Abstract
In this paper, we study the Jacobi-Dunkl convolution operators on some distribution spaces. We characterize the Jacobi-Dunkl convolution operators as those ones that commute with the Jacobi-Dunkl translations and with the Jacobi-Dunkl operators. Also we prove that the Jacobi-Dunkl convolution operators are hypercyclic and chaotic on the spaces under consideration and we give a universality property for the generalized heat equation associated with them.