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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2022, Volume 7, Issue 4, Pages 395–411
DOI: https://doi.org/10.47475/2500-0101-2022-17401 (Mi chfmj297) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Examples of generalized elementary solutions in linear inverse problems

M. Al-Mohamedab, I. V. Tikhonovac

a Lomonosov Moscow State University, Moscow, Russia
b Moscow Technical University of Communications and Informatics, Moscow, Russia
c Moscow Pedagogical State University, Moscow, Russia
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DOI: https://doi.org/10.47475/2500-0101-2022-17401
Abstract: One fragment from the theory of inverse problems for second-order abstract differential equations is presented in detail. We consider a spectral problem which related to a linear inverse problem with parameters in the final condition. It is shown that eigenvalues of the spectral problem is expressed through zeros of an elementary entire function. For certain combinations of the parameters, some zeros can be multiples with multiplicity two. Then it is possible to appear generalized elementary solutions for the inverse problem. Explicit formulas for such solutions are given. We provide specific examples of inverse problems where general ideas are put into the practice.
Keywords: abstract differential equation of the second order, inverse problem, spectral problem, multiple zeros of characteristic function, generalized elementary solutions of inverse problem.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
The work was prepared with the financial support of the Ministry of Education and Science of Russia as part of the implementation of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement № 075-15-2022-284.
Received: 11.08.2022
Revised: 23.09.2022
Bibliographic databases:
Document Type: Article
UDC: 517.95+517.984
Language: Russian
Citation: M. Al-Mohamed, I. V. Tikhonov, “Examples of generalized elementary solutions in linear inverse problems”, Chelyab. Fiz.-Mat. Zh., 7:4 (2022), 395–411
Citation in format AMSBIB
\Bibitem{AlmTik22}
\by M.~Al-Mohamed, I.~V.~Tikhonov
\paper Examples of generalized elementary solutions in linear inverse problems
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2022
\vol 7
\issue 4
\pages 395--411
\mathnet{http://mi.mathnet.ru/chfmj297}
\crossref{https://doi.org/10.47475/2500-0101-2022-17401}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4523806}
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    • This publication is cited in the following 1 articles:
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