Geodesic
On problems for linear differential operations
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 411-419 
A. A. Dezin. On problems for linear differential operations. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 411-419. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $V\subset\mathbf R^n$ be a bounded region, $H(V)\equiv H$ the Hilbert space of square-integrable complex-valued functions, and $\mathscr L$ a general differential operation of order $m\geqslant1$ that is linear and has constant coefficients. The concept of an operator $S\colon H\to H$ generated by $\mathscr L$ is introduced, and its connection with the operators determined by associating boundary conditions with $\mathscr L$ is studied. The dependence of the structure of the solutions of the equation $Su=f\in H$ on the method for defining $S$ is investigated. The abstract constructions are illustrated by examples of concrete operators. Bibliography: 7 titles.

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[2] Mamyan A. Kh., “O nekotorykh svoistvakh mnozhestva granichnykh zadach”, Matem. sb., 121(163) (1983), 370–380 | MR | Zbl

[3] Otelbaev M., Kokebaev B. K., Shynybekov A. N., “K voprosam rasshireniya i suzheniya operatorov”, DAN SSSR, 271:6 (1983), 1307–1310 | MR | Zbl

[4] Mamyan A. Kh., “Obschie granichnye zadachi v sloe”, DAN SSSR, 267:2 (1982), 292–296 | MR | Zbl

[5] Sobolev S. L., Nekotorye prilozheniya funktsionalnogo analiza v matematicheskoi fizike, LGU, L., 1950

[6] Bitsadze A. V., Samarskii A. A., “O nekotorykh prosteishikh obobscheniyakh lineinykh ellipticheskikh kraevykh zadach”, DAN SSSR, 185:4 (1969), 739–741

[7] Nakhushev A. M., “Nagruzhennye uravneniya i ikh prilozheniya”, Differents. uravneniya, 19:1 (1983), 86–94 | MR | Zbl