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    On the Determination of the Singular Sturm-Liouville Operator from Two Spectra

    Etibar S. Panakhov1, Murat Sat2

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 1-12, 2012, DOI:10.3970/cmes.2012.084.001

    Abstract 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 {λn} and {µn} 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). More >

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