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This article contains results on the range of the Radon transform $R$ on the set $\mathcal{H}$ of horocycles of a homogeneous tree $T$. Functions of compact support on $\mathcal{H}$ that satisfy two explicit {\em Radon conditions\/} constitute the image under $R$ of functions of finite support on $T$. Replacing functions on $\mathcal{H}$ by distributions, we extend these results to the non-compact case by adding decay criteria.

Copyright 1999 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 05 (1999), pp. 11-17
• Publisher Identifier: S 1079-6762(99)00055-4
• 1991 Mathematics Subject Classification. Primary 44A12
• Key words and phrases. Radon transform, homogeneous trees, horocycles, range characterizations, distributions
• Received by the editors October 15, 1998
• Posted on February 4, 1999
• Communicated by Mark Freidlin
• Comments (When Available)

Enrico Casadio Tarabusi

Dipartimento di Matematica ``G. Castelnuovo'', Universit\`{a} di Roma ``La Sapienza'', Piazzale A. Moro 2, 00185~Roma, Italy

E-mail address: casadio@alpha.science.unitn.it

Joel M. Cohen

Department of Mathematics, University of Maryland, College Park, MD 20742

E-mail address: jmc@math.umd.edu

Flavia Colonna

Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030

E-mail address: fcolonna@osf1.gmu.edu