Banach Algebras With Symbol And Singular Integral Operators

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Banach Algebras with Symbol and Singular Integral Operators

N. Krupnik
Banach Algebras with Symbol and Singular Integral Operators Book PDF

Author : N. Krupnik
Publisher : Birkhäuser
Page : 212 pages
File Size : 40,5 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.

Banach Algebras with Symbol and Singular Integral Operators

Naum Krupnik
Banach Algebras with Symbol and Singular Integral Operators Book PDF

Author : Naum Krupnik
Publisher : Birkhäuser
Page : 206 pages
File Size : 48,6 Mb
Release : 2014-10-05
Category : Science
ISBN : 3034854641

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Banach Algebras with Symbol and Singular Integral Operators by Naum 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.

Singular Integral Operators

Solomon G. Mikhlin,Siegfried Prößdorf
Singular Integral Operators Book PDF

Author : Solomon G. Mikhlin,Siegfried Prößdorf
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 51,6 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.

Singular Integral Operators and Related Topics

A. Böttcher,I. Gohberg
Singular Integral Operators and Related Topics Book PDF

Author : A. Böttcher,I. Gohberg
Publisher : Birkhäuser
Page : 325 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890403

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Singular Integral Operators and Related Topics by A. Böttcher,I. Gohberg Pdf

This volume contains a selection of papers on modern operator theory and its applications, arising from a joint workshop on linear one-dimensional singular integral equations. The book is of interest to a wide audience in the mathematical and engineering sciences.

Singular Integral Operators

S. G. Mikhlin,S. Prössdorf
Singular Integral Operators Book PDF

Author : S. G. Mikhlin,S. Prössdorf
Publisher : Walter de Gruyter GmbH & Co KG
Page : 528 pages
File Size : 42,5 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.

One-Dimensional Linear Singular Integral Equations

I. Gohberg,N. Krupnik
One Dimensional Linear Singular Integral Equations Book PDF

Author : I. Gohberg,N. Krupnik
Publisher : Birkhäuser
Page : 263 pages
File Size : 53,7 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.

Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms

Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger
Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms Book PDF

Author : Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 40,9 Mb
Release : 2019-01-08
Category : Algebra
ISBN : 9781470434380

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Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms by Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger Pdf

The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

Convolution Equations and Singular Integral Operators

Leonid Lerer,Vadim Olshevsky,Ilya M. Spitkovsky
Convolution Equations and Singular Integral Operators Book PDF

Author : Leonid Lerer,Vadim Olshevsky,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 47,8 Mb
Release : 2011-02-03
Category : Mathematics
ISBN : 9783764389567

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Convolution Equations and Singular Integral Operators by Leonid Lerer,Vadim Olshevsky,Ilya M. Spitkovsky Pdf

This book consists of translations into English of several pioneering papers in the areas of discrete and continuous convolution operators and on the theory of singular integral operators published originally in Russian. The papers were wr- ten more than thirty years ago, but time showed their importance and growing in?uence in pure and applied mathematics and engineering. The book is divided into two parts. The ?rst ?ve papers, written by I. Gohberg and G. Heinig, form the ?rst part. They are related to the inversion of ?nite block Toeplitz matrices and their continuous analogs (direct and inverse problems) and the theory of discrete and continuous resultants. The second part consists of eight papers by I. Gohberg and N. Krupnik. They are devoted to the theory of one dimensional singular integral operators with discontinuous co- cients on various spaces. Special attention is paid to localization theory, structure of the symbol, and equations with shifts. ThisbookgivesanEnglishspeakingreaderauniqueopportunitytogetfam- iarized with groundbreaking work on the theory of Toepliz matrices and singular integral operators which by now have become classical. In the process of the preparation of the book the translator and the editors took care of several misprints and unessential misstatements. The editors would like to thank the translator A. Karlovich for the thorough job he has done. Our work on this book was started when Israel Gohberg was still alive. We see this book as our tribute to a great mathematician.

Operator Theory, Operator Algebras, and Matrix Theory

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

Author : Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa
Publisher : Birkhäuser
Page : 372 pages
File Size : 44,9 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.

