Singular Integrals And Related Topics
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Singular Integrals And Related Topics
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Author : Shanzhen Lu
language : en
Publisher: World Scientific
Release Date : 2007
Singular Integrals And Related Topics written by Shanzhen 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 2007 with Mathematics categories.
This book introduces some important progress in the theory of CalderonOCoZygmund singular integrals, oscillatory singular integrals, and LittlewoodOCoPaley theory over the last decade. It includes some important research results by the authors and their cooperators, such as singular integrals with rough kernels on Block spaces and Hardy spaces, the criterion on boundedness of oscillatory singular integrals, and boundedness of the rough Marcinkiewicz integrals. These results have frequently been cited in many published papers."
Singular Integrals And Differentiability Properties Of Functions
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Author : Elias M. Stein
language : en
Publisher: Princeton University Press
Release Date : 1970
Singular Integrals And Differentiability Properties Of Functions written by Elias M. Stein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself. Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance. Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.
Singular Integral Equations
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Author : Ricardo Estrada
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Singular Integral Equations written by Ricardo Estrada and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This work focuses on the distributional solutions of singular integral equations, progressing from basic concepts of the classical theory to the more difficult two-dimensional problems.
Singularities Of Integrals
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Author : Frédéric Pham
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-22
Singularities Of Integrals written by Frédéric Pham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-22 with Mathematics categories.
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
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.
Pseudodifferential And Singular Integral Operators
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Author : Helmut Abels
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Pseudodifferential And Singular Integral Operators written by Helmut Abels and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.
Advanced Topics In Mathematical Analysis
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Author : Michael Ruzhansky
language : en
Publisher: CRC Press
Release Date : 2019-01-08
Advanced Topics In Mathematical Analysis written by Michael Ruzhansky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.
Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.
Selected Papers On Differential Equations And Analysis
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Selected Papers On Differential Equations And Analysis written by 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 2005 with Mathematics categories.
Contains translations of papers that originally appeared in the Japanese journal "Sugaku". This book covers a variety of topics, including differential equations with free boundary, singular integral operators, and operator algebras. It is suitable for graduate students and research mathematicians interested in analysis and differential equations.
Interpolation Spaces
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Author : J. Bergh
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Interpolation Spaces written by J. Bergh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.
Advances In Harmonic Analysis And Operator Theory
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Author : Alexandre Almeida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-31
Advances In Harmonic Analysis And Operator Theory written by Alexandre Almeida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Mathematics categories.
This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.