Liouville Theorem for Dunkl Polyharmonic Functions
| dc.creator | Ren, Guangbin | |
| dc.creator | Liu, Liang | |
| dc.date | 2008-11-06 | |
| dc.date.accessioned | 2026-07-07T10:16:25Z | |
| dc.date.available | 2026-07-07T10:16:25Z | |
| dc.description | Assume that $f$ is Dunkl polyharmonic in $\mathbb{R}^n$ (i.e. $(Δ_h)^p f=0$ for some integer $p$, where $Δ_h$ 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 polynomial of degree $\le s$ for $s\ge 2p-2$ is proved. As a direct corollary, a Dunkl harmonic function bounded above or below is constant. | |
| dc.description | This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0811.0962 | |
| dc.identifier | http://arxiv.org/abs/0811.0962 | |
| dc.identifier | SIGMA 4 (2008), 076, 6 pages | |
| dc.identifier | doi:10.3842/SIGMA.2008.076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173499 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Analysis of PDEs | |
| dc.title | Liouville Theorem for Dunkl Polyharmonic Functions | |
| dc.type | text |