A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential

Gift Muchatibaya and Josiah Mushanyu

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: The asymptotic and threshold behaviour of the eigenvalues of a perturbed difference operator inside a spectral gap is investigated. In particular, applications of the Titchmarsh‐Weyl m‐function theory as well as the Birman‐Schwinger principle is performed to investigate the existence and behaviour of the eigenvalues of the operator H0 + λWn inside the spectral gap of H0 in the limits λ↑∞ and λ ↓ 0.

Date: 2018
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https://doi.org/10.1155/2018/4696790

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:4696790

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