id	sid	tid	token	lemma	pos
ap-1271	1	1	ap-5-10.dvi	ap-5-10.dvi	PROPN
ap-1271	1	2	acta	acta	PROPN
ap-1271	1	3	polytechnica	polytechnica	PROPN
ap-1271	1	4	vol	vol	NOUN
ap-1271	1	5	.	.	PROPN
ap-1271	2	1	50	50	NUM
ap-1271	2	2	no	no	NOUN
ap-1271	2	3	.	.	PUNCT
ap-1271	3	1	5/2010	5/2010	DET
ap-1271	3	2	self	self	NOUN
ap-1271	3	3	-	-	PUNCT
ap-1271	3	4	adjoint	adjoint	NOUN
ap-1271	3	5	extensions	extension	NOUN
ap-1271	3	6	of	of	ADP
ap-1271	3	7	schrödinger	schrödinger	NOUN
ap-1271	3	8	operators	operator	NOUN
ap-1271	3	9	with	with	ADP
ap-1271	3	10	δ	δ	PROPN
ap-1271	3	11	-	-	PUNCT
ap-1271	3	12	magnetic	magnetic	ADJ
ap-1271	3	13	fields	field	NOUN
ap-1271	3	14	on	on	ADP
ap-1271	3	15	riemannian	riemannian	ADJ
ap-1271	3	16	manifolds	manifold	NOUN
ap-1271	3	17	t.	t.	PROPN
ap-1271	3	18	mine	mine	PRON
ap-1271	3	19	abstract	abstract	NOUN
ap-1271	3	20	we	we	PRON
ap-1271	3	21	consider	consider	VERB
ap-1271	3	22	the	the	DET
ap-1271	3	23	magnetic	magnetic	ADJ
ap-1271	3	24	schrödinger	schrödinger	NOUN
ap-1271	3	25	operator	operator	NOUN
ap-1271	3	26	on	on	ADP
ap-1271	3	27	a	a	DET
ap-1271	3	28	riemannian	riemannian	ADJ
ap-1271	3	29	manifold	manifold	ADJ
ap-1271	3	30	m	m	NOUN
ap-1271	3	31	.	.	PUNCT
ap-1271	4	1	we	we	PRON
ap-1271	4	2	assume	assume	VERB
ap-1271	4	3	the	the	DET
ap-1271	4	4	magnetic	magnetic	ADJ
ap-1271	4	5	field	field	NOUN
ap-1271	4	6	is	be	AUX
ap-1271	4	7	given	give	VERB
ap-1271	4	8	by	by	ADP
ap-1271	4	9	the	the	DET
ap-1271	4	10	sum	sum	NOUN
ap-1271	4	11	of	of	ADP
ap-1271	4	12	a	a	DET
ap-1271	4	13	regular	regular	ADJ
ap-1271	4	14	field	field	NOUN
ap-1271	4	15	and	and	CCONJ
ap-1271	4	16	the	the	DET
ap-1271	4	17	dirac	dirac	PROPN
ap-1271	4	18	δ	δ	PROPN
ap-1271	4	19	measures	measure	NOUN
ap-1271	4	20	supported	support	VERB
ap-1271	4	21	on	on	ADP
ap-1271	4	22	a	a	DET
ap-1271	4	23	discrete	discrete	ADJ
ap-1271	4	24	set	set	VERB
ap-1271	4	25	γ	γ	NOUN
ap-1271	4	26	in	in	ADP
ap-1271	4	27	m	m	PROPN
ap-1271	4	28	.	.	PUNCT
ap-1271	5	1	we	we	PRON
ap-1271	5	2	give	give	VERB
ap-1271	5	3	a	a	DET
ap-1271	5	4	complete	complete	ADJ
ap-1271	5	5	characterization	characterization	NOUN
ap-1271	5	6	of	of	ADP
ap-1271	5	7	the	the	DET
ap-1271	5	8	self	self	NOUN
ap-1271	5	9	-	-	PUNCT
ap-1271	5	10	adjoint	adjoint	NOUN
ap-1271	5	11	extensions	extension	NOUN
ap-1271	5	12	of	of	ADP
ap-1271	5	13	the	the	DET
ap-1271	5	14	minimal	minimal	ADJ
ap-1271	5	15	operator	operator	NOUN
ap-1271	5	16	,	,	PUNCT
ap-1271	5	17	in	in	ADP
ap-1271	5	18	terms	term	NOUN
ap-1271	5	19	of	of	ADP
ap-1271	5	20	the	the	DET
ap-1271	5	21	boundary	boundary	ADJ
ap-1271	5	22	conditions	condition	NOUN
ap-1271	5	23	.	.	PUNCT
ap-1271	6	1	the	the	DET
ap-1271	6	2	result	result	NOUN
ap-1271	6	3	is	be	AUX
ap-1271	6	4	an	an	DET
ap-1271	6	5	extension	extension	NOUN
ap-1271	6	6	of	of	ADP
ap-1271	6	7	the	the	DET
ap-1271	6	8	former	former	ADJ
ap-1271	6	9	results	result	NOUN
ap-1271	6	10	by	by	ADP
ap-1271	6	11	dabrowski	dabrowski	NOUN
ap-1271	6	12	-	-	PUNCT
ap-1271	6	13	šťovíček	šťovíček	PROPN
ap-1271	6	14	and	and	CCONJ
ap-1271	6	15	exner	exner	NOUN
ap-1271	6	16	-	-	PUNCT
ap-1271	6	17	šťovíček	šťovíček	NOUN
ap-1271	6	18	-	-	PUNCT
ap-1271	6	19	vytřas	vytřas	NOUN
ap-1271	6	20	.	.	PUNCT
ap-1271	7	1	keywords	keyword	NOUN
ap-1271	7	2	:	:	PUNCT
ap-1271	7	3	spectral	spectral	ADJ
ap-1271	7	4	theory	theory	NOUN
ap-1271	7	5	,	,	PUNCT
ap-1271	7	6	functional	functional	ADJ
ap-1271	7	7	analysis	analysis	NOUN
ap-1271	7	8	,	,	PUNCT
ap-1271	7	9	self	self	NOUN
ap-1271	7	10	-	-	PUNCT
ap-1271	7	11	adjointness	adjointness	NOUN
ap-1271	7	12	,	,	PUNCT
ap-1271	7	13	aharonov	aharonov	NOUN
ap-1271	7	14	-	-	PUNCT
ap-1271	7	15	bohm	bohm	PROPN
ap-1271	7	16	effect	effect	NOUN
ap-1271	7	17	,	,	PUNCT
ap-1271	7	18	quantum	quantum	NOUN
ap-1271	7	19	mechanics	mechanic	NOUN
ap-1271	7	20	,	,	PUNCT
ap-1271	7	21	differential	differential	ADJ
ap-1271	7	22	geometry	geometry	NOUN
ap-1271	7	23	,	,	PUNCT
ap-1271	7	24	schrödinger	schrödinger	ADJ
ap-1271	7	25	operator	operator	NOUN
ap-1271	7	26	.	.	PUNCT
ap-1271	8	1	1	1	NUM
ap-1271	8	2	introduction	introduction	NOUN
ap-1271	8	3	let	let	VERB
ap-1271	8	4	(	(	PUNCT
ap-1271	8	5	m	m	NOUN
ap-1271	8	6	,	,	PUNCT
ap-1271	8	7	g	g	NOUN
ap-1271	8	8	)	)	PUNCT
ap-1271	8	9	be	be	VERB
ap-1271	8	10	a	a	DET
ap-1271	8	11	two	two	NUM
ap-1271	8	12	-	-	PUNCT
ap-1271	8	13	dimensional	dimensional	ADJ
ap-1271	8	14	,	,	PUNCT
ap-1271	8	15	oriented	orient	VERB
ap-1271	8	16	,	,	PUNCT
ap-1271	8	17	connected	connected	ADJ
ap-1271	8	18	complete	complete	ADJ
ap-1271	8	19	c∞-riemannian	c∞-riemannian	PROPN
ap-1271	8	20	manifold	manifold	NOUN
ap-1271	8	21	,	,	PUNCT
ap-1271	8	22	where	where	SCONJ
ap-1271	8	23	g	g	PROPN
ap-1271	8	24	is	be	AUX
ap-1271	8	25	the	the	DET
ap-1271	8	26	riemannian	riemannian	ADJ
ap-1271	8	27	metric	metric	ADJ
ap-1271	8	28	onm	onm	NOUN
ap-1271	8	29	.	.	PUNCT
ap-1271	9	1	let	let	VERB
ap-1271	9	2	dμ	dμ	SCONJ
ap-1271	9	3	be	be	AUX
ap-1271	9	4	the	the	DET
ap-1271	9	5	measure	measure	NOUN
ap-1271	9	6	induced	induce	VERB
ap-1271	9	7	from	from	ADP
ap-1271	9	8	the	the	DET
ap-1271	9	9	riemannian	riemannian	ADJ
ap-1271	9	10	metric	metric	NOUN
ap-1271	9	11	.	.	PUNCT
ap-1271	10	1	if	if	SCONJ
ap-1271	10	2	we	we	PRON
ap-1271	10	3	take	take	VERB
ap-1271	10	4	a	a	DET
ap-1271	10	5	local	local	ADJ
ap-1271	10	6	chart	chart	NOUN
ap-1271	10	7	(	(	PUNCT
ap-1271	10	8	u	u	NOUN
ap-1271	10	9	,	,	PUNCT
ap-1271	10	10	ϕ	ϕ	NOUN
ap-1271	10	11	)	)	PUNCT
ap-1271	10	12	,	,	PUNCT
ap-1271	10	13	ϕ	ϕ	X
ap-1271	10	14	=	=	SYM
ap-1271	10	15	(	(	PUNCT
ap-1271	10	16	x1	x1	PROPN
ap-1271	10	17	,	,	PUNCT
ap-1271	10	18	x2	x2	PROPN
ap-1271	10	19	)	)	PUNCT
ap-1271	10	20	,	,	PUNCT
ap-1271	10	21	the	the	DET
ap-1271	10	22	measure	measure	NOUN
ap-1271	10	23	dμ	dμ	VERB
ap-1271	10	24	is	be	AUX
ap-1271	10	25	written	write	VERB
ap-1271	10	26	as	as	ADP
ap-1271	10	27	dμ	dμ	NOUN
ap-1271	10	28	=	=	SYM
ap-1271	10	29	√	√	PROPN
ap-1271	10	30	gdx1dx2	gdx1dx2	NOUN
ap-1271	10	31	in	in	ADP
ap-1271	10	32	u	u	PROPN
ap-1271	10	33	,	,	PUNCT
ap-1271	10	34	where	where	SCONJ
ap-1271	10	35	g	g	NOUN
ap-1271	10	36	=	=	SYM
ap-1271	10	37	det(gmn	det(gmn	PROPN
ap-1271	10	38	)	)	PUNCT
ap-1271	10	39	,	,	PUNCT
ap-1271	10	40	gmn	gmn	NOUN
ap-1271	10	41	=	=	PUNCT
ap-1271	10	42	g(∂m	g(∂m	PROPN
ap-1271	10	43	,	,	PUNCT
ap-1271	10	44	∂n	∂n	PROPN
ap-1271	10	45	)	)	PUNCT
ap-1271	10	46	,	,	PUNCT
ap-1271	10	47	and	and	CCONJ
ap-1271	10	48	∂m	∂m	PROPN
ap-1271	10	49	=	=	PUNCT
ap-1271	10	50	∂/∂xm	∂/∂xm	PROPN
ap-1271	10	51	.	.	PUNCT
ap-1271	11	1	we	we	PRON
ap-1271	11	2	denote	denote	VERB
ap-1271	11	3	l2(m	l2(m	PRON
ap-1271	11	4	)	)	PUNCT
ap-1271	11	5	=	=	SYM
ap-1271	12	1	l2(m	l2(m	PROPN
ap-1271	12	2	;	;	PUNCT
ap-1271	12	3	dμ	dμ	X
ap-1271	12	4	)	)	PUNCT
ap-1271	12	5	.	.	PUNCT
ap-1271	13	1	the	the	DET
ap-1271	13	2	set	set	NOUN
ap-1271	13	3	of	of	ADP
ap-1271	13	4	all	all	DET
ap-1271	13	5	1	1	NUM
ap-1271	13	6	-	-	NOUN
ap-1271	13	7	forms	form	NOUN
ap-1271	13	8	on	on	ADP
ap-1271	13	9	m	m	PROPN
ap-1271	13	10	is	be	AUX
ap-1271	13	11	denoted	denote	VERB
ap-1271	13	12	by	by	ADP
ap-1271	13	13	λ1(m	λ1(m	NOUN
ap-1271	13	14	)	)	PUNCT
ap-1271	13	15	.	.	PUNCT
ap-1271	14	1	in	in	ADP
ap-1271	14	2	the	the	DET
ap-1271	14	3	coordinate	coordinate	ADJ
ap-1271	14	4	neighborhood	neighborhood	NOUN
ap-1271	14	5	u	u	NOUN
ap-1271	14	6	,	,	PUNCT
ap-1271	14	7	a	a	DET
ap-1271	14	8	∈	∈	PROPN
ap-1271	14	9	λ1(m	λ1(m	NOUN
ap-1271	14	10	)	)	PUNCT
ap-1271	14	11	is	be	AUX
ap-1271	14	12	written	write	VERB
ap-1271	14	13	as	as	ADP
ap-1271	14	14	a	a	DET
ap-1271	14	15	=	=	SYM
ap-1271	14	16	a1dx1	a1dx1	PROPN
ap-1271	14	17	+	+	NOUN
ap-1271	14	18	a2dx2	a2dx2	ADJ
ap-1271	14	19	.	.	PUNCT
ap-1271	15	1	in	in	ADP
ap-1271	15	2	general	general	ADJ
ap-1271	15	3	,	,	PUNCT
ap-1271	15	4	the	the	DET
ap-1271	15	5	coefficients	coefficient	NOUN
ap-1271	15	6	a1	a1	PROPN
ap-1271	15	7	,	,	PUNCT
ap-1271	15	8	a2	a2	NOUN
ap-1271	15	9	are	be	AUX
ap-1271	15	10	complexvalued	complexvalue	VERB
ap-1271	15	11	.	.	PUNCT
ap-1271	16	1	we	we	PRON
ap-1271	16	2	say	say	VERB
ap-1271	16	3	a	a	PRON
ap-1271	16	4	is	be	AUX
ap-1271	16	5	real	real	ADV
ap-1271	16	6	-	-	PUNCT
ap-1271	16	7	valued	value	VERB
ap-1271	16	8	if	if	SCONJ
ap-1271	16	9	the	the	DET
ap-1271	16	10	coefficients	coefficient	NOUN
ap-1271	16	11	are	be	AUX
ap-1271	16	12	real	real	ADV
ap-1271	16	13	-	-	PUNCT
ap-1271	16	14	valued	value	VERB
ap-1271	16	15	.	.	PUNCT
ap-1271	17	1	we	we	PRON
ap-1271	17	2	say	say	VERB
ap-1271	17	3	a	a	DET
ap-1271	17	4	is	be	AUX
ap-1271	17	5	of	of	ADP
ap-1271	17	6	the	the	DET
ap-1271	17	7	class	class	NOUN
ap-1271	17	8	ckλ1(m	ckλ1(m	NUM
ap-1271	17	9	)	)	PUNCT
ap-1271	17	10	if	if	SCONJ
ap-1271	17	11	the	the	DET
ap-1271	17	12	coefficients	coefficient	NOUN
ap-1271	17	13	are	be	AUX
ap-1271	17	14	of	of	ADP
ap-1271	17	15	the	the	DET
ap-1271	17	16	class	class	NOUN
ap-1271	17	17	ck(u	ck(u	PUNCT
ap-1271	17	18	)	)	PUNCT
ap-1271	17	19	for	for	ADP
ap-1271	17	20	any	any	DET
ap-1271	17	21	local	local	ADJ
ap-1271	17	22	chart	chart	NOUN
ap-1271	17	23	(	(	PUNCT
ap-1271	17	24	u	u	NOUN
ap-1271	17	25	,	,	PUNCT
ap-1271	17	26	ϕ	ϕ	NOUN
ap-1271	17	27	)	)	PUNCT
ap-1271	17	28	.	.	PUNCT
ap-1271	18	1	we	we	PRON
ap-1271	18	2	define	define	VERB
ap-1271	18	3	the	the	DET
ap-1271	18	4	class	class	NOUN
ap-1271	18	5	lq	lq	NOUN
ap-1271	18	6	locλ	locλ	NOUN
ap-1271	18	7	1(m	1(m	NUM
ap-1271	18	8	)	)	PUNCT
ap-1271	18	9	(	(	PUNCT
ap-1271	18	10	1	1	NUM
ap-1271	18	11	≤	≤	NUM
ap-1271	18	12	q	q	ADJ
ap-1271	18	13	≤	≤	ADJ
ap-1271	18	14	∞)1	∞)1	PROPN
ap-1271	18	15	,	,	PUNCT
ap-1271	18	16	etc	etc	X
ap-1271	18	17	.	.	X
ap-1271	18	18	similarly	similarly	ADV
ap-1271	18	19	.	.	PUNCT
ap-1271	19	1	the	the	DET
ap-1271	19	2	2	2	NUM
ap-1271	19	3	-	-	PUNCT
ap-1271	19	4	form	form	NOUN
ap-1271	19	5	da	da	NOUN
ap-1271	19	6	is	be	AUX
ap-1271	19	7	called	call	VERB
ap-1271	19	8	the	the	DET
ap-1271	19	9	magnetic	magnetic	ADJ
ap-1271	19	10	field	field	NOUN
ap-1271	19	11	.	.	PUNCT
ap-1271	20	1	if	if	SCONJ
ap-1271	20	2	a	a	DET
ap-1271	20	3	∈	∈	PROPN
ap-1271	20	4	l1locλ	l1locλ	NOUN
ap-1271	20	5	1(m	1(m	NUM
ap-1271	20	6	)	)	PUNCT
ap-1271	20	7	,	,	PUNCT
ap-1271	20	8	da	da	PROPN
ap-1271	20	9	can	can	AUX
ap-1271	20	10	be	be	AUX
ap-1271	20	11	defined	define	VERB
ap-1271	20	12	at	at	ADP
ap-1271	20	13	least	least	ADJ
ap-1271	20	14	in	in	ADP
ap-1271	20	15	the	the	DET
ap-1271	20	16	distribution	distribution	NOUN
ap-1271	20	17	sense	sense	NOUN
ap-1271	20	18	.	.	PUNCT
ap-1271	21	1	in	in	ADP
ap-1271	21	2	u	u	PROPN
ap-1271	21	3	,	,	PUNCT
ap-1271	21	4	the	the	DET
ap-1271	21	5	magnetic	magnetic	ADJ
ap-1271	21	6	field	field	NOUN
ap-1271	21	7	is	be	AUX
ap-1271	21	8	given	give	VERB
ap-1271	21	9	by	by	ADP
ap-1271	21	10	da	da	PROPN
ap-1271	21	11	=	=	SYM
ap-1271	21	12	(	(	PUNCT
ap-1271	21	13	∂1a2	∂1a2	INTJ
ap-1271	21	14	−	−	NOUN
ap-1271	22	1	∂2a1)dx1	∂2a1)dx1	PROPN
ap-1271	22	2	∧	∧	PROPN
ap-1271	22	3	dx2	dx2	PROPN
ap-1271	22	4	.	.	PUNCT
ap-1271	23	1	let	let	VERB
ap-1271	23	2	γ	γ	X
ap-1271	23	3	=	=	PRON
ap-1271	23	4	{	{	PUNCT
ap-1271	23	5	γk}k	γk}k	X
ap-1271	23	6	k=1	k=1	X
ap-1271	23	7	be	be	AUX
ap-1271	23	8	a	a	DET
ap-1271	23	9	sequence	sequence	NOUN
ap-1271	23	10	of	of	ADP
ap-1271	23	11	mutually	mutually	ADV
ap-1271	23	12	distinct	distinct	ADJ
ap-1271	23	13	points	point	NOUN
ap-1271	23	14	in	in	ADP
ap-1271	23	15	m	m	PROPN
ap-1271	23	16	.	.	PUNCT
ap-1271	24	1	the	the	DET
ap-1271	24	2	number	number	NOUN
ap-1271	24	3	k	k	PROPN
ap-1271	24	4	may	may	AUX
ap-1271	24	5	be	be	AUX
ap-1271	24	6	infinity	infinity	NOUN
ap-1271	24	7	,	,	PUNCT
ap-1271	24	8	and	and	CCONJ
ap-1271	24	9	in	in	ADP
ap-1271	24	10	this	this	DET
ap-1271	24	11	case	case	NOUN
ap-1271	24	12	we	we	PRON
ap-1271	24	13	assume	assume	VERB
ap-1271	24	14	additionally	additionally	ADV
ap-1271	24	15	γ	γ	PROPN
ap-1271	24	16	has	have	VERB
ap-1271	24	17	no	no	DET
ap-1271	24	18	accumulation	accumulation	NOUN
ap-1271	24	19	points	point	NOUN
ap-1271	24	20	in	in	ADP
ap-1271	24	21	m	m	PROPN
ap-1271	24	22	.	.	PUNCT
ap-1271	25	1	let	let	VERB
ap-1271	25	2	a	a	PRON
ap-1271	25	3	be	be	AUX
ap-1271	25	4	a	a	DET
ap-1271	25	5	1	1	NUM
ap-1271	25	6	-	-	PUNCT
ap-1271	25	7	form	form	NOUN
ap-1271	25	8	on	on	ADP
ap-1271	25	9	m	m	AUX
ap-1271	25	10	given	give	VERB
ap-1271	25	11	by	by	ADP
ap-1271	25	12	the	the	DET
ap-1271	25	13	sum	sum	NOUN
ap-1271	25	14	of	of	ADP
ap-1271	25	15	two	two	NUM
ap-1271	25	16	1	1	NUM
ap-1271	25	17	-	-	PUNCT
ap-1271	25	18	forms	form	NOUN
ap-1271	25	19	(	(	PUNCT
ap-1271	25	20	a	a	NOUN
ap-1271	25	21	)	)	PUNCT
ap-1271	25	22	a	a	PRON
ap-1271	25	23	=	=	PUNCT
ap-1271	25	24	a(0	a(0	PROPN
ap-1271	25	25	)	)	PUNCT
ap-1271	26	1	+	+	NOUN
ap-1271	26	2	a(1	a(1	NOUN
ap-1271	26	3	)	)	PUNCT
ap-1271	26	4	.	.	PUNCT
ap-1271	27	1	the	the	DET
ap-1271	27	2	part	part	NOUN
ap-1271	27	3	a(0	a(0	VERB
ap-1271	27	4	)	)	PUNCT
ap-1271	27	5	corresponds	correspond	VERB
ap-1271	27	6	to	to	ADP
ap-1271	27	7	the	the	DET
ap-1271	27	8	δ	δ	PROPN
ap-1271	27	9	magnetic	magnetic	ADJ
ap-1271	27	10	fields	field	NOUN
ap-1271	27	11	,	,	PUNCT
ap-1271	27	12	that	that	ADV
ap-1271	27	13	is	is	ADV
ap-1271	27	14	,	,	PUNCT
ap-1271	27	15	we	we	PRON
ap-1271	27	16	assume	assume	VERB
ap-1271	27	17	the	the	DET
ap-1271	27	18	following	following	NOUN
ap-1271	27	19	.	.	PUNCT
ap-1271	28	1	(	(	PUNCT
ap-1271	28	2	a0	a0	NOUN
ap-1271	28	3	)	)	PUNCT
ap-1271	28	4	a(0	a(0	PROPN
ap-1271	28	5	)	)	PUNCT
ap-1271	28	6	∈	∈	PROPN
ap-1271	28	7	c∞λ1(m	c∞λ1(m	PROPN
ap-1271	28	8	\γ)∩l1locλ	\γ)∩l1locλ	PROPN
ap-1271	28	9	1(m	1(m	NUM
ap-1271	28	10	)	)	PUNCT
ap-1271	28	11	,	,	PUNCT
ap-1271	28	12	real	real	ADV
ap-1271	28	13	-	-	PUNCT
ap-1271	28	14	valued	value	VERB
ap-1271	28	15	,	,	PUNCT
ap-1271	28	16	and	and	CCONJ
ap-1271	28	17	da(0	da(0	NOUN
ap-1271	28	18	)	)	PUNCT
ap-1271	28	19	=	=	VERB
ap-1271	29	1	k∑	k∑	VERB
ap-1271	30	1	k=1	k=1	X
ap-1271	30	2	2παkδγk	2παkδγk	NUM
ap-1271	30	3	,	,	PUNCT
ap-1271	30	4	(	(	PUNCT
ap-1271	30	5	1	1	X
ap-1271	30	6	)	)	PUNCT
ap-1271	30	7	where	where	SCONJ
ap-1271	30	8	αk	αk	AUX
ap-1271	30	9	∈	∈	PROPN
ap-1271	30	10	r	r	NOUN
ap-1271	30	11	,	,	PUNCT
ap-1271	30	12	and	and	CCONJ
ap-1271	30	13	δγ	δγ	PROPN
ap-1271	30	14	is	be	AUX
ap-1271	30	15	the	the	DET
ap-1271	30	16	dirac	dirac	NOUN
ap-1271	30	17	measure	measure	NOUN
ap-1271	30	18	concentrated	concentrate	VERB
ap-1271	30	19	on	on	ADP
ap-1271	30	20	the	the	DET
ap-1271	30	21	point	point	NOUN
ap-1271	30	22	γ	γ	X
ap-1271	30	23	.	.	PROPN
ap-1271	30	24	more	more	ADV
ap-1271	30	25	precisely	precisely	ADV
ap-1271	30	26	,	,	PUNCT
ap-1271	30	27	(	(	PUNCT
ap-1271	30	28	1	1	X
ap-1271	30	29	)	)	PUNCT
ap-1271	30	30	means	mean	VERB
ap-1271	30	31	−	−	PROPN
ap-1271	30	32	∫	∫	PROPN
ap-1271	30	33	m	m	PROPN
ap-1271	30	34	dϕ	dϕ	PROPN
ap-1271	30	35	∧	∧	PROPN
ap-1271	30	36	a(0	a(0	PROPN
ap-1271	30	37	)	)	PUNCT
ap-1271	30	38	=	=	VERB
ap-1271	31	1	k∑	k∑	VERB
ap-1271	31	2	k=1	k=1	PROPN
ap-1271	32	1	2παkϕ(γk	2παkϕ(γk	NUM
ap-1271	32	2	)	)	PUNCT
ap-1271	32	3	,	,	PUNCT
ap-1271	32	4	for	for	ADP
ap-1271	32	5	any	any	DET
ap-1271	32	6	ϕ	ϕ	PROPN
ap-1271	32	7	∈	∈	PROPN
ap-1271	32	8	c∞	c∞	PROPN
ap-1271	32	9	0	0	NUM
ap-1271	32	10	(	(	PUNCT
ap-1271	32	11	m	m	NOUN
ap-1271	32	12	)	)	PUNCT
ap-1271	32	13	(	(	PUNCT
ap-1271	32	14	since	since	SCONJ
ap-1271	32	15	a(0	a(0	PROPN
ap-1271	32	16	)	)	PUNCT
ap-1271	32	17	∈	∈	PROPN
ap-1271	32	18	l1locλ	l1locλ	NOUN
ap-1271	32	19	1(m	1(m	NUM
ap-1271	32	20	)	)	PUNCT
ap-1271	32	21	,	,	PUNCT
ap-1271	32	22	the	the	DET
ap-1271	32	23	left	left	ADJ
ap-1271	32	24	hand	hand	NOUN
ap-1271	32	25	side	side	NOUN
ap-1271	32	26	is	be	AUX
ap-1271	32	27	well	well	ADV
ap-1271	32	28	-	-	PUNCT
ap-1271	32	29	defined	define	VERB
ap-1271	32	30	)	)	PUNCT
ap-1271	32	31	.	.	PUNCT
ap-1271	33	1	notice	notice	VERB
ap-1271	33	2	that	that	SCONJ
ap-1271	33	3	this	this	DET
ap-1271	33	4	equation	equation	NOUN
ap-1271	33	5	is	be	AUX
ap-1271	33	6	independent	independent	ADJ
ap-1271	33	7	of	of	ADP
ap-1271	33	8	the	the	DET
ap-1271	33	9	riemannian	riemannian	ADJ
ap-1271	33	10	metric	metric	ADJ
ap-1271	33	11	g.	g.	PROPN
ap-1271	33	12	for	for	ADP
ap-1271	33	13	the	the	DET
ap-1271	33	14	regular	regular	ADJ
ap-1271	33	15	part	part	NOUN
ap-1271	33	16	a(1	a(1	ADJ
ap-1271	33	17	)	)	PUNCT
ap-1271	33	18	and	and	CCONJ
ap-1271	33	19	the	the	DET
ap-1271	33	20	scalar	scalar	ADJ
ap-1271	33	21	potential	potential	ADJ
ap-1271	33	22	v	v	NOUN
ap-1271	33	23	,	,	PUNCT
ap-1271	33	24	we	we	PRON
ap-1271	33	25	assume	assume	VERB
ap-1271	33	26	the	the	DET
ap-1271	33	27	following	follow	VERB
ap-1271	33	28	:	:	PUNCT
ap-1271	33	29	(	(	PUNCT
ap-1271	33	30	a1	a1	NOUN
ap-1271	33	31	)	)	PUNCT
ap-1271	33	32	a(1	a(1	ADJ
ap-1271	33	33	)	)	PUNCT
ap-1271	33	34	∈	∈	PROPN
ap-1271	33	35	c1λ1(m	c1λ1(m	PROPN
ap-1271	33	36	)	)	PUNCT
ap-1271	33	37	,	,	PUNCT
ap-1271	33	38	real	real	ADV
ap-1271	33	39	-	-	PUNCT
ap-1271	33	40	valued	value	VERB
ap-1271	33	41	.	.	PUNCT
ap-1271	34	1	(	(	PUNCT
ap-1271	34	2	v	v	NOUN
ap-1271	34	3	)	)	PUNCT
ap-1271	34	4	v	v	NOUN
ap-1271	34	5	is	be	AUX
ap-1271	34	6	real	real	ADV
ap-1271	34	7	-	-	PUNCT
ap-1271	34	8	valued	value	VERB
ap-1271	34	9	,	,	PUNCT
ap-1271	34	10	v	v	ADP
ap-1271	34	11	∈	∈	PROPN
ap-1271	34	12	l2loc(m	l2loc(m	NOUN
ap-1271	34	13	)	)	PUNCT
ap-1271	34	14	,	,	PUNCT
ap-1271	34	15	and	and	CCONJ
ap-1271	34	16	is	be	AUX
ap-1271	34	17	bounded	bound	VERB
ap-1271	34	18	in	in	ADP
ap-1271	34	19	some	some	DET
ap-1271	34	20	open	open	ADJ
ap-1271	34	21	neighborhood	neighborhood	NOUN
ap-1271	34	22	of	of	ADP
ap-1271	34	23	γk	γk	NOUN
ap-1271	34	24	for	for	ADP
ap-1271	34	25	every	every	DET
ap-1271	34	26	k	k	NOUN
ap-1271	34	27	=	=	SYM
ap-1271	34	28	1	1	NUM
ap-1271	34	29	,	,	PUNCT
ap-1271	34	30	.	.	PUNCT
ap-1271	34	31	.	.	PUNCT
ap-1271	35	1	.	.	PUNCT
ap-1271	36	1	,	,	PUNCT
ap-1271	36	2	k.	k.	PROPN
ap-1271	36	3	using	use	VERB
ap-1271	36	4	the	the	DET
ap-1271	36	5	local	local	ADJ
ap-1271	36	6	coordinate	coordinate	NOUN
ap-1271	36	7	(	(	PUNCT
ap-1271	36	8	x1	x1	PROPN
ap-1271	36	9	,	,	PUNCT
ap-1271	36	10	x2	x2	PROPN
ap-1271	36	11	)	)	PUNCT
ap-1271	36	12	,	,	PUNCT
ap-1271	36	13	we	we	PRON
ap-1271	36	14	define	define	VERB
ap-1271	36	15	the	the	DET
ap-1271	36	16	schrödinger	schrödinger	NOUN
ap-1271	36	17	operator	operator	NOUN
ap-1271	36	18	l	l	NOUN
ap-1271	36	19	in	in	ADP
ap-1271	36	20	each	each	DET
ap-1271	36	21	coordinate	coordinate	ADJ
ap-1271	36	22	neighborhood	neighborhood	NOUN
ap-1271	36	23	by	by	ADP
ap-1271	36	24	lu	lu	PROPN
ap-1271	36	25	=	=	SYM
ap-1271	36	26	−	−	PROPN
ap-1271	36	27	1√	1√	PROPN
ap-1271	36	28	g	g	PROPN
ap-1271	36	29	∑	∑	PROPN
ap-1271	36	30	m	m	PROPN
ap-1271	36	31	,	,	PUNCT
ap-1271	36	32	n=1,2	n=1,2	ADJ
ap-1271	36	33	(	(	PUNCT
ap-1271	36	34	∂m	∂m	PROPN
ap-1271	36	35	+	+	CCONJ
ap-1271	36	36	iam	iam	PROPN
ap-1271	36	37	)	)	PUNCT
ap-1271	36	38	·	·	PUNCT
ap-1271	36	39	(	(	PUNCT
ap-1271	36	40	√	√	ADP
ap-1271	36	41	ggmn(∂n	ggmn(∂n	PROPN
ap-1271	36	42	+	+	PROPN
ap-1271	36	43	ian)u	ian)u	PROPN
ap-1271	36	44	)	)	PUNCT
ap-1271	37	1	+	+	CCONJ
ap-1271	37	2	v	v	NUM
ap-1271	37	3	u	u	NOUN
ap-1271	37	4	,	,	PUNCT
ap-1271	37	5	1the	1the	PRON
ap-1271	37	6	measure	measure	NOUN
ap-1271	37	7	dμ	dμ	ADJ
ap-1271	37	8	is	be	AUX
ap-1271	37	9	omitted	omit	VERB
ap-1271	37	10	,	,	PUNCT
ap-1271	37	11	since	since	SCONJ
ap-1271	37	12	the	the	DET
ap-1271	37	13	class	class	NOUN
ap-1271	37	14	lq	lq	VERB
ap-1271	37	15	locλ	locλ	NOUN
ap-1271	37	16	1(m	1(m	NUM
ap-1271	37	17	;	;	PUNCT
ap-1271	37	18	dμ	dμ	X
ap-1271	37	19	)	)	PUNCT
ap-1271	37	20	is	be	AUX
ap-1271	37	21	independent	independent	ADJ
ap-1271	37	22	of	of	ADP
ap-1271	37	23	the	the	DET
ap-1271	37	24	choice	choice	NOUN
ap-1271	37	25	of	of	ADP
ap-1271	37	26	dμ	dμ	NOUN
ap-1271	37	27	.	.	PUNCT
ap-1271	38	1	the	the	DET
ap-1271	38	2	coefficient	coefficient	NOUN
ap-1271	38	3	am	be	AUX
ap-1271	38	4	is	be	AUX
ap-1271	38	5	a	a	DET
ap-1271	38	6	function	function	NOUN
ap-1271	38	7	on	on	ADP
ap-1271	38	8	u	u	PROPN
ap-1271	38	9	⊂	⊂	PROPN
ap-1271	38	10	m	m	INTJ
ap-1271	38	11	,	,	PUNCT
ap-1271	38	12	however	however	ADV
ap-1271	38	13	,	,	PUNCT
ap-1271	38	14	we	we	PRON
ap-1271	38	15	denote	denote	VERB
ap-1271	38	16	the	the	DET
ap-1271	38	17	pull	pull	NOUN
ap-1271	38	18	-	-	PUNCT
ap-1271	38	19	back	back	NOUN
ap-1271	38	20	(	(	PUNCT
ap-1271	38	21	ϕ−1)∗am	ϕ−1)∗am	VERB
ap-1271	38	22	=	=	PRON
ap-1271	38	23	am	be	AUX
ap-1271	38	24	◦	◦	NOUN
ap-1271	38	25	ϕ−1	ϕ−1	X
ap-1271	38	26	on	on	ADP
ap-1271	38	27	ϕ(u	ϕ(u	NOUN
ap-1271	38	28	)	)	PUNCT
ap-1271	39	1	⊂	⊂	PROPN
ap-1271	39	2	r2	r2	PROPN
ap-1271	39	3	by	by	ADP
ap-1271	39	4	the	the	DET
ap-1271	39	5	same	same	ADJ
ap-1271	39	6	symbol	symbol	NOUN
ap-1271	39	7	am	be	AUX
ap-1271	39	8	,	,	PUNCT
ap-1271	39	9	for	for	ADP
ap-1271	39	10	simplicity	simplicity	NOUN
ap-1271	39	11	of	of	ADP
ap-1271	39	12	notations	notation	NOUN
ap-1271	39	13	.	.	PUNCT
ap-1271	40	1	this	this	DET
ap-1271	40	2	convention	convention	NOUN
ap-1271	40	3	is	be	AUX
ap-1271	40	4	frequently	frequently	ADV
ap-1271	40	5	used	use	VERB
ap-1271	40	6	in	in	ADP
ap-1271	40	7	this	this	DET
ap-1271	40	8	paper	paper	NOUN
ap-1271	40	9	.	.	PUNCT
ap-1271	41	1	62	62	NUM
ap-1271	41	2	acta	acta	PROPN
ap-1271	41	3	polytechnica	polytechnica	PROPN
ap-1271	41	4	vol	vol	NOUN
ap-1271	41	5	.	.	PROPN
ap-1271	42	1	50	50	NUM
ap-1271	42	2	no	no	NOUN
ap-1271	42	3	.	.	PUNCT
ap-1271	43	1	5/2010	5/2010	NUM
ap-1271	43	2	where	where	SCONJ
ap-1271	43	3	(	(	PUNCT
ap-1271	43	4	gmn	gmn	NOUN
ap-1271	43	5	)	)	PUNCT
ap-1271	43	6	is	be	AUX
ap-1271	43	7	the	the	DET
ap-1271	43	8	inverse	inverse	ADJ
ap-1271	43	9	matrix	matrix	NOUN
ap-1271	43	10	of	of	ADP
ap-1271	43	11	(	(	PUNCT
ap-1271	43	12	gmn	gmn	NOUN
ap-1271	43	13	)	)	PUNCT
ap-1271	43	14	.	.	PUNCT
ap-1271	44	1	this	this	DET
ap-1271	44	2	definition	definition	NOUN
ap-1271	44	3	is	be	AUX
ap-1271	44	4	independent	independent	ADJ
ap-1271	44	5	of	of	ADP
ap-1271	44	6	the	the	DET
ap-1271	44	7	choice	choice	NOUN
ap-1271	44	8	of	of	ADP
ap-1271	44	9	local	local	ADJ
ap-1271	44	10	coordinates	coordinate	NOUN
ap-1271	44	11	(	(	PUNCT
ap-1271	44	12	see	see	VERB
ap-1271	44	13	section	section	NOUN
ap-1271	44	14	2	2	NUM
ap-1271	44	15	)	)	PUNCT
ap-1271	44	16	.	.	PUNCT
ap-1271	45	1	define	define	VERB
ap-1271	45	2	the	the	DET
ap-1271	45	3	minimal	minimal	ADJ
ap-1271	45	4	operator	operator	NOUN
ap-1271	45	5	hmin	hmin	NOUN
ap-1271	45	6	by	by	ADP
ap-1271	45	7	hminu	hminu	NOUN
ap-1271	45	8	=	=	SYM
ap-1271	45	9	lu	lu	PROPN
ap-1271	45	10	,	,	PUNCT
ap-1271	45	11	d(hmin	d(hmin	PROPN
ap-1271	45	12	)	)	PUNCT
ap-1271	45	13	=	=	PRON
ap-1271	46	1	c∞	c∞	PROPN
ap-1271	46	2	0	0	PUNCT
ap-1271	47	1	(	(	PUNCT
ap-1271	47	2	m	m	PROPN
ap-1271	47	3	\	\	PROPN
ap-1271	47	4	γ	γ	NOUN
ap-1271	47	5	)	)	PUNCT
ap-1271	47	6	,	,	PUNCT
ap-1271	47	7	where	where	SCONJ
ap-1271	47	8	the	the	DET
ap-1271	47	9	overline	overline	NOUN
ap-1271	47	10	denotes	denote	VERB
ap-1271	47	11	the	the	DET
ap-1271	47	12	closure	closure	NOUN
ap-1271	47	13	with	with	ADP
ap-1271	47	14	respect	respect	NOUN
ap-1271	47	15	to	to	ADP
ap-1271	47	16	the	the	DET
ap-1271	47	17	graph	graph	NOUN
ap-1271	47	18	norm	norm	NOUN
ap-1271	47	19	.	.	PUNCT
ap-1271	48	1	define	define	VERB
ap-1271	48	2	the	the	DET
ap-1271	48	3	maximal	maximal	ADJ
ap-1271	48	4	operator	operator	NOUN
ap-1271	48	5	hmax	hmax	VERB
ap-1271	48	6	by	by	ADP
ap-1271	48	7	hmax	hmax	PROPN
ap-1271	48	8	=	=	SYM
ap-1271	48	9	h∗	h∗	PROPN
ap-1271	48	10	min	min	PROPN
ap-1271	48	11	.	.	PROPN
ap-1271	48	12	then	then	ADV
ap-1271	48	13	we	we	PRON
ap-1271	48	14	can	can	AUX
ap-1271	48	15	show	show	VERB
ap-1271	48	16	that	that	DET
ap-1271	48	17	hmaxu	hmaxu	NOUN
ap-1271	48	18	=	=	SYM
ap-1271	48	19	lu	lu	PROPN
ap-1271	48	20	,	,	PUNCT
ap-1271	48	21	d(hmax	d(hmax	NOUN
ap-1271	48	22	)	)	PUNCT
ap-1271	48	23	=	=	PUNCT
ap-1271	49	1	{	{	PUNCT
ap-1271	49	2	u	u	X
ap-1271	49	3	∈	∈	PROPN
ap-1271	49	4	l2(m	l2(m	NOUN
ap-1271	49	5	)	)	PUNCT
ap-1271	50	1	|	|	ADV
ap-1271	50	2	lu	lu	PROPN
ap-1271	50	3	∈	∈	PROPN
ap-1271	50	4	l2(m	l2(m	PROPN
ap-1271	50	5	)	)	PUNCT
ap-1271	50	6	}	}	PUNCT
ap-1271	50	7	,	,	PUNCT
ap-1271	50	8	where	where	SCONJ
ap-1271	50	9	l	l	NOUN
ap-1271	50	10	is	be	AUX
ap-1271	50	11	a	a	DET
ap-1271	50	12	differential	differential	ADJ
ap-1271	50	13	operator	operator	NOUN
ap-1271	50	14	on	on	ADP
ap-1271	50	15	d′(m	d′(m	DET
ap-1271	50	16	\	\	PROPN
ap-1271	50	17	γ	γ	X
ap-1271	50	18	)	)	PUNCT
ap-1271	50	19	.	.	PUNCT
ap-1271	51	1	we	we	PRON
ap-1271	51	2	assume	assume	VERB
ap-1271	51	3	(	(	PUNCT
ap-1271	51	4	sb	sb	X
ap-1271	51	5	)	)	PUNCT
ap-1271	51	6	the	the	DET
ap-1271	51	7	operator	operator	NOUN
ap-1271	51	8	hmin	hmin	NOUN
ap-1271	51	9	is	be	AUX
ap-1271	51	10	bounded	bound	VERB
ap-1271	51	11	from	from	ADP
ap-1271	51	12	below	below	ADV
ap-1271	51	13	.	.	PUNCT
ap-1271	52	1	in	in	ADP
ap-1271	52	2	the	the	DET
ap-1271	52	3	case	case	NOUN
ap-1271	52	4	m	m	NOUN
ap-1271	52	5	is	be	AUX
ap-1271	52	6	the	the	DET
ap-1271	52	7	flat	flat	ADJ
ap-1271	52	8	euclidean	euclidean	ADJ
ap-1271	52	9	plane	plane	NOUN
ap-1271	52	10	,	,	PUNCT
ap-1271	52	11	it	it	PRON
ap-1271	52	12	is	be	AUX
ap-1271	52	13	well	well	ADV
ap-1271	52	14	-	-	PUNCT
ap-1271	52	15	known	know	VERB
ap-1271	52	16	that	that	SCONJ
ap-1271	52	17	the	the	DET
ap-1271	52	18	operator	operator	NOUN
ap-1271	52	19	hmin	hmin	NOUN
ap-1271	52	20	is	be	AUX
ap-1271	52	21	not	not	PART
ap-1271	52	22	essentially	essentially	ADV
ap-1271	52	23	self	self	NOUN
ap-1271	52	24	-	-	PUNCT
ap-1271	52	25	adjoint	adjoint	NOUN
ap-1271	52	26	and	and	CCONJ
ap-1271	52	27	the	the	DET
ap-1271	52	28	structure	structure	NOUN
ap-1271	52	29	of	of	ADP
ap-1271	52	30	the	the	DET
ap-1271	52	31	self	self	NOUN
ap-1271	52	32	-	-	PUNCT
ap-1271	52	33	adjoint	adjoint	NOUN
ap-1271	52	34	extensions	extension	NOUN
ap-1271	52	35	ofhmin	ofhmin	ADJ
ap-1271	52	36	can	can	AUX
ap-1271	52	37	be	be	AUX
ap-1271	52	38	determined	determine	VERB
ap-1271	52	39	via	via	ADP
ap-1271	52	40	the	the	DET
ap-1271	52	41	celebrated	celebrate	VERB
ap-1271	52	42	krein	krein	PROPN
ap-1271	52	43	-	-	PUNCT
ap-1271	52	44	von	von	PROPN
ap-1271	52	45	neumann	neumann	PROPN
ap-1271	52	46	theory	theory	NOUN
ap-1271	52	47	of	of	ADP
ap-1271	52	48	self	self	NOUN
ap-1271	52	49	-	-	PUNCT
ap-1271	52	50	adjoint	adjoint	NOUN
ap-1271	52	51	extensions	extension	NOUN
ap-1271	52	52	(	(	PUNCT
ap-1271	52	53	see	see	VERB
ap-1271	52	54	e.g.	e.g.	ADV
ap-1271	52	55	reed	reed	NOUN
ap-1271	52	56	-	-	PUNCT
ap-1271	52	57	simon	simon	PROPN
ap-1271	52	58	[	[	X
ap-1271	52	59	13	13	NUM
ap-1271	52	60	]	]	PUNCT
ap-1271	52	61	)	)	PUNCT
ap-1271	52	62	.	.	PUNCT
ap-1271	53	1	in	in	ADP
ap-1271	53	2	the	the	DET
ap-1271	53	3	textbook	textbook	NOUN
ap-1271	53	4	by	by	ADP
ap-1271	53	5	albeverio	albeverio	PROPN
ap-1271	53	6	et	et	PROPN
ap-1271	53	7	al	al	PROPN
ap-1271	53	8	.	.	PUNCT
ap-1271	54	1	[	[	X
ap-1271	54	2	3	3	NUM
ap-1271	54	3	]	]	PUNCT
ap-1271	54	4	,	,	PUNCT
ap-1271	54	5	the	the	DET
ap-1271	54	6	case	case	NOUN
ap-1271	54	7	a(0	a(0	VERB
ap-1271	54	8	)	)	PUNCT
ap-1271	54	9	=	=	PUNCT
ap-1271	55	1	a(1	a(1	PROPN
ap-1271	55	2	)	)	PUNCT
ap-1271	55	3	=	=	SYM
ap-1271	55	4	0	0	NUM
ap-1271	55	5	and	and	CCONJ
ap-1271	55	6	v	v	NOUN
ap-1271	55	7	=	=	SYM
ap-1271	55	8	0	0	PUNCT
ap-1271	55	9	(	(	PUNCT
ap-1271	55	10	but	but	CCONJ
ap-1271	55	11	γ	γ	X
ap-1271	55	12	=	=	PUNCT
ap-1271	55	13	∅	∅	NOUN
ap-1271	55	14	)	)	PUNCT
ap-1271	55	15	is	be	AUX
ap-1271	55	16	exhaustively	exhaustively	ADV
ap-1271	55	17	studied	study	VERB
ap-1271	55	18	.	.	PUNCT
ap-1271	56	1	adamiteta	adamiteta	PROPN
ap-1271	57	1	[	[	X
ap-1271	57	2	1	1	NUM
ap-1271	57	3	]	]	PUNCT
ap-1271	57	4	and	and	CCONJ
ap-1271	57	5	dabrowski	dabrowski	NOUN
ap-1271	57	6	-	-	PUNCT
ap-1271	57	7	šťovíček	šťovíček	VERB
ap-1271	57	8	[	[	X
ap-1271	57	9	7	7	X
ap-1271	57	10	]	]	PUNCT
ap-1271	57	11	study	study	VERB
ap-1271	57	12	the	the	DET
ap-1271	57	13	case	case	NOUN
ap-1271	57	14	k	k	X
ap-1271	57	15	=	=	SYM
ap-1271	57	16	1	1	NUM
ap-1271	57	17	,	,	PUNCT
ap-1271	57	18	α1	α1	PROPN
ap-1271	57	19	∈	∈	PROPN
ap-1271	57	20	z	z	PROPN
ap-1271	57	21	,	,	PUNCT
ap-1271	57	22	a(1	a(1	ADJ
ap-1271	57	23	)	)	PUNCT
ap-1271	57	24	=	=	SYM
ap-1271	57	25	0	0	NUM
ap-1271	57	26	,	,	PUNCT
ap-1271	57	27	and	and	CCONJ
ap-1271	57	28	v	v	X
ap-1271	57	29	=	=	SYM
ap-1271	57	30	0	0	PROPN
ap-1271	57	31	.	.	PUNCT
ap-1271	57	32	exneršťovíček	exneršťovíček	PROPN
ap-1271	57	33	-	-	PUNCT
ap-1271	57	34	vytřas	vytřas	NOUN
ap-1271	58	1	[	[	X
ap-1271	58	2	8	8	NUM
ap-1271	58	3	]	]	PUNCT
ap-1271	58	4	study	study	VERB
ap-1271	58	5	the	the	DET
ap-1271	58	6	case	case	NOUN
ap-1271	58	7	k	k	X
ap-1271	58	8	=	=	SYM
ap-1271	58	9	1	1	NUM
ap-1271	58	10	,	,	PUNCT
ap-1271	58	11	α1	α1	PROPN
ap-1271	58	12	∈	∈	PROPN
ap-1271	58	13	z	z	PROPN
ap-1271	58	14	,	,	PUNCT
ap-1271	58	15	da(1	da(1	NOUN
ap-1271	58	16	)	)	PUNCT
ap-1271	58	17	=	=	SYM
ap-1271	58	18	bdx1	bdx1	PROPN
ap-1271	58	19	∧	∧	PROPN
ap-1271	58	20	dx2	dx2	PROPN
ap-1271	58	21	for	for	ADP
ap-1271	58	22	some	some	DET
ap-1271	58	23	non	non	ADJ
ap-1271	58	24	-	-	ADJ
ap-1271	58	25	zero	zero	ADJ
ap-1271	58	26	constant	constant	ADJ
ap-1271	58	27	b	b	NOUN
ap-1271	58	28	(	(	PUNCT
ap-1271	58	29	the	the	DET
ap-1271	58	30	constant	constant	ADJ
ap-1271	58	31	magnetic	magnetic	ADJ
ap-1271	58	32	field	field	NOUN
ap-1271	58	33	)	)	PUNCT
ap-1271	58	34	,	,	PUNCT
ap-1271	58	35	and	and	CCONJ
ap-1271	58	36	v	v	X
ap-1271	58	37	=	=	SYM
ap-1271	58	38	0	0	NUM
ap-1271	58	39	.	.	PUNCT
ap-1271	59	1	moreover	moreover	ADV
ap-1271	59	2	,	,	PUNCT
ap-1271	59	3	lisovyy	lisovyy	NOUN
ap-1271	59	4	[	[	X
ap-1271	59	5	11	11	NUM
ap-1271	59	6	]	]	PUNCT
ap-1271	59	7	studies	study	NOUN
ap-1271	59	8	the	the	DET
ap-1271	59	9	casem	casem	NOUN
ap-1271	59	10	is	be	AUX
ap-1271	59	11	the	the	DET
ap-1271	59	12	poincaré	poincaré	ADJ
ap-1271	59	13	disk	disk	NOUN
ap-1271	59	14	,	,	PUNCT
ap-1271	59	15	g	g	PROPN
ap-1271	59	16	is	be	AUX
ap-1271	59	17	the	the	DET
ap-1271	59	18	poincaré	poincaré	ADJ
ap-1271	59	19	metric	metric	NOUN
ap-1271	59	20	,	,	PUNCT
ap-1271	59	21	v	v	NOUN
ap-1271	59	22	=	=	SYM
ap-1271	59	23	0	0	NUM
ap-1271	59	24	and	and	CCONJ
ap-1271	59	25	da	da	NOUN
ap-1271	59	26	=	=	SYM
ap-1271	59	27	bωg+2παδ0	bωg+2παδ0	PROPN
ap-1271	59	28	,	,	PUNCT
ap-1271	59	29	where	where	SCONJ
ap-1271	59	30	b	b	NOUN
ap-1271	59	31	is	be	AUX
ap-1271	59	32	a	a	DET
ap-1271	59	33	non	non	ADJ
ap-1271	59	34	-	-	ADJ
ap-1271	59	35	zero	zero	ADJ
ap-1271	59	36	constant	constant	ADJ
ap-1271	59	37	and	and	CCONJ
ap-1271	59	38	ωg	ωg	PROPN
ap-1271	59	39	is	be	AUX
ap-1271	59	40	the	the	DET
ap-1271	59	41	surface	surface	NOUN
ap-1271	59	42	form	form	NOUN
ap-1271	59	43	induced	induce	VERB
ap-1271	59	44	from	from	ADP
ap-1271	59	45	the	the	DET
ap-1271	59	46	poincaré	poincaré	ADJ
ap-1271	59	47	metric	metric	ADJ
ap-1271	59	48	g.	g.	PROPN
ap-1271	59	49	in	in	ADP
ap-1271	59	50	all	all	DET
ap-1271	59	51	the	the	DET
ap-1271	59	52	results	result	NOUN
ap-1271	59	53	above	above	ADV
ap-1271	59	54	,	,	PUNCT
ap-1271	59	55	they	they	PRON
ap-1271	59	56	first	first	ADV
ap-1271	59	57	determine	determine	VERB
ap-1271	59	58	the	the	DET
ap-1271	59	59	deficiency	deficiency	NOUN
ap-1271	59	60	subspaces	subspace	VERB
ap-1271	59	61	ker(hmax	ker(hmax	PROPN
ap-1271	59	62	∓	∓	PROPN
ap-1271	59	63	i	i	X
ap-1271	59	64	)	)	PUNCT
ap-1271	59	65	and	and	CCONJ
ap-1271	59	66	apply	apply	VERB
ap-1271	59	67	the	the	DET
ap-1271	59	68	krein	krein	PROPN
ap-1271	59	69	-	-	PUNCT
ap-1271	59	70	von	von	PROPN
ap-1271	59	71	neumann	neumann	PROPN
ap-1271	59	72	theory	theory	PROPN
ap-1271	59	73	.	.	PUNCT
ap-1271	60	1	this	this	DET
ap-1271	60	2	method	method	NOUN
ap-1271	60	3	can	can	AUX
ap-1271	60	4	not	not	PART
ap-1271	60	5	be	be	AUX
ap-1271	60	6	applied	apply	VERB
ap-1271	60	7	in	in	ADP
ap-1271	60	8	the	the	DET
ap-1271	60	9	case	case	NOUN
ap-1271	60	10	k	k	PROPN
ap-1271	60	11	≥	≥	NUM
ap-1271	60	12	2	2	NUM
ap-1271	60	13	and	and	CCONJ
ap-1271	60	14	αk	αk	ADP
ap-1271	60	15	∈	∈	PROPN
ap-1271	60	16	z	z	PROPN
ap-1271	60	17	,	,	PUNCT
ap-1271	60	18	however	however	ADV
ap-1271	60	19	,	,	PUNCT
ap-1271	60	20	this	this	DET
ap-1271	60	21	case	case	NOUN
ap-1271	60	22	(	(	PUNCT
ap-1271	60	23	and	and	CCONJ
ap-1271	60	24	a(1	a(1	ADJ
ap-1271	60	25	)	)	PUNCT
ap-1271	60	26	is	be	AUX
ap-1271	60	27	the	the	DET
ap-1271	60	28	constant	constant	ADJ
ap-1271	60	29	field	field	NOUN
ap-1271	60	30	,	,	PUNCT
ap-1271	60	31	v	v	NOUN
ap-1271	60	32	=	=	SYM
ap-1271	60	33	0	0	NUM
ap-1271	60	34	)	)	PUNCT
ap-1271	60	35	on	on	ADP
ap-1271	60	36	the	the	DET
ap-1271	60	37	flat	flat	ADJ
ap-1271	60	38	euclidean	euclidean	ADJ
ap-1271	60	39	plane	plane	NOUN
ap-1271	60	40	is	be	AUX
ap-1271	60	41	studied	study	VERB
ap-1271	60	42	by	by	ADP
ap-1271	60	43	the	the	DET
ap-1271	60	44	author	author	NOUN
ap-1271	61	1	[	[	X
ap-1271	61	2	12	12	NUM
ap-1271	61	3	]	]	PUNCT
ap-1271	61	4	,	,	PUNCT
ap-1271	61	5	and	and	CCONJ
ap-1271	61	6	the	the	DET
ap-1271	61	7	structure	structure	NOUN
ap-1271	61	8	of	of	ADP
ap-1271	61	9	the	the	DET
ap-1271	61	10	self	self	NOUN
ap-1271	61	11	-	-	PUNCT
ap-1271	61	12	adjoint	adjoint	NOUN
ap-1271	61	13	extensions	extension	NOUN
ap-1271	61	14	is	be	AUX
ap-1271	61	15	determined	determine	VERB
ap-1271	61	16	.	.	PUNCT
ap-1271	62	1	our	our	PRON
ap-1271	62	2	main	main	ADJ
ap-1271	62	3	purpose	purpose	NOUN
ap-1271	62	4	in	in	ADP
ap-1271	62	5	this	this	DET
ap-1271	62	6	paper	paper	NOUN
ap-1271	62	7	is	be	AUX
ap-1271	62	8	to	to	PART
ap-1271	62	9	generalize	generalize	VERB
ap-1271	62	10	the	the	DET
ap-1271	62	11	result	result	NOUN
ap-1271	62	12	in	in	ADP
ap-1271	62	13	[	[	X
ap-1271	62	14	12	12	NUM
ap-1271	62	15	]	]	PUNCT
ap-1271	62	16	on	on	ADP
ap-1271	62	17	general	general	ADJ
ap-1271	62	18	complete	complete	ADJ
ap-1271	62	19	riemannian	riemannian	ADJ
ap-1271	62	20	manifolds	manifold	NOUN
ap-1271	62	21	and	and	CCONJ
ap-1271	62	22	for	for	ADP
