Neidhardt H., Zagrebnov V.A.
On semibounded restrictions of self-adjoint operators
(63K, LATeX 2e)

ABSTRACT.  After the von Neumann's remark about ``pathologies'' of unbounded symmetric operators and an abstract theorem
about stability domain in our previous paper, we develope here a general theory allowing to construct semibounded restrictions of
self-adjoint operators in explicit form. We apply this theory to quantum-mechanical momentum (position) operator to
describe corresponding stability domains. Generalization to the case of measurable functions of these operators is considered.
In conclusion we discuss spectral properties of self-adjoint extensions of constructed self-adjoint restrictions.