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Abstract
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We consider nonselfadjoint perturbations of semiclassical harmonic oscillators. Under
appropriate dynamical assumptions, we establish some spectral estimates such as
upper bounds on the resolvent near the real axis when no geometric control condition
is satisfied.
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Keywords
semiclassical analysis, nonselfadjoint operators, resolvent
estimates, integrable systems, averaging method
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Mathematical Subject Classification 2010
Primary: 35P20
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Milestones
Received: 27 July 2019
Revised: 21 October 2019
Accepted: 19 November 2019
Published: 22 May 2020
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