On the measure of the absolutely continuous spectrum for Jacobi matrices

Mira Shamis*, Sasha Sodin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support σac of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure of σac 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 Deift-Simon for the integrated density of states associated with the absolutely continuous spectrum to general Jacobi matrices.

Original languageEnglish
Pages (from-to)491-504
Number of pages14
JournalJournal of Approximation Theory
Volume163
Issue number4
DOIs
StatePublished - Apr 2011

Funding

FundersFunder number
United States-Israel Binational Science Foundation
Israel Academy of Sciences and Humanities
Israel Science Foundation1169/06, 2006483

    Keywords

    • Absolutely continuous spectrum
    • Chebyshev alternation theorem
    • Density of states
    • Jacobi matrices

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