Abstract & Overview
In this paper we prove that there exists a unique topological isomorphism V k from (the space of C ∞ -functions on ) onto itself which intertwines the Cherednik operators T j , j = 1, 2, . . . , d , and the partial derivatives , j = 1, 2, . . . , d , called the trigonometric Dunkl intertwining operator (this name has been proposed by G. J. Heckman). To define and study the operator V k we have introduced first the trigonometric Dunkl dual intertwining operator t V k . The operators V k and t V k are the analogue in the Dunkl theory of the Dunkl intertwining operator and its dual (see [Dunkl, Can. J. Math. 43: 1213–1227, 1991, Trimèche, Integrals Transforms Special Funct. 12: 349–374, 2001]).