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

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.

[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