The Nevanlinna-Pick interpolation problems and power moment problems for matrix-valued functions

This paper is concerned with the study of several types of matrix interpola tion problems, including The matrix Nevanlinna-Pick interpolation problem in the Nevanlinna class N- p, The matrix Nevanlinna-Pick interpolation problem in the Stieltjes class L-p , The truncated matrix power moment problem on the real axis, The Stieltjes matrix power moment problem. We use the so-called block Hankel vector approach for the treatment of thes e problems and make explicit the correspondence between solutions to the Ne vanlinna-Pick interpolation problem and solutions to an associated power mo ment problem with the block Hankel vector under consideration. This enables one not only to find existence criteria for the solutions of the Nevanlinn a-Pick interpolation problem, but also to describe the solutions based on t he results of power moment problem, and vice versa. (C) 1999 Elsevier Scien ce Inc. All rights reserved.