Abstract
It is shown that the potential of the Sturm-Liouville equation on interval [0,a] may be restored by the spectra of three boundary problems generated by the equation on the intervals [0,a], [0, 1/2a] and [1/2a,a], respectively. The algorithm of construction is given as well as the sufficient conditions for three sequences of real numbers to be the spectra of the mentioned boundary problems. The problem on [0,a] describes small vibrations of a smooth string with fixed ends. The problems on the half-intervals describe vibrations of the same string clamped at the point of equilibrium.
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