006	288	100	(	(	PUNCT
ejpam-4006	288	101	55	55	NUM
ejpam-4006	288	102	)	)	PUNCT
ejpam-4006	288	103	rh2k(x	rh2k(x	PROPN
ejpam-4006	288	104	)	)	PUNCT
ejpam-4006	288	105	=	=	SYM
ejpam-4006	288	106	u	u	NOUN
ejpam-4006	288	107	(	(	PUNCT
ejpam-4006	288	108	2k−n	2k−n	NUM
ejpam-4006	288	109	2	2	NUM
ejpam-4006	288	110	)	)	PUNCT
ejpam-4006	288	111	kn(2k	kn(2k	NOUN
ejpam-4006	288	112	)	)	PUNCT
ejpam-4006	288	113	=	=	PUNCT
ejpam-4006	288	114	(	(	PUNCT
ejpam-4006	288	115	−x21	−x21	NUM
ejpam-4006	288	116	−	−	NOUN
ejpam-4006	288	117	x22	x22	NUM
ejpam-4006	288	118	−	−	PROPN
ejpam-4006	288	119	·	·	PUNCT
ejpam-4006	288	120	·	·	PUNCT
ejpam-4006	288	121	·	·	PUNCT
ejpam-4006	289	1	−	−	PROPN
ejpam-4006	289	2	x2n	x2n	NOUN
ejpam-4006	289	3	)	)	PUNCT
ejpam-4006	289	4	(	(	PUNCT
ejpam-4006	289	5	2k−n	2k−n	NUM
ejpam-4006	289	6	2	2	NUM
ejpam-4006	289	7	)	)	PUNCT
ejpam-4006	289	8	kn(2k	kn(2k	NOUN
ejpam-4006	289	9	)	)	PUNCT
ejpam-4006	289	10	(	(	PUNCT
ejpam-4006	289	11	56	56	NUM
ejpam-4006	289	12	)	)	PUNCT
ejpam-4006	289	13	for	for	ADP
ejpam-4006	289	14	kn(2k	kn(2k	NOUN
ejpam-4006	289	15	)	)	PUNCT
ejpam-4006	289	16	=	=	PUNCT
ejpam-4006	290	1	π	π	X
ejpam-4006	290	2	n−1	n−1	PROPN
ejpam-4006	290	3	2	2	NUM
ejpam-4006	290	4	γ	γ	X
ejpam-4006	290	5	(	(	PUNCT
ejpam-4006	290	6	2	2	NUM
ejpam-4006	290	7	+	+	NOUN
ejpam-4006	290	8	2k−n	2k−n	ADJ
ejpam-4006	290	9	2	2	NUM
ejpam-4006	290	10	)	)	PUNCT
ejpam-4006	290	11	γ	γ	PROPN
ejpam-4006	290	12	(	(	PUNCT
ejpam-4006	290	13	1−2k	1−2k	NUM
ejpam-4006	290	14	2	2	NUM
ejpam-4006	290	15	)	)	PUNCT
ejpam-4006	290	16	γ(2k	γ(2k	VERB
ejpam-4006	290	17	)	)	PUNCT
ejpam-4006	290	18	γ	γ	X
ejpam-4006	290	19	(	(	PUNCT
ejpam-4006	290	20	2	2	NUM
ejpam-4006	290	21	+	+	NOUN
ejpam-4006	290	22	2k	2k	NOUN
ejpam-4006	290	23	2	2	NUM
ejpam-4006	290	24	)	)	PUNCT
ejpam-4006	290	25	γ(−2k2	γ(−2k2	X
ejpam-4006	290	26	)	)	PUNCT
ejpam-4006	290	27	,	,	PUNCT
ejpam-4006	290	28	(	(	PUNCT
ejpam-4006	290	29	57	57	NUM
ejpam-4006	290	30	)	)	PUNCT
ejpam-4006	290	31	s2k(x	s2k(x	PROPN
ejpam-4006	290	32	)	)	PUNCT
ejpam-4006	290	33	=	=	SYM
ejpam-4006	291	1	γ	γ	X
ejpam-4006	291	2	(	(	PUNCT
ejpam-4006	291	3	n−2k	n−2k	NOUN
ejpam-4006	291	4	2	2	X
ejpam-4006	291	5	)	)	PUNCT
