On a moment problem for rational matrix-valued functions.
Given a block matrix \(G\) and a sequence of complex numbers which are not located on the unit circle \(\mathbb T\), the authors consider the moment problem for rational matrix-valued functions, which entails describing the set \(\mathcal M\) of all nonnegative Hermitian Borel measures \(F\) on \(\mathbb T\) having \(G\) as the Gramian matrix. This problem can be considered as a generalization of two problems: the truncated trigonometric moment problem for matrix polynomials and the classical Carathéodory-Nevanlinna-Pick interpolation problem. The main result of the paper determines when the set \({\mathcal M}\) is nonempty and when the measure \(F\) belongs to \({\mathcal M}\) or not. In the case in which the moment problem for rational matrix-valued functions has a solution and the given matrix is nonsingular, the authors explicitly construct a particular solution.
nonnegative Hermitian Borel measures on the unit circle
scientific article; zbMATH DE number 1993116
scientific article