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

Jamel El Kamel; Chokri Yacoub — 2005

Annales mathématiques Blaise Pascal

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...

Spherical analysis on harmonic $A N$ groups

Jean-Philippe Anker; Ewa Damek; Chokri Yacoub — 1996

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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

Spherical analysis on harmonic A N groups

Spherical analysis on harmonic $A N$ groups