 01278 MARTINEZ Andre'
 Resonance Free Domains for NonAnalytic Potentials
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Jul 18, 01

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Abstract. We study the resonances of the semiclassical Schr\"odinger operator
$P=h^2\Delta
+ V$ near a nontrapping energy level $\lambda_0$ in the case when the
potential $V$ is not
necessarily analytic on all of $\R^n$ 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 $\Omega =[\lambda_0 \delta
,\lambda_0
+\delta ]i[0,C h\log (h^{1})]$ if $V$ is $C^\infty$, and
$\Omega =[\lambda_0 \delta , \lambda_0 +\delta
]i[0,\delta h^{1\frac1{s}}]$ 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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01278.tex