## 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.

Original language | English |
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Pages (from-to) | 1-29 |

Number of pages | 29 |

Journal | Monatshefte fur Mathematik |

Volume | 138 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2003 |

## Keywords

- Generalized Schur function
- Operator colligation
- Pontryagin space
- Schur algorithm
- Schur determinant

## ASJC Scopus subject areas

- Mathematics (all)