Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory - Ball, Joseph A.; Bolotnikov, Vladimir (Acta scientiarum mathematicarum (Szeged), 2013)
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.