Ishikawa Satoshi: The range of the Radon transform on the real hyperbolic Grassmann manifold. In: Acta scientiarum mathematicarum 86. pp. 225-264. (2020)
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Abstract
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.
| Item Type: | Article |
|---|---|
| Heading title: | Analysis |
| Journal or Publication Title: | Acta scientiarum mathematicarum |
| Date: | 2020 |
| Number: | 86 |
| ISSN: | 2064-8316 |
| Page Range: | pp. 225-264 |
| Related URLs: | http://acta.bibl.u-szeged.hu/69543/ |
| DOI: | 10.14232/actasm-019-773-1 |
| Uncontrolled Keywords: | Matematika |
| Additional Information: | Bibliogr.: p. 263-264. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.01. Mathematics |
| Date Deposited: | 2020. Jul. 27. 10:54 |
| Last Modified: | 2020. Jul. 27. 10:54 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/69370 |
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