id	sid	tid	token	lemma	pos
ejpam-323	1	1	12_323_khelifi.dvi	12_323_khelifi.dvi	PROPN
ejpam-323	1	2	european	european	PROPN
ejpam-323	1	3	journal	journal	PROPN
ejpam-323	1	4	of	of	ADP
ejpam-323	1	5	pure	pure	ADJ
ejpam-323	1	6	and	and	CCONJ
ejpam-323	1	7	applied	apply	VERB
ejpam-323	1	8	mathematics	mathematic	NOUN
ejpam-323	1	9	vol	vol	NOUN
ejpam-323	1	10	.	.	PUNCT
ejpam-323	2	1	3	3	NUM
ejpam-323	2	2	,	,	PUNCT
ejpam-323	2	3	no	no	INTJ
ejpam-323	2	4	.	.	NOUN
ejpam-323	2	5	2	2	NUM
ejpam-323	2	6	,	,	PUNCT
ejpam-323	2	7	2010	2010	NUM
ejpam-323	2	8	,	,	PUNCT
ejpam-323	2	9	282	282	NUM
ejpam-323	2	10	-	-	SYM
ejpam-323	2	11	294	294	NUM
ejpam-323	2	12	issn	issn	PROPN
ejpam-323	2	13	1307	1307	NUM
ejpam-323	2	14	-	-	SYM
ejpam-323	2	15	5543	5543	NUM
ejpam-323	2	16	–	–	PUNCT
ejpam-323	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-323	2	18	estimates	estimate	VERB
ejpam-323	2	19	for	for	ADP
ejpam-323	2	20	resonant	resonant	ADJ
ejpam-323	2	21	frequencies	frequency	NOUN
ejpam-323	2	22	under	under	ADP
ejpam-323	2	23	boundary	boundary	ADJ
ejpam-323	2	24	deformation	deformation	NOUN
ejpam-323	2	25	in	in	ADP
ejpam-323	2	26	multi	multi	ADJ
ejpam-323	2	27	-	-	ADJ
ejpam-323	2	28	dimensional	dimensional	ADJ
ejpam-323	2	29	space	space	NOUN
ejpam-323	2	30	abdessatar	abdessatar	NOUN
ejpam-323	2	31	khelifi∗	khelifi∗	NOUN
ejpam-323	2	32	and	and	CCONJ
ejpam-323	2	33	m.	m.	PROPN
ejpam-323	2	34	nour	nour	PROPN
ejpam-323	2	35	.	.	PUNCT
ejpam-323	3	1	shamma	shamma	PROPN
ejpam-323	3	2	department	department	PROPN
ejpam-323	3	3	of	of	ADP
ejpam-323	3	4	mathematics	mathematics	PROPN
ejpam-323	3	5	&	&	CCONJ
ejpam-323	3	6	faculty	faculty	NOUN
ejpam-323	3	7	of	of	ADP
ejpam-323	3	8	sciences	sciences	PROPN
ejpam-323	3	9	&	&	CCONJ
ejpam-323	3	10	arts	art	NOUN
ejpam-323	3	11	,	,	PUNCT
ejpam-323	3	12	al	al	PROPN
ejpam-323	3	13	gassim	gassim	PROPN
ejpam-323	3	14	university	university	PROPN
ejpam-323	3	15	,	,	PUNCT
ejpam-323	3	16	al	al	PROPN
ejpam-323	3	17	-	-	PUNCT
ejpam-323	3	18	rass	rass	PROPN
ejpam-323	3	19	province	province	NOUN
ejpam-323	3	20	,	,	PUNCT
ejpam-323	3	21	kingdom	kingdom	NOUN
ejpam-323	3	22	of	of	ADP
ejpam-323	3	23	saudi	saudi	PROPN
ejpam-323	3	24	arabia	arabia	PROPN
ejpam-323	3	25	abstract	abstract	NOUN
ejpam-323	3	26	.	.	PUNCT
ejpam-323	4	1	in	in	ADP
ejpam-323	4	2	multi	multi	ADJ
ejpam-323	4	3	-	-	ADJ
ejpam-323	4	4	dimensional	dimensional	ADJ
ejpam-323	4	5	space	space	NOUN
ejpam-323	4	6	,	,	PUNCT
ejpam-323	4	7	we	we	PRON
ejpam-323	4	8	address	address	VERB
ejpam-323	4	9	the	the	DET
ejpam-323	4	10	integral	integral	ADJ
ejpam-323	4	11	equation	equation	NOUN
ejpam-323	4	12	method	method	NOUN
ejpam-323	4	13	to	to	PART
ejpam-323	4	14	investigate	investigate	VERB
ejpam-323	4	15	the	the	DET
ejpam-323	4	16	interplay	interplay	NOUN
ejpam-323	4	17	between	between	ADP
ejpam-323	4	18	the	the	DET
ejpam-323	4	19	geometry	geometry	NOUN
ejpam-323	4	20	,	,	PUNCT
ejpam-323	4	21	boundary	boundary	ADJ
ejpam-323	4	22	conditions	condition	NOUN
ejpam-323	4	23	and	and	CCONJ
ejpam-323	4	24	the	the	DET
ejpam-323	4	25	properties	property	NOUN
ejpam-323	4	26	of	of	ADP
ejpam-323	4	27	the	the	DET
ejpam-323	4	28	resonant	resonant	ADJ
ejpam-323	4	29	frequencies	frequency	NOUN
ejpam-323	4	30	and	and	CCONJ
ejpam-323	4	31	their	their	PRON
ejpam-323	4	32	associated	associated	ADJ
ejpam-323	4	33	eigenfunctions	eigenfunction	NOUN
ejpam-323	4	34	under	under	ADP
ejpam-323	4	35	boundary	boundary	ADJ
ejpam-323	4	36	variations	variation	NOUN
ejpam-323	4	37	of	of	ADP
ejpam-323	4	38	domain	domain	NOUN
ejpam-323	4	39	.	.	PUNCT
ejpam-323	5	1	we	we	PRON
ejpam-323	5	2	provide	provide	VERB
ejpam-323	5	3	a	a	DET
ejpam-323	5	4	rigorous	rigorous	ADJ
ejpam-323	5	5	derivation	derivation	NOUN
ejpam-323	5	6	of	of	ADP
ejpam-323	5	7	asymptotic	asymptotic	ADJ
ejpam-323	5	8	expansions	expansion	NOUN
ejpam-323	5	9	for	for	ADP
ejpam-323	5	10	eigenfunctions	eigenfunction	NOUN
ejpam-323	5	11	and	and	CCONJ
ejpam-323	5	12	we	we	PRON
ejpam-323	5	13	establish	establish	VERB
ejpam-323	5	14	error	error	NOUN
ejpam-323	5	15	estimations	estimation	NOUN
ejpam-323	5	16	for	for	ADP
ejpam-323	5	17	both	both	DET
ejpam-323	5	18	resonant	resonant	ADJ
ejpam-323	5	19	frequencies	frequency	NOUN
ejpam-323	5	20	and	and	CCONJ
ejpam-323	5	21	eigenfunctions	eigenfunction	NOUN
ejpam-323	5	22	of	of	ADP
ejpam-323	5	23	the	the	DET
ejpam-323	5	24	helmholtz	helmholtz	NOUN
ejpam-323	5	25	eigenvalue	eigenvalue	PROPN
ejpam-323	5	26	problem	problem	NOUN
ejpam-323	5	27	.	.	PUNCT
ejpam-323	6	1	2000	2000	NUM
ejpam-323	6	2	mathematics	mathematic	NOUN
ejpam-323	6	3	subject	subject	NOUN
ejpam-323	6	4	classifications	classification	NOUN
ejpam-323	6	5	:	:	PUNCT
ejpam-323	6	6	35c15	35c15	NUM
ejpam-323	6	7	,	,	PUNCT
ejpam-323	6	8	35p05	35p05	NUM
ejpam-323	6	9	,	,	PUNCT
ejpam-323	6	10	45c05	45c05	NUM
ejpam-323	6	11	key	key	ADJ
ejpam-323	6	12	words	word	NOUN
ejpam-323	6	13	and	and	CCONJ
ejpam-323	6	14	phrases	phrase	NOUN
ejpam-323	6	15	:	:	PUNCT
ejpam-323	6	16	resonant	resonant	ADJ
ejpam-323	6	17	frequencies	frequency	NOUN
ejpam-323	6	18	,	,	PUNCT
ejpam-323	6	19	boundary	boundary	ADJ
ejpam-323	6	20	integral	integral	ADJ
ejpam-323	6	21	equation	equation	NOUN
ejpam-323	6	22	,	,	PUNCT
ejpam-323	6	23	error	error	NOUN
ejpam-323	6	24	estimates	estimate	VERB
ejpam-323	6	25	1	1	NUM
ejpam-323	6	26	.	.	X
ejpam-323	7	1	introduction	introduction	NOUN
ejpam-323	7	2	the	the	DET
ejpam-323	7	3	resonant	resonant	ADJ
ejpam-323	7	4	frequencies	frequency	NOUN
ejpam-323	7	5	may	may	AUX
ejpam-323	7	6	evolve	evolve	VERB
ejpam-323	7	7	under	under	ADP
ejpam-323	7	8	shape	shape	NOUN
ejpam-323	7	9	deformation	deformation	NOUN
ejpam-323	7	10	,	,	PUNCT
ejpam-323	7	11	as	as	SCONJ
ejpam-323	7	12	separated	separate	VERB
ejpam-323	7	13	,	,	PUNCT
ejpam-323	7	14	distinct	distinct	ADJ
ejpam-323	7	15	eigenvalues	eigenvalue	NOUN
ejpam-323	7	16	of	of	ADP
ejpam-323	7	17	the	the	DET
ejpam-323	7	18	helmholtz	helmholtz	NOUN
ejpam-323	7	19	eigenvalue	eigenvalue	PROPN
ejpam-323	7	20	problem	problem	NOUN
ejpam-323	7	21	.	.	PUNCT
ejpam-323	8	1	but	but	CCONJ
ejpam-323	8	2	,	,	PUNCT
ejpam-323	8	3	the	the	DET
ejpam-323	8	4	main	main	ADJ
ejpam-323	8	5	difficulty	difficulty	NOUN
ejpam-323	8	6	in	in	ADP
ejpam-323	8	7	solving	solve	VERB
ejpam-323	8	8	eigenvalue	eigenvalue	NOUN
ejpam-323	8	9	problems	problem	NOUN
ejpam-323	8	10	relates	relate	VERB
ejpam-323	8	11	to	to	ADP
ejpam-323	8	12	the	the	DET
ejpam-323	8	13	continuation	continuation	NOUN
ejpam-323	8	14	of	of	ADP
ejpam-323	8	15	multiple	multiple	ADJ
ejpam-323	8	16	eigenvalues	eigenvalue	NOUN
ejpam-323	8	17	of	of	ADP
ejpam-323	8	18	the	the	DET
ejpam-323	8	19	unperturbed	unperturbed	ADJ
ejpam-323	8	20	configuration	configuration	NOUN
ejpam-323	8	21	.	.	PUNCT
ejpam-323	9	1	the	the	DET
ejpam-323	9	2	properties	property	NOUN
ejpam-323	9	3	of	of	ADP
ejpam-323	9	4	eigenvalue	eigenvalue	ADJ
ejpam-323	9	5	problems	problem	NOUN
ejpam-323	9	6	under	under	ADP
ejpam-323	9	7	shape	shape	NOUN
ejpam-323	9	8	deformation	deformation	NOUN
ejpam-323	9	9	have	have	AUX
ejpam-323	9	10	been	be	AUX
ejpam-323	9	11	the	the	DET
ejpam-323	9	12	subject	subject	NOUN
ejpam-323	9	13	of	of	ADP
ejpam-323	9	14	comprehensive	comprehensive	ADJ
ejpam-323	9	15	studies	study	NOUN
ejpam-323	9	16	[	[	X
ejpam-323	9	17	9	9	NUM
ejpam-323	9	18	,	,	PUNCT
ejpam-323	9	19	22	22	NUM
ejpam-323	9	20	]	]	PUNCT
ejpam-323	9	21	and	and	CCONJ
ejpam-323	9	22	the	the	DET
ejpam-323	9	23	area	area	NOUN
ejpam-323	9	24	continues	continue	VERB
ejpam-323	9	25	to	to	PART
ejpam-323	9	26	carry	carry	VERB
ejpam-323	9	27	great	great	ADJ
ejpam-323	9	28	importance	importance	NOUN
ejpam-323	9	29	to	to	ADP
ejpam-323	9	30	this	this	DET
ejpam-323	9	31	day	day	NOUN
ejpam-323	10	1	[	[	X
ejpam-323	10	2	4	4	NUM
ejpam-323	10	3	,	,	PUNCT
ejpam-323	10	4	7	7	NUM
ejpam-323	10	5	,	,	PUNCT
ejpam-323	10	6	6	6	NUM
ejpam-323	10	7	,	,	PUNCT
ejpam-323	10	8	8	8	NUM
ejpam-323	10	9	,	,	PUNCT
ejpam-323	10	10	12	12	NUM
ejpam-323	10	11	,	,	PUNCT
ejpam-323	10	12	13	13	NUM
ejpam-323	10	13	,	,	PUNCT
ejpam-323	10	14	14	14	NUM
ejpam-323	10	15	,	,	PUNCT
ejpam-323	10	16	15	15	NUM
ejpam-323	10	17	]	]	PUNCT
ejpam-323	10	18	.	.	PUNCT
ejpam-323	11	1	a	a	DET
ejpam-323	11	2	substantial	substantial	ADJ
ejpam-323	11	3	portion	portion	NOUN
ejpam-323	11	4	of	of	ADP
ejpam-323	11	5	these	these	DET
ejpam-323	11	6	investigations	investigation	NOUN
ejpam-323	11	7	relate	relate	VERB
ejpam-323	11	8	to	to	ADP
ejpam-323	11	9	properties	property	NOUN
ejpam-323	11	10	of	of	ADP
ejpam-323	11	11	smoothness	smoothness	NOUN
ejpam-323	11	12	and	and	CCONJ
ejpam-323	11	13	analyticity	analyticity	NOUN
ejpam-323	11	14	of	of	ADP
ejpam-323	11	15	eigenvalues	eigenvalue	NOUN
ejpam-323	11	16	and	and	CCONJ
ejpam-323	11	17	eigenfunctions	eigenfunction	NOUN
ejpam-323	11	18	with	with	ADP
ejpam-323	11	19	respect	respect	NOUN
ejpam-323	11	20	to	to	ADP
ejpam-323	11	21	perturbations	perturbation	NOUN
ejpam-323	11	22	.	.	PUNCT
ejpam-323	12	1	bruno	bruno	PROPN
ejpam-323	12	2	and	and	CCONJ
ejpam-323	12	3	reitich	reitich	PROPN
ejpam-323	12	4	have	have	AUX
ejpam-323	12	5	presented	present	VERB
ejpam-323	12	6	in	in	ADP
ejpam-323	12	7	[	[	X
ejpam-323	12	8	4	4	NUM
ejpam-323	12	9	,	,	PUNCT
ejpam-323	12	10	theorem	theorem	ADJ
ejpam-323	12	11	2	2	NUM
ejpam-323	12	12	,	,	PUNCT
ejpam-323	12	13	p.172	p.172	NOUN
ejpam-323	12	14	and	and	CCONJ
ejpam-323	12	15	section	section	NOUN
ejpam-323	12	16	3	3	NUM
ejpam-323	12	17	,	,	PUNCT
ejpam-323	12	18	pp.180	pp.180	NOUN
ejpam-323	12	19	-	-	PUNCT
ejpam-323	12	20	183	183	NUM
ejpam-323	12	21	]	]	PUNCT
ejpam-323	12	22	some	some	DET
ejpam-323	12	23	explicit	explicit	ADJ
ejpam-323	12	24	constructions	construction	NOUN
ejpam-323	12	25	of	of	ADP
ejpam-323	12	26	high	high	ADJ
ejpam-323	12	27	-	-	PUNCT
ejpam-323	12	28	order	order	NOUN
ejpam-323	12	29	boundary	boundary	ADJ
ejpam-323	12	30	perturbation	perturbation	NOUN
ejpam-323	12	31	expansions	expansion	NOUN
ejpam-323	12	32	for	for	ADP
ejpam-323	12	33	eigenelements	eigenelement	NOUN
ejpam-323	12	34	in	in	ADP
ejpam-323	12	35	two	two	NUM
ejpam-323	12	36	dimensions	dimension	NOUN
ejpam-323	12	37	.	.	PUNCT
ejpam-323	13	1	their	their	PRON
ejpam-323	13	2	algorithm	algorithm	NOUN
ejpam-323	13	3	is	be	AUX
ejpam-323	13	4	based	base	VERB
ejpam-323	13	5	on	on	ADP
ejpam-323	13	6	certain	certain	ADJ
ejpam-323	13	7	properties	property	NOUN
ejpam-323	13	8	of	of	ADP
ejpam-323	13	9	joint	joint	ADJ
ejpam-323	13	10	analytic	analytic	ADJ
ejpam-323	13	11	dependence	dependence	NOUN
ejpam-323	13	12	on	on	ADP
ejpam-323	13	13	the	the	DET
ejpam-323	13	14	boundary	boundary	ADJ
ejpam-323	13	15	perturbations	perturbation	NOUN
ejpam-323	13	16	and	and	CCONJ
ejpam-323	13	17	spatial	spatial	ADJ
ejpam-323	13	18	variables	variable	NOUN
ejpam-323	13	19	of	of	ADP
ejpam-323	13	20	the	the	DET
ejpam-323	13	21	eigenfunctions	eigenfunction	NOUN
ejpam-323	13	22	.	.	PUNCT
ejpam-323	14	1	in	in	ADP
ejpam-323	14	2	a	a	DET
ejpam-323	14	3	series	series	NOUN
ejpam-323	14	4	of	of	ADP
ejpam-323	14	5	papers	paper	NOUN
ejpam-323	14	6	[	[	X
ejpam-323	14	7	19]-[21	19]-[21	X
ejpam-323	14	8	]	]	X
ejpam-323	14	9	,	,	PUNCT
ejpam-323	14	10	ozawa	ozawa	PROPN
ejpam-323	14	11	derived	derive	VERB
ejpam-323	14	12	the	the	DET
ejpam-323	14	13	leading	lead	VERB
ejpam-323	14	14	-	-	PUNCT
ejpam-323	14	15	order	order	NOUN
ejpam-323	14	16	term	term	NOUN
ejpam-323	14	17	in	in	ADP
ejpam-323	14	18	the	the	DET
ejpam-323	14	19	asymptotic	asymptotic	ADJ
ejpam-323	14	20	expansions	expansion	NOUN
ejpam-323	14	21	of	of	ADP
ejpam-323	14	22	simple	simple	ADJ
ejpam-323	14	23	eigenvalues	eigenvalue	NOUN
ejpam-323	14	24	in	in	ADP
ejpam-323	14	25	domain	domain	NOUN
ejpam-323	14	26	with	with	ADP
ejpam-323	14	27	a	a	DET
ejpam-323	14	28	specific	specific	ADJ
ejpam-323	14	29	geometry	geometry	NOUN
ejpam-323	14	30	.	.	PUNCT
ejpam-323	15	1	nevertheless	nevertheless	ADV
ejpam-323	15	2	,	,	PUNCT
ejpam-323	15	3	in	in	ADP
ejpam-323	15	4	our	our	PRON
ejpam-323	15	5	paper	paper	NOUN
ejpam-323	15	6	we	we	PRON
ejpam-323	15	7	remove	remove	VERB
ejpam-323	15	8	the	the	DET
ejpam-323	15	9	condition	condition	NOUN
ejpam-323	15	10	that	that	SCONJ
ejpam-323	15	11	eigenvalue	eigenvalue	PROPN
ejpam-323	15	12	is	be	AUX
ejpam-323	15	13	simple	simple	ADJ
ejpam-323	15	14	and	and	CCONJ
ejpam-323	15	15	provide	provide	VERB
ejpam-323	15	16	more	more	ADV
ejpam-323	15	17	accurate	accurate	ADJ
ejpam-323	15	18	asymptotic	asymptotic	ADJ
ejpam-323	15	19	expansions	expansion	NOUN
ejpam-323	15	20	for	for	ADP
ejpam-323	15	21	eigenfunctions	eigenfunction	NOUN
ejpam-323	15	22	in	in	ADP
ejpam-323	15	23	domain	domain	NOUN
ejpam-323	15	24	with	with	ADP
ejpam-323	15	25	more	more	ADJ
ejpam-323	15	26	general	general	ADJ
ejpam-323	15	27	shape	shape	NOUN
ejpam-323	15	28	.	.	PUNCT
ejpam-323	16	1	recently	recently	ADV
ejpam-323	16	2	,	,	PUNCT
ejpam-323	16	3	lanza	lanza	X
ejpam-323	16	4	de	de	PROPN
ejpam-323	16	5	cristoforis	cristoforis	PROPN
ejpam-323	16	6	∗corresponding	∗corresponde	VERB
ejpam-323	16	7	author	author	NOUN
ejpam-323	16	8	.	.	PUNCT
ejpam-323	17	1	email	email	NOUN
ejpam-323	17	2	addresses	address	NOUN
ejpam-323	17	3	:	:	PUNCT
ejpam-323	17	4	abdessatar.khelifi�fsb.rnu.tn	abdessatar.khelifi�fsb.rnu.tn	PROPN
ejpam-323	17	5	(	(	PUNCT
ejpam-323	17	6	a.	a.	NOUN
ejpam-323	17	7	khelifi	khelifi	PROPN
ejpam-323	17	8	)	)	PUNCT
ejpam-323	17	9	,	,	PUNCT
ejpam-323	17	10	shamman01	shamman01	PROPN
ejpam-323	17	11	�	�	PROPN
ejpam-323	17	12	yahoo	yahoo	PROPN
ejpam-323	17	13	.	.	PUNCT
ejpam-323	18	1	om	om	PROPN
ejpam-323	18	2	.	.	PUNCT
ejpam-323	19	1	(	(	PUNCT
ejpam-323	19	2	m.	m.	PROPN
ejpam-323	19	3	shamma	shamma	PROPN
ejpam-323	19	4	)	)	PUNCT
ejpam-323	20	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-323	21	1	282	282	NUM
ejpam-323	21	2	c	c	X
ejpam-323	21	3	©	©	VERB
ejpam-323	21	4	2010	2010	NUM
ejpam-323	21	5	ejpam	ejpam	NOUN
ejpam-323	21	6	all	all	DET
ejpam-323	21	7	rights	right	NOUN
ejpam-323	21	8	reserved	reserve	VERB
ejpam-323	21	9	.	.	PUNCT
ejpam-323	22	1	a.	a.	NOUN
ejpam-323	22	2	khelifi	khelifi	PROPN
ejpam-323	22	3	,	,	PUNCT
ejpam-323	22	4	m.	m.	NOUN
ejpam-323	22	5	shamma	shamma	PROPN
ejpam-323	22	6	/	/	SYM
ejpam-323	22	7	eur	eur	PROPN
ejpam-323	22	8	.	.	PUNCT
ejpam-323	23	1	j.	j.	PROPN
ejpam-323	23	2	pure	pure	PROPN
ejpam-323	23	3	appl	appl	PROPN
ejpam-323	23	4	.	.	PROPN
ejpam-323	23	5	math	math	PROPN
ejpam-323	23	6	,	,	PUNCT
ejpam-323	23	7	3	3	NUM
ejpam-323	23	8	(	(	PUNCT
ejpam-323	23	9	2010	2010	NUM
ejpam-323	23	10	)	)	PUNCT
ejpam-323	23	11	,	,	PUNCT
ejpam-323	23	12	282	282	NUM
ejpam-323	23	13	-	-	SYM
ejpam-323	23	14	294	294	NUM
ejpam-323	23	15	283	283	NUM
ejpam-323	23	16	and	and	CCONJ
ejpam-323	23	17	lamberti	lamberti	PROPN
ejpam-323	23	18	have	have	AUX
ejpam-323	23	19	developed	develop	VERB
ejpam-323	23	20	in	in	ADP
ejpam-323	23	21	[	[	X
ejpam-323	23	22	13	13	NUM
ejpam-323	23	23	]	]	PUNCT
ejpam-323	23	24	some	some	DET
ejpam-323	23	25	preliminary	preliminary	ADJ
ejpam-323	23	26	abstract	abstract	ADJ
ejpam-323	23	27	results	result	NOUN
ejpam-323	23	28	for	for	ADP
ejpam-323	23	29	the	the	DET
ejpam-323	23	30	dependence	dependence	NOUN
ejpam-323	23	31	of	of	ADP
ejpam-323	23	32	the	the	DET
ejpam-323	23	33	eigenvalues	eigenvalue	NOUN
ejpam-323	23	34	upon	upon	SCONJ
ejpam-323	23	35	perturbation	perturbation	NOUN
ejpam-323	23	36	.	.	PUNCT
ejpam-323	24	1	their	their	PRON
ejpam-323	24	2	applications	application	NOUN
ejpam-323	24	3	to	to	ADP
ejpam-323	24	4	the	the	DET
ejpam-323	24	5	dirichlet	dirichlet	PROPN
ejpam-323	24	6	eigenvalue	eigenvalue	PROPN
ejpam-323	24	7	problem	problem	NOUN
ejpam-323	24	8	for	for	ADP
ejpam-323	24	9	the	the	DET
ejpam-323	24	10	laplace	laplace	NOUN
ejpam-323	24	11	operator	operator	NOUN
ejpam-323	24	12	appear	appear	VERB
ejpam-323	24	13	clearly	clearly	ADV
ejpam-323	24	14	in	in	ADP
ejpam-323	24	15	section	section	NOUN
ejpam-323	24	16	3	3	NUM
ejpam-323	24	17	of	of	ADP
ejpam-323	24	18	their	their	PRON
ejpam-323	24	19	paper	paper	NOUN
ejpam-323	24	20	and	and	CCONJ
ejpam-323	24	21	in	in	ADP
ejpam-323	24	22	theorem	theorem	NOUN
ejpam-323	24	23	3.21	3.21	NUM
ejpam-323	24	24	when	when	SCONJ
ejpam-323	24	25	they	they	PRON
ejpam-323	24	26	justify	justify	VERB
ejpam-323	24	27	the	the	DET
ejpam-323	24	28	analyticity	analyticity	NOUN
ejpam-323	24	29	result	result	NOUN
ejpam-323	24	30	for	for	ADP
ejpam-323	24	31	some	some	DET
ejpam-323	24	32	symmetric	symmetric	ADJ
ejpam-323	24	33	functions	function	NOUN
ejpam-323	24	34	of	of	ADP
ejpam-323	24	35	eigenvalues	eigenvalue	NOUN
ejpam-323	24	36	.	.	PUNCT
ejpam-323	25	1	our	our	PRON
ejpam-323	25	2	analysis	analysis	NOUN
ejpam-323	25	3	and	and	CCONJ
ejpam-323	25	4	uniform	uniform	ADJ
ejpam-323	25	5	asymptotic	asymptotic	ADJ
ejpam-323	25	6	formulas	formula	NOUN
ejpam-323	25	7	of	of	ADP
ejpam-323	25	8	the	the	DET
ejpam-323	25	9	eigenfunctions	eigenfunction	NOUN
ejpam-323	25	10	,	,	PUNCT
ejpam-323	25	11	which	which	PRON
ejpam-323	25	12	are	be	AUX
ejpam-323	25	13	represented	represent	VERB
ejpam-323	25	14	by	by	ADP
ejpam-323	25	15	the	the	DET
ejpam-323	25	16	single	single	ADJ
ejpam-323	25	17	-	-	PUNCT
ejpam-323	25	18	layer	layer	NOUN
ejpam-323	25	19	potential	potential	NOUN
ejpam-323	25	20	involving	involve	VERB
ejpam-323	25	21	the	the	DET
ejpam-323	25	22	green	green	ADJ
ejpam-323	25	23	function	function	NOUN
ejpam-323	25	24	,	,	PUNCT
ejpam-323	25	25	are	be	AUX
ejpam-323	25	26	considerably	considerably	ADV
ejpam-323	25	27	different	different	ADJ
ejpam-323	25	28	from	from	ADP
ejpam-323	25	29	those	those	PRON
ejpam-323	25	30	in	in	ADP
ejpam-323	25	31	[	[	X
ejpam-323	25	32	12	12	NUM
ejpam-323	25	33	,	,	PUNCT
ejpam-323	25	34	13	13	NUM
ejpam-323	25	35	,	,	PUNCT
ejpam-323	25	36	10	10	NUM
ejpam-323	25	37	]	]	PUNCT
ejpam-323	25	38	.	.	PUNCT
ejpam-323	26	1	next	next	ADV
ejpam-323	26	2	,	,	PUNCT
ejpam-323	26	3	our	our	PRON
ejpam-323	26	4	method	method	NOUN
ejpam-323	26	5	differ	differ	VERB
ejpam-323	26	6	,	,	PUNCT
ejpam-323	26	7	essentially	essentially	ADV
ejpam-323	26	8	,	,	PUNCT
ejpam-323	26	9	from	from	ADP
ejpam-323	26	10	the	the	DET
ejpam-323	26	11	classical	classical	ADJ
ejpam-323	26	12	methods	method	NOUN
ejpam-323	26	13	used	use	VERB
ejpam-323	26	14	to	to	PART
ejpam-323	26	15	study	study	VERB
ejpam-323	26	16	the	the	DET
ejpam-323	26	17	analytic	analytic	ADJ
ejpam-323	26	18	dependence	dependence	NOUN
ejpam-323	26	19	of	of	ADP
ejpam-323	26	20	the	the	DET
ejpam-323	26	21	eigenfunctions	eigenfunction	NOUN
ejpam-323	26	22	of	of	ADP
ejpam-323	26	23	a	a	DET
ejpam-323	26	24	real	real	ADJ
ejpam-323	26	25	or	or	CCONJ
ejpam-323	26	26	complex	complex	ADJ
ejpam-323	26	27	parameter	parameter	NOUN
ejpam-323	26	28	and	and	CCONJ
ejpam-323	26	29	used	use	VERB
ejpam-323	26	30	to	to	PART
ejpam-323	26	31	give	give	VERB
ejpam-323	26	32	the	the	DET
ejpam-323	26	33	asymptotic	asymptotic	ADJ
ejpam-323	26	34	formulae	formulae	NOUN
ejpam-323	26	35	for	for	ADP
ejpam-323	26	36	the	the	DET
ejpam-323	26	37	eigenvalues	eigenvalue	NOUN
ejpam-323	26	38	.	.	PUNCT
ejpam-323	27	1	the	the	DET
ejpam-323	27	2	main	main	ADJ
ejpam-323	27	3	goal	goal	NOUN
ejpam-323	27	4	of	of	ADP
ejpam-323	27	5	this	this	DET
ejpam-323	27	6	paper	paper	NOUN
ejpam-323	27	7	is	be	AUX
ejpam-323	27	8	to	to	PART
ejpam-323	27	9	justify	justify	VERB
ejpam-323	27	10	and	and	CCONJ
ejpam-323	27	11	to	to	PART
ejpam-323	27	12	give	give	VERB
ejpam-323	27	13	formulae	formulae	NOUN
ejpam-323	27	14	for	for	ADP
ejpam-323	27	15	the	the	DET
ejpam-323	27	16	convergence	convergence	NOUN
ejpam-323	27	17	estimates	estimate	NOUN
ejpam-323	27	18	for	for	ADP
ejpam-323	27	19	both	both	DET
ejpam-323	27	20	resonant	resonant	ADJ
ejpam-323	27	21	frequencies	frequency	NOUN
ejpam-323	27	22	and	and	CCONJ
ejpam-323	27	23	eigenfunctions	eigenfunction	NOUN
ejpam-323	27	24	associated	associate	VERB
ejpam-323	27	25	to	to	ADP
ejpam-323	27	26	helmholtz	helmholtz	NOUN
ejpam-323	27	27	eigenvalue	eigenvalue	PROPN
ejpam-323	27	28	oroblem	oroblem	NOUN
ejpam-323	27	29	.	.	PUNCT
ejpam-323	28	1	compared	compare	VERB
ejpam-323	28	2	to	to	ADP
ejpam-323	28	3	papers	paper	NOUN
ejpam-323	28	4	in	in	ADP
ejpam-323	28	5	this	this	DET
ejpam-323	28	6	fields	field	NOUN
ejpam-323	28	7	[	[	X
ejpam-323	28	8	15	15	NUM
ejpam-323	28	9	,	,	PUNCT
ejpam-323	28	10	17	17	NUM
ejpam-323	28	11	,	,	PUNCT
ejpam-323	28	12	18	18	NUM
ejpam-323	28	13	]	]	PUNCT
ejpam-323	28	14	,	,	PUNCT
ejpam-323	28	15	one	one	PRON
ejpam-323	28	16	can	can	AUX
ejpam-323	28	17	notice	notice	VERB
ejpam-323	28	18	that	that	SCONJ
ejpam-323	28	19	our	our	PRON
ejpam-323	28	20	results	result	NOUN
ejpam-323	28	21	in	in	ADP
ejpam-323	28	22	section	section	NOUN
ejpam-323	28	23	4	4	NUM
ejpam-323	28	24	,	,	PUNCT
ejpam-323	28	25	are	be	AUX
ejpam-323	28	26	important	important	ADJ
ejpam-323	28	27	and	and	CCONJ
ejpam-323	28	28	give	give	VERB
ejpam-323	28	29	an	an	DET
ejpam-323	28	30	idea	idea	NOUN
ejpam-323	28	31	to	to	PART
ejpam-323	28	32	evaluate	evaluate	VERB
ejpam-323	28	33	the	the	DET
ejpam-323	28	34	speed	speed	NOUN
ejpam-323	28	35	of	of	ADP
ejpam-323	28	36	convergence	convergence	NOUN
ejpam-323	28	37	.	.	PUNCT
ejpam-323	29	1	the	the	DET
ejpam-323	29	2	paper	paper	NOUN
ejpam-323	29	3	is	be	AUX
ejpam-323	29	4	organized	organize	VERB
ejpam-323	29	5	as	as	SCONJ
ejpam-323	29	6	follows	follow	VERB
ejpam-323	29	7	.	.	PUNCT
ejpam-323	30	1	in	in	ADP
ejpam-323	30	2	section	section	NOUN
ejpam-323	30	3	2	2	NUM
ejpam-323	30	4	we	we	PRON
ejpam-323	30	5	describe	describe	VERB
ejpam-323	30	6	the	the	DET
ejpam-323	30	7	central	central	ADJ
ejpam-323	30	8	problem	problem	NOUN
ejpam-323	30	9	in	in	ADP
ejpam-323	30	10	this	this	DET
ejpam-323	30	11	work	work	NOUN
ejpam-323	30	12	,	,	PUNCT
ejpam-323	30	13	and	and	CCONJ
ejpam-323	30	14	we	we	PRON
ejpam-323	30	15	remember	remember	VERB
ejpam-323	30	16	some	some	DET
ejpam-323	30	17	well	well	ADV
ejpam-323	30	18	-	-	PUNCT
ejpam-323	30	19	known	know	VERB
ejpam-323	30	20	results	result	NOUN
ejpam-323	30	21	concerning	concern	VERB
ejpam-323	30	22	the	the	DET
ejpam-323	30	23	analyticity	analyticity	NOUN
ejpam-323	30	24	of	of	ADP
ejpam-323	30	25	the	the	DET
ejpam-323	30	26	eigenvalues	eigenvalue	NOUN
ejpam-323	30	27	with	with	ADP
ejpam-323	30	28	respect	respect	NOUN
ejpam-323	30	29	to	to	ADP
ejpam-323	30	30	ε	ε	PROPN
ejpam-323	30	31	.	.	PUNCT
ejpam-323	31	1	in	in	ADP
ejpam-323	31	2	section	section	NOUN
ejpam-323	31	3	3	3	NUM
ejpam-323	31	4	we	we	PRON
ejpam-323	31	5	develop	develop	VERB
ejpam-323	31	6	a	a	DET
ejpam-323	31	7	boundary	boundary	ADJ
ejpam-323	31	8	integral	integral	ADJ
ejpam-323	31	9	formulation	formulation	NOUN
ejpam-323	31	10	for	for	ADP
ejpam-323	31	11	solving	solve	VERB
ejpam-323	31	12	the	the	DET
ejpam-323	31	13	eigenvalue	eigenvalue	PROPN
ejpam-323	31	14	problem	problem	NOUN
ejpam-323	31	15	(	(	PUNCT
ejpam-323	31	16	2	2	NUM
ejpam-323	31	17	)	)	PUNCT
ejpam-323	31	18	.	.	PUNCT
ejpam-323	32	1	from	from	ADP
ejpam-323	32	2	results	result	NOUN
ejpam-323	32	3	found	find	VERB
ejpam-323	32	4	in	in	ADP
ejpam-323	32	5	[	[	X
ejpam-323	32	6	11	11	NUM
ejpam-323	32	7	]	]	PUNCT
ejpam-323	32	8	in	in	ADP
ejpam-323	32	9	two	two	NUM
ejpam-323	32	10	dimensional	dimensional	ADJ
ejpam-323	32	11	space	space	NOUN
ejpam-323	32	12	,	,	PUNCT
