Half-inverse spectral problems for Sturm--Liouville operators with singular potentials

Half-inverse spectral problem for a Sturm–Liouville operator consists in reconstruction of this operator by its spectrum and half of the potential. We give the necessary and sufficient conditions for solvability of the half-inverse spectral problem for the class of Sturm–Liouville operators with singular potentials from the space $W_2^{-1}(0,1)$ and provide the reconstruction algorithm.