id	sid	tid	token	lemma	pos
ejpam-3223	1	1	european	european	PROPN
ejpam-3223	1	2	journal	journal	PROPN
ejpam-3223	1	3	of	of	ADP
ejpam-3223	1	4	pure	pure	ADJ
ejpam-3223	1	5	and	and	CCONJ
ejpam-3223	1	6	applied	apply	VERB
ejpam-3223	1	7	mathematics	mathematic	NOUN
ejpam-3223	1	8	vol	vol	NOUN
ejpam-3223	1	9	.	.	PUNCT
ejpam-3223	2	1	11	11	NUM
ejpam-3223	2	2	,	,	PUNCT
ejpam-3223	2	3	no	no	INTJ
ejpam-3223	2	4	.	.	NOUN
ejpam-3223	2	5	2	2	NUM
ejpam-3223	2	6	,	,	PUNCT
ejpam-3223	2	7	2018	2018	NUM
ejpam-3223	2	8	,	,	PUNCT
ejpam-3223	2	9	390	390	NUM
ejpam-3223	2	10	-	-	SYM
ejpam-3223	2	11	399	399	NUM
ejpam-3223	2	12	issn	issn	PROPN
ejpam-3223	2	13	1307	1307	NUM
ejpam-3223	2	14	-	-	SYM
ejpam-3223	2	15	5543	5543	NUM
ejpam-3223	2	16	–	–	PUNCT
ejpam-3223	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3223	2	18	published	publish	VERB
ejpam-3223	2	19	by	by	ADP
ejpam-3223	2	20	new	new	PROPN
ejpam-3223	2	21	york	york	PROPN
ejpam-3223	2	22	business	business	PROPN
ejpam-3223	2	23	global	global	PROPN
ejpam-3223	2	24	on	on	ADP
ejpam-3223	2	25	the	the	DET
ejpam-3223	2	26	elementary	elementary	ADJ
ejpam-3223	2	27	solution	solution	NOUN
ejpam-3223	2	28	for	for	ADP
ejpam-3223	2	29	the	the	DET
ejpam-3223	2	30	partial	partial	ADJ
ejpam-3223	2	31	differential	differential	NOUN
ejpam-3223	2	32	operator	operator	NOUN
ejpam-3223	2	33	}	}	PUNCT
ejpam-3223	3	1	kc	kc	PROPN
ejpam-3223	3	2	related	relate	VERB
ejpam-3223	3	3	to	to	ADP
ejpam-3223	3	4	the	the	DET
ejpam-3223	3	5	wave	wave	NOUN
ejpam-3223	3	6	equation	equation	NOUN
ejpam-3223	3	7	sudprathai	sudprathai	PROPN
ejpam-3223	3	8	bupasiri	bupasiri	PROPN
ejpam-3223	3	9	department	department	PROPN
ejpam-3223	3	10	of	of	ADP
ejpam-3223	3	11	mathematics	mathematics	PROPN
ejpam-3223	3	12	,	,	PUNCT
ejpam-3223	4	1	sakon	sakon	PROPN
ejpam-3223	4	2	nakhon	nakhon	PROPN
ejpam-3223	4	3	rajabhat	rajabhat	PROPN
ejpam-3223	4	4	university	university	PROPN
ejpam-3223	4	5	,	,	PUNCT
ejpam-3223	4	6	sakon	sakon	PROPN
ejpam-3223	4	7	nakhon	nakhon	PROPN
ejpam-3223	4	8	47000	47000	NUM
ejpam-3223	4	9	,	,	PUNCT
ejpam-3223	4	10	thailand	thailand	PROPN
ejpam-3223	4	11	abstract	abstract	NOUN
ejpam-3223	4	12	.	.	PUNCT
ejpam-3223	5	1	in	in	ADP
ejpam-3223	5	2	this	this	DET
ejpam-3223	5	3	article	article	NOUN
ejpam-3223	5	4	,	,	PUNCT
ejpam-3223	5	5	we	we	PRON
ejpam-3223	5	6	study	study	VERB
ejpam-3223	5	7	an	an	DET
ejpam-3223	5	8	elementary	elementary	ADJ
ejpam-3223	5	9	solution	solution	NOUN
ejpam-3223	5	10	of	of	ADP
ejpam-3223	5	11	the	the	DET
ejpam-3223	5	12	operator	operator	NOUN
ejpam-3223	5	13	}	}	PUNCT
ejpam-3223	5	14	k	k	PROPN
ejpam-3223	5	15	c	c	PROPN
ejpam-3223	5	16	,	,	PUNCT
ejpam-3223	5	17	iterated	iterate	VERB
ejpam-3223	5	18	k	k	NOUN
ejpam-3223	5	19	-	-	PUNCT
ejpam-3223	5	20	times	time	NOUN
ejpam-3223	5	21	and	and	CCONJ
ejpam-3223	5	22	is	be	AUX
ejpam-3223	5	23	defined	define	VERB
ejpam-3223	5	24	by	by	ADP
ejpam-3223	5	25	}	}	PUNCT
ejpam-3223	5	26	k	k	PROPN
ejpam-3223	5	27	c	c	NOUN
ejpam-3223	5	28	=	=	SYM
ejpam-3223	5	29			NOUN
ejpam-3223	5	30	(	(	PUNCT
ejpam-3223	5	31	1	1	NUM
ejpam-3223	5	32	c2	c2	PROPN
ejpam-3223	5	33	p∑	p∑	PROPN
ejpam-3223	6	1	i=1	i=1	PROPN
ejpam-3223	6	2	∂2	∂2	PROPN
ejpam-3223	6	3	∂x2i	∂x2i	NOUN
ejpam-3223	7	1	+	+	PROPN
ejpam-3223	7	2	m2	m2	PROPN
ejpam-3223	7	3	)	)	PUNCT
ejpam-3223	8	1	2	2	NUM
ejpam-3223	8	2	−	−	PROPN
ejpam-3223	8	3			PROPN
ejpam-3223	8	4	p+q∑	p+q∑	PROPN
ejpam-3223	8	5	j	j	NOUN
ejpam-3223	8	6	=	=	PROPN
ejpam-3223	8	7	p+1	p+1	PROPN
ejpam-3223	8	8	∂2	∂2	PROPN
ejpam-3223	8	9	∂x2j	∂x2j	PUNCT
ejpam-3223	8	10	2	2	PROPN
ejpam-3223	8	11			PROPN
ejpam-3223	9	1	k	k	PROPN
ejpam-3223	9	2	where	where	SCONJ
ejpam-3223	9	3	p	p	NOUN
ejpam-3223	9	4	+	+	NOUN
ejpam-3223	9	5	q	q	NOUN
ejpam-3223	9	6	=	=	SYM
ejpam-3223	9	7	n	n	CCONJ
ejpam-3223	9	8	,	,	PUNCT
ejpam-3223	9	9	k	k	X
ejpam-3223	9	10	is	be	AUX
ejpam-3223	9	11	a	a	DET
ejpam-3223	9	12	nonnegative	nonnegative	ADJ
ejpam-3223	9	13	integer	integer	NOUN
ejpam-3223	9	14	,	,	PUNCT
ejpam-3223	9	15	c	c	PROPN
ejpam-3223	9	16	is	be	AUX
ejpam-3223	9	17	a	a	DET
ejpam-3223	9	18	positive	positive	ADJ
ejpam-3223	9	19	real	real	ADJ
ejpam-3223	9	20	number	number	NOUN
ejpam-3223	9	21	,	,	PUNCT
ejpam-3223	9	22	m	m	VERB
ejpam-3223	9	23	is	be	AUX
ejpam-3223	9	24	a	a	DET
ejpam-3223	9	25	nonnegative	nonnegative	ADJ
ejpam-3223	9	26	real	real	ADJ
ejpam-3223	9	27	number	number	NOUN
ejpam-3223	9	28	and	and	CCONJ
ejpam-3223	9	29	n	n	NOUN
ejpam-3223	9	30	is	be	AUX
ejpam-3223	9	31	the	the	DET
ejpam-3223	9	32	dimension	dimension	NOUN
ejpam-3223	9	33	of	of	ADP
ejpam-3223	9	34	rn	rn	PROPN
ejpam-3223	9	35	.	.	PROPN
ejpam-3223	10	1	in	in	ADP
ejpam-3223	10	2	this	this	DET
ejpam-3223	10	3	work	work	NOUN
ejpam-3223	10	4	we	we	PRON
ejpam-3223	10	5	study	study	VERB
ejpam-3223	10	6	an	an	DET
ejpam-3223	10	7	elementary	elementary	ADJ
ejpam-3223	10	8	solution	solution	NOUN
ejpam-3223	10	9	of	of	ADP
ejpam-3223	10	10	the	the	DET
ejpam-3223	10	11	operator	operator	NOUN
ejpam-3223	10	12	}	}	PUNCT
ejpam-3223	10	13	k	k	PROPN
ejpam-3223	10	14	c	c	PROPN
ejpam-3223	10	15	.	.	PUNCT
ejpam-3223	11	1	after	after	ADP
ejpam-3223	11	2	that	that	PRON
ejpam-3223	11	3	,	,	PUNCT
ejpam-3223	11	4	we	we	PRON
ejpam-3223	11	5	apply	apply	VERB
ejpam-3223	11	6	such	such	DET
ejpam-3223	11	7	an	an	DET
ejpam-3223	11	8	elementary	elementary	ADJ
ejpam-3223	11	9	solution	solution	NOUN
ejpam-3223	11	10	to	to	PART
ejpam-3223	11	11	solve	solve	VERB
ejpam-3223	11	12	the	the	DET
ejpam-3223	11	13	solution	solution	NOUN
ejpam-3223	11	14	of	of	ADP
ejpam-3223	11	15	the	the	DET
ejpam-3223	11	16	equation	equation	NOUN
ejpam-3223	11	17	}	}	PUNCT
ejpam-3223	11	18	k	k	NOUN
ejpam-3223	11	19	cu(x	cu(x	PRON
ejpam-3223	11	20	)	)	PUNCT
ejpam-3223	11	21	=	=	SYM
ejpam-3223	11	22	f(x	f(x	PROPN
ejpam-3223	11	23	)	)	PUNCT
ejpam-3223	11	24	,	,	PUNCT
ejpam-3223	11	25	where	where	SCONJ
ejpam-3223	11	26	f	f	PROPN
ejpam-3223	11	27	is	be	AUX
ejpam-3223	11	28	generalized	generalized	ADJ
ejpam-3223	11	29	function	function	NOUN
ejpam-3223	11	30	and	and	CCONJ
ejpam-3223	11	31	u(x	u(x	NOUN
ejpam-3223	11	32	)	)	PUNCT
ejpam-3223	11	33	is	be	AUX
ejpam-3223	11	34	unknown	unknown	ADJ
ejpam-3223	11	35	function	function	NOUN
ejpam-3223	11	36	for	for	ADP
ejpam-3223	11	37	x	x	PROPN
ejpam-3223	11	38	∈	∈	PROPN
ejpam-3223	11	39	rn	rn	PROPN
ejpam-3223	11	40	.	.	PROPN
ejpam-3223	11	41	2010	2010	NUM
ejpam-3223	11	42	mathematics	mathematic	NOUN
ejpam-3223	11	43	subject	subject	NOUN
ejpam-3223	11	44	classifications	classification	NOUN
ejpam-3223	11	45	:	:	PUNCT
ejpam-3223	11	46	46f10	46f10	NUM
ejpam-3223	11	47	key	key	ADJ
ejpam-3223	11	48	words	word	NOUN
ejpam-3223	11	49	and	and	CCONJ
ejpam-3223	11	50	phrases	phrase	NOUN
ejpam-3223	11	51	:	:	PUNCT
ejpam-3223	11	52	elementary	elementary	ADJ
ejpam-3223	11	53	solution	solution	NOUN
ejpam-3223	11	54	,	,	PUNCT
ejpam-3223	11	55	dirac	dirac	NOUN
ejpam-3223	11	56	-	-	PUNCT
ejpam-3223	11	57	delta	delta	NOUN
ejpam-3223	11	58	distribution	distribution	NOUN
ejpam-3223	11	59	,	,	PUNCT
ejpam-3223	11	60	temper	temper	NOUN
ejpam-3223	11	61	distribution	distribution	NOUN
ejpam-3223	11	62	1	1	NUM
ejpam-3223	11	63	.	.	PUNCT
ejpam-3223	12	1	introduction	introduction	NOUN
ejpam-3223	12	2	trione	trione	NOUN
ejpam-3223	13	1	[	[	X
ejpam-3223	13	2	10	10	NUM
ejpam-3223	13	3	]	]	PUNCT
ejpam-3223	13	4	has	have	AUX
ejpam-3223	13	5	showed	show	VERB
ejpam-3223	13	6	that	that	SCONJ
ejpam-3223	13	7	the	the	DET
ejpam-3223	13	8	generalized	generalized	ADJ
ejpam-3223	13	9	function	function	NOUN
ejpam-3223	13	10	rh2k,1(x	rh2k,1(x	NOUN
ejpam-3223	13	11	)	)	PUNCT
ejpam-3223	13	12	defined	define	VERB
ejpam-3223	13	13	by	by	ADP
ejpam-3223	13	14	(	(	PUNCT
ejpam-3223	13	15	13	13	NUM
ejpam-3223	13	16	)	)	PUNCT
ejpam-3223	13	17	is	be	AUX
ejpam-3223	13	18	the	the	DET
ejpam-3223	13	19	unique	unique	ADJ
ejpam-3223	13	20	elementary	elementary	ADJ
ejpam-3223	13	21	solution	solution	NOUN
ejpam-3223	13	22	of	of	ADP
ejpam-3223	13	23	the	the	DET
ejpam-3223	13	24	operator	operator	NOUN
ejpam-3223	13	25	�	�	NOUN
ejpam-3223	13	26	k1	k1	PROPN
ejpam-3223	13	27	,	,	PUNCT
ejpam-3223	13	28	that	that	PRON
ejpam-3223	13	29	is	be	AUX
ejpam-3223	13	30	�	�	NOUN
ejpam-3223	13	31	k1r	k1r	NOUN
ejpam-3223	13	32	h	h	NOUN
ejpam-3223	13	33	2k,1(x	2k,1(x	NUM
ejpam-3223	13	34	)	)	PUNCT
ejpam-3223	13	35	=	=	SYM
ejpam-3223	13	36	δ	δ	PROPN
ejpam-3223	13	37	where	where	SCONJ
ejpam-3223	13	38	x	x	PUNCT
ejpam-3223	13	39	∈	∈	PROPN
ejpam-3223	13	40	rn	rn	PROPN
ejpam-3223	13	41	,	,	PUNCT
ejpam-3223	13	42	with	with	ADP
ejpam-3223	13	43	n	n	CCONJ
ejpam-3223	13	44	-	-	PUNCT
ejpam-3223	13	45	dimensional	dimensional	ADJ
ejpam-3223	13	46	euclidean	euclidean	ADJ
ejpam-3223	13	47	space	space	NOUN
ejpam-3223	13	48	.	.	PUNCT
ejpam-3223	14	1	also	also	ADV
ejpam-3223	14	2	,	,	PUNCT
ejpam-3223	14	3	tellez	tellez	PROPN
ejpam-3223	14	4	(	(	PUNCT
ejpam-3223	14	5	[	[	X
ejpam-3223	14	6	7	7	NUM
ejpam-3223	14	7	]	]	PUNCT
ejpam-3223	14	8	,	,	PUNCT
ejpam-3223	14	9	p.147	p.147	NUM
ejpam-3223	14	10	-	-	PUNCT
ejpam-3223	14	11	149	149	NUM
ejpam-3223	14	12	)	)	PUNCT
ejpam-3223	14	13	has	have	AUX
ejpam-3223	14	14	proved	prove	VERB
ejpam-3223	14	15	that	that	DET
ejpam-3223	14	16	rh2k,1(x	rh2k,1(x	NOUN
ejpam-3223	14	17	)	)	PUNCT
ejpam-3223	14	18	exists	exist	VERB
ejpam-3223	14	19	only	only	ADV
ejpam-3223	14	20	if	if	SCONJ
ejpam-3223	14	21	n	n	PRON
ejpam-3223	14	22	is	be	AUX
ejpam-3223	14	23	an	an	DET
ejpam-3223	14	24	odd	odd	ADJ
ejpam-3223	14	25	with	with	ADP
ejpam-3223	14	26	p	p	X
ejpam-3223	14	27	odd	odd	ADJ
ejpam-3223	14	28	and	and	CCONJ
ejpam-3223	14	29	q	q	NOUN
ejpam-3223	14	30	even	even	ADV
ejpam-3223	14	31	,	,	PUNCT
ejpam-3223	14	32	or	or	CCONJ
ejpam-3223	14	33	only	only	ADV
ejpam-3223	14	34	n	n	PRON
ejpam-3223	14	35	is	be	AUX
ejpam-3223	14	36	an	an	DET
ejpam-3223	14	37	even	even	ADJ
ejpam-3223	14	38	with	with	ADP
ejpam-3223	14	39	p	p	X
ejpam-3223	14	40	odd	odd	ADJ
ejpam-3223	14	41	and	and	CCONJ
ejpam-3223	14	42	q	q	NOUN
ejpam-3223	14	43	odd	odd	ADJ
ejpam-3223	14	44	.	.	PUNCT
ejpam-3223	15	1	later	later	ADV
ejpam-3223	15	2	,	,	PUNCT
ejpam-3223	15	3	bupasiri	bupasiri	NOUN
ejpam-3223	15	4	[	[	X
ejpam-3223	15	5	9	9	NUM
ejpam-3223	15	6	]	]	PUNCT
ejpam-3223	15	7	has	have	AUX
ejpam-3223	15	8	showed	show	VERB
ejpam-3223	15	9	that	that	SCONJ
ejpam-3223	15	10	the	the	DET
ejpam-3223	15	11	solution	solution	NOUN
ejpam-3223	15	12	of	of	ADP
ejpam-3223	15	13	the	the	DET
ejpam-3223	15	14	convolution	convolution	NOUN
ejpam-3223	15	15	form	form	NOUN
ejpam-3223	15	16	u(x	u(x	NOUN
ejpam-3223	15	17	)	)	PUNCT
ejpam-3223	15	18	=	=	SYM
ejpam-3223	15	19	(	(	PUNCT
ejpam-3223	15	20	−1)kre2k	−1)kre2k	NOUN
ejpam-3223	15	21	,	,	PUNCT
ejpam-3223	15	22	c(x	c(x	NOUN
ejpam-3223	15	23	)	)	PUNCT
ejpam-3223	15	24	∗rh2k	∗rh2k	NOUN
ejpam-3223	15	25	,	,	PUNCT
ejpam-3223	15	26	c(x	c(x	NOUN
ejpam-3223	15	27	)	)	PUNCT
ejpam-3223	15	28	is	be	AUX
ejpam-3223	15	29	an	an	DET
ejpam-3223	15	30	elementary	elementary	ADJ
ejpam-3223	15	31	solution	solution	NOUN
ejpam-3223	15	32	of	of	ADP
ejpam-3223	15	33	the	the	DET
ejpam-3223	15	34	♦	♦	PROPN
ejpam-3223	15	35	kcu(x	kcu(x	PROPN
ejpam-3223	15	36	)	)	PUNCT
ejpam-3223	15	37	=	=	SYM
ejpam-3223	15	38	δ	δ	PROPN
ejpam-3223	15	39	,	,	PUNCT
ejpam-3223	15	40	where	where	SCONJ
ejpam-3223	15	41	the	the	DET
ejpam-3223	15	42	operator	operator	NOUN
ejpam-3223	15	43	♦	♦	PROPN
ejpam-3223	15	44	kc	kc	PROPN
ejpam-3223	15	45	is	be	AUX
ejpam-3223	15	46	defined	define	VERB
ejpam-3223	15	47	by	by	ADP
ejpam-3223	15	48	♦	♦	PROPN
ejpam-3223	15	49	kc	kc	PROPN
ejpam-3223	15	50	=	=	PROPN
ejpam-3223	15	51			PROPN
ejpam-3223	15	52	1	1	NUM
ejpam-3223	15	53	c4	c4	NOUN
ejpam-3223	15	54	(	(	PUNCT
ejpam-3223	15	55	p∑	p∑	NOUN
ejpam-3223	15	56	r=1	r=1	NOUN
ejpam-3223	15	57	∂2	∂2	NOUN
ejpam-3223	15	58	∂x2r	∂x2r	NOUN
ejpam-3223	15	59	)	)	PUNCT
ejpam-3223	15	60	2	2	NUM
ejpam-3223	15	61	−	−	NOUN
ejpam-3223	15	62			PROPN
ejpam-3223	15	63	p+q∑	p+q∑	PROPN
ejpam-3223	15	64	j	j	NOUN
ejpam-3223	15	65	=	=	PROPN
ejpam-3223	15	66	p+1	p+1	PROPN
ejpam-3223	15	67	∂2	∂2	PROPN
ejpam-3223	15	68	∂x2j	∂x2j	PUNCT
ejpam-3223	15	69	2k	2k	X
ejpam-3223	15	70	,	,	PUNCT
ejpam-3223	15	71	(	(	PUNCT
ejpam-3223	15	72	1	1	X
ejpam-3223	15	73	)	)	PUNCT
ejpam-3223	15	74	where	where	SCONJ
ejpam-3223	15	75	p	p	NOUN
ejpam-3223	15	76	+	+	NOUN
ejpam-3223	15	77	q	q	NOUN
ejpam-3223	15	78	=	=	NOUN
ejpam-3223	15	79	n	n	X
ejpam-3223	15	80	is	be	AUX
ejpam-3223	15	81	the	the	DET
ejpam-3223	15	82	dimension	dimension	NOUN
ejpam-3223	15	83	of	of	ADP
ejpam-3223	15	84	the	the	DET
ejpam-3223	15	85	euclidean	euclidean	ADJ
ejpam-3223	15	86	space	space	PROPN
ejpam-3223	15	87	rn	rn	PROPN
ejpam-3223	15	88	,	,	PUNCT
ejpam-3223	15	89	c	c	PROPN
ejpam-3223	15	90	is	be	AUX
ejpam-3223	15	91	a	a	DET
ejpam-3223	15	92	positive	positive	ADJ
ejpam-3223	15	93	real	real	ADJ
ejpam-3223	15	94	number	number	NOUN
ejpam-3223	15	95	and	and	CCONJ
ejpam-3223	15	96	k	k	PROPN
ejpam-3223	15	97	is	be	AUX
ejpam-3223	15	98	a	a	DET
ejpam-3223	15	99	nonnegative	nonnegative	ADJ
ejpam-3223	15	100	integer	integer	NOUN
ejpam-3223	15	101	.	.	PUNCT
ejpam-3223	16	1	otherwise	otherwise	ADV
ejpam-3223	16	2	,	,	PUNCT
ejpam-3223	16	3	the	the	DET
ejpam-3223	16	4	operator	operator	NOUN
ejpam-3223	16	5	♦	♦	PROPN
ejpam-3223	16	6	kc	kc	PROPN
ejpam-3223	16	7	can	can	AUX
ejpam-3223	16	8	be	be	AUX
ejpam-3223	16	9	expressed	express	VERB
ejpam-3223	16	10	in	in	ADP
ejpam-3223	16	11	the	the	DET
ejpam-3223	16	12	form	form	NOUN
ejpam-3223	16	13	email	email	NOUN
ejpam-3223	16	14	address	address	NOUN
ejpam-3223	16	15	:	:	PUNCT
ejpam-3223	16	16	sudprathai@gmail.com	sudprathai@gmail.com	X
ejpam-3223	16	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3223	17	1	390	390	NUM
ejpam-3223	17	2	c	c	X
ejpam-3223	17	3	©	©	PROPN
ejpam-3223	17	4	2018	2018	NUM
ejpam-3223	17	5	ejpam	ejpam	VERB
ejpam-3223	17	6	all	all	DET
ejpam-3223	17	7	rights	right	NOUN
ejpam-3223	17	8	reserved	reserve	VERB
ejpam-3223	17	9	.	.	PUNCT
ejpam-3223	18	1	s.	s.	PROPN
ejpam-3223	18	2	bupasiri	bupasiri	PROPN
ejpam-3223	18	3	/	/	SYM
ejpam-3223	18	4	eur	eur	PROPN
ejpam-3223	18	5	.	.	PUNCT
ejpam-3223	19	1	j.	j.	PROPN
ejpam-3223	19	2	pure	pure	PROPN
ejpam-3223	19	3	appl	appl	PROPN
ejpam-3223	19	4	.	.	PROPN
ejpam-3223	19	5	math	math	PROPN
ejpam-3223	19	6	,	,	PUNCT
ejpam-3223	19	7	11	11	NUM
ejpam-3223	19	8	(	(	PUNCT
ejpam-3223	19	9	2	2	NUM
ejpam-3223	19	10	)	)	PUNCT
ejpam-3223	19	11	(	(	PUNCT
ejpam-3223	19	12	2018	2018	NUM
ejpam-3223	19	13	)	)	PUNCT
ejpam-3223	19	14	,	,	PUNCT
ejpam-3223	19	15	390	390	NUM
ejpam-3223	19	16	-	-	SYM
ejpam-3223	19	17	399	399	NUM
ejpam-3223	19	18	391	391	NUM
ejpam-3223	19	19	♦	♦	PROPN
ejpam-3223	19	20	kc	kc	PROPN
ejpam-3223	19	21	=	=	PROPN
ejpam-3223	19	22	�	�	PROPN
ejpam-3223	19	23	kc4k	kc4k	PROPN
ejpam-3223	19	24	c	c	NOUN
ejpam-3223	20	1	=	=	SYM
ejpam-3223	20	2	4k	4k	X
ejpam-3223	20	3	c	c	X
ejpam-3223	20	4	�	�	PROPN
ejpam-3223	20	5	k	k	PROPN
ejpam-3223	20	6	c	c	PROPN
ejpam-3223	20	7	,	,	PUNCT
ejpam-3223	20	8	where	where	SCONJ
ejpam-3223	20	9	�	�	PROPN
ejpam-3223	20	10	kc	kc	PROPN
ejpam-3223	20	11	is	be	AUX
ejpam-3223	20	12	the	the	DET
ejpam-3223	20	13	operator	operator	NOUN
ejpam-3223	20	14	related	relate	VERB
ejpam-3223	20	15	to	to	ADP
ejpam-3223	20	16	the	the	DET
ejpam-3223	20	17	ultra	ultra	ADJ
ejpam-3223	20	18	-	-	ADJ
ejpam-3223	20	19	hyperbolic	hyperbolic	ADJ
ejpam-3223	20	20	operator	operator	NOUN
ejpam-3223	20	21	iterated	iterate	VERB
ejpam-3223	20	22	k	k	NOUN
ejpam-3223	20	23	-	-	PUNCT
ejpam-3223	20	24	times	time	NOUN
ejpam-3223	20	25	,	,	PUNCT
ejpam-3223	20	26	defined	define	VERB
ejpam-3223	20	27	by	by	ADP
ejpam-3223	20	28	�	�	PROPN
ejpam-3223	20	29	kc	kc	PROPN
ejpam-3223	20	30	=	=	PUNCT
ejpam-3223	20	31	(	(	PUNCT
ejpam-3223	20	32	1	1	NUM
ejpam-3223	20	33	c2	c2	PROPN
ejpam-3223	20	34	(	(	PUNCT
ejpam-3223	20	35	∂2	∂2	PROPN
ejpam-3223	20	36	∂x21	∂x21	PROPN
ejpam-3223	20	37	+	+	CCONJ
ejpam-3223	20	38	∂2	∂2	PROPN
ejpam-3223	20	39	∂x22	∂x22	PROPN
ejpam-3223	20	40	+	+	CCONJ
ejpam-3223	20	41	·	·	PUNCT
ejpam-3223	20	42	·	·	PUNCT
ejpam-3223	20	43	·	·	PUNCT
ejpam-3223	21	1	+	+	NUM
ejpam-3223	21	2	∂2	∂2	PROPN
ejpam-3223	21	3	∂x2p	∂x2p	PROPN
ejpam-3223	21	4	)	)	PUNCT
ejpam-3223	21	5	−	−	PROPN
ejpam-3223	21	6	∂2	∂2	PROPN
ejpam-3223	21	7	∂x2p+1	∂x2p+1	PROPN
ejpam-3223	21	8	−	−	PROPN
ejpam-3223	21	9	∂2	∂2	NOUN
ejpam-3223	21	10	∂x2p+2	∂x2p+2	VERB
ejpam-3223	21	11	−	−	X
ejpam-3223	21	12	·	·	PUNCT
