Multidimensional Integral Representations
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Multidimensional Integral Representations
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Author : Alexander M. Kytmanov
language : en
Publisher: Springer
Release Date : 2015-09-09
Multidimensional Integral Representations written by Alexander M. Kytmanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.
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.
Integral Representations And Residues In Multidimensional Complex Analysis
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Author : Lev Abramovich Aĭzenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Integral Representations And Residues In Multidimensional Complex Analysis written by Lev Abramovich Aĭzenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
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.
The Bochner Martinelli Integral And Its Applications
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Author : Alexander M. Kytmanov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Bochner Martinelli Integral And Its Applications written by Alexander M. Kytmanov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Holomorphic Functions And Integral Representations In Several Complex Variables
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Author : R. Michael Range
language : en
Publisher: Springer
Release Date : 2010-12-01
Holomorphic Functions And Integral Representations In Several Complex Variables written by R. Michael Range and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Mathematics categories.
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.
The Bochner Martinelli Integral And Its Applications
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Author : A. M. Kytmanov
language : en
Publisher:
Release Date : 1995
The Bochner Martinelli Integral And Its Applications written by A. M. Kytmanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Calculus categories.
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.
Integral Representation And The Computation Of Combinatorial Sums
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Author : G. P. Egorychev
language : en
Publisher: American Mathematical Soc.
Release Date : 1984-12-31
Integral Representation And The Computation Of Combinatorial Sums written by G. P. Egorychev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Mathematics categories.
This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.
Multidimensional Integral Transformations
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Author :
language : en
Publisher: CRC Press
Release Date : 1992
Multidimensional Integral Transformations written by and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
A cross between a textbook and a monograph, this extensive introduction discusses all of the most important transformations, compiling information otherwise scattered throughout the literature. Attention is concentrated on the operational calculus of the major integral transformations and some of its applications, with an investigation of transforms in spaces of functions and of distributions. Annotation copyrighted by Book News, Inc., Portland, OR
Integral Representations
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Author : I. Reiner
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1979-10
Integral Representations written by I. Reiner and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-10 with Mathematics categories.
Integral Representations For Spatial Models Of Mathematical Physics
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Author : Vladislav V Kravchenko
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Integral Representations For Spatial Models Of Mathematical Physics written by Vladislav V Kravchenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This book provides a new mathematical theory for the treatment of an ample series of spatial problems of electrodynamics, particle physics, quantum mechanics and elasticity theory. This technique proves to be as powerful for solving the spatial problems of mathematical physics as complex analysis is for solving planar problems. The main analytic tool of the book, a non-harmonic version of hypercomplex analysis recently developed by the authors, is presented in detail. There are given applications of this theory to the boundary value problems of electrodynamics and elasticity theory as well as to the problem of quark confinement. A new approach to the linearization of special classes of the self-duality equation is also considered. Detailed proofs are given throughout. The book contains an extensive bibliography on closely related topics. This book will be of particular interest to academic and professional specialists and students in mathematics and physics who are interested in integral representations for partial differential equations. The book is self-contained and could be used as a main reference for special course seminars on the subject.
Multidimensional Systems Theory And Applications
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Author : N.K. Bose
language : en
Publisher: Springer
Release Date : 2013-12-20
Multidimensional Systems Theory And Applications written by N.K. Bose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Technology & Engineering categories.
The Second Edition of this book includes an abundance of examples to illustrate advanced concepts and brings out in a text book setting the algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. Algorithms and their implementation using symbolic algebra are emphasized.