{"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"}