2 research outputs found

    Orthogonal polynomials for the weakly equilibrium Cantor sets

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    Let K(γ)K(\gamma) be the weakly equilibrium Cantor type set introduced in [10]. It is proven that the monic orthogonal polynomials Q2sQ_{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 QnQ_{n} of all degrees and the corresponding Jacobi parameters. It is shown that the sequence of the Widom factors is bounded below

    Two Measures on Cantor Sets

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    We give an example of Cantor type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in Stahl-Totik sense
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