Geodesic
Rational invariant tori and band edge spectra for non-selfadjoint operators
Journal of the European Mathematical Society, Tome 20 (2018) no. 2, pp. 391-457

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We study semiclassical asymptotics for spectra of non-selfadjoint perturbations of selfadjoint analytic h-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.
DOI : 10.4171/jems/770
Classification : 35-XX, 37-XX, 53-XX, 58-XX
Keywords: Non-selfadjoint, eigenvalue, spectral asymptotics, resolvent, semiclassical limit, completely integrable, Lagrangian torus, rational torus, secular perturbation theory, pseudospectrum, exponential weight, FBI transform 
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     author = {Michael Hitrik and Johannes Sj\"ostrand},
     title = {Rational invariant tori and band edge spectra for non-selfadjoint operators},
     journal = {Journal of the European Mathematical Society},
     pages = {391--457},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2018},
     doi = {10.4171/jems/770},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/770/}
}
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Michael Hitrik; Johannes Sjöstrand. Rational invariant tori and band edge spectra for non-selfadjoint operators. Journal of the European Mathematical Society, Tome 20 (2018) no. 2, pp. 391-457. doi: 10.4171/jems/770

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