id	sid	tid	token	lemma	pos
ejpam-6953	1	1	european	european	PROPN
ejpam-6953	1	2	journal	journal	PROPN
ejpam-6953	1	3	of	of	ADP
ejpam-6953	1	4	pure	pure	ADJ
ejpam-6953	1	5	and	and	CCONJ
ejpam-6953	1	6	applied	applied	ADJ
ejpam-6953	1	7	mathematics	mathematic	NOUN
ejpam-6953	1	8	2025	2025	NUM
ejpam-6953	1	9	,	,	PUNCT
ejpam-6953	1	10	vol	vol	NOUN
ejpam-6953	1	11	.	.	PROPN
ejpam-6953	1	12	18	18	NUM
ejpam-6953	1	13	,	,	PUNCT
ejpam-6953	1	14	issue	issue	NOUN
ejpam-6953	1	15	4	4	NUM
ejpam-6953	1	16	,	,	PUNCT
ejpam-6953	1	17	article	article	NOUN
ejpam-6953	1	18	number	number	NOUN
ejpam-6953	1	19	6953	6953	NUM
ejpam-6953	1	20	issn	issn	VERB
ejpam-6953	1	21	1307	1307	NUM
ejpam-6953	1	22	-	-	SYM
ejpam-6953	1	23	5543	5543	NUM
ejpam-6953	1	24	–	–	PUNCT
ejpam-6953	1	25	ejpam.com	ejpam.com	X
ejpam-6953	1	26	published	publish	VERB
ejpam-6953	1	27	by	by	ADP
ejpam-6953	1	28	new	new	PROPN
ejpam-6953	1	29	york	york	PROPN
ejpam-6953	1	30	business	business	PROPN
ejpam-6953	1	31	global	global	PROPN
ejpam-6953	1	32	global	global	ADJ
ejpam-6953	1	33	weighted	weight	VERB
ejpam-6953	1	34	l2	l2	NOUN
ejpam-6953	1	35	∂̄-solvability	∂̄-solvability	PROPN
ejpam-6953	1	36	on	on	ADP
ejpam-6953	1	37	noncompact	noncompact	ADJ
ejpam-6953	1	38	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	1	39	complex	complex	ADJ
ejpam-6953	1	40	lie	lie	NOUN
ejpam-6953	1	41	groups	group	NOUN
ejpam-6953	1	42	abdel	abdel	PROPN
ejpam-6953	1	43	rahman	rahman	PROPN
ejpam-6953	1	44	al	al	PROPN
ejpam-6953	1	45	-	-	PUNCT
ejpam-6953	1	46	abdallah	abdallah	PROPN
ejpam-6953	1	47	1	1	NUM
ejpam-6953	1	48	department	department	NOUN
ejpam-6953	1	49	of	of	ADP
ejpam-6953	1	50	mathematics	mathematic	NOUN
ejpam-6953	1	51	and	and	CCONJ
ejpam-6953	1	52	computer	computer	NOUN
ejpam-6953	1	53	science	science	NOUN
ejpam-6953	1	54	,	,	PUNCT
ejpam-6953	1	55	faculty	faculty	NOUN
ejpam-6953	1	56	of	of	ADP
ejpam-6953	1	57	science	science	NOUN
ejpam-6953	1	58	,	,	PUNCT
ejpam-6953	1	59	brandon	brandon	PROPN
ejpam-6953	1	60	university	university	PROPN
ejpam-6953	1	61	,	,	PUNCT
ejpam-6953	1	62	brandon	brandon	PROPN
ejpam-6953	1	63	,	,	PUNCT
ejpam-6953	1	64	manitoba	manitoba	PROPN
ejpam-6953	1	65	,	,	PUNCT
ejpam-6953	1	66	canada	canada	PROPN
ejpam-6953	1	67	abstract	abstract	NOUN
ejpam-6953	1	68	.	.	PUNCT
ejpam-6953	2	1	we	we	PRON
ejpam-6953	2	2	prove	prove	VERB
ejpam-6953	2	3	global	global	ADJ
ejpam-6953	2	4	weighted	weight	VERB
ejpam-6953	2	5	l2	l2	NOUN
ejpam-6953	2	6	solvability	solvability	NOUN
ejpam-6953	2	7	for	for	ADP
ejpam-6953	2	8	the	the	DET
ejpam-6953	2	9	∂̄-equation	∂̄-equation	NOUN
ejpam-6953	2	10	on	on	ADP
ejpam-6953	2	11	any	any	DET
ejpam-6953	2	12	connected	connected	ADJ
ejpam-6953	2	13	noncompact	noncompact	NOUN
ejpam-6953	2	14	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	2	15	complex	complex	ADJ
ejpam-6953	2	16	lie	lie	NOUN
ejpam-6953	2	17	group	group	NOUN
ejpam-6953	2	18	.	.	PUNCT
ejpam-6953	3	1	if	if	SCONJ
ejpam-6953	3	2	g	g	PROPN
ejpam-6953	3	3	is	be	AUX
ejpam-6953	3	4	a	a	DET
ejpam-6953	3	5	connected	connected	ADJ
ejpam-6953	3	6	noncompact	noncompact	NOUN
ejpam-6953	3	7	complex	complex	ADJ
ejpam-6953	3	8	lie	lie	NOUN
ejpam-6953	3	9	group	group	NOUN
ejpam-6953	3	10	admitting	admit	VERB
ejpam-6953	3	11	a	a	DET
ejpam-6953	3	12	continuous	continuous	ADJ
ejpam-6953	3	13	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	3	14	(	(	PUNCT
ejpam-6953	3	15	psh	psh	NOUN
ejpam-6953	3	16	)	)	PUNCT
ejpam-6953	3	17	exhaustion	exhaustion	NOUN
ejpam-6953	3	18	ρ	ρ	NOUN
ejpam-6953	3	19	,	,	PUNCT
ejpam-6953	3	20	then	then	ADV
ejpam-6953	3	21	for	for	ADP
ejpam-6953	3	22	every	every	DET
ejpam-6953	3	23	t	t	PROPN
ejpam-6953	3	24	≥	≥	NOUN
ejpam-6953	3	25	0	0	NUM
ejpam-6953	3	26	,	,	PUNCT
ejpam-6953	3	27	p	p	PRON
ejpam-6953	3	28	≥	≥	NOUN
ejpam-6953	3	29	0	0	NUM
ejpam-6953	3	30	and	and	CCONJ
ejpam-6953	3	31	q	q	ADJ
ejpam-6953	3	32	≥	≥	NUM
ejpam-6953	3	33	1	1	NUM
ejpam-6953	3	34	,	,	PUNCT
ejpam-6953	3	35	the	the	DET
ejpam-6953	3	36	weighted	weight	VERB
ejpam-6953	3	37	l2	l2	NOUN
ejpam-6953	3	38	dolbeault	dolbeault	VERB
ejpam-6953	3	39	cohomology	cohomology	NOUN
ejpam-6953	3	40	hp	hp	PROPN
ejpam-6953	3	41	,	,	PUNCT
ejpam-6953	3	42	q	q	NOUN
ejpam-6953	3	43	∂̄,(2),t	∂̄,(2),t	NOUN
ejpam-6953	3	44	(	(	PUNCT
ejpam-6953	3	45	g	g	NOUN
ejpam-6953	3	46	)	)	PUNCT
ejpam-6953	3	47	with	with	ADP
ejpam-6953	3	48	respect	respect	NOUN
ejpam-6953	3	49	to	to	ADP
ejpam-6953	3	50	the	the	DET
ejpam-6953	3	51	weight	weight	NOUN
ejpam-6953	3	52	e−tρ	e−tρ	NOUN
ejpam-6953	3	53	vanishes	vanish	VERB
ejpam-6953	3	54	,	,	PUNCT
ejpam-6953	3	55	and	and	CCONJ
ejpam-6953	3	56	one	one	NUM
ejpam-6953	3	57	has	have	VERB
ejpam-6953	3	58	a	a	DET
ejpam-6953	3	59	global	global	ADJ
ejpam-6953	3	60	a	a	DET
ejpam-6953	3	61	priori	priori	ADJ
ejpam-6953	3	62	estimate	estimate	NOUN
ejpam-6953	3	63	.	.	PUNCT
ejpam-6953	4	1	the	the	DET
ejpam-6953	4	2	argument	argument	NOUN
ejpam-6953	4	3	relies	rely	VERB
ejpam-6953	4	4	on	on	ADP
ejpam-6953	4	5	two	two	NUM
ejpam-6953	4	6	geometric	geometric	ADJ
ejpam-6953	4	7	uniformities	uniformity	NOUN
ejpam-6953	4	8	provided	provide	VERB
ejpam-6953	4	9	by	by	ADP
ejpam-6953	4	10	the	the	DET
ejpam-6953	4	11	lie	lie	NOUN
ejpam-6953	4	12	group	group	NOUN
ejpam-6953	4	13	structure	structure	NOUN
ejpam-6953	4	14	:	:	PUNCT
ejpam-6953	4	15	(	(	PUNCT
ejpam-6953	4	16	i	i	NOUN
ejpam-6953	4	17	)	)	PUNCT
ejpam-6953	4	18	a	a	DET
ejpam-6953	4	19	uniform	uniform	ADJ
ejpam-6953	4	20	exhaustion	exhaustion	NOUN
ejpam-6953	4	21	by	by	ADP
ejpam-6953	4	22	smoothly	smoothly	ADV
ejpam-6953	4	23	bounded	bound	VERB
ejpam-6953	4	24	strictly	strictly	ADV
ejpam-6953	4	25	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	4	26	domains	domain	NOUN
ejpam-6953	4	27	whose	whose	DET
ejpam-6953	4	28	defining	define	VERB
ejpam-6953	4	29	functions	function	NOUN
ejpam-6953	4	30	approximate	approximate	ADJ
ejpam-6953	4	31	ρ	ρ	PROPN
ejpam-6953	4	32	on	on	ADP
ejpam-6953	4	33	fixed	fix	VERB
ejpam-6953	4	34	sublevels	sublevel	NOUN
ejpam-6953	4	35	;	;	PUNCT
ejpam-6953	4	36	(	(	PUNCT
ejpam-6953	4	37	ii	ii	NOUN
ejpam-6953	4	38	)	)	PUNCT
ejpam-6953	4	39	strictly	strictly	ADV
ejpam-6953	4	40	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	4	41	reference	reference	NOUN
ejpam-6953	4	42	functions	function	NOUN
ejpam-6953	4	43	on	on	ADP
ejpam-6953	4	44	these	these	DET
ejpam-6953	4	45	domains	domain	NOUN
ejpam-6953	4	46	with	with	ADP
ejpam-6953	4	47	a	a	DET
ejpam-6953	4	48	levi	levi	PROPN
ejpam-6953	4	49	eigenvalue	eigenvalue	PROPN
ejpam-6953	4	50	lower	lower	ADV
ejpam-6953	4	51	bound	bind	VERB
ejpam-6953	4	52	independent	independent	NOUN
ejpam-6953	4	53	of	of	ADP
ejpam-6953	4	54	the	the	DET
ejpam-6953	4	55	exhaustion	exhaustion	NOUN
ejpam-6953	4	56	index	index	NOUN
ejpam-6953	4	57	.	.	PUNCT
ejpam-6953	5	1	these	these	PRON
ejpam-6953	5	2	enable	enable	ADJ
ejpam-6953	5	3	hörmander	hörmander	NOUN
ejpam-6953	5	4	-	-	PUNCT
ejpam-6953	5	5	type	type	NOUN
ejpam-6953	5	6	l2	l2	NOUN
ejpam-6953	5	7	estimates	estimate	NOUN
ejpam-6953	5	8	on	on	ADP
ejpam-6953	5	9	“	"	PUNCT
ejpam-6953	5	10	moving	move	VERB
ejpam-6953	5	11	”	"	PUNCT
ejpam-6953	5	12	domains	domain	NOUN
ejpam-6953	5	13	;	;	PUNCT
ejpam-6953	5	14	a	a	DET
ejpam-6953	5	15	mazur	mazur	PROPN
ejpam-6953	5	16	diagonal	diagonal	ADJ
ejpam-6953	5	17	convex	convex	NOUN
ejpam-6953	5	18	-	-	PUNCT
ejpam-6953	5	19	combination	combination	NOUN
ejpam-6953	5	20	argument	argument	NOUN
ejpam-6953	5	21	then	then	ADV
ejpam-6953	5	22	yields	yield	VERB
ejpam-6953	5	23	a	a	DET
ejpam-6953	5	24	single	single	ADJ
ejpam-6953	5	25	global	global	ADJ
ejpam-6953	5	26	solution	solution	NOUN
ejpam-6953	5	27	without	without	ADP
ejpam-6953	5	28	cut	cut	NOUN
ejpam-6953	5	29	-	-	PUNCT
ejpam-6953	5	30	offs	off	NOUN
ejpam-6953	5	31	.	.	PUNCT
ejpam-6953	6	1	consequences	consequence	NOUN
ejpam-6953	6	2	include	include	VERB
ejpam-6953	6	3	a	a	DET
ejpam-6953	6	4	hartogs	hartog	NOUN
ejpam-6953	6	5	-	-	PUNCT
ejpam-6953	6	6	type	type	NOUN
ejpam-6953	6	7	extension	extension	NOUN
ejpam-6953	6	8	theorem	theorem	VERB
ejpam-6953	6	9	under	under	ADP
ejpam-6953	6	10	weighted	weighted	ADJ
ejpam-6953	6	11	l2	l2	NOUN
ejpam-6953	6	12	growth	growth	NOUN
ejpam-6953	6	13	conditions	condition	NOUN
ejpam-6953	6	14	(	(	PUNCT
ejpam-6953	6	15	cf	cf	NOUN
ejpam-6953	6	16	.	.	PUNCT
ejpam-6953	7	1	[	[	X
ejpam-6953	7	2	1–4	1–4	NOUN
ejpam-6953	7	3	]	]	PUNCT
ejpam-6953	7	4	)	)	PUNCT
ejpam-6953	7	5	and	and	CCONJ
ejpam-6953	7	6	richness	richness	NOUN
ejpam-6953	7	7	of	of	ADP
ejpam-6953	7	8	weighted	weight	VERB
ejpam-6953	7	9	bergman	bergman	PROPN
ejpam-6953	7	10	spaces	space	VERB
ejpam-6953	7	11	on	on	ADP
ejpam-6953	7	12	strictly	strictly	ADV
ejpam-6953	7	13	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	7	14	sublevels	sublevel	NOUN
ejpam-6953	7	15	.	.	PUNCT
ejpam-6953	8	1	2020	2020	NUM
ejpam-6953	8	2	mathematics	mathematic	NOUN
ejpam-6953	8	3	subject	subject	NOUN
ejpam-6953	8	4	classifications	classification	NOUN
ejpam-6953	8	5	:	:	PUNCT
ejpam-6953	8	6	32w05	32w05	NUM
ejpam-6953	8	7	,	,	PUNCT
ejpam-6953	8	8	32m05	32m05	NUM
ejpam-6953	8	9	,	,	PUNCT
ejpam-6953	8	10	32f10	32f10	NUM
ejpam-6953	8	11	,	,	PUNCT
ejpam-6953	8	12	32e10	32e10	NUM
ejpam-6953	8	13	key	key	ADJ
ejpam-6953	8	14	words	word	NOUN
ejpam-6953	8	15	and	and	CCONJ
ejpam-6953	8	16	phrases	phrase	NOUN
ejpam-6953	8	17	:	:	PUNCT
ejpam-6953	8	18	complex	complex	ADJ
ejpam-6953	8	19	lie	lie	NOUN
ejpam-6953	8	20	groups	group	NOUN
ejpam-6953	8	21	,	,	PUNCT
ejpam-6953	8	22	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	8	23	(	(	PUNCT
ejpam-6953	8	24	weakly	weakly	ADJ
ejpam-6953	8	25	1	1	NUM
ejpam-6953	8	26	-	-	PUNCT
ejpam-6953	8	27	complete	complete	ADJ
ejpam-6953	8	28	)	)	PUNCT
ejpam-6953	8	29	manifolds	manifold	NOUN
ejpam-6953	8	30	,	,	PUNCT
ejpam-6953	8	31	∂̄-equation	∂̄-equation	NOUN
ejpam-6953	8	32	,	,	PUNCT
ejpam-6953	8	33	l2	l2	NOUN
ejpam-6953	8	34	dolbeault	dolbeault	VERB
ejpam-6953	8	35	cohomology	cohomology	NOUN
ejpam-6953	8	36	,	,	PUNCT
ejpam-6953	8	37	global	global	ADJ
ejpam-6953	8	38	solvability	solvability	NOUN
ejpam-6953	8	39	1	1	NUM
ejpam-6953	8	40	.	.	PUNCT
ejpam-6953	9	1	introduction	introduction	NOUN
ejpam-6953	9	2	let	let	VERB
ejpam-6953	9	3	g	g	PRON
ejpam-6953	9	4	be	be	AUX
ejpam-6953	9	5	a	a	DET
ejpam-6953	9	6	connected	connected	ADJ
ejpam-6953	9	7	noncompact	noncompact	NOUN
ejpam-6953	9	8	complex	complex	ADJ
ejpam-6953	9	9	lie	lie	NOUN
ejpam-6953	9	10	group	group	NOUN
ejpam-6953	9	11	.	.	PUNCT
ejpam-6953	10	1	global	global	ADJ
ejpam-6953	10	2	∂̄-solvability	∂̄-solvability	PROPN
ejpam-6953	10	3	on	on	ADP
ejpam-6953	10	4	noncompact	noncompact	NOUN
ejpam-6953	10	5	manifolds	manifold	NOUN
ejpam-6953	10	6	is	be	AUX
ejpam-6953	10	7	subtle	subtle	ADJ
ejpam-6953	10	8	:	:	PUNCT
ejpam-6953	10	9	while	while	SCONJ
ejpam-6953	10	10	the	the	DET
ejpam-6953	10	11	cartan	cartan	ADJ
ejpam-6953	10	12	–	–	PUNCT
ejpam-6953	10	13	serre	serre	X
ejpam-6953	10	14	vanishing	vanish	VERB
ejpam-6953	10	15	theorem	theorem	NOUN
ejpam-6953	10	16	gives	give	VERB
ejpam-6953	10	17	hp	hp	PROPN
ejpam-6953	10	18	,	,	PUNCT
ejpam-6953	10	19	q(x	q(x	PROPN
ejpam-6953	10	20	)	)	PUNCT
ejpam-6953	10	21	=	=	PUNCT
ejpam-6953	10	22	0	0	NUM
ejpam-6953	10	23	for	for	ADP
ejpam-6953	10	24	q	q	PROPN
ejpam-6953	10	25	≥	≥	NOUN
ejpam-6953	10	26	1	1	NUM
ejpam-6953	10	27	on	on	ADP
ejpam-6953	10	28	stein	stein	PROPN
ejpam-6953	10	29	manifolds	manifolds	PROPN
ejpam-6953	10	30	x	x	X
ejpam-6953	10	31	,	,	PUNCT
ejpam-6953	10	32	it	it	PRON
ejpam-6953	10	33	does	do	AUX
ejpam-6953	10	34	not	not	PART
ejpam-6953	10	35	by	by	ADP
ejpam-6953	10	36	itself	itself	PRON
ejpam-6953	10	37	furnish	furnish	VERB
ejpam-6953	10	38	a	a	DET
ejpam-6953	10	39	global	global	ADJ
ejpam-6953	10	40	l2	l2	NOUN
ejpam-6953	10	41	solution	solution	NOUN
ejpam-6953	10	42	operator	operator	NOUN
ejpam-6953	10	43	with	with	ADP
ejpam-6953	10	44	quantitative	quantitative	ADJ
ejpam-6953	10	45	control	control	NOUN
ejpam-6953	10	46	.	.	PUNCT
ejpam-6953	11	1	indeed	indeed	ADV
ejpam-6953	11	2	,	,	PUNCT
ejpam-6953	11	3	l2	l2	NOUN
ejpam-6953	11	4	dolbeault	dolbeault	NOUN
ejpam-6953	11	5	cohomology	cohomology	NOUN
ejpam-6953	11	6	can	can	AUX
ejpam-6953	11	7	be	be	AUX
ejpam-6953	11	8	highly	highly	ADV
ejpam-6953	11	9	nontrivial	nontrivial	ADJ
ejpam-6953	11	10	on	on	ADP
ejpam-6953	11	11	general	general	ADJ
ejpam-6953	11	12	noncompact	noncompact	NOUN
ejpam-6953	11	13	x	x	X
ejpam-6953	11	14	(	(	PUNCT
ejpam-6953	11	15	see	see	VERB
ejpam-6953	11	16	,	,	PUNCT
ejpam-6953	11	17	e.g.	e.g.	ADV
ejpam-6953	11	18	,	,	PUNCT
ejpam-6953	11	19	donnelly	donnelly	PROPN
ejpam-6953	11	20	–	–	PUNCT
ejpam-6953	11	21	fefferman	fefferman	NOUN
ejpam-6953	11	22	[	[	X
ejpam-6953	11	23	5	5	NUM
ejpam-6953	11	24	]	]	PUNCT
ejpam-6953	11	25	for	for	ADP
ejpam-6953	11	26	positive	positive	ADJ
ejpam-6953	11	27	results	result	NOUN
ejpam-6953	11	28	under	under	ADP
ejpam-6953	11	29	completeness	completeness	NOUN
ejpam-6953	11	30	or	or	CCONJ
ejpam-6953	11	31	curvature	curvature	NOUN
ejpam-6953	11	32	hypotheses	hypothesis	NOUN
ejpam-6953	11	33	)	)	PUNCT
ejpam-6953	11	34	.	.	PUNCT
ejpam-6953	12	1	in	in	ADP
ejpam-6953	12	2	this	this	DET
ejpam-6953	12	3	paper	paper	NOUN
ejpam-6953	12	4	we	we	PRON
ejpam-6953	12	5	assume	assume	VERB
ejpam-6953	12	6	a	a	DET
ejpam-6953	12	7	global	global	ADJ
ejpam-6953	12	8	exhaustivity	exhaustivity	NOUN
ejpam-6953	12	9	condition	condition	NOUN
ejpam-6953	12	10	in	in	ADP
ejpam-6953	12	11	place	place	NOUN
ejpam-6953	12	12	of	of	ADP
ejpam-6953	12	13	curvature	curvature	NOUN
ejpam-6953	12	14	:	:	PUNCT
ejpam-6953	12	15	namely	namely	ADV
ejpam-6953	12	16	,	,	PUNCT
ejpam-6953	12	17	that	that	SCONJ
ejpam-6953	12	18	g	g	PROPN
ejpam-6953	12	19	is	be	AUX
ejpam-6953	12	20	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	12	21	(	(	PUNCT
ejpam-6953	12	22	equivalently	equivalently	ADV
ejpam-6953	12	23	,	,	PUNCT
ejpam-6953	12	24	weakly	weakly	ADJ
ejpam-6953	12	25	1	1	NUM
ejpam-6953	12	26	-	-	PUNCT
ejpam-6953	12	27	complete	complete	ADJ
ejpam-6953	12	28	)	)	PUNCT
ejpam-6953	12	29	,	,	PUNCT
ejpam-6953	12	30	meaning	mean	VERB
ejpam-6953	12	31	there	there	PRON
ejpam-6953	12	32	exists	exist	VERB
ejpam-6953	12	33	a	a	DET
ejpam-6953	12	34	continuous	continuous	ADJ
ejpam-6953	12	35	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	12	36	exhaustion	exhaustion	NOUN
ejpam-6953	12	37	function	function	NOUN
ejpam-6953	12	38	ρ	ρ	NOUN
ejpam-6953	12	39	:	:	PUNCT
ejpam-6953	12	40	g	g	NOUN
ejpam-6953	12	41	→	→	SYM
ejpam-6953	12	42	[	[	X
ejpam-6953	12	43	0,∞	0,∞	NOUN
ejpam-6953	12	44	)	)	PUNCT
ejpam-6953	12	45	whose	whose	DET
ejpam-6953	12	46	sublevel	sublevel	NOUN
ejpam-6953	12	47	sets	set	NOUN
ejpam-6953	12	48	{	{	PUNCT
ejpam-6953	12	49	ρ	ρ	X
ejpam-6953	12	50	<	<	X
ejpam-6953	12	51	c	c	NOUN
ejpam-6953	12	52	}	}	PUNCT
ejpam-6953	12	53	are	be	AUX
ejpam-6953	12	54	all	all	PRON
ejpam-6953	12	55	relatively	relatively	ADV
ejpam-6953	12	56	compact	compact	ADJ
ejpam-6953	12	57	in	in	ADP
ejpam-6953	12	58	g	g	PROPN
ejpam-6953	12	59	(	(	PUNCT
ejpam-6953	12	60	on	on	ADP
ejpam-6953	12	61	a	a	DET
ejpam-6953	12	62	noncompact	noncompact	NOUN
ejpam-6953	12	63	x	x	NOUN
ejpam-6953	12	64	,	,	PUNCT
ejpam-6953	12	65	any	any	DET
ejpam-6953	12	66	such	such	ADJ
ejpam-6953	12	67	ρ	ρ	PROPN
ejpam-6953	12	68	is	be	AUX
ejpam-6953	12	69	doi	doi	NOUN
ejpam-6953	12	70	:	:	PUNCT
ejpam-6953	12	71	https://doi.org/10.29020/nybg.ejpam.v18i4.6953	https://doi.org/10.29020/nybg.ejpam.v18i4.6953	ADJ
ejpam-6953	12	72	email	email	NOUN
ejpam-6953	12	73	address	address	NOUN
ejpam-6953	12	74	:	:	PUNCT
ejpam-6953	12	75	al-abdallaha@brandonu.ca	al-abdallaha@brandonu.ca	NOUN
ejpam-6953	12	76	(	(	PUNCT
ejpam-6953	12	77	a.	a.	PROPN
ejpam-6953	12	78	r.	r.	PROPN
ejpam-6953	12	79	al	al	PROPN
ejpam-6953	12	80	-	-	PUNCT
ejpam-6953	12	81	abdallah	abdallah	PROPN
ejpam-6953	12	82	)	)	PUNCT
ejpam-6953	12	83	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6953	13	1	1	1	NUM
ejpam-6953	13	2	copyright	copyright	NOUN
ejpam-6953	13	3	:	:	PUNCT
ejpam-6953	13	4	©	©	PROPN
ejpam-6953	13	5	2025	2025	NUM
ejpam-6953	13	6	the	the	DET
ejpam-6953	13	7	author(s	author(s	NOUN
ejpam-6953	13	8	)	)	PUNCT
ejpam-6953	13	9	.	.	PUNCT
ejpam-6953	14	1	(	(	PUNCT
ejpam-6953	14	2	cc	cc	NOUN
ejpam-6953	14	3	by	by	ADP
ejpam-6953	14	4	-	-	PUNCT
ejpam-6953	14	5	nc	nc	PROPN
ejpam-6953	14	6	4.0	4.0	NUM
ejpam-6953	14	7	)	)	PUNCT
ejpam-6953	14	8	a.	a.	PROPN
ejpam-6953	14	9	r.	r.	PROPN
ejpam-6953	14	10	al	al	PROPN
ejpam-6953	14	11	-	-	PUNCT
ejpam-6953	14	12	abdallah	abdallah	PROPN
ejpam-6953	14	13	/	/	SYM
ejpam-6953	14	14	eur	eur	PROPN
ejpam-6953	14	15	.	.	PUNCT
ejpam-6953	15	1	j.	j.	PROPN
ejpam-6953	15	2	pure	pure	PROPN
ejpam-6953	15	3	appl	appl	PROPN
ejpam-6953	15	4	.	.	PROPN
ejpam-6953	15	5	math	math	PROPN
ejpam-6953	15	6	,	,	PUNCT
ejpam-6953	15	7	18	18	NUM
ejpam-6953	15	8	(	(	PUNCT
ejpam-6953	15	9	4	4	NUM
ejpam-6953	15	10	)	)	PUNCT
ejpam-6953	15	11	(	(	PUNCT
ejpam-6953	15	12	2025	2025	NUM
ejpam-6953	15	13	)	)	PUNCT
ejpam-6953	15	14	,	,	PUNCT
ejpam-6953	15	15	6953	6953	NUM
ejpam-6953	15	16	2	2	NUM
ejpam-6953	15	17	of	of	ADP
ejpam-6953	15	18	14	14	NUM
ejpam-6953	15	19	necessarily	necessarily	ADV
ejpam-6953	15	20	unbounded	unbounded	ADJ
ejpam-6953	15	21	and	and	CCONJ
ejpam-6953	15	22	proper	proper	ADJ
ejpam-6953	15	23	)	)	PUNCT
ejpam-6953	15	24	.	.	PUNCT
ejpam-6953	16	1	we	we	PRON
ejpam-6953	16	2	also	also	ADV
ejpam-6953	16	3	fix	fix	VERB
ejpam-6953	16	4	once	once	ADV
ejpam-6953	16	5	and	and	CCONJ
ejpam-6953	16	6	for	for	ADP
ejpam-6953	16	7	all	all	DET
ejpam-6953	16	8	a	a	DET
ejpam-6953	16	9	left	left	ADJ
ejpam-6953	16	10	-	-	PUNCT
ejpam-6953	16	11	invariant	invariant	ADJ
ejpam-6953	16	12	hermitian	hermitian	ADJ
ejpam-6953	16	13	metric	metric	PROPN
ejpam-6953	16	14	ω	ω	PROPN
ejpam-6953	16	15	on	on	ADP
ejpam-6953	16	16	g	g	NOUN
ejpam-6953	16	17	with	with	ADP
ejpam-6953	16	18	corresponding	correspond	VERB
ejpam-6953	16	19	volume	volume	NOUN
ejpam-6953	16	20	form	form	NOUN
ejpam-6953	16	21	dvω	dvω	PROPN
ejpam-6953	16	22	.	.	PUNCT
ejpam-6953	17	1	(	(	PUNCT
ejpam-6953	17	2	see	see	VERB
ejpam-6953	17	3	huckleberry	huckleberry	PROPN
ejpam-6953	17	4	[	[	X
ejpam-6953	17	5	6	6	NUM
ejpam-6953	17	6	]	]	PUNCT
ejpam-6953	17	7	for	for	ADP
ejpam-6953	17	8	background	background	NOUN
ejpam-6953	17	9	on	on	ADP
ejpam-6953	17	10	these	these	DET
ejpam-6953	17	11	notions	notion	NOUN
ejpam-6953	17	12	.	.	PUNCT
ejpam-6953	17	13	)	)	PUNCT
ejpam-6953	18	1	we	we	PRON
ejpam-6953	18	2	recall	recall	VERB
ejpam-6953	18	3	matsushima	matsushima	PROPN
ejpam-6953	18	4	’s	’s	PART
ejpam-6953	18	5	criterion	criterion	NOUN
ejpam-6953	18	6	that	that	SCONJ
ejpam-6953	18	7	a	a	DET
ejpam-6953	18	8	connected	connected	ADJ
ejpam-6953	18	9	complex	complex	ADJ
ejpam-6953	18	10	lie	lie	NOUN
ejpam-6953	18	11	group	group	NOUN
ejpam-6953	18	12	is	be	AUX
ejpam-6953	18	13	holomorphically	holomorphically	ADV
ejpam-6953	18	14	convex	convex	ADJ
ejpam-6953	18	15	(	(	PUNCT
ejpam-6953	18	16	stein	stein	PROPN
ejpam-6953	18	17	)	)	PUNCT
ejpam-6953	19	1	if	if	SCONJ
ejpam-6953	19	2	and	and	CCONJ
ejpam-6953	19	3	only	only	ADV
ejpam-6953	19	4	if	if	SCONJ
ejpam-6953	19	5	it	it	PRON
ejpam-6953	19	6	has	have	VERB
ejpam-6953	19	7	no	no	DET
ejpam-6953	19	8	nontrivial	nontrivial	ADJ
ejpam-6953	19	9	compact	compact	ADJ
ejpam-6953	19	10	complex	complex	ADJ
ejpam-6953	19	11	subgroups	subgroup	NOUN
ejpam-6953	19	12	[	[	X
ejpam-6953	19	13	7	7	NUM
ejpam-6953	19	14	]	]	PUNCT
ejpam-6953	19	15	.	.	PUNCT
ejpam-6953	20	1	(	(	PUNCT
ejpam-6953	20	2	for	for	ADP
ejpam-6953	20	3	further	further	ADJ
ejpam-6953	20	4	classification	classification	NOUN
ejpam-6953	20	5	results	result	NOUN
ejpam-6953	20	6	on	on	ADP
ejpam-6953	20	7	complex	complex	ADJ
ejpam-6953	20	8	homogeneous	homogeneous	ADJ
ejpam-6953	20	9	manifolds	manifold	NOUN
ejpam-6953	20	10	,	,	PUNCT
ejpam-6953	20	11	see	see	VERB
ejpam-6953	20	12	[	[	X
ejpam-6953	20	13	8	8	NUM
ejpam-6953	20	14	,	,	PUNCT
ejpam-6953	20	15	9	9	NUM
ejpam-6953	20	16	]	]	PUNCT
ejpam-6953	20	17	.	.	PUNCT
ejpam-6953	20	18	)	)	PUNCT
ejpam-6953	21	1	in	in	ADP
ejpam-6953	21	2	general	general	ADJ
ejpam-6953	21	3	,	,	PUNCT
ejpam-6953	21	4	however	however	ADV
ejpam-6953	21	5	,	,	PUNCT
ejpam-6953	21	6	even	even	ADV
ejpam-6953	21	7	a	a	DET
ejpam-6953	21	8	non	non	ADJ
ejpam-6953	21	9	-	-	ADJ
ejpam-6953	21	10	stein	stein	ADJ
ejpam-6953	21	11	complex	complex	ADJ
ejpam-6953	21	12	lie	lie	NOUN
ejpam-6953	21	13	group	group	NOUN
ejpam-6953	21	14	admits	admit	VERB
ejpam-6953	21	15	a	a	DET
ejpam-6953	21	16	psh	psh	NOUN
ejpam-6953	21	17	exhaustion	exhaustion	NOUN
ejpam-6953	21	18	.	.	PUNCT
ejpam-6953	22	1	in	in	ADP
ejpam-6953	22	2	fact	fact	NOUN
ejpam-6953	22	3	,	,	PUNCT
ejpam-6953	22	4	kazama	kazama	PROPN
ejpam-6953	22	5	showed	show	VERB
ejpam-6953	22	6	that	that	SCONJ
ejpam-6953	22	7	every	every	DET
ejpam-6953	22	8	complex	complex	ADJ
ejpam-6953	22	9	abelian	abelian	ADJ
ejpam-6953	22	10	lie	lie	NOUN
ejpam-6953	22	11	group	group	NOUN
ejpam-6953	22	12	is	be	AUX
ejpam-6953	22	13	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	22	14	(	(	PUNCT
ejpam-6953	22	15	weakly	weakly	ADJ
ejpam-6953	22	16	1	1	NUM
ejpam-6953	22	17	-	-	PUNCT
ejpam-6953	22	18	complete	complete	ADJ
ejpam-6953	22	19	)	)	PUNCT
ejpam-6953	23	1	[	[	X
ejpam-6953	23	2	10	10	NUM
ejpam-6953	23	3	]	]	PUNCT
ejpam-6953	23	4	.	.	PUNCT
ejpam-6953	24	1	thus	thus	ADV
ejpam-6953	24	2	all	all	DET
ejpam-6953	24	3	complex	complex	ADJ
ejpam-6953	24	4	tori	tori	NOUN
ejpam-6953	24	5	and	and	CCONJ
ejpam-6953	24	6	cousin	cousin	NOUN
ejpam-6953	24	7	groups	group	NOUN
ejpam-6953	24	8	(	(	PUNCT
ejpam-6953	24	9	quotients	quotient	NOUN
ejpam-6953	24	10	of	of	ADP
ejpam-6953	24	11	cn	cn	VERB
ejpam-6953	24	12	by	by	ADP
ejpam-6953	24	13	discrete	discrete	ADJ
ejpam-6953	24	14	subgroups	subgroup	NOUN
ejpam-6953	24	15	)	)	PUNCT
ejpam-6953	24	16	are	be	AUX
ejpam-6953	24	17	examples	example	NOUN
ejpam-6953	24	18	of	of	ADP
ejpam-6953	24	19	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	24	20	complex	complex	ADJ
ejpam-6953	24	21	lie	lie	NOUN
ejpam-6953	24	22	groups	group	NOUN
ejpam-6953	24	23	which	which	PRON
ejpam-6953	24	24	are	be	AUX
ejpam-6953	24	25	not	not	PART
ejpam-6953	24	26	stein	stein	PROPN
ejpam-6953	24	27	.	.	PUNCT
ejpam-6953	25	1	our	our	PRON
ejpam-6953	25	2	results	result	NOUN
ejpam-6953	25	3	below	below	ADV
ejpam-6953	25	4	therefore	therefore	ADV
ejpam-6953	25	5	apply	apply	VERB
ejpam-6953	25	6	to	to	ADP
ejpam-6953	25	7	a	a	DET
ejpam-6953	25	8	broad	broad	ADJ
ejpam-6953	25	9	class	class	NOUN
ejpam-6953	25	10	of	of	ADP
ejpam-6953	25	11	complex	complex	ADJ
ejpam-6953	25	12	manifolds	manifold	NOUN
ejpam-6953	25	13	beyond	beyond	ADP
ejpam-6953	25	14	the	the	DET
ejpam-6953	25	15	stein	stein	PROPN
ejpam-6953	25	16	case	case	NOUN
ejpam-6953	25	17	.	.	PUNCT
ejpam-6953	26	1	for	for	ADP
ejpam-6953	26	2	t	t	PROPN
ejpam-6953	26	3	∈	∈	PROPN
ejpam-6953	26	4	r	r	NOUN
ejpam-6953	26	5	and	and	CCONJ
ejpam-6953	26	6	bidegree	bidegree	PROPN
ejpam-6953	26	7	(	(	PUNCT
ejpam-6953	26	8	p	p	X
ejpam-6953	26	9	,	,	PUNCT
ejpam-6953	26	10	q	q	NOUN
ejpam-6953	26	11	)	)	PUNCT
ejpam-6953	26	12	,	,	PUNCT
ejpam-6953	26	13	we	we	PRON
ejpam-6953	26	14	denote	denote	VERB
ejpam-6953	26	15	by	by	ADP
ejpam-6953	26	16	l2	l2	NOUN
ejpam-6953	26	17	p	p	PRON
ejpam-6953	26	18	,	,	PUNCT
ejpam-6953	26	19	q(g	q(g	PROPN
ejpam-6953	26	20	,	,	PUNCT
ejpam-6953	26	21	e	e	PROPN
ejpam-6953	26	22	−tρ	−tρ	PROPN
ejpam-6953	26	23	)	)	PUNCT
ejpam-6953	26	24	the	the	DET
ejpam-6953	26	25	hilbert	hilbert	PROPN
ejpam-6953	26	26	space	space	NOUN
ejpam-6953	26	27	of	of	ADP
ejpam-6953	26	28	(	(	PUNCT
ejpam-6953	26	29	p	p	X
ejpam-6953	26	30	,	,	PUNCT
ejpam-6953	26	31	q)forms	q)form	NOUN
ejpam-6953	26	32	α	α	NOUN
ejpam-6953	26	33	on	on	ADP
ejpam-6953	26	34	g	g	PROPN
ejpam-6953	26	35	with	with	ADP
ejpam-6953	26	36	finite	finite	PROPN
ejpam-6953	26	37	weighted	weight	VERB
ejpam-6953	26	38	l2	l2	NOUN
ejpam-6953	26	39	-	-	PUNCT
ejpam-6953	26	40	norm	norm	NOUN
ejpam-6953	26	41	∥α∥2	∥α∥2	PROPN
ejpam-6953	26	42	t	t	PROPN
ejpam-6953	26	43	:	:	PUNCT
ejpam-6953	26	44	=	=	SYM
ejpam-6953	26	45	∫	∫	PROPN
ejpam-6953	26	46	g	g	PROPN
ejpam-6953	26	47	|α|2	|α|2	NOUN
ejpam-6953	26	48	e−tρ	e−tρ	NOUN
ejpam-6953	26	49	dvω	dvω	VERB
ejpam-6953	26	50	<	<	X
ejpam-6953	26	51	∞	∞	PROPN
ejpam-6953	26	52	.	.	PUNCT
ejpam-6953	27	1	we	we	PRON
ejpam-6953	27	2	take	take	VERB
ejpam-6953	27	3	∂̄	∂̄	NOUN
ejpam-6953	27	4	to	to	PART
ejpam-6953	27	5	be	be	AUX
ejpam-6953	27	6	the	the	DET
ejpam-6953	27	7	maximal	maximal	ADJ
ejpam-6953	27	8	closed	closed	ADJ
ejpam-6953	27	9	extension	extension	NOUN
ejpam-6953	27	10	of	of	ADP
ejpam-6953	27	11	the	the	DET
ejpam-6953	27	12	dolbeault	dolbeault	NOUN
ejpam-6953	27	13	operator	operator	NOUN
ejpam-6953	27	14	acting	act	VERB
ejpam-6953	27	15	on	on	ADP
ejpam-6953	27	16	l2	l2	NOUN
ejpam-6953	27	17	p,•(g	p,•(g	NOUN
ejpam-6953	27	18	,	,	PUNCT
ejpam-6953	27	19	e	e	PROPN
ejpam-6953	27	20	−tρ	−tρ	PROPN
ejpam-6953	27	21	)	)	PUNCT
ejpam-6953	27	22	.	.	PUNCT
ejpam-6953	28	1	that	that	PRON
ejpam-6953	28	2	is	be	AUX
ejpam-6953	28	3	,	,	PUNCT
ejpam-6953	28	4	dom(∂̄	dom(∂̄	NOUN
ejpam-6953	28	5	)	)	PUNCT
ejpam-6953	28	6	:	:	PUNCT
ejpam-6953	29	1	=	=	SYM
ejpam-6953	29	2	{	{	PUNCT
ejpam-6953	29	3	α	α	NOUN
ejpam-6953	29	4	∈	∈	PROPN
ejpam-6953	29	5	l2	l2	NOUN
ejpam-6953	29	6	p	p	NOUN
ejpam-6953	29	7	,	,	PUNCT
ejpam-6953	29	8	q(g	q(g	PROPN
ejpam-6953	29	9	,	,	PUNCT
ejpam-6953	29	10	e	e	PROPN
ejpam-6953	29	11	−tρ	−tρ	PROPN
ejpam-6953	29	12	)	)	PUNCT
ejpam-6953	29	13	:	:	PUNCT
ejpam-6953	29	14	∂̄α	∂̄α	NOUN
ejpam-6953	29	15	(	(	PUNCT
ejpam-6953	29	16	in	in	ADP
ejpam-6953	29	17	the	the	DET
ejpam-6953	29	18	sense	sense	NOUN
ejpam-6953	29	19	of	of	ADP
ejpam-6953	29	20	distributions	distribution	NOUN
ejpam-6953	29	21	)	)	PUNCT
ejpam-6953	29	22	lies	lie	VERB
ejpam-6953	29	23	in	in	ADP
ejpam-6953	29	24	l2	l2	NOUN
ejpam-6953	29	25	p	p	NOUN
ejpam-6953	29	26	,	,	PUNCT
ejpam-6953	29	27	q+1(g	q+1(g	PROPN
ejpam-6953	29	28	,	,	PUNCT
ejpam-6953	29	29	e	e	PROPN
ejpam-6953	29	30	−tρ	−tρ	PROPN
ejpam-6953	29	31	)	)	PUNCT
ejpam-6953	29	32	}	}	PUNCT
ejpam-6953	29	33	,	,	PUNCT
ejpam-6953	29	34	and	and	CCONJ
ejpam-6953	29	35	we	we	PRON
ejpam-6953	29	36	define	define	VERB
ejpam-6953	29	37	the	the	DET
ejpam-6953	29	38	corresponding	correspond	VERB
ejpam-6953	29	39	weighted	weight	VERB
ejpam-6953	29	40	l2	l2	NOUN
ejpam-6953	29	41	dolbeault	dolbeault	VERB
ejpam-6953	29	42	cohomology	cohomology	NOUN
ejpam-6953	29	43	group	group	NOUN
ejpam-6953	29	44	by	by	ADP
ejpam-6953	29	45	hp	hp	PROPN
ejpam-6953	29	46	,	,	PUNCT
ejpam-6953	29	47	q	q	NOUN
ejpam-6953	29	48	∂̄,(2),t	∂̄,(2),t	NOUN
ejpam-6953	29	49	(	(	PUNCT
ejpam-6953	29	50	g	g	NOUN
ejpam-6953	29	51	)	)	PUNCT
ejpam-6953	29	52	:	:	PUNCT
ejpam-6953	29	53	=	=	PUNCT
ejpam-6953	29	54	ker(∂̄	ker(∂̄	NOUN
ejpam-6953	29	55	:	:	PUNCT
ejpam-6953	29	56	l2	l2	NOUN
ejpam-6953	29	57	p	p	NOUN
ejpam-6953	29	58	,	,	PUNCT
ejpam-6953	29	59	q(g	q(g	PROPN
ejpam-6953	29	60	,	,	PUNCT
ejpam-6953	29	61	e	e	PROPN
ejpam-6953	29	62	−tρ	−tρ	PROPN
ejpam-6953	29	63	)	)	PUNCT
ejpam-6953	29	64	→	→	SYM
ejpam-6953	29	65	l2	l2	NOUN
ejpam-6953	29	66	p	p	NOUN
ejpam-6953	29	67	,	,	PUNCT
ejpam-6953	29	68	q+1(g	q+1(g	PROPN
ejpam-6953	29	69	,	,	PUNCT
ejpam-6953	29	70	e	e	PROPN
ejpam-6953	29	71	−tρ	−tρ	PROPN
ejpam-6953	29	72	)	)	PUNCT
ejpam-6953	29	73	)	)	PUNCT
ejpam-6953	29	74	ℑ(∂̄	ℑ(∂̄	NOUN
ejpam-6953	29	75	:	:	PUNCT
ejpam-6953	29	76	l2	l2	NOUN
ejpam-6953	29	77	p	p	PRON
ejpam-6953	29	78	,	,	PUNCT
ejpam-6953	29	79	q−1(g	q−1(g	PROPN
ejpam-6953	29	80	,	,	PUNCT
ejpam-6953	29	81	e	e	PROPN
ejpam-6953	29	82	−tρ	−tρ	PROPN
ejpam-6953	29	83	)	)	PUNCT
ejpam-6953	29	84	→	→	SYM
ejpam-6953	29	85	l2	l2	NOUN
ejpam-6953	29	86	p	p	NOUN
ejpam-6953	29	87	,	,	PUNCT
ejpam-6953	29	88	q(g	q(g	PROPN
ejpam-6953	29	89	,	,	PUNCT
ejpam-6953	29	90	e	e	PROPN
ejpam-6953	29	91	−tρ	−tρ	PROPN
ejpam-6953	29	92	)	)	PUNCT
ejpam-6953	29	93	)	)	PUNCT
ejpam-6953	29	94	.	.	PUNCT
ejpam-6953	30	1	our	our	PRON
ejpam-6953	30	2	main	main	ADJ
ejpam-6953	30	3	result	result	NOUN
ejpam-6953	30	4	is	be	AUX
ejpam-6953	30	5	as	as	SCONJ
ejpam-6953	30	6	follows	follow	VERB
ejpam-6953	30	7	:	:	PUNCT
ejpam-6953	30	8	theorem	theorem	NOUN
ejpam-6953	30	9	1	1	NUM
ejpam-6953	30	10	(	(	PUNCT
ejpam-6953	30	11	main	main	ADJ
ejpam-6953	30	12	theorem	theorem	NOUN
ejpam-6953	30	13	)	)	PUNCT
ejpam-6953	30	14	.	.	PUNCT
ejpam-6953	31	1	let	let	VERB
ejpam-6953	31	2	g	g	PRON
ejpam-6953	31	3	be	be	AUX
ejpam-6953	31	4	a	a	DET
ejpam-6953	31	5	connected	connected	ADJ
ejpam-6953	31	6	noncompact	noncompact	NOUN
ejpam-6953	31	7	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	31	8	complex	complex	ADJ
ejpam-6953	31	9	lie	lie	NOUN
ejpam-6953	31	10	group	group	NOUN
ejpam-6953	31	11	with	with	ADP
ejpam-6953	31	12	a	a	DET
ejpam-6953	31	13	fixed	fix	VERB
ejpam-6953	31	14	continuous	continuous	ADJ
ejpam-6953	31	15	psh	psh	NOUN
ejpam-6953	31	16	exhaustion	exhaustion	NOUN
ejpam-6953	31	17	ρ	ρ	NOUN
ejpam-6953	31	18	.	.	PUNCT
ejpam-6953	32	1	then	then	ADV
ejpam-6953	32	2	for	for	ADP
ejpam-6953	32	3	every	every	DET
ejpam-6953	32	4	t	t	PROPN
ejpam-6953	32	5	≥	≥	NOUN
ejpam-6953	32	6	0	0	NUM
ejpam-6953	32	7	,	,	PUNCT
ejpam-6953	32	8	p	p	PRON
ejpam-6953	32	9	≥	≥	NOUN
ejpam-6953	32	10	0	0	NUM
ejpam-6953	32	11	,	,	PUNCT
ejpam-6953	32	12	and	and	CCONJ
ejpam-6953	32	13	q	q	PRON
ejpam-6953	32	14	≥	≥	NUM
ejpam-6953	32	15	1	1	NUM
ejpam-6953	32	16	,	,	PUNCT
ejpam-6953	32	17	every	every	DET
ejpam-6953	32	18	∂̄-closed	∂̄-close	VERB
ejpam-6953	32	19	form	form	NOUN
ejpam-6953	32	20	f	f	PROPN
ejpam-6953	32	21	∈	∈	PROPN
ejpam-6953	32	22	l2	l2	NOUN
ejpam-6953	32	23	p	p	NOUN
ejpam-6953	32	24	,	,	PUNCT
ejpam-6953	32	25	q(g	q(g	PROPN
ejpam-6953	32	26	,	,	PUNCT
ejpam-6953	32	27	e	e	PROPN
ejpam-6953	32	28	−tρ	−tρ	PROPN
ejpam-6953	32	29	)	)	PUNCT
ejpam-6953	32	30	admits	admit	VERB
ejpam-6953	32	31	a	a	DET
ejpam-6953	32	32	solution	solution	NOUN
ejpam-6953	32	33	u	u	NOUN
ejpam-6953	32	34	∈	∈	NOUN
ejpam-6953	32	35	l2	l2	NOUN
ejpam-6953	32	36	p	p	NOUN
ejpam-6953	32	37	,	,	PUNCT
ejpam-6953	32	38	q−1(g	q−1(g	PROPN
ejpam-6953	32	39	,	,	PUNCT
ejpam-6953	32	40	e	e	PROPN
ejpam-6953	32	41	−tρ	−tρ	PROPN
ejpam-6953	32	42	)	)	PUNCT
ejpam-6953	32	43	to	to	ADP
ejpam-6953	32	44	∂̄u	∂̄u	PROPN
ejpam-6953	32	45	=	=	SYM
ejpam-6953	32	46	f	f	PROPN
ejpam-6953	32	47	.	.	PUNCT
ejpam-6953	33	1	equivalently	equivalently	ADV
ejpam-6953	33	2	,	,	PUNCT
ejpam-6953	33	3	hp	hp	PROPN
ejpam-6953	33	4	,	,	PUNCT
ejpam-6953	33	5	q	q	NOUN
ejpam-6953	33	6	∂̄,(2),t	∂̄,(2),t	NOUN
ejpam-6953	33	7	(	(	PUNCT
ejpam-6953	33	8	g	g	NOUN
ejpam-6953	33	9	)	)	PUNCT
ejpam-6953	33	10	=	=	SYM
ejpam-6953	33	11	0	0	NUM
ejpam-6953	33	12	for	for	ADP
ejpam-6953	33	13	all	all	DET
ejpam-6953	33	14	q	q	PRON
ejpam-6953	33	15	≥	≥	NUM
ejpam-6953	33	16	1	1	NUM
ejpam-6953	33	17	.	.	PUNCT
ejpam-6953	34	1	moreover	moreover	ADV
ejpam-6953	34	2	,	,	PUNCT
ejpam-6953	34	3	∂̄	∂̄	ADV
ejpam-6953	34	4	:	:	PUNCT
ejpam-6953	34	5	l2	l2	VERB
ejpam-6953	34	6	p	p	PRON
ejpam-6953	34	7	,	,	PUNCT
ejpam-6953	34	8	q−1(g	q−1(g	PROPN
ejpam-6953	34	9	,	,	PUNCT
ejpam-6953	34	10	e	e	PROPN
ejpam-6953	34	11	−tρ	−tρ	PROPN
ejpam-6953	34	12	)	)	PUNCT
ejpam-6953	34	13	→	→	SYM
ejpam-6953	34	14	l2	l2	NOUN
