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Weighted Bergman Spaces: Shift-Invariant Subspaces and Input/State/Output Linear Systems

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Abstract

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

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061-0123, USA

    Joseph A. Ball

  2. Department of Mathematics, The College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Vladimir Bolotnikov

Authors
  1. Joseph A. Ball
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  2. Vladimir Bolotnikov
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Correspondence to Vladimir Bolotnikov.

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The second author’s research was supported by the Plumeri Award of the College of William and Mary.

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Ball, J.A., Bolotnikov, V. Weighted Bergman Spaces: Shift-Invariant Subspaces and Input/State/Output Linear Systems. Integr. Equ. Oper. Theory 76, 301–356 (2013). https://doi.org/10.1007/s00020-013-2053-5

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  • DOI: https://doi.org/10.1007/s00020-013-2053-5

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