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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Autor principal:	Natalia P. Bondarenko
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	inverse spectral problems higher-order differential operators distribution coefficients weyl matrix uniqueness theorem Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/55fbd74c981446c3a676a5daf6abf553
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spelling	oai:doaj.org-article:55fbd74c981446c3a676a5daf6abf5532021-11-25T18:17:51ZInverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients10.3390/math92229892227-7390https://doaj.org/article/55fbd74c981446c3a676a5daf6abf5532021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2989https://doaj.org/toc/2227-7390In 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.Natalia P. BondarenkoMDPI AGarticleinverse spectral problemshigher-order differential operatorsdistribution coefficientsweyl matrixuniqueness theoremMathematicsQA1-939ENMathematics, Vol 9, Iss 2989, p 2989 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	inverse spectral problems higher-order differential operators distribution coefficients weyl matrix uniqueness theorem Mathematics QA1-939
spellingShingle	inverse spectral problems higher-order differential operators distribution coefficients weyl matrix uniqueness theorem Mathematics QA1-939 Natalia P. Bondarenko Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients
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.
format	article
author	Natalia P. Bondarenko
author_facet	Natalia P. Bondarenko
author_sort	Natalia P. Bondarenko
title	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_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_sort	inverse spectral problems for arbitrary-order differential operators with distribution coefficients
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/55fbd74c981446c3a676a5daf6abf553
work_keys_str_mv	AT nataliapbondarenko inversespectralproblemsforarbitraryorderdifferentialoperatorswithdistributioncoefficients
_version_	1718411381050441728

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

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