Open Access

ARTICLE

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

Etibar S. Panakhov¹, Murat Sat²

1 Department of Mathematics, Faculty of Science, Firat University, Elazig, 23119, Turkey. Email: epenahov@hotmail.com
2 Department of Mathematics, Faculty of Science and Art, Erzincan University, Erzincan, 24100, Turkey. Email: murat_sat24@hotmail.com

Computer Modeling in Engineering & Sciences 2012, 84(1), 1-12. https://doi.org/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 {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).

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