Rational invariant tori and band edge spectra for non-selfadjoint\n operators

2015/02/21 by Michael Hitrik, Hitrik, Michael, Sjoestrand, Johannes
Mathematics · #35P15 #35P20 #37J35 #37J40 #53D22 #58J37 #58J40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1502.06138

openalex publication_date 2015/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study semiclassical asymptotics for spectra of non-selfadjoint\nperturbations of selfadjoint analytic h-pseudodifferential operators in\ndimension 2, assuming that the classical flow of the unperturbed part is\ncompletely integrable. Complete asymptotic expansions are established for all\nindividual eigenvalues in suitable regions of the complex spectral plane, near\nthe edges of the spectral band, coming from rational flow-invariant Lagrangian\ntori.\n

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