73 citations · 117 across the 12 of their papers we have counts for
14 papers
Truncated Hermite polynomials
Diego Dominici, Francisco Marcellán
We consider the family of polynomials orthogonal with respect to the inner product \[ \left\langle f,g\right\rangle = \int_{-z}^{z} f\left( x\right) g\le…
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations
Carlos Hermoso, Edmundo J. Huertas, Alberto Lastra +1
It is well known that Sobolev-type orthogonal polynomials with respect to measures supported on the real line satisfy higher-order recurrence relations and these can be expressed a…
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…
Orthogonality of quasi-orthogonal polynomials
Cleonice F. Bracciali, Francisco Marcellán, Serhan Varma
A result of Pólya states that every sequence of quadrature formulas with nodes and positive numbers converges to the integral of a continuous function provi…
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}…
Markov-type inequalities and duality in weighted Sobolev spaces
Francisco Marcellán, Yamilet Quintana, José M. Rodríguez
The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as resul…
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…
Strong and ratio asymptotics for Laguerre polynomials revisited
Alfredo Deaño, Edmundo J. Huertas, Francisco Marcellán
In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but…
Asymptotic behaviour of zeros of exceptional Jacobi and Laguerre polynomials
David Gómez-Ullate, Francisco Marcellán, Robert Milson
The location and asymptotic behaviour for large n of the zeros of exceptional Jacobi and Laguerre polynomials are discussed. The zeros of exceptional polynomials fall into two clas…
Zeros of Orthogonal Polynomials Generated by Canonical Perturbations on Standard Measure
Edmundo J. Huertas, Francisco Marcellán, Fernando R. Rafaeli
In this contribution, the behavior of zeros of orthogonal polynomials associated with canonical linear spectral transformations of measures supported in the real line is analyzed.…
Estimates for Jacobi-Sobolev type orthogonal polynomials
Manual Alfaro, Francisco Marcellán
Let the Sobolev-type inner product <f,g> = \int fg d mu_0+ int f' g' d mu_1 with mu_0 = w + M delta_c, mu_1= N delta_c where w is the Jacobi weight, c is either 1 or -1 and M, N >=…