The Nevanlinna-Pick matrix interpolation in the Carathéodory class with infinite data both in the nondegenerate and degenerate cases

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