Extension of Holomorphic Functions 2nd Edition by Marek Jarnicki, Peter Pflug 3110627695 9783110627695

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ISBN 10: 3110627695 

ISBN 13: 9783110627695

Author: Marek Jarnicki, Peter Pflug 

This second extended edition of the classic reference on the extension problem of holomorphic functions in pluricomplex analysis contains a wealth of additional material, organized under the original chapter structure, and covers in a self-contained way all new and recent developments and theorems that appeared since the publication of the first edition about twenty years ago.

Extension of Holomorphic Functions 2nd Table of contents:

1 Riemann domains
1.1 Riemann domains over ℂn
1.2 Holomorphic functions
1.2.1 Pointwise vs. locally uniform convergence
1.2.2 Non-natural Fréchet spaces
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
1.6.1 The union of Riemann domains
1.6.2 The kernel of Riemann domains
1.6.3 The direct limit of Riemann domains
1.7 Domains of existence
1.8 Maximal holomorphic extensions
1.9 Liftings of holomorphic mappings I
1.9.1 Action of a Lie group
1.9.2 Reinhardt domains
1.10 Holomorphic convexity
1.11 Riemann surfaces
1.12 List of problems
2 Pseudoconvexity
2.1 Plurisubharmonic functions
2.1.1 Relative extremal function
2.2 Pseudoconvexity
2.3 The Kiselman minimum principle
2.4 ∂‾-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 Jöricke’s envelope of holomorphy
2.11 The division theorem
2.12 Spectrum
2.13 Liftings of holomorphic mappings II
2.13.1 Hausdorff measures
2.13.2 Proper mappings
2.14 List of problems
3 Envelopes of holomorphy for special domains
3.1 Univalent envelopes of holomorphy
3.2 Jupiter’s theorem
3.3 k-tubular domains
3.3.1 Shilov and Bergman boundaries
3.4 Matrix Reinhardt domains
3.4.1 Extended tube conjecture
3.5 The envelope of holomorphy of X∖M
3.5.1 Analytic sets
3.5.2 Singular sets
3.5.3 The Dloussky theorem
3.5.4 Reduction procedures
3.5.5 Oka theorem
3.5.6 Hartogs theorem
3.5.7 The proof of the case n=2
3.6 Extension of meromorphic functions
3.6.1 Porten’s proof of Dloussky’s theorem
3.7 Separately holomorphic functions
3.8 Generalized cross theorem
3.8.1 N-fold crosses
3.8.2 Cross theorems
3.8.3 Cross theorems with singularities
3.9 List of problems
4 Existence domains of special families of holomorphic functions
4.1 Special domains
4.1.1 ℋ∞-domains in the plane
4.1.2 Lh2-domains of holomorphy in the plane
4.1.3 Reinhardt domains
4.1.4 Balanced domains
4.1.5 Hartogs domains
4.1.6 Semitubular domains
4.1.7 Non-schlicht ℋ∞-envelopes of holomorphy
4.2 The Ohsawa–Takegoshi extension theorem
Calculation to get the estimate in Lemma
4.3 The Skoda division theorem
4.4 The Catlin–Hakim–Sibony theorem
4.5 Structure of envelopes of holomorphy
4.6 List of problems
5 List of problems
Chapter 1
Chapter 2
Chapter 3
Chapter 4

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Tags: Extension, Holomorphic Functions, Marek Jarnicki, Peter Pflug