Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T08:21:07.865Z Has data issue: false hasContentIssue false

3 - Contractive Multipliers

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

Chapter 3 introduces the notion of a contractive multiplier between weighted Hardy–Fock spaces (the analog of a Schur-class function for the classical setting). Unlike the classical case, in this general setting the notion of inner partitions into a number of distinct cases: (i) strictly inner (isometric multiplier) (ii) McCT (McCullough-Trent) inner (partially isometric multiplier), (iii) Bergman inner (contractive multiplier which is isometric when restricted to constants). For appropriately restricted pairs of input/output vectorial weighted Hardy–Fock spaces, analogs of the classical connections with dissipative/conservative linear input/state/output multidimensional linear systems, kernel decompositions, as well as corresponding generalized orthogonal decompositions of the ambient weighted Hardy–Fock space as a sum of a backward and a forward-shift-invariant subspace, are explored. These results are fundamental for the work of the succeeding Chapters.

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 [email protected] 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.

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.

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.

Available formats
×