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

  • E. S. Panakhov Firat Univ., Elazig, Turkey
  • R. Yilmazer

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 $\widetilde{q}(r) - q(r)$.
Published
25.01.2006
How to Cite
PanakhovE. S., and YilmazerR. “On Inverse Problem for Singular Sturm-Liouville Operator from Two Spectra”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 1, Jan. 2006, pp. 132–138, https://umj.imath.kiev.ua/index.php/umj/article/view/3440.
Section
Short communications