Characterization of the $L^p$-Range of the Poisson Transform in Symmetric Spaces of Real Rank One (exposé en ligne)

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

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

$(P_{\lambda }f)(x)={\int }_{K/M}{e}^{(i\lambda +\rho )A(x,b)}f(b)db,\text{for}x\in X.$

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.