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An Introduction To Complex Analysis In Several Variables
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Book Synopsis An Introduction to Complex Analysis in Several Variables by : L. Hormander
Download or read book An Introduction to Complex Analysis in Several Variables written by L. Hormander and published by Elsevier. This book was released on 1973-02-12 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Complex Analysis in Several Variables
Book Synopsis Introduction to Complex Analysis in Several Variables by : Volker Scheidemann
Download or read book Introduction to Complex Analysis in Several Variables written by Volker Scheidemann and published by Springer Nature. This book was released on 2023 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analytic Functions of Several Complex Variables by : Robert Clifford Gunning
Download or read book Analytic Functions of Several Complex Variables written by Robert Clifford Gunning and published by American Mathematical Soc.. This book was released on 2009 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic and Complex Analysis in Several Variables by : Steven G. Krantz
Download or read book Harmonic and Complex Analysis in Several Variables written by Steven G. Krantz and published by Springer. This book was released on 2017-09-20 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tasty Bits of Several Complex Variables by : Jiri Lebl
Download or read book Tasty Bits of Several Complex Variables written by Jiri Lebl and published by Lulu.com. This book was released on 2016-05-05 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Holomorphic Functions and Integral Representations in Several Complex Variables by : R. Michael Range
Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elementary Theory of Analytic Functions of One or Several Complex Variables by : Henri Cartan
Download or read book Elementary Theory of Analytic Functions of One or Several Complex Variables written by Henri Cartan and published by Courier Corporation. This book was released on 2013-04-22 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Carlos A. Berenstein Publisher :Springer Science & Business Media ISBN 13 :9780387973494 Total Pages :694 pages Book Rating :4.9/5 (734 download)
Book Synopsis Complex Variables by : Carlos A. Berenstein
Download or read book Complex Variables written by Carlos A. Berenstein and published by Springer Science & Business Media. This book was released on 1991-05-23 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text gives an overview of the basic properties of holomorphic functions of one complex variable. Topics studied in this overview include a detailed description of differential forms, homotopy theory, and homology theory, as the analytic properties of holomorphic functions, the solvability of the inhomogeneous Cauchy-Riemann equation with emphasis on the notation of compact families, the theory of growth of subharmonic functions, and an introduction to the theory of sheaves, covering spaces and Riemann surfaces. To further illuminate the material, a large number of exercises of differing levels of difficulty have been added.
Book Synopsis Several Complex Variables by : H. Grauert
Download or read book Several Complex Variables written by H. Grauert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Complex Variables by : John W. Dettman
Download or read book Applied Complex Variables written by John W. Dettman and published by Courier Corporation. This book was released on 2012-05-07 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.
Book Synopsis Function Theory of Several Complex Variables by : Steven George Krantz
Download or read book Function Theory of Several Complex Variables written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 2001 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Complex Analysis by : Friedrich Haslinger
Download or read book Complex Analysis written by Friedrich Haslinger and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-20 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. Contents Complex numbers and functions Cauchy’s Theorem and Cauchy’s formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Fréchet spaces of holomorphic functions The -complex The twisted -complex and Schrödinger operators
Book Synopsis Methods of the Theory of Functions of Many Complex Variables by : Vasiliy Sergeyevich Vladimirov
Download or read book Methods of the Theory of Functions of Many Complex Variables written by Vasiliy Sergeyevich Vladimirov and published by Courier Corporation. This book was released on 2007-01-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Analysis by : Mariano Giaquinta
Download or read book Mathematical Analysis written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2012-08-31 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Embraces a broad range of topics in analysis requiring only a sound knowledge of calculus and the functions of one variable. * Filled with beautiful illustrations, examples, exercises at the end of each chapter, and a comprehensive index.
Author :Christine Laurent-Thiébaut Publisher :Springer Science & Business Media ISBN 13 :0857290304 Total Pages :255 pages Book Rating :4.8/5 (572 download)
Book Synopsis Holomorphic Function Theory in Several Variables by : Christine Laurent-Thiébaut
Download or read book Holomorphic Function Theory in Several Variables written by Christine Laurent-Thiébaut and published by Springer Science & Business Media. This book was released on 2010-09-09 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Three appendices on differential manifolds, sheaf theory and functional analysis make the book self-contained. Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. New concepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter. Clear and succinct, this book will appeal to post-graduate students, young researchers seeking an introduction to holomorphic function theory in several variables and lecturers seeking a concise book on the subject.
Book Synopsis Holomorphic Functions of Several Variables by : Ludger Kaup
Download or read book Holomorphic Functions of Several Variables written by Ludger Kaup and published by Walter de Gruyter. This book was released on 2011-05-09 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Book Synopsis Several Complex Variables by : Raghavan Narasimhan
Download or read book Several Complex Variables written by Raghavan Narasimhan and published by University of Chicago Press. This book was released on 1971 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramified domains over C . Topics discussed are Hartogs' theory, domains in holomorphy, and automorphism of bounded domains.
