Harmonic Analysis And Boundary Value Problems In The Complex Domain
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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 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.
Geometric Harmonic Analysis V
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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-08-22
Geometric Harmonic Analysis V written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-22 with Mathematics categories.
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.
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.
Geometric Harmonic Analysis Iv
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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-07-09
Geometric Harmonic Analysis Iv written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-09 with Mathematics categories.
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Traditionally, the label “Calderón-Zygmund theory” has been applied to a distinguished body of works primarily pertaining to the mapping properties of singular integral operators on Lebesgue spaces, in various geometric settings. Volume IV amounts to a versatile Calderón-Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries, considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.
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.
Harmonic Analysis Partial Differential Equations Complex Analysis Banach Spaces And Operator Theory Volume 1
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Author : María Cristina Pereyra
language : en
Publisher: Springer
Release Date : 2016-09-15
Harmonic Analysis Partial Differential Equations Complex Analysis Banach Spaces And Operator Theory Volume 1 written by María Cristina Pereyra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-15 with Mathematics categories.
Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fields, and features fully-refereed, high-quality papers exploring new results and trends in spectral theory, mathematical physics, geometric function theory, and partial differential equations. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. Another shared research interest of the contributors of this volume lies in the area of applied harmonic analysis, where a new notion called chromatic derivatives has recently been introduced in communication engineering. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6, 2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional mathematician and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.
Harmonic Analysis And Partial Differential Equations
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Author : Michael Ruzhansky
language : en
Publisher: Springer Nature
Release Date : 2023-03-06
Harmonic Analysis And Partial Differential Equations written by Michael Ruzhansky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-06 with Mathematics categories.
This book collects papers related to the session “Harmonic Analysis and Partial Differential Equations” held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.
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.
Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems
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Author : Carlos E. Kenig
language : en
Publisher:
Release Date : 1994
Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Boundary value problems 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 migh.
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