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In this article we prove the property of unique continuation (also known forC^\infty functions as quasianalyticity) for solutions of the differentialinequality |\Delta u| \leq |Vu| for V from a wide class of potentials(including L^{d/2,\infty}_{\loc}(R^d) class) and u in a space of solutions Y_Vcontaining all eigenfunctions of the corresponding self-adjoint Schr\"odingeroperator.  Motivating question: is it true that for potentials V, for which self-adjointSchr\"odinger operator is well defined, the property of unique continuationholds?

Schr\"odinger operators and unique continuation. Towards an optimal result