id	sid	tid	token	lemma	pos
ap-1801	1	1	acta	acta	PROPN
ap-1801	1	2	polytechnica	polytechnica	PROPN
ap-1801	1	3	acta	acta	PROPN
ap-1801	1	4	polytechnica	polytechnica	PROPN
ap-1801	1	5	53(3):271–279	53(3):271–279	PROPN
ap-1801	1	6	,	,	PUNCT
ap-1801	1	7	2013	2013	NUM
ap-1801	1	8	©	©	PROPN
ap-1801	1	9	czech	czech	PROPN
ap-1801	1	10	technical	technical	PROPN
ap-1801	1	11	university	university	PROPN
ap-1801	1	12	in	in	ADP
ap-1801	1	13	prague	prague	PROPN
ap-1801	1	14	,	,	PUNCT
ap-1801	1	15	2013	2013	NUM
ap-1801	1	16	available	available	ADJ
ap-1801	1	17	online	online	ADV
ap-1801	1	18	at	at	ADP
ap-1801	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1801	1	20	spectral	spectral	ADJ
ap-1801	1	21	analysis	analysis	NOUN
ap-1801	1	22	of	of	ADP
ap-1801	1	23	schrödinger	schrödinger	ADJ
ap-1801	1	24	operators	operator	NOUN
ap-1801	1	25	with	with	ADP
ap-1801	1	26	unusual	unusual	ADJ
ap-1801	1	27	semiclassical	semiclassical	ADJ
ap-1801	1	28	behavior	behavior	NOUN
ap-1801	1	29	pavel	pavel	PROPN
ap-1801	1	30	exnera	exnera	PROPN
ap-1801	1	31	,	,	PUNCT
ap-1801	1	32	b	b	PROPN
ap-1801	1	33	,	,	PUNCT
ap-1801	1	34	diana	diana	PROPN
ap-1801	1	35	barseghyana	barseghyana	PROPN
ap-1801	1	36	,	,	PUNCT
ap-1801	1	37	b,∗	b,∗	VERB
ap-1801	1	38	a	a	DET
ap-1801	1	39	doppler	doppler	NOUN
ap-1801	1	40	institute	institute	NOUN
ap-1801	1	41	for	for	ADP
ap-1801	1	42	mathematical	mathematical	ADJ
ap-1801	1	43	physics	physics	NOUN
ap-1801	1	44	and	and	CCONJ
ap-1801	1	45	applied	apply	VERB
ap-1801	1	46	mathematics	mathematic	NOUN
ap-1801	1	47	,	,	PUNCT
ap-1801	1	48	břehová	břehová	VERB
ap-1801	1	49	7	7	NUM
ap-1801	1	50	,	,	PUNCT
ap-1801	1	51	11519	11519	NUM
ap-1801	1	52	prague	prague	PROPN
ap-1801	1	53	b	b	PROPN
ap-1801	1	54	nuclear	nuclear	PROPN
ap-1801	1	55	physics	physics	PROPN
ap-1801	1	56	institute	institute	PROPN
ap-1801	1	57	ascr	ascr	NOUN
ap-1801	1	58	,	,	PUNCT
ap-1801	1	59	25068	25068	NUM
ap-1801	1	60	řež	řež	NOUN
ap-1801	1	61	near	near	ADP
ap-1801	1	62	prague	prague	PROPN
ap-1801	1	63	,	,	PUNCT
ap-1801	1	64	czechia	czechia	VERB
ap-1801	1	65	∗	∗	NOUN
ap-1801	1	66	corresponding	corresponding	ADJ
ap-1801	1	67	author	author	NOUN
ap-1801	1	68	:	:	PUNCT
ap-1801	1	69	dianabar@ujf.cas.cz	dianabar@ujf.cas.cz	NOUN
ap-1801	1	70	abstract	abstract	NOUN
ap-1801	1	71	.	.	PUNCT
ap-1801	2	1	in	in	ADP
ap-1801	2	2	this	this	DET
ap-1801	2	3	paper	paper	NOUN
ap-1801	2	4	we	we	PRON
ap-1801	2	5	discuss	discuss	VERB
ap-1801	2	6	several	several	ADJ
ap-1801	2	7	examples	example	NOUN
ap-1801	2	8	of	of	ADP
ap-1801	2	9	schrödinger	schrödinger	ADJ
ap-1801	2	10	operators	operator	NOUN
ap-1801	2	11	describing	describe	VERB
ap-1801	2	12	a	a	DET
ap-1801	2	13	particle	particle	NOUN
ap-1801	2	14	confined	confine	VERB
ap-1801	2	15	to	to	ADP
ap-1801	2	16	a	a	DET
ap-1801	2	17	region	region	NOUN
ap-1801	2	18	with	with	ADP
ap-1801	2	19	thin	thin	ADJ
ap-1801	2	20	cusp	cusp	NOUN
ap-1801	2	21	-	-	PUNCT
ap-1801	2	22	shaped	shape	VERB
ap-1801	2	23	‘	'	PUNCT
ap-1801	2	24	channels	channel	NOUN
ap-1801	2	25	’	'	PUNCT
ap-1801	2	26	,	,	PUNCT
ap-1801	2	27	given	give	VERB
ap-1801	2	28	either	either	ADV
ap-1801	2	29	by	by	ADP
ap-1801	2	30	a	a	DET
ap-1801	2	31	potential	potential	NOUN
ap-1801	2	32	or	or	CCONJ
ap-1801	2	33	by	by	ADP
ap-1801	2	34	a	a	DET
ap-1801	2	35	dirichlet	dirichlet	PROPN
ap-1801	2	36	boundary	boundary	NOUN
ap-1801	2	37	;	;	PUNCT
ap-1801	2	38	we	we	PRON
ap-1801	2	39	focus	focus	VERB
ap-1801	2	40	on	on	ADP
ap-1801	2	41	cases	case	NOUN
ap-1801	2	42	when	when	SCONJ
ap-1801	2	43	the	the	DET
ap-1801	2	44	allowed	allow	VERB
ap-1801	2	45	phase	phase	NOUN
ap-1801	2	46	space	space	NOUN
ap-1801	2	47	is	be	AUX
ap-1801	2	48	infinite	infinite	ADJ
ap-1801	2	49	but	but	CCONJ
ap-1801	2	50	the	the	DET
ap-1801	2	51	operator	operator	NOUN
ap-1801	2	52	still	still	ADV
ap-1801	2	53	has	have	VERB
ap-1801	2	54	a	a	DET
ap-1801	2	55	discrete	discrete	ADJ
ap-1801	2	56	spectrum	spectrum	NOUN
ap-1801	2	57	.	.	PUNCT
ap-1801	3	1	first	first	ADV
ap-1801	3	2	we	we	PRON
ap-1801	3	3	analyze	analyze	VERB
ap-1801	3	4	two	two	NUM
ap-1801	3	5	-	-	PUNCT
ap-1801	3	6	dimensional	dimensional	ADJ
ap-1801	3	7	operators	operator	NOUN
ap-1801	3	8	with	with	ADP
ap-1801	3	9	the	the	DET
ap-1801	3	10	potential	potential	ADJ
ap-1801	3	11	|xy|p	|xy|p	ADP
ap-1801	3	12	−	−	NOUN
ap-1801	3	13	λ(x2	λ(x2	NOUN
ap-1801	3	14	+	+	CCONJ
ap-1801	3	15	y2)p/(p+2	y2)p/(p+2	NUM
ap-1801	3	16	)	)	PUNCT
ap-1801	4	1	where	where	SCONJ
ap-1801	4	2	p	p	PROPN
ap-1801	4	3	≥	≥	PUNCT
ap-1801	4	4	1	1	NUM
ap-1801	4	5	and	and	CCONJ
ap-1801	4	6	λ	λ	X
ap-1801	4	7	≥	≥	NOUN
ap-1801	4	8	0	0	NUM
ap-1801	4	9	.	.	PUNCT
ap-1801	4	10	we	we	PRON
ap-1801	4	11	show	show	VERB
ap-1801	4	12	that	that	SCONJ
ap-1801	4	13	there	there	PRON
ap-1801	4	14	is	be	VERB
ap-1801	4	15	a	a	DET
ap-1801	4	16	critical	critical	ADJ
ap-1801	4	17	value	value	NOUN
ap-1801	4	18	of	of	ADP
ap-1801	4	19	λ	λ	PROPN
ap-1801	4	20	such	such	ADJ
ap-1801	4	21	that	that	SCONJ
ap-1801	4	22	the	the	DET
ap-1801	4	23	spectrum	spectrum	NOUN
ap-1801	4	24	for	for	ADP
ap-1801	4	25	λ	λ	PROPN
ap-1801	4	26	<	<	X
ap-1801	4	27	λcrit	λcrit	NOUN
ap-1801	4	28	is	be	AUX
ap-1801	4	29	below	below	ADP
ap-1801	4	30	bounded	bounded	ADJ
ap-1801	4	31	and	and	CCONJ
ap-1801	4	32	purely	purely	ADV
ap-1801	4	33	discrete	discrete	ADJ
ap-1801	4	34	,	,	PUNCT
ap-1801	4	35	while	while	SCONJ
ap-1801	4	36	for	for	ADP
ap-1801	4	37	λ	λ	PROPN
ap-1801	4	38	>	>	X
ap-1801	4	39	λcrit	λcrit	NOUN
ap-1801	4	40	it	it	PRON
ap-1801	4	41	is	be	AUX
ap-1801	4	42	unbounded	unbounded	ADJ
ap-1801	4	43	from	from	ADP
ap-1801	4	44	below	below	ADV
ap-1801	4	45	.	.	PUNCT
ap-1801	5	1	in	in	ADP
ap-1801	5	2	the	the	DET
ap-1801	5	3	subcritical	subcritical	ADJ
ap-1801	5	4	case	case	NOUN
ap-1801	5	5	we	we	PRON
ap-1801	5	6	prove	prove	VERB
ap-1801	5	7	upper	upper	ADJ
ap-1801	5	8	and	and	CCONJ
ap-1801	5	9	lower	low	ADJ
ap-1801	5	10	bounds	bound	NOUN
ap-1801	5	11	for	for	ADP
ap-1801	5	12	the	the	DET
ap-1801	5	13	eigenvalue	eigenvalue	NOUN
ap-1801	5	14	sums	sum	NOUN
ap-1801	5	15	.	.	PUNCT
ap-1801	6	1	the	the	DET
ap-1801	6	2	second	second	ADJ
ap-1801	6	3	part	part	NOUN
ap-1801	6	4	of	of	ADP
ap-1801	6	5	work	work	NOUN
ap-1801	6	6	is	be	AUX
ap-1801	6	7	devoted	devote	VERB
ap-1801	6	8	to	to	ADP
ap-1801	6	9	estimates	estimate	NOUN
ap-1801	6	10	of	of	ADP
ap-1801	6	11	eigenvalue	eigenvalue	NOUN
ap-1801	6	12	moments	moment	NOUN
ap-1801	6	13	for	for	ADP
ap-1801	6	14	dirichlet	dirichlet	PROPN
ap-1801	6	15	laplacians	laplacian	NOUN
ap-1801	6	16	and	and	CCONJ
ap-1801	6	17	schrödinger	schrödinger	ADJ
ap-1801	6	18	operators	operator	NOUN
ap-1801	6	19	in	in	ADP
ap-1801	6	20	regions	region	NOUN
ap-1801	6	21	having	have	VERB
ap-1801	6	22	infinite	infinite	ADJ
ap-1801	6	23	cusps	cusps	NOUN
ap-1801	6	24	which	which	PRON
ap-1801	6	25	are	be	AUX
ap-1801	6	26	geometrically	geometrically	ADV
ap-1801	6	27	nontrivial	nontrivial	ADJ
ap-1801	6	28	being	be	AUX
ap-1801	6	29	either	either	CCONJ
ap-1801	6	30	curved	curved	ADJ
ap-1801	6	31	or	or	CCONJ
ap-1801	6	32	twisted	twisted	ADJ
ap-1801	6	33	;	;	PUNCT
ap-1801	6	34	we	we	PRON
ap-1801	6	35	are	be	AUX
ap-1801	6	36	going	go	VERB
ap-1801	6	37	to	to	PART
ap-1801	6	38	show	show	VERB
ap-1801	6	39	how	how	SCONJ
ap-1801	6	40	these	these	DET
ap-1801	6	41	geometric	geometric	ADJ
ap-1801	6	42	properties	property	NOUN
ap-1801	6	43	enter	enter	VERB
ap-1801	6	44	the	the	DET
ap-1801	6	45	eigenvalue	eigenvalue	PROPN
ap-1801	6	46	bounds	bound	NOUN
ap-1801	6	47	.	.	PUNCT
ap-1801	7	1	keywords	keyword	NOUN
ap-1801	7	2	:	:	PUNCT
ap-1801	7	3	schrödinger	schrödinger	ADJ
ap-1801	7	4	operator	operator	NOUN
ap-1801	7	5	,	,	PUNCT
ap-1801	7	6	discrete	discrete	ADJ
ap-1801	7	7	spectrum	spectrum	NOUN
ap-1801	7	8	,	,	PUNCT
ap-1801	7	9	lieb	lieb	PROPN
ap-1801	7	10	-	-	PUNCT
ap-1801	7	11	thirring	thirre	VERB
ap-1801	7	12	inequality	inequality	NOUN
ap-1801	7	13	,	,	PUNCT
ap-1801	7	14	cusp	cusp	NOUN
ap-1801	7	15	-	-	PUNCT
ap-1801	7	16	shaped	shape	VERB
ap-1801	7	17	regions	region	NOUN
ap-1801	7	18	,	,	PUNCT
ap-1801	7	19	geometrically	geometrically	ADV
ap-1801	7	20	induced	induce	VERB
ap-1801	7	21	spectrum	spectrum	NOUN
ap-1801	7	22	.	.	PUNCT
ap-1801	8	1	1	1	X
ap-1801	8	2	.	.	X
ap-1801	8	3	introduction	introduction	NOUN
ap-1801	8	4	the	the	DET
ap-1801	8	5	semiclassical	semiclassical	ADJ
ap-1801	8	6	method	method	NOUN
ap-1801	8	7	for	for	ADP
ap-1801	8	8	analyzing	analyze	VERB
ap-1801	8	9	the	the	DET
ap-1801	8	10	operator	operator	NOUN
ap-1801	8	11	has	have	AUX
ap-1801	8	12	proved	prove	VERB
ap-1801	8	13	itself	itself	PRON
ap-1801	8	14	a	a	DET
ap-1801	8	15	tremendously	tremendously	ADV
ap-1801	8	16	useful	useful	ADJ
ap-1801	8	17	tool	tool	NOUN
ap-1801	8	18	over	over	ADP
ap-1801	8	19	the	the	DET
ap-1801	8	20	century	century	NOUN
ap-1801	8	21	since	since	SCONJ
ap-1801	8	22	it	it	PRON
ap-1801	8	23	was	be	AUX
ap-1801	8	24	proposed	propose	VERB
ap-1801	8	25	by	by	ADP
ap-1801	8	26	hermann	hermann	PROPN
ap-1801	8	27	weyl	weyl	PROPN
ap-1801	8	28	.	.	PUNCT
ap-1801	9	1	nevertheless	nevertheless	ADV
ap-1801	9	2	,	,	PUNCT
ap-1801	9	3	there	there	PRON
ap-1801	9	4	are	be	VERB
ap-1801	9	5	cases	case	NOUN
ap-1801	9	6	when	when	SCONJ
ap-1801	9	7	estimates	estimate	NOUN
ap-1801	9	8	based	base	VERB
ap-1801	9	9	on	on	ADP
ap-1801	9	10	phase	phase	NOUN
ap-1801	9	11	-	-	PUNCT
ap-1801	9	12	space	space	NOUN
ap-1801	9	13	volume	volume	NOUN
ap-1801	9	14	fail	fail	ADJ
ap-1801	9	15	;	;	PUNCT
ap-1801	9	16	the	the	DET
ap-1801	9	17	classical	classical	ADJ
ap-1801	9	18	example	example	NOUN
ap-1801	9	19	is	be	AUX
ap-1801	9	20	due	due	ADJ
ap-1801	9	21	to	to	ADP
ap-1801	9	22	b.	b.	PROPN
ap-1801	9	23	simon	simon	PROPN
ap-1801	10	1	[	[	X
ap-1801	10	2	1	1	X
ap-1801	10	3	]	]	PUNCT
ap-1801	10	4	and	and	CCONJ
ap-1801	10	5	describes	describe	VERB
ap-1801	10	6	a	a	DET
ap-1801	10	7	two	two	NUM
ap-1801	10	8	-	-	PUNCT
ap-1801	10	9	dimensional	dimensional	ADJ
ap-1801	10	10	schrödinger	schrödinger	ADJ
ap-1801	10	11	operator	operator	NOUN
ap-1801	10	12	with	with	ADP
ap-1801	10	13	the	the	DET
ap-1801	10	14	potential	potential	NOUN
ap-1801	10	15	|xy|p	|xy|p	ADP
ap-1801	10	16	having	have	VERB
ap-1801	10	17	deep	deep	ADJ
ap-1801	10	18	‘	'	PUNCT
ap-1801	10	19	channels	channel	NOUN
ap-1801	10	20	’	'	PUNCT
ap-1801	10	21	the	the	DET
ap-1801	10	22	width	width	NOUN
ap-1801	10	23	of	of	ADP
ap-1801	10	24	which	which	PRON
ap-1801	10	25	is	be	AUX
ap-1801	10	26	shrinking	shrink	VERB
ap-1801	10	27	with	with	ADP
ap-1801	10	28	the	the	DET
ap-1801	10	29	distance	distance	NOUN
ap-1801	10	30	from	from	ADP
ap-1801	10	31	the	the	DET
ap-1801	10	32	origin	origin	NOUN
ap-1801	10	33	.	.	PUNCT
ap-1801	11	1	the	the	DET
ap-1801	11	2	present	present	ADJ
ap-1801	11	3	paper	paper	NOUN
ap-1801	11	4	is	be	AUX
ap-1801	11	5	devoted	devote	VERB
ap-1801	11	6	to	to	ADP
ap-1801	11	7	a	a	DET
ap-1801	11	8	discussion	discussion	NOUN
ap-1801	11	9	of	of	ADP
ap-1801	11	10	several	several	ADJ
ap-1801	11	11	models	model	NOUN
ap-1801	11	12	of	of	ADP
ap-1801	11	13	this	this	DET
ap-1801	11	14	type	type	NOUN
ap-1801	11	15	.	.	PUNCT
ap-1801	12	1	it	it	PRON
ap-1801	12	2	summarizes	summarize	VERB
ap-1801	12	3	the	the	DET
ap-1801	12	4	presentation	presentation	NOUN
ap-1801	12	5	of	of	ADP
ap-1801	12	6	the	the	DET
ap-1801	12	7	second	second	ADJ
ap-1801	12	8	named	name	VERB
ap-1801	12	9	author	author	NOUN
ap-1801	12	10	at	at	ADP
ap-1801	12	11	the	the	DET
ap-1801	12	12	conference	conference	NOUN
ap-1801	12	13	analytic	analytic	ADJ
ap-1801	12	14	and	and	CCONJ
ap-1801	12	15	algebraic	algebraic	ADJ
ap-1801	12	16	methods	method	NOUN
ap-1801	12	17	in	in	ADP
ap-1801	12	18	physics	physics	NOUN
ap-1801	12	19	x	x	PROPN
ap-1801	12	20	(	(	PUNCT
ap-1801	12	21	prague	prague	NOUN
ap-1801	12	22	,	,	PUNCT
ap-1801	12	23	2012	2012	NUM
ap-1801	12	24	)	)	PUNCT
ap-1801	12	25	based	base	VERB
ap-1801	12	26	on	on	ADP
ap-1801	12	27	the	the	DET
ap-1801	12	28	original	original	ADJ
ap-1801	12	29	papers	paper	NOUN
ap-1801	12	30	[	[	X
ap-1801	12	31	3	3	NUM
ap-1801	12	32	,	,	PUNCT
ap-1801	12	33	4	4	NUM
ap-1801	12	34	]	]	PUNCT
ap-1801	12	35	to	to	PART
ap-1801	12	36	which	which	PRON
ap-1801	12	37	we	we	PRON
ap-1801	12	38	refer	refer	VERB
ap-1801	12	39	for	for	ADP
ap-1801	12	40	details	detail	NOUN
ap-1801	12	41	of	of	ADP
ap-1801	12	42	the	the	DET
ap-1801	12	43	proofs	proof	NOUN
ap-1801	12	44	which	which	PRON
ap-1801	12	45	are	be	AUX
ap-1801	12	46	sketched	sketch	VERB
ap-1801	12	47	here	here	ADV
ap-1801	12	48	.	.	PUNCT
ap-1801	13	1	our	our	PRON
ap-1801	13	2	first	first	ADJ
ap-1801	13	3	aim	aim	NOUN
ap-1801	13	4	is	be	AUX
ap-1801	13	5	to	to	PART
ap-1801	13	6	show	show	VERB
ap-1801	13	7	that	that	SCONJ
ap-1801	13	8	the	the	DET
ap-1801	13	9	effects	effect	NOUN
ap-1801	13	10	known	know	VERB
ap-1801	13	11	from	from	ADP
ap-1801	13	12	the	the	DET
ap-1801	13	13	paper	paper	NOUN
ap-1801	13	14	[	[	X
ap-1801	13	15	1	1	X
ap-1801	13	16	]	]	PUNCT
ap-1801	13	17	can	can	AUX
ap-1801	13	18	occur	occur	VERB
ap-1801	13	19	even	even	ADV
ap-1801	13	20	if	if	SCONJ
ap-1801	13	21	the	the	DET
ap-1801	13	22	potential	potential	NOUN
ap-1801	13	23	is	be	AUX
ap-1801	13	24	unbounded	unbounded	ADJ
ap-1801	13	25	from	from	ADP
ap-1801	13	26	below	below	ADV
ap-1801	13	27	;	;	PUNCT
ap-1801	13	28	at	at	ADP
ap-1801	13	29	the	the	DET
ap-1801	13	30	same	same	ADJ
ap-1801	13	31	time	time	NOUN
ap-1801	13	32	the	the	DET
ap-1801	13	33	model	model	NOUN
ap-1801	13	34	will	will	AUX
ap-1801	13	35	exhibit	exhibit	VERB
ap-1801	13	36	a	a	DET
ap-1801	13	37	parameter	parameter	NOUN
ap-1801	13	38	transition	transition	NOUN
ap-1801	13	39	between	between	ADP
ap-1801	13	40	different	different	ADJ
ap-1801	13	41	spectral	spectral	ADJ
ap-1801	13	42	regimes	regime	NOUN
ap-1801	13	43	.	.	PUNCT
ap-1801	14	1	one	one	PRON
ap-1801	14	2	has	have	VERB
ap-1801	14	3	to	to	PART
ap-1801	14	4	add	add	VERB
ap-1801	14	5	that	that	SCONJ
ap-1801	14	6	the	the	DET
ap-1801	14	7	first	first	ADJ
ap-1801	14	8	person	person	NOUN
ap-1801	14	9	to	to	PART
ap-1801	14	10	draw	draw	VERB
ap-1801	14	11	attention	attention	NOUN
ap-1801	14	12	to	to	ADP
ap-1801	14	13	the	the	DET
ap-1801	14	14	possibility	possibility	NOUN
ap-1801	14	15	of	of	ADP
ap-1801	14	16	finding	find	VERB
ap-1801	14	17	a	a	DET
ap-1801	14	18	discrete	discrete	NOUN
ap-1801	14	19	and	and	CCONJ
ap-1801	14	20	below	below	ADP
ap-1801	14	21	bounded	bounded	ADJ
ap-1801	14	22	spectrum	spectrum	NOUN
ap-1801	14	23	in	in	ADP
ap-1801	14	24	a	a	DET
ap-1801	14	25	below	below	ADP
ap-1801	14	26	unbounded	unbounded	ADJ
ap-1801	14	27	potential	potential	NOUN
ap-1801	14	28	was	be	AUX
ap-1801	14	29	to	to	ADP
ap-1801	14	30	our	our	PRON
ap-1801	14	31	knowledge	knowledge	NOUN
ap-1801	14	32	m.	m.	NOUN
ap-1801	14	33	znojil	znojil	PROPN
ap-1801	14	34	,	,	PUNCT
ap-1801	14	35	who	who	PRON
ap-1801	14	36	analyzed	analyze	VERB
ap-1801	14	37	a	a	DET
ap-1801	14	38	related	related	ADJ
ap-1801	14	39	model	model	NOUN
ap-1801	14	40	in	in	ADP
ap-1801	14	41	[	[	X
ap-1801	14	42	2	2	NUM
ap-1801	14	43	]	]	PUNCT
ap-1801	14	44	.	.	PUNCT
ap-1801	15	1	in	in	ADP
ap-1801	15	2	the	the	DET
ap-1801	15	3	second	second	ADJ
ap-1801	15	4	part	part	NOUN
ap-1801	15	5	we	we	PRON
ap-1801	15	6	will	will	AUX
ap-1801	15	7	discuss	discuss	VERB
ap-1801	15	8	schödinger	schödinger	NOUN
ap-1801	15	9	operators	operator	NOUN
ap-1801	15	10	and	and	CCONJ
ap-1801	15	11	dirichlet	dirichlet	PROPN
ap-1801	15	12	laplacians	laplacian	NOUN
ap-1801	15	13	on	on	ADP
ap-1801	15	14	cusp	cusp	NOUN
ap-1801	15	15	-	-	PUNCT
ap-1801	15	16	shaped	shape	VERB
ap-1801	15	17	regions	region	NOUN
ap-1801	15	18	which	which	PRON
ap-1801	15	19	are	be	AUX
ap-1801	15	20	geometrically	geometrically	ADV
ap-1801	15	21	nontrivial	nontrivial	ADJ
ap-1801	15	22	,	,	PUNCT
ap-1801	15	23	being	be	AUX
ap-1801	15	24	either	either	CCONJ
ap-1801	15	25	bent	bent	ADJ
ap-1801	15	26	or	or	CCONJ
ap-1801	15	27	twisted	twisted	ADJ
ap-1801	15	28	,	,	PUNCT
ap-1801	15	29	and	and	CCONJ
ap-1801	15	30	show	show	VERB
ap-1801	15	31	how	how	SCONJ
ap-1801	15	32	their	their	PRON
ap-1801	15	33	geometry	geometry	NOUN
ap-1801	15	34	is	be	AUX
ap-1801	15	35	reflected	reflect	VERB
ap-1801	15	36	in	in	ADP
ap-1801	15	37	spectral	spectral	ADJ
ap-1801	15	38	properties	property	NOUN
ap-1801	15	39	.	.	PUNCT
ap-1801	16	1	2	2	X
ap-1801	16	2	.	.	X
ap-1801	16	3	a	a	DET
ap-1801	16	4	model	model	NOUN
ap-1801	16	5	with	with	ADP
ap-1801	16	6	potential	potential	ADJ
ap-1801	16	7	unbounded	unbounded	ADJ
ap-1801	16	8	from	from	ADP
ap-1801	16	9	below	below	ADP
ap-1801	16	10	and	and	CCONJ
ap-1801	16	11	infinite	infinite	VERB
ap-1801	16	12	phase	phase	NOUN
ap-1801	16	13	space	space	NOUN
ap-1801	16	14	we	we	PRON
ap-1801	16	15	are	be	AUX
ap-1801	16	16	going	go	VERB
ap-1801	16	17	to	to	PART
ap-1801	16	18	consider	consider	VERB
ap-1801	16	19	here	here	ADV
ap-1801	16	20	the	the	DET
ap-1801	16	21	following	follow	VERB
ap-1801	16	22	class	class	NOUN
ap-1801	16	23	of	of	ADP
ap-1801	16	24	operators	operator	NOUN
ap-1801	16	25	,	,	PUNCT
ap-1801	16	26	lp(λ	lp(λ	NUM
ap-1801	16	27	)	)	PUNCT
ap-1801	16	28	:	:	PUNCT
ap-1801	17	1	lp(λ)ψ	lp(λ)ψ	PROPN
ap-1801	17	2	=	=	X
ap-1801	17	3	−∆ψ	−∆ψ	X
ap-1801	18	1	+	+	CCONJ
ap-1801	18	2	(	(	PUNCT
ap-1801	18	3	|xy|p	|xy|p	ADP
ap-1801	18	4	−	−	NOUN
ap-1801	18	5	λ(x2	λ(x2	NOUN
ap-1801	18	6	+	+	CCONJ
ap-1801	18	7	y2)p/(p+2))ψ	y2)p/(p+2))ψ	NOUN
ap-1801	18	8	,	,	PUNCT
ap-1801	18	9	p	p	X
ap-1801	18	10	≥	≥	NUM
ap-1801	18	11	1	1	NUM
ap-1801	18	12	,	,	PUNCT
ap-1801	18	13	(	(	PUNCT
ap-1801	18	14	2.1	2.1	NUM
ap-1801	18	15	)	)	PUNCT
ap-1801	18	16	on	on	ADP
ap-1801	18	17	l2(r2	l2(r2	NOUN
ap-1801	18	18	)	)	PUNCT
ap-1801	18	19	where	where	SCONJ
ap-1801	18	20	x	x	X
ap-1801	18	21	,	,	PUNCT
ap-1801	18	22	y	y	PROPN
ap-1801	18	23	are	be	AUX
ap-1801	18	24	cartesian	cartesian	ADJ
ap-1801	18	25	coordinates	coordinate	NOUN
ap-1801	18	26	in	in	ADP
ap-1801	18	27	r2	r2	PROPN
ap-1801	18	28	.	.	PUNCT
ap-1801	19	1	the	the	DET
ap-1801	19	2	parameter	parameter	PROPN
ap-1801	19	3	λ	λ	PROPN
ap-1801	19	4	in	in	ADP
ap-1801	19	5	the	the	DET
ap-1801	19	6	second	second	ADJ
ap-1801	19	7	term	term	NOUN
ap-1801	19	8	of	of	ADP
ap-1801	19	9	the	the	DET
ap-1801	19	10	potential	potential	NOUN
ap-1801	19	11	is	be	AUX
ap-1801	19	12	assumed	assume	VERB
ap-1801	19	13	to	to	PART
ap-1801	19	14	be	be	AUX
ap-1801	19	15	non	non	ADJ
ap-1801	19	16	-	-	ADJ
ap-1801	19	17	negative	negative	ADJ
ap-1801	19	18	;	;	PUNCT
ap-1801	19	19	unless	unless	SCONJ
ap-1801	19	20	its	its	PRON
ap-1801	19	21	value	value	NOUN
ap-1801	19	22	is	be	AUX
ap-1801	19	23	important	important	ADJ
ap-1801	19	24	in	in	ADP
ap-1801	19	25	a	a	DET
ap-1801	19	26	particular	particular	ADJ
ap-1801	19	27	context	context	NOUN
ap-1801	19	28	we	we	PRON
ap-1801	19	29	write	write	VERB
ap-1801	19	30	simply	simply	ADV
ap-1801	19	31	lp	lp	ADJ
ap-1801	19	32	.	.	PUNCT
ap-1801	20	1	since	since	SCONJ
ap-1801	20	2	2p	2p	NUM
ap-1801	20	3	p+2	p+2	PROPN
ap-1801	20	4	<	<	X
ap-1801	20	5	2	2	NUM
ap-1801	20	6	the	the	DET
ap-1801	20	7	operator	operator	NOUN
ap-1801	20	8	(	(	PUNCT
ap-1801	20	9	2.1	2.1	NUM
ap-1801	20	10	)	)	PUNCT
ap-1801	20	11	is	be	AUX
ap-1801	20	12	e.s.a	e.s.a	ADJ
ap-1801	20	13	.	.	PUNCT
ap-1801	20	14	on	on	ADP
ap-1801	20	15	c∞0	c∞0	PROPN
ap-1801	20	16	(	(	PUNCT
ap-1801	20	17	r2	r2	PROPN
ap-1801	20	18	)	)	PUNCT
ap-1801	20	19	by	by	ADP
ap-1801	20	20	the	the	DET
ap-1801	20	21	faris	faris	PROPN
ap-1801	20	22	-	-	PUNCT
ap-1801	20	23	lavine	lavine	PROPN
ap-1801	20	24	theorem	theorem	NOUN
ap-1801	20	25	—	—	PUNCT
ap-1801	20	26	see	see	VERB
ap-1801	20	27	[	[	X
ap-1801	20	28	5	5	NUM
ap-1801	20	29	,	,	PUNCT
ap-1801	20	30	theorems	theorems	PROPN
ap-1801	20	31	x.28	x.28	PROPN
ap-1801	20	32	,	,	PUNCT
ap-1801	20	33	x.38	x.38	X
ap-1801	20	34	]	]	X
ap-1801	20	35	;	;	PUNCT
ap-1801	20	36	in	in	ADP
ap-1801	20	37	the	the	DET
ap-1801	20	38	following	following	NOUN
ap-1801	20	39	we	we	PRON
ap-1801	20	40	mean	mean	VERB
ap-1801	20	41	by	by	ADP
ap-1801	20	42	the	the	DET
ap-1801	20	43	symbol	symbol	NOUN
ap-1801	20	44	lp	lp	NOUN
ap-1801	20	45	or	or	CCONJ
ap-1801	20	46	lp(λ	lp(λ	PROPN
ap-1801	20	47	)	)	PUNCT
ap-1801	20	48	always	always	ADV
ap-1801	20	49	its	its	PRON
ap-1801	20	50	closure	closure	NOUN
ap-1801	20	51	.	.	PUNCT
ap-1801	21	1	we	we	PRON
ap-1801	21	2	are	be	AUX
ap-1801	21	3	going	go	VERB
ap-1801	21	4	to	to	PART
ap-1801	21	5	demonstrate	demonstrate	VERB
ap-1801	21	6	the	the	DET
ap-1801	21	7	existence	existence	NOUN
ap-1801	21	8	of	of	ADP
ap-1801	21	9	a	a	DET
ap-1801	21	10	critical	critical	ADJ
ap-1801	21	11	value	value	NOUN
ap-1801	21	12	of	of	ADP
ap-1801	21	13	the	the	DET
ap-1801	21	14	coupling	couple	VERB
ap-1801	21	15	constant	constant	ADJ
ap-1801	21	16	λ	λ	NOUN
ap-1801	21	17	,	,	PUNCT
ap-1801	21	18	expressed	express	VERB
ap-1801	21	19	explicitly	explicitly	ADV
ap-1801	21	20	in	in	ADP
ap-1801	21	21	terms	term	NOUN
ap-1801	21	22	of	of	ADP
ap-1801	21	23	the	the	DET
ap-1801	21	24	ground	ground	NOUN
ap-1801	21	25	-	-	PUNCT
ap-1801	21	26	state	state	NOUN
ap-1801	21	27	eigenvalue	eigenvalue	NOUN
ap-1801	21	28	of	of	ADP
ap-1801	21	29	the	the	DET
ap-1801	21	30	corresponding	corresponding	ADJ
ap-1801	21	31	(	(	PUNCT
ap-1801	21	32	an)harmonic	an)harmonic	ADJ
ap-1801	21	33	oscillator	oscillator	NOUN
ap-1801	21	34	hamiltonian	hamiltonian	NOUN
ap-1801	21	35	,	,	PUNCT
ap-1801	21	36	such	such	ADJ
ap-1801	21	37	that	that	SCONJ
ap-1801	21	38	the	the	DET
ap-1801	21	39	spectrum	spectrum	NOUN
ap-1801	21	40	of	of	ADP
ap-1801	21	41	lp(λ	lp(λ	PROPN
ap-1801	21	42	)	)	PUNCT
ap-1801	21	43	is	be	AUX
ap-1801	21	44	below	below	ADP
ap-1801	21	45	bounded	bounded	ADJ
ap-1801	21	46	and	and	CCONJ
ap-1801	21	47	purely	purely	ADV
ap-1801	21	48	discrete	discrete	ADJ
ap-1801	21	49	for	for	ADP
ap-1801	21	50	λ	λ	PROPN
ap-1801	21	51	<	<	X
ap-1801	21	52	λcrit	λcrit	NOUN
ap-1801	21	53	,	,	PUNCT
ap-1801	21	54	while	while	SCONJ
ap-1801	21	55	for	for	ADP
ap-1801	21	56	λ	λ	PROPN
ap-1801	21	57	>	>	X
ap-1801	21	58	λcrit	λcrit	NOUN
ap-1801	21	59	it	it	PRON
ap-1801	21	60	becomes	become	VERB
ap-1801	21	61	unbounded	unbounded	ADJ
ap-1801	21	62	from	from	ADP
ap-1801	21	63	below	below	ADV
ap-1801	21	64	.	.	PUNCT
ap-1801	22	1	in	in	ADP
ap-1801	22	2	the	the	DET
ap-1801	22	3	subcritical	subcritical	ADJ
ap-1801	22	4	case	case	NOUN
ap-1801	22	5	we	we	PRON
ap-1801	22	6	shall	shall	AUX
ap-1801	22	7	present	present	VERB
ap-1801	22	8	upper	upper	ADJ
ap-1801	22	9	and	and	CCONJ
ap-1801	22	10	lower	low	ADJ
ap-1801	22	11	bounds	bound	NOUN
ap-1801	22	12	to	to	ADP
ap-1801	22	13	the	the	DET
ap-1801	22	14	sums	sum	NOUN
ap-1801	22	15	of	of	ADP
ap-1801	22	16	the	the	DET
ap-1801	22	17	first	first	ADJ
ap-1801	22	18	n	n	NOUN
ap-1801	22	19	eigenvalues	eigenvalue	NOUN
ap-1801	22	20	of	of	ADP
ap-1801	22	21	lp(λ	lp(λ	NOUN
ap-1801	22	22	)	)	PUNCT
ap-1801	22	23	.	.	PUNCT
ap-1801	23	1	271	271	NUM
ap-1801	23	2	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1801	23	3	p.	p.	PROPN
ap-1801	23	4	exner	exner	NOUN
ap-1801	23	5	,	,	PUNCT
ap-1801	23	6	d.	d.	PROPN
ap-1801	23	7	barseghyan	barseghyan	PROPN
ap-1801	23	8	acta	acta	PROPN
ap-1801	23	9	polytechnica	polytechnica	PROPN
ap-1801	23	10	2.1	2.1	NUM
ap-1801	23	11	.	.	PUNCT
ap-1801	24	1	discreteness	discreteness	NOUN
ap-1801	24	2	of	of	ADP
ap-1801	24	3	the	the	DET
ap-1801	24	4	spectrum	spectrum	NOUN
ap-1801	24	5	let	let	VERB
ap-1801	24	6	us	we	PRON
ap-1801	24	7	first	first	ADV
ap-1801	24	8	look	look	VERB
ap-1801	24	9	at	at	ADP
ap-1801	24	10	small	small	ADJ
ap-1801	24	11	values	value	NOUN
ap-1801	24	12	of	of	ADP
ap-1801	24	13	λ	λ	PROPN
ap-1801	24	14	.	.	PUNCT
ap-1801	24	15	to	to	PART
ap-1801	24	16	speak	speak	VERB
ap-1801	24	17	quantitatively	quantitatively	ADV
ap-1801	24	18	we	we	PRON
ap-1801	24	19	need	need	VERB
ap-1801	24	20	an	an	DET
ap-1801	24	21	auxiliary	auxiliary	ADJ
ap-1801	24	22	operator	operator	NOUN
ap-1801	24	23	which	which	PRON
ap-1801	24	24	will	will	AUX
ap-1801	24	25	be	be	AUX
ap-1801	24	26	an	an	DET
ap-1801	24	27	(	(	PUNCT
ap-1801	24	28	an)harmonic	an)harmonic	ADJ
ap-1801	24	29	oscillator	oscillator	NOUN
ap-1801	24	30	hamiltonian	hamiltonian	NOUN
ap-1801	24	31	h̃p	h̃p	PROPN
ap-1801	24	32	:	:	PUNCT
ap-1801	24	33	h̃pu	h̃pu	PROPN
ap-1801	24	34	=	=	SYM
ap-1801	24	35	−u′′	−u′′	PROPN
ap-1801	25	1	+	+	PUNCT
ap-1801	25	2	|t|pu	|t|pu	NOUN
ap-1801	25	3	on	on	ADP
ap-1801	25	4	the	the	DET
ap-1801	25	5	natural	natural	ADJ
ap-1801	25	6	domain	domain	NOUN
ap-1801	25	7	in	in	ADP
ap-1801	25	8	l2(r	l2(r	PROPN
ap-1801	25	9	)	)	PUNCT
ap-1801	25	10	.	.	PUNCT
ap-1801	26	1	let	let	VERB
