Shtepina T. Integral operators on the Pseudoeuclidean spaces and the generalization of the Funk-Hecke theorem

This thesis is devoted to the study of the integral operator family that act in the space of locally integrable functions on the Lobachevski space with kernels that depend on the distance between points in hyperbolic geometry. These operators are intertwining operators of quasiregular representation of Lorentz group. This fact allows us to calculate their spectra and to diagonalize operators. The generalization of the Funk-Hecke theorem is proved for the case of pseudoeuclidean space of an arbitrary dimension. We also discuss one of the applications of the Funk-Hecke theorem to the equivariant boundary problems theory.