Dans cette note, on démontre une minoration universelle optimale sur la norme de la résolvante tronquée pour les opérateurs de Schrödinger semiclassiques près d'une énergie captive. En particulier, ce résultat implique que des majorations connues pour des captures hyperboliques sont optimales. La preuve repose sur un argument de X.P. Wang et la propagation en temps d'Ehrenfest des états cohérents.
In this note, 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.
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@article{CRMATH_2010__348_23-24_1279_0,
author = {Bony, Jean-Fran\c{c}ois and Burq, Nicolas and Ramond, Thierry},
title = {Minoration de la r\'esolvante dans le cas captif},
journal = {Comptes Rendus. Math\'ematique},
pages = {1279--1282},
publisher = {Elsevier},
volume = {348},
number = {23-24},
year = {2010},
doi = {10.1016/j.crma.2010.10.025},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.10.025/}
}
TY - JOUR AU - Bony, Jean-François AU - Burq, Nicolas AU - Ramond, Thierry TI - Minoration de la résolvante dans le cas captif JO - Comptes Rendus. Mathématique PY - 2010 SP - 1279 EP - 1282 VL - 348 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.10.025/ DO - 10.1016/j.crma.2010.10.025 LA - fr ID - CRMATH_2010__348_23-24_1279_0 ER -
%0 Journal Article %A Bony, Jean-François %A Burq, Nicolas %A Ramond, Thierry %T Minoration de la résolvante dans le cas captif %J Comptes Rendus. Mathématique %D 2010 %P 1279-1282 %V 348 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.10.025/ %R 10.1016/j.crma.2010.10.025 %G fr %F CRMATH_2010__348_23-24_1279_0
Bony, Jean-François; Burq, Nicolas; Ramond, Thierry. Minoration de la résolvante dans le cas captif. Comptes Rendus. Mathématique, Tome 348 (2010) no. 23-24, pp. 1279-1282. doi : 10.1016/j.crma.2010.10.025. http://www.numdam.org/articles/10.1016/j.crma.2010.10.025/
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