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Introduction to large truncated Toeplitz matrices.

Author: Albrecht Böttcher; Bernd Silbermann
Publisher: [S.l.] : Springer, 1999.
Series: Universitext
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Focuses on the application of functional analysis and operator theory to some concrete asymptotic problems of linear algebra. This text is useful for graduate students, teachers, and researchers for  Read more...

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Document Type: Book
All Authors / Contributors: Albrecht Böttcher; Bernd Silbermann
ISBN: 0387985700 9780387985701
OCLC Number: 468405389
Description: 258 p.
Contents: 1 Infinite Matrices.- 1.1 Boundedness and Invertibility.- 1.2 Laurent Matrices.- 1.3 Toeplitz Matrices.- 1.4 Hankel Matrices.- 1.5 Wiener-Hopf Factorization.- 1.6 Continuous Symbols.- 1.7 Locally Sectorial Symbols.- 1.8 Discontinuous Symbols.- 2 Finite Section Method and Stability.- 2.1 Approximation Methods.- 2.2 Continuous Symbols.- 2.3 Asymptotic Inverses.- 2.4 The Gohberg-Feldman Approach.- 2.5 Algebraization of Stability.- 2.6 Local Principles.- 2.7 Localization of Stability.- 3 Norms of Inverses and Pseudospectra.- 3.1C*-Algebras.- 3.2 Continuous Symbols.- 3.3 Piecewise Continuous Symbols.- 3.4 Norm of the Resolvent.- 3.5 Limits of Pseudospectra.- 3.6 Pseudospectra of Infinite Toeplitz Matrices.- 4 Moore-Penrose Inverses and Singular Values.- 4.1 Singular Values of Matrices.- 4.2 The Lowest Singular Value.- 4.3 The Splitting Phenomenon.- 4.4 Upper Singular Values.- 4.5 Moler's Phenomenon.- 4.6 Limiting Sets of Singular Values.- 4.7 The Moore-Penrose Inverse.- 4.8 Asymptotic Moore-Penrose Inversion.- 4.9 Moore-Penrose Sequences.- 4.10 Exact Moore-Penrose Sequences.- 4.11 Regularization and Kato Numbers.- 5 Determinants and Eigenvalues.- 5.1 The Strong Szegoe Limit Theorem.- 5.2 Ising Model and Onsager Formula.- 5.3 Second-Order Trace Formulas.- 5.4 The First Szegoe Limit Theorem.- 5.5 Hermitian Toeplitz Matrices.- 5.6 The Avram-Parter Theorem.- 5.7 The Algebraic Approach to Trace Formulas.- 5.8 Toeplitz Band Matrices.- 5.9 Rational Symbols.- 5.10 Continuous Symbols.- 5.11 Fisher-Hartwig Determinants.- 5.12 Piecewise Continuous Symbols.- 6 Block Toeplitz Matrices.- 6.1 Infinite Matrices.- 6.2 Finite Section Method and Stability.- 6.3 Norms of Inverses and Pseudospectra.- 6.4 Distribution of Singular Values.- 6.5 Asymptotic Moore-Penrose Inversion.- 6.6 Trace Formulas.- 6.7 The Szegoe-Widom Limit Theorem.- 6.8 Rational Matrix Symbols.- 6.9 Multilevel Toeplitz Matrices.- 7 Banach Space Phenomena.- 7.1 Boundedness.- 7.2 Fredholmness and Invertibility.- 7.3 Continuous Symbols.- 7.4 Piecewise Continuous Symbols.- 7.5 Loss of Symmetry.- References.- Symbol Index.
Series Title: Universitext
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