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Matrix Orthogonal Polynomials: A Riemann--Hilbert approach (2305.19954v1)
Published 31 May 2023 in math.CA
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.