Limit-Periodic Verblunsky Coefficients for Orthogonal Polynomials on the Unit Circle

Abstract

Avila recently introduced a new method for the study of the discrete Schrödinger Operator with limit periodic potential. I adapt this method to the context of orthogonal polynomials in the unit circle with limit periodic Verblunsky Coefficients. Specifically, I represent these Verblunsky Coefficients as a continuous sampling of the orbits of a Cantor group by a minimal translation. I then investigate the measures that arise on the unit circle as I vary the sampling function.

arXiv comment14 pages. arXiv admin note: text overlap with arXiv:0906.3337 by different authors