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


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2003-01

AUTHORS

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

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. More... »

PAGES

1-29

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00605-002-0528-6

DOI

http://dx.doi.org/10.1007/s00605-002-0528-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1034313376


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