Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-27T20:33:23.117Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)