Inversion formulas for the spherical Radon transform and the generalized cosine transform

The k-dimensional totally geodesic Radon transform on the unit sphere Sⁿ and the corresponding cosine transform can be regarded as members of the analytic family of intertwining fractional integrals d(x, ξ) being the geodesic distance between x ∈ Sⁿ and the k-geodesic ξ. We develop a unified approach to the inversion of R^α f for all α ≥ 0, 1 ≤ k ≤ n - 1, n ≥ 2. The cases of smooth f and f ∈ L^p are considered. A series of new inversion formulas is obtained. The convolution-backprojection method is developed.