ap-1801	26	2	γp	γp	PART
ap-1801	26	3	be	be	AUX
ap-1801	26	4	the	the	DET
ap-1801	26	5	minimal	minimal	ADJ
ap-1801	26	6	eigenvalue	eigenvalue	NOUN
ap-1801	26	7	of	of	ADP
ap-1801	26	8	this	this	DET
ap-1801	26	9	operator	operator	NOUN
ap-1801	26	10	;	;	PUNCT
ap-1801	26	11	in	in	ADP
ap-1801	26	12	view	view	NOUN
ap-1801	26	13	of	of	ADP
ap-1801	26	14	the	the	DET
ap-1801	26	15	mirror	mirror	NOUN
ap-1801	26	16	symmetry	symmetry	NOUN
ap-1801	26	17	we	we	PRON
ap-1801	26	18	have	have	VERB
ap-1801	26	19	γp	γp	NOUN
ap-1801	26	20	=	=	PUNCT
ap-1801	26	21	inf	inf	NOUN
ap-1801	26	22	σ(hp	σ(hp	NUM
ap-1801	26	23	)	)	PUNCT
ap-1801	26	24	,	,	PUNCT
ap-1801	26	25	where	where	SCONJ
ap-1801	26	26	hp	hp	ADJ
ap-1801	26	27	:	:	PUNCT
ap-1801	26	28	hpu	hpu	NOUN
ap-1801	26	29	=	=	SYM
ap-1801	26	30	−u′′	−u′′	X
ap-1801	26	31	+	+	CCONJ
ap-1801	26	32	tpu	tpu	X
ap-1801	26	33	(	(	PUNCT
ap-1801	26	34	2.2	2.2	NUM
ap-1801	26	35	)	)	PUNCT
ap-1801	26	36	on	on	ADP
ap-1801	26	37	the	the	DET
ap-1801	26	38	natural	natural	ADJ
ap-1801	26	39	domain	domain	NOUN
ap-1801	26	40	in	in	ADP
ap-1801	26	41	l2(r+	l2(r+	PROPN
ap-1801	26	42	)	)	PUNCT
ap-1801	26	43	with	with	ADP
ap-1801	26	44	the	the	DET
ap-1801	26	45	neumann	neumann	PROPN
ap-1801	26	46	condition	condition	NOUN
ap-1801	26	47	at	at	ADP
ap-1801	26	48	the	the	DET
ap-1801	26	49	origin	origin	NOUN
ap-1801	26	50	.	.	PUNCT
ap-1801	27	1	it	it	PRON
ap-1801	27	2	is	be	AUX
ap-1801	27	3	well	well	ADV
ap-1801	27	4	known	know	VERB
ap-1801	27	5	that	that	SCONJ
ap-1801	27	6	the	the	DET
ap-1801	27	7	quantity	quantity	NOUN
ap-1801	27	8	γp	γp	NOUN
ap-1801	27	9	depends	depend	VERB
ap-1801	27	10	smoothly	smoothly	ADV
ap-1801	27	11	on	on	ADP
ap-1801	27	12	p	p	NOUN
ap-1801	27	13	being	be	AUX
ap-1801	27	14	equal	equal	ADJ
ap-1801	27	15	to	to	ADP
ap-1801	27	16	one	one	NUM
ap-1801	27	17	for	for	ADP
ap-1801	27	18	p	p	NOUN
ap-1801	27	19	=	=	SYM
ap-1801	27	20	2	2	NUM
ap-1801	27	21	and	and	CCONJ
ap-1801	27	22	tending	tend	VERB
ap-1801	27	23	to	to	ADP
ap-1801	27	24	γ∞	γ∞	PROPN
ap-1801	27	25	=	=	SYM
ap-1801	27	26	1	1	NUM
ap-1801	27	27	4π	4π	NUM
ap-1801	27	28	2	2	NUM
ap-1801	27	29	as	as	ADP
ap-1801	27	30	p→∞	p→∞	NUM
ap-1801	27	31	;	;	PUNCT
ap-1801	27	32	a	a	DET
ap-1801	27	33	numerical	numerical	ADJ
ap-1801	27	34	analysis	analysis	NOUN
ap-1801	27	35	performed	perform	VERB
ap-1801	27	36	in	in	ADP
ap-1801	27	37	[	[	X
ap-1801	27	38	3	3	X
ap-1801	27	39	]	]	PUNCT
ap-1801	27	40	shows	show	VERB
ap-1801	27	41	that	that	SCONJ
ap-1801	27	42	the	the	DET
ap-1801	27	43	function	function	NOUN
ap-1801	27	44	p	p	PROPN
ap-1801	27	45	7→	7→	NUM
ap-1801	27	46	γp	γp	NOUN
ap-1801	27	47	is	be	AUX
ap-1801	27	48	convex	convex	ADJ
ap-1801	27	49	and	and	CCONJ
ap-1801	27	50	γp	γp	VERB
ap-1801	27	51	>	>	X
ap-1801	27	52	0.99	0.99	NUM
ap-1801	27	53	for	for	ADP
ap-1801	27	54	any	any	DET
ap-1801	27	55	p	p	NOUN
ap-1801	27	56	≥	≥	NUM
ap-1801	27	57	1	1	NUM
ap-1801	27	58	.	.	PUNCT
ap-1801	27	59	theorem	theorem	VERB
ap-1801	27	60	2.1	2.1	NUM
ap-1801	27	61	.	.	PUNCT
ap-1801	28	1	for	for	ADP
ap-1801	28	2	any	any	DET
ap-1801	28	3	λ	λ	PROPN
ap-1801	28	4	∈	∈	PROPN
ap-1801	28	5	[	[	X
ap-1801	28	6	0	0	NUM
ap-1801	28	7	,	,	PUNCT
ap-1801	28	8	λcrit	λcrit	PROPN
ap-1801	28	9	)	)	PUNCT
ap-1801	28	10	,	,	PUNCT
ap-1801	29	1	where	where	SCONJ
ap-1801	29	2	λcrit	λcrit	NOUN
ap-1801	29	3	:	:	PUNCT
ap-1801	29	4	=	=	SYM
ap-1801	29	5	γp	γp	PROPN
ap-1801	29	6	,	,	PUNCT
ap-1801	29	7	the	the	DET
ap-1801	29	8	operator	operator	NOUN
ap-1801	29	9	lp(λ	lp(λ	PUNCT
ap-1801	29	10	)	)	PUNCT
ap-1801	29	11	with	with	ADP
ap-1801	29	12	p	p	PRON
ap-1801	29	13	≥	≥	NUM
ap-1801	29	14	1	1	NUM
ap-1801	29	15	is	be	AUX
ap-1801	29	16	bounded	bound	VERB
ap-1801	29	17	from	from	ADP
ap-1801	29	18	below	below	ADV
ap-1801	29	19	and	and	CCONJ
ap-1801	29	20	its	its	PRON
ap-1801	29	21	spectrum	spectrum	NOUN
ap-1801	29	22	is	be	AUX
ap-1801	29	23	purely	purely	ADV
ap-1801	29	24	discrete	discrete	ADJ
ap-1801	29	25	.	.	PUNCT
ap-1801	30	1	sketch	sketch	NOUN
ap-1801	30	2	of	of	ADP
ap-1801	30	3	the	the	DET
ap-1801	30	4	proof	proof	NOUN
ap-1801	30	5	.	.	PUNCT
ap-1801	31	1	fix	fix	VERB
ap-1801	31	2	first	first	ADJ
ap-1801	31	3	λ	λ	X
ap-1801	31	4	<	<	X
ap-1801	31	5	γp	γp	PROPN
ap-1801	31	6	.	.	PUNCT
ap-1801	32	1	by	by	ADP
ap-1801	32	2	the	the	DET
ap-1801	32	3	minimax	minimax	NOUN
ap-1801	32	4	principle	principle	NOUN
ap-1801	32	5	we	we	PRON
ap-1801	32	6	need	need	VERB
ap-1801	32	7	to	to	PART
ap-1801	32	8	estimate	estimate	VERB
ap-1801	32	9	lp	lp	ADV
ap-1801	32	10	from	from	ADP
ap-1801	32	11	below	below	ADP
ap-1801	32	12	by	by	ADP
ap-1801	32	13	a	a	DET
ap-1801	32	14	self	self	NOUN
ap-1801	32	15	-	-	PUNCT
ap-1801	32	16	adjoint	adjoint	NOUN
ap-1801	32	17	operator	operator	NOUN
ap-1801	32	18	with	with	ADP
ap-1801	32	19	a	a	DET
ap-1801	32	20	purely	purely	ADV
ap-1801	32	21	discrete	discrete	ADJ
ap-1801	32	22	spectrum	spectrum	NOUN
ap-1801	32	23	.	.	PUNCT
ap-1801	33	1	to	to	ADP
ap-1801	33	2	this	this	DET
ap-1801	33	3	aim	aim	NOUN
ap-1801	33	4	we	we	PRON
ap-1801	33	5	employ	employ	VERB
ap-1801	33	6	a	a	DET
ap-1801	33	7	suitable	suitable	ADJ
ap-1801	33	8	bracketing	bracketing	NOUN
ap-1801	33	9	imposing	impose	VERB
ap-1801	33	10	additional	additional	ADJ
ap-1801	33	11	neumann	neumann	PROPN
ap-1801	33	12	conditions	condition	NOUN
ap-1801	33	13	at	at	ADP
ap-1801	33	14	concentric	concentric	ADJ
ap-1801	33	15	circles	circle	NOUN
ap-1801	33	16	of	of	ADP
ap-1801	33	17	radii	radius	NOUN
ap-1801	33	18	n	n	NOUN
ap-1801	33	19	=	=	SYM
ap-1801	33	20	1	1	NUM
ap-1801	33	21	,	,	PUNCT
ap-1801	33	22	2	2	NUM
ap-1801	33	23	,	,	PUNCT
ap-1801	33	24	.	.	PUNCT
ap-1801	33	25	.	.	PUNCT
ap-1801	33	26	.	.	PUNCT
ap-1801	34	1	.	.	PUNCT
ap-1801	35	1	using	use	VERB
ap-1801	35	2	the	the	DET
ap-1801	35	3	polar	polar	ADJ
ap-1801	35	4	coordinates	coordinate	NOUN
ap-1801	35	5	,	,	PUNCT
ap-1801	35	6	we	we	PRON
ap-1801	35	7	get	get	VERB
ap-1801	35	8	a	a	DET
ap-1801	35	9	direct	direct	ADJ
ap-1801	35	10	sum	sum	NOUN
ap-1801	35	11	of	of	ADP
ap-1801	35	12	operators	operator	NOUN
ap-1801	35	13	acting	act	VERB
ap-1801	35	14	as	as	ADP
ap-1801	35	15	l(1	l(1	PROPN
ap-1801	35	16	)	)	PUNCT
ap-1801	35	17	n	n	CCONJ
ap-1801	35	18	,	,	PUNCT
ap-1801	35	19	pψ	pψ	NOUN
ap-1801	35	20	=	=	SYM
ap-1801	36	1	−1	−1	NOUN
ap-1801	36	2	r	r	NOUN
ap-1801	36	3	∂	∂	NOUN
ap-1801	36	4	∂r	∂r	NOUN
ap-1801	36	5	(	(	PUNCT
ap-1801	37	1	r	r	NOUN
ap-1801	37	2	∂ψ	∂ψ	PROPN
ap-1801	38	1	∂r	∂r	INTJ
ap-1801	38	2	)	)	PUNCT
ap-1801	38	3	−	−	PROPN
ap-1801	38	4	1	1	NUM
ap-1801	38	5	n2	n2	NOUN
ap-1801	38	6	∂2ψ	∂2ψ	NOUN
ap-1801	38	7	∂ϕ2	∂ϕ2	NOUN
ap-1801	38	8	+	+	CCONJ
ap-1801	38	9	(	(	PUNCT
ap-1801	38	10	r2p	r2p	PROPN
ap-1801	38	11	2p	2p	NUM
ap-1801	38	12	|	|	NOUN
ap-1801	38	13	sin	sin	VERB
ap-1801	38	14	2ϕ|p	2ϕ|p	NOUN
ap-1801	38	15	−	−	PROPN
ap-1801	38	16	λr2p/(p+2	λr2p/(p+2	NUM
ap-1801	38	17	)	)	PUNCT
ap-1801	38	18	)	)	PUNCT
ap-1801	39	1	ψ	ψ	X
ap-1801	39	2	,	,	PUNCT
ap-1801	39	3	∂ψ	∂ψ	VERB
ap-1801	39	4	∂n	∂n	PROPN
ap-1801	39	5	∣∣∣	∣∣∣	NOUN
ap-1801	40	1	r	r	NOUN
ap-1801	40	2	=	=	NOUN
ap-1801	40	3	n−1	n−1	PROPN
ap-1801	40	4	=	=	PUNCT
ap-1801	40	5	∂ψ	∂ψ	PROPN
ap-1801	41	1	∂n	∂n	PROPN
ap-1801	41	2	∣∣∣	∣∣∣	NOUN
ap-1801	42	1	r	r	NOUN
ap-1801	42	2	=	=	NOUN
ap-1801	42	3	n	n	NOUN
ap-1801	42	4	=	=	SYM
ap-1801	42	5	0	0	NUM
ap-1801	42	6	,	,	PUNCT
ap-1801	42	7	(	(	PUNCT
ap-1801	42	8	2.3	2.3	NUM
ap-1801	42	9	)	)	PUNCT
ap-1801	42	10	on	on	ADP
ap-1801	42	11	the	the	DET
ap-1801	42	12	regions	region	NOUN
ap-1801	43	1	gn	gn	INTJ
ap-1801	43	2	:	:	PUNCT
ap-1801	43	3	=	=	SYM
ap-1801	43	4	{	{	PUNCT
ap-1801	43	5	(	(	PUNCT
ap-1801	43	6	r	r	NOUN
ap-1801	43	7	,	,	PUNCT
ap-1801	43	8	ϕ	ϕ	NOUN
ap-1801	43	9	)	)	PUNCT
ap-1801	43	10	:	:	PUNCT
ap-1801	43	11	n−	n−	NOUN
ap-1801	43	12	1	1	NUM
ap-1801	43	13	≤	≤	NOUN
ap-1801	43	14	r	r	NOUN
ap-1801	43	15	<	<	X
ap-1801	43	16	n	n	CCONJ
ap-1801	43	17	,	,	PUNCT
ap-1801	43	18	0	0	NUM
ap-1801	43	19	≤	≤	NOUN
ap-1801	43	20	ϕ	ϕ	X
ap-1801	43	21	<	<	X
ap-1801	43	22	2π	2π	PROPN
ap-1801	43	23	}	}	PUNCT
ap-1801	43	24	,	,	PUNCT
ap-1801	43	25	n	n	NOUN
ap-1801	43	26	=	=	SYM
ap-1801	43	27	1	1	NUM
ap-1801	43	28	,	,	PUNCT
ap-1801	43	29	2	2	NUM
ap-1801	43	30	,	,	PUNCT
ap-1801	43	31	.	.	PUNCT
ap-1801	43	32	.	.	PUNCT
ap-1801	43	33	.	.	PUNCT
ap-1801	43	34	.	.	PUNCT
ap-1801	44	1	each	each	PRON
ap-1801	44	2	of	of	ADP
ap-1801	44	3	these	these	DET
ap-1801	44	4	annuli	annuli	NOUN
ap-1801	44	5	is	be	AUX
ap-1801	44	6	compact	compact	ADJ
ap-1801	44	7	and	and	CCONJ
ap-1801	44	8	the	the	DET
ap-1801	44	9	potential	potential	NOUN
ap-1801	44	10	is	be	AUX
ap-1801	44	11	regular	regular	ADJ
ap-1801	44	12	on	on	ADP
ap-1801	44	13	it	it	PRON
ap-1801	44	14	,	,	PUNCT
ap-1801	44	15	hence	hence	ADV
ap-1801	44	16	σ	σ	PROPN
ap-1801	44	17	(	(	PUNCT
ap-1801	44	18	l	l	X
ap-1801	44	19	(	(	PUNCT
ap-1801	44	20	1	1	NUM
ap-1801	44	21	)	)	PUNCT
ap-1801	44	22	n	n	CCONJ
ap-1801	44	23	,	,	PUNCT
ap-1801	44	24	p	p	NOUN
ap-1801	44	25	)	)	PUNCT
ap-1801	44	26	is	be	AUX
ap-1801	44	27	purely	purely	ADV
ap-1801	44	28	discrete	discrete	ADJ
ap-1801	44	29	.	.	PUNCT
ap-1801	45	1	it	it	PRON
ap-1801	45	2	thus	thus	ADV
ap-1801	45	3	suffices	suffice	VERB
ap-1801	45	4	to	to	PART
ap-1801	45	5	check	check	VERB
ap-1801	45	6	that	that	DET
ap-1801	45	7	inf	inf	PROPN
ap-1801	45	8	σ	σ	PROPN
ap-1801	45	9	(	(	PUNCT
ap-1801	45	10	l	l	X
ap-1801	45	11	(	(	PUNCT
ap-1801	45	12	1	1	NUM
ap-1801	45	13	)	)	PUNCT
ap-1801	45	14	n	n	CCONJ
ap-1801	45	15	,	,	PUNCT
ap-1801	45	16	p	p	NOUN
ap-1801	45	17	)	)	PUNCT
ap-1801	45	18	→∞	→∞	PROPN
ap-1801	45	19	as	as	ADP
ap-1801	45	20	n→∞	n→∞	NUM
ap-1801	45	21	,	,	PUNCT
ap-1801	45	22	because	because	SCONJ
ap-1801	45	23	the	the	DET
ap-1801	45	24	spectrum	spectrum	NOUN
ap-1801	45	25	of	of	ADP
ap-1801	45	26	⊕∞	⊕∞	PROPN
ap-1801	45	27	n=1	n=1	ADP
ap-1801	45	28	l	l	PROPN
ap-1801	45	29	(	(	PUNCT
ap-1801	45	30	1	1	NUM
ap-1801	45	31	)	)	PUNCT
ap-1801	45	32	n	n	CCONJ
ap-1801	45	33	,	,	PUNCT
ap-1801	45	34	p	p	NOUN
ap-1801	45	35	below	below	ADP
ap-1801	45	36	any	any	DET
ap-1801	45	37	fixed	fix	VERB
ap-1801	45	38	value	value	NOUN
ap-1801	45	39	will	will	AUX
ap-1801	45	40	then	then	ADV
ap-1801	45	41	be	be	AUX
ap-1801	45	42	purely	purely	ADV
ap-1801	45	43	discrete	discrete	ADJ
ap-1801	45	44	.	.	PUNCT
ap-1801	46	1	we	we	PRON
ap-1801	46	2	estimate	estimate	VERB
ap-1801	46	3	l	l	NOUN
ap-1801	46	4	(	(	PUNCT
ap-1801	46	5	1	1	NUM
ap-1801	46	6	)	)	PUNCT
ap-1801	46	7	n	n	CCONJ
ap-1801	46	8	,	,	PUNCT
ap-1801	46	9	p	p	NOUN
ap-1801	46	10	from	from	ADP
ap-1801	46	11	below	below	ADP
ap-1801	46	12	by	by	ADP
ap-1801	46	13	an	an	DET
ap-1801	46	14	operator	operator	NOUN
ap-1801	46	15	with	with	ADP
ap-1801	46	16	separated	separate	VERB
ap-1801	46	17	variables	variable	NOUN
ap-1801	46	18	,	,	PUNCT
ap-1801	46	19	l(2	l(2	PROPN
ap-1801	46	20	)	)	PUNCT
ap-1801	46	21	n	n	CCONJ
ap-1801	46	22	,	,	PUNCT
ap-1801	46	23	pψ	pψ	NOUN
ap-1801	46	24	=	=	SYM
ap-1801	46	25	−1	−1	NOUN
ap-1801	46	26	r	r	NOUN
ap-1801	46	27	∂	∂	NOUN
ap-1801	46	28	∂r	∂r	NOUN
ap-1801	47	1	(	(	PUNCT
ap-1801	47	2	r	r	NOUN
ap-1801	47	3	∂ψ	∂ψ	PROPN
ap-1801	48	1	∂r	∂r	INTJ
ap-1801	48	2	)	)	PUNCT
ap-1801	48	3	−	−	PROPN
ap-1801	48	4	1	1	NUM
ap-1801	48	5	n2	n2	NOUN
ap-1801	48	6	∂2ψ	∂2ψ	NOUN
ap-1801	48	7	∂ϕ2	∂ϕ2	NOUN
ap-1801	48	8	+	+	CCONJ
ap-1801	48	9	(	(	PUNCT
ap-1801	48	10	(	(	PUNCT
ap-1801	48	11	n−	n−	NOUN
ap-1801	48	12	1)2p	1)2p	NUM
ap-1801	48	13	2p	2p	NUM
ap-1801	48	14	|sin	|sin	PROPN
ap-1801	48	15	2ϕ|p	2ϕ|p	PROPN
ap-1801	48	16	−	−	PROPN
ap-1801	48	17	λn2p/(p+2	λn2p/(p+2	NUM
ap-1801	48	18	)	)	PUNCT
ap-1801	48	19	)	)	PUNCT
ap-1801	49	1	ψ	ψ	X
ap-1801	49	2	,	,	PUNCT
ap-1801	49	3	∂ψ	∂ψ	VERB
ap-1801	49	4	∂n	∂n	PROPN
ap-1801	49	5	∣∣∣	∣∣∣	NOUN
ap-1801	50	1	r	r	NOUN
ap-1801	50	2	=	=	NOUN
ap-1801	50	3	n−1	n−1	PROPN
ap-1801	50	4	=	=	PUNCT
ap-1801	50	5	∂ψ	∂ψ	PROPN
ap-1801	51	1	∂n	∂n	PROPN
ap-1801	51	2	∣∣∣	∣∣∣	NOUN
ap-1801	52	1	r	r	NOUN
ap-1801	52	2	=	=	NOUN
ap-1801	52	3	n	n	NOUN
ap-1801	52	4	=	=	SYM
ap-1801	52	5	0	0	NUM
ap-1801	52	6	,	,	PUNCT
ap-1801	52	7	and	and	CCONJ
ap-1801	52	8	establish	establish	VERB
ap-1801	52	9	that	that	DET
ap-1801	52	10	inf	inf	PROPN
ap-1801	52	11	σ	σ	PROPN
ap-1801	52	12	(	(	PUNCT
ap-1801	52	13	l	l	X
ap-1801	52	14	(	(	PUNCT
ap-1801	52	15	3	3	NUM
ap-1801	52	16	)	)	PUNCT
ap-1801	52	17	n	n	CCONJ
ap-1801	52	18	,	,	PUNCT
ap-1801	52	19	p	p	NOUN
ap-1801	52	20	)	)	PUNCT
ap-1801	52	21	→∞	→∞	PROPN
ap-1801	52	22	as	as	ADP
ap-1801	52	23	n→∞	n→∞	NUM
ap-1801	52	24	,	,	PUNCT
ap-1801	52	25	where	where	SCONJ
ap-1801	52	26	l(3	l(3	NOUN
ap-1801	52	27	)	)	PUNCT
ap-1801	52	28	n	n	CCONJ
ap-1801	52	29	,	,	PUNCT
ap-1801	52	30	p	p	PRON
ap-1801	52	31	is	be	AUX
ap-1801	52	32	the	the	DET
ap-1801	52	33	angular	angular	ADJ
ap-1801	52	34	part	part	NOUN
ap-1801	52	35	of	of	ADP
ap-1801	52	36	l(2	l(2	PROPN
ap-1801	52	37	)	)	PUNCT
ap-1801	52	38	n	n	CCONJ
ap-1801	52	39	,	,	PUNCT
ap-1801	52	40	p.	p.	NOUN
ap-1801	52	41	the	the	DET
ap-1801	52	42	spectrum	spectrum	NOUN
ap-1801	52	43	of	of	ADP
ap-1801	52	44	l(2	l(2	PROPN
ap-1801	52	45	)	)	PUNCT
ap-1801	52	46	n	n	CCONJ
ap-1801	52	47	,	,	PUNCT
ap-1801	52	48	p	p	PRON
ap-1801	52	49	is	be	AUX
ap-1801	52	50	the	the	DET
ap-1801	52	51	‘	'	PUNCT
ap-1801	52	52	sum	sum	NOUN
ap-1801	52	53	’	'	PUNCT
ap-1801	52	54	of	of	ADP
ap-1801	52	55	the	the	DET
ap-1801	52	56	radial	radial	ADJ
ap-1801	52	57	and	and	CCONJ
ap-1801	52	58	angular	angular	ADJ
ap-1801	52	59	component	component	NOUN
ap-1801	52	60	and	and	CCONJ
ap-1801	52	61	the	the	DET
ap-1801	52	62	lowest	low	ADJ
ap-1801	52	63	radial	radial	ADJ
ap-1801	52	64	eigenvalue	eigenvalue	NOUN
ap-1801	52	65	is	be	AUX
ap-1801	52	66	zero	zero	NUM
ap-1801	52	67	corresponding	correspond	VERB
ap-1801	52	68	to	to	ADP
ap-1801	52	69	a	a	DET
ap-1801	52	70	constant	constant	ADJ
ap-1801	52	71	eigenfunction	eigenfunction	NOUN
ap-1801	52	72	.	.	PUNCT
ap-1801	53	1	one	one	NUM
ap-1801	53	2	the	the	DET
ap-1801	53	3	other	other	ADJ
ap-1801	53	4	hand	hand	NOUN
ap-1801	53	5	,	,	PUNCT
ap-1801	53	6	the	the	DET
ap-1801	53	7	angular	angular	ADJ
ap-1801	53	8	part	part	NOUN
ap-1801	53	9	behaves	behave	VERB
ap-1801	53	10	as	as	ADP
ap-1801	53	11	the	the	DET
ap-1801	53	12	anharmonic	anharmonic	ADJ
ap-1801	53	13	oscillator	oscillator	NOUN
ap-1801	53	14	around	around	ADP
ap-1801	53	15	the	the	DET
ap-1801	53	16	potential	potential	ADJ
ap-1801	53	17	minima	minima	NOUN
ap-1801	53	18	,	,	PUNCT
ap-1801	53	19	and	and	CCONJ
ap-1801	53	20	the	the	DET
ap-1801	53	21	corresponding	correspond	VERB
ap-1801	53	22	eigenvalue	eigenvalue	NOUN
ap-1801	53	23	prevails	prevail	NOUN
ap-1801	53	24	over	over	ADP
ap-1801	53	25	the	the	DET
ap-1801	53	26	negative	negative	ADJ
ap-1801	53	27	λ	λ	ADJ
ap-1801	53	28	-	-	ADJ
ap-1801	53	29	dependent	dependent	ADJ
ap-1801	53	30	term	term	NOUN
ap-1801	54	1	[	[	X
ap-1801	54	2	3	3	NUM
ap-1801	54	3	]	]	PUNCT
ap-1801	54	4	.	.	PUNCT
ap-1801	55	1	in	in	ADP
ap-1801	55	2	this	this	DET
ap-1801	55	3	way	way	NOUN
ap-1801	55	4	one	one	NUM
ap-1801	55	5	gets	get	VERB
ap-1801	55	6	inf	inf	ADJ
ap-1801	55	7	σ	σ	NOUN
ap-1801	55	8	(	(	PUNCT
ap-1801	55	9	l	l	X
ap-1801	55	10	(	(	PUNCT
ap-1801	55	11	2	2	NUM
ap-1801	55	12	)	)	PUNCT
ap-1801	55	13	n	n	CCONJ
ap-1801	55	14	,	,	PUNCT
ap-1801	55	15	p	p	NOUN
ap-1801	55	16	)	)	PUNCT
ap-1801	55	17	→∞	→∞	PROPN
ap-1801	55	18	as	as	ADP
ap-1801	55	19	n→∞	n→∞	NUM
ap-1801	55	20	,	,	PUNCT
ap-1801	55	21	which	which	PRON
ap-1801	55	22	proves	prove	VERB
ap-1801	55	23	by	by	ADP
ap-1801	55	24	the	the	DET
ap-1801	55	25	minimax	minimax	NOUN
ap-1801	55	26	principle	principle	NOUN
ap-1801	55	27	the	the	DET
ap-1801	55	28	same	same	ADJ
ap-1801	55	29	for	for	ADP
ap-1801	55	30	operator	operator	NOUN
ap-1801	55	31	l(1	l(1	NOUN
ap-1801	55	32	)	)	PUNCT
ap-1801	55	33	n	n	CCONJ
ap-1801	55	34	,	,	PUNCT
ap-1801	55	35	p.	p.	NOUN
ap-1801	55	36	2.2	2.2	NUM
ap-1801	55	37	.	.	PUNCT
ap-1801	56	1	the	the	DET
ap-1801	56	2	supercritical	supercritical	ADJ
ap-1801	56	3	case	case	NOUN
ap-1801	56	4	for	for	ADP
ap-1801	56	5	large	large	ADJ
ap-1801	56	6	λ	λ	PROPN
ap-1801	56	7	the	the	DET
ap-1801	56	8	spectral	spectral	ADJ
ap-1801	56	9	behaviour	behaviour	NOUN
ap-1801	56	10	is	be	AUX
ap-1801	56	11	different	different	ADJ
ap-1801	56	12	.	.	PUNCT
ap-1801	57	1	theorem	theorem	VERB
ap-1801	57	2	2.2	2.2	NUM
ap-1801	57	3	.	.	PUNCT
ap-1801	58	1	σ	σ	PROPN
ap-1801	58	2	(	(	PUNCT
ap-1801	58	3	lp(λ	lp(λ	NOUN
ap-1801	58	4	)	)	PUNCT
ap-1801	58	5	)	)	PUNCT
ap-1801	58	6	,	,	PUNCT
ap-1801	58	7	p	p	NOUN
ap-1801	58	8	≥	≥	NOUN
ap-1801	58	9	1	1	NUM
ap-1801	58	10	,	,	PUNCT
ap-1801	58	11	is	be	AUX
ap-1801	58	12	unbounded	unbounded	ADJ
ap-1801	58	13	from	from	ADP
ap-1801	58	14	below	below	ADP
ap-1801	58	15	if	if	SCONJ
ap-1801	58	16	λ	λ	PROPN
ap-1801	58	17	>	>	X
ap-1801	58	18	λcrit	λcrit	PROPN
ap-1801	58	19	.	.	PUNCT
ap-1801	58	20	sketch	sketch	PROPN
ap-1801	58	21	of	of	ADP
ap-1801	58	22	the	the	DET
ap-1801	58	23	proof	proof	NOUN
ap-1801	58	24	.	.	PUNCT
ap-1801	59	1	we	we	PRON
ap-1801	59	2	use	use	VERB
ap-1801	59	3	a	a	DET
ap-1801	59	4	similar	similar	ADJ
ap-1801	59	5	technique	technique	NOUN
ap-1801	59	6	,	,	PUNCT
ap-1801	59	7	this	this	DET
ap-1801	59	8	time	time	NOUN
ap-1801	59	9	looking	look	VERB
ap-1801	59	10	for	for	ADP
ap-1801	59	11	an	an	DET
ap-1801	59	12	upper	upper	ADJ
ap-1801	59	13	bound	bind	VERB
ap-1801	59	14	to	to	ADP
ap-1801	59	15	lp(λ	lp(λ	PUNCT
ap-1801	59	16	)	)	PUNCT
ap-1801	59	17	obtained	obtain	VERB
ap-1801	59	18	by	by	ADP
ap-1801	59	19	dirichlet	dirichlet	NOUN
ap-1801	59	20	bracketing	bracketing	NOUN
ap-1801	59	21	:	:	PUNCT
ap-1801	59	22	we	we	PRON
ap-1801	59	23	consider	consider	VERB
ap-1801	59	24	the	the	DET
ap-1801	59	25	operators	operator	NOUN
ap-1801	59	26	l̃(1	l̃(1	NOUN
ap-1801	59	27	)	)	PUNCT
ap-1801	59	28	n	n	CCONJ
ap-1801	59	29	,	,	PUNCT
ap-1801	59	30	p	p	NOUN
ap-1801	59	31	acting	act	VERB
ap-1801	59	32	as	as	ADP
ap-1801	59	33	(	(	PUNCT
ap-1801	59	34	2.3	2.3	NUM
ap-1801	59	35	)	)	PUNCT
ap-1801	59	36	on	on	ADP
ap-1801	59	37	the	the	DET
ap-1801	59	38	annular	annular	ADJ
ap-1801	59	39	domains	domain	NOUN
ap-1801	59	40	gn	gn	PROPN
ap-1801	59	41	with	with	ADP
ap-1801	59	42	dirichlet	dirichlet	PROPN
ap-1801	59	43	boundary	boundary	PROPN
ap-1801	59	44	conditions	condition	NOUN
ap-1801	59	45	.	.	PUNCT
ap-1801	60	1	the	the	DET
ap-1801	60	2	latter	latter	ADJ
ap-1801	60	3	give	give	VERB
ap-1801	60	4	a	a	DET
ap-1801	60	5	contribution	contribution	NOUN
ap-1801	60	6	of	of	ADP
ap-1801	60	7	order	order	NOUN
ap-1801	60	8	o(1	o(1	NOUN
ap-1801	60	9	)	)	PUNCT
ap-1801	60	10	as	as	ADP
ap-1801	60	11	n→∞	n→∞	NUM
ap-1801	60	12	and	and	CCONJ
ap-1801	60	13	since	since	SCONJ
ap-1801	60	14	the	the	DET
ap-1801	60	15	λ	λ	NOUN
ap-1801	60	16	-	-	ADJ
ap-1801	60	17	dependent	dependent	ADJ
ap-1801	60	18	term	term	NOUN
ap-1801	60	19	now	now	ADV
ap-1801	60	20	prevails	prevail	VERB
ap-1801	60	21	we	we	PRON
ap-1801	60	22	conclude	conclude	VERB
ap-1801	60	23	[	[	X
ap-1801	60	24	3	3	X
ap-1801	60	25	]	]	PUNCT
ap-1801	60	26	that	that	DET
ap-1801	60	27	inf	inf	PROPN
ap-1801	60	28	σ	σ	PROPN
ap-1801	60	29	(	(	PUNCT
ap-1801	60	30	l̃(1	l̃(1	PROPN
ap-1801	60	31	)	)	PUNCT
ap-1801	60	32	n	n	CCONJ
ap-1801	60	33	,	,	PUNCT
ap-1801	60	34	p	p	NOUN
ap-1801	60	35	)	)	PUNCT
ap-1801	60	36	→	→	PUNCT
ap-1801	60	37	−∞	−∞	PUNCT
ap-1801	60	38	as	as	ADP
ap-1801	60	39	n→∞	n→∞	NUM
ap-1801	60	40	,	,	PUNCT
ap-1801	60	41	which	which	PRON
ap-1801	60	42	means	mean	VERB
ap-1801	60	43	that	that	SCONJ
ap-1801	60	44	σ	σ	PROPN
ap-1801	60	45	(	(	PUNCT
ap-1801	60	46	lp(λ	lp(λ	NOUN
ap-1801	60	47	)	)	PUNCT
ap-1801	60	48	)	)	PUNCT
ap-1801	60	49	is	be	AUX
ap-1801	60	50	unbounded	unbounde	VERB
ap-1801	60	51	from	from	ADP
ap-1801	60	52	below	below	ADV
ap-1801	60	53	.	.	PUNCT
ap-1801	61	1	2.3	2.3	NUM
ap-1801	61	2	.	.	PUNCT
ap-1801	62	1	lower	low	ADJ
ap-1801	62	2	bounds	bound	NOUN
ap-1801	62	3	to	to	PART
ap-1801	62	4	eigenvalue	eigenvalue	VERB
ap-1801	62	5	sums	sum	NOUN
ap-1801	62	6	next	next	ADV
ap-1801	62	7	we	we	PRON
ap-1801	62	8	will	will	AUX
ap-1801	62	9	show	show	VERB
ap-1801	62	10	how	how	SCONJ
ap-1801	62	11	the	the	DET
ap-1801	62	12	eigenvalue	eigenvalue	NOUN
ap-1801	62	13	sums	sum	NOUN
ap-1801	62	14	of	of	ADP
ap-1801	62	15	operator	operator	NOUN
ap-1801	62	16	lp(λ	lp(λ	PUNCT
ap-1801	62	17	)	)	PUNCT
ap-1801	62	18	can	can	AUX
ap-1801	62	19	be	be	AUX
ap-1801	62	20	estimated	estimate	VERB
ap-1801	62	21	for	for	ADP
ap-1801	62	22	small	small	ADJ
ap-1801	62	23	values	value	NOUN
ap-1801	62	24	of	of	ADP
ap-1801	62	25	λ	λ	NOUN
ap-1801	62	26	.	.	PUNCT
ap-1801	63	1	we	we	PRON
ap-1801	63	2	introduce	introduce	VERB
ap-1801	63	3	the	the	DET
ap-1801	63	4	number	number	NOUN
ap-1801	63	5	α	α	NOUN
ap-1801	63	6	:	:	PUNCT
ap-1801	63	7	=	=	SYM
ap-1801	63	8	1	1	NUM
ap-1801	63	9	40	40	NUM
ap-1801	63	10	(	(	PUNCT
ap-1801	63	11	5	5	NUM
ap-1801	63	12	+	+	CCONJ
ap-1801	63	13	√	√	NUM
ap-1801	63	14	105	105	NUM
ap-1801	63	15	)	)	PUNCT
ap-1801	63	16	2	2	NUM
ap-1801	63	17	≈	≈	PROPN
ap-1801	63	18	5.81	5.81	NUM
ap-1801	63	19	;	;	PUNCT
ap-1801	63	20	it	it	PRON
ap-1801	63	21	is	be	AUX
ap-1801	63	22	clear	clear	ADJ
ap-1801	63	23	that	that	SCONJ
ap-1801	63	24	α−1	α−1	PROPN
ap-1801	63	25	<	<	X
ap-1801	63	26	γp	γp	PROPN
ap-1801	63	27	.	.	PUNCT
ap-1801	64	1	we	we	PRON
ap-1801	64	2	denote	denote	VERB
ap-1801	64	3	by	by	ADP
ap-1801	64	4	{	{	PUNCT
ap-1801	64	5	λj	λj	PROPN
ap-1801	64	6	,	,	PUNCT
ap-1801	64	7	p}∞j=1	p}∞j=1	VERB
ap-1801	64	8	the	the	DET
ap-1801	64	9	eigenvalues	eigenvalue	NOUN
ap-1801	64	10	of	of	ADP
ap-1801	64	11	lp(λ	lp(λ	NOUN
ap-1801	64	12	)	)	PUNCT
ap-1801	64	13	arranged	arrange	VERB
ap-1801	64	14	in	in	ADP
ap-1801	64	15	ascending	ascend	VERB
ap-1801	64	16	order	order	NOUN
ap-1801	64	17	;	;	PUNCT
ap-1801	64	18	then	then	ADV
ap-1801	64	19	we	we	PRON
ap-1801	64	20	have	have	VERB
ap-1801	64	21	the	the	DET
ap-1801	64	22	following	follow	VERB
ap-1801	64	23	result	result	NOUN
ap-1801	64	24	.	.	PUNCT
ap-1801	65	1	theorem	theorem	VERB
ap-1801	65	2	2.3	2.3	NUM
ap-1801	65	3	.	.	PUNCT
ap-1801	66	1	to	to	ADP
ap-1801	66	2	any	any	DET
ap-1801	66	3	nonnegative	nonnegative	ADJ
ap-1801	66	4	λ	λ	NOUN
ap-1801	66	5	<	<	X
ap-1801	66	6	α−1	α−1	PROPN
ap-1801	66	7	≈	≈	PROPN
ap-1801	66	8	0.172	0.172	NUM
ap-1801	66	9	there	there	PRON
ap-1801	66	10	is	be	VERB
ap-1801	66	11	a	a	DET
ap-1801	66	12	positive	positive	ADJ
ap-1801	66	13	cp	cp	NOUN
ap-1801	66	14	depending	depend	VERB
ap-1801	66	15	on	on	ADP
ap-1801	66	16	p	p	NOUN
ap-1801	66	17	only	only	ADV
ap-1801	66	18	such	such	ADJ
ap-1801	66	19	that	that	SCONJ
ap-1801	66	20	n∑	n∑	PROPN
ap-1801	66	21	j=1	j=1	PROPN
ap-1801	66	22	λj	λj	PROPN
ap-1801	66	23	,	,	PUNCT
ap-1801	66	24	p	p	NOUN
ap-1801	66	25	≥	≥	X
ap-1801	66	26	cp	cp	INTJ
ap-1801	66	27	(	(	PUNCT
ap-1801	66	28	1−	1−	NUM
ap-1801	66	29	αλ	αλ	NUM
ap-1801	66	30	)	)	PUNCT
ap-1801	66	31	n	n	CCONJ
ap-1801	66	32	(	(	PUNCT
ap-1801	66	33	2p+1)/(p+1	2p+1)/(p+1	NUM
ap-1801	66	34	)	)	PUNCT
ap-1801	66	35	(	(	PUNCT
ap-1801	66	36	lnpn	lnpn	NOUN
ap-1801	66	37	+	+	CCONJ
ap-1801	66	38	1)1/(p+1	1)1/(p+1	NOUN
ap-1801	66	39	)	)	PUNCT
ap-1801	66	40	−	−	PROPN
ap-1801	66	41	cλn	cλn	PROPN
ap-1801	66	42	,	,	PUNCT
ap-1801	66	43	n	n	NOUN
ap-1801	66	44	=	=	SYM
ap-1801	66	45	1	1	NUM
ap-1801	66	46	,	,	PUNCT
ap-1801	66	47	2	2	NUM
ap-1801	66	48	,	,	PUNCT
ap-1801	66	49	.	.	PUNCT
ap-1801	66	50	.	.	PUNCT
ap-1801	67	1	.	.	PUNCT
ap-1801	68	1	,	,	PUNCT
ap-1801	68	2	(	(	PUNCT
ap-1801	68	3	2.4	2.4	NUM
ap-1801	68	4	)	)	PUNCT
ap-1801	68	5	where	where	SCONJ
ap-1801	68	6	c	c	NOUN
ap-1801	68	7	=	=	SYM
ap-1801	68	8	2	2	NUM
ap-1801	68	9	(	(	PUNCT
ap-1801	68	10	α2	α2	NOUN
ap-1801	68	11	5	5	NUM
ap-1801	68	12	+	+	CCONJ
ap-1801	68	13	1	1	NUM
ap-1801	68	14	)	)	PUNCT
ap-1801	69	1	≈	≈	PROPN
ap-1801	69	2	15.51	15.51	NUM
ap-1801	69	3	.	.	PUNCT
ap-1801	70	1	272	272	NUM
ap-1801	70	2	vol	vol	NOUN
ap-1801	70	3	.	.	PUNCT
ap-1801	71	1	53	53	NUM
ap-1801	71	2	no	no	NOUN
ap-1801	71	3	.	.	PUNCT
ap-1801	72	1	3/2013	3/2013	PROPN
ap-1801	72	2	spectral	spectral	ADJ
ap-1801	72	3	analysis	analysis	NOUN
ap-1801	72	4	of	of	ADP
ap-1801	72	5	schrödinger	schrödinger	ADJ
ap-1801	72	6	operators	operator	NOUN
ap-1801	72	7	sketch	sketch	VERB
ap-1801	72	8	of	of	ADP
ap-1801	72	9	the	the	DET
ap-1801	72	10	proof	proof	NOUN
ap-1801	72	11	.	.	PUNCT
ap-1801	73	1	we	we	PRON
ap-1801	73	2	denote	denote	VERB
ap-1801	73	3	by	by	ADP
ap-1801	73	4	{	{	PUNCT
ap-1801	73	5	ψj	ψj	ADV
ap-1801	73	6	,	,	PUNCT
ap-1801	73	7	p}∞j=1	p}∞j=1	PROPN
ap-1801	73	8	the	the	DET
ap-1801	73	9	system	system	NOUN
ap-1801	73	10	of	of	ADP
ap-1801	73	11	normalized	normalize	VERB
ap-1801	73	12	eigenfunctions	eigenfunction	NOUN
