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The range of the Helgason-Fourier transformation on homogeneous trees

Published online by Cambridge University Press:  17 April 2009

Michael Cowling  and
Alberto G. Setti
Michael Cowling
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia e-mail: m.cowling@unsw.edu.au
Alberto G. Setti
Affiliation:
Università dell'Insubria—Polo di Como, Facoltà di Scienze, via Lucini 3, I-22100 Como, Italy e-mail: setti@fis.unico.it
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Abstract

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Let be a homogeneous tree, o be a fixed reference point in , and be the closed ball of radius N in centred at o. In this paper we characterise the image under the Helgason–Fourier transformation ℋ of , the space of functions supported in , and of , the space of rapidly decreasing functions on . In both cases our results are counterparts of known results for the Helgason–Fourier transformation on noncompact symmetric spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 237 - 246
Copyright
Copyright © Australian Mathematical Society 1999

References

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