Orthogonal polynomials on the unit circle with Verblunsky coefficients defined by the skew-shift

Details Orthogonal polynomials on the unit circle with Verblunsky coefficients defined by the skew-shift Orthogonal polynomials on the unit circle with Verblunsky coefficients defined by the skew-shift

2011-11-17

arxiv.org/abs/1111.4019v1

Mathematics

Spectral Theory

Scientific paper

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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