Articulos FC INSMAT

Permanent URI for this collection

https://repositoriovip.uasd.edu.do/handle/123456789/100

Browse

Browsing Articulos FC INSMAT by Author "Juan Hernández"

Now showing 1 - 2 of 2
  • Item
    A look at generalized degenerate Bernoulli and Euler matrices
    (2023-06-16) Juan Hernández
    In this paper, we consider the generalized degenerate Bernoulli/Euler polynomial matrices and study some algebraic properties for them. In particular, we focus our attention on some matrix-inversion formulae involving these matrices. Furthermore, we provide analytic properties for the so-called generalized degenerate Pascal matrix of the first kind, and some factorizations for the generalized degenerate Euler polynomial matrix.
  • Item
    Sequentially ordered Sobolevinner product and Laguerre – Sobolev polynomials
    (2023-04-20) Juan Hernández
    We study the sequence of polynomials {𝑆𝑛}𝑛≥0{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=0 𝜆𝑗,𝑘𝑓(𝑘)(𝑐𝑗)𝑔(𝑘)(𝑐𝑗), ⟨𝑓, 𝑔⟩{𝑠} = ∫ 𝑓(𝑥)𝑔(𝑥)𝑑𝜇(𝑥) + ∑ 𝑗=1 𝑁 ∑ 𝑘=0 𝑑𝑗𝜆𝑗,𝑘𝑓(𝑘)(𝑐𝑗)𝑔(𝑘) (𝑐𝑗) where 𝜇𝜇 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)supp𝜇 (𝑐𝑖∈R\𝐂h(supp(𝜇))∘)𝑐𝑖∈𝑅\𝐶h(supp(𝜇))∘). Under some restriction of order in the discrete part of ⟨·,·⟩𝗌⟨·,·⟩𝑠, we prove that 𝑆𝑛𝑆𝑛 has at least 𝑛−𝑑∗𝑛−𝑑* zeros on 𝐂h(supp(𝜇))∘𝐶h(supp𝜇)∘, being 𝑑∗𝑑* the number of terms in the discrete part of ⟨·,·⟩𝗌⟨·,·⟩𝑠. Finally, we obtain the outer relative asymptotic for {𝑆𝑛}{𝑆𝑛} in the case that the measure 𝜇𝜇 is the classical Laguerre measure, and for each mass point, only one order derivative appears in the discrete part of ⟨·,·⟩𝗌⟨·,·⟩𝑠.