On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum

被引：31

作者：

Buterin, S. A. ^{[1
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Saratov, Russia

来源：

DIFFERENTIAL EQUATIONS | 2010年 / 46卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Inverse Problem; Convolution Operator; Liouville Operator; Nonlinear Integral Equation; Liouville Problem;

D O I：

10.1134/S0012266110010167

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the sum of the Sturm-Liouville operator and a convolution operator. We study the inverse problem of reconstructing the convolution operator from the spectrum. This problem is reduced to a nonlinear integral equation with a singularity. We prove the global solvability of this nonlinear equation, which permits one to show that the asymptotics of the spectrum is a necessary and sufficient condition for the solvability of the inverse problem. The proof is constructive.

引用

页码：150 / 154

页数：5

共 50 条

[1] On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum
S. A. Buterin
Differential Equations, 2010, 46 : 150 - 154
[2] On the restoration of an operator of Sturm-Liouville by one spectrum
Shaldanbayev, Amir
Orazov, Isabek
Shomanbayeva, Manat
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014), 2014, 1611 : 53 - 57
[3] On the reconstruction of the potential in the inverse problem for a power of the Sturm-Liouville operator
Tomin N.G.
Journal of Mathematical Sciences, 2005, 126 (5) : 1485 - 1494
[4] Asymptotics of the Spectrum of the Sturm-Liouville Operator with Local Interaction
Ismagilov, R. S.
Kostyuchenko, A. G.
DOKLADY MATHEMATICS, 2010, 82 (01) : 596 - 598
[5] On the spectrum of the Sturm-Liouville operator with degenerate boundary conditions
Makin, A. S.
DOKLADY MATHEMATICS, 2011, 83 (02) : 161 - 164
[6] Asymptotics of the spectrum of the Sturm-Liouville operator with local interaction
R. S. Ismagilov
A. G. Kostyuchenko
Doklady Mathematics, 2010, 82 : 596 - 598
[7] Invariant transformations for the Sturm-Liouville operator
Vagharshakyan A.
Journal of Mathematical Sciences, 2006, 139 (2) : 6374 - 6392
[8] On the spectrum of the Sturm-Liouville operator with degenerate boundary conditions
A. S. Makin
Doklady Mathematics, 2011, 83 : 161 - 164
[9] Asymptotics of the spectrum of the Sturm-Liouville operator with regular boundary conditions
Makin, A. S.
DIFFERENTIAL EQUATIONS, 2008, 44 (05) : 645 - 658
[10] Characterization of the spectrum of the Sturm-Liouville operator with irregular boundary conditions
Makin, A. S.
DIFFERENTIAL EQUATIONS, 2010, 46 (10) : 1427 - 1437

← 1 2 3 4 5 →