  The paper contains the inversion formula for the weighted spherical mean. The
interest to reconstruction a function by its integral by sphere grews
tremendously in the last six decades, stimulated by the spectrum of new
problems and methods of image reconstruction. We consider a generalization of
the classical spherical mean and its inverse in the case when generalized
translation acts to function instead of regular. As a particular case this
problem includes action of spherical means on radially symmetric functions.
