Díaz González, AbelHernández, JuanPijeira Cabrera, Héctor Esteban2023-05-042023-05-042023-04-02Díaz-González, A., Hernández, J., & Pijeira-Cabrera, H. (2023). Sequentially Ordered Sobolev Inner Product and Laguerre–Sobolev Polynomials. Mathematics, 11(8), 1956.2227-7390https://hdl.handle.net/10016/37247This article belongs to the Special Issue Orthogonal Polynomials and Special Functions: Recent Trends and Their Applications.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.15eng© 2023 by the authors.Atribución 3.0 EspañaOrthogonal polynomialsSobolev orthogonalityZeros locationAsymptotic behaviorresearch articleMatemáticashttps://doi.org/10.3390/math11081956open access18, 195615Mathematics11AR/0000032766