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, p. 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 $\mathbf{c}$-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.

@article{AMBP_2005__12_1_147_0,
author = {El Kamel, Jamel and Yacoub, Chokri},
title = {Huygens' principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian},
journal = {Annales math\'ematiques Blaise Pascal},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {12},
number = {1},
year = {2005},
pages = {147-160},
doi = {10.5802/ambp.199},
mrnumber = {2126445},
zbl = {1088.35036},
language = {en},
url = {http://www.numdam.org/item/AMBP_2005__12_1_147_0}
}

El Kamel, Jamel; Yacoub, Chokri. 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. http://www.numdam.org/item/AMBP_2005__12_1_147_0/

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