Mean value characterizations of the Dunkl polyharmonic functions

We give characterizations of the Dunkl polyharmonic functions,i.e., solutions to the iteration of the Dunkl-Laplace operator \(\Delta_\kappa\) ${\mathrm{\Delta }}_{\kappa }$ whichis a differential-reflection operator associated with a Coxeter–Weil group \(W\) $W$ generatedby a finite set of reflections and an invariant multiplicity function \(\kappa\) $\kappa$ , interms of integral means over Euclidean balls and spheres.