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.

OriginalsprogEngelsk
TidsskriftPotential Analysis
Vol/bind50
Udgave nummer3
Sider (fra-til)401-413
Antal sider13
ISSN0926-2601
DOI
StatusUdgivet - 2019

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