Dispersive Decay Estimates for periodic Jacobi operators on the half-line

Fuente: arXiv
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Main Authors: Sagiv, Amir, Kassem, Remy, Weinstein, Michael I
Format: Preprint
Published: 2025
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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
id 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