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In this paper, we deal with the inverse spectral problem for the equation −(pu ) +qu = λρu on a finite interval (0, h). We give some uniqueness results on q and ρ from the Gelfand spectral data, when the coefficients p and ρ are piecewise Lipschitz and q is bounded. We also prove an equivalence result between the Gelfand spectral data and the Borg-Levinson spectral data. As a consequence, we have similar uniqueness results if we consider the Borg-Levinson spectral data. Finally, we consider thedoi:10.1088/0266-5611/20/5/002 fatcat:gddbkgx3xfhf7olzsxltgfni5a