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

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• 作者：Joseph A. Ball (1)
  Vladimir Bolotnikov (2)
  
• 关键词：47A48 ; 47A57 ; Operator ; valued functions ; Bergman space ; Beurling鈥揕ax representations ; transfer ; function realization
• 刊名：Integral Equations and Operator Theory
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：76
• 期：3
• 页码：301-356
• 全文大小：659KB
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• 作者单位：Joseph A. Ball (1)
  Vladimir Bolotnikov (2)
  
  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061-0123, USA
  2. Department of Mathematics, The College of William and Mary, Williamsburg, VA, 23187-8795, USA
  
• ISSN：1420-8989

文摘

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.