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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.

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.

Topics In Several Complex Variables

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Author : Zair Ibragimov
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-21

Topics In Several Complex Variables written by Zair Ibragimov 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 2016-04-21 with Functional analysis categories.

This volume contains the proceedings of the Special Session on Several Complex Variables, which was held during the first USA-Uzbekistan Conference on Analysis and Mathematical Physics from May 20–23, 2014, at California State University, Fullerton. This volume covers a wide variety of topics in pluripotential theory, symplectic geometry and almost complex structures, integral formulas, holomorphic extension, and complex dynamics. In particular, the reader will find articles on Lagrangian submanifolds and rational convexity, multidimensional residues, S-parabolic Stein manifolds, Segre varieties, and the theory of quasianalytic functions.

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 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 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.

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.

Geometric Harmonic Analysis Iv

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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-07-09

Geometric Harmonic Analysis Iv written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-09 with Mathematics categories.

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Traditionally, the label “Calderón-Zygmund theory” has been applied to a distinguished body of works primarily pertaining to the mapping properties of singular integral operators on Lebesgue spaces, in various geometric settings. Volume IV amounts to a versatile Calderón-Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries, considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.

Aspects Of Complex Analysis Differential Geometry Mathematical Physics And Applications Proceedings Of The Fourth International Workshop On Complex Structures And Vector Fields

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Author : Stancho Dimiev
language : en
Publisher: World Scientific
Release Date : 1999-09-17

Aspects Of Complex Analysis Differential Geometry Mathematical Physics And Applications Proceedings Of The Fourth 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 1999-09-17 with Mathematics categories.

This volume constitutes the proceedings of a workshop whose main purpose was to exchange information on current topics in complex analysis, differential geometry, mathematical physics and applications, and to group aspects of new mathematics.

The Bochner Martinelli Integral And Its Applications

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