Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator

被引：11

作者：

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

机构：

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

来源：

MATHEMATICAL NOTES | 2006年 / 80卷 / 5-6期

基金：

俄罗斯基础研究基金会;

关键词：

inverse spectral reconstruction problem; convolution operator; nonlinear integral equation; Fredholm alternative; Hilbert-Schmidt operator;

D O I：

10.1007/s11006-006-0184-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a one-dimensional perturbation of the convolution operator. We study the inverse reconstruction problem for the convolution component using the characteristic numbers under the assumption that the perturbation summand is known a priori. The problem is reduced to the solution of the so-called basic nonlinear integral equation with singularity. We prove the global solvability of this nonlinear equation. On the basis of these results, we prove a uniqueness theorem and obtain necessary and sufficient conditions for the soh.-ability of the inverse problem.

引用

页码：631 / 644

页数：14