Recent developments in harmonic approximation, with applications
The authors survey developments in the field of uniform and tangential (with a given error function) harmonic approximation. Starting point is a theorem of \textit{J. L. Walsh} [Bull. Am. Math. Soc., II. Ser. 35, 499-544 (1929; JFM 55.0889.05)], which says that every function harmonic in a neighborhood of a compact subset \(E\) of \(\mathbb{R}^n\) with connected complement can be uniformly approximated on \(E\) by functions harmonic on the whole of \(\mathbb{R}^n\). The authors present some recent extensions of this result in which approximation takes place on closed sets and they give several applications concerning universal functions, the Radon transform, the maximum principle, and the Dirichlet problem.
scientific article; zbMATH DE number 872695
scientific article