On the Carathéodory-Fejér interpolation problem for generalized Schur functions (Q1884738)

The solutions of the Carathéodory-Fejér interpolation problem for generalized Schur functions can be parameterized by a linear fractional transformation over the class of classical Schur functions. The linear fractional transformation of some of these functions may have a pole in one or more of the interpolation points or may not satisfy one or more interpolation conditions. So not all Schur functions can serve as a parameter value. This paper characterizes the excluded parameter values in terms of the related Pick matrix.