Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1090/proc12766 http://hdl.handle.net/11449/172434 |
Resumo: | The principal objective here is to look at some algebraic properties of the orthogonal polynomials Ψn (b,s,t) n with respect to the Sobolev inner product on the unit circle <f,g>S (b,s,t) = (1 − t) <f,g>μ(b) + t f(1) g(1) + s <f', g'>μ(b+1), where <f, g> μ(b) = τ(b)/2π∫2π 0 f(eiθ) g(eiθ) (eπ−θ)Im(b)(sin2(θ/2))Re(b)dθ. Here, Re(b) > −1/2, 0 ≤ t < 1, s > 0 and τ(b) is taken to be such that <1, 1>μ(b) = 1. We show that, for example, the monic Sobolev orthogonal polynomials Ψ(b,s,t) n satisfy the recurrence Ψ(b,s,t) n (z)−β(b,s,t) n Ψ(b,s,t) n−1 (z) = Φ(b,t) n (z), n ≥ 1, where Φ(b,t) n are the monic orthogonal polynomials with respect to the inner product <f, g>μ(b,t) = (1 − t) <f, g> μ(b) + t f(1) g(1). Some related bounds and asymptotic properties are also given. |
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Repositório Institucional da UNESP |
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Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circleOrthogonal polynomials on the unit circlePara-orthogonal polynomialsPositive chain sequencesSobolev orthogonal polynomials on the unit circleThe principal objective here is to look at some algebraic properties of the orthogonal polynomials Ψn (b,s,t) n with respect to the Sobolev inner product on the unit circle <f,g>S (b,s,t) = (1 − t) <f,g>μ(b) + t f(1) g(1) + s <f', g'>μ(b+1), where <f, g> μ(b) = τ(b)/2π∫2π 0 f(eiθ) g(eiθ) (eπ−θ)Im(b)(sin2(θ/2))Re(b)dθ. Here, Re(b) > −1/2, 0 ≤ t < 1, s > 0 and τ(b) is taken to be such that <1, 1>μ(b) = 1. We show that, for example, the monic Sobolev orthogonal polynomials Ψ(b,s,t) n satisfy the recurrence Ψ(b,s,t) n (z)−β(b,s,t) n Ψ(b,s,t) n−1 (z) = Φ(b,t) n (z), n ≥ 1, where Φ(b,t) n are the monic orthogonal polynomials with respect to the inner product <f, g>μ(b,t) = (1 − t) <f, g> μ(b) + t f(1) g(1). Some related bounds and asymptotic properties are also given.Departamento de Matemática Aplicada IBILCE UNESP - Universidade Estadual PaulistaDepartamento de Matemática Aplicada IBILCE UNESP - Universidade Estadual PaulistaUniversidade Estadual Paulista (Unesp)Ranga, A. Sri [UNESP]2018-12-11T17:00:20Z2018-12-11T17:00:20Z2016-03-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1129-1143application/pdfhttp://dx.doi.org/10.1090/proc12766Proceedings of the American Mathematical Society, v. 144, n. 3, p. 1129-1143, 2016.1088-68260002-9939http://hdl.handle.net/11449/17243410.1090/proc127662-s2.0-849545067962-s2.0-84954506796.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings of the American Mathematical Society1,1831,183info:eu-repo/semantics/openAccess2023-12-27T06:21:52Zoai:repositorio.unesp.br:11449/172434Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:27:17.205403Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle |
title |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle |
spellingShingle |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle Ranga, A. Sri [UNESP] Orthogonal polynomials on the unit circle Para-orthogonal polynomials Positive chain sequences Sobolev orthogonal polynomials on the unit circle |
title_short |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle |
title_full |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle |
title_fullStr |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle |
title_full_unstemmed |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle |
title_sort |
Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle |
author |
Ranga, A. Sri [UNESP] |
author_facet |
Ranga, A. Sri [UNESP] |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Ranga, A. Sri [UNESP] |
dc.subject.por.fl_str_mv |
Orthogonal polynomials on the unit circle Para-orthogonal polynomials Positive chain sequences Sobolev orthogonal polynomials on the unit circle |
topic |
Orthogonal polynomials on the unit circle Para-orthogonal polynomials Positive chain sequences Sobolev orthogonal polynomials on the unit circle |
description |
The principal objective here is to look at some algebraic properties of the orthogonal polynomials Ψn (b,s,t) n with respect to the Sobolev inner product on the unit circle <f,g>S (b,s,t) = (1 − t) <f,g>μ(b) + t f(1) g(1) + s <f', g'>μ(b+1), where <f, g> μ(b) = τ(b)/2π∫2π 0 f(eiθ) g(eiθ) (eπ−θ)Im(b)(sin2(θ/2))Re(b)dθ. Here, Re(b) > −1/2, 0 ≤ t < 1, s > 0 and τ(b) is taken to be such that <1, 1>μ(b) = 1. We show that, for example, the monic Sobolev orthogonal polynomials Ψ(b,s,t) n satisfy the recurrence Ψ(b,s,t) n (z)−β(b,s,t) n Ψ(b,s,t) n−1 (z) = Φ(b,t) n (z), n ≥ 1, where Φ(b,t) n are the monic orthogonal polynomials with respect to the inner product <f, g>μ(b,t) = (1 − t) <f, g> μ(b) + t f(1) g(1). Some related bounds and asymptotic properties are also given. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-03-01 2018-12-11T17:00:20Z 2018-12-11T17:00:20Z |
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/proc12766 Proceedings of the American Mathematical Society, v. 144, n. 3, p. 1129-1143, 2016. 1088-6826 0002-9939 http://hdl.handle.net/11449/172434 10.1090/proc12766 2-s2.0-84954506796 2-s2.0-84954506796.pdf |
url |
http://dx.doi.org/10.1090/proc12766 http://hdl.handle.net/11449/172434 |
identifier_str_mv |
Proceedings of the American Mathematical Society, v. 144, n. 3, p. 1129-1143, 2016. 1088-6826 0002-9939 10.1090/proc12766 2-s2.0-84954506796 2-s2.0-84954506796.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Proceedings of the American Mathematical Society 1,183 1,183 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1129-1143 application/pdf |
dc.source.none.fl_str_mv |
Scopus 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_ |
1808129321938714624 |