Inverse Stieltjes-like Functions and Inverse Problems for Systems with Schrödinger Operator

  • Sergey V. Belyi
  • Eduard R. Tsekanovskii
Part of the Operator Theory: Advances and Applications book series (OT, volume 197)


A class of scalar inverse Stieltjes-like functions is realized as linear-fractional transformations of transfer functions of conservative systems based on a Schrödinger operator T h in L 2au][a,+∞) with a non-selfadjoint boundary condition. In particular it is shown that any inverse Stieltjes function of this class can be realized in the unique way so that the main operator \( \mathbb{A} \) possesses a special semi-boundedness property. We derive formulas that restore the system uniquely and allow to find the exact value of a non-real boundary parameter h of the operator T h as well as a real parameter μ that appears in the construction of the elements of the realizing system. An elaborate investigation of these formulas shows the dynamics of the restored parameters h and μ in terms of the changing free term α from the integral representation of the realizable function.

Mathematics Subject Classification (2000)

Primary 47A10 47B44 Secondary 46E20 46F05 


Operator colligation conservative system transfer (characteristic) function 


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© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Sergey V. Belyi
    • 1
  • Eduard R. Tsekanovskii
    • 2
  1. 1.Department of MathematicsTroy State UniversityTroyUSA
  2. 2.Department of MathematicsNiagara UniversityNYUSA

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