Singular Integral Operators

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Singular Integral Operators

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Author : Solomon G. Mikhlin
language : en
Publisher: Springer Science & Business Media
Release Date : 1987

Singular Integral Operators written by Solomon G. Mikhlin 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 1987 with Mathematics categories.

The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.

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.

Singular Integrals And Related Topics

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Author : Shanzhen Lu
language : en
Publisher: World Scientific
Release Date : 2007-04-19

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 2007-04-19 with Mathematics categories.

This book introduces some important progress in the theory of Calderon-Zygmund singular integrals, oscillatory singular integrals, and Littlewood-Paley 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

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Author : Umberto Neri
language : en
Publisher: Springer
Release Date : 2006-11-14

Singular Integrals written by Umberto Neri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Singular Integral Operators Factorization And Applications

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Author : Albrecht Böttcher
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Singular Integral Operators Factorization And Applications written by Albrecht Böttcher 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 Mathematics categories.

This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization Theory; !> Factorization and Integrable Systems; !> Operator Theoretical Methods in Diffraction Theory; !> Algebraic Techniques in Operator Theory; !> Applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of Operator Theory in Portugal.

Lectures On Singular Integral Operators

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Author : Francis Michael Christ
language : en
Publisher: American Mathematical Soc.
Release Date : 1991-01-07

Lectures On Singular Integral Operators written by Francis Michael Christ 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 1991-01-07 with Mathematics categories.

This book represents an expanded account of lectures delivered at the NSF-CBMS Regional Conference on Singular Integral Operators, held at the University of Montana in the summer of 1989. The lectures are concerned principally with developments in the subject related to the Cauchy integral on Lipschitz curves and the T(1) theorem. The emphasis is on real-variable techniques, with a discussion of analytic capacity in one complex variable included as an application. The author has presented here a synthesized exposition of a body of results and techniques. Much of the book is introductory in character and intended to be accessible to the nonexpert, but a variety of readers should find the book useful.

Introduction To The Theory Of Singular Integral Operators With Shift

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Author : Viktor G. Kravchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To The Theory Of Singular Integral Operators With Shift written by Viktor G. Kravchenko 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.

This book is devoted to the Fredholm theory of singular integral operators with shift in Lp, 1

Multidimensional Singular Integrals And Integral Equations

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Author : Solomon Grigorʹevich Mikhlin
language : en
Publisher:
Release Date : 1965

Multidimensional Singular Integrals And Integral Equations written by Solomon Grigorʹevich Mikhlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Integral equations categories.

Wavelet Based Approximation Schemes For Singular Integral Equations

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Author : Madan Mohan Panja
language : en
Publisher: CRC Press
Release Date : 2020-06-07

Wavelet Based Approximation Schemes For Singular Integral Equations written by Madan Mohan Panja and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-07 with Mathematics categories.

Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.

Singular Integral Operators

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Author : Solomon Grigor鈋vich Mikhlin
language : en
Publisher:
Release Date : 1989

Singular Integral Operators written by Solomon Grigor鈋vich Mikhlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Integral equations categories.