Partial Information for Inverse Spectral Uniqueness in Vibration System with Multiple Frozen Arguments
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914068982398976 |
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| author | Chen, Lung-Hui |
| author_facet | Chen, Lung-Hui |
| contents | In this paper, we investigate the inverse spectral problem of the Sturm-Liouville operator with many frozen arguments fixed at the points $\{a_{1}, a_{2},\ldots,a_{N}\}$ in $(0,π)$. We start with counting the zeros or the eigenvalues of characteristic function, and then discuss how certain information provided a priori on the point set $\{a_{1}, a_{2},\ldots,a_{N}\}$ would affect the uniqueness or non-uniqueness of this vibration system with many frozen points. The knowledge at the frozen or regulator points are practical in many on-site problems. Parallelly, certain irrational independence assumption assures the inverse spectral uniqueness as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial Information for Inverse Spectral Uniqueness in Vibration System with Multiple Frozen Arguments Chen, Lung-Hui Spectral Theory In this paper, we investigate the inverse spectral problem of the Sturm-Liouville operator with many frozen arguments fixed at the points $\{a_{1}, a_{2},\ldots,a_{N}\}$ in $(0,π)$. We start with counting the zeros or the eigenvalues of characteristic function, and then discuss how certain information provided a priori on the point set $\{a_{1}, a_{2},\ldots,a_{N}\}$ would affect the uniqueness or non-uniqueness of this vibration system with many frozen points. The knowledge at the frozen or regulator points are practical in many on-site problems. Parallelly, certain irrational independence assumption assures the inverse spectral uniqueness as well. |
| title | Partial Information for Inverse Spectral Uniqueness in Vibration System with Multiple Frozen Arguments |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2507.20184 |