On boundary Nevanlinna–Pick interpolation for Carathéodory matrix functions

A matrix version of the boundary Nevanlinna-Pick interpolation problem in the class of Carathéodory matrix functions is considered. This matrix interpolation problem is reduced to a certain matrix trigonometric moment problem with specified constraints that the nonnegative matrix-valued measure has no mass distributions at a finite number of boundary points. Basing on the use of recent results due to Bolotnikov and Dym and this reduction, we obtain solvability criteria for both the boundary Nevanlinna-Pick interpolation problem and the moment problem. A parameterized description of all the solutions of each of these two problems under consideration in the nondegenerate case is given as well.