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Characterization of the range of the Radon transform on homogeneous trees
Author(s):
Enrico
Casadio
Tarabusi;
Joel
M.
Cohen;
Flavia
Colonna
Journal:
Electron. Res. Announc. Amer. Math. Soc.
5
(1999),
11-17.
MSC (1991):
Primary 44A12;
Secondary 05C05, 43A85
Posted:
February 4, 1999
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Abstract:
This article contains results on the range of the Radon transform  on the set  of horocycles of a homogeneous tree  . Functions of compact support on  that satisfy two explicit Radon conditions constitute the image under  of functions of finite support on  . Replacing functions on  by distributions, we extend these results to the non-compact case by adding decay criteria.
References:
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- G. Ahumada Bustamante, Analyse harmonique sur l'espace des chemins d'un arbre, Thesis of Doctorat d'État, Univ. of Paris-Sud (Orsay), 1988.
- [BC]
- C. A. Berenstein, E. Casadio Tarabusi, Integral geometry in hyperbolic spaces and electrical impedance tomography, SIAM. J. Appl. Math. 56 (1996), 755-764. MR 97d:53073
- [BCCP]
- C. A. Berenstein, E. Casadio Tarabusi, J. M. Cohen, M. A. Picardello, Integral geometry on trees, Amer. J. Math. 113 (1991), 441-470. MR 92g:05066
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- W. Betori, J. Faraut, M. Pagliacci, The horicycles of a tree and the Radon transform, preliminary version of [BFP].
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- -, An inversion formula for the Radon transform on trees, Math. Z. 201 (1989), 327-337. MR 90k:22004
- [BP]
- W. Betori, M. Pagliacci, The Radon transform on trees, Boll. Un. Mat. Ital. B (6) 5 (1986), 267-277. MR 87h:05073
- [CCC]
- E. Casadio Tarabusi, J. M. Cohen, F. Colonna, The range of the horocyclic Radon transform on a homogeneous tree, preprint.
- [CCP1]
- E. Casadio Tarabusi, J. M. Cohen, A. M. Picardello, The horocyclic Radon transform on non-homogeneous trees, Israel J. Math. 78 (1992), 363-380. MR 94b:44002
- [CCP2]
- -, Range of the X-ray transform on trees, Adv. Math. 109 (1994), 153-167. MR 96a:05043a
- [CC]
- J. M. Cohen, F. Colonna, The functional analysis of the X-ray transform on trees, Adv. in Appl. Math. 14 (1993), 123-138. MR 94a:05048
- [CMS]
- M. Cowling, S. Meda, A. G. Setti, An overview of harmonic analysis on the group of isometries of a homogeneous tree, preprint.
- [H]
- S. Helgason, The Radon transform, Progr. Math., vol. 5, Birkhäuser, Boston, 1980. MR 83f:43012
- [R]
- 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 [H, 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
DOI:
10.1090/S1079-6762-99-00055-4
PII:
S 1079-6762(99)00055-4
Keywords:
Radon transform,
homogeneous trees,
horocycles,
range characterizations,
distributions
Received by editor(s):
October 15, 1998
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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