Singular Integral Operators

Author : Solomon G. Mikhlin,Siegfried Prößdorf
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 52,6 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.

Author : Helmut Abels
Publisher : Walter de Gruyter
Page : 233 pages
File Size : 52,7 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 : Prof. Kevin F. Clancey,Prof. Israel Gohberg
Publisher : Birkhäuser
Page : 246 pages
File Size : 48,8 Mb
Release : 2013-11-21
Category : Science
ISBN : 9783034854924

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Factorization of Matrix Functions and Singular Integral Operators by Prof. Kevin F. Clancey,Prof. Israel Gohberg Pdf

A few years aga the authors started a project of a book on the theory of systems of one-dimensional singular integral equa tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ~~ concerning scalar equa tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions vis-a-vis appli cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represen tative variety of all kinds of methods, techniques,results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connec tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan.

Author : I. Gohberg,N. Krupnik
Publisher : Birkhäuser
Page : 263 pages
File Size : 50,9 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 : Alexander A. Borichev,Nikolai K. Nikolski
Publisher : Birkhäuser
Page : 536 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783034883627

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Systems, Approximation, Singular Integral Operators, and Related Topics by Alexander A. Borichev,Nikolai K. Nikolski Pdf

This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.

Author : S. G. Mikhlin,S. Prössdorf
Publisher : Walter de Gruyter GmbH & Co KG
Page : 528 pages
File Size : 42,7 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 9783112719152

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Singular Integral Operators by S. G. Mikhlin,S. Prössdorf Pdf

Keine ausführliche Beschreibung für "Singular Integral Operators" verfügbar.

Author : N. Krupnik
Publisher : Birkhäuser
Page : 212 pages
File Size : 42,7 Mb
Release : 2013-11-22
Category : Science
ISBN : 9783034854634

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Banach Algebras with Symbol and Singular Integral Operators by N. Krupnik Pdf

About fifty years aga S. G. Mikhlin, in solving the regularization problem for two-dimensional singular integral operators [56], assigned to each such operator a func tion which he called a symbol, and showed that regularization is possible if the infimum of the modulus of the symbol is positive. Later, the notion of a symbol was extended to multidimensional singular integral operators (of arbitrary dimension) [57, 58, 21, 22]. Subsequently, the synthesis of singular integral, and differential operators [2, 8, 9]led to the theory of pseudodifferential operators [17, 35] (see also [35(1)-35(17)]*), which are naturally characterized by their symbols. An important role in the construction of symbols for many classes of operators was played by Gelfand's theory of maximal ideals of Banach algebras [201. Using this the ory, criteria were obtained for Fredholmness of one-dimensional singular integral operators with continuous coefficients [34 (42)], Wiener-Hopf operators [37], and multidimensional singular integral operators [38 (2)]. The investigation of systems of equations involving such operators has led to the notion of matrix symbol [59, 12 (14), 39, 41]. This notion plays an essential role not only for systems, but also for singular integral operators with piecewise-continuous (scalar) coefficients [44 (4)]. At the same time, attempts to introduce a (scalar or matrix) symbol for other algebras have failed.

Author : Solomon Grigor鈋vich Mikhlin,Siegfried·Pr鑟ssdorf
Publisher : Unknown
Page : 528 pages
File Size : 45,9 Mb
Release : 1989
Category : Integral equations
ISBN : 7506204118

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Singular Integral Operators by Solomon Grigor鈋vich Mikhlin,Siegfried·Pr鑟ssdorf Pdf

Author : S. G. Mikhlin
Publisher : Elsevier
Page : 273 pages
File Size : 54,8 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 : N. I. Muskhelishvili
Publisher : Courier Corporation
Page : 466 pages
File Size : 42,7 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 : Guy David
Publisher : Springer
Page : 119 pages
File Size : 46,8 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 : Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko
Publisher : Birkhäuser
Page : 567 pages
File Size : 48,7 Mb
Release : 2016-05-11
Category : Mathematics
ISBN : 9783319210155

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Integral Operators in Non-Standard Function Spaces by Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko Pdf

This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Author : Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa
Publisher : Birkhäuser
Page : 372 pages
File Size : 52,7 Mb
Release : 2018-08-22
Category : Mathematics
ISBN : 9783319724492

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Operator Theory, Operator Algebras, and Matrix Theory by Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa Pdf

This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.

Author : Umberto Neri
Publisher : Springer
Page : 279 pages
File Size : 54,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540368649

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Singular Integrals by Umberto Neri Pdf

Author : Viktor G. Kravchenko,Georgii S. Litvinchuk
Publisher : Unknown
Page : 308 pages
File Size : 46,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401111812

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Introduction to the Theory of Singular Integral Operators with Shift by Viktor G. Kravchenko,Georgii S. Litvinchuk Pdf