id	sid	tid	token	lemma	pos
ma-265	1	1	2025	2025	NUM
ma-265	1	2	ada	ada	PROPN
ma-265	1	3	academica	academica	PROPN
ma-265	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-265	1	5	.	.	PUNCT
ma-265	2	1	j.	j.	PROPN
ma-265	2	2	math	math	PROPN
ma-265	2	3	.	.	PUNCT
ma-265	3	1	anal	anal	ADJ
ma-265	3	2	.	.	PUNCT
ma-265	4	1	5	5	NUM
ma-265	4	2	(	(	PUNCT
ma-265	4	3	2025	2025	NUM
ma-265	4	4	)	)	PUNCT
ma-265	5	1	4doi	4doi	NOUN
ma-265	5	2	:	:	PUNCT
ma-265	5	3	10.28924	10.28924	NUM
ma-265	5	4	/	/	SYM
ma-265	5	5	ada	ada	PROPN
ma-265	5	6	/	/	SYM
ma-265	5	7	ma.5.4	ma.5.4	PROPN
ma-265	5	8	correspondences	correspondence	NOUN
ma-265	5	9	among	among	ADP
ma-265	5	10	inner	inner	ADJ
ma-265	5	11	functions	function	NOUN
ma-265	5	12	,	,	PUNCT
ma-265	5	13	functions	function	NOUN
ma-265	5	14	with	with	ADP
ma-265	5	15	non	non	ADJ
ma-265	5	16	-	-	ADJ
ma-265	5	17	negative	negative	ADJ
ma-265	5	18	real	real	ADJ
ma-265	5	19	parts	part	NOUN
ma-265	5	20	and	and	CCONJ
ma-265	5	21	conformal	conformal	NOUN
ma-265	5	22	mappings	mapping	NOUN
ma-265	5	23	ronen	ronen	PROPN
ma-265	5	24	peretz	peretz	PROPN
ma-265	5	25	department	department	PROPN
ma-265	5	26	of	of	ADP
ma-265	5	27	mathematics	mathematics	PROPN
ma-265	5	28	,	,	PUNCT
ma-265	5	29	ben	ben	PROPN
ma-265	5	30	gurion	gurion	PROPN
ma-265	5	31	university	university	PROPN
ma-265	5	32	of	of	ADP
ma-265	5	33	the	the	DET
ma-265	5	34	negev	negev	NOUN
ma-265	5	35	,	,	PUNCT
ma-265	5	36	beer	beer	NOUN
ma-265	5	37	-	-	PUNCT
ma-265	5	38	sheva	sheva	PROPN
ma-265	5	39	,	,	PUNCT
ma-265	5	40	84105	84105	NUM
ma-265	5	41	,	,	PUNCT
ma-265	5	42	israelmensahyaogan2@gmailcom	israelmensahyaogan2@gmailcom	ADJ
ma-265	5	43	abstract	abstract	ADV
ma-265	5	44	.	.	PUNCT
ma-265	6	1	we	we	PRON
ma-265	6	2	study	study	VERB
ma-265	6	3	an	an	DET
ma-265	6	4	interesting	interesting	ADJ
ma-265	6	5	family	family	NOUN
ma-265	6	6	of	of	ADP
ma-265	6	7	dynamical	dynamical	ADJ
ma-265	6	8	systems	system	NOUN
ma-265	6	9	on	on	ADP
ma-265	6	10	the	the	DET
ma-265	6	11	set	set	NOUN
ma-265	6	12	of	of	ADP
ma-265	6	13	the	the	DET
ma-265	6	14	singular	singular	ADJ
ma-265	6	15	innerfunctions	innerfunction	NOUN
ma-265	6	16	(	(	PUNCT
ma-265	6	17	defined	define	VERB
ma-265	6	18	on	on	ADP
ma-265	6	19	the	the	DET
ma-265	6	20	unit	unit	NOUN
ma-265	6	21	disk	disk	NOUN
ma-265	6	22	)	)	PUNCT
ma-265	6	23	.	.	PUNCT
ma-265	7	1	starting	start	VERB
ma-265	7	2	with	with	ADP
ma-265	7	3	an	an	DET
ma-265	7	4	inner	inner	ADJ
ma-265	7	5	function	function	NOUN
ma-265	7	6	s0(z	s0(z	NOUN
ma-265	7	7	)	)	PUNCT
ma-265	7	8	,	,	PUNCT
ma-265	7	9	we	we	PRON
ma-265	7	10	obtain	obtain	VERB
ma-265	7	11	new	new	ADJ
ma-265	7	12	singularinner	singularinner	NOUN
ma-265	7	13	functions	function	NOUN
ma-265	7	14	s1(z	s1(z	NOUN
ma-265	7	15	)	)	PUNCT
ma-265	7	16	,	,	PUNCT
ma-265	7	17	s2(z	s2(z	NUM
ma-265	7	18	)	)	PUNCT
ma-265	7	19	,	,	PUNCT
ma-265	7	20	.	.	PUNCT
ma-265	7	21	.	.	PUNCT
ma-265	8	1	..	..	PUNCT
ma-265	9	1	this	this	DET
ma-265	9	2	sequence	sequence	NOUN
ma-265	9	3	converges	converge	VERB
ma-265	9	4	to	to	ADP
ma-265	9	5	a	a	DET
ma-265	9	6	holomorphic	holomorphic	ADJ
ma-265	9	7	self	self	NOUN
ma-265	9	8	-	-	PUNCT
ma-265	9	9	map	map	NOUN
ma-265	9	10	of	of	ADP
ma-265	9	11	the	the	DET
ma-265	9	12	unit	unit	NOUN
ma-265	9	13	diskwhich	diskwhich	NOUN
ma-265	9	14	we	we	PRON
ma-265	9	15	call	call	VERB
ma-265	9	16	s.	s.	PROPN
ma-265	9	17	the	the	DET
ma-265	9	18	convergence	convergence	NOUN
ma-265	9	19	is	be	AUX
ma-265	9	20	proved	prove	VERB
ma-265	9	21	with	with	ADP
ma-265	9	22	the	the	DET
ma-265	9	23	aid	aid	NOUN
ma-265	9	24	of	of	ADP
ma-265	9	25	a	a	DET
ma-265	9	26	fixed	fix	VERB
ma-265	9	27	-	-	PUNCT
ma-265	9	28	point	point	NOUN
ma-265	9	29	theorem	theorem	VERB
ma-265	9	30	,	,	PUNCT
ma-265	9	31	a	a	DET
ma-265	9	32	special	special	ADJ
ma-265	9	33	caseof	caseof	NOUN
ma-265	9	34	the	the	DET
ma-265	9	35	earle	earle	PROPN
ma-265	9	36	-	-	PUNCT
ma-265	9	37	hamilton	hamilton	PROPN
ma-265	9	38	theorem	theorem	PROPN
ma-265	9	39	.	.	PUNCT
ma-265	10	1	the	the	DET
ma-265	10	2	function	function	NOUN
ma-265	10	3	s	s	PRON
ma-265	10	4	itself	itself	PRON
ma-265	10	5	is	be	AUX
ma-265	10	6	not	not	PART
ma-265	10	7	a	a	DET
ma-265	10	8	singular	singular	ADJ
ma-265	10	9	inner	inner	ADJ
ma-265	10	10	function	function	NOUN
ma-265	10	11	as	as	ADP
ma-265	10	12	zs(z	zs(z	NUM
ma-265	10	13	)	)	PUNCT
ma-265	10	14	isa	isa	NOUN
ma-265	10	15	conformal	conformal	NOUN
ma-265	10	16	map	map	NOUN
ma-265	10	17	.	.	PUNCT
ma-265	11	1	this	this	DET
ma-265	11	2	conformal	conformal	NOUN
ma-265	11	3	map	map	NOUN
ma-265	11	4	has	have	VERB
ma-265	11	5	the	the	DET
ma-265	11	6	surprising	surprising	ADJ
ma-265	11	7	property	property	NOUN
ma-265	11	8	that	that	PRON
ma-265	11	9	its	its	PRON
ma-265	11	10	inverse	inverse	NOUN
ma-265	11	11	(	(	PUNCT
ma-265	11	12	which	which	PRON
ma-265	11	13	is	be	AUX
ma-265	11	14	a	a	DET
ma-265	11	15	prioridefined	prioridefine	VERB
ma-265	11	16	on	on	ADP
ma-265	11	17	a	a	DET
ma-265	11	18	proper	proper	ADJ
ma-265	11	19	subset	subset	NOUN
ma-265	11	20	of	of	ADP
ma-265	11	21	the	the	DET
ma-265	11	22	disk	disk	NOUN
ma-265	11	23	)	)	PUNCT
ma-265	11	24	extends	extend	VERB
ma-265	11	25	to	to	ADP
ma-265	11	26	the	the	DET
ma-265	11	27	entire	entire	ADJ
ma-265	11	28	disk	disk	NOUN
ma-265	11	29	.	.	PUNCT
ma-265	12	1	the	the	DET
ma-265	12	2	motivating	motivating	NOUN
ma-265	12	3	question	question	NOUN
ma-265	12	4	for	for	ADP
ma-265	12	5	thisresearch	thisresearch	NOUN
ma-265	12	6	is	be	AUX
ma-265	12	7	whether	whether	SCONJ
ma-265	12	8	z	z	PROPN
ma-265	12	9	times	time	VERB
ma-265	12	10	a	a	DET
ma-265	12	11	singular	singular	ADJ
ma-265	12	12	inner	inner	ADJ
ma-265	12	13	function	function	NOUN
ma-265	12	14	can	can	AUX
ma-265	12	15	have	have	VERB
ma-265	12	16	an	an	DET
ma-265	12	17	omitted	omit	VERB
ma-265	12	18	value	value	NOUN
ma-265	12	19	in	in	ADP
ma-265	12	20	the	the	DET
ma-265	12	21	unit	unit	NOUN
ma-265	12	22	disk	disk	NOUN
ma-265	12	23	.	.	PUNCT
ma-265	13	1	thisquestion	thisquestion	PROPN
ma-265	13	2	appears	appear	VERB
ma-265	13	3	within	within	ADP
ma-265	13	4	a	a	DET
ma-265	13	5	book	book	NOUN
ma-265	13	6	on	on	ADP
ma-265	13	7	the	the	DET
ma-265	13	8	krzyz	krzyz	PROPN
ma-265	13	9	problem	problem	NOUN
ma-265	13	10	written	write	VERB
ma-265	13	11	by	by	ADP
ma-265	13	12	the	the	DET
ma-265	13	13	author	author	NOUN
ma-265	13	14	.	.	PUNCT
ma-265	14	1	this	this	DET
ma-265	14	2	question	question	NOUN
ma-265	14	3	is	be	AUX
ma-265	14	4	stillopen	stillopen	ADJ
ma-265	14	5	.	.	PUNCT
ma-265	15	1	1	1	X
ma-265	15	2	.	.	X
ma-265	15	3	correspondences	correspondence	NOUN
ma-265	15	4	that	that	PRON
ma-265	15	5	involve	involve	VERB
ma-265	15	6	inner	inner	ADJ
ma-265	15	7	functions	function	NOUN
ma-265	15	8	let	let	VERB
ma-265	15	9	us	we	PRON
ma-265	15	10	recall	recall	VERB
ma-265	15	11	few	few	ADJ
ma-265	15	12	correspondences	correspondence	NOUN
ma-265	15	13	that	that	PRON
ma-265	15	14	involve	involve	VERB
ma-265	15	15	inner	inner	ADJ
ma-265	15	16	functions	function	NOUN
ma-265	15	17	in	in	ADP
ma-265	15	18	h2(u	h2(u	PROPN
ma-265	15	19	)	)	PUNCT
ma-265	15	20	.	.	PUNCT
ma-265	16	1	we	we	PRON
ma-265	16	2	denote	denote	VERB
ma-265	16	3	the	the	DET
ma-265	16	4	unitdisk	unitdisk	NOUN
ma-265	16	5	in	in	ADP
ma-265	16	6	c	c	PROPN
ma-265	16	7	by	by	ADP
ma-265	16	8	u	u	PRON
ma-265	16	9	.	.	PUNCT
ma-265	17	1	we	we	PRON
ma-265	17	2	will	will	AUX
ma-265	17	3	denote	denote	VERB
ma-265	17	4	the	the	DET
ma-265	17	5	(	(	PUNCT
ma-265	17	6	multiplicative	multiplicative	ADJ
ma-265	17	7	)	)	PUNCT
ma-265	17	8	group	group	NOUN
ma-265	17	9	of	of	ADP
ma-265	17	10	inner	inner	ADJ
ma-265	17	11	functions	function	NOUN
ma-265	17	12	in	in	ADP
ma-265	17	13	h∞(u	h∞(u	NOUN
ma-265	17	14	)	)	PUNCT
ma-265	17	15	by	by	ADP
ma-265	17	16	inn.its	inn.it	NOUN
ma-265	17	17	subgroup	subgroup	NOUN
ma-265	17	18	which	which	PRON
ma-265	17	19	contains	contain	VERB
ma-265	17	20	all	all	DET
ma-265	17	21	the	the	DET
ma-265	17	22	singular	singular	ADJ
ma-265	17	23	inner	inner	ADJ
ma-265	17	24	functions	function	NOUN
ma-265	17	25	will	will	AUX
ma-265	17	26	be	be	AUX
ma-265	17	27	denoted	denote	VERB
ma-265	17	28	by	by	ADP
ma-265	17	29	sinn	sinn	PROPN
ma-265	17	30	.	.	PUNCT
ma-265	18	1	we	we	PRON
ma-265	18	2	followthe	followthe	VERB
ma-265	18	3	notations	notation	NOUN
ma-265	18	4	in	in	ADP
ma-265	18	5	,	,	PUNCT
ma-265	18	6	[	[	X
ma-265	18	7	2	2	NUM
ma-265	18	8	]	]	PUNCT
ma-265	18	9	.	.	PUNCT
ma-265	19	1	finally	finally	ADV
ma-265	19	2	,	,	PUNCT
ma-265	19	3	the	the	DET
ma-265	19	4	(	(	PUNCT
ma-265	19	5	additive	additive	NOUN
ma-265	19	6	)	)	PUNCT
ma-265	19	7	group	group	NOUN
ma-265	19	8	of	of	ADP
ma-265	19	9	holomorphic	holomorphic	ADJ
ma-265	19	10	functions	function	NOUN
ma-265	19	11	in	in	ADP
ma-265	19	12	u	u	NOUN
ma-265	19	13	which	which	PRON
ma-265	19	14	have	have	VERB
ma-265	19	15	non	non	ADJ
ma-265	19	16	-	-	ADJ
ma-265	19	17	negative	negative	ADJ
ma-265	19	18	real	real	ADJ
ma-265	19	19	parts	part	NOUN
ma-265	19	20	and	and	CCONJ
ma-265	19	21	which	which	PRON
ma-265	19	22	have	have	VERB
ma-265	19	23	finite	finite	ADJ
ma-265	19	24	radial	radial	ADJ
ma-265	19	25	limits	limit	NOUN
ma-265	19	26	almost	almost	ADV
ma-265	19	27	everywhere	everywhere	ADV
ma-265	19	28	on	on	ADP
ma-265	19	29	t	t	PROPN
ma-265	19	30	which	which	PRON
ma-265	19	31	are	be	AUX
ma-265	19	32	purelyimaginary	purelyimaginary	ADJ
ma-265	19	33	will	will	AUX
ma-265	19	34	be	be	AUX
ma-265	19	35	denoted	denote	VERB
ma-265	19	36	by	by	ADP
ma-265	19	37	rp	rp	NOUN
ma-265	19	38	.	.	PUNCT
ma-265	20	1	later	later	ADV
ma-265	20	2	on	on	ADV
ma-265	20	3	we	we	PRON
ma-265	20	4	will	will	AUX
ma-265	20	5	add	add	VERB
ma-265	20	6	one	one	NUM
ma-265	20	7	condition	condition	NOUN
ma-265	20	8	to	to	ADP
ma-265	20	9	this	this	DET
ma-265	20	10	definition	definition	NOUN
ma-265	20	11	of	of	ADP
ma-265	20	12	rp	rp	NOUN
ma-265	20	13	butfor	butfor	ADP
ma-265	20	14	now	now	ADV
ma-265	20	15	this	this	DET
ma-265	20	16	definition	definition	NOUN
ma-265	20	17	suffices	suffice	VERB
ma-265	20	18	.	.	PUNCT
ma-265	21	1	here	here	ADV
ma-265	21	2	are	be	AUX
ma-265	21	3	a	a	DET
ma-265	21	4	few	few	ADJ
ma-265	21	5	elementary	elementary	ADJ
ma-265	21	6	facts	fact	NOUN
ma-265	21	7	that	that	PRON
ma-265	21	8	are	be	AUX
ma-265	21	9	well	well	ADV
ma-265	21	10	known:(1	known:(1	PROPN
ma-265	21	11	)	)	PUNCT
ma-265	21	12	f	f	PROPN
ma-265	21	13	∈	∈	PROPN
ma-265	21	14	rp	rp	PROPN
ma-265	21	15	⇔	⇔	PROPN
ma-265	21	16	∃w	∃w	PROPN
ma-265	21	17	∈	∈	PROPN
ma-265	21	18	inn	inn	PROPN
ma-265	21	19	such	such	ADJ
ma-265	21	20	that	that	SCONJ
ma-265	21	21	f	f	PROPN
ma-265	21	22	=	=	SYM
ma-265	21	23	1+w	1+w	NUM
ma-265	21	24	1−w	1−w	NUM
ma-265	21	25	.this	.this	PRON
ma-265	21	26	is	be	AUX
ma-265	21	27	a	a	DET
ma-265	21	28	bijection	bijection	NOUN
ma-265	21	29	since	since	SCONJ
ma-265	21	30	f	f	PROPN
ma-265	21	31	=	=	SYM
ma-265	21	32	1	1	NUM
ma-265	21	33	+	+	CCONJ
ma-265	21	34	w	w	PROPN
ma-265	21	35	1−	1−	NUM
ma-265	21	36	w	w	PROPN
ma-265	21	37	⇔	⇔	PROPN
ma-265	21	38	f	f	X
ma-265	21	39	·	·	PUNCT
ma-265	21	40	(	(	PUNCT
ma-265	21	41	1−	1−	NUM
ma-265	21	42	w	w	NOUN
ma-265	21	43	)	)	PUNCT
ma-265	21	44	=	=	SYM
ma-265	22	1	1	1	NUM
ma-265	22	2	+	+	NUM
ma-265	22	3	w	w	PROPN
ma-265	22	4	⇔	⇔	PROPN
ma-265	22	5	w	w	PROPN
ma-265	22	6	·	·	PUNCT
ma-265	22	7	(	(	PUNCT
ma-265	22	8	f	f	X
ma-265	22	9	+	+	CCONJ
ma-265	22	10	1	1	X
ma-265	22	11	)	)	PUNCT
ma-265	22	12	=	=	SYM
ma-265	23	1	f	f	PROPN
ma-265	24	1	−	−	PROPN
ma-265	24	2	1⇔	1⇔	PROPN
ma-265	25	1	w	w	PROPN
ma-265	25	2	=	=	SYM
ma-265	25	3	f	f	PROPN
ma-265	26	1	−	−	PROPN
ma-265	26	2	1	1	NUM
ma-265	26	3	f	f	NOUN
ma-265	26	4	+	+	CCONJ
ma-265	26	5	1	1	NUM
ma-265	26	6	.	.	PUNCT
ma-265	27	1	(	(	PUNCT
ma-265	27	2	2	2	X
ma-265	27	3	)	)	PUNCT
ma-265	27	4	g	g	PROPN
ma-265	27	5	∈	∈	PROPN
ma-265	27	6	sinn⇔	sinn⇔	X
ma-265	28	1	∃	∃	PROPN
ma-265	28	2	f	f	PROPN
ma-265	28	3	∈	∈	PROPN
ma-265	28	4	rp	rp	NOUN
ma-265	28	5	such	such	ADJ
ma-265	28	6	that	that	PRON
ma-265	28	7	g	g	NOUN
ma-265	28	8	=	=	SYM
ma-265	28	9	exp(−f	exp(−f	PROPN
ma-265	28	10	)	)	PUNCT
ma-265	28	11	.the	.the	PRON
ma-265	29	1	correspondence	correspondence	NOUN
ma-265	29	2	rp→	rp→	CCONJ
ma-265	29	3	sinn	sinn	PROPN
ma-265	29	4	,	,	PUNCT
ma-265	29	5	f	f	PROPN
ma-265	29	6	→	→	SYM
ma-265	29	7	g	g	PROPN
ma-265	29	8	is	be	AUX
ma-265	29	9	not	not	PART
ma-265	29	10	one	one	NUM
ma-265	29	11	-	-	PUNCT
ma-265	29	12	to	to	ADP
ma-265	29	13	-	-	PUNCT
ma-265	29	14	one	one	NUM
ma-265	29	15	.	.	PUNCT
ma-265	30	1	the	the	DET
ma-265	30	2	kernel	kernel	NOUN
ma-265	30	3	is	be	AUX
ma-265	30	4	2πiz	2πiz	NOUN
ma-265	30	5	.	.	PUNCT
ma-265	31	1	received	receive	VERB
ma-265	31	2	:	:	PUNCT
ma-265	31	3	13	13	NUM
ma-265	31	4	aug	aug	PROPN
ma-265	31	5	2024	2024	NUM
ma-265	31	6	.	.	PUNCT
ma-265	32	1	key	key	ADJ
ma-265	32	2	words	word	NOUN
ma-265	32	3	and	and	CCONJ
ma-265	32	4	phrases	phrase	NOUN
ma-265	32	5	.	.	PUNCT
ma-265	33	1	singular	singular	ADJ
ma-265	33	2	inner	inner	ADJ
ma-265	33	3	functions	function	NOUN
ma-265	33	4	;	;	PUNCT
ma-265	33	5	conformal	conformal	ADJ
ma-265	33	6	mapping	mapping	NOUN
ma-265	33	7	;	;	PUNCT
ma-265	33	8	krzyz	krzyz	PROPN
ma-265	33	9	problem	problem	NOUN
ma-265	33	10	;	;	PUNCT
ma-265	33	11	complex	complex	ADJ
ma-265	33	12	dynamical	dynamical	ADJ
ma-265	33	13	system;earle	system;earle	NOUN
ma-265	33	14	-	-	PUNCT
ma-265	33	15	hamilton	hamilton	NOUN
ma-265	33	16	fixed	fix	VERB
ma-265	33	17	-	-	PUNCT
ma-265	33	18	point	point	NOUN
ma-265	33	19	theorem	theorem	VERB
ma-265	33	20	;	;	PUNCT
ma-265	33	21	löwner	löwner	NOUN
ma-265	33	22	equation	equation	NOUN
ma-265	33	23	.	.	PUNCT
ma-265	34	1	1	1	NUM
ma-265	35	1	https://adac.ee	https://adac.ee	PROPN
ma-265	35	2	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	35	3	https://orcid.org/0000-0002-6321-479x	https://orcid.org/0000-0002-6321-479x	PROPN
ma-265	35	4	eur	eur	PROPN
ma-265	35	5	.	.	PUNCT
ma-265	36	1	j.	j.	PROPN
ma-265	36	2	math	math	PROPN
ma-265	36	3	.	.	PUNCT
ma-265	37	1	anal	anal	PROPN
ma-265	37	2	.	.	PUNCT
ma-265	38	1	10.28924	10.28924	NUM
ma-265	38	2	/	/	SYM
ma-265	38	3	ada	ada	PROPN
ma-265	38	4	/	/	SYM
ma-265	38	5	ma.5.4	ma.5.4	PROPN
ma-265	38	6	2(3	2(3	NUM
ma-265	38	7	)	)	PUNCT
ma-265	38	8	g	g	PROPN
ma-265	38	9	∈	∈	PROPN
ma-265	38	10	sinn⇔	sinn⇔	VERB
ma-265	38	11	∃w	∃w	PROPN
ma-265	38	12	∈	∈	PROPN
ma-265	38	13	inn	inn	PROPN
ma-265	38	14	such	such	ADJ
ma-265	38	15	that	that	SCONJ
ma-265	38	16	g	g	PROPN
ma-265	38	17	=	=	PUNCT
ma-265	38	18	exp	exp	NOUN
ma-265	38	19	(	(	PUNCT
ma-265	38	20	−1+w1−w	−1+w1−w	NOUN
ma-265	38	21	)	)	PUNCT
ma-265	38	22	.the	.the	PRON
ma-265	39	1	correspondence	correspondence	NOUN
ma-265	39	2	inn→	inn→	PROPN
ma-265	39	3	sinn	sinn	PROPN
ma-265	39	4	,	,	PUNCT
ma-265	39	5	w	w	PROPN
ma-265	39	6	→	→	SYM
ma-265	39	7	g	g	NOUN
ma-265	39	8	is	be	AUX
ma-265	39	9	not	not	PART
ma-265	39	10	one	one	NUM
ma-265	39	11	-	-	PUNCT
ma-265	39	12	to	to	ADP
ma-265	39	13	-	-	PUNCT
ma-265	39	14	one	one	NUM
ma-265	39	15	.	.	PUNCT
ma-265	40	1	1	1	NUM
ma-265	41	1	+	+	CCONJ
ma-265	41	2	w	w	PROPN
ma-265	41	3	1−	1−	NUM
ma-265	41	4	w	w	NOUN
ma-265	42	1	+	+	CCONJ
ma-265	43	1	2πik	2πik	NUM
ma-265	43	2	=	=	SYM
ma-265	43	3	1	1	NUM
ma-265	43	4	+	+	NUM
ma-265	43	5	v	v	ADP
ma-265	43	6	1−	1−	NUM
ma-265	43	7	v	v	ADP
ma-265	43	8	⇔	⇔	PROPN
ma-265	43	9	v	v	NOUN
ma-265	43	10	=	=	PUNCT
ma-265	43	11	(	(	PUNCT
ma-265	43	12	1	1	NUM
ma-265	43	13	+	+	CCONJ
ma-265	43	14	w	w	PROPN
ma-265	43	15	1−	1−	NUM
ma-265	43	16	w	w	NOUN
ma-265	44	1	+	+	CCONJ
ma-265	45	1	2πik	2πik	NUM
ma-265	45	2	−	−	NOUN
ma-265	45	3	1	1	NUM
ma-265	45	4	)	)	PUNCT
ma-265	45	5	/	/	SYM
ma-265	45	6	(	(	PUNCT
ma-265	45	7	1	1	NUM
ma-265	46	1	+	+	CCONJ
ma-265	46	2	w	w	PROPN
ma-265	46	3	1−	1−	NUM
ma-265	46	4	w	w	NOUN
ma-265	47	1	+	+	CCONJ
ma-265	47	2	2πik	2πik	NUM
ma-265	47	3	+	+	CCONJ
ma-265	47	4	1	1	NUM
ma-265	47	5	)	)	PUNCT
ma-265	47	6	=	=	PUNCT
ma-265	48	1	=	=	PUNCT
ma-265	48	2	πik	πik	PROPN
ma-265	49	1	+	+	CCONJ
ma-265	49	2	(	(	PUNCT
ma-265	49	3	1−	1−	NUM
ma-265	49	4	πik)w	πik)w	X
ma-265	49	5	(	(	PUNCT
ma-265	49	6	1	1	NUM
ma-265	49	7	+	+	CCONJ
ma-265	49	8	πik)−	πik)−	PROPN
ma-265	49	9	πikw	πikw	NOUN
ma-265	49	10	.so	.so	PUNCT
ma-265	49	11	if	if	SCONJ
ma-265	49	12	we	we	PRON
ma-265	49	13	denote	denote	VERB
ma-265	49	14	by	by	ADP
ma-265	49	15	φk(z	φk(z	NOUN
ma-265	49	16	)	)	PUNCT
ma-265	49	17	the	the	DET
ma-265	49	18	fractional	fractional	ADJ
ma-265	49	19	linear	linear	PROPN
ma-265	49	20	function	function	NOUN
ma-265	49	21	φk(z	φk(z	NOUN
ma-265	49	22	)	)	PUNCT
ma-265	49	23	=	=	SYM
ma-265	49	24	πik	πik	PROPN
ma-265	50	1	+	+	CCONJ
ma-265	50	2	(	(	PUNCT
ma-265	50	3	1−	1−	NUM
ma-265	50	4	πik)z	πik)z	PROPN
ma-265	50	5	(	(	PUNCT
ma-265	50	6	1	1	NUM
ma-265	50	7	+	+	X
ma-265	50	8	πik)−	πik)−	PROPN
ma-265	50	9	πikzand	πikzand	NOUN
ma-265	50	10	if	if	SCONJ
ma-265	50	11	we	we	PRON
ma-265	50	12	denote	denote	VERB
ma-265	50	13	m	m	VERB
ma-265	50	14	:	:	PUNCT
ma-265	50	15	inn→	inn→	PROPN
ma-265	50	16	sinn	sinn	PROPN
ma-265	50	17	,	,	PUNCT
ma-265	50	18	m(w	m(w	NOUN
ma-265	50	19	)	)	PUNCT
ma-265	50	20	=	=	SYM
ma-265	50	21	g	g	NOUN
ma-265	50	22	where	where	SCONJ
ma-265	50	23	m(w	m(w	NOUN
ma-265	50	24	)	)	PUNCT
ma-265	50	25	=	=	SYM
ma-265	50	26	exp	exp	NOUN
ma-265	50	27	(	(	PUNCT
ma-265	50	28	−	−	PROPN
ma-265	50	29	1	1	NUM
ma-265	51	1	+	+	CCONJ
ma-265	51	2	w	w	PROPN
ma-265	51	3	1−	1−	NUM
ma-265	51	4	w	w	NOUN
ma-265	51	5	)	)	PUNCT
ma-265	51	6	,	,	PUNCT
ma-265	51	7	then	then	ADV
ma-265	51	8	m−1(g	m−1(g	PROPN
ma-265	51	9	)	)	PUNCT
ma-265	52	1	=	=	PRON
ma-265	52	2	{	{	PUNCT
ma-265	52	3	φk(w	φk(w	NOUN
ma-265	52	4	)	)	PUNCT
ma-265	53	1	|	|	ADV
ma-265	53	2	k	k	PROPN
ma-265	53	3	∈	∈	PROPN
ma-265	53	4	z	z	PROPN
ma-265	53	5	}	}	PUNCT
ma-265	53	6	.	.	PUNCT
ma-265	54	1	2	2	X
ma-265	54	2	.	.	X
ma-265	54	3	an	an	DET
ma-265	54	4	example	example	NOUN
ma-265	54	5	of	of	ADP
ma-265	54	6	our	our	PRON
ma-265	54	7	construction	construction	NOUN
ma-265	54	8	it	it	PRON
ma-265	54	9	will	will	AUX
ma-265	54	10	be	be	AUX
ma-265	54	11	convenient	convenient	ADJ
ma-265	54	12	to	to	PART
ma-265	54	13	first	first	ADV
ma-265	54	14	demonstrate	demonstrate	VERB
ma-265	54	15	the	the	DET
ma-265	54	16	construction	construction	NOUN
ma-265	54	17	on	on	ADP
ma-265	54	18	a	a	DET
ma-265	54	19	particular	particular	ADJ
ma-265	54	20	case	case	NOUN
ma-265	54	21	where	where	SCONJ
ma-265	54	22	concretecomputations	concretecomputation	NOUN
ma-265	54	23	are	be	AUX
ma-265	54	24	possible	possible	ADJ
ma-265	54	25	.	.	PUNCT
ma-265	55	1	this	this	DET
ma-265	55	2	construction	construction	NOUN
ma-265	55	3	was	be	AUX
ma-265	55	4	motivated	motivate	VERB
ma-265	55	5	by	by	ADP
ma-265	55	6	a	a	DET
ma-265	55	7	problem	problem	NOUN
ma-265	55	8	that	that	PRON
ma-265	55	9	appeared	appear	VERB
ma-265	55	10	in	in	ADP
ma-265	55	11	thebook	thebook	NOUN
ma-265	55	12	,	,	PUNCT
ma-265	55	13	[	[	X
ma-265	55	14	4	4	NUM
ma-265	55	15	]	]	PUNCT
ma-265	55	16	:	:	PUNCT
ma-265	55	17	let	let	AUX
ma-265	55	18	s(z	s(z	PROPN
ma-265	55	19	)	)	PUNCT
ma-265	55	20	be	be	AUX
ma-265	55	21	a	a	DET
ma-265	55	22	singular	singular	ADJ
ma-265	55	23	inner	inner	ADJ
ma-265	55	24	function	function	NOUN
ma-265	55	25	(	(	PUNCT
ma-265	55	26	s	s	NOUN
ma-265	55	27	∈	∈	PROPN
ma-265	55	28	sinn	sinn	PROPN
ma-265	55	29	)	)	PUNCT
ma-265	55	30	.	.	PUNCT
ma-265	56	1	is	be	AUX
ma-265	56	2	it	it	PRON
ma-265	56	3	true	true	ADJ
ma-265	56	4	that	that	SCONJ
ma-265	56	5	the	the	DET
ma-265	56	6	inner	inner	ADJ
ma-265	56	7	function	function	NOUN
ma-265	56	8	z	z	PROPN
ma-265	56	9	·	·	PUNCT
ma-265	56	10	s(z	s(z	NOUN
ma-265	56	11	)	)	PUNCT
ma-265	56	12	is	be	AUX
ma-265	56	13	a	a	DET
ma-265	56	14	surjection	surjection	NOUN
ma-265	56	15	u	u	NOUN
ma-265	56	16	→	→	SYM
ma-265	56	17	u	u	NOUN
ma-265	56	18	?	?	PUNCT
ma-265	56	19	theorem	theorem	VERB
ma-265	56	20	2.1	2.1	NUM
ma-265	56	21	.	.	PUNCT
ma-265	57	1	let	let	VERB
ma-265	57	2	{	{	PUNCT
ma-265	57	3	sn(z)}∞n=0	sn(z)}∞n=0	NUM
ma-265	57	4	be	be	AUX
ma-265	57	5	a	a	DET
ma-265	57	6	sequence	sequence	NOUN
ma-265	57	7	of	of	ADP
ma-265	57	8	singular	singular	ADJ
ma-265	57	9	inner	inner	ADJ
ma-265	57	10	functions	function	NOUN
ma-265	57	11	defined	define	VERB
ma-265	57	12	recursively	recursively	ADV
ma-265	57	13	by	by	ADP
ma-265	57	14	:	:	PUNCT
ma-265	57	15	s0	s0	PROPN
ma-265	57	16	∈	∈	PROPN
ma-265	57	17	sinn	sinn	PROPN
ma-265	57	18	(	(	PUNCT
ma-265	57	19	an	an	DET
ma-265	57	20	arbitrary	arbitrary	ADJ
ma-265	57	21	initial	initial	ADJ
ma-265	57	22	point	point	NOUN
ma-265	57	23	)	)	PUNCT
ma-265	57	24	,	,	PUNCT
ma-265	57	25	sn+1(z	sn+1(z	VERB
ma-265	57	26	)	)	PUNCT
ma-265	57	27	=	=	SYM
ma-265	57	28	exp	exp	NOUN
ma-265	57	29	(	(	PUNCT
ma-265	57	30	−	−	PROPN
ma-265	57	31	1	1	NUM
ma-265	57	32	+	+	CCONJ
ma-265	57	33	z	z	NOUN
ma-265	57	34	·	·	PUNCT
ma-265	57	35	sn(z	sn(z	NOUN
ma-265	57	36	)	)	PUNCT
ma-265	57	37	1−	1−	NUM
ma-265	57	38	z	z	NOUN
ma-265	57	39	·	·	PUNCT
ma-265	57	40	sn(z	sn(z	NOUN
ma-265	57	41	)	)	PUNCT
ma-265	57	42	)	)	PUNCT
ma-265	57	43	for	for	ADP
ma-265	57	44	n	n	PRON
ma-265	57	45	∈	∈	PROPN
ma-265	57	46	z≥0	z≥0	PROPN
ma-265	57	47	.	.	PUNCT
ma-265	58	1	then	then	ADV
ma-265	58	2	limn→∞	limn→∞	PROPN
ma-265	58	3	sn	sn	NOUN
ma-265	58	4	=	=	X
ma-265	58	5	s	s	VERB
ma-265	58	6	uniformly	uniformly	ADV
ma-265	58	7	on	on	ADP
ma-265	58	8	compact	compact	ADJ
ma-265	58	9	subsets	subset	NOUN
ma-265	58	10	of	of	ADP
ma-265	58	11	u	u	PROPN
ma-265	58	12	.	.	PUNCT
ma-265	59	1	s(z	s(z	PROPN
ma-265	59	2	)	)	PUNCT
ma-265	59	3	is	be	AUX
ma-265	59	4	in	in	ADP
ma-265	59	5	h∞(u	h∞(u	NOUN
ma-265	59	6	)	)	PUNCT
ma-265	59	7	and	and	CCONJ
ma-265	59	8	it	it	PRON
ma-265	59	9	satisfies	satisfy	VERB
ma-265	59	10	the	the	DET
ma-265	59	11	fixed	fix	VERB
ma-265	59	12	-	-	PUNCT
ma-265	59	13	point	point	NOUN
ma-265	59	14	equation	equation	NOUN
ma-265	59	15	s	s	PART
ma-265	59	16	=	=	NOUN
ma-265	59	17	exp	exp	NOUN
ma-265	59	18	(	(	PUNCT
ma-265	59	19	−	−	PROPN
ma-265	59	20	1	1	NUM
ma-265	59	21	+	+	CCONJ
ma-265	59	22	z	z	NOUN
ma-265	59	23	·	·	PUNCT
ma-265	59	24	s	s	PART
ma-265	59	25	1−	1−	NUM
ma-265	59	26	z	z	NOUN
ma-265	59	27	·	·	PUNCT
ma-265	59	28	s	s	PART
ma-265	59	29	)	)	PUNCT
ma-265	59	30	.	.	PUNCT
ma-265	60	1	also	also	ADV
ma-265	60	2	the	the	DET
ma-265	60	3	mapping	mapping	NOUN
ma-265	60	4	z	z	NOUN
ma-265	60	5	·	·	PUNCT
ma-265	60	6	s(z	s(z	NOUN
ma-265	60	7	)	)	PUNCT
ma-265	60	8	∈	∈	PROPN
ma-265	60	9	h∞(u	h∞(u	NOUN
ma-265	60	10	)	)	PUNCT
ma-265	60	11	is	be	AUX
ma-265	60	12	injective	injective	ADJ
ma-265	60	13	u	u	NOUN
ma-265	60	14	→	→	SYM
ma-265	60	15	im(z	im(z	X
ma-265	60	16	·	·	PUNCT
ma-265	60	17	s(z	s(z	NOUN
ma-265	60	18	)	)	PUNCT
ma-265	60	19	)	)	PUNCT
ma-265	61	1	⊂	⊂	PROPN
ma-265	61	2	u	u	NOUN
ma-265	61	3	but	but	CCONJ
ma-265	61	4	it	it	PRON
ma-265	61	5	can	can	AUX
ma-265	61	6	not	not	PART
ma-265	61	7	be	be	AUX
ma-265	61	8	an	an	DET
ma-265	61	9	inner	inner	ADJ
ma-265	61	10	function	function	NOUN
ma-265	61	11	.	.	PUNCT
ma-265	62	1	proof.since	proof.since	NOUN
ma-265	62	2	s0	s0	PROPN
ma-265	62	3	∈	∈	PROPN
ma-265	62	4	sinn	sinn	PROPN
ma-265	62	5	and	and	CCONJ
ma-265	62	6	since	since	SCONJ
ma-265	62	7	an	an	DET
ma-265	62	8	inductive	inductive	ADJ
ma-265	62	9	argument	argument	NOUN
ma-265	62	10	shows	show	VERB
ma-265	62	11	that	that	SCONJ
ma-265	62	12	if	if	SCONJ
ma-265	62	13	sn	sn	PROPN
ma-265	62	14	∈	∈	PROPN
ma-265	62	15	sinn	sinn	PROPN
ma-265	62	16	then	then	ADV
ma-265	62	17	sn+1	sn+1	VERB
ma-265	62	18	=	=	SYM
ma-265	62	19	exp	exp	NOUN
ma-265	62	20	(	(	PUNCT
ma-265	62	21	−	−	PROPN
ma-265	62	22	1	1	NUM
ma-265	62	23	+	+	CCONJ
ma-265	62	24	z	z	X
ma-265	62	25	·	·	PUNCT
ma-265	62	26	sn	sn	PROPN
ma-265	62	27	1−	1−	NUM
ma-265	62	28	z	z	NOUN
ma-265	62	29	·	·	PUNCT
ma-265	62	30	sn	sn	PROPN
ma-265	62	31	)	)	PUNCT
ma-265	62	32	∈	∈	PROPN
ma-265	62	33	sinn	sinn	NOUN
ma-265	62	34	for	for	ADP
ma-265	62	35	n	n	PRON
ma-265	62	36	∈	∈	PROPN
ma-265	62	37	z≥0	z≥0	NOUN
ma-265	62	38	,	,	PUNCT
ma-265	62	39	it	it	PRON
ma-265	62	40	follows	follow	VERB
ma-265	62	41	that	that	SCONJ
ma-265	62	42	the	the	DET
ma-265	62	43	sequence	sequence	NOUN
ma-265	62	44	{	{	PUNCT
ma-265	62	45	sn(z)}∞n=0	sn(z)}∞n=0	PROPN
ma-265	62	46	is	be	AUX
ma-265	62	47	a	a	DET
ma-265	62	48	sequence	sequence	NOUN
ma-265	62	49	of	of	ADP
ma-265	62	50	singular	singular	ADJ
ma-265	62	51	inner	inner	ADJ
ma-265	62	52	functions	function	NOUN
ma-265	62	53	.	.	PUNCT
ma-265	63	1	the	the	DET
ma-265	63	2	family	family	NOUN
ma-265	63	3	offunctions	offunction	NOUN
ma-265	63	4	in	in	ADP
ma-265	63	5	the	the	DET
ma-265	63	6	sequence	sequence	NOUN
ma-265	63	7	is	be	AUX
ma-265	63	8	a	a	DET
ma-265	63	9	normal	normal	ADJ
ma-265	63	10	family	family	NOUN
ma-265	63	11	.	.	PUNCT
ma-265	64	1	even	even	ADV
ma-265	64	2	more	more	ADV
ma-265	64	3	,	,	PUNCT
ma-265	64	4	for	for	ADP
ma-265	64	5	a	a	DET
ma-265	64	6	fixed	fix	VERB
ma-265	64	7	-	-	PUNCT
ma-265	64	8	point	point	NOUN
ma-265	64	9	z	z	NOUN
ma-265	64	10	∈	∈	NOUN
ma-265	64	11	u	u	NOUN
ma-265	64	12	the	the	DET
ma-265	64	13	function	function	NOUN
ma-265	64	14	of	of	ADP
ma-265	64	15	t	t	PROPN
ma-265	64	16	∈	∈	PROPN
ma-265	64	17	u	u	NOUN
ma-265	64	18	given	give	VERB
ma-265	64	19	by	by	ADP
ma-265	64	20	exp	exp	NOUN
ma-265	64	21	(	(	PUNCT
ma-265	64	22	−	−	PROPN
ma-265	64	23	1	1	NUM
ma-265	64	24	+	+	CCONJ
ma-265	64	25	z	z	X
ma-265	64	26	·	·	PUNCT
ma-265	64	27	t	t	NOUN
ma-265	64	28	1−	1−	NUM
ma-265	64	29	z	z	NOUN
ma-265	64	30	·	·	PUNCT
ma-265	64	31	t	t	PROPN
ma-265	64	32	)	)	PUNCT
ma-265	64	33	,	,	PUNCT
ma-265	64	34	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	64	35	eur	eur	PROPN
ma-265	64	36	.	.	PUNCT
ma-265	65	1	j.	j.	PROPN
ma-265	65	2	math	math	PROPN
ma-265	65	3	.	.	PUNCT
ma-265	66	1	anal	anal	PROPN
ma-265	66	2	.	.	PUNCT
ma-265	67	1	10.28924	10.28924	NUM
ma-265	67	2	/	/	SYM
ma-265	67	3	ada	ada	PROPN
ma-265	67	4	/	/	SYM
ma-265	67	5	ma.5.4	ma.5.4	PROPN
ma-265	67	6	3is	3is	PROPN
ma-265	67	7	a	a	DET
ma-265	67	8	contraction	contraction	NOUN
ma-265	67	9	and	and	CCONJ
ma-265	67	10	so	so	ADV
ma-265	67	11	by	by	ADP
ma-265	67	12	the	the	DET
ma-265	67	13	fixed	fix	VERB
ma-265	67	14	-	-	PUNCT
ma-265	67	15	point	point	NOUN
ma-265	67	16	theorem	theorem	NOUN
ma-265	67	17	of	of	ADP
ma-265	67	18	s.	s.	PROPN
ma-265	67	19	banach	banach	PROPN
ma-265	67	20	iterations	iteration	NOUN
ma-265	67	21	of	of	ADP
ma-265	67	22	this	this	DET
ma-265	67	23	contractionconverge	contractionconverge	NOUN
ma-265	67	24	to	to	ADP
ma-265	67	25	a	a	DET
ma-265	67	26	unique	unique	ADJ
ma-265	67	27	fixed	fix	VERB
ma-265	67	28	-	-	PUNCT
ma-265	67	29	point	point	NOUN
ma-265	67	30	s(z	s(z	PROPN
ma-265	67	31	)	)	PUNCT
ma-265	67	32	.	.	PUNCT
ma-265	68	1	so	so	ADV
ma-265	68	2	limn→∞	limn→∞	PROPN
ma-265	68	3	sn	sn	NOUN
ma-265	68	4	=	=	X
ma-265	68	5	s	s	AUX
ma-265	68	6	uniformly	uniformly	ADV
ma-265	68	7	on	on	ADP
ma-265	68	8	compact	compact	ADJ
ma-265	68	9	subsets	subset	NOUN
ma-265	68	10	of	of	ADP
ma-265	68	11	u	u	NOUN
ma-265	68	12	,	,	PUNCT
ma-265	68	13	and	and	CCONJ
ma-265	68	14	s(z	s(z	PROPN
ma-265	68	15	)	)	PUNCT
ma-265	68	16	satisfies	satisfy	VERB
ma-265	68	17	the	the	DET
ma-265	68	18	fixed	fix	VERB
ma-265	68	19	-	-	PUNCT
ma-265	68	20	point	point	NOUN
ma-265	68	21	equation	equation	NOUN
ma-265	68	22	s(z	s(z	PROPN
ma-265	68	23	)	)	PUNCT
ma-265	68	24	=	=	SYM
ma-265	68	25	exp	exp	NOUN
ma-265	68	26	(	(	PUNCT
ma-265	68	27	−	−	PROPN
ma-265	68	28	1	1	NUM
ma-265	68	29	+	+	CCONJ
ma-265	69	1	z	z	NOUN
ma-265	69	2	·	·	PUNCT
ma-265	69	3	s(z	s(z	NOUN
ma-265	69	4	)	)	PUNCT
ma-265	69	5	1−	1−	NUM
ma-265	69	6	z	z	NOUN
ma-265	69	7	·	·	PUNCT
ma-265	69	8	s(z	s(z	NOUN
ma-265	69	9	)	)	PUNCT
ma-265	69	10	)	)	PUNCT
ma-265	69	11	.	.	PUNCT
ma-265	70	1	clearly	clearly	ADV
ma-265	70	2	s(z	s(z	PROPN
ma-265	70	3	)	)	PUNCT
ma-265	70	4	is	be	AUX
ma-265	70	5	a	a	DET
ma-265	70	6	non	non	ADJ
ma-265	70	7	-	-	ADJ
ma-265	70	8	vanishing	vanishing	ADJ
ma-265	70	9	function	function	NOUN
ma-265	70	10	in	in	ADP
ma-265	70	11	h∞(u	h∞(u	NOUN
ma-265	70	12	)	)	PUNCT
ma-265	70	13	.	.	PUNCT
ma-265	71	1	next	next	ADV
ma-265	71	2	,	,	PUNCT
ma-265	71	3	let	let	VERB
ma-265	71	4	us	we	PRON
ma-265	71	5	consider	consider	VERB
ma-265	71	6	the	the	DET
ma-265	71	7	following	follow	VERB
ma-265	71	8	holomorphicfunction	holomorphicfunction	NOUN
ma-265	71	9	of	of	ADP
ma-265	71	10	w	w	PROPN
ma-265	71	11	,	,	PUNCT
ma-265	71	12	defined	define	VERB
ma-265	71	13	on	on	ADP
ma-265	71	14	the	the	DET
ma-265	71	15	once	once	ADV
ma-265	71	16	punctured	punctured	ADJ
ma-265	71	17	plane	plane	NOUN
ma-265	71	18	as	as	SCONJ
ma-265	71	19	follows	follow	VERB
ma-265	71	20	:	:	PUNCT
ma-265	71	21	f	f	X
ma-265	71	22	:	:	PUNCT
ma-265	71	23	c−	c−	X
ma-265	71	24	{	{	PUNCT
ma-265	71	25	1	1	NUM
ma-265	71	26	}	}	PUNCT
ma-265	71	27	→	→	SYM
ma-265	71	28	c	c	X
ma-265	71	29	,	,	PUNCT
ma-265	71	30	f(w	f(w	PROPN
ma-265	71	31	)	)	PUNCT
ma-265	71	32	=	=	SYM
ma-265	71	33	w	w	PROPN
ma-265	71	34	exp	exp	NOUN
ma-265	71	35	(	(	PUNCT
ma-265	71	36	1+w	1+w	NUM
ma-265	71	37	1−w	1−w	NUM
ma-265	71	38	)	)	PUNCT
ma-265	71	39	.	.	PUNCT
ma-265	72	1	then	then	ADV
ma-265	72	2	by	by	ADP
ma-265	72	3	the	the	DET
ma-265	72	4	fixed	fix	VERB
ma-265	72	5	-	-	PUNCT
ma-265	72	6	point	point	NOUN
ma-265	72	7	equation	equation	NOUN
ma-265	72	8	satisfied	satisfy	VERB
ma-265	72	9	by	by	ADP
ma-265	72	10	s(z	s(z	PROPN
ma-265	72	11	)	)	PUNCT
ma-265	72	12	we	we	PRON
ma-265	72	13	get	get	VERB
ma-265	72	14	f	f	PROPN
ma-265	72	15	(	(	PUNCT
ma-265	72	16	z	z	NOUN
ma-265	72	17	·	·	PUNCT
ma-265	72	18	s(z	s(z	NOUN
ma-265	72	19	)	)	PUNCT
ma-265	72	20	)	)	PUNCT
ma-265	73	1	=	=	PUNCT
ma-265	73	2	z	z	NOUN
ma-265	73	3	.	.	PUNCT
ma-265	74	1	so	so	ADV
ma-265	74	2	f	f	PROPN
ma-265	74	3	is	be	AUX
ma-265	74	4	a	a	DET
ma-265	74	5	left	left	ADJ
ma-265	74	6	inverseof	inverseof	ADJ
ma-265	74	7	z	z	NOUN
ma-265	74	8	·	·	PUNCT
ma-265	74	9	s(z	s(z	NOUN
ma-265	74	10	)	)	PUNCT
ma-265	74	11	and	and	CCONJ
ma-265	75	1	hence	hence	ADV
ma-265	75	2	z	z	NOUN
ma-265	75	3	·	·	PUNCT
ma-265	75	4	s(z	s(z	PROPN
ma-265	75	5	)	)	PUNCT
ma-265	75	6	:	:	PUNCT
ma-265	75	7	u	u	NOUN
ma-265	75	8	→	→	SYM
ma-265	75	9	im(z	im(z	X
ma-265	75	10	·	·	PUNCT
ma-265	75	11	s(z	s(z	NOUN
ma-265	75	12	)	)	PUNCT
ma-265	75	13	)	)	PUNCT
ma-265	75	14	is	be	AUX
ma-265	75	15	an	an	DET
ma-265	75	16	injection	injection	NOUN
ma-265	75	17	.	.	PUNCT
ma-265	76	1	more	more	ADV
ma-265	76	2	concretely	concretely	ADV
ma-265	76	3	,	,	PUNCT
ma-265	76	4	if	if	SCONJ
ma-265	76	5	we	we	PRON
ma-265	76	6	denote	denote	VERB
ma-265	76	7	g(z	g(z	ADJ
ma-265	76	8	)	)	PUNCT
ma-265	76	9	=	=	PUNCT
ma-265	76	10	z	z	NOUN
ma-265	76	11	·	·	PUNCT
ma-265	76	12	s(z	s(z	NOUN
ma-265	76	13	)	)	PUNCT
ma-265	76	14	then	then	ADV
ma-265	76	15	the	the	DET
ma-265	76	16	assumption	assumption	NOUN
ma-265	76	17	g(z1	g(z1	NOUN
ma-265	76	18	)	)	PUNCT
ma-265	76	19	=	=	SYM
ma-265	76	20	g(z2	g(z2	NOUN
ma-265	76	21	)	)	PUNCT
ma-265	76	22	implies	imply	VERB
ma-265	76	23	that	that	SCONJ
ma-265	76	24	z1	z1	PROPN
ma-265	76	25	=	=	SYM
ma-265	76	26	f	f	PROPN
ma-265	76	27	(	(	PUNCT
ma-265	76	28	g(z1	g(z1	NOUN
ma-265	76	29	)	)	PUNCT
ma-265	76	30	)	)	PUNCT
ma-265	77	1	=	=	SYM
ma-265	77	2	f	f	PROPN
ma-265	77	3	(	(	PUNCT
ma-265	77	4	g(z2	g(z2	NOUN
ma-265	77	5	)	)	PUNCT
ma-265	77	6	)	)	PUNCT
ma-265	78	1	=	=	SYM
ma-265	78	2	z2.since	z2.since	NOUN
ma-265	78	3	s(z	s(z	PROPN
ma-265	78	4	)	)	PUNCT
ma-265	78	5	can	can	AUX
ma-265	78	6	not	not	PART
ma-265	78	7	be	be	AUX
ma-265	78	8	a	a	DET
ma-265	78	9	constant	constant	ADJ
ma-265	78	10	function	function	NOUN
ma-265	78	11	(	(	PUNCT
ma-265	78	12	by	by	ADP
ma-265	78	13	the	the	DET
ma-265	78	14	fixed	fix	VERB
ma-265	78	15	-	-	PUNCT
ma-265	78	16	point	point	NOUN
ma-265	78	17	equation	equation	NOUN
ma-265	78	18	)	)	PUNCT
ma-265	78	19	,	,	PUNCT
ma-265	78	20	z	z	NOUN
ma-265	78	21	·	·	PUNCT
ma-265	78	22	s(z	s(z	NOUN
ma-265	78	23	)	)	PUNCT
ma-265	78	24	can	can	AUX
ma-265	78	25	not	not	PART
ma-265	78	26	be	be	AUX
ma-265	78	27	aninner	aninner	NOUN
ma-265	78	28	function	function	NOUN
ma-265	78	29	(	(	PUNCT
ma-265	78	30	see	see	VERB
ma-265	78	31	[	[	X
ma-265	78	32	3	3	NUM
ma-265	78	33	]	]	PUNCT
ma-265	78	34	,	,	PUNCT
ma-265	78	35	remarked	remark	VERB
ma-265	78	36	by	by	ADP
ma-265	78	37	raymond	raymond	PROPN
ma-265	78	38	mortini	mortini	PROPN
ma-265	78	39	)	)	PUNCT
ma-265	78	40	.	.	PUNCT
ma-265	79	1	�	�	PROPN
ma-265	79	2	3	3	NUM
ma-265	79	3	.	.	PUNCT
ma-265	80	1	a	a	DET
ma-265	80	2	generalization	generalization	NOUN
ma-265	80	3	definition	definition	NOUN
ma-265	80	4	3.1	3.1	NUM
ma-265	80	5	.	.	PUNCT
ma-265	81	1	we	we	PRON
ma-265	81	2	will	will	AUX
ma-265	81	3	denote	denote	VERB
ma-265	81	4	by	by	ADP
ma-265	81	5	rp	rp	NOUN
ma-265	81	6	,	,	PUNCT
ma-265	81	7	the	the	DET
ma-265	81	8	family	family	NOUN
ma-265	81	9	of	of	ADP
ma-265	81	10	all	all	DET
ma-265	81	11	the	the	DET
ma-265	81	12	f	f	PROPN
ma-265	81	13	∈	∈	PROPN
ma-265	81	14	h(u	h(u	PROPN
ma-265	81	15	)	)	PUNCT
ma-265	81	16	,	,	PUNCT
ma-265	81	17	that	that	PRON
ma-265	81	18	satisfy	satisfy	VERB
ma-265	81	19	the	the	DET
ma-265	81	20	followingfour	followingfour	ADJ
ma-265	81	21	conditions:(i	conditions:(i	NOUN
ma-265	81	22	)	)	PUNCT
ma-265	82	1	<	<	X
ma-265	82	2	f	f	X
ma-265	82	3	(	(	PUNCT
ma-265	82	4	z	z	NOUN
ma-265	82	5	)	)	PUNCT
ma-265	82	6	≥	≥	NOUN
ma-265	82	7	0	0	NUM
ma-265	82	8	,	,	PUNCT
ma-265	82	9	∀	∀	PUNCT
ma-265	82	10	z	z	NOUN
ma-265	82	11	∈	∈	NOUN
ma-265	82	12	u	u	NOUN
ma-265	82	13	.(ii	.(ii	PROPN
ma-265	82	14	)	)	PUNCT
ma-265	83	1	<	<	X
ma-265	83	2	f	f	X
ma-265	83	3	(	(	PUNCT
ma-265	83	4	e	e	NOUN
ma-265	83	5	iθ	iθ	NOUN
ma-265	83	6	)	)	PUNCT
ma-265	83	7	=	=	SYM
ma-265	83	8	0	0	NUM
ma-265	83	9	almost	almost	ADV
ma-265	83	10	everywhere	everywhere	ADV
ma-265	83	11	on	on	ADP
ma-265	83	12	t	t	PROPN
ma-265	83	13	with	with	ADP
ma-265	83	14	respect	respect	NOUN
ma-265	83	15	to	to	ADP
ma-265	83	16	the	the	DET
ma-265	83	17	lebesgue	lebesgue	ADJ
ma-265	83	18	measure	measure	NOUN
ma-265	83	19	on	on	ADP
ma-265	83	20	t.(iii	t.(iii	NOUN
ma-265	83	21	)	)	PUNCT
ma-265	83	22	the	the	DET
ma-265	83	23	function	function	NOUN
ma-265	83	24	of	of	ADP
ma-265	83	25	t	t	PROPN
ma-265	83	26	∈	∈	PROPN
ma-265	83	27	u	u	NOUN
ma-265	83	28	given	give	VERB
ma-265	83	29	by	by	ADP
ma-265	83	30	exp	exp	NOUN
ma-265	83	31	(	(	PUNCT
ma-265	83	32	−f	−f	NOUN
ma-265	83	33	(	(	PUNCT
ma-265	83	34	z	z	PROPN
ma-265	83	35	·	·	PUNCT
ma-265	83	36	t	t	PROPN
ma-265	83	37	)	)	PUNCT
ma-265	83	38	)	)	PUNCT
ma-265	83	39	is	be	AUX
ma-265	83	40	a	a	DET
ma-265	83	41	contraction	contraction	NOUN
ma-265	83	42	(	(	PUNCT
ma-265	83	43	with	with	ADP
ma-265	83	44	respect	respect	NOUN
ma-265	83	45	to	to	ADP
ma-265	83	46	the	the	DET
ma-265	83	47	euclideanmetric	euclideanmetric	NOUN
ma-265	83	48	)	)	PUNCT
ma-265	83	49	where	where	SCONJ
ma-265	83	50	z	z	PROPN
ma-265	83	51	∈	∈	PROPN
ma-265	83	52	u	u	NOUN
ma-265	83	53	is	be	AUX
ma-265	83	54	fixed.(iv	fixed.(iv	ADJ
ma-265	83	55	)	)	PUNCT
ma-265	84	1	f	f	PROPN
ma-265	84	2	is	be	AUX
ma-265	84	3	a	a	DET
ma-265	84	4	non	non	ADJ
ma-265	84	5	-	-	ADJ
ma-265	84	6	constant	constant	ADJ
ma-265	84	7	function	function	NOUN
ma-265	84	8	.	.	PUNCT
ma-265	85	1	remark	remark	PROPN
ma-265	85	2	3.2	3.2	NUM
ma-265	85	3	.	.	PUNCT
ma-265	86	1	∀f	∀f	PROPN
ma-265	86	2	,	,	PUNCT
ma-265	86	3	g	g	PROPN
ma-265	86	4	∈	∈	PROPN
ma-265	86	5	rp	rp	NOUN
ma-265	86	6	,	,	PUNCT
ma-265	86	7	∀	∀	X
ma-265	86	8	a	a	DET
ma-265	86	9	,	,	PUNCT
ma-265	86	10	b	b	PROPN
ma-265	86	11	∈	∈	PROPN
ma-265	86	12	r≥0	r≥0	PROPN
ma-265	86	13	,	,	PUNCT
ma-265	86	14	such	such	ADJ
ma-265	86	15	that	that	SCONJ
ma-265	86	16	0	0	NUM
ma-265	86	17	<	<	X
ma-265	86	18	a	a	DET
ma-265	86	19	+	+	X
ma-265	86	20	b	b	NOUN
ma-265	86	21	≤	≤	NUM
ma-265	86	22	1	1	NUM
ma-265	86	23	,	,	PUNCT
ma-265	86	24	we	we	PRON
ma-265	86	25	have	have	VERB
ma-265	86	26	a	a	DET
ma-265	86	27	·	·	PUNCT
ma-265	86	28	f	f	PROPN
ma-265	87	1	+	+	CCONJ
ma-265	87	2	b	b	PROPN
ma-265	87	3	·	·	PUNCT
ma-265	87	4	g	g	NOUN
ma-265	87	5	∈	∈	PROPN
ma-265	87	6	rp.also	rp.also	PRON
ma-265	87	7	if	if	SCONJ
ma-265	87	8	f	f	PROPN
ma-265	87	9	(	(	PUNCT
ma-265	87	10	z	z	NOUN
ma-265	87	11	)	)	PUNCT
ma-265	87	12	=	=	SYM
ma-265	87	13	1+w(z	1+w(z	X
ma-265	87	14	)	)	PUNCT
ma-265	87	15	1−w(z	1−w(z	NUM
ma-265	87	16	)	)	PUNCT
ma-265	87	17	,	,	PUNCT
ma-265	87	18	where	where	SCONJ
ma-265	87	19	,	,	PUNCT
ma-265	87	20	as	as	ADP
ma-265	87	21	always	always	ADV
ma-265	87	22	w(z	w(z	NOUN
ma-265	87	23	)	)	PUNCT
ma-265	87	24	∈	∈	PROPN
ma-265	87	25	inn	inn	PROPN
ma-265	87	26	,	,	PUNCT
ma-265	87	27	then	then	ADV
ma-265	87	28	f	f	PROPN
ma-265	87	29	′(z	′(z	ADV
ma-265	87	30	)	)	PUNCT
ma-265	87	31	=	=	SYM
ma-265	87	32	2w	2w	NUM
ma-265	87	33	′(z	′(z	NOUN
ma-265	87	34	)	)	PUNCT
ma-265	87	35	(	(	PUNCT
ma-265	87	36	1−w(z))2	1−w(z))2	NUM
ma-265	87	37	.	.	PUNCT
ma-265	88	1	by	by	ADP
ma-265	88	2	d	d	X
ma-265	88	3	dt	dt	X
ma-265	88	4	exp	exp	NOUN
ma-265	88	5	(	(	PUNCT
ma-265	88	6	−f	−f	PROPN
ma-265	88	7	(	(	PUNCT
ma-265	88	8	z	z	PROPN
ma-265	88	9	·	·	PUNCT
ma-265	88	10	t	t	PROPN
ma-265	88	11	)	)	PUNCT
ma-265	88	12	)	)	PUNCT
ma-265	89	1	=	=	SYM
ma-265	89	2	−zf	−zf	NOUN
ma-265	89	3	′(z	′(z	NOUN
ma-265	89	4	·	·	PUNCT
ma-265	89	5	t	t	X
ma-265	89	6	)	)	PUNCT
ma-265	89	7	exp	exp	NOUN
ma-265	89	8	(	(	PUNCT
ma-265	89	9	−f	−f	PROPN
ma-265	89	10	(	(	PUNCT
ma-265	89	11	z	z	PROPN
ma-265	89	12	·	·	PUNCT
ma-265	89	13	t	t	PROPN
ma-265	89	14	)	)	PUNCT
ma-265	89	15	)	)	PUNCT
ma-265	89	16	,	,	PUNCT
ma-265	89	17	it	it	PRON
ma-265	89	18	follows	follow	VERB
ma-265	89	19	by	by	ADP
ma-265	89	20	(	(	PUNCT
ma-265	89	21	iii	iii	NOUN
ma-265	89	22	)	)	PUNCT
ma-265	89	23	∣∣∣∣z	∣∣∣∣z	NOUN
ma-265	89	24	2w	2w	NUM
ma-265	89	25	′(z	′(z	X
ma-265	89	26	·	·	SYM
ma-265	89	27	t	t	PROPN
ma-265	89	28	)	)	PUNCT
ma-265	89	29	(	(	PUNCT
ma-265	89	30	1−	1−	NUM
ma-265	89	31	w(z	w(z	PROPN
ma-265	89	32	·	·	PUNCT
ma-265	89	33	t))2	t))2	PROPN
ma-265	89	34	exp	exp	NOUN
ma-265	89	35	(	(	PUNCT
ma-265	89	36	−f	−f	PROPN
ma-265	89	37	(	(	PUNCT
ma-265	89	38	z	z	PROPN
ma-265	89	39	·	·	PUNCT
ma-265	89	40	t	t	PROPN
ma-265	89	41	)	)	PUNCT
ma-265	89	42	)	)	PUNCT
ma-265	89	43	∣∣∣∣	∣∣∣∣	NOUN
ma-265	89	44	≤	≤	PUNCT
ma-265	89	45	c	c	NOUN
ma-265	89	46	<	<	X
ma-265	89	47	1.in	1.in	NUM
ma-265	89	48	particular	particular	ADJ
ma-265	89	49	we	we	PRON
ma-265	89	50	obtain	obtain	VERB
ma-265	89	51	that	that	SCONJ
ma-265	89	52	the	the	DET
ma-265	89	53	generating	generate	VERB
ma-265	89	54	inner	inner	ADJ
ma-265	89	55	function	function	NOUN
ma-265	89	56	w(z	w(z	NOUN
ma-265	89	57	)	)	PUNCT
ma-265	89	58	of	of	ADP
ma-265	89	59	f	f	PROPN
ma-265	89	60	(	(	PUNCT
ma-265	89	61	z	z	NOUN
ma-265	89	62	)	)	PUNCT
ma-265	89	63	satisfies	satisfie	NOUN
ma-265	89	64	:	:	PUNCT
ma-265	89	65	|z	|z	PROPN
ma-265	89	66	|	|	ADV
ma-265	89	67	|w	|w	ADJ
ma-265	89	68	′(z	′(z	VERB
ma-265	89	69	·	·	PUNCT
ma-265	90	1	t)|	t)|	NUM
ma-265	90	2	|1−	|1−	INTJ
ma-265	90	3	w(z	w(z	PROPN
ma-265	90	4	·	·	PUNCT
ma-265	90	5	t)|2	t)|2	PROPN
ma-265	90	6	exp	exp	NOUN
ma-265	90	7	(	(	PUNCT
ma-265	90	8	−	−	PROPN
ma-265	90	9	1−	1−	NUM
ma-265	90	10	|w(z	|w(z	PROPN
ma-265	90	11	·	·	PUNCT
ma-265	90	12	t)|2	t)|2	PROPN
ma-265	90	13	|1−	|1−	X
ma-265	90	14	w(z	w(z	PROPN
ma-265	90	15	·	·	PUNCT
ma-265	90	16	t)|2	t)|2	PROPN
ma-265	90	17	)	)	PUNCT
ma-265	90	18	≤	≤	NUM
ma-265	90	19	c	c	NOUN
ma-265	90	20	2	2	NUM
ma-265	90	21	<	<	SYM
ma-265	90	22	1	1	NUM
ma-265	90	23	2	2	NUM
ma-265	90	24	.	.	PUNCT
ma-265	91	1	thus	thus	ADV
ma-265	91	2	we	we	PRON
ma-265	91	3	conclude	conclude	VERB
ma-265	91	4	that	that	SCONJ
ma-265	91	5	∀	∀	PUNCT
ma-265	91	6	z	z	NOUN
ma-265	91	7	∈	∈	PROPN
ma-265	91	8	u	u	NOUN
ma-265	91	9	and	and	CCONJ
ma-265	91	10	∀w	∀w	PROPN
ma-265	91	11	∈	∈	PROPN
ma-265	91	12	inn	inn	PROPN
ma-265	91	13	,	,	PUNCT
ma-265	92	1	such	such	ADJ
ma-265	92	2	that	that	SCONJ
ma-265	92	3	1+w1−w	1+w1−w	NUM
ma-265	92	4	∈	∈	NOUN
ma-265	92	5	rp	rp	NOUN
ma-265	92	6	we	we	PRON
ma-265	92	7	have	have	VERB
ma-265	92	8	:	:	PUNCT
ma-265	93	1	|z	|z	PROPN
ma-265	93	2	|	|	PROPN
ma-265	93	3	|w	|w	PROPN
ma-265	93	4	′(z)|	′(z)|	PROPN
ma-265	93	5	|1−	|1−	PROPN
ma-265	93	6	w(z)|2	w(z)|2	PROPN
ma-265	93	7	exp	exp	NOUN
ma-265	93	8	(	(	PUNCT
ma-265	93	9	−	−	PROPN
ma-265	93	10	1−	1−	NUM
ma-265	93	11	|w(z)|2	|w(z)|2	PUNCT
ma-265	93	12	|1−	|1−	PROPN
ma-265	93	13	w(z)|2	w(z)|2	PROPN
ma-265	93	14	)	)	PUNCT
ma-265	93	15	<	<	X
ma-265	94	1	1	1	NUM
ma-265	94	2	2	2	NUM
ma-265	94	3	.	.	PUNCT
ma-265	95	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	95	2	eur	eur	PROPN
ma-265	95	3	.	.	PUNCT
ma-265	96	1	j.	j.	PROPN
ma-265	96	2	math	math	PROPN
ma-265	96	3	.	.	PUNCT
ma-265	97	1	anal	anal	PROPN
ma-265	97	2	.	.	PUNCT
ma-265	98	1	10.28924	10.28924	NUM
ma-265	98	2	/	/	SYM
ma-265	98	3	ada	ada	PROPN
ma-265	98	4	/	/	SYM
ma-265	98	5	ma.5.4	ma.5.4	PROPN
ma-265	98	6	4	4	NUM
ma-265	98	7	the	the	DET
ma-265	98	8	construction	construction	NOUN
ma-265	98	9	.	.	PUNCT
ma-265	99	1	let	let	VERB
ma-265	99	2	f	f	PROPN
ma-265	99	3	∈	∈	PROPN
ma-265	99	4	rp	rp	NOUN
ma-265	99	5	.	.	PUNCT
ma-265	100	1	we	we	PRON
ma-265	100	2	will	will	AUX
ma-265	100	3	use	use	VERB
ma-265	100	4	f	f	X
ma-265	100	5	(	(	PUNCT
ma-265	100	6	z	z	NOUN
ma-265	100	7	)	)	PUNCT
ma-265	100	8	to	to	PART
ma-265	100	9	define	define	VERB
ma-265	100	10	a	a	DET
ma-265	100	11	sequence	sequence	NOUN
ma-265	100	12	{	{	PUNCT
ma-265	100	13	sn(z)}∞n=0	sn(z)}∞n=0	NUM
ma-265	100	14	of	of	ADP
ma-265	100	15	singular	singular	ADJ
ma-265	100	16	innerfunctions	innerfunction	NOUN
ma-265	100	17	.	.	PUNCT
ma-265	101	1	the	the	DET
ma-265	101	2	definition	definition	NOUN
ma-265	101	3	will	will	AUX
ma-265	101	4	use	use	VERB
ma-265	101	5	the	the	DET
ma-265	101	6	following	follow	VERB
ma-265	101	7	recursion	recursion	NOUN
ma-265	101	8	:	:	PUNCT
ma-265	101	9	s0	s0	PROPN
ma-265	101	10	∈	∈	PROPN
ma-265	101	11	sinn	sinn	PROPN
ma-265	101	12	(	(	PUNCT
ma-265	101	13	an	an	DET
ma-265	101	14	arbitrary	arbitrary	ADJ
ma-265	101	15	initial	initial	ADJ
ma-265	101	16	point	point	NOUN
ma-265	101	17	)	)	PUNCT
ma-265	101	18	.	.	PUNCT
ma-265	102	1	sn+1(z	sn+1(z	VERB
ma-265	102	2	)	)	PUNCT
ma-265	103	1	=	=	NOUN
ma-265	103	2	exp	exp	NOUN
ma-265	103	3	(	(	PUNCT
ma-265	103	4	−f	−f	PROPN
ma-265	103	5	(	(	PUNCT
ma-265	103	6	z	z	NOUN
ma-265	103	7	·	·	PUNCT
ma-265	103	8	sn(z	sn(z	NOUN
ma-265	103	9	)	)	PUNCT
ma-265	103	10	)	)	PUNCT
ma-265	103	11	)	)	PUNCT
ma-265	103	12	for	for	ADP
ma-265	103	13	n	n	PRON
ma-265	103	14	∈	∈	PROPN
ma-265	103	15	z≥0	z≥0	PROPN
ma-265	103	16	.	.	PUNCT
ma-265	104	1	theorem	theorem	VERB
ma-265	104	2	3.3	3.3	NUM
ma-265	104	3	.	.	PUNCT
ma-265	105	1	the	the	DET
ma-265	105	2	limit	limit	NOUN
ma-265	105	3	limn→∞	limn→∞	PROPN
ma-265	105	4	sn(z	sn(z	NOUN
ma-265	105	5	)	)	PUNCT
ma-265	105	6	=	=	SYM
ma-265	105	7	s(z	s(z	PROPN
ma-265	105	8	)	)	PUNCT
ma-265	105	9	exists	exist	VERB
ma-265	105	10	and	and	CCONJ
ma-265	105	11	is	be	AUX
ma-265	105	12	uniform	uniform	ADJ
ma-265	105	13	on	on	ADP
ma-265	105	14	compact	compact	ADJ
ma-265	105	15	subsets	subset	NOUN
ma-265	105	16	of	of	ADP
ma-265	105	17	u	u	NOUN
ma-265	105	18	.	.	PUNCT
ma-265	106	1	s	s	PART
ma-265	106	2	∈	∈	PROPN
ma-265	106	3	h(u	h(u	PROPN
ma-265	106	4	)	)	PUNCT
ma-265	106	5	satisfies	satisfy	VERB
ma-265	106	6	|s(z)|	|s(z)|	PROPN
ma-265	106	7	≤	≤	PROPN
ma-265	106	8	1∀	1∀	NUM
ma-265	106	9	z	z	SYM
ma-265	106	10	∈	∈	PROPN
ma-265	106	11	u	u	NOUN
ma-265	106	12	,	,	PUNCT
ma-265	106	13	and	and	CCONJ
ma-265	106	14	satisfies	satisfy	VERB
ma-265	106	15	the	the	DET
ma-265	106	16	following	follow	VERB
ma-265	106	17	fixed	fix	VERB
ma-265	106	18	-	-	PUNCT
ma-265	106	19	point	point	NOUN
ma-265	106	20	equation	equation	NOUN
ma-265	106	21	,	,	PUNCT
ma-265	106	22	s	s	PART
ma-265	106	23	=	=	PUNCT
ma-265	106	24	exp(−f	exp(−f	X
ma-265	106	25	(	(	PUNCT
ma-265	106	26	z	z	NOUN
ma-265	106	27	·	·	PUNCT
ma-265	106	28	s	s	X
ma-265	106	29	)	)	PUNCT
ma-265	106	30	)	)	PUNCT
ma-265	106	31	.	.	PUNCT
ma-265	107	1	the	the	DET
ma-265	107	2	function	function	NOUN
ma-265	107	3	z	z	X
ma-265	107	4	·	·	PUNCT
ma-265	107	5	s(z	s(z	NOUN
ma-265	107	6	)	)	PUNCT
ma-265	107	7	∈	∈	PROPN
ma-265	107	8	h∞(u	h∞(u	NOUN
ma-265	107	9	)	)	PUNCT
ma-265	107	10	is	be	AUX
ma-265	107	11	a	a	DET
ma-265	107	12	conformal	conformal	ADJ
ma-265	107	13	mapping	mapping	NOUN
ma-265	107	14	z	z	NOUN
ma-265	107	15	·	·	PUNCT
ma-265	107	16	s(z	s(z	PROPN
ma-265	107	17	)	)	PUNCT
ma-265	107	18	:	:	PUNCT
ma-265	107	19	u	u	NOUN
ma-265	107	20	→	→	SYM
ma-265	107	21	im(z	im(z	X
ma-265	107	22	·	·	PUNCT
ma-265	107	23	s	s	X
ma-265	107	24	)	)	PUNCT
ma-265	107	25	⊆	⊆	NUM
ma-265	107	26	u	u	NOUN
ma-265	107	27	but	but	CCONJ
ma-265	107	28	it	it	PRON
ma-265	107	29	is	be	AUX
ma-265	107	30	not	not	PART
ma-265	107	31	an	an	DET
ma-265	107	32	inner	inner	ADJ
ma-265	107	33	function	function	NOUN
ma-265	107	34	.	.	PUNCT
ma-265	108	1	proof.since	proof.since	NOUN
ma-265	108	2	s0	s0	PROPN
ma-265	108	3	∈	∈	PROPN
ma-265	108	4	sinn	sinn	PROPN
ma-265	108	5	and	and	CCONJ
ma-265	108	6	since	since	SCONJ
ma-265	108	7	an	an	DET
ma-265	108	8	inductive	inductive	ADJ
ma-265	108	9	argument	argument	NOUN
ma-265	108	10	shows	show	VERB
ma-265	108	11	that	that	SCONJ
ma-265	108	12	if	if	SCONJ
ma-265	108	13	sn	sn	PROPN
ma-265	108	14	∈	∈	PROPN
ma-265	108	15	sinn	sinn	PROPN
ma-265	108	16	,	,	PUNCT
ma-265	108	17	then	then	ADV
ma-265	108	18	sn+1	sn+1	VERB
ma-265	108	19	=	=	SYM
ma-265	108	20	exp(−f	exp(−f	X
ma-265	108	21	(	(	PUNCT
ma-265	108	22	z	z	NOUN
ma-265	108	23	·	·	PUNCT
ma-265	108	24	sn	sn	NOUN
ma-265	108	25	)	)	PUNCT
ma-265	108	26	)	)	PUNCT
ma-265	109	1	∈	∈	PROPN
ma-265	109	2	sinn	sinn	NOUN
ma-265	109	3	for	for	ADP
ma-265	109	4	n	n	PRON
ma-265	109	5	∈	∈	PROPN
ma-265	109	6	z≥0	z≥0	NOUN
ma-265	109	7	,	,	PUNCT
ma-265	109	8	it	it	PRON
ma-265	109	9	follows	follow	VERB
ma-265	109	10	that	that	SCONJ
ma-265	109	11	all	all	DET
ma-265	109	12	the	the	DET
ma-265	109	13	members	member	NOUN
ma-265	109	14	of	of	ADP
ma-265	109	15	the	the	DET
ma-265	109	16	sequence	sequence	NOUN
ma-265	109	17	{	{	PUNCT
ma-265	109	18	sn}∞n=0	sn}∞n=0	X
ma-265	109	19	belong	belong	NOUN
ma-265	109	20	to	to	ADP
ma-265	109	21	sinn	sinn	PROPN
ma-265	109	22	.	.	PUNCT
ma-265	110	1	the	the	DET
ma-265	110	2	reason	reason	NOUN
ma-265	110	3	for	for	ADP
ma-265	110	4	the	the	DET
ma-265	110	5	validity	validity	NOUN
ma-265	110	6	of	of	ADP
ma-265	110	7	the	the	DET
ma-265	110	8	inductive	inductive	ADJ
ma-265	110	9	argument	argument	NOUN
ma-265	110	10	is	be	AUX
ma-265	110	11	that	that	SCONJ
ma-265	110	12	|z	|z	PROPN
ma-265	110	13	·	·	PUNCT
ma-265	110	14	sn|	sn|	PROPN
ma-265	110	15	=	=	SYM
ma-265	110	16	|z	|z	PROPN
ma-265	110	17	||sn|	||sn|	PROPN
ma-265	110	18	≤	≤	PROPN
ma-265	110	19	|z	|z	PROPN
ma-265	111	1	|	|	ADV
ma-265	111	2	forall	forall	VERB
ma-265	111	3	z	z	PROPN
ma-265	111	4	∈	∈	PROPN
ma-265	111	5	u	u	PROPN
ma-265	111	6	,	,	PUNCT
ma-265	111	7	using	use	VERB
ma-265	111	8	the	the	DET
ma-265	111	9	induction	induction	NOUN
ma-265	111	10	hypothesis	hypothesis	NOUN
ma-265	111	11	sn	sn	PROPN
ma-265	111	12	∈	∈	PROPN
ma-265	111	13	sinn	sinn	PROPN
ma-265	111	14	.	.	PUNCT
ma-265	112	1	thus	thus	ADV
ma-265	112	2	z	z	X
ma-265	112	3	·	·	PUNCT
ma-265	112	4	sn	sn	PROPN
ma-265	112	5	∈	∈	PROPN
ma-265	112	6	bh∞	bh∞	PROPN
ma-265	112	7	,	,	PUNCT
ma-265	112	8	the	the	DET
ma-265	112	9	unit	unit	NOUN
ma-265	112	10	ball	ball	NOUN
ma-265	112	11	of	of	ADP
ma-265	112	12	h∞.also	h∞.also	ADV
ma-265	112	13	|e	|e	PROPN
ma-265	112	14	iθ	iθ	NOUN
ma-265	112	15	·	·	PUNCT
ma-265	112	16	sn(e	sn(e	PUNCT
ma-265	112	17	iθ)|	iθ)|	PROPN
ma-265	112	18	=	=	NOUN
ma-265	112	19	1	1	NUM
ma-265	112	20	almost	almost	ADV
ma-265	112	21	everywhere	everywhere	ADV
ma-265	112	22	on	on	ADP
ma-265	112	23	t	t	PROPN
ma-265	112	24	with	with	ADP
ma-265	112	25	respect	respect	NOUN
ma-265	112	26	to	to	ADP
ma-265	112	27	the	the	DET
ma-265	112	28	lebesgue	lebesgue	ADJ
ma-265	112	29	measure	measure	NOUN
ma-265	112	30	on	on	ADP
ma-265	112	31	t.also	t.also	NOUN
ma-265	112	32	this	this	PRON
ma-265	112	33	follows	follow	VERB
ma-265	112	34	by	by	ADP
ma-265	112	35	the	the	DET
ma-265	112	36	induction	induction	NOUN
ma-265	112	37	hypothesis	hypothesis	NOUN
ma-265	112	38	on	on	ADP
ma-265	112	39	sn	sn	PROPN
ma-265	112	40	.	.	PUNCT
ma-265	113	1	hence	hence	ADV
ma-265	113	2	<	<	X
ma-265	113	3	f	f	X
ma-265	113	4	(	(	PUNCT
ma-265	113	5	z	z	NOUN
ma-265	113	6	·	·	PUNCT
ma-265	113	7	sn(z	sn(z	NOUN
ma-265	113	8	)	)	PUNCT
ma-265	113	9	)	)	PUNCT
ma-265	113	10	≥	≥	NOUN
ma-265	113	11	0	0	NUM
ma-265	113	12	∀	∀	NOUN
ma-265	113	13	z	z	NOUN
ma-265	113	14	∈	∈	PROPN
ma-265	113	15	u	u	NOUN
ma-265	113	16	and	and	CCONJ
ma-265	113	17	<	<	X
ma-265	113	18	(	(	PUNCT
ma-265	113	19	e	e	NOUN
ma-265	113	20	iθ	iθ	NOUN
ma-265	113	21	·	·	PUNCT
ma-265	113	22	sn(e	sn(e	X
ma-265	113	23	iθ	iθ	NOUN
ma-265	113	24	)	)	PUNCT
ma-265	113	25	)	)	PUNCT
ma-265	114	1	=	=	SYM
ma-265	114	2	0	0	PUNCT
ma-265	115	1	almost	almost	ADV
ma-265	115	2	everywhere	everywhere	ADV
ma-265	115	3	on	on	ADP
ma-265	115	4	t	t	PROPN
ma-265	115	5	(	(	PUNCT
ma-265	115	6	recall	recall	VERB
ma-265	115	7	that	that	SCONJ
ma-265	115	8	f	f	PROPN
ma-265	115	9	∈	∈	PROPN
ma-265	115	10	rp	rp	NOUN
ma-265	115	11	satisfies	satisfie	NOUN
ma-265	115	12	by	by	ADP
ma-265	115	13	the	the	DET
ma-265	115	14	definition	definition	NOUN
ma-265	115	15	<	<	X
ma-265	115	16	f	f	X
ma-265	115	17	(	(	PUNCT
ma-265	115	18	e	e	NOUN
ma-265	115	19	iθ	iθ	NOUN
ma-265	115	20	)	)	PUNCT
ma-265	115	21	=	=	SYM
ma-265	115	22	0	0	NUM
ma-265	116	1	almost	almost	ADV
ma-265	116	2	everywhere	everywhere	ADV
ma-265	116	3	on	on	ADP
ma-265	116	4	t	t	PROPN
ma-265	116	5	)	)	PUNCT
ma-265	116	6	.	.	PUNCT
ma-265	117	1	hence	hence	ADV
ma-265	117	2	|	|	ADV
ma-265	117	3	exp	exp	NOUN
ma-265	117	4	(	(	PUNCT
ma-265	117	5	−f	−f	NOUN
ma-265	117	6	(	(	PUNCT
ma-265	117	7	z	z	NOUN
ma-265	117	8	·	·	PUNCT
ma-265	117	9	sn(z	sn(z	NOUN
ma-265	117	10	)	)	PUNCT
ma-265	117	11	)	)	PUNCT
ma-265	117	12	)	)	PUNCT
ma-265	118	1	|	|	ADV
ma-265	118	2	=	=	SYM
ma-265	118	3	exp	exp	NOUN
ma-265	118	4	(	(	PUNCT
ma-265	118	5	−<f	−<f	NOUN
ma-265	118	6	(	(	PUNCT
ma-265	118	7	z	z	NOUN
ma-265	118	8	·	·	PUNCT
ma-265	118	9	sn(z	sn(z	NOUN
ma-265	118	10	)	)	PUNCT
ma-265	118	11	)	)	PUNCT
ma-265	118	12	)	)	PUNCT
ma-265	119	1	≤	≤	ADV
ma-265	119	2	1	1	NUM
ma-265	119	3	∀	∀	NOUN
ma-265	119	4	z	z	NOUN
ma-265	119	5	∈	∈	NOUN
ma-265	119	6	uand	uand	NOUN
ma-265	119	7	also	also	ADV
ma-265	119	8	∣∣exp	∣∣exp	PROPN
ma-265	119	9	(	(	PUNCT
ma-265	119	10	−f	−f	PROPN
ma-265	119	11	(	(	PUNCT
ma-265	119	12	e	e	NOUN
ma-265	119	13	iθ	iθ	NOUN
ma-265	119	14	·	·	PUNCT
ma-265	119	15	sn(e	sn(e	NUM
ma-265	119	16	iθ)))∣∣	iθ)))∣∣	NOUN
ma-265	119	17	=	=	NOUN
ma-265	119	18	1	1	NUM
ma-265	119	19	almost	almost	ADV
ma-265	119	20	everywhere	everywhere	ADV
ma-265	119	21	on	on	ADP
ma-265	119	22	t.we	t.we	PRON
ma-265	119	23	just	just	ADV
ma-265	119	24	proved	prove	VERB
ma-265	119	25	that	that	PRON
ma-265	119	26	sn+1(z	sn+1(z	VERB
ma-265	119	27	)	)	PUNCT
ma-265	119	28	=	=	NOUN
ma-265	119	29	exp	exp	NOUN
ma-265	119	30	(	(	PUNCT
ma-265	119	31	−f	−f	PROPN
ma-265	119	32	(	(	PUNCT
ma-265	119	33	z	z	NOUN
ma-265	119	34	·	·	PUNCT
ma-265	119	35	sn(z	sn(z	NOUN
ma-265	119	36	)	)	PUNCT
ma-265	119	37	)	)	PUNCT
ma-265	119	38	)	)	PUNCT
ma-265	120	1	∈	∈	PROPN
ma-265	120	2	sinn	sinn	NOUN
ma-265	120	3	for	for	ADP
ma-265	120	4	n	n	PRON
ma-265	120	5	∈	∈	PROPN
ma-265	120	6	z≥0	z≥0	PROPN
ma-265	120	7	.	.	PUNCT
ma-265	121	1	hence	hence	ADV
ma-265	121	2	the	the	DET
ma-265	121	3	family	family	NOUN
ma-265	121	4	offunctions	offunction	NOUN
ma-265	121	5	in	in	ADP
ma-265	121	6	the	the	DET
ma-265	121	7	sequence	sequence	NOUN
ma-265	121	8	{	{	PUNCT
ma-265	121	9	sn}∞n=0	sn}∞n=0	X
ma-265	121	10	is	be	AUX
ma-265	121	11	a	a	DET
ma-265	121	12	normal	normal	ADJ
ma-265	121	13	family	family	NOUN
ma-265	121	14	.	.	PUNCT
ma-265	122	1	moreover	moreover	ADV
ma-265	122	2	,	,	PUNCT
ma-265	122	3	by	by	ADP
ma-265	122	4	condition	condition	NOUN
ma-265	122	5	(	(	PUNCT
ma-265	122	6	iii	iii	NOUN
ma-265	122	7	)	)	PUNCT
ma-265	122	8	in	in	ADP
ma-265	122	9	definition3.1	definition3.1	NUM
ma-265	122	10	,	,	PUNCT
ma-265	122	11	for	for	ADP
ma-265	122	12	a	a	DET
ma-265	122	13	fixed	fix	VERB
ma-265	122	14	z	z	NOUN
ma-265	122	15	∈	∈	PROPN
ma-265	122	16	u	u	NOUN
ma-265	122	17	iterations	iteration	NOUN
ma-265	122	18	of	of	ADP
ma-265	122	19	the	the	DET
ma-265	122	20	function	function	NOUN
ma-265	122	21	of	of	ADP
ma-265	122	22	t	t	PROPN
ma-265	122	23	∈	∈	PROPN
ma-265	122	24	u	u	NOUN
ma-265	122	25	given	give	VERB
ma-265	122	26	by	by	ADP
ma-265	122	27	exp(−f	exp(−f	PROPN
ma-265	122	28	(	(	PUNCT
ma-265	122	29	z	z	NOUN
ma-265	122	30	·	·	PUNCT
ma-265	122	31	t	t	PROPN
ma-265	122	32	)	)	PUNCT
ma-265	122	33	)	)	PUNCT
ma-265	122	34	converge(by	converge(by	VERB
ma-265	122	35	banach	banach	ADV
ma-265	122	36	fixed	fix	VERB
ma-265	122	37	-	-	PUNCT
ma-265	122	38	point	point	NOUN
ma-265	122	39	theorem	theorem	NOUN
ma-265	122	40	)	)	PUNCT
ma-265	122	41	to	to	ADP
ma-265	122	42	a	a	DET
ma-265	122	43	unique	unique	ADJ
ma-265	122	44	fixed	fix	VERB
ma-265	122	45	-	-	PUNCT
ma-265	122	46	point	point	NOUN
ma-265	122	47	t0	t0	NOUN
ma-265	122	48	=	=	PUNCT
ma-265	122	49	s(z	s(z	PROPN
ma-265	122	50	)	)	PUNCT
ma-265	122	51	.	.	PUNCT
ma-265	123	1	so	so	ADV
ma-265	123	2	limn→∞	limn→∞	PROPN
ma-265	123	3	sn(z	sn(z	NOUN
ma-265	123	4	)	)	PUNCT
ma-265	123	5	=	=	SYM
ma-265	123	6	s(z)uniformly	s(z)uniformly	ADV
ma-265	123	7	on	on	ADP
ma-265	123	8	compact	compact	ADJ
ma-265	123	9	subsets	subset	NOUN
ma-265	123	10	of	of	ADP
ma-265	123	11	u	u	NOUN
ma-265	123	12	,	,	PUNCT
ma-265	123	13	and	and	CCONJ
ma-265	123	14	s(z	s(z	PROPN
ma-265	123	15	)	)	PUNCT
ma-265	123	16	satisfies	satisfy	VERB
ma-265	123	17	the	the	DET
ma-265	123	18	fixed	fix	VERB
ma-265	123	19	-	-	PUNCT
ma-265	123	20	point	point	NOUN
ma-265	123	21	equation	equation	NOUN
ma-265	123	22	s(z	s(z	PROPN
ma-265	123	23	)	)	PUNCT
ma-265	124	1	=	=	SYM
ma-265	124	2	exp(−f	exp(−f	PROPN
ma-265	124	3	(	(	PUNCT
ma-265	124	4	z	z	NOUN
ma-265	124	5	·	·	PUNCT
ma-265	124	6	s(z	s(z	NOUN
ma-265	124	7	)	)	PUNCT
ma-265	124	8	)	)	PUNCT
ma-265	124	9	)	)	PUNCT
ma-265	124	10	.	.	PUNCT
ma-265	125	1	clearly	clearly	ADV
ma-265	125	2	,	,	PUNCT
ma-265	125	3	the	the	DET
ma-265	125	4	h∞(u	h∞(u	ADJ
ma-265	125	5	)	)	PUNCT
ma-265	125	6	function	function	NOUN
ma-265	125	7	is	be	AUX
ma-265	125	8	a	a	DET
ma-265	125	9	non	non	ADJ
ma-265	125	10	-	-	ADJ
ma-265	125	11	vanishing	vanishing	ADJ
ma-265	125	12	function	function	NOUN
ma-265	125	13	that	that	PRON
ma-265	125	14	belongs	belong	VERB
ma-265	125	15	to	to	ADP
ma-265	125	16	the	the	DET
ma-265	125	17	unit	unit	NOUN
ma-265	125	18	ball	ball	NOUN
ma-265	125	19	bh∞(u	bh∞(u	PROPN
ma-265	125	20	)	)	PUNCT
ma-265	125	21	.	.	PUNCT
ma-265	126	1	next	next	ADV
ma-265	126	2	,	,	PUNCT
ma-265	126	3	let	let	VERB
ma-265	126	4	us	we	PRON
ma-265	126	5	consider	consider	VERB
ma-265	126	6	the	the	DET
ma-265	126	7	following	follow	VERB
ma-265	126	8	holomorphic	holomorphic	ADJ
ma-265	126	9	function	function	NOUN
ma-265	126	10	of	of	ADP
ma-265	126	11	w	w	PROPN
ma-265	126	12	,	,	PUNCT
ma-265	126	13	defined	define	VERB
ma-265	126	14	on	on	ADP
ma-265	126	15	u	u	NOUN
ma-265	126	16	as	as	SCONJ
ma-265	126	17	follows	follow	VERB
ma-265	126	18	:	:	PUNCT
ma-265	127	1	f	f	X
ma-265	127	2	:	:	PUNCT
ma-265	127	3	u	u	X
ma-265	127	4	→	→	SYM
ma-265	127	5	c	c	PROPN
ma-265	127	6	,	,	PUNCT
ma-265	127	7	f(w	f(w	PROPN
ma-265	127	8	)	)	PUNCT
ma-265	127	9	=	=	SYM
ma-265	128	1	w	w	PROPN
ma-265	128	2	exp(f(w	exp(f(w	NOUN
ma-265	128	3	)	)	PUNCT
ma-265	128	4	)	)	PUNCT
ma-265	128	5	.	.	PUNCT
ma-265	129	1	then	then	ADV
ma-265	129	2	by	by	ADP
ma-265	129	3	the	the	DET
ma-265	129	4	fixed	fix	VERB
ma-265	129	5	-	-	PUNCT
ma-265	129	6	point	point	NOUN
ma-265	129	7	equation	equation	NOUN
ma-265	129	8	satisfied	satisfy	VERB
ma-265	129	9	by	by	ADP
ma-265	129	10	s(z	s(z	PROPN
ma-265	129	11	)	)	PUNCT
