Orthogonal Polynomials on the Unit Circle with quasiperiodic Verblunsky Coefficients have generic purely singular continuous spectrum
Spectral Theory
2013-01-17 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
As an application of the Gordon lemma for orthogonal polynomials on the unit circle, we prove that for a generic set of quasiperiodic Verblunsky coefficients the corresponding two-sided CMV operator has purely singular continuous spectrum. We use a similar argument to that of the Boshernitzan-Damanik result that establishes the corresponding theorem for the discrete Schr\"odinger operator.
Keywords
Cite
@article{arxiv.1301.3810,
title = {Orthogonal Polynomials on the Unit Circle with quasiperiodic Verblunsky Coefficients have generic purely singular continuous spectrum},
author = {Darren C. Ong},
journal= {arXiv preprint arXiv:1301.3810},
year = {2013}
}
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5 pages