An Introduction To Singular Integrals

Author : Jacques Peyriere
Publisher : SIAM
Page : 123 pages
File Size : 52,7 Mb
Release : 2018-11-15
Category : Mathematics
ISBN : 9781611975413

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An Introduction to Singular Integrals by Jacques Peyriere Pdf

In just over 100 pages, this book provides basic, essential knowledge of some of the tools of real analysis: the Hardy?Littlewood maximal operator, the Calder?n?Zygmund theory, the Littlewood?Paley theory, interpolation of spaces and operators, and the basics of H1 and BMO spaces. This concise text offers brief proofs and exercises of various difficulties designed to challenge and engage students. An Introduction to Singular Integrals is meant to give first-year graduate students in Fourier analysis and partial differential equations an introduction to harmonic analysis. While some background material is included in the appendices, readers should have a basic knowledge of functional analysis, some acquaintance with measure and integration theory, and familiarity with the Fourier transform in Euclidean spaces.

Author : I. Gohberg,N. Krupnik
Publisher : Birkhäuser
Page : 263 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034886475

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One-Dimensional Linear Singular Integral Equations by I. Gohberg,N. Krupnik Pdf

This book is an introduction to the theory of linear one-dimensional singular integral equations. It is essentually a graduate textbook. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form. In this book material of the monograph [2] of the authors on one-dimensional singular integral operators is widely used. This monograph appeared in 1973 in Russian and later in German translation [3]. In the final text version the authors included many addenda and changes which have in essence changed character, structure and contents of the book and have, in our opinion, made it more suitable for a wider range of readers. Only the case of singular integral operators with continuous coefficients on a closed contour is considered herein. The case of discontinuous coefficients and more general contours will be considered in the second volume. We are grateful to the editor Professor G. Heinig of the volume and to the translators Dr. B. Luderer and Dr. S. Roch, and to G. Lillack, who did the typing of the manuscript, for the work they have done on this volume.

Author : Guy David
Publisher : Springer
Page : 119 pages
File Size : 54,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540463771

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Wavelets and Singular Integrals on Curves and Surfaces by Guy David Pdf

Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics. The book begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. A second part centers on a criterion for the L2-boundedness of singular integral operators: the T(b)-theorem. It contains a full proof of that theorem. It contains a full proof of that theorem, and a few of the most striking applications (mostly to the Cauchy integral). The third part is a survey of recent attempts to understand the geometry of subsets of Rn on which analogues of the Cauchy kernel define bounded operators. The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis.

Author : Umberto Neri
Publisher : Springer
Page : 279 pages
File Size : 40,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540368649

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Singular Integrals by Umberto Neri Pdf

Author : Frédéric Pham
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 47,6 Mb
Release : 2011-04-22
Category : Mathematics
ISBN : 9780857296030

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Singularities of integrals by Frédéric Pham Pdf

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.

Author : N. I. Muskhelishvili
Publisher : Courier Corporation
Page : 466 pages
File Size : 42,6 Mb
Release : 2013-02-19
Category : Mathematics
ISBN : 9780486145068

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Singular Integral Equations by N. I. Muskhelishvili Pdf

DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div

Author : Cora Sadosky
Publisher : Unknown
Page : 395 pages
File Size : 49,6 Mb
Release : 1995
Category : Electronic
ISBN : 0783743181

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Interpolation of Operators and Singular Integrals by Cora Sadosky Pdf

Author : S. G. Mikhlin
Publisher : Elsevier
Page : 273 pages
File Size : 53,6 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483164496

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Multidimensional Singular Integrals and Integral Equations by S. G. Mikhlin Pdf

Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Author : Cora Sadosky
Publisher : Marcel Dekker Incorporated
Page : 375 pages
File Size : 51,6 Mb
Release : 1979-01-01
Category : Mathematics
ISBN : 0824768833

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Interpolation of Operators and Singular Integrals by Cora Sadosky Pdf

Author : Elias M. Stein
Publisher : Princeton University Press
Page : 304 pages
File Size : 40,8 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883882

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Singular Integrals and Differentiability Properties of Functions (PMS-30) by Elias M. Stein Pdf

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.

Author : Ricardo Estrada,Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213826

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Singular Integral Equations by Ricardo Estrada,Ram P. Kanwal Pdf

Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0

Author : Brian Street
Publisher : Princeton University Press
Page : 412 pages
File Size : 48,5 Mb
Release : 2014-10-05
Category : Mathematics
ISBN : 9781400852758

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Multi-parameter Singular Integrals. (AM-189), Volume I by Brian Street Pdf

This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. Multi-parameter Singular Integrals will interest graduate students and researchers working in singular integrals and related fields.

Author : Helmut Abels
Publisher : Walter de Gruyter
Page : 233 pages
File Size : 45,8 Mb
Release : 2011-12-23
Category : Mathematics
ISBN : 9783110250312

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Pseudodifferential and Singular Integral Operators by Helmut Abels Pdf

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.

Author : Alberto P. Calderón
Publisher : Unknown
Page : 394 pages
File Size : 47,7 Mb
Release : 1967
Category : Integral equations
ISBN : UCSD:31822028821916

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Singular Integrals by Alberto P. Calderón Pdf

Author : Adrían M. González-Pérez,Marius Junge,Javier Parcet
Publisher : American Mathematical Society
Page : 90 pages
File Size : 43,8 Mb
Release : 2021-11-16
Category : Mathematics
ISBN : 9781470449377

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Singular Integrals in Quantum Euclidean Spaces by Adrían M. González-Pérez,Marius Junge,Javier Parcet Pdf

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