Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind

Detalhes bibliográficos
Autor(a) principal: Marcellán, F.
Data de Publicação: 2017
Outros Autores: Sri Ranga, A. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s00025-016-0631-y
http://hdl.handle.net/11449/173948
Resumo: We refer to a pair of non trivial probability measures (μ0, μ1) supported on the unit circle as a coherent pair of measures of the second kind on the unit circle if the corresponding sequences of monic orthogonal polynomials {Φn(μ0;z)}n≥0 and {Φn(μ1;z)}n≥0 satisfy 1nΦn′(μ0;z)=Φn-1(μ1;z)-χnΦn-2(μ1;z), n≥ 2. It turns out that there are more interesting examples of pairs of measures on the unit circle with this latter coherency property than in the case of the standard coherence. The main objective in this contribution is to determine such pairs of measures. The polynomials orthogonal with respect to the Sobolev inner products associated with coherent pairs of measures of the second kind are also studied.
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spelling Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kindcoherent pairs of measures of the second kindOrthogonal polynomials on the unit circleSobolev orthogonal polynomials on the unit circleWe refer to a pair of non trivial probability measures (μ0, μ1) supported on the unit circle as a coherent pair of measures of the second kind on the unit circle if the corresponding sequences of monic orthogonal polynomials {Φn(μ0;z)}n≥0 and {Φn(μ1;z)}n≥0 satisfy 1nΦn′(μ0;z)=Φn-1(μ1;z)-χnΦn-2(μ1;z), n≥ 2. It turns out that there are more interesting examples of pairs of measures on the unit circle with this latter coherency property than in the case of the standard coherence. The main objective in this contribution is to determine such pairs of measures. The polynomials orthogonal with respect to the Sobolev inner products associated with coherent pairs of measures of the second kind are also studied.Ministerio de Economía y CompetitividadInstituto de Ciencias Matemáticas (ICMAT) and Departamento de Matemáticas Universidad Carlos III de MadridDepartamento de Matemática Aplicada IBILCE UNESP-Universidade Estadual PaulistaDepartamento de Matemática Aplicada IBILCE UNESP-Universidade Estadual PaulistaMinisterio de Economía y Competitividad: MTM2012-C03-01Universidad Carlos III de MadridUniversidade Estadual Paulista (Unesp)Marcellán, F.Sri Ranga, A. [UNESP]2018-12-11T17:08:27Z2018-12-11T17:08:27Z2017-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1127-1149application/pdfhttp://dx.doi.org/10.1007/s00025-016-0631-yResults in Mathematics, v. 71, n. 3-4, p. 1127-1149, 2017.1420-90121422-6383http://hdl.handle.net/11449/17394810.1007/s00025-016-0631-y2-s2.0-850064568012-s2.0-85006456801.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengResults in Mathematics0,582info:eu-repo/semantics/openAccess2023-11-15T06:14:22Zoai:repositorio.unesp.br:11449/173948Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:45:23.226382Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
title Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
spellingShingle Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
Marcellán, F.
coherent pairs of measures of the second kind
Orthogonal polynomials on the unit circle
Sobolev orthogonal polynomials on the unit circle
title_short Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
title_full Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
title_fullStr Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
title_full_unstemmed Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
title_sort Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
author Marcellán, F.
author_facet Marcellán, F.
Sri Ranga, A. [UNESP]
author_role author
author2 Sri Ranga, A. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidad Carlos III de Madrid
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Marcellán, F.
Sri Ranga, A. [UNESP]
dc.subject.por.fl_str_mv coherent pairs of measures of the second kind
Orthogonal polynomials on the unit circle
Sobolev orthogonal polynomials on the unit circle
topic coherent pairs of measures of the second kind
Orthogonal polynomials on the unit circle
Sobolev orthogonal polynomials on the unit circle
description We refer to a pair of non trivial probability measures (μ0, μ1) supported on the unit circle as a coherent pair of measures of the second kind on the unit circle if the corresponding sequences of monic orthogonal polynomials {Φn(μ0;z)}n≥0 and {Φn(μ1;z)}n≥0 satisfy 1nΦn′(μ0;z)=Φn-1(μ1;z)-χnΦn-2(μ1;z), n≥ 2. It turns out that there are more interesting examples of pairs of measures on the unit circle with this latter coherency property than in the case of the standard coherence. The main objective in this contribution is to determine such pairs of measures. The polynomials orthogonal with respect to the Sobolev inner products associated with coherent pairs of measures of the second kind are also studied.
publishDate 2017
dc.date.none.fl_str_mv 2017-06-01
2018-12-11T17:08:27Z
2018-12-11T17:08:27Z
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/10.1007/s00025-016-0631-y
Results in Mathematics, v. 71, n. 3-4, p. 1127-1149, 2017.
1420-9012
1422-6383
http://hdl.handle.net/11449/173948
10.1007/s00025-016-0631-y
2-s2.0-85006456801
2-s2.0-85006456801.pdf
url http://dx.doi.org/10.1007/s00025-016-0631-y
http://hdl.handle.net/11449/173948
identifier_str_mv Results in Mathematics, v. 71, n. 3-4, p. 1127-1149, 2017.
1420-9012
1422-6383
10.1007/s00025-016-0631-y
2-s2.0-85006456801
2-s2.0-85006456801.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Results in Mathematics
0,582
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1127-1149
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_ 1808128853988605952

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