Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime
type: Item
instance of: scholarly article
title: Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime
zbMATH Open document ID: 0960.34071
DOI: 10.1023/A:1007641323456
author: Jean Bourgain
published in: Letters in Mathematical Physics
publication date: 2000-09-14T00:00:00Z
review text: When an almost Mathieu operator on the lattice is considered, the author shows that in the limit, the integrated density of states is Hölder continuous for a certain exponent range. He shows that this result is similar to the one obtained in a perturbative regime for a one-dimensional quasiperiodic lattice of Schrödinger operators with an assumed positive Lyapunov exponent. The latest approach also provides a new way to control Green's functions.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 47B39
zbMATH DE Number: 1507910
zbMATH Keywords: almost Mathieu operator
zbMATH Keywords: Green's function
zbMATH Keywords: integrated density of states
Wikidata QID: Q97672465
reviewed by: Shlomo Carmi
MaRDI profile type: Publication
full work available at URL: a:1007641323456
OpenAlex ID: W1558901243
description: scientific article; zbMATH DE number 1507910