Abstract
The connection between factorization and invariant subspaces is developed in §4.1, where it is shown that factorization corresponds to contractive inclusion of spaces ℌ(S) and, in some cases, to invariant subspaces for the transformation f(z) into [ f(z) — f(0) ]/z When F and B are Hilbert spaces, functions SK(FB)in admit essentially unique Kreĭn-Langer factorizations, which account for indefiniteness by means of a finite Blaschke product (§4.2). In §4.3, the Potapov-Ginzburg transform is used to study the classes SK(FB) when F and B are Kreĭn spaces. These results are applied in §4.4 to construct canonical realizations for arbitrary generalized Schur functions. Canonical models are discussed in §4.5.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Basel AG
About this chapter
Cite this chapter
Alpay, D., Dijksma, A., Rovnyak, J., de Snoo, H. (1997). Structural Properties. In: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces. Operator Theory Advances and Applications, vol 96. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8908-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8908-7_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9823-2
Online ISBN: 978-3-0348-8908-7
eBook Packages: Springer Book Archive