Pablo Rom'an

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math.CA2026

Asymptotics of matrix orthogonal polynomials on the real line

Alfredo DeaÃ±o, Pablo RomÃ¡n

In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to i…

math.CA2025

An evolution of matrix-valued orthogonal polynomials

Erik Koelink, Pablo RomÃ¡n, Wadim Zudilin

We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several…

math.CA2025

A partial-sum deformation for a family of orthogonal polynomials

Erik Koelink, Pablo RomÃ¡n, Wadim Zudilin

There are several questions one may ask about polynomials $q_{m} (x) = q_{m} (x; t) = \sum_{n = 0}^{m} t^{m} p_{n} (x)$ attached to a family of orthogonal polynomials ${p_{n} (x)}_{n \geq 0}$ . In this note…

math.CA2024

Non Abelian Toda-type equations and matrix valued orthogonal polynomials

Alfredo DeaÃ±o, LucÃa Morey, Pablo RomÃ¡n

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…