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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2020, Volume 5, Issue 3, Pages 285–292
DOI: https://doi.org/10.47475/2500-0101-2020-15303
(Mi chfmj188)
 

Mathematics

On subspaces of an intermediate characteristic in C

V. I. Zalyapin, L. D. Menikhes, G. A. Shefer

South Ural State University (National Research University), Chelyabinsk, Russia
References:
Abstract: With the approximate solution of integral equations, the regularizability of the inverse mapping plays a leading role. If the inverse mapping is regularizable, then the equation can be solved by Tikhonov's method. Otherwise the regularization method is not applicable. In 1978, L.D. Menikhes built an example of integral mapping such the inverse mapping is nonregularizable. As follows from the work of V.A. Vinokurov et al. regularizability is closely related to the characteristic (index) of the image of the conjugate operator. If this characteristic is nonzero, then the inverse of the integral mapping is regularizable. The purpose of this paper is to propose a method for constructing subspaces in C with a non-trivial (intermediate between 0 and 1) characteristic.
Keywords: integral equations, regularizability, the characteristic of the subspace.
Received: 04.03.2020
Revised: 10.06.2020
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. I. Zalyapin, L. D. Menikhes, G. A. Shefer, “On subspaces of an intermediate characteristic in C”, Chelyab. Fiz.-Mat. Zh., 5:3 (2020), 285–292
Citation in format AMSBIB
\Bibitem{ZalMenShe20}
\by V.~I.~Zalyapin, L.~D.~Menikhes, G.~A.~Shefer
\paper On subspaces of an intermediate characteristic in $C^*$
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2020
\vol 5
\issue 3
\pages 285--292
\mathnet{http://mi.mathnet.ru/chfmj188}
\crossref{https://doi.org/10.47475/2500-0101-2020-15303}
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