Weighted mixed spherical means and singular ultrahyperbolic equation

Weighted mixed spherical means are constructed by using a generalized shift (in a Euclidian space a generalized shift acts with respect to one variable and a usual shift acts with respect to other variables). We obtain the differential equation for weighted mixed spherical mean and prove theorems on weighted mixed spherical means applied to the solution of the B-ultrahyperbolic equation.

On Some Boundary Value Problems for an Ultrahyperbolic Equation

The correct formulation of a characteristic problem and a Darboux type problem in the special weighted functional spaces for an ultrahyperbolic equation is investigated.

Kelvin principle for a class of singular equations

The classical Kelvin principle concerns invariance of solutions of the Laplace equation with respect to inversion in a sphere. By employing a hyperbolic-polar coordinate system, the principle is extended to cover a class of singular equations, which include the ultrahyperbolic equation.