NON SELF-ADJOINT LAPLACIANS ON A DIRECTED GRAPH

Marwa Balti (1, 2)

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

We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We analyse spectral properties of this Laplacian under a Kirchhoff assumption. Moreover we establish isoperimet-ric inequalities in terms of the numerical range to show the absence of the essential spectrum of the Laplacian on heavy end directed graphs.

Domaines: Théorie spectrale [math.SP]

Marwa Balti. NON SELF-ADJOINT LAPLACIANS ON A DIRECTED GRAPH. Filomat, 2017. ⟨hal-01674356⟩