2019
Том 71
№ 8

# Panakhov E. S.

Articles: 2
Article (English)

### Inverse problem for interior spectral data of the hydrogen atom equation

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1516-1525

We consider the inverse problem for second-order differential operators with regular singularity and show that the potential function can be uniquely determined by the set of values of eigenfunctions at some interior point and parts of two spectra.

Brief Communications (English)

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

Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 132–138

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 $\widetilde{q}(r) - q(r)$.