Inverse indefinite Sturm–Liouville problems with three spectra

We prove that the potential q ( x ) of an indefinite Sturm–Liouville problem on the closed interval [ a , b ] with the indefinite weight function w ( x ) can be determined uniquely by three spectra, which are generated by the indefinite problem defined on [ a , b ] and two right-definite problems defined on [ a , 0 ] and [ 0 , b ] , where point 0 lies in ( a , b ) and is the turning point of the weight function w ( x ) .