We obtain new descriptions of the null spaces of several projectively equivalent transforms in integral geometry. The paper deals with the hyperplane Radon transform, the totally geodesic transforms on the sphere and the hyperbolic space, the spherical slice transform, and the Cormack-Quinto spherical mean transform for spheres through the origin. The consideration extends to the corresponding dual transforms and the relevant exterior/interior modifications. The method relies on new results for the Gegenbauer-Chebyshev fractional integrals.
Publication Source (Journal or Book title)
Advances in Mathematics
Estrada, R., & Rubin, B. (2016). Null spaces of Radon transforms. Advances in Mathematics, 290, 1159-1182. https://doi.org/10.1016/j.aim.2015.12.025