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 {<i>λ<sub>n</sub></i>} and {<i>µ<sub>n</sub></i>} uniquely determine the potential function <i>q(x)</i> 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 <i>K(x,t)</i> . In particular, we obtain a new proof of the Hochstadt's theorem concerning the structure of the difference q<sup style="margin-left:-6px">~</sup>(x) - q(x).
KW  - Coulomb Potential
KW  -  Spectrum
KW  -  Singular Sturm-Liouville Operator

DO  - 10.3970/cmes.2012.084.001