de Mathématiques de Luminy
Delorme Patrick, Mezo Paul.
Twisted invariant Paley-Wiener theorem for real reductive groups.
Let G+ be the group of real points of a possibly disconnected linear reductive algebraic group defined over , which is generated by the real points of a connected component G'. Let K be a maximal compact subgroup of the group of real points of the connected component of this algebraic group. We characterize the space of maps π —> tr(π( f )), where π is an irreducible tempered representation of G+, and f varies over the space of smooth, compactly supported functions on G', which are left- and right-K-finite. This work is motivated by applications to the Arthur-Selberg trace formula.