Journal of Lie Theory Volume 6 (1996) 271–289 C ◯1996 Heldermann Verlag

Opérateurs différentiels invariants hyperboliques sur un espace symétrique ordonné

Jacques Faraut

Communicated by K.-H. Neeb

Abstract. Let M be a homogeneous and globally causal manifold and D an invariant differential operator on M. We study conditions under which D permits an causal fundamental solution. For the cases that M is an ordered symmetric space of Ol’shanskiĭ type or an ordered symmetric space of rank 1 we show that an invariant hyperbolic operator admits a causal fundamental solution.

Institut de Mathématiques de Jussieu (UMR 9994 du CNRS) Université Pierre et Martie Curie Case 247, 4 place Jussieu 75252 Paris Cedex 05 e.mail faraut@mathp6.jussieu.fr

Received May 25, 1996 and in final form September 12, 1996

ISSN 0949–5932 / $2.50 ^{_{C} ◯} Heldermann Verlag