In a bounded domain in -dimensional Euclidean space each formal, linear, partial differential operator with constant coefficients may be connected with so-called minimal and maximal operators in the Hilbert space . The operator is said to be proper if and the equation has a unique solution for any . Using the complete description of proper operators that we obtain for , in this article we discuss problems connected with the description of proper operators in the general case when .Bibliography: 8 titles.
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Aleksei A. Dezin (1976) studied this question.