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

2014/05/12 by Ball, Joseph A., Bolotnikov, Vladimir
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1405.2974

Abstract

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, operator-valued 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.

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