Author | Carmona, Renรฉ. author |
---|---|
Title | Spectral Theory of Random Schrรถdinger Operators [electronic resource] / by Renรฉ Carmona, Jean Lacroix |
Imprint | Boston, MA : Birkhรคuser Boston, 1990 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4488-2 |
Descript | XXVI, 589 p. online resource |
I Spectral Theory of Self-Adjoint Operators -- 1 Domains, Adjoints, Resolvents and Spectra -- 2 Resolutions of the Identity -- 3 Representation Theorems -- 4 The Spectral Theorem -- 5 Quadratic Forms and Self-adjoint Operators -- 6 Self-adjoint Extensions of Symmetric Operators -- 7 Problems -- 8 Notes and Complements -- II Schrรถdinger Operators -- 1 The Free Hamiltonians -- 2 Schrรถdinger Operators as Perturbations -- 3 Path Integral Formulas -- 4 Eigenfunctions -- 5 Problems -- 6 Notes and Complements -- III One-Dimensional Schrรถdinger Operators -- 1 The Continuous Case -- 2 The Lattice Case -- 3 Approximations of the Spectral Measures -- 4 Spectral Types -- 5 Quasi-one Dimensional Schrรถdinger Operators -- 6 Problems -- 7 Notes and Complements -- IV Products of Random Matrices -- 1 General Ergodic Theorems -- 2 Matrix Valued Systems -- 3 Group Action on Compact Spaces -- 4 Products of Independent Random Matrices -- 5 Markovian Multiplicative Systems -- 6 Boundaries of the Symplectic Group -- 7 Problems -- 8 Notes and Comments -- V Ergodic Families of Self-Adjoint Operators -- 1 Measurability Concepts -- 2 Spectra of Ergodic Families -- 3 The Case of Random Schrรถdinger Operators -- 4 Regularity Properties of the Lyapunov Exponents -- 5 Problems -- 6 Notes and Complements -- VI The Integrated Density of States -- 1 Existence Problems -- 2 Asymptotic Behavior and Lifschitz Tails -- 3 More on the Lattice Case -- 4 The One Dimensional Cases -- 5 Problems -- 6 Notes and Complements -- VII Absolutely Continuous Spectrum and Inverse Theory -- 1 The w-function -- 2 Periodic and Almost Periodic Potentials -- 3 The Absolutely Continuous Spectrum -- 4 Inverse Spectral Theory -- 5 Miscellaneous -- 6 Problems -- 7 Notes and Complements -- VIII Localization in One Dimension -- 1 Pointwise Theory -- 2 Perturbation Theory -- 3 Operator Theory -- 4 Localization for Singular Potentials -- 5 Non-Stationary Processes -- 6 Problems -- 7 Notes and Complements -- IX Localization in Any Dimension -- 1 Exponential Decay of the Greenโs Function at Fixed Energy -- 2 Localization for A.C. Potentials -- 3 A Direct Proof of Localization -- 4 Problems -- 5 Notes and Complements -- Notation Index