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We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and Garding-Gindikin frac- tional integrals associated to the cone of positive definite matrices. By using this connection, we obtain Abel-type representations and explicit inversion for- mulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with Lp spaces.

Radon inversion on Grassmannians via Gårding–Gindikin fractional integrals