ejpam-4006	291	6	22kπ	22kπ	NOUN
ejpam-4006	291	7	n	n	PRON
ejpam-4006	291	8	2	2	NUM
ejpam-4006	291	9	γ(k	γ(k	PROPN
ejpam-4006	291	10	)	)	PUNCT
ejpam-4006	291	11	(	(	PUNCT
ejpam-4006	291	12	−i	−i	PROPN
ejpam-4006	291	13	(	(	PUNCT
ejpam-4006	291	14	x21	x21	PROPN
ejpam-4006	291	15	+	+	CCONJ
ejpam-4006	291	16	·	·	PUNCT
ejpam-4006	291	17	·	·	PUNCT
ejpam-4006	291	18	·	·	PUNCT
ejpam-4006	291	19	+	+	NUM
ejpam-4006	291	20	x2n	x2n	NOUN
ejpam-4006	291	21	)	)	PUNCT
ejpam-4006	291	22	)	)	PUNCT
ejpam-4006	291	23	(	(	PUNCT
ejpam-4006	291	24	2k−n	2k−n	NUM
ejpam-4006	291	25	2	2	NUM
ejpam-4006	291	26	)	)	PUNCT
ejpam-4006	291	27	(	(	PUNCT
ejpam-4006	291	28	58	58	NUM
ejpam-4006	291	29	)	)	PUNCT
ejpam-4006	291	30	and	and	CCONJ
ejpam-4006	291	31	t2k(x	t2k(x	PROPN
ejpam-4006	291	32	)	)	PUNCT
ejpam-4006	291	33	=	=	SYM
ejpam-4006	292	1	γ	γ	X
ejpam-4006	292	2	(	(	PUNCT
ejpam-4006	292	3	n−2k	n−2k	NOUN
ejpam-4006	292	4	2	2	X
ejpam-4006	292	5	)	)	PUNCT
ejpam-4006	292	6	22kπ	22kπ	NOUN
ejpam-4006	292	7	n	n	PRON
ejpam-4006	292	8	2	2	NUM
ejpam-4006	292	9	γ(k	γ(k	PROPN
ejpam-4006	292	10	)	)	PUNCT
ejpam-4006	292	11	(	(	PUNCT
ejpam-4006	292	12	i	i	PRON
ejpam-4006	292	13	(	(	PUNCT
ejpam-4006	292	14	x21	x21	PROPN
ejpam-4006	292	15	+	+	CCONJ
ejpam-4006	292	16	·	·	PUNCT
ejpam-4006	292	17	·	·	PUNCT
ejpam-4006	292	18	·	·	PUNCT
ejpam-4006	292	19	+	+	NUM
ejpam-4006	292	20	x2n	x2n	NOUN
ejpam-4006	292	21	)	)	PUNCT
ejpam-4006	292	22	)	)	PUNCT
ejpam-4006	292	23	(	(	PUNCT
ejpam-4006	292	24	2k−n	2k−n	NUM
ejpam-4006	292	25	2	2	NUM
ejpam-4006	292	26	)	)	PUNCT
ejpam-4006	292	27	.	.	PUNCT
ejpam-4006	293	1	(	(	PUNCT
ejpam-4006	293	2	59	59	NUM
ejpam-4006	293	3	)	)	PUNCT
ejpam-4006	293	4	convolving	convolve	VERB
ejpam-4006	293	5	both	both	DET
ejpam-4006	293	6	sides	side	NOUN
ejpam-4006	293	7	of	of	ADP
ejpam-4006	293	8	(	(	PUNCT
ejpam-4006	293	9	54	54	NUM
ejpam-4006	293	10	)	)	PUNCT
ejpam-4006	293	11	by	by	ADP
ejpam-4006	293	12	the	the	DET
ejpam-4006	293	13	new	new	ADJ
ejpam-4006	293	14	fundamental	fundamental	ADJ
ejpam-4006	293	15	solution	solution	NOUN
ejpam-4006	293	16	h(x	h(x	PROPN
ejpam-4006	293	17	,	,	PUNCT
ejpam-4006	293	18	m	m	NOUN
ejpam-4006	293	19	)	)	PUNCT
ejpam-4006	294	1	=	=	SYM
