Document Type
Article
Publication Date
8-27-2012
Abstract
In 1927, Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on ℝ n. These formulas differ from the original ones by Radon and seem to be forgotten. We generalize Mader's formulas to totally geodesic Radon transforms in any dimension on arbitrary constant curvature space. Another new interesting inversion formula for the k-plane transform was presented in the recent book "Integral geometry and Radon transform" by S. Helgason. We extend this formula to arbitrary constant curvature space. The paper combines tools of integral geometry and complex analysis. © 2012 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
First Page
6479
Last Page
6493
Recommended Citation
Antipov, Y., & Rubin, B. (2012). A generalization of the Mader-Helgason inversion formulas for radon transforms. Transactions of the American Mathematical Society, 364 (12), 6479-6493. https://doi.org/10.1090/S0002-9947-2012-05643-1