Inverse Spectral Problem for the One-Dimensional Stark Operator on the Semiaxis

被引：2

作者：

Latifova, A. R. ^{[1
,2
,3
]}

Khanmamedov, A. Kh. ^{[1
,2
,3
]}

机构：

[1] Azerbaijan Natl Acad Sci, Inst Math & Mech, Baku, Azerbaijan

[2] Baku State Univ, Baku, Azerbaijan

[3] Azerbaijan Univ, Baku, Azerbaijan

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2020年 / 72卷 / 04期

关键词：

SCHRODINGER-EQUATION; HARMONIC-OSCILLATOR;

D O I：

10.1007/s11253-020-01801-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Stark operator T = -d(2)/dx(2) + x + q on the semiaxis 0 <= x < infinity with Dirichlet boundary condition at the origin. By the method of transformation operators, we study the direct and inverse spectral problems, deduce the main integral equation for the inverse problem, and prove that this equation is uniquely solvable. We also propose an effective algorithm of reconstruction of the perturbation potential.

引用

页码：568 / 584

页数：17

共 50 条

[1] Inverse Spectral Problem for the One-Dimensional Stark Operator on the Semiaxis
A. R. Latifova
A. Kh. Khanmamedov
Ukrainian Mathematical Journal, 2020, 72 : 568 - 584
[2] On the Inverse Spectral Problem for the One-dimensional Stark Operator on the Semiaxis
Khanmamedov, A. Kh.
Huseynova, Y. I.
AZERBAIJAN JOURNAL OF MATHEMATICS, 2024, 14 (01): : 122 - 132
[3] On Spectral Properties of the One-Dimensional Stark Operator on the Semiaxis
M. G. Makhmudova
A. Kh. Khanmamedov
Ukrainian Mathematical Journal, 2020, 71 : 1813 - 1819
[4] On Spectral Properties of the One-Dimensional Stark Operator on the Semiaxis
Makhmudova, M. G.
Khanmamedov, A. Kh
UKRAINIAN MATHEMATICAL JOURNAL, 2020, 71 (11) : 1813 - 1819
[5] One remark on the inverse scattering problem for the perturbed Stark operator on the semiaxis
Khanmamedov, Agil K.
Abbasova, Khatira E.
GEORGIAN MATHEMATICAL JOURNAL, 2022, 29 (02) : 225 - 228
[6] Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator
S. A. Buterin
Mathematical Notes, 2006, 80 : 631 - 644
[7] Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator
Buterin, S. A.
MATHEMATICAL NOTES, 2006, 80 (5-6) : 631 - 644
[8] An inverse problem of scattering theory for the perturbed Stark operator on the semiaxis
Ahmedova, Aynur R.
GEORGIAN MATHEMATICAL JOURNAL, 2015, 22 (03) : 295 - 304
[9] Inverse Spectral Problem of Teconstructing One-dimensional Perturbation of Integral Volterra Operator
Buterin, S. A.
IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2006, 6 (01): : 3 - 11
[10] Optimization Inverse Spectral Problem for the One-Dimensional Schrodinger Operator on the Entire Real Line
Sadovnichii, V. A.
Sultanaev, Ya. T.
Valeev, N. F.
DIFFERENTIAL EQUATIONS, 2024, 60 (04) : 465 - 471

← 1 2 3 4 5 →