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Radon transform on spaces of constant curvature

Authors: Carlos A. Berenstein, Enrico Casadio Tarabusi and Árpád Kurusa
Journal: Proc. Amer. Math. Soc. 125 (1997), 455-461
MSC (1991): Primary 44A12; Secondary 53C65, 51M10
MathSciNet review: 1350933
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Abstract: A correspondence among the totally geodesic Radon transforms—as well as among their duals—on the constant curvature spaces is established, and is used here to obtain various range characterizations.

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Additional Information

Carlos A. Berenstein
Affiliation: Institute for Systems Research, University of Maryland, College Park, Maryland 20742

Enrico Casadio Tarabusi
Affiliation: Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Roma, Italy

Árpád Kurusa
Affiliation: Bolyai Institute, Aradi vértanúk tere 1., 6720 Szeged, Hungary

Keywords: Radon transform, spaces of constant curvature, totally geodesic submanifolds, spherical harmonics, moment conditions
Received by editor(s): August 8, 1995
Additional Notes: The first author was partially supported by NSF grants DMS9225043 and EEC9402384. This research was in part accomplished during the second author’s stay at the University of Maryland, whose hospitality is hereby acknowledged. The third author was partially supported by the Hungarian NSF grants T4427, F016226, W075452, and T020066.
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society