Schrödinger operators and unique continuation. Towards an optimal result

Details Schrödinger operators and unique continuation. Towards an optimal result Schrödinger operators and unique continuation. Towards an optimal result

2009-02-03

arxiv.org/abs/0902.0423v2

Mathematics

Analysis of PDEs

Scientific paper

In this article we prove the property of unique continuation (also known for C^\infty functions as quasianalyticity) for solutions of the differential inequality |\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_V 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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