The degree of rational approximation to meromorphic functions
type: Item
instance of: scholarly article
title: The degree of rational approximation to meromorphic functions
zbMATH Open document ID: 0649.30031
DOI: 10.4171/ZAA/296
author: M. Freund
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1988-01-01T00:00:00Z
review text: Let S be a compact subset of \({\mathbb{C}}\), and let g be continuous on S, and holomorphic on the interior of S. Let \(E_ n(g)=\inf \| g-r_ n\|\), where the norm is the maximum norm on S, and where the infimum is taken for all rational functions \(r_ n\) of the form \(r_ n=(p_ n/q_ n)\) with polynomials \(p_ n\), \(q_ n\) of degree at most n. Let f be meromorphic on \({\mathbb{C}}\), analytic on S, and let f be of finite order \(\rho\). Under additional assumptions on the poles of f the author gives upper estimates for \(E_ n(f)\) (the case \(\rho =0\) is included), he extends a result of \textit{J. Karlsson} [J. Math. Anal. Appl. 53, 38-52 (1976; Zbl 0335.41010)].
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 4059796
reviewed by: Klaus Menke
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/296
OpenAlex ID: W2561922861
description: scientific article; zbMATH DE number 4059796