ma-265	129	12	we	we	PRON
ma-265	129	13	get	get	VERB
ma-265	129	14	:	:	PUNCT
ma-265	129	15	f	f	PROPN
ma-265	129	16	(	(	PUNCT
ma-265	129	17	z	z	NOUN
ma-265	129	18	·	·	PUNCT
ma-265	129	19	s(z	s(z	NOUN
ma-265	129	20	)	)	PUNCT
ma-265	129	21	)	)	PUNCT
ma-265	130	1	=	=	PUNCT
ma-265	130	2	z	z	NOUN
ma-265	130	3	.	.	PUNCT
ma-265	131	1	the	the	DET
ma-265	131	2	reason	reason	NOUN
ma-265	131	3	is	be	AUX
ma-265	131	4	that	that	SCONJ
ma-265	131	5	f	f	PROPN
ma-265	131	6	(	(	PUNCT
ma-265	131	7	z	z	NOUN
ma-265	131	8	·	·	PUNCT
ma-265	131	9	s(z	s(z	NOUN
ma-265	131	10	)	)	PUNCT
ma-265	131	11	)	)	PUNCT
ma-265	132	1	=	=	PUNCT
ma-265	132	2	z	z	X
ma-265	132	3	·	·	PUNCT
ma-265	132	4	s(z	s(z	NOUN
ma-265	132	5	)	)	PUNCT
ma-265	132	6	exp(f	exp(f	PROPN
ma-265	132	7	(	(	PUNCT
ma-265	132	8	z	z	NOUN
ma-265	132	9	·	·	PUNCT
ma-265	132	10	s(z	s(z	NOUN
ma-265	132	11	)	)	PUNCT
ma-265	132	12	)	)	PUNCT
ma-265	132	13	)	)	PUNCT
ma-265	133	1	=	=	PUNCT
ma-265	133	2	z	z	X
ma-265	133	3	·	·	PUNCT
ma-265	133	4	s(z	s(z	PROPN
ma-265	133	5	)	)	PUNCT
ma-265	133	6	·	·	PUNCT
ma-265	133	7	s(z)−1	s(z)−1	NOUN
ma-265	133	8	=	=	PUNCT
ma-265	133	9	z.	z.	PROPN
ma-265	133	10	thus	thus	ADV
ma-265	133	11	f	f	PROPN
ma-265	133	12	is	be	AUX
ma-265	133	13	a	a	DET
ma-265	133	14	left	left	NOUN
ma-265	133	15	is	be	AUX
ma-265	133	16	a	a	DET
ma-265	133	17	left	left	ADJ
ma-265	133	18	inverse	inverse	NOUN
ma-265	133	19	of	of	ADP
ma-265	133	20	z	z	PROPN
ma-265	133	21	·	·	PUNCT
ma-265	133	22	s(z	s(z	NOUN
ma-265	133	23	)	)	PUNCT
ma-265	133	24	and	and	CCONJ
ma-265	133	25	hence	hence	ADV
ma-265	133	26	the	the	DET
ma-265	133	27	mapping	mapping	NOUN
ma-265	133	28	:	:	PUNCT
ma-265	134	1	z	z	X
ma-265	134	2	·	·	PUNCT
ma-265	134	3	s(z	s(z	PROPN
ma-265	134	4	)	)	PUNCT
ma-265	134	5	:	:	PUNCT
ma-265	134	6	u	u	NOUN
ma-265	134	7	→	→	SYM
ma-265	134	8	im(z	im(z	PUNCT
ma-265	134	9	·	·	PUNCT
ma-265	134	10	s(z))is	s(z))is	VERB
ma-265	134	11	an	an	DET
ma-265	134	12	injection	injection	NOUN
ma-265	134	13	.	.	PUNCT
ma-265	135	1	more	more	ADV
ma-265	135	2	concretely	concretely	ADV
ma-265	135	3	,	,	PUNCT
ma-265	135	4	if	if	SCONJ
ma-265	135	5	we	we	PRON
ma-265	135	6	denote	denote	VERB
ma-265	135	7	g(z	g(z	ADJ
ma-265	135	8	)	)	PUNCT
ma-265	135	9	=	=	PUNCT
ma-265	135	10	z	z	NOUN
ma-265	135	11	·	·	PUNCT
ma-265	135	12	s(z	s(z	NOUN
ma-265	135	13	)	)	PUNCT
ma-265	135	14	then	then	ADV
ma-265	135	15	the	the	DET
ma-265	135	16	assumption	assumption	NOUN
ma-265	135	17	g(z1	g(z1	NOUN
ma-265	135	18	)	)	PUNCT
ma-265	136	1	=	=	SYM
ma-265	136	2	g(z2)implies	g(z2)implie	NOUN
ma-265	136	3	that	that	PRON
ma-265	136	4	z1	z1	PROPN
ma-265	136	5	=	=	SYM
ma-265	136	6	f	f	PROPN
ma-265	136	7	(	(	PUNCT
ma-265	136	8	g(z1	g(z1	NOUN
ma-265	136	9	)	)	PUNCT
ma-265	136	10	)	)	PUNCT
ma-265	137	1	=	=	SYM
ma-265	137	2	f	f	PROPN
ma-265	137	3	(	(	PUNCT
ma-265	137	4	g(z2	g(z2	NOUN
ma-265	137	5	)	)	PUNCT
ma-265	137	6	)	)	PUNCT
ma-265	138	1	=	=	SYM
ma-265	138	2	z2	z2	PROPN
ma-265	138	3	.	.	PUNCT
ma-265	139	1	the	the	DET
ma-265	139	2	function	function	NOUN
ma-265	139	3	s(z	s(z	PROPN
ma-265	139	4	)	)	PUNCT
ma-265	139	5	can	can	AUX
ma-265	139	6	not	not	PART
ma-265	139	7	be	be	AUX
ma-265	139	8	a	a	DET
ma-265	139	9	constant	constant	ADJ
ma-265	139	10	function	function	NOUN
ma-265	139	11	,	,	PUNCT
ma-265	139	12	forif	forif	NOUN
ma-265	139	13	s(z	s(z	PROPN
ma-265	139	14	)	)	PUNCT
ma-265	139	15	=	=	SYM
ma-265	139	16	e	e	X
ma-265	139	17	iθ0	iθ0	NOUN
ma-265	139	18	,	,	PUNCT
ma-265	139	19	then	then	ADV
ma-265	139	20	e	e	NOUN
ma-265	139	21	iθ0	iθ0	NOUN
ma-265	139	22	=	=	SYM
ma-265	139	23	exp	exp	NOUN
ma-265	139	24	(	(	PUNCT
ma-265	139	25	−f	−f	PROPN
ma-265	139	26	(	(	PUNCT
ma-265	139	27	e	e	NOUN
ma-265	139	28	iθ	iθ	NOUN
ma-265	139	29	·	·	PUNCT
ma-265	139	30	s(e	s(e	PROPN
ma-265	139	31	iθ0	iθ0	PROPN
ma-265	139	32	)	)	PUNCT
ma-265	139	33	)	)	PUNCT
ma-265	139	34	)	)	PUNCT
ma-265	140	1	=	=	SYM
ma-265	140	2	exp	exp	NOUN
ma-265	140	3	(	(	PUNCT
ma-265	140	4	−f	−f	PROPN
ma-265	140	5	(	(	PUNCT
ma-265	140	6	e	e	NOUN
ma-265	140	7	i(θ+θ0	i(θ+θ0	NOUN
ma-265	140	8	)	)	PUNCT
ma-265	140	9	)	)	PUNCT
ma-265	140	10	)	)	PUNCT
ma-265	140	11	.	.	PUNCT
ma-265	141	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	141	2	eur	eur	PROPN
ma-265	141	3	.	.	PUNCT
ma-265	142	1	j.	j.	PROPN
ma-265	142	2	math	math	PROPN
ma-265	142	3	.	.	PUNCT
ma-265	143	1	anal	anal	PROPN
ma-265	143	2	.	.	PUNCT
ma-265	144	1	10.28924	10.28924	NUM
ma-265	144	2	/	/	SYM
ma-265	144	3	ada	ada	PROPN
ma-265	144	4	/	/	SYM
ma-265	144	5	ma.5.4	ma.5.4	PROPN
ma-265	144	6	5but	5but	PROPN
ma-265	144	7	any	any	DET
ma-265	144	8	function	function	NOUN
ma-265	144	9	such	such	ADJ
ma-265	144	10	as	as	ADP
ma-265	144	11	f	f	PROPN
ma-265	144	12	in	in	ADP
ma-265	144	13	rp	rp	NOUN
ma-265	144	14	is	be	AUX
ma-265	144	15	non	non	ADJ
ma-265	144	16	-	-	ADJ
ma-265	144	17	constant	constant	ADJ
ma-265	144	18	by	by	ADP
ma-265	144	19	the	the	DET
ma-265	144	20	definition	definition	NOUN
ma-265	144	21	.	.	PUNCT
ma-265	145	1	since	since	SCONJ
ma-265	145	2	the	the	DET
ma-265	145	3	only	only	ADJ
ma-265	145	4	injective	injective	ADJ
ma-265	145	5	innerfunctions	innerfunction	NOUN
ma-265	145	6	are	be	AUX
ma-265	145	7	blaschke	blaschke	ADJ
ma-265	145	8	factors	factor	NOUN
ma-265	145	9	,	,	PUNCT
ma-265	145	10	[	[	X
ma-265	145	11	3	3	NUM
ma-265	145	12	]	]	PUNCT
ma-265	145	13	,	,	PUNCT
ma-265	145	14	z	z	NOUN
ma-265	145	15	·	·	PUNCT
ma-265	145	16	s(z	s(z	NOUN
ma-265	145	17	)	)	PUNCT
ma-265	145	18	can	can	AUX
ma-265	145	19	not	not	PART
ma-265	145	20	be	be	AUX
ma-265	145	21	an	an	DET
ma-265	145	22	inner	inner	ADJ
ma-265	145	23	function	function	NOUN
ma-265	145	24	(	(	PUNCT
ma-265	145	25	for	for	ADP
ma-265	145	26	that	that	PRON
ma-265	145	27	would	would	AUX
ma-265	145	28	imply	imply	VERB
ma-265	145	29	that	that	SCONJ
ma-265	145	30	s(z	s(z	PROPN
ma-265	145	31	)	)	PUNCT
ma-265	145	32	is	be	AUX
ma-265	145	33	a	a	DET
ma-265	145	34	unimodular	unimodular	ADJ
ma-265	145	35	constant	constant	NOUN
ma-265	145	36	)	)	PUNCT
ma-265	145	37	.	.	PUNCT
ma-265	146	1	�	�	PROPN
ma-265	146	2	4	4	NUM
ma-265	146	3	.	.	PUNCT
ma-265	147	1	a	a	DET
ma-265	147	2	parametrization	parametrization	NOUN
ma-265	147	3	of	of	ADP
ma-265	147	4	a	a	DET
ma-265	147	5	family	family	NOUN
ma-265	147	6	of	of	ADP
ma-265	147	7	conformal	conformal	ADJ
ma-265	147	8	mappings	mapping	NOUN
ma-265	147	9	by	by	ADP
ma-265	147	10	the	the	DET
ma-265	147	11	functions	function	NOUN
ma-265	147	12	in	in	ADP
ma-265	147	13	rp	rp	NOUN
ma-265	147	14	we	we	PRON
ma-265	147	15	note	note	VERB
ma-265	147	16	that	that	SCONJ
ma-265	147	17	we	we	PRON
ma-265	147	18	may	may	AUX
ma-265	147	19	replace	replace	VERB
ma-265	147	20	f	f	PROPN
ma-265	147	21	(	(	PUNCT
ma-265	147	22	z	z	NOUN
ma-265	147	23	)	)	PUNCT
ma-265	147	24	by	by	ADP
ma-265	147	25	any	any	PRON
ma-265	147	26	of	of	ADP
ma-265	147	27	the	the	DET
ma-265	147	28	functions	function	NOUN
ma-265	147	29	in	in	ADP
ma-265	147	30	the	the	DET
ma-265	147	31	sequence	sequence	NOUN
ma-265	147	32	f	f	PROPN
ma-265	147	33	(	(	PUNCT
ma-265	147	34	z	z	NOUN
ma-265	147	35	)	)	PUNCT
ma-265	148	1	+	+	NOUN
ma-265	149	1	2πiz	2πiz	NOUN
ma-265	149	2	.	.	PUNCT
ma-265	150	1	all	all	DET
ma-265	150	2	ofthese	ofthese	NOUN
ma-265	150	3	are	be	AUX
ma-265	150	4	members	member	NOUN
ma-265	150	5	of	of	ADP
ma-265	150	6	rp	rp	NOUN
ma-265	150	7	that	that	PRON
ma-265	150	8	will	will	AUX
ma-265	150	9	generate	generate	VERB
ma-265	150	10	s(z	s(z	PROPN
ma-265	150	11	)	)	PUNCT
ma-265	150	12	just	just	ADV
ma-265	150	13	as	as	SCONJ
ma-265	150	14	f	f	PROPN
ma-265	150	15	(	(	PUNCT
ma-265	150	16	z	z	NOUN
ma-265	150	17	)	)	PUNCT
ma-265	150	18	does	do	VERB
ma-265	150	19	.	.	PUNCT
ma-265	151	1	however	however	ADV
ma-265	151	2	,	,	PUNCT
ma-265	151	3	if	if	SCONJ
ma-265	151	4	g(z)−f	g(z)−f	PROPN
ma-265	151	5	(	(	PUNCT
ma-265	151	6	z	z	NOUN
ma-265	151	7	)	)	PUNCT
ma-265	151	8	6∈	6∈	NOUN
ma-265	151	9	2πizand	2πizand	NUM
ma-265	151	10	g(z	g(z	PROPN
ma-265	151	11	)	)	PUNCT
ma-265	151	12	(	(	PUNCT
ma-265	151	13	like	like	ADP
ma-265	151	14	f	f	X
ma-265	151	15	(	(	PUNCT
ma-265	151	16	z	z	NOUN
ma-265	151	17	)	)	PUNCT
ma-265	151	18	)	)	PUNCT
ma-265	151	19	belongs	belong	VERB
ma-265	151	20	to	to	ADP
ma-265	151	21	rp	rp	NOUN
ma-265	151	22	,	,	PUNCT
ma-265	151	23	then	then	ADV
ma-265	151	24	exp(−f	exp(−f	PROPN
ma-265	151	25	)	)	PUNCT
ma-265	151	26	and	and	CCONJ
ma-265	151	27	exp(−g	exp(−g	PROPN
ma-265	151	28	)	)	PUNCT
ma-265	151	29	are	be	AUX
ma-265	151	30	different	different	ADJ
ma-265	151	31	holomorphic	holomorphic	ADJ
ma-265	151	32	functions.can	functions.can	PUNCT
ma-265	151	33	they	they	PRON
ma-265	151	34	share	share	VERB
ma-265	151	35	the	the	DET
ma-265	151	36	same	same	ADJ
ma-265	151	37	fixed	fix	VERB
ma-265	151	38	-	-	PUNCT
ma-265	151	39	point	point	NOUN
ma-265	151	40	s(z	s(z	PROPN
ma-265	151	41	)	)	PUNCT
ma-265	151	42	?	?	PUNCT
ma-265	152	1	that	that	PRON
ma-265	152	2	is	be	AUX
ma-265	152	3	,	,	PUNCT
ma-265	152	4	can	can	AUX
ma-265	152	5	the	the	DET
ma-265	152	6	following	following	NOUN
ma-265	152	7	be	be	AUX
ma-265	152	8	true	true	ADJ
ma-265	152	9	?	?	PUNCT
ma-265	153	1	s(z	s(z	NOUN
ma-265	153	2	)	)	PUNCT
ma-265	153	3	=	=	SYM
ma-265	153	4	exp	exp	NOUN
ma-265	153	5	(	(	PUNCT
ma-265	153	6	−f	−f	PROPN
ma-265	153	7	(	(	PUNCT
ma-265	153	8	z	z	NOUN
ma-265	153	9	·	·	PUNCT
ma-265	153	10	s(z	s(z	PROPN
ma-265	153	11	)	)	PUNCT
ma-265	153	12	)	)	PUNCT
ma-265	153	13	)	)	PUNCT
ma-265	154	1	=	=	NOUN
ma-265	154	2	exp	exp	NOUN
ma-265	154	3	(	(	PUNCT
ma-265	154	4	−g(z	−g(z	NOUN
ma-265	154	5	·	·	PUNCT
ma-265	154	6	s(z	s(z	NOUN
ma-265	154	7	)	)	PUNCT
ma-265	154	8	)	)	PUNCT
ma-265	154	9	)	)	PUNCT
ma-265	155	1	z	z	X
ma-265	155	2	∈	∈	PROPN
ma-265	155	3	u.	u.	VERB
ma-265	155	4	by	by	ADP
ma-265	155	5	the	the	DET
ma-265	155	6	permanence	permanence	NOUN
ma-265	155	7	principle	principle	NOUN
ma-265	155	8	for	for	ADP
ma-265	155	9	holomorphic	holomorphic	ADJ
ma-265	155	10	functions	function	NOUN
ma-265	155	11	this	this	PRON
ma-265	155	12	holds	hold	VERB
ma-265	155	13	if	if	SCONJ
ma-265	155	14	and	and	CCONJ
ma-265	155	15	only	only	ADV
ma-265	156	1	if	if	SCONJ
ma-265	156	2	g	g	PROPN
ma-265	156	3	−	−	PROPN
ma-265	156	4	f	f	PROPN
ma-265	156	5	∈	∈	PROPN
ma-265	156	6	2πiz(which	2πiz(which	NUM
ma-265	156	7	is	be	AUX
ma-265	156	8	not	not	PART
ma-265	156	9	the	the	DET
ma-265	156	10	case	case	NOUN
ma-265	156	11	)	)	PUNCT
ma-265	156	12	.	.	PUNCT
ma-265	157	1	so	so	ADV
ma-265	157	2	the	the	DET
ma-265	157	3	assignment	assignment	NOUN
ma-265	157	4	:	:	PUNCT
ma-265	158	1	[	[	X
ma-265	158	2	f	f	X
ma-265	158	3	]	]	X
ma-265	158	4	:	:	PUNCT
ma-265	158	5	=	=	SYM
ma-265	158	6	f	f	PROPN
ma-265	159	1	+	+	CCONJ
ma-265	159	2	2πiz	2πiz	NUM
ma-265	159	3	→	→	SYM
ma-265	159	4	s	s	PART
ma-265	159	5	is	be	AUX
ma-265	159	6	an	an	DET
ma-265	159	7	injection	injection	NOUN
ma-265	159	8	of	of	ADP
ma-265	159	9	the	the	DET
ma-265	159	10	quotientspace	quotientspace	NOUN
ma-265	159	11	of	of	ADP
ma-265	159	12	rp	rp	NOUN
ma-265	159	13	,	,	PUNCT
ma-265	159	14	namely	namely	ADV
ma-265	159	15	of	of	ADP
ma-265	159	16	rp/2πiz	rp/2πiz	NOUN
ma-265	159	17	onto	onto	ADP
ma-265	159	18	the	the	DET
ma-265	159	19	family	family	NOUN
ma-265	159	20	of	of	ADP
ma-265	159	21	functions	function	NOUN
ma-265	159	22	s[f	s[f	NOUN
ma-265	159	23	]	]	PUNCT
ma-265	159	24	(	(	PUNCT
ma-265	159	25	z	z	NOUN
ma-265	159	26	)	)	PUNCT
ma-265	159	27	in	in	ADP
ma-265	159	28	the	the	DET
ma-265	159	29	unit	unit	NOUN
ma-265	159	30	ball	ball	NOUN
ma-265	159	31	of	of	ADP
ma-265	159	32	h∞(u),such	h∞(u),such	PROPN
ma-265	159	33	that	that	SCONJ
ma-265	159	34	z	z	NOUN
ma-265	159	35	·	·	PUNCT
ma-265	159	36	s[f	s[f	NOUN
ma-265	159	37	]	]	PUNCT
ma-265	159	38	(	(	PUNCT
ma-265	159	39	z	z	NOUN
ma-265	159	40	)	)	PUNCT
ma-265	159	41	:	:	PUNCT
ma-265	160	1	u	u	NOUN
ma-265	160	2	→	→	SYM
ma-265	160	3	im(z	im(z	X
ma-265	160	4	·	·	PUNCT
ma-265	160	5	s[f	s[f	VERB
ma-265	160	6	]	]	PUNCT
ma-265	160	7	(	(	PUNCT
ma-265	160	8	z	z	NOUN
ma-265	160	9	)	)	PUNCT
ma-265	160	10	)	)	PUNCT
ma-265	161	1	⊆	⊆	NUM
ma-265	161	2	u	u	NOUN
ma-265	161	3	is	be	AUX
ma-265	161	4	a	a	DET
ma-265	161	5	conformal	conformal	ADJ
ma-265	161	6	mapping	mapping	NOUN
ma-265	161	7	,	,	PUNCT
ma-265	161	8	where	where	SCONJ
ma-265	161	9	s[f	s[f	NOUN
ma-265	161	10	]	]	PUNCT
ma-265	161	11	is	be	AUX
ma-265	161	12	the	the	DET
ma-265	161	13	usual	usual	ADJ
ma-265	161	14	f	f	NOUN
ma-265	161	15	(	(	PUNCT
ma-265	161	16	z	z	NOUN
ma-265	161	17	)	)	PUNCT
ma-265	161	18	fixed	fix	VERB
ma-265	161	19	-	-	PUNCT
ma-265	161	20	point	point	NOUN
ma-265	161	21	:	:	PUNCT
ma-265	161	22	s[f	s[f	NOUN
ma-265	161	23	]	]	PUNCT
ma-265	161	24	=	=	PUNCT
ma-265	161	25	exp(−f	exp(−f	X
ma-265	161	26	(	(	PUNCT
ma-265	161	27	z	z	NOUN
ma-265	161	28	·	·	PUNCT
ma-265	161	29	s[f	s[f	NOUN
ma-265	161	30	]	]	PUNCT
ma-265	161	31	(	(	PUNCT
ma-265	161	32	z	z	NOUN
ma-265	161	33	)	)	PUNCT
ma-265	161	34	)	)	PUNCT
ma-265	161	35	)	)	PUNCT
ma-265	161	36	.	.	PUNCT
ma-265	162	1	here	here	ADV
ma-265	162	2	(	(	PUNCT
ma-265	162	3	in	in	ADP
ma-265	162	4	the	the	DET
ma-265	162	5	notation	notation	NOUN
ma-265	162	6	of	of	ADP
ma-265	162	7	section	section	NOUN
ma-265	162	8	3	3	NUM
ma-265	162	9	)	)	PUNCT
ma-265	163	1	[	[	X
ma-265	163	2	f	f	X
ma-265	163	3	]	]	PUNCT
ma-265	163	4	stands	stand	VERB
ma-265	163	5	forany	forany	NOUN
ma-265	163	6	of	of	ADP
ma-265	163	7	the	the	DET
ma-265	163	8	members	member	NOUN
ma-265	163	9	of	of	ADP
ma-265	163	10	the	the	DET
ma-265	163	11	equivalence	equivalence	NOUN
ma-265	163	12	class	class	NOUN
ma-265	164	1	[	[	X
ma-265	164	2	f	f	X
ma-265	164	3	]	]	X
ma-265	164	4	in	in	ADP
ma-265	164	5	rp/2πiz	rp/2πiz	PROPN
ma-265	164	6	.	.	PUNCT
ma-265	165	1	we	we	PRON
ma-265	165	2	got	get	VERB
ma-265	165	3	our	our	PRON
ma-265	165	4	parametrization	parametrization	NOUN
ma-265	165	5	thatthe	thatthe	NOUN
ma-265	165	6	title	title	NOUN
ma-265	165	7	of	of	ADP
ma-265	165	8	this	this	DET
ma-265	165	9	section	section	NOUN
ma-265	165	10	refers	refer	VERB
ma-265	165	11	to	to	ADP
ma-265	165	12	.	.	PUNCT
ma-265	166	1	[	[	X
ma-265	166	2	f	f	X
ma-265	166	3	]	]	X
ma-265	166	4	determines	determine	VERB
ma-265	166	5	the	the	DET
ma-265	166	6	conformal	conformal	ADJ
ma-265	166	7	mapping	mapping	NOUN
ma-265	166	8	z	z	NOUN
ma-265	166	9	·	·	PUNCT
ma-265	166	10	s[f	s[f	NOUN
ma-265	166	11	]	]	PUNCT
ma-265	166	12	via	via	ADP
ma-265	166	13	the	the	DET
ma-265	166	14	fixed	fix	VERB
ma-265	166	15	-	-	PUNCT
ma-265	166	16	pointequation	pointequation	NOUN
ma-265	166	17	.	.	PUNCT
ma-265	167	1	so	so	ADV
ma-265	168	1	[	[	X
ma-265	168	2	f	f	X
ma-265	168	3	]	]	X
ma-265	168	4	is	be	AUX
ma-265	168	5	the	the	DET
ma-265	168	6	parameter	parameter	NOUN
ma-265	168	7	of	of	ADP
ma-265	168	8	the	the	DET
ma-265	168	9	conformal	conformal	ADJ
ma-265	168	10	mapping	mapping	NOUN
ma-265	168	11	z	z	NOUN
ma-265	168	12	·	·	PUNCT
ma-265	168	13	s[f	s[f	NOUN
ma-265	168	14	]	]	PUNCT
ma-265	168	15	(	(	PUNCT
ma-265	168	16	z	z	NOUN
ma-265	168	17	)	)	PUNCT
ma-265	168	18	.	.	PUNCT
ma-265	169	1	if	if	SCONJ
ma-265	169	2	we	we	PRON
ma-265	169	3	define	define	VERB
ma-265	169	4	the	the	DET
ma-265	169	5	conformalmapping	conformalmapping	NOUN
ma-265	169	6	by	by	ADP
ma-265	169	7	w	w	NOUN
ma-265	169	8	=	=	SYM
ma-265	169	9	f[f	f[f	PROPN
ma-265	169	10	]	]	PUNCT
ma-265	169	11	(	(	PUNCT
ma-265	169	12	z	z	NOUN
ma-265	169	13	)	)	PUNCT
ma-265	169	14	=	=	SYM
ma-265	169	15	z	z	X
ma-265	169	16	·	·	PUNCT
ma-265	169	17	s[f	s[f	NOUN
ma-265	169	18	]	]	PUNCT
ma-265	169	19	(	(	PUNCT
ma-265	169	20	z	z	NOUN
ma-265	169	21	)	)	PUNCT
ma-265	169	22	,	,	PUNCT
ma-265	169	23	then	then	ADV
ma-265	169	24	f[f	f[f	PROPN
ma-265	169	25	]	]	PUNCT
ma-265	169	26	:	:	PUNCT
ma-265	169	27	u	u	NOUN
ma-265	169	28	→	→	SYM
ma-265	169	29	im(f[f	im(f[f	NOUN
ma-265	169	30	]	]	X
ma-265	169	31	)	)	PUNCT
ma-265	169	32	,	,	PUNCT
ma-265	169	33	is	be	AUX
ma-265	169	34	invertible	invertible	ADJ
ma-265	169	35	,	,	PUNCT
ma-265	169	36	so	so	SCONJ
ma-265	169	37	that	that	SCONJ
ma-265	169	38	z	z	NOUN
ma-265	170	1	=	=	PUNCT
ma-265	170	2	f	f	X
ma-265	170	3	−1	−1	NOUN
ma-265	171	1	[	[	X
ma-265	171	2	f	f	X
ma-265	171	3	]	]	X
ma-265	171	4	(	(	PUNCT
ma-265	171	5	w).using	w).use	VERB
ma-265	171	6	the	the	DET
ma-265	171	7	fixed	fix	VERB
ma-265	171	8	-	-	PUNCT
ma-265	171	9	point	point	NOUN
ma-265	171	10	equation	equation	NOUN
ma-265	171	11	:	:	PUNCT
ma-265	171	12	−	−	NOUN
ma-265	171	13	log	log	NOUN
ma-265	171	14	s[f	s[f	NOUN
ma-265	171	15	]	]	PUNCT
ma-265	171	16	=	=	SYM
ma-265	171	17	f	f	X
ma-265	171	18	(	(	PUNCT
ma-265	171	19	z	z	NOUN
ma-265	171	20	·	·	PUNCT
ma-265	171	21	s[f	s[f	NOUN
ma-265	171	22	]	]	PUNCT
ma-265	171	23	)	)	PUNCT
ma-265	171	24	we	we	PRON
ma-265	171	25	see	see	VERB
ma-265	171	26	that	that	SCONJ
ma-265	171	27	s[f	s[f	NOUN
ma-265	171	28	]	]	PUNCT
ma-265	171	29	determines	determine	VERB
ma-265	171	30	its	its	PRON
ma-265	171	31	parameter	parameter	NOUN
ma-265	172	1	[	[	X
ma-265	172	2	f	f	X
ma-265	172	3	]	]	PUNCT
ma-265	172	4	by	by	ADP
ma-265	172	5	:	:	PUNCT
ma-265	172	6	f	f	PROPN
ma-265	172	7	(	(	PUNCT
ma-265	172	8	w	w	NOUN
ma-265	172	9	)	)	PUNCT
ma-265	172	10	=	=	SYM
ma-265	173	1	−	−	PROPN
ma-265	173	2	log	log	NOUN
ma-265	173	3	(	(	PUNCT
ma-265	173	4	w	w	NOUN
ma-265	173	5	z	z	NOUN
ma-265	173	6	)	)	PUNCT
ma-265	173	7	=	=	SYM
ma-265	174	1	−	−	PROPN
ma-265	174	2	log	log	NOUN
ma-265	174	3	(	(	PUNCT
ma-265	174	4	w	w	NOUN
ma-265	174	5	f	f	PROPN
ma-265	174	6	−1(w	−1(w	NOUN
ma-265	174	7	)	)	PUNCT
ma-265	174	8	)	)	PUNCT
ma-265	174	9	.	.	PUNCT
ma-265	175	1	the	the	DET
ma-265	175	2	family	family	NOUN
ma-265	175	3	rp	rp	NOUN
ma-265	175	4	is	be	AUX
ma-265	175	5	algebraically	algebraically	ADV
ma-265	175	6	easy	easy	ADJ
ma-265	175	7	to	to	PART
ma-265	175	8	understand	understand	VERB
ma-265	175	9	,	,	PUNCT
ma-265	175	10	unlike	unlike	ADP
ma-265	175	11	the	the	DET
ma-265	175	12	family	family	NOUN
ma-265	175	13	of	of	ADP
ma-265	175	14	the	the	DET
ma-265	175	15	conformal	conformal	ADJ
ma-265	175	16	mappings	mapping	NOUN
ma-265	175	17	:	:	PUNCT
ma-265	175	18	{	{	PUNCT
ma-265	175	19	s[f	s[f	NOUN
ma-265	175	20	]	]	PUNCT
ma-265	176	1	|	|	ADV
ma-265	176	2	[	[	X
ma-265	176	3	f	f	X
ma-265	176	4	]	]	X
ma-265	176	5	∈	∈	PROPN
ma-265	176	6	rp/2πiz	rp/2πiz	NOUN
ma-265	176	7	}	}	PUNCT
ma-265	176	8	.	.	PUNCT
ma-265	177	1	for	for	ADP
ma-265	177	2	example	example	NOUN
ma-265	177	3	,	,	PUNCT
ma-265	177	4	see	see	VERB
ma-265	177	5	our	our	PRON
ma-265	177	6	remark	remark	NOUN
ma-265	177	7	3.2	3.2	NUM
ma-265	177	8	:	:	PUNCT
ma-265	177	9	rp	rp	NOUN
ma-265	177	10	is	be	AUX
ma-265	177	11	closed	close	VERB
ma-265	177	12	for	for	ADP
ma-265	177	13	taking	take	VERB
ma-265	177	14	linear	linear	ADJ
ma-265	177	15	combinations	combination	NOUN
ma-265	177	16	with	with	ADP
ma-265	177	17	coefficients	coefficient	NOUN
ma-265	177	18	a	a	DET
ma-265	177	19	,	,	PUNCT
ma-265	177	20	b	b	PROPN
ma-265	177	21	∈	∈	PROPN
ma-265	177	22	r≥0	r≥0	PROPN
ma-265	177	23	,	,	PUNCT
ma-265	177	24	such	such	ADJ
ma-265	177	25	that	that	SCONJ
ma-265	177	26	0	0	NUM
ma-265	177	27	<	<	X
ma-265	177	28	a+b	a+b	X
ma-265	177	29	≤	≤	NUM
ma-265	177	30	1	1	NUM
ma-265	177	31	,	,	PUNCT
ma-265	177	32	i.e.	i.e.	X
ma-265	177	33	∀f	∀f	PROPN
ma-265	177	34	,	,	PUNCT
ma-265	177	35	g	g	PROPN
ma-265	177	36	∈	∈	PROPN
ma-265	177	37	rp(or	rp(or	NOUN
ma-265	177	38	rp/2πiz	rp/2πiz	NOUN
ma-265	177	39	)	)	PUNCT
ma-265	177	40	,	,	PUNCT
ma-265	177	41	a	a	DET
ma-265	177	42	·	·	SYM
ma-265	177	43	f+b	f+b	X
ma-265	177	44	·	·	SYM
ma-265	177	45	g	g	PROPN
ma-265	177	46	∈	∈	PROPN
ma-265	177	47	rp(or	rp(or	NOUN
ma-265	177	48	rp/2πiz).geometrically	rp/2πiz).geometrically	ADV
ma-265	177	49	we	we	PRON
ma-265	177	50	are	be	AUX
ma-265	177	51	dealing	deal	VERB
ma-265	177	52	with	with	ADP
ma-265	177	53	cones	cone	NOUN
ma-265	177	54	.	.	PUNCT
ma-265	178	1	let	let	VERB
ma-265	178	2	(	(	PUNCT
ma-265	178	3	as	as	ADP
ma-265	178	4	usual	usual	ADJ
ma-265	178	5	)	)	PUNCT
ma-265	178	6	s[f	s[f	NOUN
ma-265	178	7	]	]	PUNCT
ma-265	178	8	=	=	PUNCT
ma-265	178	9	exp(−f	exp(−f	X
ma-265	178	10	(	(	PUNCT
ma-265	178	11	z	z	NOUN
ma-265	178	12	·	·	PUNCT
ma-265	178	13	s[f	s[f	NOUN
ma-265	178	14	]	]	X
ma-265	178	15	)	)	PUNCT
ma-265	178	16	)	)	PUNCT
ma-265	178	17	,	,	PUNCT
ma-265	178	18	s[g	s[g	PROPN
ma-265	178	19	]	]	X
ma-265	178	20	=	=	SYM
ma-265	178	21	exp(−g(z	exp(−g(z	PROPN
ma-265	178	22	·	·	PUNCT
ma-265	178	23	s[g	s[g	PROPN
ma-265	178	24	]	]	NUM
ma-265	178	25	)	)	PUNCT
ma-265	178	26	)	)	PUNCT
ma-265	178	27	,	,	PUNCT
ma-265	178	28	so	so	SCONJ
ma-265	178	29	that	that	SCONJ
ma-265	178	30	z	z	NOUN
ma-265	178	31	·	·	PUNCT
ma-265	178	32	s[f	s[f	NOUN
ma-265	178	33	]	]	PUNCT
ma-265	178	34	:	:	PUNCT
ma-265	178	35	u	u	NOUN
ma-265	178	36	→	→	SYM
ma-265	178	37	im(z	im(z	X
ma-265	178	38	·	·	PUNCT
ma-265	178	39	s[f	s[f	NOUN
ma-265	178	40	]	]	X
ma-265	178	41	)	)	PUNCT
ma-265	178	42	,	,	PUNCT
ma-265	178	43	z	z	NOUN
ma-265	178	44	·	·	PUNCT
ma-265	178	45	s[g	s[g	PROPN
ma-265	178	46	]	]	PUNCT
ma-265	178	47	:	:	PUNCT
ma-265	178	48	u	u	NOUN
ma-265	178	49	→	→	SYM
ma-265	178	50	im(z	im(z	X
ma-265	178	51	·	·	PUNCT
ma-265	178	52	s[g	s[g	PROPN
ma-265	178	53	]	]	PUNCT
ma-265	178	54	)	)	PUNCT
ma-265	178	55	are	be	AUX
ma-265	178	56	con	con	NOUN
ma-265	178	57	-	-	PUNCT
ma-265	178	58	formal	formal	ADJ
ma-265	178	59	mappings.then	mappings.then	ADV
ma-265	178	60	we	we	PRON
ma-265	178	61	make	make	VERB
ma-265	178	62	the	the	DET
ma-265	178	63	following	following	NOUN
ma-265	178	64	:	:	PUNCT
ma-265	178	65	definition	definition	NOUN
ma-265	178	66	4.1	4.1	NUM
ma-265	178	67	.	.	PUNCT
ma-265	178	68	∀	∀	PUNCT
ma-265	179	1	a	a	PRON
ma-265	179	2	,	,	PUNCT
ma-265	179	3	b	b	PROPN
ma-265	179	4	∈	∈	PROPN
ma-265	179	5	r≥0	r≥0	PROPN
ma-265	179	6	,	,	PUNCT
ma-265	179	7	0	0	NUM
ma-265	179	8	<	<	X
ma-265	179	9	a+b	a+b	NUM
ma-265	179	10	≤	≤	NUM
ma-265	179	11	1	1	NUM
ma-265	179	12	we	we	PRON
ma-265	179	13	define	define	VERB
ma-265	179	14	the	the	DET
ma-265	179	15	conic	conic	ADJ
ma-265	179	16	linear	linear	NOUN
ma-265	179	17	combination	combination	NOUN
ma-265	179	18	by	by	ADP
ma-265	179	19	the	the	DET
ma-265	179	20	equation	equation	NOUN
ma-265	179	21	:	:	PUNCT
ma-265	179	22	a	a	PRON
ma-265	179	23	·	·	PUNCT
ma-265	179	24	(	(	PUNCT
ma-265	179	25	z	z	NOUN
ma-265	179	26	·	·	PUNCT
ma-265	179	27	s[f	s[f	NOUN
ma-265	179	28	]	]	PUNCT
ma-265	179	29	)	)	PUNCT
ma-265	180	1	+	+	ADJ
ma-265	180	2	̂b	̂b	PROPN
ma-265	180	3	·	·	PUNCT
ma-265	180	4	(	(	PUNCT
ma-265	180	5	z	z	X
ma-265	180	6	·	·	PUNCT
ma-265	180	7	s[g	s[g	PROPN
ma-265	180	8	]	]	PUNCT
ma-265	180	9	)	)	PUNCT
ma-265	180	10	=	=	SYM
ma-265	180	11	z	z	X
ma-265	180	12	·	·	PUNCT
ma-265	180	13	s[a·f+b·g	s[a·f+b·g	NOUN
ma-265	180	14	]	]	X
ma-265	180	15	.	.	PUNCT
ma-265	181	1	this	this	DET
ma-265	181	2	definition	definition	NOUN
ma-265	181	3	(	(	PUNCT
ma-265	181	4	and	and	CCONJ
ma-265	181	5	a	a	DET
ma-265	181	6	similar	similar	ADJ
ma-265	181	7	one	one	NOUN
ma-265	181	8	for	for	ADP
ma-265	181	9	multiplication	multiplication	NOUN
ma-265	181	10	by	by	ADP
ma-265	181	11	a	a	DET
ma-265	181	12	real	real	ADJ
ma-265	181	13	non	non	ADJ
ma-265	181	14	-	-	ADJ
ma-265	181	15	negative	negative	ADJ
ma-265	181	16	scalar	scalar	ADJ
ma-265	181	17	)	)	PUNCT
ma-265	181	18	induces	induce	VERB
ma-265	181	19	onthe	onthe	NOUN
ma-265	181	20	family	family	NOUN
ma-265	181	21	of	of	ADP
ma-265	181	22	our	our	PRON
ma-265	181	23	conformal	conformal	ADJ
ma-265	181	24	mappings	mapping	NOUN
ma-265	181	25	the	the	DET
ma-265	181	26	same	same	ADJ
ma-265	181	27	conic	conic	ADJ
ma-265	181	28	structure	structure	NOUN
ma-265	181	29	as	as	ADP
ma-265	181	30	the	the	DET
ma-265	181	31	one	one	NOUN
ma-265	181	32	we	we	PRON
ma-265	181	33	easily	easily	ADV
ma-265	181	34	have	have	VERB
ma-265	181	35	on	on	ADP
ma-265	181	36	rp(or	rp(or	PROPN
ma-265	181	37	rp/2πiz	rp/2πiz	NUM
ma-265	181	38	)	)	PUNCT
ma-265	181	39	.	.	PUNCT
ma-265	182	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	182	2	eur	eur	PROPN
ma-265	182	3	.	.	PUNCT
ma-265	183	1	j.	j.	PROPN
ma-265	183	2	math	math	PROPN
ma-265	183	3	.	.	PUNCT
ma-265	184	1	anal	anal	PROPN
ma-265	184	2	.	.	PUNCT
ma-265	185	1	10.28924	10.28924	NUM
ma-265	185	2	/	/	SYM
ma-265	185	3	ada	ada	PROPN
ma-265	185	4	/	/	SYM
ma-265	185	5	ma.5.4	ma.5.4	PROPN
ma-265	185	6	6	6	NUM
ma-265	185	7	remark	remark	NOUN
ma-265	185	8	4.2	4.2	NUM
ma-265	185	9	.	.	PUNCT
ma-265	186	1	it	it	PRON
ma-265	186	2	is	be	AUX
ma-265	186	3	well	well	ADV
ma-265	186	4	known	know	VERB
ma-265	186	5	that	that	SCONJ
ma-265	186	6	there	there	PRON
ma-265	186	7	exist	exist	VERB
ma-265	186	8	natural	natural	ADJ
ma-265	186	9	and	and	CCONJ
ma-265	186	10	elementary	elementary	ADJ
ma-265	186	11	parametrizations	parametrization	NOUN
ma-265	186	12	between	between	ADP
ma-265	186	13	rp	rp	NOUN
ma-265	186	14	and	and	CCONJ
ma-265	186	15	sinn	sinn	PROPN
ma-265	186	16	and	and	CCONJ
ma-265	186	17	also	also	ADV
ma-265	186	18	between	between	ADP
ma-265	186	19	inn	inn	PROPN
ma-265	186	20	and	and	CCONJ
ma-265	186	21	sinn	sinn	PROPN
ma-265	186	22	.	.	PUNCT
ma-265	187	1	see	see	VERB
ma-265	187	2	the	the	DET
ma-265	187	3	explanations	explanation	NOUN
ma-265	187	4	in	in	ADP
ma-265	187	5	section	section	NOUN
ma-265	187	6	1	1	NUM
ma-265	187	7	.	.	PUNCT
ma-265	188	1	thus	thus	ADV
ma-265	188	2	,	,	PUNCT
ma-265	188	3	our	our	PRON
ma-265	188	4	lesselementary	lesselementary	ADJ
ma-265	188	5	parametrization	parametrization	NOUN
ma-265	188	6	of	of	ADP
ma-265	188	7	the	the	DET
ma-265	188	8	family	family	NOUN
ma-265	188	9	of	of	ADP
ma-265	188	10	conformal	conformal	ADJ
ma-265	188	11	mappings	mapping	NOUN
ma-265	188	12	z	z	NOUN
ma-265	188	13	·	·	PUNCT
ma-265	188	14	s[f	s[f	NOUN
ma-265	188	15	]	]	PUNCT
ma-265	188	16	(	(	PUNCT
ma-265	188	17	z	z	NOUN
ma-265	188	18	)	)	PUNCT
ma-265	188	19	by	by	ADP
ma-265	188	20	rp/2πiz	rp/2πiz	NOUN
ma-265	188	21	can	can	AUX
ma-265	188	22	nowbe	nowbe	VERB
ma-265	188	23	related	relate	VERB
ma-265	188	24	to	to	ADP
ma-265	188	25	the	the	DET
ma-265	188	26	tree	tree	NOUN
ma-265	188	27	of	of	ADP
ma-265	188	28	correspondences	correspondence	NOUN
ma-265	188	29	among	among	ADP
ma-265	188	30	sinn	sinn	PROPN
ma-265	188	31	,	,	PUNCT
ma-265	188	32	inn	inn	PROPN
ma-265	188	33	and	and	CCONJ
ma-265	188	34	rp	rp	NOUN
ma-265	188	35	.	.	PUNCT
ma-265	189	1	we	we	PRON
ma-265	189	2	naturally	naturally	ADV
ma-265	189	3	inquire	inquire	VERB
ma-265	189	4	as	as	ADP
ma-265	189	5	to	to	ADP
ma-265	189	6	what	what	PRON
ma-265	189	7	are	be	AUX
ma-265	189	8	the	the	DET
ma-265	189	9	conformal	conformal	ADJ
ma-265	189	10	members	member	NOUN
ma-265	189	11	that	that	PRON
ma-265	189	12	form	form	VERB
ma-265	189	13	the	the	DET
ma-265	189	14	family	family	NOUN
ma-265	189	15	of	of	ADP
ma-265	189	16	conformalmappings	conformalmapping	NOUN
ma-265	189	17	in	in	ADP
ma-265	189	18	the	the	DET
ma-265	189	19	tree	tree	NOUN
ma-265	189	20	of	of	ADP
ma-265	189	21	correspondences	correspondence	NOUN
ma-265	189	22	.	.	PUNCT
ma-265	190	1	we	we	PRON
ma-265	190	2	will	will	AUX
ma-265	190	3	deal	deal	VERB
ma-265	190	4	with	with	ADP
ma-265	190	5	that	that	PRON
ma-265	190	6	on	on	ADP
ma-265	190	7	the	the	DET
ma-265	190	8	next	next	ADJ
ma-265	190	9	section	section	NOUN
ma-265	190	10	.	.	PUNCT
ma-265	191	1	as	as	SCONJ
ma-265	191	2	expecteda	expecteda	ADJ
ma-265	191	3	main	main	ADJ
ma-265	191	4	ingredient	ingredient	NOUN
ma-265	191	5	of	of	ADP
ma-265	191	6	these	these	DET
ma-265	191	7	conformal	conformal	ADJ
ma-265	191	8	mappings	mapping	NOUN
ma-265	191	9	will	will	AUX
ma-265	191	10	be	be	AUX
ma-265	191	11	the	the	DET
ma-265	191	12	boundary	boundary	ADJ
ma-265	191	13	behaviour	behaviour	NOUN
ma-265	191	14	of	of	ADP
ma-265	191	15	the	the	DET
ma-265	191	16	inverseconformal	inverseconformal	ADJ
ma-265	191	17	mappings	mapping	NOUN
ma-265	191	18	im(z	im(z	X
ma-265	191	19	·	·	PUNCT
ma-265	191	20	s[f	s[f	VERB
ma-265	191	21	]	]	X
ma-265	191	22	)	)	PUNCT
ma-265	191	23	→	→	SYM
ma-265	191	24	u	u	NOUN
