Holomorphic Functions And Integral Representations In Several Complex Variables PDF Download
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Author | : R. Michael Range |
Publisher | : Springer Science & Business Media |
Total Pages | : 405 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475719183 |
Download Holomorphic Functions and Integral Representations in Several Complex Variables Book in PDF, ePub and Kindle
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 | : Rolf Michael Range |
Publisher | : |
Total Pages | : 388 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Holomorphic Functions and Integral Representations in Several Complex Variables Book in PDF, ePub and Kindle
Author | : Lev Abramovich Aĭzenberg |
Publisher | : American Mathematical Soc. |
Total Pages | : 296 |
Release | : 1983 |
Genre | : Mathematics |
ISBN | : 0821815504 |
Download Integral Representations and Residues in Multidimensional Complex Analysis Book in PDF, ePub and Kindle
This book deals with integral representations of holomorphic functions of several complex variables, the multidimensional logarithmic residue, and the theory of multidimensional residues. Applications are given to implicit function theory, systems of nonlinear equations, computation of the multiplicity of a zero of a mapping, and computation of combinatorial sums in closed form. Certain applications in multidimensional complex analysis are considered. The monograph is intended for specialists in theoretical and applied mathematics and theoretical physics, and for postgraduate and graduate students interested in multidimensional complex analysis or its applications.
Author | : Alexander M. Kytmanov |
Publisher | : Springer |
Total Pages | : 236 |
Release | : 2015-09-09 |
Genre | : Mathematics |
ISBN | : 3319216597 |
Download Multidimensional Integral Representations Book in PDF, ePub and Kindle
The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.
Author | : Kenzo Adachi |
Publisher | : World Scientific |
Total Pages | : 377 |
Release | : 2007 |
Genre | : Science |
ISBN | : 9812705740 |
Download Several Complex Variables and Integral Formulas Book in PDF, ePub and Kindle
This volume is an introductory text in several complex variables, using methods of integral representations and Hilbert space theory. It investigates mainly the studies of the estimate of solutions of the Cauchy?Riemann equations in pseudoconvex domains and the extension of holomorphic functions in submanifolds of pseudoconvex domains which were developed in the last 50 years. We discuss the two main studies mentioned above by two different methods: the integral formulas and the Hilbert space techniques. The theorems concerning general pseudoconvex domains are analyzed using Hilbert space theory, and the proofs for theorems concerning strictly pseudoconvex domains are solved using integral representations.This volume is written in a self-contained style, so that the proofs are easily accessible to beginners. There are exercises featured at the end of each chapter to aid readers to better understand the materials of this volume. Fairly detailed hints are articulated to solve these exercises.
Author | : Kenzo Adachi |
Publisher | : World Scientific Publishing Company |
Total Pages | : 377 |
Release | : 2007-03-21 |
Genre | : Mathematics |
ISBN | : 9813106905 |
Download Several Complex Variables And Integral Formulas Book in PDF, ePub and Kindle
This volume is an introductory text in several complex variables, using methods of integral representations and Hilbert space theory. It investigates mainly the studies of the estimate of solutions of the Cauchy-Riemann equations in pseudoconvex domains and the extension of holomorphic functions in submanifolds of pseudoconvex domains which were developed in the last 50 years. We discuss the two main studies mentioned above by two different methods: the integral formulas and the Hilbert space techniques. The theorems concerning general pseudoconvex domains are analyzed using Hilbert space theory, and the proofs for theorems concerning strictly pseudoconvex domains are solved using integral representations.This volume is written in a self-contained style, so that the proofs are easily accessible to beginners. There are exercises featured at the end of each chapter to aid readers to better understand the materials of this volume. Fairly detailed hints are articulated to solve these exercises.
Author | : Vasiliy Sergeyevich Vladimirov |
Publisher | : Courier Corporation |
Total Pages | : 370 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 0486458121 |
Download Methods of the Theory of Functions of Many Complex Variables Book in PDF, ePub and Kindle
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 | : Christine Laurent-Thiébaut |
Publisher | : Springer Science & Business Media |
Total Pages | : 255 |
Release | : 2010-09-09 |
Genre | : Mathematics |
ISBN | : 0857290304 |
Download Holomorphic Function Theory in Several Variables Book in PDF, ePub and Kindle
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.
Author | : So-chin Chen |
Publisher | : American Mathematical Soc. |
Total Pages | : 396 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9780821829615 |
Download Partial Differential Equations in Several Complex Variables Book in PDF, ePub and Kindle
This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.
Author | : Henri Cartan |
Publisher | : Courier Corporation |
Total Pages | : 242 |
Release | : 2013-04-22 |
Genre | : Mathematics |
ISBN | : 0486318672 |
Download Elementary Theory of Analytic Functions of One or Several Complex Variables Book in PDF, ePub and Kindle
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.