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 (1872), as a strengthening of a weaker criterion introduced by Rudolf Lipschitz (1864).
The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if where
ω
is the modulus of continuity of f with respect to