ap-1271	62	23	more	more	ADV
ap-1271	62	24	general	general	ADJ
ap-1271	62	25	a	a	PRON
ap-1271	62	26	and	and	CCONJ
ap-1271	62	27	v	v	NOUN
ap-1271	62	28	.	.	PUNCT
ap-1271	63	1	our	our	PRON
ap-1271	63	2	first	first	ADJ
ap-1271	63	3	result	result	NOUN
ap-1271	63	4	is	be	AUX
ap-1271	63	5	about	about	SCONJ
ap-1271	63	6	the	the	DET
ap-1271	63	7	deficiency	deficiency	NOUN
ap-1271	63	8	indices	indice	VERB
ap-1271	63	9	n±(hmin	n±(hmin	PROPN
ap-1271	63	10	)	)	PUNCT
ap-1271	63	11	=	=	PUNCT
ap-1271	63	12	dimker(hmax	dimker(hmax	PROPN
ap-1271	63	13	∓	∓	PROPN
ap-1271	63	14	i	i	NOUN
ap-1271	63	15	)	)	PUNCT
ap-1271	63	16	.	.	PUNCT
ap-1271	64	1	theorem	theorem	ADJ
ap-1271	64	2	1.1	1.1	NUM
ap-1271	64	3	assume	assume	VERB
ap-1271	64	4	(	(	PUNCT
ap-1271	64	5	a	a	NOUN
ap-1271	64	6	)	)	PUNCT
ap-1271	64	7	,	,	PUNCT
ap-1271	64	8	(	(	PUNCT
ap-1271	64	9	a0	a0	NOUN
ap-1271	64	10	)	)	PUNCT
ap-1271	64	11	,	,	PUNCT
ap-1271	64	12	(	(	PUNCT
ap-1271	64	13	a1	a1	NOUN
ap-1271	64	14	)	)	PUNCT
ap-1271	64	15	,	,	PUNCT
ap-1271	64	16	(	(	PUNCT
ap-1271	64	17	v	v	NOUN
ap-1271	64	18	)	)	PUNCT
ap-1271	64	19	,	,	PUNCT
ap-1271	64	20	and	and	CCONJ
ap-1271	64	21	(	(	PUNCT
ap-1271	64	22	sb	sb	NOUN
ap-1271	64	23	)	)	PUNCT
ap-1271	64	24	.	.	PUNCT
ap-1271	65	1	then	then	ADV
ap-1271	65	2	,	,	PUNCT
ap-1271	65	3	both	both	DET
ap-1271	65	4	deficiency	deficiency	NOUN
ap-1271	65	5	indices	indice	VERB
ap-1271	65	6	n±(hmin	n±(hmin	NOUN
ap-1271	65	7	)	)	PUNCT
ap-1271	65	8	are	be	AUX
ap-1271	65	9	equal	equal	ADJ
ap-1271	65	10	to	to	ADP
ap-1271	65	11	2k1	2k1	NUM
ap-1271	65	12	+	+	NOUN
ap-1271	65	13	k2	k2	ADJ
ap-1271	65	14	,	,	PUNCT
ap-1271	65	15	where	where	SCONJ
ap-1271	65	16	k1	k1	NOUN
ap-1271	65	17	=	=	NOUN
ap-1271	65	18	#	#	NOUN
ap-1271	65	19	{	{	PUNCT
ap-1271	65	20	αk	αk	NOUN
ap-1271	65	21	|	|	ADV
ap-1271	65	22	αk	αk	INTJ
ap-1271	65	23	∈	∈	PROPN
ap-1271	65	24	z	z	NOUN
ap-1271	65	25	}	}	PUNCT
ap-1271	65	26	,	,	PUNCT
ap-1271	65	27	k2	k2	NOUN
ap-1271	65	28	=	=	PUNCT
ap-1271	65	29	#	#	SYM
ap-1271	65	30	{	{	PUNCT
ap-1271	65	31	αk	αk	NOUN
ap-1271	65	32	|	|	ADV
ap-1271	65	33	αk	αk	INTJ
ap-1271	65	34	∈	∈	PROPN
ap-1271	65	35	z	z	NOUN
ap-1271	65	36	}	}	PUNCT
ap-1271	65	37	.	.	PUNCT
ap-1271	66	1	note	note	VERB
ap-1271	66	2	that	that	SCONJ
ap-1271	66	3	bulla	bulla	NOUN
ap-1271	66	4	-	-	PUNCT
ap-1271	66	5	gesztesy	gesztesy	NOUN
ap-1271	66	6	[	[	X
ap-1271	66	7	4	4	NUM
ap-1271	66	8	]	]	PUNCT
ap-1271	66	9	obtain	obtain	VERB
ap-1271	66	10	a	a	DET
ap-1271	66	11	similar	similar	ADJ
ap-1271	66	12	result	result	NOUN
ap-1271	66	13	in	in	ADP
ap-1271	66	14	the	the	DET
ap-1271	66	15	case	case	NOUN
ap-1271	66	16	a	a	DET
ap-1271	66	17	=	=	SYM
ap-1271	66	18	0	0	NUM
ap-1271	66	19	and	and	CCONJ
ap-1271	66	20	v	v	NOUN
ap-1271	66	21	has	have	VERB
ap-1271	66	22	singularities	singularity	NOUN
ap-1271	66	23	,	,	PUNCT
ap-1271	66	24	and	and	CCONJ
ap-1271	66	25	iwaiyabu	iwaiyabu	ADV
ap-1271	66	26	[	[	X
ap-1271	66	27	9	9	NUM
ap-1271	66	28	]	]	PUNCT
ap-1271	66	29	also	also	ADV
ap-1271	66	30	obtain	obtain	VERB
ap-1271	66	31	a	a	DET
ap-1271	66	32	similar	similar	ADJ
ap-1271	66	33	result	result	NOUN
ap-1271	66	34	on	on	ADP
ap-1271	66	35	the	the	DET
ap-1271	66	36	twodimensional	twodimensional	ADJ
ap-1271	66	37	torus	torus	NOUN
ap-1271	66	38	.	.	PUNCT
ap-1271	67	1	next	next	ADV
ap-1271	67	2	,	,	PUNCT
ap-1271	67	3	we	we	PRON
ap-1271	67	4	shall	shall	AUX
ap-1271	67	5	give	give	VERB
ap-1271	67	6	a	a	DET
ap-1271	67	7	complete	complete	ADJ
ap-1271	67	8	characterization	characterization	NOUN
ap-1271	67	9	of	of	ADP
ap-1271	67	10	the	the	DET
ap-1271	67	11	self	self	NOUN
ap-1271	67	12	-	-	PUNCT
ap-1271	67	13	adjoint	adjoint	NOUN
ap-1271	67	14	extensions	extension	NOUN
ap-1271	67	15	of	of	ADP
ap-1271	67	16	hmin	hmin	NOUN
ap-1271	67	17	.	.	PUNCT
ap-1271	68	1	to	to	ADP
ap-1271	68	2	this	this	DET
ap-1271	68	3	purpose	purpose	NOUN
ap-1271	68	4	,	,	PUNCT
ap-1271	68	5	we	we	PRON
ap-1271	68	6	introduce	introduce	VERB
ap-1271	68	7	some	some	DET
ap-1271	68	8	nice	nice	ADJ
ap-1271	68	9	coordinates	coordinate	NOUN
ap-1271	68	10	around	around	ADP
ap-1271	68	11	singularities	singularity	NOUN
ap-1271	68	12	and	and	CCONJ
ap-1271	68	13	some	some	DET
ap-1271	68	14	auxiliary	auxiliary	ADJ
ap-1271	68	15	functions	function	NOUN
ap-1271	68	16	.	.	PUNCT
ap-1271	69	1	for	for	ADP
ap-1271	69	2	simplicity	simplicity	NOUN
ap-1271	69	3	,	,	PUNCT
ap-1271	69	4	we	we	PRON
ap-1271	69	5	assume	assume	VERB
ap-1271	69	6	k	k	X
ap-1271	69	7	=	=	PUNCT
ap-1271	69	8	#	#	SYM
ap-1271	69	9	γ	γ	NOUN
ap-1271	69	10	is	be	AUX
ap-1271	69	11	finite	finite	ADJ
ap-1271	69	12	for	for	ADP
ap-1271	69	13	a	a	DET
ap-1271	69	14	while	while	NOUN
ap-1271	69	15	.	.	PUNCT
ap-1271	70	1	for	for	ADP
ap-1271	70	2	k	k	PROPN
ap-1271	70	3	=	=	SYM
ap-1271	70	4	1	1	NUM
ap-1271	70	5	,	,	PUNCT
ap-1271	70	6	.	.	PUNCT
ap-1271	70	7	.	.	PUNCT
ap-1271	70	8	.	.	PUNCT
ap-1271	71	1	,	,	PUNCT
ap-1271	71	2	k	k	X
ap-1271	71	3	,	,	PUNCT
ap-1271	71	4	let	let	VERB
ap-1271	71	5	(	(	PUNCT
ap-1271	71	6	uk	uk	PROPN
ap-1271	71	7	,	,	PUNCT
ap-1271	71	8	φk	φk	ADP
ap-1271	71	9	)	)	PUNCT
ap-1271	71	10	,	,	PUNCT
ap-1271	71	11	φk	φk	ADP
ap-1271	71	12	=	=	SYM
ap-1271	71	13	(	(	PUNCT
ap-1271	71	14	x1	x1	PROPN
ap-1271	71	15	,	,	PUNCT
ap-1271	71	16	x2	x2	PROPN
ap-1271	71	17	)	)	PUNCT
ap-1271	71	18	,	,	PUNCT
ap-1271	71	19	be	be	AUX
ap-1271	71	20	a	a	DET
ap-1271	71	21	local	local	ADJ
ap-1271	71	22	chart	chart	NOUN
ap-1271	71	23	around	around	ADV
ap-1271	71	24	γk	γk	ADP
ap-1271	71	25	such	such	ADJ
ap-1271	71	26	that	that	SCONJ
ap-1271	71	27	uk	uk	PROPN
ap-1271	71	28	is	be	AUX
ap-1271	71	29	simply	simply	ADV
ap-1271	71	30	connected	connect	VERB
ap-1271	71	31	,	,	PUNCT
ap-1271	71	32	φk(γk	φk(γk	ADJ
ap-1271	71	33	)	)	PUNCT
ap-1271	71	34	=	=	SYM
ap-1271	71	35	0	0	NUM
ap-1271	71	36	,	,	PUNCT
ap-1271	71	37	v	v	NOUN
ap-1271	71	38	is	be	AUX
ap-1271	71	39	bounded	bound	VERB
ap-1271	71	40	in	in	ADP
ap-1271	71	41	uk	uk	PROPN
ap-1271	71	42	,	,	PUNCT
ap-1271	71	43	and	and	CCONJ
ap-1271	71	44	{	{	PUNCT
ap-1271	71	45	uk}k	uk}k	PROPN
ap-1271	71	46	k=1	k=1	PROPN
ap-1271	71	47	are	be	AUX
ap-1271	71	48	disjoint	disjoint	ADJ
ap-1271	71	49	.	.	PUNCT
ap-1271	72	1	let	let	AUX
ap-1271	72	2	(	(	PUNCT
ap-1271	72	3	r	r	NOUN
ap-1271	72	4	,	,	PUNCT
ap-1271	72	5	θ	θ	NOUN
ap-1271	72	6	)	)	PUNCT
ap-1271	72	7	be	be	VERB
ap-1271	72	8	the	the	DET
ap-1271	72	9	radial	radial	ADJ
ap-1271	72	10	coordinate	coordinate	NOUN
ap-1271	72	11	in	in	ADP
ap-1271	72	12	uk	uk	PROPN
ap-1271	72	13	defined	define	VERB
ap-1271	72	14	by	by	ADP
ap-1271	72	15	x1	x1	PROPN
ap-1271	72	16	+	+	PROPN
ap-1271	72	17	ix2	ix2	PROPN
ap-1271	72	18	=	=	PROPN
ap-1271	72	19	reiθ	reiθ	PROPN
ap-1271	72	20	,	,	PUNCT
ap-1271	72	21	r	r	NOUN
ap-1271	72	22	≥	≥	NOUN
ap-1271	72	23	0	0	NUM
ap-1271	72	24	,	,	PUNCT
ap-1271	72	25	0	0	NUM
ap-1271	72	26	≤	≤	NUM
ap-1271	72	27	θ	θ	NOUN
ap-1271	72	28	<	<	X
ap-1271	72	29	2π	2π	NOUN
ap-1271	72	30	.	.	PUNCT
ap-1271	73	1	we	we	PRON
ap-1271	73	2	assume	assume	VERB
ap-1271	73	3	gmn(0	gmn(0	NOUN
ap-1271	73	4	,	,	PUNCT
ap-1271	73	5	0	0	NUM
ap-1271	73	6	)	)	PUNCT
ap-1271	73	7	=	=	SYM
ap-1271	73	8	δmn	δmn	NOUN
ap-1271	73	9	,	,	PUNCT
ap-1271	73	10	(	(	PUNCT
ap-1271	73	11	2	2	NUM
ap-1271	73	12	)	)	PUNCT
ap-1271	73	13	∂jgmn(0	∂jgmn(0	NOUN
ap-1271	73	14	,	,	PUNCT
ap-1271	73	15	0	0	NUM
ap-1271	73	16	)	)	PUNCT
ap-1271	73	17	=	=	SYM
ap-1271	73	18	0	0	PUNCT
ap-1271	73	19	(	(	PUNCT
ap-1271	73	20	m	m	PROPN
ap-1271	73	21	,	,	PUNCT
ap-1271	73	22	n	n	CCONJ
ap-1271	73	23	,	,	PUNCT
ap-1271	73	24	j	j	PROPN
ap-1271	73	25	=	=	SYM
ap-1271	73	26	1	1	NUM
ap-1271	73	27	,	,	PUNCT
ap-1271	73	28	2	2	NUM
ap-1271	73	29	)	)	PUNCT
ap-1271	73	30	,	,	PUNCT
ap-1271	73	31	where	where	SCONJ
ap-1271	73	32	δmn	δmn	NOUN
ap-1271	73	33	is	be	AUX
ap-1271	73	34	the	the	DET
ap-1271	73	35	kronecker	kronecker	NOUN
ap-1271	73	36	delta	delta	NOUN
ap-1271	73	37	.	.	PUNCT
ap-1271	74	1	condition	condition	NOUN
ap-1271	74	2	(	(	PUNCT
ap-1271	74	3	2	2	X
ap-1271	74	4	)	)	PUNCT
ap-1271	74	5	is	be	AUX
ap-1271	74	6	satisfied	satisfied	ADJ
ap-1271	74	7	,	,	PUNCT
ap-1271	74	8	for	for	ADP
ap-1271	74	9	example	example	NOUN
ap-1271	74	10	,	,	PUNCT
ap-1271	74	11	if	if	SCONJ
ap-1271	74	12	we	we	PRON
ap-1271	74	13	take	take	VERB
ap-1271	74	14	the	the	DET
ap-1271	74	15	normal	normal	ADJ
ap-1271	74	16	coordinate2	coordinate2	NOUN
ap-1271	74	17	as	as	ADP
ap-1271	74	18	(	(	PUNCT
ap-1271	74	19	x1	x1	PROPN
ap-1271	74	20	,	,	PUNCT
ap-1271	74	21	x2	x2	PROPN
ap-1271	74	22	)	)	PUNCT
ap-1271	74	23	.	.	PUNCT
ap-1271	75	1	let	let	VERB
ap-1271	75	2	βk	βk	VERB
ap-1271	75	3	be	be	AUX
ap-1271	75	4	the	the	DET
ap-1271	75	5	fractional	fractional	ADJ
ap-1271	75	6	part	part	NOUN
ap-1271	75	7	of	of	ADP
ap-1271	75	8	αk	αk	NOUN
ap-1271	75	9	,	,	PUNCT
ap-1271	75	10	that	that	ADV
ap-1271	75	11	is	is	ADV
ap-1271	75	12	,	,	PUNCT
ap-1271	75	13	αk	αk	ADP
ap-1271	75	14	=	=	SYM
ap-1271	76	1	[	[	X
ap-1271	76	2	αk	αk	X
ap-1271	76	3	]	]	X
ap-1271	76	4	+	+	CCONJ
ap-1271	76	5	βk	βk	ADJ
ap-1271	76	6	,	,	PUNCT
ap-1271	76	7	[	[	X
ap-1271	76	8	αk	αk	X
ap-1271	76	9	]	]	X
ap-1271	76	10	∈	∈	PROPN
ap-1271	76	11	z	z	NOUN
ap-1271	76	12	and	and	CCONJ
ap-1271	76	13	0	0	NUM
ap-1271	76	14	≤	≤	NUM
ap-1271	76	15	βk	βk	ADP
ap-1271	76	16	<	<	X
ap-1271	76	17	1	1	NUM
ap-1271	76	18	.	.	PUNCT
ap-1271	76	19	put3	put3	PROPN
ap-1271	76	20	ã(0	ã(0	NOUN
ap-1271	76	21	)	)	PUNCT
ap-1271	76	22	=	=	SYM
ap-1271	76	23	βkr−2(−x2dx1	βkr−2(−x2dx1	X
ap-1271	77	1	+	+	NUM
ap-1271	77	2	x1dx2	x1dx2	PROPN
ap-1271	77	3	)	)	PUNCT
ap-1271	77	4	,	,	PUNCT
ap-1271	77	5	ã(1	ã(1	NOUN
ap-1271	77	6	)	)	PUNCT
ap-1271	77	7	=	=	PUNCT
ap-1271	77	8	a(1	a(1	PROPN
ap-1271	77	9	)	)	PUNCT
ap-1271	77	10	−	−	PROPN
ap-1271	77	11	a(1)(0	a(1)(0	NUM
ap-1271	77	12	)	)	PUNCT
ap-1271	77	13	.	.	PUNCT
ap-1271	78	1	it	it	PRON
ap-1271	78	2	is	be	AUX
ap-1271	78	3	well	well	ADV
ap-1271	78	4	-	-	PUNCT
ap-1271	78	5	known	know	VERB
ap-1271	78	6	that	that	SCONJ
ap-1271	78	7	dã(0	dã(0	NOUN
ap-1271	78	8	)	)	PUNCT
ap-1271	78	9	=	=	SYM
ap-1271	78	10	2πβkδ0	2πβkδ0	NUM
ap-1271	78	11	(	(	PUNCT
ap-1271	78	12	see	see	VERB
ap-1271	78	13	e.g.	e.g.	ADV
ap-1271	78	14	aharonov	aharonov	NOUN
ap-1271	78	15	-	-	PUNCT
ap-1271	78	16	bohm	bohm	PROPN
ap-1271	78	17	[	[	X
ap-1271	78	18	2	2	NUM
ap-1271	78	19	,	,	PUNCT
ap-1271	78	20	1	1	NUM
ap-1271	78	21	]	]	PUNCT
ap-1271	78	22	or	or	CCONJ
ap-1271	78	23	[	[	X
ap-1271	78	24	7	7	NUM
ap-1271	78	25	]	]	NUM
ap-1271	78	26	)	)	PUNCT
ap-1271	78	27	.	.	PUNCT
ap-1271	79	1	define	define	VERB
ap-1271	79	2	a	a	DET
ap-1271	79	3	phase	phase	NOUN
ap-1271	79	4	function	function	NOUN
ap-1271	79	5	ψk	ψk	NOUN
ap-1271	79	6	∈	∈	PROPN
ap-1271	79	7	c∞(uk	c∞(uk	PROPN
ap-1271	79	8	\	\	PROPN
ap-1271	79	9	{	{	PUNCT
ap-1271	79	10	0	0	NUM
ap-1271	79	11	}	}	PUNCT
ap-1271	79	12	)	)	PUNCT
ap-1271	79	13	by	by	ADP
ap-1271	79	14	ψk(x	ψk(x	NOUN
ap-1271	79	15	)	)	PUNCT
ap-1271	80	1	=	=	SYM
ap-1271	80	2	exp	exp	NOUN
ap-1271	80	3	1	1	NUM
ap-1271	81	1	i	i	NOUN
ap-1271	81	2	(	(	PUNCT
ap-1271	81	3	a	a	DET
ap-1271	81	4	(	(	PUNCT
ap-1271	81	5	1	1	NUM
ap-1271	81	6	)	)	PUNCT
ap-1271	81	7	1	1	NUM
ap-1271	81	8	(	(	PUNCT
ap-1271	81	9	0)x	0)x	NOUN
ap-1271	81	10	1	1	NUM
ap-1271	81	11	+	+	NOUN
ap-1271	81	12	a	a	DET
ap-1271	81	13	(	(	PUNCT
ap-1271	81	14	1	1	NUM
ap-1271	81	15	)	)	SYM
ap-1271	81	16	2	2	NUM
ap-1271	81	17	(	(	PUNCT
ap-1271	81	18	0)x	0)x	NOUN
ap-1271	81	19	2	2	NUM
ap-1271	81	20	+	+	CCONJ
ap-1271	81	21	(	(	PUNCT
ap-1271	81	22	3)∫	3)∫	NUM
ap-1271	81	23	x	x	SYM
ap-1271	81	24	x0	x0	PROPN
ap-1271	81	25	(	(	PUNCT
ap-1271	81	26	a(0	a(0	PROPN
ap-1271	81	27	)	)	PUNCT
ap-1271	81	28	−	−	PROPN
ap-1271	81	29	ã(0	ã(0	NOUN
ap-1271	81	30	)	)	PUNCT
ap-1271	81	31	)	)	PUNCT
ap-1271	81	32	)	)	PUNCT
ap-1271	81	33	,	,	PUNCT
ap-1271	81	34	where	where	SCONJ
ap-1271	81	35	a(1	a(1	NOUN
ap-1271	81	36	)	)	PUNCT
ap-1271	81	37	=	=	SYM
ap-1271	81	38	a	a	PRON
ap-1271	81	39	(	(	PUNCT
ap-1271	81	40	1	1	NUM
ap-1271	81	41	)	)	PUNCT
ap-1271	81	42	1	1	NUM
ap-1271	81	43	dx1	dx1	PROPN
ap-1271	81	44	+	+	CCONJ
ap-1271	81	45	a	a	DET
ap-1271	81	46	(	(	PUNCT
ap-1271	81	47	1	1	NUM
ap-1271	81	48	)	)	SYM
ap-1271	81	49	2	2	NUM
ap-1271	81	50	dx2	dx2	NOUN
ap-1271	81	51	,	,	PUNCT
ap-1271	81	52	x0	x0	PROPN
ap-1271	81	53	is	be	AUX
ap-1271	81	54	some	some	DET
ap-1271	81	55	point	point	NOUN
ap-1271	81	56	in	in	ADP
ap-1271	81	57	uk	uk	PROPN
ap-1271	81	58	\	\	PROPN
ap-1271	81	59	{	{	PUNCT
ap-1271	81	60	0	0	NUM
ap-1271	81	61	}	}	PUNCT
ap-1271	81	62	,	,	PUNCT
ap-1271	81	63	and	and	CCONJ
ap-1271	81	64	the	the	DET
ap-1271	81	65	path	path	NOUN
ap-1271	81	66	of	of	ADP
ap-1271	81	67	the	the	DET
ap-1271	81	68	line	line	NOUN
ap-1271	81	69	integral	integral	ADJ
ap-1271	81	70	∫	∫	PROPN
ap-1271	81	71	x	x	PROPN
ap-1271	81	72	x0	x0	PROPN
ap-1271	81	73	lies	lie	VERB
ap-1271	81	74	in	in	ADP
ap-1271	81	75	uk	uk	PROPN
ap-1271	81	76	\	\	PROPN
ap-1271	81	77	{	{	PUNCT
ap-1271	81	78	0	0	NUM
ap-1271	81	79	}	}	PUNCT
ap-1271	81	80	.	.	PUNCT
ap-1271	82	1	notice	notice	VERB
ap-1271	82	2	that	that	SCONJ
ap-1271	82	3	the	the	DET
ap-1271	82	4	value	value	NOUN
ap-1271	82	5	of	of	ADP
ap-1271	82	6	the	the	DET
ap-1271	82	7	line	line	NOUN
ap-1271	82	8	integral	integral	ADJ
ap-1271	82	9	is	be	AUX
ap-1271	82	10	independent	independent	ADJ
ap-1271	82	11	of	of	ADP
ap-1271	82	12	the	the	DET
ap-1271	82	13	choice	choice	NOUN
ap-1271	82	14	of	of	ADP
ap-1271	82	15	paths	path	NOUN
ap-1271	82	16	modulo	modulo	NOUN
ap-1271	82	17	2πz	2πz	NOUN
ap-1271	82	18	,	,	PUNCT
ap-1271	82	19	by	by	ADP
ap-1271	82	20	the	the	DET
ap-1271	82	21	stokes	stoke	NOUN
ap-1271	82	22	theorem	theorem	NOUN
ap-1271	82	23	and	and	CCONJ
ap-1271	82	24	the	the	DET
ap-1271	82	25	assumption	assumption	NOUN
ap-1271	82	26	d(a(0	d(a(0	PROPN
ap-1271	82	27	)	)	PUNCT
ap-1271	82	28	−	−	PROPN
ap-1271	82	29	ã(0	ã(0	NOUN
ap-1271	82	30	)	)	PUNCT
ap-1271	82	31	)	)	PUNCT
ap-1271	83	1	=	=	PUNCT
ap-1271	83	2	2π[αk]δ0	2π[αk]δ0	NUM
ap-1271	83	3	in	in	ADP
ap-1271	83	4	uk	uk	PROPN
ap-1271	83	5	.	.	PUNCT
ap-1271	84	1	then	then	ADV
ap-1271	84	2	we	we	PRON
ap-1271	84	3	have	have	VERB
ap-1271	84	4	a	a	DET
ap-1271	84	5	=	=	NOUN
ap-1271	84	6	ã+	ã+	NOUN
ap-1271	84	7	iψ−1	iψ−1	PROPN
ap-1271	84	8	k	k	PROPN
ap-1271	84	9	dψk	dψk	PROPN
ap-1271	84	10	,	,	PUNCT
ap-1271	84	11	ã	ã	PROPN
ap-1271	84	12	=	=	SYM
ap-1271	84	13	ã(0	ã(0	NOUN
ap-1271	84	14	)	)	PUNCT
ap-1271	84	15	+	+	X
ap-1271	85	1	ã(1	ã(1	NOUN
ap-1271	85	2	)	)	PUNCT
ap-1271	85	3	(	(	PUNCT
ap-1271	85	4	4	4	NUM
ap-1271	85	5	)	)	PUNCT
ap-1271	85	6	and	and	CCONJ
ap-1271	85	7	l	l	NOUN
ap-1271	86	1	=	=	SYM
ap-1271	86	2	ψkl̃ψ−1	ψkl̃ψ−1	X
ap-1271	86	3	k	k	X
ap-1271	86	4	(	(	PUNCT
ap-1271	86	5	5	5	NUM
ap-1271	86	6	)	)	PUNCT
ap-1271	86	7	in	in	ADP
ap-1271	86	8	uk	uk	PROPN
ap-1271	86	9	\	\	PROPN
ap-1271	86	10	{	{	PUNCT
ap-1271	86	11	0	0	NUM
ap-1271	86	12	}	}	PUNCT
ap-1271	86	13	,	,	PUNCT
ap-1271	86	14	where	where	SCONJ
ap-1271	86	15	l̃	l̃	PROPN
ap-1271	86	16	is	be	AUX
ap-1271	86	17	the	the	DET
ap-1271	86	18	operator	operator	NOUN
ap-1271	86	19	l	l	NOUN
ap-1271	86	20	corresponding	correspond	VERB
ap-1271	86	21	to	to	ADP
ap-1271	86	22	the	the	DET
ap-1271	86	23	vector	vector	NOUN
ap-1271	86	24	potential	potential	NOUN
ap-1271	86	25	ã	ã	PROPN
ap-1271	86	26	and	and	CCONJ
ap-1271	86	27	the	the	DET
ap-1271	86	28	scalar	scalar	ADJ
ap-1271	86	29	potential	potential	ADJ
ap-1271	86	30	v	v	NOUN
ap-1271	86	31	.	.	PUNCT
ap-1271	87	1	let	let	VERB
ap-1271	87	2	k1	k1	PROPN
ap-1271	87	3	,	,	PUNCT
ap-1271	87	4	k2	k2	PROPN
ap-1271	87	5	be	be	VERB
ap-1271	87	6	the	the	DET
ap-1271	87	7	numbers	number	NOUN
ap-1271	87	8	in	in	ADP
ap-1271	87	9	theorem	theorem	ADJ
ap-1271	87	10	1.1	1.1	NUM
ap-1271	87	11	.	.	PUNCT
ap-1271	88	1	in	in	ADP
ap-1271	88	2	the	the	DET
ap-1271	88	3	sequel	sequel	NOUN
ap-1271	88	4	,	,	PUNCT
ap-1271	88	5	we	we	PRON
ap-1271	88	6	rearrange	rearrange	VERB
ap-1271	88	7	the	the	DET
ap-1271	88	8	index	index	NOUN
ap-1271	88	9	k	k	NOUN
ap-1271	89	1	so	so	ADV
ap-1271	89	2	that	that	SCONJ
ap-1271	89	3	0	0	X
ap-1271	89	4	<	<	X
ap-1271	89	5	βk	βk	X
ap-1271	89	6	<	<	X
ap-1271	89	7	1	1	NUM
ap-1271	89	8	for	for	ADP
ap-1271	89	9	1	1	NUM
ap-1271	89	10	≤	≤	NUM
ap-1271	89	11	k	k	PROPN
ap-1271	89	12	≤	≤	PROPN
ap-1271	89	13	k1	k1	NOUN
ap-1271	89	14	.	.	PUNCT
ap-1271	90	1	as	as	SCONJ
ap-1271	90	2	we	we	PRON
ap-1271	90	3	prove	prove	VERB
ap-1271	90	4	later	later	ADV
ap-1271	90	5	,	,	PUNCT
ap-1271	90	6	the	the	DET
ap-1271	90	7	2the	2the	NUM
ap-1271	90	8	coordinate	coordinate	NOUN
ap-1271	90	9	defined	define	VERB
ap-1271	90	10	by	by	ADP
ap-1271	90	11	the	the	DET
ap-1271	90	12	local	local	ADJ
ap-1271	90	13	inverse	inverse	NOUN
ap-1271	90	14	map	map	NOUN
ap-1271	90	15	of	of	ADP
ap-1271	90	16	the	the	DET
ap-1271	90	17	exponential	exponential	ADJ
ap-1271	90	18	map	map	NOUN
ap-1271	90	19	from	from	ADP
ap-1271	90	20	the	the	DET
ap-1271	90	21	tangent	tangent	ADJ
ap-1271	90	22	space	space	NOUN
ap-1271	90	23	at	at	ADP
ap-1271	90	24	γk	γk	PROPN
ap-1271	90	25	to	to	ADP
ap-1271	90	26	m	m	PROPN
ap-1271	90	27	.	.	PUNCT
ap-1271	91	1	3more	3more	NUM
ap-1271	91	2	precisely	precisely	ADV
ap-1271	91	3	,	,	PUNCT
ap-1271	91	4	the	the	DET
ap-1271	91	5	1	1	NUM
ap-1271	91	6	-	-	PUNCT
ap-1271	91	7	form	form	NOUN
ap-1271	91	8	a(1	a(1	NOUN
ap-1271	91	9	)	)	PUNCT
ap-1271	91	10	−	−	PROPN
ap-1271	91	11	a(1)(0	a(1)(0	ADV
ap-1271	91	12	)	)	PUNCT
ap-1271	91	13	is	be	AUX
ap-1271	91	14	defined	define	VERB
ap-1271	91	15	as	as	ADP
ap-1271	91	16	(	(	PUNCT
ap-1271	91	17	a(1)1	a(1)1	PROPN
ap-1271	91	18	(	(	PUNCT
ap-1271	91	19	x	x	NOUN
ap-1271	91	20	1	1	NUM
ap-1271	91	21	,	,	PUNCT
ap-1271	91	22	x2	x2	PROPN
ap-1271	91	23	)	)	PUNCT
ap-1271	91	24	−	−	PROPN
ap-1271	91	25	a	a	DET
ap-1271	91	26	(	(	PUNCT
ap-1271	91	27	1	1	NUM
ap-1271	91	28	)	)	SYM
ap-1271	91	29	1	1	NUM
ap-1271	91	30	(	(	PUNCT
ap-1271	91	31	0	0	NUM
ap-1271	91	32	,	,	PUNCT
ap-1271	91	33	0))dx1	0))dx1	NUM
ap-1271	92	1	+	+	CCONJ
ap-1271	92	2	(	(	PUNCT
ap-1271	92	3	a(1)2	a(1)2	CCONJ
ap-1271	92	4	(	(	PUNCT
ap-1271	92	5	x	x	NOUN
ap-1271	92	6	1	1	NUM
ap-1271	92	7	,	,	PUNCT
ap-1271	92	8	x2	x2	PROPN
ap-1271	92	9	)	)	PUNCT
ap-1271	92	10	−	−	PROPN
ap-1271	92	11	a	a	DET
ap-1271	92	12	(	(	PUNCT
ap-1271	92	13	1	1	NUM
ap-1271	92	14	)	)	SYM
ap-1271	92	15	2	2	NUM
ap-1271	92	16	(	(	PUNCT
ap-1271	92	17	0	0	NUM
ap-1271	92	18	,	,	PUNCT
ap-1271	92	19	0))dx2	0))dx2	NUM
ap-1271	92	20	,	,	PUNCT
ap-1271	92	21	in	in	ADP
ap-1271	92	22	the	the	DET
ap-1271	92	23	coordinate	coordinate	ADJ
ap-1271	92	24	neighborhood	neighborhood	NOUN
ap-1271	92	25	uk	uk	PROPN
ap-1271	92	26	.	.	PROPN
ap-1271	92	27	63	63	NUM
ap-1271	92	28	acta	acta	PROPN
ap-1271	92	29	polytechnica	polytechnica	PROPN
ap-1271	92	30	vol	vol	NOUN
ap-1271	92	31	.	.	PUNCT
ap-1271	93	1	50	50	NUM
ap-1271	93	2	no	no	NOUN
ap-1271	93	3	.	.	PUNCT
ap-1271	94	1	5/2010	5/2010	DET
ap-1271	94	2	asymptotics	asymptotic	NOUN
ap-1271	94	3	of	of	ADP
ap-1271	94	4	u	u	NOUN
ap-1271	94	5	∈	∈	PROPN
ap-1271	94	6	d(hmax	d(hmax	NOUN
ap-1271	94	7	)	)	PUNCT
ap-1271	94	8	in	in	ADP
ap-1271	94	9	uk	uk	PROPN
ap-1271	94	10	as	as	ADP
ap-1271	94	11	r	r	NOUN
ap-1271	94	12	→	→	SYM
ap-1271	94	13	0	0	NUM
ap-1271	94	14	is	be	AUX
ap-1271	94	15	given	give	VERB
ap-1271	94	16	by	by	ADP
ap-1271	94	17	u	u	NOUN
ap-1271	94	18	=	=	PROPN
ap-1271	94	19	⎧⎪⎪⎨⎪⎪⎩	⎧⎪⎪⎨⎪⎪⎩	PROPN
ap-1271	94	20	ψk(ck	ψk(ck	ADJ
ap-1271	94	21	1r	1r	NUM
ap-1271	94	22	βk−1e−iθ	βk−1e−iθ	PUNCT
ap-1271	95	1	+	+	CCONJ
ap-1271	95	2	ck	ck	INTJ
ap-1271	95	3	2r	2r	NUM
ap-1271	95	4	−βk+	−βk+	NOUN
ap-1271	95	5	ck	ck	PRON
ap-1271	95	6	4r	4r	NUM
ap-1271	95	7	1−βke−iθ	1−βke−iθ	NUM
ap-1271	95	8	+	+	CCONJ
ap-1271	95	9	ck	ck	PRON
ap-1271	95	10	5r	5r	NUM
ap-1271	95	11	βk	βk	NOUN
ap-1271	95	12	)	)	PUNCT
ap-1271	95	13	+	+	CCONJ
ap-1271	95	14	ξ	ξ	X
ap-1271	95	15	(	(	PUNCT
ap-1271	95	16	1	1	NUM
ap-1271	95	17	≤	≤	NUM
ap-1271	95	18	k	k	PROPN
ap-1271	95	19	≤	≤	PROPN
ap-1271	95	20	k1	k1	NOUN
ap-1271	95	21	)	)	PUNCT
ap-1271	95	22	,	,	PUNCT
ap-1271	95	23	ψk(ck	ψk(ck	NOUN
ap-1271	95	24	3	3	NUM
ap-1271	95	25	log	log	NOUN
ap-1271	95	26	r	r	NOUN
ap-1271	95	27	+	+	CCONJ
ap-1271	95	28	ck	ck	PROPN
ap-1271	95	29	6	6	NUM
ap-1271	95	30	)	)	PUNCT
ap-1271	95	31	+	+	NUM
ap-1271	95	32	ξ	ξ	X
ap-1271	95	33	(	(	PUNCT
ap-1271	95	34	k1	k1	NOUN
ap-1271	95	35	+	+	CCONJ
ap-1271	95	36	1	1	NUM
ap-1271	95	37	≤	≤	NUM
ap-1271	95	38	k	k	NOUN
ap-1271	95	39	≤	≤	PROPN
ap-1271	95	40	k	k	X
ap-1271	95	41	)	)	PUNCT
ap-1271	95	42	,	,	PUNCT
ap-1271	95	43	where	where	SCONJ
ap-1271	95	44	ck	ck	INTJ
ap-1271	95	45	1	1	NUM
ap-1271	95	46	,	,	PUNCT
ap-1271	95	47	.	.	PUNCT
ap-1271	95	48	.	.	PUNCT
ap-1271	95	49	.	.	PUNCT
ap-1271	96	1	,	,	PUNCT
ap-1271	96	2	c	c	PROPN
ap-1271	96	3	k	k	PROPN
ap-1271	96	4	6	6	NUM
ap-1271	96	5	are	be	AUX
ap-1271	96	6	constants	constant	NOUN
ap-1271	96	7	and	and	CCONJ
ap-1271	96	8	ξ	ξ	X
ap-1271	96	9	is	be	AUX
ap-1271	96	10	a	a	DET
ap-1271	96	11	regular	regular	ADJ
ap-1271	96	12	function	function	NOUN
ap-1271	96	13	in	in	ADP
ap-1271	96	14	the	the	DET
ap-1271	96	15	sense	sense	NOUN
ap-1271	96	16	ξ	ξ	PROPN
ap-1271	96	17	∈	∈	PROPN
ap-1271	96	18	d(hmin	d(hmin	NOUN
ap-1271	96	19	)	)	PUNCT
ap-1271	96	20	.	.	PUNCT
ap-1271	97	1	define	define	VERB
ap-1271	97	2	φj(u	φj(u	NOUN
ap-1271	97	3	)	)	PUNCT
ap-1271	97	4	=	=	PRON
ap-1271	97	5	{	{	PUNCT
ap-1271	97	6	t(c1j	t(c1j	NOUN
ap-1271	97	7	,	,	PUNCT
ap-1271	97	8	.	.	PUNCT
ap-1271	97	9	.	.	PUNCT
ap-1271	98	1	.	.	PUNCT
ap-1271	99	1	,	,	PUNCT
ap-1271	99	2	c	c	PROPN
ap-1271	99	3	k1	k1	PROPN
ap-1271	99	4	j	j	PROPN
ap-1271	99	5	)	)	PUNCT
ap-1271	99	6	∈	∈	PROPN
ap-1271	99	7	c	c	PROPN
ap-1271	99	8	k1	k1	PROPN
ap-1271	99	9	(	(	PUNCT
ap-1271	99	10	j	j	NOUN
ap-1271	99	11	=	=	SYM
ap-1271	99	12	1	1	NUM
ap-1271	99	13	,	,	PUNCT
ap-1271	99	14	2	2	NUM
ap-1271	99	15	,	,	PUNCT
ap-1271	99	16	4	4	NUM
ap-1271	99	17	,	,	PUNCT
ap-1271	99	18	5	5	NUM
ap-1271	99	19	)	)	PUNCT
ap-1271	99	20	,	,	PUNCT
ap-1271	99	21	t(ck1	t(ck1	PROPN
ap-1271	99	22	+	+	PROPN
ap-1271	99	23	1	1	NUM
ap-1271	99	24	j	j	NOUN
ap-1271	99	25	,	,	PUNCT
ap-1271	99	26	.	.	PUNCT
ap-1271	99	27	.	.	PUNCT
ap-1271	100	1	.	.	PUNCT
ap-1271	101	1	,	,	PUNCT
ap-1271	101	2	ck	ck	PROPN
ap-1271	101	3	j	j	PROPN
ap-1271	101	4	)	)	PUNCT
ap-1271	101	5	∈	∈	PROPN
ap-1271	101	6	ck2	ck2	NOUN
ap-1271	101	7	(	(	PUNCT
ap-1271	101	8	j	j	PROPN
ap-1271	101	9	=	=	SYM
ap-1271	101	10	3	3	NUM
ap-1271	101	11	,	,	PUNCT
ap-1271	101	12	6	6	NUM
ap-1271	101	13	)	)	PUNCT
ap-1271	101	14	,	,	PUNCT
ap-1271	101	15	φ(u	φ(u	PROPN
ap-1271	101	16	)	)	PUNCT
ap-1271	101	17	=	=	SYM
ap-1271	101	18	t(tφ1(u	t(tφ1(u	PROPN
ap-1271	101	19	)	)	PUNCT
ap-1271	101	20	·	·	PUNCT
ap-1271	101	21	·	·	PUNCT
ap-1271	101	22	·	·	PUNCT
ap-1271	101	23	tφ6(u	tφ6(u	NUM
ap-1271	101	24	)	)	PUNCT
ap-1271	101	25	)	)	PUNCT
ap-1271	101	26	∈	∈	PROPN
ap-1271	101	27	c4k1	c4k1	VERB
ap-1271	101	28	+	+	NOUN
ap-1271	101	29	2k2	2k2	NUM
ap-1271	101	30	.	.	PUNCT
ap-1271	102	1	define	define	VERB
ap-1271	102	2	a	a	DET
ap-1271	102	3	(	(	PUNCT
ap-1271	102	4	2k1	2k1	NUM
ap-1271	102	5	+	+	CCONJ
ap-1271	102	6	k2	k2	ADJ
ap-1271	102	7	)	)	PUNCT
ap-1271	102	8	×	×	NOUN
ap-1271	102	9	(	(	PUNCT
ap-1271	102	10	2k1	2k1	NUM
ap-1271	102	11	+	+	ADJ
ap-1271	102	12	k2)-diagonal	k2)-diagonal	ADJ
ap-1271	102	13	matrix	matrix	NOUN
ap-1271	102	14	d	d	NOUN
ap-1271	102	15	by	by	ADP
ap-1271	102	16	d	d	PROPN
ap-1271	102	17	=	=	SYM
ap-1271	102	18	diag	diag	X
ap-1271	102	19	(	(	PUNCT
ap-1271	102	20	1−	1−	NUM
ap-1271	102	21	β1	β1	NOUN
ap-1271	102	22	,	,	PUNCT
ap-1271	102	23	.	.	PUNCT
ap-1271	102	24	.	.	PUNCT
ap-1271	103	1	.	.	PUNCT
ap-1271	104	1	,	,	PUNCT
ap-1271	104	2	1−	1−	NUM
ap-1271	104	3	βk1	βk1	NOUN
ap-1271	104	4	,	,	PUNCT
ap-1271	104	5	β1	β1	PROPN
ap-1271	104	6	,	,	PUNCT
ap-1271	104	7	.	.	PUNCT
ap-1271	104	8	.	.	PUNCT
ap-1271	104	9	.	.	PUNCT
ap-1271	105	1	,	,	PUNCT
ap-1271	105	2	βk1	βk1	NOUN
ap-1271	105	3	,	,	PUNCT
ap-1271	105	4	(	(	PUNCT
ap-1271	105	5	6	6	X
ap-1271	105	6	)	)	PUNCT
ap-1271	105	7	−1/2	−1/2	ADJ
ap-1271	105	8	,	,	PUNCT
ap-1271	105	9	.	.	PUNCT
ap-1271	105	10	.	.	PUNCT
ap-1271	106	1	.	.	PUNCT
ap-1271	107	1	,	,	PUNCT
ap-1271	107	2	−1/2	−1/2	ADJ
ap-1271	107	3	)	)	PUNCT
ap-1271	107	4	.	.	PUNCT
ap-1271	108	1	now	now	ADV
ap-1271	108	2	our	our	PRON
ap-1271	108	3	theorem	theorem	NOUN
ap-1271	108	4	is	be	AUX
ap-1271	108	5	stated	state	VERB
ap-1271	108	6	as	as	SCONJ
ap-1271	108	7	follows	follow	VERB
ap-1271	108	8	.	.	PUNCT
ap-1271	109	1	theorem	theorem	VERB
ap-1271	109	2	1.2	1.2	NUM
ap-1271	109	3	assume	assume	VERB
ap-1271	109	4	(	(	PUNCT
ap-1271	109	5	a	a	NOUN
ap-1271	109	6	)	)	PUNCT
ap-1271	109	7	,	,	PUNCT
ap-1271	109	8	(	(	PUNCT
ap-1271	109	9	a0	a0	NOUN
ap-1271	109	10	)	)	PUNCT
ap-1271	109	11	,	,	PUNCT
ap-1271	109	12	(	(	PUNCT
ap-1271	109	13	a1	a1	NOUN
ap-1271	109	14	)	)	PUNCT
ap-1271	109	15	,	,	PUNCT
ap-1271	109	16	(	(	PUNCT
ap-1271	109	17	v	v	NOUN
ap-1271	109	18	)	)	PUNCT
ap-1271	109	19	,	,	PUNCT
ap-1271	109	20	(	(	PUNCT
ap-1271	109	21	sb	sb	X
ap-1271	109	22	)	)	PUNCT
ap-1271	109	23	and	and	CCONJ
ap-1271	109	24	k	k	X
ap-1271	109	25	<	<	X
ap-1271	109	26	∞.	∞.	PROPN
ap-1271	109	27	let	let	VERB
ap-1271	109	28	φ(u	φ(u	NOUN
ap-1271	109	29	)	)	PUNCT
ap-1271	109	30	,	,	PUNCT
ap-1271	110	1	d	d	NOUN
ap-1271	110	2	given	give	VERB
ap-1271	110	3	above	above	ADV
ap-1271	110	4	.	.	PUNCT
ap-1271	111	1	(	(	PUNCT
ap-1271	111	2	i	i	NOUN
ap-1271	111	3	)	)	PUNCT
ap-1271	111	4	let	let	VERB
ap-1271	111	5	x=	x=	PUNCT
ap-1271	112	1	(	(	PUNCT
ap-1271	112	2	x1	x1	NOUN
ap-1271	112	3	x2	x2	PROPN
ap-1271	112	4	)	)	PUNCT
ap-1271	112	5	,	,	PUNCT
ap-1271	112	6	where	where	SCONJ
ap-1271	112	7	x1	x1	X
ap-1271	112	8	,	,	PUNCT
ap-1271	112	9	x2	x2	PRON
ap-1271	112	10	are	be	AUX
ap-1271	112	11	(	(	PUNCT
ap-1271	112	12	2k1	2k1	NUM
ap-1271	112	13	+	+	NUM
ap-1271	112	14	k2)×	k2)×	NOUN
ap-1271	112	15	(	(	PUNCT
ap-1271	112	16	2k1	2k1	NUM
ap-1271	112	17	+	+	ADJ
ap-1271	112	18	k2	k2	ADJ
ap-1271	112	19	)	)	PUNCT
ap-1271	112	20	matrices	matrix	NOUN
ap-1271	112	21	satisfying	satisfy	VERB
ap-1271	112	22	rankx	rankx	NOUN
ap-1271	113	1	=	=	NOUN
ap-1271	113	2	2k1	2k1	NUM
ap-1271	114	1	+	+	ADJ
ap-1271	114	2	k2	k2	ADJ
ap-1271	114	3	,	,	PUNCT
ap-1271	114	4	x∗	x∗	X
ap-1271	114	5	1dx2	1dx2	NUM
ap-1271	114	6	=	=	SYM
ap-1271	114	7	x∗	x∗	X
ap-1271	114	8	2dx1	2dx1	NUM
ap-1271	114	9	.	.	PUNCT
ap-1271	115	1	(	(	PUNCT
ap-1271	115	2	7	7	NUM
ap-1271	115	3	)	)	PUNCT
ap-1271	115	4	then	then	ADV
ap-1271	115	5	,	,	PUNCT
ap-1271	115	6	the	the	DET
ap-1271	115	7	operator	operator	NOUN
ap-1271	115	8	hx	hx	PROPN
ap-1271	115	9	defined	define	VERB
ap-1271	115	10	by	by	ADP
ap-1271	115	11	hxu	hxu	NOUN
ap-1271	115	12	=	=	SYM
ap-1271	115	13	lu	lu	PROPN
ap-1271	115	14	,	,	PUNCT
ap-1271	115	15	d(hx	d(hx	NOUN
ap-1271	115	16	)	)	PUNCT
ap-1271	115	17	=	=	SYM
ap-1271	115	18	{	{	PUNCT
ap-1271	115	19	u	u	NOUN
ap-1271	115	20	∈	∈	PROPN
ap-1271	115	21	d(hmax	d(hmax	NOUN
ap-1271	115	22	)	)	PUNCT
ap-1271	115	23	|	|	ADV
ap-1271	115	24	φ(u	φ(u	NOUN
ap-1271	115	25	)	)	PUNCT
ap-1271	115	26	∈	∈	PROPN
ap-1271	115	27	ranx	ranx	NOUN
ap-1271	115	28	}	}	PUNCT
ap-1271	115	29	is	be	AUX
ap-1271	115	30	a	a	DET
ap-1271	115	31	self	self	NOUN
ap-1271	115	32	-	-	PUNCT
ap-1271	115	33	adjoint	adjoint	NOUN
ap-1271	115	34	extension	extension	NOUN
ap-1271	115	35	of	of	ADP
ap-1271	115	36	hmin	hmin	PROPN
ap-1271	115	37	.	.	PUNCT
ap-1271	116	1	(	(	PUNCT
ap-1271	116	2	ii	ii	NOUN
ap-1271	116	3	)	)	PUNCT
ap-1271	116	4	for	for	ADP
ap-1271	116	5	any	any	DET
ap-1271	116	6	self	self	NOUN
ap-1271	116	7	-	-	PUNCT
ap-1271	116	8	adjoint	adjoint	NOUN
ap-1271	116	9	extension	extension	NOUN
ap-1271	116	10	h	h	NOUN
ap-1271	116	11	of	of	ADP
ap-1271	116	12	hmin	hmin	NOUN
ap-1271	116	13	,	,	PUNCT
ap-1271	116	14	there	there	PRON
ap-1271	116	15	exists	exist	VERB
ap-1271	116	16	some	some	DET
ap-1271	116	17	matrix	matrix	NOUN
ap-1271	116	18	x	x	X
ap-1271	116	19	satisfying	satisfy	VERB
ap-1271	116	20	(	(	PUNCT
ap-1271	116	21	7	7	NUM
ap-1271	116	22	)	)	PUNCT
ap-1271	116	23	and	and	CCONJ
ap-1271	116	24	h	h	NOUN
ap-1271	116	25	=	=	NOUN
ap-1271	116	26	hx	hx	PROPN
ap-1271	116	27	.	.	PUNCT
ap-1271	117	1	we	we	PRON
ap-1271	117	2	can	can	AUX
ap-1271	117	3	consider	consider	VERB
ap-1271	117	4	the	the	DET
ap-1271	117	5	case	case	NOUN
ap-1271	117	6	k	k	PROPN
ap-1271	117	7	=	=	NOUN
ap-1271	117	8	∞	∞	PROPN
ap-1271	117	9	,	,	PUNCT
ap-1271	117	10	but	but	CCONJ
ap-1271	117	11	some	some	DET
ap-1271	117	12	technical	technical	ADJ
ap-1271	117	13	assumptions	assumption	NOUN
ap-1271	117	14	are	be	AUX
ap-1271	117	15	necessary	necessary	ADJ
ap-1271	117	16	.	.	PUNCT
ap-1271	118	1	we	we	PRON
ap-1271	118	2	shall	shall	AUX
ap-1271	118	3	argue	argue	VERB
ap-1271	118	4	this	this	DET
ap-1271	118	5	case	case	NOUN
ap-1271	118	6	in	in	ADP
ap-1271	118	7	section	section	NOUN
ap-1271	118	8	5	5	NUM
ap-1271	118	9	.	.	PUNCT
ap-1271	119	1	thus	thus	ADV
ap-1271	119	2	we	we	PRON
ap-1271	119	3	can	can	AUX
ap-1271	119	4	characterize	characterize	VERB
ap-1271	119	5	the	the	DET
ap-1271	119	6	self	self	NOUN
ap-1271	119	7	-	-	PUNCT
ap-1271	119	8	adjoint	adjoint	NOUN
ap-1271	119	9	extensions	extension	NOUN
ap-1271	119	10	in	in	ADP
ap-1271	119	11	terms	term	NOUN
ap-1271	119	12	of	of	ADP
ap-1271	119	13	the	the	DET
ap-1271	119	14	boundary	boundary	ADJ
ap-1271	119	15	conditions	condition	NOUN
ap-1271	119	16	.	.	PUNCT
ap-1271	120	1	we	we	PRON
ap-1271	120	2	can	can	AUX
ap-1271	120	3	easily	easily	ADV
ap-1271	120	4	prove	prove	VERB
ap-1271	120	5	that	that	SCONJ
ap-1271	120	6	the	the	DET
ap-1271	120	7	friedrichs	friedrichs	ADJ
ap-1271	120	8	extension	extension	NOUN
ap-1271	120	9	corresponds	correspond	VERB
ap-1271	120	10	to	to	ADP
ap-1271	120	11	the	the	DET
ap-1271	120	12	case	case	NOUN
ap-1271	121	1	x1	x1	NOUN
ap-1271	121	2	=	=	SYM
ap-1271	122	1	o	o	NOUN
ap-1271	122	2	,	,	PUNCT
ap-1271	122	3	x2	x2	PROPN
ap-1271	122	4	=	=	PUNCT
ap-1271	123	1	i	i	PRON
ap-1271	123	2	d.	d.	PROPN
ap-1271	123	3	in	in	ADP
ap-1271	123	4	the	the	DET
ap-1271	123	5	case	case	NOUN
ap-1271	123	6	m	m	NOUN
ap-1271	123	7	=	=	SYM
ap-1271	123	8	r	r	NOUN
ap-1271	123	9	2	2	NUM
ap-1271	123	10	and	and	CCONJ
ap-1271	123	11	k	k	NOUN
ap-1271	123	12	=	=	SYM
ap-1271	123	13	1	1	NUM
ap-1271	123	14	,	,	PUNCT
ap-1271	123	15	similar	similar	ADJ
ap-1271	123	16	results	result	NOUN
ap-1271	123	17	are	be	AUX
ap-1271	123	18	obtained	obtain	VERB
ap-1271	123	19	in	in	ADP
ap-1271	123	20	[	[	X
ap-1271	123	21	7	7	NUM
ap-1271	123	22	]	]	PUNCT
ap-1271	123	23	and	and	CCONJ
ap-1271	123	24	[	[	X
ap-1271	123	25	8	8	NUM
ap-1271	123	26	]	]	PUNCT
ap-1271	123	27	,	,	PUNCT
ap-1271	123	28	and	and	CCONJ
ap-1271	123	29	our	our	PRON
ap-1271	123	30	theorem	theorem	NOUN
ap-1271	123	31	is	be	AUX
ap-1271	123	32	a	a	DET
ap-1271	123	33	generalization	generalization	NOUN
ap-1271	123	34	of	of	ADP
ap-1271	123	35	their	their	PRON
ap-1271	123	36	results	result	NOUN
ap-1271	123	37	.	.	PUNCT
ap-1271	124	1	as	as	SCONJ
ap-1271	124	2	stated	state	VERB
ap-1271	124	3	in	in	ADP
ap-1271	124	4	their	their	PRON
ap-1271	124	5	paper	paper	NOUN
ap-1271	124	6	,	,	PUNCT
ap-1271	124	7	the	the	DET
ap-1271	124	8	choice	choice	NOUN
ap-1271	124	9	of	of	ADP
ap-1271	124	10	matrices	matrix	NOUN
ap-1271	124	11	x	x	X
ap-1271	124	12	is	be	AUX
ap-1271	124	13	of	of	ADP
ap-1271	124	14	course	course	NOUN
ap-1271	124	15	not	not	PART
ap-1271	124	16	unique	unique	ADJ
ap-1271	124	17	:	:	PUNCT
ap-1271	124	18	there	there	PRON
ap-1271	124	19	are	be	VERB
ap-1271	124	20	infinitely	infinitely	ADV
ap-1271	124	21	many	many	ADJ
ap-1271	124	22	matrices	matrix	NOUN
ap-1271	124	23	x	x	PUNCT
ap-1271	124	24	giving	give	VERB
ap-1271	124	25	same	same	ADJ
ap-1271	124	26	ranx	ranx	NOUN
ap-1271	124	27	.	.	PUNCT
ap-1271	125	1	the	the	DET
ap-1271	125	2	difficulty	difficulty	NOUN
ap-1271	125	3	in	in	ADP
ap-1271	125	4	the	the	DET
ap-1271	125	5	proof	proof	NOUN
ap-1271	125	6	is	be	AUX
ap-1271	125	7	that	that	SCONJ
ap-1271	125	8	we	we	PRON
ap-1271	125	9	can	can	AUX
ap-1271	125	10	not	not	PART
ap-1271	125	11	determine	determine	VERB
ap-1271	125	12	the	the	DET
ap-1271	125	13	deficiency	deficiency	NOUN
ap-1271	125	14	subspaces	subspace	NOUN
ap-1271	125	15	explicitly	explicitly	ADV
ap-1271	125	16	.	.	PUNCT
ap-1271	126	1	to	to	PART
ap-1271	126	2	overcome	overcome	VERB
ap-1271	126	3	this	this	DET
ap-1271	126	4	difficulty	difficulty	NOUN
ap-1271	126	5	,	,	PUNCT
ap-1271	126	6	we	we	PRON
ap-1271	126	7	describe	describe	VERB
ap-1271	126	8	the	the	DET
ap-1271	126	9	condition	condition	NOUN
ap-1271	126	10	of	of	ADP
ap-1271	126	11	the	the	DET
ap-1271	126	12	self	self	NOUN
ap-1271	126	13	-	-	PUNCT
ap-1271	126	14	adjointness	adjointness	NOUN
ap-1271	126	15	only	only	ADV
ap-1271	126	16	using	use	VERB
ap-1271	126	17	the	the	DET
ap-1271	126	18	quotient	quotient	NOUN
ap-1271	126	19	subspace	subspace	NOUN
ap-1271	126	20	d(hmax)/d(hmin	d(hmax)/d(hmin	PROPN
ap-1271	126	21	)	)	PUNCT
ap-1271	126	22	.	.	PUNCT
ap-1271	127	1	this	this	DET
ap-1271	127	2	quotient	quotient	NOUN
ap-1271	127	3	subspace	subspace	NOUN
ap-1271	127	4	is	be	AUX
ap-1271	127	5	essentially	essentially	ADV
ap-1271	127	6	the	the	DET
ap-1271	127	7	same	same	ADJ
ap-1271	127	8	object	object	NOUN
ap-1271	127	9	as	as	ADP
ap-1271	127	10	the	the	DET
ap-1271	127	11	sum	sum	NOUN
ap-1271	127	12	of	of	ADP
ap-1271	127	13	deficiency	deficiency	NOUN
ap-1271	127	14	subspaces	subspace	NOUN
ap-1271	127	15	,	,	PUNCT
ap-1271	127	16	but	but	CCONJ
ap-1271	127	17	much	much	ADV
ap-1271	127	18	easily	easily	ADV
ap-1271	127	19	tractable	tractable	ADJ
ap-1271	127	20	than	than	SCONJ
ap-1271	127	21	the	the	DET
ap-1271	127	22	deficiency	deficiency	NOUN
ap-1271	127	23	subspaces	subspace	VERB
ap-1271	127	24	themselves	themselves	PRON
ap-1271	127	25	.	.	PUNCT
ap-1271	128	1	this	this	DET
ap-1271	128	2	idea	idea	NOUN
