Instabilité spectrale semiclassique pour des opérateurs non-autoadjoints I : un modèle
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, p. 243-280

In this work, we consider a simple differential operator as well as perturbations. While the spectrum of the unperturbed operator is confined to a line inside the pseudospectrum, we show for the perturbed operators that the eigenvalues are distributed inside the pseudospectrum according to a bidimensional Weyl law.

Dans ce travail, nous considérons un opérateur différentiel simple ainsi que des perturbations. Alors que le spectre de l’opérateur non-perturbé est confiné à une droite à l’intérieur du pseudospectre, nous montrons pour les opérateurs perturbés que les valeurs propres se distribuent à l’intérieur du pseudospectre d’après une loi de Weyl.

@article{AFST_2006_6_15_2_243_0,
     author = {Hager, Mildred},
     title = {Instabilit\'e spectrale semiclassique pour des op\'erateurs non-autoadjoints~I~: un mod\`ele},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 15},
     number = {2},
     year = {2006},
     pages = {243-280},
     doi = {10.5802/afst.1121},
     mrnumber = {2244217},
     zbl = {05136604},
     language = {fr},
     url = {http://www.numdam.org/item/AFST_2006_6_15_2_243_0}
}
Hager, Mildred. Instabilité spectrale semiclassique pour des opérateurs non-autoadjoints I : un modèle. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, pp. 243-280. doi : 10.5802/afst.1121. http://www.numdam.org/item/AFST_2006_6_15_2_243_0/

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