'Nonlinear Fourier Transforms and Applications to Complex Analysis'

By Shiferaw Berhanu - June 12, 2023 - Session 3
This mini-course introduces a class of nonlinear Fourier transforms known as FBI (for Fourier, Bros, and Iagolnitzer) transforms that characterize local and microlocal smoothness, analyticity, and Gevrey regularity of functions. Applications of these transforms to the study of the regularity of solutions of systems of first order linear and nonlinear partial differential equations will be presented. In particular, applications to the holomorphic extendability of CR functions will be discussed.