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arXiv · 0902.0423

Schrödinger operators and unique continuation. Towards an optimal result

D. Kinzebulatov·L. Shartser
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Abstract

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?

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D. Kinzebulatov, L. Shartser. 2009-02-04. Schrödinger operators and unique continuation. Towards an optimal result. https://arxiv.org/abs/0902.0423

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