The FBI transforms and their use in microlocal analysis
In the paper under review, certain problems of microlocal analysis are studied. This topic deals with smooth microlocal singularities (the collection of directions in which the Fourier transform does not decay rapidly), the set of which is called a smooth wave front set. Using a more general class of FBI transforms, introduced by S. Berhanu and J. Hounie, the authors 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 as examples. They 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.
scientific article; zbMATH DE number 6891995
scientific article