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

TL;DR

This paper investigates the Nevanlinna-Pick matrix interpolation problem within the Carathéodory class for infinite data, providing an operator-theoretic framework and conditions for solution uniqueness in both degenerate and nondegenerate cases.

Contribution

It introduces an operator approach to describe all solutions and establishes criteria for problem determinacy in the infinite data setting.

Findings

Operator approach characterizes all solutions

Necessary and sufficient conditions for determinacy

Applicable to both degenerate and nondegenerate 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.