Radon-john transforms and spherical harmonics
The d-plane Radon-John transform takes functions on Rn to functions on the set of all d-dimensional planes in Rn by integration over these planes. We study the action of this transform on degenerate functions of the form f (x) = f0 (r) Yk (θ), where r = |x| > 0, θ = x/|x|, and Yk is a spherical harmonic of degree k. It is shown that the results for d < n−1 are surprisingly different from those in the known case d = n − 1.
Publication Source (Journal or Book title)
Estrada, R., & Rubin, B. (2018). Radon-john transforms and spherical harmonics. Contemporary Mathematics, 714, 131-142. https://doi.org/10.1090/conm/714/14329