Approximation of Additive Convolution-Like Operators

Victor Didenko,Bernd Silbermann
Approximation of Additive Convolution Like Operators Book PDF

Author : Victor Didenko,Bernd Silbermann
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 43,8 Mb
Release : 2008-09-19
Category : Mathematics
ISBN : 9783764387518

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Approximation of Additive Convolution-Like Operators by Victor Didenko,Bernd Silbermann Pdf

This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods. The book is self-contained and accessible to graduate students.

Toeplitz Matrices and Singular Integral Equations

Albrecht Böttcher,Israel Gohberg,P. Junghanns
Toeplitz Matrices and Singular Integral Equations Book PDF

Author : Albrecht Böttcher,Israel Gohberg,P. Junghanns
Publisher : Birkhäuser
Page : 327 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881999

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Toeplitz Matrices and Singular Integral Equations by Albrecht Böttcher,Israel Gohberg,P. Junghanns Pdf

This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.

Analysis, Partial Differential Equations and Applications

Alberto Cialdea,Flavia Lanzara,Paolo Emilio Ricci
Analysis Partial Differential Equations and Applications Book PDF

Author : Alberto Cialdea,Flavia Lanzara,Paolo Emilio Ricci
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 53,9 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9783764398989

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Analysis, Partial Differential Equations and Applications by Alberto Cialdea,Flavia Lanzara,Paolo Emilio Ricci Pdf

This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of pure and applied analysis. The book aims at spreading the seminal ideas of Maz'ya to a larger audience in faculties of sciences and engineering. In fact, all articles were inspired by previous works of Maz'ya in several frameworks, including classical and contemporary problems connected with boundary and initial value problems for elliptic, hyperbolic and parabolic operators, Schrödinger-type equations, mathematical theory of elasticity, potential theory, capacity, singular integral operators, p-Laplacians, functional analysis, and approximation theory. Maz'ya is author of more than 450 papers and 20 books. In his long career he obtained many astonishing and frequently cited results in the theory of harmonic potentials on non-smooth domains, potential and capacity theories, spaces of functions with bounded variation, maximum principle for higher-order elliptic equations, Sobolev multipliers, approximate approximations, etc. The topics included in this volume will be particularly useful to all researchers who are interested in achieving a deeper understanding of the large expertise of Vladimir Maz'ya.

Operator Algebras, Operator Theory and Applications

J. J. Grobler,L.E. Labuschagne,Manfred Möller
Operator Algebras Operator Theory and Applications Book PDF

Author : J. J. Grobler,L.E. Labuschagne,Manfred Möller
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 44,5 Mb
Release : 2009-12-24
Category : Mathematics
ISBN : 9783034601740

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Operator Algebras, Operator Theory and Applications by J. J. Grobler,L.E. Labuschagne,Manfred Möller Pdf

This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.

Operator Algebras, Toeplitz Operators and Related Topics

Wolfram Bauer,Roland Duduchava,Sergei Grudsky,Marinus A. Kaashoek
Operator Algebras Toeplitz Operators and Related Topics Book PDF

Author : Wolfram Bauer,Roland Duduchava,Sergei Grudsky,Marinus A. Kaashoek
Publisher : Springer Nature
Page : 467 pages
File Size : 48,7 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030446512

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Operator Algebras, Toeplitz Operators and Related Topics by Wolfram Bauer,Roland Duduchava,Sergei Grudsky,Marinus A. Kaashoek Pdf

This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.

Operator Theory and Related Topics

V.M. Adamyan,Israel Gohberg,Myroslav L. Gorbachuk,Valentina Gorbachuk,Marinus A. Kaashoek,H. Langer,G. Popov
Operator Theory and Related Topics Book PDF

Author : V.M. Adamyan,Israel Gohberg,Myroslav L. Gorbachuk,Valentina Gorbachuk,Marinus A. Kaashoek,H. Langer,G. Popov
Publisher : Birkhäuser
Page : 426 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884136

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Operator Theory and Related Topics by V.M. Adamyan,Israel Gohberg,Myroslav L. Gorbachuk,Valentina Gorbachuk,Marinus A. Kaashoek,H. Langer,G. Popov Pdf

The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.