Integral Equations and Operator Theory

, Volume 37, Issue 4, pp 423-436

First online:

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

  • Aurelian GheondeaAffiliated withInstitutul de Matematică al Academiei Române
  • , Raimund J. OberAffiliated withCenter for Engineering Mathematics EC35, University of Texas at Dallas

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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.

Mathematics Subject Classification

93B15 93B28 47B35 47B50