A discrete weighted Markov-Bernstein inequality for sequences and polynomials

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dc.contributor.authorDimitrov, Dimitar K. [UNESP]
dc.contributor.authorNikolov, Geno P.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionSofia Univ St Kliment Ohridski
dc.date.accessioned2021-06-25T12:21:23Z
dc.date.available2021-06-25T12:21:23Z
dc.date.issued2021-01-01
dc.description.abstractFor parameters c is an element of(0,1) and beta > 0, let l(2)(c ,beta) be the Hilbert space of real functions defined on N (i.e., real sequences), for which parallel to f parallel to(2)(c,beta) := Sigma(infinity)(k=0)(beta)(k)/k! c(k)[f(k)](2) < infinity. We study the best (i.e., the smallest possible) constant gamma(n)(c,beta) in the discrete Markov-Bernstein inequality parallel to Delta P parallel to(c,beta) <= gamma(n)(c ,beta) parallel to P parallel to(c,beta), P is an element of P-n, where P-n is the set of real algebraic polynomials of degree at most n and Delta f(x) := f(x+1)-f(x). We prove that (i) gamma(n)(c, 1) <= 1 + 1/root c for every n is an element of N and lim(n ->infinity) gamma(n)(c, 1) = 1+1/root c; (ii) For every fixed c is an element of(0,1), gamma(n)(c, beta) is a monotonically decreasing function of beta in (0,infinity); (iii) For every fixed c is an element of(0,1) and beta > 0, the best Markov-Bernstein constants gamma(n)(c,beta) are bounded uniformly with respect to n. A similar Markov-Bernstein inequality is proved for sequences, and a relation between the best Markov-Bernstein constants gamma(n)(c, beta) and the smallest eigenvalues of certain explicitly given Jacobi matrices is established. (c) 2020 Elsevier Inc. All rights reserved.en
dc.description.affiliationUniv Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.affiliationSofia Univ St Kliment Ohridski, Fac Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria
dc.description.affiliationUnespUniv Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipBulgarian National Research Fund
dc.description.sponsorshipIdCNPq: 306136/2017-1
dc.description.sponsorshipIdFAPESP: 2016/09906-0
dc.description.sponsorshipIdFAPESP: 2016/10357-1
dc.description.sponsorshipIdBulgarian National Research Fund: DN 02/14
dc.format.extent15
dc.identifierhttp://dx.doi.org/10.1016/j.jmaa.2020.124522
dc.identifier.citationJournal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 493, n. 1, 15 p., 2021.
dc.identifier.doi10.1016/j.jmaa.2020.124522
dc.identifier.issn0022-247X
dc.identifier.urihttp://hdl.handle.net/11449/209531
dc.identifier.wosWOS:000576820100029
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofJournal Of Mathematical Analysis And Applications
dc.sourceWeb of Science
dc.subjectMarkov-Bernstein inequality
dc.subjectDiscrete inequality
dc.subjectMeixner weight
dc.subjectMeixner polynomials
dc.subjectOrthogonal polynomial
dc.subjectChebyshev polynomial
dc.titleA discrete weighted Markov-Bernstein inequality for sequences and polynomialsen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderElsevier B.V.
unesp.author.orcid0000-0002-3078-2336[1]

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