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Half inverse problem for singular differential operator

A spectral analysis for the Sturm–Liouville equation defined on (0,1] and singularity of type at zero is investigated (l is an integer). As known, the potential function q(x) in the singular Sturm–Liouville problem can be uniquely determined from two spectrum. In this study, we show that if q(x) is prescribed on (1/2,1], then only one spectrum is sufficient to determine q(x) on the interval (0,1/2).