Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions

Autores
Deaño, Alfredo; Kuijlaars, Arno B. J.; Román, Pablo Manuel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider polynomials Pn orthogonal with respect to the weight Jν on [0,∞), where Jν is the Bessel function of order ν. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals. They observed that the zeros of Pn are complex and accumulate as n→∞ near the vertical line Rez=νπ2. We prove this fact for the case 0≤ν≤1/2 from strong asymptotic formulas that we derive for the polynomials Pn in the complex plane. Our main tool is the Riemann–Hilbert problem for orthogonal polynomials, suitably modified to cover the present situation, and the Deift–Zhou steepest descent method. A major part of the work is devoted to the construction of a local parametrix at the origin, for which we give an existence proof that only works for ν≤1/2.
Fil: Deaño, Alfredo. Universidad Carlos III de Madrid. Instituto de Salud; España
Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; Bélgica
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
ASYMPTOTIC REPRESENTATIONS IN THE COMPLEX DOMAIN
BESSEL FUNCTIONS
LIMITING ZERO DISTRIBUTION
ORTHOGONAL POLYNOMIALS
RIEMANN–HILBERT PROBLEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/58328
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel FunctionsDeaño, AlfredoKuijlaars, Arno B. J.Román, Pablo ManuelASYMPTOTIC REPRESENTATIONS IN THE COMPLEX DOMAINBESSEL FUNCTIONSLIMITING ZERO DISTRIBUTIONORTHOGONAL POLYNOMIALSRIEMANN–HILBERT PROBLEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider polynomials Pn orthogonal with respect to the weight Jν on [0,∞), where Jν is the Bessel function of order ν. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals. They observed that the zeros of Pn are complex and accumulate as n→∞ near the vertical line Rez=νπ2. We prove this fact for the case 0≤ν≤1/2 from strong asymptotic formulas that we derive for the polynomials Pn in the complex plane. Our main tool is the Riemann–Hilbert problem for orthogonal polynomials, suitably modified to cover the present situation, and the Deift–Zhou steepest descent method. A major part of the work is devoted to the construction of a local parametrix at the origin, for which we give an existence proof that only works for ν≤1/2.Fil: Deaño, Alfredo. Universidad Carlos III de Madrid. Instituto de Salud; EspañaFil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; BélgicaFil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaSpringer2016-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/58328Deaño, Alfredo; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions; Springer; Constructive Approximation; 43; 1; 2-2016; 153-1960176-4276CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00365-015-9300-8info:eu-repo/semantics/altIdentifier/doi/10.1007/s00365-015-9300-8info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:25:46Zoai:ri.conicet.gov.ar:11336/58328instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:25:46.356CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
title Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
spellingShingle Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
Deaño, Alfredo
ASYMPTOTIC REPRESENTATIONS IN THE COMPLEX DOMAIN
BESSEL FUNCTIONS
LIMITING ZERO DISTRIBUTION
ORTHOGONAL POLYNOMIALS
RIEMANN–HILBERT PROBLEMS
title_short Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
title_full Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
title_fullStr Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
title_full_unstemmed Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
title_sort Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
dc.creator.none.fl_str_mv Deaño, Alfredo
Kuijlaars, Arno B. J.
Román, Pablo Manuel
author Deaño, Alfredo
author_facet Deaño, Alfredo
Kuijlaars, Arno B. J.
Román, Pablo Manuel
author_role author
author2 Kuijlaars, Arno B. J.
Román, Pablo Manuel
author2_role author
author
dc.subject.none.fl_str_mv ASYMPTOTIC REPRESENTATIONS IN THE COMPLEX DOMAIN
BESSEL FUNCTIONS
LIMITING ZERO DISTRIBUTION
ORTHOGONAL POLYNOMIALS
RIEMANN–HILBERT PROBLEMS
topic ASYMPTOTIC REPRESENTATIONS IN THE COMPLEX DOMAIN
BESSEL FUNCTIONS
LIMITING ZERO DISTRIBUTION
ORTHOGONAL POLYNOMIALS
RIEMANN–HILBERT PROBLEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider polynomials Pn orthogonal with respect to the weight Jν on [0,∞), where Jν is the Bessel function of order ν. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals. They observed that the zeros of Pn are complex and accumulate as n→∞ near the vertical line Rez=νπ2. We prove this fact for the case 0≤ν≤1/2 from strong asymptotic formulas that we derive for the polynomials Pn in the complex plane. Our main tool is the Riemann–Hilbert problem for orthogonal polynomials, suitably modified to cover the present situation, and the Deift–Zhou steepest descent method. A major part of the work is devoted to the construction of a local parametrix at the origin, for which we give an existence proof that only works for ν≤1/2.
Fil: Deaño, Alfredo. Universidad Carlos III de Madrid. Instituto de Salud; España
Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; Bélgica
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We consider polynomials Pn orthogonal with respect to the weight Jν on [0,∞), where Jν is the Bessel function of order ν. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals. They observed that the zeros of Pn are complex and accumulate as n→∞ near the vertical line Rez=νπ2. We prove this fact for the case 0≤ν≤1/2 from strong asymptotic formulas that we derive for the polynomials Pn in the complex plane. Our main tool is the Riemann–Hilbert problem for orthogonal polynomials, suitably modified to cover the present situation, and the Deift–Zhou steepest descent method. A major part of the work is devoted to the construction of a local parametrix at the origin, for which we give an existence proof that only works for ν≤1/2.
publishDate 2016
dc.date.none.fl_str_mv 2016-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/58328
Deaño, Alfredo; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions; Springer; Constructive Approximation; 43; 1; 2-2016; 153-196
0176-4276
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58328
identifier_str_mv Deaño, Alfredo; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions; Springer; Constructive Approximation; 43; 1; 2-2016; 153-196
0176-4276
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00365-015-9300-8
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00365-015-9300-8
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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