Date/heure
5 janvier 2023
14:00 - 15:00
Oratrice ou orateur
Nadia Ourchane (Rabat)
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
Let $X=G/K$ be a Riemannian symmetric space of non compact type with real rank one. For $\lambda \in \mathbb{C}$ and $f$ an integrable function on the Furstenberg boundary $K/M$, the Poisson transform $P_\lambda$ of $f$ is given by
$
(P_\lambda f)(x)=\int_{K/M} e^{(i\lambda+\rho)A(x,b)}f(b)db, \quad \mbox{for} \; x\in X.
$
The aim of this talk is to present a necessary and a suffucient condition on eigenfunctions of the Laplace-Beltrami operator associated to $X$ with eigenvalue $-(\lambda^2+\rho^2)$ to have an $L^p$-Poisson integral representations on the boundary $K/M$. A special discuss of the case of the exceptional symmetric space.