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Radon transform on affine buildings of rank three

Part of: Finite geometry and special incidence structures Integral transforms, operational calculus

Published online by Cambridge University Press:  09 April 2009

Laura Atanasi
Laura Atanasi
Affiliation:
Department of Mathematics, University of Rome ‘Tor Vergata’, 00135 Rome, Italy e-mail: [email protected]
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Abstract

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We define the Radon transform for functions on the set of chambers of affine, locally finite, rank three buildings. We investigate the problem of the inversion of this transform. Explicit inversion formulas are exhibited for functions which fulfill required summability conditions.

MSC classification

Secondary: 51E24: Buildings and the geometry of diagrams 44A12: Radon transform
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 1 , February 1999 , pp. 66 - 89
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bustamante, G. Ahumada, Analyse harmonique sur l'espace des chemins d'un arbre, Tesi di dottorato di Stato, Università di Parigi Sud, Orsay, 1988.Google Scholar
[2]Atanasi, L., Trasformate di Radon su edifici affini, Tesi di dottorato, Università di Roma ‘La Sapienza’, 1996.Google Scholar
[3]Atanasi, L., ‘Radon transforms on Ãn-buildings’, preprint, (Università di Roma ‘Tor Vergata’, 1997).Google Scholar
[4]Berenstein, C. A., Tarabusi, E. Casadio, Cohen, J. M. and Picardello, M., ‘Integral geometry on trees’, Amer J. Math. 113 (1991), 441–470.Google Scholar
[5]Bourbaki, N., Integration (Hermann, Paris, 1959).Google Scholar
[6]Brown, K. S., Buildings (Springer, New York, 1989).CrossRefGoogle Scholar
[7]Carter, R. W., Simple groups of Lie type (Wiley-Interscience, New York, 1962).Google Scholar
[8]Humphreys, J. E., Reflection groups and Coxeter groups (Cambridge, 1990).Google Scholar
[9]Ronan, M., Lectures on buildings (Academic Press, Boston, 1990).Google Scholar
[10]Steger, T., personal communication.Google Scholar
[11]Tits, J., Buildings of spherical type andfinite BN-pairs, Lecture Notes in Mathematics 386 (Springer, 1974).Google Scholar
[12]Tits, J., ‘A local approach to buildings’, in: The geometric vein. The Coxeter Festschrift (Springer, New York, 1981) pp. 519–547.Google Scholar