Об одном тождестве для итерированного весового сферического среднего и его приложениях

Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We generalize iterated spherical means to weighted ones based on generalized translation operators and consider applications to $B$-hyperbolic equations and transmission tomography problems.