Several complex variables.
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| Author / Creator: | Narasimhan, Raghavan. |
|---|---|
| Imprint: | Chicago : University of Chicago Press, [1971] |
| Description: | x, 174 p. ; 21 cm. |
| Language: | English |
| Series: | Chicago lectures in mathematics. |
| Subject: | |
| Format: | Print Book |
| Local Note: | University of Chicago Library's copy 6 is a hardback; copies 7 and 8 have variant paperback covers. |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/763625 |
Table of Contents:
- Preface
- Chapter 1. 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.
- Chapter 2. Analytic Continuation: Elementary Theory
- Extension of holomorphic functions from the boundary of a polydisc. Reinhardt domains.
- Chapter 3. 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.
- Chapter 4. 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.
- Chapter 5. 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.
- Chapter 6. Analytic Continuation: Envelopes of Holomorphy
- S- extension of a domain over
