Localization Theorems for Equality of Minimal and Maximal Schrِdinger-Type Operators

Consider the operators associated in L2(Rn) with τ = −div(A(x) · grad) + q(x) where q(x) is complex. We prove the Localization Theorems in the case of A(x) ≥ 0 and without a priori restrictions on the regularity field of the operator. The same approach for the operator with singular magnetic vector potential and real q(x) enables us to include q(x) with negative fall-off at infinity.