Screen LibraryHolomorphic functions of several variables: an introduction to the fundamental theory/
Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics)
Saved in:
| Main Authors: | |
|---|---|
| Corporate Authors: | ; |
| Group Author: | ; |
| Published: |
Walter de Gruyter,
|
| Publisher Address: | Berlin: |
| Publication Dates: | [2011] |
| Literature type: | eBook |
| Language: | English |
| Series: |
De gruyter studies in mathematics
3 |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1515/9783110838350 http://www.degruyter.com/doc/cover/9783110838350.jpg |
| Summary: |
Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics) |
| Item Description: |
Bibliography: p. [325]-328 Includes index |
| Carrier Form: | 1 online ressource (xiii, 349 pages). |
| ISBN: | 9783110838350 |
| Index Number: | QA331 |
| CLC: | O174.5 |
| 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. 57 The Character Theorem and Holomorphic Hulls. 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. Interdependence of chapters; Courses and Seminars: Guide to the Essentials of Specific Topics; Part One: Function Theory on Domains in n; Chapter 0. Elementary Properties of Holomorphic Functions; 1 Definition of Holomorphic Function; 2 O (X) as a Topological Algebra; 3 Holomorphic Mappings; 4 Cauchy's Integral Formula; 4A Supplement: Cartan's Uniqueness Theorem and Automorphisms of Bounded Domains; 5 Montel's Theorem; 6 The Identity Theorem, the Maximum Principle, and Runge's Theorem; 7 The Riemann Removable Singularity Theorems; 8 The Implicite Mapping Theorem. 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 Poincar Problem; 54B Supplement: Holomorphic Line Bundles; 55 Coherent Analytic Sheaves as Fr chet Sheaves; 56 The Exhaustion Theorem. |