On Pointwise convergence of the non-linear Fourier transform

TL;DR

This paper presents a detailed proof of an analog of Carleson's Theorem, demonstrating almost everywhere convergence of a non-linear Fourier transform, extending classical Fourier analysis results to a non-linear setting.

Contribution

It provides a comprehensive exposition of Poltotaski's proof, clarifying the techniques used for establishing convergence of the non-linear Fourier transform.

Findings

Proves almost everywhere convergence of the non-linear Fourier transform.

Elaborates on the key ideas and steps in Poltotaski's proof.

Extends classical Fourier analysis results to non-linear transforms.

Abstract

A. Poltotaski proved an analog of Carleson's Theorem on almost everywhere convergence of Fourier series for a version of the non-linear Fourier transform. We aim to present his proof in full detail and elaborate on the ideas behind each step.