Complementability of spaces of harmonic functions

Abstract

Let $U$ be a bounded open set of the Euclidean space $\er^d$ and let $\Hu(U)$ denote the space of all real--valued continuous functions on $\ov{U}$ that are harmonic on $U$. We present a sufficient condition on the set $\parr U$ of all regular points of $U$ that ensures that $\Hu(U)$ is complemented in $\C(\ov{U})$.

We also present examples showing that this condition is not necessary.

Keywords

• Complementability
• spaces
• harmonic
• functions