On a Kipriyanov problem for a singular ultrahyperbolic equation

We obtain a differential equation for the spherical means generated by a multidimensional generalized shift of an arbitrary smooth “even” function. We study the Asgeirsson property of solutions of a singular ultrahyperbolic equation that includes singular differential operators Δ _B acting in Euclidean spaces, in general, of distinct dimensions. We represent the structure of a “radial” solution of the considered equation. A theorem similar to the Asgeirsson inverse theorem is proved.