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

2011/12/05 by Darren C. Ong, Ong, Darren C.
Mathematics · Physics and Astronomy · #35P05 (Secondary) #47B36 (Primary) 47B80 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35P05 #msc:47B36 #msc:47B80

paper · pdf · doi:10.48550/arxiv.1112.0988

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

arxiv created 2012/02/27 · arxiv updated 2012/02/29

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.

Related

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• Coefficients of Orthogonal Polynomials on the Unit Circle and Higher Order Szego Theorems