Radon inversion on Grassmannians via Gårding–Gindikin fractional integrals

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.

Authors

Eric L. Grinberg

Department of Mathematics
Temple University
Philadelphia, PA 19122-6082
United States

Boris Rubin

Institute of Mathematics
Hebrew University
Jerusalem
Israel