The Hamburger Criterion for Matrix Nevanlinna--Pick Interpolation
The classical Hamburger moment problem can be viewed as an interpolation problem for Nevanlinna functions. A closely related problem is the Nevanlinna--Pick interpolation problem. Each of these problems is either determinate, with a unique solution, or indeterminate, with infinitely many solutions. Hamburger established a criterion for the indeterminacy of the moment problem in terms of the convergence of two series involving the classical polynomials of the first and second kind. In this paper, we establish an analogous criterion for the matrix Nevanlinna--Pick interpolation problem. The criterion is formulated in terms of the convergence of matrix series involving the rational functions of the first and second kind.
math.CA↗