ejpam-323	32	13	we	we	PRON
ejpam-323	32	14	end	end	VERB
ejpam-323	32	15	this	this	DET
ejpam-323	32	16	section	section	NOUN
ejpam-323	32	17	by	by	ADP
ejpam-323	32	18	presenting	present	VERB
ejpam-323	32	19	the	the	DET
ejpam-323	32	20	main	main	ADJ
ejpam-323	32	21	theorem	theorem	NOUN
ejpam-323	32	22	which	which	PRON
ejpam-323	32	23	gives	give	VERB
ejpam-323	32	24	the	the	DET
ejpam-323	32	25	analyticity	analyticity	NOUN
ejpam-323	32	26	and	and	CCONJ
ejpam-323	32	27	the	the	DET
ejpam-323	32	28	uniform	uniform	ADJ
ejpam-323	32	29	asymptotic	asymptotic	ADJ
ejpam-323	32	30	expansion	expansion	NOUN
ejpam-323	32	31	for	for	ADP
ejpam-323	32	32	the	the	DET
ejpam-323	32	33	eigenfunctions	eigenfunction	NOUN
ejpam-323	32	34	.	.	PUNCT
ejpam-323	33	1	section	section	NOUN
ejpam-323	33	2	4	4	NUM
ejpam-323	33	3	contains	contain	VERB
ejpam-323	33	4	the	the	DET
ejpam-323	33	5	main	main	ADJ
ejpam-323	33	6	results	result	NOUN
ejpam-323	33	7	of	of	ADP
ejpam-323	33	8	our	our	PRON
ejpam-323	33	9	paper	paper	NOUN
ejpam-323	33	10	which	which	PRON
ejpam-323	33	11	are	be	AUX
ejpam-323	33	12	deeply	deeply	ADV
ejpam-323	33	13	based	base	VERB
ejpam-323	33	14	on	on	ADP
ejpam-323	33	15	the	the	DET
ejpam-323	33	16	osborn	osborn	PROPN
ejpam-323	33	17	’s	’s	PART
ejpam-323	33	18	theorem	theorem	PROPN
ejpam-323	33	19	.	.	PUNCT
ejpam-323	34	1	we	we	PRON
ejpam-323	34	2	then	then	ADV
ejpam-323	34	3	prove	prove	VERB
ejpam-323	34	4	some	some	DET
ejpam-323	34	5	error	error	NOUN
ejpam-323	34	6	estimates	estimate	NOUN
ejpam-323	34	7	for	for	ADP
ejpam-323	34	8	the	the	DET
ejpam-323	34	9	convergence	convergence	NOUN
ejpam-323	34	10	of	of	ADP
ejpam-323	34	11	resonant	resonant	ADJ
ejpam-323	34	12	frequencies	frequency	NOUN
ejpam-323	34	13	.	.	PUNCT
ejpam-323	35	1	2	2	X
ejpam-323	35	2	.	.	X
ejpam-323	35	3	problem	problem	NOUN
ejpam-323	35	4	description	description	NOUN
ejpam-323	35	5	let	let	VERB
ejpam-323	35	6	ω	ω	NOUN
ejpam-323	35	7	be	be	AUX
ejpam-323	35	8	a	a	DET
ejpam-323	35	9	bounded	bounded	ADJ
ejpam-323	35	10	domain	domain	NOUN
ejpam-323	35	11	in	in	ADP
ejpam-323	35	12	rd	rd	PROPN
ejpam-323	35	13	,	,	PUNCT
ejpam-323	35	14	d	d	X
ejpam-323	35	15	≥	≥	NUM
ejpam-323	35	16	2	2	NUM
ejpam-323	35	17	,	,	PUNCT
ejpam-323	35	18	with	with	ADP
ejpam-323	35	19	a	a	DET
ejpam-323	35	20	connected	connect	VERB
ejpam-323	35	21	lipschitz	lipschitz	NOUN
ejpam-323	35	22	boundary	boundary	NOUN
ejpam-323	35	23	∂ω	∂ω	ADJ
ejpam-323	35	24	and	and	CCONJ
ejpam-323	35	25	ν	ν	PROPN
ejpam-323	35	26	denotes	denote	VERB
ejpam-323	35	27	the	the	DET
ejpam-323	35	28	unit	unit	NOUN
ejpam-323	35	29	outward	outward	VERB
ejpam-323	35	30	normal	normal	ADJ
ejpam-323	35	31	to	to	ADP
ejpam-323	35	32	∂ω	∂ω	PROPN
ejpam-323	35	33	.	.	PUNCT
ejpam-323	36	1	let	let	VERB
ejpam-323	36	2	ti	ti	PROPN
ejpam-323	36	3	>	>	X
ejpam-323	36	4	0	0	NUM
ejpam-323	36	5	,	,	PUNCT
ejpam-323	36	6	for	for	ADP
ejpam-323	36	7	all	all	PRON
ejpam-323	36	8	i	i	PRON
ejpam-323	36	9	∈	∈	PROPN
ejpam-323	36	10	{	{	PUNCT
ejpam-323	36	11	1	1	NUM
ejpam-323	36	12	,	,	PUNCT
ejpam-323	36	13	·	·	PUNCT
ejpam-323	36	14	·	·	PUNCT
ejpam-323	36	15	·	·	PUNCT
ejpam-323	36	16	,	,	PUNCT
ejpam-323	37	1	d	d	X
ejpam-323	37	2	−	−	PROPN
ejpam-323	37	3	1	1	NUM
ejpam-323	37	4	}	}	PUNCT
ejpam-323	37	5	and	and	CCONJ
ejpam-323	37	6	let	let	VERB
ejpam-323	37	7	γ(t	γ(t	NOUN
ejpam-323	37	8	)	)	PUNCT
ejpam-323	37	9	,	,	PUNCT
ejpam-323	37	10	β(t	β(t	PROPN
ejpam-323	37	11	)	)	PUNCT
ejpam-323	37	12	:	:	PUNCT
ejpam-323	38	1	t	t	X
ejpam-323	38	2	=	=	SYM
ejpam-323	38	3	(	(	PUNCT
ejpam-323	38	4	t1	t1	PROPN
ejpam-323	38	5	,	,	PUNCT
ejpam-323	38	6	·	·	PUNCT
ejpam-323	38	7	·	·	PUNCT
ejpam-323	38	8	·	·	PUNCT
ejpam-323	38	9	,	,	PUNCT
ejpam-323	38	10	td−1	td−1	PROPN
ejpam-323	38	11	)	)	PUNCT
ejpam-323	38	12	∈	∈	NOUN
ejpam-323	39	1	[	[	X
ejpam-323	39	2	0	0	NUM
ejpam-323	39	3	,	,	PUNCT
ejpam-323	39	4	t1]×	t1]×	NOUN
ejpam-323	39	5	·	·	PUNCT
ejpam-323	39	6	·	·	PUNCT
ejpam-323	39	7	·	·	PUNCT
ejpam-323	39	8	×	×	NOUN
ejpam-323	39	9	[	[	X
ejpam-323	39	10	0	0	NUM
ejpam-323	39	11	,	,	PUNCT
ejpam-323	39	12	td−1]→	td−1]→	PROPN
ejpam-323	39	13	rd	rd	NOUN
ejpam-323	39	14	,	,	PUNCT
ejpam-323	39	15	be	be	AUX
ejpam-323	39	16	two	two	NUM
ejpam-323	39	17	analytic	analytic	ADJ
ejpam-323	39	18	,	,	PUNCT
ejpam-323	39	19	ti	ti	NOUN
ejpam-323	39	20	-	-	NOUN
ejpam-323	39	21	periodic	periodic	ADJ
ejpam-323	39	22	(	(	PUNCT
ejpam-323	39	23	in	in	ADP
ejpam-323	39	24	each	each	DET
ejpam-323	39	25	composite	composite	ADJ
ejpam-323	39	26	t	t	NOUN
ejpam-323	39	27	i	i	NOUN
ejpam-323	39	28	)	)	PUNCT
ejpam-323	39	29	functions	function	NOUN
ejpam-323	39	30	and	and	CCONJ
ejpam-323	39	31	satisfying	satisfy	VERB
ejpam-323	39	32	the	the	DET
ejpam-323	39	33	following	following	ADJ
ejpam-323	39	34	assumption	assumption	NOUN
ejpam-323	39	35	:	:	PUNCT
ejpam-323	39	36	〈	〈	PROPN
ejpam-323	39	37	γ′(t),β(t	γ′(t),β(t	NOUN
ejpam-323	39	38	)	)	PUNCT
ejpam-323	39	39	〉	〉	NOUN
ejpam-323	39	40	=	=	SYM
ejpam-323	39	41	0	0	NUM
ejpam-323	39	42	,	,	PUNCT
ejpam-323	39	43	for	for	ADP
ejpam-323	39	44	allt	allt	PROPN
ejpam-323	39	45	=	=	SYM
ejpam-323	39	46	(	(	PUNCT
ejpam-323	39	47	t1	t1	PROPN
ejpam-323	39	48	,	,	PUNCT
ejpam-323	39	49	·	·	PUNCT
ejpam-323	39	50	·	·	PUNCT
ejpam-323	39	51	·	·	PUNCT
ejpam-323	39	52	,	,	PUNCT
ejpam-323	39	53	td−1	td−1	PROPN
ejpam-323	39	54	)	)	PUNCT
ejpam-323	39	55	∈	∈	NOUN
ejpam-323	40	1	[	[	X
ejpam-323	40	2	0	0	NUM
ejpam-323	40	3	,	,	PUNCT
ejpam-323	40	4	t1]×	t1]×	NOUN
ejpam-323	40	5	·	·	PUNCT
ejpam-323	40	6	·	·	PUNCT
ejpam-323	40	7	·	·	PUNCT
ejpam-323	40	8	×	×	NOUN
ejpam-323	41	1	[	[	X
ejpam-323	41	2	0	0	NUM
ejpam-323	41	3	,	,	PUNCT
ejpam-323	41	4	td−1	td−1	PROPN
ejpam-323	41	5	]	]	X
ejpam-323	41	6	.	.	PUNCT
ejpam-323	42	1	(	(	PUNCT
ejpam-323	42	2	1	1	X
ejpam-323	42	3	)	)	PUNCT
ejpam-323	42	4	where	where	SCONJ
ejpam-323	42	5	〈	〈	PROPN
ejpam-323	42	6	.	.	PROPN
ejpam-323	42	7	,	,	PUNCT
ejpam-323	42	8	.	.	PUNCT
ejpam-323	43	1	〉	〉	NOUN
ejpam-323	43	2	denotes	denote	VERB
ejpam-323	43	3	the	the	DET
ejpam-323	43	4	usual	usual	ADJ
ejpam-323	43	5	product	product	NOUN
ejpam-323	43	6	scalar	scalar	ADJ
ejpam-323	43	7	in	in	ADP
ejpam-323	43	8	rd	rd	NOUN
ejpam-323	43	9	.	.	PUNCT
ejpam-323	44	1	we	we	PRON
ejpam-323	44	2	introduce	introduce	VERB
ejpam-323	44	3	,	,	PUNCT
ejpam-323	44	4	γε(t	γε(t	ADV
ejpam-323	44	5	)	)	PUNCT
ejpam-323	44	6	=	=	PUNCT
ejpam-323	45	1	γ(t	γ(t	NOUN
ejpam-323	45	2	)	)	PUNCT
ejpam-323	45	3	+	+	CCONJ
ejpam-323	45	4	εβ(t	εβ(t	NUM
ejpam-323	45	5	)	)	PUNCT
ejpam-323	45	6	,	,	PUNCT
ejpam-323	45	7	ε	ε	PROPN
ejpam-323	45	8	∈	∈	PROPN
ejpam-323	45	9	r.	r.	PROPN
ejpam-323	45	10	with	with	ADP
ejpam-323	45	11	this	this	DET
ejpam-323	45	12	definition	definition	NOUN
ejpam-323	45	13	,	,	PUNCT
ejpam-323	45	14	(	(	PUNCT
ejpam-323	45	15	t	t	PROPN
ejpam-323	45	16	,	,	PUNCT
ejpam-323	45	17	ε	ε	PROPN
ejpam-323	45	18	)	)	PUNCT
ejpam-323	45	19	7→	7→	NUM
ejpam-323	45	20	γε(t	γε(t	PUNCT
ejpam-323	45	21	)	)	PUNCT
ejpam-323	45	22	is	be	AUX
ejpam-323	45	23	an	an	DET
ejpam-323	45	24	analytic	analytic	ADJ
ejpam-323	45	25	function	function	NOUN
ejpam-323	45	26	on	on	ADP
ejpam-323	45	27	[	[	X
ejpam-323	45	28	0	0	NUM
ejpam-323	45	29	,	,	PUNCT
ejpam-323	45	30	t1	t1	NOUN
ejpam-323	45	31	]	]	X
ejpam-323	45	32	×	×	NOUN
ejpam-323	45	33	·	·	PUNCT
ejpam-323	45	34	·	·	PUNCT
ejpam-323	45	35	·	·	PUNCT
ejpam-323	46	1	×	×	NOUN
ejpam-323	46	2	[	[	X
ejpam-323	46	3	0	0	NUM
ejpam-323	46	4	,	,	PUNCT
ejpam-323	46	5	td−1	td−1	PROPN
ejpam-323	46	6	]	]	X
ejpam-323	46	7	×	×	NOUN
ejpam-323	46	8	r	r	NOUN
ejpam-323	46	9	,	,	PUNCT
ejpam-323	46	10	ti	ti	NOUN
ejpam-323	46	11	-	-	NOUN
ejpam-323	46	12	periodic	periodic	NOUN
ejpam-323	46	13	in	in	ADP
ejpam-323	46	14	each	each	DET
ejpam-323	46	15	composite	composite	ADJ
ejpam-323	46	16	t	t	NOUN
ejpam-323	46	17	i	i	PRON
ejpam-323	46	18	.	.	PUNCT
ejpam-323	47	1	we	we	PRON
ejpam-323	47	2	consider	consider	VERB
ejpam-323	47	3	the	the	DET
ejpam-323	47	4	bounded	bounded	ADJ
ejpam-323	47	5	domain	domain	NOUN
ejpam-323	47	6	ωε	ωε	NOUN
ejpam-323	47	7	in	in	ADP
ejpam-323	47	8	rd	rd	PROPN
ejpam-323	47	9	with	with	ADP
ejpam-323	47	10	smooth	smooth	ADJ
ejpam-323	47	11	boundary	boundary	ADJ
ejpam-323	47	12	∂ωε	∂ωε	NOUN
ejpam-323	47	13	parameterized	parameterize	VERB
ejpam-323	47	14	by	by	ADP
ejpam-323	47	15	the	the	DET
ejpam-323	47	16	function	function	NOUN
ejpam-323	47	17	γε(t	γε(t	PUNCT
ejpam-323	47	18	):	):	PUNCT
ejpam-323	47	19	∂ωε	∂ωε	NOUN
ejpam-323	47	20	=	=	SYM
ejpam-323	47	21	{	{	PUNCT
ejpam-323	47	22	γε(t	γε(t	NOUN
ejpam-323	47	23	)	)	PUNCT
ejpam-323	47	24	,	,	PUNCT
ejpam-323	47	25	t	t	PROPN
ejpam-323	47	26	=	=	SYM
ejpam-323	47	27	(	(	PUNCT
ejpam-323	47	28	t1	t1	PROPN
ejpam-323	47	29	,	,	PUNCT
ejpam-323	47	30	·	·	PUNCT
ejpam-323	47	31	·	·	PUNCT
ejpam-323	47	32	·	·	PUNCT
ejpam-323	47	33	,	,	PUNCT
ejpam-323	47	34	td−1	td−1	PROPN
ejpam-323	47	35	)	)	PUNCT
ejpam-323	47	36	∈	∈	NOUN
ejpam-323	48	1	[	[	X
ejpam-323	48	2	0	0	NUM
ejpam-323	48	3	,	,	PUNCT
ejpam-323	48	4	t1]×	t1]×	NOUN
ejpam-323	48	5	·	·	PUNCT
ejpam-323	48	6	·	·	PUNCT
ejpam-323	48	7	·	·	PUNCT
ejpam-323	48	8	×	×	NOUN
ejpam-323	49	1	[	[	X
ejpam-323	49	2	0	0	NUM
ejpam-323	49	3	,	,	PUNCT
ejpam-323	49	4	td−1	td−1	PROPN
ejpam-323	49	5	]	]	PUNCT
ejpam-323	49	6	}	}	PUNCT
ejpam-323	49	7	.	.	PUNCT
ejpam-323	50	1	let	let	VERB
ejpam-323	50	2	µ0	µ0	NOUN
ejpam-323	50	3	and	and	CCONJ
ejpam-323	50	4	ǫ0	ǫ0	PROPN
ejpam-323	50	5	denote	denote	VERB
ejpam-323	50	6	the	the	DET
ejpam-323	50	7	permeability	permeability	NOUN
ejpam-323	50	8	and	and	CCONJ
ejpam-323	50	9	the	the	DET
ejpam-323	50	10	permittivity	permittivity	NOUN
ejpam-323	50	11	of	of	ADP
ejpam-323	50	12	the	the	DET
ejpam-323	50	13	background	background	NOUN
ejpam-323	50	14	medium	medium	PROPN
ejpam-323	50	15	ω	ω	PROPN
ejpam-323	50	16	≡	≡	PROPN
ejpam-323	50	17	ωε=0	ωε=0	PROPN
ejpam-323	50	18	,	,	PUNCT
ejpam-323	50	19	and	and	CCONJ
ejpam-323	50	20	assume	assume	VERB
ejpam-323	50	21	that	that	SCONJ
ejpam-323	50	22	µ0	µ0	NOUN
ejpam-323	50	23	>	>	X
ejpam-323	50	24	0	0	PUNCT
ejpam-323	50	25	and	and	CCONJ
ejpam-323	50	26	ǫ0	ǫ0	PROPN
ejpam-323	50	27	>	>	SYM
ejpam-323	50	28	0	0	NUM
ejpam-323	50	29	are	be	AUX
ejpam-323	50	30	positive	positive	ADJ
ejpam-323	50	31	constants	constant	NOUN
ejpam-323	50	32	.	.	PUNCT
ejpam-323	51	1	let	let	VERB
ejpam-323	51	2	µ1	µ1	VERB
ejpam-323	51	3	>	>	X
ejpam-323	51	4	0	0	PUNCT
ejpam-323	52	1	and	and	CCONJ
ejpam-323	52	2	ǫ1	ǫ1	NUM
ejpam-323	52	3	>	>	SYM
ejpam-323	52	4	0	0	NUM
ejpam-323	52	5	a.	a.	NOUN
ejpam-323	52	6	khelifi	khelifi	PROPN
ejpam-323	52	7	,	,	PUNCT
ejpam-323	52	8	m.	m.	NOUN
ejpam-323	52	9	shamma	shamma	PROPN
ejpam-323	52	10	/	/	SYM
ejpam-323	52	11	eur	eur	PROPN
ejpam-323	52	12	.	.	PUNCT
ejpam-323	53	1	j.	j.	PROPN
ejpam-323	53	2	pure	pure	PROPN
ejpam-323	53	3	appl	appl	PROPN
ejpam-323	53	4	.	.	PROPN
ejpam-323	53	5	math	math	PROPN
ejpam-323	53	6	,	,	PUNCT
ejpam-323	53	7	3	3	NUM
ejpam-323	53	8	(	(	PUNCT
ejpam-323	53	9	2010	2010	NUM
ejpam-323	53	10	)	)	PUNCT
ejpam-323	53	11	,	,	PUNCT
ejpam-323	53	12	282	282	NUM
ejpam-323	53	13	-	-	NUM
ejpam-323	53	14	294	294	NUM
ejpam-323	53	15	284	284	NUM
ejpam-323	53	16	denote	denote	VERB
ejpam-323	53	17	the	the	DET
ejpam-323	53	18	permeability	permeability	NOUN
ejpam-323	53	19	and	and	CCONJ
ejpam-323	53	20	the	the	DET
ejpam-323	53	21	permittivity	permittivity	NOUN
ejpam-323	53	22	of	of	ADP
ejpam-323	53	23	ωε\ω0	ωε\ω0	NOUN
ejpam-323	53	24	.	.	PUNCT
ejpam-323	53	25	introduce	introduce	VERB
ejpam-323	53	26	the	the	DET
ejpam-323	53	27	piecewise	piecewise	NOUN
ejpam-323	53	28	-	-	PUNCT
ejpam-323	53	29	constant	constant	ADJ
ejpam-323	53	30	electric	electric	ADJ
ejpam-323	53	31	permittivity	permittivity	NOUN
ejpam-323	53	32	ǫε(x	ǫε(x	NUM
ejpam-323	53	33	)	)	PUNCT
ejpam-323	53	34	=	=	SYM
ejpam-323	54	1	(	(	PUNCT
ejpam-323	54	2	ǫ0	ǫ0	ADV
ejpam-323	54	3	,	,	PUNCT
ejpam-323	54	4	x	x	SYM
ejpam-323	54	5	∈	∈	PROPN
ejpam-323	54	6	ω0	ω0	NOUN
ejpam-323	54	7	,	,	PUNCT
ejpam-323	54	8	ǫ1	ǫ1	NUM
ejpam-323	54	9	,	,	PUNCT
ejpam-323	54	10	x	x	PROPN
ejpam-323	54	11	∈	∈	NOUN
ejpam-323	54	12	ωε\ω0	ωε\ω0	NOUN
ejpam-323	54	13	.	.	PUNCT
ejpam-323	55	1	if	if	SCONJ
ejpam-323	55	2	we	we	PRON
ejpam-323	55	3	allow	allow	VERB
ejpam-323	55	4	the	the	DET
ejpam-323	55	5	degenerate	degenerate	ADJ
ejpam-323	55	6	case	case	NOUN
ejpam-323	55	7	ε	ε	PROPN
ejpam-323	55	8	=	=	SYM
ejpam-323	55	9	0	0	PROPN
ejpam-323	55	10	,	,	PUNCT
ejpam-323	55	11	then	then	ADV
ejpam-323	55	12	the	the	DET
ejpam-323	55	13	function	function	NOUN
ejpam-323	55	14	ǫ0(x	ǫ0(x	NUM
ejpam-323	55	15	)	)	PUNCT
ejpam-323	55	16	equals	equal	VERB
ejpam-323	55	17	the	the	DET
ejpam-323	55	18	constant	constant	ADJ
ejpam-323	55	19	ǫ0	ǫ0	NOUN
ejpam-323	55	20	.	.	PUNCT
ejpam-323	56	1	the	the	DET
ejpam-323	56	2	piecewise	piecewise	NOUN
ejpam-323	56	3	constant	constant	ADJ
ejpam-323	56	4	magnetic	magnetic	ADJ
ejpam-323	56	5	permeability	permeability	NOUN
ejpam-323	56	6	,	,	PUNCT
ejpam-323	56	7	µε(x	µε(x	PUNCT
ejpam-323	56	8	)	)	PUNCT
ejpam-323	56	9	is	be	AUX
ejpam-323	56	10	defined	define	VERB
ejpam-323	56	11	analogously	analogously	ADV
ejpam-323	56	12	.	.	PUNCT
ejpam-323	57	1	in	in	ADP
ejpam-323	57	2	this	this	DET
ejpam-323	57	3	paper	paper	NOUN
ejpam-323	57	4	,	,	PUNCT
ejpam-323	57	5	we	we	PRON
ejpam-323	57	6	deal	deal	VERB
ejpam-323	57	7	with	with	ADP
ejpam-323	57	8	the	the	DET
ejpam-323	57	9	asymptotic	asymptotic	ADJ
ejpam-323	57	10	behavior	behavior	NOUN
ejpam-323	57	11	associated	associate	VERB
ejpam-323	57	12	with	with	ADP
ejpam-323	57	13	the	the	DET
ejpam-323	57	14	following	follow	VERB
ejpam-323	57	15	helmholtz	helmholtz	NOUN
ejpam-323	57	16	eigenvalue	eigenvalue	PROPN
ejpam-323	57	17	problem	problem	NOUN
ejpam-323	57	18	:	:	PUNCT
ejpam-323	57	19	div	div	X
ejpam-323	57	20	(	(	PUNCT
ejpam-323	57	21	1	1	NUM
ejpam-323	57	22	µε	µε	ADP
ejpam-323	57	23	grad	grad	NOUN
ejpam-323	57	24	u(ε	u(ε	PROPN
ejpam-323	57	25	)	)	PUNCT
ejpam-323	57	26	)	)	PUNCT
ejpam-323	58	1	+	+	NOUN
ejpam-323	58	2	ω2(ε)ǫεu(ε	ω2(ε)ǫεu(ε	X
ejpam-323	58	3	)	)	PUNCT
ejpam-323	58	4	=	=	SYM
ejpam-323	58	5	0	0	NUM
ejpam-323	58	6	in	in	ADP
ejpam-323	58	7	ωε	ωε	NOUN
ejpam-323	58	8	,	,	PUNCT
ejpam-323	58	9	and	and	CCONJ
ejpam-323	58	10	u(ε	u(ε	NUM
ejpam-323	58	11	)	)	PUNCT
ejpam-323	58	12	=	=	SYM
ejpam-323	58	13	0	0	NUM
ejpam-323	58	14	on	on	ADP
ejpam-323	58	15	∂ωε	∂ωε	NOUN
ejpam-323	58	16	,	,	PUNCT
ejpam-323	58	17	(	(	PUNCT
ejpam-323	58	18	2	2	X
ejpam-323	58	19	)	)	PUNCT
ejpam-323	58	20	where	where	SCONJ
ejpam-323	58	21	the	the	DET
ejpam-323	58	22	function	function	NOUN
ejpam-323	58	23	u	u	NOUN
ejpam-323	58	24	represents	represent	VERB
ejpam-323	58	25	some	some	DET
ejpam-323	58	26	electric	electric	ADJ
ejpam-323	58	27	field	field	NOUN
ejpam-323	58	28	or	or	CCONJ
ejpam-323	58	29	magnetic	magnetic	ADJ
ejpam-323	58	30	field	field	NOUN
ejpam-323	58	31	(	(	PUNCT
ejpam-323	58	32	or	or	CCONJ
ejpam-323	58	33	rather	rather	ADV
ejpam-323	58	34	,	,	PUNCT
ejpam-323	58	35	the	the	DET
ejpam-323	58	36	transversal	transversal	NOUN
ejpam-323	58	37	strength	strength	NOUN
ejpam-323	58	38	)	)	PUNCT
ejpam-323	58	39	and	and	CCONJ
ejpam-323	58	40	ω2(ε	ω2(ε	NUM
ejpam-323	58	41	)	)	PUNCT
ejpam-323	58	42	is	be	AUX
ejpam-323	58	43	the	the	DET
ejpam-323	58	44	perturbed	perturb	VERB
ejpam-323	58	45	resonant	resonant	ADJ
ejpam-323	58	46	frequency	frequency	NOUN
ejpam-323	58	47	(	(	PUNCT
ejpam-323	58	48	eigenfrequency	eigenfrequency	NOUN
ejpam-323	58	49	)	)	PUNCT
ejpam-323	58	50	associated	associate	VERB
ejpam-323	58	51	to	to	ADP
ejpam-323	58	52	the	the	DET
ejpam-323	58	53	above	above	ADJ
ejpam-323	58	54	problem	problem	NOUN
ejpam-323	58	55	(	(	PUNCT
ejpam-323	58	56	2	2	NUM
ejpam-323	58	57	)	)	PUNCT
ejpam-323	58	58	.	.	PUNCT
ejpam-323	59	1	the	the	DET
ejpam-323	59	2	eigenfunction	eigenfunction	NOUN
ejpam-323	59	3	u0	u0	ADJ
ejpam-323	59	4	,	,	PUNCT
ejpam-323	59	5	in	in	ADP
ejpam-323	59	6	the	the	DET
ejpam-323	59	7	absence	absence	NOUN
ejpam-323	59	8	of	of	ADP
ejpam-323	59	9	any	any	DET
ejpam-323	59	10	deformation	deformation	NOUN
ejpam-323	59	11	,	,	PUNCT
ejpam-323	59	12	satisfies	satisfy	VERB
ejpam-323	59	13	the	the	DET
ejpam-323	59	14	following	follow	VERB
ejpam-323	59	15	equations	equation	NOUN
ejpam-323	59	16	:	:	PUNCT
ejpam-323	59	17	−∆u0(x	−∆u0(x	NOUN
ejpam-323	59	18	)	)	PUNCT
ejpam-323	60	1	=	=	SYM
ejpam-323	60	2	ω	ω	NUM
ejpam-323	60	3	2	2	NUM
ejpam-323	60	4	0(ǫ0µ0)u0(x	0(ǫ0µ0)u0(x	NOUN
ejpam-323	60	5	)	)	PUNCT
ejpam-323	60	6	,	,	PUNCT
ejpam-323	60	7	x	x	PUNCT
ejpam-323	60	8	∈	∈	PROPN
ejpam-323	60	9	ω	ω	PROPN
ejpam-323	60	10	,	,	PUNCT
ejpam-323	60	11	and	and	CCONJ
ejpam-323	60	12	u0(x	u0(x	PRON
ejpam-323	60	13	)	)	PUNCT
ejpam-323	60	14	=	=	SYM
ejpam-323	61	1	0	0	NUM
ejpam-323	61	2	,	,	PUNCT
ejpam-323	61	3	x	x	X
ejpam-323	61	4	∈	∈	PROPN
ejpam-323	61	5	∂ω	∂ω	PROPN
ejpam-323	61	6	,	,	PUNCT
ejpam-323	61	7	(	(	PUNCT
ejpam-323	61	8	3	3	X
ejpam-323	61	9	)	)	PUNCT
ejpam-323	61	10	it	it	PRON
ejpam-323	61	11	is	be	AUX
ejpam-323	61	12	well	well	ADV
ejpam-323	61	13	known	know	VERB
ejpam-323	61	14	that	that	SCONJ
ejpam-323	61	15	the	the	DET
ejpam-323	61	16	operator	operator	NOUN
ejpam-323	61	17	−∆	−∆	NOUN
ejpam-323	61	18	on	on	ADP
ejpam-323	61	19	l2(ωε	l2(ωε	PROPN
ejpam-323	61	20	)	)	PUNCT
ejpam-323	61	21	with	with	ADP
ejpam-323	61	22	domain	domain	NOUN
ejpam-323	61	23	h2(ωε)∩h1	h2(ωε)∩h1	NOUN
ejpam-323	61	24	0(ωε	0(ωε	NOUN
ejpam-323	61	25	)	)	PUNCT
ejpam-323	61	26	is	be	AUX
ejpam-323	61	27	self	self	NOUN
ejpam-323	61	28	-	-	PUNCT
ejpam-323	61	29	adjoint	adjoint	NOUN
ejpam-323	61	30	with	with	ADP
ejpam-323	61	31	compact	compact	ADJ
ejpam-323	61	32	resolvent	resolvent	NOUN
ejpam-323	61	33	.	.	PUNCT
ejpam-323	62	1	consequently	consequently	ADV
ejpam-323	62	2	,	,	PUNCT
ejpam-323	62	3	its	its	PRON
ejpam-323	62	4	spectrum	spectrum	NOUN
ejpam-323	62	5	consists	consist	VERB
ejpam-323	62	6	entirely	entirely	ADV
ejpam-323	62	7	of	of	ADP
ejpam-323	62	8	isolated	isolated	ADJ
ejpam-323	62	9	,	,	PUNCT
ejpam-323	62	10	real	real	ADJ
ejpam-323	62	11	and	and	CCONJ
ejpam-323	62	12	positive	positive	ADJ
ejpam-323	62	13	eigenvalues	eigenvalue	NOUN
ejpam-323	62	14	with	with	ADP
ejpam-323	62	15	finite	finite	ADJ
ejpam-323	62	16	multiplicity	multiplicity	NOUN
ejpam-323	62	17	,	,	PUNCT
ejpam-323	62	18	and	and	CCONJ
ejpam-323	62	19	there	there	PRON
ejpam-323	62	20	are	be	VERB
ejpam-323	62	21	corresponding	correspond	VERB
ejpam-323	62	22	eigenfunctions	eigenfunction	NOUN
ejpam-323	62	23	which	which	PRON
ejpam-323	62	24	make	make	VERB
ejpam-323	62	25	up	up	ADP
ejpam-323	62	26	an	an	DET
ejpam-323	62	27	orthonormal	orthonormal	ADJ
ejpam-323	62	28	basis	basis	NOUN
ejpam-323	62	29	of	of	ADP
ejpam-323	62	30	l2(ωε	l2(ωε	PROPN
ejpam-323	62	31	)	)	PUNCT
ejpam-323	62	32	.	.	PUNCT
ejpam-323	63	1	by	by	ADP
ejpam-323	63	2	extending	extend	VERB
ejpam-323	63	3	our	our	PRON
ejpam-323	63	4	approach	approach	NOUN
ejpam-323	63	5	for	for	ADP
ejpam-323	63	6	treating	treat	VERB
ejpam-323	63	7	the	the	DET
ejpam-323	63	8	eigenvalue	eigenvalue	ADJ
ejpam-323	63	9	problem	problem	NOUN
ejpam-323	63	10	(	(	PUNCT
ejpam-323	63	11	3	3	X
ejpam-323	63	12	)	)	PUNCT
ejpam-323	63	13	we	we	PRON
ejpam-323	63	14	will	will	AUX
ejpam-323	63	15	investigate	investigate	VERB
ejpam-323	63	16	the	the	DET
ejpam-323	63	17	splitting	splitting	NOUN
ejpam-323	63	18	of	of	ADP
ejpam-323	63	19	the	the	DET
ejpam-323	63	20	eigenvalues	eigenvalue	NOUN
ejpam-323	63	21	and	and	CCONJ
ejpam-323	63	22	derive	derive	VERB
ejpam-323	63	23	their	their	PRON
ejpam-323	63	24	asymptotic	asymptotic	ADJ
ejpam-323	63	25	expansions	expansion	NOUN
ejpam-323	63	26	under	under	ADP
ejpam-323	63	27	boundary	boundary	ADJ
ejpam-323	63	28	perturbations	perturbation	NOUN
ejpam-323	63	29	.	.	PUNCT
ejpam-323	64	1	let	let	VERB
ejpam-323	64	2	ω2	ω2	ADV
ejpam-323	64	3	0	0	PUNCT
ejpam-323	64	4	>	>	SYM
ejpam-323	64	5	0	0	NUM
ejpam-323	64	6	denote	denote	VERB
ejpam-323	64	7	an	an	DET
ejpam-323	64	8	eigenfrequency	eigenfrequency	NOUN
ejpam-323	64	9	of	of	ADP
ejpam-323	64	10	the	the	DET
ejpam-323	64	11	eigenvalue	eigenvalue	PROPN
ejpam-323	64	12	problem	problem	NOUN
ejpam-323	64	13	(	(	PUNCT
ejpam-323	64	14	3	3	NUM
ejpam-323	64	15	)	)	PUNCT
ejpam-323	64	16	for	for	ADP
ejpam-323	64	17	ε=	ε=	NOUN
ejpam-323	64	18	0	0	NUM
ejpam-323	64	19	with	with	ADP
ejpam-323	64	20	geometric	geometric	ADJ
ejpam-323	64	21	multiplicity	multiplicity	NOUN
ejpam-323	64	22	m	m	VERB
ejpam-323	64	23	in	in	ADP
ejpam-323	64	24	the	the	DET
ejpam-323	64	25	domain	domain	NOUN
ejpam-323	64	26	ω	ω	PROPN
ejpam-323	64	27	≡	≡	PROPN
ejpam-323	64	28	ω0	ω0	NOUN
ejpam-323	64	29	.	.	PUNCT
ejpam-323	65	1	there	there	PRON
ejpam-323	65	2	exists	exist	VERB
ejpam-323	65	3	a	a	DET
ejpam-323	65	4	small	small	ADJ
ejpam-323	65	5	constant	constant	ADJ
ejpam-323	65	6	r0	r0	NOUN
ejpam-323	65	7	>	>	X
ejpam-323	65	8	0	0	NUM
ejpam-323	66	1	such	such	ADJ
ejpam-323	66	2	that	that	DET
ejpam-323	66	3	ω2	ω2	ADJ
ejpam-323	66	4	0	0	NUM
ejpam-323	66	5	is	be	AUX
ejpam-323	66	6	the	the	DET
ejpam-323	66	7	unique	unique	ADJ
ejpam-323	66	8	eigenfrequency	eigenfrequency	NOUN
ejpam-323	66	9	of	of	ADP
ejpam-323	66	10	(	(	PUNCT
ejpam-323	66	11	3	3	NUM
ejpam-323	66	12	)	)	PUNCT
ejpam-323	66	13	for	for	ADP
ejpam-323	66	14	ε=	ε=	NOUN
ejpam-323	66	15	0	0	NUM
ejpam-323	66	16	in	in	ADP
ejpam-323	66	17	the	the	DET
ejpam-323	66	18	set	set	VERB
ejpam-323	66	19	�	�	PROPN
ejpam-323	66	20	ω2,ω	ω2,ω	PROPN
ejpam-323	66	21	∈	∈	PROPN
ejpam-323	66	22	dr0	dr0	NOUN
ejpam-323	66	23	(	(	PUNCT
ejpam-323	66	24	ω0	ω0	PROPN
ejpam-323	66	25	)	)	PUNCT
ejpam-323	66	26	,	,	PUNCT
ejpam-323	66	27	where	where	SCONJ
ejpam-323	66	28	dr0	dr0	NOUN
ejpam-323	66	29	(	(	PUNCT
ejpam-323	66	30	ω0	ω0	NOUN
ejpam-323	66	31	)	)	PUNCT
ejpam-323	66	32	is	be	AUX
ejpam-323	66	33	a	a	DET
ejpam-323	66	34	disk	disk	NOUN
ejpam-323	66	35	of	of	ADP
ejpam-323	66	36	center	center	NOUN
ejpam-323	66	37	ω0	ω0	NOUN
ejpam-323	66	38	and	and	CCONJ
ejpam-323	66	39	radius	radius	NOUN
ejpam-323	66	40	r0	r0	NOUN
ejpam-323	66	41	.	.	PUNCT
ejpam-323	67	1	let	let	VERB
ejpam-323	67	2	us	we	PRON
ejpam-323	67	3	call	call	VERB
ejpam-323	67	4	the	the	DET
ejpam-323	67	5	ω0	ω0	NOUN
ejpam-323	67	6	-	-	PUNCT
ejpam-323	67	7	group	group	NOUN
ejpam-323	67	8	the	the	DET
ejpam-323	67	9	totality	totality	NOUN
ejpam-323	67	10	of	of	ADP
ejpam-323	67	11	the	the	DET
ejpam-323	67	12	perturbed	perturb	VERB
ejpam-323	67	13	eigenfrequencies	eigenfrequencie	NOUN
ejpam-323	67	14	of	of	ADP
ejpam-323	67	15	(	(	PUNCT
ejpam-323	67	16	3	3	NUM
ejpam-323	67	17	)	)	PUNCT
ejpam-323	67	18	for	for	ADP
ejpam-323	67	19	ε	ε	PROPN
ejpam-323	67	20	>	>	X
ejpam-323	67	21	0	0	NUM
ejpam-323	67	22	generated	generate	VERB
ejpam-323	67	23	by	by	ADP
ejpam-323	67	24	splitting	splitting	NOUN
ejpam-323	67	25	from	from	ADP
ejpam-323	67	26	ω2	ω2	PROPN
ejpam-323	67	27	0	0	NUM
ejpam-323	67	28	and	and	CCONJ
ejpam-323	67	29	chosen	choose	VERB
ejpam-323	67	30	to	to	PART
ejpam-323	67	31	be	be	AUX
ejpam-323	67	32	an	an	DET
ejpam-323	67	33	increasing	increase	VERB
ejpam-323	67	34	family	family	NOUN
ejpam-323	67	35	.	.	PUNCT
ejpam-323	68	1	the	the	DET
ejpam-323	68	2	following	follow	VERB
ejpam-323	68	3	analyticity	analyticity	NOUN
ejpam-323	68	4	result	result	NOUN
ejpam-323	68	5	is	be	AUX
ejpam-323	68	6	well	well	ADV
ejpam-323	68	7	-	-	PUNCT
