Half inverse problem for operators with singular potential

Abstract

A half-inverse problem for Sturm-Liouville operators consists of reconstruction of this operator by its spectrum and half of the potential. In this study, we show that if q(x) is prescribed on ( pi/2, pi), then, only one spectrum is sufficient to determine q(x) on the interval ( 0, pi/2) for the Sturm-Liouville equation having singularity type 1/sin(2) x on ( 0, pi).