Abstract.
In the first paper of this series (Daniel Alpay, Tomas Azizov, Aad Dijksma, and Heinz Langer: The Schur algorithm for generalized Schur functions I: coisometric realizations, Operator Theory: Advances and Applications 129 (2001), pp. 1–36) it was shown that for a generalized Schur function s(z), which is the characteristic function of a coisometric colligation V with state space being a Pontryagin space, the Schur transformation corresponds to a finite-dimensional reduction of the state space, and a finite-dimensional perturbation and compression of its main operator. In the present paper we show that these formulas can be explained using simple relations between V and the colligation of the reciprocal s(z)−1 of the characteristic function s(z) and general factorization results for characteristic functions.
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Received October 31, 2001; in revised form August 21, 2002
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ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday
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Alpay, D., Azizov, T., Dijksma, A. et al. The Schur Algorithm for Generalized Schur Functions II: Jordan Chains and Transformations of Characteristic Functions. Monatsh. Math. 138, 1–29 (2003). https://doi.org/10.1007/s00605-002-0528-6
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DOI: https://doi.org/10.1007/s00605-002-0528-6