Absolutely continuous Jacobi operators

被引：14

作者：

Pedersen, S ^{[1
]}

机构：

[1] Wright State Univ, Dept Math, Dayton, OH 45435 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 130卷 / 08期

关键词：

orthogonal polynomials; weighted shift; absolute continuity; Jacobi matrix;

D O I：

10.1090/S0002-9939-02-06339-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show (among other results) that a symmetric Jacobi matrix whose diagonal is the zero sequence and whose super-diagonal h(n) > 0 satisfies h(2n-1) = h(2n), h(k) less than or equal to h(k+1) and 0<b <= (h2k+2)/(k+1) <= (h2k)/(k) has purely absolutely continuous spectrum when considered as a self-adjoint operator on L-2 (N).

引用

页码：2369 / 2376

页数：8

共 18 条

[1]

Berezanskii J. M., 1968, TRANSL MATH MONOGRAP, V17

[2] A spectral analysis for self-adjoint operators generated by a class of second order difference equations [J].