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INVARIANTS OF FINITE REFLECTION GROUPS AND THE MEAN VALUE PROBLEM FOR POLYTOPES

Published online by Cambridge University Press:  01 July 1999

KATSUNORI IWASAKI
KATSUNORI IWASAKI
Affiliation:
Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan
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Abstract

Let P be an n-dimensional polytope admitting a finite reflection group G as its symmetry group. Consider the set [Hscr ]P(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 [Hscr ]G of all G-harmonic functions. Then a necessary and sufficient condition for the equality [Hscr ]P(k)=[Hscr ]G is given in terms of a distinguished invariant basis, called the canonical invariant basis, of G.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 477 - 483
Copyright
© The London Mathematical Society 1999

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