Microlocal smoothing effect for Schrödinger equations in Gevrey spaces (Q1425454)

The Cauchy problem for the Schrödinger operator is considered. Its coefficients are assumed to be in some Gevrey class \(\gamma^d\). The authors investigate a microlocal smoothing effect, i.e., if the initial data have a certain decay on the backward bicharacteristics of the operator issued from a point \(\rho_0\), then the solution belongs microlocally to some Gevrey class, which means that the point \(\rho_0\) does not belong to the (spatial) Gevrey wave front set \(WF_\sigma(u(t))\) of the solution \(u(t)\) at positive time \(t\), if \(\sigma\) is suitable.