Strichartz’s conjecture for Poisson transforms and generalized spectral projections on spinors

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

We consider the real hyperbolic space $H^n(R)$ as the symmetric space ${\mathrm{Spin}}_0(1,n)/\mathrm{Spin}(n)$.
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.