Spreading of Lagrangian regularity on rational invariant tori
| dc.creator | Wunsch, Jared | |
| dc.date | 2006-06-20 | |
| dc.date | 2007-03-06 | |
| dc.date.accessioned | 2026-07-07T07:50:07Z | |
| dc.date.available | 2026-07-07T07:50:07Z | |
| dc.description | Let $P_h$ be a self-adjoint semiclassical pseudodifferential operator on a manifold $M$ such that the bicharacteristic flow of the principal symbol on $T^*M$ is completely integrable and the subprincipal symbol of $P_h$ vanishes. Consider a semiclassical family of eigenfunctions, or, more generally, quasimodes $u_h$ of $P_h.$ We show that on a nondegenerate rational invariant torus, Lagrangian regularity of $u_h$ (regularity under test operators characteristic on the torus) propagates both along bicharacteristics, and also in an additional ``diffractive'' manner. In particular, in addition to propagating along null bicharacteristics, regularity fills in the interiors of small annular tubes of bicharacteristics. | |
| dc.description | Revised version: proof of Theorem A pruned, some examples added, hypotheses clarified | |
| dc.identifier | https://arxiv.org/abs/math/0606495 | |
| dc.identifier | http://arxiv.org/abs/math/0606495 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125061 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 35P20, 81Q20, 58F07 | |
| dc.title | Spreading of Lagrangian regularity on rational invariant tori | |
| dc.type | text |