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Inverse spectral problem for differential operators with rational scattering matrix functions. (English) Zbl 0819.47008

The authors obtain explicit formulas for the potential of an ordinary differential operator if its spectral function or its scattering functions are rational matrix functions which are analytic and invertible on the real line including infinity. The solution is given in terms of a realization of the spectral function or of the scattering function.

MSC:

47A40 Scattering theory of linear operators
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47E05 General theory of ordinary differential operators
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