Multidimensional Singular Integrals And Integral Equations

Author : S. G. Mikhlin
Publisher : Elsevier
Page : 273 pages
File Size : 45,7 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 : Solomon Grigorʹevich Mikhlin
Publisher : Unknown
Page : 0 pages
File Size : 41,9 Mb
Release : 1965
Category : Integral equations
ISBN : LCCN:64219000

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Multidimensional Singular Integrals and Integral Equations by Solomon Grigorʹevich Mikhlin Pdf

Author : Gennadi Vainikko
Publisher : Springer
Page : 169 pages
File Size : 49,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540477730

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Multidimensional Weakly Singular Integral Equations by Gennadi Vainikko Pdf

The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.

Author : Gennadi Vainikko
Publisher : Unknown
Page : 180 pages
File Size : 45,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662171597

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Multidimensional Weakly Singular Integral Equations by Gennadi Vainikko Pdf

Author : Ricardo Estrada,Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 41,9 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 : B. N. Mandal,A. Chakrabarti
Publisher : CRC Press
Page : 274 pages
File Size : 47,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439876213

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Applied Singular Integral Equations by B. N. Mandal,A. Chakrabarti Pdf

The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.

Author : L. G. Mikhailov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 232 pages
File Size : 44,9 Mb
Release : 1970-12-31
Category : Mathematics
ISBN : 9783112729151

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A New Class of Singular Integral Equations and Its Application to Differential Equations with Singular Coefficients by L. G. Mikhailov Pdf

No detailed description available for "A New Class of Singular Integral Equations and Its Application to Differential Equations with Singular Coefficients".

Author : E.G. Ladopoulos
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 45,9 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9783662042915

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Singular Integral Equations by E.G. Ladopoulos Pdf

The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Author : E.G. Ladopoulos
Publisher : Springer
Page : 551 pages
File Size : 40,6 Mb
Release : 2000-06-06
Category : Computers
ISBN : 9783540672302

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Singular Integral Equations by E.G. Ladopoulos Pdf

The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Author : N. I. Muskhelishvili,J. R. M. Radok
Publisher : Courier Corporation
Page : 466 pages
File Size : 40,7 Mb
Release : 2008-01-01
Category : Science
ISBN : 9780486462424

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Singular Integral Equations by N. I. Muskhelishvili,J. R. M. Radok Pdf

This high-level treatment considers one-dimensional singular integral equations involving Cauchy principal values, covering Hölder condition, Hilbert and Riemann-Hilbert problems, Dirichlet problems, inversion formulas for arcs, more. 1992 edition.

Author : I.K. Lifanov,L.N. Poltavskii,MG.M. Vainikko
Publisher : CRC Press
Page : 416 pages
File Size : 45,9 Mb
Release : 2003-12-29
Category : Mathematics
ISBN : 9780203402160

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Hypersingular Integral Equations and Their Applications by I.K. Lifanov,L.N. Poltavskii,MG.M. Vainikko Pdf

A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co

Author : I. Gohberg,N. Krupnik
Publisher : Birkhäuser
Page : 226 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886024

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

This monograph is the second volume of a graduate text book on the modern theory of linear one-dimensional singular integral equations. Both volumes may be regarded as unique graduate text books. Singular integral equations attract more and more attention since this class of equations appears in numerous applications, and also because they form one of the few classes of equations which can be solved explicitly. The present book is to a great extent based upon material contained in the second part of the authors' monograph [6] which appeared in 1973 in Russian, and in 1979 in German translation. The present text includes a large number of additions and complementary material, essentially changing the character, structure and contents of the book, and making it accessible to a wider audience. Our main subject in the first volume was the case of closed curves and continuous coeffi cients. Here, in the second volume, we turn to general curves and discontinuous coefficients. We are deeply grateful to the editor Professor G. Heinig, to the translator Dr. S. Roeh, and to the typist Mr. G. Lillack, for their patient work. The authors Ramat-Aviv, Ramat-Gan, May 26, 1991 11 Introduction This book is the second volume of an introduction to the theory of linear one-dimensional singular integral operators. The main topics of both parts of the book are the invertibility and Fredholmness of these operators. Special attention is paid to inversion methods.

Author : Zabreyko
Publisher : Springer
Page : 472 pages
File Size : 43,7 Mb
Release : 1975-01-09
Category : Mathematics
ISBN : UCAL:B4406097

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Integral Equations—a Reference Text by Zabreyko Pdf

The title 'Integral equations' covers many things which have very little connection with each other. However, they are united by the following important feature. In most cases, the equations involve an unknown function operated on by a bounded and often compact operator defined on some Banach space. The aim of the book is to list the main results concerning integral equations. The classical Fredholm theory and Hilbert-Schmidt theory are presented in Chapters II and III. The preceding Chapter I contains a description of the most important types of integral equations which can be solved in 'closed' form. Chapter IV is an important addition to Chapters II and III, as it contains the theory of integral equations with non-negative kernels. The development of this theory is mainly due to M. G. Krein. The content of the first four chapters is fairly elementary. It is well known that the Fredholm theory has been generalized for equations with compact operators. Chapter V is devoted tothis generalization. In Chapter VI one-dimensional (i.e. with one dependent variable) singular integral equations are considered. The last type of equations differ from that considered in the preceding chapters in that singular integral operators are not compact but only bounded in the usual functional spaces.

Author : Israel Gohberg
Publisher : Unknown
Page : 128 pages
File Size : 52,6 Mb
Release : 1991
Category : Integral operators
ISBN : OCLC:24847543

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One-dimensional Linear Singular Integral Equations by Israel Gohberg Pdf

Author : Solomon G. Mikhlin,Siegfried Prößdorf
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 41,7 Mb
Release : 1987
Category : Mathematics
ISBN : 3540159673

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Singular Integral Operators by Solomon G. Mikhlin,Siegfried Prößdorf Pdf

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.