Identification of the Domain of the Sturm–Liouville Operator on a Star Graph

This article is devoted to the unique recovering of the domain of the Sturm–Liouville operator on a star graph. The domain of the Sturm–Liouville operator is uniquely identified from the set of spectra of a finite number of specially selected canonical problems. In the general case, the domain of th...

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Main Authors:	Baltabek Kanguzhin, Ghulam Hazrat Aimal Rasa, Zhalgas Kaiyrbek
Format:	Article
Language:	English
Published:	MDPI AG 2021-07-01
Series:	Symmetry
Subjects:	boundary conditions boundary value problems canonical problems
Online Access:	https://www.mdpi.com/2073-8994/13/7/1210

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spelling	doaj-b2acae6b38b84ea6916465dc41f0b37d2021-07-23T14:09:18ZengMDPI AGSymmetry2073-89942021-07-01131210121010.3390/sym13071210Identification of the Domain of the Sturm–Liouville Operator on a Star GraphBaltabek Kanguzhin0Ghulam Hazrat Aimal Rasa1Zhalgas Kaiyrbek2Institute of Mathematics and Mathematical Modeling, Al-Farabi Kazakh National University, Almaty 050040, KazakhstanInstitute of Mathematics and Mathematical Modeling, Al-Farabi Kazakh National University, Almaty 050040, KazakhstanInstitute of Mathematics and Mathematical Modeling, Al-Farabi Kazakh National University, Almaty 050040, KazakhstanThis article is devoted to the unique recovering of the domain of the Sturm–Liouville operator on a star graph. The domain of the Sturm–Liouville operator is uniquely identified from the set of spectra of a finite number of specially selected canonical problems. In the general case, the domain of the definition of the original operator can be specified by integro-differential linear forms. In the case when the domain of the Sturm–Liouville operator on a star graph corresponds to the boundary value problem, it is sufficient to choose only finite parts of the spectra of canonical problems for a unique identification of the boundary form. Moreover, the above statement is valid only for a symmetric star graph.https://www.mdpi.com/2073-8994/13/7/1210boundary conditionsboundary value problemscanonical problems
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Baltabek Kanguzhin Ghulam Hazrat Aimal Rasa Zhalgas Kaiyrbek
spellingShingle	Baltabek Kanguzhin Ghulam Hazrat Aimal Rasa Zhalgas Kaiyrbek Identification of the Domain of the Sturm–Liouville Operator on a Star Graph Symmetry boundary conditions boundary value problems canonical problems
author_facet	Baltabek Kanguzhin Ghulam Hazrat Aimal Rasa Zhalgas Kaiyrbek
author_sort	Baltabek Kanguzhin
title	Identification of the Domain of the Sturm–Liouville Operator on a Star Graph
title_short	Identification of the Domain of the Sturm–Liouville Operator on a Star Graph
title_full	Identification of the Domain of the Sturm–Liouville Operator on a Star Graph
title_fullStr	Identification of the Domain of the Sturm–Liouville Operator on a Star Graph
title_full_unstemmed	Identification of the Domain of the Sturm–Liouville Operator on a Star Graph
title_sort	identification of the domain of the sturm–liouville operator on a star graph
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2021-07-01
description	This article is devoted to the unique recovering of the domain of the Sturm–Liouville operator on a star graph. The domain of the Sturm–Liouville operator is uniquely identified from the set of spectra of a finite number of specially selected canonical problems. In the general case, the domain of the definition of the original operator can be specified by integro-differential linear forms. In the case when the domain of the Sturm–Liouville operator on a star graph corresponds to the boundary value problem, it is sufficient to choose only finite parts of the spectra of canonical problems for a unique identification of the boundary form. Moreover, the above statement is valid only for a symmetric star graph.
topic	boundary conditions boundary value problems canonical problems
url	https://www.mdpi.com/2073-8994/13/7/1210
work_keys_str_mv	AT baltabekkanguzhin identificationofthedomainofthesturmliouvilleoperatoronastargraph AT ghulamhazrataimalrasa identificationofthedomainofthesturmliouvilleoperatoronastargraph AT zhalgaskaiyrbek identificationofthedomainofthesturmliouvilleoperatoronastargraph
_version_	1721285658977239040

Identification of the Domain of the Sturm–Liouville Operator on a Star Graph

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