An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle

Detalhes bibliográficos
Autor(a) principal: Garza, Lino G.
Data de Publicação: 2021
Outros Autores: Marcellán, F., Ranga, A. Sri [UNESP]
Tipo de documento: Capítulo de livro
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/978-3-030-75425-9_8
http://hdl.handle.net/11449/229893
Resumo: This paper deals with sequences of monic polynomials { Φn(μk;z)}n≥0, k = 0, 1, orthogonal with respect to two nontrivial Borel measures μk, k = 0, 1, supported on the unit circle, satisfying (formula presented) n ≥ 3, where bn ≠ 0. We find examples of pairs of measures (μ0, μ1) for which this property holds. The analysis of polynomials orthogonal with respect to the Sobolev inner product associated with the pair of measures (μ0, μ1) is presented. Some properties concerning their connection coefficients are given.
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spelling An Extension of the Coherent Pair of Measures of the Second Kind on the Unit CircleCoherent pairs of measures of the second kindHessenberg matricesOrthogonal polynomials on the unit circleProbability measures on the unit circleSobolev inner products on the unit circleThis paper deals with sequences of monic polynomials { Φn(μk;z)}n≥0, k = 0, 1, orthogonal with respect to two nontrivial Borel measures μk, k = 0, 1, supported on the unit circle, satisfying (formula presented) n ≥ 3, where bn ≠ 0. We find examples of pairs of measures (μ0, μ1) for which this property holds. The analysis of polynomials orthogonal with respect to the Sobolev inner product associated with the pair of measures (μ0, μ1) is presented. Some properties concerning their connection coefficients are given.Universidad Carlos III de MadridDepartamento de Física y Matemáticas Universidad de MonterreyDepartamento de Matemáticas Universidad Carlos III de MadridDepartamento de Matemática IBILCE UNESP – Universidade Estadual PaulistaDepartamento de Matemática IBILCE UNESP – Universidade Estadual PaulistaUniversidad de MonterreyUniversidad Carlos III de MadridUniversidade Estadual Paulista (UNESP)Garza, Lino G.Marcellán, F.Ranga, A. Sri [UNESP]2022-04-29T08:36:23Z2022-04-29T08:36:23Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart113-142http://dx.doi.org/10.1007/978-3-030-75425-9_8Operator Theory: Advances and Applications, v. 285, p. 113-142.2296-48780255-0156http://hdl.handle.net/11449/22989310.1007/978-3-030-75425-9_82-s2.0-85119148227Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengOperator Theory: Advances and Applicationsinfo:eu-repo/semantics/openAccess2022-04-29T08:36:23Zoai:repositorio.unesp.br:11449/229893Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-29T08:36:23Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
title An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
spellingShingle An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
Garza, Lino G.
Coherent pairs of measures of the second kind
Hessenberg matrices
Orthogonal polynomials on the unit circle
Probability measures on the unit circle
Sobolev inner products on the unit circle
title_short An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
title_full An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
title_fullStr An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
title_full_unstemmed An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
title_sort An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle
author Garza, Lino G.
author_facet Garza, Lino G.
Marcellán, F.
Ranga, A. Sri [UNESP]
author_role author
author2 Marcellán, F.
Ranga, A. Sri [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Monterrey
Universidad Carlos III de Madrid
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Garza, Lino G.
Marcellán, F.
Ranga, A. Sri [UNESP]
dc.subject.por.fl_str_mv Coherent pairs of measures of the second kind
Hessenberg matrices
Orthogonal polynomials on the unit circle
Probability measures on the unit circle
Sobolev inner products on the unit circle
topic Coherent pairs of measures of the second kind
Hessenberg matrices
Orthogonal polynomials on the unit circle
Probability measures on the unit circle
Sobolev inner products on the unit circle
description This paper deals with sequences of monic polynomials { Φn(μk;z)}n≥0, k = 0, 1, orthogonal with respect to two nontrivial Borel measures μk, k = 0, 1, supported on the unit circle, satisfying (formula presented) n ≥ 3, where bn ≠ 0. We find examples of pairs of measures (μ0, μ1) for which this property holds. The analysis of polynomials orthogonal with respect to the Sobolev inner product associated with the pair of measures (μ0, μ1) is presented. Some properties concerning their connection coefficients are given.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2022-04-29T08:36:23Z
2022-04-29T08:36:23Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/978-3-030-75425-9_8
Operator Theory: Advances and Applications, v. 285, p. 113-142.
2296-4878
0255-0156
http://hdl.handle.net/11449/229893
10.1007/978-3-030-75425-9_8
2-s2.0-85119148227
url http://dx.doi.org/10.1007/978-3-030-75425-9_8
http://hdl.handle.net/11449/229893
identifier_str_mv Operator Theory: Advances and Applications, v. 285, p. 113-142.
2296-4878
0255-0156
10.1007/978-3-030-75425-9_8
2-s2.0-85119148227
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Operator Theory: Advances and Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 113-142
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_ 1803650174044602368

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