ejpam-6953	34	15	p	p	NOUN
ejpam-6953	34	16	,	,	PUNCT
ejpam-6953	34	17	q(g	q(g	PROPN
ejpam-6953	34	18	,	,	PUNCT
ejpam-6953	34	19	e	e	PROPN
ejpam-6953	34	20	−tρ	−tρ	PROPN
ejpam-6953	34	21	)	)	PUNCT
ejpam-6953	34	22	has	have	AUX
ejpam-6953	34	23	closed	close	VERB
ejpam-6953	34	24	range	range	NOUN
ejpam-6953	34	25	,	,	PUNCT
ejpam-6953	34	26	and	and	CCONJ
ejpam-6953	34	27	there	there	PRON
ejpam-6953	34	28	exists	exist	VERB
ejpam-6953	34	29	a	a	DET
ejpam-6953	34	30	constant	constant	ADJ
ejpam-6953	34	31	c(t	c(t	NOUN
ejpam-6953	34	32	)	)	PUNCT
ejpam-6953	34	33	such	such	ADJ
ejpam-6953	34	34	that	that	PRON
ejpam-6953	34	35	for	for	ADP
ejpam-6953	34	36	all	all	DET
ejpam-6953	34	37	such	such	ADJ
ejpam-6953	34	38	f	f	NOUN
ejpam-6953	34	39	and	and	CCONJ
ejpam-6953	34	40	corresponding	corresponding	ADJ
ejpam-6953	34	41	solution	solution	NOUN
ejpam-6953	34	42	u	u	NOUN
ejpam-6953	34	43	we	we	PRON
ejpam-6953	34	44	have	have	VERB
ejpam-6953	34	45	the	the	DET
ejpam-6953	34	46	global	global	ADJ
ejpam-6953	34	47	estimate∫	estimate∫	PROPN
ejpam-6953	34	48	g	g	PROPN
ejpam-6953	34	49	|u|2	|u|2	PROPN
ejpam-6953	34	50	e−tρ	e−tρ	PROPN
ejpam-6953	34	51	dvω	dvω	PROPN
ejpam-6953	34	52	≤	≤	PROPN
ejpam-6953	34	53	c(t	c(t	PROPN
ejpam-6953	34	54	)	)	PUNCT
ejpam-6953	34	55	∫	∫	PROPN
ejpam-6953	34	56	g	g	PROPN
ejpam-6953	34	57	|f	|f	PROPN
ejpam-6953	34	58	|2	|2	NUM
ejpam-6953	34	59	e−tρ	e−tρ	NOUN
ejpam-6953	34	60	dvω	dvω	PROPN
ejpam-6953	34	61	.	.	PUNCT
ejpam-6953	35	1	(	(	PUNCT
ejpam-6953	35	2	1	1	X
ejpam-6953	35	3	)	)	PUNCT
ejpam-6953	35	4	in	in	ADP
ejpam-6953	35	5	fact	fact	NOUN
ejpam-6953	35	6	,	,	PUNCT
ejpam-6953	35	7	one	one	PRON
ejpam-6953	35	8	can	can	AUX
ejpam-6953	35	9	take	take	VERB
ejpam-6953	35	10	c(t	c(t	NOUN
ejpam-6953	35	11	)	)	PUNCT
ejpam-6953	35	12	=	=	SYM
ejpam-6953	35	13	exp	exp	NOUN
ejpam-6953	35	14	(	(	PUNCT
ejpam-6953	35	15	t	t	PROPN
ejpam-6953	35	16	2	2	NUM
ejpam-6953	35	17	+	+	CCONJ
ejpam-6953	35	18	ε∗s∗	ε∗s∗	X
ejpam-6953	35	19	)	)	PUNCT
ejpam-6953	35	20	,	,	PUNCT
ejpam-6953	35	21	with	with	ADP
ejpam-6953	35	22	explicit	explicit	ADJ
ejpam-6953	35	23	geometric	geometric	ADJ
ejpam-6953	35	24	constants	constant	NOUN
ejpam-6953	35	25	ε∗	ε∗	PROPN
ejpam-6953	35	26	,	,	PUNCT
ejpam-6953	35	27	s∗	s∗	PROPN
ejpam-6953	35	28	>	>	X
ejpam-6953	35	29	0	0	PUNCT
ejpam-6953	36	1	depending	depend	VERB
ejpam-6953	36	2	only	only	ADV
ejpam-6953	36	3	on	on	ADP
ejpam-6953	36	4	(	(	PUNCT
ejpam-6953	36	5	g	g	PROPN
ejpam-6953	36	6	,	,	PUNCT
ejpam-6953	36	7	ω	ω	NOUN
ejpam-6953	36	8	)	)	PUNCT
ejpam-6953	36	9	.	.	PUNCT
ejpam-6953	37	1	the	the	DET
ejpam-6953	37	2	inequality	inequality	NOUN
ejpam-6953	37	3	(	(	PUNCT
ejpam-6953	37	4	1	1	NUM
ejpam-6953	37	5	)	)	PUNCT
ejpam-6953	37	6	is	be	AUX
ejpam-6953	37	7	a	a	DET
ejpam-6953	37	8	global	global	ADJ
ejpam-6953	37	9	l2	l2	NOUN
ejpam-6953	37	10	-	-	PUNCT
ejpam-6953	37	11	estimate	estimate	NOUN
ejpam-6953	37	12	guaranteeing	guarantee	VERB
ejpam-6953	37	13	a	a	DET
ejpam-6953	37	14	bounded	bounded	ADJ
ejpam-6953	37	15	solution	solution	NOUN
ejpam-6953	37	16	operator	operator	NOUN
ejpam-6953	37	17	for	for	ADP
ejpam-6953	37	18	∂̄.	∂̄.	X
ejpam-6953	37	19	here	here	ADV
ejpam-6953	37	20	ε∗	ε∗	PROPN
ejpam-6953	37	21	=	=	SYM
ejpam-6953	37	22	1	1	NUM
ejpam-6953	37	23	/	/	SYM
ejpam-6953	37	24	c∗	c∗	NOUN
ejpam-6953	37	25	and	and	CCONJ
ejpam-6953	37	26	s∗	s∗	PROPN
ejpam-6953	37	27	arise	arise	VERB
ejpam-6953	37	28	from	from	ADP
ejpam-6953	37	29	the	the	DET
ejpam-6953	37	30	construction	construction	NOUN
ejpam-6953	37	31	in	in	ADP
ejpam-6953	37	32	sections	section	NOUN
ejpam-6953	37	33	3–4	3–4	NUM
ejpam-6953	37	34	below	below	ADV
ejpam-6953	37	35	.	.	PUNCT
ejpam-6953	38	1	for	for	ADP
ejpam-6953	38	2	example	example	NOUN
ejpam-6953	38	3	,	,	PUNCT
ejpam-6953	38	4	in	in	ADP
ejpam-6953	38	5	real	real	ADJ
ejpam-6953	38	6	dimension	dimension	NOUN
ejpam-6953	38	7	4	4	NUM
ejpam-6953	38	8	(	(	PUNCT
ejpam-6953	38	9	complex	complex	ADJ
ejpam-6953	38	10	dimension	dimension	NOUN
ejpam-6953	38	11	2	2	NUM
ejpam-6953	38	12	)	)	PUNCT
ejpam-6953	38	13	one	one	NOUN
ejpam-6953	38	14	can	can	AUX
ejpam-6953	38	15	cover	cover	VERB
ejpam-6953	38	16	g	g	NOUN
ejpam-6953	38	17	by	by	ADP
ejpam-6953	38	18	at	at	ADP
ejpam-6953	38	19	most	most	ADV
ejpam-6953	38	20	54	54	NUM
ejpam-6953	38	21	=	=	SYM
ejpam-6953	38	22	625	625	NUM
ejpam-6953	38	23	translated	translate	VERB
ejpam-6953	38	24	metric	metric	ADJ
ejpam-6953	38	25	balls	ball	NOUN
ejpam-6953	38	26	(	(	PUNCT
ejpam-6953	38	27	by	by	ADP
ejpam-6953	38	28	the	the	DET
ejpam-6953	38	29	besicovitch	besicovitch	PROPN
ejpam-6953	38	30	covering	covering	NOUN
ejpam-6953	38	31	theorem	theorem	VERB
ejpam-6953	38	32	,	,	PUNCT
ejpam-6953	38	33	see	see	VERB
ejpam-6953	39	1	e.g.	e.g.	ADV
ejpam-6953	39	2	[	[	X
ejpam-6953	39	3	11	11	NUM
ejpam-6953	39	4	,	,	PUNCT
ejpam-6953	39	5	12	12	NUM
ejpam-6953	39	6	]	]	PUNCT
ejpam-6953	39	7	)	)	PUNCT
ejpam-6953	39	8	.	.	PUNCT
ejpam-6953	40	1	hence	hence	ADV
ejpam-6953	40	2	one	one	NUM
ejpam-6953	40	3	a.	a.	NOUN
ejpam-6953	40	4	r.	r.	PROPN
ejpam-6953	40	5	al	al	PROPN
ejpam-6953	40	6	-	-	PUNCT
ejpam-6953	40	7	abdallah	abdallah	PROPN
ejpam-6953	40	8	/	/	SYM
ejpam-6953	40	9	eur	eur	PROPN
ejpam-6953	40	10	.	.	PUNCT
ejpam-6953	41	1	j.	j.	PROPN
ejpam-6953	41	2	pure	pure	PROPN
ejpam-6953	41	3	appl	appl	PROPN
ejpam-6953	41	4	.	.	PROPN
ejpam-6953	41	5	math	math	PROPN
ejpam-6953	41	6	,	,	PUNCT
ejpam-6953	41	7	18	18	NUM
ejpam-6953	41	8	(	(	PUNCT
ejpam-6953	41	9	4	4	NUM
ejpam-6953	41	10	)	)	PUNCT
ejpam-6953	41	11	(	(	PUNCT
ejpam-6953	41	12	2025	2025	NUM
ejpam-6953	41	13	)	)	PUNCT
ejpam-6953	41	14	,	,	PUNCT
ejpam-6953	41	15	6953	6953	NUM
ejpam-6953	41	16	3	3	NUM
ejpam-6953	41	17	of	of	ADP
ejpam-6953	41	18	14	14	NUM
ejpam-6953	41	19	may	may	AUX
ejpam-6953	41	20	take	take	VERB
ejpam-6953	41	21	ε∗	ε∗	ADV
ejpam-6953	41	22	=	=	SYM
ejpam-6953	41	23	c	c	X
ejpam-6953	41	24	/	/	SYM
ejpam-6953	41	25	λ	λ	NOUN
ejpam-6953	41	26	=	=	NOUN
ejpam-6953	41	27	625	625	NUM
ejpam-6953	41	28	/	/	SYM
ejpam-6953	41	29	λ	λ	NOUN
ejpam-6953	41	30	in	in	ADP
ejpam-6953	41	31	terms	term	NOUN
ejpam-6953	41	32	of	of	ADP
ejpam-6953	41	33	the	the	DET
ejpam-6953	41	34	besicovitch	besicovitch	ADJ
ejpam-6953	41	35	overlap	overlap	NOUN
ejpam-6953	41	36	constant	constant	ADJ
ejpam-6953	41	37	and	and	CCONJ
ejpam-6953	41	38	the	the	DET
ejpam-6953	41	39	uniform	uniform	ADJ
ejpam-6953	41	40	levi	levi	PROPN
ejpam-6953	41	41	constant	constant	PROPN
ejpam-6953	41	42	λ	λ	X
ejpam-6953	41	43	>	>	X
ejpam-6953	41	44	0	0	NUM
ejpam-6953	41	45	produced	produce	VERB
ejpam-6953	41	46	by	by	ADP
ejpam-6953	41	47	lemma	lemma	PROPN
ejpam-6953	41	48	3	3	NUM
ejpam-6953	41	49	below	below	ADV
ejpam-6953	41	50	.	.	PUNCT
ejpam-6953	42	1	then	then	ADV
ejpam-6953	42	2	c(t	c(t	PROPN
ejpam-6953	42	3	)	)	PUNCT
ejpam-6953	42	4	=	=	PUNCT
ejpam-6953	43	1	exp(t/2	exp(t/2	NOUN
ejpam-6953	43	2	+	+	CCONJ
ejpam-6953	43	3	625	625	NUM
ejpam-6953	43	4	/	/	SYM
ejpam-6953	43	5	λ	λ	NOUN
ejpam-6953	43	6	)	)	PUNCT
ejpam-6953	43	7	is	be	AUX
ejpam-6953	43	8	a	a	DET
ejpam-6953	43	9	valid	valid	ADJ
ejpam-6953	43	10	choice	choice	NOUN
ejpam-6953	43	11	.	.	PUNCT
ejpam-6953	44	1	in	in	ADP
ejpam-6953	44	2	general	general	ADJ
ejpam-6953	44	3	,	,	PUNCT
ejpam-6953	44	4	c(t	c(t	PROPN
ejpam-6953	44	5	)	)	PUNCT
ejpam-6953	44	6	depends	depend	VERB
ejpam-6953	44	7	on	on	ADP
ejpam-6953	44	8	dimcg	dimcg	NOUN
ejpam-6953	44	9	only	only	ADV
ejpam-6953	44	10	through	through	ADP
ejpam-6953	44	11	the	the	DET
ejpam-6953	44	12	besicovitch	besicovitch	ADJ
ejpam-6953	44	13	constant	constant	ADJ
ejpam-6953	44	14	c	c	PROPN
ejpam-6953	45	1	=	=	SYM
ejpam-6953	45	2	c(2	c(2	PROPN
ejpam-6953	45	3	dimcg	dimcg	PROPN
ejpam-6953	45	4	)	)	PUNCT
ejpam-6953	45	5	,	,	PUNCT
ejpam-6953	45	6	which	which	PRON
ejpam-6953	45	7	grows	grow	VERB
ejpam-6953	45	8	at	at	ADP
ejpam-6953	45	9	most	most	ADV
ejpam-6953	45	10	exponentially	exponentially	ADV
ejpam-6953	45	11	with	with	ADP
ejpam-6953	45	12	the	the	DET
ejpam-6953	45	13	complex	complex	ADJ
ejpam-6953	45	14	dimension	dimension	NOUN
ejpam-6953	45	15	(	(	PUNCT
ejpam-6953	45	16	cf	cf	NOUN
ejpam-6953	45	17	.	.	PUNCT
ejpam-6953	46	1	[	[	X
ejpam-6953	46	2	13	13	NUM
ejpam-6953	46	3	]	]	NUM
ejpam-6953	46	4	)	)	PUNCT
ejpam-6953	46	5	.	.	PUNCT
ejpam-6953	47	1	the	the	DET
ejpam-6953	47	2	proof	proof	NOUN
ejpam-6953	47	3	of	of	ADP
ejpam-6953	47	4	theorem	theorem	ADJ
ejpam-6953	47	5	1	1	NUM
ejpam-6953	47	6	uses	use	VERB
ejpam-6953	47	7	two	two	NUM
ejpam-6953	47	8	key	key	ADJ
ejpam-6953	47	9	uniformities	uniformity	NOUN
ejpam-6953	47	10	provided	provide	VERB
ejpam-6953	47	11	by	by	ADP
ejpam-6953	47	12	the	the	DET
ejpam-6953	47	13	lie	lie	NOUN
ejpam-6953	47	14	group	group	NOUN
ejpam-6953	47	15	structure	structure	NOUN
ejpam-6953	47	16	:	:	PUNCT
ejpam-6953	47	17	(	(	PUNCT
ejpam-6953	47	18	u1	u1	NOUN
ejpam-6953	47	19	)	)	PUNCT
ejpam-6953	47	20	uniform	uniform	NOUN
ejpam-6953	47	21	exhaustion	exhaustion	NOUN
ejpam-6953	47	22	by	by	ADP
ejpam-6953	47	23	strictly	strictly	ADV
ejpam-6953	47	24	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	47	25	sublevels	sublevel	NOUN
ejpam-6953	47	26	.	.	PUNCT
ejpam-6953	48	1	by	by	ADP
ejpam-6953	48	2	a	a	DET
ejpam-6953	48	3	richberg	richberg	NOUN
ejpam-6953	48	4	-	-	PUNCT
ejpam-6953	48	5	type	type	NOUN
ejpam-6953	48	6	smoothing	smoothing	NOUN
ejpam-6953	48	7	argument	argument	NOUN
ejpam-6953	48	8	(	(	PUNCT
ejpam-6953	48	9	cf	cf	NOUN
ejpam-6953	48	10	.	.	PUNCT
ejpam-6953	48	11	richberg	richberg	PROPN
ejpam-6953	49	1	[	[	X
ejpam-6953	49	2	14	14	NUM
ejpam-6953	49	3	]	]	PUNCT
ejpam-6953	49	4	and	and	CCONJ
ejpam-6953	49	5	demailly	demailly	ADV
ejpam-6953	49	6	[	[	X
ejpam-6953	49	7	15	15	NUM
ejpam-6953	49	8	,	,	PUNCT
ejpam-6953	49	9	16	16	NUM
ejpam-6953	49	10	]	]	PUNCT
ejpam-6953	49	11	)	)	PUNCT
ejpam-6953	49	12	,	,	PUNCT
ejpam-6953	49	13	we	we	PRON
ejpam-6953	49	14	can	can	AUX
ejpam-6953	49	15	approximate	approximate	VERB
ejpam-6953	49	16	the	the	DET
ejpam-6953	49	17	given	give	VERB
ejpam-6953	49	18	exhaustion	exhaustion	NOUN
ejpam-6953	49	19	ρ	ρ	NOUN
ejpam-6953	49	20	on	on	ADP
ejpam-6953	49	21	each	each	DET
ejpam-6953	49	22	sublevel	sublevel	NOUN
ejpam-6953	49	23	set	set	VERB
ejpam-6953	49	24	by	by	ADP
ejpam-6953	49	25	a	a	DET
ejpam-6953	49	26	smooth	smooth	ADJ
ejpam-6953	49	27	strictly	strictly	ADV
ejpam-6953	49	28	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	49	29	function	function	NOUN
ejpam-6953	49	30	that	that	PRON
ejpam-6953	49	31	is	be	AUX
ejpam-6953	49	32	uniformly	uniformly	ADV
ejpam-6953	49	33	close	close	ADJ
ejpam-6953	49	34	to	to	ADP
ejpam-6953	49	35	ρ	ρ	NOUN
ejpam-6953	49	36	on	on	ADP
ejpam-6953	49	37	slightly	slightly	ADV
ejpam-6953	49	38	smaller	small	ADJ
ejpam-6953	49	39	sublevels	sublevel	NOUN
ejpam-6953	49	40	.	.	PUNCT
ejpam-6953	50	1	iterating	iterate	VERB
ejpam-6953	50	2	this	this	PRON
ejpam-6953	50	3	over	over	ADP
ejpam-6953	50	4	an	an	DET
ejpam-6953	50	5	exhausting	exhausting	ADJ
ejpam-6953	50	6	sequence	sequence	NOUN
ejpam-6953	50	7	of	of	ADP
ejpam-6953	50	8	levels	level	NOUN
ejpam-6953	50	9	,	,	PUNCT
ejpam-6953	50	10	we	we	PRON
ejpam-6953	50	11	obtain	obtain	VERB
ejpam-6953	50	12	an	an	DET
ejpam-6953	50	13	exhaustion	exhaustion	NOUN
ejpam-6953	50	14	g	g	NOUN
ejpam-6953	50	15	=	=	PUNCT
ejpam-6953	50	16	⋃	⋃	NOUN
ejpam-6953	50	17	j∈n	j∈n	NOUN
ejpam-6953	50	18	ωj	ωj	ADP
ejpam-6953	50	19	by	by	ADP
ejpam-6953	50	20	smoothly	smoothly	ADV
ejpam-6953	50	21	bounded	bound	VERB
ejpam-6953	50	22	strictly	strictly	ADV
ejpam-6953	50	23	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	50	24	domains	domain	NOUN
ejpam-6953	50	25	ωj	ωj	ADP
ejpam-6953	50	26	⋐	⋐	NOUN
ejpam-6953	50	27	g	g	NOUN
ejpam-6953	50	28	,	,	PUNCT
ejpam-6953	50	29	and	and	CCONJ
ejpam-6953	50	30	smooth	smooth	ADJ
ejpam-6953	50	31	psh	psh	NOUN
ejpam-6953	50	32	functions	function	NOUN
ejpam-6953	50	33	φj	φj	X
ejpam-6953	50	34	on	on	ADP
ejpam-6953	50	35	ωj	ωj	ADP
ejpam-6953	50	36	such	such	ADJ
ejpam-6953	50	37	that	that	SCONJ
ejpam-6953	50	38	supωj−1	supωj−1	PROPN
ejpam-6953	50	39	|φj	|φj	PUNCT
ejpam-6953	50	40	−	−	PROPN
ejpam-6953	50	41	ρ|	ρ|	PROPN
ejpam-6953	50	42	is	be	AUX
ejpam-6953	50	43	uniformly	uniformly	ADV
ejpam-6953	50	44	small	small	ADJ
ejpam-6953	50	45	(	(	PUNCT
ejpam-6953	50	46	say	say	VERB
ejpam-6953	50	47	≤	≤	NUM
ejpam-6953	50	48	1/4	1/4	NUM
ejpam-6953	50	49	for	for	ADP
ejpam-6953	50	50	all	all	DET
ejpam-6953	50	51	j	j	NOUN
ejpam-6953	50	52	)	)	PUNCT
ejpam-6953	50	53	.	.	PUNCT
ejpam-6953	51	1	this	this	PRON
ejpam-6953	51	2	is	be	AUX
ejpam-6953	51	3	established	establish	VERB
ejpam-6953	51	4	in	in	ADP
ejpam-6953	51	5	lemma	lemma	PROPN
ejpam-6953	51	6	2	2	NUM
ejpam-6953	51	7	(	(	PUNCT
ejpam-6953	51	8	section	section	NOUN
ejpam-6953	51	9	3	3	NUM
ejpam-6953	51	10	)	)	PUNCT
ejpam-6953	51	11	.	.	PUNCT
ejpam-6953	52	1	(	(	PUNCT
ejpam-6953	52	2	modern	modern	ADJ
ejpam-6953	52	3	expositions	exposition	NOUN
ejpam-6953	52	4	of	of	ADP
ejpam-6953	52	5	such	such	ADJ
ejpam-6953	52	6	regularization	regularization	NOUN
ejpam-6953	52	7	on	on	ADP
ejpam-6953	52	8	manifolds	manifold	NOUN
ejpam-6953	52	9	can	can	AUX
ejpam-6953	52	10	be	be	AUX
ejpam-6953	52	11	found	find	VERB
ejpam-6953	52	12	in	in	ADP
ejpam-6953	52	13	[	[	X
ejpam-6953	52	14	16	16	NUM
ejpam-6953	52	15	,	,	PUNCT
ejpam-6953	52	16	17	17	NUM
ejpam-6953	52	17	]	]	PUNCT
ejpam-6953	52	18	.	.	PUNCT
ejpam-6953	53	1	for	for	ADP
ejpam-6953	53	2	completeness	completeness	NOUN
ejpam-6953	53	3	,	,	PUNCT
ejpam-6953	53	4	we	we	PRON
ejpam-6953	53	5	include	include	VERB
ejpam-6953	53	6	a	a	DET
ejpam-6953	53	7	simple	simple	ADJ
ejpam-6953	53	8	proof	proof	NOUN
ejpam-6953	53	9	in	in	ADP
ejpam-6953	53	10	appendix	appendix	ADJ
ejpam-6953	53	11	a.	a.	NOUN
ejpam-6953	53	12	)	)	PUNCT
ejpam-6953	53	13	(	(	PUNCT
ejpam-6953	53	14	u2	u2	NOUN
ejpam-6953	53	15	)	)	PUNCT
ejpam-6953	53	16	uniform	uniform	NOUN
ejpam-6953	53	17	strictly	strictly	ADV
ejpam-6953	53	18	psh	psh	PROPN
ejpam-6953	53	19	references	reference	NOUN
ejpam-6953	53	20	.	.	PUNCT
ejpam-6953	54	1	on	on	ADP
ejpam-6953	54	2	each	each	PRON
ejpam-6953	54	3	ωj	ωj	ADP
ejpam-6953	54	4	we	we	PRON
ejpam-6953	54	5	construct	construct	VERB
ejpam-6953	54	6	a	a	DET
ejpam-6953	54	7	smooth	smooth	ADJ
ejpam-6953	54	8	strictly	strictly	ADV
ejpam-6953	54	9	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	54	10	function	function	NOUN
ejpam-6953	54	11	σj	σj	VERB
ejpam-6953	54	12	whose	whose	DET
ejpam-6953	54	13	levi	levi	PROPN
ejpam-6953	54	14	form	form	NOUN
ejpam-6953	54	15	has	have	VERB
ejpam-6953	54	16	a	a	DET
ejpam-6953	54	17	uniform	uniform	NOUN
ejpam-6953	54	18	lower	lower	ADV
ejpam-6953	54	19	bound	bind	VERB
ejpam-6953	54	20	independent	independent	NOUN
ejpam-6953	54	21	of	of	ADP
ejpam-6953	54	22	j.	j.	PROPN
ejpam-6953	54	23	this	this	PRON
ejpam-6953	54	24	is	be	AUX
ejpam-6953	54	25	achieved	achieve	VERB
ejpam-6953	54	26	by	by	ADP
ejpam-6953	54	27	combining	combine	VERB
ejpam-6953	54	28	left	left	ADJ
ejpam-6953	54	29	-	-	PUNCT
ejpam-6953	54	30	translations	translation	NOUN
ejpam-6953	54	31	in	in	ADP
ejpam-6953	54	32	g	g	NOUN
ejpam-6953	54	33	with	with	ADP
ejpam-6953	54	34	a	a	DET
ejpam-6953	54	35	bounded	bound	VERB
ejpam-6953	54	36	-	-	PUNCT
ejpam-6953	54	37	overlap	overlap	NOUN
ejpam-6953	54	38	covering	covering	NOUN
ejpam-6953	54	39	argument	argument	NOUN
ejpam-6953	54	40	(	(	PUNCT
ejpam-6953	54	41	vitali	vitali	X
ejpam-6953	54	42	–	–	PUNCT
ejpam-6953	54	43	besicovitch	besicovitch	NOUN
ejpam-6953	54	44	covering	cover	VERB
ejpam-6953	54	45	property	property	NOUN
ejpam-6953	54	46	for	for	ADP
ejpam-6953	54	47	(	(	PUNCT
ejpam-6953	54	48	g	g	PROPN
ejpam-6953	54	49	,	,	PUNCT
ejpam-6953	54	50	ω	ω	PROPN
ejpam-6953	54	51	)	)	PUNCT
ejpam-6953	54	52	;	;	PUNCT
ejpam-6953	55	1	cf	cf	X
ejpam-6953	55	2	.	.	PUNCT
ejpam-6953	56	1	[	[	X
ejpam-6953	56	2	11	11	NUM
ejpam-6953	56	3	,	,	PUNCT
ejpam-6953	56	4	13	13	NUM
ejpam-6953	56	5	]	]	NUM
ejpam-6953	56	6	)	)	PUNCT
ejpam-6953	56	7	.	.	PUNCT
ejpam-6953	57	1	in	in	ADP
ejpam-6953	57	2	essence	essence	NOUN
ejpam-6953	57	3	,	,	PUNCT
ejpam-6953	57	4	one	one	PRON
ejpam-6953	57	5	takes	take	VERB
ejpam-6953	57	6	a	a	DET
ejpam-6953	57	7	local	local	ADJ
ejpam-6953	57	8	potential	potential	ADJ
ejpam-6953	57	9	u	u	NOUN
ejpam-6953	57	10	that	that	PRON
ejpam-6953	57	11	is	be	AUX
ejpam-6953	57	12	strictly	strictly	ADV
ejpam-6953	57	13	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	57	14	in	in	ADP
ejpam-6953	57	15	a	a	DET
ejpam-6953	57	16	neighborhood	neighborhood	NOUN
ejpam-6953	57	17	of	of	ADP
ejpam-6953	57	18	the	the	DET
ejpam-6953	57	19	identity	identity	NOUN
ejpam-6953	57	20	in	in	ADP
ejpam-6953	57	21	g	g	NOUN
ejpam-6953	57	22	,	,	PUNCT
ejpam-6953	57	23	and	and	CCONJ
ejpam-6953	57	24	one	one	NUM
ejpam-6953	57	25	averages	average	VERB
ejpam-6953	57	26	its	its	PRON
ejpam-6953	57	27	left	left	NOUN
ejpam-6953	57	28	-	-	PUNCT
ejpam-6953	57	29	translates	translate	NOUN
ejpam-6953	57	30	to	to	PART
ejpam-6953	57	31	obtain	obtain	VERB
ejpam-6953	57	32	σj	σj	NOUN
ejpam-6953	57	33	on	on	ADP
ejpam-6953	57	34	each	each	DET
ejpam-6953	57	35	ωj	ωj	NOUN
ejpam-6953	57	36	with	with	ADP
ejpam-6953	57	37	i∂∂̄σj	i∂∂̄σj	PROPN
ejpam-6953	57	38	≥	≥	NOUN
ejpam-6953	57	39	λω	λω	ADP
ejpam-6953	57	40	for	for	ADP
ejpam-6953	57	41	some	some	DET
ejpam-6953	57	42	λ	λ	PROPN
ejpam-6953	57	43	>	>	X
ejpam-6953	57	44	0	0	NUM
ejpam-6953	57	45	independent	independent	NOUN
ejpam-6953	57	46	of	of	ADP
ejpam-6953	57	47	j.	j.	PROPN
ejpam-6953	57	48	this	this	PRON
ejpam-6953	57	49	is	be	AUX
ejpam-6953	57	50	carried	carry	VERB
ejpam-6953	57	51	out	out	ADP
ejpam-6953	57	52	in	in	ADP
ejpam-6953	57	53	lemma	lemma	PROPN
ejpam-6953	57	54	3	3	NUM
ejpam-6953	57	55	(	(	PUNCT
ejpam-6953	57	56	section	section	NOUN
ejpam-6953	57	57	4	4	NUM
ejpam-6953	57	58	)	)	PUNCT
ejpam-6953	57	59	,	,	PUNCT
ejpam-6953	57	60	using	use	VERB
ejpam-6953	57	61	the	the	DET
ejpam-6953	57	62	overlap	overlap	NOUN
ejpam-6953	57	63	bound	bind	VERB
ejpam-6953	57	64	c	c	NOUN
ejpam-6953	57	65	=	=	SYM
ejpam-6953	57	66	c(dimg	c(dimg	NOUN
ejpam-6953	57	67	)	)	PUNCT
ejpam-6953	57	68	provided	provide	VERB
ejpam-6953	57	69	by	by	ADP
ejpam-6953	57	70	the	the	DET
ejpam-6953	57	71	besicovitch	besicovitch	PROPN
ejpam-6953	57	72	covering	covering	NOUN
ejpam-6953	57	73	theorem	theorem	NOUN
ejpam-6953	57	74	(	(	PUNCT
ejpam-6953	57	75	see	see	VERB
ejpam-6953	57	76	[	[	X
ejpam-6953	57	77	11	11	NUM
ejpam-6953	57	78	,	,	PUNCT
ejpam-6953	57	79	12	12	NUM
ejpam-6953	57	80	]	]	PUNCT
ejpam-6953	57	81	)	)	PUNCT
ejpam-6953	57	82	.	.	PUNCT
ejpam-6953	58	1	in	in	ADP
ejpam-6953	58	2	particular	particular	ADJ
ejpam-6953	58	3	,	,	PUNCT
ejpam-6953	58	4	we	we	PRON
ejpam-6953	58	5	obtain	obtain	VERB
ejpam-6953	58	6	fixed	fix	VERB
ejpam-6953	58	7	positive	positive	ADJ
ejpam-6953	58	8	constants	constant	NOUN
ejpam-6953	58	9	c∗	c∗	PROPN
ejpam-6953	58	10	=	=	SYM
ejpam-6953	58	11	λ	λ	PROPN
ejpam-6953	58	12	/	/	SYM
ejpam-6953	58	13	c	c	PROPN
ejpam-6953	58	14	and	and	CCONJ
ejpam-6953	58	15	s∗	s∗	PROPN
ejpam-6953	58	16	(	(	PUNCT
ejpam-6953	58	17	with	with	ADP
ejpam-6953	58	18	s∗	s∗	PROPN
ejpam-6953	58	19	=	=	SYM
ejpam-6953	58	20	1	1	NUM
ejpam-6953	58	21	in	in	ADP
ejpam-6953	58	22	our	our	PRON
ejpam-6953	58	23	construction	construction	NOUN
ejpam-6953	58	24	)	)	PUNCT
ejpam-6953	58	25	such	such	ADJ
ejpam-6953	58	26	that	that	PRON
ejpam-6953	58	27	for	for	ADP
ejpam-6953	58	28	all	all	DET
ejpam-6953	58	29	j	j	NOUN
ejpam-6953	58	30	,	,	PUNCT
ejpam-6953	58	31	i∂∂̄σj	i∂∂̄σj	PROPN
ejpam-6953	58	32	≥	≥	PROPN
ejpam-6953	58	33	c∗	c∗	PROPN
ejpam-6953	58	34	ω	ω	PROPN
ejpam-6953	58	35	on	on	ADP
ejpam-6953	58	36	ωj	ωj	ADP
ejpam-6953	58	37	,	,	PUNCT
ejpam-6953	58	38	sup	sup	NOUN
ejpam-6953	58	39	ωj	ωj	ADP
ejpam-6953	58	40	|σj	|σj	PRON
ejpam-6953	58	41	|	|	ADV
ejpam-6953	58	42	≤	≤	X
ejpam-6953	58	43	s∗	s∗	PROPN
ejpam-6953	58	44	.	.	PUNCT
ejpam-6953	59	1	with	with	ADP
ejpam-6953	59	2	(	(	PUNCT
ejpam-6953	59	3	u1)–(u2	u1)–(u2	NOUN
ejpam-6953	59	4	)	)	PUNCT
ejpam-6953	59	5	in	in	ADP
ejpam-6953	59	6	place	place	NOUN
ejpam-6953	59	7	,	,	PUNCT
ejpam-6953	59	8	hörmander	hörmander	PROPN
ejpam-6953	59	9	’s	’s	PART
ejpam-6953	59	10	l2	l2	NOUN
ejpam-6953	59	11	estimates	estimate	NOUN
ejpam-6953	59	12	for	for	ADP
ejpam-6953	59	13	the	the	DET
ejpam-6953	59	14	∂̄-neumann	∂̄-neumann	PROPN
ejpam-6953	59	15	problem	problem	NOUN
ejpam-6953	59	16	[	[	X
ejpam-6953	59	17	18	18	NUM
ejpam-6953	59	18	,	,	PUNCT
ejpam-6953	59	19	19	19	NUM
ejpam-6953	59	20	]	]	PUNCT
ejpam-6953	59	21	apply	apply	VERB
ejpam-6953	59	22	on	on	ADP
ejpam-6953	59	23	each	each	DET
ejpam-6953	59	24	ωj	ωj	X
ejpam-6953	59	25	to	to	PART
ejpam-6953	59	26	solve	solve	VERB
ejpam-6953	59	27	∂̄uj	∂̄uj	ADP
ejpam-6953	59	28	=	=	SYM
ejpam-6953	59	29	f	f	PROPN
ejpam-6953	59	30	with	with	ADP
ejpam-6953	59	31	uniform	uniform	ADJ
ejpam-6953	59	32	estimates	estimate	NOUN
ejpam-6953	59	33	that	that	PRON
ejpam-6953	59	34	depend	depend	VERB
ejpam-6953	59	35	only	only	ADV
ejpam-6953	59	36	on	on	ADP
ejpam-6953	59	37	t	t	PROPN
ejpam-6953	59	38	,	,	PUNCT
ejpam-6953	59	39	c∗	c∗	NOUN
ejpam-6953	59	40	,	,	PUNCT
ejpam-6953	59	41	and	and	CCONJ
ejpam-6953	59	42	s∗.	s∗.	ADJ
ejpam-6953	59	43	a	a	DET
ejpam-6953	59	44	mazur	mazur	PROPN
ejpam-6953	59	45	convex	convex	NOUN
ejpam-6953	59	46	combination	combination	NOUN
ejpam-6953	59	47	argument	argument	NOUN
ejpam-6953	59	48	(	(	PUNCT
ejpam-6953	59	49	as	as	ADP
ejpam-6953	59	50	in	in	ADP
ejpam-6953	59	51	[	[	X
ejpam-6953	59	52	1	1	NUM
ejpam-6953	59	53	,	,	PUNCT
ejpam-6953	59	54	20	20	NUM
ejpam-6953	59	55	]	]	PUNCT
ejpam-6953	59	56	)	)	PUNCT
ejpam-6953	59	57	then	then	ADV
ejpam-6953	59	58	upgrades	upgrade	VERB
ejpam-6953	59	59	a	a	DET
ejpam-6953	59	60	weakly	weakly	ADJ
ejpam-6953	59	61	convergent	convergent	NOUN
ejpam-6953	59	62	solving	solve	VERB
ejpam-6953	59	63	sequence	sequence	NOUN
ejpam-6953	59	64	to	to	ADP
ejpam-6953	59	65	one	one	NUM
ejpam-6953	59	66	that	that	PRON
ejpam-6953	59	67	converges	converge	VERB
ejpam-6953	59	68	strongly	strongly	ADV
ejpam-6953	59	69	on	on	ADP
ejpam-6953	59	70	each	each	DET
ejpam-6953	59	71	fixed	fix	VERB
ejpam-6953	59	72	exhaustion	exhaustion	NOUN
ejpam-6953	59	73	level	level	NOUN
ejpam-6953	59	74	.	.	PUNCT
ejpam-6953	60	1	diagonalizing	diagonalize	VERB
ejpam-6953	60	2	across	across	ADP
ejpam-6953	60	3	all	all	DET
ejpam-6953	60	4	levels	level	NOUN
ejpam-6953	60	5	,	,	PUNCT
ejpam-6953	60	6	we	we	PRON
ejpam-6953	60	7	obtain	obtain	VERB
ejpam-6953	60	8	a	a	DET
ejpam-6953	60	9	single	single	ADJ
ejpam-6953	60	10	global	global	ADJ
ejpam-6953	60	11	solution	solution	NOUN
ejpam-6953	60	12	u	u	NOUN
ejpam-6953	60	13	on	on	ADP
ejpam-6953	60	14	g	g	NOUN
ejpam-6953	60	15	without	without	ADP
ejpam-6953	60	16	cut	cut	NOUN
ejpam-6953	60	17	-	-	PUNCT
ejpam-6953	60	18	offs	off	NOUN
ejpam-6953	60	19	(	(	PUNCT
ejpam-6953	60	20	cf	cf	NOUN
ejpam-6953	60	21	.	.	PUNCT
ejpam-6953	61	1	[	[	X
ejpam-6953	61	2	1	1	NUM
ejpam-6953	61	3	]	]	PUNCT
ejpam-6953	61	4	)	)	PUNCT
ejpam-6953	61	5	.	.	PUNCT
ejpam-6953	62	1	the	the	DET
ejpam-6953	62	2	a	a	DET
ejpam-6953	62	3	priori	priori	ADJ
ejpam-6953	62	4	estimate	estimate	NOUN
ejpam-6953	62	5	(	(	PUNCT
ejpam-6953	62	6	1	1	X
ejpam-6953	62	7	)	)	PUNCT
ejpam-6953	62	8	follows	follow	VERB
ejpam-6953	62	9	from	from	ADP
ejpam-6953	62	10	these	these	DET
ejpam-6953	62	11	uniform	uniform	ADJ
ejpam-6953	62	12	local	local	ADJ
ejpam-6953	62	13	estimates	estimate	NOUN
ejpam-6953	62	14	as	as	ADV
ejpam-6953	62	15	well	well	ADV
ejpam-6953	62	16	,	,	PUNCT
ejpam-6953	62	17	yielding	yield	VERB
ejpam-6953	62	18	a	a	DET
ejpam-6953	62	19	bounded	bounded	ADJ
ejpam-6953	62	20	∂̄-solution	∂̄-solution	NOUN
ejpam-6953	62	21	operator	operator	NOUN
ejpam-6953	62	22	on	on	ADP
ejpam-6953	62	23	l2(g	l2(g	NOUN
ejpam-6953	62	24	,	,	PUNCT
ejpam-6953	62	25	e−tρ	e−tρ	NOUN
ejpam-6953	62	26	)	)	PUNCT
ejpam-6953	62	27	.	.	PUNCT
ejpam-6953	63	1	as	as	ADP
ejpam-6953	63	2	consequences	consequence	NOUN
ejpam-6953	63	3	of	of	ADP
ejpam-6953	63	4	theorem	theorem	NOUN
ejpam-6953	63	5	1	1	NUM
ejpam-6953	63	6	,	,	PUNCT
ejpam-6953	63	7	we	we	PRON
ejpam-6953	63	8	mention	mention	VERB
ejpam-6953	63	9	two	two	NUM
ejpam-6953	63	10	applications	application	NOUN
ejpam-6953	63	11	.	.	PUNCT
ejpam-6953	64	1	first	first	ADV
ejpam-6953	64	2	,	,	PUNCT
ejpam-6953	64	3	when	when	SCONJ
ejpam-6953	64	4	dimcg	dimcg	NOUN
ejpam-6953	64	5	≥	≥	NOUN
ejpam-6953	64	6	2	2	NUM
ejpam-6953	64	7	,	,	PUNCT
ejpam-6953	64	8	we	we	PRON
ejpam-6953	64	9	obtain	obtain	VERB
ejpam-6953	64	10	a	a	DET
ejpam-6953	64	11	hartogs	hartog	NOUN
ejpam-6953	64	12	-	-	PUNCT
ejpam-6953	64	13	type	type	NOUN
ejpam-6953	64	14	extension	extension	NOUN
ejpam-6953	64	15	phenomenon	phenomenon	NOUN
ejpam-6953	64	16	:	:	PUNCT
ejpam-6953	64	17	any	any	DET
ejpam-6953	64	18	holomorphic	holomorphic	ADJ
ejpam-6953	64	19	function	function	NOUN
ejpam-6953	64	20	on	on	ADP
ejpam-6953	64	21	a	a	DET
ejpam-6953	64	22	“	"	PUNCT
ejpam-6953	64	23	hole	hole	NOUN
ejpam-6953	64	24	”	"	PUNCT
ejpam-6953	64	25	e	e	NOUN
ejpam-6953	64	26	⋐	⋐	PROPN
ejpam-6953	64	27	g	g	NOUN
ejpam-6953	64	28	that	that	PRON
ejpam-6953	64	29	is	be	AUX
ejpam-6953	64	30	of	of	ADP
ejpam-6953	64	31	sufficiently	sufficiently	ADV
ejpam-6953	64	32	moderate	moderate	ADJ
ejpam-6953	64	33	growth	growth	NOUN
ejpam-6953	64	34	(	(	PUNCT
ejpam-6953	64	35	square	square	NOUN
ejpam-6953	64	36	-	-	PUNCT
ejpam-6953	64	37	integrable	integrable	ADJ
ejpam-6953	64	38	with	with	ADP
ejpam-6953	64	39	weight	weight	NOUN
ejpam-6953	64	40	e−tρ	e−tρ	NOUN
ejpam-6953	64	41	for	for	ADP
ejpam-6953	64	42	some	some	DET
ejpam-6953	64	43	t	t	NOUN
ejpam-6953	64	44	>	>	X
ejpam-6953	64	45	0	0	NUM
ejpam-6953	64	46	)	)	PUNCT
ejpam-6953	64	47	must	must	AUX
ejpam-6953	64	48	extend	extend	VERB
ejpam-6953	64	49	holomorphically	holomorphically	ADV
ejpam-6953	64	50	to	to	ADP
ejpam-6953	64	51	all	all	PRON
ejpam-6953	64	52	of	of	ADP
ejpam-6953	64	53	g.	g.	PROPN
ejpam-6953	64	54	secondly	secondly	ADV
ejpam-6953	64	55	,	,	PUNCT
ejpam-6953	64	56	our	our	PRON
ejpam-6953	64	57	results	result	NOUN
ejpam-6953	64	58	imply	imply	VERB
ejpam-6953	64	59	a	a	DET
ejpam-6953	64	60	form	form	NOUN
ejpam-6953	64	61	of	of	ADP
ejpam-6953	64	62	volume	volume	NOUN
ejpam-6953	64	63	-	-	PUNCT
ejpam-6953	64	64	growth	growth	NOUN
ejpam-6953	64	65	richness	richness	NOUN
ejpam-6953	64	66	of	of	ADP
ejpam-6953	64	67	weighted	weight	VERB
ejpam-6953	64	68	bergman	bergman	PROPN
ejpam-6953	64	69	spaces	space	VERB
ejpam-6953	64	70	on	on	ADP
ejpam-6953	64	71	strictly	strictly	ADV
ejpam-6953	64	72	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	64	73	domains	domain	NOUN
ejpam-6953	64	74	inside	inside	ADP
ejpam-6953	64	75	g.	g.	PROPN
ejpam-6953	65	1	we	we	PRON
ejpam-6953	65	2	refer	refer	VERB
ejpam-6953	65	3	to	to	ADP
ejpam-6953	65	4	section	section	NOUN
ejpam-6953	65	5	5	5	NUM
ejpam-6953	65	6	and	and	CCONJ
ejpam-6953	65	7	the	the	DET
ejpam-6953	65	8	concluding	concluding	NOUN
ejpam-6953	65	9	remarks	remark	NOUN
ejpam-6953	65	10	for	for	ADP
ejpam-6953	65	11	a	a	DET
ejpam-6953	65	12	brief	brief	ADJ
ejpam-6953	65	13	discussion	discussion	NOUN
ejpam-6953	65	14	of	of	ADP
ejpam-6953	65	15	these	these	DET
ejpam-6953	65	16	points	point	NOUN
ejpam-6953	65	17	.	.	PUNCT
ejpam-6953	66	1	a.	a.	PROPN
ejpam-6953	66	2	r.	r.	PROPN
ejpam-6953	66	3	al	al	PROPN
ejpam-6953	66	4	-	-	PUNCT
ejpam-6953	66	5	abdallah	abdallah	PROPN
ejpam-6953	66	6	/	/	SYM
ejpam-6953	66	7	eur	eur	PROPN
ejpam-6953	66	8	.	.	PUNCT
ejpam-6953	67	1	j.	j.	PROPN
ejpam-6953	67	2	pure	pure	PROPN
ejpam-6953	67	3	appl	appl	PROPN
ejpam-6953	67	4	.	.	PROPN
ejpam-6953	67	5	math	math	PROPN
ejpam-6953	67	6	,	,	PUNCT
ejpam-6953	67	7	18	18	NUM
ejpam-6953	67	8	(	(	PUNCT
ejpam-6953	67	9	4	4	NUM
ejpam-6953	67	10	)	)	PUNCT
ejpam-6953	67	11	(	(	PUNCT
ejpam-6953	67	12	2025	2025	NUM
ejpam-6953	67	13	)	)	PUNCT
ejpam-6953	67	14	,	,	PUNCT
ejpam-6953	67	15	6953	6953	NUM
ejpam-6953	67	16	4	4	NUM
ejpam-6953	67	17	of	of	ADP
ejpam-6953	67	18	14	14	NUM
ejpam-6953	67	19	it	it	PRON
ejpam-6953	67	20	is	be	AUX
ejpam-6953	67	21	also	also	ADV
ejpam-6953	67	22	worth	worth	ADJ
ejpam-6953	67	23	noting	note	VERB
ejpam-6953	67	24	an	an	DET
ejpam-6953	67	25	alternative	alternative	ADJ
ejpam-6953	67	26	analytic	analytic	ADJ
ejpam-6953	67	27	perspective	perspective	NOUN
ejpam-6953	67	28	related	relate	VERB
ejpam-6953	67	29	to	to	PART
ejpam-6953	67	30	lie	lie	VERB
ejpam-6953	67	31	theory	theory	NOUN
ejpam-6953	67	32	:	:	PUNCT
ejpam-6953	67	33	certain	certain	ADJ
ejpam-6953	67	34	complex	complex	ADJ
ejpam-6953	67	35	analysis	analysis	NOUN
ejpam-6953	67	36	problems	problem	NOUN
ejpam-6953	67	37	on	on	ADP
ejpam-6953	67	38	lie	lie	NOUN
ejpam-6953	67	39	groups	group	NOUN
ejpam-6953	67	40	can	can	AUX
ejpam-6953	67	41	be	be	AUX
ejpam-6953	67	42	approached	approach	VERB
ejpam-6953	67	43	via	via	ADP
ejpam-6953	67	44	orthogonal	orthogonal	ADJ
ejpam-6953	67	45	polynomials	polynomial	NOUN
ejpam-6953	67	46	and	and	CCONJ
ejpam-6953	67	47	special	special	ADJ
ejpam-6953	67	48	function	function	NOUN
ejpam-6953	67	49	techniques	technique	NOUN
ejpam-6953	67	50	.	.	PUNCT
ejpam-6953	68	1	for	for	ADP
ejpam-6953	68	2	example	example	NOUN
ejpam-6953	68	3	,	,	PUNCT
ejpam-6953	68	4	recent	recent	ADJ
ejpam-6953	68	5	works	work	NOUN
ejpam-6953	68	6	of	of	ADP
ejpam-6953	68	7	al	al	PROPN
ejpam-6953	68	8	-	-	PUNCT
ejpam-6953	68	9	askar	askar	NOUN
ejpam-6953	68	10	,	,	PUNCT
ejpam-6953	68	11	cesarano	cesarano	PROPN
ejpam-6953	68	12	,	,	PUNCT
ejpam-6953	68	13	mohammed	mohammed	PROPN
ejpam-6953	68	14	and	and	CCONJ
ejpam-6953	68	15	collaborators	collaborator	NOUN
ejpam-6953	68	16	have	have	AUX
ejpam-6953	68	17	used	use	VERB
ejpam-6953	68	18	lie	lie	NOUN
ejpam-6953	68	19	-	-	PUNCT
ejpam-6953	68	20	algebraic	algebraic	ADJ
ejpam-6953	68	21	expansions	expansion	NOUN
ejpam-6953	68	22	to	to	PART
ejpam-6953	68	23	solve	solve	VERB
ejpam-6953	68	24	stochastic	stochastic	ADJ
ejpam-6953	68	25	or	or	CCONJ
ejpam-6953	68	26	fractional	fractional	ADJ
ejpam-6953	68	27	differential	differential	ADJ
ejpam-6953	68	28	equations	equation	NOUN
ejpam-6953	68	29	on	on	ADP
ejpam-6953	68	30	complex	complex	ADJ
ejpam-6953	68	31	domains	domain	NOUN
ejpam-6953	68	32	(	(	PUNCT
ejpam-6953	68	33	see	see	VERB
ejpam-6953	68	34	,	,	PUNCT
ejpam-6953	68	35	e.g.	e.g.	ADV
ejpam-6953	68	36	,	,	PUNCT
ejpam-6953	68	37	[	[	X
ejpam-6953	68	38	21–23	21–23	NUM
ejpam-6953	68	39	]	]	NUM
ejpam-6953	68	40	)	)	PUNCT
ejpam-6953	68	41	.	.	PUNCT
ejpam-6953	69	1	these	these	DET
ejpam-6953	69	2	methods	method	NOUN
ejpam-6953	69	3	highlight	highlight	VERB
ejpam-6953	69	4	the	the	DET
ejpam-6953	69	5	rich	rich	ADJ
ejpam-6953	69	6	interplay	interplay	NOUN
ejpam-6953	69	7	between	between	ADP
ejpam-6953	69	8	lie	lie	NOUN
ejpam-6953	69	9	group	group	NOUN
ejpam-6953	69	10	symmetries	symmetry	NOUN
ejpam-6953	69	11	and	and	CCONJ
ejpam-6953	69	12	analytic	analytic	ADJ
ejpam-6953	69	13	function	function	NOUN
ejpam-6953	69	14	spaces	space	NOUN
ejpam-6953	69	15	.	.	PUNCT
ejpam-6953	70	1	in	in	ADP
ejpam-6953	70	2	the	the	DET
ejpam-6953	70	3	present	present	ADJ
ejpam-6953	70	4	work	work	NOUN
ejpam-6953	70	5	,	,	PUNCT
ejpam-6953	70	6	however	however	ADV
ejpam-6953	70	7	,	,	PUNCT
ejpam-6953	70	8	we	we	PRON
ejpam-6953	70	9	focus	focus	VERB
ejpam-6953	70	10	on	on	ADP
ejpam-6953	70	11	developing	develop	VERB
