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

被引：0

作者：

S. A. Buterin

机构：

[1] Saratov State University,

来源：

Differential Equations | 2010年 / 46卷

关键词：

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

D O I：

暂无

中图分类号：

学科分类号：

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：4

共 8 条

[1]

Borg G.(1946)Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe Acta Math. 78 1-96

[2]

Malamud M.M.(1993)Similar Volterra Operators and Related Aspects of the Theory of Fractional Differential Equations Tr. Mosk. Mat. Obs. 55 73-148

[3]

Eremin M.S.(1988)Inverse Problem for Second-Order Integro-Differential Equation with a Singularity Differ. Uravn. 24 350-351

[4]

Yurko V.A.(1991)Inverse Problem for Integro-Differential Operators Mat. Zametki 50 134-144

[5]

Kuryshova Yu.V.(2007)The Inverse Spectral Problem for Integro-Differential Operators Mat. Zametki 81 855-866

[6]

Buterin S.A.(2007)On an Inverse Spectral Problem for a Convolution Integro-Differential Operator Results Math. 50 173-181

[7]

Buterin S.A.(2006)The Inverse Spectral Problem of the Reconstruction of a Convolution Operator Perturbed by a One-Dimensional Operator Mat. Zametki 80 668-682

[8]

Buterin S.A.(2006)The Inverse Problem of Recovering the Volterra Convolution Operator from the Incomplete Spectrum of Its Rank-One Perturbation Inverse Problems 22 2223-2236

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