ap-1271	128	3	is	be	AUX
ap-1271	128	4	also	also	ADV
ap-1271	128	5	used	use	VERB
ap-1271	128	6	in	in	ADP
ap-1271	128	7	[	[	X
ap-1271	128	8	4	4	NUM
ap-1271	128	9	]	]	PUNCT
ap-1271	128	10	or	or	CCONJ
ap-1271	128	11	[	[	X
ap-1271	128	12	12	12	NUM
ap-1271	128	13	]	]	PUNCT
ap-1271	128	14	.	.	PUNCT
ap-1271	129	1	we	we	PRON
ap-1271	129	2	note	note	VERB
ap-1271	129	3	that	that	SCONJ
ap-1271	129	4	recently	recently	ADV
ap-1271	129	5	self	self	NOUN
ap-1271	129	6	-	-	PUNCT
ap-1271	129	7	adjoint	adjoint	NOUN
ap-1271	129	8	extensions	extension	NOUN
ap-1271	129	9	of	of	ADP
ap-1271	129	10	the	the	DET
ap-1271	129	11	schrödinger	schrödinger	NOUN
ap-1271	129	12	operators	operator	NOUN
ap-1271	129	13	on	on	ADP
ap-1271	129	14	r2	r2	PROPN
ap-1271	129	15	with	with	ADP
ap-1271	129	16	δ	δ	PROPN
ap-1271	129	17	magnetic	magnetic	ADJ
ap-1271	129	18	fields	field	NOUN
ap-1271	129	19	are	be	AUX
ap-1271	129	20	studied	study	VERB
ap-1271	129	21	from	from	ADP
ap-1271	129	22	the	the	DET
ap-1271	129	23	viewpoint	viewpoint	NOUN
ap-1271	129	24	of	of	ADP
ap-1271	129	25	the	the	DET
ap-1271	129	26	hidden	hide	VERB
ap-1271	129	27	supersymmetric	supersymmetric	ADJ
ap-1271	129	28	structure	structure	NOUN
ap-1271	129	29	;	;	PUNCT
ap-1271	129	30	see	see	VERB
ap-1271	129	31	correa	correa	PROPN
ap-1271	129	32	et	et	PROPN
ap-1271	129	33	al	al	PROPN
ap-1271	129	34	.	.	PUNCT
ap-1271	130	1	[	[	X
ap-1271	130	2	5	5	NUM
ap-1271	130	3	,	,	PUNCT
ap-1271	130	4	6	6	NUM
ap-1271	130	5	]	]	PUNCT
ap-1271	130	6	.	.	PUNCT
ap-1271	131	1	the	the	DET
ap-1271	131	2	rest	rest	NOUN
ap-1271	131	3	of	of	ADP
ap-1271	131	4	the	the	DET
ap-1271	131	5	paper	paper	NOUN
ap-1271	131	6	is	be	AUX
ap-1271	131	7	organized	organize	VERB
ap-1271	131	8	as	as	SCONJ
ap-1271	131	9	follows	follow	VERB
ap-1271	131	10	.	.	PUNCT
ap-1271	132	1	in	in	ADP
ap-1271	132	2	section	section	NOUN
ap-1271	132	3	2	2	NUM
ap-1271	132	4	,	,	PUNCT
ap-1271	132	5	we	we	PRON
ap-1271	132	6	review	review	VERB
ap-1271	132	7	basic	basic	ADJ
ap-1271	132	8	notations	notation	NOUN
ap-1271	132	9	and	and	CCONJ
ap-1271	132	10	facts	fact	NOUN
ap-1271	132	11	from	from	ADP
ap-1271	132	12	the	the	DET
ap-1271	132	13	differential	differential	ADJ
ap-1271	132	14	geometry	geometry	NOUN
ap-1271	132	15	and	and	CCONJ
ap-1271	132	16	the	the	DET
ap-1271	132	17	theory	theory	NOUN
ap-1271	132	18	of	of	ADP
ap-1271	132	19	selfadjoint	selfadjoint	NOUN
ap-1271	132	20	extensions	extension	NOUN
ap-1271	132	21	.	.	PUNCT
ap-1271	133	1	in	in	ADP
ap-1271	133	2	section	section	NOUN
ap-1271	133	3	3	3	NUM
ap-1271	133	4	,	,	PUNCT
ap-1271	133	5	we	we	PRON
ap-1271	133	6	shall	shall	AUX
ap-1271	133	7	prove	prove	VERB
ap-1271	133	8	the	the	DET
ap-1271	133	9	structure	structure	NOUN
ap-1271	133	10	of	of	ADP
ap-1271	133	11	the	the	DET
ap-1271	133	12	self	self	NOUN
ap-1271	133	13	-	-	PUNCT
ap-1271	133	14	adjoint	adjoint	NOUN
ap-1271	133	15	extensions	extension	NOUN
ap-1271	133	16	depends	depend	VERB
ap-1271	133	17	only	only	ADV
ap-1271	133	18	on	on	ADP
ap-1271	133	19	the	the	DET
ap-1271	133	20	singular	singular	ADJ
ap-1271	133	21	part	part	NOUN
ap-1271	133	22	of	of	ADP
ap-1271	133	23	the	the	DET
ap-1271	133	24	vector	vector	NOUN
ap-1271	133	25	potentials	potential	VERB
ap-1271	133	26	.	.	PUNCT
ap-1271	134	1	in	in	ADP
ap-1271	134	2	section	section	NOUN
ap-1271	134	3	4	4	NUM
ap-1271	134	4	,	,	PUNCT
ap-1271	134	5	we	we	PRON
ap-1271	134	6	shall	shall	AUX
ap-1271	134	7	prove	prove	VERB
ap-1271	134	8	the	the	DET
ap-1271	134	9	main	main	ADJ
ap-1271	134	10	theorems	theorem	NOUN
ap-1271	134	11	.	.	PUNCT
ap-1271	135	1	in	in	ADP
ap-1271	135	2	section	section	NOUN
ap-1271	135	3	5	5	NUM
ap-1271	135	4	,	,	PUNCT
ap-1271	135	5	we	we	PRON
ap-1271	135	6	shall	shall	AUX
ap-1271	135	7	consider	consider	VERB
ap-1271	135	8	the	the	DET
ap-1271	135	9	case	case	NOUN
ap-1271	135	10	k	k	NOUN
ap-1271	135	11	=	=	SYM
ap-1271	135	12	∞	∞	PROPN
ap-1271	135	13	and	and	CCONJ
ap-1271	135	14	give	give	VERB
ap-1271	135	15	a	a	DET
ap-1271	135	16	complete	complete	ADJ
ap-1271	135	17	characterization	characterization	NOUN
ap-1271	135	18	of	of	ADP
ap-1271	135	19	the	the	DET
ap-1271	135	20	self	self	NOUN
ap-1271	135	21	-	-	PUNCT
ap-1271	135	22	adjoint	adjoint	NOUN
ap-1271	135	23	extensions	extension	NOUN
ap-1271	135	24	,	,	PUNCT
ap-1271	135	25	under	under	ADP
ap-1271	135	26	some	some	DET
ap-1271	135	27	homogeneity	homogeneity	NOUN
ap-1271	135	28	conditions	condition	NOUN
ap-1271	135	29	.	.	PUNCT
ap-1271	136	1	2	2	NUM
ap-1271	136	2	basic	basic	ADJ
ap-1271	136	3	facts	fact	NOUN
ap-1271	136	4	2.1	2.1	NUM
ap-1271	136	5	formulas	formula	NOUN
ap-1271	136	6	in	in	ADP
ap-1271	136	7	differential	differential	ADJ
ap-1271	136	8	geometry	geometry	NOUN
ap-1271	136	9	we	we	PRON
ap-1271	136	10	quote	quote	VERB
ap-1271	136	11	some	some	DET
ap-1271	136	12	formulas	formula	NOUN
ap-1271	136	13	used	use	VERB
ap-1271	136	14	in	in	ADP
ap-1271	136	15	shubin	shubin	PROPN
ap-1271	137	1	[	[	X
ap-1271	137	2	14	14	NUM
ap-1271	137	3	]	]	PUNCT
ap-1271	137	4	for	for	ADP
ap-1271	137	5	the	the	DET
ap-1271	137	6	convenience	convenience	NOUN
ap-1271	137	7	of	of	ADP
ap-1271	137	8	the	the	DET
ap-1271	137	9	readers	reader	NOUN
ap-1271	137	10	.	.	PUNCT
ap-1271	138	1	take	take	VERB
ap-1271	138	2	a	a	DET
ap-1271	138	3	local	local	ADJ
ap-1271	138	4	chart	chart	NOUN
ap-1271	138	5	(	(	PUNCT
ap-1271	138	6	u	u	NOUN
ap-1271	138	7	,	,	PUNCT
ap-1271	138	8	ϕ	ϕ	NOUN
ap-1271	138	9	)	)	PUNCT
ap-1271	138	10	,	,	PUNCT
ap-1271	138	11	ϕ	ϕ	X
ap-1271	139	1	=	=	SYM
ap-1271	139	2	(	(	PUNCT
ap-1271	139	3	x1	x1	PROPN
ap-1271	139	4	,	,	PUNCT
ap-1271	139	5	x2	x2	PROPN
ap-1271	139	6	)	)	PUNCT
ap-1271	139	7	,	,	PUNCT
ap-1271	139	8	around	around	ADP
ap-1271	139	9	p	p	X
ap-1271	139	10	∈	∈	PROPN
ap-1271	139	11	m	m	VERB
ap-1271	139	12	.	.	PUNCT
ap-1271	140	1	put	put	VERB
ap-1271	140	2	gmn	gmn	NOUN
ap-1271	140	3	=	=	SYM
ap-1271	140	4	g(∂m	g(∂m	PROPN
ap-1271	140	5	,	,	PUNCT
ap-1271	140	6	∂n	∂n	PROPN
ap-1271	140	7	)	)	PUNCT
ap-1271	140	8	,	,	PUNCT
ap-1271	140	9	and	and	CCONJ
ap-1271	140	10	let	let	VERB
ap-1271	140	11	(	(	PUNCT
ap-1271	140	12	gmn	gmn	NOUN
ap-1271	140	13	)	)	PUNCT
ap-1271	140	14	be	be	VERB
ap-1271	140	15	the	the	DET
ap-1271	140	16	inverse	inverse	ADJ
ap-1271	140	17	matrix	matrix	NOUN
ap-1271	140	18	of	of	ADP
ap-1271	140	19	(	(	PUNCT
ap-1271	140	20	gmn	gmn	NOUN
ap-1271	140	21	)	)	PUNCT
ap-1271	140	22	.	.	PUNCT
ap-1271	141	1	for	for	ADP
ap-1271	141	2	α	α	NOUN
ap-1271	141	3	,	,	PUNCT
ap-1271	141	4	β	β	X
ap-1271	141	5	∈	∈	PROPN
ap-1271	141	6	λ1p(m	λ1p(m	PROPN
ap-1271	141	7	)	)	PUNCT
ap-1271	141	8	(	(	PUNCT
ap-1271	141	9	the	the	DET
ap-1271	141	10	cotangent	cotangent	NOUN
ap-1271	141	11	space	space	NOUN
ap-1271	141	12	at	at	ADP
ap-1271	141	13	p	p	NOUN
ap-1271	141	14	)	)	PUNCT
ap-1271	141	15	,	,	PUNCT
ap-1271	141	16	we	we	PRON
ap-1271	141	17	define	define	VERB
ap-1271	141	18	the	the	DET
ap-1271	141	19	scalar	scalar	ADJ
ap-1271	141	20	product	product	NOUN
ap-1271	141	21	〈	〈	PROPN
ap-1271	141	22	α	α	PRON
ap-1271	141	23	,	,	PUNCT
ap-1271	141	24	β	β	NOUN
ap-1271	141	25	〉	〉	NOUN
ap-1271	141	26	=	=	SYM
ap-1271	141	27	∑	∑	PROPN
ap-1271	141	28	m	m	PROPN
ap-1271	141	29	,	,	PUNCT
ap-1271	141	30	n=1,2	n=1,2	ADJ
ap-1271	141	31	gmnαmβn	gmnαmβn	NOUN
ap-1271	141	32	,	,	PUNCT
ap-1271	141	33	where	where	SCONJ
ap-1271	141	34	α	α	NOUN
ap-1271	141	35	=	=	PUNCT
ap-1271	141	36	α1dx1	α1dx1	PROPN
ap-1271	141	37	+	+	CCONJ
ap-1271	141	38	α2dx2	α2dx2	NOUN
ap-1271	141	39	and	and	CCONJ
ap-1271	141	40	β	β	X
ap-1271	141	41	=	=	PUNCT
ap-1271	141	42	β1dx1	β1dx1	PROPN
ap-1271	142	1	+	+	CCONJ
ap-1271	142	2	β2dx2	β2dx2	PROPN
ap-1271	142	3	.	.	PUNCT
ap-1271	143	1	put	put	VERB
ap-1271	143	2	|α|2	|α|2	NOUN
ap-1271	143	3	=	=	SYM
ap-1271	143	4	〈	〈	PROPN
ap-1271	143	5	α	α	NOUN
ap-1271	143	6	,	,	PUNCT
ap-1271	143	7	α	α	PROPN
ap-1271	143	8	〉	〉	PROPN
ap-1271	143	9	,	,	PUNCT
ap-1271	143	10	where	where	SCONJ
ap-1271	143	11	α	α	NOUN
ap-1271	143	12	=	=	PUNCT
ap-1271	143	13	α1dx1	α1dx1	PROPN
ap-1271	143	14	+	+	CCONJ
ap-1271	143	15	α2dx2	α2dx2	NOUN
ap-1271	143	16	.	.	PUNCT
ap-1271	144	1	for	for	ADP
ap-1271	144	2	a	a	DET
ap-1271	144	3	1	1	NUM
ap-1271	144	4	-	-	PUNCT
ap-1271	144	5	form	form	NOUN
ap-1271	144	6	ω	ω	NOUN
ap-1271	144	7	=	=	SYM
ap-1271	144	8	ω1dx2	ω1dx2	ADJ
ap-1271	144	9	+	+	SYM
ap-1271	144	10	ω2dx2	ω2dx2	NOUN
ap-1271	144	11	,	,	PUNCT
ap-1271	144	12	we	we	PRON
ap-1271	144	13	define	define	VERB
ap-1271	144	14	a	a	DET
ap-1271	144	15	function	function	NOUN
ap-1271	144	16	d∗ω	d∗ω	NUM
ap-1271	144	17	by	by	ADP
ap-1271	144	18	d∗ω	d∗ω	NUM
ap-1271	144	19	=	=	SYM
ap-1271	144	20	−	−	PROPN
ap-1271	144	21	1√	1√	PROPN
ap-1271	144	22	g	g	PROPN
ap-1271	144	23	∑	∑	PROPN
ap-1271	144	24	m	m	PROPN
ap-1271	144	25	,	,	PUNCT
ap-1271	144	26	n=1,2	n=1,2	PROPN
ap-1271	144	27	∂m	∂m	PROPN
ap-1271	144	28	(	(	PUNCT
ap-1271	144	29	√	√	ADP
ap-1271	144	30	ggmnωn	ggmnωn	NOUN
ap-1271	144	31	)	)	PUNCT
ap-1271	144	32	.	.	PUNCT
ap-1271	145	1	this	this	DET
ap-1271	145	2	definition	definition	NOUN
ap-1271	145	3	is	be	AUX
ap-1271	145	4	independent	independent	ADJ
ap-1271	145	5	of	of	ADP
ap-1271	145	6	the	the	DET
ap-1271	145	7	choice	choice	NOUN
ap-1271	145	8	of	of	ADP
ap-1271	145	9	local	local	ADJ
ap-1271	145	10	coordinates	coordinate	NOUN
ap-1271	145	11	.	.	PUNCT
ap-1271	146	1	actually	actually	ADV
ap-1271	146	2	,	,	PUNCT
ap-1271	146	3	operator	operator	NOUN
ap-1271	146	4	d∗	d∗	NOUN
ap-1271	146	5	is	be	AUX
ap-1271	146	6	characterized	characterize	VERB
ap-1271	146	7	by	by	ADP
ap-1271	146	8	the	the	DET
ap-1271	146	9	following	follow	VERB
ap-1271	146	10	relation:∫	relation:∫	PROPN
ap-1271	146	11	m	m	VERB
ap-1271	146	12	〈	〈	PROPN
ap-1271	146	13	du	du	X
ap-1271	146	14	,	,	PUNCT
ap-1271	146	15	ω〉dμ	ω〉dμ	NOUN
ap-1271	146	16	=	=	SYM
ap-1271	146	17	∫	∫	PROPN
ap-1271	147	1	m	m	PRON
ap-1271	147	2	ud∗ω	ud∗ω	INTJ
ap-1271	147	3	dμ	dμ	VERB
ap-1271	147	4	for	for	ADP
ap-1271	147	5	any	any	DET
ap-1271	147	6	u	u	PROPN
ap-1271	147	7	∈	∈	PROPN
ap-1271	147	8	c∞	c∞	PROPN
ap-1271	147	9	0	0	NUM
ap-1271	147	10	(	(	PUNCT
ap-1271	147	11	m	m	NOUN
ap-1271	147	12	)	)	PUNCT
ap-1271	147	13	and	and	CCONJ
ap-1271	147	14	ω	ω	NUM
ap-1271	147	15	∈	∈	PROPN
ap-1271	147	16	c∞	c∞	NOUN
ap-1271	147	17	0	0	NUM
ap-1271	147	18	λ	λ	NOUN
ap-1271	147	19	1(m	1(m	NUM
ap-1271	147	20	)	)	PUNCT
ap-1271	147	21	.	.	PUNCT
ap-1271	148	1	let	let	VERB
ap-1271	148	2	a	a	PRON
ap-1271	148	3	be	be	AUX
ap-1271	148	4	a	a	DET
ap-1271	148	5	1	1	NUM
ap-1271	148	6	-	-	PUNCT
ap-1271	148	7	form	form	NOUN
ap-1271	148	8	satisfying	satisfy	VERB
ap-1271	148	9	our	our	PRON
ap-1271	148	10	assumptions	assumption	NOUN
ap-1271	148	11	.	.	PUNCT
ap-1271	149	1	for	for	ADP
ap-1271	149	2	a	a	DET
ap-1271	149	3	function	function	NOUN
ap-1271	149	4	f	f	NOUN
ap-1271	149	5	,	,	PUNCT
ap-1271	149	6	we	we	PRON
ap-1271	149	7	define	define	VERB
ap-1271	149	8	a	a	DET
ap-1271	149	9	1	1	NUM
ap-1271	149	10	-	-	PUNCT
ap-1271	149	11	form	form	NOUN
ap-1271	149	12	daf	daf	NOUN
ap-1271	149	13	by	by	ADP
ap-1271	149	14	daf	daf	PROPN
ap-1271	149	15	=	=	SYM
ap-1271	149	16	df	df	PROPN
ap-1271	149	17	+	+	NUM
ap-1271	149	18	ifa	ifa	PROPN
ap-1271	149	19	,	,	PUNCT
ap-1271	149	20	where	where	SCONJ
ap-1271	149	21	d	d	NOUN
ap-1271	149	22	is	be	AUX
ap-1271	149	23	the	the	DET
ap-1271	149	24	exterior	exterior	ADJ
ap-1271	149	25	derivative	derivative	NOUN
ap-1271	149	26	,	,	PUNCT
ap-1271	149	27	and	and	CCONJ
ap-1271	149	28	i	i	NOUN
ap-1271	149	29	=	=	NOUN
ap-1271	149	30	√	√	NUM
ap-1271	149	31	−1	−1	NOUN
ap-1271	149	32	.	.	PUNCT
ap-1271	150	1	for	for	ADP
ap-1271	150	2	a	a	DET
ap-1271	150	3	1	1	NUM
ap-1271	150	4	-	-	PUNCT
ap-1271	150	5	form	form	NOUN
ap-1271	150	6	ω	ω	NOUN
ap-1271	150	7	,	,	PUNCT
ap-1271	150	8	we	we	PRON
ap-1271	150	9	define	define	VERB
ap-1271	150	10	d∗aω	d∗aω	PRON
ap-1271	150	11	=	=	NOUN
ap-1271	150	12	d∗ω	d∗ω	NUM
ap-1271	150	13	−	−	NOUN
ap-1271	150	14	ia∗ω	ia∗ω	NOUN
ap-1271	150	15	,	,	PUNCT
ap-1271	150	16	a∗ω	a∗ω	ADP
ap-1271	150	17	=	=	PUNCT
ap-1271	150	18	〈	〈	PROPN
ap-1271	150	19	a	a	PRON
ap-1271	150	20	,	,	PUNCT
ap-1271	150	21	ω	ω	PROPN
ap-1271	150	22	〉	〉	NOUN
ap-1271	150	23	.	.	PROPN
ap-1271	151	1	64	64	NUM
ap-1271	151	2	acta	acta	PROPN
ap-1271	151	3	polytechnica	polytechnica	PROPN
ap-1271	151	4	vol	vol	NOUN
ap-1271	151	5	.	.	PROPN
ap-1271	152	1	50	50	NUM
ap-1271	152	2	no	no	NOUN
ap-1271	152	3	.	.	PUNCT
ap-1271	153	1	5/2010	5/2010	NUM
ap-1271	153	2	then	then	ADV
ap-1271	153	3	we	we	PRON
ap-1271	153	4	obtain	obtain	VERB
ap-1271	153	5	a	a	DET
ap-1271	153	6	representation	representation	NOUN
ap-1271	153	7	of	of	ADP
ap-1271	153	8	our	our	PRON
ap-1271	153	9	schrödinger	schrödinger	NOUN
ap-1271	153	10	operator	operator	NOUN
ap-1271	153	11	l	l	NOUN
ap-1271	153	12	independent	independent	NOUN
ap-1271	153	13	of	of	ADP
ap-1271	153	14	local	local	ADJ
ap-1271	153	15	coordinates	coordinate	NOUN
ap-1271	153	16	:	:	PUNCT
ap-1271	153	17	l	l	X
ap-1271	153	18	=	=	PUNCT
ap-1271	153	19	d∗ada	d∗ada	PROPN
ap-1271	153	20	+	+	CCONJ
ap-1271	153	21	v.	v.	CCONJ
ap-1271	153	22	for	for	ADP
ap-1271	153	23	operator	operator	NOUN
ap-1271	153	24	d∗a	d∗a	PROPN
ap-1271	153	25	,	,	PUNCT
ap-1271	153	26	the	the	DET
ap-1271	153	27	following	follow	VERB
ap-1271	153	28	leibniz	leibniz	PROPN
ap-1271	153	29	formulas	formula	NOUN
ap-1271	153	30	hold	hold	VERB
ap-1271	153	31	:	:	PUNCT
ap-1271	153	32	for	for	ADP
ap-1271	153	33	an	an	DET
ap-1271	153	34	appropriate	appropriate	ADJ
ap-1271	153	35	function	function	NOUN
ap-1271	153	36	f	f	NOUN
ap-1271	153	37	and	and	CCONJ
ap-1271	153	38	1	1	NUM
ap-1271	153	39	-	-	PUNCT
ap-1271	153	40	form	form	NOUN
ap-1271	153	41	ω	ω	NOUN
ap-1271	153	42	,	,	PUNCT
ap-1271	153	43	we	we	PRON
ap-1271	153	44	have	have	VERB
ap-1271	153	45	d∗a(fω	d∗a(fω	NOUN
ap-1271	153	46	)	)	PUNCT
ap-1271	153	47	=	=	SYM
ap-1271	153	48	fd∗ω	fd∗ω	PROPN
ap-1271	153	49	−	−	PROPN
ap-1271	153	50	〈	〈	PROPN
ap-1271	153	51	df	df	PROPN
ap-1271	153	52	,	,	PUNCT
ap-1271	153	53	ω	ω	PROPN
ap-1271	153	54	〉	〉	NOUN
ap-1271	153	55	−	−	NOUN
ap-1271	153	56	if〈a	if〈a	PROPN
ap-1271	153	57	,	,	PUNCT
ap-1271	153	58	ω	ω	NOUN
ap-1271	154	1	〉	〉	NUM
ap-1271	154	2	=	=	PUNCT
ap-1271	154	3	fd∗aω	fd∗aω	PROPN
ap-1271	155	1	−	−	PROPN
ap-1271	156	1	〈	〈	PROPN
ap-1271	156	2	df	df	PROPN
ap-1271	156	3	,	,	PUNCT
ap-1271	156	4	ω	ω	NOUN
ap-1271	156	5	〉	〉	NUM
ap-1271	156	6	=	=	SYM
ap-1271	156	7	fd∗ω	fd∗ω	PROPN
ap-1271	156	8	−	−	PROPN
ap-1271	156	9	〈	〈	PROPN
ap-1271	156	10	daf	daf	PROPN
ap-1271	156	11	,	,	PUNCT
ap-1271	156	12	ω	ω	PROPN
ap-1271	156	13	〉	〉	PROPN
ap-1271	156	14	,	,	PUNCT
ap-1271	156	15	(	(	PUNCT
ap-1271	156	16	8)	8)	NUM
ap-1271	156	17	d∗ada(fg	d∗ada(fg	NOUN
ap-1271	156	18	)	)	PUNCT
ap-1271	156	19	=	=	SYM
ap-1271	156	20	fd∗adag	fd∗adag	NOUN
ap-1271	156	21	−	−	PROPN
ap-1271	156	22	2〈df	2〈df	NUM
ap-1271	156	23	,	,	PUNCT
ap-1271	156	24	dag〉+	dag〉+	PROPN
ap-1271	156	25	gd∗df	gd∗df	PROPN
ap-1271	156	26	.	.	PUNCT
ap-1271	157	1	(	(	PUNCT
ap-1271	157	2	9	9	X
ap-1271	157	3	)	)	PUNCT
ap-1271	157	4	proposition	proposition	NOUN
ap-1271	157	5	2.1	2.1	NUM
ap-1271	157	6	let	let	VERB
ap-1271	157	7	u	u	PRON
ap-1271	157	8	,	,	PUNCT
ap-1271	157	9	u	u	NOUN
ap-1271	157	10	′	′	NOUN
ap-1271	157	11	be	be	VERB
ap-1271	157	12	open	open	ADJ
ap-1271	157	13	subsets	subset	NOUN
ap-1271	157	14	of	of	ADP
ap-1271	157	15	m	m	PRON
ap-1271	157	16	\γ	\γ	NOUN
ap-1271	157	17	such	such	ADJ
ap-1271	157	18	that	that	SCONJ
ap-1271	157	19	u	u	PROPN
ap-1271	157	20	is	be	AUX
ap-1271	157	21	a	a	DET
ap-1271	157	22	compact	compact	ADJ
ap-1271	157	23	subset	subset	NOUN
ap-1271	157	24	of	of	ADP
ap-1271	157	25	u	u	NOUN
ap-1271	157	26	′	′	NOUN
ap-1271	157	27	,	,	PUNCT
ap-1271	157	28	and	and	CCONJ
ap-1271	157	29	v	v	NOUN
ap-1271	157	30	is	be	AUX
ap-1271	157	31	bounded	bound	VERB
ap-1271	157	32	in	in	ADP
ap-1271	157	33	u	u	NOUN
ap-1271	157	34	′.	′.	NOUN
ap-1271	157	35	then	then	ADV
ap-1271	157	36	,	,	PUNCT
ap-1271	157	37	there	there	PRON
ap-1271	157	38	exists	exist	VERB
ap-1271	157	39	a	a	DET
ap-1271	157	40	constant	constant	ADJ
ap-1271	157	41	c	c	NOUN
ap-1271	157	42	>	>	X
ap-1271	157	43	0	0	NUM
ap-1271	158	1	such	such	ADJ
ap-1271	158	2	that∫	that∫	NOUN
ap-1271	158	3	u	u	PROPN
ap-1271	158	4	|daf	|daf	NOUN
ap-1271	158	5	|2	|2	NUM
ap-1271	158	6	dμ	dμ	ADP
ap-1271	158	7	≤	≤	NUM
ap-1271	159	1	c	c	NOUN
ap-1271	159	2	∫	∫	PROPN
ap-1271	159	3	u	u	NOUN
ap-1271	159	4	′	′	X
ap-1271	159	5	(	(	PUNCT
ap-1271	159	6	|f	|f	PROPN
ap-1271	159	7	|2	|2	NUM
ap-1271	159	8	+	+	CCONJ
ap-1271	159	9	|lf	|lf	NOUN
ap-1271	159	10	|2	|2	NUM
ap-1271	159	11	)	)	PUNCT
ap-1271	159	12	dμ	dμ	VERB
ap-1271	159	13	(	(	PUNCT
ap-1271	159	14	10	10	NUM
ap-1271	159	15	)	)	PUNCT
ap-1271	159	16	for	for	ADP
ap-1271	159	17	f	f	PROPN
ap-1271	159	18	∈	∈	PROPN
ap-1271	159	19	d(hmax	d(hmax	NOUN
ap-1271	159	20	)	)	PUNCT
ap-1271	159	21	.	.	PUNCT
ap-1271	160	1	proof	proof	NOUN
ap-1271	160	2	.	.	PUNCT
ap-1271	161	1	according	accord	VERB
ap-1271	161	2	to	to	ADP
ap-1271	161	3	[	[	X
ap-1271	161	4	14	14	NUM
ap-1271	161	5	,	,	PUNCT
ap-1271	161	6	(	(	PUNCT
ap-1271	161	7	5.3)],4	5.3)],4	NOUN
ap-1271	161	8	we	we	PRON
ap-1271	161	9	have	have	VERB
ap-1271	161	10	(	(	PUNCT
ap-1271	161	11	l(φf	l(φf	NOUN
ap-1271	161	12	)	)	PUNCT
ap-1271	161	13	,	,	PUNCT
ap-1271	161	14	φf	φf	X
ap-1271	161	15	)	)	PUNCT
ap-1271	161	16	=	=	SYM
ap-1271	161	17	�	�	PROPN
ap-1271	161	18	(	(	PUNCT
ap-1271	161	19	φlf	φlf	PROPN
ap-1271	161	20	,	,	PUNCT
ap-1271	161	21	φf	φf	X
ap-1271	161	22	)	)	PUNCT
ap-1271	161	23	+	+	NUM
ap-1271	161	24	∫	∫	PROPN
ap-1271	161	25	m	m	VERB
ap-1271	161	26	|dφ|2|f	|dφ|2|f	PROPN
ap-1271	161	27	|2	|2	NUM
ap-1271	161	28	dμ	dμ	NOUN
ap-1271	161	29	for	for	ADP
ap-1271	161	30	f	f	PROPN
ap-1271	161	31	∈	∈	PROPN
ap-1271	161	32	d(hmax	d(hmax	NOUN
ap-1271	161	33	)	)	PUNCT
ap-1271	161	34	and	and	CCONJ
ap-1271	161	35	φ	φ	PROPN
ap-1271	161	36	∈	∈	PROPN
ap-1271	161	37	c∞	c∞	PROPN
ap-1271	161	38	0	0	NUM
ap-1271	161	39	(	(	PUNCT
ap-1271	161	40	m	m	PROPN
ap-1271	161	41	\	\	PROPN
ap-1271	161	42	γ	γ	NOUN
ap-1271	161	43	)	)	PUNCT
ap-1271	161	44	.	.	PUNCT
ap-1271	162	1	take	take	VERB
ap-1271	162	2	φ	φ	PROPN
ap-1271	162	3	∈	∈	PROPN
ap-1271	162	4	c∞	c∞	PROPN
ap-1271	162	5	0	0	PUNCT
ap-1271	163	1	(	(	PUNCT
ap-1271	163	2	u	u	NOUN
ap-1271	163	3	′	′	NOUN
ap-1271	163	4	)	)	PUNCT
ap-1271	164	1	such	such	ADJ
ap-1271	164	2	that	that	SCONJ
ap-1271	164	3	φ	φ	PROPN
ap-1271	164	4	=	=	SYM
ap-1271	164	5	1	1	NUM
ap-1271	164	6	on	on	ADP
ap-1271	164	7	u	u	PROPN
ap-1271	164	8	.	.	PUNCT
ap-1271	165	1	then	then	ADV
ap-1271	165	2	the	the	DET
ap-1271	165	3	conclusion	conclusion	NOUN
ap-1271	165	4	follows	follow	VERB
ap-1271	165	5	from	from	ADP
ap-1271	165	6	the	the	DET
ap-1271	165	7	above	above	ADJ
ap-1271	165	8	equality,∫	equality,∫	PUNCT
ap-1271	165	9	suppφ	suppφ	PROPN
ap-1271	165	10	|da(φf)|2	|da(φf)|2	PROPN
ap-1271	165	11	=	=	SYM
ap-1271	165	12	(	(	PUNCT
ap-1271	165	13	l(φf	l(φf	PROPN
ap-1271	165	14	)	)	PUNCT
ap-1271	165	15	,	,	PUNCT
ap-1271	165	16	φf	φf	X
ap-1271	165	17	)	)	PUNCT
ap-1271	165	18	−	−	PROPN
ap-1271	166	1	(	(	PUNCT
ap-1271	166	2	v	v	NOUN
ap-1271	166	3	φf	φf	ADP
ap-1271	166	4	,	,	PUNCT
ap-1271	166	5	φf	φf	NOUN
ap-1271	166	6	)	)	PUNCT
ap-1271	166	7	and	and	CCONJ
ap-1271	166	8	assumption	assumption	NOUN
ap-1271	166	9	v	v	NOUN
ap-1271	166	10	is	be	AUX
ap-1271	166	11	bounded	bound	VERB
ap-1271	166	12	.	.	PUNCT
ap-1271	167	1	�	�	PROPN
ap-1271	167	2	2.2	2.2	NUM
ap-1271	167	3	theory	theory	NOUN
ap-1271	167	4	of	of	ADP
ap-1271	167	5	self	self	NOUN
ap-1271	167	6	-	-	PUNCT
ap-1271	167	7	adjoint	adjoint	NOUN
ap-1271	167	8	extensions	extension	NOUN
ap-1271	167	9	we	we	PRON
ap-1271	167	10	quote	quote	VERB
ap-1271	167	11	some	some	DET
ap-1271	167	12	notation	notation	NOUN
ap-1271	167	13	from	from	ADP
ap-1271	167	14	the	the	DET
ap-1271	167	15	textbook	textbook	NOUN
ap-1271	167	16	[	[	X
ap-1271	167	17	13	13	NUM
ap-1271	167	18	]	]	PUNCT
ap-1271	167	19	.	.	PUNCT
ap-1271	168	1	let	let	AUX
ap-1271	168	2	h	h	PRON
ap-1271	168	3	be	be	AUX
ap-1271	168	4	a	a	DET
ap-1271	168	5	separable	separable	ADJ
ap-1271	168	6	hilbert	hilbert	NOUN
ap-1271	168	7	space	space	NOUN
ap-1271	168	8	and	and	CCONJ
ap-1271	168	9	denote	denote	VERB
ap-1271	168	10	its	its	PRON
ap-1271	168	11	inner	inner	ADJ
ap-1271	168	12	product	product	NOUN
ap-1271	168	13	by	by	ADP
ap-1271	168	14	(	(	PUNCT
ap-1271	168	15	·	·	PUNCT
ap-1271	168	16	,	,	PUNCT
ap-1271	168	17	·	·	PUNCT
ap-1271	168	18	)	)	PUNCT
ap-1271	168	19	,	,	PUNCT
ap-1271	168	20	and	and	CCONJ
ap-1271	168	21	norm	norm	NOUN
ap-1271	168	22	by	by	ADP
ap-1271	168	23	‖	‖	PROPN
ap-1271	168	24	·	·	PUNCT
ap-1271	168	25	‖.	‖.	X
ap-1271	168	26	all	all	DET
ap-1271	168	27	the	the	DET
ap-1271	168	28	linear	linear	PROPN
ap-1271	168	29	operators	operator	NOUN
ap-1271	168	30	in	in	ADP
ap-1271	168	31	this	this	DET
ap-1271	168	32	subsection	subsection	NOUN
ap-1271	168	33	are	be	AUX
ap-1271	168	34	on	on	ADP
ap-1271	168	35	the	the	DET
ap-1271	168	36	hilbert	hilbert	PROPN
ap-1271	168	37	space	space	PROPN
ap-1271	168	38	h.	h.	PROPN
ap-1271	168	39	for	for	ADP
ap-1271	168	40	a	a	DET
ap-1271	168	41	linear	linear	ADJ
ap-1271	168	42	operator	operator	NOUN
ap-1271	168	43	x	x	SYM
ap-1271	168	44	,	,	PUNCT
ap-1271	168	45	d(x	d(x	PROPN
ap-1271	168	46	)	)	PUNCT
ap-1271	168	47	denotes	denote	VERB
ap-1271	168	48	the	the	DET
ap-1271	168	49	domain	domain	NOUN
ap-1271	168	50	of	of	ADP
ap-1271	168	51	definition	definition	NOUN
ap-1271	168	52	of	of	ADP
ap-1271	168	53	x	x	X
ap-1271	168	54	,	,	PUNCT
ap-1271	168	55	x	x	PROPN
ap-1271	168	56	the	the	DET
ap-1271	168	57	closure	closure	NOUN
ap-1271	168	58	of	of	ADP
ap-1271	168	59	x	x	PRON
ap-1271	168	60	,	,	PUNCT
ap-1271	168	61	x∗	x∗	PROPN
ap-1271	168	62	the	the	DET
ap-1271	168	63	adjoint	adjoint	NOUN
ap-1271	168	64	operator	operator	NOUN
ap-1271	168	65	of	of	ADP
ap-1271	168	66	x	x	PROPN
ap-1271	168	67	.	.	PUNCT
ap-1271	169	1	for	for	ADP
ap-1271	169	2	a	a	DET
ap-1271	169	3	linear	linear	ADJ
ap-1271	169	4	operator	operator	NOUN
ap-1271	169	5	x	x	SYM
ap-1271	169	6	,	,	PUNCT
ap-1271	169	7	the	the	DET
ap-1271	169	8	graph	graph	NOUN
ap-1271	169	9	inner	inner	ADJ
ap-1271	169	10	product	product	NOUN
ap-1271	169	11	of	of	ADP
ap-1271	169	12	x	x	PROPN
ap-1271	169	13	is	be	AUX
ap-1271	169	14	defined	define	VERB
ap-1271	169	15	by	by	ADP
ap-1271	169	16	(	(	PUNCT
ap-1271	169	17	x	x	X
ap-1271	169	18	,	,	PUNCT
ap-1271	169	19	y)x	y)x	X
ap-1271	169	20	=	=	SYM
ap-1271	169	21	(	(	PUNCT
ap-1271	169	22	xx	xx	PROPN
ap-1271	169	23	,	,	PUNCT
ap-1271	169	24	xy	xy	PROPN
ap-1271	169	25	)	)	PUNCT
ap-1271	170	1	+	+	CCONJ
ap-1271	170	2	(	(	PUNCT
ap-1271	170	3	x	x	X
ap-1271	170	4	,	,	PUNCT
ap-1271	170	5	y	y	NOUN
ap-1271	170	6	)	)	PUNCT
ap-1271	170	7	for	for	ADP
ap-1271	170	8	x	x	X
ap-1271	170	9	,	,	PUNCT
ap-1271	170	10	y	y	PROPN
ap-1271	170	11	∈	∈	PROPN
ap-1271	170	12	d(x	d(x	PROPN
ap-1271	170	13	)	)	PUNCT
ap-1271	170	14	,	,	PUNCT
ap-1271	170	15	and	and	CCONJ
ap-1271	170	16	the	the	DET
ap-1271	170	17	graph	graph	NOUN
ap-1271	170	18	norm	norm	NOUN
ap-1271	170	19	by	by	ADP
ap-1271	170	20	‖x‖x	‖x‖x	PUNCT
ap-1271	170	21	=	=	SYM
ap-1271	170	22	(	(	PUNCT
ap-1271	170	23	x	x	X
ap-1271	170	24	,	,	PUNCT
ap-1271	170	25	x)1/2x	x)1/2x	PROPN
ap-1271	170	26	.	.	PUNCT
ap-1271	171	1	we	we	PRON
ap-1271	171	2	introduce	introduce	VERB
ap-1271	171	3	some	some	DET
ap-1271	171	4	equivalent	equivalent	NOUN
ap-1271	171	5	for	for	ADP
ap-1271	171	6	the	the	DET
ap-1271	171	7	sum	sum	NOUN
ap-1271	171	8	of	of	ADP
ap-1271	171	9	the	the	DET
ap-1271	171	10	deficiency	deficiency	NOUN
ap-1271	171	11	subspaces	subspace	NOUN
ap-1271	171	12	,	,	PUNCT
ap-1271	171	13	which	which	PRON
ap-1271	171	14	is	be	AUX
ap-1271	171	15	also	also	ADV
ap-1271	171	16	introduced	introduce	VERB
ap-1271	171	17	in	in	ADP
ap-1271	171	18	[	[	X
ap-1271	171	19	4	4	NUM
ap-1271	171	20	]	]	PUNCT
ap-1271	171	21	or	or	CCONJ
ap-1271	171	22	[	[	X
ap-1271	171	23	12	12	NUM
ap-1271	171	24	]	]	PUNCT
ap-1271	171	25	.	.	PUNCT
ap-1271	172	1	let	let	VERB
ap-1271	172	2	x	x	PRON
ap-1271	172	3	be	be	AUX
ap-1271	172	4	a	a	DET
ap-1271	172	5	closed	closed	ADJ
ap-1271	172	6	,	,	PUNCT
ap-1271	172	7	densely	densely	ADV
ap-1271	172	8	defined	define	VERB
ap-1271	172	9	symmetric	symmetric	ADJ
ap-1271	172	10	operator	operator	NOUN
ap-1271	172	11	.	.	PUNCT
ap-1271	173	1	let	let	VERB
ap-1271	173	2	d	d	X
ap-1271	173	3	=	=	PUNCT
ap-1271	173	4	d(x∗)/d(x	d(x∗)/d(x	PROPN
ap-1271	173	5	)	)	PUNCT
ap-1271	173	6	,	,	PUNCT
ap-1271	173	7	where	where	SCONJ
ap-1271	173	8	the	the	DET
ap-1271	173	9	right	right	ADJ
ap-1271	173	10	hand	hand	NOUN
ap-1271	173	11	side	side	NOUN
ap-1271	173	12	denotes	denote	VERB
ap-1271	173	13	the	the	DET
ap-1271	173	14	quotient	quotient	NOUN
ap-1271	173	15	space	space	NOUN
ap-1271	173	16	.	.	PUNCT
ap-1271	174	1	the	the	DET
ap-1271	174	2	space	space	NOUN
ap-1271	174	3	d	d	NOUN
ap-1271	174	4	is	be	AUX
ap-1271	174	5	a	a	DET
ap-1271	174	6	hilbert	hilbert	NOUN
ap-1271	174	7	space	space	NOUN
ap-1271	174	8	equipped	equip	VERB
ap-1271	174	9	with	with	ADP
ap-1271	174	10	the	the	DET
ap-1271	174	11	norm	norm	NOUN
ap-1271	174	12	‖[x]‖2d	‖[x]‖2d	PROPN
ap-1271	174	13	=	=	SYM
ap-1271	174	14	min	min	PROPN
ap-1271	174	15	y∈[x	y∈[x	X
ap-1271	174	16	]	]	X
ap-1271	174	17	‖y‖2x∗	‖y‖2x∗	PUNCT
ap-1271	174	18	=	=	SYM
ap-1271	174	19	‖qx‖2x∗	‖qx‖2x∗	PROPN
ap-1271	174	20	,	,	PUNCT
ap-1271	174	21	where	where	SCONJ
ap-1271	174	22	x	x	PUNCT
ap-1271	174	23	∈	∈	PROPN
ap-1271	174	24	d(x∗	d(x∗	NOUN
ap-1271	174	25	)	)	PUNCT
ap-1271	174	26	,	,	PUNCT
ap-1271	175	1	[	[	X
ap-1271	175	2	x	x	X
ap-1271	175	3	]	]	X
ap-1271	175	4	=	=	SYM
ap-1271	175	5	x+d(x	x+d(x	X
ap-1271	175	6	)	)	PUNCT
ap-1271	175	7	denotes	denote	VERB
ap-1271	175	8	the	the	DET
ap-1271	175	9	equivalence	equivalence	NOUN
ap-1271	175	10	class	class	NOUN
ap-1271	175	11	of	of	ADP
ap-1271	175	12	x	x	PUNCT
ap-1271	175	13	in	in	ADP
ap-1271	175	14	the	the	DET
ap-1271	175	15	quotient	quotient	NOUN
ap-1271	175	16	space	space	NOUN
ap-1271	175	17	d(x∗)/d(x	d(x∗)/d(x	PROPN
ap-1271	175	18	)	)	PUNCT
ap-1271	175	19	,	,	PUNCT
ap-1271	175	20	and	and	CCONJ
ap-1271	175	21	q	q	PROPN
ap-1271	175	22	denotes	denote	VERB
ap-1271	175	23	the	the	DET
ap-1271	175	24	orthogonal	orthogonal	ADJ
ap-1271	175	25	projection	projection	NOUN
ap-1271	175	26	onto	onto	ADP
ap-1271	175	27	the	the	DET
ap-1271	175	28	orthogonal	orthogonal	ADJ
ap-1271	175	29	complement	complement	NOUN
ap-1271	175	30	of	of	ADP
ap-1271	175	31	d(x	d(x	PROPN
ap-1271	175	32	)	)	PUNCT
ap-1271	175	33	in	in	ADP
ap-1271	175	34	d(x∗	d(x∗	NOUN
ap-1271	175	35	)	)	PUNCT
ap-1271	175	36	.	.	PUNCT
ap-1271	176	1	for	for	ADP
ap-1271	176	2	u	u	NOUN
ap-1271	176	3	,	,	PUNCT
ap-1271	176	4	v	v	AUX
ap-1271	176	5	∈	∈	PROPN
ap-1271	176	6	d	d	NOUN
ap-1271	176	7	,	,	PUNCT
ap-1271	176	8	define	define	VERB
ap-1271	176	9	[	[	X
ap-1271	176	10	u	u	NOUN
ap-1271	176	11	,	,	PUNCT
ap-1271	176	12	v]d	v]d	NOUN
ap-1271	176	13	=	=	SYM
ap-1271	176	14	(	(	PUNCT
ap-1271	176	15	x∗x	x∗x	PROPN
ap-1271	176	16	,	,	PUNCT
ap-1271	176	17	y)−	y)−	PROPN
ap-1271	176	18	(	(	PUNCT
ap-1271	176	19	x	x	NOUN
ap-1271	176	20	,	,	PUNCT
ap-1271	176	21	x∗y	x∗y	NUM
ap-1271	176	22	)	)	PUNCT
ap-1271	176	23	,	,	PUNCT
ap-1271	176	24	u	u	NOUN
ap-1271	176	25	=	=	PUNCT
ap-1271	177	1	[	[	X
ap-1271	177	2	x	x	X
ap-1271	177	3	]	]	X
ap-1271	177	4	,	,	PUNCT
ap-1271	177	5	v	v	NOUN
ap-1271	177	6	=	=	X
ap-1271	178	1	[	[	X
ap-1271	178	2	y	y	X
ap-1271	178	3	]	]	X
ap-1271	178	4	,	,	PUNCT
ap-1271	178	5	x	x	X
ap-1271	178	6	,	,	PUNCT
ap-1271	178	7	y	y	PROPN
ap-1271	178	8	∈	∈	PROPN
ap-1271	178	9	d(x∗	d(x∗	PROPN
ap-1271	178	10	)	)	PUNCT
ap-1271	178	11	.	.	PUNCT
ap-1271	179	1	the	the	DET
ap-1271	179	2	value	value	NOUN
ap-1271	179	3	[	[	X
ap-1271	179	4	u	u	NOUN
ap-1271	179	5	,	,	PUNCT
ap-1271	179	6	v]d	v]d	ADV
ap-1271	179	7	is	be	AUX
ap-1271	179	8	independent	independent	ADJ
ap-1271	179	9	of	of	ADP
ap-1271	179	10	the	the	DET
ap-1271	179	11	choice	choice	NOUN
ap-1271	179	12	of	of	ADP
ap-1271	179	13	the	the	DET
ap-1271	179	14	representatives	representative	NOUN
ap-1271	179	15	x	x	ADP
ap-1271	179	16	,	,	PUNCT
ap-1271	179	17	y.	y.	PROPN
ap-1271	179	18	let	let	VERB
ap-1271	179	19	p	p	PRON
ap-1271	179	20	be	be	AUX
ap-1271	179	21	the	the	DET
ap-1271	179	22	canonical	canonical	ADJ
ap-1271	179	23	projection	projection	NOUN
ap-1271	179	24	from	from	ADP
ap-1271	179	25	d(x∗	d(x∗	NOUN
ap-1271	179	26	)	)	PUNCT
ap-1271	179	27	to	to	ADP
ap-1271	179	28	d.	d.	PROPN
ap-1271	179	29	for	for	ADP
ap-1271	179	30	a	a	DET
ap-1271	179	31	closed	closed	ADJ
ap-1271	179	32	subspace	subspace	NOUN
ap-1271	179	33	v	v	ADP
ap-1271	179	34	of	of	ADP
ap-1271	179	35	d	d	PROPN
ap-1271	179	36	,	,	PUNCT
ap-1271	179	37	we	we	PRON
ap-1271	179	38	define	define	VERB
ap-1271	179	39	a	a	DET
ap-1271	179	40	closed	closed	ADJ
ap-1271	179	41	linear	linear	NOUN
ap-1271	179	42	operator	operator	NOUN
ap-1271	179	43	xv	xv	X
ap-1271	179	44	by	by	ADP
ap-1271	179	45	d(xv	d(xv	PROPN
ap-1271	179	46	)	)	PUNCT
ap-1271	180	1	=	=	SYM
ap-1271	180	2	{	{	PUNCT
ap-1271	180	3	x	x	PROPN
ap-1271	180	4	∈	∈	PROPN
ap-1271	180	5	d(x∗	d(x∗	NOUN
ap-1271	180	6	)	)	PUNCT
ap-1271	180	7	|	|	ADV
ap-1271	180	8	px	px	X
ap-1271	180	9	∈	∈	PROPN
ap-1271	180	10	v	v	ADP
ap-1271	180	11	}	}	PUNCT
ap-1271	180	12	,	,	PUNCT
ap-1271	180	13	xv	xv	X
ap-1271	180	14	x	x	X
ap-1271	180	15	=	=	PUNCT
ap-1271	180	16	x∗x	x∗x	ADJ
ap-1271	180	17	.	.	PUNCT
ap-1271	181	1	we	we	PRON
ap-1271	181	2	also	also	ADV
ap-1271	181	3	define	define	VERB
ap-1271	181	4	v	v	ADP
ap-1271	181	5	[	[	X
ap-1271	181	6	⊥	⊥	X
ap-1271	181	7	]	]	X
ap-1271	181	8	=	=	SYM
ap-1271	181	9	{	{	PUNCT
ap-1271	181	10	u	u	NOUN
ap-1271	181	11	∈	∈	PROPN
ap-1271	181	12	d	d	NOUN
ap-1271	182	1	|	|	NOUN
ap-1271	182	2	[	[	X
ap-1271	182	3	u	u	NOUN
ap-1271	182	4	,	,	PUNCT
ap-1271	182	5	v]d	v]d	ADP
ap-1271	182	6	=	=	SYM
ap-1271	182	7	0	0	NUM
ap-1271	182	8	for	for	ADP
ap-1271	182	9	any	any	DET
ap-1271	182	10	v	v	NOUN
ap-1271	182	11	∈	∈	NOUN
ap-1271	182	12	v	v	NOUN
ap-1271	182	13	}	}	PUNCT
ap-1271	182	14	.	.	PUNCT
ap-1271	183	1	then	then	ADV
ap-1271	183	2	the	the	DET
ap-1271	183	3	following	follow	VERB
ap-1271	183	4	proposition	proposition	NOUN
ap-1271	183	5	immediately	immediately	ADV
ap-1271	183	6	follows	follow	VERB
ap-1271	183	7	from	from	ADP
ap-1271	183	8	the	the	DET
ap-1271	183	9	definition	definition	NOUN
ap-1271	183	10	of	of	ADP
ap-1271	183	11	the	the	DET
ap-1271	183	12	self	self	NOUN
ap-1271	183	13	-	-	PUNCT
ap-1271	183	14	adjointness	adjointness	NOUN
ap-1271	183	15	.	.	PUNCT
ap-1271	184	1	proposition	proposition	NOUN
ap-1271	184	2	2.2	2.2	NUM
ap-1271	184	3	1	1	NUM
ap-1271	184	4	.	.	PUNCT
ap-1271	185	1	for	for	ADP
ap-1271	185	2	a	a	DET
ap-1271	185	3	closed	closed	ADJ
ap-1271	185	4	subspace	subspace	NOUN
ap-1271	185	5	v	v	ADP
ap-1271	185	6	of	of	ADP
ap-1271	185	7	d	d	PROPN
ap-1271	185	8	,	,	PUNCT
ap-1271	185	9	the	the	DET
ap-1271	185	10	operator	operator	NOUN
ap-1271	185	11	xv	xv	VERB
ap-1271	185	12	is	be	AUX
ap-1271	185	13	a	a	DET
ap-1271	185	14	self	self	NOUN
ap-1271	185	15	-	-	PUNCT
ap-1271	185	16	adjoint	adjoint	NOUN
ap-1271	185	17	extension	extension	NOUN
ap-1271	185	18	of	of	ADP
ap-1271	185	19	x	x	PRON
ap-1271	185	20	if	if	SCONJ
ap-1271	185	21	and	and	CCONJ
ap-1271	185	22	only	only	ADV
ap-1271	185	23	if	if	SCONJ
ap-1271	185	24	v	v	ADP
ap-1271	185	25	[	[	X
ap-1271	185	26	⊥	⊥	X
ap-1271	185	27	]	]	X
ap-1271	185	28	=	=	SYM
ap-1271	185	29	v.	v.	PROPN
ap-1271	185	30	(	(	PUNCT
ap-1271	185	31	11	11	NUM
ap-1271	185	32	)	)	PUNCT
ap-1271	185	33	2	2	NUM
ap-1271	185	34	.	.	X
ap-1271	185	35	for	for	ADP
ap-1271	185	36	any	any	DET
ap-1271	185	37	self	self	NOUN
ap-1271	185	38	-	-	PUNCT
ap-1271	185	39	adjoint	adjoint	NOUN
ap-1271	185	40	extension	extension	NOUN
ap-1271	185	41	x̃	x̃	PROPN
ap-1271	185	42	of	of	ADP
ap-1271	185	43	x	x	PRON
ap-1271	185	44	,	,	PUNCT
ap-1271	185	45	there	there	PRON
ap-1271	185	46	exists	exist	VERB
ap-1271	185	47	a	a	DET
ap-1271	185	48	closed	closed	ADJ
ap-1271	185	49	subspace	subspace	NOUN
ap-1271	185	50	v	v	ADP
ap-1271	185	51	of	of	ADP
ap-1271	185	52	d	d	PROPN
ap-1271	185	53	such	such	ADJ
ap-1271	185	54	that	that	PRON
ap-1271	185	55	xv	xv	VERB
ap-1271	186	1	=	=	PUNCT
ap-1271	186	2	x̃.	x̃.	ADJ
ap-1271	186	3	in	in	ADP
ap-1271	186	4	terms	term	NOUN
ap-1271	186	5	of	of	ADP
ap-1271	186	6	the	the	DET
ap-1271	186	7	above	above	ADJ
ap-1271	186	8	notations	notation	NOUN
ap-1271	186	9	,	,	PUNCT
ap-1271	186	10	the	the	DET
ap-1271	186	11	krein	krein	PROPN
ap-1271	186	12	-	-	PUNCT
ap-1271	186	13	von	von	PROPN
ap-1271	186	14	neumann	neumann	PROPN
ap-1271	186	15	theory	theory	NOUN
ap-1271	186	16	can	can	AUX
ap-1271	186	17	be	be	AUX
ap-1271	186	18	rephrased	rephrase	VERB
ap-1271	186	19	as	as	ADP
ap-1271	186	20	follows	follow	VERB
ap-1271	186	21	.	.	PUNCT
ap-1271	187	1	proposition	proposition	NOUN
ap-1271	187	2	2.3	2.3	NUM
ap-1271	187	3	let	let	VERB
ap-1271	187	4	n±	n±	PROPN
ap-1271	187	5	=	=	SYM
ap-1271	188	1	ker(x∗	ker(x∗	PROPN
ap-1271	188	2	∓	∓	PROPN
ap-1271	189	1	i	i	X
ap-1271	189	2	)	)	PUNCT
ap-1271	189	3	the	the	DET
ap-1271	189	4	deficiency	deficiency	NOUN
ap-1271	189	5	subspaces	subspace	NOUN
ap-1271	189	6	of	of	ADP
ap-1271	189	7	x	x	PRON
ap-1271	189	8	,	,	PUNCT
ap-1271	189	9	n±	n±	PROPN
ap-1271	189	10	=	=	SYM
ap-1271	189	11	dimn±	dimn±	PROPN
ap-1271	189	12	the	the	DET
ap-1271	189	13	deficiency	deficiency	NOUN
ap-1271	189	14	indices	indice	VERB
ap-1271	189	15	of	of	ADP
ap-1271	189	16	x.	x.	NOUN
ap-1271	189	17	then	then	ADV
ap-1271	189	18	,	,	PUNCT
ap-1271	189	19	the	the	DET
ap-1271	189	20	following	follow	VERB
ap-1271	189	21	holds	hold	VERB
ap-1271	189	22	.	.	PUNCT
ap-1271	190	1	(	(	PUNCT
ap-1271	190	2	i	i	NOUN
ap-1271	190	3	)	)	PUNCT
