The Radon transform for double fibrations of semisimple symmetric spaces
- 1 June 2021
- journal article
- research article
- Published by Springer Science and Business Media LLC in Acta Scientiarum Mathematicarum
- Vol. 87 (1-2), 121-162
- https://doi.org/10.14232/actasm-020-164-4
Abstract
We present the injectivity and support results of the Radon transform for the double fibrations of semisimple symmetric spaces in the setting of the inclusion incidence relation which generalizes the setting of our previous result in [Ish2]. We also generalize the projection slice theorem which relates the Radon transform with the Fourier transforms on semisimple symmetric spaces.Keywords
This publication has 21 references indexed in Scilit:
- A Paley–Wiener theorem for reductive symmetric spacesAnnals of Mathematics, 2006
- Moment conditions and support theorems for Radon transforms on affine Grassmann manifoldsAdvances in Mathematics, 2006
- Symmetric subvarieties in compactifications and the Radon transform on Riemannian symmetric spaces of noncompact typeJournal of Functional Analysis, 2003
- The range characterizations of the totally geodesic Radon transform on the real hyperbolic spaceDuke Mathematical Journal, 1997
- The Most Continuous Part of the Plancherel Decomposition for a Reductive Symmetric SpaceAnnals of Mathematics, 1997
- Support theorems for totally geodesic Radon transforms on constant curvature spacesProceedings of the American Mathematical Society, 1994
- The principal series for a reductive symmetric space. II. Eisenstein integralsJournal of Functional Analysis, 1992
- On images of Radon transformsDuke Mathematical Journal, 1985
- The orbits of affine symmetric spaces under the action of minimal parabolic subgroupsJournal of the Mathematical Society of Japan, 1979
- The Structure of Semisimple Symmetric SpacesCanadian Journal of Mathematics, 1979