INVERTING RADON TRANSFORMS : THE GROUP-THEORETIC APPROACH François Rouvière Abstract. 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 di?erential operators and harmonic analysis. We introduce a general concept of shifted Radon transform, which also leads to simple inversion formulas and solves wave equations. Mathematics Subject Classi?cation (MSC 2000): primary 44A12, secondary 43A85, 53C35, 58J70. Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Geometric setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Convolution on X and inversion of R . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Radon transforms on isotropic spaces . . . . . . . . . . . . . . . . . . . . . . . . 12 5 Harmonic analysis on X and inversion of R .
- radon transform
- invariant measure
- all ?xed
- riemannian manifold
- left-invariant measure
- transitive lie
- means ofk-invariant
- lie group