TY - EJOU
AU - Panakhov, Etibar S.
AU - Sat, Murat
TI - On the Determination of the Singular Sturm-Liouville Operator from Two Spectra
T2 - Computer Modeling in Engineering \& Sciences
PY - 2012
VL - 84
IS - 1
SN - 1526-1506
AB - In this paper an inverse problem by two given spectrum for a second-order differential operator with coulomb singularity of the type A/x in zero point ( here A is constant), is studied. It is well known that two spectrum {*λ*_{n}} and {*µ*_{n}} uniquely determine the potential function *q(x)* in the singular Sturm-Liouville equation defined on interval (0,π]. 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 q^{~}(x) - q(x).
KW - Coulomb Potential
KW - Spectrum
KW - Singular Sturm-Liouville Operator
DO - 10.3970/cmes.2012.084.001