Negative eigenvalue estimates for the 1D Schr{ö}dinger operator with measure-potential
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917762169831424 |
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| author | Fulsche, Robert Nursultanov, Medet Rozenblum, Grigori |
| author_facet | Fulsche, Robert Nursultanov, Medet Rozenblum, Grigori |
| contents | We investigate the negative part of the spectrum of the operator $-\partial^2 - μ$ on $L^2(\mathbb R)$, where a locally finite Radon measure $μ\geq 0$ is serving as a potential. We obtain estimates for the eigenvalue counting function, for individual eigenvalues and estimates of the Lieb-Thirring type. A crucial tool for our estimates is Otelbaev's function, a certain average of the measure potential $μ$, which is used both in the proofs and the formulation of most of the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Negative eigenvalue estimates for the 1D Schr{ö}dinger operator with measure-potential Fulsche, Robert Nursultanov, Medet Rozenblum, Grigori Spectral Theory Mathematical Physics 47A75, 34L15, 34E15 We investigate the negative part of the spectrum of the operator $-\partial^2 - μ$ on $L^2(\mathbb R)$, where a locally finite Radon measure $μ\geq 0$ is serving as a potential. We obtain estimates for the eigenvalue counting function, for individual eigenvalues and estimates of the Lieb-Thirring type. A crucial tool for our estimates is Otelbaev's function, a certain average of the measure potential $μ$, which is used both in the proofs and the formulation of most of the results. |
| title | Negative eigenvalue estimates for the 1D Schr{ö}dinger operator with measure-potential |
| topic | Spectral Theory Mathematical Physics 47A75, 34L15, 34E15 |
| url | https://arxiv.org/abs/2408.05980 |