By P. Bougerol, Lacroix
Bankruptcy I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. the variation equation. Hyperbolic buildings 187 2. Self adjointness of H. Spectral homes . one hundred ninety three. Slowly expanding generalized eigenfunctions 195 four. Approximations of the spectral degree 196 two hundred five. The natural element spectrum. A criterion 6. Singularity of the spectrum 202 bankruptcy II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. normal spectral houses 206 three. The Lyapunov exponent within the basic ergodie case 209 four. The Lyapunov exponent within the self reliant eas e 211 five. Absence of completely non-stop spectrum 221 224 6. Distribution of states. Thouless formulation 232 7. The natural element spectrum. Kotani's criterion eight. Asymptotic houses of the conductance in 234 the disordered twine bankruptcy III THE natural aspect SPECTRUM 237 238 1. The natural aspect spectrum. First facts 240 2. The Laplace rework on SI(2,JR) 247 three. The natural element spectrum. moment evidence 250 four. The density of states bankruptcy 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 three. Lyapunov exponents within the self reliant case. 262 The natural element spectrum (first facts) 267 four. The Laplace remodel on Sp(~,JR) 272 five. The natural element spectrum, moment facts vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This e-book offers elosely similar sequence of leetures. half A, because of P.