id	sid	tid	token	lemma	pos
ap-10553	1	1	acta	acta	PROPN
ap-10553	1	2	polytechnica	polytechnica	PROPN
ap-10553	1	3	https://doi.org/10.14311/ap.2025.65.0539	https://doi.org/10.14311/ap.2025.65.0539	PROPN
ap-10553	1	4	acta	acta	PROPN
ap-10553	1	5	polytechnica	polytechnica	PROPN
ap-10553	1	6	65(5):539–545	65(5):539–545	PROPN
ap-10553	1	7	,	,	PUNCT
ap-10553	1	8	2025	2025	NUM
ap-10553	1	9	©	©	ADP
ap-10553	1	10	2025	2025	NUM
ap-10553	1	11	the	the	DET
ap-10553	1	12	author(s	author(s	NOUN
ap-10553	1	13	)	)	PUNCT
ap-10553	1	14	.	.	PUNCT
ap-10553	2	1	licensed	license	VERB
ap-10553	2	2	under	under	ADP
ap-10553	2	3	a	a	DET
ap-10553	2	4	cc	cc	NOUN
ap-10553	2	5	-	-	PUNCT
ap-10553	2	6	by	by	ADP
ap-10553	2	7	4.0	4.0	NUM
ap-10553	2	8	licence	licence	NOUN
ap-10553	2	9	published	publish	VERB
ap-10553	2	10	by	by	ADP
ap-10553	2	11	the	the	DET
ap-10553	2	12	czech	czech	PROPN
ap-10553	2	13	technical	technical	PROPN
ap-10553	2	14	university	university	PROPN
ap-10553	2	15	in	in	ADP
ap-10553	2	16	prague	prague	NOUN
ap-10553	2	17	quantum	quantum	NOUN
ap-10553	2	18	graphs	graph	NOUN
ap-10553	2	19	featuring	feature	VERB
ap-10553	2	20	unusual	unusual	ADJ
ap-10553	2	21	self	self	NOUN
ap-10553	2	22	-	-	PUNCT
ap-10553	2	23	adjoint	adjoint	NOUN
ap-10553	2	24	extensions	extension	NOUN
ap-10553	2	25	pavel	pavel	PROPN
ap-10553	2	26	exnera	exnera	PROPN
ap-10553	2	27	,	,	PUNCT
ap-10553	2	28	b	b	PROPN
ap-10553	2	29	a	a	DET
ap-10553	2	30	czech	czech	PROPN
ap-10553	2	31	technical	technical	PROPN
ap-10553	2	32	university	university	PROPN
ap-10553	2	33	in	in	ADP
ap-10553	2	34	prague	prague	PROPN
ap-10553	2	35	,	,	PUNCT
ap-10553	2	36	doppler	doppler	NOUN
ap-10553	2	37	institute	institute	NOUN
ap-10553	2	38	for	for	ADP
ap-10553	2	39	mathematical	mathematical	ADJ
ap-10553	2	40	physics	physics	NOUN
ap-10553	2	41	and	and	CCONJ
ap-10553	2	42	applied	apply	VERB
ap-10553	2	43	mathematics	mathematic	NOUN
ap-10553	2	44	,	,	PUNCT
ap-10553	2	45	břehová	břehová	VERB
ap-10553	2	46	7	7	NUM
ap-10553	2	47	,	,	PUNCT
ap-10553	2	48	115	115	NUM
ap-10553	2	49	19	19	NUM
ap-10553	2	50	prague	prague	NOUN
ap-10553	2	51	,	,	PUNCT
ap-10553	2	52	czech	czech	PROPN
ap-10553	2	53	republic	republic	PROPN
ap-10553	2	54	b	b	PROPN
ap-10553	2	55	czech	czech	PROPN
ap-10553	2	56	academy	academy	PROPN
ap-10553	2	57	of	of	ADP
ap-10553	2	58	sciences	sciences	PROPN
ap-10553	2	59	,	,	PUNCT
ap-10553	2	60	nuclear	nuclear	ADJ
ap-10553	2	61	physics	physics	PROPN
ap-10553	2	62	institute	institute	PROPN
ap-10553	2	63	ascr	ascr	NOUN
ap-10553	2	64	,	,	PUNCT
ap-10553	2	65	department	department	NOUN
ap-10553	2	66	of	of	ADP
ap-10553	2	67	theoretical	theoretical	ADJ
ap-10553	2	68	physics	physics	NOUN
ap-10553	2	69	,	,	PUNCT
ap-10553	2	70	250	250	NUM
ap-10553	2	71	68	68	NUM
ap-10553	2	72	řež	řež	NOUN
ap-10553	2	73	,	,	PUNCT
ap-10553	2	74	czech	czech	PROPN
ap-10553	2	75	republic	republic	NOUN
ap-10553	2	76	correspondence	correspondence	NOUN
ap-10553	2	77	:	:	PUNCT
ap-10553	2	78	exner@ujf.cas.cz	exner@ujf.cas.cz	NOUN
ap-10553	2	79	abstract	abstract	ADJ
ap-10553	2	80	.	.	PUNCT
ap-10553	3	1	we	we	PRON
ap-10553	3	2	present	present	VERB
ap-10553	3	3	an	an	DET
ap-10553	3	4	example	example	NOUN
ap-10553	3	5	of	of	ADP
ap-10553	3	6	a	a	DET
ap-10553	3	7	simple	simple	ADJ
ap-10553	3	8	quantum	quantum	NOUN
ap-10553	3	9	graph	graph	NOUN
ap-10553	3	10	with	with	ADP
ap-10553	3	11	“	"	PUNCT
ap-10553	3	12	vertices	vertex	NOUN
ap-10553	3	13	at	at	ADP
ap-10553	3	14	infinity	infinity	NOUN
ap-10553	3	15	”	"	PUNCT
ap-10553	3	16	,	,	PUNCT
ap-10553	3	17	which	which	PRON
ap-10553	3	18	appear	appear	VERB
ap-10553	3	19	due	due	ADJ
ap-10553	3	20	a	a	DET
ap-10553	3	21	strongly	strongly	ADV
ap-10553	3	22	attractive	attractive	ADJ
ap-10553	3	23	potential	potential	ADJ
ap-10553	3	24	making	make	VERB
ap-10553	3	25	the	the	DET
ap-10553	3	26	spectral	spectral	ADJ
ap-10553	3	27	problem	problem	NOUN
ap-10553	3	28	quantum	quantum	NOUN
ap-10553	3	29	-	-	PUNCT
ap-10553	3	30	mechanically	mechanically	ADV
ap-10553	3	31	incomplete	incomplete	ADJ
ap-10553	3	32	.	.	PUNCT
ap-10553	4	1	we	we	PRON
ap-10553	4	2	construct	construct	VERB
ap-10553	4	3	the	the	DET
ap-10553	4	4	appropriate	appropriate	ADJ
ap-10553	4	5	self	self	NOUN
ap-10553	4	6	-	-	PUNCT
ap-10553	4	7	adjoint	adjoint	NOUN
ap-10553	4	8	extensions	extension	NOUN
ap-10553	4	9	of	of	ADP
ap-10553	4	10	the	the	DET
ap-10553	4	11	formal	formal	ADJ
ap-10553	4	12	graph	graph	NOUN
ap-10553	4	13	hamiltonian	hamiltonian	NOUN
ap-10553	4	14	,	,	PUNCT
ap-10553	4	15	and	and	CCONJ
ap-10553	4	16	derive	derive	VERB
ap-10553	4	17	their	their	PRON
ap-10553	4	18	spectral	spectral	ADJ
ap-10553	4	19	properties	property	NOUN
ap-10553	4	20	.	.	PUNCT
ap-10553	5	1	keywords	keyword	NOUN
ap-10553	5	2	:	:	PUNCT
ap-10553	5	3	quantum	quantum	NOUN
ap-10553	5	4	graphs	graph	NOUN
ap-10553	5	5	,	,	PUNCT
ap-10553	5	6	self	self	NOUN
ap-10553	5	7	-	-	PUNCT
ap-10553	5	8	adjoint	adjoint	NOUN
ap-10553	5	9	extensions	extension	NOUN
ap-10553	5	10	,	,	PUNCT
ap-10553	5	11	discrete	discrete	ADJ
ap-10553	5	12	spectrum	spectrum	NOUN
ap-10553	5	13	.	.	PUNCT
ap-10553	6	1	1	1	X
ap-10553	6	2	.	.	X
ap-10553	6	3	introduction	introduction	NOUN
ap-10553	6	4	this	this	DET
ap-10553	6	5	paper	paper	NOUN
ap-10553	6	6	is	be	AUX
ap-10553	6	7	devoted	devote	VERB
ap-10553	6	8	to	to	ADP
ap-10553	6	9	the	the	DET
ap-10553	6	10	memory	memory	NOUN
ap-10553	6	11	of	of	ADP
ap-10553	6	12	miloslav	miloslav	PROPN
ap-10553	6	13	havlíček	havlíček	PROPN
ap-10553	6	14	,	,	PUNCT
ap-10553	6	15	my	my	PRON
ap-10553	6	16	teacher	teacher	NOUN
ap-10553	6	17	,	,	PUNCT
ap-10553	6	18	colleague	colleague	NOUN
ap-10553	6	19	and	and	CCONJ
ap-10553	6	20	dear	dear	ADJ
ap-10553	6	21	friend	friend	NOUN
ap-10553	6	22	for	for	ADP
ap-10553	6	23	no	no	DET
ap-10553	6	24	less	less	ADJ
ap-10553	6	25	than	than	ADP
ap-10553	6	26	six	six	NUM
ap-10553	6	27	decades	decade	NOUN
ap-10553	6	28	,	,	PUNCT
ap-10553	6	29	who	who	PRON
ap-10553	6	30	passed	pass	VERB
ap-10553	6	31	away	away	ADV
ap-10553	6	32	last	last	ADJ
ap-10553	6	33	year	year	NOUN
ap-10553	6	34	.	.	PUNCT
ap-10553	7	1	we	we	PRON
ap-10553	7	2	worked	work	VERB
ap-10553	7	3	together	together	ADV
ap-10553	7	4	on	on	ADP
ap-10553	7	5	various	various	ADJ
ap-10553	7	6	problems	problem	NOUN
ap-10553	7	7	,	,	PUNCT
ap-10553	7	8	for	for	ADP
ap-10553	7	9	instance	instance	NOUN
ap-10553	7	10	,	,	PUNCT
ap-10553	7	11	the	the	DET
ap-10553	7	12	dynamics	dynamic	NOUN
ap-10553	7	13	of	of	ADP
ap-10553	7	14	open	open	ADJ
ap-10553	7	15	quantum	quantum	NOUN
ap-10553	7	16	systems	system	NOUN
ap-10553	7	17	or	or	CCONJ
ap-10553	7	18	canonical	canonical	ADJ
ap-10553	7	19	realisations	realisation	NOUN
ap-10553	7	20	of	of	ADP
ap-10553	7	21	lie	lie	NOUN
ap-10553	7	22	algebras	algebra	NOUN
ap-10553	7	23	.	.	PUNCT
ap-10553	8	1	we	we	PRON
ap-10553	8	2	also	also	ADV
ap-10553	8	3	wrote	write	VERB
ap-10553	8	4	and	and	CCONJ
ap-10553	8	5	rewrote	rewrote	VERB
ap-10553	8	6	,	,	PUNCT
ap-10553	8	7	coauthored	coauthore	VERB
ap-10553	8	8	by	by	ADP
ap-10553	8	9	late	late	ADJ
ap-10553	8	10	jiří	jiří	NOUN
ap-10553	8	11	blank	blank	PROPN
ap-10553	8	12	,	,	PUNCT
ap-10553	8	13	a	a	DET
ap-10553	8	14	book	book	NOUN
ap-10553	8	15	on	on	ADP
ap-10553	8	16	hilbert	hilbert	NOUN
ap-10553	8	17	space	space	NOUN
ap-10553	8	18	operators	operator	NOUN
ap-10553	8	19	in	in	ADP
ap-10553	8	20	quantum	quantum	ADJ
ap-10553	8	21	physics	physics	NOUN
ap-10553	8	22	which	which	PRON
ap-10553	8	23	became	become	VERB
ap-10553	8	24	,	,	PUNCT
ap-10553	8	25	for	for	ADP
ap-10553	8	26	many	many	ADJ
ap-10553	8	27	,	,	PUNCT
ap-10553	8	28	a	a	DET
ap-10553	8	29	standard	standard	ADJ
ap-10553	8	30	reference	reference	NOUN
ap-10553	8	31	source	source	NOUN
ap-10553	8	32	.	.	PUNCT
ap-10553	9	1	i	i	PRON
ap-10553	9	2	always	always	ADV
ap-10553	9	3	admired	admire	VERB
ap-10553	9	4	in	in	ADP
ap-10553	9	5	miloslav	miloslav	NOUN
ap-10553	9	6	his	his	PRON
ap-10553	9	7	ability	ability	NOUN
ap-10553	9	8	to	to	PART
ap-10553	9	9	go	go	VERB
ap-10553	9	10	to	to	ADP
ap-10553	9	11	the	the	DET
ap-10553	9	12	core	core	NOUN
ap-10553	9	13	of	of	ADP
ap-10553	9	14	a	a	DET
ap-10553	9	15	question	question	NOUN
ap-10553	9	16	;	;	PUNCT
ap-10553	9	17	he	he	PRON
ap-10553	9	18	liked	like	VERB
ap-10553	9	19	examples	example	NOUN
ap-10553	9	20	that	that	PRON
ap-10553	9	21	were	be	AUX
ap-10553	9	22	not	not	PART
ap-10553	9	23	overly	overly	ADV
ap-10553	9	24	technical	technical	ADJ
ap-10553	9	25	but	but	CCONJ
ap-10553	9	26	expressed	express	VERB
ap-10553	9	27	the	the	DET
ap-10553	9	28	essence	essence	NOUN
ap-10553	9	29	of	of	ADP
ap-10553	9	30	the	the	DET
ap-10553	9	31	problem	problem	NOUN
ap-10553	9	32	.	.	PUNCT
ap-10553	10	1	for	for	ADP
ap-10553	10	2	this	this	DET
ap-10553	10	3	paper	paper	NOUN
ap-10553	10	4	,	,	PUNCT
ap-10553	10	5	i	i	PRON
ap-10553	10	6	choose	choose	VERB
ap-10553	10	7	an	an	DET
ap-10553	10	8	example	example	NOUN
ap-10553	10	9	showing	show	VERB
ap-10553	10	10	an	an	DET
ap-10553	10	11	unusual	unusual	ADJ
ap-10553	10	12	behaviour	behaviour	NOUN
ap-10553	10	13	of	of	ADP
ap-10553	10	14	quantum	quantum	NOUN
ap-10553	10	15	graphs	graph	NOUN
ap-10553	10	16	;	;	PUNCT
ap-10553	10	17	i	i	PRON
ap-10553	10	18	hope	hope	VERB
ap-10553	10	19	he	he	PRON
ap-10553	10	20	would	would	AUX
ap-10553	10	21	like	like	VERB
ap-10553	10	22	it	it	PRON
ap-10553	10	23	.	.	PUNCT
ap-10553	11	1	the	the	DET
ap-10553	11	2	term	term	NOUN
ap-10553	11	3	quantum	quantum	NOUN
ap-10553	11	4	graphs	graph	NOUN
ap-10553	11	5	is	be	AUX
ap-10553	11	6	a	a	DET
ap-10553	11	7	common	common	ADJ
ap-10553	11	8	shorthand	shorthand	NOUN
ap-10553	11	9	for	for	ADP
ap-10553	11	10	models	model	NOUN
ap-10553	11	11	describing	describe	VERB
ap-10553	11	12	quantum	quantum	NOUN
ap-10553	11	13	-	-	ADJ
ap-10553	11	14	mechanical	mechanical	ADJ
ap-10553	11	15	dynamics	dynamic	NOUN
ap-10553	11	16	on	on	ADP
ap-10553	11	17	metric	metric	ADJ
ap-10553	11	18	graphs	graph	NOUN
ap-10553	11	19	,	,	PUNCT
ap-10553	11	20	described	describe	VERB
ap-10553	11	21	mostly	mostly	ADV
ap-10553	11	22	by	by	ADP
ap-10553	11	23	an	an	DET
ap-10553	11	24	appropriate	appropriate	ADJ
ap-10553	11	25	schrödinger	schrödinger	ADJ
ap-10553	11	26	operator	operator	NOUN
ap-10553	11	27	,	,	PUNCT
ap-10553	11	28	however	however	ADV
ap-10553	11	29	,	,	PUNCT
ap-10553	11	30	dirac	dirac	NOUN
ap-10553	11	31	,	,	PUNCT
ap-10553	11	32	nonlinear	nonlinear	ADJ
ap-10553	11	33	schrödinger	schrödinger	NOUN
ap-10553	11	34	,	,	PUNCT
ap-10553	11	35	and	and	CCONJ
ap-10553	11	36	other	other	ADJ
ap-10553	11	37	operators	operator	NOUN
ap-10553	11	38	are	be	AUX
ap-10553	11	39	also	also	ADV
ap-10553	11	40	considered	consider	VERB
ap-10553	11	41	in	in	ADP
ap-10553	11	42	this	this	DET
ap-10553	11	43	context	context	NOUN
ap-10553	11	44	.	.	PUNCT
ap-10553	12	1	the	the	DET
ap-10553	12	2	idea	idea	NOUN
ap-10553	12	3	can	can	AUX
ap-10553	12	4	be	be	AUX
ap-10553	12	5	traced	trace	VERB
ap-10553	12	6	back	back	ADV
ap-10553	12	7	to	to	ADP
ap-10553	12	8	a	a	DET
ap-10553	12	9	simple	simple	ADJ
ap-10553	12	10	model	model	NOUN
ap-10553	12	11	in	in	ADP
ap-10553	12	12	quantum	quantum	ADJ
ap-10553	12	13	chemistry	chemistry	NOUN
ap-10553	12	14	[	[	X
ap-10553	12	15	1	1	NUM
ap-10553	12	16	]	]	PUNCT
ap-10553	12	17	,	,	PUNCT
ap-10553	12	18	but	but	CCONJ
ap-10553	12	19	the	the	DET
ap-10553	12	20	concept	concept	NOUN
ap-10553	12	21	attracted	attract	VERB
ap-10553	12	22	attention	attention	NOUN
ap-10553	12	23	only	only	ADV
ap-10553	12	24	half	half	DET
ap-10553	12	25	a	a	DET
ap-10553	12	26	century	century	NOUN
ap-10553	12	27	later	later	ADV
ap-10553	12	28	,	,	PUNCT
ap-10553	12	29	motivated	motivate	VERB
ap-10553	12	30	in	in	ADP
ap-10553	12	31	part	part	NOUN
ap-10553	12	32	by	by	ADP
ap-10553	12	33	development	development	NOUN
ap-10553	12	34	of	of	ADP
ap-10553	12	35	microfabrication	microfabrication	NOUN
ap-10553	12	36	techniques	technique	NOUN
ap-10553	12	37	in	in	ADP
ap-10553	12	38	solid	solid	ADJ
ap-10553	12	39	-	-	PUNCT
ap-10553	12	40	state	state	NOUN
ap-10553	12	41	physics	physics	NOUN
ap-10553	12	42	.	.	PUNCT
ap-10553	13	1	since	since	SCONJ
ap-10553	13	2	then	then	ADV
ap-10553	13	3	there	there	PRON
ap-10553	13	4	was	be	VERB
ap-10553	13	5	a	a	DET
ap-10553	13	6	lot	lot	NOUN
ap-10553	13	7	of	of	ADP
ap-10553	13	8	activity	activity	NOUN
ap-10553	13	9	in	in	ADP
ap-10553	13	10	this	this	DET
ap-10553	13	11	area	area	NOUN
ap-10553	13	12	;	;	PUNCT
ap-10553	13	13	for	for	ADP
ap-10553	13	14	the	the	DET
ap-10553	13	15	current	current	ADJ
ap-10553	13	16	state	state	NOUN
ap-10553	13	17	of	of	ADP
ap-10553	13	18	art	art	NOUN
ap-10553	13	19	we	we	PRON
ap-10553	13	20	refer	refer	VERB
ap-10553	13	21	to	to	ADP
ap-10553	13	22	the	the	DET
ap-10553	13	23	monographs	monograph	NOUN
ap-10553	13	24	[	[	X
ap-10553	13	25	2–4	2–4	NUM
ap-10553	13	26	]	]	X
ap-10553	13	27	.	.	PUNCT
ap-10553	14	1	one	one	NUM
ap-10553	14	2	of	of	ADP
ap-10553	14	3	the	the	DET
ap-10553	14	4	most	most	ADV
ap-10553	14	5	common	common	ADJ
ap-10553	14	6	classes	class	NOUN
ap-10553	14	7	of	of	ADP
ap-10553	14	8	quantum	quantum	NOUN
ap-10553	14	9	graphs	graph	NOUN
ap-10553	14	10	concerns	concern	VERB
ap-10553	14	11	schrödinger	schrödinger	ADJ
ap-10553	14	12	dynamics	dynamic	NOUN
ap-10553	14	13	on	on	ADP
ap-10553	14	14	a	a	DET
ap-10553	14	15	graph	graph	NOUN
ap-10553	14	16	consisting	consist	VERB
ap-10553	14	17	of	of	ADP
ap-10553	14	18	a	a	DET
ap-10553	14	19	compact	compact	ADJ
ap-10553	14	20	core	core	NOUN
ap-10553	14	21	in	in	ADP
ap-10553	14	22	the	the	DET
ap-10553	14	23	form	form	NOUN
ap-10553	14	24	of	of	ADP
ap-10553	14	25	a	a	DET
ap-10553	14	26	finite	finite	ADJ
ap-10553	14	27	graph	graph	NOUN
ap-10553	14	28	to	to	PART
ap-10553	14	29	which	which	PRON
ap-10553	14	30	a	a	DET
ap-10553	14	31	finite	finite	ADJ
ap-10553	14	32	number	number	NOUN
ap-10553	14	33	of	of	ADP
ap-10553	14	34	semiinfinite	semiinfinite	ADJ
ap-10553	14	35	“	"	PUNCT
ap-10553	14	36	leads	lead	NOUN
ap-10553	14	37	”	"	PUNCT
ap-10553	14	38	is	be	AUX
ap-10553	14	39	connected	connect	VERB
ap-10553	14	40	;	;	PUNCT
ap-10553	14	41	one	one	PRON
ap-10553	14	42	usually	usually	ADV
ap-10553	14	43	investigates	investigate	VERB
ap-10553	14	44	spectral	spectral	ADJ
ap-10553	14	45	and	and	CCONJ
ap-10553	14	46	scattering	scatter	VERB
ap-10553	14	47	properties	property	NOUN
ap-10553	14	48	of	of	ADP
ap-10553	14	49	such	such	ADJ
ap-10553	14	50	systems	system	NOUN
ap-10553	14	51	in	in	ADP
ap-10553	14	52	dependence	dependence	NOUN
ap-10553	14	53	on	on	ADP
ap-10553	14	54	the	the	DET
ap-10553	14	55	topology	topology	NOUN
ap-10553	14	56	and	and	CCONJ
ap-10553	14	57	geometry	geometry	NOUN
ap-10553	14	58	of	of	ADP
ap-10553	14	59	the	the	DET
ap-10553	14	60	core	core	NOUN
ap-10553	14	61	and	and	CCONJ
ap-10553	14	62	coupling	coupling	NOUN
ap-10553	14	63	of	of	ADP
ap-10553	14	64	the	the	DET
ap-10553	14	65	wave	wave	NOUN
ap-10553	14	66	functions	function	NOUN
ap-10553	14	67	at	at	ADP
ap-10553	14	68	the	the	DET
ap-10553	14	69	graph	graph	NOUN
ap-10553	14	70	vertices	vertex	NOUN
ap-10553	14	71	.	.	PUNCT
ap-10553	15	1	the	the	DET
ap-10553	15	2	leads	lead	NOUN
ap-10553	15	3	in	in	ADP
ap-10553	15	4	these	these	DET
ap-10553	15	5	problems	problem	NOUN
ap-10553	15	6	play	play	VERB
ap-10553	15	7	mostly	mostly	ADV
ap-10553	15	8	a	a	DET
ap-10553	15	9	“	"	PUNCT
ap-10553	15	10	service	service	NOUN
ap-10553	15	11	role	role	NOUN
ap-10553	15	12	”	"	PUNCT
ap-10553	15	13	only	only	ADV
ap-10553	15	14	,	,	PUNCT
ap-10553	15	15	bringing	bring	VERB
ap-10553	15	16	the	the	DET
ap-10553	15	17	particles	particle	NOUN
ap-10553	15	18	in	in	ADP
ap-10553	15	19	and	and	CCONJ
ap-10553	15	20	out	out	ADV
ap-10553	15	21	;	;	PUNCT
ap-10553	15	22	they	they	PRON
ap-10553	15	23	communicate	communicate	VERB
ap-10553	15	24	mutually	mutually	ADV
ap-10553	15	25	only	only	ADV
ap-10553	15	26	through	through	ADP
ap-10553	15	27	the	the	DET
ap-10553	15	28	core	core	NOUN
ap-10553	15	29	.	.	PUNCT
ap-10553	16	1	the	the	DET
ap-10553	16	2	aim	aim	NOUN
ap-10553	16	3	of	of	ADP
ap-10553	16	4	this	this	DET
ap-10553	16	5	note	note	NOUN
ap-10553	16	6	is	be	AUX
ap-10553	16	7	to	to	PART
ap-10553	16	8	show	show	VERB
ap-10553	16	9	that	that	SCONJ
ap-10553	16	10	this	this	PRON
ap-10553	16	11	may	may	AUX
ap-10553	16	12	not	not	PART
ap-10553	16	13	be	be	AUX
ap-10553	16	14	the	the	DET
ap-10553	16	15	case	case	NOUN
ap-10553	16	16	if	if	SCONJ
ap-10553	16	17	the	the	DET
ap-10553	16	18	potential	potential	NOUN
ap-10553	16	19	of	of	ADP
ap-10553	16	20	the	the	DET
ap-10553	16	21	corresponding	correspond	VERB
ap-10553	16	22	schrödinger	schrödinger	ADJ
ap-10553	16	23	operator	operator	NOUN
ap-10553	16	24	makes	make	VERB
ap-10553	16	25	the	the	DET
ap-10553	16	26	problem	problem	NOUN
ap-10553	16	27	quantum	quantum	NOUN
ap-10553	16	28	-	-	PUNCT
ap-10553	16	29	mechanically	mechanically	ADV
ap-10553	16	30	incomplete	incomplete	ADJ
ap-10553	16	31	in	in	ADP
ap-10553	16	32	the	the	DET
ap-10553	16	33	language	language	NOUN
ap-10553	16	34	of	of	ADP
ap-10553	16	35	reed	reed	NOUN
ap-10553	16	36	and	and	CCONJ
ap-10553	16	37	simon	simon	PROPN
ap-10553	16	38	[	[	X
ap-10553	16	39	5	5	NUM
ap-10553	16	40	,	,	PUNCT
ap-10553	16	41	app	app	PROPN
ap-10553	16	42	.	.	PROPN
ap-10553	16	43	to	to	ADP
ap-10553	16	44	sec	sec	PROPN
ap-10553	16	45	.	.	PUNCT
ap-10553	17	1	x.1	x.1	PROPN
ap-10553	17	2	]	]	PUNCT
ap-10553	17	3	.	.	PUNCT
ap-10553	18	1	we	we	PRON
ap-10553	18	2	consider	consider	VERB
ap-10553	18	3	the	the	DET
ap-10553	18	4	simplest	simple	ADJ
ap-10553	18	5	situation	situation	NOUN
ap-10553	18	6	of	of	ADP
ap-10553	18	7	this	this	DET
ap-10553	18	8	type	type	NOUN
ap-10553	18	9	when	when	SCONJ
ap-10553	18	10	the	the	DET
ap-10553	18	11	core	core	NOUN
ap-10553	18	12	is	be	AUX
ap-10553	18	13	restricted	restrict	VERB
ap-10553	18	14	to	to	ADP
ap-10553	18	15	a	a	DET
ap-10553	18	16	single	single	ADJ
ap-10553	18	17	vertex	vertex	NOUN
ap-10553	18	18	in	in	ADP
ap-10553	18	19	which	which	PRON
ap-10553	18	20	n	n	PRON
ap-10553	18	21	halfline	halfline	VERB
ap-10553	18	22	edges	edge	NOUN
ap-10553	18	23	meet	meet	VERB
ap-10553	18	24	;	;	PUNCT
ap-10553	18	25	the	the	DET
ap-10553	18	26	vertex	vertex	NOUN
ap-10553	18	27	coupling	coupling	NOUN
ap-10553	18	28	is	be	AUX
ap-10553	18	29	supposed	suppose	VERB
ap-10553	18	30	to	to	PART
ap-10553	18	31	be	be	AUX
ap-10553	18	32	free	free	ADJ
ap-10553	18	33	of	of	ADP
ap-10553	18	34	any	any	DET
ap-10553	18	35	interaction	interaction	NOUN
ap-10553	18	36	being	be	AUX
ap-10553	18	37	described	describe	VERB
ap-10553	18	38	by	by	ADP
ap-10553	18	39	kirchhoff	kirchhoff	NOUN
ap-10553	18	40	conditions	condition	NOUN
ap-10553	18	41	,	,	PUNCT
ap-10553	18	42	cf	cf	INTJ
ap-10553	18	43	.	.	PUNCT
ap-10553	19	1	(	(	PUNCT
ap-10553	19	2	2	2	X
ap-10553	19	3	)	)	PUNCT
ap-10553	19	4	below	below	ADV
ap-10553	19	5	.	.	PUNCT
ap-10553	20	1	the	the	DET
ap-10553	20	2	potential	potential	NOUN
ap-10553	20	3	on	on	ADP
ap-10553	20	4	the	the	DET
ap-10553	20	5	edges	edge	NOUN
ap-10553	20	6	is	be	AUX
ap-10553	20	7	attractive	attractive	ADJ
ap-10553	20	8	and	and	CCONJ
ap-10553	20	9	decreases	decrease	VERB
ap-10553	20	10	with	with	ADP
ap-10553	20	11	the	the	DET
ap-10553	20	12	fourth	fourth	ADJ
ap-10553	20	13	power	power	NOUN
ap-10553	20	14	of	of	ADP
ap-10553	20	15	the	the	DET
ap-10553	20	16	distance	distance	NOUN
ap-10553	20	17	from	from	ADP
ap-10553	20	18	the	the	DET
ap-10553	20	19	vertex	vertex	NOUN
ap-10553	20	20	.	.	PUNCT
ap-10553	21	1	we	we	PRON
ap-10553	21	2	consider	consider	VERB
ap-10553	21	3	only	only	ADV
ap-10553	21	4	star	star	NOUN
ap-10553	21	5	graphs	graph	NOUN
ap-10553	21	6	with	with	ADP
ap-10553	21	7	a	a	DET
ap-10553	21	8	genuine	genuine	ADJ
ap-10553	21	9	branching	branching	NOUN
ap-10553	21	10	,	,	PUNCT
ap-10553	21	11	n	n	X
ap-10553	21	12	≥	≥	NOUN
ap-10553	21	13	3	3	NUM
ap-10553	21	14	.	.	PUNCT
ap-10553	22	1	the	the	DET
ap-10553	22	2	case	case	NOUN
ap-10553	22	3	n	n	NOUN
ap-10553	22	4	=	=	SYM
ap-10553	22	5	2	2	NUM
ap-10553	22	6	,	,	PUNCT
ap-10553	22	7	equivalent	equivalent	ADJ
ap-10553	22	8	to	to	ADP
ap-10553	22	9	the	the	DET
ap-10553	22	10	motion	motion	NOUN
ap-10553	22	11	on	on	ADP
ap-10553	22	12	line	line	NOUN
ap-10553	22	13	,	,	PUNCT
ap-10553	22	14	is	be	AUX
ap-10553	22	15	discussed	discuss	VERB
ap-10553	22	16	in	in	ADP
ap-10553	22	17	detail	detail	NOUN
ap-10553	22	18	in	in	ADP
ap-10553	22	19	[	[	X
ap-10553	22	20	6	6	NUM
ap-10553	22	21	]	]	PUNCT
ap-10553	22	22	,	,	PUNCT
ap-10553	22	23	including	include	VERB
ap-10553	22	24	topics	topic	NOUN
ap-10553	22	25	we	we	PRON
ap-10553	22	26	do	do	AUX
ap-10553	22	27	not	not	PART
ap-10553	22	28	touch	touch	VERB
ap-10553	22	29	here	here	ADV
ap-10553	22	30	,	,	PUNCT
ap-10553	22	31	such	such	ADJ
ap-10553	22	32	as	as	ADP
ap-10553	22	33	approximations	approximation	NOUN
ap-10553	22	34	of	of	ADP
ap-10553	22	35	self	self	NOUN
ap-10553	22	36	-	-	PUNCT
ap-10553	22	37	adjoint	adjoint	NOUN
ap-10553	22	38	extensions	extension	NOUN
ap-10553	22	39	or	or	CCONJ
ap-10553	22	40	feynman	feynman	PROPN
ap-10553	22	41	path	path	NOUN
ap-10553	22	42	-	-	PUNCT
ap-10553	22	43	integral	integral	ADJ
ap-10553	22	44	expression	expression	NOUN
ap-10553	22	45	of	of	ADP
ap-10553	22	46	the	the	DET
ap-10553	22	47	time	time	NOUN
ap-10553	22	48	evolution	evolution	NOUN
ap-10553	22	49	.	.	PUNCT
ap-10553	23	1	2	2	X
ap-10553	23	2	.	.	X
ap-10553	23	3	star	star	NOUN
ap-10553	23	4	graph	graph	NOUN
ap-10553	23	5	with	with	ADP
ap-10553	23	6	limit	limit	NOUN
ap-10553	23	7	-	-	PUNCT
ap-10553	23	8	circle	circle	NOUN
ap-10553	23	9	lead	lead	NOUN
ap-10553	23	10	ends	ends	AUX
ap-10553	23	11	consider	consider	VERB
ap-10553	23	12	a	a	DET
ap-10553	23	13	star	star	NOUN
ap-10553	23	14	graph	graph	NOUN
ap-10553	23	15	consisting	consist	VERB
ap-10553	23	16	of	of	ADP
ap-10553	23	17	n	n	PRON
ap-10553	23	18	halfline	halfline	NOUN
ap-10553	23	19	edges	edge	NOUN
ap-10553	23	20	connected	connect	VERB
ap-10553	23	21	at	at	ADP
ap-10553	23	22	a	a	DET
ap-10553	23	23	single	single	ADJ
ap-10553	23	24	vertex	vertex	NOUN
ap-10553	23	25	.	.	PUNCT
ap-10553	24	1	the	the	DET
ap-10553	24	2	state	state	PROPN
ap-10553	24	3	hilbert	hilbert	NOUN
ap-10553	24	4	space	space	NOUN
ap-10553	24	5	of	of	ADP
ap-10553	24	6	the	the	DET
ap-10553	24	7	system	system	NOUN
ap-10553	24	8	is	be	AUX
ap-10553	24	9	h	h	NOUN
ap-10553	24	10	=	=	PUNCT
ap-10553	24	11	∑	∑	PUNCT
ap-10553	24	12	j	j	PROPN
ap-10553	24	13	⊕	⊕	PROPN
ap-10553	24	14	l2(r+	l2(r+	PROPN
ap-10553	24	15	)	)	PUNCT
ap-10553	24	16	,	,	PUNCT
ap-10553	24	17	its	its	PRON
ap-10553	24	18	elements	element	NOUN
ap-10553	24	19	being	be	AUX
ap-10553	24	20	written	write	VERB
ap-10553	24	21	as	as	ADP
ap-10553	24	22	ψ	ψ	X
ap-10553	24	23	=	=	X
ap-10553	24	24	{	{	PUNCT
ap-10553	24	25	ψj	ψj	ADV
ap-10553	24	26	}	}	PUNCT
ap-10553	24	27	.	.	PUNCT
ap-10553	25	1	we	we	PRON
ap-10553	25	2	are	be	AUX
ap-10553	25	3	interested	interested	ADJ
ap-10553	25	4	in	in	ADP
ap-10553	25	5	the	the	DET
ap-10553	25	6	operator	operator	NOUN
ap-10553	25	7	h	h	NOUN
ap-10553	25	8	:	:	PUNCT
ap-10553	25	9	hψ	hψ	X
ap-10553	25	10	=	=	SYM
ap-10553	25	11	{	{	PUNCT
ap-10553	25	12	hψj	hψj	PROPN
ap-10553	25	13	}	}	PUNCT
ap-10553	25	14	acting	act	VERB
ap-10553	25	15	as	as	ADP
ap-10553	25	16	(	(	PUNCT
ap-10553	25	17	hψj)(x	hψj)(x	PROPN
ap-10553	25	18	)	)	PUNCT
ap-10553	25	19	=	=	PUNCT
ap-10553	26	1	−ψ′′	−ψ′′	ADP
ap-10553	26	2	j	j	PROPN
ap-10553	26	3	(	(	PUNCT
ap-10553	26	4	x	x	NOUN
ap-10553	26	5	)	)	PUNCT
ap-10553	26	6	−	−	PROPN
ap-10553	26	7	x4ψj(x	x4ψj(x	PROPN
ap-10553	26	8	)	)	PUNCT
ap-10553	26	9	;	;	PUNCT
ap-10553	26	10	(	(	PUNCT
ap-10553	26	11	1	1	X
ap-10553	26	12	)	)	PUNCT
ap-10553	26	13	the	the	DET
ap-10553	26	14	domain	domain	NOUN
ap-10553	26	15	d(h	d(h	PROPN
ap-10553	26	16	)	)	PUNCT
ap-10553	26	17	of	of	ADP
ap-10553	26	18	h	h	NOUN
ap-10553	26	19	is	be	AUX
ap-10553	26	20	chosen	choose	VERB
ap-10553	26	21	to	to	PART
ap-10553	26	22	consist	consist	VERB
ap-10553	26	23	of	of	ADP
ap-10553	26	24	functions	function	NOUN
ap-10553	26	25	from	from	ADP
ap-10553	26	26	∑	∑	PROPN
ap-10553	26	27	j	j	PROPN
ap-10553	26	28	⊕	⊕	PROPN
ap-10553	26	29	c∞	c∞	PROPN
ap-10553	26	30	0	0	PUNCT
ap-10553	26	31	(	(	PUNCT
ap-10553	26	32	r+	r+	X
ap-10553	26	33	)	)	PUNCT
ap-10553	26	34	satisfying	satisfy	VERB
ap-10553	26	35	the	the	DET
ap-10553	26	36	kirchhoff	kirchhoff	NOUN
ap-10553	26	37	conditions	condition	NOUN
ap-10553	26	38	at	at	ADP
ap-10553	26	39	the	the	DET
ap-10553	26	40	star	star	NOUN
ap-10553	26	41	graph	graph	NOUN
ap-10553	26	42	vertex	vertex	NOUN
ap-10553	26	43	,	,	PUNCT
ap-10553	26	44	ψj(0	ψj(0	PROPN
ap-10553	26	45	)	)	PUNCT
ap-10553	26	46	=	=	SYM
ap-10553	26	47	ψk(0	ψk(0	NOUN
ap-10553	26	48	)	)	PUNCT
ap-10553	26	49	,	,	PUNCT
ap-10553	26	50	j	j	PROPN
ap-10553	26	51	,	,	PUNCT
ap-10553	26	52	k	k	PROPN
ap-10553	26	53	=	=	SYM
ap-10553	26	54	1	1	NUM
ap-10553	26	55	,	,	PUNCT
ap-10553	26	56	.	.	PUNCT
ap-10553	26	57	.	.	PUNCT
ap-10553	27	1	.	.	PUNCT
ap-10553	28	1	,	,	PUNCT
ap-10553	28	2	n	n	CCONJ
ap-10553	28	3	,	,	PUNCT
ap-10553	28	4	(	(	PUNCT
ap-10553	28	5	2a	2a	NUM
ap-10553	28	6	)	)	PUNCT
ap-10553	29	1	n∑	n∑	NOUN
ap-10553	29	2	j=1	j=1	PROPN
ap-10553	29	3	ψ′	ψ′	PROPN
ap-10553	29	4	j(0	j(0	PROPN
ap-10553	29	5	)	)	PUNCT
ap-10553	29	6	=	=	PUNCT
ap-10553	30	1	0	0	X
ap-10553	30	2	.	.	PUNCT
ap-10553	30	3	(	(	PUNCT
ap-10553	30	4	2b	2b	NUM
ap-10553	30	5	)	)	PUNCT
