logo IMB
Retour

Séminaire de Géométrie

Resonances and residue operators for pseudo-Riemannian hyperbolic spaces

Polyxeni Spilioti (Göttingen)

Salle 2

le 17 mars 2023 à 09:30

In this talk, we present some recent 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.