On maximal weight solutions of two matricial moment problems in the nondegenerate case (Q739118)

All solutions of the matrix-valued truncated non-degenerate trigonometric moment problem can be given in the form of a matrix Möbius transform of an arbitrary matrix-valued Schur function. When the Schur function is constant, the solution is N-extremal. Among all the N-extremal solutions one may select a unique one that has a maximal weight at an arbitrary point on the unit circle. Such analysis was already performed for example in [\textit{B. Fritzsche} et al., Analysis, München 27, No. 1, 109--164 (2007; Zbl 1151.30027)]. An alternative proof is given here using orthogonal matrix polynomials and explicit expressions are given for the discrete measures that form the solutions. A link is made to the corresponding rational moment problem, in which case moments are prescribed in the spaces of rational matrix-valued functions with prescribed complex poles not on the unit circle.