On weighted polynomial approximation with gaps

Abstract

Let $\alpha$ be a nonnegative continuous function on $\mathbb{R}$. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in $C_{\alpha}$, where $C_{\alpha}$ is the weighted Banach space of complex continuous functions $f$ on $\mathbb{R}$ with $f(t) \exp (-\alpha (t))$ vanishing at infinity.