Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian
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...