This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Kraus, Christiane2016-03-242019-06-2820060946-8633https://doi.org/10.34657/1916https://oa.tib.eu/renate/handle/123456789/1826The polynomial approximation behaviour of the class of functions Fs:R2(x0,y0)−>R,Fs(x,y)=((x−x0)2+(y−y0)2)(−s),sin(0,infty), is studied in [Bra01]. There it is claimed that the obtained results can be embedded in a more general setting. This conjecture will be confirmed and complemented by a different approach than in [Bra01]. The key is to connect the approximation rate of F_s with its holomorphic continuability for which the classical Bernstein approximation theorem is linked with the convexity of best approximants. Approximation results of this kind also play a vital role in the numerical treatment of elliptic differential equations [Sau].application/pdfeng510Polynomial approximation in 2–spaceMaximal convergenceBernstein-Walsh’s type. theoremsReport