ejpam-323	68	8	known	know	VERB
ejpam-323	68	9	[	[	X
ejpam-323	68	10	9]-[22	9]-[22	NUM
ejpam-323	68	11	]	]	PUNCT
ejpam-323	68	12	.	.	PUNCT
ejpam-323	69	1	theorem	theorem	NOUN
ejpam-323	69	2	1	1	NUM
ejpam-323	69	3	.	.	PUNCT
ejpam-323	70	1	(	(	PUNCT
ejpam-323	70	2	kato	kato	PROPN
ejpam-323	70	3	[	[	X
ejpam-323	70	4	12	12	NUM
ejpam-323	70	5	,	,	PUNCT
ejpam-323	70	6	§	§	NOUN
ejpam-323	70	7	vii.6	vii.6	NOUN
ejpam-323	70	8	]	]	PUNCT
ejpam-323	70	9	,	,	PUNCT
ejpam-323	70	10	rellich	rellich	PRON
ejpam-323	71	1	[	[	X
ejpam-323	71	2	25	25	NUM
ejpam-323	71	3	,	,	PUNCT
ejpam-323	71	4	§	§	NOUN
ejpam-323	71	5	§	§	NOUN
ejpam-323	71	6	ii.2	ii.2	PROPN
ejpam-323	71	7	and	and	CCONJ
ejpam-323	71	8	ii.6	ii.6	NOUN
ejpam-323	71	9	]	]	PUNCT
ejpam-323	71	10	)	)	PUNCT
ejpam-323	71	11	there	there	PRON
ejpam-323	71	12	exits	exit	VERB
ejpam-323	71	13	ε0	ε0	PROPN
ejpam-323	71	14	>	>	X
ejpam-323	71	15	0	0	NUM
ejpam-323	71	16	such	such	ADJ
ejpam-323	71	17	that	that	PRON
ejpam-323	71	18	for	for	ADP
ejpam-323	71	19	|ε|	|ε|	PRON
ejpam-323	71	20	<	<	X
ejpam-323	71	21	ε0	ε0	PROPN
ejpam-323	71	22	,	,	PUNCT
ejpam-323	71	23	the	the	DET
ejpam-323	71	24	ω0	ω0	NOUN
ejpam-323	71	25	-	-	PUNCT
ejpam-323	71	26	group	group	NOUN
ejpam-323	71	27	consists	consist	VERB
ejpam-323	71	28	of	of	ADP
ejpam-323	71	29	m−	m−	PROPN
ejpam-323	71	30	eigenfrequencies	eigenfrequencie	NOUN
ejpam-323	71	31	,	,	PUNCT
ejpam-323	71	32	ω2	ω2	PROPN
ejpam-323	71	33	j	j	PROPN
ejpam-323	71	34	(	(	PUNCT
ejpam-323	71	35	ε	ε	PROPN
ejpam-323	71	36	)	)	PUNCT
ejpam-323	71	37	,	,	PUNCT
ejpam-323	71	38	j	j	PROPN
ejpam-323	71	39	=	=	SYM
ejpam-323	71	40	1	1	NUM
ejpam-323	71	41	,	,	PUNCT
ejpam-323	71	42	.	.	PUNCT
ejpam-323	71	43	.	.	PUNCT
ejpam-323	72	1	.	.	PUNCT
ejpam-323	73	1	,	,	PUNCT
ejpam-323	73	2	m	m	AUX
ejpam-323	73	3	(	(	PUNCT
ejpam-323	73	4	repeated	repeat	VERB
ejpam-323	73	5	according	accord	VERB
ejpam-323	73	6	to	to	ADP
ejpam-323	73	7	their	their	PRON
ejpam-323	73	8	multiplicity	multiplicity	NOUN
ejpam-323	73	9	)	)	PUNCT
ejpam-323	73	10	.	.	PUNCT
ejpam-323	74	1	moreover	moreover	ADV
ejpam-323	74	2	,	,	PUNCT
ejpam-323	74	3	they	they	PRON
ejpam-323	74	4	are	be	AUX
ejpam-323	74	5	analytic	analytic	ADJ
ejpam-323	74	6	functions	function	NOUN
ejpam-323	74	7	with	with	ADP
ejpam-323	74	8	respect	respect	NOUN
ejpam-323	74	9	to	to	ADP
ejpam-323	74	10	ε	ε	PROPN
ejpam-323	74	11	satisfying	satisfy	VERB
ejpam-323	74	12	ω2	ω2	PROPN
ejpam-323	74	13	j	j	PROPN
ejpam-323	74	14	(	(	PUNCT
ejpam-323	74	15	0	0	NUM
ejpam-323	74	16	)	)	PUNCT
ejpam-323	74	17	=	=	NOUN
ejpam-323	74	18	ω	ω	NUM
ejpam-323	74	19	2	2	NUM
ejpam-323	74	20	0	0	NUM
ejpam-323	74	21	,	,	PUNCT
ejpam-323	74	22	j	j	PROPN
ejpam-323	74	23	=	=	SYM
ejpam-323	74	24	1	1	NUM
ejpam-323	74	25	,	,	PUNCT
ejpam-323	74	26	.	.	PUNCT
ejpam-323	74	27	.	.	PUNCT
ejpam-323	75	1	.	.	PUNCT
ejpam-323	76	1	,	,	PUNCT
ejpam-323	76	2	m.	m.	NOUN
ejpam-323	76	3	the	the	DET
ejpam-323	76	4	normalized	normalize	VERB
ejpam-323	76	5	eigenfunctions	eigenfunction	NOUN
ejpam-323	76	6	associated	associate	VERB
ejpam-323	76	7	to	to	ADP
ejpam-323	76	8	the	the	DET
ejpam-323	76	9	ω0	ω0	NOUN
ejpam-323	76	10	-	-	PUNCT
ejpam-323	76	11	group	group	NOUN
ejpam-323	76	12	of	of	ADP
ejpam-323	76	13	eigenfrequencies	eigenfrequencie	NOUN
ejpam-323	76	14	are	be	AUX
ejpam-323	76	15	analytic	analytic	ADJ
ejpam-323	76	16	and	and	CCONJ
ejpam-323	76	17	their	their	PRON
ejpam-323	76	18	values	value	NOUN
ejpam-323	76	19	at	at	ADP
ejpam-323	76	20	0	0	NUM
ejpam-323	76	21	(	(	PUNCT
ejpam-323	76	22	{	{	PUNCT
ejpam-323	76	23	u	u	NOUN
ejpam-323	76	24	j	j	PROPN
ejpam-323	76	25	0	0	NUM
ejpam-323	76	26	}	}	PUNCT
ejpam-323	76	27	1≤	1≤	NUM
ejpam-323	76	28	j≤m	j≤m	NOUN
ejpam-323	76	29	)	)	PUNCT
ejpam-323	76	30	are	be	AUX
ejpam-323	76	31	m	m	VERB
ejpam-323	76	32	linearly	linearly	ADV
ejpam-323	76	33	independent	independent	ADJ
ejpam-323	76	34	solutions	solution	NOUN
ejpam-323	76	35	of	of	ADP
ejpam-323	76	36	the	the	DET
ejpam-323	76	37	unperturbed	unperturbed	ADJ
ejpam-323	76	38	eigenvalue	eigenvalue	NOUN
ejpam-323	76	39	problem	problem	NOUN
ejpam-323	76	40	.	.	PUNCT
ejpam-323	77	1	classical	classical	ADJ
ejpam-323	77	2	regularity	regularity	NOUN
ejpam-323	77	3	results	result	NOUN
ejpam-323	77	4	and	and	CCONJ
ejpam-323	77	5	the	the	DET
ejpam-323	77	6	previous	previous	ADJ
ejpam-323	77	7	theorem	theorem	NOUN
ejpam-323	77	8	imply	imply	VERB
ejpam-323	77	9	that	that	SCONJ
ejpam-323	77	10	the	the	DET
ejpam-323	77	11	eigenfunctions	eigenfunction	NOUN
ejpam-323	77	12	associated	associate	VERB
ejpam-323	77	13	to	to	ADP
ejpam-323	77	14	the	the	DET
ejpam-323	77	15	ω0	ω0	NOUN
ejpam-323	77	16	-	-	PUNCT
ejpam-323	77	17	group	group	NOUN
ejpam-323	77	18	of	of	ADP
ejpam-323	77	19	eigenvalues	eigenvalue	NOUN
ejpam-323	77	20	are	be	AUX
ejpam-323	77	21	separately	separately	ADV
ejpam-323	77	22	analytic	analytic	ADJ
ejpam-323	77	23	in	in	ADP
ejpam-323	77	24	the	the	DET
ejpam-323	77	25	small	small	ADJ
ejpam-323	77	26	parameter	parameter	NOUN
ejpam-323	77	27	ε	ε	PROPN
ejpam-323	77	28	and	and	CCONJ
ejpam-323	77	29	the	the	DET
ejpam-323	77	30	spatial	spatial	ADJ
ejpam-323	77	31	variable	variable	NOUN
ejpam-323	77	32	x	x	X
ejpam-323	77	33	.	.	PUNCT
ejpam-323	78	1	by	by	ADP
ejpam-323	78	2	an	an	DET
ejpam-323	78	3	integral	integral	ADJ
ejpam-323	78	4	equation	equation	NOUN
ejpam-323	78	5	technique	technique	NOUN
ejpam-323	78	6	we	we	PRON
ejpam-323	78	7	also	also	ADV
ejpam-323	78	8	established	establish	VERB
ejpam-323	78	9	[	[	PUNCT
ejpam-323	78	10	13	13	NUM
ejpam-323	78	11	,	,	PUNCT
ejpam-323	78	12	thm	thm	PROPN
ejpam-323	78	13	.	.	PROPN
ejpam-323	78	14	5.4	5.4	NUM
ejpam-323	78	15	,	,	PUNCT
ejpam-323	78	16	p.1219	p.1219	PROPN
ejpam-323	78	17	]	]	PUNCT
ejpam-323	79	1	the	the	DET
ejpam-323	79	2	joint	joint	ADJ
ejpam-323	79	3	analytic	analytic	ADJ
ejpam-323	79	4	dependence	dependence	NOUN
ejpam-323	79	5	of	of	ADP
ejpam-323	79	6	these	these	DET
ejpam-323	79	7	functions	function	NOUN
ejpam-323	79	8	with	with	ADP
ejpam-323	79	9	respect	respect	NOUN
ejpam-323	79	10	to	to	ADP
ejpam-323	79	11	(	(	PUNCT
ejpam-323	79	12	x	x	X
ejpam-323	79	13	,	,	PUNCT
ejpam-323	79	14	ε	ε	PROPN
ejpam-323	79	15	)	)	PUNCT
ejpam-323	79	16	.	.	PUNCT
ejpam-323	80	1	a.	a.	PROPN
ejpam-323	80	2	khelifi	khelifi	PROPN
ejpam-323	80	3	,	,	PUNCT
ejpam-323	80	4	m.	m.	NOUN
ejpam-323	80	5	shamma	shamma	PROPN
ejpam-323	80	6	/	/	SYM
ejpam-323	80	7	eur	eur	PROPN
ejpam-323	80	8	.	.	PUNCT
ejpam-323	81	1	j.	j.	PROPN
ejpam-323	81	2	pure	pure	PROPN
ejpam-323	81	3	appl	appl	PROPN
ejpam-323	81	4	.	.	PROPN
ejpam-323	81	5	math	math	PROPN
ejpam-323	81	6	,	,	PUNCT
ejpam-323	81	7	3	3	NUM
ejpam-323	81	8	(	(	PUNCT
ejpam-323	81	9	2010	2010	NUM
ejpam-323	81	10	)	)	PUNCT
ejpam-323	81	11	,	,	PUNCT
ejpam-323	81	12	282	282	NUM
ejpam-323	81	13	-	-	NUM
ejpam-323	81	14	294	294	NUM
ejpam-323	81	15	285	285	NUM
ejpam-323	81	16	we	we	PRON
ejpam-323	81	17	will	will	AUX
ejpam-323	81	18	develop	develop	VERB
ejpam-323	81	19	a	a	DET
ejpam-323	81	20	boundary	boundary	ADJ
ejpam-323	81	21	integral	integral	ADJ
ejpam-323	81	22	formulation	formulation	NOUN
ejpam-323	81	23	for	for	ADP
ejpam-323	81	24	solving	solve	VERB
ejpam-323	81	25	the	the	DET
ejpam-323	81	26	eigenvalue	eigenvalue	PROPN
ejpam-323	81	27	problem	problem	NOUN
ejpam-323	81	28	(	(	PUNCT
ejpam-323	81	29	2	2	NUM
ejpam-323	81	30	)	)	PUNCT
ejpam-323	81	31	.	.	PUNCT
ejpam-323	82	1	the	the	DET
ejpam-323	82	2	integral	integral	ADJ
ejpam-323	82	3	equations	equation	NOUN
ejpam-323	82	4	applying	apply	VERB
ejpam-323	82	5	to	to	ADP
ejpam-323	82	6	this	this	DET
ejpam-323	82	7	problem	problem	NOUN
ejpam-323	82	8	will	will	AUX
ejpam-323	82	9	be	be	AUX
ejpam-323	82	10	obtained	obtain	VERB
ejpam-323	82	11	from	from	ADP
ejpam-323	82	12	a	a	DET
ejpam-323	82	13	study	study	NOUN
ejpam-323	82	14	of	of	ADP
ejpam-323	82	15	the	the	DET
ejpam-323	82	16	layer	layer	NOUN
ejpam-323	82	17	potentials	potential	VERB
ejpam-323	82	18	for	for	ADP
ejpam-323	82	19	the	the	DET
ejpam-323	82	20	helmholtz	helmholtz	NOUN
ejpam-323	82	21	equation	equation	NOUN
ejpam-323	82	22	.	.	PUNCT
ejpam-323	83	1	2	2	NUM
ejpam-323	83	2	for	for	ADP
ejpam-323	83	3	λ	λ	PROPN
ejpam-323	83	4	>	>	X
ejpam-323	83	5	0	0	PROPN
ejpam-323	83	6	,	,	PUNCT
ejpam-323	83	7	a	a	DET
ejpam-323	83	8	fundamental	fundamental	ADJ
ejpam-323	83	9	solution	solution	NOUN
ejpam-323	83	10	γλ(x	γλ(x	NUM
ejpam-323	83	11	)	)	PUNCT
ejpam-323	83	12	to	to	ADP
ejpam-323	83	13	the	the	DET
ejpam-323	83	14	helmholtz	helmholtz	NOUN
ejpam-323	83	15	operator	operator	NOUN
ejpam-323	83	16	∆+λ2	∆+λ2	PROPN
ejpam-323	83	17	in	in	ADP
ejpam-323	83	18	rd	rd	PROPN
ejpam-323	83	19	,	,	PUNCT
ejpam-323	84	1	d	d	X
ejpam-323	84	2	=	=	SYM
ejpam-323	84	3	2,3	2,3	NUM
ejpam-323	84	4	,	,	PUNCT
ejpam-323	84	5	is	be	AUX
ejpam-323	84	6	given	give	VERB
ejpam-323	84	7	by	by	ADP
ejpam-323	84	8	γλ(x	γλ(x	NOUN
ejpam-323	84	9	)	)	PUNCT
ejpam-323	84	10	=	=	PUNCT
ejpam-323	85	1			PROPN
ejpam-323	85	2			PRON
ejpam-323	85	3			NOUN
ejpam-323	85	4	−	−	PROPN
ejpam-323	85	5	i	i	PRON
ejpam-323	85	6	4	4	NUM
ejpam-323	85	7	h	h	NOUN
ejpam-323	85	8	(	(	PUNCT
ejpam-323	85	9	1	1	NUM
ejpam-323	85	10	)	)	PUNCT
ejpam-323	85	11	0	0	NUM
ejpam-323	86	1	(	(	PUNCT
ejpam-323	86	2	λ‖x‖	λ‖x‖	PROPN
ejpam-323	86	3	)	)	PUNCT
ejpam-323	86	4	,	,	PUNCT
ejpam-323	86	5	d	d	NOUN
ejpam-323	86	6	=	=	SYM
ejpam-323	86	7	2	2	NUM
ejpam-323	86	8	,	,	PUNCT
ejpam-323	86	9	−	−	PROPN
ejpam-323	86	10	eiλ‖x‖	eiλ‖x‖	NOUN
ejpam-323	86	11	4π‖x‖	4π‖x‖	NUM
ejpam-323	86	12	,	,	PUNCT
ejpam-323	86	13	d	d	X
ejpam-323	86	14	=	=	SYM
ejpam-323	86	15	3	3	NUM
ejpam-323	86	16	,	,	PUNCT
ejpam-323	86	17	for	for	ADP
ejpam-323	86	18	x	x	SYM
ejpam-323	86	19	6=	6=	ADP
ejpam-323	86	20	0	0	NUM
ejpam-323	86	21	,	,	PUNCT
ejpam-323	86	22	where	where	SCONJ
ejpam-323	86	23	h	h	NOUN
ejpam-323	86	24	(	(	PUNCT
ejpam-323	86	25	1	1	NUM
ejpam-323	86	26	)	)	PUNCT
ejpam-323	86	27	0	0	NUM
ejpam-323	86	28	is	be	AUX
ejpam-323	86	29	the	the	DET
ejpam-323	86	30	hankel	hankel	NOUN
ejpam-323	86	31	function	function	NOUN
ejpam-323	86	32	of	of	ADP
ejpam-323	86	33	the	the	DET
ejpam-323	86	34	first	first	ADJ
ejpam-323	86	35	kind	kind	NOUN
ejpam-323	86	36	of	of	ADP
ejpam-323	86	37	order	order	NOUN
ejpam-323	86	38	0	0	PUNCT
ejpam-323	86	39	.	.	PUNCT
ejpam-323	86	40	suppose	suppose	VERB
ejpam-323	86	41	that	that	SCONJ
ejpam-323	86	42	g(x	g(x	PROPN
ejpam-323	86	43	,	,	PUNCT
ejpam-323	86	44	y	y	PROPN
ejpam-323	86	45	)	)	PUNCT
ejpam-323	86	46	=	=	PUNCT
ejpam-323	86	47	γω(ε)pµεǫε(x	γω(ε)pµεǫε(x	PROPN
ejpam-323	86	48	−	−	PROPN
ejpam-323	86	49	y	y	NOUN
ejpam-323	86	50	)	)	PUNCT
ejpam-323	86	51	.	.	PUNCT
ejpam-323	87	1	the	the	DET
ejpam-323	87	2	singularity	singularity	NOUN
ejpam-323	87	3	of	of	ADP
ejpam-323	87	4	this	this	DET
ejpam-323	87	5	function	function	NOUN
ejpam-323	87	6	has	have	VERB
ejpam-323	87	7	the	the	DET
ejpam-323	87	8	form	form	NOUN
ejpam-323	87	9	:	:	PUNCT
ejpam-323	87	10	g(x	g(x	ADJ
ejpam-323	87	11	,	,	PUNCT
ejpam-323	87	12	y	y	NOUN
ejpam-323	87	13	)	)	PUNCT
ejpam-323	87	14	∼	∼	NOUN
ejpam-323	87	15	(	(	PUNCT
ejpam-323	87	16	1	1	NUM
ejpam-323	87	17	2π	2π	NOUN
ejpam-323	87	18	log‖x	log‖x	PUNCT
ejpam-323	87	19	−	−	PROPN
ejpam-323	87	20	y‖+	y‖+	PROPN
ejpam-323	87	21	·	·	PUNCT
ejpam-323	87	22	·	·	PUNCT
ejpam-323	87	23	·	·	PUNCT
ejpam-323	87	24	as	as	SCONJ
ejpam-323	87	25	,	,	PUNCT
ejpam-323	87	26	x	x	PROPN
ejpam-323	87	27	→	→	SYM
ejpam-323	87	28	y	y	PROPN
ejpam-323	87	29	d	d	PROPN
ejpam-323	87	30	=	=	SYM
ejpam-323	87	31	2	2	NUM
ejpam-323	87	32	,	,	PUNCT
ejpam-323	87	33	1	1	NUM
ejpam-323	87	34	4π‖x−y‖	4π‖x−y‖	NUM
ejpam-323	87	35	+	+	NUM
ejpam-323	87	36	·	·	PUNCT
ejpam-323	87	37	·	·	PUNCT
ejpam-323	87	38	·	·	PUNCT
ejpam-323	87	39	as	as	ADP
ejpam-323	87	40	x	x	X
ejpam-323	87	41	→	→	SYM
ejpam-323	87	42	y	y	PROPN
ejpam-323	87	43	d	d	PROPN
ejpam-323	87	44	=	=	PROPN
ejpam-323	87	45	3	3	X
ejpam-323	87	46	.	.	PUNCT
ejpam-323	87	47	the	the	DET
ejpam-323	87	48	following	follow	VERB
ejpam-323	87	49	operator	operator	NOUN
ejpam-323	87	50	is	be	AUX
ejpam-323	87	51	well	well	ADV
ejpam-323	87	52	defined	define	VERB
ejpam-323	87	53	[	[	PUNCT
ejpam-323	87	54	2	2	NUM
ejpam-323	87	55	,	,	PUNCT
ejpam-323	87	56	16	16	NUM
ejpam-323	87	57	]	]	PUNCT
ejpam-323	87	58	s(ω	s(ω	PROPN
ejpam-323	87	59	)	)	PUNCT
ejpam-323	87	60	:	:	PUNCT
ejpam-323	88	1	h−1/2(∂ωε)→	h−1/2(∂ωε)→	NUM
ejpam-323	88	2	h1/2(∂ωε	h1/2(∂ωε	NOUN
ejpam-323	88	3	)	)	PUNCT
ejpam-323	88	4	where	where	SCONJ
ejpam-323	88	5	s(ω	s(ω	PROPN
ejpam-323	88	6	)	)	PUNCT
ejpam-323	88	7	:	:	PUNCT
ejpam-323	88	8	g→	g→	PROPN
ejpam-323	88	9	∫	∫	PROPN
ejpam-323	88	10	∂ωε	∂ωε	PROPN
ejpam-323	88	11	g	g	PROPN
ejpam-323	88	12	(	(	PUNCT
ejpam-323	88	13	·	·	PUNCT
ejpam-323	88	14	,	,	PUNCT
ejpam-323	88	15	y)g(y)dσ(y	y)g(y)dσ(y	PROPN
ejpam-323	88	16	)	)	PUNCT
ejpam-323	88	17	.	.	PUNCT
ejpam-323	89	1	for	for	ADP
ejpam-323	89	2	such	such	ADJ
ejpam-323	89	3	g	g	NOUN
ejpam-323	89	4	and	and	CCONJ
ejpam-323	89	5	every	every	DET
ejpam-323	89	6	x	x	PROPN
ejpam-323	89	7	∈	∈	PROPN
ejpam-323	89	8	∂ωε	∂ωε	NOUN
ejpam-323	89	9	,	,	PUNCT
ejpam-323	89	10	we	we	PRON
ejpam-323	89	11	denote	denote	VERB
ejpam-323	89	12	by	by	ADP
ejpam-323	89	13	g+(x	g+(x	PROPN
ejpam-323	89	14	)	)	PUNCT
ejpam-323	89	15	and	and	CCONJ
ejpam-323	89	16	g−(x	g−(x	NOUN
ejpam-323	89	17	)	)	PUNCT
ejpam-323	89	18	the	the	DET
ejpam-323	89	19	limits	limit	NOUN
ejpam-323	89	20	of	of	ADP
ejpam-323	89	21	g(y	g(y	NOUN
ejpam-323	89	22	)	)	PUNCT
ejpam-323	89	23	as	as	ADP
ejpam-323	89	24	y	y	PROPN
ejpam-323	89	25	→	→	SYM
ejpam-323	89	26	x	x	SYM
ejpam-323	89	27	,	,	PUNCT
ejpam-323	89	28	from	from	ADP
ejpam-323	89	29	y	y	PROPN
ejpam-323	89	30	∈	∈	PROPN
ejpam-323	89	31	ωε	ωε	NOUN
ejpam-323	89	32	and	and	CCONJ
ejpam-323	89	33	y	y	PROPN
ejpam-323	89	34	∈	∈	PROPN
ejpam-323	89	35	rd	rd	PROPN
ejpam-323	89	36	\ωε	\ωε	PROPN
ejpam-323	89	37	,	,	PUNCT
ejpam-323	89	38	respectively	respectively	ADV
ejpam-323	89	39	,	,	PUNCT
ejpam-323	89	40	when	when	SCONJ
ejpam-323	89	41	these	these	DET
ejpam-323	89	42	limits	limit	NOUN
ejpam-323	89	43	exist	exist	VERB
ejpam-323	89	44	.	.	PUNCT
ejpam-323	90	1	it	it	PRON
ejpam-323	90	2	is	be	AUX
ejpam-323	90	3	a	a	DET
ejpam-323	90	4	well	well	ADV
ejpam-323	90	5	-	-	PUNCT
ejpam-323	90	6	known	know	VERB
ejpam-323	90	7	classical	classical	ADJ
ejpam-323	90	8	result	result	NOUN
ejpam-323	90	9	that	that	SCONJ
ejpam-323	90	10	,	,	PUNCT
ejpam-323	90	11	for	for	ADP
ejpam-323	90	12	x	x	PROPN
ejpam-323	90	13	∈	∈	PROPN
ejpam-323	90	14	∂ωε	∂ωε	NOUN
ejpam-323	90	15	,	,	PUNCT
ejpam-323	90	16	s(ω)g(x	s(ω)g(x	NOUN
ejpam-323	90	17	)	)	PUNCT
ejpam-323	90	18	=	=	SYM
ejpam-323	90	19	(	(	PUNCT
ejpam-323	90	20	sl(ω)g)+(x	sl(ω)g)+(x	NOUN
ejpam-323	90	21	)	)	PUNCT
ejpam-323	90	22	=	=	SYM
ejpam-323	90	23	(	(	PUNCT
ejpam-323	90	24	sl(ω)g)−(x	sl(ω)g)−(x	PROPN
ejpam-323	90	25	)	)	PUNCT
ejpam-323	90	26	where	where	SCONJ
ejpam-323	90	27	the	the	DET
ejpam-323	90	28	operator	operator	NOUN
ejpam-323	90	29	sl(ω	sl(ω	NOUN
ejpam-323	90	30	)	)	PUNCT
ejpam-323	90	31	called	call	VERB
ejpam-323	90	32	single	single	ADJ
ejpam-323	90	33	-	-	PUNCT
ejpam-323	90	34	layer	layer	NOUN
ejpam-323	90	35	potential	potential	NOUN
ejpam-323	90	36	(	(	PUNCT
ejpam-323	90	37	see	see	VERB
ejpam-323	90	38	[	[	X
ejpam-323	90	39	5	5	NUM
ejpam-323	90	40	]	]	PUNCT
ejpam-323	90	41	,	,	PUNCT
ejpam-323	90	42	[	[	X
ejpam-323	90	43	16	16	NUM
ejpam-323	90	44	]	]	SYM
ejpam-323	90	45	)	)	PUNCT
ejpam-323	90	46	and	and	CCONJ
ejpam-323	90	47	s(ω	s(ω	PROPN
ejpam-323	90	48	)	)	PUNCT
ejpam-323	90	49	is	be	AUX
ejpam-323	90	50	pseudodifferential	pseudodifferential	ADJ
ejpam-323	90	51	operator	operator	NOUN
ejpam-323	90	52	of	of	ADP
ejpam-323	90	53	order	order	NOUN
ejpam-323	90	54	−1	−1	NOUN
ejpam-323	90	55	.	.	PUNCT
ejpam-323	91	1	throughout	throughout	ADP
ejpam-323	91	2	this	this	DET
ejpam-323	91	3	paper	paper	NOUN
ejpam-323	91	4	,	,	PUNCT
ejpam-323	91	5	we	we	PRON
ejpam-323	91	6	use	use	VERB
ejpam-323	91	7	for	for	ADP
ejpam-323	91	8	simplicity	simplicity	NOUN
ejpam-323	91	9	the	the	DET
ejpam-323	91	10	notation	notation	NOUN
ejpam-323	91	11	h	h	NOUN
ejpam-323	91	12	ς	ς	PROPN
ejpam-323	91	13	♯	♯	PROPN
ejpam-323	91	14	(	(	PUNCT
ejpam-323	91	15	]	]	SYM
ejpam-323	91	16	0	0	NUM
ejpam-323	91	17	,	,	PUNCT
ejpam-323	91	18	t1[×	t1[×	NOUN
ejpam-323	91	19	·	·	PUNCT
ejpam-323	91	20	·	·	PUNCT
ejpam-323	91	21	·	·	PUNCT
ejpam-323	91	22	×]0	×]0	ADP
ejpam-323	91	23	,	,	PUNCT
ejpam-323	91	24	td−1	td−1	PROPN
ejpam-323	91	25	[	[	NOUN
ejpam-323	91	26	)	)	PUNCT
ejpam-323	91	27	=	=	SYM
ejpam-323	91	28	hς(rd−1/]0	hς(rd−1/]0	PROPN
ejpam-323	91	29	,	,	PUNCT
ejpam-323	91	30	t1[×	t1[×	NOUN
ejpam-323	91	31	·	·	PUNCT
ejpam-323	91	32	·	·	PUNCT
ejpam-323	91	33	·	·	PUNCT
ejpam-323	91	34	×]0	×]0	ADP
ejpam-323	91	35	,	,	PUNCT
ejpam-323	91	36	td−1	td−1	PROPN
ejpam-323	91	37	[	[	NOUN
ejpam-323	91	38	)	)	PUNCT
ejpam-323	91	39	,	,	PUNCT
ejpam-323	91	40	for	for	ADP
ejpam-323	91	41	ς	ς	PROPN
ejpam-323	91	42	∈	∈	PROPN
ejpam-323	91	43	r	r	NOUN
ejpam-323	91	44	,	,	PUNCT
ejpam-323	91	45	where	where	SCONJ
ejpam-323	91	46	hς(rd−1/]0	hς(rd−1/]0	NOUN
ejpam-323	91	47	,	,	PUNCT
ejpam-323	91	48	t1[×	t1[×	NOUN
ejpam-323	91	49	·	·	PUNCT
ejpam-323	91	50	·	·	PUNCT
ejpam-323	91	51	·	·	PUNCT
ejpam-323	91	52	×]0	×]0	ADP
ejpam-323	91	53	,	,	PUNCT
ejpam-323	91	54	td−1	td−1	PROPN
ejpam-323	91	55	[	[	NOUN
ejpam-323	91	56	)	)	PUNCT
ejpam-323	91	57	denotes	denote	VERB
ejpam-323	91	58	the	the	DET
ejpam-323	91	59	classical	classical	ADJ
ejpam-323	91	60	sobolev	sobolev	NOUN
ejpam-323	91	61	hς	hς	PROPN
ejpam-323	91	62	-	-	NOUN
ejpam-323	91	63	space	space	NOUN
ejpam-323	91	64	on	on	ADP
ejpam-323	91	65	the	the	DET
ejpam-323	91	66	quotient	quotient	NOUN
ejpam-323	91	67	r	r	PROPN
ejpam-323	91	68	d−1/]0	d−1/]0	PROPN
ejpam-323	91	69	,	,	PUNCT
ejpam-323	91	70	t1[×	t1[×	NOUN
ejpam-323	91	71	·	·	PUNCT
ejpam-323	91	72	·	·	PUNCT
ejpam-323	91	73	·	·	PUNCT
ejpam-323	91	74	×]0	×]0	ADP
ejpam-323	91	75	,	,	PUNCT
ejpam-323	91	76	td−1	td−1	PROPN
ejpam-323	91	77	[	[	PUNCT
ejpam-323	91	78	(	(	PUNCT
ejpam-323	91	79	adams	adam	NOUN
ejpam-323	91	80	[	[	X
ejpam-323	91	81	1	1	NUM
ejpam-323	91	82	]	]	PUNCT
ejpam-323	91	83	)	)	PUNCT
ejpam-323	91	84	.	.	PUNCT
ejpam-323	92	1	using	use	VERB
ejpam-323	92	2	change	change	NOUN
ejpam-323	92	3	of	of	ADP
ejpam-323	92	4	variables	variable	NOUN
ejpam-323	92	5	and	and	CCONJ
ejpam-323	92	6	integral	integral	ADJ
ejpam-323	92	7	equations	equation	NOUN
ejpam-323	92	8	,	,	PUNCT
ejpam-323	92	9	the	the	DET
ejpam-323	92	10	following	following	ADJ
ejpam-323	92	11	result	result	NOUN
ejpam-323	92	12	immediately	immediately	ADV
ejpam-323	92	13	holds	hold	VERB
ejpam-323	92	14	(	(	PUNCT
ejpam-323	92	15	see	see	VERB
ejpam-323	92	16	[	[	X
ejpam-323	92	17	23	23	NUM
ejpam-323	92	18	]	]	NUM
ejpam-323	92	19	)	)	PUNCT
ejpam-323	92	20	.	.	PUNCT
ejpam-323	93	1	proposition	proposition	NOUN
ejpam-323	93	2	1	1	NUM
ejpam-323	93	3	.	.	PUNCT
ejpam-323	94	1	let	let	VERB
ejpam-323	94	2	aε(ω	aε(ω	NUM
ejpam-323	94	3	)	)	PUNCT
ejpam-323	94	4	:	:	PUNCT
ejpam-323	95	1	h	h	PROPN
ejpam-323	95	2	−1/2	−1/2	VERB
ejpam-323	95	3	♯	♯	PROPN
ejpam-323	95	4	(	(	PUNCT
ejpam-323	95	5	]	]	SYM
ejpam-323	95	6	0	0	NUM
ejpam-323	95	7	,	,	PUNCT
ejpam-323	95	8	t1[×	t1[×	NOUN
ejpam-323	95	9	·	·	PUNCT
ejpam-323	95	10	·	·	PUNCT
ejpam-323	95	11	·	·	PUNCT
ejpam-323	95	12	×]0	×]0	ADP
ejpam-323	95	13	,	,	PUNCT
ejpam-323	95	14	td−1[)→	td−1[)→	PROPN
ejpam-323	95	15	h	h	NOUN
ejpam-323	95	16	1/2	1/2	NUM
ejpam-323	95	17	♯	♯	PROPN
ejpam-323	95	18	(	(	PUNCT
ejpam-323	95	19	]	]	SYM
ejpam-323	95	20	0	0	NUM
ejpam-323	95	21	,	,	PUNCT
ejpam-323	95	22	t1[×	t1[×	NOUN
ejpam-323	95	23	·	·	PUNCT
ejpam-323	95	24	·	·	PUNCT
ejpam-323	95	25	·	·	PUNCT
ejpam-323	95	26	×]0	×]0	ADP
ejpam-323	95	27	,	,	PUNCT
ejpam-323	95	28	td−1	td−1	PROPN
ejpam-323	95	29	[	[	X
ejpam-323	95	30	)	)	PUNCT
ejpam-323	95	31	be	be	AUX
ejpam-323	95	32	defined	define	VERB
ejpam-323	95	33	as	as	SCONJ
ejpam-323	95	34	follows	follow	VERB
ejpam-323	95	35	:	:	PUNCT
ejpam-323	95	36	aε(ω	aε(ω	NUM
ejpam-323	95	37	)	)	PUNCT
ejpam-323	95	38	f	f	PROPN
ejpam-323	95	39	(	(	PUNCT
ejpam-323	95	40	t	t	PROPN
ejpam-323	95	41	)	)	PUNCT
ejpam-323	95	42	=	=	PROPN
ejpam-323	95	43	�	�	PROPN
ejpam-323	95	44	s(ω	s(ω	PROPN
ejpam-323	95	45	)	)	PUNCT
ejpam-323	95	46	f	f	PROPN
ejpam-323	96	1	(	(	PUNCT
ejpam-323	96	2	γ−1	γ−1	PROPN
ejpam-323	96	3	ε	ε	PROPN
ejpam-323	96	4	)	)	PUNCT
ejpam-323	96	5	�	�	PROPN
ejpam-323	96	6	(	(	PUNCT
ejpam-323	96	7	γε(t	γε(t	NOUN
ejpam-323	96	8	)	)	PUNCT
ejpam-323	96	9	)	)	PUNCT
ejpam-323	97	1	=	=	SYM
ejpam-323	97	2	∫	∫	PROPN
ejpam-323	97	3	]	]	X
ejpam-323	97	4	0,t1[×···×]0,td−1	0,t1[×···×]0,td−1	NUM
ejpam-323	97	5	[	[	PUNCT
ejpam-323	97	6	g(γε(t),γε(s))|∇γε(s)|	g(γε(t),γε(s))|∇γε(s)|	X
ejpam-323	97	7	f	f	PROPN
ejpam-323	97	8	(	(	PUNCT
ejpam-323	97	9	s)ds	s)ds	PROPN
ejpam-323	97	10	for	for	ADP
ejpam-323	97	11	f	f	PROPN
ejpam-323	97	12	∈	∈	PROPN
ejpam-323	97	13	h	h	NOUN
ejpam-323	97	14	−1/2	−1/2	VERB
ejpam-323	97	15	♯	♯	PROPN
ejpam-323	97	16	(	(	PUNCT
ejpam-323	97	17	]	]	SYM
ejpam-323	97	18	0	0	NUM
ejpam-323	97	19	,	,	PUNCT
ejpam-323	97	20	t1[×	t1[×	NOUN
ejpam-323	97	21	·	·	PUNCT
ejpam-323	97	22	·	·	PUNCT
ejpam-323	97	23	·	·	PUNCT
ejpam-323	97	24	×]0	×]0	ADP
ejpam-323	97	25	,	,	PUNCT
ejpam-323	97	26	td−1	td−1	PROPN
ejpam-323	97	27	[	[	NOUN
ejpam-323	97	28	)	)	PUNCT
ejpam-323	97	29	.	.	PUNCT
ejpam-323	98	1	a.	a.	PROPN
ejpam-323	98	2	khelifi	khelifi	PROPN
ejpam-323	98	3	,	,	PUNCT
ejpam-323	98	4	m.	m.	NOUN
ejpam-323	98	5	shamma	shamma	PROPN
ejpam-323	98	6	/	/	SYM
ejpam-323	98	7	eur	eur	PROPN
ejpam-323	98	8	.	.	PUNCT
ejpam-323	99	1	j.	j.	PROPN
ejpam-323	99	2	pure	pure	PROPN
ejpam-323	99	3	appl	appl	PROPN
ejpam-323	99	4	.	.	PROPN
ejpam-323	99	5	math	math	PROPN
ejpam-323	99	6	,	,	PUNCT
ejpam-323	99	7	3	3	NUM
ejpam-323	99	8	(	(	PUNCT
ejpam-323	99	9	2010	2010	NUM
ejpam-323	99	10	)	)	PUNCT
ejpam-323	99	11	,	,	PUNCT
ejpam-323	99	12	282	282	NUM
ejpam-323	99	13	-	-	SYM
ejpam-323	99	14	294	294	NUM
ejpam-323	99	15	286	286	NUM
ejpam-323	99	16	then	then	ADV
ejpam-323	99	17	the	the	DET
ejpam-323	99	18	operator	operator	NOUN
ejpam-323	99	19	-	-	PUNCT
ejpam-323	99	20	valued	value	VERB
ejpam-323	99	21	function	function	NOUN
ejpam-323	99	22	aε(ω	aε(ω	NUM
ejpam-323	99	23	)	)	PUNCT
ejpam-323	99	24	is	be	AUX
ejpam-323	99	25	fredholm	fredholm	NOUN
ejpam-323	99	26	analytic	analytic	ADJ
ejpam-323	99	27	with	with	ADP
ejpam-323	99	28	index	index	NOUN
ejpam-323	99	29	0	0	NUM
ejpam-323	99	30	in	in	ADP
ejpam-323	99	31	c	c	NOUN
ejpam-323	99	32	\	\	PROPN
ejpam-323	99	33	ir−.	ir−.	PROPN
ejpam-323	99	34	moreover	moreover	ADV
ejpam-323	99	35	,	,	PUNCT
ejpam-323	99	36	a−1	a−1	PROPN
ejpam-323	99	37	ε	ε	PROPN
ejpam-323	99	38	(	(	PUNCT
ejpam-323	99	39	ω	ω	NOUN
ejpam-323	99	40	)	)	PUNCT
ejpam-323	99	41	is	be	AUX
ejpam-323	99	42	a	a	DET
ejpam-323	99	43	meromorphic	meromorphic	ADJ
ejpam-323	99	44	function	function	NOUN
ejpam-323	99	45	and	and	CCONJ
ejpam-323	99	46	its	its	PRON
ejpam-323	99	47	poles	pole	NOUN
ejpam-323	99	48	are	be	AUX
ejpam-323	99	49	in	in	ADP
ejpam-323	99	50	�	�	NOUN
ejpam-323	99	51	ℑ(z	ℑ(z	NUM
ejpam-323	99	52	)	)	PUNCT
ejpam-323	99	53	≤	≤	NOUN
ejpam-323	99	54	0	0	NUM
ejpam-323	99	55	,	,	PUNCT
ejpam-323	99	56	where	where	SCONJ
ejpam-323	99	57	ℑ(z	ℑ(z	NUM
