97-393 Neidhardt H., Zagrebnov V.A.

On semibounded restrictions of self-adjoint operators (63K, LATeX 2e) Jul 6, 97

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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.

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