Essential self-adjointness of Schrödinger operators on vector bundles over infinite graphs

Ognjen Milatovic (1) , Francoise Truc (2)

1 UNF - University of North Florida [Jacksonville]
2 IF - Institut Fourier

Given a Hermitian vector bundle over an infinite weighted graph, we define the Laplacian associated to a unitary connection on this bundle and study the essential self-adjointness of a perturbation of this Laplacian by an operator-valued potential. Additionally, we give a sufficient condition for the resulting Schrödinger operator to serve as the generator of a strongly continuous contraction semigroup in the corresponding l^{p}-space.

Mots clés: vector bundles; infinite graphs; essential self-adjointness; Schrödinger operator

Domaines: Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]

Ognjen Milatovic, Francoise Truc. Essential self-adjointness of Schrödinger operators on vector bundles over infinite graphs. 2013. ⟨hal-00840850v1⟩