Almost everywhere convergence of Fourier series on SU(2): the case of Holder continuous functions

2020/05/22 by David Grow, Grow, David, Donnie Myers +1
Mathematics · #22E30 #43A50 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2005.11245

openalex publication_date 2020/05/22 · openalex created_date 2020/05/29 · openalex updated_date 2026/07/28

Abstract

We consider an aspect of the open problem: Does every square-integrable function on SU(2) have an almost everywhere convergent Fourier series? Let 0 < alpha < 1. We show that to each countable set E in SU(2) there corresponds an alpha-Holder continuous function on SU(2) whose Fourier series diverges on E. We also show that the Fourier series of each alpha-Holder continuous function on SU(2) converges almost everywhere.

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