Geodesic
Radon inversion on Grassmannians via Gårding–Gindikin fractional integrals
Eric L. Grinberg1 ; Boris Rubin2
1 Department of Mathematics, Temple University, Philadelphia, PA 19122-6082, United States
2 Institute of Mathematics, Hebrew University, Jerusalem, Israel
Annals of mathematics, Tome 159 (2004) no. 2, pp. 783-817.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2004.159.783

Eric L. Grinberg 1 ; Boris Rubin 2

1 Department of Mathematics, Temple University, Philadelphia, PA 19122-6082, United States
2 Institute of Mathematics, Hebrew University, Jerusalem, Israel 
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Eric L. Grinberg; Boris Rubin. Radon inversion on Grassmannians via Gårding–Gindikin fractional integrals. Annals of mathematics, Tome 159 (2004) no. 2, pp. 783-817. doi : 10.4007/annals.2004.159.783. http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.159.783/

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