Propagation of analytic and Gevrey singularities for operators with non- involutive characteristics (Q1323247)

The authors consider the following analytic pseudo-differential operator \[ P (t, x,D_ t,D_ x) = (tD_ t)^ m + \sum^ m_{j = 1} Q(t,x,D_ x) (tD_ t)^{m-j}, \] where \(x \in X \subset \mathbb{R}^ n \) and the \(Q_ j\)'s are analytic pseudodifferential operators with respect to the space variable \(x\) depending on \(t\) as a parameter of order \(j \delta\) with \(0<\delta<1\). They prove a result of propagation of the \(s\)- Gevrey wave front set independent of the lower order terms, \(1 \leq s<1/ \delta\), and coinciding with the splitting of the singularities observed in the \(C^ \infty\) case.