a1 School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia e-mail: email@example.com
a2 Università dell'Insubria—Polo di Como, Facoltà di Scienze, via Lucini 3, I-22100 Como, Italy e-mail: firstname.lastname@example.org
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 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.
(Received July 14 1998)