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Veronese","submitted_at":"2017-01-18T10:07:10Z","abstract_excerpt":"Given a nontrivial positive measure $\\mu$ on the unit circle, the associated Christoffel-Darboux kernels are $K_n(z, w;\\mu) = \\sum_{k=0}^{n}\\overline{\\varphi_{k}(w;\\mu)}\\,\\varphi_{k}(z;\\mu)$, $n \\geq 0$, where $\\varphi_{k}(\\cdot; \\mu)$ are the orthonormal polynomials with respect to the measure $\\mu$. Let the positive measure $\\nu$ on the unit circle be given by $d \\nu(z) = |G_{2m}(z)|\\, d \\mu(z)$, where $G_{2m}$ is a conjugate reciprocal polynomial of exact degree $2m$. We establish a determinantal formula expressing $\\{K_n(z,w;\\nu)\\}_{n \\geq 0}$ directly in terms of $\\{K_n(z,w;\\mu)\\}_{n \\geq"},"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":"1701.04995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-18T10:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"25967510ce684838a94c49f896e67003d4e5d152a0678e033557cfb347e87688","abstract_canon_sha256":"27bb3750d86bd2f6192897644597b0b7aeecba54a0d7450f19c67d5d0aa10ad9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:02.638512Z","signature_b64":"BEeFNwVAX1toGSO6h4XS80igwWjE1dUqinmMUyFQAwi/VsaRxk9QQJf67lWi2iD4xP2tf3qDaIoypWnFm2fGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a501045a9752dde7e1a4a85c3800ccfddff507523e0677ac9008189db5c4110","last_reissued_at":"2026-05-18T00:12:02.637947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:02.637947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Christoffel formula for kernel polynomials on the unit circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrei Mart\\'inez-Finkelshtein, A. Sri Ranga, Cleonice F. Bracciali, Daniel O. Veronese","submitted_at":"2017-01-18T10:07:10Z","abstract_excerpt":"Given a nontrivial positive measure $\\mu$ on the unit circle, the associated Christoffel-Darboux kernels are $K_n(z, w;\\mu) = \\sum_{k=0}^{n}\\overline{\\varphi_{k}(w;\\mu)}\\,\\varphi_{k}(z;\\mu)$, $n \\geq 0$, where $\\varphi_{k}(\\cdot; \\mu)$ are the orthonormal polynomials with respect to the measure $\\mu$. Let the positive measure $\\nu$ on the unit circle be given by $d \\nu(z) = |G_{2m}(z)|\\, d \\mu(z)$, where $G_{2m}$ is a conjugate reciprocal polynomial of exact degree $2m$. We establish a determinantal formula expressing $\\{K_n(z,w;\\nu)\\}_{n \\geq 0}$ directly in terms of $\\{K_n(z,w;\\mu)\\}_{n \\geq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04995","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":"1701.04995","created_at":"2026-05-18T00:12:02.638027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.04995v1","created_at":"2026-05-18T00:12:02.638027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04995","created_at":"2026-05-18T00:12:02.638027+00:00"},{"alias_kind":"pith_short_12","alias_value":"NJIBARNJOUW5","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NJIBARNJOUW547Q2","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NJIBARNJ","created_at":"2026-05-18T12:31:31.346846+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/NJIBARNJOUW547Q2JKC4HAAMZ7","json":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7.json","graph_json":"https://pith.science/api/pith-number/NJIBARNJOUW547Q2JKC4HAAMZ7/graph.json","events_json":"https://pith.science/api/pith-number/NJIBARNJOUW547Q2JKC4HAAMZ7/events.json","paper":"https://pith.science/paper/NJIBARNJ"},"agent_actions":{"view_html":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7","download_json":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7.json","view_paper":"https://pith.science/paper/NJIBARNJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.04995&json=true","fetch_graph":"https://pith.science/api/pith-number/NJIBARNJOUW547Q2JKC4HAAMZ7/graph.json","fetch_events":"https://pith.science/api/pith-number/NJIBARNJOUW547Q2JKC4HAAMZ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7/action/storage_attestation","attest_author":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7/action/author_attestation","sign_citation":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7/action/citation_signature","submit_replication":"https://pith.science/pith/NJIBARNJOUW547Q2JKC4HAAMZ7/action/replication_record"}},"created_at":"2026-05-18T00:12:02.638027+00:00","updated_at":"2026-05-18T00:12:02.638027+00:00"}