arXiv subjects

Lucía Morey

Publications and source records attributed to Lucía Morey.

3 recordsLinked to original sources

arXiv2024

Non Abelian Toda-type equations and matrix valued orthogonal polynomials

In this paper, we study parameter deformations of matrix valued orthogonal polynomials (MVOPs). These deformations are built on the use of certain matrix valued operators which are symmetric with respect to the matrix valued inner product defined by the orthogonality weight. We show that the recurrence coefficients associated with these operators satisfy generalizations of the non-Abelian lattice equations. We provide a Lax pair formulation for these equations, and an example of deformed Hermite-type matrix valued polynomials is discussed in detail.

math.CA↗

arXiv2023

Matrix exceptional Laguerre polynomials

We give an analog of exceptional polynomials in the matrix valued setting by considering suitable factorizations of a given second order differential operator and performing Darboux transformations. Orthogonality and density of the exceptional sequence is discussed in detail. We give an example of matrix valued exceptional Laguerre polynomials of arbitrary size.

math.CA↗

arXiv2021

Duality and difference operators for matrix valued discrete polynomials on the nonnegative integers

In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators acting on the matrix orthogonal polynomials. These operators belong to the so called Fourier algebras, which play a key role in the construction of the families. In order to illustrate duality, we describe a family of Charlier type matrix orthogonal polynomials with explicit shift operators which allow us to find explicit formulas for three term recurrences, difference operators and square norms. These are the essential ingredients for the construction of different dual families.

math.CA↗