Sparse potentials with fractional Hausdorff dimension

被引：21

作者：

Zlatos, A ^{[1
]}

机构：

[1] CALTECH, Pasadena, CA 91125 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2004年 / 207卷 / 01期

基金：

美国国家科学基金会;

关键词：

schrodinger operators; sparse potentials; singular continuous spectrum; fractional dimension;

D O I：

10.1016/S0022-1236(03)00180-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct non-random bounded discrete half-line Schrodinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case we prove and compute an exact dimension of the spectral measures. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：216 / 252

页数：37

共 10 条

[1]

CYCOON HL, 1987, SCHRODINGER OPERATOR

[2]

FAN AH, FAST BIRKHOFF AVERAG

[3] ON SUBORDINACY AND ANALYSIS OF THE SPECTRUM OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS [J].