Sequentially ordered Sobolev inner product and Laguerre-Sobolev polynomials

Díaz González, Abel; Hernández, Juan; Pijeira Cabrera, Héctor Esteban

Publication:
Sequentially ordered Sobolev inner product and Laguerre-Sobolev polynomials

dc.affiliation.dpto	UC3M. Departamento de Matemáticas	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Análisis Aplicado	es
dc.contributor.author	Díaz González, Abel
dc.contributor.author	Hernández, Juan
dc.contributor.author	Pijeira Cabrera, Héctor Esteban
dc.date.accessioned	2023-05-04T10:33:59Z
dc.date.available	2023-05-04T10:33:59Z
dc.date.issued	2023-04-02
dc.description	This article belongs to the Special Issue Orthogonal Polynomials and Special Functions: Recent Trends and Their Applications.	en
dc.description.abstract	We study the sequence of polynomials {Sn}n≥0 that are orthogonal with respect to the general discrete Sobolev-type inner product ⟨f,g⟩s=∫f(x)g(x)dμ(x)+∑Nj=1∑djk=0λj,kf(k)(cj)g(k)(cj), where μ is a finite Borel measure whose support supp(μ) is an infinite set of the real line, λj,k≥0 , and the mass points ci , i=1,…,N are real values outside the interior of the convex hull of supp(μ) (ci∈R\Ch(supp(μ))∘) . Under some restriction of order in the discrete part of ⟨⋅,⋅⟩s , we prove that Sn has at least n−d∗ zeros on Ch(supp(μ))∘ , being d∗ the number of terms in the discrete part of ⟨⋅,⋅⟩s . Finally, we obtain the outer relative asymptotic for {Sn} in the case that the measure μ is the classical Laguerre measure, and for each mass point, only one order derivative appears in the discrete part of ⟨⋅,⋅⟩s.	en
dc.description.sponsorship	The research of J. Hernández was partially supported by the Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico (FONDOCYT), Dominican Republic, under grant 2020-2021-1D1-135.	en
dc.format.extent	15
dc.identifier.bibliographicCitation	Díaz-González, A., Hernández, J., & Pijeira-Cabrera, H. (2023). Sequentially Ordered Sobolev Inner Product and Laguerre–Sobolev Polynomials. Mathematics, 11(8), 1956.	en
dc.identifier.doi	https://doi.org/10.3390/math11081956
dc.identifier.issn	2227-7390
dc.identifier.publicationfirstpage	1
dc.identifier.publicationissue	8, 1956
dc.identifier.publicationlastpage	15
dc.identifier.publicationtitle	Mathematics	en
dc.identifier.publicationvolume	11
dc.identifier.uri	https://hdl.handle.net/10016/37247
dc.identifier.uxxi	AR/0000032766
dc.language.iso	eng
dc.publisher	MDPI
dc.rights	© 2023 by the authors.	en
dc.rights	Atribución 3.0 España	*
dc.rights.accessRights	open access	en
dc.rights.uri	http://creativecommons.org/licenses/by/3.0/es/	*
dc.subject.eciencia	Matemáticas	es
dc.subject.other	Orthogonal polynomials	en
dc.subject.other	Sobolev orthogonality	en
dc.subject.other	Zeros location	en
dc.subject.other	Asymptotic behavior	en
dc.title	Sequentially ordered Sobolev inner product and Laguerre-Sobolev polynomials	en
dc.type	research article	*
dc.type.hasVersion	VoR	*
dspace.entity.type	Publication