ap-1271	190	4	the	the	DET
ap-1271	190	5	projection	projection	NOUN
ap-1271	190	6	operator	operator	NOUN
ap-1271	190	7	p	p	PROPN
ap-1271	190	8	gives	give	VERB
ap-1271	190	9	a	a	DET
ap-1271	190	10	hilbert	hilbert	NOUN
ap-1271	190	11	space	space	NOUN
ap-1271	190	12	isomorphism	isomorphism	NOUN
ap-1271	190	13	from	from	ADP
ap-1271	190	14	the	the	DET
ap-1271	190	15	direct	direct	ADJ
ap-1271	190	16	sum	sum	NOUN
ap-1271	190	17	n+	n+	PUNCT
ap-1271	190	18	⊕	⊕	PROPN
ap-1271	190	19	n−	n−	NOUN
ap-1271	190	20	to	to	AUX
ap-1271	190	21	d.	d.	VERB
ap-1271	190	22	in	in	ADP
ap-1271	190	23	particular	particular	ADJ
ap-1271	190	24	,	,	PUNCT
ap-1271	191	1	dimd	dimd	PROPN
ap-1271	191	2	=	=	PUNCT
ap-1271	191	3	n+	n+	NOUN
ap-1271	192	1	+	+	NUM
ap-1271	192	2	n−.	n−.	PROPN
ap-1271	192	3	(	(	PUNCT
ap-1271	192	4	ii	ii	NOUN
ap-1271	192	5	)	)	PUNCT
ap-1271	192	6	there	there	PRON
ap-1271	192	7	exists	exist	VERB
ap-1271	192	8	a	a	DET
ap-1271	192	9	one	one	NUM
ap-1271	192	10	-	-	PUNCT
ap-1271	192	11	to	to	ADP
ap-1271	192	12	-	-	PUNCT
ap-1271	192	13	one	one	NUM
ap-1271	192	14	correspondence	correspondence	NOUN
ap-1271	192	15	between	between	ADP
ap-1271	192	16	the	the	DET
ap-1271	192	17	closed	closed	ADJ
ap-1271	192	18	subspaces	subspace	NOUN
ap-1271	192	19	v	v	ADP
ap-1271	192	20	of	of	ADP
ap-1271	192	21	d	d	NOUN
ap-1271	192	22	satisfying	satisfy	VERB
ap-1271	192	23	(	(	PUNCT
ap-1271	192	24	11	11	NUM
ap-1271	192	25	)	)	PUNCT
ap-1271	192	26	and	and	CCONJ
ap-1271	192	27	the	the	DET
ap-1271	192	28	unitary	unitary	ADJ
ap-1271	192	29	operators	operator	NOUN
ap-1271	192	30	u	u	NOUN
ap-1271	192	31	from	from	ADP
ap-1271	192	32	h+	h+	PROPN
ap-1271	192	33	to	to	ADP
ap-1271	192	34	h−	h−	PROPN
ap-1271	192	35	,	,	PUNCT
ap-1271	192	36	given	give	VERB
ap-1271	192	37	by	by	ADP
ap-1271	192	38	v	v	NOUN
ap-1271	192	39	=	=	SYM
ap-1271	192	40	p	p	X
ap-1271	192	41	(	(	PUNCT
ap-1271	192	42	1	1	NUM
ap-1271	192	43	+	+	CCONJ
ap-1271	192	44	u)h+	u)h+	PROPN
ap-1271	192	45	.	.	PUNCT
ap-1271	193	1	this	this	DET
ap-1271	193	2	proposition	proposition	NOUN
ap-1271	193	3	says	say	VERB
ap-1271	193	4	the	the	DET
ap-1271	193	5	space	space	NOUN
ap-1271	193	6	d	d	NOUN
ap-1271	193	7	can	can	AUX
ap-1271	193	8	play	play	VERB
ap-1271	193	9	the	the	DET
ap-1271	193	10	same	same	ADJ
ap-1271	193	11	role	role	NOUN
ap-1271	193	12	as	as	ADP
ap-1271	193	13	the	the	DET
ap-1271	193	14	sum	sum	NOUN
ap-1271	193	15	of	of	ADP
ap-1271	193	16	deficiency	deficiency	NOUN
ap-1271	193	17	subspaces	subspace	NOUN
ap-1271	193	18	in	in	ADP
ap-1271	193	19	the	the	DET
ap-1271	193	20	theory	theory	NOUN
ap-1271	193	21	of	of	ADP
ap-1271	193	22	self	self	NOUN
ap-1271	193	23	-	-	PUNCT
ap-1271	193	24	adjoint	adjoint	NOUN
ap-1271	193	25	extensions	extension	NOUN
ap-1271	193	26	.	.	PUNCT
ap-1271	194	1	particularly	particularly	ADV
ap-1271	194	2	when	when	SCONJ
ap-1271	194	3	n±	n±	NOUN
ap-1271	194	4	is	be	AUX
ap-1271	194	5	difficult	difficult	ADJ
ap-1271	194	6	to	to	PART
ap-1271	194	7	determine	determine	VERB
ap-1271	194	8	explicitly	explicitly	ADV
ap-1271	194	9	(	(	PUNCT
ap-1271	194	10	as	as	ADP
ap-1271	194	11	in	in	ADP
ap-1271	194	12	our	our	PRON
ap-1271	194	13	case	case	NOUN
ap-1271	194	14	)	)	PUNCT
ap-1271	194	15	,	,	PUNCT
ap-1271	194	16	the	the	DET
ap-1271	194	17	space	space	NOUN
ap-1271	194	18	d	d	NOUN
ap-1271	194	19	is	be	AUX
ap-1271	194	20	more	more	ADV
ap-1271	194	21	tractable	tractable	ADJ
ap-1271	194	22	,	,	PUNCT
ap-1271	194	23	since	since	SCONJ
ap-1271	194	24	the	the	DET
ap-1271	194	25	element	element	NOUN
ap-1271	194	26	of	of	ADP
ap-1271	194	27	this	this	DET
ap-1271	194	28	space	space	NOUN
ap-1271	194	29	has	have	VERB
ap-1271	194	30	ambiguity	ambiguity	NOUN
ap-1271	194	31	by	by	ADP
ap-1271	194	32	d(x	d(x	PROPN
ap-1271	194	33	)	)	PUNCT
ap-1271	194	34	.	.	PUNCT
ap-1271	195	1	actually	actually	ADV
ap-1271	195	2	,	,	PUNCT
ap-1271	195	3	in	in	ADP
ap-1271	195	4	the	the	DET
ap-1271	195	5	next	next	ADJ
ap-1271	195	6	section	section	NOUN
ap-1271	195	7	we	we	PRON
ap-1271	195	8	shall	shall	AUX
ap-1271	195	9	see	see	VERB
ap-1271	195	10	that	that	SCONJ
ap-1271	195	11	the	the	DET
ap-1271	195	12	structure	structure	NOUN
ap-1271	195	13	of	of	ADP
ap-1271	195	14	d	d	PROPN
ap-1271	195	15	for	for	ADP
ap-1271	195	16	our	our	PRON
ap-1271	195	17	schrödinger	schrödinger	NOUN
ap-1271	195	18	operator	operator	NOUN
ap-1271	195	19	hmin	hmin	NOUN
ap-1271	195	20	and	and	CCONJ
ap-1271	195	21	the	the	DET
ap-1271	195	22	form	form	NOUN
ap-1271	195	23	[	[	X
ap-1271	195	24	·	·	PUNCT
ap-1271	195	25	,	,	PUNCT
ap-1271	195	26	·	·	PUNCT
ap-1271	195	27	]	]	X
ap-1271	195	28	d	d	X
ap-1271	195	29	is	be	AUX
ap-1271	195	30	determined	determine	VERB
ap-1271	195	31	only	only	ADV
ap-1271	195	32	from	from	ADP
ap-1271	195	33	the	the	DET
ap-1271	195	34	singular	singular	ADJ
ap-1271	195	35	part	part	NOUN
ap-1271	195	36	a(0	a(0	PROPN
ap-1271	195	37	)	)	PUNCT
ap-1271	195	38	of	of	ADP
ap-1271	195	39	the	the	DET
ap-1271	195	40	vector	vector	NOUN
ap-1271	195	41	potential	potential	NOUN
ap-1271	195	42	.	.	PUNCT
ap-1271	196	1	4since	4since	NUM
ap-1271	196	2	the	the	DET
ap-1271	196	3	function	function	NOUN
ap-1271	196	4	φ	φ	PROPN
ap-1271	196	5	avoids	avoid	VERB
ap-1271	196	6	the	the	DET
ap-1271	196	7	singularities	singularity	NOUN
ap-1271	196	8	,	,	PUNCT
ap-1271	196	9	the	the	DET
ap-1271	196	10	proof	proof	NOUN
ap-1271	196	11	of	of	ADP
ap-1271	196	12	[	[	X
ap-1271	196	13	14	14	NUM
ap-1271	196	14	,	,	PUNCT
ap-1271	196	15	(	(	PUNCT
ap-1271	196	16	5.3	5.3	NUM
ap-1271	196	17	)	)	PUNCT
ap-1271	196	18	]	]	PUNCT
ap-1271	196	19	is	be	AUX
ap-1271	196	20	also	also	ADV
ap-1271	196	21	available	available	ADJ
ap-1271	196	22	in	in	ADP
ap-1271	196	23	our	our	PRON
ap-1271	196	24	case	case	NOUN
ap-1271	196	25	.	.	PUNCT
ap-1271	197	1	65	65	NUM
ap-1271	197	2	acta	acta	PROPN
ap-1271	197	3	polytechnica	polytechnica	PROPN
ap-1271	197	4	vol	vol	NOUN
ap-1271	197	5	.	.	PROPN
ap-1271	198	1	50	50	NUM
ap-1271	198	2	no	no	NOUN
ap-1271	198	3	.	.	PUNCT
ap-1271	199	1	5/2010	5/2010	NUM
ap-1271	199	2	3	3	NUM
ap-1271	199	3	reduction	reduction	NOUN
ap-1271	199	4	3.1	3.1	NUM
ap-1271	199	5	division	division	NOUN
ap-1271	199	6	to	to	ADP
ap-1271	199	7	the	the	DET
ap-1271	199	8	local	local	ADJ
ap-1271	199	9	potential	potential	NOUN
ap-1271	199	10	let	let	NOUN
ap-1271	199	11	(	(	PUNCT
ap-1271	199	12	uk	uk	PROPN
ap-1271	199	13	,	,	PUNCT
ap-1271	199	14	φk	φk	ADP
ap-1271	199	15	)	)	PUNCT
ap-1271	199	16	,	,	PUNCT
ap-1271	199	17	φk	φk	ADP
ap-1271	199	18	=	=	SYM
ap-1271	199	19	(	(	PUNCT
ap-1271	199	20	x1	x1	PROPN
ap-1271	199	21	,	,	PUNCT
ap-1271	199	22	x2	x2	PROPN
ap-1271	199	23	)	)	PUNCT
ap-1271	199	24	,	,	PUNCT
ap-1271	199	25	the	the	DET
ap-1271	199	26	local	local	ADJ
ap-1271	199	27	coordinate	coordinate	NOUN
ap-1271	199	28	introduced	introduce	VERB
ap-1271	199	29	in	in	ADP
ap-1271	199	30	section	section	NOUN
ap-1271	199	31	1	1	NUM
ap-1271	199	32	.	.	PUNCT
ap-1271	200	1	let	let	VERB
ap-1271	200	2	ã	ã	PROPN
ap-1271	200	3	be	be	AUX
ap-1271	200	4	the	the	DET
ap-1271	200	5	1	1	NUM
ap-1271	200	6	-	-	PUNCT
ap-1271	200	7	form	form	NOUN
ap-1271	200	8	given	give	VERB
ap-1271	200	9	by	by	ADP
ap-1271	200	10	(	(	PUNCT
ap-1271	200	11	4	4	NUM
ap-1271	200	12	)	)	PUNCT
ap-1271	200	13	.	.	PUNCT
ap-1271	201	1	take	take	VERB
ap-1271	201	2	a	a	DET
ap-1271	201	3	positive	positive	ADJ
ap-1271	201	4	number	number	NOUN
ap-1271	201	5	εk	εk	NOUN
ap-1271	201	6	so	so	ADV
ap-1271	201	7	small	small	ADJ
ap-1271	201	8	that	that	SCONJ
ap-1271	201	9	the	the	DET
ap-1271	201	10	closed	closed	ADJ
ap-1271	201	11	disc	disc	NOUN
ap-1271	201	12	{	{	PUNCT
ap-1271	201	13	r	r	NOUN
ap-1271	201	14	≤	≤	NUM
ap-1271	201	15	2εk	2εk	NOUN
ap-1271	201	16	}	}	PUNCT
ap-1271	201	17	is	be	AUX
ap-1271	201	18	contained	contain	VERB
ap-1271	201	19	in	in	ADP
ap-1271	201	20	uk	uk	PROPN
ap-1271	201	21	.	.	PUNCT
ap-1271	202	1	let	let	VERB
ap-1271	202	2	ηk	ηk	ADP
ap-1271	202	3	∈	∈	PROPN
ap-1271	202	4	c∞	c∞	PROPN
ap-1271	202	5	0	0	NUM
ap-1271	203	1	(	(	PUNCT
ap-1271	203	2	u	u	NOUN
ap-1271	203	3	)	)	PUNCT
ap-1271	203	4	such	such	ADJ
ap-1271	203	5	that	that	SCONJ
ap-1271	203	6	0	0	NUM
ap-1271	203	7	≤	≤	NUM
ap-1271	203	8	ηk	ηk	VERB
ap-1271	203	9	≤	≤	ADV
ap-1271	203	10	1	1	NUM
ap-1271	203	11	,	,	PUNCT
ap-1271	203	12	ηk	ηk	X
ap-1271	203	13	=	=	SYM
ap-1271	203	14	1	1	NUM
ap-1271	203	15	for	for	ADP
ap-1271	203	16	r	r	NOUN
ap-1271	203	17	≤	≤	NUM
ap-1271	203	18	εk	εk	NOUN
ap-1271	203	19	,	,	PUNCT
ap-1271	203	20	ηk	ηk	X
ap-1271	203	21	=	=	SYM
ap-1271	203	22	0	0	NUM
ap-1271	203	23	for	for	ADP
ap-1271	203	24	r	r	NOUN
ap-1271	203	25	≥	≥	NOUN
ap-1271	203	26	2εk	2εk	NOUN
ap-1271	203	27	.	.	PUNCT
ap-1271	204	1	define	define	NOUN
ap-1271	204	2	functions	function	NOUN
ap-1271	204	3	ĝmn	ĝmn	PROPN
ap-1271	204	4	,	,	PUNCT
ap-1271	204	5	âm	âm	PROPN
ap-1271	204	6	and	and	CCONJ
ap-1271	204	7	v̂	v̂	NOUN
ap-1271	204	8	on	on	ADP
ap-1271	204	9	r	r	NOUN
ap-1271	204	10	2	2	NUM
ap-1271	204	11	by	by	ADP
ap-1271	204	12	ĝmn	ĝmn	NOUN
ap-1271	204	13	=	=	SYM
ap-1271	204	14	ηkgmn	ηkgmn	PROPN
ap-1271	204	15	+	+	CCONJ
ap-1271	204	16	(	(	PUNCT
ap-1271	204	17	1−	1−	NUM
ap-1271	204	18	ηk)δmn	ηk)δmn	NOUN
ap-1271	204	19	,	,	PUNCT
ap-1271	204	20	âm	âm	X
ap-1271	204	21	=	=	SYM
ap-1271	204	22	ã(0)m	ã(0)m	NOUN
ap-1271	204	23	+	+	CCONJ
ap-1271	204	24	ηkã(1)m	ηkã(1)m	NOUN
ap-1271	204	25	,	,	PUNCT
ap-1271	204	26	v̂	v̂	NOUN
ap-1271	204	27	=	=	PUNCT
ap-1271	204	28	ηkv	ηkv	ADJ
ap-1271	204	29	.	.	PUNCT
ap-1271	205	1	define	define	VERB
ap-1271	205	2	a	a	DET
ap-1271	205	3	differential	differential	ADJ
ap-1271	205	4	operator	operator	NOUN
ap-1271	205	5	lk	lk	NOUN
ap-1271	205	6	on	on	ADP
ap-1271	205	7	r	r	NOUN
ap-1271	205	8	2	2	NUM
ap-1271	205	9	by	by	ADP
ap-1271	205	10	lk	lk	NOUN
ap-1271	205	11	=	=	PUNCT
ap-1271	205	12	−	−	PROPN
ap-1271	205	13	1√	1√	PROPN
ap-1271	205	14	ĝ	ĝ	X
ap-1271	205	15	∑	∑	PROPN
ap-1271	205	16	m	m	PROPN
ap-1271	205	17	,	,	PUNCT
ap-1271	205	18	n=1,2	n=1,2	ADJ
ap-1271	205	19	(	(	PUNCT
ap-1271	205	20	∂	∂	NUM
ap-1271	205	21	∂xm	∂xm	NOUN
ap-1271	205	22	+	+	CCONJ
ap-1271	205	23	iâm	iâm	ADJ
ap-1271	205	24	)	)	PUNCT
ap-1271	205	25	·	·	PUNCT
ap-1271	205	26	√	√	NUM
ap-1271	206	1	ĝĝmn	ĝĝmn	NOUN
ap-1271	206	2	(	(	PUNCT
ap-1271	206	3	∂	∂	NUM
ap-1271	206	4	∂xn	∂xn	NOUN
ap-1271	206	5	+	+	NOUN
ap-1271	206	6	iân	iân	PROPN
ap-1271	206	7	)	)	PUNCT
ap-1271	207	1	+	+	CCONJ
ap-1271	207	2	v̂	v̂	NOUN
ap-1271	207	3	,	,	PUNCT
ap-1271	207	4	where	where	SCONJ
ap-1271	207	5	ĝ	ĝ	X
ap-1271	207	6	=	=	SYM
ap-1271	207	7	det(ĝmn	det(ĝmn	PROPN
ap-1271	207	8	)	)	PUNCT
ap-1271	207	9	,	,	PUNCT
ap-1271	207	10	and	and	CCONJ
ap-1271	207	11	(	(	PUNCT
ap-1271	207	12	ĝmn	ĝmn	NOUN
ap-1271	207	13	)	)	PUNCT
ap-1271	207	14	is	be	AUX
ap-1271	207	15	the	the	DET
ap-1271	207	16	inverse	inverse	ADJ
ap-1271	207	17	matrix	matrix	NOUN
ap-1271	207	18	of	of	ADP
ap-1271	207	19	(	(	PUNCT
ap-1271	207	20	ĝmn	ĝmn	PROPN
ap-1271	207	21	)	)	PUNCT
ap-1271	207	22	.	.	PUNCT
ap-1271	208	1	define	define	VERB
ap-1271	208	2	a	a	DET
ap-1271	208	3	linear	linear	ADJ
ap-1271	208	4	operator	operator	NOUN
ap-1271	208	5	lk	lk	NOUN
ap-1271	208	6	,	,	PUNCT
ap-1271	208	7	min	min	PROPN
ap-1271	208	8	on	on	ADP
ap-1271	208	9	l2(r2	l2(r2	NOUN
ap-1271	208	10	;	;	PUNCT
ap-1271	208	11	dμk	dμk	PROPN
ap-1271	208	12	)	)	PUNCT
ap-1271	208	13	,	,	PUNCT
ap-1271	208	14	dμk	dμk	NOUN
ap-1271	208	15	=	=	SYM
ap-1271	208	16	√	√	NOUN
ap-1271	208	17	ĝdx1dx2	ĝdx1dx2	NOUN
ap-1271	208	18	,	,	PUNCT
ap-1271	208	19	by	by	ADP
ap-1271	208	20	lk	lk	PROPN
ap-1271	208	21	,	,	PUNCT
ap-1271	208	22	minu	minu	NOUN
ap-1271	208	23	=	=	SYM
ap-1271	208	24	lku	lku	PROPN
ap-1271	208	25	,	,	PUNCT
ap-1271	208	26	d(lk	d(lk	PROPN
ap-1271	208	27	,	,	PUNCT
ap-1271	208	28	min	min	NOUN
ap-1271	208	29	)	)	PUNCT
ap-1271	208	30	=	=	PRON
ap-1271	209	1	c∞	c∞	PROPN
ap-1271	209	2	0	0	PUNCT
ap-1271	210	1	(	(	PUNCT
ap-1271	210	2	r	r	NOUN
ap-1271	210	3	2	2	NUM
ap-1271	210	4	\	\	NOUN
ap-1271	210	5	{	{	PUNCT
ap-1271	210	6	0	0	NUM
ap-1271	210	7	}	}	PUNCT
ap-1271	210	8	)	)	PUNCT
ap-1271	210	9	.	.	PUNCT
ap-1271	211	1	let	let	VERB
ap-1271	211	2	lk	lk	PROPN
ap-1271	211	3	,	,	PUNCT
ap-1271	211	4	max	max	PROPN
ap-1271	211	5	=	=	PROPN
ap-1271	211	6	l∗	l∗	PROPN
ap-1271	211	7	k	k	PROPN
ap-1271	211	8	,	,	PUNCT
ap-1271	211	9	min	min	PROPN
ap-1271	211	10	.	.	PROPN
ap-1271	212	1	then	then	ADV
ap-1271	212	2	lk	lk	PROPN
ap-1271	212	3	,	,	PUNCT
ap-1271	212	4	maxu	maxu	NOUN
ap-1271	212	5	=	=	SYM
ap-1271	212	6	lku	lku	NOUN
ap-1271	212	7	,	,	PUNCT
ap-1271	212	8	d(lk	d(lk	PROPN
ap-1271	212	9	,	,	PUNCT
ap-1271	212	10	max	max	PROPN
ap-1271	212	11	)	)	PUNCT
ap-1271	212	12	=	=	PRON
ap-1271	213	1	{	{	PUNCT
ap-1271	213	2	u	u	NOUN
ap-1271	213	3	∈	∈	NOUN
ap-1271	213	4	l2(r2	l2(r2	NOUN
ap-1271	213	5	;	;	PUNCT
ap-1271	213	6	dμk	dμk	PROPN
ap-1271	213	7	)	)	PUNCT
ap-1271	213	8	|	|	ADV
ap-1271	213	9	lku	lku	PROPN
ap-1271	213	10	∈	∈	PROPN
ap-1271	213	11	l2(r2	l2(r2	NOUN
ap-1271	213	12	;	;	PUNCT
ap-1271	213	13	dμk	dμk	PROPN
ap-1271	213	14	)	)	PUNCT
ap-1271	213	15	}	}	PUNCT
ap-1271	213	16	,	,	PUNCT
ap-1271	213	17	where	where	SCONJ
ap-1271	213	18	lk	lk	PROPN
ap-1271	213	19	is	be	AUX
ap-1271	213	20	regarded	regard	VERB
ap-1271	213	21	as	as	ADP
ap-1271	213	22	a	a	DET
ap-1271	213	23	differential	differential	ADJ
ap-1271	213	24	operator	operator	NOUN
ap-1271	213	25	on	on	ADP
ap-1271	213	26	d′(r2	d′(r2	PROPN
ap-1271	213	27	\	\	NOUN
ap-1271	213	28	0	0	NUM
ap-1271	213	29	)	)	PUNCT
ap-1271	213	30	.	.	PUNCT
ap-1271	214	1	let	let	VERB
ap-1271	214	2	d	d	NOUN
ap-1271	214	3	=	=	PUNCT
ap-1271	214	4	d(hmax)/d(hmin	d(hmax)/d(hmin	PROPN
ap-1271	214	5	)	)	PUNCT
ap-1271	214	6	,	,	PUNCT
ap-1271	214	7	dk	dk	PROPN
ap-1271	214	8	=	=	PUNCT
ap-1271	214	9	d(lk	d(lk	PROPN
ap-1271	214	10	,	,	PUNCT
ap-1271	214	11	max)/d(lk	max)/d(lk	ADJ
ap-1271	214	12	,	,	PUNCT
ap-1271	214	13	min	min	NOUN
ap-1271	214	14	)	)	PUNCT
ap-1271	214	15	.	.	PUNCT
ap-1271	215	1	let	let	VERB
ap-1271	215	2	χk	χk	PRON
ap-1271	215	3	∈	∈	PROPN
ap-1271	215	4	c∞	c∞	PROPN
ap-1271	215	5	0	0	NUM
ap-1271	216	1	(	(	PUNCT
ap-1271	216	2	m	m	NOUN
ap-1271	216	3	)	)	PUNCT
ap-1271	217	1	such	such	ADJ
ap-1271	217	2	that	that	SCONJ
ap-1271	217	3	0	0	NUM
ap-1271	217	4	≤	≤	NUM
ap-1271	217	5	χk	χk	NOUN
ap-1271	217	6	≤	≤	NUM
ap-1271	217	7	1	1	NUM
ap-1271	217	8	,	,	PUNCT
ap-1271	217	9	χk	χk	NOUN
ap-1271	217	10	=	=	SYM
ap-1271	217	11	0	0	NUM
ap-1271	217	12	for	for	ADP
ap-1271	217	13	r	r	NOUN
ap-1271	217	14	≥	≥	NOUN
ap-1271	217	15	εk	εk	NOUN
ap-1271	217	16	and	and	CCONJ
ap-1271	217	17	χk	χk	X
ap-1271	217	18	=	=	NOUN
ap-1271	217	19	1	1	NUM
ap-1271	217	20	for	for	ADP
ap-1271	217	21	r	r	NOUN
ap-1271	217	22	≤	≤	NUM
ap-1271	217	23	εk/2	εk/2	NOUN
ap-1271	217	24	.	.	PUNCT
ap-1271	218	1	define	define	VERB
ap-1271	218	2	a	a	DET
ap-1271	218	3	map	map	NOUN
ap-1271	218	4	tk	tk	NOUN
ap-1271	218	5	from	from	ADP
ap-1271	218	6	d	d	PROPN
ap-1271	218	7	to	to	ADP
ap-1271	218	8	dk	dk	PROPN
ap-1271	218	9	by	by	ADP
ap-1271	218	10	tk[f	tk[f	PROPN
ap-1271	218	11	]	]	PUNCT
ap-1271	218	12	=	=	PUNCT
ap-1271	219	1	[	[	X
ap-1271	219	2	ψ	ψ	X
ap-1271	219	3	−1	−1	NOUN
ap-1271	219	4	k	k	PROPN
ap-1271	219	5	χkf	χkf	PROPN
ap-1271	219	6	]	]	X
ap-1271	219	7	,	,	PUNCT
ap-1271	219	8	where	where	SCONJ
ap-1271	219	9	the	the	DET
ap-1271	219	10	function	function	NOUN
ap-1271	219	11	ψk	ψk	VERB
ap-1271	219	12	is	be	AUX
ap-1271	219	13	given	give	VERB
ap-1271	219	14	by	by	ADP
ap-1271	219	15	(	(	PUNCT
ap-1271	219	16	3	3	NUM
ap-1271	219	17	)	)	PUNCT
ap-1271	219	18	.	.	PUNCT
ap-1271	220	1	define	define	VERB
ap-1271	220	2	a	a	DET
ap-1271	220	3	map	map	NOUN
ap-1271	220	4	t	t	NOUN
ap-1271	220	5	from	from	ADP
ap-1271	220	6	d	d	PROPN
ap-1271	220	7	to	to	ADP
ap-1271	220	8	the	the	DET
ap-1271	220	9	direct	direct	ADJ
ap-1271	220	10	sum	sum	NOUN
ap-1271	220	11	k⊕	k⊕	NOUN
ap-1271	221	1	k=1	k=1	X
ap-1271	221	2	dk	dk	PROPN
ap-1271	221	3	by	by	ADP
ap-1271	221	4	t	t	PROPN
ap-1271	221	5	[	[	X
ap-1271	221	6	f	f	X
ap-1271	221	7	]	]	X
ap-1271	221	8	=	=	PUNCT
ap-1271	221	9	k⊕	k⊕	NOUN
ap-1271	221	10	k=1	k=1	AUX
ap-1271	221	11	tk[f	tk[f	X
ap-1271	221	12	]	]	PUNCT
ap-1271	221	13	.	.	PUNCT
ap-1271	222	1	we	we	PRON
ap-1271	222	2	also	also	ADV
ap-1271	222	3	define	define	VERB
ap-1271	222	4	a	a	DET
ap-1271	222	5	map	map	NOUN
ap-1271	222	6	s	s	VERB
ap-1271	222	7	from	from	ADP
ap-1271	222	8	k⊕	k⊕	NOUN
ap-1271	223	1	k=1	k=1	PROPN
ap-1271	223	2	dk	dk	PROPN
ap-1271	223	3	to	to	ADP
ap-1271	223	4	d	d	PROPN
ap-1271	223	5	by5	by5	PROPN
ap-1271	223	6	s	s	PART
ap-1271	223	7	k⊕	k⊕	NOUN
ap-1271	223	8	k=1	k=1	PUNCT
ap-1271	224	1	[	[	X
ap-1271	224	2	fk	fk	X
ap-1271	224	3	]	]	X
ap-1271	224	4	=	=	PUNCT
ap-1271	224	5	[	[	PUNCT
ap-1271	224	6	k∑	k∑	X
ap-1271	224	7	k=1	k=1	AUX
ap-1271	224	8	ψkχkfk	ψkχkfk	NOUN
ap-1271	224	9	]	]	PUNCT
ap-1271	224	10	.	.	PUNCT
ap-1271	225	1	in	in	ADP
ap-1271	225	2	the	the	DET
ap-1271	225	3	sequel	sequel	NOUN
ap-1271	225	4	,	,	PUNCT
ap-1271	225	5	we	we	PRON
ap-1271	225	6	sometimes	sometimes	ADV
ap-1271	225	7	write	write	VERB
ap-1271	225	8	[	[	X
ap-1271	225	9	f	f	NOUN
ap-1271	225	10	,	,	PUNCT
ap-1271	225	11	g]d	g]d	NOUN
ap-1271	225	12	=	=	PUNCT
ap-1271	226	1	[	[	X
ap-1271	226	2	[	[	X
ap-1271	226	3	f	f	X
ap-1271	226	4	]	]	X
ap-1271	226	5	,	,	PUNCT
ap-1271	226	6	[	[	X
ap-1271	226	7	g]]d	g]]d	PROPN
ap-1271	226	8	etc	etc	X
ap-1271	226	9	.	.	X
ap-1271	226	10	for	for	ADP
ap-1271	226	11	simplicity	simplicity	NOUN
ap-1271	226	12	of	of	ADP
ap-1271	226	13	notations	notation	NOUN
ap-1271	226	14	.	.	PUNCT
ap-1271	227	1	lemma	lemma	PROPN
ap-1271	227	2	3.1	3.1	NUM
ap-1271	227	3	1	1	NUM
ap-1271	227	4	.	.	PUNCT
ap-1271	228	1	assume	assume	VERB
ap-1271	228	2	k	k	X
ap-1271	228	3	<	<	X
ap-1271	228	4	∞.	∞.	PROPN
ap-1271	228	5	then	then	ADV
ap-1271	228	6	,	,	PUNCT
ap-1271	228	7	the	the	DET
ap-1271	228	8	maps	map	NOUN
ap-1271	228	9	s	s	PROPN
ap-1271	228	10	,	,	PUNCT
ap-1271	228	11	t	t	PROPN
ap-1271	228	12	defined	define	VERB
ap-1271	228	13	above	above	ADV
ap-1271	228	14	are	be	AUX
ap-1271	228	15	well	well	ADV
ap-1271	228	16	-	-	PUNCT
ap-1271	228	17	defined	define	VERB
ap-1271	228	18	and	and	CCONJ
ap-1271	228	19	mutually	mutually	ADV
ap-1271	228	20	inverse	inverse	ADJ
ap-1271	228	21	.	.	PUNCT
ap-1271	229	1	moreover	moreover	ADV
ap-1271	229	2	,	,	PUNCT
ap-1271	229	3	we	we	PRON
ap-1271	229	4	have	have	VERB
ap-1271	229	5	[	[	X
ap-1271	229	6	f	f	X
ap-1271	229	7	,	,	PUNCT
ap-1271	229	8	g]d	g]d	NOUN
ap-1271	229	9	=	=	SYM
ap-1271	230	1	k∑	k∑	VERB
ap-1271	231	1	k=1	k=1	PUNCT
ap-1271	232	1	[	[	X
ap-1271	232	2	tk[f	tk[f	X
ap-1271	232	3	]	]	PUNCT
ap-1271	232	4	,	,	PUNCT
ap-1271	232	5	tk[g]]dk	tk[g]]dk	PROPN
ap-1271	232	6	(	(	PUNCT
ap-1271	232	7	12	12	NUM
ap-1271	232	8	)	)	PUNCT
ap-1271	232	9	for	for	ADP
ap-1271	232	10	any	any	DET
ap-1271	232	11	[	[	X
ap-1271	232	12	f	f	X
ap-1271	232	13	]	]	X
ap-1271	232	14	,	,	PUNCT
ap-1271	232	15	[	[	X
ap-1271	232	16	g	g	X
ap-1271	232	17	]	]	X
ap-1271	232	18	∈	∈	PROPN
ap-1271	232	19	d.	d.	PROPN
ap-1271	232	20	2	2	NUM
ap-1271	232	21	.	.	PUNCT
ap-1271	232	22	assume	assume	VERB
ap-1271	232	23	k	k	X
ap-1271	232	24	=	=	PRON
ap-1271	232	25	∞.	∞.	PROPN
ap-1271	232	26	then	then	ADV
ap-1271	232	27	the	the	DET
ap-1271	232	28	map	map	NOUN
ap-1271	232	29	s	s	VERB
ap-1271	232	30	is	be	AUX
ap-1271	232	31	well	well	ADV
ap-1271	232	32	-	-	PUNCT
ap-1271	232	33	defined	define	VERB
ap-1271	232	34	and	and	CCONJ
ap-1271	232	35	injective	injective	ADJ
ap-1271	232	36	.	.	PUNCT
ap-1271	233	1	proof	proof	NOUN
ap-1271	233	2	.	.	PUNCT
ap-1271	234	1	(	(	PUNCT
ap-1271	234	2	i	i	NOUN
ap-1271	234	3	)	)	PUNCT
ap-1271	234	4	we	we	PRON
ap-1271	234	5	divide	divide	VERB
ap-1271	234	6	the	the	DET
ap-1271	234	7	proof	proof	NOUN
ap-1271	234	8	into	into	ADP
ap-1271	234	9	three	three	NUM
ap-1271	234	10	steps	step	NOUN
ap-1271	234	11	.	.	PUNCT
ap-1271	235	1	step	step	NOUN
ap-1271	235	2	1	1	NUM
ap-1271	235	3	.	.	PUNCT
ap-1271	236	1	the	the	DET
ap-1271	236	2	map	map	NOUN
ap-1271	236	3	d(hmax	d(hmax	NOUN
ap-1271	236	4	)	)	PUNCT
ap-1271	237	1	+	+	CCONJ
ap-1271	237	2	f	f	PROPN
ap-1271	237	3	�	�	PROPN
ap-1271	237	4	→	→	SYM
ap-1271	237	5	ψ−1	ψ−1	PROPN
ap-1271	237	6	k	k	PROPN
ap-1271	237	7	χkf	χkf	PROPN
ap-1271	237	8	∈	∈	PROPN
ap-1271	237	9	d(lk	d(lk	PROPN
ap-1271	237	10	,	,	PUNCT
ap-1271	237	11	max	max	PROPN
ap-1271	237	12	)	)	PUNCT
ap-1271	237	13	is	be	AUX
ap-1271	237	14	well	well	ADV
ap-1271	237	15	-	-	PUNCT
ap-1271	237	16	defined	define	VERB
ap-1271	237	17	and	and	CCONJ
ap-1271	237	18	continuous	continuous	ADJ
ap-1271	237	19	.	.	PUNCT
ap-1271	238	1	proof	proof	NOUN
ap-1271	238	2	.	.	PUNCT
ap-1271	239	1	clearly	clearly	ADV
ap-1271	239	2	ψ−1	ψ−1	PROPN
ap-1271	239	3	k	k	PROPN
ap-1271	239	4	χkf	χkf	PROPN
ap-1271	239	5	∈	∈	PROPN
ap-1271	239	6	l2(r2	l2(r2	NOUN
ap-1271	239	7	;	;	PUNCT
ap-1271	239	8	dμk	dμk	PROPN
ap-1271	239	9	)	)	PUNCT
ap-1271	239	10	,	,	PUNCT
ap-1271	239	11	so	so	SCONJ
ap-1271	239	12	it	it	PRON
ap-1271	239	13	suffices	suffice	VERB
ap-1271	239	14	to	to	PART
ap-1271	239	15	show	show	VERB
ap-1271	239	16	that	that	SCONJ
ap-1271	239	17	lk(ψ	lk(ψ	NOUN
ap-1271	239	18	−1	−1	NOUN
ap-1271	239	19	k	k	PROPN
ap-1271	239	20	χkf	χkf	PROPN
ap-1271	239	21	)	)	PUNCT
ap-1271	239	22	∈	∈	PROPN
ap-1271	239	23	l2(r2	l2(r2	NOUN
ap-1271	239	24	;	;	PUNCT
ap-1271	239	25	dμk	dμk	PROPN
ap-1271	239	26	)	)	PUNCT
ap-1271	239	27	.	.	PUNCT
ap-1271	240	1	by	by	ADP
ap-1271	240	2	(	(	PUNCT
ap-1271	240	3	5	5	NUM
ap-1271	240	4	)	)	PUNCT
ap-1271	240	5	and	and	CCONJ
ap-1271	240	6	the	the	DET
ap-1271	240	7	leibniz	leibniz	PROPN
ap-1271	240	8	rule	rule	NOUN
ap-1271	240	9	(	(	PUNCT
ap-1271	240	10	9	9	NUM
ap-1271	240	11	)	)	PUNCT
ap-1271	240	12	,	,	PUNCT
ap-1271	240	13	we	we	PRON
ap-1271	240	14	have	have	VERB
ap-1271	240	15	lk(ψ	lk(ψ	NUM
ap-1271	240	16	−1	−1	PROPN
ap-1271	240	17	k	k	PROPN
ap-1271	240	18	χkf	χkf	PROPN
ap-1271	240	19	)	)	PUNCT
ap-1271	241	1	=	=	PUNCT
ap-1271	241	2	ψ−1	ψ−1	PROPN
ap-1271	241	3	k	k	PROPN
ap-1271	241	4	l(χkf	l(χkf	NOUN
ap-1271	241	5	)	)	PUNCT
ap-1271	242	1	=	=	PUNCT
ap-1271	242	2	ψ−1	ψ−1	PROPN
ap-1271	242	3	k	k	X
ap-1271	242	4	(	(	PUNCT
ap-1271	242	5	χklf	χklf	VERB
ap-1271	242	6	−	−	PROPN
ap-1271	242	7	2〈dχk	2〈dχk	NOUN
ap-1271	242	8	,	,	PUNCT
ap-1271	242	9	daf〉+	daf〉+	NOUN
ap-1271	242	10	(	(	PUNCT
ap-1271	242	11	d∗dχk)f	d∗dχk)f	PROPN
ap-1271	242	12	)	)	PUNCT
ap-1271	242	13	.	.	PUNCT
ap-1271	243	1	the	the	DET
ap-1271	243	2	first	first	ADJ
ap-1271	243	3	term	term	NOUN
ap-1271	243	4	and	and	CCONJ
ap-1271	243	5	the	the	DET
ap-1271	243	6	third	third	ADJ
ap-1271	243	7	in	in	ADP
ap-1271	243	8	the	the	DET
ap-1271	243	9	parenthesis	parenthesis	NOUN
ap-1271	243	10	of	of	ADP
ap-1271	243	11	the	the	DET
ap-1271	243	12	right	right	ADJ
ap-1271	243	13	hand	hand	NOUN
ap-1271	243	14	side	side	NOUN
ap-1271	243	15	are	be	AUX
ap-1271	243	16	in	in	ADP
ap-1271	243	17	l2(r2	l2(r2	NOUN
ap-1271	243	18	;	;	PUNCT
ap-1271	243	19	dμk	dμk	PROPN
ap-1271	243	20	)	)	PUNCT
ap-1271	243	21	and	and	CCONJ
ap-1271	243	22	continuous	continuous	ADJ
ap-1271	243	23	with	with	ADP
ap-1271	243	24	respect	respect	NOUN
ap-1271	243	25	to	to	ADP
ap-1271	243	26	‖	‖	PROPN
ap-1271	243	27	·	·	SYM
ap-1271	243	28	‖hmax	‖hmax	X
ap-1271	243	29	.	.	PUNCT
ap-1271	244	1	moreover	moreover	ADV
ap-1271	244	2	,	,	PUNCT
ap-1271	244	3	we	we	PRON
ap-1271	244	4	can	can	AUX
ap-1271	244	5	prove	prove	VERB
ap-1271	244	6	the	the	DET
ap-1271	244	7	second	second	ADJ
ap-1271	244	8	term	term	NOUN
ap-1271	244	9	is	be	AUX
ap-1271	244	10	also	also	ADV
ap-1271	244	11	in	in	ADP
ap-1271	244	12	l2	l2	NOUN
ap-1271	244	13	and	and	CCONJ
ap-1271	244	14	continuous	continuous	ADJ
ap-1271	244	15	with	with	ADP
ap-1271	244	16	respect	respect	NOUN
ap-1271	244	17	to	to	ADP
ap-1271	244	18	‖	‖	PROPN
ap-1271	244	19	·	·	PUNCT
ap-1271	244	20	‖hmax	‖hmax	PUNCT
ap-1271	244	21	by	by	ADP
ap-1271	244	22	using	use	VERB
ap-1271	244	23	(	(	PUNCT
ap-1271	244	24	10	10	NUM
ap-1271	244	25	)	)	PUNCT
ap-1271	244	26	.	.	PUNCT
ap-1271	245	1	�	�	PROPN
ap-1271	245	2	step	step	VERB
ap-1271	245	3	2	2	NUM
ap-1271	245	4	.	.	PUNCT
ap-1271	246	1	let	let	VERB
ap-1271	246	2	f	f	PROPN
ap-1271	246	3	∈	∈	PROPN
ap-1271	246	4	d(hmin	d(hmin	PROPN
ap-1271	246	5	)	)	PUNCT
ap-1271	246	6	.	.	PUNCT
ap-1271	247	1	then	then	ADV
ap-1271	247	2	,	,	PUNCT
ap-1271	247	3	we	we	PRON
ap-1271	247	4	have	have	VERB
ap-1271	247	5	ψ−1	ψ−1	PROPN
ap-1271	247	6	k	k	PROPN
ap-1271	247	7	χkf	χkf	PROPN
ap-1271	247	8	∈	∈	PROPN
ap-1271	247	9	d(lk	d(lk	PROPN
ap-1271	247	10	,	,	PUNCT
ap-1271	247	11	min	min	NOUN
ap-1271	247	12	)	)	PUNCT
ap-1271	247	13	.	.	PUNCT
ap-1271	248	1	proof	proof	NOUN
ap-1271	248	2	.	.	PUNCT
ap-1271	249	1	by	by	ADP
ap-1271	249	2	definition	definition	NOUN
ap-1271	249	3	,	,	PUNCT
ap-1271	249	4	there	there	PRON
ap-1271	249	5	exists	exist	VERB
ap-1271	249	6	a	a	DET
ap-1271	249	7	sequence	sequence	NOUN
ap-1271	249	8	{	{	PUNCT
ap-1271	249	9	fn}∞n=1	fn}∞n=1	X
ap-1271	249	10	⊂	⊂	X
ap-1271	249	11	c∞	c∞	PROPN
ap-1271	249	12	0	0	PUNCT
ap-1271	249	13	(	(	PUNCT
ap-1271	249	14	m	m	PROPN
ap-1271	249	15	\γ	\γ	NOUN
ap-1271	249	16	)	)	PUNCT
ap-1271	249	17	such	such	ADJ
ap-1271	249	18	that	that	DET
ap-1271	249	19	fn	fn	PROPN
ap-1271	249	20	→	→	SYM
ap-1271	249	21	f	f	PROPN
ap-1271	249	22	in	in	ADP
ap-1271	249	23	d(hmin	d(hmin	PROPN
ap-1271	249	24	)	)	PUNCT
ap-1271	249	25	.	.	PUNCT
ap-1271	250	1	then	then	ADV
ap-1271	250	2	,	,	PUNCT
ap-1271	250	3	ψ−1	ψ−1	PROPN
ap-1271	250	4	k	k	PROPN
ap-1271	250	5	χkfn	χkfn	PROPN
ap-1271	250	6	∈	∈	PROPN
ap-1271	250	7	c∞	c∞	PROPN
ap-1271	250	8	0	0	PUNCT
ap-1271	251	1	(	(	PUNCT
ap-1271	251	2	r	r	NOUN
ap-1271	251	3	2	2	NUM
ap-1271	251	4	\	\	NOUN
ap-1271	251	5	{	{	PUNCT
ap-1271	251	6	0	0	NUM
ap-1271	251	7	}	}	PUNCT
ap-1271	251	8	)	)	PUNCT
ap-1271	251	9	and	and	CCONJ
ap-1271	251	10	ψ−1	ψ−1	PROPN
ap-1271	251	11	k	k	PROPN
ap-1271	251	12	χkfn	χkfn	PROPN
ap-1271	251	13	→	→	PUNCT
ap-1271	251	14	ψ−1	ψ−1	PROPN
ap-1271	251	15	k	k	PROPN
ap-1271	251	16	χkf	χkf	NOUN
ap-1271	251	17	in	in	ADP
ap-1271	251	18	d(lk	d(lk	PROPN
ap-1271	251	19	,	,	PUNCT
ap-1271	251	20	max	max	PROPN
ap-1271	251	21	)	)	PUNCT
ap-1271	251	22	,	,	PUNCT
ap-1271	251	23	by	by	ADP
ap-1271	251	24	step	step	NOUN
ap-1271	251	25	1	1	NUM
ap-1271	251	26	.	.	PUNCT
ap-1271	252	1	since	since	SCONJ
ap-1271	252	2	d(lk	d(lk	PROPN
ap-1271	252	3	,	,	PUNCT
ap-1271	252	4	min	min	NOUN
ap-1271	252	5	)	)	PUNCT
ap-1271	252	6	is	be	AUX
ap-1271	252	7	a	a	DET
ap-1271	252	8	closed	closed	ADJ
ap-1271	252	9	subspace	subspace	NOUN
ap-1271	252	10	of	of	ADP
ap-1271	252	11	d(lk	d(lk	PROPN
ap-1271	252	12	,	,	PUNCT
ap-1271	252	13	max	max	PROPN
ap-1271	252	14	)	)	PUNCT
ap-1271	252	15	,	,	PUNCT
ap-1271	252	16	we	we	PRON
ap-1271	252	17	have	have	VERB
ap-1271	252	18	the	the	DET
ap-1271	252	19	conclusion	conclusion	NOUN
ap-1271	252	20	.	.	PUNCT
ap-1271	253	1	�	�	PROPN
ap-1271	253	2	step	step	VERB
ap-1271	253	3	1	1	NUM
ap-1271	253	4	and	and	CCONJ
ap-1271	253	5	2	2	NUM
ap-1271	253	6	imply	imply	VERB
ap-1271	253	7	the	the	DET
ap-1271	253	8	map	map	NOUN
ap-1271	253	9	t	t	NOUN
ap-1271	253	10	is	be	AUX
ap-1271	253	11	well	well	ADV
ap-1271	253	12	-	-	PUNCT
ap-1271	253	13	defined	define	VERB
ap-1271	253	14	.	.	PUNCT
ap-1271	254	1	we	we	PRON
ap-1271	254	2	can	can	AUX
ap-1271	254	3	similarly	similarly	ADV
ap-1271	254	4	prove	prove	VERB
ap-1271	254	5	that	that	SCONJ
ap-1271	254	6	the	the	DET
ap-1271	254	7	map	map	NOUN
ap-1271	254	8	s	s	VERB
ap-1271	254	9	is	be	AUX
ap-1271	254	10	also	also	ADV
ap-1271	254	11	welldefined	welldefine	VERB
ap-1271	254	12	.	.	PUNCT
ap-1271	255	1	step	step	NOUN
ap-1271	255	2	3	3	NUM
ap-1271	255	3	.	.	PUNCT
ap-1271	256	1	the	the	DET
ap-1271	256	2	operator	operator	NOUN
ap-1271	256	3	st	st	PROPN
ap-1271	256	4	is	be	AUX
ap-1271	256	5	the	the	DET
ap-1271	256	6	identity	identity	NOUN
ap-1271	256	7	map	map	NOUN
ap-1271	256	8	on	on	ADP
ap-1271	256	9	d.	d.	PROPN
ap-1271	256	10	proof	proof	NOUN
ap-1271	256	11	.	.	PUNCT
ap-1271	257	1	by	by	ADP
ap-1271	257	2	definition	definition	NOUN
ap-1271	257	3	,	,	PUNCT
ap-1271	257	4	we	we	PRON
ap-1271	257	5	have	have	VERB
ap-1271	257	6	(	(	PUNCT
ap-1271	257	7	i	i	PRON
ap-1271	257	8	−	−	PROPN
ap-1271	257	9	st	st	PROPN
ap-1271	257	10	)	)	PUNCT
ap-1271	258	1	[	[	X
ap-1271	258	2	f	f	X
ap-1271	258	3	]	]	X
ap-1271	258	4	=	=	PUNCT
ap-1271	259	1	[	[	X
ap-1271	259	2	ψf	ψf	X
ap-1271	259	3	]	]	X
ap-1271	259	4	,	,	PUNCT
ap-1271	259	5	ψ	ψ	X
ap-1271	259	6	=	=	SYM
ap-1271	259	7	1−	1−	NUM
ap-1271	259	8	k∑	k∑	VERB
ap-1271	259	9	k=1	k=1	PROPN
ap-1271	260	1	χ2k	χ2k	PROPN
ap-1271	260	2	.	.	PUNCT
ap-1271	261	1	so	so	ADV
ap-1271	261	2	it	it	PRON
ap-1271	261	3	suffices	suffice	VERB
ap-1271	261	4	to	to	PART
ap-1271	261	5	prove	prove	VERB
ap-1271	261	6	that	that	SCONJ
ap-1271	261	7	g	g	NOUN
ap-1271	261	8	=	=	PUNCT
ap-1271	261	9	ψf	ψf	X
ap-1271	261	10	∈	∈	PROPN
ap-1271	261	11	d(hmin	d(hmin	PROPN
ap-1271	261	12	)	)	PUNCT
ap-1271	261	13	.	.	PUNCT
ap-1271	262	1	5when	5when	ADV
ap-1271	262	2	k	k	X
ap-1271	262	3	=	=	SYM
ap-1271	262	4	∞	∞	PROPN
ap-1271	262	5	,	,	PUNCT
ap-1271	262	6	we	we	PRON
ap-1271	262	7	define	define	VERB
ap-1271	262	8	the	the	DET
ap-1271	262	9	map	map	NOUN
ap-1271	262	10	s	s	VERB
ap-1271	262	11	for	for	ADP
ap-1271	262	12	the	the	DET
ap-1271	262	13	elements	element	NOUN
ap-1271	262	14	of	of	ADP
ap-1271	262	15	∞⊕	∞⊕	PROPN
ap-1271	262	16	k=1	k=1	X
ap-1271	263	1	dk	dk	PROPN
ap-1271	263	2	having	having	AUX
ap-1271	263	3	only	only	ADV
ap-1271	263	4	finite	finite	VERB
ap-1271	263	5	nonzero	nonzero	PROPN
ap-1271	263	6	components	component	NOUN
ap-1271	263	7	[	[	X
ap-1271	263	8	fk	fk	INTJ
ap-1271	263	9	]	]	X
ap-1271	263	10	.	.	PUNCT
ap-1271	264	1	so	so	ADV
ap-1271	264	2	there	there	PRON
ap-1271	264	3	is	be	VERB
ap-1271	264	4	no	no	DET
ap-1271	264	5	difficulty	difficulty	NOUN
ap-1271	264	6	in	in	ADP
ap-1271	264	7	the	the	DET
ap-1271	264	8	definition	definition	NOUN
ap-1271	264	9	of	of	ADP
ap-1271	264	10	s.	s.	PROPN
ap-1271	264	11	66	66	NUM
ap-1271	264	12	acta	acta	PROPN
ap-1271	264	13	polytechnica	polytechnica	PROPN
ap-1271	264	14	vol	vol	NOUN
ap-1271	264	15	.	.	PROPN
ap-1271	265	1	50	50	NUM
ap-1271	265	2	no	no	NOUN
ap-1271	265	3	.	.	PUNCT
ap-1271	266	1	5/2010	5/2010	PRON
ap-1271	266	2	let	let	VERB
ap-1271	266	3	(	(	PUNCT
ap-1271	266	4	r	r	NOUN
ap-1271	266	5	,	,	PUNCT
ap-1271	266	6	θ	θ	NOUN
ap-1271	266	7	)	)	PUNCT
ap-1271	266	8	be	be	VERB
ap-1271	266	9	the	the	DET
ap-1271	266	10	radial	radial	ADJ
ap-1271	266	11	coordinate	coordinate	NOUN
ap-1271	266	12	in	in	ADP
ap-1271	266	13	uk	uk	PROPN
ap-1271	266	14	and	and	CCONJ
ap-1271	266	15	put	put	VERB
ap-1271	266	16	bk	bk	PROPN
ap-1271	266	17	,	,	PUNCT
ap-1271	266	18	ε	ε	PROPN
ap-1271	266	19	=	=	PRON
ap-1271	266	20	{	{	PUNCT
ap-1271	266	21	x	x	SYM
ap-1271	266	22	∈	∈	PROPN
ap-1271	266	23	uk	uk	PROPN
ap-1271	267	1	|	|	ADV
ap-1271	267	2	r	r	X
ap-1271	267	3	<	<	X
ap-1271	267	4	ε	ε	PROPN
ap-1271	267	5	}	}	PUNCT
ap-1271	267	6	.	.	PUNCT
ap-1271	268	1	then	then	ADV
ap-1271	268	2	we	we	PRON
ap-1271	268	3	have	have	VERB
ap-1271	268	4	suppψ	suppψ	NOUN
ap-1271	268	5	⊂	⊂	PROPN
ap-1271	268	6	m	m	PROPN
ap-1271	268	7	\	\	NOUN
ap-1271	268	8	k⋃	k⋃	X
ap-1271	268	9	k=1	k=1	X
ap-1271	268	10	bk	bk	PROPN
ap-1271	268	11	,	,	PUNCT
ap-1271	268	12	εk/2	εk/2	VERB
ap-1271	268	13	.	.	PUNCT
ap-1271	269	1	for	for	ADP
ap-1271	269	2	c	c	PROPN
ap-1271	269	3	>	>	X
ap-1271	269	4	0	0	PROPN
ap-1271	269	5	,	,	PUNCT
ap-1271	269	6	let	let	VERB
ap-1271	269	7	ξc	ξc	PRON
ap-1271	269	8	∈	∈	PROPN
ap-1271	269	9	c∞(m	c∞(m	NOUN
ap-1271	269	10	)	)	PUNCT
ap-1271	269	11	such	such	ADJ
ap-1271	269	12	that	that	SCONJ
ap-1271	269	13	0	0	NUM
ap-1271	269	14	≤	≤	NUM
ap-1271	269	15	ξc	ξc	NOUN
ap-1271	269	16	≤	≤	NOUN
ap-1271	269	17	1	1	NUM
ap-1271	269	18	,	,	PUNCT
ap-1271	269	19	ξc	ξc	NOUN
ap-1271	269	20	=	=	SYM
ap-1271	269	21	1	1	NUM
ap-1271	269	22	in	in	ADP
ap-1271	269	23	m	m	PROPN
ap-1271	269	24	\	\	NOUN
ap-1271	269	25	k⋃	k⋃	X
ap-1271	269	26	k=1	k=1	X
ap-1271	269	27	bεk	bεk	PROPN
ap-1271	269	28	/	/	SYM
ap-1271	269	29	c	c	PROPN
ap-1271	269	30	,	,	PUNCT
ap-1271	269	31	ξc	ξc	NOUN
ap-1271	270	1	=	=	NOUN
ap-1271	270	2	0	0	NUM
ap-1271	270	3	in	in	ADP
ap-1271	270	4	k⋃	k⋃	X
ap-1271	270	5	k=1	k=1	X
ap-1271	270	6	bk	bk	PROPN
ap-1271	270	7	,	,	PUNCT
ap-1271	270	8	εk/(2c	εk/(2c	NOUN
ap-1271	270	9	)	)	PUNCT
ap-1271	270	10	.	.	PUNCT
ap-1271	271	1	let	let	AUX
ap-1271	271	2	l0	l0	PROPN
ap-1271	271	3	,	,	PUNCT
ap-1271	271	4	h0,min	h0,min	PROPN
ap-1271	271	5	and	and	CCONJ
ap-1271	271	6	h0,max	h0,max	PUNCT
ap-1271	271	7	be	be	AUX
ap-1271	271	8	the	the	DET
ap-1271	271	9	operators	operator	NOUN
ap-1271	271	10	corresponding	correspond	VERB
ap-1271	271	11	to	to	ADP
ap-1271	271	12	the	the	DET
ap-1271	271	13	potentials	potential	NOUN
ap-1271	271	14	ξ4a	ξ4a	PROPN
ap-1271	271	15	and	and	CCONJ
ap-1271	271	16	ξ4v	ξ4v	NOUN
ap-1271	271	17	.	.	PUNCT
ap-1271	272	1	these	these	DET
ap-1271	272	2	potentials	potential	NOUN
ap-1271	272	3	have	have	VERB
ap-1271	272	4	no	no	DET
ap-1271	272	5	singularities	singularity	NOUN
ap-1271	272	6	,	,	PUNCT
ap-1271	272	7	so	so	SCONJ
ap-1271	272	8	we	we	PRON
ap-1271	272	9	have	have	VERB
ap-1271	272	10	h0,min	h0,min	NOUN
ap-1271	272	11	=	=	PUNCT
ap-1271	272	12	h0,max	h0,max	PUNCT
ap-1271	272	13	by	by	ADP
ap-1271	272	14	[	[	X
ap-1271	272	15	14	14	NUM
ap-1271	272	16	]	]	PUNCT
ap-1271	272	17	.	.	PUNCT
ap-1271	273	1	since	since	SCONJ
ap-1271	273	2	lg	lg	PROPN
ap-1271	273	3	=	=	PROPN
ap-1271	273	4	l0	l0	PROPN
ap-1271	273	5	g	g	NOUN
ap-1271	273	6	∈	∈	PROPN
ap-1271	273	7	l2	l2	NOUN
ap-1271	273	8	,	,	PUNCT
ap-1271	273	9	we	we	PRON
ap-1271	273	10	have	have	VERB
ap-1271	273	11	g	g	PROPN
ap-1271	273	12	∈	∈	PROPN
ap-1271	273	13	d(h0,max	d(h0,max	PROPN
ap-1271	273	14	)	)	PUNCT
ap-1271	273	15	=	=	SYM
