Análise microlocal nas classes de Denjoy-Carleman

Abstract

Using a more general class of FBI transforms, introduced by S. Berhanu and J. Hounie in [16], we completely characterize regularity and microregularity in Denjoy-Carleman (non quasi analytic) classes, which includes the Gevrey classes and M. Chist FBI transform defined in [27] as examples. Using the classic FBI transform we completely describe the M—wave-front set of the boundary values of solutions in wedges W of hypo Denjoy-Carleman structures (M, V) (Definição 3.1.2) proving similar results first obtained by [1], [5], [13, 14], [35] and [43]. Inspired by [53], [56], [41] and [1] we introduce the notion of nonlinear Mizohata type equations and study microlocal Denjoy-Carleman regularity for solutions u of non linear equations, extending the main results of [1], [5], [13, 14], [35] and [43].