UID:
almahu_9947360003402882
Format:
Online-Ressource (xiii, 349 p)
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
3110041502
,
9783110041507
,
9783110838350
Series Statement:
De Gruyter studies in mathematics 3
Content:
Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics)
Note:
Bibliography: p. [325]-328
,
Includes index
,
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 ℂn; 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 Poincaré Problem; 54B Supplement: Holomorphic Line Bundles; 55 Coherent Analytic Sheaves as Fréchet Sheaves; 56 The Exhaustion Theorem.
Language:
English
DOI:
10.1515/9783110838350
URL:
http://www.degruyter.com/doi/book/10.1515/9783110838350
