The range of the Radon transform on the real hyperbolic Grassmann manifold
Let Γ n k be the space of all the k-dimensional totally geodesic submanifolds of the n-dimensional real hyperbolic space where 1 ≤ k ≤ n − 1. We prove that the Radon transform R for double fibrations of the real hyperbolic Grassmann manifolds Γ n p and Γ n q with respect to the inclusion incidence r...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2020
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| Sorozat: | Acta scientiarum mathematicarum
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| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-019-773-1 |
| Online Access: | http://acta.bibl.u-szeged.hu/69370 |
| Tartalmi kivonat: | Let Γ n k be the space of all the k-dimensional totally geodesic submanifolds of the n-dimensional real hyperbolic space where 1 ≤ k ≤ n − 1. We prove that the Radon transform R for double fibrations of the real hyperbolic Grassmann manifolds Γ n p and Γ n q with respect to the inclusion incidence relations maps C ∞0 (Γn p ) bijectively onto the space of all the functions in C ∞0 (Γn q ) which satisfy a certain system of linear partial differential equations explicitly constructed from the left infinitesimal action of the transformation group when 0 ≤ p < q ≤ n − 1 and dim Γ n p < dim Γ n q . Our approach is based on the generalized method of gnomonic projections. We also treat the dual Radon transform R. |
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| Terjedelem/Fizikai jellemzők: | 225-264 |
| ISSN: | 2064-8316 |