Abstract
We are interested in the microlocal smoothing effect for operators of real principal type. On the initial value problem for a dispersive evolution equation, we study the fact that the sufficient decay of the initial data gives th e smoothness of the solution. We develop the theory of the FBI transform in order to transform our operator of real principal type into a simple operator of first order. S ince the smoothing effect is of global nature, our transformation is realized globall y along the bicharacteristics defined from the principal symbol of the operator.
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