Skip to main content
Article thumbnail
Location of Repository

The Generalized Mader's Inversion Formulas for the Radon Transforms

By Yuri A. Antipov and Boris Rubin

Abstract

In 1927 Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $\bbr^n$. 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.Comment: 19 page

Topics: Mathematics - Complex Variables, Mathematical Physics, 44A12, 47G10
Year: 2011
OAI identifier: oai:arXiv.org:1103.2331
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1103.2331 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.