m-accretive Laplacian on a non symmetric graph

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 resu...

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Bibliographic Details
Published inIndagationes mathematicae Vol. 31; no. 2; pp. 277 - 293
Main Authors Anné, Colette, Balti, Marwa, Torki-Hamza, Nabila
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.03.2020
Elsevier Science Ltd
Elsevier
Subjects
Directed graph
Graph Laplacian
Graph theory
m-accretive Laplacian
m-sectorial Laplacian
Mathematics
Non self-adjoint operator
Numerical range
Spectral Theory
Graph Laplacian
m-sectorial Laplacian
Non self-adjoint operator
Numerical range
m-accretive Laplacian
Directed graph
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Summary: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.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2020.01.005