ap-1271	273	16	d(h0,min	d(h0,min	NOUN
ap-1271	273	17	)	)	PUNCT
ap-1271	273	18	.	.	PUNCT
ap-1271	274	1	thus	thus	ADV
ap-1271	274	2	we	we	PRON
ap-1271	274	3	can	can	AUX
ap-1271	274	4	take	take	VERB
ap-1271	274	5	a	a	DET
ap-1271	274	6	sequence	sequence	NOUN
ap-1271	274	7	{	{	PUNCT
ap-1271	274	8	gn	gn	X
ap-1271	274	9	}	}	PUNCT
ap-1271	274	10	such	such	ADJ
ap-1271	274	11	that	that	SCONJ
ap-1271	274	12	gn	gn	PROPN
ap-1271	274	13	→	→	SYM
ap-1271	274	14	g	g	PROPN
ap-1271	274	15	in	in	ADP
ap-1271	274	16	‖	‖	PROPN
ap-1271	274	17	·	·	PUNCT
ap-1271	274	18	‖h0,min	‖h0,min	PROPN
ap-1271	274	19	.	.	PUNCT
ap-1271	275	1	then	then	ADV
ap-1271	275	2	ξ2gn	ξ2gn	PUNCT
ap-1271	275	3	∈	∈	PROPN
ap-1271	275	4	c∞	c∞	PROPN
ap-1271	275	5	0	0	NUM
ap-1271	276	1	(	(	PUNCT
ap-1271	276	2	m	m	PROPN
ap-1271	276	3	\	\	PROPN
ap-1271	276	4	γ	γ	NOUN
ap-1271	276	5	)	)	PUNCT
ap-1271	276	6	and	and	CCONJ
ap-1271	276	7	ξ2gn	ξ2gn	PUNCT
ap-1271	276	8	→	→	SYM
ap-1271	276	9	ξ2	ξ2	NOUN
ap-1271	276	10	g	g	NOUN
ap-1271	276	11	=	=	SYM
ap-1271	276	12	g	g	NOUN
ap-1271	276	13	in	in	ADP
ap-1271	276	14	‖	‖	PROPN
ap-1271	276	15	·	·	PUNCT
ap-1271	276	16	‖hmin	‖hmin	X
ap-1271	276	17	.	.	PUNCT
ap-1271	277	1	thus	thus	ADV
ap-1271	277	2	we	we	PRON
ap-1271	277	3	have	have	VERB
ap-1271	277	4	g	g	PROPN
ap-1271	277	5	∈	∈	PROPN
ap-1271	277	6	d(hmin	d(hmin	PROPN
ap-1271	277	7	)	)	PUNCT
ap-1271	277	8	.	.	PUNCT
ap-1271	278	1	�	�	PROPN
ap-1271	278	2	we	we	PRON
ap-1271	278	3	can	can	AUX
ap-1271	278	4	prove	prove	VERB
ap-1271	278	5	ts	ts	ADP
ap-1271	279	1	=	=	VERB
ap-1271	279	2	i	i	PRON
ap-1271	279	3	similarly	similarly	ADV
ap-1271	279	4	.	.	PUNCT
ap-1271	280	1	then	then	ADV
ap-1271	280	2	(	(	PUNCT
ap-1271	280	3	12	12	NUM
ap-1271	280	4	)	)	PUNCT
ap-1271	280	5	follows	follow	VERB
ap-1271	280	6	from	from	ADP
ap-1271	280	7	(	(	PUNCT
ap-1271	280	8	5	5	NUM
ap-1271	280	9	)	)	PUNCT
ap-1271	280	10	and	and	CCONJ
ap-1271	280	11	the	the	DET
ap-1271	280	12	equality	equality	NOUN
ap-1271	280	13	[	[	X
ap-1271	280	14	f	f	X
ap-1271	280	15	,	,	PUNCT
ap-1271	280	16	g]d	g]d	NOUN
ap-1271	280	17	=	=	SYM
ap-1271	281	1	k∑	k∑	VERB
ap-1271	281	2	k=1	k=1	PUNCT
ap-1271	282	1	[	[	X
ap-1271	282	2	χkf	χkf	NOUN
ap-1271	282	3	,	,	PUNCT
ap-1271	282	4	χkg]d	χkg]d	PROPN
ap-1271	282	5	(	(	PUNCT
ap-1271	282	6	notice	notice	VERB
ap-1271	282	7	that	that	SCONJ
ap-1271	282	8	f	f	PROPN
ap-1271	282	9	−	−	NOUN
ap-1271	282	10	∑	∑	PUNCT
ap-1271	282	11	k	k	PROPN
ap-1271	282	12	χkf	χkf	PROPN
ap-1271	282	13	∈	∈	PROPN
ap-1271	282	14	d(hmin	d(hmin	PROPN
ap-1271	282	15	)	)	PUNCT
ap-1271	282	16	can	can	AUX
ap-1271	282	17	be	be	AUX
ap-1271	282	18	proved	prove	VERB
ap-1271	282	19	as	as	ADP
ap-1271	282	20	in	in	ADP
ap-1271	282	21	step	step	NOUN
ap-1271	282	22	3	3	NUM
ap-1271	282	23	)	)	PUNCT
ap-1271	282	24	.	.	PUNCT
ap-1271	283	1	(	(	PUNCT
ap-1271	283	2	2	2	X
ap-1271	283	3	)	)	PUNCT
ap-1271	283	4	letk	letk	NOUN
ap-1271	283	5	=	=	PROPN
ap-1271	283	6	∞.	∞.	PROPN
ap-1271	283	7	for	for	ADP
ap-1271	283	8	any	any	DET
ap-1271	283	9	positive	positive	ADJ
ap-1271	283	10	integer	integer	NOUN
ap-1271	283	11	n	n	CCONJ
ap-1271	283	12	,	,	PUNCT
ap-1271	283	13	we	we	PRON
ap-1271	283	14	can	can	AUX
ap-1271	283	15	define	define	VERB
ap-1271	283	16	t	t	PROPN
ap-1271	283	17	(	(	PUNCT
ap-1271	283	18	n	n	CCONJ
ap-1271	283	19	)	)	PUNCT
ap-1271	283	20	from	from	ADP
ap-1271	283	21	d	d	PROPN
ap-1271	283	22	to	to	ADP
ap-1271	283	23	n⊕	n⊕	NOUN
ap-1271	283	24	k=1	k=1	PUNCT
ap-1271	284	1	dk	dk	X
ap-1271	284	2	,	,	PUNCT
ap-1271	284	3	and	and	CCONJ
ap-1271	284	4	s(n	s(n	PROPN
ap-1271	284	5	)	)	PUNCT
ap-1271	284	6	from	from	ADP
ap-1271	284	7	n⊕	n⊕	PROPN
ap-1271	284	8	k=1	k=1	PUNCT
ap-1271	285	1	dk	dk	PROPN
ap-1271	285	2	to	to	ADP
ap-1271	285	3	d	d	NOUN
ap-1271	285	4	similarly	similarly	ADV
ap-1271	285	5	,	,	PUNCT
ap-1271	285	6	and	and	CCONJ
ap-1271	285	7	prove	prove	VERB
ap-1271	285	8	t	t	PROPN
ap-1271	285	9	(	(	PUNCT
ap-1271	285	10	n)s(n	n)s(n	PROPN
ap-1271	285	11	)	)	PUNCT
ap-1271	285	12	=	=	PUNCT
ap-1271	286	1	i	i	PRON
ap-1271	286	2	d.	d.	PROPN
ap-1271	286	3	this	this	PRON
ap-1271	286	4	implies	imply	VERB
ap-1271	286	5	the	the	DET
ap-1271	286	6	map	map	NOUN
ap-1271	286	7	s	s	VERB
ap-1271	286	8	is	be	AUX
ap-1271	286	9	well	well	ADV
ap-1271	286	10	-	-	PUNCT
ap-1271	286	11	defined	define	VERB
ap-1271	286	12	and	and	CCONJ
ap-1271	286	13	injective	injective	ADJ
ap-1271	286	14	.	.	PUNCT
ap-1271	287	1	�	�	PROPN
ap-1271	287	2	3.2	3.2	NUM
ap-1271	287	3	analysis	analysis	NOUN
ap-1271	287	4	of	of	ADP
ap-1271	287	5	operators	operator	NOUN
ap-1271	287	6	on	on	ADP
ap-1271	287	7	r	r	NOUN
ap-1271	287	8	2	2	NUM
ap-1271	287	9	we	we	PRON
ap-1271	287	10	shall	shall	AUX
ap-1271	287	11	analyze	analyze	VERB
ap-1271	287	12	the	the	DET
ap-1271	287	13	operator	operator	NOUN
ap-1271	287	14	lk	lk	NOUN
ap-1271	287	15	(	(	PUNCT
ap-1271	287	16	or	or	CCONJ
ap-1271	287	17	lk	lk	PROPN
ap-1271	287	18	,	,	PUNCT
ap-1271	287	19	min	min	NOUN
ap-1271	287	20	,	,	PUNCT
ap-1271	287	21	lk	lk	PROPN
ap-1271	287	22	,	,	PUNCT
ap-1271	287	23	max	max	PROPN
ap-1271	287	24	)	)	PUNCT
ap-1271	287	25	defined	define	VERB
ap-1271	287	26	in	in	ADP
ap-1271	287	27	the	the	DET
ap-1271	287	28	previous	previous	ADJ
ap-1271	287	29	subsection	subsection	NOUN
ap-1271	287	30	.	.	PUNCT
ap-1271	288	1	for	for	ADP
ap-1271	288	2	simplicity	simplicity	NOUN
ap-1271	288	3	of	of	ADP
ap-1271	288	4	notation	notation	NOUN
ap-1271	288	5	,	,	PUNCT
ap-1271	288	6	we	we	PRON
ap-1271	288	7	omitˆand˜in	omitˆand˜in	VERB
ap-1271	288	8	the	the	DET
ap-1271	288	9	definition	definition	NOUN
ap-1271	288	10	of	of	ADP
ap-1271	288	11	lk	lk	NOUN
ap-1271	288	12	in	in	ADP
ap-1271	288	13	the	the	DET
ap-1271	288	14	sequel	sequel	NOUN
ap-1271	288	15	.	.	PUNCT
ap-1271	289	1	then	then	ADV
ap-1271	289	2	our	our	PRON
ap-1271	289	3	assumptions	assumption	NOUN
ap-1271	289	4	are	be	AUX
ap-1271	289	5	the	the	DET
ap-1271	289	6	following	following	NOUN
ap-1271	289	7	:	:	PUNCT
ap-1271	289	8	1	1	X
ap-1271	289	9	.	.	X
ap-1271	289	10	lk	lk	NOUN
ap-1271	289	11	=	=	PUNCT
ap-1271	289	12	d∗ada	d∗ada	PROPN
ap-1271	289	13	+	+	CCONJ
ap-1271	289	14	v	v	NOUN
ap-1271	289	15	on	on	ADP
ap-1271	289	16	r	r	NOUN
ap-1271	289	17	2	2	NUM
ap-1271	289	18	\	\	NOUN
ap-1271	289	19	{	{	PUNCT
ap-1271	289	20	0	0	NUM
ap-1271	289	21	}	}	PUNCT
ap-1271	289	22	,	,	PUNCT
ap-1271	289	23	a	a	DET
ap-1271	289	24	=	=	PUNCT
ap-1271	289	25	a(0	a(0	PROPN
ap-1271	289	26	)	)	PUNCT
ap-1271	290	1	+	+	NOUN
ap-1271	290	2	a(1	a(1	NOUN
ap-1271	290	3	)	)	PUNCT
ap-1271	290	4	,	,	PUNCT
ap-1271	290	5	2	2	X
ap-1271	290	6	.	.	X
ap-1271	290	7	lk	lk	PROPN
ap-1271	290	8	,	,	PUNCT
ap-1271	290	9	min	min	PROPN
ap-1271	290	10	and	and	CCONJ
ap-1271	290	11	lk	lk	PROPN
ap-1271	290	12	,	,	PUNCT
ap-1271	290	13	max	max	PROPN
ap-1271	290	14	are	be	AUX
ap-1271	290	15	operators	operator	NOUN
ap-1271	290	16	on	on	ADP
ap-1271	290	17	l2(r2	l2(r2	NOUN
ap-1271	290	18	;	;	PUNCT
ap-1271	290	19	dμk	dμk	PROPN
ap-1271	290	20	)	)	PUNCT
ap-1271	290	21	,	,	PUNCT
ap-1271	290	22	dμk	dμk	NOUN
ap-1271	290	23	=	=	SYM
ap-1271	290	24	√	√	NUM
ap-1271	290	25	gdx1dx2	gdx1dx2	PROPN
ap-1271	290	26	,	,	PUNCT
ap-1271	290	27	3	3	NUM
ap-1271	290	28	.	.	PUNCT
ap-1271	291	1	a(0	a(0	PROPN
ap-1271	291	2	)	)	PUNCT
ap-1271	292	1	=	=	SYM
ap-1271	292	2	βkr−2(−x2dx1	βkr−2(−x2dx1	X
ap-1271	293	1	+	+	NUM
ap-1271	293	2	x1dx2	x1dx2	PROPN
ap-1271	293	3	)	)	PUNCT
ap-1271	293	4	,	,	PUNCT
ap-1271	293	5	0	0	NUM
ap-1271	293	6	≤	≤	NUM
ap-1271	293	7	βk	βk	ADP
ap-1271	293	8	<	<	X
ap-1271	293	9	1	1	NUM
ap-1271	293	10	,	,	PUNCT
ap-1271	293	11	4	4	NUM
ap-1271	293	12	.	.	PUNCT
ap-1271	293	13	a(1	a(1	NOUN
ap-1271	293	14	)	)	PUNCT
ap-1271	293	15	∈	∈	PROPN
ap-1271	293	16	c10λ	c10λ	NUM
ap-1271	293	17	1({r	1({r	NUM
ap-1271	293	18	<	<	X
ap-1271	293	19	2εk	2εk	NOUN
ap-1271	293	20	}	}	PUNCT
ap-1271	293	21	)	)	PUNCT
ap-1271	293	22	,	,	PUNCT
ap-1271	293	23	real	real	ADV
ap-1271	293	24	-	-	PUNCT
ap-1271	293	25	valued	value	VERB
ap-1271	293	26	,	,	PUNCT
ap-1271	293	27	a(1)(0	a(1)(0	PRON
ap-1271	293	28	)	)	PUNCT
ap-1271	293	29	=	=	SYM
ap-1271	293	30	0	0	NUM
ap-1271	293	31	,	,	PUNCT
ap-1271	293	32	5	5	NUM
ap-1271	293	33	.	.	X
ap-1271	293	34	v	v	NOUN
ap-1271	293	35	is	be	AUX
ap-1271	293	36	bounded	bound	VERB
ap-1271	293	37	,	,	PUNCT
ap-1271	293	38	real	real	ADV
ap-1271	293	39	-	-	PUNCT
ap-1271	293	40	valued	value	VERB
ap-1271	293	41	,	,	PUNCT
ap-1271	293	42	6	6	NUM
ap-1271	293	43	.	.	PUNCT
ap-1271	293	44	gmn(0	gmn(0	NOUN
ap-1271	293	45	)	)	PUNCT
ap-1271	294	1	=	=	SYM
ap-1271	294	2	δmn	δmn	NOUN
ap-1271	294	3	,	,	PUNCT
ap-1271	294	4	∂jgmn(0	∂jgmn(0	PUNCT
ap-1271	294	5	)	)	PUNCT
ap-1271	294	6	=	=	SYM
ap-1271	294	7	0	0	NUM
ap-1271	294	8	,	,	PUNCT
ap-1271	294	9	and	and	CCONJ
ap-1271	294	10	gmn	gmn	NOUN
ap-1271	294	11	=	=	PUNCT
ap-1271	294	12	δmn	δmn	PROPN
ap-1271	294	13	for	for	ADP
ap-1271	294	14	r	r	NOUN
ap-1271	294	15	≥	≥	NOUN
ap-1271	294	16	2εk	2εk	ADJ
ap-1271	294	17	.	.	PUNCT
ap-1271	295	1	we	we	PRON
ap-1271	295	2	shall	shall	AUX
ap-1271	295	3	show	show	VERB
ap-1271	295	4	that	that	SCONJ
ap-1271	295	5	gmn	gmn	NOUN
ap-1271	295	6	,	,	PUNCT
ap-1271	295	7	a(1	a(1	PROPN
ap-1271	295	8	)	)	PUNCT
ap-1271	295	9	and	and	CCONJ
ap-1271	295	10	v	v	PART
ap-1271	295	11	have	have	VERB
ap-1271	295	12	nothing	nothing	PRON
ap-1271	295	13	to	to	PART
ap-1271	295	14	do	do	VERB
ap-1271	295	15	with	with	ADP
ap-1271	295	16	the	the	DET
ap-1271	295	17	structure	structure	NOUN
ap-1271	295	18	of	of	ADP
ap-1271	295	19	the	the	DET
ap-1271	295	20	self	self	NOUN
ap-1271	295	21	-	-	PUNCT
ap-1271	295	22	adjoint	adjoint	NOUN
ap-1271	295	23	extensions	extension	NOUN
ap-1271	295	24	.	.	PUNCT
ap-1271	296	1	to	to	ADP
ap-1271	296	2	this	this	DET
ap-1271	296	3	purpose	purpose	NOUN
ap-1271	296	4	,	,	PUNCT
ap-1271	296	5	define	define	VERB
ap-1271	296	6	a	a	DET
ap-1271	296	7	differential	differential	ADJ
ap-1271	296	8	operatormk	operatormk	NOUN
ap-1271	296	9	on	on	ADP
ap-1271	296	10	r	r	NOUN
ap-1271	296	11	2	2	NUM
ap-1271	296	12	by	by	ADP
ap-1271	296	13	mk	mk	NOUN
ap-1271	296	14	=	=	SYM
ap-1271	297	1	−	−	PROPN
ap-1271	297	2	∑	∑	PUNCT
ap-1271	297	3	n=1,2	n=1,2	ADJ
ap-1271	297	4	(	(	PUNCT
ap-1271	297	5	∂	∂	NUM
ap-1271	297	6	∂xn	∂xn	NOUN
ap-1271	297	7	+	+	CCONJ
ap-1271	297	8	ian	ian	ADJ
ap-1271	297	9	)	)	PUNCT
ap-1271	297	10	2	2	NUM
ap-1271	297	11	.	.	PUNCT
ap-1271	298	1	define	define	VERB
ap-1271	298	2	a	a	DET
ap-1271	298	3	linear	linear	ADJ
ap-1271	298	4	operatormk	operatormk	NOUN
ap-1271	298	5	,	,	PUNCT
ap-1271	298	6	min	min	NOUN
ap-1271	298	7	on	on	ADP
ap-1271	298	8	l2(r2	l2(r2	NOUN
ap-1271	298	9	;	;	PUNCT
ap-1271	298	10	dx1dx2	dx1dx2	X
ap-1271	298	11	)	)	PUNCT
ap-1271	298	12	by	by	ADP
ap-1271	298	13	d(mk	d(mk	NOUN
ap-1271	298	14	,	,	PUNCT
ap-1271	298	15	min	min	NOUN
ap-1271	298	16	)	)	PUNCT
ap-1271	298	17	=	=	PRON
ap-1271	299	1	c∞	c∞	PROPN
ap-1271	299	2	0	0	PUNCT
ap-1271	300	1	(	(	PUNCT
ap-1271	300	2	r	r	NOUN
ap-1271	300	3	2	2	NUM
ap-1271	300	4	\	\	NOUN
ap-1271	300	5	{	{	PUNCT
ap-1271	300	6	0	0	NUM
ap-1271	300	7	}	}	PUNCT
ap-1271	300	8	)	)	PUNCT
ap-1271	300	9	,	,	PUNCT
ap-1271	300	10	mk	mk	PROPN
ap-1271	300	11	,	,	PUNCT
ap-1271	300	12	minu	minu	PROPN
ap-1271	300	13	=	=	PUNCT
ap-1271	300	14	mku	mku	NOUN
ap-1271	300	15	for	for	ADP
ap-1271	300	16	u	u	PROPN
ap-1271	300	17	∈	∈	PROPN
ap-1271	300	18	d(mk	d(mk	NOUN
ap-1271	300	19	,	,	PUNCT
ap-1271	300	20	min	min	NOUN
ap-1271	300	21	)	)	PUNCT
ap-1271	300	22	.	.	PUNCT
ap-1271	301	1	put	put	VERB
ap-1271	301	2	mk	mk	PROPN
ap-1271	301	3	,	,	PUNCT
ap-1271	301	4	max	max	PROPN
ap-1271	301	5	=	=	PROPN
ap-1271	301	6	m∗	m∗	PROPN
ap-1271	301	7	k	k	PROPN
ap-1271	301	8	,	,	PUNCT
ap-1271	301	9	min	min	NOUN
ap-1271	301	10	,	,	PUNCT
ap-1271	301	11	and	and	CCONJ
ap-1271	301	12	ek	ek	NOUN
ap-1271	301	13	=	=	PUNCT
ap-1271	301	14	d(mk	d(mk	NOUN
ap-1271	301	15	,	,	PUNCT
ap-1271	301	16	max)/	max)/	NOUN
ap-1271	301	17	d(mk	d(mk	NOUN
ap-1271	301	18	,	,	PUNCT
ap-1271	301	19	min	min	NOUN
ap-1271	301	20	)	)	PUNCT
ap-1271	301	21	.	.	PUNCT
ap-1271	302	1	we	we	PRON
ap-1271	302	2	also	also	ADV
ap-1271	302	3	define	define	VERB
ap-1271	302	4	m(0	m(0	PROPN
ap-1271	302	5	)	)	PUNCT
ap-1271	302	6	k	k	PROPN
ap-1271	302	7	,	,	PUNCT
ap-1271	302	8	m	m	VERB
ap-1271	302	9	(	(	PUNCT
ap-1271	302	10	0	0	NUM
ap-1271	302	11	)	)	PUNCT
ap-1271	302	12	k	k	NOUN
ap-1271	302	13	,	,	PUNCT
ap-1271	302	14	min	min	PROPN
ap-1271	302	15	,	,	PUNCT
ap-1271	302	16	m	m	VERB
ap-1271	302	17	(	(	PUNCT
ap-1271	302	18	0	0	NUM
ap-1271	302	19	)	)	PUNCT
ap-1271	302	20	k	k	NOUN
ap-1271	302	21	,	,	PUNCT
ap-1271	302	22	max	max	PROPN
ap-1271	302	23	,	,	PUNCT
ap-1271	302	24	and	and	CCONJ
ap-1271	302	25	e(0)k	e(0)k	PROPN
ap-1271	302	26	,	,	PUNCT
ap-1271	302	27	by	by	ADP
ap-1271	302	28	replacing	replace	VERB
ap-1271	302	29	an	an	DET
ap-1271	302	30	by	by	ADP
ap-1271	302	31	a(0)n	a(0)n	NOUN
ap-1271	302	32	in	in	ADP
ap-1271	302	33	the	the	DET
ap-1271	302	34	above	above	ADJ
ap-1271	302	35	definition	definition	NOUN
ap-1271	302	36	.	.	PUNCT
ap-1271	303	1	the	the	DET
ap-1271	303	2	operator	operator	NOUN
ap-1271	303	3	m(0	m(0	PROPN
ap-1271	303	4	)	)	PUNCT
ap-1271	303	5	k	k	PROPN
ap-1271	303	6	is	be	AUX
ap-1271	303	7	already	already	ADV
ap-1271	303	8	studied	study	VERB
ap-1271	303	9	in	in	ADP
ap-1271	303	10	[	[	X
ap-1271	303	11	1	1	NUM
ap-1271	303	12	]	]	PUNCT
ap-1271	303	13	and	and	CCONJ
ap-1271	303	14	[	[	X
ap-1271	303	15	7	7	NUM
ap-1271	303	16	]	]	PUNCT
ap-1271	303	17	.	.	PUNCT
ap-1271	304	1	here	here	ADV
ap-1271	304	2	we	we	PRON
ap-1271	304	3	quote	quote	VERB
ap-1271	304	4	their	their	PRON
ap-1271	304	5	results	result	NOUN
ap-1271	304	6	and	and	CCONJ
ap-1271	304	7	calculate	calculate	VERB
ap-1271	304	8	the	the	DET
ap-1271	304	9	form	form	NOUN
ap-1271	304	10	[	[	X
ap-1271	304	11	·	·	PUNCT
ap-1271	304	12	,	,	PUNCT
ap-1271	304	13	·	·	PUNCT
ap-1271	304	14	]	]	X
ap-1271	304	15	e(0	e(0	NOUN
ap-1271	304	16	)	)	PUNCT
ap-1271	304	17	k	k	PROPN
ap-1271	304	18	.	.	PUNCT
ap-1271	305	1	proposition	proposition	NOUN
ap-1271	305	2	3.2	3.2	NUM
ap-1271	305	3	let	let	VERB
ap-1271	305	4	χ	χ	PRON
ap-1271	305	5	∈	∈	PROPN
ap-1271	305	6	c∞	c∞	PROPN
ap-1271	305	7	0	0	PUNCT
ap-1271	306	1	(	(	PUNCT
ap-1271	306	2	r	r	NOUN
ap-1271	306	3	2	2	NUM
ap-1271	306	4	)	)	PUNCT
ap-1271	306	5	such	such	ADJ
ap-1271	306	6	that	that	SCONJ
ap-1271	306	7	χ	χ	X
ap-1271	306	8	=	=	SYM
ap-1271	306	9	1	1	NUM
ap-1271	306	10	in	in	ADP
ap-1271	306	11	some	some	DET
ap-1271	306	12	neighborhood	neighborhood	NOUN
ap-1271	306	13	of	of	ADP
ap-1271	306	14	0	0	NUM
ap-1271	306	15	.	.	NOUN
ap-1271	306	16	1	1	NUM
ap-1271	306	17	.	.	X
ap-1271	307	1	assume	assume	VERB
ap-1271	307	2	0	0	PUNCT
ap-1271	307	3	<	<	X
ap-1271	307	4	βk	βk	X
ap-1271	307	5	<	<	X
ap-1271	307	6	1	1	NUM
ap-1271	307	7	.	.	PUNCT
ap-1271	308	1	put	put	VERB
ap-1271	308	2	f1k	f1k	PUNCT
ap-1271	308	3	=	=	NOUN
ap-1271	308	4	χe−iθrβk−1	χe−iθrβk−1	ADJ
ap-1271	308	5	,	,	PUNCT
ap-1271	308	6	f2k	f2k	PROPN
ap-1271	308	7	=	=	SYM
ap-1271	308	8	χr−βk	χr−βk	NOUN
ap-1271	308	9	,	,	PUNCT
ap-1271	308	10	f4k	f4k	X
ap-1271	308	11	=	=	SYM
ap-1271	308	12	χe−iθr1−βk	χe−iθr1−βk	PROPN
ap-1271	308	13	,	,	PUNCT
ap-1271	308	14	f5k	f5k	PRON
ap-1271	308	15	=	=	PUNCT
ap-1271	308	16	χrβk	χrβk	NOUN
ap-1271	308	17	.	.	PUNCT
ap-1271	309	1	then	then	ADV
ap-1271	309	2	,	,	PUNCT
ap-1271	309	3	the	the	DET
ap-1271	309	4	deficiency	deficiency	NOUN
ap-1271	309	5	indices	indice	VERB
ap-1271	309	6	n±(m	n±(m	PROPN
ap-1271	309	7	(	(	PUNCT
ap-1271	309	8	0	0	NUM
ap-1271	309	9	)	)	PUNCT
ap-1271	309	10	k	k	NOUN
ap-1271	309	11	,	,	PUNCT
ap-1271	309	12	min	min	NOUN
ap-1271	309	13	)	)	PUNCT
ap-1271	309	14	=	=	SYM
ap-1271	309	15	2	2	NUM
ap-1271	309	16	,	,	PUNCT
ap-1271	309	17	dim	dim	VERB
ap-1271	309	18	e(0)k	e(0)k	PROPN
ap-1271	309	19	=	=	SYM
ap-1271	309	20	4	4	NUM
ap-1271	309	21	and	and	CCONJ
ap-1271	309	22	the	the	DET
ap-1271	309	23	vectors	vector	NOUN
ap-1271	309	24	{	{	PUNCT
ap-1271	310	1	[	[	X
ap-1271	310	2	fn	fn	X
ap-1271	310	3	k	k	X
ap-1271	310	4	]	]	X
ap-1271	310	5	}	}	PUNCT
ap-1271	310	6	n=1,2,4,5	n=1,2,4,5	NOUN
ap-1271	310	7	form	form	NOUN
ap-1271	310	8	a	a	DET
ap-1271	310	9	basis	basis	NOUN
ap-1271	310	10	of	of	ADP
ap-1271	310	11	e(0)k	e(0)k	PROPN
ap-1271	310	12	.	.	PUNCT
ap-1271	311	1	moreover	moreover	ADV
ap-1271	311	2	,	,	PUNCT
ap-1271	311	3	for	for	ADP
ap-1271	311	4	m	m	PROPN
ap-1271	311	5	,	,	PUNCT
ap-1271	311	6	n	n	PRON
ap-1271	311	7	∈	∈	PROPN
ap-1271	311	8	{	{	PUNCT
ap-1271	311	9	1	1	NUM
ap-1271	311	10	,	,	PUNCT
ap-1271	311	11	2	2	NUM
ap-1271	311	12	,	,	PUNCT
ap-1271	311	13	4	4	NUM
ap-1271	311	14	,	,	PUNCT
ap-1271	311	15	5	5	NUM
ap-1271	311	16	}	}	PUNCT
ap-1271	311	17	with	with	ADP
ap-1271	311	18	m	m	PROPN
ap-1271	311	19	≤	≤	NUM
ap-1271	311	20	n,6	n,6	NUM
ap-1271	311	21	we	we	PRON
ap-1271	311	22	have	have	VERB
ap-1271	311	23	[	[	X
ap-1271	311	24	fm	fm	X
ap-1271	311	25	k	k	NOUN
ap-1271	311	26	,	,	PUNCT
ap-1271	311	27	fn	fn	VERB
ap-1271	311	28	k	k	X
ap-1271	311	29	]	]	X
ap-1271	311	30	e(0	e(0	NOUN
ap-1271	311	31	)	)	PUNCT
ap-1271	311	32	k	k	NOUN
ap-1271	312	1	=	=	PUNCT
ap-1271	312	2	⎧⎪⎪⎨⎪⎪⎩	⎧⎪⎪⎨⎪⎪⎩	PROPN
ap-1271	312	3	4π(βk	4π(βk	NUM
ap-1271	312	4	−	−	NOUN
ap-1271	312	5	1	1	NUM
ap-1271	312	6	)	)	PUNCT
ap-1271	312	7	for	for	ADP
ap-1271	312	8	(	(	PUNCT
ap-1271	312	9	m	m	PROPN
ap-1271	312	10	,	,	PUNCT
ap-1271	312	11	n	n	CCONJ
ap-1271	312	12	)	)	PUNCT
ap-1271	312	13	=	=	SYM
ap-1271	312	14	(	(	PUNCT
ap-1271	312	15	1	1	NUM
ap-1271	312	16	,	,	PUNCT
ap-1271	312	17	4	4	NUM
ap-1271	312	18	)	)	PUNCT
ap-1271	312	19	,	,	PUNCT
ap-1271	312	20	−4πβk	−4πβk	X
ap-1271	312	21	for	for	ADP
ap-1271	312	22	(	(	PUNCT
ap-1271	312	23	m	m	PROPN
ap-1271	312	24	,	,	PUNCT
ap-1271	312	25	n	n	CCONJ
ap-1271	312	26	)	)	PUNCT
ap-1271	312	27	=	=	SYM
ap-1271	312	28	(	(	PUNCT
ap-1271	312	29	2	2	NUM
ap-1271	312	30	,	,	PUNCT
ap-1271	312	31	5	5	NUM
ap-1271	312	32	)	)	PUNCT
ap-1271	312	33	,	,	PUNCT
ap-1271	312	34	0	0	NUM
ap-1271	312	35	otherwise	otherwise	ADV
ap-1271	312	36	.	.	PUNCT
ap-1271	313	1	2	2	X
ap-1271	313	2	.	.	X
ap-1271	313	3	assume	assume	VERB
ap-1271	313	4	βk	βk	ADP
ap-1271	313	5	=	=	NOUN
ap-1271	313	6	0	0	X
ap-1271	313	7	.	.	PUNCT
ap-1271	314	1	put	put	VERB
ap-1271	314	2	f3k	f3k	PUNCT
ap-1271	315	1	=	=	SYM
ap-1271	315	2	χ	χ	NOUN
ap-1271	315	3	log	log	NOUN
ap-1271	315	4	r	r	NOUN
ap-1271	315	5	,	,	PUNCT
ap-1271	315	6	f6k	f6k	PROPN
ap-1271	315	7	=	=	SYM
ap-1271	315	8	χ	χ	NOUN
ap-1271	315	9	.	.	PUNCT
ap-1271	316	1	then	then	ADV
ap-1271	316	2	,	,	PUNCT
ap-1271	316	3	the	the	DET
ap-1271	316	4	deficiency	deficiency	NOUN
ap-1271	316	5	indices	indice	VERB
ap-1271	316	6	n±(m	n±(m	PROPN
ap-1271	316	7	(	(	PUNCT
ap-1271	316	8	0	0	NUM
ap-1271	316	9	)	)	PUNCT
ap-1271	316	10	k	k	NOUN
ap-1271	316	11	,	,	PUNCT
ap-1271	316	12	min	min	NOUN
ap-1271	316	13	)	)	PUNCT
ap-1271	316	14	=	=	SYM
ap-1271	316	15	1	1	NUM
ap-1271	316	16	,	,	PUNCT
ap-1271	316	17	dim	dim	VERB
ap-1271	316	18	e(0)k	e(0)k	PROPN
ap-1271	316	19	=	=	SYM
ap-1271	316	20	2	2	NUM
ap-1271	316	21	,	,	PUNCT
ap-1271	316	22	{	{	PUNCT
ap-1271	317	1	[	[	X
ap-1271	317	2	f	f	X
ap-1271	317	3	j	j	X
ap-1271	317	4	k	k	X
ap-1271	317	5	]	]	PUNCT
ap-1271	317	6	}	}	PUNCT
ap-1271	317	7	j=3,6	j=3,6	PROPN
ap-1271	317	8	form	form	VERB
ap-1271	317	9	a	a	DET
ap-1271	317	10	basis	basis	NOUN
ap-1271	317	11	of	of	ADP
ap-1271	317	12	e(0)k	e(0)k	PROPN
ap-1271	317	13	,	,	PUNCT
ap-1271	317	14	and	and	CCONJ
ap-1271	317	15	[	[	X
ap-1271	317	16	f3k	f3k	ADJ
ap-1271	317	17	,	,	PUNCT
ap-1271	317	18	f6k	f6k	PROPN
ap-1271	317	19	]	]	PUNCT
ap-1271	317	20	e(0	e(0	NOUN
ap-1271	317	21	)	)	PUNCT
ap-1271	317	22	k	k	NOUN
ap-1271	318	1	=	=	PUNCT
ap-1271	318	2	2π	2π	NOUN
ap-1271	318	3	,	,	PUNCT
ap-1271	318	4	[	[	X
ap-1271	318	5	f3k	f3k	ADP
ap-1271	318	6	,	,	PUNCT
ap-1271	318	7	f3k	f3k	PROPN
ap-1271	318	8	]	]	PUNCT
ap-1271	318	9	e(0	e(0	NOUN
ap-1271	318	10	)	)	PUNCT
ap-1271	318	11	k	k	NOUN
ap-1271	319	1	=	=	PUNCT
ap-1271	320	1	[	[	X
ap-1271	320	2	f6k	f6k	PROPN
ap-1271	320	3	,	,	PUNCT
ap-1271	320	4	f6k	f6k	PROPN
ap-1271	320	5	]	]	PUNCT
ap-1271	320	6	e(0	e(0	NOUN
ap-1271	320	7	)	)	PUNCT
ap-1271	320	8	k	k	NOUN
ap-1271	321	1	=	=	PUNCT
ap-1271	321	2	0	0	X
ap-1271	321	3	.	.	PUNCT
ap-1271	322	1	proof	proof	NOUN
ap-1271	322	2	.	.	PUNCT
ap-1271	323	1	(	(	PUNCT
ap-1271	323	2	i	i	NOUN
ap-1271	323	3	)	)	PUNCT
ap-1271	323	4	the	the	DET
ap-1271	323	5	first	first	ADJ
ap-1271	323	6	statement	statement	NOUN
ap-1271	323	7	follows	follow	VERB
ap-1271	323	8	from	from	ADP
ap-1271	323	9	the	the	DET
ap-1271	323	10	result	result	NOUN
ap-1271	323	11	in	in	ADP
ap-1271	323	12	[	[	X
ap-1271	323	13	7	7	NUM
ap-1271	323	14	]	]	PUNCT
ap-1271	323	15	or	or	CCONJ
ap-1271	323	16	[	[	X
ap-1271	323	17	1	1	NUM
ap-1271	323	18	]	]	PUNCT
ap-1271	323	19	.	.	PUNCT
ap-1271	324	1	for	for	ADP
ap-1271	324	2	the	the	DET
ap-1271	324	3	calculation	calculation	NOUN
ap-1271	324	4	of	of	ADP
ap-1271	324	5	[	[	X
ap-1271	324	6	u	u	NOUN
ap-1271	324	7	,	,	PUNCT
ap-1271	324	8	v]e(0	v]e(0	X
ap-1271	324	9	)	)	PUNCT
ap-1271	325	1	k	k	NOUN
ap-1271	325	2	,	,	PUNCT
ap-1271	325	3	we	we	PRON
ap-1271	325	4	use	use	VERB
ap-1271	325	5	some	some	DET
ap-1271	325	6	notation	notation	NOUN
ap-1271	325	7	in	in	ADP
ap-1271	325	8	vector	vector	NOUN
ap-1271	325	9	analysis	analysis	NOUN
ap-1271	325	10	.	.	PUNCT
ap-1271	326	1	we	we	PRON
ap-1271	326	2	use	use	VERB
ap-1271	326	3	the	the	DET
ap-1271	326	4	gradient	gradient	ADJ
ap-1271	326	5	vector	vector	NOUN
ap-1271	326	6	∇	∇	X
ap-1271	326	7	=	=	PUNCT
ap-1271	326	8	t(∂1	t(∂1	NOUN
ap-1271	326	9	,	,	PUNCT
ap-1271	326	10	∂2	∂2	PROPN
ap-1271	326	11	)	)	PUNCT
ap-1271	326	12	,	,	PUNCT
ap-1271	326	13	and	and	CCONJ
ap-1271	326	14	identify	identify	VERB
ap-1271	326	15	a	a	DET
ap-1271	326	16	1	1	NUM
ap-1271	326	17	-	-	PUNCT
ap-1271	326	18	form	form	NOUN
ap-1271	326	19	a	a	PRON
ap-1271	326	20	with	with	ADP
ap-1271	326	21	the	the	DET
ap-1271	326	22	component	component	NOUN
ap-1271	326	23	vector	vector	NOUN
ap-1271	326	24	t(a1	t(a1	NOUN
ap-1271	326	25	,	,	PUNCT
ap-1271	326	26	a2	a2	PROPN
ap-1271	326	27	)	)	PUNCT
ap-1271	326	28	.	.	PUNCT
ap-1271	327	1	the	the	DET
ap-1271	327	2	dot	dot	NOUN
ap-1271	327	3	·	·	PUNCT
ap-1271	327	4	denotes	denote	VERB
ap-1271	327	5	the	the	DET
ap-1271	327	6	euclidean	euclidean	ADJ
ap-1271	327	7	inner	inner	ADJ
ap-1271	327	8	product	product	NOUN
ap-1271	327	9	.	.	PUNCT
ap-1271	328	1	then	then	ADV
ap-1271	328	2	we	we	PRON
ap-1271	328	3	have	have	VERB
ap-1271	328	4	[	[	X
ap-1271	328	5	u	u	NOUN
ap-1271	328	6	,	,	PUNCT
ap-1271	328	7	v]e(0	v]e(0	X
ap-1271	328	8	)	)	PUNCT
ap-1271	329	1	k	k	X
ap-1271	330	1	=	=	SYM
ap-1271	330	2	lim	lim	PROPN
ap-1271	330	3	ε→0	ε→0	PROPN
ap-1271	330	4	∫	∫	PROPN
ap-1271	330	5	r≥ε	r≥ε	PROPN
ap-1271	330	6	(	(	PUNCT
ap-1271	330	7	−v(∇+	−v(∇+	NOUN
ap-1271	330	8	ia(0	ia(0	NOUN
ap-1271	330	9	)	)	PUNCT
ap-1271	330	10	)	)	PUNCT
ap-1271	330	11	·	·	PUNCT
ap-1271	331	1	(	(	PUNCT
ap-1271	331	2	∇+	∇+	NOUN
ap-1271	331	3	ia(0))u	ia(0))u	ADJ
ap-1271	331	4	+	+	CCONJ
ap-1271	331	5	u(∇+	u(∇+	PRON
ap-1271	331	6	ia(0	ia(0	NOUN
ap-1271	331	7	)	)	PUNCT
ap-1271	331	8	)	)	PUNCT
ap-1271	331	9	·	·	PUNCT
ap-1271	332	1	(	(	PUNCT
ap-1271	332	2	∇+	∇+	ADJ
ap-1271	332	3	ia(0))v	ia(0))v	ADJ
ap-1271	332	4	)	)	PUNCT
ap-1271	332	5	dx1dx2	dx1dx2	NOUN
ap-1271	332	6	=	=	PUNCT
ap-1271	333	1	6notice	6notice	NUM
ap-1271	333	2	that	that	SCONJ
ap-1271	334	1	[	[	X
ap-1271	334	2	fn	fn	X
ap-1271	334	3	k	k	NOUN
ap-1271	334	4	,	,	PUNCT
ap-1271	334	5	fm	fm	PROPN
ap-1271	334	6	k	k	X
ap-1271	334	7	]	]	X
ap-1271	334	8	e(0	e(0	NOUN
ap-1271	334	9	)	)	PUNCT
ap-1271	334	10	k	k	NOUN
ap-1271	335	1	=	=	PUNCT
ap-1271	335	2	−[fm	−[fm	X
ap-1271	336	1	k	k	NOUN
ap-1271	336	2	,	,	PUNCT
ap-1271	336	3	fn	fn	VERB
ap-1271	336	4	k	k	X
ap-1271	336	5	]	]	X
ap-1271	336	6	e(0	e(0	NOUN
ap-1271	336	7	)	)	PUNCT
ap-1271	336	8	k	k	NOUN
ap-1271	336	9	by	by	ADP
ap-1271	336	10	definition	definition	NOUN
ap-1271	336	11	.	.	PUNCT
ap-1271	337	1	67	67	NUM
ap-1271	337	2	acta	acta	PROPN
ap-1271	337	3	polytechnica	polytechnica	PROPN
ap-1271	337	4	vol	vol	NOUN
ap-1271	337	5	.	.	PROPN
ap-1271	338	1	50	50	NUM
ap-1271	338	2	no	no	NOUN
ap-1271	338	3	.	.	PUNCT
ap-1271	339	1	5/2010	5/2010	NUM
ap-1271	339	2	lim	lim	PROPN
ap-1271	339	3	ε→0	ε→0	X
ap-1271	339	4	∫	∫	PROPN
ap-1271	339	5	r	r	PROPN
ap-1271	339	6	=	=	PROPN
ap-1271	339	7	ε	ε	PROPN
ap-1271	339	8	(	(	PUNCT
ap-1271	339	9	vn	vn	PROPN
ap-1271	339	10	·	·	PUNCT
ap-1271	339	11	(	(	PUNCT
ap-1271	339	12	∇+	∇+	VERB
ap-1271	339	13	ia(0))u−	ia(0))u−	PROPN
ap-1271	339	14	un	un	PROPN
ap-1271	339	15	·	·	PUNCT
ap-1271	339	16	(	(	PUNCT
ap-1271	339	17	∇+	∇+	ADJ
ap-1271	339	18	ia(0))v	ia(0))v	NOUN
ap-1271	339	19	)	)	PUNCT
ap-1271	339	20	r	r	NOUN
ap-1271	339	21	dθ	dθ	PROPN
ap-1271	339	22	=	=	PROPN
ap-1271	339	23	lim	lim	PROPN
ap-1271	339	24	ε→0	ε→0	X
ap-1271	339	25	∫	∫	PROPN
ap-1271	339	26	r	r	PROPN
ap-1271	339	27	=	=	PROPN
ap-1271	339	28	ε	ε	X
ap-1271	339	29	(	(	PUNCT
ap-1271	339	30	v∂ru	v∂ru	NOUN
ap-1271	339	31	−	−	PROPN
ap-1271	339	32	u∂rv	u∂rv	NOUN
ap-1271	339	33	)	)	PUNCT
ap-1271	339	34	r	r	NOUN
ap-1271	339	35	dθ	dθ	PROPN
ap-1271	339	36	,	,	PUNCT
ap-1271	339	37	(	(	PUNCT
ap-1271	339	38	13	13	NUM
ap-1271	339	39	)	)	PUNCT
ap-1271	339	40	where	where	SCONJ
ap-1271	339	41	n	n	ADV
ap-1271	339	42	=	=	SYM
ap-1271	339	43	(	(	PUNCT
ap-1271	339	44	cos	cos	PROPN
ap-1271	339	45	θ	θ	PROPN
ap-1271	339	46	,	,	PUNCT
ap-1271	339	47	sin	sin	NOUN
ap-1271	339	48	θ	θ	NOUN
ap-1271	339	49	)	)	PUNCT
ap-1271	339	50	,	,	PUNCT
ap-1271	339	51	and	and	CCONJ
ap-1271	339	52	the	the	DET
ap-1271	339	53	line	line	NOUN
ap-1271	339	54	integral	integral	ADJ
ap-1271	339	55	is	be	AUX
ap-1271	339	56	taken	take	VERB
ap-1271	339	57	counterclockwise	counterclockwise	NOUN
ap-1271	339	58	.	.	PUNCT
ap-1271	340	1	we	we	PRON
ap-1271	340	2	used	use	VERB
ap-1271	340	3	the	the	DET
ap-1271	340	4	green	green	ADJ
ap-1271	340	5	formula	formula	NOUN
ap-1271	340	6	and	and	CCONJ
ap-1271	340	7	the	the	DET
ap-1271	340	8	fact	fact	NOUN
ap-1271	340	9	n	n	X
ap-1271	340	10	·	·	PUNCT
ap-1271	340	11	a(0	a(0	PROPN
ap-1271	340	12	)	)	PUNCT
ap-1271	340	13	=	=	SYM
ap-1271	341	1	0	0	X
ap-1271	341	2	.	.	PUNCT
ap-1271	342	1	then	then	ADV
ap-1271	342	2	we	we	PRON
ap-1271	342	3	can	can	AUX
ap-1271	342	4	easily	easily	ADV
ap-1271	342	5	prove	prove	VERB
ap-1271	342	6	the	the	DET
ap-1271	342	7	second	second	ADJ
ap-1271	342	8	statement	statement	NOUN
ap-1271	342	9	by	by	ADP
ap-1271	342	10	using	use	VERB
ap-1271	342	11	(	(	PUNCT
ap-1271	342	12	13	13	NUM
ap-1271	342	13	)	)	PUNCT
ap-1271	342	14	.	.	PUNCT
ap-1271	343	1	(	(	PUNCT
ap-1271	343	2	ii	ii	X
ap-1271	343	3	)	)	PUNCT
ap-1271	343	4	the	the	DET
ap-1271	343	5	first	first	ADJ
ap-1271	343	6	part	part	NOUN
ap-1271	343	7	of	of	ADP
ap-1271	343	8	the	the	DET
ap-1271	343	9	statement	statement	NOUN
ap-1271	343	10	follows	follow	VERB
ap-1271	343	11	from	from	ADP
ap-1271	343	12	the	the	DET
ap-1271	343	13	results	result	NOUN
ap-1271	343	14	in	in	ADP
ap-1271	343	15	[	[	X
ap-1271	343	16	3	3	NUM
ap-1271	343	17	]	]	PUNCT
ap-1271	343	18	.	.	PUNCT
ap-1271	344	1	the	the	DET
ap-1271	344	2	second	second	ADJ
ap-1271	344	3	statement	statement	NOUN
ap-1271	344	4	can	can	AUX
ap-1271	344	5	be	be	AUX
ap-1271	344	6	justified	justify	VERB
ap-1271	344	7	by	by	ADP
ap-1271	344	8	using	use	VERB
ap-1271	344	9	(	(	PUNCT
ap-1271	344	10	13	13	NUM
ap-1271	344	11	)	)	PUNCT
ap-1271	344	12	.	.	PUNCT
ap-1271	345	1	�	�	PROPN
ap-1271	345	2	next	next	ADV
ap-1271	345	3	,	,	PUNCT
ap-1271	345	4	we	we	PRON
ap-1271	345	5	prove	prove	VERB
ap-1271	345	6	that	that	SCONJ
ap-1271	345	7	the	the	DET
ap-1271	345	8	regular	regular	ADJ
ap-1271	345	9	part	part	NOUN
ap-1271	345	10	a(1	a(1	ADV
ap-1271	345	11	)	)	PUNCT
ap-1271	345	12	does	do	AUX
ap-1271	345	13	not	not	PART
ap-1271	345	14	affect	affect	VERB
ap-1271	345	15	the	the	DET
ap-1271	345	16	structure	structure	NOUN
ap-1271	345	17	of	of	ADP
ap-1271	345	18	ek	ek	PROPN
ap-1271	345	19	and	and	CCONJ
ap-1271	345	20	the	the	DET
ap-1271	345	21	corresponding	corresponding	ADJ
ap-1271	345	22	form	form	NOUN
ap-1271	345	23	.	.	PUNCT
ap-1271	346	1	proposition	proposition	NOUN
ap-1271	346	2	3.3	3.3	NUM
ap-1271	346	3	all	all	DET
ap-1271	346	4	the	the	DET
ap-1271	346	5	statements	statement	NOUN
ap-1271	346	6	of	of	ADP
ap-1271	346	7	proposition	proposition	NOUN
ap-1271	346	8	3.2	3.2	NUM
ap-1271	346	9	hold	hold	VERB
ap-1271	346	10	even	even	ADV
ap-1271	346	11	if	if	SCONJ
ap-1271	346	12	we	we	PRON
ap-1271	346	13	replace	replace	VERB
ap-1271	346	14	m	m	PROPN
ap-1271	346	15	(	(	PUNCT
ap-1271	346	16	0	0	NUM
ap-1271	346	17	)	)	PUNCT
ap-1271	346	18	k	k	NOUN
ap-1271	346	19	,	,	PUNCT
ap-1271	346	20	min	min	PROPN
ap-1271	346	21	by	by	ADP
ap-1271	346	22	mk	mk	PROPN
ap-1271	346	23	,	,	PUNCT
ap-1271	346	24	min	min	PROPN
ap-1271	346	25	,	,	PUNCT
ap-1271	346	26	and	and	CCONJ
ap-1271	346	27	e(0)k	e(0)k	PROPN
ap-1271	346	28	by	by	ADP
ap-1271	346	29	ek	ek	PROPN
ap-1271	346	30	.	.	PROPN
ap-1271	347	1	before	before	ADP
ap-1271	347	2	the	the	DET
ap-1271	347	3	proof	proof	NOUN
ap-1271	347	4	,	,	PUNCT
ap-1271	347	5	we	we	PRON
ap-1271	347	6	prepare	prepare	VERB
ap-1271	347	7	a	a	DET
ap-1271	347	8	perturbative	perturbative	ADJ
ap-1271	347	9	lemma	lemma	PROPN
ap-1271	347	10	,	,	PUNCT
ap-1271	347	11	which	which	PRON
ap-1271	347	12	is	be	AUX
ap-1271	347	13	an	an	DET
ap-1271	347	14	immediate	immediate	ADJ
ap-1271	347	15	corollary	corollary	NOUN
ap-1271	347	16	of	of	ADP
ap-1271	347	17	[	[	X
ap-1271	347	18	10	10	NUM
ap-1271	347	19	,	,	PUNCT
ap-1271	347	20	theorem	theorem	VERB
ap-1271	347	21	iv.5.22	iv.5.22	NOUN
ap-1271	347	22	]	]	PUNCT
ap-1271	347	23	.	.	PUNCT
ap-1271	348	1	lemma	lemma	PROPN
ap-1271	348	2	3.4	3.4	NUM
ap-1271	348	3	let	let	VERB
ap-1271	348	4	h	h	PRON
ap-1271	348	5	be	be	AUX
ap-1271	348	6	a	a	DET
ap-1271	348	7	separable	separable	ADJ
ap-1271	348	8	hilbert	hilbert	NOUN
ap-1271	348	9	space	space	NOUN
ap-1271	348	10	and	and	CCONJ
ap-1271	348	11	‖	‖	PROPN
ap-1271	348	12	·	·	PUNCT
ap-1271	348	13	‖	‖	VERB
ap-1271	348	14	its	its	PRON
ap-1271	348	15	norm	norm	NOUN
ap-1271	348	16	.	.	PUNCT
ap-1271	349	1	let	let	VERB
ap-1271	349	2	x	x	PRON
ap-1271	349	3	,	,	PUNCT
ap-1271	349	4	y	y	PROPN
ap-1271	349	5	be	be	AUX
ap-1271	349	6	densely	densely	ADV
ap-1271	349	7	defined	define	VERB
ap-1271	349	8	symmetric	symmetric	ADJ
ap-1271	349	9	operators	operator	NOUN
ap-1271	349	10	on	on	ADP
ap-1271	349	11	h.	h.	PROPN
ap-1271	349	12	assume	assume	PROPN
ap-1271	349	13	d(x	d(x	PROPN
ap-1271	349	14	)	)	PUNCT
ap-1271	350	1	⊂	⊂	PROPN
ap-1271	350	2	d(y	d(y	PROPN
ap-1271	350	3	)	)	PUNCT
ap-1271	350	4	and	and	CCONJ
ap-1271	350	5	there	there	PRON
ap-1271	350	6	exist	exist	VERB
ap-1271	350	7	positive	positive	ADJ
ap-1271	350	8	constants	constant	NOUN
ap-1271	350	9	c	c	NOUN
ap-1271	350	10	,	,	PUNCT
ap-1271	350	11	δ	δ	PROPN
ap-1271	350	12	with	with	ADP
ap-1271	350	13	0	0	NUM
ap-1271	350	14	<	<	X
ap-1271	350	15	δ	δ	X
ap-1271	350	16	<	<	X
ap-1271	350	17	1	1	NUM
ap-1271	350	18	and	and	CCONJ
ap-1271	350	19	‖y	‖y	ADV
ap-1271	350	20	u‖	u‖	ADJ
ap-1271	350	21	≤	≤	PUNCT
ap-1271	350	22	δ‖xu‖+	δ‖xu‖+	VERB
ap-1271	350	23	c‖u‖	c‖u‖	PROPN
ap-1271	350	24	for	for	ADP
ap-1271	350	25	every	every	DET
ap-1271	350	26	u	u	PROPN
ap-1271	350	27	∈	∈	PROPN
ap-1271	350	28	d(x	d(x	PROPN
ap-1271	350	29	)	)	PUNCT
ap-1271	350	30	.	.	PUNCT
ap-1271	351	1	then	then	ADV
ap-1271	351	2	,	,	PUNCT
ap-1271	351	3	we	we	PRON
ap-1271	351	4	have	have	VERB
ap-1271	351	5	d(x	d(x	NOUN
ap-1271	351	6	+	+	CCONJ
ap-1271	351	7	y	y	NOUN
ap-1271	351	8	)	)	PUNCT
ap-1271	352	1	=	=	SYM
ap-1271	352	2	d(x	d(x	PROPN
ap-1271	352	3	)	)	PUNCT
ap-1271	352	4	and	and	CCONJ
ap-1271	352	5	n±(x	n±(x	NOUN
ap-1271	352	6	+	+	CCONJ
ap-1271	352	7	y	y	PROPN
ap-1271	352	8	)	)	PUNCT
ap-1271	353	1	=	=	SYM
ap-1271	353	2	n±(x	n±(x	PROPN
ap-1271	353	3	)	)	PUNCT
ap-1271	353	4	,	,	PUNCT
ap-1271	353	5	where	where	SCONJ
ap-1271	353	6	the	the	DET
ap-1271	353	7	overline	overline	NOUN
ap-1271	353	8	denotes	denote	VERB
ap-1271	353	9	the	the	DET
ap-1271	353	10	operator	operator	NOUN
ap-1271	353	11	closure	closure	NOUN
ap-1271	353	12	.	.	PUNCT
ap-1271	354	1	proof	proof	NOUN
ap-1271	354	2	of	of	ADP
ap-1271	354	3	proposition	proposition	NOUN
ap-1271	354	4	3.3	3.3	NUM
ap-1271	354	5	we	we	PRON
ap-1271	354	6	prove	prove	VERB
ap-1271	354	7	only	only	ADV
ap-1271	354	8	statement	statement	NOUN
ap-1271	354	9	(	(	PUNCT
ap-1271	354	10	i	i	NOUN
ap-1271	354	11	)	)	PUNCT
ap-1271	354	12	.	.	PUNCT
ap-1271	355	1	statement	statement	NOUN
ap-1271	355	2	(	(	PUNCT
ap-1271	355	3	ii	ii	NOUN
ap-1271	355	4	)	)	PUNCT
ap-1271	355	5	can	can	AUX
ap-1271	355	6	be	be	AUX
ap-1271	355	7	proved	prove	VERB
ap-1271	355	8	similarly	similarly	ADV
ap-1271	355	9	.	.	PUNCT
ap-1271	356	1	by	by	ADP
ap-1271	356	2	the	the	DET
ap-1271	356	3	leibniz	leibniz	PROPN
ap-1271	356	4	formula	formula	NOUN
ap-1271	356	5	(	(	PUNCT
ap-1271	356	6	8)	8)	NUM
ap-1271	356	7	,	,	PUNCT
ap-1271	356	8	we	we	PRON
ap-1271	356	9	have	have	VERB
ap-1271	356	10	for	for	ADP
ap-1271	356	11	u	u	PROPN
ap-1271	356	12	∈	∈	PROPN
ap-1271	356	13	c∞	c∞	PROPN
ap-1271	356	14	0	0	PUNCT
ap-1271	357	1	(	(	PUNCT
ap-1271	357	2	r	r	NOUN
ap-1271	357	3	2	2	NUM
ap-1271	357	4	\	\	NOUN
ap-1271	357	5	{	{	PUNCT
ap-1271	357	6	0	0	NUM
ap-1271	357	7	}	}	PUNCT
ap-1271	357	8	)	)	PUNCT
ap-1271	357	9	(	(	PUNCT
ap-1271	357	10	mk	mk	X
ap-1271	357	11	−	−	PROPN
ap-1271	357	12	m(0	m(0	PROPN
ap-1271	357	13	)	)	PUNCT
ap-1271	357	14	k	k	NOUN
ap-1271	357	15	)	)	PUNCT
ap-1271	357	16	u	u	NOUN
ap-1271	357	17	=	=	SYM
ap-1271	357	18	i(d∗a(1))u	i(d∗a(1))u	NUM
ap-1271	357	19	−	−	PROPN
ap-1271	357	20	(	(	PUNCT
ap-1271	357	21	14	14	NUM
ap-1271	357	22	)	)	PUNCT
ap-1271	357	23	2i〈a(1	2i〈a(1	NUM
ap-1271	357	24	)	)	PUNCT
