Methods Of The Theory Of Functions Of Many Complex Variables

Author : Vasiliy Sergeyevich Vladimirov,Scripta Technica
Publisher : Courier Corporation
Page : 370 pages
File Size : 53,6 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 9780486458120

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Methods of the Theory of Functions of Many Complex Variables by Vasiliy Sergeyevich Vladimirov,Scripta Technica Pdf

This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.

Author : Vasiliĭ Sergeevich Vladimirov
Publisher : Unknown
Page : 128 pages
File Size : 44,7 Mb
Release : 2024-06-03
Category : Functions of complex variables
ISBN : OCLC:844347992

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Methods of the theory of functions of many complex variables by Vasiliĭ Sergeevich Vladimirov Pdf

Author : V. S. Vladimiroff
Publisher : MIT Press (MA)
Page : 384 pages
File Size : 52,6 Mb
Release : 1966-11-15
Category : Mathematics
ISBN : 0262220091

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Methods of the Theory of Functions of Several Complex Variables by V. S. Vladimiroff Pdf

Author : George F. Carrier,Max Krook,Carl E. Pearson
Publisher : SIAM
Page : 451 pages
File Size : 49,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0898719119

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Functions of a Complex Variable by George F. Carrier,Max Krook,Carl E. Pearson Pdf

Functions of a complex variable are used to solve applications in various branches of mathematics, science, and engineering. Functions of a Complex Variable: Theory and Technique is a book in a special category of influential classics because it is based on the authors' extensive experience in modeling complicated situations and providing analytic solutions. The book makes available to readers a comprehensive range of these analytical techniques based upon complex variable theory. Advanced topics covered include asymptotics, transforms, the Wiener-Hopf method, and dual and singular integral equations. The authors provide many exercises, incorporating them into the body of the text. Audience: intended for applied mathematicians, scientists, engineers, and senior or graduate-level students who have advanced knowledge in calculus and are interested in such subjects as complex variable theory, function theory, mathematical methods, advanced engineering mathematics, and mathematical physics.

Author : Alekseĭ Georgievich Sveshnikov,Andreĭ Nikolaevich Tikhonov
Publisher : Unknown
Page : 344 pages
File Size : 41,9 Mb
Release : 1978
Category : Functions of complex variables
ISBN : OSU:32435017113325

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The Theory of Functions of a Complex Variable by Alekseĭ Georgievich Sveshnikov,Andreĭ Nikolaevich Tikhonov Pdf

The complex variable and functions of a complex variable; Series of analytical functions; Analytic continuation elementary; The laurent series and isolated singular points; Residues and their applications; Conformal mapping; Analytic-functions in the solutions of boundary-value problems; Fundamentals of operational calculus; Saddle-point method; The wiener-hopf method; Functions of many complex variables.

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 51,9 Mb
Release : 2001
Category : Functions of several complex variables
ISBN : 9780821827246

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Function Theory of Several Complex Variables by Steven George Krantz Pdf

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.

Author : Toshio Nishino
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 45,5 Mb
Release : 2001
Category : Mathematics
ISBN : 0821808168

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Function Theory in Several Complex Variables by Toshio Nishino Pdf

'Kiyoshi Oka, at the beginning of his research, regarded the collection of problems which he encountered in the study of domains of holomorphy as large mountains which separate today and tomorrow. Thus, he believed that there could be no essential progress in analysis without climbing over these mountains ... this book is a worthwhile initial step for the reader in order to understand the mathematical world which was created by Kiyoshi Oka.' -- from the Preface. This book explains results in the theory of functions of several complex variables which were mostly established from the late nineteenth century through to the middle of the twentieth century. In the work, the author introduces the mathematical world created by his advisor, Kiyoshi Oka. In this volume, Oka's work is divided into two parts. The first is the study of analytic functions in univalent domains in ${\mathbf C}n$. Here Oka proved that three concepts are equivalent: domains of holomorphy, holomorphically convex domains, and pseudoconvex domains; and moreover that the Poincaré problem, the Cousin problems, and the Runge problem, when stated properly, can be solved in domains of holomorphy satisfying the appropriate conditions. The second part of Oka's work established a method for the study of analytic functions defined in a ramified domain over ${\mathbf C}n$ in which the branch points are considered as interior points of the domain. Here analytic functions in an analytic space are treated, which is a slight generalization of a ramified domain over ${\mathbf C}n$. In writing the book, the author's goal was to bring to readers a real understanding of Oka's original papers. This volume is an English translation of the original Japanese edition, published by the University of Tokyo Press (Japan). It would make a suitable course text for advanced graduate level introductions to several complex variables.

Author : Marston Morse
Publisher : Princeton University Press
Page : 145 pages
File Size : 44,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882342

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Topological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15 by Marston Morse Pdf

The description for this book, Topological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15, will be forthcoming.

Author : Robert C. Gunning,Hugo Rossi
Publisher : American Mathematical Society
Page : 334 pages
File Size : 48,5 Mb
Release : 2022-08-25
Category : Mathematics
ISBN : 9781470470661

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Analytic Functions of Several Complex Variables by Robert C. Gunning,Hugo Rossi Pdf

The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.

Author : Boris A. Fuks
Publisher : Unknown
Page : 412 pages
File Size : 53,8 Mb
Release : 1965
Category : Functions of complex variables
ISBN : UOM:39015017131999

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Introduction to the Theory of Analytic Functions of Several Complex Variables by Boris A. Fuks Pdf

Author : H. Grauert,K. Fritzsche
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461298748

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Several Complex Variables by H. Grauert,K. Fritzsche Pdf

The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology theory, and the real methods which stem from elliptic partial differential equations. In the first chapter we begin with the definition of holomorphic functions of several variables, their representation by the Cauchy integral, and their power series expansion on Reinhardt domains. It turns out that, in l:ontrast ~ 2 there exist domains G, G c en to the theory of a single variable, for n with G c G and G "# G such that each function holomorphic in G has a continuation on G. Domains G for which such a G does not exist are called domains of holomorphy. In Chapter 2 we give several characterizations of these domains of holomorphy (theorem of Cartan-Thullen, Levi's problem). We finally construct the holomorphic hull H(G} for each domain G, that is the largest (not necessarily schlicht) domain over en into which each function holomorphic on G can be continued.

Author : R. Michael Range
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 41,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719185

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Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range Pdf

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.

Author : Giovanni Sansone
Publisher : Unknown
Page : 506 pages
File Size : 42,9 Mb
Release : 1960
Category : Functions of complex variables
ISBN : UCR:31210010463683

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Lectures on the Theory of Functions of a Complex Variable: Holomorphic functions by Giovanni Sansone Pdf

Author : Marston Morse
Publisher : Princeton University Press
Page : 152 pages
File Size : 43,5 Mb
Release : 1948-01-20
Category : Mathematics
ISBN : 9780691095028

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Topological Methods in the Theory of Functions of a Complex Variable by Marston Morse Pdf

A classic treatment of topological methods in the theory of functions of a complex variable from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Author : John Wermer
Publisher : Springer Science & Business Media
Page : 169 pages
File Size : 46,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475738780

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Banach Algebras and Several Complex Variables by John Wermer Pdf

During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n > I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.