Weighted Bergman Spaces: Shift-Invariant Subspaces and Input/State/Output Linear Systems

It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the functional-model space for a Hilbert space contr...

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Bibliographic Details
Published in:	Integral equations and operator theory Vol. 76; no. 3; pp. 301 - 356
Main Authors:	Ball, Joseph A., Bolotnikov, Vladimir
Format:	Journal Article
Language:	English
Published:	Basel SP Birkhäuser Verlag Basel 01.07.2013
Subjects:	Analysis Mathematics Mathematics and Statistics Bergman space Operator-valued functions Beurling–Lax representations transfer-function realization 47A48 47A57
ISSN:	0378-620X, 1420-8989
Online Access:	Get full text
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Summary:	It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the functional-model space for a Hilbert space contraction operator, while forward shift-invariant subspaces have a representation in terms of an inner function. We discuss several variants of these statements in the context of weighted Bergman spaces on the unit disk.
ISSN:	0378-620X 1420-8989
DOI:	10.1007/s00020-013-2053-5