6 papers
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 \( Î(W) \) for matrix-valued orthogonal polyn…
Matrix-Valued Hermite and Laguerre polynomials via Quadratic Transformation
Inés Pacharoni, A. Victoria Torres
We present the first systematic extension of the classical Hermite-Laguerre quadratic correspondence to the matrix-valued setting. Starting from a Hermite-type weight matrix W(x) =…
The algebra via strong Darboux transformations
Ignacio Bono Parisi, Inés Pacharoni
The Matrix Bochner Problem aims to classify weight matrices such that the algebra , of all differential operators that have a sequence of matrix-valued orthogona…
Darboux transformations and the algebra
Ignacio Bono Parisi, Inés Pacharoni
The problem of finding weight matrices of size such that the associated sequence of matrix-valued orthogonal polynomials are eigenfunctions of a second-order ma…
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…
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…