Schrödinger operators and unique continuation. Towards an optimal result
Abstract
Description
In this article we prove the property of unique continuation (also known for C^\infty functions as quasianalyticity) for solutions of the differential inequality |Δu| \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_V containing all eigenfunctions of the corresponding self-adjoint Schrödinger operator.
Motivating question: is it true that for potentials V, for which self-adjoint Schrödinger operator is well defined, the property of unique continuation holds?