ejpam-323	99	58	)	)	PUNCT
ejpam-323	99	59	means	mean	VERB
ejpam-323	99	60	the	the	DET
ejpam-323	99	61	imaginary	imaginary	ADJ
ejpam-323	99	62	part	part	NOUN
ejpam-323	99	63	of	of	ADP
ejpam-323	99	64	z	z	NOUN
ejpam-323	99	65	and	and	CCONJ
ejpam-323	99	66	ℜ(z	ℜ(z	NUM
ejpam-323	99	67	)	)	PUNCT
ejpam-323	99	68	is	be	AUX
ejpam-323	99	69	the	the	DET
ejpam-323	99	70	real	real	ADJ
ejpam-323	99	71	part	part	NOUN
ejpam-323	99	72	.	.	PUNCT
ejpam-323	100	1	using	use	VERB
ejpam-323	100	2	the	the	DET
ejpam-323	100	3	proprieties	propriety	NOUN
ejpam-323	100	4	of	of	ADP
ejpam-323	100	5	the	the	DET
ejpam-323	100	6	operator	operator	NOUN
ejpam-323	100	7	-	-	PUNCT
ejpam-323	100	8	valued	value	VERB
ejpam-323	100	9	function	function	NOUN
ejpam-323	100	10	aε	aε	NOUN
ejpam-323	100	11	given	give	VERB
ejpam-323	100	12	by	by	ADP
ejpam-323	100	13	proposition	proposition	NOUN
ejpam-323	100	14	1	1	NUM
ejpam-323	100	15	and	and	CCONJ
ejpam-323	100	16	using	use	VERB
ejpam-323	100	17	the	the	DET
ejpam-323	100	18	lemma	lemma	PROPN
ejpam-323	100	19	5.3	5.3	NUM
ejpam-323	100	20	found	find	VERB
ejpam-323	100	21	in	in	ADP
ejpam-323	100	22	[	[	X
ejpam-323	100	23	11	11	NUM
ejpam-323	100	24	]	]	PUNCT
ejpam-323	100	25	,	,	PUNCT
ejpam-323	100	26	we	we	PRON
ejpam-323	100	27	can	can	AUX
ejpam-323	100	28	easily	easily	ADV
ejpam-323	100	29	prove	prove	VERB
ejpam-323	100	30	the	the	DET
ejpam-323	100	31	following	follow	VERB
ejpam-323	100	32	results	result	NOUN
ejpam-323	100	33	.	.	PUNCT
ejpam-323	101	1	theorem	theorem	NOUN
ejpam-323	101	2	2	2	NUM
ejpam-323	101	3	.	.	PUNCT
ejpam-323	102	1	let	let	VERB
ejpam-323	102	2	k	k	PROPN
ejpam-323	102	3	0	0	PUNCT
ejpam-323	102	4	be	be	AUX
ejpam-323	102	5	a	a	DET
ejpam-323	102	6	bounded	bounded	ADJ
ejpam-323	102	7	neighborhood	neighborhood	NOUN
ejpam-323	102	8	of	of	ADP
ejpam-323	102	9	ω0	ω0	PROPN
ejpam-323	102	10	in	in	ADP
ejpam-323	102	11	rd	rd	PROPN
ejpam-323	102	12	.	.	PUNCT
ejpam-323	103	1	then	then	ADV
ejpam-323	103	2	there	there	PRON
ejpam-323	103	3	exists	exist	VERB
ejpam-323	103	4	a	a	DET
ejpam-323	103	5	constant	constant	ADJ
ejpam-323	103	6	ε1	ε1	PROPN
ejpam-323	103	7	>	>	X
ejpam-323	103	8	0	0	PUNCT
ejpam-323	103	9	smaller	small	ADJ
ejpam-323	103	10	than	than	ADP
ejpam-323	103	11	ε0	ε0	NOUN
ejpam-323	103	12	such	such	ADJ
ejpam-323	103	13	that	that	SCONJ
ejpam-323	103	14	an	an	DET
ejpam-323	103	15	orthonormal	orthonormal	ADJ
ejpam-323	103	16	basis	basis	NOUN
ejpam-323	103	17	of	of	ADP
ejpam-323	103	18	eigenfunctions	eigenfunction	NOUN
ejpam-323	103	19	(	(	PUNCT
ejpam-323	103	20	u	u	NOUN
ejpam-323	103	21	j(ε	j(ε	ADJ
ejpam-323	103	22	)	)	PUNCT
ejpam-323	103	23	)	)	PUNCT
ejpam-323	104	1	j	j	PROPN
ejpam-323	104	2	corresponding	correspond	VERB
ejpam-323	104	3	to	to	ADP
ejpam-323	104	4	the	the	DET
ejpam-323	104	5	ω0	ω0	PROPN
ejpam-323	104	6	−	−	PROPN
ejpam-323	104	7	group	group	NOUN
ejpam-323	104	8	,	,	PUNCT
ejpam-323	104	9	(	(	PUNCT
ejpam-323	104	10	ω2	ω2	PROPN
ejpam-323	104	11	j	j	PROPN
ejpam-323	104	12	(	(	PUNCT
ejpam-323	104	13	ε	ε	PROPN
ejpam-323	104	14	)	)	PUNCT
ejpam-323	104	15	)	)	PUNCT
ejpam-323	105	1	j	j	PROPN
ejpam-323	105	2	,	,	PUNCT
ejpam-323	105	3	in	in	ADP
ejpam-323	105	4	h1	h1	PROPN
ejpam-323	105	5	0(ωε	0(ωε	NOUN
ejpam-323	105	6	)	)	PUNCT
ejpam-323	105	7	can	can	AUX
ejpam-323	105	8	be	be	AUX
ejpam-323	105	9	chosen	choose	VERB
ejpam-323	105	10	to	to	PART
ejpam-323	105	11	depend	depend	VERB
ejpam-323	105	12	holomorphically	holomorphically	ADV
ejpam-323	105	13	in	in	ADP
ejpam-323	105	14	(	(	PUNCT
ejpam-323	105	15	x	x	INTJ
ejpam-323	105	16	,	,	PUNCT
ejpam-323	105	17	ε	ε	PROPN
ejpam-323	105	18	)	)	PUNCT
ejpam-323	105	19	∈	∈	PROPN
ejpam-323	105	20	k0×	k0×	NOUN
ejpam-323	105	21	]	]	PUNCT
ejpam-323	105	22	−	−	PUNCT
ejpam-323	106	1	ε1,ε1	ε1,ε1	PROPN
ejpam-323	107	1	[	[	X
ejpam-323	107	2	.	.	PUNCT
ejpam-323	108	1	moreover	moreover	ADV
ejpam-323	108	2	these	these	DET
ejpam-323	108	3	eigenfunctions	eigenfunction	NOUN
ejpam-323	108	4	satisfy	satisfy	VERB
ejpam-323	108	5	the	the	DET
ejpam-323	108	6	following	follow	VERB
ejpam-323	108	7	uniform	uniform	ADJ
ejpam-323	108	8	expansion	expansion	NOUN
ejpam-323	108	9	:	:	PUNCT
ejpam-323	108	10	for	for	ADP
ejpam-323	108	11	x	x	PROPN
ejpam-323	108	12	∈	∈	PROPN
ejpam-323	108	13	k0	k0	PROPN
ejpam-323	108	14	,	,	PUNCT
ejpam-323	108	15	u	u	NOUN
ejpam-323	108	16	j(ε	j(ε	ADJ
ejpam-323	108	17	)	)	PUNCT
ejpam-323	108	18	=	=	SYM
ejpam-323	108	19	u	u	PROPN
ejpam-323	108	20	j	j	PROPN
ejpam-323	108	21	0	0	NUM
ejpam-323	109	1	+	+	CCONJ
ejpam-323	109	2	∑	∑	ADP
ejpam-323	109	3	n≥1	n≥1	NOUN
ejpam-323	109	4	u	u	NOUN
ejpam-323	109	5	(	(	PUNCT
ejpam-323	109	6	j)n	j)n	NOUN
ejpam-323	109	7	ε	ε	PROPN
ejpam-323	109	8	n	n	CCONJ
ejpam-323	109	9	,	,	PUNCT
ejpam-323	109	10	where	where	SCONJ
ejpam-323	109	11	the	the	DET
ejpam-323	109	12	family	family	NOUN
ejpam-323	109	13	u	u	NOUN
ejpam-323	109	14	j	j	PROPN
ejpam-323	109	15	0	0	PROPN
ejpam-323	109	16	builds	build	VERB
ejpam-323	109	17	a	a	DET
ejpam-323	109	18	basis	basis	NOUN
ejpam-323	109	19	of	of	ADP
ejpam-323	109	20	eigenfunctions	eigenfunction	NOUN
ejpam-323	109	21	of	of	ADP
ejpam-323	109	22	(	(	PUNCT
ejpam-323	109	23	3	3	X
ejpam-323	109	24	)	)	PUNCT
ejpam-323	109	25	associated	associate	VERB
ejpam-323	109	26	to	to	ADP
ejpam-323	109	27	ω2	ω2	PROPN
ejpam-323	109	28	0	0	NUM
ejpam-323	109	29	and	and	CCONJ
ejpam-323	109	30	normalized	normalize	VERB
ejpam-323	109	31	in	in	ADP
ejpam-323	109	32	l2(ω0	l2(ω0	ADJ
ejpam-323	109	33	)	)	PUNCT
ejpam-323	109	34	.	.	PUNCT
ejpam-323	110	1	the	the	DET
ejpam-323	110	2	terms	term	NOUN
ejpam-323	110	3	u	u	PROPN
ejpam-323	110	4	(	(	PUNCT
ejpam-323	110	5	j	j	NOUN
ejpam-323	110	6	)	)	PUNCT
ejpam-323	110	7	n	n	PRON
ejpam-323	110	8	are	be	AUX
ejpam-323	110	9	computed	compute	VERB
ejpam-323	110	10	from	from	ADP
ejpam-323	110	11	the	the	DET
ejpam-323	110	12	taylor	taylor	PROPN
ejpam-323	110	13	coefficients	coefficient	NOUN
ejpam-323	110	14	of	of	ADP
ejpam-323	110	15	the	the	DET
ejpam-323	110	16	normal	normal	ADJ
ejpam-323	110	17	derivatives	derivative	NOUN
ejpam-323	110	18	.	.	PUNCT
ejpam-323	111	1	3	3	X
ejpam-323	111	2	.	.	X
ejpam-323	111	3	convergence	convergence	NOUN
ejpam-323	111	4	estimate	estimate	NOUN
ejpam-323	111	5	in	in	ADP
ejpam-323	111	6	this	this	DET
ejpam-323	111	7	section	section	NOUN
ejpam-323	111	8	we	we	PRON
ejpam-323	111	9	are	be	AUX
ejpam-323	111	10	in	in	ADP
ejpam-323	111	11	a	a	DET
ejpam-323	111	12	position	position	NOUN
ejpam-323	111	13	to	to	PART
ejpam-323	111	14	use	use	VERB
ejpam-323	111	15	the	the	DET
ejpam-323	111	16	theorems	theorem	NOUN
ejpam-323	111	17	1	1	NUM
ejpam-323	111	18	and	and	CCONJ
ejpam-323	111	19	2	2	NUM
ejpam-323	111	20	in	in	ADP
ejpam-323	111	21	order	order	NOUN
ejpam-323	111	22	to	to	PART
ejpam-323	111	23	establish	establish	VERB
ejpam-323	111	24	certain	certain	ADJ
ejpam-323	111	25	estimates	estimate	NOUN
ejpam-323	111	26	for	for	ADP
ejpam-323	111	27	the	the	DET
ejpam-323	111	28	convergence	convergence	NOUN
ejpam-323	111	29	of	of	ADP
ejpam-323	111	30	the	the	DET
ejpam-323	111	31	eigenfunctions	eigenfunction	NOUN
ejpam-323	111	32	u	u	NOUN
ejpam-323	111	33	j(ε	j(ε	ADJ
ejpam-323	111	34	)	)	PUNCT
ejpam-323	111	35	and	and	CCONJ
ejpam-323	111	36	the	the	DET
ejpam-323	111	37	corresponding	correspond	VERB
ejpam-323	111	38	eigenfrequencies	eigenfrequencie	NOUN
ejpam-323	111	39	ω2	ω2	PROPN
ejpam-323	111	40	j	j	PROPN
ejpam-323	111	41	(	(	PUNCT
ejpam-323	111	42	ε	ε	PROPN
ejpam-323	111	43	)	)	PUNCT
ejpam-323	111	44	,	,	PUNCT
ejpam-323	111	45	for	for	ADP
ejpam-323	111	46	all	all	DET
ejpam-323	111	47	j	j	NOUN
ejpam-323	111	48	=	=	SYM
ejpam-323	111	49	1	1	NUM
ejpam-323	111	50	,	,	PUNCT
ejpam-323	111	51	·	·	PUNCT
ejpam-323	111	52	·	·	PUNCT
ejpam-323	111	53	·	·	PUNCT
ejpam-323	111	54	,	,	PUNCT
ejpam-323	111	55	m.	m.	NOUN
ejpam-323	111	56	let	let	VERB
ejpam-323	111	57	α1	α1	PROPN
ejpam-323	111	58	>	>	X
ejpam-323	111	59	0	0	PUNCT
ejpam-323	111	60	be	be	AUX
ejpam-323	111	61	the	the	DET
ejpam-323	111	62	smaller	small	ADJ
ejpam-323	111	63	positive	positive	ADJ
ejpam-323	111	64	constant	constant	ADJ
ejpam-323	111	65	such	such	ADJ
ejpam-323	111	66	that	that	SCONJ
ejpam-323	111	67	ω0	ω0	PROPN
ejpam-323	111	68	⊂	⊂	ADJ
ejpam-323	111	69	ωε	ωε	NOUN
ejpam-323	111	70	and	and	CCONJ
ejpam-323	111	71	∂ωε	∂ωε	NOUN
ejpam-323	111	72	∩	∩	NOUN
ejpam-323	111	73	∂ω0	∂ω0	PROPN
ejpam-323	111	74	=	=	PUNCT
ejpam-323	111	75	;	;	PUNCT
ejpam-323	111	76	,	,	PUNCT
ejpam-323	111	77	for	for	ADP
ejpam-323	111	78	0	0	NUM
ejpam-323	111	79	<	<	X
ejpam-323	111	80	ε	ε	PROPN
ejpam-323	111	81	<	<	X
ejpam-323	111	82	α1	α1	PROPN
ejpam-323	111	83	and	and	CCONJ
ejpam-323	111	84	define	define	VERB
ejpam-323	111	85	the	the	DET
ejpam-323	111	86	open	open	ADJ
ejpam-323	111	87	,	,	PUNCT
ejpam-323	111	88	bounded	bounded	ADJ
ejpam-323	111	89	domain	domain	NOUN
ejpam-323	111	90	ω̃ε	ω̃ε	PROPN
ejpam-323	111	91	≡	≡	PROPN
ejpam-323	111	92	ωε\ω0	ωε\ω0	NOUN
ejpam-323	111	93	.	.	PUNCT
ejpam-323	112	1	lemma	lemma	PROPN
ejpam-323	112	2	1	1	X
ejpam-323	112	3	.	.	PUNCT
ejpam-323	113	1	let	let	VERB
ejpam-323	113	2	the	the	DET
ejpam-323	113	3	functions	function	NOUN
ejpam-323	113	4	u	u	NOUN
ejpam-323	113	5	j(ε	j(ε	ADJ
ejpam-323	113	6	)	)	PUNCT
ejpam-323	113	7	and	and	CCONJ
ejpam-323	113	8	u	u	X
ejpam-323	113	9	j	j	PROPN
ejpam-323	113	10	0	0	NUM
ejpam-323	113	11	,	,	PUNCT
ejpam-323	113	12	for	for	ADP
ejpam-323	113	13	j	j	PROPN
ejpam-323	113	14	=	=	SYM
ejpam-323	113	15	1	1	NUM
ejpam-323	113	16	,	,	PUNCT
ejpam-323	113	17	·	·	PUNCT
ejpam-323	113	18	·	·	PUNCT
ejpam-323	113	19	·	·	PUNCT
ejpam-323	113	20	,	,	PUNCT
ejpam-323	113	21	m	m	VERB
ejpam-323	113	22	,	,	PUNCT
ejpam-323	113	23	be	be	AUX
ejpam-323	113	24	given	give	VERB
ejpam-323	113	25	by	by	ADP
ejpam-323	113	26	theorem	theorem	NOUN
ejpam-323	113	27	2	2	NUM
ejpam-323	113	28	.	.	PUNCT
ejpam-323	114	1	then	then	ADV
ejpam-323	114	2	,	,	PUNCT
ejpam-323	114	3	there	there	PRON
ejpam-323	114	4	exist	exist	VERB
ejpam-323	114	5	some	some	DET
ejpam-323	114	6	positive	positive	ADJ
ejpam-323	114	7	constants	constant	NOUN
ejpam-323	114	8	ε2	ε2	ADJ
ejpam-323	114	9	<	<	X
ejpam-323	114	10	ε1	ε1	PROPN
ejpam-323	114	11	and	and	CCONJ
ejpam-323	114	12	c	c	PROPN
ejpam-323	114	13	j	j	PROPN
ejpam-323	114	14	,	,	PUNCT
ejpam-323	114	15	such	such	ADJ
ejpam-323	114	16	that	that	SCONJ
ejpam-323	114	17	‖∇(u	‖∇(u	PROPN
ejpam-323	114	18	j(ε)−	j(ε)−	PROPN
ejpam-323	114	19	u	u	PROPN
ejpam-323	114	20	j	j	PROPN
ejpam-323	114	21	0)‖l2(ω̃ε	0)‖l2(ω̃ε	NOUN
ejpam-323	114	22	)	)	PUNCT
ejpam-323	114	23	≤	≤	PROPN
ejpam-323	115	1	c	c	X
ejpam-323	115	2	j|ωε\ω0|1/2	j|ωε\ω0|1/2	PROPN
ejpam-323	115	3	,	,	PUNCT
ejpam-323	115	4	for	for	ADP
ejpam-323	115	5	0	0	NUM
ejpam-323	115	6	<	<	X
ejpam-323	115	7	ε	ε	PROPN
ejpam-323	115	8	<	<	X
ejpam-323	115	9	ε2	ε2	PROPN
ejpam-323	115	10	.	.	PUNCT
ejpam-323	116	1	the	the	DET
ejpam-323	116	2	constant	constant	ADJ
ejpam-323	116	3	c	c	PROPN
ejpam-323	116	4	j	j	PROPN
ejpam-323	116	5	depends	depend	VERB
ejpam-323	116	6	on	on	ADP
ejpam-323	116	7	ω0	ω0	PROPN
ejpam-323	116	8	and	and	CCONJ
ejpam-323	116	9	u	u	NOUN
ejpam-323	116	10	j	j	PROPN
ejpam-323	116	11	0	0	NUM
ejpam-323	116	12	,	,	PUNCT
ejpam-323	116	13	but	but	CCONJ
ejpam-323	116	14	is	be	AUX
ejpam-323	116	15	otherwise	otherwise	ADV
ejpam-323	116	16	independent	independent	ADJ
ejpam-323	116	17	of	of	ADP
ejpam-323	116	18	ε	ε	PROPN
ejpam-323	116	19	.	.	PUNCT
ejpam-323	117	1	proof	proof	NOUN
ejpam-323	117	2	.	.	PUNCT
ejpam-323	118	1	define	define	VERB
ejpam-323	118	2	the	the	DET
ejpam-323	118	3	function	function	NOUN
ejpam-323	118	4	u(ε	u(ε	PROPN
ejpam-323	118	5	)	)	PUNCT
ejpam-323	119	1	=	=	SYM
ejpam-323	119	2	u	u	PROPN
ejpam-323	119	3	j(ε)−	j(ε)−	PROPN
ejpam-323	119	4	u	u	X
ejpam-323	119	5	j	j	PROPN
ejpam-323	119	6	0	0	NUM
ejpam-323	119	7	,	,	PUNCT
ejpam-323	119	8	for	for	ADP
ejpam-323	119	9	0	0	NUM
ejpam-323	119	10	<	<	X
ejpam-323	119	11	ε	ε	PROPN
ejpam-323	119	12	<	<	X
ejpam-323	119	13	inf(ε1,α1	inf(ε1,α1	PROPN
ejpam-323	119	14	)	)	PUNCT
ejpam-323	119	15	where	where	SCONJ
ejpam-323	119	16	ε1	ε1	PROPN
ejpam-323	119	17	is	be	AUX
ejpam-323	119	18	given	give	VERB
ejpam-323	119	19	by	by	ADP
ejpam-323	119	20	theorem	theorem	NOUN
ejpam-323	119	21	2	2	NUM
ejpam-323	119	22	and	and	CCONJ
ejpam-323	119	23	combine	combine	VERB
ejpam-323	119	24	the	the	DET
ejpam-323	119	25	equations	equation	NOUN
ejpam-323	119	26	(	(	PUNCT
ejpam-323	119	27	2	2	NUM
ejpam-323	119	28	)	)	PUNCT
ejpam-323	119	29	and	and	CCONJ
ejpam-323	119	30	(	(	PUNCT
ejpam-323	119	31	3	3	NUM
ejpam-323	119	32	)	)	PUNCT
ejpam-323	119	33	and	and	CCONJ
ejpam-323	119	34	let	let	VERB
ejpam-323	119	35	for	for	ADP
ejpam-323	119	36	simplicity	simplicity	NOUN
ejpam-323	119	37	ω	ω	NOUN
ejpam-323	119	38	=	=	PROPN
ejpam-323	119	39	ω	ω	X
ejpam-323	119	40	j(ε	j(ε	ADJ
ejpam-323	119	41	)	)	PUNCT
ejpam-323	119	42	p	p	NOUN
ejpam-323	119	43	µεǫε	µεǫε	NOUN
ejpam-323	119	44	,	,	PUNCT
ejpam-323	119	45	we	we	PRON
ejpam-323	119	46	compute	compute	VERB
ejpam-323	119	47	that	that	SCONJ
ejpam-323	119	48	u(ε	u(ε	PROPN
ejpam-323	119	49	)	)	PUNCT
ejpam-323	119	50	solves	solve	NOUN
ejpam-323	119	51	:	:	PUNCT
ejpam-323	119	52	−∆u	−∆u	X
ejpam-323	120	1	=	=	SYM
ejpam-323	120	2	ω2u	ω2u	PROPN
ejpam-323	120	3	+	+	CCONJ
ejpam-323	120	4	(	(	PUNCT
ejpam-323	120	5	ω2	ω2	ADV
ejpam-323	120	6	−ω2	−ω2	ADP
ejpam-323	120	7	0ǫ0µ0)u	0ǫ0µ0)u	PROPN
ejpam-323	120	8	j	j	PROPN
ejpam-323	120	9	0	0	NUM
ejpam-323	120	10	in	in	ADP
ejpam-323	120	11	ωε	ωε	NOUN
ejpam-323	120	12	.	.	PUNCT
ejpam-323	121	1	(	(	PUNCT
ejpam-323	121	2	4	4	NUM
ejpam-323	121	3	)	)	PUNCT
ejpam-323	121	4	for	for	ADP
ejpam-323	121	5	z	z	PROPN
ejpam-323	121	6	∈	∈	PROPN
ejpam-323	121	7	r	r	NOUN
ejpam-323	121	8	,	,	PUNCT
ejpam-323	121	9	we	we	PRON
ejpam-323	121	10	define	define	VERB
ejpam-323	121	11	the	the	DET
ejpam-323	121	12	function	function	NOUN
ejpam-323	121	13	ϑ	ϑ	X
ejpam-323	121	14	by	by	ADP
ejpam-323	121	15	ϑ(z	ϑ(z	NOUN
ejpam-323	121	16	)	)	PUNCT
ejpam-323	121	17	=	=	NOUN
ejpam-323	121	18	ω2z	ω2z	X
ejpam-323	121	19	+	+	CCONJ
ejpam-323	121	20	(	(	PUNCT
ejpam-323	121	21	ω2−ω2	ω2−ω2	NUM
ejpam-323	121	22	0ǫ0µ0)‖u	0ǫ0µ0)‖u	VERB
ejpam-323	121	23	j	j	PROPN
ejpam-323	121	24	0‖l∞(ω0	0‖l∞(ω0	NUM
ejpam-323	121	25	)	)	PUNCT
ejpam-323	121	26	.	.	PUNCT
ejpam-323	122	1	then	then	ADV
ejpam-323	122	2	,	,	PUNCT
ejpam-323	122	3	we	we	PRON
ejpam-323	122	4	trivially	trivially	ADV
ejpam-323	122	5	remark	remark	VERB
ejpam-323	122	6	,	,	PUNCT
ejpam-323	122	7	|ϑ(z)|	|ϑ(z)|	VERB
ejpam-323	122	8	≤	≤	NUM
ejpam-323	122	9	|ϑ(0)|+ω2|z|	|ϑ(0)|+ω2|z|	NOUN
ejpam-323	122	10	,	,	PUNCT
ejpam-323	122	11	∀z	∀z	X
ejpam-323	122	12	∈	∈	PROPN
ejpam-323	122	13	r	r	NOUN
ejpam-323	122	14	,	,	PUNCT
ejpam-323	122	15	a.	a.	NOUN
ejpam-323	122	16	khelifi	khelifi	PROPN
ejpam-323	122	17	,	,	PUNCT
ejpam-323	122	18	m.	m.	NOUN
ejpam-323	122	19	shamma	shamma	PROPN
ejpam-323	122	20	/	/	SYM
ejpam-323	122	21	eur	eur	PROPN
ejpam-323	122	22	.	.	PUNCT
ejpam-323	123	1	j.	j.	PROPN
ejpam-323	123	2	pure	pure	PROPN
ejpam-323	123	3	appl	appl	PROPN
ejpam-323	123	4	.	.	PROPN
ejpam-323	123	5	math	math	PROPN
ejpam-323	123	6	,	,	PUNCT
ejpam-323	123	7	3	3	NUM
ejpam-323	123	8	(	(	PUNCT
ejpam-323	123	9	2010	2010	NUM
ejpam-323	123	10	)	)	PUNCT
ejpam-323	123	11	,	,	PUNCT
ejpam-323	123	12	282	282	NUM
ejpam-323	123	13	-	-	NUM
ejpam-323	123	14	294	294	NUM
ejpam-323	123	15	287	287	NUM
ejpam-323	123	16	and	and	CCONJ
ejpam-323	123	17	consequently	consequently	ADV
ejpam-323	123	18	,	,	PUNCT
ejpam-323	123	19	|ϑ(u(ε))|	|ϑ(u(ε))|	PROPN
ejpam-323	123	20	≤	≤	NUM
ejpam-323	123	21	|ϑ(0)|+ω2|u(ε)|	|ϑ(0)|+ω2|u(ε)|	PROPN
ejpam-323	123	22	.	.	PROPN
ejpam-323	124	1	(	(	PUNCT
ejpam-323	124	2	5	5	X
ejpam-323	124	3	)	)	PUNCT
ejpam-323	124	4	the	the	DET
ejpam-323	124	5	fact	fact	NOUN
ejpam-323	124	6	that	that	SCONJ
ejpam-323	124	7	u	u	PRON
ejpam-323	124	8	j(ε)→	j(ε)→	PROPN
ejpam-323	124	9	u	u	PROPN
ejpam-323	124	10	j	j	PROPN
ejpam-323	124	11	0	0	PROPN
ejpam-323	124	12	implies	imply	VERB
ejpam-323	124	13	that	that	SCONJ
ejpam-323	124	14	there	there	PRON
ejpam-323	124	15	exists	exist	VERB
ejpam-323	124	16	0	0	NUM
ejpam-323	124	17	<	<	X
ejpam-323	124	18	α2	α2	ADJ
ejpam-323	124	19	<	<	X
ejpam-323	124	20	inf(ε1,α1	inf(ε1,α1	NOUN
ejpam-323	124	21	)	)	PUNCT
ejpam-323	124	22	such	such	ADJ
ejpam-323	124	23	that	that	PRON
ejpam-323	124	24	for	for	ADP
ejpam-323	124	25	0	0	NUM
ejpam-323	124	26	<	<	X
ejpam-323	124	27	ε	ε	X
ejpam-323	124	28	<	<	X
ejpam-323	124	29	α2	α2	PROPN
ejpam-323	124	30	,	,	PUNCT
ejpam-323	124	31	|u(ε)(x)|	|u(ε)(x)|	VERB
ejpam-323	124	32	≤	≤	NOUN
ejpam-323	124	33	2‖u	2‖u	NUM
ejpam-323	124	34	j	j	NOUN
ejpam-323	124	35	0‖l∞(ω0	0‖l∞(ω0	NUM
ejpam-323	124	36	)	)	PUNCT
ejpam-323	124	37	,	,	PUNCT
ejpam-323	124	38	for	for	ADP
ejpam-323	124	39	x	x	PROPN
ejpam-323	124	40	∈	∈	PROPN
ejpam-323	124	41	ωε	ωε	NOUN
ejpam-323	124	42	.	.	PUNCT
ejpam-323	125	1	(	(	PUNCT
ejpam-323	125	2	6	6	NUM
ejpam-323	125	3	)	)	PUNCT
ejpam-323	125	4	moreover	moreover	ADV
ejpam-323	125	5	,	,	PUNCT
ejpam-323	125	6	we	we	PRON
ejpam-323	125	7	remember	remember	VERB
ejpam-323	125	8	that	that	PRON
ejpam-323	125	9	ω2(ε	ω2(ε	PROPN
ejpam-323	125	10	)	)	PUNCT
ejpam-323	125	11	→	→	SYM
ejpam-323	125	12	ω2	ω2	NUM
ejpam-323	125	13	0ǫ0µ0	0ǫ0µ0	NOUN
ejpam-323	125	14	,	,	PUNCT
ejpam-323	125	15	then	then	ADV
ejpam-323	125	16	there	there	PRON
ejpam-323	125	17	exists	exist	VERB
ejpam-323	125	18	α3	α3	PROPN
ejpam-323	125	19	≥	≥	NOUN
ejpam-323	125	20	0	0	NUM
ejpam-323	126	1	such	such	ADJ
ejpam-323	126	2	that	that	PRON
ejpam-323	126	3	:	:	PUNCT
ejpam-323	126	4	ω2	ω2	ADJ
ejpam-323	126	5	≤	≤	PUNCT
ejpam-323	126	6	ω2	ω2	PROPN
ejpam-323	126	7	0ǫ0µ0	0ǫ0µ0	NOUN
ejpam-323	127	1	+	+	CCONJ
ejpam-323	127	2	1	1	NUM
ejpam-323	127	3	3	3	NUM
ejpam-323	127	4	,	,	PUNCT
ejpam-323	127	5	for	for	ADP
ejpam-323	127	6	0≤	0≤	NUM
ejpam-323	127	7	ε≤	ε≤	PROPN
ejpam-323	127	8	α3	α3	NOUN
ejpam-323	127	9	.	.	PUNCT
ejpam-323	128	1	now	now	ADV
ejpam-323	128	2	,	,	PUNCT
ejpam-323	128	3	it	it	PRON
ejpam-323	128	4	is	be	AUX
ejpam-323	128	5	useful	useful	ADJ
ejpam-323	128	6	to	to	PART
ejpam-323	128	7	introduce	introduce	VERB
ejpam-323	128	8	the	the	DET
ejpam-323	128	9	following	follow	VERB
ejpam-323	128	10	function	function	NOUN
ejpam-323	128	11	:	:	PUNCT
ejpam-323	128	12	ϑ̃(u	ϑ̃(u	ADJ
ejpam-323	128	13	)	)	PUNCT
ejpam-323	129	1	=	=	SYM
ejpam-323	129	2	ω2u	ω2u	X
ejpam-323	129	3	+	+	CCONJ
ejpam-323	129	4	(	(	PUNCT
ejpam-323	129	5	ω2	ω2	ADV
ejpam-323	129	6	−ω2	−ω2	ADP
ejpam-323	129	7	0ǫ0µ0)u	0ǫ0µ0)u	PROPN
ejpam-323	129	8	j	j	PROPN
ejpam-323	129	9	0	0	PROPN
ejpam-323	129	10	,	,	PUNCT
ejpam-323	129	11	where	where	SCONJ
ejpam-323	129	12	u	u	NOUN
ejpam-323	129	13	is	be	AUX
ejpam-323	129	14	the	the	DET
ejpam-323	129	15	solution	solution	NOUN
ejpam-323	129	16	of	of	ADP
ejpam-323	129	17	(	(	PUNCT
ejpam-323	129	18	4	4	NUM
ejpam-323	129	19	)	)	PUNCT
ejpam-323	129	20	.	.	PUNCT
ejpam-323	130	1	if	if	SCONJ
ejpam-323	130	2	we	we	PRON
ejpam-323	130	3	examine	examine	VERB
ejpam-323	130	4	each	each	DET
ejpam-323	130	5	term	term	NOUN
ejpam-323	130	6	on	on	ADP
ejpam-323	130	7	the	the	DET
ejpam-323	130	8	right	right	ADJ
ejpam-323	130	9	hand	hand	NOUN
ejpam-323	130	10	side	side	NOUN
ejpam-323	130	11	of	of	ADP
ejpam-323	130	12	(	(	PUNCT
ejpam-323	130	13	5	5	NUM
ejpam-323	130	14	)	)	PUNCT
ejpam-323	130	15	separately	separately	ADV
ejpam-323	130	16	,	,	PUNCT
ejpam-323	130	17	we	we	PRON
ejpam-323	130	18	find	find	VERB
ejpam-323	130	19	out	out	ADP
ejpam-323	130	20	that	that	SCONJ
ejpam-323	130	21	the	the	DET
ejpam-323	130	22	first	first	ADJ
ejpam-323	130	23	term	term	NOUN
ejpam-323	130	24	is	be	AUX
ejpam-323	130	25	bounded	bound	VERB
ejpam-323	130	26	by	by	ADP
ejpam-323	130	27	|ϑ(0)|	|ϑ(0)|	NOUN
ejpam-323	130	28	≤	≤	NUM
ejpam-323	130	29	1	1	NUM
ejpam-323	130	30	3	3	NUM
ejpam-323	130	31	‖u	‖u	NOUN
ejpam-323	130	32	j	j	NOUN
ejpam-323	130	33	0‖l∞(ω0	0‖l∞(ω0	NUM
ejpam-323	130	34	)	)	PUNCT
ejpam-323	130	35	,	,	PUNCT
ejpam-323	130	36	for	for	ADP
ejpam-323	130	37	0	0	NUM
ejpam-323	130	38	<	<	X
ejpam-323	130	39	ε	ε	PROPN
ejpam-323	130	40	<	<	X
ejpam-323	130	41	α3	α3	PROPN
ejpam-323	130	42	.	.	PUNCT
ejpam-323	131	1	the	the	DET
ejpam-323	131	2	second	second	ADJ
ejpam-323	131	3	term	term	NOUN
ejpam-323	131	4	is	be	AUX
ejpam-323	131	5	bounded	bound	VERB
ejpam-323	131	6	by	by	ADP
ejpam-323	131	7	ω2|u(ε)|	ω2|u(ε)|	PROPN
ejpam-323	131	8	≤	≤	PROPN
ejpam-323	131	9	2(ω2	2(ω2	NUM
ejpam-323	131	10	0ǫ0µ0	0ǫ0µ0	NOUN
ejpam-323	132	1	+	+	CCONJ
ejpam-323	132	2	1	1	NUM
ejpam-323	132	3	3	3	NUM
ejpam-323	132	4	)	)	PUNCT
ejpam-323	132	5	‖u	‖u	PROPN
ejpam-323	132	6	j	j	PROPN
ejpam-323	132	7	0‖l∞(ω0	0‖l∞(ω0	NUM
ejpam-323	132	8	)	)	PUNCT
ejpam-323	132	9	,	,	PUNCT
ejpam-323	132	10	for	for	ADP
ejpam-323	132	11	0	0	NUM
ejpam-323	132	12	<	<	X
ejpam-323	132	13	ε	ε	X
ejpam-323	132	14	<	<	X
ejpam-323	132	15	ε2	ε2	PROPN
ejpam-323	132	16	=	=	SYM
ejpam-323	132	17	inf(α2,α3	inf(α2,α3	PROPN
ejpam-323	132	18	)	)	PUNCT
ejpam-323	132	19	.	.	PUNCT
ejpam-323	133	1	these	these	DET
ejpam-323	133	2	estimates	estimate	NOUN
ejpam-323	133	3	give	give	VERB
ejpam-323	133	4	‖ϑ̃(u(ε))‖l∞(ω̃ε	‖ϑ̃(u(ε))‖l∞(ω̃ε	NOUN
ejpam-323	133	5	)	)	PUNCT
ejpam-323	133	6	≤	≤	NOUN
ejpam-323	133	7	(	(	PUNCT
ejpam-323	133	8	1	1	NUM
ejpam-323	133	9	+	+	NUM
ejpam-323	133	10	2ω2	2ω2	NUM
ejpam-323	133	11	0ǫ0µ0)‖u	0ǫ0µ0)‖u	VERB
ejpam-323	133	12	j	j	PROPN
ejpam-323	133	13	0‖l∞(ω0	0‖l∞(ω0	NUM
ejpam-323	133	14	)	)	PUNCT
ejpam-323	133	15	,	,	PUNCT
ejpam-323	133	16	for	for	ADP
ejpam-323	133	17	0	0	NUM
ejpam-323	133	18	<	<	X
ejpam-323	133	19	ε	ε	X
ejpam-323	133	20	<	<	X
ejpam-323	133	21	ε2	ε2	PROPN
ejpam-323	133	22	.	.	PUNCT
ejpam-323	134	1	(	(	PUNCT
ejpam-323	134	2	7	7	NUM
ejpam-323	134	3	)	)	PUNCT
ejpam-323	134	4	next	next	ADV
ejpam-323	134	5	,	,	PUNCT
ejpam-323	134	6	the	the	DET
ejpam-323	134	7	relation	relation	NOUN
ejpam-323	134	8	(	(	PUNCT
ejpam-323	134	9	4	4	NUM
ejpam-323	134	10	)	)	PUNCT
ejpam-323	134	11	implies	imply	VERB
ejpam-323	134	12	−∆u(ε	−∆u(ε	NOUN
ejpam-323	134	13	)	)	PUNCT
ejpam-323	134	14	=	=	SYM
ejpam-323	134	15	ϑ̃(u(ε	ϑ̃(u(ε	NOUN
ejpam-323	134	16	)	)	PUNCT
ejpam-323	134	17	)	)	PUNCT
ejpam-323	134	18	,	,	PUNCT
ejpam-323	134	19	inωε	inωε	PROPN
ejpam-323	134	20	.	.	PUNCT
ejpam-323	135	1	by	by	ADP
ejpam-323	135	2	integrating	integrate	VERB
ejpam-323	135	3	by	by	ADP
ejpam-323	135	4	parts	part	NOUN
ejpam-323	135	5	in	in	ADP
ejpam-323	135	6	ω̃ε	ω̃ε	NOUN
ejpam-323	135	7	,	,	PUNCT
ejpam-323	135	8	we	we	PRON
ejpam-323	135	9	find	find	VERB
ejpam-323	135	10	that	that	SCONJ
ejpam-323	135	11	the	the	DET
ejpam-323	135	12	function	function	NOUN
ejpam-323	135	13	u(ε	u(ε	PROPN
ejpam-323	135	14	)	)	PUNCT
ejpam-323	135	15	is	be	AUX
ejpam-323	135	16	solution	solution	NOUN
ejpam-323	135	17	to	to	ADP
ejpam-323	135	18	the	the	DET
ejpam-323	135	19	following	following	ADJ
ejpam-323	135	20	problem	problem	NOUN
ejpam-323	135	21	:	:	PUNCT
ejpam-323	135	22	∀v	∀v	PROPN
ejpam-323	135	23	∈	∈	PROPN
ejpam-323	135	24	h1(ω̃ε	h1(ω̃ε	NOUN
ejpam-323	135	25	)	)	PUNCT
ejpam-323	135	26	,	,	PUNCT
ejpam-323	135	27	∫	∫	PROPN
ejpam-323	135	28	ω̃ε	ω̃ε	PROPN
ejpam-323	135	29	∇u(ε)∇̄vd	∇u(ε)∇̄vd	NUM
ejpam-323	136	1	x	x	SYM
ejpam-323	136	2	=	=	SYM
ejpam-323	136	3	∫	∫	PROPN
ejpam-323	136	4	ω̃ε	ω̃ε	PROPN
ejpam-323	136	5	ϑ̃(u(ε))v̄d	ϑ̃(u(ε))v̄d	X
