HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES
| dc.contributor.author | Dimitrov, Dimitar K. [UNESP] | |
| dc.contributor.author | Gadjev, Ivan | |
| dc.contributor.author | Nikolov, Geno | |
| dc.contributor.author | Uluchev, Rumen | |
| dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
| dc.contributor.institution | Sofia Univ St Kliment Ohridski | |
| dc.date.accessioned | 2021-06-25T15:03:12Z | |
| dc.date.available | 2021-06-25T15:03:12Z | |
| dc.date.issued | 2021-06-01 | |
| dc.description.abstract | We study the behaviour of the smallest possible constants d(n), and c(n), in Hardy's inequalities Sigma(n)(k=1) (1/k Sigma(k)(j=1) a(j))(2) <= d(n) Sigma(n)(k=1) a(k)(2), (a(1), ..., a(n)) is an element of R-n and integral(infinity)(0) (1/x integral(x)(0) f(t) dt)(2) dx <= c(n) integral(infinity)(0) f(2)(x) dx, f is an element of H-n, for the finite dimensional spaces R-n and H-n := { f : f(o)(x) f(t)dt = e(-x/2) p(x) : p is an element of P-n,p(0) = 0}, where P-n is the set of real-valued algebraic polynomials of degree not exceeding n. The constants d(n) and c(n) are identified to be expressed in terms of the smallest zeros of the so-called continuous dual Hahn polynomials and the two-sided estimates for d(n) and c(n) of the form 4 - c/In n < d(n), c(n) < 4 - c/In-2 n, c > 0 are established. | en |
| dc.description.affiliation | Univ Estadual Paulista, Dept Matemat, IBILCE, 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, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil | |
| dc.description.sponsorship | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
| dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
| dc.description.sponsorship | Bulgarian National Research Fund | |
| dc.description.sponsorshipId | FAPESP: 2016/09906-0 | |
| dc.description.sponsorshipId | FAPESP: 2016/10357-1 | |
| dc.description.sponsorshipId | CNPq: 306136/2017-1 | |
| dc.description.sponsorshipId | Bulgarian National Research Fund: DN 02/14 | |
| dc.format.extent | 2515-2529 | |
| dc.identifier | http://dx.doi.org/10.1090/proc/15467 | |
| dc.identifier.citation | Proceedings Of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 149, n. 6, p. 2515-2529, 2021. | |
| dc.identifier.doi | 10.1090/proc/15467 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.uri | http://hdl.handle.net/11449/210267 | |
| dc.identifier.wos | WOS:000643563200022 | |
| dc.language.iso | eng | |
| dc.publisher | Amer Mathematical Soc | |
| dc.relation.ispartof | Proceedings Of The American Mathematical Society | |
| dc.source | Web of Science | |
| dc.title | HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES | en |
| dc.type | Artigo | |
| dcterms.rightsHolder | Amer Mathematical Soc | |
| unesp.author.orcid | 0000-0002-3078-2336[1] |