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Holomorphic functions of several variables : an introduction to the fundamental theory

Author: Ludger Kaup; Gottfried Barthel; Burchard Kaup
Publisher: Berlin ; New York : Walter de Gruyter, 1983.
Series: De Gruyter studies in mathematics, 3.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics).
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kaup, Ludger, 1939-
Holomorphic functions of several variables.
Berlin ; New York : Walter de Gruyter, 1983
(DLC) 83010120
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ludger Kaup; Gottfried Barthel; Burchard Kaup
ISBN: 9783110838350 3110838354
OCLC Number: 815508927
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL
Description: 1 online resource (xiii, 349 pages).
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
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.
Series Title: De Gruyter studies in mathematics, 3.
Responsibility: Ludger Kaup, Burchard Kaup ; with the assistance of Gottfried Barthel ; translated by Michael Bridgland.

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Holomorphic Functions Of Several Variables (De Gruyter Studies In Mathematics).

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