Sectoriality and Essential Spectrum of Non Symmetric Graph Laplacians
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We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We give sufficient 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.
KeywordsDirected graph Non self-adjoint Laplacian Numerical range Sectorial operator Essential spectrum
Mathematics Subject Classification47A45 47A12 47A10 47B25 39A12 47B37
We would like to thank the anonymous referees for the careful reading of our paper and the valuable comments and suggestions. The author Marwa Balti was financially supported by the DéfiMaths program of the Federation of Mathematical Research of the “Pays de Loire” and by the “PHC Utique” program of the French Ministry of Foreign Affairs and Ministry of higher education and research and the Tunisian Ministry of higher education and scientific research in the CMCU project number 13G1501 “Graphes, Géométrie et Théorie Spectrale” during her visits to the Laboratory of Mathematics Jean Leray of Nantes (LMJL). Also, the three authors would like to thank the Laboratory of Mathematics Jean Leray of Nantes (LMJL) and the research unity (UR/13ES47) of Faculty of Sciences of Bizerta (University of Carthage) for their continuous financial support.
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