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Title Convolution equations and singular integral operators : selected papers of Israel Gohberg and Georg Heinig, Israel Gohberg and Nahum Krupnik / Leonid Lerer, Vadim Olshevsky, Ilya M. Spitkovsky, editors ; translated from the Russian by Oleksiy Karlovych
Published Basel : Birkhäuser, ©2010

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Description 1 online resource (xxii, 217 pages)
Series Operator theory: advances and applications ; v. 206
Operator theory, advances and applications ; v. 206.
Contents Cover13; -- Table of Contents13; -- Preface -- Introduction -- References -- Inversion of Finite Toeplitz Matrices -- 1. Inversion of Toeplitz matrices -- 2. Inverse problem -- 3. Continual analogue -- References -- Inversion of Finite Toeplitz Matrices Consisting of Elements of a Noncommutative Algebra 13; -- 1. Theorems on inversion of Toeplitz matrices -- 2. Properties of solutions of equations -- 3. Inverse problem -- 4. Other theorems on inversion of Toeplitz matrices -- 5. Properties of solutions of equations -- 6. Inverse problem for equations -- References -- Matrix Integral Operators on a Finite Interval with Kernels Depending on the Difference of the Arguments13; -- 1. Two lemmas -- 2. The inversion formula -- 2.1. The main result of this section is the following. -- 2.2. Formula -- 3. Properties of the solutions of main equations -- 4. Inverse problem -- References -- The Resultant Matrix and its Generalizations. I. The Resultant Operator for Matrix Polynomials13; -- 1. Lemma on multiple extensions of systems of vectors -- 1.1. -- 1.2.13; -- 2. Auxiliary propositions -- 2.1. -- 2.2. -- 2.3. -- 3. Main theorem -- 3.1. -- 3.2. -- 3.3. -- 4. Applications -- 4.1. -- 4.2. -- 5. Kernel of Bezoutian -- 5.1. -- 5.2. -- References -- The Resultant Matrix and its Generalizations. II. The Continual Analogue of the Resultant Operator13; -- 1. Formulation of the main theorem -- 1.1. -- 1.2. -- 1.3. -- 1.4. -- 1.5. -- 2. A lemma -- 3. Proof of the main theorem -- 4. Scalar case -- 4.1. -- 4.2. -- 5. Applications -- 5.1. -- 5.2. -- 5.3. -- 6. Continual analogue of the Bezoutian -- References -- The Spectrum of Singular Integral Operators in Lp Spaces13; -- 1. The spectrum of discrete Wiener-Hopf equations in hp spaces -- 1.1. -- 1.2. -- 1.3. -- 2. The spectrum of singular integral operators in Lp spaces -- 3. Estimate for the norm of the singular integral operator -- 4. The spectrum of singular integral operators in symmetric spaces13; -- References -- On an Algebra Generated by the Toeplitz Matrices in the Spaces hp13; -- 1. Toeplitz operators in the spaces hp13; -- 1.1. -- 1.2. -- 2. Algebra generated by the Toeplitz operators -- 2.1. -- 2.2. -- References -- On Singular Integral Equations with Unbounded Coefficients13; -- 1. Auxiliary propositions -- 2. On the boundedness of the operator of singular integration -- 3. Operators of the form -- 4. Operators of the form -- References -- Singular Integral Equations with Continuous Coefficients on a Composed Contour13; -- 1. Auxiliary propositions and theorems on solvability13; -- 2. Quotient algebra -- 3. Normal solvability and index of operators in the algebra -- References -- On a Local Principle and Algebras Generated by Toeplitz Matrices13; -- 1. Localizing classes -- 1.1. -- 1.2. -- 1.3. -- 2. First example -- 2.1. -- 2.2. -- 3. Some properties of operators generated by Toeplitz matrices in lp spaces -- 3.1. -- 3.2. -- 3.3. -- 3.4. -- 4. Second example and its applications -- 4.1. -- 4.2. -- 5. Inversion of Toeplitz matrices -- 5.1. -- 5.2. -- 5.3. -- 6. Algebra of
Summary This volume contains English translations of 13 groundbreaking papers on Toeplitz matrices and Wiener-Hopf equations and other classes of discrete and continuous convolution operators and singular integral equations. The papers are both of theoretical and numerical interest, in particular, they examine fast algorithms for inversion of these operators, the theory of discrete and continuous resultants, inversion via factorization, and symbol construction
The papers were originally written in Russian more than thirty years ago; their English translation is published here for the first time. These papers solved difficult problems and opened new venues in the above-mentioned areas. They are still frequently quoted, and moreover, they exert a continuing influence on numerical analysis and other areas of pure and applied mathematics and engineering. The book is addressed to a wide audience of mathematicians and engineers, from graduate students to researchers, whose interests lie in the above-mentioned areas --Book Jacket
Bibliography Includes bibliographical references
Notes Translated from the Russian
Print version record
Subject Convolutions (Mathematics)
Integral equations.
Singular integrals.
MATHEMATICS -- Functional Analysis.
Ecuaciones integrales
Convoluciones (Matemáticas)
Convolutions (Mathematics)
Integral equations
Singular integrals
Faltungsoperator
Singulärer Integraloperator
Toeplitz-Matrix
Form Electronic book
Author Lerer, Leonid
Olshevsky, Vadim, 1961-
Spitkovskiĭ, Ilya M., 1953-
ISBN 9783764389567
3764389567