A Montel Theorem for Holomorphic Functions on Infinite Dimensional Spaces that Omit the Values 0 and 1
Let X be a connected complex Banach manifold. We give a proof that the set of holomorphic functions on X that omit the values 0 and 1 is a normal family.
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| Veröffentlicht in: | Computational methods and function theory Jg. 8; H. 1; S. 195 - 198 |
|---|---|
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer-Verlag
01.05.2008
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| ISSN: | 1617-9447, 2195-3724 |
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| Abstract | Let
X
be a connected complex Banach manifold. We give a proof that the set of holomorphic functions on
X
that omit the values 0 and 1 is a normal family. |
|---|---|
| AbstractList | Let
X
be a connected complex Banach manifold. We give a proof that the set of holomorphic functions on
X
that omit the values 0 and 1 is a normal family. |
| Author | Earle, Clifford J. |
| Author_xml | – sequence: 1 givenname: Clifford J. surname: Earle fullname: Earle, Clifford J. email: cliff@math.cornell.edu organization: Department of Mathematics, Cornell University |
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| Cites_doi | 10.1007/978-1-4471-0869-6 10.1090/S0002-9939-06-08681-3 |
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| Copyright | Heldermann Verlag 2008 |
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| DOI | 10.1007/BF03321682 |
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| Keywords | normal families 46G20 Montel’s Theorem |
| Language | English |
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| References | TakatsukaPNormal families of holomorphic functions on infinite dimensional spacesPort. Math. (N.S.)200663335136222549341124.46025 HarrisL ASchwarz-Pick systems of pseudometrics for domains in normed linear spacesAdvances in Holomorphy1979AmsterdamNorth Holland345406 HilleEPhillipsR SFunctional Analysis and Semi-groups1957ProvidenceAmer. Math. Soc. DineenSThe Schwarz Lemma1989OxfordClarendon Press0708.46046 DineenSComplex Analysis on Infinite Dimensional Spaces1999LondonSpringer1034.4650410.1007/978-1-4471-0869-6 MujicaJTakatsukaPA Schottky-type theorem for starlike domains in Banach spacesProc. Amer. Math. Soc.200713541141114422629171124.4602410.1090/S0002-9939-06-08681-3 CarathéodoryCTheory of Functions of a Complex Variable, Vol. II1960New YorkChelsea KelleyJ LGeneral Topology1955PrincetonVan Nostrand0066.16604 ChaeS BHolomorphy and Calculus in Normed Spaces1985New YorkMarcel Dekker0571.46031 S B Chae (BF03321682_CR2) 1985 S Dineen (BF03321682_CR4) 1999 P Takatsuka (BF03321682_CR9) 2006; 63 J L Kelley (BF03321682_CR7) 1955 C Carathéodory (BF03321682_CR1) 1960 L A Harris (BF03321682_CR5) 1979 E Hille (BF03321682_CR6) 1957 J Mujica (BF03321682_CR8) 2007; 135 S Dineen (BF03321682_CR3) 1989 |
| References_xml | – reference: ChaeS BHolomorphy and Calculus in Normed Spaces1985New YorkMarcel Dekker0571.46031 – reference: KelleyJ LGeneral Topology1955PrincetonVan Nostrand0066.16604 – reference: TakatsukaPNormal families of holomorphic functions on infinite dimensional spacesPort. Math. (N.S.)200663335136222549341124.46025 – reference: MujicaJTakatsukaPA Schottky-type theorem for starlike domains in Banach spacesProc. Amer. Math. Soc.200713541141114422629171124.4602410.1090/S0002-9939-06-08681-3 – reference: CarathéodoryCTheory of Functions of a Complex Variable, Vol. II1960New YorkChelsea – reference: HarrisL ASchwarz-Pick systems of pseudometrics for domains in normed linear spacesAdvances in Holomorphy1979AmsterdamNorth Holland345406 – reference: DineenSComplex Analysis on Infinite Dimensional Spaces1999LondonSpringer1034.4650410.1007/978-1-4471-0869-6 – reference: DineenSThe Schwarz Lemma1989OxfordClarendon Press0708.46046 – reference: HilleEPhillipsR SFunctional Analysis and Semi-groups1957ProvidenceAmer. Math. Soc. – volume-title: Complex Analysis on Infinite Dimensional Spaces year: 1999 ident: BF03321682_CR4 doi: 10.1007/978-1-4471-0869-6 – volume-title: The Schwarz Lemma year: 1989 ident: BF03321682_CR3 – start-page: 345 volume-title: Advances in Holomorphy year: 1979 ident: BF03321682_CR5 – volume-title: Holomorphy and Calculus in Normed Spaces year: 1985 ident: BF03321682_CR2 – volume-title: Theory of Functions of a Complex Variable, Vol. II year: 1960 ident: BF03321682_CR1 – volume-title: General Topology year: 1955 ident: BF03321682_CR7 – volume-title: Functional Analysis and Semi-groups year: 1957 ident: BF03321682_CR6 – volume: 135 start-page: 1141 issue: 4 year: 2007 ident: BF03321682_CR8 publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-06-08681-3 – volume: 63 start-page: 351 issue: 3 year: 2006 ident: BF03321682_CR9 publication-title: Port. Math. (N.S.) |
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| Snippet | Let
X
be a connected complex Banach manifold. We give a proof that the set of holomorphic functions on
X
that omit the values 0 and 1 is a normal family. |
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| StartPage | 195 |
| SubjectTerms | Analysis Computational Mathematics and Numerical Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics |
| Title | A Montel Theorem for Holomorphic Functions on Infinite Dimensional Spaces that Omit the Values 0 and 1 |
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