Inversion formulas of integral geometry in real hyperbolic space

William O. Bray, Missouri State University
Boris Rubin


This expository article is a brief survey of authors’ results related to inversion of Radon transforms in the n-dimensional real hyperbolic space. The exposition is focused on horospherical and totally geodesic transforms over the corresponding submanifolds of arbitrary fixed dimension d, 1 ≤ d ≤ n − 1. Our main objective is explicit inversion formulas for these transforms on Lp functions and smooth functions with suitable behavior at infinity.