On Pointwise convergence of the non-linear Fourier transform

2022/10/21 by Lukas Mauth, Mauth, Lukas
Mathematics · #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2210.12286

openalex publication_date 2022/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• The pointwise convergence of Fourier Series (II). Strong L¹ case for the lacunary Carleson operator