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Boundary Value Problems For Analytic Functions
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Book Synopsis Boundary Value Problems for Analytic Functions by : Jian-Ke Lu
Download or read book Boundary Value Problems for Analytic Functions written by Jian-Ke Lu and published by World Scientific. This book was released on 1994-02-04 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readership: Mathematicians. keywords:Cauchy Type Integral;Riemann Boundary Value Problem;Hilbert Boundary Value Problem;Index;Singular Integral Equation;Plemelj Formula;Characteristic Function;Standard Function;Noethor Theorem;Extended Residue Theorem “The book is self-contained and clearly written … It can well be used for advanced courses in complex analysis and for seminars, and is readable by graduate students themselves.” Mathematics Abstracts
Book Synopsis Harmonic Analysis and Boundary Value Problems in the Complex Domain by : M.M. Djrbashian
Download or read book Harmonic Analysis and Boundary Value Problems in the Complex Domain written by M.M. Djrbashian and published by Birkhäuser. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.
Book Synopsis Boundary Value Problems by : F. D. Gakhov
Download or read book Boundary Value Problems written by F. D. Gakhov and published by Courier Corporation. This book was released on 1990-01-01 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant monograph, directed to graduate and advanced-undergraduate students, on the theory of boundary value problems for analytic functions and its applications to the solution of singular integral equations with Cauchy and Hilbert kernels. With exercises.
Book Synopsis Boundary Value Problems by : F. D. Gakhov
Download or read book Boundary Value Problems written by F. D. Gakhov and published by Elsevier. This book was released on 2014-07-10 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.
Book Synopsis Singularly Perturbed Boundary Value Problems by : Matteo Dalla Riva
Download or read book Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and published by Springer Nature. This book was released on 2021-10-01 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.
Book Synopsis Analytical Solution Methods for Boundary Value Problems by : A.S. Yakimov
Download or read book Analytical Solution Methods for Boundary Value Problems written by A.S. Yakimov and published by Academic Press. This book was released on 2016-08-13 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content
Book Synopsis Boundary Value Problems, Weyl Functions, and Differential Operators by : Jussi Behrndt
Download or read book Boundary Value Problems, Weyl Functions, and Differential Operators written by Jussi Behrndt and published by Springer Nature. This book was released on 2020-01-03 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
Book Synopsis Solution of Initial Value Problems in Classes of Generalized Analytic Functions by : Wolfgang Tutschke
Download or read book Solution of Initial Value Problems in Classes of Generalized Analytic Functions written by Wolfgang Tutschke and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the initial value problem du CTf = f(t,u), (0. 1) u(O) = u , (0. 2) 0 where u = u(t) ist real o. r vector-valued. It is well-known that this method is also applicable if the function u belongs to a Banach space. A completely new situation arises if the right-hand side f(t,u) of the differential equation (0. 1) depends on a certain derivative Du of the sought function, i. e. , the differential equation (0,1) is replaced by the more general differential equation du dt = f(t,u,Du), (0. 3) There are diff. erential equations of type (0. 3) with smooth right-hand sides not possessing any solution to say nothing about the solvability of the initial value problem (0,3), (0,2), Assume, for instance, that the unknown function denoted by w is complex-valued and depends not only on the real variable t that can be interpreted as time but also on spacelike variables x and y, Then the differential equation (0.
Book Synopsis Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions by : v Mityushev
Download or read book Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions written by v Mityushev and published by CRC Press. This book was released on 1999-11-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for boundary value problems, both linear and nonlinear. From among the many applications to which these methods can apply, the authors focus on interesting problems associated with composite materials with a finite number of inclusions. How far can one go in the solutions of problems in nonlinear mechanics and physics using the ideas of analytic functions? What is the difference between linear and nonlinear cases from the qualitative point of view? What kinds of additional techniques should one use in investigating nonlinear problems? Constructive Methods for Linear and Nonlinear Boundary Value Problems serves to answer these questions, and presents many results to Westerners for the first time. Among the most interesting of these is the complete solution of the Riemann-Hilbert problem for multiply connected domains. The results offered in Constructive Methods for Linear and Nonlinear Boundary Value Problems are prepared for direct application. A historical survey along with background material, and an in-depth presentation of practical methods make this a self-contained volume useful to experts in analytic function theory, to non-specialists, and even to non-mathematicians who can apply the methods to their research in mechanics and physics.
