Dini criterion
In mathematics, Dini's criterion is a condition for the pointwise convergence of Fourier series, introduced by . Statement. Dini's criterion states that if a periodic function " has the property that formula_1 is locally integrable near , then the Fourier series of converges to 0 at formula_2. Dini's criterion is in some sense as strong as possible: if is a positive continuous function such that is not locally integrable near , there is a continuous function " with || ≤  whose Fourier series does not converge at .