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Characterization of the range of the Radon transform on homogeneous trees

Authors: Enrico Casadio Tarabusi, Joel M. Cohen and Flavia Colonna
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 11-17
MSC (1991): Primary 44A12; Secondary 05C05, 43A85
Published electronically: February 4, 1999
MathSciNet review: 1667635
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Abstract: 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.

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Additional Information

Enrico Casadio Tarabusi
Affiliation: Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Roma, Italy

Joel M. Cohen
Affiliation: Department of Mathematics, University of Maryland, College Park, MD 20742

Flavia Colonna
Affiliation: Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030

Keywords: Radon transform, homogeneous trees, horocycles, range characterizations, distributions
Received by editor(s): October 15, 1998
Published electronically: February 4, 1999
Additional Notes: Supported in part by an Alfred P. Sloan Research Fellowship and NSF grant DMS 95-01056.
Communicated by: Mark Freidlin
Article copyright: © Copyright 1999 American Mathematical Society

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