On weighted polynomial approximation

Abstract

Let $\Phi :{\mathbb{R}}^n\to [1,\infty )$ be a semi-continuous from below function such that $\underset{x\to \infty }{\lim }\frac{\ln \Phi (x)}{\Vert x\Vert }=+\infty$. It is shown that polynomials are dense in $C_{\Phi }({\mathbb{R}}^n)$.