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 $$\delta$$.