  We consider the horospherical transform and its inversion in 3 examples of
hyperboloids. We want to illustrate via these examples the fact that the
horospherical inversion formulas can be directly extracted from the classical
Radon inversion formula. In a more broad context, this possibility reflects the
fact that the harmonic analysis on symmetric spaces (Riemannian as well as
pseudo-Riemannian ones) is equivalent (homologous), up to the Abelian Fourier
transform, to the similar problem in the flat model. On the technical level it
is important that we work not with the usual horospherical transform, but with
its Cauchy modification.