ejpam-6953	70	12	the	the	DET
ejpam-6953	70	13	l2	l2	NOUN
ejpam-6953	70	14	∂̄-theory	∂̄-theory	ADJ
ejpam-6953	70	15	on	on	ADP
ejpam-6953	70	16	complex	complex	ADJ
ejpam-6953	70	17	lie	lie	NOUN
ejpam-6953	70	18	groups	group	NOUN
ejpam-6953	70	19	using	use	VERB
ejpam-6953	70	20	analytic	analytic	ADJ
ejpam-6953	70	21	and	and	CCONJ
ejpam-6953	70	22	geometric	geometric	ADJ
ejpam-6953	70	23	tools	tool	NOUN
ejpam-6953	70	24	as	as	SCONJ
ejpam-6953	70	25	outlined	outline	VERB
ejpam-6953	70	26	above	above	ADV
ejpam-6953	70	27	.	.	PUNCT
ejpam-6953	71	1	(	(	PUNCT
ejpam-6953	71	2	for	for	ADP
ejpam-6953	71	3	general	general	ADJ
ejpam-6953	71	4	background	background	NOUN
ejpam-6953	71	5	on	on	ADP
ejpam-6953	71	6	modern	modern	ADJ
ejpam-6953	71	7	complex	complex	ADJ
ejpam-6953	71	8	analysis	analysis	NOUN
ejpam-6953	71	9	techniques	technique	NOUN
ejpam-6953	71	10	and	and	CCONJ
ejpam-6953	71	11	l2	l2	NOUN
ejpam-6953	71	12	methods	method	NOUN
ejpam-6953	71	13	,	,	PUNCT
ejpam-6953	71	14	see	see	VERB
ejpam-6953	71	15	[	[	X
ejpam-6953	71	16	24	24	NUM
ejpam-6953	71	17	]	]	PUNCT
ejpam-6953	71	18	.	.	PUNCT
ejpam-6953	71	19	)	)	PUNCT
ejpam-6953	72	1	2	2	X
ejpam-6953	72	2	.	.	X
ejpam-6953	72	3	preliminaries	preliminary	NOUN
ejpam-6953	72	4	we	we	PRON
ejpam-6953	72	5	collect	collect	VERB
ejpam-6953	72	6	here	here	ADV
ejpam-6953	72	7	a	a	DET
ejpam-6953	72	8	few	few	ADJ
ejpam-6953	72	9	basic	basic	ADJ
ejpam-6953	72	10	lemmas	lemma	NOUN
ejpam-6953	72	11	and	and	CCONJ
ejpam-6953	72	12	setup	setup	NOUN
ejpam-6953	72	13	for	for	ADP
ejpam-6953	72	14	the	the	DET
ejpam-6953	72	15	proof	proof	NOUN
ejpam-6953	72	16	.	.	PUNCT
ejpam-6953	73	1	throughout	throughout	ADV
ejpam-6953	73	2	,	,	PUNCT
ejpam-6953	73	3	we	we	PRON
ejpam-6953	73	4	continue	continue	VERB
ejpam-6953	73	5	with	with	ADP
ejpam-6953	73	6	the	the	DET
ejpam-6953	73	7	assumptions	assumption	NOUN
ejpam-6953	73	8	and	and	CCONJ
ejpam-6953	73	9	notation	notation	NOUN
ejpam-6953	73	10	of	of	ADP
ejpam-6953	73	11	theorem	theorem	NOUN
ejpam-6953	73	12	1	1	NUM
ejpam-6953	73	13	.	.	PUNCT
ejpam-6953	74	1	in	in	ADP
ejpam-6953	74	2	particular	particular	ADJ
ejpam-6953	74	3	,	,	PUNCT
ejpam-6953	74	4	g	g	PROPN
ejpam-6953	74	5	is	be	AUX
ejpam-6953	74	6	a	a	DET
ejpam-6953	74	7	fixed	fix	VERB
ejpam-6953	74	8	connected	connected	ADJ
ejpam-6953	74	9	noncompact	noncompact	NOUN
ejpam-6953	74	10	complex	complex	ADJ
ejpam-6953	74	11	lie	lie	NOUN
ejpam-6953	74	12	group	group	NOUN
ejpam-6953	74	13	equipped	equip	VERB
ejpam-6953	74	14	with	with	ADP
ejpam-6953	74	15	a	a	DET
ejpam-6953	74	16	left	left	ADJ
ejpam-6953	74	17	-	-	PUNCT
ejpam-6953	74	18	invariant	invariant	ADJ
ejpam-6953	74	19	hermitian	hermitian	PROPN
ejpam-6953	74	20	metric	metric	PROPN
ejpam-6953	74	21	ω	ω	PROPN
ejpam-6953	74	22	,	,	PUNCT
ejpam-6953	74	23	volume	volume	NOUN
ejpam-6953	74	24	form	form	NOUN
ejpam-6953	74	25	dvω	dvω	PROPN
ejpam-6953	74	26	,	,	PUNCT
ejpam-6953	74	27	and	and	CCONJ
ejpam-6953	74	28	continuous	continuous	ADJ
ejpam-6953	74	29	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	74	30	exhaustion	exhaustion	NOUN
ejpam-6953	74	31	function	function	NOUN
ejpam-6953	74	32	ρ	ρ	NOUN
ejpam-6953	74	33	:	:	PUNCT
ejpam-6953	74	34	g→	g→	NOUN
ejpam-6953	74	35	[	[	X
ejpam-6953	74	36	0,∞	0,∞	NOUN
ejpam-6953	74	37	)	)	PUNCT
ejpam-6953	74	38	.	.	PUNCT
ejpam-6953	75	1	strictly	strictly	ADV
ejpam-6953	75	2	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	75	3	cut	cut	NOUN
ejpam-6953	75	4	-	-	PUNCT
ejpam-6953	75	5	offs	off	NOUN
ejpam-6953	75	6	and	and	CCONJ
ejpam-6953	75	7	local	local	ADJ
ejpam-6953	75	8	solutions	solution	NOUN
ejpam-6953	75	9	.	.	PUNCT
ejpam-6953	76	1	we	we	PRON
ejpam-6953	76	2	will	will	AUX
ejpam-6953	76	3	make	make	VERB
ejpam-6953	76	4	frequent	frequent	ADJ
ejpam-6953	76	5	use	use	NOUN
ejpam-6953	76	6	of	of	ADP
ejpam-6953	76	7	hörmander	hörmander	NOUN
ejpam-6953	76	8	’s	’s	PART
ejpam-6953	76	9	l2	l2	NOUN
ejpam-6953	76	10	estimate	estimate	NOUN
ejpam-6953	76	11	on	on	ADP
ejpam-6953	76	12	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	76	13	domains	domain	NOUN
ejpam-6953	76	14	.	.	PUNCT
ejpam-6953	77	1	for	for	ADP
ejpam-6953	77	2	clarity	clarity	NOUN
ejpam-6953	77	3	we	we	PRON
ejpam-6953	77	4	state	state	VERB
ejpam-6953	77	5	here	here	ADV
ejpam-6953	77	6	a	a	DET
ejpam-6953	77	7	basic	basic	ADJ
ejpam-6953	77	8	version	version	NOUN
ejpam-6953	77	9	(	(	PUNCT
ejpam-6953	77	10	cf	cf	NOUN
ejpam-6953	77	11	.	.	PUNCT
ejpam-6953	78	1	[	[	X
ejpam-6953	78	2	18	18	NUM
ejpam-6953	78	3	,	,	PUNCT
ejpam-6953	78	4	19	19	NUM
ejpam-6953	78	5	]	]	PUNCT
ejpam-6953	78	6	)	)	PUNCT
ejpam-6953	78	7	.	.	PUNCT
ejpam-6953	79	1	if	if	SCONJ
ejpam-6953	79	2	ω	ω	PROPN
ejpam-6953	79	3	⋐	⋐	NOUN
ejpam-6953	79	4	g	g	PROPN
ejpam-6953	79	5	is	be	AUX
ejpam-6953	79	6	a	a	DET
ejpam-6953	79	7	bounded	bound	VERB
ejpam-6953	79	8	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	79	9	domain	domain	NOUN
ejpam-6953	79	10	with	with	ADP
ejpam-6953	79	11	a	a	DET
ejpam-6953	79	12	smooth	smooth	ADJ
ejpam-6953	79	13	defining	define	VERB
ejpam-6953	79	14	function	function	NOUN
ejpam-6953	79	15	ψ	ψ	NOUN
ejpam-6953	79	16	that	that	PRON
ejpam-6953	79	17	is	be	AUX
ejpam-6953	79	18	strictly	strictly	ADV
ejpam-6953	79	19	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	79	20	on	on	ADP
ejpam-6953	79	21	a	a	DET
ejpam-6953	79	22	neighborhood	neighborhood	NOUN
ejpam-6953	79	23	of	of	ADP
ejpam-6953	79	24	ω	ω	NOUN
ejpam-6953	79	25	,	,	PUNCT
ejpam-6953	79	26	then	then	ADV
ejpam-6953	79	27	for	for	ADP
ejpam-6953	79	28	any	any	DET
ejpam-6953	79	29	t	t	PROPN
ejpam-6953	79	30	≥	≥	NOUN
ejpam-6953	79	31	0	0	NUM
ejpam-6953	79	32	and	and	CCONJ
ejpam-6953	79	33	q	q	ADJ
ejpam-6953	79	34	≥	≥	NUM
ejpam-6953	79	35	1	1	NUM
ejpam-6953	79	36	,	,	PUNCT
ejpam-6953	79	37	the	the	DET
ejpam-6953	79	38	∂̄-equation	∂̄-equation	NOUN
ejpam-6953	79	39	is	be	AUX
ejpam-6953	79	40	solvable	solvable	ADJ
ejpam-6953	79	41	for	for	ADP
ejpam-6953	79	42	(	(	PUNCT
ejpam-6953	79	43	p	p	X
ejpam-6953	79	44	,	,	PUNCT
ejpam-6953	79	45	q)-forms	q)-form	NOUN
ejpam-6953	79	46	on	on	ADP
ejpam-6953	79	47	ω	ω	PROPN
ejpam-6953	79	48	with	with	ADP
ejpam-6953	79	49	uniform	uniform	ADJ
ejpam-6953	79	50	l2	l2	NOUN
ejpam-6953	79	51	control	control	VERB
ejpam-6953	79	52	up	up	ADP
ejpam-6953	79	53	to	to	ADP
ejpam-6953	79	54	a	a	DET
ejpam-6953	79	55	constant	constant	ADJ
ejpam-6953	79	56	depending	depend	VERB
ejpam-6953	79	57	on	on	ADP
ejpam-6953	79	58	infω	infω	ADJ
ejpam-6953	79	59	i∂∂̄ψ	i∂∂̄ψ	NOUN
ejpam-6953	79	60	and	and	CCONJ
ejpam-6953	79	61	supω	supω	ADJ
ejpam-6953	79	62	ψ	ψ	PROPN
ejpam-6953	79	63	.	.	PUNCT
ejpam-6953	80	1	more	more	ADV
ejpam-6953	80	2	precisely	precisely	ADV
ejpam-6953	80	3	:	:	PUNCT
ejpam-6953	80	4	lemma	lemma	PROPN
ejpam-6953	80	5	1	1	NUM
ejpam-6953	80	6	(	(	PUNCT
ejpam-6953	80	7	local	local	ADJ
ejpam-6953	80	8	∂̄-solution	∂̄-solution	NOUN
ejpam-6953	80	9	with	with	ADP
ejpam-6953	80	10	estimate	estimate	NOUN
ejpam-6953	80	11	)	)	PUNCT
ejpam-6953	80	12	.	.	PUNCT
ejpam-6953	81	1	let	let	VERB
ejpam-6953	81	2	ω	ω	NUM
ejpam-6953	81	3	⋐	⋐	NOUN
ejpam-6953	81	4	g	g	NOUN
ejpam-6953	81	5	be	be	AUX
ejpam-6953	81	6	a	a	DET
ejpam-6953	81	7	smoothly	smoothly	ADV
ejpam-6953	81	8	bounded	bound	VERB
ejpam-6953	81	9	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	81	10	domain	domain	NOUN
ejpam-6953	81	11	,	,	PUNCT
ejpam-6953	81	12	and	and	CCONJ
ejpam-6953	81	13	suppose	suppose	VERB
ejpam-6953	81	14	ψ	ψ	X
ejpam-6953	81	15	∈	∈	PROPN
ejpam-6953	81	16	c∞(ω	c∞(ω	NOUN
ejpam-6953	81	17	)	)	PUNCT
ejpam-6953	81	18	satisfies	satisfie	NOUN
ejpam-6953	81	19	ψ|∂ω	ψ|∂ω	NOUN
ejpam-6953	81	20	=	=	SYM
ejpam-6953	81	21	0	0	PUNCT
ejpam-6953	82	1	and	and	CCONJ
ejpam-6953	82	2	i∂∂̄ψ	i∂∂̄ψ	ADJ
ejpam-6953	82	3	≥	≥	NOUN
ejpam-6953	82	4	µω	µω	VERB
ejpam-6953	82	5	on	on	ADP
ejpam-6953	82	6	ω	ω	NUM
ejpam-6953	82	7	for	for	ADP
ejpam-6953	82	8	some	some	DET
ejpam-6953	82	9	µ	µ	NOUN
ejpam-6953	82	10	>	>	X
ejpam-6953	82	11	0	0	NUM
ejpam-6953	82	12	.	.	PUNCT
ejpam-6953	83	1	then	then	ADV
ejpam-6953	83	2	for	for	ADP
ejpam-6953	83	3	every	every	DET
ejpam-6953	83	4	t	t	PROPN
ejpam-6953	83	5	≥	≥	NOUN
ejpam-6953	83	6	0	0	NUM
ejpam-6953	83	7	and	and	CCONJ
ejpam-6953	83	8	every	every	DET
ejpam-6953	83	9	∂̄-closed	∂̄-close	VERB
ejpam-6953	83	10	form	form	NOUN
ejpam-6953	83	11	f	f	PROPN
ejpam-6953	83	12	∈	∈	PROPN
ejpam-6953	83	13	l2	l2	NOUN
ejpam-6953	83	14	p	p	NOUN
ejpam-6953	83	15	,	,	PUNCT
ejpam-6953	83	16	q(ω	q(ω	NOUN
ejpam-6953	83	17	,	,	PUNCT
ejpam-6953	83	18	e	e	PROPN
ejpam-6953	83	19	−tρ	−tρ	PROPN
ejpam-6953	83	20	)	)	PUNCT
ejpam-6953	83	21	with	with	ADP
ejpam-6953	83	22	q	q	PROPN
ejpam-6953	83	23	≥	≥	NUM
ejpam-6953	83	24	1	1	NUM
ejpam-6953	83	25	,	,	PUNCT
ejpam-6953	83	26	there	there	PRON
ejpam-6953	83	27	exists	exist	VERB
ejpam-6953	83	28	a	a	DET
ejpam-6953	83	29	solution	solution	NOUN
ejpam-6953	83	30	u	u	NOUN
ejpam-6953	83	31	∈	∈	NOUN
ejpam-6953	83	32	l2	l2	NOUN
ejpam-6953	83	33	p	p	NOUN
ejpam-6953	83	34	,	,	PUNCT
ejpam-6953	83	35	q−1(ω	q−1(ω	PROPN
ejpam-6953	83	36	,	,	PUNCT
ejpam-6953	83	37	e	e	PROPN
ejpam-6953	83	38	−tρ	−tρ	PROPN
ejpam-6953	83	39	)	)	PUNCT
ejpam-6953	83	40	of	of	ADP
ejpam-6953	83	41	∂̄u	∂̄u	PROPN
ejpam-6953	83	42	=	=	SYM
ejpam-6953	83	43	f	f	PROPN
ejpam-6953	83	44	on	on	ADP
ejpam-6953	83	45	ω	ω	NUM
ejpam-6953	83	46	such	such	ADJ
ejpam-6953	83	47	that∫	that∫	PROPN
ejpam-6953	83	48	ω	ω	PROPN
ejpam-6953	83	49	|u|2e−tρ	|u|2e−tρ	NUM
ejpam-6953	83	50	dvω	dvω	NOUN
ejpam-6953	83	51	≤	≤	ADV
ejpam-6953	83	52	2	2	NUM
ejpam-6953	83	53	µ	µ	NOUN
ejpam-6953	83	54	q	q	X
ejpam-6953	83	55	e	e	NOUN
ejpam-6953	83	56	t	t	NOUN
ejpam-6953	83	57	supω	supω	PROPN
ejpam-6953	83	58	ψ	ψ	X
ejpam-6953	83	59	∫	∫	PROPN
ejpam-6953	83	60	ω	ω	PROPN
ejpam-6953	83	61	|f	|f	PROPN
ejpam-6953	83	62	|2e−tρ	|2e−tρ	PROPN
ejpam-6953	83	63	dvω	dvω	PROPN
ejpam-6953	83	64	.	.	PUNCT
ejpam-6953	84	1	proof	proof	NOUN
ejpam-6953	84	2	.	.	PUNCT
ejpam-6953	85	1	this	this	PRON
ejpam-6953	85	2	is	be	AUX
ejpam-6953	85	3	essentially	essentially	ADV
ejpam-6953	85	4	the	the	DET
ejpam-6953	85	5	standard	standard	ADJ
ejpam-6953	85	6	hörmander	hörmander	NOUN
ejpam-6953	85	7	estimate	estimate	NOUN
ejpam-6953	85	8	applied	apply	VERB
ejpam-6953	85	9	with	with	ADP
ejpam-6953	85	10	the	the	DET
ejpam-6953	85	11	weight	weight	NOUN
ejpam-6953	85	12	tρ	tρ	X
ejpam-6953	85	13	+	+	X
ejpam-6953	85	14	ψ	ψ	X
ejpam-6953	85	15	.	.	NOUN
ejpam-6953	85	16	indeed	indeed	ADV
ejpam-6953	85	17	,	,	PUNCT
ejpam-6953	85	18	since	since	SCONJ
ejpam-6953	85	19	∂̄f	∂̄f	PROPN
ejpam-6953	85	20	=	=	SYM
ejpam-6953	85	21	0	0	PUNCT
ejpam-6953	85	22	and	and	CCONJ
ejpam-6953	85	23	∂ψ	∂ψ	PROPN
ejpam-6953	85	24	vanishes	vanish	VERB
ejpam-6953	85	25	to	to	ADP
ejpam-6953	85	26	first	first	ADJ
ejpam-6953	85	27	order	order	NOUN
ejpam-6953	85	28	on	on	ADP
ejpam-6953	85	29	∂ω	∂ω	PROPN
ejpam-6953	85	30	,	,	PUNCT
ejpam-6953	85	31	one	one	PRON
ejpam-6953	85	32	can	can	AUX
ejpam-6953	85	33	integrate	integrate	VERB
ejpam-6953	85	34	by	by	ADP
ejpam-6953	85	35	parts	part	NOUN
ejpam-6953	85	36	(	(	PUNCT
ejpam-6953	85	37	see	see	VERB
ejpam-6953	85	38	,	,	PUNCT
ejpam-6953	85	39	e.g.	e.g.	ADV
ejpam-6953	85	40	,	,	PUNCT
ejpam-6953	85	41	[	[	X
ejpam-6953	85	42	16	16	NUM
ejpam-6953	85	43	,	,	PUNCT
ejpam-6953	85	44	§	§	NOUN
ejpam-6953	85	45	4.2	4.2	NUM
ejpam-6953	85	46	]	]	PUNCT
ejpam-6953	85	47	)	)	PUNCT
ejpam-6953	85	48	to	to	PART
ejpam-6953	85	49	get	get	VERB
ejpam-6953	85	50	∥f∥2tρ+ψ	∥f∥2tρ+ψ	PROPN
ejpam-6953	85	51	,	,	PUNCT
ejpam-6953	85	52	ω	ω	NUM
ejpam-6953	85	53	≤	≤	ADJ
ejpam-6953	85	54	⟨ñtρ+ψf	⟨ñtρ+ψf	PROPN
ejpam-6953	85	55	,	,	PUNCT
ejpam-6953	85	56	f⟩tρ+ψ	f⟩tρ+ψ	PROPN
ejpam-6953	85	57	,	,	PUNCT
ejpam-6953	85	58	ω	ω	PROPN
ejpam-6953	85	59	,	,	PUNCT
ejpam-6953	85	60	where	where	SCONJ
ejpam-6953	85	61	ñtρ+ψ	ñtρ+ψ	ADJ
ejpam-6953	85	62	is	be	AUX
ejpam-6953	85	63	the	the	DET
ejpam-6953	85	64	weighted	weight	VERB
ejpam-6953	85	65	∂̄-neumann	∂̄-neumann	PROPN
ejpam-6953	85	66	operator	operator	NOUN
ejpam-6953	85	67	on	on	ADP
ejpam-6953	85	68	ω	ω	PROPN
ejpam-6953	85	69	.	.	PUNCT
ejpam-6953	86	1	because	because	SCONJ
ejpam-6953	86	2	ψ	ψ	VERB
ejpam-6953	86	3	≤	≤	ADV
ejpam-6953	86	4	0	0	NUM
ejpam-6953	87	1	on	on	ADP
ejpam-6953	87	2	ω	ω	NUM
ejpam-6953	87	3	,	,	PUNCT
ejpam-6953	87	4	this	this	PRON
ejpam-6953	87	5	implies	imply	VERB
ejpam-6953	87	6	µ	µ	X
ejpam-6953	87	7	q	q	X
ejpam-6953	87	8	2	2	NUM
ejpam-6953	87	9	e−	e−	NUM
ejpam-6953	87	10	t	t	NOUN
ejpam-6953	87	11	supω	supω	PROPN
ejpam-6953	87	12	ψ	ψ	X
ejpam-6953	87	13	∫	∫	PROPN
ejpam-6953	87	14	ω	ω	PROPN
ejpam-6953	87	15	|u|2e−tρ	|u|2e−tρ	NUM
ejpam-6953	87	16	dvω	dvω	PROPN
ejpam-6953	88	1	≤	≤	NUM
ejpam-6953	88	2	∫	∫	PROPN
ejpam-6953	89	1	ω	ω	PROPN
ejpam-6953	89	2	|f	|f	PROPN
ejpam-6953	89	3	|2e−tρ	|2e−tρ	PROPN
ejpam-6953	89	4	dvω	dvω	PROPN
ejpam-6953	89	5	,	,	PUNCT
ejpam-6953	89	6	a.	a.	PROPN
ejpam-6953	89	7	r.	r.	PROPN
ejpam-6953	89	8	al	al	PROPN
ejpam-6953	89	9	-	-	PUNCT
ejpam-6953	89	10	abdallah	abdallah	PROPN
ejpam-6953	89	11	/	/	SYM
ejpam-6953	89	12	eur	eur	PROPN
ejpam-6953	89	13	.	.	PUNCT
ejpam-6953	90	1	j.	j.	PROPN
ejpam-6953	90	2	pure	pure	PROPN
ejpam-6953	90	3	appl	appl	PROPN
ejpam-6953	90	4	.	.	PROPN
ejpam-6953	90	5	math	math	PROPN
ejpam-6953	90	6	,	,	PUNCT
ejpam-6953	90	7	18	18	NUM
ejpam-6953	90	8	(	(	PUNCT
ejpam-6953	90	9	4	4	NUM
ejpam-6953	90	10	)	)	PUNCT
ejpam-6953	90	11	(	(	PUNCT
ejpam-6953	90	12	2025	2025	NUM
ejpam-6953	90	13	)	)	PUNCT
ejpam-6953	90	14	,	,	PUNCT
ejpam-6953	90	15	6953	6953	NUM
ejpam-6953	90	16	5	5	NUM
ejpam-6953	90	17	of	of	ADP
ejpam-6953	90	18	14	14	NUM
ejpam-6953	90	19	where	where	SCONJ
ejpam-6953	90	20	u	u	NOUN
ejpam-6953	90	21	:	:	PUNCT
ejpam-6953	90	22	=	=	PUNCT
ejpam-6953	90	23	∂̄∗tρ+ψñtρ+ψf	∂̄∗tρ+ψñtρ+ψf	INTJ
ejpam-6953	90	24	.	.	PUNCT
ejpam-6953	91	1	this	this	DET
ejpam-6953	91	2	u	u	NOUN
ejpam-6953	91	3	lies	lie	VERB
ejpam-6953	91	4	in	in	ADP
ejpam-6953	91	5	l2	l2	NOUN
ejpam-6953	91	6	p	p	NOUN
ejpam-6953	91	7	,	,	PUNCT
ejpam-6953	91	8	q−1(ω	q−1(ω	PROPN
ejpam-6953	91	9	,	,	PUNCT
ejpam-6953	91	10	e	e	NOUN
ejpam-6953	91	11	−tρ−ψ	−tρ−ψ	NOUN
ejpam-6953	91	12	)	)	PUNCT
ejpam-6953	91	13	and	and	CCONJ
ejpam-6953	91	14	satisfies	satisfy	VERB
ejpam-6953	91	15	∂̄u	∂̄u	PROPN
ejpam-6953	91	16	=	=	SYM
ejpam-6953	91	17	f	f	PROPN
ejpam-6953	91	18	.	.	PUNCT
ejpam-6953	92	1	the	the	DET
ejpam-6953	92	2	above	above	ADJ
ejpam-6953	92	3	estimate	estimate	NOUN
ejpam-6953	92	4	gives	give	VERB
ejpam-6953	92	5	∫	∫	PROPN
ejpam-6953	92	6	ω	ω	PROPN
ejpam-6953	92	7	|u|2e−tρ	|u|2e−tρ	NUM
ejpam-6953	92	8	dvω	dvω	NOUN
ejpam-6953	92	9	≤	≤	ADV
ejpam-6953	92	10	2	2	NUM
ejpam-6953	92	11	µ	µ	NOUN
ejpam-6953	92	12	q	q	X
ejpam-6953	92	13	e	e	NOUN
ejpam-6953	92	14	t	t	NOUN
ejpam-6953	92	15	supω	supω	PROPN
ejpam-6953	92	16	ψ	ψ	X
ejpam-6953	92	17	∫	∫	PROPN
ejpam-6953	92	18	ω	ω	PROPN
ejpam-6953	92	19	|f	|f	PROPN
ejpam-6953	92	20	|2e−tρ	|2e−tρ	PROPN
ejpam-6953	92	21	dvω	dvω	PROPN
ejpam-6953	92	22	.	.	PUNCT
ejpam-6953	93	1	this	this	PRON
ejpam-6953	93	2	proves	prove	VERB
ejpam-6953	93	3	the	the	DET
ejpam-6953	93	4	desired	desire	VERB
ejpam-6953	93	5	inequality	inequality	NOUN
ejpam-6953	93	6	.	.	PUNCT
ejpam-6953	94	1	3	3	X
ejpam-6953	94	2	.	.	X
ejpam-6953	94	3	exhaustion	exhaustion	NOUN
ejpam-6953	94	4	by	by	ADP
ejpam-6953	94	5	strictly	strictly	ADV
ejpam-6953	94	6	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	94	7	sublevels	sublevel	NOUN
ejpam-6953	94	8	in	in	ADP
ejpam-6953	94	9	this	this	DET
ejpam-6953	94	10	section	section	NOUN
ejpam-6953	94	11	we	we	PRON
ejpam-6953	94	12	obtain	obtain	VERB
ejpam-6953	94	13	the	the	DET
ejpam-6953	94	14	uniform	uniform	ADJ
ejpam-6953	94	15	exhaustion	exhaustion	NOUN
ejpam-6953	94	16	(	(	PUNCT
ejpam-6953	94	17	u1	u1	NOUN
ejpam-6953	94	18	)	)	PUNCT
ejpam-6953	94	19	stated	state	VERB
ejpam-6953	94	20	earlier	early	ADV
ejpam-6953	94	21	.	.	PUNCT
ejpam-6953	95	1	we	we	PRON
ejpam-6953	95	2	will	will	AUX
ejpam-6953	95	3	use	use	VERB
ejpam-6953	95	4	a	a	DET
ejpam-6953	95	5	version	version	NOUN
ejpam-6953	95	6	of	of	ADP
ejpam-6953	95	7	richberg	richberg	PROPN
ejpam-6953	95	8	’s	’s	PART
ejpam-6953	95	9	theorem	theorem	NOUN
ejpam-6953	95	10	[	[	X
ejpam-6953	95	11	14	14	NUM
ejpam-6953	95	12	]	]	PUNCT
ejpam-6953	95	13	that	that	PRON
ejpam-6953	95	14	allows	allow	VERB
ejpam-6953	95	15	us	we	PRON
ejpam-6953	95	16	to	to	PART
ejpam-6953	95	17	smoothly	smoothly	ADV
ejpam-6953	95	18	approximate	approximate	VERB
ejpam-6953	95	19	a	a	DET
ejpam-6953	95	20	continuous	continuous	ADJ
ejpam-6953	95	21	psh	psh	NOUN
ejpam-6953	95	22	function	function	NOUN
ejpam-6953	95	23	from	from	ADP
ejpam-6953	95	24	above	above	ADV
ejpam-6953	95	25	with	with	ADP
ejpam-6953	95	26	small	small	ADJ
ejpam-6953	95	27	uniform	uniform	NOUN
ejpam-6953	95	28	error	error	NOUN
ejpam-6953	95	29	.	.	PUNCT
ejpam-6953	96	1	modern	modern	ADJ
ejpam-6953	96	2	expositions	exposition	NOUN
ejpam-6953	96	3	of	of	ADP
ejpam-6953	96	4	such	such	ADJ
ejpam-6953	96	5	regularization	regularization	NOUN
ejpam-6953	96	6	on	on	ADP
ejpam-6953	96	7	manifolds	manifold	NOUN
ejpam-6953	96	8	can	can	AUX
ejpam-6953	96	9	be	be	AUX
ejpam-6953	96	10	found	find	VERB
ejpam-6953	96	11	in	in	ADP
ejpam-6953	96	12	[	[	X
ejpam-6953	96	13	16	16	NUM
ejpam-6953	96	14	,	,	PUNCT
ejpam-6953	96	15	17	17	NUM
ejpam-6953	96	16	]	]	PUNCT
ejpam-6953	96	17	.	.	PUNCT
ejpam-6953	97	1	for	for	ADP
ejpam-6953	97	2	completeness	completeness	NOUN
ejpam-6953	97	3	,	,	PUNCT
ejpam-6953	97	4	we	we	PRON
ejpam-6953	97	5	include	include	VERB
ejpam-6953	97	6	a	a	DET
ejpam-6953	97	7	simple	simple	ADJ
ejpam-6953	97	8	proof	proof	NOUN
ejpam-6953	97	9	in	in	ADP
ejpam-6953	97	10	appendix	appendix	PROPN
ejpam-6953	97	11	a.	a.	NOUN
ejpam-6953	97	12	lemma	lemma	PROPN
ejpam-6953	97	13	2	2	X
ejpam-6953	97	14	.	.	PUNCT
ejpam-6953	98	1	there	there	PRON
ejpam-6953	98	2	exists	exist	VERB
ejpam-6953	98	3	an	an	DET
ejpam-6953	98	4	exhaustion	exhaustion	NOUN
ejpam-6953	98	5	g	g	NOUN
ejpam-6953	98	6	=	=	PUNCT
ejpam-6953	98	7	⋃∞	⋃∞	X
ejpam-6953	98	8	j=1	j=1	PROPN
ejpam-6953	98	9	ωj	ωj	ADP
ejpam-6953	98	10	by	by	ADP
ejpam-6953	98	11	smoothly	smoothly	ADV
ejpam-6953	98	12	bounded	bound	VERB
ejpam-6953	98	13	strictly	strictly	ADV
ejpam-6953	98	14	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	98	15	domains	domain	NOUN
ejpam-6953	98	16	,	,	PUNCT
ejpam-6953	98	17	and	and	CCONJ
ejpam-6953	98	18	smooth	smooth	ADJ
ejpam-6953	98	19	functions	function	NOUN
ejpam-6953	98	20	φj	φj	ADP
ejpam-6953	98	21	∈	∈	PROPN
ejpam-6953	98	22	c∞(ωj	c∞(ωj	PROPN
ejpam-6953	98	23	)	)	PUNCT
ejpam-6953	98	24	,	,	PUNCT
ejpam-6953	98	25	such	such	ADJ
ejpam-6953	98	26	that	that	PRON
ejpam-6953	98	27	for	for	ADP
ejpam-6953	98	28	each	each	DET
ejpam-6953	98	29	j	j	PROPN
ejpam-6953	98	30	≥	≥	NOUN
ejpam-6953	98	31	1	1	NUM
ejpam-6953	98	32	:	:	PUNCT
ejpam-6953	98	33	(	(	PUNCT
ejpam-6953	98	34	i	i	NOUN
ejpam-6953	98	35	)	)	PUNCT
ejpam-6953	98	36	ωj	ωj	ADP
ejpam-6953	98	37	:	:	PUNCT
ejpam-6953	98	38	=	=	SYM
ejpam-6953	98	39	{	{	PUNCT
ejpam-6953	98	40	ρ	ρ	PROPN
ejpam-6953	98	41	<	<	X
ejpam-6953	98	42	rj	rj	PROPN
ejpam-6953	98	43	}	}	PUNCT
ejpam-6953	98	44	for	for	ADP
ejpam-6953	98	45	some	some	DET
ejpam-6953	98	46	rj	rj	PROPN
ejpam-6953	98	47	∈	∈	PROPN
ejpam-6953	98	48	r	r	NOUN
ejpam-6953	98	49	(	(	PUNCT
ejpam-6953	98	50	with	with	ADP
ejpam-6953	98	51	rj	rj	PROPN
ejpam-6953	98	52	→	→	SYM
ejpam-6953	98	53	∞	∞	PROPN
ejpam-6953	98	54	as	as	ADP
ejpam-6953	98	55	j	j	PROPN
ejpam-6953	98	56	→	→	SYM
ejpam-6953	98	57	∞	∞	PROPN
ejpam-6953	98	58	)	)	PUNCT
ejpam-6953	98	59	.	.	PUNCT
ejpam-6953	99	1	(	(	PUNCT
ejpam-6953	99	2	ii	ii	NOUN
ejpam-6953	99	3	)	)	PUNCT
ejpam-6953	99	4	φj	φj	PROPN
ejpam-6953	99	5	is	be	AUX
ejpam-6953	99	6	strictly	strictly	ADV
ejpam-6953	99	7	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	99	8	on	on	ADP
ejpam-6953	99	9	a	a	DET
ejpam-6953	99	10	neighborhood	neighborhood	NOUN
ejpam-6953	99	11	of	of	ADP
ejpam-6953	99	12	ωj	ωj	NOUN
ejpam-6953	99	13	,	,	PUNCT
ejpam-6953	99	14	and	and	CCONJ
ejpam-6953	99	15	φj	φj	X
ejpam-6953	99	16	|∂ωj	|∂ωj	PROPN
ejpam-6953	99	17	=	=	SYM
ejpam-6953	100	1	0	0	PROPN
ejpam-6953	100	2	.	.	PUNCT
ejpam-6953	101	1	(	(	PUNCT
ejpam-6953	101	2	iii	iii	X
ejpam-6953	101	3	)	)	PUNCT
ejpam-6953	101	4	|φj	|φj	X
ejpam-6953	101	5	−	−	PROPN
ejpam-6953	101	6	ρ|	ρ|	PROPN
ejpam-6953	101	7	<	<	X
ejpam-6953	101	8	1	1	NUM
ejpam-6953	101	9	4	4	NUM
ejpam-6953	101	10	on	on	ADP
ejpam-6953	101	11	ωj−1	ωj−1	NOUN
ejpam-6953	101	12	(	(	PUNCT
ejpam-6953	101	13	for	for	ADP
ejpam-6953	101	14	j	j	PROPN
ejpam-6953	101	15	≥	≥	PROPN
ejpam-6953	101	16	2	2	NUM
ejpam-6953	101	17	)	)	PUNCT
ejpam-6953	101	18	.	.	PUNCT
ejpam-6953	102	1	proof	proof	NOUN
ejpam-6953	102	2	.	.	PUNCT
ejpam-6953	103	1	since	since	SCONJ
ejpam-6953	103	2	ρ	ρ	PROPN
ejpam-6953	103	3	is	be	AUX
ejpam-6953	103	4	a	a	DET
ejpam-6953	103	5	continuous	continuous	ADJ
ejpam-6953	103	6	exhaustion	exhaustion	NOUN
ejpam-6953	103	7	,	,	PUNCT
ejpam-6953	103	8	its	its	PRON
ejpam-6953	103	9	sublevel	sublevel	NOUN
ejpam-6953	103	10	sets	set	NOUN
ejpam-6953	103	11	{	{	PUNCT
ejpam-6953	103	12	ρ	ρ	X
ejpam-6953	103	13	<	<	X
ejpam-6953	103	14	c	c	NOUN
ejpam-6953	103	15	}	}	PUNCT
ejpam-6953	103	16	are	be	AUX
ejpam-6953	103	17	all	all	PRON
ejpam-6953	103	18	relatively	relatively	ADV
ejpam-6953	103	19	compact	compact	ADJ
ejpam-6953	103	20	in	in	ADP
ejpam-6953	103	21	g.	g.	NOUN
ejpam-6953	103	22	we	we	PRON
ejpam-6953	103	23	inductively	inductively	ADV
ejpam-6953	103	24	define	define	VERB
ejpam-6953	103	25	a	a	DET
ejpam-6953	103	26	sequence	sequence	NOUN
ejpam-6953	103	27	r1	r1	NOUN
ejpam-6953	103	28	<	<	X
ejpam-6953	103	29	r2	r2	PROPN
ejpam-6953	103	30	<	<	X
ejpam-6953	103	31	r3	r3	PROPN
ejpam-6953	103	32	<	<	X
ejpam-6953	103	33	·	·	PUNCT
ejpam-6953	103	34	·	·	PUNCT
ejpam-6953	103	35	·	·	PUNCT
ejpam-6953	103	36	with	with	ADP
ejpam-6953	103	37	rj	rj	PROPN
ejpam-6953	103	38	→	→	SYM
ejpam-6953	103	39	∞	∞	PROPN
ejpam-6953	103	40	as	as	ADP
ejpam-6953	103	41	j	j	PROPN
ejpam-6953	103	42	→	→	SYM
ejpam-6953	103	43	∞	∞	PROPN
ejpam-6953	103	44	,	,	PUNCT
ejpam-6953	103	45	and	and	CCONJ
ejpam-6953	103	46	corresponding	correspond	VERB
ejpam-6953	103	47	φj	φj	NOUN
ejpam-6953	103	48	,	,	PUNCT
ejpam-6953	103	49	as	as	SCONJ
ejpam-6953	103	50	follows	follow	VERB
ejpam-6953	103	51	.	.	PUNCT
ejpam-6953	104	1	let	let	VERB
ejpam-6953	104	2	ω1	ω1	PROPN
ejpam-6953	104	3	:	:	PUNCT
ejpam-6953	104	4	=	=	SYM
ejpam-6953	104	5	{	{	PUNCT
ejpam-6953	104	6	ρ	ρ	PROPN
ejpam-6953	104	7	<	<	X
ejpam-6953	104	8	r1	r1	PROPN
ejpam-6953	104	9	}	}	PUNCT
ejpam-6953	104	10	for	for	ADP
ejpam-6953	104	11	some	some	DET
ejpam-6953	104	12	r1	r1	NOUN
ejpam-6953	104	13	so	so	ADV
ejpam-6953	104	14	large	large	ADJ
ejpam-6953	104	15	that	that	SCONJ
ejpam-6953	104	16	ω1	ω1	PROPN
ejpam-6953	104	17	̸=	̸=	PROPN
ejpam-6953	104	18	∅	∅	NOUN
ejpam-6953	104	19	and	and	CCONJ
ejpam-6953	104	20	ρ	ρ	NOUN
ejpam-6953	104	21	is	be	AUX
ejpam-6953	104	22	bounded	bound	VERB
ejpam-6953	104	23	on	on	ADP
ejpam-6953	104	24	ω1	ω1	PROPN
ejpam-6953	104	25	.	.	PUNCT
ejpam-6953	105	1	by	by	ADP
ejpam-6953	105	2	smoothing	smooth	VERB
ejpam-6953	105	3	ρ	ρ	NOUN
ejpam-6953	105	4	on	on	ADP
ejpam-6953	105	5	a	a	DET
ejpam-6953	105	6	slightly	slightly	ADV
ejpam-6953	105	7	larger	large	ADJ
ejpam-6953	105	8	level	level	NOUN
ejpam-6953	105	9	set	set	NOUN
ejpam-6953	105	10	,	,	PUNCT
ejpam-6953	105	11	we	we	PRON
ejpam-6953	105	12	can	can	AUX
ejpam-6953	105	13	find	find	VERB
ejpam-6953	105	14	a	a	DET
ejpam-6953	105	15	smooth	smooth	ADJ
ejpam-6953	105	16	strictly	strictly	ADV
ejpam-6953	105	17	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	105	18	function	function	NOUN
ejpam-6953	105	19	φ1	φ1	NOUN
ejpam-6953	105	20	on	on	ADP
ejpam-6953	105	21	a	a	DET
ejpam-6953	105	22	neighborhood	neighborhood	NOUN
ejpam-6953	105	23	of	of	ADP
ejpam-6953	105	24	ω1	ω1	PROPN
ejpam-6953	105	25	that	that	PRON
ejpam-6953	105	26	coincides	coincide	VERB
ejpam-6953	105	27	with	with	ADP
ejpam-6953	105	28	ρ	ρ	PROPN
ejpam-6953	105	29	near	near	ADP
ejpam-6953	105	30	∂ω1	∂ω1	PROPN
ejpam-6953	105	31	.	.	PUNCT
ejpam-6953	106	1	(	(	PUNCT
ejpam-6953	106	2	for	for	ADP
ejpam-6953	106	3	instance	instance	NOUN
ejpam-6953	106	4	,	,	PUNCT
ejpam-6953	106	5	one	one	PRON
ejpam-6953	106	6	can	can	AUX
ejpam-6953	106	7	take	take	VERB
ejpam-6953	106	8	φ1	φ1	NOUN
ejpam-6953	106	9	=	=	SYM
ejpam-6953	106	10	ρ	ρ	PROPN
ejpam-6953	106	11	∗	∗	X
ejpam-6953	106	12	χε	χε	NOUN
ejpam-6953	106	13	to	to	PART
ejpam-6953	106	14	be	be	AUX
ejpam-6953	106	15	a	a	DET
ejpam-6953	106	16	standard	standard	ADJ
ejpam-6953	106	17	mollification	mollification	NOUN
ejpam-6953	106	18	of	of	ADP
ejpam-6953	106	19	ρ	ρ	PROPN
ejpam-6953	106	20	in	in	ADP
ejpam-6953	106	21	local	local	ADJ
ejpam-6953	106	22	charts	chart	NOUN
ejpam-6953	106	23	,	,	PUNCT
ejpam-6953	106	24	for	for	ADP
ejpam-6953	106	25	sufficiently	sufficiently	ADV
ejpam-6953	106	26	small	small	ADJ
ejpam-6953	106	27	ε	ε	PROPN
ejpam-6953	106	28	>	>	X
ejpam-6953	106	29	0	0	PROPN
ejpam-6953	106	30	,	,	PUNCT
ejpam-6953	106	31	which	which	PRON
ejpam-6953	106	32	will	will	AUX
ejpam-6953	106	33	be	be	AUX
ejpam-6953	106	34	strictly	strictly	ADV
ejpam-6953	106	35	psh	psh	ADJ
ejpam-6953	106	36	on	on	ADP
ejpam-6953	106	37	ω1	ω1	PROPN
ejpam-6953	106	38	by	by	ADP
ejpam-6953	106	39	continuity	continuity	NOUN
ejpam-6953	106	40	since	since	SCONJ
ejpam-6953	106	41	ρ	ρ	PROPN
ejpam-6953	106	42	is	be	AUX
ejpam-6953	106	43	strictly	strictly	ADV
ejpam-6953	106	44	psh	psh	PROPN
ejpam-6953	106	45	near	near	ADP
ejpam-6953	106	46	∂ω1	∂ω1	PROPN
ejpam-6953	106	47	.	.	PUNCT
ejpam-6953	106	48	)	)	PUNCT
ejpam-6953	107	1	in	in	ADP
ejpam-6953	107	2	particular	particular	ADJ
ejpam-6953	107	3	φ1	φ1	NOUN
ejpam-6953	107	4	is	be	AUX
ejpam-6953	107	5	strictly	strictly	ADV
ejpam-6953	107	6	psh	psh	ADJ
ejpam-6953	107	7	on	on	ADP
ejpam-6953	107	8	ω1	ω1	PROPN
ejpam-6953	107	9	and	and	CCONJ
ejpam-6953	107	10	φ1|∂ω1	φ1|∂ω1	PROPN
ejpam-6953	107	11	=	=	SYM
ejpam-6953	107	12	ρ|∂ω1	ρ|∂ω1	PUNCT
ejpam-6953	107	13	=	=	SYM
ejpam-6953	107	14	r1	r1	PROPN
ejpam-6953	107	15	.	.	PUNCT
ejpam-6953	108	1	replacing	replace	VERB
ejpam-6953	108	2	φ1	φ1	NOUN
ejpam-6953	108	3	by	by	ADP
ejpam-6953	108	4	φ1	φ1	PROPN
ejpam-6953	108	5	−r1	−r1	PROPN
ejpam-6953	108	6	,	,	PUNCT
ejpam-6953	108	7	we	we	PRON
ejpam-6953	108	8	may	may	AUX
ejpam-6953	108	9	assume	assume	VERB
ejpam-6953	108	10	φ1|∂ω1	φ1|∂ω1	PROPN
ejpam-6953	108	11	=	=	SYM
ejpam-6953	108	12	0	0	X
ejpam-6953	108	13	.	.	PUNCT
ejpam-6953	109	1	now	now	ADV
ejpam-6953	109	2	suppose	suppose	VERB
ejpam-6953	109	3	r1	r1	PROPN
ejpam-6953	109	4	,	,	PUNCT
ejpam-6953	109	5	.	.	PUNCT
ejpam-6953	109	6	.	.	PUNCT
ejpam-6953	110	1	.	.	PUNCT
ejpam-6953	111	1	,	,	PUNCT
ejpam-6953	111	2	rj	rj	PROPN
ejpam-6953	111	3	and	and	CCONJ
ejpam-6953	111	4	φ1	φ1	PROPN
ejpam-6953	111	5	,	,	PUNCT
ejpam-6953	111	6	.	.	PUNCT
ejpam-6953	111	7	.	.	PUNCT
ejpam-6953	112	1	.	.	PUNCT
ejpam-6953	113	1	,	,	PUNCT
ejpam-6953	113	2	φj	φj	PROPN
ejpam-6953	113	3	have	have	AUX
ejpam-6953	113	4	been	be	AUX
ejpam-6953	113	5	chosen	choose	VERB
ejpam-6953	113	6	for	for	ADP
ejpam-6953	113	7	some	some	DET
ejpam-6953	113	8	j	j	PROPN
ejpam-6953	113	9	≥	≥	PROPN
ejpam-6953	113	10	1	1	NUM
ejpam-6953	113	11	.	.	PUNCT
ejpam-6953	114	1	since	since	SCONJ
ejpam-6953	114	2	ρ	ρ	PROPN
ejpam-6953	114	3	tends	tend	VERB
ejpam-6953	114	4	to	to	ADP
ejpam-6953	114	5	+	+	NOUN
ejpam-6953	114	6	∞	∞	PROPN
ejpam-6953	114	7	at	at	ADP
ejpam-6953	114	8	infinity	infinity	NOUN
ejpam-6953	114	9	,	,	PUNCT
ejpam-6953	114	10	we	we	PRON
ejpam-6953	114	11	can	can	AUX
ejpam-6953	114	12	pick	pick	VERB
ejpam-6953	114	13	rj+1	rj+1	PRON
ejpam-6953	114	14	>	>	PUNCT
ejpam-6953	114	15	rj	rj	PROPN
ejpam-6953	114	16	large	large	ADJ
ejpam-6953	114	17	enough	enough	ADV
ejpam-6953	114	18	so	so	SCONJ
ejpam-6953	114	19	that	that	SCONJ
ejpam-6953	114	20	{	{	PUNCT
ejpam-6953	114	21	ρ	ρ	X
ejpam-6953	114	22	<	<	X
ejpam-6953	114	23	rj+1	rj+1	PROPN
ejpam-6953	114	24	}	}	PUNCT
ejpam-6953	114	25	⊃	⊃	NOUN
ejpam-6953	114	26	ωj	ωj	X
ejpam-6953	114	27	and	and	CCONJ
ejpam-6953	114	28	supωj	supωj	NOUN
ejpam-6953	114	29	ρ	ρ	X
ejpam-6953	114	30	<	<	X
ejpam-6953	114	31	rj+1	rj+1	PRON
ejpam-6953	114	32	−	−	PROPN
ejpam-6953	114	33	1	1	NUM
ejpam-6953	114	34	4	4	NUM
ejpam-6953	114	35	.	.	PUNCT
ejpam-6953	115	1	set	set	VERB
ejpam-6953	115	2	ωj+1	ωj+1	NUM
ejpam-6953	115	3	:	:	PUNCT
ejpam-6953	115	4	=	=	SYM
ejpam-6953	115	5	{	{	PUNCT
ejpam-6953	115	6	ρ	ρ	X
ejpam-6953	115	7	<	<	X
ejpam-6953	115	8	rj+1	rj+1	NOUN
ejpam-6953	115	9	}	}	PUNCT
ejpam-6953	115	10	.	.	PUNCT
ejpam-6953	116	1	note	note	VERB
ejpam-6953	116	2	that	that	SCONJ
ejpam-6953	116	3	ωj+1	ωj+1	PRON
ejpam-6953	116	4	is	be	AUX
ejpam-6953	116	5	a	a	DET
ejpam-6953	116	6	larger	large	ADJ
ejpam-6953	116	7	relatively	relatively	ADV
ejpam-6953	116	8	compact	compact	ADJ
ejpam-6953	116	9	domain	domain	NOUN
ejpam-6953	116	10	containing	contain	VERB
ejpam-6953	116	11	ωj	ωj	ADP
ejpam-6953	116	12	,	,	PUNCT
ejpam-6953	116	13	and	and	CCONJ
ejpam-6953	116	14	ρ	ρ	NOUN
ejpam-6953	116	15	is	be	AUX
ejpam-6953	116	16	strictly	strictly	ADV
ejpam-6953	116	17	psh	psh	ADJ
ejpam-6953	116	18	near	near	ADP
ejpam-6953	116	19	∂ωj+1	∂ωj+1	NOUN
ejpam-6953	116	20	.	.	PUNCT
ejpam-6953	117	1	applying	apply	VERB
ejpam-6953	117	2	richberg	richberg	PROPN
ejpam-6953	117	3	’s	’s	PART
ejpam-6953	117	4	smoothing	smoothing	NOUN
ejpam-6953	117	5	theorem	theorem	NOUN
ejpam-6953	117	6	(	(	PUNCT
ejpam-6953	117	7	see	see	VERB
ejpam-6953	117	8	[	[	X
ejpam-6953	117	9	14	14	NUM
ejpam-6953	117	10	]	]	PUNCT
ejpam-6953	117	11	and	and	CCONJ
ejpam-6953	117	12	also	also	ADV
ejpam-6953	117	13	[	[	X
ejpam-6953	117	14	17	17	NUM
ejpam-6953	117	15	]	]	PUNCT
ejpam-6953	117	16	for	for	ADP
ejpam-6953	117	17	a	a	DET
ejpam-6953	117	18	modern	modern	ADJ
ejpam-6953	117	19	exposition	exposition	NOUN
ejpam-6953	117	20	)	)	PUNCT
ejpam-6953	117	21	on	on	ADP
ejpam-6953	117	22	ωj+1	ωj+1	NUM
ejpam-6953	117	23	,	,	PUNCT
ejpam-6953	117	24	we	we	PRON
ejpam-6953	117	25	obtain	obtain	VERB
ejpam-6953	117	26	a	a	DET
ejpam-6953	117	27	smooth	smooth	ADJ
ejpam-6953	117	28	strictly	strictly	ADV
ejpam-6953	117	29	psh	psh	NOUN
ejpam-6953	117	30	function	function	NOUN
ejpam-6953	117	31	φj+1	φj+1	NOUN
ejpam-6953	117	32	on	on	ADP
ejpam-6953	117	33	ωj+1	ωj+1	NUM
ejpam-6953	117	34	satisfying	satisfy	VERB
ejpam-6953	117	35	sup	sup	NOUN
ejpam-6953	117	36	ωj	ωj	ADP
ejpam-6953	117	37	|φj+1	|φj+1	NOUN
ejpam-6953	117	38	−	−	PROPN
ejpam-6953	117	39	ρ|	ρ|	PROPN
ejpam-6953	117	40	<	<	X
ejpam-6953	117	41	1	1	NUM
ejpam-6953	117	42	4	4	NUM
ejpam-6953	117	43	.	.	PUNCT
ejpam-6953	118	1	in	in	ADP
ejpam-6953	118	2	particular	particular	ADJ
ejpam-6953	118	3	,	,	PUNCT
ejpam-6953	118	4	φj+1	φj+1	NUM
ejpam-6953	118	5	<	<	X
ejpam-6953	118	6	rj+1	rj+1	NOUN
ejpam-6953	118	7	on	on	ADP
ejpam-6953	118	8	ωj	ωj	ADP
ejpam-6953	118	9	.	.	PUNCT
ejpam-6953	119	1	we	we	PRON
ejpam-6953	119	2	now	now	ADV
ejpam-6953	119	3	define	define	VERB
ejpam-6953	119	4	φ̃j+1(x	φ̃j+1(x	NOUN
ejpam-6953	119	5	)	)	PUNCT
ejpam-6953	119	6	:	:	PUNCT
ejpam-6953	119	7	=	=	SYM
ejpam-6953	119	8	max{φj+1(x	max{φj+1(x	NOUN
ejpam-6953	119	9	)	)	PUNCT
ejpam-6953	119	10	,	,	PUNCT
ejpam-6953	119	11	δ	δ	PROPN
ejpam-6953	119	12	·	·	PUNCT
ejpam-6953	119	13	dist(x	dist(x	INTJ
