On semibounded restrictions of self-adjoint operators (original) (raw)

After the yon Neumann's remark [t0] about ':pathologies" of unbounded symmetric operators and an abstract theorem about stability domain [9], we devel-.ope here a general theory allowing to construct semibounded restrictions of selfadjoint operators in explidt form. We apply this theory to quantum-mechanical momentum (position) operator to describe corresponding stability domains. Generalization to the case of measurabIe functions of these operators is considered. In conclusion we discuss spectral properties of self-adjoint extensions of constructed self-adjoint restrictions.