Embedded eigenvalues and resonances of Schrödinger operators with two channels
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 16 (2007) no. 1, pp. 179-214.

Dans cet article, nous donnons dans le régime de perturbation une condition nécessaire et suffisante sur l’existence de valeurs propres plongées entre les deux seuils. Pour une valeur propre de l’opérateur non-perturbé plongée à un seuil, nous démontrons qu’elle peut engendrer à la fois des valeurs propres discrètes et des résonances.

In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.

DOI : 10.5802/afst.1144
Wang, Xue Ping 1

1 Département de Mathématiques, UMR 6629 CNRS, Université de Nantes, 44322 Nantes Cedex France
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Wang, Xue Ping. Embedded eigenvalues and resonances of Schrödinger operators with two channels. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 16 (2007) no. 1, pp. 179-214. doi : 10.5802/afst.1144. http://www.numdam.org/articles/10.5802/afst.1144/

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