Orthogonal polynomials for the weakly equilibrium Cantor sets

Abstract

Let K ( γ ) 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 Q_{2^s} with respect to the equilibrium measure of K ( γ ) K(\gamma ) coincide with the Chebyshev polynomials of the set. Procedures are suggested to find Q n Q_{n} of all degrees and the corresponding Jacobi parameters. It is shown that the sequence of the Widom factors is bounded below.