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arXiv · 1405.2974

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

Joseph A. Ball·Vladimir Bolotnikov
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Abstract

The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ 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 $C_{\cdot 0}$ 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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Joseph A. Ball, Vladimir Bolotnikov. 2014-05-12. Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory. https://arxiv.org/abs/1405.2974

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