Inverse problem for a singular differential operator

Abstract

In this paper, we give the solution of the inverse Sturm–Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadt’s theorem concerning the structure of the difference q ( x ) − q ̃ ( x ) for the singular Sturm Liouville problem defined on the finite interval ( 0 , π ) having the singularity type 1 4 sin 2 x at the points 0 and π .