Andres Martinez - Academia.edu (original) (raw)

Andres Martinez

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Papers by Andres Martinez

Research paper thumbnail of Resonance Free Domains for Non Globally Analytic Potentials

Annales Henri Poincare, 2002

We study the resonances of the semiclassical Schrödinger operator $ P = -h^{2}\Delta + V $ near a... more 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.

Research paper thumbnail of Resonance Free Domains for Non Globally Analytic Potentials

Annales Henri Poincare, 2002

We study the resonances of the semiclassical Schrödinger operator $ P = -h^{2}\Delta + V $ near a... more 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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