The boundary control approach to inverse spectral theory
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913865896296448 |
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| author | Avdonin, S. A. Mikhaylov, V. S. |
| author_facet | Avdonin, S. A. Mikhaylov, V. S. |
| contents | We establish connections between different approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Krein method, the Simon theory, the approach proposed by Remling and the Boundary Control method. We show that the Boundary Control approach provides simple and physically motivated proofs of the central results of other theories. We demonstrate also the connections between the dynamical and spectral data and derive the local version of the classical Gelfand--Levitan equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The boundary control approach to inverse spectral theory Avdonin, S. A. Mikhaylov, V. S. Analysis of PDEs Spectral Theory We establish connections between different approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Krein method, the Simon theory, the approach proposed by Remling and the Boundary Control method. We show that the Boundary Control approach provides simple and physically motivated proofs of the central results of other theories. We demonstrate also the connections between the dynamical and spectral data and derive the local version of the classical Gelfand--Levitan equations. |
| title | The boundary control approach to inverse spectral theory |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2505.23329 |