Inverting Radon transforms: the group-theoretic approach. (Q1604959)

Summary: In the framework of homogeneous spaces of Lie groups, we propose a synthetic survey and several generalizations of various inversion formulas from the literature on Radon transforms, obtained by group-theoretic tools such as invariant differential operators and harmonic analysis. We introduce a general concept of shifted Radon transform, which also leads to simple inversion formulas and solves wave equations.