### abstract

- Realization theory is used to study Nevanlinna-Pick and Carathéodory-Fejér interpolation problems for generalized Schur classes. In the first part of the paper, conditions are given for the existence of a solution of a factorization problem that includes Nevanlinna-Pick interpolation and factorization problems of Leech type for operator-valued functions. In the second part, an analysis is made of the numbers of positive and negative eigenvalues of classical matrices which arise in coefficient problems. The complete solution of an indefinite Carathéodory-Fejér problem is obtained.