A discrete weighted Markov-Bernstein inequality for sequences and polynomials
dc.contributor.author | Dimitrov, Dimitar K. [UNESP] | |
dc.contributor.author | Nikolov, Geno P. | |
dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
dc.contributor.institution | Sofia Univ St Kliment Ohridski | |
dc.date.accessioned | 2021-06-25T12:21:23Z | |
dc.date.available | 2021-06-25T12:21:23Z | |
dc.date.issued | 2021-01-01 | |
dc.description.abstract | For 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.affiliation | Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil | |
dc.description.affiliation | Sofia Univ St Kliment Ohridski, Fac Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria | |
dc.description.affiliationUnesp | Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil | |
dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
dc.description.sponsorship | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
dc.description.sponsorship | Bulgarian National Research Fund | |
dc.description.sponsorshipId | CNPq: 306136/2017-1 | |
dc.description.sponsorshipId | FAPESP: 2016/09906-0 | |
dc.description.sponsorshipId | FAPESP: 2016/10357-1 | |
dc.description.sponsorshipId | Bulgarian National Research Fund: DN 02/14 | |
dc.format.extent | 15 | |
dc.identifier | http://dx.doi.org/10.1016/j.jmaa.2020.124522 | |
dc.identifier.citation | Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 493, n. 1, 15 p., 2021. | |
dc.identifier.doi | 10.1016/j.jmaa.2020.124522 | |
dc.identifier.issn | 0022-247X | |
dc.identifier.uri | http://hdl.handle.net/11449/209531 | |
dc.identifier.wos | WOS:000576820100029 | |
dc.language.iso | eng | |
dc.publisher | Elsevier B.V. | |
dc.relation.ispartof | Journal Of Mathematical Analysis And Applications | |
dc.source | Web of Science | |
dc.subject | Markov-Bernstein inequality | |
dc.subject | Discrete inequality | |
dc.subject | Meixner weight | |
dc.subject | Meixner polynomials | |
dc.subject | Orthogonal polynomial | |
dc.subject | Chebyshev polynomial | |
dc.title | A discrete weighted Markov-Bernstein inequality for sequences and polynomials | en |
dc.type | Artigo | |
dcterms.license | http://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy | |
dcterms.rightsHolder | Elsevier B.V. | |
unesp.author.orcid | 0000-0002-3078-2336[1] |