ejpam-4006	294	2	w2k(x	w2k(x	PROPN
ejpam-4006	294	3	,	,	PUNCT
ejpam-4006	294	4	m	m	NOUN
ejpam-4006	294	5	)	)	PUNCT
ejpam-4006	294	6	∗	∗	NOUN
ejpam-4006	294	7	y2k(x	y2k(x	PROPN
ejpam-4006	294	8	,	,	PUNCT
ejpam-4006	294	9	m	m	NOUN
ejpam-4006	294	10	)	)	PUNCT
ejpam-4006	294	11	∗m2k(x	∗m2k(x	NOUN
ejpam-4006	294	12	,	,	PUNCT
ejpam-4006	294	13	m	m	NOUN
ejpam-4006	294	14	)	)	PUNCT
ejpam-4006	294	15	∗n2k(x	∗n2k(x	NOUN
ejpam-4006	294	16	,	,	PUNCT
ejpam-4006	294	17	m	m	PROPN
ejpam-4006	294	18	)	)	PUNCT
ejpam-4006	294	19	,	,	PUNCT
ejpam-4006	294	20	we	we	PRON
ejpam-4006	294	21	obtain	obtain	VERB
ejpam-4006	294	22	that	that	SCONJ
ejpam-4006	294	23	u(x	u(x	NOUN
ejpam-4006	294	24	)	)	PUNCT
ejpam-4006	294	25	=	=	SYM
ejpam-4006	294	26	f(x	f(x	PROPN
ejpam-4006	294	27	)	)	PUNCT
ejpam-4006	294	28	∗h(x	∗h(x	PROPN
ejpam-4006	294	29	,	,	PUNCT
ejpam-4006	294	30	m	m	NOUN
ejpam-4006	294	31	)	)	PUNCT
ejpam-4006	294	32	is	be	AUX
ejpam-4006	294	33	the	the	DET
ejpam-4006	294	34	solution	solution	NOUN
ejpam-4006	294	35	of	of	ADP
ejpam-4006	294	36	(	(	PUNCT
ejpam-4006	294	37	54	54	NUM
ejpam-4006	294	38	)	)	PUNCT
ejpam-4006	294	39	.	.	PUNCT
ejpam-4006	295	1	references	reference	NOUN
ejpam-4006	295	2	894	894	NUM
ejpam-4006	295	3	acknowledgements	acknowledgement	NOUN
ejpam-4006	295	4	the	the	DET
ejpam-4006	295	5	author	author	NOUN
ejpam-4006	295	6	would	would	AUX
ejpam-4006	295	7	like	like	VERB
ejpam-4006	295	8	to	to	PART
ejpam-4006	295	9	thank	thank	VERB
ejpam-4006	295	10	the	the	DET
ejpam-4006	295	11	referees	referee	NOUN
ejpam-4006	295	12	for	for	ADP
ejpam-4006	295	13	their	their	PRON
ejpam-4006	295	14	suggestions	suggestion	NOUN
ejpam-4006	295	15	which	which	PRON
ejpam-4006	295	16	enhanced	enhance	VERB
ejpam-4006	295	17	the	the	DET
ejpam-4006	295	18	presentation	presentation	NOUN
ejpam-4006	295	19	of	of	ADP
ejpam-4006	295	20	the	the	DET
ejpam-4006	295	21	paper	paper	NOUN
ejpam-4006	295	22	.	.	PUNCT
ejpam-4006	296	1	the	the	DET
ejpam-4006	296	2	author	author	NOUN
ejpam-4006	296	3	was	be	AUX
ejpam-4006	296	4	supported	support	VERB
ejpam-4006	296	5	by	by	ADP
ejpam-4006	296	6	sakon	sakon	PROPN
ejpam-4006	296	7	nakhon	nakhon	PROPN
ejpam-4006	296	8	rajabhat	rajabhat	PROPN
