scholarly journals A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph

2017 ◽  
Vol 8 (1) ◽  
pp. 155-168 ◽  
Author(s):  
Natalia P. Bondarenko
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph ◽  
Partial Inverse Problem

scholarly journals A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph

2018 ◽  
Vol 49 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Basis Property ◽  
Singular Potentials ◽  
Main Ingredient ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph ◽  
Partial Inverse Problem ◽  
Liouville Operators

Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the potentials on the remaining edges can be constructed by fractional parts of two spectra. A uniqueness theorem is proved, and an algorithm for the constructive solution of the partial inverse problem is provided. The main ingredient of the proofs is the Riesz-basis property of specially constructed systems of functions.

scholarly journals A partial inverse problem for the Sturm-Liouville operator on the lasso-graph

2019 ◽  
Vol 13 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Chuan-Fu Yang ◽  
◽  
Natalia Pavlovna Bondarenko ◽  
◽  
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Partial Inverse Problem

Partial inverse problems for the Sturm–Liouville operator on a star-shaped graph with mixed boundary conditions

2018 ◽  
Vol 26 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Mixed Boundary ◽  
Constructive Method ◽  
Asymptotic Formulas ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph

AbstractThe Sturm–Liouville operator on a star-shaped graph with different types of boundary conditions (Robin and Dirichlet) in different vertices is studied. Asymptotic formulas for the eigenvalues are derived and partial inverse problems are solved: we show that the potential on one edge can be uniquely determined by different parts of the spectrum if the potentials on the other edges are known. We provide a constructive method for the solution of the inverse problems, based on the Riesz basis property of some systems of vector functions.

A partial inverse problem for quantum graphs with a loop

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng-Yu Guan ◽  
Chuan-Fu Yang ◽  
Dong-Jie Wu
Keyword(s):  
Inverse Problem ◽  
Internal Vertex ◽  
Boundary Vertex ◽  
Boundary Edge ◽  
Quantum Graphs ◽  
Jump Conditions ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Partial Inverse Problem ◽  
The Uniqueness Theorem

AbstractWe consider the Sturm–Liouville operator on quantum graphs with a loop with the standard matching conditions in the internal vertex and the jump conditions at the boundary vertex. Given the potential on the loop, we try to recover the potential on the boundary edge from the subspectrum. The uniqueness theorem and a constructive algorithm for the solution of this partial inverse problem are provided.

scholarly journals An inverse problem for the non-self-adjoint matrix Sturm-Liouville operator

2018 ◽  
Vol 50 (1) ◽  
pp. 71-102 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Sufficient Conditions ◽  
Adjoint Matrix ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Necessary And Sufficient

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient conditions for the solvability of the inverse problem. Our approach is based on the constructive solution of the inverse problem by the method of spectral mappings. The characterization of the spectral data in the self-adjoint case is given as a corollary of the main result.

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