English

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 LpL^p 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

R2 v1 2026-06-21T21:39:33.090Z