Abstract
We study the Radon transform $\mathcal{R}f$ of functions on Stiefel and Grassmann manifolds. We establish a connection between ${\mathcal{R}} f$ and Gårding-Gindikin fractional integrals associated to the cone of positive definite matrices. By using this connection, we obtain Abel-type representations and explicit inversion formulae for ${\mathcal{R}} f$ and the corresponding dual Radon transform. We work with the space of continuous functions and also with $L^p$ spaces.
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