ma-265	191	25	.	.	PUNCT
ma-265	192	1	5	5	X
ma-265	192	2	.	.	X
ma-265	192	3	the	the	DET
ma-265	192	4	family	family	NOUN
ma-265	192	5	of	of	ADP
ma-265	192	6	conformal	conformal	ADJ
ma-265	192	7	mappings	mapping	NOUN
ma-265	192	8	conf	conf	NOUN
ma-265	192	9	our	our	PRON
ma-265	192	10	family	family	NOUN
ma-265	192	11	of	of	ADP
ma-265	192	12	conformal	conformal	ADJ
ma-265	192	13	mappings	mapping	NOUN
ma-265	192	14	is	be	AUX
ma-265	192	15	clearly	clearly	ADV
ma-265	192	16	given	give	VERB
ma-265	192	17	by	by	ADP
ma-265	192	18	the	the	DET
ma-265	192	19	following	following	NOUN
ma-265	192	20	:	:	PUNCT
ma-265	192	21	definition	definition	NOUN
ma-265	192	22	5.1	5.1	NUM
ma-265	192	23	.	.	PUNCT
ma-265	193	1	conf	conf	NOUN
ma-265	193	2	=	=	SYM
ma-265	193	3	{	{	PUNCT
ma-265	193	4	z	z	NOUN
ma-265	193	5	·	·	PUNCT
ma-265	193	6	s[f	s[f	NOUN
ma-265	193	7	]	]	PUNCT
ma-265	193	8	∈	∈	PROPN
ma-265	193	9	h(u	h(u	PROPN
ma-265	193	10	)	)	PUNCT
ma-265	193	11	∣∣	∣∣	X
ma-265	194	1	[	[	X
ma-265	194	2	f	f	X
ma-265	194	3	]	]	X
ma-265	194	4	∈	∈	PROPN
ma-265	194	5	rp/2πiz	rp/2πiz	NOUN
ma-265	194	6	,	,	PUNCT
ma-265	194	7	s[f](z	s[f](z	PROPN
ma-265	194	8	)	)	PUNCT
ma-265	194	9	=	=	SYM
ma-265	194	10	exp	exp	NOUN
ma-265	194	11	(	(	PUNCT
ma-265	194	12	−f(z	−f(z	NOUN
ma-265	194	13	·	·	PUNCT
ma-265	194	14	s[f](z	s[f](z	PROPN
ma-265	194	15	)	)	PUNCT
ma-265	194	16	)	)	PUNCT
ma-265	194	17	)	)	PUNCT
ma-265	194	18	,	,	PUNCT
ma-265	194	19	∀z	∀z	PROPN
ma-265	194	20	∈	∈	PROPN
ma-265	194	21	u	u	NOUN
ma-265	194	22	}	}	PUNCT
ma-265	194	23	.	.	PUNCT
ma-265	195	1	we	we	PRON
ma-265	195	2	recall	recall	VERB
ma-265	195	3	the	the	DET
ma-265	195	4	following	follow	VERB
ma-265	195	5	facts:(1	facts:(1	PROPN
ma-265	195	6	)	)	PUNCT
ma-265	195	7	z	z	NOUN
ma-265	195	8	·	·	PUNCT
ma-265	195	9	s[f	s[f	NOUN
ma-265	195	10	]	]	PUNCT
ma-265	195	11	:	:	PUNCT
ma-265	195	12	u	u	NOUN
ma-265	195	13	→	→	SYM
ma-265	195	14	im(z	im(z	X
ma-265	195	15	·	·	PUNCT
ma-265	195	16	s[f	s[f	NOUN
ma-265	195	17	]	]	PUNCT
ma-265	195	18	)	)	PUNCT
ma-265	195	19	is	be	AUX
ma-265	195	20	an	an	DET
ma-265	195	21	injection.(2	injection.(2	NOUN
ma-265	195	22	)	)	PUNCT
ma-265	195	23	z	z	NOUN
ma-265	195	24	·	·	PUNCT
ma-265	195	25	s[f	s[f	NOUN
ma-265	195	26	]	]	PUNCT
ma-265	195	27	∈	∈	PROPN
ma-265	195	28	bh∞(u	bh∞(u	NOUN
ma-265	195	29	)	)	PUNCT
ma-265	195	30	−	−	PROPN
ma-265	195	31	inn	inn	PROPN
ma-265	195	32	.	.	PUNCT
ma-265	196	1	(	(	PUNCT
ma-265	196	2	[	[	X
ma-265	196	3	3]).(3	3]).(3	NUM
ma-265	196	4	)	)	PUNCT
ma-265	196	5	if	if	SCONJ
ma-265	196	6	w	w	NOUN
ma-265	196	7	=	=	SYM
ma-265	196	8	f[f	f[f	PROPN
ma-265	196	9	]	]	PUNCT
ma-265	196	10	(	(	PUNCT
ma-265	196	11	z	z	NOUN
ma-265	196	12	)	)	PUNCT
ma-265	196	13	=	=	SYM
ma-265	197	1	z	z	X
ma-265	197	2	·	·	PUNCT
ma-265	197	3	s[f	s[f	NOUN
ma-265	197	4	]	]	PUNCT
ma-265	197	5	(	(	PUNCT
ma-265	197	6	z	z	NOUN
ma-265	197	7	)	)	PUNCT
ma-265	197	8	,	,	PUNCT
ma-265	197	9	(	(	PUNCT
ma-265	197	10	z	z	NOUN
ma-265	197	11	∈	∈	PROPN
ma-265	197	12	u	u	NOUN
ma-265	197	13	)	)	PUNCT
ma-265	197	14	,	,	PUNCT
ma-265	197	15	then	then	ADV
ma-265	197	16	f	f	PROPN
ma-265	197	17	(	(	PUNCT
ma-265	197	18	w	w	PROPN
ma-265	197	19	)	)	PUNCT
ma-265	197	20	=	=	SYM
ma-265	198	1	−	−	PROPN
ma-265	198	2	log	log	NOUN
ma-265	198	3	(	(	PUNCT
ma-265	198	4	w	w	NOUN
ma-265	198	5	z	z	NOUN
ma-265	198	6	)	)	PUNCT
ma-265	198	7	=	=	SYM
ma-265	199	1	−	−	PROPN
ma-265	199	2	log	log	NOUN
ma-265	199	3	(	(	PUNCT
ma-265	199	4	w	w	NOUN
ma-265	199	5	f	f	NOUN
ma-265	199	6	−1	−1	NOUN
ma-265	200	1	[	[	X
ma-265	200	2	f	f	X
ma-265	200	3	]	]	X
ma-265	200	4	(	(	PUNCT
ma-265	200	5	w	w	NOUN
ma-265	200	6	)	)	PUNCT
ma-265	200	7	)	)	PUNCT
ma-265	200	8	,	,	PUNCT
ma-265	200	9	w	w	PROPN
ma-265	200	10	∈	∈	PROPN
ma-265	200	11	im(z	im(z	ADV
ma-265	200	12	·	·	PUNCT
ma-265	200	13	s[f	s[f	VERB
ma-265	200	14	]	]	PUNCT
ma-265	200	15	(	(	PUNCT
ma-265	200	16	z	z	NOUN
ma-265	200	17	)	)	PUNCT
ma-265	200	18	)	)	PUNCT
ma-265	200	19	.	.	PUNCT
ma-265	201	1	we	we	PRON
ma-265	201	2	would	would	AUX
ma-265	201	3	like	like	VERB
ma-265	201	4	to	to	PART
ma-265	201	5	characterize	characterize	VERB
ma-265	201	6	the	the	DET
ma-265	201	7	conformal	conformal	ADJ
ma-265	201	8	family	family	NOUN
ma-265	201	9	conf	conf	NOUN
ma-265	201	10	without	without	ADP
ma-265	201	11	any	any	DET
ma-265	201	12	reference	reference	NOUN
ma-265	201	13	to	to	ADP
ma-265	201	14	the	the	DET
ma-265	201	15	family	family	NOUN
ma-265	201	16	ofthe	ofthe	NOUN
ma-265	201	17	parameters	parameter	NOUN
ma-265	201	18	rp/2πiz	rp/2πiz	NOUN
ma-265	201	19	.	.	PUNCT
ma-265	202	1	theorem	theorem	VERB
ma-265	202	2	5.2	5.2	NUM
ma-265	202	3	.	.	PUNCT
ma-265	203	1	the	the	DET
ma-265	203	2	family	family	NOUN
ma-265	203	3	conf	conf	NOUN
ma-265	203	4	consists	consist	VERB
ma-265	203	5	of	of	ADP
ma-265	203	6	all	all	DET
ma-265	203	7	the	the	DET
ma-265	203	8	holomorphic	holomorphic	ADJ
ma-265	203	9	functions	function	NOUN
ma-265	203	10	f	f	X
ma-265	203	11	(	(	PUNCT
ma-265	203	12	z	z	NOUN
ma-265	203	13	)	)	PUNCT
ma-265	203	14	∈	∈	PROPN
ma-265	203	15	h(u	h(u	PROPN
ma-265	203	16	)	)	PUNCT
ma-265	203	17	that	that	PRON
ma-265	203	18	satisfy	satisfy	VERB
ma-265	203	19	the	the	DET
ma-265	203	20	following	following	NOUN
ma-265	203	21	:	:	PUNCT
ma-265	203	22	(	(	PUNCT
ma-265	203	23	a	a	X
ma-265	203	24	)	)	PUNCT
ma-265	203	25	f	f	NOUN
ma-265	203	26	:	:	PUNCT
ma-265	203	27	u	u	NOUN
ma-265	203	28	→	→	SYM
ma-265	203	29	im(f	im(f	NOUN
ma-265	203	30	)	)	PUNCT
ma-265	204	1	⊆	⊆	NUM
ma-265	204	2	u	u	NOUN
ma-265	204	3	is	be	AUX
ma-265	204	4	a	a	DET
ma-265	204	5	conformal	conformal	ADJ
ma-265	204	6	mapping	mapping	NOUN
ma-265	204	7	.	.	PUNCT
ma-265	205	1	(	(	PUNCT
ma-265	205	2	b	b	X
ma-265	205	3	)	)	PUNCT
ma-265	205	4	f	f	NOUN
ma-265	205	5	(	(	PUNCT
ma-265	205	6	0	0	NUM
ma-265	205	7	)	)	PUNCT
ma-265	205	8	=	=	SYM
ma-265	205	9	0	0	X
ma-265	205	10	.	.	PUNCT
ma-265	206	1	(	(	PUNCT
ma-265	206	2	c	c	X
ma-265	206	3	)	)	PUNCT
ma-265	206	4	the	the	DET
ma-265	206	5	function	function	NOUN
ma-265	206	6	:	:	PUNCT
ma-265	206	7	f	f	PROPN
ma-265	206	8	(	(	PUNCT
ma-265	206	9	w	w	NOUN
ma-265	206	10	)	)	PUNCT
ma-265	206	11	=	=	SYM
ma-265	207	1	−	−	PROPN
ma-265	207	2	log	log	NOUN
ma-265	207	3	(	(	PUNCT
ma-265	207	4	w	w	NOUN
ma-265	207	5	f	f	PROPN
ma-265	207	6	−1(w	−1(w	NOUN
ma-265	207	7	)	)	PUNCT
ma-265	207	8	)	)	PUNCT
ma-265	207	9	,	,	PUNCT
ma-265	207	10	w	w	PROPN
ma-265	207	11	∈	∈	PROPN
ma-265	207	12	im(f	im(f	NOUN
ma-265	207	13	)	)	PUNCT
ma-265	207	14	,	,	PUNCT
ma-265	207	15	can	can	AUX
ma-265	207	16	be	be	AUX
ma-265	207	17	analytically	analytically	ADV
ma-265	207	18	be	be	AUX
ma-265	207	19	defined	define	VERB
ma-265	207	20	on	on	ADP
ma-265	207	21	all	all	PRON
ma-265	207	22	of	of	ADP
ma-265	207	23	u	u	NOUN
ma-265	207	24	(	(	PUNCT
ma-265	207	25	not	not	PART
ma-265	207	26	just	just	ADV
ma-265	207	27	on	on	ADP
ma-265	207	28	im(f	im(f	NOUN
ma-265	207	29	)	)	PUNCT
ma-265	207	30	)	)	PUNCT
ma-265	207	31	,	,	PUNCT
ma-265	207	32	and	and	CCONJ
ma-265	207	33	it	it	PRON
ma-265	207	34	satisfies	satisfy	VERB
ma-265	207	35	<	<	X
ma-265	207	36	f	f	X
ma-265	207	37	(	(	PUNCT
ma-265	207	38	w	w	PROPN
ma-265	207	39	)	)	PUNCT
ma-265	207	40	≥	≥	NOUN
ma-265	207	41	0	0	NUM
ma-265	207	42	for	for	ADP
ma-265	207	43	all	all	DET
ma-265	207	44	w	w	PROPN
ma-265	207	45	∈	∈	PROPN
ma-265	207	46	im(f	im(f	NOUN
ma-265	207	47	)	)	PUNCT
ma-265	207	48	and	and	CCONJ
ma-265	207	49	<	<	X
ma-265	207	50	f	f	X
ma-265	207	51	(	(	PUNCT
ma-265	207	52	f	f	PROPN
ma-265	207	53	−1(w	−1(w	ADV
ma-265	207	54	)	)	PUNCT
ma-265	207	55	)	)	PUNCT
ma-265	208	1	=	=	SYM
ma-265	208	2	0	0	NUM
ma-265	208	3	for	for	ADP
ma-265	208	4	all	all	DET
ma-265	208	5	w	w	PROPN
ma-265	208	6	∈	∈	PROPN
ma-265	208	7	∂	∂	NOUN
ma-265	208	8	im(f	im(f	NOUN
ma-265	208	9	)	)	PUNCT
ma-265	208	10	.	.	PUNCT
ma-265	209	1	(	(	PUNCT
ma-265	209	2	d	d	X
ma-265	209	3	)	)	PUNCT
ma-265	209	4	for	for	ADP
ma-265	209	5	a	a	DET
ma-265	209	6	fixed	fix	VERB
ma-265	209	7	z	z	NOUN
ma-265	209	8	∈	∈	PROPN
ma-265	209	9	u	u	NOUN
ma-265	209	10	,	,	PUNCT
ma-265	209	11	the	the	DET
ma-265	209	12	function	function	NOUN
ma-265	209	13	z	z	PROPN
ma-265	209	14	·	·	PUNCT
ma-265	209	15	t	t	PROPN
ma-265	209	16	f	f	X
ma-265	209	17	−1(z	−1(z	X
ma-265	209	18	·	·	SYM
ma-265	209	19	t	t	PROPN
ma-265	209	20	)	)	PUNCT
ma-265	209	21	is	be	AUX
ma-265	209	22	a	a	DET
ma-265	209	23	contraction	contraction	NOUN
ma-265	209	24	in	in	ADP
ma-265	209	25	t	t	PROPN
ma-265	209	26	∈	∈	PROPN
ma-265	209	27	u	u	NOUN
ma-265	209	28	for	for	ADP
ma-265	209	29	which	which	PRON
ma-265	209	30	z	z	NOUN
ma-265	209	31	·	·	PUNCT
ma-265	209	32	t	t	PROPN
ma-265	209	33	∈	∈	PROPN
ma-265	209	34	im(f	im(f	NOUN
ma-265	209	35	)	)	PUNCT
ma-265	209	36	.	.	PUNCT
ma-265	210	1	it	it	PRON
ma-265	210	2	is	be	AUX
ma-265	210	3	a	a	DET
ma-265	210	4	contraction	contraction	NOUN
ma-265	210	5	with	with	ADP
ma-265	210	6	respect	respect	NOUN
ma-265	210	7	to	to	ADP
ma-265	210	8	the	the	DET
ma-265	210	9	euclidean	euclidean	ADJ
ma-265	210	10	metric	metric	NOUN
ma-265	210	11	.	.	PUNCT
ma-265	211	1	proof.let	proof.let	X
ma-265	211	2	us	we	PRON
ma-265	211	3	denote	denote	VERB
ma-265	211	4	the	the	DET
ma-265	211	5	family	family	NOUN
ma-265	211	6	of	of	ADP
ma-265	211	7	all	all	DET
ma-265	211	8	the	the	DET
ma-265	211	9	mappings	mapping	NOUN
ma-265	211	10	f	f	PROPN
ma-265	211	11	∈	∈	PROPN
ma-265	211	12	h(u	h(u	PROPN
ma-265	211	13	)	)	PUNCT
ma-265	211	14	that	that	PRON
ma-265	211	15	satisfy	satisfy	VERB
ma-265	211	16	(	(	PUNCT
ma-265	211	17	a	a	X
ma-265	211	18	)	)	PUNCT
ma-265	211	19	,	,	PUNCT
ma-265	211	20	(	(	PUNCT
ma-265	211	21	b	b	NOUN
ma-265	211	22	)	)	PUNCT
ma-265	211	23	,	,	PUNCT
ma-265	211	24	(	(	PUNCT
ma-265	211	25	c	c	X
ma-265	211	26	)	)	PUNCT
ma-265	211	27	and	and	CCONJ
ma-265	211	28	(	(	PUNCT
ma-265	211	29	d	d	X
ma-265	211	30	)	)	PUNCT
ma-265	211	31	by	by	ADP
ma-265	211	32	a.	a.	NOUN
ma-265	211	33	weneed	weneed	NOUN
ma-265	211	34	to	to	PART
ma-265	211	35	prove	prove	VERB
ma-265	211	36	that	that	DET
ma-265	211	37	conf	conf	NOUN
ma-265	211	38	=	=	PUNCT
ma-265	211	39	a	a	PRON
ma-265	211	40	where	where	SCONJ
ma-265	211	41	the	the	DET
ma-265	211	42	definition	definition	NOUN
ma-265	211	43	of	of	ADP
ma-265	211	44	conf	conf	NOUN
ma-265	211	45	is	be	AUX
ma-265	211	46	given	give	VERB
ma-265	211	47	in	in	ADP
ma-265	211	48	definition	definition	NOUN
ma-265	211	49	5.1	5.1	NUM
ma-265	211	50	.	.	PUNCT
ma-265	212	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	212	2	eur	eur	PROPN
ma-265	212	3	.	.	PUNCT
ma-265	213	1	j.	j.	PROPN
ma-265	213	2	math	math	PROPN
ma-265	213	3	.	.	PUNCT
ma-265	214	1	anal	anal	PROPN
ma-265	214	2	.	.	PUNCT
ma-265	215	1	10.28924	10.28924	NUM
ma-265	215	2	/	/	SYM
ma-265	215	3	ada	ada	PROPN
ma-265	215	4	/	/	SYM
ma-265	215	5	ma.5.4	ma.5.4	PROPN
ma-265	215	6	7(i	7(i	NUM
ma-265	215	7	)	)	PUNCT
ma-265	215	8	conf	conf	NOUN
ma-265	215	9	⊆	⊆	NUM
ma-265	215	10	a	a	PRON
ma-265	215	11	:	:	PUNCT
ma-265	215	12	let	let	VERB
ma-265	215	13	f[f	f[f	PROPN
ma-265	215	14	]	]	X
ma-265	215	15	(	(	PUNCT
ma-265	215	16	z	z	NOUN
ma-265	215	17	)	)	PUNCT
ma-265	215	18	=	=	SYM
ma-265	215	19	z	z	X
ma-265	215	20	·	·	PUNCT
ma-265	215	21	s[f	s[f	NOUN
ma-265	215	22	]	]	PUNCT
ma-265	215	23	(	(	PUNCT
ma-265	215	24	z	z	NOUN
ma-265	215	25	)	)	PUNCT
ma-265	215	26	∈	∈	PROPN
ma-265	215	27	conf	conf	NOUN
ma-265	215	28	.	.	PUNCT
ma-265	216	1	by	by	ADP
ma-265	216	2	fact	fact	NOUN
ma-265	216	3	(	(	PUNCT
ma-265	216	4	1	1	X
ma-265	216	5	)	)	PUNCT
ma-265	216	6	after	after	ADP
ma-265	216	7	definition	definition	NOUN
ma-265	216	8	5.1	5.1	NUM
ma-265	216	9	,	,	PUNCT
ma-265	216	10	f[f	f[f	PROPN
ma-265	216	11	]	]	PUNCT
ma-265	216	12	:	:	PUNCT
ma-265	216	13	u	u	NOUN
ma-265	216	14	→	→	SYM
ma-265	216	15	im(f[f	im(f[f	NOUN
ma-265	216	16	]	]	X
ma-265	216	17	)	)	PUNCT
ma-265	217	1	⊆	⊆	NUM
ma-265	217	2	u	u	NOUN
ma-265	217	3	is	be	AUX
ma-265	217	4	aninjection	aninjection	NOUN
ma-265	217	5	.	.	PUNCT
ma-265	218	1	clearly	clearly	ADV
ma-265	218	2	f[f	f[f	PROPN
ma-265	218	3	]	]	X
ma-265	218	4	(	(	PUNCT
ma-265	218	5	0	0	NUM
ma-265	218	6	)	)	PUNCT
ma-265	218	7	=	=	NOUN
ma-265	218	8	0	0	X
ma-265	218	9	.	.	PUNCT
ma-265	219	1	by	by	ADP
ma-265	219	2	fact	fact	NOUN
ma-265	219	3	(	(	PUNCT
ma-265	219	4	3	3	X
ma-265	219	5	)	)	PUNCT
ma-265	219	6	after	after	ADP
ma-265	219	7	definition	definition	NOUN
ma-265	219	8	5.1	5.1	NUM
ma-265	219	9	,	,	PUNCT
ma-265	219	10	f	f	PROPN
ma-265	219	11	(	(	PUNCT
ma-265	219	12	w	w	NOUN
ma-265	219	13	)	)	PUNCT
ma-265	219	14	=	=	SYM
ma-265	220	1	−	−	PROPN
ma-265	220	2	log	log	NOUN
ma-265	220	3	(	(	PUNCT
ma-265	220	4	w	w	NOUN
ma-265	220	5	f	f	NOUN
ma-265	220	6	−1	−1	NOUN
ma-265	221	1	[	[	X
ma-265	221	2	f	f	X
ma-265	221	3	]	]	X
ma-265	221	4	(	(	PUNCT
ma-265	221	5	w	w	NOUN
ma-265	221	6	)	)	PUNCT
ma-265	221	7	)	)	PUNCT
ma-265	221	8	,	,	PUNCT
ma-265	221	9	∀w	∀w	PROPN
ma-265	221	10	∈	∈	PROPN
ma-265	221	11	im(f	im(f	NOUN
ma-265	221	12	)	)	PUNCT
ma-265	221	13	.	.	PUNCT
ma-265	222	1	finally	finally	ADV
ma-265	222	2	,	,	PUNCT
ma-265	222	3	by	by	ADP
ma-265	222	4	definition	definition	NOUN
ma-265	222	5	3.1	3.1	NUM
ma-265	222	6	(	(	PUNCT
ma-265	222	7	iii	iii	NOUN
ma-265	222	8	)	)	PUNCT
ma-265	222	9	we	we	PRON
ma-265	222	10	have	have	VERB
ma-265	222	11	:	:	PUNCT
ma-265	222	12	(	(	PUNCT
ma-265	222	13	iii	iii	X
ma-265	222	14	)	)	PUNCT
ma-265	222	15	the	the	DET
ma-265	222	16	function	function	NOUN
ma-265	222	17	of	of	ADP
ma-265	222	18	t	t	PROPN
ma-265	222	19	∈	∈	PROPN
ma-265	222	20	u	u	NOUN
ma-265	222	21	given	give	VERB
ma-265	222	22	by	by	ADP
ma-265	222	23	exp	exp	NOUN
ma-265	222	24	(	(	PUNCT
ma-265	222	25	−f	−f	NOUN
ma-265	222	26	(	(	PUNCT
ma-265	222	27	z	z	PROPN
ma-265	222	28	·	·	PUNCT
ma-265	222	29	t	t	PROPN
ma-265	222	30	)	)	PUNCT
ma-265	222	31	)	)	PUNCT
ma-265	222	32	is	be	AUX
ma-265	222	33	acontraction	acontraction	NOUN
ma-265	222	34	(	(	PUNCT
ma-265	222	35	with	with	ADP
ma-265	222	36	respect	respect	NOUN
ma-265	222	37	to	to	ADP
ma-265	222	38	the	the	DET
ma-265	222	39	euclidean	euclidean	ADJ
ma-265	222	40	metric	metric	NOUN
ma-265	222	41	)	)	PUNCT
ma-265	222	42	where	where	SCONJ
ma-265	222	43	z	z	PROPN
ma-265	222	44	∈	∈	PROPN
ma-265	222	45	u	u	NOUN
ma-265	222	46	is	be	AUX
ma-265	222	47	fixed	fix	VERB
ma-265	222	48	.	.	PUNCT
ma-265	223	1	but	but	CCONJ
ma-265	223	2	exp	exp	NOUN
ma-265	223	3	(	(	PUNCT
ma-265	223	4	−f	−f	PROPN
ma-265	223	5	(	(	PUNCT
ma-265	223	6	z	z	PROPN
ma-265	223	7	·	·	PUNCT
ma-265	223	8	t	t	PROPN
ma-265	223	9	)	)	PUNCT
ma-265	223	10	)	)	PUNCT
ma-265	224	1	=	=	PUNCT
ma-265	224	2	z	z	X
ma-265	224	3	·	·	PUNCT
ma-265	224	4	t	t	PROPN
ma-265	224	5	f	f	X
ma-265	224	6	−1(z	−1(z	X
ma-265	224	7	·	·	SYM
ma-265	224	8	t	t	PROPN
ma-265	224	9	)	)	PUNCT
ma-265	224	10	which	which	PRON
ma-265	224	11	proved	prove	VERB
ma-265	224	12	(	(	PUNCT
ma-265	224	13	d	d	NOUN
ma-265	224	14	)	)	PUNCT
ma-265	225	1	and	and	CCONJ
ma-265	225	2	completes	complete	VERB
ma-265	225	3	the	the	DET
ma-265	225	4	proof	proof	NOUN
ma-265	225	5	of	of	ADP
ma-265	225	6	conf	conf	NOUN
ma-265	225	7	⊆	⊆	NUM
ma-265	225	8	a.(ii	a.(ii	NUM
ma-265	225	9	)	)	PUNCT
ma-265	225	10	a	a	DET
ma-265	225	11	⊆	⊆	NUM
ma-265	225	12	conf	conf	NOUN
ma-265	225	13	:	:	PUNCT
ma-265	225	14	let	let	VERB
ma-265	225	15	f	f	X
ma-265	225	16	:	:	PUNCT
ma-265	225	17	u	u	PROPN
ma-265	225	18	→	→	SYM
ma-265	225	19	im(f	im(f	NOUN
ma-265	225	20	)	)	PUNCT
ma-265	226	1	⊆	⊆	X
ma-265	226	2	u	u	NOUN
ma-265	226	3	be	be	VERB
ma-265	226	4	an	an	DET
ma-265	226	5	elelment	elelment	NOUN
ma-265	226	6	of	of	ADP
ma-265	226	7	a.	a.	NOUN
ma-265	226	8	then	then	ADV
ma-265	226	9	f	f	PROPN
ma-265	226	10	(	(	PUNCT
ma-265	226	11	0	0	NUM
ma-265	226	12	)	)	PUNCT
ma-265	226	13	=	=	SYM
ma-265	226	14	0	0	NUM
ma-265	226	15	and	and	CCONJ
ma-265	226	16	|f	|f	PROPN
ma-265	227	1	(	(	PUNCT
ma-265	227	2	z)|	z)|	ADP
ma-265	227	3	≤	≤	ADV
ma-265	227	4	1	1	NUM
ma-265	227	5	for	for	ADP
ma-265	227	6	all	all	DET
ma-265	227	7	z	z	NOUN
ma-265	227	8	∈	∈	PROPN
ma-265	227	9	u	u	NOUN
ma-265	227	10	.	.	PUNCT
ma-265	228	1	by	by	ADP
ma-265	228	2	theschwarz	theschwarz	PROPN
ma-265	228	3	lemma	lemma	PROPN
ma-265	228	4	we	we	PRON
ma-265	228	5	get	get	VERB
ma-265	228	6	|f	|f	PROPN
ma-265	229	1	(	(	PUNCT
ma-265	229	2	z)|	z)|	ADP
ma-265	229	3	≤	≤	PUNCT
ma-265	229	4	|z	|z	PROPN
ma-265	230	1	|	|	ADV
ma-265	230	2	for	for	ADP
ma-265	230	3	all	all	DET
ma-265	230	4	z	z	NOUN
ma-265	230	5	∈	∈	PROPN
ma-265	230	6	u	u	NOUN
ma-265	230	7	.	.	PUNCT
ma-265	231	1	hence	hence	ADV
ma-265	231	2	for	for	ADP
ma-265	231	3	all	all	DET
ma-265	231	4	w	w	PROPN
ma-265	231	5	∈	∈	PROPN
ma-265	231	6	u	u	NOUN
ma-265	231	7	where	where	SCONJ
ma-265	231	8	w	w	PROPN
ma-265	231	9	=	=	SYM
ma-265	231	10	f	f	X
ma-265	231	11	(	(	PUNCT
ma-265	231	12	z	z	X
ma-265	231	13	)	)	PUNCT
ma-265	231	14	we	we	PRON
ma-265	231	15	have∣∣∣w	have∣∣∣w	VERB
ma-265	231	16	z	z	NOUN
ma-265	231	17	∣∣∣	∣∣∣	NOUN
ma-265	231	18	≤	≤	NUM
ma-265	231	19	1	1	NUM
ma-265	232	1	so	so	ADV
ma-265	232	2	−	−	NOUN
ma-265	232	3	log	log	VERB
ma-265	232	4	∣∣∣w	∣∣∣w	NUM
ma-265	232	5	z	z	NOUN
ma-265	232	6	∣∣∣	∣∣∣	NOUN
ma-265	232	7	≥	≥	NOUN
ma-265	232	8	0	0	NUM
ma-265	232	9	.	.	PUNCT
ma-265	233	1	if	if	SCONJ
ma-265	233	2	we	we	PRON
ma-265	233	3	define	define	VERB
ma-265	233	4	ff	ff	PROPN
ma-265	233	5	(	(	PUNCT
ma-265	233	6	w	w	NOUN
ma-265	233	7	)	)	PUNCT
ma-265	233	8	=	=	SYM
ma-265	233	9	−	−	PROPN
ma-265	233	10	log	log	NOUN
ma-265	233	11	(	(	PUNCT
ma-265	233	12	w	w	NOUN
ma-265	233	13	z	z	NOUN
ma-265	233	14	)	)	PUNCT
ma-265	233	15	=	=	SYM
ma-265	234	1	−	−	PROPN
ma-265	234	2	log	log	NOUN
ma-265	234	3	(	(	PUNCT
ma-265	234	4	w	w	NOUN
ma-265	234	5	f	f	PROPN
ma-265	234	6	−1(w	−1(w	NOUN
ma-265	234	7	)	)	PUNCT
ma-265	234	8	)	)	PUNCT
ma-265	234	9	,	,	PUNCT
ma-265	234	10	then	then	ADV
ma-265	234	11	<	<	X
ma-265	234	12	ff	ff	INTJ
ma-265	234	13	(	(	PUNCT
ma-265	234	14	w	w	NOUN
ma-265	234	15	)	)	PUNCT
ma-265	234	16	≥	≥	NOUN
ma-265	234	17	0	0	NUM
ma-265	234	18	.	.	PUNCT
ma-265	235	1	now	now	ADV
ma-265	235	2	(	(	PUNCT
ma-265	235	3	ii	ii	NOUN
ma-265	235	4	)	)	PUNCT
ma-265	235	5	and	and	CCONJ
ma-265	235	6	(	(	PUNCT
ma-265	235	7	iii	iii	NOUN
ma-265	235	8	)	)	PUNCT
ma-265	235	9	in	in	ADP
ma-265	235	10	definition	definition	NOUN
ma-265	235	11	3.1	3.1	NUM
ma-265	235	12	follow	follow	NOUN
ma-265	235	13	.	.	PUNCT
ma-265	236	1	hence	hence	ADV
ma-265	236	2	f	f	PROPN
ma-265	236	3	∈	∈	PROPN
ma-265	236	4	conf	conf	NOUN
ma-265	236	5	.	.	PUNCT
ma-265	237	1	�	�	PROPN
ma-265	237	2	here	here	ADV
ma-265	237	3	is	be	AUX
ma-265	237	4	an	an	DET
ma-265	237	5	interesting	interesting	ADJ
ma-265	237	6	consequence	consequence	NOUN
ma-265	237	7	on	on	ADP
ma-265	237	8	the	the	DET
ma-265	237	9	conformal	conformal	ADJ
ma-265	237	10	mappings	mapping	NOUN
ma-265	237	11	of	of	ADP
ma-265	237	12	the	the	DET
ma-265	237	13	family	family	NOUN
ma-265	237	14	conf	conf	NOUN
ma-265	237	15	:	:	PUNCT
ma-265	237	16	corollary	corollary	ADJ
ma-265	237	17	5.3	5.3	NUM
ma-265	237	18	.	.	PUNCT
ma-265	238	1	let	let	VERB
ma-265	238	2	f	f	NOUN
ma-265	238	3	,	,	PUNCT
ma-265	238	4	g	g	PROPN
ma-265	238	5	∈	∈	PROPN
ma-265	238	6	conf	conf	NOUN
ma-265	238	7	and	and	CCONJ
ma-265	238	8	let	let	VERB
ma-265	238	9	a	a	DET
ma-265	238	10	,	,	PUNCT
ma-265	238	11	b	b	PROPN
ma-265	238	12	∈	∈	PROPN
ma-265	238	13	r≥0	r≥0	PROPN
ma-265	238	14	,	,	PUNCT
ma-265	238	15	0	0	PUNCT
ma-265	238	16	<	<	X
ma-265	238	17	a+	a+	X
ma-265	238	18	b	b	NOUN
ma-265	238	19	≤	≤	ADJ
ma-265	238	20	1	1	NUM
ma-265	238	21	.	.	PUNCT
ma-265	239	1	then	then	ADV
ma-265	239	2	∃	∃	PROPN
ma-265	239	3	ha	ha	INTJ
ma-265	239	4	,	,	PUNCT
ma-265	239	5	b	b	PROPN
ma-265	239	6	∈	∈	PROPN
ma-265	239	7	conf	conf	NOUN
ma-265	239	8	such	such	ADJ
ma-265	239	9	that	that	SCONJ
ma-265	239	10	we	we	PRON
ma-265	239	11	have	have	VERB
ma-265	239	12	the	the	DET
ma-265	239	13	following	follow	VERB
ma-265	239	14	multiplicative	multiplicative	ADJ
ma-265	239	15	relation	relation	NOUN
ma-265	239	16	among	among	ADP
ma-265	239	17	these	these	DET
ma-265	239	18	three	three	NUM
ma-265	239	19	conformal	conformal	ADJ
ma-265	239	20	mappings	mapping	NOUN
ma-265	239	21	:(	:(	PUNCT
ma-265	240	1	h−1a	h−1a	PROPN
ma-265	240	2	,	,	PUNCT
ma-265	240	3	b(w	b(w	PROPN
ma-265	240	4	)	)	PUNCT
ma-265	240	5	w	w	NOUN
ma-265	240	6	)	)	PUNCT
ma-265	241	1	=	=	PUNCT
ma-265	242	1	(	(	PUNCT
ma-265	242	2	f	f	X
ma-265	242	3	−1(w	−1(w	ADV
ma-265	242	4	)	)	PUNCT
ma-265	242	5	w	w	NOUN
ma-265	242	6	)	)	PUNCT
ma-265	242	7	a	a	DET
ma-265	242	8	(	(	PUNCT
ma-265	242	9	g−1(w	g−1(w	PROPN
ma-265	242	10	)	)	PUNCT
ma-265	242	11	w	w	NOUN
ma-265	242	12	)	)	PUNCT
ma-265	242	13	b	b	PROPN
ma-265	242	14	.	.	PUNCT
ma-265	243	1	proof.by	proof.by	X
ma-265	243	2	the	the	DET
ma-265	243	3	proof	proof	NOUN
ma-265	243	4	of	of	ADP
ma-265	243	5	theorem	theorem	ADJ
ma-265	243	6	5.2	5.2	NUM
ma-265	243	7	it	it	PRON
ma-265	243	8	follows	follow	VERB
ma-265	243	9	that	that	SCONJ
ma-265	243	10	,	,	PUNCT
ma-265	243	11	f	f	PROPN
ma-265	243	12	,	,	PUNCT
ma-265	243	13	g	g	PROPN
ma-265	243	14	∈	∈	PROPN
ma-265	243	15	conf⇔	conf⇔	X
ma-265	244	1	−	−	PROPN
ma-265	244	2	log	log	NOUN
ma-265	244	3	(	(	PUNCT
ma-265	244	4	w	w	NOUN
ma-265	244	5	f	f	PROPN
ma-265	244	6	−1(w	−1(w	NOUN
ma-265	244	7	)	)	PUNCT
ma-265	244	8	)	)	PUNCT
ma-265	244	9	,	,	PUNCT
ma-265	244	10	−	−	PROPN
ma-265	244	11	log	log	NOUN
ma-265	244	12	(	(	PUNCT
ma-265	244	13	w	w	PROPN
ma-265	244	14	g−1(w	g−1(w	PROPN
ma-265	244	15	)	)	PUNCT
ma-265	244	16	)	)	PUNCT
ma-265	245	1	∈	∈	PROPN
ma-265	245	2	rp	rp	NOUN
ma-265	245	3	.	.	PUNCT
ma-265	246	1	we	we	PRON
ma-265	246	2	note	note	VERB
ma-265	246	3	that	that	SCONJ
ma-265	246	4	in	in	ADP
ma-265	246	5	f	f	PROPN
ma-265	246	6	−1(w	−1(w	ADV
ma-265	246	7	)	)	PUNCT
ma-265	246	8	we	we	PRON
ma-265	246	9	have	have	VERB
ma-265	246	10	w	w	PROPN
ma-265	246	11	∈	∈	PROPN
ma-265	246	12	im(f	im(f	NOUN
ma-265	246	13	)	)	PUNCT
ma-265	246	14	and	and	CCONJ
ma-265	246	15	in	in	ADP
ma-265	246	16	g−1(w	g−1(w	NOUN
ma-265	246	17	)	)	PUNCT
ma-265	246	18	we	we	PRON
ma-265	246	19	have	have	VERB
ma-265	246	20	w	w	NOUN
ma-265	246	21	∈	∈	PROPN
ma-265	246	22	im(g	im(g	PRON
ma-265	246	23	)	)	PUNCT
ma-265	246	24	.	.	PUNCT
ma-265	247	1	by	by	ADP
ma-265	247	2	property	property	NOUN
ma-265	247	3	(	(	PUNCT
ma-265	247	4	5)after	5)after	NUM
ma-265	247	5	definition	definition	NOUN
ma-265	247	6	5.1	5.1	NUM
ma-265	247	7	we	we	PRON
ma-265	247	8	know	know	VERB
ma-265	247	9	that	that	SCONJ
ma-265	247	10	the	the	DET
ma-265	247	11	two	two	NUM
ma-265	247	12	-	-	PUNCT
ma-265	247	13	dimensional	dimensional	ADJ
ma-265	247	14	lebesgue	lebesgue	NOUN
ma-265	247	15	measures	measure	NOUN
ma-265	247	16	of	of	ADP
ma-265	247	17	the	the	DET
ma-265	247	18	sets	set	NOUN
ma-265	247	19	u	u	NOUN
ma-265	247	20	−	−	NOUN
ma-265	247	21	im(f	im(f	NOUN
ma-265	247	22	)	)	PUNCT
ma-265	247	23	and	and	CCONJ
ma-265	247	24	u	u	NOUN
ma-265	247	25	−	−	PROPN
ma-265	247	26	im(g	im(g	PUNCT
ma-265	247	27	)	)	PUNCT
ma-265	247	28	are	be	AUX
ma-265	247	29	zero	zero	NUM
ma-265	247	30	.	.	PUNCT
ma-265	248	1	hence	hence	ADV
ma-265	248	2	im(f	im(f	VERB
ma-265	248	3	)	)	PUNCT
ma-265	249	1	∩	∩	NOUN
ma-265	249	2	im(g	im(g	PRON
ma-265	249	3	)	)	PUNCT
ma-265	249	4	is	be	AUX
ma-265	249	5	an	an	DET
ma-265	249	6	open	open	ADJ
ma-265	249	7	subset	subset	NOUN
ma-265	249	8	of	of	ADP
ma-265	249	9	u	u	PROPN
ma-265	249	10	and	and	CCONJ
ma-265	249	11	the	the	DET
ma-265	249	12	two	two	NUM
ma-265	249	13	-	-	PUNCT
ma-265	249	14	dimensionallebesgue	dimensionallebesgue	NOUN
ma-265	249	15	measure	measure	NOUN
ma-265	249	16	of	of	ADP
ma-265	249	17	the	the	DET
ma-265	249	18	set	set	ADJ
ma-265	249	19	u−	u−	PROPN
ma-265	249	20	(	(	PUNCT
ma-265	249	21	im(f	im(f	NOUN
ma-265	249	22	)	)	PUNCT
ma-265	249	23	∩	∩	NOUN
ma-265	249	24	im(g	im(g	PRON
ma-265	249	25	)	)	PUNCT
ma-265	249	26	)	)	PUNCT
ma-265	250	1	is	be	AUX
ma-265	250	2	zero	zero	NUM
ma-265	250	3	.	.	PUNCT
ma-265	251	1	so	so	ADV
ma-265	251	2	im(f	im(f	NOUN
ma-265	251	3	)	)	PUNCT
ma-265	251	4	∩	∩	NOUN
ma-265	251	5	im(g	im(g	PRON
ma-265	251	6	)	)	PUNCT
ma-265	251	7	is	be	AUX
ma-265	251	8	a	a	DET
ma-265	251	9	large	large	ADJ
ma-265	251	10	open	open	ADJ
ma-265	251	11	subsetof	subsetof	NOUN
ma-265	251	12	u	u	NOUN
ma-265	251	13	on	on	ADP
ma-265	251	14	which	which	PRON
ma-265	251	15	both	both	CCONJ
ma-265	251	16	holomorphic	holomorphic	ADJ
ma-265	251	17	functions	function	NOUN
ma-265	251	18	−	−	PROPN
ma-265	252	1	log	log	NOUN
ma-265	252	2	(	(	PUNCT
ma-265	252	3	w	w	NOUN
ma-265	252	4	f	f	PROPN
ma-265	252	5	−1(w	−1(w	NOUN
ma-265	252	6	)	)	PUNCT
ma-265	252	7	)	)	PUNCT
ma-265	252	8	,	,	PUNCT
ma-265	252	9	and	and	CCONJ
ma-265	252	10	−	−	PROPN
ma-265	252	11	log	log	NOUN
ma-265	252	12	(	(	PUNCT
ma-265	252	13	w	w	NOUN
ma-265	252	14	g−1(w	g−1(w	PROPN
ma-265	252	15	)	)	PUNCT
ma-265	252	16	)	)	PUNCT
ma-265	252	17	,	,	PUNCT
ma-265	252	18	are	be	AUX
ma-265	252	19	defined	define	VERB
ma-265	252	20	and	and	CCONJ
ma-265	252	21	belong	belong	VERB
ma-265	252	22	to	to	ADP
ma-265	252	23	rp	rp	NOUN
ma-265	252	24	.	.	PUNCT
ma-265	253	1	i.e.	i.e.	X
ma-265	253	2	these	these	PRON
ma-265	253	3	are	be	AUX
ma-265	253	4	the	the	DET
ma-265	253	5	restrictions	restriction	NOUN
ma-265	253	6	of	of	ADP
ma-265	253	7	rp	rp	NOUN
ma-265	253	8	functions	function	NOUN
ma-265	253	9	to	to	ADP
ma-265	253	10	the	the	DET
ma-265	253	11	intersection	intersection	NOUN
ma-265	253	12	ofthe	ofthe	NOUN
ma-265	253	13	images	image	NOUN
ma-265	253	14	of	of	ADP
ma-265	253	15	the	the	DET
ma-265	253	16	conformal	conformal	NOUN
ma-265	253	17	mappings	mapping	NOUN
ma-265	253	18	f	f	PROPN
ma-265	253	19	and	and	CCONJ
ma-265	253	20	g.	g.	PROPN
ma-265	253	21	since	since	SCONJ
ma-265	253	22	:	:	PUNCT
ma-265	253	23	a	a	DET
ma-265	253	24	{	{	PUNCT
ma-265	253	25	−	−	PROPN
ma-265	253	26	log	log	NOUN
ma-265	253	27	(	(	PUNCT
ma-265	253	28	w	w	NOUN
ma-265	253	29	f	f	PROPN
ma-265	253	30	−1(w	−1(w	NOUN
ma-265	253	31	)	)	PUNCT
ma-265	253	32	)	)	PUNCT
ma-265	253	33	}	}	PUNCT
ma-265	254	1	+	+	NUM
ma-265	254	2	b	b	X
ma-265	254	3	{	{	PUNCT
ma-265	254	4	−	−	PROPN
ma-265	254	5	log	log	NOUN
ma-265	254	6	(	(	PUNCT
ma-265	254	7	w	w	NOUN
ma-265	254	8	g−1(w	g−1(w	PROPN
ma-265	254	9	)	)	PUNCT
ma-265	254	10	)	)	PUNCT
ma-265	254	11	}	}	PUNCT
ma-265	254	12	=	=	PUNCT
ma-265	255	1	−	−	NOUN
ma-265	255	2	log	log	NOUN
ma-265	255	3	(	(	PUNCT
ma-265	255	4	w	w	NOUN
ma-265	255	5	f	f	PROPN
ma-265	255	6	−1(w	−1(w	NOUN
ma-265	255	7	)	)	PUNCT
ma-265	255	8	)	)	PUNCT
ma-265	255	9	a	a	PRON
ma-265	255	10	(	(	PUNCT
ma-265	255	11	w	w	NOUN
ma-265	255	12	g−1(w	g−1(w	PROPN
ma-265	255	13	)	)	PUNCT
ma-265	255	14	)	)	PUNCT
ma-265	255	15	b	b	X
ma-265	255	16	∈	∈	PROPN
ma-265	255	17	rp	rp	NOUN
ma-265	255	18	,	,	PUNCT
ma-265	255	19	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	255	20	eur	eur	PROPN
ma-265	255	21	.	.	PUNCT
ma-265	256	1	j.	j.	PROPN
ma-265	256	2	math	math	PROPN
ma-265	256	3	.	.	PUNCT
ma-265	257	1	anal	anal	PROPN
ma-265	257	2	.	.	PUNCT
ma-265	258	1	10.28924	10.28924	NUM
ma-265	258	2	/	/	SYM
ma-265	258	3	ada	ada	PROPN
ma-265	258	4	/	/	SYM
ma-265	258	5	ma.5.4	ma.5.4	PROPN
ma-265	258	6	8it	8it	NOUN
ma-265	258	7	follows	follow	VERB
ma-265	258	8	by	by	ADP
ma-265	258	9	the	the	DET
ma-265	258	10	proof	proof	NOUN
ma-265	258	11	of	of	ADP
ma-265	258	12	theorem	theorem	ADJ
ma-265	258	13	5.2	5.2	NUM
ma-265	258	14	that	that	PRON
ma-265	258	15	∃	∃	PROPN
ma-265	258	16	ha	ha	INTJ
ma-265	258	17	,	,	PUNCT
ma-265	258	18	b	b	PROPN
ma-265	258	19	∈	∈	PROPN
ma-265	258	20	conf	conf	NOUN
ma-265	258	21	such	such	ADJ
ma-265	258	22	that	that	SCONJ
ma-265	258	23	:(	:(	PUNCT
ma-265	258	24	w	w	PROPN
ma-265	258	25	f	f	PROPN
ma-265	258	26	−1(w	−1(w	ADV
ma-265	258	27	)	)	PUNCT
ma-265	258	28	)	)	PUNCT
ma-265	258	29	a	a	DET
ma-265	258	30	(	(	PUNCT
ma-265	258	31	w	w	NOUN
ma-265	258	32	g−1(w	g−1(w	PROPN
ma-265	258	33	)	)	PUNCT
ma-265	258	34	)	)	PUNCT
ma-265	259	1	b	b	X
ma-265	260	1	=	=	PRON
ma-265	261	1	(	(	PUNCT
ma-265	261	2	w	w	PROPN
