Dans cette Note, on donne une nouvelle preuve pour lʼasymptotique forte en puissances de h de la dérivée de la fonction de décalage spectral associée au couple , près dʼune énergie non captive. Ici le potentiel V est lisse, à valeurs réelles et pour un certain , et est un petit paramètre. Ce résultat est due à D. Robert et H. Tamura et leur preuve est basée sur la construction de paramétix pour des temps grands pour lʼéquation de Schrödinger dépendant du temps. Ici on donne une méthode indépendante du temps.
In this Note, we give a new proof of a pointwise asymptotic expansion in powers of h of the derivative of the spectral shift function corresponding to the pair , near a non-trapping energy. Here the potential V is smooth, real-valued and for some , and is a small parameter. This result is originally due to D. Robert and H. Tamura and their proof is based on the construction of a long-time parametrix for the time-dependent Schrödinger equation. Here we give a time-independent method.
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@article{CRMATH_2012__350_7-8_375_0, author = {Dimassi, Mouez and Zerzeri, Maher}, title = {A time-independent approach for the study of spectral shift function}, journal = {Comptes Rendus. Math\'ematique}, pages = {375--378}, publisher = {Elsevier}, volume = {350}, number = {7-8}, year = {2012}, doi = {10.1016/j.crma.2012.03.016}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.03.016/} }
TY - JOUR AU - Dimassi, Mouez AU - Zerzeri, Maher TI - A time-independent approach for the study of spectral shift function JO - Comptes Rendus. Mathématique PY - 2012 SP - 375 EP - 378 VL - 350 IS - 7-8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.03.016/ DO - 10.1016/j.crma.2012.03.016 LA - en ID - CRMATH_2012__350_7-8_375_0 ER -
%0 Journal Article %A Dimassi, Mouez %A Zerzeri, Maher %T A time-independent approach for the study of spectral shift function %J Comptes Rendus. Mathématique %D 2012 %P 375-378 %V 350 %N 7-8 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.03.016/ %R 10.1016/j.crma.2012.03.016 %G en %F CRMATH_2012__350_7-8_375_0
Dimassi, Mouez; Zerzeri, Maher. A time-independent approach for the study of spectral shift function. Comptes Rendus. Mathématique, Tome 350 (2012) no. 7-8, pp. 375-378. doi : 10.1016/j.crma.2012.03.016. http://archive.numdam.org/articles/10.1016/j.crma.2012.03.016/
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