ejpam-6953	119	14	,	,	PUNCT
ejpam-6953	119	15	∂ωj+1	∂ωj+1	NOUN
ejpam-6953	119	16	)	)	PUNCT
ejpam-6953	119	17	}	}	PUNCT
ejpam-6953	119	18	,	,	PUNCT
ejpam-6953	119	19	x	x	PUNCT
ejpam-6953	119	20	∈	∈	NOUN
ejpam-6953	119	21	ωj+1	ωj+1	X
ejpam-6953	119	22	,	,	PUNCT
ejpam-6953	119	23	a.	a.	PROPN
ejpam-6953	119	24	r.	r.	PROPN
ejpam-6953	119	25	al	al	PROPN
ejpam-6953	119	26	-	-	PUNCT
ejpam-6953	119	27	abdallah	abdallah	PROPN
ejpam-6953	119	28	/	/	SYM
ejpam-6953	119	29	eur	eur	PROPN
ejpam-6953	119	30	.	.	PUNCT
ejpam-6953	120	1	j.	j.	PROPN
ejpam-6953	120	2	pure	pure	PROPN
ejpam-6953	120	3	appl	appl	PROPN
ejpam-6953	120	4	.	.	PROPN
ejpam-6953	120	5	math	math	PROPN
ejpam-6953	120	6	,	,	PUNCT
ejpam-6953	120	7	18	18	NUM
ejpam-6953	120	8	(	(	PUNCT
ejpam-6953	120	9	4	4	NUM
ejpam-6953	120	10	)	)	PUNCT
ejpam-6953	120	11	(	(	PUNCT
ejpam-6953	120	12	2025	2025	NUM
ejpam-6953	120	13	)	)	PUNCT
ejpam-6953	120	14	,	,	PUNCT
ejpam-6953	120	15	6953	6953	NUM
ejpam-6953	120	16	6	6	NUM
ejpam-6953	120	17	of	of	ADP
ejpam-6953	120	18	14	14	NUM
ejpam-6953	120	19	where	where	SCONJ
ejpam-6953	120	20	dist	dist	NOUN
ejpam-6953	120	21	(	(	PUNCT
ejpam-6953	120	22	·	·	PUNCT
ejpam-6953	120	23	,	,	PUNCT
ejpam-6953	120	24	∂ωj+1	∂ωj+1	NOUN
ejpam-6953	120	25	)	)	PUNCT
ejpam-6953	120	26	is	be	AUX
ejpam-6953	120	27	the	the	DET
ejpam-6953	120	28	distance	distance	NOUN
ejpam-6953	120	29	function	function	NOUN
ejpam-6953	120	30	to	to	ADP
ejpam-6953	120	31	the	the	DET
ejpam-6953	120	32	boundary	boundary	ADJ
ejpam-6953	120	33	(	(	PUNCT
ejpam-6953	120	34	with	with	ADP
ejpam-6953	120	35	respect	respect	NOUN
ejpam-6953	120	36	to	to	ADP
ejpam-6953	120	37	a	a	DET
ejpam-6953	120	38	fixed	fix	VERB
ejpam-6953	120	39	riemannian	riemannian	NOUN
ejpam-6953	120	40	metric	metric	NOUN
ejpam-6953	120	41	on	on	ADP
ejpam-6953	120	42	g	g	PROPN
ejpam-6953	120	43	)	)	PUNCT
ejpam-6953	120	44	,	,	PUNCT
ejpam-6953	120	45	and	and	CCONJ
ejpam-6953	120	46	δ	δ	PROPN
ejpam-6953	120	47	>	>	X
ejpam-6953	120	48	0	0	NUM
ejpam-6953	120	49	is	be	AUX
ejpam-6953	120	50	chosen	choose	VERB
ejpam-6953	120	51	arbitrarily	arbitrarily	ADV
ejpam-6953	120	52	small	small	ADJ
ejpam-6953	120	53	.	.	PUNCT
ejpam-6953	121	1	for	for	ADP
ejpam-6953	121	2	sufficiently	sufficiently	ADV
ejpam-6953	121	3	small	small	ADJ
ejpam-6953	121	4	δ	δ	PROPN
ejpam-6953	121	5	,	,	PUNCT
ejpam-6953	121	6	this	this	DET
ejpam-6953	121	7	φ̃j+1	φ̃j+1	PROPN
ejpam-6953	121	8	is	be	AUX
ejpam-6953	121	9	a	a	DET
ejpam-6953	121	10	smooth	smooth	ADJ
ejpam-6953	121	11	strictly	strictly	ADV
ejpam-6953	121	12	psh	psh	NOUN
ejpam-6953	121	13	function	function	NOUN
ejpam-6953	121	14	on	on	ADP
ejpam-6953	121	15	a	a	DET
ejpam-6953	121	16	neighborhood	neighborhood	NOUN
ejpam-6953	121	17	of	of	ADP
ejpam-6953	121	18	ωj+1	ωj+1	PRON
ejpam-6953	121	19	(	(	PUNCT
ejpam-6953	121	20	cf	cf	NOUN
ejpam-6953	121	21	.	.	PUNCT
ejpam-6953	122	1	[	[	X
ejpam-6953	122	2	15	15	NUM
ejpam-6953	122	3	,	,	PUNCT
ejpam-6953	122	4	p.	p.	NOUN
ejpam-6953	122	5	262	262	NUM
ejpam-6953	122	6	]	]	PUNCT
ejpam-6953	122	7	or	or	CCONJ
ejpam-6953	122	8	appendix	appendix	VERB
ejpam-6953	122	9	a	a	PRON
ejpam-6953	122	10	)	)	PUNCT
ejpam-6953	122	11	and	and	CCONJ
ejpam-6953	122	12	coincides	coincide	VERB
ejpam-6953	122	13	with	with	ADP
ejpam-6953	122	14	φj+1	φj+1	NUM
ejpam-6953	122	15	on	on	ADP
ejpam-6953	122	16	ωj	ωj	ADV
ejpam-6953	122	17	.	.	PUNCT
ejpam-6953	123	1	moreover	moreover	ADV
ejpam-6953	123	2	φ̃j+1|∂ωj	φ̃j+1|∂ωj	PRON
ejpam-6953	123	3	is	be	AUX
ejpam-6953	123	4	a	a	DET
ejpam-6953	123	5	constant	constant	ADJ
ejpam-6953	123	6	(	(	PUNCT
ejpam-6953	123	7	since	since	SCONJ
ejpam-6953	123	8	∂ωj	∂ωj	PROPN
ejpam-6953	123	9	⊂	⊂	X
ejpam-6953	123	10	ωj+1	ωj+1	NOUN
ejpam-6953	123	11	and	and	CCONJ
ejpam-6953	123	12	φ̃j+1	φ̃j+1	NOUN
ejpam-6953	123	13	is	be	AUX
ejpam-6953	123	14	constant	constant	ADJ
ejpam-6953	123	15	on	on	ADP
ejpam-6953	123	16	∂ωj+1	∂ωj+1	NOUN
ejpam-6953	123	17	)	)	PUNCT
ejpam-6953	123	18	.	.	PUNCT
ejpam-6953	124	1	thus	thus	ADV
ejpam-6953	124	2	φj+1	φj+1	NUM
ejpam-6953	124	3	,	,	PUNCT
ejpam-6953	124	4	defined	define	VERB
ejpam-6953	124	5	by	by	ADP
ejpam-6953	124	6	φj+1	φj+1	NUM
ejpam-6953	124	7	:	:	PUNCT
ejpam-6953	124	8	=	=	SYM
ejpam-6953	124	9	φ̃j+1	φ̃j+1	NOUN
ejpam-6953	124	10	−	−	NOUN
ejpam-6953	124	11	φ̃j+1|∂ωj	φ̃j+1|∂ωj	NUM
ejpam-6953	124	12	,	,	PUNCT
ejpam-6953	124	13	is	be	AUX
ejpam-6953	124	14	still	still	ADV
ejpam-6953	124	15	strictly	strictly	ADV
ejpam-6953	124	16	psh	psh	VERB
ejpam-6953	124	17	on	on	ADP
ejpam-6953	124	18	ωj+1	ωj+1	NUM
ejpam-6953	124	19	,	,	PUNCT
ejpam-6953	124	20	vanishes	vanish	VERB
ejpam-6953	124	21	on	on	ADP
ejpam-6953	124	22	∂ωj+1	∂ωj+1	NOUN
ejpam-6953	124	23	,	,	PUNCT
ejpam-6953	124	24	and	and	CCONJ
ejpam-6953	124	25	satisfies	satisfy	VERB
ejpam-6953	124	26	φj+1	φj+1	NOUN
ejpam-6953	124	27	=	=	SYM
ejpam-6953	124	28	φ̃j+1	φ̃j+1	NOUN
ejpam-6953	124	29	−	−	NOUN
ejpam-6953	124	30	const	const	NOUN
ejpam-6953	124	31	=	=	NOUN
ejpam-6953	124	32	φj+1	φj+1	NOUN
ejpam-6953	124	33	on	on	ADP
ejpam-6953	124	34	ωj	ωj	ADV
ejpam-6953	124	35	.	.	PUNCT
ejpam-6953	125	1	it	it	PRON
ejpam-6953	125	2	follows	follow	VERB
ejpam-6953	125	3	that	that	SCONJ
ejpam-6953	125	4	|φj+1	|φj+1	NOUN
ejpam-6953	125	5	−	−	PROPN
ejpam-6953	125	6	ρ|	ρ|	PROPN
ejpam-6953	125	7	<	<	X
ejpam-6953	125	8	1	1	NUM
ejpam-6953	125	9	4	4	NUM
ejpam-6953	125	10	on	on	ADP
ejpam-6953	125	11	ωj	ωj	ADP
ejpam-6953	125	12	,	,	PUNCT
ejpam-6953	125	13	as	as	SCONJ
ejpam-6953	125	14	desired	desire	VERB
ejpam-6953	125	15	.	.	PUNCT
ejpam-6953	126	1	this	this	PRON
ejpam-6953	126	2	completes	complete	VERB
ejpam-6953	126	3	the	the	DET
ejpam-6953	126	4	inductive	inductive	ADJ
ejpam-6953	126	5	step	step	NOUN
ejpam-6953	126	6	.	.	PUNCT
ejpam-6953	127	1	4	4	X
ejpam-6953	127	2	.	.	X
ejpam-6953	127	3	uniform	uniform	NOUN
ejpam-6953	127	4	strictly	strictly	ADV
ejpam-6953	127	5	psh	psh	PROPN
ejpam-6953	127	6	references	reference	NOUN
ejpam-6953	127	7	we	we	PRON
ejpam-6953	127	8	now	now	ADV
ejpam-6953	127	9	build	build	VERB
ejpam-6953	127	10	the	the	DET
ejpam-6953	127	11	uniform	uniform	ADJ
ejpam-6953	127	12	reference	reference	NOUN
ejpam-6953	127	13	functions	function	NOUN
ejpam-6953	127	14	promised	promise	VERB
ejpam-6953	127	15	in	in	ADP
ejpam-6953	127	16	(	(	PUNCT
ejpam-6953	127	17	u2	u2	PROPN
ejpam-6953	127	18	)	)	PUNCT
ejpam-6953	127	19	.	.	PUNCT
ejpam-6953	128	1	the	the	DET
ejpam-6953	128	2	construction	construction	NOUN
ejpam-6953	128	3	relies	rely	VERB
ejpam-6953	128	4	on	on	ADP
ejpam-6953	128	5	an	an	DET
ejpam-6953	128	6	elementary	elementary	ADJ
ejpam-6953	128	7	covering	cover	VERB
ejpam-6953	128	8	property	property	NOUN
ejpam-6953	128	9	of	of	ADP
ejpam-6953	128	10	(	(	PUNCT
ejpam-6953	128	11	g	g	PROPN
ejpam-6953	128	12	,	,	PUNCT
ejpam-6953	128	13	ω	ω	NOUN
ejpam-6953	128	14	)	)	PUNCT
ejpam-6953	128	15	.	.	PUNCT
ejpam-6953	129	1	we	we	PRON
ejpam-6953	129	2	recall	recall	VERB
ejpam-6953	129	3	that	that	SCONJ
ejpam-6953	129	4	a	a	DET
ejpam-6953	129	5	metric	metric	ADJ
ejpam-6953	129	6	space	space	NOUN
ejpam-6953	129	7	(	(	PUNCT
ejpam-6953	129	8	x	x	X
ejpam-6953	129	9	,	,	PUNCT
ejpam-6953	129	10	d	d	NOUN
ejpam-6953	129	11	)	)	PUNCT
ejpam-6953	129	12	is	be	AUX
ejpam-6953	129	13	said	say	VERB
ejpam-6953	129	14	to	to	PART
ejpam-6953	129	15	have	have	VERB
ejpam-6953	129	16	finite	finite	VERB
ejpam-6953	129	17	besicovitch	besicovitch	PROPN
ejpam-6953	129	18	constant	constant	ADJ
ejpam-6953	129	19	if	if	SCONJ
ejpam-6953	129	20	there	there	PRON
ejpam-6953	129	21	is	be	VERB
ejpam-6953	129	22	an	an	DET
ejpam-6953	129	23	integer	integer	NOUN
ejpam-6953	129	24	n	n	CCONJ
ejpam-6953	129	25	such	such	ADJ
ejpam-6953	129	26	that	that	PRON
ejpam-6953	129	27	for	for	SCONJ
ejpam-6953	129	28	every	every	DET
ejpam-6953	129	29	family	family	NOUN
ejpam-6953	129	30	of	of	ADP
ejpam-6953	129	31	metric	metric	ADJ
ejpam-6953	129	32	balls	ball	NOUN
ejpam-6953	129	33	covering	cover	VERB
ejpam-6953	129	34	a	a	DET
ejpam-6953	129	35	subset	subset	NOUN
ejpam-6953	129	36	e	e	X
ejpam-6953	129	37	⊂	⊂	PROPN
ejpam-6953	129	38	x	x	PROPN
ejpam-6953	129	39	,	,	PUNCT
ejpam-6953	129	40	one	one	PRON
ejpam-6953	129	41	can	can	AUX
ejpam-6953	129	42	select	select	VERB
ejpam-6953	129	43	a	a	DET
ejpam-6953	129	44	countable	countable	ADJ
ejpam-6953	129	45	subfamily	subfamily	NOUN
ejpam-6953	129	46	that	that	SCONJ
ejpam-6953	129	47	still	still	ADV
ejpam-6953	129	48	covers	cover	VERB
ejpam-6953	129	49	e	e	NOUN
ejpam-6953	129	50	and	and	CCONJ
ejpam-6953	129	51	in	in	ADP
ejpam-6953	129	52	which	which	PRON
ejpam-6953	129	53	no	no	DET
ejpam-6953	129	54	point	point	NOUN
ejpam-6953	129	55	of	of	ADP
ejpam-6953	129	56	x	x	PUNCT
ejpam-6953	129	57	is	be	AUX
ejpam-6953	129	58	covered	cover	VERB
ejpam-6953	129	59	by	by	ADP
ejpam-6953	129	60	more	more	ADJ
ejpam-6953	129	61	than	than	ADP
ejpam-6953	129	62	n	n	PRON
ejpam-6953	129	63	balls	ball	NOUN
ejpam-6953	129	64	.	.	PUNCT
ejpam-6953	130	1	it	it	PRON
ejpam-6953	130	2	is	be	AUX
ejpam-6953	130	3	a	a	DET
ejpam-6953	130	4	well	well	ADV
ejpam-6953	130	5	-	-	PUNCT
ejpam-6953	130	6	known	know	VERB
ejpam-6953	130	7	consequence	consequence	NOUN
ejpam-6953	130	8	of	of	ADP
ejpam-6953	130	9	the	the	DET
ejpam-6953	130	10	classical	classical	ADJ
ejpam-6953	130	11	besicovitch	besicovitch	NOUN
ejpam-6953	130	12	covering	covering	NOUN
ejpam-6953	130	13	theorem	theorem	NOUN
ejpam-6953	130	14	that	that	SCONJ
ejpam-6953	130	15	rm	rm	PROPN
ejpam-6953	130	16	has	have	AUX
ejpam-6953	130	17	finite	finite	VERB
ejpam-6953	130	18	besicovitch	besicovitch	PROPN
ejpam-6953	130	19	constant	constant	PROPN
ejpam-6953	130	20	n(m	n(m	PROPN
ejpam-6953	130	21	)	)	PUNCT
ejpam-6953	130	22	≤	≤	NOUN
ejpam-6953	130	23	5	5	NUM
ejpam-6953	130	24	m	m	VERB
ejpam-6953	130	25	(	(	PUNCT
ejpam-6953	130	26	see	see	VERB
ejpam-6953	130	27	[	[	X
ejpam-6953	130	28	11	11	NUM
ejpam-6953	130	29	,	,	PUNCT
ejpam-6953	130	30	12	12	NUM
ejpam-6953	130	31	]	]	PUNCT
ejpam-6953	130	32	)	)	PUNCT
ejpam-6953	130	33	.	.	PUNCT
ejpam-6953	131	1	the	the	DET
ejpam-6953	131	2	same	same	ADJ
ejpam-6953	131	3	property	property	NOUN
ejpam-6953	131	4	holds	hold	VERB
ejpam-6953	131	5	for	for	ADP
ejpam-6953	131	6	any	any	DET
ejpam-6953	131	7	left	left	ADJ
ejpam-6953	131	8	-	-	PUNCT
ejpam-6953	131	9	invariant	invariant	ADJ
ejpam-6953	131	10	metric	metric	NOUN
ejpam-6953	131	11	on	on	ADP
ejpam-6953	131	12	a	a	DET
ejpam-6953	131	13	lie	lie	NOUN
ejpam-6953	131	14	group	group	NOUN
ejpam-6953	131	15	g	g	PROPN
ejpam-6953	131	16	,	,	PUNCT
ejpam-6953	131	17	since	since	SCONJ
ejpam-6953	131	18	every	every	DET
ejpam-6953	131	19	metric	metric	ADJ
ejpam-6953	131	20	ball	ball	NOUN
ejpam-6953	131	21	in	in	ADP
ejpam-6953	131	22	(	(	PUNCT
ejpam-6953	131	23	g	g	PROPN
ejpam-6953	131	24	,	,	PUNCT
ejpam-6953	131	25	d	d	NOUN
ejpam-6953	131	26	)	)	PUNCT
ejpam-6953	131	27	is	be	AUX
ejpam-6953	131	28	isometric	isometric	ADJ
ejpam-6953	131	29	via	via	ADP
ejpam-6953	131	30	a	a	DET
ejpam-6953	131	31	left	left	ADJ
ejpam-6953	131	32	-	-	PUNCT
ejpam-6953	131	33	translation	translation	NOUN
ejpam-6953	131	34	to	to	ADP
ejpam-6953	131	35	a	a	DET
ejpam-6953	131	36	euclidean	euclidean	ADJ
ejpam-6953	131	37	ball	ball	NOUN
ejpam-6953	131	38	in	in	ADP
ejpam-6953	131	39	r2n	r2n	NOUN
ejpam-6953	131	40	(	(	PUNCT
ejpam-6953	131	41	with	with	ADP
ejpam-6953	131	42	2n	2n	NUM
ejpam-6953	131	43	=	=	SYM
ejpam-6953	131	44	dimrg	dimrg	NOUN
ejpam-6953	131	45	)	)	PUNCT
ejpam-6953	131	46	.	.	PUNCT
ejpam-6953	132	1	in	in	ADP
ejpam-6953	132	2	particular	particular	ADJ
ejpam-6953	132	3	,	,	PUNCT
ejpam-6953	132	4	(	(	PUNCT
ejpam-6953	132	5	g	g	NOUN
ejpam-6953	132	6	,	,	PUNCT
ejpam-6953	132	7	d	d	PROPN
ejpam-6953	132	8	)	)	PUNCT
ejpam-6953	132	9	enjoys	enjoy	VERB
ejpam-6953	132	10	a	a	DET
ejpam-6953	132	11	bounded	bound	VERB
ejpam-6953	132	12	-	-	PUNCT
ejpam-6953	132	13	overlap	overlap	NOUN
ejpam-6953	132	14	covering	cover	VERB
ejpam-6953	132	15	property	property	NOUN
ejpam-6953	132	16	with	with	ADP
ejpam-6953	132	17	n(2n	n(2n	NOUN
ejpam-6953	132	18	)	)	PUNCT
ejpam-6953	132	19	≤	≤	NOUN
ejpam-6953	132	20	52n	52n	NOUN
ejpam-6953	132	21	.	.	PUNCT
ejpam-6953	133	1	we	we	PRON
ejpam-6953	133	2	now	now	ADV
ejpam-6953	133	3	assume	assume	VERB
ejpam-6953	133	4	we	we	PRON
ejpam-6953	133	5	have	have	VERB
ejpam-6953	133	6	an	an	DET
ejpam-6953	133	7	exhaustion	exhaustion	NOUN
ejpam-6953	133	8	{	{	PUNCT
ejpam-6953	133	9	ωj	ωj	ADP
ejpam-6953	133	10	}	}	PUNCT
ejpam-6953	133	11	and	and	CCONJ
ejpam-6953	133	12	approximating	approximate	VERB
ejpam-6953	133	13	functions	function	NOUN
ejpam-6953	133	14	φj	φj	NOUN
ejpam-6953	133	15	as	as	SCONJ
ejpam-6953	133	16	provided	provide	VERB
ejpam-6953	133	17	by	by	ADP
ejpam-6953	133	18	lemma	lemma	PROPN
ejpam-6953	133	19	2	2	NUM
ejpam-6953	133	20	.	.	PUNCT
ejpam-6953	133	21	by	by	ADP
ejpam-6953	133	22	a	a	DET
ejpam-6953	133	23	standard	standard	ADJ
ejpam-6953	133	24	smooth	smooth	ADJ
ejpam-6953	133	25	approximation	approximation	NOUN
ejpam-6953	133	26	,	,	PUNCT
ejpam-6953	133	27	we	we	PRON
ejpam-6953	133	28	may	may	AUX
ejpam-6953	133	29	further	far	ADV
ejpam-6953	133	30	assume	assume	VERB
ejpam-6953	133	31	that	that	SCONJ
ejpam-6953	133	32	each	each	DET
ejpam-6953	133	33	φj	φj	PROPN
ejpam-6953	133	34	extends	extend	VERB
ejpam-6953	133	35	to	to	ADP
ejpam-6953	133	36	a	a	DET
ejpam-6953	133	37	smooth	smooth	ADJ
ejpam-6953	133	38	strictly	strictly	ADV
ejpam-6953	133	39	psh	psh	NOUN
ejpam-6953	133	40	function	function	NOUN
ejpam-6953	133	41	on	on	ADP
ejpam-6953	133	42	an	an	DET
ejpam-6953	133	43	open	open	ADJ
ejpam-6953	133	44	set	set	NOUN
ejpam-6953	133	45	uj	uj	PROPN
ejpam-6953	133	46	with	with	ADP
ejpam-6953	133	47	ωj	ωj	PROPN
ejpam-6953	133	48	⊂	⊂	PROPN
ejpam-6953	133	49	uj	uj	PROPN
ejpam-6953	133	50	⋐	⋐	PROPN
ejpam-6953	133	51	ωj+1	ωj+1	PROPN
ejpam-6953	133	52	.	.	PUNCT
ejpam-6953	134	1	we	we	PRON
ejpam-6953	134	2	also	also	ADV
ejpam-6953	134	3	choose	choose	VERB
ejpam-6953	134	4	an	an	DET
ejpam-6953	134	5	increasing	increase	VERB
ejpam-6953	134	6	sequence	sequence	NOUN
ejpam-6953	134	7	of	of	ADP
ejpam-6953	134	8	radii	radii	PROPN
ejpam-6953	134	9	rj	rj	PROPN
ejpam-6953	134	10	>	>	X
ejpam-6953	134	11	0	0	NUM
ejpam-6953	134	12	such	such	ADJ
ejpam-6953	134	13	that	that	SCONJ
ejpam-6953	134	14	each	each	DET
ejpam-6953	134	15	metric	metric	ADJ
ejpam-6953	134	16	ball	ball	NOUN
ejpam-6953	134	17	bj	bj	NOUN
ejpam-6953	134	18	:	:	PUNCT
ejpam-6953	134	19	=	=	SYM
ejpam-6953	134	20	bω(e	bω(e	NUM
ejpam-6953	134	21	,	,	PUNCT
ejpam-6953	134	22	rj	rj	PROPN
ejpam-6953	134	23	)	)	PUNCT
ejpam-6953	134	24	(	(	PUNCT
ejpam-6953	134	25	centered	center	VERB
ejpam-6953	134	26	at	at	ADP
ejpam-6953	134	27	the	the	DET
ejpam-6953	134	28	identity	identity	NOUN
ejpam-6953	134	29	e	e	NOUN
ejpam-6953	134	30	∈	∈	PROPN
ejpam-6953	134	31	g	g	NOUN
ejpam-6953	134	32	)	)	PUNCT
ejpam-6953	134	33	is	be	AUX
ejpam-6953	134	34	relatively	relatively	ADV
ejpam-6953	134	35	compact	compact	ADJ
ejpam-6953	134	36	in	in	ADP
ejpam-6953	134	37	u1	u1	NOUN
ejpam-6953	134	38	and	and	CCONJ
ejpam-6953	134	39	that	that	DET
ejpam-6953	134	40	5bj	5bj	ADJ
ejpam-6953	134	41	(	(	PUNCT
ejpam-6953	134	42	the	the	DET
ejpam-6953	134	43	ball	ball	NOUN
ejpam-6953	134	44	of	of	ADP
ejpam-6953	134	45	radius	radius	NOUN
ejpam-6953	134	46	5rj	5rj	NOUN
ejpam-6953	134	47	)	)	PUNCT
ejpam-6953	134	48	is	be	AUX
ejpam-6953	134	49	still	still	ADV
ejpam-6953	134	50	contained	contain	VERB
ejpam-6953	134	51	in	in	ADP
ejpam-6953	134	52	u1	u1	NOUN
ejpam-6953	134	53	.	.	PUNCT
ejpam-6953	135	1	let	let	VERB
ejpam-6953	135	2	0	0	NUM
ejpam-6953	135	3	<	<	X
ejpam-6953	135	4	λ0	λ0	NOUN
ejpam-6953	135	5	≤	≤	ADJ
ejpam-6953	135	6	λ0	λ0	NOUN
ejpam-6953	135	7	be	be	VERB
ejpam-6953	135	8	the	the	DET
ejpam-6953	135	9	minimum	minimum	NOUN
ejpam-6953	135	10	and	and	CCONJ
ejpam-6953	135	11	maximum	maximum	NOUN
ejpam-6953	135	12	of	of	ADP
ejpam-6953	135	13	i∂∂̄φ1	i∂∂̄φ1	PROPN
ejpam-6953	135	14	on	on	ADP
ejpam-6953	135	15	5bj	5bj	NOUN
ejpam-6953	135	16	.	.	PUNCT
ejpam-6953	136	1	by	by	ADP
ejpam-6953	136	2	possibly	possibly	ADV
ejpam-6953	136	3	shrinking	shrink	VERB
ejpam-6953	136	4	rj	rj	PROPN
ejpam-6953	136	5	,	,	PUNCT
ejpam-6953	136	6	we	we	PRON
ejpam-6953	136	7	can	can	AUX
ejpam-6953	136	8	ensure	ensure	VERB
ejpam-6953	136	9	λ0	λ0	NOUN
ejpam-6953	136	10	ω	ω	NOUN
ejpam-6953	136	11	≤	≤	X
ejpam-6953	136	12	i∂∂̄φ1	i∂∂̄φ1	NOUN
ejpam-6953	136	13	≤	≤	ADJ
ejpam-6953	136	14	λ0	λ0	NOUN
ejpam-6953	136	15	ω	ω	NOUN
ejpam-6953	136	16	on	on	ADP
ejpam-6953	136	17	all	all	PRON
ejpam-6953	136	18	of	of	ADP
ejpam-6953	136	19	5bj	5bj	ADJ
ejpam-6953	136	20	.	.	PUNCT
ejpam-6953	137	1	(	(	PUNCT
ejpam-6953	137	2	this	this	PRON
ejpam-6953	137	3	is	be	AUX
ejpam-6953	137	4	possible	possible	ADJ
ejpam-6953	137	5	because	because	SCONJ
ejpam-6953	137	6	bj	bj	NOUN
ejpam-6953	137	7	→	→	SYM
ejpam-6953	137	8	{	{	PUNCT
ejpam-6953	137	9	e	e	NOUN
ejpam-6953	137	10	}	}	PUNCT
ejpam-6953	137	11	as	as	ADP
ejpam-6953	137	12	j	j	PROPN
ejpam-6953	137	13	→	→	SYM
ejpam-6953	137	14	∞	∞	PROPN
ejpam-6953	137	15	,	,	PUNCT
ejpam-6953	137	16	and	and	CCONJ
ejpam-6953	137	17	φ1	φ1	NOUN
ejpam-6953	137	18	is	be	AUX
ejpam-6953	137	19	smooth	smooth	ADJ
ejpam-6953	137	20	and	and	CCONJ
ejpam-6953	137	21	strictly	strictly	ADV
ejpam-6953	137	22	psh	psh	PROPN
ejpam-6953	137	23	on	on	ADP
ejpam-6953	137	24	a	a	DET
ejpam-6953	137	25	neighborhood	neighborhood	NOUN
ejpam-6953	137	26	of	of	ADP
ejpam-6953	137	27	e.	e.	PROPN
ejpam-6953	137	28	)	)	PUNCT
ejpam-6953	137	29	lemma	lemma	PROPN
ejpam-6953	138	1	3	3	X
ejpam-6953	138	2	.	.	X
ejpam-6953	138	3	there	there	PRON
ejpam-6953	138	4	exist	exist	VERB
ejpam-6953	138	5	constants	constant	NOUN
ejpam-6953	138	6	c∗	c∗	PROPN
ejpam-6953	138	7	>	>	X
ejpam-6953	138	8	0	0	PUNCT
ejpam-6953	138	9	and	and	CCONJ
ejpam-6953	138	10	s∗	s∗	VERB
ejpam-6953	138	11	<	<	X
ejpam-6953	138	12	∞	∞	PROPN
ejpam-6953	138	13	depending	depend	VERB
ejpam-6953	138	14	only	only	ADV
ejpam-6953	138	15	on	on	ADP
ejpam-6953	138	16	(	(	PUNCT
ejpam-6953	138	17	g	g	PROPN
ejpam-6953	138	18	,	,	PUNCT
ejpam-6953	138	19	ω	ω	NOUN
ejpam-6953	138	20	)	)	PUNCT
ejpam-6953	138	21	,	,	PUNCT
ejpam-6953	138	22	and	and	CCONJ
ejpam-6953	138	23	for	for	ADP
ejpam-6953	138	24	each	each	DET
ejpam-6953	138	25	j	j	PROPN
ejpam-6953	138	26	an	an	DET
ejpam-6953	138	27	open	open	ADJ
ejpam-6953	138	28	set	set	NOUN
ejpam-6953	138	29	uj	uj	PROPN
ejpam-6953	138	30	⊃	⊃	PROPN
ejpam-6953	138	31	ωj	ωj	ADV
ejpam-6953	138	32	and	and	CCONJ
ejpam-6953	138	33	a	a	DET
ejpam-6953	138	34	function	function	NOUN
ejpam-6953	138	35	σj	σj	ADP
ejpam-6953	138	36	∈	∈	PROPN
ejpam-6953	138	37	c∞(uj	c∞(uj	NOUN
ejpam-6953	138	38	)	)	PUNCT
ejpam-6953	138	39	,	,	PUNCT
ejpam-6953	138	40	such	such	ADJ
ejpam-6953	138	41	that	that	PRON
ejpam-6953	138	42	for	for	SCONJ
ejpam-6953	138	43	every	every	DET
ejpam-6953	138	44	j	j	NOUN
ejpam-6953	138	45	:	:	PUNCT
ejpam-6953	138	46	(	(	PUNCT
ejpam-6953	138	47	i	i	NOUN
ejpam-6953	138	48	)	)	PUNCT
ejpam-6953	138	49	i∂∂̄σj	i∂∂̄σj	PROPN
ejpam-6953	138	50	≥	≥	PROPN
ejpam-6953	138	51	c∗	c∗	PROPN
ejpam-6953	138	52	ω	ω	PROPN
ejpam-6953	138	53	on	on	ADP
ejpam-6953	138	54	uj	uj	PROPN
ejpam-6953	138	55	.	.	PUNCT
ejpam-6953	138	56	(	(	PUNCT
ejpam-6953	138	57	ii	ii	PROPN
ejpam-6953	138	58	)	)	PUNCT
ejpam-6953	138	59	supωj	supωj	NOUN
ejpam-6953	138	60	|σj	|σj	PRON
ejpam-6953	138	61	|	|	ADV
ejpam-6953	138	62	≤	≤	X
ejpam-6953	138	63	s∗.	s∗.	ADJ
ejpam-6953	138	64	a.	a.	PROPN
ejpam-6953	138	65	r.	r.	PROPN
ejpam-6953	138	66	al	al	PROPN
ejpam-6953	138	67	-	-	PUNCT
ejpam-6953	138	68	abdallah	abdallah	PROPN
ejpam-6953	138	69	/	/	SYM
ejpam-6953	138	70	eur	eur	PROPN
ejpam-6953	138	71	.	.	PUNCT
ejpam-6953	139	1	j.	j.	PROPN
ejpam-6953	139	2	pure	pure	PROPN
ejpam-6953	139	3	appl	appl	PROPN
ejpam-6953	139	4	.	.	PROPN
ejpam-6953	139	5	math	math	PROPN
ejpam-6953	139	6	,	,	PUNCT
ejpam-6953	139	7	18	18	NUM
ejpam-6953	139	8	(	(	PUNCT
ejpam-6953	139	9	4	4	NUM
ejpam-6953	139	10	)	)	PUNCT
ejpam-6953	139	11	(	(	PUNCT
ejpam-6953	139	12	2025	2025	NUM
ejpam-6953	139	13	)	)	PUNCT
ejpam-6953	139	14	,	,	PUNCT
ejpam-6953	139	15	6953	6953	NUM
ejpam-6953	139	16	7	7	NUM
ejpam-6953	139	17	of	of	ADP
ejpam-6953	139	18	14	14	NUM
ejpam-6953	139	19	proof	proof	NOUN
ejpam-6953	139	20	.	.	PUNCT
ejpam-6953	140	1	for	for	ADP
ejpam-6953	140	2	each	each	DET
ejpam-6953	140	3	j	j	NOUN
ejpam-6953	140	4	,	,	PUNCT
ejpam-6953	140	5	consider	consider	VERB
ejpam-6953	140	6	the	the	DET
ejpam-6953	140	7	collection	collection	NOUN
ejpam-6953	140	8	bj	bj	VERB
ejpam-6953	140	9	=	=	PUNCT
ejpam-6953	140	10	{	{	PUNCT
ejpam-6953	140	11	g	g	NOUN
ejpam-6953	140	12	bj	bj	VERB
ejpam-6953	140	13	:	:	PUNCT
ejpam-6953	140	14	g	g	PROPN
ejpam-6953	140	15	∈	∈	PROPN
ejpam-6953	140	16	g	g	NOUN
ejpam-6953	140	17	,	,	PUNCT
ejpam-6953	140	18	g	g	NOUN
ejpam-6953	140	19	bj	bj	ADP
ejpam-6953	140	20	∩	∩	NOUN
ejpam-6953	140	21	ωj	ωj	ADP
ejpam-6953	140	22	̸=	̸=	PROPN
ejpam-6953	140	23	∅	∅	NOUN
ejpam-6953	140	24	}	}	PUNCT
ejpam-6953	140	25	of	of	ADP
ejpam-6953	140	26	metric	metric	ADJ
ejpam-6953	140	27	balls	ball	NOUN
ejpam-6953	140	28	of	of	ADP
ejpam-6953	140	29	radius	radius	NOUN
ejpam-6953	140	30	rj	rj	PROPN
ejpam-6953	140	31	whose	whose	DET
ejpam-6953	140	32	left	leave	VERB
ejpam-6953	140	33	-	-	PUNCT
ejpam-6953	140	34	translates	translate	VERB
ejpam-6953	140	35	intersect	intersect	ADJ
ejpam-6953	140	36	ωj	ωj	ADP
ejpam-6953	140	37	.	.	PUNCT
ejpam-6953	141	1	clearly	clearly	ADV
ejpam-6953	141	2	⋃	⋃	PROPN
ejpam-6953	141	3	ℓ	ℓ	PROPN
ejpam-6953	141	4	gj,ℓbj	gj,ℓbj	PROPN
ejpam-6953	141	5	⊃	⊃	PROPN
ejpam-6953	141	6	ωj	ωj	VERB
ejpam-6953	141	7	.	.	PUNCT
ejpam-6953	142	1	by	by	ADP
ejpam-6953	142	2	the	the	DET
ejpam-6953	142	3	besicovitch	besicovitch	NOUN
ejpam-6953	142	4	covering	cover	VERB
ejpam-6953	142	5	property	property	NOUN
ejpam-6953	142	6	,	,	PUNCT
ejpam-6953	142	7	we	we	PRON
ejpam-6953	142	8	can	can	AUX
ejpam-6953	142	9	find	find	VERB
ejpam-6953	142	10	a	a	DET
ejpam-6953	142	11	finite	finite	ADJ
ejpam-6953	142	12	subcollection	subcollection	NOUN
ejpam-6953	142	13	of	of	ADP
ejpam-6953	142	14	these	these	DET
ejpam-6953	142	15	balls	ball	NOUN
ejpam-6953	142	16	covering	cover	VERB
ejpam-6953	142	17	ωj	ωj	ADP
ejpam-6953	142	18	,	,	PUNCT
ejpam-6953	142	19	say	say	VERB
ejpam-6953	142	20	{	{	PUNCT
ejpam-6953	142	21	gj,1bj	gj,1bj	PROPN
ejpam-6953	142	22	,	,	PUNCT
ejpam-6953	142	23	.	.	PUNCT
ejpam-6953	142	24	.	.	PUNCT
ejpam-6953	143	1	.	.	PUNCT
ejpam-6953	144	1	,	,	PUNCT
ejpam-6953	144	2	gj	gj	PROPN
ejpam-6953	144	3	,	,	PUNCT
ejpam-6953	144	4	njbj	njbj	PROPN
ejpam-6953	144	5	}	}	PUNCT
ejpam-6953	144	6	,	,	PUNCT
ejpam-6953	144	7	such	such	ADJ
ejpam-6953	144	8	that	that	SCONJ
ejpam-6953	144	9	each	each	DET
ejpam-6953	144	10	point	point	NOUN
ejpam-6953	144	11	of	of	ADP
ejpam-6953	144	12	g	g	PROPN
ejpam-6953	144	13	is	be	AUX
ejpam-6953	144	14	contained	contain	VERB
ejpam-6953	144	15	in	in	ADP
ejpam-6953	144	16	at	at	ADP
ejpam-6953	144	17	most	most	ADJ
ejpam-6953	144	18	c	c	NOUN
ejpam-6953	144	19	of	of	ADP
ejpam-6953	144	20	these	these	DET
ejpam-6953	144	21	balls	ball	NOUN
ejpam-6953	144	22	,	,	PUNCT
ejpam-6953	144	23	where	where	SCONJ
ejpam-6953	144	24	c	c	NOUN
ejpam-6953	144	25	=	=	SYM
ejpam-6953	144	26	c(2n	c(2n	NOUN
ejpam-6953	144	27	)	)	PUNCT
ejpam-6953	144	28	≤	≤	NOUN
ejpam-6953	144	29	52n	52n	NOUN
ejpam-6953	144	30	is	be	AUX
ejpam-6953	144	31	a	a	DET
ejpam-6953	144	32	uniform	uniform	ADJ
ejpam-6953	144	33	constant	constant	ADJ
ejpam-6953	144	34	(	(	PUNCT
ejpam-6953	144	35	independent	independent	ADJ
ejpam-6953	144	36	of	of	ADP
ejpam-6953	144	37	j	j	PROPN
ejpam-6953	144	38	)	)	PUNCT
ejpam-6953	144	39	.	.	PUNCT
ejpam-6953	145	1	on	on	ADP
ejpam-6953	145	2	the	the	DET
ejpam-6953	145	3	ball	ball	NOUN
ejpam-6953	145	4	5bj	5bj	NOUN
ejpam-6953	145	5	,	,	PUNCT
ejpam-6953	145	6	the	the	DET
ejpam-6953	145	7	function	function	NOUN
ejpam-6953	145	8	φ1	φ1	PROPN
ejpam-6953	145	9	has	have	AUX
ejpam-6953	145	10	bounded	bound	VERB
ejpam-6953	145	11	geometry	geometry	NOUN
ejpam-6953	145	12	:	:	PUNCT
ejpam-6953	145	13	as	as	SCONJ
ejpam-6953	145	14	noted	note	VERB
ejpam-6953	145	15	above	above	ADV
ejpam-6953	145	16	,	,	PUNCT
ejpam-6953	145	17	λ0	λ0	NOUN
ejpam-6953	145	18	ω	ω	NOUN
ejpam-6953	145	19	≤	≤	X
ejpam-6953	145	20	i∂∂̄φ1	i∂∂̄φ1	NOUN
ejpam-6953	145	21	≤	≤	ADJ
ejpam-6953	145	22	λ0	λ0	NOUN
ejpam-6953	145	23	ω	ω	NOUN
ejpam-6953	145	24	on	on	ADP
ejpam-6953	145	25	5bj	5bj	ADJ
ejpam-6953	145	26	,	,	PUNCT
ejpam-6953	145	27	and	and	CCONJ
ejpam-6953	145	28	also	also	ADV
ejpam-6953	145	29	|φ1|	|φ1|	VERB
ejpam-6953	145	30	≤	≤	ADJ
ejpam-6953	145	31	m0	m0	NOUN
ejpam-6953	145	32	on	on	ADP
ejpam-6953	145	33	5bj	5bj	NOUN
ejpam-6953	145	34	for	for	ADP
ejpam-6953	145	35	some	some	DET
ejpam-6953	145	36	m0	m0	NOUN
ejpam-6953	145	37	(	(	PUNCT
ejpam-6953	145	38	since	since	SCONJ
ejpam-6953	145	39	5bj	5bj	ADJ
ejpam-6953	145	40	lies	lie	VERB
ejpam-6953	145	41	in	in	ADP
ejpam-6953	145	42	a	a	DET
ejpam-6953	145	43	fixed	fix	VERB
ejpam-6953	145	44	compact	compact	ADJ
ejpam-6953	145	45	set	set	VERB
ejpam-6953	145	46	u1	u1	NOUN
ejpam-6953	145	47	)	)	PUNCT
ejpam-6953	145	48	.	.	PUNCT
ejpam-6953	146	1	now	now	ADV
ejpam-6953	146	2	fix	fix	VERB
ejpam-6953	146	3	a	a	DET
ejpam-6953	146	4	smooth	smooth	ADJ
ejpam-6953	146	5	function	function	NOUN
ejpam-6953	146	6	u	u	NOUN
ejpam-6953	146	7	on	on	ADP
ejpam-6953	146	8	bj	bj	ADP
ejpam-6953	146	9	such	such	ADJ
ejpam-6953	146	10	that	that	DET
ejpam-6953	146	11	0	0	NUM
ejpam-6953	146	12	≤	≤	NUM
ejpam-6953	146	13	u	u	NOUN
ejpam-6953	146	14	≤	≤	NUM
ejpam-6953	146	15	1	1	NUM
ejpam-6953	146	16	and	and	CCONJ
ejpam-6953	146	17	i∂∂̄u	i∂∂̄u	PROPN
ejpam-6953	146	18	≥	≥	PROPN
ejpam-6953	146	19	λ0	λ0	PROPN
ejpam-6953	146	20	ω	ω	PROPN
ejpam-6953	146	21	on	on	ADP
ejpam-6953	146	22	bj	bj	NOUN
ejpam-6953	146	23	.	.	PUNCT
ejpam-6953	147	1	for	for	ADP
ejpam-6953	147	2	each	each	DET
ejpam-6953	147	3	1	1	NUM
ejpam-6953	147	4	≤	≤	NUM
ejpam-6953	147	5	ℓ	ℓ	PROPN
ejpam-6953	147	6	≤	≤	PROPN
ejpam-6953	147	7	nj	nj	PROPN
ejpam-6953	147	8	,	,	PUNCT
ejpam-6953	147	9	define	define	VERB
ejpam-6953	147	10	a	a	DET
ejpam-6953	147	11	function	function	NOUN
ejpam-6953	147	12	uj,ℓ	uj,ℓ	PUNCT
ejpam-6953	147	13	on	on	ADP
ejpam-6953	147	14	gj,ℓbj	gj,ℓbj	PROPN
ejpam-6953	147	15	by	by	ADP
ejpam-6953	147	16	left	left	ADJ
ejpam-6953	147	17	-	-	PUNCT
ejpam-6953	147	18	translating	translate	VERB
ejpam-6953	147	19	u	u	NOUN
ejpam-6953	147	20	,	,	PUNCT
ejpam-6953	147	21	namely	namely	ADV
ejpam-6953	147	22	uj,ℓ(x	uj,ℓ(x	NOUN
ejpam-6953	147	23	)	)	PUNCT
ejpam-6953	147	24	:	:	PUNCT
ejpam-6953	148	1	=	=	PUNCT
ejpam-6953	148	2	u(g−1	u(g−1	PROPN
ejpam-6953	148	3	j,ℓ	j,ℓ	INTJ
ejpam-6953	148	4	x	x	NOUN
ejpam-6953	148	5	)	)	PUNCT
ejpam-6953	148	6	,	,	PUNCT
ejpam-6953	148	7	x	x	PUNCT
ejpam-6953	148	8	∈	∈	PROPN
ejpam-6953	148	9	gj,ℓbj	gj,ℓbj	PROPN
ejpam-6953	148	10	.	.	PUNCT
ejpam-6953	149	1	since	since	SCONJ
ejpam-6953	149	2	the	the	DET
ejpam-6953	149	3	metric	metric	ADJ
ejpam-6953	149	4	ω	ω	PROPN
ejpam-6953	149	5	is	be	AUX
ejpam-6953	149	6	left	leave	VERB
ejpam-6953	149	7	-	-	PUNCT
ejpam-6953	149	8	invariant	invariant	ADJ
ejpam-6953	149	9	,	,	PUNCT
ejpam-6953	149	10	each	each	DET
ejpam-6953	149	11	uj,ℓ	uj,ℓ	NOUN
ejpam-6953	149	12	is	be	AUX
ejpam-6953	149	13	strictly	strictly	ADV
ejpam-6953	149	14	psh	psh	ADJ
ejpam-6953	149	15	on	on	ADP
ejpam-6953	149	16	gj,ℓbj	gj,ℓbj	PROPN
ejpam-6953	149	17	and	and	CCONJ
ejpam-6953	149	18	satisfies	satisfie	NOUN
ejpam-6953	149	19	i∂∂̄uj,ℓ	i∂∂̄uj,ℓ	VERB
ejpam-6953	149	20	=	=	SYM
ejpam-6953	149	21	g∗j,ℓ(i∂∂̄u	g∗j,ℓ(i∂∂̄u	PROPN
ejpam-6953	149	22	)	)	PUNCT
ejpam-6953	149	23	≥	≥	NOUN
ejpam-6953	149	24	λ0	λ0	NOUN
ejpam-6953	149	25	ω	ω	NOUN
ejpam-6953	149	26	on	on	ADP
ejpam-6953	149	27	gj,ℓbj	gj,ℓbj	PROPN
ejpam-6953	149	28	,	,	PUNCT
ejpam-6953	149	29	and	and	CCONJ
ejpam-6953	149	30	also	also	ADV
ejpam-6953	149	31	supgj,ℓbj	supgj,ℓbj	PROPN
ejpam-6953	149	32	uj,ℓ	uj,ℓ	NOUN
ejpam-6953	149	33	=	=	PUNCT
ejpam-6953	149	34	supbj	supbj	ADJ
ejpam-6953	149	35	u	u	NOUN
ejpam-6953	149	36	≤	≤	ADJ
ejpam-6953	149	37	1	1	NUM
ejpam-6953	149	38	.	.	PUNCT
ejpam-6953	150	1	we	we	PRON
ejpam-6953	150	2	now	now	ADV
ejpam-6953	150	3	define	define	VERB
ejpam-6953	150	4	σj	σj	ADJ
ejpam-6953	150	5	by	by	ADP
ejpam-6953	150	6	averaging	average	VERB
ejpam-6953	150	7	the	the	DET
ejpam-6953	150	8	uj,ℓ	uj,ℓ	NOUN
ejpam-6953	150	9	with	with	ADP
ejpam-6953	150	10	a	a	DET
ejpam-6953	150	11	large	large	ADJ
ejpam-6953	150	12	exponential	exponential	ADJ
ejpam-6953	150	13	weight	weight	NOUN
ejpam-6953	150	14	parameter	parameter	NOUN
ejpam-6953	150	15	τ	τ	PROPN
ejpam-6953	150	16	>	>	X
ejpam-6953	150	17	0	0	NUM
ejpam-6953	150	18	:	:	PUNCT
ejpam-6953	150	19	σj(x	σj(x	NUM
ejpam-6953	150	20	)	)	PUNCT
ejpam-6953	150	21	:	:	PUNCT
ejpam-6953	150	22	=	=	SYM
ejpam-6953	150	23	1	1	NUM
ejpam-6953	150	24	τ	τ	NOUN
ejpam-6953	150	25	log	log	NOUN
ejpam-6953	150	26	nj∑	nj∑	PROPN
ejpam-6953	150	27	ℓ=1	ℓ=1	ADP
ejpam-6953	150	28	1gj,ℓ5bj	1gj,ℓ5bj	NUM
ejpam-6953	150	29	(	(	PUNCT
ejpam-6953	150	30	x	x	X
ejpam-6953	150	31	)	)	PUNCT
ejpam-6953	150	32	exp{τ	exp{τ	PROPN
ejpam-6953	150	33	uj,ℓ(x	uj,ℓ(x	NOUN
ejpam-6953	150	34	)	)	PUNCT
ejpam-6953	150	35	}	}	PUNCT
ejpam-6953	150	36	,	,	PUNCT
ejpam-6953	150	37	x	x	PUNCT
ejpam-6953	150	38	∈	∈	PROPN
ejpam-6953	150	39	uj	uj	PROPN
ejpam-6953	150	40	,	,	PUNCT
ejpam-6953	150	41	where	where	SCONJ
ejpam-6953	150	42	1gj,ℓ5bj	1gj,ℓ5bj	NUM
ejpam-6953	150	43	(	(	PUNCT
ejpam-6953	150	44	x	x	X
ejpam-6953	150	45	)	)	PUNCT
ejpam-6953	150	46	is	be	AUX
ejpam-6953	150	47	1	1	NUM
ejpam-6953	150	48	if	if	SCONJ
ejpam-6953	150	49	x	x	PROPN
ejpam-6953	150	50	∈	∈	PROPN
ejpam-6953	150	51	gj,ℓ5bj	gj,ℓ5bj	PROPN
ejpam-6953	150	52	and	and	CCONJ
ejpam-6953	150	53	0	0	NUM
ejpam-6953	150	54	otherwise	otherwise	ADV
ejpam-6953	150	55	.	.	PUNCT
ejpam-6953	151	1	(	(	PUNCT
ejpam-6953	151	2	in	in	ADP
ejpam-6953	151	3	other	other	ADJ
ejpam-6953	151	4	words	word	NOUN
ejpam-6953	151	5	,	,	PUNCT
ejpam-6953	151	6	for	for	ADP
ejpam-6953	151	7	x	x	PUNCT
ejpam-6953	151	8	not	not	PART
ejpam-6953	151	9	lying	lie	VERB
ejpam-6953	151	10	in	in	ADP
ejpam-6953	151	11	the	the	DET
ejpam-6953	151	12	5bj	5bj	ADJ
ejpam-6953	151	13	-	-	PUNCT
ejpam-6953	151	14	neighborhood	neighborhood	NOUN
ejpam-6953	151	15	of	of	ADP
ejpam-6953	151	16	some	some	DET
ejpam-6953	151	17	gj,ℓbj	gj,ℓbj	PROPN
ejpam-6953	151	18	,	,	PUNCT
ejpam-6953	151	19	we	we	PRON
ejpam-6953	151	20	interpret	interpret	VERB
ejpam-6953	151	21	uj,ℓ(x	uj,ℓ(x	ADV
ejpam-6953	151	22	)	)	PUNCT
ejpam-6953	152	1	=	=	SYM
ejpam-6953	152	2	0	0	PUNCT
ejpam-6953	153	1	so	so	SCONJ
ejpam-6953	153	2	that	that	SCONJ
ejpam-6953	153	3	the	the	DET
ejpam-6953	153	4	sum	sum	NOUN
ejpam-6953	153	5	effectively	effectively	ADV
ejpam-6953	153	6	runs	run	VERB
ejpam-6953	153	7	over	over	ADP
ejpam-6953	153	8	those	those	DET
ejpam-6953	153	9	ℓ	ℓ	NOUN
ejpam-6953	153	10	for	for	ADP
ejpam-6953	153	11	which	which	PRON
ejpam-6953	153	12	x	x	SYM
ejpam-6953	153	13	∈	∈	PROPN
ejpam-6953	153	14	gj,ℓ5bj	gj,ℓ5bj	NOUN
ejpam-6953	153	15	;	;	PUNCT
ejpam-6953	153	16	note	note	NOUN
ejpam-6953	153	17	x	x	PUNCT
ejpam-6953	153	18	can	can	AUX
ejpam-6953	153	19	belong	belong	VERB
ejpam-6953	153	20	to	to	ADP
ejpam-6953	153	21	at	at	ADV
ejpam-6953	153	22	most	most	ADV
ejpam-6953	153	23	c	c	ADP
