2017
Том 69
№ 6

All Issues

On inverse problem for singular Sturm-Liouville operator from two spectra

Panakhov E. S., Yilmazer R.

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Abstract

In the paper, an inverse problem with two given spectra for second order differential operator with singularity of type $\cfrac{2}{r} + \cfrac{l(l+1)}{r^2}$ (here, $l$ is a positive integer or zero) at zero point is studied. It is well known that two spectra $\{\lambda_n\}$ and $\{\mu_n\}$ uniquely determine the potential function $q(r)$ in a singular Sturm-Liouville equation defined on interval $(0, \pi]$.
One of the aims of the paper is to prove the generalized degeneracy of the kernel $K(r, s)$. In particular, we obtain a new proof of Hochstadt's theorem concerning the structure of the difference $\widetilde{q}(r) - q(r)$.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 1, pp 147-154.

Citation Example: Panakhov E. S., Yilmazer R. On inverse problem for singular Sturm-Liouville operator from two spectra // Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 132–138.

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