Pointwise convergence of the non-linear Fourier transform

Abstract

We prove pointwise convergence for the scattering data of a Dirac system of differential equations. Equivalently, we prove an analog of Carleson's theorem on almost everywhere convergence of Fourier series for a version of the non-linear Fourier transform. Our proofs are based on the study of resonances of Dirac systems.

We make several improvements and small corrections to the last (shorter) version of the proof of the convergence result