$f(x)=|x|, x\in[-\pi,\pi[$ is a $2\pi$-periodic function. Does the Fourier series for $f(x)$ converge uniformly to $f(x),x\in\mathbb{R}$?
Answer in my book is yes, but how can it when $f'(x)=\frac{x}{|x|}$ is not defined at $x=0$ i.e. function is not piecewise differentiable (smooth)?