Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian
Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 1, pp. 147-160.

In this paper we consider the modified wave equation associated with a class of radial Laplacians L generalizing the radial part of the Laplace-Beltrami operator on hyperbolic spaces or Damek-Ricci spaces. We show that the Huygens’ principle and the equipartition of energy hold if the inverse of the Harish-Chandra c-function is a polynomial and that these two properties hold asymptotically otherwise. Similar results were established previously by Branson, Olafsson and Schlichtkrull in the case of noncompact symmetric spaces.

DOI: 10.5802/ambp.199
Jamel El Kamel 1; Chokri Yacoub 1

1 Faculty of Science of Monastir Department of Mathematics Boulevard de l’environnement Monastir Tunisia
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Jamel El Kamel; Chokri Yacoub. Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian. Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 1, pp. 147-160. doi : 10.5802/ambp.199. https://ambp.centre-mersenne.org/articles/10.5802/ambp.199/

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