Extension of Holomorphic Functions

Marek Jarnicki, Peter Pflug

• Publisher: De Gruyter
• Year: 2011
• Print ISBN:
  9783110153637
• eBook ISBN:
  9783110809787
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

No detailed description available for "Extension of Holomorphic Functions".

Table of contents

• Preface
• Chapter 1. Riemann domains
• 1.1 Riemann domains over ℂn
• 1.2 Holomorphic functions
• 1.3 Examples of Riemann regions
• 1.4 Holomorphic extension of Riemann domains
• 1.5 The boundary of a Riemann domain
• 1.6 Union, intersection, and direct limit of Riemann domains
• 1.7 Domains of existence
• 1.8 Maximal holomorphic extensions
• 1.9 Liftings of holomorphic mappings I
• 1.10 Holomorphic convexity
• 1.11 Riemann surfaces
• Chapter 2. Pseudoconvexity
• 2.1 Plurisubharmonic functions
• 2.2 Pseudoconvexity
• 2.3 The Kiselman minimum principle
• 2.4 [xxx]-operator
• 2.5 Solution of the Levi Problem
• 2.6 Regular solutions
• 2.7 Approximation
• 2.8 The Remmert embedding theorem
• 2.9 The Docquier-Grauert criteria
• 2.10 The division theorem
• 2.11 Spectrum
• 2.12 Liftings of holomorphic mappings II
• Chapter 3. Envelopes of holomorphy for special domains
• 3.1 Univalent envelopes of holomorphy
• 3.2 k-tubular domains
• 3.3 Matrix Reinhardt domains
• 3.4 The envelope of holomorphy of X\M
• 3.5 Separately holomorphic functions
• 3.6 Extension of meromorphic functions
• Chapter 4. Existence domains of special families of holomorphic functions
• 4.1 Special domains
• 4.2 The Ohsawa-Takegoshi extension theorem
• 4.3 The Skoda division theorem
• 4.4 The Catlin-Hakim-Sibony theorem
• 4.5 Structure of envelopes of holomorphy
• List of symbols
• Bibliography
• Index