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Dini–Lipschitz criterion
In mathematics, the Dini–Lipschitz criterion is a sufficient condition for the Fourier series of a periodic function to converge uniformly at all real numbers. It was introduced by , as a strengthening of a weaker criterion introduced by . The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if :\lim_{\delta\rightarrow0^+}\omega(\delta,f)\log(\delta)=0 where \omega is the modulus of continuity of f with respect to \delta.
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