Geodesic
On a family of generalized shift operators
Izvestiya. Mathematics, Tome 11 (1977) no. 4, pp. 865-888 
R. J. Grabovskaya; V. I. Kononenko; V. B. Osipov. On a family of generalized shift operators. Izvestiya. Mathematics, Tome 11 (1977) no. 4, pp. 865-888. http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper a special representation of the algebra of differential operators is constructed. Using this representation a family of generalized shift operators is studied for which the $n$th order infinitesimal operators form an arbitrary Lie algebra. Systems of differential equations with bounded operator coefficients, having $n$th order infinitesimal operators in the left sides, are also studied. Bibliography: 4 titles.

[1] Levitan B. M., Teoriya operatorov obobschennogo sdviga, Nauka, M., 1973 | MR | Zbl

[2] Levitan B. M., “Teoremy Li dlya operatorov obobschennogo sdviga”, Trudy simpoziuma, posvyaschennogo 60-letiyu akademika S. L. Soboleva, Nauka, M., 1970, 150–157 | MR

[3] Grabovskaya R. Ya., Krein S. G., “Ob odnom predstavlenii algebry differentsialnykh operatorov i svyazannykh s nim differentsialnykh uravneniyakh”, Dokl. AN SSSR, 212:2 (1973), 280–284

[4] Grabovskaya R. Ya., Kononenko V. I., Osipov V. B., “Ob odnom semeistve operatorov obobschennogo sdviga”, Dokl. AN SSSR, 223:1 (1975), 27–30 | MR | Zbl