Résumé

In this talk, we present results about resonances and residue operators for pseudo-Riemannian hyperbolic spaces. In particular, we show that for any pseudo-Riemannian hyperbolic space X, the resolvent of the Laplace--Beltrami operator can be extended meromorphically as a family of operators. Its poles are called resonances and we determine them explicitly in all cases. For each resonance, the image of the corresponding residue operator  forms a representation of the isometry group of X, which we identify with a subrepresentation of a degenerate principal series. Our study includes in particular the case of even functions on de Sitter and Anti-de Sitter spaces. This is joint work with Jan Frahm.

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