Orthogonal polynomials for the weakly equilibrium Cantor sets

Let $K(γ)$ 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 $K(γ)$ 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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