Weighted approximation in $\mathbb{C}$

TL;DR

This paper proves that the union of an increasing sequence of weighted Hilbert spaces of subharmonic functions in the complex plane is dense in the limit space, advancing understanding of weighted approximation in complex analysis.

Contribution

It establishes a density result for unions of weighted Hilbert spaces of subharmonic functions, a novel contribution to weighted approximation theory in complex analysis.

Findings

Union of increasing weighted Hilbert spaces is dense in the limit space

Provides a new approximation result for subharmonic functions in 

Enhances understanding of weighted spaces in complex analysis

Abstract

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