Third-order differential operators with a second-order distribution coefficient
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914107693727744 |
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| author | Bondarenko, Natalia P. |
| author_facet | Bondarenko, Natalia P. |
| contents | In this paper, we study differential operators associated with the formal expression $y''' + s(σ' y)' + s σ' y' + κσ'' y$ with distribution coefficient $σ'' \in W_3^{-2}$, where $s$ and $κ$ are constants. The uniqueness theorems are proved for the inverse spectral problems that consist in the recovery of $σ$ from the Weyl-Yurko matrix on a finite interval and on the half-line. In addition, we discuss the reconstruction of $σ$ and formulate some open problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_19287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Third-order differential operators with a second-order distribution coefficient Bondarenko, Natalia P. Spectral Theory 34A55 34B09 34B40 34L40 In this paper, we study differential operators associated with the formal expression $y''' + s(σ' y)' + s σ' y' + κσ'' y$ with distribution coefficient $σ'' \in W_3^{-2}$, where $s$ and $κ$ are constants. The uniqueness theorems are proved for the inverse spectral problems that consist in the recovery of $σ$ from the Weyl-Yurko matrix on a finite interval and on the half-line. In addition, we discuss the reconstruction of $σ$ and formulate some open problems. |
| title | Third-order differential operators with a second-order distribution coefficient |
| topic | Spectral Theory 34A55 34B09 34B40 34L40 |
| url | https://arxiv.org/abs/2510.19287 |