ap-1271	357	25	,	,	PUNCT
ap-1271	357	26	da(0)u〉+	da(0)u〉+	PROPN
ap-1271	357	27	|a(1)|2u	|a(1)|2u	VERB
ap-1271	357	28	.	.	PUNCT
ap-1271	358	1	we	we	PRON
ap-1271	358	2	denote	denote	VERB
ap-1271	358	3	‖u‖2	‖u‖2	PROPN
ap-1271	358	4	=	=	SYM
ap-1271	358	5	∫	∫	PROPN
ap-1271	358	6	r	r	NOUN
ap-1271	358	7	2	2	NUM
ap-1271	358	8	|u|2dx1dx2	|u|2dx1dx2	NOUN
ap-1271	358	9	for	for	ADP
ap-1271	358	10	a	a	DET
ap-1271	358	11	function	function	NOUN
ap-1271	358	12	u	u	NOUN
ap-1271	358	13	,	,	PUNCT
ap-1271	358	14	and	and	CCONJ
ap-1271	358	15	‖ω‖2	‖ω‖2	PROPN
ap-1271	358	16	=	=	SYM
ap-1271	359	1	∫	∫	PROPN
ap-1271	359	2	r	r	NOUN
ap-1271	359	3	2	2	NUM
ap-1271	359	4	|ω|2dx1dx2	|ω|2dx1dx2	NOUN
ap-1271	359	5	for	for	ADP
ap-1271	359	6	a	a	DET
ap-1271	359	7	1	1	NUM
ap-1271	359	8	-	-	PUNCT
ap-1271	359	9	form	form	NOUN
ap-1271	359	10	ω	ω	NOUN
ap-1271	359	11	(	(	PUNCT
ap-1271	359	12	notice	notice	VERB
ap-1271	359	13	that	that	SCONJ
ap-1271	359	14	|ω|2	|ω|2	NOUN
ap-1271	359	15	=	=	SYM
ap-1271	359	16	〈	〈	PROPN
ap-1271	359	17	ω	ω	PROPN
ap-1271	359	18	,	,	PUNCT
ap-1271	359	19	ω	ω	PROPN
ap-1271	359	20	〉	〉	NOUN
ap-1271	359	21	)	)	PUNCT
ap-1271	359	22	.	.	PUNCT
ap-1271	360	1	we	we	PRON
ap-1271	360	2	denote	denote	VERB
ap-1271	360	3	the	the	DET
ap-1271	360	4	essential	essential	ADJ
ap-1271	360	5	supremum	supremum	ADJ
ap-1271	360	6	norm	norm	NOUN
ap-1271	360	7	of	of	ADP
ap-1271	360	8	|u|	|u|	PROPN
ap-1271	360	9	and	and	CCONJ
ap-1271	360	10	|ω|	|ω|	VERB
ap-1271	360	11	by	by	ADP
ap-1271	360	12	‖u‖∞	‖u‖∞	NUM
ap-1271	360	13	and	and	CCONJ
ap-1271	360	14	‖ω‖∞	‖ω‖∞	PROPN
ap-1271	360	15	,	,	PUNCT
ap-1271	360	16	respectively	respectively	ADV
ap-1271	360	17	.	.	PUNCT
ap-1271	361	1	then	then	ADV
ap-1271	361	2	we	we	PRON
ap-1271	361	3	have	have	AUX
ap-1271	361	4	by	by	ADP
ap-1271	361	5	the	the	DET
ap-1271	361	6	schwarz	schwarz	PROPN
ap-1271	361	7	inequality	inequality	PROPN
ap-1271	361	8	‖(mk	‖(mk	NOUN
ap-1271	361	9	−	−	PROPN
ap-1271	361	10	m(0	m(0	PROPN
ap-1271	361	11	)	)	PUNCT
ap-1271	361	12	k	k	NOUN
ap-1271	361	13	)	)	PUNCT
ap-1271	361	14	u‖	u‖	VERB
ap-1271	361	15	≤	≤	NUM
ap-1271	361	16	‖d∗a(1)‖∞‖u‖+2‖a(1)‖∞‖da(0)u‖+	‖d∗a(1)‖∞‖u‖+2‖a(1)‖∞‖da(0)u‖+	PUNCT
ap-1271	361	17	‖a(1)‖2∞‖u‖	‖a(1)‖2∞‖u‖	PROPN
ap-1271	361	18	≤	≤	NOUN
ap-1271	361	19	(	(	PUNCT
ap-1271	361	20	‖d∗a(1)‖∞	‖d∗a(1)‖∞	ADJ
ap-1271	361	21	+	+	ADJ
ap-1271	361	22	‖a(1)‖2∞)‖u‖+	‖a(1)‖2∞)‖u‖+	NOUN
ap-1271	361	23	‖a(1)‖∞(ε‖m(0	‖a(1)‖∞(ε‖m(0	PROPN
ap-1271	361	24	)	)	PUNCT
ap-1271	361	25	k	k	PROPN
ap-1271	361	26	u‖2	u‖2	PROPN
ap-1271	362	1	+	+	CCONJ
ap-1271	362	2	ε−1‖u‖2	ε−1‖u‖2	NOUN
ap-1271	362	3	)	)	PUNCT
ap-1271	362	4	for	for	ADP
ap-1271	362	5	any	any	DET
ap-1271	362	6	ε	ε	PROPN
ap-1271	362	7	>	>	X
ap-1271	362	8	0	0	PROPN
ap-1271	362	9	,	,	PUNCT
ap-1271	362	10	where	where	SCONJ
ap-1271	362	11	we	we	PRON
ap-1271	362	12	used	use	VERB
ap-1271	362	13	the	the	DET
ap-1271	362	14	inequality	inequality	NOUN
ap-1271	362	15	‖da(0)u‖	‖da(0)u‖	PUNCT
ap-1271	362	16	=	=	PUNCT
ap-1271	363	1	(	(	PUNCT
ap-1271	363	2	m(0	m(0	PROPN
ap-1271	363	3	)	)	PUNCT
ap-1271	363	4	k	k	NOUN
ap-1271	363	5	u	u	PROPN
ap-1271	363	6	,	,	PUNCT
ap-1271	363	7	u)1/2	u)1/2	ADJ
ap-1271	363	8	≤	≤	ADJ
ap-1271	363	9	(	(	PUNCT
ap-1271	363	10	ε‖m(0	ε‖m(0	NOUN
ap-1271	363	11	)	)	PUNCT
ap-1271	363	12	k	k	PROPN
ap-1271	364	1	u‖)1/2(ε−1‖u‖)1/2	u‖)1/2(ε−1‖u‖)1/2	PROPN
ap-1271	364	2	≤	≤	NOUN
ap-1271	364	3	1	1	NUM
ap-1271	364	4	2	2	NUM
ap-1271	364	5	(	(	PUNCT
ap-1271	364	6	ε‖m(0	ε‖m(0	NOUN
ap-1271	364	7	)	)	PUNCT
ap-1271	365	1	k	k	PROPN
ap-1271	365	2	u‖+	u‖+	PROPN
ap-1271	365	3	ε−1‖u‖	ε−1‖u‖	PROPN
ap-1271	365	4	)	)	PUNCT
ap-1271	365	5	.	.	PUNCT
ap-1271	366	1	take	take	VERB
ap-1271	366	2	ε	ε	PROPN
ap-1271	366	3	>	>	X
ap-1271	366	4	0	0	PUNCT
ap-1271	367	1	sufficiently	sufficiently	ADV
ap-1271	367	2	small	small	ADJ
ap-1271	367	3	and	and	CCONJ
ap-1271	367	4	apply	apply	VERB
ap-1271	367	5	lemma	lemma	PROPN
ap-1271	367	6	3.4	3.4	NUM
ap-1271	367	7	.	.	PUNCT
ap-1271	368	1	then	then	ADV
ap-1271	368	2	we	we	PRON
ap-1271	368	3	have	have	VERB
ap-1271	368	4	n±(mk	n±(mk	NOUN
ap-1271	368	5	,	,	PUNCT
ap-1271	368	6	min	min	NOUN
ap-1271	368	7	)	)	PUNCT
ap-1271	368	8	=	=	SYM
ap-1271	368	9	n±(m	n±(m	PROPN
ap-1271	368	10	(	(	PUNCT
ap-1271	368	11	0	0	NUM
ap-1271	368	12	)	)	PUNCT
ap-1271	368	13	k	k	NOUN
ap-1271	368	14	,	,	PUNCT
ap-1271	368	15	min	min	NOUN
ap-1271	368	16	)	)	PUNCT
ap-1271	368	17	=	=	SYM
ap-1271	368	18	2	2	NUM
ap-1271	368	19	,	,	PUNCT
ap-1271	368	20	thus	thus	ADV
ap-1271	368	21	dim	dim	VERB
ap-1271	368	22	ek	ek	NOUN
ap-1271	368	23	=	=	NOUN
ap-1271	368	24	4	4	NUM
ap-1271	368	25	by	by	ADP
ap-1271	368	26	(	(	PUNCT
ap-1271	368	27	i	i	NOUN
ap-1271	368	28	)	)	PUNCT
ap-1271	368	29	of	of	ADP
ap-1271	368	30	proposition	proposition	NOUN
ap-1271	368	31	2.3	2.3	NUM
ap-1271	368	32	.	.	PUNCT
ap-1271	369	1	moreover	moreover	ADV
ap-1271	369	2	we	we	PRON
ap-1271	369	3	have	have	VERB
ap-1271	369	4	d(mk	d(mk	NOUN
ap-1271	369	5	,	,	PUNCT
ap-1271	369	6	min	min	NOUN
ap-1271	369	7	)	)	PUNCT
ap-1271	369	8	=	=	SYM
ap-1271	369	9	d(m	d(m	NOUN
ap-1271	369	10	(	(	PUNCT
ap-1271	369	11	0	0	NUM
ap-1271	369	12	)	)	PUNCT
ap-1271	369	13	k	k	NOUN
ap-1271	369	14	,	,	PUNCT
ap-1271	369	15	min	min	NOUN
ap-1271	369	16	)	)	PUNCT
ap-1271	369	17	,	,	PUNCT
ap-1271	369	18	so	so	CCONJ
ap-1271	369	19	the	the	DET
ap-1271	369	20	functions	function	NOUN
ap-1271	369	21	{	{	PUNCT
ap-1271	369	22	f	f	PROPN
ap-1271	369	23	j	j	PROPN
ap-1271	369	24	k	k	PROPN
ap-1271	369	25	}	}	PUNCT
ap-1271	369	26	(	(	PUNCT
ap-1271	369	27	j	j	NOUN
ap-1271	369	28	=	=	SYM
ap-1271	369	29	1	1	NUM
ap-1271	369	30	,	,	PUNCT
ap-1271	369	31	2	2	NUM
ap-1271	369	32	,	,	PUNCT
ap-1271	369	33	4	4	NUM
ap-1271	369	34	,	,	PUNCT
ap-1271	369	35	5	5	NUM
ap-1271	369	36	)	)	PUNCT
ap-1271	369	37	do	do	AUX
ap-1271	369	38	not	not	PART
ap-1271	369	39	belong	belong	VERB
ap-1271	369	40	to	to	ADP
ap-1271	369	41	d(mk	d(mk	NOUN
ap-1271	369	42	,	,	PUNCT
ap-1271	369	43	min	min	NOUN
ap-1271	369	44	)	)	PUNCT
ap-1271	369	45	.	.	PUNCT
ap-1271	370	1	and	and	CCONJ
ap-1271	370	2	we	we	PRON
ap-1271	370	3	can	can	AUX
ap-1271	370	4	provemkf	provemkf	VERB
ap-1271	370	5	j	j	PROPN
ap-1271	370	6	k	k	PROPN
ap-1271	370	7	∈	∈	PROPN
ap-1271	370	8	l2(r2	l2(r2	NOUN
ap-1271	370	9	)	)	PUNCT
ap-1271	370	10	by	by	ADP
ap-1271	370	11	using	use	VERB
ap-1271	370	12	(	(	PUNCT
ap-1271	370	13	14	14	NUM
ap-1271	370	14	)	)	PUNCT
ap-1271	370	15	and	and	CCONJ
ap-1271	370	16	the	the	DET
ap-1271	370	17	fact	fact	NOUN
ap-1271	370	18	|a(1)|	|a(1)|	NOUN
ap-1271	370	19	=	=	SYM
ap-1271	370	20	o(r	o(r	PROPN
ap-1271	370	21	)	)	PUNCT
ap-1271	370	22	near	near	ADP
ap-1271	370	23	the	the	DET
ap-1271	370	24	origin	origin	NOUN
ap-1271	370	25	.	.	PUNCT
ap-1271	371	1	thus	thus	ADV
ap-1271	371	2	{	{	PUNCT
ap-1271	371	3	[	[	X
ap-1271	371	4	f	f	X
ap-1271	371	5	j	j	X
ap-1271	371	6	k	k	X
ap-1271	371	7	]	]	X
ap-1271	371	8	}	}	PUNCT
ap-1271	371	9	form	form	VERB
ap-1271	371	10	a	a	DET
ap-1271	371	11	basis	basis	NOUN
ap-1271	371	12	of	of	ADP
ap-1271	371	13	ek	ek	PROPN
ap-1271	371	14	.	.	PROPN
ap-1271	371	15	for	for	ADP
ap-1271	371	16	the	the	DET
ap-1271	371	17	form	form	NOUN
ap-1271	371	18	[	[	X
ap-1271	371	19	·	·	PUNCT
ap-1271	371	20	,	,	PUNCT
ap-1271	371	21	·	·	PUNCT
ap-1271	371	22	]	]	X
ap-1271	371	23	ek	ek	X
ap-1271	371	24	,	,	PUNCT
ap-1271	371	25	we	we	PRON
ap-1271	371	26	can	can	AUX
ap-1271	371	27	prove	prove	VERB
ap-1271	371	28	the	the	DET
ap-1271	371	29	formula	formula	NOUN
ap-1271	371	30	[	[	X
ap-1271	371	31	u	u	NOUN
ap-1271	371	32	,	,	PUNCT
ap-1271	371	33	v]ek	v]ek	ADP
ap-1271	371	34	=	=	PUNCT
ap-1271	371	35	lim	lim	PROPN
ap-1271	371	36	ε→0	ε→0	X
ap-1271	371	37	∫	∫	PROPN
ap-1271	371	38	r	r	PROPN
ap-1271	371	39	=	=	PROPN
ap-1271	371	40	ε	ε	X
ap-1271	371	41	(	(	PUNCT
ap-1271	371	42	v(∂ru)−	v(∂ru)−	PROPN
ap-1271	371	43	u(∂rv)−	u(∂rv)−	ADJ
ap-1271	371	44	2i(n	2i(n	NUM
ap-1271	371	45	·	·	SYM
ap-1271	371	46	a(1))uv	a(1))uv	PROPN
ap-1271	371	47	)	)	PUNCT
ap-1271	371	48	rdθ	rdθ	VERB
ap-1271	371	49	in	in	ADP
ap-1271	371	50	a	a	DET
ap-1271	371	51	similar	similar	ADJ
ap-1271	371	52	way	way	NOUN
ap-1271	371	53	as	as	ADP
ap-1271	371	54	in	in	ADP
ap-1271	371	55	(	(	PUNCT
ap-1271	371	56	13	13	NUM
ap-1271	371	57	)	)	PUNCT
ap-1271	371	58	.	.	PUNCT
ap-1271	372	1	thus	thus	ADV
ap-1271	372	2	the	the	DET
ap-1271	372	3	value	value	NOUN
ap-1271	372	4	[	[	X
ap-1271	372	5	fm	fm	X
ap-1271	372	6	k	k	NOUN
ap-1271	372	7	,	,	PUNCT
ap-1271	372	8	fn	fn	VERB
ap-1271	372	9	k	k	X
ap-1271	372	10	]	]	X
ap-1271	372	11	ek	ek	PROPN
ap-1271	372	12	is	be	AUX
ap-1271	372	13	not	not	PART
ap-1271	372	14	affected	affect	VERB
ap-1271	372	15	by	by	ADP
ap-1271	372	16	a(1	a(1	PROPN
ap-1271	372	17	)	)	PUNCT
ap-1271	372	18	,	,	PUNCT
ap-1271	372	19	since	since	SCONJ
ap-1271	372	20	|a(1)|	|a(1)|	NOUN
ap-1271	372	21	=	=	SYM
ap-1271	372	22	o(r	o(r	PROPN
ap-1271	372	23	)	)	PUNCT
ap-1271	372	24	and	and	CCONJ
ap-1271	372	25	|fm	|fm	PROPN
ap-1271	373	1	k	k	NOUN
ap-1271	373	2	fn	fn	NOUN
ap-1271	374	1	k	k	PROPN
ap-1271	374	2	|	|	ADV
ap-1271	374	3	is	be	AUX
ap-1271	374	4	at	at	ADV
ap-1271	374	5	most	most	ADV
ap-1271	374	6	o(r−max(2βk,2(1−βk	o(r−max(2βk,2(1−βk	NOUN
ap-1271	374	7	)	)	PUNCT
ap-1271	374	8	)	)	PUNCT
ap-1271	374	9	)	)	PUNCT
ap-1271	374	10	.	.	PUNCT
ap-1271	375	1	�	�	PROPN
ap-1271	375	2	next	next	ADV
ap-1271	375	3	we	we	PRON
ap-1271	375	4	shall	shall	AUX
ap-1271	375	5	consider	consider	VERB
ap-1271	375	6	the	the	DET
ap-1271	375	7	non	non	ADJ
ap-1271	375	8	-	-	ADJ
ap-1271	375	9	flat	flat	ADJ
ap-1271	375	10	case	case	NOUN
ap-1271	375	11	.	.	PUNCT
ap-1271	376	1	we	we	PRON
ap-1271	376	2	shall	shall	AUX
ap-1271	376	3	show	show	VERB
ap-1271	376	4	that	that	SCONJ
ap-1271	376	5	metric	metric	ADJ
ap-1271	376	6	g	g	PROPN
ap-1271	376	7	also	also	ADV
ap-1271	376	8	does	do	AUX
ap-1271	376	9	not	not	PART
ap-1271	376	10	affect	affect	VERB
ap-1271	376	11	the	the	DET
ap-1271	376	12	structure	structure	NOUN
ap-1271	376	13	of	of	ADP
ap-1271	376	14	dk	dk	PROPN
ap-1271	376	15	and	and	CCONJ
ap-1271	376	16	the	the	DET
ap-1271	376	17	corresponding	corresponding	ADJ
ap-1271	376	18	form	form	NOUN
ap-1271	376	19	.	.	PUNCT
ap-1271	377	1	proposition	proposition	NOUN
ap-1271	377	2	3.5	3.5	NUM
ap-1271	377	3	all	all	DET
ap-1271	377	4	the	the	DET
ap-1271	377	5	statements	statement	NOUN
ap-1271	377	6	of	of	ADP
ap-1271	377	7	proposition	proposition	NOUN
ap-1271	377	8	3.2	3.2	NUM
ap-1271	377	9	hold	hold	VERB
ap-1271	377	10	even	even	ADV
ap-1271	377	11	if	if	SCONJ
ap-1271	377	12	we	we	PRON
ap-1271	377	13	replace	replace	VERB
ap-1271	377	14	m	m	PROPN
ap-1271	377	15	(	(	PUNCT
ap-1271	377	16	0	0	NUM
ap-1271	377	17	)	)	PUNCT
ap-1271	377	18	k	k	NOUN
ap-1271	377	19	,	,	PUNCT
ap-1271	377	20	min	min	NOUN
ap-1271	377	21	by	by	ADP
ap-1271	377	22	lk	lk	PROPN
ap-1271	377	23	,	,	PUNCT
ap-1271	377	24	min	min	PROPN
ap-1271	377	25	and	and	CCONJ
ap-1271	377	26	e(0)k	e(0)k	PROPN
ap-1271	377	27	by	by	ADP
ap-1271	377	28	dk	dk	PROPN
ap-1271	377	29	.	.	PUNCT
ap-1271	378	1	since	since	SCONJ
ap-1271	378	2	v	v	NOUN
ap-1271	378	3	is	be	AUX
ap-1271	378	4	bounded	bound	VERB
ap-1271	378	5	,	,	PUNCT
ap-1271	378	6	we	we	PRON
ap-1271	378	7	can	can	AUX
ap-1271	378	8	assume	assume	VERB
ap-1271	378	9	v	v	ADP
ap-1271	378	10	=	=	SYM
ap-1271	378	11	0	0	NUM
ap-1271	378	12	.	.	PUNCT
ap-1271	379	1	in	in	ADP
ap-1271	379	2	the	the	DET
ap-1271	379	3	sequel	sequel	NOUN
ap-1271	379	4	,	,	PUNCT
ap-1271	379	5	we	we	PRON
ap-1271	379	6	use	use	VERB
ap-1271	379	7	the	the	DET
ap-1271	379	8	following	following	ADJ
ap-1271	379	9	notation	notation	NOUN
ap-1271	379	10	:	:	PUNCT
ap-1271	379	11	l	l	X
ap-1271	380	1	=	=	PUNCT
ap-1271	381	1	g−1/2(d	g−1/2(d	PROPN
ap-1271	382	1	+	+	ADV
ap-1271	382	2	a	a	X
ap-1271	382	3	)	)	PUNCT
ap-1271	382	4	·	·	PUNCT
ap-1271	382	5	g1/2g−1(d	g1/2g−1(d	NOUN
ap-1271	382	6	+	+	NOUN
ap-1271	382	7	a	a	NOUN
ap-1271	382	8	)	)	PUNCT
ap-1271	382	9	,	,	PUNCT
ap-1271	382	10	where	where	SCONJ
ap-1271	382	11	d	d	NOUN
ap-1271	382	12	is	be	AUX
ap-1271	382	13	the	the	DET
ap-1271	382	14	column	column	NOUN
ap-1271	382	15	vector	vector	NOUN
ap-1271	382	16	t(d1	t(d1	NOUN
ap-1271	382	17	,	,	PUNCT
ap-1271	382	18	d2	d2	PROPN
ap-1271	382	19	)	)	PUNCT
ap-1271	382	20	,	,	PUNCT
ap-1271	382	21	dj	dj	NOUN
ap-1271	382	22	=	=	SYM
ap-1271	382	23	−i∂j	−i∂j	PROPN
ap-1271	382	24	,	,	PUNCT
ap-1271	382	25	a	a	PRON
ap-1271	382	26	is	be	AUX
ap-1271	382	27	identified	identify	VERB
ap-1271	382	28	with	with	ADP
ap-1271	382	29	the	the	DET
ap-1271	382	30	component	component	NOUN
ap-1271	382	31	vector	vector	NOUN
ap-1271	382	32	t(a1	t(a1	NOUN
ap-1271	382	33	,	,	PUNCT
ap-1271	382	34	a2	a2	PROPN
ap-1271	382	35	)	)	PUNCT
ap-1271	382	36	,	,	PUNCT
ap-1271	382	37	and	and	CCONJ
ap-1271	382	38	g−1	g−1	PROPN
ap-1271	382	39	is	be	AUX
ap-1271	382	40	the	the	DET
ap-1271	382	41	inverse	inverse	ADJ
ap-1271	382	42	matrix	matrix	NOUN
ap-1271	382	43	of	of	ADP
ap-1271	382	44	g	g	PROPN
ap-1271	382	45	=	=	SYM
ap-1271	382	46	(	(	PUNCT
ap-1271	382	47	gmn	gmn	NOUN
ap-1271	382	48	)	)	PUNCT
ap-1271	382	49	.	.	PUNCT
ap-1271	383	1	we	we	PRON
ap-1271	383	2	shall	shall	AUX
ap-1271	383	3	prepare	prepare	VERB
ap-1271	383	4	some	some	DET
ap-1271	383	5	elliptic	elliptic	ADJ
ap-1271	383	6	a	a	DET
ap-1271	383	7	priori	priori	ADJ
ap-1271	383	8	estimate	estimate	NOUN
ap-1271	383	9	.	.	PUNCT
ap-1271	384	1	lemma	lemma	PROPN
ap-1271	384	2	3.6	3.6	NUM
ap-1271	384	3	let	let	VERB
ap-1271	384	4	m	m	PRON
ap-1271	384	5	,	,	PUNCT
ap-1271	384	6	n	n	PRON
ap-1271	384	7	∈	∈	PROPN
ap-1271	384	8	{	{	PUNCT
ap-1271	384	9	1	1	NUM
ap-1271	384	10	,	,	PUNCT
ap-1271	384	11	2	2	NUM
ap-1271	384	12	}	}	PUNCT
ap-1271	384	13	.	.	PUNCT
ap-1271	385	1	then	then	ADV
ap-1271	385	2	,	,	PUNCT
ap-1271	385	3	there	there	PRON
ap-1271	385	4	exist	exist	VERB
ap-1271	385	5	cm	cm	NOUN
ap-1271	385	6	>	>	SYM
ap-1271	385	7	0	0	PUNCT
ap-1271	385	8	and	and	CCONJ
ap-1271	385	9	cmn	cmn	VERB
ap-1271	385	10	>	>	PUNCT
ap-1271	385	11	0	0	NUM
ap-1271	385	12	such	such	ADJ
ap-1271	385	13	that	that	PRON
ap-1271	386	1	‖(dm	‖(dm	ADP
ap-1271	386	2	+	+	NOUN
ap-1271	386	3	am)u‖	am)u‖	NOUN
ap-1271	386	4	≤	≤	ADJ
ap-1271	386	5	cm(ε‖mku‖+	cm(ε‖mku‖+	ADJ
ap-1271	386	6	ε−1‖u‖	ε−1‖u‖	NOUN
ap-1271	386	7	)	)	PUNCT
ap-1271	386	8	,	,	PUNCT
ap-1271	386	9	‖(dm	‖(dm	ADP
ap-1271	386	10	+	+	ADJ
ap-1271	386	11	am)(dn	am)(dn	X
ap-1271	386	12	+	+	NOUN
ap-1271	386	13	an)u‖	an)u‖	NOUN
ap-1271	386	14	≤	≤	ADJ
ap-1271	386	15	cmn(‖mku‖+‖u‖	cmn(‖mku‖+‖u‖	NOUN
ap-1271	386	16	)	)	PUNCT
ap-1271	386	17	(	(	PUNCT
ap-1271	386	18	15	15	NUM
ap-1271	386	19	)	)	PUNCT
ap-1271	386	20	for	for	ADP
ap-1271	386	21	every	every	DET
ap-1271	386	22	u	u	PROPN
ap-1271	386	23	∈	∈	PROPN
ap-1271	386	24	c∞	c∞	PROPN
ap-1271	386	25	0	0	PUNCT
ap-1271	387	1	(	(	PUNCT
ap-1271	387	2	r	r	NOUN
ap-1271	387	3	2	2	NUM
ap-1271	387	4	\	\	NOUN
ap-1271	387	5	{	{	PUNCT
ap-1271	387	6	0	0	NUM
ap-1271	387	7	}	}	PUNCT
ap-1271	387	8	)	)	PUNCT
ap-1271	387	9	and	and	CCONJ
ap-1271	387	10	every	every	DET
ap-1271	387	11	ε	ε	PROPN
ap-1271	387	12	>	>	X
ap-1271	387	13	0	0	PROPN
ap-1271	387	14	,	,	PUNCT
ap-1271	387	15	where	where	SCONJ
ap-1271	387	16	‖	‖	PROPN
ap-1271	387	17	·	·	SYM
ap-1271	387	18	‖	‖	PROPN
ap-1271	387	19	=	=	SYM
ap-1271	387	20	‖	‖	PROPN
ap-1271	387	21	·	·	PUNCT
ap-1271	387	22	‖	‖	ADJ
ap-1271	387	23	l2(r2	l2(r2	NOUN
ap-1271	387	24	;	;	PUNCT
ap-1271	387	25	dx1dx2	dx1dx2	PROPN
ap-1271	387	26	)	)	PUNCT
ap-1271	387	27	.	.	PUNCT
ap-1271	388	1	the	the	DET
ap-1271	388	2	difficulty	difficulty	NOUN
ap-1271	388	3	is	be	AUX
ap-1271	388	4	the	the	DET
ap-1271	388	5	singularity	singularity	NOUN
ap-1271	388	6	of	of	ADP
ap-1271	388	7	our	our	PRON
ap-1271	388	8	vector	vector	NOUN
ap-1271	388	9	potential	potential	NOUN
ap-1271	388	10	a	a	PRON
ap-1271	388	11	at	at	ADP
ap-1271	388	12	the	the	DET
ap-1271	388	13	origin	origin	NOUN
ap-1271	388	14	.	.	PUNCT
ap-1271	389	1	we	we	PRON
ap-1271	389	2	can	can	AUX
ap-1271	389	3	overcome	overcome	VERB
ap-1271	389	4	this	this	DET
ap-1271	389	5	difficulty	difficulty	NOUN
ap-1271	389	6	by	by	ADP
ap-1271	389	7	using	use	VERB
ap-1271	389	8	some	some	DET
ap-1271	389	9	commutator	commutator	NOUN
ap-1271	389	10	technique	technique	NOUN
ap-1271	389	11	.	.	PUNCT
ap-1271	390	1	proof	proof	NOUN
ap-1271	390	2	of	of	ADP
ap-1271	390	3	lemma	lemma	PROPN
ap-1271	390	4	3.6	3.6	NUM
ap-1271	390	5	put	put	NOUN
ap-1271	390	6	πj	πj	VERB
ap-1271	390	7	=	=	PUNCT
ap-1271	390	8	dj+aj	dj+aj	X
ap-1271	390	9	(	(	PUNCT
ap-1271	390	10	j	j	NOUN
ap-1271	390	11	=	=	SYM
ap-1271	390	12	1	1	NUM
ap-1271	390	13	,	,	PUNCT
ap-1271	390	14	2	2	NUM
ap-1271	390	15	)	)	PUNCT
ap-1271	390	16	.	.	PUNCT
ap-1271	391	1	then	then	ADV
ap-1271	391	2	,	,	PUNCT
ap-1271	391	3	since	since	SCONJ
ap-1271	391	4	‖πju‖2	‖πju‖2	PROPN
ap-1271	391	5	=	=	SYM
ap-1271	391	6	(	(	PUNCT
ap-1271	391	7	ε1/2π2ju	ε1/2π2ju	PROPN
ap-1271	391	8	,	,	PUNCT
ap-1271	391	9	ε−1/2u	ε−1/2u	NOUN
ap-1271	391	10	)	)	PUNCT
ap-1271	391	11	≤	≤	NUM
ap-1271	391	12	1	1	NUM
ap-1271	391	13	2	2	NUM
ap-1271	391	14	(	(	PUNCT
ap-1271	391	15	ε‖π2ju‖2	ε‖π2ju‖2	NOUN
ap-1271	391	16	+	+	CCONJ
ap-1271	391	17	ε−1‖u‖2	ε−1‖u‖2	ADJ
ap-1271	391	18	)	)	PUNCT
ap-1271	391	19	for	for	ADP
ap-1271	391	20	u	u	PROPN
ap-1271	391	21	∈	∈	PROPN
ap-1271	391	22	c∞	c∞	PROPN
ap-1271	391	23	0	0	PUNCT
ap-1271	391	24	(	(	PUNCT
ap-1271	391	25	r	r	NOUN
ap-1271	391	26	2	2	NUM
ap-1271	391	27	)	)	PUNCT
ap-1271	391	28	,	,	PUNCT
ap-1271	391	29	it	it	PRON
ap-1271	391	30	suffices	suffice	VERB
ap-1271	391	31	to	to	PART
ap-1271	391	32	prove	prove	VERB
ap-1271	391	33	(	(	PUNCT
ap-1271	391	34	15	15	NUM
ap-1271	391	35	)	)	PUNCT
ap-1271	391	36	.	.	PUNCT
ap-1271	392	1	68	68	NUM
ap-1271	392	2	acta	acta	PROPN
ap-1271	392	3	polytechnica	polytechnica	PROPN
ap-1271	392	4	vol	vol	NOUN
ap-1271	392	5	.	.	PUNCT
ap-1271	392	6	50	50	NUM
ap-1271	392	7	no	no	NOUN
ap-1271	392	8	.	.	PUNCT
ap-1271	393	1	5/2010	5/2010	NUM
ap-1271	393	2	define	define	VERB
ap-1271	393	3	auxiliary	auxiliary	ADJ
ap-1271	393	4	operators	operator	NOUN
ap-1271	393	5	a	a	DET
ap-1271	393	6	=	=	PUNCT
ap-1271	393	7	iπ1	iπ1	PROPN
ap-1271	394	1	+	+	NOUN
ap-1271	394	2	π2	π2	ADJ
ap-1271	394	3	,	,	PUNCT
ap-1271	394	4	a†	a†	NOUN
ap-1271	394	5	=	=	SYM
ap-1271	394	6	−iπ1	−iπ1	PROPN
ap-1271	395	1	+	+	NOUN
ap-1271	395	2	π2	π2	ADJ
ap-1271	395	3	.	.	PUNCT
ap-1271	396	1	let	let	VERB
ap-1271	397	1	[	[	X
ap-1271	397	2	x	x	X
ap-1271	397	3	,	,	PUNCT
ap-1271	397	4	y	y	PROPN
ap-1271	397	5	]	]	PUNCT
ap-1271	398	1	=	=	PUNCT
ap-1271	398	2	xy	xy	NOUN
ap-1271	398	3	−	−	NOUN
ap-1271	399	1	y	y	NOUN
ap-1271	399	2	x	x	PUNCT
ap-1271	399	3	be	be	AUX
ap-1271	399	4	the	the	DET
ap-1271	399	5	commutator	commutator	NOUN
ap-1271	399	6	of	of	ADP
ap-1271	399	7	operators	operator	NOUN
ap-1271	399	8	x	x	PUNCT
ap-1271	399	9	and	and	CCONJ
ap-1271	399	10	y	y	PROPN
ap-1271	399	11	.	.	PUNCT
ap-1271	400	1	then	then	ADV
ap-1271	400	2	we	we	PRON
ap-1271	400	3	have	have	VERB
ap-1271	400	4	[	[	X
ap-1271	400	5	π1,π2	π1,π2	X
ap-1271	400	6	]	]	X
ap-1271	401	1	=	=	PUNCT
ap-1271	402	1	[	[	X
ap-1271	402	2	d1	d1	PROPN
ap-1271	402	3	,	,	PUNCT
ap-1271	402	4	a2]−	a2]−	PRON
ap-1271	402	5	[	[	X
ap-1271	402	6	d2	d2	NOUN
ap-1271	402	7	,	,	PUNCT
ap-1271	402	8	a1	a1	NOUN
ap-1271	402	9	]	]	PUNCT
ap-1271	402	10	=	=	PUNCT
ap-1271	402	11	−i(b+	−i(b+	NUM
ap-1271	402	12	2πβkδ0	2πβkδ0	NUM
ap-1271	402	13	)	)	PUNCT
ap-1271	402	14	,	,	PUNCT
ap-1271	402	15	where	where	SCONJ
ap-1271	402	16	b	b	X
ap-1271	402	17	=	=	SYM
ap-1271	402	18	∂1a	∂1a	ADJ
ap-1271	402	19	(	(	PUNCT
ap-1271	402	20	1	1	NUM
ap-1271	402	21	)	)	SYM
ap-1271	402	22	2	2	NUM
ap-1271	402	23	−	−	NOUN
ap-1271	402	24	∂2a	∂2a	NOUN
ap-1271	402	25	(	(	PUNCT
ap-1271	402	26	1	1	NUM
ap-1271	402	27	)	)	PUNCT
ap-1271	402	28	1	1	NUM
ap-1271	402	29	is	be	AUX
ap-1271	402	30	the	the	DET
ap-1271	402	31	magnetic	magnetic	ADJ
ap-1271	402	32	field	field	NOUN
ap-1271	402	33	corresponding	correspond	VERB
ap-1271	402	34	to	to	ADP
ap-1271	402	35	a(1	a(1	PROPN
ap-1271	402	36	)	)	PUNCT
ap-1271	402	37	.	.	PUNCT
ap-1271	403	1	thus	thus	ADV
ap-1271	403	2	we	we	PRON
ap-1271	403	3	have	have	VERB
ap-1271	403	4	[	[	X
ap-1271	403	5	a	a	DET
ap-1271	403	6	,	,	PUNCT
ap-1271	403	7	a†	a†	NOUN
ap-1271	403	8	]	]	X
ap-1271	403	9	=	=	SYM
ap-1271	403	10	2i[π1,π2	2i[π1,π2	NUM
ap-1271	403	11	]	]	PUNCT
ap-1271	403	12	=	=	SYM
ap-1271	403	13	2(b+	2(b+	NUM
ap-1271	403	14	2πβkδ0	2πβkδ0	NUM
ap-1271	403	15	)	)	PUNCT
ap-1271	403	16	.	.	PUNCT
ap-1271	404	1	particularly	particularly	ADV
ap-1271	404	2	for	for	ADP
ap-1271	404	3	u	u	PROPN
ap-1271	404	4	∈	∈	PROPN
ap-1271	404	5	c∞	c∞	PROPN
ap-1271	404	6	0	0	PUNCT
ap-1271	405	1	(	(	PUNCT
ap-1271	405	2	r	r	NOUN
ap-1271	405	3	2	2	NUM
ap-1271	405	4	\	\	NOUN
ap-1271	405	5	{	{	PUNCT
ap-1271	405	6	0	0	NUM
ap-1271	405	7	}	}	PUNCT
ap-1271	405	8	)	)	PUNCT
ap-1271	405	9	,	,	PUNCT
ap-1271	405	10	we	we	PRON
ap-1271	405	11	have	have	VERB
ap-1271	405	12	(	(	PUNCT
ap-1271	405	13	aa†	aa†	NOUN
ap-1271	405	14	−	−	NOUN
ap-1271	406	1	a†a)u	a†a)u	NOUN
ap-1271	406	2	=	=	SYM
ap-1271	406	3	2bu	2bu	NOUN
ap-1271	406	4	.	.	PUNCT
ap-1271	407	1	moreover	moreover	ADV
ap-1271	407	2	,	,	PUNCT
ap-1271	407	3	we	we	PRON
ap-1271	407	4	have	have	VERB
ap-1271	407	5	by	by	ADP
ap-1271	407	6	definition	definition	NOUN
ap-1271	407	7	(	(	PUNCT
ap-1271	407	8	aa†	aa†	NOUN
ap-1271	407	9	+	+	NOUN
ap-1271	407	10	a†a)u	a†a)u	NOUN
ap-1271	407	11	=	=	SYM
ap-1271	407	12	2mku	2mku	NOUN
ap-1271	407	13	.	.	PUNCT
ap-1271	408	1	these	these	DET
ap-1271	408	2	equalities	equality	NOUN
ap-1271	408	3	imply	imply	VERB
ap-1271	408	4	aa†	aa†	NOUN
ap-1271	408	5	=	=	SYM
ap-1271	408	6	mk	mk	PROPN
ap-1271	408	7	+	+	CCONJ
ap-1271	408	8	b	b	PROPN
ap-1271	408	9	,	,	PUNCT
ap-1271	408	10	a†a	a†a	PROPN
ap-1271	408	11	=	=	NUM
ap-1271	408	12	mk	mk	NOUN
ap-1271	408	13	−	−	PROPN
ap-1271	408	14	b	b	PROPN
ap-1271	408	15	(	(	PUNCT
ap-1271	408	16	16	16	NUM
ap-1271	408	17	)	)	PUNCT
ap-1271	408	18	on	on	ADP
ap-1271	408	19	c∞	c∞	PROPN
ap-1271	408	20	0	0	PUNCT
ap-1271	409	1	(	(	PUNCT
ap-1271	409	2	r	r	NOUN
ap-1271	409	3	2	2	NUM
ap-1271	409	4	\	\	NOUN
ap-1271	409	5	{	{	PUNCT
ap-1271	409	6	0	0	NUM
ap-1271	409	7	}	}	PUNCT
ap-1271	409	8	)	)	PUNCT
ap-1271	409	9	.	.	PUNCT
ap-1271	410	1	since	since	SCONJ
ap-1271	410	2	πmπn	πmπn	NOUN
ap-1271	410	3	can	can	AUX
ap-1271	410	4	be	be	AUX
ap-1271	410	5	written	write	VERB
ap-1271	410	6	as	as	ADP
ap-1271	410	7	a	a	DET
ap-1271	410	8	finite	finite	ADJ
ap-1271	410	9	linear	linear	ADJ
ap-1271	410	10	combination	combination	NOUN
ap-1271	410	11	of	of	ADP
ap-1271	410	12	the	the	DET
ap-1271	410	13	operators	operator	NOUN
ap-1271	410	14	of	of	ADP
ap-1271	410	15	the	the	DET
ap-1271	410	16	formxy	formxy	NOUN
ap-1271	410	17	,	,	PUNCT
ap-1271	410	18	wherex	wherex	PROPN
ap-1271	410	19	,	,	PUNCT
ap-1271	410	20	y	y	PROPN
ap-1271	410	21	are	be	AUX
ap-1271	410	22	a	a	PRON
ap-1271	410	23	or	or	CCONJ
ap-1271	410	24	a†	a†	NOUN
ap-1271	410	25	,	,	PUNCT
ap-1271	410	26	it	it	PRON
ap-1271	410	27	suffices	suffice	VERB
ap-1271	410	28	to	to	PART
ap-1271	410	29	show	show	VERB
ap-1271	410	30	that	that	SCONJ
ap-1271	410	31	there	there	PRON
ap-1271	410	32	exists	exist	VERB
ap-1271	410	33	some	some	DET
ap-1271	410	34	constant	constant	ADJ
ap-1271	410	35	c	c	NOUN
ap-1271	410	36	>	>	X
ap-1271	410	37	0	0	NUM
ap-1271	410	38	such	such	ADJ
ap-1271	410	39	that	that	SCONJ
ap-1271	410	40	‖xy	‖xy	PROPN
ap-1271	410	41	u‖	u‖	VERB
ap-1271	410	42	≤	≤	X
ap-1271	410	43	c(‖mku‖+	c(‖mku‖+	PROPN
ap-1271	410	44	‖u‖	‖u‖	PROPN
ap-1271	410	45	)	)	PUNCT
ap-1271	410	46	(	(	PUNCT
ap-1271	410	47	17	17	NUM
ap-1271	410	48	)	)	PUNCT
ap-1271	410	49	for	for	ADP
ap-1271	410	50	u	u	PROPN
ap-1271	410	51	∈	∈	PROPN
ap-1271	410	52	c∞	c∞	PROPN
ap-1271	410	53	0	0	PUNCT
ap-1271	411	1	(	(	PUNCT
ap-1271	411	2	r	r	NOUN
ap-1271	411	3	2\{0	2\{0	NUM
ap-1271	411	4	}	}	PUNCT
ap-1271	411	5	)	)	PUNCT
ap-1271	411	6	.	.	PUNCT
ap-1271	412	1	for	for	ADP
ap-1271	412	2	(	(	PUNCT
ap-1271	412	3	x	x	X
ap-1271	412	4	,	,	PUNCT
ap-1271	412	5	y	y	PROPN
ap-1271	412	6	)	)	PUNCT
ap-1271	412	7	=	=	PUNCT
ap-1271	412	8	(	(	PUNCT
ap-1271	412	9	a	a	DET
ap-1271	412	10	,	,	PUNCT
ap-1271	412	11	a†	a†	NOUN
ap-1271	412	12	)	)	PUNCT
ap-1271	412	13	,	,	PUNCT
ap-1271	412	14	(	(	PUNCT
ap-1271	412	15	a†	a†	PROPN
ap-1271	412	16	,	,	PUNCT
ap-1271	412	17	a	a	PRON
ap-1271	412	18	)	)	PUNCT
ap-1271	412	19	,	,	PUNCT
ap-1271	412	20	(	(	PUNCT
ap-1271	412	21	17	17	NUM
ap-1271	412	22	)	)	PUNCT
ap-1271	412	23	follows	follow	VERB
ap-1271	412	24	from	from	ADP
ap-1271	412	25	(	(	PUNCT
ap-1271	412	26	16	16	NUM
ap-1271	412	27	)	)	PUNCT
ap-1271	412	28	,	,	PUNCT
ap-1271	412	29	since	since	SCONJ
ap-1271	412	30	b	b	PROPN
ap-1271	412	31	is	be	AUX
ap-1271	412	32	bounded	bound	VERB
ap-1271	412	33	.	.	PUNCT
ap-1271	413	1	to	to	PART
ap-1271	413	2	estimate	estimate	VERB
ap-1271	413	3	‖a2u‖2	‖a2u‖2	PROPN
ap-1271	413	4	,	,	PUNCT
ap-1271	413	5	we	we	PRON
ap-1271	413	6	assume	assume	VERB
ap-1271	413	7	a(1	a(1	NOUN
ap-1271	413	8	)	)	PUNCT
ap-1271	413	9	∈	∈	PROPN
ap-1271	413	10	c∞	c∞	PROPN
ap-1271	413	11	for	for	ADP
ap-1271	413	12	a	a	DET
ap-1271	413	13	while	while	NOUN
ap-1271	413	14	.	.	PUNCT
ap-1271	414	1	then	then	ADV
ap-1271	414	2	,	,	PUNCT
ap-1271	414	3	we	we	PRON
ap-1271	414	4	have	have	VERB
ap-1271	414	5	by	by	ADP
ap-1271	414	6	(	(	PUNCT
ap-1271	414	7	16	16	NUM
ap-1271	414	8	)	)	PUNCT
ap-1271	414	9	‖a2u‖2	‖a2u‖2	NOUN
ap-1271	414	10	=	=	SYM
ap-1271	414	11	(	(	PUNCT
ap-1271	414	12	a2u	a2u	PROPN
ap-1271	414	13	,	,	PUNCT
ap-1271	414	14	a2u	a2u	ADJ
ap-1271	414	15	)	)	PUNCT
ap-1271	414	16	=	=	SYM
ap-1271	414	17	(	(	PUNCT
ap-1271	414	18	(	(	PUNCT
ap-1271	414	19	a†)2a2u	a†)2a2u	ADV
ap-1271	414	20	,	,	PUNCT
ap-1271	414	21	u	u	NOUN
ap-1271	414	22	)	)	PUNCT
ap-1271	414	23	=	=	SYM
ap-1271	414	24	(	(	PUNCT
ap-1271	414	25	a†(aa†	a†(aa†	NOUN
ap-1271	414	26	−	−	PROPN
ap-1271	414	27	2b)au	2b)au	NUM
ap-1271	414	28	,	,	PUNCT
ap-1271	414	29	u	u	NOUN
ap-1271	414	30	)	)	PUNCT
ap-1271	414	31	=	=	SYM
ap-1271	415	1	‖a†au‖2	‖a†au‖2	PROPN
ap-1271	415	2	−	−	NOUN
ap-1271	415	3	2(bau	2(bau	NOUN
ap-1271	415	4	,	,	PUNCT
ap-1271	415	5	au	au	ADJ
ap-1271	415	6	)	)	PUNCT
ap-1271	415	7	≤	≤	NOUN
ap-1271	415	8	‖a†au‖2	‖a†au‖2	PUNCT
ap-1271	416	1	+	+	NUM
ap-1271	416	2	2‖b‖∞‖au‖2	2‖b‖∞‖au‖2	NUM
ap-1271	416	3	≤	≤	ADJ
ap-1271	416	4	‖a†au‖2	‖a†au‖2	PROPN
ap-1271	417	1	+	+	PROPN
ap-1271	417	2	2‖b‖∞‖a†au‖‖u‖.	2‖b‖∞‖a†au‖‖u‖.	PROPN
ap-1271	417	3	when	when	SCONJ
ap-1271	417	4	a(1	a(1	NOUN
ap-1271	417	5	)	)	PUNCT
ap-1271	417	6	∈	∈	PROPN
ap-1271	417	7	c1	c1	NOUN
ap-1271	417	8	,	,	PUNCT
ap-1271	417	9	we	we	PRON
ap-1271	417	10	approximate	approximate	VERB
ap-1271	417	11	a(1	a(1	ADV
ap-1271	417	12	)	)	PUNCT
ap-1271	417	13	by	by	ADP
ap-1271	417	14	c∞potentials	c∞potential	NOUN
ap-1271	417	15	w.r.t	w.r.t	VERB
ap-1271	417	16	.	.	PUNCT
ap-1271	418	1	c1	c1	NOUN
ap-1271	418	2	-	-	PUNCT
ap-1271	418	3	norm	norm	NOUN
ap-1271	418	4	on	on	ADP
ap-1271	418	5	some	some	DET
ap-1271	418	6	neighborhood	neighborhood	NOUN
ap-1271	418	7	of	of	ADP
ap-1271	418	8	suppu	suppu	NOUN
ap-1271	418	9	,	,	PUNCT
ap-1271	418	10	then	then	ADV
ap-1271	418	11	we	we	PRON
ap-1271	418	12	get	get	VERB
ap-1271	418	13	the	the	DET
ap-1271	418	14	above	above	ADJ
ap-1271	418	15	inequality	inequality	NOUN
ap-1271	418	16	again	again	ADV
ap-1271	418	17	.	.	PUNCT
ap-1271	419	1	then	then	ADV
ap-1271	419	2	,	,	PUNCT
ap-1271	419	3	we	we	PRON
ap-1271	419	4	have	have	VERB
ap-1271	419	5	(	(	PUNCT
ap-1271	419	6	17	17	NUM
ap-1271	419	7	)	)	PUNCT
ap-1271	419	8	by	by	ADP
ap-1271	419	9	using	use	VERB
ap-1271	419	10	(	(	PUNCT
ap-1271	419	11	16	16	NUM
ap-1271	419	12	)	)	PUNCT
ap-1271	419	13	.	.	PUNCT
ap-1271	420	1	the	the	DET
ap-1271	420	2	case	case	NOUN
ap-1271	420	3	x	x	X
ap-1271	420	4	=	=	PUNCT
ap-1271	420	5	y	y	NOUN
ap-1271	420	6	=	=	NOUN
ap-1271	420	7	a†	a†	NOUN
ap-1271	420	8	can	can	AUX
ap-1271	420	9	be	be	AUX
ap-1271	420	10	treated	treat	VERB
ap-1271	420	11	similarly	similarly	ADV
ap-1271	420	12	.	.	PUNCT
ap-1271	421	1	�	�	PROPN
ap-1271	421	2	proof	proof	NOUN
ap-1271	421	3	of	of	ADP
ap-1271	421	4	proposition	proposition	NOUN
ap-1271	421	5	3.5	3.5	NUM
ap-1271	421	6	first	first	ADV
ap-1271	421	7	,	,	PUNCT
ap-1271	421	8	by	by	ADP
ap-1271	421	9	assumption	assumption	NOUN
ap-1271	421	10	(	(	PUNCT
ap-1271	421	11	vi	vi	NOUN
ap-1271	421	12	)	)	PUNCT
ap-1271	421	13	,	,	PUNCT
ap-1271	421	14	we	we	PRON
ap-1271	421	15	have	have	VERB
ap-1271	421	16	g−1	g−1	PROPN
ap-1271	421	17	=	=	PUNCT
ap-1271	421	18	i	i	PRON
ap-1271	421	19	+	+	SYM
ap-1271	421	20	ĝ	ĝ	PROPN
ap-1271	421	21	,	,	PUNCT
ap-1271	421	22	max	max	PROPN
ap-1271	421	23	|ĝmn|	|ĝmn|	PROPN
ap-1271	421	24	=	=	SYM
ap-1271	421	25	o(r2	o(r2	NOUN
ap-1271	421	26	)	)	PUNCT
ap-1271	421	27	,	,	PUNCT
ap-1271	421	28	(	(	PUNCT
ap-1271	421	29	18	18	NUM
ap-1271	421	30	)	)	PUNCT
ap-1271	421	31	g	g	NOUN
ap-1271	421	32	=	=	SYM
ap-1271	421	33	1	1	NUM
ap-1271	421	34	+	+	NOUN
ap-1271	421	35	o(r2	o(r2	NOUN
ap-1271	421	36	)	)	PUNCT
ap-1271	421	37	,	,	PUNCT
ap-1271	421	38	|dg|	|dg|	PROPN
ap-1271	421	39	=	=	SYM
ap-1271	421	40	o(r	o(r	PROPN
ap-1271	421	41	)	)	PUNCT
ap-1271	421	42	,	,	PUNCT
ap-1271	421	43	as	as	SCONJ
ap-1271	421	44	r	r	NOUN
ap-1271	421	45	→	→	SYM
ap-1271	421	46	0	0	X
ap-1271	421	47	.	.	PUNCT
ap-1271	421	48	define	define	VERB
ap-1271	421	49	a	a	DET
ap-1271	421	50	unitary	unitary	ADJ
ap-1271	421	51	operator	operator	NOUN
ap-1271	421	52	u	u	NOUN
ap-1271	421	53	from	from	ADP
ap-1271	421	54	l2(r2	l2(r2	NOUN
ap-1271	421	55	;	;	PUNCT
ap-1271	422	1	√	√	NUM
ap-1271	422	2	gdx1dx2	gdx1dx2	PROPN
ap-1271	422	3	)	)	PUNCT
ap-1271	422	4	to	to	ADP
ap-1271	422	5	l2(r2	l2(r2	NOUN
ap-1271	422	6	;	;	PUNCT
ap-1271	422	7	dx1dx2	dx1dx2	X
ap-1271	422	8	)	)	PUNCT
ap-1271	422	9	by	by	ADP
ap-1271	422	10	uu	uu	PROPN
ap-1271	422	11	=	=	SYM
ap-1271	422	12	g1/4u	g1/4u	PROPN
ap-1271	422	13	.	.	PUNCT
ap-1271	423	1	put	put	VERB
ap-1271	423	2	l̃k	l̃k	NOUN
ap-1271	423	3	=	=	SYM
ap-1271	423	4	ulku−1	ulku−1	PROPN
ap-1271	423	5	,	,	PUNCT
ap-1271	423	6	l̃k	l̃k	NOUN
ap-1271	423	7	,	,	PUNCT
ap-1271	423	8	min	min	NOUN
ap-1271	423	9	=	=	PROPN
ap-1271	423	10	ulk	ulk	PROPN
ap-1271	423	11	,	,	PUNCT
ap-1271	423	12	minu	minu	PROPN
ap-1271	423	13	−1	−1	NOUN
ap-1271	423	14	,	,	PUNCT
ap-1271	423	15	etc	etc	X
ap-1271	423	16	.	.	X
ap-1271	424	1	then	then	ADV
ap-1271	424	2	we	we	PRON
ap-1271	424	3	have	have	VERB
ap-1271	424	4	for	for	ADP
ap-1271	424	5	v	v	PROPN
ap-1271	424	6	∈	∈	PROPN
ap-1271	424	7	c∞	c∞	PROPN
ap-1271	424	8	0	0	PUNCT
ap-1271	425	1	(	(	PUNCT
ap-1271	425	2	r	r	NOUN
ap-1271	425	3	2	2	NUM
ap-1271	425	4	\	\	NOUN
ap-1271	425	5	{	{	PUNCT
ap-1271	425	6	0	0	NUM
ap-1271	425	7	}	}	PUNCT
ap-1271	425	8	)	)	PUNCT
ap-1271	425	9	l̃k	l̃k	NOUN
ap-1271	425	10	,	,	PUNCT
ap-1271	425	11	minv	minv	NOUN
ap-1271	425	12	=	=	SYM
ap-1271	425	13	g−1/4(d	g−1/4(d	VERB
ap-1271	425	14	+	+	ADV
ap-1271	425	15	a	a	X
ap-1271	425	16	)	)	PUNCT
ap-1271	425	17	·	·	PUNCT
ap-1271	426	1	√	√	NUM
ap-1271	426	2	gg−1(d	gg−1(d	NOUN
ap-1271	426	3	+	+	NOUN
ap-1271	426	4	a)g−1/4v	a)g−1/4v	NOUN
ap-1271	426	5	.	.	PUNCT
ap-1271	427	1	thus	thus	ADV
ap-1271	427	2	we	we	PRON
ap-1271	427	3	have	have	VERB
ap-1271	427	4	l̃k	l̃k	NOUN
ap-1271	427	5	,	,	PUNCT
ap-1271	427	6	min	min	ADJ
ap-1271	427	7	=	=	NOUN
ap-1271	427	8	g−1/4(d	g−1/4(d	PRON
ap-1271	427	9	+	+	ADV
ap-1271	427	10	a	a	X
ap-1271	427	11	)	)	PUNCT
ap-1271	427	12	·	·	PUNCT
ap-1271	428	1	g1/4g−1(d	g1/4g−1(d	ADJ
ap-1271	428	2	+	+	ADV
ap-1271	428	3	a	a	X
ap-1271	428	4	)	)	PUNCT
ap-1271	429	1	+	+	CCONJ
ap-1271	429	2	g−1/4(d	g−1/4(d	VERB
ap-1271	429	3	+	+	ADV
ap-1271	429	4	a	a	X
ap-1271	429	5	)	)	PUNCT
ap-1271	429	6	·	·	PUNCT
ap-1271	430	1	√	√	ADP
ap-1271	430	2	gg−1(dg−1/4	gg−1(dg−1/4	NOUN
ap-1271	430	3	)	)	PUNCT
ap-1271	430	4	.	.	PUNCT
ap-1271	431	1	(	(	PUNCT
ap-1271	431	2	19	19	NUM
ap-1271	431	3	)	)	PUNCT
ap-1271	431	4	the	the	DET
ap-1271	431	5	second	second	ADJ
ap-1271	431	6	term	term	NOUN
ap-1271	431	7	of	of	ADP
ap-1271	431	8	(	(	PUNCT
ap-1271	431	9	19	19	NUM
ap-1271	431	10	)	)	PUNCT
ap-1271	431	11	is	be	AUX
ap-1271	431	12	written	write	VERB
ap-1271	431	13	as	as	ADP
ap-1271	431	14	g−1/4	g−1/4	PROPN
ap-1271	431	15	(	(	PUNCT
ap-1271	431	16	d	d	NOUN
ap-1271	431	17	·	·	PUNCT
ap-1271	431	18	(	(	PUNCT
ap-1271	431	19	√	√	NUM
ap-1271	431	20	gg−1(dg−1/4	gg−1(dg−1/4	NOUN
ap-1271	431	21	)	)	PUNCT
ap-1271	431	22	)	)	PUNCT
ap-1271	431	23	)	)	PUNCT
ap-1271	432	1	+	+	CCONJ
ap-1271	432	2	(	(	PUNCT
ap-1271	432	3	20	20	NUM
ap-1271	432	4	)	)	PUNCT
ap-1271	432	5	(	(	PUNCT
ap-1271	432	6	dg−1/4	dg−1/4	NOUN
ap-1271	432	7	)	)	PUNCT
ap-1271	432	8	·	·	PUNCT
ap-1271	433	1	g1/4g−1(d	g1/4g−1(d	PUNCT
ap-1271	433	2	+	+	ADV
ap-1271	433	3	a	a	X
ap-1271	433	4	)	)	PUNCT
ap-1271	433	5	.	.	PUNCT
ap-1271	434	1	the	the	DET
ap-1271	434	2	first	first	ADJ
ap-1271	434	3	term	term	NOUN
ap-1271	434	4	of	of	ADP
ap-1271	434	5	(	(	PUNCT
ap-1271	434	6	20	20	NUM
ap-1271	434	7	)	)	PUNCT
ap-1271	434	8	is	be	AUX
ap-1271	434	9	bounded	bound	VERB
ap-1271	434	10	,	,	PUNCT
ap-1271	434	11	and	and	CCONJ
ap-1271	434	12	the	the	DET
ap-1271	434	13	second	second	NOUN
ap-1271	434	14	is	be	AUX
ap-1271	434	15	infinitesimally	infinitesimally	ADV
ap-1271	434	16	small	small	ADJ
ap-1271	434	17	w.r.t	w.r.t	NOUN
ap-1271	434	18	.	.	PUNCT
ap-1271	435	1	mk	mk	PROPN
ap-1271	435	2	,	,	PUNCT
ap-1271	435	3	min	min	PROPN
ap-1271	435	4	,	,	PUNCT
ap-1271	435	5	by	by	ADP
ap-1271	435	6	lemma	lemma	PROPN
ap-1271	435	7	3.6	3.6	NUM
ap-1271	435	8	.	.	PUNCT
ap-1271	436	1	the	the	DET
ap-1271	436	2	first	first	ADJ
ap-1271	436	3	term	term	NOUN
ap-1271	436	4	of	of	ADP
ap-1271	436	5	(	(	PUNCT
ap-1271	436	6	19	19	NUM
ap-1271	436	7	)	)	PUNCT
ap-1271	436	8	is	be	AUX
ap-1271	436	9	written	write	VERB
ap-1271	436	10	as	as	ADP
