Pointwise convergence of the non-linear Fourier transform
Complex Variables
2025-12-22 v14 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2103.13349,
title = {Pointwise convergence of the non-linear Fourier transform},
author = {Alexei Poltoratski},
journal= {arXiv preprint arXiv:2103.13349},
year = {2025}
}
Comments
We make several improvements and small corrections to the last (shorter) version of the proof of the convergence result