Green's Function Estimates for Lattice Schrödinger Operators and Applications.

摘要: Acknowledgment v CHAPTER 1: Introduction 1 2: Transfer Matrix and Lyapounov Exponent 11 3: Herman's Subharmonicity Method 15 4: Estimates on Subharmonic Functions 19 5: LDT for Shift Model 25 6: Avalanche Principle in SL2( R ) 29 7: Consequences Exponent, IDS, Green's Function 31 8: Refinements 39 9: Some Facts about Semialgebraic Sets 49 10: Localization 55 11: Generalization to Certain Long-Range Models 65 12: Spectrum 75 13: Point Multifrequency at Small Disorder 87 14: A Matrix-Valued Cartan-Type Theorem 97 15: Application Jacobi Matrices Associated with Skew Shifts 105 16: the Kicked Rotor Problem 117 17: Quasi-Periodic Z d -lattice ( > 1) 123 18: An Approach Melnikov's Persistency of Non-resonant Lower Dimension Tori 133 19: Construction Solutions Nonlinear Schrodinger Equations 143 20: Wave 159 Appendix 169