ejpam-3223	21	13	·	·	PUNCT
ejpam-3223	21	14	·	·	PUNCT
ejpam-3223	22	1	−	−	PUNCT
ejpam-3223	22	2	∂2	∂2	NOUN
ejpam-3223	22	3	∂x2p+q	∂x2p+q	NOUN
ejpam-3223	22	4	)	)	PUNCT
ejpam-3223	23	1	k	k	X
ejpam-3223	23	2	,	,	PUNCT
ejpam-3223	23	3	(	(	PUNCT
ejpam-3223	23	4	2	2	NUM
ejpam-3223	23	5	)	)	PUNCT
ejpam-3223	23	6	and	and	CCONJ
ejpam-3223	23	7	4k	4k	NUM
ejpam-3223	23	8	c	c	PROPN
ejpam-3223	23	9	is	be	AUX
ejpam-3223	23	10	the	the	DET
ejpam-3223	23	11	operator	operator	NOUN
ejpam-3223	23	12	related	relate	VERB
ejpam-3223	23	13	to	to	ADP
ejpam-3223	23	14	the	the	DET
ejpam-3223	23	15	laplace	laplace	NOUN
ejpam-3223	23	16	operator	operator	NOUN
ejpam-3223	23	17	iterate	iterate	VERB
ejpam-3223	23	18	k	k	PROPN
ejpam-3223	23	19	-	-	PUNCT
ejpam-3223	23	20	times	time	NOUN
ejpam-3223	23	21	,	,	PUNCT
ejpam-3223	23	22	defined	define	VERB
ejpam-3223	23	23	by	by	ADP
ejpam-3223	23	24	4k	4k	X
ejpam-3223	23	25	c	c	NOUN
ejpam-3223	23	26	=	=	PUNCT
ejpam-3223	23	27	(	(	PUNCT
ejpam-3223	23	28	1	1	NUM
ejpam-3223	23	29	c2	c2	PROPN
ejpam-3223	23	30	(	(	PUNCT
ejpam-3223	23	31	∂2	∂2	PROPN
ejpam-3223	23	32	∂x21	∂x21	PROPN
ejpam-3223	23	33	+	+	CCONJ
ejpam-3223	23	34	∂2	∂2	PROPN
ejpam-3223	23	35	∂x22	∂x22	PROPN
ejpam-3223	23	36	+	+	X
ejpam-3223	23	37	·	·	PUNCT
ejpam-3223	23	38	·	·	PUNCT
ejpam-3223	23	39	·	·	PUNCT
ejpam-3223	23	40	∂	∂	NUM
ejpam-3223	23	41	2	2	NUM
ejpam-3223	23	42	∂x2p	∂x2p	PROPN
ejpam-3223	23	43	)	)	PUNCT
ejpam-3223	24	1	+	+	CCONJ
ejpam-3223	24	2	∂2	∂2	NUM
ejpam-3223	24	3	∂x2p+1	∂x2p+1	NOUN
ejpam-3223	24	4	+	+	CCONJ
ejpam-3223	24	5	∂2	∂2	NOUN
ejpam-3223	24	6	∂x2p+2	∂x2p+2	VERB
ejpam-3223	24	7	+	+	X
ejpam-3223	24	8	·	·	PUNCT
ejpam-3223	24	9	·	·	PUNCT
ejpam-3223	24	10	·	·	PUNCT
ejpam-3223	25	1	+	+	NUM
ejpam-3223	25	2	∂2	∂2	ADJ
ejpam-3223	25	3	∂x2p+q	∂x2p+q	NOUN
ejpam-3223	25	4	)	)	PUNCT
ejpam-3223	26	1	k	k	X
ejpam-3223	26	2	.	.	PUNCT
ejpam-3223	27	1	(	(	PUNCT
ejpam-3223	27	2	3	3	X
ejpam-3223	27	3	)	)	PUNCT
ejpam-3223	27	4	next	next	ADV
ejpam-3223	27	5	,	,	PUNCT
ejpam-3223	27	6	tellez	tellez	NOUN
ejpam-3223	27	7	[	[	X
ejpam-3223	27	8	8	8	NUM
ejpam-3223	27	9	]	]	PUNCT
ejpam-3223	27	10	has	have	AUX
ejpam-3223	27	11	studied	study	VERB
ejpam-3223	27	12	the	the	DET
ejpam-3223	27	13	convolution	convolution	NOUN
ejpam-3223	27	14	product	product	NOUN
ejpam-3223	27	15	of	of	ADP
ejpam-3223	27	16	wα(u	wα(u	PROPN
ejpam-3223	27	17	,	,	PUNCT
ejpam-3223	27	18	m	m	NOUN
ejpam-3223	27	19	)	)	PUNCT
ejpam-3223	27	20	∗wβ(u	∗wβ(u	PROPN
ejpam-3223	27	21	,	,	PUNCT
ejpam-3223	27	22	m	m	NOUN
ejpam-3223	27	23	)	)	PUNCT
ejpam-3223	27	24	.	.	PUNCT
ejpam-3223	28	1	now	now	ADV
ejpam-3223	28	2	in	in	ADP
ejpam-3223	28	3	this	this	DET
ejpam-3223	28	4	paper	paper	NOUN
ejpam-3223	28	5	,	,	PUNCT
ejpam-3223	28	6	the	the	DET
ejpam-3223	28	7	operator	operator	NOUN
ejpam-3223	28	8	}	}	PUNCT
ejpam-3223	28	9	kc	kc	PROPN
ejpam-3223	28	10	can	can	AUX
ejpam-3223	28	11	be	be	AUX
ejpam-3223	28	12	expressed	express	VERB
ejpam-3223	28	13	in	in	ADP
ejpam-3223	28	14	the	the	DET
ejpam-3223	28	15	form	form	NOUN
ejpam-3223	28	16	}	}	PUNCT
ejpam-3223	28	17	kc	kc	PROPN
ejpam-3223	28	18	=	=	SYM
ejpam-3223	28	19			PROPN
ejpam-3223	28	20	(	(	PUNCT
ejpam-3223	28	21	1	1	NUM
ejpam-3223	28	22	c2	c2	PROPN
ejpam-3223	28	23	p∑	p∑	PROPN
ejpam-3223	29	1	i=1	i=1	PROPN
ejpam-3223	29	2	∂2	∂2	PROPN
ejpam-3223	29	3	∂x2i	∂x2i	NOUN
ejpam-3223	30	1	+	+	PROPN
ejpam-3223	30	2	m2	m2	PROPN
ejpam-3223	30	3	)	)	PUNCT
ejpam-3223	31	1	2	2	NUM
ejpam-3223	31	2	−	−	PROPN
ejpam-3223	31	3			PROPN
ejpam-3223	31	4	p+q∑	p+q∑	PROPN
ejpam-3223	31	5	j	j	NOUN
ejpam-3223	31	6	=	=	PROPN
ejpam-3223	31	7	p+1	p+1	PROPN
ejpam-3223	31	8	∂2	∂2	PROPN
ejpam-3223	31	9	∂x2j	∂x2j	PUNCT
ejpam-3223	31	10	2k	2k	X
ejpam-3223	32	1	=	=	PUNCT
ejpam-3223	32	2			PROPN
ejpam-3223	32	3	1	1	NUM
ejpam-3223	32	4	c2	c2	PROPN
ejpam-3223	32	5	p∑	p∑	PROPN
ejpam-3223	32	6	i=1	i=1	PROPN
ejpam-3223	32	7	∂2	∂2	PROPN
ejpam-3223	32	8	∂x2i	∂x2i	NOUN
ejpam-3223	32	9	−	−	PROPN
ejpam-3223	32	10	p+q∑	p+q∑	PROPN
ejpam-3223	32	11	j	j	PROPN
ejpam-3223	32	12	=	=	PROPN
ejpam-3223	32	13	p+1	p+1	PROPN
ejpam-3223	32	14	∂2	∂2	PROPN
ejpam-3223	32	15	∂x2j	∂x2j	X
ejpam-3223	32	16	+m2	+m2	PROPN
ejpam-3223	32	17	k	k	PROPN
ejpam-3223	32	18	1	1	NUM
ejpam-3223	32	19	c2	c2	PROPN
ejpam-3223	32	20	p∑	p∑	PROPN
ejpam-3223	32	21	i=1	i=1	PROPN
ejpam-3223	32	22	∂2	∂2	PROPN
ejpam-3223	32	23	∂x2i	∂x2i	NOUN
ejpam-3223	32	24	+	+	CCONJ
ejpam-3223	32	25	p+q∑	p+q∑	PROPN
ejpam-3223	32	26	j	j	X
ejpam-3223	32	27	=	=	PROPN
ejpam-3223	32	28	p+1	p+1	PROPN
ejpam-3223	32	29	∂2	∂2	PROPN
ejpam-3223	32	30	∂x2j	∂x2j	PROPN
ejpam-3223	33	1	+	+	NUM
ejpam-3223	33	2	m2	m2	PROPN
ejpam-3223	33	3	k	k	PUNCT
ejpam-3223	33	4	.	.	PUNCT
ejpam-3223	34	1	(	(	PUNCT
ejpam-3223	34	2	4	4	X
ejpam-3223	34	3	)	)	PUNCT
ejpam-3223	34	4	thus	thus	ADV
ejpam-3223	34	5	equation	equation	NOUN
ejpam-3223	34	6	(	(	PUNCT
ejpam-3223	34	7	4	4	X
ejpam-3223	34	8	)	)	PUNCT
ejpam-3223	34	9	can	can	AUX
ejpam-3223	34	10	be	be	AUX
ejpam-3223	34	11	written	write	VERB
ejpam-3223	34	12	as	as	ADP
ejpam-3223	34	13	}	}	PUNCT
ejpam-3223	34	14	kc	kc	PROPN
ejpam-3223	34	15	=	=	PUNCT
ejpam-3223	34	16	(	(	PUNCT
ejpam-3223	34	17	�	�	PROPN
ejpam-3223	34	18	c	c	NOUN
ejpam-3223	34	19	+	+	NOUN
ejpam-3223	34	20	m2	m2	PROPN
ejpam-3223	34	21	)	)	PUNCT
ejpam-3223	34	22	k	k	PROPN
ejpam-3223	34	23	(	(	PUNCT
ejpam-3223	34	24	4c	4c	NOUN
ejpam-3223	34	25	+	+	NOUN
ejpam-3223	34	26	m2	m2	PROPN
ejpam-3223	35	1	)	)	PUNCT
ejpam-3223	35	2	k	k	PROPN
ejpam-3223	35	3	=	=	PUNCT
ejpam-3223	35	4	(	(	PUNCT
ejpam-3223	35	5	4c	4c	NOUN
ejpam-3223	35	6	+	+	NOUN
ejpam-3223	35	7	m2	m2	PROPN
ejpam-3223	35	8	)	)	PUNCT
ejpam-3223	35	9	k	k	PROPN
ejpam-3223	35	10	(	(	PUNCT
ejpam-3223	35	11	�	�	PROPN
ejpam-3223	35	12	c	c	NOUN
ejpam-3223	35	13	+	+	NOUN
ejpam-3223	35	14	m2	m2	PROPN
ejpam-3223	35	15	)	)	PUNCT
ejpam-3223	35	16	k	k	PROPN
ejpam-3223	35	17	,	,	PUNCT
ejpam-3223	35	18	(	(	PUNCT
ejpam-3223	35	19	5	5	NUM
ejpam-3223	35	20	)	)	PUNCT
ejpam-3223	35	21	where	where	SCONJ
ejpam-3223	35	22	(	(	PUNCT
ejpam-3223	35	23	4c	4c	NOUN
ejpam-3223	35	24	+	+	NOUN
ejpam-3223	35	25	m2	m2	PROPN
ejpam-3223	35	26	)	)	PUNCT
ejpam-3223	35	27	k	k	PROPN
ejpam-3223	35	28	is	be	AUX
ejpam-3223	35	29	the	the	DET
ejpam-3223	35	30	operator	operator	NOUN
ejpam-3223	35	31	related	relate	VERB
ejpam-3223	35	32	to	to	ADP
ejpam-3223	35	33	the	the	DET
ejpam-3223	35	34	helmholtz	helmholtz	NOUN
ejpam-3223	35	35	operator	operator	NOUN
ejpam-3223	35	36	iterated	iterate	VERB
ejpam-3223	35	37	k	k	NOUN
ejpam-3223	35	38	-	-	PUNCT
ejpam-3223	35	39	times	time	NOUN
ejpam-3223	35	40	which	which	PRON
ejpam-3223	35	41	is	be	AUX
ejpam-3223	35	42	denoted	denote	VERB
ejpam-3223	35	43	by	by	ADP
ejpam-3223	35	44	(	(	PUNCT
ejpam-3223	35	45	4c	4c	NOUN
ejpam-3223	35	46	+	+	NOUN
ejpam-3223	35	47	m2	m2	PROPN
ejpam-3223	35	48	)	)	PUNCT
ejpam-3223	35	49	k	k	PROPN
ejpam-3223	36	1	=	=	PUNCT
ejpam-3223	36	2	(	(	PUNCT
ejpam-3223	36	3	1	1	NUM
ejpam-3223	36	4	c2	c2	PROPN
ejpam-3223	36	5	(	(	PUNCT
ejpam-3223	36	6	∂2	∂2	PROPN
ejpam-3223	36	7	∂x21	∂x21	PROPN
ejpam-3223	36	8	+	+	CCONJ
ejpam-3223	36	9	∂2	∂2	PROPN
ejpam-3223	36	10	∂x22	∂x22	PROPN
ejpam-3223	36	11	+	+	X
ejpam-3223	36	12	·	·	PUNCT
ejpam-3223	36	13	·	·	PUNCT
ejpam-3223	36	14	·	·	PUNCT
ejpam-3223	36	15	∂	∂	NUM
ejpam-3223	36	16	2	2	NUM
ejpam-3223	36	17	∂x2p	∂x2p	PROPN
ejpam-3223	36	18	)	)	PUNCT
ejpam-3223	37	1	+	+	CCONJ
ejpam-3223	37	2	(	(	PUNCT
ejpam-3223	37	3	∂2	∂2	NUM
ejpam-3223	37	4	∂x2p+1	∂x2p+1	NOUN
ejpam-3223	37	5	+	+	X
ejpam-3223	37	6	·	·	PUNCT
ejpam-3223	37	7	·	·	PUNCT
ejpam-3223	37	8	·	·	PUNCT
ejpam-3223	37	9	+	+	NUM
ejpam-3223	37	10	∂2	∂2	ADJ
ejpam-3223	37	11	∂x2p+q	∂x2p+q	NOUN
ejpam-3223	37	12	)	)	PUNCT
ejpam-3223	38	1	+	+	VERB
ejpam-3223	38	2	m2	m2	X
ejpam-3223	38	3	)	)	PUNCT
ejpam-3223	38	4	k	k	PROPN
ejpam-3223	38	5	(	(	PUNCT
ejpam-3223	38	6	6	6	NUM
ejpam-3223	38	7	)	)	PUNCT
ejpam-3223	38	8	and	and	CCONJ
ejpam-3223	38	9	(	(	PUNCT
ejpam-3223	38	10	�	�	PROPN
ejpam-3223	38	11	c	c	NOUN
ejpam-3223	38	12	+	+	NOUN
ejpam-3223	38	13	m2	m2	PROPN
ejpam-3223	38	14	)	)	PUNCT
ejpam-3223	38	15	k	k	PROPN
ejpam-3223	38	16	is	be	AUX
ejpam-3223	38	17	the	the	DET
ejpam-3223	38	18	operator	operator	NOUN
ejpam-3223	38	19	related	relate	VERB
ejpam-3223	38	20	to	to	ADP
ejpam-3223	38	21	the	the	DET
ejpam-3223	38	22	klein	klein	PROPN
ejpam-3223	38	23	-	-	PUNCT
ejpam-3223	38	24	gordon	gordon	PROPN
ejpam-3223	38	25	operator	operator	NOUN
ejpam-3223	38	26	iterated	iterate	VERB
ejpam-3223	38	27	k	k	NOUN
ejpam-3223	38	28	-	-	PUNCT
ejpam-3223	38	29	times	time	NOUN
ejpam-3223	38	30	which	which	PRON
ejpam-3223	38	31	is	be	AUX
ejpam-3223	38	32	denoted	denote	VERB
ejpam-3223	38	33	by	by	ADP
ejpam-3223	38	34	(	(	PUNCT
ejpam-3223	38	35	�	�	PROPN
ejpam-3223	38	36	c	c	NOUN
ejpam-3223	38	37	+	+	NOUN
ejpam-3223	38	38	m2	m2	X
ejpam-3223	38	39	)	)	PUNCT
ejpam-3223	38	40	k	k	PROPN
ejpam-3223	39	1	=	=	PUNCT
ejpam-3223	39	2	(	(	PUNCT
ejpam-3223	39	3	1	1	NUM
ejpam-3223	39	4	c2	c2	PROPN
ejpam-3223	39	5	(	(	PUNCT
ejpam-3223	39	6	∂2	∂2	PROPN
ejpam-3223	39	7	∂x21	∂x21	PROPN
ejpam-3223	39	8	+	+	CCONJ
ejpam-3223	39	9	∂2	∂2	PROPN
ejpam-3223	39	10	∂x22	∂x22	PROPN
ejpam-3223	39	11	+	+	CCONJ
ejpam-3223	39	12	·	·	PUNCT
ejpam-3223	39	13	·	·	PUNCT
ejpam-3223	39	14	·	·	PUNCT
ejpam-3223	40	1	+	+	NUM
ejpam-3223	40	2	∂2	∂2	PROPN
ejpam-3223	40	3	∂x2p	∂x2p	PROPN
ejpam-3223	40	4	)	)	PUNCT
ejpam-3223	40	5	−	−	PROPN
ejpam-3223	41	1	(	(	PUNCT
ejpam-3223	41	2	∂2	∂2	PROPN
ejpam-3223	41	3	∂x2p+1	∂x2p+1	NOUN
ejpam-3223	41	4	+	+	X
ejpam-3223	41	5	·	·	PUNCT
ejpam-3223	41	6	·	·	PUNCT
ejpam-3223	41	7	·	·	PUNCT
ejpam-3223	41	8	+	+	NUM
ejpam-3223	41	9	∂2	∂2	ADJ
ejpam-3223	41	10	∂x2p+q	∂x2p+q	NOUN
ejpam-3223	41	11	)	)	PUNCT
ejpam-3223	42	1	+	+	VERB
ejpam-3223	42	2	m2	m2	PROPN
ejpam-3223	42	3	)	)	PUNCT
ejpam-3223	42	4	k	k	PROPN
ejpam-3223	42	5	,	,	PUNCT
ejpam-3223	42	6	(	(	PUNCT
ejpam-3223	42	7	7	7	X
ejpam-3223	42	8	)	)	PUNCT
ejpam-3223	42	9	p+	p+	NOUN
ejpam-3223	42	10	q	q	NOUN
ejpam-3223	42	11	=	=	PUNCT
ejpam-3223	42	12	n	n	PROPN
ejpam-3223	42	13	and	and	CCONJ
ejpam-3223	42	14	from	from	ADP
ejpam-3223	42	15	(	(	PUNCT
ejpam-3223	42	16	4	4	NUM
ejpam-3223	42	17	)	)	PUNCT
ejpam-3223	42	18	with	with	ADP
ejpam-3223	42	19	q	q	PROPN
ejpam-3223	42	20	=	=	SYM
ejpam-3223	42	21	0	0	NUM
ejpam-3223	42	22	,	,	PUNCT
ejpam-3223	42	23	c	c	NOUN
ejpam-3223	42	24	=	=	SYM
ejpam-3223	42	25	1	1	NUM
ejpam-3223	42	26	and	and	CCONJ
ejpam-3223	42	27	k	k	NOUN
ejpam-3223	42	28	=	=	SYM
ejpam-3223	42	29	1	1	NUM
ejpam-3223	42	30	,	,	PUNCT
ejpam-3223	42	31	we	we	PRON
ejpam-3223	42	32	obtain	obtain	VERB
ejpam-3223	42	33	}	}	PUNCT
ejpam-3223	42	34	1	1	NUM
ejpam-3223	42	35	=	=	SYM
ejpam-3223	42	36	(	(	PUNCT
ejpam-3223	42	37	4p	4p	NUM
ejpam-3223	42	38	+	+	NOUN
ejpam-3223	42	39	m2	m2	PROPN
ejpam-3223	42	40	)	)	PUNCT
ejpam-3223	42	41	2	2	NUM
ejpam-3223	42	42	(	(	PUNCT
ejpam-3223	42	43	8)	8)	NUM
ejpam-3223	42	44	where	where	SCONJ
ejpam-3223	42	45	(	(	PUNCT
ejpam-3223	42	46	4p	4p	NUM
ejpam-3223	42	47	+	+	NOUN
ejpam-3223	42	48	m2	m2	X
ejpam-3223	42	49	)	)	PUNCT
ejpam-3223	42	50	=	=	PRON
ejpam-3223	43	1	(	(	PUNCT
ejpam-3223	43	2	∂2	∂2	PROPN
ejpam-3223	43	3	∂x21	∂x21	PROPN
ejpam-3223	43	4	+	+	CCONJ
ejpam-3223	43	5	∂2	∂2	PROPN
ejpam-3223	43	6	∂x22	∂x22	PROPN
ejpam-3223	43	7	+	+	CCONJ
ejpam-3223	43	8	·	·	PUNCT
ejpam-3223	43	9	·	·	PUNCT
ejpam-3223	43	10	·	·	PUNCT
ejpam-3223	44	1	+	+	NUM
ejpam-3223	44	2	∂2	∂2	NOUN
ejpam-3223	44	3	∂x2p	∂x2p	PROPN
ejpam-3223	44	4	+	+	PROPN
ejpam-3223	44	5	m2	m2	PROPN
ejpam-3223	44	6	)	)	PUNCT
ejpam-3223	44	7	.	.	PUNCT
ejpam-3223	45	1	(	(	PUNCT
ejpam-3223	45	2	9	9	X
ejpam-3223	45	3	)	)	PUNCT
ejpam-3223	45	4	s.	s.	PROPN
ejpam-3223	45	5	bupasiri	bupasiri	PROPN
ejpam-3223	45	6	/	/	SYM
ejpam-3223	45	7	eur	eur	PROPN
ejpam-3223	45	8	.	.	PUNCT
ejpam-3223	46	1	j.	j.	PROPN
ejpam-3223	46	2	pure	pure	PROPN
ejpam-3223	46	3	appl	appl	PROPN
ejpam-3223	46	4	.	.	PROPN
ejpam-3223	46	5	math	math	PROPN
ejpam-3223	46	6	,	,	PUNCT
ejpam-3223	46	7	11	11	NUM
ejpam-3223	46	8	(	(	PUNCT
ejpam-3223	46	9	2	2	NUM
ejpam-3223	46	10	)	)	PUNCT
ejpam-3223	46	11	(	(	PUNCT
ejpam-3223	46	12	2018	2018	NUM
ejpam-3223	46	13	)	)	PUNCT
ejpam-3223	46	14	,	,	PUNCT
ejpam-3223	46	15	390	390	NUM
ejpam-3223	46	16	-	-	SYM
ejpam-3223	46	17	399	399	NUM
ejpam-3223	46	18	392	392	NUM
ejpam-3223	46	19	by	by	ADP
ejpam-3223	46	20	putting	put	VERB
ejpam-3223	46	21	p	p	NOUN
ejpam-3223	46	22	=	=	X
ejpam-3223	46	23	1,m	1,m	NOUN
ejpam-3223	46	24	=	=	SYM
ejpam-3223	46	25	0	0	NUM
ejpam-3223	46	26	,	,	PUNCT
ejpam-3223	46	27	c	c	NOUN
ejpam-3223	46	28	=	=	SYM
ejpam-3223	46	29	1	1	NUM
ejpam-3223	46	30	and	and	CCONJ
ejpam-3223	46	31	x1	x1	PROPN
ejpam-3223	46	32	=	=	SYM
ejpam-3223	46	33	t	t	PROPN
ejpam-3223	46	34	(	(	PUNCT
ejpam-3223	46	35	time	time	NOUN
ejpam-3223	46	36	)	)	PUNCT
ejpam-3223	46	37	in	in	ADP
ejpam-3223	46	38	(	(	PUNCT
ejpam-3223	46	39	7	7	X
ejpam-3223	46	40	)	)	PUNCT
ejpam-3223	46	41	then	then	ADV
ejpam-3223	46	42	we	we	PRON
ejpam-3223	46	43	obtain	obtain	VERB
ejpam-3223	46	44	the	the	DET
ejpam-3223	46	45	wave	wave	NOUN
ejpam-3223	46	46	operator	operator	NOUN
ejpam-3223	46	47	�	�	NOUN
ejpam-3223	46	48	1	1	NUM
ejpam-3223	46	49	=	=	SYM
ejpam-3223	46	50	∂2	∂2	PROPN
ejpam-3223	46	51	∂x2	∂x2	PROPN
ejpam-3223	46	52	t	t	NOUN
ejpam-3223	46	53	−	−	NOUN
ejpam-3223	46	54	n−1∑	n−1∑	NUM
ejpam-3223	46	55	j=1	j=1	PROPN
ejpam-3223	46	56	∂2	∂2	PROPN
ejpam-3223	46	57	∂x2j	∂x2j	PROPN
ejpam-3223	46	58	(	(	PUNCT
ejpam-3223	46	59	10	10	NUM
ejpam-3223	46	60	)	)	PUNCT
ejpam-3223	46	61	and	and	CCONJ
ejpam-3223	46	62	from	from	ADP
ejpam-3223	46	63	(	(	PUNCT
ejpam-3223	46	64	8)	8)	NUM
ejpam-3223	46	65	with	with	ADP
ejpam-3223	46	66	q	q	NOUN
ejpam-3223	46	67	=	=	PUNCT
ejpam-3223	46	68	0,m	0,m	PUNCT
ejpam-3223	47	1	=	=	SYM
ejpam-3223	48	1	0	0	NUM
ejpam-3223	48	2	,	,	PUNCT
ejpam-3223	48	3	c	c	NOUN
ejpam-3223	48	4	=	=	SYM
ejpam-3223	48	5	1	1	NUM
ejpam-3223	48	6	and	and	CCONJ
ejpam-3223	48	7	k	k	NOUN
ejpam-3223	48	8	=	=	SYM
ejpam-3223	48	9	1	1	NUM
ejpam-3223	48	10	,	,	PUNCT
ejpam-3223	48	11	we	we	PRON
ejpam-3223	48	12	obtain	obtain	VERB
ejpam-3223	48	13	laplace	laplace	NOUN
ejpam-3223	48	14	operator	operator	NOUN
ejpam-3223	48	15	iterated	iterate	VERB
ejpam-3223	48	16	2	2	NUM
ejpam-3223	48	17	-	-	PUNCT
ejpam-3223	48	18	times	time	NOUN
ejpam-3223	48	19	of	of	ADP
ejpam-3223	48	20	p	p	NOUN
ejpam-3223	48	21	-	-	PUNCT
ejpam-3223	48	22	dimension	dimension	NOUN
ejpam-3223	48	23	}	}	PUNCT
ejpam-3223	49	1	1	1	NUM
ejpam-3223	49	2	=	=	SYM
ejpam-3223	49	3	42	42	NUM
ejpam-3223	49	4	p.	p.	NOUN
ejpam-3223	49	5	(	(	PUNCT
ejpam-3223	49	6	11	11	NUM
ejpam-3223	49	7	)	)	PUNCT
ejpam-3223	49	8	in	in	ADP
ejpam-3223	49	9	this	this	DET
ejpam-3223	49	10	paper	paper	NOUN
ejpam-3223	49	11	,	,	PUNCT
ejpam-3223	49	12	we	we	PRON
ejpam-3223	49	13	study	study	VERB
ejpam-3223	49	14	an	an	DET
ejpam-3223	49	15	elementary	elementary	ADJ
ejpam-3223	49	16	solution	solution	NOUN
ejpam-3223	49	17	for	for	ADP
ejpam-3223	49	18	the	the	DET
ejpam-3223	49	19	operator	operator	NOUN
ejpam-3223	49	20	}	}	PUNCT
ejpam-3223	49	21	kc	kc	PROPN
ejpam-3223	49	22	,	,	PUNCT
ejpam-3223	49	23	that	that	ADV
ejpam-3223	49	24	is	is	ADV
ejpam-3223	49	25	}	}	PUNCT
ejpam-3223	49	26	kcg(x	kcg(x	PROPN
ejpam-3223	49	27	)	)	PUNCT
ejpam-3223	49	28	=	=	SYM
ejpam-3223	49	29	δ	δ	PROPN
ejpam-3223	49	30	,	,	PUNCT
ejpam-3223	49	31	where	where	SCONJ
ejpam-3223	49	32	g(x	g(x	NOUN
ejpam-3223	49	33	)	)	PUNCT
ejpam-3223	49	34	is	be	AUX
ejpam-3223	49	35	an	an	DET
ejpam-3223	49	36	elementary	elementary	ADJ
ejpam-3223	49	37	solution	solution	NOUN
ejpam-3223	49	38	,	,	PUNCT
ejpam-3223	49	39	δ	δ	PROPN
ejpam-3223	49	40	is	be	AUX
ejpam-3223	49	41	the	the	DET
ejpam-3223	49	42	dirac	dirac	NOUN
ejpam-3223	49	43	delta	delta	NOUN
ejpam-3223	49	44	distribution	distribution	NOUN
ejpam-3223	49	45	,	,	PUNCT
ejpam-3223	49	46	k	k	PROPN
ejpam-3223	49	47	is	be	AUX
ejpam-3223	49	48	a	a	DET
ejpam-3223	49	49	nonnegative	nonnegative	ADJ
ejpam-3223	49	50	integer	integer	NOUN
ejpam-3223	49	51	,	,	PUNCT
ejpam-3223	49	52	c	c	PROPN
ejpam-3223	49	53	is	be	AUX
ejpam-3223	49	54	a	a	DET
ejpam-3223	49	55	positive	positive	ADJ
ejpam-3223	49	56	real	real	ADJ
ejpam-3223	49	57	number	number	NOUN
ejpam-3223	49	58	and	and	CCONJ
ejpam-3223	49	59	m	m	NOUN
ejpam-3223	49	60	is	be	AUX
ejpam-3223	49	61	a	a	DET
ejpam-3223	49	62	nonnegative	nonnegative	ADJ
ejpam-3223	49	63	real	real	ADJ
ejpam-3223	49	64	number	number	NOUN
