Abstract
Let P be an n-dimensional polytope admitting a finite reflection group G as its symmetry group. Consider the set HP(k) of all continuous functions on Rn satisfying the mean value property with respect to the k-skeleton P(k) of P, as well as the set HG of all G-harmonic functions. Then a necessary and sufficient condition for the equality HP(k) = HG is given in terms of a distinguished invariant basis, called the canonical invariant basis, of G. 1991 Mathematics Subject Classification 20F55, 52B15.
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