The range of the Helgason-Fourier transformation on homogeneous trees

Michael Cowling, Alberto G. Setti

Type: Article

Publication Date: 1999-04-01

Citations: 20

DOI: https://doi.org/10.1017/s0004972700032858

Abstract

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.

Locations

Bulletin of the Australian Mathematical Society - View - PDF

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