Vol. 2, No. 2, 2020

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Semiclassical asymptotics for nonselfadjoint harmonic oscillators

Víctor Arnaiz and Gabriel Rivière

Vol. 2 (2020), No. 2, 427–445
Abstract

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.

Keywords
semiclassical analysis, nonselfadjoint operators, resolvent estimates, integrable systems, averaging method
Mathematical Subject Classification 2010
Primary: 35P20
Milestones
Received: 27 July 2019
Revised: 21 October 2019
Accepted: 19 November 2019
Published: 22 May 2020
Authors
Víctor Arnaiz
Université Paris-Saclay
CNRS, Laboratoire de mathématiques d’Orsay
Orsay
France
Instituto de Ciencias Matemáticas (ICMAT)
Campus de Cantoblanco, UAM
Madrid
Spain
Gabriel Rivière
Laboratoire de mathématiques Jean Leray (UMR CNRS 6629)
Université de Nantes
Nantes
France