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About: Dini–Lipschitz criterion     Goto   Sponge   NotDistinct   Permalink

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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 Ulisse Dini, as a strengthening of a weaker criterion introduced by Rudolf Lipschitz. The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if where is the modulus of continuity of f with respect to .