1301.3810 (Darren C. Ong)

Orthogonal Polynomials on the Unit Circle with quasiperiodic Verblunsky
Coefficients have generic purely singular continuous spectrum    [PDF]

Darren C. Ong

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.

View original: http://arxiv.org/abs/1301.3810