Radon-john transforms and spherical harmonics

Document Type

Article

Publication Date

1-1-2018

Abstract

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)

Contemporary Mathematics

First Page

131

Last Page

142

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