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.

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     author = {Colin de Verdi\`ere, Yves and Torki-Hamza, Nabila and Truc, Fran\c{c}oise},
     title = {Essential self-adjointness for combinatorial {Schr\"odinger} operators {III-} {Magnetic} fields},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {599--611},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 20},
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     url = {http://www.numdam.org/articles/10.5802/afst.1319/}
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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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