Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T07:51:09.001Z Has data issue: false hasContentIssue false

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
Get access

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.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • 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 Dropbox

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 Dropbox.

  • 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
×