Toeplitz Matrices and Singular Integral Equations -

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Résumé :
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.

Sommaire:
Essay on Bernd Silbermann.- Publications of Bernd Silbermann.- Toeplitz Corona Problem for Algebras of Almost Periodic Functions.- Sums of Idempotents in the Banach Algebra Generated by the Compact Operators and the Identity.- Asymptotic Formulas for the Determinants of Symmetric Toeplitz plus Hankel Matrices.- On the Determinant Formulas by Borodin, Okounkov, Baik, Deift and Rains.- On the Distance of a Large Toeplitz Band Matrix to the Nearest Singular Matrix.- Singular Integral Equations on Piecewise Smooth Curves in Spaces of Smooth Functions.- Spline Approximation Methods for the Biharmonic Dirichlet Problem on Non-smooth Domains.- On Rank Invariance of Schwarz-Pick-Potapov Block Matrices of Matrix-valued Carath?odory Functions.- Finite Section Method for Linear Ordinary Differential Equations Revisited.- Fast Algorithms for Skewsymmetric Toeplitz Matrices.- On Collocation Methods for Nonlinear Cauchy Singular Integral Equations.- Local method for nonlocal operators on Banach spaces.- Numerical Solution of Mellin Type Equations via Wiener-Hopf Equations.- A 1-parameter Scale of Closed Ideals Formed by Strictly Singular Operators.- Local Theory of the Fredholmness of Band-dominated Operators with Slowly Oscillating Coefficients.- More Inequalities and Asymptotics for Matrix Valued Linear Positive Operators: the Noncommutative Case.- Toeplitz Determinants, Random Matrices and Random Permutations....