Harmonic Analysis And Boundary Value Problems In The Complex Domain

Author : M.M. Djrbashian
Publisher : Birkhäuser
ISBN 13 : 3034885490
Total Pages : 266 pages
Book Rating : 4.92/5 ( download)

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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 266 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.

Author : Luca Capogna
Publisher : American Mathematical Soc.
ISBN 13 : 0821827456
Total Pages : 170 pages
Book Rating : 4.51/5 ( download)

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Download or read book Harmonic Analysis and Boundary Value Problems written by Luca Capogna and published by American Mathematical Soc.. This book was released on 2001 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Dorina Mitrea
Publisher : Springer Nature
ISBN 13 : 3031315618
Total Pages : 1006 pages
Book Rating : 4.19/5 ( download)

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Download or read book Geometric Harmonic Analysis V written by Dorina Mitrea and published by Springer Nature. This book was released on 2023-08-22 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
ISBN 13 : 0821803093
Total Pages : 162 pages
Book Rating : 4.97/5 ( download)

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Download or read book Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 1994 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Dorina Mitrea
Publisher : Springer Nature
ISBN 13 : 3031291794
Total Pages : 1004 pages
Book Rating : 4.91/5 ( download)

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Download or read book Geometric Harmonic Analysis IV written by Dorina Mitrea and published by Springer Nature. This book was released on 2023-07-09 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael Ruzhansky
Publisher : Springer Nature
ISBN 13 : 3031243110
Total Pages : 241 pages
Book Rating : 4.10/5 ( download)

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Download or read book Harmonic Analysis and Partial Differential Equations written by Michael Ruzhansky and published by Springer Nature. This book was released on 2023-03-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : María Cristina Pereyra
Publisher : Springer
ISBN 13 : 3319309617
Total Pages : 371 pages
Book Rating : 4.13/5 ( download)

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Download or read book Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1) written by María Cristina Pereyra and published by Springer. This book was released on 2016-09-15 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Carlos E. Kenig
Publisher :
ISBN 13 : 9781470424435
Total Pages : 146 pages
Book Rating : 4.36/5 ( download)

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Download or read book Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig and published by . This book was released on 1994 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 510 pages
Book Rating : 4.60/5 ( download)

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Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Enrique A. Gonzalez-Velasco
Publisher : Elsevier
ISBN 13 : 0080531938
Total Pages : 565 pages
Book Rating : 4.39/5 ( download)

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Download or read book Fourier Analysis and Boundary Value Problems written by Enrique A. Gonzalez-Velasco and published by Elsevier. This book was released on 1996-11-28 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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