Horocyclic Radon transform on Damek-Ricci space (Q2739296)

A rank one symmetric space of the noncompact type may be identified with a solvable Lie group \(AN\), where \(KAN\) is the Iwasawa decomposition of the associated semisimple Lie group. The group \(AN\) is a 1-dimensional extension of a nilpotent Lie group of step at most 2. Harmonic analysis on these groups \(AN\) was developed by many authors, including Harish-Chandra and S. Helgason. Some ten years ago, E.~Damek and F.~Ricci considered more general groups \(N\), and showed that the associated spaces \(AN\) enjoy many of the properties of the symmetric space, without actually being symmetric. The paper under review is a thorough working out of the generalisation of parts of semisimple analysis to the Damek-Ricci spaces \(AN\). There is a degree of overlap with the paper of \textit{J.-Ph. Anker, E. Damek} and \textit{Ch. Yacoub} [Ann. Scuola Norm. Super. Pisa Cl. Sci. (4) 23, 643--679 (1997; Zbl 0881.22008)]. A regrettable failure in the editorial process is that many of the references in this paper are published in places other than those cited.