Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913043655426048 |
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| author | Świderski, Grzegorz Trojan, Bartosz |
| author_facet | Świderski, Grzegorz Trojan, Bartosz |
| contents | We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic problem computed for the spectral parameter equal to $0$. Under certain assumptions, by studying the asymptotic behavior of Christoffel functions and density of states, we prove that the spectral density is a continuous positive everywhere function on the real line. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_12300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case Świderski, Grzegorz Trojan, Bartosz Spectral Theory Mathematical Physics Classical Analysis and ODEs 34B24, 34L05 (Primary) 34L20, 34C11 (Secondary) We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic problem computed for the spectral parameter equal to $0$. Under certain assumptions, by studying the asymptotic behavior of Christoffel functions and density of states, we prove that the spectral density is a continuous positive everywhere function on the real line. |
| title | Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case |
| topic | Spectral Theory Mathematical Physics Classical Analysis and ODEs 34B24, 34L05 (Primary) 34L20, 34C11 (Secondary) |
| url | https://arxiv.org/abs/2507.12300 |