PreprintCC BY 4.0arXiv
Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials
Abstract
In this paper, we consider one-dimensional discrete Schrödinger operators Hu(n)=(Δ+V)u(n)nonumber on ℓ2(ℕ) with a self-adjoint boundary condition at n=0, where Δ denotes the discrete Laplacian and V(n) is a real-valued perturbation satisfying V(n)=O(1)/(1+n). We determine the sharp transition for the asymptotic coefficient of V governing the existence and nonexistence of embedded eigenvalues.
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BibTeX
@misc{chu2026optimal,
title = {{Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials}},
author = {Jifeng Chu and Wencai Liu and Kang Lyu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03224},
eprint = {2609.03224},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03224},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials
AU - Jifeng Chu
AU - Wencai Liu
AU - Kang Lyu
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03224
UR - https://arxiv.org/abs/2609.03224
AB - In this paper, we consider one-dimensional discrete Schrödinger operators Hu(n)=(Δ+V)u(n)nonumber on ℓ^2(ℕ) with a self-adjoint boundary condition at n=0, where Δ denotes the discrete Laplacian and V(n) is a real-valued perturbation satisfying V(n)=O(1)/(1+n). We determine the sharp transition for the asymptotic coefficient of V governing the existence and nonexistence of embedded eigenvalues.
ER -