I've read that if we have a continuous function defined on a circle and its Fourier coefficient converges absolutely, then that implies the Fourier series converges uniformly, but I'm not quite sure why because absolute convergence does not imply uniform convergence for infinite series. I think the reason is due to the Weierstrass $M$ test correct? If the Fourier series converges absolutely, then so do the Fourier coefficients which we use for the $M$ test. Is that correct?
2026-04-17 18:06:37.1776449197
Why does $f$ continuous and its Fourier coefficient converges absolutely implies the Fourier series converges uniformly?
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