Integral Representations and Residues in Multidimensional Complex Analysis
Integral Representations and Residues in Multidimensional Complex Analysis

Author: Lev Abramovich Aĭzenberg

Publisher: American Mathematical Soc.

Published: 1983

Total Pages: 296

ISBN-13: 0821815504

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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.

Multidimensional Integral Representations
Multidimensional Integral Representations

Author: Alexander M. Kytmanov

Publisher: Springer

Published: 2015-09-09

Total Pages: 236

ISBN-13: 3319216597

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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.

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

Author: Stancho Dimiev

Publisher: World Scientific

Published: 1999-09-17

Total Pages: 382

ISBN-13: 9814543756

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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.

Introduction to Complex Analysis
Introduction to Complex Analysis

Author: E.M. Chirka

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 252

ISBN-13: 3642615252

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From the reviews: "... In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; ...for the appropriate reader, they will be valuable sources of information about modern complex analysis." Bulletin of the Am.Math.Society, 1991 "... This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables." ZAMP, Zeitschrift für Angewandte Mathematik und Physik, 1990

Complex Analysis and Dynamical Systems III
Complex Analysis and Dynamical Systems III

Author: Mark Lʹvovich Agranovskiĭ

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 482

ISBN-13: 0821841505

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The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

Identities of Algebras and their Representations
Identities of Algebras and their Representations

Author: I︠U︡riĭ Pitrimovich Razmyslov

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 468

ISBN-13: 9780821846087

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During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and *a-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and *a-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.

Encyclopaedia of Mathematics
Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 549

ISBN-13: 9401512353

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This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

The Handbook of Integration
The Handbook of Integration

Author: Daniel Zwillinger

Publisher: CRC Press

Published: 1992-11-02

Total Pages: 385

ISBN-13: 1439865841

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This book is a compilation of the most important and widely applicable methods for evaluating and approximating integrals. It is an indispensable time saver for engineers and scientists needing to evaluate integrals in their work. From the table of contents: - Applications of Integration - Concepts and Definitions - Exact Analytical Methods - Appro

Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties
Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties

Author: L a Aizenberg

Publisher: American Mathematical Soc.

Published: 2000-04-30

Total Pages: 178

ISBN-13: 082181348X

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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.