Radon Transform on Real, Complex and Quaternionic Grassmannians
نویسنده
چکیده
LetGn,k(K) be the Grassmannian manifold of k-dimensional K-subspaces in K where K = R,C,H is the field of real, complex or quaternionic numbers. For 1 ≤ k ≤ k ≤ n − 1 we define the Radon transform (Rf)(η), η ∈ Gn,k′(K), for functions f(ξ) on Gn,k(K) as an integration over all ξ ⊂ η. When k+ k ≤ n we give an inversion formula in terms of the G̊arding-Gindikin fractional integration and the Cayley type differential operator on the symmetric cone of positive k × k matrices over K. This generalizes the recent results of Grinberg-Rubin for real Grassmannians.
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