ma-265	261	3	h−1a	h−1a	PROPN
ma-265	261	4	,	,	PUNCT
ma-265	261	5	b(w	b(w	PROPN
ma-265	261	6	)	)	PUNCT
ma-265	261	7	)	)	PUNCT
ma-265	261	8	.	.	PUNCT
ma-265	262	1	our	our	PRON
ma-265	262	2	proof	proof	NOUN
ma-265	262	3	is	be	AUX
ma-265	262	4	now	now	ADV
ma-265	262	5	completed	complete	VERB
ma-265	262	6	.	.	PUNCT
ma-265	263	1	�	�	PROPN
ma-265	263	2	one	one	PRON
ma-265	263	3	can	can	AUX
ma-265	263	4	conclude	conclude	VERB
ma-265	263	5	more	more	ADV
ma-265	263	6	surprising	surprising	ADJ
ma-265	263	7	properties	property	NOUN
ma-265	263	8	on	on	ADP
ma-265	263	9	the	the	DET
ma-265	263	10	conformal	conformal	ADJ
ma-265	263	11	mappings	mapping	NOUN
ma-265	263	12	of	of	ADP
ma-265	263	13	the	the	DET
ma-265	263	14	family	family	NOUN
ma-265	263	15	conf	conf	NOUN
ma-265	263	16	.	.	PUNCT
ma-265	264	1	6	6	NUM
ma-265	264	2	.	.	X
ma-265	264	3	the	the	DET
ma-265	264	4	geometry	geometry	NOUN
ma-265	264	5	of	of	ADP
ma-265	264	6	the	the	DET
ma-265	264	7	image	image	NOUN
ma-265	264	8	of	of	ADP
ma-265	264	9	conformal	conformal	ADJ
ma-265	264	10	mappings	mapping	NOUN
ma-265	264	11	in	in	ADP
ma-265	264	12	conf	conf	NOUN
ma-265	264	13	let	let	VERB
ma-265	264	14	f	f	PROPN
ma-265	264	15	∈	∈	PROPN
ma-265	264	16	rp	rp	NOUN
ma-265	264	17	.	.	PUNCT
ma-265	265	1	we	we	PRON
ma-265	265	2	chose	choose	VERB
ma-265	265	3	an	an	DET
ma-265	265	4	arbitrary	arbitrary	ADJ
ma-265	265	5	singular	singular	ADJ
ma-265	265	6	inner	inner	ADJ
ma-265	265	7	function	function	NOUN
ma-265	265	8	s0(z	s0(z	NOUN
ma-265	265	9	)	)	PUNCT
ma-265	265	10	∈	∈	PROPN
ma-265	265	11	sinn	sinn	NOUN
ma-265	265	12	and	and	CCONJ
ma-265	265	13	we	we	PRON
ma-265	265	14	gener	gener	NOUN
ma-265	265	15	-	-	PUNCT
ma-265	265	16	ated	ate	VERB
ma-265	265	17	an	an	DET
ma-265	265	18	infinite	infinite	ADJ
ma-265	265	19	sequence	sequence	NOUN
ma-265	265	20	of	of	ADP
ma-265	265	21	singular	singular	ADJ
ma-265	265	22	inner	inner	ADJ
ma-265	265	23	functions	function	NOUN
ma-265	265	24	using	use	VERB
ma-265	265	25	the	the	DET
ma-265	265	26	following	follow	VERB
ma-265	265	27	recursion	recursion	NOUN
ma-265	265	28	:	:	PUNCT
ma-265	265	29	sn+1(z	sn+1(z	VERB
ma-265	265	30	)	)	PUNCT
ma-265	265	31	=	=	NOUN
ma-265	265	32	exp	exp	NOUN
ma-265	265	33	(	(	PUNCT
ma-265	265	34	−f	−f	PROPN
ma-265	265	35	(	(	PUNCT
ma-265	265	36	z	z	NOUN
ma-265	265	37	·	·	PUNCT
ma-265	265	38	sn(z	sn(z	NOUN
ma-265	265	39	)	)	PUNCT
ma-265	265	40	)	)	PUNCT
ma-265	265	41	)	)	PUNCT
ma-265	265	42	for	for	ADP
ma-265	265	43	n	n	PRON
ma-265	265	44	∈	∈	PROPN
ma-265	265	45	z≥0	z≥0	PROPN
ma-265	265	46	.	.	PUNCT
ma-265	266	1	the	the	DET
ma-265	266	2	limit	limit	NOUN
ma-265	266	3	s(z	s(z	PROPN
ma-265	266	4	)	)	PUNCT
ma-265	266	5	=	=	SYM
ma-265	266	6	limn→∞	limn→∞	PROPN
ma-265	266	7	sn(z	sn(z	NOUN
ma-265	266	8	)	)	PUNCT
ma-265	266	9	exists	exist	VERB
ma-265	266	10	for	for	ADP
ma-265	266	11	all	all	DET
ma-265	266	12	z	z	NOUN
ma-265	266	13	∈	∈	PROPN
ma-265	266	14	u	u	NOUN
ma-265	266	15	.	.	PUNCT
ma-265	267	1	theconvergence	theconvergence	NOUN
ma-265	267	2	is	be	AUX
ma-265	267	3	uniform	uniform	ADJ
ma-265	267	4	on	on	ADP
ma-265	267	5	compact	compact	ADJ
ma-265	267	6	subsets	subset	NOUN
ma-265	267	7	of	of	ADP
ma-265	267	8	u	u	PROPN
ma-265	267	9	.	.	PUNCT
ma-265	268	1	s(z	s(z	NOUN
ma-265	268	2	)	)	PUNCT
ma-265	268	3	satisfies	satisfy	VERB
ma-265	268	4	the	the	DET
ma-265	268	5	fixed	fix	VERB
ma-265	268	6	-	-	PUNCT
ma-265	268	7	point	point	NOUN
ma-265	268	8	equation	equation	NOUN
ma-265	268	9	s(z	s(z	PROPN
ma-265	268	10	)	)	PUNCT
ma-265	268	11	=	=	SYM
ma-265	268	12	exp	exp	NOUN
ma-265	268	13	(	(	PUNCT
ma-265	268	14	−f	−f	PROPN
ma-265	268	15	(	(	PUNCT
ma-265	268	16	z	z	NOUN
ma-265	268	17	·	·	PUNCT
ma-265	268	18	s(z	s(z	NOUN
ma-265	268	19	)	)	PUNCT
ma-265	268	20	)	)	PUNCT
ma-265	268	21	)	)	PUNCT
ma-265	268	22	,	,	PUNCT
ma-265	268	23	z	z	PROPN
ma-265	268	24	∈	∈	PROPN
ma-265	268	25	u	u	NOUN
ma-265	268	26	.	.	PUNCT
ma-265	269	1	the	the	DET
ma-265	269	2	function	function	NOUN
ma-265	269	3	g(z	g(z	PROPN
ma-265	269	4	)	)	PUNCT
ma-265	270	1	=	=	PUNCT
ma-265	270	2	z	z	X
ma-265	270	3	·	·	PUNCT
ma-265	270	4	s(z	s(z	NOUN
ma-265	270	5	)	)	PUNCT
ma-265	270	6	is	be	AUX
ma-265	270	7	a	a	DET
ma-265	270	8	conformal	conformal	ADJ
ma-265	270	9	mapping	mapping	NOUN
ma-265	270	10	u	u	NOUN
ma-265	270	11	→	→	X
ma-265	270	12	im(g	im(g	X
ma-265	270	13	)	)	PUNCT
ma-265	270	14	⊆	⊆	NUM
ma-265	270	15	u	u	NOUN
ma-265	270	16	.to	.to	PUNCT
ma-265	270	17	see	see	VERB
ma-265	270	18	that	that	SCONJ
ma-265	270	19	we	we	PRON
ma-265	270	20	defined	define	VERB
ma-265	270	21	the	the	DET
ma-265	270	22	following	follow	VERB
ma-265	270	23	holomorphic	holomorphic	ADJ
ma-265	270	24	function	function	NOUN
ma-265	270	25	defined	define	VERB
ma-265	270	26	on	on	ADP
ma-265	270	27	u	u	PROPN
ma-265	270	28	.	.	PUNCT
ma-265	271	1	f	f	X
ma-265	271	2	:	:	PUNCT
ma-265	271	3	u	u	X
ma-265	271	4	→	→	SYM
ma-265	271	5	c	c	PROPN
ma-265	271	6	,	,	PUNCT
ma-265	271	7	f(w	f(w	PROPN
ma-265	271	8	)	)	PUNCT
ma-265	272	1	=	=	SYM
ma-265	272	2	w	w	PROPN
ma-265	272	3	exp	exp	NOUN
ma-265	272	4	(	(	PUNCT
ma-265	272	5	f(w	f(w	PROPN
ma-265	272	6	)	)	PUNCT
ma-265	272	7	)	)	PUNCT
ma-265	272	8	.	.	PUNCT
ma-265	273	1	it	it	PRON
ma-265	273	2	easily	easily	ADV
ma-265	273	3	follows	follow	VERB
ma-265	273	4	by	by	ADP
ma-265	273	5	the	the	DET
ma-265	273	6	fixed	fix	VERB
ma-265	273	7	-	-	PUNCT
ma-265	273	8	point	point	NOUN
ma-265	273	9	equation	equation	NOUN
ma-265	273	10	that	that	SCONJ
ma-265	273	11	f	f	PROPN
ma-265	273	12	(	(	PUNCT
ma-265	273	13	g(z	g(z	PROPN
ma-265	273	14	)	)	PUNCT
ma-265	273	15	)	)	PUNCT
ma-265	274	1	=	=	PUNCT
ma-265	274	2	z	z	NOUN
ma-265	274	3	.	.	PUNCT
ma-265	275	1	thus	thus	ADV
ma-265	275	2	g	g	PROPN
ma-265	275	3	has	have	VERB
ma-265	275	4	a	a	DET
ma-265	275	5	left	left	ADJ
ma-265	275	6	inverse	inverse	NOUN
ma-265	275	7	f	f	NOUN
ma-265	275	8	and	and	CCONJ
ma-265	275	9	hence	hence	ADV
ma-265	275	10	g	g	PROPN
ma-265	275	11	is	be	AUX
ma-265	275	12	injective	injective	ADJ
ma-265	275	13	.	.	PUNCT
ma-265	276	1	that	that	PRON
ma-265	276	2	was	be	AUX
ma-265	276	3	the	the	DET
ma-265	276	4	first	first	ADJ
ma-265	276	5	surprise	surprise	NOUN
ma-265	276	6	.	.	PUNCT
ma-265	277	1	the	the	DET
ma-265	277	2	sequence	sequence	NOUN
ma-265	277	3	{	{	PUNCT
ma-265	277	4	sn(z)}∞n=1	sn(z)}∞n=1	NUM
ma-265	277	5	of	of	ADP
ma-265	277	6	singular	singular	ADJ
ma-265	277	7	inner	inner	ADJ
ma-265	277	8	functions	function	NOUN
ma-265	277	9	,	,	PUNCT
ma-265	277	10	each	each	PRON
ma-265	277	11	of	of	ADP
ma-265	277	12	which	which	PRON
ma-265	277	13	covers	cover	VERB
ma-265	277	14	u	u	PRON
ma-265	277	15	infinitely	infinitely	ADV
ma-265	277	16	many	many	ADJ
ma-265	277	17	times	time	NOUN
ma-265	277	18	,	,	PUNCT
ma-265	277	19	produced	produce	VERB
ma-265	277	20	the	the	DET
ma-265	277	21	limit	limit	NOUN
ma-265	277	22	s(z	s(z	PROPN
ma-265	277	23	)	)	PUNCT
ma-265	277	24	so	so	SCONJ
ma-265	277	25	that	that	SCONJ
ma-265	277	26	g(z	g(z	ADJ
ma-265	277	27	)	)	PUNCT
ma-265	277	28	=	=	PUNCT
ma-265	277	29	z	z	X
ma-265	277	30	·	·	PUNCT
ma-265	277	31	s(z	s(z	NOUN
ma-265	277	32	)	)	PUNCT
ma-265	277	33	wasinjective	wasinjective	NOUN
ma-265	277	34	.	.	PUNCT
ma-265	278	1	the	the	DET
ma-265	278	2	complete	complete	ADJ
ma-265	278	3	opposite	opposite	ADJ
ma-265	278	4	behavior	behavior	NOUN
ma-265	278	5	.	.	PUNCT
ma-265	279	1	g	g	PROPN
ma-265	279	2	covers	cover	VERB
ma-265	279	3	each	each	DET
ma-265	279	4	point	point	NOUN
ma-265	279	5	of	of	ADP
ma-265	279	6	u	u	NOUN
ma-265	279	7	at	at	ADP
ma-265	279	8	most	most	ADJ
ma-265	279	9	once.in	once.in	NOUN
ma-265	279	10	this	this	DET
ma-265	279	11	section	section	NOUN
ma-265	279	12	we	we	PRON
ma-265	279	13	will	will	AUX
ma-265	279	14	describe	describe	VERB
ma-265	279	15	the	the	DET
ma-265	279	16	image	image	NOUN
ma-265	279	17	im(g	im(g	PUNCT
ma-265	279	18	)	)	PUNCT
ma-265	279	19	by	by	ADP
ma-265	279	20	trying	try	VERB
ma-265	279	21	to	to	PART
ma-265	279	22	identify	identify	VERB
ma-265	279	23	its	its	PRON
ma-265	279	24	boundary	boundary	NOUN
ma-265	279	25	.	.	PUNCT
ma-265	280	1	at	at	ADP
ma-265	280	2	first	first	ADJ
ma-265	280	3	onemight	onemight	ADJ
ma-265	280	4	expect	expect	VERB
ma-265	280	5	a	a	DET
ma-265	280	6	very	very	ADV
ma-265	280	7	wild	wild	ADJ
ma-265	280	8	boundary	boundary	NOUN
ma-265	280	9	because	because	SCONJ
ma-265	280	10	of	of	ADP
ma-265	280	11	the	the	DET
ma-265	280	12	limit	limit	NOUN
ma-265	280	13	above	above	ADV
ma-265	280	14	.	.	PUNCT
ma-265	281	1	we	we	PRON
ma-265	281	2	will	will	AUX
ma-265	281	3	encounter	encounter	VERB
ma-265	281	4	here	here	ADV
ma-265	281	5	our	our	PRON
ma-265	281	6	secondsurprise	secondsurprise	NOUN
ma-265	281	7	.	.	PUNCT
ma-265	282	1	the	the	DET
ma-265	282	2	boundary	boundary	ADJ
ma-265	282	3	∂im(g	∂im(g	NOUN
ma-265	282	4	)	)	PUNCT
ma-265	282	5	will	will	AUX
ma-265	282	6	turn	turn	VERB
ma-265	282	7	out	out	ADP
ma-265	282	8	to	to	PART
ma-265	282	9	be	be	AUX
ma-265	282	10	completely	completely	ADV
ma-265	282	11	tame	tame	ADJ
ma-265	282	12	.	.	PUNCT
ma-265	283	1	it	it	PRON
ma-265	283	2	will	will	AUX
ma-265	283	3	be	be	AUX
ma-265	283	4	composed	compose	VERB
ma-265	283	5	of	of	ADP
ma-265	283	6	curveswhich	curveswhich	PROPN
ma-265	283	7	are	be	AUX
ma-265	283	8	the	the	DET
ma-265	283	9	zero	zero	NUM
ma-265	283	10	sets	set	NOUN
ma-265	283	11	of	of	ADP
ma-265	283	12	certain	certain	ADJ
ma-265	283	13	planar	planar	ADJ
ma-265	283	14	harmonic	harmonic	ADJ
ma-265	283	15	functions	function	NOUN
ma-265	283	16	plus	plus	CCONJ
ma-265	283	17	very	very	ADV
ma-265	283	18	few	few	ADJ
ma-265	283	19	corners	corner	NOUN
ma-265	283	20	in	in	ADP
ma-265	283	21	between	between	ADP
ma-265	283	22	thedifferent	thedifferent	NOUN
ma-265	283	23	zero	zero	NUM
ma-265	283	24	sets	set	NOUN
ma-265	283	25	.	.	PUNCT
ma-265	284	1	thus	thus	ADV
ma-265	284	2	a	a	DET
ma-265	284	3	piecewise	piecewise	NOUN
ma-265	284	4	smooth	smooth	NOUN
ma-265	284	5	closed	close	VERB
ma-265	284	6	jordan	jordan	PROPN
ma-265	284	7	curve	curve	PROPN
ma-265	284	8	.	.	PUNCT
ma-265	285	1	theorem	theorem	VERB
ma-265	285	2	6.1	6.1	NUM
ma-265	285	3	.	.	PUNCT
ma-265	286	1	the	the	DET
ma-265	286	2	image	image	NOUN
ma-265	286	3	im(g	im(g	PUNCT
ma-265	286	4	)	)	PUNCT
ma-265	286	5	=	=	PUNCT
ma-265	286	6	im(z	im(z	NOUN
ma-265	286	7	·	·	PUNCT
ma-265	286	8	s(z	s(z	NOUN
ma-265	286	9	)	)	PUNCT
ma-265	286	10	)	)	PUNCT
ma-265	286	11	of	of	ADP
ma-265	286	12	a	a	DET
ma-265	286	13	conformal	conformal	ADJ
ma-265	286	14	mapping	mapping	NOUN
ma-265	286	15	in	in	ADP
ma-265	286	16	conf	conf	NOUN
ma-265	286	17	is	be	AUX
ma-265	286	18	a	a	DET
ma-265	286	19	piecewise	piecewise	NOUN
ma-265	286	20	smooth	smooth	NOUN
ma-265	286	21	closed	close	VERB
ma-265	286	22	jordan	jordan	PROPN
ma-265	286	23	curve	curve	PROPN
ma-265	286	24	.	.	PUNCT
ma-265	287	1	it	it	PRON
ma-265	287	2	is	be	AUX
ma-265	287	3	composed	compose	VERB
ma-265	287	4	of	of	ADP
ma-265	287	5	arcs	arc	NOUN
ma-265	287	6	on	on	ADP
ma-265	287	7	t	t	PROPN
ma-265	287	8	and	and	CCONJ
ma-265	287	9	of	of	ADP
ma-265	287	10	arcs	arc	NOUN
ma-265	287	11	which	which	PRON
ma-265	287	12	are	be	AUX
ma-265	287	13	subsets	subset	NOUN
ma-265	287	14	of	of	ADP
ma-265	287	15	the	the	DET
ma-265	287	16	zero	zero	NUM
ma-265	287	17	set	set	NOUN
ma-265	287	18	of	of	ADP
ma-265	287	19	the	the	DET
ma-265	287	20	planar	planar	ADJ
ma-265	287	21	harmonic	harmonic	ADJ
ma-265	287	22	function	function	NOUN
ma-265	287	23	<	<	X
ma-265	287	24	f	f	X
ma-265	287	25	(	(	PUNCT
ma-265	287	26	w	w	NOUN
ma-265	287	27	)	)	PUNCT
ma-265	287	28	+	+	CCONJ
ma-265	287	29	log	log	VERB
ma-265	287	30	|w	|w	ADJ
ma-265	287	31	|	|	NOUN
ma-265	287	32	,	,	PUNCT
ma-265	287	33	plus	plus	CCONJ
ma-265	287	34	a	a	DET
ma-265	287	35	small	small	ADJ
ma-265	287	36	number	number	NOUN
ma-265	287	37	of	of	ADP
ma-265	287	38	corners	corner	NOUN
ma-265	287	39	.	.	PUNCT
ma-265	288	1	proof.since	proof.since	NOUN
ma-265	288	2	f	f	PROPN
ma-265	288	3	(	(	PUNCT
ma-265	288	4	w	w	NOUN
ma-265	288	5	)	)	PUNCT
ma-265	288	6	=	=	SYM
ma-265	288	7	g−1(w	g−1(w	PROPN
ma-265	288	8	)	)	PUNCT
ma-265	288	9	and	and	CCONJ
ma-265	288	10	g	g	NOUN
ma-265	288	11	:	:	PUNCT
ma-265	288	12	u	u	NOUN
ma-265	288	13	→	→	SYM
ma-265	288	14	im(g	im(g	PUNCT
ma-265	288	15	)	)	PUNCT
ma-265	288	16	⊆	⊆	NUM
ma-265	288	17	u	u	NOUN
ma-265	288	18	is	be	AUX
ma-265	288	19	conformal	conformal	ADJ
ma-265	288	20	,	,	PUNCT
ma-265	288	21	in	in	ADP
ma-265	288	22	order	order	NOUN
ma-265	288	23	to	to	PART
ma-265	288	24	to	to	PART
ma-265	288	25	identify	identify	VERB
ma-265	288	26	im(g	im(g	PRON
ma-265	288	27	)	)	PUNCT
ma-265	288	28	,	,	PUNCT
ma-265	288	29	we	we	PRON
ma-265	288	30	needto	needto	AUX
ma-265	288	31	identify	identify	VERB
ma-265	288	32	those	those	DET
ma-265	288	33	arcs	arc	NOUN
ma-265	288	34	in	in	ADP
ma-265	288	35	the	the	DET
ma-265	288	36	closure	closure	NOUN
ma-265	288	37	of	of	ADP
ma-265	288	38	the	the	DET
ma-265	288	39	unit	unit	NOUN
ma-265	288	40	disk	disk	NOUN
ma-265	288	41	u	u	NOUN
ma-265	288	42	that	that	PRON
ma-265	288	43	are	be	AUX
ma-265	288	44	mapped	map	VERB
ma-265	288	45	by	by	ADP
ma-265	288	46	f	f	PROPN
ma-265	288	47	into	into	ADP
ma-265	288	48	the	the	DET
ma-265	288	49	unit	unit	NOUN
ma-265	288	50	circle	circle	NOUN
ma-265	288	51	t	t	PROPN
ma-265	288	52	=	=	SYM
ma-265	288	53	∂u	∂u	PROPN
ma-265	288	54	.	.	PUNCT
ma-265	289	1	so	so	ADV
ma-265	289	2	we	we	PRON
ma-265	289	3	want	want	VERB
ma-265	289	4	to	to	PART
ma-265	289	5	solve	solve	VERB
ma-265	289	6	for	for	ADP
ma-265	289	7	all	all	DET
ma-265	289	8	w	w	PROPN
ma-265	289	9	∈	∈	PROPN
ma-265	289	10	u	u	NOUN
ma-265	289	11	that	that	PRON
ma-265	289	12	satisfy	satisfy	VERB
ma-265	289	13	|f	|f	PROPN
ma-265	290	1	(	(	PUNCT
ma-265	290	2	w)|	w)|	VERB
ma-265	290	3	=	=	NOUN
ma-265	290	4	1	1	X
ma-265	290	5	.	.	PUNCT
ma-265	290	6	i.e.	i.e.	X
ma-265	290	7	|w	|w	ADJ
ma-265	290	8	exp	exp	NOUN
ma-265	290	9	(	(	PUNCT
ma-265	290	10	f	f	PROPN
ma-265	290	11	(	(	PUNCT
ma-265	290	12	w))|	w))|	PROPN
ma-265	290	13	=	=	PUNCT
ma-265	290	14	1	1	X
ma-265	290	15	.	.	X
ma-265	291	1	we	we	PRON
ma-265	291	2	recall	recall	VERB
ma-265	291	3	that	that	SCONJ
ma-265	291	4	f	f	PROPN
ma-265	291	5	∈	∈	PROPN
ma-265	291	6	rp	rp	NOUN
ma-265	291	7	and	and	CCONJ
ma-265	291	8	hence	hence	ADV
ma-265	291	9	,	,	PUNCT
ma-265	291	10	by	by	ADP
ma-265	291	11	definition	definition	NOUN
ma-265	291	12	3.1	3.1	NUM
ma-265	291	13	,	,	PUNCT
ma-265	291	14	condition	condition	NOUN
ma-265	291	15	(	(	PUNCT
ma-265	291	16	ii	ii	NOUN
ma-265	291	17	)	)	PUNCT
ma-265	291	18	we	we	PRON
ma-265	291	19	know	know	VERB
ma-265	291	20	that	that	SCONJ
ma-265	291	21	<	<	X
ma-265	291	22	f	f	X
ma-265	291	23	(	(	PUNCT
ma-265	291	24	e	e	NOUN
ma-265	291	25	iθ	iθ	NOUN
ma-265	291	26	)	)	PUNCT
ma-265	291	27	=	=	SYM
ma-265	291	28	0	0	NUM
ma-265	292	1	almosteverywhere	almosteverywhere	ADV
ma-265	292	2	on	on	ADP
ma-265	292	3	t	t	PROPN
ma-265	292	4	with	with	ADP
ma-265	292	5	respect	respect	NOUN
ma-265	292	6	to	to	ADP
ma-265	292	7	the	the	DET
ma-265	292	8	lebesgue	lebesgue	ADJ
ma-265	292	9	measure	measure	NOUN
ma-265	292	10	on	on	ADP
ma-265	292	11	t.	t.	PROPN
ma-265	292	12	since	since	SCONJ
ma-265	292	13	|exp	|exp	PROPN
ma-265	292	14	(	(	PUNCT
ma-265	292	15	f	f	PROPN
ma-265	292	16	(	(	PUNCT
ma-265	292	17	w))|	w))|	PROPN
ma-265	292	18	=	=	SYM
ma-265	292	19	exp	exp	PROPN
ma-265	292	20	(	(	PUNCT
ma-265	292	21	<	<	X
ma-265	292	22	f	f	X
ma-265	292	23	(	(	PUNCT
ma-265	292	24	w))it	w))it	PROPN
ma-265	292	25	follows	follow	VERB
ma-265	292	26	that	that	PRON
ma-265	292	27	:	:	PUNCT
ma-265	292	28	∣∣e	∣∣e	PROPN
ma-265	292	29	iθ	iθ	NOUN
ma-265	292	30	exp	exp	NOUN
ma-265	292	31	(	(	PUNCT
ma-265	292	32	f	f	PROPN
ma-265	292	33	(	(	PUNCT
ma-265	292	34	e	e	NOUN
ma-265	292	35	iθ))∣∣	iθ))∣∣	NOUN
ma-265	292	36	=	=	SYM
ma-265	292	37	1	1	NUM
ma-265	292	38	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	292	39	eur	eur	PROPN
ma-265	292	40	.	.	PUNCT
ma-265	293	1	j.	j.	PROPN
ma-265	293	2	math	math	PROPN
ma-265	293	3	.	.	PUNCT
ma-265	294	1	anal	anal	PROPN
ma-265	294	2	.	.	PUNCT
ma-265	295	1	10.28924	10.28924	NUM
ma-265	295	2	/	/	SYM
ma-265	295	3	ada	ada	PROPN
ma-265	295	4	/	/	SYM
ma-265	295	5	ma.5.4	ma.5.4	PROPN
ma-265	295	6	9almost	9almost	PROPN
ma-265	295	7	everywhere	everywhere	ADV
ma-265	295	8	on	on	ADP
ma-265	295	9	t.	t.	PROPN
ma-265	296	1	so	so	ADV
ma-265	296	2	we	we	PRON
ma-265	296	3	want	want	VERB
ma-265	296	4	to	to	PART
ma-265	296	5	solve	solve	VERB
ma-265	296	6	for	for	ADP
ma-265	296	7	all	all	DET
ma-265	296	8	w	w	PROPN
ma-265	296	9	∈	∈	PROPN
ma-265	296	10	u	u	NOUN
ma-265	296	11	that	that	PRON
ma-265	296	12	satisfy	satisfy	VERB
ma-265	296	13	|f	|f	PROPN
ma-265	297	1	(	(	PUNCT
ma-265	297	2	w)|	w)|	VERB
ma-265	297	3	=	=	NOUN
ma-265	297	4	1	1	X
ma-265	297	5	.	.	PUNCT
ma-265	298	1	this	this	PRON
ma-265	298	2	means	mean	VERB
ma-265	298	3	,	,	PUNCT
ma-265	298	4	to	to	PART
ma-265	298	5	find	find	VERB
ma-265	298	6	all	all	DET
ma-265	298	7	w	w	NOUN
ma-265	298	8	∈	∈	NOUN
ma-265	298	9	u	u	NOUN
ma-265	298	10	for	for	ADP
ma-265	298	11	which	which	PRON
ma-265	298	12	|w	|w	ADJ
ma-265	298	13	exp(f	exp(f	PROPN
ma-265	298	14	(	(	PUNCT
ma-265	298	15	w))|	w))|	PROPN
ma-265	298	16	=	=	SYM
ma-265	298	17	1	1	NUM
ma-265	298	18	,	,	PUNCT
ma-265	298	19	that	that	PRON
ma-265	298	20	means	mean	VERB
ma-265	298	21	|w	|w	ADJ
ma-265	298	22	|	|	ADV
ma-265	298	23	exp(<f	exp(<f	PROPN
ma-265	298	24	(	(	PUNCT
ma-265	298	25	w	w	NOUN
ma-265	298	26	)	)	PUNCT
ma-265	298	27	)	)	PUNCT
ma-265	299	1	=	=	SYM
ma-265	299	2	1	1	NUM
ma-265	299	3	,	,	PUNCT
ma-265	299	4	i.e.	i.e.	X
ma-265	299	5	those	those	DET
ma-265	299	6	w	w	PROPN
ma-265	299	7	∈	∈	PROPN
ma-265	299	8	uthat	uthat	PRON
ma-265	299	9	satisfy	satisfy	NOUN
ma-265	299	10	:	:	PUNCT
ma-265	299	11	<	<	X
ma-265	299	12	f	f	X
ma-265	299	13	(	(	PUNCT
ma-265	299	14	w	w	NOUN
ma-265	299	15	)	)	PUNCT
ma-265	299	16	=	=	SYM
ma-265	299	17	−	−	PROPN
ma-265	299	18	log	log	NOUN
ma-265	299	19	|w	|w	ADJ
ma-265	299	20	|.this	|.this	DET
ma-265	299	21	equation	equation	NOUN
ma-265	299	22	has	have	VERB
ma-265	299	23	harmonic	harmonic	ADJ
ma-265	299	24	functions	function	NOUN
ma-265	299	25	on	on	ADP
ma-265	299	26	both	both	DET
ma-265	299	27	sides	side	NOUN
ma-265	299	28	.	.	PUNCT
ma-265	300	1	alternatively	alternatively	ADV
ma-265	300	2	we	we	PRON
ma-265	300	3	look	look	VERB
ma-265	300	4	for	for	ADP
ma-265	300	5	the	the	DET
ma-265	300	6	zero	zero	NUM
ma-265	300	7	set	set	VERB
ma-265	300	8	in	in	ADP
ma-265	300	9	u	u	NOUN
ma-265	300	10	ofthe	ofthe	NOUN
ma-265	300	11	planar	planar	ADJ
ma-265	300	12	harmonic	harmonic	ADJ
ma-265	300	13	function	function	NOUN
ma-265	300	14	<	<	X
ma-265	300	15	f	f	X
ma-265	300	16	(	(	PUNCT
ma-265	300	17	w	w	NOUN
ma-265	300	18	)	)	PUNCT
ma-265	300	19	+	+	CCONJ
ma-265	300	20	log	log	VERB
ma-265	300	21	|w	|w	ADJ
ma-265	300	22	|	|	NOUN
ma-265	300	23	.	.	PUNCT
ma-265	301	1	this	this	PRON
ma-265	301	2	proves	prove	VERB
ma-265	301	3	our	our	PRON
ma-265	301	4	theorem	theorem	NOUN
ma-265	301	5	.	.	PROPN
ma-265	301	6	�	�	PROPN
ma-265	301	7	in	in	ADP
ma-265	301	8	the	the	DET
ma-265	301	9	case	case	NOUN
ma-265	301	10	of	of	ADP
ma-265	301	11	our	our	PRON
ma-265	301	12	first	first	ADJ
ma-265	301	13	example	example	NOUN
ma-265	301	14	:	:	PUNCT
ma-265	301	15	f	f	PROPN
ma-265	301	16	(	(	PUNCT
ma-265	301	17	w	w	PROPN
ma-265	301	18	)	)	PUNCT
ma-265	301	19	=	=	SYM
ma-265	302	1	1	1	NUM
ma-265	302	2	+	+	CCONJ
ma-265	302	3	w	w	PROPN
ma-265	302	4	1−	1−	NUM
ma-265	302	5	w	w	PROPN
ma-265	302	6	.in	.in	PROPN
ma-265	302	7	this	this	DET
ma-265	302	8	case	case	NOUN
ma-265	302	9	:	:	PUNCT
ma-265	302	10	1	1	NUM
ma-265	303	1	+	+	X
ma-265	303	2	w	w	PROPN
ma-265	303	3	1−	1−	NUM
ma-265	303	4	w	w	PROPN
ma-265	303	5	=	=	SYM
ma-265	303	6	1−	1−	PROPN
ma-265	303	7	|w	|w	NOUN
ma-265	303	8	|2	|2	NUM
ma-265	303	9	|1−	|1−	PROPN
ma-265	303	10	w	w	NOUN
ma-265	303	11	|2	|2	NUM
ma-265	303	12	+	+	CCONJ
ma-265	303	13	w	w	PROPN
ma-265	303	14	−	−	PROPN
ma-265	303	15	w	w	PROPN
ma-265	303	16	|1−	|1−	PROPN
ma-265	303	17	w	w	NOUN
ma-265	303	18	|2	|2	NUM
ma-265	303	19	.our	.our	NOUN
ma-265	303	20	equation	equation	NOUN
ma-265	303	21	<	<	X
ma-265	303	22	f	f	X
ma-265	303	23	(	(	PUNCT
ma-265	303	24	w	w	NOUN
ma-265	303	25	)	)	PUNCT
ma-265	303	26	+	+	CCONJ
ma-265	303	27	log	log	VERB
ma-265	303	28	|w	|w	NOUN
ma-265	304	1	|	|	NOUN
ma-265	305	1	=	=	SYM
ma-265	305	2	0	0	NUM
ma-265	305	3	becomes	become	VERB
ma-265	305	4	:	:	PUNCT
ma-265	305	5	1−	1−	NUM
ma-265	305	6	|w	|w	ADJ
ma-265	305	7	|2	|2	NUM
ma-265	305	8	|1−	|1−	PROPN
ma-265	305	9	w	w	NOUN
ma-265	305	10	|2	|2	NUM
ma-265	305	11	+	+	CCONJ
ma-265	305	12	log	log	NOUN
ma-265	305	13	|w	|w	NOUN
ma-265	305	14	|	|	NOUN
ma-265	306	1	=	=	SYM
ma-265	307	1	0.we	0.we	NOUN
ma-265	307	2	note	note	VERB
ma-265	307	3	that	that	SCONJ
ma-265	307	4	any	any	DET
ma-265	307	5	w	w	PROPN
ma-265	307	6	∈	∈	PROPN
ma-265	307	7	t−{1	t−{1	NOUN
ma-265	307	8	}	}	PUNCT
ma-265	307	9	solves	solve	VERB
ma-265	307	10	this	this	DET
ma-265	307	11	equation	equation	NOUN
ma-265	307	12	.	.	PUNCT
ma-265	308	1	in	in	ADP
ma-265	308	2	particular	particular	ADJ
ma-265	308	3	both	both	CCONJ
ma-265	308	4	±i	±i	PRON
ma-265	308	5	are	be	AUX
ma-265	308	6	solutions	solution	NOUN
ma-265	308	7	.	.	PUNCT
ma-265	309	1	we	we	PRON
ma-265	309	2	mentionthose	mentionthose	VERB
ma-265	309	3	two	two	NUM
ma-265	309	4	in	in	ADP
ma-265	309	5	particular	particular	ADJ
ma-265	309	6	because	because	SCONJ
ma-265	309	7	we	we	PRON
ma-265	309	8	will	will	AUX
ma-265	309	9	see	see	VERB
ma-265	309	10	soon	soon	ADV
ma-265	309	11	that	that	SCONJ
ma-265	309	12	they	they	PRON
ma-265	309	13	are	be	AUX
ma-265	309	14	the	the	DET
ma-265	309	15	two	two	NUM
ma-265	309	16	zeros	zero	NOUN
ma-265	309	17	of	of	ADP
ma-265	309	18	the	the	DET
ma-265	309	19	derivative	derivative	NOUN
ma-265	309	20	of	of	ADP
ma-265	309	21	ourholomorphic	ourholomorphic	ADJ
ma-265	309	22	function	function	NOUN
ma-265	309	23	in	in	ADP
ma-265	309	24	interest	interest	NOUN
ma-265	309	25	and	and	CCONJ
ma-265	309	26	hence	hence	ADV
ma-265	309	27	this	this	DET
ma-265	309	28	function	function	NOUN
ma-265	309	29	is	be	AUX
ma-265	309	30	not	not	PART
ma-265	309	31	injective	injective	ADJ
ma-265	309	32	exactly	exactly	ADV
ma-265	309	33	at	at	ADP
ma-265	309	34	those	those	DET
ma-265	309	35	two	two	NUM
ma-265	309	36	points.we	points.we	NOUN
ma-265	309	37	can	can	AUX
ma-265	309	38	obtain	obtain	VERB
ma-265	309	39	the	the	DET
ma-265	309	40	equation	equation	NOUN
ma-265	309	41	of	of	ADP
ma-265	309	42	this	this	DET
ma-265	309	43	curve	curve	NOUN
ma-265	309	44	either	either	CCONJ
ma-265	309	45	in	in	ADP
ma-265	309	46	cartesian	cartesian	ADJ
ma-265	309	47	coordinates	coordinate	NOUN
ma-265	309	48	:	:	PUNCT
ma-265	309	49	x	x	X
ma-265	309	50	=	=	PUNCT
ma-265	309	51	<	<	X
ma-265	309	52	w	w	PROPN
ma-265	309	53	,	,	PUNCT
ma-265	309	54	y	y	PROPN
ma-265	309	55	=	=	PUNCT
ma-265	309	56	=	=	NOUN
ma-265	309	57	w	w	PROPN
ma-265	309	58	,	,	PUNCT
ma-265	309	59	|w	|w	ADJ
ma-265	309	60	|2	|2	NUM
ma-265	309	61	=	=	SYM
ma-265	309	62	x2	x2	PROPN
ma-265	310	1	+	+	CCONJ
ma-265	310	2	y2	y2	NOUN
ma-265	310	3	.	.	PUNCT
ma-265	311	1	1−	1−	NUM
ma-265	312	1	x2	x2	INTJ
ma-265	313	1	−	−	NOUN
ma-265	313	2	y2	y2	NOUN
ma-265	313	3	1	1	NUM
ma-265	314	1	+	+	NUM
ma-265	314	2	x2	x2	PROPN
ma-265	315	1	+	+	CCONJ
ma-265	316	1	y2	y2	PROPN
ma-265	316	2	−	−	NOUN
ma-265	317	1	2x	2x	NUM
ma-265	317	2	+	+	CCONJ
ma-265	317	3	1	1	NUM
ma-265	317	4	2	2	NUM
ma-265	317	5	log(x2	log(x2	NOUN
ma-265	317	6	+	+	CCONJ
ma-265	317	7	y2	y2	NOUN
ma-265	317	8	)	)	PUNCT
ma-265	318	1	=	=	SYM
ma-265	318	2	0,or	0,or	X
ma-265	318	3	better	well	ADV
ma-265	318	4	in	in	ADP
ma-265	318	5	polar	polar	ADJ
ma-265	318	6	coordinates	coordinate	NOUN
ma-265	318	7	:	:	PUNCT
ma-265	318	8	x	x	SYM
ma-265	318	9	=	=	PUNCT
ma-265	318	10	r	r	NOUN
ma-265	318	11	cos	cos	PROPN
ma-265	318	12	θ	θ	PROPN
ma-265	318	13	,	,	PUNCT
ma-265	318	14	y	y	NOUN
ma-265	319	1	=	=	PUNCT
ma-265	319	2	r	r	NOUN
ma-265	319	3	sin	sin	NOUN
ma-265	319	4	θ	θ	PROPN
ma-265	319	5	.	.	PROPN
ma-265	319	6	1−	1−	NUM
ma-265	319	7	r2	r2	PROPN
ma-265	319	8	1	1	NUM
ma-265	319	9	+	+	NUM
ma-265	319	10	r2	r2	PROPN
ma-265	319	11	−	−	PROPN
ma-265	319	12	2r	2r	NUM
ma-265	319	13	cos	cos	PROPN
ma-265	319	14	θ	θ	PROPN
ma-265	319	15	+	+	CCONJ
ma-265	319	16	log	log	NOUN
ma-265	319	17	r	r	NOUN
ma-265	319	18	=	=	SYM
ma-265	319	19	0.solving	0.solve	VERB
ma-265	319	20	for	for	ADP
ma-265	319	21	cos	cos	ADP
ma-265	319	22	θ	θ	PROPN
ma-265	319	23	this	this	PRON
ma-265	319	24	is	be	AUX
ma-265	319	25	:	:	PUNCT
ma-265	319	26	cos	cos	PROPN
ma-265	319	27	θ	θ	PROPN
ma-265	319	28	=	=	SYM
ma-265	319	29	1	1	NUM
ma-265	319	30	2r	2r	NUM
ma-265	319	31	{	{	PUNCT
ma-265	319	32	1	1	NUM
ma-265	319	33	+	+	NUM
ma-265	319	34	r2	r2	PROPN
ma-265	319	35	+	+	CCONJ
ma-265	319	36	1−	1−	NUM
ma-265	319	37	r2	r2	PROPN
ma-265	319	38	log	log	NOUN
ma-265	319	39	r	r	NOUN
ma-265	319	40	}	}	PUNCT
ma-265	319	41	.	.	PUNCT
ma-265	320	1	remark	remark	VERB
ma-265	320	2	6.2	6.2	NUM
ma-265	320	3	.	.	PUNCT
ma-265	321	1	we	we	PRON
ma-265	321	2	note	note	VERB
ma-265	321	3	that	that	SCONJ
ma-265	321	4	:	:	PUNCT
ma-265	321	5	lim	lim	PROPN
ma-265	321	6	r→1−	r→1−	PROPN
ma-265	321	7	1	1	NUM
ma-265	321	8	2r	2r	NUM
ma-265	321	9	{	{	PUNCT
ma-265	321	10	1	1	NUM
ma-265	321	11	+	+	NUM
ma-265	321	12	r2	r2	PROPN
ma-265	321	13	+	+	CCONJ
ma-265	321	14	1−	1−	NUM
ma-265	321	15	r2	r2	PROPN
ma-265	321	16	log	log	NOUN
ma-265	321	17	r	r	NOUN
ma-265	321	18	}	}	PUNCT
ma-265	321	19	=	=	SYM
ma-265	321	20	0	0	NUM
ma-265	321	21	,	,	PUNCT
ma-265	321	22	so	so	ADV
ma-265	321	23	the	the	DET
ma-265	321	24	equation	equation	NOUN
ma-265	321	25	above	above	ADV
ma-265	321	26	has	have	VERB
ma-265	321	27	exactly	exactly	ADV
ma-265	321	28	two	two	NUM
ma-265	321	29	solutions	solution	NOUN
ma-265	321	30	in	in	ADP
ma-265	321	31	[	[	X
ma-265	321	32	−π	−π	PROPN
ma-265	321	33	,	,	PUNCT
ma-265	321	34	π	π	X
ma-265	321	35	]	]	X
ma-265	321	36	,	,	PUNCT
ma-265	321	37	and	and	CCONJ
ma-265	321	38	these	these	PRON
ma-265	321	39	are	be	AUX
ma-265	321	40	±π2	±π2	NOUN
ma-265	321	41	.	.	PUNCT
ma-265	322	1	these	these	DET
ma-265	322	2	correspondto	correspondto	PROPN
ma-265	322	3	±i	±i	PROPN
ma-265	322	4	.	.	PUNCT
ma-265	323	1	the	the	DET
ma-265	323	2	zero	zero	NUM
ma-265	323	3	set	set	VERB
ma-265	323	4	within	within	ADP
ma-265	323	5	u	u	NOUN
ma-265	323	6	is	be	AUX
ma-265	323	7	the	the	DET
ma-265	323	8	given	give	VERB
ma-265	323	9	by	by	ADP
ma-265	323	10	θ(r	θ(r	NOUN
ma-265	323	11	)	)	PUNCT
ma-265	324	1	=	=	SYM
ma-265	324	2	cos−1	cos−1	NOUN
ma-265	324	3	{	{	PUNCT
ma-265	324	4	1	1	NUM
ma-265	324	5	2r	2r	NUM
ma-265	324	6	(	(	PUNCT
ma-265	324	7	1	1	NUM
ma-265	324	8	+	+	NUM
ma-265	324	9	r2	r2	PROPN
ma-265	324	10	+	+	CCONJ
ma-265	324	11	1−	1−	NUM
ma-265	324	12	r2	r2	PROPN
ma-265	324	13	log	log	NOUN
ma-265	324	14	r	r	NOUN
ma-265	324	15	)	)	PUNCT
ma-265	324	16	}	}	PUNCT
ma-265	324	17	.	.	PUNCT
ma-265	325	1	this	this	DET
ma-265	325	2	intersects	intersect	VERB
ma-265	325	3	the	the	DET
ma-265	325	4	x	x	NOUN
ma-265	325	5	-	-	NOUN
ma-265	325	6	axis	axis	NOUN
ma-265	325	7	to	to	ADP
ma-265	325	8	the	the	DET
ma-265	325	9	right	right	NOUN
ma-265	325	10	of	of	ADP
ma-265	325	11	0	0	NUM
ma-265	325	12	,	,	PUNCT
ma-265	325	13	for	for	ADP
ma-265	325	14	θ	θ	PROPN
ma-265	325	15	=	=	SYM
ma-265	325	16	0	0	PUNCT
ma-265	326	1	so	so	ADV
ma-265	326	2	cos	cos	ADP
ma-265	326	3	θ	θ	PROPN
ma-265	326	4	=	=	SYM
ma-265	326	5	1	1	NUM
ma-265	326	6	:	:	SYM
ma-265	326	7	1	1	NUM
ma-265	326	8	=	=	SYM
ma-265	326	9	1	1	NUM
ma-265	326	10	2r	2r	NUM
ma-265	326	11	{	{	PUNCT
ma-265	326	12	1	1	NUM
ma-265	326	13	+	+	NUM
ma-265	326	14	r2	r2	PROPN
ma-265	326	15	+	+	CCONJ
ma-265	326	16	1−	1−	NUM
ma-265	326	17	r2	r2	PROPN
ma-265	326	18	log	log	NOUN
ma-265	326	19	r	r	NOUN
ma-265	326	20	}	}	PUNCT
ma-265	326	21	⇒	⇒	NOUN
ma-265	326	22	(	(	PUNCT
