[PDF] Harmonic Analysis Partial Differential Equations And Applications eBook

Author : Sagun Chanillo
Publisher : Birkhäuser
Page : 319 pages
File Size : 10,8 MB
Release : 2017-02-20
Category : Mathematics
ISBN : 3319527428

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This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.

Author : Dorina Mitrea
Publisher : American Mathematical Soc.
Page : 446 pages
File Size : 38,66 MB
Release : 2008
Category : Mathematics
ISBN : 0821844245

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This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.

Author : Dorina Mitrea
Publisher : Springer
Page : 600 pages
File Size : 25,31 MB
Release : 2018-12-29
Category : Mathematics
ISBN : 3030032965

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The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity. The main additions to the current, second edition, pertain to fundamental solutions (through the inclusion of the Helmholtz operator, the perturbed Dirac operator, and their iterations) and the theory of Sobolev spaces (built systematically from the ground up, exploiting natural connections with the Fourier Analysis developed earlier in the monograph).

Author : Alberto P. Calderón
Publisher : University of Chicago Press
Page : 388 pages
File Size : 16,59 MB
Release : 1999
Category : Mathematics
ISBN : 9780226104560

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Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day. In 1996, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book is essential reading for researchers in these and other related fields.

Author : María Cristina Pereyra
Publisher : Springer
Page : 469 pages
File Size : 50,90 MB
Release : 2017-07-10
Category : Mathematics
ISBN : 3319515934

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This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic harmonic analysis. 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. A survey of the two weight problem for the Hilbert transform and an expository article on the Clark model to the case of non-singular measures and applications to the study of rank-one perturbations are included. 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 scientist 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 : Michael Ruzhansky
Publisher : Springer Nature
Page : 241 pages
File Size : 16,2 MB
Release : 2023-03-06
Category : Mathematics
ISBN : 3031243110

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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 : Mario Milman
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 15,82 MB
Release : 1990
Category : Mathematics
ISBN : 0821851136

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Illuminates the relationship between harmonic analysis and partial differential equations. This book covers topics such as application of fully nonlinear, uniformly elliptic equations to the Monge Ampere equation; and estimates for Green functions for the purpose of studying Dirichlet problems for operators in non-divergence form.

Author : Isaac Pesenson
Publisher : Birkhäuser
Page : 512 pages
File Size : 33,85 MB
Release : 2017-08-09
Category : Mathematics
ISBN : 3319555561

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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 : Giovanna Citti
Publisher : Birkhäuser
Page : 178 pages
File Size : 25,82 MB
Release : 2015-04-28
Category : Mathematics
ISBN : 3034804083

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This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and the Heisenberg group to understand human vision. The second and third series of lectures cover some of the main topics on linear and multilinear harmonic analysis. The last one is a clear introduction to a deep result of De Giorgi, Moser and Nash on regularity of elliptic partial differential equations in divergence form.

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 32,51 MB
Release : 2009-05-24
Category : Mathematics
ISBN : 0817646698

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This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.