ap-1801	73	13	corresponding	correspond	VERB
ap-1801	73	14	to	to	ADP
ap-1801	73	15	{	{	PUNCT
ap-1801	73	16	λj	λj	PROPN
ap-1801	73	17	,	,	PUNCT
ap-1801	73	18	p}∞j=1	p}∞j=1	PROPN
ap-1801	73	19	,	,	PUNCT
ap-1801	73	20	−∆ψj	−∆ψj	NOUN
ap-1801	73	21	,	,	PUNCT
ap-1801	73	22	p	p	X
ap-1801	73	23	+	+	X
ap-1801	73	24	(	(	PUNCT
ap-1801	73	25	|xy|p	|xy|p	ADP
ap-1801	73	26	−	−	NOUN
ap-1801	73	27	λ(x2	λ(x2	NOUN
ap-1801	73	28	+	+	CCONJ
ap-1801	73	29	y2)p)/(p+2))ψj	y2)p)/(p+2))ψj	NOUN
ap-1801	73	30	,	,	PUNCT
ap-1801	73	31	p	p	NOUN
ap-1801	73	32	=	=	SYM
ap-1801	73	33	λj	λj	PROPN
ap-1801	73	34	,	,	PUNCT
ap-1801	73	35	pψj	pψj	ADV
ap-1801	73	36	,	,	PUNCT
ap-1801	73	37	p	p	X
ap-1801	73	38	,	,	PUNCT
ap-1801	73	39	j	j	PROPN
ap-1801	73	40	=	=	SYM
ap-1801	73	41	1	1	NUM
ap-1801	73	42	,	,	PUNCT
ap-1801	73	43	2	2	NUM
ap-1801	73	44	,	,	PUNCT
ap-1801	73	45	.	.	PUNCT
ap-1801	73	46	.	.	PUNCT
ap-1801	73	47	.	.	PUNCT
ap-1801	74	1	;	;	PUNCT
ap-1801	74	2	without	without	ADP
ap-1801	74	3	loss	loss	NOUN
ap-1801	74	4	of	of	ADP
ap-1801	74	5	generality	generality	NOUN
ap-1801	74	6	we	we	PRON
ap-1801	74	7	may	may	AUX
ap-1801	74	8	assume	assume	VERB
ap-1801	74	9	these	these	DET
ap-1801	74	10	functions	function	NOUN
ap-1801	74	11	to	to	PART
ap-1801	74	12	be	be	AUX
ap-1801	74	13	real	real	ADV
ap-1801	74	14	-	-	PUNCT
ap-1801	74	15	valued	value	VERB
ap-1801	74	16	.	.	PUNCT
ap-1801	75	1	our	our	PRON
ap-1801	75	2	potential	potential	ADJ
ap-1801	75	3	form	form	NOUN
ap-1801	75	4	hyperbolic	hyperbolic	ADV
ap-1801	75	5	-	-	PUNCT
ap-1801	75	6	shaped	shape	VERB
ap-1801	75	7	‘	'	PUNCT
ap-1801	75	8	channels	channel	NOUN
ap-1801	75	9	’	'	PUNCT
ap-1801	75	10	and	and	CCONJ
ap-1801	75	11	we	we	PRON
ap-1801	75	12	have	have	VERB
ap-1801	75	13	first	first	ADJ
ap-1801	75	14	to	to	PART
ap-1801	75	15	estimate	estimate	VERB
ap-1801	75	16	eigenfunction	eigenfunction	NOUN
ap-1801	75	17	integrals	integral	NOUN
ap-1801	75	18	in	in	ADP
ap-1801	75	19	the	the	DET
ap-1801	75	20	corresponding	correspond	VERB
ap-1801	75	21	parts	part	NOUN
ap-1801	75	22	of	of	ADP
ap-1801	75	23	the	the	DET
ap-1801	75	24	plane	plane	NOUN
ap-1801	75	25	.	.	PUNCT
ap-1801	76	1	we	we	PRON
ap-1801	76	2	establish	establish	VERB
ap-1801	76	3	[	[	X
ap-1801	76	4	3	3	NUM
ap-1801	76	5	]	]	PUNCT
ap-1801	76	6	that	that	SCONJ
ap-1801	76	7	for	for	ADP
ap-1801	76	8	any	any	DET
ap-1801	76	9	natural	natural	ADJ
ap-1801	76	10	j	j	PROPN
ap-1801	76	11	and	and	CCONJ
ap-1801	76	12	a	a	DET
ap-1801	76	13	δ	δ	NOUN
ap-1801	76	14	>	>	X
ap-1801	76	15	0	0	NUM
ap-1801	77	1	one	one	NUM
ap-1801	77	2	has	have	VERB
ap-1801	77	3	∫	∫	PROPN
ap-1801	77	4	∞	∞	NUM
ap-1801	77	5	1	1	NUM
ap-1801	77	6	∫	∫	PROPN
ap-1801	77	7	(	(	PUNCT
ap-1801	77	8	1+δ)y−p/(p+2	1+δ)y−p/(p+2	PROPN
ap-1801	77	9	)	)	PUNCT
ap-1801	77	10	0	0	PUNCT
ap-1801	78	1	y2p/(p+2)ψ2	y2p/(p+2)ψ2	PROPN
ap-1801	78	2	j	j	PROPN
ap-1801	78	3	,	,	PUNCT
ap-1801	78	4	p(x	p(x	PROPN
ap-1801	78	5	,	,	PUNCT
ap-1801	78	6	y	y	PROPN
ap-1801	78	7	)	)	PUNCT
ap-1801	78	8	dxdy	dxdy	PROPN
ap-1801	78	9	≤	≤	ADV
ap-1801	78	10	5	5	NUM
ap-1801	78	11	2(1	2(1	NUM
ap-1801	78	12	+	+	CCONJ
ap-1801	78	13	δ)2	δ)2	PROPN
ap-1801	78	14	∫	∫	PROPN
ap-1801	78	15	∞	∞	PROPN
ap-1801	78	16	1	1	NUM
ap-1801	78	17	∫	∫	NOUN
ap-1801	78	18	∞	∞	PROPN
ap-1801	78	19	0	0	NUM
ap-1801	78	20	(	(	PUNCT
ap-1801	78	21	∂ψj	∂ψj	PROPN
ap-1801	78	22	,	,	PUNCT
ap-1801	78	23	p	p	NOUN
ap-1801	78	24	∂x	∂x	PROPN
ap-1801	78	25	)	)	PUNCT
ap-1801	78	26	2	2	NUM
ap-1801	78	27	(	(	PUNCT
ap-1801	78	28	x	x	NOUN
ap-1801	78	29	,	,	PUNCT
ap-1801	78	30	y	y	PROPN
ap-1801	78	31	)	)	PUNCT
ap-1801	78	32	dxdy	dxdy	NOUN
ap-1801	78	33	+	+	CCONJ
ap-1801	78	34	21	21	NUM
ap-1801	78	35	+	+	CCONJ
ap-1801	78	36	δ	δ	PROPN
ap-1801	78	37	δ	δ	X
ap-1801	78	38	∫	∫	PROPN
ap-1801	78	39	∞	∞	NUM
ap-1801	78	40	1	1	NUM
ap-1801	78	41	∫	∫	PROPN
ap-1801	78	42	(	(	PUNCT
ap-1801	78	43	1+δ)y−p/(p+2	1+δ)y−p/(p+2	PROPN
ap-1801	78	44	)	)	PUNCT
ap-1801	78	45	0	0	NUM
ap-1801	78	46	xpypψ2	xpypψ2	PROPN
ap-1801	79	1	j	j	PROPN
ap-1801	79	2	,	,	PUNCT
ap-1801	79	3	p(x	p(x	PROPN
ap-1801	79	4	,	,	PUNCT
ap-1801	79	5	y	y	PROPN
ap-1801	79	6	)	)	PUNCT
ap-1801	79	7	dx	dx	PROPN
ap-1801	79	8	dy	dy	NOUN
ap-1801	79	9	and	and	CCONJ
ap-1801	79	10	that	that	SCONJ
ap-1801	79	11	for	for	ADP
ap-1801	79	12	an	an	DET
ap-1801	79	13	arbitrary	arbitrary	ADJ
ap-1801	79	14	ε	ε	PROPN
ap-1801	79	15	>	>	X
ap-1801	79	16	0	0	PUNCT
ap-1801	80	1	there	there	PRON
ap-1801	80	2	is	be	VERB
ap-1801	80	3	a	a	DET
ap-1801	80	4	number	number	NOUN
ap-1801	80	5	θ(ε	θ(ε	NOUN
ap-1801	80	6	)	)	PUNCT
ap-1801	80	7	∈	∈	PROPN
ap-1801	81	1	[	[	X
ap-1801	81	2	1	1	NUM
ap-1801	81	3	,	,	PUNCT
ap-1801	81	4	1	1	NUM
ap-1801	81	5	+	+	NUM
ap-1801	81	6	δ	δ	X
ap-1801	81	7	]	]	X
ap-1801	81	8	such	such	ADJ
ap-1801	81	9	that∫	that∫	NOUN
ap-1801	81	10	∞	∞	NUM
ap-1801	81	11	1	1	NUM
ap-1801	81	12	yp/(p+2)ψ2	yp/(p+2)ψ2	PROPN
ap-1801	81	13	j	j	PROPN
ap-1801	81	14	,	,	PUNCT
ap-1801	81	15	p	p	X
ap-1801	81	16	(	(	PUNCT
ap-1801	81	17	θ(ε	θ(ε	PROPN
ap-1801	81	18	)	)	PUNCT
ap-1801	81	19	yp/(p+2	yp/(p+2	PROPN
ap-1801	81	20	)	)	PUNCT
ap-1801	81	21	,	,	PUNCT
ap-1801	81	22	y	y	PROPN
ap-1801	81	23	)	)	PUNCT
ap-1801	81	24	dy	dy	VERB
ap-1801	81	25	<	<	X
ap-1801	81	26	1	1	NUM
ap-1801	81	27	δ	δ	NOUN
ap-1801	81	28	∫	∫	NOUN
ap-1801	81	29	∞	∞	NUM
ap-1801	81	30	1	1	NUM
ap-1801	81	31	∫	∫	PROPN
ap-1801	81	32	(	(	PUNCT
ap-1801	81	33	1+δ)y−p/(p+2	1+δ)y−p/(p+2	PROPN
ap-1801	81	34	)	)	PUNCT
ap-1801	81	35	y−p/(p+2	y−p/(p+2	PROPN
ap-1801	81	36	)	)	PUNCT
ap-1801	81	37	xpypψ2	xpypψ2	PROPN
ap-1801	82	1	j	j	PROPN
ap-1801	82	2	,	,	PUNCT
ap-1801	82	3	p(x	p(x	PROPN
ap-1801	82	4	,	,	PUNCT
ap-1801	82	5	y	y	NOUN
ap-1801	82	6	)	)	PUNCT
ap-1801	82	7	dxdy	dxdy	NOUN
ap-1801	82	8	+	+	CCONJ
ap-1801	82	9	ε	ε	PROPN
ap-1801	82	10	.	.	PUNCT
ap-1801	83	1	using	use	VERB
ap-1801	83	2	the	the	DET
ap-1801	83	3	potential	potential	ADJ
ap-1801	83	4	symmetry	symmetry	NOUN
ap-1801	83	5	we	we	PRON
ap-1801	83	6	get	get	VERB
ap-1801	83	7	an	an	DET
ap-1801	83	8	analogous	analogous	ADJ
ap-1801	83	9	bound	bind	VERB
ap-1801	83	10	for	for	ADP
ap-1801	83	11	the	the	DET
ap-1801	83	12	other	other	ADJ
ap-1801	83	13	‘	'	PUNCT
ap-1801	83	14	channels	channel	NOUN
ap-1801	83	15	’	'	PUNCT
ap-1801	83	16	.	.	PUNCT
ap-1801	84	1	using	use	VERB
ap-1801	84	2	next	next	ADJ
ap-1801	84	3	the	the	DET
ap-1801	84	4	normalization	normalization	NOUN
ap-1801	84	5	‖ψj	‖ψj	NUM
ap-1801	84	6	,	,	PUNCT
ap-1801	84	7	p‖	p‖	NOUN
ap-1801	84	8	=	=	SYM
ap-1801	84	9	1	1	NUM
ap-1801	84	10	and	and	CCONJ
ap-1801	84	11	the	the	DET
ap-1801	84	12	mentioned	mention	VERB
ap-1801	84	13	estimates	estimate	NOUN
ap-1801	84	14	we	we	PRON
ap-1801	84	15	find∫	find∫	VERB
ap-1801	84	16	r2	r2	PROPN
ap-1801	84	17	(	(	PUNCT
ap-1801	84	18	x2	x2	PROPN
ap-1801	84	19	+	+	CCONJ
ap-1801	84	20	y2	y2	NOUN
ap-1801	84	21	)	)	PUNCT
ap-1801	85	1	p	p	PROPN
ap-1801	85	2	p+2ψ2	p+2ψ2	PROPN
ap-1801	85	3	j	j	PROPN
ap-1801	85	4	,	,	PUNCT
ap-1801	85	5	p(x	p(x	PROPN
ap-1801	85	6	,	,	PUNCT
ap-1801	85	7	y	y	PROPN
ap-1801	85	8	)	)	PUNCT
ap-1801	85	9	dxdy	dxdy	PROPN
ap-1801	85	10	≤	≤	PROPN
ap-1801	85	11	(	(	PUNCT
ap-1801	85	12	∫	∫	PROPN
ap-1801	85	13	|y|≥1	|y|≥1	PROPN
ap-1801	85	14	∫	∫	PROPN
ap-1801	85	15	|x|≤(1+δ)|y|−p/(p+2	|x|≤(1+δ)|y|−p/(p+2	CCONJ
ap-1801	85	16	)	)	PUNCT
ap-1801	85	17	|y|2p/(p+2)ψ2	|y|2p/(p+2)ψ2	PROPN
ap-1801	85	18	j	j	PROPN
ap-1801	85	19	,	,	PUNCT
ap-1801	85	20	p(x	p(x	PROPN
ap-1801	85	21	,	,	PUNCT
ap-1801	85	22	y	y	NOUN
ap-1801	85	23	)	)	PUNCT
ap-1801	85	24	dxdy	dxdy	PROPN
ap-1801	85	25	+	+	CCONJ
ap-1801	85	26	∫	∫	PROPN
ap-1801	85	27	|y|≥1	|y|≥1	PROPN
ap-1801	85	28	∫	∫	PROPN
ap-1801	85	29	|x|>(1+δ)|y|−p/(p+2	|x|>(1+δ)|y|−p/(p+2	X
ap-1801	85	30	)	)	PUNCT
ap-1801	85	31	|y|2p/(p+2)ψ2	|y|2p/(p+2)ψ2	PROPN
ap-1801	85	32	j	j	PROPN
ap-1801	85	33	,	,	PUNCT
ap-1801	85	34	p(x	p(x	PROPN
ap-1801	85	35	,	,	PUNCT
ap-1801	85	36	y	y	NOUN
ap-1801	85	37	)	)	PUNCT
ap-1801	85	38	dxdy	dxdy	PROPN
ap-1801	85	39	+	+	CCONJ
ap-1801	85	40	∫	∫	PROPN
ap-1801	85	41	|x|≥1	|x|≥1	PROPN
ap-1801	85	42	∫	∫	PROPN
ap-1801	85	43	|y|≤(1+δ)|x|−p/(p+2	|y|≤(1+δ)|x|−p/(p+2	NUM
ap-1801	85	44	)	)	PUNCT
ap-1801	85	45	|x|2p/(p+2)ψ2	|x|2p/(p+2)ψ2	PROPN
ap-1801	85	46	j	j	PROPN
ap-1801	85	47	,	,	PUNCT
ap-1801	85	48	p(x	p(x	PROPN
ap-1801	85	49	,	,	PUNCT
ap-1801	85	50	y	y	NOUN
ap-1801	85	51	)	)	PUNCT
ap-1801	85	52	dy	dy	NOUN
ap-1801	85	53	dx	dx	PROPN
ap-1801	86	1	+	+	CCONJ
ap-1801	86	2	∫	∫	PROPN
ap-1801	86	3	|x|≥1	|x|≥1	PROPN
ap-1801	86	4	∫	∫	PROPN
ap-1801	86	5	(	(	PUNCT
ap-1801	86	6	1+δ)|x|−p/(p+2)<|y|<1	1+δ)|x|−p/(p+2)<|y|<1	PROPN
ap-1801	86	7	|x|2p/(p+2)ψ2	|x|2p/(p+2)ψ2	PROPN
ap-1801	86	8	j	j	PROPN
ap-1801	86	9	,	,	PUNCT
ap-1801	86	10	p(x	p(x	PROPN
ap-1801	86	11	,	,	PUNCT
ap-1801	86	12	y	y	NOUN
ap-1801	86	13	)	)	PUNCT
ap-1801	86	14	dy	dy	PROPN
ap-1801	86	15	dx	dx	PROPN
ap-1801	86	16	)	)	PUNCT
ap-1801	87	1	+	+	CCONJ
ap-1801	87	2	2	2	NUM
ap-1801	87	3	≤	≤	NOUN
ap-1801	87	4	(	(	PUNCT
ap-1801	87	5	1	1	NUM
ap-1801	87	6	+	+	CCONJ
ap-1801	87	7	δ	δ	PROPN
ap-1801	87	8	)	)	PUNCT
ap-1801	87	9	max	max	PROPN
ap-1801	87	10	{	{	PUNCT
ap-1801	87	11	5	5	NUM
ap-1801	87	12	2(1	2(1	NUM
ap-1801	87	13	+	+	CCONJ
ap-1801	87	14	δ	δ	PROPN
ap-1801	87	15	)	)	PUNCT
ap-1801	87	16	,	,	PUNCT
ap-1801	87	17	2	2	NUM
ap-1801	87	18	δ	δ	NOUN
ap-1801	87	19	}	}	PUNCT
ap-1801	87	20	(	(	PUNCT
ap-1801	87	21	∫	∫	PROPN
ap-1801	87	22	r2	r2	PROPN
ap-1801	87	23	|∇ψj	|∇ψj	PROPN
ap-1801	87	24	,	,	PUNCT
ap-1801	87	25	p|2	p|2	PROPN
ap-1801	87	26	(	(	PUNCT
ap-1801	87	27	x	x	NOUN
ap-1801	87	28	,	,	PUNCT
ap-1801	87	29	y	y	PROPN
ap-1801	87	30	)	)	PUNCT
ap-1801	87	31	dx	dx	PROPN
ap-1801	88	1	dy	dy	NOUN
ap-1801	88	2	+	+	CCONJ
ap-1801	88	3	∫	∫	PROPN
ap-1801	88	4	r2	r2	PROPN
ap-1801	88	5	|xy|pψ2	|xy|pψ2	PROPN
ap-1801	88	6	j	j	PROPN
ap-1801	88	7	,	,	PUNCT
ap-1801	88	8	p(x	p(x	PROPN
ap-1801	88	9	,	,	PUNCT
ap-1801	88	10	y	y	PROPN
ap-1801	88	11	)	)	PUNCT
ap-1801	88	12	dx	dx	PROPN
ap-1801	89	1	dy	dy	NOUN
ap-1801	89	2	+	+	CCONJ
ap-1801	89	3	(	(	PUNCT
ap-1801	89	4	1	1	NUM
ap-1801	89	5	+	+	CCONJ
ap-1801	89	6	δ)2	δ)2	NOUN
ap-1801	89	7	)	)	PUNCT
ap-1801	90	1	+	+	CCONJ
ap-1801	90	2	2	2	NUM
ap-1801	90	3	,	,	PUNCT
ap-1801	90	4	where	where	SCONJ
ap-1801	90	5	we	we	PRON
ap-1801	90	6	have	have	AUX
ap-1801	90	7	used	use	VERB
ap-1801	90	8	the	the	DET
ap-1801	90	9	inequality	inequality	NOUN
ap-1801	90	10	|xy|p	|xy|p	ADP
ap-1801	90	11	>	>	X
ap-1801	90	12	|y|2p/(p+2	|y|2p/(p+2	ADJ
ap-1801	90	13	)	)	PUNCT
ap-1801	90	14	valid	valid	NOUN
ap-1801	90	15	on	on	ADP
ap-1801	90	16	the	the	DET
ap-1801	90	17	domain	domain	NOUN
ap-1801	90	18	of	of	ADP
ap-1801	90	19	the	the	DET
ap-1801	90	20	second	second	NOUN
ap-1801	90	21	of	of	ADP
ap-1801	90	22	the	the	DET
ap-1801	90	23	four	four	NUM
ap-1801	90	24	integrals	integral	NOUN
ap-1801	90	25	and	and	CCONJ
ap-1801	90	26	an	an	DET
ap-1801	90	27	analogous	analogous	ADJ
ap-1801	90	28	bound	bind	VERB
ap-1801	90	29	for	for	ADP
ap-1801	90	30	the	the	DET
ap-1801	90	31	fourth	fourth	ADJ
ap-1801	90	32	integral	integral	NOUN
ap-1801	90	33	;	;	PUNCT
ap-1801	90	34	the	the	DET
ap-1801	90	35	factor	factor	NOUN
ap-1801	90	36	(	(	PUNCT
ap-1801	90	37	1	1	NUM
ap-1801	90	38	+	+	NUM
ap-1801	90	39	δ)2	δ)2	NOUN
ap-1801	90	40	prevents	prevent	VERB
ap-1801	90	41	double	double	ADJ
ap-1801	90	42	counting	count	VERB
ap-1801	90	43	the	the	DET
ap-1801	90	44	‘	'	PUNCT
ap-1801	90	45	corner	corner	NOUN
ap-1801	90	46	regions	region	NOUN
ap-1801	90	47	’	'	PUNCT
ap-1801	90	48	with	with	ADP
ap-1801	90	49	|x|	|x|	PROPN
ap-1801	90	50	,	,	PUNCT
ap-1801	90	51	|y|	|y|	ADJ
ap-1801	90	52	≥	≥	NOUN
ap-1801	90	53	1	1	NUM
ap-1801	90	54	and	and	CCONJ
ap-1801	90	55	|y|	|y|	PROPN
ap-1801	90	56	≤	≤	NOUN
ap-1801	90	57	(	(	PUNCT
ap-1801	90	58	1	1	NUM
ap-1801	90	59	+	+	CCONJ
ap-1801	90	60	δ)|x|−p/(p+2	δ)|x|−p/(p+2	PUNCT
ap-1801	90	61	)	)	PUNCT
ap-1801	90	62	.	.	PUNCT
ap-1801	91	1	choosing	choose	VERB
ap-1801	91	2	δ	δ	X
ap-1801	91	3	=	=	PUNCT
ap-1801	92	1	−5	−5	PROPN
ap-1801	92	2	+	+	ADJ
ap-1801	92	3	√	√	NUM
ap-1801	92	4	105	105	NUM
ap-1801	92	5	10	10	NUM
ap-1801	92	6	we	we	PRON
ap-1801	92	7	arrive	arrive	VERB
ap-1801	92	8	at∫	at∫	NOUN
ap-1801	92	9	r2	r2	PROPN
ap-1801	92	10	(	(	PUNCT
ap-1801	92	11	x2	x2	PROPN
ap-1801	92	12	+	+	CCONJ
ap-1801	92	13	y2	y2	NOUN
ap-1801	92	14	)	)	PUNCT
ap-1801	93	1	p	p	PROPN
ap-1801	93	2	p+2ψ2	p+2ψ2	PROPN
ap-1801	93	3	j	j	PROPN
ap-1801	93	4	,	,	PUNCT
ap-1801	93	5	p(x	p(x	PROPN
ap-1801	93	6	,	,	PUNCT
ap-1801	93	7	y	y	PROPN
ap-1801	93	8	)	)	PUNCT
ap-1801	93	9	dx	dx	PROPN
ap-1801	93	10	dy	dy	VERB
ap-1801	93	11	≤	≤	NUM
ap-1801	93	12	α	α	PROPN
ap-1801	93	13	(	(	PUNCT
ap-1801	93	14	∫	∫	PROPN
ap-1801	93	15	r2	r2	PROPN
ap-1801	93	16	|∇ψj	|∇ψj	PROPN
ap-1801	93	17	,	,	PUNCT
ap-1801	93	18	p||2(x	p||2(x	NOUN
ap-1801	93	19	,	,	PUNCT
ap-1801	93	20	y	y	PROPN
ap-1801	93	21	)	)	PUNCT
ap-1801	93	22	dx	dx	PROPN
ap-1801	94	1	dy	dy	NOUN
ap-1801	94	2	+	+	CCONJ
ap-1801	94	3	∫	∫	PROPN
ap-1801	94	4	r2	r2	PROPN
ap-1801	94	5	|xy|pψ2	|xy|pψ2	PROPN
ap-1801	94	6	j	j	PROPN
ap-1801	94	7	,	,	PUNCT
ap-1801	94	8	p(x	p(x	PROPN
ap-1801	94	9	,	,	PUNCT
ap-1801	94	10	y	y	PROPN
ap-1801	94	11	)	)	PUNCT
ap-1801	94	12	dx	dx	PROPN
ap-1801	94	13	dy	dy	X
ap-1801	94	14	)	)	PUNCT
ap-1801	95	1	+	+	CCONJ
ap-1801	96	1	c	c	X
ap-1801	96	2	,	,	PUNCT
ap-1801	96	3	where	where	SCONJ
ap-1801	96	4	c	c	X
ap-1801	96	5	:	:	PUNCT
ap-1801	96	6	=	=	SYM
ap-1801	96	7	α(1	α(1	PROPN
ap-1801	96	8	+	+	PUNCT
ap-1801	96	9	δ)2	δ)2	NOUN
ap-1801	96	10	+	+	CCONJ
ap-1801	96	11	2	2	NUM
ap-1801	96	12	=	=	SYM
ap-1801	96	13	2	2	NUM
ap-1801	96	14	(	(	PUNCT
ap-1801	96	15	α2	α2	NOUN
ap-1801	96	16	5	5	NUM
ap-1801	96	17	+	+	CCONJ
ap-1801	96	18	1	1	NUM
ap-1801	96	19	)	)	PUNCT
ap-1801	96	20	.	.	PUNCT
ap-1801	97	1	since	since	SCONJ
ap-1801	97	2	λj	λj	PROPN
ap-1801	97	3	,	,	PUNCT
ap-1801	97	4	p	p	PROPN
ap-1801	97	5	is	be	AUX
ap-1801	97	6	the	the	DET
ap-1801	97	7	eigenvalue	eigenvalue	NOUN
ap-1801	97	8	corresponding	corresponding	NOUN
ap-1801	97	9	to	to	ADP
ap-1801	97	10	the	the	DET
ap-1801	97	11	eigenfunction	eigenfunction	NOUN
ap-1801	97	12	ψj	ψj	ADP
ap-1801	97	13	,	,	PUNCT
ap-1801	97	14	p	p	NOUN
ap-1801	97	15	the	the	DET
ap-1801	97	16	inequality	inequality	NOUN
ap-1801	97	17	derived	derive	VERB
ap-1801	97	18	above	above	ADP
ap-1801	97	19	implies∫	implies∫	PROPN
ap-1801	97	20	r2	r2	PROPN
ap-1801	97	21	|∇ψj	|∇ψj	PROPN
ap-1801	97	22	,	,	PUNCT
ap-1801	97	23	p|2	p|2	PROPN
ap-1801	97	24	dx	dx	PROPN
ap-1801	97	25	dy	dy	PROPN
ap-1801	97	26	+	+	CCONJ
ap-1801	97	27	∫	∫	PROPN
ap-1801	97	28	r2	r2	PROPN
ap-1801	97	29	|xy|pψ2	|xy|pψ2	PROPN
ap-1801	97	30	j	j	PROPN
ap-1801	97	31	,	,	PUNCT
ap-1801	97	32	p	p	PROPN
ap-1801	97	33	dxdy	dxdy	PROPN
ap-1801	97	34	≤	≤	ADV
ap-1801	97	35	1	1	NUM
ap-1801	97	36	1−	1−	NUM
ap-1801	97	37	αλ	αλ	PRON
ap-1801	97	38	(	(	PUNCT
ap-1801	97	39	λj	λj	PROPN
ap-1801	97	40	,	,	PUNCT
ap-1801	97	41	p	p	X
ap-1801	97	42	+	+	X
ap-1801	97	43	cλ	cλ	PROPN
ap-1801	97	44	)	)	PUNCT
ap-1801	97	45	,	,	PUNCT
ap-1801	98	1	j	j	PROPN
ap-1801	98	2	=	=	SYM
ap-1801	98	3	1	1	NUM
ap-1801	98	4	,	,	PUNCT
ap-1801	98	5	2	2	NUM
ap-1801	98	6	,	,	PUNCT
ap-1801	98	7	.	.	PUNCT
ap-1801	98	8	.	.	PUNCT
ap-1801	98	9	.	.	PUNCT
ap-1801	99	1	.	.	PUNCT
ap-1801	100	1	next	next	ADV
ap-1801	100	2	we	we	PRON
ap-1801	100	3	use	use	VERB
ap-1801	100	4	plancherel	plancherel	PROPN
ap-1801	100	5	’s	’s	PART
ap-1801	100	6	theorem	theorem	NOUN
ap-1801	100	7	to	to	PART
ap-1801	100	8	express	express	VERB
ap-1801	100	9	the	the	DET
ap-1801	100	10	gradients	gradient	NOUN
ap-1801	100	11	of	of	ADP
ap-1801	100	12	ψj	ψj	ADP
ap-1801	100	13	,	,	PUNCT
ap-1801	100	14	p	p	NOUN
ap-1801	100	15	in	in	ADP
ap-1801	100	16	the	the	DET
ap-1801	100	17	first	first	ADJ
ap-1801	100	18	integral	integral	ADJ
ap-1801	100	19	and	and	CCONJ
ap-1801	100	20	then	then	ADV
ap-1801	100	21	apply	apply	VERB
ap-1801	100	22	the	the	DET
ap-1801	100	23	following	follow	VERB
ap-1801	100	24	lieb	lieb	PROPN
ap-1801	100	25	-	-	PUNCT
ap-1801	100	26	thirring	thirring	NOUN
ap-1801	100	27	-	-	PUNCT
ap-1801	100	28	type	type	NOUN
ap-1801	100	29	inequality	inequality	NOUN
ap-1801	100	30	to	to	ADP
ap-1801	100	31	the	the	DET
ap-1801	100	32	resulting	result	VERB
ap-1801	100	33	orthonormal	orthonormal	ADJ
ap-1801	100	34	series	series	NOUN
ap-1801	100	35	:	:	PUNCT
ap-1801	100	36	lemma	lemma	PROPN
ap-1801	100	37	2.4	2.4	NUM
ap-1801	100	38	.	.	PUNCT
ap-1801	101	1	there	there	PRON
ap-1801	101	2	is	be	VERB
ap-1801	101	3	a	a	DET
ap-1801	101	4	constant	constant	ADJ
ap-1801	101	5	c	c	NOUN
ap-1801	101	6	′p	′p	VERB
ap-1801	101	7	such	such	ADJ
ap-1801	101	8	that	that	PRON
ap-1801	101	9	for	for	ADP
ap-1801	101	10	any	any	DET
ap-1801	101	11	orthonormal	orthonormal	ADJ
ap-1801	101	12	system	system	NOUN
ap-1801	101	13	of	of	ADP
ap-1801	101	14	real	real	ADV
ap-1801	101	15	-	-	PUNCT
ap-1801	101	16	valued	value	VERB
ap-1801	101	17	function	function	NOUN
ap-1801	101	18	,	,	PUNCT
ap-1801	101	19	φ	φ	PROPN
ap-1801	101	20	=	=	SYM
ap-1801	101	21	{	{	PUNCT
ap-1801	101	22	ϕj}nj=1	ϕj}nj=1	PROPN
ap-1801	101	23	⊂	⊂	PROPN
ap-1801	101	24	l2(r2	l2(r2	NOUN
ap-1801	101	25	)	)	PUNCT
ap-1801	101	26	,	,	PUNCT
ap-1801	101	27	n	n	NOUN
ap-1801	101	28	=	=	SYM
ap-1801	101	29	1	1	NUM
ap-1801	101	30	,	,	PUNCT
ap-1801	101	31	2	2	NUM
ap-1801	101	32	,	,	PUNCT
ap-1801	101	33	.	.	PUNCT
ap-1801	101	34	.	.	PUNCT
ap-1801	102	1	.	.	PUNCT
ap-1801	103	1	,	,	PUNCT
ap-1801	103	2	the	the	DET
ap-1801	103	3	inequality	inequality	NOUN
ap-1801	103	4	∫	∫	PROPN
ap-1801	103	5	r2	r2	PROPN
ap-1801	103	6	ρp+1	ρp+1	PROPN
ap-1801	103	7	φ	φ	PROPN
ap-1801	103	8	dxdy	dxdy	PROPN
ap-1801	103	9	≤	≤	PROPN
ap-1801	103	10	c	c	PUNCT
ap-1801	104	1	′p(lnpn	′p(lnpn	NOUN
ap-1801	104	2	+	+	CCONJ
ap-1801	104	3	1	1	X
ap-1801	104	4	)	)	PUNCT
ap-1801	104	5	n∑	n∑	NOUN
ap-1801	104	6	j=1	j=1	ADJ
ap-1801	104	7	∫	∫	PROPN
ap-1801	104	8	r2	r2	PROPN
ap-1801	104	9	|ξη|p|ϕ̂j	|ξη|p|ϕ̂j	PROPN
ap-1801	104	10	|2	|2	VERB
ap-1801	105	1	dξ	dξ	ADP
ap-1801	105	2	dη	dη	PROPN
ap-1801	105	3	,	,	PUNCT
ap-1801	105	4	holds	hold	VERB
ap-1801	105	5	true	true	ADJ
ap-1801	105	6	,	,	PUNCT
ap-1801	105	7	where	where	SCONJ
ap-1801	105	8	ρφ	ρφ	NOUN
ap-1801	105	9	:	:	PUNCT
ap-1801	105	10	=	=	SYM
ap-1801	106	1	∑n	∑n	PROPN
ap-1801	106	2	j=1	j=1	PROPN
ap-1801	106	3	ϕ	ϕ	PROPN
ap-1801	106	4	2	2	NUM
ap-1801	106	5	j	j	PROPN
ap-1801	106	6	.	.	PUNCT
ap-1801	107	1	this	this	DET
ap-1801	107	2	claim	claim	NOUN
ap-1801	107	3	was	be	AUX
ap-1801	107	4	proved	prove	VERB
ap-1801	107	5	as	as	ADP
ap-1801	107	6	theorem	theorem	ADJ
ap-1801	107	7	2	2	NUM
ap-1801	107	8	in	in	ADP
ap-1801	107	9	[	[	X
ap-1801	107	10	6	6	NUM
ap-1801	107	11	]	]	PUNCT
ap-1801	107	12	for	for	ADP
ap-1801	107	13	p	p	NOUN
ap-1801	107	14	=	=	SYM
ap-1801	107	15	1	1	NUM
ap-1801	108	1	and	and	CCONJ
ap-1801	108	2	it	it	PRON
ap-1801	108	3	is	be	AUX
ap-1801	108	4	straightforward	straightforward	ADJ
ap-1801	108	5	to	to	PART
ap-1801	108	6	extend	extend	VERB
ap-1801	108	7	the	the	DET
ap-1801	108	8	argument	argument	NOUN
ap-1801	108	9	to	to	ADP
ap-1801	108	10	any	any	DET
ap-1801	108	11	p	p	NOUN
ap-1801	108	12	≥	≥	NOUN
ap-1801	108	13	1	1	NUM
ap-1801	108	14	.	.	PUNCT
ap-1801	109	1	after	after	ADP
ap-1801	109	2	a	a	DET
ap-1801	109	3	few	few	ADJ
ap-1801	109	4	simple	simple	ADJ
ap-1801	109	5	manipulations	manipulation	NOUN
ap-1801	109	6	for	for	ADP
ap-1801	109	7	any	any	DET
ap-1801	109	8	non	non	ADJ
ap-1801	109	9	-	-	ADJ
ap-1801	109	10	negative	negative	ADJ
ap-1801	109	11	parameter	parameter	NOUN
ap-1801	109	12	%	%	INTJ
ap-1801	109	13	we	we	PRON
ap-1801	109	14	get	get	VERB
ap-1801	109	15	c	c	PROPN
ap-1801	109	16	′′p	′′p	NOUN
ap-1801	109	17	(	(	PUNCT
ap-1801	109	18	1	1	NUM
ap-1801	109	19	+	+	NUM
ap-1801	109	20	lnpn)1	lnpn)1	NOUN
ap-1801	109	21	/	/	SYM
ap-1801	109	22	p	p	NOUN
ap-1801	109	23	%	%	NOUN
ap-1801	109	24	(	(	PUNCT
ap-1801	109	25	2p+1)/p	2p+1)/p	NUM
ap-1801	109	26	≥	≥	X
ap-1801	109	27	n%−	n%−	NOUN
ap-1801	109	28	1	1	NUM
ap-1801	109	29	1−	1−	NUM
ap-1801	109	30	αλ	αλ	NUM
ap-1801	109	31	n∑	n∑	NOUN
ap-1801	110	1	j=1	j=1	NOUN
ap-1801	110	2	(	(	PUNCT
ap-1801	110	3	λj	λj	PROPN
ap-1801	110	4	,	,	PUNCT
ap-1801	110	5	p	p	X
ap-1801	110	6	+	+	X
ap-1801	110	7	cλ	cλ	PROPN
ap-1801	110	8	)	)	PUNCT
ap-1801	110	9	273	273	NUM
ap-1801	110	10	p.	p.	NOUN
ap-1801	110	11	exner	exner	NOUN
ap-1801	110	12	,	,	PUNCT
ap-1801	110	13	d.	d.	PROPN
ap-1801	110	14	barseghyan	barseghyan	PROPN
ap-1801	110	15	acta	acta	PROPN
ap-1801	110	16	polytechnica	polytechnica	PROPN
ap-1801	110	17	with	with	ADP
ap-1801	110	18	a	a	DET
ap-1801	110	19	new	new	ADJ
ap-1801	110	20	positive	positive	ADJ
ap-1801	110	21	constant	constant	ADJ
ap-1801	110	22	c	c	NOUN
ap-1801	110	23	′′p	′′p	NOUN
ap-1801	110	24	.	.	PUNCT
ap-1801	111	1	in	in	ADP
ap-1801	111	2	the	the	DET
ap-1801	111	3	final	final	ADJ
ap-1801	111	4	step	step	NOUN
ap-1801	111	5	we	we	PRON
ap-1801	111	6	consider	consider	VERB
ap-1801	111	7	g̃(n	g̃(n	PROPN
ap-1801	111	8	)	)	PUNCT
ap-1801	111	9	=	=	SYM
ap-1801	112	1	max	max	PROPN
ap-1801	112	2	%	%	INTJ
ap-1801	112	3	≥0	≥0	X
ap-1801	112	4	(	(	PUNCT
ap-1801	112	5	n%−	n%−	PRON
ap-1801	112	6	c	c	NOUN
ap-1801	112	7	′′p	′′p	NOUN
ap-1801	113	1	%	%	INTJ
ap-1801	113	2	(	(	PUNCT
ap-1801	113	3	2p+1)/p(1	2p+1)/p(1	NUM
ap-1801	113	4	+	+	CCONJ
ap-1801	113	5	lnpn)1	lnpn)1	PROPN
ap-1801	113	6	/	/	SYM
ap-1801	113	7	p	p	NOUN
ap-1801	113	8	)	)	PUNCT
ap-1801	113	9	.	.	PUNCT
ap-1801	114	1	denoting	denote	VERB
ap-1801	114	2	now	now	ADV
ap-1801	114	3	the	the	DET
ap-1801	114	4	expression	expression	NOUN
ap-1801	114	5	in	in	ADP
ap-1801	114	6	the	the	DET
ap-1801	114	7	bracket	bracket	NOUN
ap-1801	114	8	as	as	ADP
ap-1801	114	9	h(%	h(%	PROPN
ap-1801	114	10	)	)	PUNCT
ap-1801	114	11	we	we	PRON
ap-1801	114	12	check	check	VERB
ap-1801	114	13	easily	easily	ADV
ap-1801	114	14	that	that	PRON
ap-1801	114	15	reaches	reach	VERB
ap-1801	114	16	its	its	PRON
ap-1801	114	17	maximum	maximum	NOUN
ap-1801	114	18	at	at	ADP
ap-1801	114	19	the	the	DET
ap-1801	114	20	point	point	NOUN
ap-1801	114	21	%	%	NOUN
ap-1801	114	22	max	max	PROPN
ap-1801	114	23	=	=	SYM
ap-1801	114	24	(	(	PUNCT
ap-1801	114	25	p/(2p+	p/(2p+	INTJ
ap-1801	114	26	1)c	1)c	NUM
ap-1801	114	27	′′p	′′p	ADJ
ap-1801	114	28	)	)	PUNCT
ap-1801	114	29	p/(p+1	p/(p+1	NOUN
ap-1801	114	30	)	)	PUNCT
ap-1801	114	31	np/(p+1)(1	np/(p+1)(1	NOUN
ap-1801	114	32	+	+	PUNCT
ap-1801	114	33	lnpn)−1/(p+1	lnpn)−1/(p+1	PUNCT
ap-1801	114	34	)	)	PUNCT
ap-1801	114	35	and	and	CCONJ
ap-1801	114	36	its	its	PRON
ap-1801	114	37	value	value	NOUN
ap-1801	114	38	there	there	ADV
ap-1801	114	39	equals	equal	VERB
ap-1801	114	40	g̃(n	g̃(n	PROPN
ap-1801	114	41	)	)	PUNCT
ap-1801	114	42	=	=	SYM
ap-1801	114	43	h(%max	h(%max	NOUN
ap-1801	114	44	)	)	PUNCT
ap-1801	115	1	=	=	SYM
ap-1801	115	2	cp	cp	INTJ
ap-1801	115	3	n	n	PROPN
ap-1801	115	4	(	(	PUNCT
ap-1801	115	5	2p+1)/(p+1	2p+1)/(p+1	NUM
ap-1801	115	6	)	)	PUNCT
ap-1801	115	7	(	(	PUNCT
ap-1801	115	8	1	1	NUM
ap-1801	115	9	+	+	CCONJ
ap-1801	115	10	lnpn)1/(p+1	lnpn)1/(p+1	NOUN
ap-1801	115	11	)	)	PUNCT
ap-1801	115	12	with	with	ADP
ap-1801	115	13	some	some	DET
ap-1801	115	14	constant	constant	ADJ
ap-1801	115	15	cp	cp	INTJ
ap-1801	115	16	>	>	X
ap-1801	115	17	0	0	X
ap-1801	115	18	.	.	PUNCT
ap-1801	116	1	in	in	ADP
ap-1801	116	2	this	this	DET
ap-1801	116	3	way	way	NOUN
ap-1801	116	4	we	we	PRON
ap-1801	116	5	arrive	arrive	VERB
ap-1801	116	6	at	at	ADP
ap-1801	116	7	the	the	DET
ap-1801	116	8	bound	bind	VERB
ap-1801	116	9	1	1	NUM
ap-1801	116	10	1−	1−	NUM
ap-1801	116	11	αpλ	αpλ	NOUN
ap-1801	116	12	n∑	n∑	PROPN
ap-1801	116	13	j=1	j=1	NOUN
ap-1801	116	14	(	(	PUNCT
ap-1801	116	15	λj	λj	PROPN
ap-1801	116	16	,	,	PUNCT
ap-1801	116	17	p	p	NOUN
ap-1801	116	18	+	+	X
ap-1801	116	19	cpλ	cpλ	ADJ
ap-1801	116	20	)	)	PUNCT
ap-1801	116	21	≥	≥	PROPN
ap-1801	116	22	h	h	NOUN
ap-1801	117	1	(	(	PUNCT
ap-1801	117	2	%	%	INTJ
ap-1801	117	3	max	max	PROPN
ap-1801	117	4	)	)	PUNCT
ap-1801	117	5	=	=	SYM
ap-1801	117	6	g̃(n	g̃(n	PROPN
ap-1801	117	7	)	)	PUNCT
ap-1801	117	8	.	.	PUNCT
ap-1801	118	1	which	which	PRON
ap-1801	118	2	is	be	AUX
ap-1801	118	3	equivalent	equivalent	ADJ
ap-1801	118	4	to	to	ADP
ap-1801	118	5	the	the	DET
ap-1801	118	6	claim	claim	NOUN
ap-1801	118	7	of	of	ADP
ap-1801	118	8	the	the	DET
ap-1801	118	9	theorem	theorem	NOUN
ap-1801	118	10	.	.	PROPN
ap-1801	118	11	2.4	2.4	NUM
ap-1801	118	12	.	.	PUNCT
ap-1801	119	1	upper	upper	ADJ
ap-1801	119	2	bounds	bound	NOUN
ap-1801	119	3	next	next	ADV
ap-1801	119	4	we	we	PRON
ap-1801	119	5	estimate	estimate	VERB
ap-1801	119	6	spectral	spectral	ADJ
ap-1801	119	7	sums	sum	NOUN
ap-1801	119	8	of	of	ADP
ap-1801	119	9	lp(λ	lp(λ	NOUN
ap-1801	119	10	)	)	PUNCT
ap-1801	119	11	,	,	PUNCT
