Abstract: | Let t = (t1, …, tn) be a point of ?n. We shall write . We put by definition Rα(u) = u(α?n)/2/Kn(α); here α is a complex parameter, n the dimension of the space, and Kn(α) is a constant. First we evaluate □Rα(u) = Rα(u), where □ the ultrahyperbolic operator. Then we obtain the following results: R?2k(u) = □kδ; R0(u) = δ; and □kR2k(u) = δ, k = 0, 1, …. The first result is the n-dimensional ultrahyperbolic correlative of the well-known one-dimensional formula . Equivalent formulas have been proved by Nozaki by a completely different method. The particular case µ = 1 was solved previously. |