### Approximation on the boundary and sets of determination for harmonic functions

Stephen J. Gardiner and Jordi Pau
Source: Illinois J. Math. Volume 47, Number 4 (2003), 1115-1136.

#### 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.

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Primary Subjects: 31B05
Full-text: Open access