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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Bibliographic Details
Published in:Nonlinear Semigroups, Fixed Points, And Geometry Of Domains In Banach Spaces pp. 51 - 79
Main Authors: Simeon Reich, David Shoikhet
Format: Book Chapter
Language:English
Published: Singapore World Scientific Publishing Company 2005
PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO
Subjects:
Differential equations
ISBN:9781860945755, 1860945759, 9781783260218, 1783260211, 186094714X, 9781860947148
Online Access:Get full text
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Summary: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
ISBN:9781860945755
1860945759
9781783260218
1783260211
186094714X
9781860947148
DOI:10.1142/9781860947148_0002