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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Vydané v:Integral equations and operator theory Ročník 76; číslo 3; s. 301 - 356
Hlavní autori: Ball, Joseph A., Bolotnikov, Vladimir
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel SP Birkhäuser Verlag Basel 01.07.2013
Predmet:
Analysis
Mathematics
Mathematics and Statistics
Bergman space
Operator-valued functions
Beurling–Lax representations
transfer-function realization
47A48
47A57
ISSN:0378-620X, 1420-8989
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Popis
Shrnutí: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