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Funktsional'nyi Analiz i ego Prilozheniya, 2012, Volume 46, Issue 1, Pages 65–70
DOI: https://doi.org/10.4213/faa3062 (Mi faa3062) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Brief communications

Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for the Matrix Sturm–Liouville Operator

N. P. Bondarenko

Saratov State University named after N. G. Chernyshevsky
Full-text PDF (196 kB) Citations (8)
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DOI: https://doi.org/10.4213/faa3062
Abstract: The matrix Sturm–Liouville operator on a finite interval with Dirichlet boundary conditions is studied. Properties of its spectral characteristics and the inverse problem of recovering the operator from these characteristics are investigated. Necessary and sufficient conditions on the spectral data of the operator are obtained. Research is conducted in the general case, with no a priori restrictions on the spectrum. A constructive algorithm for solving the inverse problem is provided.
Keywords: matrix Sturm–Liouville operator, spectral data, inverse spectral problem, necessary and sufficient condition.
Received: 13.01.2011
English version:
Functional Analysis and Its Applications, 2012, Volume 46, Issue 1, Pages 53–57
DOI: https://doi.org/10.1007/s10688-012-0006-4
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: N. P. Bondarenko, “Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for the Matrix Sturm–Liouville Operator”, Funktsional. Anal. i Prilozhen., 46:1 (2012), 65–70; Funct. Anal. Appl., 46:1 (2012), 53–57
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/faa3062
  • https://doi.org/10.4213/faa3062
  • https://www.mathnet.ru/eng/faa/v46/i1/p65
    Erratum
    This publication is cited in the following 8 articles:
    1. Bondarenko N.P., “Inverse Problem Solution and Spectral Data Characterization For the Matrix Sturm-Liouville Operator With Singular Potential”, Anal. Math. Phys., 11:4 (2021), 145  crossref  mathscinet  isi
    2. Bondarenko N.P., “Constructive Solution of the Inverse Spectral Problem For the Matrix Sturm-Liouville Operator”, Inverse Probl. Sci. Eng., 28:9 (2020), 1307–1330  crossref  mathscinet  isi
    3. Bondarenko N.P., “Spectral Data Characterization For the Sturm-Liouville Operator on the Star-Shaped Graph”, Anal. Math. Phys., 10:4 (2020), 83  crossref  mathscinet  zmath  isi  scopus
    4. Bondarenko N., “Recovery of the matrix quadratic differential pencil from the spectral data”, J. Inverse Ill-Posed Probl., 24:3 (2016), 245–263  crossref  mathscinet  zmath  isi  elib  scopus
    5. B. Chanane, “Eigenvalues of vectorial Sturm-Liouville problems with parameter dependent boundary conditions”, Abstr. Appl. Anal., 2015, 796086, 9 pp.  crossref  mathscinet  scopus
    6. N. Bondarenko, G. Freiling, “An inverse problem for the quadratic pencil of non-self-adjoint matrix operators on the half-line”, J. Inverse Ill-Posed Probl., 22:4 (2014), 467–495  crossref  mathscinet  zmath  isi  scopus
    7. N. P. Bondarenko, “An inverse problem for the matrix quadratic pencil on a finite interval”, Eurasian Math. J., 4:3 (2013), 20–31  mathnet
    8. V. Yurko, “Recovering arbitrary order differential operators on noncompact star-type graphs”, Methods Funct. Anal. Topology, 18:1 (2012), 90–100  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    References:108
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