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Introduction to Large Truncated Toeplitz Matrices [[electronic resource] /] / by Albrecht Böttcher, Bernd Silbermann
| Introduction to Large Truncated Toeplitz Matrices [[electronic resource] /] / by Albrecht Böttcher, Bernd Silbermann |
| Autore | Böttcher Albrecht |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 259 p.) |
| Disciplina | 514 |
| Collana | Universitext |
| Soggetto topico |
Topology
Matrix theory Algebra Mathematical analysis Analysis (Mathematics) Linear and Multilinear Algebras, Matrix Theory Analysis |
| ISBN | 1-4612-1426-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 Szegö Limit Theorem -- 5.2 Ising Model and Onsager Formula -- 5.3 Second-Order Trace Formulas -- 5.4 The First Szegö 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 Szegö-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. |
| Record Nr. | UNINA-9910480322303321 |
Böttcher Albrecht
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to Large Truncated Toeplitz Matrices [[electronic resource] /] / by Albrecht Böttcher, Bernd Silbermann
| Introduction to Large Truncated Toeplitz Matrices [[electronic resource] /] / by Albrecht Böttcher, Bernd Silbermann |
| Autore | Böttcher Albrecht |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 259 p.) |
| Disciplina | 514 |
| Collana | Universitext |
| Soggetto topico |
Topology
Matrix theory Algebra Mathematical analysis Analysis (Mathematics) Linear and Multilinear Algebras, Matrix Theory Analysis |
| ISBN | 1-4612-1426-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 Szegö Limit Theorem -- 5.2 Ising Model and Onsager Formula -- 5.3 Second-Order Trace Formulas -- 5.4 The First Szegö 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 Szegö-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. |
| Record Nr. | UNINA-9910789218803321 |
|
Böttcher Albrecht
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to Large Truncated Toeplitz Matrices / / by Albrecht Böttcher, Bernd Silbermann
| Introduction to Large Truncated Toeplitz Matrices / / by Albrecht Böttcher, Bernd Silbermann |
| Autore | Böttcher Albrecht |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 259 p.) |
| Disciplina | 514 |
| Collana | Universitext |
| Soggetto topico |
Topology
Matrix theory Algebra Mathematical analysis Analysis (Mathematics) Linear and Multilinear Algebras, Matrix Theory Analysis |
| ISBN | 1-4612-1426-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 Szegö Limit Theorem -- 5.2 Ising Model and Onsager Formula -- 5.3 Second-Order Trace Formulas -- 5.4 The First Szegö 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 Szegö-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. |
| Record Nr. | UNINA-9910828902203321 |
|
Böttcher Albrecht
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||