ma-265	326	23	1−	1−	NUM
ma-265	326	24	r	r	NOUN
ma-265	326	25	)	)	PUNCT
ma-265	326	26	{	{	PUNCT
ma-265	326	27	1−	1−	NUM
ma-265	326	28	r	r	NOUN
ma-265	326	29	+	+	NOUN
ma-265	326	30	1	1	NUM
ma-265	327	1	+	+	CCONJ
ma-265	327	2	r	r	NOUN
ma-265	327	3	log	log	NOUN
ma-265	327	4	r	r	NOUN
ma-265	327	5	}	}	PUNCT
ma-265	327	6	=	=	SYM
ma-265	327	7	0	0	X
ma-265	327	8	.	.	PUNCT
ma-265	328	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	328	2	eur	eur	PROPN
ma-265	328	3	.	.	PUNCT
ma-265	329	1	j.	j.	PROPN
ma-265	329	2	math	math	PROPN
ma-265	329	3	.	.	PUNCT
ma-265	330	1	anal	anal	PROPN
ma-265	330	2	.	.	PUNCT
ma-265	331	1	10.28924	10.28924	NUM
ma-265	331	2	/	/	SYM
ma-265	331	3	ada	ada	PROPN
ma-265	331	4	/	/	SYM
ma-265	331	5	ma.5.4	ma.5.4	PROPN
ma-265	331	6	10one	10one	NOUN
ma-265	331	7	solution	solution	NOUN
ma-265	331	8	is	be	AUX
ma-265	331	9	r	r	NOUN
ma-265	331	10	=	=	PUNCT
ma-265	331	11	x	x	SYM
ma-265	331	12	=	=	SYM
ma-265	331	13	1	1	NUM
ma-265	331	14	and	and	CCONJ
ma-265	331	15	others	other	NOUN
ma-265	331	16	we	we	PRON
ma-265	331	17	obtain	obtain	VERB
ma-265	331	18	by	by	ADP
ma-265	331	19	:	:	PUNCT
ma-265	331	20	1−	1−	NUM
ma-265	331	21	x	x	SYM
ma-265	332	1	+	+	NUM
ma-265	332	2	1	1	NUM
ma-265	332	3	+	+	CCONJ
ma-265	332	4	x	x	SYM
ma-265	332	5	log	log	NOUN
ma-265	332	6	x	x	SYM
ma-265	332	7	=	=	SYM
ma-265	332	8	0	0	NUM
ma-265	332	9	or	or	CCONJ
ma-265	332	10	1	1	NUM
ma-265	332	11	+	+	CCONJ
ma-265	332	12	x	x	SYM
ma-265	333	1	+	+	PUNCT
ma-265	333	2	(	(	PUNCT
ma-265	333	3	1−	1−	NUM
ma-265	333	4	x	x	NOUN
ma-265	333	5	)	)	PUNCT
ma-265	333	6	log	log	NOUN
ma-265	333	7	x	x	NOUN
ma-265	334	1	=	=	NOUN
ma-265	334	2	0	0	X
ma-265	334	3	.	.	PUNCT
ma-265	335	1	we	we	PRON
ma-265	335	2	easily	easily	ADV
ma-265	335	3	check	check	VERB
ma-265	335	4	that	that	SCONJ
ma-265	335	5	(	(	PUNCT
ma-265	335	6	1	1	NUM
ma-265	335	7	+	+	CCONJ
ma-265	335	8	x	x	PUNCT
ma-265	335	9	+	+	ADJ
ma-265	335	10	(	(	PUNCT
ma-265	335	11	1−	1−	NUM
ma-265	335	12	x	x	NOUN
ma-265	335	13	)	)	PUNCT
ma-265	335	14	log	log	VERB
ma-265	335	15	x)′	x)′	PROPN
ma-265	335	16	>	>	X
ma-265	335	17	0	0	PUNCT
ma-265	336	1	for	for	ADP
ma-265	336	2	0	0	NUM
ma-265	336	3	<	<	X
ma-265	336	4	x	x	X
ma-265	336	5	<	<	X
ma-265	336	6	1	1	NUM
ma-265	337	1	and	and	CCONJ
ma-265	337	2	so	so	ADV
ma-265	337	3	there	there	PRON
ma-265	337	4	is	be	VERB
ma-265	337	5	exactly	exactly	ADV
ma-265	337	6	one	one	NUM
ma-265	337	7	solution	solution	NOUN
ma-265	337	8	x	x	PUNCT
ma-265	338	1	=	=	SYM
ma-265	338	2	x0	x0	PROPN
ma-265	338	3	of	of	ADP
ma-265	338	4	1−	1−	NUM
ma-265	338	5	x	x	PUNCT
ma-265	339	1	+	+	CCONJ
ma-265	339	2	1	1	NUM
ma-265	339	3	+	+	CCONJ
ma-265	339	4	x	x	SYM
ma-265	339	5	log	log	NOUN
ma-265	339	6	x	x	SYM
ma-265	339	7	=	=	SYM
ma-265	339	8	0	0	NUM
ma-265	339	9	,	,	PUNCT
ma-265	339	10	in	in	ADP
ma-265	339	11	0	0	NUM
ma-265	339	12	<	<	X
ma-265	339	13	x	x	X
ma-265	339	14	<	<	X
ma-265	339	15	1	1	NUM
ma-265	339	16	.	.	PUNCT
ma-265	340	1	a	a	DET
ma-265	340	2	similar	similar	ADJ
ma-265	340	3	computation	computation	NOUN
ma-265	340	4	shows	show	VERB
ma-265	340	5	that	that	SCONJ
ma-265	340	6	the	the	DET
ma-265	340	7	curve	curve	NOUN
ma-265	340	8	:	:	PUNCT
ma-265	340	9	1−	1−	NUM
ma-265	340	10	x2	x2	INTJ
ma-265	341	1	−	−	PROPN
ma-265	341	2	y2	y2	NOUN
ma-265	341	3	1	1	NUM
ma-265	342	1	+	+	NUM
ma-265	342	2	x2	x2	PROPN
ma-265	343	1	+	+	CCONJ
ma-265	344	1	y2	y2	PROPN
ma-265	344	2	−	−	NOUN
ma-265	345	1	2x	2x	NUM
ma-265	345	2	+	+	CCONJ
ma-265	345	3	1	1	NUM
ma-265	345	4	2	2	NUM
ma-265	345	5	log(x2	log(x2	NOUN
ma-265	345	6	+	+	CCONJ
ma-265	345	7	y2	y2	NOUN
ma-265	345	8	)	)	PUNCT
ma-265	345	9	=	=	SYM
ma-265	345	10	0	0	NUM
ma-265	345	11	,	,	PUNCT
ma-265	345	12	determines	determine	VERB
ma-265	345	13	x	x	PUNCT
ma-265	345	14	as	as	ADP
ma-265	345	15	a	a	DET
ma-265	345	16	function	function	NOUN
ma-265	345	17	of	of	ADP
ma-265	345	18	y	y	PROPN
ma-265	345	19	in	in	ADP
ma-265	345	20	[	[	X
ma-265	345	21	−1	−1	NOUN
ma-265	345	22	,	,	PUNCT
ma-265	345	23	1	1	NUM
ma-265	345	24	]	]	PUNCT
ma-265	345	25	.	.	PUNCT
ma-265	346	1	it	it	PRON
ma-265	346	2	connects	connect	VERB
ma-265	346	3	−i	−i	PROPN
ma-265	346	4	=	=	PUNCT
ma-265	346	5	(	(	PUNCT
ma-265	346	6	0,−1	0,−1	PROPN
ma-265	346	7	)	)	PUNCT
ma-265	346	8	to	to	ADP
ma-265	346	9	i	i	PRON
ma-265	346	10	=	=	PUNCT
ma-265	346	11	(	(	PUNCT
ma-265	346	12	0	0	NUM
ma-265	346	13	,	,	PUNCT
ma-265	346	14	1	1	NUM
ma-265	346	15	)	)	PUNCT
ma-265	346	16	.	.	PUNCT
ma-265	347	1	if	if	SCONJ
ma-265	347	2	goes	go	VERB
ma-265	347	3	through	through	ADP
ma-265	347	4	(	(	PUNCT
ma-265	347	5	x0	x0	PROPN
ma-265	347	6	,	,	PUNCT
ma-265	347	7	0	0	NUM
ma-265	347	8	)	)	PUNCT
ma-265	347	9	and	and	CCONJ
ma-265	347	10	is	be	AUX
ma-265	347	11	symmetric	symmetric	ADJ
ma-265	347	12	with	with	ADP
ma-265	347	13	respect	respect	NOUN
ma-265	347	14	to	to	ADP
ma-265	347	15	the	the	DET
ma-265	347	16	x	x	NOUN
ma-265	347	17	-	-	NOUN
ma-265	347	18	axis	axis	ADJ
ma-265	347	19	.	.	PUNCT
ma-265	348	1	it	it	PRON
ma-265	348	2	is	be	AUX
ma-265	348	3	strictly	strictly	ADV
ma-265	348	4	monotonic	monotonic	ADJ
ma-265	348	5	decreasing	decrease	VERB
ma-265	348	6	from	from	ADP
ma-265	348	7	(	(	PUNCT
ma-265	348	8	x0	x0	PROPN
ma-265	348	9	,	,	PUNCT
ma-265	348	10	0)to	0)to	X
ma-265	348	11	(	(	PUNCT
ma-265	348	12	0	0	NUM
ma-265	348	13	,	,	PUNCT
ma-265	348	14	1	1	NUM
ma-265	348	15	)	)	PUNCT
ma-265	348	16	and	and	CCONJ
ma-265	348	17	by	by	ADP
ma-265	348	18	symmetry	symmetry	NOUN
ma-265	348	19	with	with	ADP
ma-265	348	20	respect	respect	NOUN
ma-265	348	21	to	to	ADP
ma-265	348	22	the	the	DET
ma-265	348	23	x	x	NOUN
ma-265	348	24	-	-	NOUN
ma-265	348	25	axis	axis	ADJ
ma-265	348	26	it	it	PRON
ma-265	348	27	is	be	AUX
ma-265	348	28	strictly	strictly	ADV
ma-265	348	29	monotonic	monotonic	ADJ
ma-265	348	30	increasing	increase	VERB
ma-265	348	31	from	from	ADP
ma-265	348	32	(	(	PUNCT
ma-265	348	33	0,−1)to	0,−1)to	NOUN
ma-265	348	34	(	(	PUNCT
ma-265	348	35	x0	x0	PROPN
ma-265	348	36	,	,	PUNCT
ma-265	348	37	0	0	NUM
ma-265	348	38	)	)	PUNCT
ma-265	348	39	.	.	PUNCT
ma-265	349	1	thus	thus	ADV
ma-265	349	2	u	u	NOUN
ma-265	349	3	is	be	AUX
ma-265	349	4	divided	divide	VERB
ma-265	349	5	into	into	ADP
ma-265	349	6	two	two	NUM
ma-265	349	7	parts	part	NOUN
ma-265	349	8	by	by	ADP
ma-265	349	9	that	that	DET
ma-265	349	10	zero	zero	NUM
ma-265	349	11	set	set	NOUN
ma-265	349	12	.	.	PUNCT
ma-265	350	1	the	the	DET
ma-265	350	2	part	part	NOUN
ma-265	350	3	in	in	ADP
ma-265	350	4	u	u	NOUN
ma-265	350	5	to	to	ADP
ma-265	350	6	the	the	DET
ma-265	350	7	left	left	NOUN
ma-265	350	8	of	of	ADP
ma-265	350	9	the	the	DET
ma-265	350	10	curveand	curveand	NOUN
ma-265	350	11	the	the	DET
ma-265	350	12	part	part	NOUN
ma-265	350	13	to	to	ADP
ma-265	350	14	the	the	DET
ma-265	350	15	right	right	NOUN
ma-265	350	16	of	of	ADP
ma-265	350	17	that	that	DET
ma-265	350	18	zero	zero	NUM
ma-265	350	19	set	set	NOUN
ma-265	350	20	.	.	PUNCT
ma-265	351	1	since	since	SCONJ
ma-265	351	2	the	the	DET
ma-265	351	3	left	left	ADJ
ma-265	351	4	part	part	NOUN
ma-265	351	5	contains	contain	VERB
ma-265	351	6	the	the	DET
ma-265	351	7	origin	origin	NOUN
ma-265	351	8	(	(	PUNCT
ma-265	351	9	by	by	ADP
ma-265	351	10	x0	x0	PROPN
ma-265	351	11	>	>	X
ma-265	351	12	0	0	NUM
ma-265	351	13	)	)	PUNCT
ma-265	351	14	it	it	PRON
ma-265	351	15	isthat	isthat	PROPN
ma-265	351	16	left	leave	VERB
ma-265	351	17	part	part	NOUN
ma-265	351	18	that	that	PRON
ma-265	351	19	is	be	AUX
ma-265	351	20	the	the	DET
ma-265	351	21	image	image	NOUN
ma-265	351	22	of	of	ADP
ma-265	351	23	our	our	PRON
ma-265	351	24	conformal	conformal	NOUN
ma-265	351	25	mapping	mapping	NOUN
ma-265	351	26	in	in	ADP
ma-265	351	27	this	this	DET
ma-265	351	28	example	example	NOUN
ma-265	351	29	,	,	PUNCT
ma-265	351	30	that	that	PRON
ma-265	351	31	corresponds	correspond	VERB
ma-265	351	32	to	to	ADP
ma-265	351	33	thefunction	thefunction	NOUN
ma-265	351	34	in	in	ADP
ma-265	351	35	rp	rp	NOUN
ma-265	351	36	given	give	VERB
ma-265	351	37	by	by	ADP
ma-265	351	38	:	:	PUNCT
ma-265	351	39	f	f	PROPN
ma-265	351	40	(	(	PUNCT
ma-265	351	41	z	z	NOUN
ma-265	351	42	)	)	PUNCT
ma-265	351	43	=	=	SYM
ma-265	352	1	1	1	NUM
ma-265	352	2	+	+	CCONJ
ma-265	352	3	z	z	NOUN
ma-265	352	4	1−	1−	NUM
ma-265	352	5	z	z	NOUN
ma-265	352	6	.	.	PUNCT
ma-265	353	1	7	7	X
ma-265	353	2	.	.	X
ma-265	353	3	combining	combine	VERB
ma-265	353	4	two	two	NUM
ma-265	353	5	dynamical	dynamical	ADJ
ma-265	353	6	systems	system	NOUN
ma-265	353	7	next	next	ADV
ma-265	353	8	we	we	PRON
ma-265	353	9	will	will	AUX
ma-265	353	10	make	make	VERB
ma-265	353	11	use	use	NOUN
ma-265	353	12	of	of	ADP
ma-265	353	13	two	two	NUM
ma-265	353	14	dynamical	dynamical	ADJ
ma-265	353	15	systems	system	NOUN
ma-265	353	16	.	.	PUNCT
ma-265	354	1	the	the	DET
ma-265	354	2	first	first	ADJ
ma-265	354	3	is	be	AUX
ma-265	354	4	the	the	DET
ma-265	354	5	discrete	discrete	ADJ
ma-265	354	6	dynamical	dynamical	ADJ
ma-265	354	7	systemwe	systemwe	NOUN
ma-265	354	8	used	use	VERB
ma-265	354	9	above	above	ADV
ma-265	354	10	.	.	PUNCT
ma-265	355	1	it	it	PRON
ma-265	355	2	is	be	AUX
ma-265	355	3	controlled	control	VERB
ma-265	355	4	by	by	ADP
ma-265	355	5	a	a	DET
ma-265	355	6	simple	simple	ADJ
ma-265	355	7	recursion	recursion	NOUN
ma-265	355	8	which	which	PRON
ma-265	355	9	is	be	AUX
ma-265	355	10	generated	generate	VERB
ma-265	355	11	by	by	ADP
ma-265	355	12	a	a	DET
ma-265	355	13	function	function	NOUN
ma-265	355	14	in	in	ADP
ma-265	355	15	rp.the	rp.the	DET
ma-265	355	16	second	second	NOUN
ma-265	355	17	is	be	AUX
ma-265	355	18	the	the	DET
ma-265	355	19	continuous	continuous	ADJ
ma-265	355	20	dynamical	dynamical	ADJ
ma-265	355	21	system	system	NOUN
ma-265	355	22	of	of	ADP
ma-265	355	23	löwner	löwner	NOUN
ma-265	355	24	type	type	NOUN
ma-265	355	25	that	that	PRON
ma-265	355	26	is	be	AUX
ma-265	355	27	controlled	control	VERB
ma-265	355	28	by	by	ADP
ma-265	355	29	the	the	DET
ma-265	355	30	partialdifferential	partialdifferential	ADJ
ma-265	355	31	equation	equation	NOUN
ma-265	355	32	for	for	ADP
ma-265	355	33	b	b	NOUN
ma-265	355	34	,	,	PUNCT
ma-265	355	35	the	the	DET
ma-265	355	36	class	class	NOUN
ma-265	355	37	of	of	ADP
ma-265	355	38	bounded	bounded	ADJ
ma-265	355	39	non	non	ADJ
ma-265	355	40	-	-	ADJ
ma-265	355	41	vanishing	vanishing	ADJ
ma-265	355	42	functions	function	NOUN
ma-265	355	43	.	.	PUNCT
ma-265	356	1	in	in	ADP
ma-265	356	2	fact	fact	NOUN
ma-265	356	3	b	b	NOUN
ma-265	356	4	=	=	SYM
ma-265	356	5	sinn	sinn	PROPN
ma-265	356	6	the	the	DET
ma-265	356	7	classof	classof	NOUN
ma-265	356	8	the	the	DET
ma-265	356	9	singular	singular	ADJ
ma-265	356	10	inner	inner	ADJ
ma-265	356	11	functions	function	NOUN
ma-265	356	12	.	.	PUNCT
ma-265	357	1	the	the	DET
ma-265	357	2	notation	notation	PROPN
ma-265	357	3	b	b	PROPN
ma-265	357	4	as	as	ADV
ma-265	357	5	well	well	ADV
ma-265	357	6	as	as	ADP
ma-265	357	7	its	its	PRON
ma-265	357	8	differential	differential	ADJ
ma-265	357	9	equation	equation	NOUN
ma-265	357	10	were	be	AUX
ma-265	357	11	describedin	describedin	VERB
ma-265	357	12	section	section	NOUN
ma-265	357	13	2	2	NUM
ma-265	357	14	of	of	ADP
ma-265	357	15	the	the	DET
ma-265	357	16	basic	basic	ADJ
ma-265	357	17	paper	paper	NOUN
ma-265	357	18	[	[	X
ma-265	357	19	1	1	NUM
ma-265	357	20	]	]	PUNCT
ma-265	357	21	.	.	PUNCT
ma-265	358	1	the	the	DET
ma-265	358	2	notation	notation	NOUN
ma-265	358	3	sinn	sinn	PROPN
ma-265	358	4	was	be	AUX
ma-265	358	5	used	use	VERB
ma-265	358	6	in	in	ADP
ma-265	358	7	[	[	X
ma-265	358	8	2	2	NUM
ma-265	358	9	]	]	PUNCT
ma-265	358	10	.	.	PUNCT
ma-265	359	1	we	we	PRON
ma-265	359	2	recall	recall	VERB
ma-265	359	3	facts	fact	NOUN
ma-265	359	4	from	from	ADP
ma-265	359	5	section2	section2	NOUN
ma-265	359	6	of	of	ADP
ma-265	359	7	[	[	X
ma-265	359	8	1	1	NUM
ma-265	359	9	]	]	PUNCT
ma-265	359	10	.	.	PUNCT
ma-265	360	1	suppose	suppose	VERB
ma-265	360	2	f	f	PROPN
ma-265	360	3	∈	∈	PROPN
ma-265	360	4	b	b	PROPN
ma-265	360	5	has	have	VERB
ma-265	360	6	the	the	DET
ma-265	360	7	herglotz	herglotz	NOUN
ma-265	360	8	representation	representation	NOUN
ma-265	360	9	f	f	X
ma-265	360	10	(	(	PUNCT
ma-265	360	11	z	z	NOUN
ma-265	360	12	)	)	PUNCT
ma-265	360	13	=	=	NOUN
ma-265	360	14	exp	exp	NOUN
ma-265	360	15	(	(	PUNCT
ma-265	360	16	−	−	PROPN
ma-265	360	17	∫	∫	PROPN
ma-265	360	18	2π	2π	PROPN
ma-265	360	19	0	0	PUNCT
ma-265	361	1	e	e	NOUN
ma-265	361	2	iθ	iθ	NOUN
ma-265	361	3	+	+	NOUN
ma-265	361	4	z	z	NOUN
ma-265	361	5	e	e	NOUN
ma-265	361	6	iθ	iθ	NOUN
ma-265	361	7	−	−	PROPN
ma-265	361	8	z	z	NOUN
ma-265	361	9	h(θ)dθ	h(θ)dθ	PROPN
ma-265	361	10	)	)	PUNCT
ma-265	361	11	,	,	PUNCT
ma-265	361	12	where	where	SCONJ
ma-265	361	13	h(θ	h(θ	PROPN
ma-265	361	14	)	)	PUNCT
ma-265	361	15	≥	≥	NOUN
ma-265	361	16	0	0	NUM
ma-265	361	17	.	.	PUNCT
ma-265	362	1	the	the	DET
ma-265	362	2	collection	collection	NOUN
ma-265	362	3	of	of	ADP
ma-265	362	4	such	such	ADJ
ma-265	362	5	functions	function	NOUN
ma-265	362	6	is	be	AUX
ma-265	362	7	dense	dense	ADJ
ma-265	362	8	in	in	ADP
ma-265	362	9	the	the	DET
ma-265	362	10	subfamily	subfamily	NOUN
ma-265	362	11	of	of	ADP
ma-265	362	12	b	b	NOUN
ma-265	362	13	consisting	consist	VERB
ma-265	362	14	offunctions	offunction	NOUN
ma-265	362	15	for	for	ADP
ma-265	362	16	which	which	PRON
ma-265	362	17	f	f	X
ma-265	362	18	(	(	PUNCT
ma-265	362	19	0	0	NUM
ma-265	362	20	)	)	PUNCT
ma-265	362	21	>	>	X
ma-265	362	22	0	0	X
ma-265	362	23	.	.	X
ma-265	363	1	changing	change	VERB
ma-265	363	2	variable	variable	NOUN
ma-265	363	3	by	by	ADP
ma-265	363	4	the	the	DET
ma-265	363	5	substitution	substitution	NOUN
ma-265	363	6	τ	τ	NOUN
ma-265	363	7	=	=	SYM
ma-265	363	8	τ(θ	τ(θ	X
ma-265	363	9	)	)	PUNCT
ma-265	363	10	=	=	SYM
ma-265	364	1	∫	∫	PROPN
ma-265	364	2	θ0	θ0	PROPN
ma-265	364	3	h(φ)dφ	h(φ)dφ	PART
ma-265	364	4	,	,	PUNCT
ma-265	364	5	andputting	andputte	VERB
ma-265	364	6	k(τ	k(τ	PROPN
ma-265	364	7	)	)	PUNCT
ma-265	365	1	=	=	PUNCT
ma-265	365	2	e	e	NOUN
ma-265	365	3	iθ	iθ	NOUN
ma-265	365	4	leads	lead	VERB
ma-265	365	5	to	to	ADP
ma-265	365	6	the	the	DET
ma-265	365	7	formula	formula	NOUN
ma-265	365	8	,	,	PUNCT
ma-265	365	9	f	f	PROPN
ma-265	365	10	(	(	PUNCT
ma-265	365	11	z	z	NOUN
ma-265	365	12	)	)	PUNCT
ma-265	365	13	=	=	NOUN
ma-265	365	14	exp	exp	NOUN
ma-265	365	15	(	(	PUNCT
ma-265	365	16	−	−	PROPN
ma-265	365	17	∫	∫	PROPN
ma-265	365	18	t0	t0	PROPN
ma-265	365	19	0	0	NUM
ma-265	365	20	1	1	NUM
ma-265	365	21	+	+	CCONJ
ma-265	365	22	k(τ)z	k(τ)z	PROPN
ma-265	365	23	1−	1−	NUM
ma-265	365	24	k(τ)z	k(τ)z	PROPN
ma-265	365	25	dτ	dτ	PROPN
ma-265	365	26	)	)	PUNCT
ma-265	365	27	,	,	PUNCT
ma-265	365	28	(	(	PUNCT
ma-265	365	29	7.1	7.1	NUM
ma-265	365	30	)	)	PUNCT
ma-265	365	31	where	where	SCONJ
ma-265	365	32	t0	t0	NOUN
ma-265	365	33	=	=	SYM
ma-265	365	34	τ(2π	τ(2π	NUM
ma-265	365	35	)	)	PUNCT
ma-265	365	36	=	=	PUNCT
ma-265	366	1	−	−	PROPN
ma-265	366	2	log	log	NOUN
ma-265	366	3	f	f	X
ma-265	366	4	(	(	PUNCT
ma-265	366	5	0	0	NUM
ma-265	366	6	)	)	PUNCT
ma-265	366	7	.	.	PUNCT
ma-265	367	1	conversely	conversely	ADV
ma-265	367	2	,	,	PUNCT
ma-265	367	3	if	if	SCONJ
ma-265	367	4	k(τ	k(τ	PROPN
ma-265	367	5	)	)	PUNCT
ma-265	367	6	is	be	AUX
ma-265	367	7	a	a	DET
ma-265	367	8	measurable	measurable	ADJ
ma-265	367	9	function	function	NOUN
ma-265	367	10	of	of	ADP
ma-265	367	11	τ	τ	PROPN
ma-265	367	12	which	which	PRON
ma-265	367	13	satisfies	satisfy	VERB
ma-265	367	14	|k(τ)|	|k(τ)|	PROPN
ma-265	367	15	=	=	SYM
ma-265	367	16	1	1	NUM
ma-265	367	17	,	,	PUNCT
ma-265	367	18	τ	τ	PROPN
ma-265	367	19	∈	∈	PROPN
ma-265	367	20	r	r	NOUN
ma-265	367	21	,	,	PUNCT
ma-265	367	22	then	then	ADV
ma-265	367	23	equation	equation	NOUN
ma-265	367	24	(	(	PUNCT
ma-265	367	25	7.1	7.1	NUM
ma-265	367	26	)	)	PUNCT
ma-265	367	27	defines	define	VERB
ma-265	367	28	a	a	DET
ma-265	367	29	function	function	NOUN
ma-265	367	30	of	of	ADP
ma-265	367	31	class	class	PROPN
ma-265	367	32	b.	b.	PROPN
ma-265	367	33	given	give	VERB
ma-265	367	34	f	f	PROPN
ma-265	367	35	(	(	PUNCT
ma-265	367	36	z	z	NOUN
ma-265	367	37	)	)	PUNCT
ma-265	367	38	as	as	ADP
ma-265	367	39	in	in	ADP
ma-265	367	40	equation(7.1	equation(7.1	NOUN
ma-265	367	41	)	)	PUNCT
ma-265	367	42	,	,	PUNCT
ma-265	367	43	we	we	PRON
ma-265	367	44	set	set	VERB
ma-265	367	45	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	367	46	eur	eur	PROPN
ma-265	367	47	.	.	PUNCT
ma-265	368	1	j.	j.	PROPN
ma-265	368	2	math	math	PROPN
ma-265	368	3	.	.	PUNCT
ma-265	369	1	anal	anal	PROPN
ma-265	369	2	.	.	PUNCT
ma-265	370	1	10.28924	10.28924	NUM
ma-265	370	2	/	/	SYM
ma-265	370	3	ada	ada	PROPN
ma-265	370	4	/	/	SYM
ma-265	370	5	ma.5.4	ma.5.4	PROPN
ma-265	370	6	11	11	NUM
ma-265	370	7	f	f	NOUN
ma-265	370	8	(	(	PUNCT
ma-265	370	9	z	z	PROPN
ma-265	370	10	,	,	PUNCT
ma-265	370	11	t	t	PROPN
ma-265	370	12	)	)	PUNCT
ma-265	370	13	=	=	NOUN
ma-265	370	14	exp	exp	NOUN
ma-265	370	15	(	(	PUNCT
ma-265	370	16	−	−	PROPN
ma-265	370	17	∫	∫	PROPN
ma-265	370	18	t	t	NOUN
ma-265	370	19	0	0	NUM
ma-265	370	20	1	1	NUM
ma-265	370	21	+	+	CCONJ
ma-265	370	22	k(τ)z	k(τ)z	PROPN
ma-265	370	23	1−	1−	NUM
ma-265	370	24	k(τ)z	k(τ)z	PROPN
ma-265	370	25	dτ	dτ	PROPN
ma-265	370	26	)	)	PUNCT
ma-265	370	27	,	,	PUNCT
ma-265	370	28	0	0	NUM
ma-265	370	29	≤	≤	NUM
ma-265	370	30	t	t	PROPN
ma-265	370	31	≤	≤	NUM
ma-265	370	32	t0	t0	PROPN
ma-265	370	33	.	.	PUNCT
ma-265	371	1	(	(	PUNCT
ma-265	371	2	7.2	7.2	NUM
ma-265	371	3	)	)	PUNCT
ma-265	371	4	then	then	ADV
ma-265	371	5	f	f	X
ma-265	371	6	(	(	PUNCT
ma-265	371	7	z	z	PROPN
ma-265	371	8	,	,	PUNCT
ma-265	371	9	t	t	PROPN
ma-265	371	10	)	)	PUNCT
ma-265	371	11	∈	∈	PROPN
ma-265	371	12	b	b	PROPN
ma-265	371	13	for	for	ADP
ma-265	371	14	all	all	DET
ma-265	371	15	t	t	NOUN
ma-265	371	16	∈	∈	PROPN
ma-265	372	1	[	[	X
ma-265	372	2	0	0	NUM
ma-265	372	3	,	,	PUNCT
ma-265	372	4	t0	t0	PROPN
ma-265	372	5	]	]	PUNCT
ma-265	372	6	,	,	PUNCT
ma-265	372	7	f	f	PROPN
ma-265	372	8	(	(	PUNCT
ma-265	372	9	z	z	PROPN
ma-265	372	10	,	,	PUNCT
ma-265	372	11	t0	t0	NOUN
ma-265	372	12	)	)	PUNCT
ma-265	372	13	=	=	SYM
ma-265	372	14	f	f	X
ma-265	372	15	(	(	PUNCT
ma-265	372	16	z	z	NOUN
ma-265	372	17	)	)	PUNCT
ma-265	372	18	,	,	PUNCT
ma-265	372	19	and	and	CCONJ
ma-265	372	20	f	f	PROPN
ma-265	372	21	(	(	PUNCT
ma-265	372	22	z	z	NOUN
ma-265	372	23	,	,	PUNCT
ma-265	372	24	0	0	NUM
ma-265	372	25	)	)	PUNCT
ma-265	372	26	=	=	SYM
ma-265	372	27	1	1	X
ma-265	372	28	.	.	PUNCT
ma-265	373	1	it	it	PRON
ma-265	373	2	follows	follow	VERB
ma-265	373	3	from	from	ADP
ma-265	373	4	equation	equation	NOUN
ma-265	373	5	(	(	PUNCT
ma-265	373	6	7.2)that	7.2)that	NUM
ma-265	373	7	for	for	ADP
ma-265	373	8	almost	almost	ADV
ma-265	373	9	all	all	PRON
ma-265	373	10	t	t	NOUN
ma-265	373	11	,	,	PUNCT
ma-265	373	12	∂f	∂f	PROPN
ma-265	373	13	(	(	PUNCT
ma-265	373	14	z	z	PROPN
ma-265	373	15	,	,	PUNCT
ma-265	373	16	t	t	PROPN
ma-265	373	17	)	)	PUNCT
ma-265	374	1	∂t	∂t	PROPN
ma-265	374	2	=	=	SYM
ma-265	374	3	−f	−f	PROPN
ma-265	374	4	(	(	PUNCT
ma-265	374	5	z	z	PROPN
ma-265	374	6	,	,	PUNCT
ma-265	374	7	t	t	PROPN
ma-265	374	8	)	)	PUNCT
ma-265	374	9	·	·	PUNCT
ma-265	374	10	1	1	NUM
ma-265	374	11	+	+	CCONJ
ma-265	374	12	k(t	k(t	X
ma-265	374	13	)	)	PUNCT
ma-265	374	14	·	·	PUNCT
ma-265	374	15	z	z	NOUN
ma-265	374	16	1−	1−	NUM
ma-265	374	17	k(t	k(t	X
ma-265	374	18	)	)	PUNCT
ma-265	374	19	·	·	PUNCT
ma-265	374	20	z	z	X
ma-265	374	21	.	.	PUNCT
ma-265	375	1	(	(	PUNCT
ma-265	375	2	7.3	7.3	NUM
ma-265	375	3	)	)	PUNCT
ma-265	375	4	this	this	PRON
ma-265	375	5	is	be	AUX
ma-265	375	6	the	the	DET
ma-265	375	7	differential	differential	ADJ
ma-265	375	8	equation	equation	NOUN
ma-265	375	9	for	for	ADP
ma-265	375	10	b.we	b.we	PRON
ma-265	375	11	recall	recall	VERB
ma-265	375	12	our	our	PRON
ma-265	375	13	discrete	discrete	ADJ
ma-265	375	14	dynamical	dynamical	ADJ
ma-265	375	15	system	system	NOUN
ma-265	375	16	:	:	PUNCT
ma-265	375	17	let	let	VERB
ma-265	375	18	g	g	PROPN
ma-265	375	19	∈	∈	PROPN
ma-265	375	20	rp	rp	NOUN
ma-265	375	21	.	.	PUNCT
ma-265	376	1	we	we	PRON
ma-265	376	2	will	will	AUX
ma-265	376	3	use	use	VERB
ma-265	376	4	the	the	DET
ma-265	376	5	function	function	NOUN
ma-265	376	6	g(z	g(z	PROPN
ma-265	376	7	)	)	PUNCT
ma-265	376	8	to	to	PART
ma-265	376	9	generate	generate	VERB
ma-265	376	10	a	a	DET
ma-265	376	11	sequence	sequence	NOUN
ma-265	376	12	{	{	PUNCT
ma-265	376	13	sn}∞n=0	sn}∞n=0	X
ma-265	376	14	of	of	ADP
ma-265	376	15	singular	singular	ADJ
ma-265	376	16	innerfunctions	innerfunction	NOUN
ma-265	376	17	.	.	PUNCT
ma-265	377	1	it	it	PRON
ma-265	377	2	is	be	AUX
ma-265	377	3	controlled	control	VERB
ma-265	377	4	by	by	ADP
ma-265	377	5	the	the	DET
ma-265	377	6	following	follow	VERB
ma-265	377	7	recursion	recursion	NOUN
ma-265	377	8	,	,	PUNCT
ma-265	377	9	s0(z	s0(z	SYM
ma-265	377	10	)	)	PUNCT
ma-265	377	11	∈	∈	PROPN
ma-265	377	12	sinn	sinn	NOUN
ma-265	377	13	(	(	PUNCT
ma-265	377	14	an	an	DET
ma-265	377	15	arbitrary	arbitrary	ADJ
ma-265	377	16	initial	initial	ADJ
ma-265	377	17	point	point	NOUN
ma-265	377	18	)	)	PUNCT
ma-265	377	19	.	.	PUNCT
ma-265	378	1	sn+1(z	sn+1(z	VERB
ma-265	378	2	)	)	PUNCT
ma-265	379	1	=	=	NOUN
ma-265	379	2	exp	exp	NOUN
ma-265	379	3	(	(	PUNCT
ma-265	379	4	−g(z	−g(z	NOUN
ma-265	379	5	·	·	PUNCT
ma-265	379	6	sn(z	sn(z	NOUN
ma-265	379	7	)	)	PUNCT
ma-265	379	8	)	)	PUNCT
ma-265	379	9	)	)	PUNCT
ma-265	379	10	for	for	ADP
ma-265	379	11	n	n	PRON
ma-265	379	12	∈	∈	PROPN
ma-265	379	13	z≥0	z≥0	PROPN
ma-265	379	14	.	.	PUNCT
ma-265	380	1	(	(	PUNCT
ma-265	380	2	7.4	7.4	NUM
ma-265	380	3	)	)	PUNCT
ma-265	380	4	we	we	PRON
ma-265	380	5	proved	prove	VERB
ma-265	380	6	in	in	ADP
ma-265	380	7	theorem	theorem	ADJ
ma-265	380	8	3.3	3.3	NUM
ma-265	380	9	,	,	PUNCT
ma-265	380	10	the	the	DET
ma-265	380	11	following	following	NOUN
ma-265	380	12	:	:	PUNCT
ma-265	380	13	the	the	DET
ma-265	380	14	limit	limit	NOUN
ma-265	380	15	s(z	s(z	PROPN
ma-265	380	16	)	)	PUNCT
ma-265	380	17	=	=	SYM
ma-265	380	18	limn→∞	limn→∞	PROPN
ma-265	380	19	sn(z	sn(z	NOUN
ma-265	380	20	)	)	PUNCT
ma-265	380	21	exists	exist	VERB
ma-265	380	22	and	and	CCONJ
ma-265	380	23	is	be	AUX
ma-265	380	24	uniform	uniform	ADJ
ma-265	380	25	on	on	ADP
ma-265	380	26	compact	compact	ADJ
ma-265	380	27	subsets	subset	NOUN
ma-265	380	28	of	of	ADP
ma-265	380	29	u	u	NOUN
ma-265	380	30	.	.	PUNCT
ma-265	381	1	s	s	PART
ma-265	381	2	∈	∈	PROPN
ma-265	381	3	h(u	h(u	PROPN
ma-265	381	4	)	)	PUNCT
ma-265	381	5	satisfies	satisfy	VERB
ma-265	381	6	|s(z)|	|s(z)|	PROPN
ma-265	381	7	≤	≤	ADJ
ma-265	381	8	1	1	NUM
ma-265	381	9	∀	∀	NOUN
ma-265	381	10	z	z	NOUN
ma-265	381	11	∈	∈	PROPN
ma-265	381	12	u	u	NOUN
ma-265	381	13	,	,	PUNCT
ma-265	381	14	and	and	CCONJ
ma-265	381	15	satisfies	satisfy	VERB
ma-265	381	16	the	the	DET
ma-265	381	17	following	follow	VERB
ma-265	381	18	fixed	fix	VERB
ma-265	381	19	-	-	PUNCT
ma-265	381	20	point	point	NOUN
ma-265	381	21	equation	equation	NOUN
ma-265	381	22	,	,	PUNCT
ma-265	381	23	s(z	s(z	PROPN
ma-265	381	24	)	)	PUNCT
ma-265	381	25	=	=	SYM
ma-265	381	26	exp	exp	NOUN
ma-265	381	27	(	(	PUNCT
ma-265	381	28	−g(z	−g(z	NOUN
ma-265	381	29	·	·	PUNCT
ma-265	381	30	s(z))).the	s(z))).the	PRON
ma-265	381	31	function	function	NOUN
ma-265	381	32	z	z	NOUN
ma-265	381	33	·	·	PUNCT
ma-265	381	34	s(z	s(z	NOUN
ma-265	381	35	)	)	PUNCT
ma-265	381	36	∈	∈	PROPN
ma-265	381	37	bh∞(u	bh∞(u	NOUN
ma-265	381	38	)	)	PUNCT
ma-265	381	39	,	,	PUNCT
ma-265	381	40	the	the	DET
ma-265	381	41	unit	unit	NOUN
ma-265	381	42	ball	ball	NOUN
ma-265	381	43	of	of	ADP
ma-265	381	44	h∞(u	h∞(u	NOUN
ma-265	381	45	)	)	PUNCT
ma-265	381	46	.	.	PUNCT
ma-265	382	1	z	z	NOUN
ma-265	382	2	·	·	PUNCT
ma-265	382	3	s(z	s(z	PROPN
ma-265	382	4	)	)	PUNCT
ma-265	382	5	is	be	AUX
ma-265	382	6	a	a	DET
ma-265	382	7	conformal	conformal	ADJ
ma-265	382	8	mapping	mapping	NOUN
ma-265	382	9	(	(	PUNCT
ma-265	382	10	it	it	PRON
ma-265	382	11	belongsto	belongsto	NOUN
ma-265	382	12	conf	conf	NOUN
ma-265	382	13	)	)	PUNCT
ma-265	382	14	.	.	PUNCT
ma-265	383	1	thus	thus	ADV
ma-265	383	2	z	z	X
ma-265	383	3	·	·	PUNCT
ma-265	383	4	s(z	s(z	PROPN
ma-265	383	5	)	)	PUNCT
ma-265	383	6	:	:	PUNCT
ma-265	383	7	u	u	NOUN
ma-265	383	8	→	→	SYM
ma-265	383	9	im(z	im(z	X
ma-265	383	10	·	·	PUNCT
ma-265	383	11	s(z	s(z	PROPN
ma-265	383	12	)	)	PUNCT
ma-265	383	13	)	)	PUNCT
ma-265	384	1	⊆	⊆	NUM
ma-265	384	2	u	u	NOUN
ma-265	384	3	,	,	PUNCT
ma-265	384	4	but	but	CCONJ
ma-265	384	5	it	it	PRON
ma-265	384	6	is	be	AUX
ma-265	384	7	not	not	PART
ma-265	384	8	an	an	DET
ma-265	384	9	inner	inner	ADJ
ma-265	384	10	function	function	NOUN
ma-265	384	11	,	,	PUNCT
ma-265	384	12	see	see	VERB
ma-265	384	13	for	for	ADP
ma-265	384	14	example	example	NOUN
ma-265	384	15	[	[	X
ma-265	384	16	3].let	3].let	NUM
ma-265	384	17	us	we	PRON
ma-265	384	18	denote	denote	VERB
ma-265	384	19	the	the	DET
ma-265	384	20	following	follow	VERB
ma-265	384	21	correspondence	correspondence	NOUN
ma-265	384	22	by	by	ADP
ma-265	384	23	f	f	PROPN
ma-265	384	24	:	:	PUNCT
ma-265	384	25	f	f	X
ma-265	384	26	:	:	PUNCT
ma-265	384	27	sinn→	sinn→	PRON
ma-265	384	28	conf	conf	NOUN
ma-265	384	29	,	,	PUNCT
ma-265	384	30	f	f	PROPN
ma-265	384	31	(	(	PUNCT
ma-265	384	32	s0	s0	PROPN
ma-265	384	33	)	)	PUNCT
ma-265	384	34	=	=	PUNCT
ma-265	384	35	z	z	NOUN
ma-265	384	36	·	·	PUNCT
ma-265	384	37	s(z	s(z	NOUN
ma-265	384	38	)	)	PUNCT
ma-265	384	39	.	.	PUNCT
ma-265	385	1	one	one	NUM
ma-265	385	2	result	result	VERB
ma-265	385	3	that	that	SCONJ
ma-265	385	4	we	we	PRON
ma-265	385	5	will	will	AUX
ma-265	385	6	demonstrate	demonstrate	VERB
ma-265	385	7	below	below	ADV
ma-265	385	8	is	be	AUX
ma-265	385	9	that	that	SCONJ
ma-265	385	10	the	the	DET
ma-265	385	11	correspondence	correspondence	NOUN
ma-265	385	12	f	f	PROPN
ma-265	385	13	is	be	AUX
ma-265	385	14	,	,	PUNCT
ma-265	385	15	in	in	ADP
ma-265	385	16	fact	fact	NOUN
ma-265	385	17	,	,	PUNCT
ma-265	385	18	a	a	DET
ma-265	385	19	constant	constant	ADJ
ma-265	385	20	.	.	PUNCT
ma-265	386	1	wewill	wewill	PROPN
ma-265	386	2	give	give	VERB
ma-265	386	3	two	two	NUM
ma-265	386	4	different	different	ADJ
ma-265	386	5	proofs	proof	NOUN
ma-265	386	6	for	for	ADP
ma-265	386	7	that	that	DET
ma-265	386	8	result	result	NOUN
ma-265	386	9	.	.	PUNCT
ma-265	387	1	this	this	DET
ma-265	387	2	result	result	NOUN
ma-265	387	3	might	might	AUX
ma-265	387	4	seem	seem	VERB
ma-265	387	5	to	to	PART
ma-265	387	6	be	be	AUX
ma-265	387	7	surprising	surprising	ADJ
ma-265	387	8	at	at	ADP
ma-265	387	9	first	first	ADV
ma-265	387	10	.	.	PUNCT
ma-265	388	1	but	but	CCONJ
ma-265	388	2	itis	itis	NOUN
ma-265	388	3	not	not	PART
ma-265	388	4	really	really	ADV
ma-265	388	5	surprising	surprising	ADJ
ma-265	388	6	.	.	PUNCT
ma-265	389	1	remark	remark	NOUN
ma-265	389	2	7.1	7.1	NUM
ma-265	389	3	.	.	PUNCT
ma-265	390	1	we	we	PRON
ma-265	390	2	clearly	clearly	ADV
ma-265	390	3	have	have	VERB
ma-265	390	4	∀	∀	NOUN
ma-265	390	5	n	n	PRON
ma-265	390	6	∈	∈	PROPN
ma-265	390	7	z≥0	z≥0	NOUN
ma-265	390	8	,	,	PUNCT
ma-265	390	9	f	f	PROPN
ma-265	390	10	(	(	PUNCT
ma-265	390	11	sn	sn	PROPN
ma-265	390	12	)	)	PUNCT
ma-265	390	13	=	=	SYM
ma-265	390	14	z	z	NOUN
ma-265	390	15	·	·	PUNCT
ma-265	390	16	s(z	s(z	NOUN
ma-265	390	17	)	)	PUNCT
ma-265	390	18	.	.	PUNCT
ma-265	391	1	so	so	ADV
ma-265	391	2	the	the	DET
ma-265	391	3	correspondence	correspondence	NOUN
ma-265	391	4	f	f	PROPN
ma-265	391	5	is	be	AUX
ma-265	391	6	certainlyconstant	certainlyconstant	ADJ
ma-265	391	7	on	on	ADP
ma-265	391	8	the	the	DET
ma-265	391	9	sequence	sequence	NOUN
ma-265	391	10	{	{	PUNCT
ma-265	391	11	sn(z)}∞n=0	sn(z)}∞n=0	NUM
ma-265	391	12	which	which	PRON
ma-265	391	13	is	be	AUX
ma-265	391	14	the	the	DET
ma-265	391	15	output	output	NOUN
ma-265	391	16	of	of	ADP
ma-265	391	17	our	our	PRON
ma-265	391	18	recursion	recursion	NOUN
ma-265	391	19	,	,	PUNCT
ma-265	391	20	that	that	PRON
ma-265	391	21	generates	generate	VERB
ma-265	391	22	thediscrete	thediscrete	ADJ
ma-265	391	23	dynamical	dynamical	ADJ
ma-265	391	24	system	system	NOUN
ma-265	391	25	.	.	PUNCT
ma-265	392	1	so	so	ADV
ma-265	392	2	we	we	PRON
ma-265	392	3	can	can	AUX
ma-265	392	4	view	view	VERB
