On an analogue of the runge theorem for harmonic differential forms

Abstract

A variant of the classical theorem of Runge is established for harmonic differenrial forms on an open subset of ℝn. It generalizes the case of analytic functions for n=2. Harmonic forms with point singularities are introduced, and a theorem of displacement of poles is proved. An integral representation analogous to the Cauchy formula is constructed. Bibliography: 5 titles.