Recent Progress in Polyhedral Harmonics |
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Authors: | Katsunori Iwasaki |
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Affiliation: | (1) Graduate School of Mathematics, Kyushu University, 6–10–1 Hakozaki, Higashi-ku, Fukuoka, 812–8581, Japan. e-mail |
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Abstract: | Polyhedral harmonics is a subject which deals with the problem of characterizing the continuous functions satisfying the mean value property with respect to a polytope. The main feature of it is the finite dimensionality of the space of polyhedral harmonic functions. The theory involves not only analysis but also algebra and combinatorics, and has a rather different flavor from classical harmonic analysis. This paper aims at providing a survey on the subject, focusing on the author's recent results. |
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Keywords: | polytope mean value property harmonic function invariant |
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