Trace ideals and their applications / Barry Simon.
Series Mathematical surveys and monographs: no. 120.Editor: Providence, RI : American Mathematical Society, 2005Edición: 2nd edDescripción: viii, 150 p. : il. ; 26 cmISBN: 0821835815 (alk. paper); 9780821849880 (softcover)Tema(s): Operator theory | Hilbert space | Ideals (Algebra) | Mathematical physicsOtra clasificación: 47L20 (47A40 47A55 47B10 47B36 47E05 81Q15 81U99)Preface to the Second Edition v Preface to the First Edition vii Chapter 1. Preliminaries [1] 1.1. Absolute Value and Polar Decomposition [1] 1.2. Compact Operators and the Canonical Decomposition [1] 1.3. Inequalities on Singular Values, I [3] 1.4. Rearrangement Inequalities and All That [4] 1.5. Antisymmetric Tensor Products [6] 1.6. Inequalities on Eigenvalues, I [8] 1.7. Symmetrically Normed Spaces [8] 1.8. Inequalities on Singular Values and Eigenvalues, II [11] 1.9. Clarkson-McCarthy Inequalities [14] Chapter 2. Calkin’s Theory of Operator Ideals and Symmetrically Normed Ideals; Convergence Theorems for Jp [17] Chapter 3. Trace, Determinant, and Lidskii’s Theorem [31] Chapter 4. f(x)g(-iV) [37] Chapter 5. Fredholm Theory [45] Chapter 6. Scattering With a Trace Condition [53] Chapter 7. Bound State Problems [61] Chapter 8. Lots of Inequalities [67] 8.1. Golden-Thompson Inequalities [67] 8.2. Lieb’s Inequalities [70] 8.3. Peierls-Bogoliubov and Berezin Inequalities [71] 8.4. Lieb Concavity [72] Chapter 9. Regularized Determinants and Renormalization in Quantum Field Theory [75] Chapter 10. An Introduction to the Theory on a Banach Space [81] Chapter 11. Borel Transforms, the Krein Spectral Shift, and All That [85] 11.1. Borel Transforms of Measures [86] 11.2. Rank One Perturbations: The Set-Up and Basic Formulae [90] 11.3. The Integral Formula [92] 11.4. The Krein Spectral Shift [93] Appendix to Section 11.4: The Krein Spectral Shift for Trace Class Perturbations [96] 11.5. Infinite Coupling [97] 11.6. Boundary Condition Variation of ODE’s [100] 11.7. Jacobi Matrices [102] Chapter 12. Spectral Theory of Rank One Perturbations [105] 12.1. Invariance of the Absolutely Continuous Spectrum [105] 12.2. The Aronszajn-Donoghue Theory [105] 12.3. The Simon-Wolff Criterion [107] 12.4. Instability of Point Spectrum [109] 12.5. Examples [110] Chapter 13. Localization in the Anderson Model Following Aizenman-Molchanov [113] Chapter 14. The Xi Function [117] 14.1. Abstract Trace Formula [118] 14.2. The Trace Formula for Schrodinger Operators [119] 14.3. Examples [120] 14.4. The Trace Formula for Jacobi Matrices [122] 14.5. A Regularity Theorem for the A.C. Spectrum [123] 14.6. Inverse Problems [124] Appendix. Addenda [127] Bibliography [135] Index [149]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
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Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 47 Si594 (Browse shelf) | Available | A-9291 |
Incluye referencias bibliográficas (p. 135-147) e índice.
Preface to the Second Edition v --
Preface to the First Edition vii --
Chapter 1. Preliminaries [1] --
1.1. Absolute Value and Polar Decomposition [1] --
1.2. Compact Operators and the Canonical Decomposition [1] --
1.3. Inequalities on Singular Values, I [3] --
1.4. Rearrangement Inequalities and All That [4] --
1.5. Antisymmetric Tensor Products [6] --
1.6. Inequalities on Eigenvalues, I [8] --
1.7. Symmetrically Normed Spaces [8] --
1.8. Inequalities on Singular Values and Eigenvalues, II [11] --
1.9. Clarkson-McCarthy Inequalities [14] --
Chapter 2. Calkin’s Theory of Operator Ideals and Symmetrically Normed Ideals; Convergence Theorems for Jp [17] --
Chapter 3. Trace, Determinant, and Lidskii’s Theorem [31] --
Chapter 4. f(x)g(-iV) [37] --
Chapter 5. Fredholm Theory [45] --
Chapter 6. Scattering With a Trace Condition [53] --
Chapter 7. Bound State Problems [61] --
Chapter 8. Lots of Inequalities [67] --
8.1. Golden-Thompson Inequalities [67] --
8.2. Lieb’s Inequalities [70] --
8.3. Peierls-Bogoliubov and Berezin Inequalities [71] --
8.4. Lieb Concavity [72] --
Chapter 9. Regularized Determinants and Renormalization in Quantum Field Theory [75] --
Chapter 10. An Introduction to the Theory on a Banach Space [81] --
Chapter 11. Borel Transforms, the Krein Spectral Shift, and All That [85] --
11.1. Borel Transforms of Measures [86] --
11.2. Rank One Perturbations: The Set-Up and Basic Formulae [90] --
11.3. The Integral Formula [92] --
11.4. The Krein Spectral Shift [93] --
Appendix to Section 11.4: The Krein Spectral Shift for Trace Class Perturbations [96] --
11.5. Infinite Coupling [97] --
11.6. Boundary Condition Variation of ODE’s [100] --
11.7. Jacobi Matrices [102] --
Chapter 12. Spectral Theory of Rank One Perturbations [105] --
12.1. Invariance of the Absolutely Continuous Spectrum [105] --
12.2. The Aronszajn-Donoghue Theory [105] --
12.3. The Simon-Wolff Criterion [107] --
12.4. Instability of Point Spectrum [109] --
12.5. Examples [110] --
Chapter 13. Localization in the Anderson Model Following Aizenman-Molchanov [113] --
Chapter 14. The Xi Function [117] --
14.1. Abstract Trace Formula [118] --
14.2. The Trace Formula for Schrodinger Operators [119] --
14.3. Examples [120] --
14.4. The Trace Formula for Jacobi Matrices [122] --
14.5. A Regularity Theorem for the A.C. Spectrum [123] --
14.6. Inverse Problems [124] --
Appendix. Addenda [127] --
Bibliography [135] --
Index [149] --
MR, MR2154153
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