scholarly journals Inverse problem solution and spectral data characterization for the matrix Sturm–Liouville operator with singular potential

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Natalia P. Bondarenko
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Liouville Operator ◽  
Singular Potential ◽  
Problem Solution ◽  
Inverse Problem Solution ◽  
The Matrix ◽  
Sturm Liouville

scholarly journals Recovery of the matrix quadratic differential pencil from the spectral data

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Natalia Bondarenko
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Spectral Data ◽  
Quadratic Differential ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
The Matrix ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Liouville Operators

AbstractWe consider a pencil of matrix Sturm–Liouville operators on a finite interval. We study the properties of its spectral characteristics and inverse problems that consist in the recovering of the pencil by the spectral data, that is, eigenvalues and so-called weight matrices. This inverse problem is reduced to a linear equation in a Banach space by the method of spectral mappings. A constructive algorithm for the solution of the inverse problem is provided.

scholarly journals Solving An Inverse Problem For The Sturm-Liouville Operator With A Singular Potential By Yurko's Method

2020 ◽  
Vol 52 (1) ◽  
Author(s):  
Natalia P. Bondarenko
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Singular Potential ◽  
Inverse Spectral Problem ◽  
Sufficient Conditions ◽  
The Self ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
The Uniqueness Theorem

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint cases.

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