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

摘要

Avila recently introduced a new method for the study of the discreteSchr\"odinger Operator with limit periodic potential. I adapt this method tothe context of orthogonal polynomials in the unit circle with limit periodicVerblunsky Coefficients. Specifically, I represent these VerblunskyCoefficients as a continuous sampling of the orbits of a Cantor group by aminimal translation. I then investigate the measures that arise on the unitcircle as I vary the sampling function.