The range of the Radon transform on the real hyperbolic Grassmann manifold

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: https://doi.org/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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