Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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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)
  • Received : 2021.01.13
  • Accepted : 2021.04.01
  • Published : 2021.12.15
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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.

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References

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