A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros

Detalhes bibliográficos
Autor(a) principal: Bracciali, Cleonice F. [UNESP]
Data de Publicação: 2021
Outros Autores: da Silva, Jéssica V. [UNESP], Sri Ranga, A. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.jat.2021.105604
http://hdl.handle.net/11449/228998
Resumo: This paper deals with orthogonal polynomials and associated connection coefficients with respect to a class of Sobolev inner products on the unit circle. Under certain conditions on the parameters in the inner product it is shown that the connection coefficients are related to a subfamily of the continuous dual Hahn polynomials. Properties regarding bounds and asymptotics are also established with respect to these parameters. Criteria for knowing when the zeros of the (Sobolev) orthogonal polynomials and also the zeros of their derivatives stay within the unit disk have also been addressed. By numerical experiments some further information on the parameters is also found so that the zeros remain within the unit disk.
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spelling A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zerosCircular Jacobi polynomialsContinuous dual Hahn polynomialsSobolev orthogonal polynomials on the unit circleThis paper deals with orthogonal polynomials and associated connection coefficients with respect to a class of Sobolev inner products on the unit circle. Under certain conditions on the parameters in the inner product it is shown that the connection coefficients are related to a subfamily of the continuous dual Hahn polynomials. Properties regarding bounds and asymptotics are also established with respect to these parameters. Criteria for knowing when the zeros of the (Sobolev) orthogonal polynomials and also the zeros of their derivatives stay within the unit disk have also been addressed. By numerical experiments some further information on the parameters is also found so that the zeros remain within the unit disk.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Departamento de Matemática IBILCE UNESP-Universidade Estadual PaulistaDepartamento de Matemática IBILCE UNESP-Universidade Estadual PaulistaFAPESP: 2016/09906-0FAPESP: 2020/14244-2CNPq: 304087/2018-1Universidade Estadual Paulista (UNESP)Bracciali, Cleonice F. [UNESP]da Silva, Jéssica V. [UNESP]Sri Ranga, A. [UNESP]2022-04-29T08:29:43Z2022-04-29T08:29:43Z2021-08-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jat.2021.105604Journal of Approximation Theory, v. 268.1096-04300021-9045http://hdl.handle.net/11449/22899810.1016/j.jat.2021.1056042-s2.0-85108259358Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Approximation Theoryinfo:eu-repo/semantics/openAccess2022-04-29T08:29:44Zoai:repositorio.unesp.br:11449/228998Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-06T00:03:41.327639Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
title A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
spellingShingle A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
Bracciali, Cleonice F. [UNESP]
Circular Jacobi polynomials
Continuous dual Hahn polynomials
Sobolev orthogonal polynomials on the unit circle
title_short A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
title_full A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
title_fullStr A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
title_full_unstemmed A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
title_sort A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
author Bracciali, Cleonice F. [UNESP]
author_facet Bracciali, Cleonice F. [UNESP]
da Silva, Jéssica V. [UNESP]
Sri Ranga, A. [UNESP]
author_role author
author2 da Silva, Jéssica V. [UNESP]
Sri Ranga, A. [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Bracciali, Cleonice F. [UNESP]
da Silva, Jéssica V. [UNESP]
Sri Ranga, A. [UNESP]
dc.subject.por.fl_str_mv Circular Jacobi polynomials
Continuous dual Hahn polynomials
Sobolev orthogonal polynomials on the unit circle
topic Circular Jacobi polynomials
Continuous dual Hahn polynomials
Sobolev orthogonal polynomials on the unit circle
description This paper deals with orthogonal polynomials and associated connection coefficients with respect to a class of Sobolev inner products on the unit circle. Under certain conditions on the parameters in the inner product it is shown that the connection coefficients are related to a subfamily of the continuous dual Hahn polynomials. Properties regarding bounds and asymptotics are also established with respect to these parameters. Criteria for knowing when the zeros of the (Sobolev) orthogonal polynomials and also the zeros of their derivatives stay within the unit disk have also been addressed. By numerical experiments some further information on the parameters is also found so that the zeros remain within the unit disk.
publishDate 2021
dc.date.none.fl_str_mv 2021-08-01
2022-04-29T08:29:43Z
2022-04-29T08:29:43Z
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/10.1016/j.jat.2021.105604
Journal of Approximation Theory, v. 268.
1096-0430
0021-9045
http://hdl.handle.net/11449/228998
10.1016/j.jat.2021.105604
2-s2.0-85108259358
url http://dx.doi.org/10.1016/j.jat.2021.105604
http://hdl.handle.net/11449/228998
identifier_str_mv Journal of Approximation Theory, v. 268.
1096-0430
0021-9045
10.1016/j.jat.2021.105604
2-s2.0-85108259358
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Approximation Theory
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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
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