Geodesic
Application of Simonenko–Kozak's local principe in the section method theory of solving convolution equations with operator coefficients
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 55-66 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this work we generalize the Simonenko–Kozak's local structure to algebras generated by multidimensional operators with compact coefficients. Then we apply this local structure to receive the criteria of applicability the method of solving equations for multidimensional convolution operators with compact coefficients. 
@article{VMJ_2016_18_2_a6,
     author = {A. V. Lukin},
     title = {Application of {Simonenko{\textendash}Kozak's} local principe in the section method theory of solving convolution equations with operator coefficients},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {55--66},
     year = {2016},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a6/}
}
TY  - JOUR
AU  - A. V. Lukin
TI  - Application of Simonenko–Kozak's local principe in the section method theory of solving convolution equations with operator coefficients
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 55
EP  - 66
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a6/
LA  - ru
ID  - VMJ_2016_18_2_a6
ER  - 
%0 Journal Article
%A A. V. Lukin
%T Application of Simonenko–Kozak's local principe in the section method theory of solving convolution equations with operator coefficients
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 55-66
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a6/
%G ru
%F VMJ_2016_18_2_a6
A. V. Lukin. Application of Simonenko–Kozak's local principe in the section method theory of solving convolution equations with operator coefficients. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 55-66. http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a6/

[1] Gokhberg I. Ts., Feldman I. A., Uravneniya v svertkakh i proektsionnye metody ikh resheniya, Nauka, M., 1971, 352 pp. | MR

[2] Kozak A. V., “Lokalnyi printsip v teorii proektsionnykh metodov”, Dif. i integralnye uravneniya i ikh prilozheniya, Sb. nauch. trudov, Izd-vo KalmGU, Elista, 1983, 58–73 | MR

[3] Simonenko I. B., “Novyi obschii metod issledovaniya lineinykh operatornykh integralnykh uravnenii. I”, Izv. AN SSSR. Ser. mat., 29:3 (1965), 567–586 | MR | Zbl

[4] Simonenko I. B., Lokalnyi metod v teorii invariantnykh otnositelno sdviga operatorov i ikh ogibayuschikh, TsVVR, Rostov-n/D., 2007, 120 pp.

[5] Deundyak V. M., Miroshnikova E. I., “Ob ogranichennosti i fredgolmovosti integralnykh operatorov s anizotropno odnorodnymi yadrami kompaktnogo tipa i peremennymi koeffitsientami”, Izv. vuzov. Matem., 2012, no. 7, 3–17 | MR

[6] Deundyak V. M., Lukin A. V., “Priblizhennyi metod resheniya operatornykh uravnenii svertki na gruppe $\mathbb R^n$ s kompaktnymi koeffitsientami i prilozheniya”, Izv. vuzov Severo-Kavkazskii region, 2013, no. 6, 5–8

[7] Lukin A. V., “Proektsionnyi metod resheniya uravnenii svertki s operatornymi koeffitsientami”, Tez. dokl. mezhdunar. konf. “Sovremennye metody i problemy teorii operatorov i garmonicheskogo analiza i ikh prilozheniya – IV”, Rostov-n/D., 2014, 36

[8] Pilidi V. S., “O bisingulyarnom uravnenii v prostranstve $L_p$”, Mat. issledovaniya, 7:3 (1972), 167–175 | MR | Zbl

[9] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969, 456 pp. | MR

[10] Lyusternik L. A., Sobolev V. I., Kratkii kurs funktsionalnogo analiza, Vysshaya shkola, M., 1982, 271 pp. | MR