Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (2): 876-896.doi: 10.1007/s10473-026-0218-y

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LIMITING ABSORPTION PRINCIPLE FOR LONG-RANGE PERTURBATION IN THE DISCRETE TRIANGULAR LATTICE SETTING

Nassim ATHMOUNI1, Marwa ENNACEUR2, Sylvain GOL ÉNIA3,*, Amel JADLAOUI4   

  1. 1. Universit é de Gafsa, Campus Universitaire, 2112, Tunisie;
    2. Department of Mathematics, College of Science, University of Hail, Hail 81451, Saudi Arabia;
    3. Univ. Bordeaux, Bordeaux INP, CNRS, IMB, UMR 5251, F-33400 Talence, France;
    4. Universit_e de Sfax. Route de la Soukra km 4-B.P. n 802-3038 Sfax, Tunisie
  • Received:2024-11-20 Revised:2025-07-05 Published:2026-05-22
  • Contact: *Sylvain GOL ÉNIA, E-mail: sylvain.golenia@math.u-bordeaux.fr
  • About author:Nassim ATHMOUNI, E-mail: nassim.athmouni@fsgf.u-gafsa.tn; Marwa ENNACEUR, E-mail: mar.ennaceur@uoh.edu.sa; Amel JADLAOUI, E-mail: amel.jadlaoui@yahoo.com

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.

Key words: commutator, Mourre estimate, Limiting Absorption Principle, discrete Laplacian, triangular lattice

CLC Number: 

  • 81Q10
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