Almost everywhere convergence of Fourier series on compact connected Lie groups
Classical Analysis and ODEs
2021-08-31 v1
Abstract
We consider the open problem: Does every square-integrable function f on a compact, connected Lie group G have an almost everywhere convergent Fourier series? We prove a general theorem from which it follows that if the integral modulus of continuity of f is O(t^a) for some a > 0 then the Fourier series of f converges almost everywhere on G. In particular, the Fourier series of any Holder continuous function of degree a > 0 on G converges almost everywhere. On the other hand, we show that to each countable subset E of G = SU(2) and each 0 < a < 1 there corresponds an Holder continuous function of degree a on SU(2) whose Fourier series diverges on E.
Keywords
Cite
@article{arxiv.2108.12997,
title = {Almost everywhere convergence of Fourier series on compact connected Lie groups},
author = {David Grow and Donnie Myers},
journal= {arXiv preprint arXiv:2108.12997},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2005.11245