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arXiv · 1610.06384

Barrier-top resonances for non globally analytic potentials

Jean-Francois Bony·Setsuro Fujiie·Thierry Ramond·Maher Zerzeri
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Abstract

We give the semiclassical asymptotic of barrier-top resonances for Schr\"{o}dinger operators on ${\mathbb R}^{n}$, $n \geq 1$, whose potential is $C^{\infty}$ everywhere and analytic at infinity. In the globally analytic setting, this has already been obtained. Our proof is based on a propagation of singularities theorem at a hyperbolic fixed point that we establish here. This last result refines a theorem of the same authors, and its proof follows another approach.

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Jean-Francois Bony, Setsuro Fujiie, Thierry Ramond, Maher Zerzeri. 2016-10-20. Barrier-top resonances for non globally analytic potentials. https://arxiv.org/abs/1610.06384

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