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.

scholarly journals An inverse spectral problem for non-selfadjoint Sturm-Liouville operators with nonseparated boundary conditions

2012 ◽  
Vol 43 (2) ◽  
pp. 289-299 ◽  
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Inverse Spectral Problem ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Nonseparated Boundary Conditions ◽  
Sturm Liouville ◽  
Liouville Operators

Non-selfadjoint Sturm-Liouville operators on a finite interval with nonseparated boundary conditions are studied. We establish properties of the spectral characteristics and investigate an inverse problem of recovering the operators from their spectral data. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing the solution.

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.

scholarly journals Inverse spectral problems for differential operators on a graph with a rooted cycle

2009 ◽  
Vol 40 (3) ◽  
pp. 271-286 ◽  
Author(s):  
V. Yurko
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Inverse Spectral Problems ◽  
Matching Conditions ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral

An inverse spectral problem is studied for Sturm-Liouville differential operators on graphs with a cycle and with standard matching conditions in internal vertices. A uniqueness theorem is proved, and a constructive procedure for the solution is provided.

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 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.

scholarly journals An inverse spectral problem for differential operators with integral delay

2011 ◽  
Vol 42 (3) ◽  
pp. 295-303 ◽  
Author(s):  
Yulia Kuryshova
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Integral Transform ◽  
Main Tool ◽  
One Dimensional ◽  
Sturm Liouville ◽  
The Uniqueness Theorem

The uniqueness theorem is proved for the solution of the inverse spec- tral problem for second-order integro-di®erential operators on a ¯nite interval. These operators are perturbations of the Sturm-Liouville operator with convolution and one- dimensional operators. The main tool is an integral transform connected with solutions of integro-di®erential operators.

scholarly journals INVERSE SPECTRAL PROBLEMS FOR SINGULAR RANK-ONE PERTURBATIONS OF A HILL OPERATOR

2009 ◽  
Vol 87 (3) ◽  
pp. 421-428
Author(s):  
KAZUSHI YOSHITOMI
Keyword(s):  
Inverse Spectral Problem ◽  
Real Sequence ◽  
Inverse Spectral Problems ◽  
Necessary And Sufficient Condition ◽  
Hill Operator ◽  
Rank One Perturbation ◽  
Rank One ◽  
Inverse Spectral ◽  
Necessary And Sufficient ◽  
The Hill

AbstractWe investigate an inverse spectral problem for the singular rank-one perturbations of a Hill operator. We give a necessary and sufficient condition for a real sequence to be the spectrum of a singular rank-one perturbation of the Hill operator.

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