MICROLOCAL SMOOTHING EFFECT FOR SCHRÖDINGER EQUATIONS IN GEVREY SPACES

We consider the Gevrey smoothing effects of the solutions to the Cauchy problem for Schrödinger-type equations.

We prove that if the initial data decay like e^-c〈x〉κ, where c > 0 and 0 < κ < 1, in a neighborhood of the x-projection of the backward bicharacteristic issuing from a point (y₀,η₀), then (y₀, η₀) does not belong to the Gevrey wave front set of order 1/κ of the solution.