Generic Spectral Results for CMV Matrices with Dynamically Defined Verblunsky Coefficients
Spectral Theory
2020-01-06 v1 Mathematical Physics
Dynamical Systems
math.MP
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.
Cite
@article{arxiv.2001.00845,
title = {Generic Spectral Results for CMV Matrices with Dynamically Defined Verblunsky Coefficients},
author = {Licheng Fang and David Damanik and Shuzheng Guo},
journal= {arXiv preprint arXiv:2001.00845},
year = {2020}
}
Comments
20 pages