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Matematicheskie Trudy, 2021, Volume 24, Number 2, Pages 105–121
DOI: https://doi.org/10.33048/mattrudy.2021.24.207 (Mi mt653) 		 
The inversion of series of resolvents of a closed operator and some of its applications

A. R. Mirotin

Gomel State University named after Francisk Skorina
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DOI: https://doi.org/10.33048/mattrudy.2021.24.207
Abstract: We describe the left inverse for operators representable by a sum of a series in the values of the resolvent of a densely defined closed operator in a complex Banach space. We give some applications of this result to regularization of the corresponding equations of the first kind and consider several examples.
Key words: closed operator, inverse operator, regularization strategy, ill-posed problem, integral equation of a first kind, inverse problem, recursive filter.
Received: 20.04.2020
Revised: 12.03.2021
Accepted: 31.03.2021
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. R. Mirotin, “The inversion of series of resolvents of a closed operator and some of its applications”, Mat. Tr., 24:2 (2021), 105–121
Citation in format AMSBIB
\Bibitem{Mir21}
\by A.~R.~Mirotin
\paper The inversion of series of resolvents of a closed operator and some of its applications
\jour Mat. Tr.
\yr 2021
\vol 24
\issue 2
\pages 105--121
\mathnet{http://mi.mathnet.ru/mt653}
\crossref{https://doi.org/10.33048/mattrudy.2021.24.207}
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