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

2013; Birkhäuser; Volume: 79; Issue: 3-4 Linguagem: Inglês

10.1007/bf03651344

2064-8316

Joseph A. Ball, Vladimir Bolotnikov,

Spectral Theory in Mathematical Physics

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.