Spectral Theory for Sturm-Liouville operators with measure potentials through Otelbaev's function
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866916291019800576 |
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| author | Fulsche, Robert Nursultanov, Medet |
| author_facet | Fulsche, Robert Nursultanov, Medet |
| contents | We investigate the spectral properties of Sturm-Liouville operators with measure potentials. We obtain two-sided estimates for the spectral distribution function of the eigenvalues. As a corollary, we derive a criterion for the discreteness of the spectrum and a criterion for the membership of the resolvents to Schatten classes. We give two side estimates for the lower bound of the essential spectrum. Our main tool in achieving this is Otelbaev's function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2007_01624 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Spectral Theory for Sturm-Liouville operators with measure potentials through Otelbaev's function Fulsche, Robert Nursultanov, Medet Functional Analysis Spectral Theory Primary 34L15, 34L20, Secondary 34E15 We investigate the spectral properties of Sturm-Liouville operators with measure potentials. We obtain two-sided estimates for the spectral distribution function of the eigenvalues. As a corollary, we derive a criterion for the discreteness of the spectrum and a criterion for the membership of the resolvents to Schatten classes. We give two side estimates for the lower bound of the essential spectrum. Our main tool in achieving this is Otelbaev's function. |
| title | Spectral Theory for Sturm-Liouville operators with measure potentials through Otelbaev's function |
| topic | Functional Analysis Spectral Theory Primary 34L15, 34L20, Secondary 34E15 |
| url | https://arxiv.org/abs/2007.01624 |