Abstract
Let be the Grassmannian manifold of -dimensional -subspaces in , where is the field of real, complex, or quaternionic numbers. For , we define the Radon transform , , for functions on as an integration over all . When , we give an inversion formula in terms of the Gårding-Gindikin fractional integration and the Cayley-type differential operator on the symmetric cone of positive ()-matrices over . This generalizes the recent results of Grinberg and Rubin [4] for real Grassmannians
Citation
Genkai Zhang. "Radon transform on real, complex, and quaternionic Grassmannians." Duke Math. J. 138 (1) 137 - 160, 15 May 2007. https://doi.org/10.1215/S0012-7094-07-13814-6
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