Holomorphic Functions And Integral Representations In Several Complex Variables

Author : R. Michael Range
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 46,5 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 : Rolf Michael Range
Publisher : Unknown
Page : 388 pages
File Size : 50,6 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:1088189787

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

Author : Lev Abramovich Aĭzenberg,Aleksandr Petrovich I︠U︡zhakov
Publisher : American Mathematical Soc.
Page : 283 pages
File Size : 49,9 Mb
Release : 1983
Category : Mathematics
ISBN : 9780821815502

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Integral Representations and Residues in Multidimensional Complex Analysis by Lev Abramovich Aĭzenberg,Aleksandr Petrovich I︠U︡zhakov Pdf

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,Simona G. Myslivets
Publisher : Springer
Page : 225 pages
File Size : 47,6 Mb
Release : 2015-09-09
Category : Mathematics
ISBN : 9783319216591

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Multidimensional Integral Representations by Alexander M. Kytmanov,Simona G. Myslivets Pdf

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 Publishing Company
Page : 376 pages
File Size : 47,7 Mb
Release : 2007-03-21
Category : Mathematics
ISBN : 9789813106901

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Several Complex Variables and Integral Formulas by Kenzo Adachi Pdf

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,Scripta Technica
Publisher : Courier Corporation
Page : 370 pages
File Size : 41,5 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 : Jiri Lebl
Publisher : Lulu.com
Page : 142 pages
File Size : 49,6 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781365095573

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Tasty Bits of Several Complex Variables by Jiri Lebl Pdf

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.

Author : L a Aizenberg
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 50,6 Mb
Release : 2000-04-30
Category : Mathematics
ISBN : 9780821813485

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Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties by L a Aizenberg Pdf

The authors consider the problem of characterizing the exterior differential forms which are orthogonal to holomorphic functions (or forms) in a domain $D\subset {\mathbf C}^n$ with respect to integration over the boundary, and some related questions. They give a detailed account of the derivation of the Bochner-Martinelli-Koppelman integral representation of exterior differential forms, which was obtained in 1967 and has already found many important applications. They study the properties of $\overline \partial$-closed forms of type $(p, n - 1), 0\leq p\leq n - 1$, which turn out to be the duals (with respect to the orthogonality mentioned above) to holomorphic functions (or forms) in several complex variables, and resemble holomorphic functions of one complex variable in their properties.

Author : Christine Laurent-Thiébaut
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 52,6 Mb
Release : 2010-09-09
Category : Mathematics
ISBN : 9780857290304

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Holomorphic Function Theory in Several Variables by Christine Laurent-Thiébaut Pdf

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 : R Michael Range
Publisher : World Scientific Publishing Company
Page : 372 pages
File Size : 41,6 Mb
Release : 2015-08-20
Category : Mathematics
ISBN : 9789814644501

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What is Calculus? by R Michael Range Pdf

This unique book provides a new and well-motivated introduction to calculus and analysis, historically significant fundamental areas of mathematics that are widely used in many disciplines. It begins with familiar elementary high school geometry and algebra, and develops important concepts such as tangents and derivatives without using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject. This simple algebraic method is a modern version of an idea that goes back to René Descartes and that has been largely forgotten. Moving beyond algebra, the need for new analytic concepts based on completeness, continuity, and limits becomes clearly visible to the reader while investigating exponential functions. The author carefully develops the necessary foundations while minimizing the use of technical language. He expertly guides the reader to deep fundamental analysis results, including completeness, key differential equations, definite integrals, Taylor series for standard functions, and the Euler identity. This pioneering book takes the sophisticated reader from simple familiar algebra to the heart of analysis. Furthermore, it should be of interest as a source of new ideas and as supplementary reading for high school teachers, and for students and instructors of calculus and analysis.

Author : Reynaldo Rocha-Chavez,Michael Shapiro,Frank Sommen
Publisher : CRC Press
Page : 216 pages
File Size : 49,6 Mb
Release : 2001-08-03
Category : Mathematics
ISBN : 9781420035513

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Integral Theorems for Functions and Differential Forms in C(m) by Reynaldo Rocha-Chavez,Michael Shapiro,Frank Sommen Pdf

The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories. The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory. That is, they sought a reproducing kernel for the whole class that is universal and from same class. Integral Theorems for Functions and Differential Forms in Cm documents their success. Their highly original approach allowed them to obtain new results and refine some well-known results from the classical theory of several complex variables. The 'hyperholomorphic" theory they developed proved to be a kind of direct sum of function theories for two Dirac-type operators of Clifford analysis considered in the same domain. In addition to new results and methods, this work presents a first-look at a brand new setting, based upon the natural language of differential forms, for complex analysis. Integral Theorems for Functions and Differential Forms in Cm reveals a deep link between the fields of several complex variables theory and Clifford analysis. It will have a strong influence on researchers in both areas, and undoubtedly will change the general viewpoint on the methods and ideas of several complex variables theory.

Author : So-chin Chen,Mei-Chi Shaw
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 51,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0821829610

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Partial Differential Equations in Several Complex Variables by So-chin Chen,Mei-Chi Shaw Pdf

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 : Alexander M. Kytmanov
Publisher : Birkhäuser
Page : 318 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890946

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The Bochner-Martinelli Integral and Its Applications by Alexander M. Kytmanov Pdf

The Bochner-Martinelli integral representation for holomorphic functions or'sev eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's. It was the first essen tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n > 1, the Bochner-Martinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the Bochner-Martinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood Brown) on removability of compact singularities of holomorphic functions in en when n > 1. In the 1950's and 1960's, only isolated works appeared that studied the boundary behavior of Bochner-Martinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the Bochner-Martinelli integral being the sum of a double-layer potential and the tangential derivative of a single-layer potential. Therefore the Bochner-Martinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the double-layer potential. Thus, the Bochner-Martinelli integral combines properties of the Cauchy integral and the double-layer potential.

Author : Henri Cartan
Publisher : Courier Corporation
Page : 242 pages
File Size : 45,7 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486318677

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Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan Pdf

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 : Kehe Zhu
Publisher : Springer
Page : 0 pages
File Size : 51,6 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387501398

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Spaces of Holomorphic Functions in the Unit Ball by Kehe Zhu Pdf

Can be used as a graduate text Contains many exercises Contains new results