Abstract.
We study the resonances of the semiclassical Schrödinger operator \( P = -h^{2}\Delta + V \) near a non-trapping energy level \( \lambda_0 \) in the case when the potential V is not necessarily analytic on all of \( \mathbb{R}^n \) but only outside some compact set. Then we prove that for some \( \delta > 0 \) and for any C > 0, P admits no resonance in the domain \( \Omega = [ \lambda_{0}-\delta, \lambda_{0}+\delta] - i[0, Ch \textrm{log}(h^{-1})] \) if V is \( C^\infty \), and \( \Omega = [ \lambda_{0}-\delta, \lambda_{0}+\delta] - i[0, \delta h^{1-{1 \over s}}] \) if V is Gevrey with index s. Here \( \delta > 0 \) does not depend on h and the results are uniform with respect to h > 0 small enough.
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Submitted 05/02/02, accepted 06/05/02
An erratum to this article is available at 10.1007/s00023-007-0340-x.
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Martinez, A. Resonance Free Domains for Non Globally Analytic Potentials. Ann. Henri Poincaré 3, 739–756 (2002). https://doi.org/10.1007/s00023-002-8634-5
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DOI: https://doi.org/10.1007/s00023-002-8634-5