March 3, 2026

Spectral enclosures for non-self-adjoint Jacobi operators

Key Points

Eigenvalues are located for non-self-adjoint Jacobi operators through ℓp perturbations of the discrete Laplacian, indicating complex behavior.
Optimal bounds under rank-one and rank-two perturbations were derived, revealing how perturbations affect spectrum.
The method involved norm estimates for the Birman-Schwinger operator, which plays a key role in spectral analysis.
Results highlight the importance of spectral bounds for different values of p, contributing to theoretical understanding.

Abstract

We study the ℓp-perturbations of the discrete Laplacian and obtain the spectral enclosures of corresponding non-self-adjoint Jacobi operator. By invoking the Birman-Schwinger principle and establishing norm estimates for the Birman-Schwinger operator, for p = 1, we get the location of the eigenvalues, and the optimal bounds is given under the rank-one and rank-two perturbations. For 1 p ≤ ∞, we get the spectral bounds.

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Cite This Study

Fu et al. (Thu,) studied this question.

synapsesocial.com/papers/69a75a73c6e9836116a20484 https://doi.org/https://doi.org/10.1063/5.0291195

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