Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911232434372608 |
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| author | Cuenin, Jean-Claude |
| author_facet | Cuenin, Jean-Claude |
| contents | We prove eigenvalue bounds for Schrödinger operator $-Δ_g+V$ on compact manifolds with complex potentials $V$. The bounds depend only on an $L^q$-norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank's \cite{MR2820160} results in the Euclidean case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds Cuenin, Jean-Claude Spectral Theory Analysis of PDEs We prove eigenvalue bounds for Schrödinger operator $-Δ_g+V$ on compact manifolds with complex potentials $V$. The bounds depend only on an $L^q$-norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank's \cite{MR2820160} results in the Euclidean case. |
| title | Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds |
| topic | Spectral Theory Analysis of PDEs |
| url | https://arxiv.org/abs/2411.16984 |