Dans le cadre de l'étude des résonances semiclassiques, on précise le lien entre majoration polynomiale du prolongement de la résolvante et propagation des singularités à travers l'ensemble capté. Cette approche permet d'éliminer l'infini et de concentrer l'étude près de l'ensemble capté. Nous l'avons utilisée dans des travaux antérieurs pour obtenir l'asymptotique des résonances dans diverses situations géométriques.
In the framework of semiclassical resonances, we make more precise the link between the polynomial estimates of the extension of the resolvent and the propagation of the singularities through the trapped set. This approach makes it possible to eliminate infinity and to concentrate the study near the trapped set. It has allowed us in previous papers to obtain the asymptotic of resonances in various geometric situations.
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@article{CRMATH_2017__355_8_887_0,
author = {Bony, Jean-Fran\c{c}ois and Fujii\'e, Setsuro and Ramond, Thierry and Zerzeri, Maher},
title = {Propagation des singularit\'es et r\'esonances},
journal = {Comptes Rendus. Math\'ematique},
pages = {887--891},
publisher = {Elsevier},
volume = {355},
number = {8},
year = {2017},
doi = {10.1016/j.crma.2017.06.008},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.06.008/}
}
TY - JOUR AU - Bony, Jean-François AU - Fujiié, Setsuro AU - Ramond, Thierry AU - Zerzeri, Maher TI - Propagation des singularités et résonances JO - Comptes Rendus. Mathématique PY - 2017 SP - 887 EP - 891 VL - 355 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.06.008/ DO - 10.1016/j.crma.2017.06.008 LA - fr ID - CRMATH_2017__355_8_887_0 ER -
%0 Journal Article %A Bony, Jean-François %A Fujiié, Setsuro %A Ramond, Thierry %A Zerzeri, Maher %T Propagation des singularités et résonances %J Comptes Rendus. Mathématique %D 2017 %P 887-891 %V 355 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.06.008/ %R 10.1016/j.crma.2017.06.008 %G fr %F CRMATH_2017__355_8_887_0
Bony, Jean-François; Fujiié, Setsuro; Ramond, Thierry; Zerzeri, Maher. Propagation des singularités et résonances. Comptes Rendus. Mathématique, Tome 355 (2017) no. 8, pp. 887-891. doi : 10.1016/j.crma.2017.06.008. http://www.numdam.org/articles/10.1016/j.crma.2017.06.008/
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