Hausdorff Dimension of Spectrum of One-Dimensional Schrödinger Operator with Sturmian Potentials

被引：0

作者：

Qing-Hui Liu

Zhi-Ying Wen

机构：

[1] Beijing Institute of Technology,Department of Computer Science and Engineering

[2] Tsinghua University,Department of Mathematics

来源：

Potential Analysis | 2004年 / 20卷

关键词：

one-dimensional Schrödinger operators; Sturmian sequence; Hausdorff dimension;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let β∈(0,1) be an irrational, and [a1,a2,...] be the continued fraction expansion of β. Let Hβ be the one-dimensional Schrödinger operator with Sturmian potentials. We show that if the potential strength V>20, then the Hausdorff dimension of the spectrum σ(Hβ) is strictly great than zero for any irrational β, and is strictly less than 1 if and only if lim inf k→∞(a1a2⋅⋅⋅ak))1/k<∞.

引用

页码：33 / 59

页数：26

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