Spectral analysis of the Laplacian acting on discrete cusps and funnels

We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from the possible embedded eigenvalues. The approach is based on a positive commutator technique

Spectral analysis of the Laplacian acting on discrete cusps and funnels

Nous étudions le Laplacien agissant sur un cusp discret et un funnel discret. Nous ajoutons une perturbation longue-portée à la métrique. Puis, nous établissons un principe d'absorption limite en dehors des possibles valeurs propres plongées. Notre approche est basée sur une technique de commutateurs positifs.We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from the possible embedded eigenvalues. The approach is based on a positive commutator technique

THE DISCRETE LAPLACIAN ASSOCIATED TO EDGES WITH APPLICATIONTO MAGNETIC ADJACENCY MATRIX

This paper is devoted to the investigation of the question of the essential self-adjointness of discrete magnetic Laplacian operators on pseudo-cochains. We consider the notion of χ−completness of the locally finite graph and we approach this geometric hypothesis for the weighted magnetic graph. Moreover, we establish a link between the magnetic adjacency matrix on line graph and the magnetic discrete Laplacian on 1-forms

LIMITING ABSORPTION PRINCIPLE FOR LONG-RANGE PERTURBATION IN THE DISCRETE TRIANGULAR LATTICE SETTING

We study the discrete Laplacian acting on a triangular lattice. We perturb the metric and the potential in a long-range way. We aim at proving a Limiting Absorption Principle away the possible embedded eigenvalues. The approach is based on a positive commutator technique