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Range of the \(k\)-dimensional Radon transform in real hyperbolic spaces. (English) Zbl 0786.44004

Authors’ summary: Characterizations of the range of the totally geodesic \(k\)-dimensional Radon transform on the \(n\)-dimensional hyperbolic space are given both as the kernel of a differential operator and in terms of moment conditions. It is shown in particular that, unlike in the Euclidean case, the latter are sufficient for all \(k\) also in the Schwartz space of fast decreasing functions.

MSC:

44A12 Radon transform
53C65 Integral geometry
51M10 Hyperbolic and elliptic geometries (general) and generalizations
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