ap-10553	30	6	speaking	speak	VERB
ap-10553	30	7	of	of	ADP
ap-10553	30	8	c∞	c∞	PROPN
ap-10553	30	9	0	0	PUNCT
ap-10553	30	10	(	(	PUNCT
ap-10553	30	11	r+	r+	X
ap-10553	30	12	)	)	PUNCT
ap-10553	30	13	,	,	PUNCT
ap-10553	30	14	we	we	PRON
ap-10553	30	15	suppose	suppose	VERB
ap-10553	30	16	that	that	SCONJ
ap-10553	30	17	the	the	DET
ap-10553	30	18	supports	support	NOUN
ap-10553	30	19	of	of	ADP
ap-10553	30	20	the	the	DET
ap-10553	30	21	functions	function	NOUN
ap-10553	30	22	may	may	AUX
ap-10553	30	23	contain	contain	VERB
ap-10553	30	24	zero	zero	NUM
ap-10553	30	25	,	,	PUNCT
ap-10553	30	26	and	and	CCONJ
ap-10553	30	27	ψj(0	ψj(0	PROPN
ap-10553	30	28	)	)	PUNCT
ap-10553	30	29	and	and	CCONJ
ap-10553	30	30	ψ′	ψ′	PROPN
ap-10553	30	31	j(0	j(0	PROPN
ap-10553	30	32	)	)	PUNCT
ap-10553	30	33	539	539	NUM
ap-10553	30	34	https://doi.org/10.14311/ap.2025.65.0539	https://doi.org/10.14311/ap.2025.65.0539	NOUN
ap-10553	30	35	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10553	30	36	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-10553	30	37	pavel	pavel	PROPN
ap-10553	30	38	exner	exner	PROPN
ap-10553	30	39	acta	acta	PROPN
ap-10553	30	40	polytechnica	polytechnica	PROPN
ap-10553	30	41	are	be	AUX
ap-10553	30	42	understood	understand	VERB
ap-10553	30	43	as	as	ADP
ap-10553	30	44	right	right	ADJ
ap-10553	30	45	limits	limit	NOUN
ap-10553	30	46	there	there	ADV
ap-10553	30	47	.	.	PUNCT
ap-10553	31	1	as	as	ADP
ap-10553	31	2	such	such	ADJ
ap-10553	31	3	,	,	PUNCT
ap-10553	31	4	the	the	DET
ap-10553	31	5	operator	operator	NOUN
ap-10553	31	6	is	be	AUX
ap-10553	31	7	densely	densely	ADV
ap-10553	31	8	defined	define	VERB
ap-10553	31	9	and	and	CCONJ
ap-10553	31	10	symmetric	symmetric	ADJ
ap-10553	31	11	but	but	CCONJ
ap-10553	31	12	not	not	PART
ap-10553	31	13	closed	closed	ADJ
ap-10553	31	14	;	;	PUNCT
ap-10553	31	15	it	it	PRON
ap-10553	31	16	is	be	AUX
ap-10553	31	17	straightforward	straightforward	ADJ
ap-10553	31	18	to	to	PART
ap-10553	31	19	find	find	VERB
ap-10553	31	20	its	its	PRON
ap-10553	31	21	adjoint	adjoint	NOUN
ap-10553	31	22	which	which	PRON
ap-10553	31	23	acts	act	VERB
ap-10553	31	24	as	as	ADP
ap-10553	31	25	(	(	PUNCT
ap-10553	31	26	1	1	NUM
ap-10553	31	27	)	)	PUNCT
ap-10553	31	28	again	again	ADV
ap-10553	31	29	on	on	ADP
ap-10553	31	30	the	the	DET
ap-10553	31	31	definition	definition	NOUN
ap-10553	31	32	domain	domain	NOUN
ap-10553	31	33	d(h∗	d(h∗	NOUN
ap-10553	31	34	)	)	PUNCT
ap-10553	31	35	,	,	PUNCT
ap-10553	31	36	consisting	consist	VERB
ap-10553	31	37	of	of	ADP
ap-10553	31	38	all	all	DET
ap-10553	31	39	vector	vector	NOUN
ap-10553	31	40	-	-	PUNCT
ap-10553	31	41	valued	value	VERB
ap-10553	31	42	functions	function	NOUN
ap-10553	31	43	ψ	ψ	ADP
ap-10553	31	44	∈	∈	NOUN
ap-10553	31	45	h	h	NOUN
ap-10553	31	46	such	such	ADJ
ap-10553	31	47	that	that	SCONJ
ap-10553	31	48	ψj	ψj	ADV
ap-10553	31	49	∈	∈	PROPN
ap-10553	31	50	h2	h2	NOUN
ap-10553	31	51	loc(r+	loc(r+	X
ap-10553	31	52	)	)	PUNCT
ap-10553	31	53	and	and	CCONJ
ap-10553	31	54	−ψ′′	−ψ′′	ADP
ap-10553	31	55	j	j	PROPN
ap-10553	31	56	−	−	PROPN
ap-10553	31	57	x4ψj	x4ψj	PROPN
ap-10553	31	58	understood	understand	VERB
ap-10553	31	59	in	in	ADP
ap-10553	31	60	the	the	DET
ap-10553	31	61	sense	sense	NOUN
ap-10553	31	62	of	of	ADP
ap-10553	31	63	distributions	distribution	NOUN
ap-10553	31	64	belongs	belong	VERB
ap-10553	31	65	to	to	ADP
ap-10553	31	66	l2(r+	l2(r+	PROPN
ap-10553	31	67	)	)	PUNCT
ap-10553	31	68	.	.	PUNCT
ap-10553	32	1	the	the	DET
ap-10553	32	2	operator	operator	NOUN
ap-10553	32	3	h	h	NOUN
ap-10553	32	4	is	be	AUX
ap-10553	32	5	symmetric	symmetric	ADJ
ap-10553	32	6	but	but	CCONJ
ap-10553	32	7	not	not	PART
ap-10553	32	8	essentially	essentially	ADV
ap-10553	32	9	self	self	NOUN
ap-10553	32	10	-	-	PUNCT
ap-10553	32	11	adjoint	adjoint	NOUN
ap-10553	32	12	because	because	SCONJ
ap-10553	32	13	h∗	h∗	PROPN
ap-10553	32	14	is	be	AUX
ap-10553	32	15	not	not	PART
ap-10553	32	16	symmetric	symmetric	ADJ
ap-10553	32	17	;	;	PUNCT
ap-10553	32	18	as	as	SCONJ
ap-10553	32	19	is	be	AUX
ap-10553	32	20	usual	usual	ADJ
ap-10553	32	21	with	with	ADP
ap-10553	32	22	sturmliouville	sturmliouville	NOUN
ap-10553	32	23	-	-	PUNCT
ap-10553	32	24	type	type	NOUN
ap-10553	32	25	operators	operator	NOUN
ap-10553	32	26	,	,	PUNCT
ap-10553	32	27	this	this	PRON
ap-10553	32	28	would	would	AUX
ap-10553	32	29	require	require	VERB
ap-10553	32	30	the	the	DET
ap-10553	32	31	boundary	boundary	ADJ
ap-10553	32	32	form	form	NOUN
ap-10553	32	33	b(ϕ	b(ϕ	NOUN
ap-10553	32	34	,	,	PUNCT
ap-10553	32	35	ψ	ψ	NOUN
ap-10553	32	36	)	)	PUNCT
ap-10553	32	37	:	:	PUNCT
ap-10553	32	38	=	=	SYM
ap-10553	32	39	(	(	PUNCT
ap-10553	32	40	h∗ϕ	h∗ϕ	NOUN
ap-10553	32	41	,	,	PUNCT
ap-10553	32	42	ψ	ψ	NOUN
ap-10553	32	43	)	)	PUNCT
ap-10553	32	44	−	−	PROPN
ap-10553	32	45	(	(	PUNCT
ap-10553	32	46	ϕ,h∗ψ	ϕ,h∗ψ	NOUN
ap-10553	32	47	)	)	PUNCT
ap-10553	32	48	(	(	PUNCT
ap-10553	32	49	3a	3a	NUM
ap-10553	32	50	)	)	PUNCT
ap-10553	32	51	to	to	PART
ap-10553	32	52	vanish	vanish	VERB
ap-10553	32	53	for	for	ADP
ap-10553	32	54	all	all	DET
ap-10553	32	55	ϕ	ϕ	NOUN
ap-10553	32	56	,	,	PUNCT
ap-10553	32	57	ψ	ψ	X
ap-10553	32	58	∈	∈	PROPN
ap-10553	32	59	d(h∗	d(h∗	NOUN
ap-10553	32	60	)	)	PUNCT
ap-10553	32	61	.	.	PUNCT
ap-10553	33	1	this	this	DET
ap-10553	33	2	form	form	NOUN
ap-10553	33	3	can	can	AUX
ap-10553	33	4	be	be	AUX
ap-10553	33	5	expressed	express	VERB
ap-10553	33	6	explicitly	explicitly	ADV
ap-10553	33	7	through	through	ADP
ap-10553	33	8	integration	integration	NOUN
ap-10553	33	9	by	by	ADP
ap-10553	33	10	parts	part	NOUN
ap-10553	33	11	and	and	CCONJ
ap-10553	33	12	decomposes	decompose	VERB
ap-10553	33	13	naturally	naturally	ADV
ap-10553	33	14	into	into	ADP
ap-10553	33	15	the	the	DET
ap-10553	33	16	sum	sum	NOUN
ap-10553	33	17	b(ϕ	b(ϕ	NOUN
ap-10553	33	18	,	,	PUNCT
ap-10553	33	19	ψ	ψ	NOUN
ap-10553	33	20	)	)	PUNCT
ap-10553	33	21	=	=	SYM
ap-10553	33	22	b0(ϕ	b0(ϕ	PROPN
ap-10553	33	23	,	,	PUNCT
ap-10553	33	24	ψ	ψ	NOUN
ap-10553	33	25	)	)	PUNCT
ap-10553	34	1	+	+	CCONJ
ap-10553	34	2	b∞(ϕ	b∞(ϕ	PROPN
ap-10553	34	3	,	,	PUNCT
ap-10553	34	4	ψ	ψ	NOUN
ap-10553	34	5	)	)	PUNCT
ap-10553	34	6	,	,	PUNCT
ap-10553	34	7	(	(	PUNCT
ap-10553	34	8	3b	3b	NUM
ap-10553	34	9	)	)	PUNCT
ap-10553	34	10	where	where	SCONJ
ap-10553	34	11	b0(ϕ	b0(ϕ	NOUN
ap-10553	34	12	,	,	PUNCT
ap-10553	34	13	ψ	ψ	NOUN
ap-10553	34	14	)	)	PUNCT
ap-10553	34	15	:	:	PUNCT
ap-10553	35	1	=	=	SYM
ap-10553	35	2	n∑	n∑	NOUN
ap-10553	35	3	j=1	j=1	NOUN
ap-10553	35	4	(	(	PUNCT
ap-10553	35	5	ϕ̄′ψ	ϕ̄′ψ	PROPN
ap-10553	35	6	−	−	PROPN
ap-10553	35	7	ϕ̄ψ′)(0	ϕ̄ψ′)(0	PROPN
ap-10553	35	8	)	)	PUNCT
ap-10553	35	9	(	(	PUNCT
ap-10553	35	10	3c	3c	NUM
ap-10553	35	11	)	)	PUNCT
ap-10553	35	12	and	and	CCONJ
ap-10553	35	13	the	the	DET
ap-10553	35	14	other	other	ADJ
ap-10553	35	15	part	part	NOUN
ap-10553	35	16	related	relate	VERB
ap-10553	35	17	to	to	ADP
ap-10553	35	18	the	the	DET
ap-10553	35	19	behaviour	behaviour	NOUN
ap-10553	35	20	of	of	ADP
ap-10553	35	21	functions	function	NOUN
ap-10553	35	22	from	from	ADP
ap-10553	35	23	d(h∗	d(h∗	NOUN
ap-10553	35	24	)	)	PUNCT
ap-10553	35	25	at	at	ADP
ap-10553	35	26	large	large	ADJ
ap-10553	35	27	values	value	NOUN
ap-10553	35	28	of	of	ADP
ap-10553	35	29	the	the	DET
ap-10553	35	30	argument	argument	NOUN
ap-10553	35	31	we	we	PRON
ap-10553	35	32	shall	shall	AUX
ap-10553	35	33	specify	specify	VERB
ap-10553	35	34	later	later	ADV
ap-10553	35	35	.	.	PUNCT
ap-10553	36	1	the	the	DET
ap-10553	36	2	choice	choice	NOUN
ap-10553	36	3	of	of	ADP
ap-10553	36	4	the	the	DET
ap-10553	36	5	conditions	condition	NOUN
ap-10553	36	6	(	(	PUNCT
ap-10553	36	7	2	2	X
ap-10553	36	8	)	)	PUNCT
ap-10553	36	9	ensures	ensure	VERB
ap-10553	36	10	that	that	SCONJ
ap-10553	36	11	the	the	DET
ap-10553	36	12	operator	operator	NOUN
ap-10553	36	13	is	be	AUX
ap-10553	36	14	“	"	PUNCT
ap-10553	36	15	locally	locally	ADV
ap-10553	36	16	self	self	NOUN
ap-10553	36	17	-	-	PUNCT
ap-10553	36	18	adjoint	adjoint	NOUN
ap-10553	36	19	”	"	PUNCT
ap-10553	36	20	,	,	PUNCT
ap-10553	36	21	meaning	mean	VERB
ap-10553	36	22	that	that	SCONJ
ap-10553	36	23	b0(ϕ	b0(ϕ	NOUN
ap-10553	36	24	,	,	PUNCT
ap-10553	36	25	ψ	ψ	NOUN
ap-10553	36	26	)	)	PUNCT
ap-10553	36	27	=	=	SYM
ap-10553	36	28	0	0	NUM
ap-10553	36	29	holds	hold	NOUN
ap-10553	36	30	,	,	PUNCT
ap-10553	36	31	or	or	CCONJ
ap-10553	36	32	in	in	ADP
ap-10553	36	33	other	other	ADJ
ap-10553	36	34	words	word	NOUN
ap-10553	36	35	,	,	PUNCT
ap-10553	36	36	that	that	SCONJ
ap-10553	36	37	the	the	DET
ap-10553	36	38	probability	probability	NOUN
ap-10553	36	39	current	current	NOUN
ap-10553	36	40	is	be	AUX
ap-10553	36	41	conserved	conserve	VERB
ap-10553	36	42	at	at	ADP
ap-10553	36	43	the	the	DET
ap-10553	36	44	vertex	vertex	NOUN
ap-10553	36	45	.	.	PUNCT
ap-10553	37	1	in	in	ADP
ap-10553	37	2	view	view	NOUN
ap-10553	37	3	of	of	ADP
ap-10553	37	4	the	the	DET
ap-10553	37	5	strong	strong	ADJ
ap-10553	37	6	negative	negative	ADJ
ap-10553	37	7	potential	potential	NOUN
ap-10553	37	8	,	,	PUNCT
ap-10553	37	9	however	however	ADV
ap-10553	37	10	,	,	PUNCT
ap-10553	37	11	it	it	PRON
ap-10553	37	12	is	be	AUX
ap-10553	37	13	not	not	PART
ap-10553	37	14	“	"	PUNCT
ap-10553	37	15	globally	globally	ADV
ap-10553	37	16	”	"	PUNCT
ap-10553	37	17	self	self	NOUN
ap-10553	37	18	-	-	PUNCT
ap-10553	37	19	adjoint	adjoint	NOUN
ap-10553	37	20	:	:	PUNCT
ap-10553	37	21	proposition	proposition	NOUN
ap-10553	37	22	2.1	2.1	NUM
ap-10553	37	23	.	.	PUNCT
ap-10553	38	1	operator	operator	NOUN
ap-10553	38	2	(	(	PUNCT
ap-10553	38	3	1	1	X
ap-10553	38	4	)	)	PUNCT
ap-10553	38	5	has	have	VERB
ap-10553	38	6	deficiency	deficiency	NOUN
ap-10553	38	7	indices	index	NOUN
ap-10553	38	8	(	(	PUNCT
ap-10553	38	9	n	n	X
ap-10553	38	10	,	,	PUNCT
ap-10553	38	11	n	n	CCONJ
ap-10553	38	12	)	)	PUNCT
ap-10553	38	13	and	and	CCONJ
ap-10553	38	14	is	be	AUX
ap-10553	38	15	bounded	bound	VERB
ap-10553	38	16	neither	neither	CCONJ
ap-10553	38	17	from	from	ADP
ap-10553	38	18	above	above	ADV
ap-10553	38	19	nor	nor	CCONJ
ap-10553	38	20	from	from	ADP
ap-10553	38	21	below	below	ADV
ap-10553	38	22	.	.	PUNCT
ap-10553	39	1	any	any	DET
ap-10553	39	2	self	self	NOUN
ap-10553	39	3	-	-	PUNCT
ap-10553	39	4	adjoint	adjoint	NOUN
ap-10553	39	5	extension	extension	NOUN
ap-10553	39	6	of	of	ADP
ap-10553	39	7	it	it	PRON
ap-10553	39	8	has	have	VERB
ap-10553	39	9	a	a	DET
ap-10553	39	10	purely	purely	ADV
ap-10553	39	11	discrete	discrete	ADJ
ap-10553	39	12	spectrum	spectrum	NOUN
ap-10553	39	13	of	of	ADP
ap-10553	39	14	multiplicity	multiplicity	NOUN
ap-10553	39	15	not	not	PART
ap-10553	39	16	exceeding	exceed	VERB
ap-10553	39	17	n	n	PRON
ap-10553	39	18	.	.	PUNCT
ap-10553	40	1	proof	proof	NOUN
ap-10553	40	2	.	.	PUNCT
ap-10553	41	1	the	the	DET
ap-10553	41	2	“	"	PUNCT
ap-10553	41	3	two	two	NUM
ap-10553	41	4	-	-	PUNCT
ap-10553	41	5	sided	sided	ADJ
ap-10553	41	6	”	"	PUNCT
ap-10553	41	7	unboundedness	unboundedness	NOUN
ap-10553	41	8	of	of	ADP
ap-10553	41	9	h	h	NOUN
ap-10553	41	10	is	be	AUX
ap-10553	41	11	easy	easy	ADJ
ap-10553	41	12	to	to	PART
ap-10553	41	13	check	check	VERB
ap-10553	41	14	.	.	PUNCT
ap-10553	42	1	it	it	PRON
ap-10553	42	2	is	be	AUX
ap-10553	42	3	sufficient	sufficient	ADJ
ap-10553	42	4	to	to	PART
ap-10553	42	5	choose	choose	VERB
ap-10553	42	6	a	a	DET
ap-10553	42	7	suitable	suitable	ADJ
ap-10553	42	8	family	family	NOUN
ap-10553	42	9	of	of	ADP
ap-10553	42	10	functions	function	NOUN
ap-10553	42	11	of	of	ADP
ap-10553	42	12	the	the	DET
ap-10553	42	13	domain	domain	NOUN
ap-10553	42	14	,	,	PUNCT
ap-10553	42	15	say	say	VERB
ap-10553	42	16	,	,	PUNCT
ap-10553	42	17	ψσ	ψσ	ADP
ap-10553	42	18	=	=	SYM
ap-10553	42	19	{	{	PUNCT
ap-10553	42	20	δj1σ	δj1σ	NOUN
ap-10553	42	21	−	−	NOUN
ap-10553	42	22	1	1	NUM
ap-10553	42	23	2	2	NUM
ap-10553	42	24	f	f	X
ap-10553	42	25	(	(	PUNCT
ap-10553	42	26	·	·	PUNCT
ap-10553	42	27	σ	σ	X
ap-10553	42	28	)	)	PUNCT
ap-10553	42	29	}	}	PUNCT
ap-10553	42	30	with	with	ADP
ap-10553	42	31	σ	σ	PROPN
ap-10553	42	32	>	>	X
ap-10553	42	33	0	0	PROPN
ap-10553	42	34	,	,	PUNCT
ap-10553	42	35	where	where	SCONJ
ap-10553	42	36	f	f	PROPN
ap-10553	42	37	is	be	AUX
ap-10553	42	38	a	a	DET
ap-10553	42	39	non	non	ADJ
ap-10553	42	40	-	-	ADJ
ap-10553	42	41	vanishing	vanishing	ADJ
ap-10553	42	42	function	function	NOUN
ap-10553	42	43	from	from	ADP
ap-10553	42	44	c∞	c∞	PROPN
ap-10553	42	45	0	0	PUNCT
ap-10553	42	46	(	(	PUNCT
ap-10553	42	47	r+	r+	X
ap-10553	42	48	)	)	PUNCT
ap-10553	42	49	with	with	ADP
ap-10553	42	50	supp	supp	PROPN
ap-10553	42	51	f	f	PROPN
ap-10553	42	52	⊂	⊂	PROPN
ap-10553	43	1	[	[	X
ap-10553	43	2	1	1	NUM
ap-10553	43	3	,	,	PUNCT
ap-10553	43	4	2	2	NUM
ap-10553	43	5	]	]	PUNCT
ap-10553	43	6	;	;	PUNCT
ap-10553	43	7	then	then	ADV
ap-10553	43	8	a	a	DET
ap-10553	43	9	straightforward	straightforward	ADJ
ap-10553	43	10	computation	computation	NOUN
ap-10553	43	11	yields	yield	VERB
ap-10553	43	12	the	the	DET
ap-10553	43	13	expression	expression	NOUN
ap-10553	43	14	(	(	PUNCT
ap-10553	43	15	ψσ	ψσ	ADP
ap-10553	43	16	,	,	PUNCT
ap-10553	43	17	hψσ	hψσ	NOUN
ap-10553	43	18	)	)	PUNCT
ap-10553	43	19	=	=	PUNCT
ap-10553	44	1	σ−2∥f	σ−2∥f	PROPN
ap-10553	44	2	′∥2	′∥2	VERB
ap-10553	44	3	−	−	PROPN
ap-10553	44	4	σ4∥x2f∥2	σ4∥x2f∥2	PROPN
ap-10553	44	5	,	,	PUNCT
ap-10553	44	6	which	which	PRON
ap-10553	44	7	tends	tend	VERB
ap-10553	44	8	to	to	PART
ap-10553	44	9	±∞	±∞	PROPN
ap-10553	44	10	as	as	ADP
ap-10553	44	11	σ	σ	PROPN
ap-10553	44	12	→	→	SYM
ap-10553	44	13	0	0	NUM
ap-10553	44	14	+	+	NUM
ap-10553	44	15	and	and	CCONJ
ap-10553	44	16	σ	σ	PROPN
ap-10553	44	17	→	→	SYM
ap-10553	44	18	∞	∞	PROPN
ap-10553	44	19	,	,	PUNCT
ap-10553	44	20	respectively	respectively	ADV
ap-10553	44	21	.	.	PUNCT
ap-10553	45	1	consider	consider	VERB
ap-10553	45	2	next	next	ADP
ap-10553	45	3	the	the	DET
ap-10553	45	4	dirichlet	dirichlet	NOUN
ap-10553	45	5	-	-	PUNCT
ap-10553	45	6	decoupled	decouple	VERB
ap-10553	45	7	counterpart	counterpart	NOUN
ap-10553	45	8	to	to	ADP
ap-10553	45	9	h	h	NOUN
ap-10553	45	10	,	,	PUNCT
ap-10553	45	11	i.e.	i.e.	X
ap-10553	45	12	the	the	DET
ap-10553	45	13	direct	direct	ADJ
ap-10553	45	14	sum	sum	NOUN
ap-10553	45	15	hd	hd	PROPN
ap-10553	46	1	=	=	PRON
ap-10553	46	2	∑	∑	PUNCT
ap-10553	46	3	j	j	PROPN
ap-10553	46	4	⊕	⊕	PROPN
ap-10553	46	5	hd	hd	PROPN
ap-10553	46	6	j	j	PROPN
ap-10553	46	7	,	,	PUNCT
ap-10553	46	8	where	where	SCONJ
ap-10553	46	9	the	the	DET
ap-10553	46	10	operators	operator	NOUN
ap-10553	46	11	hd	hd	VERB
ap-10553	46	12	j	j	PROPN
ap-10553	46	13	on	on	ADP
ap-10553	46	14	l2(r+	l2(r+	PROPN
ap-10553	46	15	)	)	PUNCT
ap-10553	46	16	act	act	NOUN
ap-10553	46	17	as	as	ADP
ap-10553	46	18	(	(	PUNCT
ap-10553	46	19	1	1	NUM
ap-10553	46	20	)	)	PUNCT
ap-10553	46	21	on	on	ADP
ap-10553	46	22	functions	function	NOUN
ap-10553	46	23	from	from	ADP
ap-10553	46	24	c∞	c∞	PROPN
ap-10553	46	25	0	0	PUNCT
ap-10553	46	26	(	(	PUNCT
ap-10553	46	27	r+	r+	X
ap-10553	46	28	)	)	PUNCT
ap-10553	46	29	satisfying	satisfy	VERB
ap-10553	46	30	ψj(0	ψj(0	PROPN
ap-10553	46	31	)	)	PUNCT
ap-10553	46	32	=	=	NOUN
ap-10553	47	1	0	0	X
ap-10553	47	2	.	.	PUNCT
ap-10553	48	1	as	as	SCONJ
ap-10553	48	2	hd	hd	PROPN
ap-10553	48	3	is	be	AUX
ap-10553	48	4	a	a	DET
ap-10553	48	5	direct	direct	ADJ
ap-10553	48	6	sum	sum	NOUN
ap-10553	48	7	,	,	PUNCT
ap-10553	48	8	its	its	PRON
ap-10553	48	9	spectral	spectral	ADJ
ap-10553	48	10	properties	property	NOUN
ap-10553	48	11	are	be	AUX
ap-10553	48	12	determined	determine	VERB
ap-10553	48	13	by	by	ADP
ap-10553	48	14	those	those	PRON
ap-10553	48	15	of	of	ADP
ap-10553	48	16	its	its	PRON
ap-10553	48	17	components	component	NOUN
ap-10553	48	18	.	.	PUNCT
ap-10553	49	1	the	the	DET
ap-10553	49	2	latter	latter	ADJ
ap-10553	49	3	have	have	AUX
ap-10553	49	4	fixed	fix	VERB
ap-10553	49	5	boundary	boundary	ADJ
ap-10553	49	6	condition	condition	NOUN
ap-10553	49	7	at	at	ADP
ap-10553	49	8	zero	zero	NUM
ap-10553	49	9	and	and	CCONJ
ap-10553	49	10	are	be	AUX
ap-10553	49	11	limit	limit	VERB
ap-10553	49	12	circle	circle	NOUN
ap-10553	49	13	at	at	ADP
ap-10553	49	14	infinity	infinity	NOUN
ap-10553	49	15	as	as	SCONJ
ap-10553	49	16	we	we	PRON
ap-10553	49	17	shall	shall	AUX
ap-10553	49	18	see	see	VERB
ap-10553	49	19	a	a	DET
ap-10553	49	20	little	little	ADJ
ap-10553	49	21	below	below	ADV
ap-10553	49	22	,	,	PUNCT
ap-10553	49	23	hence	hence	ADV
ap-10553	49	24	each	each	PRON
ap-10553	49	25	of	of	ADP
ap-10553	49	26	them	they	PRON
ap-10553	49	27	has	have	VERB
ap-10553	49	28	deficiency	deficiency	NOUN
ap-10553	49	29	indices	index	NOUN
ap-10553	49	30	(	(	PUNCT
ap-10553	49	31	1	1	NUM
ap-10553	49	32	,	,	PUNCT
ap-10553	49	33	1	1	NUM
ap-10553	49	34	)	)	PUNCT
ap-10553	49	35	,	,	PUNCT
ap-10553	50	1	[	[	X
ap-10553	50	2	7	7	NUM
ap-10553	50	3	,	,	PUNCT
ap-10553	50	4	sec	sec	PROPN
ap-10553	50	5	.	.	PUNCT
ap-10553	51	1	xiii.6	xiii.6	PROPN
ap-10553	51	2	]	]	PUNCT
ap-10553	51	3	or	or	CCONJ
ap-10553	51	4	[	[	X
ap-10553	51	5	5	5	NUM
ap-10553	51	6	,	,	PUNCT
ap-10553	51	7	app	app	PROPN
ap-10553	51	8	.	.	PROPN
ap-10553	51	9	to	to	ADP
ap-10553	51	10	sec	sec	PROPN
ap-10553	51	11	.	.	PUNCT
ap-10553	52	1	x.1	x.1	PROPN
ap-10553	53	1	]	]	PUNCT
ap-10553	53	2	,	,	PUNCT
ap-10553	53	3	and	and	CCONJ
ap-10553	53	4	consequently	consequently	ADV
ap-10553	53	5	,	,	PUNCT
ap-10553	53	6	the	the	DET
ap-10553	53	7	deficiency	deficiency	NOUN
ap-10553	53	8	indices	index	NOUN
ap-10553	53	9	of	of	ADP
ap-10553	53	10	hd	hd	NOUN
ap-10553	53	11	are	be	AUX
ap-10553	53	12	(	(	PUNCT
ap-10553	53	13	n	n	X
ap-10553	53	14	,	,	PUNCT
ap-10553	53	15	n	n	CCONJ
ap-10553	53	16	)	)	PUNCT
ap-10553	53	17	.	.	PUNCT
ap-10553	54	1	since	since	SCONJ
ap-10553	54	2	the	the	DET
ap-10553	54	3	deficiency	deficiency	NOUN
ap-10553	54	4	indices	index	NOUN
ap-10553	54	5	are	be	AUX
ap-10553	54	6	finite	finite	ADJ
ap-10553	54	7	and	and	CCONJ
ap-10553	54	8	equal	equal	ADJ
ap-10553	54	9	,	,	PUNCT
ap-10553	54	10	every	every	DET
ap-10553	54	11	maximal	maximal	ADJ
ap-10553	54	12	symmetric	symmetric	ADJ
ap-10553	54	13	extension	extension	NOUN
ap-10553	54	14	of	of	ADP
ap-10553	54	15	hd	hd	PROPN
ap-10553	54	16	is	be	AUX
ap-10553	54	17	selfadjoint	selfadjoint	NOUN
ap-10553	54	18	;	;	PUNCT
ap-10553	54	19	the	the	DET
ap-10553	54	20	family	family	NOUN
ap-10553	54	21	of	of	ADP
ap-10553	54	22	such	such	ADJ
ap-10553	54	23	extensions	extension	NOUN
ap-10553	54	24	depends	depend	VERB
ap-10553	54	25	on	on	ADP
ap-10553	54	26	n2	n2	ADJ
ap-10553	54	27	real	real	ADJ
ap-10553	54	28	parameters	parameter	NOUN
ap-10553	54	29	.	.	PUNCT
ap-10553	55	1	let	let	VERB
ap-10553	55	2	ĥd	ĥd	X
ap-10553	55	3	be	be	AUX
ap-10553	55	4	a	a	DET
ap-10553	55	5	fixed	fix	VERB
ap-10553	55	6	self	self	NOUN
ap-10553	55	7	-	-	PUNCT
ap-10553	55	8	adjoint	adjoint	NOUN
ap-10553	55	9	extension	extension	NOUN
ap-10553	55	10	.	.	PUNCT
ap-10553	56	1	its	its	PRON
ap-10553	56	2	essential	essential	ADJ
ap-10553	56	3	spectrum	spectrum	NOUN
ap-10553	56	4	is	be	AUX
ap-10553	56	5	empty	empty	ADJ
ap-10553	56	6	:	:	PUNCT
ap-10553	56	7	since	since	SCONJ
ap-10553	56	8	for	for	ADP
ap-10553	56	9	our	our	PRON
ap-10553	56	10	edge	edge	NOUN
ap-10553	56	11	potential	potential	ADJ
ap-10553	56	12	v(x	v(x	NOUN
ap-10553	56	13	)	)	PUNCT
ap-10553	56	14	=	=	SYM
ap-10553	56	15	−x4	−x4	NOUN
ap-10553	56	16	,	,	PUNCT
ap-10553	56	17	both	both	CCONJ
ap-10553	56	18	the	the	DET
ap-10553	56	19	functions	function	NOUN
ap-10553	56	20	x	x	SYM
ap-10553	56	21	7→	7→	NUM
ap-10553	56	22	|v(x)|−	|v(x)|−	VERB
ap-10553	56	23	1	1	NUM
ap-10553	56	24	2	2	NUM
ap-10553	56	25	=	=	SYM
ap-10553	56	26	x−2	x−2	PROPN
ap-10553	56	27	and	and	CCONJ
ap-10553	56	28	x	x	SYM
ap-10553	56	29	7→	7→	NUM
ap-10553	56	30	(	(	PUNCT
ap-10553	56	31	(	(	PUNCT
ap-10553	56	32	v′	v′	NOUN
ap-10553	56	33	|v|	|v|	VERB
ap-10553	56	34	3	3	NUM
ap-10553	56	35	2	2	NUM
ap-10553	56	36	)	)	PUNCT
ap-10553	56	37	′	′	NOUN
ap-10553	57	1	−	−	NOUN
ap-10553	57	2	1	1	NUM
ap-10553	57	3	4	4	NUM
ap-10553	57	4	(	(	PUNCT
ap-10553	57	5	v′)2	v′)2	NOUN
ap-10553	57	6	|v|	|v|	NUM
ap-10553	57	7	5	5	NUM
ap-10553	57	8	2	2	NUM
ap-10553	57	9	)	)	PUNCT
ap-10553	57	10	(	(	PUNCT
ap-10553	57	11	x	x	X
ap-10553	57	12	)	)	PUNCT
ap-10553	57	13	=	=	SYM
ap-10553	57	14	−16x−4	−16x−4	NOUN
ap-10553	57	15	belong	belong	VERB
ap-10553	57	16	to	to	ADP
ap-10553	57	17	l(1,∞	l(1,∞	PROPN
ap-10553	57	18	)	)	PUNCT
ap-10553	57	19	,	,	PUNCT
ap-10553	57	20	we	we	PRON
ap-10553	57	21	infer	infer	VERB
ap-10553	57	22	that	that	SCONJ
ap-10553	57	23	σess(hd	σess(hd	PROPN
ap-10553	57	24	j	j	PROPN
ap-10553	57	25	)	)	PUNCT
ap-10553	58	1	=	=	NOUN
ap-10553	58	2	∅	∅	NOUN
ap-10553	58	3	holds	hold	VERB
ap-10553	58	4	for	for	ADP
ap-10553	58	5	j	j	PROPN
ap-10553	58	6	=	=	SYM
ap-10553	58	7	1	1	PROPN
ap-10553	58	8	,	,	PUNCT
ap-10553	58	9	.	.	PUNCT
ap-10553	58	10	.	.	PUNCT
ap-10553	59	1	.	.	PUNCT
ap-10553	60	1	,	,	PUNCT
ap-10553	60	2	n	n	X
ap-10553	60	3	,	,	PUNCT
ap-10553	60	4	cf	cf	NOUN
ap-10553	60	5	.	.	PUNCT
ap-10553	61	1	[	[	X
ap-10553	61	2	7	7	NUM
ap-10553	61	3	,	,	PUNCT
ap-10553	61	4	sec	sec	PROPN
ap-10553	61	5	.	.	PUNCT
ap-10553	62	1	xiii.7.16	xiii.7.16	PROPN
ap-10553	62	2	]	]	X
ap-10553	62	3	,	,	PUNCT
ap-10553	62	4	and	and	CCONJ
ap-10553	62	5	the	the	DET
ap-10553	62	6	same	same	ADJ
ap-10553	62	7	is	be	AUX
ap-10553	62	8	true	true	ADJ
ap-10553	62	9	for	for	ADP
ap-10553	62	10	σess(hd	σess(hd	PROPN
ap-10553	62	11	)	)	PUNCT
ap-10553	62	12	,	,	PUNCT
ap-10553	62	13	hence	hence	ADV
ap-10553	62	14	the	the	DET
ap-10553	62	15	spectrum	spectrum	NOUN
ap-10553	62	16	of	of	ADP
ap-10553	62	17	ĥd	ĥd	NOUN
ap-10553	62	18	is	be	AUX
ap-10553	62	19	purely	purely	ADV
ap-10553	62	20	discrete	discrete	ADJ
ap-10553	62	21	.	.	PUNCT
ap-10553	63	1	we	we	PRON
ap-10553	63	2	note	note	VERB
ap-10553	63	3	that	that	SCONJ
ap-10553	63	4	the	the	DET
ap-10553	63	5	adjoint	adjoint	NOUN
ap-10553	63	6	of	of	ADP
ap-10553	63	7	hd	hd	PROPN
ap-10553	63	8	is	be	AUX
ap-10553	63	9	also	also	ADV
ap-10553	63	10	a	a	DET
ap-10553	63	11	direct	direct	ADJ
ap-10553	63	12	sum	sum	NOUN
ap-10553	63	13	,	,	PUNCT
ap-10553	63	14	(	(	PUNCT
ap-10553	63	15	hd)∗	hd)∗	PROPN
ap-10553	63	16	=	=	SYM
ap-10553	63	17	∑	∑	PUNCT
ap-10553	63	18	j	j	PROPN
ap-10553	63	19	⊕(hd	⊕(hd	PROPN
ap-10553	63	20	j	j	PROPN
ap-10553	63	21	)	)	PUNCT
ap-10553	63	22	∗	∗	NOUN
ap-10553	63	23	,	,	PUNCT
ap-10553	63	24	and	and	CCONJ
ap-10553	63	25	the	the	DET
ap-10553	63	26	family	family	NOUN
ap-10553	63	27	of	of	ADP
ap-10553	63	28	self	self	NOUN
ap-10553	63	29	-	-	PUNCT
ap-10553	63	30	adjoint	adjoint	NOUN
ap-10553	63	31	extensions	extension	NOUN
ap-10553	63	32	of	of	ADP
ap-10553	63	33	hd	hd	NOUN
ap-10553	63	34	contains	contain	VERB
ap-10553	63	35	those	those	PRON
ap-10553	63	36	which	which	PRON
ap-10553	63	37	preserve	preserve	VERB
ap-10553	63	38	the	the	DET
ap-10553	63	39	direct	direct	ADJ
ap-10553	63	40	-	-	PUNCT
ap-10553	63	41	sum	sum	NOUN
ap-10553	63	42	form	form	NOUN
ap-10553	63	43	,	,	PUNCT
ap-10553	63	44	obtained	obtain	VERB
ap-10553	63	45	by	by	ADP
ap-10553	63	46	imposing	impose	VERB
ap-10553	63	47	boundary	boundary	ADJ
ap-10553	63	48	condition	condition	NOUN
ap-10553	63	49	at	at	ADP
ap-10553	63	50	infinity	infinity	NOUN
ap-10553	63	51	componentwise	componentwise	NOUN
ap-10553	63	52	.	.	PUNCT
ap-10553	64	1	we	we	PRON
ap-10553	64	2	pick	pick	VERB
ap-10553	64	3	one	one	NUM
ap-10553	64	4	such	such	ADJ
ap-10553	64	5	extension	extension	NOUN
ap-10553	64	6	with	with	ADP
ap-10553	64	7	the	the	DET
ap-10553	64	8	property	property	NOUN
ap-10553	64	9	that	that	PRON
ap-10553	64	10	the	the	DET
ap-10553	64	11	boundary	boundary	ADJ
ap-10553	64	12	condition	condition	NOUN
ap-10553	64	13	at	at	ADP
ap-10553	64	14	infinity	infinity	NOUN
ap-10553	64	15	is	be	AUX
ap-10553	64	16	the	the	DET
ap-10553	64	17	same	same	ADJ
ap-10553	64	18	at	at	ADP
ap-10553	64	19	each	each	DET
ap-10553	64	20	edge	edge	NOUN
ap-10553	64	21	,	,	PUNCT
ap-10553	64	22	denoting	denote	VERB
ap-10553	64	23	it	it	PRON
ap-10553	64	24	as	as	ADP
ap-10553	64	25	h̃d	h̃d	NOUN
ap-10553	64	26	;	;	PUNCT
ap-10553	64	27	as	as	SCONJ
ap-10553	64	28	is	be	AUX
ap-10553	64	29	usual	usual	ADJ
ap-10553	64	30	with	with	ADP
ap-10553	64	31	sturm	sturm	NOUN
ap-10553	64	32	-	-	PUNCT
ap-10553	64	33	liouville	liouville	NOUN
ap-10553	64	34	problems	problem	NOUN
ap-10553	64	35	,	,	PUNCT
ap-10553	64	36	eigenvalues	eigenvalue	VERB
ap-10553	64	37	of	of	ADP
ap-10553	64	38	its	its	PRON
ap-10553	64	39	component	component	NOUN
ap-10553	64	40	operators	operator	NOUN
ap-10553	64	41	are	be	AUX
ap-10553	64	42	simple	simple	ADJ
ap-10553	64	43	,	,	PUNCT
ap-10553	64	44	and	and	CCONJ
ap-10553	64	45	consequently	consequently	ADV
ap-10553	64	46	,	,	PUNCT
ap-10553	64	47	eigenvalues	eigenvalue	NOUN
ap-10553	64	48	of	of	ADP
ap-10553	64	49	h̃d	h̃d	NOUN
ap-10553	64	50	,	,	PUNCT
ap-10553	64	51	which	which	PRON
ap-10553	64	52	is	be	AUX
ap-10553	64	53	a	a	DET
ap-10553	64	54	direct	direct	ADJ
ap-10553	64	55	sum	sum	NOUN
ap-10553	64	56	of	of	ADP
ap-10553	64	57	copies	copy	NOUN
ap-10553	64	58	of	of	ADP
ap-10553	64	59	the	the	DET
ap-10553	64	60	same	same	ADJ
ap-10553	64	61	operator	operator	NOUN
ap-10553	64	62	,	,	PUNCT
ap-10553	64	63	are	be	AUX
ap-10553	64	64	of	of	ADP
ap-10553	64	65	multiplicity	multiplicity	NOUN
ap-10553	64	66	n	n	NOUN
ap-10553	64	67	.	.	PUNCT
ap-10553	65	1	we	we	PRON
ap-10553	65	2	observe	observe	VERB
ap-10553	65	3	that	that	SCONJ
ap-10553	65	4	ĥd	ĥd	PRON
ap-10553	65	5	and	and	CCONJ
ap-10553	65	6	h̃d	h̃d	NOUN
ap-10553	65	7	are	be	AUX
ap-10553	65	8	self	self	NOUN
ap-10553	65	9	-	-	PUNCT
ap-10553	65	10	adjoint	adjoint	NOUN
