Orthogonal polynomials for the weakly equilibrium Cantor sets

Alpan, Gökalp; Goncharov, Alexander

doi:10.1090/proc/13025

Orthogonal polynomials for the weakly equilibrium Cantor sets
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by Gökalp Alpan and Alexander Goncharov

Proc. Amer. Math. Soc. 144 (2016), 3781-3795

DOI: https://doi.org/10.1090/proc/13025

Published electronically: May 6, 2016

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Abstract:

Let $K(\gamma )$ be the weakly equilibrium Cantor-type set introduced by the second author in an earlier work. It is proven that the monic orthogonal polynomials $Q_{2^s}$ with respect to the equilibrium measure of $K(\gamma )$ coincide with the Chebyshev polynomials of the set. Procedures are suggested to find $Q_{n}$ of all degrees and the corresponding Jacobi parameters. It is shown that the sequence of the Widom factors is bounded below.

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