Approximation on the boundary and sets of determination for harmonic functions

Abstract

Let $E$ be a subset of a domain $\Omega $ in Euclidean space. This paper deals with the representation, or approximation, of functions on the boundary of $\Omega $ by sums of Poisson, Green or Martin kernels associated with the set $E$, and with the related issue of whether $E$ can be used to determine the suprema of certain harmonic functions on $\Omega $. The results address several questions raised by Hayman.