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Huygens' principle and a Paley-Wiener type Theorem on Damek-Ricci spaces

Abstract:
We prove that Huygens' principle and the principle of equipartition of energy hold for the modified wave equation on odd dimensional Damek-Ricci spaces. We also prove a Paley-Wiener type theorem for the inverse of the Helgason Fourier transform on Damek-Ricci spaces.

Keywords:
Wave equation, Damek-Ricci spaces

MSC:
43