On universality and convergence of the Fourier series of functions in the disc algebra

2015/03/11 by Christos Papachristodoulos, Papachristodoulos, Christos, Michael Papadimitrakis +1
Engineering · Mathematics · #Advanced Banach Space Theory #Advanced Numerical Analysis Techniques #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1503.03426

openalex publication_date 2015/03/11 · arxiv created 2015/12/10 · arxiv updated 2015/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct functions in the disc algebra with pointwise universal Fourier series on sets which are G-delta and dense and at the same time with Fourier series whose set of divergence is of Hausdorff dimension zero. We also see that some classes of closed sets of measure zero do not accept uniformly universal Fourier series, although all such sets accept divergent Fourier series.

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