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 0 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 .

References

Fourier series