Borg-type theorem for a class of higher-order differential operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910959881158656 |
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| author | Guan, Ai-Wei Wu, Dong-Jie Yang, Chuan-Fu Bondarenko, Natalia P. |
| author_facet | Guan, Ai-Wei Wu, Dong-Jie Yang, Chuan-Fu Bondarenko, Natalia P. |
| contents | In this paper, we study an inverse spectral operator for the higher-order differential equation $(-1)^my^{(2m)}+ q y = λy$, where $q \in L^2(0,π)$. We prove that if $\|q\|_2$ is sufficiently small, the two spectra corresponding to the both Dirichlet boundary conditions and to the Dirichlet-Neumann ones uniquely determine the potential $q$. The result extends the Borg theorem from the second order to all even higher orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Borg-type theorem for a class of higher-order differential operators Guan, Ai-Wei Wu, Dong-Jie Yang, Chuan-Fu Bondarenko, Natalia P. Spectral Theory In this paper, we study an inverse spectral operator for the higher-order differential equation $(-1)^my^{(2m)}+ q y = λy$, where $q \in L^2(0,π)$. We prove that if $\|q\|_2$ is sufficiently small, the two spectra corresponding to the both Dirichlet boundary conditions and to the Dirichlet-Neumann ones uniquely determine the potential $q$. The result extends the Borg theorem from the second order to all even higher orders. |
| title | Borg-type theorem for a class of higher-order differential operators |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2505.15675 |