{"paper":{"title":"Optimal concentration in the Paley-Wiener space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Lu\\'is Daniel Abreu, Michael Speckbacher","submitted_at":"2026-07-21T15:28:42Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}$ be a bounded interval and let $PW(\\Omega )$ be the corresponding Paley--Wiener space. For a measurable set $E\\subset \\mathbb{R}$ of finite measure, consider the largest possible fraction of the $L^{2}$-mass of a function in $PW(\\Omega )$ that can lie in $E$. We prove that this concentration is no larger than the concentration attained on an interval of measure $\\lvert E\\rvert $. Thus, \\emph{intervals optimize concentration in the Paley-Wiener space of band-limited functions.}\n  The proof, based on an universality-type limit of the reproducing kernel of analytic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19192","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/2607.19192/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"}