Ebook: Toeplitz Matrices and Singular Integral Equations: The Bernd Silbermann Anniversary Volume

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.

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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.
Content:
Front Matter....Pages i-viii
Essay on Bernd Silbermann....Pages 1-12
Publications of Bernd Silbermann....Pages 13-23
Toeplitz Corona Problem for Algebras of Almost Periodic Functions....Pages 25-37
Sums of Idempotents in the Banach Algebra Generated by the Compact Operators and the Identity....Pages 39-60
Asymptotic Formulas for the Determinants of Symmetric Toeplitz plus Hankel Matrices....Pages 61-90
On the Determinant Formulas by Borodin, Okounkov, Baik, Deift and Rains....Pages 91-99
On the Distance of a Large Toeplitz Band Matrix to the Nearest Singular Matrix....Pages 101-106
Singular Integral Equations on Piecewise Smooth Curves in Spaces of Smooth Functions....Pages 107-144
Spline Approximation Methods for the Biharmonic Dirichlet Problem on Non-Smooth Domains....Pages 145-160
On Rank Invariance of Schwarz-Pick-Potapov Block Matrices of Matrix-Valued Carath?odory Functions....Pages 161-181
Finite Section Method for Linear Ordinary Differential Equations Revisited....Pages 183-191
Fast Algorithms for Skewsymmetric Toeplitz Matrices....Pages 193-208
On Collocation Methods for Nonlinear Cauchy Singular Integral Equations....Pages 209-233
Local Method for Nonlocal Operators on Banach Spaces....Pages 235-247
Numerical Solution of Mellin Type Equations via Wiener-Hopf Equations....Pages 249-260
A 1-parameter Scale of Closed Ideals Formed by Strictly Singular Operators....Pages 261-265
Local Theory of the Fredholmness of Band-Dominated Operators with Slowly Oscillating Coefficients....Pages 267-291
More Inequalities and Asymptotics for Matrix Valued Linear Positive Operators: the Noncommutative Case....Pages 293-315
Toeplitz Determinants, Random Matrices and Random Permutations....Pages 317-328

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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.
Content:
Front Matter....Pages i-viii
Essay on Bernd Silbermann....Pages 1-12
Publications of Bernd Silbermann....Pages 13-23
Toeplitz Corona Problem for Algebras of Almost Periodic Functions....Pages 25-37
Sums of Idempotents in the Banach Algebra Generated by the Compact Operators and the Identity....Pages 39-60
Asymptotic Formulas for the Determinants of Symmetric Toeplitz plus Hankel Matrices....Pages 61-90
On the Determinant Formulas by Borodin, Okounkov, Baik, Deift and Rains....Pages 91-99
On the Distance of a Large Toeplitz Band Matrix to the Nearest Singular Matrix....Pages 101-106
Singular Integral Equations on Piecewise Smooth Curves in Spaces of Smooth Functions....Pages 107-144
Spline Approximation Methods for the Biharmonic Dirichlet Problem on Non-Smooth Domains....Pages 145-160
On Rank Invariance of Schwarz-Pick-Potapov Block Matrices of Matrix-Valued Carath?odory Functions....Pages 161-181
Finite Section Method for Linear Ordinary Differential Equations Revisited....Pages 183-191
Fast Algorithms for Skewsymmetric Toeplitz Matrices....Pages 193-208
On Collocation Methods for Nonlinear Cauchy Singular Integral Equations....Pages 209-233
Local Method for Nonlocal Operators on Banach Spaces....Pages 235-247
Numerical Solution of Mellin Type Equations via Wiener-Hopf Equations....Pages 249-260
A 1-parameter Scale of Closed Ideals Formed by Strictly Singular Operators....Pages 261-265
Local Theory of the Fredholmness of Band-Dominated Operators with Slowly Oscillating Coefficients....Pages 267-291
More Inequalities and Asymptotics for Matrix Valued Linear Positive Operators: the Noncommutative Case....Pages 293-315
Toeplitz Determinants, Random Matrices and Random Permutations....Pages 317-328
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