ejpam-6953	153	24	such	such	ADJ
ejpam-6953	153	25	balls	ball	NOUN
ejpam-6953	153	26	by	by	ADP
ejpam-6953	153	27	the	the	DET
ejpam-6953	153	28	overlap	overlap	NOUN
ejpam-6953	153	29	property	property	NOUN
ejpam-6953	153	30	.	.	PUNCT
ejpam-6953	153	31	)	)	PUNCT
ejpam-6953	154	1	the	the	DET
ejpam-6953	154	2	function	function	NOUN
ejpam-6953	154	3	σj	σj	VERB
ejpam-6953	154	4	is	be	AUX
ejpam-6953	154	5	well	well	ADV
ejpam-6953	154	6	-	-	PUNCT
ejpam-6953	154	7	defined	define	VERB
ejpam-6953	154	8	and	and	CCONJ
ejpam-6953	154	9	smooth	smooth	ADJ
ejpam-6953	154	10	on	on	ADP
ejpam-6953	154	11	uj	uj	PROPN
ejpam-6953	154	12	when	when	SCONJ
ejpam-6953	154	13	τ	τ	PROPN
ejpam-6953	154	14	is	be	AUX
ejpam-6953	154	15	large	large	ADJ
ejpam-6953	154	16	,	,	PUNCT
ejpam-6953	154	17	and	and	CCONJ
ejpam-6953	154	18	σj	σj	VERB
ejpam-6953	154	19	decreases	decrease	NOUN
ejpam-6953	154	20	pointwise	pointwise	NOUN
ejpam-6953	154	21	to	to	ADP
ejpam-6953	154	22	max{uj,1	max{uj,1	PROPN
ejpam-6953	154	23	,	,	PUNCT
ejpam-6953	154	24	.	.	PUNCT
ejpam-6953	154	25	.	.	PUNCT
ejpam-6953	155	1	.	.	PUNCT
ejpam-6953	156	1	,	,	PUNCT
ejpam-6953	156	2	uj	uj	PROPN
ejpam-6953	156	3	,	,	PUNCT
ejpam-6953	156	4	nj	nj	PROPN
ejpam-6953	156	5	}	}	PUNCT
ejpam-6953	156	6	as	as	ADP
ejpam-6953	156	7	τ	τ	PROPN
ejpam-6953	156	8	→	→	SYM
ejpam-6953	156	9	+	+	PROPN
ejpam-6953	156	10	∞.	∞.	PROPN
ejpam-6953	156	11	by	by	ADP
ejpam-6953	156	12	standard	standard	ADJ
ejpam-6953	156	13	calculations	calculation	NOUN
ejpam-6953	156	14	(	(	PUNCT
ejpam-6953	156	15	see	see	VERB
ejpam-6953	156	16	appendix	appendix	VERB
ejpam-6953	156	17	a	a	DET
ejpam-6953	156	18	or	or	CCONJ
ejpam-6953	156	19	[	[	X
ejpam-6953	156	20	15	15	NUM
ejpam-6953	156	21	,	,	PUNCT
ejpam-6953	156	22	p.	p.	NOUN
ejpam-6953	156	23	261	261	NUM
ejpam-6953	156	24	]	]	PUNCT
ejpam-6953	156	25	)	)	PUNCT
ejpam-6953	156	26	,	,	PUNCT
ejpam-6953	156	27	one	one	PRON
ejpam-6953	156	28	has	have	AUX
ejpam-6953	156	29	i∂∂̄σj	i∂∂̄σj	VERB
ejpam-6953	156	30	≥	≥	NOUN
ejpam-6953	156	31	λ0	λ0	NOUN
ejpam-6953	156	32	ω	ω	NOUN
ejpam-6953	156	33	at	at	ADP
ejpam-6953	156	34	every	every	DET
ejpam-6953	156	35	point	point	NOUN
ejpam-6953	156	36	of	of	ADP
ejpam-6953	156	37	uj	uj	PROPN
ejpam-6953	156	38	,	,	PUNCT
ejpam-6953	156	39	so	so	CCONJ
ejpam-6953	156	40	(	(	PUNCT
ejpam-6953	156	41	i	i	NOUN
ejpam-6953	156	42	)	)	PUNCT
ejpam-6953	156	43	holds	hold	VERB
ejpam-6953	156	44	with	with	ADP
ejpam-6953	156	45	c∗	c∗	NOUN
ejpam-6953	156	46	:	:	PUNCT
ejpam-6953	156	47	=	=	SYM
ejpam-6953	156	48	λ0	λ0	NOUN
ejpam-6953	156	49	.	.	PUNCT
ejpam-6953	157	1	meanwhile	meanwhile	ADV
ejpam-6953	157	2	,	,	PUNCT
ejpam-6953	157	3	since	since	SCONJ
ejpam-6953	157	4	each	each	DET
ejpam-6953	157	5	uj,ℓ	uj,ℓ	NOUN
ejpam-6953	157	6	≤	≤	NUM
ejpam-6953	157	7	1	1	NUM
ejpam-6953	157	8	,	,	PUNCT
ejpam-6953	157	9	we	we	PRON
ejpam-6953	157	10	have	have	AUX
ejpam-6953	157	11	sup	sup	NOUN
ejpam-6953	157	12	uj	uj	NUM
ejpam-6953	157	13	σj	σj	VERB
ejpam-6953	157	14	≤	≤	NUM
ejpam-6953	157	15	1	1	NUM
ejpam-6953	157	16	+	+	CCONJ
ejpam-6953	157	17	1	1	NUM
ejpam-6953	157	18	τ	τ	NOUN
ejpam-6953	157	19	lognj	lognj	NOUN
ejpam-6953	157	20	.	.	PUNCT
ejpam-6953	158	1	choosing	choose	VERB
ejpam-6953	158	2	,	,	PUNCT
ejpam-6953	158	3	for	for	ADP
ejpam-6953	158	4	example	example	NOUN
ejpam-6953	158	5	,	,	PUNCT
ejpam-6953	158	6	τ	τ	PROPN
ejpam-6953	158	7	=	=	SYM
ejpam-6953	158	8	1	1	NUM
ejpam-6953	158	9	gives	give	VERB
ejpam-6953	158	10	supuj	supuj	NOUN
ejpam-6953	158	11	σj	σj	VERB
ejpam-6953	158	12	≤	≤	NUM
ejpam-6953	158	13	1	1	NUM
ejpam-6953	158	14	+	+	NUM
ejpam-6953	158	15	lognj	lognj	NOUN
ejpam-6953	158	16	.	.	PUNCT
ejpam-6953	159	1	but	but	CCONJ
ejpam-6953	159	2	nj	nj	PROPN
ejpam-6953	159	3	,	,	PUNCT
ejpam-6953	159	4	the	the	DET
ejpam-6953	159	5	number	number	NOUN
ejpam-6953	159	6	of	of	ADP
ejpam-6953	159	7	covering	cover	VERB
ejpam-6953	159	8	balls	ball	NOUN
ejpam-6953	159	9	,	,	PUNCT
ejpam-6953	159	10	can	can	AUX
ejpam-6953	159	11	be	be	AUX
ejpam-6953	159	12	bounded	bound	VERB
ejpam-6953	159	13	in	in	ADP
ejpam-6953	159	14	terms	term	NOUN
ejpam-6953	159	15	of	of	ADP
ejpam-6953	159	16	the	the	DET
ejpam-6953	159	17	volume	volume	NOUN
ejpam-6953	159	18	of	of	ADP
ejpam-6953	159	19	ωj	ωj	ADP
ejpam-6953	159	20	relative	relative	ADJ
ejpam-6953	159	21	to	to	ADP
ejpam-6953	159	22	a	a	DET
ejpam-6953	159	23	ball	ball	NOUN
ejpam-6953	159	24	of	of	ADP
ejpam-6953	159	25	radius	radius	PROPN
ejpam-6953	159	26	rj	rj	PROPN
ejpam-6953	159	27	.	.	PUNCT
ejpam-6953	160	1	more	more	ADV
ejpam-6953	160	2	concretely	concretely	ADV
ejpam-6953	160	3	,	,	PUNCT
ejpam-6953	160	4	nj	nj	PROPN
ejpam-6953	160	5	=	=	SYM
ejpam-6953	160	6	#	#	ADJ
ejpam-6953	160	7	{	{	PUNCT
ejpam-6953	160	8	gbj	gbj	VERB
ejpam-6953	160	9	:	:	PUNCT
ejpam-6953	160	10	gbj	gbj	VERB
ejpam-6953	160	11	∩	∩	NOUN
ejpam-6953	160	12	ωj	ωj	ADP
ejpam-6953	160	13	̸=	̸=	PROPN
ejpam-6953	160	14	∅	∅	NOUN
ejpam-6953	160	15	}	}	PUNCT
ejpam-6953	160	16	≤	≤	PROPN
ejpam-6953	160	17	vol(ωj+1	vol(ωj+1	PROPN
ejpam-6953	160	18	)	)	PUNCT
ejpam-6953	160	19	vol(bj	vol(bj	NOUN
ejpam-6953	160	20	)	)	PUNCT
ejpam-6953	160	21	,	,	PUNCT
ejpam-6953	160	22	since	since	SCONJ
ejpam-6953	160	23	distinct	distinct	ADJ
ejpam-6953	160	24	left	left	NOUN
ejpam-6953	160	25	-	-	PUNCT
ejpam-6953	160	26	translates	translate	NOUN
ejpam-6953	160	27	of	of	ADP
ejpam-6953	160	28	bj	bj	NOUN
ejpam-6953	160	29	are	be	AUX
ejpam-6953	160	30	disjoint	disjoint	ADJ
ejpam-6953	160	31	.	.	PUNCT
ejpam-6953	161	1	thus	thus	ADV
ejpam-6953	161	2	we	we	PRON
ejpam-6953	161	3	can	can	AUX
ejpam-6953	161	4	set	set	VERB
ejpam-6953	161	5	s∗	s∗	PROPN
ejpam-6953	161	6	:	:	PUNCT
ejpam-6953	161	7	=	=	SYM
ejpam-6953	162	1	1	1	NUM
ejpam-6953	163	1	+	+	CCONJ
ejpam-6953	163	2	sup	sup	NOUN
ejpam-6953	163	3	j	j	PROPN
ejpam-6953	163	4	log	log	PROPN
ejpam-6953	163	5	vol(ωj+1	vol(ωj+1	PROPN
ejpam-6953	163	6	)	)	PUNCT
ejpam-6953	163	7	vol(bj	vol(bj	NOUN
ejpam-6953	163	8	)	)	PUNCT
ejpam-6953	163	9	,	,	PUNCT
ejpam-6953	163	10	a.	a.	PROPN
ejpam-6953	163	11	r.	r.	PROPN
ejpam-6953	163	12	al	al	PROPN
ejpam-6953	163	13	-	-	PUNCT
ejpam-6953	163	14	abdallah	abdallah	PROPN
ejpam-6953	163	15	/	/	SYM
ejpam-6953	163	16	eur	eur	PROPN
ejpam-6953	163	17	.	.	PUNCT
ejpam-6953	164	1	j.	j.	PROPN
ejpam-6953	164	2	pure	pure	PROPN
ejpam-6953	164	3	appl	appl	PROPN
ejpam-6953	164	4	.	.	PROPN
ejpam-6953	164	5	math	math	PROPN
ejpam-6953	164	6	,	,	PUNCT
ejpam-6953	164	7	18	18	NUM
ejpam-6953	164	8	(	(	PUNCT
ejpam-6953	164	9	4	4	NUM
ejpam-6953	164	10	)	)	PUNCT
ejpam-6953	164	11	(	(	PUNCT
ejpam-6953	164	12	2025	2025	NUM
ejpam-6953	164	13	)	)	PUNCT
ejpam-6953	164	14	,	,	PUNCT
ejpam-6953	164	15	6953	6953	NUM
ejpam-6953	164	16	8	8	NUM
ejpam-6953	164	17	of	of	ADP
ejpam-6953	164	18	14	14	NUM
ejpam-6953	164	19	which	which	PRON
ejpam-6953	164	20	is	be	AUX
ejpam-6953	164	21	finite	finite	ADJ
ejpam-6953	164	22	because	because	SCONJ
ejpam-6953	164	23	,	,	PUNCT
ejpam-6953	164	24	by	by	ADP
ejpam-6953	164	25	choosing	choose	VERB
ejpam-6953	164	26	rj	rj	PROPN
ejpam-6953	164	27	sufficiently	sufficiently	ADV
ejpam-6953	164	28	small	small	ADJ
ejpam-6953	164	29	for	for	ADP
ejpam-6953	164	30	large	large	ADJ
ejpam-6953	164	31	j	j	PROPN
ejpam-6953	164	32	,	,	PUNCT
ejpam-6953	164	33	one	one	PRON
ejpam-6953	164	34	can	can	AUX
ejpam-6953	164	35	keep	keep	VERB
ejpam-6953	164	36	vol(ωj+1	vol(ωj+1	PROPN
ejpam-6953	164	37	)	)	PUNCT
ejpam-6953	164	38	vol(bj	vol(bj	NOUN
ejpam-6953	164	39	)	)	PUNCT
ejpam-6953	164	40	bounded	bound	VERB
ejpam-6953	164	41	uniformly	uniformly	ADV
ejpam-6953	164	42	in	in	ADP
ejpam-6953	164	43	j.	j.	PROPN
ejpam-6953	164	44	(	(	PUNCT
ejpam-6953	164	45	for	for	ADP
ejpam-6953	164	46	instance	instance	NOUN
ejpam-6953	164	47	,	,	PUNCT
ejpam-6953	164	48	in	in	ADP
ejpam-6953	164	49	r4	r4	PROPN
ejpam-6953	164	50	one	one	NUM
ejpam-6953	164	51	has	have	AUX
ejpam-6953	164	52	vol(ωj+1	vol(ωj+1	PROPN
ejpam-6953	164	53	)	)	PUNCT
ejpam-6953	164	54	vol(bj+1	vol(bj+1	PROPN
ejpam-6953	164	55	)	)	PUNCT
ejpam-6953	164	56	≤	≤	NOUN
ejpam-6953	164	57	625	625	NUM
ejpam-6953	164	58	as	as	ADP
ejpam-6953	164	59	in	in	ADP
ejpam-6953	164	60	the	the	DET
ejpam-6953	164	61	discussion	discussion	NOUN
ejpam-6953	164	62	above	above	ADP
ejpam-6953	164	63	.	.	PUNCT
ejpam-6953	164	64	)	)	PUNCT
ejpam-6953	165	1	thus	thus	ADV
ejpam-6953	165	2	(	(	PUNCT
ejpam-6953	165	3	ii	ii	NOUN
ejpam-6953	165	4	)	)	PUNCT
ejpam-6953	165	5	holds	hold	VERB
ejpam-6953	165	6	.	.	PUNCT
ejpam-6953	166	1	5	5	X
ejpam-6953	166	2	.	.	X
ejpam-6953	166	3	global	global	ADJ
ejpam-6953	166	4	weighted	weight	VERB
ejpam-6953	166	5	l2	l2	NOUN
ejpam-6953	166	6	solvability	solvability	NOUN
ejpam-6953	166	7	with	with	ADP
ejpam-6953	166	8	the	the	DET
ejpam-6953	166	9	preparations	preparation	NOUN
ejpam-6953	166	10	of	of	ADP
ejpam-6953	166	11	the	the	DET
ejpam-6953	166	12	previous	previous	ADJ
ejpam-6953	166	13	sections	section	NOUN
ejpam-6953	166	14	,	,	PUNCT
ejpam-6953	166	15	we	we	PRON
ejpam-6953	166	16	can	can	AUX
ejpam-6953	166	17	now	now	ADV
ejpam-6953	166	18	prove	prove	VERB
ejpam-6953	166	19	the	the	DET
ejpam-6953	166	20	main	main	ADJ
ejpam-6953	166	21	theorem	theorem	NOUN
ejpam-6953	166	22	.	.	PUNCT
ejpam-6953	167	1	let	let	VERB
ejpam-6953	167	2	f	f	PROPN
ejpam-6953	167	3	∈	∈	PROPN
ejpam-6953	167	4	l2	l2	NOUN
ejpam-6953	167	5	p	p	NOUN
ejpam-6953	167	6	,	,	PUNCT
ejpam-6953	167	7	q(g	q(g	PROPN
ejpam-6953	167	8	,	,	PUNCT
ejpam-6953	167	9	e	e	PROPN
ejpam-6953	167	10	−tρ	−tρ	PROPN
ejpam-6953	167	11	)	)	PUNCT
ejpam-6953	167	12	be	be	VERB
ejpam-6953	167	13	an	an	DET
ejpam-6953	167	14	arbitrary	arbitrary	ADJ
ejpam-6953	167	15	∂̄-closed	∂̄-close	VERB
ejpam-6953	167	16	form	form	NOUN
ejpam-6953	167	17	with	with	ADP
ejpam-6953	167	18	q	q	PROPN
ejpam-6953	167	19	≥	≥	NUM
ejpam-6953	167	20	1	1	NUM
ejpam-6953	167	21	.	.	PUNCT
ejpam-6953	168	1	we	we	PRON
ejpam-6953	168	2	aim	aim	VERB
ejpam-6953	168	3	to	to	PART
ejpam-6953	168	4	produce	produce	VERB
ejpam-6953	168	5	a	a	DET
ejpam-6953	168	6	solution	solution	NOUN
ejpam-6953	168	7	u	u	NOUN
ejpam-6953	168	8	∈	∈	NOUN
ejpam-6953	168	9	l2	l2	NOUN
ejpam-6953	168	10	p	p	NOUN
ejpam-6953	168	11	,	,	PUNCT
ejpam-6953	168	12	q−1(g	q−1(g	PROPN
ejpam-6953	168	13	,	,	PUNCT
ejpam-6953	168	14	e	e	PROPN
ejpam-6953	168	15	−tρ	−tρ	PROPN
ejpam-6953	168	16	)	)	PUNCT
ejpam-6953	168	17	such	such	ADJ
ejpam-6953	168	18	that	that	SCONJ
ejpam-6953	168	19	∂̄u	∂̄u	PROPN
ejpam-6953	169	1	=	=	SYM
ejpam-6953	169	2	f	f	PROPN
ejpam-6953	169	3	.	.	PUNCT
ejpam-6953	170	1	let	let	VERB
ejpam-6953	170	2	ωj	ωj	VERB
ejpam-6953	170	3	,	,	PUNCT
ejpam-6953	170	4	φj	φj	INTJ
ejpam-6953	170	5	,	,	PUNCT
ejpam-6953	170	6	and	and	CCONJ
ejpam-6953	170	7	σj	σj	ADJ
ejpam-6953	170	8	be	be	AUX
ejpam-6953	170	9	as	as	ADP
ejpam-6953	170	10	in	in	ADP
ejpam-6953	170	11	lemmas	lemmas	PROPN
ejpam-6953	170	12	2	2	NUM
ejpam-6953	170	13	and	and	CCONJ
ejpam-6953	170	14	3	3	NUM
ejpam-6953	170	15	.	.	PUNCT
ejpam-6953	171	1	by	by	ADP
ejpam-6953	171	2	compactness	compactness	NOUN
ejpam-6953	171	3	,	,	PUNCT
ejpam-6953	171	4	there	there	PRON
ejpam-6953	171	5	exists	exist	VERB
ejpam-6953	171	6	some	some	DET
ejpam-6953	171	7	index	index	NOUN
ejpam-6953	171	8	j0	j0	PROPN
ejpam-6953	171	9	such	such	ADJ
ejpam-6953	171	10	that	that	DET
ejpam-6953	171	11	suppf	suppf	NOUN
ejpam-6953	171	12	⊂	⊂	PROPN
ejpam-6953	171	13	ωj0	ωj0	PROPN
ejpam-6953	171	14	.	.	PUNCT
ejpam-6953	172	1	we	we	PRON
ejpam-6953	172	2	may	may	AUX
ejpam-6953	172	3	assume	assume	VERB
ejpam-6953	172	4	j0	j0	PROPN
ejpam-6953	172	5	=	=	SYM
ejpam-6953	172	6	1	1	NUM
ejpam-6953	172	7	without	without	ADP
ejpam-6953	172	8	loss	loss	NOUN
ejpam-6953	172	9	of	of	ADP
ejpam-6953	172	10	generality	generality	NOUN
ejpam-6953	172	11	(	(	PUNCT
ejpam-6953	172	12	i.e.	i.e.	X
ejpam-6953	172	13	,	,	PUNCT
ejpam-6953	172	14	f	f	PROPN
ejpam-6953	172	15	is	be	AUX
ejpam-6953	172	16	supported	support	VERB
ejpam-6953	172	17	in	in	ADP
ejpam-6953	172	18	ω1	ω1	PROPN
ejpam-6953	172	19	)	)	PUNCT
ejpam-6953	172	20	.	.	PUNCT
ejpam-6953	173	1	for	for	ADP
ejpam-6953	173	2	each	each	DET
ejpam-6953	173	3	j	j	PROPN
ejpam-6953	173	4	≥	≥	NUM
ejpam-6953	173	5	1	1	NUM
ejpam-6953	173	6	,	,	PUNCT
ejpam-6953	173	7	consider	consider	VERB
ejpam-6953	173	8	the	the	DET
ejpam-6953	173	9	bounded	bounded	ADJ
ejpam-6953	173	10	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	173	11	domain	domain	NOUN
ejpam-6953	173	12	ω̃j	ω̃j	NOUN
ejpam-6953	173	13	:	:	PUNCT
ejpam-6953	173	14	=	=	SYM
ejpam-6953	173	15	ωj+1	ωj+1	X
ejpam-6953	173	16	\	\	PROPN
ejpam-6953	173	17	ωj	ωj	ADP
ejpam-6953	173	18	⋐	⋐	NOUN
ejpam-6953	173	19	g	g	NOUN
ejpam-6953	173	20	(	(	PUNCT
ejpam-6953	173	21	with	with	ADP
ejpam-6953	173	22	smooth	smooth	ADJ
ejpam-6953	173	23	boundary	boundary	NOUN
ejpam-6953	173	24	,	,	PUNCT
ejpam-6953	173	25	possibly	possibly	ADV
ejpam-6953	173	26	disconnected	disconnect	VERB
ejpam-6953	173	27	)	)	PUNCT
ejpam-6953	173	28	,	,	PUNCT
ejpam-6953	173	29	and	and	CCONJ
ejpam-6953	173	30	the	the	DET
ejpam-6953	173	31	function	function	NOUN
ejpam-6953	173	32	ψj	ψj	ADP
ejpam-6953	173	33	:	:	PUNCT
ejpam-6953	173	34	=	=	SYM
ejpam-6953	173	35	φj+1	φj+1	X
ejpam-6953	173	36	+	+	NUM
ejpam-6953	173	37	ε∗(σj	ε∗(σj	PROPN
ejpam-6953	173	38	−	−	PROPN
ejpam-6953	173	39	s∗	s∗	PROPN
ejpam-6953	173	40	)	)	PUNCT
ejpam-6953	173	41	,	,	PUNCT
ejpam-6953	173	42	where	where	SCONJ
ejpam-6953	173	43	ε∗	ε∗	PROPN
ejpam-6953	173	44	and	and	CCONJ
ejpam-6953	173	45	s∗	s∗	PROPN
ejpam-6953	173	46	are	be	AUX
ejpam-6953	173	47	the	the	DET
ejpam-6953	173	48	constants	constant	NOUN
ejpam-6953	173	49	from	from	ADP
ejpam-6953	173	50	lemma	lemma	PROPN
ejpam-6953	173	51	3	3	NUM
ejpam-6953	173	52	.	.	PUNCT
ejpam-6953	174	1	by	by	ADP
ejpam-6953	174	2	construction	construction	NOUN
ejpam-6953	174	3	we	we	PRON
ejpam-6953	174	4	have	have	VERB
ejpam-6953	174	5	ψj	ψj	ADV
ejpam-6953	174	6	=	=	SYM
ejpam-6953	174	7	φj+1	φj+1	X
ejpam-6953	174	8	≥	≥	NOUN
ejpam-6953	174	9	0	0	NUM
ejpam-6953	174	10	on	on	ADP
ejpam-6953	174	11	∂ωj+1	∂ωj+1	NOUN
ejpam-6953	174	12	and	and	CCONJ
ejpam-6953	174	13	ψj	ψj	ADV
ejpam-6953	174	14	=	=	PROPN
ejpam-6953	174	15	ε∗(σj−s∗	ε∗(σj−s∗	PROPN
ejpam-6953	174	16	)	)	PUNCT
ejpam-6953	174	17	≤	≤	NOUN
ejpam-6953	174	18	0	0	NUM
ejpam-6953	175	1	on	on	ADP
ejpam-6953	175	2	∂ωj	∂ωj	NOUN
ejpam-6953	175	3	(	(	PUNCT
ejpam-6953	175	4	because	because	SCONJ
ejpam-6953	175	5	σj	σj	ADJ
ejpam-6953	175	6	≤	≤	PROPN
ejpam-6953	175	7	s∗	s∗	PROPN
ejpam-6953	175	8	on	on	ADP
ejpam-6953	175	9	ωj	ωj	ADP
ejpam-6953	175	10	)	)	PUNCT
ejpam-6953	175	11	.	.	PUNCT
ejpam-6953	176	1	thus	thus	ADV
ejpam-6953	176	2	ψj	ψj	ADV
ejpam-6953	176	3	is	be	AUX
ejpam-6953	176	4	a	a	DET
ejpam-6953	176	5	smooth	smooth	ADJ
ejpam-6953	176	6	function	function	NOUN
ejpam-6953	176	7	on	on	ADP
ejpam-6953	176	8	ω̃j	ω̃j	NOUN
ejpam-6953	176	9	that	that	PRON
ejpam-6953	176	10	vanishes	vanish	VERB
ejpam-6953	176	11	on	on	ADP
ejpam-6953	176	12	∂ω̃j	∂ω̃j	PROPN
ejpam-6953	176	13	.	.	PUNCT
ejpam-6953	177	1	moreover	moreover	ADV
ejpam-6953	177	2	,	,	PUNCT
ejpam-6953	177	3	on	on	ADP
ejpam-6953	177	4	ω̃j	ω̃j	NOUN
ejpam-6953	177	5	we	we	PRON
ejpam-6953	177	6	have	have	VERB
ejpam-6953	177	7	i∂∂̄ψj	i∂∂̄ψj	NUM
ejpam-6953	177	8	≥	≥	NOUN
ejpam-6953	177	9	i∂∂̄φj+1	i∂∂̄φj+1	NOUN
ejpam-6953	177	10	+	+	CCONJ
ejpam-6953	177	11	ε∗(i∂∂̄σj	ε∗(i∂∂̄σj	PROPN
ejpam-6953	177	12	)	)	PUNCT
ejpam-6953	177	13	≥	≥	PRON
ejpam-6953	177	14	ε∗c∗ω	ε∗c∗ω	VERB
ejpam-6953	177	15	=	=	X
ejpam-6953	177	16	:	:	PUNCT
ejpam-6953	177	17	λ∗ω	λ∗ω	NUM
ejpam-6953	177	18	,	,	PUNCT
ejpam-6953	177	19	where	where	SCONJ
ejpam-6953	177	20	λ∗	λ∗	NOUN
ejpam-6953	177	21	:	:	PUNCT
ejpam-6953	177	22	=	=	SYM
ejpam-6953	178	1	ε∗c∗	ε∗c∗	PROPN
ejpam-6953	178	2	>	>	X
ejpam-6953	178	3	0	0	PUNCT
ejpam-6953	178	4	is	be	AUX
ejpam-6953	178	5	a	a	DET
ejpam-6953	178	6	fixed	fix	VERB
ejpam-6953	178	7	constant	constant	ADJ
ejpam-6953	178	8	.	.	PUNCT
ejpam-6953	179	1	in	in	ADP
ejpam-6953	179	2	other	other	ADJ
ejpam-6953	179	3	words	word	NOUN
ejpam-6953	179	4	,	,	PUNCT
ejpam-6953	179	5	ψj	ψj	ADV
ejpam-6953	179	6	is	be	AUX
ejpam-6953	179	7	a	a	DET
ejpam-6953	179	8	fixed	fix	VERB
ejpam-6953	179	9	multiple	multiple	NOUN
ejpam-6953	179	10	of	of	ADP
ejpam-6953	179	11	a	a	DET
ejpam-6953	179	12	strictly	strictly	ADV
ejpam-6953	179	13	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	179	14	defining	define	VERB
ejpam-6953	179	15	function	function	NOUN
ejpam-6953	179	16	for	for	ADP
ejpam-6953	179	17	ω̃j	ω̃j	NOUN
ejpam-6953	179	18	,	,	PUNCT
ejpam-6953	179	19	with	with	ADP
ejpam-6953	179	20	a	a	DET
ejpam-6953	179	21	uniform	uniform	ADJ
ejpam-6953	179	22	levi	levi	PROPN
ejpam-6953	179	23	bound	bind	VERB
ejpam-6953	179	24	independent	independent	ADJ
ejpam-6953	179	25	of	of	ADP
ejpam-6953	179	26	j.	j.	PROPN
ejpam-6953	179	27	now	now	ADV
ejpam-6953	179	28	,	,	PUNCT
ejpam-6953	179	29	on	on	ADP
ejpam-6953	179	30	each	each	DET
ejpam-6953	179	31	ω̃j	ω̃j	NOUN
ejpam-6953	179	32	we	we	PRON
ejpam-6953	179	33	can	can	AUX
ejpam-6953	179	34	solve	solve	VERB
ejpam-6953	179	35	∂̄uj	∂̄uj	ADP
ejpam-6953	179	36	=	=	SYM
ejpam-6953	179	37	f	f	PROPN
ejpam-6953	179	38	with	with	ADP
ejpam-6953	179	39	uniform	uniform	ADJ
ejpam-6953	179	40	estimates	estimate	NOUN
ejpam-6953	179	41	thanks	thank	NOUN
ejpam-6953	179	42	to	to	ADP
ejpam-6953	179	43	lemma	lemma	PROPN
ejpam-6953	179	44	1	1	NUM
ejpam-6953	179	45	.	.	PUNCT
ejpam-6953	179	46	indeed	indeed	ADV
ejpam-6953	179	47	,	,	PUNCT
ejpam-6953	179	48	applying	apply	VERB
ejpam-6953	179	49	lemma	lemma	PROPN
ejpam-6953	179	50	1	1	NUM
ejpam-6953	179	51	on	on	ADP
ejpam-6953	179	52	ω̃j	ω̃j	NOUN
ejpam-6953	179	53	with	with	ADP
ejpam-6953	179	54	the	the	DET
ejpam-6953	179	55	weight	weight	NOUN
ejpam-6953	179	56	e−tρ	e−tρ	NOUN
ejpam-6953	179	57	and	and	CCONJ
ejpam-6953	179	58	the	the	DET
ejpam-6953	179	59	strictly	strictly	ADV
ejpam-6953	179	60	psh	psh	NOUN
ejpam-6953	179	61	cut	cut	NOUN
ejpam-6953	179	62	-	-	PUNCT
ejpam-6953	179	63	off	off	NOUN
ejpam-6953	179	64	ψj	ψj	ADV
ejpam-6953	179	65	,	,	PUNCT
ejpam-6953	179	66	we	we	PRON
ejpam-6953	179	67	obtain	obtain	VERB
ejpam-6953	179	68	a	a	DET
ejpam-6953	179	69	solution	solution	NOUN
ejpam-6953	179	70	uj	uj	PROPN
ejpam-6953	179	71	∈	∈	PROPN
ejpam-6953	179	72	l2	l2	NOUN
ejpam-6953	179	73	p	p	NOUN
ejpam-6953	179	74	,	,	PUNCT
ejpam-6953	179	75	q−1(ω̃j	q−1(ω̃j	X
ejpam-6953	179	76	,	,	PUNCT
ejpam-6953	179	77	e	e	PROPN
ejpam-6953	179	78	−tρ	−tρ	PROPN
ejpam-6953	179	79	)	)	PUNCT
ejpam-6953	179	80	such	such	ADJ
ejpam-6953	179	81	that	that	SCONJ
ejpam-6953	179	82	∂̄uj	∂̄uj	PROPN
ejpam-6953	179	83	=	=	SYM
ejpam-6953	179	84	f	f	PROPN
ejpam-6953	179	85	on	on	ADP
ejpam-6953	179	86	ω̃j	ω̃j	NOUN
ejpam-6953	179	87	and∫	and∫	X
ejpam-6953	179	88	ω̃j	ω̃j	NOUN
ejpam-6953	179	89	|uj	|uj	NOUN
ejpam-6953	179	90	|2	|2	NUM
ejpam-6953	179	91	e−tρ	e−tρ	NOUN
ejpam-6953	179	92	≤	≤	ADV
ejpam-6953	179	93	2	2	NUM
ejpam-6953	179	94	λ∗	λ∗	NOUN
ejpam-6953	179	95	q	q	PROPN
ejpam-6953	179	96	e	e	NOUN
ejpam-6953	179	97	t	t	PROPN
ejpam-6953	179	98	sup	sup	NOUN
ejpam-6953	179	99	ω̃j	ω̃j	NOUN
ejpam-6953	179	100	ψj	ψj	ADV
ejpam-6953	179	101	∫	∫	PROPN
ejpam-6953	179	102	ω̃j	ω̃j	PROPN
ejpam-6953	179	103	|f	|f	PROPN
ejpam-6953	179	104	|2	|2	NUM
ejpam-6953	179	105	e−tρ	e−tρ	NOUN
ejpam-6953	179	106	dvω	dvω	PROPN
ejpam-6953	179	107	.	.	PUNCT
ejpam-6953	180	1	(	(	PUNCT
ejpam-6953	180	2	2	2	X
ejpam-6953	180	3	)	)	PUNCT
ejpam-6953	180	4	using	use	VERB
ejpam-6953	180	5	the	the	DET
ejpam-6953	180	6	properties	property	NOUN
ejpam-6953	180	7	of	of	ADP
ejpam-6953	180	8	ψj	ψj	ADV
ejpam-6953	180	9	,	,	PUNCT
ejpam-6953	180	10	we	we	PRON
ejpam-6953	180	11	can	can	AUX
ejpam-6953	180	12	simplify	simplify	VERB
ejpam-6953	180	13	sup	sup	NOUN
ejpam-6953	180	14	ω̃j	ω̃j	NOUN
ejpam-6953	180	15	ψj	ψj	ADV
ejpam-6953	180	16	.	.	PUNCT
ejpam-6953	181	1	on	on	ADP
ejpam-6953	181	2	ωj	ωj	INTJ
ejpam-6953	181	3	we	we	PRON
ejpam-6953	181	4	have	have	VERB
ejpam-6953	181	5	ψj	ψj	ADV
ejpam-6953	181	6	≤	≤	NUM
ejpam-6953	181	7	0	0	NUM
ejpam-6953	181	8	,	,	PUNCT
ejpam-6953	181	9	whereas	whereas	SCONJ
ejpam-6953	181	10	on	on	ADP
ejpam-6953	181	11	ωj+1	ωj+1	NOUN
ejpam-6953	181	12	we	we	PRON
ejpam-6953	181	13	have	have	VERB
ejpam-6953	181	14	ψj	ψj	ADV
ejpam-6953	181	15	≤	≤	NUM
ejpam-6953	181	16	rj+1	rj+1	NOUN
ejpam-6953	181	17	+	+	CCONJ
ejpam-6953	181	18	1	1	NUM
ejpam-6953	181	19	4	4	NUM
ejpam-6953	181	20	(	(	PUNCT
ejpam-6953	181	21	since	since	SCONJ
ejpam-6953	181	22	|φj+1	|φj+1	NOUN
ejpam-6953	181	23	−	−	PROPN
ejpam-6953	181	24	ρ|	ρ|	PROPN
ejpam-6953	181	25	<	<	X
ejpam-6953	181	26	1/4	1/4	NUM
ejpam-6953	181	27	on	on	ADP
ejpam-6953	181	28	ωj	ωj	ADP
ejpam-6953	181	29	and	and	CCONJ
ejpam-6953	181	30	ρ	ρ	NOUN
ejpam-6953	181	31	<	<	X
ejpam-6953	181	32	rj+1	rj+1	NOUN
ejpam-6953	181	33	on	on	ADP
ejpam-6953	181	34	ωj+1	ωj+1	NOUN
ejpam-6953	181	35	)	)	PUNCT
ejpam-6953	181	36	.	.	PUNCT
ejpam-6953	182	1	thus	thus	ADV
ejpam-6953	182	2	sup	sup	NOUN
ejpam-6953	182	3	ω̃j	ω̃j	NOUN
ejpam-6953	182	4	ψj	ψj	ADV
ejpam-6953	182	5	≤	≤	ADJ
ejpam-6953	182	6	rj+1	rj+1	NOUN
ejpam-6953	182	7	+	+	CCONJ
ejpam-6953	182	8	1	1	NUM
ejpam-6953	182	9	4	4	NUM
ejpam-6953	182	10	.	.	PUNCT
ejpam-6953	183	1	from	from	ADP
ejpam-6953	183	2	(	(	PUNCT
ejpam-6953	183	3	2	2	X
ejpam-6953	183	4	)	)	PUNCT
ejpam-6953	183	5	we	we	PRON
ejpam-6953	183	6	deduce	deduce	VERB
ejpam-6953	183	7	that∫	that∫	NOUN
ejpam-6953	183	8	ω̃j	ω̃j	NOUN
ejpam-6953	183	9	|uj	|uj	PROPN
ejpam-6953	183	10	|2e−tρ	|2e−tρ	PROPN
ejpam-6953	183	11	≤	≤	NUM
ejpam-6953	183	12	2	2	NUM
ejpam-6953	183	13	λ∗	λ∗	NOUN
ejpam-6953	183	14	q	q	PROPN
ejpam-6953	183	15	e	e	PROPN
ejpam-6953	183	16	t	t	PROPN
ejpam-6953	183	17	(	(	PUNCT
ejpam-6953	183	18	rj+1	rj+1	NOUN
ejpam-6953	183	19	+	+	NOUN
ejpam-6953	183	20	1/4	1/4	NUM
ejpam-6953	183	21	)	)	PUNCT
ejpam-6953	183	22	∫	∫	PROPN
ejpam-6953	183	23	g	g	PROPN
ejpam-6953	183	24	|f	|f	PROPN
ejpam-6953	183	25	|2e−tρ	|2e−tρ	PROPN
ejpam-6953	183	26	dvω	dvω	PROPN
ejpam-6953	183	27	,	,	PUNCT
ejpam-6953	183	28	since	since	SCONJ
ejpam-6953	183	29	f	f	PROPN
ejpam-6953	183	30	is	be	AUX
ejpam-6953	183	31	supported	support	VERB
ejpam-6953	183	32	in	in	ADP
ejpam-6953	183	33	ω1	ω1	PROPN
ejpam-6953	183	34	⊂	⊂	PROPN
ejpam-6953	183	35	ω̃j	ω̃j	NOUN
ejpam-6953	183	36	for	for	ADP
ejpam-6953	183	37	all	all	DET
ejpam-6953	183	38	j.	j.	PROPN
ejpam-6953	183	39	in	in	ADP
ejpam-6953	183	40	particular	particular	ADJ
ejpam-6953	183	41	,	,	PUNCT
ejpam-6953	183	42	uj	uj	PROPN
ejpam-6953	183	43	has	have	AUX
ejpam-6953	183	44	uniformly	uniformly	ADV
ejpam-6953	183	45	bounded	bound	VERB
ejpam-6953	183	46	l2	l2	NOUN
ejpam-6953	183	47	norm	norm	NOUN
ejpam-6953	183	48	(	(	PUNCT
ejpam-6953	183	49	with	with	ADP
ejpam-6953	183	50	respect	respect	NOUN
ejpam-6953	183	51	to	to	ADP
ejpam-6953	183	52	e−tρdvω	e−tρdvω	NOUN
ejpam-6953	183	53	)	)	PUNCT
ejpam-6953	183	54	on	on	ADP
ejpam-6953	183	55	the	the	DET
ejpam-6953	183	56	exhausting	exhausting	ADJ
ejpam-6953	183	57	sequence	sequence	NOUN
ejpam-6953	183	58	ω̃j	ω̃j	X
ejpam-6953	183	59	↑	↑	PROPN
ejpam-6953	183	60	g.	g.	PROPN
ejpam-6953	183	61	a.	a.	PROPN
ejpam-6953	183	62	r.	r.	PROPN
ejpam-6953	183	63	al	al	PROPN
ejpam-6953	183	64	-	-	PUNCT
ejpam-6953	183	65	abdallah	abdallah	PROPN
ejpam-6953	183	66	/	/	SYM
ejpam-6953	183	67	eur	eur	PROPN
ejpam-6953	183	68	.	.	PUNCT
ejpam-6953	184	1	j.	j.	PROPN
ejpam-6953	184	2	pure	pure	PROPN
ejpam-6953	184	3	appl	appl	PROPN
ejpam-6953	184	4	.	.	PROPN
ejpam-6953	184	5	math	math	PROPN
ejpam-6953	184	6	,	,	PUNCT
ejpam-6953	184	7	18	18	NUM
ejpam-6953	184	8	(	(	PUNCT
ejpam-6953	184	9	4	4	NUM
ejpam-6953	184	10	)	)	PUNCT
ejpam-6953	184	11	(	(	PUNCT
ejpam-6953	184	12	2025	2025	NUM
ejpam-6953	184	13	)	)	PUNCT
ejpam-6953	184	14	,	,	PUNCT
ejpam-6953	184	15	6953	6953	NUM
ejpam-6953	184	16	9	9	NUM
ejpam-6953	184	17	of	of	ADP
ejpam-6953	184	18	14	14	NUM
ejpam-6953	184	19	since	since	SCONJ
ejpam-6953	184	20	the	the	DET
ejpam-6953	184	21	ω̃j	ω̃j	NOUN
ejpam-6953	184	22	form	form	VERB
ejpam-6953	184	23	an	an	DET
ejpam-6953	184	24	increasing	increase	VERB
ejpam-6953	184	25	sequence	sequence	NOUN
ejpam-6953	184	26	whose	whose	DET
ejpam-6953	184	27	union	union	NOUN
ejpam-6953	184	28	is	be	AUX
ejpam-6953	184	29	g	g	NOUN
ejpam-6953	184	30	,	,	PUNCT
ejpam-6953	184	31	and	and	CCONJ
ejpam-6953	184	32	since	since	SCONJ
ejpam-6953	184	33	the	the	DET
ejpam-6953	184	34	norms	norm	NOUN
ejpam-6953	184	35	∥uj∥l2(g	∥uj∥l2(g	NOUN
ejpam-6953	184	36	,	,	PUNCT
ejpam-6953	184	37	e−tρ	e−tρ	NOUN
ejpam-6953	184	38	)	)	PUNCT
ejpam-6953	184	39	are	be	AUX
ejpam-6953	184	40	uniformly	uniformly	ADV
ejpam-6953	184	41	bounded	bound	VERB
ejpam-6953	184	42	,	,	PUNCT
ejpam-6953	184	43	we	we	PRON
ejpam-6953	184	44	can	can	AUX
ejpam-6953	184	45	extract	extract	VERB
ejpam-6953	184	46	from	from	ADP
ejpam-6953	184	47	{	{	PUNCT
ejpam-6953	184	48	uj	uj	PROPN
ejpam-6953	184	49	}	}	PUNCT
ejpam-6953	184	50	a	a	DET
ejpam-6953	184	51	subsequence	subsequence	NOUN
ejpam-6953	184	52	that	that	PRON
ejpam-6953	184	53	converges	converge	VERB
ejpam-6953	184	54	weakly	weakly	ADV
ejpam-6953	184	55	in	in	ADP
ejpam-6953	184	56	l2	l2	NOUN
ejpam-6953	184	57	p	p	NOUN
ejpam-6953	184	58	,	,	PUNCT
ejpam-6953	184	59	q−1(g	q−1(g	PROPN
ejpam-6953	184	60	,	,	PUNCT
ejpam-6953	184	61	e	e	PROPN
ejpam-6953	184	62	−tρ	−tρ	PROPN
ejpam-6953	184	63	)	)	PUNCT
ejpam-6953	184	64	to	to	ADP
ejpam-6953	184	65	some	some	DET
ejpam-6953	184	66	u	u	NOUN
ejpam-6953	184	67	∈	∈	PROPN
ejpam-6953	184	68	l2	l2	NOUN
ejpam-6953	184	69	p	p	NOUN
ejpam-6953	184	70	,	,	PUNCT
ejpam-6953	184	71	q−1(g	q−1(g	PROPN
ejpam-6953	184	72	,	,	PUNCT
ejpam-6953	184	73	e	e	PROPN
ejpam-6953	184	74	−tρ	−tρ	PROPN
ejpam-6953	184	75	)	)	PUNCT
ejpam-6953	184	76	.	.	PUNCT
ejpam-6953	185	1	passing	pass	VERB
ejpam-6953	185	2	to	to	ADP
ejpam-6953	185	3	a	a	DET
ejpam-6953	185	4	diagonal	diagonal	ADJ
ejpam-6953	185	5	subsequence	subsequence	NOUN
ejpam-6953	185	6	if	if	SCONJ
ejpam-6953	185	7	necessary	necessary	ADJ
ejpam-6953	185	8	,	,	PUNCT
ejpam-6953	185	9	we	we	PRON
ejpam-6953	185	10	may	may	AUX
ejpam-6953	185	11	assume	assume	VERB
ejpam-6953	185	12	uj	uj	PROPN
ejpam-6953	185	13	→	→	SYM
ejpam-6953	185	14	u	u	PROPN
ejpam-6953	185	15	in	in	ADP
ejpam-6953	185	16	the	the	DET
ejpam-6953	185	17	weak	weak	ADJ
ejpam-6953	185	18	l2	l2	NOUN
ejpam-6953	185	19	sense	sense	NOUN
ejpam-6953	185	20	on	on	ADP
ejpam-6953	185	21	each	each	DET
ejpam-6953	185	22	fixed	fix	VERB
ejpam-6953	185	23	ω̃m	ω̃m	NOUN
ejpam-6953	185	24	as	as	ADP
ejpam-6953	185	25	j	j	PROPN
ejpam-6953	185	26	→	→	SYM
ejpam-6953	185	27	∞	∞	PROPN
ejpam-6953	185	28	,	,	PUNCT
ejpam-6953	185	29	for	for	ADP
ejpam-6953	185	30	every	every	DET
ejpam-6953	185	31	m.	m.	NOUN
ejpam-6953	185	32	in	in	ADP
ejpam-6953	185	33	particular	particular	ADJ
ejpam-6953	185	34	,	,	PUNCT
ejpam-6953	185	35	for	for	ADP
ejpam-6953	185	36	each	each	DET
ejpam-6953	185	37	m	m	VERB
ejpam-6953	185	38	we	we	PRON
ejpam-6953	185	39	have∫	have∫	VERB
ejpam-6953	185	40	ω̃m	ω̃m	NOUN
ejpam-6953	185	41	⟨uj	⟨uj	PROPN
ejpam-6953	185	42	,	,	PUNCT
ejpam-6953	185	43	ϕ⟩	ϕ⟩	NOUN
ejpam-6953	185	44	e−tρdvω	e−tρdvω	X
ejpam-6953	185	45	→	→	SYM
ejpam-6953	185	46	∫	∫	PROPN
ejpam-6953	185	47	ω̃m	ω̃m	NUM
ejpam-6953	185	48	⟨u	⟨u	NOUN
ejpam-6953	185	49	,	,	PUNCT
ejpam-6953	185	50	ϕ⟩	ϕ⟩	ADJ
ejpam-6953	185	51	e−tρdvω	e−tρdvω	NOUN
ejpam-6953	185	52	,	,	PUNCT
ejpam-6953	185	53	∀ϕ	∀ϕ	PROPN
ejpam-6953	185	54	∈	∈	PROPN
ejpam-6953	185	55	l2	l2	NOUN
ejpam-6953	185	56	p	p	X
ejpam-6953	185	57	,	,	PUNCT
ejpam-6953	185	58	q−1(ω̃m	q−1(ω̃m	PROPN
ejpam-6953	185	59	,	,	PUNCT
ejpam-6953	185	60	e	e	PROPN
ejpam-6953	185	61	−tρ	−tρ	PROPN
ejpam-6953	185	62	)	)	PUNCT
ejpam-6953	185	63	.	.	PUNCT
ejpam-6953	186	1	using	use	VERB
ejpam-6953	186	2	this	this	PRON
ejpam-6953	186	3	against	against	ADP
ejpam-6953	186	4	smooth	smooth	NOUN
ejpam-6953	186	5	compactly	compactly	ADV
ejpam-6953	186	6	supported	support	VERB
ejpam-6953	186	7	forms	form	NOUN
ejpam-6953	186	8	ϕ	ϕ	NOUN
ejpam-6953	186	9	,	,	PUNCT
ejpam-6953	186	10	we	we	PRON
ejpam-6953	186	11	see	see	VERB
ejpam-6953	186	12	that	that	SCONJ
ejpam-6953	186	13	∂̄u	∂̄u	PROPN
ejpam-6953	186	14	=	=	SYM
ejpam-6953	186	15	f	f	PROPN
ejpam-6953	186	16	holds	hold	VERB
ejpam-6953	186	17	in	in	ADP
ejpam-6953	186	18	the	the	DET
ejpam-6953	186	19	sense	sense	NOUN
ejpam-6953	186	20	of	of	ADP
ejpam-6953	186	21	distributions	distribution	NOUN
ejpam-6953	186	22	on	on	ADP
ejpam-6953	186	23	ωm	ωm	NOUN
ejpam-6953	186	24	,	,	PUNCT
ejpam-6953	186	25	hence	hence	ADV
ejpam-6953	186	26	classically	classically	ADV
ejpam-6953	186	27	on	on	ADP
ejpam-6953	186	28	ωm	ωm	NOUN
ejpam-6953	186	29	.	.	PUNCT
ejpam-6953	186	30	since	since	SCONJ
ejpam-6953	186	31	m	m	PROPN
ejpam-6953	186	32	was	be	AUX
ejpam-6953	186	33	arbitrary	arbitrary	ADJ
ejpam-6953	186	34	,	,	PUNCT
ejpam-6953	186	35	∂̄u	∂̄u	X
ejpam-6953	186	36	=	=	SYM
ejpam-6953	186	37	f	f	PROPN
ejpam-6953	186	38	on	on	ADP
ejpam-6953	186	39	all	all	PRON
ejpam-6953	186	40	of	of	ADP
ejpam-6953	186	41	g.	g.	PROPN
ejpam-6953	186	42	finally	finally	ADV
ejpam-6953	186	43	,	,	PUNCT
ejpam-6953	186	44	by	by	ADP
ejpam-6953	186	45	the	the	DET
ejpam-6953	186	46	weak	weak	ADJ
ejpam-6953	186	47	lower	low	ADJ
ejpam-6953	186	48	semicontinuity	semicontinuity	NOUN
ejpam-6953	186	49	of	of	ADP
ejpam-6953	186	50	the	the	DET
ejpam-6953	186	51	l2	l2	NOUN
ejpam-6953	186	52	norm	norm	NOUN
ejpam-6953	186	53	(	(	PUNCT
ejpam-6953	186	54	see	see	VERB
ejpam-6953	186	55	,	,	PUNCT
ejpam-6953	186	56	e.g.	e.g.	ADV
ejpam-6953	186	57	,	,	PUNCT
ejpam-6953	186	58	[	[	X
ejpam-6953	186	59	25	25	NUM
ejpam-6953	186	60	,	,	PUNCT
ejpam-6953	186	61	ch	ch	NOUN
ejpam-6953	186	62	.	.	NOUN
ejpam-6953	186	63	3	3	NUM
ejpam-6953	186	64	]	]	NUM
ejpam-6953	186	65	)	)	PUNCT
ejpam-6953	186	66	,	,	PUNCT
ejpam-6953	186	67	we	we	PRON
ejpam-6953	186	68	have	have	VERB
ejpam-6953	186	69	∫	∫	PROPN
ejpam-6953	186	70	g	g	PROPN
ejpam-6953	186	71	|u|2e−tρ	|u|2e−tρ	NUM
ejpam-6953	186	72	dvω	dvω	PROPN
ejpam-6953	186	73	≤	≤	PROPN
ejpam-6953	186	74	lim	lim	PROPN
ejpam-6953	186	75	inf	inf	PROPN
ejpam-6953	186	76	j→∞	j→∞	NUM
ejpam-6953	186	77	∫	∫	PROPN
ejpam-6953	186	78	ω̃j	ω̃j	PROPN
ejpam-6953	186	79	|uj	|uj	PROPN
ejpam-6953	186	80	|2e−tρ	|2e−tρ	PROPN
ejpam-6953	186	81	dvω	dvω	PROPN
ejpam-6953	186	82	.	.	PUNCT
ejpam-6953	187	1	using	use	VERB
ejpam-6953	187	2	(	(	PUNCT
ejpam-6953	187	3	2	2	NUM
ejpam-6953	187	4	)	)	PUNCT
ejpam-6953	187	5	and	and	CCONJ
ejpam-6953	187	6	taking	take	VERB
ejpam-6953	187	7	j	j	PROPN
ejpam-6953	187	8	→	→	SYM
ejpam-6953	187	9	∞	∞	PROPN
ejpam-6953	187	10	(	(	PUNCT
ejpam-6953	187	11	so	so	SCONJ
ejpam-6953	187	12	that	that	SCONJ
ejpam-6953	187	13	rj+1	rj+1	X
ejpam-6953	187	14	→	→	SYM
ejpam-6953	187	15	∞	∞	NUM
ejpam-6953	187	16	)	)	PUNCT
ejpam-6953	187	17	,	,	PUNCT
ejpam-6953	187	18	we	we	PRON
ejpam-6953	187	19	deduce∫	deduce∫	VERB
ejpam-6953	187	20	g	g	PROPN
ejpam-6953	187	21	|u|2e−tρ	|u|2e−tρ	NUM
ejpam-6953	187	22	dvω	dvω	NOUN
ejpam-6953	187	23	≤	≤	ADV
ejpam-6953	187	24	2	2	NUM
ejpam-6953	187	25	λ∗	λ∗	NOUN
ejpam-6953	187	26	q	q	PROPN
ejpam-6953	187	27	e	e	PROPN
ejpam-6953	187	28	t	t	PROPN
ejpam-6953	187	29	(	(	PUNCT
ejpam-6953	187	30	rj+1	rj+1	NOUN
ejpam-6953	187	31	+	+	NOUN
ejpam-6953	187	32	1/4	1/4	NUM
ejpam-6953	187	33	)	)	PUNCT
ejpam-6953	187	34	∫	∫	PROPN
ejpam-6953	188	1	g	g	PROPN
ejpam-6953	188	2	|f	|f	PROPN
ejpam-6953	188	3	|2e−tρ	|2e−tρ	PROPN
ejpam-6953	188	4	dvω	dvω	PROPN
ejpam-6953	188	5	,	,	PUNCT
ejpam-6953	188	6	for	for	ADP
ejpam-6953	188	7	arbitrarily	arbitrarily	ADV
ejpam-6953	188	8	large	large	ADJ
ejpam-6953	188	9	rj+1	rj+1	NOUN
ejpam-6953	188	10	.	.	PUNCT
ejpam-6953	189	1	this	this	PRON
ejpam-6953	189	2	proves	prove	VERB
ejpam-6953	189	3	an	an	DET
ejpam-6953	189	4	a	a	DET
ejpam-6953	189	5	priori	priori	ADV
ejpam-6953	189	6	bound	bind	VERB
ejpam-6953	189	7	of	of	ADP
ejpam-6953	189	8	the	the	DET
ejpam-6953	189	9	form	form	NOUN
ejpam-6953	189	10	(	(	PUNCT
ejpam-6953	189	11	1	1	NUM
ejpam-6953	189	12	)	)	PUNCT
ejpam-6953	189	13	for	for	ADP
ejpam-6953	189	14	u	u	PROPN
ejpam-6953	189	15	(	(	PUNCT
ejpam-6953	189	16	with	with	ADP
ejpam-6953	189	17	a	a	DET
ejpam-6953	189	18	constant	constant	ADJ
ejpam-6953	189	19	c(t	c(t	PROPN
ejpam-6953	189	20	)	)	PUNCT
ejpam-6953	189	21	=	=	SYM
ejpam-6953	189	22	2	2	NUM
ejpam-6953	189	23	λ∗q	λ∗q	NUM
ejpam-6953	189	24	depending	depend	VERB
ejpam-6953	189	25	on	on	ADP
ejpam-6953	189	26	t	t	PROPN
ejpam-6953	189	27	and	and	CCONJ
ejpam-6953	189	28	q	q	NOUN
ejpam-6953	189	29	)	)	PUNCT
ejpam-6953	189	30	.	.	PUNCT
ejpam-6953	190	1	in	in	ADP
ejpam-6953	190	2	fact	fact	NOUN
ejpam-6953	190	3	,	,	PUNCT
ejpam-6953	190	4	by	by	ADP
ejpam-6953	190	5	optimizing	optimize	VERB
ejpam-6953	190	6	the	the	DET
ejpam-6953	190	7	uniform	uniform	ADJ
ejpam-6953	190	8	estimate	estimate	NOUN
ejpam-6953	190	9	(	(	PUNCT
ejpam-6953	190	10	2	2	NUM
ejpam-6953	190	11	)	)	PUNCT
ejpam-6953	190	12	over	over	ADP
ejpam-6953	190	13	q	q	PROPN
ejpam-6953	190	14	(	(	PUNCT
ejpam-6953	190	15	see	see	INTJ
ejpam-6953	190	16	remark	remark	NOUN
ejpam-6953	190	17	5.1	5.1	NUM
ejpam-6953	190	18	in	in	ADP
ejpam-6953	190	19	[	[	X
ejpam-6953	190	20	19	19	NUM
ejpam-6953	190	21	]	]	NUM
ejpam-6953	190	22	)	)	PUNCT
ejpam-6953	190	23	,	,	PUNCT
ejpam-6953	190	24	one	one	PRON
ejpam-6953	190	25	can	can	AUX
ejpam-6953	190	26	remove	remove	VERB
ejpam-6953	190	27	the	the	DET
ejpam-6953	190	28	explicit	explicit	ADJ
ejpam-6953	190	29	1	1	NUM
ejpam-6953	190	30	/	/	SYM
ejpam-6953	190	31	q	q	NOUN
ejpam-6953	190	32	dependence	dependence	NOUN
ejpam-6953	190	33	and	and	CCONJ
ejpam-6953	190	34	arrange	arrange	NOUN
ejpam-6953	190	35	that	that	SCONJ
ejpam-6953	190	36	c(t	c(t	PROPN
ejpam-6953	190	37	)	)	PUNCT
ejpam-6953	190	38	=	=	PUNCT
ejpam-6953	191	1	exp(t/2	exp(t/2	NOUN
ejpam-6953	191	2	+	+	CCONJ
ejpam-6953	191	3	ε∗s∗	ε∗s∗	X
ejpam-6953	191	4	)	)	PUNCT
ejpam-6953	191	5	as	as	ADP
ejpam-6953	191	6	in	in	ADP
ejpam-6953	191	7	theorem	theorem	NOUN
ejpam-6953	191	8	1	1	NUM
ejpam-6953	191	9	.	.	PUNCT
ejpam-6953	192	1	this	this	PRON
ejpam-6953	192	2	completes	complete	VERB
ejpam-6953	192	3	the	the	DET
ejpam-6953	192	4	proof	proof	NOUN
ejpam-6953	192	5	of	of	ADP
ejpam-6953	192	6	global	global	ADJ
ejpam-6953	192	7	solvability	solvability	NOUN
ejpam-6953	192	8	.	.	PUNCT
ejpam-6953	193	1	6	6	X
ejpam-6953	193	2	.	.	X
ejpam-6953	193	3	examples	example	NOUN
ejpam-6953	193	4	we	we	PRON
ejpam-6953	193	5	illustrate	illustrate	VERB
ejpam-6953	193	6	theorem	theorem	NOUN
ejpam-6953	193	7	1	1	NUM
ejpam-6953	193	8	with	with	ADP
ejpam-6953	193	9	several	several	ADJ
ejpam-6953	193	10	classes	class	NOUN
ejpam-6953	193	11	of	of	ADP
ejpam-6953	193	12	complex	complex	ADJ
ejpam-6953	193	13	lie	lie	NOUN
ejpam-6953	193	14	groups	group	NOUN
ejpam-6953	193	15	.	.	PUNCT
ejpam-6953	194	1	these	these	DET
ejpam-6953	194	2	examples	example	NOUN
ejpam-6953	194	3	also	also	ADV
ejpam-6953	194	4	highlight	highlight	VERB
ejpam-6953	194	5	that	that	SCONJ
ejpam-6953	194	6	the	the	DET
ejpam-6953	194	7	vanishing	vanishing	NOUN
ejpam-6953	194	8	of	of	ADP
ejpam-6953	194	9	weighted	weight	VERB
ejpam-6953	194	10	l2	l2	NOUN
ejpam-6953	194	11	dolbeault	dolbeault	NOUN
ejpam-6953	194	12	cohomology	cohomology	NOUN
ejpam-6953	194	13	is	be	AUX
ejpam-6953	194	14	a	a	DET
ejpam-6953	194	15	strictly	strictly	ADV
ejpam-6953	194	16	broader	broad	ADJ
ejpam-6953	194	17	phenomenon	phenomenon	NOUN
ejpam-6953	194	18	than	than	ADP
ejpam-6953	194	19	the	the	DET
ejpam-6953	194	20	vanishing	vanishing	NOUN
ejpam-6953	194	21	of	of	ADP
ejpam-6953	194	22	ordinary	ordinary	ADJ
ejpam-6953	194	23	dolbeault	dolbeault	NOUN
ejpam-6953	194	24	cohomology	cohomology	NOUN
ejpam-6953	194	25	.	.	PUNCT
ejpam-6953	195	1	example	example	NOUN
ejpam-6953	196	1	1	1	NUM
ejpam-6953	196	2	.	.	X
ejpam-6953	196	3	take	take	VERB
ejpam-6953	196	4	ρ(z	ρ(z	NOUN
ejpam-6953	196	5	)	)	PUNCT
ejpam-6953	197	1	=	=	SYM
ejpam-6953	197	2	|z|2	|z|2	NOUN
ejpam-6953	197	3	(	(	PUNCT
ejpam-6953	197	4	the	the	DET
ejpam-6953	197	5	squared	square	VERB
ejpam-6953	197	6	euclidean	euclidean	ADJ
ejpam-6953	197	7	norm	norm	NOUN
ejpam-6953	197	8	)	)	PUNCT
ejpam-6953	197	9	on	on	ADP
ejpam-6953	197	10	g	g	PROPN
ejpam-6953	197	11	=	=	SYM
ejpam-6953	197	12	cn	cn	PROPN
ejpam-6953	197	13	,	,	PUNCT
ejpam-6953	197	14	with	with	ADP
ejpam-6953	197	15	the	the	DET
ejpam-6953	197	16	standard	standard	ADJ
ejpam-6953	197	17	euclidean	euclidean	ADJ
ejpam-6953	197	18	metric	metric	NOUN
ejpam-6953	197	19	.	.	PUNCT
ejpam-6953	198	1	then	then	ADV
ejpam-6953	198	2	one	one	PRON
ejpam-6953	198	3	can	can	AUX
ejpam-6953	198	4	take	take	VERB
ejpam-6953	198	5	φj	φj	X
ejpam-6953	198	6	=	=	PUNCT
ejpam-6953	198	7	ρ	ρ	PROPN
ejpam-6953	198	8	for	for	ADP
ejpam-6953	198	9	all	all	DET
ejpam-6953	198	10	j	j	NOUN
ejpam-6953	198	11	,	,	PUNCT
ejpam-6953	198	12	so	so	SCONJ
ejpam-6953	198	13	that	that	SCONJ
ejpam-6953	198	14	ωj	ωj	ADP
ejpam-6953	198	15	=	=	SYM
ejpam-6953	198	16	{	{	PUNCT
ejpam-6953	198	17	|z|	|z|	PROPN
ejpam-6953	198	18	<	<	X
ejpam-6953	198	19	rj	rj	PROPN
ejpam-6953	198	20	}	}	PUNCT
ejpam-6953	198	21	is	be	AUX
ejpam-6953	198	22	a	a	DET
ejpam-6953	198	23	euclidean	euclidean	ADJ
ejpam-6953	198	24	ball	ball	NOUN
ejpam-6953	198	25	exhausting	exhaust	VERB
ejpam-6953	198	26	cn	cn	PROPN
ejpam-6953	198	27	.	.	PUNCT
ejpam-6953	199	1	moreover	moreover	ADV
ejpam-6953	199	2	,	,	PUNCT
ejpam-6953	199	3	one	one	PRON
ejpam-6953	199	4	may	may	AUX
ejpam-6953	199	5	take	take	AUX
ejpam-6953	199	6	σj	σj	VERB
ejpam-6953	199	7	compactly	compactly	ADV
ejpam-6953	199	8	supported	support	VERB
ejpam-6953	199	9	near	near	ADP
ejpam-6953	199	10	∂ωj	∂ωj	PROPN
ejpam-6953	199	11	(	(	PUNCT
ejpam-6953	199	12	or	or	CCONJ
ejpam-6953	199	13	simply	simply	ADV
ejpam-6953	199	14	use	use	VERB
ejpam-6953	199	15	a	a	DET
ejpam-6953	199	16	fixed	fix	VERB
ejpam-6953	199	17	quadratic	quadratic	ADJ
ejpam-6953	199	18	potential	potential	NOUN
ejpam-6953	199	19	transplanted	transplant	VERB
ejpam-6953	199	20	to	to	ADP
ejpam-6953	199	21	each	each	DET
ejpam-6953	199	22	ωj	ωj	NOUN
ejpam-6953	199	23	)	)	PUNCT
ejpam-6953	199	24	.	.	PUNCT
ejpam-6953	200	1	all	all	DET
ejpam-6953	200	2	the	the	DET
ejpam-6953	200	3	uniformity	uniformity	NOUN
ejpam-6953	200	4	conditions	condition	NOUN
ejpam-6953	200	5	are	be	AUX
ejpam-6953	200	6	trivially	trivially	ADV
ejpam-6953	200	7	satisfied	satisfied	ADJ
ejpam-6953	200	8	,	,	PUNCT
ejpam-6953	200	9	and	and	CCONJ
ejpam-6953	200	10	theorem	theorem	VERB
ejpam-6953	200	11	1	1	NUM
ejpam-6953	200	12	recovers	recover	NOUN
ejpam-6953	200	13	hp	hp	VERB
ejpam-6953	200	14	,	,	PUNCT
ejpam-6953	200	15	q	q	NOUN
ejpam-6953	200	16	∂̄,(2),t	∂̄,(2),t	NOUN
ejpam-6953	200	17	(	(	PUNCT
ejpam-6953	200	18	cn	cn	PROPN
ejpam-6953	200	19	)	)	PUNCT
ejpam-6953	200	20	=	=	SYM
ejpam-6953	200	21	0	0	NUM
ejpam-6953	200	22	for	for	ADP
ejpam-6953	200	23	q	q	PROPN
ejpam-6953	200	24	≥	≥	NUM
ejpam-6953	200	25	1	1	NUM
ejpam-6953	200	26	,	,	PUNCT
ejpam-6953	200	27	with	with	ADP
ejpam-6953	200	28	explicit	explicit	ADJ
ejpam-6953	200	29	constants	constant	NOUN
ejpam-6953	200	30	.	.	PUNCT
ejpam-6953	201	1	example	example	NOUN
ejpam-6953	201	2	2	2	NUM
ejpam-6953	201	3	(	(	PUNCT
ejpam-6953	201	4	solvable	solvable	PROPN
ejpam-6953	201	5	borel	borel	PROPN
ejpam-6953	201	6	subgroup	subgroup	NOUN
ejpam-6953	201	7	of	of	ADP
ejpam-6953	201	8	sl(2,c	sl(2,c	NOUN
ejpam-6953	201	9	)	)	PUNCT
ejpam-6953	201	10	)	)	PUNCT
ejpam-6953	201	11	.	.	PUNCT
ejpam-6953	202	1	let	let	VERB
ejpam-6953	202	2	g	g	PRON
ejpam-6953	202	3	be	be	AUX
ejpam-6953	202	4	the	the	DET
ejpam-6953	202	5	borel	borel	PROPN
ejpam-6953	202	6	subgroup	subgroup	NOUN
ejpam-6953	202	7	of	of	ADP
ejpam-6953	202	8	sl(2,c	sl(2,c	NOUN
ejpam-6953	202	9	)	)	PUNCT
ejpam-6953	202	10	,	,	PUNCT
ejpam-6953	202	11	consisting	consist	VERB
ejpam-6953	202	12	of	of	ADP
ejpam-6953	202	13	all	all	DET
ejpam-6953	202	14	complex	complex	ADJ
ejpam-6953	202	15	2	2	NUM
ejpam-6953	202	16	×	×	NOUN
ejpam-6953	202	17	2	2	NUM
ejpam-6953	202	18	upper	upper	ADJ
ejpam-6953	202	19	-	-	PUNCT
ejpam-6953	202	20	triangular	triangular	NOUN
ejpam-6953	202	21	matrices	matrix	NOUN
ejpam-6953	202	22	with	with	ADP
ejpam-6953	202	23	determinant	determinant	ADJ
ejpam-6953	202	24	1	1	NUM
ejpam-6953	202	25	.	.	PUNCT
ejpam-6953	203	1	every	every	DET
ejpam-6953	203	2	element	element	NOUN
ejpam-6953	203	3	can	can	AUX
ejpam-6953	203	4	be	be	AUX
ejpam-6953	203	5	written	write	VERB
ejpam-6953	203	6	as	as	ADP
ejpam-6953	203	7	(	(	PUNCT
ejpam-6953	203	8	a	a	DET
ejpam-6953	203	9	b	b	PROPN
ejpam-6953	203	10	0	0	NUM
ejpam-6953	203	11	a−1	a−1	PROPN
ejpam-6953	203	12	)	)	PUNCT
ejpam-6953	203	13	,	,	PUNCT
ejpam-6953	203	14	a	a	DET
ejpam-6953	203	15	∈	∈	PROPN
ejpam-6953	203	16	c∗	c∗	NOUN
ejpam-6953	203	17	,	,	PUNCT
ejpam-6953	203	18	b	b	PROPN
ejpam-6953	203	19	∈	∈	PROPN
ejpam-6953	203	20	c	c	X
ejpam-6953	203	21	.	.	PUNCT
ejpam-6953	204	1	a.	a.	PROPN
ejpam-6953	204	2	r.	r.	PROPN
ejpam-6953	204	3	al	al	PROPN
ejpam-6953	204	4	-	-	PUNCT
ejpam-6953	204	5	abdallah	abdallah	PROPN
ejpam-6953	204	6	/	/	SYM
ejpam-6953	204	7	eur	eur	PROPN
ejpam-6953	204	8	.	.	PUNCT
ejpam-6953	205	1	j.	j.	PROPN
ejpam-6953	205	2	pure	pure	PROPN
ejpam-6953	205	3	appl	appl	PROPN
ejpam-6953	205	4	.	.	PROPN
ejpam-6953	205	5	math	math	PROPN
ejpam-6953	205	6	,	,	PUNCT
ejpam-6953	205	7	18	18	NUM
ejpam-6953	205	8	(	(	PUNCT
ejpam-6953	205	9	4	4	NUM
ejpam-6953	205	10	)	)	PUNCT
ejpam-6953	205	11	(	(	PUNCT
ejpam-6953	205	12	2025	2025	NUM
ejpam-6953	205	13	)	)	PUNCT
ejpam-6953	205	14	,	,	PUNCT
ejpam-6953	205	15	6953	6953	NUM
ejpam-6953	205	16	10	10	NUM
ejpam-6953	205	17	of	of	ADP
ejpam-6953	205	18	14	14	NUM
ejpam-6953	205	19	thus	thus	ADV
ejpam-6953	205	20	g	g	PROPN
ejpam-6953	205	21	is	be	AUX
ejpam-6953	205	22	biholomorphic	biholomorphic	ADJ
ejpam-6953	205	23	to	to	ADP
ejpam-6953	205	24	the	the	DET
ejpam-6953	205	25	affine	affine	ADJ
ejpam-6953	205	26	variety	variety	NOUN
ejpam-6953	205	27	c∗	c∗	PROPN
ejpam-6953	205	28	×	×	PROPN
ejpam-6953	205	29	c	c	NOUN
ejpam-6953	205	30	and	and	CCONJ
ejpam-6953	205	31	is	be	AUX
ejpam-6953	205	32	a	a	DET
ejpam-6953	205	33	noncompact	noncompact	ADJ
ejpam-6953	205	34	complex	complex	ADJ
ejpam-6953	205	35	lie	lie	NOUN
ejpam-6953	205	36	group	group	NOUN
ejpam-6953	205	37	of	of	ADP
ejpam-6953	205	38	complex	complex	ADJ
ejpam-6953	205	39	dimension	dimension	NOUN
ejpam-6953	205	40	2	2	NUM
ejpam-6953	205	41	.	.	PUNCT
ejpam-6953	205	42	being	be	AUX
ejpam-6953	205	43	an	an	DET
ejpam-6953	205	44	affine	affine	ADJ
ejpam-6953	205	45	algebraic	algebraic	ADJ
ejpam-6953	205	46	group	group	NOUN
ejpam-6953	205	47	,	,	PUNCT
ejpam-6953	205	48	g	g	PROPN
ejpam-6953	205	49	is	be	AUX
ejpam-6953	205	50	stein	stein	PROPN
ejpam-6953	205	51	and	and	CCONJ
ejpam-6953	205	52	admits	admit	VERB
ejpam-6953	205	53	a	a	DET
ejpam-6953	205	54	continuous	continuous	ADJ
ejpam-6953	205	55	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	205	56	exhaustion	exhaustion	NOUN
ejpam-6953	205	57	.	.	PUNCT
ejpam-6953	206	1	for	for	ADP
ejpam-6953	206	2	instance	instance	NOUN
ejpam-6953	206	3	,	,	PUNCT
ejpam-6953	206	4	we	we	PRON
ejpam-6953	206	5	may	may	AUX
ejpam-6953	206	6	take	take	VERB
ejpam-6953	206	7	ρ(a	ρ(a	PROPN
ejpam-6953	206	8	,	,	PUNCT
ejpam-6953	206	9	b	b	NOUN
ejpam-6953	206	10	)	)	PUNCT
ejpam-6953	206	11	=	=	SYM
ejpam-6953	206	12	|a|2	|a|2	PROPN
ejpam-6953	206	13	+	+	CCONJ
ejpam-6953	206	14	|a|−2	|a|−2	PROPN
ejpam-6953	206	15	+	+	CCONJ
ejpam-6953	206	16	|b|2	|b|2	PROPN
ejpam-6953	206	17	,	,	PUNCT
ejpam-6953	206	18	which	which	PRON
ejpam-6953	206	19	is	be	AUX
ejpam-6953	206	20	a	a	DET
ejpam-6953	206	21	proper	proper	ADJ
ejpam-6953	206	22	continuous	continuous	ADJ
ejpam-6953	206	23	psh	psh	NOUN
ejpam-6953	206	24	exhaustion	exhaustion	NOUN
ejpam-6953	206	25	of	of	ADP
ejpam-6953	206	26	g	g	PROPN
ejpam-6953	206	27	(	(	PUNCT
ejpam-6953	206	28	indeed	indeed	ADV
ejpam-6953	206	29	,	,	PUNCT
ejpam-6953	206	30	i∂∂̄(|a|2	i∂∂̄(|a|2	PROPN
ejpam-6953	206	31	+	+	SYM
ejpam-6953	206	32	|a|−2	|a|−2	PROPN
ejpam-6953	206	33	)	)	PUNCT
ejpam-6953	206	34	≥	≥	NOUN
ejpam-6953	206	35	0	0	NUM
ejpam-6953	206	36	on	on	ADP
ejpam-6953	206	37	c∗	c∗	PROPN
ejpam-6953	206	38	and	and	CCONJ
ejpam-6953	206	39	|b|2	|b|2	PROPN
ejpam-6953	206	40	is	be	AUX
ejpam-6953	206	41	psh	psh	NOUN
ejpam-6953	206	42	on	on	ADP
ejpam-6953	206	43	c	c	NOUN
ejpam-6953	206	44	)	)	PUNCT
ejpam-6953	206	45	.	.	PUNCT
ejpam-6953	207	1	applying	apply	VERB
ejpam-6953	207	2	lemma	lemma	PROPN
ejpam-6953	207	3	2	2	NUM
ejpam-6953	207	4	,	,	PUNCT
ejpam-6953	207	5	we	we	PRON
ejpam-6953	207	6	obtain	obtain	VERB
ejpam-6953	207	7	an	an	DET
ejpam-6953	207	8	exhaustion	exhaustion	NOUN
ejpam-6953	207	9	{	{	PUNCT
ejpam-6953	207	10	ωj	ωj	ADP
ejpam-6953	207	11	}	}	PUNCT
ejpam-6953	207	12	of	of	ADP
ejpam-6953	207	13	g	g	NOUN
ejpam-6953	207	14	by	by	ADP
ejpam-6953	207	15	smoothly	smoothly	ADV
ejpam-6953	207	16	bounded	bound	VERB
ejpam-6953	207	17	strictly	strictly	ADV
ejpam-6953	207	18	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	207	19	domains	domain	NOUN
ejpam-6953	207	20	and	and	CCONJ
ejpam-6953	207	21	smooth	smooth	ADJ
ejpam-6953	207	22	functions	function	NOUN
ejpam-6953	207	23	φj	φj	X
ejpam-6953	207	24	with	with	ADP
ejpam-6953	207	25	supωj+1	supωj+1	NOUN
ejpam-6953	207	26	|φj	|φj	PUNCT
ejpam-6953	207	27	−	−	PROPN
ejpam-6953	207	28	ρ|	ρ|	PROPN
ejpam-6953	207	29	≤	≤	NOUN
ejpam-6953	207	30	1/4	1/4	NUM
ejpam-6953	207	31	.	.	PUNCT
ejpam-6953	208	1	next	next	ADV
ejpam-6953	208	2	,	,	PUNCT
ejpam-6953	208	3	to	to	PART
ejpam-6953	208	4	construct	construct	VERB
ejpam-6953	208	5	the	the	DET
ejpam-6953	208	6	uniform	uniform	ADJ
ejpam-6953	208	7	reference	reference	NOUN
ejpam-6953	208	8	functions	function	NOUN
ejpam-6953	208	9	,	,	PUNCT
ejpam-6953	208	10	we	we	PRON
ejpam-6953	208	11	choose	choose	VERB
ejpam-6953	208	12	a	a	DET
ejpam-6953	208	13	left	left	ADJ
ejpam-6953	208	14	-	-	PUNCT
ejpam-6953	208	15	invariant	invariant	ADJ
ejpam-6953	208	16	hermitian	hermitian	ADJ
ejpam-6953	208	17	metric	metric	NOUN
ejpam-6953	208	18	on	on	ADP
ejpam-6953	208	19	g	g	NOUN
ejpam-6953	208	20	;	;	PUNCT
ejpam-6953	208	21	for	for	ADP
ejpam-6953	208	22	example	example	NOUN
ejpam-6953	208	23	,	,	PUNCT
ejpam-6953	208	24	one	one	PRON
ejpam-6953	208	25	can	can	AUX
ejpam-6953	208	26	take	take	VERB
ejpam-6953	208	27	the	the	DET
ejpam-6953	208	28	product	product	NOUN
ejpam-6953	208	29	metric	metric	NOUN
ejpam-6953	208	30	induced	induce	VERB
ejpam-6953	208	31	by	by	ADP
ejpam-6953	208	32	coordinates	coordinate	NOUN
ejpam-6953	208	33	(	(	PUNCT
ejpam-6953	208	34	log	log	VERB
ejpam-6953	208	35	a	a	PRON
ejpam-6953	208	36	,	,	PUNCT
ejpam-6953	208	37	b	b	NOUN
ejpam-6953	208	38	)	)	PUNCT
ejpam-6953	208	39	∈	∈	PROPN
ejpam-6953	208	40	c	c	PROPN
ejpam-6953	208	41	×	×	PROPN
ejpam-6953	208	42	c.	c.	NOUN
ejpam-6953	208	43	in	in	ADP
ejpam-6953	208	44	the	the	DET
ejpam-6953	208	45	coordinate	coordinate	NOUN
ejpam-6953	208	46	chart	chart	NOUN
ejpam-6953	208	47	b	b	NOUN
ejpam-6953	208	48	around	around	ADP
ejpam-6953	208	49	the	the	DET
ejpam-6953	208	50	identity	identity	NOUN
ejpam-6953	208	51	element	element	NOUN
ejpam-6953	208	52	(	(	PUNCT
ejpam-6953	208	53	a	a	PRON
ejpam-6953	208	54	=	=	SYM
ejpam-6953	208	55	1	1	NUM
ejpam-6953	208	56	,	,	PUNCT
ejpam-6953	208	57	b	b	NOUN
ejpam-6953	208	58	=	=	SYM
ejpam-6953	208	59	0	0	NUM
ejpam-6953	208	60	)	)	PUNCT
ejpam-6953	208	61	,	,	PUNCT
ejpam-6953	208	62	one	one	PRON
ejpam-6953	208	63	can	can	AUX
ejpam-6953	208	64	take	take	VERB
ejpam-6953	208	65	u(x	u(x	NOUN
ejpam-6953	208	66	,	,	PUNCT
ejpam-6953	208	67	y	y	NOUN
ejpam-6953	208	68	)	)	PUNCT
ejpam-6953	208	69	=	=	PUNCT
ejpam-6953	208	70	|x|2	|x|2	PROPN
ejpam-6953	208	71	+	+	CCONJ
ejpam-6953	208	72	|y|2	|y|2	ADJ
ejpam-6953	208	73	as	as	ADP
ejpam-6953	208	74	in	in	ADP
ejpam-6953	208	75	the	the	DET
ejpam-6953	208	76	proof	proof	NOUN
ejpam-6953	208	77	of	of	ADP
ejpam-6953	208	78	lemma	lemma	PROPN
ejpam-6953	208	79	3	3	NUM
ejpam-6953	208	80	.	.	PUNCT
ejpam-6953	209	1	then	then	ADV
ejpam-6953	209	2	i∂∂̄u	i∂∂̄u	PROPN
ejpam-6953	209	3	≥	≥	NUM
ejpam-6953	209	4	λω	λω	ADP
ejpam-6953	209	5	on	on	ADP
ejpam-6953	209	6	b	b	NOUN
ejpam-6953	209	7	for	for	ADP
ejpam-6953	209	8	some	some	DET
ejpam-6953	209	9	λ	λ	PROPN
ejpam-6953	209	10	>	>	X
ejpam-6953	209	11	0	0	NUM
ejpam-6953	209	12	.	.	PUNCT
ejpam-6953	210	1	by	by	ADP
ejpam-6953	210	2	left	left	ADJ
ejpam-6953	210	3	-	-	PUNCT
ejpam-6953	210	4	translating	translate	VERB
ejpam-6953	210	5	u	u	NOUN
ejpam-6953	210	6	and	and	CCONJ
ejpam-6953	210	7	covering	cover	VERB
ejpam-6953	210	8	each	each	PRON
ejpam-6953	210	9	ωj	ωj	ADP
ejpam-6953	210	10	by	by	ADP
ejpam-6953	210	11	at	at	ADV
ejpam-6953	210	12	most	most	ADV
ejpam-6953	210	13	c	c	ADP
ejpam-6953	210	14	such	such	ADJ
ejpam-6953	210	15	translated	translate	VERB
ejpam-6953	210	16	balls	ball	NOUN
ejpam-6953	210	17	(	(	PUNCT
ejpam-6953	210	18	here	here	ADV
ejpam-6953	210	19	c	c	X
ejpam-6953	210	20	can	can	AUX
ejpam-6953	210	21	be	be	AUX
ejpam-6953	210	22	taken	take	VERB
ejpam-6953	210	23	,	,	PUNCT
ejpam-6953	210	24	for	for	ADP
ejpam-6953	210	25	instance	instance	NOUN
ejpam-6953	210	26	,	,	PUNCT
ejpam-6953	210	27	as	as	ADP
ejpam-6953	210	28	54	54	NUM
ejpam-6953	210	29	=	=	SYM
ejpam-6953	210	30	625	625	NUM
ejpam-6953	210	31	in	in	ADP
ejpam-6953	210	32	real	real	ADJ
ejpam-6953	210	33	dimension	dimension	NOUN
ejpam-6953	210	34	4	4	NUM
ejpam-6953	210	35	)	)	PUNCT
ejpam-6953	210	36	,	,	PUNCT
ejpam-6953	210	37	we	we	PRON
ejpam-6953	210	38	obtain	obtain	VERB
ejpam-6953	210	39	σj	σj	VERB
ejpam-6953	210	40	such	such	ADJ
ejpam-6953	210	41	that	that	PRON
ejpam-6953	210	42	i∂∂̄σj	i∂∂̄σj	PROPN
ejpam-6953	210	43	≥	≥	X
ejpam-6953	210	44	(	(	PUNCT
ejpam-6953	210	45	λ	λ	NOUN
ejpam-6953	210	46	/	/	SYM
ejpam-6953	210	47	c)ω	c)ω	NOUN
ejpam-6953	210	48	on	on	ADP
ejpam-6953	210	49	ωj	ωj	ADP
ejpam-6953	210	50	.	.	PUNCT
ejpam-6953	211	1	thus	thus	ADV
ejpam-6953	211	2	conditions	condition	NOUN
ejpam-6953	211	3	(	(	PUNCT
ejpam-6953	211	4	u1	u1	NOUN
ejpam-6953	211	5	)	)	PUNCT
ejpam-6953	211	6	and	and	CCONJ
ejpam-6953	211	7	(	(	PUNCT
ejpam-6953	211	8	u2	u2	NOUN
ejpam-6953	211	9	)	)	PUNCT
ejpam-6953	211	10	are	be	AUX
ejpam-6953	211	11	satisfied	satisfied	ADJ
ejpam-6953	211	12	with	with	ADP
ejpam-6953	211	13	c∗	c∗	PROPN
ejpam-6953	211	14	=	=	SYM
ejpam-6953	211	15	λ	λ	PROPN
ejpam-6953	211	16	/	/	SYM
ejpam-6953	211	17	c	c	PROPN
ejpam-6953	211	18	and	and	CCONJ
ejpam-6953	211	19	s∗	s∗	PROPN
ejpam-6953	211	20	=	=	SYM
ejpam-6953	212	1	1	1	X
ejpam-6953	212	2	.	.	PUNCT
ejpam-6953	213	1	in	in	ADP
ejpam-6953	213	2	particular	particular	ADJ
ejpam-6953	213	3	,	,	PUNCT
ejpam-6953	213	4	ε∗	ε∗	PROPN
ejpam-6953	213	5	=	=	SYM
ejpam-6953	213	6	1	1	NUM
ejpam-6953	213	7	/	/	SYM
ejpam-6953	213	8	c∗	c∗	NOUN
ejpam-6953	213	9	=	=	SYM
ejpam-6953	213	10	c	c	X
ejpam-6953	213	11	/	/	SYM
ejpam-6953	213	12	λ	λ	NOUN
ejpam-6953	213	13	.	.	PUNCT
ejpam-6953	214	1	plugging	plug	VERB
ejpam-6953	214	2	these	these	PRON
ejpam-6953	214	3	into	into	ADP
ejpam-6953	214	4	the	the	DET
ejpam-6953	214	5	estimate	estimate	NOUN
ejpam-6953	214	6	(	(	PUNCT
ejpam-6953	214	7	1	1	NUM
ejpam-6953	214	8	)	)	PUNCT
ejpam-6953	214	9	,	,	PUNCT
ejpam-6953	214	10	we	we	PRON
ejpam-6953	214	11	get	get	VERB
ejpam-6953	214	12	an	an	DET
ejpam-6953	214	13	explicit	explicit	ADJ
ejpam-6953	214	14	constant	constant	ADJ
ejpam-6953	214	15	c(t	c(t	PROPN
ejpam-6953	214	16	)	)	PUNCT
ejpam-6953	214	17	=	=	NOUN
ejpam-6953	214	18	exp	exp	NOUN
ejpam-6953	214	19	(	(	PUNCT
ejpam-6953	214	20	t/2	t/2	NUM
ejpam-6953	215	1	+	+	X
ejpam-6953	215	2	ε∗s∗	ε∗s∗	X
ejpam-6953	215	3	)	)	PUNCT
ejpam-6953	215	4	=	=	SYM
ejpam-6953	215	5	exp	exp	NOUN
ejpam-6953	215	6	(	(	PUNCT
ejpam-6953	215	7	t/2	t/2	NUM
ejpam-6953	215	8	+	+	CCONJ
ejpam-6953	215	9	c	c	NOUN
ejpam-6953	215	10	λ	λ	NOUN
ejpam-6953	215	11	)	)	PUNCT
ejpam-6953	215	12	in	in	ADP
ejpam-6953	215	13	the	the	DET
ejpam-6953	215	14	global	global	ADJ
ejpam-6953	215	15	l2	l2	NOUN
ejpam-6953	215	16	estimate	estimate	VERB
ejpam-6953	215	17	for	for	ADP
ejpam-6953	215	18	∂̄.	∂̄.	NOUN
ejpam-6953	215	19	for	for	ADP
ejpam-6953	215	20	instance	instance	NOUN
ejpam-6953	215	21	,	,	PUNCT
ejpam-6953	215	22	choosing	choose	VERB
ejpam-6953	215	23	the	the	DET
ejpam-6953	215	24	metric	metric	ADJ
ejpam-6953	215	25	normalization	normalization	NOUN
ejpam-6953	215	26	such	such	ADJ
ejpam-6953	215	27	that	that	PRON
ejpam-6953	215	28	λ	λ	NOUN
ejpam-6953	215	29	=	=	SYM
ejpam-6953	215	30	1	1	NUM
ejpam-6953	215	31	and	and	CCONJ
ejpam-6953	215	32	c	c	NOUN
ejpam-6953	215	33	=	=	SYM
ejpam-6953	215	34	625	625	NUM
ejpam-6953	215	35	,	,	PUNCT
ejpam-6953	215	36	one	one	PRON
ejpam-6953	215	37	finds	find	VERB
ejpam-6953	215	38	c(t	c(t	NOUN
ejpam-6953	215	39	)	)	PUNCT
ejpam-6953	215	40	=	=	PUNCT
ejpam-6953	216	1	exp(t/2	exp(t/2	NOUN
ejpam-6953	216	2	+	+	PUNCT
ejpam-6953	216	3	625	625	NUM
ejpam-6953	216	4	)	)	PUNCT
ejpam-6953	216	5	as	as	ADP
ejpam-6953	216	6	a	a	DET
ejpam-6953	216	7	valid	valid	ADJ
ejpam-6953	216	8	constant	constant	ADJ
ejpam-6953	216	9	in	in	ADP
ejpam-6953	216	10	theorem	theorem	NOUN
ejpam-6953	216	11	1	1	NUM
ejpam-6953	216	12	for	for	ADP
ejpam-6953	216	13	the	the	DET
ejpam-6953	216	14	borel	borel	PROPN
ejpam-6953	216	15	group	group	NOUN
ejpam-6953	216	16	.	.	PUNCT
ejpam-6953	217	1	example	example	NOUN
ejpam-6953	218	1	3	3	X
ejpam-6953	218	2	.	.	PUNCT
ejpam-6953	218	3	let	let	VERB
ejpam-6953	218	4	g	g	NOUN
ejpam-6953	218	5	=	=	SYM
ejpam-6953	218	6	(	(	PUNCT
ejpam-6953	218	7	c∗)n	c∗)n	NOUN
ejpam-6953	218	8	with	with	ADP
ejpam-6953	218	9	the	the	DET
ejpam-6953	218	10	product	product	NOUN
ejpam-6953	218	11	metric	metric	ADJ
ejpam-6953	218	12	.	.	PUNCT
ejpam-6953	219	1	as	as	ADP
ejpam-6953	219	2	an	an	DET
ejpam-6953	219	3	explicit	explicit	ADJ
ejpam-6953	219	4	example	example	NOUN
ejpam-6953	219	5	of	of	ADP
ejpam-6953	219	6	a	a	DET
ejpam-6953	219	7	continuous	continuous	ADJ
ejpam-6953	219	8	psh	psh	NOUN
ejpam-6953	219	9	exhaustion	exhaustion	NOUN
ejpam-6953	219	10	,	,	PUNCT
ejpam-6953	219	11	take	take	VERB
ejpam-6953	219	12	ρ(z	ρ(z	NOUN
ejpam-6953	219	13	)	)	PUNCT
ejpam-6953	220	1	=	=	PUNCT
ejpam-6953	221	1	n∑	n∑	NOUN
ejpam-6953	221	2	k=1	k=1	PUNCT
ejpam-6953	222	1	(	(	PUNCT
ejpam-6953	222	2	|	|	ADV
ejpam-6953	222	3	log	log	VERB
ejpam-6953	222	4	|zk||2	|zk||2	PROPN
ejpam-6953	222	5	+	+	NUM
ejpam-6953	222	6	|zk|−2	|zk|−2	NOUN
ejpam-6953	222	7	+	+	NOUN
ejpam-6953	222	8	|zk|2	|zk|2	PUNCT
ejpam-6953	222	9	)	)	PUNCT
ejpam-6953	222	10	.	.	PUNCT
ejpam-6953	223	1	then	then	ADV
ejpam-6953	223	2	ρ	ρ	PROPN
ejpam-6953	223	3	is	be	AUX
ejpam-6953	223	4	proper	proper	ADJ
ejpam-6953	223	5	and	and	CCONJ
ejpam-6953	223	6	continuous	continuous	ADJ
ejpam-6953	223	7	psh	psh	NOUN
ejpam-6953	223	8	on	on	ADP
ejpam-6953	223	9	g	g	NOUN
ejpam-6953	223	10	,	,	PUNCT
ejpam-6953	223	11	and	and	CCONJ
ejpam-6953	223	12	theorem	theorem	VERB
ejpam-6953	223	13	1	1	NUM
ejpam-6953	223	14	applies	apply	VERB
ejpam-6953	223	15	to	to	PART
ejpam-6953	223	16	give	give	VERB
ejpam-6953	223	17	global	global	ADJ
ejpam-6953	223	18	weighted	weight	VERB
ejpam-6953	223	19	l2	l2	NOUN
ejpam-6953	223	20	∂̄-solvability	∂̄-solvability	PROPN
ejpam-6953	223	21	in	in	ADP
ejpam-6953	223	22	all	all	DET
ejpam-6953	223	23	positive	positive	ADJ
ejpam-6953	223	24	anti	anti	ADJ
ejpam-6953	223	25	-	-	ADJ
ejpam-6953	223	26	holomorphic	holomorphic	ADJ
ejpam-6953	223	27	degrees	degree	NOUN
ejpam-6953	223	28	.	.	PUNCT
ejpam-6953	224	1	note	note	VERB
ejpam-6953	224	2	that	that	SCONJ
ejpam-6953	224	3	although	although	SCONJ
ejpam-6953	224	4	the	the	DET
ejpam-6953	224	5	ordinary	ordinary	ADJ
ejpam-6953	224	6	dolbeault	dolbeault	NOUN
ejpam-6953	224	7	cohomology	cohomology	NOUN
ejpam-6953	224	8	of	of	ADP
ejpam-6953	224	9	(	(	PUNCT
ejpam-6953	224	10	c∗)n	c∗)n	PROPN
ejpam-6953	224	11	is	be	AUX
ejpam-6953	224	12	nontrivial	nontrivial	ADJ
ejpam-6953	224	13	(	(	PUNCT
ejpam-6953	224	14	indeed	indeed	ADV
ejpam-6953	224	15	h0,1(g	h0,1(g	ADV
ejpam-6953	224	16	)	)	PUNCT
ejpam-6953	225	1	∼=	∼=	PROPN
ejpam-6953	225	2	h1(g	h1(g	NOUN
ejpam-6953	225	3	,	,	PUNCT
ejpam-6953	225	4	o	o	NOUN
ejpam-6953	225	5	)	)	PUNCT
ejpam-6953	225	6	∼=	∼=	PROPN
ejpam-6953	225	7	cn	cn	PROPN
ejpam-6953	225	8	)	)	PUNCT
ejpam-6953	225	9	,	,	PUNCT
ejpam-6953	225	10	its	its	PRON
ejpam-6953	225	11	weighted	weight	VERB
ejpam-6953	225	12	l2	l2	NOUN
ejpam-6953	225	13	dolbeault	dolbeault	VERB
ejpam-6953	225	14	cohomology	cohomology	NOUN
ejpam-6953	225	15	in	in	ADP
ejpam-6953	225	16	degrees	degree	NOUN
ejpam-6953	225	17	q	q	PROPN
ejpam-6953	225	18	≥	≥	NUM
ejpam-6953	225	19	1	1	NUM
ejpam-6953	225	20	vanishes	vanish	VERB
ejpam-6953	225	21	by	by	ADP
ejpam-6953	225	22	our	our	PRON
ejpam-6953	225	23	result	result	NOUN
ejpam-6953	225	24	.	.	PUNCT
ejpam-6953	226	1	example	example	NOUN
ejpam-6953	226	2	4	4	NUM
ejpam-6953	226	3	(	(	PUNCT
ejpam-6953	226	4	a	a	DET
ejpam-6953	226	5	cousin	cousin	NOUN
ejpam-6953	226	6	group	group	NOUN
ejpam-6953	226	7	)	)	PUNCT
ejpam-6953	226	8	.	.	PUNCT
ejpam-6953	227	1	consider	consider	VERB
ejpam-6953	227	2	the	the	DET
ejpam-6953	227	3	complex	complex	ADJ
ejpam-6953	227	4	abelian	abelian	ADJ
ejpam-6953	227	5	lie	lie	NOUN
ejpam-6953	227	6	group	group	NOUN
ejpam-6953	227	7	g	g	PROPN
ejpam-6953	227	8	=	=	PROPN
ejpam-6953	227	9	c2	c2	PROPN
ejpam-6953	227	10	/	/	SYM
ejpam-6953	227	11	γ	γ	PROPN
ejpam-6953	227	12	,	,	PUNCT
ejpam-6953	227	13	where	where	SCONJ
ejpam-6953	227	14	γ	γ	X
ejpam-6953	227	15	=	=	PUNCT
ejpam-6953	227	16	⟨(1	⟨(1	NOUN
ejpam-6953	227	17	,	,	PUNCT
ejpam-6953	227	18	0	0	NUM
ejpam-6953	227	19	)	)	PUNCT
ejpam-6953	227	20	,	,	PUNCT
ejpam-6953	227	21	(	(	PUNCT
ejpam-6953	227	22	0	0	NUM
ejpam-6953	227	23	,	,	PUNCT
ejpam-6953	227	24	1	1	NUM
ejpam-6953	227	25	)	)	PUNCT
ejpam-6953	227	26	,	,	PUNCT
ejpam-6953	227	27	(	(	PUNCT
ejpam-6953	227	28	i	i	PRON
ejpam-6953	227	29	,	,	PUNCT
ejpam-6953	227	30	i	i	PRON
ejpam-6953	227	31	√	√	PROPN
ejpam-6953	227	32	2)⟩z	2)⟩z	NUM
ejpam-6953	227	33	is	be	AUX
ejpam-6953	227	34	the	the	DET
ejpam-6953	227	35	rank-3	rank-3	PROPN
ejpam-6953	227	36	lattice	lattice	NOUN
ejpam-6953	227	37	in	in	ADP
ejpam-6953	227	38	c2	c2	PROPN
ejpam-6953	227	39	generated	generate	VERB
ejpam-6953	227	40	by	by	ADP
ejpam-6953	227	41	(	(	PUNCT
ejpam-6953	227	42	1	1	NUM
ejpam-6953	227	43	,	,	PUNCT
ejpam-6953	227	44	0	0	NUM
ejpam-6953	227	45	)	)	PUNCT
ejpam-6953	227	46	,	,	PUNCT
ejpam-6953	227	47	(	(	PUNCT
ejpam-6953	227	48	0	0	NUM
ejpam-6953	227	49	,	,	PUNCT
ejpam-6953	227	50	1	1	NUM
ejpam-6953	227	51	)	)	PUNCT
ejpam-6953	227	52	,	,	PUNCT
ejpam-6953	227	53	and	and	CCONJ
ejpam-6953	227	54	(	(	PUNCT
ejpam-6953	227	55	i	i	INTJ
ejpam-6953	227	56	,	,	PUNCT
ejpam-6953	227	57	i	i	PRON
ejpam-6953	227	58	√	√	VERB
ejpam-6953	227	59	2	2	NUM
ejpam-6953	227	60	)	)	PUNCT
ejpam-6953	227	61	.	.	PUNCT
ejpam-6953	228	1	this	this	DET
ejpam-6953	228	2	g	g	PROPN
ejpam-6953	228	3	is	be	AUX
ejpam-6953	228	4	a	a	DET
ejpam-6953	228	5	noncompact	noncompact	ADJ
ejpam-6953	228	6	complex	complex	ADJ
ejpam-6953	228	7	two	two	NUM
ejpam-6953	228	8	-	-	PUNCT
ejpam-6953	228	9	dimensional	dimensional	ADJ
ejpam-6953	228	10	lie	lie	NOUN
ejpam-6953	228	11	group	group	NOUN
ejpam-6953	228	12	which	which	PRON
ejpam-6953	228	13	is	be	AUX
ejpam-6953	228	14	not	not	PART
ejpam-6953	228	15	stein	stein	PROPN
ejpam-6953	228	16	.	.	PUNCT
ejpam-6953	229	1	(	(	PUNCT
ejpam-6953	229	2	indeed	indeed	ADV
ejpam-6953	229	3	,	,	PUNCT
ejpam-6953	229	4	g	g	PROPN
ejpam-6953	229	5	contains	contain	VERB
ejpam-6953	229	6	a	a	DET
ejpam-6953	229	7	one	one	NUM
ejpam-6953	229	8	-	-	PUNCT
ejpam-6953	229	9	dimensional	dimensional	ADJ
ejpam-6953	229	10	complex	complex	ADJ
ejpam-6953	229	11	torus	torus	NOUN
ejpam-6953	229	12	c/⟨1⟩	c/⟨1⟩	NOUN
ejpam-6953	229	13	as	as	ADP
ejpam-6953	229	14	a	a	DET
ejpam-6953	229	15	closed	closed	ADJ
ejpam-6953	229	16	complex	complex	ADJ
ejpam-6953	229	17	subgroup	subgroup	NOUN
ejpam-6953	229	18	,	,	PUNCT
ejpam-6953	229	19	so	so	SCONJ
ejpam-6953	229	20	g	g	PROPN
ejpam-6953	229	21	fails	fail	VERB
ejpam-6953	229	22	matsushima	matsushima	PROPN
ejpam-6953	229	23	’s	’s	PROPN
ejpam-6953	229	24	stein	stein	PROPN
ejpam-6953	229	25	criterion	criterion	PROPN
ejpam-6953	229	26	.	.	PUNCT
ejpam-6953	229	27	)	)	PUNCT
ejpam-6953	230	1	however	however	ADV
ejpam-6953	230	2	,	,	PUNCT
ejpam-6953	230	3	by	by	ADP
ejpam-6953	230	4	a	a	DET
ejpam-6953	230	5	theorem	theorem	NOUN
ejpam-6953	230	6	of	of	ADP
ejpam-6953	230	7	kazama	kazama	PROPN
ejpam-6953	230	8	a.	a.	PROPN
ejpam-6953	230	9	r.	r.	PROPN
ejpam-6953	230	10	al	al	PROPN
ejpam-6953	230	11	-	-	PUNCT
ejpam-6953	230	12	abdallah	abdallah	PROPN
ejpam-6953	230	13	/	/	SYM
ejpam-6953	230	14	eur	eur	PROPN
ejpam-6953	230	15	.	.	PUNCT
ejpam-6953	231	1	j.	j.	PROPN
ejpam-6953	231	2	pure	pure	PROPN
ejpam-6953	231	3	appl	appl	PROPN
ejpam-6953	231	4	.	.	PROPN
ejpam-6953	231	5	math	math	PROPN
ejpam-6953	231	6	,	,	PUNCT
ejpam-6953	231	7	18	18	NUM
ejpam-6953	231	8	(	(	PUNCT
ejpam-6953	231	9	4	4	NUM
ejpam-6953	231	10	)	)	PUNCT
ejpam-6953	231	11	(	(	PUNCT
ejpam-6953	231	12	2025	2025	NUM
ejpam-6953	231	13	)	)	PUNCT
ejpam-6953	231	14	,	,	PUNCT
ejpam-6953	231	15	6953	6953	NUM
ejpam-6953	231	16	11	11	NUM
ejpam-6953	231	17	of	of	ADP
ejpam-6953	231	18	14	14	NUM
ejpam-6953	232	1	[	[	X
ejpam-6953	232	2	10	10	NUM
ejpam-6953	232	3	]	]	PUNCT
ejpam-6953	232	4	,	,	PUNCT
ejpam-6953	232	5	g	g	PROPN
ejpam-6953	232	6	is	be	AUX
ejpam-6953	232	7	pseudoconvex	pseudoconvex	PROPN
ejpam-6953	232	8	,	,	PUNCT
ejpam-6953	232	9	i.e.	i.e.	X
ejpam-6953	232	10	admits	admit	VERB
ejpam-6953	232	11	a	a	DET
ejpam-6953	232	12	continuous	continuous	ADJ
ejpam-6953	232	13	psh	psh	NOUN
ejpam-6953	232	14	exhaustion	exhaustion	NOUN
ejpam-6953	232	15	.	.	PUNCT
ejpam-6953	233	1	for	for	ADP
ejpam-6953	233	2	example	example	NOUN
ejpam-6953	233	3	,	,	PUNCT
ejpam-6953	233	4	one	one	NUM
ejpam-6953	233	5	convenient	convenient	ADJ
ejpam-6953	233	6	choice	choice	NOUN
ejpam-6953	233	7	is	be	AUX
ejpam-6953	233	8	ρ([z1	ρ([z1	NOUN
ejpam-6953	233	9	,	,	PUNCT
ejpam-6953	233	10	z2	z2	NOUN
ejpam-6953	233	11	]	]	PUNCT
ejpam-6953	233	12	)	)	PUNCT
ejpam-6953	234	1	:	:	PUNCT
ejpam-6953	234	2	=	=	SYM
ejpam-6953	234	3	(	(	PUNCT
ejpam-6953	234	4	ℑz2	ℑz2	NOUN
ejpam-6953	234	5	−	−	PROPN
ejpam-6953	234	6	√	√	PROPN
ejpam-6953	234	7	2ℑz1)2	2ℑz1)2	NUM
ejpam-6953	234	8	,	,	PUNCT
ejpam-6953	234	9	which	which	PRON
ejpam-6953	234	10	is	be	AUX
ejpam-6953	234	11	well	well	ADV
ejpam-6953	234	12	-	-	PUNCT
ejpam-6953	234	13	defined	define	VERB
ejpam-6953	234	14	on	on	ADP
ejpam-6953	234	15	the	the	DET
ejpam-6953	234	16	quotient	quotient	NOUN
ejpam-6953	234	17	g	g	NOUN
ejpam-6953	234	18	because	because	SCONJ
ejpam-6953	234	19	ℑz2−	ℑz2−	NOUN
