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
DOI:
https://doi.org/10.1090/S1079-6762-99-00055-4
Published electronically:
February 4, 1999
MathSciNet review:
1667635
Full-text PDF Free Access
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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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- ---, An inversion formula for the Radon transform on trees, Math. Z. 201 (1989), 327–337.
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- ---, Range of the X-ray transform on trees, Adv. Math. 109 (1994), 153–167.
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- M. Cowling, S. Meda, A. G. Setti, An overview of harmonic analysis on the group of isometries of a homogeneous tree, preprint.
- S. Helgason, The Radon transform, Progr. Math., vol. 5, Birkhäuser, Boston, 1980.
- J. Radon, Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten, Ber. Verh. Sächs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 69 (1917), 262–277; reprinted in S. Helgason, The Radon transform, Progr. Math., vol. 5, Birkhäuser, Boston, 1980, pp. 177–192.
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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
Email:
casadio@alpha.science.unitn.it
Joel M. Cohen
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742
Email:
jmc@math.umd.edu
Flavia Colonna
Affiliation:
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030
Email:
fcolonna@osf1.gmu.edu
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
