Title: A generalization of the Mader-Helgason inversion formulas for Radon transforms
Abstract: In 1927, Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $\mathbb {R}^n$. These formulas differ from the original ones by Radon and seem to be forgotten. We generalize Maderâs 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 âIntegral geometry and Radon transformâ by S. Helgason. We extend this formula to arbitrary constant curvature space. The paper combines tools of integral geometry and complex analysis.