Berenstein, Carlos A.; Tarabusi, Enrico Casadio Range of the \(k\)-dimensional Radon transform in real hyperbolic spaces. (English) Zbl 0786.44004 Forum Math. 5, No. 6, 603-616 (1993). 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. Reviewer: H.-J.Glaeske (Jena) Cited in 1 ReviewCited in 8 Documents MSC: 44A12 Radon transform 53C65 Integral geometry 51M10 Hyperbolic and elliptic geometries (general) and generalizations Keywords:totally geodesic \(k\)-dimensional Radon transform; range; hyperbolic space; Schwartz space PDFBibTeX XMLCite \textit{C. A. Berenstein} and \textit{E. C. Tarabusi}, Forum Math. 5, No. 6, 603--616 (1993; Zbl 0786.44004) Full Text: DOI EuDML