Semi-Fredholmness of the discrete Gauss-Bonnet Operator

Hèla Ayadi (1, 2)

1 Faculté des Sciences de Bizerte [Université de Carthage]
2 LMJL - Laboratoire de Mathématiques Jean Leray

In the context of an infinite locally finite weighted graph, we give a necessary and sufficient condition for semi-Fredholmness of the Gauss-Bonnet operator. This result is a discrete version of the theorem of Gilles Carron in the continuous case [5]. In addition, using a criterion of Anghel [2], we give a sufficient condition to have an operator of Gauss-Bonnet with closed range. Finally, this work can be considered as an extension of the work of Colette Anné and Nabila Torki-Hamza [3].

Mots clés: Closed Range Operator.; Discrete Gauss-Bonnet Operator; Non-parabolicity at Infinity; Infinite weighted graph

Domaines: Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]

Hèla Ayadi. Semi-Fredholmness of the discrete Gauss-Bonnet Operator. Filomat, 2017. ⟨hal-01412045⟩