Schr\"odinger operators and unique continuation. Towards an optimal result
Analysis of PDEs
2009-02-04 v2 Mathematical Physics
math.MP
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 |\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?
Keywords
Cite
@article{arxiv.0902.0423,
title = {Schr\"odinger operators and unique continuation. Towards an optimal result},
author = {D. Kinzebulatov and L. Shartser},
journal= {arXiv preprint arXiv:0902.0423},
year = {2009}
}