Generic Spectral Results for CMV Matrices with Dynamically Defined Verblunsky Coefficients

2020/01/03 by Licheng Fang, David Damanik, Fang, Licheng +3
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2001.00845

openalex publication_date 2020/01/03 · openalex created_date 2020/01/10 · openalex updated_date 2026/07/28

Abstract

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.

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