Coherent pairs and Sobolev-type orthogonal polynomials on the real line: An extension to the matrix case

In this contribution, we extend the concept of coherent pair for two quasi-definite matrix linear functionals u0 and u1. Necessary and sufficient conditions for these functionals to constitute a coherent pair are determined, when one of them satisfies a matrix Pearson-type equation. Moreover, we deduce algebraic properties of the matrix orthogonal polynomials associated with the Sobolev-type inner product(sic)p, q(sic)(s) = (sic)p,q(sic)(u0) + (sic)p'M-1, q'M-2(sic)(u1) ,where M-1 and M-2 are m x m non-singular matrices and p, q are matrix polynomials.(c) 2022 Elsevier Inc. All rights reserved.