ap-1271	436	11	(	(	PUNCT
ap-1271	436	12	d	d	PROPN
ap-1271	436	13	+	+	NOUN
ap-1271	436	14	a	a	X
ap-1271	436	15	)	)	PUNCT
ap-1271	436	16	·	·	PUNCT
ap-1271	437	1	g−1(d	g−1(d	ADJ
ap-1271	437	2	+	+	ADV
ap-1271	437	3	a	a	X
ap-1271	437	4	)	)	PUNCT
ap-1271	437	5	+	+	CCONJ
ap-1271	437	6	(	(	PUNCT
ap-1271	437	7	21	21	NUM
ap-1271	437	8	)	)	PUNCT
ap-1271	437	9	g−1/4(dg1/4	g−1/4(dg1/4	PROPN
ap-1271	437	10	)	)	PUNCT
ap-1271	437	11	·	·	PUNCT
ap-1271	438	1	g−1(d	g−1(d	ADJ
ap-1271	438	2	+	+	ADV
ap-1271	438	3	a	a	NOUN
ap-1271	438	4	)	)	PUNCT
ap-1271	438	5	.	.	PUNCT
ap-1271	439	1	the	the	DET
ap-1271	439	2	second	second	ADJ
ap-1271	439	3	term	term	NOUN
ap-1271	439	4	of	of	ADP
ap-1271	439	5	(	(	PUNCT
ap-1271	439	6	21	21	NUM
ap-1271	439	7	)	)	PUNCT
ap-1271	439	8	is	be	AUX
ap-1271	439	9	also	also	ADV
ap-1271	439	10	infinitesimally	infinitesimally	ADV
ap-1271	439	11	small	small	ADJ
ap-1271	439	12	w.r.t	w.r.t	NOUN
ap-1271	439	13	.	.	PUNCT
ap-1271	440	1	mk	mk	PROPN
ap-1271	440	2	,	,	PUNCT
ap-1271	440	3	min	min	PROPN
ap-1271	440	4	,	,	PUNCT
ap-1271	440	5	by	by	ADP
ap-1271	440	6	lemma	lemma	PROPN
ap-1271	440	7	3.6	3.6	NUM
ap-1271	440	8	.	.	PUNCT
ap-1271	441	1	the	the	DET
ap-1271	441	2	first	first	ADJ
ap-1271	441	3	term	term	NOUN
ap-1271	441	4	of	of	ADP
ap-1271	441	5	(	(	PUNCT
ap-1271	441	6	21	21	NUM
ap-1271	441	7	)	)	PUNCT
ap-1271	441	8	is	be	AUX
ap-1271	441	9	written	write	VERB
ap-1271	441	10	as	as	ADP
ap-1271	441	11	mk	mk	PROPN
ap-1271	441	12	,	,	PUNCT
ap-1271	441	13	min	min	PROPN
ap-1271	441	14	+	+	CCONJ
ap-1271	441	15	(	(	PUNCT
ap-1271	441	16	d	d	PROPN
ap-1271	441	17	+	+	NOUN
ap-1271	441	18	a	a	X
ap-1271	441	19	)	)	PUNCT
ap-1271	441	20	·	·	PUNCT
ap-1271	441	21	ĝ(d	ĝ(d	NOUN
ap-1271	442	1	+	+	ADV
ap-1271	442	2	a	a	X
ap-1271	442	3	)	)	PUNCT
ap-1271	442	4	.	.	PUNCT
ap-1271	443	1	the	the	DET
ap-1271	443	2	second	second	ADJ
ap-1271	443	3	term	term	NOUN
ap-1271	443	4	of	of	ADP
ap-1271	443	5	this	this	DET
ap-1271	443	6	expression	expression	NOUN
ap-1271	443	7	is	be	AUX
ap-1271	443	8	written	write	VERB
ap-1271	443	9	as∑	as∑	PROPN
ap-1271	443	10	m	m	PROPN
ap-1271	443	11	,	,	PUNCT
ap-1271	443	12	n=1,2	n=1,2	ADJ
ap-1271	443	13	(	(	PUNCT
ap-1271	443	14	dmĝmn)(dn	dmĝmn)(dn	PROPN
ap-1271	444	1	+	+	NOUN
ap-1271	444	2	an	an	X
ap-1271	444	3	)	)	PUNCT
ap-1271	444	4	+	+	CCONJ
ap-1271	444	5	(	(	PUNCT
ap-1271	444	6	22	22	NUM
ap-1271	444	7	)	)	PUNCT
ap-1271	444	8	∑	∑	NOUN
ap-1271	444	9	m	m	PROPN
ap-1271	444	10	,	,	PUNCT
ap-1271	444	11	n=1,2	n=1,2	ADJ
ap-1271	444	12	ĝmn(dm	ĝmn(dm	PROPN
ap-1271	444	13	+	+	PROPN
ap-1271	444	14	am)(dn	am)(dn	PROPN
ap-1271	444	15	+	+	NOUN
ap-1271	444	16	an	an	NOUN
ap-1271	444	17	)	)	PUNCT
ap-1271	444	18	.	.	PUNCT
ap-1271	445	1	the	the	DET
ap-1271	445	2	first	first	ADJ
ap-1271	445	3	sum	sum	NOUN
ap-1271	445	4	of	of	ADP
ap-1271	445	5	(	(	PUNCT
ap-1271	445	6	22	22	NUM
ap-1271	445	7	)	)	PUNCT
ap-1271	445	8	is	be	AUX
ap-1271	445	9	infinitesimally	infinitesimally	ADV
ap-1271	445	10	small	small	ADJ
ap-1271	445	11	w.r.t	w.r.t	NOUN
ap-1271	445	12	.	.	PUNCT
ap-1271	446	1	mk	mk	PROPN
ap-1271	446	2	,	,	PUNCT
ap-1271	446	3	min	min	PROPN
ap-1271	446	4	.	.	PROPN
ap-1271	447	1	if	if	SCONJ
ap-1271	447	2	we	we	PRON
ap-1271	447	3	take	take	VERB
ap-1271	447	4	εk	εk	NOUN
ap-1271	447	5	sufficiently	sufficiently	ADV
ap-1271	447	6	small	small	ADJ
ap-1271	447	7	,	,	PUNCT
ap-1271	447	8	the	the	DET
ap-1271	447	9	second	second	ADJ
ap-1271	447	10	sum	sum	NOUN
ap-1271	447	11	ismk	ismk	NOUN
ap-1271	447	12	,	,	PUNCT
ap-1271	447	13	min	min	NOUN
ap-1271	447	14	-	-	NOUN
ap-1271	447	15	bounded	bounded	ADJ
ap-1271	447	16	with	with	ADP
ap-1271	447	17	relative	relative	ADJ
ap-1271	447	18	bound	bind	VERB
ap-1271	447	19	less	less	ADJ
ap-1271	447	20	than	than	ADP
ap-1271	447	21	1	1	NUM
ap-1271	447	22	,	,	PUNCT
ap-1271	447	23	by	by	ADP
ap-1271	447	24	lemma	lemma	PROPN
ap-1271	447	25	3.6	3.6	NUM
ap-1271	447	26	.	.	PUNCT
ap-1271	448	1	now	now	ADV
ap-1271	448	2	we	we	PRON
ap-1271	448	3	can	can	AUX
ap-1271	448	4	apply	apply	VERB
ap-1271	448	5	lemma	lemma	PROPN
ap-1271	448	6	3.4	3.4	NUM
ap-1271	448	7	,	,	PUNCT
ap-1271	448	8	and	and	CCONJ
ap-1271	448	9	conclude	conclude	VERB
ap-1271	448	10	that	that	SCONJ
ap-1271	448	11	d(l̃k	d(l̃k	PROPN
ap-1271	448	12	,	,	PUNCT
ap-1271	448	13	min	min	NOUN
ap-1271	448	14	)	)	PUNCT
ap-1271	448	15	=	=	SYM
ap-1271	448	16	d(mk	d(mk	NOUN
ap-1271	448	17	,	,	PUNCT
ap-1271	448	18	min	min	NOUN
ap-1271	448	19	)	)	PUNCT
ap-1271	449	1	=	=	SYM
ap-1271	449	2	d(m	d(m	NOUN
ap-1271	449	3	(	(	PUNCT
ap-1271	449	4	0	0	NUM
ap-1271	449	5	)	)	PUNCT
ap-1271	449	6	k	k	NOUN
ap-1271	449	7	,	,	PUNCT
ap-1271	449	8	min	min	NOUN
ap-1271	449	9	)	)	PUNCT
ap-1271	449	10	,	,	PUNCT
ap-1271	449	11	and	and	CCONJ
ap-1271	449	12	n±(lk	n±(lk	PROPN
ap-1271	449	13	,	,	PUNCT
ap-1271	449	14	min	min	NOUN
ap-1271	449	15	)	)	PUNCT
ap-1271	449	16	=	=	SYM
ap-1271	449	17	n±(l̃k	n±(l̃k	PROPN
ap-1271	449	18	,	,	PUNCT
ap-1271	449	19	min	min	NOUN
ap-1271	449	20	)	)	PUNCT
ap-1271	449	21	=	=	PUNCT
ap-1271	449	22	n±(mk	n±(mk	PROPN
ap-1271	449	23	,	,	PUNCT
ap-1271	449	24	min	min	NOUN
ap-1271	449	25	)	)	PUNCT
ap-1271	449	26	=	=	SYM
ap-1271	449	27	n±(m	n±(m	PROPN
ap-1271	449	28	(	(	PUNCT
ap-1271	449	29	0	0	NUM
ap-1271	449	30	)	)	PUNCT
ap-1271	449	31	k	k	NOUN
ap-1271	449	32	,	,	PUNCT
ap-1271	449	33	min	min	NOUN
ap-1271	449	34	)	)	PUNCT
ap-1271	449	35	.	.	PUNCT
ap-1271	450	1	moreover	moreover	ADV
ap-1271	450	2	,	,	PUNCT
ap-1271	450	3	one	one	PRON
ap-1271	450	4	can	can	AUX
ap-1271	450	5	show	show	VERB
ap-1271	450	6	that	that	DET
ap-1271	450	7	multiplication	multiplication	NOUN
ap-1271	450	8	by	by	ADP
ap-1271	450	9	g1/4	g1/4	NOUN
ap-1271	450	10	is	be	AUX
ap-1271	450	11	a	a	DET
ap-1271	450	12	bijective	bijective	ADJ
ap-1271	450	13	continuous	continuous	ADJ
ap-1271	450	14	map	map	NOUN
ap-1271	450	15	on	on	ADP
ap-1271	450	16	d(m	d(m	PROPN
ap-1271	450	17	(	(	PUNCT
ap-1271	450	18	0	0	NUM
ap-1271	450	19	)	)	PUNCT
ap-1271	450	20	k	k	NOUN
ap-1271	450	21	,	,	PUNCT
ap-1271	450	22	min	min	NOUN
ap-1271	450	23	)	)	PUNCT
ap-1271	450	24	.	.	PUNCT
ap-1271	451	1	thus	thus	ADV
ap-1271	451	2	we	we	PRON
ap-1271	451	3	have	have	VERB
ap-1271	451	4	d(lk	d(lk	PROPN
ap-1271	451	5	,	,	PUNCT
ap-1271	451	6	min	min	NOUN
ap-1271	451	7	)	)	PUNCT
ap-1271	451	8	=	=	SYM
ap-1271	451	9	u−1d(l̃k	u−1d(l̃k	NOUN
ap-1271	451	10	,	,	PUNCT
ap-1271	451	11	min	min	NOUN
ap-1271	451	12	)	)	PUNCT
ap-1271	451	13	=	=	SYM
ap-1271	451	14	g−1/4d(m	g−1/4d(m	NOUN
ap-1271	451	15	(	(	PUNCT
ap-1271	451	16	0	0	NUM
ap-1271	451	17	)	)	PUNCT
ap-1271	451	18	k	k	NOUN
ap-1271	451	19	,	,	PUNCT
ap-1271	451	20	min	min	NOUN
ap-1271	451	21	)	)	PUNCT
ap-1271	451	22	=	=	SYM
ap-1271	451	23	d(m	d(m	NOUN
ap-1271	451	24	(	(	PUNCT
ap-1271	451	25	0	0	NUM
ap-1271	451	26	)	)	PUNCT
ap-1271	451	27	k	k	NOUN
ap-1271	451	28	,	,	PUNCT
ap-1271	451	29	min	min	NOUN
ap-1271	451	30	)	)	PUNCT
ap-1271	451	31	.	.	PUNCT
ap-1271	452	1	and	and	CCONJ
ap-1271	452	2	then	then	ADV
ap-1271	452	3	we	we	PRON
ap-1271	452	4	can	can	AUX
ap-1271	452	5	prove	prove	VERB
ap-1271	452	6	lkfm	lkfm	PROPN
ap-1271	452	7	k	k	PROPN
ap-1271	452	8	∈	∈	PROPN
ap-1271	452	9	l2(r2	l2(r2	NOUN
ap-1271	452	10	;	;	PUNCT
ap-1271	452	11	dμk	dμk	PROPN
ap-1271	452	12	)	)	PUNCT
ap-1271	452	13	by	by	ADP
ap-1271	452	14	the	the	DET
ap-1271	452	15	leibniz	leibniz	PROPN
ap-1271	452	16	formula	formula	NOUN
ap-1271	452	17	and	and	CCONJ
ap-1271	452	18	(	(	PUNCT
ap-1271	452	19	18	18	NUM
ap-1271	452	20	)	)	PUNCT
ap-1271	452	21	,	,	PUNCT
ap-1271	452	22	and	and	CCONJ
ap-1271	452	23	thus	thus	ADV
ap-1271	452	24	{	{	PUNCT
ap-1271	452	25	[	[	X
ap-1271	452	26	fm	fm	X
ap-1271	452	27	k	k	X
ap-1271	452	28	]	]	PUNCT
ap-1271	452	29	}	}	PUNCT
ap-1271	452	30	m	m	VERB
ap-1271	452	31	form	form	VERB
ap-1271	452	32	a	a	DET
ap-1271	452	33	basis	basis	NOUN
ap-1271	452	34	of	of	ADP
ap-1271	452	35	dk	dk	PROPN
ap-1271	452	36	.	.	PROPN
ap-1271	452	37	69	69	NUM
ap-1271	452	38	acta	acta	PROPN
ap-1271	452	39	polytechnica	polytechnica	PROPN
ap-1271	452	40	vol	vol	NOUN
ap-1271	452	41	.	.	PROPN
ap-1271	453	1	50	50	NUM
ap-1271	453	2	no	no	NOUN
ap-1271	453	3	.	.	PUNCT
ap-1271	454	1	5/2010	5/2010	NUM
ap-1271	454	2	in	in	ADP
ap-1271	454	3	a	a	DET
ap-1271	454	4	similar	similar	ADJ
ap-1271	454	5	way	way	NOUN
ap-1271	454	6	as	as	ADP
ap-1271	454	7	in	in	ADP
ap-1271	454	8	(	(	PUNCT
ap-1271	454	9	13	13	NUM
ap-1271	454	10	)	)	PUNCT
ap-1271	454	11	,	,	PUNCT
ap-1271	454	12	we	we	PRON
ap-1271	454	13	have	have	VERB
ap-1271	454	14	[	[	X
ap-1271	454	15	u	u	NOUN
ap-1271	454	16	,	,	PUNCT
ap-1271	454	17	v]dk	v]dk	PROPN
ap-1271	454	18	=	=	SYM
ap-1271	454	19	lim	lim	PROPN
ap-1271	454	20	ε→0	ε→0	X
ap-1271	454	21	∫	∫	PROPN
ap-1271	454	22	r	r	PROPN
ap-1271	454	23	=	=	PROPN
ap-1271	454	24	ε	ε	X
ap-1271	454	25	(	(	PUNCT
ap-1271	454	26	vn	vn	PROPN
ap-1271	454	27	·	·	PUNCT
ap-1271	454	28	√	√	PROPN
ap-1271	454	29	gg−1(∇+	gg−1(∇+	NOUN
ap-1271	454	30	ia)u−	ia)u−	NOUN
ap-1271	454	31	−un	−un	PROPN
ap-1271	454	32	·	·	PUNCT
ap-1271	454	33	√	√	PROPN
ap-1271	454	34	gg−1(∇+	gg−1(∇+	PROPN
ap-1271	454	35	ia)v	ia)v	PROPN
ap-1271	454	36	)	)	PUNCT
ap-1271	454	37	r	r	NOUN
ap-1271	454	38	dθ	dθ	PROPN
ap-1271	454	39	.	.	PUNCT
ap-1271	455	1	since	since	SCONJ
ap-1271	455	2	√	√	PROPN
ap-1271	455	3	gg−1	gg−1	PROPN
ap-1271	455	4	=	=	PUNCT
ap-1271	455	5	i	i	PRON
ap-1271	455	6	+	+	CCONJ
ap-1271	455	7	o(r2	o(r2	NOUN
ap-1271	455	8	)	)	PUNCT
ap-1271	455	9	,	,	PUNCT
ap-1271	455	10	we	we	PRON
ap-1271	455	11	can	can	AUX
ap-1271	455	12	replace	replace	VERB
ap-1271	455	13	√	√	PROPN
ap-1271	455	14	gg−1	gg−1	VERB
ap-1271	455	15	by	by	ADP
ap-1271	455	16	i	i	PRON
ap-1271	455	17	in	in	ADP
ap-1271	455	18	the	the	DET
ap-1271	455	19	calculation	calculation	NOUN
ap-1271	455	20	of	of	ADP
ap-1271	455	21	[	[	X
ap-1271	455	22	fm	fm	PROPN
ap-1271	455	23	k	k	NOUN
ap-1271	455	24	,	,	PUNCT
ap-1271	455	25	fn	fn	VERB
ap-1271	455	26	k	k	X
ap-1271	456	1	]	]	X
ap-1271	456	2	dk	dk	X
ap-1271	456	3	,	,	PUNCT
ap-1271	456	4	and	and	CCONJ
ap-1271	456	5	we	we	PRON
ap-1271	456	6	have	have	VERB
ap-1271	456	7	[	[	X
ap-1271	456	8	fm	fm	X
ap-1271	456	9	k	k	NOUN
ap-1271	456	10	,	,	PUNCT
ap-1271	456	11	fn	fn	VERB
ap-1271	456	12	k	k	X
ap-1271	457	1	]	]	X
ap-1271	457	2	dk	dk	X
ap-1271	458	1	=	=	PUNCT
ap-1271	458	2	[	[	X
ap-1271	458	3	fm	fm	X
ap-1271	458	4	k	k	NOUN
ap-1271	458	5	,	,	PUNCT
ap-1271	458	6	fn	fn	VERB
ap-1271	458	7	k	k	X
ap-1271	458	8	]	]	X
ap-1271	458	9	ek	ek	PROPN
ap-1271	458	10	.	.	PUNCT
ap-1271	459	1	thus	thus	ADV
ap-1271	459	2	we	we	PRON
ap-1271	459	3	have	have	VERB
ap-1271	459	4	the	the	DET
ap-1271	459	5	conclusion	conclusion	NOUN
ap-1271	459	6	.	.	PUNCT
ap-1271	460	1	�	�	NOUN
ap-1271	460	2	4	4	NUM
ap-1271	460	3	proof	proof	NOUN
ap-1271	460	4	of	of	ADP
ap-1271	460	5	main	main	ADJ
ap-1271	460	6	theorems	theorem	NOUN
ap-1271	460	7	proof	proof	NOUN
ap-1271	460	8	of	of	ADP
ap-1271	460	9	theorem	theorem	ADJ
ap-1271	460	10	1.1	1.1	NUM
ap-1271	460	11	since	since	SCONJ
ap-1271	460	12	hmin	hmin	NOUN
ap-1271	460	13	is	be	AUX
ap-1271	460	14	semibounded	semibounde	VERB
ap-1271	460	15	,	,	PUNCT
ap-1271	460	16	we	we	PRON
ap-1271	460	17	have	have	VERB
ap-1271	460	18	n+(hmin	n+(hmin	NOUN
ap-1271	460	19	)	)	PUNCT
ap-1271	460	20	=	=	SYM
ap-1271	460	21	n−(hmin	n−(hmin	PROPN
ap-1271	460	22	)	)	PUNCT
ap-1271	460	23	=	=	SYM
ap-1271	460	24	dimd/2	dimd/2	PROPN
ap-1271	460	25	.	.	PROPN
ap-1271	460	26	by	by	ADP
ap-1271	460	27	lemma	lemma	PROPN
ap-1271	460	28	3.1	3.1	NUM
ap-1271	460	29	and	and	CCONJ
ap-1271	460	30	proposition	proposition	NOUN
ap-1271	460	31	3.5	3.5	NUM
ap-1271	460	32	,	,	PUNCT
ap-1271	460	33	we	we	PRON
ap-1271	460	34	have	have	VERB
ap-1271	460	35	for	for	ADP
ap-1271	460	36	k	k	PROPN
ap-1271	460	37	<	<	X
ap-1271	460	38	∞	∞	PROPN
ap-1271	460	39	dimd	dimd	PROPN
ap-1271	460	40	=	=	PUNCT
ap-1271	460	41	k∑	k∑	PROPN
ap-1271	461	1	k=1	k=1	X
ap-1271	461	2	dimdk	dimdk	NOUN
ap-1271	461	3	=	=	PUNCT
ap-1271	461	4	4k1	4k1	NUM
ap-1271	461	5	+	+	CCONJ
ap-1271	461	6	2k2	2k2	NUM
ap-1271	461	7	,	,	PUNCT
ap-1271	461	8	and	and	CCONJ
ap-1271	461	9	for	for	ADP
ap-1271	461	10	k	k	PROPN
ap-1271	461	11	=	=	PROPN
ap-1271	461	12	∞	∞	PROPN
ap-1271	461	13	dimd	dimd	PROPN
ap-1271	461	14	≥	≥	NOUN
ap-1271	461	15	∞∑	∞∑	NUM
ap-1271	461	16	k=1	k=1	PART
ap-1271	461	17	dimdk	dimdk	NOUN
ap-1271	461	18	=	=	NOUN
ap-1271	461	19	∞.	∞.	PROPN
ap-1271	461	20	thus	thus	ADV
ap-1271	461	21	we	we	PRON
ap-1271	461	22	have	have	VERB
ap-1271	461	23	the	the	DET
ap-1271	461	24	conclusion	conclusion	NOUN
ap-1271	461	25	.	.	PUNCT
ap-1271	462	1	�	�	PROPN
ap-1271	462	2	proof	proof	NOUN
ap-1271	462	3	of	of	ADP
ap-1271	462	4	theorem	theorem	ADJ
ap-1271	462	5	1.2	1.2	NUM
ap-1271	462	6	by	by	ADP
ap-1271	462	7	lemma	lemma	PROPN
ap-1271	462	8	3.1	3.1	NUM
ap-1271	462	9	and	and	CCONJ
ap-1271	462	10	proposition	proposition	NOUN
ap-1271	462	11	3.5	3.5	NUM
ap-1271	462	12	,	,	PUNCT
ap-1271	462	13	we	we	PRON
ap-1271	462	14	have	have	VERB
ap-1271	462	15	for	for	ADP
ap-1271	462	16	u	u	NOUN
ap-1271	462	17	,	,	PUNCT
ap-1271	462	18	v	v	NOUN
ap-1271	462	19	∈	∈	NOUN
ap-1271	462	20	d(hmax	d(hmax	NOUN
ap-1271	462	21	)	)	PUNCT
ap-1271	463	1	[	[	X
ap-1271	463	2	u	u	NOUN
ap-1271	463	3	,	,	PUNCT
ap-1271	463	4	v]d	v]d	ADP
ap-1271	463	5	=	=	SYM
ap-1271	463	6	4πφ(u)∗	4πφ(u)∗	PROPN
ap-1271	463	7	(	(	PUNCT
ap-1271	463	8	o	o	PROPN
ap-1271	463	9	−d	−d	PROPN
ap-1271	463	10	d	d	X
ap-1271	463	11	o	o	PROPN
ap-1271	463	12	)	)	PUNCT
ap-1271	463	13	φ(v	φ(v	NOUN
ap-1271	463	14	)	)	PUNCT
ap-1271	463	15	,	,	PUNCT
ap-1271	463	16	where	where	SCONJ
ap-1271	463	17	φ(u)∗	φ(u)∗	NOUN
ap-1271	463	18	is	be	AUX
ap-1271	463	19	the	the	DET
ap-1271	463	20	row	row	NOUN
ap-1271	463	21	-	-	PUNCT
ap-1271	463	22	vector	vector	NOUN
ap-1271	463	23	tφ(u	tφ(u	NOUN
ap-1271	463	24	)	)	PUNCT
ap-1271	463	25	and	and	CCONJ
ap-1271	463	26	d	d	PROPN
ap-1271	463	27	is	be	AUX
ap-1271	463	28	the	the	DET
ap-1271	463	29	matrix	matrix	NOUN
ap-1271	463	30	given	give	VERB
ap-1271	463	31	by	by	ADP
ap-1271	463	32	(	(	PUNCT
ap-1271	463	33	6	6	NUM
ap-1271	463	34	)	)	PUNCT
ap-1271	463	35	.	.	PUNCT
ap-1271	464	1	let	let	VERB
ap-1271	464	2	x	x	PUNCT
ap-1271	464	3	=	=	SYM
ap-1271	464	4	t(x1	t(x1	NOUN
ap-1271	464	5	,	,	PUNCT
ap-1271	464	6	x2	x2	PRON
ap-1271	464	7	)	)	PUNCT
ap-1271	464	8	be	be	VERB
ap-1271	464	9	the	the	DET
ap-1271	464	10	matrix	matrix	NOUN
ap-1271	464	11	satisfying	satisfying	NOUN
ap-1271	464	12	(	(	PUNCT
ap-1271	464	13	7	7	NUM
ap-1271	464	14	)	)	PUNCT
ap-1271	464	15	.	.	PUNCT
ap-1271	465	1	then	then	ADV
ap-1271	465	2	we	we	PRON
ap-1271	465	3	have	have	VERB
ap-1271	465	4	x∗	x∗	PROPN
ap-1271	465	5	(	(	PUNCT
ap-1271	465	6	o	o	NOUN
ap-1271	465	7	−d	−d	PROPN
ap-1271	465	8	d	d	X
ap-1271	465	9	o	o	NOUN
ap-1271	465	10	)	)	PUNCT
ap-1271	465	11	x	x	X
ap-1271	466	1	=	=	SYM
ap-1271	466	2	o	o	NOUN
ap-1271	466	3	,	,	PUNCT
ap-1271	466	4	which	which	PRON
ap-1271	466	5	implies	imply	VERB
ap-1271	466	6	v	v	NUM
ap-1271	466	7	⊂	⊂	PROPN
ap-1271	466	8	v	v	ADP
ap-1271	466	9	[	[	X
ap-1271	466	10	⊥	⊥	X
ap-1271	466	11	]	]	X
ap-1271	466	12	for	for	ADP
ap-1271	466	13	v	v	NOUN
ap-1271	466	14	=	=	SYM
ap-1271	466	15	ranx	ranx	NOUN
ap-1271	466	16	.	.	PUNCT
ap-1271	467	1	moreover	moreover	ADV
ap-1271	467	2	,	,	PUNCT
ap-1271	467	3	if	if	SCONJ
ap-1271	467	4	rankx	rankx	NOUN
ap-1271	467	5	=	=	SYM
ap-1271	467	6	2k1	2k1	NUM
ap-1271	467	7	+	+	SYM
ap-1271	467	8	k2	k2	ADJ
ap-1271	467	9	,	,	PUNCT
ap-1271	467	10	we	we	PRON
ap-1271	467	11	have	have	AUX
ap-1271	467	12	dim	dim	VERB
ap-1271	467	13	v	v	ADP
ap-1271	467	14	[	[	X
ap-1271	467	15	⊥	⊥	X
ap-1271	467	16	]	]	X
ap-1271	467	17	=	=	X
ap-1271	467	18	4k1	4k1	NUM
ap-1271	467	19	+	+	NOUN
ap-1271	467	20	2k2−dimv	2k2−dimv	NUM
ap-1271	467	21	=	=	SYM
ap-1271	467	22	2k1+k2	2k1+k2	NUM
ap-1271	467	23	=	=	SYM
ap-1271	467	24	dimv	dimv	NOUN
ap-1271	467	25	.	.	PUNCT
ap-1271	468	1	thus	thus	ADV
ap-1271	468	2	we	we	PRON
ap-1271	468	3	have	have	VERB
ap-1271	468	4	(	(	PUNCT
ap-1271	468	5	11	11	NUM
ap-1271	468	6	)	)	PUNCT
ap-1271	468	7	,	,	PUNCT
ap-1271	468	8	and	and	CCONJ
ap-1271	468	9	therefore	therefore	ADV
ap-1271	468	10	hx	hx	PROPN
ap-1271	468	11	is	be	AUX
ap-1271	468	12	self	self	NOUN
ap-1271	468	13	-	-	PUNCT
ap-1271	468	14	adjoint	adjoint	NOUN
ap-1271	468	15	.	.	PUNCT
ap-1271	469	1	conversely	conversely	ADV
ap-1271	469	2	,	,	PUNCT
ap-1271	469	3	for	for	ADP
ap-1271	469	4	a	a	DET
ap-1271	469	5	given	give	VERB
ap-1271	469	6	self	self	NOUN
ap-1271	469	7	-	-	PUNCT
ap-1271	469	8	adjoint	adjoint	NOUN
ap-1271	469	9	extension	extension	NOUN
ap-1271	469	10	h	h	NOUN
ap-1271	469	11	of	of	ADP
ap-1271	469	12	hmin	hmin	NOUN
ap-1271	469	13	,	,	PUNCT
ap-1271	469	14	we	we	PRON
ap-1271	469	15	can	can	AUX
ap-1271	469	16	construct	construct	VERB
ap-1271	469	17	a	a	DET
ap-1271	469	18	(	(	PUNCT
ap-1271	469	19	4k1	4k1	NUM
ap-1271	469	20	+	+	NOUN
ap-1271	469	21	2k2)×	2k2)×	NUM
ap-1271	469	22	(	(	PUNCT
ap-1271	469	23	2k1+k2)matrix	2k1+k2)matrix	NOUN
ap-1271	469	24	x	x	VERB
ap-1271	469	25	by	by	ADP
ap-1271	469	26	arranging	arrange	VERB
ap-1271	469	27	the	the	DET
ap-1271	469	28	coefficients	coefficient	NOUN
ap-1271	469	29	of	of	ADP
ap-1271	469	30	an	an	DET
ap-1271	469	31	arbitrary	arbitrary	ADJ
ap-1271	469	32	basis	basis	NOUN
ap-1271	469	33	of	of	ADP
ap-1271	469	34	v	v	NOUN
ap-1271	469	35	=	=	SYM
ap-1271	469	36	pd(h	pd(h	NOUN
ap-1271	469	37	)	)	PUNCT
ap-1271	469	38	with	with	ADP
ap-1271	469	39	respect	respect	NOUN
ap-1271	469	40	to	to	ADP
ap-1271	469	41	the	the	DET
ap-1271	469	42	basis	basis	NOUN
ap-1271	469	43	{	{	PUNCT
ap-1271	470	1	[	[	X
ap-1271	470	2	ψkf	ψkf	X
ap-1271	470	3	j	j	PROPN
ap-1271	470	4	k	k	X
ap-1271	470	5	]	]	PUNCT
ap-1271	470	6	}	}	PUNCT
ap-1271	470	7	.	.	PUNCT
ap-1271	471	1	�	�	PROPN
ap-1271	471	2	5	5	NUM
ap-1271	471	3	infinite	infinite	ADJ
ap-1271	471	4	singularities	singularity	NOUN
ap-1271	471	5	let	let	VERB
ap-1271	471	6	us	we	PRON
ap-1271	471	7	consider	consider	VERB
ap-1271	471	8	the	the	DET
ap-1271	471	9	case	case	NOUN
ap-1271	471	10	k	k	X
ap-1271	471	11	=	=	SYM
ap-1271	471	12	∞	∞	PROPN
ap-1271	471	13	,	,	PUNCT
ap-1271	471	14	and	and	CCONJ
ap-1271	471	15	extend	extend	VERB
ap-1271	471	16	theorem	theorem	ADJ
ap-1271	471	17	1.2	1.2	NUM
ap-1271	471	18	.	.	PUNCT
ap-1271	472	1	even	even	ADV
ap-1271	472	2	in	in	ADP
ap-1271	472	3	this	this	DET
ap-1271	472	4	case	case	NOUN
ap-1271	472	5	,	,	PUNCT
ap-1271	472	6	for	for	ADP
ap-1271	472	7	u	u	PROPN
ap-1271	472	8	∈	∈	PROPN
ap-1271	472	9	d(hmax	d(hmax	NOUN
ap-1271	472	10	)	)	PUNCT
ap-1271	472	11	and	and	CCONJ
ap-1271	472	12	for	for	ADP
ap-1271	472	13	each	each	DET
ap-1271	472	14	k	k	NOUN
ap-1271	472	15	,	,	PUNCT
ap-1271	472	16	we	we	PRON
ap-1271	472	17	can	can	AUX
ap-1271	472	18	define	define	VERB
ap-1271	472	19	the	the	DET
ap-1271	472	20	asymptotic	asymptotic	ADJ
ap-1271	472	21	coefficients	coefficient	NOUN
ap-1271	472	22	ck	ck	INTJ
ap-1271	472	23	j	j	PROPN
ap-1271	472	24	at	at	ADP
ap-1271	472	25	γk	γk	PROPN
ap-1271	472	26	.	.	PUNCT
ap-1271	473	1	however	however	ADV
ap-1271	473	2	,	,	PUNCT
ap-1271	473	3	the	the	DET
ap-1271	473	4	sequence	sequence	NOUN
ap-1271	473	5	φj(u	φj(u	NOUN
ap-1271	473	6	)	)	PUNCT
ap-1271	473	7	is	be	AUX
ap-1271	473	8	an	an	DET
ap-1271	473	9	infinite	infinite	ADJ
ap-1271	473	10	sequence	sequence	NOUN
ap-1271	473	11	.	.	PUNCT
ap-1271	474	1	we	we	PRON
ap-1271	474	2	shall	shall	AUX
ap-1271	474	3	find	find	VERB
ap-1271	474	4	appropriate	appropriate	ADJ
ap-1271	474	5	assumptions	assumption	NOUN
ap-1271	474	6	which	which	PRON
ap-1271	474	7	make	make	VERB
ap-1271	474	8	these	these	DET
ap-1271	474	9	infinite	infinite	ADJ
ap-1271	474	10	sequences	sequence	NOUN
ap-1271	474	11	square	square	ADJ
ap-1271	474	12	summable	summable	ADJ
ap-1271	474	13	.	.	PUNCT
ap-1271	475	1	in	in	ADP
ap-1271	475	2	the	the	DET
ap-1271	475	3	sequel	sequel	NOUN
ap-1271	475	4	,	,	PUNCT
ap-1271	475	5	uk	uk	PROPN
ap-1271	475	6	,	,	PUNCT
ap-1271	475	7	βk	βk	NOUN
ap-1271	475	8	,	,	PUNCT
ap-1271	475	9	gmn	gmn	PROPN
ap-1271	475	10	are	be	AUX
ap-1271	475	11	those	those	PRON
ap-1271	475	12	introduced	introduce	VERB
ap-1271	475	13	in	in	ADP
ap-1271	475	14	section	section	NOUN
ap-1271	475	15	1	1	NUM
ap-1271	475	16	.	.	PUNCT
ap-1271	476	1	however	however	ADV
ap-1271	476	2	,	,	PUNCT
ap-1271	476	3	we	we	PRON
ap-1271	476	4	may	may	AUX
ap-1271	476	5	replace	replace	VERB
ap-1271	476	6	ψk	ψk	ADV
ap-1271	476	7	defined	define	VERB
ap-1271	476	8	by	by	ADP
ap-1271	476	9	(	(	PUNCT
ap-1271	476	10	3	3	NUM
ap-1271	476	11	)	)	PUNCT
ap-1271	476	12	more	more	ADV
ap-1271	476	13	appropriate	appropriate	ADJ
ap-1271	476	14	one	one	NUM
ap-1271	476	15	satisfying	satisfying	NOUN
ap-1271	476	16	(	(	PUNCT
ap-1271	476	17	4	4	NUM
ap-1271	476	18	)	)	PUNCT
ap-1271	476	19	,	,	PUNCT
ap-1271	476	20	if	if	SCONJ
ap-1271	476	21	such	such	ADJ
ap-1271	476	22	one	one	NUM
ap-1271	476	23	exists	exist	VERB
ap-1271	476	24	.	.	PUNCT
ap-1271	477	1	for	for	ADP
ap-1271	477	2	simplicity	simplicity	NOUN
ap-1271	477	3	,	,	PUNCT
ap-1271	477	4	we	we	PRON
ap-1271	477	5	assume	assume	VERB
ap-1271	477	6	v	v	ADP
ap-1271	477	7	=	=	SYM
ap-1271	477	8	0	0	PROPN
ap-1271	477	9	.	.	PUNCT
ap-1271	478	1	(	(	PUNCT
ap-1271	478	2	u	u	NOUN
ap-1271	478	3	)	)	PUNCT
ap-1271	478	4	(	(	PUNCT
ap-1271	478	5	i	i	NOUN
ap-1271	478	6	)	)	PUNCT
ap-1271	478	7	there	there	PRON
ap-1271	478	8	exists	exist	VERB
ap-1271	478	9	ε0	ε0	PROPN
ap-1271	478	10	>	>	X
ap-1271	478	11	0	0	PROPN
ap-1271	478	12	,	,	PUNCT
ap-1271	478	13	independent	independent	ADJ
ap-1271	478	14	of	of	ADP
ap-1271	478	15	k	k	PROPN
ap-1271	478	16	,	,	PUNCT
ap-1271	479	1	such	such	ADJ
ap-1271	479	2	that	that	SCONJ
ap-1271	479	3	uk	uk	PROPN
ap-1271	479	4	=	=	PRON
ap-1271	479	5	{	{	PUNCT
ap-1271	479	6	r	r	NOUN
ap-1271	479	7	<	<	X
ap-1271	479	8	ε0	ε0	NOUN
ap-1271	479	9	}	}	PUNCT
ap-1271	479	10	for	for	ADP
ap-1271	479	11	every	every	DET
ap-1271	479	12	k.	k.	PROPN
ap-1271	479	13	(	(	PUNCT
ap-1271	479	14	ii	ii	PROPN
ap-1271	479	15	)	)	PUNCT
ap-1271	479	16	there	there	PRON
ap-1271	479	17	exist	exist	VERB
ap-1271	479	18	β−	β−	PRON
ap-1271	479	19	,	,	PUNCT
ap-1271	479	20	β+	β+	PUNCT
ap-1271	479	21	such	such	ADJ
ap-1271	479	22	that	that	SCONJ
ap-1271	479	23	0	0	NUM
ap-1271	479	24	<	<	X
ap-1271	479	25	β−	β−	PUNCT
ap-1271	479	26	≤	≤	NOUN
ap-1271	479	27	βk	βk	ADP
ap-1271	479	28	≤	≤	NOUN
ap-1271	479	29	β+	β+	PUNCT
ap-1271	479	30	<	<	X
ap-1271	479	31	1	1	NUM
ap-1271	479	32	or	or	CCONJ
ap-1271	479	33	βk	βk	NOUN
ap-1271	479	34	=	=	NOUN
ap-1271	479	35	0	0	NUM
ap-1271	479	36	,	,	PUNCT
ap-1271	479	37	for	for	ADP
ap-1271	479	38	every	every	DET
ap-1271	479	39	k.	k.	PROPN
ap-1271	479	40	(	(	PUNCT
ap-1271	479	41	iii	iii	X
ap-1271	479	42	)	)	PUNCT
ap-1271	479	43	there	there	PRON
ap-1271	479	44	exists	exist	VERB
ap-1271	479	45	c1	c1	PROPN
ap-1271	479	46	>	>	X
ap-1271	479	47	0	0	PUNCT
ap-1271	480	1	independent	independent	ADJ
ap-1271	480	2	of	of	ADP
ap-1271	480	3	k	k	PROPN
ap-1271	480	4	such	such	ADJ
ap-1271	480	5	that	that	SCONJ
ap-1271	480	6	gmn	gmn	PROPN
ap-1271	480	7	satisfies	satisfie	NOUN
ap-1271	480	8	(	(	PUNCT
ap-1271	480	9	2	2	NUM
ap-1271	480	10	)	)	PUNCT
ap-1271	480	11	and	and	CCONJ
ap-1271	480	12	|∂i∂jgmn|	|∂i∂jgmn|	PROPN
ap-1271	480	13	≤	≤	PROPN
ap-1271	480	14	c1	c1	PROPN
ap-1271	480	15	in	in	ADP
ap-1271	480	16	uk	uk	PROPN
ap-1271	480	17	,	,	PUNCT
ap-1271	480	18	for	for	ADP
ap-1271	480	19	every	every	DET
ap-1271	480	20	i	i	PROPN
ap-1271	480	21	,	,	PUNCT
ap-1271	480	22	j	j	PROPN
ap-1271	480	23	,	,	PUNCT
ap-1271	480	24	m	m	PROPN
ap-1271	480	25	,	,	PUNCT
ap-1271	480	26	n	n	NOUN
ap-1271	480	27	=	=	SYM
ap-1271	480	28	1	1	NUM
ap-1271	480	29	,	,	PUNCT
ap-1271	480	30	2	2	NUM
ap-1271	480	31	.	.	PUNCT
ap-1271	480	32	(	(	PUNCT
ap-1271	480	33	iv	iv	X
ap-1271	480	34	)	)	PUNCT
ap-1271	480	35	there	there	PRON
ap-1271	480	36	exists	exist	VERB
ap-1271	480	37	c2	c2	PROPN
ap-1271	480	38	>	>	X
ap-1271	480	39	0	0	PROPN
ap-1271	481	1	independent	independent	ADJ
ap-1271	481	2	of	of	ADP
ap-1271	481	3	k	k	PROPN
ap-1271	481	4	,	,	PUNCT
ap-1271	481	5	and	and	CCONJ
ap-1271	481	6	phase	phase	NOUN
ap-1271	481	7	functions	function	NOUN
ap-1271	481	8	ψk	ψk	ADP
ap-1271	481	9	∈	∈	PROPN
ap-1271	481	10	c∞(uk	c∞(uk	PROPN
ap-1271	481	11	\	\	PROPN
ap-1271	481	12	{	{	PUNCT
ap-1271	481	13	0	0	NUM
ap-1271	481	14	}	}	PUNCT
ap-1271	481	15	)	)	PUNCT
ap-1271	481	16	satisfying	satisfy	VERB
ap-1271	481	17	|ψk|	|ψk|	NOUN
ap-1271	481	18	=	=	NOUN
ap-1271	481	19	1	1	NUM
ap-1271	481	20	,	,	PUNCT
ap-1271	481	21	(	(	PUNCT
ap-1271	481	22	4	4	NUM
ap-1271	481	23	)	)	PUNCT
ap-1271	481	24	and	and	CCONJ
ap-1271	481	25	|∂ja	|∂ja	NUM
ap-1271	481	26	(	(	PUNCT
ap-1271	481	27	1	1	X
ap-1271	481	28	)	)	PUNCT
ap-1271	481	29	m	m	VERB
ap-1271	481	30	|	|	ADV
ap-1271	481	31	≤	≤	NUM
ap-1271	481	32	c2	c2	PROPN
ap-1271	481	33	in	in	ADP
ap-1271	481	34	uk	uk	PROPN
ap-1271	481	35	,	,	PUNCT
ap-1271	481	36	for	for	ADP
ap-1271	481	37	j	j	PROPN
ap-1271	481	38	,	,	PUNCT
ap-1271	481	39	m	m	VERB
ap-1271	481	40	=	=	NOUN
ap-1271	481	41	1	1	NUM
ap-1271	481	42	,	,	PUNCT
ap-1271	481	43	2	2	NUM
ap-1271	481	44	.	.	PUNCT
ap-1271	482	1	thus	thus	ADV
ap-1271	482	2	we	we	PRON
ap-1271	482	3	assume	assume	VERB
ap-1271	482	4	some	some	DET
ap-1271	482	5	homogeneity	homogeneity	NOUN
ap-1271	482	6	for	for	ADP
ap-1271	482	7	g	g	NOUN
ap-1271	482	8	,	,	PUNCT
ap-1271	482	9	a(0	a(0	PROPN
ap-1271	482	10	)	)	PUNCT
ap-1271	482	11	,	,	PUNCT
ap-1271	482	12	and	and	CCONJ
ap-1271	482	13	a(1	a(1	NOUN
ap-1271	482	14	)	)	PUNCT
ap-1271	482	15	.	.	PUNCT
ap-1271	483	1	since	since	SCONJ
ap-1271	483	2	the	the	DET
ap-1271	483	3	open	open	ADJ
ap-1271	483	4	sets	set	NOUN
ap-1271	483	5	{	{	PUNCT
ap-1271	483	6	uk}∞k=1	uk}∞k=1	PRON
ap-1271	483	7	are	be	AUX
ap-1271	483	8	required	require	VERB
ap-1271	483	9	to	to	PART
ap-1271	483	10	be	be	AUX
ap-1271	483	11	disjoint	disjoint	NOUN
ap-1271	483	12	,	,	PUNCT
ap-1271	483	13	assumption	assumption	NOUN
ap-1271	483	14	(	(	PUNCT
ap-1271	483	15	i	i	NOUN
ap-1271	483	16	)	)	PUNCT
ap-1271	483	17	says	say	VERB
ap-1271	483	18	the	the	DET
ap-1271	483	19	points	point	NOUN
ap-1271	483	20	of	of	ADP
ap-1271	483	21	γ	γ	NOUN
ap-1271	483	22	are	be	AUX
ap-1271	483	23	uniformly	uniformly	ADV
ap-1271	483	24	separated	separate	VERB
ap-1271	483	25	in	in	ADP
ap-1271	483	26	some	some	DET
ap-1271	483	27	sense	sense	NOUN
ap-1271	483	28	.	.	PUNCT
ap-1271	484	1	assumption	assumption	NOUN
ap-1271	484	2	(	(	PUNCT
ap-1271	484	3	ii	ii	NOUN
ap-1271	484	4	)	)	PUNCT
ap-1271	484	5	seems	seem	VERB
ap-1271	484	6	a	a	DET
ap-1271	484	7	little	little	ADJ
ap-1271	484	8	strange	strange	ADJ
ap-1271	484	9	,	,	PUNCT
ap-1271	484	10	but	but	CCONJ
ap-1271	484	11	we	we	PRON
ap-1271	484	12	need	need	VERB
ap-1271	484	13	this	this	DET
ap-1271	484	14	assumption	assumption	NOUN
ap-1271	484	15	if	if	SCONJ
ap-1271	484	16	we	we	PRON
ap-1271	484	17	want	want	VERB
ap-1271	484	18	to	to	PART
ap-1271	484	19	make	make	VERB
ap-1271	484	20	the	the	DET
ap-1271	484	21	boundary	boundary	ADJ
ap-1271	484	22	value	value	NOUN
ap-1271	484	23	φ(u	φ(u	NOUN
ap-1271	484	24	)	)	PUNCT
ap-1271	484	25	square	square	ADJ
ap-1271	484	26	summable.7	summable.7	PROPN
ap-1271	484	27	assumption	assumption	NOUN
ap-1271	484	28	(	(	PUNCT
ap-1271	484	29	iii	iii	NOUN
ap-1271	484	30	)	)	PUNCT
ap-1271	484	31	binds	bind	VERB
ap-1271	484	32	the	the	DET
ap-1271	484	33	curvature	curvature	NOUN
ap-1271	484	34	of	of	ADP
ap-1271	484	35	m	m	PROPN
ap-1271	484	36	,	,	PUNCT
ap-1271	484	37	and	and	CCONJ
ap-1271	484	38	(	(	PUNCT
ap-1271	484	39	iv	iv	X
ap-1271	484	40	)	)	PUNCT
ap-1271	484	41	the	the	DET
ap-1271	484	42	intensity	intensity	NOUN
ap-1271	484	43	of	of	ADP
ap-1271	484	44	the	the	DET
ap-1271	484	45	magnetic	magnetic	ADJ
ap-1271	484	46	field	field	NOUN
ap-1271	484	47	.	.	PUNCT
ap-1271	485	1	in	in	ADP
ap-1271	485	2	[	[	X
ap-1271	485	3	12	12	NUM
ap-1271	485	4	]	]	PUNCT
ap-1271	485	5	,	,	PUNCT
ap-1271	485	6	the	the	DET
ap-1271	485	7	author	author	NOUN
ap-1271	485	8	considers	consider	VERB
ap-1271	485	9	a	a	DET
ap-1271	485	10	similar	similar	ADJ
ap-1271	485	11	assumption	assumption	NOUN
ap-1271	485	12	when	when	SCONJ
ap-1271	485	13	m	m	PROPN
ap-1271	485	14	is	be	AUX
ap-1271	485	15	the	the	DET
ap-1271	485	16	flat	flat	ADJ
ap-1271	485	17	euclidean	euclidean	ADJ
ap-1271	485	18	plane	plane	NOUN
ap-1271	485	19	and	and	CCONJ
ap-1271	485	20	da(1	da(1	NOUN
ap-1271	485	21	)	)	PUNCT
ap-1271	485	22	is	be	AUX
ap-1271	485	23	a	a	DET
ap-1271	485	24	constant	constant	ADJ
ap-1271	485	25	magnetic	magnetic	ADJ
ap-1271	485	26	field	field	NOUN
ap-1271	485	27	.	.	PUNCT
ap-1271	486	1	in	in	ADP
ap-1271	486	2	the	the	DET
ap-1271	486	3	sequel	sequel	NOUN
ap-1271	486	4	,	,	PUNCT
ap-1271	486	5	we	we	PRON
ap-1271	486	6	use	use	VERB
ap-1271	486	7	the	the	DET
ap-1271	486	8	notation	notation	NOUN
ap-1271	486	9	c	c	NOUN
ap-1271	486	10	∞	∞	NOUN
ap-1271	486	11	=	=	SYM
ap-1271	486	12	l2	l2	NOUN
ap-1271	486	13	=	=	SYM
ap-1271	486	14	{	{	PUNCT
ap-1271	486	15	(	(	PUNCT
ap-1271	486	16	cj)∞j=1	cj)∞j=1	NOUN
ap-1271	486	17	|	|	ADV
ap-1271	486	18	∞∑	∞∑	NUM
ap-1271	486	19	j=1	j=1	NOUN
ap-1271	486	20	|cj	|cj	X
ap-1271	486	21	|2	|2	X
ap-1271	486	22	<	<	X
ap-1271	486	23	∞	∞	NUM
ap-1271	486	24	}	}	PUNCT
ap-1271	486	25	,	,	PUNCT
ap-1271	486	26	and	and	CCONJ
ap-1271	486	27	define	define	VERB
ap-1271	486	28	its	its	PRON
ap-1271	486	29	inner	inner	ADJ
ap-1271	486	30	product	product	NOUN
ap-1271	486	31	by	by	ADP
ap-1271	486	32	usual	usual	ADJ
ap-1271	486	33	l2	l2	NOUN
ap-1271	486	34	-	-	PUNCT
ap-1271	486	35	inner	inner	ADJ
ap-1271	486	36	product	product	NOUN
ap-1271	486	37	.	.	PUNCT
ap-1271	487	1	let	let	VERB
ap-1271	487	2	h	h	NOUN
ap-1271	487	3	=	=	PUNCT
ap-1271	487	4	c	c	PROPN
ap-1271	487	5	k1	k1	PROPN
ap-1271	487	6	⊕	⊕	PROPN
ap-1271	487	7	c	c	PROPN
ap-1271	487	8	k1	k1	PROPN
ap-1271	487	9	⊕	⊕	PROPN
ap-1271	487	10	c	c	PROPN
ap-1271	487	11	k2	k2	PROPN
ap-1271	487	12	.	.	PUNCT
ap-1271	488	1	proposition	proposition	NOUN
ap-1271	488	2	5.1	5.1	NUM
ap-1271	488	3	assume	assume	VERB
ap-1271	488	4	(	(	PUNCT
ap-1271	488	5	a	a	X
ap-1271	488	6	)	)	PUNCT
ap-1271	488	7	,	,	PUNCT
ap-1271	488	8	(	(	PUNCT
ap-1271	488	9	a0	a0	NOUN
ap-1271	488	10	)	)	PUNCT
ap-1271	488	11	,	,	PUNCT
ap-1271	488	12	(	(	PUNCT
ap-1271	488	13	a1	a1	NOUN
ap-1271	488	14	)	)	PUNCT
ap-1271	488	15	,	,	PUNCT
ap-1271	488	16	(	(	PUNCT
ap-1271	488	17	sb	sb	X
ap-1271	488	18	)	)	PUNCT
ap-1271	488	19	,	,	PUNCT
ap-1271	488	20	(	(	PUNCT
ap-1271	488	21	u	u	NOUN
ap-1271	488	22	)	)	PUNCT
ap-1271	488	23	,	,	PUNCT
ap-1271	488	24	v	v	NOUN
ap-1271	488	25	=	=	SYM
ap-1271	488	26	0	0	NUM
ap-1271	488	27	,	,	PUNCT
ap-1271	488	28	and	and	CCONJ
ap-1271	488	29	k	k	PROPN
ap-1271	488	30	=	=	PROPN
ap-1271	488	31	∞.	∞.	PROPN
ap-1271	488	32	then	then	ADV
ap-1271	488	33	,	,	PUNCT
ap-1271	488	34	the	the	DET
ap-1271	488	35	following	follow	VERB
ap-1271	488	36	linear	linear	PROPN
ap-1271	488	37	map	map	NOUN
ap-1271	488	38	7if	7if	NOUN
ap-1271	488	39	we	we	PRON
ap-1271	488	40	consider	consider	VERB
ap-1271	488	41	another	another	DET
ap-1271	488	42	type	type	NOUN
ap-1271	488	43	of	of	ADP
ap-1271	488	44	characterization	characterization	NOUN
ap-1271	488	45	,	,	PUNCT
ap-1271	488	46	assumption	assumption	NOUN
ap-1271	488	47	(	(	PUNCT
ap-1271	488	48	ii	ii	NOUN
ap-1271	488	49	)	)	PUNCT
ap-1271	488	50	may	may	AUX
ap-1271	488	51	be	be	AUX
ap-1271	488	52	dropped	drop	VERB
ap-1271	488	53	.	.	PUNCT
ap-1271	489	1	70	70	NUM
ap-1271	489	2	acta	acta	PROPN
ap-1271	489	3	polytechnica	polytechnica	PROPN
ap-1271	489	4	vol	vol	NOUN
ap-1271	489	5	.	.	PROPN
ap-1271	490	1	50	50	NUM
ap-1271	490	2	no	no	NOUN
ap-1271	490	3	.	.	PUNCT
ap-1271	491	1	5/2010	5/2010	NUM
ap-1271	492	1	d	d	NOUN
ap-1271	492	2	+	+	PROPN
ap-1271	493	1	[	[	X
ap-1271	493	2	u	u	X
ap-1271	493	3	]	]	X
ap-1271	493	4	�	�	PROPN
ap-1271	493	5	→	→	SYM
ap-1271	493	6	φ(u	φ(u	NOUN
ap-1271	493	7	)	)	PUNCT
ap-1271	493	8	∈	∈	PROPN
ap-1271	493	9	h	h	NOUN
ap-1271	493	10	⊕	⊕	PROPN
ap-1271	493	11	h	h	PROPN
ap-1271	493	12	,	,	PUNCT
ap-1271	493	13	(	(	PUNCT
ap-1271	493	14	23	23	NUM
ap-1271	493	15	)	)	PUNCT
ap-1271	493	16	is	be	AUX
ap-1271	493	17	a	a	DET
ap-1271	493	18	well	well	ADV
ap-1271	493	19	-	-	PUNCT
ap-1271	493	20	defined	define	VERB
ap-1271	493	21	homeomorphism	homeomorphism	NOUN
ap-1271	493	22	.	.	PUNCT
ap-1271	494	1	moreover	moreover	ADV
ap-1271	494	2	,	,	PUNCT
ap-1271	494	3	[	[	X
ap-1271	494	4	u	u	NOUN
ap-1271	494	5	,	,	PUNCT
ap-1271	494	6	v]d	v]d	ADP
ap-1271	494	7	=	=	SYM
ap-1271	494	8	4π(φ(u	4π(φ(u	NUM
ap-1271	494	9	)	)	PUNCT
ap-1271	494	10	,	,	PUNCT
ap-1271	494	11	d̃φ(v	d̃φ(v	NOUN
ap-1271	494	12	)	)	PUNCT
ap-1271	494	13	)	)	PUNCT
ap-1271	494	14	,	,	PUNCT
ap-1271	494	15	(	(	PUNCT
ap-1271	494	16	24	24	NUM
ap-1271	494	17	)	)	PUNCT
ap-1271	494	18	d̃	d̃	PROPN
ap-1271	495	1	=	=	SYM
ap-1271	495	2	(	(	PUNCT
ap-1271	495	3	o	o	X
ap-1271	495	4	−d	−d	PROPN
ap-1271	495	5	d	d	X
ap-1271	495	6	o	o	PROPN
ap-1271	495	7	)	)	PUNCT
ap-1271	495	8	,	,	PUNCT
ap-1271	495	9	where	where	SCONJ
ap-1271	495	10	d	d	NOUN
ap-1271	495	11	is	be	AUX
ap-1271	495	12	a	a	DET
ap-1271	495	13	bounded	bounded	ADJ
ap-1271	495	14	operator	operator	NOUN
ap-1271	495	15	on	on	ADP
ap-1271	495	16	h	h	NOUN
ap-1271	495	17	defined	define	VERB
ap-1271	495	18	by	by	ADP
ap-1271	495	19	(	(	PUNCT
ap-1271	495	20	6	6	NUM
ap-1271	495	21	)	)	PUNCT
ap-1271	495	22	.	.	PUNCT
ap-1271	496	1	once	once	SCONJ
ap-1271	496	2	this	this	DET
ap-1271	496	3	proposition	proposition	NOUN
ap-1271	496	4	is	be	AUX
ap-1271	496	5	established	establish	VERB
ap-1271	496	6	,	,	PUNCT
ap-1271	496	7	our	our	PRON
ap-1271	496	8	theorem	theorem	NOUN
ap-1271	496	9	can	can	AUX
ap-1271	496	10	be	be	AUX
ap-1271	496	11	proved	prove	VERB
ap-1271	496	12	similarly	similarly	ADV
ap-1271	496	13	as	as	ADP
