Abstract
This article is devoted to the investigation of remarkable properties of extremal solutions F [U] and G [U] with a q × q unitary parameter U and their distinguished one-parameter families and with |w| = 1 within the solution sets of Problem (C) (the matricial Carathéodory problem) and Problem (NP) (a certain Nevanlinna–Pick-type interpolation for Carathéodory matrix functions), respectively, in the nondegenerate case. We show connections between the poles of the functions F [U] and at the unit circle of the complex plane and their Riesz–Herglotz measures, and discuss closely related matters for the extremal solutions F [U] and . These results further serve as a starting point to look for corresponding properties of the functions G [U] and based on the so-called modified block Toeplitz vector approach.
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