ap-10553	65	11	extensions	extension	NOUN
ap-10553	65	12	of	of	ADP
ap-10553	65	13	the	the	DET
ap-10553	65	14	same	same	ADJ
ap-10553	65	15	symmetric	symmetric	ADJ
ap-10553	65	16	operator	operator	NOUN
ap-10553	65	17	of	of	ADP
ap-10553	65	18	the	the	DET
ap-10553	65	19	deficiency	deficiency	NOUN
ap-10553	65	20	indices	indice	VERB
ap-10553	65	21	not	not	PART
ap-10553	65	22	exceeding	exceed	VERB
ap-10553	65	23	n	n	PRON
ap-10553	65	24	,	,	PUNCT
ap-10553	65	25	namely	namely	ADV
ap-10553	65	26	hd	hd	VERB
ap-10553	65	27	;	;	PUNCT
ap-10553	65	28	in	in	ADP
ap-10553	65	29	such	such	DET
ap-10553	65	30	a	a	DET
ap-10553	65	31	case	case	NOUN
ap-10553	65	32	,	,	PUNCT
ap-10553	65	33	in	in	ADP
ap-10553	65	34	each	each	DET
ap-10553	65	35	spectral	spectral	ADJ
ap-10553	65	36	gap	gap	NOUN
ap-10553	65	37	of	of	ADP
ap-10553	65	38	h̃d	h̃d	NOUN
ap-10553	65	39	there	there	PRON
ap-10553	65	40	is	be	VERB
ap-10553	65	41	at	at	ADP
ap-10553	65	42	most	most	ADJ
ap-10553	65	43	n	n	PRON
ap-10553	65	44	eigenvalues	eigenvalue	NOUN
ap-10553	65	45	of	of	ADP
ap-10553	65	46	ĥd	ĥd	NOUN
ap-10553	65	47	,	,	PUNCT
ap-10553	65	48	counting	count	VERB
ap-10553	65	49	multiplicity	multiplicity	NOUN
ap-10553	65	50	,	,	PUNCT
ap-10553	65	51	cf	cf	NOUN
ap-10553	65	52	.	.	PUNCT
ap-10553	66	1	[	[	X
ap-10553	66	2	8	8	NUM
ap-10553	66	3	,	,	PUNCT
ap-10553	66	4	corr	corr	NOUN
ap-10553	66	5	.	.	PUNCT
ap-10553	67	1	1	1	NUM
ap-10553	67	2	to	to	ADP
ap-10553	67	3	thm	thm	PRON
ap-10553	67	4	.	.	PUNCT
ap-10553	68	1	8.19	8.19	NUM
ap-10553	68	2	]	]	PUNCT
ap-10553	68	3	,	,	PUNCT
ap-10553	68	4	hence	hence	ADV
ap-10553	68	5	the	the	DET
ap-10553	68	6	multiplicity	multiplicity	NOUN
ap-10553	68	7	σdisc(ĥd	σdisc(ĥd	NOUN
ap-10553	68	8	)	)	PUNCT
ap-10553	68	9	can	can	AUX
ap-10553	68	10	not	not	PART
ap-10553	68	11	exceed	exceed	VERB
ap-10553	68	12	that	that	PRON
ap-10553	68	13	of	of	ADP
ap-10553	68	14	σdisc(h̃d	σdisc(h̃d	NOUN
ap-10553	68	15	)	)	PUNCT
ap-10553	68	16	.	.	PUNCT
ap-10553	69	1	next	next	ADV
ap-10553	69	2	,	,	PUNCT
ap-10553	69	3	we	we	PRON
ap-10553	69	4	apply	apply	VERB
ap-10553	69	5	the	the	DET
ap-10553	69	6	analogous	analogous	ADJ
ap-10553	69	7	argument	argument	NOUN
ap-10553	69	8	at	at	ADP
ap-10553	69	9	the	the	DET
ap-10553	69	10	“	"	PUNCT
ap-10553	69	11	other	other	ADJ
ap-10553	69	12	end	end	NOUN
ap-10553	69	13	”	"	PUNCT
ap-10553	69	14	of	of	ADP
ap-10553	69	15	the	the	DET
ap-10553	69	16	edges	edge	NOUN
ap-10553	69	17	.	.	PUNCT
ap-10553	70	1	we	we	PRON
ap-10553	70	2	consider	consider	VERB
ap-10553	70	3	the	the	DET
ap-10553	70	4	self	self	NOUN
ap-10553	70	5	-	-	PUNCT
ap-10553	70	6	adjoint	adjoint	NOUN
ap-10553	70	7	extension	extension	NOUN
ap-10553	70	8	ĥ	ĥ	PROPN
ap-10553	70	9	of	of	ADP
ap-10553	70	10	the	the	DET
ap-10553	70	11	original	original	ADJ
ap-10553	70	12	operator	operator	NOUN
ap-10553	70	13	h	h	NOUN
ap-10553	70	14	obtained	obtain	VERB
ap-10553	70	15	by	by	ADP
ap-10553	70	16	modifying	modify	VERB
ap-10553	70	17	ĥd	ĥd	NOUN
ap-10553	70	18	:	:	PUNCT
ap-10553	70	19	we	we	PRON
ap-10553	70	20	keep	keep	VERB
ap-10553	70	21	the	the	DET
ap-10553	70	22	requirements	requirement	NOUN
ap-10553	70	23	on	on	ADP
ap-10553	70	24	the	the	DET
ap-10553	70	25	behavior	behavior	NOUN
ap-10553	70	26	of	of	ADP
ap-10553	70	27	the	the	DET
ap-10553	70	28	functions	function	NOUN
ap-10553	70	29	at	at	ADP
ap-10553	70	30	infinity	infinity	NOUN
ap-10553	70	31	that	that	PRON
ap-10553	70	32	guarantee	guarantee	VERB
ap-10553	70	33	vanishing	vanishing	NOUN
ap-10553	70	34	of	of	ADP
ap-10553	70	35	the	the	DET
ap-10553	70	36	form	form	NOUN
ap-10553	70	37	b∞	b∞	PROPN
ap-10553	70	38	(	(	PUNCT
ap-10553	70	39	·	·	PUNCT
ap-10553	70	40	,	,	PUNCT
ap-10553	70	41	·	·	PUNCT
ap-10553	70	42	)	)	PUNCT
ap-10553	70	43	,	,	PUNCT
ap-10553	70	44	but	but	CCONJ
ap-10553	70	45	replace	replace	VERB
ap-10553	70	46	the	the	DET
ap-10553	70	47	dirichlet	dirichlet	NOUN
ap-10553	70	48	condition	condition	NOUN
ap-10553	70	49	at	at	ADP
ap-10553	70	50	the	the	DET
ap-10553	70	51	vertex	vertex	NOUN
ap-10553	70	52	by	by	ADP
ap-10553	70	53	(	(	PUNCT
ap-10553	70	54	2	2	NUM
ap-10553	70	55	)	)	PUNCT
ap-10553	70	56	.	.	PUNCT
ap-10553	71	1	by	by	ADP
ap-10553	71	2	krein	krein	PROPN
ap-10553	71	3	’s	’s	PART
ap-10553	71	4	formula	formula	NOUN
ap-10553	71	5	[	[	X
ap-10553	71	6	9	9	X
ap-10553	71	7	]	]	PUNCT
ap-10553	71	8	the	the	DET
ap-10553	71	9	resolvents	resolvent	NOUN
ap-10553	71	10	of	of	ADP
ap-10553	71	11	ĥ	ĥ	PUNCT
ap-10553	71	12	and	and	CCONJ
ap-10553	71	13	hd	hd	NOUN
ap-10553	71	14	differ	differ	VERB
ap-10553	71	15	by	by	ADP
ap-10553	71	16	an	an	DET
ap-10553	71	17	operator	operator	NOUN
ap-10553	71	18	of	of	ADP
ap-10553	71	19	rank	rank	NOUN
ap-10553	71	20	not	not	PART
ap-10553	71	21	exceeding	exceed	VERB
ap-10553	71	22	n	n	PROPN
ap-10553	71	23	(	(	PUNCT
ap-10553	71	24	in	in	ADP
ap-10553	71	25	fact	fact	NOUN
ap-10553	71	26	,	,	PUNCT
ap-10553	71	27	equal	equal	ADJ
ap-10553	71	28	to	to	ADP
ap-10553	71	29	n	n	NOUN
ap-10553	71	30	−	−	PROPN
ap-10553	71	31	1	1	NUM
ap-10553	71	32	)	)	PUNCT
ap-10553	71	33	,	,	PUNCT
ap-10553	71	34	hence	hence	ADV
ap-10553	71	35	their	their	PRON
ap-10553	71	36	essential	essential	ADJ
ap-10553	71	37	spectra	spectra	ADJ
ap-10553	71	38	coincide	coincide	NOUN
ap-10553	71	39	and	and	CCONJ
ap-10553	71	40	we	we	PRON
ap-10553	71	41	get	get	VERB
ap-10553	71	42	σess(ĥ	σess(ĥ	PRON
ap-10553	71	43	)	)	PUNCT
ap-10553	72	1	=	=	VERB
ap-10553	72	2	∅.	∅.	ADP
ap-10553	72	3	furthermore	furthermore	ADV
ap-10553	72	4	,	,	PUNCT
ap-10553	72	5	both	both	PRON
ap-10553	72	6	ĥ	ĥ	X
ap-10553	72	7	and	and	CCONJ
ap-10553	72	8	hd	hd	PROPN
ap-10553	72	9	are	be	AUX
ap-10553	72	10	self	self	NOUN
ap-10553	72	11	-	-	PUNCT
ap-10553	72	12	adjoint	adjoint	NOUN
ap-10553	72	13	extensions	extension	NOUN
ap-10553	72	14	of	of	ADP
ap-10553	72	15	the	the	DET
ap-10553	72	16	same	same	ADJ
ap-10553	72	17	symmetric	symmetric	ADJ
ap-10553	72	18	operator	operator	NOUN
ap-10553	72	19	of	of	ADP
ap-10553	72	20	the	the	DET
ap-10553	72	21	deficiency	deficiency	NOUN
ap-10553	72	22	indices	indice	VERB
ap-10553	72	23	not	not	PART
ap-10553	72	24	exceeding	exceed	VERB
ap-10553	72	25	n	n	PRON
ap-10553	72	26	(	(	PUNCT
ap-10553	72	27	the	the	DET
ap-10553	72	28	domain	domain	NOUN
ap-10553	72	29	of	of	ADP
ap-10553	72	30	which	which	PRON
ap-10553	72	31	is	be	AUX
ap-10553	72	32	obtained	obtain	VERB
ap-10553	72	33	by	by	ADP
ap-10553	72	34	imposing	impose	VERB
ap-10553	72	35	the	the	DET
ap-10553	72	36	conditions	condition	NOUN
ap-10553	72	37	ψj(0	ψj(0	NOUN
ap-10553	72	38	)	)	PUNCT
ap-10553	72	39	=	=	PRON
ap-10553	72	40	ψ′	ψ′	PROPN
ap-10553	72	41	j(0	j(0	PROPN
ap-10553	72	42	)	)	PUNCT
ap-10553	73	1	=	=	PUNCT
ap-10553	73	2	0	0	NUM
ap-10553	74	1	for	for	ADP
ap-10553	74	2	j	j	PROPN
ap-10553	74	3	=	=	SYM
ap-10553	74	4	1	1	PROPN
ap-10553	74	5	,	,	PUNCT
ap-10553	74	6	.	.	PUNCT
ap-10553	74	7	.	.	PUNCT
ap-10553	74	8	.	.	PUNCT
ap-10553	74	9	,	,	PUNCT
ap-10553	74	10	n	n	CCONJ
ap-10553	74	11	)	)	PUNCT
ap-10553	74	12	,	,	PUNCT
ap-10553	74	13	and	and	CCONJ
ap-10553	74	14	since	since	SCONJ
ap-10553	74	15	the	the	DET
ap-10553	74	16	eigenvalues	eigenvalue	NOUN
ap-10553	74	17	come	come	VERB
ap-10553	74	18	from	from	ADP
ap-10553	74	19	zeros	zero	NOUN
ap-10553	74	20	of	of	ADP
ap-10553	74	21	(	(	PUNCT
ap-10553	74	22	the	the	DET
ap-10553	74	23	determinant	determinant	NOUN
ap-10553	74	24	of	of	ADP
ap-10553	74	25	)	)	PUNCT
ap-10553	74	26	the	the	DET
ap-10553	74	27	denominator	denominator	NOUN
ap-10553	74	28	of	of	ADP
ap-10553	74	29	the	the	DET
ap-10553	74	30	second	second	ADJ
ap-10553	74	31	term	term	NOUN
ap-10553	74	32	in	in	ADP
ap-10553	74	33	krein	krein	PROPN
ap-10553	74	34	’s	’s	PART
ap-10553	74	35	formula	formula	NOUN
ap-10553	74	36	which	which	PRON
ap-10553	74	37	is	be	AUX
ap-10553	74	38	an	an	DET
ap-10553	74	39	analytic	analytic	ADJ
ap-10553	74	40	matrix	matrix	NOUN
ap-10553	74	41	-	-	PUNCT
ap-10553	74	42	valued	value	VERB
ap-10553	74	43	function	function	NOUN
ap-10553	74	44	of	of	ADP
ap-10553	74	45	the	the	DET
ap-10553	74	46	spectral	spectral	ADJ
ap-10553	74	47	parameter	parameter	NOUN
ap-10553	74	48	of	of	ADP
ap-10553	74	49	the	the	DET
ap-10553	74	50	rank	rank	NOUN
ap-10553	74	51	not	not	PART
ap-10553	74	52	exceeding	exceed	VERB
ap-10553	74	53	n	n	PRON
ap-10553	74	54	,	,	PUNCT
ap-10553	74	55	the	the	DET
ap-10553	74	56	multiplicity	multiplicity	NOUN
ap-10553	74	57	σdisc(ĥ	σdisc(ĥ	NOUN
ap-10553	74	58	)	)	PUNCT
ap-10553	74	59	can	can	AUX
ap-10553	74	60	not	not	PART
ap-10553	74	61	exceed	exceed	VERB
ap-10553	74	62	that	that	PRON
ap-10553	74	63	of	of	ADP
ap-10553	74	64	σdisc(ĥd	σdisc(ĥd	NOUN
ap-10553	74	65	)	)	PUNCT
ap-10553	74	66	.	.	PUNCT
ap-10553	75	1	after	after	ADP
ap-10553	75	2	this	this	DET
ap-10553	75	3	preliminary	preliminary	NOUN
ap-10553	75	4	,	,	PUNCT
ap-10553	75	5	let	let	VERB
ap-10553	75	6	us	we	PRON
ap-10553	75	7	look	look	VERB
ap-10553	75	8	how	how	SCONJ
ap-10553	75	9	the	the	DET
ap-10553	75	10	selfadjoint	selfadjoint	NOUN
ap-10553	75	11	extensions	extension	NOUN
ap-10553	75	12	of	of	ADP
ap-10553	75	13	h	h	NOUN
ap-10553	75	14	look	look	VERB
ap-10553	75	15	like	like	ADP
ap-10553	75	16	.	.	PUNCT
ap-10553	76	1	since	since	SCONJ
ap-10553	76	2	every	every	DET
ap-10553	76	3	extension	extension	NOUN
ap-10553	76	4	refers	refer	VERB
ap-10553	76	5	to	to	ADP
ap-10553	76	6	a	a	DET
ap-10553	76	7	subspace	subspace	NOUN
ap-10553	76	8	of	of	ADP
ap-10553	76	9	d(h∗	d(h∗	NOUN
ap-10553	76	10	)	)	PUNCT
ap-10553	76	11	,	,	PUNCT
ap-10553	76	12	we	we	PRON
ap-10553	76	13	employ	employ	VERB
ap-10553	76	14	the	the	DET
ap-10553	76	15	standard	standard	ADJ
ap-10553	76	16	decomposition	decomposition	NOUN
ap-10553	76	17	of	of	ADP
ap-10553	76	18	this	this	DET
ap-10553	76	19	set	set	NOUN
ap-10553	76	20	,	,	PUNCT
ap-10553	76	21	d(h∗	d(h∗	NOUN
ap-10553	76	22	)	)	PUNCT
ap-10553	76	23	=	=	SYM
ap-10553	76	24	d(h̄	d(h̄	NOUN
ap-10553	76	25	)	)	PUNCT
ap-10553	76	26	⊕	⊕	PROPN
ap-10553	76	27	k+	k+	PROPN
ap-10553	76	28	⊕	⊕	PROPN
ap-10553	76	29	k−	k−	PROPN
ap-10553	76	30	,	,	PUNCT
ap-10553	76	31	(	(	PUNCT
ap-10553	76	32	4	4	X
ap-10553	76	33	)	)	PUNCT
ap-10553	76	34	540	540	NUM
ap-10553	76	35	vol	vol	NOUN
ap-10553	76	36	.	.	PUNCT
ap-10553	77	1	65	65	NUM
ap-10553	77	2	no	no	NOUN
ap-10553	77	3	.	.	PUNCT
ap-10553	78	1	5/2025	5/2025	NUM
ap-10553	78	2	quantum	quantum	NOUN
ap-10553	78	3	graphs	graph	NOUN
ap-10553	78	4	featuring	feature	VERB
ap-10553	78	5	unusual	unusual	ADJ
ap-10553	78	6	self	self	NOUN
ap-10553	78	7	-	-	PUNCT
ap-10553	78	8	adjoint	adjoint	NOUN
ap-10553	78	9	extensions	extension	NOUN
ap-10553	78	10	where	where	SCONJ
ap-10553	78	11	k±	k±	PROPN
ap-10553	78	12	=	=	PUNCT
ap-10553	78	13	ker(h∗	ker(h∗	X
ap-10553	78	14	∓	∓	PROPN
ap-10553	78	15	i	i	PRON
ap-10553	78	16	)	)	PUNCT
ap-10553	78	17	are	be	AUX
ap-10553	78	18	the	the	DET
ap-10553	78	19	deficiency	deficiency	NOUN
ap-10553	78	20	spaces	space	NOUN
ap-10553	78	21	;	;	PUNCT
ap-10553	78	22	we	we	PRON
ap-10553	78	23	already	already	ADV
ap-10553	78	24	know	know	VERB
ap-10553	78	25	that	that	SCONJ
ap-10553	78	26	in	in	ADP
ap-10553	78	27	our	our	PRON
ap-10553	78	28	case	case	NOUN
ap-10553	78	29	,	,	PUNCT
ap-10553	78	30	their	their	PRON
ap-10553	78	31	dimension	dimension	NOUN
ap-10553	78	32	is	be	AUX
ap-10553	78	33	n	n	PRON
ap-10553	78	34	.	.	PUNCT
ap-10553	79	1	to	to	PART
ap-10553	79	2	construct	construct	VERB
ap-10553	79	3	the	the	DET
ap-10553	79	4	extensions	extension	NOUN
ap-10553	79	5	,	,	PUNCT
ap-10553	79	6	one	one	PRON
ap-10553	79	7	can	can	AUX
ap-10553	79	8	use	use	VERB
ap-10553	79	9	different	different	ADJ
ap-10553	79	10	methods	method	NOUN
ap-10553	79	11	.	.	PUNCT
ap-10553	80	1	the	the	DET
ap-10553	80	2	classical	classical	ADJ
ap-10553	80	3	one	one	NOUN
ap-10553	80	4	,	,	PUNCT
ap-10553	80	5	due	due	ADP
ap-10553	80	6	to	to	ADP
ap-10553	80	7	j.	j.	PROPN
ap-10553	80	8	von	von	PROPN
ap-10553	80	9	neumann	neumann	PROPN
ap-10553	80	10	,	,	PUNCT
ap-10553	80	11	uses	use	VERB
ap-10553	80	12	isometric	isometric	ADJ
ap-10553	80	13	maps	map	NOUN
ap-10553	80	14	from	from	ADP
ap-10553	80	15	k+	k+	NOUN
ap-10553	80	16	to	to	ADP
ap-10553	80	17	k−	k−	PROPN
ap-10553	81	1	[	[	X
ap-10553	81	2	5	5	NUM
ap-10553	81	3	,	,	PUNCT
ap-10553	81	4	sec	sec	PROPN
ap-10553	81	5	.	.	PROPN
ap-10553	81	6	x.1	x.1	PROPN
ap-10553	81	7	]	]	X
ap-10553	81	8	.	.	PUNCT
ap-10553	82	1	if	if	SCONJ
ap-10553	82	2	the	the	DET
ap-10553	82	3	operator	operator	NOUN
ap-10553	82	4	in	in	ADP
ap-10553	82	5	question	question	NOUN
ap-10553	82	6	is	be	AUX
ap-10553	82	7	differential	differential	ADJ
ap-10553	82	8	,	,	PUNCT
ap-10553	82	9	it	it	PRON
ap-10553	82	10	is	be	AUX
ap-10553	82	11	usually	usually	ADV
ap-10553	82	12	simpler	simple	ADJ
ap-10553	82	13	to	to	PART
ap-10553	82	14	employ	employ	VERB
ap-10553	82	15	appropriate	appropriate	ADJ
ap-10553	82	16	boundary	boundary	ADJ
ap-10553	82	17	conditions	condition	NOUN
ap-10553	82	18	;	;	PUNCT
ap-10553	82	19	this	this	DET
ap-10553	82	20	approach	approach	NOUN
ap-10553	82	21	finds	find	VERB
ap-10553	82	22	its	its	PRON
ap-10553	82	23	abstract	abstract	ADJ
ap-10553	82	24	form	form	NOUN
ap-10553	82	25	in	in	ADP
ap-10553	82	26	the	the	DET
ap-10553	82	27	theory	theory	NOUN
ap-10553	82	28	of	of	ADP
ap-10553	82	29	boundary	boundary	ADJ
ap-10553	82	30	triples	triple	NOUN
ap-10553	82	31	[	[	X
ap-10553	82	32	10	10	NUM
ap-10553	82	33	]	]	PUNCT
ap-10553	82	34	.	.	PUNCT
ap-10553	83	1	here	here	ADV
ap-10553	83	2	,	,	PUNCT
ap-10553	83	3	we	we	PRON
ap-10553	83	4	follow	follow	VERB
ap-10553	83	5	neither	neither	PRON
ap-10553	83	6	of	of	ADP
ap-10553	83	7	the	the	DET
ap-10553	83	8	two	two	NUM
ap-10553	83	9	paths	path	NOUN
ap-10553	83	10	,	,	PUNCT
ap-10553	83	11	but	but	CCONJ
ap-10553	83	12	our	our	PRON
ap-10553	83	13	construction	construction	NOUN
ap-10553	83	14	is	be	AUX
ap-10553	83	15	closer	close	ADJ
ap-10553	83	16	to	to	ADP
ap-10553	83	17	the	the	DET
ap-10553	83	18	latter	latter	ADJ
ap-10553	83	19	since	since	SCONJ
ap-10553	83	20	it	it	PRON
ap-10553	83	21	expresses	express	VERB
ap-10553	83	22	the	the	DET
ap-10553	83	23	second	second	ADJ
ap-10553	83	24	part	part	NOUN
ap-10553	83	25	of	of	ADP
ap-10553	83	26	the	the	DET
ap-10553	83	27	form	form	NOUN
ap-10553	83	28	(	(	PUNCT
ap-10553	83	29	3b	3b	NUM
ap-10553	83	30	)	)	PUNCT
ap-10553	83	31	by	by	ADP
ap-10553	83	32	means	mean	NOUN
ap-10553	83	33	of	of	ADP
ap-10553	83	34	generalised	generalised	ADJ
ap-10553	83	35	boundary	boundary	ADJ
ap-10553	83	36	values	value	NOUN
ap-10553	83	37	.	.	PUNCT
ap-10553	84	1	to	to	PART
ap-10553	84	2	define	define	VERB
ap-10553	84	3	them	they	PRON
ap-10553	84	4	,	,	PUNCT
ap-10553	84	5	we	we	PRON
ap-10553	84	6	note	note	VERB
ap-10553	84	7	that	that	SCONJ
ap-10553	84	8	while	while	SCONJ
ap-10553	84	9	we	we	PRON
ap-10553	84	10	can	can	AUX
ap-10553	84	11	not	not	PART
ap-10553	84	12	solve	solve	VERB
ap-10553	84	13	the	the	DET
ap-10553	84	14	deficiency	deficiency	NOUN
ap-10553	84	15	equations	equation	NOUN
ap-10553	84	16	,	,	PUNCT
ap-10553	84	17	−ψ′′(x	−ψ′′(x	NOUN
ap-10553	84	18	)	)	PUNCT
ap-10553	84	19	−	−	PROPN
ap-10553	85	1	(	(	PUNCT
ap-10553	85	2	x4	x4	PROPN
ap-10553	85	3	±	±	PROPN
ap-10553	85	4	i)ψ(x	i)ψ(x	NOUN
ap-10553	85	5	)	)	PUNCT
ap-10553	85	6	=	=	SYM
ap-10553	85	7	0	0	NUM
ap-10553	85	8	,	,	PUNCT
ap-10553	85	9	explicitly	explicitly	ADV
ap-10553	85	10	,	,	PUNCT
ap-10553	85	11	the	the	DET
ap-10553	85	12	knowledge	knowledge	NOUN
ap-10553	85	13	of	of	ADP
ap-10553	85	14	the	the	DET
ap-10553	85	15	potential	potential	NOUN
ap-10553	85	16	allows	allow	VERB
ap-10553	85	17	us	we	PRON
ap-10553	85	18	to	to	PART
ap-10553	85	19	determine	determine	VERB
ap-10553	85	20	the	the	DET
ap-10553	85	21	asymptotic	asymptotic	ADJ
ap-10553	85	22	behaviour	behaviour	NOUN
ap-10553	85	23	for	for	ADP
ap-10553	85	24	large	large	ADJ
ap-10553	85	25	values	value	NOUN
ap-10553	85	26	of	of	ADP
ap-10553	85	27	the	the	DET
ap-10553	85	28	argument	argument	NOUN
ap-10553	85	29	,	,	PUNCT
ap-10553	85	30	which	which	PRON
ap-10553	85	31	is	be	AUX
ap-10553	85	32	what	what	PRON
ap-10553	85	33	would	would	AUX
ap-10553	85	34	matter	matter	VERB
ap-10553	85	35	:	:	PUNCT
ap-10553	85	36	components	component	NOUN
ap-10553	85	37	of	of	ADP
ap-10553	85	38	any	any	DET
ap-10553	85	39	such	such	ADJ
ap-10553	85	40	solution	solution	NOUN
ap-10553	85	41	are	be	AUX
ap-10553	85	42	linear	linear	ADJ
ap-10553	85	43	combinations	combination	NOUN
ap-10553	85	44	of	of	ADP
ap-10553	85	45	a	a	DET
ap-10553	85	46	pair	pair	NOUN
ap-10553	85	47	of	of	ADP
ap-10553	85	48	functions	function	NOUN
ap-10553	85	49	satisfying	satisfy	VERB
ap-10553	85	50	φ±(x	φ±(x	NOUN
ap-10553	85	51	)	)	PUNCT
ap-10553	86	1	=	=	PUNCT
ap-10553	86	2	e±	e±	VERB
ap-10553	86	3	ix3	ix3	PROPN
ap-10553	86	4	3	3	NUM
ap-10553	86	5	x	x	SYM
ap-10553	86	6	(	(	PUNCT
ap-10553	86	7	1	1	NUM
ap-10553	86	8	+	+	CCONJ
ap-10553	86	9	o(x−1	o(x−1	NOUN
ap-10553	86	10	)	)	PUNCT
ap-10553	86	11	)	)	PUNCT
ap-10553	86	12	,	,	PUNCT
ap-10553	86	13	(	(	PUNCT
ap-10553	86	14	5a	5a	NUM
ap-10553	86	15	)	)	PUNCT
ap-10553	86	16	φ′	φ′	NUM
ap-10553	86	17	±(x	±(x	NOUN
ap-10553	86	18	)	)	PUNCT
ap-10553	87	1	=	=	PRON
ap-10553	87	2	±ix	±ix	PROPN
ap-10553	87	3	e±	e±	PROPN
ap-10553	87	4	ix3	ix3	PROPN
ap-10553	87	5	3	3	NUM
ap-10553	87	6	(	(	PUNCT
ap-10553	87	7	1	1	NUM
ap-10553	87	8	+	+	CCONJ
ap-10553	87	9	o(x−1	o(x−1	NOUN
ap-10553	87	10	)	)	PUNCT
ap-10553	87	11	)	)	PUNCT
ap-10553	87	12	,	,	PUNCT
ap-10553	87	13	(	(	PUNCT
ap-10553	87	14	5b	5b	NUM
ap-10553	87	15	)	)	PUNCT
ap-10553	87	16	cf	cf	NOUN
ap-10553	87	17	.	.	PUNCT
ap-10553	88	1	[	[	X
ap-10553	88	2	11	11	NUM
ap-10553	88	3	,	,	PUNCT
ap-10553	88	4	thm	thm	PROPN
ap-10553	88	5	.	.	PUNCT
ap-10553	89	1	6.2.2	6.2.2	NUM
ap-10553	89	2	]	]	PUNCT
ap-10553	89	3	;	;	PUNCT
ap-10553	89	4	since	since	SCONJ
ap-10553	89	5	the	the	DET
ap-10553	89	6	solutions	solution	NOUN
ap-10553	89	7	belong	belong	VERB
ap-10553	89	8	,	,	PUNCT
ap-10553	89	9	in	in	ADP
ap-10553	89	10	view	view	NOUN
ap-10553	89	11	of	of	ADP
ap-10553	89	12	elliptic	elliptic	ADJ
ap-10553	89	13	regularity	regularity	NOUN
ap-10553	89	14	,	,	PUNCT
ap-10553	89	15	to	to	ADP
ap-10553	89	16	c∞(r+	c∞(r+	PROPN
ap-10553	89	17	)	)	PUNCT
ap-10553	89	18	,	,	PUNCT
ap-10553	89	19	both	both	DET
ap-10553	89	20	functions	function	NOUN
ap-10553	89	21	(	(	PUNCT
ap-10553	89	22	5a	5a	NUM
ap-10553	89	23	)	)	PUNCT
ap-10553	89	24	are	be	AUX
ap-10553	89	25	obviously	obviously	ADV
ap-10553	89	26	elements	element	NOUN
ap-10553	89	27	of	of	ADP
ap-10553	89	28	l2(r+	l2(r+	PROPN
ap-10553	89	29	)	)	PUNCT
ap-10553	89	30	.	.	PUNCT
ap-10553	90	1	to	to	PART
ap-10553	90	2	use	use	VERB
ap-10553	90	3	the	the	DET
ap-10553	90	4	asymptotics	asymptotic	NOUN
ap-10553	90	5	(	(	PUNCT
ap-10553	90	6	5	5	NUM
ap-10553	90	7	)	)	PUNCT
ap-10553	90	8	,	,	PUNCT
ap-10553	90	9	one	one	PRON
ap-10553	90	10	has	have	VERB
ap-10553	90	11	to	to	PART
ap-10553	90	12	make	make	VERB
ap-10553	90	13	sure	sure	ADJ
ap-10553	90	14	that	that	SCONJ
ap-10553	90	15	the	the	DET
ap-10553	90	16	sought	seek	VERB
ap-10553	90	17	boundary	boundary	ADJ
ap-10553	90	18	values	value	NOUN
ap-10553	90	19	will	will	AUX
ap-10553	90	20	be	be	AUX
ap-10553	90	21	determined	determine	VERB
ap-10553	90	22	by	by	ADP
ap-10553	90	23	elements	element	NOUN
ap-10553	90	24	of	of	ADP
ap-10553	90	25	the	the	DET
ap-10553	90	26	deficiency	deficiency	NOUN
ap-10553	90	27	subspaces	subspace	VERB
ap-10553	90	28	only	only	ADV
ap-10553	90	29	.	.	PUNCT
ap-10553	91	1	lemma	lemma	PROPN
ap-10553	91	2	2.2	2.2	NUM
ap-10553	91	3	.	.	PUNCT
ap-10553	92	1	the	the	DET
ap-10553	92	2	domain	domain	NOUN
ap-10553	92	3	d(h̄	d(h̄	NOUN
ap-10553	92	4	)	)	PUNCT
ap-10553	92	5	of	of	ADP
ap-10553	92	6	the	the	DET
ap-10553	92	7	closure	closure	NOUN
ap-10553	92	8	h̄	h̄	NOUN
ap-10553	92	9	consists	consist	VERB
ap-10553	92	10	of	of	ADP
ap-10553	92	11	all	all	DET
ap-10553	92	12	the	the	DET
ap-10553	92	13	functions	function	NOUN
ap-10553	92	14	ψ	ψ	X
ap-10553	92	15	∈	∈	PROPN
ap-10553	92	16	d(h∗	d(h∗	NOUN
ap-10553	92	17	)	)	PUNCT
ap-10553	92	18	satisfying	satisfy	VERB
ap-10553	92	19	lim	lim	PROPN
ap-10553	92	20	x→∞	x→∞	NUM
ap-10553	92	21	xψj(x	xψj(x	PROPN
ap-10553	92	22	)	)	PUNCT
ap-10553	93	1	=	=	SYM
ap-10553	93	2	lim	lim	PROPN
ap-10553	93	3	x→∞	x→∞	NUM
ap-10553	93	4	ψ′	ψ′	NUM
ap-10553	93	5	j(x	j(x	NOUN
ap-10553	93	6	)	)	PUNCT
ap-10553	93	7	x	x	PUNCT
ap-10553	94	1	=	=	SYM
ap-10553	94	2	0	0	NUM
ap-10553	94	3	,	,	PUNCT
ap-10553	94	4	j	j	PROPN
ap-10553	94	5	=	=	SYM
ap-10553	94	6	1	1	NUM
ap-10553	94	7	,	,	PUNCT
ap-10553	94	8	.	.	PUNCT
ap-10553	94	9	.	.	PUNCT
ap-10553	94	10	.	.	PUNCT
ap-10553	95	1	,	,	PUNCT
ap-10553	95	2	n.	n.	NOUN
ap-10553	95	3	proof	proof	NOUN
ap-10553	95	4	.	.	PUNCT
ap-10553	96	1	recall	recall	VERB
ap-10553	96	2	that	that	SCONJ
ap-10553	96	3	the	the	DET
ap-10553	96	4	decomposition	decomposition	NOUN
ap-10553	96	5	(	(	PUNCT
ap-10553	96	6	4	4	X
ap-10553	96	7	)	)	PUNCT
ap-10553	96	8	is	be	AUX
ap-10553	96	9	orthogonal	orthogonal	ADJ
ap-10553	96	10	with	with	ADP
ap-10553	96	11	respect	respect	NOUN
ap-10553	96	12	to	to	ADP
ap-10553	96	13	the	the	DET
ap-10553	96	14	scalar	scalar	ADJ
ap-10553	96	15	product	product	NOUN
ap-10553	96	16	(	(	PUNCT
ap-10553	96	17	ϕ	ϕ	NOUN
ap-10553	96	18	,	,	PUNCT
ap-10553	96	19	ψ)h	ψ)h	PUNCT
ap-10553	96	20	:	:	PUNCT
ap-10553	96	21	=	=	SYM
ap-10553	96	22	(	(	PUNCT
ap-10553	96	23	ϕ	ϕ	NOUN
ap-10553	96	24	,	,	PUNCT
ap-10553	96	25	ψ	ψ	NOUN
ap-10553	96	26	)	)	PUNCT
ap-10553	96	27	+	+	CCONJ
ap-10553	96	28	(	(	PUNCT
ap-10553	96	29	h∗ϕ,h∗ψ	h∗ϕ,h∗ψ	NOUN
ap-10553	96	30	)	)	PUNCT
ap-10553	96	31	.	.	PUNCT
ap-10553	97	1	in	in	ADP
ap-10553	97	2	particular	particular	ADJ
ap-10553	97	3	,	,	PUNCT
ap-10553	97	4	any	any	DET
ap-10553	97	5	vectors	vector	NOUN
ap-10553	97	6	ψ	ψ	VERB
ap-10553	97	7	∈	∈	PROPN
ap-10553	97	8	d(h̄	d(h̄	NOUN
ap-10553	97	9	)	)	PUNCT
ap-10553	97	10	and	and	CCONJ
ap-10553	97	11	ϕ	ϕ	PROPN
ap-10553	97	12	∈	∈	PROPN
ap-10553	97	13	k+	k+	NOUN
ap-10553	97	14	are	be	AUX
ap-10553	97	15	in	in	ADP
ap-10553	97	16	this	this	DET
ap-10553	97	17	sense	sense	NOUN
ap-10553	97	18	orthogonal	orthogonal	NOUN
ap-10553	97	19	,	,	PUNCT
ap-10553	97	20	and	and	CCONJ
ap-10553	97	21	since	since	SCONJ
ap-10553	97	22	h∗ϕ	h∗ϕ	NOUN
ap-10553	97	23	=	=	SYM
ap-10553	97	24	iϕ	iϕ	NOUN
ap-10553	97	25	,	,	PUNCT
ap-10553	97	26	we	we	PRON
ap-10553	97	27	have	have	VERB
ap-10553	97	28	(	(	PUNCT
ap-10553	97	29	ψ	ψ	X
ap-10553	97	30	,	,	PUNCT
ap-10553	97	31	ϕ	ϕ	NOUN
ap-10553	97	32	)	)	PUNCT
ap-10553	98	1	+	+	CCONJ
ap-10553	98	2	i(h∗ψ	i(h∗ψ	NOUN
ap-10553	98	3	,	,	PUNCT
ap-10553	98	4	ϕ	ϕ	NOUN
ap-10553	98	5	)	)	PUNCT
ap-10553	98	6	=	=	SYM
ap-10553	98	7	0	0	NUM
ap-10553	98	8	,	,	PUNCT
ap-10553	98	9	or	or	CCONJ
ap-10553	98	10	n∑	n∑	ADJ
ap-10553	98	11	j=1	j=1	NOUN
ap-10553	98	12	(	(	PUNCT
ap-10553	98	13	(	(	PUNCT
ap-10553	98	14	ψj	ψj	ADV
ap-10553	98	15	,	,	PUNCT
ap-10553	98	16	ϕj	ϕj	PROPN
ap-10553	98	17	)	)	PUNCT
ap-10553	99	1	+	+	CCONJ
ap-10553	99	2	i(h∗ψj	i(h∗ψj	PROPN
ap-10553	99	3	,	,	PUNCT
ap-10553	99	4	ϕj	ϕj	PROPN
ap-10553	99	5	)	)	PUNCT
ap-10553	99	6	)	)	PUNCT
ap-10553	100	1	=	=	SYM
ap-10553	100	2	0	0	PUNCT
ap-10553	100	3	(	(	PUNCT
ap-10553	100	4	6	6	NUM
ap-10553	100	5	)	)	PUNCT
ap-10553	100	6	(	(	PUNCT
ap-10553	100	7	we	we	PRON
ap-10553	100	8	use	use	VERB
ap-10553	100	9	here	here	ADV
ap-10553	100	10	the	the	DET
ap-10553	100	11	convention	convention	NOUN
ap-10553	100	12	in	in	ADP
ap-10553	100	13	which	which	PRON
ap-10553	100	14	the	the	DET
ap-10553	100	15	scalar	scalar	ADJ
ap-10553	100	16	product	product	NOUN
ap-10553	100	17	is	be	AUX
ap-10553	100	18	linear	linear	ADJ
ap-10553	100	19	in	in	ADP
ap-10553	100	20	the	the	DET
ap-10553	100	21	second	second	ADJ
ap-10553	100	22	argument	argument	NOUN
ap-10553	100	23	)	)	PUNCT
ap-10553	100	24	.	.	PUNCT
ap-10553	101	1	next	next	ADV
ap-10553	101	2	,	,	PUNCT
ap-10553	101	3	we	we	PRON
ap-10553	101	4	use	use	VERB
ap-10553	101	5	the	the	DET
ap-10553	101	6	explicit	explicit	ADJ
ap-10553	101	7	expression	expression	NOUN
ap-10553	101	8	of	of	ADP
ap-10553	101	9	the	the	DET
ap-10553	101	10	second	second	ADJ
ap-10553	101	11	part	part	NOUN
ap-10553	101	12	on	on	ADP
ap-10553	101	13	the	the	DET
ap-10553	101	14	left	left	ADJ
ap-10553	101	15	-	-	PUNCT
ap-10553	101	16	hand	hand	NOUN
ap-10553	101	17	side	side	NOUN
ap-10553	101	18	and	and	CCONJ
ap-10553	101	19	move	move	VERB
ap-10553	101	20	h∗	h∗	PROPN
ap-10553	101	21	to	to	ADP
ap-10553	101	22	the	the	DET
ap-10553	101	23	other	other	ADJ
ap-10553	101	24	side	side	NOUN
ap-10553	101	25	of	of	ADP
ap-10553	101	26	the	the	DET
ap-10553	101	27	scalar	scalar	ADJ
ap-10553	101	28	product	product	NOUN
ap-10553	101	29	using	use	VERB
ap-10553	101	30	double	double	ADJ
ap-10553	101	31	integration	integration	NOUN
ap-10553	101	32	by	by	ADP
ap-10553	101	33	parts	part	NOUN
ap-10553	101	34	over	over	ADP
ap-10553	101	35	the	the	DET
ap-10553	101	36	interval	interval	NOUN
ap-10553	101	37	[	[	X
ap-10553	101	38	0	0	NUM
ap-10553	101	39	,	,	PUNCT
ap-10553	101	40	x̃	x̃	PROPN
ap-10553	101	41	)	)	PUNCT
ap-10553	101	42	,	,	PUNCT
ap-10553	101	43	and	and	CCONJ
ap-10553	101	44	since	since	SCONJ
ap-10553	101	45	h∗ϕj	h∗ϕj	NOUN
ap-10553	101	46	=	=	PUNCT
ap-10553	101	47	iϕj	iϕj	VERB
ap-10553	101	48	by	by	ADP
ap-10553	101	49	assumption	assumption	NOUN
ap-10553	101	50	,	,	PUNCT
ap-10553	101	51	we	we	PRON
ap-10553	101	52	arrive	arrive	VERB
ap-10553	101	53	at	at	ADP
ap-10553	101	54	the	the	DET
