Landau and Kolmogoroff type polynomial inequalities
Autor(a) principal: | |
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Data de Publicação: | 1999 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1155/S1025583499000430 http://hdl.handle.net/11449/21719 |
Resumo: | Let 0<j<m less than or equal to n be integers. Denote by parallel to . parallel to the norm parallel to f parallel to(2) = integral(-infinity)(infinity) f(2)(x) exp(-x(2)) dx. For various positive values of A and B we establish Kolmogoroff type inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained. |
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Landau and Kolmogoroff type polynomial inequalitiesLandau and Kolmogoroff type inequalitiesMarkov's inequalityhermite polynomialsextremal polynomialsRayleigh-Ritz theoremLet 0<j<m less than or equal to n be integers. Denote by parallel to . parallel to the norm parallel to f parallel to(2) = integral(-infinity)(infinity) f(2)(x) exp(-x(2)) dx. For various positive values of A and B we establish Kolmogoroff type inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained.Univ Estadual Paulista, Dept Ciências Comp & Estatist, IBILCE, BR-15054000 Sao Jose do Rio Preto, SP, BrazilUniv Estadual Paulista, Dept Ciências Comp & Estatist, IBILCE, BR-15054000 Sao Jose do Rio Preto, SP, BrazilGordon Breach Sci Publ LtdUniversidade Estadual Paulista (Unesp)Alves, CRRDimitrov, D. K.2014-05-20T14:01:33Z2014-05-20T14:01:33Z1999-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article327-338application/pdfhttp://dx.doi.org/10.1155/S1025583499000430Journal of Inequalities and Applications. Reading: Gordon Breach Sci Publ Ltd, v. 4, n. 4, p. 327-338, 1999.1025-5834http://hdl.handle.net/11449/2171910.1155/S1025583499000430WOS:000083720600004WOS000083720600004.pdf1681267716971253Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Inequalities and Applications0,546info:eu-repo/semantics/openAccess2023-12-23T06:17:33Zoai:repositorio.unesp.br:11449/21719Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:05:15.209189Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Landau and Kolmogoroff type polynomial inequalities |
title |
Landau and Kolmogoroff type polynomial inequalities |
spellingShingle |
Landau and Kolmogoroff type polynomial inequalities Alves, CRR Landau and Kolmogoroff type inequalities Markov's inequality hermite polynomials extremal polynomials Rayleigh-Ritz theorem |
title_short |
Landau and Kolmogoroff type polynomial inequalities |
title_full |
Landau and Kolmogoroff type polynomial inequalities |
title_fullStr |
Landau and Kolmogoroff type polynomial inequalities |
title_full_unstemmed |
Landau and Kolmogoroff type polynomial inequalities |
title_sort |
Landau and Kolmogoroff type polynomial inequalities |
author |
Alves, CRR |
author_facet |
Alves, CRR Dimitrov, D. K. |
author_role |
author |
author2 |
Dimitrov, D. K. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Alves, CRR Dimitrov, D. K. |
dc.subject.por.fl_str_mv |
Landau and Kolmogoroff type inequalities Markov's inequality hermite polynomials extremal polynomials Rayleigh-Ritz theorem |
topic |
Landau and Kolmogoroff type inequalities Markov's inequality hermite polynomials extremal polynomials Rayleigh-Ritz theorem |
description |
Let 0<j<m less than or equal to n be integers. Denote by parallel to . parallel to the norm parallel to f parallel to(2) = integral(-infinity)(infinity) f(2)(x) exp(-x(2)) dx. For various positive values of A and B we establish Kolmogoroff type inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained. |
publishDate |
1999 |
dc.date.none.fl_str_mv |
1999-01-01 2014-05-20T14:01:33Z 2014-05-20T14:01:33Z |
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/10.1155/S1025583499000430 Journal of Inequalities and Applications. Reading: Gordon Breach Sci Publ Ltd, v. 4, n. 4, p. 327-338, 1999. 1025-5834 http://hdl.handle.net/11449/21719 10.1155/S1025583499000430 WOS:000083720600004 WOS000083720600004.pdf 1681267716971253 |
url |
http://dx.doi.org/10.1155/S1025583499000430 http://hdl.handle.net/11449/21719 |
identifier_str_mv |
Journal of Inequalities and Applications. Reading: Gordon Breach Sci Publ Ltd, v. 4, n. 4, p. 327-338, 1999. 1025-5834 10.1155/S1025583499000430 WOS:000083720600004 WOS000083720600004.pdf 1681267716971253 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Inequalities and Applications 0,546 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
327-338 application/pdf |
dc.publisher.none.fl_str_mv |
Gordon Breach Sci Publ Ltd |
publisher.none.fl_str_mv |
Gordon Breach Sci Publ Ltd |
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 |
|
_version_ |
1808129282419982336 |