Toeplitz Matrices And Operators

Author by : Nikolaï Nikolski
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
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Description : A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.


Large Truncated Toeplitz Matrices Toeplitz Operators And Related Topics

Author by : Dario A. Bini
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 82
Total Download : 131
File Size : 40,6 Mb
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Description : This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Böttcher’s 60th birthday. Albrecht Böttcher himself has made substantial contributions to the subject in the past. The book also includes a biographical essay, a complete bibliography of Albrecht Böttcher’s work and brief informal notes on personal encounters with him. The book is of interest to graduate and advanced undergraduate students majoring in mathematics, researchers in matrix and operator theory as well as engineers and applied mathematicians.


Toeplitz Matrices And Operators

Author by : Nikolaï Nikolski
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 75
Total Download : 631
File Size : 40,9 Mb
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Description : The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others. This friendly introduction to Toeplitz theory covers the classical spectral theory of Toeplitz forms and Wiener–Hopf integral operators and their manifestations throughout modern functional analysis. Numerous solved exercises illustrate the results of the main text and introduce subsidiary topics, including recent developments. Each chapter ends with a survey of the present state of the theory, making this a valuable work for the beginning graduate student and established researcher alike. With biographies of the principal creators of the theory and historical context also woven into the text, this book is a complete source on Toeplitz theory.


Introduction To Large Truncated Toeplitz Matrices

Author by : Albrecht Böttcher
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 87
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Description : Applying functional analysis and operator theory to some concrete asymptotic problems of linear algebra, this book contains results on the stability of projection methods, deals with asymptotic inverses and Moore-Penrose inversion of large Toeplitz matrices, and embarks on the asymptotic behaviour of the norms of inverses, the pseudospectra, the singular values, and the eigenvalues of large Toeplitz matrices. The approach is heavily based on Banach algebra techniques and nicely demonstrates the usefulness of C*-algebras and local principles in numerical analysis, including classical topics as well as results and methods from the last few years. Though employing modern tools, the exposition is elementary and points out the mathematical background behind some interesting phenomena encountered with large Toeplitz matrices. Accessible to readers with basic knowledge in functional analysis, the book addresses graduates, teachers, and researchers and should be of interest to everyone who has to deal with infinite matrices (Toeplitz or not) and their large truncations.


Toeplitz Operators And Related Topics

Author by : Estelle L. Basor
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 95
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Description : 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.


Toeplitz Matrices And Singular Integral Equations

Author by : Albrecht Böttcher
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 82
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Description : 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.


Spectral Properties Of Banded Toeplitz Matrices

Author by : Albrecht Boettcher
Languange : en
Publisher by : SIAM
Format Available : PDF, ePub, Mobi
Total Read : 52
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File Size : 49,9 Mb
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Description : “This is a wonderful book, full of the latest material on Toeplitz matrices and operators, including norms, spectra, pseudospectra, fields of values, and polynomial hulls. The notes at the end of the chapters are especially interesting and the exercises are challenging. The writing is careful and precise but also entertaining.” --Anne Greenbaum, Professor of Mathematics, University of Washington.“This book is a tremendous resource for all aspects of the spectral theory of banded Toeplitz matrices. It will be the first place I turn when looking for many results in this field, and given this book's amazing breadth and depth, I expect to find just what I need.” -- Mark Embree, Assistant Professor of Computational and Applied Mathematics, Rice University.This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge. Covering everything from classic results to the most recent developments, Spectral Properties of Banded Toeplitz Matrices is an important resource. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers. The book may serve both as a text for introducing the material and as a reference. The approach is based on the know-how and experience of the authors in combining functional analytical methods with hard analysis and in applying operator theoretical methods to matrix theory, which reveals the essence of several phenomena and leads to significant improvements in existing results. All basic results presented in the book are precisely stated as theorems and accompanied by full proofs.Audience This book is written for applied mathematicians, engineers, and scientists who encounter Toeplitz matrices in their research. It also will be of interest to mathematicians in the fields of operator theory, numerical analysis, structured matrices, or random matrix theory, and physicists, chemists, biologists, and economists who deal with stationary statistical and stochastic problems. Parts of the book are suitable for use as a graduate-level text on Toeplitz matrices or analysis.Contents Preface; Chapter 1: Infinite Matrices; Chapter 2: Determinants; Chapter 3: Stability; Chapter 4: Instability; Chapter 5: Norms; Chapter 6: Condition Numbers; Chapter 7: Substitutes for the Spectrum; Chapter 8: Transient Behavior; Chapter 9: Singular Values; Chapter 10: Extreme Eigenvalues; Chapter 11: Eigenvalue Distribution; Chapter 12: Eigenvectors and Pseudomodes; Chapter 13: Structured Perturbations; Chapter 14: Impurities; Bibliography; Index.


Block Toeplitz Operators

Author by : Abraham Konegerie
Languange : en
Publisher by : LAP Lambert Academic Publishing
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Description : In this dissertation we study the modern state space method for inverting semi-infinite block Toeplitz operators with rational matrix symbols explicitly from the representation of its symbol in realization form. The method for constructing explicit formulas for the inverse of a semi-infinite block Toeplitz operator with rational symbol is well-known for rational matrix functions that are analytic and invertible at infinity. However, in this work, we emphasize the case where the matrix function does not have these properties at infinity. In the main results in Chapter 2 we give necessary and sufficient conditions for the equivalence between block Toeplitz operators with rational symbol and discrete singular systems with boundary conditions. We also deal with the special case of finite block Toeplitz matrices. Different Fredholm characteristics are computed in Chapter 3, and a Riemann-Hilbert problem is solved as an application. This book should be useful to individuals who study Operator Theory in Mathematics and Control Sytems in Engineering.


