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arXiv · 1603.04937

Julia sets of Orthogonal polynomials

Jacob Stordahl Christiansen·Christian Henriksen·Henrik Laurberg Pedersen·Carsten Lunde Petersen
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Abstract

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 $K$.

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Jacob Stordahl Christiansen, Christian Henriksen, Henrik Laurberg Pedersen, Carsten Lunde Petersen. 2016-03-16. Julia sets of Orthogonal polynomials. https://arxiv.org/abs/1603.04937

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