SECTORIALITY AND ESSENTIAL SPECTRUM OF NON SYMMETRIC GRAPH LAPLACIANS

Colette Anné (1) , Marwa Balti (2, 1) , Nabila Torki-Hamza (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Faculté des Sciences de Bizerte [Université de Carthage]
3 ISIG-K - Institut Supérieur d'Informatique et de Gestion de Kairouan

We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We give necessary conditions for this Laplacian to be sectorial. We introduce a special self-adjoint operator and compare its essential spectrum with that of the non self-adjoint Laplacian considered.

Domaines: Théorie spectrale [math.SP]

Colette Anné, Marwa Balti, Nabila Torki-Hamza. SECTORIALITY AND ESSENTIAL SPECTRUM OF NON SYMMETRIC GRAPH LAPLACIANS. Complex Analysis and Operator Theory, 2018, 13 (3), pp.967-983. ⟨10.1007/s11785-018-0817-2⟩. ⟨hal-01671142⟩