On Resolvent Matrix, Dyukarev–Stieltjes Parameters and Orthogonal Matrix Polynomials via $$[0, \infty )$$ [ 0 , ∞ ) -Stieltjes Transformed Sequences

Abstract

By using Schur transformed sequences and Dyukarev–Stieltjes parameters we obtain a new representation of the resolvent matrix corresponding to the truncated matricial Stieltjes moment problem. Explicit relations between orthogonal matrix polynomials and matrix polynomials of the second kind constructed from consecutive Schur transformed sequences are obtained. Additionally, a non-negative Hermitian measure for which the matrix polynomials of the second kind are the orthogonal matrix polynomials is found.