scholarly journals Direct and Inverse Spectral Problems for Rank-One Perturbations of Self-adjoint Operators

2021 ◽  
Vol 93 (2) ◽  
Author(s):  
Oles Dobosevych ◽  
Rostyslav Hryniv
Keyword(s):  
Inverse Problem ◽  
Discrete Spectrum ◽  
Adjoint Operator ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Rank One ◽  
Inverse Spectral ◽  
Adjoint Operators

AbstractFor a given self-adjoint operator A with discrete spectrum, we completely characterise possible eigenvalues of its rank-one perturbations B and discuss the inverse problem of reconstructing B from its spectrum.

scholarly journals NUMERICAL METHOD FOR SOLVING INVERSE SPECTRAL PROBLEMS GENERATED BY PERTURBED SELF-ADJOINT OPERATORS

2017 ◽  
Vol 19 (9.1) ◽  
pp. 5-11
Author(s):  
S.I. Kadchenko
Keyword(s):  
Numerical Method ◽  
Computational Efficiency ◽  
Spectral Characteristics ◽  
Adjoint Operator ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Discrete Operators ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Adjoint Operators

A new numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators from their spectral characteristics is developed. The method was tested on the problems for perturbed Sturm - Liouville operator. The results of numerous calculations have shown its computational efficiency. The simple algebraic formulas for finding the eigenvalues of discrete operators was found. At that the calculation of eigenvalues of perturbed self-adjoint operator can start from any number, no matter known the eigenvalues from previous numbers or not.

scholarly journals Determination of differential pencils with impulse from interior spectral data

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongxia Guo ◽  
Guangsheng Wei ◽  
Ruoxia Yao
Keyword(s):  
Spectral Data ◽  
Interior Point ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral ◽  
Differential Pencils ◽  
Second Spectrum

Abstract In this paper, we are concerned with the inverse spectral problems for differential pencils defined on $[0,\pi ]$ [ 0 , π ] with an interior discontinuity. We prove that two potential functions are determined uniquely by one spectrum and a set of values of eigenfunctions at some interior point $b\in (0,\pi )$ b ∈ ( 0 , π ) in the situation of $b=\pi /2$ b = π / 2 and $b\neq \pi /2$ b ≠ π / 2 . For the latter, we need the knowledge of a part of the second spectrum.

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