M-accretive Laplacian on a non symmetric graph

2019/06/18 by Anné, Colette, Balti, Marwa, Torki-Hamza, Nabila · 1 citation
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1906.07596

Abstract

We consider a non self-adjoint Laplacian on a directed graph with non symmetric weights on edges. We give a criterion for the m-accretiveness and the m-sectoriality of this Laplacian. Our results are based on a comparison of this operator with its symmetric part for which we can apply dierent results concerning essential self-adjointness of a symmetric Laplace operator on an innite graph. This gives results on the heat operator related to our non-symmetric Laplacian.

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• Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs

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