The Nevanlinna–Pick interpolation problems and power moment problems for matrix-valued functions III: The infinitely many data case

AbstractThe objective of this paper is to establish an intrinsic and simple correspondence between a multiple Nevanlinna–Pick matrix interpolation (NP) problem in the Nevanlinna class Np with a denumerable set of nodes and a certain full Hamburger matrix moment problem. With the help of the indicated correspondence, the solution of an infinite NP problem in Np can be reduced to what amounts to the study of the associated full Hamburger matrix moment problem with the so-called block Hankel vector of the former, and vice versa. These investigations can be regarded as a natural extension of our previous work on both the NP problems with a finite set of interpolation data and the truncated power matrix moment problems