Unitarization and Inversion Formulae for the Radon Transform between Dual Pairs

30 Oct 2018  ·  Alberti Giovanni S., Bartolucci Francesca, De Mari Filippo, De Vito Ernesto ·

We consider the Radon transform associated to dual pairs $(X,\Xi)$ in the sense of Helgason, with $X=G/K$ and $\Xi=G/H$, where $G=\mathbb{R}^d\rtimes K$, $K$ is a closed subgroup of ${\rm GL}(d,\mathbb{R})$ and $H$ is a closed subgroup of $G$. Under some technical assumptions, we prove that if the quasi regular representations of $G$ acting on $L^2(X)$ and $L^2(\Xi)$ are irreducible, then the Radon transform admits a unitarization intertwining the two representations... If, in addition, the representations are square integrable, we provide an inversion formula for the Radon transform based on the voice transform associated to these representations. read more

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Representation Theory Functional Analysis