Geodesic
On subspaces of an intermediate characteristic in $C^*$
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 285-292

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CHFMJ_2020_5_3_a2,
     author = {V. I. Zalyapin and L. D. Menikhes and G. A. Shefer},
     title = {On subspaces of an intermediate characteristic in $C^*$},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {285--292},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a2/}
}
TY  - JOUR
AU  - V. I. Zalyapin
AU  - L. D. Menikhes
AU  - G. A. Shefer
TI  - On subspaces of an intermediate characteristic in $C^*$
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2020
SP  - 285
EP  - 292
VL  - 5
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a2/
LA  - ru
ID  - CHFMJ_2020_5_3_a2
ER  - 
%0 Journal Article
%A V. I. Zalyapin
%A L. D. Menikhes
%A G. A. Shefer
%T On subspaces of an intermediate characteristic in $C^*$
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2020
%P 285-292
%V 5
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a2/
%G ru
%F CHFMJ_2020_5_3_a2
V. I. Zalyapin; L. D. Menikhes; G. A. Shefer. On subspaces of an intermediate characteristic in $C^*$. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 285-292. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a2/