Harmonic approximation and Sarasonʹs-type theorem Original Research Article

In this paper uniform approximation of bounded harmonic functions on an arbitrary open set in Euclidean space by harmonic functions arising as solutions of the classical or generalized Dirichlet problem is studied. In particular, an analogue of Sarasonʹs H∞+C theorem (known from the theory of algebras of analytic functions) is established for harmonic functions.