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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
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
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
Linking options:
https://www.mathnet.ru/eng/chfmj188 https://www.mathnet.ru/eng/chfmj/v5/i3/p285
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Abstract page: | 258 | Full-text PDF : | 95 | References: | 61 |
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