On the chaotic behavior of the Dunkl heat semigroup on weighted L p spaces

In this paper we study the chaotic behavior of the heat semigroup generated by the Dunkl-Laplacian on weighted Lp spaces. In the case of the heat semigroup associated to the standard Laplacian we obtain a complete picture on the spaces Lp(Rn, (φiρ(x))2dx) where φiρ is the Euclidean spherical function. The behavior is very similar to the case of the Laplace–Beltrami operator on non-compact Riemannian symmetric spaces studied by Pramanik and Sarkar.