Orthogonal polynomials for the weakly equilibrium Cantor sets

Gokalp Alpan; Alexander Goncharov

doi:10.1090/proc/13025

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arXiv · 1506.05734

Orthogonal polynomials for the weakly equilibrium Cantor sets

Gokalp Alpan·Alexander Goncharov

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Abstract

Let $K(\gamma)$ be the weakly equilibrium Cantor type set introduced in [10]. 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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BibTeX RIS

Gokalp Alpan, Alexander Goncharov. 2015-06-18. Orthogonal polynomials for the weakly equilibrium Cantor sets. https://doi.org/10.1090/proc%2F13025

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