The shifted wave equation on Damek--Ricci spaces and on homogeneous trees

Abstract : We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' principle. A similar analysis is carried out in the discrete setting of homogeneous trees.
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Jean-Philippe Anker, Pierre Martinot, Emmanuel Pedon, Alberto Setti. The shifted wave equation on Damek--Ricci spaces and on homogeneous trees. M.A. Picardello. Trends in Harmonic Analysis (dedicated to A. Figà-Talamanca on the occasion of his retirement), 3, Springer-Verlag, pp.1-25, 2013, INdAM Ser., ⟨10.1007/978-88-470-2853-1_1⟩. ⟨hal-00705135v3⟩

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