ejpam-6953	234	20	√	√	NUM
ejpam-6953	234	21	2ℑz1	2ℑz1	PROPN
ejpam-6953	234	22	is	be	AUX
ejpam-6953	234	23	invariant	invariant	ADJ
ejpam-6953	234	24	under	under	ADP
ejpam-6953	234	25	the	the	DET
ejpam-6953	234	26	period	period	NOUN
ejpam-6953	234	27	lattice	lattice	PROPN
ejpam-6953	234	28	γ	γ	PROPN
ejpam-6953	234	29	.	.	PROPN
ejpam-6953	234	30	note	note	NOUN
ejpam-6953	234	31	that	that	SCONJ
ejpam-6953	234	32	ρ	ρ	PROPN
ejpam-6953	234	33	is	be	AUX
ejpam-6953	234	34	unbounded	unbounded	ADJ
ejpam-6953	234	35	on	on	ADP
ejpam-6953	234	36	g	g	PROPN
ejpam-6953	234	37	and	and	CCONJ
ejpam-6953	234	38	{	{	PUNCT
ejpam-6953	234	39	ρ	ρ	NOUN
ejpam-6953	234	40	<	<	X
ejpam-6953	234	41	c	c	X
ejpam-6953	234	42	}	}	PUNCT
ejpam-6953	234	43	is	be	AUX
ejpam-6953	234	44	relatively	relatively	ADV
ejpam-6953	234	45	compact	compact	ADJ
ejpam-6953	234	46	for	for	ADP
ejpam-6953	234	47	each	each	DET
ejpam-6953	234	48	c	c	NOUN
ejpam-6953	234	49	,	,	PUNCT
ejpam-6953	234	50	so	so	ADV
ejpam-6953	234	51	ρ	ρ	PROPN
ejpam-6953	234	52	is	be	AUX
ejpam-6953	234	53	a	a	DET
ejpam-6953	234	54	continuous	continuous	ADJ
ejpam-6953	234	55	exhaustion	exhaustion	NOUN
ejpam-6953	234	56	of	of	ADP
ejpam-6953	234	57	g.	g.	PROPN
ejpam-6953	234	58	moreover	moreover	ADV
ejpam-6953	234	59	,	,	PUNCT
ejpam-6953	234	60	ρ	ρ	PROPN
ejpam-6953	234	61	is	be	AUX
ejpam-6953	234	62	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	234	63	:	:	PUNCT
ejpam-6953	234	64	it	it	PRON
ejpam-6953	234	65	is	be	AUX
ejpam-6953	234	66	the	the	DET
ejpam-6953	234	67	square	square	NOUN
ejpam-6953	234	68	of	of	ADP
ejpam-6953	234	69	the	the	DET
ejpam-6953	234	70	imaginary	imaginary	ADJ
ejpam-6953	234	71	part	part	NOUN
ejpam-6953	234	72	of	of	ADP
ejpam-6953	234	73	the	the	DET
ejpam-6953	234	74	holomorphic	holomorphic	ADJ
ejpam-6953	234	75	1	1	NUM
ejpam-6953	234	76	-	-	PUNCT
ejpam-6953	234	77	form	form	NOUN
ejpam-6953	234	78	dz2	dz2	NOUN
ejpam-6953	234	79	−	−	NOUN
ejpam-6953	234	80	√	√	NOUN
ejpam-6953	234	81	2	2	NUM
ejpam-6953	234	82	dz1	dz1	VERB
ejpam-6953	234	83	on	on	ADP
ejpam-6953	234	84	c2	c2	PROPN
ejpam-6953	234	85	,	,	PUNCT
ejpam-6953	234	86	hence	hence	ADV
ejpam-6953	234	87	ρ	ρ	PROPN
ejpam-6953	234	88	is	be	AUX
ejpam-6953	234	89	psh	psh	NOUN
ejpam-6953	234	90	(	(	PUNCT
ejpam-6953	234	91	in	in	ADP
ejpam-6953	234	92	fact	fact	NOUN
ejpam-6953	234	93	pluriharmonic	pluriharmonic	ADJ
ejpam-6953	234	94	)	)	PUNCT
ejpam-6953	234	95	on	on	ADP
ejpam-6953	234	96	c2	c2	PROPN
ejpam-6953	234	97	,	,	PUNCT
ejpam-6953	234	98	and	and	CCONJ
ejpam-6953	234	99	it	it	PRON
ejpam-6953	234	100	descends	descend	VERB
ejpam-6953	234	101	to	to	ADP
ejpam-6953	234	102	a	a	DET
ejpam-6953	234	103	continuous	continuous	ADJ
ejpam-6953	234	104	psh	psh	NOUN
ejpam-6953	234	105	function	function	NOUN
ejpam-6953	234	106	on	on	ADP
ejpam-6953	234	107	g.	g.	PROPN
ejpam-6953	234	108	the	the	DET
ejpam-6953	234	109	sublevel	sublevel	NOUN
ejpam-6953	234	110	sets	set	NOUN
ejpam-6953	234	111	ωc	ωc	X
ejpam-6953	234	112	:	:	PUNCT
ejpam-6953	234	113	=	=	SYM
ejpam-6953	234	114	{	{	PUNCT
ejpam-6953	234	115	ρ	ρ	X
ejpam-6953	234	116	<	<	X
ejpam-6953	234	117	c	c	X
ejpam-6953	234	118	}	}	PUNCT
ejpam-6953	234	119	are	be	AUX
ejpam-6953	234	120	therefore	therefore	ADV
ejpam-6953	234	121	smoothly	smoothly	ADV
ejpam-6953	234	122	bounded	bound	VERB
ejpam-6953	234	123	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	234	124	domains	domain	NOUN
ejpam-6953	234	125	in	in	ADP
ejpam-6953	234	126	g.	g.	NOUN
ejpam-6953	234	127	applying	apply	VERB
ejpam-6953	234	128	lemma	lemma	PROPN
ejpam-6953	234	129	2	2	NUM
ejpam-6953	234	130	,	,	PUNCT
ejpam-6953	234	131	we	we	PRON
ejpam-6953	234	132	approximate	approximate	VERB
ejpam-6953	234	133	ρ	ρ	PROPN
ejpam-6953	234	134	uniformly	uniformly	ADV
ejpam-6953	234	135	on	on	ADP
ejpam-6953	234	136	these	these	DET
ejpam-6953	234	137	sublevels	sublevel	NOUN
ejpam-6953	234	138	by	by	ADP
ejpam-6953	234	139	smooth	smooth	ADJ
ejpam-6953	234	140	strictly	strictly	ADV
ejpam-6953	234	141	psh	psh	PROPN
ejpam-6953	234	142	functions	function	NOUN
ejpam-6953	234	143	φj	φj	NOUN
ejpam-6953	234	144	,	,	PUNCT
ejpam-6953	234	145	and	and	CCONJ
ejpam-6953	234	146	then	then	ADV
ejpam-6953	234	147	lemma	lemma	PROPN
ejpam-6953	234	148	3	3	NUM
ejpam-6953	234	149	provides	provide	VERB
ejpam-6953	234	150	strictly	strictly	ADV
ejpam-6953	234	151	psh	psh	NOUN
ejpam-6953	234	152	reference	reference	NOUN
ejpam-6953	234	153	functions	function	NOUN
ejpam-6953	234	154	σj	σj	VERB
ejpam-6953	234	155	with	with	ADP
ejpam-6953	234	156	uniform	uniform	ADJ
ejpam-6953	234	157	levi	levi	PROPN
ejpam-6953	234	158	bound	bind	VERB
ejpam-6953	234	159	.	.	PUNCT
ejpam-6953	235	1	all	all	DET
ejpam-6953	235	2	assumptions	assumption	NOUN
ejpam-6953	235	3	(	(	PUNCT
ejpam-6953	235	4	u1	u1	NOUN
ejpam-6953	235	5	)	)	PUNCT
ejpam-6953	235	6	and	and	CCONJ
ejpam-6953	235	7	(	(	PUNCT
ejpam-6953	235	8	u2	u2	NOUN
ejpam-6953	235	9	)	)	PUNCT
ejpam-6953	235	10	are	be	AUX
ejpam-6953	235	11	thus	thus	ADV
ejpam-6953	235	12	satisfied	satisfied	ADJ
ejpam-6953	235	13	.	.	PUNCT
ejpam-6953	236	1	by	by	ADP
ejpam-6953	236	2	theorem	theorem	NOUN
ejpam-6953	236	3	1	1	NUM
ejpam-6953	236	4	,	,	PUNCT
ejpam-6953	236	5	we	we	PRON
ejpam-6953	236	6	conclude	conclude	VERB
ejpam-6953	236	7	that	that	SCONJ
ejpam-6953	236	8	hp	hp	PROPN
ejpam-6953	236	9	,	,	PUNCT
ejpam-6953	236	10	q	q	NOUN
ejpam-6953	236	11	∂̄,(2),t	∂̄,(2),t	NOUN
ejpam-6953	236	12	(	(	PUNCT
ejpam-6953	236	13	g	g	NOUN
ejpam-6953	236	14	)	)	PUNCT
ejpam-6953	236	15	=	=	SYM
ejpam-6953	236	16	0	0	NUM
ejpam-6953	236	17	for	for	ADP
ejpam-6953	236	18	all	all	DET
ejpam-6953	236	19	q	q	PRON
ejpam-6953	236	20	≥	≥	NUM
ejpam-6953	236	21	1	1	NUM
ejpam-6953	236	22	and	and	CCONJ
ejpam-6953	236	23	all	all	PRON
ejpam-6953	236	24	t	t	PROPN
ejpam-6953	236	25	≥	≥	NOUN
ejpam-6953	236	26	0	0	NUM
ejpam-6953	236	27	,	,	PUNCT
ejpam-6953	236	28	and	and	CCONJ
ejpam-6953	236	29	obtain	obtain	VERB
ejpam-6953	236	30	a	a	DET
ejpam-6953	236	31	global	global	ADJ
ejpam-6953	236	32	∂̄-solution	∂̄-solution	NOUN
ejpam-6953	236	33	operator	operator	NOUN
ejpam-6953	236	34	on	on	ADP
ejpam-6953	236	35	l2(g	l2(g	NOUN
ejpam-6953	236	36	,	,	PUNCT
ejpam-6953	236	37	e−tρ	e−tρ	NOUN
ejpam-6953	236	38	)	)	PUNCT
ejpam-6953	236	39	.	.	PUNCT
ejpam-6953	237	1	in	in	ADP
ejpam-6953	237	2	particular	particular	ADJ
ejpam-6953	237	3	,	,	PUNCT
ejpam-6953	237	4	this	this	PRON
ejpam-6953	237	5	shows	show	VERB
ejpam-6953	237	6	that	that	SCONJ
ejpam-6953	237	7	even	even	ADV
ejpam-6953	237	8	non	non	ADJ
ejpam-6953	237	9	-	-	ADJ
ejpam-6953	237	10	stein	stein	ADJ
ejpam-6953	237	11	complex	complex	ADJ
ejpam-6953	237	12	lie	lie	NOUN
ejpam-6953	237	13	groups	group	NOUN
ejpam-6953	237	14	(	(	PUNCT
ejpam-6953	237	15	such	such	ADJ
ejpam-6953	237	16	as	as	ADP
ejpam-6953	237	17	the	the	DET
ejpam-6953	237	18	above	above	ADJ
ejpam-6953	237	19	cousin	cousin	NOUN
ejpam-6953	237	20	group	group	NOUN
ejpam-6953	237	21	)	)	PUNCT
ejpam-6953	237	22	enjoy	enjoy	VERB
ejpam-6953	237	23	a	a	DET
ejpam-6953	237	24	robust	robust	ADJ
ejpam-6953	237	25	∂̄-solvability	∂̄-solvability	NOUN
ejpam-6953	237	26	in	in	ADP
ejpam-6953	237	27	the	the	DET
ejpam-6953	237	28	l2	l2	NOUN
ejpam-6953	237	29	sense	sense	NOUN
ejpam-6953	237	30	.	.	PUNCT
ejpam-6953	238	1	7	7	X
ejpam-6953	238	2	.	.	X
ejpam-6953	238	3	concluding	conclude	VERB
ejpam-6953	238	4	remarks	remark	NOUN
ejpam-6953	238	5	we	we	PRON
ejpam-6953	238	6	have	have	AUX
ejpam-6953	238	7	exhibited	exhibit	VERB
ejpam-6953	238	8	a	a	DET
ejpam-6953	238	9	robust	robust	ADJ
ejpam-6953	238	10	global	global	ADJ
ejpam-6953	238	11	l2	l2	NOUN
ejpam-6953	238	12	∂̄-theory	∂̄-theory	ADJ
ejpam-6953	238	13	on	on	ADP
ejpam-6953	238	14	noncompact	noncompact	ADJ
ejpam-6953	238	15	pseudoconvex	pseudoconvex	NOUN
ejpam-6953	238	16	complex	complex	ADJ
ejpam-6953	238	17	lie	lie	NOUN
ejpam-6953	238	18	groups	group	NOUN
ejpam-6953	238	19	,	,	PUNCT
ejpam-6953	238	20	with	with	ADP
ejpam-6953	238	21	explicit	explicit	ADJ
ejpam-6953	238	22	estimates	estimate	NOUN
ejpam-6953	238	23	and	and	CCONJ
ejpam-6953	238	24	analytic	analytic	ADJ
ejpam-6953	238	25	consequences	consequence	NOUN
ejpam-6953	238	26	.	.	PUNCT
ejpam-6953	239	1	in	in	ADP
ejpam-6953	239	2	a	a	DET
ejpam-6953	239	3	forthcoming	forthcoming	ADJ
ejpam-6953	239	4	paper	paper	NOUN
ejpam-6953	239	5	,	,	PUNCT
ejpam-6953	239	6	we	we	PRON
ejpam-6953	239	7	also	also	ADV
ejpam-6953	239	8	extend	extend	VERB
ejpam-6953	239	9	the	the	DET
ejpam-6953	239	10	main	main	ADJ
ejpam-6953	239	11	theorem	theorem	NOUN
ejpam-6953	239	12	to	to	ADP
ejpam-6953	239	13	(	(	PUNCT
ejpam-6953	239	14	p	p	X
ejpam-6953	239	15	,	,	PUNCT
ejpam-6953	239	16	q)-forms	q)-form	NOUN
ejpam-6953	239	17	with	with	ADP
ejpam-6953	239	18	values	value	NOUN
ejpam-6953	239	19	in	in	ADP
ejpam-6953	239	20	holomorphic	holomorphic	ADJ
ejpam-6953	239	21	vector	vector	NOUN
ejpam-6953	239	22	bundles	bundle	NOUN
ejpam-6953	239	23	(	(	PUNCT
ejpam-6953	239	24	the	the	DET
ejpam-6953	239	25	bundle	bundle	NOUN
ejpam-6953	239	26	curvature	curvature	NOUN
ejpam-6953	239	27	contributes	contribute	VERB
ejpam-6953	239	28	an	an	DET
ejpam-6953	239	29	additional	additional	ADJ
ejpam-6953	239	30	nakano	nakano	ADJ
ejpam-6953	239	31	-	-	PUNCT
ejpam-6953	239	32	nonnegative	nonnegative	ADJ
ejpam-6953	239	33	term	term	NOUN
ejpam-6953	239	34	to	to	ADP
ejpam-6953	239	35	the	the	DET
ejpam-6953	239	36	weight	weight	NOUN
ejpam-6953	239	37	)	)	PUNCT
ejpam-6953	239	38	.	.	PUNCT
ejpam-6953	240	1	on	on	ADP
ejpam-6953	240	2	the	the	DET
ejpam-6953	240	3	other	other	ADJ
ejpam-6953	240	4	hand	hand	NOUN
ejpam-6953	240	5	,	,	PUNCT
ejpam-6953	240	6	identifying	identify	VERB
ejpam-6953	240	7	geometric	geometric	ADJ
ejpam-6953	240	8	conditions	condition	NOUN
ejpam-6953	240	9	beyond	beyond	ADP
ejpam-6953	240	10	lie	lie	NOUN
ejpam-6953	240	11	groups	group	NOUN
ejpam-6953	240	12	that	that	PRON
ejpam-6953	240	13	guarantee	guarantee	VERB
ejpam-6953	240	14	the	the	DET
ejpam-6953	240	15	key	key	ADJ
ejpam-6953	240	16	uniformities	uniformity	NOUN
ejpam-6953	240	17	(	(	PUNCT
ejpam-6953	240	18	u1)–(u2	u1)–(u2	PROPN
ejpam-6953	240	19	)	)	PUNCT
ejpam-6953	240	20	is	be	AUX
ejpam-6953	240	21	a	a	DET
ejpam-6953	240	22	natural	natural	ADJ
ejpam-6953	240	23	direction	direction	NOUN
ejpam-6953	240	24	for	for	ADP
ejpam-6953	240	25	future	future	ADJ
ejpam-6953	240	26	work	work	NOUN
ejpam-6953	240	27	.	.	PUNCT
ejpam-6953	241	1	appendix	appendix	VERB
ejpam-6953	241	2	a.	a.	NOUN
ejpam-6953	241	3	regularized	regularize	VERB
ejpam-6953	241	4	maxima	maxima	NOUN
ejpam-6953	241	5	of	of	ADP
ejpam-6953	241	6	strictly	strictly	ADV
ejpam-6953	241	7	psh	psh	NOUN
ejpam-6953	241	8	functions	function	NOUN
ejpam-6953	241	9	we	we	PRON
ejpam-6953	241	10	outline	outline	VERB
ejpam-6953	241	11	the	the	DET
ejpam-6953	241	12	construction	construction	NOUN
ejpam-6953	241	13	of	of	ADP
ejpam-6953	241	14	the	the	DET
ejpam-6953	241	15	auxiliary	auxiliary	ADJ
ejpam-6953	241	16	functions	function	NOUN
ejpam-6953	241	17	σj	σj	AUX
ejpam-6953	241	18	used	use	VERB
ejpam-6953	241	19	in	in	ADP
ejpam-6953	241	20	lemma	lemma	PROPN
ejpam-6953	241	21	3	3	X
ejpam-6953	241	22	.	.	PUNCT
ejpam-6953	242	1	let	let	VERB
ejpam-6953	242	2	u1	u1	VERB
ejpam-6953	242	3	,	,	PUNCT
ejpam-6953	242	4	.	.	PUNCT
ejpam-6953	242	5	.	.	PUNCT
ejpam-6953	243	1	.	.	PUNCT
ejpam-6953	244	1	,	,	PUNCT
ejpam-6953	244	2	un	un	PROPN
ejpam-6953	244	3	be	be	VERB
ejpam-6953	244	4	strictly	strictly	ADV
ejpam-6953	244	5	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	244	6	functions	function	NOUN
ejpam-6953	244	7	on	on	ADP
ejpam-6953	244	8	a	a	DET
ejpam-6953	244	9	complex	complex	ADJ
ejpam-6953	244	10	manifold	manifold	NOUN
ejpam-6953	244	11	(	(	PUNCT
ejpam-6953	244	12	say	say	INTJ
ejpam-6953	244	13	,	,	PUNCT
ejpam-6953	244	14	on	on	ADP
ejpam-6953	244	15	an	an	DET
ejpam-6953	244	16	open	open	ADJ
ejpam-6953	244	17	set	set	NOUN
ejpam-6953	244	18	in	in	ADP
ejpam-6953	244	19	cn	cn	PROPN
ejpam-6953	244	20	)	)	PUNCT
ejpam-6953	244	21	such	such	ADJ
ejpam-6953	244	22	that	that	SCONJ
ejpam-6953	244	23	i∂∂̄ui	i∂∂̄ui	ADV
ejpam-6953	244	24	≥	≥	X
ejpam-6953	244	25	λi	λi	X
ejpam-6953	244	26	ω	ω	NUM
ejpam-6953	244	27	for	for	ADP
ejpam-6953	244	28	some	some	PRON
ejpam-6953	244	29	λi	λi	ADP
ejpam-6953	244	30	>	>	X
ejpam-6953	244	31	0	0	X
ejpam-6953	244	32	.	.	PUNCT
ejpam-6953	245	1	consider	consider	VERB
ejpam-6953	245	2	the	the	DET
ejpam-6953	245	3	regularized	regularize	VERB
ejpam-6953	245	4	maximum	maximum	NOUN
ejpam-6953	245	5	mτ	mτ	NOUN
ejpam-6953	245	6	(	(	PUNCT
ejpam-6953	245	7	u1	u1	PROPN
ejpam-6953	245	8	,	,	PUNCT
ejpam-6953	245	9	.	.	PUNCT
ejpam-6953	245	10	.	.	PUNCT
ejpam-6953	246	1	.	.	PUNCT
ejpam-6953	247	1	,	,	PUNCT
ejpam-6953	247	2	un	un	PROPN
ejpam-6953	247	3	)	)	PUNCT
ejpam-6953	247	4	(	(	PUNCT
ejpam-6953	248	1	z	z	NOUN
ejpam-6953	248	2	)	)	PUNCT
ejpam-6953	248	3	:	:	PUNCT
ejpam-6953	248	4	=	=	SYM
ejpam-6953	248	5	1	1	NUM
ejpam-6953	248	6	τ	τ	NUM
ejpam-6953	248	7	log	log	NOUN
ejpam-6953	248	8	(	(	PUNCT
ejpam-6953	248	9	eτu1(z	eτu1(z	NUM
ejpam-6953	248	10	)	)	PUNCT
ejpam-6953	248	11	+	+	CCONJ
ejpam-6953	248	12	·	·	PUNCT
ejpam-6953	248	13	·	·	PUNCT
ejpam-6953	248	14	·	·	PUNCT
ejpam-6953	249	1	+	+	CCONJ
ejpam-6953	249	2	eτun	eτun	NOUN
ejpam-6953	249	3	(	(	PUNCT
ejpam-6953	249	4	z	z	NOUN
ejpam-6953	249	5	)	)	PUNCT
ejpam-6953	249	6	)	)	PUNCT
ejpam-6953	249	7	,	,	PUNCT
ejpam-6953	249	8	depending	depend	VERB
ejpam-6953	249	9	on	on	ADP
ejpam-6953	249	10	a	a	DET
ejpam-6953	249	11	large	large	ADJ
ejpam-6953	249	12	parameter	parameter	NOUN
ejpam-6953	249	13	τ	τ	PROPN
ejpam-6953	249	14	>	>	X
ejpam-6953	249	15	0	0	PROPN
ejpam-6953	249	16	.	.	PUNCT
ejpam-6953	250	1	one	one	NUM
ejpam-6953	250	2	checks	check	NOUN
ejpam-6953	250	3	that	that	PRON
ejpam-6953	250	4	mτ	mτ	NOUN
ejpam-6953	250	5	(	(	PUNCT
ejpam-6953	250	6	u1	u1	PROPN
ejpam-6953	250	7	,	,	PUNCT
ejpam-6953	250	8	.	.	PUNCT
ejpam-6953	250	9	.	.	PUNCT
ejpam-6953	250	10	.	.	PUNCT
ejpam-6953	251	1	,	,	PUNCT
ejpam-6953	251	2	un	un	PROPN
ejpam-6953	251	3	)	)	PUNCT
ejpam-6953	251	4	is	be	AUX
ejpam-6953	251	5	a	a	DET
ejpam-6953	251	6	smooth	smooth	ADJ
ejpam-6953	251	7	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	251	8	function	function	NOUN
ejpam-6953	251	9	which	which	PRON
ejpam-6953	251	10	decreases	decrease	VERB
ejpam-6953	251	11	pointwise	pointwise	NOUN
ejpam-6953	251	12	to	to	ADP
ejpam-6953	251	13	max{u1	max{u1	NUM
ejpam-6953	251	14	,	,	PUNCT
ejpam-6953	251	15	.	.	PUNCT
ejpam-6953	251	16	.	.	PUNCT
ejpam-6953	252	1	.	.	PUNCT
ejpam-6953	253	1	,	,	PUNCT
ejpam-6953	253	2	un	un	PROPN
ejpam-6953	253	3	}	}	PUNCT
ejpam-6953	253	4	as	as	ADP
ejpam-6953	253	5	τ	τ	PROPN
ejpam-6953	253	6	→	→	SYM
ejpam-6953	253	7	∞.	∞.	PROPN
ejpam-6953	253	8	a	a	DET
ejpam-6953	253	9	direct	direct	ADJ
ejpam-6953	253	10	computation	computation	NOUN
ejpam-6953	253	11	of	of	ADP
ejpam-6953	253	12	the	the	DET
ejpam-6953	253	13	levi	levi	PROPN
ejpam-6953	253	14	form	form	NOUN
ejpam-6953	253	15	(	(	PUNCT
ejpam-6953	253	16	see	see	VERB
ejpam-6953	253	17	,	,	PUNCT
ejpam-6953	253	18	e.g.	e.g.	ADV
ejpam-6953	253	19	,	,	PUNCT
ejpam-6953	253	20	[	[	X
ejpam-6953	253	21	15	15	NUM
ejpam-6953	253	22	,	,	PUNCT
ejpam-6953	253	23	p.	p.	NOUN
ejpam-6953	253	24	262	262	NUM
ejpam-6953	253	25	]	]	PUNCT
ejpam-6953	253	26	)	)	PUNCT
ejpam-6953	253	27	shows	show	VERB
ejpam-6953	253	28	that	that	SCONJ
ejpam-6953	253	29	i∂∂̄mτ	i∂∂̄mτ	NOUN
ejpam-6953	253	30	(	(	PUNCT
ejpam-6953	253	31	u1	u1	NOUN
ejpam-6953	253	32	,	,	PUNCT
ejpam-6953	253	33	.	.	PUNCT
ejpam-6953	253	34	.	.	PUNCT
ejpam-6953	254	1	.	.	PUNCT
ejpam-6953	255	1	,	,	PUNCT
ejpam-6953	255	2	un	un	PROPN
ejpam-6953	255	3	)	)	PUNCT
ejpam-6953	256	1	=	=	PUNCT
ejpam-6953	257	1	n∑	n∑	PROPN
ejpam-6953	257	2	i=1	i=1	PROPN
ejpam-6953	257	3	αi(z	αi(z	NOUN
ejpam-6953	257	4	)	)	PUNCT
ejpam-6953	257	5	i∂∂̄ui(z	i∂∂̄ui(z	NOUN
ejpam-6953	257	6	)	)	PUNCT
ejpam-6953	258	1	+	+	CCONJ
ejpam-6953	259	1	n∑	n∑	X
ejpam-6953	259	2	i=1	i=1	X
ejpam-6953	259	3	αi(z)βi(z	αi(z)βi(z	PRON
ejpam-6953	259	4	)	)	PUNCT
ejpam-6953	259	5	,	,	PUNCT
ejpam-6953	259	6	where	where	SCONJ
ejpam-6953	259	7	αi(z	αi(z	VERB
ejpam-6953	259	8	)	)	PUNCT
ejpam-6953	259	9	=	=	PRON
ejpam-6953	259	10	eτui(z)∑n	eτui(z)∑n	NOUN
ejpam-6953	259	11	k=1	k=1	X
ejpam-6953	259	12	e	e	X
ejpam-6953	259	13	τuk(z	τuk(z	PROPN
ejpam-6953	259	14	)	)	PUNCT
ejpam-6953	259	15	≥	≥	NOUN
ejpam-6953	259	16	0	0	NUM
ejpam-6953	259	17	,	,	PUNCT
ejpam-6953	259	18	n∑	n∑	PROPN
ejpam-6953	259	19	i=1	i=1	PROPN
ejpam-6953	259	20	αi(z	αi(z	ADV
ejpam-6953	259	21	)	)	PUNCT
ejpam-6953	259	22	=	=	SYM
ejpam-6953	259	23	1	1	NUM
ejpam-6953	259	24	,	,	PUNCT
ejpam-6953	259	25	a.	a.	PROPN
ejpam-6953	259	26	r.	r.	PROPN
ejpam-6953	259	27	al	al	PROPN
ejpam-6953	259	28	-	-	PUNCT
ejpam-6953	259	29	abdallah	abdallah	PROPN
ejpam-6953	259	30	/	/	SYM
ejpam-6953	259	31	eur	eur	PROPN
ejpam-6953	259	32	.	.	PUNCT
ejpam-6953	260	1	j.	j.	PROPN
ejpam-6953	260	2	pure	pure	PROPN
ejpam-6953	260	3	appl	appl	PROPN
ejpam-6953	260	4	.	.	PROPN
ejpam-6953	260	5	math	math	PROPN
ejpam-6953	260	6	,	,	PUNCT
ejpam-6953	260	7	18	18	NUM
ejpam-6953	260	8	(	(	PUNCT
ejpam-6953	260	9	4	4	NUM
ejpam-6953	260	10	)	)	PUNCT
ejpam-6953	260	11	(	(	PUNCT
ejpam-6953	260	12	2025	2025	NUM
ejpam-6953	260	13	)	)	PUNCT
ejpam-6953	260	14	,	,	PUNCT
ejpam-6953	260	15	6953	6953	NUM
ejpam-6953	260	16	12	12	NUM
ejpam-6953	260	17	of	of	ADP
ejpam-6953	260	18	14	14	NUM
ejpam-6953	260	19	and	and	CCONJ
ejpam-6953	260	20	βi(z	βi(z	NUM
ejpam-6953	260	21	)	)	PUNCT
ejpam-6953	260	22	is	be	AUX
ejpam-6953	260	23	a	a	DET
ejpam-6953	260	24	positive	positive	ADJ
ejpam-6953	260	25	semidefinite	semidefinite	NOUN
ejpam-6953	260	26	(	(	PUNCT
ejpam-6953	260	27	1	1	NUM
ejpam-6953	260	28	,	,	PUNCT
ejpam-6953	260	29	1)-form	1)-form	PROPN
ejpam-6953	260	30	.	.	PUNCT
ejpam-6953	261	1	in	in	ADP
ejpam-6953	261	2	particular	particular	ADJ
ejpam-6953	261	3	,	,	PUNCT
ejpam-6953	261	4	if	if	SCONJ
ejpam-6953	261	5	each	each	DET
ejpam-6953	261	6	i∂∂̄ui	i∂∂̄ui	ADV
ejpam-6953	261	7	≥	≥	X
ejpam-6953	261	8	λω	λω	ADP
ejpam-6953	261	9	,	,	PUNCT
ejpam-6953	261	10	then	then	ADV
ejpam-6953	261	11	i∂∂̄mτ	i∂∂̄mτ	PROPN
ejpam-6953	261	12	(	(	PUNCT
ejpam-6953	261	13	u1	u1	NOUN
ejpam-6953	261	14	,	,	PUNCT
ejpam-6953	261	15	.	.	PUNCT
ejpam-6953	261	16	.	.	PUNCT
ejpam-6953	261	17	.	.	PUNCT
ejpam-6953	262	1	,	,	PUNCT
ejpam-6953	262	2	un	un	PROPN
ejpam-6953	262	3	)	)	PUNCT
ejpam-6953	262	4	≥	≥	PROPN
ejpam-6953	262	5	λω	λω	ADP
ejpam-6953	262	6	for	for	ADP
ejpam-6953	262	7	every	every	DET
ejpam-6953	262	8	τ	τ	PROPN
ejpam-6953	262	9	>	>	X
ejpam-6953	262	10	0	0	PROPN
ejpam-6953	262	11	.	.	PUNCT
ejpam-6953	263	1	now	now	ADV
ejpam-6953	263	2	suppose	suppose	VERB
ejpam-6953	263	3	each	each	DET
ejpam-6953	263	4	ui	ui	NOUN
ejpam-6953	263	5	vanishes	vanish	VERB
ejpam-6953	263	6	outside	outside	ADP
ejpam-6953	263	7	some	some	DET
ejpam-6953	263	8	relatively	relatively	ADV
ejpam-6953	263	9	compact	compact	ADJ
ejpam-6953	263	10	domain	domain	NOUN
ejpam-6953	263	11	and	and	CCONJ
ejpam-6953	263	12	that	that	SCONJ
ejpam-6953	263	13	at	at	ADP
ejpam-6953	263	14	most	most	ADJ
ejpam-6953	263	15	c	c	NOUN
ejpam-6953	263	16	of	of	ADP
ejpam-6953	263	17	the	the	DET
ejpam-6953	263	18	functions	function	NOUN
ejpam-6953	263	19	ui	ui	NOUN
ejpam-6953	263	20	are	be	AUX
ejpam-6953	263	21	simultaneously	simultaneously	ADV
ejpam-6953	263	22	nonzero	nonzero	ADJ
ejpam-6953	263	23	at	at	ADP
ejpam-6953	263	24	any	any	DET
ejpam-6953	263	25	given	give	VERB
ejpam-6953	263	26	point	point	NOUN
ejpam-6953	263	27	.	.	PUNCT
ejpam-6953	264	1	in	in	ADP
ejpam-6953	264	2	that	that	DET
ejpam-6953	264	3	case	case	NOUN
ejpam-6953	264	4	,	,	PUNCT
ejpam-6953	264	5	one	one	PRON
ejpam-6953	264	6	can	can	AUX
ejpam-6953	264	7	choose	choose	VERB
ejpam-6953	264	8	a	a	DET
ejpam-6953	264	9	finite	finite	NOUN
ejpam-6953	264	10	τ	τ	PROPN
ejpam-6953	264	11	large	large	ADJ
ejpam-6953	264	12	enough	enough	ADV
ejpam-6953	264	13	that	that	SCONJ
ejpam-6953	264	14	at	at	ADP
ejpam-6953	264	15	every	every	DET
ejpam-6953	264	16	point	point	NOUN
ejpam-6953	264	17	z	z	PROPN
ejpam-6953	264	18	,	,	PUNCT
ejpam-6953	264	19	the	the	DET
ejpam-6953	264	20	weights	weight	NOUN
ejpam-6953	264	21	αi(z	αi(z	NOUN
ejpam-6953	264	22	)	)	PUNCT
ejpam-6953	264	23	are	be	AUX
ejpam-6953	264	24	concentrated	concentrate	VERB
ejpam-6953	264	25	on	on	ADP
ejpam-6953	264	26	at	at	ADP
ejpam-6953	264	27	most	most	ADJ
ejpam-6953	264	28	c	c	NOUN
ejpam-6953	264	29	terms	term	NOUN
ejpam-6953	264	30	.	.	PUNCT
ejpam-6953	265	1	it	it	PRON
ejpam-6953	265	2	follows	follow	VERB
ejpam-6953	265	3	that	that	SCONJ
ejpam-6953	265	4	mτ	mτ	NOUN
ejpam-6953	265	5	(	(	PUNCT
ejpam-6953	265	6	u1	u1	PROPN
ejpam-6953	265	7	,	,	PUNCT
ejpam-6953	265	8	.	.	PUNCT
ejpam-6953	265	9	.	.	PUNCT
ejpam-6953	265	10	.	.	PUNCT
ejpam-6953	266	1	,	,	PUNCT
ejpam-6953	266	2	un	un	PROPN
ejpam-6953	266	3	)	)	PUNCT
ejpam-6953	266	4	is	be	AUX
ejpam-6953	266	5	strictly	strictly	ADV
ejpam-6953	266	6	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	266	7	with	with	ADP
ejpam-6953	266	8	i∂∂̄mτ	i∂∂̄mτ	NOUN
ejpam-6953	266	9	(	(	PUNCT
ejpam-6953	266	10	u1	u1	NOUN
ejpam-6953	266	11	,	,	PUNCT
ejpam-6953	266	12	.	.	PUNCT
ejpam-6953	266	13	.	.	PUNCT
ejpam-6953	267	1	.	.	PUNCT
ejpam-6953	268	1	,	,	PUNCT
ejpam-6953	268	2	un	un	PROPN
ejpam-6953	268	3	)	)	PUNCT
ejpam-6953	268	4	≥	≥	PROPN
ejpam-6953	268	5	(	(	PUNCT
ejpam-6953	268	6	min	min	NOUN
ejpam-6953	268	7	i	i	PRON
ejpam-6953	268	8	λi	λi	NOUN
ejpam-6953	268	9	/	/	SYM
ejpam-6953	268	10	c)ω	c)ω	NOUN
ejpam-6953	268	11	.	.	PUNCT
ejpam-6953	269	1	finally	finally	ADV
ejpam-6953	269	2	,	,	PUNCT
ejpam-6953	269	3	by	by	ADP
ejpam-6953	269	4	mollifying	mollify	VERB
ejpam-6953	269	5	mτ	mτ	NOUN
ejpam-6953	269	6	(	(	PUNCT
ejpam-6953	269	7	u1	u1	PROPN
ejpam-6953	269	8	,	,	PUNCT
ejpam-6953	269	9	.	.	PUNCT
ejpam-6953	269	10	.	.	PUNCT
ejpam-6953	269	11	.	.	PUNCT
ejpam-6953	270	1	,	,	PUNCT
ejpam-6953	270	2	un	un	PROPN
ejpam-6953	270	3	)	)	PUNCT
ejpam-6953	270	4	if	if	SCONJ
ejpam-6953	270	5	necessary	necessary	ADJ
ejpam-6953	270	6	,	,	PUNCT
ejpam-6953	270	7	we	we	PRON
ejpam-6953	270	8	can	can	AUX
ejpam-6953	270	9	obtain	obtain	VERB
ejpam-6953	270	10	a	a	DET
ejpam-6953	270	11	c∞	c∞	ADJ
ejpam-6953	270	12	function	function	NOUN
ejpam-6953	270	13	σ	σ	NOUN
ejpam-6953	270	14	satisfying	satisfy	VERB
ejpam-6953	270	15	σ	σ	PROPN
ejpam-6953	270	16	≥	≥	NUM
ejpam-6953	270	17	max(u1	max(u1	NOUN
ejpam-6953	270	18	,	,	PUNCT
ejpam-6953	270	19	.	.	PUNCT
ejpam-6953	270	20	.	.	PUNCT
ejpam-6953	271	1	.	.	PUNCT
ejpam-6953	272	1	,	,	PUNCT
ejpam-6953	272	2	un	un	PROPN
ejpam-6953	272	3	)	)	PUNCT
ejpam-6953	272	4	and	and	CCONJ
ejpam-6953	272	5	i∂∂̄σ	i∂∂̄σ	PROPN
ejpam-6953	272	6	≥	≥	PROPN
ejpam-6953	272	7	(	(	PUNCT
ejpam-6953	272	8	mini	mini	ADJ
ejpam-6953	272	9	λi	λi	NOUN
ejpam-6953	272	10	/	/	SYM
ejpam-6953	272	11	c)ω	c)ω	NOUN
ejpam-6953	272	12	.	.	PUNCT
ejpam-6953	273	1	this	this	DET
ejpam-6953	273	2	σ	σ	PROPN
ejpam-6953	273	3	serves	serve	VERB
ejpam-6953	273	4	as	as	ADP
ejpam-6953	273	5	the	the	DET
ejpam-6953	273	6	desired	desire	VERB
ejpam-6953	273	7	reference	reference	NOUN
ejpam-6953	273	8	function	function	NOUN
ejpam-6953	273	9	.	.	PUNCT
ejpam-6953	274	1	appendix	appendix	PROPN
ejpam-6953	274	2	b.	b.	PROPN
ejpam-6953	274	3	bounded	bound	VERB
ejpam-6953	274	4	-	-	PUNCT
ejpam-6953	274	5	overlap	overlap	NOUN
ejpam-6953	274	6	coverings	covering	NOUN
ejpam-6953	274	7	in	in	ADP
ejpam-6953	274	8	left	left	ADJ
ejpam-6953	274	9	-	-	PUNCT
ejpam-6953	274	10	invariant	invariant	ADJ
ejpam-6953	274	11	metrics	metric	NOUN
ejpam-6953	274	12	any	any	DET
ejpam-6953	274	13	left	left	ADJ
ejpam-6953	274	14	-	-	PUNCT
ejpam-6953	274	15	invariant	invariant	ADJ
ejpam-6953	274	16	riemannian	riemannian	ADJ
ejpam-6953	274	17	metric	metric	NOUN
ejpam-6953	274	18	(	(	PUNCT
ejpam-6953	274	19	or	or	CCONJ
ejpam-6953	274	20	hermitian	hermitian	ADJ
ejpam-6953	274	21	metric	metric	NOUN
ejpam-6953	274	22	)	)	PUNCT
ejpam-6953	274	23	on	on	ADP
ejpam-6953	274	24	a	a	DET
ejpam-6953	274	25	complex	complex	ADJ
ejpam-6953	274	26	lie	lie	NOUN
ejpam-6953	274	27	group	group	NOUN
ejpam-6953	274	28	g	g	PROPN
ejpam-6953	274	29	induces	induce	VERB
ejpam-6953	274	30	a	a	DET
ejpam-6953	274	31	distance	distance	NOUN
ejpam-6953	274	32	function	function	NOUN
ejpam-6953	274	33	d	d	NOUN
ejpam-6953	274	34	ong	ong	INTJ
ejpam-6953	274	35	that	that	PRON
ejpam-6953	274	36	is	be	AUX
ejpam-6953	274	37	homogeneous	homogeneous	ADJ
ejpam-6953	274	38	in	in	ADP
ejpam-6953	274	39	the	the	DET
ejpam-6953	274	40	sense	sense	NOUN
ejpam-6953	274	41	that	that	SCONJ
ejpam-6953	274	42	d(gx	d(gx	PROPN
ejpam-6953	274	43	,	,	PUNCT
ejpam-6953	274	44	gy	gy	NOUN
ejpam-6953	274	45	)	)	PUNCT
ejpam-6953	274	46	=	=	SYM
ejpam-6953	274	47	d(x	d(x	PROPN
ejpam-6953	274	48	,	,	PUNCT
ejpam-6953	274	49	y	y	NOUN
ejpam-6953	274	50	)	)	PUNCT
ejpam-6953	274	51	for	for	ADP
ejpam-6953	274	52	all	all	DET
ejpam-6953	274	53	g	g	NOUN
ejpam-6953	274	54	,	,	PUNCT
ejpam-6953	274	55	x	x	PRON
ejpam-6953	274	56	,	,	PUNCT
ejpam-6953	274	57	y	y	PROPN
ejpam-6953	274	58	∈	∈	PROPN
ejpam-6953	274	59	g.	g.	PROPN
ejpam-6953	274	60	moreover	moreover	ADV
ejpam-6953	274	61	,	,	PUNCT
ejpam-6953	274	62	(	(	PUNCT
ejpam-6953	274	63	g	g	NOUN
ejpam-6953	274	64	,	,	PUNCT
ejpam-6953	274	65	d	d	NOUN
ejpam-6953	274	66	)	)	PUNCT
ejpam-6953	274	67	has	have	AUX
ejpam-6953	274	68	finite	finite	VERB
ejpam-6953	274	69	besicovitch	besicovitch	PROPN
ejpam-6953	274	70	constant	constant	ADJ
ejpam-6953	274	71	,	,	PUNCT
ejpam-6953	274	72	depending	depend	VERB
ejpam-6953	274	73	only	only	ADV
ejpam-6953	274	74	on	on	ADP
ejpam-6953	274	75	the	the	DET
ejpam-6953	274	76	real	real	ADJ
ejpam-6953	274	77	dimension	dimension	NOUN
ejpam-6953	274	78	of	of	ADP
ejpam-6953	274	79	g.	g.	PROPN
ejpam-6953	274	80	this	this	PRON
ejpam-6953	274	81	is	be	AUX
ejpam-6953	274	82	a	a	DET
ejpam-6953	274	83	consequence	consequence	NOUN
ejpam-6953	274	84	of	of	ADP
ejpam-6953	274	85	the	the	DET
ejpam-6953	274	86	besicovitch	besicovitch	NOUN
ejpam-6953	274	87	covering	covering	NOUN
ejpam-6953	274	88	theorem	theorem	NOUN
ejpam-6953	274	89	in	in	ADP
ejpam-6953	274	90	euclidean	euclidean	ADJ
ejpam-6953	274	91	space	space	NOUN
ejpam-6953	274	92	(	(	PUNCT
ejpam-6953	274	93	see	see	VERB
ejpam-6953	274	94	,	,	PUNCT
ejpam-6953	274	95	e.g.	e.g.	ADV
ejpam-6953	274	96	,	,	PUNCT
ejpam-6953	274	97	[	[	X
ejpam-6953	274	98	11–13	11–13	NUM
ejpam-6953	274	99	]	]	NUM
ejpam-6953	274	100	)	)	PUNCT
ejpam-6953	274	101	,	,	PUNCT
ejpam-6953	274	102	since	since	SCONJ
ejpam-6953	274	103	any	any	DET
ejpam-6953	274	104	metric	metric	ADJ
ejpam-6953	274	105	ball	ball	NOUN
ejpam-6953	274	106	in	in	ADP
ejpam-6953	274	107	(	(	PUNCT
ejpam-6953	274	108	g	g	PROPN
ejpam-6953	274	109	,	,	PUNCT
ejpam-6953	274	110	d	d	NOUN
ejpam-6953	274	111	)	)	PUNCT
ejpam-6953	274	112	is	be	AUX
ejpam-6953	274	113	isometric	isometric	ADJ
ejpam-6953	274	114	(	(	PUNCT
ejpam-6953	274	115	via	via	ADP
ejpam-6953	274	116	lefttranslation	lefttranslation	NOUN
ejpam-6953	274	117	and	and	CCONJ
ejpam-6953	274	118	the	the	DET
ejpam-6953	274	119	exponential	exponential	ADJ
ejpam-6953	274	120	map	map	NOUN
ejpam-6953	274	121	at	at	ADP
ejpam-6953	274	122	the	the	DET
ejpam-6953	274	123	identity	identity	NOUN
ejpam-6953	274	124	)	)	PUNCT
ejpam-6953	274	125	to	to	ADP
ejpam-6953	274	126	a	a	DET
ejpam-6953	274	127	euclidean	euclidean	ADJ
ejpam-6953	274	128	ball	ball	NOUN
ejpam-6953	274	129	in	in	ADP
ejpam-6953	274	130	r2n	r2n	NOUN
ejpam-6953	274	131	.	.	PUNCT
ejpam-6953	275	1	concretely	concretely	ADV
ejpam-6953	275	2	,	,	PUNCT
ejpam-6953	275	3	the	the	DET
ejpam-6953	275	4	besicovitch	besicovitch	ADJ
ejpam-6953	275	5	property	property	NOUN
ejpam-6953	275	6	implies	imply	VERB
ejpam-6953	275	7	that	that	SCONJ
ejpam-6953	275	8	there	there	PRON
ejpam-6953	275	9	exists	exist	VERB
ejpam-6953	275	10	an	an	DET
ejpam-6953	275	11	integer	integer	NOUN
ejpam-6953	275	12	n	n	NOUN
ejpam-6953	275	13	=	=	SYM
ejpam-6953	275	14	n(dimg	n(dimg	NOUN
ejpam-6953	275	15	)	)	PUNCT
ejpam-6953	275	16	with	with	ADP
ejpam-6953	275	17	the	the	DET
ejpam-6953	275	18	following	follow	VERB
ejpam-6953	275	19	property	property	NOUN
ejpam-6953	275	20	:	:	PUNCT
ejpam-6953	275	21	given	give	VERB
ejpam-6953	275	22	any	any	DET
ejpam-6953	275	23	family	family	NOUN
ejpam-6953	275	24	of	of	ADP
ejpam-6953	275	25	metric	metric	ADJ
ejpam-6953	275	26	balls	ball	NOUN
ejpam-6953	275	27	in	in	ADP
ejpam-6953	275	28	(	(	PUNCT
ejpam-6953	275	29	g	g	NOUN
ejpam-6953	275	30	,	,	PUNCT
ejpam-6953	275	31	d	d	NOUN
ejpam-6953	275	32	)	)	PUNCT
ejpam-6953	275	33	covering	cover	VERB
ejpam-6953	275	34	a	a	DET
ejpam-6953	275	35	set	set	NOUN
ejpam-6953	275	36	e	e	PROPN
ejpam-6953	275	37	⊂	⊂	PROPN
ejpam-6953	275	38	g	g	PROPN
ejpam-6953	275	39	,	,	PUNCT
ejpam-6953	275	40	one	one	PRON
ejpam-6953	275	41	can	can	AUX
ejpam-6953	275	42	extract	extract	VERB
ejpam-6953	275	43	a	a	DET
ejpam-6953	275	44	countable	countable	ADJ
ejpam-6953	275	45	subcollection	subcollection	NOUN
ejpam-6953	275	46	of	of	ADP
ejpam-6953	275	47	these	these	DET
ejpam-6953	275	48	balls	ball	NOUN
ejpam-6953	275	49	which	which	PRON
ejpam-6953	275	50	still	still	ADV
ejpam-6953	275	51	covers	cover	VERB
ejpam-6953	275	52	e	e	NOUN
ejpam-6953	275	53	and	and	CCONJ
ejpam-6953	275	54	such	such	ADJ
ejpam-6953	275	55	that	that	SCONJ
ejpam-6953	275	56	no	no	DET
ejpam-6953	275	57	point	point	NOUN
ejpam-6953	275	58	of	of	ADP
ejpam-6953	275	59	g	g	NOUN
ejpam-6953	275	60	is	be	AUX
ejpam-6953	275	61	contained	contain	VERB
ejpam-6953	275	62	in	in	ADP
ejpam-6953	275	63	more	more	ADJ
ejpam-6953	275	64	than	than	ADP
ejpam-6953	275	65	n	n	PRON
ejpam-6953	275	66	balls	ball	NOUN
ejpam-6953	275	67	from	from	ADP
ejpam-6953	275	68	the	the	DET
ejpam-6953	275	69	subcollection	subcollection	NOUN
ejpam-6953	275	70	.	.	PUNCT
ejpam-6953	276	1	in	in	ADP
ejpam-6953	276	2	particular	particular	ADJ
ejpam-6953	276	3	,	,	PUNCT
ejpam-6953	276	4	by	by	ADP
ejpam-6953	276	5	applying	apply	VERB
ejpam-6953	276	6	this	this	PRON
ejpam-6953	276	7	to	to	ADP
ejpam-6953	276	8	a	a	DET
ejpam-6953	276	9	cover	cover	NOUN
ejpam-6953	276	10	of	of	ADP
ejpam-6953	276	11	ωj	ωj	ADP
ejpam-6953	276	12	by	by	ADP
ejpam-6953	276	13	sufficiently	sufficiently	ADV
ejpam-6953	276	14	small	small	ADJ
ejpam-6953	276	15	balls	ball	NOUN
ejpam-6953	276	16	,	,	PUNCT
ejpam-6953	276	17	one	one	PRON
ejpam-6953	276	18	obtains	obtain	VERB
ejpam-6953	276	19	a	a	DET
ejpam-6953	276	20	finite	finite	ADJ
ejpam-6953	276	21	subcover	subcover	NOUN
ejpam-6953	276	22	of	of	ADP
ejpam-6953	276	23	ωj	ωj	PROPN
ejpam-6953	276	24	with	with	ADP
ejpam-6953	276	25	the	the	DET
ejpam-6953	276	26	bounded	bounded	ADJ
ejpam-6953	276	27	overlap	overlap	NOUN
ejpam-6953	276	28	property	property	NOUN
ejpam-6953	276	29	used	use	VERB
ejpam-6953	276	30	in	in	ADP
ejpam-6953	276	31	lemma	lemma	PROPN
ejpam-6953	276	32	3	3	NUM
ejpam-6953	276	33	.	.	PUNCT
ejpam-6953	276	34	one	one	NUM
ejpam-6953	276	35	classical	classical	ADJ
ejpam-6953	276	36	proof	proof	NOUN
ejpam-6953	276	37	of	of	ADP
ejpam-6953	276	38	the	the	DET
ejpam-6953	276	39	besicovitch	besicovitch	NOUN
ejpam-6953	276	40	covering	cover	VERB
ejpam-6953	276	41	lemma	lemma	PROPN
ejpam-6953	276	42	shows	show	VERB
