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VOL. 27 | 2000 Polytopes, Invariants and Harmonic Functions

Abstract

The classical harmonic functions are characterized in terms of the mean value property with respect to the unit ball. Replacing the ball by a polytope, we are led to the notion of polyhedral harmonic functions, i.e., those continuous functions which satisfy the mean value property with respect to a given polytope. The study of polyhedral harmonic functions involves not only analysis but also algebra, including combinatorics of polytopes and invariant theory for finite reflection groups. We give a brief survey on this subject, focusing on some recent results obtained by the author.

Information

Published: 1 January 2000
First available in Project Euclid: 20 August 2018

zbMATH: 0969.31005
MathSciNet: MR1796897

Digital Object Identifier: 10.2969/aspm/02710145

Rights: Copyright © 2000 Mathematical Society of Japan

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