ejpam-3223	49	65	.	.	PUNCT
ejpam-3223	50	1	we	we	PRON
ejpam-3223	50	2	then	then	ADV
ejpam-3223	50	3	also	also	ADV
ejpam-3223	50	4	apply	apply	VERB
ejpam-3223	50	5	such	such	DET
ejpam-3223	50	6	an	an	DET
ejpam-3223	50	7	elementary	elementary	ADJ
ejpam-3223	50	8	solution	solution	NOUN
ejpam-3223	50	9	to	to	PART
ejpam-3223	50	10	solve	solve	VERB
ejpam-3223	50	11	the	the	DET
ejpam-3223	50	12	solution	solution	NOUN
ejpam-3223	50	13	of	of	ADP
ejpam-3223	50	14	the	the	DET
ejpam-3223	50	15	equation	equation	NOUN
ejpam-3223	50	16	}	}	PUNCT
ejpam-3223	50	17	kcu(x	kcu(x	PROPN
ejpam-3223	50	18	)	)	PUNCT
ejpam-3223	50	19	=	=	SYM
ejpam-3223	50	20	f(x	f(x	PROPN
ejpam-3223	50	21	)	)	PUNCT
ejpam-3223	50	22	,	,	PUNCT
ejpam-3223	50	23	where	where	SCONJ
ejpam-3223	50	24	f(x	f(x	PROPN
ejpam-3223	50	25	)	)	PUNCT
ejpam-3223	50	26	is	be	AUX
ejpam-3223	50	27	a	a	DET
ejpam-3223	50	28	given	give	VERB
ejpam-3223	50	29	generalized	generalized	ADJ
ejpam-3223	50	30	function	function	NOUN
ejpam-3223	50	31	and	and	CCONJ
ejpam-3223	50	32	u(x	u(x	NOUN
ejpam-3223	50	33	)	)	PUNCT
ejpam-3223	50	34	is	be	AUX
ejpam-3223	50	35	an	an	DET
ejpam-3223	50	36	unknown	unknown	ADJ
ejpam-3223	50	37	function	function	NOUN
ejpam-3223	50	38	for	for	ADP
ejpam-3223	50	39	x	x	PROPN
ejpam-3223	50	40	∈	∈	PROPN
ejpam-3223	50	41	rn	rn	PROPN
ejpam-3223	50	42	.	.	PROPN
ejpam-3223	50	43	2	2	NUM
ejpam-3223	50	44	.	.	PUNCT
ejpam-3223	50	45	preliminaries	preliminary	NOUN
ejpam-3223	50	46	definition	definition	NOUN
ejpam-3223	50	47	1	1	X
ejpam-3223	50	48	.	.	PUNCT
ejpam-3223	51	1	let	let	VERB
ejpam-3223	51	2	x	x	PUNCT
ejpam-3223	51	3	=	=	SYM
ejpam-3223	51	4	(	(	PUNCT
ejpam-3223	51	5	x1	x1	PROPN
ejpam-3223	51	6	,	,	PUNCT
ejpam-3223	51	7	x2	x2	PROPN
ejpam-3223	51	8	,	,	PUNCT
ejpam-3223	51	9	.	.	PUNCT
ejpam-3223	51	10	.	.	PUNCT
ejpam-3223	52	1	.	.	PUNCT
ejpam-3223	53	1	,	,	PUNCT
ejpam-3223	53	2	xn	xn	X
ejpam-3223	53	3	)	)	PUNCT
ejpam-3223	53	4	be	be	VERB
ejpam-3223	53	5	a	a	DET
ejpam-3223	53	6	point	point	NOUN
ejpam-3223	53	7	of	of	ADP
ejpam-3223	53	8	the	the	DET
ejpam-3223	53	9	n	n	CCONJ
ejpam-3223	53	10	dimensional	dimensional	ADJ
ejpam-3223	53	11	space	space	NOUN
ejpam-3223	53	12	rn	rn	PROPN
ejpam-3223	53	13	,	,	PUNCT
ejpam-3223	53	14	u	u	PROPN
ejpam-3223	53	15	=	=	PROPN
ejpam-3223	53	16	c2	c2	PROPN
ejpam-3223	53	17	(	(	PUNCT
ejpam-3223	53	18	x21	x21	PROPN
ejpam-3223	54	1	+	+	NUM
ejpam-3223	54	2	x22	x22	NUM
ejpam-3223	54	3	+	+	CCONJ
ejpam-3223	54	4	·	·	PUNCT
ejpam-3223	54	5	·	·	PUNCT
ejpam-3223	54	6	·	·	PUNCT
ejpam-3223	55	1	+	+	NUM
ejpam-3223	55	2	x2p	x2p	PUNCT
ejpam-3223	55	3	)	)	PUNCT
ejpam-3223	56	1	−	−	PROPN
ejpam-3223	57	1	x2p+1	x2p+1	NUM
ejpam-3223	58	1	−	−	PROPN
ejpam-3223	58	2	x2p+2	x2p+2	ADJ
ejpam-3223	59	1	−	−	PROPN
ejpam-3223	59	2	·	·	PUNCT
ejpam-3223	59	3	·	·	PUNCT
ejpam-3223	59	4	·	·	PUNCT
ejpam-3223	60	1	−	−	NOUN
ejpam-3223	60	2	x2p+q	x2p+q	NOUN
ejpam-3223	60	3	,	,	PUNCT
ejpam-3223	60	4	(	(	PUNCT
ejpam-3223	60	5	12	12	NUM
ejpam-3223	60	6	)	)	PUNCT
ejpam-3223	60	7	where	where	SCONJ
ejpam-3223	60	8	c	c	NOUN
ejpam-3223	60	9	is	be	AUX
ejpam-3223	60	10	a	a	DET
ejpam-3223	60	11	positive	positive	ADJ
ejpam-3223	60	12	real	real	ADJ
ejpam-3223	60	13	number	number	NOUN
ejpam-3223	60	14	,	,	PUNCT
ejpam-3223	60	15	p	p	NOUN
ejpam-3223	60	16	+	+	NOUN
ejpam-3223	60	17	q	q	NOUN
ejpam-3223	60	18	=	=	PUNCT
ejpam-3223	60	19	n.	n.	NOUN
ejpam-3223	60	20	define	define	VERB
ejpam-3223	60	21	γ+	γ+	PUNCT
ejpam-3223	60	22	=	=	SYM
ejpam-3223	60	23	{	{	PUNCT
ejpam-3223	60	24	x	x	PROPN
ejpam-3223	60	25	∈	∈	PROPN
ejpam-3223	60	26	rn	rn	PROPN
ejpam-3223	60	27	:	:	PUNCT
ejpam-3223	60	28	x1	x1	PROPN
ejpam-3223	60	29	>	>	X
ejpam-3223	60	30	0	0	PUNCT
ejpam-3223	60	31	and	and	CCONJ
ejpam-3223	60	32	u	u	X
ejpam-3223	60	33	>	>	X
ejpam-3223	60	34	0	0	NUM
ejpam-3223	60	35	}	}	PUNCT
ejpam-3223	60	36	which	which	PRON
ejpam-3223	60	37	designates	designate	VERB
ejpam-3223	60	38	the	the	DET
ejpam-3223	60	39	interior	interior	NOUN
ejpam-3223	60	40	of	of	ADP
ejpam-3223	60	41	the	the	DET
ejpam-3223	60	42	forward	forward	ADJ
ejpam-3223	60	43	cone	cone	NOUN
ejpam-3223	60	44	and	and	CCONJ
ejpam-3223	60	45	γ+	γ+	PRON
ejpam-3223	60	46	designates	designate	VERB
ejpam-3223	60	47	its	its	PRON
ejpam-3223	60	48	closure	closure	NOUN
ejpam-3223	60	49	and	and	CCONJ
ejpam-3223	60	50	the	the	DET
ejpam-3223	60	51	following	follow	VERB
ejpam-3223	60	52	functions	function	NOUN
ejpam-3223	60	53	introduce	introduce	VERB
ejpam-3223	60	54	by	by	ADP
ejpam-3223	60	55	nozaki	nozaki	NOUN
ejpam-3223	60	56	(	(	PUNCT
ejpam-3223	60	57	[	[	X
ejpam-3223	60	58	12	12	NUM
ejpam-3223	60	59	]	]	PUNCT
ejpam-3223	60	60	,	,	PUNCT
ejpam-3223	60	61	p.72	p.72	NOUN
ejpam-3223	60	62	)	)	PUNCT
ejpam-3223	60	63	that	that	SCONJ
ejpam-3223	60	64	rhα	rhα	ADJ
ejpam-3223	60	65	,	,	PUNCT
ejpam-3223	60	66	c(x	c(x	NOUN
ejpam-3223	60	67	)	)	PUNCT
ejpam-3223	60	68	=	=	PRON
ejpam-3223	60	69	{	{	PUNCT
ejpam-3223	60	70	u	u	NOUN
ejpam-3223	60	71	α−n	α−n	PROPN
ejpam-3223	60	72	2	2	NUM
ejpam-3223	60	73	kn(α	kn(α	PUNCT
ejpam-3223	60	74	)	)	PUNCT
ejpam-3223	60	75	if	if	SCONJ
ejpam-3223	60	76	x	x	PUNCT
ejpam-3223	60	77	∈	∈	NOUN
ejpam-3223	60	78	γ+	γ+	PUNCT
ejpam-3223	60	79	0	0	PUNCT
ejpam-3223	61	1	if	if	SCONJ
ejpam-3223	61	2	x	x	PROPN
ejpam-3223	61	3	6∈	6∈	PROPN
ejpam-3223	61	4	γ+	γ+	PRON
ejpam-3223	61	5	,	,	PUNCT
ejpam-3223	61	6	(	(	PUNCT
ejpam-3223	61	7	13	13	NUM
ejpam-3223	61	8	)	)	PUNCT
ejpam-3223	61	9	rhα,1(x	rhα,1(x	NOUN
ejpam-3223	61	10	)	)	PUNCT
ejpam-3223	61	11	is	be	AUX
ejpam-3223	61	12	called	call	VERB
ejpam-3223	61	13	the	the	DET
ejpam-3223	61	14	ultra	ultra	ADJ
ejpam-3223	61	15	-	-	ADJ
ejpam-3223	61	16	hyperbolic	hyperbolic	ADJ
ejpam-3223	61	17	kernel	kernel	NOUN
ejpam-3223	61	18	of	of	ADP
ejpam-3223	61	19	marcel	marcel	PROPN
ejpam-3223	61	20	riesz	riesz	PROPN
ejpam-3223	61	21	.	.	PUNCT
ejpam-3223	62	1	here	here	ADV
ejpam-3223	62	2	α	α	PROPN
ejpam-3223	62	3	is	be	AUX
ejpam-3223	62	4	a	a	DET
ejpam-3223	62	5	complex	complex	ADJ
ejpam-3223	62	6	parameter	parameter	NOUN
ejpam-3223	62	7	and	and	CCONJ
ejpam-3223	62	8	n	n	DET
ejpam-3223	62	9	the	the	DET
ejpam-3223	62	10	dimension	dimension	NOUN
ejpam-3223	62	11	of	of	ADP
ejpam-3223	62	12	the	the	DET
ejpam-3223	62	13	space	space	NOUN
ejpam-3223	62	14	.	.	PUNCT
ejpam-3223	63	1	the	the	DET
ejpam-3223	63	2	constant	constant	ADJ
ejpam-3223	63	3	kn(α	kn(α	PRON
ejpam-3223	63	4	)	)	PUNCT
ejpam-3223	63	5	is	be	AUX
ejpam-3223	63	6	defined	define	VERB
ejpam-3223	63	7	by	by	ADP
ejpam-3223	63	8	kn(α	kn(α	NOUN
ejpam-3223	63	9	)	)	PUNCT
ejpam-3223	63	10	=	=	PUNCT
ejpam-3223	64	1	π	π	X
ejpam-3223	64	2	n−1	n−1	PROPN
ejpam-3223	64	3	2	2	NUM
ejpam-3223	64	4	γ	γ	X
ejpam-3223	64	5	(	(	PUNCT
ejpam-3223	64	6	2+α−n	2+α−n	PROPN
ejpam-3223	64	7	2	2	NUM
ejpam-3223	64	8	)	)	PUNCT
ejpam-3223	64	9	γ	γ	X
ejpam-3223	64	10	(	(	PUNCT
ejpam-3223	64	11	1−α	1−α	NUM
ejpam-3223	64	12	2	2	NUM
ejpam-3223	64	13	)	)	PUNCT
ejpam-3223	64	14	γ(α	γ(α	PROPN
ejpam-3223	64	15	)	)	PUNCT
ejpam-3223	64	16	γ	γ	PROPN
ejpam-3223	64	17	(	(	PUNCT
ejpam-3223	64	18	2+α−p	2+α−p	NUM
ejpam-3223	64	19	2	2	NUM
ejpam-3223	64	20	)	)	PUNCT
ejpam-3223	64	21	γ	γ	X
ejpam-3223	64	22	(	(	PUNCT
ejpam-3223	64	23	p−α	p−α	NOUN
ejpam-3223	64	24	2	2	NUM
ejpam-3223	64	25	)	)	PUNCT
ejpam-3223	64	26	(	(	PUNCT
ejpam-3223	64	27	14	14	NUM
ejpam-3223	64	28	)	)	PUNCT
ejpam-3223	64	29	and	and	CCONJ
ejpam-3223	64	30	p	p	NOUN
ejpam-3223	64	31	is	be	AUX
ejpam-3223	64	32	the	the	DET
ejpam-3223	64	33	number	number	NOUN
ejpam-3223	64	34	of	of	ADP
ejpam-3223	64	35	positive	positive	ADJ
ejpam-3223	64	36	terms	term	NOUN
ejpam-3223	64	37	of	of	ADP
ejpam-3223	64	38	u	u	NOUN
ejpam-3223	64	39	=	=	PROPN
ejpam-3223	64	40	c2	c2	PROPN
ejpam-3223	64	41	(	(	PUNCT
ejpam-3223	64	42	x21	x21	PROPN
ejpam-3223	64	43	+	+	NUM
ejpam-3223	64	44	x22	x22	NUM
ejpam-3223	64	45	+	+	CCONJ
ejpam-3223	64	46	·	·	PUNCT
ejpam-3223	64	47	·	·	PUNCT
ejpam-3223	64	48	·	·	PUNCT
ejpam-3223	65	1	+	+	NUM
ejpam-3223	65	2	x2p	x2p	PUNCT
ejpam-3223	65	3	)	)	PUNCT
ejpam-3223	66	1	−	−	PROPN
ejpam-3223	67	1	x2p+1	x2p+1	NUM
ejpam-3223	68	1	−	−	PROPN
ejpam-3223	68	2	x2p+2	x2p+2	ADJ
ejpam-3223	69	1	−	−	PROPN
ejpam-3223	69	2	·	·	PUNCT
ejpam-3223	69	3	·	·	PUNCT
ejpam-3223	69	4	·	·	PUNCT
ejpam-3223	70	1	−	−	NOUN
ejpam-3223	70	2	x2p+q	x2p+q	X
ejpam-3223	70	3	,	,	PUNCT
ejpam-3223	70	4	p+	p+	VERB
ejpam-3223	70	5	q	q	NOUN
ejpam-3223	70	6	=	=	PUNCT
ejpam-3223	70	7	n	n	PROPN
ejpam-3223	70	8	and	and	CCONJ
ejpam-3223	70	9	let	let	VERB
ejpam-3223	70	10	supp	supp	PROPN
ejpam-3223	70	11	rhα	rhα	VERB
ejpam-3223	70	12	,	,	PUNCT
ejpam-3223	70	13	c(x	c(x	NOUN
ejpam-3223	70	14	)	)	PUNCT
ejpam-3223	70	15	⊂	⊂	PROPN
ejpam-3223	70	16	γ+	γ+	PROPN
ejpam-3223	70	17	.	.	PUNCT
ejpam-3223	71	1	now	now	ADV
ejpam-3223	71	2	rhα	rhα	ADJ
ejpam-3223	71	3	,	,	PUNCT
ejpam-3223	71	4	c(x	c(x	NOUN
ejpam-3223	71	5	)	)	PUNCT
ejpam-3223	71	6	is	be	AUX
ejpam-3223	71	7	an	an	DET
ejpam-3223	71	8	ordinary	ordinary	ADJ
ejpam-3223	71	9	function	function	NOUN
ejpam-3223	71	10	if	if	SCONJ
ejpam-3223	71	11	re	re	X
ejpam-3223	71	12	(	(	PUNCT
ejpam-3223	71	13	α	α	NOUN
ejpam-3223	71	14	,	,	PUNCT
ejpam-3223	71	15	c	c	NOUN
ejpam-3223	71	16	)	)	PUNCT
ejpam-3223	71	17	≥	≥	NOUN
ejpam-3223	71	18	n	n	CCONJ
ejpam-3223	71	19	and	and	CCONJ
ejpam-3223	71	20	is	be	AUX
ejpam-3223	71	21	a	a	DET
ejpam-3223	71	22	distribution	distribution	NOUN
ejpam-3223	71	23	of	of	ADP
ejpam-3223	71	24	α	α	PRON
ejpam-3223	71	25	if	if	SCONJ
ejpam-3223	71	26	re	re	X
ejpam-3223	71	27	(	(	PUNCT
ejpam-3223	71	28	α	α	NOUN
ejpam-3223	71	29	,	,	PUNCT
ejpam-3223	71	30	c	c	NOUN
ejpam-3223	71	31	)	)	PUNCT
ejpam-3223	71	32	<	<	X
ejpam-3223	71	33	n.	n.	PROPN
ejpam-3223	71	34	s.	s.	PROPN
ejpam-3223	71	35	bupasiri	bupasiri	PROPN
ejpam-3223	71	36	/	/	SYM
ejpam-3223	71	37	eur	eur	PROPN
ejpam-3223	71	38	.	.	PUNCT
ejpam-3223	72	1	j.	j.	PROPN
ejpam-3223	72	2	pure	pure	PROPN
ejpam-3223	72	3	appl	appl	PROPN
ejpam-3223	72	4	.	.	PROPN
ejpam-3223	72	5	math	math	PROPN
ejpam-3223	72	6	,	,	PUNCT
ejpam-3223	72	7	11	11	NUM
ejpam-3223	72	8	(	(	PUNCT
ejpam-3223	72	9	2	2	NUM
ejpam-3223	72	10	)	)	PUNCT
ejpam-3223	72	11	(	(	PUNCT
ejpam-3223	72	12	2018	2018	NUM
ejpam-3223	72	13	)	)	PUNCT
ejpam-3223	72	14	,	,	PUNCT
ejpam-3223	72	15	390	390	NUM
ejpam-3223	72	16	-	-	SYM
ejpam-3223	72	17	399	399	NUM
ejpam-3223	72	18	393	393	NUM
ejpam-3223	72	19	now	now	ADV
ejpam-3223	72	20	,	,	PUNCT
ejpam-3223	72	21	if	if	SCONJ
ejpam-3223	72	22	p	p	NOUN
ejpam-3223	72	23	=	=	NOUN
ejpam-3223	72	24	1	1	NUM
ejpam-3223	72	25	then	then	ADV
ejpam-3223	72	26	(	(	PUNCT
ejpam-3223	72	27	13	13	NUM
ejpam-3223	72	28	)	)	PUNCT
ejpam-3223	72	29	reduces	reduce	VERB
ejpam-3223	72	30	to	to	ADP
ejpam-3223	72	31	the	the	DET
ejpam-3223	72	32	function	function	NOUN
ejpam-3223	72	33	mα	mα	PROPN
ejpam-3223	72	34	,	,	PUNCT
ejpam-3223	72	35	c(u	c(u	PROPN
ejpam-3223	72	36	)	)	PUNCT
ejpam-3223	72	37	say	say	VERB
ejpam-3223	72	38	,	,	PUNCT
ejpam-3223	72	39	and	and	CCONJ
ejpam-3223	72	40	defined	define	VERB
ejpam-3223	72	41	by	by	ADP
ejpam-3223	72	42	mα	mα	PROPN
ejpam-3223	72	43	,	,	PUNCT
ejpam-3223	72	44	c(u	c(u	PROPN
ejpam-3223	72	45	)	)	PUNCT
ejpam-3223	73	1	=	=	PRON
ejpam-3223	73	2	{	{	PUNCT
ejpam-3223	73	3	u	u	NOUN
ejpam-3223	73	4	α−n	α−n	PROPN
ejpam-3223	73	5	2	2	NUM
ejpam-3223	73	6	hn(α	hn(α	PUNCT
ejpam-3223	73	7	)	)	PUNCT
ejpam-3223	73	8	if	if	SCONJ
ejpam-3223	73	9	x	x	SYM
ejpam-3223	73	10	∈	∈	NOUN
ejpam-3223	73	11	γ+	γ+	PUNCT
ejpam-3223	73	12	0	0	PUNCT
ejpam-3223	74	1	if	if	SCONJ
ejpam-3223	74	2	x	x	PROPN
ejpam-3223	74	3	6∈	6∈	PROPN
ejpam-3223	74	4	γ+	γ+	PRON
ejpam-3223	74	5	,	,	PUNCT
ejpam-3223	74	6	(	(	PUNCT
ejpam-3223	74	7	15	15	NUM
ejpam-3223	74	8	)	)	PUNCT
ejpam-3223	74	9	where	where	SCONJ
ejpam-3223	74	10	u	u	NOUN
ejpam-3223	74	11	=	=	PUNCT
ejpam-3223	74	12	c2x21	c2x21	PROPN
ejpam-3223	74	13	−	−	NUM
ejpam-3223	74	14	x22	x22	NOUN
ejpam-3223	74	15	−	−	PROPN
ejpam-3223	74	16	·	·	PUNCT
ejpam-3223	74	17	·	·	PUNCT
ejpam-3223	74	18	·	·	PUNCT
ejpam-3223	75	1	−	−	PROPN
ejpam-3223	76	1	x2n	x2n	PROPN
ejpam-3223	76	2	and	and	CCONJ
ejpam-3223	76	3	hn(α	hn(α	PUNCT
ejpam-3223	76	4	)	)	PUNCT
ejpam-3223	76	5	=	=	SYM
ejpam-3223	76	6	π	π	X
ejpam-3223	76	7	(	(	PUNCT
ejpam-3223	76	8	n−1	n−1	PROPN
ejpam-3223	76	9	)	)	PUNCT
ejpam-3223	76	10	2	2	NUM
ejpam-3223	76	11	2α−1γ(α−n+2	2α−1γ(α−n+2	NUM
ejpam-3223	76	12	2	2	NUM
ejpam-3223	76	13	)	)	PUNCT
ejpam-3223	76	14	.	.	PUNCT
ejpam-3223	77	1	the	the	DET
ejpam-3223	77	2	function	function	NOUN
ejpam-3223	77	3	mα,1(u	mα,1(u	PROPN
ejpam-3223	77	4	)	)	PUNCT
ejpam-3223	77	5	is	be	AUX
ejpam-3223	77	6	called	call	VERB
ejpam-3223	77	7	the	the	DET
ejpam-3223	77	8	hyperbolic	hyperbolic	ADJ
ejpam-3223	77	9	kernel	kernel	NOUN
ejpam-3223	77	10	of	of	ADP
ejpam-3223	77	11	marcel	marcel	PROPN
ejpam-3223	77	12	riesz	riesz	PROPN
ejpam-3223	77	13	.	.	PUNCT
ejpam-3223	78	1	definition	definition	NOUN
ejpam-3223	78	2	2	2	NUM
ejpam-3223	78	3	.	.	PUNCT
ejpam-3223	79	1	let	let	VERB
ejpam-3223	79	2	x	x	PUNCT
ejpam-3223	79	3	=	=	SYM
ejpam-3223	79	4	(	(	PUNCT
ejpam-3223	79	5	x1	x1	PROPN
ejpam-3223	79	6	,	,	PUNCT
ejpam-3223	79	7	x2	x2	PROPN
ejpam-3223	79	8	,	,	PUNCT
ejpam-3223	79	9	.	.	PUNCT
ejpam-3223	79	10	.	.	PUNCT
ejpam-3223	80	1	.	.	PUNCT
ejpam-3223	81	1	,	,	PUNCT
ejpam-3223	81	2	xn	xn	X
ejpam-3223	81	3	)	)	PUNCT
ejpam-3223	81	4	∈	∈	PROPN
ejpam-3223	81	5	rn	rn	PROPN
ejpam-3223	81	6	and	and	CCONJ
ejpam-3223	81	7	v	v	NOUN
ejpam-3223	81	8	=	=	SYM
ejpam-3223	81	9	c2	c2	PROPN
ejpam-3223	81	10	(	(	PUNCT
ejpam-3223	81	11	x21	x21	PROPN
ejpam-3223	82	1	+	+	NUM
ejpam-3223	82	2	x22	x22	NUM
ejpam-3223	82	3	+	+	CCONJ
ejpam-3223	82	4	·	·	PUNCT
ejpam-3223	82	5	·	·	PUNCT
ejpam-3223	82	6	·	·	PUNCT
ejpam-3223	83	1	+	+	NUM
ejpam-3223	83	2	x2p	x2p	PUNCT
ejpam-3223	83	3	)	)	PUNCT
ejpam-3223	84	1	+	+	CCONJ
ejpam-3223	84	2	x2p+1	x2p+1	PROPN
ejpam-3223	85	1	+	+	CCONJ
ejpam-3223	85	2	x2p+2	x2p+2	ADJ
ejpam-3223	86	1	+	+	CCONJ
ejpam-3223	86	2	·	·	PUNCT
ejpam-3223	86	3	·	·	PUNCT
ejpam-3223	86	4	·	·	PUNCT
ejpam-3223	86	5	+	+	NUM
ejpam-3223	86	6	x2p+q	x2p+q	X
ejpam-3223	86	7	,	,	PUNCT
ejpam-3223	86	8	p+	p+	VERB
ejpam-3223	86	9	q	q	NOUN
ejpam-3223	86	10	=	=	PUNCT
ejpam-3223	86	11	n.	n.	NOUN
ejpam-3223	86	12	(	(	PUNCT
ejpam-3223	86	13	16	16	NUM
ejpam-3223	86	14	)	)	PUNCT
ejpam-3223	86	15	for	for	ADP
ejpam-3223	86	16	any	any	DET
ejpam-3223	86	17	complex	complex	ADJ
ejpam-3223	86	18	number	number	NOUN
ejpam-3223	86	19	β	β	NOUN
ejpam-3223	86	20	,	,	PUNCT
ejpam-3223	86	21	we	we	PRON
ejpam-3223	86	22	define	define	VERB
ejpam-3223	86	23	the	the	DET
ejpam-3223	86	24	function	function	NOUN
ejpam-3223	86	25	reβ	reβ	NOUN
ejpam-3223	86	26	,	,	PUNCT
ejpam-3223	86	27	c(v	c(v	PROPN
ejpam-3223	86	28	)	)	PUNCT
ejpam-3223	86	29	=	=	SYM
ejpam-3223	87	1	2−βπ−n/2γ	2−βπ−n/2γ	NUM
ejpam-3223	87	2	(	(	PUNCT
ejpam-3223	87	3	n−	n−	NOUN
ejpam-3223	87	4	β	β	X
ejpam-3223	87	5	2	2	NUM
ejpam-3223	87	6	)	)	PUNCT
ejpam-3223	87	7	v(β−n)/2	v(β−n)/2	NOUN
ejpam-3223	87	8	γ(β/2	γ(β/2	PROPN
ejpam-3223	87	9	)	)	PUNCT
ejpam-3223	87	10	.	.	PUNCT
ejpam-3223	88	1	(	(	PUNCT
ejpam-3223	88	2	17	17	NUM
ejpam-3223	88	3	)	)	PUNCT
ejpam-3223	88	4	the	the	DET
ejpam-3223	88	5	function	function	NOUN
ejpam-3223	88	6	reβ,1(v	reβ,1(v	NOUN
ejpam-3223	88	7	)	)	PUNCT
ejpam-3223	88	8	is	be	AUX
ejpam-3223	88	9	called	call	VERB
ejpam-3223	88	10	the	the	DET
ejpam-3223	88	11	elliptic	elliptic	ADJ
ejpam-3223	88	12	kernel	kernel	NOUN
ejpam-3223	88	13	of	of	ADP
ejpam-3223	88	14	marcel	marcel	PROPN
ejpam-3223	88	15	riesz	riesz	PROPN
ejpam-3223	88	16	.	.	PUNCT
ejpam-3223	89	1	it	it	PRON
ejpam-3223	89	2	is	be	AUX
ejpam-3223	89	3	an	an	DET
ejpam-3223	89	4	ordinary	ordinary	ADJ
ejpam-3223	89	5	function	function	NOUN
ejpam-3223	89	6	if	if	SCONJ
ejpam-3223	89	7	re(β	re(β	NOUN
ejpam-3223	89	8	,	,	PUNCT
ejpam-3223	89	9	c	c	NOUN
ejpam-3223	89	10	)	)	PUNCT
ejpam-3223	89	11	≥	≥	NOUN
ejpam-3223	89	12	n	n	PROPN
ejpam-3223	89	13	and	and	CCONJ
ejpam-3223	89	14	a	a	DET
ejpam-3223	89	15	distribution	distribution	NOUN
ejpam-3223	89	16	of	of	ADP
ejpam-3223	89	17	β	β	PRON
ejpam-3223	89	18	if	if	SCONJ
ejpam-3223	89	19	re(β	re(β	NOUN
ejpam-3223	89	20	,	,	PUNCT
ejpam-3223	89	21	c	c	X
ejpam-3223	89	22	)	)	PUNCT
ejpam-3223	89	23	<	<	X
ejpam-3223	89	24	n.	n.	PROPN
ejpam-3223	89	25	lemma	lemma	PROPN
ejpam-3223	89	26	1	1	NUM
ejpam-3223	89	27	.	.	PUNCT
ejpam-3223	89	28	given	give	VERB
ejpam-3223	89	29	the	the	DET
ejpam-3223	89	30	equation	equation	NOUN
