On problems for linear differential operations

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.