On the spectral properties of long-range perturbations of a class of block finite difference operators

2025/11/01 by Olivier Bourget, Bourget, Olivier, Angela Vargas-Mancipe +1
Mathematics · #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2511.00332

Abstract

We analyze spectral properties of a family of self-adjoint first-order finite difference operators acting on ℓ²(ℤ; ℂ²) or ℓ²(ℤ₊; ℂ²). Applying the conjugate operator method, we prove the existence of limiting absorption principles and the absence of singular continuous spectrum for these operators. Our results cover classes of admissible long-range perturbations that have not been previously addressed.

Citations

• Remarks on discrete Dirac operators and their continuum limits
• Spectral and scattering theory for perturbed block Toeplitz operators
• Spectral theory of a class of Block Jacobi matrices and applications
• Spectral stability for compact perturbations of Toeplitz matrices
• On the a.c. spectrum of 1D discrete Dirac operator
• The electronic properties of graphene

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