Dini–Lipschitz criterion

Template: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 Template:Harvs, as a strengthening of a weaker criterion introduced by Template:Harvs. The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if

$\underset{\delta \to 0^{+}}{\lim }\omega (\delta ,f)\log (\delta )=0$

where $\omega$ is the modulus of continuity of f with respect to $\delta$.

References

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