Modul:   BZ001  The BZ Seminar in Analysis - Basel, Zurich

Localization of orthonormal functions in spectral clusters

Talk by Rupert L. Frank

Speaker invited by: Prof. Dr. Benjamin Schlein

Date: 25.05.18  Time: 16.00 - 18.15  Room: Y27H25

We generalize the Lp spectral cluster bounds of Sogge for the Laplace-Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. We show that these bounds are optimal on any manifold in a very strong sense. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators and their optimality follows by semi-classical analysis. The talk is based on joint work with Julien Sabin.