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: |
Bolyai Institute, University of Szeged
Szeged
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 |
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| 008 | 200727s2020 hu o 000 eng d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-019-773-1 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Ishikawa Satoshi | |
| 245 | 1 | 4 | |a The range of the Radon transform on the real hyperbolic Grassmann manifold |h [elektronikus dokumentum] / |c Ishikawa Satoshi |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2020 | ||
| 300 | |a 225-264 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum | |
| 520 | 3 | |a 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. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Matematika | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/69370/1/math_086_numb_001-002_225-264.pdf |z Dokumentum-elérés |