Harmonic Analysis And Boundary Value Problems

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Harmonic Analysis And Boundary Value Problems In The Complex Domain

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Author : M.M. Djrbashian
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Harmonic Analysis And Boundary Value Problems In The Complex Domain written by M.M. Djrbashian 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 Social Science categories.

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.

Harmonic Analysis And Boundary Value Problems

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Author : Luca Capogna
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Harmonic Analysis And Boundary Value Problems written by Luca Capogna 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 2001 with Mathematics categories.

This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ``two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.

Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems

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Author : Carlos E. Kenig
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig 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 1994 with Mathematics categories.

In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.

Polyharmonic Boundary Value Problems

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Author : Filippo Gazzola
language : en
Publisher: Springer
Release Date : 2010-05-26

Polyharmonic Boundary Value Problems written by Filippo Gazzola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-26 with Mathematics categories.

This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.

Fourier Analysis And Boundary Value Problems

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Author : Enrique A. Gonzalez-Velasco
language : en
Publisher: Elsevier
Release Date : 1996-11-28

Fourier Analysis And Boundary Value Problems written by Enrique A. Gonzalez-Velasco and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-28 with Mathematics categories.

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field. - Topics are covered from a historical perspective with biographical information on key contributors to the field - The text contains more than 500 exercises - Includes practical applications of the equations to problems in both engineering and physics

Boundary Value Problems For Analytic Functions

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Author : Jian-Ke Lu
language : en
Publisher: World Scientific
Release Date : 1993

Boundary Value Problems For Analytic Functions written by Jian-Ke Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincar‚-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter I describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals; Chapters II and III study, respectively, fundamental boundary value problems and their applications to singular integral equations for closed contours; Chapters IV and V discuss the same problems for curves with nodes (including open arcs); Chaper VI deals with similar problems for systems of functions; Chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of these exercises.For graduate students or seniors, all the 7 chapters can be used for a full year course, while the first 3 chapters may be used for a one-semester course.

Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science

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Author : Isaac Pesenson
language : en
Publisher: Birkhäuser
Release Date : 2017-08-09

Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science written by Isaac Pesenson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-09 with Mathematics categories.

The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Solving Ordinary And Partial Boundary Value Problems In Science And Engineering

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Author : Karel Rektorys
language : en
Publisher: CRC Press
Release Date : 2024-11-01

Solving Ordinary And Partial Boundary Value Problems In Science And Engineering written by Karel Rektorys and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.

This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.

Real Variable Methods In Harmonic Analysis

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Author :
language : en
Publisher: Academic Press
Release Date : 1986-11-06

Real Variable Methods In Harmonic Analysis written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-11-06 with Mathematics categories.

Real-variable Methods in Harmonic Analysis