Английская Википедия:Dini–Lipschitz criterion
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Шаблон:Distinguish 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 Шаблон:Harvs, as a strengthening of a weaker criterion introduced by Шаблон:Harvs. The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if
- <math>\lim_{\delta\rightarrow0^+}\omega(\delta,f)\log(\delta)=0</math>
where <math>\omega</math> is the modulus of continuity of f with respect to <math>\delta</math>.
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