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arXiv · 2108.12997

Almost everywhere convergence of Fourier series on compact connected Lie groups

David Grow·Donnie Myers
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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.

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David Grow, Donnie Myers. 2021-08-30. Almost everywhere convergence of Fourier series on compact connected Lie groups. https://arxiv.org/abs/2108.12997

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