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Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

Mathematical Physics 2009-11-10 v1 math.MP Spectral Theory

Abstract

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectrum

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Cite

@article{arxiv.math-ph/0402019,
  title  = {Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation},
  author = {Tuncay Aktosun and Ricardo Weder},
  journal= {arXiv preprint arXiv:math-ph/0402019},
  year   = {2009}
}