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On the missing bound state data of inverse spectral-scattering problems on the half-line

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  • The inverse spectral-scattering problems for the radial Schrödinger equation on the half-line are considered with a real-valued integrable potential with a finite moment. It is shown that if the potential is sufficiently smooth in a neighborhood of the origin and its derivatives are known, then it is uniquely determined on the half-line in terms of the amplitude or scattering phase of the Jost function without bound state data, that is, the bound state data is missing.
    Mathematics Subject Classification: Primary: 34A55; Secondary: 34L40, 34L20.


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