Tuncay Aktosun and Ricardo Weder
Inverse Spectral-Scattering Problem
with Two Sets of Discrete Spectra
for the Radial Schroedinger Equation
(102K, AMS TEX)
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.