ejpam-3223	89	31	4k	4k	NOUN
ejpam-3223	89	32	cu(x	cu(x	VERB
ejpam-3223	89	33	)	)	PUNCT
ejpam-3223	89	34	=	=	SYM
ejpam-3223	89	35	δ	δ	PROPN
ejpam-3223	89	36	for	for	ADP
ejpam-3223	89	37	x	x	PROPN
ejpam-3223	89	38	∈	∈	PROPN
ejpam-3223	89	39	rn	rn	PROPN
ejpam-3223	89	40	,	,	PUNCT
ejpam-3223	89	41	where	where	SCONJ
ejpam-3223	89	42	4k	4k	PRON
ejpam-3223	89	43	c	c	PROPN
ejpam-3223	89	44	is	be	AUX
ejpam-3223	89	45	the	the	DET
ejpam-3223	89	46	operator	operator	NOUN
ejpam-3223	89	47	related	relate	VERB
ejpam-3223	89	48	to	to	ADP
ejpam-3223	89	49	the	the	DET
ejpam-3223	89	50	laplace	laplace	NOUN
ejpam-3223	89	51	operator	operator	NOUN
ejpam-3223	89	52	iterated	iterate	VERB
ejpam-3223	89	53	k	k	NOUN
ejpam-3223	89	54	-	-	PUNCT
ejpam-3223	89	55	times	time	NOUN
ejpam-3223	89	56	defined	define	VERB
ejpam-3223	89	57	by	by	ADP
ejpam-3223	89	58	(	(	PUNCT
ejpam-3223	89	59	3	3	NUM
ejpam-3223	89	60	)	)	PUNCT
ejpam-3223	89	61	.	.	PUNCT
ejpam-3223	90	1	then	then	ADV
ejpam-3223	90	2	u(x	u(x	VERB
ejpam-3223	90	3	)	)	PUNCT
ejpam-3223	90	4	=	=	SYM
ejpam-3223	90	5	(	(	PUNCT
ejpam-3223	90	6	−1)kre2k	−1)kre2k	PROPN
ejpam-3223	90	7	,	,	PUNCT
ejpam-3223	90	8	c(v	c(v	PROPN
ejpam-3223	90	9	)	)	PUNCT
ejpam-3223	90	10	is	be	AUX
ejpam-3223	90	11	an	an	DET
ejpam-3223	90	12	elementary	elementary	ADJ
ejpam-3223	90	13	solution	solution	NOUN
ejpam-3223	90	14	of	of	ADP
ejpam-3223	90	15	the	the	DET
ejpam-3223	90	16	operator	operator	NOUN
ejpam-3223	90	17	4k	4k	NOUN
ejpam-3223	90	18	c	c	PROPN
ejpam-3223	90	19	,	,	PUNCT
ejpam-3223	90	20	with	with	ADP
ejpam-3223	90	21	β	β	X
ejpam-3223	90	22	=	=	SYM
ejpam-3223	90	23	2k	2k	NUM
ejpam-3223	90	24	.	.	PUNCT
ejpam-3223	91	1	proof	proof	NOUN
ejpam-3223	91	2	.	.	PUNCT
ejpam-3223	92	1	see	see	VERB
ejpam-3223	92	2	[	[	X
ejpam-3223	92	3	2	2	NUM
ejpam-3223	92	4	]	]	PUNCT
ejpam-3223	92	5	.	.	PUNCT
ejpam-3223	93	1	lemma	lemma	PROPN
ejpam-3223	93	2	2	2	X
ejpam-3223	93	3	.	.	PUNCT
ejpam-3223	94	1	if	if	SCONJ
ejpam-3223	94	2	�	�	NOUN
ejpam-3223	94	3	kcu(x	kcu(x	PROPN
ejpam-3223	94	4	)	)	PUNCT
ejpam-3223	94	5	=	=	SYM
ejpam-3223	94	6	δ	δ	PROPN
ejpam-3223	94	7	for	for	ADP
ejpam-3223	94	8	x	x	PROPN
ejpam-3223	94	9	∈	∈	PROPN
ejpam-3223	94	10	γ+	γ+	PUNCT
ejpam-3223	94	11	=	=	SYM
ejpam-3223	94	12	{	{	PUNCT
ejpam-3223	94	13	x	x	PROPN
ejpam-3223	94	14	∈	∈	PROPN
ejpam-3223	94	15	rn	rn	PROPN
ejpam-3223	94	16	:	:	PUNCT
ejpam-3223	94	17	x1	x1	PROPN
ejpam-3223	94	18	>	>	X
ejpam-3223	94	19	0	0	PUNCT
ejpam-3223	94	20	and	and	CCONJ
ejpam-3223	94	21	u	u	X
ejpam-3223	94	22	>	>	X
ejpam-3223	94	23	0	0	NUM
ejpam-3223	94	24	}	}	PUNCT
ejpam-3223	94	25	,	,	PUNCT
ejpam-3223	94	26	where	where	SCONJ
ejpam-3223	94	27	�	�	PROPN
ejpam-3223	94	28	kc	kc	PROPN
ejpam-3223	94	29	is	be	AUX
ejpam-3223	94	30	the	the	DET
ejpam-3223	94	31	operator	operator	NOUN
ejpam-3223	94	32	related	relate	VERB
ejpam-3223	94	33	to	to	ADP
ejpam-3223	94	34	the	the	DET
ejpam-3223	94	35	ultra	ultra	ADJ
ejpam-3223	94	36	-	-	ADJ
ejpam-3223	94	37	hyperbolic	hyperbolic	ADJ
ejpam-3223	94	38	operator	operator	NOUN
ejpam-3223	94	39	iterated	iterate	VERB
ejpam-3223	94	40	k	k	NOUN
ejpam-3223	94	41	-	-	PUNCT
ejpam-3223	94	42	times	time	NOUN
ejpam-3223	94	43	defined	define	VERB
ejpam-3223	94	44	by	by	ADP
ejpam-3223	94	45	(	(	PUNCT
ejpam-3223	94	46	2	2	NUM
ejpam-3223	94	47	)	)	PUNCT
ejpam-3223	94	48	.	.	PUNCT
ejpam-3223	95	1	then	then	ADV
ejpam-3223	95	2	u(x	u(x	VERB
ejpam-3223	95	3	)	)	PUNCT
ejpam-3223	95	4	=	=	SYM
ejpam-3223	95	5	rh2k	rh2k	PROPN
ejpam-3223	95	6	,	,	PUNCT
ejpam-3223	95	7	c(u	c(u	PROPN
ejpam-3223	95	8	)	)	PUNCT
ejpam-3223	95	9	is	be	AUX
ejpam-3223	95	10	the	the	DET
ejpam-3223	95	11	unique	unique	ADJ
ejpam-3223	95	12	elementary	elementary	ADJ
ejpam-3223	95	13	solution	solution	NOUN
ejpam-3223	95	14	of	of	ADP
ejpam-3223	95	15	the	the	DET
ejpam-3223	95	16	operator	operator	NOUN
ejpam-3223	95	17	�	�	PROPN
ejpam-3223	95	18	kc	kc	PROPN
ejpam-3223	95	19	,	,	PUNCT
ejpam-3223	95	20	with	with	ADP
ejpam-3223	95	21	α	α	NOUN
ejpam-3223	95	22	=	=	SYM
ejpam-3223	95	23	2k	2k	NUM
ejpam-3223	95	24	.	.	PUNCT
ejpam-3223	96	1	proof	proof	NOUN
ejpam-3223	96	2	.	.	PUNCT
ejpam-3223	97	1	see	see	VERB
ejpam-3223	97	2	[	[	X
ejpam-3223	97	3	10	10	NUM
ejpam-3223	97	4	]	]	PUNCT
ejpam-3223	97	5	.	.	PUNCT
ejpam-3223	98	1	lemma	lemma	PROPN
ejpam-3223	98	2	3	3	X
ejpam-3223	98	3	.	.	PUNCT
ejpam-3223	98	4	given	give	VERB
ejpam-3223	98	5	the	the	DET
ejpam-3223	98	6	equation	equation	NOUN
ejpam-3223	98	7	(	(	PUNCT
ejpam-3223	98	8	�	�	PROPN
ejpam-3223	98	9	c	c	NOUN
ejpam-3223	98	10	+	+	NOUN
ejpam-3223	98	11	m2	m2	X
ejpam-3223	98	12	)	)	PUNCT
ejpam-3223	98	13	k	k	PROPN
ejpam-3223	98	14	u(x	u(x	PROPN
ejpam-3223	98	15	)	)	PUNCT
ejpam-3223	98	16	=	=	SYM
ejpam-3223	98	17	δ	δ	PROPN
ejpam-3223	98	18	for	for	ADP
ejpam-3223	98	19	x	x	PROPN
ejpam-3223	98	20	∈	∈	PROPN
ejpam-3223	98	21	rn	rn	PROPN
ejpam-3223	98	22	,	,	PUNCT
ejpam-3223	98	23	where	where	SCONJ
ejpam-3223	98	24	(	(	PUNCT
ejpam-3223	98	25	�	�	PROPN
ejpam-3223	98	26	c	c	NOUN
ejpam-3223	98	27	+	+	NOUN
ejpam-3223	98	28	m2	m2	PROPN
ejpam-3223	98	29	)	)	PUNCT
ejpam-3223	98	30	k	k	PROPN
ejpam-3223	98	31	is	be	AUX
ejpam-3223	98	32	the	the	DET
ejpam-3223	98	33	operator	operator	NOUN
ejpam-3223	98	34	related	relate	VERB
ejpam-3223	98	35	to	to	ADP
ejpam-3223	98	36	the	the	DET
ejpam-3223	98	37	klein	klein	PROPN
ejpam-3223	98	38	-	-	PUNCT
ejpam-3223	98	39	gordon	gordon	PROPN
ejpam-3223	98	40	operator	operator	NOUN
ejpam-3223	98	41	iterated	iterate	VERB
ejpam-3223	98	42	k	k	NOUN
ejpam-3223	98	43	-	-	PUNCT
ejpam-3223	98	44	times	time	NOUN
ejpam-3223	98	45	defined	define	VERB
ejpam-3223	98	46	by	by	ADP
ejpam-3223	98	47	equation	equation	NOUN
ejpam-3223	98	48	(	(	PUNCT
ejpam-3223	98	49	7	7	NUM
ejpam-3223	98	50	)	)	PUNCT
ejpam-3223	98	51	,	,	PUNCT
ejpam-3223	98	52	δ	δ	PROPN
ejpam-3223	98	53	is	be	AUX
ejpam-3223	98	54	the	the	DET
ejpam-3223	98	55	dirac	dirac	NOUN
ejpam-3223	98	56	-	-	PUNCT
ejpam-3223	98	57	delta	delta	NOUN
ejpam-3223	98	58	distribution	distribution	NOUN
ejpam-3223	98	59	,	,	PUNCT
ejpam-3223	98	60	k	k	PROPN
ejpam-3223	98	61	is	be	AUX
ejpam-3223	98	62	a	a	DET
ejpam-3223	98	63	nonnegative	nonnegative	ADJ
ejpam-3223	98	64	integer	integer	NOUN
ejpam-3223	98	65	and	and	CCONJ
ejpam-3223	98	66	m	m	NOUN
ejpam-3223	98	67	is	be	AUX
ejpam-3223	98	68	a	a	DET
ejpam-3223	98	69	nonnegative	nonnegative	ADJ
ejpam-3223	98	70	real	real	ADJ
ejpam-3223	98	71	number	number	NOUN
ejpam-3223	98	72	,	,	PUNCT
ejpam-3223	98	73	then	then	ADV
ejpam-3223	98	74	u(x	u(x	VERB
ejpam-3223	98	75	)	)	PUNCT
ejpam-3223	98	76	=	=	SYM
ejpam-3223	98	77	w2k	w2k	PROPN
ejpam-3223	98	78	,	,	PUNCT
ejpam-3223	98	79	c(u	c(u	PROPN
ejpam-3223	98	80	,	,	PUNCT
ejpam-3223	98	81	m	m	PRON
ejpam-3223	98	82	)	)	PUNCT
ejpam-3223	98	83	is	be	AUX
ejpam-3223	98	84	an	an	DET
ejpam-3223	98	85	elementary	elementary	ADJ
ejpam-3223	98	86	solution	solution	NOUN
ejpam-3223	98	87	of	of	ADP
ejpam-3223	98	88	the	the	DET
ejpam-3223	98	89	operator	operator	NOUN
ejpam-3223	98	90	(	(	PUNCT
ejpam-3223	98	91	�	�	PROPN
ejpam-3223	98	92	c	c	NOUN
ejpam-3223	98	93	+	+	NOUN
ejpam-3223	98	94	m2	m2	PROPN
ejpam-3223	98	95	)	)	PUNCT
ejpam-3223	98	96	k	k	PROPN
ejpam-3223	98	97	,	,	PUNCT
ejpam-3223	98	98	where	where	SCONJ
ejpam-3223	98	99	w2k	w2k	PROPN
ejpam-3223	98	100	,	,	PUNCT
ejpam-3223	98	101	c(u	c(u	PROPN
ejpam-3223	98	102	,	,	PUNCT
ejpam-3223	98	103	m	m	NOUN
ejpam-3223	98	104	)	)	PUNCT
ejpam-3223	98	105	=	=	PUNCT
ejpam-3223	99	1	∞∑	∞∑	NUM
ejpam-3223	99	2	r=0	r=0	PROPN
ejpam-3223	99	3	(	(	PUNCT
ejpam-3223	99	4	−k	−k	NOUN
ejpam-3223	99	5	r	r	NOUN
ejpam-3223	99	6	)	)	PUNCT
ejpam-3223	100	1	m2rrh2k+2r	m2rrh2k+2r	ADV
ejpam-3223	100	2	,	,	PUNCT
ejpam-3223	100	3	c(u	c(u	PROPN
ejpam-3223	100	4	)	)	PUNCT
ejpam-3223	100	5	,	,	PUNCT
ejpam-3223	100	6	(	(	PUNCT
ejpam-3223	100	7	18	18	NUM
ejpam-3223	100	8	)	)	PUNCT
ejpam-3223	100	9	rh2k	rh2k	PROPN
ejpam-3223	100	10	,	,	PUNCT
ejpam-3223	100	11	c(u	c(u	PROPN
ejpam-3223	100	12	)	)	PUNCT
ejpam-3223	100	13	is	be	AUX
ejpam-3223	100	14	defined	define	VERB
ejpam-3223	100	15	by	by	ADP
ejpam-3223	100	16	(	(	PUNCT
ejpam-3223	100	17	13	13	NUM
ejpam-3223	100	18	)	)	PUNCT
ejpam-3223	100	19	.	.	PUNCT
ejpam-3223	101	1	proof	proof	NOUN
ejpam-3223	101	2	.	.	PUNCT
ejpam-3223	102	1	see	see	VERB
ejpam-3223	102	2	[	[	X
ejpam-3223	102	3	6	6	NUM
ejpam-3223	102	4	]	]	PUNCT
ejpam-3223	102	5	.	.	PUNCT
ejpam-3223	103	1	s.	s.	PROPN
ejpam-3223	103	2	bupasiri	bupasiri	PROPN
ejpam-3223	103	3	/	/	SYM
ejpam-3223	103	4	eur	eur	PROPN
ejpam-3223	103	5	.	.	PUNCT
ejpam-3223	104	1	j.	j.	PROPN
ejpam-3223	104	2	pure	pure	PROPN
ejpam-3223	104	3	appl	appl	PROPN
ejpam-3223	104	4	.	.	PROPN
ejpam-3223	104	5	math	math	PROPN
ejpam-3223	104	6	,	,	PUNCT
ejpam-3223	104	7	11	11	NUM
ejpam-3223	104	8	(	(	PUNCT
ejpam-3223	104	9	2	2	NUM
ejpam-3223	104	10	)	)	PUNCT
ejpam-3223	104	11	(	(	PUNCT
ejpam-3223	104	12	2018	2018	NUM
ejpam-3223	104	13	)	)	PUNCT
ejpam-3223	104	14	,	,	PUNCT
ejpam-3223	104	15	390	390	NUM
ejpam-3223	104	16	-	-	SYM
ejpam-3223	104	17	399	399	NUM
ejpam-3223	104	18	394	394	NUM
ejpam-3223	104	19	lemma	lemma	PROPN
ejpam-3223	104	20	4	4	NUM
ejpam-3223	104	21	.	.	PUNCT
ejpam-3223	105	1	let	let	VERB
ejpam-3223	105	2	�	�	PROPN
ejpam-3223	105	3	c	c	PROPN
ejpam-3223	105	4	be	be	AUX
ejpam-3223	105	5	the	the	DET
ejpam-3223	105	6	operator	operator	NOUN
ejpam-3223	105	7	related	relate	VERB
ejpam-3223	105	8	to	to	ADP
ejpam-3223	105	9	the	the	DET
ejpam-3223	105	10	ultra	ultra	ADJ
ejpam-3223	105	11	-	-	ADJ
ejpam-3223	105	12	hyperbolic	hyperbolic	ADJ
ejpam-3223	105	13	operator	operator	NOUN
ejpam-3223	105	14	,	,	PUNCT
ejpam-3223	105	15	defined	define	VERB
ejpam-3223	105	16	by	by	ADP
ejpam-3223	105	17	(	(	PUNCT
ejpam-3223	105	18	2	2	NUM
ejpam-3223	105	19	)	)	PUNCT
ejpam-3223	105	20	and	and	CCONJ
ejpam-3223	105	21	δ	δ	PROPN
ejpam-3223	105	22	is	be	AUX
ejpam-3223	105	23	the	the	DET
ejpam-3223	105	24	dirac	dirac	NOUN
ejpam-3223	105	25	delta	delta	NOUN
ejpam-3223	105	26	distribution	distribution	NOUN
ejpam-3223	105	27	for	for	ADP
ejpam-3223	105	28	x	x	PROPN
ejpam-3223	105	29	∈	∈	PROPN
ejpam-3223	105	30	rn	rn	PROPN
ejpam-3223	105	31	,	,	PUNCT
ejpam-3223	105	32	then	then	ADV
ejpam-3223	105	33	(	(	PUNCT
ejpam-3223	105	34	�	�	PROPN
ejpam-3223	105	35	c	c	PROPN
ejpam-3223	105	36	+	+	NOUN
ejpam-3223	105	37	m2	m2	X
ejpam-3223	105	38	)	)	PUNCT
ejpam-3223	106	1	k	k	PROPN
ejpam-3223	106	2	δ	δ	PROPN
ejpam-3223	106	3	=	=	SYM
ejpam-3223	106	4	w−2k	w−2k	NOUN
ejpam-3223	106	5	,	,	PUNCT
ejpam-3223	106	6	c(u	c(u	PROPN
ejpam-3223	106	7	,	,	PUNCT
ejpam-3223	106	8	m	m	NOUN
ejpam-3223	106	9	)	)	PUNCT
ejpam-3223	106	10	,	,	PUNCT
ejpam-3223	106	11	where	where	SCONJ
ejpam-3223	106	12	w−2k	w−2k	NOUN
ejpam-3223	106	13	,	,	PUNCT
ejpam-3223	106	14	c(u	c(u	PROPN
ejpam-3223	106	15	,	,	PUNCT
ejpam-3223	106	16	m	m	PRON
ejpam-3223	106	17	)	)	PUNCT
ejpam-3223	106	18	is	be	AUX
ejpam-3223	106	19	the	the	DET
ejpam-3223	106	20	inverse	inverse	NOUN
ejpam-3223	106	21	of	of	ADP
ejpam-3223	106	22	w2k	w2k	PROPN
ejpam-3223	106	23	,	,	PUNCT
ejpam-3223	106	24	c(u	c(u	PROPN
ejpam-3223	106	25	,	,	PUNCT
ejpam-3223	106	26	m	m	NOUN
ejpam-3223	106	27	)	)	PUNCT
ejpam-3223	106	28	in	in	ADP
ejpam-3223	106	29	the	the	DET
ejpam-3223	106	30	convolution	convolution	NOUN
ejpam-3223	106	31	algebra	algebra	NOUN
ejpam-3223	106	32	.	.	PUNCT
ejpam-3223	107	1	proof	proof	NOUN
ejpam-3223	107	2	.	.	PUNCT
ejpam-3223	108	1	let	let	VERB
ejpam-3223	108	2	v	v	X
ejpam-3223	108	3	(	(	PUNCT
ejpam-3223	108	4	x	x	NOUN
ejpam-3223	108	5	)	)	PUNCT
ejpam-3223	108	6	=	=	SYM
ejpam-3223	108	7	(	(	PUNCT
ejpam-3223	108	8	�	�	PROPN
ejpam-3223	108	9	c	c	NOUN
ejpam-3223	108	10	+	+	NOUN
ejpam-3223	108	11	m2	m2	X
ejpam-3223	108	12	)	)	PUNCT
ejpam-3223	108	13	k	k	PROPN
ejpam-3223	108	14	δ	δ	PROPN
ejpam-3223	108	15	,	,	PUNCT
ejpam-3223	108	16	convolving	convolve	VERB
ejpam-3223	108	17	both	both	DET
ejpam-3223	108	18	sides	side	NOUN
ejpam-3223	108	19	by	by	ADP
ejpam-3223	108	20	w2k	w2k	PROPN
ejpam-3223	108	21	,	,	PUNCT
ejpam-3223	108	22	c(u	c(u	PROPN
ejpam-3223	108	23	,	,	PUNCT
ejpam-3223	108	24	m	m	PROPN
ejpam-3223	108	25	)	)	PUNCT
ejpam-3223	108	26	,	,	PUNCT
ejpam-3223	108	27	then	then	ADV
ejpam-3223	108	28	w2k	w2k	PROPN
ejpam-3223	108	29	,	,	PUNCT
ejpam-3223	108	30	c(u	c(u	PROPN
ejpam-3223	108	31	,	,	PUNCT
ejpam-3223	108	32	m	m	NOUN
ejpam-3223	108	33	)	)	PUNCT
ejpam-3223	108	34	∗	∗	NOUN
ejpam-3223	108	35	v	v	NOUN
ejpam-3223	108	36	(	(	PUNCT
ejpam-3223	108	37	x	x	NOUN
ejpam-3223	108	38	)	)	PUNCT
ejpam-3223	108	39	=	=	SYM
ejpam-3223	108	40	w2k	w2k	PROPN
ejpam-3223	108	41	,	,	PUNCT
ejpam-3223	108	42	c(u	c(u	PROPN
ejpam-3223	108	43	,	,	PUNCT
ejpam-3223	108	44	m	m	NOUN
ejpam-3223	108	45	)	)	PUNCT
ejpam-3223	108	46	∗	∗	NOUN
ejpam-3223	108	47	(	(	PUNCT
ejpam-3223	108	48	�	�	PROPN
ejpam-3223	108	49	c	c	NOUN
ejpam-3223	108	50	+	+	NOUN
ejpam-3223	108	51	m2	m2	X
ejpam-3223	108	52	)	)	PUNCT
ejpam-3223	108	53	k	k	PROPN
ejpam-3223	108	54	δ	δ	PROPN
ejpam-3223	108	55	=	=	PRON
ejpam-3223	108	56	(	(	PUNCT
ejpam-3223	108	57	�	�	PROPN
ejpam-3223	108	58	c	c	NOUN
ejpam-3223	108	59	+	+	NOUN
ejpam-3223	108	60	m2	m2	X
ejpam-3223	108	61	)	)	PUNCT
ejpam-3223	108	62	k	k	PROPN
ejpam-3223	108	63	w2k	w2k	PROPN
ejpam-3223	108	64	,	,	PUNCT
ejpam-3223	108	65	c(u	c(u	PROPN
ejpam-3223	108	66	,	,	PUNCT
ejpam-3223	108	67	m	m	NOUN
ejpam-3223	108	68	)	)	PUNCT
ejpam-3223	108	69	∗	∗	NOUN
ejpam-3223	108	70	δ	δ	PROPN
ejpam-3223	108	71	=	=	SYM
ejpam-3223	108	72	δ	δ	PROPN
ejpam-3223	108	73	.	.	PUNCT
ejpam-3223	109	1	(	(	PUNCT
ejpam-3223	109	2	19	19	NUM
ejpam-3223	109	3	)	)	PUNCT
ejpam-3223	109	4	since	since	SCONJ
ejpam-3223	109	5	w2k	w2k	PROPN
ejpam-3223	109	6	,	,	PUNCT
ejpam-3223	109	7	c(u	c(u	PROPN
ejpam-3223	109	8	,	,	PUNCT
ejpam-3223	109	9	m	m	PRON
ejpam-3223	109	10	)	)	PUNCT
ejpam-3223	109	11	is	be	AUX
ejpam-3223	109	12	lie	lie	NOUN
ejpam-3223	109	13	in	in	ADP
ejpam-3223	109	14	s′	s′	NOUN
ejpam-3223	109	15	,	,	PUNCT
ejpam-3223	109	16	where	where	SCONJ
ejpam-3223	109	17	s′	s′	ADJ
ejpam-3223	109	18	is	be	AUX
ejpam-3223	109	19	a	a	DET
ejpam-3223	109	20	space	space	NOUN
ejpam-3223	109	21	of	of	ADP
ejpam-3223	109	22	tempered	temper	VERB
ejpam-3223	109	23	distribution	distribution	NOUN
ejpam-3223	109	24	,	,	PUNCT
ejpam-3223	109	25	choose	choose	VERB
ejpam-3223	109	26	s′	s′	ADJ
ejpam-3223	109	27	⊂	⊂	PROPN
ejpam-3223	109	28	d′r	d′r	NOUN
ejpam-3223	109	29	,	,	PUNCT
ejpam-3223	109	30	where	where	SCONJ
ejpam-3223	109	31	d′r	d′r	NOUN
ejpam-3223	109	32	is	be	AUX
ejpam-3223	109	33	the	the	DET
ejpam-3223	109	34	right	right	ADJ
ejpam-3223	109	35	-	-	PUNCT
ejpam-3223	109	36	side	side	NOUN
ejpam-3223	109	37	distribution	distribution	NOUN
ejpam-3223	109	38	which	which	PRON
ejpam-3223	109	39	is	be	AUX
ejpam-3223	109	40	a	a	DET
ejpam-3223	109	41	subspace	subspace	NOUN
ejpam-3223	109	42	of	of	ADP
ejpam-3223	109	43	d′	d′	PRON
ejpam-3223	109	44	of	of	ADP
ejpam-3223	109	45	distribution	distribution	NOUN
ejpam-3223	109	46	.	.	PUNCT
ejpam-3223	110	1	thus	thus	ADV
ejpam-3223	110	2	w2k	w2k	PROPN
ejpam-3223	110	3	,	,	PUNCT
ejpam-3223	110	4	c(u	c(u	PROPN
ejpam-3223	110	5	,	,	PUNCT
ejpam-3223	110	6	m	m	NOUN
ejpam-3223	110	7	)	)	PUNCT
ejpam-3223	110	8	∈	∈	PROPN
ejpam-3223	110	9	d′r	d′r	NOUN
ejpam-3223	110	10	,	,	PUNCT
ejpam-3223	110	11	it	it	PRON
ejpam-3223	110	12	follow	follow	VERB
ejpam-3223	110	13	that	that	SCONJ
ejpam-3223	110	14	w2k	w2k	PROPN
ejpam-3223	110	15	,	,	PUNCT
ejpam-3223	110	16	c(u	c(u	PROPN
ejpam-3223	110	17	,	,	PUNCT
ejpam-3223	110	18	m	m	PRON
ejpam-3223	110	19	)	)	PUNCT
ejpam-3223	110	20	is	be	AUX
ejpam-3223	110	21	an	an	DET
ejpam-3223	110	22	element	element	NOUN
ejpam-3223	110	23	of	of	ADP
ejpam-3223	110	24	convolution	convolution	NOUN
ejpam-3223	110	25	algebra	algebra	NOUN
ejpam-3223	110	26	,	,	PUNCT
ejpam-3223	110	27	thus	thus	ADV
ejpam-3223	110	28	by	by	ADP
ejpam-3223	110	29	(	(	PUNCT
ejpam-3223	110	30	[	[	X
ejpam-3223	110	31	1	1	NUM
ejpam-3223	110	32	]	]	PUNCT
ejpam-3223	110	33	,	,	PUNCT
ejpam-3223	110	34	p.150	p.150	PROPN
ejpam-3223	110	35	-	-	SYM
ejpam-3223	110	36	151	151	NUM
ejpam-3223	110	37	)	)	PUNCT
ejpam-3223	110	38	,	,	PUNCT
ejpam-3223	110	39	we	we	PRON
ejpam-3223	110	40	have	have	VERB
ejpam-3223	110	41	that	that	SCONJ
ejpam-3223	110	42	the	the	DET
ejpam-3223	110	43	equation	equation	NOUN
ejpam-3223	110	44	(	(	PUNCT
ejpam-3223	110	45	19	19	NUM
ejpam-3223	110	46	)	)	PUNCT
ejpam-3223	110	47	has	have	VERB
ejpam-3223	110	48	a	a	DET
