Spectral analysis of the Laplacian acting on discrete cusps and funnels

2019/02/12 by Athmouni, Nassim, Ennaceur, Marwa, Golenia, Sylvain · 5 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1902.04467

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.

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