The inverse scattering problem for a discrete Sturm-Liouville equation on the line

被引：3

作者：

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

机构：

[1] Baku State Univ, Baku, Azerbaijan

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

来源：

SBORNIK MATHEMATICS | 2011年 / 202卷 / 07期

关键词：

the inverse spectral problem; Jacobi operators; scattering problem; Weyl function;

D O I：

10.1070/SM2011v202n07ABEH004178

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates the inverse scattering problem for a discrete Sturm-Liouville equation on the entire line with coefficients that stabilize to zero in one direction. We derive a necessary and a sufficient condition on the scattering data so that the inverse problem is uniquely solvable.

引用

页码：1071 / 1083

页数：13

共 50 条

[1] Inverse Scattering Problem for a Difference Sturm-Liouville Equation on the Line
Khanmamedov, A. Kh.
Makhmudova, M. G.
[J]. AZERBAIJAN JOURNAL OF MATHEMATICS, 2012, 2 (01): : 24 - 36
[2] Inverse scattering problem for a discrete Sturm-Liouville operator on the entire line
Ag. Kh. Khanmamedov
[J]. Doklady Mathematics, 2010, 81 : 188 - 189
[3] Inverse scattering problem for a discrete Sturm-Liouville operator on the entire line
Khanmamedov, Ag. Kh.
[J]. DOKLADY MATHEMATICS, 2010, 81 (02) : 188 - 189
[4] Inverse scattering on the line for the matrix Sturm-Liouville equation
Bondarenko, Natalia
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (03) : 2073 - 2105
[5] Inverse spectral problem for the Sturm-Liouville equation
Brown, BM
Samko, VS
Knowles, IW
Marletta, M
[J]. INVERSE PROBLEMS, 2003, 19 (01) : 235 - 252
[6] Inverse scattering problem with Levinson formula for eigenparameter-dependent discrete Sturm-Liouville equation
Koprubasi, Turhan
Mohapatra, Ram N.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (02) : 1466 - 1478
[7] THE SCATTERING PROBLEM FOR A DISCRETE STURM-LIOUVILLE OPERATOR
APTEKAREV, AI
NIKISHIN, EM
[J]. MATHEMATICS OF THE USSR-SBORNIK, 1983, 121 (3-4): : 325 - 355
[8] Corrigendum to "Inverse scattering problem with Levinson formula for eigenparameter-dependent discrete Sturm-Liouville equation"
Koprubasi, Turhan
Mohapatra, R. N.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (18) : 19452 - 19458
[9] Inverse Hochstadt problem for singular Sturm-Liouville equation
Gasimov, ZM
[J]. PROCEEDINGS OF THE SECOND ISAAC CONGRESS, VOLS 1 AND 2, 2000, 7 : 1249 - 1254
[10] Inverse problem for the Sturm-Liouville equation on a simple graph
Pivovarchik, V
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 32 (04) : 801 - 819

← 1 2 3 4 5 →