2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173499Assume 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.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/Classical Analysis and ODEsAnalysis of PDEstext