ap-10553	101	55	relation	relation	NOUN
ap-10553	101	56	lim	lim	PROPN
ap-10553	101	57	x̃→∞	x̃→∞	PUNCT
ap-10553	102	1	n∑	n∑	INTJ
ap-10553	102	2	j=1	j=1	NOUN
ap-10553	102	3	[	[	PUNCT
ap-10553	102	4	−	−	NOUN
ap-10553	102	5	ψ′	ψ′	NUM
ap-10553	102	6	j(x)ϕj(x	j(x)ϕj(x	NOUN
ap-10553	102	7	)	)	PUNCT
ap-10553	102	8	+	+	CCONJ
ap-10553	102	9	ψj(x)ϕ′	ψj(x)ϕ′	PUNCT
ap-10553	102	10	j(x	j(x	PROPN
ap-10553	102	11	)	)	PUNCT
ap-10553	103	1	]	]	PUNCT
ap-10553	103	2	x̃	x̃	PROPN
ap-10553	103	3	0	0	PUNCT
ap-10553	103	4	=	=	SYM
ap-10553	103	5	0	0	X
ap-10553	103	6	.	.	PUNCT
ap-10553	104	1	furthermore	furthermore	ADV
ap-10553	104	2	,	,	PUNCT
ap-10553	104	3	the	the	DET
ap-10553	104	4	contribution	contribution	NOUN
ap-10553	104	5	from	from	ADP
ap-10553	104	6	the	the	DET
ap-10553	104	7	values	value	NOUN
ap-10553	104	8	at	at	ADP
ap-10553	104	9	x	x	X
ap-10553	104	10	=	=	SYM
ap-10553	104	11	0	0	NUM
ap-10553	104	12	vanishes	vanish	VERB
ap-10553	104	13	in	in	ADP
ap-10553	104	14	view	view	NOUN
ap-10553	104	15	of	of	ADP
ap-10553	104	16	condition	condition	NOUN
ap-10553	104	17	(	(	PUNCT
ap-10553	104	18	2	2	NUM
ap-10553	104	19	)	)	PUNCT
ap-10553	104	20	,	,	PUNCT
ap-10553	104	21	and	and	CCONJ
ap-10553	104	22	since	since	SCONJ
ap-10553	104	23	there	there	PRON
ap-10553	104	24	is	be	VERB
ap-10553	104	25	no	no	DET
ap-10553	104	26	correlation	correlation	NOUN
ap-10553	104	27	between	between	ADP
ap-10553	104	28	the	the	DET
ap-10553	104	29	values	value	NOUN
ap-10553	104	30	as	as	ADP
ap-10553	104	31	x	x	X
ap-10553	104	32	→	→	SYM
ap-10553	104	33	∞	∞	PROPN
ap-10553	104	34	,	,	PUNCT
ap-10553	104	35	we	we	PRON
ap-10553	104	36	get	get	VERB
ap-10553	104	37	lim	lim	PROPN
ap-10553	104	38	x→∞	x→∞	X
ap-10553	105	1	[	[	PUNCT
ap-10553	105	2	−	−	PROPN
ap-10553	105	3	ψ′	ψ′	NUM
ap-10553	105	4	j(x)ϕj(x	j(x)ϕj(x	NOUN
ap-10553	105	5	)	)	PUNCT
ap-10553	105	6	+	+	CCONJ
ap-10553	105	7	ψj(x)ϕ′	ψj(x)ϕ′	PUNCT
ap-10553	105	8	j(x	j(x	PROPN
ap-10553	105	9	)	)	PUNCT
ap-10553	105	10	]	]	PUNCT
ap-10553	106	1	=	=	PUNCT
ap-10553	106	2	0	0	PUNCT
ap-10553	106	3	(	(	PUNCT
ap-10553	106	4	7a	7a	NUM
ap-10553	106	5	)	)	PUNCT
ap-10553	106	6	for	for	ADP
ap-10553	106	7	any	any	DET
ap-10553	106	8	j	j	PROPN
ap-10553	106	9	=	=	SYM
ap-10553	106	10	1	1	NUM
ap-10553	106	11	,	,	PUNCT
ap-10553	106	12	.	.	PUNCT
ap-10553	106	13	.	.	PUNCT
ap-10553	106	14	.	.	PUNCT
ap-10553	107	1	,	,	PUNCT
ap-10553	107	2	n	n	X
ap-10553	107	3	.	.	PUNCT
ap-10553	108	1	the	the	DET
ap-10553	108	2	vector	vector	PROPN
ap-10553	108	3	ψ	ψ	X
ap-10553	108	4	∈	∈	PROPN
ap-10553	108	5	d(h̄	d(h̄	NOUN
ap-10553	108	6	)	)	PUNCT
ap-10553	108	7	was	be	AUX
ap-10553	108	8	supposed	suppose	VERB
ap-10553	108	9	to	to	PART
ap-10553	108	10	be	be	AUX
ap-10553	108	11	arbitrary	arbitrary	ADJ
ap-10553	108	12	,	,	PUNCT
ap-10553	108	13	in	in	ADP
ap-10553	108	14	particular	particular	ADJ
ap-10553	108	15	,	,	PUNCT
ap-10553	108	16	we	we	PRON
ap-10553	108	17	can	can	AUX
ap-10553	108	18	choose	choose	VERB
ap-10553	108	19	it	it	PRON
ap-10553	108	20	real	real	ADV
ap-10553	108	21	-	-	PUNCT
ap-10553	108	22	valued	value	VERB
ap-10553	108	23	;	;	PUNCT
ap-10553	108	24	taking	take	VERB
ap-10553	108	25	complex	complex	ADJ
ap-10553	108	26	conjugate	conjugate	NOUN
ap-10553	108	27	,	,	PUNCT
ap-10553	108	28	we	we	PRON
ap-10553	108	29	also	also	ADV
ap-10553	108	30	get	get	VERB
ap-10553	108	31	lim	lim	PROPN
ap-10553	108	32	x→∞	x→∞	X
ap-10553	109	1	[	[	PUNCT
ap-10553	109	2	−	−	PROPN
ap-10553	109	3	ψ′	ψ′	NUM
ap-10553	109	4	j(x)ϕj(x	j(x)ϕj(x	NOUN
ap-10553	109	5	)	)	PUNCT
ap-10553	109	6	+	+	CCONJ
ap-10553	109	7	ψj(x)ϕ′	ψj(x)ϕ′	PUNCT
ap-10553	109	8	j(x	j(x	PROPN
ap-10553	109	9	)	)	PUNCT
ap-10553	109	10	]	]	PUNCT
ap-10553	110	1	=	=	PUNCT
ap-10553	110	2	0	0	X
ap-10553	110	3	.	.	PUNCT
ap-10553	111	1	(	(	PUNCT
ap-10553	111	2	7b	7b	NUM
ap-10553	111	3	)	)	PUNCT
ap-10553	111	4	we	we	PRON
ap-10553	111	5	denote	denote	VERB
ap-10553	111	6	the	the	DET
ap-10553	111	7	left	left	ADJ
ap-10553	111	8	-	-	PUNCT
ap-10553	111	9	hand	hand	NOUN
ap-10553	111	10	side	side	NOUN
ap-10553	111	11	of	of	ADP
ap-10553	111	12	(	(	PUNCT
ap-10553	111	13	7a	7a	NUM
ap-10553	111	14	)	)	PUNCT
ap-10553	111	15	by	by	ADP
ap-10553	111	16	b(ψj	b(ψj	PROPN
ap-10553	111	17	,	,	PUNCT
ap-10553	111	18	ϕj	ϕj	PROPN
ap-10553	111	19	)	)	PUNCT
ap-10553	111	20	and	and	CCONJ
ap-10553	111	21	choose	choose	VERB
ap-10553	111	22	for	for	ADP
ap-10553	111	23	ϕj	ϕj	INTJ
ap-10553	111	24	a	a	DET
ap-10553	111	25	vector	vector	NOUN
ap-10553	111	26	with	with	ADP
ap-10553	111	27	one	one	NUM
ap-10553	111	28	of	of	ADP
ap-10553	111	29	the	the	DET
ap-10553	111	30	asymptotics	asymptotic	NOUN
ap-10553	111	31	(	(	PUNCT
ap-10553	111	32	5	5	NUM
ap-10553	111	33	)	)	PUNCT
ap-10553	111	34	;	;	PUNCT
ap-10553	111	35	then	then	ADV
ap-10553	111	36	b(ψj	b(ψj	NOUN
ap-10553	111	37	,	,	PUNCT
ap-10553	111	38	φ+	φ+	NOUN
ap-10553	111	39	)	)	PUNCT
ap-10553	112	1	=	=	SYM
ap-10553	112	2	b(ψj	b(ψj	NOUN
ap-10553	112	3	,	,	PUNCT
ap-10553	112	4	φ−	φ−	PROPN
ap-10553	112	5	)	)	PUNCT
ap-10553	112	6	equals	equal	VERB
ap-10553	112	7	b(ψj	b(ψj	NOUN
ap-10553	112	8	,	,	PUNCT
ap-10553	112	9	φ+	φ+	NOUN
ap-10553	112	10	)	)	PUNCT
ap-10553	112	11	=	=	SYM
ap-10553	112	12	lim	lim	PROPN
ap-10553	112	13	x→∞	x→∞	X
ap-10553	113	1	[	[	PUNCT
ap-10553	113	2	−	−	NUM
ap-10553	113	3	ψ′	ψ′	NUM
ap-10553	113	4	j(x	j(x	NOUN
ap-10553	113	5	)	)	PUNCT
ap-10553	113	6	x	x	PUNCT
ap-10553	114	1	−	−	PROPN
ap-10553	114	2	ixψj(x	ixψj(x	NOUN
ap-10553	114	3	)	)	PUNCT
ap-10553	114	4	]	]	PUNCT
ap-10553	115	1	e−	e−	PROPN
ap-10553	115	2	ix3	ix3	PROPN
ap-10553	115	3	3	3	NUM
ap-10553	115	4	=	=	SYM
ap-10553	115	5	0	0	NUM
ap-10553	115	6	,	,	PUNCT
ap-10553	115	7	and	and	CCONJ
ap-10553	115	8	similarly	similarly	ADV
ap-10553	115	9	,	,	PUNCT
ap-10553	115	10	from	from	ADP
ap-10553	115	11	(	(	PUNCT
ap-10553	115	12	7b	7b	NOUN
ap-10553	115	13	)	)	PUNCT
ap-10553	115	14	we	we	PRON
ap-10553	115	15	get	get	VERB
ap-10553	115	16	b(ψj	b(ψj	NOUN
ap-10553	115	17	,	,	PUNCT
ap-10553	115	18	φ̄−	φ̄−	ADJ
ap-10553	115	19	)	)	PUNCT
ap-10553	115	20	=	=	VERB
ap-10553	115	21	lim	lim	PROPN
ap-10553	115	22	x→∞	x→∞	X
ap-10553	116	1	[	[	PUNCT
ap-10553	116	2	−	−	NUM
ap-10553	116	3	ψ′	ψ′	NUM
ap-10553	116	4	j(x	j(x	NOUN
ap-10553	116	5	)	)	PUNCT
ap-10553	116	6	x	x	PUNCT
ap-10553	117	1	+	+	PUNCT
ap-10553	117	2	ixψj(x	ixψj(x	X
ap-10553	117	3	)	)	PUNCT
ap-10553	117	4	]	]	PUNCT
ap-10553	118	1	e−	e−	PROPN
ap-10553	118	2	ix3	ix3	PROPN
ap-10553	118	3	3	3	NUM
ap-10553	118	4	=	=	SYM
ap-10553	118	5	0	0	NUM
ap-10553	118	6	.	.	PUNCT
ap-10553	119	1	thus	thus	ADV
ap-10553	119	2	the	the	DET
ap-10553	119	3	limits	limit	NOUN
ap-10553	119	4	of	of	ADP
ap-10553	119	5	the	the	DET
ap-10553	119	6	two	two	NUM
ap-10553	119	7	square	square	ADJ
ap-10553	119	8	brackets	bracket	NOUN
ap-10553	119	9	have	have	VERB
ap-10553	119	10	to	to	PART
ap-10553	119	11	be	be	AUX
ap-10553	119	12	simultaneously	simultaneously	ADV
ap-10553	119	13	zero	zero	NUM
ap-10553	119	14	,	,	PUNCT
ap-10553	119	15	from	from	ADP
ap-10553	119	16	which	which	PRON
ap-10553	119	17	the	the	DET
ap-10553	119	18	claim	claim	NOUN
ap-10553	119	19	follows	follow	VERB
ap-10553	119	20	.	.	PUNCT
ap-10553	120	1	it	it	PRON
ap-10553	120	2	follows	follow	VERB
ap-10553	120	3	from	from	ADP
ap-10553	120	4	(	(	PUNCT
ap-10553	120	5	5	5	NUM
ap-10553	120	6	)	)	PUNCT
ap-10553	120	7	and	and	CCONJ
ap-10553	120	8	the	the	DET
ap-10553	120	9	above	above	ADJ
ap-10553	120	10	lemma	lemma	PROPN
ap-10553	120	11	that	that	PRON
ap-10553	120	12	away	away	ADV
ap-10553	120	13	from	from	ADP
ap-10553	120	14	the	the	DET
ap-10553	120	15	vertex	vertex	NOUN
ap-10553	120	16	,	,	PUNCT
ap-10553	120	17	the	the	DET
ap-10553	120	18	components	component	NOUN
ap-10553	120	19	of	of	ADP
ap-10553	120	20	any	any	DET
ap-10553	120	21	vector	vector	NOUN
ap-10553	120	22	ψ	ψ	ADP
ap-10553	120	23	∈	∈	PROPN
ap-10553	120	24	d(h∗	d(h∗	NOUN
ap-10553	120	25	)	)	PUNCT
ap-10553	120	26	can	can	AUX
ap-10553	120	27	be	be	AUX
ap-10553	120	28	expressed	express	VERB
ap-10553	120	29	as	as	ADP
ap-10553	120	30	ψj(x	ψj(x	PUNCT
ap-10553	120	31	)	)	PUNCT
ap-10553	121	1	=	=	SYM
ap-10553	121	2	ain	ain	PROPN
ap-10553	121	3	j	j	PROPN
ap-10553	121	4	(	(	PUNCT
ap-10553	121	5	ψ	ψ	NOUN
ap-10553	121	6	)	)	PUNCT
ap-10553	121	7	e	e	NOUN
ap-10553	121	8	ix3	ix3	PROPN
ap-10553	121	9	3	3	NUM
ap-10553	121	10	x	x	X
ap-10553	121	11	+	+	PROPN
ap-10553	121	12	aout	aout	PROPN
ap-10553	121	13	j	j	PROPN
ap-10553	121	14	(	(	PUNCT
ap-10553	121	15	ψ	ψ	NOUN
ap-10553	121	16	)	)	PUNCT
ap-10553	121	17	e−	e−	PROPN
ap-10553	121	18	ix3	ix3	PROPN
ap-10553	121	19	3	3	NUM
ap-10553	121	20	x	x	SYM
ap-10553	121	21	+	+	CCONJ
ap-10553	121	22	uj(x	uj(x	NOUN
ap-10553	121	23	)	)	PUNCT
ap-10553	121	24	(	(	PUNCT
ap-10553	121	25	8)	8)	NUM
ap-10553	121	26	with	with	ADP
ap-10553	121	27	some	some	DET
ap-10553	121	28	u	u	NOUN
ap-10553	121	29	=	=	PUNCT
ap-10553	121	30	{	{	PUNCT
ap-10553	121	31	uj	uj	PROPN
ap-10553	121	32	}	}	PUNCT
ap-10553	121	33	∈	∈	PROPN
ap-10553	121	34	d(h̄	d(h̄	NOUN
ap-10553	121	35	)	)	PUNCT
ap-10553	121	36	and	and	CCONJ
ap-10553	121	37	the	the	DET
ap-10553	121	38	amplitudes	amplitude	NOUN
ap-10553	121	39	a	a	DET
ap-10553	121	40	in	in	ADP
ap-10553	121	41	/	/	SYM
ap-10553	121	42	out	out	ADP
ap-10553	121	43	j	j	PROPN
ap-10553	121	44	(	(	PUNCT
ap-10553	121	45	ψ	ψ	NOUN
ap-10553	121	46	)	)	PUNCT
ap-10553	121	47	:	:	PUNCT
ap-10553	122	1	=	=	SYM
ap-10553	122	2	1	1	NUM
ap-10553	122	3	2i	2i	NUM
ap-10553	122	4	lim	lim	PROPN
ap-10553	122	5	x→∞	x→∞	PROPN
ap-10553	123	1	(	(	PUNCT
ap-10553	123	2	ixψj(x	ixψj(x	PROPN
ap-10553	123	3	)	)	PUNCT
ap-10553	123	4	±	±	NUM
ap-10553	123	5	ψ′	ψ′	NUM
ap-10553	123	6	j(x	j(x	NOUN
ap-10553	123	7	)	)	PUNCT
ap-10553	123	8	x	x	X
ap-10553	123	9	)	)	PUNCT
ap-10553	124	1	e∓	e∓	PROPN
ap-10553	124	2	ix3	ix3	PROPN
ap-10553	124	3	3	3	NUM
ap-10553	124	4	,	,	PUNCT
ap-10553	124	5	(	(	PUNCT
ap-10553	124	6	9	9	X
ap-10553	124	7	)	)	PUNCT
ap-10553	124	8	which	which	PRON
ap-10553	124	9	are	be	AUX
ap-10553	124	10	the	the	DET
ap-10553	124	11	sought	seek	VERB
ap-10553	124	12	generalised	generalise	VERB
ap-10553	124	13	boundary	boundary	ADJ
ap-10553	124	14	values	value	NOUN
ap-10553	124	15	;	;	PUNCT
ap-10553	124	16	by	by	ADP
ap-10553	124	17	the	the	DET
ap-10553	124	18	lemma	lemma	PROPN
ap-10553	124	19	,	,	PUNCT
ap-10553	124	20	ain	ain	PROPN
ap-10553	124	21	/	/	SYM
ap-10553	124	22	out	out	NOUN
ap-10553	124	23	j	j	PROPN
ap-10553	124	24	(	(	PUNCT
ap-10553	124	25	ψ	ψ	NOUN
ap-10553	124	26	)	)	PUNCT
ap-10553	124	27	=	=	SYM
ap-10553	124	28	0	0	NUM
ap-10553	124	29	holds	hold	VERB
ap-10553	124	30	for	for	ADP
ap-10553	124	31	any	any	DET
ap-10553	124	32	ψ	ψ	X
ap-10553	124	33	∈	∈	NOUN
ap-10553	124	34	d(h̄	d(h̄	NOUN
ap-10553	124	35	)	)	PUNCT
ap-10553	124	36	.	.	PUNCT
ap-10553	125	1	to	to	PART
ap-10553	125	2	find	find	VERB
ap-10553	125	3	self	self	NOUN
ap-10553	125	4	-	-	PUNCT
ap-10553	125	5	adjoint	adjoint	NOUN
ap-10553	125	6	extension	extension	NOUN
ap-10553	125	7	of	of	ADP
ap-10553	125	8	h	h	NOUN
ap-10553	125	9	we	we	PRON
ap-10553	125	10	have	have	VERB
ap-10553	125	11	to	to	PART
ap-10553	125	12	evaluate	evaluate	VERB
ap-10553	125	13	the	the	DET
ap-10553	125	14	form	form	NOUN
ap-10553	125	15	b∞	b∞	PROPN
ap-10553	125	16	:	:	PUNCT
ap-10553	125	17	d(h∗	d(h∗	X
ap-10553	125	18	)	)	PUNCT
ap-10553	125	19	×d(h∗	×d(h∗	PROPN
ap-10553	125	20	)	)	PUNCT
ap-10553	126	1	→	→	SYM
ap-10553	126	2	c	c	NOUN
ap-10553	126	3	given	give	VERB
ap-10553	126	4	by	by	ADP
ap-10553	126	5	b∞(ϕ	b∞(ϕ	NOUN
ap-10553	126	6	,	,	PUNCT
ap-10553	126	7	ψ	ψ	NOUN
ap-10553	126	8	)	)	PUNCT
ap-10553	126	9	:	:	PUNCT
ap-10553	126	10	=	=	SYM
ap-10553	126	11	lim	lim	PROPN
ap-10553	126	12	x→∞	x→∞	NUM
ap-10553	127	1	n∑	n∑	INTJ
ap-10553	127	2	j=1	j=1	NOUN
ap-10553	127	3	(	(	PUNCT
ap-10553	127	4	ϕ̄ψ′	ϕ̄ψ′	ADV
ap-10553	127	5	−	−	PROPN
ap-10553	127	6	ϕ̄′ψ	ϕ̄′ψ	PROPN
ap-10553	127	7	)	)	PUNCT
ap-10553	127	8	(	(	PUNCT
ap-10553	127	9	x	x	NOUN
ap-10553	127	10	)	)	PUNCT
ap-10553	127	11	.	.	PUNCT
ap-10553	128	1	substituting	substitute	VERB
ap-10553	128	2	from	from	ADP
ap-10553	128	3	(	(	PUNCT
ap-10553	128	4	9	9	NUM
ap-10553	128	5	)	)	PUNCT
ap-10553	128	6	and	and	CCONJ
ap-10553	128	7	using	use	VERB
ap-10553	128	8	lemma	lemma	PROPN
ap-10553	128	9	2.2	2.2	NUM
ap-10553	128	10	,	,	PUNCT
ap-10553	128	11	we	we	PRON
ap-10553	128	12	obtain	obtain	VERB
ap-10553	128	13	by	by	ADP
ap-10553	128	14	a	a	DET
ap-10553	128	15	straightforward	straightforward	ADJ
ap-10553	128	16	computation	computation	NOUN
ap-10553	128	17	b∞(ϕ	b∞(ϕ	NOUN
ap-10553	128	18	,	,	PUNCT
ap-10553	128	19	ψ	ψ	NOUN
ap-10553	128	20	)	)	PUNCT
ap-10553	128	21	=	=	SYM
ap-10553	128	22	2i	2i	NUM
ap-10553	129	1	n∑	n∑	NOUN
ap-10553	130	1	j=1	j=1	NOUN
ap-10553	131	1	(	(	PUNCT
ap-10553	131	2	ain	ain	PROPN
ap-10553	131	3	j	j	PROPN
ap-10553	131	4	(	(	PUNCT
ap-10553	131	5	ϕ)ain	ϕ)ain	PROPN
ap-10553	131	6	j	j	PROPN
ap-10553	131	7	(	(	PUNCT
ap-10553	131	8	ψ	ψ	NOUN
ap-10553	131	9	)	)	PUNCT
ap-10553	131	10	−aout	−aout	ADP
ap-10553	131	11	j	j	PROPN
ap-10553	131	12	(	(	PUNCT
ap-10553	131	13	ϕ)aout	ϕ)aout	NUM
ap-10553	131	14	j	j	X
ap-10553	131	15	(	(	PUNCT
ap-10553	131	16	ψ	ψ	NOUN
ap-10553	131	17	)	)	PUNCT
ap-10553	131	18	)	)	PUNCT
ap-10553	131	19	;	;	PUNCT
ap-10553	131	20	(	(	PUNCT
ap-10553	131	21	10a	10a	NOUN
ap-10553	131	22	)	)	PUNCT
ap-10553	131	23	introducing	introduce	VERB
ap-10553	131	24	vector	vector	NOUN
ap-10553	131	25	functions	function	NOUN
ap-10553	131	26	ain	ain	PROPN
ap-10553	131	27	/	/	SYM
ap-10553	131	28	out	out	PROPN
ap-10553	131	29	(	(	PUNCT
ap-10553	131	30	·	·	PUNCT
ap-10553	131	31	)	)	PUNCT
ap-10553	131	32	=	=	PRON
ap-10553	131	33	{	{	PUNCT
ap-10553	131	34	ain	ain	PROPN
ap-10553	131	35	/	/	SYM
ap-10553	131	36	out	out	NOUN
ap-10553	131	37	j	j	PROPN
ap-10553	131	38	(	(	PUNCT
ap-10553	131	39	·	·	PUNCT
ap-10553	131	40	)	)	PUNCT
ap-10553	131	41	}	}	PUNCT
ap-10553	131	42	with	with	ADP
ap-10553	131	43	values	value	NOUN
ap-10553	131	44	in	in	ADP
ap-10553	131	45	cn	cn	PROPN
ap-10553	131	46	,	,	PUNCT
ap-10553	131	47	we	we	PRON
ap-10553	131	48	can	can	AUX
ap-10553	131	49	rewrite	rewrite	VERB
ap-10553	131	50	it	it	PRON
ap-10553	131	51	concisely	concisely	ADV
ap-10553	131	52	as	as	ADP
ap-10553	131	53	b∞(ϕ	b∞(ϕ	PROPN
ap-10553	131	54	,	,	PUNCT
ap-10553	131	55	ψ	ψ	NOUN
ap-10553	131	56	)	)	PUNCT
ap-10553	131	57	=	=	SYM
ap-10553	131	58	2i	2i	NUM
ap-10553	131	59	(	(	PUNCT
ap-10553	131	60	(	(	PUNCT
ap-10553	131	61	ain(ϕ	ain(ϕ	PROPN
ap-10553	131	62	)	)	PUNCT
ap-10553	131	63	,	,	PUNCT
ap-10553	131	64	ain(ψ	ain(ψ	PROPN
ap-10553	131	65	)	)	PUNCT
ap-10553	131	66	)	)	PUNCT
ap-10553	132	1	−	−	PROPN
ap-10553	133	1	(	(	PUNCT
ap-10553	133	2	aout(ϕ	aout(ϕ	PROPN
ap-10553	133	3	)	)	PUNCT
ap-10553	133	4	,	,	PUNCT
ap-10553	133	5	aout(ψ	aout(ψ	ADP
ap-10553	133	6	)	)	PUNCT
ap-10553	133	7	)	)	PUNCT
ap-10553	133	8	)	)	PUNCT
ap-10553	133	9	.	.	PUNCT
ap-10553	134	1	(	(	PUNCT
ap-10553	134	2	10b	10b	NOUN
ap-10553	134	3	)	)	PUNCT
ap-10553	134	4	this	this	PRON
ap-10553	134	5	has	have	VERB
ap-10553	134	6	an	an	DET
ap-10553	134	7	easy	easy	ADJ
ap-10553	134	8	consequence	consequence	NOUN
ap-10553	134	9	:	:	PUNCT
ap-10553	134	10	theorem	theorem	VERB
ap-10553	134	11	2.3	2.3	NUM
ap-10553	134	12	.	.	PUNCT
ap-10553	135	1	there	there	PRON
ap-10553	135	2	is	be	VERB
ap-10553	135	3	a	a	DET
ap-10553	135	4	bijective	bijective	ADJ
ap-10553	135	5	correspondence	correspondence	NOUN
ap-10553	135	6	between	between	ADP
ap-10553	135	7	self	self	NOUN
ap-10553	135	8	-	-	PUNCT
ap-10553	135	9	adjoint	adjoint	NOUN
ap-10553	135	10	extensions	extension	NOUN
ap-10553	135	11	of	of	ADP
ap-10553	135	12	operator	operator	NOUN
ap-10553	135	13	h	h	NOUN
ap-10553	135	14	and	and	CCONJ
ap-10553	135	15	2×2	2×2	NUM
ap-10553	135	16	unitary	unitary	ADJ
ap-10553	135	17	matrices	matrix	NOUN
ap-10553	135	18	allowing	allow	VERB
ap-10553	135	19	us	we	PRON
ap-10553	135	20	to	to	PART
ap-10553	135	21	use	use	VERB
ap-10553	135	22	such	such	ADJ
ap-10553	135	23	matrices	matrix	NOUN
ap-10553	135	24	as	as	ADP
ap-10553	135	25	the	the	DET
ap-10553	135	26	extension	extension	NOUN
ap-10553	135	27	label	label	NOUN
ap-10553	135	28	.	.	PUNCT
ap-10553	136	1	the	the	DET
ap-10553	136	2	domain	domain	NOUN
ap-10553	136	3	of	of	ADP
ap-10553	136	4	an	an	DET
ap-10553	136	5	extension	extension	NOUN
ap-10553	136	6	hu	hu	NOUN
ap-10553	136	7	consist	consist	NOUN
ap-10553	136	8	of	of	ADP
ap-10553	136	9	those	those	PRON
ap-10553	136	10	ψ	ψ	X
ap-10553	136	11	∈	∈	PROPN
ap-10553	136	12	d(h∗	d(h∗	NOUN
ap-10553	136	13	)	)	PUNCT
ap-10553	136	14	,	,	PUNCT
ap-10553	136	15	which	which	PRON
ap-10553	136	16	satisfy	satisfy	VERB
ap-10553	136	17	ain(ψ	ain(ψ	NOUN
ap-10553	136	18	)	)	PUNCT
ap-10553	136	19	=	=	SYM
ap-10553	136	20	uaout(ψ	uaout(ψ	NOUN
ap-10553	136	21	)	)	PUNCT
ap-10553	136	22	.	.	PUNCT
ap-10553	137	1	(	(	PUNCT
ap-10553	137	2	11	11	NUM
ap-10553	137	3	)	)	PUNCT
ap-10553	137	4	remark	remark	NOUN
ap-10553	137	5	2.4	2.4	NUM
ap-10553	137	6	.	.	PUNCT
ap-10553	138	1	mathematically	mathematically	ADV
ap-10553	138	2	speaking	speak	VERB
ap-10553	138	3	,	,	PUNCT
ap-10553	138	4	it	it	PRON
ap-10553	138	5	makes	make	VERB
ap-10553	138	6	no	no	DET
ap-10553	138	7	difference	difference	NOUN
ap-10553	138	8	if	if	SCONJ
ap-10553	138	9	we	we	PRON
ap-10553	138	10	put	put	VERB
ap-10553	138	11	u	u	NOUN
ap-10553	138	12	or	or	CCONJ
ap-10553	138	13	u∗	u∗	VERB
ap-10553	138	14	on	on	ADP
ap-10553	138	15	the	the	DET
ap-10553	138	16	right	right	ADJ
ap-10553	138	17	-	-	PUNCT
ap-10553	138	18	hand	hand	NOUN
ap-10553	138	19	side	side	NOUN
ap-10553	138	20	of	of	ADP
ap-10553	138	21	(	(	PUNCT
ap-10553	138	22	11	11	NUM
ap-10553	138	23	)	)	PUNCT
ap-10553	138	24	.	.	PUNCT
ap-10553	139	1	we	we	PRON
ap-10553	139	2	made	make	VERB
ap-10553	139	3	this	this	DET
ap-10553	139	4	choice	choice	NOUN
ap-10553	139	5	to	to	PART
ap-10553	139	6	stress	stress	VERB
ap-10553	139	7	the	the	DET
ap-10553	139	8	heuristic	heuristic	ADJ
ap-10553	139	9	“	"	PUNCT
ap-10553	139	10	scattering	scatter	VERB
ap-10553	139	11	-	-	PUNCT
ap-10553	139	12	at	at	ADP
ap-10553	139	13	-	-	PUNCT
ap-10553	139	14	infinity	infinity	NOUN
ap-10553	139	15	”	"	PUNCT
ap-10553	139	16	character	character	NOUN
ap-10553	139	17	of	of	ADP
ap-10553	139	18	the	the	DET
ap-10553	139	19	condition	condition	NOUN
ap-10553	139	20	(	(	PUNCT
ap-10553	139	21	11	11	NUM
ap-10553	139	22	)	)	PUNCT
ap-10553	139	23	,	,	PUNCT
ap-10553	139	24	namely	namely	ADV
ap-10553	139	25	that	that	SCONJ
ap-10553	139	26	the	the	DET
ap-10553	139	27	particle	particle	NOUN
ap-10553	139	28	moving	move	VERB
ap-10553	139	29	away	away	ADV
ap-10553	139	30	from	from	ADP
ap-10553	139	31	the	the	DET
ap-10553	139	32	vertex	vertex	NOUN
ap-10553	139	33	reaches	reach	VERB
ap-10553	139	34	infinity	infinity	NOUN
ap-10553	139	35	at	at	ADP
ap-10553	139	36	a	a	DET
ap-10553	139	37	finite	finite	ADJ
ap-10553	139	38	time	time	NOUN
ap-10553	139	39	and	and	CCONJ
ap-10553	139	40	reenters	reenter	VERB
ap-10553	139	41	the	the	DET
ap-10553	139	42	edges	edge	NOUN
ap-10553	139	43	from	from	ADP
ap-10553	139	44	their	their	PRON
ap-10553	139	45	infinitely	infinitely	ADV
ap-10553	139	46	distant	distant	ADJ
ap-10553	139	47	“	"	PUNCT
ap-10553	139	48	endpoints	endpoint	NOUN
ap-10553	139	49	”	"	PUNCT
ap-10553	139	50	.	.	PUNCT
ap-10553	140	1	541	541	NUM
ap-10553	140	2	pavel	pavel	PROPN
ap-10553	140	3	exner	exner	PROPN
ap-10553	140	4	acta	acta	PROPN
ap-10553	140	5	polytechnica	polytechnica	PROPN
ap-10553	140	6	3	3	X
ap-10553	140	7	.	.	PUNCT
ap-10553	140	8	properties	property	NOUN
ap-10553	140	9	of	of	ADP
ap-10553	140	10	the	the	DET
ap-10553	140	11	extensions	extension	NOUN
ap-10553	140	12	let	let	VERB
ap-10553	140	13	us	we	PRON
ap-10553	140	14	now	now	ADV
ap-10553	140	15	look	look	VERB
ap-10553	140	16	at	at	ADP
ap-10553	140	17	properties	property	NOUN
ap-10553	140	18	of	of	ADP
ap-10553	140	19	various	various	ADJ
ap-10553	140	20	self	self	NOUN
ap-10553	140	21	-	-	PUNCT
ap-10553	140	22	adjoint	adjoint	NOUN
ap-10553	140	23	extensions	extension	NOUN
ap-10553	140	24	we	we	PRON
ap-10553	140	25	have	have	AUX
ap-10553	140	26	obtained	obtain	VERB
ap-10553	140	27	.	.	PUNCT
ap-10553	141	1	to	to	PART
ap-10553	141	2	begin	begin	VERB
ap-10553	141	3	with	with	ADP
ap-10553	141	4	,	,	PUNCT
ap-10553	141	5	it	it	PRON
ap-10553	141	6	follows	follow	VERB
ap-10553	141	7	from	from	ADP
ap-10553	141	8	(	(	PUNCT
ap-10553	141	9	11	11	NUM
ap-10553	141	10	)	)	PUNCT
ap-10553	141	11	that	that	SCONJ
ap-10553	141	12	for	for	ADP
ap-10553	141	13	any	any	DET
ap-10553	141	14	hu	hu	NOUN
ap-10553	141	15	,	,	PUNCT
ap-10553	141	16	we	we	PRON
ap-10553	141	17	have	have	VERB
ap-10553	141	18	n∑	n∑	ADJ
ap-10553	141	19	j=1	j=1	NOUN
ap-10553	141	20	(	(	PUNCT
ap-10553	141	21	|aout	|aout	PROPN
ap-10553	141	22	j	j	PROPN
ap-10553	141	23	(	(	PUNCT
ap-10553	141	24	ψ)|2	ψ)|2	X
ap-10553	141	25	−	−	PROPN
ap-10553	142	1	|ain	|ain	PROPN
ap-10553	142	2	j	j	PROPN
ap-10553	142	3	(	(	PUNCT
ap-10553	142	4	ψ)|2	ψ)|2	X
ap-10553	142	5	)	)	PUNCT
ap-10553	143	1	=	=	SYM
ap-10553	143	2	0	0	NUM
ap-10553	143	3	,	,	PUNCT
ap-10553	143	4	(	(	PUNCT
ap-10553	143	5	12	12	NUM
ap-10553	143	6	)	)	PUNCT
ap-10553	143	7	which	which	PRON
ap-10553	143	8	expresses	express	VERB
ap-10553	143	9	the	the	DET
ap-10553	143	10	current	current	ADJ
ap-10553	143	11	conservation	conservation	NOUN
ap-10553	143	12	;	;	PUNCT
ap-10553	143	13	recall	recall	VERB
ap-10553	143	14	that	that	PRON
ap-10553	143	15	jj(ψ	jj(ψ	PUNCT
ap-10553	143	16	)	)	PUNCT
ap-10553	143	17	:	:	PUNCT
ap-10553	144	1	=	=	PUNCT
ap-10553	144	2	|aout	|aout	PROPN
ap-10553	144	3	j	j	PROPN
ap-10553	144	4	(	(	PUNCT
ap-10553	144	5	ψ)|2	ψ)|2	X
ap-10553	144	6	−	−	PROPN
ap-10553	144	7	|ain	|ain	PROPN
ap-10553	144	8	j	j	PROPN
ap-10553	144	9	(	(	PUNCT
ap-10553	144	10	ψ)|2	ψ)|2	PRON
ap-10553	144	11	is	be	AUX
ap-10553	144	12	the	the	DET
ap-10553	144	13	net	net	ADJ
ap-10553	144	14	outward	outward	ADJ
ap-10553	144	15	probability	probability	NOUN
ap-10553	144	16	current	current	ADJ
ap-10553	144	17	on	on	ADP
ap-10553	144	18	the	the	DET
ap-10553	144	19	jth	jth	PROPN
ap-10553	144	20	edge	edge	NOUN
ap-10553	144	21	.	.	PUNCT
ap-10553	145	1	in	in	ADP
ap-10553	145	2	particular	particular	ADJ
ap-10553	145	3	,	,	PUNCT
ap-10553	145	4	the	the	DET
ap-10553	145	5	jth	jth	PROPN
ap-10553	145	6	current	current	ADJ
ap-10553	145	7	component	component	NOUN
ap-10553	145	8	vanishes	vanish	VERB
ap-10553	145	9	if	if	SCONJ
ap-10553	145	10	ain	ain	PROPN
ap-10553	145	11	j	j	PROPN
ap-10553	145	12	(	(	PUNCT
ap-10553	145	13	ψ	ψ	NOUN
ap-10553	145	14	)	)	PUNCT
ap-10553	145	15	=	=	VERB
ap-10553	146	1	eiθjain	eiθjain	PROPN
ap-10553	146	2	j	j	PROPN
ap-10553	146	3	(	(	PUNCT
ap-10553	146	4	ψ	ψ	NOUN
ap-10553	146	5	)	)	PUNCT
ap-10553	146	6	for	for	ADP
ap-10553	146	7	some	some	DET
ap-10553	146	8	θj	θj	NOUN
ap-10553	146	9	∈	∈	PROPN
ap-10553	146	10	r.	r.	NOUN
ap-10553	146	11	the	the	DET
ap-10553	146	12	graph	graph	NOUN
ap-10553	146	13	supports	support	VERB
ap-10553	146	14	no	no	DET
ap-10553	146	15	current	current	NOUN
ap-10553	146	16	at	at	ADV
ap-10553	146	17	all	all	ADV
ap-10553	146	18	if	if	SCONJ
ap-10553	146	19	and	and	CCONJ
ap-10553	146	20	only	only	ADV
ap-10553	146	21	if	if	SCONJ
ap-10553	146	22	the	the	DET
ap-10553	146	23	matrix	matrix	NOUN
ap-10553	146	24	u	u	NOUN
ap-10553	146	25	is	be	AUX
ap-10553	146	26	diagonal	diagonal	ADJ
ap-10553	146	27	,	,	PUNCT
ap-10553	146	28	u	u	NOUN
ap-10553	146	29	=	=	PUNCT
ap-10553	146	30	diag	diag	X
ap-10553	146	31	(	(	PUNCT
ap-10553	146	32	eiθ1	eiθ1	PROPN
ap-10553	146	33	,	,	PUNCT
ap-10553	146	34	.	.	PUNCT
ap-10553	146	35	.	.	PUNCT
ap-10553	146	36	.	.	PUNCT
ap-10553	147	1	,	,	PUNCT
ap-10553	147	2	eiθn	eiθn	NOUN
ap-10553	147	3	)	)	PUNCT
ap-10553	147	4	(	(	PUNCT
ap-10553	147	5	13	13	NUM
ap-10553	147	6	)	)	PUNCT
ap-10553	147	7	for	for	ADP
ap-10553	147	8	some	some	DET
ap-10553	147	9	θj	θj	NOUN
ap-10553	147	10	∈	∈	PROPN
ap-10553	147	11	(	(	PUNCT
ap-10553	147	12	−π	−π	PROPN
ap-10553	147	13	,	,	PUNCT
ap-10553	147	14	π	π	PROPN
ap-10553	147	15	]	]	X
ap-10553	147	16	;	;	PUNCT
ap-10553	147	17	in	in	ADP
ap-10553	147	18	such	such	DET
ap-10553	147	19	a	a	DET
ap-10553	147	20	case	case	NOUN
ap-10553	147	21	,	,	PUNCT
ap-10553	147	22	we	we	PRON
ap-10553	147	23	speak	speak	VERB
ap-10553	147	24	of	of	ADP
ap-10553	147	25	boundary	boundary	ADJ
ap-10553	147	26	conditions	condition	NOUN
ap-10553	147	27	fully	fully	ADV
ap-10553	147	28	separated	separate	VERB
ap-10553	147	29	at	at	ADP
ap-10553	147	30	infinity	infinity	NOUN
ap-10553	147	31	.	.	PUNCT
ap-10553	148	1	the	the	DET
ap-10553	148	2	separation	separation	NOUN
ap-10553	148	3	at	at	ADP
ap-10553	148	4	infinity	infinity	NOUN
ap-10553	148	5	can	can	AUX
ap-10553	148	6	be	be	AUX
ap-10553	148	7	partial	partial	ADJ
ap-10553	148	8	only	only	ADV
ap-10553	148	9	;	;	PUNCT
ap-10553	148	10	this	this	PRON
ap-10553	148	11	happens	happen	VERB
ap-10553	148	12	if	if	SCONJ
ap-10553	148	13	there	there	PRON
ap-10553	148	14	is	be	VERB
ap-10553	148	15	a	a	DET
ap-10553	148	16	nonempty	nonempty	NOUN
ap-10553	148	17	k	k	X
ap-10553	148	18	⊂	⊂	X
ap-10553	148	19	{	{	PUNCT
ap-10553	148	20	1	1	NUM
ap-10553	148	21	,	,	PUNCT
ap-10553	148	22	.	.	PUNCT
ap-10553	148	23	.	.	PUNCT
ap-10553	149	1	.	.	PUNCT
ap-10553	150	1	,	,	PUNCT
ap-10553	150	2	n	n	CCONJ
ap-10553	150	3	}	}	PUNCT
ap-10553	150	4	with	with	ADP
ap-10553	150	5	#	#	SYM
ap-10553	150	6	k	k	NOUN
ap-10553	150	7	<	<	X
ap-10553	150	8	n	n	CCONJ
