Inverse spectral problems for Sturm-Liouville operators with singular   potentials
  The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized. 
R. O. Hryniv and Ya. V. Mykytyuk