In this paper we consider the modified wave equation associated with a class of radial Laplacians 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 -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{\textquoteright} principle and equipartition of energy for the modified wave equation associated to a generalized radial {Laplacian}},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {147--160},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {12},
number = {1},
year = {2005},
doi = {10.5802/ambp.199},
zbl = {1088.35036},
mrnumber = {2126445},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.199/}
}
TY - JOUR AU - El Kamel, Jamel AU - Yacoub, Chokri TI - Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian JO - Annales mathématiques Blaise Pascal PY - 2005 SP - 147 EP - 160 VL - 12 IS - 1 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.199/ DO - 10.5802/ambp.199 LA - en ID - AMBP_2005__12_1_147_0 ER -
%0 Journal Article %A El Kamel, Jamel %A Yacoub, Chokri %T Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian %J Annales mathématiques Blaise Pascal %D 2005 %P 147-160 %V 12 %N 1 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.199/ %R 10.5802/ambp.199 %G en %F 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, Tome 12 (2005) no. 1, pp. 147-160. doi : 10.5802/ambp.199. http://www.numdam.org/articles/10.5802/ambp.199/
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