A Radon transform on the cylinder

We define a parametric Radon transform R that assigns to a Sobolev function on the cylinder S x R in R-3 its mean values along sets E-zeta formed by the intersections of planes through the origin and the cylinder. We show that R is a continuous operator, prove an inversion formula, provide a support theorem, as well as a characterization of its null space. We conclude by presenting a formula for the dual transform R*. We show that R and its dual R* are related to the right-sided and left-sided Chebyshev fractional integrals. Using this relationship, we characterize the null space of R and R* and provide an inversion formula for R*. (C) 2022 Elsevier Inc. All rights reserved.