A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential
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 o...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/4696790 |
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| _version_ | 1832560784464412672 |
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| author | Gift Muchatibaya Josiah Mushanyu |
| author_facet | Gift Muchatibaya Josiah Mushanyu |
| author_sort | Gift Muchatibaya |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0c2fcfe1ba254ca48cf16f5a6de5e105 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0c2fcfe1ba254ca48cf16f5a6de5e1052025-02-03T01:26:36ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/46967904696790A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic PotentialGift Muchatibaya0Josiah Mushanyu1Department of Mathematics, University of Zimbabwe, MP 167, Mt Pleasant, Harare, ZimbabweDepartment of Mathematics, University of Zimbabwe, MP 167, Mt Pleasant, Harare, ZimbabweThe 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.http://dx.doi.org/10.1155/2018/4696790 |
| spellingShingle | Gift Muchatibaya Josiah Mushanyu A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential Advances in Mathematical Physics |
| title | A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential |
| title_full | A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential |
| title_fullStr | A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential |
| title_full_unstemmed | A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential |
| title_short | A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential |
| title_sort | note on the asymptotic and threshold behaviour of discrete eigenvalues inside the spectral gaps of the difference operator with a periodic potential |
| url | http://dx.doi.org/10.1155/2018/4696790 |
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