Rational approximation with varying weights. III (Q1971924)

[For part II see \textit{E. A. Rakhmanov, E. B. Saff} and \textit{P. C. Simeonov}, J. Approximation Theory 92, No. 2, 331--338 (1998; Zbl 0907.41013).] The authors investigate the uniform approximation of continuous real-valued functions \(f\) defined on compact subsets \(E\) of \(\mathbb{R}\) by weighted rational functions of the form \(w^nr_n\), where \(r_n\) is a rational function and \(w\) the so called admissible weight. The problem considered in this third paper is to characterize the largest set \(E\) depending of the given weight, having the property that every continuous function \(f\) is the uniform limit on \(E\) of a sequence \(\{w^nr_n\}\).