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arXiv · 1207.5178

On the Funk-Radon-Helgason Inversion Method in Integral Geometry

Boris Rubin
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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 $L^p$ 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.

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Boris Rubin. 2012-07-21. On the Funk-Radon-Helgason Inversion Method in Integral Geometry. https://arxiv.org/abs/1207.5178

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