On the determination of the singular sturm-liouville operator from two spectra

In this paper an inverse problem by two given spectrum for a secondorder differential operator with coulomb singularity of the type Ax in zero point ( here A is constant), is studied. It is well known that two spectrum λn and μn uniquely determine the potential function q(x) in the singular Sturm-Liouville equation defined on interval (0;p] : The aim of this paper is to prove the generalized degeneracy of the kernel K(x; t) . In particular, we obtain a new proof of the Hochstadt's theorem concerning the structure of the difference eq(x)q∼(x). Copyright © 2012 Tech Science Press.