Abstract
LetP be ann-dimensional regular simplex in ℝn centered at the origin, and let P(k) be thek-skeleton ofP fork = 0, 1,…,n. Then the set\({\mathcal{H}}_{P(k)} \) of all continuous functions in ℝn satisfying the mean value property with respect to P(k) forms a finite-dimensional linear space of harmonic polynomials. In this paper the function space\({\mathcal{H}}_{P(k)} \) is explicitly determined by group theoretic and combinatorial arguments for symmetric polynomials.
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Iwasaki, K. Regular simplices, symmetric polynomials and the mean value property. J. Anal. Math. 72, 279–298 (1997). https://doi.org/10.1007/BF02843162
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DOI: https://doi.org/10.1007/BF02843162