Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients
In this paper, we propose an approach to inverse spectral problems for the <i>n</i>-th order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo&g...
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| 语言: | English |
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MDPI AG
2021-11-01
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| 丛编: | Mathematics |
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| 在线阅读: | https://www.mdpi.com/2227-7390/9/22/2989 |
| _version_ | 1827676155623243776 |
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| author | Natalia P. Bondarenko |
| author_facet | Natalia P. Bondarenko |
| author_sort | Natalia P. Bondarenko |
| collection | DOAJ |
| description | In this paper, we propose an approach to inverse spectral problems for the <i>n</i>-th order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-10T05:17:43Z |
| format | Article |
| id | doaj.art-55fbd74c981446c3a676a5daf6abf553 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:17:43Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-55fbd74c981446c3a676a5daf6abf5532023-11-23T00:16:08ZengMDPI AGMathematics2227-73902021-11-01922298910.3390/math9222989Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution CoefficientsNatalia P. Bondarenko0Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, 443086 Samara, RussiaIn this paper, we propose an approach to inverse spectral problems for the <i>n</i>-th order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/9/22/2989inverse spectral problemshigher-order differential operatorsdistribution coefficientsweyl matrixuniqueness theorem |
| spellingShingle | Natalia P. Bondarenko Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients Mathematics inverse spectral problems higher-order differential operators distribution coefficients weyl matrix uniqueness theorem |
| title | Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients |
| title_full | Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients |
| title_fullStr | Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients |
| title_full_unstemmed | Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients |
| title_short | Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients |
| title_sort | inverse spectral problems for arbitrary order differential operators with distribution coefficients |
| topic | inverse spectral problems higher-order differential operators distribution coefficients weyl matrix uniqueness theorem |
| url | https://www.mdpi.com/2227-7390/9/22/2989 |
| work_keys_str_mv | AT nataliapbondarenko inversespectralproblemsforarbitraryorderdifferentialoperatorswithdistributioncoefficients |