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The Bochner Martinelli Integral And Its Applications

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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.

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.

Some Applications Of The Bochner Martinelli Integral

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Author : A. M. Kytmanov
language : en
Publisher:
Release Date : 1999

Some Applications Of The Bochner Martinelli Integral 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 1999 with Bochner-Martinelli representation formula categories.

Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations

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Author : A S A Mshimba
language : en
Publisher: World Scientific
Release Date : 1995-10-17

Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations written by A S A Mshimba and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-17 with categories.

These proceedings concentrate on recent results in the following fields of complex analysis: complex methods for solving boundary value problems with piecewise smooth boundary data, complex methods for linear and nonlinear differential equations and systems of second order, and applications of scales of Banach spaces to initial value problems.Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed.Particular emphasis is placed on Symbolic Computation in Complex Analysis and on the new approaches to teach mathematical analysis based on interactions between complex analysis and partial differential equations.

Integral Theorems For Functions And Differential Forms In C M

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Author : Reynaldo Rocha-Chavez
language : en
Publisher: CRC Press
Release Date : 2001-08-03

Integral Theorems For Functions And Differential Forms In C M written by Reynaldo Rocha-Chavez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-03 with Mathematics categories.

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

Geometric Theory Of Generalized Functions With Applications To General Relativity

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Author : M. Grosser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Geometric Theory Of Generalized Functions With Applications To General Relativity written by M. Grosser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.

Topics In Complex Analysis Differential Geometry And Methematical Physics Proceedings Of The Third International Workshop On Complex Structures And Vector Fields

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Author : Stancho Dimiev
language : en
Publisher: World Scientific
Release Date : 1997-07-01

Topics In Complex Analysis Differential Geometry And Methematical Physics Proceedings Of The Third International Workshop On Complex Structures And Vector Fields written by Stancho Dimiev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-01 with categories.

The Third International Workshop on Complex Structures and Vector Fields was held to exchange information on current topics in complex analysis, differential geometry and mathematical physics, and to find new subjects in these fields.This volume contains many interesting and important articles in complex analysis (including quaternionic analysis), functional analysis, topology, differential geometry (hermitian geometry, surface theory), and mathematical physics (quantum mechanics, hamilton mechanics).

Linear Functional Equations Operator Approach

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Author : Anatolij Antonevich
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Linear Functional Equations Operator Approach written by Anatolij Antonevich 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.

In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ ual representatives are related with problems arising in various areas of mathemat ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au tomorphisms of Banach algebras, and other problems.

Integral Representations For Spatial Models Of Mathematical Physics

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Author : Vladislav V Kravchenko
language : en
Publisher: CRC Press
Release Date : 2020-11-25

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 2020-11-25 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 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.

The Bochner Martinelli Integral And Its Applications

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