On quasi-periodic lattice Schrödinger operators.
type: Item
instance of: scholarly article
title: On quasi-periodic lattice Schrödinger operators.
zbMATH Open document ID: 1059.35091
author: Jean Bourgain
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-07-01T00:00:00Z
review text: The aim of the paper is to review a number of developments over the recent years on the following topics: (1) spectrum and eigenfunctions of Schrödinger operators on \(\mathbb{Z}\) and \(\mathbb{Z}^D\) with a quasi-periodic potential, (2) linear Schrödinger equations with time periodic potential, (3) KAM theory for nonlinear PDE. The paper mainly surveys the works of the author and his collaborators. Compared with earlier research in the areas listed above, there are two new methods extensively used in the contributions considered: (1) subharmonic function techniques, (2) the theory of semi-algebraic sets.
reviewed by: Pavel Dyshlovenko
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 37K55
Mathematics Subject Classification ID: 47B80
zbMATH DE Number: 2077708
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: spectrum
zbMATH Keywords: KAM theory
zbMATH Keywords: Melnikov problems
zbMATH Keywords: review
zbMATH Keywords: subharmonic function
zbMATH Keywords: semi-algebraic sets
MaRDI profile type: Publication
full work available at URL: dcds.2004.10.75
OpenAlex ID: W2072186054
DOI: 10.3934/DCDS.2004.10.75
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description: scientific article; zbMATH DE number 2077708