ejpam-3223	110	49	unique	unique	ADJ
ejpam-3223	110	50	solution	solution	NOUN
ejpam-3223	110	51	v	v	NOUN
ejpam-3223	110	52	(	(	PUNCT
ejpam-3223	110	53	x	x	NOUN
ejpam-3223	110	54	)	)	PUNCT
ejpam-3223	110	55	=	=	SYM
ejpam-3223	110	56	w−2k	w−2k	NOUN
ejpam-3223	110	57	,	,	PUNCT
ejpam-3223	110	58	c(u	c(u	PROPN
ejpam-3223	110	59	,	,	PUNCT
ejpam-3223	110	60	m	m	NOUN
ejpam-3223	110	61	)	)	PUNCT
ejpam-3223	110	62	∗	∗	NOUN
ejpam-3223	110	63	δ	δ	NOUN
ejpam-3223	110	64	=	=	SYM
ejpam-3223	110	65	w−2k	w−2k	NOUN
ejpam-3223	110	66	,	,	PUNCT
ejpam-3223	110	67	c(u	c(u	PROPN
ejpam-3223	110	68	,	,	PUNCT
ejpam-3223	110	69	m	m	NOUN
ejpam-3223	110	70	)	)	PUNCT
ejpam-3223	110	71	.	.	PUNCT
ejpam-3223	111	1	(	(	PUNCT
ejpam-3223	111	2	20	20	NUM
ejpam-3223	111	3	)	)	PUNCT
ejpam-3223	111	4	that	that	PRON
ejpam-3223	111	5	complete	complete	VERB
ejpam-3223	111	6	the	the	DET
ejpam-3223	111	7	proof	proof	NOUN
ejpam-3223	111	8	.	.	PUNCT
ejpam-3223	112	1	lemma	lemma	PROPN
ejpam-3223	112	2	5	5	NUM
ejpam-3223	112	3	.	.	PUNCT
ejpam-3223	113	1	given	give	VERB
ejpam-3223	113	2	the	the	DET
ejpam-3223	113	3	equation	equation	NOUN
ejpam-3223	113	4	(	(	PUNCT
ejpam-3223	113	5	4c	4c	NOUN
ejpam-3223	113	6	+	+	NOUN
ejpam-3223	113	7	m2	m2	PROPN
ejpam-3223	113	8	)	)	PUNCT
ejpam-3223	113	9	k	k	PROPN
ejpam-3223	113	10	u(x	u(x	PROPN
ejpam-3223	113	11	)	)	PUNCT
ejpam-3223	113	12	=	=	SYM
ejpam-3223	113	13	δ	δ	PROPN
ejpam-3223	113	14	for	for	ADP
ejpam-3223	113	15	x	x	PROPN
ejpam-3223	113	16	∈	∈	PROPN
ejpam-3223	113	17	rn	rn	PROPN
ejpam-3223	113	18	,	,	PUNCT
ejpam-3223	113	19	where	where	SCONJ
ejpam-3223	113	20	(	(	PUNCT
ejpam-3223	113	21	4c	4c	NOUN
ejpam-3223	113	22	+	+	NOUN
ejpam-3223	113	23	m2	m2	PROPN
ejpam-3223	113	24	)	)	PUNCT
ejpam-3223	113	25	k	k	PROPN
ejpam-3223	113	26	is	be	AUX
ejpam-3223	113	27	the	the	DET
ejpam-3223	113	28	operator	operator	NOUN
ejpam-3223	113	29	related	relate	VERB
ejpam-3223	113	30	to	to	ADP
ejpam-3223	113	31	the	the	DET
ejpam-3223	113	32	helmholtz	helmholtz	NOUN
ejpam-3223	113	33	operator	operator	NOUN
ejpam-3223	113	34	iterated	iterate	VERB
ejpam-3223	113	35	k	k	NOUN
ejpam-3223	113	36	-	-	PUNCT
ejpam-3223	113	37	times	time	NOUN
ejpam-3223	113	38	defined	define	VERB
ejpam-3223	113	39	by	by	ADP
ejpam-3223	113	40	equation	equation	NOUN
ejpam-3223	113	41	(	(	PUNCT
ejpam-3223	113	42	6	6	NUM
ejpam-3223	113	43	)	)	PUNCT
ejpam-3223	113	44	,	,	PUNCT
ejpam-3223	113	45	δ	δ	PROPN
ejpam-3223	113	46	is	be	AUX
ejpam-3223	113	47	the	the	DET
ejpam-3223	113	48	dirac	dirac	NOUN
ejpam-3223	113	49	-	-	PUNCT
ejpam-3223	113	50	delta	delta	NOUN
ejpam-3223	113	51	distribution	distribution	NOUN
ejpam-3223	113	52	,	,	PUNCT
ejpam-3223	113	53	k	k	PROPN
ejpam-3223	113	54	is	be	AUX
ejpam-3223	113	55	a	a	DET
ejpam-3223	113	56	nonnegative	nonnegative	ADJ
ejpam-3223	113	57	integer	integer	NOUN
ejpam-3223	113	58	,	,	PUNCT
ejpam-3223	113	59	then	then	ADV
ejpam-3223	113	60	u(x	u(x	VERB
ejpam-3223	113	61	)	)	PUNCT
ejpam-3223	113	62	=	=	SYM
ejpam-3223	113	63	y2k	y2k	PROPN
ejpam-3223	113	64	,	,	PUNCT
ejpam-3223	113	65	c(v	c(v	PROPN
ejpam-3223	113	66	,	,	PUNCT
ejpam-3223	113	67	m	m	NOUN
ejpam-3223	113	68	)	)	PUNCT
ejpam-3223	113	69	is	be	AUX
ejpam-3223	113	70	an	an	DET
ejpam-3223	113	71	elementary	elementary	ADJ
ejpam-3223	113	72	solution	solution	NOUN
ejpam-3223	113	73	of	of	ADP
ejpam-3223	113	74	the	the	DET
ejpam-3223	113	75	operator	operator	NOUN
ejpam-3223	113	76	(	(	PUNCT
ejpam-3223	113	77	4c	4c	NOUN
ejpam-3223	113	78	+	+	NOUN
ejpam-3223	113	79	m2	m2	PROPN
ejpam-3223	113	80	)	)	PUNCT
ejpam-3223	113	81	k	k	PROPN
ejpam-3223	113	82	,	,	PUNCT
ejpam-3223	113	83	where	where	SCONJ
ejpam-3223	113	84	y2k	y2k	NOUN
ejpam-3223	113	85	,	,	PUNCT
ejpam-3223	113	86	c(v	c(v	PROPN
ejpam-3223	113	87	,	,	PUNCT
ejpam-3223	113	88	m	m	NOUN
ejpam-3223	113	89	)	)	PUNCT
ejpam-3223	113	90	=	=	PUNCT
ejpam-3223	114	1	∞∑	∞∑	NUM
ejpam-3223	114	2	r=0	r=0	PROPN
ejpam-3223	114	3	(	(	PUNCT
ejpam-3223	114	4	−k	−k	NOUN
ejpam-3223	114	5	r	r	NOUN
ejpam-3223	114	6	)	)	PUNCT
ejpam-3223	114	7	m2r(−1)k+rre2k+2r	m2r(−1)k+rre2k+2r	NOUN
ejpam-3223	114	8	,	,	PUNCT
ejpam-3223	114	9	c(v	c(v	PROPN
ejpam-3223	114	10	)	)	PUNCT
ejpam-3223	114	11	,	,	PUNCT
ejpam-3223	114	12	(	(	PUNCT
ejpam-3223	114	13	21	21	NUM
ejpam-3223	114	14	)	)	PUNCT
ejpam-3223	114	15	re2k	re2k	NOUN
ejpam-3223	114	16	,	,	PUNCT
ejpam-3223	114	17	c(v	c(v	PROPN
ejpam-3223	114	18	)	)	PUNCT
ejpam-3223	114	19	is	be	AUX
ejpam-3223	114	20	defined	define	VERB
ejpam-3223	114	21	by	by	ADP
ejpam-3223	114	22	(	(	PUNCT
ejpam-3223	114	23	17	17	NUM
ejpam-3223	114	24	)	)	PUNCT
ejpam-3223	114	25	.	.	PUNCT
ejpam-3223	115	1	proof	proof	NOUN
ejpam-3223	115	2	.	.	PUNCT
ejpam-3223	116	1	see	see	VERB
ejpam-3223	116	2	[	[	X
ejpam-3223	116	3	6	6	NUM
ejpam-3223	116	4	]	]	PUNCT
ejpam-3223	116	5	.	.	PUNCT
ejpam-3223	117	1	lemma	lemma	PROPN
ejpam-3223	117	2	6	6	NUM
ejpam-3223	117	3	.	.	PUNCT
ejpam-3223	118	1	let	let	VERB
ejpam-3223	118	2	4c	4c	NOUN
ejpam-3223	118	3	be	be	AUX
ejpam-3223	118	4	the	the	DET
ejpam-3223	118	5	operator	operator	NOUN
ejpam-3223	118	6	related	relate	VERB
ejpam-3223	118	7	to	to	ADP
ejpam-3223	118	8	the	the	DET
ejpam-3223	118	9	laplace	laplace	NOUN
ejpam-3223	118	10	operator	operator	NOUN
ejpam-3223	118	11	,	,	PUNCT
ejpam-3223	118	12	defined	define	VERB
ejpam-3223	118	13	by	by	ADP
ejpam-3223	118	14	(	(	PUNCT
ejpam-3223	118	15	3	3	NUM
ejpam-3223	118	16	)	)	PUNCT
ejpam-3223	118	17	and	and	CCONJ
ejpam-3223	118	18	δ	δ	PROPN
ejpam-3223	118	19	is	be	AUX
ejpam-3223	118	20	the	the	DET
ejpam-3223	118	21	dirac	dirac	NOUN
ejpam-3223	118	22	delta	delta	NOUN
ejpam-3223	118	23	distribution	distribution	NOUN
ejpam-3223	118	24	for	for	ADP
ejpam-3223	118	25	x	x	PROPN
ejpam-3223	118	26	∈	∈	PROPN
ejpam-3223	118	27	rn	rn	PROPN
ejpam-3223	118	28	,	,	PUNCT
ejpam-3223	118	29	then	then	ADV
ejpam-3223	118	30	(	(	PUNCT
ejpam-3223	118	31	4c	4c	NUM
ejpam-3223	118	32	+	+	NOUN
ejpam-3223	118	33	m2	m2	PROPN
ejpam-3223	118	34	)	)	PUNCT
ejpam-3223	119	1	k	k	PROPN
ejpam-3223	119	2	δ	δ	PROPN
ejpam-3223	119	3	=	=	PUNCT
ejpam-3223	119	4	y−2k	y−2k	NOUN
ejpam-3223	119	5	,	,	PUNCT
ejpam-3223	119	6	c(v	c(v	PROPN
ejpam-3223	119	7	,	,	PUNCT
ejpam-3223	119	8	m	m	NOUN
ejpam-3223	119	9	)	)	PUNCT
ejpam-3223	119	10	,	,	PUNCT
ejpam-3223	119	11	where	where	SCONJ
ejpam-3223	119	12	y−2k	y−2k	NOUN
ejpam-3223	119	13	,	,	PUNCT
ejpam-3223	119	14	c(v	c(v	PROPN
ejpam-3223	119	15	,	,	PUNCT
ejpam-3223	119	16	m	m	NOUN
ejpam-3223	119	17	)	)	PUNCT
ejpam-3223	119	18	is	be	AUX
ejpam-3223	119	19	the	the	DET
ejpam-3223	119	20	inverse	inverse	NOUN
ejpam-3223	119	21	of	of	ADP
ejpam-3223	119	22	y2k	y2k	PROPN
ejpam-3223	119	23	,	,	PUNCT
ejpam-3223	119	24	c(v	c(v	PROPN
ejpam-3223	119	25	,	,	PUNCT
ejpam-3223	119	26	m	m	NOUN
ejpam-3223	119	27	)	)	PUNCT
ejpam-3223	119	28	in	in	ADP
ejpam-3223	119	29	the	the	DET
ejpam-3223	119	30	convolution	convolution	NOUN
ejpam-3223	119	31	algebra	algebra	NOUN
ejpam-3223	119	32	.	.	PUNCT
ejpam-3223	120	1	proof	proof	NOUN
ejpam-3223	120	2	.	.	PUNCT
ejpam-3223	121	1	the	the	DET
ejpam-3223	121	2	proof	proof	NOUN
ejpam-3223	121	3	of	of	ADP
ejpam-3223	121	4	this	this	DET
ejpam-3223	121	5	lemma	lemma	PROPN
ejpam-3223	121	6	similar	similar	ADJ
ejpam-3223	121	7	lemma	lemma	PROPN
ejpam-3223	121	8	4	4	NUM
ejpam-3223	121	9	.	.	PUNCT
ejpam-3223	122	1	s.	s.	PROPN
ejpam-3223	122	2	bupasiri	bupasiri	PROPN
ejpam-3223	122	3	/	/	SYM
ejpam-3223	122	4	eur	eur	PROPN
ejpam-3223	122	5	.	.	PUNCT
ejpam-3223	123	1	j.	j.	PROPN
ejpam-3223	123	2	pure	pure	PROPN
ejpam-3223	123	3	appl	appl	PROPN
ejpam-3223	123	4	.	.	PROPN
ejpam-3223	123	5	math	math	PROPN
ejpam-3223	123	6	,	,	PUNCT
ejpam-3223	123	7	11	11	NUM
ejpam-3223	123	8	(	(	PUNCT
ejpam-3223	123	9	2	2	NUM
ejpam-3223	123	10	)	)	PUNCT
ejpam-3223	123	11	(	(	PUNCT
ejpam-3223	123	12	2018	2018	NUM
ejpam-3223	123	13	)	)	PUNCT
ejpam-3223	123	14	,	,	PUNCT
ejpam-3223	123	15	390	390	NUM
ejpam-3223	123	16	-	-	SYM
ejpam-3223	123	17	399	399	NUM
ejpam-3223	123	18	395	395	NUM
ejpam-3223	123	19	lemma	lemma	PROPN
ejpam-3223	123	20	7	7	NUM
ejpam-3223	123	21	.	.	PUNCT
ejpam-3223	124	1	the	the	DET
ejpam-3223	124	2	convolution	convolution	NOUN
ejpam-3223	124	3	w2k	w2k	PROPN
ejpam-3223	124	4	,	,	PUNCT
ejpam-3223	124	5	c(u	c(u	PROPN
ejpam-3223	124	6	,	,	PUNCT
ejpam-3223	124	7	m)∗y2k	m)∗y2k	PROPN
ejpam-3223	124	8	,	,	PUNCT
ejpam-3223	124	9	c(v	c(v	PROPN
ejpam-3223	124	10	,	,	PUNCT
ejpam-3223	124	11	m	m	NOUN
ejpam-3223	124	12	)	)	PUNCT
ejpam-3223	124	13	exists	exist	VERB
ejpam-3223	124	14	and	and	CCONJ
ejpam-3223	124	15	is	be	AUX
ejpam-3223	124	16	a	a	DET
ejpam-3223	124	17	tempered	temper	VERB
ejpam-3223	124	18	distribution	distribution	NOUN
ejpam-3223	124	19	where	where	SCONJ
ejpam-3223	124	20	w2k	w2k	PROPN
ejpam-3223	124	21	,	,	PUNCT
ejpam-3223	124	22	c(u	c(u	PROPN
ejpam-3223	124	23	,	,	PUNCT
ejpam-3223	124	24	m	m	NOUN
ejpam-3223	124	25	)	)	PUNCT
ejpam-3223	124	26	and	and	CCONJ
ejpam-3223	124	27	y2k	y2k	PROPN
ejpam-3223	124	28	,	,	PUNCT
ejpam-3223	124	29	c(v	c(v	PROPN
ejpam-3223	124	30	,	,	PUNCT
ejpam-3223	124	31	m	m	VERB
ejpam-3223	124	32	)	)	PUNCT
ejpam-3223	124	33	be	be	AUX
ejpam-3223	124	34	defined	define	VERB
ejpam-3223	124	35	by	by	ADP
ejpam-3223	124	36	(	(	PUNCT
ejpam-3223	124	37	18	18	NUM
ejpam-3223	124	38	)	)	PUNCT
ejpam-3223	124	39	and	and	CCONJ
ejpam-3223	124	40	(	(	PUNCT
ejpam-3223	124	41	21	21	NUM
ejpam-3223	124	42	)	)	PUNCT
ejpam-3223	124	43	,	,	PUNCT
ejpam-3223	124	44	respectively	respectively	ADV
ejpam-3223	124	45	.	.	PUNCT
ejpam-3223	125	1	proof	proof	NOUN
ejpam-3223	125	2	.	.	PUNCT
ejpam-3223	126	1	from	from	ADP
ejpam-3223	126	2	(	(	PUNCT
ejpam-3223	126	3	18	18	NUM
ejpam-3223	126	4	)	)	PUNCT
ejpam-3223	126	5	and	and	CCONJ
ejpam-3223	126	6	(	(	PUNCT
ejpam-3223	126	7	21	21	NUM
ejpam-3223	126	8	)	)	PUNCT
ejpam-3223	126	9	,	,	PUNCT
ejpam-3223	126	10	we	we	PRON
ejpam-3223	126	11	have	have	VERB
ejpam-3223	126	12	w2k	w2k	PROPN
ejpam-3223	126	13	,	,	PUNCT
ejpam-3223	126	14	c(u	c(u	PROPN
ejpam-3223	126	15	,	,	PUNCT
ejpam-3223	126	16	m	m	NOUN
ejpam-3223	126	17	)	)	PUNCT
ejpam-3223	126	18	∗	∗	NOUN
ejpam-3223	126	19	y2k	y2k	PROPN
ejpam-3223	126	20	,	,	PUNCT
ejpam-3223	126	21	c(v	c(v	PROPN
ejpam-3223	126	22	,	,	PUNCT
ejpam-3223	126	23	m	m	NOUN
ejpam-3223	126	24	)	)	PUNCT
ejpam-3223	126	25	=	=	SYM
ejpam-3223	127	1	(	(	PUNCT
ejpam-3223	127	2	∞∑	∞∑	NUM
ejpam-3223	127	3	r=0	r=0	PROPN
ejpam-3223	127	4	(	(	PUNCT
ejpam-3223	127	5	−k	−k	NOUN
ejpam-3223	127	6	r	r	NOUN
ejpam-3223	127	7	)	)	PUNCT
ejpam-3223	127	8	m2rrh2k+2r	m2rrh2k+2r	ADV
ejpam-3223	127	9	,	,	PUNCT
ejpam-3223	127	10	c(u	c(u	PROPN
ejpam-3223	127	11	)	)	PUNCT
ejpam-3223	127	12	)	)	PUNCT
ejpam-3223	128	1	∗	∗	NOUN
ejpam-3223	128	2	(	(	PUNCT
ejpam-3223	128	3	∞∑	∞∑	PROPN
ejpam-3223	128	4	r=0	r=0	PROPN
ejpam-3223	128	5	(	(	PUNCT
ejpam-3223	128	6	−k	−k	NOUN
ejpam-3223	128	7	r	r	NOUN
ejpam-3223	128	8	)	)	PUNCT
ejpam-3223	128	9	m2r(−1)k+rre2k+2r	m2r(−1)k+rre2k+2r	NOUN
ejpam-3223	128	10	,	,	PUNCT
ejpam-3223	128	11	c(v	c(v	PROPN
ejpam-3223	128	12	)	)	PUNCT
ejpam-3223	128	13	)	)	PUNCT
ejpam-3223	129	1	=	=	PUNCT
ejpam-3223	130	1	∞∑	∞∑	NUM
ejpam-3223	130	2	r=0	r=0	NUM
ejpam-3223	130	3	∞∑	∞∑	NUM
ejpam-3223	130	4	s=0	s=0	NOUN
ejpam-3223	130	5	(	(	PUNCT
ejpam-3223	130	6	−k	−k	NOUN
ejpam-3223	130	7	r	r	NOUN
ejpam-3223	130	8	)	)	PUNCT
ejpam-3223	130	9	(	(	PUNCT
ejpam-3223	130	10	−k	−k	PROPN
ejpam-3223	130	11	s	s	PART
ejpam-3223	130	12	)	)	PUNCT
ejpam-3223	130	13	m2r+2s(−1)k+rre2k+2r	m2r+2s(−1)k+rre2k+2r	PROPN
ejpam-3223	130	14	,	,	PUNCT
ejpam-3223	130	15	c(v	c(v	PROPN
ejpam-3223	130	16	)	)	PUNCT
ejpam-3223	130	17	∗rh2k+2s	∗rh2k+2	NOUN
ejpam-3223	130	18	,	,	PUNCT
ejpam-3223	130	19	c(u	c(u	PROPN
ejpam-3223	130	20	)	)	PUNCT
ejpam-3223	130	21	.	.	PUNCT
ejpam-3223	131	1	since	since	SCONJ
ejpam-3223	131	2	the	the	DET
ejpam-3223	131	3	function	function	NOUN
ejpam-3223	131	4	re2k+2r	re2k+2r	NOUN
ejpam-3223	131	5	,	,	PUNCT
ejpam-3223	131	6	c(v	c(v	PROPN
ejpam-3223	131	7	)	)	PUNCT
ejpam-3223	131	8	and	and	CCONJ
ejpam-3223	131	9	rh2k+2s	rh2k+2	NOUN
ejpam-3223	131	10	,	,	PUNCT
ejpam-3223	131	11	c(u	c(u	PROPN
ejpam-3223	131	12	)	)	PUNCT
ejpam-3223	131	13	are	be	AUX
ejpam-3223	131	14	tempered	temper	VERB
ejpam-3223	131	15	distributions	distribution	NOUN
ejpam-3223	131	16	,	,	PUNCT
ejpam-3223	131	17	see([3	see([3	ADP
ejpam-3223	131	18	]	]	X
ejpam-3223	131	19	,	,	PUNCT
ejpam-3223	131	20	p.34	p.34	PROPN
ejpam-3223	131	21	,	,	PUNCT
ejpam-3223	131	22	[	[	X
ejpam-3223	131	23	5	5	NUM
ejpam-3223	131	24	]	]	PUNCT
ejpam-3223	131	25	,	,	PUNCT
ejpam-3223	131	26	p.302	p.302	NOUN
ejpam-3223	131	27	and	and	CCONJ
ejpam-3223	131	28	[	[	X
ejpam-3223	131	29	4	4	NUM
ejpam-3223	131	30	]	]	PUNCT
ejpam-3223	131	31	,	,	PUNCT
ejpam-3223	131	32	p.97	p.97	NOUN
ejpam-3223	131	33	)	)	PUNCT
ejpam-3223	131	34	and	and	CCONJ
ejpam-3223	131	35	the	the	DET
ejpam-3223	131	36	convolution	convolution	NOUN
ejpam-3223	131	37	of	of	ADP
ejpam-3223	131	38	functions	function	NOUN
ejpam-3223	131	39	(	(	PUNCT
ejpam-3223	131	40	−1)k+rrh2k+2r	−1)k+rrh2k+2r	NUM
ejpam-3223	131	41	,	,	PUNCT
ejpam-3223	131	42	c(u	c(u	PROPN
ejpam-3223	131	43	)	)	PUNCT
ejpam-3223	131	44	∗re2k+2s	∗re2k+2	NOUN
ejpam-3223	131	45	,	,	PUNCT
ejpam-3223	131	46	c(v	c(v	PROPN
ejpam-3223	131	47	)	)	PUNCT
ejpam-3223	131	48	exists	exist	VERB
ejpam-3223	131	49	and	and	CCONJ
ejpam-3223	131	50	is	be	AUX
ejpam-3223	131	51	also	also	ADV
ejpam-3223	131	52	a	a	DET
ejpam-3223	131	53	tempered	temper	VERB
ejpam-3223	131	54	distribution	distribution	NOUN
ejpam-3223	131	55	,	,	PUNCT
ejpam-3223	131	56	see	see	VERB
ejpam-3223	131	57	(	(	PUNCT
ejpam-3223	131	58	[	[	X
ejpam-3223	131	59	11	11	NUM
ejpam-3223	131	60	]	]	PUNCT
ejpam-3223	131	61	,	,	PUNCT
ejpam-3223	131	62	p.152	p.152	NUM
ejpam-3223	131	63	)	)	PUNCT
ejpam-3223	131	64	.	.	PUNCT
ejpam-3223	132	1	thus	thus	ADV
ejpam-3223	132	2	,	,	PUNCT
ejpam-3223	132	3	w2k	w2k	PROPN
ejpam-3223	132	4	,	,	PUNCT
ejpam-3223	132	5	c(u	c(u	PROPN
ejpam-3223	132	6	,	,	PUNCT
ejpam-3223	132	7	m)∗y2k	m)∗y2k	PROPN
ejpam-3223	132	8	,	,	PUNCT
ejpam-3223	132	9	c(v	c(v	PROPN
ejpam-3223	132	10	,	,	PUNCT
ejpam-3223	132	11	m	m	NOUN
ejpam-3223	132	12	)	)	PUNCT
ejpam-3223	132	13	exists	exist	VERB
ejpam-3223	132	14	and	and	CCONJ
ejpam-3223	132	15	also	also	ADV
ejpam-3223	132	16	is	be	AUX
ejpam-3223	132	17	a	a	DET
ejpam-3223	132	18	tempered	temper	VERB
ejpam-3223	132	19	distribution	distribution	NOUN
ejpam-3223	132	20	.	.	PUNCT
ejpam-3223	133	1	3	3	X
ejpam-3223	133	2	.	.	X
ejpam-3223	133	3	main	main	ADJ
ejpam-3223	133	4	results	result	NOUN
ejpam-3223	133	5	theorem	theorem	VERB
ejpam-3223	133	6	1	1	NUM
ejpam-3223	133	7	.	.	PUNCT
ejpam-3223	134	1	given	give	VERB
ejpam-3223	134	2	the	the	DET
ejpam-3223	134	3	equation	equation	NOUN
ejpam-3223	134	4	}	}	PUNCT
ejpam-3223	134	5	kcg(x	kcg(x	PROPN
ejpam-3223	134	6	)	)	PUNCT
ejpam-3223	134	7	=	=	SYM
ejpam-3223	134	8	δ	δ	PROPN
ejpam-3223	134	9	(	(	PUNCT
ejpam-3223	134	10	22	22	NUM
ejpam-3223	134	11	)	)	PUNCT
ejpam-3223	134	12	for	for	ADP
ejpam-3223	134	13	x	x	PROPN
ejpam-3223	134	14	∈	∈	PROPN
ejpam-3223	134	15	rn	rn	PROPN
ejpam-3223	134	16	,	,	PUNCT
ejpam-3223	134	17	where	where	SCONJ
ejpam-3223	134	18	}	}	PUNCT
ejpam-3223	134	19	kc	kc	PROPN
ejpam-3223	134	20	is	be	AUX
ejpam-3223	134	21	the	the	DET
ejpam-3223	134	22	operator	operator	NOUN
ejpam-3223	134	23	related	relate	VERB
ejpam-3223	134	24	to	to	ADP
ejpam-3223	134	25	the	the	DET
ejpam-3223	134	26	helmhotz	helmhotz	NOUN
ejpam-3223	134	27	operator	operator	NOUN
ejpam-3223	134	28	and	and	CCONJ
ejpam-3223	134	29	klein	klein	PROPN
ejpam-3223	134	30	-	-	PUNCT
ejpam-3223	134	31	gordon	gordon	PROPN
ejpam-3223	134	32	operator	operator	NOUN
ejpam-3223	134	33	iterated	iterate	VERB
ejpam-3223	134	34	k	k	NOUN
ejpam-3223	134	35	-	-	PUNCT
ejpam-3223	134	36	times	time	NOUN
ejpam-3223	134	37	defined	define	VERB
ejpam-3223	134	38	by	by	ADP
ejpam-3223	134	39	(	(	PUNCT
ejpam-3223	134	40	4	4	NUM
ejpam-3223	134	41	)	)	PUNCT
ejpam-3223	134	42	,	,	PUNCT
ejpam-3223	134	43	then	then	ADV
ejpam-3223	134	44	g(x	g(x	NOUN
ejpam-3223	134	45	)	)	PUNCT
ejpam-3223	134	46	=	=	SYM
ejpam-3223	134	47	w2k	w2k	PROPN
ejpam-3223	134	48	,	,	PUNCT
ejpam-3223	134	49	c(u	c(u	PROPN
ejpam-3223	134	50	,	,	PUNCT
ejpam-3223	134	51	m	m	NOUN
ejpam-3223	134	52	)	)	PUNCT
ejpam-3223	134	53	∗	∗	NOUN
ejpam-3223	134	54	y2k	y2k	PROPN
ejpam-3223	134	55	,	,	PUNCT
ejpam-3223	134	56	c(v	c(v	PROPN
ejpam-3223	134	57	,	,	PUNCT
