Abstract
For s is an element of R, denote by P-k(s) f the "projection" of a function f in D(R-d) into the eigenspaces of the Dunkl Laplacian Delta(k) corresponding to the eigenvalue -s(2): The parameter k comes from Dunkl's theory of differential-difference operators. We shall characterize the range of P-k(s) on the space of functions f is an element of D(R-d) supported inside the closed ball <(B(O, R))over bar>. As an application, we provide a spectral version of the Paley-Wiener theorem for the Dunkl transform.