Several Complex Variables

By: Raghavan Narasimhan

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Paperback | 27 February 1995 | Edition Number 1

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184 Pages

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2.01 x 1.39 x 0.12

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Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramified domains over C . Topics discussed are Hartogs' theory, domains in holomorphy, and automorphism of bounded domains.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis Probability & Statistics Applied Mathematics Miscellaneous Items

Preface
Elementary Properties of Functions of Several Complex Variables
Notations. Holomorphic functions. Cauchy's formula and some consequences. The open mapping theorem. Weierstrass' and Montel's theorems.
Analytic Continuation: Elementary Theory
Extension of holomorphic functions from the boundary of a polydisc. Reinhardt domains.
Subharmonic Functions and Hartogs' Theorem
Definition and basic properties of harmonic and subharmonic functions. Some examples and applications. Hartogs' theorem on separate analyticity. Exceptional sets of subharmonic functions.
Hartogs' Theorem on the Singularities of Holomorphic Functions
Analytic sets. The Riemann continuation theorem. Rado's theorem. Hartogs' continuity theorem. Properties of the Hartogs radius. Analyticity of certain singular sets.
Automorphisms of Bounded Domains
Cartan's uniqueness theorem. Automorphisms of circular domains, in particular of polydiscs. Poincare's theorem that the polydisc and the ball are analytically distinct. Proper holomorphic maps. A theorem of Remmert-Stein and some generalizations.
Limits of automorphisms: Cartan's theorem. Action of Aut(D) on D, finite generation of some discrete groups. An injective holomorphic map from D C Cn into Cn is an isomorphism.
Analytic Continuation: Envelopes of Holomorphy
S- extension of a domain over
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Several Complex Variables

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