caa a22 4500 38809236X CHVBK 20180307125255.0 cr unu---uuuuu 161130e199904 xx s 000 0 eng 10.1017/S0004972700032858 doi S0004972700032858 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700032858 The range of the Helgason-Fourier transformation on homogeneous trees [Elektronische Daten] 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. Copyright © Australian Mathematical Society 1999 Cowling Michael School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia e-mail: m.cowling@unsw.edu.au Setti Alberto G. Università dell'Insubria—Polo di Como, Facoltà di Scienze, via Lucini 3, I-22100 Como, Italy e-mail: setti@fis.unico.it Bulletin of the Australian Mathematical Society Cambridge University Press 59/2(1999-04), 237-246 0004-9727 59:2<237 1999 59 BAZ https://doi.org/10.1017/S0004972700032858 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700032858 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cowling Michael School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia e-mail: m.cowling@unsw.edu.au NATIONALLICENCE 700 1- Setti Alberto G. Università dell'Insubria—Polo di Como, Facoltà di Scienze, via Lucini 3, I-22100 Como, Italy e-mail: setti@fis.unico.it NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 59/2(1999-04), 237-246 0004-9727 59:2<237 1999 59 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge