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Introduction to Complex Analysis in Several Variables

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ISBN-10: 376437490X

ISBN-13: 9783764374907

Edition: 2005

Authors: Volker Scheidemann

List price: $49.99
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Description:

This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as possible. Many cross-references to other parts of mathematics, such as functional analysis or algebras, are pointed out in order to broaden the view and the understanding of the chosen topics. A major focus is extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who…    
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Book details

List price: $49.99
Copyright year: 2005
Publisher: Springer Basel AG
Publication date: 9/16/2005
Binding: Paperback
Pages: 171
Size: 6.50" wide x 9.00" long x 0.50" tall
Weight: 0.748
Language: English

Preface
Elementary theory of several complex variables
Geometry of <$>{\op C}^n<$>
Holomorphic functions in several complex variables
Definition of a holomorphic function
Basic properties of holomorphic functions
Partially holomorphic functions and the Cauchy-Riemann differential equations
The Cauchy Integral Formula
<$>{\cal O}<$> (U) as a topological space
Locally convex spaces
The compact-open topology on <$>{\cal C}<$> (U, E)
The Theorems of Arzel�-Ascoli and Montel
Power series and Taylor series
Summable families in Banach spaces
Power series
Reinhardt domains and Laurent expansion
Continuation on circular and polycircular domains
Holomorphic continuation
Representation-theoretic interpretation of the Laurent series
Hartogs' Kugelsatz, Special case
Biholomorphic maps
The Inverse Function Theorem and Implicit Functions
The Riemann Mapping Problem
Cartan's Uniqueness Theorem
Analytic Sets
Elementary properties of analytic sets
The Riemann Removable Singularity Theorems
Hartogs' Kugelsatz
Holomorphic Differential Forms
Multilinear forms
Complex differential forms
The inhomogenous Cauchy-Riemann Differential Equations
Dolbeaut's Lemma
The Kugelsatz of Hartogs
Continuation on Tubular Domains
Convex hulls
Holomorphically convex hulls
Bochner's Theorem
Cartan-Thullen Theory
Holomorphically convex sets
Domains of Holomorphy
The Theorem of Cartan-Thullen
Holomorphically convex Reinhardt domains
Local Properties of holomorphic functions
Local representation of a holomorphic function
Germ of a holomorphic function
The algebras of formal and of convergent power series
The Weierstrass Theorems
The Weierstrass Division Formula
The Weierstrass Preparation Theorem
Algebraic properties of <$>{\op C} \{z_1, \ldots, z_n\}<$>
Hilbert's Nullstellensatz
Germs of a set
The radical of an ideal
Hilbert's Nullstellensatz for principal ideals
Register of Symbols
Bibliography
Index