m-ACCRETIVE LAPLACIAN ON A NON SYMMETRIC GRAPH

Colette Anné (1) , Marwa Balti (1) , Nabila Torki-Hamza (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LR/18ES15 - Université de Monastir

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 different results concerning essential self-adjointness of a symmetric Laplace operator on an infinite graph. This gives results on the heat operator related to our non-symmetric Laplacian.

Domaines: Théorie spectrale [math.SP]

Colette Anné, Marwa Balti, Nabila Torki-Hamza. m-ACCRETIVE LAPLACIAN ON A NON SYMMETRIC GRAPH. Indagationes Mathematicae, 2020. ⟨hal-02158296v1⟩