Matrix Orthogonal Polynomials: A Riemann--Hilbert approach

2023/05/31 by Branquinho, Amílcar, Foulquié-Moreno, Ana, Fradi, Assil +1 · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.19954

Abstract

In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain information about the matrix orthogonal polynomials and functions of second kind associated with a weight matrix. We deduce properties for the recurrence relation coefficients from differential properties of the weight matrix. We take the matrix polynomials of Hermite, Laguerre and Jacobi type as a case study.

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• Non-commutative multiple bi-orthogonal polynomials: formal approach and integrability

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