Methods of the Theory of Functions of Many Complex Variables
Methods of the Theory of Functions of Many Complex Variables

Author: Vasiliy Sergeyevich Vladimirov

Publisher: Courier Corporation

Published: 2007-01-01

Total Pages: 370

ISBN-13: 0486458121

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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.

Methods of the Theory of Generalized Functions
Methods of the Theory of Generalized Functions

Author: V. S. Vladimirov

Publisher: CRC Press

Published: 2002-08-15

Total Pages: 332

ISBN-13: 9780415273565

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This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.

The Theory of Functions of a Complex Variable
The Theory of Functions of a Complex Variable

Author: Alekseĭ Georgievich Sveshnikov

Publisher:

Published: 1978

Total Pages: 344

ISBN-13:

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The complex variable and functions of a complex variable; Series of analytical functions; Analytic continuation elementary; The laurent series and isolated singular points; Residues and their applications; Conformal mapping; Analytic-functions in the solutions of boundary-value problems; Fundamentals of operational calculus; Saddle-point method; The wiener-hopf method; Functions of many complex variables.

Mathematics for Physical Science and Engineering
Mathematics for Physical Science and Engineering

Author: Frank E. Harris

Publisher: Academic Press

Published: 2014-05-24

Total Pages: 787

ISBN-13: 0128010495

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Mathematics for Physical Science and Engineering is a complete text in mathematics for physical science that includes the use of symbolic computation to illustrate the mathematical concepts and enable the solution of a broader range of practical problems. This book enables professionals to connect their knowledge of mathematics to either or both of the symbolic languages Maple and Mathematica. The book begins by introducing the reader to symbolic computation and how it can be applied to solve a broad range of practical problems. Chapters cover topics that include: infinite series; complex numbers and functions; vectors and matrices; vector analysis; tensor analysis; ordinary differential equations; general vector spaces; Fourier series; partial differential equations; complex variable theory; and probability and statistics. Each important concept is clarified to students through the use of a simple example and often an illustration. This book is an ideal reference for upper level undergraduates in physical chemistry, physics, engineering, and advanced/applied mathematics courses. It will also appeal to graduate physicists, engineers and related specialties seeking to address practical problems in physical science. - Clarifies each important concept to students through the use of a simple example and often an illustration - Provides quick-reference for students through multiple appendices, including an overview of terms in most commonly used applications (Mathematica, Maple) - Shows how symbolic computing enables solving a broad range of practical problems

Generalized Functions, Convergence Structures, and Their Applications
Generalized Functions, Convergence Structures, and Their Applications

Author: Bogoljub Stankovic

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 432

ISBN-13: 1461310555

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This Proceedings consists of a collection of papers presented at the International Conference "Generalized functions, convergence structures and their applications" held from June 23-27, 1987 in Dubrovnik, Yugoslavia (GFCA-87): 71 participants from 21 countr~es from allover the world took part in the Conference. Proceedings reflects the work of the Conference. Plenary lectures of J. Burzyk, J. F. Colombeau, W. Gahler, H. Keiter, H. Komatsu, B. Stankovic, H. G. Tillman, V. S. Vladimirov provide an up-to-date account of the cur rent state of the subject. All these lectures, except H. G. Tillman's, are published in this volume. The published communications give the contemporary problems and achievements in the theory of generalized functions, in the theory of convergence structures and in their applications, specially in the theory of partial differential equations and in the mathematical physics. New approaches to the theory of generalized functions are presented, moti vated by concrete problems of applications. The presence of articles of experts in mathematical physics contributed to this aim. At the end of the volume one can find presented open problems which also point to further course of development in the theory of generalized functions and convergence structures. We are very grateful to Mr. Milan Manojlovic who typed these Proce edings with extreme skill and diligence and with inexhaustible patience.

A Guide to Distribution Theory and Fourier Transforms
A Guide to Distribution Theory and Fourier Transforms

Author: Robert S. Strichartz

Publisher: World Scientific

Published: 2003

Total Pages: 238

ISBN-13: 9789812384300

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This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.

Functions of a Complex Variable
Functions of a Complex Variable

Author: George F. Carrier

Publisher: SIAM

Published: 2005-01-01

Total Pages: 451

ISBN-13: 9780898719116

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Functions of a complex variable are used to solve applications in various branches of mathematics, science, and engineering. Functions of a Complex Variable: Theory and Technique is a book in a special category of influential classics because it is based on the authors' extensive experience in modeling complicated situations and providing analytic solutions. The book makes available to readers a comprehensive range of these analytical techniques based upon complex variable theory. Advanced topics covered include asymptotics, transforms, the Wiener-Hopf method, and dual and singular integral equations. The authors provide many exercises, incorporating them into the body of the text. Audience: intended for applied mathematicians, scientists, engineers, and senior or graduate-level students who have advanced knowledge in calculus and are interested in such subjects as complex variable theory, function theory, mathematical methods, advanced engineering mathematics, and mathematical physics.

An Introduction to Complex Function Theory
An Introduction to Complex Function Theory

Author: Bruce P. Palka

Publisher: Springer Science & Business Media

Published: 1991

Total Pages: 585

ISBN-13: 038797427X

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This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.