Weighted Bergman spaces: shift-invariant subspaces and\n input/state/output linear systems

2012/09/17 by Joseph A. Ball, Ball, Joseph A., Vladimir Bolotnikov +1
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1209.3687

Abstract

It is well known that subspaces of the Hardy space over the unit disk which\nare invariant under the backward shift occur as the image of an observability\noperator associated with a discrete-time linear system with stable\nstate-dynamics, as well as the functional-model space for a Hilbert space\ncontraction operator, while forward shift-invariant subspaces have a\nrepresentation in terms of an inner function. We discuss several variants of\nthese statements in the context of weighted Bergman spaces on the unit disk.\n

Citations

• On two problems concerning linear transformations in hilbert space

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