Radon transforms over lower-dimensional horospheres in real hyperbolic space
We study horospherical Radon transforms that integrate functions on the n-dimensional real hyperbolic space over horospheres of arbitrary fixed dimension 1 ≤ d ≤ n-1. Exact existence conditions and new explicit inversion formulas are obtained for these transforms acting on smooth functions and functions belonging to Lp. The case d = n 1 agrees with the well-known Gelfand-Graev transform.
Horospherical transforms, Inversion formulas, L -spaces p, Radon transforms, Real hyperbolic space
Bray, William, and Boris Rubin. "Radon transforms over lower-dimensional horospheres in real hyperbolic space." Transactions of the American Mathematical Society 372, no. 2 (2019): 1091-1112.
Transactions of the American Mathematical Society