Abstract
Let $G\subset C $ be a finite Jordan domain, $z_{0}\in G;$ $B\Subset G$ be an arbitrary closed disk with $z_{0}\in B,$ and $w=\varphi (z,z_{0})$ be the conformal mapping of $G$ onto a disk $\{w:\left| w\right| <r\}$ normalized by $\varphi (z_{0},z_{0})=0$, $\varphi ^{\prime }(z_{0},z_{0})=1$ . It is well known that the Bieberbach polynomials $\{\pi _{n}(z,z_{0})\}$ for the pair $(G,z_{0})$ converge uniformly to $\varphi (z,z_{0})$ on compact subsets of the Jordan domain $G.$ In this paper we study the speed of $\left\| \varphi -\pi _{n}\right\| _{C(B)}\rightarrow 0,$ $n\rightarrow \infty ,$ in domains of the complex plane with a complicated boundary structure.
Citation
F.G. Abdullayev. M. Küçükaslan. T. Tunç. "Convergence of Bieberbach polynomials inside domains of the complex plane." Bull. Belg. Math. Soc. Simon Stevin 13 (4) 657 - 671, December 2006. https://doi.org/10.36045/bbms/1168957342
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