Multidimensional Complex Analysis And Partial Differential Equations

Author : Steven G. Krantz
Publisher : CRC Press
Page : 322 pages
File Size : 47,9 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351425803

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Partial Differential Equations and Complex Analysis by Steven G. Krantz Pdf

Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.

Author : Francois Treves,Paulo D. Cordaro,Howard Jacobowitz
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 43,7 Mb
Release : 1997
Category : Analyse fonctionnelle - Congrès
ISBN : 9780821805091

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Multidimensional Complex Analysis and Partial Differential Equations by Francois Treves,Paulo D. Cordaro,Howard Jacobowitz Pdf

This collection of papers by outstanding contributors in analysis, partial differential equations and several complex variables is dedicated to Professor Treves in honour of his 65th birthday. There are five excellent survey articles covering analytic singularities, holomorphically nondegenerate algebraic hypersurfaces, analyticity of CR mappings, removable singularities of vector fields and local solvability for systems of vector fields. The other papers are original research contributions on topics such as Klein-Gordon and Dirac equations, Toeplitz operators, elliptic structures, complexification of Lie groups, and pseudo-differential operators.

Author : Manfred Kracht,Erwin Kreyszig
Publisher : New York ; Toronto : Wiley
Page : 424 pages
File Size : 52,9 Mb
Release : 1988
Category : Mathematics
ISBN : UCAL:B4406640

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Methods of Complex Analysis in Partial Differential Equations with Applications by Manfred Kracht,Erwin Kreyszig Pdf

This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of analytic behaviour of solutions. It presents basic facts of the subject and includes recent results, emphasizing the method of integral operators and the method of differential operators. The first chapter gives a motivation for and the underlying ideas of, the later chapters. Chapters 2 to 7 give a detailed exposition of the basic concepts and fundamental theorems, as well as their most recent development. Chapters 8 to 13 are concerned with the application of the theory to three important classes of differential equations of mathematical physics.

Author : So-chin Chen,Mei-Chi Shaw
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 44,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0821829610

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Partial Differential Equations in Several Complex Variables by So-chin Chen,Mei-Chi Shaw Pdf

This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.

Author : H Begehr,Abduhamid Dzhuraev
Publisher : Chapman and Hall/CRC
Page : 464 pages
File Size : 55,7 Mb
Release : 1997-07-09
Category : Mathematics
ISBN : 0582255007

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An Introduction to Several Complex Variables and Partial Differential Equations by H Begehr,Abduhamid Dzhuraev Pdf

Author : G.M. Khenkin
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580116

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Several Complex Variables V by G.M. Khenkin Pdf

This volume of the Encyclopaedia contains three contributions in the field of complex analysis; on mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. It is immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theory and general relativity.

Author : A S A Mshimba,Wolfgang Tutschke
Publisher : World Scientific
Page : 442 pages
File Size : 43,7 Mb
Release : 1995-10-17
Category : Electronic
ISBN : 9789814548533

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Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations by A S A Mshimba,Wolfgang Tutschke Pdf

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.

Author : H. F. Weinberger
Publisher : Courier Corporation
Page : 482 pages
File Size : 50,5 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486132044

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A First Course in Partial Differential Equations by H. F. Weinberger Pdf

Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.

Author : Heinrich G W Begehr
Publisher : World Scientific Publishing Company
Page : 284 pages
File Size : 53,8 Mb
Release : 1994-11-15
Category : Mathematics
ISBN : 9789813104686

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Complex Analytic Methods for Partial Differential Equations by Heinrich G W Begehr Pdf

This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincaré problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.

Author : Heinrich Begehr,A. Okay Celebi,W. Tutschke
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 40,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332916

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Complex Methods for Partial Differential Equations by Heinrich Begehr,A. Okay Celebi,W. Tutschke Pdf

This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these methods are not only applied. Whithin the framework of holomorphic functions but are also combined with properties of generalized analytic functions. This can be seen by the many books which recently were published in this field and also by the proceedings in this ISAAC series and the ISAAC congresses and workshops.

Author : Tomasz Radożycki
Publisher : Springer Nature
Page : 384 pages
File Size : 43,9 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9783030368487

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Solving Problems in Mathematical Analysis, Part II by Tomasz Radożycki Pdf

This textbook offers an extensive list of completely solved problems in mathematical analysis. This second of three volumes covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

Author : Anton Savin,Boris Sternin
Publisher : Birkhäuser
Page : 138 pages
File Size : 45,5 Mb
Release : 2017-03-28
Category : Mathematics
ISBN : 9783319517445

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Introduction to Complex Theory of Differential Equations by Anton Savin,Boris Sternin Pdf

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.

Author : H Begehr,Alan Jeffrey
Publisher : Chapman and Hall/CRC
Page : 232 pages
File Size : 44,6 Mb
Release : 1992-11-02
Category : Mathematics
ISBN : 0582096405

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Partial Differential Equations With Complex Analysis by H Begehr,Alan Jeffrey Pdf

A collection of papers on function theory and function-theoretic methods in PDEs. Results are obtained using a variety of complex analytic methods e.g. Bergman and Vekua, geometric function theory and the Riemann-Hilbert boundary value problem.

Author : Theodore V. Hromadka
Publisher : Computational Mechanics
Page : 0 pages
File Size : 40,7 Mb
Release : 2002
Category : Boundary element methods
ISBN : 1853129089

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A Multi-dimensional Complex Variable Boundary Element Method by Theodore V. Hromadka Pdf

The Complex Variable Boundary Element Method (CVBEM) is a numerical technique useful in developing approximations of boundary value problems involving the LaPlace and Poisson partial differential equations. Because the CVBEM is based upon the Cauchy integral theorem of complex variables, it has so far been limited to two-dimensional geometry applications.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 351 pages
File Size : 54,7 Mb
Release : 2019-04-16
Category : Mathematics
ISBN : 9781000000351

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Complex Variables by Steven G. Krantz Pdf

The idea of complex numbers dates back at least 300 years—to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. Features: This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis This book has an exceptionally large number of examples and a large number of figures. The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking. Incisive applications appear throughout the book. Partial differential equations are used as a unifying theme.