{"paper":{"title":"On the failure of the Nehari Theorem for Paley-Wiener spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Konstantinos Bampouras","submitted_at":"2023-03-02T12:48:54Z","abstract_excerpt":"Let $\\Omega$ be a nonempty, open and convex subset of $\\mathbb{R}^{n}$. The Paley-Wiener space with respect to $\\Omega$ is defined to be the closed subspace of $L^{2}(\\mathbb{R}^{n})$ of functions with Fourier transform supported in $2\\Omega$. For a tempered distribution $\\phi$ we define a Hankel operator to be the densely defined operator:\n  $$\\widehat{H_{\\phi}f}(x)=\\int_{\\Omega}\\widehat{f}(y)\\widehat{\\phi}(x+y)dy,\\text{ for $x\\in\\Omega$}.$$ We say that the Nehari theorem is true for $\\Omega$, if every bounded Hankel operator is generated by a bounded function. In this paper we prove that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01208","kind":"arxiv","version":2},"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/2303.01208/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"}