Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients

We consider CMV matrices with dynamically defined Verblunsky coefficients. These coefficients are obtained by continuous sampling along the orbits of an ergodic transformation. We investigate whether certain spectral phenomena are generic in the sense that for a fixed base transformation, the set of...

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Bibliographic Details
Published inJournal of functional analysis Vol. 279; no. 12; p. 108803
Main Authors Fang, Licheng, Damanik, David, Guo, Shuzheng
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.12.2020
Subjects
CMV matrices
Ergodic Verblunsky coefficients
Kotani theory
Kotani theory
CMV matrices
Ergodic Verblunsky coefficients
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Summary:We consider CMV matrices with dynamically defined Verblunsky coefficients. These coefficients are obtained by continuous sampling along the orbits of an ergodic transformation. We investigate whether certain spectral phenomena are generic in the sense that for a fixed base transformation, the set of continuous sampling functions for which the spectral phenomenon occurs is residual. Among the phenomena we discuss are the absence of absolutely continuous spectrum and the vanishing of the Lebesgue measure of the spectrum.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108803