5 citations · 6 across the 8 of their papers we have counts for
8 papers
Using quasi-Darboux transformations to construct exceptional matrix polynomials
Ignacio Bono Parisi, Antonio J. Durán, Ignacio N. Zurrián
We introduce a couple of methods to construct exceptional matrix polynomials. One of them uses what we have called quasi-Darboux transformations. This seems to be a more powerful m…
Matrix-valued bispectral discrete orthogonal polynomials
Ignacio Bono Parisi
We develop a unified construction of matrix-valued orthogonal polynomials associated with discrete weights, yielding bispectral sequences as eigenfunctions of second-order differen…
A singular solution to the Matrix Bochner Problem with not of the form
Ignacio Bono Parisi
The Matrix Bochner Problem aims to classify weight matrices whose sequences of orthogonal polynomials are eigenfunctions of a second-order differential operator. A major breakthrou…
Explicit construction of matrix-valued orthogonal polynomials of arbitrary size
Ignacio Bono Parisi
In this paper, we explicitly provide expressions for a sequence of orthogonal polynomials associated with a weight matrix of size constructed from a collection of scalar weight…
Structure of operator algebras for matrix orthogonal polynomials
Ignacio Bono Parisi, Inés Pacharoni
In this paper, we study the structure of the differential operator algebra \( \mathcal{D}(W) \) and its associated eigenvalue algebra \( Λ(W) \) for matrix-valued orthogonal polyno…
Singular solutions of the matrix Bochner problem: the -dimensional cases
Ignacio Bono Parisi, Inés Pacharoni
In the theory of matrix-valued orthogonal polynomials, there exists a longstanding problem known as the Matrix Bochner Problem: the classification of all weight matric…
On a new equivalence relation for matrix-valued orthogonal polynomials
Ignacio Bono Parisi, Inés Pacharoni, Ignacio Zurrián
In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and how to build suc…
Singular examples of the Matrix Bochner Problem
Ignacio Bono Parisi, Inés Pacharoni
The Matrix Bochner Problem aims to classify which weight matrices have their sequence of orthogonal polynomials as eigenfunctions of a second-order differential operator. Casper an…