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1 - Introduction

Published online by Cambridge University Press:  09 December 2021

Joseph A. Ball
Affiliation:
Virginia Tech
Vladimir Bolotnikov
Affiliation:
College of William and Mary, Virginia
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Summary

The Introduction of the book reviews the confluence of system-theory ideas and reproducing-kernel techniques which lead to representations of backward-shift invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspaces form an in general generalized orthogonal decomposition (in the sense of de Branges–Rovnyak) of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert-space contraction operator.

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Publisher: Cambridge University Press
Print publication year: 2021
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  • Introduction
  • Joseph A. Ball, Vladimir Bolotnikov, College of William and Mary, Virginia
  • Book: Noncommutative Function-Theoretic Operator Theory and Applications
  • Online publication: 09 December 2021
  • Chapter DOI: https://doi.org/10.1017/9781009004305.003
Available formats
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  • Introduction
  • Joseph A. Ball, Vladimir Bolotnikov, College of William and Mary, Virginia
  • Book: Noncommutative Function-Theoretic Operator Theory and Applications
  • Online publication: 09 December 2021
  • Chapter DOI: https://doi.org/10.1017/9781009004305.003
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Introduction
  • Joseph A. Ball, Vladimir Bolotnikov, College of William and Mary, Virginia
  • Book: Noncommutative Function-Theoretic Operator Theory and Applications
  • Online publication: 09 December 2021
  • Chapter DOI: https://doi.org/10.1017/9781009004305.003
Available formats
×