Integral Equations and Operator Theory

, Volume 37, Issue 4, pp 423–436

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


  • Aurelian Gheondea
    • Institutul de Matematică al Academiei Române
  • Raimund J. Ober
    • Center for Engineering Mathematics EC35University of Texas at Dallas

DOI: 10.1007/BF01192830

Cite this article as:
Gheondea, A. & Ober, R.J. Integr equ oper theory (2000) 37: 423. doi:10.1007/BF01192830


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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© Birkhäuser Verlag 2000