Erdélyi–Kober fractional integrals and Radon transforms for mutually orthogonal affine planes

Document Type

Article

Publication Date

8-1-2020

Abstract

We apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in Rn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j+k = n−1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

Publication Source (Journal or Book title)

Fractional Calculus and Applied Analysis

First Page

967

Last Page

979

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