Diophantine tori and spectral asymptotics for non-selfadjoint operators

dc.creatorHitrik, Michael
dc.creatorSjoestrand, Johannes
dc.creatorNgoc, San Vu
dc.date2005-02-01
dc.date.accessioned2026-07-07T05:16:36Z
dc.date.available2026-07-07T05:16:36Z
dc.descriptionWe study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori enjoying a Diophantine property. We get complete asymptotic expansions for all eigenvalues in certain rectangles in the complex plane in two different cases: in the first case, we assume that the strength $ε$ of the perturbation is ${\cal O}(h^δ)$ for some $δ>0$ and is bounded from below by a fixed positive power of $h$. In the second case, $ε$ is assumed to be sufficiently small but independent of $h$, and we describe the eigenvalues completely in a fixed $h$-independent domain in the complex spectral plane.
dc.description81 pages
dc.identifierhttps://arxiv.org/abs/math/0502032
dc.identifierhttp://arxiv.org/abs/math/0502032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74044
dc.subjectSpectral Theory
dc.subjectAnalysis of PDEs
dc.subject35P15; 35P20; 37J35; 37J40; 53D22; 58J37; 70H08
dc.titleDiophantine tori and spectral asymptotics for non-selfadjoint operators
dc.typetext

Files

Collections