ap-1801	119	12	p	p	NOUN
ap-1801	119	13	≥	≥	NUM
ap-1801	119	14	1	1	NUM
ap-1801	119	15	,	,	PUNCT
ap-1801	119	16	from	from	ADP
ap-1801	119	17	above	above	ADP
ap-1801	119	18	for	for	ADP
ap-1801	119	19	any	any	DET
ap-1801	119	20	subcritical	subcritical	ADJ
ap-1801	119	21	λ	λ	NOUN
ap-1801	119	22	.	.	PUNCT
ap-1801	120	1	it	it	PRON
ap-1801	120	2	will	will	AUX
ap-1801	120	3	show	show	VERB
ap-1801	120	4	,	,	PUNCT
ap-1801	120	5	in	in	ADP
ap-1801	120	6	particular	particular	ADJ
ap-1801	120	7	,	,	PUNCT
ap-1801	120	8	that	that	SCONJ
ap-1801	120	9	in	in	ADP
ap-1801	120	10	the	the	DET
ap-1801	120	11	case	case	NOUN
ap-1801	120	12	λ	λ	NOUN
ap-1801	120	13	=	=	SYM
ap-1801	120	14	0	0	NUM
ap-1801	120	15	the	the	DET
ap-1801	120	16	asymptotics	asymptotic	NOUN
ap-1801	120	17	given	give	VERB
ap-1801	120	18	by	by	ADP
ap-1801	120	19	theorem	theorem	ADJ
ap-1801	120	20	2.3	2.3	NUM
ap-1801	120	21	is	be	AUX
ap-1801	120	22	exact	exact	ADJ
ap-1801	120	23	up	up	ADP
ap-1801	120	24	the	the	DET
ap-1801	120	25	value	value	NOUN
ap-1801	120	26	of	of	ADP
ap-1801	120	27	the	the	DET
ap-1801	120	28	constant	constant	ADJ
ap-1801	120	29	.	.	PUNCT
ap-1801	121	1	theorem	theorem	VERB
ap-1801	121	2	2.5	2.5	NUM
ap-1801	121	3	.	.	PUNCT
ap-1801	122	1	to	to	ADP
ap-1801	122	2	any	any	DET
ap-1801	122	3	p	p	PRON
ap-1801	122	4	≥	≥	NUM
ap-1801	122	5	1	1	NUM
ap-1801	122	6	there	there	PRON
ap-1801	122	7	is	be	VERB
ap-1801	122	8	a	a	DET
ap-1801	122	9	constant	constant	ADJ
ap-1801	122	10	c̃p	c̃p	NOUN
ap-1801	122	11	>	>	X
ap-1801	122	12	0	0	NUM
ap-1801	123	1	such	such	ADJ
ap-1801	123	2	that	that	SCONJ
ap-1801	123	3	n∑	n∑	PROPN
ap-1801	123	4	j=1	j=1	PROPN
ap-1801	123	5	λj	λj	PROPN
ap-1801	123	6	,	,	PUNCT
ap-1801	123	7	p	p	PROPN
ap-1801	123	8	≤	≤	ADJ
ap-1801	123	9	c̃p	c̃p	PROPN
ap-1801	123	10	n	n	PROPN
ap-1801	123	11	(	(	PUNCT
ap-1801	123	12	2p+1)/(p+1	2p+1)/(p+1	NUM
ap-1801	123	13	)	)	PUNCT
ap-1801	123	14	(	(	PUNCT
ap-1801	123	15	1	1	NUM
ap-1801	123	16	+	+	CCONJ
ap-1801	123	17	lnpn)1/(p+1	lnpn)1/(p+1	NOUN
ap-1801	123	18	)	)	PUNCT
ap-1801	123	19	,	,	PUNCT
ap-1801	123	20	n	n	NOUN
ap-1801	123	21	=	=	SYM
ap-1801	123	22	1	1	NUM
ap-1801	123	23	,	,	PUNCT
ap-1801	123	24	2	2	NUM
ap-1801	123	25	,	,	PUNCT
ap-1801	123	26	.	.	PUNCT
ap-1801	123	27	.	.	PUNCT
ap-1801	123	28	.	.	PUNCT
ap-1801	124	1	holds	hold	VERB
ap-1801	124	2	for	for	ADP
ap-1801	124	3	any	any	DET
ap-1801	124	4	0	0	NUM
ap-1801	124	5	≤	≤	NUM
ap-1801	124	6	λ	λ	X
ap-1801	124	7	<	<	X
ap-1801	124	8	γp	γp	PROPN
ap-1801	124	9	.	.	PUNCT
ap-1801	124	10	sketch	sketch	NOUN
ap-1801	124	11	of	of	ADP
ap-1801	124	12	the	the	DET
ap-1801	124	13	proof	proof	NOUN
ap-1801	124	14	.	.	PUNCT
ap-1801	125	1	it	it	PRON
ap-1801	125	2	clearly	clearly	ADV
ap-1801	125	3	suffices	suffice	VERB
ap-1801	125	4	to	to	PART
ap-1801	125	5	prove	prove	VERB
ap-1801	125	6	the	the	DET
ap-1801	125	7	claim	claim	NOUN
ap-1801	125	8	for	for	ADP
ap-1801	125	9	λ	λ	PROPN
ap-1801	125	10	=	=	SYM
ap-1801	125	11	0	0	X
ap-1801	125	12	.	.	PUNCT
ap-1801	126	1	consider	consider	VERB
ap-1801	126	2	the	the	DET
ap-1801	126	3	operator	operator	NOUN
ap-1801	126	4	ĥp	ĥp	PROPN
ap-1801	126	5	=	=	SYM
ap-1801	127	1	−∆	−∆	NOUN
ap-1801	127	2	+	+	ADJ
ap-1801	127	3	q	q	ADJ
ap-1801	127	4	,	,	PUNCT
ap-1801	127	5	where	where	SCONJ
ap-1801	127	6	q(x	q(x	PROPN
ap-1801	127	7	,	,	PUNCT
ap-1801	127	8	y	y	NOUN
ap-1801	127	9	)	)	PUNCT
ap-1801	127	10	=	=	SYM
ap-1801	127	11	|xy|p	|xy|p	ADP
ap-1801	127	12	+	+	CCONJ
ap-1801	127	13	|x|p	|x|p	PROPN
ap-1801	127	14	+	+	CCONJ
ap-1801	127	15	|y|p	|y|p	VERB
ap-1801	127	16	+	+	NOUN
ap-1801	127	17	1	1	NUM
ap-1801	127	18	in	in	ADP
ap-1801	127	19	l2(r2	l2(r2	NOUN
ap-1801	127	20	)	)	PUNCT
ap-1801	127	21	.	.	PUNCT
ap-1801	128	1	its	its	PRON
ap-1801	128	2	spectrum	spectrum	NOUN
ap-1801	128	3	is	be	AUX
ap-1801	128	4	discrete	discrete	ADJ
ap-1801	128	5	by	by	ADP
ap-1801	128	6	theorem	theorem	NOUN
ap-1801	128	7	2.1	2.1	NUM
ap-1801	128	8	in	in	ADP
ap-1801	128	9	combination	combination	NOUN
ap-1801	128	10	with	with	ADP
ap-1801	128	11	the	the	DET
ap-1801	128	12	minimax	minimax	NOUN
ap-1801	128	13	principle	principle	NOUN
ap-1801	128	14	since	since	SCONJ
ap-1801	128	15	hp	hp	PROPN
ap-1801	128	16	≥	≥	PROPN
ap-1801	128	17	lp	lp	PROPN
ap-1801	128	18	,	,	PUNCT
ap-1801	128	19	thus	thus	ADV
ap-1801	128	20	we	we	PRON
ap-1801	128	21	have	have	VERB
ap-1801	128	22	to	to	PART
ap-1801	128	23	establish	establish	VERB
ap-1801	128	24	the	the	DET
ap-1801	128	25	bound	bind	VERB
ap-1801	128	26	of	of	ADP
ap-1801	128	27	the	the	DET
ap-1801	128	28	indicated	indicate	VERB
ap-1801	128	29	type	type	NOUN
ap-1801	128	30	for	for	ADP
ap-1801	128	31	the	the	DET
ap-1801	128	32	eigenvalues	eigenvalue	NOUN
ap-1801	129	1	0	0	SYM
ap-1801	129	2	≤	≤	NUM
ap-1801	129	3	β1,p	β1,p	PROPN
ap-1801	129	4	≤	≤	PROPN
ap-1801	129	5	β2,p	β2,p	PROPN
ap-1801	129	6	≤	≤	NOUN
ap-1801	129	7	·	·	PUNCT
ap-1801	129	8	·	·	PUNCT
ap-1801	129	9	·	·	PUNCT
ap-1801	129	10	of	of	ADP
ap-1801	129	11	the	the	DET
ap-1801	129	12	estimating	estimate	VERB
ap-1801	129	13	operator	operator	NOUN
ap-1801	129	14	ĥp	ĥp	PROPN
ap-1801	129	15	.	.	PUNCT
ap-1801	130	1	we	we	PRON
ap-1801	130	2	employ	employ	VERB
ap-1801	130	3	weyl	weyl	VERB
ap-1801	130	4	asymptotics	asymptotic	NOUN
ap-1801	130	5	for	for	ADP
ap-1801	130	6	the	the	DET
ap-1801	130	7	number	number	NOUN
ap-1801	130	8	of	of	ADP
ap-1801	130	9	eigenvalues	eigenvalue	NOUN
ap-1801	130	10	of	of	ADP
ap-1801	130	11	below	below	ADP
ap-1801	130	12	-	-	PUNCT
ap-1801	130	13	bounded	bound	VERB
ap-1801	130	14	differential	differential	NOUN
ap-1801	130	15	operators	operator	NOUN
ap-1801	130	16	in	in	ADP
ap-1801	130	17	a	a	DET
ap-1801	130	18	version	version	NOUN
ap-1801	130	19	due	due	ADP
ap-1801	130	20	to	to	ADP
ap-1801	130	21	g.	g.	PROPN
ap-1801	130	22	rozenblum	rozenblum	PROPN
ap-1801	130	23	.	.	PUNCT
ap-1801	131	1	let	let	VERB
ap-1801	131	2	t	t	NOUN
ap-1801	131	3	=	=	PUNCT
ap-1801	131	4	−∆	−∆	NOUN
ap-1801	131	5	+	+	CCONJ
ap-1801	131	6	v	v	NOUN
ap-1801	131	7	in	in	ADP
ap-1801	131	8	rm	rm	PROPN
ap-1801	131	9	,	,	PUNCT
ap-1801	131	10	where	where	SCONJ
ap-1801	131	11	the	the	DET
ap-1801	131	12	potential	potential	ADJ
ap-1801	131	13	v	v	X
ap-1801	131	14	(	(	PUNCT
ap-1801	131	15	x	x	NOUN
ap-1801	131	16	)	)	PUNCT
ap-1801	131	17	≥	≥	NOUN
ap-1801	131	18	1	1	NUM
ap-1801	131	19	and	and	CCONJ
ap-1801	131	20	tends	tend	VERB
ap-1801	131	21	to	to	PART
ap-1801	131	22	infinity	infinity	VERB
ap-1801	131	23	as	as	ADP
ap-1801	131	24	|x|	|x|	PROPN
ap-1801	131	25	→	→	SYM
ap-1801	131	26	∞.	∞.	PROPN
ap-1801	131	27	we	we	PRON
ap-1801	131	28	denote	denote	VERB
ap-1801	131	29	by	by	ADP
ap-1801	131	30	e(λ	e(λ	PROPN
ap-1801	131	31	,	,	PUNCT
ap-1801	131	32	v	v	NOUN
ap-1801	131	33	)	)	PUNCT
ap-1801	131	34	the	the	DET
ap-1801	131	35	set	set	NOUN
ap-1801	131	36	{	{	PUNCT
ap-1801	131	37	x	x	SYM
ap-1801	131	38	∈	∈	PROPN
ap-1801	131	39	rm	rm	NOUN
ap-1801	131	40	:	:	PUNCT
ap-1801	131	41	v	v	PROPN
ap-1801	131	42	(	(	PUNCT
ap-1801	131	43	x	x	X
ap-1801	131	44	)	)	PUNCT
ap-1801	131	45	<	<	X
ap-1801	131	46	λ	λ	X
ap-1801	131	47	}	}	PUNCT
ap-1801	131	48	and	and	CCONJ
ap-1801	131	49	put	put	VERB
ap-1801	131	50	σ(λ	σ(λ	PROPN
ap-1801	131	51	,	,	PUNCT
ap-1801	131	52	v	v	NOUN
ap-1801	131	53	)	)	PUNCT
ap-1801	132	1	=	=	PUNCT
ap-1801	132	2	mese(λ	mese(λ	PROPN
ap-1801	132	3	,	,	PUNCT
ap-1801	132	4	v	v	NOUN
ap-1801	132	5	)	)	PUNCT
ap-1801	132	6	.	.	PUNCT
ap-1801	133	1	for	for	ADP
ap-1801	133	2	any	any	DET
ap-1801	133	3	unit	unit	NOUN
ap-1801	133	4	cube	cube	NOUN
ap-1801	133	5	d	d	PROPN
ap-1801	133	6	⊂	⊂	PROPN
ap-1801	133	7	rm	rm	PROPN
ap-1801	133	8	we	we	PRON
ap-1801	133	9	denote	denote	VERB
ap-1801	133	10	the	the	DET
ap-1801	133	11	mean	mean	ADJ
ap-1801	133	12	value	value	NOUN
ap-1801	133	13	of	of	ADP
ap-1801	133	14	the	the	DET
ap-1801	133	15	function	function	NOUN
ap-1801	133	16	v	v	NOUN
ap-1801	133	17	in	in	ADP
ap-1801	133	18	d	d	NOUN
ap-1801	133	19	by	by	ADP
ap-1801	133	20	vd	vd	NOUN
ap-1801	133	21	.	.	PUNCT
ap-1801	134	1	furthermore	furthermore	ADV
ap-1801	134	2	,	,	PUNCT
ap-1801	134	3	given	give	VERB
ap-1801	134	4	a	a	DET
ap-1801	134	5	function	function	NOUN
ap-1801	134	6	f	f	PROPN
ap-1801	134	7	∈	∈	PROPN
ap-1801	134	8	l1(d	l1(d	X
ap-1801	134	9	)	)	PUNCT
ap-1801	134	10	and	and	CCONJ
ap-1801	134	11	t	t	X
ap-1801	134	12	≤	≤	NUM
ap-1801	134	13	√	√	NUM
ap-1801	134	14	m	m	VERB
ap-1801	134	15	we	we	PRON
ap-1801	134	16	define	define	VERB
ap-1801	134	17	its	its	PRON
ap-1801	134	18	l1	l1	NOUN
ap-1801	134	19	-	-	PUNCT
ap-1801	134	20	modulus	modulus	NOUN
ap-1801	134	21	of	of	ADP
ap-1801	134	22	continuity	continuity	NOUN
ap-1801	134	23	by	by	ADP
ap-1801	134	24	the	the	DET
ap-1801	134	25	formula	formula	NOUN
ap-1801	134	26	ω1(f	ω1(f	PROPN
ap-1801	134	27	,	,	PUNCT
ap-1801	134	28	t	t	PROPN
ap-1801	134	29	,	,	PUNCT
ap-1801	134	30	d	d	PROPN
ap-1801	134	31	)	)	PUNCT
ap-1801	134	32	:	:	PUNCT
ap-1801	134	33	=	=	SYM
ap-1801	134	34	sup	sup	PROPN
ap-1801	134	35	|z|<t	|z|<t	PROPN
ap-1801	134	36	∫	∫	PROPN
ap-1801	134	37	x∈d	x∈d	PROPN
ap-1801	134	38	,	,	PUNCT
ap-1801	134	39	x+z∈d	x+z∈d	PROPN
ap-1801	134	40	∣∣f(x+	∣∣f(x+	PROPN
ap-1801	134	41	z)−	z)−	PROPN
ap-1801	134	42	f(x	f(x	PROPN
ap-1801	134	43	)	)	PUNCT
ap-1801	134	44	∣∣dx	∣∣dx	NOUN
ap-1801	134	45	.	.	PUNCT
ap-1801	135	1	then	then	ADV
ap-1801	135	2	we	we	PRON
ap-1801	135	3	have	have	VERB
ap-1801	135	4	the	the	DET
ap-1801	135	5	following	following	ADJ
ap-1801	135	6	result	result	NOUN
ap-1801	135	7	[	[	X
ap-1801	135	8	7	7	NUM
ap-1801	135	9	]	]	PUNCT
ap-1801	135	10	:	:	PUNCT
ap-1801	135	11	lemma	lemma	PROPN
ap-1801	135	12	2.6	2.6	NUM
ap-1801	135	13	.	.	PUNCT
ap-1801	135	14	suppose	suppose	VERB
ap-1801	135	15	that	that	SCONJ
ap-1801	135	16	the	the	DET
ap-1801	135	17	potential	potential	NOUN
ap-1801	135	18	v	v	NOUN
ap-1801	135	19	satisfies	satisfy	VERB
ap-1801	135	20	the	the	DET
ap-1801	135	21	conditions	condition	NOUN
ap-1801	135	22	:	:	PUNCT
ap-1801	135	23	(	(	PUNCT
ap-1801	135	24	1	1	NUM
ap-1801	135	25	.	.	PUNCT
ap-1801	135	26	)	)	PUNCT
ap-1801	136	1	there	there	PRON
ap-1801	136	2	is	be	VERB
ap-1801	136	3	c	c	NOUN
ap-1801	136	4	>	>	X
ap-1801	136	5	0	0	NUM
ap-1801	136	6	such	such	ADJ
ap-1801	136	7	that	that	SCONJ
ap-1801	136	8	σ(2λ	σ(2λ	NOUN
ap-1801	136	9	,	,	PUNCT
ap-1801	136	10	v	v	NOUN
ap-1801	136	11	)	)	PUNCT
ap-1801	136	12	≤	≤	NOUN
ap-1801	136	13	cσ(λ	cσ(λ	NOUN
ap-1801	136	14	,	,	PUNCT
ap-1801	136	15	v	v	NOUN
ap-1801	136	16	)	)	PUNCT
ap-1801	136	17	holds	hold	VERB
ap-1801	136	18	all	all	DET
ap-1801	136	19	λ	λ	NOUN
ap-1801	136	20	large	large	ADJ
ap-1801	136	21	enough	enough	ADV
ap-1801	136	22	.	.	PUNCT
ap-1801	137	1	(	(	PUNCT
ap-1801	137	2	2	2	NUM
ap-1801	137	3	.	.	NUM
ap-1801	137	4	)	)	PUNCT
ap-1801	138	1	v	v	X
ap-1801	138	2	(	(	PUNCT
ap-1801	138	3	y	y	NOUN
ap-1801	138	4	)	)	PUNCT
ap-1801	138	5	≤	≤	NOUN
ap-1801	138	6	cv	cv	PROPN
ap-1801	138	7	(	(	PUNCT
ap-1801	138	8	x	x	NOUN
ap-1801	138	9	)	)	PUNCT
ap-1801	138	10	holds	hold	VERB
ap-1801	138	11	if	if	SCONJ
ap-1801	138	12	as	as	SCONJ
ap-1801	138	13	|x−	|x−	NOUN
ap-1801	138	14	y|	y|	NOUN
ap-1801	138	15	≤	≤	NOUN
ap-1801	138	16	1	1	NUM
ap-1801	138	17	.	.	PUNCT
ap-1801	139	1	(	(	PUNCT
ap-1801	139	2	3	3	NUM
ap-1801	139	3	.	.	PUNCT
ap-1801	139	4	)	)	PUNCT
ap-1801	140	1	there	there	PRON
ap-1801	140	2	is	be	VERB
ap-1801	140	3	a	a	DET
ap-1801	140	4	continuous	continuous	ADJ
ap-1801	140	5	and	and	CCONJ
ap-1801	140	6	monotonous	monotonous	ADJ
ap-1801	140	7	function	function	NOUN
ap-1801	140	8	η	η	PROPN
ap-1801	140	9	:	:	PUNCT
ap-1801	140	10	t	t	PROPN
ap-1801	140	11	∈	∈	PROPN
ap-1801	141	1	[	[	X
ap-1801	141	2	0	0	NUM
ap-1801	141	3	,	,	PUNCT
ap-1801	141	4	√	√	ADV
ap-1801	141	5	m	m	VERB
ap-1801	141	6	]	]	PUNCT
ap-1801	141	7	→	→	PUNCT
ap-1801	141	8	r+	r+	NOUN
ap-1801	141	9	with	with	ADP
ap-1801	141	10	η(0	η(0	PROPN
ap-1801	141	11	)	)	PUNCT
ap-1801	142	1	=	=	SYM
ap-1801	142	2	0	0	NUM
ap-1801	142	3	and	and	CCONJ
ap-1801	142	4	a	a	DET
ap-1801	142	5	number	number	NOUN
ap-1801	142	6	β	β	X
ap-1801	142	7	∈	∈	PROPN
ap-1801	143	1	[	[	X
ap-1801	143	2	0	0	NUM
ap-1801	143	3	,	,	PUNCT
ap-1801	143	4	1	1	NUM
ap-1801	143	5	2	2	NUM
ap-1801	143	6	)	)	PUNCT
ap-1801	143	7	such	such	ADJ
ap-1801	143	8	that	that	PRON
ap-1801	143	9	for	for	ADP
ap-1801	143	10	any	any	DET
ap-1801	143	11	unit	unit	NOUN
ap-1801	143	12	square	square	PROPN
ap-1801	144	1	d	d	INTJ
ap-1801	144	2	we	we	PRON
ap-1801	144	3	have	have	VERB
ap-1801	144	4	ω1(v	ω1(v	NUM
ap-1801	144	5	,	,	PUNCT
ap-1801	144	6	t	t	PROPN
ap-1801	144	7	,	,	PUNCT
ap-1801	144	8	d	d	NOUN
ap-1801	144	9	)	)	PUNCT
ap-1801	144	10	≤	≤	NUM
ap-1801	144	11	η(t	η(t	NOUN
ap-1801	144	12	)	)	PUNCT
ap-1801	144	13	t2β	t2β	PROPN
ap-1801	144	14	v	v	ADP
ap-1801	144	15	1+β	1+β	PROPN
ap-1801	145	1	d	d	NOUN
ap-1801	145	2	.	.	PUNCT
ap-1801	146	1	274	274	NUM
ap-1801	146	2	vol	vol	NOUN
ap-1801	146	3	.	.	PUNCT
ap-1801	147	1	53	53	NUM
ap-1801	147	2	no	no	NOUN
ap-1801	147	3	.	.	PUNCT
ap-1801	148	1	3/2013	3/2013	PROPN
ap-1801	148	2	spectral	spectral	ADJ
ap-1801	148	3	analysis	analysis	NOUN
ap-1801	148	4	of	of	ADP
ap-1801	148	5	schrödinger	schrödinger	ADJ
ap-1801	148	6	operators	operator	NOUN
ap-1801	148	7	under	under	ADP
ap-1801	148	8	these	these	DET
ap-1801	148	9	assumptions	assumption	NOUN
ap-1801	148	10	the	the	DET
ap-1801	148	11	asymptotic	asymptotic	ADJ
ap-1801	148	12	formula	formula	NOUN
ap-1801	148	13	n(λ	n(λ	PROPN
ap-1801	148	14	,	,	PUNCT
ap-1801	148	15	v	v	NOUN
ap-1801	148	16	)	)	PUNCT
ap-1801	148	17	∼	∼	NOUN
ap-1801	148	18	γmφ(λ	γmφ(λ	PROPN
ap-1801	148	19	,	,	PUNCT
ap-1801	148	20	v	v	NOUN
ap-1801	148	21	)	)	PUNCT
ap-1801	148	22	holds	hold	VERB
ap-1801	148	23	for	for	ADP
ap-1801	148	24	the	the	DET
ap-1801	148	25	operator	operator	NOUN
ap-1801	148	26	t	t	NOUN
ap-1801	148	27	=	=	SYM
ap-1801	149	1	−4	−4	PROPN
ap-1801	149	2	+	+	X
ap-1801	149	3	v	v	NOUN
ap-1801	149	4	,	,	PUNCT
ap-1801	149	5	where	where	SCONJ
ap-1801	149	6	n(λ	n(λ	PROPN
ap-1801	149	7	,	,	PUNCT
ap-1801	149	8	v	v	NOUN
ap-1801	149	9	)	)	PUNCT
ap-1801	149	10	is	be	AUX
ap-1801	149	11	the	the	DET
ap-1801	149	12	number	number	NOUN
ap-1801	149	13	of	of	ADP
ap-1801	149	14	eigenvalues	eigenvalue	NOUN
ap-1801	149	15	of	of	ADP
ap-1801	149	16	t	t	NOUN
ap-1801	149	17	smaller	small	ADJ
ap-1801	149	18	than	than	ADP
ap-1801	149	19	λ	λ	PROPN
ap-1801	149	20	,	,	PUNCT
ap-1801	149	21	unit	unit	NOUN
ap-1801	149	22	-	-	PUNCT
ap-1801	149	23	ball	ball	NOUN
ap-1801	149	24	volume	volume	NOUN
ap-1801	149	25	γm	γm	X
ap-1801	149	26	=	=	SYM
ap-1801	149	27	(	(	PUNCT
ap-1801	149	28	2	2	NUM
ap-1801	149	29	√	√	NUM
ap-1801	149	30	π)−m	π)−m	NUM
ap-1801	149	31	(	(	PUNCT
ap-1801	149	32	γ(m2	γ(m2	X
ap-1801	150	1	+	+	CCONJ
ap-1801	150	2	1	1	NUM
ap-1801	150	3	)	)	PUNCT
ap-1801	150	4	)	)	PUNCT
ap-1801	151	1	−1	−1	NOUN
ap-1801	151	2	,	,	PUNCT
ap-1801	151	3	and	and	CCONJ
ap-1801	151	4	φ(λ	φ(λ	PROPN
ap-1801	151	5	,	,	PUNCT
ap-1801	151	6	v	v	NOUN
ap-1801	151	7	)	)	PUNCT
ap-1801	151	8	=	=	SYM
ap-1801	152	1	∫	∫	PROPN
ap-1801	152	2	r2	r2	PROPN
ap-1801	152	3	(	(	PUNCT
ap-1801	152	4	λ−	λ−	PROPN
ap-1801	152	5	v	v	PROPN
ap-1801	152	6	)	)	PUNCT
ap-1801	152	7	m/2	m/2	NUM
ap-1801	152	8	+	+	CCONJ
ap-1801	152	9	dxdy	dxdy	NOUN
ap-1801	152	10	.	.	PUNCT
ap-1801	153	1	it	it	PRON
ap-1801	153	2	is	be	AUX
ap-1801	153	3	straightforward	straightforward	ADJ
ap-1801	153	4	to	to	PART
ap-1801	153	5	check	check	VERB
ap-1801	153	6	the	the	DET
ap-1801	153	7	hypotheses	hypothesis	NOUN
ap-1801	153	8	of	of	ADP
ap-1801	153	9	the	the	DET
ap-1801	153	10	lemma	lemma	PROPN
ap-1801	153	11	for	for	ADP
ap-1801	153	12	the	the	DET
ap-1801	153	13	operator	operator	NOUN
ap-1801	153	14	ĥp	ĥp	PROPN
ap-1801	153	15	,	,	PUNCT
ap-1801	153	16	which	which	PRON
ap-1801	153	17	gives	give	VERB
ap-1801	153	18	an	an	DET
ap-1801	153	19	asymptotic	asymptotic	ADJ
ap-1801	153	20	formula	formula	NOUN
ap-1801	153	21	for	for	ADP
ap-1801	153	22	spectral	spectral	ADJ
ap-1801	153	23	distribution	distribution	NOUN
ap-1801	153	24	function	function	NOUN
ap-1801	153	25	n(λ	n(λ	PROPN
ap-1801	153	26	,	,	PUNCT
ap-1801	153	27	ĥp	ĥp	NUM
ap-1801	153	28	)	)	PUNCT
ap-1801	153	29	.	.	PUNCT
ap-1801	154	1	after	after	ADP
ap-1801	154	2	some	some	DET
ap-1801	154	3	simple	simple	ADJ
ap-1801	154	4	estimates	estimate	NOUN
ap-1801	154	5	[	[	X
ap-1801	154	6	3	3	X
ap-1801	154	7	]	]	PUNCT
ap-1801	154	8	we	we	PRON
ap-1801	154	9	arrive	arrive	VERB
ap-1801	154	10	at	at	ADP
ap-1801	154	11	the	the	DET
ap-1801	154	12	following	follow	VERB
ap-1801	154	13	upper	upper	NOUN
ap-1801	154	14	bound	bind	VERB
ap-1801	154	15	on	on	ADP
ap-1801	154	16	the	the	DET
ap-1801	154	17	spectrum	spectrum	NOUN
ap-1801	154	18	of	of	ADP
ap-1801	154	19	the	the	DET
ap-1801	154	20	operator	operator	NOUN
ap-1801	154	21	ĥp	ĥp	PROPN
ap-1801	154	22	,	,	PUNCT
ap-1801	154	23	n∑	n∑	PROPN
ap-1801	154	24	j=1	j=1	PROPN
ap-1801	154	25	βj	βj	X
ap-1801	154	26	,	,	PUNCT
ap-1801	154	27	p	p	NOUN
ap-1801	154	28	≤	≤	ADJ
ap-1801	154	29	c̃p	c̃p	PROPN
ap-1801	154	30	n	n	PROPN
ap-1801	154	31	(	(	PUNCT
ap-1801	154	32	2p+1)/(p+1	2p+1)/(p+1	NUM
ap-1801	154	33	)	)	PUNCT
ap-1801	154	34	(	(	PUNCT
ap-1801	154	35	lnn	lnn	NOUN
ap-1801	154	36	+	+	NOUN
ap-1801	154	37	1)p/(p+1	1)p/(p+1	NUM
ap-1801	154	38	)	)	PUNCT
ap-1801	154	39	with	with	ADP
ap-1801	154	40	a	a	DET
ap-1801	154	41	constant	constant	ADJ
ap-1801	154	42	c̃p	c̃p	NOUN
ap-1801	154	43	depending	depend	VERB
ap-1801	154	44	on	on	ADP
ap-1801	154	45	p	p	NOUN
ap-1801	154	46	only	only	ADV
ap-1801	154	47	;	;	PUNCT
ap-1801	154	48	this	this	PRON
ap-1801	154	49	proves	prove	VERB
ap-1801	154	50	the	the	DET
ap-1801	154	51	theorem	theorem	NOUN
ap-1801	154	52	.	.	PROPN
ap-1801	155	1	3	3	X
ap-1801	155	2	.	.	X
ap-1801	155	3	schrödinger	schrödinger	ADJ
ap-1801	155	4	operators	operator	NOUN
ap-1801	155	5	in	in	ADP
ap-1801	155	6	cusps	cusps	NOUN
ap-1801	155	7	with	with	ADP
ap-1801	155	8	non	non	ADJ
ap-1801	155	9	-	-	ADJ
ap-1801	155	10	trivial	trivial	ADJ
ap-1801	155	11	geometry	geometry	NOUN
ap-1801	155	12	in	in	ADP
ap-1801	155	13	the	the	DET
ap-1801	155	14	second	second	ADJ
ap-1801	155	15	part	part	NOUN
ap-1801	155	16	of	of	ADP
ap-1801	155	17	the	the	DET
ap-1801	155	18	paper	paper	NOUN
ap-1801	155	19	we	we	PRON
ap-1801	155	20	shall	shall	AUX
ap-1801	155	21	discuss	discuss	VERB
ap-1801	155	22	schrödinger	schrödinger	ADJ
ap-1801	155	23	type	type	NOUN
ap-1801	155	24	operators	operator	NOUN
ap-1801	155	25	hω	hω	ADP
ap-1801	155	26	=	=	SYM
ap-1801	155	27	−∆ω	−∆ω	NOUN
ap-1801	155	28	d	d	NOUN
ap-1801	155	29	−	−	PROPN
ap-1801	155	30	v	v	NOUN
ap-1801	155	31	(	(	PUNCT
ap-1801	155	32	3.1	3.1	NUM
ap-1801	155	33	)	)	PUNCT
ap-1801	155	34	with	with	ADP
ap-1801	155	35	a	a	DET
ap-1801	155	36	bounded	bound	VERB
ap-1801	155	37	measurable	measurable	ADJ
ap-1801	155	38	potential	potential	NOUN
ap-1801	155	39	v	v	ADP
ap-1801	155	40	≥	≥	NOUN
ap-1801	155	41	0	0	NUM
ap-1801	155	42	on	on	ADP
ap-1801	155	43	l2(ω	l2(ω	PROPN
ap-1801	155	44	)	)	PUNCT
ap-1801	155	45	,	,	PUNCT
ap-1801	155	46	where	where	SCONJ
ap-1801	155	47	−∆ω	−∆ω	NOUN
ap-1801	155	48	d	d	NOUN
ap-1801	155	49	is	be	AUX
ap-1801	155	50	the	the	DET
ap-1801	155	51	dirichlet	dirichlet	PROPN
ap-1801	155	52	laplacian	laplacian	NOUN
ap-1801	155	53	on	on	ADP
ap-1801	155	54	a	a	DET
ap-1801	155	55	region	region	NOUN
ap-1801	156	1	ω	ω	PROPN
ap-1801	156	2	⊂	⊂	PROPN
ap-1801	156	3	rd	rd	PROPN
ap-1801	156	4	.	.	PROPN
ap-1801	157	1	in	in	ADP
ap-1801	157	2	the	the	DET
ap-1801	157	3	spirit	spirit	NOUN
ap-1801	157	4	of	of	ADP
ap-1801	157	5	the	the	DET
ap-1801	157	6	previous	previous	ADJ
ap-1801	157	7	considerations	consideration	NOUN
ap-1801	157	8	we	we	PRON
ap-1801	157	9	will	will	AUX
ap-1801	157	10	be	be	AUX
ap-1801	157	11	particularly	particularly	ADV
ap-1801	157	12	interested	interested	ADJ
ap-1801	157	13	in	in	ADP
ap-1801	157	14	situations	situation	NOUN
ap-1801	157	15	where	where	SCONJ
ap-1801	157	16	ω	ω	NOUN
ap-1801	157	17	is	be	AUX
ap-1801	157	18	unbounded	unbounded	ADJ
ap-1801	157	19	but	but	CCONJ
ap-1801	157	20	hω	hω	ADP
ap-1801	157	21	still	still	ADV
ap-1801	157	22	has	have	VERB
ap-1801	157	23	a	a	DET
ap-1801	157	24	purely	purely	ADV
ap-1801	157	25	discrete	discrete	ADJ
ap-1801	157	26	spectrum	spectrum	NOUN
ap-1801	157	27	.	.	PUNCT
ap-1801	158	1	it	it	PRON
ap-1801	158	2	is	be	AUX
ap-1801	158	3	well	well	ADV
ap-1801	158	4	known	known	ADJ
ap-1801	158	5	[	[	X
ap-1801	158	6	1	1	NUM
ap-1801	158	7	,	,	PUNCT
ap-1801	158	8	9	9	NUM
ap-1801	158	9	]	]	PUNCT
ap-1801	158	10	that	that	SCONJ
ap-1801	158	11	for	for	ADP
ap-1801	158	12	some	some	DET
ap-1801	158	13	unbounded	unbounded	ADJ
ap-1801	158	14	regions	region	NOUN
ap-1801	158	15	the	the	DET
ap-1801	158	16	spectrum	spectrum	NOUN
ap-1801	158	17	may	may	AUX
ap-1801	158	18	be	be	AUX
ap-1801	158	19	purely	purely	ADV
ap-1801	158	20	discrete	discrete	ADJ
ap-1801	158	21	;	;	PUNCT
ap-1801	158	22	typically	typically	ADV
ap-1801	158	23	this	this	PRON
ap-1801	158	24	happens	happen	VERB
ap-1801	158	25	if	if	SCONJ
ap-1801	158	26	ω	ω	NOUN
ap-1801	158	27	has	have	VERB
ap-1801	158	28	cusps	cusps	NOUN
ap-1801	158	29	.	.	PUNCT
ap-1801	159	1	the	the	DET
ap-1801	159	2	negative	negative	ADJ
ap-1801	159	3	spectrum	spectrum	NOUN
ap-1801	159	4	of	of	ADP
ap-1801	159	5	hω	hω	ADP
ap-1801	159	6	consists	consist	NOUN
ap-1801	159	7	of	of	ADP
ap-1801	159	8	a	a	DET
ap-1801	159	9	finite	finite	ADJ
ap-1801	159	10	number	number	NOUN
ap-1801	159	11	of	of	ADP
ap-1801	159	12	eigenvalues	eigenvalue	NOUN
ap-1801	159	13	counted	count	VERB
ap-1801	159	14	with	with	ADP
ap-1801	159	15	their	their	PRON
ap-1801	159	16	multiplicities	multiplicity	NOUN
ap-1801	159	17	;	;	PUNCT
ap-1801	159	18	it	it	PRON
ap-1801	159	19	is	be	AUX
ap-1801	159	20	natural	natural	ADJ
ap-1801	159	21	to	to	PART
ap-1801	159	22	ask	ask	VERB
ap-1801	159	23	about	about	ADP
ap-1801	159	24	bounds	bound	NOUN
ap-1801	159	25	on	on	ADP
ap-1801	159	26	the	the	DET
ap-1801	159	27	negative	negative	ADJ
ap-1801	159	28	spectrum	spectrum	NOUN
ap-1801	159	29	moments	moment	NOUN
ap-1801	159	30	in	in	ADP
ap-1801	159	31	terms	term	NOUN
ap-1801	159	32	of	of	ADP
ap-1801	159	33	their	their	PRON
ap-1801	159	34	geometrical	geometrical	ADJ
ap-1801	159	35	properties	property	NOUN
ap-1801	159	36	,	,	PUNCT
ap-1801	159	37	in	in	ADP
ap-1801	159	38	the	the	DET
ap-1801	159	39	spirit	spirit	NOUN
ap-1801	159	40	the	the	DET
ap-1801	159	41	seminal	seminal	ADJ
ap-1801	159	42	work	work	NOUN
ap-1801	159	43	of	of	ADP
ap-1801	159	44	lieb	lieb	PROPN
ap-1801	159	45	and	and	CCONJ
ap-1801	159	46	thirring	thirre	VERB
ap-1801	159	47	[	[	X
ap-1801	159	48	10	10	NUM
ap-1801	159	49	]	]	PUNCT
ap-1801	159	50	,	,	PUNCT
ap-1801	159	51	or	or	CCONJ
ap-1801	159	52	in	in	ADP
ap-1801	159	53	the	the	DET
ap-1801	159	54	present	present	ADJ
ap-1801	159	55	context	context	NOUN
ap-1801	159	56	referring	refer	VERB
ap-1801	159	57	to	to	ADP
ap-1801	159	58	berezin	berezin	PROPN
ap-1801	159	59	,	,	PUNCT
ap-1801	159	60	lieb	lieb	PROPN
ap-1801	159	61	,	,	PUNCT
ap-1801	159	62	li	li	PROPN
ap-1801	159	63	and	and	CCONJ
ap-1801	159	64	yau	yau	PROPN
ap-1801	160	1	[	[	X
ap-1801	160	2	11–14	11–14	NUM
ap-1801	160	3	]	]	PUNCT
ap-1801	160	4	.	.	PUNCT
ap-1801	161	1	note	note	VERB
ap-1801	161	2	that	that	SCONJ
ap-1801	161	3	estimates	estimate	NOUN
ap-1801	161	4	of	of	ADP
ap-1801	161	5	this	this	DET
ap-1801	161	6	type	type	NOUN
ap-1801	161	7	have	have	AUX
ap-1801	161	8	been	be	AUX
ap-1801	161	9	derived	derive	VERB
ap-1801	161	10	recently	recently	ADV
ap-1801	161	11	in	in	ADP
ap-1801	161	12	[	[	X
ap-1801	161	13	5	5	NUM
ap-1801	161	14	]	]	PUNCT
ap-1801	161	15	for	for	ADP
ap-1801	161	16	various	various	ADJ
ap-1801	161	17	cusped	cusped	ADJ
ap-1801	161	18	regions	region	NOUN
ap-1801	161	19	;	;	PUNCT
ap-1801	161	20	a	a	DET
ap-1801	161	21	typical	typical	ADJ
ap-1801	161	22	example	example	NOUN
ap-1801	161	23	is	be	AUX
ap-1801	161	24	ω	ω	NOUN
ap-1801	161	25	=	=	SYM
ap-1801	161	26	{	{	PUNCT
ap-1801	161	27	(	(	PUNCT
ap-1801	161	28	x	x	NOUN
ap-1801	161	29	,	,	PUNCT
ap-1801	161	30	y	y	NOUN
ap-1801	161	31	)	)	PUNCT
ap-1801	161	32	∈	∈	PROPN
ap-1801	161	33	r2	r2	NOUN
ap-1801	161	34	:	:	PUNCT
ap-1801	161	35	|xy|	|xy|	NOUN
ap-1801	161	36	<	<	X
ap-1801	161	37	1	1	NUM
ap-1801	161	38	}	}	PUNCT
ap-1801	161	39	with	with	ADP
ap-1801	161	40	hyperbolic	hyperbolic	ADJ
ap-1801	161	41	ends	end	NOUN
ap-1801	161	42	.	.	PUNCT
ap-1801	162	1	our	our	PRON
ap-1801	162	2	goal	goal	NOUN
ap-1801	162	3	is	be	AUX
ap-1801	162	4	to	to	PART
ap-1801	162	5	discuss	discuss	VERB
ap-1801	162	6	situations	situation	NOUN
ap-1801	162	7	when	when	SCONJ
ap-1801	162	8	such	such	ADJ
