Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): Rupert L. Frank, Julien Sabin
We generalize the $L^p$ spectral cluster bounds of Sogge for the Laplace–Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.