Absolutely continuous spectrum of Dirac operators with square-integrable potentials

被引：4

作者：

Hughes, Daniel ^{[1
]}

Schmidt, Karl Michael ^{[1
]}

机构：

[1] Cardiff Univ, Sch Math, Cardiff CF24 4AG, S Glam, Wales

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2014年 / 144卷 / 03期

关键词：

DIMENSIONAL SCHRODINGER-OPERATORS; DENSE POINT SPECTRUM; DECAYING POTENTIALS; SUBORDINACY;

D O I：

10.1017/S0308210512001187

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (-infinity, -1] boolean OR [1, infinity). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a subsequent limiting procedure for the spectral function. Furthermore, we show that the absolutely continuous spectrum persists when an angular momentum term is added, thus also establishing the result for spherically symmetric Dirac operators in higher dimensions.

引用

页码：533 / 555

页数：23