On the non-trivial solvability of one integral geometry problem

Abstract

The non-trivial solvability of the homogeneous problem of integral geometry is investigated. The problem is posed on a sphere generated with a cut of n-1-dimensional unit sphere by a hyperplane perpendicular to generatrices of a cone given by symbol of ultrahyperbolic operator. The connection of the problem under consideration with the Dirichlet problem for ultrahyperbolic equation in a ball is broadly used.