Convergence of Bieberbach polynomials in domains with quasiconformal boundary
type: Item
instance of: scholarly article
title: Convergence of Bieberbach polynomials in domains with quasiconformal boundary
zbMATH Open document ID: 0536.30006
DOI: 10.1007/BF01092167
published in: Ukrainian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: G est l'intérieur d'une courbe de Jordan L et \(z_ 0\) est un point donné de G; \(w=\phi(z)\) représente conformément G sur un disque de centre 0, avec \(\phi(z_ 0)=0,\quad \phi '(z_ 0)=1.\) Le polynôme \(P_ n\) minimise \(\iint_{G}| P'(z)|^ 2dxdy\) parmi les polynômes de degré n au plus vérifiant \(P(z_ 0)=0,\quad P'(z_ 0)=1.\) Si la courbe L est quasiconforme, l'A. établit la convergence des \(P_ n\) vers \(\phi\) selon la loi \(\| \phi -P_ n\| =O(n^{- \gamma})\) (norme de la convergence uniforme sur \(\bar G\), constante \(\gamma>0)\).
Mathematics Subject Classification ID: 30C20
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 3851445
zbMATH Keywords: Bieberbach polynomials
zbMATH Keywords: quasiconformal curves
author: V. V. Andrievskii
MaRDI profile type: Publication
cites work: Q5638542
cites work: Q5685358
cites work: Q5512337
cites work: Q3937799
cites work: Approximation of functions by partial sums of series of Faber polynomials on continua with nonzero local geometric characteristic
cites work: Q5641585
description: scientific article; zbMATH DE number 3851445