First Steps In Several Complex Variables
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First Steps In Several Complex Variables
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Author : Marek Jarnicki
language : en
Publisher: European Mathematical Society
Release Date : 2008
First Steps In Several Complex Variables written by Marek Jarnicki and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book provides a comprehensive introduction to the field of several complex variables in the setting of a very special but basic class of domains, the so-called Reinhardt domains. In this way the reader may learn much about this area without encountering too many technical difficulties. Chapter 1 describes the fundamental notions and the phenomenon of simultaneous holomorphic extension. Chapter 2 presents a fairly complete discussion of biholomorphisms of bounded (complete) Reinhardt domains in the two dimensional case. The third chapter gives a classification of Reinhardt domains of existence for the most important classes of holomorphic functions. The last chapter deals with invariant functions and gives explicit calculations of many of them on certain Reinhardt domains. Numerous exercises are included to help the readers with their understanding of the material. Further results and open problems are added which may be useful as seminar topics. The primary aim of this book is to introduce students or non-experts to some of the main research areas in several complex variables. The book provides a friendly invitation to this field as the only prerequisite is a basic knowledge of analysis.
Basic Oka Theory In Several Complex Variables
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Author : Junjiro Noguchi
language : en
Publisher: Springer Nature
Release Date : 2024-07-19
Basic Oka Theory In Several Complex Variables written by Junjiro Noguchi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-19 with Mathematics categories.
This book provides a new, comprehensive, and self-contained account of Oka theory as an introduction to function theory of several complex variables, mainly concerned with the Three Big Problems (Approximation, Cousin, Pseudoconvexity) that were solved by Kiyoshi Oka and form the basics of the theory. The purpose of the volume is to serve as a textbook in lecture courses right after complex function theory of one variable. The presentation aims to be readable and enjoyable both for those who are beginners in mathematics and for researchers interested in complex analysis in several variables and complex geometry. The nature of the present book is evinced by its approach following Oka’s unpublished five papers of 1943 with his guiding methodological principle termed the “Joku-Iko Principle”, where historically the Pseudoconvexity Problem (Hartogs, Levi) was first solved in all dimensions, even for unramified Riemann domains as well. The method that is used in the book is elementary and direct, not relying on the cohomology theory of sheaves nor on the L2-∂-bar method, but yet reaches the core of the theory with the complete proofs. Two proofs for Levi’s Problem are provided: One is Oka’s original with the Fredholm integral equation of the second kind combined with the Joku-Iko Principle, and the other is Grauert’s by the well-known “bumping-method” with L. Schwartz’s Fredholm theorem, of which a self-contained, rather simple and short proof is given. The comparison of them should be interesting even for specialists. In addition to the Three Big Problems, other basic material is dealt with, such as Poincaré’s non-biholomorphism between balls and polydisks, the Cartan–Thullen theorem on holomorphic convexity, Hartogs’ separate analyticity, Bochner’s tube theorem, analytic interpolation, and others. It is valuable for students and researchers alike to look into the original works of Kiyoshi Oka, which are not easy to find in books or monographs.
Several Complex Variables Part 1
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Author : Raymond O'Neil Wells
language : en
Publisher: American Mathematical Soc.
Release Date : 1977
Several Complex Variables Part 1 written by Raymond O'Neil Wells and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.
Contains sections on Singularities of analytic spaces, Function theory and real analysis, Compact complex manifolds, and Survey papers.
Several Complex Variables
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Author : Michael Schneider
language : en
Publisher: Cambridge University Press
Release Date : 1999
Several Complex Variables written by Michael Schneider and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.
Function Theory Of Several Complex Variables
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Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Function Theory Of Several Complex Variables written by Steven George Krantz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
Theory Of Analytic Functions Of Several Complex Variables
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Author : Boris Abramovich Fuks
language : en
Publisher: American Mathematical Soc.
Release Date : 1963
Theory Of Analytic Functions Of Several Complex Variables written by Boris Abramovich Fuks and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematics categories.
Fourier Analysis In Several Complex Variables
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Author : Leon Ehrenpreis
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
Fourier Analysis In Several Complex Variables written by Leon Ehrenpreis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.
Tasty Bits Of Several Complex Variables
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Author : Jiri Lebl
language : en
Publisher: Lulu.com
Release Date : 2016-05-05
Tasty Bits Of Several Complex Variables written by Jiri Lebl and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Science categories.
This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.
L2 Approaches In Several Complex Variables
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Author : Takeo Ohsawa
language : en
Publisher: Springer
Release Date : 2018-11-28
L2 Approaches In Several Complex Variables written by Takeo Ohsawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Mathematics categories.
This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the L2 extension of holomorphic functions in the past 5 years.In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L2 method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka–Cartan theory is given by this method. The L2 extension theorem with an optimal constant is included, obtained recently by Z. Błocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, Guan–Zhou, and Berndtsson–Lempert. Most of these results are obtained by the L2 method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L2 method obtained during the past 15 years.
Several Complex Variables And Complex Geometry Part I
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Author : Eric Bedford
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Several Complex Variables And Complex Geometry Part I written by Eric Bedford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.