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Nanosystems: Physics, Chemistry, Mathematics, 2015, Volume 6, Issue 1, Pages 63–78
DOI: https://doi.org/10.17586/2220-8054-2015-6-1-63-78 (Mi nano920) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On some applications of the boundary control method to spectral estimation and inverse problems

S. A. Avdonina, A. S. Mikhailovbc, V. S. Mikhailovbd

a Department of Mathematics and Statistics, University of Alaska, Fairbanks, USA
b St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academyof Sciences, St. Petersburg, Russia
c St. Petersburg State University, Faculty of Mathematics and Mechanics, St. Petersburg, Russia
d St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia
Full-text PDF (259 kB) Citations (5)
DOI: https://doi.org/10.17586/2220-8054-2015-6-1-63-78
Abstract: We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method for these problems and show that the solvability of these equations crucially depends on the controllability properties of the corresponding dynamical system and properties of the corresponding families of exponentials.
Keywords: spectral estimation problem, boundary control method, identification problem, inverse problem, Schrödinger equation, hyperbolic system.
Funding agency Grant number
National Science Foundation 1411564
Ministry of Education and Science of the Russian Federation НШ-1771.2014.1
11.38.263.2014
Russian Foundation for Basic Research 14-01-00306
14-01-00535
14-01-31388
International Research Staff Exchange Scheme FP7-PEOPLE-2012
Sergei Avdonin was supported by the NSF grant DMS 1411564; Alexander Mikhaylov was supported by NSh-1771.2014.1, RFBR 14-01-00306, IRSES (FP7-PEOPLE-2012-IRSES Marie Curie Actions); Victor Mikhaylov was supported by RFBR 14-01-00535, RFBR 14-01-31388 and NIR SPbGU 11.38.263.2014.
Received: 05.12.2014
Bibliographic databases:
Document Type: Article
PACS: 02.30 Zz, 02.30 Yy, 02.30 Nw
Language: English
Citation: S. A. Avdonin, A. S. Mikhailov, V. S. Mikhailov, “On some applications of the boundary control method to spectral estimation and inverse problems”, Nanosystems: Physics, Chemistry, Mathematics, 6:1 (2015), 63–78
Citation in format AMSBIB
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\by S.~A.~Avdonin, A.~S.~Mikhailov, V.~S.~Mikhailov
\paper On some applications of the boundary control method to spectral estimation and inverse problems
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2015
\vol 6
\issue 1
\pages 63--78
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\crossref{https://doi.org/10.17586/2220-8054-2015-6-1-63-78}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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