On the Weyl Matrix Balls Associated with Nondegenerate Matrix-Valued Carathéodory Functions

Inspired by SCHUR's and R. NEVANLINNA's famous papers [20] and [18], ARTEMENKO [2] and GERONIMUS [13] completely solved the interpolation problems named now after Carathéodory and Schur. Additionally, given a fixed point z0 of the open unit disc, they observed that the set of the values at z0 of all solutions of the interpolation problem under consideration fills a closed disc, the center and the radii of which can be explicitly expressed by the given data. In connection with boundary value problems the study of certain families of nested discs originates in WEYL's " . Habilitationsschrift" [22] in which there are treated singular differential equations of second order. In the context of discrete interpolation problems, Weyl's method of nested discs was first applied by HELLINGER [14]. In their approach to matrix versions of classical interpolation problems, V.P. Potapov and his pupils worked out a natural matricial generalization of Weyl's method (see, e.g., KOVALISHINA and .POTAPOV [17], KOVALISHINA [16], DUBOVOJ [5]). Hereby, discs are replaced by so-called matrix balls which had, been treated in detail before by SMULJAN [21]. Note that particular aspects of the matricial generalization of Weyl's method were also touched in the context of Nevanlinna-Pick interpolation by' DELSARTE/GENIN/KAMP[4]. The study of matrix and operator balls in connection with