  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.
