The FBI transforms and their use in microlocal analysis

Using a more general class of FBI transforms introduced by S. Berhanu and J. Hounie in {[}12] we completely characterize regularity and microregularity in Denjoy-Carleman (non quasi analytic) classes, which includes the Gevrey classes and M. Christ version of the FBI transform defined in {[}22] as examples. We also exhibit a result on microlocal regularity for solutions of first order partial differential equations in these classes, that do not seem possible to prove using the classical FBI transform. (C) 2018 Elsevier Inc. All rights reserved. (AU)