On dynamics of asymptotically minimal polynomials

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Bayraktar T., Efe M.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 295
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.jat.2023.105956
  • Dergi Adı: Journal of Approximation Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Brolin measure, Extremal polynomials, Julia set, Klimek topology
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.