scholarly journals On a Discrete Inverse Problem for Two Spectra

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Gusein Sh. Guseinov
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Finite Order ◽  
Inverse Spectral Problem ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Symmetric Matrices ◽  
The Matrix ◽  
Inverse Spectral

A version of the inverse spectral problem for two spectra of finite-order real Jacobi matrices (tridiagonal symmetric matrices) is investigated. The problem is to reconstruct the matrix using two sets of eigenvalues: one for the original Jacobi matrix and one for the matrix obtained by deleting the last row and last column of the Jacobi matrix.

Inverse problem about two-spectra for finite Jacobi matrices with zero diagonal

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Adil Huseynov
Keyword(s):  
Inverse Problem ◽  
Finite Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Jacobi Matrices ◽  
The Matrix ◽  
Explicit Procedure ◽  
Necessary And Sufficient

AbstractThe necessary and sufficient conditions for solvability of the inverse problem about two-spectra for finite order real Jacobi matrices with zero-diagonal elements are established. An explicit procedure of reconstruction of the matrix from the two-spectra is given.

scholarly journals On an inverse spectral problem for a quadratic Jacobi matrix pencil

2005 ◽  
Vol 306 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Yuri Agranovich ◽  
Tomas Azizov ◽  
Andrei Barsukov ◽  
Aad Dijksma
Keyword(s):  
Spectral Problem ◽  
Inverse Spectral Problem ◽  
Jacobi Matrix ◽  
Matrix Pencil ◽  
Inverse Spectral

scholarly journals An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
I. Dehghani Tazehkand ◽  
A. Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Spectral Characteristics ◽  
Star Graph ◽  
Dirichlet Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Robin Boundary

We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

On an inverse spectral problem for one integro-differential operator of fractional order

2019 ◽  
Vol 27 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Mikhail Ignatiev
Keyword(s):  
Inverse Problem ◽  
Differential Operator ◽  
Spectral Problem ◽  
Fractional Order ◽  
Inverse Spectral Problem ◽  
A Priori ◽  
A Priori Information ◽  
Inverse Spectral ◽  
Priori Information

Abstract An inverse spectral problem for some integro-differential operator of fractional order {\alpha\in(1,2)} is studied. We show that the specification of the spectrum together with a certain a priori information about the structure of the operator determines such operator uniquely. The proof is constructive and provides a procedure for solving the inverse problem.

scholarly journals Inverse spectral problem for the Hill operator on the graph with a loop

2020 ◽  
Author(s):  
Rakib Efendiev
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Spectral Properties ◽  
Inverse Spectral Problem ◽  
Hill Operator ◽  
Inverse Spectral ◽  
Definition Of ◽  
The Hill ◽  
The Uniqueness Theorem

In this paper, we investigate a generalization of the classical a PT-symmetric Hill operator to lasso graph. The definition of the PT-symmetric Hill operator on lasso graph is given and derived its spectral properties. We solved the inverse problem, proved the uniqueness theorem and provided a constructive procedure for the solution of the inverse problem.

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