ejpam-323	136	6	x	x	PUNCT
ejpam-323	137	1	+	+	NUM
ejpam-323	137	2	∫	∫	PROPN
ejpam-323	137	3	∂	∂	NUM
ejpam-323	137	4	ω̃ε	ω̃ε	PROPN
ejpam-323	137	5	∂	∂	NUM
ejpam-323	137	6	u	u	NOUN
ejpam-323	137	7	∂	∂	NOUN
ejpam-323	137	8	ν	ν	X
ejpam-323	137	9	v̄ds(x	v̄ds(x	PROPN
ejpam-323	137	10	)	)	PUNCT
ejpam-323	137	11	.	.	PUNCT
ejpam-323	138	1	(	(	PUNCT
ejpam-323	138	2	8)	8)	NUM
ejpam-323	138	3	on	on	ADP
ejpam-323	138	4	the	the	DET
ejpam-323	138	5	other	other	ADJ
ejpam-323	138	6	hand	hand	NOUN
ejpam-323	138	7	,	,	PUNCT
ejpam-323	138	8	it	it	PRON
ejpam-323	138	9	is	be	AUX
ejpam-323	138	10	not	not	PART
ejpam-323	138	11	hard	hard	ADJ
ejpam-323	138	12	to	to	PART
ejpam-323	138	13	see	see	VERB
ejpam-323	138	14	that	that	PRON
ejpam-323	138	15	(	(	PUNCT
ejpam-323	138	16	trace	trace	NOUN
ejpam-323	138	17	theorem	theorem	VERB
ejpam-323	138	18	)	)	PUNCT
ejpam-323	138	19	,	,	PUNCT
ejpam-323	138	20	�	�	PROPN
ejpam-323	138	21	�	�	PROPN
ejpam-323	138	22	∫	∫	PROPN
ejpam-323	138	23	∂	∂	NUM
ejpam-323	138	24	ω̃ε	ω̃ε	PROPN
ejpam-323	138	25	∂	∂	NUM
ejpam-323	138	26	u	u	NOUN
ejpam-323	138	27	∂	∂	NOUN
ejpam-323	138	28	ν	ν	X
ejpam-323	138	29	v̄ds(x	v̄ds(x	PROPN
ejpam-323	138	30	)	)	PUNCT
ejpam-323	138	31	�	�	PROPN
ejpam-323	138	32	�	�	PROPN
ejpam-323	138	33	≤	≤	PROPN
ejpam-323	138	34	|ω̃ε|1/2	|ω̃ε|1/2	NUM
ejpam-323	138	35	sup	sup	NOUN
ejpam-323	138	36	z∈∂	z∈∂	PROPN
ejpam-323	138	37	ω̃ε	ω̃ε	NOUN
ejpam-323	138	38	|∂	|∂	NUM
ejpam-323	138	39	u(z	u(z	NOUN
ejpam-323	138	40	)	)	PUNCT
ejpam-323	138	41	∂	∂	NUM
ejpam-323	138	42	ν	ν	NOUN
ejpam-323	138	43	|.‖v‖l2(ω̃ε	|.‖v‖l2(ω̃ε	NUM
ejpam-323	138	44	)	)	PUNCT
ejpam-323	138	45	.	.	PUNCT
ejpam-323	139	1	but	but	CCONJ
ejpam-323	139	2	,	,	PUNCT
ejpam-323	139	3	the	the	DET
ejpam-323	139	4	relation	relation	NOUN
ejpam-323	139	5	(	(	PUNCT
ejpam-323	139	6	6	6	NUM
ejpam-323	139	7	)	)	PUNCT
ejpam-323	139	8	implies	imply	VERB
ejpam-323	139	9	that	that	SCONJ
ejpam-323	139	10	supz∈∂	supz∈∂	PROPN
ejpam-323	139	11	ω̃ε	ω̃ε	NUM
ejpam-323	139	12	|	|	NOUN
ejpam-323	139	13	∂	∂	NUM
ejpam-323	139	14	u(z	u(z	NOUN
ejpam-323	139	15	)	)	PUNCT
ejpam-323	139	16	∂	∂	NUM
ejpam-323	139	17	ν	ν	NOUN
ejpam-323	139	18	|	|	ADV
ejpam-323	139	19	is	be	AUX
ejpam-323	139	20	a	a	DET
ejpam-323	139	21	positive	positive	ADJ
ejpam-323	139	22	constant	constant	ADJ
ejpam-323	139	23	c∗	c∗	NOUN
ejpam-323	139	24	independent	independent	NOUN
ejpam-323	139	25	of	of	ADP
ejpam-323	139	26	ε	ε	PROPN
ejpam-323	139	27	.	.	PUNCT
ejpam-323	140	1	if	if	SCONJ
ejpam-323	140	2	we	we	PRON
ejpam-323	140	3	choose	choose	VERB
ejpam-323	140	4	v	v	NOUN
ejpam-323	140	5	=	=	SYM
ejpam-323	140	6	u(ε	u(ε	PROPN
ejpam-323	140	7	)	)	PUNCT
ejpam-323	140	8	and	and	CCONJ
ejpam-323	140	9	if	if	SCONJ
ejpam-323	140	10	we	we	PRON
ejpam-323	140	11	consider	consider	VERB
ejpam-323	140	12	relations	relation	NOUN
ejpam-323	140	13	(	(	PUNCT
ejpam-323	140	14	7	7	NUM
ejpam-323	140	15	)	)	PUNCT
ejpam-323	140	16	and	and	CCONJ
ejpam-323	140	17	(	(	PUNCT
ejpam-323	140	18	8)	8)	NUM
ejpam-323	140	19	we	we	PRON
ejpam-323	140	20	deduce	deduce	VERB
ejpam-323	140	21	that	that	SCONJ
ejpam-323	140	22	,	,	PUNCT
ejpam-323	140	23	‖∇u‖2	‖∇u‖2	PROPN
ejpam-323	140	24	l2(ω̃ε	l2(ω̃ε	NOUN
ejpam-323	140	25	)	)	PUNCT
ejpam-323	140	26	≤	≤	NOUN
ejpam-323	141	1	[	[	X
ejpam-323	141	2	c∗	c∗	NOUN
ejpam-323	141	3	+	+	CCONJ
ejpam-323	141	4	(	(	PUNCT
ejpam-323	141	5	1	1	NUM
ejpam-323	141	6	+	+	NUM
ejpam-323	141	7	2ω2	2ω2	NUM
ejpam-323	141	8	0ǫ0µ0)‖u	0ǫ0µ0)‖u	VERB
ejpam-323	141	9	j	j	PROPN
ejpam-323	141	10	0‖l∞(ω0	0‖l∞(ω0	PROPN
ejpam-323	141	11	)	)	PUNCT
ejpam-323	141	12	]	]	PUNCT
ejpam-323	141	13	|ω̃ε|1/2‖u‖l2(ω̃ε	|ω̃ε|1/2‖u‖l2(ω̃ε	X
ejpam-323	141	14	)	)	PUNCT
ejpam-323	141	15	.	.	PUNCT
ejpam-323	142	1	(	(	PUNCT
ejpam-323	142	2	9	9	X
ejpam-323	142	3	)	)	PUNCT
ejpam-323	142	4	a.	a.	NOUN
ejpam-323	142	5	khelifi	khelifi	PROPN
ejpam-323	142	6	,	,	PUNCT
ejpam-323	142	7	m.	m.	NOUN
ejpam-323	142	8	shamma	shamma	PROPN
ejpam-323	142	9	/	/	SYM
ejpam-323	142	10	eur	eur	PROPN
ejpam-323	142	11	.	.	PUNCT
ejpam-323	143	1	j.	j.	PROPN
ejpam-323	143	2	pure	pure	PROPN
ejpam-323	143	3	appl	appl	PROPN
ejpam-323	143	4	.	.	PROPN
ejpam-323	143	5	math	math	PROPN
ejpam-323	143	6	,	,	PUNCT
ejpam-323	143	7	3	3	NUM
ejpam-323	143	8	(	(	PUNCT
ejpam-323	143	9	2010	2010	NUM
ejpam-323	143	10	)	)	PUNCT
ejpam-323	143	11	,	,	PUNCT
ejpam-323	143	12	282	282	NUM
ejpam-323	143	13	-	-	SYM
ejpam-323	143	14	294	294	NUM
ejpam-323	143	15	288	288	NUM
ejpam-323	143	16	by	by	ADP
ejpam-323	143	17	poincare	poincare	PROPN
ejpam-323	143	18	’s	’s	PART
ejpam-323	143	19	inequality	inequality	NOUN
ejpam-323	144	1	,	,	PUNCT
ejpam-323	144	2	there	there	PRON
ejpam-323	144	3	exists	exist	VERB
ejpam-323	144	4	some	some	DET
ejpam-323	144	5	positive	positive	ADJ
ejpam-323	144	6	constant	constant	ADJ
ejpam-323	144	7	c(ω̃ε	c(ω̃ε	NOUN
ejpam-323	144	8	)	)	PUNCT
ejpam-323	144	9	such	such	ADJ
ejpam-323	144	10	that	that	SCONJ
ejpam-323	144	11	‖u‖l2(ω̃ε	‖u‖l2(ω̃ε	NOUN
ejpam-323	144	12	)	)	PUNCT
ejpam-323	144	13	≤	≤	NUM
ejpam-323	144	14	c(ω̃ε)‖∇u‖l2(ω̃ε	c(ω̃ε)‖∇u‖l2(ω̃ε	NUM
ejpam-323	144	15	)	)	PUNCT
ejpam-323	144	16	.	.	PUNCT
ejpam-323	145	1	the	the	DET
ejpam-323	145	2	fact	fact	NOUN
ejpam-323	145	3	u	u	NOUN
ejpam-323	145	4	and	and	CCONJ
ejpam-323	145	5	∇u	∇u	PROPN
ejpam-323	145	6	are	be	AUX
ejpam-323	145	7	uniformly	uniformly	ADV
ejpam-323	145	8	bounded	bound	VERB
ejpam-323	145	9	on	on	ADP
ejpam-323	145	10	ωε	ωε	NOUN
ejpam-323	145	11	implies	implie	NOUN
ejpam-323	145	12	there	there	PRON
ejpam-323	145	13	exists	exist	VERB
ejpam-323	145	14	some	some	DET
ejpam-323	145	15	constant	constant	ADJ
ejpam-323	145	16	c0	c0	NOUN
ejpam-323	145	17	independent	independent	ADJ
ejpam-323	145	18	of	of	ADP
ejpam-323	145	19	ε	ε	PROPN
ejpam-323	145	20	(	(	PUNCT
ejpam-323	145	21	e.g.[13	e.g.[13	PROPN
ejpam-323	145	22	,	,	PUNCT
ejpam-323	145	23	p.33	p.33	PROPN
ejpam-323	145	24	]	]	X
ejpam-323	145	25	)	)	PUNCT
ejpam-323	145	26	such	such	ADJ
ejpam-323	145	27	that	that	DET
ejpam-323	145	28	c(ω̃ε)≤	c(ω̃ε)≤	PROPN
ejpam-323	145	29	c0	c0	PROPN
ejpam-323	145	30	,	,	PUNCT
ejpam-323	145	31	(	(	PUNCT
ejpam-323	145	32	10	10	NUM
ejpam-323	145	33	)	)	PUNCT
ejpam-323	145	34	and	and	CCONJ
ejpam-323	145	35	therefore	therefore	ADV
ejpam-323	145	36	the	the	DET
ejpam-323	145	37	relation	relation	NOUN
ejpam-323	145	38	(	(	PUNCT
ejpam-323	145	39	9	9	X
ejpam-323	145	40	)	)	PUNCT
ejpam-323	145	41	becomes	become	VERB
ejpam-323	145	42	‖∇u‖l2(ω̃ε	‖∇u‖l2(ω̃ε	NOUN
ejpam-323	145	43	)	)	PUNCT
ejpam-323	145	44	≤	≤	NOUN
ejpam-323	145	45	c0[c∗	c0[c∗	PROPN
ejpam-323	145	46	+	+	CCONJ
ejpam-323	145	47	(	(	PUNCT
ejpam-323	145	48	1	1	NUM
ejpam-323	145	49	+	+	NUM
ejpam-323	145	50	2ω2	2ω2	NUM
ejpam-323	145	51	0ǫ0µ0)‖u	0ǫ0µ0)‖u	VERB
ejpam-323	145	52	j	j	PROPN
ejpam-323	145	53	0‖l∞(ω0	0‖l∞(ω0	PROPN
ejpam-323	145	54	)	)	PUNCT
ejpam-323	145	55	]	]	PUNCT
ejpam-323	145	56	|ω̃ε|1/2	|ω̃ε|1/2	NUM
ejpam-323	145	57	.	.	PUNCT
ejpam-323	146	1	we	we	PRON
ejpam-323	146	2	take	take	VERB
ejpam-323	146	3	c	c	PROPN
ejpam-323	146	4	j	j	PROPN
ejpam-323	146	5	=	=	SYM
ejpam-323	146	6	c0[c∗	c0[c∗	PROPN
ejpam-323	146	7	+	+	CCONJ
ejpam-323	146	8	(	(	PUNCT
ejpam-323	146	9	1	1	NUM
ejpam-323	146	10	+	+	NUM
ejpam-323	146	11	2ω2	2ω2	NUM
ejpam-323	146	12	0ǫ0µ0)‖u	0ǫ0µ0)‖u	VERB
ejpam-323	146	13	j	j	PROPN
ejpam-323	146	14	0‖l∞(ω0	0‖l∞(ω0	PROPN
ejpam-323	146	15	)	)	PUNCT
ejpam-323	146	16	]	]	PUNCT
ejpam-323	146	17	which	which	PRON
ejpam-323	146	18	concludes	conclude	VERB
ejpam-323	146	19	the	the	DET
ejpam-323	146	20	proof	proof	NOUN
ejpam-323	146	21	.	.	PUNCT
ejpam-323	147	1	the	the	DET
ejpam-323	147	2	following	follow	VERB
ejpam-323	147	3	main	main	ADJ
ejpam-323	147	4	result	result	NOUN
ejpam-323	147	5	holds	hold	NOUN
ejpam-323	147	6	.	.	PUNCT
ejpam-323	148	1	theorem	theorem	NOUN
ejpam-323	148	2	3	3	X
ejpam-323	148	3	.	.	PUNCT
ejpam-323	149	1	let	let	VERB
ejpam-323	149	2	γ	γ	PRON
ejpam-323	149	3	,	,	PUNCT
ejpam-323	149	4	β	β	X
ejpam-323	149	5	and	and	CCONJ
ejpam-323	149	6	ωε	ωε	NOUN
ejpam-323	149	7	be	be	AUX
ejpam-323	149	8	defined	define	VERB
ejpam-323	149	9	as	as	ADP
ejpam-323	149	10	in	in	ADP
ejpam-323	149	11	section	section	NOUN
ejpam-323	149	12	2	2	NUM
ejpam-323	149	13	and	and	CCONJ
ejpam-323	149	14	let	let	VERB
ejpam-323	149	15	the	the	DET
ejpam-323	149	16	functions	function	NOUN
ejpam-323	149	17	u	u	NOUN
ejpam-323	149	18	j(ε	j(ε	ADJ
ejpam-323	149	19	)	)	PUNCT
ejpam-323	149	20	and	and	CCONJ
ejpam-323	149	21	u	u	X
ejpam-323	149	22	j	j	PROPN
ejpam-323	149	23	0	0	NUM
ejpam-323	149	24	,	,	PUNCT
ejpam-323	149	25	for	for	ADP
ejpam-323	149	26	j	j	PROPN
ejpam-323	149	27	=	=	SYM
ejpam-323	149	28	1	1	NUM
ejpam-323	149	29	,	,	PUNCT
ejpam-323	149	30	·	·	PUNCT
ejpam-323	149	31	·	·	PUNCT
ejpam-323	149	32	·	·	PUNCT
ejpam-323	149	33	,	,	PUNCT
ejpam-323	149	34	m	m	VERB
ejpam-323	149	35	,	,	PUNCT
ejpam-323	149	36	be	be	AUX
ejpam-323	149	37	given	give	VERB
ejpam-323	149	38	by	by	ADP
ejpam-323	149	39	theorem	theorem	NOUN
ejpam-323	149	40	2	2	NUM
ejpam-323	149	41	.	.	PUNCT
ejpam-323	150	1	then	then	ADV
ejpam-323	150	2	,	,	PUNCT
ejpam-323	150	3	there	there	PRON
ejpam-323	150	4	exist	exist	VERB
ejpam-323	150	5	some	some	PRON
ejpam-323	150	6	constant	constant	ADJ
ejpam-323	150	7	0	0	PUNCT
ejpam-323	150	8	<	<	X
ejpam-323	150	9	ε3	ε3	PROPN
ejpam-323	150	10	≤	≤	NUM
ejpam-323	150	11	1	1	NUM
ejpam-323	150	12	/	/	SYM
ejpam-323	150	13	m	m	PROPN
ejpam-323	150	14	,	,	PUNCT
ejpam-323	150	15	m	m	VERB
ejpam-323	150	16	=	=	PUNCT
ejpam-323	150	17	maxt∈[0,t1]×···×[0,td−1	maxt∈[0,t1]×···×[0,td−1	PROPN
ejpam-323	150	18	]	]	X
ejpam-323	150	19	|β(t)|	|β(t)|	PROPN
ejpam-323	150	20	and	and	CCONJ
ejpam-323	150	21	some	some	DET
ejpam-323	150	22	positive	positive	ADJ
ejpam-323	150	23	constant	constant	ADJ
ejpam-323	150	24	κ	κ	X
ejpam-323	150	25	j	j	PROPN
ejpam-323	150	26	dependent	dependent	ADJ
ejpam-323	150	27	on	on	ADP
ejpam-323	150	28	ω0	ω0	PROPN
ejpam-323	150	29	,	,	PUNCT
ejpam-323	150	30	u	u	PROPN
ejpam-323	150	31	j	j	PROPN
ejpam-323	150	32	0	0	NUM
ejpam-323	150	33	,	,	PUNCT
ejpam-323	150	34	|γ|	|γ|	PROPN
ejpam-323	150	35	and	and	CCONJ
ejpam-323	150	36	m	m	PROPN
ejpam-323	150	37	but	but	CCONJ
ejpam-323	150	38	otherwise	otherwise	ADV
ejpam-323	150	39	independent	independent	ADJ
ejpam-323	150	40	of	of	ADP
ejpam-323	150	41	ε	ε	PROPN
ejpam-323	150	42	such	such	ADJ
ejpam-323	150	43	that	that	SCONJ
ejpam-323	150	44	,	,	PUNCT
ejpam-323	150	45	‖u	‖u	PROPN
ejpam-323	150	46	j(ε)−	j(ε)−	PROPN
ejpam-323	150	47	u	u	PROPN
ejpam-323	150	48	j	j	PROPN
ejpam-323	150	49	0‖l2(ω̃ε	0‖l2(ω̃ε	NOUN
ejpam-323	150	50	)	)	PUNCT
ejpam-323	150	51	≤	≤	NUM
ejpam-323	150	52	κ	κ	NOUN
ejpam-323	150	53	jε	jε	PROPN
ejpam-323	150	54	1/2	1/2	NUM
ejpam-323	150	55	,	,	PUNCT
ejpam-323	150	56	for	for	ADP
ejpam-323	150	57	0	0	NUM
ejpam-323	150	58	<	<	X
ejpam-323	150	59	ε	ε	X
ejpam-323	150	60	<	<	X
ejpam-323	150	61	ε3	ε3	PROPN
ejpam-323	150	62	.	.	PUNCT
ejpam-323	151	1	proof	proof	NOUN
ejpam-323	151	2	.	.	PUNCT
ejpam-323	152	1	for	for	ADP
ejpam-323	152	2	simplicity	simplicity	NOUN
ejpam-323	152	3	we	we	PRON
ejpam-323	152	4	can	can	AUX
ejpam-323	152	5	suppose	suppose	VERB
ejpam-323	152	6	that	that	SCONJ
ejpam-323	152	7	ω0	ω0	PROPN
ejpam-323	152	8	is	be	AUX
ejpam-323	152	9	a	a	DET
ejpam-323	152	10	disk	disk	NOUN
ejpam-323	152	11	with	with	ADP
ejpam-323	152	12	radius	radius	NOUN
ejpam-323	152	13	̺0	̺0	NOUN
ejpam-323	152	14	>	>	X
ejpam-323	152	15	0	0	PUNCT
ejpam-323	152	16	in	in	ADP
ejpam-323	152	17	r2	r2	PROPN
ejpam-323	152	18	.	.	PUNCT
ejpam-323	153	1	it	it	PRON
ejpam-323	153	2	then	then	ADV
ejpam-323	153	3	follows	follow	VERB
ejpam-323	153	4	that	that	SCONJ
ejpam-323	153	5	|γ(t)|	|γ(t)|	PROPN
ejpam-323	153	6	=	=	SYM
ejpam-323	153	7	̺0	̺0	NOUN
ejpam-323	153	8	.	.	PUNCT
ejpam-323	154	1	the	the	DET
ejpam-323	154	2	proof	proof	NOUN
ejpam-323	154	3	is	be	AUX
ejpam-323	154	4	simple	simple	ADJ
ejpam-323	154	5	if	if	SCONJ
ejpam-323	154	6	we	we	PRON
ejpam-323	154	7	calculate	calculate	VERB
ejpam-323	154	8	the	the	DET
ejpam-323	154	9	area	area	NOUN
ejpam-323	154	10	|ω̃ε|	|ω̃ε|	NOUN
ejpam-323	154	11	of	of	ADP
ejpam-323	154	12	the	the	DET
ejpam-323	154	13	domain	domain	NOUN
ejpam-323	154	14	ω̃ε	ω̃ε	NOUN
ejpam-323	154	15	.	.	PUNCT
ejpam-323	155	1	but	but	CCONJ
ejpam-323	155	2	it	it	PRON
ejpam-323	155	3	is	be	AUX
ejpam-323	155	4	not	not	PART
ejpam-323	155	5	hard	hard	ADJ
ejpam-323	155	6	to	to	PART
ejpam-323	155	7	see	see	VERB
ejpam-323	155	8	that	that	PRON
ejpam-323	155	9	,	,	PUNCT
ejpam-323	155	10	in	in	ADP
ejpam-323	155	11	polar	polar	ADJ
ejpam-323	155	12	coordinates	coordinate	NOUN
ejpam-323	155	13	(	(	PUNCT
ejpam-323	155	14	̺,θ	̺,θ	PROPN
ejpam-323	155	15	)	)	PUNCT
ejpam-323	155	16	,	,	PUNCT
ejpam-323	155	17	there	there	PRON
ejpam-323	155	18	exists	exist	VERB
ejpam-323	155	19	a	a	DET
ejpam-323	155	20	regular	regular	ADJ
ejpam-323	155	21	function	function	NOUN
ejpam-323	155	22	υ	υ	NOUN
ejpam-323	156	1	:	:	PUNCT
ejpam-323	156	2	[	[	X
ejpam-323	156	3	0,2π]→	0,2π]→	NOUN
ejpam-323	156	4	r+	r+	X
ejpam-323	156	5	;	;	PUNCT
ejpam-323	156	6	υ(θ	υ(θ	X
ejpam-323	156	7	)	)	PUNCT
ejpam-323	156	8	=	=	PUNCT
ejpam-323	156	9	|β(θ)|	|β(θ)|	ADP
ejpam-323	156	10	such	such	ADJ
ejpam-323	156	11	that	that	SCONJ
ejpam-323	156	12	the	the	DET
ejpam-323	156	13	boundary	boundary	ADJ
ejpam-323	156	14	∂ωε	∂ωε	NOUN
ejpam-323	156	15	can	can	AUX
ejpam-323	156	16	be	be	AUX
ejpam-323	156	17	re	re	VERB
ejpam-323	156	18	-	-	ADJ
ejpam-323	156	19	parameterized	parameterized	ADJ
ejpam-323	156	20	by	by	ADP
ejpam-323	156	21	̺	̺	PROPN
ejpam-323	156	22	=	=	SYM
ejpam-323	156	23	̺(ε	̺(ε	PROPN
ejpam-323	156	24	,	,	PUNCT
ejpam-323	156	25	θ	θ	NOUN
ejpam-323	156	26	)	)	PUNCT
ejpam-323	156	27	=	=	PUNCT
ejpam-323	157	1	̺0	̺0	X
ejpam-323	157	2	+	+	ADJ
ejpam-323	157	3	ευ(θ	ευ(θ	NOUN
ejpam-323	157	4	)	)	PUNCT
ejpam-323	157	5	;	;	PUNCT
ejpam-323	157	6	θ	θ	PROPN
ejpam-323	157	7	∈	∈	PROPN
ejpam-323	158	1	[	[	X
ejpam-323	158	2	0,2π	0,2π	NOUN
ejpam-323	158	3	]	]	PUNCT
ejpam-323	158	4	.	.	PUNCT
ejpam-323	159	1	therefore	therefore	ADV
ejpam-323	159	2	|ω̃ε|	|ω̃ε|	NOUN
ejpam-323	159	3	=	=	SYM
ejpam-323	159	4	∫	∫	PROPN
ejpam-323	159	5	2π	2π	PROPN
ejpam-323	159	6	0	0	PUNCT
ejpam-323	160	1	[	[	PUNCT
ejpam-323	160	2	∫	∫	PROPN
ejpam-323	160	3	̺0+ευ(θ	̺0+ευ(θ	PROPN
ejpam-323	160	4	)	)	PUNCT
ejpam-323	161	1	̺0	̺0	VERB
ejpam-323	161	2	̺d̺]dθ	̺d̺]dθ	NOUN
ejpam-323	161	3	=	=	SYM
ejpam-323	161	4	1	1	NUM
ejpam-323	161	5	2	2	NUM
ejpam-323	161	6	∫	∫	NOUN
ejpam-323	161	7	2π	2π	NOUN
ejpam-323	161	8	0	0	PUNCT
ejpam-323	162	1	[	[	X
ejpam-323	162	2	ε2υ2(θ	ε2υ2(θ	X
ejpam-323	162	3	)	)	PUNCT
ejpam-323	162	4	+	+	NUM
ejpam-323	162	5	2ε̺0υ(θ)]dθ	2ε̺0υ(θ)]dθ	NUM
ejpam-323	162	6	.	.	PUNCT
ejpam-323	163	1	(	(	PUNCT
ejpam-323	163	2	11	11	NUM
ejpam-323	163	3	)	)	PUNCT
ejpam-323	163	4	for	for	ADP
ejpam-323	163	5	ε	ε	PROPN
ejpam-323	163	6	<	<	X
ejpam-323	163	7	ε3	ε3	PROPN
ejpam-323	163	8	=	=	SYM
ejpam-323	163	9	inf(ε2	inf(ε2	PROPN
ejpam-323	163	10	,	,	PUNCT
ejpam-323	163	11	1	1	NUM
ejpam-323	163	12	/	/	SYM
ejpam-323	163	13	m	m	NOUN
ejpam-323	163	14	)	)	PUNCT
ejpam-323	163	15	,	,	PUNCT
ejpam-323	163	16	we	we	PRON
ejpam-323	163	17	can	can	AUX
ejpam-323	163	18	write	write	VERB
ejpam-323	163	19	:	:	PUNCT
ejpam-323	163	20	ε2	ε2	ADJ
ejpam-323	163	21	≤	≤	NUM
ejpam-323	163	22	ε	ε	PROPN
ejpam-323	163	23	/	/	SYM
ejpam-323	163	24	m	m	PROPN
ejpam-323	163	25	;	;	PUNCT
ejpam-323	163	26	which	which	PRON
ejpam-323	163	27	implies	imply	VERB
ejpam-323	163	28	ε2m2	ε2m2	PROPN
ejpam-323	163	29	≤	≤	NUM
ejpam-323	163	30	εm	εm	NOUN
ejpam-323	163	31	.	.	PUNCT
ejpam-323	164	1	consequently	consequently	ADV
ejpam-323	164	2	the	the	DET
ejpam-323	164	3	equality	equality	NOUN
ejpam-323	164	4	(	(	PUNCT
ejpam-323	164	5	11	11	NUM
ejpam-323	164	6	)	)	PUNCT
ejpam-323	164	7	gives	give	VERB
ejpam-323	164	8	|ω̃ε|	|ω̃ε|	ADP
ejpam-323	164	9	≤	≤	ADJ
ejpam-323	164	10	πm(1	πm(1	NOUN
ejpam-323	164	11	+	+	CCONJ
ejpam-323	164	12	2̺0)ε	2̺0)ε	NUM
ejpam-323	164	13	.	.	PUNCT
ejpam-323	165	1	(	(	PUNCT
ejpam-323	165	2	12	12	NUM
ejpam-323	165	3	)	)	PUNCT
ejpam-323	165	4	by	by	ADP
ejpam-323	165	5	poincare	poincare	PROPN
ejpam-323	165	6	’s	’s	PART
ejpam-323	165	7	inequality	inequality	NOUN
ejpam-323	165	8	and	and	CCONJ
ejpam-323	165	9	lemma	lemma	PROPN
ejpam-323	165	10	1	1	NUM
ejpam-323	165	11	we	we	PRON
ejpam-323	165	12	write	write	VERB
ejpam-323	165	13	,	,	PUNCT
ejpam-323	165	14	‖u	‖u	PROPN
ejpam-323	165	15	j(ε)−	j(ε)−	PROPN
ejpam-323	165	16	u	u	PROPN
ejpam-323	165	17	j	j	PROPN
ejpam-323	165	18	0‖l2(ω̃ε	0‖l2(ω̃ε	PROPN
ejpam-323	165	19	)	)	PUNCT
ejpam-323	165	20	≤	≤	NOUN
ejpam-323	165	21	c(ω̃ε)c	c(ω̃ε)c	NOUN
ejpam-323	165	22	j|ω̃ε|1/2	j|ω̃ε|1/2	PROPN
ejpam-323	165	23	.	.	PUNCT
ejpam-323	166	1	a.	a.	PROPN
ejpam-323	166	2	khelifi	khelifi	PROPN
ejpam-323	166	3	,	,	PUNCT
ejpam-323	166	4	m.	m.	NOUN
ejpam-323	166	5	shamma	shamma	PROPN
ejpam-323	166	6	/	/	SYM
ejpam-323	166	7	eur	eur	PROPN
ejpam-323	166	8	.	.	PUNCT
ejpam-323	167	1	j.	j.	PROPN
ejpam-323	167	2	pure	pure	PROPN
ejpam-323	167	3	appl	appl	PROPN
ejpam-323	167	4	.	.	PROPN
ejpam-323	167	5	math	math	PROPN
ejpam-323	167	6	,	,	PUNCT
ejpam-323	167	7	3	3	NUM
ejpam-323	167	8	(	(	PUNCT
ejpam-323	167	9	2010	2010	NUM
ejpam-323	167	10	)	)	PUNCT
ejpam-323	167	11	,	,	PUNCT
ejpam-323	167	12	282	282	NUM
ejpam-323	167	13	-	-	SYM
ejpam-323	167	14	294	294	NUM
ejpam-323	167	15	289	289	NUM
ejpam-323	167	16	finally	finally	ADV
ejpam-323	167	17	,	,	PUNCT
ejpam-323	167	18	we	we	PRON
ejpam-323	167	19	obtain	obtain	VERB
ejpam-323	167	20	the	the	DET
ejpam-323	167	21	desired	desire	VERB
ejpam-323	167	22	result	result	NOUN
ejpam-323	167	23	if	if	SCONJ
ejpam-323	167	24	we	we	PRON
ejpam-323	167	25	consider	consider	VERB
ejpam-323	167	26	the	the	DET
ejpam-323	167	27	relations	relation	NOUN
ejpam-323	167	28	(	(	PUNCT
ejpam-323	167	29	10	10	NUM
ejpam-323	167	30	)	)	PUNCT
ejpam-323	167	31	and	and	CCONJ
ejpam-323	167	32	(	(	PUNCT
ejpam-323	167	33	12	12	NUM
ejpam-323	167	34	)	)	PUNCT
ejpam-323	167	35	and	and	CCONJ
ejpam-323	167	36	if	if	SCONJ
ejpam-323	167	37	we	we	PRON
ejpam-323	167	38	choose	choose	VERB
ejpam-323	167	39	the	the	DET
ejpam-323	167	40	constant	constant	ADJ
ejpam-323	167	41	κ	κ	PROPN
ejpam-323	167	42	j	j	PROPN
ejpam-323	167	43	=	=	PUNCT
ejpam-323	167	44	c	c	PROPN
ejpam-323	168	1	jc0	jc0	NOUN
ejpam-323	168	2	p	p	NOUN
ejpam-323	168	3	πm(1	πm(1	PROPN
ejpam-323	168	4	+	+	PROPN
ejpam-323	168	5	2̺0	2̺0	NUM
ejpam-323	168	6	)	)	PUNCT
ejpam-323	168	7	.	.	PUNCT
ejpam-323	169	1	to	to	PART
ejpam-323	169	2	derive	derive	VERB
ejpam-323	169	3	the	the	DET
ejpam-323	169	4	corresponding	correspond	VERB
ejpam-323	169	5	formulae	formulae	NOUN
ejpam-323	169	6	for	for	ADP
ejpam-323	169	7	the	the	DET
ejpam-323	169	8	eigenvalues	eigenvalue	NOUN
ejpam-323	169	9	we	we	PRON
ejpam-323	169	10	will	will	AUX
ejpam-323	169	11	use	use	VERB
ejpam-323	169	12	an	an	DET
ejpam-323	169	13	idea	idea	NOUN
ejpam-323	169	14	close	close	ADV
ejpam-323	169	15	to	to	ADP
ejpam-323	169	16	the	the	DET
ejpam-323	169	17	theorem	theorem	NOUN
ejpam-323	169	18	of	of	ADP
ejpam-323	169	19	osborn	osborn	PROPN
ejpam-323	170	1	[	[	X
ejpam-323	170	2	18	18	NUM
ejpam-323	170	3	]	]	PUNCT
ejpam-323	170	4	which	which	PRON
ejpam-323	170	5	gives	give	VERB
ejpam-323	170	6	estimates	estimate	NOUN
ejpam-323	170	7	for	for	ADP
ejpam-323	170	8	the	the	DET
ejpam-323	170	9	convergence	convergence	NOUN
ejpam-323	170	10	of	of	ADP
ejpam-323	170	11	the	the	DET
ejpam-323	170	12	eigenvalues	eigenvalue	NOUN
ejpam-323	170	13	of	of	ADP
ejpam-323	170	14	a	a	DET
ejpam-323	170	15	sequence	sequence	NOUN
ejpam-323	170	16	of	of	ADP
ejpam-323	170	17	compact	compact	ADJ
ejpam-323	170	18	operators	operator	NOUN
ejpam-323	170	19	.	.	PUNCT
ejpam-323	171	1	for	for	ADP
ejpam-323	171	2	our	our	PRON
ejpam-323	171	3	case	case	NOUN
ejpam-323	171	4	we	we	PRON
ejpam-323	171	5	consider	consider	VERB
ejpam-323	171	6	the	the	DET
ejpam-323	171	7	hilbert	hilbert	NOUN
ejpam-323	171	8	space	space	NOUN
ejpam-323	171	9	l2(ωε	l2(ωε	PROPN
ejpam-323	171	10	)	)	PUNCT
ejpam-323	171	11	with	with	ADP
ejpam-323	171	12	the	the	DET
ejpam-323	171	13	standard	standard	ADJ
ejpam-323	171	14	inner	inner	ADJ
ejpam-323	171	15	product	product	NOUN
ejpam-323	171	16	〈	〈	PROPN
ejpam-323	171	17	.	.	PROPN
ejpam-323	171	18	,	,	PUNCT
ejpam-323	171	19	.	.	PUNCT
ejpam-323	172	1	〉	〉	NOUN
ejpam-323	172	2	.	.	PUNCT
ejpam-323	173	1	for	for	ADP
ejpam-323	173	2	any	any	DET
ejpam-323	173	3	ϕ	ϕ	PROPN
ejpam-323	173	4	∈	∈	PROPN
ejpam-323	173	5	l2(ωε	l2(ωε	PROPN
ejpam-323	173	6	)	)	PUNCT
ejpam-323	173	7	,	,	PUNCT
ejpam-323	173	8	define	define	VERB
ejpam-323	173	9	the	the	DET
ejpam-323	173	10	operator	operator	NOUN
ejpam-323	173	11	tεϕ	tεϕ	NOUN
ejpam-323	173	12	=	=	PUNCT
ejpam-323	173	13	vε	vε	PROPN
ejpam-323	173	14	,	,	PUNCT
ejpam-323	173	15	where	where	SCONJ
ejpam-323	173	16	vε	vε	NOUN
ejpam-323	173	17	is	be	AUX
ejpam-323	173	18	the	the	DET
ejpam-323	173	19	solution	solution	NOUN
ejpam-323	173	20	to	to	ADP
ejpam-323	173	21	the	the	DET
ejpam-323	173	22	problem	problem	NOUN
ejpam-323	173	23	(	(	PUNCT
ejpam-323	173	24	−∆vε	−∆vε	PROPN
ejpam-323	173	25	=	=	SYM
ejpam-323	173	26	ϕ	ϕ	PROPN
ejpam-323	173	27	in	in	ADP
ejpam-323	173	28	ωε	ωε	NOUN
ejpam-323	173	29	,	,	PUNCT
ejpam-323	173	30	vε	vε	VERB
ejpam-323	173	31	=	=	SYM
ejpam-323	173	32	0	0	NUM
ejpam-323	173	33	on	on	ADP
ejpam-323	173	34	∂ωε	∂ωε	NOUN
ejpam-323	173	35	.	.	PUNCT
ejpam-323	174	1	(	(	PUNCT
ejpam-323	174	2	13	13	NUM
ejpam-323	174	3	)	)	PUNCT
ejpam-323	174	4	and	and	CCONJ
ejpam-323	174	5	we	we	PRON
ejpam-323	174	6	define	define	VERB
ejpam-323	174	7	the	the	DET
ejpam-323	174	8	operator	operator	NOUN
ejpam-323	174	9	t0ϕ	t0ϕ	PROPN
ejpam-323	175	1	=	=	SYM
ejpam-323	175	2	v0	v0	PROPN
ejpam-323	175	3	,	,	PUNCT
ejpam-323	175	4	where	where	SCONJ
ejpam-323	175	5	v0	v0	NOUN
ejpam-323	175	6	is	be	AUX
ejpam-323	175	7	the	the	DET
ejpam-323	175	8	solution	solution	NOUN
ejpam-323	175	9	to	to	ADP
ejpam-323	175	10	the	the	DET
ejpam-323	175	11	problem	problem	NOUN
ejpam-323	175	12	(	(	PUNCT
ejpam-323	175	13	−∆v0	−∆v0	NOUN
ejpam-323	175	14	=	=	SYM
ejpam-323	175	15	ϕ	ϕ	PROPN
ejpam-323	175	16	in	in	ADP
ejpam-323	175	17	ω0	ω0	NOUN
ejpam-323	175	18	,	,	PUNCT
ejpam-323	175	19	v0	v0	NOUN
ejpam-323	175	20	=	=	SYM
ejpam-323	175	21	0	0	NUM
ejpam-323	175	22	on	on	ADP
ejpam-323	175	23	∂ω0	∂ω0	PROPN
ejpam-323	175	24	.	.	PUNCT
ejpam-323	176	1	(	(	PUNCT
ejpam-323	176	2	14	14	NUM
ejpam-323	176	3	)	)	PUNCT
ejpam-323	176	4	the	the	DET
ejpam-323	176	5	function	function	NOUN
ejpam-323	176	6	ϕ	ϕ	PROPN
ejpam-323	176	7	7→	7→	NUM
ejpam-323	176	8	(	(	PUNCT
ejpam-323	176	9	−∆)−1ϕ	−∆)−1ϕ	NOUN
ejpam-323	176	10	is	be	AUX
ejpam-323	176	11	continuous	continuous	ADJ
ejpam-323	176	12	from	from	ADP
ejpam-323	176	13	l2(ωε	l2(ωε	PROPN
ejpam-323	176	14	)	)	PUNCT
ejpam-323	176	15	to	to	PART
ejpam-323	176	16	h1	h1	VERB
ejpam-323	176	17	0(ωε	0(ωε	NOUN
ejpam-323	176	18	)	)	PUNCT
ejpam-323	176	19	.	.	PUNCT
ejpam-323	177	1	clearly	clearly	ADV
ejpam-323	177	2	tε	tε	ADP
ejpam-323	177	3	and	and	CCONJ
ejpam-323	177	4	t0	t0	PROPN
ejpam-323	177	5	are	be	AUX
ejpam-323	177	6	compact	compact	ADJ
ejpam-323	177	7	operators	operator	NOUN
ejpam-323	177	8	from	from	ADP
ejpam-323	177	9	l2(ω0	l2(ω0	ADJ
ejpam-323	177	10	)	)	PUNCT
ejpam-323	177	11	to	to	PART
