Polynomial inequalities and universal Taylor series

Abstract

We derive several new properties concerning both universal Taylor series and Fekete universal series from classical polynomial inequalities. In particular, we study some density properties of their approximating subsequences. Moreover we exhibit summability methods which preserve or imply the universality of Taylor series in the complex plane. Likewise we show that the partial sums of the Taylor expansion around zero of a \(C^{\infty }\) function is universal if and only if the sequence of its Cesaro means satisfies the same universal approximation property.