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Half-inverse spectral problem for a Sturm--Liouville operator consists inreconstruction of this operator by its spectrum and half of the potential. Wegive the necessary and sufficient conditions for solvability of thehalf-inverse spectral problem for the class of Sturm--Liouville operators withsingular potentials from the space $W^{-1}_2(0,1)$ and provide thereconstruction algorithm.Comment: 21 page

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