Orthogonal polynomials for the weakly equilibrium cantor sets

Abstract

Let K(γ) be the weakly equilibrium Cantor-type set introduced by the second author in an earlier work. It is proven that the monic orthogonal polynomials Q2 s with respect to the equilibrium measure of K(γ) coincide with the Chebyshev polynomials of the set. Procedures are suggested to find Qn of all degrees and the corresponding Jacobi parameters. It is shown that the sequence of the Widom factors is bounded below. © 2016 American Mathematical Society.