Spectral analysis of the Laplacian acting on discrete cusps and funnels
Spectral Theory
2020-03-31 v2 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1902.04467,
title = {Spectral analysis of the Laplacian acting on discrete cusps and funnels},
author = {Nassim Athmouni and Marwa Ennaceur and Sylvain Golenia},
journal= {arXiv preprint arXiv:1902.04467},
year = {2020}
}