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) over tilde (x) for the singular Sturm Liouville problem defined on the finite interval (0, pi) having the singularity type 1/4sin(2)x at the points 0 and pi. (c) 2007 Elsevier Ltd. All rights reserved.