ap-10553	150	9	such	such	ADJ
ap-10553	150	10	that	that	PRON
ap-10553	150	11	ain(ψ	ain(ψ	NOUN
ap-10553	150	12	)	)	PUNCT
ap-10553	150	13	=	=	SYM
ap-10553	150	14	eiθkaout(ψ	eiθkaout(ψ	NOUN
ap-10553	150	15	)	)	PUNCT
ap-10553	150	16	for	for	ADP
ap-10553	150	17	k	k	PROPN
ap-10553	150	18	∈	∈	PROPN
ap-10553	150	19	k	k	PROPN
ap-10553	150	20	,	,	PUNCT
ap-10553	150	21	i.e.	i.e.	X
ap-10553	150	22	when	when	SCONJ
ap-10553	150	23	u	u	PROPN
ap-10553	150	24	=	=	PROPN
ap-10553	150	25	dm	dm	PROPN
ap-10553	150	26	⊕	⊕	PROPN
ap-10553	150	27	ũ	ũ	PROPN
ap-10553	150	28	where	where	SCONJ
ap-10553	150	29	ũ	ũ	PROPN
ap-10553	150	30	is	be	AUX
ap-10553	150	31	an	an	DET
ap-10553	150	32	(	(	PUNCT
ap-10553	150	33	n	n	CCONJ
ap-10553	150	34	−	−	PROPN
ap-10553	150	35	m	m	NOUN
ap-10553	150	36	)	)	PUNCT
ap-10553	150	37	×	×	NOUN
ap-10553	150	38	(	(	PUNCT
ap-10553	150	39	n	n	CCONJ
ap-10553	150	40	−	−	PROPN
ap-10553	150	41	m	m	NOUN
ap-10553	150	42	)	)	PUNCT
ap-10553	150	43	non	non	ADJ
ap-10553	150	44	-	-	ADJ
ap-10553	150	45	diagonal	diagonal	ADJ
ap-10553	150	46	unitary	unitary	ADJ
ap-10553	150	47	matrix	matrix	NOUN
ap-10553	150	48	and	and	CCONJ
ap-10553	150	49	dm	dm	PROPN
ap-10553	150	50	is	be	AUX
ap-10553	150	51	m×m	m×m	PROPN
ap-10553	150	52	of	of	ADP
ap-10553	150	53	the	the	DET
ap-10553	150	54	type	type	NOUN
ap-10553	150	55	(	(	PUNCT
ap-10553	150	56	13	13	NUM
ap-10553	150	57	)	)	PUNCT
ap-10553	150	58	.	.	PUNCT
ap-10553	151	1	one	one	PRON
ap-10553	151	2	can	can	AUX
ap-10553	151	3	label	label	VERB
ap-10553	151	4	such	such	DET
ap-10553	151	5	a	a	DET
ap-10553	151	6	separation	separation	NOUN
ap-10553	151	7	at	at	ADP
ap-10553	151	8	infinity	infinity	NOUN
ap-10553	151	9	dirichlet	dirichlet	PROPN
ap-10553	151	10	(	(	PUNCT
ap-10553	151	11	neumann	neumann	PROPN
ap-10553	151	12	,	,	PUNCT
ap-10553	151	13	robin	robin	PROPN
ap-10553	151	14	)	)	PUNCT
ap-10553	151	15	,	,	PUNCT
ap-10553	151	16	if	if	SCONJ
ap-10553	151	17	θk	θk	NOUN
ap-10553	151	18	=	=	SYM
ap-10553	151	19	π	π	PROPN
ap-10553	151	20	(	(	PUNCT
ap-10553	151	21	θk	θk	NOUN
ap-10553	151	22	=	=	SYM
ap-10553	151	23	0	0	NUM
ap-10553	151	24	or	or	CCONJ
ap-10553	151	25	θk	θk	PROPN
ap-10553	151	26	̸=	̸=	PROPN
ap-10553	151	27	0	0	NUM
ap-10553	151	28	(	(	PUNCT
ap-10553	151	29	mod	mod	PROPN
ap-10553	151	30	π	π	PROPN
ap-10553	151	31	)	)	PUNCT
ap-10553	151	32	)	)	PUNCT
ap-10553	151	33	,	,	PUNCT
ap-10553	151	34	respectively	respectively	ADV
ap-10553	151	35	.	.	PUNCT
ap-10553	152	1	on	on	ADP
ap-10553	152	2	any	any	DET
ap-10553	152	3	edge	edge	NOUN
ap-10553	152	4	with	with	ADP
ap-10553	152	5	separation	separation	NOUN
ap-10553	152	6	at	at	ADP
ap-10553	152	7	infinity	infinity	NOUN
ap-10553	152	8	,	,	PUNCT
ap-10553	152	9	the	the	DET
ap-10553	152	10	probability	probability	NOUN
ap-10553	152	11	current	current	NOUN
ap-10553	152	12	is	be	AUX
ap-10553	152	13	naturally	naturally	ADV
ap-10553	152	14	zero	zero	NUM
ap-10553	152	15	.	.	PUNCT
ap-10553	153	1	another	another	DET
ap-10553	153	2	important	important	ADJ
ap-10553	153	3	class	class	NOUN
ap-10553	153	4	of	of	ADP
ap-10553	153	5	the	the	DET
ap-10553	153	6	extension	extension	NOUN
ap-10553	153	7	are	be	AUX
ap-10553	153	8	those	those	PRON
ap-10553	153	9	invariant	invariant	ADJ
ap-10553	153	10	with	with	ADP
ap-10553	153	11	respect	respect	NOUN
ap-10553	153	12	to	to	ADP
ap-10553	153	13	the	the	DET
ap-10553	153	14	time	time	NOUN
ap-10553	153	15	reversal	reversal	NOUN
ap-10553	153	16	.	.	PUNCT
ap-10553	154	1	in	in	ADP
ap-10553	154	2	the	the	DET
ap-10553	154	3	absence	absence	NOUN
ap-10553	154	4	of	of	ADP
ap-10553	154	5	internal	internal	ADJ
ap-10553	154	6	degrees	degree	NOUN
ap-10553	154	7	of	of	ADP
ap-10553	154	8	freedom	freedom	NOUN
ap-10553	154	9	,	,	PUNCT
ap-10553	154	10	the	the	DET
ap-10553	154	11	swap	swap	NOUN
ap-10553	154	12	of	of	ADP
ap-10553	154	13	the	the	DET
ap-10553	154	14	time	time	NOUN
ap-10553	154	15	arrow	arrow	NOUN
ap-10553	154	16	orientation	orientation	NOUN
ap-10553	154	17	is	be	AUX
ap-10553	154	18	described	describe	VERB
ap-10553	154	19	by	by	ADP
ap-10553	154	20	the	the	DET
ap-10553	154	21	antilinear	antilinear	ADJ
ap-10553	154	22	operator	operator	NOUN
ap-10553	154	23	ψ	ψ	ADP
ap-10553	154	24	7→	7→	NUM
ap-10553	154	25	ψ̄.	ψ̄.	PUNCT
ap-10553	154	26	the	the	DET
ap-10553	154	27	invariance	invariance	NOUN
ap-10553	154	28	thus	thus	ADV
ap-10553	154	29	means	mean	VERB
ap-10553	154	30	that	that	SCONJ
ap-10553	154	31	ū	ū	NOUN
ap-10553	154	32	=	=	SYM
ap-10553	154	33	u	u	NOUN
ap-10553	154	34	,	,	PUNCT
ap-10553	154	35	and	and	CCONJ
ap-10553	154	36	since	since	SCONJ
ap-10553	154	37	u	u	NOUN
ap-10553	154	38	is	be	AUX
ap-10553	154	39	unitary	unitary	ADJ
ap-10553	154	40	,	,	PUNCT
ap-10553	154	41	we	we	PRON
ap-10553	154	42	see	see	VERB
ap-10553	154	43	that	that	SCONJ
ap-10553	154	44	hu	hu	PROPN
ap-10553	154	45	is	be	AUX
ap-10553	154	46	timereversal	timereversal	ADJ
ap-10553	154	47	-	-	PUNCT
ap-10553	154	48	invariant	invariant	ADJ
ap-10553	154	49	if	if	SCONJ
ap-10553	154	50	and	and	CCONJ
ap-10553	154	51	only	only	ADV
ap-10553	154	52	if	if	SCONJ
ap-10553	154	53	matrix	matrix	NOUN
ap-10553	154	54	u	u	NOUN
ap-10553	154	55	is	be	AUX
ap-10553	154	56	invariant	invariant	ADJ
ap-10553	154	57	with	with	ADP
ap-10553	154	58	respect	respect	NOUN
ap-10553	154	59	to	to	ADP
ap-10553	154	60	the	the	DET
ap-10553	154	61	transposal	transposal	NOUN
ap-10553	154	62	,	,	PUNCT
ap-10553	154	63	u	u	NOUN
ap-10553	154	64	=	=	PROPN
ap-10553	154	65	ut	ut	PROPN
ap-10553	154	66	.	.	PROPN
ap-10553	155	1	(	(	PUNCT
ap-10553	155	2	14	14	NUM
ap-10553	155	3	)	)	PUNCT
ap-10553	155	4	furthermore	furthermore	ADV
ap-10553	155	5	,	,	PUNCT
ap-10553	155	6	it	it	PRON
ap-10553	155	7	follows	follow	VERB
ap-10553	155	8	easily	easily	ADV
ap-10553	155	9	from	from	ADP
ap-10553	155	10	(	(	PUNCT
ap-10553	155	11	9	9	NUM
ap-10553	155	12	)	)	PUNCT
ap-10553	155	13	that	that	PRON
ap-10553	155	14	a	a	DET
ap-10553	155	15	in	in	ADP
ap-10553	155	16	/	/	SYM
ap-10553	155	17	out	out	ADP
ap-10553	155	18	j	j	PROPN
ap-10553	155	19	(	(	PUNCT
ap-10553	155	20	ψ	ψ	NOUN
ap-10553	155	21	)	)	PUNCT
ap-10553	155	22	=	=	PUNCT
ap-10553	155	23	a	a	DET
ap-10553	155	24	out	out	NOUN
ap-10553	155	25	/	/	SYM
ap-10553	155	26	in	in	ADP
ap-10553	155	27	j	j	PROPN
ap-10553	155	28	(	(	PUNCT
ap-10553	155	29	ψ̄	ψ̄	NUM
ap-10553	155	30	)	)	PUNCT
ap-10553	155	31	for	for	ADP
ap-10553	155	32	any	any	DET
ap-10553	155	33	ψ	ψ	X
ap-10553	155	34	∈	∈	PROPN
ap-10553	155	35	d(h∗	d(h∗	NOUN
ap-10553	155	36	)	)	PUNCT
ap-10553	155	37	;	;	PUNCT
ap-10553	155	38	(	(	PUNCT
ap-10553	155	39	15	15	NUM
ap-10553	155	40	)	)	PUNCT
ap-10553	155	41	thus	thus	ADV
ap-10553	155	42	indicating	indicate	VERB
ap-10553	155	43	the	the	DET
ap-10553	155	44	dependence	dependence	NOUN
ap-10553	155	45	of	of	ADP
ap-10553	155	46	the	the	DET
ap-10553	155	47	probability	probability	NOUN
ap-10553	155	48	current	current	NOUN
ap-10553	155	49	on	on	ADP
ap-10553	155	50	the	the	DET
ap-10553	155	51	chosen	choose	VERB
ap-10553	155	52	extension	extension	NOUN
ap-10553	155	53	,	,	PUNCT
ap-10553	155	54	we	we	PRON
ap-10553	155	55	get	get	VERB
ap-10553	155	56	jj(ψ;ut	jj(ψ;ut	NOUN
ap-10553	155	57	)	)	PUNCT
ap-10553	155	58	=	=	SYM
ap-10553	156	1	−jj(ψ;u	−jj(ψ;u	ADJ
ap-10553	156	2	)	)	PUNCT
ap-10553	156	3	,	,	PUNCT
ap-10553	156	4	j	j	PROPN
ap-10553	156	5	=	=	SYM
ap-10553	156	6	1	1	NUM
ap-10553	156	7	,	,	PUNCT
ap-10553	156	8	.	.	PUNCT
ap-10553	156	9	.	.	PUNCT
ap-10553	157	1	.	.	PUNCT
ap-10553	158	1	,	,	PUNCT
ap-10553	158	2	n	n	CCONJ
ap-10553	158	3	,	,	PUNCT
ap-10553	158	4	(	(	PUNCT
ap-10553	158	5	16	16	NUM
ap-10553	158	6	)	)	PUNCT
ap-10553	158	7	as	as	SCONJ
ap-10553	158	8	one	one	PRON
ap-10553	158	9	should	should	AUX
ap-10553	158	10	naturally	naturally	ADV
ap-10553	158	11	expect	expect	VERB
ap-10553	158	12	.	.	PUNCT
ap-10553	159	1	remark	remark	PROPN
ap-10553	159	2	3.1	3.1	NUM
ap-10553	159	3	.	.	PUNCT
ap-10553	160	1	the	the	DET
ap-10553	160	2	jth	jth	PROPN
ap-10553	160	3	component	component	NOUN
ap-10553	160	4	of	of	ADP
ap-10553	160	5	the	the	DET
ap-10553	160	6	probability	probability	NOUN
ap-10553	160	7	current	current	NOUN
ap-10553	160	8	vanishes	vanish	VERB
ap-10553	160	9	for	for	ADP
ap-10553	160	10	a	a	DET
ap-10553	160	11	given	give	VERB
ap-10553	160	12	u	u	PRON
ap-10553	160	13	if	if	SCONJ
ap-10553	160	14	and	and	CCONJ
ap-10553	160	15	only	only	ADV
ap-10553	160	16	if	if	SCONJ
ap-10553	160	17	|aout	|aout	PROPN
ap-10553	160	18	j	j	PROPN
ap-10553	160	19	(	(	PUNCT
ap-10553	160	20	ψ)|	ψ)|	NOUN
ap-10553	160	21	=	=	PUNCT
ap-10553	160	22	|ain	|ain	PROPN
ap-10553	160	23	j	j	X
ap-10553	160	24	(	(	PUNCT
ap-10553	160	25	ψ)|	ψ)|	PROPN
ap-10553	160	26	holds	hold	VERB
ap-10553	160	27	for	for	ADP
ap-10553	160	28	all	all	DET
ap-10553	160	29	ψ	ψ	PRON
ap-10553	160	30	∈	∈	PRON
ap-10553	160	31	d(hu	d(hu	PROPN
ap-10553	160	32	)	)	PUNCT
ap-10553	160	33	.	.	PUNCT
ap-10553	161	1	the	the	DET
ap-10553	161	2	corresponding	correspond	VERB
ap-10553	161	3	asymptotics	asymptotic	NOUN
ap-10553	161	4	of	of	ADP
ap-10553	161	5	the	the	DET
ap-10553	161	6	jth	jth	PROPN
ap-10553	161	7	component	component	NOUN
ap-10553	161	8	of	of	ADP
ap-10553	161	9	those	those	DET
ap-10553	161	10	functions	function	NOUN
ap-10553	161	11	,	,	PUNCT
ap-10553	161	12	in	in	ADP
ap-10553	161	13	particular	particular	ADJ
ap-10553	161	14	,	,	PUNCT
ap-10553	161	15	of	of	ADP
ap-10553	161	16	any	any	DET
ap-10553	161	17	eigenvector	eigenvector	NOUN
ap-10553	161	18	of	of	ADP
ap-10553	161	19	hu	hu	PROPN
ap-10553	161	20	,	,	PUNCT
ap-10553	161	21	is	be	AUX
ap-10553	161	22	then	then	ADV
ap-10553	161	23	real	real	ADV
ap-10553	161	24	-	-	PUNCT
ap-10553	161	25	valued	value	VERB
ap-10553	161	26	up	up	ADP
ap-10553	161	27	to	to	ADP
ap-10553	161	28	an	an	DET
ap-10553	161	29	overall	overall	ADJ
ap-10553	161	30	phase	phase	NOUN
ap-10553	161	31	factor	factor	NOUN
ap-10553	161	32	,	,	PUNCT
ap-10553	161	33	ψj(x	ψj(x	PUNCT
ap-10553	161	34	)	)	PUNCT
ap-10553	162	1	=	=	SYM
ap-10553	162	2	cj	cj	NOUN
ap-10553	163	1	cos	cos	PROPN
ap-10553	163	2	(	(	PUNCT
ap-10553	163	3	x3	x3	NOUN
ap-10553	163	4	3	3	NUM
ap-10553	163	5	+	+	CCONJ
ap-10553	163	6	ηj	ηj	NOUN
ap-10553	163	7	)	)	PUNCT
ap-10553	163	8	(	(	PUNCT
ap-10553	163	9	1	1	NUM
ap-10553	163	10	+	+	CCONJ
ap-10553	163	11	o(x−1	o(x−1	NOUN
ap-10553	163	12	)	)	PUNCT
ap-10553	163	13	)	)	PUNCT
ap-10553	163	14	with	with	ADP
ap-10553	163	15	some	some	PRON
ap-10553	163	16	ηj	ηj	ADP
ap-10553	163	17	∈	∈	PROPN
ap-10553	163	18	(	(	PUNCT
ap-10553	163	19	−π	−π	PROPN
ap-10553	163	20	,	,	PUNCT
ap-10553	163	21	π	π	X
ap-10553	163	22	]	]	PUNCT
ap-10553	163	23	as	as	SCONJ
ap-10553	163	24	x	x	X
ap-10553	163	25	→	→	PUNCT
ap-10553	163	26	∞.	∞.	PROPN
ap-10553	163	27	another	another	DET
ap-10553	163	28	subclass	subclass	NOUN
ap-10553	163	29	consists	consist	VERB
ap-10553	163	30	of	of	ADP
ap-10553	163	31	the	the	DET
ap-10553	163	32	extension	extension	NOUN
ap-10553	163	33	that	that	PRON
ap-10553	163	34	are	be	AUX
ap-10553	163	35	invariant	invariant	ADJ
ap-10553	163	36	with	with	ADP
ap-10553	163	37	respect	respect	NOUN
ap-10553	163	38	to	to	ADP
ap-10553	163	39	all	all	DET
ap-10553	163	40	permutations	permutation	NOUN
ap-10553	163	41	of	of	ADP
ap-10553	163	42	the	the	DET
ap-10553	163	43	star	star	NOUN
ap-10553	163	44	edges	edge	NOUN
ap-10553	163	45	.	.	PUNCT
ap-10553	164	1	such	such	DET
ap-10553	164	2	a	a	DET
ap-10553	164	3	transformation	transformation	NOUN
ap-10553	164	4	leads	lead	VERB
ap-10553	164	5	to	to	ADP
ap-10553	164	6	a	a	DET
ap-10553	164	7	simultaneous	simultaneous	ADJ
ap-10553	164	8	permutation	permutation	NOUN
ap-10553	164	9	of	of	ADP
ap-10553	164	10	the	the	DET
ap-10553	164	11	rows	row	NOUN
ap-10553	164	12	and	and	CCONJ
ap-10553	164	13	columns	column	NOUN
ap-10553	164	14	of	of	ADP
ap-10553	164	15	the	the	DET
ap-10553	164	16	matrix	matrix	NOUN
ap-10553	164	17	u	u	NOUN
ap-10553	164	18	.	.	PUNCT
ap-10553	165	1	should	should	AUX
ap-10553	165	2	this	this	PRON
ap-10553	165	3	include	include	VERB
ap-10553	165	4	all	all	DET
ap-10553	165	5	such	such	ADJ
ap-10553	165	6	permutations	permutation	NOUN
ap-10553	165	7	,	,	PUNCT
ap-10553	165	8	it	it	PRON
ap-10553	165	9	is	be	AUX
ap-10553	165	10	easy	easy	ADJ
ap-10553	165	11	to	to	PART
ap-10553	165	12	see	see	VERB
ap-10553	165	13	that	that	SCONJ
ap-10553	165	14	it	it	PRON
ap-10553	165	15	singles	single	VERB
ap-10553	165	16	out	out	ADP
ap-10553	165	17	of	of	ADP
ap-10553	165	18	the	the	DET
ap-10553	165	19	entire	entire	ADJ
ap-10553	165	20	n2	n2	ADJ
ap-10553	165	21	-	-	PUNCT
ap-10553	165	22	parameter	parameter	NOUN
ap-10553	165	23	family	family	NOUN
ap-10553	165	24	of	of	ADP
ap-10553	165	25	the	the	DET
ap-10553	165	26	operators	operator	NOUN
ap-10553	165	27	hu	hu	PROPN
ap-10553	166	1	a	a	DET
ap-10553	166	2	two	two	NUM
ap-10553	166	3	-	-	PUNCT
ap-10553	166	4	parameter	parameter	NOUN
ap-10553	166	5	subfamily	subfamily	ADV
ap-10553	166	6	,	,	PUNCT
ap-10553	166	7	namely	namely	ADV
ap-10553	166	8	those	those	PRON
ap-10553	166	9	with	with	ADP
ap-10553	166	10	u	u	NOUN
ap-10553	166	11	=	=	PUNCT
ap-10553	166	12	(	(	PUNCT
ap-10553	166	13	uij	uij	PROPN
ap-10553	166	14	)	)	PUNCT
ap-10553	166	15	,	,	PUNCT
ap-10553	166	16	uij	uij	PRON
ap-10553	166	17	=	=	SYM
ap-10553	166	18	b−	b−	NOUN
ap-10553	166	19	aδij	aδij	NOUN
ap-10553	166	20	,	,	PUNCT
ap-10553	166	21	(	(	PUNCT
ap-10553	166	22	17a	17a	X
ap-10553	166	23	)	)	PUNCT
ap-10553	166	24	where	where	SCONJ
ap-10553	166	25	the	the	DET
ap-10553	166	26	unitarity	unitarity	NOUN
ap-10553	166	27	requires	require	VERB
ap-10553	166	28	the	the	DET
ap-10553	166	29	numbers	number	NOUN
ap-10553	166	30	a	a	PRON
ap-10553	166	31	,	,	PUNCT
ap-10553	166	32	b	b	PROPN
ap-10553	166	33	∈	∈	PROPN
ap-10553	166	34	c	c	NOUN
ap-10553	166	35	to	to	PART
ap-10553	166	36	obey	obey	VERB
ap-10553	167	1	|a|	|a|	PROPN
ap-10553	167	2	=	=	PROPN
ap-10553	167	3	1	1	NUM
ap-10553	167	4	and	and	CCONJ
ap-10553	167	5	|a+nb|	|a+nb|	PROPN
ap-10553	167	6	=	=	SYM
ap-10553	167	7	1	1	NUM
ap-10553	167	8	;	;	PUNCT
ap-10553	167	9	(	(	PUNCT
ap-10553	167	10	17b	17b	NUM
ap-10553	167	11	)	)	PUNCT
ap-10553	167	12	such	such	DET
ap-10553	167	13	a	a	DET
ap-10553	167	14	matrix	matrix	NOUN
ap-10553	167	15	is	be	AUX
ap-10553	167	16	hermitean	hermitean	NOUN
ap-10553	167	17	having	have	VERB
ap-10553	167	18	simple	simple	ADJ
ap-10553	167	19	eigenvalue	eigenvalue	PROPN
ap-10553	167	20	a	a	PRON
ap-10553	167	21	and	and	CCONJ
ap-10553	167	22	eigenvalue	eigenvalue	PROPN
ap-10553	167	23	a+nb	a+nb	NOUN
ap-10553	167	24	of	of	ADP
ap-10553	167	25	multiplicity	multiplicity	NOUN
ap-10553	167	26	n	n	CCONJ
ap-10553	167	27	−	−	PROPN
ap-10553	167	28	1	1	NUM
ap-10553	167	29	,	,	PUNCT
ap-10553	167	30	cf	cf	NOUN
ap-10553	167	31	.	.	PUNCT
ap-10553	168	1	[	[	X
ap-10553	168	2	12	12	NUM
ap-10553	168	3	]	]	PUNCT
ap-10553	168	4	.	.	PUNCT
ap-10553	169	1	a	a	DET
ap-10553	169	2	particular	particular	ADJ
ap-10553	169	3	case	case	NOUN
ap-10553	169	4	with	with	ADP
ap-10553	169	5	a	a	DET
ap-10553	169	6	=	=	SYM
ap-10553	169	7	−1	−1	NOUN
ap-10553	169	8	,	,	PUNCT
ap-10553	169	9	b	b	NOUN
ap-10553	169	10	=	=	SYM
ap-10553	169	11	2	2	NUM
ap-10553	169	12	n	n	NOUN
ap-10553	169	13	,	,	PUNCT
ap-10553	169	14	(	(	PUNCT
ap-10553	169	15	18	18	NUM
ap-10553	169	16	)	)	PUNCT
ap-10553	169	17	is	be	AUX
ap-10553	169	18	a	a	DET
ap-10553	169	19	natural	natural	ADJ
ap-10553	169	20	counterpart	counterpart	NOUN
ap-10553	169	21	of	of	ADP
ap-10553	169	22	the	the	DET
ap-10553	169	23	condition	condition	NOUN
ap-10553	169	24	(	(	PUNCT
ap-10553	169	25	2	2	X
ap-10553	169	26	)	)	PUNCT
ap-10553	169	27	imposed	impose	VERB
ap-10553	169	28	at	at	ADP
ap-10553	169	29	the	the	DET
ap-10553	169	30	vertex	vertex	NOUN
ap-10553	169	31	;	;	PUNCT
ap-10553	169	32	we	we	PRON
ap-10553	169	33	call	call	VERB
ap-10553	169	34	it	it	PRON
ap-10553	169	35	kirchhoff	kirchhoff	NOUN
ap-10553	169	36	condition	condition	NOUN
ap-10553	169	37	at	at	ADP
ap-10553	169	38	infinity	infinity	NOUN
ap-10553	169	39	.	.	PUNCT
ap-10553	170	1	a	a	DET
ap-10553	170	2	wider	wide	ADJ
ap-10553	170	3	,	,	PUNCT
ap-10553	170	4	n	n	CCONJ
ap-10553	170	5	-parameter	-parameter	NOUN
ap-10553	170	6	family	family	NOUN
ap-10553	170	7	of	of	ADP
ap-10553	170	8	extensions	extension	NOUN
ap-10553	170	9	corresponds	correspond	VERB
ap-10553	170	10	to	to	ADP
ap-10553	170	11	the	the	DET
ap-10553	170	12	situations	situation	NOUN
ap-10553	170	13	when	when	SCONJ
ap-10553	170	14	the	the	DET
ap-10553	170	15	matrix	matrix	NOUN
ap-10553	170	16	is	be	AUX
ap-10553	170	17	circulant	circulant	ADJ
ap-10553	170	18	[	[	X
ap-10553	170	19	13	13	NUM
ap-10553	170	20	]	]	PUNCT
ap-10553	170	21	.	.	PUNCT
ap-10553	171	1	recall	recall	VERB
ap-10553	171	2	that	that	SCONJ
ap-10553	171	3	in	in	ADP
ap-10553	171	4	general	general	ADJ
ap-10553	171	5	,	,	PUNCT
ap-10553	171	6	such	such	ADJ
ap-10553	171	7	matrices	matrix	NOUN
ap-10553	171	8	are	be	AUX
ap-10553	171	9	of	of	ADP
ap-10553	171	10	the	the	DET
ap-10553	171	11	form	form	NOUN
ap-10553	171	12	c0	c0	PROPN
ap-10553	171	13	c1	c1	PROPN
ap-10553	171	14	·	·	PUNCT
ap-10553	171	15	·	·	PUNCT
ap-10553	171	16	·	·	PUNCT
ap-10553	172	1	cn−2	cn−2	PROPN
ap-10553	172	2	cn−1	cn−1	PROPN
ap-10553	172	3	cn−1	cn−1	PROPN
ap-10553	172	4	c0	c0	PROPN
ap-10553	172	5	c1	c1	PROPN
ap-10553	172	6	cn−2	cn−2	PROPN
ap-10553	172	7	...	...	PUNCT
ap-10553	173	1	cn−1	cn−1	PROPN
ap-10553	173	2	c0	c0	PROPN
ap-10553	173	3	.	.	PUNCT
ap-10553	173	4	.	.	PUNCT
ap-10553	173	5	.	.	PUNCT
ap-10553	174	1	...	...	PUNCT
ap-10553	175	1	c2	c2	PROPN
ap-10553	175	2	.	.	PUNCT
ap-10553	175	3	.	.	PUNCT
ap-10553	175	4	.	.	PUNCT
ap-10553	175	5	.	.	PUNCT
ap-10553	175	6	.	.	PUNCT
ap-10553	175	7	.	.	PUNCT
ap-10553	176	1	c1	c1	PROPN
ap-10553	176	2	c1	c1	PROPN
ap-10553	176	3	c2	c2	PROPN
ap-10553	176	4	·	·	PUNCT
ap-10553	176	5	·	·	PUNCT
ap-10553	176	6	·	·	PUNCT
ap-10553	176	7	cn−1	cn−1	PROPN
ap-10553	176	8	c0	c0	PROPN
ap-10553	176	9			ADP
ap-10553	176	10	(	(	PUNCT
ap-10553	176	11	19	19	NUM
ap-10553	176	12	)	)	PUNCT
ap-10553	176	13	and	and	CCONJ
ap-10553	176	14	that	that	SCONJ
ap-10553	176	15	they	they	PRON
ap-10553	176	16	belong	belong	VERB
ap-10553	176	17	to	to	ADP
ap-10553	176	18	the	the	DET
ap-10553	176	19	class	class	NOUN
ap-10553	176	20	of	of	ADP
ap-10553	176	21	toeplitz	toeplitz	NOUN
ap-10553	176	22	matrices	matrix	NOUN
ap-10553	176	23	in	in	ADP
ap-10553	176	24	which	which	PRON
ap-10553	176	25	they	they	PRON
ap-10553	176	26	are	be	AUX
ap-10553	176	27	distinguished	distinguish	VERB
ap-10553	176	28	by	by	ADP
ap-10553	176	29	the	the	DET
ap-10553	176	30	“	"	PUNCT
ap-10553	176	31	two	two	NUM
ap-10553	176	32	-	-	PUNCT
ap-10553	176	33	sided	sided	ADJ
ap-10553	176	34	cyclicity	cyclicity	NOUN
ap-10553	176	35	”	"	PUNCT
ap-10553	176	36	in	in	ADP
ap-10553	176	37	the	the	DET
ap-10553	176	38	antidiagonal	antidiagonal	ADJ
ap-10553	176	39	direction	direction	NOUN
ap-10553	176	40	;	;	PUNCT
ap-10553	176	41	matrices	matrix	NOUN
ap-10553	176	42	(	(	PUNCT
ap-10553	176	43	17	17	NUM
ap-10553	176	44	)	)	PUNCT
ap-10553	176	45	represent	represent	VERB
ap-10553	176	46	a	a	DET
ap-10553	176	47	particular	particular	ADJ
ap-10553	176	48	case	case	NOUN
ap-10553	176	49	with	with	ADP
ap-10553	176	50	c0	c0	PROPN
ap-10553	176	51	=	=	PUNCT
ap-10553	176	52	b−	b−	PROPN
ap-10553	176	53	a	a	PROPN
ap-10553	176	54	and	and	CCONJ
ap-10553	176	55	ck	ck	NOUN
ap-10553	176	56	=	=	SYM
ap-10553	176	57	b	b	PROPN
ap-10553	176	58	for	for	ADP
ap-10553	176	59	k	k	PROPN
ap-10553	176	60	=	=	SYM
ap-10553	176	61	1	1	NUM
ap-10553	176	62	,	,	PUNCT
ap-10553	176	63	.	.	PUNCT
ap-10553	176	64	.	.	PUNCT
ap-10553	177	1	.	.	PUNCT
ap-10553	178	1	,	,	PUNCT
ap-10553	178	2	n−1	n−1	PROPN
ap-10553	178	3	.	.	PROPN
ap-10553	178	4	not	not	PART
ap-10553	178	5	every	every	DET
ap-10553	178	6	such	such	ADJ
ap-10553	178	7	matrix	matrix	NOUN
ap-10553	178	8	is	be	AUX
ap-10553	178	9	unitary	unitary	ADJ
ap-10553	178	10	,	,	PUNCT
ap-10553	178	11	of	of	ADP
ap-10553	178	12	course	course	NOUN
ap-10553	178	13	;	;	PUNCT
ap-10553	178	14	to	to	PART
ap-10553	178	15	find	find	VERB
ap-10553	178	16	the	the	DET
ap-10553	178	17	condition	condition	NOUN
ap-10553	178	18	which	which	PRON
ap-10553	178	19	ensures	ensure	VERB
ap-10553	178	20	unitarity	unitarity	NOUN
ap-10553	178	21	,	,	PUNCT
ap-10553	178	22	generalising	generalise	VERB
ap-10553	178	23	(	(	PUNCT
ap-10553	178	24	17b	17b	NUM
ap-10553	178	25	)	)	PUNCT
ap-10553	178	26	,	,	PUNCT
ap-10553	178	27	we	we	PRON
ap-10553	178	28	recall	recall	VERB
ap-10553	178	29	that	that	SCONJ
ap-10553	178	30	all	all	DET
ap-10553	178	31	circulant	circulant	ADJ
ap-10553	178	32	matrices	matrix	NOUN
ap-10553	178	33	of	of	ADP
ap-10553	178	34	the	the	DET
ap-10553	178	35	same	same	ADJ
ap-10553	178	36	dimension	dimension	NOUN
ap-10553	178	37	have	have	VERB
ap-10553	178	38	a	a	DET
ap-10553	178	39	common	common	ADJ
ap-10553	178	40	orthonormal	orthonormal	ADJ
ap-10553	178	41	basis	basis	NOUN
ap-10553	178	42	of	of	ADP
ap-10553	178	43	eigenvectors	eigenvector	NOUN
ap-10553	178	44	,	,	PUNCT
ap-10553	178	45	namely	namely	ADV
ap-10553	178	46	vk	vk	VERB
ap-10553	178	47	=	=	SYM
ap-10553	178	48	1√	1√	PROPN
ap-10553	178	49	n	n	CCONJ
ap-10553	178	50	(	(	PUNCT
ap-10553	178	51	1	1	NUM
ap-10553	178	52	,	,	PUNCT
ap-10553	178	53	ωk	ωk	ADV
ap-10553	178	54	,	,	PUNCT
ap-10553	178	55	ω2k	ω2k	PROPN
ap-10553	178	56	,	,	PUNCT
ap-10553	178	57	.	.	PUNCT
ap-10553	178	58	.	.	PUNCT
ap-10553	178	59	.	.	PUNCT
ap-10553	179	1	,	,	PUNCT
ap-10553	179	2	ω(n−1)k	ω(n−1)k	ADV
ap-10553	179	3	)	)	PUNCT
ap-10553	179	4	t	t	PROPN
ap-10553	179	5	(	(	PUNCT
ap-10553	179	6	20	20	NUM
ap-10553	179	7	)	)	PUNCT
ap-10553	179	8	with	with	ADP
ap-10553	179	9	k	k	PROPN
ap-10553	179	10	=	=	SYM
ap-10553	179	11	0	0	NUM
ap-10553	179	12	,	,	PUNCT
ap-10553	179	13	1	1	NUM
ap-10553	179	14	,	,	PUNCT
ap-10553	179	15	.	.	PUNCT
ap-10553	179	16	.	.	PUNCT
ap-10553	179	17	.	.	PUNCT
ap-10553	180	1	,	,	PUNCT
ap-10553	181	1	n	n	CCONJ
ap-10553	181	2	−	−	PROPN
ap-10553	181	3	1	1	NUM
ap-10553	181	4	,	,	PUNCT
ap-10553	181	5	where	where	SCONJ
ap-10553	181	6	ω	ω	X
ap-10553	181	7	:	:	PUNCT
ap-10553	181	8	=	=	SYM
ap-10553	181	9	e	e	NOUN
ap-10553	181	10	2πi	2πi	NOUN
ap-10553	181	11	n	n	PRON
ap-10553	181	12	are	be	AUX
ap-10553	181	13	complex	complex	ADJ
ap-10553	181	14	roots	root	NOUN
ap-10553	181	15	of	of	ADP
ap-10553	181	16	unity	unity	NOUN
ap-10553	181	17	,	,	PUNCT
ap-10553	181	18	and	and	CCONJ
ap-10553	181	19	the	the	DET
ap-10553	181	20	kth	kth	PROPN
ap-10553	181	21	eigenvalue	eigenvalue	PROPN
ap-10553	181	22	is	be	AUX
ap-10553	181	23	λk	λk	ADP
ap-10553	181	24	=	=	SYM
ap-10553	181	25	c0	c0	PROPN
ap-10553	181	26	+	+	CCONJ
ap-10553	181	27	c1ω	c1ω	X
ap-10553	182	1	k	k	X
ap-10553	183	1	+	+	CCONJ
ap-10553	183	2	c2ω	c2ω	DET
ap-10553	183	3	2k	2k	NOUN
ap-10553	183	4	+	+	CCONJ
ap-10553	183	5	·	·	PUNCT
ap-10553	183	6	·	·	PUNCT
ap-10553	183	7	·	·	PUNCT
ap-10553	184	1	+	+	CCONJ
ap-10553	184	2	cn−1ω	cn−1ω	NOUN
ap-10553	184	3	(	(	PUNCT
ap-10553	184	4	n−1)k	n−1)k	NUM
ap-10553	184	5	;	;	PUNCT
ap-10553	184	6	(	(	PUNCT
ap-10553	184	7	21	21	NUM
ap-10553	184	8	)	)	PUNCT
ap-10553	184	9	therefore	therefore	ADV
ap-10553	184	10	,	,	PUNCT
ap-10553	184	11	to	to	PART
ap-10553	184	12	get	get	VERB
ap-10553	184	13	a	a	DET
ap-10553	184	14	unitary	unitary	ADJ
ap-10553	184	15	circulant	circulant	ADJ
ap-10553	184	16	matrix	matrix	NOUN
ap-10553	184	17	,	,	PUNCT
ap-10553	184	18	the	the	DET
ap-10553	184	19	generating	generate	VERB
ap-10553	184	20	sequence	sequence	NOUN
ap-10553	184	21	(	(	PUNCT
ap-10553	184	22	c0	c0	NOUN
ap-10553	184	23	,	,	PUNCT
ap-10553	184	24	.	.	PUNCT
ap-10553	184	25	.	.	PUNCT
ap-10553	184	26	.	.	PUNCT
ap-10553	185	1	,	,	PUNCT
ap-10553	185	2	cn−1	cn−1	PROPN
ap-10553	185	3	)	)	PUNCT
ap-10553	185	4	must	must	AUX
ap-10553	185	5	satisfy	satisfy	VERB
ap-10553	185	6	|λk|	|λk|	PUNCT
ap-10553	186	1	=	=	NOUN
ap-10553	186	2	1	1	NUM
ap-10553	186	3	for	for	ADP
ap-10553	186	4	k	k	PROPN
ap-10553	186	5	=	=	SYM
ap-10553	186	6	0	0	PROPN
ap-10553	186	7	,	,	PUNCT
ap-10553	186	8	.	.	PUNCT
ap-10553	186	9	.	.	PUNCT
ap-10553	187	1	.	.	PUNCT
ap-10553	188	1	,	,	PUNCT
ap-10553	189	1	n	n	CCONJ
ap-10553	189	2	−	−	PROPN
ap-10553	189	3	1	1	X
ap-10553	189	4	.	.	PUNCT
ap-10553	190	1	let	let	VERB
ap-10553	190	2	us	we	PRON
ap-10553	190	3	also	also	ADV
ap-10553	190	4	recall	recall	VERB
ap-10553	190	5	that	that	SCONJ
ap-10553	190	6	every	every	DET
ap-10553	190	7	circulant	circulant	ADJ
ap-10553	190	8	matrix	matrix	NOUN
ap-10553	190	9	is	be	AUX
ap-10553	190	10	diagonalised	diagonalise	VERB
ap-10553	190	11	by	by	ADP
ap-10553	190	12	the	the	DET
ap-10553	190	13	discrete	discrete	ADJ
ap-10553	190	14	fourier	fourier	NOUN
ap-10553	190	15	transform	transform	NOUN
ap-10553	190	16	represented	represent	VERB
ap-10553	190	17	by	by	ADP
ap-10553	190	18	the	the	DET
ap-10553	190	19	matrix	matrix	NOUN
ap-10553	191	1	f	f	NOUN
ap-10553	191	2	=	=	PUNCT
ap-10553	191	3			ADJ
ap-10553	191	4	1	1	NUM
ap-10553	191	5	1	1	NUM
ap-10553	191	6	1	1	NUM
ap-10553	191	7	1	1	NUM
ap-10553	191	8	.	.	PUNCT
ap-10553	191	9	.	.	PUNCT
ap-10553	191	10	.	.	PUNCT
ap-10553	192	1	1	1	NUM
ap-10553	192	2	1	1	NUM
ap-10553	192	3	ω	ω	NUM
ap-10553	192	4	ω2	ω2	ADJ
ap-10553	192	5	ω3	ω3	NOUN
ap-10553	192	6	.	.	PUNCT
ap-10553	192	7	.	.	PUNCT
ap-10553	192	8	.	.	PUNCT
ap-10553	193	1	ω(n−1	ω(n−1	X
ap-10553	193	2	)	)	PUNCT
ap-10553	193	3	1	1	NUM
ap-10553	193	4	ω2	ω2	NOUN
ap-10553	193	5	ω4	ω4	NUM
