Convolution Operators And Factorization Of Almost Periodic Matrix Functions

Author : Albrecht Böttcher,Yuri I. Karlovich,Ilya M. Spitkovsky
Publisher : Birkhäuser
Page : 464 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881524

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Convolution Operators and Factorization of Almost Periodic Matrix Functions by Albrecht Böttcher,Yuri I. Karlovich,Ilya M. Spitkovsky Pdf

Many problems of the engineering sciences, physics, and mathematics lead to con volution equations and their various modifications. Convolution equations on a half-line can be studied by having recourse to the methods and results of the theory of Toeplitz and Wiener-Hopf operators. Convolutions by integrable kernels have continuous symbols and the Cauchy singular integral operator is the most prominent example of a convolution operator with a piecewise continuous symbol. The Fredholm theory of Toeplitz and Wiener-Hopf operators with continuous and piecewise continuous (matrix) symbols is well presented in a series of classical and recent monographs. Symbols beyond piecewise continuous symbols have discontinuities of oscillating type. Such symbols emerge very naturally. For example, difference operators are nothing but convolution operators with almost periodic symbols: the operator defined by (A

Author : Vladimir Dybin,Sergei M. Grudsky
Publisher : Birkhäuser
Page : 306 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882132

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Introduction to the Theory of Toeplitz Operators with Infinite Index by Vladimir Dybin,Sergei M. Grudsky Pdf

This book is devoted to Toeplitz and singular integral operators with symbols that have discontinuities of the oscillating type. Criteria for the normal solvability of such operators are established and several methods for describing the kernel and image spaces of the operators are presented. The approach is based on the idea of modelling discontinuities with an "infinite index" by appropriate inner functions, especially by infinite Blaschke products. The corresponding techniques have been elaborated by the authors during the last two decades, and they are applicable to both symbols with slowly and rapidly increasing arguments. Moreover, the book reveals exciting connections between invariant subspaces of the shift operator, bases in Banach spaces, and various classes of entire and meromorphic functions. The book aims at making advanced topics accessible to a broad readership. It is addressed to graduate and postgraduate students and to mathematicians interested in functional analysis, the theory of functions of a complex variable, or mathematical physics.

Author : A. Böttcher,I. Gohberg
Publisher : Birkhäuser
Page : 325 pages
File Size : 53,5 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.

Author : H. Bart,I. Gohberg,A.C.M. Ran
Publisher : Birkhäuser
Page : 460 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882835

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Operator Theory and Analysis by H. Bart,I. Gohberg,A.C.M. Ran Pdf

On November 12-14, 1997 a workshop was held at the Vrije Universiteit Amsterdam on the occasion of the sixtieth birthday ofM. A. Kaashoek. The present volume contains the proceedings of this workshop. The workshop was attended by 44 participants from all over the world: partici pants came from Austria, Belgium, Canada, Germany, Ireland, Israel, Italy, The Netherlands, South Africa, Switzerland, Ukraine and the USA. The atmosphere at the workshop was very warm and friendly. There where 21 plenary lectures, and each lecture was followed by a lively discussion. The workshop was supported by: the Vakgroep Wiskunde of the Vrije Univer siteit, the department of Mathematics and Computer Science of the Vrije Univer siteit, the Stichting VU Computer Science & Mathematics Research Centre, the Thomas Stieltjes Institute for Mathematics, and the department of Economics of the Erasmus University Rotterdam. The organizers would like to take this opportunity to express their gratitude for the support. Without it the workshop would not have been so successful as it was. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Photograph of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Curriculum Vitae of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Publications of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix l. Gohberg Opening Address . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi H. Bart, A. C. M. Ran and H. I. Woerdeman Personal Reminiscences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxv V. Adamyan and R. Mennicken On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Conditions for the Separation of Spectral Components . . . . . . . 4 3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Author : Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 45,8 Mb
Release : 2011-02-09
Category : Mathematics
ISBN : 9783034601580

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Topics in Operator Theory by Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky Pdf

This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Author : Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos
Publisher : Birkhäuser
Page : 227 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880039

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Factorization and Integrable Systems by Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos Pdf

This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.

