(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given each of the functions f below, describe the set of points at which the Fourier

series converges to f.

b) f(x) = abs(sqrt(x)) for x on [-pi, pi] with f(x+2pi)=f(x)

2. Relevant equations

Theorem: If f(x) is absolutely integrable, then its fourier series converges to f at the points where f is also holder continuous or differentiable.

3. The attempt at a solution

I managed to prove that f(x) is holder continuous on [-pi,pi] so by the theorem above since f(x) is absolutely integrable its fourier series converges to f(x) at every point on this interval. But f(x) is not differentiable at x=0. What did I analyze incorrectly? Or in this context are holder continuity and differentiability not equivalent conditions (i.e. one can fail and the other can hold)?

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# Fourier series convergence - holder continuity and differentiability

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