Dini criterion

In mathematics, Dini's criterion is a condition for the pointwise convergence of Fourier series, introduced by Ulisse Dini (1880).

Dini's criterion states that if a periodic function

is locally integrable near

, then the Fourier series of

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

whose Fourier series does not converge at