2008
DOI: 10.1007/s11118-008-9098-0
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Complementability of Spaces of Harmonic Functions

Abstract: Let U be a bounded open set of the Euclidean space R d and let H(U) denote the space of all real-valued continuous functions on U that are harmonic on U. We present a sufficient condition on the set ∂ reg U of all regular points of U that ensures that H(U) is complemented in C U . We also present examples showing that this condition is not necessary. The proof of the positive result is based upon a general result on complementability of a simplicial function space in a C(K) space.

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