An inverse sturm-Liouville problem by three spectra

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.