ma-265	392	5	f	f	PROPN
ma-265	392	6	as	as	ADP
ma-265	392	7	a	a	DET
ma-265	392	8	correspondence	correspondence	NOUN
ma-265	392	9	sinn/{{sn(z)}∞n=0	sinn/{{sn(z)}∞n=0	NOUN
ma-265	392	10	}	}	PUNCT
ma-265	392	11	→	→	SYM
ma-265	392	12	conf.however	conf.however	X
ma-265	392	13	,	,	PUNCT
ma-265	392	14	since	since	SCONJ
ma-265	392	15	we	we	PRON
ma-265	392	16	will	will	AUX
ma-265	392	17	prove	prove	VERB
ma-265	392	18	that	that	SCONJ
ma-265	392	19	f	f	PROPN
ma-265	392	20	is	be	AUX
ma-265	392	21	a	a	DET
ma-265	392	22	constant	constant	ADJ
ma-265	392	23	correspondence	correspondence	NOUN
ma-265	392	24	(	(	PUNCT
ma-265	392	25	given	give	VERB
ma-265	392	26	a	a	DET
ma-265	392	27	g	g	PROPN
ma-265	392	28	∈	∈	PROPN
ma-265	392	29	rp	rp	NOUN
ma-265	392	30	)	)	PUNCT
ma-265	392	31	we	we	PRON
ma-265	392	32	willconclude	willconclude	VERB
ma-265	392	33	that	that	SCONJ
ma-265	392	34	the	the	DET
ma-265	392	35	truly	truly	ADV
ma-265	392	36	interesting	interesting	ADJ
ma-265	392	37	correspondence	correspondence	NOUN
ma-265	392	38	is	be	AUX
ma-265	392	39	not	not	PART
ma-265	392	40	sinn→	sinn→	PRON
ma-265	392	41	conf	conf	NOUN
ma-265	392	42	,	,	PUNCT
ma-265	392	43	but	but	CCONJ
ma-265	392	44	is	be	AUX
ma-265	392	45	t	t	NOUN
ma-265	392	46	:	:	PUNCT
ma-265	392	47	rp→	rp→	PROPN
ma-265	392	48	conf	conf	NOUN
ma-265	392	49	,	,	PUNCT
ma-265	392	50	t	t	PROPN
ma-265	392	51	(	(	PUNCT
ma-265	392	52	g(z	g(z	PROPN
ma-265	392	53	)	)	PUNCT
ma-265	392	54	)	)	PUNCT
ma-265	393	1	=	=	PUNCT
ma-265	393	2	z	z	X
ma-265	393	3	·	·	PUNCT
ma-265	393	4	s(z	s(z	NOUN
ma-265	393	5	)	)	PUNCT
ma-265	393	6	.	.	PUNCT
ma-265	394	1	we	we	PRON
ma-265	394	2	combine	combine	VERB
ma-265	394	3	the	the	DET
ma-265	394	4	continuous	continuous	ADJ
ma-265	394	5	dynamical	dynamical	ADJ
ma-265	394	6	system	system	NOUN
ma-265	394	7	that	that	PRON
ma-265	394	8	was	be	AUX
ma-265	394	9	described	describe	VERB
ma-265	394	10	in	in	ADP
ma-265	394	11	equation	equation	NOUN
ma-265	394	12	(	(	PUNCT
ma-265	394	13	7.3	7.3	NUM
ma-265	394	14	)	)	PUNCT
ma-265	394	15	,	,	PUNCT
ma-265	394	16	with	with	SCONJ
ma-265	394	17	our	our	PRON
ma-265	394	18	g	g	NOUN
ma-265	394	19	-	-	PUNCT
ma-265	394	20	discrete	discrete	ADJ
ma-265	394	21	dynamical	dynamical	ADJ
ma-265	394	22	system	system	NOUN
ma-265	394	23	(	(	PUNCT
ma-265	394	24	g	g	PROPN
ma-265	394	25	∈	∈	PROPN
ma-265	394	26	rp	rp	NOUN
ma-265	394	27	)	)	PUNCT
ma-265	394	28	that	that	PRON
ma-265	394	29	was	be	AUX
ma-265	394	30	described	describe	VERB
ma-265	394	31	in	in	ADP
ma-265	394	32	equation	equation	NOUN
ma-265	394	33	(	(	PUNCT
ma-265	394	34	7.4	7.4	NUM
ma-265	394	35	)	)	PUNCT
ma-265	394	36	,	,	PUNCT
ma-265	394	37	as	as	SCONJ
ma-265	394	38	follows	follow	VERB
ma-265	394	39	:	:	PUNCT
ma-265	394	40	f	f	X
ma-265	394	41	:	:	PUNCT
ma-265	394	42	{	{	PUNCT
ma-265	394	43	f	f	X
ma-265	394	44	(	(	PUNCT
ma-265	394	45	z	z	PROPN
ma-265	394	46	,	,	PUNCT
ma-265	394	47	t	t	PROPN
ma-265	394	48	)	)	PUNCT
ma-265	394	49	|	|	ADV
ma-265	394	50	0	0	NUM
ma-265	394	51	≤	≤	NOUN
ma-265	394	52	t	t	PROPN
ma-265	394	53	≤	≤	NUM
ma-265	394	54	t0	t0	PROPN
ma-265	394	55	}	}	PUNCT
ma-265	394	56	→	→	SYM
ma-265	394	57	conf	conf	NOUN
ma-265	394	58	,	,	PUNCT
ma-265	394	59	f	f	PROPN
ma-265	394	60	(	(	PUNCT
ma-265	394	61	f	f	X
ma-265	394	62	(	(	PUNCT
ma-265	394	63	z	z	PROPN
ma-265	394	64	,	,	PUNCT
ma-265	394	65	t	t	PROPN
ma-265	394	66	)	)	PUNCT
ma-265	394	67	)	)	PUNCT
ma-265	395	1	=	=	PUNCT
ma-265	396	1	z	z	X
ma-265	396	2	·	·	PUNCT
ma-265	396	3	s(z	s(z	PROPN
ma-265	396	4	,	,	PUNCT
ma-265	396	5	t	t	PROPN
ma-265	396	6	)	)	PUNCT
ma-265	396	7	.	.	PUNCT
ma-265	397	1	here	here	ADV
ma-265	397	2	the	the	DET
ma-265	397	3	starting	starting	NOUN
ma-265	397	4	point	point	NOUN
ma-265	397	5	of	of	ADP
ma-265	397	6	the	the	DET
ma-265	397	7	recursion	recursion	NOUN
ma-265	397	8	is	be	AUX
ma-265	397	9	s0(z	s0(z	NOUN
ma-265	397	10	,	,	PUNCT
ma-265	397	11	t	t	PROPN
ma-265	397	12	)	)	PUNCT
ma-265	398	1	=	=	SYM
ma-265	398	2	f	f	X
ma-265	398	3	(	(	PUNCT
ma-265	398	4	z	z	PROPN
ma-265	398	5	,	,	PUNCT
ma-265	398	6	t	t	PROPN
ma-265	398	7	)	)	PUNCT
ma-265	398	8	and	and	CCONJ
ma-265	398	9	sn+1(z	sn+1(z	VERB
ma-265	398	10	,	,	PUNCT
ma-265	398	11	t	t	PROPN
ma-265	398	12	)	)	PUNCT
ma-265	398	13	=	=	NOUN
ma-265	398	14	exp	exp	NOUN
ma-265	398	15	(	(	PUNCT
ma-265	398	16	−g(z	−g(z	NOUN
ma-265	398	17	·	·	PUNCT
ma-265	398	18	sn(z	sn(z	NOUN
ma-265	398	19	,	,	PUNCT
ma-265	398	20	t)))for	t)))for	ADP
ma-265	398	21	n	n	PRON
ma-265	398	22	∈	∈	PROPN
ma-265	398	23	z≥0	z≥0	PROPN
ma-265	398	24	.	.	PUNCT
ma-265	399	1	s(z	s(z	PROPN
ma-265	399	2	,	,	PUNCT
ma-265	399	3	t	t	PROPN
ma-265	399	4	)	)	PUNCT
ma-265	399	5	=	=	SYM
ma-265	399	6	limn→∞	limn→∞	PROPN
ma-265	399	7	sn(z	sn(z	NOUN
ma-265	399	8	,	,	PUNCT
ma-265	399	9	t	t	PROPN
ma-265	399	10	)	)	PUNCT
ma-265	399	11	for	for	ADP
ma-265	399	12	z	z	PROPN
ma-265	399	13	∈	∈	PROPN
ma-265	399	14	u	u	NOUN
ma-265	399	15	(	(	PUNCT
ma-265	399	16	as	as	SCONJ
ma-265	399	17	was	be	AUX
ma-265	399	18	mentioned	mention	VERB
ma-265	399	19	above	above	ADP
ma-265	399	20	)	)	PUNCT
ma-265	399	21	,	,	PUNCT
ma-265	399	22	also	also	ADV
ma-265	399	23	s(z	s(z	PROPN
ma-265	399	24	,	,	PUNCT
ma-265	399	25	t	t	PROPN
ma-265	399	26	)	)	PUNCT
ma-265	399	27	=	=	NOUN
ma-265	399	28	exp	exp	NOUN
ma-265	399	29	(	(	PUNCT
ma-265	399	30	−g(z	−g(z	NOUN
ma-265	399	31	·	·	PUNCT
ma-265	399	32	s(z	s(z	PROPN
ma-265	399	33	,	,	PUNCT
ma-265	399	34	t	t	PROPN
ma-265	399	35	)	)	PUNCT
ma-265	399	36	)	)	PUNCT
ma-265	399	37	)	)	PUNCT
ma-265	399	38	for	for	ADP
ma-265	399	39	z	z	PROPN
ma-265	399	40	∈	∈	PROPN
ma-265	399	41	u	u	NOUN
ma-265	399	42	,	,	PUNCT
ma-265	399	43	and	and	CCONJ
ma-265	399	44	z	z	NOUN
ma-265	399	45	·	·	PUNCT
ma-265	400	1	s(z	s(z	PROPN
ma-265	400	2	,	,	PUNCT
ma-265	400	3	t	t	PROPN
ma-265	400	4	)	)	PUNCT
ma-265	400	5	∈	∈	PROPN
ma-265	400	6	conf	conf	NOUN
ma-265	400	7	for	for	ADP
ma-265	400	8	each	each	DET
ma-265	400	9	0	0	NUM
ma-265	400	10	≤	≤	NUM
ma-265	400	11	t	t	PROPN
ma-265	400	12	≤	≤	NUM
ma-265	400	13	t0	t0	PROPN
ma-265	400	14	.	.	PUNCT
ma-265	401	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	401	2	eur	eur	PROPN
ma-265	401	3	.	.	PUNCT
ma-265	402	1	j.	j.	PROPN
ma-265	402	2	math	math	PROPN
ma-265	402	3	.	.	PUNCT
ma-265	403	1	anal	anal	PROPN
ma-265	403	2	.	.	PUNCT
ma-265	404	1	10.28924	10.28924	NUM
ma-265	404	2	/	/	SYM
ma-265	404	3	ada	ada	PROPN
ma-265	404	4	/	/	SYM
ma-265	404	5	ma.5.4	ma.5.4	PROPN
ma-265	404	6	128	128	NUM
ma-265	404	7	.	.	PUNCT
ma-265	405	1	more	more	ADJ
ma-265	405	2	results	result	VERB
ma-265	405	3	those	those	DET
ma-265	405	4	results	result	NOUN
ma-265	405	5	will	will	AUX
ma-265	405	6	be	be	AUX
ma-265	405	7	summarized	summarize	VERB
ma-265	405	8	in	in	ADP
ma-265	405	9	three	three	NUM
ma-265	405	10	theorems	theorem	NOUN
ma-265	405	11	and	and	CCONJ
ma-265	405	12	one	one	NUM
ma-265	405	13	corollary	corollary	NOUN
ma-265	405	14	.	.	PUNCT
ma-265	406	1	we	we	PRON
ma-265	406	2	begin	begin	VERB
ma-265	406	3	with	with	ADP
ma-265	406	4	thecorresponding	thecorresponde	VERB
ma-265	406	5	computations	computation	NOUN
ma-265	406	6	.	.	PUNCT
ma-265	407	1	by	by	ADP
ma-265	407	2	the	the	DET
ma-265	407	3	differential	differential	ADJ
ma-265	407	4	equation	equation	NOUN
ma-265	407	5	for	for	ADP
ma-265	407	6	b	b	NOUN
ma-265	407	7	,	,	PUNCT
ma-265	407	8	in	in	ADP
ma-265	407	9	equation	equation	NOUN
ma-265	407	10	(	(	PUNCT
ma-265	407	11	7.3	7.3	NUM
ma-265	407	12	)	)	PUNCT
ma-265	407	13	and	and	CCONJ
ma-265	407	14	by	by	ADP
ma-265	407	15	therecursion	therecursion	NOUN
ma-265	407	16	,	,	PUNCT
ma-265	407	17	in	in	ADP
ma-265	407	18	equation	equation	NOUN
ma-265	407	19	(	(	PUNCT
ma-265	407	20	7.4	7.4	NUM
ma-265	407	21	)	)	PUNCT
ma-265	407	22	we	we	PRON
ma-265	407	23	have	have	VERB
ma-265	407	24	,	,	PUNCT
ma-265	407	25	∂s1(z	∂s1(z	PROPN
ma-265	407	26	,	,	PUNCT
ma-265	407	27	t	t	PROPN
ma-265	407	28	)	)	PUNCT
ma-265	408	1	∂t	∂t	PROPN
ma-265	408	2	=	=	SYM
ma-265	408	3	∂	∂	PROPN
ma-265	409	1	∂s0	∂s0	PRON
ma-265	409	2	{	{	PUNCT
ma-265	409	3	exp	exp	NOUN
ma-265	409	4	(	(	PUNCT
ma-265	409	5	−g(z	−g(z	NOUN
ma-265	409	6	·	·	SYM
ma-265	409	7	s0	s0	NOUN
ma-265	409	8	)	)	PUNCT
ma-265	409	9	)	)	PUNCT
ma-265	409	10	}	}	PUNCT
ma-265	409	11	·	·	PUNCT
ma-265	410	1	∂s0(z	∂s0(z	ADJ
ma-265	410	2	,	,	PUNCT
ma-265	410	3	t	t	PROPN
ma-265	410	4	)	)	PUNCT
ma-265	410	5	∂t	∂t	PROPN
ma-265	410	6	=	=	PUNCT
ma-265	410	7	=	=	SYM
ma-265	410	8	s1(z	s1(z	PROPN
ma-265	410	9	,	,	PUNCT
ma-265	410	10	t	t	PROPN
ma-265	410	11	)	)	PUNCT
ma-265	410	12	·	·	PUNCT
ma-265	410	13	{	{	PUNCT
ma-265	410	14	−z	−z	NOUN
ma-265	410	15	·	·	PUNCT
ma-265	410	16	∂g(w	∂g(w	X
ma-265	410	17	)	)	PUNCT
ma-265	410	18	∂w	∂w	PROPN
ma-265	410	19	|w	|w	NOUN
ma-265	410	20	=	=	PROPN
ma-265	410	21	z	z	NOUN
ma-265	410	22	·	·	SYM
ma-265	410	23	s0(z	s0(z	PROPN
ma-265	410	24	,	,	PUNCT
ma-265	410	25	t	t	PROPN
ma-265	410	26	)	)	PUNCT
ma-265	410	27	}	}	PUNCT
ma-265	410	28	·	·	PUNCT
ma-265	411	1	∂s0(z	∂s0(z	ADJ
ma-265	411	2	,	,	PUNCT
ma-265	411	3	t	t	PROPN
ma-265	411	4	)	)	PUNCT
ma-265	411	5	∂t	∂t	PROPN
ma-265	411	6	=	=	PUNCT
ma-265	411	7	=	=	SYM
ma-265	411	8	s1(z	s1(z	PROPN
ma-265	411	9	,	,	PUNCT
ma-265	411	10	t	t	PROPN
ma-265	411	11	)	)	PUNCT
ma-265	411	12	·	·	PUNCT
ma-265	411	13	{	{	PUNCT
ma-265	411	14	−z	−z	NOUN
ma-265	411	15	·	·	PUNCT
ma-265	411	16	∂g(w	∂g(w	X
ma-265	411	17	)	)	PUNCT
ma-265	411	18	∂w	∂w	PROPN
ma-265	411	19	|w	|w	NOUN
ma-265	411	20	=	=	PROPN
ma-265	411	21	z	z	NOUN
ma-265	411	22	·	·	SYM
ma-265	411	23	s0(z	s0(z	PROPN
ma-265	411	24	,	,	PUNCT
ma-265	411	25	t	t	PROPN
ma-265	411	26	)	)	PUNCT
ma-265	411	27	}	}	PUNCT
ma-265	411	28	·	·	PUNCT
ma-265	411	29	{	{	PUNCT
ma-265	411	30	−s0(z	−s0(z	PROPN
ma-265	411	31	,	,	PUNCT
ma-265	411	32	t	t	PROPN
ma-265	411	33	)	)	PUNCT
ma-265	411	34	·	·	PUNCT
ma-265	411	35	1	1	NUM
ma-265	412	1	+	+	CCONJ
ma-265	412	2	k(t)z	k(t)z	PROPN
ma-265	412	3	1−	1−	NUM
ma-265	412	4	k(t)z	k(t)z	NOUN
ma-265	412	5	}	}	PUNCT
ma-265	412	6	=	=	PUNCT
ma-265	413	1	=	=	SYM
ma-265	413	2	s0(z	s0(z	PROPN
ma-265	413	3	,	,	PUNCT
ma-265	413	4	t	t	PROPN
ma-265	413	5	)	)	PUNCT
ma-265	413	6	·	·	PUNCT
ma-265	413	7	s1(z	s1(z	PROPN
ma-265	413	8	,	,	PUNCT
ma-265	413	9	t	t	PROPN
ma-265	413	10	)	)	PUNCT
ma-265	413	11	·	·	PUNCT
ma-265	414	1	z	z	X
ma-265	414	2	·	·	PUNCT
ma-265	414	3	∂g(w	∂g(w	X
ma-265	414	4	)	)	PUNCT
ma-265	414	5	∂w	∂w	PROPN
ma-265	414	6	|w	|w	NOUN
ma-265	414	7	=	=	PROPN
ma-265	414	8	z	z	NOUN
ma-265	414	9	·	·	SYM
ma-265	414	10	s0(z	s0(z	PROPN
ma-265	414	11	,	,	PUNCT
ma-265	414	12	t	t	PROPN
ma-265	414	13	)	)	PUNCT
ma-265	414	14	·	·	PUNCT
ma-265	414	15	{	{	PUNCT
ma-265	415	1	1	1	NUM
ma-265	415	2	+	+	NUM
ma-265	415	3	k(t)z	k(t)z	PROPN
ma-265	415	4	1−	1−	NUM
ma-265	415	5	k(t)z	k(t)z	PROPN
ma-265	415	6	}	}	PUNCT
ma-265	415	7	.	.	PUNCT
ma-265	416	1	next	next	ADV
ma-265	416	2	,	,	PUNCT
ma-265	416	3	∂s2(z	∂s2(z	PROPN
ma-265	416	4	,	,	PUNCT
ma-265	416	5	t	t	PROPN
ma-265	416	6	)	)	PUNCT
ma-265	416	7	∂t	∂t	PROPN
ma-265	416	8	=	=	SYM
ma-265	416	9	∂	∂	PROPN
ma-265	416	10	∂s1	∂s1	NOUN
ma-265	416	11	{	{	PUNCT
ma-265	416	12	exp	exp	NOUN
ma-265	416	13	(	(	PUNCT
ma-265	416	14	−g(z	−g(z	NOUN
ma-265	416	15	·	·	SYM
ma-265	416	16	s1	s1	NOUN
ma-265	416	17	)	)	PUNCT
ma-265	416	18	)	)	PUNCT
ma-265	416	19	}	}	PUNCT
ma-265	416	20	·	·	PUNCT
ma-265	417	1	∂s1(z	∂s1(z	VERB
ma-265	417	2	,	,	PUNCT
ma-265	417	3	t	t	PROPN
ma-265	417	4	)	)	PUNCT
ma-265	417	5	∂t	∂t	PROPN
ma-265	417	6	=	=	PUNCT
ma-265	417	7	=	=	SYM
ma-265	417	8	s2(z	s2(z	NUM
ma-265	417	9	,	,	PUNCT
ma-265	417	10	t	t	PROPN
ma-265	417	11	)	)	PUNCT
ma-265	417	12	·	·	PUNCT
ma-265	417	13	{	{	PUNCT
ma-265	417	14	−z	−z	NOUN
ma-265	417	15	·	·	PUNCT
ma-265	417	16	∂g(w	∂g(w	X
ma-265	417	17	)	)	PUNCT
ma-265	417	18	∂w	∂w	PROPN
ma-265	417	19	|w	|w	NOUN
ma-265	417	20	=	=	PROPN
ma-265	417	21	z	z	PROPN
ma-265	417	22	·	·	PUNCT
ma-265	417	23	s1(z	s1(z	PROPN
ma-265	417	24	,	,	PUNCT
ma-265	417	25	t	t	PROPN
ma-265	417	26	)	)	PUNCT
ma-265	417	27	}	}	PUNCT
ma-265	417	28	·	·	PUNCT
ma-265	418	1	∂s1(z	∂s1(z	VERB
ma-265	418	2	,	,	PUNCT
ma-265	418	3	t	t	PROPN
ma-265	418	4	)	)	PUNCT
ma-265	418	5	∂t	∂t	PROPN
ma-265	418	6	=	=	PUNCT
ma-265	418	7	=	=	SYM
ma-265	418	8	s2(z	s2(z	NUM
ma-265	418	9	,	,	PUNCT
ma-265	418	10	t	t	PROPN
ma-265	418	11	)	)	PUNCT
ma-265	418	12	·	·	PUNCT
ma-265	418	13	{	{	PUNCT
ma-265	418	14	−z	−z	NOUN
ma-265	418	15	·	·	PUNCT
ma-265	418	16	∂g(w	∂g(w	X
ma-265	418	17	)	)	PUNCT
ma-265	418	18	∂w	∂w	PROPN
ma-265	418	19	|w	|w	NOUN
ma-265	418	20	=	=	PROPN
ma-265	418	21	z	z	PROPN
ma-265	418	22	·	·	PUNCT
ma-265	418	23	s1(z	s1(z	PROPN
ma-265	418	24	,	,	PUNCT
ma-265	418	25	t	t	PROPN
ma-265	418	26	)	)	PUNCT
ma-265	418	27	}	}	PUNCT
ma-265	418	28	·	·	PUNCT
ma-265	418	29	s0(z	s0(z	PROPN
ma-265	418	30	,	,	PUNCT
ma-265	418	31	t	t	PROPN
ma-265	418	32	)	)	PUNCT
ma-265	418	33	·	·	PUNCT
ma-265	418	34	s1(z	s1(z	PROPN
ma-265	418	35	,	,	PUNCT
ma-265	418	36	t	t	PROPN
ma-265	418	37	)	)	PUNCT
ma-265	418	38	·	·	PUNCT
ma-265	419	1	z	z	X
ma-265	419	2	·	·	PUNCT
ma-265	419	3	∂g(w	∂g(w	X
ma-265	419	4	)	)	PUNCT
ma-265	419	5	∂w	∂w	PROPN
ma-265	419	6	|w	|w	NOUN
ma-265	419	7	=	=	PROPN
ma-265	419	8	z	z	NOUN
ma-265	419	9	·	·	SYM
ma-265	419	10	s0(z	s0(z	PROPN
ma-265	419	11	,	,	PUNCT
ma-265	419	12	t	t	PROPN
ma-265	419	13	)	)	PUNCT
ma-265	419	14	·	·	PUNCT
ma-265	419	15	{	{	PUNCT
ma-265	420	1	1	1	NUM
ma-265	420	2	+	+	NUM
ma-265	420	3	k(t)z	k(t)z	PROPN
ma-265	420	4	1−	1−	NUM
ma-265	420	5	k(t)z	k(t)z	NOUN
ma-265	420	6	}	}	PUNCT
ma-265	420	7	=	=	PUNCT
ma-265	421	1	=	=	PUNCT
ma-265	421	2	−s0(z	−s0(z	PROPN
ma-265	421	3	,	,	PUNCT
ma-265	421	4	t	t	PROPN
ma-265	421	5	)	)	PUNCT
ma-265	421	6	·	·	PUNCT
ma-265	422	1	s1(z	s1(z	PROPN
ma-265	422	2	,	,	PUNCT
ma-265	422	3	t	t	PROPN
ma-265	422	4	)	)	PUNCT
ma-265	422	5	·	·	PUNCT
ma-265	423	1	s2(z	s2(z	NUM
ma-265	423	2	,	,	PUNCT
ma-265	423	3	t	t	PROPN
ma-265	423	4	)	)	PUNCT
ma-265	423	5	·	·	PUNCT
ma-265	424	1	z2	z2	NUM
ma-265	424	2	·	·	PUNCT
ma-265	424	3	∂g(w	∂g(w	X
ma-265	424	4	)	)	PUNCT
ma-265	424	5	∂w	∂w	PROPN
ma-265	424	6	|w	|w	NOUN
ma-265	424	7	=	=	PROPN
ma-265	424	8	z	z	NOUN
ma-265	424	9	·	·	SYM
ma-265	424	10	s0(z	s0(z	PROPN
ma-265	424	11	,	,	PUNCT
ma-265	424	12	t	t	PROPN
ma-265	424	13	)	)	PUNCT
ma-265	424	14	·	·	PUNCT
ma-265	425	1	∂g(w	∂g(w	X
ma-265	425	2	)	)	PUNCT
ma-265	425	3	∂w	∂w	PROPN
ma-265	425	4	|w	|w	NOUN
ma-265	425	5	=	=	PROPN
ma-265	425	6	z	z	PROPN
ma-265	425	7	·	·	PUNCT
ma-265	425	8	s1(z	s1(z	PROPN
ma-265	425	9	,	,	PUNCT
ma-265	425	10	t	t	PROPN
ma-265	425	11	)	)	PUNCT
ma-265	425	12	·	·	PUNCT
ma-265	425	13	1	1	NUM
ma-265	426	1	+	+	CCONJ
ma-265	426	2	k(t)z	k(t)z	PROPN
ma-265	426	3	1−	1−	NUM
ma-265	426	4	k(t)z	k(t)z	PROPN
ma-265	426	5	.inductive	.inductive	VERB
ma-265	426	6	arguments	argument	NOUN
ma-265	426	7	prove	prove	VERB
ma-265	426	8	:	:	PUNCT
ma-265	426	9	theorem	theorem	VERB
ma-265	426	10	8.1	8.1	NUM
ma-265	426	11	.	.	PUNCT
ma-265	427	1	∂sn(z	∂sn(z	PROPN
ma-265	427	2	,	,	PUNCT
ma-265	427	3	t	t	NOUN
ma-265	427	4	)	)	PUNCT
ma-265	427	5	∂t	∂t	PROPN
ma-265	427	6	=	=	PUNCT
ma-265	427	7	(	(	PUNCT
ma-265	427	8	−1)n+1	−1)n+1	PROPN
ma-265	427	9	·	·	PUNCT
ma-265	427	10			PUNCT
ma-265	427	11	n∏	n∏	NOUN
ma-265	427	12	j=0	j=0	PROPN
ma-265	427	13	sj(z	sj(z	NOUN
ma-265	427	14	,	,	PUNCT
ma-265	427	15	t	t	NOUN
ma-265	427	16	)	)	PUNCT
ma-265	428	1			NOUN
ma-265	428	2	·	·	PUNCT
ma-265	428	3	zn	zn	X
ma-265	428	4	·	·	PUNCT
ma-265	428	5	n−1∏	n−1∏	NUM
ma-265	428	6	j=0	j=0	PROPN
ma-265	428	7	(	(	PUNCT
ma-265	428	8	∂g(w	∂g(w	PROPN
ma-265	428	9	)	)	PUNCT
ma-265	428	10	∂w	∂w	PROPN
ma-265	428	11	|w	|w	NOUN
ma-265	428	12	=	=	ADJ
ma-265	428	13	z	z	X
ma-265	428	14	·	·	PUNCT
ma-265	428	15	sj	sj	INTJ
ma-265	428	16	(	(	PUNCT
ma-265	428	17	z	z	PROPN
ma-265	428	18	,	,	PUNCT
ma-265	428	19	t	t	PROPN
ma-265	428	20	)	)	PUNCT
ma-265	428	21	)	)	PUNCT
ma-265	429	1			NOUN
ma-265	429	2	·	·	PUNCT
ma-265	429	3	{	{	PUNCT
ma-265	429	4	1	1	NUM
ma-265	429	5	+	+	NUM
ma-265	429	6	k(t)z	k(t)z	PROPN
ma-265	429	7	1−	1−	NUM
ma-265	429	8	k(t)z	k(t)z	PROPN
ma-265	429	9	}	}	PUNCT
ma-265	429	10	.	.	PUNCT
ma-265	430	1	theorem	theorem	VERB
ma-265	430	2	8.2	8.2	NUM
ma-265	430	3	.	.	PUNCT
ma-265	431	1	there	there	PRON
ma-265	431	2	exists	exist	VERB
ma-265	431	3	a	a	DET
ma-265	431	4	unique	unique	ADJ
ma-265	431	5	s(z	s(z	PROPN
ma-265	431	6	)	)	PUNCT
ma-265	431	7	∈	∈	PROPN
ma-265	431	8	h(u	h(u	PROPN
ma-265	431	9	)	)	PUNCT
ma-265	431	10	such	such	ADJ
ma-265	431	11	that	that	SCONJ
ma-265	431	12	it	it	PRON
ma-265	431	13	is	be	AUX
ma-265	431	14	the	the	DET
ma-265	431	15	only	only	ADJ
ma-265	431	16	fixed	fix	VERB
ma-265	431	17	-	-	PUNCT
ma-265	431	18	point	point	NOUN
ma-265	431	19	of	of	ADP
ma-265	431	20	the	the	DET
ma-265	431	21	function	function	NOUN
ma-265	431	22	exp	exp	NOUN
ma-265	431	23	(	(	PUNCT
ma-265	431	24	−g(z	−g(z	NOUN
ma-265	431	25	·	·	PUNCT
ma-265	431	26	w	w	NOUN
ma-265	431	27	)	)	PUNCT
ma-265	431	28	)	)	PUNCT
ma-265	431	29	,	,	PUNCT
ma-265	431	30	i.e.	i.e.	X
ma-265	431	31	s(z	s(z	PROPN
ma-265	431	32	)	)	PUNCT
ma-265	431	33	=	=	SYM
ma-265	431	34	exp	exp	NOUN
ma-265	431	35	(	(	PUNCT
ma-265	431	36	−g(z	−g(z	NOUN
ma-265	431	37	·	·	PUNCT
ma-265	431	38	s(z	s(z	NOUN
ma-265	431	39	)	)	PUNCT
ma-265	431	40	)	)	PUNCT
ma-265	431	41	)	)	PUNCT
ma-265	431	42	.	.	PUNCT
ma-265	432	1	moreover	moreover	ADV
ma-265	432	2	,	,	PUNCT
ma-265	432	3	∀s0(z	∀s0(z	ADJ
ma-265	432	4	)	)	PUNCT
ma-265	432	5	∈	∈	PROPN
ma-265	432	6	sinn	sinn	PROPN
ma-265	432	7	,	,	PUNCT
ma-265	432	8	the	the	DET
ma-265	432	9	recursion	recursion	NOUN
ma-265	432	10	sn+1(z	sn+1(z	VERB
ma-265	432	11	)	)	PUNCT
ma-265	432	12	=	=	NOUN
ma-265	432	13	exp	exp	NOUN
ma-265	432	14	(	(	PUNCT
ma-265	432	15	−g(z	−g(z	NOUN
ma-265	432	16	·	·	PUNCT
ma-265	432	17	sn(z	sn(z	NOUN
ma-265	432	18	)	)	PUNCT
ma-265	432	19	)	)	PUNCT
ma-265	432	20	)	)	PUNCT
ma-265	432	21	,	,	PUNCT
ma-265	432	22	n	n	PROPN
ma-265	432	23	∈	∈	PROPN
ma-265	432	24	z≥0	z≥0	NOUN
ma-265	432	25	,	,	PUNCT
ma-265	432	26	defines	define	VERB
ma-265	432	27	a	a	DET
ma-265	432	28	sequence	sequence	NOUN
ma-265	432	29	of	of	ADP
ma-265	432	30	singular	singular	ADJ
ma-265	432	31	inner	inner	ADJ
ma-265	432	32	functions	function	NOUN
ma-265	432	33	{	{	PUNCT
ma-265	432	34	sn(z)}∞n=0	sn(z)}∞n=0	NUM
ma-265	432	35	.	.	PUNCT
ma-265	433	1	this	this	DET
ma-265	433	2	sequence	sequence	NOUN
ma-265	433	3	converges	converge	VERB
ma-265	433	4	uniformly	uniformly	ADV
ma-265	433	5	on	on	ADP
ma-265	433	6	compact	compact	ADJ
ma-265	433	7	subsets	subset	NOUN
ma-265	433	8	of	of	ADP
ma-265	433	9	u	u	NOUN
ma-265	433	10	to	to	ADP
ma-265	433	11	the	the	DET
ma-265	433	12	fixed	fix	VERB
ma-265	433	13	-	-	PUNCT
ma-265	433	14	point	point	NOUN
ma-265	433	15	s(z	s(z	PROPN
ma-265	433	16	)	)	PUNCT
ma-265	433	17	,	,	PUNCT
ma-265	433	18	i.e.	i.e.	X
ma-265	433	19	s(z	s(z	PROPN
ma-265	433	20	)	)	PUNCT
ma-265	433	21	=	=	SYM
ma-265	433	22	limn→∞	limn→∞	PROPN
ma-265	433	23	sn(z	sn(z	NOUN
ma-265	433	24	)	)	PUNCT
ma-265	433	25	uniformly	uniformly	ADV
ma-265	433	26	on	on	ADP
ma-265	433	27	compact	compact	ADJ
ma-265	433	28	subsets	subset	NOUN
ma-265	433	29	of	of	ADP
ma-265	433	30	u	u	PROPN
ma-265	433	31	.	.	PUNCT
ma-265	434	1	so	so	ADV
ma-265	434	2	s(z	s(z	PROPN
ma-265	434	3	)	)	PUNCT
ma-265	434	4	is	be	AUX
ma-265	434	5	determined	determine	VERB
ma-265	434	6	by	by	ADP
ma-265	434	7	the	the	DET
ma-265	434	8	recursion	recursion	NOUN
ma-265	434	9	but	but	CCONJ
ma-265	434	10	independently	independently	ADV
ma-265	434	11	of	of	ADP
ma-265	434	12	the	the	DET
ma-265	434	13	initial	initial	ADJ
ma-265	434	14	singular	singular	ADJ
ma-265	434	15	inner	inner	ADJ
ma-265	434	16	function	function	NOUN
ma-265	434	17	s0(z	s0(z	NOUN
ma-265	434	18	)	)	PUNCT
ma-265	434	19	.	.	PUNCT
ma-265	435	1	thus	thus	ADV
ma-265	435	2	∀s0(z	∀s0(z	NUM
ma-265	435	3	)	)	PUNCT
ma-265	435	4	,	,	PUNCT
ma-265	435	5	t0(z	t0(z	X
ma-265	435	6	)	)	PUNCT
ma-265	435	7	∈	∈	PROPN
ma-265	435	8	sinn	sinn	PROPN
ma-265	435	9	,	,	PUNCT
ma-265	435	10	sn+1(z	sn+1(z	X
ma-265	435	11	)	)	PUNCT
ma-265	435	12	=	=	NOUN
ma-265	435	13	exp	exp	NOUN
ma-265	435	14	(	(	PUNCT
ma-265	435	15	−g(z	−g(z	NOUN
ma-265	435	16	·	·	PUNCT
ma-265	435	17	sn(z	sn(z	NOUN
ma-265	435	18	)	)	PUNCT
ma-265	435	19	)	)	PUNCT
ma-265	435	20	)	)	PUNCT
ma-265	435	21	,	,	PUNCT
ma-265	435	22	tn+1(z	tn+1(z	PROPN
ma-265	435	23	)	)	PUNCT
ma-265	436	1	=	=	SYM
ma-265	436	2	exp	exp	NOUN
ma-265	436	3	(	(	PUNCT
ma-265	436	4	−g(z	−g(z	NOUN
ma-265	436	5	·	·	PUNCT
ma-265	436	6	tn(z	tn(z	NUM
ma-265	436	7	)	)	PUNCT
ma-265	436	8	)	)	PUNCT
ma-265	436	9	)	)	PUNCT
ma-265	437	1	and	and	CCONJ
ma-265	437	2	we	we	PRON
ma-265	437	3	have	have	VERB
ma-265	437	4	:	:	PUNCT
ma-265	437	5	limn→∞	limn→∞	PROPN
ma-265	437	6	sn(z	sn(z	NOUN
ma-265	437	7	)	)	PUNCT
ma-265	437	8	=	=	SYM
ma-265	437	9	limn→∞	limn→∞	NOUN
ma-265	437	10	tn(z	tn(z	PUNCT
ma-265	437	11	)	)	PUNCT
ma-265	437	12	=	=	SYM
ma-265	437	13	s(z	s(z	PROPN
ma-265	437	14	)	)	PUNCT
ma-265	437	15	,	,	PUNCT
ma-265	437	16	uniformly	uniformly	ADV
ma-265	437	17	on	on	ADP
ma-265	437	18	compact	compact	ADJ
ma-265	437	19	subsets	subset	NOUN
ma-265	437	20	of	of	ADP
ma-265	437	21	u	u	PROPN
ma-265	437	22	.	.	PUNCT
ma-265	438	1	proof.we	proof.we	NOUN
ma-265	438	2	will	will	AUX
ma-265	438	3	outline	outline	VERB
ma-265	438	4	two	two	NUM
ma-265	438	5	proofs	proof	NOUN
ma-265	438	6	.	.	PUNCT
ma-265	439	1	the	the	DET
ma-265	439	2	first	first	ADJ
ma-265	439	3	proof	proof	NOUN
ma-265	439	4	is	be	AUX
ma-265	439	5	using	use	VERB
ma-265	439	6	the	the	DET
ma-265	439	7	banach	banach	ADV
ma-265	439	8	fixed	fix	VERB
ma-265	439	9	-	-	PUNCT
ma-265	439	10	point	point	NOUN
ma-265	439	11	theorem	theorem	VERB
ma-265	439	12	.	.	PUNCT
ma-265	440	1	namely	namely	ADV
ma-265	440	2	,	,	PUNCT
ma-265	440	3	∀	∀	X
ma-265	440	4	z	z	NOUN
ma-265	440	5	∈	∈	PROPN
ma-265	440	6	u	u	NOUN
ma-265	440	7	,	,	PUNCT
ma-265	440	8	the	the	DET
ma-265	440	9	function	function	NOUN
ma-265	440	10	of	of	ADP
ma-265	440	11	w	w	PROPN
ma-265	440	12	∈	∈	PROPN
ma-265	440	13	u	u	NOUN
ma-265	440	14	given	give	VERB
ma-265	440	15	by	by	ADP
ma-265	440	16	:	:	PUNCT
ma-265	440	17	exp	exp	NOUN
ma-265	440	18	(	(	PUNCT
ma-265	440	19	−g(z	−g(z	NOUN
ma-265	440	20	·	·	SYM
ma-265	440	21	w	w	NOUN
ma-265	440	22	)	)	PUNCT
ma-265	440	23	)	)	PUNCT
ma-265	440	24	is	be	AUX
ma-265	440	25	a	a	DET
ma-265	440	26	contraction	contraction	NOUN
ma-265	440	27	and	and	CCONJ
ma-265	440	28	so	so	ADV
ma-265	440	29	by	by	ADP
ma-265	440	30	the	the	DET
ma-265	440	31	theoremof	theoremof	NOUN
ma-265	440	32	banach	banach	NOUN
ma-265	440	33	it	it	PRON
ma-265	440	34	has	have	VERB
ma-265	440	35	a	a	DET
ma-265	440	36	unique	unique	ADJ
ma-265	440	37	fixed	fix	VERB
ma-265	440	38	-	-	PUNCT
ma-265	440	39	point	point	NOUN
ma-265	440	40	w	w	NOUN
ma-265	440	41	=	=	SYM
ma-265	440	42	s(z	s(z	PROPN
ma-265	440	43	)	)	PUNCT
ma-265	440	44	.	.	PUNCT
ma-265	441	1	moreover	moreover	ADV
ma-265	441	2	,	,	PUNCT
ma-265	441	3	this	this	DET
ma-265	441	4	fixed	fix	VERB
ma-265	441	5	-	-	PUNCT
ma-265	441	6	point	point	NOUN
ma-265	441	7	is	be	AUX
ma-265	441	8	the	the	DET
ma-265	441	9	limit	limit	NOUN
ma-265	441	10	of	of	ADP
ma-265	441	11	the	the	DET
ma-265	441	12	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	441	13	eur	eur	PROPN
ma-265	441	14	.	.	PUNCT
ma-265	442	1	j.	j.	PROPN
ma-265	442	2	math	math	PROPN
ma-265	442	3	.	.	PUNCT
ma-265	443	1	anal	anal	PROPN
ma-265	443	2	.	.	PUNCT
ma-265	444	1	10.28924	10.28924	NUM
ma-265	444	2	/	/	SYM
ma-265	444	3	ada	ada	PROPN
ma-265	444	4	/	/	SYM
ma-265	444	5	ma.5.4	ma.5.4	PROPN
ma-265	444	6	13sequence	13sequence	NOUN
ma-265	444	7	,	,	PUNCT
ma-265	444	8	defined	define	VERB
ma-265	444	9	by	by	ADP
ma-265	444	10	the	the	DET
ma-265	444	11	recursion	recursion	NOUN
ma-265	444	12	wn+1	wn+1	NOUN
ma-265	444	13	=	=	SYM
ma-265	444	14	exp	exp	NOUN
ma-265	444	15	(	(	PUNCT
ma-265	444	16	−g(z	−g(z	NOUN
ma-265	444	17	·	·	PUNCT
ma-265	444	18	wn	wn	NOUN
ma-265	444	19	)	)	PUNCT
ma-265	444	20	)	)	PUNCT
ma-265	444	21	,	,	PUNCT
ma-265	444	22	independently	independently	ADV
ma-265	444	23	of	of	ADP
ma-265	444	24	the	the	DET
ma-265	444	25	initial	initial	ADJ
ma-265	444	26	point	point	NOUN
ma-265	444	27	w0.from	w0.from	ADP
ma-265	444	28	this	this	PRON
ma-265	444	29	we	we	PRON
ma-265	444	30	get	get	VERB
ma-265	444	31	our	our	PRON
ma-265	444	32	conclusions	conclusion	NOUN
ma-265	444	33	.	.	PUNCT
ma-265	445	1	a	a	DET
ma-265	445	2	second	second	ADJ
ma-265	445	3	proof	proof	NOUN
ma-265	445	4	uses	use	VERB
ma-265	445	5	the	the	DET
ma-265	445	6	differential	differential	ADJ
ma-265	445	7	equation	equation	NOUN
ma-265	445	8	of	of	ADP
ma-265	445	9	b	b	NOUN
ma-265	445	10	,	,	PUNCT
ma-265	445	11	namely	namely	ADV
ma-265	445	12	we	we	PRON
ma-265	445	13	start	start	VERB
ma-265	445	14	at	at	ADP
ma-265	445	15	the	the	DET
ma-265	445	16	beginning	beginning	NOUN
ma-265	445	17	of	of	ADP
ma-265	445	18	chain	chain	NOUN
ma-265	445	19	s0(z	s0(z	PROPN
ma-265	445	20	,	,	PUNCT
ma-265	445	21	t	t	PROPN
ma-265	445	22	)	)	PUNCT
ma-265	446	1	=	=	SYM
ma-265	446	2	f	f	X
ma-265	446	3	(	(	PUNCT
ma-265	446	4	z	z	PROPN
ma-265	446	5	,	,	PUNCT
ma-265	446	6	t	t	PROPN
ma-265	446	7	)	)	PUNCT
ma-265	446	8	and	and	CCONJ
ma-265	446	9	generate	generate	VERB
ma-265	446	10	the	the	DET
ma-265	446	11	sequence	sequence	NOUN
ma-265	446	12	of	of	ADP
ma-265	446	13	singular	singular	ADJ
ma-265	446	14	inner	inner	ADJ
ma-265	446	15	functions	function	NOUN
ma-265	446	16	by	by	ADP
ma-265	446	17	our	our	PRON
ma-265	446	18	recursion	recursion	NOUN
ma-265	446	19	:	:	PUNCT
ma-265	446	20	sn+1(z	sn+1(z	VERB
ma-265	446	21	)	)	PUNCT
ma-265	446	22	=	=	NOUN
ma-265	446	23	exp	exp	NOUN
ma-265	446	24	(	(	PUNCT
ma-265	446	25	−g(z	−g(z	NOUN
ma-265	446	26	·	·	PUNCT
ma-265	446	27	sn(z	sn(z	NOUN
ma-265	446	28	)	)	PUNCT
ma-265	446	29	)	)	PUNCT
ma-265	446	30	)	)	PUNCT
ma-265	446	31	.	.	PUNCT
ma-265	447	1	we	we	PRON
ma-265	447	2	obtain	obtain	VERB
ma-265	447	3	the	the	DET
ma-265	447	4	limit	limit	NOUN
ma-265	447	5	uniformly	uniformly	ADV
ma-265	447	6	on	on	ADP
ma-265	447	7	compact	compact	ADJ
ma-265	447	8	subsets	subset	NOUN
ma-265	447	9	of	of	ADP
ma-265	447	10	u	u	PROPN
ma-265	447	11	,	,	PUNCT
ma-265	447	12	s(z	s(z	PROPN
ma-265	447	13	,	,	PUNCT
ma-265	447	14	t	t	PROPN
ma-265	447	15	)	)	PUNCT
ma-265	447	16	=	=	SYM
ma-265	448	1	limn→∞	limn→∞	PROPN
ma-265	448	2	sn(z	sn(z	NOUN
ma-265	448	3	,	,	PUNCT
ma-265	448	4	t	t	PROPN
ma-265	448	5	)	)	PUNCT
ma-265	448	6	.	.	PUNCT
ma-265	449	1	s(z	s(z	PROPN
ma-265	449	2	,	,	PUNCT
ma-265	449	3	t	t	PROPN
ma-265	449	4	)	)	PUNCT
ma-265	449	5	is	be	AUX
ma-265	449	6	a	a	DET
ma-265	449	7	fixed	fix	VERB
ma-265	449	8	-	-	PUNCT
ma-265	449	9	point	point	NOUN
ma-265	449	10	s(z	s(z	PROPN
ma-265	449	11	,	,	PUNCT
ma-265	449	12	t	t	PROPN
ma-265	449	13	)	)	PUNCT
ma-265	450	1	=	=	NOUN
ma-265	450	2	exp	exp	NOUN
ma-265	450	3	(	(	PUNCT
ma-265	450	4	−g(z	−g(z	NOUN
ma-265	450	5	·	·	PUNCT
ma-265	450	6	s(z	s(z	PROPN
ma-265	450	7	,	,	PUNCT
ma-265	450	8	t	t	PROPN
ma-265	450	9	)	)	PUNCT
ma-265	450	10	)	)	PUNCT
ma-265	450	11	)	)	PUNCT
ma-265	451	1	.we	.we	PUNCT
ma-265	451	2	apply	apply	VERB
ma-265	451	3	the	the	DET
ma-265	451	4	operator	operator	NOUN
ma-265	451	5	∂	∂	NOUN
ma-265	451	6	∂t	∂t	PROPN
ma-265	451	7	to	to	ADP
ma-265	451	8	both	both	DET
ma-265	451	9	sides	side	NOUN
ma-265	451	10	of	of	ADP
ma-265	451	11	the	the	DET
ma-265	451	12	fixed	fix	VERB
ma-265	451	13	-	-	PUNCT
ma-265	451	14	point	point	NOUN
ma-265	451	15	equation	equation	NOUN
ma-265	451	16	(	(	PUNCT
ma-265	451	17	justified	justify	VERB
ma-265	451	18	by	by	ADP
ma-265	451	19	our	our	PRON
ma-265	451	20	assumptionson	assumptionson	PROPN
ma-265	451	21	s0(z	s0(z	PROPN
ma-265	451	22	,	,	PUNCT
ma-265	451	23	t	t	PROPN
ma-265	451	24	)	)	PUNCT
ma-265	451	25	)	)	PUNCT
ma-265	451	26	.	.	PUNCT
ma-265	452	1	we	we	PRON
ma-265	452	2	obtain	obtain	VERB
ma-265	452	3	:	:	PUNCT
ma-265	452	4	∂s(z	∂s(z	PROPN
ma-265	452	5	,	,	PUNCT
