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Minoration de la résolvante dans le cas captif. (Lower bound on the resolvent for trapped situations.) (French) Zbl 1206.35182
Summary: We prove an optimal universal lower bound on the truncated resolvent for semiclassical Schrödinger operators near a trapping energy. In particular, this shows that known upper bounds for hyperbolic trapping are optimal. The proof rely on an idea of X. P. Wang, and on propagation of coherent states for Ehrenfest times.

MSC:
35P15 Estimates of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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