THE DISTRIBUTIONAL CONVOLUTION PRODUCTS

In this note we establish the distributional eonvolution produets of the form (P ± iD)> ' * c5(Io} (p+) (e.E. (1,2,12), (1,1,40), (1, 1,41), (1, 1,42) and (1,1,43)) and (m2 + P ± iD)> ' * c5(Io} (m2 + P) (e.E. (1,3,4), (1,3,5), (1,3,6), (1,3, 7) and (1,3,8)). We obtain the results by using systematieally the Fourier transformation and to obtain (m2 + P ± iD)a-l * c5(Io} (m2 + P) we have employ the expansion c5(Io} (m2 + P) = L: (:2r c5(Io+JI}(P+) JI?:,:o (e.E. [2] , page 6, formula (1, 1,24)). The eonvolution produet (P ± iD)> ' * c5(Io} (p+) generalizes the result ([1] , page 13, formula (1,3,6))