A PAIR OF GENERALIZED HANKEL-CLIFFORD TRANSFORMATIONS AND THEIR APPLICATIONS

Two variants of the Hankel transform, which will be called Hankel-Clifford transformations, are simultaneously investigated in certain spaces of distributions by the procedure of the adjoint operator. For this purpose, we exploit the fact that a Parseval equation involving both transforms can be constructed, so we propose to define the first generalized transformation as the adjoint operator of the second one, and conversely. Finally, these transforms are used in the solution of some partial differential equations of Kepinski type. © 1991.