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E-raamat: Extension of Holomorphic Functions

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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, Aix-Marseille Université, France 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 Urbaski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Botjan Gabrovek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Preface vii
Riemann domains
1(95)
Riemann domains over Cn
3(15)
Holomorphic functions
18(3)
Examples of Riemann regions
21(4)
Holomorphic extension of Riemann domains
25(4)
The boundary of a Riemann domain
29(10)
Union, Intersection, and direct limit of Riemann domains
39(11)
Domains of existence
50(4)
Maximal holomorphic extensions
54(8)
Liftings of holomorphic mappings I
62(13)
Holomorphic convexity
75(11)
Riemann surfaces
86(10)
Pseudoconvexity
96(139)
Plurisubharmonic functions
96(33)
Pseudoconvexity
129(24)
The Kiselman minimum principle
153(6)
∂-operator
159(18)
Solution of the Levi Problem
177(7)
Regular solutions
184(6)
Approximation
190(5)
The Remmert Embedding theorem
195(6)
The Deocquier-Grauert criteria
201(7)
The division theorem
208(11)
Spectrum
219(5)
Liftings of holomorphic mappings II
224(11)
Envelopes of holomorphy for special domains
235(106)
Univalent envelopes of holomorphy
235(23)
k-tubular domains
258(26)
Matrix Reinhardt domains
284(18)
The envelope of holomorphy of X \ M
302(22)
Separately holomorphic functions
324(10)
Extension of meromorphic functions
334(7)
Existence domains of special families of holomorphic functions
341(120)
Special domains
341(47)
The Ohsawa-Takegoshi extension theorem
388(22)
The Skoda division theorem
410(12)
The Catlin-Hakim-Sibony theorem
422(19)
Structure of envelopes of holomorphy
441(20)
List of symbols 461(8)
Bibliography 469(14)
Index 483