ap-1801	162	9	infinite	infinite	ADJ
ap-1801	162	10	cusps	cusps	NOUN
ap-1801	162	11	of	of	ADP
ap-1801	162	12	ω	ω	PROPN
ap-1801	162	13	are	be	AUX
ap-1801	162	14	geometrically	geometrically	ADV
ap-1801	162	15	nontrivial	nontrivial	ADJ
ap-1801	162	16	,	,	PUNCT
ap-1801	162	17	being	be	AUX
ap-1801	162	18	curved	curve	VERB
ap-1801	162	19	or	or	CCONJ
ap-1801	162	20	twisted	twisted	ADJ
ap-1801	162	21	,	,	PUNCT
ap-1801	162	22	to	to	PART
ap-1801	162	23	see	see	VERB
ap-1801	162	24	in	in	ADP
ap-1801	162	25	which	which	DET
ap-1801	162	26	way	way	NOUN
ap-1801	162	27	the	the	DET
ap-1801	162	28	geometry	geometry	NOUN
ap-1801	162	29	influences	influence	VERB
ap-1801	162	30	the	the	DET
ap-1801	162	31	spectral	spectral	ADJ
ap-1801	162	32	estimates	estimate	NOUN
ap-1801	162	33	.	.	PUNCT
ap-1801	163	1	first	first	ADV
ap-1801	163	2	we	we	PRON
ap-1801	163	3	will	will	AUX
ap-1801	163	4	discuss	discuss	VERB
ap-1801	163	5	a	a	DET
ap-1801	163	6	curved	curved	ADJ
ap-1801	163	7	planar	planar	ADJ
ap-1801	163	8	cusp	cusp	NOUN
ap-1801	163	9	and	and	CCONJ
ap-1801	163	10	derive	derive	ADJ
ap-1801	163	11	estimates	estimate	NOUN
ap-1801	163	12	on	on	ADP
ap-1801	163	13	negative	negative	ADJ
ap-1801	163	14	spectrum	spectrum	NOUN
ap-1801	163	15	moments	moment	NOUN
ap-1801	163	16	which	which	PRON
ap-1801	163	17	include	include	VERB
ap-1801	163	18	a	a	DET
ap-1801	163	19	curvature	curvature	NOUN
ap-1801	163	20	-	-	PUNCT
ap-1801	163	21	induced	induce	VERB
ap-1801	163	22	potential	potential	NOUN
ap-1801	163	23	.	.	PUNCT
ap-1801	164	1	this	this	DET
ap-1801	164	2	result	result	NOUN
ap-1801	164	3	can	can	AUX
ap-1801	164	4	be	be	AUX
ap-1801	164	5	generalized	generalize	VERB
ap-1801	164	6	for	for	ADP
ap-1801	164	7	bent	bent	ADJ
ap-1801	164	8	cusps	cusps	NOUN
ap-1801	164	9	with	with	ADP
ap-1801	164	10	a	a	DET
ap-1801	164	11	circular	circular	ADJ
ap-1801	164	12	cross	cross	NOUN
ap-1801	164	13	section	section	NOUN
ap-1801	164	14	;	;	PUNCT
ap-1801	164	15	we	we	PRON
ap-1801	164	16	refer	refer	VERB
ap-1801	164	17	to	to	ADP
ap-1801	164	18	[	[	X
ap-1801	164	19	4	4	X
ap-1801	164	20	]	]	PUNCT
ap-1801	164	21	for	for	ADP
ap-1801	164	22	a	a	DET
ap-1801	164	23	description	description	NOUN
ap-1801	164	24	.	.	PUNCT
ap-1801	165	1	then	then	ADV
ap-1801	165	2	,	,	PUNCT
ap-1801	165	3	in	in	ADP
ap-1801	165	4	section	section	NOUN
ap-1801	165	5	3.2	3.2	NUM
ap-1801	165	6	,	,	PUNCT
ap-1801	165	7	we	we	PRON
ap-1801	165	8	will	will	AUX
ap-1801	165	9	consider	consider	VERB
ap-1801	165	10	cusps	cusps	NOUN
ap-1801	165	11	of	of	ADP
ap-1801	165	12	a	a	DET
ap-1801	165	13	non	non	ADJ
ap-1801	165	14	-	-	ADJ
ap-1801	165	15	circular	circular	ADJ
ap-1801	165	16	cross	cross	NOUN
ap-1801	165	17	section	section	NOUN
ap-1801	165	18	in	in	ADP
ap-1801	165	19	r3	r3	PROPN
ap-1801	165	20	which	which	PRON
ap-1801	165	21	are	be	AUX
ap-1801	165	22	straight	straight	ADJ
ap-1801	165	23	but	but	CCONJ
ap-1801	165	24	twisted	twisted	ADJ
ap-1801	165	25	.	.	PUNCT
ap-1801	166	1	the	the	DET
ap-1801	166	2	geometry	geometry	NOUN
ap-1801	166	3	of	of	ADP
ap-1801	166	4	the	the	DET
ap-1801	166	5	region	region	NOUN
ap-1801	166	6	will	will	AUX
ap-1801	166	7	again	again	ADV
ap-1801	166	8	be	be	AUX
ap-1801	166	9	involved	involve	VERB
ap-1801	166	10	in	in	ADP
ap-1801	166	11	the	the	DET
ap-1801	166	12	obtained	obtain	VERB
ap-1801	166	13	eigenvalue	eigenvalue	PROPN
ap-1801	166	14	estimates	estimate	NOUN
ap-1801	166	15	,	,	PUNCT
ap-1801	166	16	now	now	ADV
ap-1801	166	17	in	in	ADP
ap-1801	166	18	a	a	DET
ap-1801	166	19	different	different	ADJ
ap-1801	166	20	way	way	NOUN
ap-1801	166	21	than	than	ADP
ap-1801	166	22	for	for	ADP
ap-1801	166	23	curved	curved	ADJ
ap-1801	166	24	cusps	cusps	NOUN
ap-1801	166	25	,	,	PUNCT
ap-1801	166	26	because	because	SCONJ
ap-1801	166	27	the	the	DET
ap-1801	166	28	effective	effective	ADJ
ap-1801	166	29	interaction	interaction	NOUN
ap-1801	166	30	associated	associate	VERB
ap-1801	166	31	with	with	ADP
ap-1801	166	32	twisting	twisting	NOUN
ap-1801	166	33	is	be	AUX
ap-1801	166	34	repulsive	repulsive	ADJ
ap-1801	166	35	rather	rather	ADV
ap-1801	166	36	than	than	ADP
ap-1801	166	37	attractive	attractive	ADJ
ap-1801	166	38	.	.	PUNCT
ap-1801	167	1	3.1	3.1	NUM
ap-1801	167	2	.	.	PUNCT
ap-1801	168	1	curved	curve	VERB
ap-1801	168	2	planar	planar	ADJ
ap-1801	168	3	cusps	cusps	NOUN
ap-1801	168	4	we	we	PRON
ap-1801	168	5	consider	consider	VERB
ap-1801	168	6	an	an	DET
ap-1801	168	7	infinite	infinite	ADJ
ap-1801	168	8	cusp	cusp	NOUN
ap-1801	168	9	-	-	PUNCT
ap-1801	168	10	shaped	shape	VERB
ap-1801	168	11	ω	ω	NUM
ap-1801	168	12	⊂	⊂	PROPN
ap-1801	168	13	r2	r2	PROPN
ap-1801	168	14	assuming	assume	VERB
ap-1801	168	15	that	that	SCONJ
ap-1801	168	16	its	its	PRON
ap-1801	168	17	boundary	boundary	NOUN
ap-1801	168	18	is	be	AUX
ap-1801	168	19	smooth	smooth	ADJ
ap-1801	168	20	,	,	PUNCT
ap-1801	168	21	so	so	SCONJ
ap-1801	168	22	one	one	PRON
ap-1801	168	23	can	can	AUX
ap-1801	168	24	describe	describe	VERB
ap-1801	168	25	it	it	PRON
ap-1801	168	26	by	by	ADP
ap-1801	168	27	specifying	specify	VERB
ap-1801	168	28	its	its	PRON
ap-1801	168	29	axis	axis	NOUN
ap-1801	168	30	and	and	CCONJ
ap-1801	168	31	the	the	DET
ap-1801	168	32	cusp	cusp	NOUN
ap-1801	168	33	width	width	NOUN
ap-1801	168	34	at	at	ADP
ap-1801	168	35	each	each	DET
ap-1801	168	36	point	point	NOUN
ap-1801	168	37	of	of	ADP
ap-1801	168	38	it	it	PRON
ap-1801	168	39	.	.	PUNCT
ap-1801	169	1	this	this	PRON
ap-1801	169	2	will	will	AUX
ap-1801	169	3	allow	allow	VERB
ap-1801	169	4	us	we	PRON
ap-1801	169	5	to	to	PART
ap-1801	169	6	employ	employ	VERB
ap-1801	169	7	natural	natural	ADJ
ap-1801	169	8	curvilinear	curvilinear	NOUN
ap-1801	169	9	coordinates	coordinate	NOUN
ap-1801	169	10	by	by	ADP
ap-1801	169	11	analogy	analogy	NOUN
ap-1801	169	12	with	with	ADP
ap-1801	169	13	the	the	DET
ap-1801	169	14	theory	theory	NOUN
ap-1801	169	15	of	of	ADP
ap-1801	169	16	quantum	quantum	ADJ
ap-1801	169	17	waveguides	waveguide	NOUN
ap-1801	169	18	[	[	X
ap-1801	169	19	15	15	NUM
ap-1801	169	20	]	]	PUNCT
ap-1801	169	21	and	and	CCONJ
ap-1801	169	22	to	to	PART
ap-1801	169	23	‘	'	PUNCT
ap-1801	169	24	straighten	straighten	VERB
ap-1801	169	25	’	'	PUNCT
ap-1801	169	26	the	the	DET
ap-1801	169	27	cusp	cusp	NOUN
ap-1801	169	28	,	,	PUNCT
ap-1801	169	29	translating	translate	VERB
ap-1801	169	30	its	its	PRON
ap-1801	169	31	geometric	geometric	ADJ
ap-1801	169	32	properties	property	NOUN
ap-1801	169	33	into	into	ADP
ap-1801	169	34	the	the	DET
ap-1801	169	35	coefficients	coefficient	NOUN
ap-1801	169	36	of	of	ADP
ap-1801	169	37	the	the	DET
ap-1801	169	38	resulting	result	VERB
ap-1801	169	39	operator	operator	NOUN
ap-1801	169	40	.	.	PUNCT
ap-1801	170	1	to	to	PART
ap-1801	170	2	be	be	AUX
ap-1801	170	3	specific	specific	ADJ
ap-1801	170	4	,	,	PUNCT
ap-1801	170	5	we	we	PRON
ap-1801	170	6	characterize	characterize	VERB
ap-1801	170	7	our	our	PRON
ap-1801	170	8	region	region	NOUN
ap-1801	170	9	by	by	ADP
ap-1801	170	10	three	three	NUM
ap-1801	170	11	functions	function	NOUN
ap-1801	170	12	:	:	PUNCT
ap-1801	170	13	sufficiently	sufficiently	ADV
ap-1801	170	14	smooth	smooth	VERB
ap-1801	170	15	a	a	PRON
ap-1801	170	16	,	,	PUNCT
ap-1801	170	17	b	b	NOUN
ap-1801	170	18	:	:	PUNCT
ap-1801	170	19	r→	r→	PROPN
ap-1801	170	20	r2	r2	PROPN
ap-1801	170	21	and	and	CCONJ
ap-1801	170	22	a	a	DET
ap-1801	170	23	positive	positive	ADJ
ap-1801	170	24	and	and	CCONJ
ap-1801	170	25	continuous	continuous	ADJ
ap-1801	170	26	f	f	X
ap-1801	170	27	:	:	PUNCT
ap-1801	170	28	r→	r→	NOUN
ap-1801	170	29	r+	r+	NOUN
ap-1801	170	30	in	in	ADP
ap-1801	170	31	such	such	DET
ap-1801	170	32	a	a	DET
ap-1801	170	33	way	way	NOUN
ap-1801	170	34	that	that	PRON
ap-1801	170	35	ω	ω	X
ap-1801	170	36	:	:	PUNCT
ap-1801	170	37	=	=	SYM
ap-1801	170	38	{	{	PUNCT
ap-1801	170	39	(	(	PUNCT
ap-1801	170	40	a(s)−	a(s)−	PROPN
ap-1801	170	41	uḃ(s	uḃ(s	PROPN
ap-1801	170	42	)	)	PUNCT
ap-1801	170	43	,	,	PUNCT
ap-1801	170	44	b(s	b(	NOUN
ap-1801	170	45	)	)	PUNCT
ap-1801	171	1	+	+	CCONJ
ap-1801	171	2	uȧ(s	uȧ(	NOUN
ap-1801	171	3	)	)	PUNCT
ap-1801	171	4	)	)	PUNCT
ap-1801	171	5	:	:	PUNCT
ap-1801	172	1	s	s	AUX
ap-1801	172	2	∈	∈	PROPN
ap-1801	172	3	r	r	NOUN
ap-1801	172	4	,	,	PUNCT
ap-1801	172	5	|u|	|u|	X
ap-1801	172	6	<	<	X
ap-1801	172	7	f(s	f(s	ADV
ap-1801	172	8	)	)	PUNCT
ap-1801	172	9	}	}	PUNCT
ap-1801	172	10	,	,	PUNCT
ap-1801	172	11	(	(	PUNCT
ap-1801	172	12	3.2	3.2	NUM
ap-1801	172	13	)	)	PUNCT
ap-1801	172	14	where	where	SCONJ
ap-1801	172	15	the	the	DET
ap-1801	172	16	dot	dot	NOUN
ap-1801	172	17	marks	mark	VERB
ap-1801	172	18	the	the	DET
ap-1801	172	19	derivative	derivative	NOUN
ap-1801	172	20	with	with	ADP
ap-1801	172	21	respect	respect	NOUN
ap-1801	172	22	to	to	ADP
ap-1801	172	23	s	s	PRON
ap-1801	172	24	;	;	PUNCT
ap-1801	172	25	to	to	PART
ap-1801	172	26	make	make	VERB
ap-1801	172	27	the	the	DET
ap-1801	172	28	region	region	NOUN
ap-1801	172	29	ω	ω	PROPN
ap-1801	172	30	cusp	cusp	NOUN
ap-1801	172	31	-	-	PUNCT
ap-1801	172	32	shaped	shape	VERB
ap-1801	172	33	we	we	PRON
ap-1801	172	34	shall	shall	AUX
ap-1801	172	35	always	always	ADV
ap-1801	172	36	suppose	suppose	VERB
ap-1801	172	37	that	that	SCONJ
ap-1801	172	38	lim	lim	PROPN
ap-1801	172	39	|s|→∞	|s|→∞	PRON
ap-1801	172	40	f(s	f(	VERB
ap-1801	172	41	)	)	PUNCT
ap-1801	172	42	=	=	SYM
ap-1801	172	43	0	0	X
ap-1801	172	44	.	.	PUNCT
ap-1801	173	1	(	(	PUNCT
ap-1801	173	2	3.3	3.3	NUM
ap-1801	173	3	)	)	PUNCT
ap-1801	173	4	since	since	SCONJ
ap-1801	173	5	the	the	DET
ap-1801	173	6	reference	reference	NOUN
ap-1801	173	7	curve	curve	VERB
ap-1801	173	8	γ	γ	X
ap-1801	173	9	=	=	SYM
ap-1801	173	10	{	{	PUNCT
ap-1801	173	11	(	(	PUNCT
ap-1801	173	12	a(s	a(s	PROPN
ap-1801	173	13	)	)	PUNCT
ap-1801	173	14	,	,	PUNCT
ap-1801	173	15	b(s	b(	NOUN
ap-1801	173	16	)	)	PUNCT
ap-1801	173	17	)	)	PUNCT
ap-1801	173	18	:	:	PUNCT
ap-1801	173	19	s	s	AUX
ap-1801	173	20	∈	∈	PROPN
ap-1801	173	21	r	r	NOUN
ap-1801	173	22	}	}	PUNCT
ap-1801	173	23	can	can	AUX
ap-1801	173	24	always	always	ADV
ap-1801	173	25	be	be	AUX
ap-1801	173	26	parametrized	parametrize	VERB
ap-1801	173	27	by	by	ADP
ap-1801	173	28	its	its	PRON
ap-1801	173	29	arc	arc	NOUN
ap-1801	173	30	length	length	NOUN
ap-1801	173	31	we	we	PRON
ap-1801	173	32	may	may	AUX
ap-1801	173	33	suppose	suppose	VERB
ap-1801	173	34	without	without	ADP
ap-1801	173	35	loss	loss	NOUN
ap-1801	173	36	of	of	ADP
ap-1801	173	37	generality	generality	NOUN
ap-1801	173	38	that	that	PRON
ap-1801	173	39	ȧ(s)2	ȧ(s)2	PROPN
ap-1801	173	40	+	+	CCONJ
ap-1801	173	41	ḃ(s)2	ḃ(s)2	NOUN
ap-1801	173	42	=	=	SYM
ap-1801	173	43	1	1	NUM
ap-1801	173	44	and	and	CCONJ
ap-1801	173	45	s	s	NOUN
ap-1801	173	46	is	be	AUX
ap-1801	173	47	the	the	DET
ap-1801	173	48	arc	arc	NOUN
ap-1801	173	49	length	length	NOUN
ap-1801	173	50	.	.	PUNCT
ap-1801	174	1	the	the	DET
ap-1801	174	2	signed	sign	VERB
ap-1801	174	3	curvature	curvature	NOUN
ap-1801	174	4	γ(s	γ(	NOUN
ap-1801	174	5	)	)	PUNCT
ap-1801	174	6	of	of	ADP
ap-1801	174	7	γ	γ	PROPN
ap-1801	174	8	is	be	AUX
ap-1801	174	9	then	then	ADV
ap-1801	174	10	given	give	VERB
ap-1801	174	11	by	by	ADP
ap-1801	174	12	γ(s	γ(	NOUN
ap-1801	174	13	)	)	PUNCT
ap-1801	175	1	=	=	SYM
ap-1801	175	2	ḃ(s)ä(s)−	ḃ(s)ä(s)−	NOUN
ap-1801	175	3	ȧ(s)b̈(s	ȧ(s)b̈(s	PROPN
ap-1801	175	4	)	)	PUNCT
ap-1801	175	5	;	;	PUNCT
ap-1801	175	6	275	275	NUM
ap-1801	175	7	p.	p.	NOUN
ap-1801	175	8	exner	exner	NOUN
ap-1801	175	9	,	,	PUNCT
ap-1801	175	10	d.	d.	PROPN
ap-1801	175	11	barseghyan	barseghyan	PROPN
ap-1801	175	12	acta	acta	PROPN
ap-1801	175	13	polytechnica	polytechnica	PROPN
ap-1801	175	14	knowing	know	VERB
ap-1801	175	15	this	this	DET
ap-1801	175	16	one	one	NOUN
ap-1801	175	17	can	can	AUX
ap-1801	175	18	reconstruct	reconstruct	VERB
ap-1801	175	19	the	the	DET
ap-1801	175	20	functions	function	NOUN
ap-1801	175	21	a	a	PRON
ap-1801	175	22	,	,	PUNCT
ap-1801	175	23	b	b	NOUN
ap-1801	175	24	describing	describe	VERB
ap-1801	175	25	the	the	DET
ap-1801	175	26	cartesian	cartesian	ADJ
ap-1801	175	27	coordinates	coordinate	NOUN
ap-1801	175	28	of	of	ADP
ap-1801	175	29	the	the	DET
ap-1801	175	30	cusps	cusps	NOUN
ap-1801	175	31	axis	axis	NOUN
ap-1801	175	32	,	,	PUNCT
ap-1801	175	33	modulo	modulo	NOUN
ap-1801	175	34	euclidean	euclidean	ADJ
ap-1801	175	35	transformations	transformation	NOUN
ap-1801	175	36	.	.	PUNCT
ap-1801	176	1	under	under	ADP
ap-1801	176	2	the	the	DET
ap-1801	176	3	condition	condition	NOUN
ap-1801	176	4	(	(	PUNCT
ap-1801	176	5	3.3	3.3	NUM
ap-1801	176	6	)	)	PUNCT
ap-1801	176	7	the	the	DET
ap-1801	176	8	region	region	NOUN
ap-1801	176	9	is	be	AUX
ap-1801	176	10	quasi	quasi	ADJ
ap-1801	176	11	-	-	VERB
ap-1801	176	12	bounded	bounded	ADJ
ap-1801	176	13	so	so	SCONJ
ap-1801	176	14	it	it	PRON
ap-1801	176	15	may	may	AUX
ap-1801	176	16	have	have	VERB
ap-1801	176	17	a	a	DET
ap-1801	176	18	purely	purely	ADV
ap-1801	176	19	discrete	discrete	ADJ
ap-1801	176	20	spectrum	spectrum	NOUN
ap-1801	176	21	.	.	PUNCT
ap-1801	177	1	this	this	PRON
ap-1801	177	2	is	be	AUX
ap-1801	177	3	indeed	indeed	ADV
ap-1801	177	4	the	the	DET
ap-1801	177	5	case	case	NOUN
ap-1801	177	6	;	;	PUNCT
ap-1801	177	7	recall	recall	VERB
ap-1801	177	8	that	that	SCONJ
ap-1801	177	9	the	the	DET
ap-1801	177	10	necessary	necessary	ADJ
ap-1801	177	11	and	and	CCONJ
ap-1801	177	12	sufficient	sufficient	ADJ
ap-1801	177	13	condition	condition	NOUN
ap-1801	177	14	for	for	ADP
ap-1801	177	15	the	the	DET
ap-1801	177	16	purely	purely	ADV
ap-1801	177	17	discrete	discrete	ADJ
ap-1801	177	18	spectral	spectral	ADJ
ap-1801	177	19	character	character	NOUN
ap-1801	177	20	[	[	X
ap-1801	177	21	16	16	NUM
ap-1801	177	22	,	,	PUNCT
ap-1801	177	23	thm	thm	PROPN
ap-1801	177	24	2.8	2.8	NUM
ap-1801	177	25	]	]	PUNCT
ap-1801	177	26	is	be	AUX
ap-1801	177	27	that	that	SCONJ
ap-1801	177	28	we	we	PRON
ap-1801	177	29	can	can	AUX
ap-1801	177	30	cover	cover	VERB
ap-1801	177	31	ω	ω	NUM
ap-1801	177	32	by	by	ADP
ap-1801	177	33	a	a	DET
ap-1801	177	34	family	family	NOUN
ap-1801	177	35	of	of	ADP
ap-1801	177	36	unit	unit	NOUN
ap-1801	177	37	balls	ball	NOUN
ap-1801	177	38	whose	whose	DET
ap-1801	177	39	centres	centre	NOUN
ap-1801	177	40	tend	tend	VERB
ap-1801	177	41	to	to	PART
ap-1801	177	42	infinity	infinity	VERB
ap-1801	177	43	in	in	ADP
ap-1801	177	44	such	such	DET
ap-1801	177	45	a	a	DET
ap-1801	177	46	way	way	NOUN
ap-1801	177	47	that	that	PRON
ap-1801	177	48	the	the	DET
ap-1801	177	49	volumes	volume	NOUN
ap-1801	177	50	of	of	ADP
ap-1801	177	51	their	their	PRON
ap-1801	177	52	intersections	intersection	NOUN
ap-1801	177	53	with	with	ADP
ap-1801	177	54	ω	ω	NOUN
ap-1801	177	55	tend	tend	VERB
ap-1801	177	56	to	to	ADP
ap-1801	177	57	zero	zero	NUM
ap-1801	177	58	;	;	PUNCT
ap-1801	177	59	it	it	PRON
ap-1801	177	60	is	be	AUX
ap-1801	177	61	not	not	PART
ap-1801	177	62	difficult	difficult	ADJ
ap-1801	177	63	to	to	PART
ap-1801	177	64	construct	construct	VERB
ap-1801	177	65	such	such	DET
ap-1801	177	66	a	a	DET
ap-1801	177	67	ball	ball	NOUN
ap-1801	177	68	sequence	sequence	NOUN
ap-1801	177	69	if	if	SCONJ
ap-1801	177	70	(	(	PUNCT
ap-1801	177	71	3.3	3.3	NUM
ap-1801	177	72	)	)	PUNCT
ap-1801	177	73	is	be	AUX
ap-1801	177	74	valid	valid	ADJ
ap-1801	177	75	.	.	PUNCT
ap-1801	178	1	our	our	PRON
ap-1801	178	2	main	main	ADJ
ap-1801	178	3	aim	aim	NOUN
ap-1801	178	4	is	be	AUX
ap-1801	178	5	to	to	PART
ap-1801	178	6	provide	provide	VERB
ap-1801	178	7	bounds	bound	NOUN
ap-1801	178	8	on	on	ADP
ap-1801	178	9	the	the	DET
ap-1801	178	10	eigenvalue	eigenvalue	ADJ
ap-1801	178	11	moments	moment	NOUN
ap-1801	178	12	;	;	PUNCT
ap-1801	178	13	as	as	ADP
ap-1801	178	14	usual	usual	ADJ
ap-1801	178	15	when	when	SCONJ
ap-1801	178	16	dealing	deal	VERB
ap-1801	178	17	with	with	ADP
ap-1801	178	18	a	a	DET
ap-1801	178	19	lieb	lieb	PROPN
ap-1801	178	20	-	-	PUNCT
ap-1801	178	21	thirring	thirre	VERB
ap-1801	178	22	type	type	NOUN
ap-1801	178	23	problem	problem	NOUN
ap-1801	178	24	we	we	PRON
ap-1801	178	25	restrict	restrict	VERB
ap-1801	178	26	our	our	PRON
ap-1801	178	27	attention	attention	NOUN
ap-1801	178	28	to	to	ADP
ap-1801	178	29	the	the	DET
ap-1801	178	30	negative	negative	ADJ
ap-1801	178	31	part	part	NOUN
ap-1801	178	32	of	of	ADP
ap-1801	178	33	the	the	DET
ap-1801	178	34	spectrum	spectrum	NOUN
ap-1801	178	35	noting	note	VERB
ap-1801	178	36	that	that	SCONJ
ap-1801	178	37	it	it	PRON
ap-1801	178	38	can	can	AUX
ap-1801	178	39	be	be	AUX
ap-1801	178	40	always	always	ADV
ap-1801	178	41	made	make	VERB
ap-1801	178	42	non	non	ADJ
ap-1801	178	43	-	-	ADJ
ap-1801	178	44	empty	empty	ADJ
ap-1801	178	45	by	by	ADP
ap-1801	178	46	including	include	VERB
ap-1801	178	47	a	a	DET
ap-1801	178	48	suitable	suitable	ADJ
ap-1801	178	49	constant	constant	NOUN
ap-1801	178	50	into	into	ADP
ap-1801	178	51	the	the	DET
ap-1801	178	52	potential	potential	NOUN
ap-1801	178	53	.	.	PUNCT
ap-1801	179	1	theorem	theorem	NOUN
ap-1801	179	2	3.1	3.1	NUM
ap-1801	179	3	.	.	PUNCT
ap-1801	180	1	consider	consider	VERB
ap-1801	180	2	the	the	DET
ap-1801	180	3	schrödinger	schrödinger	ADJ
ap-1801	180	4	operator	operator	NOUN
ap-1801	180	5	(	(	PUNCT
ap-1801	180	6	3.1	3.1	NUM
ap-1801	180	7	)	)	PUNCT
ap-1801	180	8	on	on	ADP
ap-1801	180	9	the	the	DET
ap-1801	180	10	region	region	NOUN
ap-1801	180	11	(	(	PUNCT
ap-1801	180	12	3.2	3.2	NUM
ap-1801	180	13	)	)	PUNCT
ap-1801	180	14	.	.	PUNCT
ap-1801	181	1	suppose	suppose	VERB
ap-1801	181	2	that	that	SCONJ
ap-1801	181	3	the	the	DET
ap-1801	181	4	curvature	curvature	NOUN
ap-1801	181	5	γ	γ	PROPN
ap-1801	181	6	∈	∈	PROPN
ap-1801	181	7	c4	c4	NOUN
ap-1801	181	8	,	,	PUNCT
ap-1801	181	9	the	the	DET
ap-1801	181	10	inequality	inequality	NOUN
ap-1801	181	11	∥∥f(·)γ	∥∥f(·)γ	PROPN
ap-1801	181	12	(	(	PUNCT
ap-1801	181	13	·	·	PUNCT
ap-1801	181	14	)	)	PUNCT
ap-1801	181	15	∥∥	∥∥	X
ap-1801	181	16	l∞(r	l∞(r	PROPN
ap-1801	181	17	)	)	PUNCT
ap-1801	181	18	<	<	X
ap-1801	181	19	1	1	NUM
ap-1801	181	20	holds	hold	VERB
ap-1801	181	21	true	true	ADJ
ap-1801	181	22	,	,	PUNCT
ap-1801	181	23	and	and	CCONJ
ap-1801	181	24	ω	ω	PROPN
ap-1801	181	25	does	do	AUX
ap-1801	181	26	not	not	PART
ap-1801	181	27	intersect	intersect	VERB
ap-1801	181	28	itself	itself	PRON
ap-1801	181	29	.	.	PUNCT
ap-1801	182	1	then	then	ADV
ap-1801	182	2	for	for	ADP
ap-1801	182	3	any	any	DET
ap-1801	182	4	σ	σ	PROPN
ap-1801	182	5	≥	≥	NUM
ap-1801	182	6	3/2	3/2	NUM
ap-1801	182	7	we	we	PRON
ap-1801	182	8	have	have	VERB
ap-1801	182	9	the	the	DET
ap-1801	182	10	estimate	estimate	NOUN
ap-1801	182	11	tr(hω)σ−	tr(hω)σ−	NOUN
ap-1801	182	12	≤	≤	PROPN
ap-1801	183	1	∥∥1	∥∥1	PROPN
ap-1801	184	1	+	+	NUM
ap-1801	184	2	f	f	X
ap-1801	184	3	|γ|	|γ|	VERB
ap-1801	184	4	∥∥−2σ	∥∥−2σ	NOUN
ap-1801	184	5	∞	∞	NUM
ap-1801	184	6	lcl	lcl	PROPN
ap-1801	184	7	σ,1	σ,1	PRON
ap-1801	184	8	∫	∫	NOUN
ap-1801	184	9	r	r	NOUN
ap-1801	184	10	∞∑	∞∑	PROPN
ap-1801	184	11	j=1	j=1	NOUN
ap-1801	184	12	(	(	PUNCT
ap-1801	184	13	−	−	PROPN
ap-1801	184	14	(	(	PUNCT
ap-1801	184	15	πj	πj	VERB
ap-1801	184	16	2f(s	2f(s	NUM
ap-1801	184	17	)	)	PUNCT
ap-1801	184	18	)	)	PUNCT
ap-1801	184	19	2	2	NUM
ap-1801	185	1	+	+	CCONJ
ap-1801	185	2	∥∥1	∥∥1	PROPN
ap-1801	186	1	+	+	NUM
ap-1801	186	2	f	f	X
ap-1801	186	3	|γ|	|γ|	VERB
ap-1801	186	4	∥∥2	∥∥2	PROPN
ap-1801	186	5	∞w	∞w	NOUN
ap-1801	186	6	−(s	−(s	ADV
ap-1801	186	7	)	)	PUNCT
ap-1801	187	1	+	+	CCONJ
ap-1801	188	1	∥∥1	∥∥1	PROPN
ap-1801	189	1	+	+	NUM
ap-1801	189	2	f	f	AUX
ap-1801	189	3	|γ|	|γ|	VERB
ap-1801	189	4	∥∥2	∥∥2	NOUN
ap-1801	190	1	∞	∞	NUM
ap-1801	190	2	∥∥ṽ	∥∥ṽ	NOUN
ap-1801	190	3	(	(	PUNCT
ap-1801	190	4	s	s	PROPN
ap-1801	190	5	,	,	PUNCT
ap-1801	190	6	·	·	PUNCT
ap-1801	190	7	)	)	PUNCT
ap-1801	190	8	∥∥	∥∥	X
ap-1801	190	9	∞	∞	NUM
ap-1801	190	10	)	)	PUNCT
ap-1801	190	11	σ+1/2	σ+1/2	PROPN
ap-1801	191	1	+	+	CCONJ
ap-1801	191	2	ds	ds	ADJ
ap-1801	191	3	,	,	PUNCT
ap-1801	191	4	(	(	PUNCT
ap-1801	191	5	3.4	3.4	NUM
ap-1801	191	6	)	)	PUNCT
ap-1801	191	7	where	where	SCONJ
ap-1801	191	8	‖·‖∞	‖·‖∞	VERB
ap-1801	191	9	≡	≡	PROPN
ap-1801	191	10	‖·‖l∞(r	‖·‖l∞(r	PROPN
ap-1801	191	11	)	)	PUNCT
ap-1801	191	12	and	and	CCONJ
ap-1801	191	13	lcl	lcl	PROPN
ap-1801	191	14	σ,1	σ,1	PROPN
ap-1801	191	15	is	be	AUX
ap-1801	191	16	the	the	DET
ap-1801	191	17	semiclassical	semiclassical	ADJ
ap-1801	191	18	constant	constant	ADJ
ap-1801	191	19	,	,	PUNCT
ap-1801	191	20	lcl	lcl	PROPN
ap-1801	191	21	σ,1	σ,1	NOUN
ap-1801	191	22	:	:	PUNCT
ap-1801	191	23	=	=	PUNCT
ap-1801	191	24	γ(σ	γ(σ	X
ap-1801	191	25	+	+	PROPN
ap-1801	191	26	1)√	1)√	NUM
ap-1801	191	27	4π	4π	NUM
ap-1801	191	28	γ(σ	γ(σ	ADJ
ap-1801	191	29	+	+	CCONJ
ap-1801	191	30	3	3	NUM
ap-1801	191	31	2	2	NUM
ap-1801	191	32	)	)	PUNCT
ap-1801	191	33	,	,	PUNCT
ap-1801	191	34	(	(	PUNCT
ap-1801	191	35	3.5	3.5	NUM
ap-1801	191	36	)	)	PUNCT
ap-1801	191	37	and	and	CCONJ
ap-1801	191	38	furthermore	furthermore	ADV
ap-1801	191	39	,	,	PUNCT
ap-1801	191	40	we	we	PRON
ap-1801	191	41	have	have	AUX
ap-1801	191	42	introduced	introduce	VERB
ap-1801	191	43	w−(s	w−(	VERB
ap-1801	191	44	)	)	PUNCT
ap-1801	191	45	:	:	PUNCT
ap-1801	192	1	=	=	SYM
ap-1801	192	2	γ(s)2	γ(s)2	ADJ
ap-1801	192	3	4	4	NUM
ap-1801	192	4	(	(	PUNCT
ap-1801	192	5	1−	1−	NUM
ap-1801	192	6	f(s)|γ(s)|	f(s)|γ(s)|	NUM
ap-1801	192	7	)	)	PUNCT
ap-1801	192	8	2	2	NUM
ap-1801	192	9	+	+	NUM
ap-1801	192	10	f(s	f(	NOUN
ap-1801	192	11	)	)	PUNCT
ap-1801	192	12	∣∣γ̈(s	∣∣γ̈(s	PROPN
ap-1801	192	13	)	)	PUNCT
ap-1801	192	14	∣∣	∣∣	X
ap-1801	192	15	2	2	NUM
ap-1801	192	16	(	(	PUNCT
ap-1801	192	17	1−	1−	NUM
ap-1801	192	18	f(s)|γ(s)|	f(s)|γ(s)|	NUM
ap-1801	192	19	)	)	PUNCT
ap-1801	192	20	3	3	NUM
ap-1801	193	1	+	+	CCONJ
ap-1801	193	2	5f2(s)γ̇(s)2	5f2(s)γ̇(s)2	NOUN
ap-1801	193	3	4	4	NUM
ap-1801	193	4	(	(	PUNCT
ap-1801	193	5	1−	1−	NUM
ap-1801	193	6	f(s)|γ(s)|	f(s)|γ(s)|	NUM
ap-1801	193	7	)	)	PUNCT
ap-1801	193	8	4	4	NUM
ap-1801	193	9	and	and	CCONJ
ap-1801	193	10	ṽ	ṽ	PROPN
ap-1801	193	11	(	(	PUNCT
ap-1801	193	12	s	s	PROPN
ap-1801	193	13	,	,	PUNCT
ap-1801	193	14	u	u	NOUN
ap-1801	193	15	)	)	PUNCT
ap-1801	193	16	:	:	PUNCT
ap-1801	194	1	=	=	SYM
ap-1801	194	2	v	v	X
ap-1801	194	3	(	(	PUNCT
ap-1801	194	4	a(s)−	a(s)−	PROPN
ap-1801	194	5	uḃ(s	uḃ(s	PROPN
ap-1801	194	6	)	)	PUNCT
ap-1801	194	7	,	,	PUNCT
ap-1801	194	8	b(s	b(	NOUN
ap-1801	194	9	)	)	PUNCT
ap-1801	194	10	+	+	CCONJ
ap-1801	194	11	uȧ(s	uȧ(	NOUN
ap-1801	194	12	)	)	PUNCT
ap-1801	194	13	)	)	PUNCT
ap-1801	194	14	.	.	PUNCT
ap-1801	195	1	sketch	sketch	NOUN
ap-1801	195	2	of	of	ADP
ap-1801	195	3	the	the	DET
ap-1801	195	4	proof	proof	NOUN
ap-1801	195	5	.	.	PUNCT
ap-1801	196	1	using	use	VERB
ap-1801	196	2	the	the	DET
ap-1801	196	3	mentioned	mention	VERB
ap-1801	196	4	‘	'	PUNCT
ap-1801	196	5	straightening	straightening	NOUN
ap-1801	196	6	’	'	PUNCT
ap-1801	196	7	transformation	transformation	NOUN
ap-1801	196	8	[	[	X
ap-1801	196	9	15	15	NUM
ap-1801	196	10	]	]	X
ap-1801	196	11	we	we	PRON
ap-1801	196	12	infer	infer	VERB
ap-1801	196	13	that	that	SCONJ
ap-1801	196	14	hω	hω	ADP
ap-1801	196	15	is	be	AUX
ap-1801	196	16	unitarily	unitarily	ADV
ap-1801	196	17	equivalent	equivalent	ADJ
ap-1801	196	18	to	to	ADP
ap-1801	196	19	the	the	DET
ap-1801	196	20	operator	operator	NOUN
ap-1801	196	21	h0	h0	NOUN
ap-1801	196	22	on	on	ADP
ap-1801	196	23	l2(ω0	l2(ω0	ADJ
ap-1801	196	24	)	)	PUNCT
ap-1801	196	25	acting	act	VERB
ap-1801	196	26	as	as	ADP
ap-1801	196	27	(	(	PUNCT
ap-1801	196	28	h0ψ)(s	h0ψ)(s	PROPN
ap-1801	196	29	,	,	PUNCT
ap-1801	196	30	u	u	NOUN
ap-1801	196	31	)	)	PUNCT
ap-1801	196	32	=	=	SYM
ap-1801	196	33	−	−	PROPN
ap-1801	196	34	∂	∂	NUM
ap-1801	196	35	∂s	∂s	PROPN
ap-1801	196	36	(	(	PUNCT
ap-1801	196	37	1	1	NUM
ap-1801	196	38	(	(	PUNCT
ap-1801	196	39	1	1	NUM
ap-1801	196	40	+	+	CCONJ
ap-1801	196	41	uγ(s))2	uγ(s))2	PROPN
ap-1801	196	42	∂ψ	∂ψ	PROPN
ap-1801	196	43	∂s	∂s	PROPN
ap-1801	196	44	(	(	PUNCT
ap-1801	196	45	s	s	PROPN
ap-1801	196	46	,	,	PUNCT
ap-1801	196	47	u	u	NOUN
ap-1801	196	48	)	)	PUNCT
ap-1801	196	49	)	)	PUNCT
ap-1801	197	1	−	−	PROPN
ap-1801	198	1	∂2ψ	∂2ψ	PROPN
ap-1801	198	2	∂u2	∂u2	NOUN
ap-1801	198	3	(	(	PUNCT
ap-1801	198	4	s	s	PROPN
ap-1801	198	5	,	,	PUNCT
ap-1801	198	6	u	u	NOUN
ap-1801	198	7	)	)	PUNCT
ap-1801	198	8	+	+	CCONJ
ap-1801	198	9	(	(	PUNCT
ap-1801	198	10	(	(	PUNCT
ap-1801	198	11	w	w	PROPN
ap-1801	198	12	−	−	PROPN
ap-1801	198	13	ṽ	ṽ	PROPN
ap-1801	198	14	)	)	PUNCT
ap-1801	198	15	ψ	ψ	NOUN
ap-1801	198	16	)	)	PUNCT
ap-1801	198	17	(	(	PUNCT
ap-1801	198	18	s	s	X
ap-1801	198	19	,	,	PUNCT
ap-1801	198	20	u	u	NOUN
ap-1801	198	21	)	)	PUNCT
ap-1801	198	22	,	,	PUNCT
ap-1801	198	23	where	where	SCONJ
ap-1801	198	24	ω0	ω0	ADV
ap-1801	198	25	=	=	SYM
ap-1801	198	26	{	{	PUNCT
ap-1801	198	27	(	(	PUNCT
ap-1801	198	28	s	s	X
ap-1801	198	29	,	,	PUNCT
