Diophantine tori and spectral asymptotics for non-selfadjoint operators
| dc.creator | Hitrik, Michael | |
| dc.creator | Sjoestrand, Johannes | |
| dc.creator | Ngoc, San Vu | |
| dc.date | 2005-02-01 | |
| dc.date.accessioned | 2026-07-07T05:16:36Z | |
| dc.date.available | 2026-07-07T05:16:36Z | |
| dc.description | We 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.description | 81 pages | |
| dc.identifier | https://arxiv.org/abs/math/0502032 | |
| dc.identifier | http://arxiv.org/abs/math/0502032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74044 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P15; 35P20; 37J35; 37J40; 53D22; 58J37; 70H08 | |
| dc.title | Diophantine tori and spectral asymptotics for non-selfadjoint operators | |
| dc.type | text |