[Des minorations de la fonction de comptage de résonances pour une perturbation d'un opérateur de Schrödinger périodique par un potientiel décroissant]
We are interested here in the counting function of resonances N(h) for a perturbation of a periodic Schrödinger operator P0 by decreasing potential W(hx) (). We obtain a lower bound for N(h) near some singularities of the density of states measure, associated to the unperturbed Hamiltonian P0.
On s'intéresse ici à la fonction de comptage N(h) du nombre de résonances de l'opérateur de Schrödinger périodique P0 perturbé par un potentiel décroissant W(hx) (). Nous obtenons une minoration de N(h) près de certaines singularités de la densité d'états associée à l'opérateur non perturbé P0.
Accepté le :
Publié le :
Dimassi, Mouez 1 ; Mnif, Maher 2
@article{CRMATH_2002__335_12_1013_0,
author = {Dimassi, Mouez and Mnif, Maher},
title = {Lower bounds for the counting function of resonances for a perturbation of a periodic {Schr\"odinger} operator by decreasing potential},
journal = {Comptes Rendus. Math\'ematique},
pages = {1013--1016},
year = {2002},
publisher = {Elsevier},
volume = {335},
number = {12},
doi = {10.1016/S1631-073X(02)02600-6},
language = {en},
url = {https://www.numdam.org/articles/10.1016/S1631-073X(02)02600-6/}
}
TY - JOUR AU - Dimassi, Mouez AU - Mnif, Maher TI - Lower bounds for the counting function of resonances for a perturbation of a periodic Schrödinger operator by decreasing potential JO - Comptes Rendus. Mathématique PY - 2002 SP - 1013 EP - 1016 VL - 335 IS - 12 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/S1631-073X(02)02600-6/ DO - 10.1016/S1631-073X(02)02600-6 LA - en ID - CRMATH_2002__335_12_1013_0 ER -
%0 Journal Article %A Dimassi, Mouez %A Mnif, Maher %T Lower bounds for the counting function of resonances for a perturbation of a periodic Schrödinger operator by decreasing potential %J Comptes Rendus. Mathématique %D 2002 %P 1013-1016 %V 335 %N 12 %I Elsevier %U https://www.numdam.org/articles/10.1016/S1631-073X(02)02600-6/ %R 10.1016/S1631-073X(02)02600-6 %G en %F CRMATH_2002__335_12_1013_0
Dimassi, Mouez; Mnif, Maher. Lower bounds for the counting function of resonances for a perturbation of a periodic Schrödinger operator by decreasing potential. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1013-1016. doi: 10.1016/S1631-073X(02)02600-6
[1] M. Dimassi, M. Zerzeri, A local trace formula for resonances of perturbed periodic Schrödinger operators, J. Funct. Anal., à paraı̂tre
[2] Localisation of resonances for matrix Schrödinger operators, Duke Math. J., Volume 106 (2001) no. 2, pp. 209-236
[3] Methods of Modern Mathematical Physics, Analysis Operators, Academic Press, New York, 1978
[4] J. Sjöstrand, A trace formula for resonances and application to semi-classical Schrödinger operators, Séminaire équations aux dérivées partielles, Exposé no 11 (1996–97)
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