ejpam-4006	296	9	university	university	PROPN
ejpam-4006	296	10	.	.	PUNCT
ejpam-4006	297	1	references	reference	NOUN
ejpam-4006	297	2	[	[	X
ejpam-4006	297	3	1	1	X
ejpam-4006	297	4	]	]	PUNCT
ejpam-4006	297	5	s.	s.	PROPN
ejpam-4006	297	6	suantai	suantai	VERB
ejpam-4006	297	7	a.	a.	PROPN
ejpam-4006	297	8	kananthai	kananthai	PROPN
ejpam-4006	297	9	and	and	CCONJ
ejpam-4006	297	10	v.	v.	ADP
ejpam-4006	297	11	longani	longani	PROPN
ejpam-4006	297	12	.	.	PUNCT
ejpam-4006	298	1	on	on	ADP
ejpam-4006	298	2	the	the	DET
ejpam-4006	298	3	weak	weak	ADJ
ejpam-4006	298	4	solution	solution	NOUN
ejpam-4006	298	5	of	of	ADP
ejpam-4006	298	6	the	the	DET
ejpam-4006	298	7	equation	equation	NOUN
ejpam-4006	298	8	related	relate	VERB
ejpam-4006	298	9	to	to	ADP
ejpam-4006	298	10	the	the	DET
ejpam-4006	298	11	diamond	diamond	NOUN
ejpam-4006	298	12	operator	operator	NOUN
ejpam-4006	298	13	.	.	PUNCT
ejpam-4006	299	1	computational	computational	ADJ
ejpam-4006	299	2	technologies	technology	NOUN
ejpam-4006	299	3	,	,	PUNCT
ejpam-4006	299	4	5:42–48	5:42–48	NUM
ejpam-4006	299	5	,	,	PUNCT
ejpam-4006	299	6	2000	2000	NUM
ejpam-4006	299	7	.	.	PUNCT
ejpam-4006	300	1	[	[	X
ejpam-4006	300	2	2	2	X
ejpam-4006	300	3	]	]	PUNCT
ejpam-4006	300	4	s.	s.	PROPN
ejpam-4006	300	5	suantai	suantai	VERB
ejpam-4006	300	6	a.	a.	PROPN
ejpam-4006	300	7	kananthai	kananthai	PROPN
ejpam-4006	300	8	and	and	CCONJ
ejpam-4006	300	9	v.	v.	ADP
ejpam-4006	300	10	longani	longani	PROPN
ejpam-4006	300	11	.	.	PUNCT
ejpam-4006	301	1	on	on	ADP
ejpam-4006	301	2	the	the	DET
ejpam-4006	301	3	operator	operator	NOUN
ejpam-4006	301	4	⊕k	⊕k	NOUN
ejpam-4006	301	5	related	relate	VERB
ejpam-4006	301	6	to	to	ADP
ejpam-4006	301	7	the	the	DET
ejpam-4006	301	8	wave	wave	NOUN
ejpam-4006	301	9	equation	equation	NOUN
ejpam-4006	301	10	and	and	CCONJ
ejpam-4006	301	11	laplacian	laplacian	PROPN
ejpam-4006	301	12	.	.	PUNCT
ejpam-4006	301	13	appl	appl	PROPN
ejpam-4006	301	14	.	.	PROPN
ejpam-4006	301	15	math	math	PROPN
ejpam-4006	301	16	.	.	PUNCT
ejpam-4006	302	1	comput	comput	NOUN
ejpam-4006	302	2	.	.	PUNCT
ejpam-4006	302	3	,	,	PUNCT
ejpam-4006	302	4	132:219–229	132:219–229	NUM
ejpam-4006	302	5	,	,	PUNCT
ejpam-4006	302	6	2002	2002	NUM
ejpam-4006	302	7	.	.	PUNCT