ap-1271	496	14	in	in	ADP
ap-1271	496	15	the	the	DET
ap-1271	496	16	proof	proof	NOUN
ap-1271	496	17	of	of	ADP
ap-1271	496	18	theorem	theorem	ADJ
ap-1271	496	19	1.2	1.2	NUM
ap-1271	496	20	.	.	PUNCT
ap-1271	497	1	so	so	ADV
ap-1271	497	2	we	we	PRON
ap-1271	497	3	omit	omit	VERB
ap-1271	497	4	the	the	DET
ap-1271	497	5	proof	proof	NOUN
ap-1271	497	6	.	.	PUNCT
ap-1271	498	1	theorem	theorem	VERB
ap-1271	498	2	5.2	5.2	NUM
ap-1271	498	3	assume	assume	VERB
ap-1271	498	4	the	the	DET
ap-1271	498	5	same	same	ADJ
ap-1271	498	6	conditions	condition	NOUN
ap-1271	498	7	as	as	ADP
ap-1271	498	8	in	in	ADP
ap-1271	498	9	proposition	proposition	NOUN
ap-1271	498	10	5.1	5.1	NUM
ap-1271	498	11	.	.	PUNCT
ap-1271	499	1	then	then	ADV
ap-1271	499	2	,	,	PUNCT
ap-1271	499	3	the	the	DET
ap-1271	499	4	statements	statement	NOUN
ap-1271	499	5	of	of	ADP
ap-1271	499	6	theorem	theorem	ADJ
ap-1271	499	7	1.2	1.2	NUM
ap-1271	499	8	hold	hold	NOUN
ap-1271	499	9	with	with	ADP
ap-1271	499	10	the	the	DET
ap-1271	499	11	following	follow	VERB
ap-1271	499	12	changes	change	NOUN
ap-1271	499	13	:	:	PUNCT
ap-1271	499	14	x1	x1	X
ap-1271	499	15	,	,	PUNCT
ap-1271	499	16	x2	x2	PROPN
ap-1271	499	17	are	be	AUX
ap-1271	499	18	bounded	bound	VERB
ap-1271	499	19	operators	operator	NOUN
ap-1271	499	20	on	on	ADP
ap-1271	499	21	h	h	NOUN
ap-1271	499	22	,	,	PUNCT
ap-1271	499	23	and	and	CCONJ
ap-1271	499	24	condition	condition	NOUN
ap-1271	499	25	(	(	PUNCT
ap-1271	499	26	7	7	X
ap-1271	499	27	)	)	PUNCT
ap-1271	499	28	is	be	AUX
ap-1271	499	29	replaced	replace	VERB
ap-1271	499	30	by	by	ADP
ap-1271	499	31	the	the	DET
ap-1271	499	32	condition	condition	NOUN
ap-1271	499	33	ranx	ranx	NOUN
ap-1271	499	34	=	=	SYM
ap-1271	499	35	kerx∗d̃	kerx∗d̃	PROPN
ap-1271	499	36	,	,	PUNCT
ap-1271	499	37	where	where	SCONJ
ap-1271	499	38	d̃	d̃	PROPN
ap-1271	499	39	is	be	AUX
ap-1271	499	40	the	the	DET
ap-1271	499	41	bounded	bounded	ADJ
ap-1271	499	42	operator	operator	NOUN
ap-1271	499	43	on	on	ADP
ap-1271	499	44	h	h	PROPN
ap-1271	499	45	⊕	⊕	PROPN
ap-1271	499	46	h	h	PROPN
ap-1271	499	47	defined	define	VERB
ap-1271	499	48	in	in	ADP
ap-1271	499	49	proposition	proposition	NOUN
ap-1271	499	50	5.1	5.1	NUM
ap-1271	499	51	.	.	PUNCT
ap-1271	500	1	we	we	PRON
ap-1271	500	2	conclude	conclude	VERB
ap-1271	500	3	this	this	DET
ap-1271	500	4	paper	paper	NOUN
ap-1271	500	5	by	by	ADP
ap-1271	500	6	proving	prove	VERB
ap-1271	500	7	proposition	proposition	NOUN
ap-1271	500	8	5.1	5.1	NUM
ap-1271	500	9	.	.	PUNCT
ap-1271	501	1	proof	proof	NOUN
ap-1271	501	2	of	of	ADP
ap-1271	501	3	proposition	proposition	NOUN
ap-1271	501	4	5.1	5.1	NUM
ap-1271	501	5	.	.	PUNCT
ap-1271	502	1	we	we	PRON
ap-1271	502	2	divide	divide	VERB
ap-1271	502	3	the	the	DET
ap-1271	502	4	proof	proof	NOUN
ap-1271	502	5	into	into	ADP
ap-1271	502	6	two	two	NUM
ap-1271	502	7	steps	step	NOUN
ap-1271	502	8	.	.	PUNCT
ap-1271	503	1	step	step	NOUN
ap-1271	503	2	1	1	NUM
ap-1271	503	3	.	.	PUNCT
ap-1271	504	1	the	the	DET
ap-1271	504	2	map	map	NOUN
ap-1271	505	1	d	d	X
ap-1271	505	2	+	+	X
ap-1271	506	1	[	[	X
ap-1271	506	2	f	f	X
ap-1271	506	3	]	]	PUNCT
ap-1271	506	4	�	�	PROPN
ap-1271	506	5	→	→	SYM
ap-1271	506	6	∞⊕	∞⊕	PROPN
ap-1271	507	1	k=1	k=1	AUX
ap-1271	507	2	tk[f	tk[f	X
ap-1271	507	3	]	]	PUNCT
ap-1271	508	1	∈	∈	PROPN
ap-1271	508	2	∞⊕	∞⊕	NOUN
ap-1271	509	1	k=1	k=1	X
ap-1271	510	1	dk	dk	PROPN
ap-1271	510	2	is	be	AUX
ap-1271	510	3	continuous	continuous	ADJ
ap-1271	510	4	,	,	PUNCT
ap-1271	510	5	bijective	bijective	ADJ
ap-1271	510	6	and	and	CCONJ
ap-1271	510	7	its	its	PRON
ap-1271	510	8	inverse	inverse	NOUN
ap-1271	510	9	is	be	AUX
ap-1271	510	10	also	also	ADV
ap-1271	510	11	continuous	continuous	ADJ
ap-1271	510	12	.	.	PUNCT
ap-1271	511	1	proof	proof	NOUN
ap-1271	511	2	.	.	PUNCT
ap-1271	512	1	by	by	ADP
ap-1271	512	2	our	our	PRON
ap-1271	512	3	assumption	assumption	NOUN
ap-1271	512	4	(	(	PUNCT
ap-1271	512	5	u	u	NOUN
ap-1271	512	6	)	)	PUNCT
ap-1271	512	7	and	and	CCONJ
ap-1271	512	8	the	the	DET
ap-1271	512	9	calculation	calculation	NOUN
ap-1271	512	10	in	in	ADP
ap-1271	512	11	section	section	NOUN
ap-1271	512	12	3	3	NUM
ap-1271	512	13	,	,	PUNCT
ap-1271	512	14	we	we	PRON
ap-1271	512	15	can	can	AUX
ap-1271	512	16	prove	prove	VERB
ap-1271	512	17	there	there	PRON
ap-1271	512	18	exists	exist	VERB
ap-1271	512	19	c	c	NOUN
ap-1271	512	20	>	>	X
ap-1271	512	21	0	0	PROPN
ap-1271	512	22	independent	independent	ADJ
ap-1271	512	23	of	of	ADP
ap-1271	512	24	k	k	PROPN
ap-1271	512	25	such	such	ADJ
ap-1271	512	26	that	that	SCONJ
ap-1271	512	27	‖ψ−1	‖ψ−1	DET
ap-1271	512	28	k	k	PROPN
ap-1271	512	29	χkf‖2lk	χkf‖2lk	NOUN
ap-1271	512	30	,	,	PUNCT
ap-1271	512	31	max	max	PROPN
ap-1271	512	32	≤	≤	PROPN
ap-1271	512	33	c	c	PROPN
ap-1271	512	34	∫	∫	PROPN
ap-1271	512	35	uk	uk	PROPN
ap-1271	512	36	(	(	PUNCT
ap-1271	512	37	|lf	|lf	NOUN
ap-1271	512	38	|2	|2	NUM
ap-1271	512	39	+	+	X
ap-1271	512	40	|f	|f	PROPN
ap-1271	512	41	|2)dμk	|2)dμk	PROPN
ap-1271	512	42	.	.	PUNCT
ap-1271	513	1	summing	sum	VERB
ap-1271	513	2	up	up	ADP
ap-1271	513	3	these	these	DET
ap-1271	513	4	equalities	equality	NOUN
ap-1271	513	5	with	with	ADP
ap-1271	513	6	respect	respect	NOUN
ap-1271	513	7	to	to	ADP
ap-1271	513	8	k	k	NOUN
ap-1271	513	9	,	,	PUNCT
ap-1271	513	10	we	we	PRON
ap-1271	513	11	conclude	conclude	VERB
ap-1271	513	12	the	the	DET
ap-1271	513	13	map	map	NOUN
ap-1271	513	14	d(hmax	d(hmax	NOUN
ap-1271	513	15	)	)	PUNCT
ap-1271	514	1	+	+	CCONJ
ap-1271	514	2	f	f	PROPN
ap-1271	514	3	�	�	PROPN
ap-1271	514	4	→	→	SYM
ap-1271	514	5	∞⊕	∞⊕	PROPN
ap-1271	514	6	k=1	k=1	PUNCT
ap-1271	515	1	ψ−1	ψ−1	PROPN
ap-1271	515	2	k	k	X
ap-1271	515	3	χkf	χkf	PROPN
ap-1271	516	1	∈	∈	PROPN
ap-1271	516	2	∞⊕	∞⊕	PUNCT
ap-1271	517	1	k=1	k=1	X
ap-1271	517	2	d(lk	d(lk	PROPN
ap-1271	517	3	,	,	PUNCT
ap-1271	517	4	max	max	PROPN
ap-1271	517	5	)	)	PUNCT
ap-1271	517	6	is	be	AUX
ap-1271	517	7	continuous	continuous	ADJ
ap-1271	517	8	.	.	PUNCT
ap-1271	518	1	then	then	ADV
ap-1271	518	2	the	the	DET
ap-1271	518	3	well	well	NOUN
ap-1271	518	4	-	-	PUNCT
ap-1271	518	5	definedness	definedness	NOUN
ap-1271	518	6	of	of	ADP
ap-1271	518	7	the	the	DET
ap-1271	518	8	map	map	NOUN
ap-1271	518	9	(	(	PUNCT
ap-1271	518	10	23	23	NUM
ap-1271	518	11	)	)	PUNCT
ap-1271	518	12	can	can	AUX
ap-1271	518	13	be	be	AUX
ap-1271	518	14	proved	prove	VERB
ap-1271	518	15	similarly	similarly	ADV
ap-1271	518	16	as	as	ADP
ap-1271	518	17	in	in	ADP
ap-1271	518	18	section	section	NOUN
ap-1271	518	19	3	3	NUM
ap-1271	518	20	.	.	PUNCT
ap-1271	519	1	since	since	SCONJ
ap-1271	519	2	d	d	PROPN
ap-1271	519	3	is	be	AUX
ap-1271	519	4	identified	identify	VERB
ap-1271	519	5	with	with	ADP
ap-1271	519	6	the	the	DET
ap-1271	519	7	closed	closed	ADJ
ap-1271	519	8	subspace	subspace	NOUN
ap-1271	519	9	d(hmin)⊥	d(hmin)⊥	NOUN
ap-1271	519	10	of	of	ADP
ap-1271	519	11	d(hmax	d(hmax	NOUN
ap-1271	519	12	)	)	PUNCT
ap-1271	519	13	and	and	CCONJ
ap-1271	519	14	the	the	DET
ap-1271	519	15	projection	projection	NOUN
ap-1271	519	16	from	from	ADP
ap-1271	519	17	d(lk	d(lk	PROPN
ap-1271	519	18	,	,	PUNCT
ap-1271	519	19	max	max	PROPN
ap-1271	519	20	)	)	PUNCT
ap-1271	519	21	to	to	ADP
ap-1271	519	22	dk	dk	PROPN
ap-1271	519	23	is	be	AUX
ap-1271	519	24	continuous	continuous	ADJ
ap-1271	519	25	,	,	PUNCT
ap-1271	519	26	we	we	PRON
ap-1271	519	27	conclude	conclude	VERB
ap-1271	519	28	the	the	DET
ap-1271	519	29	map	map	NOUN
ap-1271	519	30	(	(	PUNCT
ap-1271	519	31	23	23	NUM
ap-1271	519	32	)	)	PUNCT
ap-1271	519	33	is	be	AUX
ap-1271	519	34	continuous	continuous	ADJ
ap-1271	519	35	.	.	PUNCT
ap-1271	520	1	moreover	moreover	ADV
ap-1271	520	2	,	,	PUNCT
ap-1271	520	3	we	we	PRON
ap-1271	520	4	can	can	AUX
ap-1271	520	5	prove	prove	VERB
ap-1271	520	6	the	the	DET
ap-1271	520	7	inverse	inverse	NOUN
ap-1271	520	8	map	map	NOUN
ap-1271	520	9	is	be	AUX
ap-1271	520	10	also	also	ADV
ap-1271	520	11	well	well	ADV
ap-1271	520	12	-	-	PUNCT
ap-1271	520	13	defined	define	VERB
ap-1271	520	14	and	and	CCONJ
ap-1271	520	15	continuous	continuous	ADJ
ap-1271	520	16	,	,	PUNCT
ap-1271	520	17	so	so	SCONJ
ap-1271	520	18	we	we	PRON
ap-1271	520	19	have	have	VERB
ap-1271	520	20	the	the	DET
ap-1271	520	21	conclusion	conclusion	NOUN
ap-1271	520	22	.	.	PUNCT
ap-1271	521	1	�	�	PROPN
ap-1271	521	2	step	step	VERB
ap-1271	521	3	2	2	NUM
ap-1271	521	4	.	.	PUNCT
ap-1271	522	1	there	there	PRON
ap-1271	522	2	exists	exist	VERB
ap-1271	522	3	c	c	NOUN
ap-1271	522	4	>	>	X
ap-1271	522	5	1	1	NUM
ap-1271	522	6	independent	independent	NOUN
ap-1271	522	7	of	of	ADP
ap-1271	522	8	k	k	PROPN
ap-1271	522	9	such	such	ADJ
ap-1271	522	10	that	that	SCONJ
ap-1271	522	11	c−1|ck|	c−1|ck|	PROPN
ap-1271	522	12	≤	≤	PROPN
ap-1271	522	13	‖[u]‖dk	‖[u]‖dk	ADV
ap-1271	522	14	≤	≤	PROPN
ap-1271	523	1	c|ck|	c|ck|	PROPN
ap-1271	523	2	for	for	ADP
ap-1271	523	3	every	every	DET
ap-1271	523	4	[	[	X
ap-1271	523	5	u	u	X
ap-1271	523	6	]	]	X
ap-1271	523	7	∈	∈	PROPN
ap-1271	523	8	dk	dk	NOUN
ap-1271	523	9	,	,	PUNCT
ap-1271	523	10	where	where	SCONJ
ap-1271	523	11	ck	ck	ADV
ap-1271	523	12	=	=	SYM
ap-1271	523	13	(	(	PUNCT
ap-1271	523	14	ck	ck	INTJ
ap-1271	523	15	1	1	NUM
ap-1271	523	16	,	,	PUNCT
ap-1271	523	17	c	c	PROPN
ap-1271	523	18	k	k	PROPN
ap-1271	523	19	2	2	NUM
ap-1271	523	20	,	,	PUNCT
ap-1271	523	21	c	c	PROPN
ap-1271	523	22	k	k	PROPN
ap-1271	523	23	4	4	NUM
ap-1271	523	24	,	,	PUNCT
ap-1271	523	25	c	c	PROPN
ap-1271	523	26	k	k	PROPN
ap-1271	523	27	5	5	NUM
ap-1271	523	28	)	)	PUNCT
ap-1271	523	29	for	for	ADP
ap-1271	523	30	0	0	NUM
ap-1271	523	31	<	<	X
ap-1271	523	32	βk	βk	ADP
ap-1271	523	33	<	<	X
ap-1271	523	34	1	1	NUM
ap-1271	523	35	,	,	PUNCT
ap-1271	523	36	ck	ck	NOUN
ap-1271	523	37	=	=	SYM
ap-1271	523	38	(	(	PUNCT
ap-1271	523	39	ck	ck	INTJ
ap-1271	523	40	3	3	NUM
ap-1271	523	41	,	,	PUNCT
ap-1271	523	42	c	c	PROPN
ap-1271	523	43	k	k	PROPN
ap-1271	523	44	6	6	NUM
ap-1271	523	45	)	)	PUNCT
ap-1271	523	46	for	for	ADP
ap-1271	523	47	βk	βk	NOUN
ap-1271	523	48	=	=	SYM
ap-1271	523	49	0	0	NUM
ap-1271	523	50	,	,	PUNCT
ap-1271	523	51	and	and	CCONJ
ap-1271	523	52	ck	ck	INTJ
ap-1271	523	53	j	j	PROPN
ap-1271	523	54	are	be	AUX
ap-1271	523	55	asymptotic	asymptotic	ADJ
ap-1271	523	56	coefficients	coefficient	NOUN
ap-1271	523	57	of	of	ADP
ap-1271	523	58	u	u	NOUN
ap-1271	523	59	defined	define	VERB
ap-1271	523	60	in	in	ADP
ap-1271	523	61	section	section	NOUN
ap-1271	523	62	1	1	NUM
ap-1271	523	63	.	.	PUNCT
ap-1271	524	1	proof	proof	NOUN
ap-1271	524	2	.	.	PUNCT
ap-1271	525	1	we	we	PRON
ap-1271	525	2	only	only	ADV
ap-1271	525	3	consider	consider	VERB
ap-1271	525	4	the	the	DET
ap-1271	525	5	case	case	NOUN
ap-1271	525	6	0	0	PUNCT
ap-1271	525	7	<	<	X
ap-1271	525	8	βk	βk	X
ap-1271	525	9	<	<	X
ap-1271	525	10	1	1	NUM
ap-1271	525	11	.	.	PUNCT
ap-1271	525	12	consider	consider	VERB
ap-1271	525	13	the	the	DET
ap-1271	525	14	following	follow	VERB
ap-1271	525	15	formula	formula	NOUN
ap-1271	525	16	for	for	ADP
ap-1271	525	17	ck	ck	PROPN
ap-1271	526	1	1	1	NUM
ap-1271	526	2	ck	ck	NOUN
ap-1271	526	3	1	1	NUM
ap-1271	526	4	=	=	SYM
ap-1271	526	5	1	1	NUM
ap-1271	526	6	4π(1−	4π(1−	NUM
ap-1271	526	7	βk	βk	NOUN
ap-1271	526	8	)	)	PUNCT
ap-1271	526	9	[	[	X
ap-1271	526	10	f4k	f4k	X
ap-1271	526	11	,	,	PUNCT
ap-1271	526	12	u]dk	u]dk	PROPN
ap-1271	526	13	,	,	PUNCT
ap-1271	526	14	which	which	PRON
ap-1271	526	15	can	can	AUX
ap-1271	526	16	be	be	AUX
ap-1271	526	17	verified	verify	VERB
ap-1271	526	18	by	by	ADP
ap-1271	526	19	substituting	substitute	VERB
ap-1271	526	20	all	all	DET
ap-1271	526	21	the	the	DET
ap-1271	526	22	basis	basis	NOUN
ap-1271	526	23	functions	function	NOUN
ap-1271	526	24	into	into	ADP
ap-1271	526	25	u.	u.	NOUN
ap-1271	526	26	by	by	ADP
ap-1271	526	27	choosing	choose	VERB
ap-1271	526	28	the	the	DET
ap-1271	526	29	representative	representative	ADJ
ap-1271	526	30	u	u	PROPN
ap-1271	526	31	∈	∈	PROPN
ap-1271	526	32	d(lk	d(lk	PROPN
ap-1271	526	33	,	,	PUNCT
ap-1271	526	34	min)⊥	min)⊥	PROPN
ap-1271	526	35	(	(	PUNCT
ap-1271	526	36	so	so	ADV
ap-1271	526	37	‖u‖lk	‖u‖lk	NOUN
ap-1271	526	38	,	,	PUNCT
ap-1271	526	39	max	max	PROPN
ap-1271	526	40	=	=	SYM
ap-1271	526	41	‖[u]‖dk	‖[u]‖dk	NOUN
ap-1271	526	42	)	)	PUNCT
ap-1271	526	43	and	and	CCONJ
ap-1271	526	44	using	use	VERB
ap-1271	526	45	the	the	DET
ap-1271	526	46	schwarz	schwarz	PROPN
ap-1271	526	47	inequality	inequality	NOUN
ap-1271	526	48	,	,	PUNCT
ap-1271	526	49	we	we	PRON
ap-1271	526	50	have	have	VERB
ap-1271	526	51	|ck	|ck	ADP
ap-1271	526	52	1	1	NUM
ap-1271	526	53	|	|	ADV
ap-1271	526	54	≤	≤	NUM
ap-1271	526	55	1	1	NUM
ap-1271	526	56	2π(1	2π(1	NUM
ap-1271	526	57	−	−	NOUN
ap-1271	526	58	βk	βk	NOUN
ap-1271	526	59	)	)	PUNCT
ap-1271	526	60	‖f4k‖lk	‖f4k‖lk	ADJ
ap-1271	526	61	,	,	PUNCT
ap-1271	526	62	max‖[u]‖dk	max‖[u]‖dk	PROPN
ap-1271	526	63	.	.	PUNCT
ap-1271	527	1	the	the	DET
ap-1271	527	2	fraction	fraction	NOUN
ap-1271	527	3	is	be	AUX
ap-1271	527	4	bounded	bound	VERB
ap-1271	527	5	uniformly	uniformly	ADV
ap-1271	527	6	w.r.t	w.r.t	NOUN
ap-1271	527	7	.	.	PUNCT
ap-1271	528	1	k	k	X
ap-1271	528	2	,	,	PUNCT
ap-1271	528	3	by	by	ADP
ap-1271	528	4	our	our	PRON
ap-1271	528	5	assumption	assumption	NOUN
ap-1271	528	6	(	(	PUNCT
ap-1271	528	7	ii	ii	NOUN
ap-1271	528	8	)	)	PUNCT
ap-1271	528	9	of	of	ADP
ap-1271	528	10	(	(	PUNCT
ap-1271	528	11	u	u	NOUN
ap-1271	528	12	)	)	PUNCT
ap-1271	528	13	.	.	PUNCT
ap-1271	529	1	moreover	moreover	ADV
ap-1271	529	2	,	,	PUNCT
ap-1271	529	3	we	we	PRON
ap-1271	529	4	can	can	AUX
ap-1271	529	5	prove	prove	VERB
ap-1271	529	6	‖f	‖f	SCONJ
ap-1271	529	7	j	j	PROPN
ap-1271	529	8	k‖lk	k‖lk	PROPN
ap-1271	529	9	,	,	PUNCT
ap-1271	529	10	max	max	PROPN
ap-1271	529	11	is	be	AUX
ap-1271	529	12	also	also	ADV
ap-1271	529	13	uniformly	uniformly	ADV
ap-1271	529	14	bounded	bound	VERB
ap-1271	529	15	,	,	PUNCT
ap-1271	529	16	by	by	ADP
ap-1271	529	17	(	(	PUNCT
ap-1271	529	18	u	u	NOUN
ap-1271	529	19	)	)	PUNCT
ap-1271	529	20	and	and	CCONJ
ap-1271	529	21	the	the	DET
ap-1271	529	22	calculations	calculation	NOUN
ap-1271	529	23	in	in	ADP
ap-1271	529	24	section	section	NOUN
ap-1271	529	25	3	3	NUM
ap-1271	529	26	(	(	PUNCT
ap-1271	529	27	first	first	ADJ
ap-1271	529	28	decompose	decompose	NOUN
ap-1271	529	29	lk	lk	NOUN
ap-1271	529	30	as	as	ADP
ap-1271	529	31	in	in	ADP
ap-1271	529	32	section	section	NOUN
ap-1271	529	33	3	3	NUM
ap-1271	529	34	,	,	PUNCT
ap-1271	529	35	and	and	CCONJ
ap-1271	529	36	estimate	estimate	VERB
ap-1271	529	37	all	all	DET
ap-1271	529	38	terms	term	NOUN
ap-1271	529	39	)	)	PUNCT
ap-1271	529	40	.	.	PUNCT
ap-1271	530	1	thus	thus	ADV
ap-1271	530	2	we	we	PRON
ap-1271	530	3	have	have	VERB
ap-1271	530	4	|ck	|ck	ADP
ap-1271	530	5	j	j	PROPN
ap-1271	530	6	|	|	ADV
ap-1271	530	7	≤	≤	NUM
ap-1271	530	8	c‖[u]‖dk	c‖[u]‖dk	NOUN
ap-1271	530	9	.	.	PUNCT
ap-1271	531	1	for	for	ADP
ap-1271	531	2	j	j	PROPN
ap-1271	531	3	=	=	SYM
ap-1271	531	4	1	1	X
ap-1271	531	5	.	.	PUNCT
ap-1271	532	1	the	the	DET
ap-1271	532	2	case	case	NOUN
ap-1271	532	3	j	j	PROPN
ap-1271	532	4	=	=	SYM
ap-1271	532	5	2	2	NUM
ap-1271	532	6	,	,	PUNCT
ap-1271	532	7	4	4	NUM
ap-1271	532	8	,	,	PUNCT
ap-1271	532	9	5	5	NUM
ap-1271	532	10	can	can	AUX
ap-1271	532	11	be	be	AUX
ap-1271	532	12	treated	treat	VERB
ap-1271	532	13	similarly	similarly	ADV
ap-1271	532	14	.	.	PUNCT
ap-1271	533	1	conversely,∑	conversely,∑	PROPN
ap-1271	533	2	j=1,2,4,5	j=1,2,4,5	NOUN
ap-1271	533	3	‖ck	‖ck	NUM
ap-1271	533	4	j	j	NOUN
ap-1271	534	1	[	[	X
ap-1271	534	2	f	f	X
ap-1271	534	3	j	j	PROPN
ap-1271	534	4	k	k	X
ap-1271	534	5	]	]	X
ap-1271	534	6	‖dk	‖dk	PROPN
ap-1271	534	7	≤	≤	PROPN
ap-1271	534	8	|ck|	|ck|	PROPN
ap-1271	534	9	(	(	PUNCT
ap-1271	534	10	∑	∑	PROPN
ap-1271	534	11	j=1,2,4,5	j=1,2,4,5	PROPN
ap-1271	534	12	‖f	‖f	PRON
ap-1271	534	13	j	j	PROPN
ap-1271	534	14	k‖2lk	k‖2lk	PROPN
ap-1271	534	15	,	,	PUNCT
ap-1271	534	16	max	max	PROPN
ap-1271	534	17	)	)	PUNCT
ap-1271	534	18	1/2	1/2	NUM
ap-1271	534	19	,	,	PUNCT
ap-1271	534	20	and	and	CCONJ
ap-1271	534	21	the	the	DET
ap-1271	534	22	sum	sum	NOUN
ap-1271	534	23	in	in	ADP
ap-1271	534	24	the	the	DET
ap-1271	534	25	right	right	ADJ
ap-1271	534	26	hand	hand	NOUN
ap-1271	534	27	side	side	NOUN
ap-1271	534	28	is	be	AUX
ap-1271	534	29	uniformly	uniformly	ADV
ap-1271	534	30	bounded	bound	VERB
ap-1271	534	31	.	.	PUNCT
ap-1271	535	1	thus	thus	ADV
ap-1271	535	2	the	the	DET
ap-1271	535	3	conclusion	conclusion	NOUN
ap-1271	535	4	holds	hold	VERB
ap-1271	535	5	.	.	PUNCT
ap-1271	536	1	�	�	PROPN
ap-1271	536	2	by	by	ADP
ap-1271	536	3	step	step	NOUN
ap-1271	536	4	1	1	NUM
ap-1271	536	5	and	and	CCONJ
ap-1271	536	6	2	2	NUM
ap-1271	536	7	,	,	PUNCT
ap-1271	536	8	we	we	PRON
ap-1271	536	9	have	have	AUX
ap-1271	536	10	proved	prove	VERB
ap-1271	536	11	the	the	DET
ap-1271	536	12	map	map	NOUN
ap-1271	536	13	(	(	PUNCT
ap-1271	536	14	23	23	NUM
ap-1271	536	15	)	)	PUNCT
ap-1271	536	16	is	be	AUX
ap-1271	536	17	well	well	ADV
ap-1271	536	18	-	-	PUNCT
ap-1271	536	19	defined	define	VERB
ap-1271	536	20	and	and	CCONJ
ap-1271	536	21	homeomorphism	homeomorphism	X
ap-1271	536	22	.	.	PUNCT
ap-1271	537	1	equation	equation	NOUN
ap-1271	537	2	(	(	PUNCT
ap-1271	537	3	24	24	NUM
ap-1271	537	4	)	)	PUNCT
ap-1271	537	5	is	be	AUX
ap-1271	537	6	confirmed	confirm	VERB
ap-1271	537	7	by	by	ADP
ap-1271	537	8	substituting	substitute	VERB
ap-1271	537	9	each	each	DET
ap-1271	537	10	f	f	PROPN
ap-1271	537	11	j	j	PROPN
ap-1271	537	12	k	k	PROPN
ap-1271	537	13	as	as	SCONJ
ap-1271	537	14	u	u	PROPN
ap-1271	537	15	or	or	CCONJ
ap-1271	537	16	v.	v.	ADP
ap-1271	537	17	�	�	PROPN
ap-1271	537	18	acknowledgement	acknowledgement	NOUN
ap-1271	537	19	this	this	DET
ap-1271	537	20	work	work	NOUN
ap-1271	537	21	was	be	AUX
ap-1271	537	22	partially	partially	ADV
ap-1271	537	23	supported	support	VERB
ap-1271	537	24	by	by	ADP
ap-1271	537	25	doppler	doppler	NOUN
ap-1271	537	26	institute	institute	NOUN
ap-1271	537	27	for	for	ADP
ap-1271	537	28	mathematical	mathematical	ADJ
ap-1271	537	29	physics	physics	NOUN
ap-1271	537	30	and	and	CCONJ
ap-1271	537	31	applied	apply	VERB
ap-1271	537	32	mathematics	mathematic	NOUN
ap-1271	537	33	,	,	PUNCT
ap-1271	537	34	kit	kit	NOUN
ap-1271	537	35	faculty	faculty	NOUN
ap-1271	537	36	research	research	NOUN
ap-1271	537	37	abroad	abroad	ADV
ap-1271	537	38	fellowship	fellowship	NOUN
ap-1271	537	39	program	program	NOUN
ap-1271	537	40	,	,	PUNCT
ap-1271	537	41	and	and	CCONJ
ap-1271	537	42	jsps	jsps	PROPN
ap-1271	537	43	grant	grant	PROPN
ap-1271	537	44	wakate	wakate	PROPN
ap-1271	537	45	20740093	20740093	NUM
ap-1271	537	46	.	.	PUNCT
ap-1271	538	1	references	reference	NOUN
ap-1271	538	2	[	[	X
ap-1271	538	3	1	1	NUM
ap-1271	538	4	]	]	PUNCT
ap-1271	538	5	adami	adami	NOUN
ap-1271	538	6	,	,	PUNCT
ap-1271	538	7	r.	r.	PROPN
ap-1271	538	8	,	,	PUNCT
ap-1271	538	9	teta	teta	PROPN
ap-1271	538	10	,	,	PUNCT
ap-1271	538	11	a.	a.	NOUN
ap-1271	538	12	:	:	PUNCT
ap-1271	538	13	on	on	ADP
ap-1271	538	14	the	the	DET
ap-1271	538	15	aharonov	aharonov	PROPN
ap-1271	538	16	-	-	PUNCT
ap-1271	538	17	bohm	bohm	PROPN
ap-1271	538	18	hamiltonian	hamiltonian	NOUN
ap-1271	538	19	,	,	PUNCT
ap-1271	538	20	lett	lett	PROPN
ap-1271	538	21	.	.	PUNCT
ap-1271	538	22	math	math	NOUN
ap-1271	538	23	.	.	PUNCT
ap-1271	539	1	phys	phy	NOUN
ap-1271	539	2	.	.	PUNCT
ap-1271	540	1	43	43	NUM
ap-1271	540	2	(	(	PUNCT
ap-1271	540	3	1998	1998	NUM
ap-1271	540	4	)	)	PUNCT
ap-1271	540	5	,	,	PUNCT
ap-1271	540	6	43–54	43–54	X
ap-1271	540	7	.	.	PUNCT
ap-1271	541	1	[	[	X
ap-1271	541	2	2	2	NUM
ap-1271	541	3	]	]	PUNCT
ap-1271	541	4	aharonov	aharonov	NOUN
ap-1271	541	5	,	,	PUNCT
ap-1271	541	6	y.	y.	PROPN
ap-1271	541	7	,	,	PUNCT
ap-1271	541	8	bohm	bohm	PROPN
ap-1271	541	9	,	,	PUNCT
ap-1271	541	10	d.	d.	NOUN
ap-1271	541	11	:	:	PUNCT
ap-1271	541	12	significance	significance	NOUN
ap-1271	541	13	of	of	ADP
ap-1271	541	14	electromagnetic	electromagnetic	ADJ
ap-1271	541	15	potentials	potential	NOUN
ap-1271	541	16	in	in	ADP
ap-1271	541	17	the	the	DET
ap-1271	541	18	quantum	quantum	ADJ
ap-1271	541	19	theory	theory	NOUN
ap-1271	541	20	,	,	PUNCT
ap-1271	541	21	phys	phy	NOUN
ap-1271	541	22	.	.	PUNCT
ap-1271	542	1	rev	rev	PROPN
ap-1271	542	2	.	.	PROPN
ap-1271	542	3	115	115	NUM
ap-1271	542	4	(	(	PUNCT
ap-1271	542	5	1959	1959	NUM
ap-1271	542	6	)	)	PUNCT
ap-1271	542	7	,	,	PUNCT
ap-1271	542	8	485–491	485–491	NUM
ap-1271	542	9	.	.	PUNCT
ap-1271	542	10	71	71	NUM
ap-1271	542	11	acta	acta	PROPN
ap-1271	542	12	polytechnica	polytechnica	PROPN
ap-1271	542	13	vol	vol	NOUN
ap-1271	542	14	.	.	PROPN
ap-1271	543	1	50	50	NUM
ap-1271	543	2	no	no	NOUN
ap-1271	543	3	.	.	PUNCT
ap-1271	544	1	5/2010	5/2010	NUM
ap-1271	545	1	[	[	X
ap-1271	545	2	3	3	NUM
ap-1271	545	3	]	]	PUNCT
ap-1271	545	4	albeverio	albeverio	PROPN
ap-1271	545	5	,	,	PUNCT
ap-1271	545	6	s.	s.	PROPN
ap-1271	545	7	,	,	PUNCT
ap-1271	545	8	gesztesy	gesztesy	PROPN
ap-1271	545	9	,	,	PUNCT
ap-1271	545	10	f.	f.	PROPN
ap-1271	545	11	,	,	PUNCT
ap-1271	545	12	høegh	høegh	VERB
ap-1271	545	13	-	-	PUNCT
ap-1271	545	14	krohn	krohn	PROPN
ap-1271	545	15	,	,	PUNCT
ap-1271	545	16	r.	r.	PROPN
ap-1271	545	17	,	,	PUNCT
ap-1271	545	18	holden	holden	PROPN
ap-1271	545	19	,	,	PUNCT
ap-1271	545	20	h.	h.	PROPN
ap-1271	545	21	:	:	PUNCT
ap-1271	545	22	solvable	solvable	ADJ
ap-1271	545	23	models	model	NOUN
ap-1271	545	24	in	in	ADP
ap-1271	545	25	quantum	quantum	ADJ
ap-1271	545	26	mechanics	mechanic	NOUN
ap-1271	545	27	.	.	PUNCT
ap-1271	546	1	texts	text	NOUN
ap-1271	546	2	and	and	CCONJ
ap-1271	546	3	monographs	monograph	NOUN
ap-1271	546	4	in	in	ADP
ap-1271	546	5	physics	physics	PROPN
ap-1271	546	6	.	.	PUNCT
ap-1271	546	7	,	,	PUNCT
ap-1271	546	8	springer	springer	NOUN
ap-1271	546	9	-	-	PUNCT
ap-1271	546	10	verlag	verlag	PROPN
ap-1271	546	11	,	,	PUNCT
ap-1271	546	12	new	new	PROPN
ap-1271	546	13	york	york	PROPN
ap-1271	546	14	,	,	PUNCT
ap-1271	546	15	1988	1988	NUM
ap-1271	546	16	.	.	PUNCT
ap-1271	547	1	[	[	X
ap-1271	547	2	4	4	NUM
ap-1271	547	3	]	]	SYM
ap-1271	547	4	bulla	bulla	X
ap-1271	547	5	,	,	PUNCT
ap-1271	547	6	w.	w.	PROPN
ap-1271	547	7	,	,	PUNCT
ap-1271	547	8	gesztesy	gesztesy	PROPN
ap-1271	547	9	,	,	PUNCT
ap-1271	547	10	f.	f.	PROPN
ap-1271	547	11	:	:	PUNCT
ap-1271	547	12	deficiency	deficiency	NOUN
ap-1271	547	13	indices	index	NOUN
ap-1271	547	14	and	and	CCONJ
ap-1271	547	15	singular	singular	ADJ
ap-1271	547	16	boundary	boundary	ADJ
ap-1271	547	17	conditions	condition	NOUN
ap-1271	547	18	in	in	ADP
ap-1271	547	19	quantum	quantum	ADJ
ap-1271	547	20	mechanics	mechanic	NOUN
ap-1271	547	21	,	,	PUNCT
ap-1271	547	22	j.	j.	PROPN
ap-1271	547	23	math	math	PROPN
ap-1271	547	24	.	.	PUNCT
ap-1271	548	1	phys	phy	NOUN
ap-1271	548	2	.	.	PUNCT
ap-1271	549	1	26	26	NUM
ap-1271	549	2	no	no	NOUN
ap-1271	549	3	.	.	PROPN
ap-1271	549	4	10	10	NUM
ap-1271	549	5	(	(	PUNCT
ap-1271	549	6	1985	1985	NUM
ap-1271	549	7	)	)	PUNCT
ap-1271	549	8	,	,	PUNCT
ap-1271	549	9	2	2	NUM
ap-1271	549	10	520–2	520–2	NUM
ap-1271	549	11	528	528	NUM
ap-1271	549	12	.	.	PUNCT
ap-1271	550	1	[	[	X
ap-1271	550	2	5	5	NUM
ap-1271	550	3	]	]	X
ap-1271	550	4	correa	correa	PROPN
ap-1271	550	5	,	,	PUNCT
ap-1271	550	6	f.	f.	PROPN
ap-1271	550	7	,	,	PUNCT
ap-1271	550	8	falomir	falomir	PROPN
ap-1271	550	9	,	,	PUNCT
ap-1271	550	10	h.	h.	PROPN
ap-1271	550	11	,	,	PUNCT
ap-1271	550	12	jakubsky	jakubsky	PROPN
ap-1271	550	13	,	,	PUNCT
ap-1271	550	14	v.	v.	PROPN
ap-1271	550	15	,	,	PUNCT
ap-1271	550	16	plyushchay	plyushchay	PROPN
ap-1271	550	17	,	,	PUNCT
ap-1271	550	18	m.	m.	NOUN
ap-1271	550	19	s.	s.	PROPN
ap-1271	550	20	:	:	PUNCT
ap-1271	550	21	hidden	hide	VERB
ap-1271	550	22	superconformal	superconformal	ADJ
ap-1271	550	23	symmetry	symmetry	NOUN
ap-1271	550	24	of	of	ADP
ap-1271	550	25	spinless	spinless	ADJ
ap-1271	550	26	aharonov	aharonov	PROPN
ap-1271	550	27	-	-	PUNCT
ap-1271	550	28	bohm	bohm	PROPN
ap-1271	550	29	system	system	NOUN
ap-1271	550	30	preprint	preprint	NOUN
ap-1271	550	31	,	,	PUNCT
ap-1271	550	32	url	url	PROPN
ap-1271	550	33	:	:	PUNCT
ap-1271	550	34	http://arxiv.org/abs/0906.4055	http://arxiv.org/abs/0906.4055	NOUN
ap-1271	550	35	[	[	X
ap-1271	550	36	6	6	NUM
ap-1271	550	37	]	]	X
ap-1271	550	38	correa	correa	PROPN
ap-1271	550	39	,	,	PUNCT
ap-1271	550	40	f.	f.	PROPN
ap-1271	550	41	,	,	PUNCT
ap-1271	550	42	falomir	falomir	PROPN
ap-1271	550	43	,	,	PUNCT
ap-1271	550	44	h.	h.	PROPN
ap-1271	550	45	,	,	PUNCT
ap-1271	550	46	jakubsky	jakubsky	PROPN
ap-1271	550	47	,	,	PUNCT
ap-1271	550	48	v.	v.	PROPN
ap-1271	550	49	,	,	PUNCT
ap-1271	550	50	plyushchay	plyushchay	PROPN
ap-1271	550	51	,	,	PUNCT
ap-1271	550	52	m.	m.	NOUN
ap-1271	550	53	s.	s.	PROPN
ap-1271	550	54	:	:	PUNCT
ap-1271	550	55	supersymmetries	supersymmetry	NOUN
ap-1271	550	56	of	of	ADP
ap-1271	550	57	the	the	DET
ap-1271	550	58	spin1/2	spin1/2	ADJ
ap-1271	550	59	particle	particle	NOUN
ap-1271	550	60	in	in	ADP
ap-1271	550	61	the	the	DET
ap-1271	550	62	field	field	NOUN
ap-1271	550	63	of	of	ADP
ap-1271	550	64	magnetic	magnetic	ADJ
ap-1271	550	65	vortex	vortex	NOUN
ap-1271	550	66	,	,	PUNCT
ap-1271	550	67	and	and	CCONJ
ap-1271	550	68	anyons	anyon	NOUN
ap-1271	550	69	,	,	PUNCT
ap-1271	550	70	preprint	preprint	NOUN
ap-1271	550	71	,	,	PUNCT
ap-1271	550	72	url	url	PROPN
ap-1271	550	73	:	:	PUNCT
ap-1271	550	74	http://arxiv.org/abs/1003.1434	http://arxiv.org/abs/1003.1434	PROPN
ap-1271	550	75	[	[	X
ap-1271	550	76	7	7	NUM
ap-1271	550	77	]	]	PUNCT
ap-1271	550	78	dabrowski	dabrowski	NOUN
ap-1271	550	79	,	,	PUNCT
ap-1271	550	80	l.	l.	PROPN
ap-1271	550	81	,	,	PUNCT
ap-1271	550	82	šťovíček	šťovíček	PROPN
ap-1271	550	83	,	,	PUNCT
ap-1271	550	84	p.	p.	NOUN
ap-1271	550	85	:	:	PUNCT
ap-1271	550	86	aharonov	aharonov	NOUN
ap-1271	550	87	–	–	PUNCT
ap-1271	550	88	bohm	bohm	PROPN
ap-1271	550	89	effect	effect	NOUN
ap-1271	550	90	with	with	ADP
ap-1271	550	91	δ	δ	NOUN
ap-1271	550	92	-	-	PUNCT
ap-1271	550	93	type	type	NOUN
ap-1271	550	94	interaction	interaction	NOUN
ap-1271	550	95	,	,	PUNCT
ap-1271	550	96	j.	j.	PROPN
ap-1271	550	97	math	math	PROPN
ap-1271	550	98	.	.	PUNCT
ap-1271	551	1	phys	phy	NOUN
ap-1271	551	2	.	.	PUNCT
ap-1271	552	1	39	39	NUM
ap-1271	552	2	,	,	PUNCT
ap-1271	552	3	no	no	INTJ
ap-1271	552	4	.	.	NOUN
ap-1271	552	5	1	1	NUM
ap-1271	552	6	(	(	PUNCT
ap-1271	552	7	1998	1998	NUM
ap-1271	552	8	)	)	PUNCT
ap-1271	552	9	,	,	PUNCT
ap-1271	552	10	47–62	47–62	NUM
ap-1271	552	11	.	.	PUNCT
ap-1271	553	1	[	[	X
ap-1271	553	2	8	8	NUM
ap-1271	553	3	]	]	SYM
ap-1271	553	4	exner	exner	NOUN
ap-1271	553	5	,	,	PUNCT
ap-1271	553	6	p.	p.	PROPN
ap-1271	553	7	,	,	PUNCT
ap-1271	553	8	šťovíček	šťovíček	PROPN
ap-1271	553	9	,	,	PUNCT
ap-1271	553	10	p.	p.	NOUN
ap-1271	553	11	,	,	PUNCT
ap-1271	553	12	vytřas	vytřas	NOUN
ap-1271	553	13	,	,	PUNCT
ap-1271	553	14	p.	p.	NOUN
ap-1271	553	15	:	:	PUNCT
ap-1271	554	1	generalized	generalize	VERB
ap-1271	554	2	boundary	boundary	ADJ
ap-1271	554	3	conditions	condition	NOUN
ap-1271	554	4	for	for	ADP
ap-1271	554	5	the	the	DET
ap-1271	554	6	aharonovbohm	aharonovbohm	PROPN
ap-1271	554	7	effect	effect	NOUN
ap-1271	554	8	combined	combine	VERB
ap-1271	554	9	with	with	ADP
ap-1271	554	10	a	a	DET
ap-1271	554	11	homogeneous	homogeneous	ADJ
ap-1271	554	12	magnetic	magnetic	ADJ
ap-1271	554	13	field	field	NOUN
ap-1271	554	14	,	,	PUNCT
ap-1271	554	15	j.	j.	PROPN
ap-1271	554	16	math	math	PROPN
ap-1271	554	17	.	.	PUNCT
ap-1271	555	1	phys	phy	NOUN
ap-1271	555	2	.	.	PUNCT
ap-1271	556	1	43	43	NUM
ap-1271	556	2	,	,	PUNCT
ap-1271	556	3	no	no	INTJ
ap-1271	556	4	.	.	NOUN
ap-1271	556	5	5	5	NUM
ap-1271	556	6	(	(	PUNCT
ap-1271	556	7	2002	2002	NUM
ap-1271	556	8	)	)	PUNCT
ap-1271	556	9	,	,	PUNCT
ap-1271	556	10	2	2	NUM
ap-1271	556	11	151–2	151–2	NUM
ap-1271	556	12	167	167	NUM
ap-1271	556	13	.	.	PUNCT
ap-1271	557	1	[	[	X
ap-1271	557	2	9	9	NUM
ap-1271	557	3	]	]	PUNCT
ap-1271	557	4	iwai	iwai	NOUN
ap-1271	557	5	,	,	PUNCT
ap-1271	557	6	t.	t.	PROPN
ap-1271	557	7	,	,	PUNCT
ap-1271	557	8	yabu	yabu	PROPN
ap-1271	557	9	,	,	PUNCT
ap-1271	557	10	y.	y.	PROPN
ap-1271	557	11	:	:	PUNCT
ap-1271	557	12	aharonov	aharonov	PROPN
ap-1271	557	13	-	-	PUNCT
ap-1271	557	14	bohm	bohm	PROPN
ap-1271	557	15	quantum	quantum	NOUN
ap-1271	557	16	systems	system	NOUN
ap-1271	557	17	on	on	ADP
ap-1271	557	18	a	a	DET
ap-1271	557	19	punctured	punctured	ADJ
ap-1271	557	20	2	2	NUM
ap-1271	557	21	-	-	PUNCT
ap-1271	557	22	torus	torus	NOUN
ap-1271	557	23	,	,	PUNCT
ap-1271	557	24	j.	j.	PROPN
ap-1271	557	25	phys	phys	PROPN
ap-1271	557	26	.	.	PUNCT
ap-1271	558	1	a	a	DET
ap-1271	558	2	:	:	PUNCT
ap-1271	558	3	math	math	NOUN
ap-1271	558	4	.	.	PUNCT
ap-1271	559	1	gen	gen	PROPN
ap-1271	559	2	.	.	PROPN
ap-1271	559	3	39	39	NUM
ap-1271	559	4	(	(	PUNCT
ap-1271	559	5	2006	2006	NUM
ap-1271	559	6	)	)	PUNCT
ap-1271	559	7	739–777	739–777	NUM
ap-1271	559	8	.	.	PUNCT
ap-1271	560	1	[	[	X
ap-1271	560	2	10	10	NUM
ap-1271	560	3	]	]	X
ap-1271	560	4	kato	kato	PROPN
ap-1271	560	5	,	,	PUNCT
ap-1271	560	6	t.	t.	PROPN
ap-1271	560	7	:	:	PUNCT
ap-1271	560	8	perturbation	perturbation	NOUN
ap-1271	560	9	theory	theory	NOUN
ap-1271	560	10	for	for	ADP
ap-1271	560	11	linear	linear	PROPN
ap-1271	560	12	operators	operator	NOUN
ap-1271	560	13	.	.	PUNCT
ap-1271	561	1	springer	springer	NOUN
ap-1271	561	2	,	,	PUNCT
ap-1271	561	3	1966	1966	NUM
ap-1271	561	4	.	.	PUNCT
ap-1271	562	1	[	[	X
ap-1271	562	2	11	11	NUM
ap-1271	562	3	]	]	PUNCT
ap-1271	562	4	lisovyy	lisovyy	NOUN
ap-1271	562	5	,	,	PUNCT
ap-1271	562	6	o.	o.	NOUN
ap-1271	562	7	:	:	PUNCT
ap-1271	562	8	aharonov	aharonov	PROPN
ap-1271	562	9	-	-	PUNCT
ap-1271	562	10	bohm	bohm	PROPN
ap-1271	562	11	effect	effect	NOUN
ap-1271	562	12	on	on	ADP
ap-1271	562	13	the	the	DET
ap-1271	562	14	poincaré	poincaré	ADJ
ap-1271	562	15	disk	disk	NOUN
ap-1271	562	16	,	,	PUNCT
ap-1271	562	17	j.	j.	PROPN
ap-1271	562	18	math	math	PROPN
ap-1271	562	19	.	.	PUNCT
ap-1271	563	1	phys	phy	NOUN
ap-1271	563	2	.	.	PUNCT
ap-1271	564	1	48	48	NUM
ap-1271	564	2	(	(	PUNCT
ap-1271	564	3	2007	2007	NUM
ap-1271	564	4	)	)	PUNCT
ap-1271	564	5	,	,	PUNCT
ap-1271	564	6	no	no	INTJ
ap-1271	564	7	.	.	NOUN
ap-1271	564	8	5	5	NUM
ap-1271	564	9	,	,	PUNCT
ap-1271	564	10	052112	052112	NUM
ap-1271	564	11	.	.	PUNCT
ap-1271	565	1	[	[	X
ap-1271	565	2	12	12	NUM
ap-1271	565	3	]	]	X
ap-1271	565	4	mine	mine	NOUN
ap-1271	565	5	,	,	PUNCT
ap-1271	565	6	t.	t.	PROPN
ap-1271	565	7	:	:	PUNCT
ap-1271	565	8	the	the	DET
ap-1271	565	9	aharonov	aharonov	PROPN
ap-1271	565	10	-	-	PUNCT
ap-1271	565	11	bohm	bohm	PROPN
ap-1271	565	12	solenoids	solenoid	NOUN
ap-1271	565	13	in	in	ADP
ap-1271	565	14	a	a	DET
ap-1271	565	15	constant	constant	ADJ
ap-1271	565	16	magnetic	magnetic	ADJ
ap-1271	565	17	field	field	NOUN
ap-1271	565	18	.	.	PUNCT
ap-1271	566	1	ann	ann	PROPN
ap-1271	566	2	.	.	PUNCT
ap-1271	567	1	henri	henri	PROPN
ap-1271	567	2	poincaré	poincaré	ADJ
ap-1271	567	3	6	6	NUM
ap-1271	567	4	(	(	PUNCT
ap-1271	567	5	2005	2005	NUM
ap-1271	567	6	)	)	PUNCT
ap-1271	567	7	,	,	PUNCT
ap-1271	567	8	no	no	INTJ
ap-1271	567	9	.	.	NOUN
ap-1271	567	10	1	1	NUM
ap-1271	567	11	,	,	PUNCT
ap-1271	567	12	125–154	125–154	NUM
ap-1271	567	13	.	.	PUNCT
ap-1271	568	1	[	[	X
ap-1271	568	2	13	13	NUM
ap-1271	568	3	]	]	SYM
ap-1271	568	4	reed	reed	NOUN
ap-1271	568	5	,	,	PUNCT
ap-1271	568	6	m.	m.	NOUN
ap-1271	568	7	,	,	PUNCT
ap-1271	568	8	simon	simon	PROPN
ap-1271	568	9	,	,	PUNCT
ap-1271	568	10	b.	b.	PROPN
ap-1271	568	11	:	:	PUNCT
ap-1271	568	12	methods	method	NOUN
ap-1271	568	13	of	of	ADP
ap-1271	568	14	modern	modern	ADJ
ap-1271	568	15	mathematical	mathematical	ADJ
ap-1271	568	16	physics	physics	PROPN
ap-1271	568	17	.	.	PUNCT
ap-1271	569	1	ii	ii	PROPN
ap-1271	569	2	.	.	PUNCT
ap-1271	570	1	fourier	fouri	ADJ
ap-1271	570	2	analysis	analysis	NOUN
ap-1271	570	3	,	,	PUNCT
ap-1271	570	4	selfadjointness	selfadjointness	NOUN
ap-1271	570	5	,	,	PUNCT
ap-1271	570	6	academic	academic	ADJ
ap-1271	570	7	press	press	NOUN
ap-1271	570	8	,	,	PUNCT
ap-1271	570	9	new	new	PROPN
ap-1271	570	10	york	york	PROPN
ap-1271	570	11	-	-	PUNCT
ap-1271	570	12	london	london	PROPN
ap-1271	570	13	,	,	PUNCT
ap-1271	570	14	1975	1975	NUM
ap-1271	570	15	.	.	PUNCT
ap-1271	571	1	[	[	X
ap-1271	571	2	14	14	NUM
ap-1271	571	3	]	]	X
ap-1271	571	4	shubin	shubin	PROPN
ap-1271	571	5	,	,	PUNCT
ap-1271	571	6	m.	m.	NOUN
ap-1271	571	7	:	:	PUNCT
ap-1271	571	8	essential	essential	ADJ
ap-1271	571	9	self	self	NOUN
ap-1271	571	10	-	-	PUNCT
ap-1271	571	11	adjointness	adjointness	NOUN
ap-1271	571	12	for	for	ADP
ap-1271	571	13	semibounded	semibounde	VERB
ap-1271	571	14	magnetic	magnetic	ADJ
ap-1271	571	15	schrödinger	schrödinger	NOUN
ap-1271	571	16	operators	operator	NOUN
ap-1271	571	17	on	on	ADP
ap-1271	571	18	non	non	ADJ
ap-1271	571	19	-	-	ADJ
ap-1271	571	20	compact	compact	ADJ
ap-1271	571	21	manifolds	manifold	NOUN
ap-1271	571	22	,	,	PUNCT
ap-1271	571	23	j.	j.	PROPN
ap-1271	571	24	funct	funct	PROPN
ap-1271	571	25	.	.	PUNCT
ap-1271	572	1	anal	anal	PROPN
ap-1271	572	2	.	.	PUNCT
ap-1271	573	1	186	186	NUM
ap-1271	573	2	(	(	PUNCT
ap-1271	573	3	2001	2001	NUM
ap-1271	573	4	)	)	PUNCT
ap-1271	573	5	,	,	PUNCT
ap-1271	574	1	92–116	92–116	PROPN
ap-1271	574	2	.	.	PUNCT
ap-1271	575	1	dr	dr	PROPN
ap-1271	575	2	.	.	PROPN
ap-1271	575	3	takuya	takuya	PROPN
ap-1271	575	4	mine	mine	PROPN
ap-1271	575	5	e	e	NOUN
ap-1271	575	6	-	-	NOUN
ap-1271	575	7	mail	mail	NOUN
ap-1271	575	8	:	:	PUNCT
ap-1271	575	9	mine@kit.ac.jp	mine@kit.ac.jp	ADJ
ap-1271	575	10	kyoto	kyoto	PROPN
ap-1271	575	11	institute	institute	PROPN
ap-1271	575	12	of	of	ADP
ap-1271	575	13	technology	technology	PROPN
ap-1271	575	14	matsugasaki	matsugasaki	PROPN
ap-1271	575	15	,	,	PUNCT
ap-1271	575	16	sakyo	sakyo	PROPN
ap-1271	575	17	-	-	PUNCT
ap-1271	575	18	ku	ku	PROPN
ap-1271	575	19	kyoto	kyoto	PROPN
ap-1271	575	20	606	606	NUM
ap-1271	575	21	-	-	SYM
ap-1271	575	22	8585	8585	NUM
ap-1271	575	23	,	,	PUNCT
ap-1271	575	24	japan	japan	PROPN
ap-1271	575	25	72	72	NUM