The Shifted Wave Equation on Damek–Ricci Spaces and on Homogeneous Trees

Pierre Martinot,Emmanuel Pedon,Alberto G Setti,Jean-Philippe Anker

doi:10.1007/978-88-470-2853-1_1

The Shifted Wave Equation on Damek–Ricci Spaces and on Homogeneous Trees

Pierre Martinot, Emmanuel Pedon + Show 2 more

Open Access

https://doi.org/10.1007/978-88-470-2853-1_1

Copy DOI

Publication Date: Jul 23, 2012

Citations: 33

Affiliation: University of Reims Champagne-Ardenne, Laboratoire de Mathématiques, University of Insubria, Laboratoire de Mathématiques Analyse, Probabilités, Modélisation Orléans, University of Orléans, French National Centre for Scientific Research

#Damek Ricci Spaces #Shifted Wave Equation + Show 4 more

Abstract
Full-Text PDF
Similar Papers

Abstract

AbstractWe solve explicitly the shifted wave equation on Damek–Ricci spaces, using the inverse dual Abel transform and Ásgeirsson’s theorem. As an application, we investigate Huygens’ principle. A similar analysis is carried out in the discrete setting of homogeneous trees.KeywordsAbel transformDamek–Ricci spaceHomogeneous treeHuygens’ principleHyperbolic spaceWave equationWave propagationMathematics Subject Classification (2010)35L0543A8520F6722E3022E3533C8043A8058J45

Full Text