Limiting absorption principle for long-range perturbation in the discrete triangular lattice setting
Functional Analysis
2025-06-09 v4 Spectral Theory
Abstract
We examine the discrete Laplacian acting on a triangular lattice, introducing long-range perturbations to both the metric and the potential. Our goal is to establish a Limiting Absorption Principle away from possible embedded eigenvalues. Our study relies on a positive commutator technique.
Cite
@article{arxiv.2403.06578,
title = {Limiting absorption principle for long-range perturbation in the discrete triangular lattice setting},
author = {Nassim Athmouni and Marwa Ennaceur and Sylvain Golenia and Amel Jadlaoui},
journal= {arXiv preprint arXiv:2403.06578},
year = {2025}
}