{"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"}