Potentials Associated to Rational Weights

  • D. Alpay
  • I. Gohberg
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)


In this paper we consider the problem of building the spectral function of a canonical differential equation when the potential is given. We restrict ourselves to the case where the spectral function is rational. An algorithm is proposed which allows the construction of the spectral function from the values of the potential and of a number of its derivatives at the origin. The approach is based on the solution of the partial realization problem for systems.


Spectral Function Rational Weight Laurent Expansion Minimal Realization Riesz Projection 
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • D. Alpay
    • 1
  • I. Gohberg
    • 2
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityRamat-AvivIsrael

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