Sharp geometric conditions for a spectral inequality in the whole space
Gilles Lebeau  1  
1 : Laboratoire Jean Alexandre Dieudonné  (JAD)  -  Website
Université Nice Sophia Antipolis (UNS), CNRS : UMR7351
Université de Nice - Sophia Antipolis U.M.R. no 6621 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France -  France

We will present sharp quantifications of the uncertainty principle for a Schrödinger operator with a potential function $V=V(x)$, which is assumed to be an analytic symbol of negative degree, hence not necessarily a short range perturbation. Our approach relies on spectral inequalities, adapted to the unbounded case using holomorphic extension, spectral projections and suitable Carleman estimates for the D-bar operator. These results are motivated from control theory.
Joint work with Iván Moyano, Center for Mathematical Sciences, University of Cambridge.

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