Range of the horocyclic Radon transform on trees

Annales de l'Institut Fourier

Volumn 50, Issue 1, 2000, Pages 211-234

  Casadio Tarabusi, Enrico ^a   Cohen, Joel M ^b   Colonna, Flavia ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b Bldg 142   (United States)

^c GEORGE MASON UNIVERSITY   (United States)

Author keywords

Distributions; Homogeneous trees; Horocycles; Radon transform; Range characterizations

Indexed keywords

EID: 0034364963     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1752     Document Type: Article

References (15)

1. G. AHUMADA BUSTAMANTE, Analyse harmonique sur l'espace des chemins d'un arbre, Thèse de Doctorat d'État, Université de Paris-Sud (Orsay), 1988.
2. C.A. BERENSTEIN, E. CASADIO TARABUSI, Integral geometry in hyperbolic spaces and electrical impedance tomography, SIAM. J. Appl. Math., 56 (1996), 755-764.
3. C.A. BERBNSTEIN, E. CASADIO TARABUSI, J.M. COHEN, M.A. PICARDELLO, Integral geometry on trees, Amer. J. Math., 113 (1991), 441-470.
4. W. BETORI, J. FARAUT, M. PAGLIACCI, The horicycles of a tree and the Radon transform, preliminary version of [BFP].
5. W. BETORI, J. FARAUT, M. PAGLIACCI, An inversion formula for the Radon transform on trees, Math. Z., 201 (1989), 327-337.
6. W. BETORI, M. PAGLIACCI, The Radon transform on trees, Boll. Un. Mat. Ital. B (6), 5 (1986), 267-277.
7. E. CASADIO TARABUSI, J.M. COHEN, F. COLONNA, Characterization of the range of the Radon transform on homogeneous trees, Electron. Res. Announc. Amer. Math. Soc., 5 (1999), 11-17.
8. E. CASADIO TARABUSI, J.M. COHEN, A.M. PICARDELLO, The horocyclic Radon transform on non-homogeneous trees, Israel J. Math., 78 (1992), 363-380.
9. E. CASADIO TARABUSI, J.M. COHEN, A.M. PICARDELLO, Range of the X-ray transform on trees, Adv. Math., 109 (1994), 153-167.
10. J.M. COHEN, F. COLONNA, The functional analysis of the X-ray transform on trees, Adv. in Appl. Math., 14 (1993), 123-138.
11. J.M. COHEN, L. DE MICHELE, The radial Fourier-Stieltjes algebra of free groups, Contemp. Math., 10 (1982), 33-40.
12. M.G. COWLING, S. MEDA, A.G. SETTI, An overview of harmonic analysis on the group of isometries of a homogeneous tree, Exposition. Math., 16 (1998), 385-423.
13. M.G. COWLING, A.G. SETTI, The range of the Helgason-Fourier transformation on homogeneous trees, Bull. Austral. Math. Soc., 59 (1999), 237-246.
14. S. HELGASON, The Radon transform, Progr. Math., 5, Birkhäuser, Boston, 1980.
15. 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].