Toeplitz operators with analytic symbols
Résumé
We provide asymptotic formulas for the Bergman projector and Berezin-Toeplitz operators on a compact Kähler manifold. These objects depend on an integer N and we study, in the limit N → +∞, situations in which one can control them up to an error O(e −cN) for some c > 0. We develop a calculus of Toeplitz operators with real-analytic symbols, which applies to Kähler man-ifolds with real-analytic metrics. In particular, we prove that the Bergman kernel is controlled up to O(e −cN) on any real-analytic Kähler manifold as N → +∞. We also prove that Toeplitz operators with analytic symbols can be composed and inverted up to O(e −cN). As an application, we study eigenfunction concentration for Toeplitz operators if both the manifold and the symbol are real-analytic. In this case we prove exponential decay in the classically forbidden region.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...