Julia Sets of Orthogonal Polynomials

Jacob Stordal Christiansen, Christian Henriksen, Henrik Laurberg Petersen, Carsten Lunde Petersen

Research output: Contribution to journalJournal articleResearchpeer-review

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 fPng to properties of the support. More precisely
we relate the Julia set of Pn to the outer boundary of the support, the lled
Julia set to the polynomial convex hull K of the support, and the Green's
function associated with Pn to the Green's function for the complement
of K.
Translated title of the contributionJuliamængder for orthogonale polynomier
Original languageEnglish
JournalPotential Analysis
Volume50
Pages (from-to)401-413
Number of pages13
ISSN0926-2601
DOIs
Publication statusPublished - 2019

Bibliographical note

Publisher's note about the attached Accepted Manuscript of the article (embargoed until february 2019): “This is a post-peer-review, pre-copyedit version of an article published in 'Potential Analysis'. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11118-018-9687-5”.

Keywords

  • Orthogonal Polynomials
  • Green's function
  • Julia set

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