ejpam-323	177	12	l2(ω0	l2(ω0	VERB
ejpam-323	177	13	)	)	PUNCT
ejpam-323	177	14	.	.	PUNCT
ejpam-323	178	1	from	from	ADP
ejpam-323	178	2	the	the	DET
ejpam-323	178	3	standard	standard	ADJ
ejpam-323	178	4	h1	h1	NOUN
ejpam-323	178	5	estimates	estimate	NOUN
ejpam-323	178	6	for	for	ADP
ejpam-323	178	7	vε	vε	ADP
ejpam-323	178	8	which	which	PRON
ejpam-323	178	9	are	be	AUX
ejpam-323	178	10	independent	independent	ADJ
ejpam-323	178	11	of	of	ADP
ejpam-323	178	12	ε	ε	PROPN
ejpam-323	178	13	,	,	PUNCT
ejpam-323	178	14	we	we	PRON
ejpam-323	178	15	see	see	VERB
ejpam-323	178	16	that	that	SCONJ
ejpam-323	178	17	the	the	DET
ejpam-323	178	18	set	set	NOUN
ejpam-323	178	19	{	{	PUNCT
ejpam-323	178	20	tε	tε	NOUN
ejpam-323	178	21	}	}	PUNCT
ejpam-323	178	22	is	be	AUX
ejpam-323	178	23	collectively	collectively	ADV
ejpam-323	178	24	compact	compact	ADJ
ejpam-323	178	25	.	.	PUNCT
ejpam-323	179	1	hence	hence	ADV
ejpam-323	179	2	all	all	DET
ejpam-323	179	3	hypotheses	hypothesis	NOUN
ejpam-323	179	4	hold	hold	VERB
ejpam-323	179	5	for	for	ADP
ejpam-323	179	6	the	the	DET
ejpam-323	179	7	theorem	theorem	NOUN
ejpam-323	179	8	of	of	ADP
ejpam-323	179	9	osborn	osborn	PROPN
ejpam-323	179	10	.	.	PUNCT
ejpam-323	180	1	now	now	ADV
ejpam-323	180	2	if	if	SCONJ
ejpam-323	180	3	we	we	PRON
ejpam-323	180	4	set	set	VERB
ejpam-323	180	5	,	,	PUNCT
ejpam-323	180	6	λ0	λ0	NOUN
ejpam-323	180	7	=	=	SYM
ejpam-323	180	8	1	1	NUM
ejpam-323	180	9	ω2	ω2	NUM
ejpam-323	180	10	0	0	NUM
ejpam-323	180	11	and	and	CCONJ
ejpam-323	180	12	λ	λ	X
ejpam-323	180	13	j(ε	j(ε	ADJ
ejpam-323	180	14	)	)	PUNCT
ejpam-323	181	1	=	=	SYM
ejpam-323	181	2	1	1	NUM
ejpam-323	182	1	ω2	ω2	NUM
ejpam-323	182	2	j	j	PROPN
ejpam-323	182	3	(	(	PUNCT
ejpam-323	182	4	ε	ε	PROPN
ejpam-323	182	5	)	)	PUNCT
ejpam-323	182	6	,	,	PUNCT
ejpam-323	182	7	then	then	ADV
ejpam-323	182	8	according	accord	VERB
ejpam-323	182	9	to	to	ADP
ejpam-323	182	10	the	the	DET
ejpam-323	182	11	problem	problem	NOUN
ejpam-323	182	12	(	(	PUNCT
ejpam-323	182	13	13)(resp	13)(resp	NUM
ejpam-323	182	14	.	.	PUNCT
ejpam-323	183	1	(	(	PUNCT
ejpam-323	183	2	14	14	NUM
ejpam-323	183	3	)	)	PUNCT
ejpam-323	183	4	)	)	PUNCT
ejpam-323	184	1	we	we	PRON
ejpam-323	184	2	can	can	AUX
ejpam-323	184	3	see	see	VERB
ejpam-323	184	4	that	that	PRON
ejpam-323	184	5	(	(	PUNCT
ejpam-323	184	6	λ	λ	X
ejpam-323	184	7	j(ε),u	j(ε),u	PROPN
ejpam-323	184	8	j(ε	j(ε	ADJ
ejpam-323	184	9	)	)	PUNCT
ejpam-323	184	10	)	)	PUNCT
ejpam-323	184	11	(	(	PUNCT
ejpam-323	184	12	resp.(λ0,u	resp.(λ0,u	PROPN
ejpam-323	184	13	j	j	PROPN
ejpam-323	184	14	0	0	NUM
ejpam-323	184	15	)	)	PUNCT
ejpam-323	184	16	)	)	PUNCT
ejpam-323	184	17	is	be	AUX
ejpam-323	184	18	eigenpairs	eigenpair	NOUN
ejpam-323	184	19	of	of	ADP
ejpam-323	184	20	tε	tε	PROPN
ejpam-323	184	21	(	(	PUNCT
ejpam-323	184	22	resp	resp	NOUN
ejpam-323	184	23	.	.	PUNCT
ejpam-323	184	24	of	of	ADP
ejpam-323	184	25	t0	t0	PROPN
ejpam-323	184	26	)	)	PUNCT
ejpam-323	184	27	with	with	ADP
ejpam-323	184	28	ϕ	ϕ	NOUN
ejpam-323	184	29	=	=	SYM
ejpam-323	184	30	1	1	NUM
ejpam-323	184	31	ω2	ω2	NUM
ejpam-323	184	32	j	j	PROPN
ejpam-323	184	33	(	(	PUNCT
ejpam-323	184	34	ε	ε	PROPN
ejpam-323	184	35	)	)	PUNCT
ejpam-323	184	36	u	u	NOUN
ejpam-323	184	37	j(ε	j(ε	ADJ
ejpam-323	184	38	)	)	PUNCT
ejpam-323	184	39	.	.	PUNCT
ejpam-323	185	1	we	we	PRON
ejpam-323	185	2	remember	remember	VERB
ejpam-323	185	3	that	that	SCONJ
ejpam-323	185	4	ω2	ω2	ADJ
ejpam-323	185	5	0	0	NUM
ejpam-323	185	6	is	be	AUX
ejpam-323	185	7	an	an	DET
ejpam-323	185	8	eigenfrequency	eigenfrequency	NOUN
ejpam-323	185	9	of	of	ADP
ejpam-323	185	10	multiplicity	multiplicity	NOUN
ejpam-323	185	11	m	m	VERB
ejpam-323	185	12	with	with	ADP
ejpam-323	185	13	a	a	DET
ejpam-323	185	14	corresponding	corresponding	ADJ
ejpam-323	185	15	set	set	NOUN
ejpam-323	185	16	of	of	ADP
ejpam-323	185	17	orthonormal	orthonormal	ADJ
ejpam-323	185	18	eigenfunctions	eigenfunction	NOUN
ejpam-323	185	19	{	{	PUNCT
ejpam-323	185	20	u	u	NOUN
ejpam-323	185	21	j	j	PROPN
ejpam-323	185	22	0	0	NUM
ejpam-323	185	23	}	}	PUNCT
ejpam-323	185	24	and	and	CCONJ
ejpam-323	185	25	then	then	ADV
ejpam-323	185	26	r(p(0	r(p(0	ADJ
ejpam-323	185	27	)	)	PUNCT
ejpam-323	185	28	)	)	PUNCT
ejpam-323	185	29	is	be	AUX
ejpam-323	185	30	just	just	ADV
ejpam-323	185	31	the	the	DET
ejpam-323	185	32	m−dimensional	m−dimensional	ADJ
ejpam-323	185	33	subspace	subspace	NOUN
ejpam-323	185	34	generated	generate	VERB
ejpam-323	185	35	by	by	ADP
ejpam-323	185	36	{	{	PUNCT
ejpam-323	185	37	u	u	PROPN
ejpam-323	185	38	j	j	PROPN
ejpam-323	185	39	0}(where	0}(where	NUM
ejpam-323	185	40	p(0	p(0	PROPN
ejpam-323	185	41	)	)	PUNCT
ejpam-323	185	42	means	mean	VERB
ejpam-323	185	43	the	the	DET
ejpam-323	185	44	spectral	spectral	ADJ
ejpam-323	185	45	projection	projection	NOUN
ejpam-323	185	46	associated	associate	VERB
ejpam-323	185	47	with	with	ADP
ejpam-323	185	48	t0	t0	PROPN
ejpam-323	185	49	and	and	CCONJ
ejpam-323	185	50	means	mean	VERB
ejpam-323	185	51	the	the	DET
ejpam-323	185	52	projection	projection	NOUN
ejpam-323	185	53	onto	onto	ADP
ejpam-323	185	54	the	the	DET
ejpam-323	185	55	space	space	NOUN
ejpam-323	185	56	associated	associate	VERB
ejpam-323	185	57	to	to	ADP
ejpam-323	185	58	{	{	PUNCT
ejpam-323	185	59	u	u	PROPN
ejpam-323	185	60	j	j	PROPN
ejpam-323	185	61	0	0	NUM
ejpam-323	185	62	}	}	PUNCT
ejpam-323	185	63	)	)	PUNCT
ejpam-323	185	64	.	.	PUNCT
ejpam-323	186	1	although	although	SCONJ
ejpam-323	186	2	each	each	PRON
ejpam-323	186	3	of	of	ADP
ejpam-323	186	4	the	the	DET
ejpam-323	186	5	eigenvalues	eigenvalues	PROPN
ejpam-323	186	6	λ1(ε	λ1(ε	NOUN
ejpam-323	186	7	)	)	PUNCT
ejpam-323	186	8	,	,	PUNCT
ejpam-323	186	9	·	·	PUNCT
ejpam-323	186	10	·	·	PUNCT
ejpam-323	186	11	·	·	PUNCT
ejpam-323	186	12	,	,	PUNCT
ejpam-323	186	13	λm(ε	λm(ε	NUM
ejpam-323	186	14	)	)	PUNCT
ejpam-323	186	15	are	be	AUX
ejpam-323	186	16	close	close	ADJ
ejpam-323	186	17	to	to	ADP
ejpam-323	186	18	λ0	λ0	NOUN
ejpam-323	186	19	,	,	PUNCT
ejpam-323	186	20	their	their	PRON
ejpam-323	186	21	arithmetic	arithmetic	ADJ
ejpam-323	186	22	mean	mean	NOUN
ejpam-323	186	23	is	be	AUX
ejpam-323	186	24	generally	generally	ADV
ejpam-323	186	25	a	a	DET
ejpam-323	186	26	closer	close	ADJ
ejpam-323	186	27	approximation	approximation	NOUN
ejpam-323	186	28	[	[	X
ejpam-323	186	29	3	3	NUM
ejpam-323	186	30	]	]	PUNCT
ejpam-323	186	31	.	.	PUNCT
ejpam-323	187	1	thus	thus	ADV
ejpam-323	187	2	we	we	PRON
ejpam-323	187	3	define	define	VERB
ejpam-323	187	4	λ̂(ε	λ̂(ε	NUM
ejpam-323	187	5	)	)	PUNCT
ejpam-323	187	6	=	=	SYM
ejpam-323	188	1	1	1	NUM
ejpam-323	188	2	m	m	NOUN
ejpam-323	188	3	m	m	VERB
ejpam-323	188	4	∑	∑	ADJ
ejpam-323	188	5	j=1	j=1	ADJ
ejpam-323	188	6	1	1	NUM
ejpam-323	188	7	ω2	ω2	NUM
ejpam-323	188	8	j	j	PROPN
ejpam-323	188	9	(	(	PUNCT
ejpam-323	188	10	ε	ε	PROPN
ejpam-323	188	11	)	)	PUNCT
ejpam-323	188	12	.	.	PUNCT
ejpam-323	189	1	(	(	PUNCT
ejpam-323	189	2	15	15	NUM
ejpam-323	189	3	)	)	PUNCT
ejpam-323	189	4	in	in	ADP
ejpam-323	189	5	the	the	DET
ejpam-323	189	6	terminology	terminology	NOUN
ejpam-323	189	7	of	of	ADP
ejpam-323	189	8	[	[	X
ejpam-323	189	9	9	9	NUM
ejpam-323	189	10	]	]	PUNCT
ejpam-323	189	11	this	this	PRON
ejpam-323	189	12	is	be	AUX
ejpam-323	189	13	the	the	DET
ejpam-323	189	14	weighted	weighted	ADJ
ejpam-323	189	15	mean	mean	NOUN
ejpam-323	189	16	of	of	ADP
ejpam-323	189	17	the	the	DET
ejpam-323	189	18	λ0−group	λ0−group	NOUN
ejpam-323	189	19	.	.	PUNCT
ejpam-323	190	1	the	the	DET
ejpam-323	190	2	next	next	ADJ
ejpam-323	190	3	lemma	lemma	PROPN
ejpam-323	190	4	gives	give	VERB
ejpam-323	190	5	an	an	DET
ejpam-323	190	6	estimate	estimate	NOUN
ejpam-323	190	7	for	for	ADP
ejpam-323	190	8	λ0	λ0	NOUN
ejpam-323	190	9	−	−	PROPN
ejpam-323	190	10	λ̂(ε	λ̂(ε	NOUN
ejpam-323	190	11	)	)	PUNCT
ejpam-323	190	12	which	which	PRON
ejpam-323	190	13	will	will	AUX
ejpam-323	190	14	be	be	AUX
ejpam-323	190	15	useful	useful	ADJ
ejpam-323	190	16	to	to	PART
ejpam-323	190	17	prove	prove	VERB
ejpam-323	190	18	our	our	PRON
ejpam-323	190	19	main	main	ADJ
ejpam-323	190	20	result	result	NOUN
ejpam-323	190	21	.	.	PUNCT
ejpam-323	191	1	lemma	lemma	PROPN
ejpam-323	191	2	2	2	X
ejpam-323	191	3	.	.	PUNCT
ejpam-323	192	1	let	let	VERB
ejpam-323	192	2	ε3	ε3	PROPN
ejpam-323	192	3	be	be	AUX
ejpam-323	192	4	the	the	DET
ejpam-323	192	5	positive	positive	ADJ
ejpam-323	192	6	constant	constant	NOUN
ejpam-323	192	7	given	give	VERB
ejpam-323	192	8	by	by	ADP
ejpam-323	192	9	theorem	theorem	NOUN
ejpam-323	192	10	3	3	NUM
ejpam-323	192	11	.	.	PUNCT
ejpam-323	193	1	then	then	ADV
ejpam-323	193	2	there	there	PRON
ejpam-323	193	3	exists	exist	VERB
ejpam-323	193	4	a	a	DET
ejpam-323	193	5	positive	positive	ADJ
ejpam-323	193	6	constant	constant	ADJ
ejpam-323	193	7	k1	k1	NOUN
ejpam-323	193	8	such	such	ADJ
ejpam-323	193	9	that	that	PRON
ejpam-323	193	10	for	for	ADP
ejpam-323	193	11	ε	ε	PROPN
ejpam-323	193	12	<	<	X
ejpam-323	193	13	ε3	ε3	PROPN
ejpam-323	193	14	,	,	PUNCT
ejpam-323	193	15	|λ0−	|λ0−	NOUN
ejpam-323	193	16	λ̂(ε)|	λ̂(ε)|	X
ejpam-323	193	17	≤	≤	ADV
ejpam-323	193	18	k1ε	k1ε	PROPN
ejpam-323	193	19	1/2	1/2	NUM
ejpam-323	193	20	.	.	PUNCT
ejpam-323	194	1	a.	a.	NOUN
ejpam-323	194	2	khelifi	khelifi	PROPN
ejpam-323	194	3	,	,	PUNCT
ejpam-323	194	4	m.	m.	NOUN
ejpam-323	194	5	shamma	shamma	PROPN
ejpam-323	194	6	/	/	SYM
ejpam-323	194	7	eur	eur	PROPN
ejpam-323	194	8	.	.	PUNCT
ejpam-323	195	1	j.	j.	PROPN
ejpam-323	195	2	pure	pure	PROPN
ejpam-323	195	3	appl	appl	PROPN
ejpam-323	195	4	.	.	PROPN
ejpam-323	195	5	math	math	PROPN
ejpam-323	195	6	,	,	PUNCT
ejpam-323	195	7	3	3	NUM
ejpam-323	195	8	(	(	PUNCT
ejpam-323	195	9	2010	2010	NUM
ejpam-323	195	10	)	)	PUNCT
ejpam-323	195	11	,	,	PUNCT
ejpam-323	195	12	282	282	NUM
ejpam-323	195	13	-	-	NUM
ejpam-323	195	14	294	294	NUM
ejpam-323	195	15	290	290	NUM
ejpam-323	195	16	proof	proof	NOUN
ejpam-323	195	17	.	.	PUNCT
ejpam-323	196	1	we	we	PRON
ejpam-323	196	2	write	write	VERB
ejpam-323	196	3	,	,	PUNCT
ejpam-323	196	4	‖tεu	‖tεu	PROPN
ejpam-323	196	5	j	j	PROPN
ejpam-323	196	6	0	0	NUM
ejpam-323	197	1	−	−	PROPN
ejpam-323	197	2	t0u	t0u	ADP
ejpam-323	197	3	j	j	NOUN
ejpam-323	197	4	0‖l2(ω̃ε	0‖l2(ω̃ε	PROPN
ejpam-323	197	5	)	)	PUNCT
ejpam-323	198	1	=	=	SYM
ejpam-323	198	2	‖tεu	‖tεu	NOUN
ejpam-323	198	3	j(ε	j(ε	ADJ
ejpam-323	198	4	)	)	PUNCT
ejpam-323	199	1	+	+	CCONJ
ejpam-323	199	2	tεu	tεu	VERB
ejpam-323	199	3	j	j	NOUN
ejpam-323	199	4	0	0	NUM
ejpam-323	199	5	−	−	PROPN
ejpam-323	199	6	tεu	tεu	NOUN
ejpam-323	199	7	j(ε)−	j(ε)−	PROPN
ejpam-323	199	8	t0u	t0u	NOUN
ejpam-323	199	9	j	j	NOUN
ejpam-323	199	10	0‖l2(ω̃ε	0‖l2(ω̃ε	PROPN
ejpam-323	199	11	)	)	PUNCT
ejpam-323	199	12	≤	≤	NOUN
ejpam-323	199	13	‖	‖	PROPN
ejpam-323	199	14	1	1	NUM
ejpam-323	199	15	ω2	ω2	PROPN
ejpam-323	199	16	j	j	PROPN
ejpam-323	199	17	(	(	PUNCT
ejpam-323	199	18	ε	ε	PROPN
ejpam-323	199	19	)	)	PUNCT
ejpam-323	199	20	u	u	NOUN
ejpam-323	199	21	j(ε)−	j(ε)−	PROPN
ejpam-323	199	22	1	1	NUM
ejpam-323	199	23	ω2	ω2	ADJ
ejpam-323	199	24	0	0	NUM
ejpam-323	199	25	u0‖l2(ω̃ε	u0‖l2(ω̃ε	NOUN
ejpam-323	199	26	)	)	PUNCT
ejpam-323	200	1	+	+	CCONJ
ejpam-323	200	2	‖tεu	‖tεu	NUM
ejpam-323	200	3	j	j	NOUN
ejpam-323	200	4	0	0	NUM
ejpam-323	200	5	−	−	PROPN
ejpam-323	200	6	tεu	tεu	NOUN
ejpam-323	200	7	j(ε)‖l2(ω̃ε	j(ε)‖l2(ω̃ε	NOUN
ejpam-323	200	8	)	)	PUNCT
ejpam-323	200	9	.	.	PUNCT
ejpam-323	201	1	(	(	PUNCT
ejpam-323	201	2	16	16	NUM
ejpam-323	201	3	)	)	PUNCT
ejpam-323	201	4	if	if	SCONJ
ejpam-323	201	5	we	we	PRON
ejpam-323	201	6	set	set	VERB
ejpam-323	201	7	z	z	NOUN
ejpam-323	201	8	j(ε	j(ε	ADJ
ejpam-323	201	9	)	)	PUNCT
ejpam-323	201	10	=	=	SYM
ejpam-323	201	11	1	1	NUM
ejpam-323	201	12	ω2	ω2	NUM
ejpam-323	201	13	j	j	PROPN
ejpam-323	201	14	(	(	PUNCT
ejpam-323	201	15	ε	ε	PROPN
ejpam-323	201	16	)	)	PUNCT
ejpam-323	201	17	u	u	NOUN
ejpam-323	201	18	j(ε	j(ε	ADJ
ejpam-323	201	19	)	)	PUNCT
ejpam-323	201	20	and	and	CCONJ
ejpam-323	201	21	z	z	NOUN
ejpam-323	201	22	j	j	NOUN
ejpam-323	201	23	0	0	PUNCT
ejpam-323	202	1	=	=	SYM
ejpam-323	202	2	1	1	NUM
ejpam-323	202	3	ω2	ω2	ADJ
ejpam-323	202	4	0	0	NUM
ejpam-323	202	5	u	u	NOUN
ejpam-323	202	6	j	j	PROPN
ejpam-323	202	7	0	0	NUM
ejpam-323	202	8	,	,	PUNCT
ejpam-323	202	9	we	we	PRON
ejpam-323	202	10	see	see	VERB
ejpam-323	202	11	that	that	SCONJ
ejpam-323	202	12	z	z	NOUN
ejpam-323	202	13	j(ε	j(ε	ADJ
ejpam-323	202	14	)	)	PUNCT
ejpam-323	202	15	and	and	CCONJ
ejpam-323	202	16	z	z	PROPN
ejpam-323	202	17	j	j	PROPN
ejpam-323	202	18	0	0	NUM
ejpam-323	202	19	are	be	AUX
ejpam-323	202	20	solutions	solution	NOUN
ejpam-323	202	21	to	to	ADP
ejpam-323	202	22	the	the	DET
ejpam-323	202	23	problems	problem	NOUN
ejpam-323	202	24	(	(	PUNCT
ejpam-323	202	25	3	3	NUM
ejpam-323	202	26	)	)	PUNCT
ejpam-323	202	27	and	and	CCONJ
ejpam-323	202	28	(	(	PUNCT
ejpam-323	202	29	2	2	X
ejpam-323	202	30	)	)	PUNCT
ejpam-323	202	31	respectively	respectively	ADV
ejpam-323	202	32	and	and	CCONJ
ejpam-323	203	1	z	z	NOUN
ejpam-323	203	2	j(ε)→	j(ε)→	PROPN
ejpam-323	204	1	z	z	PROPN
ejpam-323	204	2	j	j	PROPN
ejpam-323	204	3	0	0	PUNCT
ejpam-323	204	4	as	as	SCONJ
ejpam-323	204	5	ε	ε	PROPN
ejpam-323	204	6	tends	tend	VERB
ejpam-323	204	7	to	to	ADP
ejpam-323	204	8	0	0	NUM
ejpam-323	204	9	.	.	PUNCT
ejpam-323	205	1	therefore	therefore	ADV
ejpam-323	205	2	,	,	PUNCT
ejpam-323	205	3	theorem	theorem	VERB
ejpam-323	205	4	3	3	NUM
ejpam-323	205	5	gives	give	VERB
ejpam-323	205	6	for	for	ADP
ejpam-323	205	7	ε	ε	PROPN
ejpam-323	205	8	<	<	X
ejpam-323	205	9	ε3	ε3	PROPN
ejpam-323	205	10	,	,	PUNCT
ejpam-323	205	11	‖z	‖z	NOUN
ejpam-323	205	12	j(ε)−	j(ε)−	PROPN
ejpam-323	205	13	z	z	PROPN
ejpam-323	205	14	j	j	NOUN
ejpam-323	205	15	0‖l2(ω̃ε	0‖l2(ω̃ε	PROPN
ejpam-323	205	16	)	)	PUNCT
ejpam-323	205	17	≤	≤	NUM
ejpam-323	205	18	κ	κ	NOUN
ejpam-323	205	19	jε	jε	PROPN
ejpam-323	205	20	1/2	1/2	NUM
ejpam-323	205	21	.	.	PUNCT
ejpam-323	206	1	in	in	ADP
ejpam-323	206	2	other	other	ADJ
ejpam-323	206	3	words	word	NOUN
ejpam-323	206	4	,	,	PUNCT
ejpam-323	206	5	for	for	ADP
ejpam-323	206	6	reasons	reason	NOUN
ejpam-323	206	7	of	of	ADP
ejpam-323	206	8	compactness	compactness	NOUN
ejpam-323	206	9	of	of	ADP
ejpam-323	206	10	tε	tε	NOUN
ejpam-323	206	11	and	and	CCONJ
ejpam-323	206	12	according	accord	VERB
ejpam-323	206	13	to	to	ADP
ejpam-323	206	14	theorem	theorem	NOUN
ejpam-323	206	15	3	3	NUM
ejpam-323	206	16	we	we	PRON
ejpam-323	206	17	have	have	VERB
ejpam-323	206	18	‖tεu	‖tεu	NUM
ejpam-323	206	19	j	j	PROPN
ejpam-323	206	20	0	0	NUM
ejpam-323	206	21	−	−	PROPN
ejpam-323	206	22	tεu	tεu	NOUN
ejpam-323	206	23	j(ε)‖l2(ω̃ε	j(ε)‖l2(ω̃ε	NOUN
ejpam-323	206	24	)	)	PUNCT
ejpam-323	206	25	=	=	PUNCT
ejpam-323	207	1	‖tε(u	‖tε(u	PUNCT
ejpam-323	207	2	j	j	PROPN
ejpam-323	207	3	0	0	PUNCT
ejpam-323	207	4	−	−	PROPN
ejpam-323	207	5	u	u	PROPN
ejpam-323	207	6	j(ε))‖l2(ω̃ε	j(ε))‖l2(ω̃ε	PROPN
ejpam-323	207	7	)	)	PUNCT
ejpam-323	207	8	≤	≤	NUM
ejpam-323	208	1	k‖u	k‖u	NOUN
ejpam-323	208	2	j	j	PROPN
ejpam-323	208	3	0	0	NUM
ejpam-323	208	4	−	−	PROPN
ejpam-323	208	5	u	u	NOUN
ejpam-323	208	6	j(ε)‖l2(ω̃ε	j(ε)‖l2(ω̃ε	PROPN
ejpam-323	208	7	)	)	PUNCT
ejpam-323	208	8	≤	≤	PUNCT
ejpam-323	209	1	k	k	X
ejpam-323	209	2	.κ	.κ	PROPN
ejpam-323	209	3	jε	jε	PROPN
ejpam-323	209	4	1/2	1/2	NUM
ejpam-323	209	5	.	.	PUNCT
ejpam-323	210	1	then	then	ADV
ejpam-323	210	2	,	,	PUNCT
ejpam-323	210	3	the	the	DET
ejpam-323	210	4	relation	relation	NOUN
ejpam-323	210	5	(	(	PUNCT
ejpam-323	210	6	16	16	NUM
ejpam-323	210	7	)	)	PUNCT
ejpam-323	210	8	becomes	become	VERB
ejpam-323	210	9	‖tεu	‖tεu	PROPN
ejpam-323	210	10	j	j	PROPN
ejpam-323	210	11	0	0	NUM
ejpam-323	211	1	−	−	PROPN
ejpam-323	212	1	t0u	t0u	ADP
ejpam-323	212	2	j	j	PROPN
ejpam-323	212	3	0	0	NUM
ejpam-323	212	4	‖l2(ω̃ε	‖l2(ω̃ε	NUM
ejpam-323	212	5	)	)	PUNCT
ejpam-323	212	6	≤	≤	NOUN
ejpam-323	212	7	κ	κ	PROPN
ejpam-323	212	8	j(1	j(1	PROPN
ejpam-323	212	9	+	+	PROPN
ejpam-323	212	10	k)ε1/2	k)ε1/2	NOUN
ejpam-323	212	11	.	.	PUNCT
ejpam-323	213	1	(	(	PUNCT
ejpam-323	213	2	17	17	NUM
ejpam-323	213	3	)	)	PUNCT
ejpam-323	213	4	inserting	insert	VERB
ejpam-323	213	5	all	all	DET
ejpam-323	213	6	this	this	DET
ejpam-323	213	7	information	information	NOUN
ejpam-323	213	8	into	into	ADP
ejpam-323	213	9	the	the	DET
ejpam-323	213	10	theorem	theorem	NOUN
ejpam-323	213	11	of	of	ADP
ejpam-323	213	12	osborn	osborn	PROPN
ejpam-323	213	13	[	[	X
ejpam-323	213	14	21	21	NUM
ejpam-323	213	15	,	,	PUNCT
ejpam-323	213	16	thm.3	thm.3	PROPN
ejpam-323	213	17	]	]	PUNCT
ejpam-323	213	18	,	,	PUNCT
ejpam-323	213	19	we	we	PRON
ejpam-323	213	20	obtain	obtain	VERB
ejpam-323	213	21	1	1	NUM
ejpam-323	213	22	ω2	ω2	ADJ
ejpam-323	213	23	0	0	NUM
ejpam-323	214	1	−	−	PROPN
ejpam-323	214	2	1	1	NUM
ejpam-323	214	3	m	m	NOUN
ejpam-323	214	4	m	m	VERB
ejpam-323	214	5	∑	∑	ADJ
ejpam-323	214	6	j=1	j=1	ADJ
ejpam-323	214	7	1	1	NUM
ejpam-323	214	8	ω2	ω2	NUM
ejpam-323	214	9	j	j	PROPN
ejpam-323	214	10	(	(	PUNCT
ejpam-323	214	11	ε	ε	PROPN
ejpam-323	214	12	)	)	PUNCT
ejpam-323	214	13	=	=	SYM
ejpam-323	215	1	1	1	NUM
ejpam-323	215	2	m	m	NOUN
ejpam-323	215	3	m	m	VERB
ejpam-323	215	4	∑	∑	ADV
ejpam-323	215	5	j=1	j=1	PROPN
ejpam-323	215	6	〈	〈	PROPN
ejpam-323	215	7	(	(	PUNCT
ejpam-323	215	8	t0	t0	NOUN
ejpam-323	215	9	−	−	PROPN
ejpam-323	215	10	tε)u	tε)u	PROPN
ejpam-323	215	11	j	j	PROPN
ejpam-323	215	12	0,u	0,u	ADP
ejpam-323	215	13	j	j	PROPN
ejpam-323	215	14	0〉+	0〉+	PUNCT
ejpam-323	215	15	ε1/2o(1	ε1/2o(1	NOUN
ejpam-323	215	16	)	)	PUNCT
ejpam-323	215	17	.	.	PUNCT
ejpam-323	216	1	the	the	DET
ejpam-323	216	2	proof	proof	NOUN
ejpam-323	216	3	follows	follow	VERB
ejpam-323	216	4	by	by	ADP
ejpam-323	216	5	reconsidering	reconsider	VERB
ejpam-323	216	6	again	again	ADV
ejpam-323	216	7	relation	relation	NOUN
ejpam-323	216	8	(	(	PUNCT
ejpam-323	216	9	17	17	NUM
ejpam-323	216	10	)	)	PUNCT
ejpam-323	216	11	.	.	PUNCT
ejpam-323	217	1	next	next	ADV
ejpam-323	217	2	,	,	PUNCT
ejpam-323	217	3	to	to	ADP
ejpam-323	217	4	estimating	estimate	VERB
ejpam-323	217	5	|ω2	|ω2	NOUN
ejpam-323	217	6	0−ω2	0−ω2	NUM
ejpam-323	217	7	j	j	PROPN
ejpam-323	217	8	(	(	PUNCT
ejpam-323	217	9	ε)|	ε)|	PROPN
ejpam-323	217	10	we	we	PRON
ejpam-323	217	11	may	may	AUX
ejpam-323	217	12	,	,	PUNCT
ejpam-323	217	13	firstly	firstly	ADV
ejpam-323	217	14	,	,	PUNCT
ejpam-323	217	15	estimate	estimate	VERB
ejpam-323	217	16	|λ0−λ	|λ0−λ	PROPN
ejpam-323	217	17	j(ε)|	j(ε)|	NOUN
ejpam-323	217	18	for	for	ADP
ejpam-323	217	19	each	each	DET
ejpam-323	217	20	j.	j.	PROPN
ejpam-323	217	21	lemma	lemma	PROPN
ejpam-323	218	1	3	3	X
ejpam-323	218	2	.	.	X
ejpam-323	219	1	there	there	PRON
ejpam-323	219	2	exist	exist	VERB
ejpam-323	219	3	some	some	DET
ejpam-323	219	4	constants	constant	NOUN
ejpam-323	219	5	0	0	NUM
ejpam-323	219	6	<	<	X
ejpam-323	219	7	ε4	ε4	NOUN
ejpam-323	219	8	≤	≤	PROPN
ejpam-323	219	9	ε3	ε3	PROPN
ejpam-323	219	10	and	and	CCONJ
ejpam-323	219	11	k	k	X
ejpam-323	219	12	(	(	PUNCT
ejpam-323	219	13	1	1	X
ejpam-323	219	14	)	)	PUNCT
ejpam-323	219	15	j	j	NOUN
ejpam-323	219	16	such	such	ADJ
ejpam-323	219	17	that	that	PRON
ejpam-323	219	18	for	for	ADP
ejpam-323	219	19	all	all	DET
ejpam-323	219	20	j	j	NOUN
ejpam-323	219	21	=	=	SYM
ejpam-323	219	22	1	1	NUM
ejpam-323	219	23	,	,	PUNCT
ejpam-323	219	24	·	·	PUNCT
ejpam-323	219	25	·	·	PUNCT
ejpam-323	219	26	·	·	PUNCT
ejpam-323	219	27	,	,	PUNCT
ejpam-323	219	28	m	m	PROPN
ejpam-323	219	29	,	,	PUNCT
ejpam-323	219	30	|λ0−λ	|λ0−λ	PROPN
ejpam-323	219	31	j(ε)|m	j(ε)|m	PROPN
ejpam-323	219	32	≤	≤	PROPN
ejpam-323	219	33	k	k	PROPN
ejpam-323	219	34	(	(	PUNCT
ejpam-323	219	35	1	1	X
ejpam-323	219	36	)	)	PUNCT
ejpam-323	219	37	j	j	NOUN
ejpam-323	219	38	ε5/2	ε5/2	NOUN
ejpam-323	219	39	,	,	PUNCT
ejpam-323	219	40	for	for	ADP
ejpam-323	219	41	0≤	0≤	NUM
ejpam-323	219	42	ε≤	ε≤	PROPN
ejpam-323	219	43	ε4	ε4	NOUN
ejpam-323	219	44	.	.	PUNCT
ejpam-323	220	1	proof	proof	NOUN
ejpam-323	220	2	.	.	PUNCT
ejpam-323	221	1	let	let	VERB
ejpam-323	221	2	tε(yε	tε(yε	NOUN
ejpam-323	221	3	)	)	PUNCT
ejpam-323	222	1	=	=	PUNCT
ejpam-323	222	2	λ	λ	PROPN
ejpam-323	222	3	j(ε)yε	j(ε)yε	NOUN
ejpam-323	222	4	such	such	ADJ
ejpam-323	222	5	that	that	SCONJ
ejpam-323	222	6	‖yε‖=	‖yε‖=	ADP
ejpam-323	222	7	1	1	X
ejpam-323	222	8	.	.	PUNCT
ejpam-323	223	1	we	we	PRON
ejpam-323	223	2	can	can	AUX
ejpam-323	223	3	then	then	ADV
ejpam-323	223	4	choose̟∗	choose̟∗	VERB
ejpam-323	223	5	∈	∈	PROPN
ejpam-323	224	1	ker((λ0−t	ker((λ0−t	PROPN
ejpam-323	224	2	∗0	∗0	PROPN
ejpam-323	224	3	)	)	PUNCT
ejpam-323	224	4	m	m	PROPN
ejpam-323	224	5	)	)	PUNCT
ejpam-323	224	6	in	in	ADP
ejpam-323	224	7	such	such	DET
ejpam-323	224	8	a	a	DET
ejpam-323	224	9	way	way	NOUN
ejpam-323	224	10	that	that	PRON
ejpam-323	224	11	〈	〈	NOUN
ejpam-323	224	12	yε,̟∗	yε,̟∗	NOUN
ejpam-323	224	13	〉	〉	NOUN
ejpam-323	224	14	=	=	SYM
ejpam-323	224	15	1	1	X
ejpam-323	224	16	.	.	PUNCT
ejpam-323	224	17	then	then	ADV
ejpam-323	224	18	,	,	PUNCT
ejpam-323	224	19	〈	〈	PROPN
ejpam-323	224	20	(	(	PUNCT
ejpam-323	224	21	λ0	λ0	NOUN
ejpam-323	224	22	−	−	PROPN
ejpam-323	224	23	t	t	PROPN
ejpam-323	224	24	∗0	∗0	PROPN
ejpam-323	224	25	)	)	PUNCT
ejpam-323	224	26	m̟∗	m̟∗	NOUN
ejpam-323	224	27	,	,	PUNCT
ejpam-323	224	28	yε	yε	ADJ
ejpam-323	224	29	〉	〉	NOUN
ejpam-323	224	30	=	=	SYM
ejpam-323	224	31	0	0	NUM
ejpam-323	224	32	and	and	CCONJ
ejpam-323	224	33	therefore	therefore	ADV
ejpam-323	224	34	,	,	PUNCT
ejpam-323	224	35	|〈(λ0−λ	|〈(λ0−λ	X
ejpam-323	224	36	j(ε	j(ε	ADJ
ejpam-323	224	37	)	)	PUNCT
ejpam-323	224	38	)	)	PUNCT
ejpam-323	224	39	m̟∗	m̟∗	NOUN
ejpam-323	224	40	,	,	PUNCT
ejpam-323	224	41	yε〉|	yε〉|	PROPN
ejpam-323	224	42	=	=	X
ejpam-323	224	43	|〈(λ0−λ	|〈(λ0−λ	X
ejpam-323	224	44	j(ε	j(ε	ADJ
ejpam-323	224	45	)	)	PUNCT
ejpam-323	224	46	)	)	PUNCT
ejpam-323	225	1	m̟∗	m̟∗	NOUN
ejpam-323	225	2	,	,	PUNCT
ejpam-323	225	3	yε	yε	ADP
ejpam-323	225	4	〉	〉	NOUN
ejpam-323	225	5	−	−	NOUN
ejpam-323	225	6	〈	〈	PROPN
ejpam-323	225	7	(	(	PUNCT
ejpam-323	225	8	λ0	λ0	NOUN
ejpam-323	225	9	−	−	PROPN
ejpam-323	225	10	t	t	PROPN
ejpam-323	225	11	∗0	∗0	PROPN
ejpam-323	225	12	)	)	PUNCT
ejpam-323	225	13	m̟∗	m̟∗	NOUN
ejpam-323	225	14	,	,	PUNCT
ejpam-323	225	15	yε〉|	yε〉|	PROPN
ejpam-323	225	16	=	=	PUNCT
ejpam-323	226	1	|	|	ADV
ejpam-323	226	2	−	−	PROPN
ejpam-323	226	3	m−1	m−1	PROPN
ejpam-323	226	4	∑	∑	PUNCT
ejpam-323	227	1	l=0	l=0	PROPN
ejpam-323	227	2	(	(	PUNCT
ejpam-323	227	3	λ0−λ	λ0−λ	PROPN
ejpam-323	227	4	j(ε	j(ε	ADJ
ejpam-323	227	5	)	)	PUNCT
ejpam-323	227	6	)	)	PUNCT
ejpam-323	228	1	l〈(λ0−	l〈(λ0−	PROPN
ejpam-323	228	2	t	t	NOUN
ejpam-323	228	3	∗0	∗0	PROPN
ejpam-323	228	4	)	)	PUNCT
ejpam-323	228	5	m−1−l(λ	m−1−l(λ	ADP
ejpam-323	228	6	j(ε)−	j(ε)−	PROPN
ejpam-323	228	7	t	t	PROPN
ejpam-323	228	8	∗0	∗0	PROPN
ejpam-323	228	9	)	)	PUNCT
ejpam-323	228	10	̟	̟	PRON
ejpam-323	228	11	∗	∗	NOUN
ejpam-323	228	12	,	,	PUNCT
ejpam-323	228	13	yε〉|	yε〉|	PROPN
ejpam-323	228	14	.	.	PUNCT
ejpam-323	229	1	(	(	PUNCT
ejpam-323	229	2	18	18	NUM
ejpam-323	229	3	)	)	PUNCT
ejpam-323	229	4	a.	a.	NOUN
ejpam-323	229	5	khelifi	khelifi	PROPN
ejpam-323	229	6	,	,	PUNCT
ejpam-323	229	7	m.	m.	NOUN
ejpam-323	229	8	shamma	shamma	PROPN
ejpam-323	229	9	/	/	SYM
ejpam-323	229	10	eur	eur	PROPN
ejpam-323	229	11	.	.	PUNCT
ejpam-323	230	1	j.	j.	PROPN
ejpam-323	230	2	pure	pure	PROPN
ejpam-323	230	3	appl	appl	PROPN
ejpam-323	230	4	.	.	PROPN
ejpam-323	230	5	math	math	PROPN
ejpam-323	230	6	,	,	PUNCT
ejpam-323	230	7	3	3	NUM
ejpam-323	230	8	(	(	PUNCT
ejpam-323	230	9	2010	2010	NUM
ejpam-323	230	10	)	)	PUNCT
ejpam-323	230	11	,	,	PUNCT
