Orthogonal polynomials on the unit circle with Verblunsky coefficients defined by the skew-shift
Spectral Theory
2011-11-18 v1
Abstract
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.
Cite
@article{arxiv.1111.4019,
title = {Orthogonal polynomials on the unit circle with Verblunsky coefficients defined by the skew-shift},
author = {Helge Krueger},
journal= {arXiv preprint arXiv:1111.4019},
year = {2011}
}