SPECTRA OF LAPLACIANS ON FORMS ON AN INFINITE GRAPH

Ayadi Hela , Hèla Ayadi (1)

1 Faculté des Sciences de Bizerte [Université de Carthage]

In the context of infinite weighted graphs, we consider the discrete Laplacians on 0-forms and 1-forms. Using Weyl's criterion, we prove the relation between the nonzero spectrum of ∆0 and that of ∆1. Moreover, we give an extension of the work of John Lott to characterize the 0-spectrum of these two Laplacians.

Domaines: Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]; Mathématiques [math]

Ayadi Hela, Hèla Ayadi. SPECTRA OF LAPLACIANS ON FORMS ON AN INFINITE GRAPH. Operators and Matrices, 2017. ⟨hal-01710216⟩