2019
Том 71
№ 11

All Issues

Khanmamedov A. Kh.

Articles: 4
Brief Communications (Russian)

On the spectral properties of the one-dimensional Stark operator on the half-line

Khanmamedov A. Kh., Makhmudova M. G.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1579-1584

UDC 517.9
We consider a one-dimensional Stark operator on a half-line with the Dirichlet boundary condition at zero. The asymptotic behavior of the eigenvalues at infinity is found.

Article (Russian)

On the inverse scattering problem for the one-dimensional Schrödinger equation with growing potential

Guseinov I. M., Khanmamedov A. Kh.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 10. - pp. 1390-1402

We consider a one-dimensional Schrödinger equation on the entire axis whose potential rapidly decreases at the left end and infinitely increases at the right end. By the method of transformation operators, we study the inverse scattering problem. We establish conditions for the scattering data under which the inverse problem is solvable. The basic Marchenko-type integral equations are investigated and their unique solvability is established.

Brief Communications (Russian)

On conditions for the discreteness of the spectrum of a semiinfinite Jacobi matrix with zero diagonal

Khanmamedov A. Kh., Masmaliev G. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 285–288

We establish sufficient conditions for the discreteness of the spectrum of a second-order self-adjoint difference operator generated by a semiinfinite Jacobi matrix with zero principal diagonal.

Brief Communications (Russian)

Rapidly Decreasing Solution of the Initial Boundary-Value Problem for the Toda Lattice

Khanmamedov A. Kh.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1144 – 1152

Using the inverse scattering transform, we investigate an initial boundary-value problem with zero boundary condition for the Toda lattice. We prove the existence and uniqueness of a rapidly decreasing solution and determine a class of initial data that guarantees the existence of a rapidly decreasing solution.