Reconstruction of Higher-Order Differential Operators by Their Spectral Data
This paper is concerned with inverse spectral problems for higher-order (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>2</mn></mrow>&l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/20/3882 |
| _version_ | 1797471728443588608 |
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| author | Natalia P. Bondarenko |
| author_facet | Natalia P. Bondarenko |
| author_sort | Natalia P. Bondarenko |
| collection | DOAJ |
| description | This paper is concerned with inverse spectral problems for higher-order (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula>) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either regular or distribution coefficients. Our approach is based on the reduction of an inverse problem to a linear equation in the Banach space of bounded infinite sequences. This equation is derived in a general form that can be applied to various classes of differential operators. The unique solvability of the linear main equation is also proved. By using the solution of the main equation, we derive reconstruction formulas for the differential expression coefficients in the form of series and prove the convergence of these series for several classes of operators. The results of this paper can be used for the constructive solution of inverse spectral problems and for the investigation of their solvability and stability. |
| first_indexed | 2024-03-09T19:52:20Z |
| format | Article |
| id | doaj.art-93eb0f934d9449f38e46cbb4cdaddb9c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T19:52:20Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-93eb0f934d9449f38e46cbb4cdaddb9c2023-11-24T01:07:57ZengMDPI AGMathematics2227-73902022-10-011020388210.3390/math10203882Reconstruction of Higher-Order Differential Operators by Their Spectral DataNatalia P. Bondarenko0Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara 443086, RussiaThis paper is concerned with inverse spectral problems for higher-order (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula>) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either regular or distribution coefficients. Our approach is based on the reduction of an inverse problem to a linear equation in the Banach space of bounded infinite sequences. This equation is derived in a general form that can be applied to various classes of differential operators. The unique solvability of the linear main equation is also proved. By using the solution of the main equation, we derive reconstruction formulas for the differential expression coefficients in the form of series and prove the convergence of these series for several classes of operators. The results of this paper can be used for the constructive solution of inverse spectral problems and for the investigation of their solvability and stability.https://www.mdpi.com/2227-7390/10/20/3882inverse spectral problemshigher-order differential operatorsdistribution coefficientsconstructive solutionmethod of spectral mappings |
| spellingShingle | Natalia P. Bondarenko Reconstruction of Higher-Order Differential Operators by Their Spectral Data Mathematics inverse spectral problems higher-order differential operators distribution coefficients constructive solution method of spectral mappings |
| title | Reconstruction of Higher-Order Differential Operators by Their Spectral Data |
| title_full | Reconstruction of Higher-Order Differential Operators by Their Spectral Data |
| title_fullStr | Reconstruction of Higher-Order Differential Operators by Their Spectral Data |
| title_full_unstemmed | Reconstruction of Higher-Order Differential Operators by Their Spectral Data |
| title_short | Reconstruction of Higher-Order Differential Operators by Their Spectral Data |
| title_sort | reconstruction of higher order differential operators by their spectral data |
| topic | inverse spectral problems higher-order differential operators distribution coefficients constructive solution method of spectral mappings |
| url | https://www.mdpi.com/2227-7390/10/20/3882 |
| work_keys_str_mv | AT nataliapbondarenko reconstructionofhigherorderdifferentialoperatorsbytheirspectraldata |