Realization theory for operator colligations on Pontryagin spaces is used to study interpolation and factorization in generalized Schur classes. Several criteria are derived which imply that a given function is almost the restriction of a generalized Schur function. The role of realization theory in coefficient problems is also discussed; a solution of an indefinite Carathéodory-Fejér problem is obtained, as well as a result that relates the number of negative (positive) squares of the reproducing kernels associated with the canonical coisometric, isometric, and unitary realizations of a generalized Schur function to the number of negative (positive) eigenvalues of matrices derived from their Taylor coefficients.
D. Alpay, T. Constantinescu, A. Dijksma and J. Rovnyak. A note on interpolation in the generalized Schur class. I. Applications of realization theory. Operator Theory: Advances and Applications, vol. 134 (2002) pp. 67-97.