Self-adjointness of elliptic operators with infinitely many variables
The author studies the selfadjointness of infinite-dimensional differential operators of Schrödinger type. Let \({\mathcal L}u(x)=Lu(x)+p(x)u(x)\) be a differential operator on some Hilbert space, where L is a strongly symmetric infinite-dimensional differential operator on this Hilbert space [see the author, Mat. Zametki 24, no. 2, 241-248 (1978; Zbl 0414.47031)]. Of the function p assume that it is real-valued, measurable with respect to a Gaussian measure \(\mu\) and bounded on each bounded set of the Hilbert space under consideration. The results of this note are summarized in one theorem. In this theorem the author estalishes that if the operator \({\mathcal L}\) is bounded below then its closure is selfadjoint.
selfadjointness of infinite-dimensional differential operators of Schrödinger
scientific article; zbMATH DE number 4058262