{"title":"Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets","authors":"V'ictor Arnaiz","doi":"10.4171/jst/418","DOIUrl":null,"url":null,"abstract":"We construct quasimodes for non-selfadjoint semiclassical operators using propagation of Hagedorn wave-packets. Assuming that the imaginary part of the principal symbol of the operator is non-negative and vanishes on certain points of the phase-space satisfying a finite-type dynamical condition, we construct quasimodes that concentrate on these non-damped points. More generally, we apply this technique to construct quasimodes for non-selfadjoint semiclassical perturbations of the harmonic oscillator that concentrate on periodic orbits or invariant tori.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Spectral Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jst/418","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We construct quasimodes for non-selfadjoint semiclassical operators using propagation of Hagedorn wave-packets. Assuming that the imaginary part of the principal symbol of the operator is non-negative and vanishes on certain points of the phase-space satisfying a finite-type dynamical condition, we construct quasimodes that concentrate on these non-damped points. More generally, we apply this technique to construct quasimodes for non-selfadjoint semiclassical perturbations of the harmonic oscillator that concentrate on periodic orbits or invariant tori.
期刊介绍：
The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome.
The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory.
Schrödinger operators, scattering theory and resonances;
eigenvalues: perturbation theory, asymptotics and inequalities;
quantum graphs, graph Laplacians;
pseudo-differential operators and semi-classical analysis;
random matrix theory;
the Anderson model and other random media;
non-self-adjoint matrices and operators, including Toeplitz operators;
spectral geometry, including manifolds and automorphic forms;
linear and nonlinear differential operators, especially those arising in geometry and physics;
orthogonal polynomials;
inverse problems.
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