Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 20 (2011) no. 3, pp. 599-611.

On définit l’opérateur de Schrödinger avec champ magnétique sur un graphe infini par la donnée d’un champ magnétique, de poids sur les sommets et de poids sur les arêtes. Lorsque le graphe est de degré borné, on étudie le caractère essentiellement auto-adjoint d’un tel opérateur. Le résultat principal est une version discrète d’un résultat de deux des auteurs du présent article.

We define the magnetic Schrödinger operator on an infinite graph by the data of a magnetic field, some weights on vertices and some weights on edges. We discuss essential self-adjointness of this operator for graphs of bounded degree. The main result is a discrete version of a result of two authors of the present paper.

DOI : 10.5802/afst.1319
Colin de Verdière, Yves 1 ; Torki-Hamza, Nabila 2 ; Truc, Françoise 1

1 Grenoble University, Institut Fourier, Unité mixte de recherche CNRS-UJF 5582, BP 74, 38402-Saint Martin d’Hères Cedex (France)
2 Université de Carthage, Faculté des Sciences de Bizerte, Mathématiques et Applications (05/UR/15-02), 7021-Bizerte (Tunisie)
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     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Colin de Verdière, Yves; Torki-Hamza, Nabila; Truc, Françoise. Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 20 (2011) no. 3, pp. 599-611. doi : 10.5802/afst.1319. http://www.numdam.org/articles/10.5802/afst.1319/

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