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http://dx.doi.org/10.22771/nfaa.2021.26.04.04

ESSENTIAL SPECTRUM OF A WEIGHTED GEOMETRIC REALIZATION  

Hatim, Khalid (Departement de Mathematiques et Informatique, Faculte des Sciences Ain Chock Universite Hassan II de Casablanca, Laboratoire de Modelisation, Analyse, Controle et Statistiques)
Baalal, Azeddine (Departement de Mathematiques et Informatique, Faculte des Sciences Ain Chock Universite Hassan II de Casablanca, Laboratoire de Modelisation, Analyse, Controle et Statistiques)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.4, 2021 , pp. 701-716 More about this Journal
Abstract
In this present article, we construct a new framework that's we call the weighted geometric realization of 2 and 3-simplexes. On this new weighted framework, we construct a nonself-adjoint 2-simplex Laplacian L and a self-adjoint 2-simplex Laplacian N. We propose general conditions to ensure sectoriality for our new nonself-adjoint 2-simplex Laplacian L. We show the relation between the essential spectra of L and N. Finally, we prove the absence of the essential spectrum for our 2-simplex Laplacians L and N.
Keywords
Weighted geometric realization; nonself-adjoint 2-simplex Laplacian; numerical range; essential spectrum; sectoriality;
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