ejpam-323	230	12	282	282	NUM
ejpam-323	230	13	-	-	SYM
ejpam-323	230	14	294	294	NUM
ejpam-323	230	15	291	291	NUM
ejpam-323	230	16	now	now	ADV
ejpam-323	230	17	we	we	PRON
ejpam-323	230	18	prove	prove	VERB
ejpam-323	230	19	that	that	SCONJ
ejpam-323	230	20	|λ0−λp(ε)|	|λ0−λp(ε)|	PROPN
ejpam-323	230	21	≤	≤	PROPN
ejpam-323	230	22	|λ0−	|λ0−	NOUN
ejpam-323	230	23	λ̂(ε)|	λ̂(ε)|	NOUN
ejpam-323	230	24	,	,	PUNCT
ejpam-323	230	25	for	for	ADP
ejpam-323	230	26	each	each	DET
ejpam-323	230	27	positive	positive	ADJ
ejpam-323	230	28	integer	integer	NOUN
ejpam-323	230	29	p.	p.	NOUN
ejpam-323	230	30	but	but	CCONJ
ejpam-323	230	31	,	,	PUNCT
ejpam-323	230	32	the	the	DET
ejpam-323	230	33	relation	relation	NOUN
ejpam-323	230	34	,	,	PUNCT
ejpam-323	230	35	λ0−	λ0−	PROPN
ejpam-323	230	36	λ̂(ε)−	λ̂(ε)−	PROPN
ejpam-323	230	37	(	(	PUNCT
ejpam-323	230	38	λ0−λp(ε	λ0−λp(ε	NOUN
ejpam-323	230	39	)	)	PUNCT
ejpam-323	230	40	)	)	PUNCT
ejpam-323	231	1	=	=	PUNCT
ejpam-323	231	2	λp(ε)−	λp(ε)−	X
ejpam-323	231	3	1	1	NUM
ejpam-323	231	4	m	m	VERB
ejpam-323	231	5	m	m	VERB
ejpam-323	231	6	∑	∑	ADV
ejpam-323	231	7	j=1	j=1	PROPN
ejpam-323	231	8	λ	λ	X
ejpam-323	231	9	j(ε	j(ε	ADJ
ejpam-323	231	10	)	)	PUNCT
ejpam-323	231	11	implies	imply	VERB
ejpam-323	231	12	that	that	SCONJ
ejpam-323	231	13	,	,	PUNCT
ejpam-323	231	14	for	for	ADP
ejpam-323	231	15	p	p	PROPN
ejpam-323	231	16	and	and	CCONJ
ejpam-323	231	17	q	q	NOUN
ejpam-323	231	18	the	the	DET
ejpam-323	231	19	integers	integer	NOUN
ejpam-323	231	20	such	such	ADJ
ejpam-323	231	21	that	that	SCONJ
ejpam-323	231	22	λp	λp	X
ejpam-323	231	23	=	=	PUNCT
ejpam-323	231	24	sup1≤	sup1≤	ADJ
ejpam-323	231	25	j≤m	j≤m	NOUN
ejpam-323	231	26	|λ	|λ	CCONJ
ejpam-323	231	27	j(ε)|	j(ε)|	PROPN
ejpam-323	231	28	and	and	CCONJ
ejpam-323	231	29	λq	λq	ADJ
ejpam-323	231	30	=	=	PUNCT
ejpam-323	231	31	inf1≤	inf1≤	PROPN
ejpam-323	231	32	j≤m	j≤m	PROPN
ejpam-323	231	33	|λ	|λ	CCONJ
ejpam-323	231	34	j(ε)|	j(ε)|	NOUN
ejpam-323	231	35	,	,	PUNCT
ejpam-323	231	36	the	the	DET
ejpam-323	231	37	following	follow	VERB
ejpam-323	231	38	relation	relation	NOUN
ejpam-323	231	39	holds(the	holds(the	PROPN
ejpam-323	231	40	family	family	NOUN
ejpam-323	231	41	(	(	PUNCT
ejpam-323	231	42	ω2	ω2	PROPN
ejpam-323	231	43	j	j	PROPN
ejpam-323	231	44	)	)	PUNCT
ejpam-323	231	45	j	j	PROPN
ejpam-323	231	46	is	be	AUX
ejpam-323	231	47	increasing	increase	VERB
ejpam-323	231	48	):	):	PUNCT
ejpam-323	231	49	|λ0−	|λ0−	NOUN
ejpam-323	231	50	λ̂(ε)|	λ̂(ε)|	PROPN
ejpam-323	231	51	≥	≥	PROPN
ejpam-323	231	52	sup(|λ0−λp(ε)|	sup(|λ0−λp(ε)|	PROPN
ejpam-323	231	53	,	,	PUNCT
ejpam-323	231	54	|λ0−λq(ε)|	|λ0−λq(ε)|	PROPN
ejpam-323	231	55	)	)	PUNCT
ejpam-323	231	56	which	which	PRON
ejpam-323	231	57	gives	give	VERB
ejpam-323	231	58	that	that	DET
ejpam-323	231	59	|λ0−λ	|λ0−λ	PROPN
ejpam-323	231	60	j(ε)|	j(ε)|	PROPN
ejpam-323	231	61	≤	≤	PROPN
ejpam-323	231	62	|λ0−λ̂(ε)|	|λ0−λ̂(ε)|	NOUN
ejpam-323	231	63	for	for	ADP
ejpam-323	231	64	1≤	1≤	PROPN
ejpam-323	231	65	j	j	PROPN
ejpam-323	231	66	≤	≤	PROPN
ejpam-323	231	67	m.	m.	NOUN
ejpam-323	231	68	therefore	therefore	ADV
ejpam-323	231	69	,	,	PUNCT
ejpam-323	231	70	the	the	DET
ejpam-323	231	71	fact	fact	NOUN
ejpam-323	231	72	that	that	SCONJ
ejpam-323	231	73	λ0−λ̂(ε)→	λ0−λ̂(ε)→	PROPN
ejpam-323	231	74	0	0	NUM
ejpam-323	231	75	implies	imply	VERB
ejpam-323	231	76	that	that	SCONJ
ejpam-323	231	77	there	there	PRON
ejpam-323	231	78	exists	exist	VERB
ejpam-323	231	79	δ1	δ1	NOUN
ejpam-323	231	80	>	>	X
ejpam-323	231	81	0	0	NUM
ejpam-323	232	1	such	such	ADJ
ejpam-323	232	2	that	that	PRON
ejpam-323	232	3	for	for	ADP
ejpam-323	232	4	all	all	DET
ejpam-323	232	5	0≤	0≤	ADJ
ejpam-323	232	6	l	l	NOUN
ejpam-323	232	7	≤	≤	NOUN
ejpam-323	232	8	m−	m−	PROPN
ejpam-323	232	9	1	1	NUM
ejpam-323	232	10	,	,	PUNCT
ejpam-323	232	11	|λ0−λ	|λ0−λ	PROPN
ejpam-323	232	12	j(ε)|l	j(ε)|l	PROPN
ejpam-323	232	13	≤	≤	PROPN
ejpam-323	232	14	|λ0−	|λ0−	NOUN
ejpam-323	232	15	λ̂(ε)|	λ̂(ε)|	NOUN
ejpam-323	232	16	,	,	PUNCT
ejpam-323	232	17	for	for	ADP
ejpam-323	232	18	0	0	NUM
ejpam-323	232	19	<	<	X
ejpam-323	232	20	ε	ε	PROPN
ejpam-323	232	21	<	<	X
ejpam-323	232	22	δ1	δ1	PROPN
ejpam-323	232	23	.	.	PUNCT
ejpam-323	233	1	(	(	PUNCT
ejpam-323	233	2	19	19	NUM
ejpam-323	233	3	)	)	PUNCT
ejpam-323	233	4	next	next	ADV
ejpam-323	233	5	,	,	PUNCT
ejpam-323	233	6	if	if	SCONJ
ejpam-323	233	7	we	we	PRON
ejpam-323	233	8	insert	insert	VERB
ejpam-323	233	9	the	the	DET
ejpam-323	233	10	relation	relation	NOUN
ejpam-323	233	11	(	(	PUNCT
ejpam-323	233	12	19	19	NUM
ejpam-323	233	13	)	)	PUNCT
ejpam-323	233	14	into	into	ADP
ejpam-323	233	15	(	(	PUNCT
ejpam-323	233	16	18	18	NUM
ejpam-323	233	17	)	)	PUNCT
ejpam-323	233	18	we	we	PRON
ejpam-323	233	19	obtain	obtain	VERB
ejpam-323	233	20	the	the	DET
ejpam-323	233	21	following	follow	VERB
ejpam-323	233	22	inequality	inequality	NOUN
ejpam-323	233	23	|λ0−λ	|λ0−λ	PROPN
ejpam-323	233	24	j(ε)|m	j(ε)|m	PROPN
ejpam-323	233	25	≤	≤	PROPN
ejpam-323	233	26	|λ0−	|λ0−	NOUN
ejpam-323	233	27	λ̂(ε)|	λ̂(ε)|	X
ejpam-323	234	1	m−1	m−1	PROPN
ejpam-323	234	2	∑	∑	PUNCT
ejpam-323	234	3	l=0	l=0	PROPN
ejpam-323	234	4	‖λ0−t	‖λ0−t	PROPN
ejpam-323	235	1	∗0	∗0	X
ejpam-323	235	2	‖m−1−l	‖m−1−l	DET
ejpam-323	235	3	max	max	PROPN
ejpam-323	235	4	‖ψ∗‖=1	‖ψ∗‖=1	PROPN
ejpam-323	235	5	|〈(λ	|〈(λ	PROPN
ejpam-323	235	6	j(ε)−t0)yε	j(ε)−t0)yε	PROPN
ejpam-323	235	7	,	,	PUNCT
ejpam-323	235	8	ψ	ψ	X
ejpam-323	235	9	∗〉|	∗〉|	PROPN
ejpam-323	235	10	,	,	PUNCT
ejpam-323	235	11	for	for	ADP
ejpam-323	235	12	0	0	NUM
ejpam-323	235	13	<	<	X
ejpam-323	235	14	ε	ε	PROPN
ejpam-323	235	15	<	<	X
ejpam-323	235	16	δ1	δ1	PROPN
ejpam-323	235	17	.	.	PUNCT
ejpam-323	236	1	(	(	PUNCT
ejpam-323	236	2	20	20	NUM
ejpam-323	236	3	)	)	PUNCT
ejpam-323	236	4	for	for	ADP
ejpam-323	236	5	any	any	DET
ejpam-323	236	6	ψ∗	ψ∗	NOUN
ejpam-323	236	7	∈	∈	PROPN
ejpam-323	236	8	r(p(0)∗	r(p(0)∗	PROPN
ejpam-323	236	9	)	)	PUNCT
ejpam-323	236	10	,	,	PUNCT
ejpam-323	236	11	with	with	ADP
ejpam-323	236	12	‖ψ∗‖	‖ψ∗‖	PROPN
ejpam-323	236	13	=	=	SYM
ejpam-323	236	14	1	1	NUM
ejpam-323	236	15	,	,	PUNCT
ejpam-323	236	16	and	and	CCONJ
ejpam-323	236	17	the	the	DET
ejpam-323	236	18	fact	fact	NOUN
ejpam-323	236	19	that	that	SCONJ
ejpam-323	236	20	pj(ε	pj(ε	X
ejpam-323	236	21	)	)	PUNCT
ejpam-323	236	22	−1pj(ε	−1pj(ε	ADJ
ejpam-323	236	23	)	)	PUNCT
ejpam-323	236	24	is	be	AUX
ejpam-323	236	25	the	the	DET
ejpam-323	236	26	identity	identity	NOUN
ejpam-323	236	27	on	on	ADP
ejpam-323	236	28	r(p(0	r(p(0	NOUN
ejpam-323	236	29	)	)	PUNCT
ejpam-323	236	30	)	)	PUNCT
ejpam-323	236	31	(	(	PUNCT
ejpam-323	236	32	where	where	SCONJ
ejpam-323	236	33	pj(ε	pj(ε	NUM
ejpam-323	236	34	)	)	PUNCT
ejpam-323	236	35	means	mean	VERB
ejpam-323	236	36	the	the	DET
ejpam-323	236	37	spectral	spectral	ADJ
ejpam-323	236	38	projection	projection	NOUN
ejpam-323	236	39	associated	associate	VERB
ejpam-323	236	40	with	with	ADP
ejpam-323	236	41	tε	tε	NOUN
ejpam-323	236	42	and	and	CCONJ
ejpam-323	236	43	is	be	AUX
ejpam-323	236	44	a	a	DET
ejpam-323	236	45	projection	projection	NOUN
ejpam-323	236	46	onto	onto	ADP
ejpam-323	236	47	the	the	DET
ejpam-323	236	48	direct	direct	ADJ
ejpam-323	236	49	sum	sum	NOUN
ejpam-323	236	50	of	of	ADP
ejpam-323	236	51	the	the	DET
ejpam-323	236	52	spaces	space	NOUN
ejpam-323	236	53	of	of	ADP
ejpam-323	236	54	the	the	DET
ejpam-323	236	55	eigenvectors	eigenvector	NOUN
ejpam-323	236	56	corresponding	correspond	VERB
ejpam-323	236	57	to	to	ADP
ejpam-323	236	58	tε	tε	NUM
ejpam-323	236	59	)	)	PUNCT
ejpam-323	236	60	we	we	PRON
ejpam-323	236	61	write	write	VERB
ejpam-323	236	62	,	,	PUNCT
ejpam-323	236	63	|〈(λ	|〈(λ	PROPN
ejpam-323	236	64	j(ε)−	j(ε)−	PROPN
ejpam-323	236	65	t0)yε	t0)yε	PROPN
ejpam-323	236	66	,	,	PUNCT
ejpam-323	236	67	ψ	ψ	PROPN
ejpam-323	236	68	∗〉|	∗〉|	PROPN
ejpam-323	236	69	=	=	SYM
ejpam-323	236	70	|〈pj(ε	|〈pj(ε	ADJ
ejpam-323	236	71	)	)	PUNCT
ejpam-323	236	72	−1pj(ε)(tε−	−1pj(ε)(tε−	NOUN
ejpam-323	236	73	t0)yε	t0)yε	PROPN
ejpam-323	236	74	,	,	PUNCT
ejpam-323	236	75	ψ	ψ	PROPN
ejpam-323	236	76	∗〉|	∗〉|	PROPN
ejpam-323	236	77	=	=	SYM
ejpam-323	236	78	|〈(tε−	|〈(tε−	PROPN
ejpam-323	236	79	t0)yε	t0)yε	PROPN
ejpam-323	236	80	,	,	PUNCT
ejpam-323	236	81	(	(	PUNCT
ejpam-323	236	82	pj(ε	pj(ε	ADJ
ejpam-323	236	83	)	)	PUNCT
ejpam-323	236	84	−1pj(ε	−1pj(ε	ADJ
ejpam-323	236	85	)	)	PUNCT
ejpam-323	236	86	)	)	PUNCT
ejpam-323	236	87	∗ψ∗〉|	∗ψ∗〉|	NOUN
ejpam-323	236	88	.	.	PUNCT
ejpam-323	237	1	due	due	ADP
ejpam-323	237	2	to	to	ADP
ejpam-323	237	3	the	the	DET
ejpam-323	237	4	estimate	estimate	NOUN
ejpam-323	237	5	(	(	PUNCT
ejpam-323	237	6	4.10	4.10	NUM
ejpam-323	237	7	)	)	PUNCT
ejpam-323	237	8	found	find	VERB
ejpam-323	237	9	in	in	ADP
ejpam-323	237	10	[	[	X
ejpam-323	237	11	21	21	NUM
ejpam-323	237	12	,	,	PUNCT
ejpam-323	237	13	p.722	p.722	NOUN
ejpam-323	237	14	]	]	PUNCT
ejpam-323	237	15	,	,	PUNCT
ejpam-323	237	16	we	we	PRON
ejpam-323	237	17	obtain	obtain	VERB
ejpam-323	237	18	|〈(tε−	|〈(tε−	PROPN
ejpam-323	237	19	t0)yε	t0)yε	PROPN
ejpam-323	237	20	,	,	PUNCT
ejpam-323	237	21	(	(	PUNCT
ejpam-323	237	22	pj(ε	pj(ε	ADJ
ejpam-323	237	23	)	)	PUNCT
ejpam-323	237	24	−1pj(ε	−1pj(ε	ADJ
ejpam-323	237	25	)	)	PUNCT
ejpam-323	237	26	)	)	PUNCT
ejpam-323	238	1	∗ψ∗〉|	∗ψ∗〉|	NOUN
ejpam-323	239	1	≤	≤	PROPN
ejpam-323	239	2	c.ε2‖yε‖l2	c.ε2‖yε‖l2	PROPN
ejpam-323	239	3	.‖(pj(ε	.‖(pj(ε	PUNCT
ejpam-323	239	4	)	)	PUNCT
ejpam-323	239	5	−1pj(ε	−1pj(ε	ADJ
ejpam-323	239	6	)	)	PUNCT
ejpam-323	239	7	)	)	PUNCT
ejpam-323	240	1	∗ψ∗‖l2	∗ψ∗‖l2	PROPN
ejpam-323	240	2	,	,	PUNCT
ejpam-323	240	3	for	for	ADP
ejpam-323	240	4	0	0	NUM
ejpam-323	240	5	<	<	X
ejpam-323	240	6	ε	ε	PROPN
ejpam-323	240	7	<	<	X
ejpam-323	240	8	δ1	δ1	PROPN
ejpam-323	240	9	,	,	PUNCT
ejpam-323	240	10	where	where	SCONJ
ejpam-323	240	11	c	c	PROPN
ejpam-323	240	12	is	be	AUX
ejpam-323	240	13	a	a	DET
ejpam-323	240	14	positive	positive	ADJ
ejpam-323	240	15	constant	constant	NOUN
ejpam-323	240	16	.	.	PUNCT
ejpam-323	241	1	then	then	ADV
ejpam-323	241	2	,	,	PUNCT
ejpam-323	241	3	|〈(tε	|〈(tε	PUNCT
ejpam-323	241	4	−	−	PROPN
ejpam-323	241	5	t0)yε	t0)yε	PROPN
ejpam-323	241	6	,	,	PUNCT
ejpam-323	241	7	(	(	PUNCT
ejpam-323	241	8	pj(ε	pj(ε	ADJ
ejpam-323	241	9	)	)	PUNCT
ejpam-323	241	10	−1pj(ε	−1pj(ε	ADJ
ejpam-323	241	11	)	)	PUNCT
ejpam-323	241	12	)	)	PUNCT
ejpam-323	241	13	∗ψ∗〉|	∗ψ∗〉|	X
ejpam-323	241	14	≤	≤	PROPN
ejpam-323	241	15	c.ε2‖yε‖l2	c.ε2‖yε‖l2	PROPN
ejpam-323	241	16	.‖pj(ε	.‖pj(ε	NUM
ejpam-323	241	17	)	)	PUNCT
ejpam-323	242	1	−1‖.‖pj(ε)‖.‖ψ∗‖l2	−1‖.‖pj(ε)‖.‖ψ∗‖l2	NOUN
ejpam-323	242	2	.	.	PUNCT
ejpam-323	243	1	the	the	DET
ejpam-323	243	2	norm	norm	NOUN
ejpam-323	243	3	‖pj(ε)‖	‖pj(ε)‖	NUM
ejpam-323	243	4	is	be	AUX
ejpam-323	243	5	bounded	bound	VERB
ejpam-323	243	6	in	in	ADP
ejpam-323	243	7	ε	ε	PROPN
ejpam-323	243	8	since	since	SCONJ
ejpam-323	243	9	pj(ε)→	pj(ε)→	ADP
ejpam-323	243	10	p(0	p(0	PROPN
ejpam-323	243	11	)	)	PUNCT
ejpam-323	243	12	pointwise	pointwise	NOUN
ejpam-323	243	13	.	.	PUNCT
ejpam-323	244	1	in	in	ADP
ejpam-323	244	2	other	other	ADJ
ejpam-323	244	3	words	word	NOUN
ejpam-323	244	4	,	,	PUNCT
ejpam-323	244	5	for	for	ADP
ejpam-323	244	6	ε	ε	PROPN
ejpam-323	244	7	small	small	ADJ
ejpam-323	244	8	enough	enough	ADV
ejpam-323	244	9	and	and	CCONJ
ejpam-323	244	10	for	for	ADP
ejpam-323	244	11	f	f	PROPN
ejpam-323	244	12	∈	∈	PROPN
ejpam-323	244	13	r(p(0	r(p(0	PROPN
ejpam-323	244	14	)	)	PUNCT
ejpam-323	244	15	)	)	PUNCT
ejpam-323	244	16	with	with	ADP
ejpam-323	244	17	‖	‖	PROPN
ejpam-323	244	18	f	f	PROPN
ejpam-323	244	19	‖	‖	PROPN
ejpam-323	244	20	=	=	SYM
ejpam-323	244	21	1	1	NUM
ejpam-323	244	22	,	,	PUNCT
ejpam-323	244	23	we	we	PRON
ejpam-323	244	24	have	have	VERB
ejpam-323	244	25	1−‖pj(ε	1−‖pj(ε	NUM
ejpam-323	244	26	)	)	PUNCT
ejpam-323	245	1	f	f	PROPN
ejpam-323	245	2	‖=	‖=	PROPN
ejpam-323	245	3	‖p(0	‖p(0	PROPN
ejpam-323	245	4	)	)	PUNCT
ejpam-323	245	5	f	f	PROPN
ejpam-323	246	1	‖	‖	PROPN
ejpam-323	246	2	−	−	PROPN
ejpam-323	246	3	‖pj(ε	‖pj(ε	PROPN
ejpam-323	246	4	)	)	PUNCT
ejpam-323	246	5	f	f	PROPN
ejpam-323	246	6	‖	‖	PROPN
ejpam-323	246	7	≤	≤	PROPN
ejpam-323	246	8	‖(p(0)−	‖(p(0)−	NOUN
ejpam-323	246	9	pj(ε	pj(ε	NUM
ejpam-323	246	10	)	)	PUNCT
ejpam-323	246	11	)	)	PUNCT
ejpam-323	247	1	f	f	PROPN
ejpam-323	247	2	‖	‖	PROPN
ejpam-323	247	3	≤	≤	PROPN
ejpam-323	247	4	1	1	NUM
ejpam-323	247	5	2	2	NUM
ejpam-323	247	6	and	and	CCONJ
ejpam-323	247	7	hence	hence	ADV
ejpam-323	247	8	‖p(ε	‖p(ε	NOUN
ejpam-323	247	9	)	)	PUNCT
ejpam-323	247	10	f	f	PROPN
ejpam-323	247	11	‖	‖	PROPN
ejpam-323	247	12	≥	≥	NUM
ejpam-323	247	13	1	1	NUM
ejpam-323	247	14	2	2	NUM
ejpam-323	247	15	which	which	PRON
ejpam-323	247	16	implies	imply	VERB
ejpam-323	247	17	‖p(ε)−1‖	‖p(ε)−1‖	PROPN
ejpam-323	247	18	≤	≤	ADV
ejpam-323	247	19	2	2	NUM
ejpam-323	247	20	for	for	ADP
ejpam-323	247	21	ε	ε	PROPN
ejpam-323	247	22	small	small	ADJ
ejpam-323	247	23	enough	enough	ADV
ejpam-323	247	24	,	,	PUNCT
ejpam-323	247	25	say	say	VERB
ejpam-323	247	26	for	for	ADP
ejpam-323	247	27	0	0	NUM
ejpam-323	247	28	≤	≤	NUM
ejpam-323	247	29	ε	ε	PROPN
ejpam-323	247	30	≤	≤	X
ejpam-323	247	31	δ2	δ2	VERB
ejpam-323	247	32	where	where	SCONJ
ejpam-323	247	33	δ2	δ2	PROPN
ejpam-323	247	34	is	be	AUX
ejpam-323	247	35	a	a	DET
ejpam-323	247	36	positive	positive	ADJ
ejpam-323	247	37	constant	constant	NOUN
ejpam-323	247	38	.	.	PUNCT
ejpam-323	248	1	then	then	ADV
ejpam-323	248	2	the	the	DET
ejpam-323	248	3	relation	relation	NOUN
ejpam-323	248	4	(	(	PUNCT
ejpam-323	248	5	20	20	NUM
ejpam-323	248	6	)	)	PUNCT
ejpam-323	248	7	becomes	become	VERB
ejpam-323	248	8	,	,	PUNCT
ejpam-323	249	1	|λ0−λ	|λ0−λ	PROPN
ejpam-323	249	2	j(ε)|m	j(ε)|m	PROPN
ejpam-323	249	3	≤	≤	PROPN
ejpam-323	249	4	c′.ε2|λ0−	c′.ε2|λ0−	NOUN
ejpam-323	249	5	λ̂(ε)|	λ̂(ε)|	PROPN
ejpam-323	249	6	.	.	PROPN
ejpam-323	249	7	(	(	PUNCT
ejpam-323	249	8	21	21	NUM
ejpam-323	249	9	)	)	PUNCT
ejpam-323	249	10	the	the	DET
ejpam-323	249	11	proof	proof	NOUN
ejpam-323	249	12	is	be	AUX
ejpam-323	249	13	achieved	achieve	VERB
ejpam-323	249	14	if	if	SCONJ
ejpam-323	249	15	we	we	PRON
ejpam-323	249	16	use	use	VERB
ejpam-323	249	17	lemma	lemma	PROPN
ejpam-323	249	18	2	2	NUM
ejpam-323	249	19	and	and	CCONJ
ejpam-323	249	20	we	we	PRON
ejpam-323	249	21	take	take	VERB
ejpam-323	249	22	ε4	ε4	NOUN
ejpam-323	249	23	=	=	SYM
ejpam-323	249	24	inf(ε3,δ1,δ2	inf(ε3,δ1,δ2	PROPN
ejpam-323	249	25	)	)	PUNCT
ejpam-323	249	26	and	and	CCONJ
ejpam-323	249	27	k	k	X
ejpam-323	249	28	(	(	PUNCT
ejpam-323	249	29	1	1	X
ejpam-323	249	30	)	)	PUNCT
ejpam-323	249	31	j	j	NOUN
ejpam-323	249	32	=	=	SYM
ejpam-323	249	33	c′k1	c′k1	PROPN
ejpam-323	249	34	.	.	PUNCT
ejpam-323	250	1	the	the	DET
ejpam-323	250	2	main	main	ADJ
ejpam-323	250	3	estimate	estimate	NOUN
ejpam-323	250	4	will	will	AUX
ejpam-323	250	5	be	be	AUX
ejpam-323	250	6	given	give	VERB
ejpam-323	250	7	in	in	ADP
ejpam-323	250	8	the	the	DET
ejpam-323	250	9	following	following	NOUN
ejpam-323	250	10	theorem	theorem	NOUN
ejpam-323	250	11	which	which	PRON
ejpam-323	250	12	its	its	PRON
ejpam-323	250	13	proof	proof	NOUN
ejpam-323	250	14	follows	follow	VERB
ejpam-323	250	15	easily	easily	ADV
ejpam-323	250	16	by	by	ADP
ejpam-323	250	17	lemma	lemma	PROPN
ejpam-323	250	18	3	3	NUM
ejpam-323	250	19	.	.	PROPN
ejpam-323	250	20	references	reference	NOUN
ejpam-323	250	21	292	292	NUM
ejpam-323	250	22	theorem	theorem	NOUN
ejpam-323	250	23	4	4	NUM
ejpam-323	250	24	.	.	PUNCT
ejpam-323	251	1	let	let	VERB
ejpam-323	251	2	ω2	ω2	ADV
ejpam-323	251	3	0	0	PUNCT
ejpam-323	251	4	>	>	SYM
ejpam-323	251	5	0	0	NUM
ejpam-323	251	6	be	be	AUX
ejpam-323	251	7	the	the	DET
ejpam-323	251	8	eigenfrequency	eigenfrequency	NOUN
ejpam-323	251	9	of	of	ADP
ejpam-323	251	10	the	the	DET
ejpam-323	251	11	problem	problem	NOUN
ejpam-323	251	12	(	(	PUNCT
ejpam-323	251	13	2	2	NUM
ejpam-323	251	14	)	)	PUNCT
ejpam-323	251	15	with	with	ADP
ejpam-323	251	16	geometric	geometric	ADJ
ejpam-323	251	17	multiplicity	multiplicity	NOUN
ejpam-323	251	18	m	m	NOUN
ejpam-323	251	19	,	,	PUNCT
ejpam-323	251	20	and	and	CCONJ
ejpam-323	251	21	ω2	ω2	ADJ
ejpam-323	251	22	j	j	PROPN
ejpam-323	251	23	(	(	PUNCT
ejpam-323	251	24	ε	ε	PROPN
ejpam-323	251	25	)	)	PUNCT
ejpam-323	251	26	,	,	PUNCT
ejpam-323	251	27	for	for	ADP
ejpam-323	251	28	j	j	PROPN
ejpam-323	251	29	=	=	SYM
ejpam-323	251	30	1	1	NUM
ejpam-323	251	31	,	,	PUNCT
ejpam-323	251	32	·	·	PUNCT
ejpam-323	251	33	·	·	PUNCT
ejpam-323	251	34	·	·	PUNCT
ejpam-323	251	35	,	,	PUNCT
ejpam-323	251	36	m	m	AUX
ejpam-323	251	37	given	give	VERB
ejpam-323	251	38	by	by	ADP
ejpam-323	251	39	theorem	theorem	NOUN
ejpam-323	251	40	1	1	NUM
ejpam-323	251	41	.	.	PUNCT
ejpam-323	252	1	then	then	ADV
ejpam-323	252	2	,	,	PUNCT
ejpam-323	252	3	there	there	PRON
ejpam-323	252	4	exist	exist	VERB
ejpam-323	252	5	some	some	DET
ejpam-323	252	6	positive	positive	ADJ
ejpam-323	252	7	constants	constant	NOUN
ejpam-323	252	8	0	0	NUM
ejpam-323	252	9	<	<	X
ejpam-323	252	10	ε5	ε5	PROPN
ejpam-323	252	11	≤	≤	PROPN
ejpam-323	252	12	ε4	ε4	PROPN
ejpam-323	252	13	and	and	CCONJ
ejpam-323	252	14	k	k	PROPN
ejpam-323	252	15	(	(	PUNCT
ejpam-323	252	16	2	2	X
ejpam-323	252	17	)	)	PUNCT
ejpam-323	252	18	j	j	NOUN
ejpam-323	252	19	such	such	ADJ
ejpam-323	252	20	that	that	SCONJ
ejpam-323	252	21	|ω2	|ω2	PROPN
ejpam-323	252	22	0	0	NUM
ejpam-323	253	1	−ω2	−ω2	ADP
ejpam-323	253	2	j	j	PROPN
ejpam-323	253	3	(	(	PUNCT
ejpam-323	253	4	ε)|	ε)|	PROPN
ejpam-323	253	5	≤	≤	PROPN
ejpam-323	253	6	k	k	X
ejpam-323	253	7	(	(	PUNCT
ejpam-323	253	8	2	2	X
ejpam-323	253	9	)	)	PUNCT
ejpam-323	253	10	j	j	NOUN
ejpam-323	253	11	ε	ε	PROPN
ejpam-323	253	12	5	5	NUM
ejpam-323	253	13	2	2	NUM
ejpam-323	253	14	m	m	NOUN
ejpam-323	253	15	,	,	PUNCT
ejpam-323	253	16	for	for	ADP
ejpam-323	253	17	0	0	NUM
ejpam-323	253	18	<	<	X
ejpam-323	253	19	ε≤	ε≤	PROPN
ejpam-323	253	20	ε5	ε5	NOUN
ejpam-323	253	21	.	.	PUNCT
ejpam-323	253	22	proof	proof	NOUN
ejpam-323	253	23	.	.	PUNCT
ejpam-323	254	1	it	it	PRON
ejpam-323	254	2	is	be	AUX
ejpam-323	254	3	not	not	PART
ejpam-323	254	4	hard	hard	ADJ
ejpam-323	254	5	to	to	PART
ejpam-323	254	6	see	see	VERB
ejpam-323	254	7	that	that	PRON
ejpam-323	254	8	for	for	ADP
ejpam-323	254	9	all	all	PRON
ejpam-323	254	10	j	j	NOUN
ejpam-323	254	11	=	=	SYM
ejpam-323	254	12	1	1	NUM
ejpam-323	254	13	,	,	PUNCT
ejpam-323	254	14	·	·	PUNCT
ejpam-323	254	15	·	·	PUNCT
ejpam-323	254	16	·	·	PUNCT
ejpam-323	254	17	,	,	PUNCT
ejpam-323	254	18	m	m	PROPN
ejpam-323	254	19	,	,	PUNCT
ejpam-323	254	20	|λ0−λ	|λ0−λ	PROPN
ejpam-323	254	21	j(ε)|=	j(ε)|=	PROPN
ejpam-323	254	22	�	�	PROPN
ejpam-323	254	23	�	�	PROPN
ejpam-323	254	24	�	�	PROPN
ejpam-323	254	25	ω2	ω2	PROPN
ejpam-323	254	26	j	j	PROPN
ejpam-323	254	27	(	(	PUNCT
ejpam-323	254	28	ε)−ω2	ε)−ω2	PROPN
ejpam-323	254	29	0	0	NUM
ejpam-323	254	30	�	�	PROPN
ejpam-323	254	31	ω0ω	ω0ω	PROPN
ejpam-323	254	32	j(ε	j(ε	PROPN
ejpam-323	254	33	)	)	PUNCT
ejpam-323	254	34	�	�	PROPN
ejpam-323	254	35	2	2	NUM
ejpam-323	254	36	�	�	PROPN
ejpam-323	254	37	�	�	PROPN
ejpam-323	254	38	�	�	PROPN
ejpam-323	254	39	(	(	PUNCT
ejpam-323	254	40	22	22	NUM
ejpam-323	254	41	)	)	PUNCT
ejpam-323	254	42	but	but	CCONJ
ejpam-323	254	43	the	the	DET
ejpam-323	254	44	fact	fact	NOUN
ejpam-323	254	45	ω2	ω2	PROPN
ejpam-323	254	46	j	j	PROPN
ejpam-323	254	47	(	(	PUNCT
ejpam-323	254	48	ε)→	ε)→	NOUN
ejpam-323	254	49	ω2	ω2	ADJ
ejpam-323	254	50	0	0	PUNCT
ejpam-323	254	51	as	as	SCONJ
ejpam-323	254	52	ε	ε	PROPN
ejpam-323	254	53	tends	tend	VERB
ejpam-323	254	54	to	to	ADP
ejpam-323	254	55	0	0	NUM
ejpam-323	254	56	implies	imply	VERB
ejpam-323	254	57	that	that	SCONJ
ejpam-323	254	58	there	there	PRON
ejpam-323	254	59	exists	exist	VERB
ejpam-323	254	60	some	some	DET
ejpam-323	254	61	constant	constant	ADJ
ejpam-323	254	62	δ3	δ3	NOUN
ejpam-323	254	63	>	>	X
ejpam-323	254	64	0	0	NUM
ejpam-323	254	65	such	such	ADJ
ejpam-323	254	66	that	that	SCONJ
ejpam-323	254	67	|	|	NOUN
ejpam-323	254	68	�	�	PROPN
ejpam-323	254	69	ω	ω	PROPN
ejpam-323	254	70	j(ε)ω0	j(ε)ω0	PROPN
ejpam-323	254	71	�	�	PROPN
ejpam-323	254	72	2|	2|	PROPN
ejpam-323	254	73	<	<	X
ejpam-323	254	74	3	3	NUM
ejpam-323	254	75	2	2	NUM
ejpam-323	254	76	ω4	ω4	NUM
ejpam-323	254	77	0	0	NUM
ejpam-323	254	78	,	,	PUNCT
ejpam-323	254	79	for	for	ADP
ejpam-323	254	80	0	0	NUM
ejpam-323	254	81	<	<	X
ejpam-323	254	82	ε	ε	PROPN
ejpam-323	254	83	<	<	X
ejpam-323	254	84	δ3	δ3	PROPN
ejpam-323	254	85	.	.	PUNCT
ejpam-323	255	1	the	the	DET
ejpam-323	255	2	relation	relation	NOUN
ejpam-323	255	3	(	(	PUNCT
ejpam-323	255	4	22	22	NUM
ejpam-323	255	5	)	)	PUNCT
ejpam-323	255	6	implies	imply	VERB
ejpam-323	255	7	,	,	PUNCT
ejpam-323	255	8	|ω2	|ω2	PROPN
ejpam-323	255	9	j	j	PROPN
ejpam-323	255	10	(	(	PUNCT
ejpam-323	255	11	ε)−ω2	ε)−ω2	NOUN
ejpam-323	255	12	0|	0|	VERB
ejpam-323	255	13	≤	≤	NUM
ejpam-323	255	14	3	3	NUM
ejpam-323	255	15	2	2	NUM
ejpam-323	255	16	ω4	ω4	NUM
ejpam-323	255	17	0|λ0−λ	0|λ0−λ	PROPN
ejpam-323	255	18	j(ε)|	j(ε)|	NOUN
ejpam-323	255	19	,	,	PUNCT
ejpam-323	255	20	for	for	ADP
ejpam-323	255	21	0	0	NUM
ejpam-323	255	22	<	<	X
ejpam-323	255	23	ε	ε	PROPN
ejpam-323	255	24	<	<	X
ejpam-323	255	25	δ3	δ3	PROPN
ejpam-323	255	26	.	.	PUNCT
ejpam-323	256	1	the	the	DET
ejpam-323	256	2	theorem	theorem	NOUN
ejpam-323	256	3	follows	follow	VERB
ejpam-323	256	4	immediately	immediately	ADV
ejpam-323	256	5	by	by	ADP
ejpam-323	256	6	considering	consider	VERB
ejpam-323	256	7	lemma	lemma	PROPN
ejpam-323	256	8	3	3	NUM
ejpam-323	256	9	,	,	PUNCT
ejpam-323	256	10	we	we	PRON
ejpam-323	256	11	take	take	VERB
ejpam-323	256	12	ε5	ε5	NOUN
ejpam-323	256	13	=	=	SYM
ejpam-323	256	14	inf(δ3,ε4	inf(δ3,ε4	NOUN
ejpam-323	256	15	)	)	PUNCT
ejpam-323	256	16	and	and	CCONJ
ejpam-323	256	17	we	we	PRON
ejpam-323	256	18	choose	choose	VERB
ejpam-323	256	19	k	k	X
ejpam-323	256	20	(	(	PUNCT
ejpam-323	256	21	2	2	NUM
ejpam-323	256	22	)	)	PUNCT
ejpam-323	256	23	j	j	NOUN
ejpam-323	257	1	=	=	SYM
ejpam-323	257	2	3	3	NUM
ejpam-323	257	3	2	2	NUM
ejpam-323	257	4	ω4	ω4	NUM
ejpam-323	257	5	0(k	0(k	NUM
ejpam-323	257	6	(	(	PUNCT
ejpam-323	257	7	1	1	X
ejpam-323	257	8	)	)	PUNCT
ejpam-323	257	9	j	j	NOUN
ejpam-323	257	10	)	)	PUNCT
ejpam-323	257	11	1	1	NUM
ejpam-323	257	12	/	/	SYM
ejpam-323	257	13	m.	m.	NOUN
ejpam-323	257	14	references	reference	NOUN
ejpam-323	257	15	[	[	X
ejpam-323	257	16	1	1	NUM
ejpam-323	257	17	]	]	X
ejpam-323	257	18	r.	r.	PROPN
ejpam-323	257	19	adams	adams	PROPN
ejpam-323	257	20	,	,	PUNCT
ejpam-323	257	21	sobolev	sobolev	NOUN
ejpam-323	257	22	spaces	space	NOUN
ejpam-323	257	23	,	,	PUNCT
ejpam-323	257	24	academic	academic	ADJ
ejpam-323	257	25	press	press	NOUN
ejpam-323	257	26	,	,	PUNCT
ejpam-323	257	27	new	new	PROPN
ejpam-323	257	28	york	york	PROPN
ejpam-323	257	29	,	,	PUNCT
ejpam-323	257	30	1975	1975	NUM
ejpam-323	257	31	.	.	PUNCT
ejpam-323	258	1	[	[	X
ejpam-323	258	2	2	2	X
ejpam-323	258	3	]	]	X
ejpam-323	258	4	h.	h.	NOUN
ejpam-323	258	5	ammari	ammari	PROPN
ejpam-323	258	6	,	,	PUNCT
ejpam-323	258	7	and	and	CCONJ
ejpam-323	258	8	h.	h.	PROPN
ejpam-323	258	9	kang	kang	PROPN
ejpam-323	258	10	,	,	PUNCT
ejpam-323	258	11	reconstruction	reconstruction	NOUN
ejpam-323	258	12	of	of	ADP
ejpam-323	258	13	small	small	ADJ
ejpam-323	258	14	inhomogeneities	inhomogeneity	NOUN
ejpam-323	258	15	from	from	ADP
ejpam-323	258	16	boundary	boundary	ADJ
ejpam-323	258	17	measurements	measurement	NOUN
ejpam-323	258	18	,	,	PUNCT
ejpam-323	258	19	lecture	lecture	NOUN
ejpam-323	258	20	notes	note	NOUN
ejpam-323	258	21	in	in	ADP
