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We associate with this problem the map $F:\\, W^\\theta_2\\to l_B^\\theta,\\ F(\\sigma) =\\{s_k\\}_1^\\infty$, where $W^\\theta_2 = W^\\theta_2[0,\\pi]$ are Sobolev spaces with $\\theta\\geqslant 0$, $\\sigma=\\int q$ is a primitive of the potential $q$ and $l_B^\\theta$ are special Hilbert spaces which we construct to place in the regularized spectral data $\\bold s = \\{s_k\\}_1^\\infty$. 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