Abstract
We discuss extremal solutions of a certain finite moment problem for rational matrix functions which satisfy an additional rank condition.W e will see, among other things, that these solutions are molecular nonnegative Hermitian matrix-valued Borel measures on the unit circle and that these measures have a particular structure.W e study the above-mentioned solutions in all generality, but later focus on the nondegenerate case.In this case, the family of these special solutions can be parametrized by the set of unitary matrices.T his realization allows us to further examine the structure of these solutions.H ere, the analysis of the structural properties relies, to a great extent, on the theory of orthogonal rational matrix functions on the unit circle.
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