On the singular spectrum of Schrodinger operators with decaying potential

被引：5

作者：

Denisov, S ^{[1
]}

Kupin, S ^{[1
]}

机构：

[1] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 04期

关键词：

Schrodinger operators; Dirac operators; Krein systems; singular part of the spectral measure;

D O I：

10.1090/S0002-9947-04-03553-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The relation between Hausdorff dimension of the singular spectrum of a Schrodinger operator and the decay of its potential has been extensively studied in many papers. In this work, we address similar questions from a different point of view. Our approach relies on the study of the so-called Krein systems. For Schrodinger operators, we show that some bounds on the singular spectrum, obtained recently by Remling and Christ-Kiselev, are optimal.

引用

页码：1525 / 1544

页数：20

共 31 条

[1]

Akhiezer N.I, 1992, Theory of Approximation

[2]

AKHIEZER NI, 1968, UKRAINIAN MATH J, V20, P3

[3] WKB and spectral analysis of one-dimensional Schrodinger operators with slowly varying potentials [J].