Toeplitz Matrices and Singular Integral Equations

Toeplitz Matrices and Singular Integral Equations
Author :
Publisher : Birkhäuser
Total Pages : 327
Release :
ISBN-10 : 9783034881999
ISBN-13 : 3034881991
Rating : 4/5 (99 Downloads)

Synopsis Toeplitz Matrices and Singular Integral Equations by : Albrecht Böttcher

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.

Toeplitz Matrices and Singular Integral Equations

Toeplitz Matrices and Singular Integral Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 350
Release :
ISBN-10 : 3764368772
ISBN-13 : 9783764368777
Rating : 4/5 (72 Downloads)

Synopsis Toeplitz Matrices and Singular Integral Equations by : Bernd Silbermann

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.

Toeplitz Matrices and Operators

Toeplitz Matrices and Operators
Author :
Publisher : Cambridge University Press
Total Pages : 453
Release :
ISBN-10 : 9781107198500
ISBN-13 : 110719850X
Rating : 4/5 (00 Downloads)

Synopsis Toeplitz Matrices and Operators by : Nikolaï Nikolski

A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.

Toeplitz and Circulant Matrices

Toeplitz and Circulant Matrices
Author :
Publisher : Now Publishers Inc
Total Pages : 105
Release :
ISBN-10 : 9781933019239
ISBN-13 : 1933019239
Rating : 4/5 (39 Downloads)

Synopsis Toeplitz and Circulant Matrices by : Robert M. Gray

The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.

Numerical Methods for Structured Matrices and Applications

Numerical Methods for Structured Matrices and Applications
Author :
Publisher : Springer Science & Business Media
Total Pages : 439
Release :
ISBN-10 : 9783764389963
ISBN-13 : 3764389966
Rating : 4/5 (63 Downloads)

Synopsis Numerical Methods for Structured Matrices and Applications by : Dario Andrea Bini

This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.

Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics

Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics
Author :
Publisher : Birkhäuser
Total Pages : 757
Release :
ISBN-10 : 9783319491820
ISBN-13 : 3319491822
Rating : 4/5 (20 Downloads)

Synopsis Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics by : Dario A. Bini

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.

Convolution Equations and Singular Integral Operators

Convolution Equations and Singular Integral Operators
Author :
Publisher : Springer Science & Business Media
Total Pages : 232
Release :
ISBN-10 : 9783764389567
ISBN-13 : 3764389567
Rating : 4/5 (67 Downloads)

Synopsis Convolution Equations and Singular Integral Operators by : Leonid Lerer

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.

Singular Integral Equations and Discrete Vortices

Singular Integral Equations and Discrete Vortices
Author :
Publisher : Walter de Gruyter GmbH & Co KG
Total Pages : 488
Release :
ISBN-10 : 9783110926040
ISBN-13 : 3110926040
Rating : 4/5 (40 Downloads)

Synopsis Singular Integral Equations and Discrete Vortices by : I. K. Lifanov

This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Proceedings of the Norbert Wiener Centenary Congress, 1994

Proceedings of the Norbert Wiener Centenary Congress, 1994
Author :
Publisher : American Mathematical Soc.
Total Pages : 622
Release :
ISBN-10 : 0821867571
ISBN-13 : 9780821867570
Rating : 4/5 (71 Downloads)

Synopsis Proceedings of the Norbert Wiener Centenary Congress, 1994 by : Vidyadhar Mandrekar

A mathematician on par with the greatest in the century, Norbert Wiener was a universal thinker of colossal proportions. This book contains the proceedings of the Norbert Wiener Centenary Congress held at Michigan State University on November 27-December 2, 1994. The aim of the Congress was to reveal the depth and strong coherence of thought that runs through Wiener's legacy, and to exhibit its continuation in on-going research. This volume brings together the great minds who have furthered Wiener's ideas in physics, stochastics, harmonic analysis, philosophy, prosthesis and cybernetics. The presentations coherently lay out the developments of the subjects from their inception. This volume provides an excellent pathway for new investigators who may wish to pursue these developments by following the footsteps of world experts. There is no other book available in which experts in the various fields in which Wiener worked have presented his thoughts and contributions insuch a coherent and lucid manner.

Orthogonal Polynomials on the Unit Circle

Orthogonal Polynomials on the Unit Circle
Author :
Publisher : American Mathematical Soc.
Total Pages : 498
Release :
ISBN-10 : 9780821848630
ISBN-13 : 0821848631
Rating : 4/5 (30 Downloads)

Synopsis Orthogonal Polynomials on the Unit Circle by : Barry Simon

This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szego's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.