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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/58328
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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 Técnicas2025-09-29T10:28:41Zoai: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:34982025-09-29 10:28:41.659CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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