The Schur Algorithm for Generalized Schur Functions II: Jordan Chains and Transformations of Characteristic Functions

D. Alpay; T. Ya Azizov; A. Dijksma; H. Langer

doi:10.1007/s00605-002-0528-6

The Schur Algorithm for Generalized Schur Functions II: Jordan Chains and Transformations of Characteristic Functions

D. Alpay, T. Ya Azizov, A. Dijksma, H. Langer

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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
Pages (from-to)	1-29
Number of pages	29
Journal	Monatshefte fur Mathematik
Volume	138
Issue number	1
DOIs	https://doi.org/10.1007/s00605-002-0528-6
State	Published - 1 Jan 2003

Keywords

Generalized Schur function
Operator colligation
Pontryagin space
Schur algorithm
Schur determinant

ASJC Scopus subject areas

Mathematics (all)

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10.1007/s00605-002-0528-6

Cite this

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AU - Langer, H.

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The Schur Algorithm for Generalized Schur Functions II: Jordan Chains and Transformations of Characteristic Functions

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Keywords

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