Holomorphic functions of several variables : an introduction to the fundamental theory /
Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics).
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Full text (MCPHS users only) |
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| Main Author: | |
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English German |
| Published: |
Berlin ; New York :
Walter de Gruyter,
1983
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| Series: | De Gruyter studies in mathematics ;
3. |
| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- 24 Analytic AlgebrasChapter 3 Complex Manifolds and the Elementary Theory of Complex Spaces; 30 Bringing in the Sheaves; 31 Ringed Spaces and Local Models of Complex Spaces; 32 Complex Manifolds and Reduced Complex Spaces; 32A Supplement: Submersions and Immersions; 32B Supplement: Examples of Complex Manifolds; 33 Zeros of Polynomials; 33A Supplement: Resultants and Discriminants; 33B Supplement: Proper Mappings and Equivalence Relations; Chapter 4 Complex Spaces; 41 Coherent Sheaves; 42 The Coherence of nO; 43 Complex Spaces.
- 44 Germs of Complex Spaces and Analytic Algebras 45 Discrete and Finite Holomorphic Mappings; 45A Supplement: Image Sheaves; 45B Supplement: The Analytic Spectrum; 46 The Representation Theorem for Prime Germs; 46A Supplement: Injective Holomorphic Mappings between Manifolds of the Same Dimension; 46B Supplement: Universal Denominators for Prime Germs; 47 Hilbert's Nullstellensatz and Cartan's Coherence Theorem; 48 Dimension Theory; 49 Set of Singular Points and Decomposition into Irreducible Components; 49A Supplement: Fiber Products and Quotients.
- Chapter 1 Regions of Holomorphy 11 Domains of Convergence of Power Series and Reinhardt Domains; 12 Regions of Holomorphy and Holomorphic Convexit; 12A Supplement: Further Extension Theorems for Holomorphic Functions; 12B Supplement: The Edge-of-the-Wedge Theorem; 13 Plurisubharmonic Functions; 14 Pseudoconvex Domains; Part Two: Function Theory on Analytic Sets; Chapter 2 The Weierstrass Preparation Theorem and its Applications; 21 Power Series Algebras; 22 The Weierstrass Theorems; 23 Algebraic Properties of nO0 and; 23A Supplement: Finite Ring-extensions, Normality.
- Part Three: Function Theory on Stein SpacesChapter 5 Applications of Theorem B; 50 Introductory Remarks on Cohomology; 50A Supplement: Automorphic Functions; 51 Stein Spaces; 51A Supplement: Countable Topology in Complex Spaces; 52 Theorem B and B-Spaces; 53 The Additive Cousin Problem; 53A Supplement: Meromorphic Functions on Reduced Complex Spaces; 54 The Multiplicative Cousin Problem; 54 A Supplement: The Poincaré Problem; 54B Supplement: Holomorphic Line Bundles; 55 Coherent Analytic Sheaves as Fréchet Sheaves; 56 The Exhaustion Theorem.
