Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval

Deaño Cabrera, Alfredo

Publication:
Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval

dc.affiliation.dpto	UC3M. Departamento de Matemáticas	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Análisis Aplicado	es
dc.contributor.author	Deaño Cabrera, Alfredo
dc.date.accessioned	2016-07-20T08:25:38Z
dc.date.available	2016-11-01T23:00:09Z
dc.date.issued	2014-10
dc.description.abstract	We consider polynomials pω n (x) that are orthogonal with respect to the oscillatory weight w(x) = eiωx on [−1, 1], where ω > 0 is a real parameter. A first analysis of pω n (x) for large values of ω was carried out in Asheim et al. (2014), in connection with complex Gaussian quadrature rules with uniform good properties in ω. In this contribution we study the existence, asymptotic behavior and asymptotic distribution of the roots of pω n (x) in the complex plane as n → ∞. The parameter ω grows with n linearly. The tools used are logarithmic potential theory and the S-property, together with the Riemann–Hilbert formulation and the Deift–Zhou steepest descent method.	en
dc.description.sponsorship	The author gratefully acknowledges financial support from projects FWO G.0617.10 and FWO G.0641.11, funded by FWO (Fonds Wetenschappelijk Onderzoek, Research Fund Flanders, Belgium), and projects MTM2012-34787 and MTM2012-36732-C03-01, from the Spanish Ministry of Economy and Competitivity. The author also thanks Daan Huybrechs and Pablo Rom´an for many stimulating and useful discussions on the topic and scope of this paper, and the two anonymous referees for comments, corrections and suggestions to improve its presentation.	en
dc.format.extent	32
dc.format.mimetype	application/pdf
dc.identifier.bibliographicCitation	Journal of Approximation Theory, October 2014, Vol.186, October 2014, pp. 33–63
dc.identifier.doi	10.1016/j.jat.2014.07.004
dc.identifier.issn	0021-9045
dc.identifier.publicationfirstpage	33
dc.identifier.publicationissue	Journal of Approximation Theory, 2014, v. 186, pp. 33-63.	en
dc.identifier.publicationlastpage	63
dc.identifier.publicationtitle	Journal of approximation theory	en
dc.identifier.publicationvolume	186
dc.identifier.uri	http://hdl.handle.net/10016/23386
dc.identifier.uxxi	AR/0000015689
dc.language.iso	eng
dc.publisher	Elsevier	en
dc.relation.projectID	Gobierno de España. MTM2012-34787	es
dc.relation.projectID	Gobierno de España. MTM2012-36732-C03-01	es
dc.relation.publisherversion	http://dx.doi.org/10.1016/j.jat.2014.07.004
dc.rights	© Elsevier 2014
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRights	open access
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.eciencia	Matemáticas	es
dc.subject.other	Orthogonal polynomials in the complex plane	en
dc.subject.other	Strong asymptotics	en
dc.subject.other	Zero distribution	en
dc.subject.other	Logarithmic potential theory	en
dc.subject.other	S-property	en
dc.subject.other	Steepest descent method	en
dc.subject.other	Riemann-Hilbert problem	en
dc.title	Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval	en
dc.type	research article	*
dc.type.hasVersion	AM	*
dspace.entity.type	Publication