{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:KU72633JIHMU5ZQ7M5KATZV45H","short_pith_number":"pith:KU72633J","schema_version":"1.0","canonical_sha256":"553faf6f6941d94ee61f675409e6bce9c23dc28439028df6286074f812ebf9ea","source":{"kind":"arxiv","id":"2303.01208","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2303.01208","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2023-03-02T12:48:54Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"67f06345933f42de72a6ce0590b67cd5c7868a9819c9d9ee3ceb39f98aa46e01","abstract_canon_sha256":"b5e9453d83b63dbec78f5f779807f066ee851ed5af3ab5ba3a0ac8286012dadb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:10:46.360728Z","signature_b64":"LDLZVXUC7OXYrwUqYtrDTLqRgm2N/XmWIzXy3ZV/aQg+ydCMb1O5SoOWScm/V7ayyEpRDuwGvwjRTEOmEbZXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"553faf6f6941d94ee61f675409e6bce9c23dc28439028df6286074f812ebf9ea","last_reissued_at":"2026-07-05T07:10:46.360155Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:10:46.360155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2303.01208","created_at":"2026-07-05T07:10:46.360271+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.01208v2","created_at":"2026-07-05T07:10:46.360271+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01208","created_at":"2026-07-05T07:10:46.360271+00:00"},{"alias_kind":"pith_short_12","alias_value":"KU72633JIHMU","created_at":"2026-07-05T07:10:46.360271+00:00"},{"alias_kind":"pith_short_16","alias_value":"KU72633JIHMU5ZQ7","created_at":"2026-07-05T07:10:46.360271+00:00"},{"alias_kind":"pith_short_8","alias_value":"KU72633J","created_at":"2026-07-05T07:10:46.360271+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H","json":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H.json","graph_json":"https://pith.science/api/pith-number/KU72633JIHMU5ZQ7M5KATZV45H/graph.json","events_json":"https://pith.science/api/pith-number/KU72633JIHMU5ZQ7M5KATZV45H/events.json","paper":"https://pith.science/paper/KU72633J"},"agent_actions":{"view_html":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H","download_json":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H.json","view_paper":"https://pith.science/paper/KU72633J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.01208&json=true","fetch_graph":"https://pith.science/api/pith-number/KU72633JIHMU5ZQ7M5KATZV45H/graph.json","fetch_events":"https://pith.science/api/pith-number/KU72633JIHMU5ZQ7M5KATZV45H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H/action/storage_attestation","attest_author":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H/action/author_attestation","sign_citation":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H/action/citation_signature","submit_replication":"https://pith.science/pith/KU72633JIHMU5ZQ7M5KATZV45H/action/replication_record"}},"created_at":"2026-07-05T07:10:46.360271+00:00","updated_at":"2026-07-05T07:10:46.360271+00:00"}