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

Darren C. Ong

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arXiv · 1112.0988

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

Darren C. Ong

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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.

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BibTeX RIS

Darren C. Ong. 2012-02-27. Limit-Periodic Verblunsky Coefficients for Orthogonal Polynomials on the Unit Circle. https://arxiv.org/abs/1112.0988

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