Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912015142879232 |
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| author | Cuenin, Jean-Claude Keedle-Isack, Solomon |
| author_facet | Cuenin, Jean-Claude Keedle-Isack, Solomon |
| contents | We consider eigenvalue sums of Schrödinger operators $-Δ+V$ on $L^2(\R^d)$ with complex radial potentials $V\in L^q(\R^d)$, $q<d$. We prove quantitative bounds on the distribution of the eigenvlaues in terms of the $L^q$ norm of $V$. A consequence of our bounds is that, if the eigenvlaues $(z_j)$ accumulates to a point in $(0,\infty)$, then $(\im z_j)$ is summable. The key technical tools are resolvent estimates in Schatten spaces. We show that these resolvent estimates follow from spectral measure estimates by an epsilon removal argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials Cuenin, Jean-Claude Keedle-Isack, Solomon Spectral Theory Mathematical Physics Analysis of PDEs We consider eigenvalue sums of Schrödinger operators $-Δ+V$ on $L^2(\R^d)$ with complex radial potentials $V\in L^q(\R^d)$, $q<d$. We prove quantitative bounds on the distribution of the eigenvlaues in terms of the $L^q$ norm of $V$. A consequence of our bounds is that, if the eigenvlaues $(z_j)$ accumulates to a point in $(0,\infty)$, then $(\im z_j)$ is summable. The key technical tools are resolvent estimates in Schatten spaces. We show that these resolvent estimates follow from spectral measure estimates by an epsilon removal argument. |
| title | Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2408.15783 |