Orthogonal Polynomials on the Unit Circle with Verblunsky Coefficients Defined by the Skew-shift
نویسنده
چکیده
I give an example of a family of orthogonal polynomials on the unit circle with Verblunsky coefficients given by the skew-shift for which the associated measures are supported on the entire unit circle and almost-every Aleksandrov measure is pure point. Furthermore, I show in the case of the two dimensional skew-shift the zeros of para-orthogonal polynomials obey the same statistics as an appropriate irrational rotation. The proof is based on an analysis of the associated CMV matrices.
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Matrix measures on the unit circle, moment spaces, orthogonal polynomials and the Geronimus relations
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