Thursday, January 17, 2013

1301.3810 (Darren C. Ong)

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

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.
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