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 Carathéodory class with infinite data (both in the nondegenerate and degenerate cases). We develop the Szökefalvi-Nagy and Korányi 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.

arXiv comment16 pages