Abstract
In an ongoing collaboration with Pierre Germain and Tristan Léger, we are interested in the L2 - Lp norms of spectral projectors in small spectral windows on hyperbolic surfaces of infinite area. In the absence of " cusps ", we obtain near-optimal estimates that are better than with non-negative curvature. After an historical review of the subject, which goes back to the Stein-Tomas restriction theorem, we will give an overview of the methods used to achieve this result.
