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| Preface 1 Infinite Toeplitz Matrices 1.1 Boundedness 1.2 Compactness and Selfadjointness 1.3 C*-Algebras 1.4 Fredhohn Operators 1.5 Continuous Symbols 1.6 Notes 2 C*-Algebras in Action 2.1 Finite Section Method 2.2 Perturbed Toeplitz Matrices 2.3 Algebraization of Stability 2.4 Stability Criteria 2.5 Asymptotic Inverses 2.6 Norms 2.7 Norms of Inverses 2.8 Condition Numbers 2.9 Eigenvalues of Hermitian Matrices 2.10 Singular Values 2.11 Pseudospectra 2.12 Notes 3 Instability 3.1 Some Standard Tricks 3.2 At Least Polynomial Growth 3.3 At Most Polynomial Growth 3.4 Semi-Definite Hermitian Matrices 3.5 Exponential Growth 3.6 Notes 4 Condition Numbers 4.1 Norms of Pure Toeplitz Matrices 4.2 Structure of the Inverse 4.3 Perturbed Toeplitz Band Matrices 4.4 Norms of the Inverses of Toeplitz Matrices 4.5 Condition Numbers of Toeplitz Matrices 4.6 Condition Numbers of Toeplitz-Like Matrices 4.7 Notes 5 Singular Values 5.1 Basic Facts 5.2 The Splitting Phenomenon 5.3 Extreme Singular Values 5.4 The First Szeg5 Limit Theorem 5.5 The Avram-Parter Theorem 5.6 Circulants 5.7 Toeplitz Band Matrices 5.8 Zizler, Zuidwijk, Taylor, Arimoto 5.9 Notes Bibliography Notation Index Subject Index |
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