Müntz's theorem and rational approximation (Q1235856)

The authors prove a Müntz type theorem, using the usual Müntz-Szaz theorem, for approximating the reciprocal of a nonvanishing continuous functions \(f\) with reciprocals of polynomials in \(x^{n_k}\) on the positive real axis. The result is that reciprocals of these polynomials are dense in the class of \(1/f\) with limit 0 at infinity if the usual conditions \(\Sigma1/n_k\) diverges is satisfied.