On the measure of the absolutely continuous spectrum for Jacobi matrices

JOURNAL OF APPROXIMATION THEORY

卷:163

Article

Shamis, Mira¹  Sodin, Sasha² 

[1] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

[2] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

关键词: Jacobi matrices;    Absolutely continuous spectrum;    Density of states;    Chebyshev alternation theorem;   

DOI  :  10.1016/j.jat.2010.12.003

来源: Elsevier

【 摘 要 】

We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support Sigma(ac) of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure of Sigma(ac) which takes into account the value distribution of the diagonal elements, and implies the bound due to Deift-Simon and Poltoratski-Remling. Second, we generalise the differential inequality of Delft-Simon for the integrated density of states associated with the absolutely continuous spectrum to general Jacobi matrices. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free