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

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

2011-12-05

arxiv.org/abs/1112.0988v3

Mathematics

Spectral Theory

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

Scientific paper

Avila recently introduced a new method for the study of the discrete Schr\"odinger 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.

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