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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.

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Published date: December 2000

Identifiers

Local EPrints ID: 424913
URI: https://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

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Date deposited: 05 Oct 2018 16:30
Last modified: 14 Mar 2019 01:21

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

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