Rational invariant tori and band edge spectra for non-selfadjoint operators
Michael Hitrik
University of California, Los Angeles, USAJohannes Sjöstrand
Université de Bourgogne Franche-Comté, Dijon, France
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Abstract
We study semiclassical asymptotics for spectra of non-selfadjoint perturbations of selfadjoint analytic -pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Complete asymptotic expansions are established for all individual eigenvalues in suitable regions of the complex spectral plane, near the edges of the spectral band, coming from rational flow-invariant Lagrangian tori.
Cite this article
Michael Hitrik, Johannes Sjöstrand, Rational invariant tori and band edge spectra for non-selfadjoint operators. J. Eur. Math. Soc. 20 (2018), no. 2, pp. 391–457
DOI 10.4171/JEMS/770