{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:YGCJLI7O6ORGWVLHZNIOVBBLVT","short_pith_number":"pith:YGCJLI7O","schema_version":"1.0","canonical_sha256":"c18495a3eef3a26b5567cb50ea842bace5ded1a885fadfce8ef233921473bf88","source":{"kind":"arxiv","id":"2411.16359","version":1},"attestation_state":"computed","paper":{"title":"Exact $L_2$ Bernstein-Markov inequalities for generalized weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Heping Wang, Jiansong Li, Jiaxin Geng, Yun Ling","submitted_at":"2024-11-25T13:11:36Z","abstract_excerpt":"In this paper, we obtain some exact $L_2$ Bernstein-Markov inequalities for generalized Hermite and Gegenbauer weight. More precisely, we determine the exact values of the extremal problem $$M_n^2(L_2(W_\\lambda),{\\rm D}):=\\sup_{0\\neq p\\in\\mathcal{P}_n}\\frac{\\int_I\\left|{\\rm D} p(x)\\right|^2W_\\lambda(x){\\rm d}x}{\\int_I| p(x)|^2W_\\lambda(x){\\rm d}x},\\ \\lambda>0,$$ where $\\mathcal{P}_n$ denotes the set of all algebraic polynomials of degree at most $n$, ${\\rm D}$ is the differential operator given by $${\\rm D}=\\Bigg\\{\\begin{aligned}&\\frac {\\rm d}{{\\rm d}x}\\ {\\rm or}\\ \\mathcal{D}_\\lambda, &&{\\rm i"},"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":"2411.16359","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-11-25T13:11:36Z","cross_cats_sorted":[],"title_canon_sha256":"3fff52c44fe0a359cd489c03216e590d6f9950b07f5b6929c30ae230890d1387","abstract_canon_sha256":"e5e08d7c2383900b965e44bd5df0d9d0299d93bd0a618ad3f3fb475b5b9de6d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:08.189004Z","signature_b64":"dYaaLBwW6hkjEERzsndTfTbNthMW+dc3aw8CGNdjnH2B13Zq0R8ET+VHfzdlherv+W4jzYfUAx6NVa/3EtZ2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c18495a3eef3a26b5567cb50ea842bace5ded1a885fadfce8ef233921473bf88","last_reissued_at":"2026-07-05T09:40:08.188595Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:08.188595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact $L_2$ Bernstein-Markov inequalities for generalized weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Heping Wang, Jiansong Li, Jiaxin Geng, Yun Ling","submitted_at":"2024-11-25T13:11:36Z","abstract_excerpt":"In this paper, we obtain some exact $L_2$ Bernstein-Markov inequalities for generalized Hermite and Gegenbauer weight. More precisely, we determine the exact values of the extremal problem $$M_n^2(L_2(W_\\lambda),{\\rm D}):=\\sup_{0\\neq p\\in\\mathcal{P}_n}\\frac{\\int_I\\left|{\\rm D} p(x)\\right|^2W_\\lambda(x){\\rm d}x}{\\int_I| p(x)|^2W_\\lambda(x){\\rm d}x},\\ \\lambda>0,$$ where $\\mathcal{P}_n$ denotes the set of all algebraic polynomials of degree at most $n$, ${\\rm D}$ is the differential operator given by $${\\rm D}=\\Bigg\\{\\begin{aligned}&\\frac {\\rm d}{{\\rm d}x}\\ {\\rm or}\\ \\mathcal{D}_\\lambda, &&{\\rm i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16359","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.16359/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.16359","created_at":"2026-07-05T09:40:08.188648+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.16359v1","created_at":"2026-07-05T09:40:08.188648+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16359","created_at":"2026-07-05T09:40:08.188648+00:00"},{"alias_kind":"pith_short_12","alias_value":"YGCJLI7O6ORG","created_at":"2026-07-05T09:40:08.188648+00:00"},{"alias_kind":"pith_short_16","alias_value":"YGCJLI7O6ORGWVLH","created_at":"2026-07-05T09:40:08.188648+00:00"},{"alias_kind":"pith_short_8","alias_value":"YGCJLI7O","created_at":"2026-07-05T09:40:08.188648+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/YGCJLI7O6ORGWVLHZNIOVBBLVT","json":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT.json","graph_json":"https://pith.science/api/pith-number/YGCJLI7O6ORGWVLHZNIOVBBLVT/graph.json","events_json":"https://pith.science/api/pith-number/YGCJLI7O6ORGWVLHZNIOVBBLVT/events.json","paper":"https://pith.science/paper/YGCJLI7O"},"agent_actions":{"view_html":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT","download_json":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT.json","view_paper":"https://pith.science/paper/YGCJLI7O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.16359&json=true","fetch_graph":"https://pith.science/api/pith-number/YGCJLI7O6ORGWVLHZNIOVBBLVT/graph.json","fetch_events":"https://pith.science/api/pith-number/YGCJLI7O6ORGWVLHZNIOVBBLVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT/action/storage_attestation","attest_author":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT/action/author_attestation","sign_citation":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT/action/citation_signature","submit_replication":"https://pith.science/pith/YGCJLI7O6ORGWVLHZNIOVBBLVT/action/replication_record"}},"created_at":"2026-07-05T09:40:08.188648+00:00","updated_at":"2026-07-05T09:40:08.188648+00:00"}