English

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}
}