ejpam-4006	303	1	[	[	X
ejpam-4006	303	2	3	3	NUM
ejpam-4006	303	3	]	]	X
ejpam-4006	303	4	w.f	w.f	PROPN
ejpam-4006	303	5	.	.	PROPN
ejpam-4006	303	6	donoghue	donoghue	PROPN
ejpam-4006	303	7	.	.	PUNCT
ejpam-4006	304	1	distribution	distribution	NOUN
ejpam-4006	304	2	and	and	CCONJ
ejpam-4006	304	3	fourier	fourier	NOUN
ejpam-4006	304	4	transform	transform	NOUN
ejpam-4006	304	5	.	.	PUNCT
ejpam-4006	305	1	academic	academic	ADJ
ejpam-4006	305	2	press	press	NOUN
ejpam-4006	305	3	,	,	PUNCT
ejpam-4006	305	4	new	new	PROPN
ejpam-4006	305	5	york	york	PROPN
ejpam-4006	305	6	,	,	PUNCT
ejpam-4006	305	7	1969	1969	NUM
ejpam-4006	305	8	.	.	PUNCT
ejpam-4006	306	1	[	[	X
ejpam-4006	306	2	4	4	NUM
ejpam-4006	306	3	]	]	PUNCT
ejpam-4006	306	4	a.	a.	NOUN
ejpam-4006	306	5	kananthai	kananthai	PROPN
ejpam-4006	306	6	.	.	PUNCT
ejpam-4006	307	1	on	on	ADP
ejpam-4006	307	2	the	the	DET
ejpam-4006	307	3	solutions	solution	NOUN
ejpam-4006	307	4	of	of	ADP
ejpam-4006	307	5	the	the	DET
ejpam-4006	307	6	n	n	ADV
ejpam-4006	307	7	-	-	PUNCT
ejpam-4006	307	8	dimensional	dimensional	ADJ
ejpam-4006	307	9	diamond	diamond	NOUN
ejpam-4006	307	10	operator	operator	NOUN
ejpam-4006	307	11	.	.	PUNCT
ejpam-4006	308	1	appl	appl	PROPN
ejpam-4006	308	2	.	.	PROPN
ejpam-4006	308	3	math	math	PROPN
ejpam-4006	308	4	.	.	PUNCT
ejpam-4006	309	1	comput	comput	NOUN
ejpam-4006	309	2	.	.	PUNCT
ejpam-4006	309	3	,	,	PUNCT
ejpam-4006	309	4	88:27–37	88:27–37	NUM
ejpam-4006	309	5	,	,	PUNCT
ejpam-4006	309	6	1997	1997	NUM
ejpam-4006	309	7	.	.	PUNCT
ejpam-4006	310	1	[	[	X
ejpam-4006	310	2	5	5	NUM
ejpam-4006	310	3	]	]	PUNCT
ejpam-4006	310	4	a.	a.	NOUN
ejpam-4006	310	5	kananthai	kananthai	PROPN
ejpam-4006	310	6	.	.	PUNCT
ejpam-4006	311	1	on	on	ADP
ejpam-4006	311	2	the	the	DET
ejpam-4006	311	3	convolution	convolution	NOUN
ejpam-4006	311	4	equation	equation	NOUN
ejpam-4006	311	5	related	relate	VERB
ejpam-4006	311	6	to	to	ADP
ejpam-4006	311	7	the	the	DET
ejpam-4006	311	8	diamond	diamond	NOUN
ejpam-4006	311	9	kernel	kernel	NOUN
ejpam-4006	311	10	of	of	ADP
ejpam-4006	311	11	marcel	marcel	PROPN
ejpam-4006	311	12	riesz	riesz	PROPN
ejpam-4006	311	13	.	.	PUNCT
ejpam-4006	312	1	j.	j.	PROPN
ejpam-4006	312	2	comp	comp	PROPN
