ESSENTIAL SPECTRUM OF A WEIGHTED GEOMETRIC REALIZATION

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.