Explicit sharp bounds for all nodes of Sturm-Liouville operators with potentials in $L^1$ balls
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909972479082496 |
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| author | Chu, Jifeng Guo, Shuyuan Meng, Gang Zhang, Meirong |
| author_facet | Chu, Jifeng Guo, Shuyuan Meng, Gang Zhang, Meirong |
| contents | For the classical Sturm-Liouville operators, we prove the sharp bounds for all nodes of eigenfunctions by regarding these nodes as nonlinear functionals of potential $q\in L^1[0,1]$. By studying the optimization problems to minimize or to maximize the nodes $\{ T_{i,m}\}$ subject to the constraint $\|q\|_{1}=r$ with $r>0$ and using the strong continuity of the nodes in potentials, we obtain the explicit expressions for the sharp bounds, which are given as elementary functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18404 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit sharp bounds for all nodes of Sturm-Liouville operators with potentials in $L^1$ balls Chu, Jifeng Guo, Shuyuan Meng, Gang Zhang, Meirong Spectral Theory 34B24, 34L40, 49J40 For the classical Sturm-Liouville operators, we prove the sharp bounds for all nodes of eigenfunctions by regarding these nodes as nonlinear functionals of potential $q\in L^1[0,1]$. By studying the optimization problems to minimize or to maximize the nodes $\{ T_{i,m}\}$ subject to the constraint $\|q\|_{1}=r$ with $r>0$ and using the strong continuity of the nodes in potentials, we obtain the explicit expressions for the sharp bounds, which are given as elementary functions. |
| title | Explicit sharp bounds for all nodes of Sturm-Liouville operators with potentials in $L^1$ balls |
| topic | Spectral Theory 34B24, 34L40, 49J40 |
| url | https://arxiv.org/abs/2512.18404 |