ap-10553	193	6	ω6	ω6	PROPN
ap-10553	193	7	.	.	PUNCT
ap-10553	193	8	.	.	PUNCT
ap-10553	193	9	.	.	PUNCT
ap-10553	194	1	ω2(n−1	ω2(n−1	ADJ
ap-10553	194	2	)	)	PUNCT
ap-10553	194	3	...	...	PUNCT
ap-10553	194	4	...	...	PUNCT
ap-10553	194	5	...	...	PUNCT
ap-10553	194	6	...	...	PUNCT
ap-10553	195	1	...	...	PUNCT
ap-10553	195	2	1	1	NUM
ap-10553	195	3	ωn−1	ωn−1	PROPN
ap-10553	195	4	ω2(n−1	ω2(n−1	NUM
ap-10553	195	5	)	)	PUNCT
ap-10553	195	6	ω3(n−1	ω3(n−1	ADJ
ap-10553	195	7	)	)	PUNCT
ap-10553	195	8	.	.	PUNCT
ap-10553	195	9	.	.	PUNCT
ap-10553	195	10	.	.	PUNCT
ap-10553	196	1	ω(n−1)2	ω(n−1)2	PROPN
ap-10553	196	2			PROPN
ap-10553	196	3	,	,	PUNCT
ap-10553	196	4	542	542	NUM
ap-10553	196	5	vol	vol	NOUN
ap-10553	196	6	.	.	PUNCT
ap-10553	197	1	65	65	NUM
ap-10553	197	2	no	no	NOUN
ap-10553	197	3	.	.	PUNCT
ap-10553	198	1	5/2025	5/2025	NUM
ap-10553	198	2	quantum	quantum	NOUN
ap-10553	198	3	graphs	graph	NOUN
ap-10553	198	4	featuring	feature	VERB
ap-10553	198	5	unusual	unusual	ADJ
ap-10553	198	6	self	self	NOUN
ap-10553	198	7	-	-	PUNCT
ap-10553	198	8	adjoint	adjoint	NOUN
ap-10553	198	9	extensions	extension	NOUN
ap-10553	198	10	so	so	SCONJ
ap-10553	198	11	that	that	SCONJ
ap-10553	199	1	d	d	NOUN
ap-10553	199	2	=	=	SYM
ap-10553	199	3	1	1	NUM
ap-10553	199	4	n	n	NOUN
ap-10553	199	5	f	f	NOUN
ap-10553	199	6	∗cf	∗cf	NOUN
ap-10553	199	7	=	=	PUNCT
ap-10553	199	8	diag	diag	PROPN
ap-10553	199	9	(	(	PUNCT
ap-10553	199	10	λ0	λ0	NOUN
ap-10553	199	11	,	,	PUNCT
ap-10553	199	12	λ1	λ1	ADJ
ap-10553	199	13	,	,	PUNCT
ap-10553	199	14	.	.	PUNCT
ap-10553	199	15	.	.	PUNCT
ap-10553	199	16	.	.	PUNCT
ap-10553	200	1	,	,	PUNCT
ap-10553	200	2	λn−1	λn−1	PROPN
ap-10553	200	3	)	)	PUNCT
ap-10553	200	4	.	.	PUNCT
ap-10553	201	1	(	(	PUNCT
ap-10553	201	2	22	22	NUM
ap-10553	201	3	)	)	PUNCT
ap-10553	201	4	since	since	SCONJ
ap-10553	201	5	f	f	PROPN
ap-10553	201	6	is	be	AUX
ap-10553	201	7	unitary	unitary	ADJ
ap-10553	201	8	,	,	PUNCT
ap-10553	201	9	we	we	PRON
ap-10553	201	10	have	have	VERB
ap-10553	201	11	c	c	NOUN
ap-10553	201	12	=	=	SYM
ap-10553	201	13	1	1	NUM
ap-10553	201	14	n	n	NUM
ap-10553	201	15	fdf	fdf	ADJ
ap-10553	201	16	∗	∗	NOUN
ap-10553	201	17	,	,	PUNCT
ap-10553	201	18	which	which	PRON
ap-10553	201	19	yields	yield	VERB
ap-10553	201	20	ck	ck	NOUN
ap-10553	201	21	=	=	SYM
ap-10553	201	22	1	1	NUM
ap-10553	201	23	n	n	CCONJ
ap-10553	201	24	(	(	PUNCT
ap-10553	201	25	λ0	λ0	NOUN
ap-10553	201	26	+	+	CCONJ
ap-10553	201	27	λ1ω	λ1ω	NOUN
ap-10553	201	28	−k	−k	ADJ
ap-10553	201	29	+	+	X
ap-10553	201	30	·	·	PUNCT
ap-10553	201	31	·	·	PUNCT
ap-10553	201	32	·	·	PUNCT
ap-10553	202	1	+	+	CCONJ
ap-10553	202	2	λn−1ω	λn−1ω	NUM
ap-10553	202	3	−(n−1)k	−(n−1)k	PROPN
ap-10553	202	4	)	)	PUNCT
ap-10553	202	5	;	;	PUNCT
ap-10553	202	6	(	(	PUNCT
ap-10553	202	7	23	23	NUM
ap-10553	202	8	)	)	PUNCT
ap-10553	202	9	hence	hence	ADV
ap-10553	202	10	n	n	CCONJ
ap-10553	202	11	×n	×n	PRON
ap-10553	202	12	unitary	unitary	ADJ
ap-10553	202	13	circulant	circulant	ADJ
ap-10553	202	14	matrices	matrix	NOUN
ap-10553	202	15	can	can	AUX
ap-10553	202	16	be	be	AUX
ap-10553	202	17	indeed	indeed	ADV
ap-10553	202	18	characterised	characterise	VERB
ap-10553	202	19	by	by	ADP
ap-10553	202	20	n	n	CCONJ
ap-10553	202	21	real	real	ADJ
ap-10553	202	22	parameters	parameter	NOUN
ap-10553	202	23	.	.	PUNCT
ap-10553	203	1	the	the	DET
ap-10553	203	2	symmetries	symmetry	NOUN
ap-10553	203	3	considered	consider	VERB
ap-10553	203	4	up	up	ADP
ap-10553	203	5	to	to	ADP
ap-10553	203	6	now	now	ADV
ap-10553	203	7	did	do	AUX
ap-10553	203	8	not	not	PART
ap-10553	203	9	require	require	VERB
ap-10553	203	10	to	to	PART
ap-10553	203	11	consider	consider	VERB
ap-10553	203	12	the	the	DET
ap-10553	203	13	star	star	NOUN
ap-10553	203	14	graph	graph	NOUN
ap-10553	203	15	as	as	ADV
ap-10553	203	16	embedded	embed	VERB
ap-10553	203	17	in	in	ADP
ap-10553	203	18	a	a	DET
ap-10553	203	19	euclidean	euclidean	ADJ
ap-10553	203	20	space	space	NOUN
ap-10553	203	21	;	;	PUNCT
ap-10553	203	22	if	if	SCONJ
ap-10553	203	23	this	this	PRON
ap-10553	203	24	is	be	AUX
ap-10553	203	25	the	the	DET
ap-10553	203	26	case	case	NOUN
ap-10553	203	27	,	,	PUNCT
ap-10553	203	28	other	other	ADJ
ap-10553	203	29	possibilities	possibility	NOUN
ap-10553	203	30	open	open	VERB
ap-10553	203	31	.	.	PUNCT
ap-10553	204	1	for	for	ADP
ap-10553	204	2	simplicity	simplicity	NOUN
ap-10553	204	3	,	,	PUNCT
ap-10553	204	4	let	let	VERB
ap-10553	204	5	us	we	PRON
ap-10553	204	6	restrict	restrict	VERB
ap-10553	204	7	to	to	ADP
ap-10553	204	8	the	the	DET
ap-10553	204	9	situation	situation	NOUN
ap-10553	204	10	where	where	SCONJ
ap-10553	204	11	the	the	DET
ap-10553	204	12	star	star	NOUN
ap-10553	204	13	is	be	AUX
ap-10553	204	14	planar	planar	ADJ
ap-10553	204	15	,	,	PUNCT
ap-10553	204	16	that	that	ADV
ap-10553	204	17	is	is	ADV
ap-10553	204	18	,	,	PUNCT
ap-10553	204	19	embedded	embed	VERB
ap-10553	204	20	in	in	ADP
ap-10553	204	21	r2	r2	PROPN
ap-10553	204	22	.	.	PUNCT
ap-10553	205	1	the	the	DET
ap-10553	205	2	edges	edge	NOUN
ap-10553	205	3	numbering	number	VERB
ap-10553	205	4	then	then	ADV
ap-10553	205	5	defines	define	VERB
ap-10553	205	6	the	the	DET
ap-10553	205	7	order	order	NOUN
ap-10553	205	8	in	in	ADP
ap-10553	205	9	which	which	PRON
ap-10553	205	10	they	they	PRON
ap-10553	205	11	appear	appear	VERB
ap-10553	205	12	if	if	SCONJ
ap-10553	205	13	we	we	PRON
ap-10553	205	14	go	go	VERB
ap-10553	205	15	around	around	ADP
ap-10553	205	16	the	the	DET
ap-10553	205	17	vertex	vertex	NOUN
ap-10553	205	18	.	.	PUNCT
ap-10553	206	1	observing	observe	VERB
ap-10553	206	2	such	such	DET
ap-10553	206	3	a	a	DET
ap-10553	206	4	graph	graph	NOUN
ap-10553	206	5	in	in	ADP
ap-10553	206	6	a	a	DET
ap-10553	206	7	mirror	mirror	NOUN
ap-10553	206	8	,	,	PUNCT
ap-10553	206	9	the	the	DET
ap-10553	206	10	order	order	NOUN
ap-10553	206	11	is	be	AUX
ap-10553	206	12	reversed	reverse	VERB
ap-10553	206	13	,	,	PUNCT
ap-10553	206	14	which	which	PRON
ap-10553	206	15	means	mean	VERB
ap-10553	206	16	that	that	SCONJ
ap-10553	206	17	we	we	PRON
ap-10553	206	18	can	can	AUX
ap-10553	206	19	associate	associate	VERB
ap-10553	206	20	the	the	DET
ap-10553	206	21	parity	parity	NOUN
ap-10553	206	22	transformation	transformation	NOUN
ap-10553	206	23	of	of	ADP
ap-10553	206	24	a	a	DET
ap-10553	206	25	planar	planar	ADJ
ap-10553	206	26	star	star	NOUN
ap-10553	206	27	graph	graph	NOUN
ap-10553	206	28	with	with	ADP
ap-10553	206	29	the	the	DET
ap-10553	206	30	passage	passage	NOUN
ap-10553	206	31	from	from	ADP
ap-10553	206	32	hu	hu	PROPN
ap-10553	206	33	to	to	ADP
ap-10553	206	34	hut	hut	NOUN
ap-10553	206	35	.	.	PUNCT
ap-10553	207	1	a	a	DET
ap-10553	207	2	comparison	comparison	NOUN
ap-10553	207	3	with	with	ADP
ap-10553	207	4	(	(	PUNCT
ap-10553	207	5	15	15	NUM
ap-10553	207	6	)	)	PUNCT
ap-10553	207	7	then	then	ADV
ap-10553	207	8	shows	show	VERB
ap-10553	207	9	that	that	SCONJ
ap-10553	207	10	star	star	NOUN
ap-10553	207	11	graphs	graph	NOUN
ap-10553	207	12	with	with	ADP
ap-10553	207	13	a	a	DET
ap-10553	207	14	circulant	circulant	ADJ
ap-10553	207	15	coupling	coupling	NOUN
ap-10553	207	16	are	be	AUX
ap-10553	207	17	pt	pt	X
ap-10553	207	18	-symmetric	-symmetric	NOUN
ap-10553	207	19	,	,	PUNCT
ap-10553	207	20	i.e.	i.e.	X
ap-10553	207	21	invariant	invariant	ADJ
ap-10553	207	22	with	with	ADP
ap-10553	207	23	respect	respect	NOUN
ap-10553	207	24	to	to	ADP
ap-10553	207	25	the	the	DET
ap-10553	207	26	combination	combination	NOUN
ap-10553	207	27	of	of	ADP
ap-10553	207	28	the	the	DET
ap-10553	207	29	parity	parity	NOUN
ap-10553	207	30	and	and	CCONJ
ap-10553	207	31	time	time	NOUN
ap-10553	207	32	reversal	reversal	NOUN
ap-10553	207	33	transformations	transformation	NOUN
ap-10553	207	34	.	.	PUNCT
ap-10553	208	1	in	in	ADP
ap-10553	208	2	more	more	ADJ
ap-10553	208	3	detail	detail	NOUN
ap-10553	208	4	,	,	PUNCT
ap-10553	208	5	an	an	DET
ap-10553	208	6	(	(	PUNCT
ap-10553	208	7	⌊	⌊	PROPN
ap-10553	208	8	n	n	PRON
ap-10553	208	9	2	2	NUM
ap-10553	208	10	⌋	⌋	NOUN
ap-10553	208	11	+	+	CCONJ
ap-10553	208	12	1	1	X
ap-10553	208	13	)	)	PUNCT
ap-10553	208	14	-parameter	-parameter	ADJ
ap-10553	208	15	part	part	NOUN
ap-10553	208	16	of	of	ADP
ap-10553	208	17	this	this	DET
ap-10553	208	18	family	family	NOUN
ap-10553	208	19	exhibits	exhibit	VERB
ap-10553	208	20	these	these	DET
ap-10553	208	21	symmetries	symmetry	NOUN
ap-10553	208	22	separately	separately	ADV
ap-10553	208	23	,	,	PUNCT
ap-10553	208	24	while	while	SCONJ
ap-10553	208	25	its	its	PRON
ap-10553	208	26	(	(	PUNCT
ap-10553	208	27	⌊	⌊	PROPN
ap-10553	208	28	n−1	n−1	PROPN
ap-10553	208	29	2	2	NUM
ap-10553	208	30	⌋	⌋	NOUN
ap-10553	208	31	)	)	PUNCT
ap-10553	208	32	-parameter	-parameter	ADJ
ap-10553	208	33	counterpart	counterpart	NOUN
ap-10553	208	34	for	for	ADP
ap-10553	208	35	which	which	PRON
ap-10553	208	36	u	u	NOUN
ap-10553	208	37	̸=	̸=	PROPN
ap-10553	208	38	ut	ut	PROPN
ap-10553	208	39	shows	show	VERB
ap-10553	208	40	a	a	DET
ap-10553	208	41	“	"	PUNCT
ap-10553	208	42	genuine	genuine	ADJ
ap-10553	208	43	”	"	PUNCT
ap-10553	208	44	pt	pt	NOUN
ap-10553	208	45	-symmetry	-symmetry	NOUN
ap-10553	208	46	.	.	PUNCT
ap-10553	209	1	to	to	PART
ap-10553	209	2	put	put	VERB
ap-10553	209	3	this	this	DET
ap-10553	209	4	observation	observation	NOUN
ap-10553	209	5	in	in	ADP
ap-10553	209	6	context	context	NOUN
ap-10553	209	7	,	,	PUNCT
ap-10553	209	8	let	let	VERB
ap-10553	209	9	us	we	PRON
ap-10553	209	10	add	add	VERB
ap-10553	209	11	that	that	SCONJ
ap-10553	209	12	circulant	circulant	ADJ
ap-10553	209	13	matrices	matrix	NOUN
ap-10553	209	14	in	in	ADP
ap-10553	209	15	relation	relation	NOUN
ap-10553	209	16	to	to	ADP
ap-10553	209	17	quantum	quantum	NOUN
ap-10553	209	18	graphs	graph	NOUN
ap-10553	209	19	were	be	AUX
ap-10553	209	20	first	first	ADV
ap-10553	209	21	considered	consider	VERB
ap-10553	209	22	by	by	ADP
ap-10553	209	23	astudillo	astudillo	PROPN
ap-10553	209	24	et	et	PROPN
ap-10553	209	25	al	al	PROPN
ap-10553	209	26	.	.	PUNCT
ap-10553	210	1	[	[	X
ap-10553	210	2	14	14	NUM
ap-10553	210	3	]	]	PUNCT
ap-10553	210	4	,	,	PUNCT
ap-10553	210	5	but	but	CCONJ
ap-10553	210	6	those	those	DET
ap-10553	210	7	authors	author	NOUN
ap-10553	210	8	looked	look	VERB
ap-10553	210	9	,	,	PUNCT
ap-10553	210	10	in	in	ADP
ap-10553	210	11	the	the	DET
ap-10553	210	12	spirit	spirit	NOUN
ap-10553	210	13	of	of	ADP
ap-10553	210	14	[	[	X
ap-10553	210	15	15	15	NUM
ap-10553	210	16	]	]	PUNCT
ap-10553	210	17	,	,	PUNCT
ap-10553	210	18	for	for	ADP
ap-10553	210	19	graphs	graph	NOUN
ap-10553	210	20	with	with	ADP
ap-10553	210	21	non	non	ADJ
ap-10553	210	22	-	-	ADJ
ap-10553	210	23	selfadjoint	selfadjoint	ADJ
ap-10553	210	24	dynamics	dynamic	NOUN
ap-10553	210	25	having	have	VERB
ap-10553	210	26	a	a	DET
ap-10553	210	27	real	real	ADJ
ap-10553	210	28	spectrum	spectrum	NOUN
ap-10553	210	29	.	.	PUNCT
ap-10553	211	1	a	a	DET
ap-10553	211	2	nontrivial	nontrivial	ADJ
ap-10553	211	3	pt	pt	NOUN
ap-10553	211	4	-symmetry	-symmetry	NOUN
ap-10553	211	5	of	of	ADP
ap-10553	211	6	self	self	NOUN
ap-10553	211	7	-	-	PUNCT
ap-10553	211	8	adjoint	adjoint	NOUN
ap-10553	211	9	quantum	quantum	NOUN
ap-10553	211	10	graph	graph	NOUN
ap-10553	211	11	hamiltonians	hamiltonian	NOUN
ap-10553	211	12	was	be	AUX
ap-10553	211	13	noted	note	VERB
ap-10553	211	14	in	in	ADP
ap-10553	211	15	[	[	X
ap-10553	211	16	16	16	NUM
ap-10553	211	17	]	]	PUNCT
ap-10553	211	18	for	for	ADP
ap-10553	211	19	graphs	graph	NOUN
ap-10553	211	20	with	with	ADP
ap-10553	211	21	the	the	DET
ap-10553	211	22	“	"	PUNCT
ap-10553	211	23	usual	usual	ADJ
ap-10553	211	24	”	"	PUNCT
ap-10553	211	25	vertices	vertex	NOUN
ap-10553	211	26	;	;	PUNCT
ap-10553	211	27	the	the	DET
ap-10553	211	28	present	present	ADJ
ap-10553	211	29	discussion	discussion	NOUN
ap-10553	211	30	shows	show	VERB
ap-10553	211	31	that	that	SCONJ
ap-10553	211	32	the	the	DET
ap-10553	211	33	observation	observation	NOUN
ap-10553	211	34	also	also	ADV
ap-10553	211	35	extends	extend	VERB
ap-10553	211	36	to	to	ADP
ap-10553	211	37	situations	situation	NOUN
ap-10553	211	38	with	with	ADP
ap-10553	211	39	a	a	DET
ap-10553	211	40	“	"	PUNCT
ap-10553	211	41	coupling	coupling	NOUN
ap-10553	211	42	at	at	ADP
ap-10553	211	43	infinity	infinity	NOUN
ap-10553	211	44	”	"	PUNCT
ap-10553	211	45	.	.	PUNCT
ap-10553	212	1	4	4	X
ap-10553	212	2	.	.	X
ap-10553	212	3	spectrum	spectrum	NOUN
ap-10553	212	4	of	of	ADP
ap-10553	212	5	hu	hu	PROPN
ap-10553	212	6	let	let	VERB
ap-10553	212	7	us	we	PRON
ap-10553	212	8	turn	turn	VERB
ap-10553	212	9	to	to	ADP
ap-10553	212	10	spectral	spectral	ADJ
ap-10553	212	11	properties	property	NOUN
ap-10553	212	12	of	of	ADP
ap-10553	212	13	the	the	DET
ap-10553	212	14	obtained	obtain	VERB
ap-10553	212	15	selfadjoint	selfadjoint	NOUN
ap-10553	212	16	extensions	extension	NOUN
ap-10553	212	17	.	.	PUNCT
ap-10553	213	1	we	we	PRON
ap-10553	213	2	know	know	VERB
ap-10553	213	3	from	from	ADP
ap-10553	213	4	proposition	proposition	NOUN
ap-10553	213	5	2.1	2.1	NUM
ap-10553	213	6	that	that	SCONJ
ap-10553	213	7	the	the	DET
ap-10553	213	8	spectrum	spectrum	NOUN
ap-10553	213	9	of	of	ADP
ap-10553	213	10	any	any	DET
ap-10553	213	11	operator	operator	NOUN
ap-10553	213	12	hu	hu	PROPN
ap-10553	213	13	is	be	AUX
ap-10553	213	14	purely	purely	ADV
ap-10553	213	15	discrete	discrete	ADJ
ap-10553	213	16	and	and	CCONJ
ap-10553	213	17	its	its	PRON
ap-10553	213	18	multiplicity	multiplicity	NOUN
ap-10553	213	19	does	do	AUX
ap-10553	213	20	not	not	PART
ap-10553	213	21	exceed	exceed	VERB
ap-10553	213	22	n	n	NOUN
ap-10553	213	23	;	;	PUNCT
ap-10553	213	24	now	now	ADV
ap-10553	213	25	we	we	PRON
ap-10553	213	26	can	can	AUX
ap-10553	213	27	say	say	VERB
ap-10553	213	28	more	more	ADJ
ap-10553	213	29	.	.	PUNCT
ap-10553	214	1	as	as	ADP
ap-10553	214	2	a	a	DET
ap-10553	214	3	preliminary	preliminary	NOUN
ap-10553	214	4	,	,	PUNCT
ap-10553	214	5	let	let	VERB
ap-10553	214	6	us	we	PRON
ap-10553	214	7	fix	fix	VERB
ap-10553	214	8	a	a	DET
ap-10553	214	9	family	family	NOUN
ap-10553	214	10	of	of	ADP
ap-10553	214	11	parameters	parameter	NOUN
ap-10553	214	12	characterising	characterise	VERB
ap-10553	214	13	n	n	PRON
ap-10553	214	14	×n	×n	PRON
ap-10553	214	15	unitary	unitary	ADJ
ap-10553	214	16	matrices	matrix	NOUN
ap-10553	214	17	,	,	PUNCT
ap-10553	214	18	as	as	ADP
ap-10553	214	19	a	a	DET
ap-10553	214	20	subset	subset	NOUN
ap-10553	214	21	of	of	ADP
ap-10553	214	22	rn2	rn2	PROPN
ap-10553	214	23	.	.	PUNCT
ap-10553	215	1	we	we	PRON
ap-10553	215	2	use	use	VERB
ap-10553	215	3	the	the	DET
ap-10553	215	4	relation	relation	NOUN
ap-10553	215	5	u	u	NOUN
ap-10553	215	6	=	=	PROPN
ap-10553	215	7	coth	coth	PROPN
ap-10553	215	8	a+i	a+i	X
ap-10553	215	9	coth	coth	PROPN
ap-10553	215	10	a−i	a−i	NOUN
ap-10553	215	11	,	,	PUNCT
ap-10553	215	12	which	which	PRON
ap-10553	215	13	defines	define	VERB
ap-10553	215	14	a	a	DET
ap-10553	215	15	bijection	bijection	NOUN
ap-10553	215	16	between	between	ADP
ap-10553	215	17	our	our	PRON
ap-10553	215	18	unitary	unitary	ADJ
ap-10553	215	19	matrices	matrix	NOUN
ap-10553	215	20	and	and	CCONJ
ap-10553	215	21	hermitean	hermitean	NOUN
ap-10553	215	22	matrices	matrix	NOUN
ap-10553	215	23	a	a	PRON
ap-10553	215	24	with	with	ADP
ap-10553	215	25	∥a∥	∥a∥	NOUN
ap-10553	215	26	≤	≤	NUM
ap-10553	215	27	1	1	NUM
ap-10553	215	28	,	,	PUNCT
ap-10553	215	29	and	and	CCONJ
ap-10553	215	30	use	use	VERB
ap-10553	215	31	the	the	DET
ap-10553	215	32	elements	element	NOUN
ap-10553	215	33	of	of	ADP
ap-10553	215	34	the	the	DET
ap-10553	215	35	unit	unit	NOUN
ap-10553	215	36	ball	ball	NOUN
ap-10553	215	37	in	in	ADP
ap-10553	215	38	rn2	rn2	PROPN
ap-10553	215	39	with	with	ADP
ap-10553	215	40	the	the	DET
ap-10553	215	41	coordinates	coordinate	NOUN
ap-10553	215	42	being	be	AUX
ap-10553	215	43	n	n	DET
ap-10553	215	44	real	real	ADJ
ap-10553	215	45	numbers	number	NOUN
ap-10553	215	46	for	for	ADP
ap-10553	215	47	the	the	DET
ap-10553	215	48	diagonal	diagonal	ADJ
ap-10553	215	49	elements	element	NOUN
ap-10553	215	50	of	of	ADP
ap-10553	215	51	a	a	DET
ap-10553	215	52	together	together	NOUN
ap-10553	215	53	with	with	ADP
ap-10553	215	54	1	1	NUM
ap-10553	215	55	2n(n	2n(n	NUM
ap-10553	215	56	−	−	NOUN
ap-10553	215	57	1	1	X
ap-10553	215	58	)	)	PUNCT
ap-10553	215	59	pairs	pair	NOUN
ap-10553	215	60	of	of	ADP
ap-10553	215	61	real	real	ADJ
ap-10553	215	62	numbers	number	NOUN
ap-10553	215	63	characterising	characterise	VERB
ap-10553	215	64	the	the	DET
ap-10553	215	65	complex	complex	ADJ
ap-10553	215	66	above	above	ADP
ap-10553	215	67	-	-	PUNCT
ap-10553	215	68	diagonal	diagonal	ADJ
ap-10553	215	69	elements	element	NOUN
ap-10553	215	70	.	.	PUNCT
ap-10553	216	1	theorem	theorem	VERB
ap-10553	216	2	4.1	4.1	NUM
ap-10553	216	3	.	.	PUNCT
ap-10553	217	1	(	(	PUNCT
ap-10553	217	2	i	i	NOUN
ap-10553	217	3	)	)	PUNCT
ap-10553	217	4	the	the	DET
ap-10553	217	5	spectrum	spectrum	NOUN
ap-10553	217	6	is	be	AUX
ap-10553	217	7	not	not	PART
ap-10553	217	8	simple	simple	ADJ
ap-10553	217	9	if	if	SCONJ
ap-10553	217	10	the	the	DET
ap-10553	217	11	hu	hu	PROPN
ap-10553	217	12	is	be	AUX
ap-10553	217	13	time	time	NOUN
ap-10553	217	14	-	-	PUNCT
ap-10553	217	15	reversal	reversal	NOUN
ap-10553	217	16	invariant	invariant	NOUN
ap-10553	217	17	and	and	CCONJ
ap-10553	217	18	there	there	PRON
ap-10553	217	19	are	be	VERB
ap-10553	217	20	an	an	DET
ap-10553	217	21	index	index	NOUN
ap-10553	217	22	j	j	NOUN
ap-10553	217	23	and	and	CCONJ
ap-10553	217	24	a	a	DET
ap-10553	217	25	function	function	NOUN
ap-10553	217	26	ψ	ψ	X
ap-10553	217	27	∈	∈	PROPN
ap-10553	217	28	d(hu	d(hu	PROPN
ap-10553	217	29	)	)	PUNCT
ap-10553	217	30	such	such	ADJ
ap-10553	217	31	that	that	PRON
ap-10553	217	32	jj(ψ	jj(ψ	NOUN
ap-10553	217	33	)	)	PUNCT
ap-10553	217	34	̸=	̸=	PROPN
ap-10553	217	35	0	0	NUM
ap-10553	217	36	.	.	PUNCT
ap-10553	218	1	(	(	PUNCT
ap-10553	218	2	ii	ii	NOUN
ap-10553	218	3	)	)	PUNCT
ap-10553	218	4	as	as	ADP
ap-10553	218	5	a	a	DET
ap-10553	218	6	function	function	NOUN
ap-10553	218	7	of	of	ADP
ap-10553	218	8	u	u	PROPN
ap-10553	218	9	,	,	PUNCT
ap-10553	218	10	the	the	DET
ap-10553	218	11	spectrum	spectrum	NOUN
ap-10553	218	12	of	of	ADP
ap-10553	218	13	hu	hu	PROPN
ap-10553	218	14	is	be	AUX
ap-10553	218	15	generically	generically	ADV
ap-10553	218	16	simple	simple	ADJ
ap-10553	218	17	,	,	PUNCT
ap-10553	218	18	that	that	ADV
ap-10553	218	19	is	is	ADV
ap-10553	218	20	,	,	PUNCT
ap-10553	218	21	the	the	DET
ap-10553	218	22	subset	subset	NOUN
ap-10553	218	23	of	of	ADP
ap-10553	218	24	the	the	DET
ap-10553	218	25	parameter	parameter	NOUN
ap-10553	218	26	space	space	NOUN
ap-10553	218	27	for	for	ADP
ap-10553	218	28	which	which	PRON
ap-10553	218	29	this	this	PRON
ap-10553	218	30	is	be	AUX
ap-10553	218	31	not	not	PART
ap-10553	218	32	true	true	ADJ
ap-10553	218	33	has	have	VERB
ap-10553	218	34	lebesgue	lebesgue	NOUN
ap-10553	218	35	measure	measure	NOUN
ap-10553	218	36	zero	zero	NUM
ap-10553	218	37	.	.	PUNCT
ap-10553	219	1	(	(	PUNCT
ap-10553	219	2	iii	iii	X
ap-10553	219	3	)	)	PUNCT
ap-10553	219	4	there	there	PRON
ap-10553	219	5	are	be	VERB
ap-10553	219	6	matrices	matrix	NOUN
ap-10553	219	7	u	u	PRON
ap-10553	219	8	such	such	ADJ
ap-10553	219	9	that	that	SCONJ
ap-10553	219	10	every	every	DET
ap-10553	219	11	eigenvalue	eigenvalue	NOUN
ap-10553	219	12	of	of	ADP
ap-10553	219	13	hu	hu	PROPN
ap-10553	219	14	is	be	AUX
ap-10553	219	15	either	either	CCONJ
ap-10553	219	16	simple	simple	ADJ
ap-10553	219	17	or	or	CCONJ
ap-10553	219	18	it	it	PRON
ap-10553	219	19	has	have	VERB
ap-10553	219	20	multiplicity	multiplicity	NOUN
ap-10553	219	21	n	n	CCONJ
ap-10553	219	22	−	−	PROPN
ap-10553	219	23	1	1	NUM
ap-10553	219	24	.	.	PUNCT
ap-10553	220	1	proof	proof	NOUN
ap-10553	220	2	.	.	PUNCT
ap-10553	221	1	(	(	PUNCT
ap-10553	221	2	i	i	NOUN
ap-10553	221	3	)	)	PUNCT
ap-10553	221	4	if	if	SCONJ
ap-10553	221	5	ψ	ψ	NOUN
ap-10553	221	6	is	be	AUX
ap-10553	221	7	an	an	DET
ap-10553	221	8	eigenfunction	eigenfunction	NOUN
ap-10553	221	9	of	of	ADP
ap-10553	221	10	a	a	DET
ap-10553	221	11	time	time	NOUN
ap-10553	221	12	-	-	PUNCT
ap-10553	221	13	reversal	reversal	NOUN
ap-10553	221	14	invariant	invariant	ADJ
ap-10553	221	15	operatorhu	operatorhu	NOUN
ap-10553	221	16	,	,	PUNCT
ap-10553	221	17	the	the	DET
ap-10553	221	18	same	same	ADJ
ap-10553	221	19	is	be	AUX
ap-10553	221	20	true	true	ADJ
ap-10553	221	21	for	for	ADP
ap-10553	221	22	its	its	PRON
ap-10553	221	23	complex	complex	ADJ
ap-10553	221	24	conjugate	conjugate	ADJ
ap-10553	221	25	function	function	NOUN
ap-10553	221	26	ψ̄.	ψ̄.	PUNCT
ap-10553	221	27	since	since	SCONJ
ap-10553	221	28	|aout	|aout	PROPN
ap-10553	221	29	j	j	PROPN
ap-10553	221	30	(	(	PUNCT
ap-10553	221	31	ψ)|	ψ)|	PROPN
ap-10553	221	32	̸=	̸=	PROPN
ap-10553	221	33	|ain	|ain	PROPN
ap-10553	221	34	j	j	PROPN
ap-10553	221	35	(	(	PUNCT
ap-10553	221	36	ψ)|	ψ)|	PROPN
ap-10553	221	37	by	by	ADP
ap-10553	221	38	assumption	assumption	NOUN
ap-10553	221	39	,	,	PUNCT
ap-10553	221	40	the	the	DET
ap-10553	221	41	asymptotics	asymptotic	NOUN
ap-10553	221	42	of	of	ADP
ap-10553	221	43	ψ	ψ	NOUN
ap-10553	221	44	can	can	AUX
ap-10553	221	45	not	not	PART
ap-10553	221	46	be	be	AUX
ap-10553	221	47	represented	represent	VERB
ap-10553	221	48	by	by	ADP
ap-10553	221	49	a	a	DET
ap-10553	221	50	real	real	ADJ
ap-10553	221	51	function	function	NOUN
ap-10553	221	52	,	,	PUNCT
ap-10553	222	1	cf	cf	X
ap-10553	222	2	.	.	PUNCT
ap-10553	222	3	remark	remark	PROPN
ap-10553	222	4	3.1	3.1	NUM
ap-10553	222	5	,	,	PUNCT
ap-10553	222	6	which	which	PRON
ap-10553	222	7	means	mean	VERB
ap-10553	222	8	that	that	SCONJ
ap-10553	222	9	ψ	ψ	NOUN
ap-10553	222	10	and	and	CCONJ
ap-10553	222	11	ψ̄	ψ̄	NOUN
ap-10553	222	12	must	must	AUX
ap-10553	222	13	be	be	AUX
ap-10553	222	14	linearly	linearly	ADV
ap-10553	222	15	independent	independent	ADJ
ap-10553	222	16	.	.	PUNCT
ap-10553	223	1	(	(	PUNCT
ap-10553	223	2	ii	ii	NOUN
ap-10553	223	3	)	)	PUNCT
ap-10553	223	4	we	we	PRON
ap-10553	223	5	employ	employ	VERB
ap-10553	223	6	the	the	DET
ap-10553	223	7	above	above	ADV
ap-10553	223	8	described	describe	VERB
ap-10553	223	9	parametrisation	parametrisation	NOUN
ap-10553	223	10	.	.	PUNCT
ap-10553	224	1	by	by	ADP
ap-10553	224	2	negation	negation	NOUN
ap-10553	224	3	of	of	ADP
ap-10553	224	4	the	the	DET
ap-10553	224	5	previous	previous	ADJ
ap-10553	224	6	claim	claim	NOUN
ap-10553	224	7	,	,	PUNCT
ap-10553	224	8	if	if	SCONJ
ap-10553	224	9	the	the	DET
ap-10553	224	10	spectrum	spectrum	NOUN
ap-10553	224	11	is	be	AUX
ap-10553	224	12	simple	simple	ADJ
ap-10553	224	13	,	,	PUNCT
ap-10553	224	14	then	then	ADV
ap-10553	224	15	u	u	PROPN
ap-10553	224	16	̸=	̸=	PROPN
ap-10553	224	17	ut	ut	PROPN
ap-10553	224	18	or	or	CCONJ
ap-10553	224	19	jj(ψ	jj(ψ	PUNCT
ap-10553	224	20	)	)	PUNCT
ap-10553	225	1	=	=	SYM
ap-10553	225	2	0	0	NUM
ap-10553	225	3	for	for	ADP
ap-10553	225	4	all	all	DET
ap-10553	225	5	j	j	PROPN
ap-10553	225	6	and	and	CCONJ
ap-10553	225	7	ψ	ψ	X
ap-10553	225	8	∈	∈	PROPN
ap-10553	225	9	d(hu	d(hu	PROPN
ap-10553	225	10	)	)	PUNCT
ap-10553	225	11	.	.	PUNCT
ap-10553	226	1	the	the	DET
ap-10553	226	2	first	first	ADJ
ap-10553	226	3	condition	condition	NOUN
ap-10553	226	4	excludes	exclude	VERB
ap-10553	226	5	only	only	ADV
ap-10553	226	6	transposal	transposal	ADJ
ap-10553	226	7	-	-	PUNCT
ap-10553	226	8	invariant	invariant	ADJ
ap-10553	226	9	matrices	matrix	NOUN
ap-10553	226	10	u	u	NOUN
ap-10553	226	11	to	to	PART
ap-10553	226	12	which	which	PRON
ap-10553	226	13	transposal	transposal	ADJ
ap-10553	226	14	invariant	invariant	ADJ
ap-10553	226	15	hermitean	hermitean	NOUN
ap-10553	226	16	matrices	matrix	NOUN
ap-10553	226	17	a	a	DET
ap-10553	226	18	correspond	correspond	NOUN
ap-10553	226	19	,	,	PUNCT
ap-10553	226	20	i.e.	i.e.	X
ap-10553	226	21	those	those	PRON
ap-10553	226	22	with	with	ADP
ap-10553	226	23	real	real	ADJ
ap-10553	226	24	off	off	ADP
ap-10553	226	25	-	-	PUNCT
ap-10553	226	26	diagonal	diagonal	ADJ
ap-10553	226	27	elements	element	NOUN
ap-10553	226	28	.	.	PUNCT
ap-10553	227	1	they	they	PRON
ap-10553	227	2	refer	refer	VERB
ap-10553	227	3	to	to	ADP
ap-10553	227	4	vectors	vector	NOUN
ap-10553	227	5	in	in	ADP
ap-10553	227	6	the	the	DET
ap-10553	227	7	intersection	intersection	NOUN
ap-10553	227	8	of	of	ADP
ap-10553	227	9	the	the	DET
ap-10553	227	10	ball	ball	NOUN
ap-10553	227	11	with	with	ADP
ap-10553	227	12	the	the	DET
ap-10553	227	13	hyperplane	hyperplane	NOUN
ap-10553	227	14	at	at	ADP
ap-10553	227	15	which	which	PRON
ap-10553	227	16	1	1	NUM
ap-10553	227	17	2n(n	2n(n	NUM
ap-10553	227	18	−1	−1	NOUN
ap-10553	227	19	)	)	PUNCT
ap-10553	227	20	out	out	ADP
ap-10553	227	21	of	of	ADP
ap-10553	227	22	the	the	DET
ap-10553	227	23	n2	n2	ADJ
ap-10553	227	24	coordinates	coordinate	NOUN
ap-10553	227	25	of	of	ADP
ap-10553	227	26	the	the	DET
ap-10553	227	27	parameter	parameter	NOUN
ap-10553	227	28	vector	vector	NOUN
ap-10553	227	29	are	be	AUX
ap-10553	227	30	zero	zero	NUM
ap-10553	227	31	,	,	PUNCT
ap-10553	227	32	certainly	certainly	ADV
ap-10553	227	33	a	a	DET
ap-10553	227	34	zero	zero	NUM
ap-10553	227	35	measure	measure	NOUN
ap-10553	227	36	set	set	VERB
ap-10553	227	37	.	.	PUNCT
ap-10553	228	1	the	the	DET
ap-10553	228	2	second	second	ADJ
ap-10553	228	3	condition	condition	NOUN
ap-10553	228	4	excludes	exclude	VERB
ap-10553	228	5	only	only	ADV
ap-10553	228	6	separated	separate	VERB
ap-10553	228	7	boundary	boundary	ADJ
ap-10553	228	8	conditions	condition	NOUN
ap-10553	228	9	with	with	ADP
ap-10553	228	10	u	u	NOUN
ap-10553	228	11	given	give	VERB
ap-10553	228	12	by	by	ADP
ap-10553	228	13	(	(	PUNCT
