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

被引：32

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

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