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X-ray transform on Damek-Ricci spaces
| 1. | Laboratoire J.A. Dieudonné, Université de Nice, Parc Valrose, 06108 Nice cedex 2, France |
Using suitably chosen totally geodesic submanifolds we reduce the problems to similar questions on low-dimensional hyperbolic spaces.
References:
| [1] |
M. Cowling, A. Dooley, A. Korányi and F. Ricci, $H$-type groups and Iwasawa decompositions, Adv. Math., 87 (1991), 1-41.
doi: doi:10.1016/0001-8708(91)90060-K. |
| [2] |
M. Cowling, A. Dooley, A. Korányi and F. Ricci, An approach to symmetric spaces of rank one via groups of Heisenberg type, J. Geom. Anal., 8 (1998), 199-237. |
| [3] |
E. Damek and F. Ricci, A class of nonsymmetric harmonic Riemannian spaces, Bull. Amer. Math. Soc., 27 (1992), 139-142.
doi: doi:10.1090/S0273-0979-1992-00293-8. |
| [4] |
E. Damek and F. Ricci, Harmonic analysis on solvable extensions of $H$-type groups, J. Geom. Anal., 2 (1992), 213-248. |
| [5] |
S. Helgason, "Differential Geometry, Lie Groups and Symmetric Spaces," Academic Press, 1978. |
| [6] |
S. Helgason, "The Radon Transform," second edition, Birkhäuser, 1999. |
| [7] |
S. Helgason, The Abel, Fourier and Radon transforms on symmetric spaces, Indag. Math., 16 (2005), 531-551, arXiv:math/0506049. |
| [8] |
F. Rouvière, Espaces de Damek-Ricci, géométrie et analyse, Sémin. Congr., 7, Soc. Math. France, 2003, 45-100. |
| [9] |
, revised version of [8] at http://math.unice.fr/ frou/recherche/Damek-Ricci.pdf |
| [10] |
F. Rouvière, Transformation aux rayons X sur un espace symétrique, C. R. Math. Acad. Sci. Paris, 342 (2006), 1-6. |
show all references
References:
| [1] |
M. Cowling, A. Dooley, A. Korányi and F. Ricci, $H$-type groups and Iwasawa decompositions, Adv. Math., 87 (1991), 1-41.
doi: doi:10.1016/0001-8708(91)90060-K. |
| [2] |
M. Cowling, A. Dooley, A. Korányi and F. Ricci, An approach to symmetric spaces of rank one via groups of Heisenberg type, J. Geom. Anal., 8 (1998), 199-237. |
| [3] |
E. Damek and F. Ricci, A class of nonsymmetric harmonic Riemannian spaces, Bull. Amer. Math. Soc., 27 (1992), 139-142.
doi: doi:10.1090/S0273-0979-1992-00293-8. |
| [4] |
E. Damek and F. Ricci, Harmonic analysis on solvable extensions of $H$-type groups, J. Geom. Anal., 2 (1992), 213-248. |
| [5] |
S. Helgason, "Differential Geometry, Lie Groups and Symmetric Spaces," Academic Press, 1978. |
| [6] |
S. Helgason, "The Radon Transform," second edition, Birkhäuser, 1999. |
| [7] |
S. Helgason, The Abel, Fourier and Radon transforms on symmetric spaces, Indag. Math., 16 (2005), 531-551, arXiv:math/0506049. |
| [8] |
F. Rouvière, Espaces de Damek-Ricci, géométrie et analyse, Sémin. Congr., 7, Soc. Math. France, 2003, 45-100. |
| [9] |
, revised version of [8] at http://math.unice.fr/ frou/recherche/Damek-Ricci.pdf |
| [10] |
F. Rouvière, Transformation aux rayons X sur un espace symétrique, C. R. Math. Acad. Sci. Paris, 342 (2006), 1-6. |
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