Elementary proofs of Paley-Wiener theorems for the Dunkl transform on   the real line
  We give an elementary proof of the Paley-Wiener theorem for smooth functions for the Dunkl transforms on the real line, establish a similar theorem for L^2-functions and prove identities in the spirit of Bang for L^p-functions. The proofs seem to be new also in the special case of the Fourier transform. 
Nils Byrial Andersen and Marcel de Jeu