Convergence of Bieberbach polynomials inside domains of the complex plane

Küçükaslan M., Tunç T., ABDULLAYEV F.

Bulletin of the Belgian Mathematical Society - Simon Stevin, vol.13, no.4, pp.657-671, 2006 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 4
  • Publication Date: 2006
  • Doi Number: 10.36045/bbms/1168957342
  • Journal Name: Bulletin of the Belgian Mathematical Society - Simon Stevin
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.657-671
  • Keywords: Bieberbach polynomials, Complex approximation, Conformal mapping, Quasiconformal curve
  • Uşak University Affiliated: No

Abstract

Let G ⊂ C be a finite Jordan domain, z0 ∈ G; B ⊂ G be an arbitrary closed disk with z0 ∈ B, and w = φ(z, z 0) be the conformal mapping of G onto a disk {w : |w| < r} normalized by φ(z0, z0} = 0, φ(z0, z0) = 1 . It is well known that the Bieberbach polynomials {πn(z, z0)} for the pair (G, z0) converge uniformly to φ(z, z0) on compact subsets of the Jordan domain G. In this paper we study the speed of ||φ - πn||C(B) → 0, n → ∞, in domains of the complex plane with a complicated boundary structure.