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Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse Problems

Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 165)

Abstract

We study the inverse problems associated to the characteristic spectral functions of first-order discrete systems. We focus on the case where the coefficients defining the discrete system are strictly pseudo-exponential. The arguments use methods from system theory. An important role is played by the description of the unitary solutions of a related Nehari interpolation problem and by Hankel operators with unimodular symbols. An application to inverse problems for Jacobi matrices is also given.

Keywords

Inverse problems scattering matrix Schur parameters state space method 

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© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-Aviv, Ramat-AvivIsrael

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