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Inverse spectral problems for difference operators with rational scattering matrix function

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Abstract

In this paper we obtain explicit formulas for the coefficients of a second order difference block operator if its spectral or its scattering functions are rational matrix functions analytic and invertible on the unit circle. The solutions are given in terms of realizations of the spectral or scattering function.

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Alpay, D., Gohberg, I. Inverse spectral problems for difference operators with rational scattering matrix function. Integr equ oper theory 20, 125–170 (1994). https://doi.org/10.1007/BF01679669

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AMS Subject Classification Numbers

  • 47A40
  • 33C45
  • 81U40