HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1090/proc/15467 http://hdl.handle.net/11449/210267 |
Resumo: | 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. |
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HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACESWe 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.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Bulgarian National Research FundUniv Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilSofia Univ St Kliment Ohridski, Fac Math & Informat, 5 James Bourchier Blvd, Sofia 1164, BulgariaUniv Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilFAPESP: 2016/09906-0FAPESP: 2016/10357-1CNPq: 306136/2017-1Bulgarian National Research Fund: DN 02/14Amer Mathematical SocUniversidade Estadual Paulista (Unesp)Sofia Univ St Kliment OhridskiDimitrov, Dimitar K. [UNESP]Gadjev, IvanNikolov, GenoUluchev, Rumen2021-06-25T15:03:12Z2021-06-25T15:03:12Z2021-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2515-2529http://dx.doi.org/10.1090/proc/15467Proceedings Of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 149, n. 6, p. 2515-2529, 2021.0002-9939http://hdl.handle.net/11449/21026710.1090/proc/15467WOS:000643563200022Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings Of The American Mathematical Societyinfo:eu-repo/semantics/openAccess2021-10-23T20:17:26Zoai:repositorio.unesp.br:11449/210267Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:53:14.926256Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES |
title |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES |
spellingShingle |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES Dimitrov, Dimitar K. [UNESP] |
title_short |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES |
title_full |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES |
title_fullStr |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES |
title_full_unstemmed |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES |
title_sort |
HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES |
author |
Dimitrov, Dimitar K. [UNESP] |
author_facet |
Dimitrov, Dimitar K. [UNESP] Gadjev, Ivan Nikolov, Geno Uluchev, Rumen |
author_role |
author |
author2 |
Gadjev, Ivan Nikolov, Geno Uluchev, Rumen |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Sofia Univ St Kliment Ohridski |
dc.contributor.author.fl_str_mv |
Dimitrov, Dimitar K. [UNESP] Gadjev, Ivan Nikolov, Geno Uluchev, Rumen |
description |
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. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T15:03:12Z 2021-06-25T15:03:12Z 2021-06-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1090/proc/15467 Proceedings Of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 149, n. 6, p. 2515-2529, 2021. 0002-9939 http://hdl.handle.net/11449/210267 10.1090/proc/15467 WOS:000643563200022 |
url |
http://dx.doi.org/10.1090/proc/15467 http://hdl.handle.net/11449/210267 |
identifier_str_mv |
Proceedings Of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 149, n. 6, p. 2515-2529, 2021. 0002-9939 10.1090/proc/15467 WOS:000643563200022 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Proceedings Of The American Mathematical Society |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
2515-2529 |
dc.publisher.none.fl_str_mv |
Amer Mathematical Soc |
publisher.none.fl_str_mv |
Amer Mathematical Soc |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
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1808128995617669120 |