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