Julia Sets of Orthogonal Polynomials

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For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials {P n } to properties of the support. More precisely we relate the Julia set of P n to the outer boundary of the support, the filled Julia set to the polynomial convex hull K of the support, and the Green’s function associated with P n to the Green’s function for the complement of K.

Original languageEnglish
JournalPotential Analysis
Issue number3
Pages (from-to)401-413
Number of pages13
Publication statusPublished - 2019

    Research areas

  • Green’s function, Julia set, Orthogonal polynomials

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