On Maximal Weight Solutions of a Moment Problem for Rational Matrix-valued Functions
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We study some special solutions of a finite moment problem for rational matrix functions. Roughly speaking, we discuss a family of molecular non-negative Hermitian matrix-valued Borel measures on the unit circle with a special structure. As one of the main results, we will see that each member of this family offers an extremal property in the solution set of the moment problem concerning the weight assigned to some point of the open unit disk. Our approach uses the theory of orthogonal rational matrix functions.
KeywordsNon-negative Hermitian matrix measures matrix moment problem matricial Carathéodory functions orthogonal rational matrix functions.
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