{"paper":{"title":"Point evaluation in Paley--Wiener spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.CA","authors_text":"Andr\\'es Chirre, Joaquim Ortega-Cerd\\`a, Kristian Seip, Ole Fredrik Brevig","submitted_at":"2022-10-25T11:20:30Z","abstract_excerpt":"We study the norm of point evaluation at the origin in the Paley--Wiener space $PW^p$ for $0 < p < \\infty$, i. e., we search for the smallest positive constant $C$, called $\\mathscr{C}_p$, such that the inequality $|f(0)|^p \\leq C \\|f\\|_p^p$ holds for every $f$ in $PW^p$. We present evidence and prove several results supporting the following monotonicity conjecture: The function $p\\mapsto \\mathscr{C}_p/p$ is strictly decreasing on the half-line $(0,\\infty)$. Our main result implies that $\\mathscr{C}_p <p/2$ for $2<p<\\infty$, and we verify numerically that $\\mathscr{C}_p > p/2$ for $1 \\leq p < "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.13922","kind":"arxiv","version":4},"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/2210.13922/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"}