# IJPAM: Volume 35, No. 3 (2007)

CAUSAL (ANTICAUSAL) CONVOLUTION PRODUCTS OF
THE DISTRIBUTIONAL FAMILIES RELATED TO
THE ULTRAHYPERBOLIC KLEIN GORDON OPERATOR,
ULTRAHYPERBOLIC OPERATOR, LAPLACIAN
OPERATOR AND THE DIAMOND OPERATOR

Manuel A. Aguirre T.
Pinto 399, Tandil, 7000, ARGENTINA
e-mail: maguirre@exa.unicen.edu.ar

Abstract.Let and the convolution distributional functions families defined by and where is the causal (anticausal) distribution defined by ()(cf. [#!T1!#]) and is causal (anticausal) analogues of the elliptic kernel of M.Riesz (cf. [#!T1!#]) defined by () and is the elliptic kernel of Marcel Riesz defined by (). In this paper we give a sense to convolution product of and for all complex numbers such that and . As consequence of our formula we give a sense to convolution product of: and , where is the -dimensions ultrahyperbolic Klein Gordon operator iterated -times, is the ultrahyperbolic operator iterated -times, is the Laplacian operator iterated -times and is the Diamond operator iterated -times.