Orthogonal polynomials for the weakly equilibrium Cantor sets

Abstract

Let $K(\gamma )$ 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 $K(\gamma )$ 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.

References in corpus (3)

• Two Measures on Cantor Sets
• Chebyshev polynomials on generalized Julia sets
• Finite Gap Jacobi Matrices: A Review

Cited by in corpus (2)

• Spacing properties of the zeros of orthogonal polynomials on Cantor sets via a sequence of polynomial mappings
• Orthogonal polynomials on Cantor sets of zero Lebesgue measure