Weighted approximation in $\mathbb{C}$

Abstract

We prove that if $\{{\phi }_j{\}}_j$ is a sequence of subharmonic functions which are increasing to some subharmonic function $\phi$ in $\mathbb{C}$, then the union of all the weighted Hilbert spaces $H({\phi }_j)$ is dense in the weighted Hilbert space $H(\phi )$.