On the rate of rational approximation to functions with a finite number of poles
type: Item
instance of: scholarly article
title: On the rate of rational approximation to functions with a finite number of poles
zbMATH Open document ID: 0717.30033
DOI: 10.1016/0022-247X(90)90111-R
author: M. Freund
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Let K be a compact subset of \({\mathbb{C}}\) bounded by a Jordan curve C. Let \(\Gamma_ R=\phi (\{| z| =R\})\) \((R>1)\) be the level line of the corresponding conformal mapping \(\phi\) of \(\{| z| >1\}\) onto \({\hat {\mathbb{C}}}\setminus K\), and let \(E_ R\) be the interior of \(\Gamma_ R\), such that \(K\subset E_ R\). Let f be meromorphic on \(E_ R\) with precisely \(\nu\) poles. For the case that C is sufficiently smooth (more exactly: if K is a Faber set), the author describes the asymptotic behaviour of \[ \max_{w\in K}| f(w)-R_{n\nu}(w)|, \] where \(R_{n\nu}\) is the best rational approximation (admitting \(\nu\) poles) to f on K, in terms of the growth of f. Further, he extends his results to the case of interpolation and investigates some other related topics.
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 4181719
reviewed by: Klaus Menke
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4181719