Julia sets of Orthogonal polynomials

Jacob Stordahl Christiansen; Christian Henriksen; Henrik Laurberg Pedersen; Carsten Lunde Petersen

Julia sets of Orthogonal polynomials

Complex Variables 2019-10-29 v3

Authors: Jacob Stordahl Christiansen , Christian Henriksen , Henrik Laurberg Pedersen , Carsten Lunde Petersen

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 $K$ .

Keywords

julia set orthogonal polynomials

Cite

@article{arxiv.1603.04937,
  title  = {Julia sets of Orthogonal polynomials},
  author = {Jacob Stordahl Christiansen and Christian Henriksen and Henrik Laurberg Pedersen and Carsten Lunde Petersen},
  journal= {arXiv preprint arXiv:1603.04937},
  year   = {2019}
}

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14 pages, 1 illustration

Julia sets of Orthogonal polynomials

Abstract

Keywords

Cite

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