RT Journal Article
T1 Sequentially ordered Sobolev inner product and Laguerre-Sobolev polynomials
A1 Díaz González, Abel
A1 Hernández, Juan
A1 Pijeira Cabrera, Héctor Esteban
AB 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.
PB MDPI
SN 2227-7390
YR 2023
FD 2023-04-02
LK https://hdl.handle.net/10016/37247
UL https://hdl.handle.net/10016/37247
LA eng
NO This article belongs to the Special Issue Orthogonal Polynomials and Special Functions: Recent Trends and Their Applications.
NO 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.
DS e-Archivo
RD 17 jul. 2024