Geodesic
Characterization of the range of the Radon transform on homogeneous trees
Tarabusi, Enrico1 ; Cohen, Joel2 ; Colonna, Flavia3
1 Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Roma, Italy
2 Department of Mathematics, University of Maryland, College Park, MD 20742
3 Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 11-17 Cet article a éte moissonné depuis la source American Mathematical Society

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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 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.
DOI : 10.1090/S1079-6762-99-00055-4

Tarabusi, Enrico 1 ; Cohen, Joel 2 ; Colonna, Flavia 3

1 Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Roma, Italy
2 Department of Mathematics, University of Maryland, College Park, MD 20742
3 Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030 
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Tarabusi, Enrico; Cohen, Joel; Colonna, Flavia. Characterization of the range of the Radon transform on homogeneous trees. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 11-17. doi: 10.1090/S1079-6762-99-00055-4

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