45 citations · 121 across the 10 of their papers we have counts for
10 papers · 1 filter
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…
Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems
Gerardo Ariznabarreta, Manuel Mañas, Piergiulio Tempesta
We introduce a large class of Sobolev bi-orthogonal polynomial sequences arising from a -factorizable moment matrix and associated with a suitable measure matrix that character…
CMV biorthogonal Laurent polynomials. II: Christoffel formulas for Geronimus-Uvarov perturbations
Gerardo Ariznabarreta, Manuel Mañas, Alfredo Toledano
This paper is a continuation of the recent paper "CMV biorthogonal Laurent polynomials: Christoffel formulas for Christoffel and Geronimus transformations" by the same authors. The…
CMV biorthogonal Laurent polynomials: Christoffel formulas for Christoffel and Geronimus perturbations
Gerardo Ariznabarreta, Manuel Mañas, Alfredo Toledano
Quasidefinite sesquilinear forms for Laurent polynomials in the complex plane and corresponding CMV biorthogonal Laurent polynomial families are studied. Bivariate linear functiona…
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…
Linear spectral transformations for multivariate orthogonal polynomials and multispectral Toda hierarchies
Gerardo Ariznabarreta, Manuel Mañas
Linear spectral transformations of orthogonal polynomials in the real line, and in particular Geronimus transformations, are extended to orthogonal polynomials depending on several…
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}…
Multivariate orthogonal Laurent polynomials and integrable systems
Gerardo Ariznabarreta, Manuel Mañas
An ordering for Laurent polynomials in the algebraic torus , inspired by the Cantero-Moral-Velázquez approach to orthogonal Laurent polynomials in the unit circle,…
Darboux transformations for multivariate orthogonal polynomials
Gerardo Ariznabarreta, Manuel Mañas
Darboux transformations for polynomial perturbations of a real multivariate measure are found. The 1D Christoffel formula is extended to the multidimensional realm: multivariate or…
Matrix Orthogonal Laurent Polynomials on the Unit Circle and Toda Type Integrable Systems
Gerardo Ariznabarreta, Manuel Manas
Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of two, left and a right,…