Representation of Harmonic Functions with Asymptotic Boundary Conditions PDF

Keywords

harmonic function, infinity, inversion transformation

Abstract

The representation of a harmonic function outside a compact set in IR^n is obtained, subject to one-sided growth condition at infinity. By an inversion transformation, this result is used to characterize the behavior of a harmonic function in the neighbourhood of an isolated singular point, and leads to a generalized version of Bocher's theorem