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

الأصل · EN

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 Lᵖ functions from their Radon transforms. New inversion formulas involving Erdélyi-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.