ap-1801	198	30	u	u	NOUN
ap-1801	198	31	)	)	PUNCT
ap-1801	198	32	:	:	PUNCT
ap-1801	198	33	s	s	VERB
ap-1801	198	34	∈	∈	PROPN
ap-1801	198	35	r	r	NOUN
ap-1801	198	36	,	,	PUNCT
ap-1801	198	37	|u|	|u|	X
ap-1801	198	38	<	<	X
ap-1801	198	39	f(s	f(	NOUN
ap-1801	198	40	)	)	PUNCT
ap-1801	198	41	}	}	PUNCT
ap-1801	198	42	,	,	PUNCT
ap-1801	198	43	the	the	DET
ap-1801	198	44	curvature	curvature	NOUN
ap-1801	198	45	-	-	PUNCT
ap-1801	198	46	induced	induce	VERB
ap-1801	198	47	potential	potential	NOUN
ap-1801	198	48	is	be	AUX
ap-1801	198	49	w	w	NOUN
ap-1801	198	50	(	(	PUNCT
ap-1801	198	51	s	s	PROPN
ap-1801	198	52	,	,	PUNCT
ap-1801	198	53	u	u	NOUN
ap-1801	198	54	)	)	PUNCT
ap-1801	198	55	:	:	PUNCT
ap-1801	199	1	=	=	PUNCT
ap-1801	199	2	−	−	PROPN
ap-1801	199	3	γ2(s	γ2(s	PROPN
ap-1801	199	4	)	)	PUNCT
ap-1801	199	5	4	4	NUM
ap-1801	199	6	(	(	PUNCT
ap-1801	199	7	1	1	NUM
ap-1801	199	8	+	+	NUM
ap-1801	199	9	uγ(s	uγ(	NOUN
ap-1801	199	10	)	)	PUNCT
ap-1801	199	11	)	)	PUNCT
ap-1801	199	12	2	2	NUM
ap-1801	199	13	+	+	CCONJ
ap-1801	199	14	uγ̈(s	uγ̈(	NOUN
ap-1801	199	15	)	)	PUNCT
ap-1801	199	16	2	2	NUM
ap-1801	199	17	(	(	PUNCT
ap-1801	199	18	1	1	NUM
ap-1801	199	19	+	+	NUM
ap-1801	199	20	uγ(s	uγ(	NOUN
ap-1801	199	21	)	)	PUNCT
ap-1801	199	22	)	)	PUNCT
ap-1801	199	23	3	3	NUM
ap-1801	199	24	−	−	NOUN
ap-1801	199	25	5	5	NUM
ap-1801	199	26	4	4	NUM
ap-1801	199	27	u2γ̇2(s	u2γ̇2(s	NOUN
ap-1801	199	28	)	)	PUNCT
ap-1801	199	29	(	(	PUNCT
ap-1801	199	30	1	1	NUM
ap-1801	199	31	+	+	NUM
ap-1801	199	32	uγ(s	uγ(	NOUN
ap-1801	199	33	)	)	PUNCT
ap-1801	199	34	)	)	PUNCT
ap-1801	199	35	4	4	NUM
ap-1801	199	36	and	and	CCONJ
ap-1801	199	37	dirichlet	dirichlet	PROPN
ap-1801	199	38	boundary	boundary	ADJ
ap-1801	199	39	conditions	condition	NOUN
ap-1801	199	40	are	be	AUX
ap-1801	199	41	imposed	impose	VERB
ap-1801	199	42	at	at	ADP
ap-1801	199	43	u	u	NOUN
ap-1801	199	44	=	=	PROPN
ap-1801	199	45	±f(s	±f(s	PROPN
ap-1801	199	46	)	)	PUNCT
ap-1801	199	47	.	.	PUNCT
ap-1801	200	1	in	in	ADP
ap-1801	200	2	view	view	NOUN
ap-1801	200	3	of	of	ADP
ap-1801	200	4	the	the	DET
ap-1801	200	5	unitary	unitary	ADJ
ap-1801	200	6	equivalence	equivalence	NOUN
ap-1801	200	7	it	it	PRON
ap-1801	200	8	is	be	AUX
ap-1801	200	9	enough	enough	ADJ
ap-1801	200	10	to	to	PART
ap-1801	200	11	establish	establish	VERB
ap-1801	200	12	inequality	inequality	NOUN
ap-1801	200	13	(	(	PUNCT
ap-1801	200	14	3.4	3.4	NUM
ap-1801	200	15	)	)	PUNCT
ap-1801	200	16	for	for	ADP
ap-1801	200	17	the	the	DET
ap-1801	200	18	operator	operator	NOUN
ap-1801	200	19	h0	h0	NOUN
ap-1801	200	20	.	.	PUNCT
ap-1801	201	1	we	we	PRON
ap-1801	201	2	employ	employ	VERB
ap-1801	201	3	the	the	DET
ap-1801	201	4	minimax	minimax	NOUN
ap-1801	201	5	principle	principle	NOUN
ap-1801	201	6	:	:	PUNCT
ap-1801	201	7	consider	consider	VERB
ap-1801	201	8	the	the	DET
ap-1801	201	9	operator	operator	NOUN
ap-1801	201	10	h−0	h−0	PROPN
ap-1801	201	11	defined	define	VERB
ap-1801	201	12	on	on	ADP
ap-1801	201	13	the	the	DET
ap-1801	201	14	domain	domain	NOUN
ap-1801	201	15	h2	h2	NOUN
ap-1801	201	16	0(ω0	0(ω0	NUM
ap-1801	201	17	)	)	PUNCT
ap-1801	201	18	in	in	ADP
ap-1801	201	19	l2(ω0	l2(ω0	ADJ
ap-1801	201	20	)	)	PUNCT
ap-1801	201	21	by	by	ADP
ap-1801	201	22	h−0	h−0	PROPN
ap-1801	201	23	=	=	SYM
ap-1801	201	24	−∆ω0	−∆ω0	PROPN
ap-1801	202	1	d	d	NOUN
ap-1801	202	2	−	−	PROPN
ap-1801	203	1	∥∥1	∥∥1	PROPN
ap-1801	203	2	+	+	NUM
ap-1801	204	1	f	f	AUX
ap-1801	204	2	|γ|	|γ|	VERB
ap-1801	204	3	∥∥2	∥∥2	NOUN
ap-1801	205	1	∞	∞	NUM
ap-1801	206	1	(	(	PUNCT
ap-1801	206	2	w−	w−	NOUN
ap-1801	206	3	+	+	X
ap-1801	206	4	ṽ	ṽ	PROPN
ap-1801	206	5	)	)	PUNCT
ap-1801	206	6	,	,	PUNCT
ap-1801	206	7	where	where	SCONJ
ap-1801	206	8	−∆ω0	−∆ω0	PUNCT
ap-1801	206	9	d	d	NOUN
ap-1801	206	10	is	be	AUX
ap-1801	206	11	as	as	ADV
ap-1801	206	12	usual	usual	ADJ
ap-1801	206	13	the	the	DET
ap-1801	206	14	corresponding	corresponding	ADJ
ap-1801	206	15	dirichlet	dirichlet	PROPN
ap-1801	206	16	laplacian	laplacian	PROPN
ap-1801	206	17	;	;	PUNCT
ap-1801	206	18	it	it	PRON
ap-1801	206	19	is	be	AUX
ap-1801	206	20	obvious	obvious	ADJ
ap-1801	206	21	that	that	SCONJ
ap-1801	206	22	h0	h0	PROPN
ap-1801	206	23	≥	≥	PRON
ap-1801	206	24	∥∥1	∥∥1	PROPN
ap-1801	207	1	+	+	NUM
ap-1801	207	2	f	f	X
ap-1801	207	3	|γ|	|γ|	ADJ
ap-1801	207	4	∥∥−2	∥∥−2	NUM
ap-1801	207	5	∞	∞	PROPN
ap-1801	207	6	h−0	h−0	PROPN
ap-1801	207	7	(	(	PUNCT
ap-1801	207	8	3.6	3.6	NUM
ap-1801	207	9	)	)	PUNCT
ap-1801	207	10	holds	hold	VERB
ap-1801	207	11	true	true	ADJ
ap-1801	207	12	,	,	PUNCT
ap-1801	207	13	therefore	therefore	ADV
ap-1801	207	14	it	it	PRON
ap-1801	207	15	is	be	AUX
ap-1801	207	16	sufficient	sufficient	ADJ
ap-1801	207	17	to	to	PART
ap-1801	207	18	get	get	VERB
ap-1801	207	19	the	the	DET
ap-1801	207	20	upper	upper	ADJ
ap-1801	207	21	bound	bind	VERB
ap-1801	207	22	for	for	ADP
ap-1801	207	23	negative	negative	ADJ
ap-1801	207	24	eigenvalue	eigenvalue	ADJ
ap-1801	207	25	moments	moment	NOUN
ap-1801	207	26	of	of	ADP
ap-1801	207	27	operator	operator	NOUN
ap-1801	207	28	h−0	h−0	PROPN
ap-1801	207	29	.	.	PUNCT
ap-1801	208	1	we	we	PRON
ap-1801	208	2	use	use	VERB
ap-1801	208	3	a	a	DET
ap-1801	208	4	variational	variational	ADJ
ap-1801	208	5	argument	argument	NOUN
ap-1801	208	6	—	—	PUNCT
ap-1801	208	7	see	see	VERB
ap-1801	208	8	[	[	X
ap-1801	208	9	17	17	NUM
ap-1801	208	10	]	]	PUNCT
ap-1801	208	11	—	—	PUNCT
ap-1801	208	12	to	to	PART
ap-1801	208	13	estimate	estimate	VERB
ap-1801	208	14	the	the	DET
ap-1801	208	15	negative	negative	ADJ
ap-1801	208	16	eigenvalue	eigenvalue	ADJ
ap-1801	208	17	moments	moment	NOUN
ap-1801	208	18	of	of	ADP
ap-1801	208	19	h−0	h−0	PROPN
ap-1801	208	20	by	by	ADP
ap-1801	208	21	the	the	DET
ap-1801	208	22	negative	negative	ADJ
ap-1801	208	23	eigenvalue	eigenvalue	ADJ
ap-1801	208	24	moments	moment	NOUN
ap-1801	208	25	of	of	ADP
ap-1801	208	26	the	the	DET
ap-1801	208	27	other	other	ADJ
ap-1801	208	28	operator	operator	NOUN
ap-1801	208	29	with	with	ADP
ap-1801	208	30	the	the	DET
ap-1801	208	31	operator	operator	NOUN
ap-1801	208	32	-	-	PUNCT
ap-1801	208	33	valued	value	VERB
ap-1801	208	34	potential	potential	NOUN
ap-1801	208	35	defined	define	VERB
ap-1801	208	36	on	on	ADP
ap-1801	208	37	domain	domain	NOUN
ap-1801	208	38	h1	h1	NOUN
ap-1801	208	39	(	(	PUNCT
ap-1801	208	40	r	r	NOUN
ap-1801	208	41	,	,	PUNCT
ap-1801	208	42	l2(r	l2(r	NOUN
ap-1801	208	43	)	)	PUNCT
ap-1801	208	44	)	)	PUNCT
ap-1801	208	45	and	and	CCONJ
ap-1801	208	46	given	give	VERB
ap-1801	208	47	as	as	SCONJ
ap-1801	208	48	follows	follow	VERB
ap-1801	208	49	−	−	PROPN
ap-1801	208	50	∂2	∂2	PROPN
ap-1801	208	51	∂s2	∂s2	PROPN
ap-1801	208	52	⊗	⊗	PROPN
ap-1801	208	53	il2(r	il2(r	PROPN
ap-1801	208	54	)	)	PUNCT
ap-1801	209	1	+	+	NUM
ap-1801	209	2	h	h	NOUN
ap-1801	209	3	(	(	PUNCT
ap-1801	209	4	s	s	PROPN
ap-1801	209	5	,	,	PUNCT
ap-1801	209	6	ṽ	ṽ	PROPN
ap-1801	209	7	,	,	PUNCT
ap-1801	209	8	w−	w−	PROPN
ap-1801	209	9	)	)	PUNCT
ap-1801	209	10	,	,	PUNCT
ap-1801	209	11	where	where	SCONJ
ap-1801	209	12	h	h	PROPN
ap-1801	209	13	(	(	PUNCT
ap-1801	209	14	s	s	PROPN
ap-1801	209	15	,	,	PUNCT
ap-1801	209	16	ṽ	ṽ	PROPN
ap-1801	209	17	,	,	PUNCT
ap-1801	209	18	w−	w−	PROPN
ap-1801	209	19	)	)	PUNCT
ap-1801	209	20	is	be	AUX
ap-1801	209	21	the	the	DET
ap-1801	209	22	negative	negative	ADJ
ap-1801	209	23	part	part	NOUN
ap-1801	209	24	of	of	ADP
ap-1801	209	25	the	the	DET
ap-1801	209	26	sturm	sturm	NOUN
ap-1801	209	27	-	-	PUNCT
ap-1801	209	28	liouville	liouville	NOUN
ap-1801	209	29	operator	operator	NOUN
ap-1801	209	30	−	−	PROPN
ap-1801	209	31	d2	d2	PROPN
ap-1801	210	1	du2	du2	PROPN
ap-1801	211	1	−	−	PROPN
ap-1801	211	2	∥∥1	∥∥1	PROPN
ap-1801	212	1	+	+	NUM
ap-1801	212	2	f	f	X
ap-1801	212	3	|γ|	|γ|	VERB
ap-1801	212	4	∥∥2	∥∥2	NOUN
ap-1801	212	5	∞	∞	NUM
ap-1801	213	1	(	(	PUNCT
ap-1801	213	2	w−	w−	X
ap-1801	213	3	+	+	X
ap-1801	213	4	ṽ	ṽ	PROPN
ap-1801	213	5	)	)	PUNCT
ap-1801	213	6	.	.	PUNCT
ap-1801	214	1	276	276	NUM
ap-1801	214	2	vol	vol	NOUN
ap-1801	214	3	.	.	PUNCT
ap-1801	215	1	53	53	NUM
ap-1801	215	2	no	no	NOUN
ap-1801	215	3	.	.	PUNCT
ap-1801	216	1	3/2013	3/2013	PROPN
ap-1801	216	2	spectral	spectral	ADJ
ap-1801	216	3	analysis	analysis	NOUN
ap-1801	216	4	of	of	ADP
ap-1801	216	5	schrödinger	schrödinger	ADJ
ap-1801	216	6	operators	operator	NOUN
ap-1801	216	7	consequently	consequently	ADV
ap-1801	216	8	,	,	PUNCT
ap-1801	216	9	tr	tr	ADP
ap-1801	216	10	(	(	PUNCT
ap-1801	216	11	h−0	h−0	PROPN
ap-1801	216	12	)	)	PUNCT
ap-1801	216	13	σ−	σ−	NOUN
ap-1801	216	14	≤	≤	NOUN
ap-1801	216	15	tr	tr	VERB
ap-1801	216	16	(	(	PUNCT
ap-1801	216	17	−	−	PROPN
ap-1801	216	18	∂2	∂2	NOUN
ap-1801	216	19	∂	∂	NOUN
ap-1801	216	20	s2	s2	PROPN
ap-1801	216	21	⊗	⊗	PROPN
ap-1801	216	22	il2(r	il2(r	PROPN
ap-1801	216	23	)	)	PUNCT
ap-1801	217	1	+	+	NOUN
ap-1801	217	2	h	h	NOUN
ap-1801	217	3	(	(	PUNCT
ap-1801	217	4	s	s	PROPN
ap-1801	217	5	,	,	PUNCT
ap-1801	217	6	ṽ	ṽ	PROPN
ap-1801	217	7	,	,	PUNCT
ap-1801	217	8	w−	w−	PROPN
ap-1801	217	9	)	)	PUNCT
ap-1801	217	10	)	)	PUNCT
ap-1801	218	1	σ	σ	NOUN
ap-1801	218	2	−	−	PROPN
ap-1801	218	3	holds	hold	VERB
ap-1801	218	4	for	for	ADP
ap-1801	218	5	any	any	DET
ap-1801	218	6	nonnegative	nonnegative	ADJ
ap-1801	218	7	number	number	NOUN
ap-1801	218	8	σ	σ	PROPN
ap-1801	218	9	.	.	PUNCT
ap-1801	219	1	this	this	PRON
ap-1801	219	2	makes	make	VERB
ap-1801	219	3	it	it	PRON
ap-1801	219	4	possible	possible	ADJ
ap-1801	219	5	to	to	PART
ap-1801	219	6	employ	employ	VERB
ap-1801	219	7	the	the	DET
ap-1801	219	8	version	version	NOUN
ap-1801	219	9	of	of	ADP
ap-1801	219	10	lieb	lieb	PROPN
ap-1801	219	11	-	-	PUNCT
ap-1801	219	12	thirring	thirre	VERB
ap-1801	219	13	inequality	inequality	NOUN
ap-1801	219	14	for	for	ADP
ap-1801	219	15	operator	operator	NOUN
ap-1801	219	16	-	-	PUNCT
ap-1801	219	17	valued	value	VERB
ap-1801	219	18	potentials	potential	NOUN
ap-1801	219	19	[	[	X
ap-1801	219	20	18	18	NUM
ap-1801	219	21	]	]	PUNCT
ap-1801	219	22	for	for	ADP
ap-1801	219	23	operator	operator	NOUN
ap-1801	219	24	-	-	PUNCT
ap-1801	219	25	valued	value	VERB
ap-1801	219	26	potentials	potential	NOUN
ap-1801	219	27	,	,	PUNCT
ap-1801	219	28	which	which	PRON
ap-1801	219	29	yields	yield	VERB
ap-1801	219	30	tr(h−0	tr(h−0	ADJ
ap-1801	219	31	)	)	PUNCT
ap-1801	219	32	σ−	σ−	NOUN
ap-1801	219	33	≤	≤	NUM
ap-1801	219	34	lcl	lcl	NOUN
ap-1801	219	35	σ,1	σ,1	PRON
ap-1801	219	36	∫	∫	NOUN
ap-1801	219	37	r	r	NOUN
ap-1801	219	38	tr	tr	PUNCT
ap-1801	219	39	(	(	PUNCT
ap-1801	219	40	h	h	NOUN
ap-1801	219	41	(	(	PUNCT
ap-1801	219	42	s	s	PROPN
ap-1801	219	43	,	,	PUNCT
ap-1801	219	44	ṽ	ṽ	PROPN
ap-1801	219	45	,	,	PUNCT
ap-1801	219	46	w−	w−	NOUN
ap-1801	219	47	)	)	PUNCT
ap-1801	219	48	)	)	PUNCT
ap-1801	220	1	σ+1/2	σ+1/2	NOUN
ap-1801	220	2	−	−	PROPN
ap-1801	220	3	ds	ds	PROPN
ap-1801	220	4	,	,	PUNCT
ap-1801	220	5	σ	σ	X
ap-1801	220	6	≥	≥	NOUN
ap-1801	220	7	3/2	3/2	NUM
ap-1801	220	8	,	,	PUNCT
ap-1801	220	9	(	(	PUNCT
ap-1801	220	10	3.7	3.7	NUM
ap-1801	220	11	)	)	PUNCT
ap-1801	220	12	with	with	ADP
ap-1801	220	13	the	the	DET
ap-1801	220	14	semiclassical	semiclassical	ADJ
ap-1801	220	15	constant	constant	ADJ
ap-1801	220	16	lcl	lcl	NOUN
ap-1801	220	17	σ,1	σ,1	PROPN
ap-1801	220	18	.	.	PUNCT
ap-1801	221	1	it	it	PRON
ap-1801	221	2	remains	remain	VERB
ap-1801	221	3	to	to	PART
ap-1801	221	4	estimate	estimate	VERB
ap-1801	221	5	the	the	DET
ap-1801	221	6	negative	negative	ADJ
ap-1801	221	7	spectrum	spectrum	NOUN
ap-1801	221	8	of	of	ADP
ap-1801	221	9	the	the	DET
ap-1801	221	10	sturm	sturm	NOUN
ap-1801	221	11	-	-	PUNCT
ap-1801	221	12	liouville	liouville	NOUN
ap-1801	221	13	operator	operator	NOUN
ap-1801	222	1	−	−	PROPN
ap-1801	222	2	d2	d2	PROPN
ap-1801	222	3	du2	du2	PROPN
ap-1801	223	1	−	−	PROPN
ap-1801	223	2	∥∥1	∥∥1	PROPN
ap-1801	224	1	+	+	NUM
ap-1801	224	2	f	f	AUX
ap-1801	224	3	|γ|	|γ|	VERB
ap-1801	224	4	∥∥2	∥∥2	NOUN
ap-1801	224	5	∞	∞	PRON
ap-1801	224	6	(	(	PUNCT
ap-1801	224	7	w−(s	w−(s	ADJ
ap-1801	224	8	)	)	PUNCT
ap-1801	225	1	+	+	CCONJ
ap-1801	225	2	∥∥ṽ	∥∥ṽ	ADJ
ap-1801	225	3	(	(	PUNCT
ap-1801	225	4	s	s	PROPN
ap-1801	225	5	,	,	PUNCT
ap-1801	225	6	·	·	PUNCT
ap-1801	225	7	)	)	PUNCT
ap-1801	225	8	∥∥	∥∥	PROPN
ap-1801	225	9	∞	∞	PROPN
ap-1801	225	10	)	)	PUNCT
ap-1801	225	11	which	which	PRON
ap-1801	225	12	is	be	AUX
ap-1801	225	13	easily	easily	ADV
ap-1801	225	14	done	do	VERB
ap-1801	225	15	,	,	PUNCT
ap-1801	225	16	(	(	PUNCT
ap-1801	225	17	(	(	PUNCT
ap-1801	225	18	πj	πj	VERB
ap-1801	225	19	2f(s	2f(s	NUM
ap-1801	225	20	)	)	PUNCT
ap-1801	225	21	)	)	PUNCT
ap-1801	225	22	2	2	NUM
ap-1801	225	23	−	−	PROPN
ap-1801	225	24	∥∥1	∥∥1	PROPN
ap-1801	226	1	+	+	NUM
ap-1801	226	2	f	f	X
ap-1801	226	3	|γ|	|γ|	PRON
ap-1801	226	4	∥∥2	∥∥2	PROPN
ap-1801	226	5	∞w	∞w	NOUN
ap-1801	226	6	−(s)−	−(s)−	NUM
ap-1801	226	7	∥∥1	∥∥1	PROPN
ap-1801	227	1	+	+	NUM
ap-1801	227	2	f	f	AUX
ap-1801	227	3	|γ|	|γ|	VERB
ap-1801	227	4	∥∥2	∥∥2	NOUN
ap-1801	228	1	∞	∞	NUM
ap-1801	228	2	∥∥ṽ	∥∥ṽ	NOUN
ap-1801	228	3	(	(	PUNCT
ap-1801	228	4	s	s	PROPN
ap-1801	228	5	,	,	PUNCT
ap-1801	228	6	·	·	PUNCT
ap-1801	228	7	)	)	PUNCT
ap-1801	228	8	∥∥	∥∥	PROPN
ap-1801	228	9	∞	∞	NUM
ap-1801	228	10	)	)	PUNCT
ap-1801	228	11	−	−	NOUN
ap-1801	228	12	;	;	PUNCT
ap-1801	228	13	hence	hence	ADV
ap-1801	228	14	in	in	ADP
ap-1801	228	15	view	view	NOUN
ap-1801	228	16	of	of	ADP
ap-1801	228	17	(	(	PUNCT
ap-1801	228	18	3.6	3.6	NUM
ap-1801	228	19	)	)	PUNCT
ap-1801	228	20	and	and	CCONJ
ap-1801	228	21	(	(	PUNCT
ap-1801	228	22	3.7	3.7	NUM
ap-1801	228	23	)	)	PUNCT
ap-1801	228	24	we	we	PRON
ap-1801	228	25	find	find	VERB
ap-1801	228	26	that	that	SCONJ
ap-1801	228	27	tr(h0)σ−	tr(h0)σ−	PROPN
ap-1801	228	28	≤	≤	X
ap-1801	228	29	∥∥1	∥∥1	PROPN
ap-1801	229	1	+	+	NUM
ap-1801	229	2	f	f	X
ap-1801	229	3	|γ|	|γ|	VERB
ap-1801	229	4	∥∥−2σ	∥∥−2σ	NOUN
ap-1801	229	5	∞	∞	NUM
ap-1801	229	6	lcl	lcl	PROPN
ap-1801	230	1	σ,1	σ,1	PRON
ap-1801	230	2	∫	∫	NOUN
ap-1801	230	3	r	r	NOUN
ap-1801	230	4	∞∑	∞∑	PROPN
ap-1801	230	5	j=1	j=1	NOUN
ap-1801	230	6	(	(	PUNCT
ap-1801	230	7	−	−	PROPN
ap-1801	230	8	(	(	PUNCT
ap-1801	230	9	πj	πj	VERB
ap-1801	230	10	2f(s	2f(s	NUM
ap-1801	230	11	)	)	PUNCT
ap-1801	230	12	)	)	PUNCT
ap-1801	230	13	2	2	NUM
ap-1801	231	1	+	+	CCONJ
ap-1801	231	2	∥∥1	∥∥1	PROPN
ap-1801	232	1	+	+	NUM
ap-1801	232	2	f	f	X
ap-1801	232	3	|γ|	|γ|	VERB
ap-1801	232	4	∥∥2	∥∥2	PROPN
ap-1801	232	5	∞w	∞w	NOUN
ap-1801	232	6	−(s	−(s	ADV
ap-1801	232	7	)	)	PUNCT
ap-1801	233	1	+	+	CCONJ
ap-1801	234	1	∥∥1	∥∥1	PROPN
ap-1801	235	1	+	+	NUM
ap-1801	235	2	f	f	AUX
ap-1801	235	3	|γ|	|γ|	VERB
ap-1801	235	4	∥∥2	∥∥2	NOUN
ap-1801	236	1	∞	∞	NUM
ap-1801	236	2	∥∥ṽ	∥∥ṽ	NOUN
ap-1801	236	3	(	(	PUNCT
ap-1801	236	4	s	s	PROPN
ap-1801	236	5	,	,	PUNCT
ap-1801	236	6	·	·	PUNCT
ap-1801	236	7	)	)	PUNCT
ap-1801	236	8	∥∥	∥∥	X
ap-1801	236	9	∞	∞	NUM
ap-1801	236	10	)	)	PUNCT
ap-1801	236	11	σ+1/2	σ+1/2	PROPN
ap-1801	237	1	+	+	CCONJ
ap-1801	237	2	ds	ds	PROPN
ap-1801	237	3	,	,	PUNCT
ap-1801	237	4	which	which	PRON
ap-1801	237	5	proves	prove	VERB
ap-1801	237	6	the	the	DET
ap-1801	237	7	theorem	theorem	NOUN
ap-1801	237	8	.	.	PUNCT
ap-1801	238	1	we	we	PRON
ap-1801	238	2	finish	finish	VERB
ap-1801	238	3	this	this	DET
ap-1801	238	4	section	section	NOUN
ap-1801	238	5	with	with	ADP
ap-1801	238	6	two	two	NUM
ap-1801	238	7	remarks	remark	NOUN
ap-1801	238	8	.	.	PUNCT
ap-1801	239	1	first	first	ADV
ap-1801	239	2	we	we	PRON
ap-1801	239	3	note	note	VERB
ap-1801	239	4	that	that	SCONJ
ap-1801	239	5	while	while	SCONJ
ap-1801	239	6	the	the	DET
ap-1801	239	7	standard	standard	ADJ
ap-1801	239	8	phase	phase	NOUN
ap-1801	239	9	-	-	PUNCT
ap-1801	239	10	space	space	NOUN
ap-1801	239	11	-	-	PUNCT
ap-1801	239	12	volume	volume	NOUN
ap-1801	239	13	estimates	estimate	NOUN
ap-1801	239	14	give	give	VERB
ap-1801	239	15	correct	correct	ADJ
ap-1801	239	16	high	high	ADJ
ap-1801	239	17	-	-	PUNCT
ap-1801	239	18	energy	energy	NOUN
ap-1801	239	19	behaviour	behaviour	NOUN
ap-1801	239	20	one	one	PRON
ap-1801	239	21	can	can	AUX
ap-1801	239	22	find	find	VERB
ap-1801	239	23	finite	finite	ADJ
ap-1801	239	24	regions	region	NOUN
ap-1801	239	25	ω	ω	X
ap-1801	239	26	for	for	ADP
ap-1801	239	27	which	which	PRON
ap-1801	239	28	there	there	PRON
ap-1801	239	29	exists	exist	VERB
ap-1801	239	30	an	an	DET
ap-1801	239	31	intermediate	intermediate	ADJ
ap-1801	239	32	energy	energy	NOUN
ap-1801	239	33	region	region	NOUN
ap-1801	239	34	where	where	SCONJ
ap-1801	239	35	the	the	DET
ap-1801	239	36	bound	bind	VERB
ap-1801	239	37	(	(	PUNCT
ap-1801	239	38	3.4	3.4	NUM
ap-1801	239	39	)	)	PUNCT
ap-1801	239	40	is	be	AUX
ap-1801	239	41	much	much	ADV
ap-1801	239	42	stronger	strong	ADJ
ap-1801	239	43	than	than	ADP
ap-1801	239	44	the	the	DET
ap-1801	239	45	berezin	berezin	PROPN
ap-1801	239	46	-	-	PUNCT
ap-1801	239	47	li	li	PROPN
ap-1801	239	48	-	-	PROPN
ap-1801	239	49	yau	yau	PROPN
ap-1801	239	50	inequality	inequality	NOUN
ap-1801	239	51	.	.	PUNCT
ap-1801	240	1	an	an	DET
ap-1801	240	2	example	example	NOUN
ap-1801	240	3	is	be	AUX
ap-1801	240	4	given	give	VERB
ap-1801	240	5	in	in	ADP
ap-1801	240	6	paper	paper	NOUN
ap-1801	240	7	[	[	X
ap-1801	240	8	4	4	NUM
ap-1801	240	9	]	]	PUNCT
ap-1801	240	10	,	,	PUNCT
ap-1801	240	11	to	to	PART
ap-1801	240	12	which	which	PRON
ap-1801	240	13	we	we	PRON
ap-1801	240	14	refer	refer	VERB
ap-1801	240	15	also	also	ADV
ap-1801	240	16	for	for	ADP
ap-1801	240	17	the	the	DET
ap-1801	240	18	mentioned	mention	VERB
ap-1801	240	19	generalization	generalization	NOUN
ap-1801	240	20	of	of	ADP
ap-1801	240	21	theorem	theorem	ADJ
ap-1801	240	22	3.1	3.1	NUM
ap-1801	240	23	to	to	ADP
ap-1801	240	24	higher	high	ADJ
ap-1801	240	25	dimensions	dimension	NOUN
ap-1801	240	26	.	.	PUNCT
ap-1801	241	1	3.2	3.2	NUM
ap-1801	241	2	.	.	PUNCT
ap-1801	241	3	twisted	twisted	ADJ
ap-1801	241	4	cusps	cusps	NOUN
ap-1801	241	5	of	of	ADP
ap-1801	241	6	non	non	ADJ
ap-1801	241	7	-	-	ADJ
ap-1801	241	8	circular	circular	ADJ
ap-1801	241	9	cross	cross	NOUN
ap-1801	241	10	section	section	NOUN
ap-1801	241	11	in	in	ADP
ap-1801	241	12	r3	r3	PROPN
ap-1801	241	13	let	let	VERB
ap-1801	241	14	us	we	PRON
ap-1801	241	15	now	now	ADV
ap-1801	241	16	look	look	VERB
ap-1801	241	17	at	at	ADP
ap-1801	241	18	another	another	DET
ap-1801	241	19	type	type	NOUN
ap-1801	241	20	of	of	ADP
ap-1801	241	21	nontrivial	nontrivial	ADJ
ap-1801	241	22	cusp	cusp	NOUN
ap-1801	241	23	geometry	geometry	NOUN
ap-1801	241	24	.	.	PUNCT
ap-1801	242	1	as	as	SCONJ
ap-1801	242	2	before	before	SCONJ
ap-1801	242	3	we	we	PRON
ap-1801	242	4	will	will	AUX
ap-1801	242	5	suppose	suppose	VERB
ap-1801	242	6	that	that	SCONJ
ap-1801	242	7	its	its	PRON
ap-1801	242	8	cross	cross	NOUN
ap-1801	242	9	section	section	NOUN
ap-1801	242	10	changes	change	NOUN
ap-1801	242	11	along	along	ADP
ap-1801	242	12	the	the	DET
ap-1801	242	13	curve	curve	NOUN
ap-1801	242	14	playing	playing	NOUN
ap-1801	242	15	role	role	NOUN
ap-1801	242	16	of	of	ADP
ap-1801	242	17	the	the	DET
ap-1801	242	18	axis	axis	NOUN
ap-1801	242	19	,	,	PUNCT
ap-1801	242	20	however	however	ADV
ap-1801	242	21	,	,	PUNCT
ap-1801	242	22	now	now	ADV
ap-1801	242	23	we	we	PRON
ap-1801	242	24	allow	allow	VERB
ap-1801	242	25	it	it	PRON
ap-1801	242	26	to	to	PART
ap-1801	242	27	be	be	AUX
ap-1801	242	28	non	non	ADJ
ap-1801	242	29	-	-	ADJ
ap-1801	242	30	circular	circular	ADJ
ap-1801	242	31	.	.	PUNCT
ap-1801	243	1	consider	consider	VERB
ap-1801	243	2	an	an	DET
ap-1801	243	3	open	open	ADJ
ap-1801	243	4	connected	connect	VERB
ap-1801	243	5	set	set	NOUN
ap-1801	243	6	ω0	ω0	PROPN
ap-1801	243	7	⊂	⊂	ADJ
ap-1801	243	8	r2	r2	PROPN
ap-1801	243	9	and	and	CCONJ
ap-1801	243	10	a	a	DET
ap-1801	243	11	positive	positive	ADJ
ap-1801	243	12	function	function	NOUN
ap-1801	244	1	f	f	NOUN
ap-1801	244	2	:	:	PUNCT
ap-1801	244	3	r→	r→	VERB
ap-1801	244	4	r	r	NOUN
ap-1801	244	5	satisfying	satisfy	VERB
ap-1801	244	6	the	the	DET
ap-1801	244	7	condition	condition	NOUN
ap-1801	244	8	(	(	PUNCT
ap-1801	244	9	3.3	3.3	NUM
ap-1801	244	10	)	)	PUNCT
ap-1801	244	11	,	,	PUNCT
ap-1801	244	12	and	and	CCONJ
ap-1801	244	13	set	set	VERB
ap-1801	244	14	ωs	ωs	PRON
ap-1801	244	15	:	:	PUNCT
ap-1801	244	16	=	=	SYM
ap-1801	244	17	f(s)ω0	f(s)ω0	PROPN
ap-1801	244	18	,	,	PUNCT
ap-1801	244	19	(	(	PUNCT
ap-1801	244	20	3.8	3.8	NUM
ap-1801	244	21	)	)	PUNCT
ap-1801	244	22	where	where	SCONJ
ap-1801	244	23	we	we	PRON
ap-1801	244	24	use	use	VERB
ap-1801	244	25	the	the	DET
ap-1801	244	26	conventional	conventional	ADJ
ap-1801	244	27	shorthand	shorthand	NOUN
ap-1801	244	28	αa	αa	NOUN
ap-1801	244	29	:	:	PUNCT
ap-1801	244	30	=	=	SYM
ap-1801	244	31	{	{	PUNCT
ap-1801	244	32	(	(	PUNCT
ap-1801	244	33	αx	αx	INTJ
ap-1801	244	34	,	,	PUNCT
ap-1801	244	35	αy	αy	NOUN
ap-1801	244	36	)	)	PUNCT
ap-1801	244	37	:	:	PUNCT
ap-1801	244	38	(	(	PUNCT
ap-1801	244	39	x	x	X
ap-1801	244	40	,	,	PUNCT
ap-1801	244	41	y	y	PROPN
ap-1801	244	42	)	)	PUNCT
ap-1801	244	43	∈	∈	PROPN
ap-1801	244	44	a	a	PRON
ap-1801	244	45	}	}	PUNCT
ap-1801	244	46	for	for	ADP
ap-1801	244	47	α	α	PROPN
ap-1801	244	48	>	>	X
ap-1801	244	49	0	0	PROPN
ap-1801	244	50	and	and	CCONJ
ap-1801	244	51	a	a	DET
ap-1801	244	52	⊂	⊂	PROPN
ap-1801	244	53	r2	r2	PROPN
ap-1801	244	54	.	.	PUNCT
ap-1801	245	1	using	use	VERB
ap-1801	245	2	(	(	PUNCT
ap-1801	245	3	3.8	3.8	NUM
ap-1801	245	4	)	)	PUNCT
ap-1801	245	5	we	we	PRON
ap-1801	245	6	define	define	VERB
ap-1801	245	7	a	a	DET
ap-1801	245	8	straight	straight	ADJ
ap-1801	245	9	cusped	cuspe	VERB
ap-1801	245	10	region	region	NOUN
ap-1801	245	11	determined	determine	VERB
ap-1801	245	12	by	by	ADP
ap-1801	245	13	ω0	ω0	NOUN
ap-1801	245	14	and	and	CCONJ
ap-1801	245	15	the	the	DET
ap-1801	245	16	function	function	NOUN
ap-1801	245	17	f	f	PROPN
ap-1801	245	18	as	as	ADP
ap-1801	245	19	ω0	ω0	ADV
ap-1801	245	20	:	:	PUNCT
ap-1801	245	21	=	=	SYM
ap-1801	245	22	{	{	PUNCT
ap-1801	245	23	(	(	PUNCT
ap-1801	245	24	s	s	X
ap-1801	245	25	,	,	PUNCT
ap-1801	245	26	x	x	NOUN
ap-1801	245	27	,	,	PUNCT
ap-1801	245	28	y	y	PROPN
ap-1801	245	29	)	)	PUNCT
ap-1801	245	30	:	:	PUNCT
ap-1801	245	31	s	s	VERB
ap-1801	245	32	∈	∈	PROPN
ap-1801	245	33	r	r	NOUN
ap-1801	245	34	,	,	PUNCT
ap-1801	245	35	(	(	PUNCT
ap-1801	245	36	x	x	NOUN
ap-1801	245	37	,	,	PUNCT
ap-1801	245	38	y	y	NOUN
ap-1801	245	39	)	)	PUNCT
ap-1801	245	40	∈	∈	NOUN
ap-1801	245	41	ωs	ωs	X
ap-1801	245	42	}	}	PUNCT
ap-1801	245	43	.	.	PUNCT
ap-1801	246	1	next	next	ADV
ap-1801	246	2	we	we	PRON
ap-1801	246	3	twist	twist	VERB
ap-1801	246	4	the	the	DET
ap-1801	246	5	region	region	NOUN
ap-1801	246	6	ω0	ω0	NOUN
ap-1801	246	7	.	.	PUNCT
ap-1801	247	1	we	we	PRON
ap-1801	247	2	fix	fix	VERB
ap-1801	247	3	a	a	DET
ap-1801	247	4	c1	c1	NOUN
ap-1801	247	5	-	-	PUNCT
ap-1801	247	6	smooth	smooth	ADJ
ap-1801	247	7	function	function	NOUN
ap-1801	247	8	θ	θ	NOUN
ap-1801	247	9	:	:	PUNCT
ap-1801	247	10	r→	r→	VERB
ap-1801	247	11	r	r	NOUN
ap-1801	247	12	with	with	ADP
ap-1801	247	13	a	a	DET
ap-1801	247	14	bounded	bounded	ADJ
ap-1801	247	15	derivative	derivative	NOUN
ap-1801	247	16	,	,	PUNCT
ap-1801	247	17	∥∥θ̇∥∥∞	∥∥θ̇∥∥∞	X
ap-1801	247	18	<	<	X
ap-1801	247	19	∞	∞	PROPN
ap-1801	247	20	,	,	PUNCT
ap-1801	247	21	and	and	CCONJ
ap-1801	247	22	introduce	introduce	VERB
ap-1801	247	23	the	the	DET
ap-1801	247	24	set	set	NOUN
ap-1801	247	25	ωθ	ωθ	NOUN
ap-1801	247	26	as	as	ADP
ap-1801	247	27	the	the	DET
ap-1801	247	28	image	image	NOUN
ap-1801	247	29	ωθ	ωθ	INTJ
ap-1801	247	30	:	:	PUNCT
ap-1801	247	31	=	=	NOUN
ap-1801	247	32	lθ(ω0	lθ(ω0	ADJ
ap-1801	247	33	)	)	PUNCT
ap-1801	247	34	,	,	PUNCT
ap-1801	247	35	(	(	PUNCT
ap-1801	247	36	3.9	3.9	NUM
ap-1801	247	37	)	)	PUNCT
ap-1801	247	38	where	where	SCONJ
ap-1801	247	39	the	the	DET
ap-1801	247	40	map	map	NOUN
ap-1801	247	41	lθ	lθ	X
ap-1801	247	42	:	:	PUNCT
ap-1801	247	43	r3	r3	PROPN
ap-1801	247	44	→	→	SYM
ap-1801	247	45	r3	r3	PROPN
ap-1801	247	46	is	be	AUX
ap-1801	247	47	given	give	VERB
ap-1801	247	48	by	by	ADP
ap-1801	247	49	lθ(s	lθ(s	PROPN
ap-1801	247	50	,	,	PUNCT
ap-1801	247	51	x	x	X
ap-1801	247	52	,	,	PUNCT
ap-1801	247	53	y	y	PROPN
ap-1801	247	54	)	)	PUNCT
ap-1801	247	55	:	:	PUNCT
ap-1801	248	1	=	=	PUNCT
ap-1801	248	2	(	(	PUNCT
ap-1801	248	3	s	s	X
ap-1801	248	4	,	,	PUNCT
ap-1801	248	5	x	x	X
ap-1801	248	6	cos	cos	ADP
ap-1801	248	7	θ(s	θ(s	PROPN
ap-1801	248	8	)	)	PUNCT
ap-1801	249	1	+	+	CCONJ
ap-1801	249	2	y	y	PROPN
ap-1801	249	3	sin	sin	NOUN
ap-1801	249	4	θ(s),−x	θ(s),−x	NOUN
ap-1801	249	5	sin	sin	NOUN
ap-1801	249	6	θ(s	θ(s	NOUN
ap-1801	249	7	)	)	PUNCT
ap-1801	250	1	+	+	CCONJ
ap-1801	250	2	y	y	PROPN
ap-1801	250	3	cos	cos	PROPN
ap-1801	250	4	θ(s	θ(s	PROPN
ap-1801	250	5	)	)	PUNCT
ap-1801	250	6	)	)	PUNCT
ap-1801	250	7	.	.	PUNCT
ap-1801	251	1	(	(	PUNCT
ap-1801	251	2	3.10	3.10	NUM
ap-1801	251	3	)	)	PUNCT
ap-1801	251	4	we	we	PRON
ap-1801	251	5	are	be	AUX
