Schr\"odinger operators and unique continuation. Towards an optimal result
Abstract
In this article we prove the property of unique continuation (also known for C∞ functions as quasianalyticity) for solutions of the differential inequality | u| ≤ |Vu| for V from a wide class of potentials (including Ld/2,∞(Rd) class) and u in a space of solutions YV containing all eigenfunctions of the corresponding self-adjoint Schr\"odinger operator. Motivating question: is it true that for potentials V, for which self-adjoint Schr\"odinger operator is well defined, the property of unique continuation holds?
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