The degree of rational approximation to meromorphic functions (Q1105730)

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)].