Author : Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck
Publisher : Birkhäuser
Page : 393 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880077

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Singular Integral Operators, Factorization and Applications by Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck Pdf

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.

Author : Estelle L. Basor,I. Gohberg
Publisher : Birkhäuser
Page : 208 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885430

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Toeplitz Operators and Related Topics by Estelle L. Basor,I. Gohberg Pdf

This volume is dedicated to Harold Widom, a distinguished mathematician and renowned expert in the area of Toeplitz, Wiener-Hopf and pseudodifferential operators, on the occasion of his sixtieth birthday. The book opens with biographical material and a list of the mathematician's publications, this being followed by two papers based on Toeplitz lectures which he delivered at Tel Aviv University in March, 1993. The rest of the book consists of a selection of papers containing some recent achievements in the following areas: Szegö-Widom asymptotic formulas for determinants of finite sections of Toeplitz matrices and their generalizations, the Fisher-Hartwig conjecture, random matrices, analysis of kernels of Toeplitz matrices, projectional methods and eigenvalue distribution for Toeplitz matrices, the Fredholm theory for convolution type operators, the Nehari interpolation problem with generalizations and applications, and Toeplitz-Hausdorff type theorems. The book will appeal to a wide audience of pure and applied mathematicians.

Author : Marek Ptak
Publisher : Springer Nature
Page : 423 pages
File Size : 40,5 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9783031506130

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Operator and Matrix Theory, Function Spaces, and Applications by Marek Ptak Pdf

Author : Albrecht Böttcher,Israel Gohberg,P. Junghanns
Publisher : Birkhäuser
Page : 327 pages
File Size : 42,9 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.

Author : Deguang Han,Palle E. T. Jørgensen,David R. Larson
Publisher : American Mathematical Soc.
Page : 440 pages
File Size : 48,9 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839232

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Operator Theory, Operator Algebras, and Applications by Deguang Han,Palle E. T. Jørgensen,David R. Larson Pdf

This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.

Author : Maria Amélia Bastos,Israel Gohberg,Amarino Brites Lebre,Frank-Olme Speck
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 51,7 Mb
Release : 2008-05-27
Category : Mathematics
ISBN : 9783764386849

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Operator Algebras, Operator Theory and Applications by Maria Amélia Bastos,Israel Gohberg,Amarino Brites Lebre,Frank-Olme Speck Pdf

This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.

Author : Robert Ellis,Israel Gohberg
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 51,8 Mb
Release : 2003
Category : Mathematics
ISBN : 3764369299

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Orthogonal Systems and Convolution Operators by Robert Ellis,Israel Gohberg Pdf

The main concern of this book is the distribution of zeros of polynomials that are orthogonal on the unit circle with respect to an indefinite weighted scalar or inner product. The first theorem of this type, proved by M. G. Krein, was a far-reaching generalization of G. Szegö's result for the positive definite case. A continuous analogue of that theorem was proved by Krein and H. Langer. These results, as well as many generalizations and extensions, are thoroughly treated in this book. A unifying theme is the general problem of orthogonalization with invertible squares in modules over C*-algebras. Particular modules that are considered in detail include modules of matrices, matrix polynomials, matrix-valued functions, linear operators, and others. One of the central features of this book is the interplay between orthogonal polynomials and their generalizations on the one hand, and operator theory, especially the theory of Toeplitz marices and operators, and Fredholm and Wiener-Hopf operators, on the other hand. The book is of interest to both engineers and specialists in analysis.

Author : M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Publisher : Springer Nature
Page : 654 pages
File Size : 44,8 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030519452

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Operator Theory, Functional Analysis and Applications by M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich Pdf

This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Author : Alexandre Almeida,Luís Castro,Frank-Olme Speck
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 48,5 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9783034805162

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Advances in Harmonic Analysis and Operator Theory by Alexandre Almeida,Luís Castro,Frank-Olme Speck Pdf

This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.