Translator Disclaimer
15 May 2007 Radon transform on real, complex, and quaternionic Grassmannians
Genkai Zhang
Author Affiliations +
Duke Math. J. 138(1): 137-160 (15 May 2007). DOI: 10.1215/S0012-7094-07-13814-6

Abstract

Let Gn,k(K) be the Grassmannian manifold of k-dimensional K-subspaces in Kn, where K=R,C,H is the field of real, complex, or quaternionic numbers. For 1k<k'n1, we define the Radon transform (Rf)(η), ηGn,k'(K), for functions f(ξ) on Gn,k(K) as an integration over all ξη. When k+k'n, 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 (k×k)-matrices over K. This generalizes the recent results of Grinberg and Rubin [4] for real Grassmannians

Citation

Download 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

Information

Published: 15 May 2007
First available in Project Euclid: 9 May 2007

zbMATH: 1125.26013
MathSciNet: MR2309157
Digital Object Identifier: 10.1215/S0012-7094-07-13814-6

Subjects:
Primary: 26A33 , 44A12 , 53C65
Secondary: 43A85 , 57S15

Rights: Copyright © 2007 Duke University Press

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.138 • No. 1 • 15 May 2007
Back to Top