Document Type
Article
Publication Date
5-1-2022
Abstract
We study the spherical slice transform which assigns to a function f on the unit sphere Sn in n+1 the integrals of f over cross-sections of Sn by k-dimensional affine planes passing through the north pole (0,..., 0, 1). These transforms are known when k = n. We consider all 2 ≤ k ≤ n and obtain an explicit formula connecting with the classical (k - 1)-plane Radon-John transform Rk-1 on n. Using this connection, known facts for Rk-1, like inversion formulas, support theorems, representation on zonal functions, and some others, are reformulated for .
Publication Source (Journal or Book title)
Analysis and Applications
First Page
483
Last Page
497
Recommended Citation
Rubin, B. (2022). On the spherical slice transform. Analysis and Applications, 20 (3), 483-497. https://doi.org/10.1142/S021953052150024X