Date/heure
21 septembre 2023
15:45 - 16:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Khalid Koufany
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
We consider the real hyperbolic space $H^n(R)$ as the symmetric space $\operatorname{Spin}_0(1, n) / \operatorname{Spin}(n)$.
We prove that the Poisson transform is an isomorphism between the space of $L^2$-spinors on the unit sphere $S^{n-1}$ and a certain weighted $L^2$-space consisting of joint eigenspinors on $H^n(R)$. For this purpose, we prove a Fourier restriction estimate and an asymptotic formula for the Poisson transform.
As a consequence we prove a characterization for the generalized spectral projections.
This is a joint work with A. Boussejra.