Polynomial approximation in weighted Dirichlet spaces

TL;DR

This paper provides a straightforward proof that polynomials are dense in weighted Dirichlet spaces with superharmonic weights, extending classical approximation results to a broader function space context.

Contribution

It offers an elementary proof of polynomial density in weighted Dirichlet spaces with superharmonic weights, simplifying previous approaches.

Findings

Polynomials are dense in weighted Dirichlet spaces with superharmonic weights.

The proof extends Fejér's theorem analogue to these spaces.

Provides a simple method for approximation in these function spaces.

Abstract

We give an elementary proof of an analogue of Fej\'er's theorem in weighted Dirichlet spaces with superharmonic weights. This provides a simple way of seeing that polynomials are dense in such spaces.