Abstract:
In this paper a new method of definition of differential operators with an infinite number of independent variables is proposed, and an analysis of the selfadjointness in the corresponding Hilbert spaces is carried out. Certain spectral properties of such operators are also investigated. In contrast with previous analyses, the spaces of functions of an infinite number of variables in which the operators being studied act are, in general, not infinite tensor products of spaces of functions of a finite number of variables.
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