The University of Southampton
University of Southampton Institutional Repository

A note on the existence, uniqueness and symmetry of par-balanced realizations

A note on the existence, uniqueness and symmetry of par-balanced realizations
A note on the existence, uniqueness and symmetry of par-balanced realizations

We give a proof of the realization theorem of N.J. Young which states that analytic functions which are symbols of bounded Hankel operators admit par-balanced realizations. The main tool used in this proof is the induced Hilbert spaces and a lifting lemma of Kreǐn-Reid-Lax-Dieudonné. Alternatively one can use the Loewner inequality. A short proof of the uniqueness of par-balanced realizations is included. As an application, it is proved that par-balanced realizations of real symmetric transfer functions are J-self-adjoint.

0378-620X
423-436
Gheondea, Aurelian
97dd2d38-c290-4cd8-9f95-b580a9501f8b
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Gheondea, Aurelian
97dd2d38-c290-4cd8-9f95-b580a9501f8b
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Gheondea, Aurelian and Ober, Raimund J. (2000) A note on the existence, uniqueness and symmetry of par-balanced realizations. Integral Equations and Operator Theory, 37 (4), 423-436. (doi:10.1007/BF01192830).

Record type: Article

Abstract

We give a proof of the realization theorem of N.J. Young which states that analytic functions which are symbols of bounded Hankel operators admit par-balanced realizations. The main tool used in this proof is the induced Hilbert spaces and a lifting lemma of Kreǐn-Reid-Lax-Dieudonné. Alternatively one can use the Loewner inequality. A short proof of the uniqueness of par-balanced realizations is included. As an application, it is proved that par-balanced realizations of real symmetric transfer functions are J-self-adjoint.

This record has no associated files available for download.

More information

Published date: December 2000

Identifiers

Local EPrints ID: 424913
URI: http://eprints.soton.ac.uk/id/eprint/424913
ISSN: 0378-620X
PURE UUID: 17dd6064-6ae4-4bb4-ab1c-f31b7c637f08
ORCID for Raimund J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 05 Oct 2018 16:30
Last modified: 18 Mar 2024 03:48

Export record

Altmetrics

Contributors

Author: Aurelian Gheondea
Author: Raimund J. Ober ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×