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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.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Operator Theory: Advances and Applications, volume 134, in 2002 following peer review. The final publication is available at Springer via DOI: 10.1007/978-3-0348-8215-6_5

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