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Range of the horocyclic Radon transform on trees

Enrico Casadio Tarabusi, Joel M. Cohen, Flavia Colonna (2000)

Annales de l'institut Fourier

In this paper we study the Radon transform R on the set of horocycles of a homogeneous tree T , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit Radon conditions constitute the image under R of functions of finite support on T . We extend these results to spaces of functions with suitable decay on T , whose image under R satisfies corresponding decay conditions and contains distributions on that are not defined pointwise....

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