Products of Random Matrices with Applications to Schrödinger Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1985
|
| Schriftenreihe: | Progress in Probability and Statistics
8 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties . 190 3. Slowly increasing generalized eigenfunctions 195 4. Approximations of the spectral measure 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P. |
| Beschreibung: | 1 Online-Ressource (XI, 284 p) |
| ISBN: | 9781468491722 9781468491746 |
| DOI: | 10.1007/978-1-4684-9172-2 |
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| 500 | |a CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties . 190 3. Slowly increasing generalized eigenfunctions 195 4. Approximations of the spectral measure 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P. | ||
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| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468491722 9781468491746 |
| language | English |
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| spelling | Bougerol, Philippe Verfasser aut Products of Random Matrices with Applications to Schrödinger Operators edited by Philippe Bougerol, Jean Lacroix Boston, MA Birkhäuser Boston 1985 1 Online-Ressource (XI, 284 p) txt rdacontent c rdamedia cr rdacarrier Progress in Probability and Statistics 8 CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties . 190 3. Slowly increasing generalized eigenfunctions 195 4. Approximations of the spectral measure 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P. Mathematics Matrix theory Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Linear and Multilinear Algebras, Matrix Theory Partial Differential Equations Mathematik Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 s Hamilton-Operator (DE-588)4072278-8 s 1\p DE-604 Lacroix, Jean Sonstige oth https://doi.org/10.1007/978-1-4684-9172-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bougerol, Philippe Products of Random Matrices with Applications to Schrödinger Operators Mathematics Matrix theory Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Linear and Multilinear Algebras, Matrix Theory Partial Differential Equations Mathematik Hamilton-Operator (DE-588)4072278-8 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| subject_GND | (DE-588)4072278-8 (DE-588)4057624-3 |
| title | Products of Random Matrices with Applications to Schrödinger Operators |
| title_auth | Products of Random Matrices with Applications to Schrödinger Operators |
| title_exact_search | Products of Random Matrices with Applications to Schrödinger Operators |
| title_full | Products of Random Matrices with Applications to Schrödinger Operators edited by Philippe Bougerol, Jean Lacroix |
| title_fullStr | Products of Random Matrices with Applications to Schrödinger Operators edited by Philippe Bougerol, Jean Lacroix |
| title_full_unstemmed | Products of Random Matrices with Applications to Schrödinger Operators edited by Philippe Bougerol, Jean Lacroix |
| title_short | Products of Random Matrices with Applications to Schrödinger Operators |
| title_sort | products of random matrices with applications to schrodinger operators |
| topic | Mathematics Matrix theory Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Linear and Multilinear Algebras, Matrix Theory Partial Differential Equations Mathematik Hamilton-Operator (DE-588)4072278-8 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| topic_facet | Mathematics Matrix theory Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Linear and Multilinear Algebras, Matrix Theory Partial Differential Equations Mathematik Hamilton-Operator Stochastische Matrix |
| url | https://doi.org/10.1007/978-1-4684-9172-2 |
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