The distribution of negative eigenvalues of Schrödinger operators on asymptotically hyperbolic manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916577201356800 |
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| author | Barreto, Antônio Sá Wang, Yiran |
| author_facet | Barreto, Antônio Sá Wang, Yiran |
| contents | We study the asymptotic behavior of the counting function of negative eigenvalues of Schrödinger operators with real valued potentials on asymptotically hyperbolic manifolds. We establish conditions on the potential that determine if there are finitely or infinitely many negative eigenvalues. In the latter case, they may only accumulate at zero and we obtain the asymptotic behavior of the counting function of eigenvalues in an interval $(-\infty,-E)$ as $E\rightarrow 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The distribution of negative eigenvalues of Schrödinger operators on asymptotically hyperbolic manifolds Barreto, Antônio Sá Wang, Yiran Spectral Theory Analysis of PDEs We study the asymptotic behavior of the counting function of negative eigenvalues of Schrödinger operators with real valued potentials on asymptotically hyperbolic manifolds. We establish conditions on the potential that determine if there are finitely or infinitely many negative eigenvalues. In the latter case, they may only accumulate at zero and we obtain the asymptotic behavior of the counting function of eigenvalues in an interval $(-\infty,-E)$ as $E\rightarrow 0$. |
| title | The distribution of negative eigenvalues of Schrödinger operators on asymptotically hyperbolic manifolds |
| topic | Spectral Theory Analysis of PDEs |
| url | https://arxiv.org/abs/2501.12606 |