ap-1801	251	6	interested	interested	ADJ
ap-1801	251	7	primarily	primarily	ADV
ap-1801	251	8	in	in	ADP
ap-1801	251	9	nontrivial	nontrivial	ADJ
ap-1801	251	10	situations	situation	NOUN
ap-1801	251	11	,	,	PUNCT
ap-1801	251	12	assuming	assume	VERB
ap-1801	251	13	that	that	SCONJ
ap-1801	251	14	(	(	PUNCT
ap-1801	251	15	1	1	NUM
ap-1801	251	16	.	.	PUNCT
ap-1801	251	17	)	)	PUNCT
ap-1801	252	1	the	the	DET
ap-1801	252	2	function	function	NOUN
ap-1801	252	3	θ	θ	PROPN
ap-1801	252	4	is	be	AUX
ap-1801	252	5	not	not	PART
ap-1801	252	6	constant	constant	ADJ
ap-1801	252	7	,	,	PUNCT
ap-1801	252	8	(	(	PUNCT
ap-1801	252	9	2	2	NUM
ap-1801	252	10	.	.	PUNCT
ap-1801	252	11	)	)	PUNCT
ap-1801	252	12	ω0	ω0	PROPN
ap-1801	252	13	is	be	AUX
ap-1801	252	14	not	not	PART
ap-1801	252	15	rotationally	rotationally	ADV
ap-1801	252	16	symmetric	symmetric	ADJ
ap-1801	252	17	with	with	ADP
ap-1801	252	18	respect	respect	NOUN
ap-1801	252	19	to	to	ADP
ap-1801	252	20	the	the	DET
ap-1801	252	21	origin	origin	NOUN
ap-1801	252	22	in	in	ADP
ap-1801	252	23	r2	r2	PROPN
ap-1801	252	24	.	.	PUNCT
ap-1801	253	1	to	to	PART
ap-1801	253	2	formulate	formulate	VERB
ap-1801	253	3	the	the	DET
ap-1801	253	4	result	result	NOUN
ap-1801	253	5	of	of	ADP
ap-1801	253	6	this	this	DET
ap-1801	253	7	section	section	NOUN
ap-1801	253	8	,	,	PUNCT
ap-1801	253	9	we	we	PRON
ap-1801	253	10	need	need	VERB
ap-1801	253	11	a	a	DET
ap-1801	253	12	few	few	ADJ
ap-1801	253	13	more	more	ADJ
ap-1801	253	14	preliminaries	preliminary	NOUN
ap-1801	253	15	.	.	PUNCT
ap-1801	254	1	first	first	ADV
ap-1801	254	2	of	of	ADP
ap-1801	254	3	all	all	PRON
ap-1801	254	4	,	,	PUNCT
ap-1801	254	5	we	we	PRON
ap-1801	254	6	introduce	introduce	VERB
ap-1801	254	7	%	%	NOUN
ap-1801	254	8	:	:	PUNCT
ap-1801	254	9	=	=	SYM
ap-1801	254	10	sup(x	sup(x	PROPN
ap-1801	254	11	,	,	PUNCT
ap-1801	254	12	y)∈ω0	y)∈ω0	NOUN
ap-1801	254	13	√	√	PROPN
ap-1801	254	14	x2	x2	NOUN
ap-1801	255	1	+	+	CCONJ
ap-1801	255	2	y2	y2	PROPN
ap-1801	255	3	and	and	CCONJ
ap-1801	255	4	assume	assume	VERB
ap-1801	255	5	that	that	SCONJ
ap-1801	255	6	%	%	NOUN
ap-1801	255	7	∥∥f(·)θ̇	∥∥f(·)θ̇	CCONJ
ap-1801	255	8	(	(	PUNCT
ap-1801	255	9	·	·	PUNCT
ap-1801	255	10	)	)	PUNCT
ap-1801	255	11	∥∥	∥∥	X
ap-1801	256	1	∞	∞	NOUN
ap-1801	256	2	<	<	X
ap-1801	256	3	1	1	NUM
ap-1801	256	4	.	.	PUNCT
ap-1801	257	1	(	(	PUNCT
ap-1801	257	2	3.11	3.11	NUM
ap-1801	257	3	)	)	PUNCT
ap-1801	257	4	next	next	ADV
ap-1801	257	5	we	we	PRON
ap-1801	257	6	set	set	VERB
ap-1801	257	7	ṽ	ṽ	PROPN
ap-1801	257	8	(	(	PUNCT
ap-1801	257	9	s	s	PROPN
ap-1801	257	10	,	,	PUNCT
ap-1801	257	11	x	x	NOUN
ap-1801	257	12	,	,	PUNCT
ap-1801	257	13	y	y	PROPN
ap-1801	257	14	)	)	PUNCT
ap-1801	257	15	:	:	PUNCT
ap-1801	257	16	=	=	SYM
ap-1801	257	17	v	v	X
ap-1801	257	18	(	(	PUNCT
ap-1801	257	19	lθ(s	lθ(s	X
ap-1801	257	20	,	,	PUNCT
ap-1801	257	21	x	x	X
ap-1801	257	22	,	,	PUNCT
ap-1801	257	23	y	y	PROPN
ap-1801	257	24	)	)	PUNCT
ap-1801	257	25	)	)	PUNCT
ap-1801	257	26	by	by	ADP
ap-1801	257	27	analogy	analogy	NOUN
ap-1801	257	28	with	with	ADP
ap-1801	257	29	the	the	DET
ap-1801	257	30	corresponding	corresponding	ADJ
ap-1801	257	31	definitions	definition	NOUN
ap-1801	257	32	in	in	ADP
ap-1801	257	33	the	the	DET
ap-1801	257	34	previous	previous	ADJ
ap-1801	257	35	sections	section	NOUN
ap-1801	257	36	,	,	PUNCT
ap-1801	257	37	and	and	CCONJ
ap-1801	257	38	finally	finally	ADV
ap-1801	257	39	,	,	PUNCT
ap-1801	257	40	we	we	PRON
ap-1801	257	41	introduce	introduce	VERB
ap-1801	257	42	the	the	DET
ap-1801	257	43	operator	operator	NOUN
ap-1801	257	44	ltrans	ltran	NOUN
ap-1801	257	45	:	:	PUNCT
ap-1801	257	46	=	=	SYM
ap-1801	257	47	−i	−i	ADJ
ap-1801	257	48	(	(	PUNCT
ap-1801	257	49	x	x	SYM
ap-1801	257	50	∂	∂	NUM
ap-1801	257	51	∂y	∂y	NOUN
ap-1801	257	52	−	−	PROPN
ap-1801	257	53	y	y	PROPN
ap-1801	257	54	∂	∂	NOUN
ap-1801	257	55	∂x	∂x	PROPN
ap-1801	257	56	)	)	PUNCT
ap-1801	257	57	,	,	PUNCT
ap-1801	257	58	dom(ltrans	dom(ltrans	PROPN
ap-1801	257	59	)	)	PUNCT
ap-1801	257	60	=	=	SYM
ap-1801	257	61	h1	h1	PROPN
ap-1801	257	62	0(ω0	0(ω0	NUM
ap-1801	257	63	)	)	PUNCT
ap-1801	257	64	,	,	PUNCT
ap-1801	257	65	describing	describe	VERB
ap-1801	257	66	the	the	DET
ap-1801	257	67	angular	angular	ADJ
ap-1801	257	68	momentum	momentum	NOUN
ap-1801	257	69	component	component	NOUN
ap-1801	257	70	canonically	canonically	ADV
ap-1801	257	71	associated	associate	VERB
ap-1801	257	72	with	with	ADP
ap-1801	257	73	rotations	rotation	NOUN
ap-1801	257	74	in	in	ADP
ap-1801	257	75	the	the	DET
ap-1801	257	76	transverse	transverse	NOUN
ap-1801	257	77	plane	plane	NOUN
ap-1801	257	78	.	.	PUNCT
ap-1801	258	1	we	we	PRON
ap-1801	258	2	have	have	VERB
ap-1801	258	3	the	the	DET
ap-1801	258	4	following	follow	VERB
ap-1801	258	5	claim	claim	NOUN
ap-1801	258	6	:	:	PUNCT
ap-1801	258	7	277	277	NUM
ap-1801	258	8	p.	p.	NOUN
ap-1801	258	9	exner	exner	NOUN
ap-1801	258	10	,	,	PUNCT
ap-1801	258	11	d.	d.	PROPN
ap-1801	258	12	barseghyan	barseghyan	PROPN
ap-1801	258	13	acta	acta	PROPN
ap-1801	258	14	polytechnica	polytechnica	PROPN
ap-1801	258	15	theorem	theorem	VERB
ap-1801	258	16	3.2	3.2	NUM
ap-1801	258	17	.	.	PUNCT
ap-1801	259	1	let	let	VERB
ap-1801	259	2	hωθ	hωθ	NOUN
ap-1801	259	3	be	be	AUX
ap-1801	259	4	the	the	DET
ap-1801	259	5	operator	operator	NOUN
ap-1801	259	6	(	(	PUNCT
ap-1801	259	7	3.1	3.1	NUM
ap-1801	259	8	)	)	PUNCT
ap-1801	259	9	referring	refer	VERB
ap-1801	259	10	to	to	ADP
ap-1801	259	11	the	the	DET
ap-1801	259	12	region	region	NOUN
ap-1801	259	13	ωθ	ωθ	NUM
ap-1801	259	14	defined	define	VERB
ap-1801	259	15	by	by	ADP
ap-1801	259	16	(	(	PUNCT
ap-1801	259	17	3.9	3.9	NUM
ap-1801	259	18	)	)	PUNCT
ap-1801	259	19	and	and	CCONJ
ap-1801	259	20	(	(	PUNCT
ap-1801	259	21	3.10	3.10	NUM
ap-1801	259	22	)	)	PUNCT
ap-1801	259	23	with	with	ADP
ap-1801	259	24	a	a	DET
ap-1801	259	25	potential	potential	ADJ
ap-1801	259	26	v	v	ADP
ap-1801	259	27	≥	≥	NOUN
ap-1801	259	28	0	0	NUM
ap-1801	259	29	which	which	PRON
ap-1801	259	30	is	be	AUX
ap-1801	259	31	bounded	bound	VERB
ap-1801	259	32	and	and	CCONJ
ap-1801	259	33	measurable	measurable	ADJ
ap-1801	259	34	.	.	PUNCT
ap-1801	260	1	under	under	ADP
ap-1801	260	2	the	the	DET
ap-1801	260	3	assumption	assumption	NOUN
ap-1801	260	4	(	(	PUNCT
ap-1801	260	5	3.11	3.11	NUM
ap-1801	260	6	)	)	PUNCT
ap-1801	260	7	for	for	ADP
ap-1801	260	8	the	the	DET
ap-1801	260	9	negative	negative	ADJ
ap-1801	260	10	spectrum	spectrum	NOUN
ap-1801	260	11	of	of	ADP
ap-1801	260	12	hωθ	hωθ	PROPN
ap-1801	260	13	the	the	DET
ap-1801	260	14	inequality	inequality	NOUN
ap-1801	260	15	tr	tr	VERB
ap-1801	260	16	(	(	PUNCT
ap-1801	260	17	hωθ	hωθ	PROPN
ap-1801	260	18	d	d	NOUN
ap-1801	260	19	)	)	PUNCT
ap-1801	260	20	σ	σ	PROPN
ap-1801	260	21	−	−	PROPN
ap-1801	260	22	≤	≤	NOUN
ap-1801	260	23	l	l	NOUN
ap-1801	260	24	cl	cl	NOUN
ap-1801	260	25	σ,1	σ,1	NOUN
ap-1801	260	26	(	(	PUNCT
ap-1801	260	27	1−	1−	NUM
ap-1801	260	28	%	%	NOUN
ap-1801	260	29	∥∥fθ̇∥∥∞)σ	∥∥fθ̇∥∥∞)σ	PUNCT
ap-1801	260	30	∫	∫	NOUN
ap-1801	260	31	r	r	NOUN
ap-1801	260	32	∞∑	∞∑	PROPN
ap-1801	260	33	j=1	j=1	NOUN
ap-1801	260	34	(	(	PUNCT
ap-1801	260	35	−λ0,j(s	−λ0,j(s	PROPN
ap-1801	260	36	)	)	PUNCT
ap-1801	260	37	f2(s	f2(s	NOUN
ap-1801	260	38	)	)	PUNCT
ap-1801	261	1	+	+	CCONJ
ap-1801	261	2	∥∥ṽ	∥∥ṽ	ADJ
ap-1801	261	3	∥∥∞	∥∥∞	NOUN
ap-1801	261	4	1−	1−	NUM
ap-1801	261	5	%	%	NOUN
ap-1801	261	6	∥∥fθ̇∥∥∞	∥∥fθ̇∥∥∞	PROPN
ap-1801	261	7	)	)	PUNCT
ap-1801	262	1	σ+1/2	σ+1/2	NOUN
ap-1801	263	1	+	+	CCONJ
ap-1801	263	2	ds	ds	ADJ
ap-1801	263	3	holds	hold	NOUN
ap-1801	263	4	true	true	ADJ
ap-1801	263	5	for	for	ADP
ap-1801	263	6	σ	σ	PROPN
ap-1801	263	7	≥	≥	PROPN
ap-1801	263	8	3/2	3/2	NUM
ap-1801	263	9	,	,	PUNCT
ap-1801	263	10	where	where	SCONJ
ap-1801	263	11	lcl	lcl	PROPN
ap-1801	263	12	σ,1	σ,1	PROPN
ap-1801	263	13	is	be	AUX
ap-1801	263	14	the	the	DET
ap-1801	263	15	constant	constant	ADJ
ap-1801	263	16	(	(	PUNCT
ap-1801	263	17	3.5	3.5	NUM
ap-1801	263	18	)	)	PUNCT
ap-1801	263	19	and	and	CCONJ
ap-1801	263	20	λ0,j(s	λ0,j(s	NUM
ap-1801	263	21	)	)	PUNCT
ap-1801	263	22	,	,	PUNCT
ap-1801	263	23	j	j	PROPN
ap-1801	264	1	=	=	SYM
ap-1801	264	2	1	1	NUM
ap-1801	264	3	,	,	PUNCT
ap-1801	264	4	2	2	NUM
ap-1801	264	5	,	,	PUNCT
ap-1801	264	6	.	.	PUNCT
ap-1801	264	7	.	.	PUNCT
ap-1801	265	1	.	.	PUNCT
ap-1801	266	1	,	,	PUNCT
ap-1801	266	2	are	be	AUX
ap-1801	266	3	the	the	DET
ap-1801	266	4	eigenvalues	eigenvalue	NOUN
ap-1801	266	5	of	of	ADP
ap-1801	266	6	the	the	DET
ap-1801	266	7	operator	operator	NOUN
ap-1801	266	8	hf	hf	NOUN
ap-1801	266	9	,	,	PUNCT
ap-1801	266	10	θ(s	θ(s	PROPN
ap-1801	266	11	)	)	PUNCT
ap-1801	266	12	:	:	PUNCT
ap-1801	267	1	=	=	PUNCT
ap-1801	267	2	−∆ω0	−∆ω0	PROPN
ap-1801	268	1	d	d	X
ap-1801	268	2	+	+	CCONJ
ap-1801	268	3	f2(s)θ̇2(s)l2	f2(s)θ̇2(s)l2	VERB
ap-1801	268	4	trans	tran	NOUN
ap-1801	268	5	defined	define	VERB
ap-1801	268	6	on	on	ADP
ap-1801	268	7	the	the	DET
ap-1801	268	8	domain	domain	NOUN
ap-1801	268	9	h2	h2	NOUN
ap-1801	268	10	0(ω0	0(ω0	NUM
ap-1801	268	11	)	)	PUNCT
ap-1801	268	12	in	in	ADP
ap-1801	268	13	l2(ω0	l2(ω0	ADJ
ap-1801	268	14	)	)	PUNCT
ap-1801	268	15	.	.	PUNCT
ap-1801	269	1	sketch	sketch	NOUN
ap-1801	269	2	of	of	ADP
ap-1801	269	3	the	the	DET
ap-1801	269	4	proof	proof	NOUN
ap-1801	269	5	.	.	PUNCT
ap-1801	270	1	as	as	ADP
ap-1801	270	2	before	before	ADV
ap-1801	270	3	,	,	PUNCT
ap-1801	270	4	we	we	PRON
ap-1801	270	5	employ	employ	VERB
ap-1801	270	6	suitable	suitable	ADJ
ap-1801	270	7	curvilinear	curvilinear	PROPN
ap-1801	270	8	coordinates	coordinate	NOUN
ap-1801	270	9	,	,	PUNCT
ap-1801	270	10	this	this	DET
ap-1801	270	11	time	time	NOUN
ap-1801	270	12	to	to	PART
ap-1801	270	13	‘	'	PUNCT
ap-1801	270	14	untwist	untwist	VERB
ap-1801	270	15	’	'	PUNCT
ap-1801	270	16	the	the	DET
ap-1801	270	17	region	region	NOUN
ap-1801	270	18	.	.	PUNCT
ap-1801	271	1	we	we	PRON
ap-1801	271	2	define	define	VERB
ap-1801	271	3	a	a	DET
ap-1801	271	4	unitary	unitary	ADJ
ap-1801	271	5	operator	operator	NOUN
ap-1801	271	6	from	from	ADP
ap-1801	271	7	l2(ωθ	l2(ωθ	PROPN
ap-1801	271	8	)	)	PUNCT
ap-1801	271	9	to	to	PART
ap-1801	271	10	l2(ω0	l2(ω0	VERB
ap-1801	271	11	)	)	PUNCT
ap-1801	271	12	by	by	ADP
ap-1801	271	13	uθψ	uθψ	NOUN
ap-1801	271	14	:	:	PUNCT
ap-1801	271	15	=	=	SYM
ap-1801	271	16	ψ	ψ	PART
ap-1801	271	17	◦	◦	NOUN
ap-1801	271	18	lθ	lθ	PRON
ap-1801	271	19	which	which	PRON
ap-1801	271	20	allows	allow	VERB
ap-1801	271	21	us	we	PRON
ap-1801	271	22	to	to	PART
ap-1801	271	23	pass	pass	VERB
ap-1801	271	24	from	from	ADP
ap-1801	271	25	hd	hd	NOUN
ap-1801	271	26	ωθ	ωθ	NOUN
ap-1801	271	27	to	to	ADP
ap-1801	271	28	the	the	DET
ap-1801	271	29	operator	operator	NOUN
ap-1801	271	30	h0	h0	NOUN
ap-1801	271	31	:	:	PUNCT
ap-1801	271	32	=	=	SYM
ap-1801	271	33	uθ	uθ	X
ap-1801	271	34	(	(	PUNCT
ap-1801	271	35	hd	hd	PROPN
ap-1801	271	36	ωθ	ωθ	NOUN
ap-1801	271	37	)	)	PUNCT
ap-1801	271	38	u−1	u−1	PROPN
ap-1801	271	39	θ	θ	PROPN
ap-1801	271	40	in	in	ADP
ap-1801	271	41	l2(ω0	l2(ω0	ADJ
ap-1801	271	42	)	)	PUNCT
ap-1801	271	43	.	.	PUNCT
ap-1801	272	1	from	from	ADP
ap-1801	272	2	paper	paper	NOUN
ap-1801	272	3	[	[	X
ap-1801	272	4	19	19	NUM
ap-1801	272	5	]	]	X
ap-1801	272	6	we	we	PRON
ap-1801	272	7	know	know	VERB
ap-1801	272	8	that	that	DET
ap-1801	272	9	h0	h0	PROPN
ap-1801	272	10	is	be	AUX
ap-1801	272	11	the	the	DET
ap-1801	272	12	self	self	NOUN
ap-1801	272	13	-	-	PUNCT
ap-1801	272	14	adjoint	adjoint	NOUN
ap-1801	272	15	operator	operator	NOUN
ap-1801	272	16	associated	associate	VERB
ap-1801	272	17	with	with	ADP
ap-1801	272	18	the	the	DET
ap-1801	272	19	quadratic	quadratic	ADJ
ap-1801	272	20	form	form	NOUN
ap-1801	272	21	q0	q0	NOUN
ap-1801	272	22	:	:	PUNCT
ap-1801	272	23	q0[ψ	q0[ψ	VERB
ap-1801	272	24	]	]	X
ap-1801	272	25	:	:	PUNCT
ap-1801	272	26	=	=	SYM
ap-1801	273	1	∥∥∂sψ	∥∥∂sψ	PROPN
ap-1801	273	2	+	+	CCONJ
ap-1801	273	3	iθ̇ltransψ	iθ̇ltransψ	VERB
ap-1801	273	4	∥∥2	∥∥2	NOUN
ap-1801	274	1	+	+	CCONJ
ap-1801	274	2	∥∥∇′ψ∥∥2	∥∥∇′ψ∥∥2	PROPN
ap-1801	274	3	−	−	PROPN
ap-1801	274	4	∫	∫	PROPN
ap-1801	274	5	ω0	ω0	PROPN
ap-1801	274	6	(	(	PUNCT
ap-1801	274	7	ṽ	ṽ	PROPN
ap-1801	274	8	|ψ|2	|ψ|2	PROPN
ap-1801	274	9	)	)	PUNCT
ap-1801	274	10	(	(	PUNCT
ap-1801	274	11	s	s	X
ap-1801	274	12	,	,	PUNCT
ap-1801	274	13	x	x	NOUN
ap-1801	274	14	,	,	PUNCT
ap-1801	274	15	y	y	NOUN
ap-1801	274	16	)	)	PUNCT
ap-1801	274	17	dsdxdy	dsdxdy	NOUN
ap-1801	274	18	defined	define	VERB
ap-1801	274	19	on	on	ADP
ap-1801	274	20	h1	h1	PROPN
ap-1801	274	21	0	0	NUM
ap-1801	274	22	,	,	PUNCT
ap-1801	274	23	where	where	SCONJ
ap-1801	274	24	∇′	∇′	PROPN
ap-1801	274	25	:	:	PUNCT
ap-1801	274	26	=	=	SYM
ap-1801	274	27	(	(	PUNCT
ap-1801	274	28	∂x	∂x	PROPN
ap-1801	274	29	,	,	PUNCT
ap-1801	274	30	∂y	∂y	PROPN
ap-1801	274	31	)	)	PUNCT
ap-1801	274	32	is	be	AUX
ap-1801	274	33	the	the	DET
ap-1801	274	34	transversal	transversal	ADJ
ap-1801	274	35	gradient	gradient	NOUN
ap-1801	274	36	and	and	CCONJ
ap-1801	274	37	the	the	DET
ap-1801	274	38	norms	norm	NOUN
ap-1801	274	39	refer	refer	VERB
ap-1801	274	40	to	to	ADP
ap-1801	274	41	l2(ω0	l2(ω0	ADJ
ap-1801	274	42	)	)	PUNCT
ap-1801	274	43	.	.	PUNCT
ap-1801	275	1	for	for	ADP
ap-1801	275	2	any	any	DET
ap-1801	275	3	function	function	NOUN
ap-1801	275	4	ψ	ψ	X
ap-1801	275	5	∈	∈	PROPN
ap-1801	275	6	h1	h1	NOUN
ap-1801	275	7	0	0	NUM
ap-1801	275	8	(	(	PUNCT
ap-1801	275	9	ωs	ωs	PROPN
ap-1801	275	10	)	)	PUNCT
ap-1801	275	11	we	we	PRON
ap-1801	275	12	have	have	VERB
ap-1801	275	13	|ltransψ|	|ltransψ|	NUM
ap-1801	275	14	≤	≤	NUM
ap-1801	275	15	%	%	NOUN
ap-1801	275	16	f(s)|∇′ψ|	f(s)|∇′ψ|	PROPN
ap-1801	275	17	and	and	CCONJ
ap-1801	275	18	applying	apply	VERB
ap-1801	275	19	the	the	DET
ap-1801	275	20	cauchy	cauchy	NOUN
ap-1801	275	21	-	-	PUNCT
ap-1801	275	22	schwarz	schwarz	PROPN
ap-1801	275	23	inequality	inequality	NOUN
ap-1801	275	24	we	we	PRON
ap-1801	275	25	infer	infer	VERB
ap-1801	275	26	2	2	NUM
ap-1801	275	27	∣∣∣∣∫	∣∣∣∣∫	NOUN
ap-1801	275	28	ω0	ω0	ADV
ap-1801	275	29	θ̇∂sψltransψ	θ̇∂sψltransψ	PRON
ap-1801	275	30	dsdxdy	dsdxdy	NOUN
ap-1801	275	31	∣∣∣∣	∣∣∣∣	PROPN
ap-1801	275	32	≤	≤	NUM
ap-1801	275	33	%	%	NOUN
ap-1801	275	34	∥∥fθ̇∥∥∞(∥∥∂sψ∥∥2	∥∥fθ̇∥∥∞(∥∥∂sψ∥∥2	PROPN
ap-1801	275	35	l2(ω0	l2(ω0	ADJ
ap-1801	275	36	)	)	PUNCT
ap-1801	276	1	+	+	CCONJ
ap-1801	277	1	∥∥∇′ψ∥∥2	∥∥∇′ψ∥∥2	PROPN
ap-1801	277	2	l2(ω0	l2(ω0	ADJ
ap-1801	277	3	)	)	PUNCT
ap-1801	277	4	)	)	PUNCT
ap-1801	277	5	,	,	PUNCT
ap-1801	277	6	thus	thus	ADV
ap-1801	277	7	q0[ψ	q0[ψ	VERB
ap-1801	277	8	]	]	PUNCT
ap-1801	277	9	can	can	AUX
ap-1801	277	10	be	be	AUX
ap-1801	277	11	estimated	estimate	VERB
ap-1801	277	12	from	from	ADP
ap-1801	277	13	below	below	ADP
ap-1801	277	14	by	by	ADP
ap-1801	277	15	(	(	PUNCT
ap-1801	277	16	1−	1−	NUM
ap-1801	277	17	%	%	NOUN
ap-1801	277	18	∥∥fθ̇∥∥∞)(∥∥∇ψ∥∥2	∥∥fθ̇∥∥∞)(∥∥∇ψ∥∥2	PROPN
ap-1801	277	19	l2(ω0	l2(ω0	ADJ
ap-1801	277	20	)	)	PUNCT
ap-1801	278	1	+	+	CCONJ
ap-1801	278	2	∥∥θ̇ltransψ	∥∥θ̇ltransψ	PROPN
ap-1801	278	3	∥∥2	∥∥2	PROPN
ap-1801	278	4	l2(ω0	l2(ω0	ADJ
ap-1801	278	5	)	)	PUNCT
ap-1801	278	6	)	)	PUNCT
ap-1801	279	1	−	−	NUM
ap-1801	279	2	∫	∫	PROPN
ap-1801	279	3	ω0	ω0	PROPN
ap-1801	279	4	∥∥ṽ	∥∥ṽ	NOUN
ap-1801	279	5	(	(	PUNCT
ap-1801	279	6	s	s	PROPN
ap-1801	279	7	,	,	PUNCT
ap-1801	279	8	·	·	PUNCT
ap-1801	279	9	)	)	PUNCT
ap-1801	279	10	∥∥	∥∥	PROPN
ap-1801	279	11	∞|ψ|	∞|ψ|	PROPN
ap-1801	279	12	2	2	NUM
ap-1801	279	13	dsdxdy	dsdxdy	NOUN
ap-1801	279	14	.	.	PUNCT
ap-1801	280	1	we	we	PRON
ap-1801	280	2	introduce	introduce	VERB
ap-1801	280	3	the	the	DET
ap-1801	280	4	operator	operator	NOUN
ap-1801	280	5	h−0	h−0	PROPN
ap-1801	280	6	=	=	PUNCT
ap-1801	280	7	−∆ω0	−∆ω0	PROPN
ap-1801	281	1	d	d	X
ap-1801	281	2	+	+	CCONJ
ap-1801	281	3	θ̇2l2	θ̇2l2	VERB
ap-1801	281	4	trans	tran	NOUN
ap-1801	281	5	−	−	PROPN
ap-1801	281	6	1	1	NUM
ap-1801	281	7	1−	1−	NUM
ap-1801	281	8	%	%	NOUN
ap-1801	281	9	∥∥fθ̇∥∥∞	∥∥fθ̇∥∥∞	NOUN
ap-1801	281	10	∥∥ṽ	∥∥ṽ	NOUN
ap-1801	281	11	(	(	PUNCT
ap-1801	281	12	s	s	PROPN
ap-1801	281	13	,	,	PUNCT
ap-1801	281	14	·	·	PUNCT
ap-1801	281	15	)	)	PUNCT
ap-1801	281	16	∥∥	∥∥	PUNCT
ap-1801	282	1	∞	∞	NUM
ap-1801	282	2	defined	define	VERB
ap-1801	282	3	on	on	ADP
ap-1801	282	4	h2	h2	PROPN
ap-1801	282	5	0	0	NUM
ap-1801	282	6	(	(	PUNCT
ap-1801	282	7	ω0	ω0	PROPN
ap-1801	282	8	)	)	PUNCT
ap-1801	282	9	,	,	PUNCT
ap-1801	282	10	then	then	ADV
ap-1801	282	11	the	the	DET
ap-1801	282	12	above	above	ADJ
ap-1801	282	13	estimate	estimate	NOUN
ap-1801	282	14	implies	imply	VERB
ap-1801	282	15	h0	h0	PROPN
ap-1801	282	16	≥	≥	PRON
ap-1801	282	17	(	(	PUNCT
ap-1801	282	18	1−	1−	NUM
ap-1801	282	19	%	%	NOUN
ap-1801	282	20	∥∥fθ̇∥∥∞)h−0	∥∥fθ̇∥∥∞)h−0	PROPN
ap-1801	282	21	,	,	PUNCT
ap-1801	282	22	(	(	PUNCT
ap-1801	282	23	3.12	3.12	NUM
ap-1801	282	24	)	)	PUNCT
ap-1801	282	25	hence	hence	ADV
ap-1801	282	26	by	by	ADP
ap-1801	282	27	the	the	DET
ap-1801	282	28	minimax	minimax	NOUN
ap-1801	282	29	principle	principle	NOUN
ap-1801	282	30	and	and	CCONJ
ap-1801	282	31	the	the	DET
ap-1801	282	32	condition	condition	NOUN
ap-1801	282	33	(	(	PUNCT
ap-1801	282	34	3.11	3.11	NUM
ap-1801	282	35	)	)	PUNCT
ap-1801	282	36	it	it	PRON
ap-1801	282	37	is	be	AUX
ap-1801	282	38	enough	enough	ADJ
ap-1801	282	39	to	to	PART
ap-1801	282	40	establish	establish	VERB
ap-1801	282	41	the	the	DET
ap-1801	282	42	upper	upper	ADJ
ap-1801	282	43	estimate	estimate	NOUN
ap-1801	282	44	for	for	ADP
ap-1801	282	45	the	the	DET
ap-1801	282	46	negative	negative	ADJ
ap-1801	282	47	spectrum	spectrum	NOUN
ap-1801	282	48	of	of	ADP
ap-1801	282	49	operator	operator	NOUN
ap-1801	282	50	h−0	h−0	PROPN
ap-1801	282	51	.	.	PUNCT
ap-1801	283	1	using	use	VERB
ap-1801	283	2	again	again	ADV
ap-1801	283	3	the	the	DET
ap-1801	283	4	variational	variational	ADJ
ap-1801	283	5	technique	technique	NOUN
ap-1801	283	6	one	one	PRON
ap-1801	283	7	can	can	AUX
ap-1801	283	8	estimate	estimate	VERB
ap-1801	283	9	the	the	DET
ap-1801	283	10	negative	negative	ADJ
ap-1801	283	11	eigenvalue	eigenvalue	ADJ
ap-1801	283	12	moments	moment	NOUN
ap-1801	283	13	of	of	ADP
ap-1801	283	14	operator	operator	NOUN
ap-1801	283	15	h−0	h−0	PROPN
ap-1801	283	16	by	by	ADP
ap-1801	283	17	the	the	DET
ap-1801	283	18	moments	moment	NOUN
ap-1801	283	19	of	of	ADP
ap-1801	283	20	the	the	DET
ap-1801	283	21	operator	operator	NOUN
ap-1801	283	22	with	with	ADP
ap-1801	283	23	separated	separate	VERB
ap-1801	283	24	variables	variable	NOUN
ap-1801	283	25	,	,	PUNCT
ap-1801	283	26	−	−	PROPN
ap-1801	283	27	∂2	∂2	NOUN
ap-1801	283	28	∂	∂	NOUN
ap-1801	283	29	s2	s2	NOUN
ap-1801	283	30	⊗	⊗	NUM
ap-1801	283	31	il2(r2	il2(r2	NUM
ap-1801	283	32	)	)	PUNCT
ap-1801	283	33	+	+	CCONJ
ap-1801	283	34	h(s	h(s	PROPN
ap-1801	283	35	,	,	PUNCT
ap-1801	283	36	ṽ	ṽ	PROPN
ap-1801	283	37	)	)	PUNCT
ap-1801	283	38	,	,	PUNCT
ap-1801	283	39	defined	define	VERB
ap-1801	283	40	on	on	ADP
ap-1801	283	41	the	the	DET
ap-1801	283	42	domain	domain	NOUN
ap-1801	283	43	h1	h1	NOUN
ap-1801	283	44	(	(	PUNCT
ap-1801	283	45	r	r	NOUN
ap-1801	283	46	,	,	PUNCT
ap-1801	283	47	l2(r2	l2(r2	NOUN
ap-1801	283	48	)	)	PUNCT
ap-1801	283	49	)	)	PUNCT
ap-1801	283	50	,	,	PUNCT
ap-1801	283	51	i.e.	i.e.	X
ap-1801	283	52	tr	tr	X
ap-1801	283	53	(	(	PUNCT
ap-1801	283	54	h−0	h−0	PROPN
ap-1801	283	55	)	)	PUNCT
ap-1801	283	56	σ	σ	PROPN
ap-1801	283	57	−	−	PROPN
ap-1801	283	58	≤	≤	NOUN
ap-1801	283	59	tr	tr	PUNCT
ap-1801	283	60	(	(	PUNCT
ap-1801	283	61	−	−	PROPN
ap-1801	283	62	∂2	∂2	PROPN
ap-1801	283	63	∂s2	∂s2	PROPN
ap-1801	283	64	⊗	⊗	PROPN
ap-1801	283	65	il2(r2	il2(r2	PROPN
ap-1801	283	66	)	)	PUNCT
ap-1801	284	1	+	+	ADJ
ap-1801	284	2	h(s	h(s	PROPN
ap-1801	284	3	,	,	PUNCT
ap-1801	284	4	ṽ	ṽ	PROPN
ap-1801	284	5	)	)	PUNCT
ap-1801	284	6	)	)	PUNCT
ap-1801	285	1	σ	σ	PROPN
ap-1801	285	2	−	−	PROPN
ap-1801	285	3	,	,	PUNCT
ap-1801	285	4	σ	σ	X
ap-1801	285	5	≥	≥	PROPN
ap-1801	285	6	0	0	NUM
ap-1801	285	7	.	.	PUNCT
ap-1801	286	1	in	in	ADP
ap-1801	286	2	view	view	NOUN
ap-1801	286	3	of	of	ADP
ap-1801	286	4	the	the	DET
ap-1801	286	5	lieb	lieb	PROPN
ap-1801	286	6	-	-	PUNCT
ap-1801	286	7	thirring	thirre	VERB
ap-1801	286	8	inequality	inequality	NOUN
ap-1801	286	9	for	for	ADP
ap-1801	286	10	operator	operator	NOUN
ap-1801	286	11	valued	value	VERB
ap-1801	286	12	potentials	potential	VERB
ap-1801	286	13	this	this	PRON
ap-1801	286	14	implies	imply	VERB
ap-1801	286	15	tr	tr	VERB
ap-1801	286	16	(	(	PUNCT
ap-1801	286	17	h−0	h−0	PROPN
ap-1801	286	18	)	)	PUNCT
ap-1801	286	19	σ	σ	PROPN
ap-1801	287	1	−	−	PROPN
ap-1801	287	2	≤	≤	NUM
ap-1801	287	3	l	l	NOUN
ap-1801	287	4	cl	cl	NOUN
ap-1801	287	5	σ,1	σ,1	PRON
ap-1801	287	6	∫	∫	NOUN
ap-1801	287	7	r	r	NOUN
ap-1801	287	8	trh	trh	NOUN
ap-1801	287	9	(	(	PUNCT
ap-1801	287	10	s	s	PROPN
ap-1801	287	11	,	,	PUNCT
ap-1801	287	12	ṽ	ṽ	PROPN
ap-1801	287	13	)	)	PUNCT
ap-1801	287	14	σ+1/2	σ+1/2	NOUN
ap-1801	288	1	−	−	PROPN
ap-1801	288	2	d	d	PROPN
ap-1801	288	3	s	s	PROPN
ap-1801	288	4	,	,	PUNCT
ap-1801	288	5	for	for	ADP
ap-1801	288	6	any	any	DET
ap-1801	288	7	σ	σ	PROPN
ap-1801	288	8	≥	≥	NUM
ap-1801	288	9	3/2	3/2	NUM
ap-1801	288	10	(	(	PUNCT
ap-1801	288	11	3.13	3.13	NUM
ap-1801	288	12	)	)	PUNCT
ap-1801	288	13	with	with	ADP
ap-1801	288	14	the	the	DET
ap-1801	288	15	semiclassical	semiclassical	ADJ
ap-1801	288	16	constant	constant	ADJ
ap-1801	288	17	lcl	lcl	NOUN
ap-1801	288	18	σ,1	σ,1	PROPN
ap-1801	288	19	.	.	PUNCT
ap-1801	289	1	then	then	ADV
ap-1801	289	2	,	,	PUNCT
ap-1801	289	3	by	by	ADP
ap-1801	289	4	virtue	virtue	NOUN
ap-1801	289	5	of	of	ADP
ap-1801	289	6	unitary	unitary	ADJ
ap-1801	289	7	equivalence	equivalence	NOUN
ap-1801	289	8	of	of	ADP
ap-1801	289	9	operators	operator	NOUN
ap-1801	289	10	hωθ	hωθ	PROPN
ap-1801	289	11	d	d	NOUN
ap-1801	289	12	and	and	CCONJ
ap-1801	289	13	h0	h0	PROPN
ap-1801	289	14	,	,	PUNCT
ap-1801	289	15	inequalities	inequality	NOUN
ap-1801	289	16	(	(	PUNCT
ap-1801	289	17	3.12	3.12	NUM
ap-1801	289	18	)	)	PUNCT
ap-1801	289	19	,	,	PUNCT
ap-1801	289	20	(	(	PUNCT
ap-1801	289	21	3.13	3.13	NUM
ap-1801	289	22	)	)	PUNCT
ap-1801	289	23	and	and	CCONJ
ap-1801	289	24	the	the	DET
ap-1801	289	25	condition	condition	NOUN
ap-1801	289	26	(	(	PUNCT
ap-1801	289	27	3.11	3.11	NUM
ap-1801	289	28	)	)	PUNCT
ap-1801	289	29	we	we	PRON
ap-1801	289	30	get	get	VERB
ap-1801	289	31	tr	tr	VERB
ap-1801	289	32	(	(	PUNCT
ap-1801	289	33	hωθ	hωθ	PROPN
ap-1801	289	34	d	d	NOUN
ap-1801	289	35	)	)	PUNCT
ap-1801	289	36	σ	σ	PROPN
ap-1801	289	37	−	−	PROPN
ap-1801	289	38	≤	≤	NOUN
ap-1801	289	39	l	l	NOUN
ap-1801	289	40	cl	cl	NOUN
ap-1801	289	41	σ,1	σ,1	NOUN
ap-1801	289	42	(	(	PUNCT
ap-1801	289	43	1−	1−	NUM
ap-1801	289	44	%	%	NOUN
ap-1801	289	45	∥∥fθ̇∥∥∞)σ	∥∥fθ̇∥∥∞)σ	PUNCT
ap-1801	289	46	∫	∫	PROPN
ap-1801	289	47	r	r	NOUN
ap-1801	289	48	trh	trh	NOUN
ap-1801	289	49	(	(	PUNCT
ap-1801	289	50	s	s	PROPN
ap-1801	289	51	,	,	PUNCT
ap-1801	289	52	ṽ	ṽ	PROPN
ap-1801	289	53	)	)	PUNCT
ap-1801	289	54	σ+1/2	σ+1/2	NOUN
ap-1801	290	1	−	−	NOUN
ap-1801	290	2	ds	ds	NOUN
ap-1801	290	3	for	for	ADP
ap-1801	290	4	σ	σ	PROPN
ap-1801	290	5	≥	≥	PROPN
ap-1801	290	6	3/2	3/2	NUM
ap-1801	290	7	.	.	PUNCT
ap-1801	291	1	(	(	PUNCT
ap-1801	291	2	3.14	3.14	NUM
ap-1801	291	3	)	)	PUNCT
ap-1801	291	4	278	278	NUM
ap-1801	291	5	vol	vol	NOUN
ap-1801	291	6	.	.	PUNCT
ap-1801	292	1	53	53	NUM
ap-1801	292	2	no	no	NOUN
ap-1801	292	3	.	.	PUNCT
ap-1801	293	1	3/2013	3/2013	PROPN
ap-1801	293	2	spectral	spectral	ADJ
ap-1801	293	3	analysis	analysis	NOUN
ap-1801	293	4	of	of	ADP
ap-1801	293	5	schrödinger	schrödinger	ADJ
ap-1801	293	6	operators	operator	NOUN
ap-1801	293	7	it	it	PRON
ap-1801	293	8	is	be	AUX
ap-1801	293	9	easy	easy	ADJ
ap-1801	293	10	to	to	PART
ap-1801	293	11	see	see	VERB
ap-1801	293	12	that	that	SCONJ
ap-1801	293	13	the	the	DET
ap-1801	293	14	eigenvalues	eigenvalue	NOUN
ap-1801	293	15	of	of	ADP
ap-1801	293	16	operator	operator	NOUN
ap-1801	293	17	h(s	h(s	PROPN
ap-1801	293	18	,	,	PUNCT
ap-1801	293	19	ṽ	ṽ	PROPN
ap-1801	293	20	)	)	PUNCT
ap-1801	293	21	are(λ0,j(s	are(λ0,j(s	PROPN
ap-1801	293	22	)	)	PUNCT
ap-1801	293	23	f2(s	f2(s	PROPN
ap-1801	293	24	)	)	PUNCT
ap-1801	294	1	−	−	NOUN
ap-1801	294	2	1	1	NUM
ap-1801	294	3	1−	1−	NUM
ap-1801	294	4	%	%	NOUN
ap-1801	294	5	∥∥fθ̇∥∥∞	∥∥fθ̇∥∥∞	NOUN
ap-1801	294	6	∥∥ṽ	∥∥ṽ	NOUN
ap-1801	294	7	(	(	PUNCT
ap-1801	294	8	s	s	PROPN
ap-1801	294	9	,	,	PUNCT
ap-1801	294	10	·	·	PUNCT
ap-1801	294	11	)	)	PUNCT
ap-1801	294	12	∥∥	∥∥	PROPN
ap-1801	294	13	∞	∞	NUM
ap-1801	294	14	)	)	PUNCT
ap-1801	294	15	−	−	PROPN
ap-1801	294	16	,	,	PUNCT
ap-1801	294	17	j	j	PROPN
ap-1801	294	18	=	=	SYM
ap-1801	294	19	1	1	NUM
ap-1801	294	20	,	,	PUNCT
ap-1801	294	21	2	2	NUM
ap-1801	294	22	,	,	PUNCT
ap-1801	294	23	.	.	PUNCT
ap-1801	294	24	.	.	PUNCT
ap-1801	294	25	.	.	PUNCT
ap-1801	295	1	,	,	PUNCT
ap-1801	295	2	(	(	PUNCT
ap-1801	295	3	3.15	3.15	NUM
ap-1801	295	4	)	)	PUNCT
