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Specifically, if $\\{\\phi_\\alpha(x): \\alpha\\in A\\}$ is a regular family of interpolators and $\\{x_n: n\\in \\mathbb{Z}\\}$ is a complete interpolating sequence for $L^2([-\\pi,\\pi])$, then the family $\\{ e^{2\\pi i m x}\\phi_{\\alpha}(x-x_n): m,n\\in \\mathbb{Z}, \\alpha\\in A \\} $ may be used to recover $f\\in(PW,l^1)$."},"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":"1311.5169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-20T18:53:45Z","cross_cats_sorted":[],"title_canon_sha256":"64d3dfe8ff9127383e0d14b5ad009b96241724c9815943d9fd316c59831fdf82","abstract_canon_sha256":"2f238da17d260a5e8c0456365aa7f0111da09611a69ba9561b5f05e203593a4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:35.066980Z","signature_b64":"JZVIWGflJJYyl7jFUdunIPmMNsrI9J380oQpruqd8CYTF0Sgb87TdlBX7xLXriYtOTNYzWhUJzNyuCsQdtYbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4edf9e58a2ac8e318fd082cf9a410a36d8f2b77f09344c9b7ab59b457f256dde","last_reissued_at":"2026-05-18T03:06:35.066338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:35.066338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recovering functions from the Paley-Wiener amalgam space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jeff Ledford","submitted_at":"2013-11-20T18:53:45Z","abstract_excerpt":"In this paper we show that functions from the Paley-Wiener amalgam space $(PW,l^1)=\\{f\\in L^2(\\mathbb{R}): \\sum\\|\\hat{f}(\\xi+2\\pi m) \\|_{L^2([-\\pi,\\pi])} < \\infty\\}$ enjoy similar recovery properties as the classical Paley-Wiener space. Specifically, if $\\{\\phi_\\alpha(x): \\alpha\\in A\\}$ is a regular family of interpolators and $\\{x_n: n\\in \\mathbb{Z}\\}$ is a complete interpolating sequence for $L^2([-\\pi,\\pi])$, then the family $\\{ e^{2\\pi i m x}\\phi_{\\alpha}(x-x_n): m,n\\in \\mathbb{Z}, \\alpha\\in A \\} $ may be used to recover $f\\in(PW,l^1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5169","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":""},"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":"1311.5169","created_at":"2026-05-18T03:06:35.066430+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.5169v1","created_at":"2026-05-18T03:06:35.066430+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5169","created_at":"2026-05-18T03:06:35.066430+00:00"},{"alias_kind":"pith_short_12","alias_value":"J3PZ4WFCVSHD","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"J3PZ4WFCVSHDDD6Q","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"J3PZ4WFC","created_at":"2026-05-18T12:27:49.015174+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/J3PZ4WFCVSHDDD6QQLHZUQIKG3","json":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3.json","graph_json":"https://pith.science/api/pith-number/J3PZ4WFCVSHDDD6QQLHZUQIKG3/graph.json","events_json":"https://pith.science/api/pith-number/J3PZ4WFCVSHDDD6QQLHZUQIKG3/events.json","paper":"https://pith.science/paper/J3PZ4WFC"},"agent_actions":{"view_html":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3","download_json":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3.json","view_paper":"https://pith.science/paper/J3PZ4WFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.5169&json=true","fetch_graph":"https://pith.science/api/pith-number/J3PZ4WFCVSHDDD6QQLHZUQIKG3/graph.json","fetch_events":"https://pith.science/api/pith-number/J3PZ4WFCVSHDDD6QQLHZUQIKG3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3/action/storage_attestation","attest_author":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3/action/author_attestation","sign_citation":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3/action/citation_signature","submit_replication":"https://pith.science/pith/J3PZ4WFCVSHDDD6QQLHZUQIKG3/action/replication_record"}},"created_at":"2026-05-18T03:06:35.066430+00:00","updated_at":"2026-05-18T03:06:35.066430+00:00"}