An Introduction to Complex Analysis in Several Variables

An Introduction to Complex Analysis in Several Variables
Title An Introduction to Complex Analysis in Several Variables PDF eBook
Author L. Hormander
Publisher Elsevier
Pages 227
Release 1973-02-12
Genre Mathematics
ISBN 0444105239

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An Introduction to Complex Analysis in Several Variables

Introduction to Complex Analysis in Several Variables

Introduction to Complex Analysis in Several Variables
Title Introduction to Complex Analysis in Several Variables PDF eBook
Author Volker Scheidemann
Publisher Springer Nature
Pages 239
Release 2023
Genre Functions of complex variables
ISBN 3031264282

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This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.

Analytic Functions of Several Complex Variables

Analytic Functions of Several Complex Variables
Title Analytic Functions of Several Complex Variables PDF eBook
Author Robert Clifford Gunning
Publisher American Mathematical Soc.
Pages 338
Release 2009
Genre Mathematics
ISBN 0821821652

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The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.

Harmonic and Complex Analysis in Several Variables

Harmonic and Complex Analysis in Several Variables
Title Harmonic and Complex Analysis in Several Variables PDF eBook
Author Steven G. Krantz
Publisher Springer
Pages 429
Release 2017-09-20
Genre Mathematics
ISBN 3319632310

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Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

Elementary Theory of Analytic Functions of One or Several Complex Variables

Elementary Theory of Analytic Functions of One or Several Complex Variables
Title Elementary Theory of Analytic Functions of One or Several Complex Variables PDF eBook
Author Henri Cartan
Publisher Courier Corporation
Pages 242
Release 2013-04-22
Genre Mathematics
ISBN 0486318672

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Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.

Tasty Bits of Several Complex Variables

Tasty Bits of Several Complex Variables
Title Tasty Bits of Several Complex Variables PDF eBook
Author Jiri Lebl
Publisher Lulu.com
Pages 142
Release 2016-05-05
Genre Science
ISBN 1365095576

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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.

Holomorphic Functions and Integral Representations in Several Complex Variables

Holomorphic Functions and Integral Representations in Several Complex Variables
Title Holomorphic Functions and Integral Representations in Several Complex Variables PDF eBook
Author R. Michael Range
Publisher Springer Science & Business Media
Pages 405
Release 2013-03-09
Genre Mathematics
ISBN 1475719183

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The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.