On dynamics of asymptotically minimal polynomials


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Bayraktar T., Efe M.

Journal of Approximation Theory, vol.295, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 295
  • Publication Date: 2023
  • Doi Number: 10.1016/j.jat.2023.105956
  • Journal Name: Journal of Approximation Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Keywords: Brolin measure, Extremal polynomials, Julia set, Klimek topology
  • Istanbul University Affiliated: Yes

Abstract

We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set E. In particular, we prove that if the zeros of such polynomials are uniformly bounded then their Brolin measures converge weakly to the equilibrium measure of E. In addition, if E is regular and the zeros of such polynomials are sufficiently close to E then we show that the filled Julia sets converge to polynomial convex hull of E in the Klimek topology.