ap-10553	228	14	13	13	NUM
ap-10553	228	15	)	)	PUNCT
ap-10553	228	16	to	to	PART
ap-10553	228	17	which	which	PRON
ap-10553	228	18	a	a	DET
ap-10553	228	19	diagonal	diagonal	ADJ
ap-10553	228	20	a	a	DET
ap-10553	228	21	corresponds	correspond	NOUN
ap-10553	228	22	,	,	PUNCT
ap-10553	228	23	i.e.	i.e.	X
ap-10553	228	24	the	the	DET
ap-10553	228	25	parameters	parameter	NOUN
ap-10553	228	26	belonging	belong	VERB
ap-10553	228	27	to	to	ADP
ap-10553	228	28	the	the	DET
ap-10553	228	29	intersection	intersection	NOUN
ap-10553	228	30	of	of	ADP
ap-10553	228	31	the	the	DET
ap-10553	228	32	ball	ball	NOUN
ap-10553	228	33	with	with	ADP
ap-10553	228	34	the	the	DET
ap-10553	228	35	hyperplane	hyperplane	NOUN
ap-10553	228	36	of	of	ADP
ap-10553	228	37	vectors	vector	NOUN
ap-10553	228	38	with	with	ADP
ap-10553	228	39	even	even	ADV
ap-10553	228	40	n(n	n(n	NOUN
ap-10553	228	41	−	−	NOUN
ap-10553	228	42	1	1	NUM
ap-10553	228	43	)	)	PUNCT
ap-10553	228	44	components	component	NOUN
ap-10553	228	45	vanishing	vanish	VERB
ap-10553	228	46	,	,	PUNCT
ap-10553	228	47	no	no	ADV
ap-10553	228	48	doubt	doubt	ADV
ap-10553	228	49	a	a	DET
ap-10553	228	50	zero	zero	NUM
ap-10553	228	51	measure	measure	NOUN
ap-10553	228	52	set	set	VERB
ap-10553	228	53	again	again	ADV
ap-10553	228	54	.	.	PUNCT
ap-10553	229	1	(	(	PUNCT
ap-10553	229	2	iii	iii	X
ap-10553	229	3	)	)	PUNCT
ap-10553	229	4	each	each	DET
ap-10553	229	5	matrix	matrix	NOUN
ap-10553	229	6	u	u	NOUN
ap-10553	229	7	can	can	AUX
ap-10553	229	8	be	be	AUX
ap-10553	229	9	,	,	PUNCT
ap-10553	229	10	of	of	ADP
ap-10553	229	11	course	course	NOUN
ap-10553	229	12	,	,	PUNCT
ap-10553	229	13	diagonalised	diagonalise	VERB
ap-10553	229	14	:	:	PUNCT
ap-10553	229	15	there	there	PRON
ap-10553	229	16	is	be	VERB
ap-10553	229	17	a	a	DET
ap-10553	229	18	unitary	unitary	ADJ
ap-10553	229	19	v	v	NOUN
ap-10553	229	20	such	such	DET
ap-10553	229	21	that	that	DET
ap-10553	229	22	v	v	NOUN
ap-10553	229	23	uv	uv	NOUN
ap-10553	229	24	∗	∗	NOUN
ap-10553	229	25	=	=	SYM
ap-10553	229	26	diag	diag	NOUN
ap-10553	229	27	(	(	PUNCT
ap-10553	229	28	eiθ1	eiθ1	PROPN
ap-10553	229	29	,	,	PUNCT
ap-10553	229	30	.	.	PUNCT
ap-10553	229	31	.	.	PUNCT
ap-10553	230	1	.	.	PUNCT
ap-10553	231	1	,	,	PUNCT
ap-10553	231	2	eiθn	eiθn	NOUN
ap-10553	231	3	)	)	PUNCT
ap-10553	231	4	,	,	PUNCT
ap-10553	231	5	(	(	PUNCT
ap-10553	231	6	24	24	NUM
ap-10553	231	7	)	)	PUNCT
ap-10553	231	8	and	and	CCONJ
ap-10553	231	9	since	since	SCONJ
ap-10553	231	10	v	v	NUM
ap-10553	231	11	ain	ain	PROPN
ap-10553	231	12	/	/	SYM
ap-10553	231	13	out(ψ	out(ψ	PROPN
ap-10553	231	14	)	)	PUNCT
ap-10553	231	15	=	=	SYM
ap-10553	231	16	ain	ain	PROPN
ap-10553	231	17	/	/	SYM
ap-10553	231	18	out(v	out(v	PROPN
ap-10553	231	19	ψ	ψ	NOUN
ap-10553	231	20	)	)	PUNCT
ap-10553	231	21	obviously	obviously	ADV
ap-10553	231	22	holds	hold	VERB
ap-10553	231	23	,	,	PUNCT
ap-10553	231	24	relation	relation	NOUN
ap-10553	231	25	(	(	PUNCT
ap-10553	231	26	11	11	NUM
ap-10553	231	27	)	)	PUNCT
ap-10553	231	28	defining	define	VERB
ap-10553	231	29	the	the	DET
ap-10553	231	30	self	self	NOUN
ap-10553	231	31	-	-	PUNCT
ap-10553	231	32	adjoint	adjoint	NOUN
ap-10553	231	33	extension	extension	NOUN
ap-10553	231	34	gives	give	VERB
ap-10553	231	35	ain	ain	PROPN
ap-10553	231	36	j	j	PROPN
ap-10553	231	37	(	(	PUNCT
ap-10553	231	38	v	v	NOUN
ap-10553	231	39	ψ	ψ	NOUN
ap-10553	231	40	)	)	PUNCT
ap-10553	231	41	=	=	SYM
ap-10553	232	1	eiθjaout	eiθjaout	PROPN
ap-10553	232	2	j	j	PROPN
ap-10553	232	3	(	(	PUNCT
ap-10553	232	4	v	v	NOUN
ap-10553	232	5	ψ	ψ	NOUN
ap-10553	232	6	)	)	PUNCT
ap-10553	232	7	,	,	PUNCT
ap-10553	232	8	j	j	PROPN
ap-10553	232	9	=	=	SYM
ap-10553	232	10	1	1	NUM
ap-10553	232	11	,	,	PUNCT
ap-10553	232	12	.	.	PUNCT
ap-10553	232	13	.	.	PUNCT
ap-10553	232	14	.	.	PUNCT
ap-10553	233	1	,	,	PUNCT
ap-10553	233	2	n.	n.	PROPN
ap-10553	233	3	(	(	PUNCT
ap-10553	233	4	25	25	NUM
ap-10553	233	5	)	)	PUNCT
ap-10553	233	6	in	in	ADP
ap-10553	233	7	particular	particular	ADJ
ap-10553	233	8	,	,	PUNCT
ap-10553	233	9	if	if	SCONJ
ap-10553	233	10	all	all	DET
ap-10553	233	11	the	the	DET
ap-10553	233	12	θj	θj	NOUN
ap-10553	233	13	are	be	AUX
ap-10553	233	14	the	the	DET
ap-10553	233	15	same	same	ADJ
ap-10553	233	16	,	,	PUNCT
ap-10553	233	17	i.e.	i.e.	X
ap-10553	233	18	u	u	X
ap-10553	233	19	=	=	PRON
ap-10553	233	20	eiθi	eiθi	NOUN
ap-10553	233	21	for	for	ADP
ap-10553	233	22	some	some	DET
ap-10553	233	23	θ	θ	PROPN
ap-10553	233	24	∈	∈	PROPN
ap-10553	233	25	(	(	PUNCT
ap-10553	233	26	−π	−π	PROPN
ap-10553	233	27	,	,	PUNCT
ap-10553	233	28	π	π	PROPN
ap-10553	233	29	]	]	X
ap-10553	233	30	,	,	PUNCT
ap-10553	233	31	any	any	DET
ap-10553	233	32	unitary	unitary	ADJ
ap-10553	233	33	matrix	matrix	NOUN
ap-10553	233	34	v	v	NOUN
ap-10553	233	35	does	do	AUX
ap-10553	233	36	the	the	DET
ap-10553	233	37	job	job	NOUN
ap-10553	233	38	.	.	PUNCT
ap-10553	234	1	we	we	PRON
ap-10553	234	2	can	can	AUX
ap-10553	234	3	then	then	ADV
ap-10553	234	4	choose	choose	VERB
ap-10553	234	5	v	v	ADP
ap-10553	234	6	which	which	PRON
ap-10553	234	7	diagonalizes	diagonalize	VERB
ap-10553	234	8	similarly	similarly	ADV
ap-10553	234	9	the	the	DET
ap-10553	234	10	coupling	coupling	NOUN
ap-10553	234	11	(	(	PUNCT
ap-10553	234	12	2	2	NUM
ap-10553	234	13	)	)	PUNCT
ap-10553	234	14	at	at	ADP
ap-10553	234	15	the	the	DET
ap-10553	234	16	star	star	NOUN
ap-10553	234	17	vertex	vertex	NOUN
ap-10553	234	18	.	.	PUNCT
ap-10553	235	1	it	it	PRON
ap-10553	235	2	is	be	AUX
ap-10553	235	3	well	well	ADV
ap-10553	235	4	known	know	VERB
ap-10553	235	5	that	that	SCONJ
ap-10553	235	6	this	this	PRON
ap-10553	235	7	leads	lead	VERB
ap-10553	235	8	to	to	ADP
ap-10553	235	9	the	the	DET
ap-10553	235	10	simple	simple	ADJ
ap-10553	235	11	neumann	neumann	PROPN
ap-10553	235	12	condition	condition	NOUN
ap-10553	235	13	and	and	CCONJ
ap-10553	235	14	the	the	DET
ap-10553	235	15	dirichlet	dirichlet	PROPN
ap-10553	235	16	one	one	NUM
ap-10553	235	17	of	of	ADP
ap-10553	235	18	multiplicity	multiplicity	NOUN
ap-10553	235	19	n	n	CCONJ
ap-10553	235	20	−	−	PROPN
ap-10553	235	21	1	1	NUM
ap-10553	235	22	.	.	PUNCT
ap-10553	236	1	in	in	ADP
ap-10553	236	2	this	this	DET
ap-10553	236	3	way	way	NOUN
ap-10553	236	4	,	,	PUNCT
ap-10553	236	5	the	the	DET
ap-10553	236	6	problem	problem	NOUN
ap-10553	236	7	is	be	AUX
ap-10553	236	8	unitarily	unitarily	ADV
ap-10553	236	9	equivalent	equivalent	ADJ
ap-10553	236	10	to	to	ADP
ap-10553	236	11	the	the	DET
ap-10553	236	12	analysis	analysis	NOUN
ap-10553	236	13	of	of	ADP
ap-10553	236	14	a	a	DET
ap-10553	236	15	direct	direct	ADJ
ap-10553	236	16	sum	sum	NOUN
ap-10553	236	17	of	of	ADP
ap-10553	236	18	n	n	NUM
ap-10553	236	19	halfline	halfline	NOUN
ap-10553	236	20	operators	operator	NOUN
ap-10553	236	21	.	.	PUNCT
ap-10553	237	1	all	all	PRON
ap-10553	237	2	of	of	ADP
ap-10553	237	3	them	they	PRON
ap-10553	237	4	satisfy	satisfy	VERB
ap-10553	237	5	the	the	DET
ap-10553	237	6	condition	condition	NOUN
ap-10553	237	7	ain	ain	PROPN
ap-10553	237	8	j	j	PROPN
ap-10553	237	9	(	(	PUNCT
ap-10553	237	10	v	v	NOUN
ap-10553	237	11	ψ	ψ	NOUN
ap-10553	237	12	)	)	PUNCT
ap-10553	237	13	=	=	PUNCT
ap-10553	237	14	eiθaout	eiθaout	PROPN
ap-10553	237	15	j	j	PROPN
ap-10553	237	16	(	(	PUNCT
ap-10553	237	17	v	v	NOUN
ap-10553	237	18	ψ	ψ	NOUN
ap-10553	237	19	)	)	PUNCT
ap-10553	237	20	at	at	ADP
ap-10553	237	21	infinity	infinity	NOUN
ap-10553	237	22	;	;	PUNCT
ap-10553	237	23	one	one	NUM
ap-10553	237	24	is	be	AUX
ap-10553	237	25	neumann	neumann	NOUN
ap-10553	237	26	at	at	ADP
ap-10553	237	27	the	the	DET
ap-10553	237	28	origin	origin	NOUN
ap-10553	237	29	and	and	CCONJ
ap-10553	237	30	n	n	CCONJ
ap-10553	237	31	−	−	PROPN
ap-10553	237	32	1	1	NUM
ap-10553	237	33	satisfy	satisfy	NOUN
ap-10553	237	34	dirichlet	dirichlet	PROPN
ap-10553	237	35	condition	condition	NOUN
ap-10553	237	36	there	there	ADV
ap-10553	237	37	.	.	PUNCT
ap-10553	238	1	consequently	consequently	ADV
ap-10553	238	2	,	,	PUNCT
ap-10553	238	3	the	the	DET
ap-10553	238	4	spectrum	spectrum	NOUN
ap-10553	238	5	of	of	ADP
ap-10553	238	6	the	the	DET
ap-10553	238	7	operators	operator	NOUN
ap-10553	238	8	hu	hu	PROPN
ap-10553	238	9	with	with	SCONJ
ap-10553	238	10	u	u	NOUN
ap-10553	238	11	=	=	NOUN
ap-10553	238	12	eiθi	eiθi	NOUN
ap-10553	238	13	consists	consist	VERB
ap-10553	238	14	of	of	ADP
ap-10553	238	15	two	two	NUM
ap-10553	238	16	interlaced	interlaced	ADJ
ap-10553	238	17	series	series	NOUN
ap-10553	238	18	of	of	ADP
ap-10553	238	19	eigenvalues	eigenvalue	NOUN
ap-10553	238	20	:	:	PUNCT
ap-10553	238	21	the	the	DET
ap-10553	238	22	elements	element	NOUN
ap-10553	238	23	of	of	ADP
ap-10553	238	24	one	one	NUM
ap-10553	238	25	of	of	ADP
ap-10553	238	26	them	they	PRON
ap-10553	238	27	have	have	VERB
ap-10553	238	28	all	all	DET
ap-10553	238	29	multiplicity	multiplicity	NOUN
ap-10553	239	1	n	n	DET
ap-10553	239	2	−	−	NUM
ap-10553	239	3	1	1	NUM
ap-10553	239	4	while	while	SCONJ
ap-10553	239	5	the	the	DET
ap-10553	239	6	elements	element	NOUN
ap-10553	239	7	of	of	ADP
ap-10553	239	8	the	the	DET
ap-10553	239	9	other	other	ADJ
ap-10553	239	10	referring	refer	VERB
ap-10553	239	11	to	to	ADP
ap-10553	239	12	the	the	DET
ap-10553	239	13	neumann	neumann	PROPN
ap-10553	239	14	condition	condition	NOUN
ap-10553	239	15	at	at	ADP
ap-10553	239	16	the	the	DET
ap-10553	239	17	origin	origin	NOUN
ap-10553	239	18	are	be	AUX
ap-10553	239	19	simple	simple	ADJ
ap-10553	239	20	.	.	PUNCT
ap-10553	240	1	remarks	remark	VERB
ap-10553	240	2	4.2	4.2	NUM
ap-10553	240	3	.	.	PUNCT
ap-10553	241	1	(	(	PUNCT
ap-10553	241	2	a	a	X
ap-10553	241	3	)	)	PUNCT
ap-10553	241	4	we	we	PRON
ap-10553	241	5	proved	prove	VERB
ap-10553	241	6	claim	claim	NOUN
ap-10553	241	7	(	(	PUNCT
ap-10553	241	8	ii	ii	NOUN
ap-10553	241	9	)	)	PUNCT
ap-10553	241	10	for	for	ADP
ap-10553	241	11	a	a	DET
ap-10553	241	12	particular	particular	ADJ
ap-10553	241	13	parametrisation	parametrisation	NOUN
ap-10553	241	14	of	of	ADP
ap-10553	241	15	the	the	DET
ap-10553	241	16	family	family	NOUN
ap-10553	241	17	of	of	ADP
ap-10553	241	18	matrices	matrix	NOUN
ap-10553	241	19	u	u	NOUN
ap-10553	241	20	but	but	CCONJ
ap-10553	241	21	its	its	PRON
ap-10553	241	22	validity	validity	NOUN
ap-10553	241	23	extends	extend	VERB
ap-10553	241	24	to	to	ADP
ap-10553	241	25	other	other	ADJ
ap-10553	241	26	parametrisations	parametrisation	NOUN
ap-10553	241	27	as	as	ADP
ap-10553	241	28	543	543	NUM
ap-10553	241	29	pavel	pavel	PROPN
ap-10553	241	30	exner	exner	NOUN
ap-10553	241	31	acta	acta	PROPN
ap-10553	241	32	polytechnica	polytechnica	PROPN
ap-10553	241	33	long	long	ADV
ap-10553	241	34	as	as	SCONJ
ap-10553	241	35	the	the	DET
ap-10553	241	36	corresponding	corresponding	ADJ
ap-10553	241	37	parameter	parameter	NOUN
ap-10553	241	38	space	space	NOUN
ap-10553	241	39	is	be	AUX
ap-10553	241	40	related	relate	VERB
ap-10553	241	41	to	to	ADP
ap-10553	241	42	the	the	DET
ap-10553	241	43	indicated	indicate	VERB
ap-10553	241	44	one	one	NUM
ap-10553	241	45	by	by	ADP
ap-10553	241	46	a	a	DET
ap-10553	241	47	bijective	bijective	ADJ
ap-10553	241	48	and	and	CCONJ
ap-10553	241	49	bicontinous	bicontinous	ADJ
ap-10553	241	50	mapping	mapping	NOUN
ap-10553	241	51	preserving	preserve	VERB
ap-10553	241	52	zero	zero	NUM
ap-10553	241	53	lebesgue	lebesgue	NOUN
ap-10553	241	54	measure	measure	NOUN
ap-10553	241	55	sets	set	NOUN
ap-10553	241	56	,	,	PUNCT
ap-10553	241	57	in	in	ADP
ap-10553	241	58	particular	particular	ADJ
ap-10553	241	59	,	,	PUNCT
ap-10553	241	60	to	to	ADP
ap-10553	241	61	various	various	ADJ
ap-10553	241	62	commonly	commonly	ADV
ap-10553	241	63	used	use	VERB
ap-10553	241	64	parametrisations	parametrisation	NOUN
ap-10553	241	65	.	.	PUNCT
ap-10553	242	1	(	(	PUNCT
ap-10553	242	2	b	b	X
ap-10553	242	3	)	)	PUNCT
ap-10553	242	4	a	a	DET
ap-10553	242	5	natural	natural	ADJ
ap-10553	242	6	counterpart	counterpart	NOUN
ap-10553	242	7	to	to	ADP
ap-10553	242	8	(	(	PUNCT
ap-10553	242	9	2	2	X
ap-10553	242	10	)	)	PUNCT
ap-10553	242	11	is	be	AUX
ap-10553	242	12	the	the	DET
ap-10553	242	13	kirchhoff	kirchhoff	NOUN
ap-10553	242	14	condition	condition	NOUN
ap-10553	242	15	at	at	ADP
ap-10553	242	16	infinity	infinity	NOUN
ap-10553	242	17	(	(	PUNCT
ap-10553	242	18	18	18	NUM
ap-10553	242	19	)	)	PUNCT
ap-10553	242	20	.	.	PUNCT
ap-10553	243	1	in	in	ADP
ap-10553	243	2	this	this	DET
ap-10553	243	3	case	case	NOUN
ap-10553	243	4	,	,	PUNCT
ap-10553	243	5	there	there	PRON
ap-10553	243	6	is	be	VERB
ap-10553	243	7	a	a	DET
ap-10553	243	8	matrix	matrix	NOUN
ap-10553	243	9	v	v	NOUN
ap-10553	243	10	,	,	PUNCT
ap-10553	243	11	which	which	PRON
ap-10553	243	12	diagonalises	diagonalise	VERB
ap-10553	243	13	the	the	DET
ap-10553	243	14	problem	problem	NOUN
ap-10553	243	15	at	at	ADP
ap-10553	243	16	zero	zero	NUM
ap-10553	243	17	and	and	CCONJ
ap-10553	243	18	infinity	infinity	NOUN
ap-10553	243	19	simultaneously	simultaneously	ADV
ap-10553	243	20	,	,	PUNCT
ap-10553	243	21	and	and	CCONJ
ap-10553	243	22	the	the	DET
ap-10553	243	23	problem	problem	NOUN
ap-10553	243	24	splits	split	VERB
ap-10553	243	25	into	into	ADP
ap-10553	243	26	a	a	DET
ap-10553	243	27	family	family	NOUN
ap-10553	243	28	of	of	ADP
ap-10553	243	29	halfline	halfline	ADJ
ap-10553	243	30	ones	one	NOUN
ap-10553	243	31	,	,	PUNCT
ap-10553	243	32	a	a	DET
ap-10553	243	33	single	single	ADJ
ap-10553	243	34	with	with	ADP
ap-10553	243	35	neumann	neumann	PROPN
ap-10553	243	36	condition	condition	NOUN
ap-10553	243	37	at	at	ADP
ap-10553	243	38	zero	zero	NUM
ap-10553	243	39	and	and	CCONJ
ap-10553	243	40	infinity	infinity	NOUN
ap-10553	243	41	,	,	PUNCT
ap-10553	243	42	(	(	PUNCT
ap-10553	243	43	ain(v	ain(v	PROPN
ap-10553	243	44	ψ))1	ψ))1	NOUN
ap-10553	243	45	=	=	PUNCT
ap-10553	243	46	(	(	PUNCT
ap-10553	243	47	aout(v	aout(v	PROPN
ap-10553	243	48	ψ))1	ψ))1	PROPN
ap-10553	243	49	,	,	PUNCT
ap-10553	243	50	and	and	CCONJ
ap-10553	243	51	n	n	DET
ap-10553	243	52	−	−	PROPN
ap-10553	243	53	1	1	NUM
ap-10553	243	54	copies	copy	NOUN
ap-10553	243	55	of	of	ADP
ap-10553	243	56	the	the	DET
ap-10553	243	57	one	one	NOUN
ap-10553	243	58	with	with	ADP
ap-10553	243	59	dirichlet	dirichlet	PROPN
ap-10553	243	60	at	at	ADP
ap-10553	243	61	zero	zero	NUM
ap-10553	243	62	and	and	CCONJ
ap-10553	243	63	infinity	infinity	NOUN
ap-10553	243	64	,	,	PUNCT
ap-10553	243	65	(	(	PUNCT
ap-10553	243	66	ain(v	ain(v	PROPN
ap-10553	243	67	ψ))j	ψ))j	NOUN
ap-10553	243	68	=	=	PUNCT
ap-10553	243	69	−(aout(v	−(aout(v	NOUN
ap-10553	243	70	ψ))j	ψ))j	NOUN
ap-10553	243	71	for	for	ADP
ap-10553	243	72	j	j	PROPN
ap-10553	243	73	=	=	SYM
ap-10553	243	74	2	2	NUM
ap-10553	243	75	,	,	PUNCT
ap-10553	243	76	.	.	PUNCT
ap-10553	243	77	.	.	PUNCT
ap-10553	244	1	.	.	PUNCT
ap-10553	245	1	,	,	PUNCT
ap-10553	246	1	n	n	CCONJ
ap-10553	246	2	−	−	PROPN
ap-10553	246	3	1	1	NUM
ap-10553	246	4	.	.	PUNCT
ap-10553	247	1	the	the	DET
ap-10553	247	2	latter	latter	ADJ
ap-10553	247	3	give	give	VERB
ap-10553	247	4	rise	rise	NOUN
ap-10553	247	5	to	to	ADP
ap-10553	247	6	eigenvalues	eigenvalue	NOUN
ap-10553	247	7	of	of	ADP
ap-10553	247	8	multiplicity	multiplicity	NOUN
ap-10553	247	9	n	n	CCONJ
ap-10553	247	10	−	−	PROPN
ap-10553	247	11	1	1	NUM
ap-10553	247	12	,	,	PUNCT
ap-10553	247	13	but	but	CCONJ
ap-10553	247	14	we	we	PRON
ap-10553	247	15	do	do	AUX
ap-10553	247	16	not	not	PART
ap-10553	247	17	know	know	VERB
ap-10553	247	18	whether	whether	SCONJ
ap-10553	247	19	those	those	DET
ap-10553	247	20	coincide	coincide	NOUN
ap-10553	247	21	with	with	ADP
ap-10553	247	22	the	the	DET
ap-10553	247	23	eigenvalues	eigenvalue	NOUN
ap-10553	247	24	of	of	ADP
ap-10553	247	25	the	the	DET
ap-10553	247	26	neumann	neumann	PROPN
ap-10553	247	27	part	part	NOUN
ap-10553	247	28	of	of	ADP
ap-10553	247	29	the	the	DET
ap-10553	247	30	problem	problem	NOUN
ap-10553	247	31	or	or	CCONJ
ap-10553	247	32	not	not	PART
ap-10553	247	33	.	.	PUNCT
ap-10553	248	1	(	(	PUNCT
ap-10553	248	2	c	c	X
ap-10553	248	3	)	)	PUNCT
ap-10553	248	4	if	if	SCONJ
ap-10553	248	5	we	we	PRON
ap-10553	248	6	replace	replace	VERB
ap-10553	248	7	the	the	DET
ap-10553	248	8	initial	initial	ADJ
ap-10553	248	9	operator	operator	NOUN
ap-10553	248	10	h	h	NOUN
ap-10553	248	11	satisfying	satisfy	VERB
ap-10553	248	12	condition	condition	NOUN
ap-10553	248	13	(	(	PUNCT
ap-10553	248	14	2	2	NUM
ap-10553	248	15	)	)	PUNCT
ap-10553	248	16	by	by	ADP
ap-10553	248	17	hd	hd	NOUN
ap-10553	248	18	from	from	ADP
ap-10553	248	19	the	the	DET
ap-10553	248	20	proof	proof	NOUN
ap-10553	248	21	of	of	ADP
ap-10553	248	22	proposition	proposition	NOUN
ap-10553	248	23	2.1	2.1	NUM
ap-10553	248	24	,	,	PUNCT
ap-10553	248	25	dirichlet	dirichlet	PROPN
ap-10553	248	26	decoupled	decouple	VERB
ap-10553	248	27	at	at	ADP
ap-10553	248	28	the	the	DET
ap-10553	248	29	vertex	vertex	NOUN
ap-10553	248	30	,	,	PUNCT
ap-10553	248	31	and	and	CCONJ
ap-10553	248	32	choose	choose	VERB
ap-10553	248	33	u	u	NOUN
ap-10553	248	34	=	=	NOUN
ap-10553	248	35	eiθi	eiθi	NOUN
ap-10553	248	36	,	,	PUNCT
ap-10553	248	37	we	we	PRON
ap-10553	248	38	get	get	VERB
ap-10553	248	39	an	an	DET
ap-10553	248	40	operator	operator	NOUN
ap-10553	248	41	each	each	DET
ap-10553	248	42	eigenvalue	eigenvalue	NOUN
ap-10553	248	43	of	of	ADP
ap-10553	248	44	which	which	PRON
ap-10553	248	45	has	have	VERB
ap-10553	248	46	multiplicity	multiplicity	NOUN
ap-10553	248	47	n	n	NOUN
ap-10553	248	48	.	.	PUNCT
ap-10553	249	1	if	if	SCONJ
ap-10553	249	2	u	u	NOUN
ap-10553	249	3	is	be	AUX
ap-10553	249	4	non	non	ADJ
ap-10553	249	5	-	-	ADJ
ap-10553	249	6	diagonal	diagonal	ADJ
ap-10553	249	7	,	,	PUNCT
ap-10553	249	8	we	we	PRON
ap-10553	249	9	get	get	VERB
ap-10553	249	10	a	a	DET
ap-10553	249	11	graph	graph	NOUN
ap-10553	249	12	the	the	DET
ap-10553	249	13	edges	edge	NOUN
ap-10553	249	14	of	of	ADP
ap-10553	249	15	which	which	PRON
ap-10553	249	16	are	be	AUX
ap-10553	249	17	decoupled	decouple	VERB
ap-10553	249	18	at	at	ADP
ap-10553	249	19	the	the	DET
ap-10553	249	20	vertex	vertex	NOUN
ap-10553	249	21	,	,	PUNCT
ap-10553	249	22	but	but	CCONJ
ap-10553	249	23	some	some	PRON
ap-10553	249	24	or	or	CCONJ
ap-10553	249	25	all	all	PRON
ap-10553	249	26	of	of	ADP
ap-10553	249	27	them	they	PRON
ap-10553	249	28	are	be	AUX
ap-10553	249	29	coupled	couple	VERB
ap-10553	249	30	at	at	ADP
ap-10553	249	31	infinity	infinity	NOUN
ap-10553	249	32	.	.	PUNCT
ap-10553	250	1	(	(	PUNCT
ap-10553	250	2	d	d	X
ap-10553	250	3	)	)	PUNCT
ap-10553	250	4	the	the	DET
ap-10553	250	5	case	case	NOUN
ap-10553	250	6	n	n	NOUN
ap-10553	250	7	=	=	SYM
ap-10553	250	8	2	2	NUM
ap-10553	250	9	considered	consider	VERB
ap-10553	250	10	in	in	ADP
ap-10553	250	11	[	[	X
ap-10553	250	12	6	6	NUM
ap-10553	250	13	]	]	PUNCT
ap-10553	250	14	,	,	PUNCT
ap-10553	250	15	i.e.	i.e.	X
ap-10553	250	16	schrödinger	schrödinger	ADJ
ap-10553	250	17	operator	operator	NOUN
ap-10553	250	18	on	on	ADP
ap-10553	250	19	line	line	NOUN
ap-10553	250	20	with	with	ADP
ap-10553	250	21	the	the	DET
ap-10553	250	22	potential	potential	ADJ
ap-10553	250	23	−x4	−x4	NOUN
ap-10553	250	24	,	,	PUNCT
ap-10553	250	25	fits	fit	VERB
ap-10553	250	26	the	the	DET
ap-10553	250	27	scheme	scheme	NOUN
ap-10553	250	28	.	.	PUNCT
ap-10553	251	1	the	the	DET
ap-10553	251	2	matrix	matrix	NOUN
ap-10553	251	3	u	u	NOUN
ap-10553	251	4	has	have	VERB
ap-10553	251	5	now	now	ADV
ap-10553	251	6	a	a	DET
ap-10553	251	7	conventional	conventional	ADJ
ap-10553	251	8	parametrization	parametrization	NOUN
ap-10553	251	9	u	u	NOUN
ap-10553	251	10	=	=	X
ap-10553	251	11	eiη	eiη	PROPN
ap-10553	251	12	(	(	PUNCT
ap-10553	251	13	r	r	NOUN
ap-10553	251	14	eiθ	eiθ	PROPN
ap-10553	252	1	−	−	NOUN
ap-10553	252	2	√	√	NOUN
ap-10553	252	3	1	1	NUM
ap-10553	252	4	−	−	PROPN
ap-10553	252	5	r2	r2	NOUN
ap-10553	252	6	e−iϕ	e−iϕ	PROPN
ap-10553	252	7	√	√	ADV
ap-10553	252	8	1	1	NUM
ap-10553	252	9	−	−	NOUN
ap-10553	252	10	r2	r2	NOUN
ap-10553	252	11	eiϕ	eiϕ	PRON
ap-10553	252	12	r	r	NOUN
ap-10553	252	13	e−iθ	e−iθ	PROPN
ap-10553	252	14	)	)	PUNCT
ap-10553	252	15	,	,	PUNCT
ap-10553	252	16	and	and	CCONJ
ap-10553	252	17	the	the	DET
ap-10553	252	18	spectrum	spectrum	NOUN
ap-10553	252	19	of	of	ADP
ap-10553	252	20	hu	hu	PROPN
ap-10553	252	21	is	be	AUX
ap-10553	252	22	simple	simple	ADJ
ap-10553	252	23	unless	unless	SCONJ
ap-10553	252	24	r	r	NOUN
ap-10553	252	25	∈	∈	PROPN
ap-10553	253	1	[	[	X
ap-10553	253	2	0	0	NUM
ap-10553	253	3	,	,	PUNCT
ap-10553	253	4	1	1	NUM
ap-10553	253	5	)	)	PUNCT
ap-10553	253	6	and	and	CCONJ
ap-10553	253	7	ϕ	ϕ	X
ap-10553	253	8	=	=	SYM
ap-10553	253	9	±	±	NUM
ap-10553	253	10	π	π	NOUN
ap-10553	253	11	2	2	NUM
ap-10553	253	12	;	;	PUNCT
ap-10553	253	13	otherwise	otherwise	ADV
ap-10553	253	14	,	,	PUNCT
ap-10553	253	15	it	it	PRON
ap-10553	253	16	has	have	VERB
ap-10553	253	17	multiplicity	multiplicity	NOUN
ap-10553	253	18	two	two	NUM
ap-10553	253	19	.	.	PUNCT
ap-10553	254	1	in	in	ADP
ap-10553	254	2	contrast	contrast	NOUN
ap-10553	254	3	,	,	PUNCT
ap-10553	254	4	for	for	ADP
ap-10553	254	5	n	n	PROPN
ap-10553	254	6	>	>	SYM
ap-10553	254	7	2	2	NUM
ap-10553	254	8	the	the	DET
ap-10553	254	9	eigenvalue	eigenvalue	PROPN
ap-10553	254	10	multiplicities	multiplicity	NOUN
ap-10553	254	11	may	may	AUX
ap-10553	254	12	be	be	AUX
ap-10553	254	13	different	different	ADJ
ap-10553	254	14	as	as	ADP
ap-10553	254	15	the	the	DET
ap-10553	254	16	claim	claim	NOUN
ap-10553	254	17	(	(	PUNCT
ap-10553	254	18	iii	iii	NOUN
ap-10553	254	19	)	)	PUNCT
ap-10553	254	20	of	of	ADP
ap-10553	254	21	theorem	theorem	ADJ
ap-10553	254	22	4.1	4.1	NUM
ap-10553	254	23	shows	show	NOUN
ap-10553	254	24	and	and	CCONJ
ap-10553	254	25	we	we	PRON
ap-10553	254	26	can	can	AUX
ap-10553	254	27	not	not	PART
ap-10553	254	28	even	even	ADV
ap-10553	254	29	guarantee	guarantee	VERB
ap-10553	254	30	that	that	SCONJ
ap-10553	254	31	all	all	DET
ap-10553	254	32	nonsimple	nonsimple	NOUN
ap-10553	254	33	eigenvalues	eigenvalue	VERB
ap-10553	254	34	have	have	VERB
ap-10553	254	35	the	the	DET
ap-10553	254	36	same	same	ADJ
ap-10553	254	37	multiplicity	multiplicity	NOUN
ap-10553	254	38	.	.	PUNCT
ap-10553	255	1	5	5	X
ap-10553	255	2	.	.	X
ap-10553	255	3	concluding	conclude	VERB
ap-10553	255	4	remarks	remark	VERB
ap-10553	255	5	the	the	DET
ap-10553	255	6	present	present	ADJ
ap-10553	255	7	example	example	NOUN
ap-10553	255	8	underlines	underline	VERB
ap-10553	255	9	one	one	NUM
ap-10553	255	10	more	more	ADJ
ap-10553	255	11	time	time	NOUN
ap-10553	255	12	the	the	DET
ap-10553	255	13	importance	importance	NOUN
ap-10553	255	14	of	of	ADP
ap-10553	255	15	self	self	NOUN
ap-10553	255	16	-	-	PUNCT
ap-10553	255	17	adjointness	adjointness	NOUN
ap-10553	255	18	in	in	ADP
ap-10553	255	19	quantum	quantum	ADJ
ap-10553	255	20	mechanics	mechanic	NOUN
ap-10553	255	21	:	:	PUNCT
ap-10553	255	22	a	a	DET
ap-10553	255	23	formally	formally	ADV
ap-10553	255	24	“	"	PUNCT
ap-10553	255	25	hermitean	hermitean	ADJ
ap-10553	255	26	”	"	PUNCT
ap-10553	255	27	operator	operator	NOUN
ap-10553	255	28	can	can	AUX
ap-10553	255	29	have	have	VERB
ap-10553	255	30	a	a	DET
ap-10553	255	31	nontrivial	nontrivial	ADJ
ap-10553	255	32	family	family	NOUN
ap-10553	255	33	of	of	ADP
ap-10553	255	34	self	self	NOUN
ap-10553	255	35	-	-	PUNCT
ap-10553	255	36	adjoint	adjoint	NOUN
ap-10553	255	37	realisations	realisation	NOUN
ap-10553	255	38	,	,	PUNCT
ap-10553	255	39	each	each	PRON
ap-10553	255	40	of	of	ADP
ap-10553	255	41	which	which	PRON
ap-10553	255	42	describes	describe	VERB
ap-10553	255	43	a	a	DET
ap-10553	255	44	different	different	ADJ
ap-10553	255	45	physics	physics	NOUN
ap-10553	255	46	.	.	PUNCT
ap-10553	256	1	in	in	ADP
ap-10553	256	2	some	some	DET
ap-10553	256	3	situations	situation	NOUN
ap-10553	256	4	,	,	PUNCT
ap-10553	256	5	this	this	DET
ap-10553	256	6	fact	fact	NOUN
ap-10553	256	7	is	be	AUX
ap-10553	256	8	obvious	obvious	ADJ
ap-10553	256	9	;	;	PUNCT
ap-10553	256	10	even	even	ADV
ap-10553	256	11	a	a	DET
ap-10553	256	12	hard	hard	ADJ
ap-10553	256	13	-	-	PUNCT
ap-10553	256	14	core	core	NOUN
ap-10553	256	15	physicist	physicist	NOUN
ap-10553	256	16	would	would	AUX
ap-10553	256	17	not	not	PART
ap-10553	256	18	object	object	VERB
ap-10553	256	19	against	against	ADP
ap-10553	256	20	the	the	DET
ap-10553	256	21	necessity	necessity	NOUN
ap-10553	256	22	to	to	PART
ap-10553	256	23	impose	impose	VERB
ap-10553	256	24	condition	condition	NOUN
ap-10553	256	25	matching	matching	NOUN
ap-10553	256	26	wave	wave	NOUN
ap-10553	256	27	functions	function	NOUN
ap-10553	256	28	at	at	ADP
ap-10553	256	29	the	the	DET
ap-10553	256	30	graph	graph	NOUN
ap-10553	256	31	vertices	vertex	NOUN
ap-10553	256	32	.	.	PUNCT
ap-10553	257	1	what	what	PRON
ap-10553	257	2	we	we	PRON
ap-10553	257	3	tried	try	VERB
ap-10553	257	4	to	to	PART
ap-10553	257	5	illustrate	illustrate	VERB
ap-10553	257	6	here	here	ADV
ap-10553	257	7	was	be	AUX
ap-10553	257	8	that	that	SCONJ
ap-10553	257	9	the	the	DET
ap-10553	257	10	necessity	necessity	NOUN
ap-10553	257	11	to	to	PART
ap-10553	257	12	check	check	VERB
ap-10553	257	13	the	the	DET
ap-10553	257	14	self	self	NOUN
ap-10553	257	15	-	-	PUNCT
ap-10553	257	16	adjointness	adjointness	NOUN
ap-10553	257	17	may	may	AUX
ap-10553	257	18	come	come	VERB
ap-10553	257	19	from	from	ADP
ap-10553	257	20	less	less	ADV
ap-10553	257	21	conspicuous	conspicuous	ADJ
ap-10553	257	22	places	place	NOUN
ap-10553	257	23	.	.	PUNCT
ap-10553	258	1	the	the	DET
ap-10553	258	2	situation	situation	NOUN
ap-10553	258	3	we	we	PRON
ap-10553	258	4	discussed	discuss	VERB
ap-10553	258	5	in	in	ADP
ap-10553	258	6	this	this	DET
ap-10553	258	7	short	short	ADJ
ap-10553	258	8	paper	paper	NOUN
