Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory

The Sz.-Nagy-Foias model theory for C ·0 contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operatorvalued inner functions, conservative discrete-time input/state/output linear systems, and C...

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Vydané v:Acta scientiarum mathematicarum (Szeged) Ročník 79; číslo 3-4; s. 623 - 686
Hlavní autori: Ball, Joseph A., Bolotnikov, Vladimir
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.12.2013
Predmet:
Functional Analysis
Mathematics
Operator Theory
Beurling-Lax theorem
dilation theory
weighted Hardy space
Bergman inner functions
47A57
Operator-valued functions
hypercontraction operators
characteristic function
ISSN:0001-6969, 2064-8316
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Popis
Shrnutí:The Sz.-Nagy-Foias model theory for C ·0 contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operatorvalued inner functions, conservative discrete-time input/state/output linear systems, and C ·0 Hilbert-space contraction operators. We discuss an analogue of all these ideas in the context of weighted Hardy spaces over the unit disk and an associated class of hypercontraction operators.
ISSN:0001-6969
2064-8316
DOI:10.1007/BF03651344