Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1111/sapm.12583 http://hdl.handle.net/11449/248861 |
Resumo: | The aim here is to consider the orthogonal polynomials (Formula presented.) with respect to an inner product of the type (Formula presented.), where (Formula presented.) and (Formula presented.) is a coherent pair of positive measures of the second kind on the real line (CPPM2K on the real line). Properties of (Formula presented.) and the connection formulas they satisfy with the orthogonal polynomials associated with the measure ν0 are analyzed. It is also shown that the zeros of (Formula presented.) are the eigenvalues of a matrix, which is a single line modification of the (Formula presented.) Jacobi matrix associated with the measure ν0. The paper also looks at a special example of a CPPM2K on the real line, where one of the measures is the Jacobi measure, and provides a much more detailed study of the properties of the orthogonal polynomials and the corresponding connection coefficients. In particular, the relation that these connection coefficients have with the Wilson polynomials is exposed. |
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Repositório Institucional da UNESP |
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Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi caseSobolev orthogonal polynomialsWilson polynomialszerosThe aim here is to consider the orthogonal polynomials (Formula presented.) with respect to an inner product of the type (Formula presented.), where (Formula presented.) and (Formula presented.) is a coherent pair of positive measures of the second kind on the real line (CPPM2K on the real line). Properties of (Formula presented.) and the connection formulas they satisfy with the orthogonal polynomials associated with the measure ν0 are analyzed. It is also shown that the zeros of (Formula presented.) are the eigenvalues of a matrix, which is a single line modification of the (Formula presented.) Jacobi matrix associated with the measure ν0. The paper also looks at a special example of a CPPM2K on the real line, where one of the measures is the Jacobi measure, and provides a much more detailed study of the properties of the orthogonal polynomials and the corresponding connection coefficients. In particular, the relation that these connection coefficients have with the Wilson polynomials is exposed.Departamento de Matemática IBILCE UNESP - Universidade Estadual Paulista, São PauloDepartamento de Matemáticas Universidad Carlos III de MadridDepartamento de Matemática IBILCE UNESP - Universidade Estadual Paulista, São PauloUniversidade Estadual Paulista (UNESP)Universidad Carlos III de MadridMarcato, G. A. [UNESP]Marcellán, F.Ranga, A. Sri [UNESP]Lun, Yen Chi [UNESP]2023-07-29T13:55:44Z2023-07-29T13:55:44Z2023-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1111/sapm.12583Studies in Applied Mathematics.1467-95900022-2526http://hdl.handle.net/11449/24886110.1111/sapm.125832-s2.0-85159916859Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengStudies in Applied Mathematicsinfo:eu-repo/semantics/openAccess2023-07-29T13:55:44Zoai:repositorio.unesp.br:11449/248861Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T13:55:44Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case |
title |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case |
spellingShingle |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case Marcato, G. A. [UNESP] Sobolev orthogonal polynomials Wilson polynomials zeros |
title_short |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case |
title_full |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case |
title_fullStr |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case |
title_full_unstemmed |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case |
title_sort |
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case |
author |
Marcato, G. A. [UNESP] |
author_facet |
Marcato, G. A. [UNESP] Marcellán, F. Ranga, A. Sri [UNESP] Lun, Yen Chi [UNESP] |
author_role |
author |
author2 |
Marcellán, F. Ranga, A. Sri [UNESP] Lun, Yen Chi [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Universidad Carlos III de Madrid |
dc.contributor.author.fl_str_mv |
Marcato, G. A. [UNESP] Marcellán, F. Ranga, A. Sri [UNESP] Lun, Yen Chi [UNESP] |
dc.subject.por.fl_str_mv |
Sobolev orthogonal polynomials Wilson polynomials zeros |
topic |
Sobolev orthogonal polynomials Wilson polynomials zeros |
description |
The aim here is to consider the orthogonal polynomials (Formula presented.) with respect to an inner product of the type (Formula presented.), where (Formula presented.) and (Formula presented.) is a coherent pair of positive measures of the second kind on the real line (CPPM2K on the real line). Properties of (Formula presented.) and the connection formulas they satisfy with the orthogonal polynomials associated with the measure ν0 are analyzed. It is also shown that the zeros of (Formula presented.) are the eigenvalues of a matrix, which is a single line modification of the (Formula presented.) Jacobi matrix associated with the measure ν0. The paper also looks at a special example of a CPPM2K on the real line, where one of the measures is the Jacobi measure, and provides a much more detailed study of the properties of the orthogonal polynomials and the corresponding connection coefficients. In particular, the relation that these connection coefficients have with the Wilson polynomials is exposed. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-29T13:55:44Z 2023-07-29T13:55:44Z 2023-01-01 |
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/10.1111/sapm.12583 Studies in Applied Mathematics. 1467-9590 0022-2526 http://hdl.handle.net/11449/248861 10.1111/sapm.12583 2-s2.0-85159916859 |
url |
http://dx.doi.org/10.1111/sapm.12583 http://hdl.handle.net/11449/248861 |
identifier_str_mv |
Studies in Applied Mathematics. 1467-9590 0022-2526 10.1111/sapm.12583 2-s2.0-85159916859 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Studies in Applied Mathematics |
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 |
|
_version_ |
1799965347278749696 |