New Inversion Formulas for the Horospherical Transform

The following two inversion methods for totally geodesic Radon transforms on constant curvature spaces are well known in integral geometry. The first method employs mean value operators in accordance with the classical Funk–Radon–Helgason scheme. The second one relies on the properties of potentials that can be inverted by polynomials of the Beltrami–Laplace operator. Using tools of harmonic analysis, we show that both methods are also applicable to the horospherical transform on the real hyperbolic space.