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Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation.

Authors :
Shi, Yunfeng
Source :
Journal d'Analyse Mathématique; Oct2022, Vol. 148 Issue 1, p305-338, 34p
Publication Year :
2022

Abstract

In this paper we study the multi-frequency quasi-periodic operator with a Gevrey type perturbation. We first establish the large deviation theorem (LDT) for the multi-dimensional operator with a sub-exponential (or Gevrey) long-range hopping, and then prove the pure point spectrum property. Based on the LDT and the Aubry duality, we show the absence of a point spectrum for the 1D exponential long-range operator with a multi-frequency and a Gevrey potential. We also prove the spectrum has positive Lebesgue measure. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00217670
Volume :
148
Issue :
1
Database :
Complementary Index
Journal :
Journal d'Analyse Mathématique
Publication Type :
Academic Journal
Accession number :
160955253
Full Text :
https://doi.org/10.1007/s11854-022-0230-7