scholarly journals Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2989
Author(s):  
Natalia P. Bondarenko
Keyword(s):  
Inverse Problems ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Distribution Coefficients ◽  
Inverse Spectral Problems ◽  
Singular Potentials ◽  
Spectral Problems ◽  
Weyl Matrix ◽  
Method Of Spectral Mappings ◽  
Inverse Spectral

In this paper, we propose an approach to inverse spectral problems for the n-th order (n≥2) ordinary differential operators with distribution coefficients. The inverse problems which consist in the reconstruction of the differential expression coefficients by the Weyl matrix and by several spectra are studied. We prove the uniqueness of solution for these inverse problems, by developing the method of spectral mappings. The results of this paper generalize the previously known results for the second-order differential operators with singular potentials and for the higher-order differential operators with regular coefficients. In the future, the approach of this paper can be used for constructive solution and for investigation of solvability of the considered inverse problems.

Inverse spectral problems for differential operators with non-separated boundary conditions

2020 ◽  
Vol 28 (4) ◽  
pp. 567-616
Author(s):  
Vjacheslav A. Yurko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Short Review ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Separated Boundary Conditions ◽  
Inverse Spectral ◽  
Type Boundary

AbstractWe give a short review of results on inverse spectral problems for second-order differential operators on an interval with non-separated boundary conditions. We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential operators from given spectral characteristics. In the first part of the review, we provide the main results and methods related to inverse problems for Sturm–Liouville operators with non-separated boundary conditions: periodic, quasi-periodic and Robin-type boundary conditions. At the end, we present the main results on inverse problems for differential pencils with non-separated boundary conditions.

scholarly journals Partial inverse problems for Sturm–Liouville operators on trees

2017 ◽  
Vol 147 (5) ◽  
pp. 917-933 ◽  
Author(s):  
Natalia Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Sets ◽  
Spectral Problems ◽  
Partial Inverse ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper, inverse spectral problems for Sturm–Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b – 1 spectral sets uniquely determine the potential functions on a tree with b external edges. Constructive solutions, based on the method of spectral mappings, are provided for the considered inverse problems.

scholarly journals INVERSE SPECTRAL PROBLEMS FOR STURM–LIOUVILLE OPERATORS WITH SINGULAR POTENTIALS. IV. POTENTIALS IN THE SOBOLEV SPACE SCALE

2006 ◽  
Vol 49 (2) ◽  
pp. 309-329 ◽  
Author(s):  
Rostyslav O. Hryniv ◽  
Yaroslav V. Mykytyuk
Keyword(s):  
Sobolev Space ◽  
Spectral Data ◽  
Sufficient Conditions ◽  
Inverse Spectral Problems ◽  
Singular Potentials ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Necessary And Sufficient ◽  
Liouville Operators

AbstractWe solve the inverse spectral problems for the class of Sturm–Liouville operators with singular real-valued potentials from the Sobolev space $W^{s-1}_2(0,1)$, $s\in[0,1]$. The potential is recovered from two spectra or from one spectrum and the norming constants. Necessary and sufficient conditions for the spectral data to correspond to a potential in $W^{s-1}_2(0,1)$ are established.

scholarly journals Inverse problems for the differential operator on the graph with a cycle with different orders on different edges

2015 ◽  
Vol 46 (3) ◽  
pp. 229-243 ◽  
Author(s):  
Natalia Bondarenko
Keyword(s):  
Differential Operator ◽  
Inverse Problems ◽  
Order Differential Operator ◽  
Variable Order ◽  
Uniqueness Theorems ◽  
Inverse Spectral Problems ◽  
Constructive Algorithms ◽  
Spectral Problems ◽  
Inverse Spectral

We consider a variable order differential operator on a graph with a cycle. We study inverse spectral problems for this operator by the system of spectra. Uniqueness theorems are proved, and constructive algorithms are obtained for the solution of the inverse problems.

Sign in / Sign up

Export Citation Format

Share Document