Inverse spectral problem for the one-dimensional Stark operator on the half-axis

  • A. R. Latifova Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku; Baku. state university; Azerbaijan University, Baku
  • A. Kh. Khanmamedov Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku; Baku. state university; Azerbaijan University, Baku
Keywords: one-dimensional Stark operator, inverse spectral problem, spectral data, transformation operator

Abstract

UDC 517.91

We consider the Stark operator $T=-\dfrac{d^{2}}{dx^{2}}+x+q\left(x\right)$ on the half-axis $0\le x<\infty $ with a Dirichlet boundary condition at zero.
By using transformation operators, we study the direct and inverse spectral problems and obtain the main integral equation for the inverse problem.
We prove that the main integral equation is uniquely solvable and suggest an effective algorithm of reconstruction for the perturbed potential.

Author Biography

A. Kh. Khanmamedov, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku; Baku. state university; Azerbaijan University, Baku

 

 

 

 

 

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Published
28.03.2020
How to Cite
LatifovaA. R., and KhanmamedovA. K. “Inverse Spectral Problem for the One-Dimensional Stark Operator on the Half-Axis”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 4, Mar. 2020, pp. 494-08, doi:10.37863/umzh.v72i4.2302.
Section
Research articles