{"paper":{"title":"Dispersive Decay Estimates for periodic Jacobi operators on the half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.SP","authors_text":"Amir Sagiv, Michael I Weinstein, Remy Kassem","submitted_at":"2025-05-20T15:27:34Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14498","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.14498/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}