On the convergence of series that define eigenfunctions of Dunkl–Darboux operators

Earlier we gave a talk about formal solutions of an equation for eigenfunctions of the Dunkl-Darboux operator. These solutions are represented by functional series of special type. In some general settings, we construct a convergent series that determines an eigenfunction of the Dunkl-Darboux operator. In the talk we explain a construction of this series and the main steps of the proof of its convergence.