ejpam-3223	134	58	m	m	NOUN
ejpam-3223	134	59	)	)	PUNCT
ejpam-3223	134	60	(	(	PUNCT
ejpam-3223	134	61	23	23	NUM
ejpam-3223	134	62	)	)	PUNCT
ejpam-3223	134	63	is	be	AUX
ejpam-3223	134	64	an	an	DET
ejpam-3223	134	65	elementary	elementary	ADJ
ejpam-3223	134	66	solution	solution	NOUN
ejpam-3223	134	67	of	of	ADP
ejpam-3223	134	68	(	(	PUNCT
ejpam-3223	134	69	22	22	NUM
ejpam-3223	134	70	)	)	PUNCT
ejpam-3223	134	71	,	,	PUNCT
ejpam-3223	134	72	where	where	SCONJ
ejpam-3223	134	73	w2k	w2k	PROPN
ejpam-3223	134	74	,	,	PUNCT
ejpam-3223	134	75	c(u	c(u	PROPN
ejpam-3223	134	76	,	,	PUNCT
ejpam-3223	134	77	m	m	NOUN
ejpam-3223	134	78	)	)	PUNCT
ejpam-3223	134	79	and	and	CCONJ
ejpam-3223	134	80	y2k	y2k	PROPN
ejpam-3223	134	81	,	,	PUNCT
ejpam-3223	134	82	c(v	c(v	PROPN
ejpam-3223	134	83	,	,	PUNCT
ejpam-3223	134	84	m	m	NOUN
ejpam-3223	134	85	)	)	PUNCT
ejpam-3223	134	86	are	be	AUX
ejpam-3223	134	87	defined	define	VERB
ejpam-3223	134	88	by	by	ADP
ejpam-3223	134	89	(	(	PUNCT
ejpam-3223	134	90	18	18	NUM
ejpam-3223	134	91	)	)	PUNCT
ejpam-3223	134	92	and	and	CCONJ
ejpam-3223	134	93	(	(	PUNCT
ejpam-3223	134	94	21	21	NUM
ejpam-3223	134	95	)	)	PUNCT
ejpam-3223	134	96	,	,	PUNCT
ejpam-3223	134	97	respectively	respectively	ADV
ejpam-3223	134	98	,	,	PUNCT
ejpam-3223	134	99	k	k	PROPN
ejpam-3223	134	100	is	be	AUX
ejpam-3223	134	101	a	a	DET
ejpam-3223	134	102	nonnegative	nonnegative	ADJ
ejpam-3223	134	103	integer	integer	NOUN
ejpam-3223	134	104	and	and	CCONJ
ejpam-3223	134	105	m	m	NOUN
ejpam-3223	134	106	is	be	AUX
ejpam-3223	134	107	a	a	DET
ejpam-3223	134	108	nonnegative	nonnegative	ADJ
ejpam-3223	134	109	real	real	ADJ
ejpam-3223	134	110	number	number	NOUN
ejpam-3223	134	111	.	.	PUNCT
ejpam-3223	135	1	moreover	moreover	ADV
ejpam-3223	135	2	,	,	PUNCT
ejpam-3223	135	3	from	from	ADP
ejpam-3223	135	4	(	(	PUNCT
ejpam-3223	135	5	23	23	NUM
ejpam-3223	135	6	)	)	PUNCT
ejpam-3223	135	7	we	we	PRON
ejpam-3223	135	8	obtain	obtain	VERB
ejpam-3223	135	9	w−2k	w−2k	NOUN
ejpam-3223	135	10	,	,	PUNCT
ejpam-3223	135	11	c(u	c(u	PROPN
ejpam-3223	135	12	,	,	PUNCT
ejpam-3223	135	13	m	m	NOUN
ejpam-3223	135	14	)	)	PUNCT
ejpam-3223	135	15	∗g(x	∗g(x	NUM
ejpam-3223	135	16	)	)	PUNCT
ejpam-3223	135	17	=	=	SYM
ejpam-3223	135	18	y2k	y2k	PROPN
ejpam-3223	135	19	,	,	PUNCT
ejpam-3223	135	20	c(v	c(v	PROPN
ejpam-3223	135	21	,	,	PUNCT
ejpam-3223	135	22	m	m	NOUN
ejpam-3223	135	23	)	)	PUNCT
ejpam-3223	135	24	(	(	PUNCT
ejpam-3223	135	25	24	24	NUM
ejpam-3223	135	26	)	)	PUNCT
ejpam-3223	135	27	as	as	ADP
ejpam-3223	135	28	the	the	DET
ejpam-3223	135	29	elementary	elementary	ADJ
ejpam-3223	135	30	solution	solution	NOUN
ejpam-3223	135	31	of	of	ADP
ejpam-3223	135	32	the	the	DET
ejpam-3223	135	33	operator	operator	NOUN
ejpam-3223	135	34	(	(	PUNCT
ejpam-3223	135	35	4c	4c	NOUN
ejpam-3223	135	36	+	+	CCONJ
ejpam-3223	135	37	m2)k	m2)k	NOUN
ejpam-3223	135	38	related	relate	VERB
ejpam-3223	135	39	to	to	ADP
ejpam-3223	135	40	the	the	DET
ejpam-3223	135	41	helmholtz	helmholtz	NOUN
ejpam-3223	135	42	operator	operator	NOUN
ejpam-3223	135	43	iterated	iterate	VERB
ejpam-3223	135	44	k	k	NOUN
ejpam-3223	135	45	-	-	PUNCT
ejpam-3223	135	46	times	time	NOUN
ejpam-3223	135	47	defined	define	VERB
ejpam-3223	135	48	by	by	ADP
ejpam-3223	135	49	(	(	PUNCT
ejpam-3223	135	50	6	6	NUM
ejpam-3223	135	51	)	)	PUNCT
ejpam-3223	135	52	and	and	CCONJ
ejpam-3223	135	53	in	in	ADP
ejpam-3223	135	54	particular	particular	ADJ
ejpam-3223	135	55	,	,	PUNCT
ejpam-3223	135	56	for	for	ADP
ejpam-3223	135	57	q	q	NOUN
ejpam-3223	135	58	=	=	SYM
ejpam-3223	135	59	0	0	NUM
ejpam-3223	135	60	and	and	CCONJ
ejpam-3223	135	61	c	c	NOUN
ejpam-3223	135	62	=	=	NOUN
ejpam-3223	135	63	1	1	NUM
ejpam-3223	135	64	then	then	ADV
ejpam-3223	135	65	}	}	PUNCT
ejpam-3223	135	66	kc	kc	PROPN
ejpam-3223	135	67	reduces	reduce	VERB
ejpam-3223	135	68	to	to	ADP
ejpam-3223	135	69	the	the	DET
ejpam-3223	135	70	helmhotz	helmhotz	NOUN
ejpam-3223	135	71	operator	operator	NOUN
ejpam-3223	135	72	(	(	PUNCT
ejpam-3223	135	73	4p	4p	NUM
ejpam-3223	135	74	+	+	NOUN
ejpam-3223	135	75	m2	m2	PROPN
ejpam-3223	135	76	)	)	PUNCT
ejpam-3223	135	77	2k	2k	NOUN
ejpam-3223	135	78	of	of	ADP
ejpam-3223	135	79	p	p	NOUN
ejpam-3223	135	80	-	-	PUNCT
ejpam-3223	135	81	dimension	dimension	NOUN
ejpam-3223	135	82	iterated	iterate	VERB
ejpam-3223	135	83	2k	2k	NUM
ejpam-3223	135	84	-	-	PUNCT
ejpam-3223	135	85	times	time	NOUN
ejpam-3223	135	86	and	and	CCONJ
ejpam-3223	135	87	is	be	AUX
ejpam-3223	135	88	defined	define	VERB
ejpam-3223	135	89	by	by	ADP
ejpam-3223	135	90	(	(	PUNCT
ejpam-3223	135	91	9	9	NUM
ejpam-3223	135	92	)	)	PUNCT
ejpam-3223	135	93	,	,	PUNCT
ejpam-3223	135	94	where	where	SCONJ
ejpam-3223	135	95	4p	4p	NOUN
ejpam-3223	135	96	=	=	SYM
ejpam-3223	135	97	1	1	NUM
ejpam-3223	135	98	c2	c2	PROPN
ejpam-3223	135	99	(	(	PUNCT
ejpam-3223	135	100	∂2	∂2	PROPN
ejpam-3223	135	101	∂x21	∂x21	PROPN
ejpam-3223	135	102	+	+	CCONJ
ejpam-3223	135	103	∂2	∂2	PROPN
ejpam-3223	135	104	∂x22	∂x22	PROPN
ejpam-3223	135	105	+	+	CCONJ
ejpam-3223	135	106	·	·	PUNCT
ejpam-3223	135	107	·	·	PUNCT
ejpam-3223	135	108	·	·	PUNCT
ejpam-3223	135	109	+	+	NUM
ejpam-3223	135	110	∂2	∂2	PROPN
ejpam-3223	135	111	∂x2p	∂x2p	PROPN
ejpam-3223	135	112	)	)	PUNCT
ejpam-3223	135	113	,	,	PUNCT
ejpam-3223	135	114	thus	thus	ADV
ejpam-3223	135	115	(	(	PUNCT
ejpam-3223	135	116	22	22	NUM
ejpam-3223	135	117	)	)	PUNCT
ejpam-3223	135	118	becomes	become	VERB
ejpam-3223	135	119	(	(	PUNCT
ejpam-3223	135	120	4p	4p	NOUN
ejpam-3223	135	121	+	+	NOUN
ejpam-3223	135	122	m2	m2	PROPN
ejpam-3223	135	123	)	)	PUNCT
ejpam-3223	135	124	2k	2k	PROPN
ejpam-3223	135	125	g(x	g(x	NOUN
ejpam-3223	135	126	)	)	PUNCT
ejpam-3223	136	1	=	=	SYM
ejpam-3223	136	2	δ	δ	PROPN
ejpam-3223	136	3	,	,	PUNCT
ejpam-3223	136	4	(	(	PUNCT
ejpam-3223	136	5	25	25	NUM
ejpam-3223	136	6	)	)	PUNCT
ejpam-3223	136	7	s.	s.	PROPN
ejpam-3223	136	8	bupasiri	bupasiri	PROPN
ejpam-3223	136	9	/	/	SYM
ejpam-3223	136	10	eur	eur	PROPN
ejpam-3223	136	11	.	.	PUNCT
ejpam-3223	137	1	j.	j.	PROPN
ejpam-3223	137	2	pure	pure	PROPN
ejpam-3223	137	3	appl	appl	PROPN
ejpam-3223	137	4	.	.	PROPN
ejpam-3223	137	5	math	math	PROPN
ejpam-3223	137	6	,	,	PUNCT
ejpam-3223	137	7	11	11	NUM
ejpam-3223	137	8	(	(	PUNCT
ejpam-3223	137	9	2	2	NUM
ejpam-3223	137	10	)	)	PUNCT
ejpam-3223	137	11	(	(	PUNCT
ejpam-3223	137	12	2018	2018	NUM
ejpam-3223	137	13	)	)	PUNCT
ejpam-3223	137	14	,	,	PUNCT
ejpam-3223	137	15	390	390	NUM
ejpam-3223	137	16	-	-	SYM
ejpam-3223	137	17	399	399	NUM
ejpam-3223	137	18	396	396	NUM
ejpam-3223	137	19	we	we	PRON
ejpam-3223	137	20	obtain	obtain	VERB
ejpam-3223	137	21	g(x	g(x	NOUN
ejpam-3223	137	22	)	)	PUNCT
ejpam-3223	138	1	=	=	SYM
ejpam-3223	138	2	y4k,1(v	y4k,1(v	PROPN
ejpam-3223	138	3	,	,	PUNCT
ejpam-3223	138	4	m	m	PROPN
ejpam-3223	138	5	)	)	PUNCT
ejpam-3223	138	6	(	(	PUNCT
ejpam-3223	138	7	26	26	NUM
ejpam-3223	138	8	)	)	PUNCT
ejpam-3223	138	9	is	be	AUX
ejpam-3223	138	10	an	an	DET
ejpam-3223	138	11	elementary	elementary	ADJ
ejpam-3223	138	12	solution	solution	NOUN
ejpam-3223	138	13	of	of	ADP
ejpam-3223	138	14	(	(	PUNCT
ejpam-3223	138	15	25	25	NUM
ejpam-3223	138	16	)	)	PUNCT
ejpam-3223	138	17	and	and	CCONJ
ejpam-3223	138	18	from	from	ADP
ejpam-3223	138	19	(	(	PUNCT
ejpam-3223	138	20	23	23	NUM
ejpam-3223	138	21	)	)	PUNCT
ejpam-3223	138	22	.	.	PUNCT
ejpam-3223	139	1	moreover	moreover	ADV
ejpam-3223	139	2	,	,	PUNCT
ejpam-3223	139	3	y−2k	y−2k	NOUN
ejpam-3223	139	4	,	,	PUNCT
ejpam-3223	139	5	c(u	c(u	PROPN
ejpam-3223	139	6	,	,	PUNCT
ejpam-3223	139	7	m	m	NOUN
ejpam-3223	139	8	)	)	PUNCT
ejpam-3223	139	9	∗g(x	∗g(x	NUM
ejpam-3223	139	10	)	)	PUNCT
ejpam-3223	139	11	=	=	SYM
ejpam-3223	139	12	w2k	w2k	PROPN
ejpam-3223	139	13	,	,	PUNCT
ejpam-3223	139	14	c(u	c(u	PROPN
ejpam-3223	139	15	,	,	PUNCT
ejpam-3223	139	16	m	m	NOUN
ejpam-3223	139	17	)	)	PUNCT
ejpam-3223	139	18	(	(	PUNCT
ejpam-3223	139	19	27	27	NUM
ejpam-3223	139	20	)	)	PUNCT
ejpam-3223	139	21	is	be	AUX
ejpam-3223	139	22	an	an	DET
ejpam-3223	139	23	elementary	elementary	ADJ
ejpam-3223	139	24	solution	solution	NOUN
ejpam-3223	139	25	of	of	ADP
ejpam-3223	139	26	operator	operator	NOUN
ejpam-3223	139	27	related	relate	VERB
ejpam-3223	139	28	to	to	ADP
ejpam-3223	139	29	the	the	DET
ejpam-3223	139	30	klein	klein	PROPN
ejpam-3223	139	31	-	-	PUNCT
ejpam-3223	139	32	gordon	gordon	PROPN
ejpam-3223	139	33	operator	operator	NOUN
ejpam-3223	139	34	.	.	PUNCT
ejpam-3223	140	1	in	in	ADP
ejpam-3223	140	2	particular	particular	ADJ
ejpam-3223	140	3	,	,	PUNCT
ejpam-3223	140	4	we	we	PRON
ejpam-3223	140	5	obtain	obtain	VERB
ejpam-3223	140	6	(	(	PUNCT
ejpam-3223	140	7	−1)kre−2,1(v	−1)kre−2,1(v	NOUN
ejpam-3223	140	8	)	)	PUNCT
ejpam-3223	140	9	∗g(x	∗g(x	NOUN
ejpam-3223	140	10	)	)	PUNCT
ejpam-3223	140	11	=	=	SYM
ejpam-3223	141	1	m2,1(u	m2,1(u	PROPN
ejpam-3223	141	2	)	)	PUNCT
ejpam-3223	141	3	is	be	AUX
ejpam-3223	141	4	an	an	DET
ejpam-3223	141	5	elementary	elementary	ADJ
ejpam-3223	141	6	solution	solution	NOUN
ejpam-3223	141	7	of	of	ADP
ejpam-3223	141	8	the	the	DET
ejpam-3223	141	9	wave	wave	NOUN
ejpam-3223	141	10	operator	operator	NOUN
ejpam-3223	141	11	defined	define	VERB
ejpam-3223	141	12	by	by	ADP
ejpam-3223	141	13	(	(	PUNCT
ejpam-3223	141	14	10	10	NUM
ejpam-3223	141	15	)	)	PUNCT
ejpam-3223	141	16	where	where	SCONJ
ejpam-3223	141	17	u	u	NOUN
ejpam-3223	141	18	=	=	PROPN
ejpam-3223	141	19	t2	t2	PROPN
ejpam-3223	141	20	−	−	PROPN
ejpam-3223	141	21	x21	x21	NUM
ejpam-3223	141	22	−	−	PROPN
ejpam-3223	141	23	x22	x22	NOUN
ejpam-3223	141	24	−	−	PROPN
ejpam-3223	141	25	·	·	PUNCT
ejpam-3223	141	26	·	·	PUNCT
ejpam-3223	141	27	·	·	PUNCT
ejpam-3223	142	1	−	−	PROPN
ejpam-3223	143	1	x2n−1	x2n−1	PROPN
ejpam-3223	143	2	.	.	PUNCT
ejpam-3223	144	1	also	also	ADV
ejpam-3223	144	2	,	,	PUNCT
ejpam-3223	144	3	for	for	ADP
ejpam-3223	144	4	m	m	PROPN
ejpam-3223	144	5	=	=	SYM
ejpam-3223	144	6	0	0	NUM
ejpam-3223	144	7	,	,	PUNCT
ejpam-3223	144	8	q	q	NOUN
ejpam-3223	144	9	=	=	SYM
ejpam-3223	144	10	0	0	NUM
ejpam-3223	144	11	and	and	CCONJ
ejpam-3223	144	12	c	c	NOUN
ejpam-3223	144	13	=	=	SYM
ejpam-3223	144	14	1	1	NUM
ejpam-3223	144	15	then	then	ADV
ejpam-3223	144	16	(	(	PUNCT
ejpam-3223	144	17	25	25	NUM
ejpam-3223	144	18	)	)	PUNCT
ejpam-3223	144	19	becomes	become	VERB
ejpam-3223	144	20	42k	42k	NUM
ejpam-3223	144	21	p	p	X
ejpam-3223	144	22	g(x	g(x	NOUN
ejpam-3223	144	23	)	)	PUNCT
ejpam-3223	145	1	=	=	SYM
ejpam-3223	145	2	δ	δ	PROPN
ejpam-3223	145	3	(	(	PUNCT
ejpam-3223	145	4	28	28	NUM
ejpam-3223	145	5	)	)	PUNCT
ejpam-3223	145	6	where	where	SCONJ
ejpam-3223	145	7	42k	42k	NOUN
ejpam-3223	145	8	p	p	NOUN
ejpam-3223	145	9	is	be	AUX
ejpam-3223	145	10	the	the	DET
ejpam-3223	145	11	laplacian	laplacian	NOUN
ejpam-3223	145	12	of	of	ADP
ejpam-3223	145	13	p	p	ADJ
ejpam-3223	145	14	-	-	PUNCT
ejpam-3223	145	15	dimension	dimension	NOUN
ejpam-3223	145	16	iterated	iterate	VERB
ejpam-3223	145	17	2k	2k	NUM
ejpam-3223	145	18	-	-	PUNCT
ejpam-3223	145	19	times	time	NOUN
ejpam-3223	145	20	.	.	PUNCT
ejpam-3223	146	1	we	we	PRON
ejpam-3223	146	2	have	have	VERB
ejpam-3223	146	3	g(x	g(x	NOUN
ejpam-3223	146	4	)	)	PUNCT
ejpam-3223	147	1	=	=	SYM
ejpam-3223	147	2	re4k,1(v	re4k,1(v	PROPN
ejpam-3223	147	3	)	)	PUNCT
ejpam-3223	147	4	is	be	AUX
ejpam-3223	147	5	an	an	DET
ejpam-3223	147	6	elementary	elementary	ADJ
ejpam-3223	147	7	solution	solution	NOUN
ejpam-3223	147	8	of	of	ADP
ejpam-3223	147	9	(	(	PUNCT
ejpam-3223	147	10	28	28	NUM
ejpam-3223	147	11	)	)	PUNCT
ejpam-3223	147	12	where	where	SCONJ
ejpam-3223	147	13	v	v	NOUN
ejpam-3223	147	14	=	=	SYM
ejpam-3223	147	15	c2	c2	PROPN
ejpam-3223	147	16	(	(	PUNCT
ejpam-3223	147	17	x21	x21	PROPN
ejpam-3223	147	18	+	+	NUM
ejpam-3223	147	19	x22	x22	NUM
ejpam-3223	147	20	+	+	CCONJ
ejpam-3223	147	21	·	·	PUNCT
ejpam-3223	147	22	·	·	PUNCT
ejpam-3223	147	23	·	·	PUNCT
ejpam-3223	148	1	+	+	NUM
ejpam-3223	148	2	x2p	x2p	NUM
ejpam-3223	148	3	)	)	PUNCT
ejpam-3223	148	4	.	.	PUNCT
ejpam-3223	149	1	proof	proof	NOUN
ejpam-3223	149	2	.	.	PUNCT
ejpam-3223	150	1	from	from	ADP
ejpam-3223	150	2	(	(	PUNCT
ejpam-3223	150	3	5	5	NUM
ejpam-3223	150	4	)	)	PUNCT
ejpam-3223	150	5	and	and	CCONJ
ejpam-3223	150	6	(	(	PUNCT
ejpam-3223	150	7	22	22	NUM
ejpam-3223	150	8	)	)	PUNCT
ejpam-3223	150	9	we	we	PRON
ejpam-3223	150	10	have	have	VERB
ejpam-3223	150	11	}	}	PUNCT
ejpam-3223	150	12	kcg(x	kcg(x	PROPN
ejpam-3223	150	13	)	)	PUNCT
ejpam-3223	150	14	=	=	SYM
ejpam-3223	151	1	(	(	PUNCT
ejpam-3223	151	2	(	(	PUNCT
ejpam-3223	151	3	�	�	PROPN
ejpam-3223	151	4	c	c	NOUN
ejpam-3223	151	5	+	+	NOUN
ejpam-3223	151	6	m2	m2	PROPN
ejpam-3223	151	7	)	)	PUNCT
ejpam-3223	151	8	k	k	PROPN
ejpam-3223	151	9	(	(	PUNCT
ejpam-3223	151	10	4c	4c	NOUN
ejpam-3223	151	11	+	+	NOUN
ejpam-3223	151	12	m2	m2	PROPN
ejpam-3223	151	13	)	)	PUNCT
ejpam-3223	151	14	k	k	NOUN
ejpam-3223	151	15	)	)	PUNCT
ejpam-3223	151	16	g(x	g(x	NOUN
ejpam-3223	151	17	)	)	PUNCT
ejpam-3223	152	1	=	=	SYM
ejpam-3223	152	2	δ	δ	PROPN
ejpam-3223	152	3	.	.	PUNCT
ejpam-3223	153	1	convolving	convolve	VERB
ejpam-3223	153	2	both	both	DET
ejpam-3223	153	3	sides	side	NOUN
ejpam-3223	153	4	of	of	ADP
ejpam-3223	153	5	the	the	DET
ejpam-3223	153	6	above	above	ADJ
ejpam-3223	153	7	equation	equation	NOUN
ejpam-3223	153	8	by	by	ADP
ejpam-3223	153	9	the	the	DET
ejpam-3223	153	10	convolution	convolution	NOUN
ejpam-3223	153	11	w2k	w2k	PROPN
ejpam-3223	153	12	,	,	PUNCT
ejpam-3223	153	13	c(u	c(u	PROPN
ejpam-3223	153	14	,	,	PUNCT
ejpam-3223	153	15	m	m	NOUN
ejpam-3223	153	16	)	)	PUNCT
ejpam-3223	153	17	∗	∗	NOUN
ejpam-3223	153	18	y2k	y2k	PROPN
ejpam-3223	153	19	,	,	PUNCT
ejpam-3223	153	20	c(v	c(v	PROPN
ejpam-3223	153	21	,	,	PUNCT
ejpam-3223	153	22	m	m	NOUN
ejpam-3223	153	23	)	)	PUNCT
ejpam-3223	153	24	and	and	CCONJ
ejpam-3223	153	25	the	the	DET
ejpam-3223	153	26	properties	property	NOUN
ejpam-3223	153	27	of	of	ADP
ejpam-3223	153	28	convolution	convolution	NOUN
ejpam-3223	153	29	with	with	ADP
ejpam-3223	153	30	derivatives	derivative	NOUN
ejpam-3223	153	31	,	,	PUNCT
ejpam-3223	153	32	we	we	PRON
ejpam-3223	153	33	obtain	obtain	VERB
ejpam-3223	153	34	(	(	PUNCT
ejpam-3223	153	35	�	�	PROPN
ejpam-3223	153	36	c	c	NOUN
ejpam-3223	153	37	+	+	NOUN
ejpam-3223	153	38	m2	m2	X
ejpam-3223	153	39	)	)	PUNCT
ejpam-3223	153	40	k	k	PROPN
ejpam-3223	153	41	w2k	w2k	PROPN
ejpam-3223	153	42	,	,	PUNCT
ejpam-3223	153	43	c(u	c(u	PROPN
ejpam-3223	153	44	,	,	PUNCT
ejpam-3223	153	45	m	m	NOUN
ejpam-3223	153	46	)	)	PUNCT
ejpam-3223	153	47	∗	∗	NOUN
ejpam-3223	153	48	(	(	PUNCT
ejpam-3223	153	49	4c	4c	NOUN
ejpam-3223	153	50	+	+	NOUN
ejpam-3223	153	51	m2	m2	PROPN
ejpam-3223	153	52	)	)	PUNCT
ejpam-3223	153	53	k	k	PROPN
ejpam-3223	153	54	y2k	y2k	PROPN
ejpam-3223	153	55	,	,	PUNCT
ejpam-3223	153	56	c(v	c(v	PROPN
ejpam-3223	153	57	,	,	PUNCT
ejpam-3223	153	58	m	m	NOUN
ejpam-3223	153	59	)	)	PUNCT
ejpam-3223	153	60	∗g(x	∗g(x	NUM
ejpam-3223	153	61	)	)	PUNCT
ejpam-3223	153	62	=	=	SYM
ejpam-3223	154	1	w2k	w2k	PROPN
ejpam-3223	154	2	,	,	PUNCT
ejpam-3223	154	3	c(u	c(u	PROPN
ejpam-3223	154	4	,	,	PUNCT
ejpam-3223	154	5	m	m	NOUN
ejpam-3223	154	6	)	)	PUNCT
ejpam-3223	154	7	∗	∗	NOUN
ejpam-3223	154	8	y2k	y2k	PROPN
ejpam-3223	154	9	,	,	PUNCT
ejpam-3223	154	10	c(v	c(v	PROPN
ejpam-3223	154	11	,	,	PUNCT
ejpam-3223	154	12	m	m	NOUN
ejpam-3223	154	13	)	)	PUNCT
ejpam-3223	154	14	∗	∗	PROPN
ejpam-3223	154	15	δ	δ	PROPN
ejpam-3223	154	16	.	.	PUNCT
ejpam-3223	155	1	(	(	PUNCT
ejpam-3223	155	2	29	29	NUM
ejpam-3223	155	3	)	)	PUNCT
ejpam-3223	155	4	thus	thus	ADV
ejpam-3223	155	5	g(x	g(x	NOUN
ejpam-3223	155	6	)	)	PUNCT
ejpam-3223	156	1	=	=	SYM
ejpam-3223	156	2	δ	δ	PROPN
ejpam-3223	156	3	∗	∗	NOUN
ejpam-3223	156	4	δ	δ	PROPN
ejpam-3223	156	5	∗g(x	∗g(x	NOUN
ejpam-3223	156	6	)	)	PUNCT
ejpam-3223	156	7	=	=	SYM
ejpam-3223	157	1	w2k	w2k	PROPN
ejpam-3223	157	2	,	,	PUNCT
ejpam-3223	157	3	c(u	c(u	PROPN
ejpam-3223	157	4	,	,	PUNCT
ejpam-3223	157	5	m	m	NOUN
ejpam-3223	157	6	)	)	PUNCT
ejpam-3223	157	7	∗	∗	NOUN
ejpam-3223	157	8	y2k	y2k	PROPN
ejpam-3223	157	9	,	,	PUNCT
ejpam-3223	157	10	c(v	c(v	PROPN
ejpam-3223	157	11	,	,	PUNCT
ejpam-3223	157	12	m	m	NOUN
ejpam-3223	157	13	)	)	PUNCT
ejpam-3223	157	14	(	(	PUNCT
ejpam-3223	157	15	30	30	NUM
ejpam-3223	157	16	)	)	PUNCT
ejpam-3223	157	17	by	by	ADP
ejpam-3223	157	18	lemma	lemma	PROPN
ejpam-3223	157	19	3	3	NUM
ejpam-3223	157	20	and	and	CCONJ
ejpam-3223	157	21	5	5	NUM
ejpam-3223	157	22	.	.	PUNCT
ejpam-3223	157	23	now	now	ADV
ejpam-3223	157	24	from	from	ADP
ejpam-3223	157	25	(	(	PUNCT
ejpam-3223	157	26	23	23	NUM
ejpam-3223	157	27	)	)	PUNCT
