{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:INGUC42LQZ6QR5BOV43PQAI7NC","short_pith_number":"pith:INGUC42L","schema_version":"1.0","canonical_sha256":"434d41734b867d08f42eaf36f8011f68b91778867a301f6d98effa385dc087ff","source":{"kind":"arxiv","id":"1105.0660","version":1},"attestation_state":"computed","paper":{"title":"Pade interpolation by F-polynomials and transfinite diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dan Coman, Evgeny A. Poletsky","submitted_at":"2011-05-03T19:27:58Z","abstract_excerpt":"We define $F$-polynomials as linear combinations of dilations by some frequencies of an entire function $F$. In this paper we use Pade interpolation of holomorphic functions in the unit disk by $F$-polynomials to obtain explicitly approximating $F$-polynomials with sharp estimates on their coefficients. We show that when frequencies lie in a compact set $K\\subset\\mathbb C$ then optimal choices for the frequencies of interpolating polynomials are similar to Fekete points. Moreover, the minimal norms of the interpolating operators form a sequence whose rate of growth is determined by the transfi"},"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":"1105.0660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-05-03T19:27:58Z","cross_cats_sorted":[],"title_canon_sha256":"1eebc0b103ae84a2a35ee4cdd78933288ab6a12bc1c8ccce9d61261888f68cc3","abstract_canon_sha256":"45fb1df898c099ec2f4bf36b114de5ef3799923a3798e767788b2c69eb58df22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:10.942885Z","signature_b64":"ewStJ7GrWXDREG4VgHQ8PtXBQJRdIL/E1iS0SpdE9jRCV95hIOB45PcIs2fihJAWEmbvw7WQrgP3kMBXYXcsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"434d41734b867d08f42eaf36f8011f68b91778867a301f6d98effa385dc087ff","last_reissued_at":"2026-05-18T04:23:10.942457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:10.942457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pade interpolation by F-polynomials and transfinite diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dan Coman, Evgeny A. Poletsky","submitted_at":"2011-05-03T19:27:58Z","abstract_excerpt":"We define $F$-polynomials as linear combinations of dilations by some frequencies of an entire function $F$. In this paper we use Pade interpolation of holomorphic functions in the unit disk by $F$-polynomials to obtain explicitly approximating $F$-polynomials with sharp estimates on their coefficients. We show that when frequencies lie in a compact set $K\\subset\\mathbb C$ then optimal choices for the frequencies of interpolating polynomials are similar to Fekete points. Moreover, the minimal norms of the interpolating operators form a sequence whose rate of growth is determined by the transfi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0660","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":"1105.0660","created_at":"2026-05-18T04:23:10.942534+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.0660v1","created_at":"2026-05-18T04:23:10.942534+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0660","created_at":"2026-05-18T04:23:10.942534+00:00"},{"alias_kind":"pith_short_12","alias_value":"INGUC42LQZ6Q","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"INGUC42LQZ6QR5BO","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"INGUC42L","created_at":"2026-05-18T12:26:32.869790+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/INGUC42LQZ6QR5BOV43PQAI7NC","json":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC.json","graph_json":"https://pith.science/api/pith-number/INGUC42LQZ6QR5BOV43PQAI7NC/graph.json","events_json":"https://pith.science/api/pith-number/INGUC42LQZ6QR5BOV43PQAI7NC/events.json","paper":"https://pith.science/paper/INGUC42L"},"agent_actions":{"view_html":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC","download_json":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC.json","view_paper":"https://pith.science/paper/INGUC42L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.0660&json=true","fetch_graph":"https://pith.science/api/pith-number/INGUC42LQZ6QR5BOV43PQAI7NC/graph.json","fetch_events":"https://pith.science/api/pith-number/INGUC42LQZ6QR5BOV43PQAI7NC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC/action/storage_attestation","attest_author":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC/action/author_attestation","sign_citation":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC/action/citation_signature","submit_replication":"https://pith.science/pith/INGUC42LQZ6QR5BOV43PQAI7NC/action/replication_record"}},"created_at":"2026-05-18T04:23:10.942534+00:00","updated_at":"2026-05-18T04:23:10.942534+00:00"}