ap-10553	258	9	is	be	AUX
ap-10553	258	10	rather	rather	ADV
ap-10553	258	11	particular	particular	ADJ
ap-10553	258	12	and	and	CCONJ
ap-10553	258	13	the	the	DET
ap-10553	258	14	conclusions	conclusion	NOUN
ap-10553	258	15	allow	allow	VERB
ap-10553	258	16	for	for	ADP
ap-10553	258	17	various	various	ADJ
ap-10553	258	18	generalisations	generalisation	NOUN
ap-10553	258	19	.	.	PUNCT
ap-10553	259	1	for	for	ADP
ap-10553	259	2	instance	instance	NOUN
ap-10553	259	3	,	,	PUNCT
ap-10553	259	4	the	the	DET
ap-10553	259	5	graph	graph	NOUN
ap-10553	259	6	topology	topology	NOUN
ap-10553	259	7	can	can	AUX
ap-10553	259	8	be	be	AUX
ap-10553	259	9	more	more	ADV
ap-10553	259	10	complicated	complicated	ADJ
ap-10553	259	11	;	;	PUNCT
ap-10553	259	12	the	the	DET
ap-10553	259	13	same	same	ADJ
ap-10553	259	14	reasoning	reasoning	NOUN
ap-10553	259	15	would	would	AUX
ap-10553	259	16	clearly	clearly	ADV
ap-10553	259	17	work	work	VERB
ap-10553	259	18	as	as	ADV
ap-10553	259	19	long	long	ADV
ap-10553	259	20	as	as	SCONJ
ap-10553	259	21	the	the	DET
ap-10553	259	22	graph	graph	NOUN
ap-10553	259	23	has	have	VERB
ap-10553	259	24	a	a	DET
ap-10553	259	25	compact	compact	ADJ
ap-10553	259	26	core	core	NOUN
ap-10553	259	27	to	to	PART
ap-10553	259	28	which	which	PRON
ap-10553	259	29	a	a	DET
ap-10553	259	30	finite	finite	ADJ
ap-10553	259	31	number	number	NOUN
ap-10553	259	32	of	of	ADP
ap-10553	259	33	edges	edge	NOUN
ap-10553	259	34	is	be	AUX
ap-10553	259	35	attached	attach	VERB
ap-10553	259	36	.	.	PUNCT
ap-10553	260	1	likewise	likewise	ADV
ap-10553	260	2	,	,	PUNCT
ap-10553	260	3	the	the	DET
ap-10553	260	4	attractive	attractive	ADJ
ap-10553	260	5	potential	potential	NOUN
ap-10553	260	6	on	on	ADP
ap-10553	260	7	the	the	DET
ap-10553	260	8	leads	lead	NOUN
ap-10553	260	9	,	,	PUNCT
ap-10553	260	10	which	which	PRON
ap-10553	260	11	is	be	AUX
ap-10553	260	12	the	the	DET
ap-10553	260	13	reason	reason	NOUN
ap-10553	260	14	behind	behind	ADP
ap-10553	260	15	the	the	DET
ap-10553	260	16	quantum	quantum	NOUN
ap-10553	260	17	-	-	ADJ
ap-10553	260	18	mechanical	mechanical	ADJ
ap-10553	260	19	incompleteness	incompleteness	NOUN
ap-10553	260	20	,	,	PUNCT
ap-10553	260	21	can	can	AUX
ap-10553	260	22	be	be	AUX
ap-10553	260	23	modified	modify	VERB
ap-10553	260	24	;	;	PUNCT
ap-10553	260	25	staying	stay	VERB
ap-10553	260	26	in	in	ADP
ap-10553	260	27	the	the	DET
ap-10553	260	28	class	class	NOUN
ap-10553	260	29	of	of	ADP
ap-10553	260	30	powerlike	powerlike	ADJ
ap-10553	260	31	ones	one	NOUN
ap-10553	260	32	only	only	ADV
ap-10553	260	33	,	,	PUNCT
ap-10553	260	34	−xp	−xp	NOUN
ap-10553	260	35	with	with	SCONJ
ap-10553	260	36	any	any	DET
ap-10553	260	37	p	p	X
ap-10553	260	38	>	>	X
ap-10553	260	39	2	2	NUM
ap-10553	260	40	will	will	AUX
ap-10553	260	41	do	do	VERB
ap-10553	260	42	.	.	PUNCT
ap-10553	261	1	this	this	PRON
ap-10553	261	2	does	do	AUX
ap-10553	261	3	not	not	PART
ap-10553	261	4	say	say	VERB
ap-10553	261	5	that	that	SCONJ
ap-10553	261	6	the	the	DET
ap-10553	261	7	analysis	analysis	NOUN
ap-10553	261	8	of	of	ADP
ap-10553	261	9	our	our	PRON
ap-10553	261	10	example	example	NOUN
ap-10553	261	11	is	be	AUX
ap-10553	261	12	complete	complete	ADJ
ap-10553	261	13	.	.	PUNCT
ap-10553	262	1	one	one	PRON
ap-10553	262	2	can	can	AUX
ap-10553	262	3	ask	ask	VERB
ap-10553	262	4	,	,	PUNCT
ap-10553	262	5	for	for	ADP
ap-10553	262	6	example	example	NOUN
ap-10553	262	7	,	,	PUNCT
ap-10553	262	8	about	about	ADP
ap-10553	262	9	the	the	DET
ap-10553	262	10	asymptotic	asymptotic	ADJ
ap-10553	262	11	distribution	distribution	NOUN
ap-10553	262	12	of	of	ADP
ap-10553	262	13	the	the	DET
ap-10553	262	14	eigenvalues	eigenvalue	NOUN
ap-10553	262	15	of	of	ADP
ap-10553	262	16	both	both	DET
ap-10553	262	17	directions	direction	NOUN
ap-10553	262	18	,	,	PUNCT
ap-10553	262	19	or	or	CCONJ
ap-10553	262	20	for	for	ADP
ap-10553	262	21	the	the	DET
ap-10553	262	22	allowed	allow	VERB
ap-10553	262	23	values	value	NOUN
ap-10553	262	24	of	of	ADP
ap-10553	262	25	multiplicities	multiplicity	NOUN
ap-10553	262	26	in	in	ADP
ap-10553	262	27	the	the	DET
ap-10553	262	28	situations	situation	NOUN
ap-10553	262	29	where	where	SCONJ
ap-10553	262	30	the	the	DET
ap-10553	262	31	spectrum	spectrum	NOUN
ap-10553	262	32	is	be	AUX
ap-10553	262	33	not	not	PART
ap-10553	262	34	simple	simple	ADJ
ap-10553	262	35	.	.	PUNCT
ap-10553	263	1	another	another	DET
ap-10553	263	2	question	question	NOUN
ap-10553	263	3	concerns	concern	VERB
ap-10553	263	4	the	the	DET
ap-10553	263	5	existence	existence	NOUN
ap-10553	263	6	of	of	ADP
ap-10553	263	7	effects	effect	NOUN
ap-10553	263	8	analogous	analogous	ADJ
ap-10553	263	9	to	to	ADP
ap-10553	263	10	those	those	PRON
ap-10553	263	11	discussed	discuss	VERB
ap-10553	263	12	in	in	ADP
ap-10553	263	13	[	[	X
ap-10553	263	14	16	16	NUM
ap-10553	263	15	]	]	PUNCT
ap-10553	263	16	in	in	ADP
ap-10553	263	17	cases	case	NOUN
ap-10553	263	18	when	when	SCONJ
ap-10553	263	19	the	the	DET
ap-10553	263	20	matrix	matrix	NOUN
ap-10553	263	21	u	u	NOUN
ap-10553	263	22	is	be	AUX
ap-10553	263	23	circulant	circulant	ADJ
ap-10553	263	24	and	and	CCONJ
ap-10553	263	25	the	the	DET
ap-10553	263	26	time	time	NOUN
ap-10553	263	27	-	-	PUNCT
ap-10553	263	28	reversal	reversal	NOUN
ap-10553	263	29	invariance	invariance	NOUN
ap-10553	263	30	is	be	AUX
ap-10553	263	31	violated	violate	VERB
ap-10553	263	32	.	.	PUNCT
ap-10553	264	1	we	we	PRON
ap-10553	264	2	leave	leave	VERB
ap-10553	264	3	these	these	DET
ap-10553	264	4	problems	problem	NOUN
ap-10553	264	5	to	to	ADP
ap-10553	264	6	a	a	DET
ap-10553	264	7	future	future	ADJ
ap-10553	264	8	publication	publication	NOUN
ap-10553	264	9	.	.	PUNCT
ap-10553	265	1	acknowledgements	acknowledgement	NOUN
ap-10553	265	2	the	the	DET
ap-10553	265	3	work	work	NOUN
ap-10553	265	4	was	be	AUX
ap-10553	265	5	partially	partially	ADV
ap-10553	265	6	supported	support	VERB
ap-10553	265	7	by	by	ADP
ap-10553	265	8	the	the	DET
ap-10553	265	9	european	european	PROPN
ap-10553	265	10	union	union	PROPN
ap-10553	265	11	’s	’s	PART
ap-10553	265	12	horizon	horizon	NOUN
ap-10553	265	13	2020	2020	NUM
ap-10553	265	14	research	research	NOUN
ap-10553	265	15	and	and	CCONJ
ap-10553	265	16	innovation	innovation	NOUN
ap-10553	265	17	programme	programme	NOUN
ap-10553	265	18	under	under	ADP
ap-10553	265	19	the	the	DET
ap-10553	265	20	marie	marie	PROPN
ap-10553	265	21	skłodowska	skłodowska	PROPN
ap-10553	265	22	-	-	PUNCT
ap-10553	265	23	curie	curie	PROPN
ap-10553	265	24	grant	grant	NOUN
ap-10553	265	25	agreement	agreement	NOUN
ap-10553	265	26	no	no	INTJ
ap-10553	265	27	.	.	NOUN
ap-10553	265	28	873071	873071	NUM
ap-10553	265	29	.	.	PUNCT
ap-10553	266	1	thanks	thank	NOUN
ap-10553	266	2	also	also	ADV
ap-10553	266	3	go	go	VERB
ap-10553	266	4	to	to	ADP
ap-10553	266	5	the	the	DET
ap-10553	266	6	referee	referee	NOUN
ap-10553	266	7	for	for	ADP
ap-10553	266	8	pointing	point	VERB
ap-10553	266	9	out	out	ADP
ap-10553	266	10	a	a	DET
ap-10553	266	11	few	few	ADJ
ap-10553	266	12	typos	typo	NOUN
ap-10553	266	13	and	and	CCONJ
ap-10553	266	14	minor	minor	ADJ
ap-10553	266	15	inconsistencies	inconsistency	NOUN
ap-10553	266	16	.	.	PUNCT
ap-10553	267	1	references	reference	NOUN
ap-10553	267	2	[	[	X
ap-10553	267	3	1	1	NUM
ap-10553	267	4	]	]	PUNCT
ap-10553	267	5	l.	l.	PROPN
ap-10553	267	6	pauling	pauling	PROPN
ap-10553	267	7	.	.	PUNCT
ap-10553	268	1	the	the	DET
ap-10553	268	2	diamagnetic	diamagnetic	ADJ
ap-10553	268	3	anisotropy	anisotropy	NOUN
ap-10553	268	4	of	of	ADP
ap-10553	268	5	aromatic	aromatic	ADJ
ap-10553	268	6	molecules	molecule	NOUN
ap-10553	268	7	.	.	PUNCT
ap-10553	269	1	the	the	DET
ap-10553	269	2	journal	journal	PROPN
ap-10553	269	3	of	of	ADP
ap-10553	269	4	chemical	chemical	PROPN
ap-10553	269	5	physics	physics	PROPN
ap-10553	269	6	4(10):673	4(10):673	PROPN
ap-10553	269	7	–	–	PUNCT
ap-10553	269	8	677	677	NUM
ap-10553	269	9	,	,	PUNCT
ap-10553	269	10	1936	1936	NUM
ap-10553	269	11	.	.	PUNCT
ap-10553	270	1	https://doi.org/10.1063/1.1749766	https://doi.org/10.1063/1.1749766	PROPN
ap-10553	271	1	[	[	X
ap-10553	271	2	2	2	NUM
ap-10553	271	3	]	]	X
ap-10553	271	4	g.	g.	NOUN
ap-10553	271	5	berkolaiko	berkolaiko	NOUN
ap-10553	271	6	,	,	PUNCT
ap-10553	271	7	p.	p.	PROPN
ap-10553	271	8	kuchment	kuchment	PROPN
ap-10553	271	9	.	.	PUNCT
ap-10553	272	1	introduction	introduction	NOUN
ap-10553	272	2	to	to	ADP
ap-10553	272	3	quantum	quantum	NOUN
ap-10553	272	4	graphs	graph	NOUN
ap-10553	272	5	.	.	PUNCT
ap-10553	273	1	american	american	PROPN
ap-10553	273	2	mathematical	mathematical	PROPN
ap-10553	273	3	society	society	NOUN
ap-10553	273	4	,	,	PUNCT
ap-10553	273	5	providence	providence	NOUN
ap-10553	273	6	,	,	PUNCT
ap-10553	273	7	rhode	rhode	PROPN
ap-10553	273	8	island	island	NOUN
ap-10553	273	9	,	,	PUNCT
ap-10553	273	10	usa	usa	PROPN
ap-10553	273	11	,	,	PUNCT
ap-10553	273	12	2013	2013	NUM
ap-10553	273	13	.	.	PUNCT
ap-10553	274	1	isbn	isbn	ADJ
ap-10553	274	2	978	978	NUM
ap-10553	274	3	-	-	SYM
ap-10553	274	4	0	0	NUM
ap-10553	274	5	-	-	PUNCT
ap-10553	274	6	8218	8218	NUM
ap-10553	274	7	-	-	PUNCT
ap-10553	274	8	9211	9211	NUM
ap-10553	274	9	-	-	PUNCT
ap-10553	274	10	4	4	NUM
ap-10553	274	11	.	.	PUNCT
ap-10553	275	1	[	[	X
ap-10553	275	2	3	3	NUM
ap-10553	275	3	]	]	PUNCT
ap-10553	275	4	a.	a.	NOUN
ap-10553	275	5	kostenko	kostenko	PROPN
ap-10553	275	6	,	,	PUNCT
ap-10553	275	7	n.	n.	PROPN
ap-10553	275	8	nicolussi	nicolussi	PROPN
ap-10553	275	9	.	.	PUNCT
ap-10553	276	1	laplacians	laplacian	NOUN
ap-10553	276	2	on	on	ADP
ap-10553	276	3	infinite	infinite	ADJ
ap-10553	276	4	graphs	graph	NOUN
ap-10553	276	5	.	.	PUNCT
ap-10553	277	1	european	european	PROPN
ap-10553	277	2	mathematical	mathematical	PROPN
ap-10553	277	3	society	society	PROPN
ap-10553	277	4	press	press	PROPN
ap-10553	277	5	,	,	PUNCT
ap-10553	277	6	berlin	berlin	PROPN
ap-10553	277	7	,	,	PUNCT
ap-10553	277	8	germany	germany	PROPN
ap-10553	277	9	,	,	PUNCT
ap-10553	277	10	2023	2023	NUM
ap-10553	277	11	.	.	PUNCT
ap-10553	278	1	https://doi.org/10.4171/mems/3	https://doi.org/10.4171/mems/3	PROPN
ap-10553	278	2	[	[	X
ap-10553	278	3	4	4	X
ap-10553	278	4	]	]	PUNCT
ap-10553	278	5	p.	p.	NOUN
ap-10553	278	6	kurasov	kurasov	PROPN
ap-10553	278	7	.	.	PUNCT
ap-10553	279	1	spectral	spectral	ADJ
ap-10553	279	2	geometry	geometry	NOUN
ap-10553	279	3	of	of	ADP
ap-10553	279	4	graphs	graph	NOUN
ap-10553	279	5	.	.	PUNCT
ap-10553	280	1	birkhäuser	birkhäuser	ADJ
ap-10553	280	2	,	,	PUNCT
ap-10553	280	3	berlin	berlin	PROPN
ap-10553	280	4	,	,	PUNCT
ap-10553	280	5	germany	germany	PROPN
ap-10553	280	6	,	,	PUNCT
ap-10553	280	7	2024	2024	NUM
ap-10553	280	8	.	.	PUNCT
ap-10553	281	1	isbn	isbn	ADJ
ap-10553	281	2	978	978	NUM
ap-10553	281	3	-	-	SYM
ap-10553	281	4	3	3	NUM
ap-10553	281	5	-	-	PUNCT
ap-10553	281	6	662	662	NUM
ap-10553	281	7	-	-	PUNCT
ap-10553	281	8	67870	67870	NUM
ap-10553	281	9	-	-	SYM
ap-10553	281	10	1	1	NUM
ap-10553	281	11	.	.	PUNCT
ap-10553	282	1	https://doi.org/10.1007/978-3-662-67872-5	https://doi.org/10.1007/978-3-662-67872-5	NOUN
ap-10553	282	2	[	[	X
ap-10553	282	3	5	5	NUM
ap-10553	282	4	]	]	PUNCT
ap-10553	282	5	m.	m.	NOUN
ap-10553	282	6	reed	reed	PROPN
ap-10553	282	7	,	,	PUNCT
ap-10553	282	8	b.	b.	PROPN
ap-10553	282	9	simon	simon	PROPN
ap-10553	282	10	.	.	PUNCT
ap-10553	283	1	methods	method	NOUN
ap-10553	283	2	of	of	ADP
ap-10553	283	3	modern	modern	ADJ
ap-10553	283	4	mathematical	mathematical	ADJ
ap-10553	283	5	physics	physics	PROPN
ap-10553	283	6	.	.	PUNCT
ap-10553	284	1	ii	ii	PROPN
ap-10553	284	2	.	.	PUNCT
ap-10553	285	1	fourier	fouri	ADJ
ap-10553	285	2	analysis	analysis	NOUN
ap-10553	285	3	.	.	PUNCT
ap-10553	286	1	self	self	NOUN
ap-10553	286	2	-	-	PUNCT
ap-10553	286	3	adjointness	adjointness	NOUN
ap-10553	286	4	.	.	PUNCT
ap-10553	287	1	academic	academic	ADJ
ap-10553	287	2	press	press	NOUN
ap-10553	287	3	,	,	PUNCT
ap-10553	287	4	new	new	PROPN
ap-10553	287	5	york	york	PROPN
ap-10553	287	6	,	,	PUNCT
ap-10553	287	7	usa	usa	PROPN
ap-10553	287	8	,	,	PUNCT
ap-10553	287	9	1975	1975	NUM
ap-10553	287	10	.	.	PUNCT
ap-10553	288	1	isbn	isbn	ADJ
ap-10553	288	2	978	978	NUM
ap-10553	288	3	-	-	SYM
ap-10553	288	4	0125850025	0125850025	NUM
ap-10553	288	5	.	.	PUNCT
ap-10553	289	1	[	[	X
ap-10553	289	2	6	6	NUM
ap-10553	289	3	]	]	PUNCT
ap-10553	289	4	p.	p.	NOUN
ap-10553	289	5	exner	exner	NOUN
ap-10553	289	6	,	,	PUNCT
ap-10553	289	7	t.	t.	PROPN
ap-10553	289	8	ichinose	ichinose	PROPN
ap-10553	289	9	,	,	PUNCT
ap-10553	289	10	j.	j.	PROPN
ap-10553	289	11	klauder	klauder	PROPN
ap-10553	289	12	.	.	PUNCT
ap-10553	290	1	on	on	ADP
ap-10553	290	2	the	the	DET
ap-10553	290	3	schrödinger	schrödinger	ADJ
ap-10553	290	4	operator	operator	NOUN
ap-10553	290	5	with	with	ADP
ap-10553	290	6	a	a	DET
ap-10553	290	7	negative	negative	ADJ
ap-10553	290	8	quartic	quartic	ADJ
ap-10553	290	9	potential	potential	NOUN
ap-10553	290	10	.	.	PUNCT
ap-10553	291	1	in	in	ADP
ap-10553	291	2	preparation	preparation	NOUN
ap-10553	291	3	.	.	PUNCT
ap-10553	292	1	[	[	X
ap-10553	292	2	7	7	X
ap-10553	292	3	]	]	X
ap-10553	292	4	n.	n.	PROPN
ap-10553	292	5	dunford	dunford	PROPN
ap-10553	292	6	,	,	PUNCT
ap-10553	292	7	j.	j.	PROPN
ap-10553	292	8	t.	t.	PROPN
ap-10553	292	9	schwartz	schwartz	PROPN
ap-10553	292	10	.	.	PUNCT
ap-10553	293	1	linear	linear	PROPN
ap-10553	293	2	operators	operator	NOUN
ap-10553	293	3	.	.	PUNCT
ap-10553	294	1	part	part	NOUN
ap-10553	294	2	ii	ii	PROPN
ap-10553	294	3	:	:	PUNCT
ap-10553	294	4	spectral	spectral	ADJ
ap-10553	294	5	theory	theory	NOUN
ap-10553	294	6	.	.	PUNCT
ap-10553	295	1	interscience	interscience	NOUN
ap-10553	295	2	,	,	PUNCT
ap-10553	295	3	new	new	PROPN
ap-10553	295	4	york	york	PROPN
ap-10553	295	5	,	,	PUNCT
ap-10553	295	6	usa	usa	PROPN
ap-10553	295	7	,	,	PUNCT
ap-10553	295	8	1963	1963	NUM
ap-10553	295	9	.	.	PUNCT
ap-10553	296	1	isbn	isbn	ADJ
ap-10553	296	2	13	13	NUM
ap-10553	296	3	-	-	SYM
ap-10553	296	4	978	978	NUM
ap-10553	296	5	-	-	PUNCT
ap-10553	296	6	0471608479	0471608479	NUM
ap-10553	296	7	.	.	PUNCT
ap-10553	297	1	[	[	X
ap-10553	297	2	8	8	X
ap-10553	297	3	]	]	X
ap-10553	297	4	j.	j.	PROPN
ap-10553	297	5	weidmann	weidmann	PROPN
ap-10553	297	6	.	.	PUNCT
ap-10553	298	1	linear	linear	PROPN
ap-10553	298	2	operators	operator	NOUN
ap-10553	298	3	in	in	ADP
ap-10553	298	4	hilbert	hilbert	PROPN
ap-10553	298	5	spaces	space	NOUN
ap-10553	298	6	.	.	PUNCT
ap-10553	299	1	springer	springer	NOUN
ap-10553	299	2	,	,	PUNCT
ap-10553	299	3	new	new	PROPN
ap-10553	299	4	york	york	PROPN
ap-10553	299	5	,	,	PUNCT
ap-10553	299	6	usa	usa	PROPN
ap-10553	299	7	,	,	PUNCT
ap-10553	299	8	1980	1980	NUM
ap-10553	299	9	.	.	PUNCT
ap-10553	300	1	isbn	isbn	ADJ
ap-10553	300	2	978	978	NUM
ap-10553	300	3	-	-	SYM
ap-10553	300	4	1461260295	1461260295	NUM
ap-10553	300	5	.	.	PUNCT
ap-10553	301	1	[	[	X
ap-10553	301	2	9	9	NUM
ap-10553	301	3	]	]	X
ap-10553	301	4	s.	s.	PROPN
ap-10553	301	5	albeverio	albeverio	PROPN
ap-10553	301	6	,	,	PUNCT
ap-10553	301	7	k.	k.	PROPN
ap-10553	301	8	pankrashkin	pankrashkin	PROPN
ap-10553	301	9	.	.	PUNCT
ap-10553	302	1	a	a	DET
ap-10553	302	2	remark	remark	NOUN
ap-10553	302	3	on	on	ADP
ap-10553	302	4	krein	krein	PROPN
ap-10553	302	5	’s	’s	PART
ap-10553	302	6	resolvent	resolvent	ADJ
ap-10553	302	7	formula	formula	NOUN
ap-10553	302	8	and	and	CCONJ
ap-10553	302	9	boundary	boundary	ADJ
ap-10553	302	10	conditions	condition	NOUN
ap-10553	302	11	.	.	PUNCT
ap-10553	303	1	journal	journal	PROPN
ap-10553	303	2	of	of	ADP
ap-10553	303	3	physics	physics	PROPN
ap-10553	303	4	a	a	PRON
ap-10553	303	5	:	:	PUNCT
ap-10553	303	6	mathematical	mathematical	ADJ
ap-10553	303	7	and	and	CCONJ
ap-10553	303	8	general	general	ADJ
ap-10553	303	9	38(22):4859	38(22):4859	NUM
ap-10553	303	10	,	,	PUNCT
ap-10553	303	11	2005	2005	NUM
ap-10553	303	12	.	.	PUNCT
ap-10553	304	1	https://doi.org/10.1088/0305-4470/38/22/010	https://doi.org/10.1088/0305-4470/38/22/010	NOUN
ap-10553	304	2	[	[	X
ap-10553	304	3	10	10	NUM
ap-10553	304	4	]	]	X
ap-10553	304	5	j.	j.	PROPN
ap-10553	304	6	behrndt	behrndt	PROPN
ap-10553	304	7	,	,	PUNCT
ap-10553	304	8	s.	s.	PROPN
ap-10553	304	9	hassi	hassi	PROPN
ap-10553	304	10	,	,	PUNCT
ap-10553	304	11	h.	h.	PROPN
ap-10553	304	12	de	de	PROPN
ap-10553	304	13	snoo	snoo	PROPN
ap-10553	304	14	.	.	PUNCT
ap-10553	305	1	boundary	boundary	ADJ
ap-10553	305	2	value	value	NOUN
ap-10553	305	3	problems	problem	NOUN
ap-10553	305	4	,	,	PUNCT
ap-10553	305	5	weyl	weyl	ADJ
ap-10553	305	6	functions	function	NOUN
ap-10553	305	7	,	,	PUNCT
ap-10553	305	8	and	and	CCONJ
ap-10553	305	9	differential	differential	ADJ
ap-10553	305	10	operators	operator	NOUN
ap-10553	305	11	.	.	PUNCT
ap-10553	306	1	birkhäuser	birkhäuser	PROPN
ap-10553	306	2	,	,	PUNCT
ap-10553	306	3	cham	cham	PROPN
ap-10553	306	4	,	,	PUNCT
ap-10553	306	5	germany	germany	PROPN
ap-10553	306	6	,	,	PUNCT
ap-10553	306	7	2020	2020	NUM
ap-10553	306	8	.	.	PUNCT
ap-10553	307	1	isbn	isbn	ADJ
ap-10553	307	2	978	978	NUM
ap-10553	307	3	-	-	SYM
ap-10553	307	4	3	3	NUM
ap-10553	307	5	-	-	PUNCT
ap-10553	307	6	030	030	NUM
ap-10553	307	7	-	-	PUNCT
ap-10553	307	8	36713	36713	NUM
ap-10553	307	9	-	-	SYM
ap-10553	307	10	8	8	NUM
ap-10553	307	11	.	.	PUNCT
ap-10553	307	12	https://doi.org/10.1007/978-3-030-36714-5	https://doi.org/10.1007/978-3-030-36714-5	PROPN
ap-10553	308	1	[	[	X
ap-10553	308	2	11	11	NUM
ap-10553	308	3	]	]	X
ap-10553	308	4	f.	f.	PROPN
ap-10553	308	5	w.	w.	PROPN
ap-10553	308	6	j.	j.	PROPN
ap-10553	308	7	olver	olver	PROPN
ap-10553	308	8	.	.	PUNCT
ap-10553	309	1	asymptotics	asymptotic	NOUN
ap-10553	309	2	and	and	CCONJ
ap-10553	309	3	special	special	ADJ
ap-10553	309	4	functions	function	NOUN
ap-10553	309	5	.	.	PUNCT
ap-10553	310	1	crc	crc	PROPN
ap-10553	310	2	press	press	PROPN
ap-10553	310	3	,	,	PUNCT
ap-10553	310	4	new	new	PROPN
ap-10553	310	5	york	york	PROPN
ap-10553	310	6	,	,	PUNCT
ap-10553	310	7	usa	usa	PROPN
ap-10553	310	8	,	,	PUNCT
ap-10553	310	9	1st	1st	ADJ
ap-10553	310	10	edn	edn	PROPN
ap-10553	310	11	.	.	PUNCT
ap-10553	310	12	,	,	PUNCT
ap-10553	310	13	1997	1997	NUM
ap-10553	310	14	.	.	PUNCT
ap-10553	311	1	https://doi.org/10.1201/9781439864548	https://doi.org/10.1201/9781439864548	AUX
ap-10553	311	2	544	544	NUM
ap-10553	311	3	https://doi.org/10.1063/1.1749766	https://doi.org/10.1063/1.1749766	NOUN
ap-10553	311	4	https://doi.org/10.4171/mems/3	https://doi.org/10.4171/mems/3	PROPN
ap-10553	311	5	https://doi.org/10.1007/978-3-662-67872-5	https://doi.org/10.1007/978-3-662-67872-5	ADV
ap-10553	311	6	https://doi.org/10.1088/0305-4470/38/22/010	https://doi.org/10.1088/0305-4470/38/22/010	PROPN
ap-10553	311	7	https://doi.org/10.1007/978-3-030-36714-5	https://doi.org/10.1007/978-3-030-36714-5	PROPN
ap-10553	311	8	https://doi.org/10.1201/9781439864548	https://doi.org/10.1201/9781439864548	AUX
ap-10553	311	9	vol	vol	NOUN
ap-10553	311	10	.	.	PUNCT
ap-10553	312	1	65	65	NUM
ap-10553	312	2	no	no	NOUN
ap-10553	312	3	.	.	PUNCT
ap-10553	313	1	5/2025	5/2025	NUM
ap-10553	313	2	quantum	quantum	NOUN
ap-10553	313	3	graphs	graph	NOUN
ap-10553	313	4	featuring	feature	VERB
ap-10553	313	5	unusual	unusual	ADJ
ap-10553	313	6	self	self	NOUN
ap-10553	313	7	-	-	PUNCT
ap-10553	313	8	adjoint	adjoint	NOUN
ap-10553	313	9	extensions	extension	NOUN
ap-10553	313	10	[	[	X
ap-10553	313	11	12	12	NUM
ap-10553	313	12	]	]	PUNCT
ap-10553	313	13	o.	o.	NOUN
ap-10553	313	14	turek	turek	PROPN
ap-10553	313	15	,	,	PUNCT
ap-10553	313	16	t.	t.	PROPN
ap-10553	313	17	cheon	cheon	PROPN
ap-10553	313	18	.	.	PUNCT
ap-10553	314	1	quantum	quantum	ADJ
ap-10553	314	2	graph	graph	NOUN
ap-10553	314	3	vertices	vertex	NOUN
ap-10553	314	4	with	with	ADP
ap-10553	314	5	permutation	permutation	NOUN
ap-10553	314	6	-	-	PUNCT
ap-10553	314	7	symmetric	symmetric	ADJ
ap-10553	314	8	scattering	scatter	VERB
ap-10553	314	9	probabilities	probability	NOUN
ap-10553	314	10	.	.	PUNCT
ap-10553	315	1	physics	physics	NOUN
ap-10553	315	2	letters	letter	NOUN
ap-10553	315	3	a	a	DET
ap-10553	315	4	375(43):3775–3780	375(43):3775–3780	NUM
ap-10553	315	5	,	,	PUNCT
ap-10553	315	6	2011	2011	NUM
ap-10553	315	7	.	.	PUNCT
ap-10553	316	1	https://doi.org/10.1016/j.physleta.2011.09.006	https://doi.org/10.1016/j.physleta.2011.09.006	VERB
ap-10553	316	2	[	[	PUNCT
ap-10553	316	3	13	13	NUM
ap-10553	316	4	]	]	PUNCT
ap-10553	316	5	p.	p.	PROPN
ap-10553	316	6	j.	j.	PROPN
ap-10553	316	7	davis	davis	PROPN
ap-10553	316	8	.	.	PUNCT
ap-10553	317	1	circulant	circulant	ADJ
ap-10553	317	2	matrices	matrix	NOUN
ap-10553	317	3	.	.	PUNCT
ap-10553	318	1	wiley	wiley	PROPN
ap-10553	318	2	,	,	PUNCT
ap-10553	318	3	new	new	PROPN
ap-10553	318	4	york	york	PROPN
ap-10553	318	5	,	,	PUNCT
ap-10553	318	6	usa	usa	PROPN
ap-10553	318	7	,	,	PUNCT
ap-10553	318	8	1979	1979	NUM
ap-10553	318	9	.	.	PUNCT
ap-10553	319	1	[	[	X
ap-10553	319	2	14	14	NUM
ap-10553	319	3	]	]	PUNCT
ap-10553	319	4	m.	m.	NOUN
ap-10553	319	5	astudillo	astudillo	PROPN
ap-10553	319	6	,	,	PUNCT
ap-10553	319	7	p.	p.	PROPN
ap-10553	319	8	kurasov	kurasov	PROPN
ap-10553	319	9	,	,	PUNCT
ap-10553	319	10	m.	m.	NOUN
ap-10553	319	11	usman	usman	PROPN
ap-10553	319	12	.	.	PUNCT
ap-10553	320	1	rt	rt	PROPN
ap-10553	320	2	-symmetric	-symmetric	ADJ
ap-10553	320	3	laplace	laplace	NOUN
ap-10553	320	4	operators	operator	NOUN
ap-10553	320	5	on	on	ADP
ap-10553	320	6	star	star	NOUN
ap-10553	320	7	graphs	graph	NOUN
ap-10553	320	8	:	:	PUNCT
ap-10553	320	9	real	real	ADJ
ap-10553	320	10	spectrum	spectrum	NOUN
ap-10553	320	11	and	and	CCONJ
ap-10553	320	12	self	self	NOUN
ap-10553	320	13	-	-	PUNCT
ap-10553	320	14	adjointness	adjointness	NOUN
ap-10553	320	15	.	.	PUNCT
ap-10553	321	1	advances	advance	NOUN
ap-10553	321	2	in	in	ADP
ap-10553	321	3	mathematical	mathematical	ADJ
ap-10553	321	4	physics	physics	NOUN
ap-10553	321	5	2015(1):649795	2015(1):649795	NUM
ap-10553	321	6	,	,	PUNCT
ap-10553	321	7	2015	2015	NUM
ap-10553	321	8	.	.	PUNCT
ap-10553	322	1	https://doi.org/10.1155/2015/649795	https://doi.org/10.1155/2015/649795	PROPN
ap-10553	323	1	[	[	X
ap-10553	323	2	15	15	NUM
ap-10553	323	3	]	]	X
ap-10553	323	4	c.	c.	PROPN
ap-10553	323	5	m.	m.	PROPN
ap-10553	323	6	bender	bender	PROPN
ap-10553	323	7	,	,	PUNCT
ap-10553	323	8	s.	s.	PROPN
ap-10553	323	9	boettcher	boettcher	PROPN
ap-10553	323	10	.	.	PUNCT
ap-10553	324	1	real	real	ADJ
ap-10553	324	2	spectra	spectra	NOUN
ap-10553	324	3	in	in	ADP
ap-10553	324	4	non	non	ADJ
ap-10553	324	5	-	-	ADJ
ap-10553	324	6	hermitian	hermitian	ADJ
ap-10553	324	7	hamiltonians	hamiltonian	NOUN
ap-10553	324	8	having	have	VERB
ap-10553	324	9	pt	pt	PRON
ap-10553	324	10	symmetry	symmetry	NOUN
ap-10553	324	11	.	.	PUNCT
ap-10553	325	1	physical	physical	ADJ
ap-10553	325	2	review	review	NOUN
ap-10553	325	3	letters	letter	NOUN
ap-10553	325	4	80:5243–5246	80:5243–5246	NUM
ap-10553	325	5	,	,	PUNCT
ap-10553	325	6	1998	1998	NUM
ap-10553	325	7	.	.	PUNCT
ap-10553	326	1	https://doi.org/10.1103/physrevlett.80.5243	https://doi.org/10.1103/physrevlett.80.5243	PROPN
ap-10553	327	1	[	[	X
ap-10553	327	2	16	16	NUM
ap-10553	327	3	]	]	PUNCT
ap-10553	327	4	p.	p.	NOUN
ap-10553	327	5	exner	exner	PROPN
ap-10553	327	6	,	,	PUNCT
ap-10553	327	7	m.	m.	NOUN
ap-10553	327	8	tater	tater	NOUN
ap-10553	327	9	.	.	PUNCT
ap-10553	328	1	quantum	quantum	NOUN
ap-10553	328	2	graphs	graph	NOUN
ap-10553	328	3	:	:	PUNCT
ap-10553	328	4	self	self	NOUN
ap-10553	328	5	-	-	PUNCT
ap-10553	328	6	adjoint	adjoint	NOUN
ap-10553	328	7	,	,	PUNCT
ap-10553	328	8	and	and	CCONJ
ap-10553	328	9	yet	yet	ADV
ap-10553	328	10	exhibiting	exhibit	VERB
ap-10553	328	11	a	a	DET
ap-10553	328	12	nontrivial	nontrivial	ADJ
ap-10553	328	13	pt	pt	PROPN
ap-10553	328	14	-symmetry	-symmetry	PROPN
ap-10553	328	15	.	.	PUNCT
ap-10553	329	1	physics	physics	NOUN
ap-10553	329	2	letters	letter	VERB
ap-10553	329	3	a	a	DET
ap-10553	329	4	416:127669	416:127669	NUM
ap-10553	329	5	,	,	PUNCT
ap-10553	329	6	2021	2021	NUM
ap-10553	329	7	.	.	PUNCT
ap-10553	330	1	https://doi.org/10.1016/j.physleta.2021.127669	https://doi.org/10.1016/j.physleta.2021.127669	NOUN
ap-10553	330	2	545	545	NUM
ap-10553	330	3	https://doi.org/10.1016/j.physleta.2011.09.006	https://doi.org/10.1016/j.physleta.2011.09.006	NUM
ap-10553	330	4	https://doi.org/10.1155/2015/649795	https://doi.org/10.1155/2015/649795	PROPN
ap-10553	330	5	https://doi.org/10.1103/physrevlett.80.5243	https://doi.org/10.1103/physrevlett.80.5243	NOUN
ap-10553	330	6	https://doi.org/10.1016/j.physleta.2021.127669	https://doi.org/10.1016/j.physleta.2021.127669	PROPN
ap-10553	330	7	acta	acta	PROPN
ap-10553	330	8	polytechnica	polytechnica	PROPN
ap-10553	330	9	65(5):539–545	65(5):539–545	PROPN
ap-10553	330	10	,	,	PUNCT
ap-10553	330	11	2025	2025	NUM
ap-10553	330	12	1	1	NUM
ap-10553	330	13	introduction	introduction	NOUN
ap-10553	330	14	2	2	NUM
ap-10553	330	15	star	star	NOUN
ap-10553	330	16	graph	graph	NOUN
ap-10553	330	17	with	with	ADP
ap-10553	330	18	limit	limit	NOUN
ap-10553	330	19	-	-	PUNCT
ap-10553	330	20	circle	circle	NOUN
ap-10553	330	21	lead	lead	NOUN
ap-10553	330	22	ends	end	VERB
ap-10553	330	23	3	3	NUM
ap-10553	330	24	properties	property	NOUN
ap-10553	330	25	of	of	ADP
ap-10553	330	26	the	the	DET
ap-10553	330	27	extensions	extension	NOUN
ap-10553	330	28	4	4	NUM
ap-10553	330	29	spectrum	spectrum	NOUN
ap-10553	330	30	of	of	ADP
ap-10553	330	31	hu	hu	PROPN
ap-10553	330	32	5	5	NUM
ap-10553	330	33	concluding	conclude	VERB
ap-10553	330	34	remarks	remark	VERB
ap-10553	330	35	acknowledgements	acknowledgement	NOUN
ap-10553	330	36	references	reference	NOUN