{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:C5O2LTS7UQHCZDLCH7VDZ3RCA7","short_pith_number":"pith:C5O2LTS7","schema_version":"1.0","canonical_sha256":"175da5ce5fa40e2c8d623fea3cee2207fbb1130fa99ae10a1458d3e5284afd8f","source":{"kind":"arxiv","id":"1612.08304","version":2},"attestation_state":"computed","paper":{"title":"A generalized Hilbert operator acting on conformally invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniel Girela, Noel Merch\\'an","submitted_at":"2016-12-25T23:07:47Z","abstract_excerpt":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\\mathcal H_\\mu $ be the Hankel matrix $\\mathcal H_\\mu =(\\mu_{n, k})_{n,k\\ge 0}$ with entries $\\mu_{n, k}=\\mu_{n+k}$, where, for $n\\,=\\,0, 1, 2, \\dots $, $\\mu_n$ denotes the moment of orden $n$ of $\\mu $. This matrix induces formally the operator $$\\mathcal{H}_\\mu (f)(z)= \\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty} \\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\D $. This is a natural generalization of the classical Hilbert operator. The action of the ope"},"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":"1612.08304","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-25T23:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"26db73aa73289c25552954894d73c61bbba606e3e5fbea83e4bc9ae39b619592","abstract_canon_sha256":"6548c1f3e0376dd1edd0ca2badcb5089b7ad4645d327eb2880bfdca42781ff00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:24.678665Z","signature_b64":"38F0s/8s75qZznuvl4pAneCdDaxwYeo6LTfklyTKZWau17C0LnIAlSJLmnxRr9p5jQrRkIxqJvXJaH7Ak1/8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"175da5ce5fa40e2c8d623fea3cee2207fbb1130fa99ae10a1458d3e5284afd8f","last_reissued_at":"2026-05-18T00:15:24.678157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:24.678157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A generalized Hilbert operator acting on conformally invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniel Girela, Noel Merch\\'an","submitted_at":"2016-12-25T23:07:47Z","abstract_excerpt":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\\mathcal H_\\mu $ be the Hankel matrix $\\mathcal H_\\mu =(\\mu_{n, k})_{n,k\\ge 0}$ with entries $\\mu_{n, k}=\\mu_{n+k}$, where, for $n\\,=\\,0, 1, 2, \\dots $, $\\mu_n$ denotes the moment of orden $n$ of $\\mu $. This matrix induces formally the operator $$\\mathcal{H}_\\mu (f)(z)= \\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty} \\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\D $. This is a natural generalization of the classical Hilbert operator. The action of the ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08304","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":""},"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":"1612.08304","created_at":"2026-05-18T00:15:24.678237+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08304v2","created_at":"2026-05-18T00:15:24.678237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08304","created_at":"2026-05-18T00:15:24.678237+00:00"},{"alias_kind":"pith_short_12","alias_value":"C5O2LTS7UQHC","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C5O2LTS7UQHCZDLC","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C5O2LTS7","created_at":"2026-05-18T12:30:09.641336+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/C5O2LTS7UQHCZDLCH7VDZ3RCA7","json":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7.json","graph_json":"https://pith.science/api/pith-number/C5O2LTS7UQHCZDLCH7VDZ3RCA7/graph.json","events_json":"https://pith.science/api/pith-number/C5O2LTS7UQHCZDLCH7VDZ3RCA7/events.json","paper":"https://pith.science/paper/C5O2LTS7"},"agent_actions":{"view_html":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7","download_json":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7.json","view_paper":"https://pith.science/paper/C5O2LTS7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08304&json=true","fetch_graph":"https://pith.science/api/pith-number/C5O2LTS7UQHCZDLCH7VDZ3RCA7/graph.json","fetch_events":"https://pith.science/api/pith-number/C5O2LTS7UQHCZDLCH7VDZ3RCA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/action/storage_attestation","attest_author":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/action/author_attestation","sign_citation":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/action/citation_signature","submit_replication":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/action/replication_record"}},"created_at":"2026-05-18T00:15:24.678237+00:00","updated_at":"2026-05-18T00:15:24.678237+00:00"}