# Introduction to Complex Analysis in Several Variables

## Edition: 2005

List price: $49.99 30 day, 100% satisfaction guarantee! Out of stock what's this? Rush Rewards U Members Receive: You have reached 400 XP and carrot coins. That is the daily max! ### 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… Customers also bought ### Book details List price:$49.99
 Preface Elementary theory of several complex variables Geometry of <$>{\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}<$> (U, E) The Theorems of Arzelï¿½-Ascoli and Montel Power series and Taylor series Summable families in Banach spaces Power series Reinhardt domains and Laurent expansion Continuation on circular and polycircular domains Holomorphic continuation Representation-theoretic interpretation of the Laurent series Hartogs' Kugelsatz, Special case Biholomorphic maps The Inverse Function Theorem and Implicit Functions The Riemann Mapping Problem Cartan's Uniqueness Theorem Analytic Sets Elementary properties of analytic sets The Riemann Removable Singularity Theorems Hartogs' Kugelsatz Holomorphic Differential Forms Multilinear forms Complex differential forms The inhomogenous Cauchy-Riemann Differential Equations Dolbeaut's Lemma The Kugelsatz of Hartogs Continuation on Tubular Domains Convex hulls Holomorphically convex hulls Bochner's Theorem Cartan-Thullen Theory Holomorphically convex sets Domains of Holomorphy The Theorem of Cartan-Thullen Holomorphically convex Reinhardt domains Local Properties of holomorphic functions Local representation of a holomorphic function Germ of a holomorphic function The algebras of formal and of convergent power series The Weierstrass Theorems The Weierstrass Division Formula The Weierstrass Preparation Theorem Algebraic properties of <$>{\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