ejpam-4006	312	3	.	.	PUNCT
ejpam-4006	313	1	appl	appl	PROPN
ejpam-4006	313	2	.	.	PROPN
ejpam-4006	313	3	math	math	PROPN
ejpam-4006	313	4	.	.	PUNCT
ejpam-4006	313	5	,	,	PUNCT
ejpam-4006	313	6	100:33–39	100:33–39	PROPN
ejpam-4006	313	7	,	,	PUNCT
ejpam-4006	313	8	1998	1998	NUM
ejpam-4006	313	9	.	.	PUNCT
ejpam-4006	314	1	[	[	X
ejpam-4006	314	2	6	6	NUM
ejpam-4006	314	3	]	]	PUNCT
ejpam-4006	314	4	a.	a.	NOUN
ejpam-4006	314	5	kananthai	kananthai	PROPN
ejpam-4006	314	6	.	.	PUNCT
ejpam-4006	315	1	on	on	ADP
ejpam-4006	315	2	the	the	DET
ejpam-4006	315	3	convolutions	convolution	NOUN
ejpam-4006	315	4	of	of	ADP
ejpam-4006	315	5	the	the	DET
ejpam-4006	315	6	diamond	diamond	NOUN
ejpam-4006	315	7	kernel	kernel	NOUN
ejpam-4006	315	8	of	of	ADP
ejpam-4006	315	9	marcel	marcel	PROPN
ejpam-4006	315	10	riesz	riesz	PROPN
ejpam-4006	315	11	.	.	PUNCT
ejpam-4006	315	12	appl	appl	PROPN
ejpam-4006	315	13	.	.	PROPN
ejpam-4006	315	14	math	math	PROPN
ejpam-4006	315	15	.	.	PUNCT
ejpam-4006	316	1	comput	comput	NOUN
ejpam-4006	316	2	.	.	PUNCT
ejpam-4006	316	3	,	,	PUNCT
ejpam-4006	316	4	114:95–101	114:95–101	NUM
ejpam-4006	316	5	,	,	PUNCT
ejpam-4006	316	6	2000	2000	NUM
ejpam-4006	316	7	.	.	PUNCT
ejpam-4006	317	1	[	[	X
ejpam-4006	317	2	7	7	X
ejpam-4006	317	3	]	]	PUNCT
ejpam-4006	317	4	a.	a.	NOUN
ejpam-4006	317	5	kananthai	kananthai	PROPN
ejpam-4006	317	6	.	.	PUNCT
ejpam-4006	318	1	on	on	ADP
ejpam-4006	318	2	the	the	DET
ejpam-4006	318	3	green	green	ADJ
ejpam-4006	318	4	function	function	NOUN
ejpam-4006	318	5	of	of	ADP
ejpam-4006	318	6	the	the	DET
ejpam-4006	318	7	diamond	diamond	NOUN
ejpam-4006	318	8	operator	operator	NOUN
ejpam-4006	318	9	related	relate	VERB
ejpam-4006	318	10	to	to	ADP
ejpam-4006	318	11	the	the	DET
ejpam-4006	318	12	kleingordon	kleingordon	PROPN
ejpam-4006	318	13	operato	operato	PROPN
ejpam-4006	318	14	.	.	PROPN
ejpam-4006	318	15	bull	bull	PROPN
ejpam-4006	318	16	.	.	PUNCT
ejpam-4006	319	1	cal	cal	PROPN
ejpam-4006	319	2	.	.	PUNCT
ejpam-4006	320	1	math	math	NOUN
ejpam-4006	320	2	.	.	PUNCT
ejpam-4006	321	1	soc	soc	PROPN
ejpam-4006	321	2	.	.	PROPN
ejpam-4006	321	3	,	,	PUNCT
ejpam-4006	321	4	93:353–360	93:353–360	NUM
ejpam-4006	321	5	,	,	PUNCT
