Complementability of spaces of harmonic functions
Let \(U\) be a bounded open set in finite dimensions and let \({\mathbf H}(U)\) stand for the space of functions harmonic on \(U\) and continuous on the closure \(\overline U\) of \(U\). The author gives conditions on the set of regular points of \(\overline U\) garanteeing that \({\mathbf H}(U)\) is complemented in \(C({\overline U})\). The proof bases on a thorough analysis of complementarity of a simplicial function space.
scientific article; zbMATH DE number 5373446
scientific article