Microlocalization and stationary phase
| dc.creator | Lopez, Ricardo Garcia | |
| dc.date | 2003-07-28 | |
| dc.date.accessioned | 2026-07-07T04:59:56Z | |
| dc.date.available | 2026-07-07T04:59:56Z | |
| dc.description | Let M be a holonomic module over the Weyl algebra K[t]<\partial_t>, K a field of characteristic zero. We prove a stationary phase formula which expresses the formalization of the germ at infinity of the Fourier transform of M in terms of a sum of local contributions depending on the germs defined by M at its singular points and at infinity. For this purpose, we consider formal analogues of the local Fourier transforms defined by G. Laumon in the l-adic setting (for instance, the transformation labelled (0,\infty) by Laumon corresponds in our context to formal microlocalization). When K is the field of complex numbers we can describe in a similar way the 1-Gevrey germ at infinity defined by M. When K is a p-adic field, we make a modest attempt to reproduce a small part of these constructions in the p-adic setting. We define a ring of p-adic microdifferential operators (of finite order) and we prove a p-adic stationary phase formula in some special cases. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307366 | |
| dc.identifier | http://arxiv.org/abs/math/0307366 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68191 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32C38;35A27 | |
| dc.title | Microlocalization and stationary phase | |
| dc.type | text |