ejpam-3223	157	28	and	and	CCONJ
ejpam-3223	157	29	by	by	ADP
ejpam-3223	157	30	lemma	lemma	PROPN
ejpam-3223	157	31	3	3	NUM
ejpam-3223	157	32	and	and	CCONJ
ejpam-3223	157	33	lemma	lemma	PROPN
ejpam-3223	157	34	4	4	NUM
ejpam-3223	157	35	and	and	CCONJ
ejpam-3223	157	36	properties	property	NOUN
ejpam-3223	157	37	of	of	ADP
ejpam-3223	157	38	inverses	inverse	NOUN
ejpam-3223	157	39	in	in	ADP
ejpam-3223	157	40	the	the	DET
ejpam-3223	157	41	convolution	convolution	NOUN
ejpam-3223	157	42	algebra	algebra	NOUN
ejpam-3223	157	43	,	,	PUNCT
ejpam-3223	157	44	we	we	PRON
ejpam-3223	157	45	obtain	obtain	VERB
ejpam-3223	157	46	w−2k	w−2k	NOUN
ejpam-3223	157	47	,	,	PUNCT
ejpam-3223	157	48	c(u	c(u	PROPN
ejpam-3223	157	49	,	,	PUNCT
ejpam-3223	157	50	m	m	NOUN
ejpam-3223	157	51	)	)	PUNCT
ejpam-3223	157	52	∗g(x	∗g(x	NUM
ejpam-3223	157	53	)	)	PUNCT
ejpam-3223	157	54	=	=	SYM
ejpam-3223	158	1	δ	δ	PROPN
ejpam-3223	158	2	∗	∗	VERB
ejpam-3223	158	3	y2k	y2k	PROPN
ejpam-3223	158	4	,	,	PUNCT
ejpam-3223	158	5	c(v	c(v	PROPN
ejpam-3223	158	6	,	,	PUNCT
ejpam-3223	158	7	m	m	NOUN
ejpam-3223	158	8	)	)	PUNCT
ejpam-3223	158	9	=	=	SYM
ejpam-3223	158	10	y2k	y2k	PROPN
ejpam-3223	158	11	,	,	PUNCT
ejpam-3223	158	12	c(v	c(v	PROPN
ejpam-3223	158	13	,	,	PUNCT
ejpam-3223	158	14	m	m	NOUN
ejpam-3223	158	15	)	)	PUNCT
ejpam-3223	158	16	is	be	AUX
ejpam-3223	158	17	an	an	DET
ejpam-3223	158	18	elementary	elementary	ADJ
ejpam-3223	158	19	solution	solution	NOUN
ejpam-3223	158	20	of	of	ADP
ejpam-3223	158	21	operator	operator	NOUN
ejpam-3223	158	22	related	relate	VERB
ejpam-3223	158	23	to	to	ADP
ejpam-3223	158	24	the	the	DET
ejpam-3223	158	25	helmhotz	helmhotz	NOUN
ejpam-3223	158	26	operator	operator	NOUN
ejpam-3223	158	27	iterated	iterate	VERB
ejpam-3223	158	28	k	k	NOUN
ejpam-3223	158	29	-	-	PUNCT
ejpam-3223	158	30	times	time	NOUN
ejpam-3223	158	31	defined	define	VERB
ejpam-3223	158	32	by	by	ADP
ejpam-3223	158	33	(	(	PUNCT
ejpam-3223	158	34	6	6	NUM
ejpam-3223	158	35	)	)	PUNCT
ejpam-3223	158	36	.	.	PUNCT
ejpam-3223	159	1	in	in	ADP
ejpam-3223	159	2	particular	particular	ADJ
ejpam-3223	159	3	,	,	PUNCT
ejpam-3223	159	4	for	for	ADP
ejpam-3223	159	5	q	q	NOUN
ejpam-3223	159	6	=	=	SYM
ejpam-3223	159	7	0	0	NUM
ejpam-3223	159	8	and	and	CCONJ
ejpam-3223	159	9	c	c	NOUN
ejpam-3223	159	10	=	=	SYM
ejpam-3223	159	11	1	1	NUM
ejpam-3223	159	12	then	then	ADV
ejpam-3223	159	13	(	(	PUNCT
ejpam-3223	159	14	22	22	NUM
ejpam-3223	159	15	)	)	PUNCT
ejpam-3223	159	16	becomes	become	VERB
ejpam-3223	159	17	(	(	PUNCT
ejpam-3223	159	18	4p	4p	NUM
ejpam-3223	159	19	+	+	NOUN
ejpam-3223	159	20	m2	m2	PROPN
ejpam-3223	159	21	)	)	PUNCT
ejpam-3223	159	22	2k	2k	NOUN
ejpam-3223	159	23	g(x	g(x	NOUN
ejpam-3223	159	24	)	)	PUNCT
ejpam-3223	159	25	=	=	SYM
ejpam-3223	159	26	δ	δ	PROPN
ejpam-3223	159	27	(	(	PUNCT
ejpam-3223	159	28	31	31	NUM
ejpam-3223	159	29	)	)	PUNCT
ejpam-3223	159	30	s.	s.	PROPN
ejpam-3223	159	31	bupasiri	bupasiri	PROPN
ejpam-3223	159	32	/	/	SYM
ejpam-3223	159	33	eur	eur	PROPN
ejpam-3223	159	34	.	.	PUNCT
ejpam-3223	160	1	j.	j.	PROPN
ejpam-3223	160	2	pure	pure	PROPN
ejpam-3223	160	3	appl	appl	PROPN
ejpam-3223	160	4	.	.	PROPN
ejpam-3223	160	5	math	math	PROPN
ejpam-3223	160	6	,	,	PUNCT
ejpam-3223	160	7	11	11	NUM
ejpam-3223	160	8	(	(	PUNCT
ejpam-3223	160	9	2	2	NUM
ejpam-3223	160	10	)	)	PUNCT
ejpam-3223	160	11	(	(	PUNCT
ejpam-3223	160	12	2018	2018	NUM
ejpam-3223	160	13	)	)	PUNCT
ejpam-3223	160	14	,	,	PUNCT
ejpam-3223	160	15	390	390	NUM
ejpam-3223	160	16	-	-	SYM
ejpam-3223	160	17	399	399	NUM
ejpam-3223	160	18	397	397	NUM
ejpam-3223	160	19	where	where	SCONJ
ejpam-3223	160	20	(	(	PUNCT
ejpam-3223	160	21	4p	4p	NUM
ejpam-3223	160	22	+	+	NOUN
ejpam-3223	160	23	m2	m2	PROPN
ejpam-3223	160	24	)	)	PUNCT
ejpam-3223	160	25	2k	2k	PROPN
ejpam-3223	160	26	is	be	AUX
ejpam-3223	160	27	the	the	DET
ejpam-3223	160	28	helmholtz	helmholtz	NOUN
ejpam-3223	160	29	operator	operator	NOUN
ejpam-3223	160	30	of	of	ADP
ejpam-3223	160	31	p	p	NOUN
ejpam-3223	160	32	-	-	PUNCT
ejpam-3223	160	33	dimension	dimension	NOUN
ejpam-3223	160	34	,	,	PUNCT
ejpam-3223	160	35	iterated	iterate	VERB
ejpam-3223	160	36	2k	2k	NUM
ejpam-3223	160	37	-	-	PUNCT
ejpam-3223	160	38	times	time	NOUN
ejpam-3223	160	39	and	and	CCONJ
ejpam-3223	160	40	is	be	AUX
ejpam-3223	160	41	defined	define	VERB
ejpam-3223	160	42	by	by	ADP
ejpam-3223	160	43	(	(	PUNCT
ejpam-3223	160	44	9	9	NUM
ejpam-3223	160	45	)	)	PUNCT
ejpam-3223	160	46	.	.	PUNCT
ejpam-3223	161	1	by	by	ADP
ejpam-3223	161	2	lemma	lemma	PROPN
ejpam-3223	161	3	5	5	NUM
ejpam-3223	161	4	,	,	PUNCT
ejpam-3223	161	5	we	we	PRON
ejpam-3223	161	6	have	have	VERB
ejpam-3223	161	7	g(x	g(x	NOUN
ejpam-3223	161	8	)	)	PUNCT
ejpam-3223	162	1	=	=	SYM
ejpam-3223	162	2	y4k,1(v	y4k,1(v	PROPN
ejpam-3223	162	3	,	,	PUNCT
ejpam-3223	162	4	m	m	PROPN
ejpam-3223	162	5	)	)	PUNCT
ejpam-3223	162	6	(	(	PUNCT
ejpam-3223	162	7	32	32	NUM
ejpam-3223	162	8	)	)	PUNCT
ejpam-3223	162	9	is	be	AUX
ejpam-3223	162	10	an	an	DET
ejpam-3223	162	11	elementary	elementary	ADJ
ejpam-3223	162	12	solution	solution	NOUN
ejpam-3223	162	13	of	of	ADP
ejpam-3223	162	14	(	(	PUNCT
ejpam-3223	162	15	31	31	NUM
ejpam-3223	162	16	)	)	PUNCT
ejpam-3223	162	17	.	.	PUNCT
ejpam-3223	163	1	moreover	moreover	ADV
ejpam-3223	163	2	,	,	PUNCT
ejpam-3223	163	3	from	from	ADP
ejpam-3223	163	4	(	(	PUNCT
ejpam-3223	163	5	23	23	NUM
ejpam-3223	163	6	)	)	PUNCT
ejpam-3223	163	7	and	and	CCONJ
ejpam-3223	163	8	by	by	ADP
ejpam-3223	163	9	lemma	lemma	PROPN
ejpam-3223	163	10	6	6	NUM
ejpam-3223	163	11	and	and	CCONJ
ejpam-3223	163	12	lemma	lemma	PROPN
ejpam-3223	163	13	5	5	NUM
ejpam-3223	163	14	and	and	CCONJ
ejpam-3223	163	15	properties	property	NOUN
ejpam-3223	163	16	of	of	ADP
ejpam-3223	163	17	inverses	inverse	NOUN
ejpam-3223	163	18	in	in	ADP
ejpam-3223	163	19	the	the	DET
ejpam-3223	163	20	convolution	convolution	NOUN
ejpam-3223	163	21	algebra	algebra	NOUN
ejpam-3223	163	22	,	,	PUNCT
ejpam-3223	163	23	we	we	PRON
ejpam-3223	163	24	obtain	obtain	VERB
ejpam-3223	163	25	y−2k	y−2k	NOUN
ejpam-3223	163	26	,	,	PUNCT
ejpam-3223	163	27	c(u	c(u	PROPN
ejpam-3223	163	28	,	,	PUNCT
ejpam-3223	163	29	m	m	NOUN
ejpam-3223	163	30	)	)	PUNCT
ejpam-3223	163	31	∗g(x	∗g(x	NUM
ejpam-3223	163	32	)	)	PUNCT
ejpam-3223	163	33	=	=	SYM
ejpam-3223	163	34	w2k	w2k	PROPN
ejpam-3223	163	35	,	,	PUNCT
ejpam-3223	163	36	c(u	c(u	PROPN
ejpam-3223	163	37	,	,	PUNCT
ejpam-3223	163	38	m	m	NOUN
ejpam-3223	163	39	)	)	PUNCT
ejpam-3223	163	40	∗	∗	NOUN
ejpam-3223	163	41	δ	δ	PROPN
ejpam-3223	163	42	=	=	SYM
ejpam-3223	163	43	w2k	w2k	PROPN
ejpam-3223	163	44	,	,	PUNCT
ejpam-3223	163	45	c(u	c(u	PROPN
ejpam-3223	163	46	,	,	PUNCT
ejpam-3223	163	47	m	m	PRON
ejpam-3223	163	48	)	)	PUNCT
ejpam-3223	163	49	is	be	AUX
ejpam-3223	163	50	an	an	DET
ejpam-3223	163	51	elementary	elementary	ADJ
ejpam-3223	163	52	solution	solution	NOUN
ejpam-3223	163	53	of	of	ADP
ejpam-3223	163	54	operator	operator	NOUN
ejpam-3223	163	55	related	relate	VERB
ejpam-3223	163	56	to	to	ADP
ejpam-3223	163	57	the	the	DET
ejpam-3223	163	58	klein	klein	PROPN
ejpam-3223	163	59	-	-	PUNCT
ejpam-3223	163	60	gordon	gordon	PROPN
ejpam-3223	163	61	operator	operator	NOUN
ejpam-3223	163	62	.	.	PUNCT
ejpam-3223	164	1	in	in	ADP
ejpam-3223	164	2	particular	particular	ADJ
ejpam-3223	164	3	,	,	PUNCT
ejpam-3223	164	4	by	by	ADP
ejpam-3223	164	5	putting	put	VERB
ejpam-3223	164	6	p	p	NOUN
ejpam-3223	164	7	=	=	NOUN
ejpam-3223	164	8	1	1	NUM
ejpam-3223	164	9	,	,	PUNCT
ejpam-3223	164	10	q	q	NOUN
ejpam-3223	164	11	=	=	PUNCT
ejpam-3223	164	12	n−	n−	NOUN
ejpam-3223	164	13	1	1	NUM
ejpam-3223	164	14	,	,	PUNCT
ejpam-3223	164	15	k	k	NOUN
ejpam-3223	164	16	=	=	SYM
ejpam-3223	164	17	1	1	NUM
ejpam-3223	164	18	,	,	PUNCT
ejpam-3223	164	19	x1	x1	PROPN
ejpam-3223	164	20	=	=	SYM
ejpam-3223	164	21	t	t	PROPN
ejpam-3223	164	22	,	,	PUNCT
ejpam-3223	164	23	c	c	NOUN
ejpam-3223	164	24	=	=	SYM
ejpam-3223	164	25	1	1	NUM
ejpam-3223	164	26	and	and	CCONJ
ejpam-3223	164	27	m	m	PROPN
ejpam-3223	164	28	=	=	NOUN
ejpam-3223	164	29	0	0	NUM
ejpam-3223	164	30	in	in	ADP
ejpam-3223	164	31	(	(	PUNCT
ejpam-3223	164	32	23	23	NUM
ejpam-3223	164	33	)	)	PUNCT
ejpam-3223	164	34	and	and	CCONJ
ejpam-3223	164	35	(	(	PUNCT
ejpam-3223	164	36	27	27	NUM
ejpam-3223	164	37	)	)	PUNCT
ejpam-3223	164	38	,	,	PUNCT
ejpam-3223	164	39	w2,1(u	w2,1(u	PROPN
ejpam-3223	164	40	,	,	PUNCT
ejpam-3223	164	41	m	m	VERB
ejpam-3223	164	42	=	=	NOUN
ejpam-3223	164	43	0	0	NUM
ejpam-3223	164	44	)	)	PUNCT
ejpam-3223	164	45	=	=	SYM
ejpam-3223	164	46	rh2,1(u	rh2,1(u	NOUN
ejpam-3223	164	47	)	)	PUNCT
ejpam-3223	164	48	reduces	reduce	VERB
ejpam-3223	164	49	to	to	ADP
ejpam-3223	164	50	m2,1(u	m2,1(u	NOUN
ejpam-3223	164	51	)	)	PUNCT
ejpam-3223	164	52	where	where	SCONJ
ejpam-3223	164	53	m2,1(u	m2,1(u	NOUN
ejpam-3223	164	54	)	)	PUNCT
ejpam-3223	164	55	is	be	AUX
ejpam-3223	164	56	defined	define	VERB
ejpam-3223	164	57	by	by	ADP
ejpam-3223	164	58	(	(	PUNCT
ejpam-3223	164	59	15	15	NUM
ejpam-3223	164	60	)	)	PUNCT
ejpam-3223	164	61	with	with	ADP
ejpam-3223	164	62	α	α	NOUN
ejpam-3223	164	63	=	=	SYM
ejpam-3223	164	64	2	2	NUM
ejpam-3223	164	65	.	.	PUNCT
ejpam-3223	165	1	thus	thus	ADV
ejpam-3223	165	2	we	we	PRON
ejpam-3223	165	3	obtain	obtain	VERB
ejpam-3223	165	4	(	(	PUNCT
ejpam-3223	165	5	−1)kre−2,1(v	−1)kre−2,1(v	NOUN
ejpam-3223	165	6	)	)	PUNCT
ejpam-3223	165	7	∗g(x	∗g(x	NOUN
ejpam-3223	165	8	)	)	PUNCT
ejpam-3223	165	9	=	=	SYM
ejpam-3223	166	1	m2,1(u	m2,1(u	PROPN
ejpam-3223	166	2	)	)	PUNCT
ejpam-3223	166	3	is	be	AUX
ejpam-3223	166	4	an	an	DET
ejpam-3223	166	5	elementary	elementary	ADJ
ejpam-3223	166	6	solution	solution	NOUN
ejpam-3223	166	7	of	of	ADP
ejpam-3223	166	8	the	the	DET
ejpam-3223	166	9	wave	wave	NOUN
ejpam-3223	166	10	operator	operator	NOUN
ejpam-3223	166	11	defined	define	VERB
ejpam-3223	166	12	by	by	ADP
ejpam-3223	166	13	(	(	PUNCT
ejpam-3223	166	14	10	10	NUM
ejpam-3223	166	15	)	)	PUNCT
ejpam-3223	166	16	where	where	SCONJ
ejpam-3223	166	17	u	u	NOUN
ejpam-3223	166	18	=	=	PROPN
ejpam-3223	166	19	t2	t2	PROPN
ejpam-3223	166	20	−	−	PROPN
ejpam-3223	166	21	x21	x21	NUM
ejpam-3223	166	22	−	−	PROPN
ejpam-3223	166	23	x22	x22	NOUN
ejpam-3223	166	24	−	−	PROPN
ejpam-3223	166	25	·	·	PUNCT
ejpam-3223	166	26	·	·	PUNCT
ejpam-3223	166	27	·	·	PUNCT
ejpam-3223	167	1	−	−	PROPN
ejpam-3223	168	1	x2n−1	x2n−1	PROPN
ejpam-3223	168	2	.	.	PUNCT
ejpam-3223	169	1	also	also	ADV
ejpam-3223	169	2	,	,	PUNCT
ejpam-3223	169	3	for	for	ADP
ejpam-3223	169	4	m	m	PROPN
ejpam-3223	169	5	=	=	SYM
ejpam-3223	169	6	0	0	NUM
ejpam-3223	169	7	,	,	PUNCT
ejpam-3223	169	8	c	c	NOUN
ejpam-3223	169	9	=	=	SYM
ejpam-3223	169	10	1	1	NUM
ejpam-3223	169	11	and	and	CCONJ
ejpam-3223	169	12	q	q	NOUN
ejpam-3223	170	1	=	=	NOUN
ejpam-3223	170	2	0	0	NUM
ejpam-3223	171	1	then	then	ADV
ejpam-3223	171	2	(	(	PUNCT
ejpam-3223	171	3	25	25	NUM
ejpam-3223	171	4	)	)	PUNCT
ejpam-3223	171	5	becomes	become	VERB
ejpam-3223	171	6	42k	42k	NUM
ejpam-3223	171	7	p	p	X
ejpam-3223	171	8	g(x	g(x	NOUN
ejpam-3223	171	9	)	)	PUNCT
ejpam-3223	171	10	=	=	SYM
ejpam-3223	171	11	δ	δ	PROPN
ejpam-3223	171	12	(	(	PUNCT
ejpam-3223	171	13	33	33	NUM
ejpam-3223	171	14	)	)	PUNCT
ejpam-3223	171	15	where	where	SCONJ
ejpam-3223	171	16	42k	42k	NOUN
ejpam-3223	171	17	p	p	NOUN
ejpam-3223	171	18	is	be	AUX
ejpam-3223	171	19	the	the	DET
ejpam-3223	171	20	laplacian	laplacian	NOUN
ejpam-3223	171	21	of	of	ADP
ejpam-3223	171	22	p	p	ADJ
ejpam-3223	171	23	-	-	PUNCT
ejpam-3223	171	24	dimension	dimension	NOUN
ejpam-3223	171	25	iterated	iterate	VERB
ejpam-3223	171	26	2k	2k	NUM
ejpam-3223	171	27	-	-	PUNCT
ejpam-3223	171	28	times	time	NOUN
ejpam-3223	171	29	.	.	PUNCT
ejpam-3223	172	1	by	by	ADP
ejpam-3223	172	2	lemma	lemma	PROPN
ejpam-3223	172	3	1	1	NUM
ejpam-3223	172	4	,	,	PUNCT
ejpam-3223	172	5	we	we	PRON
ejpam-3223	172	6	have	have	VERB
ejpam-3223	172	7	g(x	g(x	NOUN
ejpam-3223	172	8	)	)	PUNCT
ejpam-3223	173	1	=	=	SYM
ejpam-3223	173	2	(	(	PUNCT
ejpam-3223	173	3	−1)2kre4k,1(v	−1)2kre4k,1(v	NOUN
ejpam-3223	173	4	)	)	PUNCT
ejpam-3223	173	5	=	=	SYM
ejpam-3223	173	6	re4k,1(v	re4k,1(v	PROPN
ejpam-3223	173	7	)	)	PUNCT
ejpam-3223	173	8	is	be	AUX
ejpam-3223	173	9	an	an	DET
ejpam-3223	173	10	elementary	elementary	ADJ
ejpam-3223	173	11	solution	solution	NOUN
ejpam-3223	173	12	of	of	ADP
ejpam-3223	173	13	(	(	PUNCT
ejpam-3223	173	14	33	33	NUM
ejpam-3223	173	15	)	)	PUNCT
ejpam-3223	173	16	where	where	SCONJ
ejpam-3223	173	17	v	v	NOUN
ejpam-3223	173	18	=	=	SYM
ejpam-3223	173	19	c2(x21	c2(x21	NOUN
ejpam-3223	174	1	+	+	CCONJ
ejpam-3223	174	2	x22	x22	NUM
ejpam-3223	174	3	+	+	CCONJ
ejpam-3223	174	4	·	·	PUNCT
ejpam-3223	174	5	·	·	PUNCT
ejpam-3223	174	6	·	·	PUNCT
ejpam-3223	174	7	+	+	NUM
ejpam-3223	174	8	x2p	x2p	NUM
ejpam-3223	174	9	)	)	PUNCT
ejpam-3223	174	10	.	.	PUNCT
ejpam-3223	175	1	on	on	ADP
ejpam-3223	175	2	the	the	DET
ejpam-3223	175	3	other	other	ADJ
ejpam-3223	175	4	hand	hand	NOUN
ejpam-3223	175	5	,	,	PUNCT
ejpam-3223	175	6	we	we	PRON
ejpam-3223	175	7	can	can	AUX
ejpam-3223	175	8	also	also	ADV
ejpam-3223	175	9	find	find	VERB
ejpam-3223	175	10	g(x	g(x	NOUN
ejpam-3223	175	11	)	)	PUNCT
ejpam-3223	175	12	from	from	ADP
ejpam-3223	175	13	(	(	PUNCT
ejpam-3223	175	14	23	23	NUM
ejpam-3223	175	15	)	)	PUNCT
ejpam-3223	175	16	,	,	PUNCT
ejpam-3223	175	17	since	since	SCONJ
ejpam-3223	175	18	q	q	PROPN
ejpam-3223	175	19	=	=	SYM
ejpam-3223	175	20	0	0	NUM
ejpam-3223	175	21	,	,	PUNCT
ejpam-3223	175	22	c	c	NOUN
ejpam-3223	175	23	=	=	SYM
ejpam-3223	175	24	1	1	NUM
ejpam-3223	175	25	and	and	CCONJ
ejpam-3223	175	26	m	m	PROPN
ejpam-3223	175	27	=	=	ADJ
ejpam-3223	175	28	0	0	NUM
ejpam-3223	175	29	,	,	PUNCT
ejpam-3223	175	30	we	we	PRON
ejpam-3223	175	31	have	have	VERB
ejpam-3223	175	32	w2k,1(u	w2k,1(u	NOUN
ejpam-3223	175	33	,	,	PUNCT
ejpam-3223	175	34	m	m	NOUN
ejpam-3223	175	35	=	=	NOUN
ejpam-3223	175	36	0	0	NUM
ejpam-3223	175	37	)	)	PUNCT
ejpam-3223	175	38	=	=	SYM
ejpam-3223	175	39	rh2k,1(u	rh2k,1(u	NOUN
ejpam-3223	175	40	)	)	PUNCT
ejpam-3223	175	41	reduces	reduce	VERB
ejpam-3223	175	42	to	to	ADP
ejpam-3223	175	43	(	(	PUNCT
ejpam-3223	175	44	−1)kre2k,1(v	−1)kre2k,1(v	NOUN
ejpam-3223	175	45	)	)	PUNCT
ejpam-3223	175	46	,	,	PUNCT
ejpam-3223	175	47	where	where	SCONJ
ejpam-3223	175	48	v	v	NOUN
ejpam-3223	175	49	=	=	SYM
ejpam-3223	175	50	c2(x21	c2(x21	NOUN
ejpam-3223	176	1	+	+	CCONJ
ejpam-3223	176	2	x22	x22	NUM
ejpam-3223	176	3	+	+	CCONJ
ejpam-3223	176	4	·	·	PUNCT
ejpam-3223	176	5	·	·	PUNCT
ejpam-3223	176	6	·	·	PUNCT
ejpam-3223	177	1	+	+	CCONJ
ejpam-3223	177	2	x2p	x2p	NUM
ejpam-3223	177	3	)	)	PUNCT
ejpam-3223	177	4	.	.	PUNCT
ejpam-3223	178	1	thus	thus	ADV
ejpam-3223	178	2	,	,	PUNCT
ejpam-3223	178	3	by	by	ADP
ejpam-3223	178	4	(	(	PUNCT
ejpam-3223	178	5	23	23	NUM
ejpam-3223	178	6	)	)	PUNCT
ejpam-3223	178	7	for	for	ADP
ejpam-3223	178	8	q	q	NOUN
ejpam-3223	178	9	=	=	SYM
ejpam-3223	178	10	0	0	NUM
ejpam-3223	178	11	,	,	PUNCT
ejpam-3223	178	12	c	c	NOUN
ejpam-3223	178	13	=	=	SYM
ejpam-3223	178	14	1	1	NUM
ejpam-3223	178	15	and	and	CCONJ
ejpam-3223	178	16	m	m	PROPN
ejpam-3223	178	17	=	=	ADJ
ejpam-3223	178	18	0	0	NUM
ejpam-3223	178	19	,	,	PUNCT
ejpam-3223	178	20	we	we	PRON
ejpam-3223	178	21	obtain	obtain	VERB
ejpam-3223	178	22	g(x	g(x	NOUN
ejpam-3223	178	23	)	)	PUNCT
ejpam-3223	179	1	=	=	SYM
ejpam-3223	179	2	(	(	PUNCT
ejpam-3223	179	3	−1)kre2k,1(v	−1)kre2k,1(v	NOUN
ejpam-3223	179	4	)	)	PUNCT
ejpam-3223	179	5	∗	∗	NOUN
ejpam-3223	179	6	(	(	PUNCT
ejpam-3223	179	7	−1)kre2k,1(v	−1)kre2k,1(v	NOUN
ejpam-3223	179	8	)	)	PUNCT
ejpam-3223	179	9	=	=	SYM
ejpam-3223	179	10	(	(	PUNCT
ejpam-3223	179	11	−1)2kre2k+2k,1(v	−1)2kre2k+2k,1(v	PROPN
ejpam-3223	179	12	)	)	PUNCT
ejpam-3223	179	13	=	=	SYM
ejpam-3223	179	14	re4k,1(v	re4k,1(v	PROPN
ejpam-3223	179	15	)	)	PUNCT
ejpam-3223	179	16	by	by	ADP
ejpam-3223	179	17	w.f	w.f	PROPN
ejpam-3223	179	18	.	.	PROPN
ejpam-3223	179	19	donoghue	donoghue	PROPN
ejpam-3223	179	20	(	(	PUNCT
ejpam-3223	180	1	[	[	X
ejpam-3223	180	2	11],p	11],p	NUM
ejpam-3223	180	3	158	158	NUM
ejpam-3223	180	4	)	)	PUNCT
ejpam-3223	180	5	.	.	PUNCT
ejpam-3223	181	1	that	that	PRON
ejpam-3223	181	2	complete	complete	VERB
ejpam-3223	181	3	the	the	DET
ejpam-3223	181	4	proofs	proof	NOUN
ejpam-3223	181	5	.	.	PUNCT
ejpam-3223	182	1	theorem	theorem	NOUN
ejpam-3223	182	2	2	2	NUM
ejpam-3223	182	3	.	.	PUNCT
ejpam-3223	182	4	given	give	VERB
ejpam-3223	182	5	the	the	DET
ejpam-3223	182	6	equation	equation	NOUN
ejpam-3223	182	7	}	}	PUNCT
ejpam-3223	182	8	kcu(x	kcu(x	PROPN
ejpam-3223	182	9	)	)	PUNCT
ejpam-3223	182	10	=	=	SYM