ejpam-4006	321	6	2001	2001	NUM
ejpam-4006	321	7	.	.	PUNCT
ejpam-4006	322	1	[	[	X
ejpam-4006	322	2	8	8	NUM
ejpam-4006	322	3	]	]	X
ejpam-4006	322	4	a.	a.	NOUN
ejpam-4006	322	5	kananthai	kananthai	PROPN
ejpam-4006	322	6	.	.	PUNCT
ejpam-4006	323	1	on	on	ADP
ejpam-4006	323	2	the	the	DET
ejpam-4006	323	3	inversion	inversion	NOUN
ejpam-4006	323	4	of	of	ADP
ejpam-4006	323	5	the	the	DET
ejpam-4006	323	6	kernel	kernel	NOUN
ejpam-4006	323	7	kα	kα	PROPN
ejpam-4006	323	8	,	,	PUNCT
ejpam-4006	323	9	β	β	X
ejpam-4006	323	10	,	,	PUNCT
ejpam-4006	323	11	γ	γ	X
ejpam-4006	323	12	,	,	PUNCT
ejpam-4006	323	13	ν	ν	NOUN
ejpam-4006	323	14	related	relate	VERB
ejpam-4006	323	15	to	to	ADP
ejpam-4006	323	16	the	the	DET
ejpam-4006	323	17	operator	operator	NOUN
ejpam-4006	323	18	⊕k	⊕k	NOUN
ejpam-4006	323	19	.	.	PUNCT
ejpam-4006	324	1	indian	indian	PROPN
ejpam-4006	324	2	j.	j.	PROPN
ejpam-4006	324	3	pure	pure	PROPN
ejpam-4006	324	4	appl	appl	PROPN
ejpam-4006	324	5	.	.	PUNCT
ejpam-4006	324	6	math	math	PROPN
ejpam-4006	324	7	.	.	PUNCT
ejpam-4006	324	8	,	,	PUNCT
ejpam-4006	324	9	34:1419–1429	34:1419–1429	NUM
ejpam-4006	324	10	,	,	PUNCT
ejpam-4006	324	11	2003	2003	NUM
ejpam-4006	324	12	.	.	PUNCT
ejpam-4006	325	1	[	[	X
ejpam-4006	325	2	9	9	NUM
ejpam-4006	325	3	]	]	X
ejpam-4006	325	4	y.	y.	PROPN
ejpam-4006	325	5	nozaki	nozaki	PROPN
ejpam-4006	325	6	.	.	PUNCT
ejpam-4006	326	1	on	on	ADP
ejpam-4006	326	2	riemann	riemann	PROPN
ejpam-4006	326	3	-	-	PUNCT
ejpam-4006	326	4	liouville	liouville	VERB
ejpam-4006	326	5	integral	integral	ADJ
ejpam-4006	326	6	of	of	ADP
ejpam-4006	326	7	ultra	ultra	ADJ
ejpam-4006	326	8	-	-	ADJ
ejpam-4006	326	9	hyperbolic	hyperbolic	ADJ
ejpam-4006	326	10	type	type	NOUN
ejpam-4006	326	11	.	.	PUNCT
ejpam-4006	327	1	kodai	kodai	PROPN
ejpam-4006	327	2	mathematical	mathematical	ADJ
ejpam-4006	327	3	seminar	seminar	NOUN
ejpam-4006	327	4	reports	report	NOUN
ejpam-4006	327	5	,	,	PUNCT
ejpam-4006	327	6	6:69–87	6:69–87	NUM
ejpam-4006	327	7	,	,	PUNCT
ejpam-4006	327	8	1964	1964	NUM
ejpam-4006	327	9	.	.	PUNCT
ejpam-4006	328	1	[	[	X
ejpam-4006	328	2	10	10	NUM
ejpam-4006	328	3	]	]	X
ejpam-4006	328	4	m.a	m.a	PROPN
ejpam-4006	328	5	.	.	PROPN
ejpam-4006	328	6	tellez	tellez	PROPN
