Green's Function Estimates for Lattice Schr�dinger Operators and Applications. (AM-158) (Annals of Mathematics Studies, 158) - Hardcover

Bourgain, Jean

9780691120973: Green's Function Estimates for Lattice Schr�dinger Operators and Applications. (AM-158) (Annals of Mathematics Studies, 158)

Hardcover

ISBN 10: 0691120978 ISBN 13: 9780691120973

Publisher: Princeton University Press, 2004

This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schr�dinger 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 R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations.

Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."

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About the Author:

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 Schr�dinger Equations.

Review:

"This text is an up to date introduction to localization problems for lattice Schr�dinger operations with deterministic ergodic potentials by one of the leading experts. . . . I can recommend it to any graduate student or researcher in the field."---G. Teschl, Monatschefte f�r Mathematik

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