Microlocal smoothing effect for the Schrödinger evolution equation in a Gevrey class (Q1006621)

The author considers a time-independent Schrödinger equation with variable coefficients, and studies the propagation of the Gevrey regularity of the solution along non-trapping Hamilton vector fields. He proves that if the initial data decays (in some conical direction), then the solution becomes regular (in a corresponding microlocal direction). For this purpose he studies the propagation of the homogeneous Gevrey wave front set, which is a refinement of the usual wave front set. Such a result is already known in analytic cases, and the author extends it to Gevrey cases using almost analytic extensions of Gevrey functions.