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- W2963258903 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 two-sided 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. I show that generically the spectrum is a Cantor set and we have empty point spectrum. Furthermore, there exists a dense set of sampling functions for which the corresponding spectrum is a Cantor set of positive Lebesgue measure, and all corresponding spectral measures are purely absolutely continuous." @default.
- W2963258903 created "2019-07-30" @default.
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- W2963258903 date "2012-10-01" @default.
- W2963258903 modified "2023-09-28" @default.
- W2963258903 title "Limit-periodic Verblunsky coefficients for orthogonal polynomials on the unit circle" @default.
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- W2963258903 doi "https://doi.org/10.1016/j.jmaa.2012.04.082" @default.
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