Approximation by weighted polynomials
The paper is devoted to the study of approximation by weighted polynomials. The author proves that if \(xQ'(x)\) is increasing on \((0,\infty)\) and \(w(x)= \exp(-Q(x))\) is the corresponding weight on \([0,\infty)\), then every continuous function that vanishes outside. The support of the extremal measure associated with \(w\) can be uniformly approximated by weighted polynomials of the form \(w^nP_n\). In connection with the Borwein-Saff conjecture Totik [\textit{V. Totik} Constructive Approximation 16, 261-281 (2000; Zbl 0955.41005)] proved a similar result for convex \(Q\).
scientific article; zbMATH DE number 1891281