Minoration de la resolvante dans le cas captif

摘要

In this note, we prove an optimal universal lower bound on the truncatedresolvent for semiclassical Schroedinger operators near a trapping energy. Inparticular, this shows that known upper bounds for hyperbolic trapping areoptimal. The proof rely on an idea of X. P. Wang, and on propagation ofcoherent states for Ehrenfest times.