Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces

Astengo, Francesca; Di Blasio, Bianca

Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 327-340

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.

Classification : 43A80, 22E25
Keywords: Wave equation, Damek–Ricci space

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