ejpam-6953	276	43	that	that	SCONJ
ejpam-6953	276	44	one	one	PRON
ejpam-6953	276	45	can	can	AUX
ejpam-6953	276	46	take	take	VERB
ejpam-6953	276	47	n	n	NOUN
ejpam-6953	276	48	=	=	SYM
ejpam-6953	276	49	5	5	NUM
ejpam-6953	276	50	m	m	NOUN
ejpam-6953	276	51	in	in	ADP
ejpam-6953	276	52	rm	rm	PROPN
ejpam-6953	276	53	(	(	PUNCT
ejpam-6953	276	54	see	see	VERB
ejpam-6953	276	55	[	[	X
ejpam-6953	276	56	11	11	NUM
ejpam-6953	276	57	]	]	NUM
ejpam-6953	276	58	)	)	PUNCT
ejpam-6953	276	59	,	,	PUNCT
ejpam-6953	276	60	so	so	CCONJ
ejpam-6953	276	61	for	for	ADP
ejpam-6953	276	62	dimrg	dimrg	NOUN
ejpam-6953	276	63	=	=	SYM
ejpam-6953	276	64	2n	2n	NUM
ejpam-6953	276	65	one	one	PRON
ejpam-6953	276	66	may	may	AUX
ejpam-6953	276	67	take	take	VERB
ejpam-6953	276	68	c	c	NOUN
ejpam-6953	276	69	=	=	SYM
ejpam-6953	276	70	n(2n	n(2n	NOUN
ejpam-6953	276	71	)	)	PUNCT
ejpam-6953	276	72	≤	≤	NOUN
ejpam-6953	276	73	52n	52n	NOUN
ejpam-6953	276	74	in	in	ADP
ejpam-6953	276	75	lemma	lemma	PROPN
ejpam-6953	276	76	3	3	NUM
ejpam-6953	276	77	.	.	PUNCT
ejpam-6953	277	1	thus	thus	ADV
ejpam-6953	277	2	,	,	PUNCT
ejpam-6953	277	3	for	for	ADP
ejpam-6953	277	4	instance	instance	NOUN
ejpam-6953	277	5	,	,	PUNCT
ejpam-6953	277	6	c	c	PROPN
ejpam-6953	277	7	=	=	SYM
ejpam-6953	277	8	54	54	NUM
ejpam-6953	277	9	=	=	SYM
ejpam-6953	277	10	625	625	NUM
ejpam-6953	277	11	is	be	AUX
ejpam-6953	277	12	valid	valid	ADJ
ejpam-6953	277	13	for	for	ADP
ejpam-6953	277	14	any	any	DET
ejpam-6953	277	15	left	left	ADJ
ejpam-6953	277	16	-	-	PUNCT
ejpam-6953	277	17	invariant	invariant	ADJ
ejpam-6953	277	18	metric	metric	NOUN
ejpam-6953	277	19	on	on	ADP
ejpam-6953	277	20	a	a	DET
ejpam-6953	277	21	real	real	ADJ
ejpam-6953	277	22	4	4	NUM
ejpam-6953	277	23	-	-	PUNCT
ejpam-6953	277	24	dimensional	dimensional	ADJ
ejpam-6953	277	25	lie	lie	NOUN
ejpam-6953	277	26	group	group	NOUN
ejpam-6953	277	27	(	(	PUNCT
ejpam-6953	277	28	such	such	ADJ
ejpam-6953	277	29	as	as	ADP
ejpam-6953	277	30	the	the	DET
ejpam-6953	277	31	borel	borel	PROPN
ejpam-6953	277	32	group	group	NOUN
ejpam-6953	277	33	in	in	ADP
ejpam-6953	277	34	example	example	NOUN
ejpam-6953	277	35	6.2	6.2	NUM
ejpam-6953	277	36	)	)	PUNCT
ejpam-6953	277	37	.	.	PUNCT
ejpam-6953	278	1	references	reference	NOUN
ejpam-6953	278	2	[	[	X
ejpam-6953	278	3	1	1	NUM
ejpam-6953	278	4	]	]	X
ejpam-6953	278	5	takeo	takeo	PROPN
ejpam-6953	278	6	ohsawa	ohsawa	PROPN
ejpam-6953	278	7	and	and	CCONJ
ejpam-6953	278	8	kensho	kensho	PROPN
ejpam-6953	278	9	takegoshi	takegoshi	PROPN
ejpam-6953	278	10	.	.	PUNCT
ejpam-6953	279	1	on	on	ADP
ejpam-6953	279	2	the	the	DET
ejpam-6953	279	3	extension	extension	NOUN
ejpam-6953	279	4	of	of	ADP
ejpam-6953	279	5	l2	l2	NOUN
ejpam-6953	279	6	holomorphic	holomorphic	ADJ
ejpam-6953	279	7	functions	function	NOUN
ejpam-6953	279	8	.	.	PUNCT
ejpam-6953	280	1	mathematische	mathematische	PROPN
ejpam-6953	280	2	zeitschrift	zeitschrift	PROPN
ejpam-6953	280	3	,	,	PUNCT
ejpam-6953	280	4	195(2):197–204	195(2):197–204	NUM
ejpam-6953	280	5	,	,	PUNCT
ejpam-6953	280	6	1987	1987	NUM
ejpam-6953	280	7	.	.	PUNCT
ejpam-6953	281	1	[	[	X
ejpam-6953	281	2	2	2	X
ejpam-6953	281	3	]	]	PUNCT
ejpam-6953	281	4	bo	bo	NOUN
ejpam-6953	281	5	berndtsson	berndtsson	PROPN
ejpam-6953	281	6	and	and	CCONJ
ejpam-6953	281	7	lászló	lászló	PROPN
ejpam-6953	281	8	lempert	lempert	X
ejpam-6953	281	9	.	.	PUNCT
ejpam-6953	282	1	a	a	DET
ejpam-6953	282	2	proof	proof	NOUN
ejpam-6953	282	3	of	of	ADP
ejpam-6953	282	4	the	the	DET
ejpam-6953	282	5	ohsawa	ohsawa	PROPN
ejpam-6953	282	6	–	–	PUNCT
ejpam-6953	282	7	takegoshi	takegoshi	PROPN
ejpam-6953	282	8	theorem	theorem	VERB
ejpam-6953	282	9	with	with	ADP
ejpam-6953	282	10	sharp	sharp	ADJ
ejpam-6953	282	11	estimates	estimate	NOUN
ejpam-6953	282	12	.	.	PUNCT
ejpam-6953	283	1	journal	journal	NOUN
ejpam-6953	283	2	of	of	ADP
ejpam-6953	283	3	the	the	DET
ejpam-6953	283	4	mathematical	mathematical	ADJ
ejpam-6953	283	5	society	society	NOUN
ejpam-6953	283	6	of	of	ADP
ejpam-6953	283	7	japan	japan	PROPN
ejpam-6953	283	8	,	,	PUNCT
ejpam-6953	283	9	68(4):1461–1472	68(4):1461–1472	NUM
ejpam-6953	283	10	,	,	PUNCT
ejpam-6953	283	11	2016	2016	NUM
ejpam-6953	283	12	.	.	PUNCT
ejpam-6953	284	1	[	[	X
ejpam-6953	284	2	3	3	X
ejpam-6953	284	3	]	]	PUNCT
ejpam-6953	284	4	qi’an	qi’an	PROPN
ejpam-6953	284	5	guan	guan	PROPN
ejpam-6953	284	6	and	and	CCONJ
ejpam-6953	284	7	xiangyu	xiangyu	VERB
ejpam-6953	284	8	zhou	zhou	PROPN
ejpam-6953	284	9	.	.	PUNCT
ejpam-6953	285	1	a	a	DET
ejpam-6953	285	2	solution	solution	NOUN
ejpam-6953	285	3	of	of	ADP
ejpam-6953	285	4	an	an	DET
ejpam-6953	285	5	l2	l2	NOUN
ejpam-6953	285	6	extension	extension	NOUN
ejpam-6953	285	7	problem	problem	NOUN
ejpam-6953	285	8	with	with	ADP
ejpam-6953	285	9	an	an	DET
ejpam-6953	285	10	optimal	optimal	ADJ
ejpam-6953	285	11	estimate	estimate	NOUN
ejpam-6953	285	12	and	and	CCONJ
ejpam-6953	285	13	applications	application	NOUN
ejpam-6953	285	14	.	.	PUNCT
ejpam-6953	286	1	annals	annal	NOUN
ejpam-6953	286	2	of	of	ADP
ejpam-6953	286	3	mathematics	mathematic	NOUN
ejpam-6953	286	4	,	,	PUNCT
ejpam-6953	286	5	181(3):1139–1208	181(3):1139–1208	NUM
ejpam-6953	286	6	,	,	PUNCT
ejpam-6953	286	7	2015	2015	NUM
ejpam-6953	286	8	.	.	PUNCT
ejpam-6953	287	1	[	[	X
ejpam-6953	287	2	4	4	X
ejpam-6953	287	3	]	]	PUNCT
ejpam-6953	287	4	qi’an	qi’an	PROPN
ejpam-6953	287	5	guan	guan	PROPN
ejpam-6953	287	6	and	and	CCONJ
ejpam-6953	287	7	xiangyu	xiangyu	VERB
ejpam-6953	287	8	zhou	zhou	PROPN
ejpam-6953	287	9	.	.	PUNCT
ejpam-6953	288	1	optimal	optimal	ADJ
ejpam-6953	288	2	constant	constant	ADJ
ejpam-6953	288	3	in	in	ADP
ejpam-6953	288	4	an	an	DET
ejpam-6953	288	5	l2	l2	NOUN
ejpam-6953	288	6	extension	extension	NOUN
ejpam-6953	288	7	problem	problem	NOUN
ejpam-6953	288	8	and	and	CCONJ
ejpam-6953	288	9	a	a	DET
ejpam-6953	288	10	proof	proof	NOUN
ejpam-6953	288	11	of	of	ADP
ejpam-6953	288	12	a	a	DET
ejpam-6953	288	13	conjecture	conjecture	NOUN
ejpam-6953	288	14	of	of	ADP
ejpam-6953	288	15	ohsawa	ohsawa	PROPN
ejpam-6953	288	16	.	.	PUNCT
ejpam-6953	289	1	science	science	PROPN
ejpam-6953	289	2	china	china	PROPN
ejpam-6953	289	3	mathematics	mathematics	PROPN
ejpam-6953	289	4	,	,	PUNCT
ejpam-6953	289	5	58(1):35–59	58(1):35–59	NUM
ejpam-6953	289	6	,	,	PUNCT
ejpam-6953	289	7	2015	2015	NUM
ejpam-6953	289	8	.	.	PUNCT
ejpam-6953	290	1	a.	a.	PROPN
ejpam-6953	290	2	r.	r.	PROPN
ejpam-6953	290	3	al	al	PROPN
ejpam-6953	290	4	-	-	PUNCT
ejpam-6953	290	5	abdallah	abdallah	PROPN
ejpam-6953	290	6	/	/	SYM
ejpam-6953	290	7	eur	eur	PROPN
ejpam-6953	290	8	.	.	PUNCT
ejpam-6953	291	1	j.	j.	PROPN
ejpam-6953	291	2	pure	pure	PROPN
ejpam-6953	291	3	appl	appl	PROPN
ejpam-6953	291	4	.	.	PROPN
ejpam-6953	291	5	math	math	PROPN
ejpam-6953	291	6	,	,	PUNCT
ejpam-6953	291	7	18	18	NUM
ejpam-6953	291	8	(	(	PUNCT
ejpam-6953	291	9	4	4	NUM
ejpam-6953	291	10	)	)	PUNCT
ejpam-6953	291	11	(	(	PUNCT
ejpam-6953	291	12	2025	2025	NUM
ejpam-6953	291	13	)	)	PUNCT
ejpam-6953	291	14	,	,	PUNCT
ejpam-6953	291	15	6953	6953	NUM
ejpam-6953	291	16	13	13	NUM
ejpam-6953	291	17	of	of	ADP
ejpam-6953	291	18	14	14	NUM
ejpam-6953	292	1	[	[	SYM
ejpam-6953	292	2	5	5	NUM
ejpam-6953	292	3	]	]	PUNCT
ejpam-6953	292	4	harold	harold	PROPN
ejpam-6953	292	5	donnelly	donnelly	PROPN
ejpam-6953	292	6	and	and	CCONJ
ejpam-6953	292	7	charles	charles	PROPN
ejpam-6953	292	8	fefferman	fefferman	PROPN
ejpam-6953	292	9	.	.	PUNCT
ejpam-6953	293	1	l2	l2	NOUN
ejpam-6953	293	2	-	-	PUNCT
ejpam-6953	293	3	cohomology	cohomology	NOUN
ejpam-6953	293	4	and	and	CCONJ
ejpam-6953	293	5	index	index	NOUN
ejpam-6953	293	6	theorem	theorem	NOUN
ejpam-6953	293	7	for	for	ADP
ejpam-6953	293	8	the	the	DET
ejpam-6953	293	9	bergman	bergman	PROPN
ejpam-6953	293	10	metric	metric	PROPN
ejpam-6953	293	11	.	.	PUNCT
ejpam-6953	294	1	annals	annal	NOUN
ejpam-6953	294	2	of	of	ADP
ejpam-6953	294	3	mathematics	mathematic	NOUN
ejpam-6953	294	4	,	,	PUNCT
ejpam-6953	294	5	118(3):593–618	118(3):593–618	NUM
ejpam-6953	294	6	,	,	PUNCT
ejpam-6953	294	7	1983	1983	NUM
ejpam-6953	294	8	.	.	PUNCT
ejpam-6953	295	1	[	[	X
ejpam-6953	295	2	6	6	NUM
ejpam-6953	295	3	]	]	PUNCT
ejpam-6953	295	4	alan	alan	PROPN
ejpam-6953	295	5	t.	t.	PROPN
ejpam-6953	295	6	huckleberry	huckleberry	PROPN
ejpam-6953	295	7	.	.	PUNCT
ejpam-6953	296	1	actions	action	NOUN
ejpam-6953	296	2	of	of	ADP
ejpam-6953	296	3	groups	group	NOUN
ejpam-6953	296	4	of	of	ADP
ejpam-6953	296	5	holomorphic	holomorphic	ADJ
ejpam-6953	296	6	transformations	transformation	NOUN
ejpam-6953	296	7	.	.	PUNCT
ejpam-6953	297	1	in	in	ADP
ejpam-6953	297	2	wolf	wolf	PROPN
ejpam-6953	297	3	barth	barth	NOUN
ejpam-6953	297	4	and	and	CCONJ
ejpam-6953	297	5	raghavan	raghavan	PROPN
ejpam-6953	297	6	narasimhan	narasimhan	PROPN
ejpam-6953	297	7	,	,	PUNCT
ejpam-6953	297	8	editors	editor	NOUN
ejpam-6953	297	9	,	,	PUNCT
ejpam-6953	297	10	several	several	ADJ
ejpam-6953	297	11	complex	complex	ADJ
ejpam-6953	297	12	variables	variable	NOUN
ejpam-6953	297	13	vi	vi	NOUN
ejpam-6953	297	14	,	,	PUNCT
ejpam-6953	297	15	volume	volume	NOUN
ejpam-6953	297	16	69	69	NUM
ejpam-6953	297	17	of	of	ADP
ejpam-6953	297	18	encyclopaedia	encyclopaedia	NOUN
ejpam-6953	297	19	of	of	ADP
ejpam-6953	297	20	mathematical	mathematical	ADJ
ejpam-6953	297	21	sciences	science	NOUN
ejpam-6953	297	22	,	,	PUNCT
ejpam-6953	297	23	pages	page	NOUN
ejpam-6953	297	24	143–196	143–196	NUM
ejpam-6953	297	25	.	.	PUNCT
ejpam-6953	298	1	springer	springer	NOUN
ejpam-6953	298	2	,	,	PUNCT
ejpam-6953	298	3	berlin	berlin	PROPN
ejpam-6953	298	4	,	,	PUNCT
ejpam-6953	298	5	heidelberg	heidelberg	NOUN
ejpam-6953	298	6	,	,	PUNCT
ejpam-6953	298	7	1991	1991	NUM
ejpam-6953	298	8	.	.	PUNCT
ejpam-6953	299	1	[	[	X
ejpam-6953	299	2	7	7	NUM
ejpam-6953	299	3	]	]	SYM
ejpam-6953	299	4	yozô	yozô	NOUN
ejpam-6953	299	5	matsushima	matsushima	PROPN
ejpam-6953	299	6	.	.	PUNCT
ejpam-6953	300	1	sur	sur	PROPN
ejpam-6953	300	2	la	la	PROPN
ejpam-6953	300	3	structure	structure	PROPN
ejpam-6953	300	4	du	du	PROPN
ejpam-6953	300	5	groupe	groupe	PROPN
ejpam-6953	300	6	d’homéomorphismes	d’homéomorphismes	PROPN
ejpam-6953	300	7	analytiques	analytique	NOUN
ejpam-6953	300	8	d’une	d’une	VERB
ejpam-6953	300	9	certaine	certaine	PROPN
ejpam-6953	300	10	variété	variété	PROPN
ejpam-6953	300	11	kählérienne	kählérienne	PROPN
ejpam-6953	300	12	.	.	PUNCT
ejpam-6953	301	1	nagoya	nagoya	PROPN
ejpam-6953	301	2	mathematical	mathematical	PROPN
ejpam-6953	301	3	journal	journal	PROPN
ejpam-6953	301	4	,	,	PUNCT
ejpam-6953	301	5	11(2):145–150	11(2):145–150	PROPN
ejpam-6953	301	6	,	,	PUNCT
ejpam-6953	301	7	1957	1957	NUM
ejpam-6953	301	8	.	.	PUNCT
ejpam-6953	302	1	[	[	X
ejpam-6953	302	2	8	8	NUM
ejpam-6953	302	3	]	]	X
ejpam-6953	302	4	dmitri	dmitri	PROPN
ejpam-6953	302	5	n.	n.	PROPN
ejpam-6953	302	6	akhiezer	akhiezer	PROPN
ejpam-6953	302	7	.	.	PUNCT
ejpam-6953	303	1	homogeneous	homogeneous	ADJ
ejpam-6953	303	2	complex	complex	ADJ
ejpam-6953	303	3	manifolds	manifold	NOUN
ejpam-6953	303	4	.	.	PUNCT
ejpam-6953	304	1	in	in	ADP
ejpam-6953	304	2	s.	s.	PROPN
ejpam-6953	304	3	g.	g.	PROPN
ejpam-6953	304	4	gindikin	gindikin	PROPN
ejpam-6953	304	5	and	and	CCONJ
ejpam-6953	304	6	g.	g.	PROPN
ejpam-6953	304	7	m.	m.	PROPN
ejpam-6953	304	8	khenkin	khenkin	PROPN
ejpam-6953	304	9	,	,	PUNCT
ejpam-6953	304	10	editors	editor	NOUN
ejpam-6953	304	11	,	,	PUNCT
ejpam-6953	304	12	several	several	ADJ
ejpam-6953	304	13	complex	complex	ADJ
ejpam-6953	304	14	variables	variable	NOUN
ejpam-6953	304	15	iv	iv	NUM
ejpam-6953	304	16	,	,	PUNCT
ejpam-6953	304	17	volume	volume	NOUN
ejpam-6953	304	18	10	10	NUM
ejpam-6953	304	19	of	of	ADP
ejpam-6953	304	20	encyclopaedia	encyclopaedia	NOUN
ejpam-6953	304	21	of	of	ADP
ejpam-6953	304	22	mathematical	mathematical	ADJ
ejpam-6953	304	23	sciences	science	NOUN
ejpam-6953	304	24	,	,	PUNCT
ejpam-6953	304	25	pages	page	NOUN
ejpam-6953	304	26	195–244	195–244	NUM
ejpam-6953	304	27	.	.	PUNCT
ejpam-6953	305	1	springer	springer	NOUN
ejpam-6953	305	2	,	,	PUNCT
ejpam-6953	305	3	berlin	berlin	PROPN
ejpam-6953	305	4	,	,	PUNCT
ejpam-6953	305	5	heidelberg	heidelberg	NOUN
ejpam-6953	305	6	,	,	PUNCT
ejpam-6953	305	7	1990	1990	NUM
ejpam-6953	305	8	.	.	PUNCT
ejpam-6953	306	1	[	[	X
ejpam-6953	306	2	9	9	NUM
ejpam-6953	306	3	]	]	PUNCT
ejpam-6953	306	4	alan	alan	PROPN
ejpam-6953	306	5	t.	t.	PROPN
ejpam-6953	306	6	huckleberry	huckleberry	PROPN
ejpam-6953	306	7	and	and	CCONJ
ejpam-6953	306	8	daniel	daniel	PROPN
ejpam-6953	306	9	snow	snow	PROPN
ejpam-6953	306	10	.	.	PUNCT
ejpam-6953	307	1	a	a	DET
ejpam-6953	307	2	classification	classification	NOUN
ejpam-6953	307	3	of	of	ADP
ejpam-6953	307	4	strictly	strictly	ADV
ejpam-6953	307	5	pseudoconcave	pseudoconcave	VERB
ejpam-6953	307	6	homogeneous	homogeneous	ADJ
ejpam-6953	307	7	manifolds	manifold	NOUN
ejpam-6953	307	8	.	.	PUNCT
ejpam-6953	308	1	annali	annali	PROPN
ejpam-6953	308	2	della	della	PROPN
ejpam-6953	308	3	scuola	scuola	PROPN
ejpam-6953	308	4	normale	normale	PROPN
ejpam-6953	308	5	superiore	superiore	PROPN
ejpam-6953	308	6	di	di	PROPN
ejpam-6953	308	7	pisa	pisa	PROPN
ejpam-6953	308	8	—	—	PUNCT
ejpam-6953	308	9	classe	classe	PROPN
ejpam-6953	308	10	di	di	PROPN
ejpam-6953	308	11	scienze	scienze	PROPN
ejpam-6953	308	12	,	,	PUNCT
ejpam-6953	308	13	8(2):231–255	8(2):231–255	NUM
ejpam-6953	308	14	,	,	PUNCT
ejpam-6953	308	15	1981	1981	NUM
ejpam-6953	308	16	.	.	PUNCT
ejpam-6953	309	1	dedicated	dedicate	VERB
ejpam-6953	309	2	to	to	ADP
ejpam-6953	309	3	the	the	DET
ejpam-6953	309	4	memory	memory	NOUN
ejpam-6953	309	5	of	of	ADP
ejpam-6953	309	6	aldo	aldo	PROPN
ejpam-6953	309	7	andreotti	andreotti	PROPN
ejpam-6953	309	8	.	.	PUNCT
ejpam-6953	310	1	[	[	X
ejpam-6953	310	2	10	10	NUM
ejpam-6953	310	3	]	]	X
ejpam-6953	310	4	hideaki	hideaki	PROPN
ejpam-6953	310	5	kazama	kazama	PROPN
ejpam-6953	310	6	.	.	PUNCT
ejpam-6953	311	1	on	on	ADP
ejpam-6953	311	2	pseudoconvexity	pseudoconvexity	NOUN
ejpam-6953	311	3	of	of	ADP
ejpam-6953	311	4	complex	complex	ADJ
ejpam-6953	311	5	abelian	abelian	ADJ
ejpam-6953	311	6	lie	lie	NOUN
ejpam-6953	311	7	groups	group	NOUN
ejpam-6953	311	8	.	.	PUNCT
ejpam-6953	312	1	journal	journal	NOUN
ejpam-6953	312	2	of	of	ADP
ejpam-6953	312	3	the	the	DET
ejpam-6953	312	4	mathematical	mathematical	ADJ
ejpam-6953	312	5	society	society	NOUN
ejpam-6953	312	6	of	of	ADP
ejpam-6953	312	7	japan	japan	PROPN
ejpam-6953	312	8	,	,	PUNCT
ejpam-6953	312	9	25(2):329–333	25(2):329–333	NUM
ejpam-6953	312	10	,	,	PUNCT
ejpam-6953	312	11	1973	1973	NUM
ejpam-6953	312	12	.	.	PUNCT
ejpam-6953	313	1	[	[	X
ejpam-6953	313	2	11	11	NUM
ejpam-6953	313	3	]	]	X
ejpam-6953	313	4	juha	juha	PROPN
ejpam-6953	313	5	heinonen	heinonen	PROPN
ejpam-6953	313	6	.	.	PUNCT
ejpam-6953	314	1	lectures	lecture	NOUN
ejpam-6953	314	2	on	on	ADP
ejpam-6953	314	3	analysis	analysis	NOUN
ejpam-6953	314	4	on	on	ADP
ejpam-6953	314	5	metric	metric	ADJ
ejpam-6953	314	6	spaces	space	NOUN
ejpam-6953	314	7	.	.	PUNCT
ejpam-6953	315	1	universitext	universitext	PROPN
ejpam-6953	315	2	.	.	PUNCT
ejpam-6953	315	3	springer	springer	PROPN
ejpam-6953	315	4	,	,	PUNCT
ejpam-6953	315	5	new	new	PROPN
ejpam-6953	315	6	york	york	PROPN
ejpam-6953	315	7	,	,	PUNCT
ejpam-6953	315	8	2001	2001	NUM
ejpam-6953	315	9	.	.	PUNCT
ejpam-6953	316	1	[	[	X
ejpam-6953	316	2	12	12	NUM
ejpam-6953	316	3	]	]	X
ejpam-6953	316	4	antonio	antonio	PROPN
ejpam-6953	317	1	córdoba	córdoba	PROPN
ejpam-6953	317	2	.	.	PROPN
ejpam-6953	318	1	on	on	ADP
ejpam-6953	318	2	the	the	DET
ejpam-6953	318	3	vitali	vitali	PROPN
ejpam-6953	318	4	covering	cover	VERB
ejpam-6953	318	5	properties	property	NOUN
ejpam-6953	318	6	of	of	ADP
ejpam-6953	318	7	a	a	DET
ejpam-6953	318	8	differentiation	differentiation	NOUN
ejpam-6953	318	9	basis	basis	NOUN
ejpam-6953	318	10	.	.	PUNCT
ejpam-6953	319	1	studia	studia	PROPN
ejpam-6953	319	2	mathematica	mathematica	PROPN
ejpam-6953	319	3	,	,	PUNCT
ejpam-6953	319	4	57(1):91–95	57(1):91–95	NUM
ejpam-6953	319	5	,	,	PUNCT
ejpam-6953	319	6	1976	1976	NUM
ejpam-6953	319	7	.	.	PUNCT
ejpam-6953	320	1	[	[	X
ejpam-6953	320	2	13	13	NUM
ejpam-6953	320	3	]	]	PUNCT
ejpam-6953	320	4	j.	j.	PROPN
ejpam-6953	320	5	m.	m.	PROPN
ejpam-6953	320	6	aldaz	aldaz	PROPN
ejpam-6953	320	7	.	.	PUNCT
ejpam-6953	321	1	besicovitch	besicovitch	VERB
ejpam-6953	321	2	and	and	CCONJ
ejpam-6953	321	3	doubling	double	VERB
ejpam-6953	321	4	type	type	NOUN
ejpam-6953	321	5	properties	property	NOUN
ejpam-6953	321	6	in	in	ADP
ejpam-6953	321	7	metric	metric	ADJ
ejpam-6953	321	8	spaces	space	NOUN
ejpam-6953	321	9	.	.	PUNCT
ejpam-6953	322	1	hokkaido	hokkaido	PROPN
ejpam-6953	322	2	mathematical	mathematical	PROPN
ejpam-6953	322	3	journal	journal	PROPN
ejpam-6953	322	4	,	,	PUNCT
ejpam-6953	322	5	52(2):267–283	52(2):267–283	PROPN
ejpam-6953	322	6	,	,	PUNCT
ejpam-6953	322	7	2023	2023	NUM
ejpam-6953	322	8	.	.	PUNCT
ejpam-6953	323	1	[	[	X
ejpam-6953	323	2	14	14	NUM
ejpam-6953	323	3	]	]	PUNCT
ejpam-6953	323	4	rolf	rolf	PROPN
ejpam-6953	323	5	richberg	richberg	PROPN
ejpam-6953	323	6	.	.	PUNCT
ejpam-6953	324	1	stetige	stetige	PROPN
ejpam-6953	324	2	streng	streng	PROPN
ejpam-6953	324	3	pseudokonvexe	pseudokonvexe	PROPN
ejpam-6953	324	4	funktionen	funktionen	PROPN
ejpam-6953	324	5	.	.	PUNCT
ejpam-6953	325	1	mathematische	mathematische	PROPN
ejpam-6953	325	2	annalen	annalen	PROPN
ejpam-6953	325	3	,	,	PUNCT
ejpam-6953	325	4	175(4):257–286	175(4):257–286	NUM
ejpam-6953	325	5	,	,	PUNCT
ejpam-6953	325	6	1967	1967	NUM
ejpam-6953	325	7	.	.	PUNCT
ejpam-6953	326	1	[	[	X
ejpam-6953	326	2	15	15	NUM
ejpam-6953	326	3	]	]	X
ejpam-6953	326	4	jean	jean	NOUN
ejpam-6953	326	5	-	-	PUNCT
ejpam-6953	326	6	pierre	pierre	PROPN
ejpam-6953	326	7	demailly	demailly	NOUN
ejpam-6953	326	8	.	.	PUNCT
ejpam-6953	327	1	regularization	regularization	NOUN
ejpam-6953	327	2	of	of	ADP
ejpam-6953	327	3	closed	closed	ADJ
ejpam-6953	327	4	positive	positive	ADJ
ejpam-6953	327	5	currents	current	NOUN
ejpam-6953	327	6	of	of	ADP
ejpam-6953	327	7	type	type	NOUN
ejpam-6953	327	8	(	(	PUNCT
ejpam-6953	327	9	1,1	1,1	NUM
ejpam-6953	327	10	)	)	PUNCT
ejpam-6953	327	11	by	by	ADP
ejpam-6953	327	12	the	the	DET
ejpam-6953	327	13	flow	flow	NOUN
ejpam-6953	327	14	of	of	ADP
ejpam-6953	327	15	a	a	DET
ejpam-6953	327	16	chern	chern	NOUN
ejpam-6953	327	17	connection	connection	NOUN
ejpam-6953	327	18	.	.	PUNCT
ejpam-6953	328	1	in	in	ADP
ejpam-6953	328	2	henri	henri	PROPN
ejpam-6953	328	3	skoda	skoda	PROPN
ejpam-6953	328	4	and	and	CCONJ
ejpam-6953	328	5	jean	jean	PROPN
ejpam-6953	328	6	-	-	PUNCT
ejpam-6953	328	7	marie	marie	PROPN
ejpam-6953	328	8	trépreau	trépreau	PROPN
ejpam-6953	328	9	,	,	PUNCT
ejpam-6953	328	10	editors	editor	NOUN
ejpam-6953	328	11	,	,	PUNCT
ejpam-6953	328	12	contributions	contribution	NOUN
ejpam-6953	328	13	to	to	ADP
ejpam-6953	328	14	complex	complex	ADJ
ejpam-6953	328	15	analysis	analysis	NOUN
ejpam-6953	328	16	and	and	CCONJ
ejpam-6953	328	17	analytic	analytic	ADJ
ejpam-6953	328	18	geometry	geometry	NOUN
ejpam-6953	328	19	,	,	PUNCT
ejpam-6953	328	20	volume	volume	NOUN
ejpam-6953	328	21	e	e	PROPN
ejpam-6953	328	22	26	26	NUM
ejpam-6953	328	23	of	of	ADP
ejpam-6953	328	24	aspects	aspect	NOUN
ejpam-6953	328	25	of	of	ADP
ejpam-6953	328	26	mathematics	mathematic	NOUN
ejpam-6953	328	27	,	,	PUNCT
ejpam-6953	328	28	pages	page	NOUN
ejpam-6953	328	29	105–126	105–126	NUM
ejpam-6953	328	30	.	.	PUNCT
ejpam-6953	329	1	vieweg+teubner	vieweg+teubner	PROPN
ejpam-6953	329	2	verlag	verlag	PROPN
ejpam-6953	329	3	,	,	PUNCT
ejpam-6953	329	4	wiesbaden	wiesbaden	PROPN
ejpam-6953	329	5	,	,	PUNCT
ejpam-6953	329	6	1994	1994	NUM
ejpam-6953	329	7	.	.	PUNCT
ejpam-6953	330	1	[	[	X
ejpam-6953	330	2	16	16	NUM
ejpam-6953	330	3	]	]	X
ejpam-6953	330	4	jean	jean	PROPN
ejpam-6953	330	5	-	-	PUNCT
ejpam-6953	330	6	pierre	pierre	PROPN
ejpam-6953	330	7	demailly	demailly	NOUN
ejpam-6953	330	8	.	.	PUNCT
ejpam-6953	331	1	complex	complex	ADJ
ejpam-6953	331	2	analytic	analytic	ADJ
ejpam-6953	331	3	and	and	CCONJ
ejpam-6953	331	4	differential	differential	ADJ
ejpam-6953	331	5	geometry	geometry	NOUN
ejpam-6953	331	6	.	.	PUNCT
ejpam-6953	332	1	2012	2012	NUM
ejpam-6953	332	2	.	.	PUNCT
ejpam-6953	333	1	opencontent	opencontent	PROPN
ejpam-6953	333	2	book	book	NOUN
ejpam-6953	333	3	.	.	PUNCT
ejpam-6953	334	1	[	[	X
ejpam-6953	334	2	17	17	NUM
ejpam-6953	334	3	]	]	X
ejpam-6953	334	4	zbigniew	zbigniew	PROPN
ejpam-6953	334	5	b	b	X
ejpam-6953	334	6	locki	locki	PROPN
ejpam-6953	334	7	and	and	CCONJ
ejpam-6953	334	8	s	s	PRON
ejpam-6953	334	9	lawomir	lawomir	NOUN
ejpam-6953	334	10	ko	ko	PROPN
ejpam-6953	334	11	lodziej	lodziej	PROPN
ejpam-6953	334	12	.	.	PUNCT
ejpam-6953	335	1	on	on	ADP
ejpam-6953	335	2	regularization	regularization	NOUN
ejpam-6953	335	3	of	of	ADP
ejpam-6953	335	4	plurisubharmonic	plurisubharmonic	ADJ
ejpam-6953	335	5	functions	function	NOUN
ejpam-6953	335	6	on	on	ADP
ejpam-6953	335	7	manifolds	manifold	NOUN
ejpam-6953	335	8	.	.	PUNCT
ejpam-6953	336	1	proceedings	proceeding	NOUN
ejpam-6953	336	2	of	of	ADP
ejpam-6953	336	3	the	the	DET
ejpam-6953	336	4	american	american	PROPN
ejpam-6953	336	5	mathematical	mathematical	PROPN
ejpam-6953	336	6	society	society	NOUN
ejpam-6953	336	7	,	,	PUNCT
ejpam-6953	336	8	135(7):2089	135(7):2089	PROPN
ejpam-6953	336	9	–	–	PUNCT
ejpam-6953	336	10	2093	2093	NUM
ejpam-6953	336	11	,	,	PUNCT
ejpam-6953	336	12	2007	2007	NUM
ejpam-6953	336	13	.	.	PUNCT
ejpam-6953	337	1	[	[	X
ejpam-6953	337	2	18	18	NUM
ejpam-6953	337	3	]	]	PUNCT
ejpam-6953	337	4	lars	lars	PROPN
ejpam-6953	337	5	hörmander	hörmander	PROPN
ejpam-6953	337	6	.	.	PUNCT
ejpam-6953	338	1	l2	l2	NOUN
ejpam-6953	338	2	estimates	estimate	NOUN
ejpam-6953	338	3	and	and	CCONJ
ejpam-6953	338	4	existence	existence	NOUN
ejpam-6953	338	5	theorems	theorem	VERB
ejpam-6953	338	6	for	for	ADP
ejpam-6953	338	7	the	the	DET
ejpam-6953	338	8	∂̄	∂̄	ADJ
ejpam-6953	338	9	operator	operator	NOUN
ejpam-6953	338	10	.	.	PUNCT
ejpam-6953	339	1	acta	acta	PROPN
ejpam-6953	339	2	mathematica	mathematica	PROPN
ejpam-6953	339	3	,	,	PUNCT
ejpam-6953	339	4	113:89–152	113:89–152	NUM
ejpam-6953	339	5	,	,	PUNCT
ejpam-6953	339	6	1965	1965	NUM
ejpam-6953	339	7	.	.	PUNCT
ejpam-6953	340	1	[	[	X
ejpam-6953	340	2	19	19	NUM
ejpam-6953	340	3	]	]	X
ejpam-6953	340	4	aldo	aldo	PROPN
ejpam-6953	340	5	andreotti	andreotti	PROPN
ejpam-6953	340	6	and	and	CCONJ
ejpam-6953	340	7	edoardo	edoardo	PROPN
ejpam-6953	340	8	vesentini	vesentini	PROPN
ejpam-6953	340	9	.	.	PUNCT
ejpam-6953	341	1	erratum	erratum	PROPN
ejpam-6953	341	2	:	:	PUNCT
ejpam-6953	341	3	carleman	carleman	ADJ
ejpam-6953	341	4	estimates	estimate	NOUN
ejpam-6953	341	5	for	for	ADP
ejpam-6953	341	6	the	the	DET
ejpam-6953	341	7	laplace	laplace	NOUN
ejpam-6953	341	8	–	–	PUNCT
ejpam-6953	341	9	beltrami	beltrami	ADJ
ejpam-6953	341	10	equation	equation	NOUN
ejpam-6953	341	11	on	on	ADP
ejpam-6953	341	12	complex	complex	ADJ
ejpam-6953	341	13	manifolds	manifold	NOUN
ejpam-6953	341	14	.	.	PUNCT
ejpam-6953	342	1	publications	publication	NOUN
ejpam-6953	342	2	mathématiques	mathématiques	PROPN
ejpam-6953	342	3	de	de	X
ejpam-6953	342	4	l’ihés	l’ihés	PROPN
ejpam-6953	342	5	,	,	PUNCT
ejpam-6953	342	6	27:153–155	27:153–155	NUM
ejpam-6953	342	7	,	,	PUNCT
ejpam-6953	342	8	1965	1965	NUM
ejpam-6953	342	9	.	.	PUNCT
ejpam-6953	343	1	[	[	X
ejpam-6953	343	2	20	20	NUM
ejpam-6953	343	3	]	]	PUNCT
ejpam-6953	343	4	stanis	stanis	PROPN
ejpam-6953	343	5	law	law	PROPN
ejpam-6953	343	6	mazur	mazur	PROPN
ejpam-6953	343	7	.	.	PUNCT
ejpam-6953	343	8	über	über	PROPN
ejpam-6953	343	9	konvexe	konvexe	PROPN
ejpam-6953	343	10	mengen	mengen	VERB
ejpam-6953	343	11	in	in	ADP
ejpam-6953	343	12	linearen	linearen	NOUN
ejpam-6953	343	13	normierten	normierten	ADJ
ejpam-6953	343	14	räumen	räuman	NOUN
ejpam-6953	343	15	.	.	PUNCT
ejpam-6953	344	1	studia	studia	PROPN
ejpam-6953	344	2	mathematica	mathematica	PROPN
ejpam-6953	344	3	,	,	PUNCT
ejpam-6953	344	4	4(1):70–84	4(1):70–84	NUM
ejpam-6953	344	5	,	,	PUNCT
ejpam-6953	344	6	1933	1933	NUM
ejpam-6953	344	7	.	.	PUNCT
ejpam-6953	345	1	[	[	X
ejpam-6953	345	2	21	21	NUM
ejpam-6953	345	3	]	]	X
ejpam-6953	345	4	wael	wael	PROPN
ejpam-6953	345	5	w.	w.	PROPN
ejpam-6953	345	6	mohammed	mohammed	PROPN
ejpam-6953	345	7	,	,	PUNCT
ejpam-6953	345	8	farah	farah	PROPN
ejpam-6953	345	9	m.	m.	PROPN
ejpam-6953	345	10	al	al	PROPN
ejpam-6953	345	11	-	-	PUNCT
ejpam-6953	345	12	askar	askar	ADJ
ejpam-6953	345	13	,	,	PUNCT
ejpam-6953	345	14	and	and	CCONJ
ejpam-6953	345	15	clemente	clemente	PROPN
ejpam-6953	345	16	cesarano	cesarano	PROPN
ejpam-6953	345	17	.	.	PUNCT
ejpam-6953	346	1	the	the	DET
ejpam-6953	346	2	analytical	analytical	ADJ
ejpam-6953	346	3	solutions	solution	NOUN
ejpam-6953	346	4	of	of	ADP
ejpam-6953	346	5	the	the	DET
ejpam-6953	346	6	stochastic	stochastic	ADJ
ejpam-6953	346	7	mkdv	mkdv	NOUN
ejpam-6953	346	8	equation	equation	NOUN
ejpam-6953	346	9	via	via	ADP
ejpam-6953	346	10	the	the	DET
ejpam-6953	346	11	mapping	mapping	NOUN
ejpam-6953	346	12	method	method	NOUN
ejpam-6953	346	13	.	.	PUNCT
ejpam-6953	347	1	mathematics	mathematic	NOUN
ejpam-6953	347	2	,	,	PUNCT
ejpam-6953	347	3	10(22):4212	10(22):4212	NUM
ejpam-6953	347	4	,	,	PUNCT
ejpam-6953	347	5	2022	2022	NUM
ejpam-6953	347	6	.	.	PUNCT
ejpam-6953	348	1	a.	a.	PROPN
ejpam-6953	348	2	r.	r.	PROPN
ejpam-6953	348	3	al	al	PROPN
ejpam-6953	348	4	-	-	PUNCT
ejpam-6953	348	5	abdallah	abdallah	PROPN
ejpam-6953	348	6	/	/	SYM
ejpam-6953	348	7	eur	eur	PROPN
ejpam-6953	348	8	.	.	PUNCT
ejpam-6953	349	1	j.	j.	PROPN
ejpam-6953	349	2	pure	pure	PROPN
ejpam-6953	349	3	appl	appl	PROPN
ejpam-6953	349	4	.	.	PROPN
ejpam-6953	349	5	math	math	PROPN
ejpam-6953	349	6	,	,	PUNCT
ejpam-6953	349	7	18	18	NUM
ejpam-6953	349	8	(	(	PUNCT
ejpam-6953	349	9	4	4	NUM
ejpam-6953	349	10	)	)	PUNCT
ejpam-6953	349	11	(	(	PUNCT
ejpam-6953	349	12	2025	2025	NUM
ejpam-6953	349	13	)	)	PUNCT
ejpam-6953	349	14	,	,	PUNCT
ejpam-6953	349	15	6953	6953	NUM
ejpam-6953	349	16	14	14	NUM
ejpam-6953	349	17	of	of	ADP
ejpam-6953	349	18	14	14	NUM
ejpam-6953	349	19	[	[	SYM
ejpam-6953	349	20	22	22	NUM
ejpam-6953	349	21	]	]	PUNCT
ejpam-6953	349	22	farah	farah	PROPN
ejpam-6953	349	23	m.	m.	PROPN
ejpam-6953	349	24	al	al	PROPN
ejpam-6953	349	25	-	-	PUNCT
ejpam-6953	349	26	askar	askar	PROPN
ejpam-6953	349	27	,	,	PUNCT
ejpam-6953	349	28	clemente	clemente	PROPN
ejpam-6953	349	29	cesarano	cesarano	PROPN
ejpam-6953	349	30	,	,	PUNCT
ejpam-6953	349	31	and	and	CCONJ
ejpam-6953	349	32	wael	wael	PROPN
ejpam-6953	349	33	w.	w.	PROPN
ejpam-6953	349	34	mohammed	mohammed	PROPN
ejpam-6953	349	35	.	.	PUNCT
ejpam-6953	350	1	multiplicative	multiplicative	PROPN
ejpam-6953	350	2	brownian	brownian	ADJ
ejpam-6953	350	3	motion	motion	NOUN
ejpam-6953	350	4	stabilizes	stabilize	VERB
ejpam-6953	350	5	the	the	DET
ejpam-6953	350	6	exact	exact	ADJ
ejpam-6953	350	7	stochastic	stochastic	ADJ
ejpam-6953	350	8	solutions	solution	NOUN
ejpam-6953	350	9	of	of	ADP
ejpam-6953	350	10	the	the	DET
ejpam-6953	350	11	davey	davey	NOUN
ejpam-6953	350	12	–	–	PUNCT
ejpam-6953	350	13	stewartson	stewartson	NOUN
ejpam-6953	350	14	equations	equation	NOUN
ejpam-6953	350	15	.	.	PUNCT
ejpam-6953	351	1	symmetry	symmetry	PROPN
ejpam-6953	351	2	,	,	PUNCT
ejpam-6953	351	3	14(10):2176	14(10):2176	NUM
ejpam-6953	351	4	,	,	PUNCT
ejpam-6953	351	5	2022	2022	NUM
ejpam-6953	351	6	.	.	PUNCT
ejpam-6953	352	1	[	[	X
ejpam-6953	352	2	23	23	NUM
ejpam-6953	352	3	]	]	PUNCT
ejpam-6953	352	4	farah	farah	PROPN
ejpam-6953	352	5	m.	m.	PROPN
ejpam-6953	352	6	al	al	PROPN
ejpam-6953	352	7	-	-	PUNCT
ejpam-6953	352	8	askar	askar	PROPN
ejpam-6953	352	9	,	,	PUNCT
ejpam-6953	352	10	clemente	clemente	PROPN
ejpam-6953	352	11	cesarano	cesarano	PROPN
ejpam-6953	352	12	,	,	PUNCT
ejpam-6953	352	13	and	and	CCONJ
ejpam-6953	352	14	wael	wael	PROPN
ejpam-6953	352	15	w.	w.	PROPN
ejpam-6953	352	16	mohammed	mohammed	PROPN
ejpam-6953	352	17	.	.	PUNCT
ejpam-6953	353	1	the	the	DET
ejpam-6953	353	2	analytical	analytical	ADJ
ejpam-6953	353	3	solutions	solution	NOUN
ejpam-6953	353	4	of	of	ADP
ejpam-6953	353	5	stochastic	stochastic	ADJ
ejpam-6953	353	6	–	–	PUNCT
ejpam-6953	353	7	fractional	fractional	ADJ
ejpam-6953	353	8	drinfel’d	drinfel’d	NOUN
ejpam-6953	353	9	–	–	PUNCT
ejpam-6953	353	10	sokolov	sokolov	NOUN
ejpam-6953	353	11	–	–	PUNCT
ejpam-6953	353	12	wilson	wilson	PROPN
ejpam-6953	353	13	equations	equation	NOUN
ejpam-6953	353	14	via	via	ADP
ejpam-6953	353	15	g′/g	g′/g	NOUN
ejpam-6953	353	16	-	-	PUNCT
ejpam-6953	353	17	expansion	expansion	NOUN
ejpam-6953	353	18	method	method	NOUN
ejpam-6953	353	19	.	.	PUNCT
ejpam-6953	354	1	symmetry	symmetry	NOUN
ejpam-6953	354	2	,	,	PUNCT
ejpam-6953	354	3	14(10):2105	14(10):2105	NUM
ejpam-6953	354	4	,	,	PUNCT
ejpam-6953	354	5	2022	2022	NUM
ejpam-6953	354	6	.	.	PUNCT
ejpam-6953	355	1	[	[	X
ejpam-6953	355	2	24	24	NUM
ejpam-6953	355	3	]	]	PUNCT
ejpam-6953	355	4	bo	bo	PROPN
ejpam-6953	355	5	berndtsson	berndtsson	PROPN
ejpam-6953	355	6	.	.	PUNCT
ejpam-6953	356	1	an	an	DET
ejpam-6953	356	2	introduction	introduction	NOUN
ejpam-6953	356	3	to	to	ADP
ejpam-6953	356	4	things	thing	NOUN
ejpam-6953	356	5	∂̄.	∂̄.	PUNCT
ejpam-6953	356	6	in	in	ADP
ejpam-6953	356	7	jeffery	jeffery	PROPN
ejpam-6953	356	8	d.	d.	PROPN
ejpam-6953	356	9	mcneal	mcneal	PROPN
ejpam-6953	356	10	and	and	CCONJ
ejpam-6953	356	11	mircea	mircea	PROPN
ejpam-6953	356	12	mustaţă	mustaţă	PROPN
ejpam-6953	356	13	,	,	PUNCT
ejpam-6953	356	14	editors	editor	NOUN
ejpam-6953	356	15	,	,	PUNCT
ejpam-6953	356	16	analytic	analytic	ADJ
ejpam-6953	356	17	and	and	CCONJ
ejpam-6953	356	18	algebraic	algebraic	ADJ
ejpam-6953	356	19	geometry	geometry	NOUN
ejpam-6953	356	20	,	,	PUNCT
ejpam-6953	356	21	volume	volume	NOUN
ejpam-6953	356	22	17	17	NUM
ejpam-6953	356	23	of	of	ADP
ejpam-6953	356	24	ias	ias	PROPN
ejpam-6953	356	25	/	/	SYM
ejpam-6953	356	26	park	park	NOUN
ejpam-6953	356	27	city	city	NOUN
ejpam-6953	356	28	mathematics	mathematics	PROPN
ejpam-6953	356	29	series	series	PROPN
ejpam-6953	356	30	,	,	PUNCT
ejpam-6953	356	31	pages	page	VERB
ejpam-6953	356	32	7–76	7–76	PROPN
ejpam-6953	356	33	.	.	PUNCT
ejpam-6953	357	1	american	american	PROPN
ejpam-6953	357	2	mathematical	mathematical	PROPN
ejpam-6953	357	3	society	society	NOUN
ejpam-6953	357	4	,	,	PUNCT
ejpam-6953	357	5	providence	providence	NOUN
ejpam-6953	357	6	,	,	PUNCT
ejpam-6953	357	7	ri	ri	PROPN
ejpam-6953	357	8	,	,	PUNCT
ejpam-6953	357	9	2010	2010	NUM
ejpam-6953	357	10	.	.	PUNCT
ejpam-6953	358	1	lecture	lecture	NOUN
ejpam-6953	358	2	notes	note	NOUN
ejpam-6953	358	3	,	,	PUNCT
ejpam-6953	358	4	pcmi	pcmi	NOUN
ejpam-6953	358	5	2008	2008	NUM
ejpam-6953	358	6	.	.	PUNCT
ejpam-6953	359	1	[	[	X
ejpam-6953	359	2	25	25	NUM
ejpam-6953	359	3	]	]	PUNCT
ejpam-6953	359	4	haim	haim	NOUN
ejpam-6953	359	5	brezis	brezis	NOUN
ejpam-6953	359	6	.	.	PUNCT
ejpam-6953	360	1	functional	functional	ADJ
ejpam-6953	360	2	analysis	analysis	NOUN
ejpam-6953	360	3	,	,	PUNCT
ejpam-6953	360	4	sobolev	sobolev	NOUN
ejpam-6953	360	5	spaces	space	NOUN
ejpam-6953	360	6	and	and	CCONJ
ejpam-6953	360	7	partial	partial	ADJ
ejpam-6953	360	8	differential	differential	ADJ
ejpam-6953	360	9	equations	equation	NOUN
ejpam-6953	360	10	.	.	PUNCT
ejpam-6953	361	1	universitext	universitext	PROPN
ejpam-6953	361	2	.	.	PUNCT
ejpam-6953	361	3	springer	springer	PROPN
ejpam-6953	361	4	,	,	PUNCT
ejpam-6953	361	5	new	new	PROPN
ejpam-6953	361	6	york	york	PROPN
ejpam-6953	361	7	,	,	PUNCT
ejpam-6953	361	8	2011	2011	NUM
ejpam-6953	361	9	.	.	PUNCT