- 08-211 S. Fujii\'e, A. Lahmar-Benbernou, A. Martinez
- Width of Shape Resonances for Non Globally Analytic Potentials
(162K, LATeX 2e)
Nov 5, 08
(auto. generated ps),
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Abstract. We consider the semiclassical Schroedinger operator with a ''well in an
island'' potential, on which we assume smoothness only, except near
infinity. We give the asymptotic expansion of the imaginary part of the
shape resonance at the bottom of the well. This is a generalization of
a result by Helffer and Sjoestrand in the globally analytic case.
We use an almost analytic extension in order to continue the WKB
solution coming from the well beyond the caustic set, and, for the
justification of the accuracy of this approximation, we develop some
refined microlocal arguments in h-dependent small regions.