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

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.