Abstract:

Let t = (t1, ..., tn) be a point of ℝn. 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. © 2015 Wiley Periodicals, Inc., A Wiley Company.