ma-265	452	6	t	t	PROPN
ma-265	452	7	)	)	PUNCT
ma-265	452	8	∂t	∂t	PROPN
ma-265	452	9	=	=	PUNCT
ma-265	452	10	−z	−z	PROPN
ma-265	452	11	·	·	PUNCT
ma-265	453	1	s(z	s(z	PROPN
ma-265	453	2	,	,	PUNCT
ma-265	453	3	t	t	PROPN
ma-265	453	4	)	)	PUNCT
ma-265	453	5	·	·	PUNCT
ma-265	453	6	{	{	PUNCT
ma-265	453	7	∂g(w	∂g(w	X
ma-265	453	8	)	)	PUNCT
ma-265	453	9	∂w	∂w	PROPN
ma-265	453	10	|w	|w	NOUN
ma-265	453	11	=	=	PROPN
ma-265	453	12	z	z	NOUN
ma-265	453	13	·	·	PUNCT
ma-265	453	14	s(z	s(z	PROPN
ma-265	453	15	,	,	PUNCT
ma-265	453	16	t	t	PROPN
ma-265	453	17	)	)	PUNCT
ma-265	453	18	}	}	PUNCT
ma-265	453	19	·	·	PUNCT
ma-265	454	1	∂s(z	∂s(z	NUM
ma-265	454	2	,	,	PUNCT
ma-265	454	3	t	t	PROPN
ma-265	454	4	)	)	PUNCT
ma-265	454	5	∂t	∂t	PROPN
ma-265	454	6	.	.	PUNCT
ma-265	455	1	we	we	PRON
ma-265	455	2	claim	claim	VERB
ma-265	455	3	that	that	SCONJ
ma-265	455	4	∂s(z	∂s(z	PROPN
ma-265	455	5	,	,	PUNCT
ma-265	455	6	t	t	PROPN
ma-265	455	7	)	)	PUNCT
ma-265	455	8	∂t	∂t	PROPN
ma-265	456	1	=	=	NOUN
ma-265	456	2	0	0	PROPN
ma-265	456	3	for	for	ADP
ma-265	456	4	all	all	DET
ma-265	456	5	t	t	PROPN
ma-265	456	6	.	.	PUNCT
ma-265	457	1	for	for	ADP
ma-265	457	2	if	if	SCONJ
ma-265	457	3	there	there	PRON
ma-265	457	4	were	be	VERB
ma-265	457	5	an	an	DET
ma-265	457	6	open	open	ADJ
ma-265	457	7	non	non	ADJ
ma-265	457	8	-	-	ADJ
ma-265	457	9	empty	empty	ADJ
ma-265	457	10	interval	interval	NOUN
ma-265	457	11	of	of	ADP
ma-265	457	12	t	t	PROPN
ma-265	457	13	,	,	PUNCT
ma-265	457	14	over	over	ADP
ma-265	457	15	which	which	PRON
ma-265	457	16	∂s(z	∂s(z	PROPN
ma-265	457	17	,	,	PUNCT
ma-265	457	18	t	t	PROPN
ma-265	457	19	)	)	PUNCT
ma-265	457	20	∂t	∂t	PROPN
ma-265	457	21	6=	6=	ADP
ma-265	457	22	0	0	NUM
ma-265	457	23	,	,	PUNCT
ma-265	457	24	then	then	ADV
ma-265	457	25	by	by	ADP
ma-265	457	26	the	the	DET
ma-265	457	27	equation	equation	NOUN
ma-265	457	28	above	above	ADV
ma-265	457	29	:	:	PUNCT
ma-265	457	30	{	{	PUNCT
ma-265	457	31	w	w	PROPN
ma-265	457	32	·	·	PUNCT
ma-265	457	33	∂g(w	∂g(w	X
ma-265	457	34	)	)	PUNCT
ma-265	457	35	∂w	∂w	PROPN
ma-265	457	36	|w	|w	NOUN
ma-265	457	37	=	=	PROPN
ma-265	457	38	z	z	NOUN
ma-265	457	39	·	·	PUNCT
ma-265	457	40	s(z	s(z	PROPN
ma-265	457	41	,	,	PUNCT
ma-265	457	42	t	t	PROPN
ma-265	457	43	)	)	PUNCT
ma-265	457	44	}	}	PUNCT
ma-265	457	45	=	=	PUNCT
ma-265	457	46	−1	−1	NOUN
ma-265	457	47	.	.	PUNCT
ma-265	458	1	so	so	ADV
ma-265	458	2	z	z	NOUN
ma-265	458	3	·	·	PUNCT
ma-265	458	4	s(z	s(z	PROPN
ma-265	458	5	,	,	PUNCT
ma-265	458	6	t	t	PROPN
ma-265	458	7	)	)	PUNCT
ma-265	458	8	can	can	AUX
ma-265	458	9	be	be	AUX
ma-265	458	10	one	one	NUM
ma-265	458	11	of	of	ADP
ma-265	458	12	a	a	DET
ma-265	458	13	discrete	discrete	ADJ
ma-265	458	14	set	set	NOUN
ma-265	458	15	which	which	PRON
ma-265	458	16	are	be	AUX
ma-265	458	17	the	the	DET
ma-265	458	18	zeros	zero	NOUN
ma-265	458	19	of	of	ADP
ma-265	458	20	the	the	DET
ma-265	458	21	non	non	ADJ
ma-265	458	22	-	-	ADJ
ma-265	458	23	zero	zero	ADJ
ma-265	458	24	holomorphic	holomorphic	ADJ
ma-265	458	25	function	function	NOUN
ma-265	458	26	w	w	PROPN
ma-265	458	27	·	·	PUNCT
ma-265	458	28	∂g(w	∂g(w	X
ma-265	459	1	)	)	PUNCT
ma-265	459	2	∂w	∂w	PROPN
ma-265	460	1	+	+	NUM
ma-265	460	2	1	1	NUM
ma-265	460	3	.	.	X
ma-265	460	4	hence	hence	ADV
ma-265	460	5	z	z	NOUN
ma-265	460	6	·	·	PUNCT
ma-265	460	7	s(z	s(z	PROPN
ma-265	460	8	,	,	PUNCT
ma-265	460	9	t	t	PROPN
ma-265	460	10	)	)	PUNCT
ma-265	460	11	6∈	6∈	PROPN
ma-265	460	12	conf	conf	NOUN
ma-265	460	13	,	,	PUNCT
ma-265	460	14	a	a	DET
ma-265	460	15	contradiction	contradiction	NOUN
ma-265	460	16	.	.	PUNCT
ma-265	461	1	hence	hence	ADV
ma-265	461	2	indeed	indeed	ADV
ma-265	461	3	s(z	s(z	PROPN
ma-265	461	4	,	,	PUNCT
ma-265	461	5	t	t	PROPN
ma-265	461	6	)	)	PUNCT
ma-265	461	7	=	=	SYM
ma-265	461	8	s(z	s(z	PROPN
ma-265	461	9	)	)	PUNCT
ma-265	461	10	is	be	AUX
ma-265	461	11	independent	independent	ADJ
ma-265	461	12	of	of	ADP
ma-265	461	13	t	t	PROPN
ma-265	461	14	.since	.since	NOUN
ma-265	461	15	the	the	DET
ma-265	461	16	beginning	beginning	NOUN
ma-265	461	17	of	of	ADP
ma-265	461	18	the	the	DET
ma-265	461	19	chain	chain	NOUN
ma-265	461	20	{	{	PUNCT
ma-265	461	21	f	f	PROPN
ma-265	461	22	(	(	PUNCT
ma-265	461	23	z	z	PROPN
ma-265	461	24	,	,	PUNCT
ma-265	461	25	t	t	PROPN
ma-265	461	26	)	)	PUNCT
ma-265	461	27	}	}	PUNCT
ma-265	461	28	equals	equal	VERB
ma-265	461	29	the	the	DET
ma-265	461	30	first	first	ADJ
ma-265	461	31	element	element	NOUN
ma-265	461	32	of	of	ADP
ma-265	461	33	the	the	DET
ma-265	461	34	sequence	sequence	NOUN
ma-265	461	35	of	of	ADP
ma-265	461	36	the	the	DET
ma-265	461	37	singularinner	singularinner	NOUN
ma-265	461	38	functions	function	NOUN
ma-265	461	39	,	,	PUNCT
ma-265	461	40	s0(z	s0(z	PROPN
ma-265	461	41	,	,	PUNCT
ma-265	461	42	t	t	PROPN
ma-265	461	43	)	)	PUNCT
ma-265	461	44	=	=	SYM
ma-265	461	45	f	f	X
ma-265	461	46	(	(	PUNCT
ma-265	461	47	z	z	PROPN
ma-265	461	48	,	,	PUNCT
ma-265	461	49	t	t	PROPN
ma-265	461	50	)	)	PUNCT
ma-265	461	51	,	,	PUNCT
ma-265	461	52	this	this	PRON
ma-265	461	53	again	again	ADV
ma-265	461	54	,	,	PUNCT
ma-265	461	55	implies	imply	VERB
ma-265	461	56	the	the	DET
ma-265	461	57	conclusions	conclusion	NOUN
ma-265	461	58	of	of	ADP
ma-265	461	59	theorem	theorem	ADJ
ma-265	461	60	3.3	3.3	NUM
ma-265	461	61	.	.	PUNCT
ma-265	462	1	�	�	PROPN
ma-265	462	2	theorem	theorem	VERB
ma-265	462	3	8.3	8.3	NUM
ma-265	462	4	.	.	PUNCT
ma-265	463	1	lim	lim	PROPN
ma-265	463	2	n→∞	n→∞	NUM
ma-265	463	3			PUNCT
ma-265	463	4	n∏	n∏	PROPN
ma-265	463	5	j=0	j=0	PROPN
ma-265	463	6	sj(z	sj(z	NOUN
ma-265	463	7	,	,	PUNCT
ma-265	463	8	t	t	NOUN
ma-265	463	9	)	)	PUNCT
ma-265	463	10			NOUN
ma-265	463	11	·	·	PUNCT
ma-265	463	12	zn	zn	X
ma-265	463	13	·	·	PUNCT
ma-265	463	14	n−1∏	n−1∏	NUM
ma-265	463	15	j=0	j=0	PROPN
ma-265	463	16	(	(	PUNCT
ma-265	463	17	∂g(w	∂g(w	PROPN
ma-265	463	18	)	)	PUNCT
ma-265	463	19	∂w	∂w	PROPN
ma-265	463	20	|w	|w	NOUN
ma-265	463	21	=	=	ADJ
ma-265	463	22	z	z	X
ma-265	463	23	·	·	PUNCT
ma-265	463	24	sj	sj	INTJ
ma-265	463	25	(	(	PUNCT
ma-265	463	26	z	z	PROPN
ma-265	463	27	,	,	PUNCT
ma-265	463	28	t	t	PROPN
ma-265	463	29	)	)	PUNCT
ma-265	463	30	)	)	PUNCT
ma-265	464	1			NOUN
ma-265	464	2	=	=	PUNCT
ma-265	464	3	0	0	X
ma-265	464	4	.	.	PUNCT
ma-265	465	1	proof.by	proof.by	PROPN
ma-265	465	2	theorem	theorem	VERB
ma-265	465	3	6.1	6.1	NUM
ma-265	465	4	and	and	CCONJ
ma-265	465	5	theorem	theorem	VERB
ma-265	465	6	8.1	8.1	NUM
ma-265	465	7	where	where	SCONJ
ma-265	465	8	we	we	PRON
ma-265	465	9	use	use	VERB
ma-265	465	10	limn→∞	limn→∞	ADJ
ma-265	465	11	∂sn(z	∂sn(z	PROPN
ma-265	465	12	,	,	PUNCT
ma-265	465	13	t	t	NOUN
ma-265	465	14	)	)	PUNCT
ma-265	465	15	∂t	∂t	PROPN
ma-265	465	16	=	=	SYM
ma-265	465	17	0	0	PROPN
ma-265	465	18	.	.	X
ma-265	465	19	�	�	PROPN
ma-265	465	20	in	in	ADP
ma-265	465	21	particular	particular	ADJ
ma-265	465	22	,	,	PUNCT
ma-265	465	23	if	if	SCONJ
ma-265	465	24	we	we	PRON
ma-265	465	25	start	start	VERB
ma-265	465	26	our	our	PRON
ma-265	465	27	recursion	recursion	NOUN
ma-265	465	28	from	from	ADP
ma-265	465	29	its	its	PRON
ma-265	465	30	fixed	fix	VERB
ma-265	465	31	-	-	PUNCT
ma-265	465	32	point	point	NOUN
ma-265	465	33	s0(z	s0(z	PROPN
ma-265	465	34	,	,	PUNCT
ma-265	465	35	t	t	PROPN
ma-265	465	36	)	)	PUNCT
ma-265	465	37	=	=	SYM
ma-265	465	38	s(z	s(z	PROPN
ma-265	465	39	)	)	PUNCT
ma-265	465	40	,	,	PUNCT
ma-265	465	41	then	then	ADV
ma-265	465	42	our	our	PRON
ma-265	465	43	sequenceis	sequenceis	NOUN
ma-265	465	44	stationary	stationary	NOUN
ma-265	465	45	,	,	PUNCT
ma-265	465	46	sj(z	sj(z	NOUN
ma-265	465	47	,	,	PUNCT
ma-265	465	48	t	t	PROPN
ma-265	465	49	)	)	PUNCT
ma-265	465	50	=	=	SYM
ma-265	465	51	s(z	s(z	PROPN
ma-265	465	52	)	)	PUNCT
ma-265	465	53	for	for	ADP
ma-265	465	54	all	all	DET
ma-265	465	55	j	j	PROPN
ma-265	465	56	∈	∈	PROPN
ma-265	465	57	z≥0	z≥0	PROPN
ma-265	465	58	,	,	PUNCT
ma-265	465	59	and	and	CCONJ
ma-265	465	60	the	the	DET
ma-265	465	61	formula	formula	NOUN
ma-265	465	62	of	of	ADP
ma-265	465	63	theorem	theorem	ADJ
ma-265	465	64	5.2	5.2	NUM
ma-265	465	65	gives	give	VERB
ma-265	465	66	us	we	PRON
ma-265	465	67	,	,	PUNCT
ma-265	465	68	corollary	corollary	ADJ
ma-265	465	69	8.4	8.4	NUM
ma-265	465	70	.	.	PUNCT
ma-265	466	1	lim	lim	PROPN
ma-265	466	2	n→∞	n→∞	X
ma-265	466	3	(	(	PUNCT
ma-265	466	4	z	z	NOUN
ma-265	466	5	·	·	PUNCT
ma-265	466	6	s(z))n	s(z))n	NOUN
ma-265	466	7	·	·	PUNCT
ma-265	466	8	{	{	PUNCT
ma-265	466	9	∂g(w	∂g(w	NOUN
ma-265	466	10	)	)	PUNCT
ma-265	466	11	∂w	∂w	PROPN
ma-265	466	12	|w	|w	NOUN
ma-265	466	13	=	=	PROPN
ma-265	466	14	z	z	NOUN
ma-265	466	15	·	·	PUNCT
ma-265	466	16	s(z	s(z	PROPN
ma-265	466	17	)	)	PUNCT
ma-265	466	18	}	}	PUNCT
ma-265	466	19	n	n	NOUN
ma-265	466	20	=	=	SYM
ma-265	466	21	0	0	NUM
ma-265	466	22	∀	∀	NOUN
ma-265	466	23	z	z	NOUN
ma-265	466	24	∈	∈	SYM
ma-265	466	25	u	u	NOUN
ma-265	466	26	,	,	PUNCT
ma-265	466	27	equivalently	equivalently	ADV
ma-265	466	28	lim	lim	PROPN
ma-265	466	29	n→∞	n→∞	NUM
ma-265	466	30	{	{	PUNCT
ma-265	466	31	(	(	PUNCT
ma-265	466	32	w	w	PROPN
ma-265	466	33	·	·	PUNCT
ma-265	466	34	∂g(w	∂g(w	X
ma-265	466	35	)	)	PUNCT
ma-265	466	36	∂w	∂w	PROPN
ma-265	466	37	)	)	PUNCT
ma-265	466	38	|w	|w	NOUN
ma-265	466	39	=	=	SYM
ma-265	466	40	z	z	NOUN
ma-265	466	41	·	·	PUNCT
ma-265	466	42	s(z	s(z	PROPN
ma-265	466	43	)	)	PUNCT
ma-265	466	44	}	}	PUNCT
ma-265	466	45	n	n	NOUN
ma-265	466	46	=	=	SYM
ma-265	466	47	0	0	NUM
ma-265	466	48	∀	∀	NOUN
ma-265	466	49	z	z	NOUN
ma-265	466	50	∈	∈	PROPN
ma-265	466	51	u	u	NOUN
ma-265	466	52	,	,	PUNCT
ma-265	466	53	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	466	54	eur	eur	PROPN
ma-265	466	55	.	.	PUNCT
ma-265	467	1	j.	j.	PROPN
ma-265	467	2	math	math	PROPN
ma-265	467	3	.	.	PUNCT
ma-265	468	1	anal	anal	PROPN
ma-265	468	2	.	.	PUNCT
ma-265	469	1	10.28924	10.28924	NUM
ma-265	469	2	/	/	SYM
ma-265	469	3	ada	ada	PROPN
ma-265	469	4	/	/	SYM
ma-265	469	5	ma.5.4	ma.5.4	PROPN
ma-265	469	6	14	14	NUM
ma-265	469	7	equivalently	equivalently	ADV
ma-265	469	8	∣∣∣∣{(w	∣∣∣∣{(w	ADJ
ma-265	469	9	·	·	PUNCT
ma-265	469	10	∂g(w)∂w	∂g(w)∂w	NOUN
ma-265	469	11	)	)	PUNCT
ma-265	469	12	|w	|w	PROPN
ma-265	469	13	=	=	SYM
ma-265	469	14	z	z	NOUN
ma-265	469	15	·	·	PUNCT
ma-265	469	16	s(z	s(z	PROPN
ma-265	469	17	)	)	PUNCT
ma-265	469	18	}	}	PUNCT
ma-265	469	19	∣∣∣∣	∣∣∣∣	NOUN
ma-265	469	20	<	<	X
ma-265	469	21	1	1	NUM
ma-265	469	22	∀	∀	NOUN
ma-265	469	23	z	z	NOUN
ma-265	469	24	∈	∈	PROPN
ma-265	469	25	u.	u.	VERB
ma-265	469	26	the	the	DET
ma-265	469	27	last	last	ADJ
ma-265	469	28	inequality	inequality	NOUN
ma-265	469	29	can	can	AUX
ma-265	469	30	be	be	AUX
ma-265	469	31	written	write	VERB
ma-265	469	32	as	as	SCONJ
ma-265	469	33	follows	follow	VERB
ma-265	469	34	:	:	PUNCT
ma-265	469	35	z	z	NOUN
ma-265	469	36	·	·	PUNCT
ma-265	469	37	s(z	s(z	NOUN
ma-265	469	38	)	)	PUNCT
ma-265	469	39	·	·	PUNCT
ma-265	470	1	g′(z	g′(z	X
ma-265	470	2	·	·	PUNCT
ma-265	470	3	s(z	s(z	NOUN
ma-265	470	4	)	)	PUNCT
ma-265	470	5	)	)	PUNCT
ma-265	471	1	∈	∈	PROPN
ma-265	471	2	bh∞(u	bh∞(u	NOUN
ma-265	471	3	)	)	PUNCT
ma-265	471	4	where	where	SCONJ
ma-265	471	5	∣∣z	∣∣z	PROPN
ma-265	471	6	·	·	PUNCT
ma-265	471	7	s(z	s(z	PROPN
ma-265	471	8	)	)	PUNCT
ma-265	471	9	·	·	PUNCT
ma-265	471	10	g′(z	g′(z	X
ma-265	471	11	·	·	PUNCT
ma-265	472	1	s(z))∣∣	s(z))∣∣	X
ma-265	472	2	<	<	X
ma-265	472	3	1	1	NUM
ma-265	472	4	∀	∀	NOUN
ma-265	472	5	z	z	NOUN
ma-265	472	6	∈	∈	NOUN
ma-265	472	7	u.	u.	NOUN
ma-265	473	1	we	we	PRON
ma-265	473	2	end	end	VERB
ma-265	473	3	our	our	PRON
ma-265	473	4	paper	paper	NOUN
ma-265	473	5	with	with	ADP
ma-265	473	6	the	the	DET
ma-265	473	7	example	example	NOUN
ma-265	473	8	g(w	g(w	PROPN
ma-265	473	9	)	)	PUNCT
ma-265	473	10	=	=	PUNCT
ma-265	474	1	1+w	1+w	NUM
ma-265	474	2	1−w	1−w	NUM
ma-265	474	3	.	.	PUNCT
ma-265	475	1	on	on	ADP
ma-265	475	2	the	the	DET
ma-265	475	3	next	next	ADJ
ma-265	475	4	we	we	PRON
ma-265	475	5	will	will	AUX
ma-265	475	6	present	present	VERB
ma-265	475	7	the	the	DET
ma-265	475	8	formulas	formula	NOUN
ma-265	475	9	weproved	weprove	VERB
ma-265	475	10	,	,	PUNCT
ma-265	475	11	for	for	ADP
ma-265	475	12	this	this	DET
ma-265	475	13	particular	particular	ADJ
ma-265	475	14	case	case	NOUN
ma-265	475	15	.	.	PUNCT
ma-265	476	1	9	9	X
ma-265	476	2	.	.	X
ma-265	476	3	an	an	DET
ma-265	476	4	example	example	NOUN
ma-265	476	5	let	let	VERB
ma-265	476	6	us	we	PRON
ma-265	476	7	consider	consider	VERB
ma-265	476	8	g(w	g(w	ADJ
ma-265	476	9	)	)	PUNCT
ma-265	476	10	=	=	SYM
ma-265	477	1	1	1	NUM
ma-265	477	2	+	+	CCONJ
ma-265	477	3	w	w	PROPN
ma-265	477	4	1−	1−	NUM
ma-265	477	5	w	w	PROPN
ma-265	477	6	∈	∈	PROPN
ma-265	477	7	rp.let	rp.let	VERB
ma-265	477	8	s0(z	s0(z	PROPN
ma-265	477	9	,	,	PUNCT
ma-265	477	10	t	t	PROPN
ma-265	477	11	)	)	PUNCT
ma-265	478	1	=	=	SYM
ma-265	478	2	f	f	X
ma-265	478	3	(	(	PUNCT
ma-265	478	4	z	z	PROPN
ma-265	478	5	,	,	PUNCT
ma-265	478	6	t	t	PROPN
ma-265	478	7	)	)	PUNCT
ma-265	478	8	and	and	CCONJ
ma-265	478	9	sn+1(z	sn+1(z	VERB
ma-265	478	10	,	,	PUNCT
ma-265	478	11	t	t	PROPN
ma-265	478	12	)	)	PUNCT
ma-265	478	13	=	=	NOUN
ma-265	478	14	exp	exp	NOUN
ma-265	478	15	(	(	PUNCT
ma-265	478	16	−	−	PROPN
ma-265	478	17	1	1	NUM
ma-265	478	18	+	+	CCONJ
ma-265	478	19	z	z	NOUN
ma-265	478	20	·	·	PUNCT
ma-265	478	21	sn(z	sn(z	NOUN
ma-265	478	22	,	,	PUNCT
ma-265	478	23	t	t	PROPN
ma-265	478	24	)	)	PUNCT
ma-265	478	25	1−	1−	NUM
ma-265	478	26	z	z	NOUN
ma-265	478	27	·	·	PUNCT
ma-265	478	28	sn(z	sn(z	NOUN
ma-265	478	29	,	,	PUNCT
ma-265	478	30	t	t	PROPN
ma-265	478	31	)	)	PUNCT
ma-265	478	32	)	)	PUNCT
ma-265	478	33	for	for	ADP
ma-265	478	34	n	n	PRON
ma-265	478	35	∈	∈	PROPN
ma-265	478	36	z≥0	z≥0	PROPN
ma-265	478	37	s(z	s(z	PROPN
ma-265	478	38	,	,	PUNCT
ma-265	478	39	t	t	PROPN
ma-265	478	40	)	)	PUNCT
ma-265	478	41	=	=	SYM
ma-265	479	1	limn→∞	limn→∞	PROPN
ma-265	479	2	sn(z	sn(z	NOUN
ma-265	479	3	,	,	PUNCT
ma-265	479	4	t	t	NOUN
ma-265	479	5	)	)	PUNCT
ma-265	479	6	uniformly	uniformly	ADV
ma-265	479	7	on	on	ADP
ma-265	479	8	compact	compact	ADJ
ma-265	479	9	subsets	subset	NOUN
ma-265	479	10	of	of	ADP
ma-265	479	11	u	u	NOUN
ma-265	479	12	,	,	PUNCT
ma-265	479	13	so	so	SCONJ
ma-265	479	14	that	that	SCONJ
ma-265	479	15	s(z	s(z	PROPN
ma-265	479	16	,	,	PUNCT
ma-265	479	17	t	t	PROPN
ma-265	479	18	)	)	PUNCT
ma-265	479	19	=	=	NOUN
ma-265	479	20	exp	exp	NOUN
ma-265	479	21	(	(	PUNCT
ma-265	479	22	−	−	PROPN
ma-265	479	23	1	1	NUM
ma-265	479	24	+	+	CCONJ
ma-265	479	25	z	z	NOUN
ma-265	479	26	·	·	PUNCT
ma-265	480	1	s(z	s(z	PROPN
ma-265	480	2	,	,	PUNCT
ma-265	480	3	t	t	PROPN
ma-265	480	4	)	)	PUNCT
ma-265	480	5	1−	1−	NUM
ma-265	480	6	z	z	NOUN
ma-265	480	7	·	·	PUNCT
ma-265	480	8	s(z	s(z	PROPN
ma-265	480	9	,	,	PUNCT
ma-265	480	10	t	t	PROPN
ma-265	480	11	)	)	PUNCT
ma-265	480	12	)	)	PUNCT
ma-265	480	13	∀	∀	X
ma-265	481	1	z	z	NOUN
ma-265	481	2	∈	∈	PROPN
ma-265	481	3	u	u	NOUN
ma-265	481	4	and	and	CCONJ
ma-265	481	5	z	z	PROPN
ma-265	481	6	·	·	PUNCT
ma-265	482	1	s(z	s(z	PROPN
ma-265	482	2	,	,	PUNCT
ma-265	482	3	t	t	PROPN
ma-265	482	4	)	)	PUNCT
ma-265	482	5	∈	∈	PROPN
ma-265	482	6	conf	conf	NOUN
ma-265	482	7	,	,	PUNCT
ma-265	482	8	∀	∀	X
ma-265	482	9	0	0	NUM
ma-265	482	10	≤	≤	NUM
ma-265	482	11	t	t	PROPN
ma-265	482	12	≤	≤	NUM
ma-265	482	13	t0	t0	NOUN
ma-265	482	14	.	.	PUNCT
ma-265	483	1	we	we	PRON
ma-265	483	2	have	have	VERB
ma-265	483	3	the	the	DET
ma-265	483	4	following	follow	VERB
ma-265	483	5	results	result	NOUN
ma-265	483	6	:	:	PUNCT
ma-265	483	7	(	(	PUNCT
ma-265	483	8	9.5	9.5	NUM
ma-265	483	9	)	)	PUNCT
ma-265	483	10	∂sn(z	∂sn(z	NOUN
ma-265	483	11	,	,	PUNCT
ma-265	483	12	t	t	NOUN
ma-265	483	13	)	)	PUNCT
ma-265	483	14	∂t	∂t	PROPN
ma-265	483	15	=	=	PUNCT
ma-265	483	16	(	(	PUNCT
ma-265	483	17	−1)n+1	−1)n+1	PROPN
ma-265	483	18	·	·	PUNCT
ma-265	483	19			PUNCT
ma-265	483	20	n∏	n∏	NOUN
ma-265	483	21	j=0	j=0	PROPN
ma-265	483	22	sj(z	sj(z	NOUN
ma-265	483	23	,	,	PUNCT
ma-265	483	24	t	t	NOUN
ma-265	483	25	)	)	PUNCT
ma-265	483	26			NOUN
ma-265	483	27	·	·	PUNCT
ma-265	483	28	{	{	PUNCT
ma-265	483	29	(	(	PUNCT
ma-265	483	30	2z)n∏n−1	2z)n∏n−1	NUM
ma-265	483	31	j=0	j=0	PROPN
ma-265	483	32	(	(	PUNCT
ma-265	483	33	1−	1−	NUM
ma-265	483	34	z	z	NOUN
ma-265	483	35	·	·	PUNCT
ma-265	483	36	sj(z	sj(z	NOUN
ma-265	483	37	,	,	PUNCT
ma-265	483	38	t))2	t))2	NOUN
ma-265	483	39	}	}	PUNCT
ma-265	483	40	·	·	PUNCT
ma-265	483	41	{	{	PUNCT
ma-265	484	1	1	1	NUM
ma-265	484	2	+	+	NUM
ma-265	484	3	k(t)z	k(t)z	PROPN
ma-265	484	4	1−	1−	NUM
ma-265	484	5	k(t)z	k(t)z	PROPN
ma-265	484	6	}	}	PUNCT
ma-265	484	7	.	.	PUNCT
ma-265	485	1	this	this	PRON
ma-265	485	2	follows	follow	VERB
ma-265	485	3	by	by	ADP
ma-265	485	4	theorem	theorem	NOUN
ma-265	485	5	2.1	2.1	NUM
ma-265	485	6	.	.	PUNCT
ma-265	486	1	there	there	PRON
ma-265	486	2	exists	exist	VERB
ma-265	486	3	a	a	DET
ma-265	486	4	unique	unique	ADJ
ma-265	486	5	s(z	s(z	PROPN
ma-265	486	6	)	)	PUNCT
ma-265	486	7	∈	∈	PROPN
ma-265	486	8	h(u	h(u	PROPN
ma-265	486	9	)	)	PUNCT
ma-265	486	10	such	such	ADJ
ma-265	486	11	that	that	SCONJ
ma-265	486	12	it	it	PRON
ma-265	486	13	is	be	AUX
ma-265	486	14	the	the	DET
ma-265	486	15	only	only	ADJ
ma-265	486	16	fixed	fix	VERB
ma-265	486	17	-	-	PUNCT
ma-265	486	18	point	point	NOUN
ma-265	486	19	of	of	ADP
ma-265	486	20	the	the	DET
ma-265	486	21	function	function	NOUN
ma-265	486	22	exp	exp	NOUN
ma-265	486	23	(	(	PUNCT
ma-265	486	24	−1+z	−1+z	PROPN
ma-265	486	25	·	·	PROPN
ma-265	486	26	w1−z	w1−z	PROPN
ma-265	486	27	·	·	PUNCT
ma-265	486	28	w	w	PROPN
ma-265	486	29	)	)	PUNCT
ma-265	486	30	,	,	PUNCT
ma-265	486	31	i.e.	i.e.	X
ma-265	486	32	s(z	s(z	NOUN
ma-265	486	33	)	)	PUNCT
ma-265	486	34	=	=	SYM
ma-265	486	35	exp	exp	NOUN
ma-265	486	36	(	(	PUNCT
ma-265	486	37	−	−	PROPN
ma-265	486	38	1	1	NUM
ma-265	486	39	+	+	CCONJ
ma-265	486	40	z	z	NOUN
ma-265	486	41	·	·	PUNCT
ma-265	486	42	s(z	s(z	NOUN
ma-265	486	43	)	)	PUNCT
ma-265	486	44	1−	1−	NUM
ma-265	486	45	z	z	NOUN
ma-265	486	46	·	·	PUNCT
ma-265	486	47	s(z	s(z	NOUN
ma-265	486	48	)	)	PUNCT
ma-265	486	49	)	)	PUNCT
ma-265	486	50	.	.	PUNCT
ma-265	487	1	moreover	moreover	ADV
ma-265	487	2	∀s0(z	∀s0(z	NUM
ma-265	487	3	)	)	PUNCT
ma-265	487	4	∈	∈	PROPN
ma-265	487	5	sinn	sinn	PROPN
ma-265	487	6	,	,	PUNCT
ma-265	487	7	the	the	DET
ma-265	487	8	recursion	recursion	NOUN
ma-265	487	9	sn+1(z	sn+1(z	VERB
ma-265	487	10	,	,	PUNCT
ma-265	487	11	t	t	PROPN
ma-265	487	12	)	)	PUNCT
ma-265	487	13	=	=	NOUN
ma-265	487	14	exp	exp	NOUN
ma-265	487	15	(	(	PUNCT
ma-265	487	16	−	−	PROPN
ma-265	487	17	1	1	NUM
ma-265	487	18	+	+	CCONJ
ma-265	487	19	z	z	NOUN
ma-265	487	20	·	·	PUNCT
ma-265	487	21	sn(z	sn(z	NOUN
ma-265	487	22	,	,	PUNCT
ma-265	487	23	t	t	PROPN
ma-265	487	24	)	)	PUNCT
ma-265	487	25	1−	1−	NUM
ma-265	487	26	z	z	NOUN
ma-265	487	27	·	·	PUNCT
ma-265	487	28	sn(z	sn(z	NOUN
ma-265	487	29	,	,	PUNCT
ma-265	487	30	t	t	PROPN
ma-265	487	31	)	)	PUNCT
ma-265	487	32	)	)	PUNCT
ma-265	487	33	for	for	ADP
ma-265	487	34	n	n	DET
ma-265	487	35	∈	∈	PROPN
ma-265	487	36	z≥0	z≥0	PROPN
ma-265	487	37	defines	define	VERB
ma-265	487	38	a	a	DET
ma-265	487	39	sequence	sequence	NOUN
ma-265	487	40	of	of	ADP
ma-265	487	41	singular	singular	ADJ
ma-265	487	42	inner	inner	ADJ
ma-265	487	43	functions	function	NOUN
ma-265	487	44	{	{	PUNCT
ma-265	487	45	sn(z)}∞n=0	sn(z)}∞n=0	NUM
ma-265	487	46	.	.	PUNCT
ma-265	488	1	this	this	DET
ma-265	488	2	sequence	sequence	NOUN
ma-265	488	3	converges	converge	VERB
ma-265	488	4	uniformlyon	uniformlyon	VERB
ma-265	488	5	compact	compact	ADJ
ma-265	488	6	subsets	subset	NOUN
ma-265	488	7	of	of	ADP
ma-265	488	8	u	u	NOUN
ma-265	488	9	to	to	ADP
ma-265	488	10	the	the	DET
ma-265	488	11	fixed	fix	VERB
ma-265	488	12	-	-	PUNCT
ma-265	488	13	point	point	NOUN
ma-265	488	14	s(z),i.e	s(z),i.e	NOUN
ma-265	488	15	.	.	PUNCT
ma-265	489	1	s(z	s(z	PROPN
ma-265	489	2	)	)	PUNCT
ma-265	490	1	=	=	SYM
ma-265	490	2	limn→∞	limn→∞	PROPN
ma-265	490	3	sn(z	sn(z	NOUN
ma-265	490	4	)	)	PUNCT
ma-265	490	5	uniformly	uniformly	ADV
ma-265	490	6	on	on	ADP
ma-265	490	7	compactsubsets	compactsubset	NOUN
ma-265	490	8	of	of	ADP
ma-265	490	9	u	u	PROPN
ma-265	490	10	.so	.so	PUNCT
ma-265	490	11	s(z	s(z	PROPN
ma-265	490	12	)	)	PUNCT
ma-265	490	13	is	be	AUX
ma-265	490	14	determined	determine	VERB
ma-265	490	15	by	by	ADP
ma-265	490	16	the	the	DET
ma-265	490	17	recursion	recursion	NOUN
ma-265	490	18	independently	independently	ADV
ma-265	490	19	of	of	ADP
ma-265	490	20	the	the	DET
ma-265	490	21	initial	initial	ADJ
ma-265	490	22	singular	singular	ADJ
ma-265	490	23	inner	inner	ADJ
ma-265	490	24	function	function	NOUN
ma-265	490	25	s0(z).this	s0(z).this	PROPN
ma-265	490	26	follows	follow	VERB
ma-265	490	27	by	by	ADP
ma-265	490	28	theorem	theorem	ADJ
ma-265	490	29	3.3	3.3	NUM
ma-265	490	30	.	.	PUNCT
ma-265	491	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	491	2	eur	eur	PROPN
ma-265	491	3	.	.	PUNCT
ma-265	492	1	j.	j.	PROPN
ma-265	492	2	math	math	PROPN
ma-265	492	3	.	.	PUNCT
ma-265	493	1	anal	anal	PROPN
ma-265	493	2	.	.	PUNCT
ma-265	494	1	10.28924	10.28924	NUM
ma-265	494	2	/	/	SYM
ma-265	494	3	ada	ada	PROPN
ma-265	494	4	/	/	SYM
ma-265	494	5	ma.5.4	ma.5.4	PROPN
ma-265	494	6	15	15	NUM
ma-265	494	7	lim	lim	PROPN
ma-265	494	8	n→∞	n→∞	X
ma-265	494	9	(	(	PUNCT
ma-265	494	10	2z)n	2z)n	NUM
ma-265	494	11	·	·	SYM
ma-265	494	12	∏n	∏n	ADJ
ma-265	494	13	j=0	j=0	PROPN
ma-265	494	14	sj(z	sj(z	NOUN
ma-265	494	15	,	,	PUNCT
ma-265	494	16	t)∏n−1	t)∏n−1	PROPN
ma-265	494	17	j=0	j=0	PROPN
ma-265	494	18	(	(	PUNCT
ma-265	494	19	1−	1−	NUM
ma-265	494	20	z	z	NOUN
ma-265	494	21	·	·	PUNCT
ma-265	494	22	sj(z	sj(z	NOUN
ma-265	494	23	,	,	PUNCT
ma-265	494	24	t))2	t))2	NOUN
ma-265	494	25	=	=	SYM
ma-265	494	26	0	0	X
ma-265	494	27	.	.	PUNCT
ma-265	495	1	(	(	PUNCT
ma-265	495	2	9.6	9.6	NUM
ma-265	495	3	)	)	PUNCT
ma-265	495	4	this	this	PRON
ma-265	495	5	follows	follow	VERB
ma-265	495	6	by	by	ADP
ma-265	495	7	theorem	theorem	NOUN
ma-265	495	8	8.2	8.2	NUM
ma-265	495	9	.	.	PUNCT
ma-265	496	1	∣∣∣∣	∣∣∣∣	NOUN
ma-265	496	2	2z	2z	NOUN
ma-265	496	3	·	·	PUNCT
ma-265	497	1	s(z	s(z	NOUN
ma-265	497	2	)	)	PUNCT
ma-265	497	3	(	(	PUNCT
ma-265	497	4	1−	1−	NUM
ma-265	497	5	z	z	NOUN
ma-265	497	6	·	·	PUNCT
ma-265	497	7	s(z))2	s(z))2	PROPN
ma-265	497	8	∣∣∣∣	∣∣∣∣	NOUN
ma-265	497	9	<	<	X
ma-265	497	10	1	1	NUM
ma-265	497	11	∀	∀	NOUN
ma-265	497	12	z	z	NOUN
ma-265	497	13	∈	∈	SYM
ma-265	497	14	u	u	NOUN
ma-265	497	15	,	,	PUNCT
ma-265	497	16	(	(	PUNCT
ma-265	497	17	9.7	9.7	NUM
ma-265	497	18	)	)	PUNCT
ma-265	497	19	equivalently	equivalently	ADV
ma-265	497	20	(	(	PUNCT
ma-265	497	21	1−	1−	NUM
ma-265	497	22	|z	|z	PROPN
ma-265	497	23	|	|	ADV
ma-265	497	24	·	·	PUNCT
ma-265	497	25	|s(z)|)2	|s(z)|)2	NOUN
ma-265	497	26	>	>	X
ma-265	497	27	2<{z	2<{z	PROPN
ma-265	497	28	·	·	PUNCT
ma-265	497	29	s(z	s(z	NOUN
ma-265	497	30	)	)	PUNCT
ma-265	497	31	}	}	PUNCT
ma-265	497	32	∀	∀	PUNCT
ma-265	497	33	z	z	NOUN
ma-265	497	34	∈	∈	NOUN
ma-265	497	35	u	u	NOUN
ma-265	497	36	.	.	PUNCT
ma-265	498	1	this	this	PRON
ma-265	498	2	follows	follow	VERB
ma-265	498	3	by	by	ADP
ma-265	498	4	corollary	corollary	ADJ
ma-265	498	5	5.3	5.3	NUM
ma-265	498	6	.	.	PUNCT
ma-265	499	1	references	reference	NOUN
ma-265	499	2	[	[	X
ma-265	499	3	1	1	NUM
ma-265	499	4	]	]	X
ma-265	499	5	j.a	j.a	PROPN
ma-265	499	6	.	.	PROPN
ma-265	499	7	hummel	hummel	PROPN
ma-265	499	8	,	,	PUNCT
ma-265	499	9	s.	s.	PROPN
ma-265	499	10	scheinberg	scheinberg	PROPN
ma-265	499	11	,	,	PUNCT
ma-265	499	12	l.	l.	PROPN
ma-265	499	13	zalcman	zalcman	PROPN
ma-265	499	14	,	,	PUNCT
ma-265	499	15	a	a	DET
ma-265	499	16	coefficient	coefficient	NOUN
ma-265	499	17	problem	problem	NOUN
ma-265	499	18	for	for	ADP
ma-265	499	19	bounded	bounded	ADJ
ma-265	499	20	nonvanishing	nonvanishing	NOUN
ma-265	499	21	functions	function	NOUN
ma-265	499	22	,	,	PUNCT
ma-265	499	23	j.	j.	PROPN
ma-265	499	24	anal	anal	PROPN
ma-265	499	25	.	.	PUNCT
ma-265	500	1	math.31	math.31	PROPN
ma-265	500	2	(	(	PUNCT
ma-265	500	3	1977	1977	NUM
ma-265	500	4	)	)	PUNCT
ma-265	500	5	169	169	NUM
ma-265	500	6	-	-	SYM
ma-265	500	7	190.[2	190.[2	NUM
ma-265	500	8	]	]	X
ma-265	500	9	o.	o.	PROPN
ma-265	500	10	ivrii	ivrii	PROPN
ma-265	500	11	,	,	PUNCT
ma-265	500	12	critical	critical	ADJ
ma-265	500	13	structures	structure	NOUN
ma-265	500	14	of	of	ADP
ma-265	500	15	inner	inner	ADJ
ma-265	500	16	functions	function	NOUN
ma-265	500	17	,	,	PUNCT
ma-265	500	18	j.	j.	PROPN
ma-265	500	19	funct	funct	PROPN
ma-265	500	20	.	.	PUNCT
ma-265	501	1	anal	anal	PROPN
ma-265	501	2	.	.	PUNCT
ma-265	502	1	281	281	NUM
ma-265	502	2	(	(	PUNCT
ma-265	502	3	2021	2021	NUM
ma-265	502	4	)	)	PUNCT
ma-265	502	5	109	109	NUM
ma-265	502	6	-	-	SYM
ma-265	502	7	198.[3	198.[3	NUM
ma-265	502	8	]	]	PUNCT
ma-265	502	9	r.	r.	PROPN
ma-265	502	10	mclaughlin	mclaughlin	PROPN
ma-265	502	11	,	,	PUNCT
ma-265	502	12	exceptional	exceptional	ADJ
ma-265	502	13	sets	set	NOUN
ma-265	502	14	for	for	ADP
ma-265	502	15	inner	inner	ADJ
ma-265	502	16	functions	function	NOUN
ma-265	502	17	,	,	PUNCT
ma-265	502	18	j.	j.	PROPN
ma-265	502	19	london	london	PROPN
ma-265	502	20	math	math	PROPN
ma-265	502	21	.	.	PUNCT
ma-265	503	1	soc	soc	PROPN
ma-265	503	2	.	.	PUNCT
ma-265	504	1	s2	s2	PROPN
ma-265	504	2	-	-	PUNCT
ma-265	504	3	4	4	NUM
ma-265	504	4	(	(	PUNCT
ma-265	504	5	4	4	NUM
ma-265	504	6	)	)	PUNCT
ma-265	504	7	(	(	PUNCT
ma-265	504	8	1972	1972	NUM
ma-265	504	9	)	)	PUNCT
ma-265	504	10	696	696	NUM
ma-265	504	11	-	-	SYM
ma-265	504	12	700.[4	700.[4	NUM
ma-265	504	13	]	]	X
ma-265	504	14	r.	r.	PROPN
ma-265	504	15	peretz	peretz	PROPN
ma-265	504	16	,	,	PUNCT
ma-265	504	17	the	the	DET
ma-265	504	18	krzyż	krzyż	NOUN
ma-265	504	19	conjecture	conjecture	NOUN
ma-265	504	20	theory	theory	NOUN
ma-265	504	21	and	and	CCONJ
ma-265	504	22	methods	method	NOUN
ma-265	504	23	,	,	PUNCT
ma-265	504	24	world	world	NOUN
ma-265	504	25	scientific	scientific	PROPN
ma-265	504	26	,	,	PUNCT
ma-265	504	27	singapore	singapore	PROPN
ma-265	504	28	,	,	PUNCT
ma-265	504	29	2021	2021	NUM
ma-265	504	30	.	.	PUNCT
ma-265	505	1	https://doi.org/10.28924/ada/ma.5.4	https://doi.org/10.28924/ada/ma.5.4	PROPN
ma-265	505	2	1	1	NUM
ma-265	505	3	.	.	PUNCT
ma-265	505	4	correspondences	correspondence	NOUN
ma-265	505	5	that	that	PRON
ma-265	505	6	involve	involve	VERB
ma-265	505	7	inner	inner	ADJ
ma-265	505	8	functions	function	NOUN
ma-265	505	9	2	2	NUM
ma-265	505	10	.	.	PUNCT
ma-265	506	1	an	an	DET
ma-265	506	2	example	example	NOUN
ma-265	506	3	of	of	ADP
ma-265	506	4	our	our	PRON
ma-265	506	5	construction	construction	NOUN
ma-265	506	6	3	3	NUM
ma-265	506	7	.	.	PUNCT
ma-265	507	1	a	a	DET
ma-265	507	2	generalization	generalization	NOUN
ma-265	507	3	4	4	NUM
ma-265	507	4	.	.	PUNCT
ma-265	507	5	a	a	DET
ma-265	507	6	parametrization	parametrization	NOUN
ma-265	507	7	of	of	ADP
ma-265	507	8	a	a	DET
ma-265	507	9	family	family	NOUN
ma-265	507	10	of	of	ADP
ma-265	507	11	conformal	conformal	ADJ
ma-265	507	12	mappings	mapping	NOUN
ma-265	507	13	by	by	ADP
ma-265	507	14	the	the	DET
ma-265	507	15	functions	function	NOUN
ma-265	507	16	in	in	ADP
ma-265	507	17	rp	rp	NOUN
ma-265	507	18	5	5	NUM
ma-265	507	19	.	.	PUNCT
ma-265	508	1	the	the	DET
ma-265	508	2	family	family	NOUN
ma-265	508	3	of	of	ADP
ma-265	508	4	conformal	conformal	ADJ
ma-265	508	5	mappings	mapping	NOUN
ma-265	508	6	conf	conf	NOUN
ma-265	508	7	6	6	NUM
ma-265	508	8	.	.	PUNCT
ma-265	509	1	the	the	DET
ma-265	509	2	geometry	geometry	NOUN
ma-265	509	3	of	of	ADP
ma-265	509	4	the	the	DET
ma-265	509	5	image	image	NOUN
ma-265	509	6	of	of	ADP
ma-265	509	7	conformal	conformal	ADJ
ma-265	509	8	mappings	mapping	NOUN
ma-265	509	9	in	in	ADP
ma-265	509	10	conf	conf	NOUN
ma-265	509	11	7	7	NUM
ma-265	509	12	.	.	PUNCT
ma-265	509	13	combining	combine	VERB
ma-265	509	14	two	two	NUM
ma-265	509	15	dynamical	dynamical	ADJ
ma-265	509	16	systems	system	NOUN
ma-265	509	17	8	8	NUM
ma-265	509	18	.	.	PUNCT
ma-265	510	1	more	more	ADJ
ma-265	510	2	results	result	NOUN
ma-265	510	3	9	9	NUM
ma-265	510	4	.	.	PUNCT
ma-265	511	1	an	an	DET
ma-265	511	2	example	example	NOUN
ma-265	511	3	references	reference	NOUN