INVERSE SINGULAR SPECTRAL PROBLEM VIA HOCSHTADT-LIEBERMAN METHOD

Abstract

In this paper, it is proved that if q (x) is defined on (pi/2, pi], then just one spectrum is enough to determine q (x) on the interval (0,pi/2] for the Sturm-Lioville equation having singularity type delta/x(p), on (0,pi], i.e. if the potential on the half-interval is known, then, it is necessary to reconstruct the potential on the whole interval.