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

1. Auflage 2004
ISBN: 978-1-4008-3714-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 158, 200 Seiten

Reihe: Annals of Mathematics Studies

BourgainJean:

Jean Bourgain is Professor of Mathematics at the Institute for Advanced Study and J. Doob Professor of Mathematics at the University of Illinois, Urbana-Champaign. He is the author of Global Solutions of Nonlinear Schrödinger Equations.Jean Bourgain is Professor of Mathematics at the Institute for Advanced Study and J. Doob Professor of Mathematics at the University of Illinois, Urbana-Champaign. He is the author of Global Solutions of Nonlinear Schrödinger Equations.

Autoren/Hrsg.

Bourgain, Jean

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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

Über Autor(innen)

Jean Bourgain is Professor of Mathematics at the Institute for Advanced Study and J. Doob Professor of Mathematics at the University of Illinois, Urbana-Champaign. He is the author of Global Solutions of Nonlinear Schrödinger Equations.