Geodesic
On problems for linear differential operations
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 411-419 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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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