{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KU72633JIHMU5ZQ7M5KATZV45H","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b5e9453d83b63dbec78f5f779807f066ee851ed5af3ab5ba3a0ac8286012dadb","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2023-03-02T12:48:54Z","title_canon_sha256":"67f06345933f42de72a6ce0590b67cd5c7868a9819c9d9ee3ceb39f98aa46e01"},"schema_version":"1.0","source":{"id":"2303.01208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01208","created_at":"2026-07-05T07:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01208v2","created_at":"2026-07-05T07:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01208","created_at":"2026-07-05T07:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"KU72633JIHMU","created_at":"2026-07-05T07:10:46Z"},{"alias_kind":"pith_short_16","alias_value":"KU72633JIHMU5ZQ7","created_at":"2026-07-05T07:10:46Z"},{"alias_kind":"pith_short_8","alias_value":"KU72633J","created_at":"2026-07-05T07:10:46Z"}],"graph_snapshots":[{"event_id":"sha256:de1f16c834bf830d3e3114334766a8a4743010fc011cec2b1fff0c6a19af4e57","target":"graph","created_at":"2026-07-05T07:10:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.01208/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Konstantinos Bampouras","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2023-03-02T12:48:54Z","title":"On the failure of the Nehari Theorem for Paley-Wiener spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01208","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:87d31b59fb019b48c50d7e2183cbcc7b13ab1f8c92bbd8be24d2916ac9ddb03e","target":"record","created_at":"2026-07-05T07:10:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b5e9453d83b63dbec78f5f779807f066ee851ed5af3ab5ba3a0ac8286012dadb","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2023-03-02T12:48:54Z","title_canon_sha256":"67f06345933f42de72a6ce0590b67cd5c7868a9819c9d9ee3ceb39f98aa46e01"},"schema_version":"1.0","source":{"id":"2303.01208","kind":"arxiv","version":2}},"canonical_sha256":"553faf6f6941d94ee61f675409e6bce9c23dc28439028df6286074f812ebf9ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"553faf6f6941d94ee61f675409e6bce9c23dc28439028df6286074f812ebf9ea","first_computed_at":"2026-07-05T07:10:46.360155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:10:46.360155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDLZVXUC7OXYrwUqYtrDTLqRgm2N/XmWIzXy3ZV/aQg+ydCMb1O5SoOWScm/V7ayyEpRDuwGvwjRTEOmEbZXDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:10:46.360728Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.01208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87d31b59fb019b48c50d7e2183cbcc7b13ab1f8c92bbd8be24d2916ac9ddb03e","sha256:de1f16c834bf830d3e3114334766a8a4743010fc011cec2b1fff0c6a19af4e57"],"state_sha256":"b9dd8ebd0cf1ba1485909b2583310268a71b4b1469ae5955e814867a39a37823"}