ap-1801	295	5	where	where	SCONJ
ap-1801	295	6	λ0,j(s	λ0,j(s	X
ap-1801	295	7	)	)	PUNCT
ap-1801	295	8	,	,	PUNCT
ap-1801	295	9	j	j	PROPN
ap-1801	295	10	=	=	SYM
ap-1801	295	11	1	1	NUM
ap-1801	295	12	,	,	PUNCT
ap-1801	295	13	2	2	NUM
ap-1801	295	14	,	,	PUNCT
ap-1801	295	15	.	.	PUNCT
ap-1801	295	16	.	.	PUNCT
ap-1801	295	17	.	.	PUNCT
ap-1801	296	1	are	be	AUX
ap-1801	296	2	eigenvalues	eigenvalue	NOUN
ap-1801	296	3	of	of	ADP
ap-1801	296	4	the	the	DET
ap-1801	296	5	operator	operator	NOUN
ap-1801	296	6	hf	hf	NOUN
ap-1801	296	7	,	,	PUNCT
ap-1801	296	8	θ(s	θ(s	PROPN
ap-1801	296	9	)	)	PUNCT
ap-1801	296	10	:	:	PUNCT
ap-1801	297	1	=	=	PUNCT
ap-1801	297	2	−∆ω0	−∆ω0	PROPN
ap-1801	298	1	d	d	X
ap-1801	298	2	+	+	CCONJ
ap-1801	298	3	f2(s)θ̇2(s)l2	f2(s)θ̇2(s)l2	VERB
ap-1801	298	4	trans	tran	NOUN
ap-1801	298	5	.	.	PROPN
ap-1801	299	1	from	from	ADP
ap-1801	299	2	inequalities	inequality	NOUN
ap-1801	299	3	(	(	PUNCT
ap-1801	299	4	3.14	3.14	NUM
ap-1801	299	5	)	)	PUNCT
ap-1801	299	6	and	and	CCONJ
ap-1801	299	7	(	(	PUNCT
ap-1801	299	8	3.15	3.15	NUM
ap-1801	299	9	)	)	PUNCT
ap-1801	299	10	it	it	PRON
ap-1801	299	11	follows	follow	VERB
ap-1801	299	12	that	that	SCONJ
ap-1801	299	13	tr	tr	PUNCT
ap-1801	299	14	(	(	PUNCT
ap-1801	299	15	hωθ	hωθ	PROPN
ap-1801	299	16	d	d	NOUN
ap-1801	299	17	)	)	PUNCT
ap-1801	299	18	σ	σ	NOUN
ap-1801	299	19	−	−	PROPN
ap-1801	299	20	is	be	AUX
ap-1801	299	21	estimated	estimate	VERB
ap-1801	299	22	by	by	ADP
ap-1801	299	23	lcl	lcl	PROPN
ap-1801	299	24	σ,1	σ,1	PROPN
ap-1801	299	25	(	(	PUNCT
ap-1801	299	26	1−	1−	NUM
ap-1801	299	27	%	%	NOUN
ap-1801	299	28	∥∥fθ̇∥∥∞)σ	∥∥fθ̇∥∥∞)σ	PUNCT
ap-1801	299	29	∫	∫	NOUN
ap-1801	300	1	r	r	NOUN
ap-1801	300	2	∞∑	∞∑	PROPN
ap-1801	300	3	j=1	j=1	NOUN
ap-1801	300	4	(	(	PUNCT
ap-1801	300	5	−λ0,j(s	−λ0,j(s	PROPN
ap-1801	300	6	)	)	PUNCT
ap-1801	300	7	f2(s	f2(s	NOUN
ap-1801	300	8	)	)	PUNCT
ap-1801	301	1	+	+	CCONJ
ap-1801	301	2	1	1	NUM
ap-1801	301	3	1−	1−	NUM
ap-1801	301	4	%	%	NOUN
ap-1801	301	5	∥∥fθ̇∥∥∞	∥∥fθ̇∥∥∞	NOUN
ap-1801	301	6	∥∥ṽ	∥∥ṽ	NOUN
ap-1801	301	7	(	(	PUNCT
ap-1801	301	8	s	s	PROPN
ap-1801	301	9	,	,	PUNCT
ap-1801	301	10	·	·	PUNCT
ap-1801	301	11	)	)	PUNCT
ap-1801	301	12	∥∥	∥∥	X
ap-1801	301	13	∞	∞	NUM
ap-1801	301	14	)	)	PUNCT
ap-1801	302	1	σ+1/2	σ+1/2	PROPN
ap-1801	303	1	+	+	CCONJ
ap-1801	303	2	ds	ds	ADJ
ap-1801	303	3	,	,	PUNCT
ap-1801	303	4	for	for	ADP
ap-1801	303	5	any	any	DET
ap-1801	303	6	σ	σ	PROPN
ap-1801	303	7	≥	≥	NUM
ap-1801	303	8	3/2	3/2	NUM
ap-1801	303	9	which	which	PRON
ap-1801	303	10	proves	prove	VERB
ap-1801	303	11	the	the	DET
ap-1801	303	12	theorem	theorem	NOUN
ap-1801	303	13	.	.	PUNCT
ap-1801	304	1	acknowledgements	acknowledgement	VERB
ap-1801	304	2	the	the	DET
ap-1801	304	3	research	research	NOUN
ap-1801	304	4	presented	present	VERB
ap-1801	304	5	here	here	ADV
ap-1801	304	6	was	be	AUX
ap-1801	304	7	supported	support	VERB
ap-1801	304	8	by	by	ADP
ap-1801	304	9	the	the	DET
ap-1801	304	10	czech	czech	PROPN
ap-1801	304	11	science	science	NOUN
ap-1801	304	12	foundation	foundation	PROPN
ap-1801	304	13	within	within	ADP
ap-1801	304	14	project	project	NOUN
ap-1801	304	15	p203/11/0701	p203/11/0701	NOUN
ap-1801	304	16	.	.	PUNCT
ap-1801	305	1	the	the	DET
ap-1801	305	2	authors	author	NOUN
ap-1801	305	3	are	be	AUX
ap-1801	305	4	grateful	grateful	ADJ
ap-1801	305	5	to	to	ADP
ap-1801	305	6	the	the	DET
ap-1801	305	7	referees	referee	NOUN
ap-1801	305	8	for	for	ADP
ap-1801	305	9	reading	read	VERB
ap-1801	305	10	the	the	DET
ap-1801	305	11	manuscript	manuscript	NOUN
ap-1801	305	12	carefully	carefully	ADV
ap-1801	305	13	and	and	CCONJ
ap-1801	305	14	pointing	point	VERB
ap-1801	305	15	out	out	ADP
ap-1801	305	16	some	some	DET
ap-1801	305	17	minor	minor	ADJ
ap-1801	305	18	slips	slip	NOUN
ap-1801	305	19	of	of	ADP
ap-1801	305	20	the	the	DET
ap-1801	305	21	pen	pen	NOUN
ap-1801	305	22	.	.	PUNCT
ap-1801	306	1	references	reference	NOUN
ap-1801	306	2	[	[	X
ap-1801	306	3	1	1	X
ap-1801	306	4	]	]	X
ap-1801	306	5	simon	simon	PROPN
ap-1801	306	6	b.	b.	PROPN
ap-1801	306	7	:	:	PUNCT
ap-1801	306	8	some	some	DET
ap-1801	306	9	quantum	quantum	NOUN
ap-1801	306	10	operators	operator	NOUN
ap-1801	306	11	with	with	ADP
ap-1801	306	12	discrete	discrete	ADJ
ap-1801	306	13	spectrum	spectrum	NOUN
ap-1801	306	14	but	but	CCONJ
ap-1801	306	15	classically	classically	ADV
ap-1801	306	16	continuous	continuous	ADJ
ap-1801	306	17	spectrum	spectrum	NOUN
ap-1801	306	18	,	,	PUNCT
ap-1801	306	19	ann	ann	PROPN
ap-1801	306	20	.	.	PUNCT
ap-1801	307	1	phys	phys	PROPN
ap-1801	307	2	.	.	PUNCT
ap-1801	308	1	146	146	NUM
ap-1801	308	2	(	(	PUNCT
ap-1801	308	3	1983	1983	NUM
ap-1801	308	4	)	)	PUNCT
ap-1801	308	5	,	,	PUNCT
ap-1801	308	6	209–220	209–220	NUM
ap-1801	308	7	.	.	PUNCT
ap-1801	309	1	[	[	X
ap-1801	309	2	2	2	NUM
ap-1801	309	3	]	]	SYM
ap-1801	309	4	znojil	znojil	NOUN
ap-1801	309	5	m.	m.	NOUN
ap-1801	309	6	:	:	PUNCT
ap-1801	309	7	quantum	quantum	NOUN
ap-1801	309	8	exotic	exotic	NOUN
ap-1801	309	9	:	:	PUNCT
ap-1801	309	10	a	a	DET
ap-1801	309	11	repulsive	repulsive	ADJ
ap-1801	309	12	and	and	CCONJ
ap-1801	309	13	bottomless	bottomless	ADJ
ap-1801	309	14	confining	confining	NOUN
ap-1801	309	15	potential	potential	NOUN
ap-1801	309	16	,	,	PUNCT
ap-1801	309	17	j.	j.	PROPN
ap-1801	309	18	phys	phys	PROPN
ap-1801	309	19	.	.	PUNCT
ap-1801	310	1	a	a	DET
ap-1801	310	2	:	:	PUNCT
ap-1801	310	3	math	math	NOUN
ap-1801	310	4	.	.	PUNCT
ap-1801	311	1	gen	gen	PROPN
ap-1801	311	2	.	.	PROPN
ap-1801	311	3	31	31	NUM
ap-1801	311	4	(	(	PUNCT
ap-1801	311	5	1998	1998	NUM
ap-1801	311	6	)	)	PUNCT
ap-1801	311	7	,	,	PUNCT
ap-1801	311	8	3349–3355	3349–3355	NUM
ap-1801	311	9	.	.	PUNCT
ap-1801	312	1	[	[	X
ap-1801	312	2	3	3	X
ap-1801	312	3	]	]	PUNCT
ap-1801	312	4	exner	exner	NOUN
ap-1801	312	5	p.	p.	PROPN
ap-1801	312	6	,	,	PUNCT
ap-1801	312	7	barseghyan	barseghyan	PROPN
ap-1801	312	8	d.	d.	PROPN
ap-1801	312	9	:	:	PUNCT
ap-1801	312	10	spectral	spectral	ADJ
ap-1801	312	11	estimates	estimate	NOUN
ap-1801	312	12	for	for	ADP
ap-1801	312	13	a	a	DET
ap-1801	312	14	class	class	NOUN
ap-1801	312	15	of	of	ADP
ap-1801	312	16	schrödinger	schrödinger	ADJ
ap-1801	312	17	operators	operator	NOUN
ap-1801	312	18	with	with	ADP
ap-1801	312	19	infinite	infinite	ADJ
ap-1801	312	20	phase	phase	NOUN
ap-1801	312	21	space	space	NOUN
ap-1801	312	22	and	and	CCONJ
ap-1801	312	23	potential	potential	ADJ
ap-1801	312	24	unbounded	unbounded	ADJ
ap-1801	312	25	from	from	ADP
ap-1801	312	26	below	below	ADV
ap-1801	312	27	,	,	PUNCT
ap-1801	312	28	j.	j.	PROPN
ap-1801	312	29	phys	phys	PROPN
ap-1801	312	30	.	.	PUNCT
ap-1801	313	1	a	a	DET
ap-1801	313	2	:	:	PUNCT
ap-1801	313	3	math	math	NOUN
ap-1801	313	4	.	.	PUNCT
ap-1801	314	1	theor	theor	PROPN
ap-1801	314	2	.	.	PUNCT
ap-1801	315	1	45	45	NUM
ap-1801	315	2	(	(	PUNCT
ap-1801	315	3	2012	2012	NUM
ap-1801	315	4	)	)	PUNCT
ap-1801	315	5	,	,	PUNCT
ap-1801	315	6	075204	075204	NUM
ap-1801	315	7	.	.	PUNCT
ap-1801	316	1	[	[	X
ap-1801	316	2	4	4	NUM
ap-1801	316	3	]	]	PUNCT
ap-1801	316	4	exner	exner	NOUN
ap-1801	316	5	p.	p.	PROPN
ap-1801	316	6	,	,	PUNCT
ap-1801	316	7	barseghyan	barseghyan	PROPN
ap-1801	316	8	d.	d.	PROPN
ap-1801	316	9	:	:	PUNCT
ap-1801	316	10	spectral	spectral	ADJ
ap-1801	316	11	estimates	estimate	NOUN
ap-1801	316	12	for	for	ADP
ap-1801	316	13	dirichlet	dirichlet	PROPN
ap-1801	316	14	laplacians	laplacian	NOUN
ap-1801	316	15	and	and	CCONJ
ap-1801	316	16	schrödinger	schrödinger	ADJ
ap-1801	316	17	operators	operator	NOUN
ap-1801	316	18	on	on	ADP
ap-1801	316	19	geometrically	geometrically	ADV
ap-1801	316	20	nontrivial	nontrivial	ADJ
ap-1801	316	21	cusps	cusps	NOUN
ap-1801	316	22	,	,	PUNCT
ap-1801	316	23	to	to	PART
ap-1801	316	24	appear	appear	VERB
ap-1801	316	25	in	in	ADP
ap-1801	316	26	j.	j.	PROPN
ap-1801	316	27	spect	spect	PROPN
ap-1801	316	28	.	.	PUNCT
ap-1801	317	1	theory	theory	NOUN
ap-1801	317	2	,	,	PUNCT
ap-1801	317	3	arxiv:1203.2098	arxiv:1203.2098	PROPN
ap-1801	317	4	.	.	PUNCT
ap-1801	318	1	[	[	X
ap-1801	318	2	5	5	NUM
ap-1801	318	3	]	]	PUNCT
ap-1801	318	4	reed	reed	NOUN
ap-1801	318	5	m.	m.	NOUN
ap-1801	318	6	,	,	PUNCT
ap-1801	318	7	simon	simon	PROPN
ap-1801	318	8	b.	b.	PROPN
ap-1801	318	9	:	:	PUNCT
ap-1801	318	10	methods	method	NOUN
ap-1801	318	11	of	of	ADP
ap-1801	318	12	modern	modern	ADJ
ap-1801	318	13	mathematical	mathematical	ADJ
ap-1801	318	14	physics	physics	PROPN
ap-1801	318	15	,	,	PUNCT
ap-1801	318	16	ii	ii	PROPN
ap-1801	318	17	.	.	PUNCT
ap-1801	319	1	fourier	fourier	PROPN
ap-1801	319	2	analysis	analysis	NOUN
ap-1801	319	3	.	.	PUNCT
ap-1801	320	1	self	self	NOUN
ap-1801	320	2	-	-	PUNCT
ap-1801	320	3	adjointness	adjointness	NOUN
ap-1801	320	4	,	,	PUNCT
ap-1801	320	5	academic	academic	ADJ
ap-1801	320	6	press	press	NOUN
ap-1801	320	7	,	,	PUNCT
ap-1801	320	8	new	new	PROPN
ap-1801	320	9	york	york	PROPN
ap-1801	320	10	1975	1975	NUM
ap-1801	320	11	.	.	PUNCT
ap-1801	321	1	[	[	X
ap-1801	321	2	6	6	NUM
ap-1801	321	3	]	]	PUNCT
ap-1801	321	4	barseghyan	barseghyan	X
ap-1801	321	5	d.	d.	PROPN
ap-1801	321	6	:	:	PUNCT
ap-1801	321	7	on	on	ADP
ap-1801	321	8	the	the	DET
ap-1801	321	9	possibility	possibility	NOUN
ap-1801	321	10	of	of	ADP
ap-1801	321	11	strengthening	strengthen	VERB
ap-1801	321	12	the	the	DET
ap-1801	321	13	lieb	lieb	PROPN
ap-1801	321	14	-	-	PUNCT
ap-1801	321	15	thirring	thirre	VERB
ap-1801	321	16	inequality	inequality	NOUN
ap-1801	321	17	,	,	PUNCT
ap-1801	321	18	math	math	NOUN
ap-1801	321	19	.	.	PUNCT
ap-1801	322	1	notes	note	VERB
ap-1801	322	2	86	86	NUM
ap-1801	322	3	(	(	PUNCT
ap-1801	322	4	2009	2009	NUM
ap-1801	322	5	)	)	PUNCT
ap-1801	322	6	,	,	PUNCT
ap-1801	322	7	803–818	803–818	NUM
ap-1801	322	8	.	.	PUNCT
ap-1801	323	1	[	[	X
ap-1801	323	2	7	7	NUM
ap-1801	323	3	]	]	ADJ
ap-1801	323	4	rozenblum	rozenblum	NOUN
ap-1801	323	5	.	.	PUNCT
ap-1801	324	1	g.	g.	NOUN
ap-1801	324	2	:	:	PUNCT
ap-1801	324	3	asymptotics	asymptotic	NOUN
ap-1801	324	4	of	of	ADP
ap-1801	324	5	the	the	DET
ap-1801	324	6	eigenvalues	eigenvalue	NOUN
ap-1801	324	7	of	of	ADP
ap-1801	324	8	schrödinger	schrödinger	ADJ
ap-1801	324	9	operator	operator	NOUN
ap-1801	324	10	,	,	PUNCT
ap-1801	324	11	mat	mat	NOUN
ap-1801	324	12	.	.	X
ap-1801	324	13	sbornik	sbornik	X
ap-1801	324	14	(	(	PUNCT
ap-1801	324	15	n.s	n.s	PROPN
ap-1801	324	16	.	.	PROPN
ap-1801	324	17	)	)	PUNCT
ap-1801	324	18	93(135	93(135	PROPN
ap-1801	324	19	)	)	PUNCT
ap-1801	324	20	(	(	PUNCT
ap-1801	324	21	1974	1974	NUM
ap-1801	324	22	)	)	PUNCT
ap-1801	324	23	,	,	PUNCT
ap-1801	324	24	347–367	347–367	NUM
ap-1801	324	25	.	.	PUNCT
ap-1801	325	1	[	[	X
ap-1801	325	2	8	8	NUM
ap-1801	325	3	]	]	X
ap-1801	325	4	adams	adams	PROPN
ap-1801	325	5	r.a	r.a	PROPN
ap-1801	325	6	.	.	PROPN
ap-1801	325	7	,	,	PUNCT
ap-1801	325	8	fournier	fournier	PROPN
ap-1801	325	9	j.f	j.f	PROPN
ap-1801	325	10	.	.	PROPN
ap-1801	325	11	:	:	PUNCT
ap-1801	326	1	sobolev	sobolev	NOUN
ap-1801	326	2	spaces	space	VERB
ap-1801	326	3	,	,	PUNCT
ap-1801	326	4	2nd	2nd	ADJ
ap-1801	326	5	ed	ed	NOUN
ap-1801	326	6	.	.	PROPN
ap-1801	326	7	,	,	PUNCT
ap-1801	326	8	academic	academic	ADJ
ap-1801	326	9	press	press	NOUN
ap-1801	326	10	,	,	PUNCT
ap-1801	326	11	new	new	PROPN
ap-1801	326	12	york	york	PROPN
ap-1801	326	13	2003	2003	NUM
ap-1801	326	14	.	.	PUNCT
ap-1801	327	1	[	[	X
ap-1801	327	2	9	9	NUM
ap-1801	327	3	]	]	PUNCT
ap-1801	327	4	geisinger	geisinger	PROPN
ap-1801	327	5	l.	l.	PROPN
ap-1801	327	6	,	,	PUNCT
ap-1801	327	7	weidl	weidl	PROPN
ap-1801	327	8	t.	t.	PROPN
ap-1801	327	9	:	:	PUNCT
ap-1801	327	10	sharp	sharp	ADJ
ap-1801	327	11	spectral	spectral	ADJ
ap-1801	327	12	estimates	estimate	NOUN
ap-1801	327	13	in	in	ADP
ap-1801	327	14	domains	domain	NOUN
ap-1801	327	15	of	of	ADP
ap-1801	327	16	infinite	infinite	ADJ
ap-1801	327	17	volume	volume	NOUN
ap-1801	327	18	,	,	PUNCT
ap-1801	327	19	rev	rev	PROPN
ap-1801	327	20	.	.	PROPN
ap-1801	327	21	math	math	NOUN
ap-1801	327	22	.	.	PUNCT
ap-1801	328	1	phys	phy	NOUN
ap-1801	328	2	.	.	PUNCT
ap-1801	329	1	23	23	NUM
ap-1801	329	2	(	(	PUNCT
ap-1801	329	3	2011	2011	NUM
ap-1801	329	4	)	)	PUNCT
ap-1801	329	5	,	,	PUNCT
ap-1801	329	6	615–641	615–641	NUM
ap-1801	329	7	.	.	PUNCT
ap-1801	330	1	[	[	X
ap-1801	330	2	10	10	NUM
ap-1801	330	3	]	]	X
ap-1801	330	4	lieb	lieb	PROPN
ap-1801	330	5	e.h	e.h	PROPN
ap-1801	330	6	.	.	PROPN
ap-1801	330	7	,	,	PUNCT
ap-1801	330	8	thirring	thirre	VERB
ap-1801	330	9	w.	w.	NOUN
ap-1801	330	10	:	:	PUNCT
ap-1801	330	11	inequalities	inequality	NOUN
ap-1801	330	12	for	for	ADP
ap-1801	330	13	the	the	DET
ap-1801	330	14	moments	moment	NOUN
ap-1801	330	15	of	of	ADP
ap-1801	330	16	the	the	DET
ap-1801	330	17	eigenvalues	eigenvalue	NOUN
ap-1801	330	18	of	of	ADP
ap-1801	330	19	the	the	DET
ap-1801	330	20	schrödinger	schrödinger	ADJ
ap-1801	330	21	hamiltonian	hamiltonian	NOUN
ap-1801	330	22	and	and	CCONJ
ap-1801	330	23	their	their	PRON
ap-1801	330	24	relation	relation	NOUN
ap-1801	330	25	to	to	ADP
ap-1801	330	26	sobolev	sobolev	NOUN
ap-1801	330	27	inequalities	inequality	NOUN
ap-1801	330	28	,	,	PUNCT
ap-1801	330	29	in	in	ADP
ap-1801	330	30	studies	study	NOUN
ap-1801	330	31	in	in	ADP
ap-1801	330	32	math	math	NOUN
ap-1801	330	33	.	.	PUNCT
ap-1801	331	1	phys	phy	NOUN
ap-1801	331	2	.	.	PUNCT
ap-1801	331	3	,	,	PUNCT
ap-1801	331	4	essays	essay	NOUN
ap-1801	331	5	in	in	ADP
ap-1801	331	6	honor	honor	NOUN
ap-1801	331	7	of	of	ADP
ap-1801	331	8	valentine	valentine	PROPN
ap-1801	331	9	bargmann	bargmann	PROPN
ap-1801	331	10	(	(	PUNCT
ap-1801	331	11	e.	e.	PROPN
ap-1801	331	12	lieb	lieb	PROPN
ap-1801	331	13	,	,	PUNCT
ap-1801	331	14	b.	b.	PROPN
ap-1801	331	15	simon	simon	PROPN
ap-1801	331	16	and	and	CCONJ
ap-1801	331	17	a.s	a.s	PROPN
ap-1801	331	18	.	.	PROPN
ap-1801	331	19	wightman	wightman	PROPN
ap-1801	331	20	,	,	PUNCT
ap-1801	331	21	eds	eds	PROPN
ap-1801	331	22	.	.	PUNCT
ap-1801	331	23	)	)	PUNCT
ap-1801	331	24	;	;	PUNCT
ap-1801	331	25	princeton	princeton	PROPN
ap-1801	331	26	univ	univ	PROPN
ap-1801	331	27	.	.	PUNCT
ap-1801	332	1	press	press	PROPN
ap-1801	332	2	,	,	PUNCT
ap-1801	332	3	princeton	princeton	PROPN
ap-1801	332	4	1976	1976	NUM
ap-1801	332	5	;	;	PUNCT
ap-1801	332	6	pp	pp	ADP
ap-1801	332	7	.	.	PUNCT
ap-1801	333	1	269–330	269–330	NUM
ap-1801	333	2	.	.	PUNCT
ap-1801	334	1	[	[	X
ap-1801	334	2	11	11	NUM
ap-1801	334	3	]	]	PUNCT
ap-1801	334	4	berezin	berezin	PROPN
ap-1801	334	5	f.a	f.a	PROPN
ap-1801	334	6	.	.	PROPN
ap-1801	334	7	:	:	PUNCT
ap-1801	334	8	covariant	covariant	PROPN
ap-1801	334	9	and	and	CCONJ
ap-1801	334	10	contravariant	contravariant	ADJ
ap-1801	334	11	symbols	symbol	NOUN
ap-1801	334	12	of	of	ADP
ap-1801	334	13	operators	operator	NOUN
ap-1801	334	14	,	,	PUNCT
ap-1801	334	15	izv	izv	PROPN
ap-1801	334	16	.	.	PROPN
ap-1801	334	17	akad	akad	PROPN
ap-1801	334	18	.	.	PUNCT
ap-1801	335	1	nauk	nauk	PROPN
ap-1801	335	2	sssr	sssr	PROPN
ap-1801	335	3	ser	ser	PROPN
ap-1801	335	4	.	.	PROPN
ap-1801	336	1	mat	mat	PROPN
ap-1801	336	2	.	.	PROPN
ap-1801	336	3	36	36	NUM
ap-1801	336	4	(	(	PUNCT
ap-1801	336	5	1972	1972	NUM
ap-1801	336	6	)	)	PUNCT
ap-1801	336	7	,	,	PUNCT
ap-1801	336	8	1134–1167	1134–1167	NUM
ap-1801	336	9	.	.	PUNCT
ap-1801	337	1	[	[	X
ap-1801	337	2	12	12	NUM
ap-1801	337	3	]	]	PUNCT
ap-1801	337	4	berezin	berezin	PROPN
ap-1801	338	1	f.a	f.a	PROPN
ap-1801	338	2	.	.	PROPN
ap-1801	338	3	:	:	PUNCT
ap-1801	339	1	convex	convex	NOUN
ap-1801	339	2	functions	function	NOUN
ap-1801	339	3	of	of	ADP
ap-1801	339	4	operators	operator	NOUN
ap-1801	339	5	,	,	PUNCT
ap-1801	339	6	mat	mat	PROPN
ap-1801	339	7	.	.	PUNCT
ap-1801	339	8	sb	sb	PROPN
ap-1801	339	9	.	.	PROPN
ap-1801	339	10	(	(	PUNCT
ap-1801	339	11	ns	ns	NOUN
ap-1801	339	12	)	)	PUNCT
ap-1801	339	13	36(130	36(130	NOUN
ap-1801	339	14	)	)	PUNCT
ap-1801	339	15	(	(	PUNCT
ap-1801	339	16	1972	1972	NUM
ap-1801	339	17	)	)	PUNCT
ap-1801	339	18	,	,	PUNCT
ap-1801	339	19	268–276	268–276	NUM
ap-1801	339	20	.	.	PUNCT
ap-1801	340	1	[	[	X
ap-1801	340	2	13	13	NUM
ap-1801	340	3	]	]	X
ap-1801	340	4	lieb	lieb	PROPN
ap-1801	340	5	e.h	e.h	PROPN
ap-1801	340	6	.	.	PROPN
ap-1801	340	7	:	:	PUNCT
ap-1801	341	1	the	the	DET
ap-1801	341	2	classical	classical	ADJ
ap-1801	341	3	limit	limit	NOUN
ap-1801	341	4	of	of	ADP
ap-1801	341	5	quantum	quantum	NOUN
ap-1801	341	6	spin	spin	NOUN
ap-1801	341	7	systems	system	NOUN
ap-1801	341	8	,	,	PUNCT
ap-1801	341	9	commun	commun	PROPN
ap-1801	341	10	.	.	PUNCT
ap-1801	341	11	math	math	NOUN
ap-1801	341	12	.	.	PUNCT
ap-1801	342	1	phys	phy	NOUN
ap-1801	342	2	.	.	PUNCT
ap-1801	343	1	31	31	NUM
ap-1801	343	2	(	(	PUNCT
ap-1801	343	3	1973	1973	NUM
ap-1801	343	4	)	)	PUNCT
ap-1801	343	5	,	,	PUNCT
ap-1801	343	6	327–340	327–340	NUM
ap-1801	343	7	.	.	PUNCT
ap-1801	344	1	[	[	X
ap-1801	344	2	14	14	NUM
ap-1801	344	3	]	]	X
ap-1801	344	4	li	li	PROPN
ap-1801	344	5	p.	p.	PROPN
ap-1801	344	6	,	,	PUNCT
ap-1801	344	7	yau	yau	PROPN
ap-1801	344	8	s.t	s.t	PROPN
ap-1801	344	9	.	.	PUNCT
ap-1801	344	10	:	:	PUNCT
ap-1801	345	1	on	on	ADP
ap-1801	345	2	the	the	DET
ap-1801	345	3	schrödinger	schrödinger	ADJ
ap-1801	345	4	equation	equation	NOUN
ap-1801	345	5	and	and	CCONJ
ap-1801	345	6	the	the	DET
ap-1801	345	7	eigenvalue	eigenvalue	PROPN
ap-1801	345	8	problem	problem	NOUN
ap-1801	345	9	,	,	PUNCT
ap-1801	345	10	commun	commun	PROPN
ap-1801	345	11	.	.	PUNCT
ap-1801	345	12	math	math	NOUN
ap-1801	345	13	.	.	PUNCT
ap-1801	346	1	phys	phy	NOUN
ap-1801	346	2	.	.	PUNCT
ap-1801	347	1	88	88	NUM
ap-1801	347	2	(	(	PUNCT
ap-1801	347	3	1983	1983	NUM
ap-1801	347	4	)	)	PUNCT
ap-1801	347	5	,	,	PUNCT
ap-1801	347	6	309–318	309–318	NUM
ap-1801	347	7	.	.	PUNCT
ap-1801	348	1	[	[	X
ap-1801	348	2	15	15	NUM
ap-1801	348	3	]	]	PUNCT
ap-1801	348	4	exner	exner	NOUN
ap-1801	348	5	p.	p.	PROPN
ap-1801	348	6	,	,	PUNCT
ap-1801	348	7	šeba	šeba	PROPN
ap-1801	348	8	p.	p.	NOUN
ap-1801	348	9	:	:	PUNCT
ap-1801	348	10	bound	bind	VERB
ap-1801	348	11	states	state	NOUN
ap-1801	348	12	in	in	ADP
ap-1801	348	13	curved	curved	ADJ
ap-1801	348	14	quantum	quantum	ADJ
ap-1801	348	15	wavequides	wavequide	NOUN
ap-1801	348	16	,	,	PUNCT
ap-1801	348	17	j.	j.	PROPN
ap-1801	348	18	math	math	PROPN
ap-1801	348	19	.	.	PUNCT
ap-1801	349	1	phys	phy	NOUN
ap-1801	349	2	.	.	PUNCT
ap-1801	350	1	30	30	NUM
ap-1801	350	2	(	(	PUNCT
ap-1801	350	3	1989	1989	NUM
ap-1801	350	4	)	)	PUNCT
ap-1801	350	5	,	,	PUNCT
ap-1801	350	6	2574–2580	2574–2580	NUM
ap-1801	350	7	.	.	PUNCT
ap-1801	351	1	[	[	X
ap-1801	351	2	16	16	NUM
ap-1801	351	3	]	]	X
ap-1801	351	4	berger	berger	PROPN
ap-1801	351	5	m.s	m.s	PROPN
ap-1801	351	6	.	.	PROPN
ap-1801	351	7	,	,	PUNCT
ap-1801	351	8	schechter	schechter	NOUN
ap-1801	351	9	m.	m.	NOUN
ap-1801	351	10	:	:	PUNCT
ap-1801	351	11	embedding	embed	VERB
ap-1801	351	12	theorems	theorem	NOUN
ap-1801	351	13	and	and	CCONJ
ap-1801	351	14	quasi	quasi	ADJ
ap-1801	351	15	-	-	ADJ
ap-1801	351	16	linear	linear	ADJ
ap-1801	351	17	elliptic	elliptic	ADJ
ap-1801	351	18	boundary	boundary	ADJ
ap-1801	351	19	value	value	NOUN
ap-1801	351	20	problems	problem	NOUN
ap-1801	351	21	for	for	ADP
ap-1801	351	22	unbounded	unbounded	ADJ
ap-1801	351	23	domain	domain	NOUN
ap-1801	351	24	,	,	PUNCT
ap-1801	351	25	trans	trans	PROPN
ap-1801	351	26	.	.	PROPN
ap-1801	351	27	am	be	AUX
ap-1801	351	28	.	.	PUNCT
ap-1801	352	1	math	math	NOUN
ap-1801	352	2	.	.	PUNCT
ap-1801	353	1	soc	soc	PROPN
ap-1801	353	2	.	.	PUNCT
ap-1801	354	1	172	172	NUM
ap-1801	354	2	(	(	PUNCT
ap-1801	354	3	1972	1972	NUM
ap-1801	354	4	)	)	PUNCT
ap-1801	354	5	,	,	PUNCT
ap-1801	354	6	261–278	261–278	NUM
ap-1801	354	7	.	.	PUNCT
ap-1801	355	1	[	[	X
ap-1801	355	2	17	17	NUM
ap-1801	355	3	]	]	X
ap-1801	355	4	weidl	weidl	NOUN
ap-1801	355	5	t.	t.	PROPN
ap-1801	355	6	:	:	PUNCT
ap-1801	355	7	improved	improved	ADJ
ap-1801	355	8	berezin	berezin	PROPN
ap-1801	355	9	-	-	PUNCT
ap-1801	355	10	li	li	PROPN
ap-1801	355	11	-	-	PROPN
ap-1801	355	12	yau	yau	PROPN
ap-1801	355	13	inequalities	inequality	NOUN
ap-1801	355	14	with	with	ADP
ap-1801	355	15	a	a	DET
ap-1801	355	16	remainder	remainder	NOUN
ap-1801	355	17	term	term	NOUN
ap-1801	355	18	,	,	PUNCT
ap-1801	355	19	in	in	ADP
ap-1801	355	20	spectral	spectral	ADJ
ap-1801	355	21	theory	theory	NOUN
ap-1801	355	22	of	of	ADP
ap-1801	355	23	differential	differential	ADJ
ap-1801	355	24	operators	operator	NOUN
ap-1801	355	25	,	,	PUNCT
ap-1801	355	26	amer	amer	PROPN
ap-1801	355	27	.	.	PROPN
ap-1801	355	28	math	math	PROPN
ap-1801	355	29	.	.	PUNCT
ap-1801	356	1	soc	soc	PROPN
ap-1801	356	2	.	.	PUNCT
ap-1801	357	1	transl	transl	PROPN
ap-1801	357	2	.	.	PUNCT
ap-1801	358	1	225	225	NUM
ap-1801	358	2	(	(	PUNCT
ap-1801	358	3	2008	2008	NUM
ap-1801	358	4	)	)	PUNCT
ap-1801	358	5	,	,	PUNCT
ap-1801	358	6	253–263	253–263	NUM
ap-1801	358	7	.	.	PUNCT
ap-1801	359	1	[	[	X
ap-1801	359	2	18	18	NUM
ap-1801	359	3	]	]	X
ap-1801	359	4	laptev	laptev	PROPN
ap-1801	359	5	a.	a.	NOUN
ap-1801	359	6	,	,	PUNCT
ap-1801	359	7	weidl	weidl	PROPN
ap-1801	359	8	t.	t.	PROPN
ap-1801	359	9	:	:	PUNCT
ap-1801	359	10	sharp	sharp	ADJ
ap-1801	359	11	lieb	lieb	PROPN
ap-1801	359	12	-	-	PUNCT
ap-1801	359	13	thirring	thirre	VERB
ap-1801	359	14	inequalities	inequality	NOUN
ap-1801	359	15	in	in	ADP
ap-1801	359	16	high	high	ADJ
ap-1801	359	17	dimensions	dimension	NOUN
ap-1801	359	18	,	,	PUNCT
ap-1801	359	19	acta	acta	PROPN
ap-1801	359	20	math	math	NOUN
ap-1801	359	21	.	.	PUNCT
ap-1801	360	1	184	184	NUM
ap-1801	360	2	(	(	PUNCT
ap-1801	360	3	2000	2000	NUM
ap-1801	360	4	)	)	PUNCT
ap-1801	360	5	,	,	PUNCT
ap-1801	360	6	87–100	87–100	PROPN
ap-1801	360	7	.	.	PUNCT
ap-1801	361	1	[	[	X
ap-1801	361	2	19	19	NUM
ap-1801	361	3	]	]	X
ap-1801	361	4	krejčiřík	krejčiřík	PROPN
ap-1801	361	5	d.	d.	PROPN
ap-1801	361	6	,	,	PUNCT
ap-1801	361	7	zuazua	zuazua	PROPN
ap-1801	361	8	e.	e.	PROPN
ap-1801	361	9	:	:	PUNCT
ap-1801	361	10	the	the	DET
ap-1801	361	11	hardy	hardy	ADJ
ap-1801	361	12	inequality	inequality	NOUN
ap-1801	361	13	and	and	CCONJ
ap-1801	361	14	the	the	DET
ap-1801	361	15	heat	heat	NOUN
ap-1801	361	16	equation	equation	NOUN
ap-1801	361	17	in	in	ADP
ap-1801	361	18	the	the	DET
ap-1801	361	19	twisted	twisted	ADJ
ap-1801	361	20	tubes	tube	NOUN
ap-1801	361	21	,	,	PUNCT
ap-1801	361	22	j.	j.	PROPN
ap-1801	361	23	diff	diff	PROPN
ap-1801	361	24	.	.	PUNCT
ap-1801	362	1	eqs	eqs	PROPN
ap-1801	362	2	.	.	PROPN
ap-1801	363	1	250	250	NUM
ap-1801	363	2	(	(	PUNCT
ap-1801	363	3	2011	2011	NUM
ap-1801	363	4	)	)	PUNCT
ap-1801	363	5	,	,	PUNCT
ap-1801	363	6	2334–2346	2334–2346	NUM
ap-1801	363	7	.	.	PUNCT
ap-1801	364	1	279	279	NUM
ap-1801	364	2	http://arxiv.org/abs/1203.2098	http://arxiv.org/abs/1203.2098	PROPN
ap-1801	364	3	acta	acta	PROPN
ap-1801	364	4	polytechnica	polytechnica	PROPN
ap-1801	364	5	53(3):271–279	53(3):271–279	PROPN
ap-1801	364	6	,	,	PUNCT
ap-1801	364	7	2013	2013	NUM
ap-1801	364	8	1	1	NUM
ap-1801	364	9	introduction	introduction	NOUN
ap-1801	364	10	2	2	NUM
ap-1801	364	11	a	a	DET
ap-1801	364	12	model	model	NOUN
ap-1801	364	13	with	with	ADP
ap-1801	364	14	potential	potential	ADJ
ap-1801	364	15	unbounded	unbounded	ADJ
ap-1801	364	16	from	from	ADP
ap-1801	364	17	below	below	ADP
ap-1801	364	18	and	and	CCONJ
ap-1801	364	19	infinite	infinite	VERB
ap-1801	364	20	phase	phase	NOUN
ap-1801	364	21	space	space	NOUN
ap-1801	364	22	2.1	2.1	NUM
ap-1801	364	23	discreteness	discreteness	NOUN
ap-1801	364	24	of	of	ADP
ap-1801	364	25	the	the	DET
ap-1801	364	26	spectrum	spectrum	NOUN
ap-1801	364	27	2.2	2.2	NUM
ap-1801	364	28	the	the	DET
ap-1801	364	29	supercritical	supercritical	ADJ
ap-1801	364	30	case	case	NOUN
ap-1801	364	31	2.3	2.3	NUM
ap-1801	364	32	lower	low	ADJ
ap-1801	364	33	bounds	bound	NOUN
ap-1801	364	34	to	to	PART
ap-1801	364	35	eigenvalue	eigenvalue	VERB
ap-1801	364	36	sums	sum	VERB
ap-1801	364	37	2.4	2.4	NUM
ap-1801	364	38	upper	upper	ADJ
ap-1801	364	39	bounds	bound	NOUN
ap-1801	364	40	3	3	NUM
ap-1801	364	41	schrödinger	schrödinger	ADJ
ap-1801	364	42	operators	operator	NOUN
ap-1801	364	43	in	in	ADP
ap-1801	364	44	cusps	cusps	NOUN
ap-1801	364	45	with	with	ADP
ap-1801	364	46	non	non	ADJ
ap-1801	364	47	-	-	ADJ
ap-1801	364	48	trivial	trivial	ADJ
ap-1801	364	49	geometry	geometry	NOUN
ap-1801	364	50	3.1	3.1	NUM
ap-1801	364	51	curved	curved	ADJ
ap-1801	364	52	planar	planar	ADJ
ap-1801	364	53	cusps	cusps	NOUN
ap-1801	364	54	3.2	3.2	NUM
ap-1801	364	55	twisted	twisted	ADJ
ap-1801	364	56	cusps	cusps	NOUN
ap-1801	364	57	of	of	ADP
ap-1801	364	58	non	non	ADJ
ap-1801	364	59	-	-	ADJ
ap-1801	364	60	circular	circular	ADJ
ap-1801	364	61	cross	cross	NOUN
ap-1801	364	62	section	section	NOUN
ap-1801	364	63	in	in	ADP
ap-1801	364	64	rˆ3	rˆ3	NOUN
ap-1801	364	65	acknowledgements	acknowledgement	NOUN
ap-1801	364	66	references	reference	NOUN