30 citations · 41 across the 9 of their papers we have counts for
11 papers
A class of Truncated Freud polynomials
Juan Carlos García-Ardila, Francisco Marcellán, Misael E. Marriaga
Consider the following truncated Freud linear functional depending on a parameter , The…
Generalized Gauss-Rys orthogonal polynomials
Juan C. García-Ardila, Francisco Marcellán
Let be the sequence of monic orthogonal polynomials with respect to the symmetric linear functional defined by $$\langle\mathbf{s},p\rangle=\i…
A note on Laguerre truncated polynomials and quadrature formula
Juan C. García-Ardila, Francisco Marcellán
In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function supported on an interval , $…
Uvarov Perturbations for Matrix Orthogonal Polynomials
Gerardo Ariznabarreta, Juan C. García-Ardila, Manuel Mañas +1
Additive perturbations, specifically, matrix Uvarov transformations for matrix orthogonal polynomials, are under consideration. Christoffel-Uvarov formulas are deduced for the pert…
Symmetrization process and truncated orthogonal polynomials
Diego Dominici, Juan C. García-Ardila, Francisco Marcellán
We define the family of truncated Laguerre polynomials , orthogonal with respect to the linear functional defined by $$\langle{\ell,p\rangle}=\int_{0}^zp(x)x^αe^{-…
Associated orthogonal polynomials of the first kind and Darboux transformations
Juan C. García-Ardila, Francisco Marcellán, Paul H. Villamil-Hernández
Let $\un,$ be a quasi-definite linear functional defined on the space of polynomials For such a functional we can define a sequence of monic orthogonal polynomials (S…
Matrix biorthogonal polynomials, associated polynomials and functions of the second kind
Amilcar Branquinho, Juan Carlos García-Ardila, Francisco Marcellán
In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the -th associated matrix polynomials and the second kind matr…
Ratio asymptotic for bi-orthogonal matrix polynomials with unbounded recurrence coefficients
Amilcar Branquinho, Juan Carlos García-Ardila, Francisco Marcellán
In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for…
Transformation theory and Christoffel formulas for matrix biorthogonal polynomials on the real line
Carlos Álvarez-Fernández, Gerardo Ariznabarreta, Juan C. García-Ardila +2
In this paper transformations for matrix orthogonal polynomials in the real line are studied. The orthogonality is understood in a broad sense, and is given in terms of a nondegene…
Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy
Carlos Álvarez-Fernández, Gerardo Ariznabarreta, Juan Carlos García-Ardila +2
Given a matrix polynomial , matrix bi-orthogonal polynomials with respect to the sesquilinear form $\langle P(x),Q(x)\rangle_W=\int P(x) W(x)\operatorname{d}μ(x)(Q(x))^{\top}…
Multiple Geronimus transformations
Maxim Derevyagin, Juan Carlos García-Ardila, Francisco Marcellán
We consider multiple Geronimus transformations and show that they lead to discrete (non-diagonal) Sobolev type inner products. Moreover, it is shown that every discrete Sobolev inn…