On the Funk-Radon-Helgason Inversion Method in Integral Geometry
Functional Analysis
2012-07-24 v1
Abstract
The paper deals with totally geodesic Radon transforms on constant curvature spaces. We study applicability of the historically the first Funk-Radon-Helgason method of mean value operators to reconstruction of continuous and functions from their Radon transforms. New inversion formulas involving Erd\'elyi-Kober type fractional integrals are obtained. Particular emphasis is placed on the choice of the differentiation operator in the spirit of the recent Helgason's formula.
Keywords
Cite
@article{arxiv.1207.5178,
title = {On the Funk-Radon-Helgason Inversion Method in Integral Geometry},
author = {Boris Rubin},
journal= {arXiv preprint arXiv:1207.5178},
year = {2012}
}
Comments
29 pages