JournalsjemsVol. 20, No. 2pp. 391–457

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

  • Michael Hitrik

    University of California, Los Angeles, USA
  • Johannes Sjöstrand

    Université de Bourgogne Franche-Comté, Dijon, France
Rational invariant tori and band edge spectra for non-selfadjoint operators cover

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Abstract

We study semiclassical asymptotics for spectra of non-selfadjoint perturbations of selfadjoint analytic hh-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