ORTHOGONAL POLYNOMIALS FOR THE WEAKLY EQUILIBRIUM CANTOR SETS

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.