THE ADJACENCY MATRIX AND THE DISCRETE LAPLACIAN ACTING ON FORMS

Hatem Baloudi (1) , Sylvain Golenia (2) , Aref Jeribi (1)

1 FSS - Faculté des Sciences de Sfax
2 IMB - Institut de Mathématiques de Bordeaux

We study the relationship between the adjacency matrix and the discrete Laplacian acting on 1-forms. We also prove that if the adjacency matrix is bounded from below it is not necessarily essentially self-adjoint. We discuss the question of essential self-adjointness and the notion of completeness.

Mots clés: adjacency matrix; self-adjoint extension; locally finite graphs; discrete Laplacian; forms

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

Hatem Baloudi, Sylvain Golenia, Aref Jeribi. THE ADJACENCY MATRIX AND THE DISCRETE LAPLACIAN ACTING ON FORMS. 2015. ⟨hal-01148783⟩