The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual

Abstract

In this paper we prove that the Dunkl intertwining operator V_k defined only on the space of polynomials on can also be extended to an operator on spaces of functions and distributions. We study also its dual ^tV_k and we prove that for each there exists a positive measure v_y on the Borel ω-algebra of with support in such that for all function f continuous on and with compact support, we have