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

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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 Kreîn-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 areJ-self-adjoint.

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Authors and Affiliations

  1. Institutul de Matematică al Academiei Române, C.P. 1-764, 70700, Bucureşti, Romănia

    Aurelian Gheondea

  2. Center for Engineering Mathematics EC35, University of Texas at Dallas, 75083-0688, Richardson, Texas, USA

    Raimund J. Ober

Authors
  1. Aurelian Gheondea
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  2. Raimund J. Ober
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Additional information

Research supported in part by the Romanian Academy grant GAR-6645/1996.

This research was supported in part by NSF grant DMS-9501223.

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Gheondea, A., Ober, R.J. A note on the existence, uniqueness and symmetry of par-balanced realizations. Integr equ oper theory 37, 423–436 (2000). https://doi.org/10.1007/BF01192830

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  • DOI: https://doi.org/10.1007/BF01192830

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