ejpam-323	258	22	mathematics	mathematic	NOUN
ejpam-323	258	23	,	,	PUNCT
ejpam-323	258	24	vol.1846	vol.1846	NUM
ejpam-323	258	25	,	,	PUNCT
ejpam-323	258	26	springer	springer	NOUN
ejpam-323	258	27	-	-	PUNCT
ejpam-323	258	28	verlag	verlag	PROPN
ejpam-323	258	29	,	,	PUNCT
ejpam-323	258	30	berlin	berlin	PROPN
ejpam-323	258	31	(	(	PUNCT
ejpam-323	258	32	2004	2004	NUM
ejpam-323	258	33	)	)	PUNCT
ejpam-323	258	34	.	.	PUNCT
ejpam-323	259	1	[	[	X
ejpam-323	259	2	3	3	X
ejpam-323	259	3	]	]	X
ejpam-323	259	4	j.h	j.h	PROPN
ejpam-323	259	5	.	.	PROPN
ejpam-323	259	6	bramble	bramble	NOUN
ejpam-323	259	7	and	and	CCONJ
ejpam-323	259	8	j.e	j.e	PROPN
ejpam-323	259	9	.	.	PROPN
ejpam-323	259	10	osborn	osborn	PROPN
ejpam-323	259	11	,	,	PUNCT
ejpam-323	259	12	rate	rate	NOUN
ejpam-323	259	13	of	of	ADP
ejpam-323	259	14	convergence	convergence	NOUN
ejpam-323	259	15	estimates	estimate	NOUN
ejpam-323	259	16	for	for	ADP
ejpam-323	259	17	nonselfadjoint	nonselfadjoint	NOUN
ejpam-323	259	18	eigenvalue	eigenvalue	NOUN
ejpam-323	259	19	approximations	approximation	NOUN
ejpam-323	259	20	,	,	PUNCT
ejpam-323	259	21	math	math	NOUN
ejpam-323	259	22	.	.	PUNCT
ejpam-323	260	1	comp	comp	PROPN
ejpam-323	260	2	.	.	PUNCT
ejpam-323	261	1	vol	vol	NOUN
ejpam-323	261	2	.	.	PROPN
ejpam-323	262	1	27	27	NUM
ejpam-323	262	2	(	(	PUNCT
ejpam-323	262	3	1973	1973	NUM
ejpam-323	262	4	)	)	PUNCT
ejpam-323	262	5	,	,	PUNCT
ejpam-323	262	6	525	525	NUM
ejpam-323	262	7	-	-	SYM
ejpam-323	262	8	549	549	NUM
ejpam-323	262	9	.	.	PUNCT
ejpam-323	263	1	[	[	X
ejpam-323	263	2	4	4	X
ejpam-323	263	3	]	]	PUNCT
ejpam-323	263	4	o.	o.	PROPN
ejpam-323	264	1	p.	p.	PROPN
ejpam-323	264	2	bruno	bruno	PROPN
ejpam-323	264	3	and	and	CCONJ
ejpam-323	264	4	f.	f.	PROPN
ejpam-323	264	5	reitich	reitich	PROPN
ejpam-323	264	6	,	,	PUNCT
ejpam-323	264	7	boundary	boundary	ADJ
ejpam-323	264	8	-	-	PUNCT
ejpam-323	264	9	variation	variation	NOUN
ejpam-323	264	10	solution	solution	NOUN
ejpam-323	264	11	of	of	ADP
ejpam-323	264	12	eigenvalue	eigenvalue	NOUN
ejpam-323	264	13	problems	problem	NOUN
ejpam-323	264	14	for	for	ADP
ejpam-323	264	15	elliptic	elliptic	ADJ
ejpam-323	264	16	operators	operator	NOUN
ejpam-323	264	17	,	,	PUNCT
ejpam-323	264	18	j.	j.	PROPN
ejpam-323	264	19	fourier	fourier	PROPN
ejpam-323	264	20	anal	anal	PROPN
ejpam-323	264	21	.	.	PUNCT
ejpam-323	265	1	appl	appl	PROPN
ejpam-323	265	2	.	.	PROPN
ejpam-323	265	3	7	7	NUM
ejpam-323	265	4	(	(	PUNCT
ejpam-323	265	5	2001	2001	NUM
ejpam-323	265	6	)	)	PUNCT
ejpam-323	265	7	,	,	PUNCT
ejpam-323	265	8	169	169	NUM
ejpam-323	265	9	-	-	SYM
ejpam-323	265	10	187	187	NUM
ejpam-323	265	11	.	.	PUNCT
ejpam-323	266	1	[	[	X
ejpam-323	266	2	5	5	X
ejpam-323	266	3	]	]	X
ejpam-323	266	4	d.	d.	PROPN
ejpam-323	266	5	colton	colton	PROPN
ejpam-323	266	6	and	and	CCONJ
ejpam-323	266	7	r.	r.	PROPN
ejpam-323	266	8	kress	kress	PROPN
ejpam-323	266	9	,	,	PUNCT
ejpam-323	266	10	integral	integral	ADJ
ejpam-323	266	11	equation	equation	NOUN
ejpam-323	266	12	methods	method	NOUN
ejpam-323	266	13	in	in	ADP
ejpam-323	266	14	scattering	scatter	VERB
ejpam-323	266	15	theory	theory	NOUN
ejpam-323	266	16	,	,	PUNCT
ejpam-323	266	17	new	new	PROPN
ejpam-323	266	18	york	york	PROPN
ejpam-323	266	19	:	:	PUNCT
ejpam-323	266	20	john	john	PROPN
ejpam-323	266	21	wiley	wiley	PROPN
ejpam-323	266	22	(	(	PUNCT
ejpam-323	266	23	1983	1983	NUM
ejpam-323	266	24	)	)	PUNCT
ejpam-323	266	25	.	.	PUNCT
ejpam-323	267	1	[	[	X
ejpam-323	267	2	6	6	NUM
ejpam-323	267	3	]	]	X
ejpam-323	267	4	c.	c.	PROPN
ejpam-323	267	5	conca	conca	PROPN
ejpam-323	267	6	,	,	PUNCT
ejpam-323	267	7	m.	m.	NOUN
ejpam-323	267	8	duran	duran	PROPN
ejpam-323	267	9	and	and	CCONJ
ejpam-323	267	10	j.	j.	PROPN
ejpam-323	267	11	rappaz	rappaz	PROPN
ejpam-323	267	12	,	,	PUNCT
ejpam-323	267	13	rate	rate	NOUN
ejpam-323	267	14	of	of	ADP
ejpam-323	267	15	convergence	convergence	NOUN
ejpam-323	267	16	estimates	estimate	NOUN
ejpam-323	267	17	for	for	ADP
ejpam-323	267	18	the	the	DET
ejpam-323	267	19	spectral	spectral	ADJ
ejpam-323	267	20	approximation	approximation	NOUN
ejpam-323	267	21	of	of	ADP
ejpam-323	267	22	a	a	DET
ejpam-323	267	23	generalized	generalize	VERB
ejpam-323	267	24	eigenvalue	eigenvalue	NOUN
ejpam-323	267	25	problem	problem	NOUN
ejpam-323	267	26	,	,	PUNCT
ejpam-323	267	27	numer	numer	PROPN
ejpam-323	267	28	.	.	PUNCT
ejpam-323	267	29	math	math	NOUN
ejpam-323	267	30	.	.	PUNCT
ejpam-323	268	1	79	79	NUM
ejpam-323	268	2	,	,	PUNCT
ejpam-323	268	3	no3	no3	NOUN
ejpam-323	268	4	,	,	PUNCT
ejpam-323	268	5	(	(	PUNCT
ejpam-323	268	6	1998	1998	NUM
ejpam-323	268	7	)	)	PUNCT
ejpam-323	268	8	,	,	PUNCT
ejpam-323	268	9	349	349	NUM
ejpam-323	268	10	-	-	SYM
ejpam-323	268	11	369	369	NUM
ejpam-323	268	12	.	.	PUNCT
ejpam-323	269	1	[	[	X
ejpam-323	269	2	7	7	X
ejpam-323	269	3	]	]	PUNCT
ejpam-323	269	4	s.	s.	PROPN
ejpam-323	269	5	j.	j.	PROPN
ejpam-323	269	6	cox	cox	PROPN
ejpam-323	269	7	,	,	PUNCT
ejpam-323	269	8	the	the	DET
ejpam-323	269	9	generalized	generalize	VERB
ejpam-323	269	10	gradient	gradient	NOUN
ejpam-323	269	11	at	at	ADP
ejpam-323	269	12	a	a	DET
ejpam-323	269	13	multiple	multiple	ADJ
ejpam-323	269	14	eigenvalue	eigenvalue	NOUN
ejpam-323	269	15	,	,	PUNCT
ejpam-323	269	16	j.	j.	PROPN
ejpam-323	269	17	func	func	PROPN
ejpam-323	269	18	.	.	PUNCT
ejpam-323	270	1	anal	anal	ADJ
ejpam-323	270	2	,	,	PUNCT
ejpam-323	270	3	133	133	NUM
ejpam-323	270	4	,	,	PUNCT
ejpam-323	270	5	(	(	PUNCT
ejpam-323	270	6	1995	1995	NUM
ejpam-323	270	7	)	)	PUNCT
ejpam-323	270	8	,	,	PUNCT
ejpam-323	270	9	30	30	NUM
ejpam-323	270	10	-	-	SYM
ejpam-323	270	11	40	40	NUM
ejpam-323	270	12	.	.	PUNCT
ejpam-323	270	13	references	reference	NOUN
ejpam-323	270	14	293	293	NUM
ejpam-323	271	1	[	[	X
ejpam-323	271	2	8	8	NUM
ejpam-323	271	3	]	]	X
ejpam-323	271	4	r.	r.	PROPN
ejpam-323	271	5	r.	r.	PROPN
ejpam-323	271	6	gadyl’shin	gadyl’shin	PROPN
ejpam-323	271	7	and	and	CCONJ
ejpam-323	271	8	a.	a.	NOUN
ejpam-323	271	9	m.	m.	NOUN
ejpam-323	271	10	il’in	il’in	VERB
ejpam-323	271	11	,	,	PUNCT
ejpam-323	271	12	asymptotic	asymptotic	ADJ
ejpam-323	271	13	behavior	behavior	NOUN
ejpam-323	271	14	of	of	ADP
ejpam-323	271	15	the	the	DET
ejpam-323	271	16	eigenvalues	eigenvalue	NOUN
ejpam-323	271	17	of	of	ADP
ejpam-323	271	18	the	the	DET
ejpam-323	271	19	dirichlet	dirichlet	PROPN
ejpam-323	271	20	problem	problem	NOUN
ejpam-323	271	21	in	in	ADP
ejpam-323	271	22	a	a	DET
ejpam-323	271	23	domain	domain	NOUN
ejpam-323	271	24	with	with	ADP
ejpam-323	271	25	a	a	DET
ejpam-323	271	26	narrow	narrow	ADJ
ejpam-323	271	27	crack	crack	NOUN
ejpam-323	271	28	,	,	PUNCT
ejpam-323	271	29	sbornik	sbornik	ADJ
ejpam-323	271	30	math	math	NOUN
ejpam-323	271	31	.	.	PUNCT
ejpam-323	272	1	189	189	NUM
ejpam-323	272	2	(	(	PUNCT
ejpam-323	272	3	1998	1998	NUM
ejpam-323	272	4	)	)	PUNCT
ejpam-323	272	5	,	,	PUNCT
ejpam-323	272	6	503	503	NUM
ejpam-323	272	7	-	-	SYM
ejpam-323	272	8	526	526	NUM
ejpam-323	272	9	.	.	PUNCT
ejpam-323	273	1	[	[	X
ejpam-323	273	2	9	9	NUM
ejpam-323	273	3	]	]	PUNCT
ejpam-323	273	4	t.	t.	PROPN
ejpam-323	273	5	kato	kato	PROPN
ejpam-323	273	6	,	,	PUNCT
ejpam-323	273	7	perturbation	perturbation	NOUN
ejpam-323	273	8	theory	theory	NOUN
ejpam-323	273	9	for	for	ADP
ejpam-323	273	10	linear	linear	PROPN
ejpam-323	273	11	operators	operator	NOUN
ejpam-323	273	12	,	,	PUNCT
ejpam-323	273	13	2end	2end	PROPN
ejpam-323	273	14	edition	edition	NOUN
ejpam-323	273	15	,	,	PUNCT
ejpam-323	273	16	springer	springer	NOUN
ejpam-323	273	17	-	-	PUNCT
ejpam-323	273	18	verlag	verlag	PROPN
ejpam-323	273	19	,	,	PUNCT
ejpam-323	273	20	berlin	berlin	PROPN
ejpam-323	273	21	(	(	PUNCT
ejpam-323	273	22	1980	1980	NUM
ejpam-323	273	23	)	)	PUNCT
ejpam-323	273	24	.	.	PUNCT
ejpam-323	274	1	[	[	X
ejpam-323	274	2	10	10	NUM
ejpam-323	274	3	]	]	PUNCT
ejpam-323	274	4	a.	a.	NOUN
ejpam-323	274	5	khelifi	khelifi	PROPN
ejpam-323	274	6	,	,	PUNCT
ejpam-323	274	7	diffraction	diffraction	NOUN
ejpam-323	274	8	d’ondes	d’ondes	PROPN
ejpam-323	274	9	électromagnétiques	électromagnétique	VERB
ejpam-323	274	10	par	par	PROPN
ejpam-323	274	11	des	des	PROPN
ejpam-323	274	12	inhomogénéités	inhomogénéités	PROPN
ejpam-323	274	13	diélectriques	diélectrique	NOUN
ejpam-323	274	14	,	,	PUNCT
ejpam-323	274	15	phd	phd	NOUN
ejpam-323	274	16	.	.	PUNCT
ejpam-323	275	1	thesis	thesis	PROPN
ejpam-323	275	2	,	,	PUNCT
ejpam-323	275	3	applied	apply	VERB
ejpam-323	275	4	mathematics	mathematic	NOUN
ejpam-323	275	5	,	,	PUNCT
ejpam-323	275	6	ecole	ecole	X
ejpam-323	275	7	polytechnique	polytechnique	PROPN
ejpam-323	275	8	france	france	PROPN
ejpam-323	275	9	,	,	PUNCT
ejpam-323	275	10	february	february	PROPN
ejpam-323	275	11	(	(	PUNCT
ejpam-323	275	12	2002	2002	NUM
ejpam-323	275	13	)	)	PUNCT
ejpam-323	275	14	.	.	PUNCT
ejpam-323	276	1	[	[	X
ejpam-323	276	2	11	11	NUM
ejpam-323	276	3	]	]	PUNCT
ejpam-323	276	4	a.	a.	NOUN
ejpam-323	276	5	khelifi	khelifi	PROPN
ejpam-323	276	6	,	,	PUNCT
ejpam-323	276	7	the	the	DET
ejpam-323	276	8	integral	integral	ADJ
ejpam-323	276	9	equation	equation	NOUN
ejpam-323	276	10	methods	method	NOUN
ejpam-323	276	11	for	for	ADP
ejpam-323	276	12	the	the	DET
ejpam-323	276	13	perturbed	perturb	VERB
ejpam-323	276	14	helmholtz	helmholtz	NOUN
ejpam-323	276	15	eigenvalue	eigenvalue	NOUN
ejpam-323	276	16	problems	problem	NOUN
ejpam-323	276	17	,	,	PUNCT
ejpam-323	276	18	int	int	NOUN
ejpam-323	276	19	.	.	PUNCT
ejpam-323	277	1	j.	j.	PROPN
ejpam-323	277	2	math	math	PROPN
ejpam-323	277	3	.	.	PUNCT
ejpam-323	278	1	math	math	NOUN
ejpam-323	278	2	.	.	PUNCT
ejpam-323	279	1	sc	sc	PROPN
ejpam-323	279	2	.	.	PROPN
ejpam-323	279	3	80,(2005	80,(2005	NUM
ejpam-323	279	4	)	)	PUNCT
ejpam-323	279	5	,	,	PUNCT
ejpam-323	279	6	1201	1201	NUM
ejpam-323	279	7	-	-	SYM
ejpam-323	279	8	1220	1220	NUM
ejpam-323	279	9	.	.	PUNCT
ejpam-323	280	1	[	[	X
ejpam-323	280	2	12	12	NUM
ejpam-323	280	3	]	]	X
ejpam-323	280	4	p.d	p.d	PROPN
ejpam-323	280	5	.	.	PROPN
ejpam-323	280	6	lamberti	lamberti	PROPN
ejpam-323	280	7	,	,	PUNCT
ejpam-323	280	8	and	and	CCONJ
ejpam-323	280	9	m.	m.	NOUN
ejpam-323	280	10	lanza	lanza	PROPN
ejpam-323	280	11	de	de	PROPN
ejpam-323	280	12	cristoforis	cristoforis	PROPN
ejpam-323	280	13	,	,	PUNCT
ejpam-323	280	14	a	a	DET
ejpam-323	280	15	real	real	ADJ
ejpam-323	280	16	analyticity	analyticity	NOUN
ejpam-323	280	17	result	result	NOUN
ejpam-323	280	18	for	for	ADP
ejpam-323	280	19	symmetric	symmetric	ADJ
ejpam-323	280	20	functions	function	NOUN
ejpam-323	280	21	of	of	ADP
ejpam-323	280	22	the	the	DET
ejpam-323	280	23	eigenvalues	eigenvalue	NOUN
ejpam-323	280	24	of	of	ADP
ejpam-323	280	25	a	a	DET
ejpam-323	280	26	domain	domain	NOUN
ejpam-323	280	27	dependent	dependent	ADJ
ejpam-323	280	28	dirichlet	dirichlet	PROPN
ejpam-323	280	29	problem	problem	NOUN
ejpam-323	280	30	for	for	ADP
ejpam-323	280	31	the	the	DET
ejpam-323	280	32	laplace	laplace	NOUN
ejpam-323	280	33	operator	operator	NOUN
ejpam-323	280	34	.	.	PUNCT
ejpam-323	281	1	j.	j.	PROPN
ejpam-323	281	2	nonlin	nonlin	PROPN
ejpam-323	281	3	.	.	PUNCT
ejpam-323	282	1	con	con	PROPN
ejpam-323	282	2	.	.	PUNCT
ejpam-323	283	1	anal	anal	PROPN
ejpam-323	283	2	.	.	PUNCT
ejpam-323	284	1	vol	vol	NOUN
ejpam-323	284	2	5	5	NUM
ejpam-323	284	3	,	,	PUNCT
ejpam-323	284	4	no	no	DET
ejpam-323	284	5	1,(2004	1,(2004	PROPN
ejpam-323	284	6	)	)	PUNCT
ejpam-323	284	7	,	,	PUNCT
ejpam-323	284	8	19	19	NUM
ejpam-323	284	9	-	-	SYM
ejpam-323	284	10	42	42	NUM
ejpam-323	284	11	.	.	PUNCT
ejpam-323	285	1	[	[	X
ejpam-323	285	2	13	13	NUM
ejpam-323	285	3	]	]	X
ejpam-323	285	4	p.d	p.d	PROPN
ejpam-323	285	5	.	.	PROPN
ejpam-323	285	6	lamberti	lamberti	PROPN
ejpam-323	285	7	,	,	PUNCT
ejpam-323	285	8	and	and	CCONJ
ejpam-323	285	9	m.	m.	NOUN
ejpam-323	285	10	lanza	lanza	PROPN
ejpam-323	285	11	de	de	PROPN
ejpam-323	285	12	cristoforis	cristoforis	PROPN
ejpam-323	285	13	,	,	PUNCT
ejpam-323	285	14	an	an	DET
ejpam-323	285	15	analyticity	analyticity	NOUN
ejpam-323	285	16	result	result	NOUN
ejpam-323	285	17	for	for	ADP
ejpam-323	285	18	the	the	DET
ejpam-323	285	19	dependence	dependence	NOUN
ejpam-323	285	20	of	of	ADP
ejpam-323	285	21	multiple	multiple	ADJ
ejpam-323	285	22	eigenvalues	eigenvalue	NOUN
ejpam-323	285	23	and	and	CCONJ
ejpam-323	285	24	eigenspaces	eigenspace	NOUN
ejpam-323	285	25	of	of	ADP
ejpam-323	285	26	the	the	DET
ejpam-323	285	27	laplace	laplace	NOUN
ejpam-323	285	28	operator	operator	NOUN
ejpam-323	285	29	upon	upon	SCONJ
ejpam-323	285	30	perturbation	perturbation	NOUN
ejpam-323	285	31	of	of	ADP
ejpam-323	285	32	the	the	DET
ejpam-323	285	33	domain	domain	NOUN
ejpam-323	285	34	.	.	PUNCT
ejpam-323	286	1	glasgow	glasgow	PROPN
ejpam-323	286	2	math	math	PROPN
ejpam-323	286	3	j.	j.	PROPN
ejpam-323	287	1	no	no	DET
ejpam-323	287	2	1,(2002	1,(2002	NOUN
ejpam-323	287	3	)	)	PUNCT
ejpam-323	287	4	,	,	PUNCT
ejpam-323	287	5	29	29	NUM
ejpam-323	287	6	-	-	SYM
ejpam-323	287	7	43	43	NUM
ejpam-323	287	8	.	.	PUNCT
ejpam-323	288	1	[	[	X
ejpam-323	288	2	14	14	NUM
ejpam-323	288	3	]	]	X
ejpam-323	288	4	d.	d.	PROPN
ejpam-323	288	5	lupo	lupo	PROPN
ejpam-323	288	6	,	,	PUNCT
ejpam-323	288	7	and	and	CCONJ
ejpam-323	288	8	a.	a.	NOUN
ejpam-323	288	9	m.	m.	NOUN
ejpam-323	288	10	micheletti	micheletti	PROPN
ejpam-323	288	11	,	,	PUNCT
ejpam-323	288	12	on	on	ADP
ejpam-323	288	13	multiple	multiple	ADJ
ejpam-323	288	14	eigenvalues	eigenvalue	NOUN
ejpam-323	288	15	of	of	ADP
ejpam-323	288	16	selfadjoint	selfadjoint	NOUN
ejpam-323	288	17	compact	compact	ADJ
ejpam-323	288	18	operators	operator	NOUN
ejpam-323	288	19	,	,	PUNCT
ejpam-323	288	20	j.	j.	PROPN
ejpam-323	288	21	math	math	PROPN
ejpam-323	288	22	.	.	PUNCT
ejpam-323	289	1	anal	anal	PROPN
ejpam-323	289	2	.	.	PUNCT
ejpam-323	290	1	appl	appl	PROPN
ejpam-323	290	2	.	.	PUNCT
ejpam-323	291	1	172	172	NUM
ejpam-323	291	2	,	,	PUNCT
ejpam-323	291	3	(	(	PUNCT
ejpam-323	291	4	1993	1993	NUM
ejpam-323	291	5	)	)	PUNCT
ejpam-323	291	6	,	,	PUNCT
ejpam-323	291	7	106	106	NUM
ejpam-323	291	8	-	-	SYM
ejpam-323	291	9	116	116	NUM
ejpam-323	291	10	.	.	PUNCT
ejpam-323	292	1	[	[	X
ejpam-323	292	2	15	15	NUM
ejpam-323	292	3	]	]	X
ejpam-323	292	4	s.	s.	PROPN
ejpam-323	292	5	moskow	moskow	PROPN
ejpam-323	292	6	and	and	CCONJ
ejpam-323	292	7	m.	m.	NOUN
ejpam-323	292	8	vogelius	vogelius	NOUN
ejpam-323	292	9	,	,	PUNCT
ejpam-323	292	10	first	first	ADJ
ejpam-323	292	11	order	order	NOUN
ejpam-323	292	12	correction	correction	NOUN
ejpam-323	292	13	to	to	ADP
ejpam-323	292	14	the	the	DET
ejpam-323	292	15	homogenized	homogenized	ADJ
ejpam-323	292	16	eigenvalues	eigenvalue	NOUN
ejpam-323	292	17	of	of	ADP
ejpam-323	292	18	a	a	DET
ejpam-323	292	19	periodic	periodic	ADJ
ejpam-323	292	20	composite	composite	ADJ
ejpam-323	292	21	medium	medium	NOUN
ejpam-323	292	22	.	.	PUNCT
ejpam-323	293	1	the	the	DET
ejpam-323	293	2	case	case	NOUN
ejpam-323	293	3	of	of	ADP
ejpam-323	293	4	neumann	neumann	PROPN
ejpam-323	293	5	boundary	boundary	ADJ
ejpam-323	293	6	conditions	condition	NOUN
ejpam-323	293	7	,	,	PUNCT
ejpam-323	293	8	to	to	PART
ejpam-323	293	9	appear	appear	VERB
ejpam-323	293	10	in	in	ADP
ejpam-323	293	11	j.	j.	PROPN
ejpam-323	293	12	indiana	indiana	PROPN
ejpam-323	293	13	.	.	PUNCT
ejpam-323	294	1	univ	univ	PROPN
ejpam-323	294	2	.	.	PROPN
ejpam-323	294	3	,	,	PUNCT
ejpam-323	294	4	(	(	PUNCT
ejpam-323	294	5	2006	2006	NUM
ejpam-323	294	6	)	)	PUNCT
ejpam-323	294	7	.	.	PUNCT
ejpam-323	295	1	[	[	X
ejpam-323	295	2	16	16	NUM
ejpam-323	295	3	]	]	X
ejpam-323	295	4	j.	j.	PROPN
ejpam-323	295	5	c.	c.	PROPN
ejpam-323	295	6	nédélec	nédélec	PROPN
ejpam-323	295	7	,	,	PUNCT
ejpam-323	295	8	acoustic	acoustic	ADJ
ejpam-323	295	9	and	and	CCONJ
ejpam-323	295	10	electromagnetic	electromagnetic	ADJ
ejpam-323	295	11	equations	equation	NOUN
ejpam-323	295	12	.	.	PUNCT
ejpam-323	296	1	integral	integral	ADJ
ejpam-323	296	2	representation	representation	NOUN
ejpam-323	296	3	for	for	ADP
ejpam-323	296	4	harmonic	harmonic	ADJ
ejpam-323	296	5	problem	problem	NOUN
ejpam-323	296	6	,	,	PUNCT
ejpam-323	296	7	springer	springer	NOUN
ejpam-323	296	8	-	-	PUNCT
ejpam-323	296	9	verlag	verlag	PROPN
ejpam-323	296	10	,	,	PUNCT
ejpam-323	296	11	new	new	PROPN
ejpam-323	296	12	york	york	PROPN
ejpam-323	296	13	,	,	PUNCT
ejpam-323	296	14	2001	2001	NUM
ejpam-323	296	15	.	.	PUNCT
ejpam-323	297	1	[	[	X
ejpam-323	297	2	17	17	NUM
ejpam-323	297	3	]	]	PUNCT
ejpam-323	297	4	k.	k.	PROPN
ejpam-323	297	5	neymeyr	neymeyr	PROPN
ejpam-323	297	6	,	,	PUNCT
ejpam-323	297	7	a	a	DET
ejpam-323	297	8	posteriori	posteriori	NOUN
ejpam-323	297	9	error	error	NOUN
ejpam-323	297	10	estimation	estimation	NOUN
ejpam-323	297	11	for	for	ADP
ejpam-323	297	12	elliptic	elliptic	ADJ
ejpam-323	297	13	eigenproblems	eigenproblem	NOUN
ejpam-323	297	14	,	,	PUNCT
ejpam-323	297	15	num	num	PROPN
ejpam-323	297	16	.	.	PUNCT
ejpam-323	298	1	lin	lin	PROPN
ejpam-323	298	2	.	.	PUNCT
ejpam-323	299	1	alg	alg	PROPN
ejpam-323	299	2	.	.	PUNCT
ejpam-323	299	3	appl	appl	PROPN
ejpam-323	299	4	.	.	PROPN
ejpam-323	300	1	9	9	NUM
ejpam-323	300	2	(	(	PUNCT
ejpam-323	300	3	2002	2002	NUM
ejpam-323	300	4	)	)	PUNCT
ejpam-323	300	5	,	,	PUNCT
ejpam-323	300	6	263	263	NUM
ejpam-323	300	7	-	-	SYM
ejpam-323	300	8	279	279	NUM
ejpam-323	300	9	.	.	PUNCT
ejpam-323	301	1	[	[	X
ejpam-323	301	2	18	18	NUM
ejpam-323	301	3	]	]	X
ejpam-323	301	4	j.e	j.e	PROPN
ejpam-323	301	5	.	.	PROPN
ejpam-323	301	6	osborn	osborn	PROPN
ejpam-323	301	7	,	,	PUNCT
ejpam-323	301	8	spectral	spectral	ADJ
ejpam-323	301	9	approximations	approximation	NOUN
ejpam-323	301	10	for	for	ADP
ejpam-323	301	11	compact	compact	ADJ
ejpam-323	301	12	operators	operator	NOUN
ejpam-323	301	13	,	,	PUNCT
ejpam-323	301	14	math	math	NOUN
ejpam-323	301	15	.	.	PUNCT
ejpam-323	302	1	comp	comp	PROPN
ejpam-323	302	2	.	.	PUNCT
ejpam-323	302	3	,	,	PUNCT
ejpam-323	302	4	vol	vol	NOUN
ejpam-323	302	5	29	29	NUM
ejpam-323	302	6	(	(	PUNCT
ejpam-323	302	7	1975	1975	NUM
ejpam-323	302	8	)	)	PUNCT
ejpam-323	302	9	,	,	PUNCT
ejpam-323	302	10	712	712	NUM
ejpam-323	302	11	-	-	SYM
ejpam-323	302	12	725	725	NUM
ejpam-323	302	13	.	.	PUNCT
ejpam-323	303	1	[	[	X
ejpam-323	303	2	19	19	NUM
ejpam-323	303	3	]	]	X
ejpam-323	303	4	s.	s.	PROPN
ejpam-323	303	5	ozawa	ozawa	PROPN
ejpam-323	303	6	,	,	PUNCT
ejpam-323	303	7	eigenvalues	eigenvalue	VERB
ejpam-323	303	8	of	of	ADP
ejpam-323	303	9	the	the	DET
ejpam-323	303	10	laplacian	laplacian	NOUN
ejpam-323	303	11	under	under	ADP
ejpam-323	303	12	singular	singular	ADJ
ejpam-323	303	13	variation	variation	NOUN
ejpam-323	303	14	of	of	ADP
ejpam-323	303	15	domains	domain	NOUN
ejpam-323	303	16	-	-	PUNCT
ejpam-323	303	17	the	the	DET
ejpam-323	303	18	robin	robin	PROPN
ejpam-323	303	19	problem	problem	NOUN
ejpam-323	303	20	with	with	ADP
ejpam-323	303	21	obstacle	obstacle	NOUN
ejpam-323	303	22	of	of	ADP
ejpam-323	303	23	general	general	ADJ
ejpam-323	303	24	shape	shape	NOUN
ejpam-323	303	25	,	,	PUNCT
ejpam-323	303	26	proc.japan	proc.japan	NOUN
ejpam-323	303	27	acad	acad	NOUN
ejpam-323	303	28	.	.	PUNCT
ejpam-323	304	1	ser.a	ser.a	ADJ
ejpam-323	304	2	math.sci.72	math.sci.72	NOUN
ejpam-323	304	3	(	(	PUNCT
ejpam-323	304	4	1996	1996	NUM
ejpam-323	304	5	)	)	PUNCT
ejpam-323	304	6	,	,	PUNCT
ejpam-323	304	7	124134	124134	NUM
ejpam-323	304	8	.	.	PUNCT
ejpam-323	305	1	[	[	X
ejpam-323	305	2	20	20	NUM
ejpam-323	305	3	]	]	PUNCT
ejpam-323	305	4	s.	s.	PROPN
ejpam-323	305	5	ozawa	ozawa	PROPN
ejpam-323	305	6	,	,	PUNCT
ejpam-323	305	7	asymptotic	asymptotic	ADJ
ejpam-323	305	8	property	property	NOUN
ejpam-323	305	9	of	of	ADP
ejpam-323	305	10	eigenfunction	eigenfunction	NOUN
ejpam-323	305	11	of	of	ADP
ejpam-323	305	12	the	the	DET
ejpam-323	305	13	laplacian	laplacian	NOUN
ejpam-323	305	14	under	under	ADP
ejpam-323	305	15	singular	singular	ADJ
ejpam-323	305	16	variation	variation	NOUN
ejpam-323	305	17	of	of	ADP
ejpam-323	305	18	domains	domain	NOUN
ejpam-323	305	19	-	-	PUNCT
ejpam-323	305	20	the	the	DET
ejpam-323	305	21	neumann	neumann	PROPN
ejpam-323	305	22	condition	condition	NOUN
ejpam-323	305	23	,	,	PUNCT
ejpam-323	305	24	osaka	osaka	PROPN
ejpam-323	305	25	j.math.22(1985	j.math.22(1985	PROPN
ejpam-323	305	26	)	)	PUNCT
ejpam-323	305	27	,	,	PUNCT
ejpam-323	305	28	639	639	NUM
ejpam-323	305	29	-	-	SYM
ejpam-323	305	30	655	655	NUM
ejpam-323	305	31	.	.	PUNCT
ejpam-323	306	1	[	[	X
ejpam-323	306	2	21	21	NUM
ejpam-323	306	3	]	]	X
ejpam-323	306	4	s.	s.	PROPN
ejpam-323	306	5	ozawa	ozawa	PROPN
ejpam-323	306	6	,	,	PUNCT
ejpam-323	306	7	an	an	DET
ejpam-323	306	8	asymptotic	asymptotic	ADJ
ejpam-323	306	9	formula	formula	NOUN
ejpam-323	306	10	for	for	ADP
ejpam-323	306	11	the	the	DET
ejpam-323	306	12	eigenvalues	eigenvalue	NOUN
ejpam-323	306	13	of	of	ADP
ejpam-323	306	14	the	the	DET
ejpam-323	306	15	laplacian	laplacian	NOUN
ejpam-323	306	16	in	in	ADP
ejpam-323	306	17	a	a	DET
ejpam-323	306	18	threedimensional	threedimensional	ADJ
ejpam-323	306	19	domain	domain	NOUN
ejpam-323	306	20	with	with	ADP
ejpam-323	306	21	a	a	DET
ejpam-323	306	22	small	small	ADJ
ejpam-323	306	23	hole	hole	NOUN
ejpam-323	306	24	,	,	PUNCT
ejpam-323	306	25	j.	j.	PROPN
ejpam-323	306	26	fac	fac	PROPN
ejpam-323	306	27	.	.	PUNCT
ejpam-323	307	1	sci	sci	PROPN
ejpam-323	307	2	.	.	PROPN
ejpam-323	307	3	univ	univ	PROPN
ejpam-323	307	4	.	.	PUNCT
ejpam-323	308	1	tokyo	tokyo	PROPN
ejpam-323	308	2	sect	sect	NOUN
ejpam-323	308	3	.	.	PUNCT
ejpam-323	309	1	ia	ia	PROPN
ejpam-323	309	2	30	30	NUM
ejpam-323	309	3	(	(	PUNCT
ejpam-323	309	4	1983	1983	NUM
ejpam-323	309	5	)	)	PUNCT
ejpam-323	309	6	,	,	PUNCT
ejpam-323	309	7	243257	243257	NUM
ejpam-323	309	8	.	.	PUNCT
ejpam-323	310	1	references	reference	NOUN
ejpam-323	310	2	294	294	NUM
ejpam-323	311	1	[	[	X
ejpam-323	311	2	22	22	NUM
ejpam-323	311	3	]	]	PUNCT
ejpam-323	311	4	f.	f.	PROPN
ejpam-323	311	5	rellich	rellich	PROPN
ejpam-323	311	6	,	,	PUNCT
ejpam-323	311	7	perturbation	perturbation	NOUN
ejpam-323	311	8	theory	theory	NOUN
ejpam-323	311	9	of	of	ADP
ejpam-323	311	10	eigenvalue	eigenvalue	PROPN
ejpam-323	311	11	problems	problem	NOUN
ejpam-323	311	12	,	,	PUNCT
ejpam-323	311	13	gordon	gordon	PROPN
ejpam-323	311	14	and	and	CCONJ
ejpam-323	311	15	breach	breach	VERB
ejpam-323	311	16	science	science	NOUN
ejpam-323	311	17	publishers	publisher	NOUN
ejpam-323	311	18	,	,	PUNCT
ejpam-323	311	19	new	new	PROPN
ejpam-323	311	20	york	york	PROPN
ejpam-323	311	21	(	(	PUNCT
ejpam-323	311	22	1969	1969	NUM
ejpam-323	311	23	)	)	PUNCT
ejpam-323	311	24	.	.	PUNCT
ejpam-323	312	1	[	[	X
ejpam-323	312	2	23	23	NUM
ejpam-323	312	3	]	]	PUNCT
ejpam-323	312	4	m.	m.	PROPN
ejpam-323	312	5	e.	e.	PROPN
ejpam-323	312	6	taylor	taylor	PROPN
ejpam-323	312	7	,	,	PUNCT
ejpam-323	312	8	partial	partial	ADJ
ejpam-323	312	9	differential	differential	PROPN
ejpam-323	312	10	equations	equation	NOUN
ejpam-323	312	11	ii	ii	PROPN
ejpam-323	312	12	,	,	PUNCT
ejpam-323	312	13	qualitative	qualitative	ADJ
ejpam-323	312	14	studies	study	NOUN
ejpam-323	312	15	of	of	ADP
ejpam-323	312	16	linear	linear	PROPN
ejpam-323	312	17	equations	equation	NOUN
ejpam-323	312	18	,	,	PUNCT
ejpam-323	312	19	applied	apply	VERB
ejpam-323	312	20	mathematical	mathematical	ADJ
ejpam-323	312	21	sciences	science	NOUN
ejpam-323	312	22	116	116	NUM
ejpam-323	312	23	,	,	PUNCT
ejpam-323	312	24	springerverlag	springerverlag	NOUN
ejpam-323	312	25	,	,	PUNCT
ejpam-323	312	26	(	(	PUNCT
ejpam-323	312	27	1996	1996	NUM
ejpam-323	312	28	)	)	PUNCT
ejpam-323	312	29	.	.	PUNCT