Book Synopsis Boundary-value Problems with Free Boundaries for Elliptic Systems of Equations by : Valentin Nikolaevich Monakhov
Download or read book Boundary-value Problems with Free Boundaries for Elliptic Systems of Equations written by Valentin Nikolaevich Monakhov and published by American Mathematical Soc.. This book was released on 1983 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.
Book Synopsis Boundary Value Problems by : Fedor Dmitrievich Gakhov
Download or read book Boundary Value Problems written by Fedor Dmitrievich Gakhov and published by . This book was released on 1966 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical-Analytic Methods in the Theory of Boundary-Value Problems by : M Ronto
Download or read book Numerical-Analytic Methods in the Theory of Boundary-Value Problems written by M Ronto and published by World Scientific. This book was released on 2000-06-30 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs. The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari–Hale and Lyapunov–Schmidt methods. Contents:Numerical-Analytic Method of Successive Approximations for Two-Point Boundary-Value ProblemsModification of the Numerical-Analytic Method for Two-Point Boundary-Value ProblemsNumerical-Analytic Method for Boundary-Value Problems with Parameters in Boundary ConditionsCollocation Method for Boundary-Value Problems with ImpulsesThe Theory of the Numerical-Analytic Method: Achievements and New Trends of Development Readership: Researchers on differential equations. Keywords:Ordinary Differential Equations;Nonlinear Boundary Value Problems;Periodic Boundary Value Problems;Nonlinear Boundary Conditions;Parametrized Boundary Value Problems;Numerical-Analytic Method;Successive Approximations;Determining Equations;Trigonometric Collocation;Impulsive Systems
Book Synopsis Integral Equations And Boundary Value Problems - Proceedings Of The International Conference by : Guo Chun Wen
Download or read book Integral Equations And Boundary Value Problems - Proceedings Of The International Conference written by Guo Chun Wen and published by #N/A. This book was released on 1991-03-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings covers the following topics: Boundary value problems of partial differential equations including free boundary problems; Theory and methods of integral equations including singular integral equations; Applications of integral equations and boundary value problems to mechanics and physics; and numerical methods for integral equations and boundary value problems.
Book Synopsis Generalized Analytic Functions by : I. N. Vekua
Download or read book Generalized Analytic Functions written by I. N. Vekua and published by Elsevier. This book was released on 2014-07-17 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Analytic Functions is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells. Some classes of functions and operators are discussed, along with the reduction of a positive differential quadratic form to the canonical form. Boundary value problems and infinitesimal bendings of surfaces are also considered. Comprised of six chapters, this volume begins with a detailed treatment of various problems of the general theory of generalized analytic functions as as well as boundary value problems. The reader is introduced to some classes of functions and functional spaces, with emphasis on functions of two independent variables. Subsequent chapters focus on the problem of reducing a positive differential quadratic form to the canonical form; basic properties of solutions of elliptic systems of partial differential equations of the first order, in a two-dimensional domain; and some boundary value problems for an elliptic system of equations of the first order and for an elliptic equation of the second order, in a two-dimensional domain. The final part of the book deals with problems of the theory of surfaces and the membrane theory of shells. This book is intended for students of advanced courses of the mechanico-mathematical faculties, postgraduates, and research workers.
Book Synopsis Boundary Value Problems, Integral Equations And Related Problems - Proceedings Of The International Conference by : Guo Chun Wen
Download or read book Boundary Value Problems, Integral Equations And Related Problems - Proceedings Of The International Conference written by Guo Chun Wen and published by World Scientific. This book was released on 2000-02-22 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.
Book Synopsis Distributions and the Boundary Values of Analytic Functions by : E. J. Beltrami
Download or read book Distributions and the Boundary Values of Analytic Functions written by E. J. Beltrami and published by Academic Press. This book was released on 2014-05-12 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.
Author :Heinrich G W Begehr Publisher :World Scientific Publishing Company ISBN 13 :9813104686 Total Pages :284 pages Book Rating :4.8/5 (131 download)
Book Synopsis Complex Analytic Methods for Partial Differential Equations by : Heinrich G W Begehr
Download or read book Complex Analytic Methods for Partial Differential Equations written by Heinrich G W Begehr and published by World Scientific Publishing Company. This book was released on 1994-11-15 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
