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 is locally integrable near, then the Fourier series of converges to at.
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.