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In this paper we study the Nevanlinna-Pick matrix interpolation problem inthe Carath\'eodory class with infinite data (both in the nondegenerate anddegenerate cases). We develop the Sz\"okefalvi-Nagy and Kor\'anyi operatorapproach to obtain an analytic description of all solutions of the problem.Simple necessary and sufficient conditions for the determinacy of the problemare given.

The Nevanlinna-Pick matrix interpolation in the Carath\'eodory class with infinite data both in the nondegenerate and degenerate cases