Schrodinger operators and unique continuation. Towards an optimal result

摘要

In this article we prove the property of unique continuation (also known for C-infinity functions as quasi-analyticity) for solutions of the differential inequality |Delta u| <= |Vu| for V from a wide class of potentials (including L-loc(d/2,infinity) (R-d) class) and it in a space of solutions Y-V containing all eigenfunctions of the corresponding self-adjoint Schrodinger operator. Motivating question: is it true that for potentials V, for which self-adjoint Schrodinger operator is well defined, the property Of unique continuation holds'?