Differentiable and Holomorphic Mappings in Banach Spaces
The following sections are included: Differentiable Mappings. Fréchet Derivatives Examples Holomorphic Mappings The Cauchy integral formula Power series representation The maximum modulus theorem Topologies in ${\rm Hol}(\mathcal {D}, Y)$ T-topology and compact open topology on ${\rm Hol}(\mathcal {...
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| Veröffentlicht in: | Nonlinear Semigroups, Fixed Points, And Geometry Of Domains In Banach Spaces S. 51 - 79 |
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| Hauptverfasser: | , |
| Format: | Buchkapitel |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore
World Scientific Publishing Company
2005
PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO |
| Schlagworte: | |
| ISBN: | 9781860945755, 1860945759, 9781783260218, 1783260211, 186094714X, 9781860947148 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The following sections are included:
Differentiable Mappings. Fréchet Derivatives
Examples
Holomorphic Mappings
The Cauchy integral formula
Power series representation
The maximum modulus theorem
Topologies in ${\rm Hol}(\mathcal {D}, Y)$
T-topology and compact open topology on ${\rm Hol}(\mathcal {D}, Y)$
Montel's theorem
Vitali's theorem
Elements of Functional Analytic Calculus
Symbolic calculus on Banach algebras
The spectral mapping theorem,
Some*-algebras
l-analytic functions on unital J*-algebras
The Schwarz Lemma
The classical Schwarz Lemma and Cartan's uniqueness theorem
Automorphisms
The unit disk
The poly disk in ℂn
The Euclidean ball in ℂn and the Hilbert ball
Unital J*-algebras
The Schwarz–Pick lemma |
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| ISBN: | 9781860945755 1860945759 9781783260218 1783260211 186094714X 9781860947148 |
| DOI: | 10.1142/9781860947148_0002 |