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Holomorphic functions of several variables : an introduction to the fundamental theory / Ludger Kaup, Burchard Kaup ; with the assistance of Gottfried Barthel ; translated by Michael Bridgland

Author
Kaup, Ludger, 1939-
Published
Berlin ; New York : Walter de Gruyter, 1983.
Physical Description
1 online resource (xiii, 349 pages).
Additional Creators
Barthel, Gottfried and Kaup, Burchard, 1940-
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Series
Language Note
English.
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., and Front matter -- Part One: Function Theory on Domains in ℂn -- Chapter 0. Elementary Properties of Holomorphic Functions -- Chapter 1 Regions of Ηolomorphy -- Part Two: Function Theory on Analytic Sets -- Chapter 2 The Weierstrass Preparation Theorem and its Applications -- Chapter 3 Complex Manifolds and the Elementary Theory of Complex Spaces -- Chapter 4 Complex Spaces -- Part Three: Function Theory on Stein Spaces -- Chapter 5 Applications of Theorem Β -- Chapter 6 Proof of Theorem Β -- Supplement: Chapter 7 Normal Complex Spaces -- List of Examples -- Bibliography -- Glossary of Notations -- Index -- Backmatter
Summary
Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics).
Subject(s)
ISBN
9783110838350 (electronic bk.)
3110838354 (electronic bk.)
3110041502
9783110041507
Digital File Characteristics
data file
Bibliography Note
Includes bibliographical references (pages 325-328) and index.
View MARC record | catkey: 43616311