2021/11/19 by Coyoli, Alejandro
#26A33 #42A16 #44A12 #45Q05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.10397
We define a parametric Radon transform R that assigns to a Sobolev function on the cylinder \mathbbS× ℝ in ℝ3 its mean values along sets Eζ 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^*.