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

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.

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.

@article{AFST_2007_6_16_1_179_0,
     author = {Wang, Xue Ping},
     title = {Embedded eigenvalues and resonances of Schr\"odinger operators with two channels},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 16},
     number = {1},
     year = {2007},
     pages = {179-214},
     doi = {10.5802/afst.1144},
     mrnumber = {2325597},
     zbl = {pre05247244},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2007_6_16_1_179_0}
}
Wang, Xue Ping. Embedded eigenvalues and resonances of Schrödinger operators with two channels. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, pp. 179-214. doi : 10.5802/afst.1144. http://www.numdam.org/item/AFST_2007_6_16_1_179_0/

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