Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / / Jean Bourgain.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Bourgain, Jean,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2004]; ©2005
• Year of Publication: 2004
• Language: English
• Series: Annals of Mathematics Studies ; 158
• Physical Description: 1 online resource (200 p.) :; 14 line illus.

This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas...

Table of Contents

• Frontmatter
• Contents
• Acknowledgment
• Chapter 1. Introduction
• Chapter 2. Transfer Matrix and Lyapounov Exponent
• Chapter 3. Herman's Subharmonicity Method
• Chapter 4. Estimates on Subharmonic Functions
• Chapter 5. LDT for Shift Model
• Chapter 6. Avalanche Principle in SL2(R)
• Chapter 7. Consequences for Lyapounov Exponent, IDS, and Green's Function
• Chapter 8. Refinements
• Chapter 9. Some Facts about Semialgebraic Sets
• Chapter 10. Localization
• Chapter 11. Generalization to Certain Long-Range Models
• Chapter 12. Lyapounov Exponent and Spectrum
• Chapter 13. Point Spectrum in Multifrequency Models at Small Disorder
• Chapter 14. A Matrix-Valued Cartan-Type Theorem
• Chapter 15. Application to Jacobi Matrices Associated with Skew Shifts
• Chapter 16. Application to the Kicked Rotor Problem
• Chapter 17. Quasi-Periodic Localization on the Zd-lattice (d > 1)
• Chapter 18. An Approach to Melnikov's Theorem on Persistency of Nonresonant Lower Dimension Tori
• Chapter 19. Application to the Construction of Quasi-Periodic Solutions of Nonlinear Schrödinger Equations
• Chapter 20. Construction of Quasi-Periodic Solutions of Nonlinear Wave Equations
• Appendix