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Spectral analysis of the Laplacian acting on discrete cusps and funnels

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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https://hal.archives-ouvertes.fr/hal-02000996
Contributor : Sylvain Golenia <>
Submitted on : Thursday, March 26, 2020 - 6:19:55 PM
Last modification on : Tuesday, March 31, 2020 - 2:06:22 AM

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  • HAL Id : hal-02000996, version 2
  • ARXIV : 1902.04467

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Nassim Athmouni, Marwa Ennaceur, Sylvain Golenia. Spectral analysis of the Laplacian acting on discrete cusps and funnels. 2020. ⟨hal-02000996v2⟩

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