Dispersive Decay Estimates for periodic Jacobi operators on the half-line
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913848977522688 |
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| author | Sagiv, Amir Kassem, Remy Weinstein, Michael I |
| author_facet | Sagiv, Amir Kassem, Remy Weinstein, Michael I |
| contents | We establish dispersive time-decay estimates for periodic Jacobi operators on the discrete half-line, $\N$. Specifically, we prove $t^{-1/2}$ decay in the weighted $\ell^\infty_{-1}$ norm for all such operators. For the global $\ell^1 \to \ell^\infty$ decay estimate, we show that $t^{-1/3}$ decay holds under a nondegeneracy condition on the discriminant. Alternatively, for any even period $q\geq2$, if the continuous spectrum consists of exactly $q$ disjoint intervals (bands), we obtain a $t^{-1/(q+1)}$ decay rate without any further assumptions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_14498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dispersive Decay Estimates for periodic Jacobi operators on the half-line Sagiv, Amir Kassem, Remy Weinstein, Michael I Spectral Theory Mathematical Physics Classical Analysis and ODEs 47B36, 37L50, 42Axx, 81U30 We establish dispersive time-decay estimates for periodic Jacobi operators on the discrete half-line, $\N$. Specifically, we prove $t^{-1/2}$ decay in the weighted $\ell^\infty_{-1}$ norm for all such operators. For the global $\ell^1 \to \ell^\infty$ decay estimate, we show that $t^{-1/3}$ decay holds under a nondegeneracy condition on the discriminant. Alternatively, for any even period $q\geq2$, if the continuous spectrum consists of exactly $q$ disjoint intervals (bands), we obtain a $t^{-1/(q+1)}$ decay rate without any further assumptions. |
| title | Dispersive Decay Estimates for periodic Jacobi operators on the half-line |
| topic | Spectral Theory Mathematical Physics Classical Analysis and ODEs 47B36, 37L50, 42Axx, 81U30 |
| url | https://arxiv.org/abs/2505.14498 |