ejpam-4006	328	7	and	and	CCONJ
ejpam-4006	328	8	s.e	s.e	PROPN
ejpam-4006	328	9	.	.	PROPN
ejpam-4006	328	10	trione	trione	NOUN
ejpam-4006	328	11	.	.	PUNCT
ejpam-4006	329	1	the	the	DET
ejpam-4006	329	2	distributional	distributional	ADJ
ejpam-4006	329	3	convolution	convolution	NOUN
ejpam-4006	329	4	products	product	NOUN
ejpam-4006	329	5	of	of	ADP
ejpam-4006	329	6	marcel	marcel	PROPN
ejpam-4006	329	7	riesz	riesz	PROPN
ejpam-4006	329	8	’s	’s	PART
ejpam-4006	329	9	ultra	ultra	ADJ
ejpam-4006	329	10	-	-	ADJ
ejpam-4006	329	11	hyperbolic	hyperbolic	ADJ
ejpam-4006	329	12	kernel	kernel	NOUN
ejpam-4006	329	13	.	.	PUNCT
ejpam-4006	330	1	revista	revista	PROPN
ejpam-4006	330	2	de	de	PROPN
ejpam-4006	330	3	la	la	PROPN
ejpam-4006	330	4	union	union	PROPN
ejpam-4006	330	5	matematica	matematica	PROPN
ejpam-4006	330	6	argentina	argentina	PROPN
ejpam-4006	330	7	,	,	PUNCT
ejpam-4006	330	8	39	39	NUM
ejpam-4006	330	9	,	,	PUNCT
ejpam-4006	330	10	1995	1995	NUM
ejpam-4006	330	11	.	.	PUNCT
ejpam-4006	331	1	[	[	X
ejpam-4006	331	2	11	11	NUM
ejpam-4006	331	3	]	]	X
ejpam-4006	331	4	s.e	s.e	PROPN
ejpam-4006	331	5	.	.	PROPN
ejpam-4006	331	6	trione	trione	NOUN
ejpam-4006	331	7	.	.	PUNCT
ejpam-4006	332	1	on	on	ADP
ejpam-4006	332	2	the	the	DET
ejpam-4006	332	3	elementary	elementary	ADJ
ejpam-4006	332	4	retared	retared	ADJ
ejpam-4006	332	5	,	,	PUNCT
ejpam-4006	332	6	ultra	ultra	ADJ
ejpam-4006	332	7	-	-	ADJ
ejpam-4006	332	8	hyperbolic	hyperbolic	ADJ
ejpam-4006	332	9	solution	solution	NOUN
ejpam-4006	332	10	of	of	ADP
ejpam-4006	332	11	the	the	DET
ejpam-4006	332	12	klein	klein	PROPN
ejpam-4006	332	13	-	-	PUNCT
ejpam-4006	332	14	gordon	gordon	PROPN
ejpam-4006	332	15	operator	operator	NOUN
ejpam-4006	332	16	iterated	iterate	VERB
ejpam-4006	332	17	k	k	NOUN
ejpam-4006	332	18	-	-	PUNCT
ejpam-4006	332	19	times	time	NOUN
ejpam-4006	332	20	.	.	PUNCT
ejpam-4006	333	1	studies	study	NOUN
ejpam-4006	333	2	in	in	ADP
ejpam-4006	333	3	applied	applied	ADJ
ejpam-4006	333	4	mathematics	mathematic	NOUN
ejpam-4006	333	5	,	,	PUNCT
ejpam-4006	333	6	89:121	89:121	NUM
ejpam-4006	333	7	–	–	PUNCT
ejpam-4006	333	8	141	141	NUM
ejpam-4006	333	9	,	,	PUNCT
ejpam-4006	333	10	1988	1988	NUM
ejpam-4006	333	11	.	.	PUNCT