Explicit solution of the wave equation in a symmetric space of non-compact type of rank 1. (Solution explicite de l’équation des ondes dans un espace symétrique de type non compact de rang 1.) (French) Zbl 0912.58038

Séminaire de théorie spectrale et géométrie. Année 1993-1994. Chambéry: Univ. de Savoie, Fac. des Sciences, Service de Math. Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 12, 25-28 (1994).
From the text (translated from the French): “in [J. Funct. Anal. 46, 280-350 (1982; Zbl 0497.30036)], P. D. Lax and R. S. Phillips have obtained an explicit solution of the wave equation on the real hyperbolic space of dimension \(n\). Here, we give the solution in the case of a general hyperbolic space \((\mathbb{K} H^n,ds)\) where \(\mathbb{K}\) is one of the classic fields \(\mathbb{R}\), \(\mathbb{C}\), \(\mathbb{H}\) or \(Ca\)”.
For the entire collection see [Zbl 0812.00007].


58J45 Hyperbolic equations on manifolds
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)


Zbl 0497.30036
Full Text: EuDML