Extension of Holomorphic Functions

Marek Jarnicki, Peter Pflug

Walter de Gruyter, Jun 24, 2011 - Mathematics - 497 pages

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject.

Editorial Board

Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Honorary Editor

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Titles in planning include

Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Contents

• Chapter 1 Riemann domains: 1
• 11 Riemann domains over Cn: 3
• 12 Holomorphic functions: 18
• 13 Examples of Riemann regions: 21
• 14 Holomorphic extension of Riemann domains: 25
• 15 The boundary of a Riemann domain: 29
• 16 Union intersection and direct limit of Riemann domains: 39
• 17 Domains of existence: 50
• 18 Maximal holomorphic extensions: 54
• 19 Liftings of holomorphic mappings I: 62
• 110 Holomorphic convexity: 75
• 111 Riemann surfaces: 86
• Chapter 2 Pseudoconvexity: 96
• 22 Pseudoconvexity: 129
• 23 The Kiselman minimum principle: 153
• 24 xxxoperator: 159
• 25 Solution of the Levi Problem: 177
• 26 Regular solutions: 184
• 27 Approximation: 190
• 28 The Remmert embedding theorem: 195
• 29 The DocquierGrauert criteria: 201
• 210 The division theorem: 208
• 211 Spectrum: 219
• 212 Liftings of holomorphic mappings II: 224
• Chapter 3 Envelopes of holomorphy for special domains: 235
• 32 ktubular domains: 258
• 33 Matrix Reinhardt domains: 284
• 34 The envelope of holomorphy of XM: 302
• 35 Separately holomorphic functions: 324
• 36 Extension of meromorphic functions: 334
• Chapter 4 Existence domains of special families of holomorphic functions: 341
• 42 The OhsawaTakegoshi extension theorem: 388
• 43 The Skoda division theorem: 410
• 44 The CatlinHakimSibony theorem: 422
• 45 Structure of envelopes of holomorphy: 441
• List of symbols: 461
• Bibliography: 469
• Index: 483

Bibliographic information

• Title: Extension of Holomorphic Functions; Volume 34 of De Gruyter Expositions in Mathematics
• Authors: Marek Jarnicki, Peter Pflug
• Edition: reprint
• Publisher: Walter de Gruyter, 2011
• ISBN: 3110809788, 9783110809787
• Length: 497 pages
• Subjects: Mathematics / Calculus; Mathematics / General; Mathematics / Mathematical Analysis