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.
De Shintaro Nishikawa
De Juliette Coutens
De Yiannis Sakellaridis
De Bernhard Krötz
De Yoshiki Oshima
De Yiannis Sakellaridis
De Bernhard Krötz
De Polyxeni Spilioti
De Alain Connes
De Karl-Hermann Neeb
De Karl-Hermann Neeb
