Semi-Fredholmness of the discrete Gauss-Bonnet Operator

2016/12/12 by Ayadi, Hèla
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1612.03750

Abstract

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

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