Recent Advances In Matrix And Operator Theory

Author by : Joseph A. Ball
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 10
Total Download : 778
File Size : 54,7 Mb
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Description : This volume comprises the proceedings of the International Workshop on Operator Theory and Its Applications held at the University of Connecticut in July 2005.


Toeplitz Matrices Asymptotic Linear Algebra And Functional Analysis

Author by : Albrecht Böttcher
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 27
Total Download : 390
File Size : 52,9 Mb
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Description : This text is a self-contained introduction to some problems for Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The text looks at Toeplitz matrices with rational symbols, and focuses attention on the asymptotic behavior of the singular values, which includes the behavior of the norms, the norms of the inverses, and the condition numbers as special cases. The text illustrates that the asymptotics of several linear algebra characteristics depend in a fascinating way on functional analytic properties of infinite matrices. Many convergence results can very comfortably be obtained by working with appropriate C*-algebras, while refinements of these results, for example, estimates of the convergence speed, nevertheless require hard analysis.


Infinite Matrices Of Operators

Author by : I.J. Maddox
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 44
Total Download : 388
File Size : 46,8 Mb
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Description :


Analysis Of Toeplitz Operators

Author by : Albrecht Böttcher
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 26
Total Download : 129
File Size : 43,7 Mb
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Description : This book was originally intended as an extended version of our book "Invertibility and Asymptotics of Toeplitz Matrices", which appeared in 1983. We planned to discuss several topics in more detail, but our main concern was to incorporate a whole series of new results obtained during the last few years. However, we soon realized that the program we had in mind required new thoughts from both the methodological and substantial point of view, and so we decided to attempt writing a completely new book on the analysis of Toeplitz operators. There are at least two reasons for the continuous and increasing interest in Toeplitz operators. On the one hand, Toeplitz operators are of importance in connection with a variety of problems in physics, probability theory, information and control theory, and several other fields. Although we shall not embark on these problems, the selection of the material of this book is to a certain extent determined by such applications. On the other hand, besides the differential operators, Toeplitz operators constitute one of the most important classes of non-selfadjoint operators and they are a fascinating example of the fruitful interplay between such topics as operator theory, function theory, and the theory of Banach algebras. One main purpose of this book is to elucidate some of the ideas and methods illustrating just the latter aspect.


Infinite Matrices Of Operators

Author by : Ivor John Maddox
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 73
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File Size : 48,6 Mb
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Toeplitz Matrices Asymptotic Linear Algebra And Functional Analysis

Author by : Albrecht Böttcher
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 88
Total Download : 314
File Size : 54,5 Mb
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Description : This text is a self-contained introduction to some problems for Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The text looks at Toeplitz matrices with rational symbols, and focuses attention on the asymptotic behavior of the singular values, which includes the behavior of the norms, the norms of the inverses, and the condition numbers as special cases. The text illustrates that the asymptotics of several linear algebra characteristics depend in a fascinating way on functional analytic properties of infinite matrices. Many convergence results can very comfortably be obtained by working with appropriate C*-algebras, while refinements of these results, for example, estimates of the convergence speed, nevertheless require hard analysis.


Matrix And Operator Valued Functions

Author by : I. Gohberg
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 40
Total Download : 781
File Size : 41,6 Mb
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Description : A collection of papers on different aspects of operator theory and complex analysis, covering the recent achievements of the Odessa-Kharkov school, where Potapov was very active. The book appeals to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.


Spectra And Pseudospectra

Author by : Lloyd N. Trefethen
Languange : en
Publisher by : Princeton University Press
Format Available : PDF, ePub, Mobi
Total Read : 30
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File Size : 49,6 Mb
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Description : Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.


Recent Advances In Operator Theory And Its Applications

Author by : Israel Gohberg
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 119
File Size : 51,9 Mb
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Description : This book contains a selection of carefully refereed research papers, most of which were presented at the fourteenth International Workshop on Operator Theory and its Applications (IWOTA), held at Cagliari, Italy, from June 24-27, 2003. The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.


Encyclopaedia Of Mathematics

Author by : Michiel Hazewinkel
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 64
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Description : This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.


Recent Trends In Toeplitz And Pseudodifferential Operators

Author by : Roland V. Duduchava
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 82
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Description : The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory and differential geometry to some problems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points. Moreover, the book comprises new results in the theory of Wiener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics.


Current Trends In Operator Theory And Its Applications

Author by : Joseph A. Ball
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 41
Total Download : 865
File Size : 51,8 Mb
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Description : Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.


Operator Theory Operator Algebras And Matrix Theory

Author by : Carlos André
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 26
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Description : 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.


Recent Progress In Operator Theory And Its Applications

Author by : Joseph A. Ball
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 67
Total Download : 676
File Size : 55,8 Mb
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Description : This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers, each carefully refereed. The contributions reflect recent developments in operator theory and its applications. Consistent with the topics of recent IWOTA meetings, IWOTA 2009 was designed as a comprehensive, inclusive conference covering all aspects of theoretical and applied operator theory, ranging from classical analysis, differential and integral equations, complex and harmonic analysis to mathematical physics, mathematical systems and control theory, signal processing and numerical analysis. The conference brought together international experts for a week-long stay at Hotel Real de Minas, in an atmosphere conducive to fruitful professional interactions. These Proceedings reflect the high quality of the papers presented at the conference.


Recent Progress In Operator Theory

Author by : Israel C. Gohberg
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 44
Total Download : 881
File Size : 45,8 Mb
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Description : This volume brings readers up to date on different aspects of operator theory and its applications, including mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and systems. Of practical use to a wide readership in pure and applied mathematics, physics and engineering sciences.


Handbook Of Linear Algebra

Author by : Leslie Hogben
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 86
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File Size : 51,6 Mb
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Description : With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and