{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KW4XHNPHB7QRWEUXUO5RK7PNHT","short_pith_number":"pith:KW4XHNPH","schema_version":"1.0","canonical_sha256":"55b973b5e70fe11b1297a3bb157ded3cd27009df931f36715a3aa7e1b41afa87","source":{"kind":"arxiv","id":"1309.7130","version":1},"attestation_state":"computed","paper":{"title":"The Beurling--Malliavin Multiplier Theorem and its analogs for the de Branges spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Victor Havin, Yurii Belov","submitted_at":"2013-09-27T06:44:32Z","abstract_excerpt":"Let $\\omega$ be a non-negative function on $\\mathbb{R}$. We are looking for a non-zero $f$ from a given space of entire functions $X$ satisfying $$(a) \\quad|f|\\leq \\omega\\text{\\quad or\\quad(b)}\\quad |f|\\asymp\\omega.$$ The classical Beurling--Malliavin Multiplier Theorem corresponds to $(a)$ and the classical Paley--Wiener space as $X$. We survey recent results for the case when $X$ is a de Branges space $\\he$. Numerous answers mainly depend on the behaviour of the phase function of the generating function $E$."},"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":"1309.7130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-09-27T06:44:32Z","cross_cats_sorted":[],"title_canon_sha256":"f6aab338766327a29f6df636030ffc63c09adba3977c190d9dff0b2da1a4b563","abstract_canon_sha256":"20cf13c3e33e440102e147e4b6862e226faa0513936b48ee863d4e6fa47d61f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:00.148924Z","signature_b64":"wfx9z6KgRF/wiy32B3FQxwVvcNAOcVQRhzfCEgj6kT/+f4W60S+sDVT5+/djRXXomF3jbhQTtD5I/Gakj0zRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55b973b5e70fe11b1297a3bb157ded3cd27009df931f36715a3aa7e1b41afa87","last_reissued_at":"2026-05-18T03:12:00.148129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:00.148129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Beurling--Malliavin Multiplier Theorem and its analogs for the de Branges spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Victor Havin, Yurii Belov","submitted_at":"2013-09-27T06:44:32Z","abstract_excerpt":"Let $\\omega$ be a non-negative function on $\\mathbb{R}$. We are looking for a non-zero $f$ from a given space of entire functions $X$ satisfying $$(a) \\quad|f|\\leq \\omega\\text{\\quad or\\quad(b)}\\quad |f|\\asymp\\omega.$$ The classical Beurling--Malliavin Multiplier Theorem corresponds to $(a)$ and the classical Paley--Wiener space as $X$. We survey recent results for the case when $X$ is a de Branges space $\\he$. Numerous answers mainly depend on the behaviour of the phase function of the generating function $E$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7130","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":"1309.7130","created_at":"2026-05-18T03:12:00.148258+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7130v1","created_at":"2026-05-18T03:12:00.148258+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7130","created_at":"2026-05-18T03:12:00.148258+00:00"},{"alias_kind":"pith_short_12","alias_value":"KW4XHNPHB7QR","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"KW4XHNPHB7QRWEUX","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"KW4XHNPH","created_at":"2026-05-18T12:27:51.066281+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/KW4XHNPHB7QRWEUXUO5RK7PNHT","json":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT.json","graph_json":"https://pith.science/api/pith-number/KW4XHNPHB7QRWEUXUO5RK7PNHT/graph.json","events_json":"https://pith.science/api/pith-number/KW4XHNPHB7QRWEUXUO5RK7PNHT/events.json","paper":"https://pith.science/paper/KW4XHNPH"},"agent_actions":{"view_html":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT","download_json":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT.json","view_paper":"https://pith.science/paper/KW4XHNPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7130&json=true","fetch_graph":"https://pith.science/api/pith-number/KW4XHNPHB7QRWEUXUO5RK7PNHT/graph.json","fetch_events":"https://pith.science/api/pith-number/KW4XHNPHB7QRWEUXUO5RK7PNHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT/action/storage_attestation","attest_author":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT/action/author_attestation","sign_citation":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT/action/citation_signature","submit_replication":"https://pith.science/pith/KW4XHNPHB7QRWEUXUO5RK7PNHT/action/replication_record"}},"created_at":"2026-05-18T03:12:00.148258+00:00","updated_at":"2026-05-18T03:12:00.148258+00:00"}