Radon, cosine and sine transforms on real hyperbolic space (Q1851238)

The author obtains some new inversion formulae for the \(d\)-dimensional totally geodesic Radon transform on the \(n\)-dimensional real hyperbolic space, \(1\leq d\leq n-1\), in terms of polynomials of the Laplace-Beltrami operator and intertwining fractional integrals. Similar results are also established for hyperbolic cosine and sine transforms. See the remarks by \textit{B. Rubin} in Adv. Math. 192, No. 1, 225 (2005).