WKB Approximation and Krall-Type Orthogonal Polynomials

Detalhes bibliográficos
Autor(a) principal: Álvarez-Nodarse, R.
Data de Publicação: 1998
Outros Autores: Marcellán, F., Petronilho, J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/7743
https://doi.org/10.1023/A:1006006519197
Resumo: We give a unified approach to the Krall-type polynomials orthogonal withrespect to a positive measure consisting of an absolutely continuous one‘perturbed’ by the addition of one or more Dirac deltafunctions. Some examples studied by different authors are considered from aunique point of view. Also some properties of the Krall-type polynomials arestudied. The three-term recurrence relation is calculated explicitly, aswell as some asymptotic formulas. With special emphasis will be consideredthe second order differential equations that such polynomials satisfy. Theyallow us to obtain the central moments and the WKB approximation of thedistribution of zeros. Some examples coming from quadratic polynomialmappings and tridiagonal periodic matrices are also studied.
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spelling WKB Approximation and Krall-Type Orthogonal PolynomialsWe give a unified approach to the Krall-type polynomials orthogonal withrespect to a positive measure consisting of an absolutely continuous one‘perturbed’ by the addition of one or more Dirac deltafunctions. Some examples studied by different authors are considered from aunique point of view. Also some properties of the Krall-type polynomials arestudied. The three-term recurrence relation is calculated explicitly, aswell as some asymptotic formulas. With special emphasis will be consideredthe second order differential equations that such polynomials satisfy. Theyallow us to obtain the central moments and the WKB approximation of thedistribution of zeros. Some examples coming from quadratic polynomialmappings and tridiagonal periodic matrices are also studied.1998info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/7743http://hdl.handle.net/10316/7743https://doi.org/10.1023/A:1006006519197engActa Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications. 54:1 (1998) 27-58Álvarez-Nodarse, R.Marcellán, F.Petronilho, J.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2020-05-25T09:46:17Zoai:estudogeral.uc.pt:10316/7743Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:44.542311Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv WKB Approximation and Krall-Type Orthogonal Polynomials
title WKB Approximation and Krall-Type Orthogonal Polynomials
spellingShingle WKB Approximation and Krall-Type Orthogonal Polynomials
Álvarez-Nodarse, R.
title_short WKB Approximation and Krall-Type Orthogonal Polynomials
title_full WKB Approximation and Krall-Type Orthogonal Polynomials
title_fullStr WKB Approximation and Krall-Type Orthogonal Polynomials
title_full_unstemmed WKB Approximation and Krall-Type Orthogonal Polynomials
title_sort WKB Approximation and Krall-Type Orthogonal Polynomials
author Álvarez-Nodarse, R.
author_facet Álvarez-Nodarse, R.
Marcellán, F.
Petronilho, J.
author_role author
author2 Marcellán, F.
Petronilho, J.
author2_role author
author
dc.contributor.author.fl_str_mv Álvarez-Nodarse, R.
Marcellán, F.
Petronilho, J.
description We give a unified approach to the Krall-type polynomials orthogonal withrespect to a positive measure consisting of an absolutely continuous one‘perturbed’ by the addition of one or more Dirac deltafunctions. Some examples studied by different authors are considered from aunique point of view. Also some properties of the Krall-type polynomials arestudied. The three-term recurrence relation is calculated explicitly, aswell as some asymptotic formulas. With special emphasis will be consideredthe second order differential equations that such polynomials satisfy. Theyallow us to obtain the central moments and the WKB approximation of thedistribution of zeros. Some examples coming from quadratic polynomialmappings and tridiagonal periodic matrices are also studied.
publishDate 1998
dc.date.none.fl_str_mv 1998
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10316/7743
http://hdl.handle.net/10316/7743
https://doi.org/10.1023/A:1006006519197
url http://hdl.handle.net/10316/7743
https://doi.org/10.1023/A:1006006519197
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications. 54:1 (1998) 27-58
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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