Point spectrum for quasi-periodic long range operators

被引：4

作者：

You, Jiangong ^{[1
]}

Zhang, Shiwen ^{[1
]}

Zhou, Qi ^{[2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[2] Univ Paris 06, Lab Probabilites & Modeles aleatoires, F-75252 Paris 05, France

来源：

JOURNAL OF SPECTRAL THEORY | 2014年 / 4卷 / 04期

关键词：

Point spectrum; quasi-periodic; long-range operator; reducibility; REDUCIBILITY; THEOREM;

D O I：

10.4171/JST/85

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We generalize Gordon type argument to quasi- periodic operators with finite range interaction and prove that these operators have no point spectrum when the rational approximation rate of the base frequency is relatively large. We also show that, for any irrational frequency, there are operators with in finite range interaction possessing point spectrum. This is a new phenomenon which can not happen in the finite range interaction case.

引用

页码：769 / 781

页数：13

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