Semiclassical asymptotics for nonselfadjoint harmonic oscillators

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 22 May 2020Embargo end date: 01 Jan 2018 France English Publisher:Mathematical Sciences PublishersJournal:Pure and Applied Analysis, volume 2, pages 427-445 (issn: 2578-5893, eissn: 2578-5885,

Copyright policy )Funded by:ANR | CEMPI, ANR | GeRaSic

Authors: Arnaiz, Victor; Rivière, Gabriel;

doi: 10.2140/paa.2020.2.427 , 10.48550/arxiv.1812.02022

arXiv: 1812.02022

handle: 10261/233740

Semiclassical asymptotics for nonselfadjoint harmonic oscillators

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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.

Country

France

Related Organizations

University of Paris-Saclay
France
French National Centre for Scientific Research
France
Laboratoire de Mathématiques Jean Leray
France
Université de Nantes
France
Spanish National Research Council
Spain

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Keywords

Harmonic oscillators, Semiclassical analysis, FOS: Physical sciences, 510, Mathematics - Spectral Theory, Resolvent estimates, Mathematics - Analysis of PDEs, integrable systems, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 35P20, nonselfadjoint operators, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Spectral Theory (math.SP), Mathematical Physics, Asymptotic distributions of eigenvalues in context of PDEs, resolvent estimates, averaging method, Mathematical Physics (math-ph), [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP], semiclassical analysis, Analysis of PDEs (math.AP)

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