ejpam-3223	182	11	f(x	f(x	PROPN
ejpam-3223	182	12	)	)	PUNCT
ejpam-3223	182	13	,	,	PUNCT
ejpam-3223	182	14	(	(	PUNCT
ejpam-3223	182	15	34	34	NUM
ejpam-3223	182	16	)	)	PUNCT
ejpam-3223	182	17	where	where	SCONJ
ejpam-3223	182	18	f	f	PROPN
ejpam-3223	182	19	is	be	AUX
ejpam-3223	182	20	a	a	DET
ejpam-3223	182	21	given	give	VERB
ejpam-3223	182	22	generalized	generalized	ADJ
ejpam-3223	182	23	function	function	NOUN
ejpam-3223	182	24	and	and	CCONJ
ejpam-3223	182	25	u(x	u(x	NOUN
ejpam-3223	182	26	)	)	PUNCT
ejpam-3223	182	27	is	be	AUX
ejpam-3223	182	28	an	an	DET
ejpam-3223	182	29	unknown	unknown	ADJ
ejpam-3223	182	30	function	function	NOUN
ejpam-3223	182	31	,	,	PUNCT
ejpam-3223	182	32	we	we	PRON
ejpam-3223	182	33	obtain	obtain	VERB
ejpam-3223	182	34	u(x	u(x	NOUN
ejpam-3223	182	35	)	)	PUNCT
ejpam-3223	182	36	=	=	SYM
ejpam-3223	182	37	g(x	g(x	NOUN
ejpam-3223	182	38	)	)	PUNCT
ejpam-3223	182	39	∗	∗	NOUN
ejpam-3223	182	40	f(x	f(x	PROPN
ejpam-3223	182	41	)	)	PUNCT
ejpam-3223	182	42	is	be	AUX
ejpam-3223	182	43	a	a	DET
ejpam-3223	182	44	solution	solution	NOUN
ejpam-3223	182	45	of	of	ADP
ejpam-3223	182	46	the	the	DET
ejpam-3223	182	47	equation	equation	NOUN
ejpam-3223	182	48	(	(	PUNCT
ejpam-3223	182	49	34	34	NUM
ejpam-3223	182	50	)	)	PUNCT
ejpam-3223	182	51	,	,	PUNCT
ejpam-3223	182	52	where	where	SCONJ
ejpam-3223	182	53	g(x	g(x	NOUN
ejpam-3223	182	54	)	)	PUNCT
ejpam-3223	182	55	is	be	AUX
ejpam-3223	182	56	an	an	DET
ejpam-3223	182	57	elementary	elementary	ADJ
ejpam-3223	182	58	solution	solution	NOUN
ejpam-3223	182	59	for	for	ADP
ejpam-3223	182	60	}	}	PUNCT
ejpam-3223	182	61	kc	kc	PROPN
ejpam-3223	182	62	operator	operator	NOUN
ejpam-3223	182	63	.	.	PUNCT
ejpam-3223	183	1	references	reference	NOUN
ejpam-3223	183	2	398	398	NUM
ejpam-3223	183	3	proof	proof	NOUN
ejpam-3223	183	4	.	.	PUNCT
ejpam-3223	184	1	convolving	convolve	VERB
ejpam-3223	184	2	both	both	DET
ejpam-3223	184	3	sides	side	NOUN
ejpam-3223	184	4	of	of	ADP
ejpam-3223	184	5	(	(	PUNCT
ejpam-3223	184	6	34	34	NUM
ejpam-3223	184	7	)	)	PUNCT
ejpam-3223	184	8	by	by	ADP
ejpam-3223	184	9	g(x	g(x	PROPN
ejpam-3223	184	10	)	)	PUNCT
ejpam-3223	184	11	,	,	PUNCT
ejpam-3223	184	12	where	where	SCONJ
ejpam-3223	184	13	g(x	g(x	NOUN
ejpam-3223	184	14	)	)	PUNCT
ejpam-3223	184	15	is	be	AUX
ejpam-3223	184	16	an	an	DET
ejpam-3223	184	17	elementary	elementary	ADJ
ejpam-3223	184	18	solution	solution	NOUN
ejpam-3223	184	19	of	of	ADP
ejpam-3223	184	20	}	}	PUNCT
ejpam-3223	184	21	kc	kc	PROPN
ejpam-3223	184	22	in	in	ADP
ejpam-3223	184	23	theorem	theorem	NOUN
ejpam-3223	184	24	1	1	NUM
ejpam-3223	184	25	,	,	PUNCT
ejpam-3223	184	26	we	we	PRON
ejpam-3223	184	27	obtain	obtain	VERB
ejpam-3223	184	28	g(x	g(x	NOUN
ejpam-3223	184	29	)	)	PUNCT
ejpam-3223	184	30	∗}kcu(x	∗}kcu(x	PROPN
ejpam-3223	184	31	)	)	PUNCT
ejpam-3223	184	32	=	=	SYM
ejpam-3223	184	33	g(x	g(x	NOUN
ejpam-3223	184	34	)	)	PUNCT
ejpam-3223	184	35	∗	∗	NOUN
ejpam-3223	184	36	f(x	f(x	PROPN
ejpam-3223	184	37	)	)	PUNCT
ejpam-3223	184	38	or	or	CCONJ
ejpam-3223	184	39	,	,	PUNCT
ejpam-3223	184	40	}	}	PUNCT
ejpam-3223	184	41	kcg(x	kcg(x	PROPN
ejpam-3223	184	42	)	)	PUNCT
ejpam-3223	184	43	∗	∗	NOUN
ejpam-3223	184	44	u(x	u(x	PROPN
ejpam-3223	184	45	)	)	PUNCT
ejpam-3223	184	46	=	=	SYM
ejpam-3223	184	47	g(x	g(x	NOUN
ejpam-3223	184	48	)	)	PUNCT
ejpam-3223	184	49	∗	∗	NOUN
ejpam-3223	184	50	f(x	f(x	PROPN
ejpam-3223	184	51	)	)	PUNCT
ejpam-3223	184	52	applying	apply	VERB
ejpam-3223	184	53	the	the	DET
ejpam-3223	184	54	theorem	theorem	NOUN
ejpam-3223	184	55	1	1	NUM
ejpam-3223	184	56	,	,	PUNCT
ejpam-3223	184	57	we	we	PRON
ejpam-3223	184	58	have	have	VERB
ejpam-3223	184	59	δ	δ	PROPN
ejpam-3223	184	60	∗	∗	X
ejpam-3223	184	61	u(x	u(x	NOUN
ejpam-3223	184	62	)	)	PUNCT
ejpam-3223	184	63	=	=	SYM
ejpam-3223	184	64	g(x	g(x	NOUN
ejpam-3223	184	65	)	)	PUNCT
ejpam-3223	184	66	∗	∗	NOUN
ejpam-3223	184	67	f(x	f(x	PROPN
ejpam-3223	184	68	)	)	PUNCT
ejpam-3223	184	69	.	.	PUNCT
ejpam-3223	185	1	therefore	therefore	ADV
ejpam-3223	185	2	,	,	PUNCT
ejpam-3223	185	3	u(x	u(x	PROPN
ejpam-3223	185	4	)	)	PUNCT
ejpam-3223	185	5	=	=	SYM
ejpam-3223	186	1	g(x	g(x	NOUN
ejpam-3223	186	2	)	)	PUNCT
ejpam-3223	186	3	∗	∗	NOUN
ejpam-3223	186	4	f(x	f(x	PROPN
ejpam-3223	186	5	)	)	PUNCT
ejpam-3223	186	6	.	.	PUNCT
ejpam-3223	187	1	acknowledgements	acknowledgement	VERB
ejpam-3223	187	2	the	the	DET
ejpam-3223	187	3	author	author	NOUN
ejpam-3223	187	4	would	would	AUX
ejpam-3223	187	5	like	like	VERB
ejpam-3223	187	6	to	to	PART
ejpam-3223	187	7	thank	thank	VERB
ejpam-3223	187	8	the	the	DET
ejpam-3223	187	9	referee	referee	NOUN
ejpam-3223	187	10	for	for	ADP
ejpam-3223	187	11	his	his	PRON
ejpam-3223	187	12	suggestions	suggestion	NOUN
ejpam-3223	187	13	which	which	PRON
ejpam-3223	187	14	enhanced	enhance	VERB
ejpam-3223	187	15	the	the	DET
ejpam-3223	187	16	presentation	presentation	NOUN
ejpam-3223	187	17	of	of	ADP
ejpam-3223	187	18	the	the	DET
ejpam-3223	187	19	paper	paper	NOUN
ejpam-3223	187	20	.	.	PUNCT
ejpam-3223	188	1	the	the	DET
ejpam-3223	188	2	author	author	NOUN
ejpam-3223	188	3	was	be	AUX
ejpam-3223	188	4	supported	support	VERB
ejpam-3223	188	5	by	by	ADP
ejpam-3223	188	6	sakon	sakon	PROPN
ejpam-3223	188	7	nakhon	nakhon	PROPN
ejpam-3223	188	8	rajabhat	rajabhat	PROPN
ejpam-3223	188	9	university	university	PROPN
ejpam-3223	188	10	.	.	PUNCT
ejpam-3223	189	1	references	reference	NOUN
ejpam-3223	189	2	[	[	X
ejpam-3223	189	3	1	1	NUM
ejpam-3223	189	4	]	]	PUNCT
ejpam-3223	189	5	a.	a.	NOUN
ejpam-3223	189	6	h.	h.	PROPN
ejpam-3223	189	7	zemanian	zemanian	PROPN
ejpam-3223	189	8	,	,	PUNCT
ejpam-3223	189	9	distribution	distribution	NOUN
ejpam-3223	189	10	theory	theory	NOUN
ejpam-3223	189	11	and	and	CCONJ
ejpam-3223	189	12	transform	transform	VERB
ejpam-3223	189	13	analysis	analysis	NOUN
ejpam-3223	189	14	,	,	PUNCT
ejpam-3223	189	15	new	new	PROPN
ejpam-3223	189	16	york	york	PROPN
ejpam-3223	189	17	,	,	PUNCT
ejpam-3223	189	18	mcgraw	mcgraw	PROPN
ejpam-3223	189	19	-	-	PUNCT
ejpam-3223	189	20	hill	hill	NOUN
ejpam-3223	189	21	,	,	PUNCT
ejpam-3223	189	22	1964	1964	NUM
ejpam-3223	189	23	.	.	PUNCT
ejpam-3223	190	1	[	[	X
ejpam-3223	190	2	2	2	NUM
ejpam-3223	190	3	]	]	PUNCT
ejpam-3223	190	4	a.	a.	NOUN
ejpam-3223	190	5	kananthai	kananthai	PROPN
ejpam-3223	190	6	,	,	PUNCT
ejpam-3223	190	7	on	on	ADP
ejpam-3223	190	8	the	the	DET
ejpam-3223	190	9	solutions	solution	NOUN
ejpam-3223	190	10	of	of	ADP
ejpam-3223	190	11	the	the	DET
ejpam-3223	190	12	n	n	ADV
ejpam-3223	190	13	-	-	PUNCT
ejpam-3223	190	14	dimensional	dimensional	ADJ
ejpam-3223	190	15	diamond	diamond	NOUN
ejpam-3223	190	16	operator	operator	NOUN
ejpam-3223	190	17	,	,	PUNCT
ejpam-3223	190	18	appl	appl	PROPN
ejpam-3223	190	19	.	.	PROPN
ejpam-3223	190	20	math	math	PROPN
ejpam-3223	190	21	.	.	PUNCT
ejpam-3223	191	1	comput	comput	NOUN
ejpam-3223	191	2	.	.	PUNCT
ejpam-3223	192	1	88	88	NUM
ejpam-3223	192	2	(	(	PUNCT
ejpam-3223	192	3	1997	1997	NUM
ejpam-3223	192	4	)	)	PUNCT
ejpam-3223	192	5	,	,	PUNCT
ejpam-3223	192	6	27–37	27–37	NUM
ejpam-3223	192	7	.	.	PUNCT
ejpam-3223	193	1	[	[	X
ejpam-3223	193	2	3	3	NUM
ejpam-3223	193	3	]	]	PUNCT
ejpam-3223	193	4	a.	a.	NOUN
ejpam-3223	193	5	kananthai	kananthai	PROPN
ejpam-3223	193	6	,	,	PUNCT
ejpam-3223	193	7	on	on	ADP
ejpam-3223	193	8	the	the	DET
ejpam-3223	193	9	convolution	convolution	NOUN
ejpam-3223	193	10	equation	equation	NOUN
ejpam-3223	193	11	related	relate	VERB
ejpam-3223	193	12	to	to	ADP
ejpam-3223	193	13	the	the	DET
ejpam-3223	193	14	diamond	diamond	NOUN
ejpam-3223	193	15	kernel	kernel	NOUN
ejpam-3223	193	16	of	of	ADP
ejpam-3223	193	17	marcel	marcel	PROPN
ejpam-3223	193	18	riesz	riesz	PROPN
ejpam-3223	193	19	,	,	PUNCT
ejpam-3223	193	20	j.	j.	PROPN
ejpam-3223	193	21	comp	comp	PROPN
ejpam-3223	193	22	.	.	PUNCT
ejpam-3223	194	1	appl	appl	PROPN
ejpam-3223	194	2	.	.	PROPN
ejpam-3223	194	3	math	math	NOUN
ejpam-3223	194	4	.	.	PUNCT
ejpam-3223	195	1	100	100	NUM
ejpam-3223	195	2	(	(	PUNCT
ejpam-3223	195	3	1998	1998	NUM
ejpam-3223	195	4	)	)	PUNCT
ejpam-3223	195	5	,	,	PUNCT
ejpam-3223	196	1	33–39	33–39	NUM
ejpam-3223	196	2	.	.	PUNCT
ejpam-3223	197	1	[	[	X
ejpam-3223	197	2	4	4	NUM
ejpam-3223	197	3	]	]	PUNCT
ejpam-3223	197	4	a.	a.	NOUN
ejpam-3223	197	5	kananthai	kananthai	PROPN
ejpam-3223	197	6	,	,	PUNCT
ejpam-3223	197	7	on	on	ADP
ejpam-3223	197	8	the	the	DET
ejpam-3223	197	9	convolution	convolution	NOUN
ejpam-3223	197	10	of	of	ADP
ejpam-3223	197	11	the	the	DET
ejpam-3223	197	12	diamond	diamond	NOUN
ejpam-3223	197	13	kernel	kernel	NOUN
ejpam-3223	197	14	of	of	ADP
ejpam-3223	197	15	marcel	marcel	PROPN
ejpam-3223	197	16	riesz	riesz	PROPN
ejpam-3223	197	17	,	,	PUNCT
ejpam-3223	197	18	appl	appl	PROPN
ejpam-3223	197	19	.	.	PROPN
ejpam-3223	197	20	math	math	NOUN
ejpam-3223	197	21	.	.	PUNCT
ejpam-3223	198	1	comput	comput	NOUN
ejpam-3223	198	2	.	.	PUNCT
ejpam-3223	199	1	114	114	NUM
ejpam-3223	199	2	(	(	PUNCT
ejpam-3223	199	3	2000	2000	NUM
ejpam-3223	199	4	)	)	PUNCT
ejpam-3223	199	5	,	,	PUNCT
ejpam-3223	200	1	95–101	95–101	PRON
ejpam-3223	200	2	.	.	PUNCT
ejpam-3223	201	1	[	[	X
ejpam-3223	201	2	5	5	NUM
ejpam-3223	201	3	]	]	PUNCT
ejpam-3223	201	4	a.	a.	NOUN
ejpam-3223	201	5	kananthai	kananthai	PROPN
ejpam-3223	201	6	,	,	PUNCT
ejpam-3223	201	7	on	on	ADP
ejpam-3223	201	8	the	the	DET
ejpam-3223	201	9	convolution	convolution	NOUN
ejpam-3223	201	10	equation	equation	NOUN
ejpam-3223	201	11	related	relate	VERB
ejpam-3223	201	12	to	to	ADP
ejpam-3223	201	13	the	the	DET
ejpam-3223	201	14	n	n	CCONJ
ejpam-3223	201	15	-dimensional	-dimensional	ADJ
ejpam-3223	201	16	ultrahyperbolic	ultrahyperbolic	ADJ
ejpam-3223	201	17	operator	operator	NOUN
ejpam-3223	201	18	,	,	PUNCT
ejpam-3223	201	19	j.	j.	PROPN
ejpam-3223	201	20	comp	comp	PROPN
ejpam-3223	201	21	.	.	PUNCT
ejpam-3223	202	1	appl	appl	PROPN
ejpam-3223	202	2	.	.	PROPN
ejpam-3223	202	3	math	math	NOUN
ejpam-3223	202	4	.	.	PUNCT
ejpam-3223	203	1	115	115	NUM
ejpam-3223	203	2	(	(	PUNCT
ejpam-3223	203	3	2000	2000	NUM
ejpam-3223	203	4	)	)	PUNCT
ejpam-3223	203	5	,	,	PUNCT
ejpam-3223	203	6	301–308	301–308	NUM
ejpam-3223	203	7	.	.	PUNCT
ejpam-3223	204	1	[	[	X
ejpam-3223	204	2	6	6	NUM
ejpam-3223	204	3	]	]	PUNCT
ejpam-3223	204	4	j.	j.	PROPN
ejpam-3223	204	5	tariboon	tariboon	PROPN
ejpam-3223	204	6	,	,	PUNCT
ejpam-3223	204	7	and	and	CCONJ
ejpam-3223	204	8	a.	a.	NOUN
ejpam-3223	204	9	kananthai	kananthai	PROPN
ejpam-3223	204	10	,	,	PUNCT
ejpam-3223	204	11	on	on	ADP
ejpam-3223	204	12	the	the	DET
ejpam-3223	204	13	green	green	ADJ
ejpam-3223	204	14	function	function	NOUN
ejpam-3223	204	15	of	of	ADP
ejpam-3223	204	16	the	the	DET
ejpam-3223	204	17	(	(	PUNCT
ejpam-3223	204	18	⊕	⊕	PROPN
ejpam-3223	204	19	+	+	CCONJ
ejpam-3223	204	20	m2	m2	PROPN
ejpam-3223	204	21	)	)	PUNCT
ejpam-3223	204	22	operator	operator	NOUN
ejpam-3223	204	23	,	,	PUNCT
ejpam-3223	204	24	integral	integral	ADJ
ejpam-3223	204	25	transform	transform	NOUN
ejpam-3223	204	26	and	and	CCONJ
ejpam-3223	204	27	special	special	ADJ
ejpam-3223	204	28	functions	function	NOUN
ejpam-3223	204	29	18	18	NUM
ejpam-3223	204	30	(	(	PUNCT
ejpam-3223	204	31	2007	2007	NUM
ejpam-3223	204	32	)	)	PUNCT
ejpam-3223	204	33	,	,	PUNCT
ejpam-3223	204	34	297–304	297–304	NUM
ejpam-3223	204	35	.	.	PUNCT
ejpam-3223	205	1	[	[	X
ejpam-3223	205	2	7	7	X
ejpam-3223	205	3	]	]	X
ejpam-3223	205	4	m.	m.	NOUN
ejpam-3223	205	5	a.	a.	NOUN
ejpam-3223	205	6	tellez	tellez	PROPN
ejpam-3223	205	7	,	,	PUNCT
ejpam-3223	205	8	the	the	DET
ejpam-3223	205	9	distributional	distributional	ADJ
ejpam-3223	205	10	hankel	hankel	NOUN
ejpam-3223	205	11	transform	transform	NOUN
ejpam-3223	205	12	of	of	ADP
ejpam-3223	205	13	marcel	marcel	PROPN
ejpam-3223	205	14	riesz	riesz	PROPN
ejpam-3223	205	15	’s	’s	PART
ejpam-3223	205	16	ultra	ultra	ADJ
ejpam-3223	205	17	-	-	ADJ
ejpam-3223	205	18	hyperbolic	hyperbolic	ADJ
ejpam-3223	205	19	kernel	kernel	NOUN
ejpam-3223	205	20	,	,	PUNCT
ejpam-3223	205	21	studies	study	NOUN
ejpam-3223	205	22	in	in	ADP
ejpam-3223	205	23	applied	applied	ADJ
ejpam-3223	205	24	mathematics	mathematic	NOUN
ejpam-3223	205	25	93	93	NUM
ejpam-3223	205	26	(	(	PUNCT
ejpam-3223	205	27	1994	1994	NUM
ejpam-3223	205	28	)	)	PUNCT
ejpam-3223	205	29	,	,	PUNCT
ejpam-3223	205	30	133–162	133–162	NUM
ejpam-3223	205	31	.	.	PUNCT
ejpam-3223	206	1	[	[	X
ejpam-3223	206	2	8	8	NUM
ejpam-3223	206	3	]	]	X
ejpam-3223	206	4	m.	m.	NOUN
ejpam-3223	206	5	a.	a.	NOUN
ejpam-3223	206	6	tellez	tellez	PROPN
ejpam-3223	206	7	,	,	PUNCT
ejpam-3223	206	8	the	the	DET
ejpam-3223	206	9	convolution	convolution	NOUN
ejpam-3223	206	10	product	product	NOUN
ejpam-3223	206	11	of	of	ADP
ejpam-3223	206	12	wα(u	wα(u	NOUN
ejpam-3223	206	13	,	,	PUNCT
ejpam-3223	206	14	m)∗wβ(u	m)∗wβ(u	PROPN
ejpam-3223	206	15	,	,	PUNCT
ejpam-3223	206	16	m	m	PROPN
ejpam-3223	206	17	)	)	PUNCT
ejpam-3223	206	18	,	,	PUNCT
ejpam-3223	206	19	mathematic	mathematic	ADJ
ejpam-3223	206	20	38	38	NUM
ejpam-3223	206	21	(	(	PUNCT
ejpam-3223	206	22	195196	195196	NUM
ejpam-3223	206	23	)	)	PUNCT
ejpam-3223	206	24	,	,	PUNCT
ejpam-3223	206	25	105–111	105–111	NUM
ejpam-3223	206	26	.	.	PUNCT
ejpam-3223	206	27	references	reference	NOUN
ejpam-3223	206	28	399	399	NUM
ejpam-3223	207	1	[	[	X
ejpam-3223	207	2	9	9	NUM
ejpam-3223	207	3	]	]	PUNCT
ejpam-3223	207	4	s.	s.	PROPN
ejpam-3223	207	5	bupasiri	bupasiri	PROPN
ejpam-3223	207	6	,	,	PUNCT
ejpam-3223	207	7	on	on	ADP
ejpam-3223	207	8	the	the	DET
ejpam-3223	207	9	solution	solution	NOUN
ejpam-3223	207	10	of	of	ADP
ejpam-3223	207	11	the	the	DET
ejpam-3223	207	12	n	n	CCONJ
ejpam-3223	207	13	-	-	PUNCT
ejpam-3223	207	14	dimentional	dimentional	ADJ
ejpam-3223	207	15	operator	operator	NOUN
ejpam-3223	207	16	related	relate	VERB
ejpam-3223	207	17	to	to	ADP
ejpam-3223	207	18	the	the	DET
ejpam-3223	207	19	diamond	diamond	NOUN
ejpam-3223	207	20	operator	operator	NOUN
ejpam-3223	207	21	,	,	PUNCT
ejpam-3223	207	22	fjms	fjms	NOUN
ejpam-3223	207	23	.	.	PROPN
ejpam-3223	208	1	45	45	NUM
ejpam-3223	208	2	(	(	PUNCT
ejpam-3223	208	3	2010	2010	NUM
ejpam-3223	208	4	)	)	PUNCT
ejpam-3223	208	5	,	,	PUNCT
ejpam-3223	208	6	69–80	69–80	NUM
ejpam-3223	208	7	.	.	PUNCT
ejpam-3223	209	1	[	[	X
ejpam-3223	209	2	10	10	NUM
ejpam-3223	209	3	]	]	PUNCT
ejpam-3223	209	4	s.	s.	PROPN
ejpam-3223	209	5	e.	e.	PROPN
ejpam-3223	209	6	trione	trione	PROPN
ejpam-3223	209	7	,	,	PUNCT
ejpam-3223	209	8	on	on	ADP
ejpam-3223	209	9	marcel	marcel	PROPN
ejpam-3223	209	10	riesz	riesz	PROPN
ejpam-3223	209	11	’s	’s	PART
ejpam-3223	209	12	ultra	ultra	ADJ
ejpam-3223	209	13	-	-	ADJ
ejpam-3223	209	14	hyperbolic	hyperbolic	ADJ
ejpam-3223	209	15	kernel	kernel	NOUN
ejpam-3223	209	16	,	,	PUNCT
ejpam-3223	209	17	trabajos	trabajos	PROPN
ejpam-3223	209	18	de	de	PROPN
ejpam-3223	209	19	mathematica	mathematica	PROPN
ejpam-3223	209	20	116	116	NUM
ejpam-3223	209	21	(	(	PUNCT
ejpam-3223	209	22	1987	1987	NUM
ejpam-3223	209	23	)	)	PUNCT
ejpam-3223	209	24	.	.	PUNCT
ejpam-3223	210	1	[	[	X
ejpam-3223	210	2	11	11	NUM
ejpam-3223	210	3	]	]	PUNCT
ejpam-3223	210	4	w.	w.	PROPN
ejpam-3223	210	5	f.	f.	PROPN
ejpam-3223	210	6	donoghue	donoghue	PROPN
ejpam-3223	210	7	,	,	PUNCT
ejpam-3223	210	8	distribution	distribution	NOUN
ejpam-3223	210	9	and	and	CCONJ
ejpam-3223	210	10	fourier	fourier	NOUN
ejpam-3223	210	11	transform	transform	NOUN
ejpam-3223	210	12	,	,	PUNCT
ejpam-3223	210	13	new	new	PROPN
ejpam-3223	210	14	york	york	PROPN
ejpam-3223	210	15	,	,	PUNCT
ejpam-3223	210	16	academic	academic	ADJ
ejpam-3223	210	17	press	press	NOUN
ejpam-3223	210	18	,	,	PUNCT
ejpam-3223	210	19	1969	1969	NUM
ejpam-3223	210	20	.	.	PUNCT
ejpam-3223	211	1	[	[	X
ejpam-3223	211	2	12	12	NUM
ejpam-3223	211	3	]	]	X
ejpam-3223	211	4	y.	y.	PROPN
ejpam-3223	211	5	nozaki	nozaki	PROPN
ejpam-3223	211	6	,	,	PUNCT
ejpam-3223	211	7	on	on	ADP
ejpam-3223	211	8	reimann	reimann	NOUN
ejpam-3223	211	9	-	-	PUNCT
ejpam-3223	211	10	liouvlle	liouvlle	NOUN
ejpam-3223	211	11	integral	integral	ADJ
ejpam-3223	211	12	of	of	ADP
ejpam-3223	211	13	ultra	ultra	ADJ
ejpam-3223	211	14	-	-	ADJ
ejpam-3223	211	15	hyperbolic	hyperbolic	ADJ
ejpam-3223	211	16	type	type	NOUN
ejpam-3223	211	17	,	,	PUNCT
ejpam-3223	211	18	kodai	kodai	PROPN
ejpam-3223	211	19	mathemaical	mathemaical	ADJ
ejpam-3223	211	20	seminar	seminar	NOUN
ejpam-3223	211	21	report	report	NOUN
ejpam-3223	211	22	6	6	NUM
ejpam-3223	211	23	(	(	PUNCT
ejpam-3223	211	24	1964	1964	NUM
ejpam-3223	211	25	)	)	PUNCT
ejpam-3223	211	26	,	,	PUNCT
ejpam-3223	211	27	69–87	69–87	NUM
ejpam-3223	211	28	.	.	PUNCT