{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4HJYUOWIGRRJGFC6FZOSKATTIL","short_pith_number":"pith:4HJYUOWI","schema_version":"1.0","canonical_sha256":"e1d38a3ac8346293145e2e5d25027342f4816c14b7b860830c6684848110f185","source":{"kind":"arxiv","id":"1403.6927","version":2},"attestation_state":"computed","paper":{"title":"On a Theorem by Bojanov and Naidenov applied to families of Gegenbauer-Sobolev polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dilcia P\\'erez, Vanessa G. Paschoa, Yamilet Quintana","submitted_at":"2014-03-27T06:43:55Z","abstract_excerpt":"Let $\\{Q^{(\\alpha)}_{n,\\lambda}\\}_{n\\geq 0}$ be the sequence of monic orthogonal polynomials with respect the Gegenbauer-Sobolev inner product $$\\langle f,g\\rangle_{S}:=\\int_{-1}^{1}f(x)g(x)(1-x^{2})^{\\alpha-\\frac{1}{2}}dx+\\lambda \\int_{-1}^{1}f'(x)g'(x)(1-x^{2})^{\\alpha-\\frac{1}{2}} dx,$$ where $\\alpha>-\\frac{1}{2}$ and $\\lambda\\geq 0$. In this paper we use a recent result due to B.D. Bojanov and N.\n  Naidenov \\cite{BN2010}, in order to study the maximization of a local extremum of the $k$th derivative $\\frac{d^k}{dx^k}Q^{(\\alpha)}_{n,\\lambda}$ in $[-M_{n,\\lambda}, M_{n,\\lambda}]$, where\n  $M"},"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":"1403.6927","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-27T06:43:55Z","cross_cats_sorted":[],"title_canon_sha256":"8a221f3fae7af69423de66f60a21dd56e3cfe17aeaed3aeb80eacc01d11d8180","abstract_canon_sha256":"b4eb642780ef3edb47a24372d18153765fe1d1dd335f0d3e966a5dba7ee6c599"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:20.191743Z","signature_b64":"JnKUWIwo09EgyNdqpSQgQlbfcu0AF6CB9QwaF4lr86t1RjTfn4qeKp3j/RK410VuADRZw1+LcA3bbI0lKA6NAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1d38a3ac8346293145e2e5d25027342f4816c14b7b860830c6684848110f185","last_reissued_at":"2026-05-18T02:55:20.191375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:20.191375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Theorem by Bojanov and Naidenov applied to families of Gegenbauer-Sobolev polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dilcia P\\'erez, Vanessa G. Paschoa, Yamilet Quintana","submitted_at":"2014-03-27T06:43:55Z","abstract_excerpt":"Let $\\{Q^{(\\alpha)}_{n,\\lambda}\\}_{n\\geq 0}$ be the sequence of monic orthogonal polynomials with respect the Gegenbauer-Sobolev inner product $$\\langle f,g\\rangle_{S}:=\\int_{-1}^{1}f(x)g(x)(1-x^{2})^{\\alpha-\\frac{1}{2}}dx+\\lambda \\int_{-1}^{1}f'(x)g'(x)(1-x^{2})^{\\alpha-\\frac{1}{2}} dx,$$ where $\\alpha>-\\frac{1}{2}$ and $\\lambda\\geq 0$. In this paper we use a recent result due to B.D. Bojanov and N.\n  Naidenov \\cite{BN2010}, in order to study the maximization of a local extremum of the $k$th derivative $\\frac{d^k}{dx^k}Q^{(\\alpha)}_{n,\\lambda}$ in $[-M_{n,\\lambda}, M_{n,\\lambda}]$, where\n  $M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6927","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":"1403.6927","created_at":"2026-05-18T02:55:20.191441+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.6927v2","created_at":"2026-05-18T02:55:20.191441+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6927","created_at":"2026-05-18T02:55:20.191441+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HJYUOWIGRRJ","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HJYUOWIGRRJGFC6","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HJYUOWI","created_at":"2026-05-18T12:28:14.216126+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/4HJYUOWIGRRJGFC6FZOSKATTIL","json":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL.json","graph_json":"https://pith.science/api/pith-number/4HJYUOWIGRRJGFC6FZOSKATTIL/graph.json","events_json":"https://pith.science/api/pith-number/4HJYUOWIGRRJGFC6FZOSKATTIL/events.json","paper":"https://pith.science/paper/4HJYUOWI"},"agent_actions":{"view_html":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL","download_json":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL.json","view_paper":"https://pith.science/paper/4HJYUOWI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.6927&json=true","fetch_graph":"https://pith.science/api/pith-number/4HJYUOWIGRRJGFC6FZOSKATTIL/graph.json","fetch_events":"https://pith.science/api/pith-number/4HJYUOWIGRRJGFC6FZOSKATTIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL/action/storage_attestation","attest_author":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL/action/author_attestation","sign_citation":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL/action/citation_signature","submit_replication":"https://pith.science/pith/4HJYUOWIGRRJGFC6FZOSKATTIL/action/replication_record"}},"created_at":"2026-05-18T02:55:20.191441+00:00","updated_at":"2026-05-18T02:55:20.191441+00:00"}