Liouville Theorem for Dunkl Polyharmonic Functions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Authors: Ren, G., Liu, L.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148992
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Liouville Theorem for Dunkl Polyharmonic Functions / G. Ren, L. Liu // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліор.: 17 назв. — англ.

Assume that f is Dunkl polyharmonic in Rn (i.e. (Δh)p f = 0 for some integer p, where Δh is the Dunkl Laplacian associated to a root system R and to a multiplicity function κ, defined on R and invariant with respect to the finite Coxeter group). Necessary and successful condition that f is a polynom...