Pure Mathematics
The Schur Algorithm for Generalized Schur Functions II: Jordan Chains and Transformations of Characteristic Functions
2003-01
https://scigraph.springernature.com/explorer/license/
2019-04-10T15:01
en
2003-01-01
1-29
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.
research_article
http://link.springer.com/10.1007%2Fs00605-002-0528-6
true
articles
H.
Langer
Voronezh State University, Voronezh, Russia, RU
Voronezh State University
Alpay
D.
Dijksma
A.
Mathematical Sciences
1
Ben-Gurion University of the Negev
Ben-Gurion University of the Negev, Beer Sheva, Israel, IL
0026-9255
1436-5081
Monatshefte für Mathematik
Azizov
T. Ya.
Springer Nature - SN SciGraph project
readcube_id
a3745d5726ae4c0ec09fe7d1191886e324758fa0ded9072adbab349ad0a87bda
doi
10.1007/s00605-002-0528-6
University of Groningen, The Netherlands, NL
University of Groningen
138
dimensions_id
pub.1034313376
Vienna University of Technology, Austria, AT
TU Wien